Properties

Label 8043.2.a.t.1.15
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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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 1.15
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.58348 q^{2}\) \(-1.00000 q^{3}\) \(+0.507395 q^{4}\) \(-2.03406 q^{5}\) \(+1.58348 q^{6}\) \(+1.00000 q^{7}\) \(+2.36350 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.58348 q^{2}\) \(-1.00000 q^{3}\) \(+0.507395 q^{4}\) \(-2.03406 q^{5}\) \(+1.58348 q^{6}\) \(+1.00000 q^{7}\) \(+2.36350 q^{8}\) \(+1.00000 q^{9}\) \(+3.22089 q^{10}\) \(+1.17498 q^{11}\) \(-0.507395 q^{12}\) \(+3.73140 q^{13}\) \(-1.58348 q^{14}\) \(+2.03406 q^{15}\) \(-4.75734 q^{16}\) \(-8.09560 q^{17}\) \(-1.58348 q^{18}\) \(-8.31210 q^{19}\) \(-1.03207 q^{20}\) \(-1.00000 q^{21}\) \(-1.86056 q^{22}\) \(+2.49738 q^{23}\) \(-2.36350 q^{24}\) \(-0.862589 q^{25}\) \(-5.90858 q^{26}\) \(-1.00000 q^{27}\) \(+0.507395 q^{28}\) \(-3.50435 q^{29}\) \(-3.22089 q^{30}\) \(+10.4075 q^{31}\) \(+2.80612 q^{32}\) \(-1.17498 q^{33}\) \(+12.8192 q^{34}\) \(-2.03406 q^{35}\) \(+0.507395 q^{36}\) \(-2.40440 q^{37}\) \(+13.1620 q^{38}\) \(-3.73140 q^{39}\) \(-4.80752 q^{40}\) \(-6.51764 q^{41}\) \(+1.58348 q^{42}\) \(+6.17846 q^{43}\) \(+0.596180 q^{44}\) \(-2.03406 q^{45}\) \(-3.95454 q^{46}\) \(-8.33923 q^{47}\) \(+4.75734 q^{48}\) \(+1.00000 q^{49}\) \(+1.36589 q^{50}\) \(+8.09560 q^{51}\) \(+1.89329 q^{52}\) \(+4.21927 q^{53}\) \(+1.58348 q^{54}\) \(-2.38999 q^{55}\) \(+2.36350 q^{56}\) \(+8.31210 q^{57}\) \(+5.54906 q^{58}\) \(+9.57535 q^{59}\) \(+1.03207 q^{60}\) \(-13.7336 q^{61}\) \(-16.4800 q^{62}\) \(+1.00000 q^{63}\) \(+5.07125 q^{64}\) \(-7.58990 q^{65}\) \(+1.86056 q^{66}\) \(+2.82956 q^{67}\) \(-4.10767 q^{68}\) \(-2.49738 q^{69}\) \(+3.22089 q^{70}\) \(+3.19338 q^{71}\) \(+2.36350 q^{72}\) \(-4.96110 q^{73}\) \(+3.80731 q^{74}\) \(+0.862589 q^{75}\) \(-4.21751 q^{76}\) \(+1.17498 q^{77}\) \(+5.90858 q^{78}\) \(+10.7268 q^{79}\) \(+9.67673 q^{80}\) \(+1.00000 q^{81}\) \(+10.3205 q^{82}\) \(-12.9827 q^{83}\) \(-0.507395 q^{84}\) \(+16.4670 q^{85}\) \(-9.78343 q^{86}\) \(+3.50435 q^{87}\) \(+2.77708 q^{88}\) \(-12.6293 q^{89}\) \(+3.22089 q^{90}\) \(+3.73140 q^{91}\) \(+1.26716 q^{92}\) \(-10.4075 q^{93}\) \(+13.2050 q^{94}\) \(+16.9073 q^{95}\) \(-2.80612 q^{96}\) \(-12.2662 q^{97}\) \(-1.58348 q^{98}\) \(+1.17498 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58348 −1.11969 −0.559843 0.828599i \(-0.689139\pi\)
−0.559843 + 0.828599i \(0.689139\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.507395 0.253697
\(5\) −2.03406 −0.909660 −0.454830 0.890578i \(-0.650300\pi\)
−0.454830 + 0.890578i \(0.650300\pi\)
\(6\) 1.58348 0.646451
\(7\) 1.00000 0.377964
\(8\) 2.36350 0.835625
\(9\) 1.00000 0.333333
\(10\) 3.22089 1.01853
\(11\) 1.17498 0.354271 0.177135 0.984187i \(-0.443317\pi\)
0.177135 + 0.984187i \(0.443317\pi\)
\(12\) −0.507395 −0.146472
\(13\) 3.73140 1.03490 0.517452 0.855712i \(-0.326881\pi\)
0.517452 + 0.855712i \(0.326881\pi\)
\(14\) −1.58348 −0.423202
\(15\) 2.03406 0.525193
\(16\) −4.75734 −1.18933
\(17\) −8.09560 −1.96347 −0.981736 0.190248i \(-0.939071\pi\)
−0.981736 + 0.190248i \(0.939071\pi\)
\(18\) −1.58348 −0.373229
\(19\) −8.31210 −1.90693 −0.953463 0.301510i \(-0.902509\pi\)
−0.953463 + 0.301510i \(0.902509\pi\)
\(20\) −1.03207 −0.230778
\(21\) −1.00000 −0.218218
\(22\) −1.86056 −0.396672
\(23\) 2.49738 0.520739 0.260370 0.965509i \(-0.416156\pi\)
0.260370 + 0.965509i \(0.416156\pi\)
\(24\) −2.36350 −0.482448
\(25\) −0.862589 −0.172518
\(26\) −5.90858 −1.15877
\(27\) −1.00000 −0.192450
\(28\) 0.507395 0.0958886
\(29\) −3.50435 −0.650742 −0.325371 0.945586i \(-0.605489\pi\)
−0.325371 + 0.945586i \(0.605489\pi\)
\(30\) −3.22089 −0.588051
\(31\) 10.4075 1.86924 0.934618 0.355654i \(-0.115742\pi\)
0.934618 + 0.355654i \(0.115742\pi\)
\(32\) 2.80612 0.496057
\(33\) −1.17498 −0.204538
\(34\) 12.8192 2.19847
\(35\) −2.03406 −0.343819
\(36\) 0.507395 0.0845658
\(37\) −2.40440 −0.395282 −0.197641 0.980275i \(-0.563328\pi\)
−0.197641 + 0.980275i \(0.563328\pi\)
\(38\) 13.1620 2.13516
\(39\) −3.73140 −0.597502
\(40\) −4.80752 −0.760135
\(41\) −6.51764 −1.01788 −0.508942 0.860801i \(-0.669963\pi\)
−0.508942 + 0.860801i \(0.669963\pi\)
\(42\) 1.58348 0.244336
\(43\) 6.17846 0.942206 0.471103 0.882078i \(-0.343856\pi\)
0.471103 + 0.882078i \(0.343856\pi\)
\(44\) 0.596180 0.0898775
\(45\) −2.03406 −0.303220
\(46\) −3.95454 −0.583065
\(47\) −8.33923 −1.21640 −0.608201 0.793783i \(-0.708109\pi\)
−0.608201 + 0.793783i \(0.708109\pi\)
\(48\) 4.75734 0.686663
\(49\) 1.00000 0.142857
\(50\) 1.36589 0.193166
\(51\) 8.09560 1.13361
\(52\) 1.89329 0.262552
\(53\) 4.21927 0.579562 0.289781 0.957093i \(-0.406418\pi\)
0.289781 + 0.957093i \(0.406418\pi\)
\(54\) 1.58348 0.215484
\(55\) −2.38999 −0.322266
\(56\) 2.36350 0.315837
\(57\) 8.31210 1.10096
\(58\) 5.54906 0.728627
\(59\) 9.57535 1.24660 0.623302 0.781981i \(-0.285791\pi\)
0.623302 + 0.781981i \(0.285791\pi\)
\(60\) 1.03207 0.133240
\(61\) −13.7336 −1.75841 −0.879204 0.476446i \(-0.841925\pi\)
−0.879204 + 0.476446i \(0.841925\pi\)
\(62\) −16.4800 −2.09296
\(63\) 1.00000 0.125988
\(64\) 5.07125 0.633907
\(65\) −7.58990 −0.941411
\(66\) 1.86056 0.229019
\(67\) 2.82956 0.345686 0.172843 0.984949i \(-0.444705\pi\)
0.172843 + 0.984949i \(0.444705\pi\)
\(68\) −4.10767 −0.498128
\(69\) −2.49738 −0.300649
\(70\) 3.22089 0.384970
\(71\) 3.19338 0.378985 0.189492 0.981882i \(-0.439316\pi\)
0.189492 + 0.981882i \(0.439316\pi\)
\(72\) 2.36350 0.278542
\(73\) −4.96110 −0.580653 −0.290326 0.956928i \(-0.593764\pi\)
−0.290326 + 0.956928i \(0.593764\pi\)
\(74\) 3.80731 0.442591
\(75\) 0.862589 0.0996032
\(76\) −4.21751 −0.483782
\(77\) 1.17498 0.133902
\(78\) 5.90858 0.669015
\(79\) 10.7268 1.20686 0.603432 0.797414i \(-0.293799\pi\)
0.603432 + 0.797414i \(0.293799\pi\)
\(80\) 9.67673 1.08189
\(81\) 1.00000 0.111111
\(82\) 10.3205 1.13971
\(83\) −12.9827 −1.42503 −0.712516 0.701655i \(-0.752445\pi\)
−0.712516 + 0.701655i \(0.752445\pi\)
\(84\) −0.507395 −0.0553613
\(85\) 16.4670 1.78609
\(86\) −9.78343 −1.05497
\(87\) 3.50435 0.375706
\(88\) 2.77708 0.296037
\(89\) −12.6293 −1.33871 −0.669353 0.742945i \(-0.733429\pi\)
−0.669353 + 0.742945i \(0.733429\pi\)
\(90\) 3.22089 0.339511
\(91\) 3.73140 0.391157
\(92\) 1.26716 0.132110
\(93\) −10.4075 −1.07920
\(94\) 13.2050 1.36199
\(95\) 16.9073 1.73466
\(96\) −2.80612 −0.286399
\(97\) −12.2662 −1.24544 −0.622720 0.782445i \(-0.713972\pi\)
−0.622720 + 0.782445i \(0.713972\pi\)
\(98\) −1.58348 −0.159955
\(99\) 1.17498 0.118090
\(100\) −0.437673 −0.0437673
\(101\) 10.4030 1.03514 0.517568 0.855642i \(-0.326837\pi\)
0.517568 + 0.855642i \(0.326837\pi\)
\(102\) −12.8192 −1.26929
\(103\) 15.2288 1.50054 0.750269 0.661132i \(-0.229924\pi\)
0.750269 + 0.661132i \(0.229924\pi\)
\(104\) 8.81918 0.864791
\(105\) 2.03406 0.198504
\(106\) −6.68111 −0.648927
\(107\) 1.38838 0.134219 0.0671097 0.997746i \(-0.478622\pi\)
0.0671097 + 0.997746i \(0.478622\pi\)
\(108\) −0.507395 −0.0488241
\(109\) 2.93650 0.281266 0.140633 0.990062i \(-0.455086\pi\)
0.140633 + 0.990062i \(0.455086\pi\)
\(110\) 3.78449 0.360837
\(111\) 2.40440 0.228216
\(112\) −4.75734 −0.449526
\(113\) −4.96451 −0.467021 −0.233511 0.972354i \(-0.575021\pi\)
−0.233511 + 0.972354i \(0.575021\pi\)
\(114\) −13.1620 −1.23273
\(115\) −5.07982 −0.473696
\(116\) −1.77809 −0.165091
\(117\) 3.73140 0.344968
\(118\) −15.1623 −1.39581
\(119\) −8.09560 −0.742123
\(120\) 4.80752 0.438864
\(121\) −9.61941 −0.874492
\(122\) 21.7468 1.96887
\(123\) 6.51764 0.587676
\(124\) 5.28069 0.474220
\(125\) 11.9249 1.06659
\(126\) −1.58348 −0.141067
\(127\) 4.90100 0.434893 0.217447 0.976072i \(-0.430227\pi\)
0.217447 + 0.976072i \(0.430227\pi\)
\(128\) −13.6425 −1.20583
\(129\) −6.17846 −0.543983
\(130\) 12.0184 1.05409
\(131\) 13.3143 1.16328 0.581639 0.813447i \(-0.302412\pi\)
0.581639 + 0.813447i \(0.302412\pi\)
\(132\) −0.596180 −0.0518908
\(133\) −8.31210 −0.720750
\(134\) −4.48055 −0.387060
\(135\) 2.03406 0.175064
\(136\) −19.1340 −1.64073
\(137\) 20.6490 1.76416 0.882082 0.471095i \(-0.156141\pi\)
0.882082 + 0.471095i \(0.156141\pi\)
\(138\) 3.95454 0.336632
\(139\) −7.72470 −0.655201 −0.327600 0.944816i \(-0.606240\pi\)
−0.327600 + 0.944816i \(0.606240\pi\)
\(140\) −1.03207 −0.0872260
\(141\) 8.33923 0.702290
\(142\) −5.05664 −0.424344
\(143\) 4.38433 0.366636
\(144\) −4.75734 −0.396445
\(145\) 7.12807 0.591954
\(146\) 7.85578 0.650149
\(147\) −1.00000 −0.0824786
\(148\) −1.21998 −0.100282
\(149\) −13.2763 −1.08763 −0.543817 0.839204i \(-0.683021\pi\)
−0.543817 + 0.839204i \(0.683021\pi\)
\(150\) −1.36589 −0.111524
\(151\) 1.33666 0.108776 0.0543879 0.998520i \(-0.482679\pi\)
0.0543879 + 0.998520i \(0.482679\pi\)
\(152\) −19.6457 −1.59347
\(153\) −8.09560 −0.654491
\(154\) −1.86056 −0.149928
\(155\) −21.1694 −1.70037
\(156\) −1.89329 −0.151585
\(157\) −5.99064 −0.478105 −0.239053 0.971007i \(-0.576837\pi\)
−0.239053 + 0.971007i \(0.576837\pi\)
\(158\) −16.9857 −1.35131
\(159\) −4.21927 −0.334610
\(160\) −5.70783 −0.451244
\(161\) 2.49738 0.196821
\(162\) −1.58348 −0.124410
\(163\) 10.6974 0.837886 0.418943 0.908012i \(-0.362401\pi\)
0.418943 + 0.908012i \(0.362401\pi\)
\(164\) −3.30701 −0.258234
\(165\) 2.38999 0.186060
\(166\) 20.5577 1.59559
\(167\) −12.7413 −0.985949 −0.492975 0.870044i \(-0.664090\pi\)
−0.492975 + 0.870044i \(0.664090\pi\)
\(168\) −2.36350 −0.182348
\(169\) 0.923340 0.0710261
\(170\) −26.0750 −1.99986
\(171\) −8.31210 −0.635642
\(172\) 3.13492 0.239035
\(173\) −17.7462 −1.34922 −0.674610 0.738174i \(-0.735688\pi\)
−0.674610 + 0.738174i \(0.735688\pi\)
\(174\) −5.54906 −0.420673
\(175\) −0.862589 −0.0652056
\(176\) −5.58979 −0.421347
\(177\) −9.57535 −0.719727
\(178\) 19.9982 1.49893
\(179\) −6.76582 −0.505701 −0.252850 0.967505i \(-0.581368\pi\)
−0.252850 + 0.967505i \(0.581368\pi\)
\(180\) −1.03207 −0.0769261
\(181\) 11.0685 0.822716 0.411358 0.911474i \(-0.365055\pi\)
0.411358 + 0.911474i \(0.365055\pi\)
\(182\) −5.90858 −0.437973
\(183\) 13.7336 1.01522
\(184\) 5.90256 0.435143
\(185\) 4.89071 0.359572
\(186\) 16.4800 1.20837
\(187\) −9.51220 −0.695601
\(188\) −4.23128 −0.308598
\(189\) −1.00000 −0.0727393
\(190\) −26.7723 −1.94227
\(191\) −19.4885 −1.41014 −0.705068 0.709140i \(-0.749084\pi\)
−0.705068 + 0.709140i \(0.749084\pi\)
\(192\) −5.07125 −0.365986
\(193\) 3.02241 0.217558 0.108779 0.994066i \(-0.465306\pi\)
0.108779 + 0.994066i \(0.465306\pi\)
\(194\) 19.4232 1.39450
\(195\) 7.58990 0.543524
\(196\) 0.507395 0.0362425
\(197\) −25.2988 −1.80247 −0.901233 0.433335i \(-0.857337\pi\)
−0.901233 + 0.433335i \(0.857337\pi\)
\(198\) −1.86056 −0.132224
\(199\) 3.49513 0.247764 0.123882 0.992297i \(-0.460466\pi\)
0.123882 + 0.992297i \(0.460466\pi\)
\(200\) −2.03873 −0.144160
\(201\) −2.82956 −0.199582
\(202\) −16.4729 −1.15903
\(203\) −3.50435 −0.245957
\(204\) 4.10767 0.287594
\(205\) 13.2573 0.925929
\(206\) −24.1144 −1.68013
\(207\) 2.49738 0.173580
\(208\) −17.7515 −1.23085
\(209\) −9.76657 −0.675568
\(210\) −3.22089 −0.222262
\(211\) 6.26977 0.431629 0.215814 0.976434i \(-0.430759\pi\)
0.215814 + 0.976434i \(0.430759\pi\)
\(212\) 2.14084 0.147033
\(213\) −3.19338 −0.218807
\(214\) −2.19846 −0.150284
\(215\) −12.5674 −0.857087
\(216\) −2.36350 −0.160816
\(217\) 10.4075 0.706505
\(218\) −4.64988 −0.314930
\(219\) 4.96110 0.335240
\(220\) −1.21267 −0.0817580
\(221\) −30.2079 −2.03200
\(222\) −3.80731 −0.255530
\(223\) −3.40829 −0.228236 −0.114118 0.993467i \(-0.536404\pi\)
−0.114118 + 0.993467i \(0.536404\pi\)
\(224\) 2.80612 0.187492
\(225\) −0.862589 −0.0575060
\(226\) 7.86117 0.522917
\(227\) −25.8890 −1.71831 −0.859156 0.511714i \(-0.829011\pi\)
−0.859156 + 0.511714i \(0.829011\pi\)
\(228\) 4.21751 0.279312
\(229\) −6.00764 −0.396996 −0.198498 0.980101i \(-0.563606\pi\)
−0.198498 + 0.980101i \(0.563606\pi\)
\(230\) 8.04377 0.530391
\(231\) −1.17498 −0.0773082
\(232\) −8.28255 −0.543776
\(233\) −10.3213 −0.676168 −0.338084 0.941116i \(-0.609779\pi\)
−0.338084 + 0.941116i \(0.609779\pi\)
\(234\) −5.90858 −0.386256
\(235\) 16.9625 1.10651
\(236\) 4.85848 0.316260
\(237\) −10.7268 −0.696783
\(238\) 12.8192 0.830945
\(239\) −16.2362 −1.05023 −0.525117 0.851030i \(-0.675978\pi\)
−0.525117 + 0.851030i \(0.675978\pi\)
\(240\) −9.67673 −0.624630
\(241\) 12.5949 0.811310 0.405655 0.914026i \(-0.367043\pi\)
0.405655 + 0.914026i \(0.367043\pi\)
\(242\) 15.2321 0.979157
\(243\) −1.00000 −0.0641500
\(244\) −6.96836 −0.446103
\(245\) −2.03406 −0.129951
\(246\) −10.3205 −0.658012
\(247\) −31.0158 −1.97349
\(248\) 24.5981 1.56198
\(249\) 12.9827 0.822743
\(250\) −18.8827 −1.19425
\(251\) 22.8035 1.43935 0.719673 0.694314i \(-0.244292\pi\)
0.719673 + 0.694314i \(0.244292\pi\)
\(252\) 0.507395 0.0319629
\(253\) 2.93438 0.184483
\(254\) −7.76061 −0.486944
\(255\) −16.4670 −1.03120
\(256\) 11.4600 0.716249
\(257\) 18.2621 1.13916 0.569580 0.821936i \(-0.307106\pi\)
0.569580 + 0.821936i \(0.307106\pi\)
\(258\) 9.78343 0.609090
\(259\) −2.40440 −0.149402
\(260\) −3.85107 −0.238833
\(261\) −3.50435 −0.216914
\(262\) −21.0829 −1.30251
\(263\) 26.3782 1.62655 0.813274 0.581881i \(-0.197683\pi\)
0.813274 + 0.581881i \(0.197683\pi\)
\(264\) −2.77708 −0.170917
\(265\) −8.58226 −0.527204
\(266\) 13.1620 0.807014
\(267\) 12.6293 0.772902
\(268\) 1.43571 0.0876997
\(269\) −7.27730 −0.443705 −0.221852 0.975080i \(-0.571210\pi\)
−0.221852 + 0.975080i \(0.571210\pi\)
\(270\) −3.22089 −0.196017
\(271\) −10.6407 −0.646378 −0.323189 0.946334i \(-0.604755\pi\)
−0.323189 + 0.946334i \(0.604755\pi\)
\(272\) 38.5135 2.33523
\(273\) −3.73140 −0.225835
\(274\) −32.6972 −1.97531
\(275\) −1.01353 −0.0611180
\(276\) −1.26716 −0.0762738
\(277\) −30.1397 −1.81092 −0.905459 0.424434i \(-0.860473\pi\)
−0.905459 + 0.424434i \(0.860473\pi\)
\(278\) 12.2319 0.733619
\(279\) 10.4075 0.623079
\(280\) −4.80752 −0.287304
\(281\) −21.8838 −1.30548 −0.652739 0.757583i \(-0.726380\pi\)
−0.652739 + 0.757583i \(0.726380\pi\)
\(282\) −13.2050 −0.786345
\(283\) 15.4851 0.920495 0.460248 0.887791i \(-0.347761\pi\)
0.460248 + 0.887791i \(0.347761\pi\)
\(284\) 1.62031 0.0961474
\(285\) −16.9073 −1.00150
\(286\) −6.94248 −0.410517
\(287\) −6.51764 −0.384724
\(288\) 2.80612 0.165352
\(289\) 48.5388 2.85522
\(290\) −11.2871 −0.662803
\(291\) 12.2662 0.719055
\(292\) −2.51724 −0.147310
\(293\) 9.98207 0.583158 0.291579 0.956547i \(-0.405819\pi\)
0.291579 + 0.956547i \(0.405819\pi\)
\(294\) 1.58348 0.0923502
\(295\) −19.4769 −1.13399
\(296\) −5.68282 −0.330307
\(297\) −1.17498 −0.0681794
\(298\) 21.0226 1.21781
\(299\) 9.31871 0.538915
\(300\) 0.437673 0.0252691
\(301\) 6.17846 0.356120
\(302\) −2.11657 −0.121795
\(303\) −10.4030 −0.597636
\(304\) 39.5435 2.26797
\(305\) 27.9350 1.59955
\(306\) 12.8192 0.732824
\(307\) 4.79874 0.273879 0.136939 0.990579i \(-0.456273\pi\)
0.136939 + 0.990579i \(0.456273\pi\)
\(308\) 0.596180 0.0339705
\(309\) −15.2288 −0.866336
\(310\) 33.5213 1.90388
\(311\) −5.91843 −0.335603 −0.167802 0.985821i \(-0.553667\pi\)
−0.167802 + 0.985821i \(0.553667\pi\)
\(312\) −8.81918 −0.499288
\(313\) 8.13144 0.459616 0.229808 0.973236i \(-0.426190\pi\)
0.229808 + 0.973236i \(0.426190\pi\)
\(314\) 9.48603 0.535328
\(315\) −2.03406 −0.114606
\(316\) 5.44274 0.306178
\(317\) 4.12351 0.231600 0.115800 0.993273i \(-0.463057\pi\)
0.115800 + 0.993273i \(0.463057\pi\)
\(318\) 6.68111 0.374658
\(319\) −4.11755 −0.230539
\(320\) −10.3152 −0.576640
\(321\) −1.38838 −0.0774916
\(322\) −3.95454 −0.220378
\(323\) 67.2914 3.74420
\(324\) 0.507395 0.0281886
\(325\) −3.21867 −0.178539
\(326\) −16.9391 −0.938170
\(327\) −2.93650 −0.162389
\(328\) −15.4045 −0.850569
\(329\) −8.33923 −0.459757
\(330\) −3.78449 −0.208329
\(331\) −7.88009 −0.433129 −0.216565 0.976268i \(-0.569485\pi\)
−0.216565 + 0.976268i \(0.569485\pi\)
\(332\) −6.58734 −0.361527
\(333\) −2.40440 −0.131761
\(334\) 20.1755 1.10395
\(335\) −5.75551 −0.314457
\(336\) 4.75734 0.259534
\(337\) 5.71700 0.311425 0.155712 0.987802i \(-0.450233\pi\)
0.155712 + 0.987802i \(0.450233\pi\)
\(338\) −1.46209 −0.0795270
\(339\) 4.96451 0.269635
\(340\) 8.35525 0.453127
\(341\) 12.2286 0.662215
\(342\) 13.1620 0.711720
\(343\) 1.00000 0.0539949
\(344\) 14.6028 0.787330
\(345\) 5.07982 0.273488
\(346\) 28.1007 1.51070
\(347\) −17.0545 −0.915536 −0.457768 0.889072i \(-0.651351\pi\)
−0.457768 + 0.889072i \(0.651351\pi\)
\(348\) 1.77809 0.0953156
\(349\) 7.88885 0.422280 0.211140 0.977456i \(-0.432282\pi\)
0.211140 + 0.977456i \(0.432282\pi\)
\(350\) 1.36589 0.0730099
\(351\) −3.73140 −0.199167
\(352\) 3.29715 0.175739
\(353\) −12.6774 −0.674752 −0.337376 0.941370i \(-0.609539\pi\)
−0.337376 + 0.941370i \(0.609539\pi\)
\(354\) 15.1623 0.805869
\(355\) −6.49554 −0.344747
\(356\) −6.40805 −0.339626
\(357\) 8.09560 0.428465
\(358\) 10.7135 0.566226
\(359\) −34.5229 −1.82205 −0.911023 0.412355i \(-0.864706\pi\)
−0.911023 + 0.412355i \(0.864706\pi\)
\(360\) −4.80752 −0.253378
\(361\) 50.0910 2.63637
\(362\) −17.5267 −0.921183
\(363\) 9.61941 0.504888
\(364\) 1.89329 0.0992355
\(365\) 10.0912 0.528197
\(366\) −21.7468 −1.13672
\(367\) 4.22048 0.220307 0.110154 0.993915i \(-0.464866\pi\)
0.110154 + 0.993915i \(0.464866\pi\)
\(368\) −11.8809 −0.619333
\(369\) −6.51764 −0.339295
\(370\) −7.74432 −0.402608
\(371\) 4.21927 0.219054
\(372\) −5.28069 −0.273791
\(373\) 33.9458 1.75765 0.878823 0.477148i \(-0.158329\pi\)
0.878823 + 0.477148i \(0.158329\pi\)
\(374\) 15.0623 0.778854
\(375\) −11.9249 −0.615798
\(376\) −19.7098 −1.01646
\(377\) −13.0761 −0.673455
\(378\) 1.58348 0.0814452
\(379\) 32.6135 1.67524 0.837620 0.546253i \(-0.183946\pi\)
0.837620 + 0.546253i \(0.183946\pi\)
\(380\) 8.57869 0.440077
\(381\) −4.90100 −0.251086
\(382\) 30.8595 1.57891
\(383\) −1.00000 −0.0510976
\(384\) 13.6425 0.696188
\(385\) −2.38999 −0.121805
\(386\) −4.78591 −0.243597
\(387\) 6.17846 0.314069
\(388\) −6.22378 −0.315965
\(389\) 19.2296 0.974978 0.487489 0.873129i \(-0.337913\pi\)
0.487489 + 0.873129i \(0.337913\pi\)
\(390\) −12.0184 −0.608576
\(391\) −20.2178 −1.02246
\(392\) 2.36350 0.119375
\(393\) −13.3143 −0.671619
\(394\) 40.0600 2.01820
\(395\) −21.8191 −1.09784
\(396\) 0.596180 0.0299592
\(397\) −7.72827 −0.387871 −0.193935 0.981014i \(-0.562125\pi\)
−0.193935 + 0.981014i \(0.562125\pi\)
\(398\) −5.53446 −0.277417
\(399\) 8.31210 0.416125
\(400\) 4.10363 0.205182
\(401\) 33.9001 1.69289 0.846444 0.532477i \(-0.178739\pi\)
0.846444 + 0.532477i \(0.178739\pi\)
\(402\) 4.48055 0.223469
\(403\) 38.8344 1.93448
\(404\) 5.27842 0.262611
\(405\) −2.03406 −0.101073
\(406\) 5.54906 0.275395
\(407\) −2.82513 −0.140037
\(408\) 19.1340 0.947274
\(409\) 1.66653 0.0824048 0.0412024 0.999151i \(-0.486881\pi\)
0.0412024 + 0.999151i \(0.486881\pi\)
\(410\) −20.9926 −1.03675
\(411\) −20.6490 −1.01854
\(412\) 7.72701 0.380683
\(413\) 9.57535 0.471172
\(414\) −3.95454 −0.194355
\(415\) 26.4076 1.29630
\(416\) 10.4708 0.513372
\(417\) 7.72470 0.378280
\(418\) 15.4651 0.756424
\(419\) 27.9606 1.36597 0.682983 0.730434i \(-0.260682\pi\)
0.682983 + 0.730434i \(0.260682\pi\)
\(420\) 1.03207 0.0503600
\(421\) −0.833488 −0.0406217 −0.0203109 0.999794i \(-0.506466\pi\)
−0.0203109 + 0.999794i \(0.506466\pi\)
\(422\) −9.92803 −0.483289
\(423\) −8.33923 −0.405467
\(424\) 9.97227 0.484296
\(425\) 6.98318 0.338734
\(426\) 5.05664 0.244995
\(427\) −13.7336 −0.664616
\(428\) 0.704455 0.0340511
\(429\) −4.38433 −0.211677
\(430\) 19.9001 0.959669
\(431\) −13.2665 −0.639025 −0.319513 0.947582i \(-0.603519\pi\)
−0.319513 + 0.947582i \(0.603519\pi\)
\(432\) 4.75734 0.228888
\(433\) −26.6116 −1.27887 −0.639436 0.768845i \(-0.720832\pi\)
−0.639436 + 0.768845i \(0.720832\pi\)
\(434\) −16.4800 −0.791064
\(435\) −7.12807 −0.341765
\(436\) 1.48997 0.0713565
\(437\) −20.7584 −0.993011
\(438\) −7.85578 −0.375364
\(439\) −3.42227 −0.163336 −0.0816680 0.996660i \(-0.526025\pi\)
−0.0816680 + 0.996660i \(0.526025\pi\)
\(440\) −5.64875 −0.269294
\(441\) 1.00000 0.0476190
\(442\) 47.8335 2.27521
\(443\) 30.7219 1.45964 0.729821 0.683638i \(-0.239603\pi\)
0.729821 + 0.683638i \(0.239603\pi\)
\(444\) 1.21998 0.0578978
\(445\) 25.6888 1.21777
\(446\) 5.39694 0.255553
\(447\) 13.2763 0.627946
\(448\) 5.07125 0.239594
\(449\) 21.0431 0.993087 0.496544 0.868012i \(-0.334602\pi\)
0.496544 + 0.868012i \(0.334602\pi\)
\(450\) 1.36589 0.0643886
\(451\) −7.65811 −0.360606
\(452\) −2.51896 −0.118482
\(453\) −1.33666 −0.0628017
\(454\) 40.9946 1.92397
\(455\) −7.58990 −0.355820
\(456\) 19.6457 0.919993
\(457\) 25.9974 1.21611 0.608054 0.793896i \(-0.291950\pi\)
0.608054 + 0.793896i \(0.291950\pi\)
\(458\) 9.51296 0.444511
\(459\) 8.09560 0.377870
\(460\) −2.57747 −0.120175
\(461\) 20.8371 0.970479 0.485239 0.874381i \(-0.338732\pi\)
0.485239 + 0.874381i \(0.338732\pi\)
\(462\) 1.86056 0.0865609
\(463\) 33.4805 1.55597 0.777986 0.628281i \(-0.216241\pi\)
0.777986 + 0.628281i \(0.216241\pi\)
\(464\) 16.6714 0.773950
\(465\) 21.1694 0.981709
\(466\) 16.3435 0.757096
\(467\) −15.8486 −0.733386 −0.366693 0.930342i \(-0.619510\pi\)
−0.366693 + 0.930342i \(0.619510\pi\)
\(468\) 1.89329 0.0875175
\(469\) 2.82956 0.130657
\(470\) −26.8597 −1.23895
\(471\) 5.99064 0.276034
\(472\) 22.6314 1.04169
\(473\) 7.25958 0.333796
\(474\) 16.9857 0.780179
\(475\) 7.16993 0.328979
\(476\) −4.10767 −0.188275
\(477\) 4.21927 0.193187
\(478\) 25.7097 1.17593
\(479\) 34.1683 1.56119 0.780595 0.625037i \(-0.214916\pi\)
0.780595 + 0.625037i \(0.214916\pi\)
\(480\) 5.70783 0.260526
\(481\) −8.97179 −0.409078
\(482\) −19.9437 −0.908413
\(483\) −2.49738 −0.113635
\(484\) −4.88084 −0.221856
\(485\) 24.9501 1.13293
\(486\) 1.58348 0.0718279
\(487\) −37.5504 −1.70157 −0.850785 0.525513i \(-0.823873\pi\)
−0.850785 + 0.525513i \(0.823873\pi\)
\(488\) −32.4594 −1.46937
\(489\) −10.6974 −0.483754
\(490\) 3.22089 0.145505
\(491\) −14.0685 −0.634904 −0.317452 0.948274i \(-0.602827\pi\)
−0.317452 + 0.948274i \(0.602827\pi\)
\(492\) 3.30701 0.149092
\(493\) 28.3698 1.27771
\(494\) 49.1127 2.20968
\(495\) −2.38999 −0.107422
\(496\) −49.5118 −2.22315
\(497\) 3.19338 0.143243
\(498\) −20.5577 −0.921214
\(499\) 7.63867 0.341954 0.170977 0.985275i \(-0.445308\pi\)
0.170977 + 0.985275i \(0.445308\pi\)
\(500\) 6.05062 0.270592
\(501\) 12.7413 0.569238
\(502\) −36.1088 −1.61161
\(503\) −13.4944 −0.601686 −0.300843 0.953674i \(-0.597268\pi\)
−0.300843 + 0.953674i \(0.597268\pi\)
\(504\) 2.36350 0.105279
\(505\) −21.1603 −0.941623
\(506\) −4.64651 −0.206563
\(507\) −0.923340 −0.0410070
\(508\) 2.48674 0.110331
\(509\) −2.95066 −0.130786 −0.0653928 0.997860i \(-0.520830\pi\)
−0.0653928 + 0.997860i \(0.520830\pi\)
\(510\) 26.0750 1.15462
\(511\) −4.96110 −0.219466
\(512\) 9.13830 0.403860
\(513\) 8.31210 0.366988
\(514\) −28.9176 −1.27550
\(515\) −30.9763 −1.36498
\(516\) −3.13492 −0.138007
\(517\) −9.79846 −0.430936
\(518\) 3.80731 0.167284
\(519\) 17.7462 0.778973
\(520\) −17.9388 −0.786667
\(521\) −16.1698 −0.708413 −0.354206 0.935167i \(-0.615249\pi\)
−0.354206 + 0.935167i \(0.615249\pi\)
\(522\) 5.54906 0.242876
\(523\) 23.4396 1.02494 0.512471 0.858704i \(-0.328730\pi\)
0.512471 + 0.858704i \(0.328730\pi\)
\(524\) 6.75562 0.295121
\(525\) 0.862589 0.0376465
\(526\) −41.7692 −1.82122
\(527\) −84.2547 −3.67019
\(528\) 5.58979 0.243265
\(529\) −16.7631 −0.728831
\(530\) 13.5898 0.590303
\(531\) 9.57535 0.415535
\(532\) −4.21751 −0.182852
\(533\) −24.3199 −1.05341
\(534\) −19.9982 −0.865408
\(535\) −2.82404 −0.122094
\(536\) 6.68769 0.288864
\(537\) 6.76582 0.291967
\(538\) 11.5234 0.496810
\(539\) 1.17498 0.0506101
\(540\) 1.03207 0.0444133
\(541\) −36.5762 −1.57253 −0.786267 0.617887i \(-0.787989\pi\)
−0.786267 + 0.617887i \(0.787989\pi\)
\(542\) 16.8493 0.723741
\(543\) −11.0685 −0.474995
\(544\) −22.7173 −0.973994
\(545\) −5.97303 −0.255857
\(546\) 5.90858 0.252864
\(547\) 27.1642 1.16146 0.580728 0.814098i \(-0.302768\pi\)
0.580728 + 0.814098i \(0.302768\pi\)
\(548\) 10.4772 0.447564
\(549\) −13.7336 −0.586136
\(550\) 1.60490 0.0684330
\(551\) 29.1285 1.24092
\(552\) −5.90256 −0.251230
\(553\) 10.7268 0.456152
\(554\) 47.7255 2.02766
\(555\) −4.89071 −0.207599
\(556\) −3.91947 −0.166223
\(557\) 17.2971 0.732901 0.366451 0.930438i \(-0.380573\pi\)
0.366451 + 0.930438i \(0.380573\pi\)
\(558\) −16.4800 −0.697652
\(559\) 23.0543 0.975092
\(560\) 9.67673 0.408916
\(561\) 9.51220 0.401605
\(562\) 34.6525 1.46173
\(563\) −34.5133 −1.45456 −0.727280 0.686341i \(-0.759216\pi\)
−0.727280 + 0.686341i \(0.759216\pi\)
\(564\) 4.23128 0.178169
\(565\) 10.0981 0.424831
\(566\) −24.5203 −1.03067
\(567\) 1.00000 0.0419961
\(568\) 7.54757 0.316689
\(569\) 8.65891 0.363000 0.181500 0.983391i \(-0.441905\pi\)
0.181500 + 0.983391i \(0.441905\pi\)
\(570\) 26.7723 1.12137
\(571\) −4.29822 −0.179875 −0.0899375 0.995947i \(-0.528667\pi\)
−0.0899375 + 0.995947i \(0.528667\pi\)
\(572\) 2.22459 0.0930146
\(573\) 19.4885 0.814142
\(574\) 10.3205 0.430770
\(575\) −2.15421 −0.0898368
\(576\) 5.07125 0.211302
\(577\) 36.4562 1.51769 0.758845 0.651271i \(-0.225764\pi\)
0.758845 + 0.651271i \(0.225764\pi\)
\(578\) −76.8600 −3.19695
\(579\) −3.02241 −0.125607
\(580\) 3.61675 0.150177
\(581\) −12.9827 −0.538612
\(582\) −19.4232 −0.805116
\(583\) 4.95757 0.205322
\(584\) −11.7256 −0.485208
\(585\) −7.58990 −0.313804
\(586\) −15.8064 −0.652955
\(587\) 24.6640 1.01799 0.508996 0.860769i \(-0.330017\pi\)
0.508996 + 0.860769i \(0.330017\pi\)
\(588\) −0.507395 −0.0209246
\(589\) −86.5079 −3.56449
\(590\) 30.8411 1.26971
\(591\) 25.2988 1.04065
\(592\) 11.4386 0.470122
\(593\) −3.78538 −0.155447 −0.0777234 0.996975i \(-0.524765\pi\)
−0.0777234 + 0.996975i \(0.524765\pi\)
\(594\) 1.86056 0.0763396
\(595\) 16.4670 0.675080
\(596\) −6.73631 −0.275930
\(597\) −3.49513 −0.143046
\(598\) −14.7560 −0.603416
\(599\) 21.6900 0.886228 0.443114 0.896465i \(-0.353874\pi\)
0.443114 + 0.896465i \(0.353874\pi\)
\(600\) 2.03873 0.0832310
\(601\) 0.767439 0.0313045 0.0156522 0.999877i \(-0.495018\pi\)
0.0156522 + 0.999877i \(0.495018\pi\)
\(602\) −9.78343 −0.398743
\(603\) 2.82956 0.115229
\(604\) 0.678214 0.0275961
\(605\) 19.5665 0.795491
\(606\) 16.4729 0.669165
\(607\) −10.5297 −0.427386 −0.213693 0.976901i \(-0.568549\pi\)
−0.213693 + 0.976901i \(0.568549\pi\)
\(608\) −23.3248 −0.945944
\(609\) 3.50435 0.142004
\(610\) −44.2344 −1.79100
\(611\) −31.1170 −1.25886
\(612\) −4.10767 −0.166043
\(613\) 14.3641 0.580161 0.290080 0.957002i \(-0.406318\pi\)
0.290080 + 0.957002i \(0.406318\pi\)
\(614\) −7.59869 −0.306658
\(615\) −13.2573 −0.534585
\(616\) 2.77708 0.111892
\(617\) 12.2239 0.492114 0.246057 0.969255i \(-0.420865\pi\)
0.246057 + 0.969255i \(0.420865\pi\)
\(618\) 24.1144 0.970025
\(619\) −49.0827 −1.97280 −0.986400 0.164363i \(-0.947443\pi\)
−0.986400 + 0.164363i \(0.947443\pi\)
\(620\) −10.7413 −0.431379
\(621\) −2.49738 −0.100216
\(622\) 9.37168 0.375770
\(623\) −12.6293 −0.505983
\(624\) 17.7515 0.710630
\(625\) −19.9430 −0.797720
\(626\) −12.8759 −0.514626
\(627\) 9.76657 0.390039
\(628\) −3.03962 −0.121294
\(629\) 19.4651 0.776124
\(630\) 3.22089 0.128323
\(631\) 27.3662 1.08943 0.544716 0.838620i \(-0.316637\pi\)
0.544716 + 0.838620i \(0.316637\pi\)
\(632\) 25.3529 1.00849
\(633\) −6.26977 −0.249201
\(634\) −6.52948 −0.259319
\(635\) −9.96894 −0.395605
\(636\) −2.14084 −0.0848897
\(637\) 3.73140 0.147843
\(638\) 6.52005 0.258131
\(639\) 3.19338 0.126328
\(640\) 27.7496 1.09690
\(641\) 30.0221 1.18580 0.592900 0.805276i \(-0.297983\pi\)
0.592900 + 0.805276i \(0.297983\pi\)
\(642\) 2.19846 0.0867663
\(643\) 36.6432 1.44507 0.722534 0.691335i \(-0.242977\pi\)
0.722534 + 0.691335i \(0.242977\pi\)
\(644\) 1.26716 0.0499329
\(645\) 12.5674 0.494840
\(646\) −106.554 −4.19233
\(647\) 17.2026 0.676306 0.338153 0.941091i \(-0.390198\pi\)
0.338153 + 0.941091i \(0.390198\pi\)
\(648\) 2.36350 0.0928472
\(649\) 11.2509 0.441635
\(650\) 5.09668 0.199908
\(651\) −10.4075 −0.407901
\(652\) 5.42781 0.212570
\(653\) 14.1311 0.552993 0.276496 0.961015i \(-0.410827\pi\)
0.276496 + 0.961015i \(0.410827\pi\)
\(654\) 4.64988 0.181825
\(655\) −27.0822 −1.05819
\(656\) 31.0066 1.21060
\(657\) −4.96110 −0.193551
\(658\) 13.2050 0.514783
\(659\) 19.4818 0.758901 0.379451 0.925212i \(-0.376113\pi\)
0.379451 + 0.925212i \(0.376113\pi\)
\(660\) 1.21267 0.0472030
\(661\) −22.5821 −0.878344 −0.439172 0.898403i \(-0.644728\pi\)
−0.439172 + 0.898403i \(0.644728\pi\)
\(662\) 12.4779 0.484969
\(663\) 30.2079 1.17318
\(664\) −30.6846 −1.19079
\(665\) 16.9073 0.655638
\(666\) 3.80731 0.147530
\(667\) −8.75169 −0.338867
\(668\) −6.46485 −0.250133
\(669\) 3.40829 0.131772
\(670\) 9.11371 0.352093
\(671\) −16.1368 −0.622952
\(672\) −2.80612 −0.108249
\(673\) −19.5706 −0.754390 −0.377195 0.926134i \(-0.623111\pi\)
−0.377195 + 0.926134i \(0.623111\pi\)
\(674\) −9.05273 −0.348698
\(675\) 0.862589 0.0332011
\(676\) 0.468498 0.0180191
\(677\) −29.1476 −1.12023 −0.560117 0.828413i \(-0.689244\pi\)
−0.560117 + 0.828413i \(0.689244\pi\)
\(678\) −7.86117 −0.301907
\(679\) −12.2662 −0.470732
\(680\) 38.9197 1.49250
\(681\) 25.8890 0.992068
\(682\) −19.3637 −0.741474
\(683\) −40.4250 −1.54682 −0.773410 0.633906i \(-0.781450\pi\)
−0.773410 + 0.633906i \(0.781450\pi\)
\(684\) −4.21751 −0.161261
\(685\) −42.0014 −1.60479
\(686\) −1.58348 −0.0604574
\(687\) 6.00764 0.229206
\(688\) −29.3930 −1.12060
\(689\) 15.7438 0.599791
\(690\) −8.04377 −0.306221
\(691\) 47.9232 1.82308 0.911541 0.411208i \(-0.134893\pi\)
0.911541 + 0.411208i \(0.134893\pi\)
\(692\) −9.00434 −0.342294
\(693\) 1.17498 0.0446339
\(694\) 27.0054 1.02511
\(695\) 15.7125 0.596010
\(696\) 8.28255 0.313949
\(697\) 52.7642 1.99859
\(698\) −12.4918 −0.472822
\(699\) 10.3213 0.390386
\(700\) −0.437673 −0.0165425
\(701\) −44.1271 −1.66666 −0.833329 0.552778i \(-0.813568\pi\)
−0.833329 + 0.552778i \(0.813568\pi\)
\(702\) 5.90858 0.223005
\(703\) 19.9856 0.753773
\(704\) 5.95864 0.224575
\(705\) −16.9625 −0.638846
\(706\) 20.0744 0.755510
\(707\) 10.4030 0.391245
\(708\) −4.85848 −0.182593
\(709\) −33.6912 −1.26530 −0.632650 0.774438i \(-0.718033\pi\)
−0.632650 + 0.774438i \(0.718033\pi\)
\(710\) 10.2855 0.386009
\(711\) 10.7268 0.402288
\(712\) −29.8495 −1.11866
\(713\) 25.9914 0.973384
\(714\) −12.8192 −0.479746
\(715\) −8.91800 −0.333514
\(716\) −3.43294 −0.128295
\(717\) 16.2362 0.606353
\(718\) 54.6661 2.04012
\(719\) 18.9323 0.706057 0.353029 0.935613i \(-0.385152\pi\)
0.353029 + 0.935613i \(0.385152\pi\)
\(720\) 9.67673 0.360630
\(721\) 15.2288 0.567150
\(722\) −79.3178 −2.95190
\(723\) −12.5949 −0.468410
\(724\) 5.61610 0.208721
\(725\) 3.02282 0.112265
\(726\) −15.2321 −0.565317
\(727\) 6.78906 0.251792 0.125896 0.992043i \(-0.459819\pi\)
0.125896 + 0.992043i \(0.459819\pi\)
\(728\) 8.81918 0.326860
\(729\) 1.00000 0.0370370
\(730\) −15.9792 −0.591415
\(731\) −50.0183 −1.84999
\(732\) 6.96836 0.257558
\(733\) 21.4982 0.794054 0.397027 0.917807i \(-0.370042\pi\)
0.397027 + 0.917807i \(0.370042\pi\)
\(734\) −6.68303 −0.246675
\(735\) 2.03406 0.0750275
\(736\) 7.00795 0.258316
\(737\) 3.32469 0.122467
\(738\) 10.3205 0.379904
\(739\) 4.08334 0.150208 0.0751041 0.997176i \(-0.476071\pi\)
0.0751041 + 0.997176i \(0.476071\pi\)
\(740\) 2.48152 0.0912225
\(741\) 31.0158 1.13939
\(742\) −6.68111 −0.245271
\(743\) −2.66701 −0.0978431 −0.0489216 0.998803i \(-0.515578\pi\)
−0.0489216 + 0.998803i \(0.515578\pi\)
\(744\) −24.5981 −0.901809
\(745\) 27.0048 0.989378
\(746\) −53.7523 −1.96801
\(747\) −12.9827 −0.475011
\(748\) −4.82644 −0.176472
\(749\) 1.38838 0.0507302
\(750\) 18.8827 0.689500
\(751\) 51.9749 1.89659 0.948295 0.317391i \(-0.102807\pi\)
0.948295 + 0.317391i \(0.102807\pi\)
\(752\) 39.6726 1.44671
\(753\) −22.8035 −0.831006
\(754\) 20.7057 0.754059
\(755\) −2.71885 −0.0989491
\(756\) −0.507395 −0.0184538
\(757\) 14.3161 0.520326 0.260163 0.965565i \(-0.416224\pi\)
0.260163 + 0.965565i \(0.416224\pi\)
\(758\) −51.6426 −1.87574
\(759\) −2.93438 −0.106511
\(760\) 39.9605 1.44952
\(761\) −1.05740 −0.0383307 −0.0191653 0.999816i \(-0.506101\pi\)
−0.0191653 + 0.999816i \(0.506101\pi\)
\(762\) 7.76061 0.281137
\(763\) 2.93650 0.106309
\(764\) −9.88834 −0.357748
\(765\) 16.4670 0.595364
\(766\) 1.58348 0.0572133
\(767\) 35.7294 1.29012
\(768\) −11.4600 −0.413526
\(769\) 37.7716 1.36208 0.681040 0.732246i \(-0.261528\pi\)
0.681040 + 0.732246i \(0.261528\pi\)
\(770\) 3.78449 0.136384
\(771\) −18.2621 −0.657695
\(772\) 1.53356 0.0551939
\(773\) 36.3383 1.30700 0.653498 0.756928i \(-0.273301\pi\)
0.653498 + 0.756928i \(0.273301\pi\)
\(774\) −9.78343 −0.351658
\(775\) −8.97737 −0.322477
\(776\) −28.9911 −1.04072
\(777\) 2.40440 0.0862575
\(778\) −30.4495 −1.09167
\(779\) 54.1752 1.94103
\(780\) 3.85107 0.137891
\(781\) 3.75217 0.134263
\(782\) 32.0144 1.14483
\(783\) 3.50435 0.125235
\(784\) −4.75734 −0.169905
\(785\) 12.1853 0.434913
\(786\) 21.0829 0.752003
\(787\) −3.97456 −0.141678 −0.0708388 0.997488i \(-0.522568\pi\)
−0.0708388 + 0.997488i \(0.522568\pi\)
\(788\) −12.8365 −0.457281
\(789\) −26.3782 −0.939088
\(790\) 34.5500 1.22923
\(791\) −4.96451 −0.176518
\(792\) 2.77708 0.0986791
\(793\) −51.2456 −1.81978
\(794\) 12.2375 0.434293
\(795\) 8.58226 0.304382
\(796\) 1.77341 0.0628569
\(797\) 41.3980 1.46639 0.733196 0.680018i \(-0.238028\pi\)
0.733196 + 0.680018i \(0.238028\pi\)
\(798\) −13.1620 −0.465930
\(799\) 67.5111 2.38837
\(800\) −2.42053 −0.0855787
\(801\) −12.6293 −0.446235
\(802\) −53.6799 −1.89550
\(803\) −5.82921 −0.205708
\(804\) −1.43571 −0.0506334
\(805\) −5.07982 −0.179040
\(806\) −61.4933 −2.16601
\(807\) 7.27730 0.256173
\(808\) 24.5875 0.864986
\(809\) −47.1729 −1.65851 −0.829256 0.558869i \(-0.811236\pi\)
−0.829256 + 0.558869i \(0.811236\pi\)
\(810\) 3.22089 0.113170
\(811\) 45.1440 1.58522 0.792610 0.609728i \(-0.208721\pi\)
0.792610 + 0.609728i \(0.208721\pi\)
\(812\) −1.77809 −0.0623987
\(813\) 10.6407 0.373187
\(814\) 4.47353 0.156797
\(815\) −21.7592 −0.762192
\(816\) −38.5135 −1.34824
\(817\) −51.3559 −1.79672
\(818\) −2.63891 −0.0922675
\(819\) 3.73140 0.130386
\(820\) 6.72667 0.234906
\(821\) 15.9729 0.557459 0.278730 0.960370i \(-0.410087\pi\)
0.278730 + 0.960370i \(0.410087\pi\)
\(822\) 32.6972 1.14045
\(823\) 23.6259 0.823547 0.411773 0.911286i \(-0.364910\pi\)
0.411773 + 0.911286i \(0.364910\pi\)
\(824\) 35.9933 1.25389
\(825\) 1.01353 0.0352865
\(826\) −15.1623 −0.527565
\(827\) 26.3407 0.915955 0.457978 0.888964i \(-0.348574\pi\)
0.457978 + 0.888964i \(0.348574\pi\)
\(828\) 1.26716 0.0440367
\(829\) −18.4133 −0.639519 −0.319760 0.947499i \(-0.603602\pi\)
−0.319760 + 0.947499i \(0.603602\pi\)
\(830\) −41.8157 −1.45144
\(831\) 30.1397 1.04553
\(832\) 18.9229 0.656032
\(833\) −8.09560 −0.280496
\(834\) −12.2319 −0.423555
\(835\) 25.9165 0.896879
\(836\) −4.95551 −0.171390
\(837\) −10.4075 −0.359735
\(838\) −44.2750 −1.52945
\(839\) −35.0262 −1.20924 −0.604620 0.796514i \(-0.706675\pi\)
−0.604620 + 0.796514i \(0.706675\pi\)
\(840\) 4.80752 0.165875
\(841\) −16.7195 −0.576535
\(842\) 1.31981 0.0454836
\(843\) 21.8838 0.753718
\(844\) 3.18125 0.109503
\(845\) −1.87813 −0.0646097
\(846\) 13.2050 0.453996
\(847\) −9.61941 −0.330527
\(848\) −20.0725 −0.689293
\(849\) −15.4851 −0.531448
\(850\) −11.0577 −0.379276
\(851\) −6.00470 −0.205839
\(852\) −1.62031 −0.0555107
\(853\) 7.20790 0.246794 0.123397 0.992357i \(-0.460621\pi\)
0.123397 + 0.992357i \(0.460621\pi\)
\(854\) 21.7468 0.744161
\(855\) 16.9073 0.578218
\(856\) 3.28143 0.112157
\(857\) 7.31936 0.250025 0.125012 0.992155i \(-0.460103\pi\)
0.125012 + 0.992155i \(0.460103\pi\)
\(858\) 6.94248 0.237012
\(859\) −49.4834 −1.68835 −0.844176 0.536065i \(-0.819910\pi\)
−0.844176 + 0.536065i \(0.819910\pi\)
\(860\) −6.37661 −0.217441
\(861\) 6.51764 0.222120
\(862\) 21.0072 0.715508
\(863\) −46.5393 −1.58422 −0.792108 0.610381i \(-0.791016\pi\)
−0.792108 + 0.610381i \(0.791016\pi\)
\(864\) −2.80612 −0.0954663
\(865\) 36.0969 1.22733
\(866\) 42.1388 1.43193
\(867\) −48.5388 −1.64846
\(868\) 5.28069 0.179238
\(869\) 12.6039 0.427557
\(870\) 11.2871 0.382669
\(871\) 10.5582 0.357752
\(872\) 6.94044 0.235033
\(873\) −12.2662 −0.415146
\(874\) 32.8705 1.11186
\(875\) 11.9249 0.403134
\(876\) 2.51724 0.0850495
\(877\) 12.5085 0.422382 0.211191 0.977445i \(-0.432266\pi\)
0.211191 + 0.977445i \(0.432266\pi\)
\(878\) 5.41908 0.182885
\(879\) −9.98207 −0.336687
\(880\) 11.3700 0.383282
\(881\) 40.5582 1.36644 0.683221 0.730212i \(-0.260579\pi\)
0.683221 + 0.730212i \(0.260579\pi\)
\(882\) −1.58348 −0.0533184
\(883\) 16.9527 0.570503 0.285251 0.958453i \(-0.407923\pi\)
0.285251 + 0.958453i \(0.407923\pi\)
\(884\) −15.3273 −0.515514
\(885\) 19.4769 0.654707
\(886\) −48.6474 −1.63434
\(887\) 3.93843 0.132240 0.0661198 0.997812i \(-0.478938\pi\)
0.0661198 + 0.997812i \(0.478938\pi\)
\(888\) 5.68282 0.190703
\(889\) 4.90100 0.164374
\(890\) −40.6776 −1.36352
\(891\) 1.17498 0.0393634
\(892\) −1.72935 −0.0579029
\(893\) 69.3165 2.31959
\(894\) −21.0226 −0.703102
\(895\) 13.7621 0.460016
\(896\) −13.6425 −0.455762
\(897\) −9.31871 −0.311143
\(898\) −33.3213 −1.11195
\(899\) −36.4714 −1.21639
\(900\) −0.437673 −0.0145891
\(901\) −34.1576 −1.13795
\(902\) 12.1264 0.403766
\(903\) −6.17846 −0.205606
\(904\) −11.7336 −0.390255
\(905\) −22.5140 −0.748392
\(906\) 2.11657 0.0703183
\(907\) 22.2551 0.738968 0.369484 0.929237i \(-0.379534\pi\)
0.369484 + 0.929237i \(0.379534\pi\)
\(908\) −13.1359 −0.435931
\(909\) 10.4030 0.345046
\(910\) 12.0184 0.398407
\(911\) −27.1176 −0.898447 −0.449224 0.893419i \(-0.648299\pi\)
−0.449224 + 0.893419i \(0.648299\pi\)
\(912\) −39.5435 −1.30942
\(913\) −15.2544 −0.504847
\(914\) −41.1663 −1.36166
\(915\) −27.9350 −0.923503
\(916\) −3.04825 −0.100717
\(917\) 13.3143 0.439678
\(918\) −12.8192 −0.423096
\(919\) −0.0136658 −0.000450794 0 −0.000225397 1.00000i \(-0.500072\pi\)
−0.000225397 1.00000i \(0.500072\pi\)
\(920\) −12.0062 −0.395832
\(921\) −4.79874 −0.158124
\(922\) −32.9950 −1.08663
\(923\) 11.9158 0.392213
\(924\) −0.596180 −0.0196129
\(925\) 2.07401 0.0681931
\(926\) −53.0156 −1.74220
\(927\) 15.2288 0.500180
\(928\) −9.83364 −0.322805
\(929\) 35.1265 1.15246 0.576232 0.817286i \(-0.304522\pi\)
0.576232 + 0.817286i \(0.304522\pi\)
\(930\) −33.5213 −1.09921
\(931\) −8.31210 −0.272418
\(932\) −5.23695 −0.171542
\(933\) 5.91843 0.193761
\(934\) 25.0959 0.821162
\(935\) 19.3484 0.632760
\(936\) 8.81918 0.288264
\(937\) 9.27557 0.303020 0.151510 0.988456i \(-0.451586\pi\)
0.151510 + 0.988456i \(0.451586\pi\)
\(938\) −4.48055 −0.146295
\(939\) −8.13144 −0.265359
\(940\) 8.60669 0.280719
\(941\) −47.5286 −1.54939 −0.774693 0.632337i \(-0.782096\pi\)
−0.774693 + 0.632337i \(0.782096\pi\)
\(942\) −9.48603 −0.309072
\(943\) −16.2770 −0.530052
\(944\) −45.5532 −1.48263
\(945\) 2.03406 0.0661681
\(946\) −11.4954 −0.373747
\(947\) 40.3978 1.31275 0.656376 0.754434i \(-0.272089\pi\)
0.656376 + 0.754434i \(0.272089\pi\)
\(948\) −5.44274 −0.176772
\(949\) −18.5118 −0.600920
\(950\) −11.3534 −0.368353
\(951\) −4.12351 −0.133714
\(952\) −19.1340 −0.620136
\(953\) −2.58733 −0.0838117 −0.0419059 0.999122i \(-0.513343\pi\)
−0.0419059 + 0.999122i \(0.513343\pi\)
\(954\) −6.68111 −0.216309
\(955\) 39.6408 1.28275
\(956\) −8.23817 −0.266442
\(957\) 4.11755 0.133102
\(958\) −54.1047 −1.74804
\(959\) 20.6490 0.666792
\(960\) 10.3152 0.332923
\(961\) 77.3153 2.49404
\(962\) 14.2066 0.458039
\(963\) 1.38838 0.0447398
\(964\) 6.39060 0.205827
\(965\) −6.14777 −0.197904
\(966\) 3.95454 0.127235
\(967\) −28.0460 −0.901899 −0.450949 0.892550i \(-0.648914\pi\)
−0.450949 + 0.892550i \(0.648914\pi\)
\(968\) −22.7355 −0.730747
\(969\) −67.2914 −2.16171
\(970\) −39.5079 −1.26852
\(971\) −25.9142 −0.831625 −0.415813 0.909450i \(-0.636503\pi\)
−0.415813 + 0.909450i \(0.636503\pi\)
\(972\) −0.507395 −0.0162747
\(973\) −7.72470 −0.247643
\(974\) 59.4601 1.90523
\(975\) 3.21867 0.103080
\(976\) 65.3354 2.09134
\(977\) −6.52762 −0.208837 −0.104419 0.994533i \(-0.533298\pi\)
−0.104419 + 0.994533i \(0.533298\pi\)
\(978\) 16.9391 0.541653
\(979\) −14.8392 −0.474264
\(980\) −1.03207 −0.0329683
\(981\) 2.93650 0.0937554
\(982\) 22.2772 0.710894
\(983\) 60.1942 1.91990 0.959949 0.280175i \(-0.0903926\pi\)
0.959949 + 0.280175i \(0.0903926\pi\)
\(984\) 15.4045 0.491076
\(985\) 51.4594 1.63963
\(986\) −44.9229 −1.43064
\(987\) 8.33923 0.265441
\(988\) −15.7372 −0.500668
\(989\) 15.4299 0.490643
\(990\) 3.78449 0.120279
\(991\) −53.8861 −1.71175 −0.855874 0.517184i \(-0.826980\pi\)
−0.855874 + 0.517184i \(0.826980\pi\)
\(992\) 29.2046 0.927248
\(993\) 7.88009 0.250067
\(994\) −5.05664 −0.160387
\(995\) −7.10932 −0.225381
\(996\) 6.58734 0.208728
\(997\) −26.1583 −0.828442 −0.414221 0.910176i \(-0.635946\pi\)
−0.414221 + 0.910176i \(0.635946\pi\)
\(998\) −12.0956 −0.382881
\(999\) 2.40440 0.0760720
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 \(a_p\))