Properties

Label 6026.2.a.h.1.19
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.72713 q^{3}\) \(+1.00000 q^{4}\) \(+0.546511 q^{5}\) \(-1.72713 q^{6}\) \(+2.37970 q^{7}\) \(-1.00000 q^{8}\) \(-0.0170298 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.72713 q^{3}\) \(+1.00000 q^{4}\) \(+0.546511 q^{5}\) \(-1.72713 q^{6}\) \(+2.37970 q^{7}\) \(-1.00000 q^{8}\) \(-0.0170298 q^{9}\) \(-0.546511 q^{10}\) \(-1.95450 q^{11}\) \(+1.72713 q^{12}\) \(-3.17542 q^{13}\) \(-2.37970 q^{14}\) \(+0.943895 q^{15}\) \(+1.00000 q^{16}\) \(-0.643138 q^{17}\) \(+0.0170298 q^{18}\) \(+0.483782 q^{19}\) \(+0.546511 q^{20}\) \(+4.11005 q^{21}\) \(+1.95450 q^{22}\) \(-1.00000 q^{23}\) \(-1.72713 q^{24}\) \(-4.70133 q^{25}\) \(+3.17542 q^{26}\) \(-5.21080 q^{27}\) \(+2.37970 q^{28}\) \(+6.04235 q^{29}\) \(-0.943895 q^{30}\) \(-4.23490 q^{31}\) \(-1.00000 q^{32}\) \(-3.37568 q^{33}\) \(+0.643138 q^{34}\) \(+1.30053 q^{35}\) \(-0.0170298 q^{36}\) \(-6.91135 q^{37}\) \(-0.483782 q^{38}\) \(-5.48435 q^{39}\) \(-0.546511 q^{40}\) \(+1.46356 q^{41}\) \(-4.11005 q^{42}\) \(+7.54748 q^{43}\) \(-1.95450 q^{44}\) \(-0.00930697 q^{45}\) \(+1.00000 q^{46}\) \(-12.7339 q^{47}\) \(+1.72713 q^{48}\) \(-1.33702 q^{49}\) \(+4.70133 q^{50}\) \(-1.11078 q^{51}\) \(-3.17542 q^{52}\) \(+13.4183 q^{53}\) \(+5.21080 q^{54}\) \(-1.06816 q^{55}\) \(-2.37970 q^{56}\) \(+0.835553 q^{57}\) \(-6.04235 q^{58}\) \(-3.90994 q^{59}\) \(+0.943895 q^{60}\) \(+1.06084 q^{61}\) \(+4.23490 q^{62}\) \(-0.0405258 q^{63}\) \(+1.00000 q^{64}\) \(-1.73540 q^{65}\) \(+3.37568 q^{66}\) \(-9.73931 q^{67}\) \(-0.643138 q^{68}\) \(-1.72713 q^{69}\) \(-1.30053 q^{70}\) \(-15.5760 q^{71}\) \(+0.0170298 q^{72}\) \(-4.64800 q^{73}\) \(+6.91135 q^{74}\) \(-8.11979 q^{75}\) \(+0.483782 q^{76}\) \(-4.65113 q^{77}\) \(+5.48435 q^{78}\) \(+14.7471 q^{79}\) \(+0.546511 q^{80}\) \(-8.94862 q^{81}\) \(-1.46356 q^{82}\) \(+13.0716 q^{83}\) \(+4.11005 q^{84}\) \(-0.351482 q^{85}\) \(-7.54748 q^{86}\) \(+10.4359 q^{87}\) \(+1.95450 q^{88}\) \(-5.56625 q^{89}\) \(+0.00930697 q^{90}\) \(-7.55655 q^{91}\) \(-1.00000 q^{92}\) \(-7.31421 q^{93}\) \(+12.7339 q^{94}\) \(+0.264392 q^{95}\) \(-1.72713 q^{96}\) \(+8.21629 q^{97}\) \(+1.33702 q^{98}\) \(+0.0332848 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.72713 0.997158 0.498579 0.866844i \(-0.333855\pi\)
0.498579 + 0.866844i \(0.333855\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.546511 0.244407 0.122204 0.992505i \(-0.461004\pi\)
0.122204 + 0.992505i \(0.461004\pi\)
\(6\) −1.72713 −0.705097
\(7\) 2.37970 0.899442 0.449721 0.893169i \(-0.351523\pi\)
0.449721 + 0.893169i \(0.351523\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.0170298 −0.00567659
\(10\) −0.546511 −0.172822
\(11\) −1.95450 −0.589305 −0.294652 0.955604i \(-0.595204\pi\)
−0.294652 + 0.955604i \(0.595204\pi\)
\(12\) 1.72713 0.498579
\(13\) −3.17542 −0.880703 −0.440351 0.897826i \(-0.645146\pi\)
−0.440351 + 0.897826i \(0.645146\pi\)
\(14\) −2.37970 −0.636002
\(15\) 0.943895 0.243713
\(16\) 1.00000 0.250000
\(17\) −0.643138 −0.155984 −0.0779919 0.996954i \(-0.524851\pi\)
−0.0779919 + 0.996954i \(0.524851\pi\)
\(18\) 0.0170298 0.00401396
\(19\) 0.483782 0.110987 0.0554936 0.998459i \(-0.482327\pi\)
0.0554936 + 0.998459i \(0.482327\pi\)
\(20\) 0.546511 0.122204
\(21\) 4.11005 0.896886
\(22\) 1.95450 0.416701
\(23\) −1.00000 −0.208514
\(24\) −1.72713 −0.352548
\(25\) −4.70133 −0.940265
\(26\) 3.17542 0.622751
\(27\) −5.21080 −1.00282
\(28\) 2.37970 0.449721
\(29\) 6.04235 1.12204 0.561019 0.827803i \(-0.310410\pi\)
0.561019 + 0.827803i \(0.310410\pi\)
\(30\) −0.943895 −0.172331
\(31\) −4.23490 −0.760610 −0.380305 0.924861i \(-0.624181\pi\)
−0.380305 + 0.924861i \(0.624181\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.37568 −0.587630
\(34\) 0.643138 0.110297
\(35\) 1.30053 0.219830
\(36\) −0.0170298 −0.00283830
\(37\) −6.91135 −1.13622 −0.568110 0.822953i \(-0.692325\pi\)
−0.568110 + 0.822953i \(0.692325\pi\)
\(38\) −0.483782 −0.0784798
\(39\) −5.48435 −0.878199
\(40\) −0.546511 −0.0864111
\(41\) 1.46356 0.228570 0.114285 0.993448i \(-0.463542\pi\)
0.114285 + 0.993448i \(0.463542\pi\)
\(42\) −4.11005 −0.634194
\(43\) 7.54748 1.15098 0.575490 0.817809i \(-0.304811\pi\)
0.575490 + 0.817809i \(0.304811\pi\)
\(44\) −1.95450 −0.294652
\(45\) −0.00930697 −0.00138740
\(46\) 1.00000 0.147442
\(47\) −12.7339 −1.85742 −0.928712 0.370801i \(-0.879083\pi\)
−0.928712 + 0.370801i \(0.879083\pi\)
\(48\) 1.72713 0.249289
\(49\) −1.33702 −0.191003
\(50\) 4.70133 0.664868
\(51\) −1.11078 −0.155540
\(52\) −3.17542 −0.440351
\(53\) 13.4183 1.84314 0.921570 0.388213i \(-0.126907\pi\)
0.921570 + 0.388213i \(0.126907\pi\)
\(54\) 5.21080 0.709099
\(55\) −1.06816 −0.144030
\(56\) −2.37970 −0.318001
\(57\) 0.835553 0.110672
\(58\) −6.04235 −0.793400
\(59\) −3.90994 −0.509030 −0.254515 0.967069i \(-0.581916\pi\)
−0.254515 + 0.967069i \(0.581916\pi\)
\(60\) 0.943895 0.121856
\(61\) 1.06084 0.135827 0.0679134 0.997691i \(-0.478366\pi\)
0.0679134 + 0.997691i \(0.478366\pi\)
\(62\) 4.23490 0.537833
\(63\) −0.0405258 −0.00510577
\(64\) 1.00000 0.125000
\(65\) −1.73540 −0.215250
\(66\) 3.37568 0.415517
\(67\) −9.73931 −1.18985 −0.594923 0.803783i \(-0.702817\pi\)
−0.594923 + 0.803783i \(0.702817\pi\)
\(68\) −0.643138 −0.0779919
\(69\) −1.72713 −0.207922
\(70\) −1.30053 −0.155444
\(71\) −15.5760 −1.84854 −0.924268 0.381743i \(-0.875324\pi\)
−0.924268 + 0.381743i \(0.875324\pi\)
\(72\) 0.0170298 0.00200698
\(73\) −4.64800 −0.544008 −0.272004 0.962296i \(-0.587686\pi\)
−0.272004 + 0.962296i \(0.587686\pi\)
\(74\) 6.91135 0.803429
\(75\) −8.11979 −0.937592
\(76\) 0.483782 0.0554936
\(77\) −4.65113 −0.530046
\(78\) 5.48435 0.620981
\(79\) 14.7471 1.65918 0.829589 0.558375i \(-0.188575\pi\)
0.829589 + 0.558375i \(0.188575\pi\)
\(80\) 0.546511 0.0611018
\(81\) −8.94862 −0.994291
\(82\) −1.46356 −0.161624
\(83\) 13.0716 1.43479 0.717397 0.696665i \(-0.245333\pi\)
0.717397 + 0.696665i \(0.245333\pi\)
\(84\) 4.11005 0.448443
\(85\) −0.351482 −0.0381236
\(86\) −7.54748 −0.813865
\(87\) 10.4359 1.11885
\(88\) 1.95450 0.208351
\(89\) −5.56625 −0.590021 −0.295011 0.955494i \(-0.595323\pi\)
−0.295011 + 0.955494i \(0.595323\pi\)
\(90\) 0.00930697 0.000981041 0
\(91\) −7.55655 −0.792141
\(92\) −1.00000 −0.104257
\(93\) −7.31421 −0.758449
\(94\) 12.7339 1.31340
\(95\) 0.264392 0.0271261
\(96\) −1.72713 −0.176274
\(97\) 8.21629 0.834238 0.417119 0.908852i \(-0.363040\pi\)
0.417119 + 0.908852i \(0.363040\pi\)
\(98\) 1.33702 0.135060
\(99\) 0.0332848 0.00334524
\(100\) −4.70133 −0.470133
\(101\) −7.17468 −0.713907 −0.356954 0.934122i \(-0.616185\pi\)
−0.356954 + 0.934122i \(0.616185\pi\)
\(102\) 1.11078 0.109984
\(103\) −7.41808 −0.730925 −0.365462 0.930826i \(-0.619089\pi\)
−0.365462 + 0.930826i \(0.619089\pi\)
\(104\) 3.17542 0.311375
\(105\) 2.24619 0.219205
\(106\) −13.4183 −1.30330
\(107\) −11.5349 −1.11512 −0.557562 0.830136i \(-0.688263\pi\)
−0.557562 + 0.830136i \(0.688263\pi\)
\(108\) −5.21080 −0.501409
\(109\) 1.66673 0.159644 0.0798220 0.996809i \(-0.474565\pi\)
0.0798220 + 0.996809i \(0.474565\pi\)
\(110\) 1.06816 0.101845
\(111\) −11.9368 −1.13299
\(112\) 2.37970 0.224861
\(113\) 0.628262 0.0591019 0.0295510 0.999563i \(-0.490592\pi\)
0.0295510 + 0.999563i \(0.490592\pi\)
\(114\) −0.835553 −0.0782568
\(115\) −0.546511 −0.0509625
\(116\) 6.04235 0.561019
\(117\) 0.0540767 0.00499939
\(118\) 3.90994 0.359939
\(119\) −1.53048 −0.140298
\(120\) −0.943895 −0.0861654
\(121\) −7.17992 −0.652720
\(122\) −1.06084 −0.0960441
\(123\) 2.52776 0.227921
\(124\) −4.23490 −0.380305
\(125\) −5.30189 −0.474215
\(126\) 0.0405258 0.00361032
\(127\) −2.76031 −0.244938 −0.122469 0.992472i \(-0.539081\pi\)
−0.122469 + 0.992472i \(0.539081\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 13.0355 1.14771
\(130\) 1.73540 0.152205
\(131\) −1.00000 −0.0873704
\(132\) −3.37568 −0.293815
\(133\) 1.15126 0.0998266
\(134\) 9.73931 0.841348
\(135\) −2.84776 −0.245096
\(136\) 0.643138 0.0551486
\(137\) −13.4677 −1.15062 −0.575312 0.817934i \(-0.695119\pi\)
−0.575312 + 0.817934i \(0.695119\pi\)
\(138\) 1.72713 0.147023
\(139\) −7.38074 −0.626026 −0.313013 0.949749i \(-0.601338\pi\)
−0.313013 + 0.949749i \(0.601338\pi\)
\(140\) 1.30053 0.109915
\(141\) −21.9930 −1.85215
\(142\) 15.5760 1.30711
\(143\) 6.20636 0.519002
\(144\) −0.0170298 −0.00141915
\(145\) 3.30222 0.274234
\(146\) 4.64800 0.384672
\(147\) −2.30921 −0.190461
\(148\) −6.91135 −0.568110
\(149\) −19.9014 −1.63038 −0.815191 0.579192i \(-0.803368\pi\)
−0.815191 + 0.579192i \(0.803368\pi\)
\(150\) 8.11979 0.662978
\(151\) −2.49936 −0.203395 −0.101697 0.994815i \(-0.532427\pi\)
−0.101697 + 0.994815i \(0.532427\pi\)
\(152\) −0.483782 −0.0392399
\(153\) 0.0109525 0.000885457 0
\(154\) 4.65113 0.374799
\(155\) −2.31442 −0.185899
\(156\) −5.48435 −0.439100
\(157\) −3.33070 −0.265819 −0.132909 0.991128i \(-0.542432\pi\)
−0.132909 + 0.991128i \(0.542432\pi\)
\(158\) −14.7471 −1.17322
\(159\) 23.1750 1.83790
\(160\) −0.546511 −0.0432055
\(161\) −2.37970 −0.187547
\(162\) 8.94862 0.703070
\(163\) −0.880629 −0.0689762 −0.0344881 0.999405i \(-0.510980\pi\)
−0.0344881 + 0.999405i \(0.510980\pi\)
\(164\) 1.46356 0.114285
\(165\) −1.84485 −0.143621
\(166\) −13.0716 −1.01455
\(167\) −9.52175 −0.736815 −0.368408 0.929664i \(-0.620097\pi\)
−0.368408 + 0.929664i \(0.620097\pi\)
\(168\) −4.11005 −0.317097
\(169\) −2.91672 −0.224363
\(170\) 0.351482 0.0269574
\(171\) −0.00823870 −0.000630029 0
\(172\) 7.54748 0.575490
\(173\) 1.88911 0.143627 0.0718133 0.997418i \(-0.477121\pi\)
0.0718133 + 0.997418i \(0.477121\pi\)
\(174\) −10.4359 −0.791145
\(175\) −11.1877 −0.845714
\(176\) −1.95450 −0.147326
\(177\) −6.75296 −0.507584
\(178\) 5.56625 0.417208
\(179\) 17.6151 1.31661 0.658305 0.752751i \(-0.271274\pi\)
0.658305 + 0.752751i \(0.271274\pi\)
\(180\) −0.00930697 −0.000693701 0
\(181\) 5.16895 0.384205 0.192103 0.981375i \(-0.438469\pi\)
0.192103 + 0.981375i \(0.438469\pi\)
\(182\) 7.55655 0.560128
\(183\) 1.83221 0.135441
\(184\) 1.00000 0.0737210
\(185\) −3.77713 −0.277700
\(186\) 7.31421 0.536304
\(187\) 1.25701 0.0919220
\(188\) −12.7339 −0.928712
\(189\) −12.4001 −0.901977
\(190\) −0.264392 −0.0191810
\(191\) 13.6429 0.987162 0.493581 0.869700i \(-0.335688\pi\)
0.493581 + 0.869700i \(0.335688\pi\)
\(192\) 1.72713 0.124645
\(193\) −22.4970 −1.61937 −0.809685 0.586865i \(-0.800362\pi\)
−0.809685 + 0.586865i \(0.800362\pi\)
\(194\) −8.21629 −0.589895
\(195\) −2.99726 −0.214638
\(196\) −1.33702 −0.0955017
\(197\) 18.2682 1.30155 0.650777 0.759269i \(-0.274443\pi\)
0.650777 + 0.759269i \(0.274443\pi\)
\(198\) −0.0332848 −0.00236544
\(199\) −12.1348 −0.860215 −0.430108 0.902778i \(-0.641524\pi\)
−0.430108 + 0.902778i \(0.641524\pi\)
\(200\) 4.70133 0.332434
\(201\) −16.8210 −1.18646
\(202\) 7.17468 0.504809
\(203\) 14.3790 1.00921
\(204\) −1.11078 −0.0777702
\(205\) 0.799854 0.0558642
\(206\) 7.41808 0.516842
\(207\) 0.0170298 0.00118365
\(208\) −3.17542 −0.220176
\(209\) −0.945554 −0.0654053
\(210\) −2.24619 −0.155002
\(211\) 12.8114 0.881973 0.440987 0.897514i \(-0.354629\pi\)
0.440987 + 0.897514i \(0.354629\pi\)
\(212\) 13.4183 0.921570
\(213\) −26.9018 −1.84328
\(214\) 11.5349 0.788511
\(215\) 4.12478 0.281308
\(216\) 5.21080 0.354550
\(217\) −10.0778 −0.684125
\(218\) −1.66673 −0.112885
\(219\) −8.02770 −0.542461
\(220\) −1.06816 −0.0720152
\(221\) 2.04223 0.137375
\(222\) 11.9368 0.801145
\(223\) −26.3483 −1.76442 −0.882208 0.470861i \(-0.843943\pi\)
−0.882208 + 0.470861i \(0.843943\pi\)
\(224\) −2.37970 −0.159000
\(225\) 0.0800625 0.00533750
\(226\) −0.628262 −0.0417914
\(227\) 20.9614 1.39126 0.695628 0.718402i \(-0.255126\pi\)
0.695628 + 0.718402i \(0.255126\pi\)
\(228\) 0.835553 0.0553359
\(229\) −11.2178 −0.741291 −0.370645 0.928774i \(-0.620863\pi\)
−0.370645 + 0.928774i \(0.620863\pi\)
\(230\) 0.546511 0.0360359
\(231\) −8.03310 −0.528539
\(232\) −6.04235 −0.396700
\(233\) 21.6622 1.41914 0.709568 0.704637i \(-0.248890\pi\)
0.709568 + 0.704637i \(0.248890\pi\)
\(234\) −0.0540767 −0.00353510
\(235\) −6.95920 −0.453968
\(236\) −3.90994 −0.254515
\(237\) 25.4701 1.65446
\(238\) 1.53048 0.0992060
\(239\) −1.69920 −0.109912 −0.0549561 0.998489i \(-0.517502\pi\)
−0.0549561 + 0.998489i \(0.517502\pi\)
\(240\) 0.943895 0.0609282
\(241\) −4.52346 −0.291382 −0.145691 0.989330i \(-0.546540\pi\)
−0.145691 + 0.989330i \(0.546540\pi\)
\(242\) 7.17992 0.461543
\(243\) 0.176977 0.0113531
\(244\) 1.06084 0.0679134
\(245\) −0.730699 −0.0466827
\(246\) −2.52776 −0.161164
\(247\) −1.53621 −0.0977467
\(248\) 4.23490 0.268916
\(249\) 22.5763 1.43072
\(250\) 5.30189 0.335321
\(251\) 18.7370 1.18267 0.591335 0.806426i \(-0.298601\pi\)
0.591335 + 0.806426i \(0.298601\pi\)
\(252\) −0.0405258 −0.00255288
\(253\) 1.95450 0.122879
\(254\) 2.76031 0.173197
\(255\) −0.607054 −0.0380152
\(256\) 1.00000 0.0625000
\(257\) 12.2418 0.763624 0.381812 0.924240i \(-0.375300\pi\)
0.381812 + 0.924240i \(0.375300\pi\)
\(258\) −13.0355 −0.811552
\(259\) −16.4470 −1.02196
\(260\) −1.73540 −0.107625
\(261\) −0.102900 −0.00636935
\(262\) 1.00000 0.0617802
\(263\) 29.5109 1.81972 0.909860 0.414916i \(-0.136189\pi\)
0.909860 + 0.414916i \(0.136189\pi\)
\(264\) 3.37568 0.207759
\(265\) 7.33323 0.450477
\(266\) −1.15126 −0.0705881
\(267\) −9.61362 −0.588344
\(268\) −9.73931 −0.594923
\(269\) −4.96244 −0.302565 −0.151283 0.988491i \(-0.548340\pi\)
−0.151283 + 0.988491i \(0.548340\pi\)
\(270\) 2.84776 0.173309
\(271\) −21.3809 −1.29880 −0.649399 0.760448i \(-0.724980\pi\)
−0.649399 + 0.760448i \(0.724980\pi\)
\(272\) −0.643138 −0.0389959
\(273\) −13.0511 −0.789890
\(274\) 13.4677 0.813614
\(275\) 9.18875 0.554103
\(276\) −1.72713 −0.103961
\(277\) 21.2840 1.27883 0.639415 0.768862i \(-0.279177\pi\)
0.639415 + 0.768862i \(0.279177\pi\)
\(278\) 7.38074 0.442667
\(279\) 0.0721194 0.00431768
\(280\) −1.30053 −0.0777218
\(281\) 16.7218 0.997536 0.498768 0.866735i \(-0.333786\pi\)
0.498768 + 0.866735i \(0.333786\pi\)
\(282\) 21.9930 1.30966
\(283\) 27.1756 1.61542 0.807711 0.589579i \(-0.200706\pi\)
0.807711 + 0.589579i \(0.200706\pi\)
\(284\) −15.5760 −0.924268
\(285\) 0.456640 0.0270490
\(286\) −6.20636 −0.366990
\(287\) 3.48284 0.205586
\(288\) 0.0170298 0.00100349
\(289\) −16.5864 −0.975669
\(290\) −3.30222 −0.193913
\(291\) 14.1906 0.831866
\(292\) −4.64800 −0.272004
\(293\) −1.47593 −0.0862249 −0.0431125 0.999070i \(-0.513727\pi\)
−0.0431125 + 0.999070i \(0.513727\pi\)
\(294\) 2.30921 0.134676
\(295\) −2.13683 −0.124411
\(296\) 6.91135 0.401714
\(297\) 10.1845 0.590966
\(298\) 19.9014 1.15285
\(299\) 3.17542 0.183639
\(300\) −8.11979 −0.468796
\(301\) 17.9607 1.03524
\(302\) 2.49936 0.143822
\(303\) −12.3916 −0.711878
\(304\) 0.483782 0.0277468
\(305\) 0.579762 0.0331971
\(306\) −0.0109525 −0.000626112 0
\(307\) −30.2166 −1.72455 −0.862275 0.506440i \(-0.830961\pi\)
−0.862275 + 0.506440i \(0.830961\pi\)
\(308\) −4.65113 −0.265023
\(309\) −12.8120 −0.728847
\(310\) 2.31442 0.131450
\(311\) −7.36136 −0.417424 −0.208712 0.977977i \(-0.566927\pi\)
−0.208712 + 0.977977i \(0.566927\pi\)
\(312\) 5.48435 0.310490
\(313\) 1.26962 0.0717630 0.0358815 0.999356i \(-0.488576\pi\)
0.0358815 + 0.999356i \(0.488576\pi\)
\(314\) 3.33070 0.187962
\(315\) −0.0221478 −0.00124789
\(316\) 14.7471 0.829589
\(317\) −29.5320 −1.65868 −0.829342 0.558742i \(-0.811284\pi\)
−0.829342 + 0.558742i \(0.811284\pi\)
\(318\) −23.1750 −1.29959
\(319\) −11.8098 −0.661222
\(320\) 0.546511 0.0305509
\(321\) −19.9223 −1.11195
\(322\) 2.37970 0.132616
\(323\) −0.311138 −0.0173122
\(324\) −8.94862 −0.497146
\(325\) 14.9287 0.828094
\(326\) 0.880629 0.0487735
\(327\) 2.87866 0.159190
\(328\) −1.46356 −0.0808118
\(329\) −30.3028 −1.67065
\(330\) 1.84485 0.101555
\(331\) 14.3844 0.790640 0.395320 0.918543i \(-0.370634\pi\)
0.395320 + 0.918543i \(0.370634\pi\)
\(332\) 13.0716 0.717397
\(333\) 0.117699 0.00644986
\(334\) 9.52175 0.521007
\(335\) −5.32265 −0.290807
\(336\) 4.11005 0.224221
\(337\) −10.2218 −0.556815 −0.278408 0.960463i \(-0.589807\pi\)
−0.278408 + 0.960463i \(0.589807\pi\)
\(338\) 2.91672 0.158648
\(339\) 1.08509 0.0589339
\(340\) −0.351482 −0.0190618
\(341\) 8.27712 0.448231
\(342\) 0.00823870 0.000445498 0
\(343\) −19.8396 −1.07124
\(344\) −7.54748 −0.406933
\(345\) −0.943895 −0.0508176
\(346\) −1.88911 −0.101559
\(347\) 11.9664 0.642390 0.321195 0.947013i \(-0.395916\pi\)
0.321195 + 0.947013i \(0.395916\pi\)
\(348\) 10.4359 0.559424
\(349\) 2.63119 0.140845 0.0704223 0.997517i \(-0.477565\pi\)
0.0704223 + 0.997517i \(0.477565\pi\)
\(350\) 11.1877 0.598010
\(351\) 16.5465 0.883185
\(352\) 1.95450 0.104175
\(353\) −20.3242 −1.08175 −0.540874 0.841104i \(-0.681906\pi\)
−0.540874 + 0.841104i \(0.681906\pi\)
\(354\) 6.75296 0.358916
\(355\) −8.51249 −0.451796
\(356\) −5.56625 −0.295011
\(357\) −2.64333 −0.139900
\(358\) −17.6151 −0.930984
\(359\) −10.2530 −0.541132 −0.270566 0.962701i \(-0.587211\pi\)
−0.270566 + 0.962701i \(0.587211\pi\)
\(360\) 0.00930697 0.000490520 0
\(361\) −18.7660 −0.987682
\(362\) −5.16895 −0.271674
\(363\) −12.4006 −0.650865
\(364\) −7.55655 −0.396071
\(365\) −2.54019 −0.132959
\(366\) −1.83221 −0.0957711
\(367\) −13.1647 −0.687193 −0.343597 0.939117i \(-0.611645\pi\)
−0.343597 + 0.939117i \(0.611645\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −0.0249242 −0.00129750
\(370\) 3.77713 0.196364
\(371\) 31.9314 1.65780
\(372\) −7.31421 −0.379224
\(373\) −27.9871 −1.44912 −0.724559 0.689213i \(-0.757956\pi\)
−0.724559 + 0.689213i \(0.757956\pi\)
\(374\) −1.25701 −0.0649987
\(375\) −9.15703 −0.472867
\(376\) 12.7339 0.656699
\(377\) −19.1870 −0.988181
\(378\) 12.4001 0.637794
\(379\) 0.505238 0.0259523 0.0129762 0.999916i \(-0.495869\pi\)
0.0129762 + 0.999916i \(0.495869\pi\)
\(380\) 0.264392 0.0135630
\(381\) −4.76741 −0.244242
\(382\) −13.6429 −0.698029
\(383\) 19.9129 1.01750 0.508752 0.860913i \(-0.330107\pi\)
0.508752 + 0.860913i \(0.330107\pi\)
\(384\) −1.72713 −0.0881371
\(385\) −2.54190 −0.129547
\(386\) 22.4970 1.14507
\(387\) −0.128532 −0.00653364
\(388\) 8.21629 0.417119
\(389\) −7.22207 −0.366174 −0.183087 0.983097i \(-0.558609\pi\)
−0.183087 + 0.983097i \(0.558609\pi\)
\(390\) 2.99726 0.151772
\(391\) 0.643138 0.0325249
\(392\) 1.33702 0.0675299
\(393\) −1.72713 −0.0871221
\(394\) −18.2682 −0.920338
\(395\) 8.05945 0.405515
\(396\) 0.0332848 0.00167262
\(397\) 37.1412 1.86406 0.932032 0.362375i \(-0.118034\pi\)
0.932032 + 0.362375i \(0.118034\pi\)
\(398\) 12.1348 0.608264
\(399\) 1.98837 0.0995429
\(400\) −4.70133 −0.235066
\(401\) −13.2667 −0.662507 −0.331254 0.943542i \(-0.607472\pi\)
−0.331254 + 0.943542i \(0.607472\pi\)
\(402\) 16.8210 0.838957
\(403\) 13.4476 0.669872
\(404\) −7.17468 −0.356954
\(405\) −4.89052 −0.243012
\(406\) −14.3790 −0.713618
\(407\) 13.5083 0.669580
\(408\) 1.11078 0.0549918
\(409\) 22.9714 1.13586 0.567932 0.823075i \(-0.307743\pi\)
0.567932 + 0.823075i \(0.307743\pi\)
\(410\) −0.799854 −0.0395020
\(411\) −23.2604 −1.14735
\(412\) −7.41808 −0.365462
\(413\) −9.30448 −0.457843
\(414\) −0.0170298 −0.000836968 0
\(415\) 7.14378 0.350674
\(416\) 3.17542 0.155688
\(417\) −12.7475 −0.624247
\(418\) 0.945554 0.0462485
\(419\) 6.32609 0.309050 0.154525 0.987989i \(-0.450615\pi\)
0.154525 + 0.987989i \(0.450615\pi\)
\(420\) 2.24619 0.109603
\(421\) 30.0999 1.46698 0.733491 0.679699i \(-0.237890\pi\)
0.733491 + 0.679699i \(0.237890\pi\)
\(422\) −12.8114 −0.623649
\(423\) 0.216855 0.0105438
\(424\) −13.4183 −0.651648
\(425\) 3.02360 0.146666
\(426\) 26.9018 1.30340
\(427\) 2.52449 0.122168
\(428\) −11.5349 −0.557562
\(429\) 10.7192 0.517527
\(430\) −4.12478 −0.198915
\(431\) 6.24375 0.300751 0.150376 0.988629i \(-0.451952\pi\)
0.150376 + 0.988629i \(0.451952\pi\)
\(432\) −5.21080 −0.250705
\(433\) −5.09446 −0.244824 −0.122412 0.992479i \(-0.539063\pi\)
−0.122412 + 0.992479i \(0.539063\pi\)
\(434\) 10.0778 0.483750
\(435\) 5.70335 0.273455
\(436\) 1.66673 0.0798220
\(437\) −0.483782 −0.0231424
\(438\) 8.02770 0.383578
\(439\) −5.68741 −0.271446 −0.135723 0.990747i \(-0.543336\pi\)
−0.135723 + 0.990747i \(0.543336\pi\)
\(440\) 1.06816 0.0509224
\(441\) 0.0227692 0.00108425
\(442\) −2.04223 −0.0971390
\(443\) −10.0320 −0.476634 −0.238317 0.971187i \(-0.576596\pi\)
−0.238317 + 0.971187i \(0.576596\pi\)
\(444\) −11.9368 −0.566495
\(445\) −3.04202 −0.144206
\(446\) 26.3483 1.24763
\(447\) −34.3722 −1.62575
\(448\) 2.37970 0.112430
\(449\) 5.34635 0.252310 0.126155 0.992011i \(-0.459736\pi\)
0.126155 + 0.992011i \(0.459736\pi\)
\(450\) −0.0800625 −0.00377418
\(451\) −2.86054 −0.134698
\(452\) 0.628262 0.0295510
\(453\) −4.31671 −0.202817
\(454\) −20.9614 −0.983766
\(455\) −4.12974 −0.193605
\(456\) −0.835553 −0.0391284
\(457\) 10.4118 0.487042 0.243521 0.969896i \(-0.421698\pi\)
0.243521 + 0.969896i \(0.421698\pi\)
\(458\) 11.2178 0.524172
\(459\) 3.35126 0.156423
\(460\) −0.546511 −0.0254812
\(461\) 30.0568 1.39989 0.699943 0.714199i \(-0.253209\pi\)
0.699943 + 0.714199i \(0.253209\pi\)
\(462\) 8.03310 0.373734
\(463\) 22.3224 1.03741 0.518705 0.854953i \(-0.326414\pi\)
0.518705 + 0.854953i \(0.326414\pi\)
\(464\) 6.04235 0.280509
\(465\) −3.99730 −0.185370
\(466\) −21.6622 −1.00348
\(467\) 1.09494 0.0506677 0.0253339 0.999679i \(-0.491935\pi\)
0.0253339 + 0.999679i \(0.491935\pi\)
\(468\) 0.0540767 0.00249970
\(469\) −23.1766 −1.07020
\(470\) 6.95920 0.321004
\(471\) −5.75254 −0.265063
\(472\) 3.90994 0.179969
\(473\) −14.7516 −0.678278
\(474\) −25.4701 −1.16988
\(475\) −2.27442 −0.104357
\(476\) −1.53048 −0.0701492
\(477\) −0.228510 −0.0104628
\(478\) 1.69920 0.0777197
\(479\) 37.4579 1.71150 0.855748 0.517392i \(-0.173097\pi\)
0.855748 + 0.517392i \(0.173097\pi\)
\(480\) −0.943895 −0.0430827
\(481\) 21.9464 1.00067
\(482\) 4.52346 0.206038
\(483\) −4.11005 −0.187014
\(484\) −7.17992 −0.326360
\(485\) 4.49029 0.203894
\(486\) −0.176977 −0.00802782
\(487\) 10.6622 0.483149 0.241575 0.970382i \(-0.422336\pi\)
0.241575 + 0.970382i \(0.422336\pi\)
\(488\) −1.06084 −0.0480220
\(489\) −1.52096 −0.0687801
\(490\) 0.730699 0.0330096
\(491\) −30.9746 −1.39787 −0.698933 0.715187i \(-0.746342\pi\)
−0.698933 + 0.715187i \(0.746342\pi\)
\(492\) 2.52776 0.113960
\(493\) −3.88607 −0.175020
\(494\) 1.53621 0.0691174
\(495\) 0.0181905 0.000817602 0
\(496\) −4.23490 −0.190153
\(497\) −37.0663 −1.66265
\(498\) −22.5763 −1.01167
\(499\) −36.8800 −1.65098 −0.825488 0.564419i \(-0.809100\pi\)
−0.825488 + 0.564419i \(0.809100\pi\)
\(500\) −5.30189 −0.237108
\(501\) −16.4453 −0.734721
\(502\) −18.7370 −0.836274
\(503\) −10.0464 −0.447946 −0.223973 0.974595i \(-0.571903\pi\)
−0.223973 + 0.974595i \(0.571903\pi\)
\(504\) 0.0405258 0.00180516
\(505\) −3.92104 −0.174484
\(506\) −1.95450 −0.0868883
\(507\) −5.03754 −0.223725
\(508\) −2.76031 −0.122469
\(509\) 26.4236 1.17121 0.585604 0.810598i \(-0.300858\pi\)
0.585604 + 0.810598i \(0.300858\pi\)
\(510\) 0.607054 0.0268808
\(511\) −11.0609 −0.489304
\(512\) −1.00000 −0.0441942
\(513\) −2.52089 −0.111300
\(514\) −12.2418 −0.539964
\(515\) −4.05406 −0.178643
\(516\) 13.0355 0.573854
\(517\) 24.8884 1.09459
\(518\) 16.4470 0.722638
\(519\) 3.26274 0.143218
\(520\) 1.73540 0.0761024
\(521\) 31.2568 1.36939 0.684694 0.728831i \(-0.259936\pi\)
0.684694 + 0.728831i \(0.259936\pi\)
\(522\) 0.102900 0.00450381
\(523\) 0.444611 0.0194415 0.00972074 0.999953i \(-0.496906\pi\)
0.00972074 + 0.999953i \(0.496906\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −19.3227 −0.843310
\(526\) −29.5109 −1.28674
\(527\) 2.72362 0.118643
\(528\) −3.37568 −0.146907
\(529\) 1.00000 0.0434783
\(530\) −7.33323 −0.318535
\(531\) 0.0665854 0.00288956
\(532\) 1.15126 0.0499133
\(533\) −4.64743 −0.201302
\(534\) 9.61362 0.416022
\(535\) −6.30397 −0.272544
\(536\) 9.73931 0.420674
\(537\) 30.4234 1.31287
\(538\) 4.96244 0.213946
\(539\) 2.61322 0.112559
\(540\) −2.84776 −0.122548
\(541\) −36.1722 −1.55516 −0.777582 0.628781i \(-0.783554\pi\)
−0.777582 + 0.628781i \(0.783554\pi\)
\(542\) 21.3809 0.918389
\(543\) 8.92744 0.383113
\(544\) 0.643138 0.0275743
\(545\) 0.910888 0.0390182
\(546\) 13.0511 0.558536
\(547\) 2.08286 0.0890567 0.0445284 0.999008i \(-0.485821\pi\)
0.0445284 + 0.999008i \(0.485821\pi\)
\(548\) −13.4677 −0.575312
\(549\) −0.0180659 −0.000771034 0
\(550\) −9.18875 −0.391810
\(551\) 2.92318 0.124532
\(552\) 1.72713 0.0735114
\(553\) 35.0937 1.49233
\(554\) −21.2840 −0.904269
\(555\) −6.52359 −0.276911
\(556\) −7.38074 −0.313013
\(557\) −32.0391 −1.35754 −0.678769 0.734352i \(-0.737486\pi\)
−0.678769 + 0.734352i \(0.737486\pi\)
\(558\) −0.0721194 −0.00305306
\(559\) −23.9664 −1.01367
\(560\) 1.30053 0.0549576
\(561\) 2.17102 0.0916607
\(562\) −16.7218 −0.705365
\(563\) 31.6883 1.33550 0.667750 0.744385i \(-0.267257\pi\)
0.667750 + 0.744385i \(0.267257\pi\)
\(564\) −21.9930 −0.926073
\(565\) 0.343352 0.0144449
\(566\) −27.1756 −1.14228
\(567\) −21.2950 −0.894308
\(568\) 15.5760 0.653556
\(569\) 2.77931 0.116515 0.0582575 0.998302i \(-0.481446\pi\)
0.0582575 + 0.998302i \(0.481446\pi\)
\(570\) −0.456640 −0.0191265
\(571\) −30.8292 −1.29016 −0.645081 0.764115i \(-0.723176\pi\)
−0.645081 + 0.764115i \(0.723176\pi\)
\(572\) 6.20636 0.259501
\(573\) 23.5630 0.984357
\(574\) −3.48284 −0.145371
\(575\) 4.70133 0.196059
\(576\) −0.0170298 −0.000709574 0
\(577\) 23.8845 0.994325 0.497162 0.867657i \(-0.334375\pi\)
0.497162 + 0.867657i \(0.334375\pi\)
\(578\) 16.5864 0.689902
\(579\) −38.8552 −1.61477
\(580\) 3.30222 0.137117
\(581\) 31.1065 1.29051
\(582\) −14.1906 −0.588218
\(583\) −26.2260 −1.08617
\(584\) 4.64800 0.192336
\(585\) 0.0295535 0.00122189
\(586\) 1.47593 0.0609702
\(587\) −18.9053 −0.780305 −0.390152 0.920750i \(-0.627578\pi\)
−0.390152 + 0.920750i \(0.627578\pi\)
\(588\) −2.30921 −0.0952303
\(589\) −2.04877 −0.0844180
\(590\) 2.13683 0.0879717
\(591\) 31.5515 1.29786
\(592\) −6.91135 −0.284055
\(593\) 31.2873 1.28482 0.642408 0.766363i \(-0.277936\pi\)
0.642408 + 0.766363i \(0.277936\pi\)
\(594\) −10.1845 −0.417876
\(595\) −0.836422 −0.0342900
\(596\) −19.9014 −0.815191
\(597\) −20.9584 −0.857770
\(598\) −3.17542 −0.129853
\(599\) 1.49047 0.0608990 0.0304495 0.999536i \(-0.490306\pi\)
0.0304495 + 0.999536i \(0.490306\pi\)
\(600\) 8.11979 0.331489
\(601\) −30.8448 −1.25819 −0.629093 0.777330i \(-0.716574\pi\)
−0.629093 + 0.777330i \(0.716574\pi\)
\(602\) −17.9607 −0.732025
\(603\) 0.165858 0.00675427
\(604\) −2.49936 −0.101697
\(605\) −3.92391 −0.159530
\(606\) 12.3916 0.503374
\(607\) 34.0014 1.38008 0.690038 0.723773i \(-0.257594\pi\)
0.690038 + 0.723773i \(0.257594\pi\)
\(608\) −0.483782 −0.0196200
\(609\) 24.8344 1.00634
\(610\) −0.579762 −0.0234739
\(611\) 40.4353 1.63584
\(612\) 0.0109525 0.000442728 0
\(613\) −3.92414 −0.158495 −0.0792473 0.996855i \(-0.525252\pi\)
−0.0792473 + 0.996855i \(0.525252\pi\)
\(614\) 30.2166 1.21944
\(615\) 1.38145 0.0557055
\(616\) 4.65113 0.187399
\(617\) 7.93988 0.319648 0.159824 0.987146i \(-0.448907\pi\)
0.159824 + 0.987146i \(0.448907\pi\)
\(618\) 12.8120 0.515373
\(619\) −8.76103 −0.352135 −0.176068 0.984378i \(-0.556338\pi\)
−0.176068 + 0.984378i \(0.556338\pi\)
\(620\) −2.31442 −0.0929494
\(621\) 5.21080 0.209102
\(622\) 7.36136 0.295164
\(623\) −13.2460 −0.530690
\(624\) −5.48435 −0.219550
\(625\) 20.6091 0.824363
\(626\) −1.26962 −0.0507441
\(627\) −1.63309 −0.0652194
\(628\) −3.33070 −0.132909
\(629\) 4.44495 0.177232
\(630\) 0.0221478 0.000882390 0
\(631\) −9.12805 −0.363382 −0.181691 0.983356i \(-0.558157\pi\)
−0.181691 + 0.983356i \(0.558157\pi\)
\(632\) −14.7471 −0.586608
\(633\) 22.1269 0.879466
\(634\) 29.5320 1.17287
\(635\) −1.50854 −0.0598647
\(636\) 23.1750 0.918950
\(637\) 4.24561 0.168217
\(638\) 11.8098 0.467554
\(639\) 0.265257 0.0104934
\(640\) −0.546511 −0.0216028
\(641\) −25.5876 −1.01065 −0.505325 0.862929i \(-0.668627\pi\)
−0.505325 + 0.862929i \(0.668627\pi\)
\(642\) 19.9223 0.786270
\(643\) −13.0608 −0.515069 −0.257534 0.966269i \(-0.582910\pi\)
−0.257534 + 0.966269i \(0.582910\pi\)
\(644\) −2.37970 −0.0937733
\(645\) 7.12403 0.280508
\(646\) 0.311138 0.0122416
\(647\) −20.6107 −0.810290 −0.405145 0.914252i \(-0.632779\pi\)
−0.405145 + 0.914252i \(0.632779\pi\)
\(648\) 8.94862 0.351535
\(649\) 7.64198 0.299974
\(650\) −14.9287 −0.585551
\(651\) −17.4056 −0.682181
\(652\) −0.880629 −0.0344881
\(653\) 9.83847 0.385009 0.192505 0.981296i \(-0.438339\pi\)
0.192505 + 0.981296i \(0.438339\pi\)
\(654\) −2.87866 −0.112564
\(655\) −0.546511 −0.0213540
\(656\) 1.46356 0.0571426
\(657\) 0.0791545 0.00308811
\(658\) 30.3028 1.18133
\(659\) 25.0150 0.974447 0.487224 0.873277i \(-0.338010\pi\)
0.487224 + 0.873277i \(0.338010\pi\)
\(660\) −1.84485 −0.0718105
\(661\) 16.9679 0.659976 0.329988 0.943985i \(-0.392955\pi\)
0.329988 + 0.943985i \(0.392955\pi\)
\(662\) −14.3844 −0.559067
\(663\) 3.52719 0.136985
\(664\) −13.0716 −0.507276
\(665\) 0.629175 0.0243984
\(666\) −0.117699 −0.00456074
\(667\) −6.04235 −0.233961
\(668\) −9.52175 −0.368408
\(669\) −45.5069 −1.75940
\(670\) 5.32265 0.205632
\(671\) −2.07342 −0.0800434
\(672\) −4.11005 −0.158549
\(673\) −37.5800 −1.44860 −0.724301 0.689484i \(-0.757837\pi\)
−0.724301 + 0.689484i \(0.757837\pi\)
\(674\) 10.2218 0.393728
\(675\) 24.4976 0.942915
\(676\) −2.91672 −0.112181
\(677\) −29.0960 −1.11825 −0.559125 0.829083i \(-0.688863\pi\)
−0.559125 + 0.829083i \(0.688863\pi\)
\(678\) −1.08509 −0.0416726
\(679\) 19.5523 0.750349
\(680\) 0.351482 0.0134787
\(681\) 36.2030 1.38730
\(682\) −8.27712 −0.316947
\(683\) −45.8677 −1.75508 −0.877540 0.479503i \(-0.840817\pi\)
−0.877540 + 0.479503i \(0.840817\pi\)
\(684\) −0.00823870 −0.000315015 0
\(685\) −7.36025 −0.281221
\(686\) 19.8396 0.757480
\(687\) −19.3745 −0.739184
\(688\) 7.54748 0.287745
\(689\) −42.6086 −1.62326
\(690\) 0.943895 0.0359335
\(691\) 19.4795 0.741034 0.370517 0.928826i \(-0.379180\pi\)
0.370517 + 0.928826i \(0.379180\pi\)
\(692\) 1.88911 0.0718133
\(693\) 0.0792078 0.00300885
\(694\) −11.9664 −0.454238
\(695\) −4.03366 −0.153005
\(696\) −10.4359 −0.395572
\(697\) −0.941273 −0.0356532
\(698\) −2.63119 −0.0995922
\(699\) 37.4133 1.41510
\(700\) −11.1877 −0.422857
\(701\) 2.42730 0.0916780 0.0458390 0.998949i \(-0.485404\pi\)
0.0458390 + 0.998949i \(0.485404\pi\)
\(702\) −16.5465 −0.624506
\(703\) −3.34359 −0.126106
\(704\) −1.95450 −0.0736631
\(705\) −12.0194 −0.452678
\(706\) 20.3242 0.764912
\(707\) −17.0736 −0.642118
\(708\) −6.75296 −0.253792
\(709\) −10.6282 −0.399149 −0.199575 0.979883i \(-0.563956\pi\)
−0.199575 + 0.979883i \(0.563956\pi\)
\(710\) 8.51249 0.319468
\(711\) −0.251140 −0.00941847
\(712\) 5.56625 0.208604
\(713\) 4.23490 0.158598
\(714\) 2.64333 0.0989240
\(715\) 3.39185 0.126848
\(716\) 17.6151 0.658305
\(717\) −2.93474 −0.109600
\(718\) 10.2530 0.382638
\(719\) 18.2529 0.680717 0.340358 0.940296i \(-0.389452\pi\)
0.340358 + 0.940296i \(0.389452\pi\)
\(720\) −0.00930697 −0.000346850 0
\(721\) −17.6528 −0.657425
\(722\) 18.7660 0.698397
\(723\) −7.81259 −0.290553
\(724\) 5.16895 0.192103
\(725\) −28.4071 −1.05501
\(726\) 12.4006 0.460231
\(727\) 42.3362 1.57016 0.785082 0.619392i \(-0.212621\pi\)
0.785082 + 0.619392i \(0.212621\pi\)
\(728\) 7.55655 0.280064
\(729\) 27.1515 1.00561
\(730\) 2.54019 0.0940166
\(731\) −4.85407 −0.179534
\(732\) 1.83221 0.0677204
\(733\) 13.5595 0.500833 0.250417 0.968138i \(-0.419432\pi\)
0.250417 + 0.968138i \(0.419432\pi\)
\(734\) 13.1647 0.485919
\(735\) −1.26201 −0.0465500
\(736\) 1.00000 0.0368605
\(737\) 19.0355 0.701182
\(738\) 0.0249242 0.000917471 0
\(739\) 10.5758 0.389038 0.194519 0.980899i \(-0.437685\pi\)
0.194519 + 0.980899i \(0.437685\pi\)
\(740\) −3.77713 −0.138850
\(741\) −2.65323 −0.0974689
\(742\) −31.9314 −1.17224
\(743\) 13.3752 0.490690 0.245345 0.969436i \(-0.421099\pi\)
0.245345 + 0.969436i \(0.421099\pi\)
\(744\) 7.31421 0.268152
\(745\) −10.8763 −0.398477
\(746\) 27.9871 1.02468
\(747\) −0.222606 −0.00814474
\(748\) 1.25701 0.0459610
\(749\) −27.4497 −1.00299
\(750\) 9.15703 0.334368
\(751\) −47.8751 −1.74699 −0.873493 0.486837i \(-0.838151\pi\)
−0.873493 + 0.486837i \(0.838151\pi\)
\(752\) −12.7339 −0.464356
\(753\) 32.3612 1.17931
\(754\) 19.1870 0.698750
\(755\) −1.36593 −0.0497112
\(756\) −12.4001 −0.450989
\(757\) 11.1899 0.406703 0.203351 0.979106i \(-0.434817\pi\)
0.203351 + 0.979106i \(0.434817\pi\)
\(758\) −0.505238 −0.0183511
\(759\) 3.37568 0.122529
\(760\) −0.264392 −0.00959052
\(761\) −45.7341 −1.65786 −0.828929 0.559353i \(-0.811050\pi\)
−0.828929 + 0.559353i \(0.811050\pi\)
\(762\) 4.76741 0.172705
\(763\) 3.96632 0.143591
\(764\) 13.6429 0.493581
\(765\) 0.00598566 0.000216412 0
\(766\) −19.9129 −0.719483
\(767\) 12.4157 0.448304
\(768\) 1.72713 0.0623224
\(769\) −10.4570 −0.377090 −0.188545 0.982065i \(-0.560377\pi\)
−0.188545 + 0.982065i \(0.560377\pi\)
\(770\) 2.54190 0.0916036
\(771\) 21.1432 0.761454
\(772\) −22.4970 −0.809685
\(773\) −43.3159 −1.55797 −0.778983 0.627046i \(-0.784264\pi\)
−0.778983 + 0.627046i \(0.784264\pi\)
\(774\) 0.128532 0.00461998
\(775\) 19.9096 0.715175
\(776\) −8.21629 −0.294948
\(777\) −28.4060 −1.01906
\(778\) 7.22207 0.258924
\(779\) 0.708046 0.0253684
\(780\) −2.99726 −0.107319
\(781\) 30.4434 1.08935
\(782\) −0.643138 −0.0229986
\(783\) −31.4855 −1.12520
\(784\) −1.33702 −0.0477509
\(785\) −1.82027 −0.0649681
\(786\) 1.72713 0.0616046
\(787\) −27.1636 −0.968278 −0.484139 0.874991i \(-0.660867\pi\)
−0.484139 + 0.874991i \(0.660867\pi\)
\(788\) 18.2682 0.650777
\(789\) 50.9691 1.81455
\(790\) −8.05945 −0.286742
\(791\) 1.49508 0.0531588
\(792\) −0.0332848 −0.00118272
\(793\) −3.36862 −0.119623
\(794\) −37.1412 −1.31809
\(795\) 12.6654 0.449196
\(796\) −12.1348 −0.430108
\(797\) −19.1475 −0.678239 −0.339119 0.940743i \(-0.610129\pi\)
−0.339119 + 0.940743i \(0.610129\pi\)
\(798\) −1.98837 −0.0703874
\(799\) 8.18963 0.289728
\(800\) 4.70133 0.166217
\(801\) 0.0947920 0.00334931
\(802\) 13.2667 0.468463
\(803\) 9.08454 0.320586
\(804\) −16.8210 −0.593232
\(805\) −1.30053 −0.0458378
\(806\) −13.4476 −0.473671
\(807\) −8.57076 −0.301705
\(808\) 7.17468 0.252404
\(809\) 27.6318 0.971482 0.485741 0.874103i \(-0.338550\pi\)
0.485741 + 0.874103i \(0.338550\pi\)
\(810\) 4.89052 0.171835
\(811\) −41.5638 −1.45950 −0.729751 0.683713i \(-0.760364\pi\)
−0.729751 + 0.683713i \(0.760364\pi\)
\(812\) 14.3790 0.504604
\(813\) −36.9276 −1.29511
\(814\) −13.5083 −0.473464
\(815\) −0.481274 −0.0168583
\(816\) −1.11078 −0.0388851
\(817\) 3.65133 0.127744
\(818\) −22.9714 −0.803178
\(819\) 0.128686 0.00449666
\(820\) 0.799854 0.0279321
\(821\) 9.63216 0.336165 0.168082 0.985773i \(-0.446243\pi\)
0.168082 + 0.985773i \(0.446243\pi\)
\(822\) 23.2604 0.811301
\(823\) −32.4335 −1.13056 −0.565280 0.824899i \(-0.691232\pi\)
−0.565280 + 0.824899i \(0.691232\pi\)
\(824\) 7.41808 0.258421
\(825\) 15.8702 0.552528
\(826\) 9.30448 0.323744
\(827\) −20.7850 −0.722767 −0.361383 0.932417i \(-0.617695\pi\)
−0.361383 + 0.932417i \(0.617695\pi\)
\(828\) 0.0170298 0.000591826 0
\(829\) −31.8344 −1.10565 −0.552827 0.833296i \(-0.686451\pi\)
−0.552827 + 0.833296i \(0.686451\pi\)
\(830\) −7.14378 −0.247964
\(831\) 36.7601 1.27520
\(832\) −3.17542 −0.110088
\(833\) 0.859891 0.0297934
\(834\) 12.7475 0.441409
\(835\) −5.20375 −0.180083
\(836\) −0.945554 −0.0327027
\(837\) 22.0672 0.762754
\(838\) −6.32609 −0.218531
\(839\) 14.1644 0.489010 0.244505 0.969648i \(-0.421375\pi\)
0.244505 + 0.969648i \(0.421375\pi\)
\(840\) −2.24619 −0.0775008
\(841\) 7.51005 0.258967
\(842\) −30.0999 −1.03731
\(843\) 28.8806 0.994701
\(844\) 12.8114 0.440987
\(845\) −1.59402 −0.0548359
\(846\) −0.216855 −0.00745563
\(847\) −17.0861 −0.587084
\(848\) 13.4183 0.460785
\(849\) 46.9357 1.61083
\(850\) −3.02360 −0.103709
\(851\) 6.91135 0.236918
\(852\) −26.9018 −0.921641
\(853\) 16.6441 0.569883 0.284942 0.958545i \(-0.408026\pi\)
0.284942 + 0.958545i \(0.408026\pi\)
\(854\) −2.52449 −0.0863861
\(855\) −0.00450255 −0.000153984 0
\(856\) 11.5349 0.394256
\(857\) −16.6186 −0.567680 −0.283840 0.958872i \(-0.591608\pi\)
−0.283840 + 0.958872i \(0.591608\pi\)
\(858\) −10.7192 −0.365947
\(859\) −6.30950 −0.215277 −0.107639 0.994190i \(-0.534329\pi\)
−0.107639 + 0.994190i \(0.534329\pi\)
\(860\) 4.12478 0.140654
\(861\) 6.01531 0.205001
\(862\) −6.24375 −0.212663
\(863\) 40.4821 1.37803 0.689013 0.724749i \(-0.258044\pi\)
0.689013 + 0.724749i \(0.258044\pi\)
\(864\) 5.21080 0.177275
\(865\) 1.03242 0.0351034
\(866\) 5.09446 0.173117
\(867\) −28.6468 −0.972896
\(868\) −10.0778 −0.342063
\(869\) −28.8232 −0.977761
\(870\) −5.70335 −0.193362
\(871\) 30.9264 1.04790
\(872\) −1.66673 −0.0564427
\(873\) −0.139922 −0.00473563
\(874\) 0.483782 0.0163642
\(875\) −12.6169 −0.426529
\(876\) −8.02770 −0.271231
\(877\) −24.4482 −0.825557 −0.412778 0.910831i \(-0.635442\pi\)
−0.412778 + 0.910831i \(0.635442\pi\)
\(878\) 5.68741 0.191941
\(879\) −2.54912 −0.0859798
\(880\) −1.06816 −0.0360076
\(881\) 17.2779 0.582107 0.291054 0.956707i \(-0.405994\pi\)
0.291054 + 0.956707i \(0.405994\pi\)
\(882\) −0.0227692 −0.000766680 0
\(883\) 1.67355 0.0563194 0.0281597 0.999603i \(-0.491035\pi\)
0.0281597 + 0.999603i \(0.491035\pi\)
\(884\) 2.04223 0.0686877
\(885\) −3.69057 −0.124057
\(886\) 10.0320 0.337031
\(887\) −1.47471 −0.0495160 −0.0247580 0.999693i \(-0.507882\pi\)
−0.0247580 + 0.999693i \(0.507882\pi\)
\(888\) 11.9368 0.400573
\(889\) −6.56872 −0.220308
\(890\) 3.04202 0.101969
\(891\) 17.4901 0.585941
\(892\) −26.3483 −0.882208
\(893\) −6.16042 −0.206150
\(894\) 34.3722 1.14958
\(895\) 9.62683 0.321789
\(896\) −2.37970 −0.0795002
\(897\) 5.48435 0.183117
\(898\) −5.34635 −0.178410
\(899\) −25.5888 −0.853433
\(900\) 0.0800625 0.00266875
\(901\) −8.62979 −0.287500
\(902\) 2.86054 0.0952455
\(903\) 31.0205 1.03230
\(904\) −0.628262 −0.0208957
\(905\) 2.82489 0.0939026
\(906\) 4.31671 0.143413
\(907\) −37.5448 −1.24666 −0.623328 0.781961i \(-0.714220\pi\)
−0.623328 + 0.781961i \(0.714220\pi\)
\(908\) 20.9614 0.695628
\(909\) 0.122183 0.00405256
\(910\) 4.12974 0.136900
\(911\) 32.8640 1.08883 0.544416 0.838815i \(-0.316751\pi\)
0.544416 + 0.838815i \(0.316751\pi\)
\(912\) 0.835553 0.0276679
\(913\) −25.5485 −0.845531
\(914\) −10.4118 −0.344391
\(915\) 1.00132 0.0331027
\(916\) −11.2178 −0.370645
\(917\) −2.37970 −0.0785846
\(918\) −3.35126 −0.110608
\(919\) −46.6207 −1.53788 −0.768938 0.639323i \(-0.779215\pi\)
−0.768938 + 0.639323i \(0.779215\pi\)
\(920\) 0.546511 0.0180179
\(921\) −52.1878 −1.71965
\(922\) −30.0568 −0.989869
\(923\) 49.4605 1.62801
\(924\) −8.03310 −0.264270
\(925\) 32.4925 1.06835
\(926\) −22.3224 −0.733560
\(927\) 0.126328 0.00414916
\(928\) −6.04235 −0.198350
\(929\) 48.1697 1.58040 0.790199 0.612850i \(-0.209977\pi\)
0.790199 + 0.612850i \(0.209977\pi\)
\(930\) 3.99730 0.131077
\(931\) −0.646828 −0.0211989
\(932\) 21.6622 0.709568
\(933\) −12.7140 −0.416238
\(934\) −1.09494 −0.0358275
\(935\) 0.686973 0.0224664
\(936\) −0.0540767 −0.00176755
\(937\) −36.1130 −1.17976 −0.589879 0.807491i \(-0.700825\pi\)
−0.589879 + 0.807491i \(0.700825\pi\)
\(938\) 23.1766 0.756744
\(939\) 2.19279 0.0715590
\(940\) −6.95920 −0.226984
\(941\) −5.16644 −0.168421 −0.0842106 0.996448i \(-0.526837\pi\)
−0.0842106 + 0.996448i \(0.526837\pi\)
\(942\) 5.75254 0.187428
\(943\) −1.46356 −0.0476602
\(944\) −3.90994 −0.127258
\(945\) −6.77682 −0.220450
\(946\) 14.7516 0.479615
\(947\) −34.5463 −1.12260 −0.561302 0.827611i \(-0.689699\pi\)
−0.561302 + 0.827611i \(0.689699\pi\)
\(948\) 25.4701 0.827231
\(949\) 14.7594 0.479109
\(950\) 2.27442 0.0737918
\(951\) −51.0056 −1.65397
\(952\) 1.53048 0.0496030
\(953\) −7.60552 −0.246367 −0.123183 0.992384i \(-0.539310\pi\)
−0.123183 + 0.992384i \(0.539310\pi\)
\(954\) 0.228510 0.00739828
\(955\) 7.45598 0.241270
\(956\) −1.69920 −0.0549561
\(957\) −20.3970 −0.659342
\(958\) −37.4579 −1.21021
\(959\) −32.0491 −1.03492
\(960\) 0.943895 0.0304641
\(961\) −13.0656 −0.421472
\(962\) −21.9464 −0.707582
\(963\) 0.196437 0.00633010
\(964\) −4.52346 −0.145691
\(965\) −12.2949 −0.395786
\(966\) 4.11005 0.132239
\(967\) −2.09433 −0.0673490 −0.0336745 0.999433i \(-0.510721\pi\)
−0.0336745 + 0.999433i \(0.510721\pi\)
\(968\) 7.17992 0.230771
\(969\) −0.537376 −0.0172630
\(970\) −4.49029 −0.144175
\(971\) 38.5936 1.23853 0.619264 0.785183i \(-0.287431\pi\)
0.619264 + 0.785183i \(0.287431\pi\)
\(972\) 0.176977 0.00567653
\(973\) −17.5640 −0.563075
\(974\) −10.6622 −0.341638
\(975\) 25.7837 0.825740
\(976\) 1.06084 0.0339567
\(977\) 24.8868 0.796199 0.398100 0.917342i \(-0.369670\pi\)
0.398100 + 0.917342i \(0.369670\pi\)
\(978\) 1.52096 0.0486349
\(979\) 10.8792 0.347702
\(980\) −0.730699 −0.0233413
\(981\) −0.0283841 −0.000906234 0
\(982\) 30.9746 0.988441
\(983\) −36.0099 −1.14854 −0.574268 0.818667i \(-0.694713\pi\)
−0.574268 + 0.818667i \(0.694713\pi\)
\(984\) −2.52776 −0.0805821
\(985\) 9.98377 0.318109
\(986\) 3.88607 0.123758
\(987\) −52.3368 −1.66590
\(988\) −1.53621 −0.0488734
\(989\) −7.54748 −0.239996
\(990\) −0.0181905 −0.000578132 0
\(991\) 7.78476 0.247291 0.123646 0.992326i \(-0.460541\pi\)
0.123646 + 0.992326i \(0.460541\pi\)
\(992\) 4.23490 0.134458
\(993\) 24.8438 0.788393
\(994\) 37.0663 1.17567
\(995\) −6.63182 −0.210243
\(996\) 22.5763 0.715358
\(997\) −6.89443 −0.218349 −0.109174 0.994023i \(-0.534821\pi\)
−0.109174 + 0.994023i \(0.534821\pi\)
\(998\) 36.8800 1.16742
\(999\) 36.0137 1.13942
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 \(a_p\))