Properties

Label 8043.2.a.t.1.3
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56328 q^{2}\) \(-1.00000 q^{3}\) \(+4.57042 q^{4}\) \(-4.02293 q^{5}\) \(+2.56328 q^{6}\) \(+1.00000 q^{7}\) \(-6.58873 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56328 q^{2}\) \(-1.00000 q^{3}\) \(+4.57042 q^{4}\) \(-4.02293 q^{5}\) \(+2.56328 q^{6}\) \(+1.00000 q^{7}\) \(-6.58873 q^{8}\) \(+1.00000 q^{9}\) \(+10.3119 q^{10}\) \(-2.04432 q^{11}\) \(-4.57042 q^{12}\) \(-3.98824 q^{13}\) \(-2.56328 q^{14}\) \(+4.02293 q^{15}\) \(+7.74793 q^{16}\) \(-2.64291 q^{17}\) \(-2.56328 q^{18}\) \(+0.955824 q^{19}\) \(-18.3865 q^{20}\) \(-1.00000 q^{21}\) \(+5.24017 q^{22}\) \(+5.68481 q^{23}\) \(+6.58873 q^{24}\) \(+11.1839 q^{25}\) \(+10.2230 q^{26}\) \(-1.00000 q^{27}\) \(+4.57042 q^{28}\) \(+2.11501 q^{29}\) \(-10.3119 q^{30}\) \(-3.54335 q^{31}\) \(-6.68269 q^{32}\) \(+2.04432 q^{33}\) \(+6.77453 q^{34}\) \(-4.02293 q^{35}\) \(+4.57042 q^{36}\) \(+7.26134 q^{37}\) \(-2.45005 q^{38}\) \(+3.98824 q^{39}\) \(+26.5060 q^{40}\) \(-2.24510 q^{41}\) \(+2.56328 q^{42}\) \(+9.17675 q^{43}\) \(-9.34340 q^{44}\) \(-4.02293 q^{45}\) \(-14.5718 q^{46}\) \(-10.5562 q^{47}\) \(-7.74793 q^{48}\) \(+1.00000 q^{49}\) \(-28.6676 q^{50}\) \(+2.64291 q^{51}\) \(-18.2280 q^{52}\) \(+0.903669 q^{53}\) \(+2.56328 q^{54}\) \(+8.22414 q^{55}\) \(-6.58873 q^{56}\) \(-0.955824 q^{57}\) \(-5.42137 q^{58}\) \(-5.90876 q^{59}\) \(+18.3865 q^{60}\) \(-4.64238 q^{61}\) \(+9.08261 q^{62}\) \(+1.00000 q^{63}\) \(+1.63378 q^{64}\) \(+16.0444 q^{65}\) \(-5.24017 q^{66}\) \(-5.76668 q^{67}\) \(-12.0792 q^{68}\) \(-5.68481 q^{69}\) \(+10.3119 q^{70}\) \(-5.68274 q^{71}\) \(-6.58873 q^{72}\) \(-12.0298 q^{73}\) \(-18.6129 q^{74}\) \(-11.1839 q^{75}\) \(+4.36852 q^{76}\) \(-2.04432 q^{77}\) \(-10.2230 q^{78}\) \(-2.09234 q^{79}\) \(-31.1694 q^{80}\) \(+1.00000 q^{81}\) \(+5.75484 q^{82}\) \(-0.102376 q^{83}\) \(-4.57042 q^{84}\) \(+10.6322 q^{85}\) \(-23.5226 q^{86}\) \(-2.11501 q^{87}\) \(+13.4695 q^{88}\) \(-9.25679 q^{89}\) \(+10.3119 q^{90}\) \(-3.98824 q^{91}\) \(+25.9820 q^{92}\) \(+3.54335 q^{93}\) \(+27.0585 q^{94}\) \(-3.84521 q^{95}\) \(+6.68269 q^{96}\) \(+17.4113 q^{97}\) \(-2.56328 q^{98}\) \(-2.04432 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56328 −1.81252 −0.906258 0.422726i \(-0.861073\pi\)
−0.906258 + 0.422726i \(0.861073\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.57042 2.28521
\(5\) −4.02293 −1.79911 −0.899554 0.436810i \(-0.856108\pi\)
−0.899554 + 0.436810i \(0.856108\pi\)
\(6\) 2.56328 1.04646
\(7\) 1.00000 0.377964
\(8\) −6.58873 −2.32947
\(9\) 1.00000 0.333333
\(10\) 10.3119 3.26091
\(11\) −2.04432 −0.616385 −0.308192 0.951324i \(-0.599724\pi\)
−0.308192 + 0.951324i \(0.599724\pi\)
\(12\) −4.57042 −1.31937
\(13\) −3.98824 −1.10614 −0.553070 0.833135i \(-0.686544\pi\)
−0.553070 + 0.833135i \(0.686544\pi\)
\(14\) −2.56328 −0.685066
\(15\) 4.02293 1.03872
\(16\) 7.74793 1.93698
\(17\) −2.64291 −0.641000 −0.320500 0.947248i \(-0.603851\pi\)
−0.320500 + 0.947248i \(0.603851\pi\)
\(18\) −2.56328 −0.604172
\(19\) 0.955824 0.219281 0.109640 0.993971i \(-0.465030\pi\)
0.109640 + 0.993971i \(0.465030\pi\)
\(20\) −18.3865 −4.11134
\(21\) −1.00000 −0.218218
\(22\) 5.24017 1.11721
\(23\) 5.68481 1.18536 0.592682 0.805437i \(-0.298069\pi\)
0.592682 + 0.805437i \(0.298069\pi\)
\(24\) 6.58873 1.34492
\(25\) 11.1839 2.23679
\(26\) 10.2230 2.00489
\(27\) −1.00000 −0.192450
\(28\) 4.57042 0.863729
\(29\) 2.11501 0.392747 0.196374 0.980529i \(-0.437083\pi\)
0.196374 + 0.980529i \(0.437083\pi\)
\(30\) −10.3119 −1.88269
\(31\) −3.54335 −0.636404 −0.318202 0.948023i \(-0.603079\pi\)
−0.318202 + 0.948023i \(0.603079\pi\)
\(32\) −6.68269 −1.18134
\(33\) 2.04432 0.355870
\(34\) 6.77453 1.16182
\(35\) −4.02293 −0.679999
\(36\) 4.57042 0.761737
\(37\) 7.26134 1.19376 0.596878 0.802332i \(-0.296407\pi\)
0.596878 + 0.802332i \(0.296407\pi\)
\(38\) −2.45005 −0.397450
\(39\) 3.98824 0.638630
\(40\) 26.5060 4.19096
\(41\) −2.24510 −0.350626 −0.175313 0.984513i \(-0.556094\pi\)
−0.175313 + 0.984513i \(0.556094\pi\)
\(42\) 2.56328 0.395523
\(43\) 9.17675 1.39944 0.699721 0.714416i \(-0.253308\pi\)
0.699721 + 0.714416i \(0.253308\pi\)
\(44\) −9.34340 −1.40857
\(45\) −4.02293 −0.599703
\(46\) −14.5718 −2.14849
\(47\) −10.5562 −1.53978 −0.769890 0.638177i \(-0.779689\pi\)
−0.769890 + 0.638177i \(0.779689\pi\)
\(48\) −7.74793 −1.11832
\(49\) 1.00000 0.142857
\(50\) −28.6676 −4.05421
\(51\) 2.64291 0.370082
\(52\) −18.2280 −2.52776
\(53\) 0.903669 0.124128 0.0620642 0.998072i \(-0.480232\pi\)
0.0620642 + 0.998072i \(0.480232\pi\)
\(54\) 2.56328 0.348819
\(55\) 8.22414 1.10894
\(56\) −6.58873 −0.880456
\(57\) −0.955824 −0.126602
\(58\) −5.42137 −0.711861
\(59\) −5.90876 −0.769255 −0.384627 0.923072i \(-0.625670\pi\)
−0.384627 + 0.923072i \(0.625670\pi\)
\(60\) 18.3865 2.37369
\(61\) −4.64238 −0.594395 −0.297198 0.954816i \(-0.596052\pi\)
−0.297198 + 0.954816i \(0.596052\pi\)
\(62\) 9.08261 1.15349
\(63\) 1.00000 0.125988
\(64\) 1.63378 0.204222
\(65\) 16.0444 1.99006
\(66\) −5.24017 −0.645020
\(67\) −5.76668 −0.704512 −0.352256 0.935904i \(-0.614585\pi\)
−0.352256 + 0.935904i \(0.614585\pi\)
\(68\) −12.0792 −1.46482
\(69\) −5.68481 −0.684370
\(70\) 10.3119 1.23251
\(71\) −5.68274 −0.674417 −0.337208 0.941430i \(-0.609483\pi\)
−0.337208 + 0.941430i \(0.609483\pi\)
\(72\) −6.58873 −0.776489
\(73\) −12.0298 −1.40798 −0.703989 0.710211i \(-0.748599\pi\)
−0.703989 + 0.710211i \(0.748599\pi\)
\(74\) −18.6129 −2.16370
\(75\) −11.1839 −1.29141
\(76\) 4.36852 0.501104
\(77\) −2.04432 −0.232972
\(78\) −10.2230 −1.15753
\(79\) −2.09234 −0.235406 −0.117703 0.993049i \(-0.537553\pi\)
−0.117703 + 0.993049i \(0.537553\pi\)
\(80\) −31.1694 −3.48484
\(81\) 1.00000 0.111111
\(82\) 5.75484 0.635516
\(83\) −0.102376 −0.0112372 −0.00561860 0.999984i \(-0.501788\pi\)
−0.00561860 + 0.999984i \(0.501788\pi\)
\(84\) −4.57042 −0.498674
\(85\) 10.6322 1.15323
\(86\) −23.5226 −2.53651
\(87\) −2.11501 −0.226753
\(88\) 13.4695 1.43585
\(89\) −9.25679 −0.981218 −0.490609 0.871380i \(-0.663226\pi\)
−0.490609 + 0.871380i \(0.663226\pi\)
\(90\) 10.3119 1.08697
\(91\) −3.98824 −0.418081
\(92\) 25.9820 2.70881
\(93\) 3.54335 0.367428
\(94\) 27.0585 2.79087
\(95\) −3.84521 −0.394510
\(96\) 6.68269 0.682049
\(97\) 17.4113 1.76785 0.883923 0.467632i \(-0.154893\pi\)
0.883923 + 0.467632i \(0.154893\pi\)
\(98\) −2.56328 −0.258931
\(99\) −2.04432 −0.205462
\(100\) 51.1154 5.11154
\(101\) 4.05370 0.403358 0.201679 0.979452i \(-0.435360\pi\)
0.201679 + 0.979452i \(0.435360\pi\)
\(102\) −6.77453 −0.670779
\(103\) −6.68168 −0.658365 −0.329183 0.944266i \(-0.606773\pi\)
−0.329183 + 0.944266i \(0.606773\pi\)
\(104\) 26.2774 2.57671
\(105\) 4.02293 0.392597
\(106\) −2.31636 −0.224985
\(107\) 15.9187 1.53892 0.769460 0.638695i \(-0.220525\pi\)
0.769460 + 0.638695i \(0.220525\pi\)
\(108\) −4.57042 −0.439789
\(109\) 0.670528 0.0642249 0.0321124 0.999484i \(-0.489777\pi\)
0.0321124 + 0.999484i \(0.489777\pi\)
\(110\) −21.0808 −2.00998
\(111\) −7.26134 −0.689216
\(112\) 7.74793 0.732111
\(113\) 5.49468 0.516896 0.258448 0.966025i \(-0.416789\pi\)
0.258448 + 0.966025i \(0.416789\pi\)
\(114\) 2.45005 0.229468
\(115\) −22.8696 −2.13260
\(116\) 9.66649 0.897511
\(117\) −3.98824 −0.368713
\(118\) 15.1458 1.39429
\(119\) −2.64291 −0.242275
\(120\) −26.5060 −2.41965
\(121\) −6.82077 −0.620070
\(122\) 11.8997 1.07735
\(123\) 2.24510 0.202434
\(124\) −16.1946 −1.45432
\(125\) −24.8776 −2.22512
\(126\) −2.56328 −0.228355
\(127\) −7.83776 −0.695489 −0.347744 0.937589i \(-0.613052\pi\)
−0.347744 + 0.937589i \(0.613052\pi\)
\(128\) 9.17755 0.811189
\(129\) −9.17675 −0.807968
\(130\) −41.1264 −3.60702
\(131\) 13.3048 1.16244 0.581221 0.813746i \(-0.302575\pi\)
0.581221 + 0.813746i \(0.302575\pi\)
\(132\) 9.34340 0.813238
\(133\) 0.955824 0.0828804
\(134\) 14.7816 1.27694
\(135\) 4.02293 0.346238
\(136\) 17.4134 1.49319
\(137\) −12.5012 −1.06805 −0.534024 0.845469i \(-0.679321\pi\)
−0.534024 + 0.845469i \(0.679321\pi\)
\(138\) 14.5718 1.24043
\(139\) 3.94608 0.334702 0.167351 0.985897i \(-0.446479\pi\)
0.167351 + 0.985897i \(0.446479\pi\)
\(140\) −18.3865 −1.55394
\(141\) 10.5562 0.888992
\(142\) 14.5665 1.22239
\(143\) 8.15323 0.681807
\(144\) 7.74793 0.645661
\(145\) −8.50853 −0.706595
\(146\) 30.8357 2.55198
\(147\) −1.00000 −0.0824786
\(148\) 33.1874 2.72799
\(149\) −14.7408 −1.20761 −0.603807 0.797130i \(-0.706350\pi\)
−0.603807 + 0.797130i \(0.706350\pi\)
\(150\) 28.6676 2.34070
\(151\) −0.942868 −0.0767295 −0.0383647 0.999264i \(-0.512215\pi\)
−0.0383647 + 0.999264i \(0.512215\pi\)
\(152\) −6.29766 −0.510808
\(153\) −2.64291 −0.213667
\(154\) 5.24017 0.422265
\(155\) 14.2546 1.14496
\(156\) 18.2280 1.45940
\(157\) −1.74511 −0.139275 −0.0696376 0.997572i \(-0.522184\pi\)
−0.0696376 + 0.997572i \(0.522184\pi\)
\(158\) 5.36325 0.426678
\(159\) −0.903669 −0.0716656
\(160\) 26.8840 2.12537
\(161\) 5.68481 0.448025
\(162\) −2.56328 −0.201391
\(163\) 5.76830 0.451808 0.225904 0.974150i \(-0.427466\pi\)
0.225904 + 0.974150i \(0.427466\pi\)
\(164\) −10.2611 −0.801256
\(165\) −8.22414 −0.640248
\(166\) 0.262418 0.0203676
\(167\) −9.38778 −0.726448 −0.363224 0.931702i \(-0.618324\pi\)
−0.363224 + 0.931702i \(0.618324\pi\)
\(168\) 6.58873 0.508331
\(169\) 2.90607 0.223544
\(170\) −27.2534 −2.09024
\(171\) 0.955824 0.0730937
\(172\) 41.9417 3.19802
\(173\) −1.87702 −0.142707 −0.0713535 0.997451i \(-0.522732\pi\)
−0.0713535 + 0.997451i \(0.522732\pi\)
\(174\) 5.42137 0.410993
\(175\) 11.1839 0.845427
\(176\) −15.8392 −1.19393
\(177\) 5.90876 0.444130
\(178\) 23.7278 1.77847
\(179\) −20.4454 −1.52816 −0.764079 0.645123i \(-0.776806\pi\)
−0.764079 + 0.645123i \(0.776806\pi\)
\(180\) −18.3865 −1.37045
\(181\) 8.66454 0.644030 0.322015 0.946735i \(-0.395640\pi\)
0.322015 + 0.946735i \(0.395640\pi\)
\(182\) 10.2230 0.757779
\(183\) 4.64238 0.343174
\(184\) −37.4556 −2.76127
\(185\) −29.2118 −2.14770
\(186\) −9.08261 −0.665969
\(187\) 5.40295 0.395103
\(188\) −48.2463 −3.51872
\(189\) −1.00000 −0.0727393
\(190\) 9.85636 0.715056
\(191\) −21.0559 −1.52355 −0.761775 0.647842i \(-0.775672\pi\)
−0.761775 + 0.647842i \(0.775672\pi\)
\(192\) −1.63378 −0.117908
\(193\) −24.3282 −1.75118 −0.875590 0.483054i \(-0.839527\pi\)
−0.875590 + 0.483054i \(0.839527\pi\)
\(194\) −44.6300 −3.20425
\(195\) −16.0444 −1.14896
\(196\) 4.57042 0.326459
\(197\) 9.16186 0.652755 0.326378 0.945239i \(-0.394172\pi\)
0.326378 + 0.945239i \(0.394172\pi\)
\(198\) 5.24017 0.372402
\(199\) −15.8809 −1.12576 −0.562882 0.826537i \(-0.690308\pi\)
−0.562882 + 0.826537i \(0.690308\pi\)
\(200\) −73.6880 −5.21053
\(201\) 5.76668 0.406750
\(202\) −10.3908 −0.731093
\(203\) 2.11501 0.148445
\(204\) 12.0792 0.845715
\(205\) 9.03189 0.630815
\(206\) 17.1270 1.19330
\(207\) 5.68481 0.395121
\(208\) −30.9006 −2.14257
\(209\) −1.95401 −0.135161
\(210\) −10.3119 −0.711589
\(211\) 11.3669 0.782528 0.391264 0.920278i \(-0.372038\pi\)
0.391264 + 0.920278i \(0.372038\pi\)
\(212\) 4.13015 0.283660
\(213\) 5.68274 0.389375
\(214\) −40.8042 −2.78932
\(215\) −36.9174 −2.51775
\(216\) 6.58873 0.448306
\(217\) −3.54335 −0.240538
\(218\) −1.71875 −0.116409
\(219\) 12.0298 0.812896
\(220\) 37.5878 2.53417
\(221\) 10.5406 0.709035
\(222\) 18.6129 1.24921
\(223\) 16.2233 1.08639 0.543196 0.839606i \(-0.317214\pi\)
0.543196 + 0.839606i \(0.317214\pi\)
\(224\) −6.68269 −0.446506
\(225\) 11.1839 0.745596
\(226\) −14.0844 −0.936882
\(227\) −6.93735 −0.460448 −0.230224 0.973138i \(-0.573946\pi\)
−0.230224 + 0.973138i \(0.573946\pi\)
\(228\) −4.36852 −0.289312
\(229\) 1.57459 0.104052 0.0520259 0.998646i \(-0.483432\pi\)
0.0520259 + 0.998646i \(0.483432\pi\)
\(230\) 58.6212 3.86537
\(231\) 2.04432 0.134506
\(232\) −13.9352 −0.914892
\(233\) −6.63984 −0.434990 −0.217495 0.976061i \(-0.569789\pi\)
−0.217495 + 0.976061i \(0.569789\pi\)
\(234\) 10.2230 0.668298
\(235\) 42.4668 2.77023
\(236\) −27.0055 −1.75791
\(237\) 2.09234 0.135912
\(238\) 6.77453 0.439128
\(239\) 7.77321 0.502807 0.251403 0.967882i \(-0.419108\pi\)
0.251403 + 0.967882i \(0.419108\pi\)
\(240\) 31.1694 2.01197
\(241\) −17.0364 −1.09741 −0.548707 0.836015i \(-0.684880\pi\)
−0.548707 + 0.836015i \(0.684880\pi\)
\(242\) 17.4836 1.12389
\(243\) −1.00000 −0.0641500
\(244\) −21.2176 −1.35832
\(245\) −4.02293 −0.257015
\(246\) −5.75484 −0.366915
\(247\) −3.81205 −0.242555
\(248\) 23.3462 1.48248
\(249\) 0.102376 0.00648780
\(250\) 63.7682 4.03306
\(251\) −29.1693 −1.84115 −0.920576 0.390563i \(-0.872280\pi\)
−0.920576 + 0.390563i \(0.872280\pi\)
\(252\) 4.57042 0.287910
\(253\) −11.6215 −0.730640
\(254\) 20.0904 1.26058
\(255\) −10.6322 −0.665817
\(256\) −26.7922 −1.67451
\(257\) 15.1827 0.947070 0.473535 0.880775i \(-0.342978\pi\)
0.473535 + 0.880775i \(0.342978\pi\)
\(258\) 23.5226 1.46445
\(259\) 7.26134 0.451198
\(260\) 73.3297 4.54772
\(261\) 2.11501 0.130916
\(262\) −34.1039 −2.10694
\(263\) 27.1481 1.67403 0.837013 0.547183i \(-0.184300\pi\)
0.837013 + 0.547183i \(0.184300\pi\)
\(264\) −13.4695 −0.828987
\(265\) −3.63539 −0.223320
\(266\) −2.45005 −0.150222
\(267\) 9.25679 0.566507
\(268\) −26.3562 −1.60996
\(269\) 2.49848 0.152335 0.0761675 0.997095i \(-0.475732\pi\)
0.0761675 + 0.997095i \(0.475732\pi\)
\(270\) −10.3119 −0.627563
\(271\) −5.52726 −0.335757 −0.167878 0.985808i \(-0.553692\pi\)
−0.167878 + 0.985808i \(0.553692\pi\)
\(272\) −20.4771 −1.24161
\(273\) 3.98824 0.241379
\(274\) 32.0441 1.93585
\(275\) −22.8635 −1.37872
\(276\) −25.9820 −1.56393
\(277\) 4.50271 0.270541 0.135271 0.990809i \(-0.456810\pi\)
0.135271 + 0.990809i \(0.456810\pi\)
\(278\) −10.1149 −0.606653
\(279\) −3.54335 −0.212135
\(280\) 26.5060 1.58403
\(281\) 1.30509 0.0778550 0.0389275 0.999242i \(-0.487606\pi\)
0.0389275 + 0.999242i \(0.487606\pi\)
\(282\) −27.0585 −1.61131
\(283\) −4.46319 −0.265309 −0.132655 0.991162i \(-0.542350\pi\)
−0.132655 + 0.991162i \(0.542350\pi\)
\(284\) −25.9725 −1.54119
\(285\) 3.84521 0.227771
\(286\) −20.8990 −1.23579
\(287\) −2.24510 −0.132524
\(288\) −6.68269 −0.393781
\(289\) −10.0150 −0.589119
\(290\) 21.8098 1.28071
\(291\) −17.4113 −1.02067
\(292\) −54.9811 −3.21753
\(293\) 0.00623872 0.000364470 0 0.000182235 1.00000i \(-0.499942\pi\)
0.000182235 1.00000i \(0.499942\pi\)
\(294\) 2.56328 0.149494
\(295\) 23.7705 1.38397
\(296\) −47.8430 −2.78082
\(297\) 2.04432 0.118623
\(298\) 37.7849 2.18882
\(299\) −22.6724 −1.31118
\(300\) −51.1154 −2.95115
\(301\) 9.17675 0.528939
\(302\) 2.41684 0.139073
\(303\) −4.05370 −0.232879
\(304\) 7.40566 0.424743
\(305\) 18.6759 1.06938
\(306\) 6.77453 0.387274
\(307\) −25.8509 −1.47539 −0.737694 0.675135i \(-0.764085\pi\)
−0.737694 + 0.675135i \(0.764085\pi\)
\(308\) −9.34340 −0.532389
\(309\) 6.68168 0.380107
\(310\) −36.5387 −2.07526
\(311\) 8.78160 0.497959 0.248979 0.968509i \(-0.419905\pi\)
0.248979 + 0.968509i \(0.419905\pi\)
\(312\) −26.2774 −1.48767
\(313\) −18.0846 −1.02220 −0.511101 0.859521i \(-0.670762\pi\)
−0.511101 + 0.859521i \(0.670762\pi\)
\(314\) 4.47322 0.252439
\(315\) −4.02293 −0.226666
\(316\) −9.56287 −0.537953
\(317\) 4.96903 0.279088 0.139544 0.990216i \(-0.455436\pi\)
0.139544 + 0.990216i \(0.455436\pi\)
\(318\) 2.31636 0.129895
\(319\) −4.32375 −0.242083
\(320\) −6.57256 −0.367417
\(321\) −15.9187 −0.888496
\(322\) −14.5718 −0.812053
\(323\) −2.52616 −0.140559
\(324\) 4.57042 0.253912
\(325\) −44.6043 −2.47420
\(326\) −14.7858 −0.818909
\(327\) −0.670528 −0.0370803
\(328\) 14.7924 0.816773
\(329\) −10.5562 −0.581982
\(330\) 21.0808 1.16046
\(331\) −9.09624 −0.499974 −0.249987 0.968249i \(-0.580426\pi\)
−0.249987 + 0.968249i \(0.580426\pi\)
\(332\) −0.467901 −0.0256794
\(333\) 7.26134 0.397919
\(334\) 24.0635 1.31670
\(335\) 23.1989 1.26749
\(336\) −7.74793 −0.422684
\(337\) −19.0399 −1.03717 −0.518585 0.855026i \(-0.673541\pi\)
−0.518585 + 0.855026i \(0.673541\pi\)
\(338\) −7.44907 −0.405176
\(339\) −5.49468 −0.298430
\(340\) 48.5938 2.63537
\(341\) 7.24373 0.392270
\(342\) −2.45005 −0.132483
\(343\) 1.00000 0.0539949
\(344\) −60.4631 −3.25995
\(345\) 22.8696 1.23126
\(346\) 4.81133 0.258659
\(347\) 16.9033 0.907414 0.453707 0.891151i \(-0.350101\pi\)
0.453707 + 0.891151i \(0.350101\pi\)
\(348\) −9.66649 −0.518178
\(349\) 15.3604 0.822221 0.411110 0.911586i \(-0.365141\pi\)
0.411110 + 0.911586i \(0.365141\pi\)
\(350\) −28.6676 −1.53235
\(351\) 3.98824 0.212877
\(352\) 13.6615 0.728163
\(353\) −2.26559 −0.120585 −0.0602925 0.998181i \(-0.519203\pi\)
−0.0602925 + 0.998181i \(0.519203\pi\)
\(354\) −15.1458 −0.804992
\(355\) 22.8612 1.21335
\(356\) −42.3075 −2.24229
\(357\) 2.64291 0.139878
\(358\) 52.4072 2.76981
\(359\) −7.90961 −0.417453 −0.208727 0.977974i \(-0.566932\pi\)
−0.208727 + 0.977974i \(0.566932\pi\)
\(360\) 26.5060 1.39699
\(361\) −18.0864 −0.951916
\(362\) −22.2097 −1.16731
\(363\) 6.82077 0.357997
\(364\) −18.2280 −0.955404
\(365\) 48.3949 2.53310
\(366\) −11.8997 −0.622009
\(367\) 23.0178 1.20152 0.600758 0.799431i \(-0.294865\pi\)
0.600758 + 0.799431i \(0.294865\pi\)
\(368\) 44.0455 2.29603
\(369\) −2.24510 −0.116875
\(370\) 74.8782 3.89273
\(371\) 0.903669 0.0469161
\(372\) 16.1946 0.839652
\(373\) 0.910604 0.0471493 0.0235746 0.999722i \(-0.492495\pi\)
0.0235746 + 0.999722i \(0.492495\pi\)
\(374\) −13.8493 −0.716130
\(375\) 24.8776 1.28467
\(376\) 69.5519 3.58687
\(377\) −8.43517 −0.434433
\(378\) 2.56328 0.131841
\(379\) 12.6111 0.647788 0.323894 0.946093i \(-0.395008\pi\)
0.323894 + 0.946093i \(0.395008\pi\)
\(380\) −17.5742 −0.901539
\(381\) 7.83776 0.401541
\(382\) 53.9722 2.76146
\(383\) −1.00000 −0.0510976
\(384\) −9.17755 −0.468340
\(385\) 8.22414 0.419141
\(386\) 62.3600 3.17404
\(387\) 9.17675 0.466481
\(388\) 79.5769 4.03991
\(389\) −6.87183 −0.348416 −0.174208 0.984709i \(-0.555736\pi\)
−0.174208 + 0.984709i \(0.555736\pi\)
\(390\) 41.1264 2.08251
\(391\) −15.0244 −0.759818
\(392\) −6.58873 −0.332781
\(393\) −13.3048 −0.671136
\(394\) −23.4844 −1.18313
\(395\) 8.41732 0.423521
\(396\) −9.34340 −0.469523
\(397\) −18.1901 −0.912935 −0.456467 0.889740i \(-0.650886\pi\)
−0.456467 + 0.889740i \(0.650886\pi\)
\(398\) 40.7072 2.04047
\(399\) −0.955824 −0.0478510
\(400\) 86.6524 4.33262
\(401\) −13.1933 −0.658840 −0.329420 0.944183i \(-0.606853\pi\)
−0.329420 + 0.944183i \(0.606853\pi\)
\(402\) −14.7816 −0.737241
\(403\) 14.1317 0.703952
\(404\) 18.5271 0.921759
\(405\) −4.02293 −0.199901
\(406\) −5.42137 −0.269058
\(407\) −14.8445 −0.735814
\(408\) −17.4134 −0.862093
\(409\) −30.4427 −1.50530 −0.752648 0.658423i \(-0.771224\pi\)
−0.752648 + 0.658423i \(0.771224\pi\)
\(410\) −23.1513 −1.14336
\(411\) 12.5012 0.616638
\(412\) −30.5381 −1.50450
\(413\) −5.90876 −0.290751
\(414\) −14.5718 −0.716163
\(415\) 0.411850 0.0202169
\(416\) 26.6522 1.30673
\(417\) −3.94608 −0.193240
\(418\) 5.00867 0.244982
\(419\) −3.12119 −0.152480 −0.0762400 0.997089i \(-0.524292\pi\)
−0.0762400 + 0.997089i \(0.524292\pi\)
\(420\) 18.3865 0.897169
\(421\) −27.5179 −1.34114 −0.670570 0.741846i \(-0.733950\pi\)
−0.670570 + 0.741846i \(0.733950\pi\)
\(422\) −29.1365 −1.41834
\(423\) −10.5562 −0.513260
\(424\) −5.95403 −0.289153
\(425\) −29.5582 −1.43378
\(426\) −14.5665 −0.705748
\(427\) −4.64238 −0.224660
\(428\) 72.7553 3.51676
\(429\) −8.15323 −0.393642
\(430\) 94.6298 4.56345
\(431\) 28.6289 1.37900 0.689502 0.724284i \(-0.257829\pi\)
0.689502 + 0.724284i \(0.257829\pi\)
\(432\) −7.74793 −0.372773
\(433\) 2.89495 0.139123 0.0695613 0.997578i \(-0.477840\pi\)
0.0695613 + 0.997578i \(0.477840\pi\)
\(434\) 9.08261 0.435979
\(435\) 8.50853 0.407953
\(436\) 3.06460 0.146768
\(437\) 5.43367 0.259928
\(438\) −30.8357 −1.47339
\(439\) 37.3897 1.78451 0.892256 0.451530i \(-0.149122\pi\)
0.892256 + 0.451530i \(0.149122\pi\)
\(440\) −54.1866 −2.58325
\(441\) 1.00000 0.0476190
\(442\) −27.0185 −1.28514
\(443\) −2.85854 −0.135813 −0.0679066 0.997692i \(-0.521632\pi\)
−0.0679066 + 0.997692i \(0.521632\pi\)
\(444\) −33.1874 −1.57500
\(445\) 37.2394 1.76532
\(446\) −41.5849 −1.96910
\(447\) 14.7408 0.697217
\(448\) 1.63378 0.0771886
\(449\) −6.77794 −0.319871 −0.159935 0.987127i \(-0.551129\pi\)
−0.159935 + 0.987127i \(0.551129\pi\)
\(450\) −28.6676 −1.35140
\(451\) 4.58970 0.216121
\(452\) 25.1130 1.18122
\(453\) 0.942868 0.0442998
\(454\) 17.7824 0.834570
\(455\) 16.0444 0.752173
\(456\) 6.29766 0.294915
\(457\) 3.47991 0.162783 0.0813916 0.996682i \(-0.474064\pi\)
0.0813916 + 0.996682i \(0.474064\pi\)
\(458\) −4.03612 −0.188595
\(459\) 2.64291 0.123361
\(460\) −104.524 −4.87344
\(461\) 17.4648 0.813415 0.406708 0.913558i \(-0.366677\pi\)
0.406708 + 0.913558i \(0.366677\pi\)
\(462\) −5.24017 −0.243795
\(463\) 6.87390 0.319457 0.159729 0.987161i \(-0.448938\pi\)
0.159729 + 0.987161i \(0.448938\pi\)
\(464\) 16.3869 0.760745
\(465\) −14.2546 −0.661043
\(466\) 17.0198 0.788427
\(467\) 17.8400 0.825535 0.412768 0.910836i \(-0.364562\pi\)
0.412768 + 0.910836i \(0.364562\pi\)
\(468\) −18.2280 −0.842588
\(469\) −5.76668 −0.266280
\(470\) −108.854 −5.02108
\(471\) 1.74511 0.0804106
\(472\) 38.9312 1.79195
\(473\) −18.7602 −0.862595
\(474\) −5.36325 −0.246342
\(475\) 10.6899 0.490485
\(476\) −12.0792 −0.553650
\(477\) 0.903669 0.0413761
\(478\) −19.9249 −0.911345
\(479\) −7.67759 −0.350798 −0.175399 0.984497i \(-0.556122\pi\)
−0.175399 + 0.984497i \(0.556122\pi\)
\(480\) −26.8840 −1.22708
\(481\) −28.9600 −1.32046
\(482\) 43.6693 1.98908
\(483\) −5.68481 −0.258668
\(484\) −31.1738 −1.41699
\(485\) −70.0443 −3.18055
\(486\) 2.56328 0.116273
\(487\) 5.06733 0.229622 0.114811 0.993387i \(-0.463374\pi\)
0.114811 + 0.993387i \(0.463374\pi\)
\(488\) 30.5874 1.38462
\(489\) −5.76830 −0.260851
\(490\) 10.3119 0.465844
\(491\) 28.4086 1.28206 0.641031 0.767515i \(-0.278507\pi\)
0.641031 + 0.767515i \(0.278507\pi\)
\(492\) 10.2611 0.462605
\(493\) −5.58978 −0.251751
\(494\) 9.77138 0.439635
\(495\) 8.22414 0.369648
\(496\) −27.4536 −1.23270
\(497\) −5.68274 −0.254906
\(498\) −0.262418 −0.0117592
\(499\) −20.3883 −0.912706 −0.456353 0.889799i \(-0.650844\pi\)
−0.456353 + 0.889799i \(0.650844\pi\)
\(500\) −113.701 −5.08486
\(501\) 9.38778 0.419415
\(502\) 74.7693 3.33712
\(503\) 26.0575 1.16185 0.580923 0.813958i \(-0.302692\pi\)
0.580923 + 0.813958i \(0.302692\pi\)
\(504\) −6.58873 −0.293485
\(505\) −16.3077 −0.725684
\(506\) 29.7893 1.32430
\(507\) −2.90607 −0.129063
\(508\) −35.8219 −1.58934
\(509\) 34.9571 1.54945 0.774724 0.632300i \(-0.217889\pi\)
0.774724 + 0.632300i \(0.217889\pi\)
\(510\) 27.2534 1.20680
\(511\) −12.0298 −0.532165
\(512\) 50.3210 2.22389
\(513\) −0.955824 −0.0422006
\(514\) −38.9175 −1.71658
\(515\) 26.8799 1.18447
\(516\) −41.9417 −1.84638
\(517\) 21.5802 0.949097
\(518\) −18.6129 −0.817803
\(519\) 1.87702 0.0823919
\(520\) −105.712 −4.63579
\(521\) 5.04523 0.221036 0.110518 0.993874i \(-0.464749\pi\)
0.110518 + 0.993874i \(0.464749\pi\)
\(522\) −5.42137 −0.237287
\(523\) −39.3182 −1.71927 −0.859633 0.510912i \(-0.829308\pi\)
−0.859633 + 0.510912i \(0.829308\pi\)
\(524\) 60.8084 2.65643
\(525\) −11.1839 −0.488107
\(526\) −69.5884 −3.03420
\(527\) 9.36476 0.407935
\(528\) 15.8392 0.689314
\(529\) 9.31701 0.405087
\(530\) 9.31854 0.404772
\(531\) −5.90876 −0.256418
\(532\) 4.36852 0.189399
\(533\) 8.95402 0.387841
\(534\) −23.7278 −1.02680
\(535\) −64.0398 −2.76868
\(536\) 37.9951 1.64114
\(537\) 20.4454 0.882282
\(538\) −6.40431 −0.276109
\(539\) −2.04432 −0.0880550
\(540\) 18.3865 0.791228
\(541\) −15.1529 −0.651474 −0.325737 0.945460i \(-0.605612\pi\)
−0.325737 + 0.945460i \(0.605612\pi\)
\(542\) 14.1679 0.608564
\(543\) −8.66454 −0.371831
\(544\) 17.6618 0.757242
\(545\) −2.69748 −0.115547
\(546\) −10.2230 −0.437504
\(547\) 1.85970 0.0795149 0.0397575 0.999209i \(-0.487341\pi\)
0.0397575 + 0.999209i \(0.487341\pi\)
\(548\) −57.1357 −2.44072
\(549\) −4.64238 −0.198132
\(550\) 58.6057 2.49896
\(551\) 2.02158 0.0861220
\(552\) 37.4556 1.59422
\(553\) −2.09234 −0.0889752
\(554\) −11.5417 −0.490361
\(555\) 29.2118 1.23997
\(556\) 18.0353 0.764866
\(557\) 38.2706 1.62158 0.810790 0.585338i \(-0.199038\pi\)
0.810790 + 0.585338i \(0.199038\pi\)
\(558\) 9.08261 0.384498
\(559\) −36.5991 −1.54798
\(560\) −31.1694 −1.31715
\(561\) −5.40295 −0.228113
\(562\) −3.34531 −0.141113
\(563\) −21.6875 −0.914021 −0.457011 0.889461i \(-0.651080\pi\)
−0.457011 + 0.889461i \(0.651080\pi\)
\(564\) 48.2463 2.03154
\(565\) −22.1047 −0.929951
\(566\) 11.4404 0.480877
\(567\) 1.00000 0.0419961
\(568\) 37.4420 1.57103
\(569\) −18.5523 −0.777755 −0.388877 0.921289i \(-0.627137\pi\)
−0.388877 + 0.921289i \(0.627137\pi\)
\(570\) −9.85636 −0.412838
\(571\) −0.274191 −0.0114745 −0.00573726 0.999984i \(-0.501826\pi\)
−0.00573726 + 0.999984i \(0.501826\pi\)
\(572\) 37.2637 1.55807
\(573\) 21.0559 0.879622
\(574\) 5.75484 0.240202
\(575\) 63.5785 2.65141
\(576\) 1.63378 0.0680740
\(577\) 41.8550 1.74245 0.871224 0.490886i \(-0.163327\pi\)
0.871224 + 0.490886i \(0.163327\pi\)
\(578\) 25.6713 1.06779
\(579\) 24.3282 1.01104
\(580\) −38.8876 −1.61472
\(581\) −0.102376 −0.00424726
\(582\) 44.6300 1.84997
\(583\) −1.84739 −0.0765109
\(584\) 79.2608 3.27984
\(585\) 16.0444 0.663354
\(586\) −0.0159916 −0.000660607 0
\(587\) 22.8612 0.943584 0.471792 0.881710i \(-0.343607\pi\)
0.471792 + 0.881710i \(0.343607\pi\)
\(588\) −4.57042 −0.188481
\(589\) −3.38682 −0.139551
\(590\) −60.9306 −2.50847
\(591\) −9.16186 −0.376868
\(592\) 56.2604 2.31229
\(593\) −12.5229 −0.514253 −0.257127 0.966378i \(-0.582776\pi\)
−0.257127 + 0.966378i \(0.582776\pi\)
\(594\) −5.24017 −0.215007
\(595\) 10.6322 0.435879
\(596\) −67.3718 −2.75966
\(597\) 15.8809 0.649961
\(598\) 58.1157 2.37653
\(599\) −13.0209 −0.532019 −0.266009 0.963970i \(-0.585705\pi\)
−0.266009 + 0.963970i \(0.585705\pi\)
\(600\) 73.6880 3.00830
\(601\) 11.7006 0.477279 0.238640 0.971108i \(-0.423299\pi\)
0.238640 + 0.971108i \(0.423299\pi\)
\(602\) −23.5226 −0.958711
\(603\) −5.76668 −0.234837
\(604\) −4.30931 −0.175343
\(605\) 27.4394 1.11557
\(606\) 10.3908 0.422096
\(607\) −32.1572 −1.30522 −0.652610 0.757694i \(-0.726326\pi\)
−0.652610 + 0.757694i \(0.726326\pi\)
\(608\) −6.38748 −0.259046
\(609\) −2.11501 −0.0857045
\(610\) −47.8717 −1.93827
\(611\) 42.1007 1.70321
\(612\) −12.0792 −0.488274
\(613\) −13.8065 −0.557639 −0.278819 0.960344i \(-0.589943\pi\)
−0.278819 + 0.960344i \(0.589943\pi\)
\(614\) 66.2632 2.67416
\(615\) −9.03189 −0.364201
\(616\) 13.4695 0.542700
\(617\) 30.2406 1.21744 0.608720 0.793385i \(-0.291683\pi\)
0.608720 + 0.793385i \(0.291683\pi\)
\(618\) −17.1270 −0.688951
\(619\) 38.6627 1.55398 0.776992 0.629511i \(-0.216745\pi\)
0.776992 + 0.629511i \(0.216745\pi\)
\(620\) 65.1498 2.61648
\(621\) −5.68481 −0.228123
\(622\) −22.5097 −0.902558
\(623\) −9.25679 −0.370866
\(624\) 30.9006 1.23701
\(625\) 44.1609 1.76643
\(626\) 46.3560 1.85276
\(627\) 1.95401 0.0780355
\(628\) −7.97591 −0.318273
\(629\) −19.1911 −0.765198
\(630\) 10.3119 0.410836
\(631\) −27.1322 −1.08011 −0.540057 0.841628i \(-0.681597\pi\)
−0.540057 + 0.841628i \(0.681597\pi\)
\(632\) 13.7858 0.548371
\(633\) −11.3669 −0.451793
\(634\) −12.7370 −0.505852
\(635\) 31.5307 1.25126
\(636\) −4.13015 −0.163771
\(637\) −3.98824 −0.158020
\(638\) 11.0830 0.438780
\(639\) −5.68274 −0.224806
\(640\) −36.9206 −1.45942
\(641\) −44.4324 −1.75497 −0.877487 0.479601i \(-0.840781\pi\)
−0.877487 + 0.479601i \(0.840781\pi\)
\(642\) 40.8042 1.61041
\(643\) 30.7327 1.21198 0.605989 0.795473i \(-0.292778\pi\)
0.605989 + 0.795473i \(0.292778\pi\)
\(644\) 25.9820 1.02383
\(645\) 36.9174 1.45362
\(646\) 6.47526 0.254766
\(647\) −45.6093 −1.79309 −0.896543 0.442956i \(-0.853930\pi\)
−0.896543 + 0.442956i \(0.853930\pi\)
\(648\) −6.58873 −0.258830
\(649\) 12.0794 0.474157
\(650\) 114.333 4.48452
\(651\) 3.54335 0.138875
\(652\) 26.3636 1.03248
\(653\) −8.67504 −0.339480 −0.169740 0.985489i \(-0.554293\pi\)
−0.169740 + 0.985489i \(0.554293\pi\)
\(654\) 1.71875 0.0672085
\(655\) −53.5241 −2.09136
\(656\) −17.3949 −0.679157
\(657\) −12.0298 −0.469326
\(658\) 27.0585 1.05485
\(659\) −12.9070 −0.502784 −0.251392 0.967885i \(-0.580888\pi\)
−0.251392 + 0.967885i \(0.580888\pi\)
\(660\) −37.5878 −1.46310
\(661\) 22.2481 0.865350 0.432675 0.901550i \(-0.357570\pi\)
0.432675 + 0.901550i \(0.357570\pi\)
\(662\) 23.3162 0.906211
\(663\) −10.5406 −0.409362
\(664\) 0.674526 0.0261767
\(665\) −3.84521 −0.149111
\(666\) −18.6129 −0.721234
\(667\) 12.0234 0.465548
\(668\) −42.9061 −1.66009
\(669\) −16.2233 −0.627228
\(670\) −59.4654 −2.29735
\(671\) 9.49049 0.366376
\(672\) 6.68269 0.257790
\(673\) −3.96523 −0.152849 −0.0764243 0.997075i \(-0.524350\pi\)
−0.0764243 + 0.997075i \(0.524350\pi\)
\(674\) 48.8047 1.87989
\(675\) −11.1839 −0.430470
\(676\) 13.2820 0.510844
\(677\) 8.87621 0.341140 0.170570 0.985346i \(-0.445439\pi\)
0.170570 + 0.985346i \(0.445439\pi\)
\(678\) 14.0844 0.540909
\(679\) 17.4113 0.668183
\(680\) −70.0529 −2.68641
\(681\) 6.93735 0.265840
\(682\) −18.5677 −0.710996
\(683\) −0.742743 −0.0284203 −0.0142101 0.999899i \(-0.504523\pi\)
−0.0142101 + 0.999899i \(0.504523\pi\)
\(684\) 4.36852 0.167035
\(685\) 50.2913 1.92153
\(686\) −2.56328 −0.0978666
\(687\) −1.57459 −0.0600743
\(688\) 71.1009 2.71069
\(689\) −3.60405 −0.137303
\(690\) −58.6212 −2.23167
\(691\) 41.0374 1.56114 0.780568 0.625071i \(-0.214930\pi\)
0.780568 + 0.625071i \(0.214930\pi\)
\(692\) −8.57877 −0.326116
\(693\) −2.04432 −0.0776572
\(694\) −43.3278 −1.64470
\(695\) −15.8748 −0.602166
\(696\) 13.9352 0.528213
\(697\) 5.93361 0.224752
\(698\) −39.3729 −1.49029
\(699\) 6.63984 0.251142
\(700\) 51.1154 1.93198
\(701\) −12.6077 −0.476186 −0.238093 0.971242i \(-0.576522\pi\)
−0.238093 + 0.971242i \(0.576522\pi\)
\(702\) −10.2230 −0.385842
\(703\) 6.94056 0.261768
\(704\) −3.33996 −0.125879
\(705\) −42.4668 −1.59939
\(706\) 5.80734 0.218562
\(707\) 4.05370 0.152455
\(708\) 27.0055 1.01493
\(709\) −25.6422 −0.963014 −0.481507 0.876442i \(-0.659910\pi\)
−0.481507 + 0.876442i \(0.659910\pi\)
\(710\) −58.5998 −2.19921
\(711\) −2.09234 −0.0784688
\(712\) 60.9905 2.28572
\(713\) −20.1433 −0.754371
\(714\) −6.77453 −0.253530
\(715\) −32.7998 −1.22664
\(716\) −93.4439 −3.49216
\(717\) −7.77321 −0.290296
\(718\) 20.2746 0.756640
\(719\) 44.4331 1.65708 0.828538 0.559933i \(-0.189173\pi\)
0.828538 + 0.559933i \(0.189173\pi\)
\(720\) −31.1694 −1.16161
\(721\) −6.68168 −0.248839
\(722\) 46.3606 1.72536
\(723\) 17.0364 0.633592
\(724\) 39.6006 1.47175
\(725\) 23.6541 0.878493
\(726\) −17.4836 −0.648876
\(727\) −13.7089 −0.508434 −0.254217 0.967147i \(-0.581818\pi\)
−0.254217 + 0.967147i \(0.581818\pi\)
\(728\) 26.2774 0.973907
\(729\) 1.00000 0.0370370
\(730\) −124.050 −4.59129
\(731\) −24.2533 −0.897042
\(732\) 21.2176 0.784226
\(733\) −5.94860 −0.219716 −0.109858 0.993947i \(-0.535040\pi\)
−0.109858 + 0.993947i \(0.535040\pi\)
\(734\) −59.0010 −2.17777
\(735\) 4.02293 0.148388
\(736\) −37.9898 −1.40032
\(737\) 11.7889 0.434250
\(738\) 5.75484 0.211839
\(739\) −30.8869 −1.13619 −0.568096 0.822962i \(-0.692320\pi\)
−0.568096 + 0.822962i \(0.692320\pi\)
\(740\) −133.511 −4.90794
\(741\) 3.81205 0.140039
\(742\) −2.31636 −0.0850362
\(743\) −12.5600 −0.460781 −0.230391 0.973098i \(-0.574000\pi\)
−0.230391 + 0.973098i \(0.574000\pi\)
\(744\) −23.3462 −0.855912
\(745\) 59.3012 2.17263
\(746\) −2.33414 −0.0854588
\(747\) −0.102376 −0.00374573
\(748\) 24.6938 0.902894
\(749\) 15.9187 0.581657
\(750\) −63.7682 −2.32849
\(751\) 27.2977 0.996108 0.498054 0.867146i \(-0.334048\pi\)
0.498054 + 0.867146i \(0.334048\pi\)
\(752\) −81.7887 −2.98253
\(753\) 29.1693 1.06299
\(754\) 21.6217 0.787417
\(755\) 3.79309 0.138045
\(756\) −4.57042 −0.166225
\(757\) −5.20830 −0.189299 −0.0946495 0.995511i \(-0.530173\pi\)
−0.0946495 + 0.995511i \(0.530173\pi\)
\(758\) −32.3258 −1.17413
\(759\) 11.6215 0.421835
\(760\) 25.3350 0.918998
\(761\) 35.6890 1.29373 0.646863 0.762607i \(-0.276081\pi\)
0.646863 + 0.762607i \(0.276081\pi\)
\(762\) −20.0904 −0.727799
\(763\) 0.670528 0.0242747
\(764\) −96.2343 −3.48163
\(765\) 10.6322 0.384409
\(766\) 2.56328 0.0926152
\(767\) 23.5656 0.850903
\(768\) 26.7922 0.966781
\(769\) 14.3693 0.518168 0.259084 0.965855i \(-0.416579\pi\)
0.259084 + 0.965855i \(0.416579\pi\)
\(770\) −21.0808 −0.759699
\(771\) −15.1827 −0.546791
\(772\) −111.190 −4.00182
\(773\) 41.4087 1.48937 0.744684 0.667417i \(-0.232600\pi\)
0.744684 + 0.667417i \(0.232600\pi\)
\(774\) −23.5226 −0.845503
\(775\) −39.6286 −1.42350
\(776\) −114.718 −4.11814
\(777\) −7.26134 −0.260499
\(778\) 17.6145 0.631509
\(779\) −2.14592 −0.0768857
\(780\) −73.3297 −2.62563
\(781\) 11.6173 0.415700
\(782\) 38.5119 1.37718
\(783\) −2.11501 −0.0755843
\(784\) 7.74793 0.276712
\(785\) 7.02047 0.250571
\(786\) 34.1039 1.21644
\(787\) −8.15910 −0.290840 −0.145420 0.989370i \(-0.546453\pi\)
−0.145420 + 0.989370i \(0.546453\pi\)
\(788\) 41.8736 1.49168
\(789\) −27.1481 −0.966499
\(790\) −21.5760 −0.767639
\(791\) 5.49468 0.195368
\(792\) 13.4695 0.478616
\(793\) 18.5149 0.657484
\(794\) 46.6264 1.65471
\(795\) 3.63539 0.128934
\(796\) −72.5823 −2.57261
\(797\) 45.9056 1.62606 0.813029 0.582223i \(-0.197817\pi\)
0.813029 + 0.582223i \(0.197817\pi\)
\(798\) 2.45005 0.0867307
\(799\) 27.8991 0.986999
\(800\) −74.7389 −2.64242
\(801\) −9.25679 −0.327073
\(802\) 33.8181 1.19416
\(803\) 24.5927 0.867856
\(804\) 26.3562 0.929510
\(805\) −22.8696 −0.806046
\(806\) −36.2236 −1.27592
\(807\) −2.49848 −0.0879506
\(808\) −26.7087 −0.939609
\(809\) −42.2943 −1.48699 −0.743493 0.668743i \(-0.766833\pi\)
−0.743493 + 0.668743i \(0.766833\pi\)
\(810\) 10.3119 0.362323
\(811\) −12.2425 −0.429891 −0.214945 0.976626i \(-0.568957\pi\)
−0.214945 + 0.976626i \(0.568957\pi\)
\(812\) 9.66649 0.339227
\(813\) 5.52726 0.193849
\(814\) 38.0506 1.33367
\(815\) −23.2054 −0.812851
\(816\) 20.4771 0.716842
\(817\) 8.77136 0.306871
\(818\) 78.0334 2.72837
\(819\) −3.98824 −0.139360
\(820\) 41.2796 1.44155
\(821\) −43.1325 −1.50533 −0.752667 0.658401i \(-0.771233\pi\)
−0.752667 + 0.658401i \(0.771233\pi\)
\(822\) −32.0441 −1.11767
\(823\) −22.2274 −0.774797 −0.387398 0.921912i \(-0.626626\pi\)
−0.387398 + 0.921912i \(0.626626\pi\)
\(824\) 44.0238 1.53364
\(825\) 22.8635 0.796006
\(826\) 15.1458 0.526991
\(827\) 18.5947 0.646603 0.323301 0.946296i \(-0.395207\pi\)
0.323301 + 0.946296i \(0.395207\pi\)
\(828\) 25.9820 0.902936
\(829\) 42.8336 1.48767 0.743837 0.668362i \(-0.233004\pi\)
0.743837 + 0.668362i \(0.233004\pi\)
\(830\) −1.05569 −0.0366435
\(831\) −4.50271 −0.156197
\(832\) −6.51589 −0.225898
\(833\) −2.64291 −0.0915714
\(834\) 10.1149 0.350251
\(835\) 37.7663 1.30696
\(836\) −8.93064 −0.308873
\(837\) 3.54335 0.122476
\(838\) 8.00049 0.276372
\(839\) 16.0338 0.553548 0.276774 0.960935i \(-0.410735\pi\)
0.276774 + 0.960935i \(0.410735\pi\)
\(840\) −26.5060 −0.914543
\(841\) −24.5267 −0.845750
\(842\) 70.5362 2.43084
\(843\) −1.30509 −0.0449496
\(844\) 51.9514 1.78824
\(845\) −11.6909 −0.402179
\(846\) 27.0585 0.930291
\(847\) −6.82077 −0.234364
\(848\) 7.00156 0.240435
\(849\) 4.46319 0.153176
\(850\) 75.7660 2.59875
\(851\) 41.2793 1.41504
\(852\) 25.9725 0.889804
\(853\) 10.2883 0.352265 0.176132 0.984367i \(-0.443641\pi\)
0.176132 + 0.984367i \(0.443641\pi\)
\(854\) 11.8997 0.407200
\(855\) −3.84521 −0.131503
\(856\) −104.884 −3.58486
\(857\) 31.2063 1.06599 0.532994 0.846119i \(-0.321067\pi\)
0.532994 + 0.846119i \(0.321067\pi\)
\(858\) 20.8990 0.713482
\(859\) 45.8315 1.56375 0.781876 0.623434i \(-0.214263\pi\)
0.781876 + 0.623434i \(0.214263\pi\)
\(860\) −168.728 −5.75359
\(861\) 2.24510 0.0765129
\(862\) −73.3839 −2.49947
\(863\) 55.0210 1.87294 0.936469 0.350750i \(-0.114073\pi\)
0.936469 + 0.350750i \(0.114073\pi\)
\(864\) 6.68269 0.227350
\(865\) 7.55110 0.256745
\(866\) −7.42059 −0.252162
\(867\) 10.0150 0.340128
\(868\) −16.1946 −0.549681
\(869\) 4.27740 0.145101
\(870\) −21.8098 −0.739420
\(871\) 22.9989 0.779288
\(872\) −4.41792 −0.149610
\(873\) 17.4113 0.589282
\(874\) −13.9280 −0.471123
\(875\) −24.8776 −0.841015
\(876\) 54.9811 1.85764
\(877\) −31.9097 −1.07751 −0.538756 0.842462i \(-0.681106\pi\)
−0.538756 + 0.842462i \(0.681106\pi\)
\(878\) −95.8404 −3.23446
\(879\) −0.00623872 −0.000210427 0
\(880\) 63.7201 2.14800
\(881\) 41.2680 1.39035 0.695177 0.718839i \(-0.255326\pi\)
0.695177 + 0.718839i \(0.255326\pi\)
\(882\) −2.56328 −0.0863103
\(883\) −8.13370 −0.273721 −0.136860 0.990590i \(-0.543701\pi\)
−0.136860 + 0.990590i \(0.543701\pi\)
\(884\) 48.1749 1.62030
\(885\) −23.7705 −0.799037
\(886\) 7.32725 0.246164
\(887\) −5.50769 −0.184930 −0.0924651 0.995716i \(-0.529475\pi\)
−0.0924651 + 0.995716i \(0.529475\pi\)
\(888\) 47.8430 1.60551
\(889\) −7.83776 −0.262870
\(890\) −95.4552 −3.19966
\(891\) −2.04432 −0.0684872
\(892\) 74.1473 2.48263
\(893\) −10.0899 −0.337644
\(894\) −37.7849 −1.26372
\(895\) 82.2502 2.74932
\(896\) 9.17755 0.306601
\(897\) 22.6724 0.757008
\(898\) 17.3738 0.579771
\(899\) −7.49422 −0.249946
\(900\) 51.1154 1.70385
\(901\) −2.38832 −0.0795663
\(902\) −11.7647 −0.391722
\(903\) −9.17675 −0.305383
\(904\) −36.2029 −1.20409
\(905\) −34.8568 −1.15868
\(906\) −2.41684 −0.0802940
\(907\) 34.5792 1.14818 0.574091 0.818791i \(-0.305355\pi\)
0.574091 + 0.818791i \(0.305355\pi\)
\(908\) −31.7067 −1.05222
\(909\) 4.05370 0.134453
\(910\) −41.1264 −1.36333
\(911\) 29.1614 0.966159 0.483080 0.875576i \(-0.339518\pi\)
0.483080 + 0.875576i \(0.339518\pi\)
\(912\) −7.40566 −0.245226
\(913\) 0.209289 0.00692644
\(914\) −8.91999 −0.295047
\(915\) −18.6759 −0.617408
\(916\) 7.19654 0.237780
\(917\) 13.3048 0.439362
\(918\) −6.77453 −0.223593
\(919\) −14.1196 −0.465762 −0.232881 0.972505i \(-0.574815\pi\)
−0.232881 + 0.972505i \(0.574815\pi\)
\(920\) 150.681 4.96781
\(921\) 25.8509 0.851816
\(922\) −44.7672 −1.47433
\(923\) 22.6641 0.745999
\(924\) 9.34340 0.307375
\(925\) 81.2104 2.67018
\(926\) −17.6198 −0.579021
\(927\) −6.68168 −0.219455
\(928\) −14.1340 −0.463970
\(929\) −8.43203 −0.276646 −0.138323 0.990387i \(-0.544171\pi\)
−0.138323 + 0.990387i \(0.544171\pi\)
\(930\) 36.5387 1.19815
\(931\) 0.955824 0.0313259
\(932\) −30.3469 −0.994045
\(933\) −8.78160 −0.287497
\(934\) −45.7289 −1.49630
\(935\) −21.7357 −0.710832
\(936\) 26.2774 0.858905
\(937\) 24.2574 0.792455 0.396227 0.918152i \(-0.370319\pi\)
0.396227 + 0.918152i \(0.370319\pi\)
\(938\) 14.7816 0.482637
\(939\) 18.0846 0.590169
\(940\) 194.091 6.33056
\(941\) −37.8015 −1.23229 −0.616146 0.787632i \(-0.711307\pi\)
−0.616146 + 0.787632i \(0.711307\pi\)
\(942\) −4.47322 −0.145745
\(943\) −12.7630 −0.415620
\(944\) −45.7807 −1.49003
\(945\) 4.02293 0.130866
\(946\) 48.0877 1.56347
\(947\) −0.353923 −0.0115010 −0.00575048 0.999983i \(-0.501830\pi\)
−0.00575048 + 0.999983i \(0.501830\pi\)
\(948\) 9.56287 0.310588
\(949\) 47.9776 1.55742
\(950\) −27.4012 −0.889012
\(951\) −4.96903 −0.161132
\(952\) 17.4134 0.564372
\(953\) 4.13854 0.134060 0.0670302 0.997751i \(-0.478648\pi\)
0.0670302 + 0.997751i \(0.478648\pi\)
\(954\) −2.31636 −0.0749949
\(955\) 84.7063 2.74103
\(956\) 35.5268 1.14902
\(957\) 4.32375 0.139767
\(958\) 19.6799 0.635827
\(959\) −12.5012 −0.403684
\(960\) 6.57256 0.212128
\(961\) −18.4447 −0.594989
\(962\) 74.2326 2.39336
\(963\) 15.9187 0.512973
\(964\) −77.8638 −2.50782
\(965\) 97.8705 3.15056
\(966\) 14.5718 0.468839
\(967\) −47.0116 −1.51179 −0.755895 0.654693i \(-0.772798\pi\)
−0.755895 + 0.654693i \(0.772798\pi\)
\(968\) 44.9402 1.44443
\(969\) 2.52616 0.0811518
\(970\) 179.543 5.76479
\(971\) 34.4310 1.10494 0.552472 0.833531i \(-0.313685\pi\)
0.552472 + 0.833531i \(0.313685\pi\)
\(972\) −4.57042 −0.146596
\(973\) 3.94608 0.126506
\(974\) −12.9890 −0.416194
\(975\) 44.6043 1.42848
\(976\) −35.9688 −1.15133
\(977\) 42.9239 1.37326 0.686628 0.727009i \(-0.259090\pi\)
0.686628 + 0.727009i \(0.259090\pi\)
\(978\) 14.7858 0.472797
\(979\) 18.9238 0.604808
\(980\) −18.3865 −0.587335
\(981\) 0.670528 0.0214083
\(982\) −72.8193 −2.32376
\(983\) 0.191557 0.00610972 0.00305486 0.999995i \(-0.499028\pi\)
0.00305486 + 0.999995i \(0.499028\pi\)
\(984\) −14.7924 −0.471564
\(985\) −36.8575 −1.17438
\(986\) 14.3282 0.456303
\(987\) 10.5562 0.336007
\(988\) −17.4227 −0.554290
\(989\) 52.1681 1.65885
\(990\) −21.0808 −0.669992
\(991\) 54.9608 1.74589 0.872943 0.487822i \(-0.162208\pi\)
0.872943 + 0.487822i \(0.162208\pi\)
\(992\) 23.6791 0.751813
\(993\) 9.09624 0.288660
\(994\) 14.5665 0.462020
\(995\) 63.8876 2.02537
\(996\) 0.467901 0.0148260
\(997\) 55.9528 1.77204 0.886022 0.463644i \(-0.153458\pi\)
0.886022 + 0.463644i \(0.153458\pi\)
\(998\) 52.2610 1.65429
\(999\) −7.26134 −0.229739
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 \(a_p\))