Properties

Label 4033.2.a.d.1.20
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.74629 q^{2}\) \(+2.61915 q^{3}\) \(+1.04954 q^{4}\) \(-0.0450252 q^{5}\) \(-4.57381 q^{6}\) \(-1.64580 q^{7}\) \(+1.65978 q^{8}\) \(+3.85995 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.74629 q^{2}\) \(+2.61915 q^{3}\) \(+1.04954 q^{4}\) \(-0.0450252 q^{5}\) \(-4.57381 q^{6}\) \(-1.64580 q^{7}\) \(+1.65978 q^{8}\) \(+3.85995 q^{9}\) \(+0.0786272 q^{10}\) \(-1.43541 q^{11}\) \(+2.74891 q^{12}\) \(+2.18651 q^{13}\) \(+2.87405 q^{14}\) \(-0.117928 q^{15}\) \(-4.99755 q^{16}\) \(-4.11109 q^{17}\) \(-6.74060 q^{18}\) \(-7.92373 q^{19}\) \(-0.0472559 q^{20}\) \(-4.31060 q^{21}\) \(+2.50665 q^{22}\) \(+8.12033 q^{23}\) \(+4.34720 q^{24}\) \(-4.99797 q^{25}\) \(-3.81830 q^{26}\) \(+2.25233 q^{27}\) \(-1.72734 q^{28}\) \(+5.25757 q^{29}\) \(+0.205936 q^{30}\) \(+8.11228 q^{31}\) \(+5.40763 q^{32}\) \(-3.75956 q^{33}\) \(+7.17917 q^{34}\) \(+0.0741025 q^{35}\) \(+4.05118 q^{36}\) \(-1.00000 q^{37}\) \(+13.8372 q^{38}\) \(+5.72680 q^{39}\) \(-0.0747317 q^{40}\) \(-3.25013 q^{41}\) \(+7.52758 q^{42}\) \(-1.02152 q^{43}\) \(-1.50653 q^{44}\) \(-0.173795 q^{45}\) \(-14.1805 q^{46}\) \(+0.633654 q^{47}\) \(-13.0893 q^{48}\) \(-4.29134 q^{49}\) \(+8.72793 q^{50}\) \(-10.7676 q^{51}\) \(+2.29484 q^{52}\) \(-8.79066 q^{53}\) \(-3.93323 q^{54}\) \(+0.0646297 q^{55}\) \(-2.73166 q^{56}\) \(-20.7534 q^{57}\) \(-9.18126 q^{58}\) \(-7.03026 q^{59}\) \(-0.123770 q^{60}\) \(-7.72486 q^{61}\) \(-14.1664 q^{62}\) \(-6.35271 q^{63}\) \(+0.551770 q^{64}\) \(-0.0984481 q^{65}\) \(+6.56530 q^{66}\) \(-13.4734 q^{67}\) \(-4.31477 q^{68}\) \(+21.2684 q^{69}\) \(-0.129405 q^{70}\) \(+10.3308 q^{71}\) \(+6.40665 q^{72}\) \(+9.59743 q^{73}\) \(+1.74629 q^{74}\) \(-13.0904 q^{75}\) \(-8.31630 q^{76}\) \(+2.36241 q^{77}\) \(-10.0007 q^{78}\) \(+9.98476 q^{79}\) \(+0.225015 q^{80}\) \(-5.68065 q^{81}\) \(+5.67568 q^{82}\) \(-1.30660 q^{83}\) \(-4.52417 q^{84}\) \(+0.185102 q^{85}\) \(+1.78387 q^{86}\) \(+13.7704 q^{87}\) \(-2.38246 q^{88}\) \(-7.22191 q^{89}\) \(+0.303497 q^{90}\) \(-3.59857 q^{91}\) \(+8.52264 q^{92}\) \(+21.2473 q^{93}\) \(-1.10655 q^{94}\) \(+0.356767 q^{95}\) \(+14.1634 q^{96}\) \(-9.33511 q^{97}\) \(+7.49394 q^{98}\) \(-5.54062 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.74629 −1.23482 −0.617408 0.786643i \(-0.711817\pi\)
−0.617408 + 0.786643i \(0.711817\pi\)
\(3\) 2.61915 1.51217 0.756083 0.654475i \(-0.227110\pi\)
0.756083 + 0.654475i \(0.227110\pi\)
\(4\) 1.04954 0.524772
\(5\) −0.0450252 −0.0201359 −0.0100679 0.999949i \(-0.503205\pi\)
−0.0100679 + 0.999949i \(0.503205\pi\)
\(6\) −4.57381 −1.86725
\(7\) −1.64580 −0.622055 −0.311027 0.950401i \(-0.600673\pi\)
−0.311027 + 0.950401i \(0.600673\pi\)
\(8\) 1.65978 0.586819
\(9\) 3.85995 1.28665
\(10\) 0.0786272 0.0248641
\(11\) −1.43541 −0.432793 −0.216397 0.976306i \(-0.569430\pi\)
−0.216397 + 0.976306i \(0.569430\pi\)
\(12\) 2.74891 0.793543
\(13\) 2.18651 0.606430 0.303215 0.952922i \(-0.401940\pi\)
0.303215 + 0.952922i \(0.401940\pi\)
\(14\) 2.87405 0.768123
\(15\) −0.117928 −0.0304488
\(16\) −4.99755 −1.24939
\(17\) −4.11109 −0.997085 −0.498542 0.866865i \(-0.666131\pi\)
−0.498542 + 0.866865i \(0.666131\pi\)
\(18\) −6.74060 −1.58878
\(19\) −7.92373 −1.81783 −0.908914 0.416983i \(-0.863087\pi\)
−0.908914 + 0.416983i \(0.863087\pi\)
\(20\) −0.0472559 −0.0105667
\(21\) −4.31060 −0.940651
\(22\) 2.50665 0.534420
\(23\) 8.12033 1.69321 0.846603 0.532225i \(-0.178644\pi\)
0.846603 + 0.532225i \(0.178644\pi\)
\(24\) 4.34720 0.887369
\(25\) −4.99797 −0.999595
\(26\) −3.81830 −0.748829
\(27\) 2.25233 0.433461
\(28\) −1.72734 −0.326437
\(29\) 5.25757 0.976306 0.488153 0.872758i \(-0.337671\pi\)
0.488153 + 0.872758i \(0.337671\pi\)
\(30\) 0.205936 0.0375987
\(31\) 8.11228 1.45701 0.728504 0.685041i \(-0.240216\pi\)
0.728504 + 0.685041i \(0.240216\pi\)
\(32\) 5.40763 0.955944
\(33\) −3.75956 −0.654456
\(34\) 7.17917 1.23122
\(35\) 0.0741025 0.0125256
\(36\) 4.05118 0.675197
\(37\) −1.00000 −0.164399
\(38\) 13.8372 2.24468
\(39\) 5.72680 0.917023
\(40\) −0.0747317 −0.0118161
\(41\) −3.25013 −0.507584 −0.253792 0.967259i \(-0.581678\pi\)
−0.253792 + 0.967259i \(0.581678\pi\)
\(42\) 7.52758 1.16153
\(43\) −1.02152 −0.155780 −0.0778899 0.996962i \(-0.524818\pi\)
−0.0778899 + 0.996962i \(0.524818\pi\)
\(44\) −1.50653 −0.227118
\(45\) −0.173795 −0.0259078
\(46\) −14.1805 −2.09080
\(47\) 0.633654 0.0924279 0.0462140 0.998932i \(-0.485284\pi\)
0.0462140 + 0.998932i \(0.485284\pi\)
\(48\) −13.0893 −1.88928
\(49\) −4.29134 −0.613048
\(50\) 8.72793 1.23432
\(51\) −10.7676 −1.50776
\(52\) 2.29484 0.318237
\(53\) −8.79066 −1.20749 −0.603745 0.797178i \(-0.706325\pi\)
−0.603745 + 0.797178i \(0.706325\pi\)
\(54\) −3.93323 −0.535245
\(55\) 0.0646297 0.00871467
\(56\) −2.73166 −0.365034
\(57\) −20.7534 −2.74886
\(58\) −9.18126 −1.20556
\(59\) −7.03026 −0.915262 −0.457631 0.889142i \(-0.651302\pi\)
−0.457631 + 0.889142i \(0.651302\pi\)
\(60\) −0.123770 −0.0159787
\(61\) −7.72486 −0.989067 −0.494534 0.869158i \(-0.664661\pi\)
−0.494534 + 0.869158i \(0.664661\pi\)
\(62\) −14.1664 −1.79914
\(63\) −6.35271 −0.800366
\(64\) 0.551770 0.0689712
\(65\) −0.0984481 −0.0122110
\(66\) 6.56530 0.808133
\(67\) −13.4734 −1.64603 −0.823017 0.568017i \(-0.807711\pi\)
−0.823017 + 0.568017i \(0.807711\pi\)
\(68\) −4.31477 −0.523242
\(69\) 21.2684 2.56041
\(70\) −0.129405 −0.0154668
\(71\) 10.3308 1.22604 0.613019 0.790068i \(-0.289955\pi\)
0.613019 + 0.790068i \(0.289955\pi\)
\(72\) 6.40665 0.755030
\(73\) 9.59743 1.12329 0.561647 0.827377i \(-0.310168\pi\)
0.561647 + 0.827377i \(0.310168\pi\)
\(74\) 1.74629 0.203003
\(75\) −13.0904 −1.51155
\(76\) −8.31630 −0.953946
\(77\) 2.36241 0.269221
\(78\) −10.0007 −1.13235
\(79\) 9.98476 1.12337 0.561686 0.827350i \(-0.310153\pi\)
0.561686 + 0.827350i \(0.310153\pi\)
\(80\) 0.225015 0.0251575
\(81\) −5.68065 −0.631184
\(82\) 5.67568 0.626774
\(83\) −1.30660 −0.143418 −0.0717092 0.997426i \(-0.522845\pi\)
−0.0717092 + 0.997426i \(0.522845\pi\)
\(84\) −4.52417 −0.493627
\(85\) 0.185102 0.0200772
\(86\) 1.78387 0.192359
\(87\) 13.7704 1.47634
\(88\) −2.38246 −0.253972
\(89\) −7.22191 −0.765521 −0.382761 0.923848i \(-0.625027\pi\)
−0.382761 + 0.923848i \(0.625027\pi\)
\(90\) 0.303497 0.0319914
\(91\) −3.59857 −0.377232
\(92\) 8.52264 0.888547
\(93\) 21.2473 2.20324
\(94\) −1.10655 −0.114132
\(95\) 0.356767 0.0366035
\(96\) 14.1634 1.44555
\(97\) −9.33511 −0.947837 −0.473919 0.880569i \(-0.657161\pi\)
−0.473919 + 0.880569i \(0.657161\pi\)
\(98\) 7.49394 0.757002
\(99\) −5.54062 −0.556853
\(100\) −5.24559 −0.524559
\(101\) −15.6227 −1.55451 −0.777257 0.629183i \(-0.783390\pi\)
−0.777257 + 0.629183i \(0.783390\pi\)
\(102\) 18.8033 1.86181
\(103\) −10.9414 −1.07809 −0.539047 0.842276i \(-0.681215\pi\)
−0.539047 + 0.842276i \(0.681215\pi\)
\(104\) 3.62912 0.355865
\(105\) 0.194086 0.0189408
\(106\) 15.3511 1.49103
\(107\) 5.70963 0.551970 0.275985 0.961162i \(-0.410996\pi\)
0.275985 + 0.961162i \(0.410996\pi\)
\(108\) 2.36392 0.227468
\(109\) −1.00000 −0.0957826
\(110\) −0.112862 −0.0107610
\(111\) −2.61915 −0.248599
\(112\) 8.22497 0.777187
\(113\) −11.1040 −1.04457 −0.522287 0.852770i \(-0.674921\pi\)
−0.522287 + 0.852770i \(0.674921\pi\)
\(114\) 36.2416 3.39434
\(115\) −0.365619 −0.0340942
\(116\) 5.51805 0.512338
\(117\) 8.43982 0.780262
\(118\) 12.2769 1.13018
\(119\) 6.76603 0.620241
\(120\) −0.195733 −0.0178679
\(121\) −8.93959 −0.812690
\(122\) 13.4899 1.22132
\(123\) −8.51257 −0.767552
\(124\) 8.51420 0.764597
\(125\) 0.450160 0.0402636
\(126\) 11.0937 0.988305
\(127\) 11.1808 0.992137 0.496069 0.868283i \(-0.334776\pi\)
0.496069 + 0.868283i \(0.334776\pi\)
\(128\) −11.7788 −1.04111
\(129\) −2.67550 −0.235565
\(130\) 0.171919 0.0150783
\(131\) −3.46874 −0.303065 −0.151532 0.988452i \(-0.548421\pi\)
−0.151532 + 0.988452i \(0.548421\pi\)
\(132\) −3.94583 −0.343440
\(133\) 13.0409 1.13079
\(134\) 23.5285 2.03255
\(135\) −0.101411 −0.00872811
\(136\) −6.82348 −0.585109
\(137\) 2.12643 0.181673 0.0908365 0.995866i \(-0.471046\pi\)
0.0908365 + 0.995866i \(0.471046\pi\)
\(138\) −37.1408 −3.16164
\(139\) 6.19785 0.525695 0.262847 0.964837i \(-0.415338\pi\)
0.262847 + 0.964837i \(0.415338\pi\)
\(140\) 0.0777738 0.00657309
\(141\) 1.65963 0.139766
\(142\) −18.0406 −1.51393
\(143\) −3.13855 −0.262459
\(144\) −19.2903 −1.60752
\(145\) −0.236723 −0.0196588
\(146\) −16.7599 −1.38706
\(147\) −11.2397 −0.927031
\(148\) −1.04954 −0.0862720
\(149\) −18.8125 −1.54118 −0.770590 0.637332i \(-0.780038\pi\)
−0.770590 + 0.637332i \(0.780038\pi\)
\(150\) 22.8598 1.86649
\(151\) 20.4681 1.66567 0.832836 0.553520i \(-0.186716\pi\)
0.832836 + 0.553520i \(0.186716\pi\)
\(152\) −13.1516 −1.06674
\(153\) −15.8686 −1.28290
\(154\) −4.12546 −0.332439
\(155\) −0.365257 −0.0293381
\(156\) 6.01053 0.481228
\(157\) −10.5586 −0.842669 −0.421334 0.906905i \(-0.638438\pi\)
−0.421334 + 0.906905i \(0.638438\pi\)
\(158\) −17.4363 −1.38716
\(159\) −23.0241 −1.82593
\(160\) −0.243480 −0.0192487
\(161\) −13.3645 −1.05327
\(162\) 9.92009 0.779396
\(163\) 16.3370 1.27961 0.639805 0.768538i \(-0.279015\pi\)
0.639805 + 0.768538i \(0.279015\pi\)
\(164\) −3.41115 −0.266366
\(165\) 0.169275 0.0131780
\(166\) 2.28171 0.177095
\(167\) −19.4715 −1.50675 −0.753375 0.657591i \(-0.771576\pi\)
−0.753375 + 0.657591i \(0.771576\pi\)
\(168\) −7.15463 −0.551992
\(169\) −8.21916 −0.632243
\(170\) −0.323243 −0.0247916
\(171\) −30.5852 −2.33891
\(172\) −1.07213 −0.0817489
\(173\) 15.2285 1.15780 0.578899 0.815399i \(-0.303483\pi\)
0.578899 + 0.815399i \(0.303483\pi\)
\(174\) −24.0471 −1.82301
\(175\) 8.22567 0.621802
\(176\) 7.17354 0.540726
\(177\) −18.4133 −1.38403
\(178\) 12.6116 0.945278
\(179\) −15.7451 −1.17685 −0.588423 0.808553i \(-0.700251\pi\)
−0.588423 + 0.808553i \(0.700251\pi\)
\(180\) −0.182405 −0.0135957
\(181\) −15.8223 −1.17606 −0.588032 0.808838i \(-0.700097\pi\)
−0.588032 + 0.808838i \(0.700097\pi\)
\(182\) 6.28416 0.465813
\(183\) −20.2326 −1.49564
\(184\) 13.4779 0.993606
\(185\) 0.0450252 0.00331032
\(186\) −37.1040 −2.72060
\(187\) 5.90111 0.431532
\(188\) 0.665048 0.0485036
\(189\) −3.70689 −0.269636
\(190\) −0.623021 −0.0451987
\(191\) −9.93374 −0.718780 −0.359390 0.933187i \(-0.617015\pi\)
−0.359390 + 0.933187i \(0.617015\pi\)
\(192\) 1.44517 0.104296
\(193\) 3.50234 0.252104 0.126052 0.992024i \(-0.459769\pi\)
0.126052 + 0.992024i \(0.459769\pi\)
\(194\) 16.3019 1.17041
\(195\) −0.257850 −0.0184650
\(196\) −4.50395 −0.321710
\(197\) 18.6570 1.32926 0.664630 0.747173i \(-0.268589\pi\)
0.664630 + 0.747173i \(0.268589\pi\)
\(198\) 9.67555 0.687612
\(199\) −5.26760 −0.373410 −0.186705 0.982416i \(-0.559781\pi\)
−0.186705 + 0.982416i \(0.559781\pi\)
\(200\) −8.29551 −0.586581
\(201\) −35.2888 −2.48908
\(202\) 27.2818 1.91954
\(203\) −8.65292 −0.607316
\(204\) −11.3010 −0.791230
\(205\) 0.146337 0.0102206
\(206\) 19.1070 1.33125
\(207\) 31.3440 2.17856
\(208\) −10.9272 −0.757665
\(209\) 11.3738 0.786744
\(210\) −0.338930 −0.0233884
\(211\) −14.0681 −0.968491 −0.484245 0.874932i \(-0.660906\pi\)
−0.484245 + 0.874932i \(0.660906\pi\)
\(212\) −9.22618 −0.633657
\(213\) 27.0579 1.85398
\(214\) −9.97069 −0.681582
\(215\) 0.0459939 0.00313676
\(216\) 3.73836 0.254363
\(217\) −13.3512 −0.906339
\(218\) 1.74629 0.118274
\(219\) 25.1371 1.69861
\(220\) 0.0678317 0.00457321
\(221\) −8.98894 −0.604662
\(222\) 4.57381 0.306974
\(223\) −5.17280 −0.346397 −0.173198 0.984887i \(-0.555410\pi\)
−0.173198 + 0.984887i \(0.555410\pi\)
\(224\) −8.89990 −0.594649
\(225\) −19.2919 −1.28613
\(226\) 19.3908 1.28986
\(227\) 22.4132 1.48762 0.743809 0.668392i \(-0.233017\pi\)
0.743809 + 0.668392i \(0.233017\pi\)
\(228\) −21.7816 −1.44252
\(229\) 21.2559 1.40463 0.702313 0.711868i \(-0.252151\pi\)
0.702313 + 0.711868i \(0.252151\pi\)
\(230\) 0.638479 0.0421000
\(231\) 6.18750 0.407107
\(232\) 8.72638 0.572915
\(233\) 28.4334 1.86274 0.931368 0.364079i \(-0.118616\pi\)
0.931368 + 0.364079i \(0.118616\pi\)
\(234\) −14.7384 −0.963480
\(235\) −0.0285304 −0.00186112
\(236\) −7.37857 −0.480304
\(237\) 26.1516 1.69873
\(238\) −11.8155 −0.765884
\(239\) −10.4662 −0.677002 −0.338501 0.940966i \(-0.609920\pi\)
−0.338501 + 0.940966i \(0.609920\pi\)
\(240\) 0.589349 0.0380423
\(241\) −4.50370 −0.290109 −0.145054 0.989424i \(-0.546336\pi\)
−0.145054 + 0.989424i \(0.546336\pi\)
\(242\) 15.6112 1.00352
\(243\) −21.6355 −1.38792
\(244\) −8.10759 −0.519035
\(245\) 0.193218 0.0123442
\(246\) 14.8654 0.947786
\(247\) −17.3253 −1.10238
\(248\) 13.4646 0.855001
\(249\) −3.42219 −0.216872
\(250\) −0.786112 −0.0497181
\(251\) −0.600811 −0.0379229 −0.0189614 0.999820i \(-0.506036\pi\)
−0.0189614 + 0.999820i \(0.506036\pi\)
\(252\) −6.66745 −0.420010
\(253\) −11.6560 −0.732808
\(254\) −19.5250 −1.22511
\(255\) 0.484811 0.0303600
\(256\) 19.4657 1.21661
\(257\) −20.0350 −1.24975 −0.624876 0.780724i \(-0.714850\pi\)
−0.624876 + 0.780724i \(0.714850\pi\)
\(258\) 4.67222 0.290880
\(259\) 1.64580 0.102265
\(260\) −0.103326 −0.00640798
\(261\) 20.2939 1.25616
\(262\) 6.05743 0.374230
\(263\) −9.89890 −0.610392 −0.305196 0.952290i \(-0.598722\pi\)
−0.305196 + 0.952290i \(0.598722\pi\)
\(264\) −6.24003 −0.384047
\(265\) 0.395801 0.0243138
\(266\) −22.7732 −1.39632
\(267\) −18.9153 −1.15760
\(268\) −14.1409 −0.863793
\(269\) 15.2630 0.930600 0.465300 0.885153i \(-0.345946\pi\)
0.465300 + 0.885153i \(0.345946\pi\)
\(270\) 0.177094 0.0107776
\(271\) −10.8655 −0.660030 −0.330015 0.943976i \(-0.607054\pi\)
−0.330015 + 0.943976i \(0.607054\pi\)
\(272\) 20.5453 1.24574
\(273\) −9.42519 −0.570438
\(274\) −3.71337 −0.224333
\(275\) 7.17416 0.432618
\(276\) 22.3221 1.34363
\(277\) 12.3196 0.740213 0.370106 0.928989i \(-0.379321\pi\)
0.370106 + 0.928989i \(0.379321\pi\)
\(278\) −10.8233 −0.649136
\(279\) 31.3130 1.87466
\(280\) 0.122994 0.00735027
\(281\) −2.82215 −0.168356 −0.0841778 0.996451i \(-0.526826\pi\)
−0.0841778 + 0.996451i \(0.526826\pi\)
\(282\) −2.89821 −0.172586
\(283\) 13.7311 0.816229 0.408114 0.912931i \(-0.366186\pi\)
0.408114 + 0.912931i \(0.366186\pi\)
\(284\) 10.8426 0.643391
\(285\) 0.934427 0.0553507
\(286\) 5.48083 0.324088
\(287\) 5.34906 0.315745
\(288\) 20.8732 1.22996
\(289\) −0.0989699 −0.00582176
\(290\) 0.413388 0.0242750
\(291\) −24.4501 −1.43329
\(292\) 10.0729 0.589473
\(293\) −15.6542 −0.914531 −0.457265 0.889330i \(-0.651171\pi\)
−0.457265 + 0.889330i \(0.651171\pi\)
\(294\) 19.6277 1.14471
\(295\) 0.316539 0.0184296
\(296\) −1.65978 −0.0964725
\(297\) −3.23302 −0.187599
\(298\) 32.8521 1.90307
\(299\) 17.7552 1.02681
\(300\) −13.7390 −0.793221
\(301\) 1.68121 0.0969035
\(302\) −35.7434 −2.05680
\(303\) −40.9181 −2.35069
\(304\) 39.5992 2.27117
\(305\) 0.347813 0.0199157
\(306\) 27.7112 1.58414
\(307\) 29.6010 1.68942 0.844709 0.535226i \(-0.179773\pi\)
0.844709 + 0.535226i \(0.179773\pi\)
\(308\) 2.47945 0.141280
\(309\) −28.6573 −1.63026
\(310\) 0.637846 0.0362272
\(311\) −31.4219 −1.78177 −0.890887 0.454225i \(-0.849916\pi\)
−0.890887 + 0.454225i \(0.849916\pi\)
\(312\) 9.50521 0.538127
\(313\) −27.4364 −1.55080 −0.775399 0.631472i \(-0.782451\pi\)
−0.775399 + 0.631472i \(0.782451\pi\)
\(314\) 18.4384 1.04054
\(315\) 0.286032 0.0161161
\(316\) 10.4794 0.589515
\(317\) −4.18255 −0.234915 −0.117458 0.993078i \(-0.537474\pi\)
−0.117458 + 0.993078i \(0.537474\pi\)
\(318\) 40.2068 2.25468
\(319\) −7.54678 −0.422539
\(320\) −0.0248435 −0.00138880
\(321\) 14.9544 0.834672
\(322\) 23.3383 1.30059
\(323\) 32.5751 1.81253
\(324\) −5.96209 −0.331227
\(325\) −10.9281 −0.606184
\(326\) −28.5291 −1.58008
\(327\) −2.61915 −0.144839
\(328\) −5.39448 −0.297860
\(329\) −1.04287 −0.0574952
\(330\) −0.295604 −0.0162725
\(331\) −25.3147 −1.39142 −0.695710 0.718322i \(-0.744910\pi\)
−0.695710 + 0.718322i \(0.744910\pi\)
\(332\) −1.37134 −0.0752619
\(333\) −3.85995 −0.211524
\(334\) 34.0030 1.86056
\(335\) 0.606641 0.0331443
\(336\) 21.5424 1.17524
\(337\) 14.7711 0.804636 0.402318 0.915500i \(-0.368205\pi\)
0.402318 + 0.915500i \(0.368205\pi\)
\(338\) 14.3531 0.780704
\(339\) −29.0830 −1.57957
\(340\) 0.194273 0.0105359
\(341\) −11.6445 −0.630584
\(342\) 53.4107 2.88812
\(343\) 18.5833 1.00340
\(344\) −1.69549 −0.0914146
\(345\) −0.957611 −0.0515561
\(346\) −26.5934 −1.42967
\(347\) −30.6522 −1.64549 −0.822747 0.568407i \(-0.807560\pi\)
−0.822747 + 0.568407i \(0.807560\pi\)
\(348\) 14.4526 0.774741
\(349\) 17.2810 0.925030 0.462515 0.886611i \(-0.346947\pi\)
0.462515 + 0.886611i \(0.346947\pi\)
\(350\) −14.3644 −0.767812
\(351\) 4.92475 0.262864
\(352\) −7.76219 −0.413726
\(353\) −10.6330 −0.565938 −0.282969 0.959129i \(-0.591319\pi\)
−0.282969 + 0.959129i \(0.591319\pi\)
\(354\) 32.1551 1.70902
\(355\) −0.465145 −0.0246873
\(356\) −7.57972 −0.401724
\(357\) 17.7213 0.937908
\(358\) 27.4956 1.45319
\(359\) −27.8224 −1.46841 −0.734205 0.678928i \(-0.762445\pi\)
−0.734205 + 0.678928i \(0.762445\pi\)
\(360\) −0.288460 −0.0152032
\(361\) 43.7855 2.30450
\(362\) 27.6304 1.45222
\(363\) −23.4141 −1.22892
\(364\) −3.77686 −0.197961
\(365\) −0.432126 −0.0226185
\(366\) 35.3320 1.84684
\(367\) 22.7747 1.18883 0.594415 0.804159i \(-0.297384\pi\)
0.594415 + 0.804159i \(0.297384\pi\)
\(368\) −40.5817 −2.11547
\(369\) −12.5453 −0.653083
\(370\) −0.0786272 −0.00408763
\(371\) 14.4677 0.751125
\(372\) 22.3000 1.15620
\(373\) −3.41513 −0.176829 −0.0884143 0.996084i \(-0.528180\pi\)
−0.0884143 + 0.996084i \(0.528180\pi\)
\(374\) −10.3051 −0.532863
\(375\) 1.17904 0.0608852
\(376\) 1.05172 0.0542385
\(377\) 11.4957 0.592061
\(378\) 6.47332 0.332952
\(379\) −23.5744 −1.21093 −0.605467 0.795870i \(-0.707014\pi\)
−0.605467 + 0.795870i \(0.707014\pi\)
\(380\) 0.374443 0.0192085
\(381\) 29.2842 1.50028
\(382\) 17.3472 0.887562
\(383\) 7.65425 0.391114 0.195557 0.980692i \(-0.437349\pi\)
0.195557 + 0.980692i \(0.437349\pi\)
\(384\) −30.8505 −1.57433
\(385\) −0.106368 −0.00542100
\(386\) −6.11611 −0.311302
\(387\) −3.94300 −0.200434
\(388\) −9.79761 −0.497398
\(389\) 18.9416 0.960375 0.480187 0.877166i \(-0.340569\pi\)
0.480187 + 0.877166i \(0.340569\pi\)
\(390\) 0.450282 0.0228009
\(391\) −33.3834 −1.68827
\(392\) −7.12265 −0.359748
\(393\) −9.08514 −0.458285
\(394\) −32.5807 −1.64139
\(395\) −0.449565 −0.0226201
\(396\) −5.81512 −0.292221
\(397\) −12.0372 −0.604131 −0.302066 0.953287i \(-0.597676\pi\)
−0.302066 + 0.953287i \(0.597676\pi\)
\(398\) 9.19878 0.461093
\(399\) 34.1561 1.70994
\(400\) 24.9776 1.24888
\(401\) −5.39260 −0.269294 −0.134647 0.990894i \(-0.542990\pi\)
−0.134647 + 0.990894i \(0.542990\pi\)
\(402\) 61.6246 3.07356
\(403\) 17.7376 0.883573
\(404\) −16.3967 −0.815766
\(405\) 0.255772 0.0127094
\(406\) 15.1105 0.749924
\(407\) 1.43541 0.0711508
\(408\) −17.8717 −0.884782
\(409\) 15.6185 0.772284 0.386142 0.922439i \(-0.373807\pi\)
0.386142 + 0.922439i \(0.373807\pi\)
\(410\) −0.255548 −0.0126206
\(411\) 5.56943 0.274720
\(412\) −11.4835 −0.565753
\(413\) 11.5704 0.569343
\(414\) −54.7359 −2.69012
\(415\) 0.0588300 0.00288785
\(416\) 11.8239 0.579712
\(417\) 16.2331 0.794938
\(418\) −19.8621 −0.971485
\(419\) −13.7547 −0.671960 −0.335980 0.941869i \(-0.609067\pi\)
−0.335980 + 0.941869i \(0.609067\pi\)
\(420\) 0.203701 0.00993961
\(421\) 23.6585 1.15305 0.576523 0.817081i \(-0.304409\pi\)
0.576523 + 0.817081i \(0.304409\pi\)
\(422\) 24.5671 1.19591
\(423\) 2.44587 0.118922
\(424\) −14.5905 −0.708578
\(425\) 20.5471 0.996681
\(426\) −47.2510 −2.28932
\(427\) 12.7136 0.615254
\(428\) 5.99251 0.289659
\(429\) −8.22033 −0.396881
\(430\) −0.0803189 −0.00387332
\(431\) −4.35928 −0.209979 −0.104989 0.994473i \(-0.533481\pi\)
−0.104989 + 0.994473i \(0.533481\pi\)
\(432\) −11.2561 −0.541560
\(433\) 18.4637 0.887310 0.443655 0.896198i \(-0.353681\pi\)
0.443655 + 0.896198i \(0.353681\pi\)
\(434\) 23.3151 1.11916
\(435\) −0.620013 −0.0297273
\(436\) −1.04954 −0.0502640
\(437\) −64.3433 −3.07796
\(438\) −43.8968 −2.09747
\(439\) −28.8537 −1.37711 −0.688557 0.725183i \(-0.741755\pi\)
−0.688557 + 0.725183i \(0.741755\pi\)
\(440\) 0.107271 0.00511394
\(441\) −16.5643 −0.788777
\(442\) 15.6973 0.746646
\(443\) −18.0891 −0.859438 −0.429719 0.902963i \(-0.641387\pi\)
−0.429719 + 0.902963i \(0.641387\pi\)
\(444\) −2.74891 −0.130458
\(445\) 0.325168 0.0154144
\(446\) 9.03324 0.427736
\(447\) −49.2727 −2.33052
\(448\) −0.908104 −0.0429039
\(449\) 3.76252 0.177564 0.0887822 0.996051i \(-0.471702\pi\)
0.0887822 + 0.996051i \(0.471702\pi\)
\(450\) 33.6894 1.58813
\(451\) 4.66527 0.219679
\(452\) −11.6541 −0.548164
\(453\) 53.6091 2.51877
\(454\) −39.1401 −1.83694
\(455\) 0.162026 0.00759590
\(456\) −34.4461 −1.61308
\(457\) 1.33547 0.0624705 0.0312352 0.999512i \(-0.490056\pi\)
0.0312352 + 0.999512i \(0.490056\pi\)
\(458\) −37.1190 −1.73446
\(459\) −9.25952 −0.432197
\(460\) −0.383733 −0.0178917
\(461\) 32.9332 1.53385 0.766927 0.641734i \(-0.221785\pi\)
0.766927 + 0.641734i \(0.221785\pi\)
\(462\) −10.8052 −0.502703
\(463\) 21.3658 0.992955 0.496478 0.868050i \(-0.334626\pi\)
0.496478 + 0.868050i \(0.334626\pi\)
\(464\) −26.2749 −1.21978
\(465\) −0.956662 −0.0443641
\(466\) −49.6531 −2.30014
\(467\) −8.72214 −0.403613 −0.201806 0.979425i \(-0.564681\pi\)
−0.201806 + 0.979425i \(0.564681\pi\)
\(468\) 8.85797 0.409460
\(469\) 22.1745 1.02392
\(470\) 0.0498224 0.00229814
\(471\) −27.6546 −1.27426
\(472\) −11.6687 −0.537093
\(473\) 1.46630 0.0674204
\(474\) −45.6683 −2.09762
\(475\) 39.6026 1.81709
\(476\) 7.10125 0.325485
\(477\) −33.9315 −1.55362
\(478\) 18.2771 0.835973
\(479\) 29.3328 1.34025 0.670125 0.742248i \(-0.266240\pi\)
0.670125 + 0.742248i \(0.266240\pi\)
\(480\) −0.637709 −0.0291073
\(481\) −2.18651 −0.0996964
\(482\) 7.86478 0.358231
\(483\) −35.0035 −1.59272
\(484\) −9.38249 −0.426477
\(485\) 0.420315 0.0190855
\(486\) 37.7819 1.71382
\(487\) −34.5610 −1.56611 −0.783055 0.621952i \(-0.786340\pi\)
−0.783055 + 0.621952i \(0.786340\pi\)
\(488\) −12.8215 −0.580404
\(489\) 42.7889 1.93498
\(490\) −0.337416 −0.0152429
\(491\) 11.4040 0.514657 0.257329 0.966324i \(-0.417158\pi\)
0.257329 + 0.966324i \(0.417158\pi\)
\(492\) −8.93431 −0.402790
\(493\) −21.6143 −0.973460
\(494\) 30.2551 1.36124
\(495\) 0.249467 0.0112127
\(496\) −40.5415 −1.82037
\(497\) −17.0024 −0.762663
\(498\) 5.97615 0.267798
\(499\) 16.0261 0.717426 0.358713 0.933448i \(-0.383216\pi\)
0.358713 + 0.933448i \(0.383216\pi\)
\(500\) 0.472463 0.0211292
\(501\) −50.9988 −2.27846
\(502\) 1.04919 0.0468278
\(503\) −21.5723 −0.961862 −0.480931 0.876758i \(-0.659701\pi\)
−0.480931 + 0.876758i \(0.659701\pi\)
\(504\) −10.5441 −0.469670
\(505\) 0.703414 0.0313015
\(506\) 20.3549 0.904884
\(507\) −21.5272 −0.956057
\(508\) 11.7348 0.520646
\(509\) 37.7441 1.67298 0.836489 0.547984i \(-0.184605\pi\)
0.836489 + 0.547984i \(0.184605\pi\)
\(510\) −0.846622 −0.0374891
\(511\) −15.7955 −0.698750
\(512\) −10.4353 −0.461179
\(513\) −17.8469 −0.787958
\(514\) 34.9871 1.54321
\(515\) 0.492640 0.0217083
\(516\) −2.80806 −0.123618
\(517\) −0.909555 −0.0400022
\(518\) −2.87405 −0.126279
\(519\) 39.8856 1.75078
\(520\) −0.163402 −0.00716564
\(521\) −11.2384 −0.492362 −0.246181 0.969224i \(-0.579176\pi\)
−0.246181 + 0.969224i \(0.579176\pi\)
\(522\) −35.4392 −1.55113
\(523\) −1.35953 −0.0594482 −0.0297241 0.999558i \(-0.509463\pi\)
−0.0297241 + 0.999558i \(0.509463\pi\)
\(524\) −3.64059 −0.159040
\(525\) 21.5443 0.940269
\(526\) 17.2864 0.753723
\(527\) −33.3503 −1.45276
\(528\) 18.7886 0.817668
\(529\) 42.9398 1.86695
\(530\) −0.691185 −0.0300231
\(531\) −27.1364 −1.17762
\(532\) 13.6870 0.593406
\(533\) −7.10644 −0.307814
\(534\) 33.0316 1.42942
\(535\) −0.257077 −0.0111144
\(536\) −22.3628 −0.965925
\(537\) −41.2388 −1.77959
\(538\) −26.6537 −1.14912
\(539\) 6.15984 0.265323
\(540\) −0.106436 −0.00458027
\(541\) −5.66000 −0.243342 −0.121671 0.992570i \(-0.538825\pi\)
−0.121671 + 0.992570i \(0.538825\pi\)
\(542\) 18.9743 0.815017
\(543\) −41.4410 −1.77840
\(544\) −22.2312 −0.953157
\(545\) 0.0450252 0.00192867
\(546\) 16.4592 0.704387
\(547\) 10.7923 0.461444 0.230722 0.973020i \(-0.425891\pi\)
0.230722 + 0.973020i \(0.425891\pi\)
\(548\) 2.23178 0.0953369
\(549\) −29.8176 −1.27258
\(550\) −12.5282 −0.534204
\(551\) −41.6596 −1.77476
\(552\) 35.3007 1.50250
\(553\) −16.4329 −0.698799
\(554\) −21.5136 −0.914027
\(555\) 0.117928 0.00500575
\(556\) 6.50491 0.275870
\(557\) 21.4129 0.907294 0.453647 0.891182i \(-0.350123\pi\)
0.453647 + 0.891182i \(0.350123\pi\)
\(558\) −54.6817 −2.31486
\(559\) −2.23356 −0.0944694
\(560\) −0.370331 −0.0156493
\(561\) 15.4559 0.652548
\(562\) 4.92831 0.207888
\(563\) −35.4522 −1.49413 −0.747066 0.664750i \(-0.768538\pi\)
−0.747066 + 0.664750i \(0.768538\pi\)
\(564\) 1.74186 0.0733455
\(565\) 0.499958 0.0210334
\(566\) −23.9785 −1.00789
\(567\) 9.34923 0.392631
\(568\) 17.1468 0.719463
\(569\) 0.107921 0.00452428 0.00226214 0.999997i \(-0.499280\pi\)
0.00226214 + 0.999997i \(0.499280\pi\)
\(570\) −1.63178 −0.0683479
\(571\) −11.6760 −0.488623 −0.244312 0.969697i \(-0.578562\pi\)
−0.244312 + 0.969697i \(0.578562\pi\)
\(572\) −3.29405 −0.137731
\(573\) −26.0179 −1.08692
\(574\) −9.34104 −0.389887
\(575\) −40.5852 −1.69252
\(576\) 2.12980 0.0887418
\(577\) −24.9028 −1.03672 −0.518358 0.855164i \(-0.673457\pi\)
−0.518358 + 0.855164i \(0.673457\pi\)
\(578\) 0.172831 0.00718880
\(579\) 9.17315 0.381223
\(580\) −0.248451 −0.0103164
\(581\) 2.15041 0.0892140
\(582\) 42.6970 1.76985
\(583\) 12.6182 0.522594
\(584\) 15.9296 0.659170
\(585\) −0.380004 −0.0157112
\(586\) 27.3369 1.12928
\(587\) −15.4685 −0.638455 −0.319228 0.947678i \(-0.603423\pi\)
−0.319228 + 0.947678i \(0.603423\pi\)
\(588\) −11.7965 −0.486480
\(589\) −64.2795 −2.64859
\(590\) −0.552770 −0.0227572
\(591\) 48.8656 2.01006
\(592\) 4.99755 0.205398
\(593\) −27.0894 −1.11243 −0.556215 0.831038i \(-0.687747\pi\)
−0.556215 + 0.831038i \(0.687747\pi\)
\(594\) 5.64581 0.231650
\(595\) −0.304642 −0.0124891
\(596\) −19.7445 −0.808768
\(597\) −13.7966 −0.564659
\(598\) −31.0058 −1.26792
\(599\) −9.51041 −0.388585 −0.194292 0.980944i \(-0.562241\pi\)
−0.194292 + 0.980944i \(0.562241\pi\)
\(600\) −21.7272 −0.887009
\(601\) −33.4852 −1.36589 −0.682944 0.730470i \(-0.739301\pi\)
−0.682944 + 0.730470i \(0.739301\pi\)
\(602\) −2.93589 −0.119658
\(603\) −52.0065 −2.11787
\(604\) 21.4822 0.874098
\(605\) 0.402506 0.0163642
\(606\) 71.4551 2.90267
\(607\) 13.1301 0.532934 0.266467 0.963844i \(-0.414144\pi\)
0.266467 + 0.963844i \(0.414144\pi\)
\(608\) −42.8486 −1.73774
\(609\) −22.6633 −0.918363
\(610\) −0.607384 −0.0245923
\(611\) 1.38549 0.0560510
\(612\) −16.6548 −0.673229
\(613\) 20.7261 0.837118 0.418559 0.908190i \(-0.362535\pi\)
0.418559 + 0.908190i \(0.362535\pi\)
\(614\) −51.6921 −2.08612
\(615\) 0.383280 0.0154553
\(616\) 3.92106 0.157984
\(617\) 23.1147 0.930561 0.465281 0.885163i \(-0.345953\pi\)
0.465281 + 0.885163i \(0.345953\pi\)
\(618\) 50.0441 2.01307
\(619\) 17.0980 0.687225 0.343613 0.939111i \(-0.388349\pi\)
0.343613 + 0.939111i \(0.388349\pi\)
\(620\) −0.383353 −0.0153958
\(621\) 18.2897 0.733939
\(622\) 54.8719 2.20016
\(623\) 11.8858 0.476196
\(624\) −28.6200 −1.14572
\(625\) 24.9696 0.998784
\(626\) 47.9121 1.91495
\(627\) 29.7898 1.18969
\(628\) −11.0817 −0.442209
\(629\) 4.11109 0.163920
\(630\) −0.499495 −0.0199004
\(631\) −8.94391 −0.356052 −0.178026 0.984026i \(-0.556971\pi\)
−0.178026 + 0.984026i \(0.556971\pi\)
\(632\) 16.5725 0.659217
\(633\) −36.8466 −1.46452
\(634\) 7.30396 0.290077
\(635\) −0.503418 −0.0199775
\(636\) −24.1648 −0.958195
\(637\) −9.38306 −0.371770
\(638\) 13.1789 0.521758
\(639\) 39.8763 1.57748
\(640\) 0.530343 0.0209637
\(641\) −17.5564 −0.693436 −0.346718 0.937969i \(-0.612704\pi\)
−0.346718 + 0.937969i \(0.612704\pi\)
\(642\) −26.1147 −1.03067
\(643\) −23.5400 −0.928328 −0.464164 0.885749i \(-0.653645\pi\)
−0.464164 + 0.885749i \(0.653645\pi\)
\(644\) −14.0266 −0.552725
\(645\) 0.120465 0.00474330
\(646\) −56.8858 −2.23814
\(647\) 23.2768 0.915104 0.457552 0.889183i \(-0.348726\pi\)
0.457552 + 0.889183i \(0.348726\pi\)
\(648\) −9.42861 −0.370391
\(649\) 10.0913 0.396119
\(650\) 19.0837 0.748526
\(651\) −34.9688 −1.37054
\(652\) 17.1464 0.671503
\(653\) 32.6530 1.27781 0.638905 0.769286i \(-0.279388\pi\)
0.638905 + 0.769286i \(0.279388\pi\)
\(654\) 4.57381 0.178850
\(655\) 0.156180 0.00610247
\(656\) 16.2426 0.634169
\(657\) 37.0455 1.44528
\(658\) 1.82116 0.0709960
\(659\) −34.4340 −1.34136 −0.670678 0.741748i \(-0.733997\pi\)
−0.670678 + 0.741748i \(0.733997\pi\)
\(660\) 0.177661 0.00691546
\(661\) −32.2787 −1.25550 −0.627748 0.778417i \(-0.716023\pi\)
−0.627748 + 0.778417i \(0.716023\pi\)
\(662\) 44.2069 1.71815
\(663\) −23.5434 −0.914349
\(664\) −2.16867 −0.0841606
\(665\) −0.587168 −0.0227694
\(666\) 6.74060 0.261193
\(667\) 42.6932 1.65309
\(668\) −20.4362 −0.790700
\(669\) −13.5483 −0.523809
\(670\) −1.05937 −0.0409271
\(671\) 11.0884 0.428062
\(672\) −23.3102 −0.899209
\(673\) 21.6164 0.833252 0.416626 0.909078i \(-0.363213\pi\)
0.416626 + 0.909078i \(0.363213\pi\)
\(674\) −25.7948 −0.993578
\(675\) −11.2571 −0.433285
\(676\) −8.62637 −0.331784
\(677\) −2.81215 −0.108080 −0.0540398 0.998539i \(-0.517210\pi\)
−0.0540398 + 0.998539i \(0.517210\pi\)
\(678\) 50.7875 1.95048
\(679\) 15.3637 0.589607
\(680\) 0.307228 0.0117817
\(681\) 58.7036 2.24953
\(682\) 20.3347 0.778655
\(683\) −27.5881 −1.05563 −0.527814 0.849360i \(-0.676988\pi\)
−0.527814 + 0.849360i \(0.676988\pi\)
\(684\) −32.1005 −1.22739
\(685\) −0.0957427 −0.00365814
\(686\) −32.4519 −1.23902
\(687\) 55.6723 2.12403
\(688\) 5.10507 0.194629
\(689\) −19.2209 −0.732257
\(690\) 1.67227 0.0636623
\(691\) 17.4897 0.665338 0.332669 0.943044i \(-0.392051\pi\)
0.332669 + 0.943044i \(0.392051\pi\)
\(692\) 15.9829 0.607580
\(693\) 9.11876 0.346393
\(694\) 53.5277 2.03188
\(695\) −0.279059 −0.0105853
\(696\) 22.8557 0.866343
\(697\) 13.3615 0.506105
\(698\) −30.1777 −1.14224
\(699\) 74.4714 2.81677
\(700\) 8.63321 0.326305
\(701\) 23.4285 0.884882 0.442441 0.896798i \(-0.354113\pi\)
0.442441 + 0.896798i \(0.354113\pi\)
\(702\) −8.60006 −0.324588
\(703\) 7.92373 0.298849
\(704\) −0.792018 −0.0298503
\(705\) −0.0747253 −0.00281432
\(706\) 18.5684 0.698830
\(707\) 25.7118 0.966993
\(708\) −19.3256 −0.726300
\(709\) 16.2789 0.611366 0.305683 0.952133i \(-0.401115\pi\)
0.305683 + 0.952133i \(0.401115\pi\)
\(710\) 0.812281 0.0304843
\(711\) 38.5406 1.44539
\(712\) −11.9868 −0.449223
\(713\) 65.8744 2.46702
\(714\) −30.9465 −1.15814
\(715\) 0.141314 0.00528483
\(716\) −16.5252 −0.617576
\(717\) −27.4125 −1.02374
\(718\) 48.5861 1.81322
\(719\) 18.8813 0.704155 0.352078 0.935971i \(-0.385475\pi\)
0.352078 + 0.935971i \(0.385475\pi\)
\(720\) 0.868547 0.0323688
\(721\) 18.0075 0.670633
\(722\) −76.4624 −2.84564
\(723\) −11.7959 −0.438693
\(724\) −16.6062 −0.617165
\(725\) −26.2772 −0.975910
\(726\) 40.8880 1.51749
\(727\) −6.51462 −0.241614 −0.120807 0.992676i \(-0.538548\pi\)
−0.120807 + 0.992676i \(0.538548\pi\)
\(728\) −5.97281 −0.221367
\(729\) −39.6246 −1.46758
\(730\) 0.754618 0.0279297
\(731\) 4.19954 0.155326
\(732\) −21.2350 −0.784868
\(733\) 15.2451 0.563091 0.281546 0.959548i \(-0.409153\pi\)
0.281546 + 0.959548i \(0.409153\pi\)
\(734\) −39.7713 −1.46799
\(735\) 0.506067 0.0186666
\(736\) 43.9118 1.61861
\(737\) 19.3399 0.712393
\(738\) 21.9078 0.806437
\(739\) 49.1695 1.80873 0.904365 0.426759i \(-0.140345\pi\)
0.904365 + 0.426759i \(0.140345\pi\)
\(740\) 0.0472559 0.00173716
\(741\) −45.3777 −1.66699
\(742\) −25.2648 −0.927501
\(743\) −30.5878 −1.12216 −0.561079 0.827762i \(-0.689614\pi\)
−0.561079 + 0.827762i \(0.689614\pi\)
\(744\) 35.2657 1.29290
\(745\) 0.847035 0.0310330
\(746\) 5.96382 0.218351
\(747\) −5.04342 −0.184529
\(748\) 6.19347 0.226456
\(749\) −9.39692 −0.343356
\(750\) −2.05895 −0.0751821
\(751\) −7.57697 −0.276488 −0.138244 0.990398i \(-0.544146\pi\)
−0.138244 + 0.990398i \(0.544146\pi\)
\(752\) −3.16671 −0.115478
\(753\) −1.57361 −0.0573457
\(754\) −20.0749 −0.731086
\(755\) −0.921580 −0.0335397
\(756\) −3.89054 −0.141498
\(757\) 32.7115 1.18892 0.594460 0.804125i \(-0.297366\pi\)
0.594460 + 0.804125i \(0.297366\pi\)
\(758\) 41.1678 1.49528
\(759\) −30.5289 −1.10813
\(760\) 0.592154 0.0214797
\(761\) −5.23114 −0.189629 −0.0948144 0.995495i \(-0.530226\pi\)
−0.0948144 + 0.995495i \(0.530226\pi\)
\(762\) −51.1389 −1.85257
\(763\) 1.64580 0.0595820
\(764\) −10.4259 −0.377196
\(765\) 0.714485 0.0258323
\(766\) −13.3666 −0.482954
\(767\) −15.3718 −0.555042
\(768\) 50.9837 1.83972
\(769\) −46.9816 −1.69420 −0.847101 0.531432i \(-0.821654\pi\)
−0.847101 + 0.531432i \(0.821654\pi\)
\(770\) 0.185749 0.00669394
\(771\) −52.4748 −1.88983
\(772\) 3.67586 0.132297
\(773\) 24.2523 0.872296 0.436148 0.899875i \(-0.356342\pi\)
0.436148 + 0.899875i \(0.356342\pi\)
\(774\) 6.88563 0.247499
\(775\) −40.5450 −1.45642
\(776\) −15.4942 −0.556209
\(777\) 4.31060 0.154642
\(778\) −33.0775 −1.18589
\(779\) 25.7531 0.922701
\(780\) −0.270625 −0.00968994
\(781\) −14.8289 −0.530621
\(782\) 58.2972 2.08470
\(783\) 11.8418 0.423191
\(784\) 21.4461 0.765934
\(785\) 0.475403 0.0169679
\(786\) 15.8653 0.565898
\(787\) 3.13846 0.111874 0.0559369 0.998434i \(-0.482185\pi\)
0.0559369 + 0.998434i \(0.482185\pi\)
\(788\) 19.5814 0.697558
\(789\) −25.9267 −0.923015
\(790\) 0.785073 0.0279316
\(791\) 18.2750 0.649782
\(792\) −9.19618 −0.326772
\(793\) −16.8905 −0.599800
\(794\) 21.0205 0.745991
\(795\) 1.03666 0.0367666
\(796\) −5.52858 −0.195955
\(797\) 16.8411 0.596544 0.298272 0.954481i \(-0.403590\pi\)
0.298272 + 0.954481i \(0.403590\pi\)
\(798\) −59.6465 −2.11146
\(799\) −2.60501 −0.0921585
\(800\) −27.0272 −0.955556
\(801\) −27.8762 −0.984957
\(802\) 9.41707 0.332528
\(803\) −13.7763 −0.486154
\(804\) −37.0371 −1.30620
\(805\) 0.601737 0.0212084
\(806\) −30.9751 −1.09105
\(807\) 39.9760 1.40722
\(808\) −25.9301 −0.912219
\(809\) −7.10227 −0.249702 −0.124851 0.992175i \(-0.539845\pi\)
−0.124851 + 0.992175i \(0.539845\pi\)
\(810\) −0.446654 −0.0156938
\(811\) 29.6680 1.04179 0.520893 0.853622i \(-0.325599\pi\)
0.520893 + 0.853622i \(0.325599\pi\)
\(812\) −9.08162 −0.318702
\(813\) −28.4583 −0.998076
\(814\) −2.50665 −0.0878582
\(815\) −0.735574 −0.0257660
\(816\) 53.8113 1.88377
\(817\) 8.09422 0.283181
\(818\) −27.2745 −0.953630
\(819\) −13.8903 −0.485366
\(820\) 0.153588 0.00536351
\(821\) −48.1826 −1.68159 −0.840793 0.541357i \(-0.817911\pi\)
−0.840793 + 0.541357i \(0.817911\pi\)
\(822\) −9.72587 −0.339229
\(823\) −30.1699 −1.05166 −0.525829 0.850590i \(-0.676245\pi\)
−0.525829 + 0.850590i \(0.676245\pi\)
\(824\) −18.1604 −0.632646
\(825\) 18.7902 0.654191
\(826\) −20.2054 −0.703034
\(827\) 22.2195 0.772649 0.386325 0.922363i \(-0.373744\pi\)
0.386325 + 0.922363i \(0.373744\pi\)
\(828\) 32.8970 1.14325
\(829\) −55.5836 −1.93050 −0.965249 0.261333i \(-0.915838\pi\)
−0.965249 + 0.261333i \(0.915838\pi\)
\(830\) −0.102734 −0.00356597
\(831\) 32.2669 1.11933
\(832\) 1.20645 0.0418262
\(833\) 17.6421 0.611261
\(834\) −28.3478 −0.981603
\(835\) 0.876708 0.0303397
\(836\) 11.9373 0.412861
\(837\) 18.2715 0.631556
\(838\) 24.0197 0.829748
\(839\) −4.92119 −0.169898 −0.0849492 0.996385i \(-0.527073\pi\)
−0.0849492 + 0.996385i \(0.527073\pi\)
\(840\) 0.322138 0.0111148
\(841\) −1.35797 −0.0468267
\(842\) −41.3148 −1.42380
\(843\) −7.39164 −0.254582
\(844\) −14.7651 −0.508237
\(845\) 0.370069 0.0127308
\(846\) −4.27121 −0.146847
\(847\) 14.7128 0.505538
\(848\) 43.9317 1.50862
\(849\) 35.9638 1.23427
\(850\) −35.8813 −1.23072
\(851\) −8.12033 −0.278361
\(852\) 28.3984 0.972914
\(853\) 28.0324 0.959812 0.479906 0.877320i \(-0.340671\pi\)
0.479906 + 0.877320i \(0.340671\pi\)
\(854\) −22.2017 −0.759726
\(855\) 1.37710 0.0470959
\(856\) 9.47670 0.323907
\(857\) −4.28492 −0.146370 −0.0731851 0.997318i \(-0.523316\pi\)
−0.0731851 + 0.997318i \(0.523316\pi\)
\(858\) 14.3551 0.490076
\(859\) 55.0243 1.87741 0.938703 0.344728i \(-0.112029\pi\)
0.938703 + 0.344728i \(0.112029\pi\)
\(860\) 0.0482726 0.00164608
\(861\) 14.0100 0.477459
\(862\) 7.61258 0.259285
\(863\) −27.3096 −0.929631 −0.464815 0.885408i \(-0.653879\pi\)
−0.464815 + 0.885408i \(0.653879\pi\)
\(864\) 12.1798 0.414364
\(865\) −0.685663 −0.0233133
\(866\) −32.2431 −1.09567
\(867\) −0.259217 −0.00880347
\(868\) −14.0127 −0.475621
\(869\) −14.3323 −0.486188
\(870\) 1.08272 0.0367078
\(871\) −29.4597 −0.998204
\(872\) −1.65978 −0.0562071
\(873\) −36.0330 −1.21953
\(874\) 112.362 3.80071
\(875\) −0.740875 −0.0250461
\(876\) 26.3825 0.891382
\(877\) −36.2740 −1.22489 −0.612443 0.790515i \(-0.709813\pi\)
−0.612443 + 0.790515i \(0.709813\pi\)
\(878\) 50.3871 1.70048
\(879\) −41.0008 −1.38292
\(880\) −0.322990 −0.0108880
\(881\) −27.6231 −0.930644 −0.465322 0.885141i \(-0.654062\pi\)
−0.465322 + 0.885141i \(0.654062\pi\)
\(882\) 28.9262 0.973995
\(883\) −1.50723 −0.0507223 −0.0253612 0.999678i \(-0.508074\pi\)
−0.0253612 + 0.999678i \(0.508074\pi\)
\(884\) −9.43429 −0.317310
\(885\) 0.829062 0.0278686
\(886\) 31.5888 1.06125
\(887\) −1.36407 −0.0458011 −0.0229005 0.999738i \(-0.507290\pi\)
−0.0229005 + 0.999738i \(0.507290\pi\)
\(888\) −4.34720 −0.145883
\(889\) −18.4014 −0.617164
\(890\) −0.567839 −0.0190340
\(891\) 8.15408 0.273172
\(892\) −5.42909 −0.181779
\(893\) −5.02090 −0.168018
\(894\) 86.0447 2.87776
\(895\) 0.708927 0.0236968
\(896\) 19.3856 0.647628
\(897\) 46.5035 1.55271
\(898\) −6.57048 −0.219260
\(899\) 42.6509 1.42249
\(900\) −20.2477 −0.674924
\(901\) 36.1392 1.20397
\(902\) −8.14694 −0.271263
\(903\) 4.40335 0.146534
\(904\) −18.4301 −0.612977
\(905\) 0.712402 0.0236811
\(906\) −93.6172 −3.11022
\(907\) 58.1615 1.93122 0.965611 0.259991i \(-0.0837197\pi\)
0.965611 + 0.259991i \(0.0837197\pi\)
\(908\) 23.5237 0.780660
\(909\) −60.3027 −2.00011
\(910\) −0.282945 −0.00937954
\(911\) 45.8785 1.52002 0.760011 0.649911i \(-0.225194\pi\)
0.760011 + 0.649911i \(0.225194\pi\)
\(912\) 103.716 3.43439
\(913\) 1.87552 0.0620705
\(914\) −2.33212 −0.0771396
\(915\) 0.910975 0.0301159
\(916\) 22.3090 0.737109
\(917\) 5.70885 0.188523
\(918\) 16.1698 0.533685
\(919\) 50.0523 1.65107 0.825536 0.564349i \(-0.190873\pi\)
0.825536 + 0.564349i \(0.190873\pi\)
\(920\) −0.606846 −0.0200071
\(921\) 77.5295 2.55468
\(922\) −57.5111 −1.89403
\(923\) 22.5884 0.743506
\(924\) 6.49405 0.213639
\(925\) 4.99797 0.164332
\(926\) −37.3111 −1.22612
\(927\) −42.2334 −1.38713
\(928\) 28.4310 0.933293
\(929\) −10.1654 −0.333515 −0.166757 0.985998i \(-0.553330\pi\)
−0.166757 + 0.985998i \(0.553330\pi\)
\(930\) 1.67061 0.0547816
\(931\) 34.0034 1.11442
\(932\) 29.8421 0.977512
\(933\) −82.2988 −2.69434
\(934\) 15.2314 0.498388
\(935\) −0.265698 −0.00868926
\(936\) 14.0082 0.457873
\(937\) 27.8302 0.909172 0.454586 0.890703i \(-0.349787\pi\)
0.454586 + 0.890703i \(0.349787\pi\)
\(938\) −38.7232 −1.26436
\(939\) −71.8601 −2.34507
\(940\) −0.0299439 −0.000976661 0
\(941\) 50.5334 1.64734 0.823671 0.567067i \(-0.191922\pi\)
0.823671 + 0.567067i \(0.191922\pi\)
\(942\) 48.2930 1.57347
\(943\) −26.3921 −0.859445
\(944\) 35.1341 1.14352
\(945\) 0.166903 0.00542936
\(946\) −2.56059 −0.0832519
\(947\) 41.6600 1.35377 0.676884 0.736090i \(-0.263330\pi\)
0.676884 + 0.736090i \(0.263330\pi\)
\(948\) 27.4472 0.891445
\(949\) 20.9849 0.681198
\(950\) −69.1578 −2.24377
\(951\) −10.9547 −0.355231
\(952\) 11.2301 0.363970
\(953\) −2.56093 −0.0829568 −0.0414784 0.999139i \(-0.513207\pi\)
−0.0414784 + 0.999139i \(0.513207\pi\)
\(954\) 59.2543 1.91843
\(955\) 0.447268 0.0144733
\(956\) −10.9847 −0.355272
\(957\) −19.7662 −0.638949
\(958\) −51.2237 −1.65496
\(959\) −3.49968 −0.113011
\(960\) −0.0650689 −0.00210009
\(961\) 34.8091 1.12287
\(962\) 3.81830 0.123107
\(963\) 22.0389 0.710192
\(964\) −4.72683 −0.152241
\(965\) −0.157693 −0.00507633
\(966\) 61.1264 1.96671
\(967\) −4.48369 −0.144186 −0.0720929 0.997398i \(-0.522968\pi\)
−0.0720929 + 0.997398i \(0.522968\pi\)
\(968\) −14.8377 −0.476902
\(969\) 85.3192 2.74085
\(970\) −0.733994 −0.0235671
\(971\) −37.6981 −1.20979 −0.604895 0.796305i \(-0.706785\pi\)
−0.604895 + 0.796305i \(0.706785\pi\)
\(972\) −22.7074 −0.728339
\(973\) −10.2004 −0.327011
\(974\) 60.3538 1.93386
\(975\) −28.6224 −0.916651
\(976\) 38.6054 1.23573
\(977\) −14.1754 −0.453512 −0.226756 0.973952i \(-0.572812\pi\)
−0.226756 + 0.973952i \(0.572812\pi\)
\(978\) −74.7221 −2.38935
\(979\) 10.3664 0.331313
\(980\) 0.202791 0.00647792
\(981\) −3.85995 −0.123239
\(982\) −19.9148 −0.635507
\(983\) −20.5890 −0.656687 −0.328343 0.944558i \(-0.606490\pi\)
−0.328343 + 0.944558i \(0.606490\pi\)
\(984\) −14.1290 −0.450414
\(985\) −0.840036 −0.0267658
\(986\) 37.7450 1.20204
\(987\) −2.73143 −0.0869424
\(988\) −18.1837 −0.578501
\(989\) −8.29505 −0.263767
\(990\) −0.435643 −0.0138456
\(991\) 34.4809 1.09532 0.547661 0.836701i \(-0.315518\pi\)
0.547661 + 0.836701i \(0.315518\pi\)
\(992\) 43.8682 1.39282
\(993\) −66.3029 −2.10406
\(994\) 29.6912 0.941749
\(995\) 0.237175 0.00751894
\(996\) −3.59174 −0.113809
\(997\) −62.8352 −1.99001 −0.995005 0.0998249i \(-0.968172\pi\)
−0.995005 + 0.0998249i \(0.968172\pi\)
\(998\) −27.9863 −0.885889
\(999\) −2.25233 −0.0712605
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 \(a_p\))