Properties

Label 4019.2.a.b.1.18
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.40616 q^{2}\) \(-0.556574 q^{3}\) \(+3.78961 q^{4}\) \(+1.68267 q^{5}\) \(+1.33921 q^{6}\) \(+2.28423 q^{7}\) \(-4.30608 q^{8}\) \(-2.69023 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.40616 q^{2}\) \(-0.556574 q^{3}\) \(+3.78961 q^{4}\) \(+1.68267 q^{5}\) \(+1.33921 q^{6}\) \(+2.28423 q^{7}\) \(-4.30608 q^{8}\) \(-2.69023 q^{9}\) \(-4.04878 q^{10}\) \(+2.91752 q^{11}\) \(-2.10920 q^{12}\) \(+6.13861 q^{13}\) \(-5.49623 q^{14}\) \(-0.936532 q^{15}\) \(+2.78191 q^{16}\) \(-7.57808 q^{17}\) \(+6.47311 q^{18}\) \(+8.35943 q^{19}\) \(+6.37667 q^{20}\) \(-1.27134 q^{21}\) \(-7.02002 q^{22}\) \(-4.30211 q^{23}\) \(+2.39665 q^{24}\) \(-2.16861 q^{25}\) \(-14.7705 q^{26}\) \(+3.16703 q^{27}\) \(+8.65634 q^{28}\) \(-2.31811 q^{29}\) \(+2.25345 q^{30}\) \(+10.1378 q^{31}\) \(+1.91844 q^{32}\) \(-1.62382 q^{33}\) \(+18.2341 q^{34}\) \(+3.84361 q^{35}\) \(-10.1949 q^{36}\) \(-2.31179 q^{37}\) \(-20.1141 q^{38}\) \(-3.41659 q^{39}\) \(-7.24573 q^{40}\) \(-0.874310 q^{41}\) \(+3.05906 q^{42}\) \(+0.103907 q^{43}\) \(+11.0563 q^{44}\) \(-4.52677 q^{45}\) \(+10.3516 q^{46}\) \(+0.979261 q^{47}\) \(-1.54834 q^{48}\) \(-1.78229 q^{49}\) \(+5.21803 q^{50}\) \(+4.21776 q^{51}\) \(+23.2629 q^{52}\) \(+2.46421 q^{53}\) \(-7.62039 q^{54}\) \(+4.90923 q^{55}\) \(-9.83609 q^{56}\) \(-4.65264 q^{57}\) \(+5.57773 q^{58}\) \(+7.94536 q^{59}\) \(-3.54909 q^{60}\) \(-0.119062 q^{61}\) \(-24.3931 q^{62}\) \(-6.14509 q^{63}\) \(-10.1799 q^{64}\) \(+10.3293 q^{65}\) \(+3.90716 q^{66}\) \(+13.0806 q^{67}\) \(-28.7179 q^{68}\) \(+2.39444 q^{69}\) \(-9.24835 q^{70}\) \(-1.52675 q^{71}\) \(+11.5843 q^{72}\) \(-5.80152 q^{73}\) \(+5.56254 q^{74}\) \(+1.20699 q^{75}\) \(+31.6789 q^{76}\) \(+6.66429 q^{77}\) \(+8.22087 q^{78}\) \(+3.24083 q^{79}\) \(+4.68104 q^{80}\) \(+6.30799 q^{81}\) \(+2.10373 q^{82}\) \(+1.20009 q^{83}\) \(-4.81789 q^{84}\) \(-12.7514 q^{85}\) \(-0.250016 q^{86}\) \(+1.29020 q^{87}\) \(-12.5631 q^{88}\) \(+3.53011 q^{89}\) \(+10.8921 q^{90}\) \(+14.0220 q^{91}\) \(-16.3033 q^{92}\) \(-5.64241 q^{93}\) \(-2.35626 q^{94}\) \(+14.0662 q^{95}\) \(-1.06776 q^{96}\) \(-4.69774 q^{97}\) \(+4.28848 q^{98}\) \(-7.84879 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40616 −1.70141 −0.850706 0.525642i \(-0.823825\pi\)
−0.850706 + 0.525642i \(0.823825\pi\)
\(3\) −0.556574 −0.321338 −0.160669 0.987008i \(-0.551365\pi\)
−0.160669 + 0.987008i \(0.551365\pi\)
\(4\) 3.78961 1.89480
\(5\) 1.68267 0.752514 0.376257 0.926515i \(-0.377211\pi\)
0.376257 + 0.926515i \(0.377211\pi\)
\(6\) 1.33921 0.546729
\(7\) 2.28423 0.863358 0.431679 0.902027i \(-0.357921\pi\)
0.431679 + 0.902027i \(0.357921\pi\)
\(8\) −4.30608 −1.52243
\(9\) −2.69023 −0.896742
\(10\) −4.04878 −1.28034
\(11\) 2.91752 0.879666 0.439833 0.898080i \(-0.355038\pi\)
0.439833 + 0.898080i \(0.355038\pi\)
\(12\) −2.10920 −0.608873
\(13\) 6.13861 1.70254 0.851272 0.524725i \(-0.175832\pi\)
0.851272 + 0.524725i \(0.175832\pi\)
\(14\) −5.49623 −1.46893
\(15\) −0.936532 −0.241812
\(16\) 2.78191 0.695478
\(17\) −7.57808 −1.83795 −0.918977 0.394311i \(-0.870983\pi\)
−0.918977 + 0.394311i \(0.870983\pi\)
\(18\) 6.47311 1.52573
\(19\) 8.35943 1.91778 0.958892 0.283772i \(-0.0915858\pi\)
0.958892 + 0.283772i \(0.0915858\pi\)
\(20\) 6.37667 1.42587
\(21\) −1.27134 −0.277430
\(22\) −7.02002 −1.49667
\(23\) −4.30211 −0.897052 −0.448526 0.893770i \(-0.648051\pi\)
−0.448526 + 0.893770i \(0.648051\pi\)
\(24\) 2.39665 0.489215
\(25\) −2.16861 −0.433723
\(26\) −14.7705 −2.89673
\(27\) 3.16703 0.609496
\(28\) 8.65634 1.63589
\(29\) −2.31811 −0.430461 −0.215231 0.976563i \(-0.569050\pi\)
−0.215231 + 0.976563i \(0.569050\pi\)
\(30\) 2.25345 0.411421
\(31\) 10.1378 1.82079 0.910397 0.413736i \(-0.135776\pi\)
0.910397 + 0.413736i \(0.135776\pi\)
\(32\) 1.91844 0.339136
\(33\) −1.62382 −0.282670
\(34\) 18.2341 3.12712
\(35\) 3.84361 0.649689
\(36\) −10.1949 −1.69915
\(37\) −2.31179 −0.380056 −0.190028 0.981779i \(-0.560858\pi\)
−0.190028 + 0.981779i \(0.560858\pi\)
\(38\) −20.1141 −3.26294
\(39\) −3.41659 −0.547093
\(40\) −7.24573 −1.14565
\(41\) −0.874310 −0.136544 −0.0682721 0.997667i \(-0.521749\pi\)
−0.0682721 + 0.997667i \(0.521749\pi\)
\(42\) 3.05906 0.472023
\(43\) 0.103907 0.0158456 0.00792282 0.999969i \(-0.497478\pi\)
0.00792282 + 0.999969i \(0.497478\pi\)
\(44\) 11.0563 1.66679
\(45\) −4.52677 −0.674811
\(46\) 10.3516 1.52625
\(47\) 0.979261 0.142840 0.0714199 0.997446i \(-0.477247\pi\)
0.0714199 + 0.997446i \(0.477247\pi\)
\(48\) −1.54834 −0.223484
\(49\) −1.78229 −0.254613
\(50\) 5.21803 0.737941
\(51\) 4.21776 0.590605
\(52\) 23.2629 3.22599
\(53\) 2.46421 0.338485 0.169242 0.985574i \(-0.445868\pi\)
0.169242 + 0.985574i \(0.445868\pi\)
\(54\) −7.62039 −1.03700
\(55\) 4.90923 0.661960
\(56\) −9.83609 −1.31440
\(57\) −4.65264 −0.616257
\(58\) 5.57773 0.732392
\(59\) 7.94536 1.03440 0.517199 0.855865i \(-0.326975\pi\)
0.517199 + 0.855865i \(0.326975\pi\)
\(60\) −3.54909 −0.458185
\(61\) −0.119062 −0.0152443 −0.00762216 0.999971i \(-0.502426\pi\)
−0.00762216 + 0.999971i \(0.502426\pi\)
\(62\) −24.3931 −3.09792
\(63\) −6.14509 −0.774209
\(64\) −10.1799 −1.27249
\(65\) 10.3293 1.28119
\(66\) 3.90716 0.480939
\(67\) 13.0806 1.59805 0.799026 0.601297i \(-0.205349\pi\)
0.799026 + 0.601297i \(0.205349\pi\)
\(68\) −28.7179 −3.48256
\(69\) 2.39444 0.288257
\(70\) −9.24835 −1.10539
\(71\) −1.52675 −0.181192 −0.0905960 0.995888i \(-0.528877\pi\)
−0.0905960 + 0.995888i \(0.528877\pi\)
\(72\) 11.5843 1.36523
\(73\) −5.80152 −0.679017 −0.339508 0.940603i \(-0.610261\pi\)
−0.339508 + 0.940603i \(0.610261\pi\)
\(74\) 5.56254 0.646632
\(75\) 1.20699 0.139372
\(76\) 31.6789 3.63382
\(77\) 6.66429 0.759466
\(78\) 8.22087 0.930830
\(79\) 3.24083 0.364622 0.182311 0.983241i \(-0.441642\pi\)
0.182311 + 0.983241i \(0.441642\pi\)
\(80\) 4.68104 0.523357
\(81\) 6.30799 0.700887
\(82\) 2.10373 0.232318
\(83\) 1.20009 0.131728 0.0658638 0.997829i \(-0.479020\pi\)
0.0658638 + 0.997829i \(0.479020\pi\)
\(84\) −4.81789 −0.525675
\(85\) −12.7514 −1.38309
\(86\) −0.250016 −0.0269600
\(87\) 1.29020 0.138324
\(88\) −12.5631 −1.33923
\(89\) 3.53011 0.374191 0.187095 0.982342i \(-0.440093\pi\)
0.187095 + 0.982342i \(0.440093\pi\)
\(90\) 10.8921 1.14813
\(91\) 14.0220 1.46991
\(92\) −16.3033 −1.69974
\(93\) −5.64241 −0.585091
\(94\) −2.35626 −0.243030
\(95\) 14.0662 1.44316
\(96\) −1.06776 −0.108977
\(97\) −4.69774 −0.476983 −0.238491 0.971145i \(-0.576653\pi\)
−0.238491 + 0.971145i \(0.576653\pi\)
\(98\) 4.28848 0.433202
\(99\) −7.84879 −0.788833
\(100\) −8.21820 −0.821820
\(101\) 6.03244 0.600250 0.300125 0.953900i \(-0.402972\pi\)
0.300125 + 0.953900i \(0.402972\pi\)
\(102\) −10.1486 −1.00486
\(103\) 12.3773 1.21957 0.609787 0.792565i \(-0.291255\pi\)
0.609787 + 0.792565i \(0.291255\pi\)
\(104\) −26.4334 −2.59200
\(105\) −2.13926 −0.208770
\(106\) −5.92927 −0.575902
\(107\) 7.95681 0.769213 0.384607 0.923081i \(-0.374337\pi\)
0.384607 + 0.923081i \(0.374337\pi\)
\(108\) 12.0018 1.15487
\(109\) 15.7072 1.50448 0.752240 0.658889i \(-0.228973\pi\)
0.752240 + 0.658889i \(0.228973\pi\)
\(110\) −11.8124 −1.12627
\(111\) 1.28668 0.122127
\(112\) 6.35453 0.600446
\(113\) −4.43851 −0.417540 −0.208770 0.977965i \(-0.566946\pi\)
−0.208770 + 0.977965i \(0.566946\pi\)
\(114\) 11.1950 1.04851
\(115\) −7.23904 −0.675044
\(116\) −8.78471 −0.815640
\(117\) −16.5142 −1.52674
\(118\) −19.1178 −1.75994
\(119\) −17.3101 −1.58681
\(120\) 4.03278 0.368141
\(121\) −2.48807 −0.226189
\(122\) 0.286482 0.0259369
\(123\) 0.486618 0.0438769
\(124\) 38.4181 3.45005
\(125\) −12.0624 −1.07890
\(126\) 14.7861 1.31725
\(127\) 1.16954 0.103780 0.0518902 0.998653i \(-0.483475\pi\)
0.0518902 + 0.998653i \(0.483475\pi\)
\(128\) 20.6576 1.82589
\(129\) −0.0578318 −0.00509181
\(130\) −24.8539 −2.17983
\(131\) 11.4104 0.996927 0.498464 0.866911i \(-0.333898\pi\)
0.498464 + 0.866911i \(0.333898\pi\)
\(132\) −6.15363 −0.535605
\(133\) 19.0949 1.65573
\(134\) −31.4741 −2.71894
\(135\) 5.32908 0.458654
\(136\) 32.6318 2.79816
\(137\) 3.91272 0.334286 0.167143 0.985933i \(-0.446546\pi\)
0.167143 + 0.985933i \(0.446546\pi\)
\(138\) −5.76141 −0.490444
\(139\) −17.6305 −1.49540 −0.747700 0.664037i \(-0.768842\pi\)
−0.747700 + 0.664037i \(0.768842\pi\)
\(140\) 14.5658 1.23103
\(141\) −0.545031 −0.0458999
\(142\) 3.67361 0.308282
\(143\) 17.9095 1.49767
\(144\) −7.48397 −0.623664
\(145\) −3.90061 −0.323928
\(146\) 13.9594 1.15529
\(147\) 0.991977 0.0818169
\(148\) −8.76078 −0.720132
\(149\) 4.06396 0.332932 0.166466 0.986047i \(-0.446764\pi\)
0.166466 + 0.986047i \(0.446764\pi\)
\(150\) −2.90422 −0.237129
\(151\) −0.855728 −0.0696381 −0.0348191 0.999394i \(-0.511085\pi\)
−0.0348191 + 0.999394i \(0.511085\pi\)
\(152\) −35.9964 −2.91969
\(153\) 20.3867 1.64817
\(154\) −16.0353 −1.29217
\(155\) 17.0585 1.37017
\(156\) −12.9475 −1.03663
\(157\) −9.90959 −0.790872 −0.395436 0.918494i \(-0.629406\pi\)
−0.395436 + 0.918494i \(0.629406\pi\)
\(158\) −7.79796 −0.620373
\(159\) −1.37151 −0.108768
\(160\) 3.22811 0.255204
\(161\) −9.82701 −0.774477
\(162\) −15.1780 −1.19250
\(163\) −9.27230 −0.726263 −0.363131 0.931738i \(-0.618292\pi\)
−0.363131 + 0.931738i \(0.618292\pi\)
\(164\) −3.31329 −0.258725
\(165\) −2.73235 −0.212713
\(166\) −2.88762 −0.224123
\(167\) 13.8101 1.06866 0.534328 0.845277i \(-0.320565\pi\)
0.534328 + 0.845277i \(0.320565\pi\)
\(168\) 5.47451 0.422368
\(169\) 24.6825 1.89866
\(170\) 30.6820 2.35320
\(171\) −22.4887 −1.71976
\(172\) 0.393766 0.0300244
\(173\) −4.08808 −0.310811 −0.155405 0.987851i \(-0.549668\pi\)
−0.155405 + 0.987851i \(0.549668\pi\)
\(174\) −3.10442 −0.235346
\(175\) −4.95362 −0.374458
\(176\) 8.11628 0.611788
\(177\) −4.42218 −0.332392
\(178\) −8.49401 −0.636653
\(179\) −9.57235 −0.715471 −0.357736 0.933823i \(-0.616451\pi\)
−0.357736 + 0.933823i \(0.616451\pi\)
\(180\) −17.1547 −1.27863
\(181\) −9.28015 −0.689788 −0.344894 0.938642i \(-0.612085\pi\)
−0.344894 + 0.938642i \(0.612085\pi\)
\(182\) −33.7392 −2.50091
\(183\) 0.0662668 0.00489858
\(184\) 18.5252 1.36570
\(185\) −3.88999 −0.285997
\(186\) 13.5765 0.995481
\(187\) −22.1092 −1.61678
\(188\) 3.71101 0.270654
\(189\) 7.23423 0.526213
\(190\) −33.8455 −2.45541
\(191\) −15.0179 −1.08666 −0.543329 0.839520i \(-0.682836\pi\)
−0.543329 + 0.839520i \(0.682836\pi\)
\(192\) 5.66587 0.408899
\(193\) −11.0433 −0.794917 −0.397459 0.917620i \(-0.630108\pi\)
−0.397459 + 0.917620i \(0.630108\pi\)
\(194\) 11.3035 0.811544
\(195\) −5.74901 −0.411695
\(196\) −6.75418 −0.482441
\(197\) −25.7060 −1.83148 −0.915738 0.401777i \(-0.868393\pi\)
−0.915738 + 0.401777i \(0.868393\pi\)
\(198\) 18.8854 1.34213
\(199\) 8.87747 0.629307 0.314654 0.949207i \(-0.398112\pi\)
0.314654 + 0.949207i \(0.398112\pi\)
\(200\) 9.33823 0.660313
\(201\) −7.28033 −0.513515
\(202\) −14.5150 −1.02127
\(203\) −5.29509 −0.371642
\(204\) 15.9837 1.11908
\(205\) −1.47118 −0.102751
\(206\) −29.7818 −2.07500
\(207\) 11.5736 0.804424
\(208\) 17.0771 1.18408
\(209\) 24.3888 1.68701
\(210\) 5.14739 0.355204
\(211\) −25.8826 −1.78183 −0.890917 0.454166i \(-0.849937\pi\)
−0.890917 + 0.454166i \(0.849937\pi\)
\(212\) 9.33837 0.641362
\(213\) 0.849751 0.0582240
\(214\) −19.1453 −1.30875
\(215\) 0.174841 0.0119241
\(216\) −13.6375 −0.927915
\(217\) 23.1570 1.57200
\(218\) −37.7941 −2.55974
\(219\) 3.22898 0.218194
\(220\) 18.6041 1.25429
\(221\) −46.5189 −3.12920
\(222\) −3.09597 −0.207788
\(223\) 23.0931 1.54643 0.773214 0.634145i \(-0.218648\pi\)
0.773214 + 0.634145i \(0.218648\pi\)
\(224\) 4.38217 0.292796
\(225\) 5.83406 0.388937
\(226\) 10.6798 0.710407
\(227\) −20.1279 −1.33594 −0.667969 0.744189i \(-0.732836\pi\)
−0.667969 + 0.744189i \(0.732836\pi\)
\(228\) −17.6317 −1.16769
\(229\) 8.30562 0.548851 0.274425 0.961608i \(-0.411512\pi\)
0.274425 + 0.961608i \(0.411512\pi\)
\(230\) 17.4183 1.14853
\(231\) −3.70917 −0.244046
\(232\) 9.98195 0.655347
\(233\) 1.42485 0.0933447 0.0466724 0.998910i \(-0.485138\pi\)
0.0466724 + 0.998910i \(0.485138\pi\)
\(234\) 39.7359 2.59762
\(235\) 1.64777 0.107489
\(236\) 30.1098 1.95998
\(237\) −1.80376 −0.117167
\(238\) 41.6508 2.69982
\(239\) 29.1802 1.88751 0.943755 0.330644i \(-0.107266\pi\)
0.943755 + 0.330644i \(0.107266\pi\)
\(240\) −2.60535 −0.168175
\(241\) −28.4431 −1.83218 −0.916092 0.400968i \(-0.868674\pi\)
−0.916092 + 0.400968i \(0.868674\pi\)
\(242\) 5.98671 0.384840
\(243\) −13.0120 −0.834718
\(244\) −0.451198 −0.0288850
\(245\) −2.99901 −0.191600
\(246\) −1.17088 −0.0746527
\(247\) 51.3153 3.26511
\(248\) −43.6540 −2.77203
\(249\) −0.667942 −0.0423291
\(250\) 29.0241 1.83565
\(251\) 6.97150 0.440037 0.220019 0.975496i \(-0.429388\pi\)
0.220019 + 0.975496i \(0.429388\pi\)
\(252\) −23.2875 −1.46697
\(253\) −12.5515 −0.789106
\(254\) −2.81411 −0.176573
\(255\) 7.09711 0.444439
\(256\) −29.3457 −1.83410
\(257\) 5.37505 0.335286 0.167643 0.985848i \(-0.446384\pi\)
0.167643 + 0.985848i \(0.446384\pi\)
\(258\) 0.139153 0.00866327
\(259\) −5.28066 −0.328124
\(260\) 39.1439 2.42760
\(261\) 6.23623 0.386013
\(262\) −27.4551 −1.69618
\(263\) −11.7684 −0.725671 −0.362836 0.931853i \(-0.618191\pi\)
−0.362836 + 0.931853i \(0.618191\pi\)
\(264\) 6.99229 0.430346
\(265\) 4.14645 0.254714
\(266\) −45.9453 −2.81709
\(267\) −1.96477 −0.120242
\(268\) 49.5704 3.02799
\(269\) 10.1204 0.617053 0.308527 0.951216i \(-0.400164\pi\)
0.308527 + 0.951216i \(0.400164\pi\)
\(270\) −12.8226 −0.780360
\(271\) −15.4078 −0.935959 −0.467979 0.883739i \(-0.655018\pi\)
−0.467979 + 0.883739i \(0.655018\pi\)
\(272\) −21.0815 −1.27826
\(273\) −7.80429 −0.472337
\(274\) −9.41464 −0.568759
\(275\) −6.32698 −0.381531
\(276\) 9.07400 0.546191
\(277\) −11.1500 −0.669940 −0.334970 0.942229i \(-0.608726\pi\)
−0.334970 + 0.942229i \(0.608726\pi\)
\(278\) 42.4218 2.54429
\(279\) −27.2728 −1.63278
\(280\) −16.5509 −0.989106
\(281\) −8.70776 −0.519461 −0.259731 0.965681i \(-0.583634\pi\)
−0.259731 + 0.965681i \(0.583634\pi\)
\(282\) 1.31143 0.0780947
\(283\) 18.9866 1.12864 0.564319 0.825557i \(-0.309139\pi\)
0.564319 + 0.825557i \(0.309139\pi\)
\(284\) −5.78579 −0.343323
\(285\) −7.82887 −0.463742
\(286\) −43.0932 −2.54815
\(287\) −1.99713 −0.117887
\(288\) −5.16104 −0.304117
\(289\) 40.4273 2.37808
\(290\) 9.38550 0.551135
\(291\) 2.61464 0.153273
\(292\) −21.9855 −1.28660
\(293\) 29.4454 1.72022 0.860110 0.510108i \(-0.170395\pi\)
0.860110 + 0.510108i \(0.170395\pi\)
\(294\) −2.38686 −0.139204
\(295\) 13.3694 0.778399
\(296\) 9.95476 0.578609
\(297\) 9.23988 0.536152
\(298\) −9.77854 −0.566455
\(299\) −26.4090 −1.52727
\(300\) 4.57404 0.264082
\(301\) 0.237347 0.0136805
\(302\) 2.05902 0.118483
\(303\) −3.35750 −0.192883
\(304\) 23.2552 1.33378
\(305\) −0.200342 −0.0114716
\(306\) −49.0538 −2.80422
\(307\) −3.60190 −0.205571 −0.102786 0.994704i \(-0.532776\pi\)
−0.102786 + 0.994704i \(0.532776\pi\)
\(308\) 25.2550 1.43904
\(309\) −6.88890 −0.391896
\(310\) −41.0455 −2.33123
\(311\) 21.8332 1.23805 0.619025 0.785372i \(-0.287528\pi\)
0.619025 + 0.785372i \(0.287528\pi\)
\(312\) 14.7121 0.832910
\(313\) 12.6608 0.715628 0.357814 0.933793i \(-0.383522\pi\)
0.357814 + 0.933793i \(0.383522\pi\)
\(314\) 23.8441 1.34560
\(315\) −10.3402 −0.582603
\(316\) 12.2815 0.690888
\(317\) 27.2151 1.52855 0.764275 0.644891i \(-0.223097\pi\)
0.764275 + 0.644891i \(0.223097\pi\)
\(318\) 3.30008 0.185059
\(319\) −6.76312 −0.378662
\(320\) −17.1294 −0.957565
\(321\) −4.42855 −0.247178
\(322\) 23.6454 1.31770
\(323\) −63.3484 −3.52480
\(324\) 23.9048 1.32804
\(325\) −13.3123 −0.738432
\(326\) 22.3106 1.23567
\(327\) −8.74224 −0.483447
\(328\) 3.76485 0.207879
\(329\) 2.23686 0.123322
\(330\) 6.57448 0.361913
\(331\) 20.6735 1.13632 0.568160 0.822918i \(-0.307655\pi\)
0.568160 + 0.822918i \(0.307655\pi\)
\(332\) 4.54789 0.249598
\(333\) 6.21924 0.340812
\(334\) −33.2293 −1.81823
\(335\) 22.0104 1.20256
\(336\) −3.53677 −0.192946
\(337\) 7.85757 0.428029 0.214015 0.976830i \(-0.431346\pi\)
0.214015 + 0.976830i \(0.431346\pi\)
\(338\) −59.3901 −3.23040
\(339\) 2.47036 0.134171
\(340\) −48.3229 −2.62068
\(341\) 29.5771 1.60169
\(342\) 54.1115 2.92602
\(343\) −20.0608 −1.08318
\(344\) −0.447431 −0.0241239
\(345\) 4.02906 0.216917
\(346\) 9.83657 0.528817
\(347\) −9.71597 −0.521581 −0.260790 0.965395i \(-0.583983\pi\)
−0.260790 + 0.965395i \(0.583983\pi\)
\(348\) 4.88934 0.262096
\(349\) 1.76402 0.0944258 0.0472129 0.998885i \(-0.484966\pi\)
0.0472129 + 0.998885i \(0.484966\pi\)
\(350\) 11.9192 0.637108
\(351\) 19.4412 1.03769
\(352\) 5.59710 0.298326
\(353\) 2.65431 0.141275 0.0706373 0.997502i \(-0.477497\pi\)
0.0706373 + 0.997502i \(0.477497\pi\)
\(354\) 10.6405 0.565535
\(355\) −2.56902 −0.136350
\(356\) 13.3777 0.709018
\(357\) 9.63435 0.509904
\(358\) 23.0326 1.21731
\(359\) 19.5283 1.03066 0.515331 0.856991i \(-0.327669\pi\)
0.515331 + 0.856991i \(0.327669\pi\)
\(360\) 19.4926 1.02735
\(361\) 50.8800 2.67789
\(362\) 22.3295 1.17361
\(363\) 1.38480 0.0726831
\(364\) 53.1379 2.78518
\(365\) −9.76206 −0.510970
\(366\) −0.159448 −0.00833451
\(367\) 20.2910 1.05918 0.529591 0.848253i \(-0.322345\pi\)
0.529591 + 0.848253i \(0.322345\pi\)
\(368\) −11.9681 −0.623880
\(369\) 2.35209 0.122445
\(370\) 9.35993 0.486600
\(371\) 5.62881 0.292233
\(372\) −21.3825 −1.10863
\(373\) −17.8583 −0.924669 −0.462335 0.886706i \(-0.652988\pi\)
−0.462335 + 0.886706i \(0.652988\pi\)
\(374\) 53.1983 2.75082
\(375\) 6.71364 0.346691
\(376\) −4.21678 −0.217464
\(377\) −14.2299 −0.732880
\(378\) −17.4067 −0.895305
\(379\) 38.1531 1.95979 0.979897 0.199506i \(-0.0639336\pi\)
0.979897 + 0.199506i \(0.0639336\pi\)
\(380\) 53.3053 2.73450
\(381\) −0.650938 −0.0333486
\(382\) 36.1355 1.84885
\(383\) 3.62027 0.184987 0.0924935 0.995713i \(-0.470516\pi\)
0.0924935 + 0.995713i \(0.470516\pi\)
\(384\) −11.4975 −0.586728
\(385\) 11.2138 0.571509
\(386\) 26.5721 1.35248
\(387\) −0.279533 −0.0142094
\(388\) −17.8026 −0.903789
\(389\) −4.81242 −0.243999 −0.122000 0.992530i \(-0.538931\pi\)
−0.122000 + 0.992530i \(0.538931\pi\)
\(390\) 13.8330 0.700463
\(391\) 32.6017 1.64874
\(392\) 7.67469 0.387630
\(393\) −6.35071 −0.320351
\(394\) 61.8527 3.11609
\(395\) 5.45326 0.274383
\(396\) −29.7438 −1.49468
\(397\) −19.1435 −0.960785 −0.480393 0.877054i \(-0.659506\pi\)
−0.480393 + 0.877054i \(0.659506\pi\)
\(398\) −21.3606 −1.07071
\(399\) −10.6277 −0.532051
\(400\) −6.03289 −0.301645
\(401\) 33.2623 1.66104 0.830520 0.556989i \(-0.188044\pi\)
0.830520 + 0.556989i \(0.188044\pi\)
\(402\) 17.5177 0.873701
\(403\) 62.2317 3.09998
\(404\) 22.8606 1.13736
\(405\) 10.6143 0.527427
\(406\) 12.7408 0.632317
\(407\) −6.74470 −0.334322
\(408\) −18.1620 −0.899155
\(409\) 23.3100 1.15260 0.576302 0.817237i \(-0.304495\pi\)
0.576302 + 0.817237i \(0.304495\pi\)
\(410\) 3.53989 0.174823
\(411\) −2.17772 −0.107419
\(412\) 46.9052 2.31085
\(413\) 18.1490 0.893056
\(414\) −27.8480 −1.36866
\(415\) 2.01937 0.0991268
\(416\) 11.7766 0.577394
\(417\) 9.81268 0.480529
\(418\) −58.6833 −2.87030
\(419\) 27.0258 1.32030 0.660148 0.751136i \(-0.270494\pi\)
0.660148 + 0.751136i \(0.270494\pi\)
\(420\) −8.10694 −0.395578
\(421\) −7.31578 −0.356549 −0.178275 0.983981i \(-0.557052\pi\)
−0.178275 + 0.983981i \(0.557052\pi\)
\(422\) 62.2778 3.03163
\(423\) −2.63443 −0.128090
\(424\) −10.6111 −0.515319
\(425\) 16.4339 0.797163
\(426\) −2.04464 −0.0990630
\(427\) −0.271965 −0.0131613
\(428\) 30.1532 1.45751
\(429\) −9.96798 −0.481259
\(430\) −0.420696 −0.0202877
\(431\) −2.22051 −0.106958 −0.0534791 0.998569i \(-0.517031\pi\)
−0.0534791 + 0.998569i \(0.517031\pi\)
\(432\) 8.81040 0.423891
\(433\) −2.88593 −0.138689 −0.0693445 0.997593i \(-0.522091\pi\)
−0.0693445 + 0.997593i \(0.522091\pi\)
\(434\) −55.7194 −2.67461
\(435\) 2.17098 0.104091
\(436\) 59.5242 2.85069
\(437\) −35.9632 −1.72035
\(438\) −7.76944 −0.371238
\(439\) 4.61864 0.220436 0.110218 0.993907i \(-0.464845\pi\)
0.110218 + 0.993907i \(0.464845\pi\)
\(440\) −21.1396 −1.00779
\(441\) 4.79476 0.228322
\(442\) 111.932 5.32406
\(443\) −12.0674 −0.573341 −0.286671 0.958029i \(-0.592549\pi\)
−0.286671 + 0.958029i \(0.592549\pi\)
\(444\) 4.87602 0.231406
\(445\) 5.94002 0.281584
\(446\) −55.5657 −2.63111
\(447\) −2.26189 −0.106984
\(448\) −23.2532 −1.09861
\(449\) −30.7493 −1.45115 −0.725574 0.688144i \(-0.758426\pi\)
−0.725574 + 0.688144i \(0.758426\pi\)
\(450\) −14.0377 −0.661743
\(451\) −2.55082 −0.120113
\(452\) −16.8202 −0.791156
\(453\) 0.476276 0.0223774
\(454\) 48.4310 2.27298
\(455\) 23.5944 1.10612
\(456\) 20.0347 0.938209
\(457\) 0.367359 0.0171843 0.00859216 0.999963i \(-0.497265\pi\)
0.00859216 + 0.999963i \(0.497265\pi\)
\(458\) −19.9846 −0.933821
\(459\) −24.0000 −1.12023
\(460\) −27.4331 −1.27908
\(461\) −17.8744 −0.832496 −0.416248 0.909251i \(-0.636655\pi\)
−0.416248 + 0.909251i \(0.636655\pi\)
\(462\) 8.92486 0.415222
\(463\) −19.9222 −0.925863 −0.462932 0.886394i \(-0.653202\pi\)
−0.462932 + 0.886394i \(0.653202\pi\)
\(464\) −6.44876 −0.299376
\(465\) −9.49433 −0.440289
\(466\) −3.42841 −0.158818
\(467\) −16.7977 −0.777305 −0.388653 0.921384i \(-0.627059\pi\)
−0.388653 + 0.921384i \(0.627059\pi\)
\(468\) −62.5825 −2.89288
\(469\) 29.8791 1.37969
\(470\) −3.96481 −0.182883
\(471\) 5.51542 0.254137
\(472\) −34.2134 −1.57480
\(473\) 0.303150 0.0139389
\(474\) 4.34015 0.199350
\(475\) −18.1284 −0.831787
\(476\) −65.5984 −3.00670
\(477\) −6.62927 −0.303533
\(478\) −70.2123 −3.21143
\(479\) 17.5135 0.800211 0.400105 0.916469i \(-0.368974\pi\)
0.400105 + 0.916469i \(0.368974\pi\)
\(480\) −1.79668 −0.0820070
\(481\) −14.1912 −0.647062
\(482\) 68.4388 3.11730
\(483\) 5.46946 0.248869
\(484\) −9.42883 −0.428583
\(485\) −7.90475 −0.358936
\(486\) 31.3089 1.42020
\(487\) −20.7302 −0.939377 −0.469689 0.882832i \(-0.655634\pi\)
−0.469689 + 0.882832i \(0.655634\pi\)
\(488\) 0.512690 0.0232084
\(489\) 5.16073 0.233376
\(490\) 7.21610 0.325990
\(491\) 19.8753 0.896959 0.448480 0.893793i \(-0.351966\pi\)
0.448480 + 0.893793i \(0.351966\pi\)
\(492\) 1.84409 0.0831381
\(493\) 17.5668 0.791168
\(494\) −123.473 −5.55530
\(495\) −13.2069 −0.593608
\(496\) 28.2023 1.26632
\(497\) −3.48745 −0.156434
\(498\) 1.60718 0.0720192
\(499\) −8.12700 −0.363815 −0.181907 0.983316i \(-0.558227\pi\)
−0.181907 + 0.983316i \(0.558227\pi\)
\(500\) −45.7119 −2.04430
\(501\) −7.68634 −0.343400
\(502\) −16.7746 −0.748685
\(503\) −30.4466 −1.35755 −0.678773 0.734348i \(-0.737488\pi\)
−0.678773 + 0.734348i \(0.737488\pi\)
\(504\) 26.4613 1.17868
\(505\) 10.1506 0.451696
\(506\) 30.2009 1.34259
\(507\) −13.7377 −0.610111
\(508\) 4.43212 0.196643
\(509\) 31.9373 1.41559 0.707797 0.706416i \(-0.249689\pi\)
0.707797 + 0.706416i \(0.249689\pi\)
\(510\) −17.0768 −0.756173
\(511\) −13.2520 −0.586235
\(512\) 29.2952 1.29468
\(513\) 26.4746 1.16888
\(514\) −12.9332 −0.570460
\(515\) 20.8270 0.917746
\(516\) −0.219160 −0.00964798
\(517\) 2.85701 0.125651
\(518\) 12.7061 0.558275
\(519\) 2.27532 0.0998754
\(520\) −44.4787 −1.95052
\(521\) 1.94539 0.0852292 0.0426146 0.999092i \(-0.486431\pi\)
0.0426146 + 0.999092i \(0.486431\pi\)
\(522\) −15.0054 −0.656767
\(523\) 22.3009 0.975151 0.487576 0.873081i \(-0.337881\pi\)
0.487576 + 0.873081i \(0.337881\pi\)
\(524\) 43.2408 1.88898
\(525\) 2.75705 0.120328
\(526\) 28.3167 1.23467
\(527\) −76.8247 −3.34654
\(528\) −4.51731 −0.196591
\(529\) −4.49186 −0.195298
\(530\) −9.97702 −0.433374
\(531\) −21.3748 −0.927588
\(532\) 72.3620 3.13729
\(533\) −5.36705 −0.232473
\(534\) 4.72755 0.204581
\(535\) 13.3887 0.578844
\(536\) −56.3262 −2.43292
\(537\) 5.32773 0.229908
\(538\) −24.3514 −1.04986
\(539\) −5.19987 −0.223974
\(540\) 20.1951 0.869059
\(541\) 34.7892 1.49571 0.747853 0.663865i \(-0.231085\pi\)
0.747853 + 0.663865i \(0.231085\pi\)
\(542\) 37.0737 1.59245
\(543\) 5.16509 0.221655
\(544\) −14.5381 −0.623316
\(545\) 26.4301 1.13214
\(546\) 18.7784 0.803640
\(547\) 38.6167 1.65113 0.825565 0.564307i \(-0.190857\pi\)
0.825565 + 0.564307i \(0.190857\pi\)
\(548\) 14.8277 0.633407
\(549\) 0.320303 0.0136702
\(550\) 15.2237 0.649142
\(551\) −19.3780 −0.825532
\(552\) −10.3107 −0.438851
\(553\) 7.40281 0.314800
\(554\) 26.8287 1.13984
\(555\) 2.16507 0.0919019
\(556\) −66.8127 −2.83349
\(557\) 6.86687 0.290958 0.145479 0.989361i \(-0.453528\pi\)
0.145479 + 0.989361i \(0.453528\pi\)
\(558\) 65.6228 2.77803
\(559\) 0.637843 0.0269779
\(560\) 10.6926 0.451844
\(561\) 12.3054 0.519535
\(562\) 20.9523 0.883818
\(563\) 1.08013 0.0455219 0.0227609 0.999741i \(-0.492754\pi\)
0.0227609 + 0.999741i \(0.492754\pi\)
\(564\) −2.06545 −0.0869713
\(565\) −7.46855 −0.314204
\(566\) −45.6849 −1.92028
\(567\) 14.4089 0.605117
\(568\) 6.57432 0.275852
\(569\) 3.84367 0.161135 0.0805676 0.996749i \(-0.474327\pi\)
0.0805676 + 0.996749i \(0.474327\pi\)
\(570\) 18.8375 0.789017
\(571\) 26.2993 1.10059 0.550295 0.834970i \(-0.314515\pi\)
0.550295 + 0.834970i \(0.314515\pi\)
\(572\) 67.8701 2.83779
\(573\) 8.35858 0.349185
\(574\) 4.80540 0.200574
\(575\) 9.32962 0.389072
\(576\) 27.3862 1.14109
\(577\) −39.9218 −1.66197 −0.830984 0.556296i \(-0.812222\pi\)
−0.830984 + 0.556296i \(0.812222\pi\)
\(578\) −97.2745 −4.04609
\(579\) 6.14644 0.255437
\(580\) −14.7818 −0.613780
\(581\) 2.74129 0.113728
\(582\) −6.29124 −0.260780
\(583\) 7.18937 0.297753
\(584\) 24.9818 1.03376
\(585\) −27.7881 −1.14889
\(586\) −70.8504 −2.92680
\(587\) −16.5921 −0.684828 −0.342414 0.939549i \(-0.611245\pi\)
−0.342414 + 0.939549i \(0.611245\pi\)
\(588\) 3.75920 0.155027
\(589\) 84.7458 3.49189
\(590\) −32.1690 −1.32438
\(591\) 14.3073 0.588523
\(592\) −6.43120 −0.264320
\(593\) 16.1580 0.663531 0.331765 0.943362i \(-0.392356\pi\)
0.331765 + 0.943362i \(0.392356\pi\)
\(594\) −22.2326 −0.912216
\(595\) −29.1272 −1.19410
\(596\) 15.4008 0.630842
\(597\) −4.94097 −0.202221
\(598\) 63.5442 2.59852
\(599\) −19.9373 −0.814615 −0.407308 0.913291i \(-0.633532\pi\)
−0.407308 + 0.913291i \(0.633532\pi\)
\(600\) −5.19742 −0.212184
\(601\) 23.1243 0.943260 0.471630 0.881796i \(-0.343666\pi\)
0.471630 + 0.881796i \(0.343666\pi\)
\(602\) −0.571095 −0.0232761
\(603\) −35.1898 −1.43304
\(604\) −3.24287 −0.131951
\(605\) −4.18661 −0.170210
\(606\) 8.07868 0.328174
\(607\) −26.8611 −1.09026 −0.545130 0.838352i \(-0.683520\pi\)
−0.545130 + 0.838352i \(0.683520\pi\)
\(608\) 16.0371 0.650389
\(609\) 2.94711 0.119423
\(610\) 0.482055 0.0195178
\(611\) 6.01130 0.243191
\(612\) 77.2577 3.12296
\(613\) 4.29756 0.173577 0.0867884 0.996227i \(-0.472340\pi\)
0.0867884 + 0.996227i \(0.472340\pi\)
\(614\) 8.66674 0.349761
\(615\) 0.818819 0.0330180
\(616\) −28.6970 −1.15623
\(617\) 38.2377 1.53939 0.769695 0.638411i \(-0.220408\pi\)
0.769695 + 0.638411i \(0.220408\pi\)
\(618\) 16.5758 0.666776
\(619\) −36.9349 −1.48454 −0.742270 0.670101i \(-0.766251\pi\)
−0.742270 + 0.670101i \(0.766251\pi\)
\(620\) 64.6451 2.59621
\(621\) −13.6249 −0.546749
\(622\) −52.5343 −2.10643
\(623\) 8.06358 0.323061
\(624\) −9.50466 −0.380491
\(625\) −9.45404 −0.378162
\(626\) −30.4638 −1.21758
\(627\) −13.5742 −0.542100
\(628\) −37.5535 −1.49855
\(629\) 17.5189 0.698526
\(630\) 24.8801 0.991248
\(631\) −20.1757 −0.803181 −0.401590 0.915819i \(-0.631542\pi\)
−0.401590 + 0.915819i \(0.631542\pi\)
\(632\) −13.9553 −0.555112
\(633\) 14.4056 0.572572
\(634\) −65.4838 −2.60069
\(635\) 1.96796 0.0780961
\(636\) −5.19750 −0.206094
\(637\) −10.9408 −0.433490
\(638\) 16.2732 0.644260
\(639\) 4.10731 0.162483
\(640\) 34.7600 1.37401
\(641\) 39.2156 1.54892 0.774462 0.632621i \(-0.218021\pi\)
0.774462 + 0.632621i \(0.218021\pi\)
\(642\) 10.6558 0.420551
\(643\) 40.4232 1.59414 0.797068 0.603889i \(-0.206383\pi\)
0.797068 + 0.603889i \(0.206383\pi\)
\(644\) −37.2405 −1.46748
\(645\) −0.0973120 −0.00383166
\(646\) 152.426 5.99714
\(647\) −27.6683 −1.08775 −0.543876 0.839165i \(-0.683044\pi\)
−0.543876 + 0.839165i \(0.683044\pi\)
\(648\) −27.1627 −1.06705
\(649\) 23.1808 0.909924
\(650\) 32.0315 1.25638
\(651\) −12.8886 −0.505143
\(652\) −35.1384 −1.37613
\(653\) −34.5177 −1.35078 −0.675390 0.737460i \(-0.736025\pi\)
−0.675390 + 0.737460i \(0.736025\pi\)
\(654\) 21.0352 0.822543
\(655\) 19.1999 0.750202
\(656\) −2.43225 −0.0949635
\(657\) 15.6074 0.608903
\(658\) −5.38224 −0.209821
\(659\) −23.8792 −0.930202 −0.465101 0.885258i \(-0.653982\pi\)
−0.465101 + 0.885258i \(0.653982\pi\)
\(660\) −10.3545 −0.403050
\(661\) −8.13565 −0.316440 −0.158220 0.987404i \(-0.550576\pi\)
−0.158220 + 0.987404i \(0.550576\pi\)
\(662\) −49.7438 −1.93335
\(663\) 25.8912 1.00553
\(664\) −5.16771 −0.200546
\(665\) 32.1304 1.24596
\(666\) −14.9645 −0.579862
\(667\) 9.97274 0.386146
\(668\) 52.3348 2.02489
\(669\) −12.8530 −0.496927
\(670\) −52.9605 −2.04604
\(671\) −0.347365 −0.0134099
\(672\) −2.43900 −0.0940865
\(673\) 1.53057 0.0589993 0.0294996 0.999565i \(-0.490609\pi\)
0.0294996 + 0.999565i \(0.490609\pi\)
\(674\) −18.9066 −0.728254
\(675\) −6.86807 −0.264352
\(676\) 93.5371 3.59758
\(677\) 9.94538 0.382232 0.191116 0.981567i \(-0.438789\pi\)
0.191116 + 0.981567i \(0.438789\pi\)
\(678\) −5.94408 −0.228281
\(679\) −10.7307 −0.411807
\(680\) 54.9087 2.10565
\(681\) 11.2027 0.429288
\(682\) −71.1672 −2.72513
\(683\) −48.6450 −1.86135 −0.930674 0.365849i \(-0.880779\pi\)
−0.930674 + 0.365849i \(0.880779\pi\)
\(684\) −85.2235 −3.25860
\(685\) 6.58383 0.251555
\(686\) 48.2694 1.84294
\(687\) −4.62269 −0.176367
\(688\) 0.289059 0.0110203
\(689\) 15.1268 0.576285
\(690\) −9.69457 −0.369066
\(691\) 36.2774 1.38006 0.690028 0.723783i \(-0.257598\pi\)
0.690028 + 0.723783i \(0.257598\pi\)
\(692\) −15.4922 −0.588926
\(693\) −17.9284 −0.681045
\(694\) 23.3782 0.887424
\(695\) −29.6663 −1.12531
\(696\) −5.55570 −0.210588
\(697\) 6.62559 0.250962
\(698\) −4.24452 −0.160657
\(699\) −0.793032 −0.0299952
\(700\) −18.7723 −0.709525
\(701\) −17.2324 −0.650857 −0.325429 0.945567i \(-0.605509\pi\)
−0.325429 + 0.945567i \(0.605509\pi\)
\(702\) −46.7786 −1.76554
\(703\) −19.3252 −0.728865
\(704\) −29.7001 −1.11936
\(705\) −0.917109 −0.0345403
\(706\) −6.38670 −0.240366
\(707\) 13.7795 0.518230
\(708\) −16.7583 −0.629817
\(709\) 33.8268 1.27039 0.635196 0.772351i \(-0.280920\pi\)
0.635196 + 0.772351i \(0.280920\pi\)
\(710\) 6.18148 0.231987
\(711\) −8.71857 −0.326972
\(712\) −15.2009 −0.569679
\(713\) −43.6137 −1.63335
\(714\) −23.1818 −0.867556
\(715\) 30.1359 1.12702
\(716\) −36.2755 −1.35568
\(717\) −16.2410 −0.606530
\(718\) −46.9882 −1.75358
\(719\) −12.0771 −0.450398 −0.225199 0.974313i \(-0.572303\pi\)
−0.225199 + 0.974313i \(0.572303\pi\)
\(720\) −12.5931 −0.469316
\(721\) 28.2727 1.05293
\(722\) −122.425 −4.55620
\(723\) 15.8307 0.588751
\(724\) −35.1681 −1.30701
\(725\) 5.02708 0.186701
\(726\) −3.33205 −0.123664
\(727\) −20.6823 −0.767065 −0.383533 0.923527i \(-0.625293\pi\)
−0.383533 + 0.923527i \(0.625293\pi\)
\(728\) −60.3799 −2.23783
\(729\) −11.6818 −0.432661
\(730\) 23.4891 0.869370
\(731\) −0.787414 −0.0291236
\(732\) 0.251125 0.00928185
\(733\) −8.93399 −0.329985 −0.164992 0.986295i \(-0.552760\pi\)
−0.164992 + 0.986295i \(0.552760\pi\)
\(734\) −48.8234 −1.80211
\(735\) 1.66917 0.0615683
\(736\) −8.25335 −0.304222
\(737\) 38.1630 1.40575
\(738\) −5.65951 −0.208329
\(739\) 44.9249 1.65259 0.826295 0.563237i \(-0.190444\pi\)
0.826295 + 0.563237i \(0.190444\pi\)
\(740\) −14.7415 −0.541909
\(741\) −28.5607 −1.04921
\(742\) −13.5438 −0.497210
\(743\) 52.5320 1.92721 0.963606 0.267327i \(-0.0861404\pi\)
0.963606 + 0.267327i \(0.0861404\pi\)
\(744\) 24.2967 0.890760
\(745\) 6.83831 0.250536
\(746\) 42.9700 1.57324
\(747\) −3.22852 −0.118126
\(748\) −83.7852 −3.06349
\(749\) 18.1752 0.664107
\(750\) −16.1541 −0.589864
\(751\) 50.4441 1.84073 0.920365 0.391059i \(-0.127891\pi\)
0.920365 + 0.391059i \(0.127891\pi\)
\(752\) 2.72422 0.0993419
\(753\) −3.88016 −0.141401
\(754\) 34.2395 1.24693
\(755\) −1.43991 −0.0524037
\(756\) 27.4149 0.997071
\(757\) −28.4695 −1.03474 −0.517371 0.855761i \(-0.673089\pi\)
−0.517371 + 0.855761i \(0.673089\pi\)
\(758\) −91.8025 −3.33442
\(759\) 6.98584 0.253570
\(760\) −60.5701 −2.19711
\(761\) −28.2130 −1.02272 −0.511361 0.859366i \(-0.670858\pi\)
−0.511361 + 0.859366i \(0.670858\pi\)
\(762\) 1.56626 0.0567397
\(763\) 35.8789 1.29890
\(764\) −56.9120 −2.05900
\(765\) 34.3042 1.24027
\(766\) −8.71094 −0.314739
\(767\) 48.7735 1.76111
\(768\) 16.3330 0.589368
\(769\) 18.4467 0.665205 0.332602 0.943067i \(-0.392073\pi\)
0.332602 + 0.943067i \(0.392073\pi\)
\(770\) −26.9822 −0.972372
\(771\) −2.99161 −0.107740
\(772\) −41.8499 −1.50621
\(773\) −32.3116 −1.16217 −0.581083 0.813844i \(-0.697371\pi\)
−0.581083 + 0.813844i \(0.697371\pi\)
\(774\) 0.672600 0.0241761
\(775\) −21.9849 −0.789720
\(776\) 20.2288 0.726173
\(777\) 2.93908 0.105439
\(778\) 11.5794 0.415143
\(779\) −7.30873 −0.261862
\(780\) −21.7865 −0.780081
\(781\) −4.45433 −0.159388
\(782\) −78.4450 −2.80519
\(783\) −7.34152 −0.262364
\(784\) −4.95817 −0.177078
\(785\) −16.6746 −0.595142
\(786\) 15.2808 0.545049
\(787\) 35.5540 1.26736 0.633682 0.773593i \(-0.281543\pi\)
0.633682 + 0.773593i \(0.281543\pi\)
\(788\) −97.4156 −3.47029
\(789\) 6.54999 0.233186
\(790\) −13.1214 −0.466839
\(791\) −10.1386 −0.360486
\(792\) 33.7975 1.20094
\(793\) −0.730875 −0.0259541
\(794\) 46.0624 1.63469
\(795\) −2.30781 −0.0818495
\(796\) 33.6421 1.19241
\(797\) −16.7698 −0.594017 −0.297009 0.954875i \(-0.595989\pi\)
−0.297009 + 0.954875i \(0.595989\pi\)
\(798\) 25.5720 0.905238
\(799\) −7.42092 −0.262533
\(800\) −4.16036 −0.147091
\(801\) −9.49679 −0.335552
\(802\) −80.0344 −2.82611
\(803\) −16.9261 −0.597308
\(804\) −27.5896 −0.973010
\(805\) −16.5356 −0.582805
\(806\) −149.739 −5.27435
\(807\) −5.63277 −0.198283
\(808\) −25.9762 −0.913838
\(809\) 50.1650 1.76371 0.881855 0.471521i \(-0.156295\pi\)
0.881855 + 0.471521i \(0.156295\pi\)
\(810\) −25.5396 −0.897372
\(811\) −33.2954 −1.16916 −0.584579 0.811337i \(-0.698740\pi\)
−0.584579 + 0.811337i \(0.698740\pi\)
\(812\) −20.0663 −0.704189
\(813\) 8.57560 0.300759
\(814\) 16.2288 0.568820
\(815\) −15.6022 −0.546523
\(816\) 11.7334 0.410753
\(817\) 0.868601 0.0303885
\(818\) −56.0875 −1.96106
\(819\) −37.7223 −1.31813
\(820\) −5.57518 −0.194694
\(821\) −27.9620 −0.975881 −0.487940 0.872877i \(-0.662252\pi\)
−0.487940 + 0.872877i \(0.662252\pi\)
\(822\) 5.23994 0.182764
\(823\) 19.1976 0.669186 0.334593 0.942363i \(-0.391401\pi\)
0.334593 + 0.942363i \(0.391401\pi\)
\(824\) −53.2978 −1.85672
\(825\) 3.52143 0.122601
\(826\) −43.6695 −1.51946
\(827\) 5.55876 0.193297 0.0966484 0.995319i \(-0.469188\pi\)
0.0966484 + 0.995319i \(0.469188\pi\)
\(828\) 43.8596 1.52423
\(829\) 10.1057 0.350986 0.175493 0.984481i \(-0.443848\pi\)
0.175493 + 0.984481i \(0.443848\pi\)
\(830\) −4.85892 −0.168656
\(831\) 6.20581 0.215277
\(832\) −62.4905 −2.16647
\(833\) 13.5063 0.467967
\(834\) −23.6109 −0.817578
\(835\) 23.2378 0.804179
\(836\) 92.4240 3.19655
\(837\) 32.1066 1.10977
\(838\) −65.0284 −2.24637
\(839\) −24.7698 −0.855148 −0.427574 0.903980i \(-0.640632\pi\)
−0.427574 + 0.903980i \(0.640632\pi\)
\(840\) 9.21181 0.317838
\(841\) −23.6264 −0.814703
\(842\) 17.6029 0.606637
\(843\) 4.84651 0.166923
\(844\) −98.0850 −3.37623
\(845\) 41.5326 1.42877
\(846\) 6.33887 0.217935
\(847\) −5.68334 −0.195282
\(848\) 6.85520 0.235409
\(849\) −10.5675 −0.362675
\(850\) −39.5427 −1.35630
\(851\) 9.94558 0.340930
\(852\) 3.22022 0.110323
\(853\) −30.9842 −1.06088 −0.530439 0.847723i \(-0.677973\pi\)
−0.530439 + 0.847723i \(0.677973\pi\)
\(854\) 0.654391 0.0223928
\(855\) −37.8412 −1.29414
\(856\) −34.2627 −1.17107
\(857\) −47.2147 −1.61282 −0.806412 0.591354i \(-0.798594\pi\)
−0.806412 + 0.591354i \(0.798594\pi\)
\(858\) 23.9846 0.818819
\(859\) 20.1118 0.686206 0.343103 0.939298i \(-0.388522\pi\)
0.343103 + 0.939298i \(0.388522\pi\)
\(860\) 0.662579 0.0225938
\(861\) 1.11155 0.0378815
\(862\) 5.34290 0.181980
\(863\) 7.46998 0.254281 0.127141 0.991885i \(-0.459420\pi\)
0.127141 + 0.991885i \(0.459420\pi\)
\(864\) 6.07577 0.206702
\(865\) −6.87890 −0.233889
\(866\) 6.94401 0.235967
\(867\) −22.5008 −0.764167
\(868\) 87.7558 2.97863
\(869\) 9.45520 0.320746
\(870\) −5.22373 −0.177101
\(871\) 80.2968 2.72075
\(872\) −67.6366 −2.29047
\(873\) 12.6380 0.427730
\(874\) 86.5331 2.92703
\(875\) −27.5534 −0.931474
\(876\) 12.2366 0.413435
\(877\) 16.7380 0.565201 0.282600 0.959238i \(-0.408803\pi\)
0.282600 + 0.959238i \(0.408803\pi\)
\(878\) −11.1132 −0.375052
\(879\) −16.3886 −0.552773
\(880\) 13.6570 0.460379
\(881\) −53.0385 −1.78691 −0.893455 0.449152i \(-0.851726\pi\)
−0.893455 + 0.449152i \(0.851726\pi\)
\(882\) −11.5370 −0.388470
\(883\) 11.5588 0.388983 0.194492 0.980904i \(-0.437694\pi\)
0.194492 + 0.980904i \(0.437694\pi\)
\(884\) −176.288 −5.92922
\(885\) −7.44109 −0.250129
\(886\) 29.0362 0.975490
\(887\) 45.4621 1.52647 0.763235 0.646121i \(-0.223610\pi\)
0.763235 + 0.646121i \(0.223610\pi\)
\(888\) −5.54056 −0.185929
\(889\) 2.67151 0.0895996
\(890\) −14.2926 −0.479090
\(891\) 18.4037 0.616546
\(892\) 87.5138 2.93018
\(893\) 8.18606 0.273936
\(894\) 5.44248 0.182024
\(895\) −16.1071 −0.538402
\(896\) 47.1867 1.57640
\(897\) 14.6986 0.490770
\(898\) 73.9877 2.46900
\(899\) −23.5004 −0.783781
\(900\) 22.1088 0.736960
\(901\) −18.6739 −0.622119
\(902\) 6.13767 0.204362
\(903\) −0.132101 −0.00439605
\(904\) 19.1126 0.635675
\(905\) −15.6155 −0.519075
\(906\) −1.14600 −0.0380732
\(907\) 16.5695 0.550182 0.275091 0.961418i \(-0.411292\pi\)
0.275091 + 0.961418i \(0.411292\pi\)
\(908\) −76.2769 −2.53134
\(909\) −16.2286 −0.538269
\(910\) −56.7720 −1.88197
\(911\) 23.4779 0.777857 0.388928 0.921268i \(-0.372845\pi\)
0.388928 + 0.921268i \(0.372845\pi\)
\(912\) −12.9432 −0.428593
\(913\) 3.50130 0.115876
\(914\) −0.883924 −0.0292376
\(915\) 0.111505 0.00368625
\(916\) 31.4750 1.03996
\(917\) 26.0639 0.860705
\(918\) 57.7479 1.90597
\(919\) 53.7691 1.77368 0.886839 0.462079i \(-0.152896\pi\)
0.886839 + 0.462079i \(0.152896\pi\)
\(920\) 31.1719 1.02771
\(921\) 2.00472 0.0660578
\(922\) 43.0088 1.41642
\(923\) −9.37213 −0.308488
\(924\) −14.0563 −0.462419
\(925\) 5.01338 0.164839
\(926\) 47.9360 1.57528
\(927\) −33.2978 −1.09364
\(928\) −4.44715 −0.145985
\(929\) 32.5623 1.06833 0.534167 0.845379i \(-0.320625\pi\)
0.534167 + 0.845379i \(0.320625\pi\)
\(930\) 22.8449 0.749113
\(931\) −14.8989 −0.488292
\(932\) 5.39960 0.176870
\(933\) −12.1518 −0.397833
\(934\) 40.4180 1.32252
\(935\) −37.2025 −1.21665
\(936\) 71.1117 2.32436
\(937\) −46.1034 −1.50613 −0.753066 0.657945i \(-0.771426\pi\)
−0.753066 + 0.657945i \(0.771426\pi\)
\(938\) −71.8940 −2.34742
\(939\) −7.04665 −0.229959
\(940\) 6.24442 0.203671
\(941\) 6.64359 0.216575 0.108287 0.994120i \(-0.465463\pi\)
0.108287 + 0.994120i \(0.465463\pi\)
\(942\) −13.2710 −0.432392
\(943\) 3.76138 0.122487
\(944\) 22.1033 0.719401
\(945\) 12.1728 0.395983
\(946\) −0.729428 −0.0237157
\(947\) 8.65510 0.281253 0.140627 0.990063i \(-0.455088\pi\)
0.140627 + 0.990063i \(0.455088\pi\)
\(948\) −6.83556 −0.222009
\(949\) −35.6133 −1.15606
\(950\) 43.6198 1.41521
\(951\) −15.1472 −0.491182
\(952\) 74.5386 2.41581
\(953\) 30.0422 0.973161 0.486581 0.873636i \(-0.338244\pi\)
0.486581 + 0.873636i \(0.338244\pi\)
\(954\) 15.9511 0.516435
\(955\) −25.2702 −0.817725
\(956\) 110.582 3.57646
\(957\) 3.76418 0.121679
\(958\) −42.1402 −1.36149
\(959\) 8.93756 0.288609
\(960\) 9.53380 0.307702
\(961\) 71.7740 2.31529
\(962\) 34.1463 1.10092
\(963\) −21.4056 −0.689786
\(964\) −107.788 −3.47163
\(965\) −18.5823 −0.598186
\(966\) −13.1604 −0.423429
\(967\) −49.5192 −1.59243 −0.796215 0.605014i \(-0.793167\pi\)
−0.796215 + 0.605014i \(0.793167\pi\)
\(968\) 10.7139 0.344356
\(969\) 35.2581 1.13265
\(970\) 19.0201 0.610698
\(971\) −41.5437 −1.33320 −0.666601 0.745415i \(-0.732251\pi\)
−0.666601 + 0.745415i \(0.732251\pi\)
\(972\) −49.3102 −1.58163
\(973\) −40.2721 −1.29106
\(974\) 49.8803 1.59827
\(975\) 7.40927 0.237287
\(976\) −0.331220 −0.0106021
\(977\) 37.0902 1.18662 0.593310 0.804974i \(-0.297821\pi\)
0.593310 + 0.804974i \(0.297821\pi\)
\(978\) −12.4175 −0.397069
\(979\) 10.2992 0.329163
\(980\) −11.3651 −0.363044
\(981\) −42.2560 −1.34913
\(982\) −47.8231 −1.52610
\(983\) −38.8827 −1.24016 −0.620082 0.784537i \(-0.712901\pi\)
−0.620082 + 0.784537i \(0.712901\pi\)
\(984\) −2.09542 −0.0667995
\(985\) −43.2547 −1.37821
\(986\) −42.2685 −1.34610
\(987\) −1.24498 −0.0396281
\(988\) 194.465 6.18675
\(989\) −0.447018 −0.0142144
\(990\) 31.7780 1.00997
\(991\) −55.1144 −1.75077 −0.875383 0.483430i \(-0.839391\pi\)
−0.875383 + 0.483430i \(0.839391\pi\)
\(992\) 19.4487 0.617497
\(993\) −11.5064 −0.365143
\(994\) 8.39137 0.266158
\(995\) 14.9379 0.473563
\(996\) −2.53124 −0.0802053
\(997\) −5.89602 −0.186729 −0.0933644 0.995632i \(-0.529762\pi\)
−0.0933644 + 0.995632i \(0.529762\pi\)
\(998\) 19.5549 0.618999
\(999\) −7.32152 −0.231643
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 \(a_p\))