Properties

Label 8035.2.a.e.1.15
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.33215 q^{2}\) \(-3.21462 q^{3}\) \(+3.43894 q^{4}\) \(+1.00000 q^{5}\) \(+7.49699 q^{6}\) \(-4.86714 q^{7}\) \(-3.35583 q^{8}\) \(+7.33378 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.33215 q^{2}\) \(-3.21462 q^{3}\) \(+3.43894 q^{4}\) \(+1.00000 q^{5}\) \(+7.49699 q^{6}\) \(-4.86714 q^{7}\) \(-3.35583 q^{8}\) \(+7.33378 q^{9}\) \(-2.33215 q^{10}\) \(+5.00642 q^{11}\) \(-11.0549 q^{12}\) \(+0.810556 q^{13}\) \(+11.3509 q^{14}\) \(-3.21462 q^{15}\) \(+0.948436 q^{16}\) \(+3.45990 q^{17}\) \(-17.1035 q^{18}\) \(-1.22672 q^{19}\) \(+3.43894 q^{20}\) \(+15.6460 q^{21}\) \(-11.6757 q^{22}\) \(-4.23007 q^{23}\) \(+10.7877 q^{24}\) \(+1.00000 q^{25}\) \(-1.89034 q^{26}\) \(-13.9315 q^{27}\) \(-16.7378 q^{28}\) \(-3.93790 q^{29}\) \(+7.49699 q^{30}\) \(+10.6735 q^{31}\) \(+4.49977 q^{32}\) \(-16.0937 q^{33}\) \(-8.06901 q^{34}\) \(-4.86714 q^{35}\) \(+25.2205 q^{36}\) \(+3.60402 q^{37}\) \(+2.86091 q^{38}\) \(-2.60563 q^{39}\) \(-3.35583 q^{40}\) \(-9.85216 q^{41}\) \(-36.4889 q^{42}\) \(+0.0946578 q^{43}\) \(+17.2168 q^{44}\) \(+7.33378 q^{45}\) \(+9.86516 q^{46}\) \(+8.64538 q^{47}\) \(-3.04886 q^{48}\) \(+16.6891 q^{49}\) \(-2.33215 q^{50}\) \(-11.1223 q^{51}\) \(+2.78745 q^{52}\) \(+12.0939 q^{53}\) \(+32.4903 q^{54}\) \(+5.00642 q^{55}\) \(+16.3333 q^{56}\) \(+3.94345 q^{57}\) \(+9.18379 q^{58}\) \(-0.143658 q^{59}\) \(-11.0549 q^{60}\) \(-3.98793 q^{61}\) \(-24.8922 q^{62}\) \(-35.6946 q^{63}\) \(-12.3910 q^{64}\) \(+0.810556 q^{65}\) \(+37.5331 q^{66}\) \(+6.47252 q^{67}\) \(+11.8984 q^{68}\) \(+13.5981 q^{69}\) \(+11.3509 q^{70}\) \(-9.29484 q^{71}\) \(-24.6110 q^{72}\) \(+14.5566 q^{73}\) \(-8.40513 q^{74}\) \(-3.21462 q^{75}\) \(-4.21863 q^{76}\) \(-24.3670 q^{77}\) \(+6.07673 q^{78}\) \(+15.0284 q^{79}\) \(+0.948436 q^{80}\) \(+22.7830 q^{81}\) \(+22.9768 q^{82}\) \(+5.15508 q^{83}\) \(+53.8057 q^{84}\) \(+3.45990 q^{85}\) \(-0.220756 q^{86}\) \(+12.6589 q^{87}\) \(-16.8007 q^{88}\) \(+6.41139 q^{89}\) \(-17.1035 q^{90}\) \(-3.94509 q^{91}\) \(-14.5469 q^{92}\) \(-34.3112 q^{93}\) \(-20.1623 q^{94}\) \(-1.22672 q^{95}\) \(-14.4650 q^{96}\) \(+1.28356 q^{97}\) \(-38.9214 q^{98}\) \(+36.7160 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.33215 −1.64908 −0.824541 0.565802i \(-0.808567\pi\)
−0.824541 + 0.565802i \(0.808567\pi\)
\(3\) −3.21462 −1.85596 −0.927981 0.372628i \(-0.878457\pi\)
−0.927981 + 0.372628i \(0.878457\pi\)
\(4\) 3.43894 1.71947
\(5\) 1.00000 0.447214
\(6\) 7.49699 3.06063
\(7\) −4.86714 −1.83961 −0.919803 0.392380i \(-0.871652\pi\)
−0.919803 + 0.392380i \(0.871652\pi\)
\(8\) −3.35583 −1.18647
\(9\) 7.33378 2.44459
\(10\) −2.33215 −0.737492
\(11\) 5.00642 1.50949 0.754746 0.656017i \(-0.227760\pi\)
0.754746 + 0.656017i \(0.227760\pi\)
\(12\) −11.0549 −3.19127
\(13\) 0.810556 0.224808 0.112404 0.993663i \(-0.464145\pi\)
0.112404 + 0.993663i \(0.464145\pi\)
\(14\) 11.3509 3.03366
\(15\) −3.21462 −0.830011
\(16\) 0.948436 0.237109
\(17\) 3.45990 0.839148 0.419574 0.907721i \(-0.362179\pi\)
0.419574 + 0.907721i \(0.362179\pi\)
\(18\) −17.1035 −4.03134
\(19\) −1.22672 −0.281430 −0.140715 0.990050i \(-0.544940\pi\)
−0.140715 + 0.990050i \(0.544940\pi\)
\(20\) 3.43894 0.768971
\(21\) 15.6460 3.41424
\(22\) −11.6757 −2.48928
\(23\) −4.23007 −0.882030 −0.441015 0.897500i \(-0.645381\pi\)
−0.441015 + 0.897500i \(0.645381\pi\)
\(24\) 10.7877 2.20204
\(25\) 1.00000 0.200000
\(26\) −1.89034 −0.370726
\(27\) −13.9315 −2.68111
\(28\) −16.7378 −3.16315
\(29\) −3.93790 −0.731250 −0.365625 0.930762i \(-0.619145\pi\)
−0.365625 + 0.930762i \(0.619145\pi\)
\(30\) 7.49699 1.36876
\(31\) 10.6735 1.91702 0.958508 0.285066i \(-0.0920157\pi\)
0.958508 + 0.285066i \(0.0920157\pi\)
\(32\) 4.49977 0.795454
\(33\) −16.0937 −2.80156
\(34\) −8.06901 −1.38382
\(35\) −4.86714 −0.822697
\(36\) 25.2205 4.20341
\(37\) 3.60402 0.592497 0.296249 0.955111i \(-0.404264\pi\)
0.296249 + 0.955111i \(0.404264\pi\)
\(38\) 2.86091 0.464101
\(39\) −2.60563 −0.417234
\(40\) −3.35583 −0.530604
\(41\) −9.85216 −1.53865 −0.769325 0.638858i \(-0.779407\pi\)
−0.769325 + 0.638858i \(0.779407\pi\)
\(42\) −36.4889 −5.63036
\(43\) 0.0946578 0.0144352 0.00721759 0.999974i \(-0.497703\pi\)
0.00721759 + 0.999974i \(0.497703\pi\)
\(44\) 17.2168 2.59553
\(45\) 7.33378 1.09326
\(46\) 9.86516 1.45454
\(47\) 8.64538 1.26106 0.630529 0.776166i \(-0.282838\pi\)
0.630529 + 0.776166i \(0.282838\pi\)
\(48\) −3.04886 −0.440065
\(49\) 16.6891 2.38415
\(50\) −2.33215 −0.329816
\(51\) −11.1223 −1.55743
\(52\) 2.78745 0.386550
\(53\) 12.0939 1.66123 0.830614 0.556849i \(-0.187990\pi\)
0.830614 + 0.556849i \(0.187990\pi\)
\(54\) 32.4903 4.42137
\(55\) 5.00642 0.675066
\(56\) 16.3333 2.18263
\(57\) 3.94345 0.522323
\(58\) 9.18379 1.20589
\(59\) −0.143658 −0.0187027 −0.00935136 0.999956i \(-0.502977\pi\)
−0.00935136 + 0.999956i \(0.502977\pi\)
\(60\) −11.0549 −1.42718
\(61\) −3.98793 −0.510602 −0.255301 0.966862i \(-0.582175\pi\)
−0.255301 + 0.966862i \(0.582175\pi\)
\(62\) −24.8922 −3.16132
\(63\) −35.6946 −4.49709
\(64\) −12.3910 −1.54888
\(65\) 0.810556 0.100537
\(66\) 37.5331 4.62000
\(67\) 6.47252 0.790744 0.395372 0.918521i \(-0.370616\pi\)
0.395372 + 0.918521i \(0.370616\pi\)
\(68\) 11.8984 1.44289
\(69\) 13.5981 1.63701
\(70\) 11.3509 1.35669
\(71\) −9.29484 −1.10309 −0.551547 0.834144i \(-0.685962\pi\)
−0.551547 + 0.834144i \(0.685962\pi\)
\(72\) −24.6110 −2.90043
\(73\) 14.5566 1.70372 0.851862 0.523767i \(-0.175474\pi\)
0.851862 + 0.523767i \(0.175474\pi\)
\(74\) −8.40513 −0.977076
\(75\) −3.21462 −0.371192
\(76\) −4.21863 −0.483910
\(77\) −24.3670 −2.77687
\(78\) 6.07673 0.688054
\(79\) 15.0284 1.69082 0.845411 0.534116i \(-0.179355\pi\)
0.845411 + 0.534116i \(0.179355\pi\)
\(80\) 0.948436 0.106038
\(81\) 22.7830 2.53145
\(82\) 22.9768 2.53736
\(83\) 5.15508 0.565843 0.282922 0.959143i \(-0.408696\pi\)
0.282922 + 0.959143i \(0.408696\pi\)
\(84\) 53.8057 5.87068
\(85\) 3.45990 0.375278
\(86\) −0.220756 −0.0238048
\(87\) 12.6589 1.35717
\(88\) −16.8007 −1.79096
\(89\) 6.41139 0.679606 0.339803 0.940497i \(-0.389640\pi\)
0.339803 + 0.940497i \(0.389640\pi\)
\(90\) −17.1035 −1.80287
\(91\) −3.94509 −0.413558
\(92\) −14.5469 −1.51662
\(93\) −34.3112 −3.55791
\(94\) −20.1623 −2.07959
\(95\) −1.22672 −0.125859
\(96\) −14.4650 −1.47633
\(97\) 1.28356 0.130325 0.0651627 0.997875i \(-0.479243\pi\)
0.0651627 + 0.997875i \(0.479243\pi\)
\(98\) −38.9214 −3.93166
\(99\) 36.7160 3.69010
\(100\) 3.43894 0.343894
\(101\) 7.49239 0.745521 0.372761 0.927928i \(-0.378411\pi\)
0.372761 + 0.927928i \(0.378411\pi\)
\(102\) 25.9388 2.56832
\(103\) −15.3350 −1.51100 −0.755501 0.655148i \(-0.772606\pi\)
−0.755501 + 0.655148i \(0.772606\pi\)
\(104\) −2.72009 −0.266727
\(105\) 15.6460 1.52689
\(106\) −28.2049 −2.73950
\(107\) 1.06772 0.103221 0.0516103 0.998667i \(-0.483565\pi\)
0.0516103 + 0.998667i \(0.483565\pi\)
\(108\) −47.9095 −4.61009
\(109\) 18.1476 1.73823 0.869113 0.494614i \(-0.164690\pi\)
0.869113 + 0.494614i \(0.164690\pi\)
\(110\) −11.6757 −1.11324
\(111\) −11.5856 −1.09965
\(112\) −4.61617 −0.436187
\(113\) 5.13782 0.483325 0.241663 0.970360i \(-0.422307\pi\)
0.241663 + 0.970360i \(0.422307\pi\)
\(114\) −9.19673 −0.861353
\(115\) −4.23007 −0.394456
\(116\) −13.5422 −1.25736
\(117\) 5.94444 0.549564
\(118\) 0.335033 0.0308423
\(119\) −16.8398 −1.54370
\(120\) 10.7877 0.984780
\(121\) 14.0643 1.27857
\(122\) 9.30047 0.842025
\(123\) 31.6710 2.85567
\(124\) 36.7055 3.29625
\(125\) 1.00000 0.0894427
\(126\) 83.2452 7.41607
\(127\) −15.1824 −1.34722 −0.673611 0.739086i \(-0.735258\pi\)
−0.673611 + 0.739086i \(0.735258\pi\)
\(128\) 19.8982 1.75877
\(129\) −0.304289 −0.0267911
\(130\) −1.89034 −0.165794
\(131\) −9.92424 −0.867085 −0.433542 0.901133i \(-0.642737\pi\)
−0.433542 + 0.901133i \(0.642737\pi\)
\(132\) −55.3455 −4.81720
\(133\) 5.97064 0.517720
\(134\) −15.0949 −1.30400
\(135\) −13.9315 −1.19903
\(136\) −11.6108 −0.995621
\(137\) 7.59754 0.649102 0.324551 0.945868i \(-0.394787\pi\)
0.324551 + 0.945868i \(0.394787\pi\)
\(138\) −31.7128 −2.69957
\(139\) −0.411264 −0.0348829 −0.0174415 0.999848i \(-0.505552\pi\)
−0.0174415 + 0.999848i \(0.505552\pi\)
\(140\) −16.7378 −1.41460
\(141\) −27.7916 −2.34048
\(142\) 21.6770 1.81909
\(143\) 4.05798 0.339346
\(144\) 6.95562 0.579635
\(145\) −3.93790 −0.327025
\(146\) −33.9483 −2.80958
\(147\) −53.6490 −4.42489
\(148\) 12.3940 1.01878
\(149\) 16.0485 1.31474 0.657372 0.753566i \(-0.271668\pi\)
0.657372 + 0.753566i \(0.271668\pi\)
\(150\) 7.49699 0.612127
\(151\) 0.866470 0.0705123 0.0352562 0.999378i \(-0.488775\pi\)
0.0352562 + 0.999378i \(0.488775\pi\)
\(152\) 4.11668 0.333907
\(153\) 25.3741 2.05138
\(154\) 56.8275 4.57929
\(155\) 10.6735 0.857315
\(156\) −8.96060 −0.717422
\(157\) −19.3393 −1.54344 −0.771721 0.635961i \(-0.780604\pi\)
−0.771721 + 0.635961i \(0.780604\pi\)
\(158\) −35.0484 −2.78830
\(159\) −38.8774 −3.08317
\(160\) 4.49977 0.355738
\(161\) 20.5883 1.62259
\(162\) −53.1335 −4.17457
\(163\) −2.55217 −0.199901 −0.0999506 0.994992i \(-0.531868\pi\)
−0.0999506 + 0.994992i \(0.531868\pi\)
\(164\) −33.8810 −2.64566
\(165\) −16.0937 −1.25290
\(166\) −12.0224 −0.933122
\(167\) 9.51681 0.736433 0.368217 0.929740i \(-0.379969\pi\)
0.368217 + 0.929740i \(0.379969\pi\)
\(168\) −52.5054 −4.05088
\(169\) −12.3430 −0.949462
\(170\) −8.06901 −0.618865
\(171\) −8.99653 −0.687982
\(172\) 0.325523 0.0248209
\(173\) 14.7683 1.12281 0.561406 0.827540i \(-0.310261\pi\)
0.561406 + 0.827540i \(0.310261\pi\)
\(174\) −29.5224 −2.23809
\(175\) −4.86714 −0.367921
\(176\) 4.74827 0.357914
\(177\) 0.461807 0.0347116
\(178\) −14.9523 −1.12073
\(179\) −22.1672 −1.65685 −0.828425 0.560099i \(-0.810763\pi\)
−0.828425 + 0.560099i \(0.810763\pi\)
\(180\) 25.2205 1.87982
\(181\) 22.4873 1.67146 0.835732 0.549137i \(-0.185043\pi\)
0.835732 + 0.549137i \(0.185043\pi\)
\(182\) 9.20055 0.681990
\(183\) 12.8197 0.947659
\(184\) 14.1954 1.04650
\(185\) 3.60402 0.264973
\(186\) 80.0190 5.86728
\(187\) 17.3217 1.26669
\(188\) 29.7309 2.16835
\(189\) 67.8064 4.93219
\(190\) 2.86091 0.207552
\(191\) −3.76100 −0.272136 −0.136068 0.990699i \(-0.543447\pi\)
−0.136068 + 0.990699i \(0.543447\pi\)
\(192\) 39.8324 2.87466
\(193\) 6.63664 0.477716 0.238858 0.971055i \(-0.423227\pi\)
0.238858 + 0.971055i \(0.423227\pi\)
\(194\) −2.99345 −0.214917
\(195\) −2.60563 −0.186593
\(196\) 57.3927 4.09948
\(197\) 3.76296 0.268099 0.134050 0.990975i \(-0.457202\pi\)
0.134050 + 0.990975i \(0.457202\pi\)
\(198\) −85.6274 −6.08527
\(199\) 13.8550 0.982156 0.491078 0.871116i \(-0.336603\pi\)
0.491078 + 0.871116i \(0.336603\pi\)
\(200\) −3.35583 −0.237293
\(201\) −20.8067 −1.46759
\(202\) −17.4734 −1.22943
\(203\) 19.1663 1.34521
\(204\) −38.2488 −2.67795
\(205\) −9.85216 −0.688105
\(206\) 35.7636 2.49177
\(207\) −31.0224 −2.15621
\(208\) 0.768760 0.0533039
\(209\) −6.14150 −0.424816
\(210\) −36.4889 −2.51797
\(211\) −8.71099 −0.599689 −0.299845 0.953988i \(-0.596935\pi\)
−0.299845 + 0.953988i \(0.596935\pi\)
\(212\) 41.5903 2.85643
\(213\) 29.8794 2.04730
\(214\) −2.49009 −0.170219
\(215\) 0.0946578 0.00645561
\(216\) 46.7517 3.18105
\(217\) −51.9494 −3.52655
\(218\) −42.3230 −2.86648
\(219\) −46.7940 −3.16205
\(220\) 17.2168 1.16076
\(221\) 2.80444 0.188647
\(222\) 27.0193 1.81342
\(223\) 17.4190 1.16646 0.583231 0.812306i \(-0.301788\pi\)
0.583231 + 0.812306i \(0.301788\pi\)
\(224\) −21.9010 −1.46332
\(225\) 7.33378 0.488919
\(226\) −11.9822 −0.797043
\(227\) 22.2581 1.47732 0.738662 0.674076i \(-0.235458\pi\)
0.738662 + 0.674076i \(0.235458\pi\)
\(228\) 13.5613 0.898119
\(229\) −2.26616 −0.149752 −0.0748760 0.997193i \(-0.523856\pi\)
−0.0748760 + 0.997193i \(0.523856\pi\)
\(230\) 9.86516 0.650490
\(231\) 78.3305 5.15377
\(232\) 13.2149 0.867603
\(233\) −18.2828 −1.19774 −0.598872 0.800844i \(-0.704384\pi\)
−0.598872 + 0.800844i \(0.704384\pi\)
\(234\) −13.8633 −0.906275
\(235\) 8.64538 0.563962
\(236\) −0.494033 −0.0321588
\(237\) −48.3105 −3.13810
\(238\) 39.2730 2.54569
\(239\) −11.5672 −0.748217 −0.374108 0.927385i \(-0.622051\pi\)
−0.374108 + 0.927385i \(0.622051\pi\)
\(240\) −3.04886 −0.196803
\(241\) 20.0007 1.28836 0.644180 0.764874i \(-0.277199\pi\)
0.644180 + 0.764874i \(0.277199\pi\)
\(242\) −32.8000 −2.10846
\(243\) −31.4444 −2.01716
\(244\) −13.7143 −0.877966
\(245\) 16.6891 1.06622
\(246\) −73.8616 −4.70924
\(247\) −0.994328 −0.0632676
\(248\) −35.8185 −2.27447
\(249\) −16.5716 −1.05018
\(250\) −2.33215 −0.147498
\(251\) −18.1086 −1.14301 −0.571503 0.820600i \(-0.693639\pi\)
−0.571503 + 0.820600i \(0.693639\pi\)
\(252\) −122.751 −7.73262
\(253\) −21.1775 −1.33142
\(254\) 35.4077 2.22168
\(255\) −11.1223 −0.696502
\(256\) −21.6237 −1.35148
\(257\) −5.79003 −0.361172 −0.180586 0.983559i \(-0.557799\pi\)
−0.180586 + 0.983559i \(0.557799\pi\)
\(258\) 0.709648 0.0441808
\(259\) −17.5413 −1.08996
\(260\) 2.78745 0.172871
\(261\) −28.8797 −1.78761
\(262\) 23.1448 1.42989
\(263\) −4.25235 −0.262211 −0.131105 0.991368i \(-0.541853\pi\)
−0.131105 + 0.991368i \(0.541853\pi\)
\(264\) 54.0079 3.32396
\(265\) 12.0939 0.742923
\(266\) −13.9244 −0.853762
\(267\) −20.6102 −1.26132
\(268\) 22.2586 1.35966
\(269\) −20.2782 −1.23639 −0.618193 0.786026i \(-0.712135\pi\)
−0.618193 + 0.786026i \(0.712135\pi\)
\(270\) 32.4903 1.97730
\(271\) 1.06346 0.0646005 0.0323003 0.999478i \(-0.489717\pi\)
0.0323003 + 0.999478i \(0.489717\pi\)
\(272\) 3.28149 0.198970
\(273\) 12.6820 0.767547
\(274\) −17.7186 −1.07042
\(275\) 5.00642 0.301899
\(276\) 46.7629 2.81480
\(277\) 4.27136 0.256641 0.128320 0.991733i \(-0.459041\pi\)
0.128320 + 0.991733i \(0.459041\pi\)
\(278\) 0.959130 0.0575248
\(279\) 78.2771 4.68633
\(280\) 16.3333 0.976102
\(281\) −8.93717 −0.533147 −0.266574 0.963815i \(-0.585892\pi\)
−0.266574 + 0.963815i \(0.585892\pi\)
\(282\) 64.8143 3.85963
\(283\) 18.8278 1.11920 0.559598 0.828764i \(-0.310955\pi\)
0.559598 + 0.828764i \(0.310955\pi\)
\(284\) −31.9644 −1.89674
\(285\) 3.94345 0.233590
\(286\) −9.46384 −0.559609
\(287\) 47.9519 2.83051
\(288\) 33.0003 1.94456
\(289\) −5.02912 −0.295831
\(290\) 9.18379 0.539291
\(291\) −4.12615 −0.241879
\(292\) 50.0594 2.92950
\(293\) −8.68587 −0.507434 −0.253717 0.967279i \(-0.581653\pi\)
−0.253717 + 0.967279i \(0.581653\pi\)
\(294\) 125.118 7.29701
\(295\) −0.143658 −0.00836411
\(296\) −12.0945 −0.702978
\(297\) −69.7468 −4.04712
\(298\) −37.4276 −2.16812
\(299\) −3.42870 −0.198287
\(300\) −11.0549 −0.638254
\(301\) −0.460713 −0.0265550
\(302\) −2.02074 −0.116281
\(303\) −24.0852 −1.38366
\(304\) −1.16347 −0.0667295
\(305\) −3.98793 −0.228348
\(306\) −59.1764 −3.38289
\(307\) −1.88844 −0.107779 −0.0538896 0.998547i \(-0.517162\pi\)
−0.0538896 + 0.998547i \(0.517162\pi\)
\(308\) −83.7965 −4.77475
\(309\) 49.2962 2.80436
\(310\) −24.8922 −1.41378
\(311\) −25.0546 −1.42072 −0.710359 0.703839i \(-0.751468\pi\)
−0.710359 + 0.703839i \(0.751468\pi\)
\(312\) 8.74405 0.495035
\(313\) −29.3596 −1.65950 −0.829750 0.558135i \(-0.811517\pi\)
−0.829750 + 0.558135i \(0.811517\pi\)
\(314\) 45.1022 2.54526
\(315\) −35.6946 −2.01116
\(316\) 51.6816 2.90732
\(317\) −4.46268 −0.250649 −0.125325 0.992116i \(-0.539997\pi\)
−0.125325 + 0.992116i \(0.539997\pi\)
\(318\) 90.6680 5.08441
\(319\) −19.7148 −1.10382
\(320\) −12.3910 −0.692679
\(321\) −3.43232 −0.191574
\(322\) −48.0151 −2.67578
\(323\) −4.24434 −0.236161
\(324\) 78.3495 4.35275
\(325\) 0.810556 0.0449615
\(326\) 5.95205 0.329653
\(327\) −58.3377 −3.22608
\(328\) 33.0622 1.82556
\(329\) −42.0783 −2.31985
\(330\) 37.5331 2.06613
\(331\) −18.4637 −1.01486 −0.507429 0.861694i \(-0.669404\pi\)
−0.507429 + 0.861694i \(0.669404\pi\)
\(332\) 17.7280 0.972951
\(333\) 26.4311 1.44842
\(334\) −22.1947 −1.21444
\(335\) 6.47252 0.353632
\(336\) 14.8392 0.809547
\(337\) −14.8510 −0.808987 −0.404494 0.914541i \(-0.632552\pi\)
−0.404494 + 0.914541i \(0.632552\pi\)
\(338\) 28.7858 1.56574
\(339\) −16.5161 −0.897034
\(340\) 11.8984 0.645280
\(341\) 53.4360 2.89372
\(342\) 20.9813 1.13454
\(343\) −47.1580 −2.54629
\(344\) −0.317656 −0.0171268
\(345\) 13.5981 0.732095
\(346\) −34.4419 −1.85161
\(347\) −8.69189 −0.466605 −0.233303 0.972404i \(-0.574953\pi\)
−0.233303 + 0.972404i \(0.574953\pi\)
\(348\) 43.5331 2.33362
\(349\) −25.0983 −1.34348 −0.671740 0.740787i \(-0.734453\pi\)
−0.671740 + 0.740787i \(0.734453\pi\)
\(350\) 11.3509 0.606732
\(351\) −11.2922 −0.602735
\(352\) 22.5277 1.20073
\(353\) 19.3176 1.02817 0.514087 0.857738i \(-0.328131\pi\)
0.514087 + 0.857738i \(0.328131\pi\)
\(354\) −1.07701 −0.0572422
\(355\) −9.29484 −0.493319
\(356\) 22.0484 1.16856
\(357\) 54.1336 2.86505
\(358\) 51.6972 2.73228
\(359\) 24.6251 1.29966 0.649832 0.760078i \(-0.274839\pi\)
0.649832 + 0.760078i \(0.274839\pi\)
\(360\) −24.6110 −1.29711
\(361\) −17.4951 −0.920797
\(362\) −52.4438 −2.75638
\(363\) −45.2113 −2.37298
\(364\) −13.5669 −0.711100
\(365\) 14.5566 0.761928
\(366\) −29.8975 −1.56277
\(367\) −31.5955 −1.64927 −0.824636 0.565664i \(-0.808620\pi\)
−0.824636 + 0.565664i \(0.808620\pi\)
\(368\) −4.01195 −0.209137
\(369\) −72.2536 −3.76137
\(370\) −8.40513 −0.436962
\(371\) −58.8628 −3.05600
\(372\) −117.994 −6.11772
\(373\) 26.8388 1.38966 0.694829 0.719175i \(-0.255480\pi\)
0.694829 + 0.719175i \(0.255480\pi\)
\(374\) −40.3969 −2.08887
\(375\) −3.21462 −0.166002
\(376\) −29.0124 −1.49620
\(377\) −3.19189 −0.164391
\(378\) −158.135 −8.13359
\(379\) −22.4961 −1.15555 −0.577774 0.816197i \(-0.696079\pi\)
−0.577774 + 0.816197i \(0.696079\pi\)
\(380\) −4.21863 −0.216411
\(381\) 48.8057 2.50039
\(382\) 8.77122 0.448775
\(383\) −6.29305 −0.321560 −0.160780 0.986990i \(-0.551401\pi\)
−0.160780 + 0.986990i \(0.551401\pi\)
\(384\) −63.9653 −3.26421
\(385\) −24.3670 −1.24186
\(386\) −15.4777 −0.787792
\(387\) 0.694200 0.0352881
\(388\) 4.41407 0.224091
\(389\) 5.91388 0.299846 0.149923 0.988698i \(-0.452097\pi\)
0.149923 + 0.988698i \(0.452097\pi\)
\(390\) 6.07673 0.307707
\(391\) −14.6356 −0.740153
\(392\) −56.0057 −2.82871
\(393\) 31.9027 1.60928
\(394\) −8.77579 −0.442118
\(395\) 15.0284 0.756159
\(396\) 126.264 6.34502
\(397\) −19.7314 −0.990293 −0.495146 0.868810i \(-0.664886\pi\)
−0.495146 + 0.868810i \(0.664886\pi\)
\(398\) −32.3120 −1.61966
\(399\) −19.1933 −0.960868
\(400\) 0.948436 0.0474218
\(401\) −22.7282 −1.13499 −0.567497 0.823375i \(-0.692088\pi\)
−0.567497 + 0.823375i \(0.692088\pi\)
\(402\) 48.5244 2.42018
\(403\) 8.65146 0.430960
\(404\) 25.7659 1.28190
\(405\) 22.7830 1.13210
\(406\) −44.6988 −2.21836
\(407\) 18.0432 0.894370
\(408\) 37.3244 1.84783
\(409\) 35.1010 1.73563 0.867817 0.496884i \(-0.165523\pi\)
0.867817 + 0.496884i \(0.165523\pi\)
\(410\) 22.9768 1.13474
\(411\) −24.4232 −1.20471
\(412\) −52.7361 −2.59812
\(413\) 0.699206 0.0344057
\(414\) 72.3490 3.55576
\(415\) 5.15508 0.253053
\(416\) 3.64731 0.178824
\(417\) 1.32206 0.0647414
\(418\) 14.3229 0.700557
\(419\) −9.80104 −0.478812 −0.239406 0.970920i \(-0.576953\pi\)
−0.239406 + 0.970920i \(0.576953\pi\)
\(420\) 53.8057 2.62545
\(421\) 4.96796 0.242124 0.121062 0.992645i \(-0.461370\pi\)
0.121062 + 0.992645i \(0.461370\pi\)
\(422\) 20.3154 0.988937
\(423\) 63.4033 3.08277
\(424\) −40.5852 −1.97099
\(425\) 3.45990 0.167830
\(426\) −69.6833 −3.37617
\(427\) 19.4098 0.939307
\(428\) 3.67184 0.177485
\(429\) −13.0449 −0.629812
\(430\) −0.220756 −0.0106458
\(431\) 20.4221 0.983697 0.491849 0.870681i \(-0.336321\pi\)
0.491849 + 0.870681i \(0.336321\pi\)
\(432\) −13.2131 −0.635716
\(433\) −5.93424 −0.285181 −0.142591 0.989782i \(-0.545543\pi\)
−0.142591 + 0.989782i \(0.545543\pi\)
\(434\) 121.154 5.81557
\(435\) 12.6589 0.606946
\(436\) 62.4086 2.98883
\(437\) 5.18912 0.248229
\(438\) 109.131 5.21447
\(439\) −7.82584 −0.373507 −0.186754 0.982407i \(-0.559797\pi\)
−0.186754 + 0.982407i \(0.559797\pi\)
\(440\) −16.8007 −0.800943
\(441\) 122.394 5.82828
\(442\) −6.54038 −0.311094
\(443\) 22.6915 1.07811 0.539053 0.842272i \(-0.318782\pi\)
0.539053 + 0.842272i \(0.318782\pi\)
\(444\) −39.8421 −1.89082
\(445\) 6.41139 0.303929
\(446\) −40.6238 −1.92359
\(447\) −51.5898 −2.44012
\(448\) 60.3088 2.84932
\(449\) 34.0951 1.60905 0.804524 0.593920i \(-0.202420\pi\)
0.804524 + 0.593920i \(0.202420\pi\)
\(450\) −17.1035 −0.806267
\(451\) −49.3241 −2.32258
\(452\) 17.6687 0.831064
\(453\) −2.78537 −0.130868
\(454\) −51.9094 −2.43623
\(455\) −3.94509 −0.184949
\(456\) −13.2336 −0.619718
\(457\) −27.4681 −1.28490 −0.642452 0.766326i \(-0.722083\pi\)
−0.642452 + 0.766326i \(0.722083\pi\)
\(458\) 5.28503 0.246953
\(459\) −48.2014 −2.24985
\(460\) −14.5469 −0.678255
\(461\) −31.2058 −1.45340 −0.726701 0.686954i \(-0.758947\pi\)
−0.726701 + 0.686954i \(0.758947\pi\)
\(462\) −182.679 −8.49899
\(463\) 33.4282 1.55354 0.776770 0.629785i \(-0.216857\pi\)
0.776770 + 0.629785i \(0.216857\pi\)
\(464\) −3.73485 −0.173386
\(465\) −34.3112 −1.59114
\(466\) 42.6383 1.97518
\(467\) 9.19614 0.425546 0.212773 0.977102i \(-0.431750\pi\)
0.212773 + 0.977102i \(0.431750\pi\)
\(468\) 20.4426 0.944959
\(469\) −31.5027 −1.45466
\(470\) −20.1623 −0.930020
\(471\) 62.1685 2.86457
\(472\) 0.482094 0.0221902
\(473\) 0.473897 0.0217898
\(474\) 112.667 5.17499
\(475\) −1.22672 −0.0562859
\(476\) −57.9111 −2.65435
\(477\) 88.6942 4.06103
\(478\) 26.9764 1.23387
\(479\) 9.47974 0.433141 0.216570 0.976267i \(-0.430513\pi\)
0.216570 + 0.976267i \(0.430513\pi\)
\(480\) −14.4650 −0.660236
\(481\) 2.92126 0.133198
\(482\) −46.6447 −2.12461
\(483\) −66.1836 −3.01146
\(484\) 48.3662 2.19846
\(485\) 1.28356 0.0582833
\(486\) 73.3332 3.32646
\(487\) −38.3713 −1.73877 −0.869386 0.494134i \(-0.835485\pi\)
−0.869386 + 0.494134i \(0.835485\pi\)
\(488\) 13.3828 0.605812
\(489\) 8.20425 0.371009
\(490\) −38.9214 −1.75829
\(491\) −14.9402 −0.674242 −0.337121 0.941461i \(-0.609453\pi\)
−0.337121 + 0.941461i \(0.609453\pi\)
\(492\) 108.915 4.91025
\(493\) −13.6247 −0.613627
\(494\) 2.31893 0.104333
\(495\) 36.7160 1.65026
\(496\) 10.1231 0.454542
\(497\) 45.2393 2.02926
\(498\) 38.6476 1.73184
\(499\) 15.5537 0.696280 0.348140 0.937443i \(-0.386813\pi\)
0.348140 + 0.937443i \(0.386813\pi\)
\(500\) 3.43894 0.153794
\(501\) −30.5929 −1.36679
\(502\) 42.2321 1.88491
\(503\) −3.64734 −0.162627 −0.0813135 0.996689i \(-0.525911\pi\)
−0.0813135 + 0.996689i \(0.525911\pi\)
\(504\) 119.785 5.33565
\(505\) 7.49239 0.333407
\(506\) 49.3892 2.19562
\(507\) 39.6781 1.76216
\(508\) −52.2115 −2.31651
\(509\) 8.97536 0.397826 0.198913 0.980017i \(-0.436259\pi\)
0.198913 + 0.980017i \(0.436259\pi\)
\(510\) 25.9388 1.14859
\(511\) −70.8491 −3.13418
\(512\) 10.6333 0.469931
\(513\) 17.0901 0.754545
\(514\) 13.5032 0.595603
\(515\) −15.3350 −0.675740
\(516\) −1.04643 −0.0460666
\(517\) 43.2824 1.90356
\(518\) 40.9089 1.79744
\(519\) −47.4744 −2.08390
\(520\) −2.72009 −0.119284
\(521\) 19.3820 0.849139 0.424570 0.905395i \(-0.360425\pi\)
0.424570 + 0.905395i \(0.360425\pi\)
\(522\) 67.3519 2.94791
\(523\) −37.0328 −1.61933 −0.809666 0.586891i \(-0.800352\pi\)
−0.809666 + 0.586891i \(0.800352\pi\)
\(524\) −34.1289 −1.49093
\(525\) 15.6460 0.682848
\(526\) 9.91713 0.432407
\(527\) 36.9292 1.60866
\(528\) −15.2639 −0.664275
\(529\) −5.10654 −0.222024
\(530\) −28.2049 −1.22514
\(531\) −1.05356 −0.0457206
\(532\) 20.5327 0.890204
\(533\) −7.98573 −0.345900
\(534\) 48.0661 2.08002
\(535\) 1.06772 0.0461617
\(536\) −21.7207 −0.938191
\(537\) 71.2590 3.07505
\(538\) 47.2920 2.03890
\(539\) 83.5524 3.59886
\(540\) −47.9095 −2.06170
\(541\) −3.70791 −0.159416 −0.0797078 0.996818i \(-0.525399\pi\)
−0.0797078 + 0.996818i \(0.525399\pi\)
\(542\) −2.48015 −0.106532
\(543\) −72.2880 −3.10218
\(544\) 15.5687 0.667504
\(545\) 18.1476 0.777358
\(546\) −29.5763 −1.26575
\(547\) 42.5162 1.81786 0.908931 0.416947i \(-0.136900\pi\)
0.908931 + 0.416947i \(0.136900\pi\)
\(548\) 26.1275 1.11611
\(549\) −29.2466 −1.24822
\(550\) −11.6757 −0.497855
\(551\) 4.83072 0.205795
\(552\) −45.6328 −1.94226
\(553\) −73.1451 −3.11045
\(554\) −9.96146 −0.423222
\(555\) −11.5856 −0.491779
\(556\) −1.41431 −0.0599802
\(557\) 37.3924 1.58437 0.792183 0.610284i \(-0.208944\pi\)
0.792183 + 0.610284i \(0.208944\pi\)
\(558\) −182.554 −7.72813
\(559\) 0.0767254 0.00324514
\(560\) −4.61617 −0.195069
\(561\) −55.6827 −2.35092
\(562\) 20.8429 0.879203
\(563\) −5.97462 −0.251800 −0.125900 0.992043i \(-0.540182\pi\)
−0.125900 + 0.992043i \(0.540182\pi\)
\(564\) −95.5737 −4.02438
\(565\) 5.13782 0.216150
\(566\) −43.9093 −1.84565
\(567\) −110.888 −4.65687
\(568\) 31.1919 1.30878
\(569\) 45.5515 1.90962 0.954810 0.297217i \(-0.0960586\pi\)
0.954810 + 0.297217i \(0.0960586\pi\)
\(570\) −9.19673 −0.385209
\(571\) 10.4378 0.436809 0.218404 0.975858i \(-0.429915\pi\)
0.218404 + 0.975858i \(0.429915\pi\)
\(572\) 13.9552 0.583495
\(573\) 12.0902 0.505074
\(574\) −111.831 −4.66774
\(575\) −4.23007 −0.176406
\(576\) −90.8731 −3.78638
\(577\) 13.9660 0.581414 0.290707 0.956812i \(-0.406110\pi\)
0.290707 + 0.956812i \(0.406110\pi\)
\(578\) 11.7287 0.487849
\(579\) −21.3343 −0.886622
\(580\) −13.5422 −0.562310
\(581\) −25.0905 −1.04093
\(582\) 9.62281 0.398878
\(583\) 60.5472 2.50761
\(584\) −48.8496 −2.02141
\(585\) 5.94444 0.245772
\(586\) 20.2568 0.836800
\(587\) −15.3599 −0.633972 −0.316986 0.948430i \(-0.602671\pi\)
−0.316986 + 0.948430i \(0.602671\pi\)
\(588\) −184.496 −7.60847
\(589\) −13.0934 −0.539505
\(590\) 0.335033 0.0137931
\(591\) −12.0965 −0.497582
\(592\) 3.41818 0.140486
\(593\) 2.46420 0.101193 0.0505963 0.998719i \(-0.483888\pi\)
0.0505963 + 0.998719i \(0.483888\pi\)
\(594\) 162.660 6.67403
\(595\) −16.8398 −0.690364
\(596\) 55.1898 2.26066
\(597\) −44.5386 −1.82284
\(598\) 7.99626 0.326992
\(599\) 13.7218 0.560658 0.280329 0.959904i \(-0.409556\pi\)
0.280329 + 0.959904i \(0.409556\pi\)
\(600\) 10.7877 0.440407
\(601\) 44.3413 1.80872 0.904359 0.426772i \(-0.140349\pi\)
0.904359 + 0.426772i \(0.140349\pi\)
\(602\) 1.07445 0.0437914
\(603\) 47.4681 1.93305
\(604\) 2.97974 0.121244
\(605\) 14.0643 0.571793
\(606\) 56.1704 2.28177
\(607\) −19.7309 −0.800852 −0.400426 0.916329i \(-0.631138\pi\)
−0.400426 + 0.916329i \(0.631138\pi\)
\(608\) −5.51997 −0.223864
\(609\) −61.6124 −2.49666
\(610\) 9.30047 0.376565
\(611\) 7.00756 0.283495
\(612\) 87.2601 3.52728
\(613\) 4.03142 0.162827 0.0814137 0.996680i \(-0.474057\pi\)
0.0814137 + 0.996680i \(0.474057\pi\)
\(614\) 4.40414 0.177737
\(615\) 31.6710 1.27710
\(616\) 81.7714 3.29467
\(617\) 21.3458 0.859348 0.429674 0.902984i \(-0.358629\pi\)
0.429674 + 0.902984i \(0.358629\pi\)
\(618\) −114.966 −4.62462
\(619\) −24.5807 −0.987981 −0.493991 0.869467i \(-0.664462\pi\)
−0.493991 + 0.869467i \(0.664462\pi\)
\(620\) 36.7055 1.47413
\(621\) 58.9310 2.36482
\(622\) 58.4313 2.34288
\(623\) −31.2051 −1.25021
\(624\) −2.47127 −0.0989300
\(625\) 1.00000 0.0400000
\(626\) 68.4710 2.73665
\(627\) 19.7426 0.788443
\(628\) −66.5067 −2.65391
\(629\) 12.4695 0.497193
\(630\) 83.2452 3.31657
\(631\) 36.9713 1.47181 0.735903 0.677087i \(-0.236758\pi\)
0.735903 + 0.677087i \(0.236758\pi\)
\(632\) −50.4327 −2.00610
\(633\) 28.0025 1.11300
\(634\) 10.4077 0.413341
\(635\) −15.1824 −0.602496
\(636\) −133.697 −5.30143
\(637\) 13.5274 0.535975
\(638\) 45.9779 1.82028
\(639\) −68.1663 −2.69662
\(640\) 19.8982 0.786547
\(641\) −9.99365 −0.394725 −0.197363 0.980331i \(-0.563238\pi\)
−0.197363 + 0.980331i \(0.563238\pi\)
\(642\) 8.00471 0.315921
\(643\) −41.1307 −1.62204 −0.811018 0.585021i \(-0.801086\pi\)
−0.811018 + 0.585021i \(0.801086\pi\)
\(644\) 70.8020 2.78999
\(645\) −0.304289 −0.0119814
\(646\) 9.89844 0.389449
\(647\) −47.9171 −1.88382 −0.941908 0.335870i \(-0.890970\pi\)
−0.941908 + 0.335870i \(0.890970\pi\)
\(648\) −76.4561 −3.00348
\(649\) −0.719215 −0.0282316
\(650\) −1.89034 −0.0741452
\(651\) 166.998 6.54515
\(652\) −8.77675 −0.343724
\(653\) 32.3242 1.26494 0.632472 0.774583i \(-0.282040\pi\)
0.632472 + 0.774583i \(0.282040\pi\)
\(654\) 136.052 5.32007
\(655\) −9.92424 −0.387772
\(656\) −9.34415 −0.364828
\(657\) 106.755 4.16491
\(658\) 98.1330 3.82562
\(659\) 6.51593 0.253825 0.126912 0.991914i \(-0.459493\pi\)
0.126912 + 0.991914i \(0.459493\pi\)
\(660\) −55.3455 −2.15432
\(661\) −45.2602 −1.76042 −0.880209 0.474585i \(-0.842598\pi\)
−0.880209 + 0.474585i \(0.842598\pi\)
\(662\) 43.0602 1.67358
\(663\) −9.01520 −0.350121
\(664\) −17.2996 −0.671354
\(665\) 5.97064 0.231531
\(666\) −61.6414 −2.38856
\(667\) 16.6576 0.644984
\(668\) 32.7278 1.26628
\(669\) −55.9955 −2.16491
\(670\) −15.0949 −0.583167
\(671\) −19.9653 −0.770751
\(672\) 70.4034 2.71587
\(673\) 11.4554 0.441573 0.220787 0.975322i \(-0.429138\pi\)
0.220787 + 0.975322i \(0.429138\pi\)
\(674\) 34.6349 1.33409
\(675\) −13.9315 −0.536223
\(676\) −42.4469 −1.63257
\(677\) −7.59709 −0.291980 −0.145990 0.989286i \(-0.546637\pi\)
−0.145990 + 0.989286i \(0.546637\pi\)
\(678\) 38.5182 1.47928
\(679\) −6.24725 −0.239747
\(680\) −11.6108 −0.445255
\(681\) −71.5515 −2.74186
\(682\) −124.621 −4.77198
\(683\) 14.1937 0.543105 0.271553 0.962424i \(-0.412463\pi\)
0.271553 + 0.962424i \(0.412463\pi\)
\(684\) −30.9385 −1.18296
\(685\) 7.59754 0.290287
\(686\) 109.980 4.19904
\(687\) 7.28484 0.277934
\(688\) 0.0897768 0.00342271
\(689\) 9.80279 0.373457
\(690\) −31.7128 −1.20728
\(691\) 5.70299 0.216952 0.108476 0.994099i \(-0.465403\pi\)
0.108476 + 0.994099i \(0.465403\pi\)
\(692\) 50.7873 1.93064
\(693\) −178.702 −6.78833
\(694\) 20.2708 0.769470
\(695\) −0.411264 −0.0156001
\(696\) −42.4810 −1.61024
\(697\) −34.0875 −1.29115
\(698\) 58.5331 2.21551
\(699\) 58.7722 2.22297
\(700\) −16.7378 −0.632630
\(701\) 44.1636 1.66804 0.834019 0.551736i \(-0.186034\pi\)
0.834019 + 0.551736i \(0.186034\pi\)
\(702\) 26.3352 0.993959
\(703\) −4.42114 −0.166746
\(704\) −62.0347 −2.33802
\(705\) −27.7916 −1.04669
\(706\) −45.0517 −1.69554
\(707\) −36.4665 −1.37147
\(708\) 1.58813 0.0596855
\(709\) −4.50089 −0.169035 −0.0845173 0.996422i \(-0.526935\pi\)
−0.0845173 + 0.996422i \(0.526935\pi\)
\(710\) 21.6770 0.813523
\(711\) 110.215 4.13338
\(712\) −21.5155 −0.806329
\(713\) −45.1496 −1.69086
\(714\) −126.248 −4.72470
\(715\) 4.05798 0.151760
\(716\) −76.2315 −2.84891
\(717\) 37.1840 1.38866
\(718\) −57.4296 −2.14325
\(719\) 16.4800 0.614600 0.307300 0.951613i \(-0.400574\pi\)
0.307300 + 0.951613i \(0.400574\pi\)
\(720\) 6.95562 0.259221
\(721\) 74.6375 2.77965
\(722\) 40.8014 1.51847
\(723\) −64.2947 −2.39115
\(724\) 77.3324 2.87404
\(725\) −3.93790 −0.146250
\(726\) 105.440 3.91323
\(727\) −25.9429 −0.962169 −0.481084 0.876674i \(-0.659757\pi\)
−0.481084 + 0.876674i \(0.659757\pi\)
\(728\) 13.2391 0.490672
\(729\) 32.7327 1.21232
\(730\) −33.9483 −1.25648
\(731\) 0.327506 0.0121132
\(732\) 44.0862 1.62947
\(733\) 3.96885 0.146593 0.0732964 0.997310i \(-0.476648\pi\)
0.0732964 + 0.997310i \(0.476648\pi\)
\(734\) 73.6856 2.71978
\(735\) −53.6490 −1.97887
\(736\) −19.0343 −0.701614
\(737\) 32.4042 1.19362
\(738\) 168.507 6.20281
\(739\) 5.71693 0.210301 0.105150 0.994456i \(-0.466468\pi\)
0.105150 + 0.994456i \(0.466468\pi\)
\(740\) 12.3940 0.455613
\(741\) 3.19639 0.117422
\(742\) 137.277 5.03960
\(743\) 29.9779 1.09978 0.549891 0.835237i \(-0.314669\pi\)
0.549891 + 0.835237i \(0.314669\pi\)
\(744\) 115.143 4.22134
\(745\) 16.0485 0.587971
\(746\) −62.5921 −2.29166
\(747\) 37.8062 1.38326
\(748\) 59.5683 2.17803
\(749\) −5.19676 −0.189885
\(750\) 7.49699 0.273751
\(751\) −8.59257 −0.313547 −0.156774 0.987635i \(-0.550109\pi\)
−0.156774 + 0.987635i \(0.550109\pi\)
\(752\) 8.19959 0.299008
\(753\) 58.2123 2.12138
\(754\) 7.44397 0.271093
\(755\) 0.866470 0.0315341
\(756\) 233.182 8.48076
\(757\) −41.1434 −1.49538 −0.747690 0.664048i \(-0.768837\pi\)
−0.747690 + 0.664048i \(0.768837\pi\)
\(758\) 52.4644 1.90559
\(759\) 68.0776 2.47106
\(760\) 4.11668 0.149328
\(761\) 19.1139 0.692880 0.346440 0.938072i \(-0.387390\pi\)
0.346440 + 0.938072i \(0.387390\pi\)
\(762\) −113.822 −4.12335
\(763\) −88.3270 −3.19765
\(764\) −12.9338 −0.467930
\(765\) 25.3741 0.917403
\(766\) 14.6764 0.530279
\(767\) −0.116443 −0.00420452
\(768\) 69.5120 2.50830
\(769\) 29.9515 1.08008 0.540039 0.841640i \(-0.318410\pi\)
0.540039 + 0.841640i \(0.318410\pi\)
\(770\) 56.8275 2.04792
\(771\) 18.6128 0.670322
\(772\) 22.8230 0.821418
\(773\) −19.6544 −0.706919 −0.353459 0.935450i \(-0.614995\pi\)
−0.353459 + 0.935450i \(0.614995\pi\)
\(774\) −1.61898 −0.0581930
\(775\) 10.6735 0.383403
\(776\) −4.30740 −0.154627
\(777\) 56.3885 2.02293
\(778\) −13.7921 −0.494470
\(779\) 12.0859 0.433022
\(780\) −8.96060 −0.320841
\(781\) −46.5339 −1.66511
\(782\) 34.1324 1.22057
\(783\) 54.8608 1.96056
\(784\) 15.8285 0.565304
\(785\) −19.3393 −0.690249
\(786\) −74.4019 −2.65383
\(787\) 32.4426 1.15645 0.578227 0.815876i \(-0.303745\pi\)
0.578227 + 0.815876i \(0.303745\pi\)
\(788\) 12.9406 0.460989
\(789\) 13.6697 0.486653
\(790\) −35.0484 −1.24697
\(791\) −25.0065 −0.889128
\(792\) −123.213 −4.37818
\(793\) −3.23244 −0.114787
\(794\) 46.0167 1.63307
\(795\) −38.8774 −1.37884
\(796\) 47.6466 1.68879
\(797\) −20.6978 −0.733155 −0.366577 0.930388i \(-0.619470\pi\)
−0.366577 + 0.930388i \(0.619470\pi\)
\(798\) 44.7618 1.58455
\(799\) 29.9121 1.05821
\(800\) 4.49977 0.159091
\(801\) 47.0197 1.66136
\(802\) 53.0058 1.87170
\(803\) 72.8766 2.57176
\(804\) −71.5530 −2.52348
\(805\) 20.5883 0.725643
\(806\) −20.1765 −0.710688
\(807\) 65.1868 2.29468
\(808\) −25.1432 −0.884536
\(809\) 51.4718 1.80965 0.904826 0.425782i \(-0.140001\pi\)
0.904826 + 0.425782i \(0.140001\pi\)
\(810\) −53.1335 −1.86692
\(811\) 30.3516 1.06579 0.532894 0.846182i \(-0.321104\pi\)
0.532894 + 0.846182i \(0.321104\pi\)
\(812\) 65.9118 2.31305
\(813\) −3.41862 −0.119896
\(814\) −42.0796 −1.47489
\(815\) −2.55217 −0.0893985
\(816\) −10.5487 −0.369280
\(817\) −0.116119 −0.00406249
\(818\) −81.8610 −2.86220
\(819\) −28.9324 −1.01098
\(820\) −33.8810 −1.18318
\(821\) −4.71388 −0.164516 −0.0822578 0.996611i \(-0.526213\pi\)
−0.0822578 + 0.996611i \(0.526213\pi\)
\(822\) 56.9587 1.98666
\(823\) 26.0254 0.907189 0.453594 0.891208i \(-0.350142\pi\)
0.453594 + 0.891208i \(0.350142\pi\)
\(824\) 51.4617 1.79275
\(825\) −16.0937 −0.560312
\(826\) −1.63065 −0.0567377
\(827\) 12.2546 0.426136 0.213068 0.977037i \(-0.431654\pi\)
0.213068 + 0.977037i \(0.431654\pi\)
\(828\) −106.684 −3.70753
\(829\) −8.24782 −0.286459 −0.143229 0.989690i \(-0.545749\pi\)
−0.143229 + 0.989690i \(0.545749\pi\)
\(830\) −12.0224 −0.417305
\(831\) −13.7308 −0.476316
\(832\) −10.0436 −0.348200
\(833\) 57.7424 2.00065
\(834\) −3.08324 −0.106764
\(835\) 9.51681 0.329343
\(836\) −21.1202 −0.730459
\(837\) −148.697 −5.13973
\(838\) 22.8575 0.789601
\(839\) 19.2777 0.665540 0.332770 0.943008i \(-0.392017\pi\)
0.332770 + 0.943008i \(0.392017\pi\)
\(840\) −52.5054 −1.81161
\(841\) −13.4929 −0.465274
\(842\) −11.5860 −0.399281
\(843\) 28.7296 0.989501
\(844\) −29.9566 −1.03115
\(845\) −12.3430 −0.424612
\(846\) −147.866 −5.08375
\(847\) −68.4527 −2.35206
\(848\) 11.4703 0.393892
\(849\) −60.5242 −2.07719
\(850\) −8.06901 −0.276765
\(851\) −15.2452 −0.522600
\(852\) 102.753 3.52027
\(853\) −18.1561 −0.621655 −0.310827 0.950466i \(-0.600606\pi\)
−0.310827 + 0.950466i \(0.600606\pi\)
\(854\) −45.2667 −1.54899
\(855\) −8.99653 −0.307675
\(856\) −3.58310 −0.122468
\(857\) −5.75210 −0.196488 −0.0982440 0.995162i \(-0.531323\pi\)
−0.0982440 + 0.995162i \(0.531323\pi\)
\(858\) 30.4227 1.03861
\(859\) −2.85866 −0.0975363 −0.0487681 0.998810i \(-0.515530\pi\)
−0.0487681 + 0.998810i \(0.515530\pi\)
\(860\) 0.325523 0.0111002
\(861\) −154.147 −5.25332
\(862\) −47.6275 −1.62220
\(863\) 40.5535 1.38046 0.690229 0.723591i \(-0.257510\pi\)
0.690229 + 0.723591i \(0.257510\pi\)
\(864\) −62.6884 −2.13270
\(865\) 14.7683 0.502137
\(866\) 13.8396 0.470287
\(867\) 16.1667 0.549051
\(868\) −178.651 −6.06381
\(869\) 75.2383 2.55228
\(870\) −29.5224 −1.00090
\(871\) 5.24634 0.177765
\(872\) −60.9003 −2.06235
\(873\) 9.41332 0.318593
\(874\) −12.1018 −0.409351
\(875\) −4.86714 −0.164539
\(876\) −160.922 −5.43705
\(877\) −1.64895 −0.0556810 −0.0278405 0.999612i \(-0.508863\pi\)
−0.0278405 + 0.999612i \(0.508863\pi\)
\(878\) 18.2511 0.615944
\(879\) 27.9218 0.941778
\(880\) 4.74827 0.160064
\(881\) 21.9368 0.739068 0.369534 0.929217i \(-0.379517\pi\)
0.369534 + 0.929217i \(0.379517\pi\)
\(882\) −285.441 −9.61131
\(883\) −23.9698 −0.806648 −0.403324 0.915057i \(-0.632145\pi\)
−0.403324 + 0.915057i \(0.632145\pi\)
\(884\) 9.64430 0.324373
\(885\) 0.461807 0.0155235
\(886\) −52.9201 −1.77789
\(887\) −1.22863 −0.0412534 −0.0206267 0.999787i \(-0.506566\pi\)
−0.0206267 + 0.999787i \(0.506566\pi\)
\(888\) 38.8792 1.30470
\(889\) 73.8950 2.47836
\(890\) −14.9523 −0.501204
\(891\) 114.061 3.82120
\(892\) 59.9029 2.00570
\(893\) −10.6055 −0.354899
\(894\) 120.315 4.02395
\(895\) −22.1672 −0.740966
\(896\) −96.8475 −3.23545
\(897\) 11.0220 0.368013
\(898\) −79.5151 −2.65345
\(899\) −42.0311 −1.40182
\(900\) 25.2205 0.840682
\(901\) 41.8437 1.39402
\(902\) 115.031 3.83013
\(903\) 1.48102 0.0492851
\(904\) −17.2417 −0.573449
\(905\) 22.4873 0.747502
\(906\) 6.49592 0.215812
\(907\) 44.1056 1.46450 0.732251 0.681035i \(-0.238470\pi\)
0.732251 + 0.681035i \(0.238470\pi\)
\(908\) 76.5444 2.54022
\(909\) 54.9476 1.82250
\(910\) 9.20055 0.304995
\(911\) −7.18242 −0.237964 −0.118982 0.992896i \(-0.537963\pi\)
−0.118982 + 0.992896i \(0.537963\pi\)
\(912\) 3.74011 0.123847
\(913\) 25.8085 0.854137
\(914\) 64.0599 2.11891
\(915\) 12.8197 0.423806
\(916\) −7.79319 −0.257494
\(917\) 48.3026 1.59509
\(918\) 112.413 3.71019
\(919\) 25.7823 0.850480 0.425240 0.905081i \(-0.360190\pi\)
0.425240 + 0.905081i \(0.360190\pi\)
\(920\) 14.1954 0.468008
\(921\) 6.07063 0.200034
\(922\) 72.7768 2.39678
\(923\) −7.53398 −0.247984
\(924\) 269.374 8.86176
\(925\) 3.60402 0.118499
\(926\) −77.9597 −2.56191
\(927\) −112.464 −3.69379
\(928\) −17.7196 −0.581676
\(929\) 8.34401 0.273758 0.136879 0.990588i \(-0.456293\pi\)
0.136879 + 0.990588i \(0.456293\pi\)
\(930\) 80.0190 2.62393
\(931\) −20.4729 −0.670971
\(932\) −62.8734 −2.05949
\(933\) 80.5412 2.63680
\(934\) −21.4468 −0.701761
\(935\) 17.3217 0.566480
\(936\) −19.9485 −0.652039
\(937\) 18.1316 0.592333 0.296167 0.955136i \(-0.404292\pi\)
0.296167 + 0.955136i \(0.404292\pi\)
\(938\) 73.4690 2.39885
\(939\) 94.3798 3.07997
\(940\) 29.7309 0.969716
\(941\) −2.70252 −0.0880995 −0.0440497 0.999029i \(-0.514026\pi\)
−0.0440497 + 0.999029i \(0.514026\pi\)
\(942\) −144.986 −4.72391
\(943\) 41.6753 1.35713
\(944\) −0.136251 −0.00443459
\(945\) 67.8064 2.20574
\(946\) −1.10520 −0.0359332
\(947\) −8.03292 −0.261035 −0.130517 0.991446i \(-0.541664\pi\)
−0.130517 + 0.991446i \(0.541664\pi\)
\(948\) −166.137 −5.39587
\(949\) 11.7989 0.383010
\(950\) 2.86091 0.0928201
\(951\) 14.3458 0.465196
\(952\) 56.5115 1.83155
\(953\) 9.92017 0.321346 0.160673 0.987008i \(-0.448634\pi\)
0.160673 + 0.987008i \(0.448634\pi\)
\(954\) −206.848 −6.69697
\(955\) −3.76100 −0.121703
\(956\) −39.7788 −1.28654
\(957\) 63.3756 2.04864
\(958\) −22.1082 −0.714284
\(959\) −36.9783 −1.19409
\(960\) 39.8324 1.28559
\(961\) 82.9234 2.67495
\(962\) −6.81282 −0.219654
\(963\) 7.83045 0.252333
\(964\) 68.7813 2.21530
\(965\) 6.63664 0.213641
\(966\) 154.350 4.96614
\(967\) −28.7663 −0.925061 −0.462530 0.886603i \(-0.653058\pi\)
−0.462530 + 0.886603i \(0.653058\pi\)
\(968\) −47.1973 −1.51698
\(969\) 13.6439 0.438306
\(970\) −2.99345 −0.0961139
\(971\) −17.6300 −0.565775 −0.282887 0.959153i \(-0.591292\pi\)
−0.282887 + 0.959153i \(0.591292\pi\)
\(972\) −108.135 −3.46845
\(973\) 2.00168 0.0641708
\(974\) 89.4879 2.86738
\(975\) −2.60563 −0.0834469
\(976\) −3.78230 −0.121068
\(977\) −57.4458 −1.83785 −0.918927 0.394429i \(-0.870942\pi\)
−0.918927 + 0.394429i \(0.870942\pi\)
\(978\) −19.1336 −0.611824
\(979\) 32.0981 1.02586
\(980\) 57.3927 1.83334
\(981\) 133.091 4.24926
\(982\) 34.8429 1.11188
\(983\) −7.60234 −0.242477 −0.121239 0.992623i \(-0.538687\pi\)
−0.121239 + 0.992623i \(0.538687\pi\)
\(984\) −106.282 −3.38816
\(985\) 3.76296 0.119898
\(986\) 31.7750 1.01192
\(987\) 135.266 4.30555
\(988\) −3.41943 −0.108787
\(989\) −0.400409 −0.0127323
\(990\) −85.6274 −2.72142
\(991\) −16.5524 −0.525805 −0.262903 0.964822i \(-0.584680\pi\)
−0.262903 + 0.964822i \(0.584680\pi\)
\(992\) 48.0282 1.52490
\(993\) 59.3539 1.88354
\(994\) −105.505 −3.34641
\(995\) 13.8550 0.439233
\(996\) −56.9888 −1.80576
\(997\) −3.08664 −0.0977550 −0.0488775 0.998805i \(-0.515564\pi\)
−0.0488775 + 0.998805i \(0.515564\pi\)
\(998\) −36.2737 −1.14822
\(999\) −50.2093 −1.58855
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 \(a_p\))