Properties

Label 6017.2.a.c.1.10
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.43520 q^{2}\) \(-0.763891 q^{3}\) \(+3.93019 q^{4}\) \(+1.56797 q^{5}\) \(+1.86023 q^{6}\) \(+2.19104 q^{7}\) \(-4.70040 q^{8}\) \(-2.41647 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.43520 q^{2}\) \(-0.763891 q^{3}\) \(+3.93019 q^{4}\) \(+1.56797 q^{5}\) \(+1.86023 q^{6}\) \(+2.19104 q^{7}\) \(-4.70040 q^{8}\) \(-2.41647 q^{9}\) \(-3.81832 q^{10}\) \(+1.00000 q^{11}\) \(-3.00224 q^{12}\) \(+2.36121 q^{13}\) \(-5.33563 q^{14}\) \(-1.19776 q^{15}\) \(+3.58603 q^{16}\) \(-7.19121 q^{17}\) \(+5.88459 q^{18}\) \(-5.00968 q^{19}\) \(+6.16243 q^{20}\) \(-1.67372 q^{21}\) \(-2.43520 q^{22}\) \(+5.48829 q^{23}\) \(+3.59060 q^{24}\) \(-2.54147 q^{25}\) \(-5.75002 q^{26}\) \(+4.13759 q^{27}\) \(+8.61122 q^{28}\) \(+3.08689 q^{29}\) \(+2.91678 q^{30}\) \(+0.979432 q^{31}\) \(+0.668107 q^{32}\) \(-0.763891 q^{33}\) \(+17.5120 q^{34}\) \(+3.43549 q^{35}\) \(-9.49720 q^{36}\) \(-10.5213 q^{37}\) \(+12.1996 q^{38}\) \(-1.80371 q^{39}\) \(-7.37010 q^{40}\) \(-6.32400 q^{41}\) \(+4.07584 q^{42}\) \(+12.6521 q^{43}\) \(+3.93019 q^{44}\) \(-3.78896 q^{45}\) \(-13.3651 q^{46}\) \(+8.78320 q^{47}\) \(-2.73934 q^{48}\) \(-2.19933 q^{49}\) \(+6.18898 q^{50}\) \(+5.49330 q^{51}\) \(+9.28002 q^{52}\) \(-0.712147 q^{53}\) \(-10.0759 q^{54}\) \(+1.56797 q^{55}\) \(-10.2988 q^{56}\) \(+3.82685 q^{57}\) \(-7.51719 q^{58}\) \(+5.94876 q^{59}\) \(-4.70742 q^{60}\) \(-8.95486 q^{61}\) \(-2.38511 q^{62}\) \(-5.29459 q^{63}\) \(-8.79904 q^{64}\) \(+3.70231 q^{65}\) \(+1.86023 q^{66}\) \(+15.3258 q^{67}\) \(-28.2628 q^{68}\) \(-4.19245 q^{69}\) \(-8.36611 q^{70}\) \(+10.1508 q^{71}\) \(+11.3584 q^{72}\) \(+5.23097 q^{73}\) \(+25.6214 q^{74}\) \(+1.94140 q^{75}\) \(-19.6890 q^{76}\) \(+2.19104 q^{77}\) \(+4.39239 q^{78}\) \(-2.02337 q^{79}\) \(+5.62280 q^{80}\) \(+4.08874 q^{81}\) \(+15.4002 q^{82}\) \(-10.2756 q^{83}\) \(-6.57803 q^{84}\) \(-11.2756 q^{85}\) \(-30.8105 q^{86}\) \(-2.35805 q^{87}\) \(-4.70040 q^{88}\) \(-9.97324 q^{89}\) \(+9.22686 q^{90}\) \(+5.17352 q^{91}\) \(+21.5700 q^{92}\) \(-0.748179 q^{93}\) \(-21.3888 q^{94}\) \(-7.85503 q^{95}\) \(-0.510361 q^{96}\) \(-9.49463 q^{97}\) \(+5.35580 q^{98}\) \(-2.41647 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43520 −1.72195 −0.860973 0.508651i \(-0.830144\pi\)
−0.860973 + 0.508651i \(0.830144\pi\)
\(3\) −0.763891 −0.441033 −0.220516 0.975383i \(-0.570774\pi\)
−0.220516 + 0.975383i \(0.570774\pi\)
\(4\) 3.93019 1.96510
\(5\) 1.56797 0.701218 0.350609 0.936522i \(-0.385975\pi\)
0.350609 + 0.936522i \(0.385975\pi\)
\(6\) 1.86023 0.759434
\(7\) 2.19104 0.828136 0.414068 0.910246i \(-0.364107\pi\)
0.414068 + 0.910246i \(0.364107\pi\)
\(8\) −4.70040 −1.66184
\(9\) −2.41647 −0.805490
\(10\) −3.81832 −1.20746
\(11\) 1.00000 0.301511
\(12\) −3.00224 −0.866672
\(13\) 2.36121 0.654883 0.327441 0.944872i \(-0.393814\pi\)
0.327441 + 0.944872i \(0.393814\pi\)
\(14\) −5.33563 −1.42601
\(15\) −1.19776 −0.309260
\(16\) 3.58603 0.896508
\(17\) −7.19121 −1.74412 −0.872062 0.489395i \(-0.837218\pi\)
−0.872062 + 0.489395i \(0.837218\pi\)
\(18\) 5.88459 1.38701
\(19\) −5.00968 −1.14930 −0.574650 0.818400i \(-0.694862\pi\)
−0.574650 + 0.818400i \(0.694862\pi\)
\(20\) 6.16243 1.37796
\(21\) −1.67372 −0.365235
\(22\) −2.43520 −0.519186
\(23\) 5.48829 1.14439 0.572194 0.820119i \(-0.306093\pi\)
0.572194 + 0.820119i \(0.306093\pi\)
\(24\) 3.59060 0.732927
\(25\) −2.54147 −0.508293
\(26\) −5.75002 −1.12767
\(27\) 4.13759 0.796280
\(28\) 8.61122 1.62737
\(29\) 3.08689 0.573221 0.286610 0.958047i \(-0.407471\pi\)
0.286610 + 0.958047i \(0.407471\pi\)
\(30\) 2.91678 0.532529
\(31\) 0.979432 0.175911 0.0879556 0.996124i \(-0.471967\pi\)
0.0879556 + 0.996124i \(0.471967\pi\)
\(32\) 0.668107 0.118106
\(33\) −0.763891 −0.132976
\(34\) 17.5120 3.00329
\(35\) 3.43549 0.580704
\(36\) −9.49720 −1.58287
\(37\) −10.5213 −1.72968 −0.864842 0.502043i \(-0.832582\pi\)
−0.864842 + 0.502043i \(0.832582\pi\)
\(38\) 12.1996 1.97903
\(39\) −1.80371 −0.288825
\(40\) −7.37010 −1.16531
\(41\) −6.32400 −0.987643 −0.493821 0.869563i \(-0.664400\pi\)
−0.493821 + 0.869563i \(0.664400\pi\)
\(42\) 4.07584 0.628915
\(43\) 12.6521 1.92943 0.964717 0.263289i \(-0.0848072\pi\)
0.964717 + 0.263289i \(0.0848072\pi\)
\(44\) 3.93019 0.592499
\(45\) −3.78896 −0.564824
\(46\) −13.3651 −1.97057
\(47\) 8.78320 1.28116 0.640580 0.767891i \(-0.278694\pi\)
0.640580 + 0.767891i \(0.278694\pi\)
\(48\) −2.73934 −0.395389
\(49\) −2.19933 −0.314190
\(50\) 6.18898 0.875253
\(51\) 5.49330 0.769216
\(52\) 9.28002 1.28691
\(53\) −0.712147 −0.0978209 −0.0489105 0.998803i \(-0.515575\pi\)
−0.0489105 + 0.998803i \(0.515575\pi\)
\(54\) −10.0759 −1.37115
\(55\) 1.56797 0.211425
\(56\) −10.2988 −1.37623
\(57\) 3.82685 0.506878
\(58\) −7.51719 −0.987055
\(59\) 5.94876 0.774462 0.387231 0.921983i \(-0.373432\pi\)
0.387231 + 0.921983i \(0.373432\pi\)
\(60\) −4.70742 −0.607726
\(61\) −8.95486 −1.14655 −0.573276 0.819362i \(-0.694328\pi\)
−0.573276 + 0.819362i \(0.694328\pi\)
\(62\) −2.38511 −0.302910
\(63\) −5.29459 −0.667056
\(64\) −8.79904 −1.09988
\(65\) 3.70231 0.459215
\(66\) 1.86023 0.228978
\(67\) 15.3258 1.87234 0.936172 0.351544i \(-0.114343\pi\)
0.936172 + 0.351544i \(0.114343\pi\)
\(68\) −28.2628 −3.42737
\(69\) −4.19245 −0.504712
\(70\) −8.36611 −0.999941
\(71\) 10.1508 1.20468 0.602340 0.798240i \(-0.294235\pi\)
0.602340 + 0.798240i \(0.294235\pi\)
\(72\) 11.3584 1.33860
\(73\) 5.23097 0.612238 0.306119 0.951993i \(-0.400969\pi\)
0.306119 + 0.951993i \(0.400969\pi\)
\(74\) 25.6214 2.97842
\(75\) 1.94140 0.224174
\(76\) −19.6890 −2.25848
\(77\) 2.19104 0.249693
\(78\) 4.39239 0.497340
\(79\) −2.02337 −0.227647 −0.113824 0.993501i \(-0.536310\pi\)
−0.113824 + 0.993501i \(0.536310\pi\)
\(80\) 5.62280 0.628648
\(81\) 4.08874 0.454305
\(82\) 15.4002 1.70067
\(83\) −10.2756 −1.12789 −0.563946 0.825812i \(-0.690717\pi\)
−0.563946 + 0.825812i \(0.690717\pi\)
\(84\) −6.57803 −0.717722
\(85\) −11.2756 −1.22301
\(86\) −30.8105 −3.32238
\(87\) −2.35805 −0.252809
\(88\) −4.70040 −0.501065
\(89\) −9.97324 −1.05716 −0.528581 0.848883i \(-0.677276\pi\)
−0.528581 + 0.848883i \(0.677276\pi\)
\(90\) 9.22686 0.972597
\(91\) 5.17352 0.542332
\(92\) 21.5700 2.24883
\(93\) −0.748179 −0.0775826
\(94\) −21.3888 −2.20609
\(95\) −7.85503 −0.805909
\(96\) −0.510361 −0.0520885
\(97\) −9.49463 −0.964034 −0.482017 0.876162i \(-0.660096\pi\)
−0.482017 + 0.876162i \(0.660096\pi\)
\(98\) 5.35580 0.541018
\(99\) −2.41647 −0.242864
\(100\) −9.98845 −0.998845
\(101\) −5.22934 −0.520339 −0.260169 0.965563i \(-0.583778\pi\)
−0.260169 + 0.965563i \(0.583778\pi\)
\(102\) −13.3773 −1.32455
\(103\) −14.4770 −1.42646 −0.713231 0.700929i \(-0.752769\pi\)
−0.713231 + 0.700929i \(0.752769\pi\)
\(104\) −11.0987 −1.08831
\(105\) −2.62434 −0.256109
\(106\) 1.73422 0.168442
\(107\) −5.54375 −0.535935 −0.267967 0.963428i \(-0.586352\pi\)
−0.267967 + 0.963428i \(0.586352\pi\)
\(108\) 16.2615 1.56477
\(109\) 3.82204 0.366085 0.183043 0.983105i \(-0.441405\pi\)
0.183043 + 0.983105i \(0.441405\pi\)
\(110\) −3.81832 −0.364063
\(111\) 8.03710 0.762847
\(112\) 7.85715 0.742431
\(113\) −4.62935 −0.435493 −0.217746 0.976005i \(-0.569871\pi\)
−0.217746 + 0.976005i \(0.569871\pi\)
\(114\) −9.31914 −0.872817
\(115\) 8.60548 0.802465
\(116\) 12.1321 1.12643
\(117\) −5.70580 −0.527501
\(118\) −14.4864 −1.33358
\(119\) −15.7563 −1.44437
\(120\) 5.62995 0.513942
\(121\) 1.00000 0.0909091
\(122\) 21.8069 1.97430
\(123\) 4.83084 0.435583
\(124\) 3.84936 0.345683
\(125\) −11.8248 −1.05764
\(126\) 12.8934 1.14863
\(127\) −14.0517 −1.24689 −0.623446 0.781867i \(-0.714268\pi\)
−0.623446 + 0.781867i \(0.714268\pi\)
\(128\) 20.0912 1.77583
\(129\) −9.66486 −0.850943
\(130\) −9.01587 −0.790744
\(131\) 12.8505 1.12276 0.561378 0.827560i \(-0.310272\pi\)
0.561378 + 0.827560i \(0.310272\pi\)
\(132\) −3.00224 −0.261311
\(133\) −10.9764 −0.951777
\(134\) −37.3213 −3.22407
\(135\) 6.48763 0.558366
\(136\) 33.8016 2.89846
\(137\) 11.4305 0.976576 0.488288 0.872683i \(-0.337622\pi\)
0.488288 + 0.872683i \(0.337622\pi\)
\(138\) 10.2095 0.869087
\(139\) −16.1763 −1.37206 −0.686028 0.727575i \(-0.740647\pi\)
−0.686028 + 0.727575i \(0.740647\pi\)
\(140\) 13.5021 1.14114
\(141\) −6.70940 −0.565034
\(142\) −24.7192 −2.07439
\(143\) 2.36121 0.197455
\(144\) −8.66554 −0.722129
\(145\) 4.84015 0.401953
\(146\) −12.7384 −1.05424
\(147\) 1.68005 0.138568
\(148\) −41.3506 −3.39900
\(149\) 7.67056 0.628396 0.314198 0.949357i \(-0.398264\pi\)
0.314198 + 0.949357i \(0.398264\pi\)
\(150\) −4.72770 −0.386015
\(151\) 12.8964 1.04950 0.524748 0.851258i \(-0.324160\pi\)
0.524748 + 0.851258i \(0.324160\pi\)
\(152\) 23.5475 1.90996
\(153\) 17.3774 1.40488
\(154\) −5.33563 −0.429957
\(155\) 1.53572 0.123352
\(156\) −7.08892 −0.567568
\(157\) −20.5437 −1.63956 −0.819782 0.572676i \(-0.805905\pi\)
−0.819782 + 0.572676i \(0.805905\pi\)
\(158\) 4.92731 0.391996
\(159\) 0.544003 0.0431422
\(160\) 1.04757 0.0828179
\(161\) 12.0251 0.947709
\(162\) −9.95690 −0.782288
\(163\) −16.4075 −1.28514 −0.642569 0.766228i \(-0.722131\pi\)
−0.642569 + 0.766228i \(0.722131\pi\)
\(164\) −24.8545 −1.94081
\(165\) −1.19776 −0.0932454
\(166\) 25.0231 1.94217
\(167\) −16.4271 −1.27117 −0.635584 0.772032i \(-0.719240\pi\)
−0.635584 + 0.772032i \(0.719240\pi\)
\(168\) 7.86715 0.606964
\(169\) −7.42468 −0.571129
\(170\) 27.4584 2.10596
\(171\) 12.1057 0.925749
\(172\) 49.7254 3.79152
\(173\) 15.9620 1.21357 0.606783 0.794867i \(-0.292460\pi\)
0.606783 + 0.794867i \(0.292460\pi\)
\(174\) 5.74231 0.435323
\(175\) −5.56846 −0.420936
\(176\) 3.58603 0.270307
\(177\) −4.54420 −0.341563
\(178\) 24.2868 1.82037
\(179\) 6.85535 0.512393 0.256197 0.966625i \(-0.417531\pi\)
0.256197 + 0.966625i \(0.417531\pi\)
\(180\) −14.8913 −1.10993
\(181\) −8.42470 −0.626203 −0.313101 0.949720i \(-0.601368\pi\)
−0.313101 + 0.949720i \(0.601368\pi\)
\(182\) −12.5985 −0.933866
\(183\) 6.84054 0.505667
\(184\) −25.7972 −1.90179
\(185\) −16.4970 −1.21289
\(186\) 1.82197 0.133593
\(187\) −7.19121 −0.525873
\(188\) 34.5197 2.51761
\(189\) 9.06564 0.659429
\(190\) 19.1286 1.38773
\(191\) 25.0042 1.80924 0.904621 0.426217i \(-0.140154\pi\)
0.904621 + 0.426217i \(0.140154\pi\)
\(192\) 6.72150 0.485083
\(193\) −4.22340 −0.304007 −0.152003 0.988380i \(-0.548572\pi\)
−0.152003 + 0.988380i \(0.548572\pi\)
\(194\) 23.1213 1.66001
\(195\) −2.82816 −0.202529
\(196\) −8.64379 −0.617414
\(197\) −10.9462 −0.779881 −0.389941 0.920840i \(-0.627504\pi\)
−0.389941 + 0.920840i \(0.627504\pi\)
\(198\) 5.88459 0.418199
\(199\) 11.5026 0.815397 0.407698 0.913117i \(-0.366332\pi\)
0.407698 + 0.913117i \(0.366332\pi\)
\(200\) 11.9459 0.844704
\(201\) −11.7072 −0.825764
\(202\) 12.7345 0.895995
\(203\) 6.76350 0.474705
\(204\) 21.5897 1.51158
\(205\) −9.91585 −0.692553
\(206\) 35.2544 2.45629
\(207\) −13.2623 −0.921793
\(208\) 8.46738 0.587107
\(209\) −5.00968 −0.346527
\(210\) 6.39079 0.441007
\(211\) −10.5438 −0.725868 −0.362934 0.931815i \(-0.618225\pi\)
−0.362934 + 0.931815i \(0.618225\pi\)
\(212\) −2.79888 −0.192228
\(213\) −7.75411 −0.531303
\(214\) 13.5001 0.922851
\(215\) 19.8382 1.35295
\(216\) −19.4484 −1.32329
\(217\) 2.14598 0.145679
\(218\) −9.30743 −0.630379
\(219\) −3.99589 −0.270017
\(220\) 6.16243 0.415471
\(221\) −16.9800 −1.14220
\(222\) −19.5719 −1.31358
\(223\) −2.22968 −0.149310 −0.0746552 0.997209i \(-0.523786\pi\)
−0.0746552 + 0.997209i \(0.523786\pi\)
\(224\) 1.46385 0.0978077
\(225\) 6.14138 0.409425
\(226\) 11.2734 0.749895
\(227\) −20.4542 −1.35759 −0.678797 0.734326i \(-0.737498\pi\)
−0.678797 + 0.734326i \(0.737498\pi\)
\(228\) 15.0403 0.996065
\(229\) 0.879388 0.0581116 0.0290558 0.999578i \(-0.490750\pi\)
0.0290558 + 0.999578i \(0.490750\pi\)
\(230\) −20.9561 −1.38180
\(231\) −1.67372 −0.110123
\(232\) −14.5096 −0.952603
\(233\) −15.6972 −1.02836 −0.514179 0.857683i \(-0.671903\pi\)
−0.514179 + 0.857683i \(0.671903\pi\)
\(234\) 13.8948 0.908329
\(235\) 13.7718 0.898373
\(236\) 23.3798 1.52189
\(237\) 1.54564 0.100400
\(238\) 38.3696 2.48713
\(239\) −25.8453 −1.67179 −0.835897 0.548887i \(-0.815052\pi\)
−0.835897 + 0.548887i \(0.815052\pi\)
\(240\) −4.29520 −0.277254
\(241\) −7.20437 −0.464074 −0.232037 0.972707i \(-0.574539\pi\)
−0.232037 + 0.972707i \(0.574539\pi\)
\(242\) −2.43520 −0.156541
\(243\) −15.5361 −0.996643
\(244\) −35.1943 −2.25309
\(245\) −3.44849 −0.220316
\(246\) −11.7641 −0.750050
\(247\) −11.8289 −0.752656
\(248\) −4.60373 −0.292337
\(249\) 7.84943 0.497437
\(250\) 28.7957 1.82120
\(251\) 17.5250 1.10617 0.553083 0.833126i \(-0.313451\pi\)
0.553083 + 0.833126i \(0.313451\pi\)
\(252\) −20.8088 −1.31083
\(253\) 5.48829 0.345046
\(254\) 34.2188 2.14708
\(255\) 8.61334 0.539388
\(256\) −31.3280 −1.95800
\(257\) 10.3216 0.643842 0.321921 0.946766i \(-0.395671\pi\)
0.321921 + 0.946766i \(0.395671\pi\)
\(258\) 23.5359 1.46528
\(259\) −23.0525 −1.43242
\(260\) 14.5508 0.902403
\(261\) −7.45937 −0.461724
\(262\) −31.2936 −1.93332
\(263\) 24.7141 1.52394 0.761970 0.647612i \(-0.224232\pi\)
0.761970 + 0.647612i \(0.224232\pi\)
\(264\) 3.59060 0.220986
\(265\) −1.11663 −0.0685938
\(266\) 26.7298 1.63891
\(267\) 7.61846 0.466242
\(268\) 60.2333 3.67933
\(269\) −15.2288 −0.928518 −0.464259 0.885700i \(-0.653679\pi\)
−0.464259 + 0.885700i \(0.653679\pi\)
\(270\) −15.7987 −0.961476
\(271\) 9.43014 0.572840 0.286420 0.958104i \(-0.407535\pi\)
0.286420 + 0.958104i \(0.407535\pi\)
\(272\) −25.7879 −1.56362
\(273\) −3.95200 −0.239186
\(274\) −27.8356 −1.68161
\(275\) −2.54147 −0.153256
\(276\) −16.4772 −0.991808
\(277\) −7.19599 −0.432365 −0.216183 0.976353i \(-0.569361\pi\)
−0.216183 + 0.976353i \(0.569361\pi\)
\(278\) 39.3925 2.36260
\(279\) −2.36677 −0.141695
\(280\) −16.1482 −0.965040
\(281\) 20.3404 1.21341 0.606703 0.794929i \(-0.292492\pi\)
0.606703 + 0.794929i \(0.292492\pi\)
\(282\) 16.3387 0.972957
\(283\) 7.22134 0.429264 0.214632 0.976695i \(-0.431145\pi\)
0.214632 + 0.976695i \(0.431145\pi\)
\(284\) 39.8947 2.36731
\(285\) 6.00039 0.355432
\(286\) −5.75002 −0.340006
\(287\) −13.8562 −0.817903
\(288\) −1.61446 −0.0951330
\(289\) 34.7135 2.04197
\(290\) −11.7867 −0.692141
\(291\) 7.25286 0.425170
\(292\) 20.5587 1.20311
\(293\) −17.8132 −1.04066 −0.520330 0.853965i \(-0.674191\pi\)
−0.520330 + 0.853965i \(0.674191\pi\)
\(294\) −4.09125 −0.238607
\(295\) 9.32748 0.543067
\(296\) 49.4542 2.87447
\(297\) 4.13759 0.240087
\(298\) −18.6793 −1.08206
\(299\) 12.9590 0.749439
\(300\) 7.63009 0.440523
\(301\) 27.7214 1.59783
\(302\) −31.4053 −1.80717
\(303\) 3.99464 0.229486
\(304\) −17.9649 −1.03036
\(305\) −14.0410 −0.803983
\(306\) −42.3173 −2.41912
\(307\) −10.3194 −0.588960 −0.294480 0.955658i \(-0.595146\pi\)
−0.294480 + 0.955658i \(0.595146\pi\)
\(308\) 8.61122 0.490670
\(309\) 11.0588 0.629116
\(310\) −3.73979 −0.212406
\(311\) −21.5717 −1.22322 −0.611609 0.791160i \(-0.709477\pi\)
−0.611609 + 0.791160i \(0.709477\pi\)
\(312\) 8.47816 0.479981
\(313\) 1.96689 0.111175 0.0555877 0.998454i \(-0.482297\pi\)
0.0555877 + 0.998454i \(0.482297\pi\)
\(314\) 50.0279 2.82324
\(315\) −8.30177 −0.467752
\(316\) −7.95224 −0.447349
\(317\) 27.5855 1.54936 0.774679 0.632355i \(-0.217911\pi\)
0.774679 + 0.632355i \(0.217911\pi\)
\(318\) −1.32475 −0.0742885
\(319\) 3.08689 0.172833
\(320\) −13.7966 −0.771255
\(321\) 4.23482 0.236365
\(322\) −29.2835 −1.63190
\(323\) 36.0257 2.00452
\(324\) 16.0695 0.892753
\(325\) −6.00094 −0.332872
\(326\) 39.9556 2.21294
\(327\) −2.91962 −0.161456
\(328\) 29.7253 1.64131
\(329\) 19.2444 1.06098
\(330\) 2.91678 0.160564
\(331\) −0.589243 −0.0323877 −0.0161939 0.999869i \(-0.505155\pi\)
−0.0161939 + 0.999869i \(0.505155\pi\)
\(332\) −40.3850 −2.21642
\(333\) 25.4243 1.39324
\(334\) 40.0033 2.18888
\(335\) 24.0304 1.31292
\(336\) −6.00201 −0.327436
\(337\) −26.7165 −1.45534 −0.727669 0.685928i \(-0.759396\pi\)
−0.727669 + 0.685928i \(0.759396\pi\)
\(338\) 18.0806 0.983453
\(339\) 3.53632 0.192066
\(340\) −44.3153 −2.40334
\(341\) 0.979432 0.0530392
\(342\) −29.4799 −1.59409
\(343\) −20.1561 −1.08833
\(344\) −59.4702 −3.20642
\(345\) −6.57365 −0.353913
\(346\) −38.8706 −2.08970
\(347\) −15.0308 −0.806893 −0.403447 0.915003i \(-0.632188\pi\)
−0.403447 + 0.915003i \(0.632188\pi\)
\(348\) −9.26757 −0.496794
\(349\) −21.4996 −1.15085 −0.575423 0.817856i \(-0.695162\pi\)
−0.575423 + 0.817856i \(0.695162\pi\)
\(350\) 13.5603 0.724829
\(351\) 9.76974 0.521470
\(352\) 0.668107 0.0356102
\(353\) −4.39168 −0.233746 −0.116873 0.993147i \(-0.537287\pi\)
−0.116873 + 0.993147i \(0.537287\pi\)
\(354\) 11.0660 0.588153
\(355\) 15.9162 0.844743
\(356\) −39.1967 −2.07742
\(357\) 12.0361 0.637016
\(358\) −16.6941 −0.882313
\(359\) −26.7658 −1.41265 −0.706323 0.707889i \(-0.749648\pi\)
−0.706323 + 0.707889i \(0.749648\pi\)
\(360\) 17.8096 0.938650
\(361\) 6.09689 0.320889
\(362\) 20.5158 1.07829
\(363\) −0.763891 −0.0400939
\(364\) 20.3329 1.06574
\(365\) 8.20201 0.429313
\(366\) −16.6581 −0.870731
\(367\) 4.48215 0.233966 0.116983 0.993134i \(-0.462678\pi\)
0.116983 + 0.993134i \(0.462678\pi\)
\(368\) 19.6812 1.02595
\(369\) 15.2818 0.795536
\(370\) 40.1736 2.08852
\(371\) −1.56034 −0.0810091
\(372\) −2.94049 −0.152457
\(373\) 21.9987 1.13905 0.569524 0.821975i \(-0.307128\pi\)
0.569524 + 0.821975i \(0.307128\pi\)
\(374\) 17.5120 0.905525
\(375\) 9.03286 0.466455
\(376\) −41.2846 −2.12909
\(377\) 7.28880 0.375392
\(378\) −22.0766 −1.13550
\(379\) −3.88775 −0.199700 −0.0998502 0.995002i \(-0.531836\pi\)
−0.0998502 + 0.995002i \(0.531836\pi\)
\(380\) −30.8718 −1.58369
\(381\) 10.7340 0.549920
\(382\) −60.8903 −3.11542
\(383\) 6.79431 0.347173 0.173587 0.984819i \(-0.444464\pi\)
0.173587 + 0.984819i \(0.444464\pi\)
\(384\) −15.3475 −0.783198
\(385\) 3.43549 0.175089
\(386\) 10.2848 0.523483
\(387\) −30.5735 −1.55414
\(388\) −37.3157 −1.89442
\(389\) 24.9260 1.26380 0.631899 0.775051i \(-0.282276\pi\)
0.631899 + 0.775051i \(0.282276\pi\)
\(390\) 6.88714 0.348744
\(391\) −39.4674 −1.99595
\(392\) 10.3377 0.522135
\(393\) −9.81640 −0.495172
\(394\) 26.6561 1.34291
\(395\) −3.17259 −0.159630
\(396\) −9.49720 −0.477252
\(397\) 7.15999 0.359349 0.179675 0.983726i \(-0.442495\pi\)
0.179675 + 0.983726i \(0.442495\pi\)
\(398\) −28.0111 −1.40407
\(399\) 8.38479 0.419765
\(400\) −9.11378 −0.455689
\(401\) 3.12648 0.156129 0.0780645 0.996948i \(-0.475126\pi\)
0.0780645 + 0.996948i \(0.475126\pi\)
\(402\) 28.5094 1.42192
\(403\) 2.31265 0.115201
\(404\) −20.5523 −1.02252
\(405\) 6.41103 0.318567
\(406\) −16.4705 −0.817416
\(407\) −10.5213 −0.521520
\(408\) −25.8207 −1.27832
\(409\) 27.6544 1.36742 0.683711 0.729753i \(-0.260365\pi\)
0.683711 + 0.729753i \(0.260365\pi\)
\(410\) 24.1471 1.19254
\(411\) −8.73167 −0.430702
\(412\) −56.8974 −2.80313
\(413\) 13.0340 0.641360
\(414\) 32.2963 1.58728
\(415\) −16.1118 −0.790898
\(416\) 1.57754 0.0773454
\(417\) 12.3569 0.605121
\(418\) 12.1996 0.596700
\(419\) 7.58206 0.370408 0.185204 0.982700i \(-0.440705\pi\)
0.185204 + 0.982700i \(0.440705\pi\)
\(420\) −10.3142 −0.503280
\(421\) 0.627076 0.0305618 0.0152809 0.999883i \(-0.495136\pi\)
0.0152809 + 0.999883i \(0.495136\pi\)
\(422\) 25.6763 1.24990
\(423\) −21.2243 −1.03196
\(424\) 3.34738 0.162563
\(425\) 18.2762 0.886527
\(426\) 18.8828 0.914875
\(427\) −19.6205 −0.949502
\(428\) −21.7880 −1.05316
\(429\) −1.80371 −0.0870839
\(430\) −48.3100 −2.32971
\(431\) 38.8000 1.86893 0.934465 0.356054i \(-0.115878\pi\)
0.934465 + 0.356054i \(0.115878\pi\)
\(432\) 14.8375 0.713872
\(433\) −13.6308 −0.655056 −0.327528 0.944842i \(-0.606216\pi\)
−0.327528 + 0.944842i \(0.606216\pi\)
\(434\) −5.22588 −0.250850
\(435\) −3.69735 −0.177274
\(436\) 15.0214 0.719393
\(437\) −27.4946 −1.31524
\(438\) 9.73078 0.464955
\(439\) −17.9114 −0.854867 −0.427433 0.904047i \(-0.640582\pi\)
−0.427433 + 0.904047i \(0.640582\pi\)
\(440\) −7.37010 −0.351356
\(441\) 5.31462 0.253077
\(442\) 41.3496 1.96680
\(443\) −7.11797 −0.338185 −0.169093 0.985600i \(-0.554084\pi\)
−0.169093 + 0.985600i \(0.554084\pi\)
\(444\) 31.5873 1.49907
\(445\) −15.6377 −0.741300
\(446\) 5.42971 0.257104
\(447\) −5.85947 −0.277143
\(448\) −19.2791 −0.910851
\(449\) 24.1884 1.14152 0.570761 0.821116i \(-0.306648\pi\)
0.570761 + 0.821116i \(0.306648\pi\)
\(450\) −14.9555 −0.705008
\(451\) −6.32400 −0.297785
\(452\) −18.1942 −0.855785
\(453\) −9.85145 −0.462862
\(454\) 49.8100 2.33770
\(455\) 8.11193 0.380293
\(456\) −17.9877 −0.842353
\(457\) −7.74850 −0.362459 −0.181230 0.983441i \(-0.558008\pi\)
−0.181230 + 0.983441i \(0.558008\pi\)
\(458\) −2.14148 −0.100065
\(459\) −29.7543 −1.38881
\(460\) 33.8212 1.57692
\(461\) −11.6350 −0.541898 −0.270949 0.962594i \(-0.587337\pi\)
−0.270949 + 0.962594i \(0.587337\pi\)
\(462\) 4.07584 0.189625
\(463\) 27.3291 1.27009 0.635046 0.772474i \(-0.280981\pi\)
0.635046 + 0.772474i \(0.280981\pi\)
\(464\) 11.0697 0.513897
\(465\) −1.17312 −0.0544023
\(466\) 38.2258 1.77077
\(467\) −9.16785 −0.424238 −0.212119 0.977244i \(-0.568036\pi\)
−0.212119 + 0.977244i \(0.568036\pi\)
\(468\) −22.4249 −1.03659
\(469\) 33.5795 1.55056
\(470\) −33.5371 −1.54695
\(471\) 15.6931 0.723101
\(472\) −27.9616 −1.28704
\(473\) 12.6521 0.581746
\(474\) −3.76393 −0.172883
\(475\) 12.7319 0.584181
\(476\) −61.9251 −2.83833
\(477\) 1.72088 0.0787938
\(478\) 62.9384 2.87874
\(479\) −32.8967 −1.50309 −0.751545 0.659681i \(-0.770691\pi\)
−0.751545 + 0.659681i \(0.770691\pi\)
\(480\) −0.800231 −0.0365254
\(481\) −24.8429 −1.13274
\(482\) 17.5441 0.799111
\(483\) −9.18585 −0.417971
\(484\) 3.93019 0.178645
\(485\) −14.8873 −0.675998
\(486\) 37.8336 1.71617
\(487\) 9.10966 0.412798 0.206399 0.978468i \(-0.433825\pi\)
0.206399 + 0.978468i \(0.433825\pi\)
\(488\) 42.0915 1.90539
\(489\) 12.5336 0.566788
\(490\) 8.39775 0.379372
\(491\) −26.9215 −1.21495 −0.607475 0.794339i \(-0.707817\pi\)
−0.607475 + 0.794339i \(0.707817\pi\)
\(492\) 18.9862 0.855962
\(493\) −22.1985 −0.999768
\(494\) 28.8058 1.29603
\(495\) −3.78896 −0.170301
\(496\) 3.51228 0.157706
\(497\) 22.2409 0.997639
\(498\) −19.1149 −0.856560
\(499\) −2.27222 −0.101718 −0.0508592 0.998706i \(-0.516196\pi\)
−0.0508592 + 0.998706i \(0.516196\pi\)
\(500\) −46.4738 −2.07837
\(501\) 12.5485 0.560626
\(502\) −42.6768 −1.90476
\(503\) −2.44008 −0.108798 −0.0543990 0.998519i \(-0.517324\pi\)
−0.0543990 + 0.998519i \(0.517324\pi\)
\(504\) 24.8867 1.10854
\(505\) −8.19945 −0.364871
\(506\) −13.3651 −0.594150
\(507\) 5.67164 0.251886
\(508\) −55.2261 −2.45026
\(509\) −39.0193 −1.72950 −0.864751 0.502201i \(-0.832524\pi\)
−0.864751 + 0.502201i \(0.832524\pi\)
\(510\) −20.9752 −0.928797
\(511\) 11.4613 0.507017
\(512\) 36.1075 1.59574
\(513\) −20.7280 −0.915164
\(514\) −25.1351 −1.10866
\(515\) −22.6995 −1.00026
\(516\) −37.9848 −1.67219
\(517\) 8.78320 0.386285
\(518\) 56.1375 2.46654
\(519\) −12.1932 −0.535223
\(520\) −17.4024 −0.763144
\(521\) −15.1687 −0.664552 −0.332276 0.943182i \(-0.607817\pi\)
−0.332276 + 0.943182i \(0.607817\pi\)
\(522\) 18.1651 0.795063
\(523\) −18.0898 −0.791011 −0.395506 0.918464i \(-0.629431\pi\)
−0.395506 + 0.918464i \(0.629431\pi\)
\(524\) 50.5050 2.20632
\(525\) 4.25370 0.185647
\(526\) −60.1839 −2.62414
\(527\) −7.04331 −0.306811
\(528\) −2.73934 −0.119214
\(529\) 7.12132 0.309622
\(530\) 2.71921 0.118115
\(531\) −14.3750 −0.623822
\(532\) −43.1395 −1.87033
\(533\) −14.9323 −0.646790
\(534\) −18.5525 −0.802844
\(535\) −8.69245 −0.375807
\(536\) −72.0374 −3.11154
\(537\) −5.23674 −0.225982
\(538\) 37.0852 1.59886
\(539\) −2.19933 −0.0947318
\(540\) 25.4976 1.09724
\(541\) −14.2429 −0.612350 −0.306175 0.951975i \(-0.599049\pi\)
−0.306175 + 0.951975i \(0.599049\pi\)
\(542\) −22.9643 −0.986400
\(543\) 6.43555 0.276176
\(544\) −4.80450 −0.205991
\(545\) 5.99285 0.256706
\(546\) 9.62392 0.411866
\(547\) 1.00000 0.0427569
\(548\) 44.9242 1.91907
\(549\) 21.6392 0.923537
\(550\) 6.18898 0.263899
\(551\) −15.4643 −0.658802
\(552\) 19.7062 0.838753
\(553\) −4.43330 −0.188523
\(554\) 17.5237 0.744510
\(555\) 12.6019 0.534922
\(556\) −63.5760 −2.69622
\(557\) 32.2993 1.36857 0.684283 0.729217i \(-0.260115\pi\)
0.684283 + 0.729217i \(0.260115\pi\)
\(558\) 5.76355 0.243991
\(559\) 29.8744 1.26355
\(560\) 12.3198 0.520606
\(561\) 5.49330 0.231927
\(562\) −49.5329 −2.08942
\(563\) −34.4539 −1.45206 −0.726030 0.687663i \(-0.758637\pi\)
−0.726030 + 0.687663i \(0.758637\pi\)
\(564\) −26.3693 −1.11035
\(565\) −7.25869 −0.305375
\(566\) −17.5854 −0.739169
\(567\) 8.95861 0.376226
\(568\) −47.7129 −2.00199
\(569\) −6.32001 −0.264948 −0.132474 0.991186i \(-0.542292\pi\)
−0.132474 + 0.991186i \(0.542292\pi\)
\(570\) −14.6121 −0.612035
\(571\) 7.02090 0.293816 0.146908 0.989150i \(-0.453068\pi\)
0.146908 + 0.989150i \(0.453068\pi\)
\(572\) 9.28002 0.388017
\(573\) −19.1005 −0.797935
\(574\) 33.7425 1.40838
\(575\) −13.9483 −0.581684
\(576\) 21.2626 0.885942
\(577\) −13.5808 −0.565376 −0.282688 0.959212i \(-0.591226\pi\)
−0.282688 + 0.959212i \(0.591226\pi\)
\(578\) −84.5343 −3.51616
\(579\) 3.22622 0.134077
\(580\) 19.0227 0.789876
\(581\) −22.5142 −0.934048
\(582\) −17.6622 −0.732120
\(583\) −0.712147 −0.0294941
\(584\) −24.5877 −1.01744
\(585\) −8.94653 −0.369894
\(586\) 43.3788 1.79196
\(587\) −33.2500 −1.37237 −0.686186 0.727426i \(-0.740717\pi\)
−0.686186 + 0.727426i \(0.740717\pi\)
\(588\) 6.60291 0.272300
\(589\) −4.90664 −0.202175
\(590\) −22.7143 −0.935131
\(591\) 8.36167 0.343953
\(592\) −37.7296 −1.55068
\(593\) −48.5792 −1.99491 −0.997454 0.0713146i \(-0.977281\pi\)
−0.997454 + 0.0713146i \(0.977281\pi\)
\(594\) −10.0759 −0.413418
\(595\) −24.7054 −1.01282
\(596\) 30.1468 1.23486
\(597\) −8.78672 −0.359616
\(598\) −31.5578 −1.29049
\(599\) 35.9532 1.46901 0.734504 0.678604i \(-0.237415\pi\)
0.734504 + 0.678604i \(0.237415\pi\)
\(600\) −9.12538 −0.372542
\(601\) 1.55862 0.0635775 0.0317888 0.999495i \(-0.489880\pi\)
0.0317888 + 0.999495i \(0.489880\pi\)
\(602\) −67.5071 −2.75138
\(603\) −37.0343 −1.50815
\(604\) 50.6854 2.06236
\(605\) 1.56797 0.0637471
\(606\) −9.72775 −0.395163
\(607\) −32.4058 −1.31531 −0.657655 0.753319i \(-0.728452\pi\)
−0.657655 + 0.753319i \(0.728452\pi\)
\(608\) −3.34700 −0.135739
\(609\) −5.16658 −0.209360
\(610\) 34.1925 1.38442
\(611\) 20.7390 0.839010
\(612\) 68.2963 2.76072
\(613\) −38.1965 −1.54274 −0.771370 0.636387i \(-0.780428\pi\)
−0.771370 + 0.636387i \(0.780428\pi\)
\(614\) 25.1298 1.01416
\(615\) 7.57462 0.305438
\(616\) −10.2988 −0.414950
\(617\) −25.4434 −1.02431 −0.512156 0.858892i \(-0.671153\pi\)
−0.512156 + 0.858892i \(0.671153\pi\)
\(618\) −26.9305 −1.08330
\(619\) −15.9094 −0.639451 −0.319726 0.947510i \(-0.603591\pi\)
−0.319726 + 0.947510i \(0.603591\pi\)
\(620\) 6.03568 0.242399
\(621\) 22.7083 0.911253
\(622\) 52.5313 2.10631
\(623\) −21.8518 −0.875474
\(624\) −6.46816 −0.258934
\(625\) −5.83361 −0.233345
\(626\) −4.78978 −0.191438
\(627\) 3.82685 0.152830
\(628\) −80.7406 −3.22190
\(629\) 75.6606 3.01679
\(630\) 20.2165 0.805443
\(631\) −16.5748 −0.659832 −0.329916 0.944010i \(-0.607020\pi\)
−0.329916 + 0.944010i \(0.607020\pi\)
\(632\) 9.51067 0.378314
\(633\) 8.05434 0.320131
\(634\) −67.1763 −2.66791
\(635\) −22.0327 −0.874342
\(636\) 2.13804 0.0847786
\(637\) −5.19308 −0.205758
\(638\) −7.51719 −0.297608
\(639\) −24.5291 −0.970358
\(640\) 31.5024 1.24524
\(641\) 4.80188 0.189663 0.0948314 0.995493i \(-0.469769\pi\)
0.0948314 + 0.995493i \(0.469769\pi\)
\(642\) −10.3126 −0.407007
\(643\) −3.25443 −0.128342 −0.0641711 0.997939i \(-0.520440\pi\)
−0.0641711 + 0.997939i \(0.520440\pi\)
\(644\) 47.2609 1.86234
\(645\) −15.1542 −0.596697
\(646\) −87.7297 −3.45168
\(647\) −18.8073 −0.739390 −0.369695 0.929153i \(-0.620538\pi\)
−0.369695 + 0.929153i \(0.620538\pi\)
\(648\) −19.2187 −0.754984
\(649\) 5.94876 0.233509
\(650\) 14.6135 0.573188
\(651\) −1.63929 −0.0642490
\(652\) −64.4848 −2.52542
\(653\) 23.5446 0.921373 0.460686 0.887563i \(-0.347603\pi\)
0.460686 + 0.887563i \(0.347603\pi\)
\(654\) 7.10986 0.278018
\(655\) 20.1492 0.787296
\(656\) −22.6781 −0.885430
\(657\) −12.6405 −0.493152
\(658\) −46.8639 −1.82694
\(659\) −34.9931 −1.36314 −0.681569 0.731753i \(-0.738702\pi\)
−0.681569 + 0.731753i \(0.738702\pi\)
\(660\) −4.70742 −0.183236
\(661\) 10.3438 0.402327 0.201163 0.979558i \(-0.435528\pi\)
0.201163 + 0.979558i \(0.435528\pi\)
\(662\) 1.43492 0.0557699
\(663\) 12.9709 0.503746
\(664\) 48.2994 1.87438
\(665\) −17.2107 −0.667403
\(666\) −61.9133 −2.39909
\(667\) 16.9417 0.655986
\(668\) −64.5617 −2.49797
\(669\) 1.70323 0.0658507
\(670\) −58.5188 −2.26078
\(671\) −8.95486 −0.345699
\(672\) −1.11822 −0.0431364
\(673\) 22.2648 0.858245 0.429123 0.903246i \(-0.358823\pi\)
0.429123 + 0.903246i \(0.358823\pi\)
\(674\) 65.0599 2.50601
\(675\) −10.5156 −0.404744
\(676\) −29.1804 −1.12232
\(677\) −51.4181 −1.97616 −0.988078 0.153953i \(-0.950800\pi\)
−0.988078 + 0.153953i \(0.950800\pi\)
\(678\) −8.61164 −0.330728
\(679\) −20.8032 −0.798352
\(680\) 52.9999 2.03245
\(681\) 15.6248 0.598743
\(682\) −2.38511 −0.0913307
\(683\) −4.18932 −0.160300 −0.0801500 0.996783i \(-0.525540\pi\)
−0.0801500 + 0.996783i \(0.525540\pi\)
\(684\) 47.5779 1.81919
\(685\) 17.9227 0.684792
\(686\) 49.0842 1.87404
\(687\) −0.671757 −0.0256291
\(688\) 45.3710 1.72975
\(689\) −1.68153 −0.0640612
\(690\) 16.0081 0.609419
\(691\) 32.3996 1.23254 0.616270 0.787535i \(-0.288643\pi\)
0.616270 + 0.787535i \(0.288643\pi\)
\(692\) 62.7337 2.38478
\(693\) −5.29459 −0.201125
\(694\) 36.6029 1.38943
\(695\) −25.3640 −0.962110
\(696\) 11.0838 0.420129
\(697\) 45.4772 1.72257
\(698\) 52.3557 1.98169
\(699\) 11.9909 0.453539
\(700\) −21.8851 −0.827180
\(701\) −11.5464 −0.436102 −0.218051 0.975937i \(-0.569970\pi\)
−0.218051 + 0.975937i \(0.569970\pi\)
\(702\) −23.7912 −0.897943
\(703\) 52.7081 1.98793
\(704\) −8.79904 −0.331626
\(705\) −10.5202 −0.396212
\(706\) 10.6946 0.402497
\(707\) −11.4577 −0.430911
\(708\) −17.8596 −0.671204
\(709\) −22.4188 −0.841957 −0.420978 0.907071i \(-0.638313\pi\)
−0.420978 + 0.907071i \(0.638313\pi\)
\(710\) −38.7591 −1.45460
\(711\) 4.88942 0.183368
\(712\) 46.8782 1.75684
\(713\) 5.37541 0.201311
\(714\) −29.3102 −1.09691
\(715\) 3.70231 0.138459
\(716\) 26.9429 1.00690
\(717\) 19.7430 0.737316
\(718\) 65.1801 2.43250
\(719\) 11.1796 0.416928 0.208464 0.978030i \(-0.433154\pi\)
0.208464 + 0.978030i \(0.433154\pi\)
\(720\) −13.5873 −0.506370
\(721\) −31.7197 −1.18130
\(722\) −14.8471 −0.552553
\(723\) 5.50335 0.204672
\(724\) −33.1107 −1.23055
\(725\) −7.84522 −0.291364
\(726\) 1.86023 0.0690395
\(727\) −28.4724 −1.05598 −0.527992 0.849249i \(-0.677055\pi\)
−0.527992 + 0.849249i \(0.677055\pi\)
\(728\) −24.3176 −0.901271
\(729\) −0.398319 −0.0147526
\(730\) −19.9735 −0.739253
\(731\) −90.9843 −3.36517
\(732\) 26.8846 0.993685
\(733\) −14.9133 −0.550837 −0.275418 0.961324i \(-0.588816\pi\)
−0.275418 + 0.961324i \(0.588816\pi\)
\(734\) −10.9149 −0.402877
\(735\) 2.63427 0.0971664
\(736\) 3.66676 0.135159
\(737\) 15.3258 0.564533
\(738\) −37.2141 −1.36987
\(739\) −16.3153 −0.600167 −0.300084 0.953913i \(-0.597015\pi\)
−0.300084 + 0.953913i \(0.597015\pi\)
\(740\) −64.8365 −2.38344
\(741\) 9.03600 0.331946
\(742\) 3.79975 0.139493
\(743\) 21.0138 0.770921 0.385460 0.922724i \(-0.374043\pi\)
0.385460 + 0.922724i \(0.374043\pi\)
\(744\) 3.51675 0.128930
\(745\) 12.0272 0.440643
\(746\) −53.5711 −1.96138
\(747\) 24.8306 0.908506
\(748\) −28.2628 −1.03339
\(749\) −12.1466 −0.443827
\(750\) −21.9968 −0.803210
\(751\) 33.4990 1.22239 0.611197 0.791478i \(-0.290688\pi\)
0.611197 + 0.791478i \(0.290688\pi\)
\(752\) 31.4968 1.14857
\(753\) −13.3872 −0.487856
\(754\) −17.7497 −0.646405
\(755\) 20.2212 0.735925
\(756\) 35.6297 1.29584
\(757\) −27.7614 −1.00900 −0.504502 0.863410i \(-0.668324\pi\)
−0.504502 + 0.863410i \(0.668324\pi\)
\(758\) 9.46745 0.343873
\(759\) −4.19245 −0.152176
\(760\) 36.9218 1.33930
\(761\) 5.16706 0.187306 0.0936529 0.995605i \(-0.470146\pi\)
0.0936529 + 0.995605i \(0.470146\pi\)
\(762\) −26.1394 −0.946932
\(763\) 8.37426 0.303169
\(764\) 98.2714 3.55534
\(765\) 27.2472 0.985124
\(766\) −16.5455 −0.597813
\(767\) 14.0463 0.507182
\(768\) 23.9312 0.863541
\(769\) −23.3969 −0.843713 −0.421856 0.906663i \(-0.638621\pi\)
−0.421856 + 0.906663i \(0.638621\pi\)
\(770\) −8.36611 −0.301494
\(771\) −7.88456 −0.283956
\(772\) −16.5988 −0.597403
\(773\) 38.8786 1.39837 0.699184 0.714942i \(-0.253547\pi\)
0.699184 + 0.714942i \(0.253547\pi\)
\(774\) 74.4526 2.67615
\(775\) −2.48919 −0.0894145
\(776\) 44.6286 1.60207
\(777\) 17.6096 0.631742
\(778\) −60.6997 −2.17619
\(779\) 31.6812 1.13510
\(780\) −11.1152 −0.397989
\(781\) 10.1508 0.363225
\(782\) 96.1111 3.43693
\(783\) 12.7723 0.456444
\(784\) −7.88687 −0.281674
\(785\) −32.2119 −1.14969
\(786\) 23.9049 0.852659
\(787\) 27.5709 0.982795 0.491397 0.870936i \(-0.336486\pi\)
0.491397 + 0.870936i \(0.336486\pi\)
\(788\) −43.0205 −1.53254
\(789\) −18.8789 −0.672107
\(790\) 7.72589 0.274875
\(791\) −10.1431 −0.360647
\(792\) 11.3584 0.403603
\(793\) −21.1443 −0.750857
\(794\) −17.4360 −0.618780
\(795\) 0.852980 0.0302521
\(796\) 45.2074 1.60233
\(797\) −5.25809 −0.186251 −0.0931255 0.995654i \(-0.529686\pi\)
−0.0931255 + 0.995654i \(0.529686\pi\)
\(798\) −20.4186 −0.722812
\(799\) −63.1618 −2.23450
\(800\) −1.69797 −0.0600323
\(801\) 24.1000 0.851533
\(802\) −7.61360 −0.268846
\(803\) 5.23097 0.184597
\(804\) −46.0117 −1.62271
\(805\) 18.8550 0.664551
\(806\) −5.63176 −0.198370
\(807\) 11.6332 0.409507
\(808\) 24.5800 0.864722
\(809\) 8.87182 0.311917 0.155958 0.987764i \(-0.450153\pi\)
0.155958 + 0.987764i \(0.450153\pi\)
\(810\) −15.6121 −0.548554
\(811\) −38.8083 −1.36274 −0.681372 0.731938i \(-0.738616\pi\)
−0.681372 + 0.731938i \(0.738616\pi\)
\(812\) 26.5819 0.932841
\(813\) −7.20360 −0.252641
\(814\) 25.6214 0.898028
\(815\) −25.7265 −0.901162
\(816\) 19.6992 0.689608
\(817\) −63.3832 −2.21750
\(818\) −67.3440 −2.35463
\(819\) −12.5017 −0.436843
\(820\) −38.9712 −1.36093
\(821\) −16.7312 −0.583922 −0.291961 0.956430i \(-0.594308\pi\)
−0.291961 + 0.956430i \(0.594308\pi\)
\(822\) 21.2634 0.741645
\(823\) −41.0599 −1.43126 −0.715630 0.698480i \(-0.753860\pi\)
−0.715630 + 0.698480i \(0.753860\pi\)
\(824\) 68.0478 2.37056
\(825\) 1.94140 0.0675910
\(826\) −31.7403 −1.10439
\(827\) −18.6710 −0.649255 −0.324627 0.945842i \(-0.605239\pi\)
−0.324627 + 0.945842i \(0.605239\pi\)
\(828\) −52.1234 −1.81141
\(829\) 1.24073 0.0430923 0.0215462 0.999768i \(-0.493141\pi\)
0.0215462 + 0.999768i \(0.493141\pi\)
\(830\) 39.2355 1.36188
\(831\) 5.49695 0.190687
\(832\) −20.7764 −0.720292
\(833\) 15.8158 0.547987
\(834\) −30.0916 −1.04199
\(835\) −25.7572 −0.891365
\(836\) −19.6890 −0.680959
\(837\) 4.05249 0.140075
\(838\) −18.4638 −0.637823
\(839\) 36.9217 1.27468 0.637340 0.770583i \(-0.280035\pi\)
0.637340 + 0.770583i \(0.280035\pi\)
\(840\) 12.3355 0.425614
\(841\) −19.4711 −0.671418
\(842\) −1.52705 −0.0526258
\(843\) −15.5378 −0.535152
\(844\) −41.4393 −1.42640
\(845\) −11.6417 −0.400486
\(846\) 51.6855 1.77698
\(847\) 2.19104 0.0752851
\(848\) −2.55378 −0.0876972
\(849\) −5.51631 −0.189319
\(850\) −44.5062 −1.52655
\(851\) −57.7437 −1.97943
\(852\) −30.4752 −1.04406
\(853\) 47.8695 1.63902 0.819510 0.573065i \(-0.194246\pi\)
0.819510 + 0.573065i \(0.194246\pi\)
\(854\) 47.7798 1.63499
\(855\) 18.9815 0.649152
\(856\) 26.0579 0.890640
\(857\) −24.0450 −0.821361 −0.410681 0.911779i \(-0.634709\pi\)
−0.410681 + 0.911779i \(0.634709\pi\)
\(858\) 4.39239 0.149954
\(859\) −23.7542 −0.810483 −0.405242 0.914210i \(-0.632813\pi\)
−0.405242 + 0.914210i \(0.632813\pi\)
\(860\) 77.9680 2.65869
\(861\) 10.5846 0.360722
\(862\) −94.4857 −3.21820
\(863\) 55.6395 1.89399 0.946995 0.321250i \(-0.104103\pi\)
0.946995 + 0.321250i \(0.104103\pi\)
\(864\) 2.76435 0.0940452
\(865\) 25.0279 0.850975
\(866\) 33.1938 1.12797
\(867\) −26.5173 −0.900576
\(868\) 8.43411 0.286272
\(869\) −2.02337 −0.0686382
\(870\) 9.00378 0.305257
\(871\) 36.1874 1.22616
\(872\) −17.9651 −0.608376
\(873\) 22.9435 0.776520
\(874\) 66.9547 2.26478
\(875\) −25.9087 −0.875872
\(876\) −15.7046 −0.530610
\(877\) 13.8784 0.468640 0.234320 0.972160i \(-0.424714\pi\)
0.234320 + 0.972160i \(0.424714\pi\)
\(878\) 43.6179 1.47203
\(879\) 13.6074 0.458965
\(880\) 5.62280 0.189544
\(881\) 28.4446 0.958322 0.479161 0.877727i \(-0.340941\pi\)
0.479161 + 0.877727i \(0.340941\pi\)
\(882\) −12.9421 −0.435785
\(883\) 6.14593 0.206827 0.103413 0.994638i \(-0.467024\pi\)
0.103413 + 0.994638i \(0.467024\pi\)
\(884\) −66.7346 −2.24453
\(885\) −7.12518 −0.239510
\(886\) 17.3337 0.582336
\(887\) −1.54466 −0.0518645 −0.0259322 0.999664i \(-0.508255\pi\)
−0.0259322 + 0.999664i \(0.508255\pi\)
\(888\) −37.7776 −1.26773
\(889\) −30.7880 −1.03260
\(890\) 38.0810 1.27648
\(891\) 4.08874 0.136978
\(892\) −8.76307 −0.293409
\(893\) −44.0010 −1.47244
\(894\) 14.2690 0.477226
\(895\) 10.7490 0.359299
\(896\) 44.0207 1.47063
\(897\) −9.89927 −0.330527
\(898\) −58.9037 −1.96564
\(899\) 3.02340 0.100836
\(900\) 24.1368 0.804560
\(901\) 5.12120 0.170612
\(902\) 15.4002 0.512770
\(903\) −21.1761 −0.704697
\(904\) 21.7598 0.723721
\(905\) −13.2097 −0.439105
\(906\) 23.9902 0.797023
\(907\) 36.6993 1.21858 0.609290 0.792948i \(-0.291455\pi\)
0.609290 + 0.792948i \(0.291455\pi\)
\(908\) −80.3890 −2.66780
\(909\) 12.6365 0.419128
\(910\) −19.7542 −0.654844
\(911\) −30.1967 −1.00046 −0.500230 0.865893i \(-0.666751\pi\)
−0.500230 + 0.865893i \(0.666751\pi\)
\(912\) 13.7232 0.454421
\(913\) −10.2756 −0.340072
\(914\) 18.8691 0.624135
\(915\) 10.7258 0.354583
\(916\) 3.45616 0.114195
\(917\) 28.1560 0.929795
\(918\) 72.4576 2.39146
\(919\) 22.7262 0.749667 0.374833 0.927092i \(-0.377700\pi\)
0.374833 + 0.927092i \(0.377700\pi\)
\(920\) −40.4492 −1.33357
\(921\) 7.88291 0.259751
\(922\) 28.3336 0.933119
\(923\) 23.9682 0.788924
\(924\) −6.57803 −0.216401
\(925\) 26.7394 0.879187
\(926\) −66.5519 −2.18703
\(927\) 34.9832 1.14900
\(928\) 2.06237 0.0677006
\(929\) −8.05096 −0.264143 −0.132072 0.991240i \(-0.542163\pi\)
−0.132072 + 0.991240i \(0.542163\pi\)
\(930\) 2.85679 0.0936778
\(931\) 11.0179 0.361098
\(932\) −61.6930 −2.02082
\(933\) 16.4784 0.539479
\(934\) 22.3255 0.730514
\(935\) −11.2756 −0.368752
\(936\) 26.8196 0.876625
\(937\) 1.10645 0.0361461 0.0180731 0.999837i \(-0.494247\pi\)
0.0180731 + 0.999837i \(0.494247\pi\)
\(938\) −81.7727 −2.66997
\(939\) −1.50249 −0.0490320
\(940\) 54.1258 1.76539
\(941\) 35.6500 1.16216 0.581079 0.813847i \(-0.302631\pi\)
0.581079 + 0.813847i \(0.302631\pi\)
\(942\) −38.2159 −1.24514
\(943\) −34.7079 −1.13025
\(944\) 21.3324 0.694312
\(945\) 14.2147 0.462403
\(946\) −30.8105 −1.00174
\(947\) 26.4446 0.859333 0.429666 0.902988i \(-0.358631\pi\)
0.429666 + 0.902988i \(0.358631\pi\)
\(948\) 6.07465 0.197295
\(949\) 12.3514 0.400944
\(950\) −31.0048 −1.00593
\(951\) −21.0723 −0.683317
\(952\) 74.0608 2.40032
\(953\) −28.9222 −0.936883 −0.468441 0.883495i \(-0.655184\pi\)
−0.468441 + 0.883495i \(0.655184\pi\)
\(954\) −4.19069 −0.135679
\(955\) 39.2059 1.26867
\(956\) −101.577 −3.28524
\(957\) −2.35805 −0.0762248
\(958\) 80.1101 2.58824
\(959\) 25.0448 0.808738
\(960\) 10.5391 0.340149
\(961\) −30.0407 −0.969055
\(962\) 60.4975 1.95052
\(963\) 13.3963 0.431690
\(964\) −28.3146 −0.911951
\(965\) −6.62217 −0.213175
\(966\) 22.3694 0.719723
\(967\) −22.1638 −0.712740 −0.356370 0.934345i \(-0.615986\pi\)
−0.356370 + 0.934345i \(0.615986\pi\)
\(968\) −4.70040 −0.151077
\(969\) −27.5197 −0.884059
\(970\) 36.2536 1.16403
\(971\) 6.91747 0.221992 0.110996 0.993821i \(-0.464596\pi\)
0.110996 + 0.993821i \(0.464596\pi\)
\(972\) −61.0600 −1.95850
\(973\) −35.4430 −1.13625
\(974\) −22.1838 −0.710816
\(975\) 4.58407 0.146808
\(976\) −32.1124 −1.02789
\(977\) −12.9607 −0.414650 −0.207325 0.978272i \(-0.566476\pi\)
−0.207325 + 0.978272i \(0.566476\pi\)
\(978\) −30.5217 −0.975978
\(979\) −9.97324 −0.318746
\(980\) −13.5532 −0.432942
\(981\) −9.23585 −0.294878
\(982\) 65.5591 2.09208
\(983\) 23.6571 0.754545 0.377272 0.926102i \(-0.376862\pi\)
0.377272 + 0.926102i \(0.376862\pi\)
\(984\) −22.7069 −0.723870
\(985\) −17.1633 −0.546867
\(986\) 54.0577 1.72155
\(987\) −14.7006 −0.467925
\(988\) −46.4899 −1.47904
\(989\) 69.4386 2.20802
\(990\) 9.22686 0.293249
\(991\) 30.7144 0.975674 0.487837 0.872935i \(-0.337786\pi\)
0.487837 + 0.872935i \(0.337786\pi\)
\(992\) 0.654365 0.0207761
\(993\) 0.450117 0.0142840
\(994\) −54.1609 −1.71788
\(995\) 18.0357 0.571771
\(996\) 30.8498 0.977512
\(997\) −19.1273 −0.605768 −0.302884 0.953028i \(-0.597949\pi\)
−0.302884 + 0.953028i \(0.597949\pi\)
\(998\) 5.53330 0.175153
\(999\) −43.5327 −1.37731
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 \(a_p\))