Properties

Label 6041.2.a.f.1.5
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.71866 q^{2}\) \(-0.898623 q^{3}\) \(+5.39111 q^{4}\) \(+3.58669 q^{5}\) \(+2.44305 q^{6}\) \(+1.00000 q^{7}\) \(-9.21926 q^{8}\) \(-2.19248 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.71866 q^{2}\) \(-0.898623 q^{3}\) \(+5.39111 q^{4}\) \(+3.58669 q^{5}\) \(+2.44305 q^{6}\) \(+1.00000 q^{7}\) \(-9.21926 q^{8}\) \(-2.19248 q^{9}\) \(-9.75100 q^{10}\) \(-6.15231 q^{11}\) \(-4.84457 q^{12}\) \(+0.437075 q^{13}\) \(-2.71866 q^{14}\) \(-3.22309 q^{15}\) \(+14.2818 q^{16}\) \(-4.15017 q^{17}\) \(+5.96060 q^{18}\) \(-2.98619 q^{19}\) \(+19.3362 q^{20}\) \(-0.898623 q^{21}\) \(+16.7260 q^{22}\) \(+3.64443 q^{23}\) \(+8.28464 q^{24}\) \(+7.86437 q^{25}\) \(-1.18826 q^{26}\) \(+4.66608 q^{27}\) \(+5.39111 q^{28}\) \(-7.47833 q^{29}\) \(+8.76247 q^{30}\) \(-0.0845463 q^{31}\) \(-20.3889 q^{32}\) \(+5.52861 q^{33}\) \(+11.2829 q^{34}\) \(+3.58669 q^{35}\) \(-11.8199 q^{36}\) \(+4.52200 q^{37}\) \(+8.11843 q^{38}\) \(-0.392766 q^{39}\) \(-33.0667 q^{40}\) \(+5.05744 q^{41}\) \(+2.44305 q^{42}\) \(+11.2055 q^{43}\) \(-33.1678 q^{44}\) \(-7.86374 q^{45}\) \(-9.90795 q^{46}\) \(-6.30676 q^{47}\) \(-12.8340 q^{48}\) \(+1.00000 q^{49}\) \(-21.3805 q^{50}\) \(+3.72943 q^{51}\) \(+2.35632 q^{52}\) \(-10.0023 q^{53}\) \(-12.6855 q^{54}\) \(-22.0665 q^{55}\) \(-9.21926 q^{56}\) \(+2.68346 q^{57}\) \(+20.3310 q^{58}\) \(+1.07947 q^{59}\) \(-17.3760 q^{60}\) \(-5.39020 q^{61}\) \(+0.229853 q^{62}\) \(-2.19248 q^{63}\) \(+26.8667 q^{64}\) \(+1.56766 q^{65}\) \(-15.0304 q^{66}\) \(+0.429232 q^{67}\) \(-22.3740 q^{68}\) \(-3.27497 q^{69}\) \(-9.75100 q^{70}\) \(+13.6946 q^{71}\) \(+20.2130 q^{72}\) \(-13.2913 q^{73}\) \(-12.2938 q^{74}\) \(-7.06710 q^{75}\) \(-16.0989 q^{76}\) \(-6.15231 q^{77}\) \(+1.06780 q^{78}\) \(+4.10176 q^{79}\) \(+51.2245 q^{80}\) \(+2.38438 q^{81}\) \(-13.7494 q^{82}\) \(-1.17732 q^{83}\) \(-4.84457 q^{84}\) \(-14.8854 q^{85}\) \(-30.4639 q^{86}\) \(+6.72020 q^{87}\) \(+56.7198 q^{88}\) \(-14.0167 q^{89}\) \(+21.3788 q^{90}\) \(+0.437075 q^{91}\) \(+19.6475 q^{92}\) \(+0.0759753 q^{93}\) \(+17.1459 q^{94}\) \(-10.7105 q^{95}\) \(+18.3219 q^{96}\) \(+2.83308 q^{97}\) \(-2.71866 q^{98}\) \(+13.4888 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71866 −1.92238 −0.961191 0.275884i \(-0.911030\pi\)
−0.961191 + 0.275884i \(0.911030\pi\)
\(3\) −0.898623 −0.518820 −0.259410 0.965767i \(-0.583528\pi\)
−0.259410 + 0.965767i \(0.583528\pi\)
\(4\) 5.39111 2.69555
\(5\) 3.58669 1.60402 0.802009 0.597312i \(-0.203765\pi\)
0.802009 + 0.597312i \(0.203765\pi\)
\(6\) 2.44305 0.997371
\(7\) 1.00000 0.377964
\(8\) −9.21926 −3.25950
\(9\) −2.19248 −0.730826
\(10\) −9.75100 −3.08354
\(11\) −6.15231 −1.85499 −0.927496 0.373834i \(-0.878043\pi\)
−0.927496 + 0.373834i \(0.878043\pi\)
\(12\) −4.84457 −1.39851
\(13\) 0.437075 0.121223 0.0606114 0.998161i \(-0.480695\pi\)
0.0606114 + 0.998161i \(0.480695\pi\)
\(14\) −2.71866 −0.726592
\(15\) −3.22309 −0.832197
\(16\) 14.2818 3.57045
\(17\) −4.15017 −1.00656 −0.503281 0.864123i \(-0.667874\pi\)
−0.503281 + 0.864123i \(0.667874\pi\)
\(18\) 5.96060 1.40493
\(19\) −2.98619 −0.685078 −0.342539 0.939504i \(-0.611287\pi\)
−0.342539 + 0.939504i \(0.611287\pi\)
\(20\) 19.3362 4.32372
\(21\) −0.898623 −0.196096
\(22\) 16.7260 3.56600
\(23\) 3.64443 0.759916 0.379958 0.925004i \(-0.375939\pi\)
0.379958 + 0.925004i \(0.375939\pi\)
\(24\) 8.28464 1.69110
\(25\) 7.86437 1.57287
\(26\) −1.18826 −0.233037
\(27\) 4.66608 0.897987
\(28\) 5.39111 1.01882
\(29\) −7.47833 −1.38869 −0.694345 0.719642i \(-0.744306\pi\)
−0.694345 + 0.719642i \(0.744306\pi\)
\(30\) 8.76247 1.59980
\(31\) −0.0845463 −0.0151850 −0.00759248 0.999971i \(-0.502417\pi\)
−0.00759248 + 0.999971i \(0.502417\pi\)
\(32\) −20.3889 −3.60427
\(33\) 5.52861 0.962407
\(34\) 11.2829 1.93500
\(35\) 3.58669 0.606262
\(36\) −11.8199 −1.96998
\(37\) 4.52200 0.743412 0.371706 0.928351i \(-0.378773\pi\)
0.371706 + 0.928351i \(0.378773\pi\)
\(38\) 8.11843 1.31698
\(39\) −0.392766 −0.0628929
\(40\) −33.0667 −5.22830
\(41\) 5.05744 0.789839 0.394920 0.918716i \(-0.370772\pi\)
0.394920 + 0.918716i \(0.370772\pi\)
\(42\) 2.44305 0.376971
\(43\) 11.2055 1.70882 0.854410 0.519600i \(-0.173919\pi\)
0.854410 + 0.519600i \(0.173919\pi\)
\(44\) −33.1678 −5.00023
\(45\) −7.86374 −1.17226
\(46\) −9.90795 −1.46085
\(47\) −6.30676 −0.919935 −0.459967 0.887936i \(-0.652139\pi\)
−0.459967 + 0.887936i \(0.652139\pi\)
\(48\) −12.8340 −1.85242
\(49\) 1.00000 0.142857
\(50\) −21.3805 −3.02366
\(51\) 3.72943 0.522225
\(52\) 2.35632 0.326763
\(53\) −10.0023 −1.37393 −0.686964 0.726692i \(-0.741057\pi\)
−0.686964 + 0.726692i \(0.741057\pi\)
\(54\) −12.6855 −1.72627
\(55\) −22.0665 −2.97544
\(56\) −9.21926 −1.23198
\(57\) 2.68346 0.355433
\(58\) 20.3310 2.66959
\(59\) 1.07947 0.140536 0.0702678 0.997528i \(-0.477615\pi\)
0.0702678 + 0.997528i \(0.477615\pi\)
\(60\) −17.3760 −2.24323
\(61\) −5.39020 −0.690145 −0.345072 0.938576i \(-0.612146\pi\)
−0.345072 + 0.938576i \(0.612146\pi\)
\(62\) 0.229853 0.0291913
\(63\) −2.19248 −0.276226
\(64\) 26.8667 3.35834
\(65\) 1.56766 0.194444
\(66\) −15.0304 −1.85011
\(67\) 0.429232 0.0524391 0.0262195 0.999656i \(-0.491653\pi\)
0.0262195 + 0.999656i \(0.491653\pi\)
\(68\) −22.3740 −2.71324
\(69\) −3.27497 −0.394260
\(70\) −9.75100 −1.16547
\(71\) 13.6946 1.62525 0.812627 0.582784i \(-0.198037\pi\)
0.812627 + 0.582784i \(0.198037\pi\)
\(72\) 20.2130 2.38213
\(73\) −13.2913 −1.55563 −0.777816 0.628492i \(-0.783672\pi\)
−0.777816 + 0.628492i \(0.783672\pi\)
\(74\) −12.2938 −1.42912
\(75\) −7.06710 −0.816039
\(76\) −16.0989 −1.84667
\(77\) −6.15231 −0.701121
\(78\) 1.06780 0.120904
\(79\) 4.10176 0.461484 0.230742 0.973015i \(-0.425885\pi\)
0.230742 + 0.973015i \(0.425885\pi\)
\(80\) 51.2245 5.72707
\(81\) 2.38438 0.264932
\(82\) −13.7494 −1.51837
\(83\) −1.17732 −0.129227 −0.0646137 0.997910i \(-0.520582\pi\)
−0.0646137 + 0.997910i \(0.520582\pi\)
\(84\) −4.84457 −0.528586
\(85\) −14.8854 −1.61455
\(86\) −30.4639 −3.28500
\(87\) 6.72020 0.720481
\(88\) 56.7198 6.04635
\(89\) −14.0167 −1.48577 −0.742885 0.669419i \(-0.766543\pi\)
−0.742885 + 0.669419i \(0.766543\pi\)
\(90\) 21.3788 2.25353
\(91\) 0.437075 0.0458179
\(92\) 19.6475 2.04839
\(93\) 0.0759753 0.00787827
\(94\) 17.1459 1.76847
\(95\) −10.7105 −1.09888
\(96\) 18.3219 1.86997
\(97\) 2.83308 0.287655 0.143828 0.989603i \(-0.454059\pi\)
0.143828 + 0.989603i \(0.454059\pi\)
\(98\) −2.71866 −0.274626
\(99\) 13.4888 1.35568
\(100\) 42.3976 4.23976
\(101\) 10.2894 1.02384 0.511918 0.859034i \(-0.328935\pi\)
0.511918 + 0.859034i \(0.328935\pi\)
\(102\) −10.1391 −1.00392
\(103\) 6.29641 0.620404 0.310202 0.950671i \(-0.399603\pi\)
0.310202 + 0.950671i \(0.399603\pi\)
\(104\) −4.02951 −0.395126
\(105\) −3.22309 −0.314541
\(106\) 27.1930 2.64121
\(107\) −13.8880 −1.34261 −0.671303 0.741183i \(-0.734265\pi\)
−0.671303 + 0.741183i \(0.734265\pi\)
\(108\) 25.1553 2.42057
\(109\) 8.66578 0.830031 0.415015 0.909814i \(-0.363776\pi\)
0.415015 + 0.909814i \(0.363776\pi\)
\(110\) 59.9912 5.71993
\(111\) −4.06357 −0.385697
\(112\) 14.2818 1.34950
\(113\) 12.1592 1.14384 0.571921 0.820308i \(-0.306198\pi\)
0.571921 + 0.820308i \(0.306198\pi\)
\(114\) −7.29540 −0.683277
\(115\) 13.0714 1.21892
\(116\) −40.3164 −3.74329
\(117\) −0.958277 −0.0885928
\(118\) −2.93472 −0.270163
\(119\) −4.15017 −0.380445
\(120\) 29.7145 2.71255
\(121\) 26.8509 2.44099
\(122\) 14.6541 1.32672
\(123\) −4.54473 −0.409784
\(124\) −0.455798 −0.0409319
\(125\) 10.2736 0.918900
\(126\) 5.96060 0.531012
\(127\) −11.9245 −1.05813 −0.529064 0.848582i \(-0.677457\pi\)
−0.529064 + 0.848582i \(0.677457\pi\)
\(128\) −32.2637 −2.85174
\(129\) −10.0695 −0.886570
\(130\) −4.26192 −0.373795
\(131\) 10.5085 0.918135 0.459068 0.888401i \(-0.348184\pi\)
0.459068 + 0.888401i \(0.348184\pi\)
\(132\) 29.8053 2.59422
\(133\) −2.98619 −0.258935
\(134\) −1.16694 −0.100808
\(135\) 16.7358 1.44039
\(136\) 38.2615 3.28089
\(137\) 4.88617 0.417454 0.208727 0.977974i \(-0.433068\pi\)
0.208727 + 0.977974i \(0.433068\pi\)
\(138\) 8.90352 0.757918
\(139\) −16.0765 −1.36359 −0.681795 0.731543i \(-0.738801\pi\)
−0.681795 + 0.731543i \(0.738801\pi\)
\(140\) 19.3362 1.63421
\(141\) 5.66740 0.477281
\(142\) −37.2310 −3.12436
\(143\) −2.68902 −0.224867
\(144\) −31.3125 −2.60938
\(145\) −26.8225 −2.22748
\(146\) 36.1346 2.99052
\(147\) −0.898623 −0.0741172
\(148\) 24.3786 2.00391
\(149\) 16.2761 1.33339 0.666694 0.745332i \(-0.267709\pi\)
0.666694 + 0.745332i \(0.267709\pi\)
\(150\) 19.2130 1.56874
\(151\) −12.4912 −1.01652 −0.508259 0.861204i \(-0.669711\pi\)
−0.508259 + 0.861204i \(0.669711\pi\)
\(152\) 27.5304 2.23301
\(153\) 9.09914 0.735622
\(154\) 16.7260 1.34782
\(155\) −0.303242 −0.0243570
\(156\) −2.11744 −0.169531
\(157\) 19.2088 1.53303 0.766516 0.642225i \(-0.221989\pi\)
0.766516 + 0.642225i \(0.221989\pi\)
\(158\) −11.1513 −0.887148
\(159\) 8.98834 0.712822
\(160\) −73.1286 −5.78132
\(161\) 3.64443 0.287221
\(162\) −6.48233 −0.509300
\(163\) −4.70230 −0.368313 −0.184156 0.982897i \(-0.558955\pi\)
−0.184156 + 0.982897i \(0.558955\pi\)
\(164\) 27.2652 2.12905
\(165\) 19.8294 1.54372
\(166\) 3.20073 0.248424
\(167\) 16.3733 1.26701 0.633503 0.773740i \(-0.281616\pi\)
0.633503 + 0.773740i \(0.281616\pi\)
\(168\) 8.28464 0.639174
\(169\) −12.8090 −0.985305
\(170\) 40.4682 3.10377
\(171\) 6.54715 0.500673
\(172\) 60.4099 4.60621
\(173\) −0.149213 −0.0113444 −0.00567222 0.999984i \(-0.501806\pi\)
−0.00567222 + 0.999984i \(0.501806\pi\)
\(174\) −18.2699 −1.38504
\(175\) 7.86437 0.594490
\(176\) −87.8662 −6.62316
\(177\) −0.970041 −0.0729127
\(178\) 38.1067 2.85622
\(179\) −8.21822 −0.614258 −0.307129 0.951668i \(-0.599368\pi\)
−0.307129 + 0.951668i \(0.599368\pi\)
\(180\) −42.3943 −3.15988
\(181\) 21.2890 1.58240 0.791198 0.611561i \(-0.209458\pi\)
0.791198 + 0.611561i \(0.209458\pi\)
\(182\) −1.18826 −0.0880796
\(183\) 4.84376 0.358061
\(184\) −33.5989 −2.47695
\(185\) 16.2190 1.19245
\(186\) −0.206551 −0.0151450
\(187\) 25.5331 1.86717
\(188\) −34.0004 −2.47973
\(189\) 4.66608 0.339407
\(190\) 29.1183 2.11246
\(191\) 19.2441 1.39245 0.696226 0.717823i \(-0.254861\pi\)
0.696226 + 0.717823i \(0.254861\pi\)
\(192\) −24.1430 −1.74237
\(193\) 1.70644 0.122832 0.0614160 0.998112i \(-0.480438\pi\)
0.0614160 + 0.998112i \(0.480438\pi\)
\(194\) −7.70217 −0.552984
\(195\) −1.40873 −0.100881
\(196\) 5.39111 0.385079
\(197\) −11.3972 −0.812016 −0.406008 0.913869i \(-0.633080\pi\)
−0.406008 + 0.913869i \(0.633080\pi\)
\(198\) −36.6714 −2.60613
\(199\) 18.3993 1.30429 0.652144 0.758095i \(-0.273870\pi\)
0.652144 + 0.758095i \(0.273870\pi\)
\(200\) −72.5037 −5.12678
\(201\) −0.385718 −0.0272064
\(202\) −27.9734 −1.96820
\(203\) −7.47833 −0.524876
\(204\) 20.1058 1.40769
\(205\) 18.1395 1.26692
\(206\) −17.1178 −1.19265
\(207\) −7.99032 −0.555366
\(208\) 6.24223 0.432821
\(209\) 18.3720 1.27081
\(210\) 8.76247 0.604668
\(211\) 5.86906 0.404043 0.202021 0.979381i \(-0.435249\pi\)
0.202021 + 0.979381i \(0.435249\pi\)
\(212\) −53.9237 −3.70350
\(213\) −12.3063 −0.843214
\(214\) 37.7568 2.58100
\(215\) 40.1906 2.74098
\(216\) −43.0178 −2.92699
\(217\) −0.0845463 −0.00573938
\(218\) −23.5593 −1.59564
\(219\) 11.9439 0.807093
\(220\) −118.963 −8.02046
\(221\) −1.81393 −0.122018
\(222\) 11.0475 0.741457
\(223\) −0.238872 −0.0159960 −0.00799802 0.999968i \(-0.502546\pi\)
−0.00799802 + 0.999968i \(0.502546\pi\)
\(224\) −20.3889 −1.36229
\(225\) −17.2424 −1.14950
\(226\) −33.0568 −2.19890
\(227\) −23.3285 −1.54837 −0.774183 0.632962i \(-0.781839\pi\)
−0.774183 + 0.632962i \(0.781839\pi\)
\(228\) 14.4668 0.958087
\(229\) −22.6685 −1.49798 −0.748989 0.662582i \(-0.769461\pi\)
−0.748989 + 0.662582i \(0.769461\pi\)
\(230\) −35.5368 −2.34323
\(231\) 5.52861 0.363756
\(232\) 68.9446 4.52644
\(233\) −11.7360 −0.768849 −0.384424 0.923156i \(-0.625600\pi\)
−0.384424 + 0.923156i \(0.625600\pi\)
\(234\) 2.60523 0.170309
\(235\) −22.6204 −1.47559
\(236\) 5.81956 0.378821
\(237\) −3.68593 −0.239427
\(238\) 11.2829 0.731361
\(239\) 25.4338 1.64518 0.822588 0.568638i \(-0.192530\pi\)
0.822588 + 0.568638i \(0.192530\pi\)
\(240\) −46.0315 −2.97132
\(241\) −4.81627 −0.310244 −0.155122 0.987895i \(-0.549577\pi\)
−0.155122 + 0.987895i \(0.549577\pi\)
\(242\) −72.9985 −4.69252
\(243\) −16.1409 −1.03544
\(244\) −29.0592 −1.86032
\(245\) 3.58669 0.229145
\(246\) 12.3556 0.787762
\(247\) −1.30519 −0.0830472
\(248\) 0.779455 0.0494954
\(249\) 1.05796 0.0670458
\(250\) −27.9305 −1.76648
\(251\) 18.2117 1.14951 0.574757 0.818324i \(-0.305097\pi\)
0.574757 + 0.818324i \(0.305097\pi\)
\(252\) −11.8199 −0.744582
\(253\) −22.4217 −1.40964
\(254\) 32.4186 2.03412
\(255\) 13.3763 0.837659
\(256\) 33.9806 2.12379
\(257\) −1.85367 −0.115629 −0.0578144 0.998327i \(-0.518413\pi\)
−0.0578144 + 0.998327i \(0.518413\pi\)
\(258\) 27.3755 1.70433
\(259\) 4.52200 0.280983
\(260\) 8.45139 0.524133
\(261\) 16.3961 1.01489
\(262\) −28.5691 −1.76501
\(263\) −15.3998 −0.949591 −0.474795 0.880096i \(-0.657478\pi\)
−0.474795 + 0.880096i \(0.657478\pi\)
\(264\) −50.9697 −3.13697
\(265\) −35.8753 −2.20381
\(266\) 8.11843 0.497773
\(267\) 12.5958 0.770848
\(268\) 2.31404 0.141352
\(269\) −18.4640 −1.12577 −0.562884 0.826536i \(-0.690308\pi\)
−0.562884 + 0.826536i \(0.690308\pi\)
\(270\) −45.4989 −2.76898
\(271\) 1.99413 0.121135 0.0605673 0.998164i \(-0.480709\pi\)
0.0605673 + 0.998164i \(0.480709\pi\)
\(272\) −59.2719 −3.59389
\(273\) −0.392766 −0.0237713
\(274\) −13.2838 −0.802506
\(275\) −48.3840 −2.91767
\(276\) −17.6557 −1.06275
\(277\) 27.2755 1.63882 0.819412 0.573205i \(-0.194300\pi\)
0.819412 + 0.573205i \(0.194300\pi\)
\(278\) 43.7065 2.62134
\(279\) 0.185366 0.0110976
\(280\) −33.0667 −1.97611
\(281\) 21.7734 1.29889 0.649447 0.760407i \(-0.275000\pi\)
0.649447 + 0.760407i \(0.275000\pi\)
\(282\) −15.4077 −0.917516
\(283\) 15.5606 0.924983 0.462491 0.886624i \(-0.346956\pi\)
0.462491 + 0.886624i \(0.346956\pi\)
\(284\) 73.8292 4.38096
\(285\) 9.62474 0.570120
\(286\) 7.31054 0.432281
\(287\) 5.05744 0.298531
\(288\) 44.7021 2.63410
\(289\) 0.223872 0.0131689
\(290\) 72.9211 4.28208
\(291\) −2.54587 −0.149241
\(292\) −71.6549 −4.19329
\(293\) −20.3666 −1.18983 −0.594916 0.803788i \(-0.702815\pi\)
−0.594916 + 0.803788i \(0.702815\pi\)
\(294\) 2.44305 0.142482
\(295\) 3.87174 0.225422
\(296\) −41.6895 −2.42315
\(297\) −28.7072 −1.66576
\(298\) −44.2491 −2.56328
\(299\) 1.59289 0.0921192
\(300\) −38.0995 −2.19968
\(301\) 11.2055 0.645873
\(302\) 33.9593 1.95414
\(303\) −9.24632 −0.531187
\(304\) −42.6482 −2.44604
\(305\) −19.3330 −1.10700
\(306\) −24.7375 −1.41415
\(307\) 22.5602 1.28758 0.643788 0.765204i \(-0.277362\pi\)
0.643788 + 0.765204i \(0.277362\pi\)
\(308\) −33.1678 −1.88991
\(309\) −5.65810 −0.321878
\(310\) 0.824411 0.0468234
\(311\) 11.9761 0.679104 0.339552 0.940587i \(-0.389724\pi\)
0.339552 + 0.940587i \(0.389724\pi\)
\(312\) 3.62101 0.204999
\(313\) 24.1029 1.36237 0.681187 0.732109i \(-0.261464\pi\)
0.681187 + 0.732109i \(0.261464\pi\)
\(314\) −52.2223 −2.94707
\(315\) −7.86374 −0.443072
\(316\) 22.1130 1.24395
\(317\) 6.87592 0.386190 0.193095 0.981180i \(-0.438147\pi\)
0.193095 + 0.981180i \(0.438147\pi\)
\(318\) −24.4362 −1.37032
\(319\) 46.0090 2.57601
\(320\) 96.3627 5.38684
\(321\) 12.4801 0.696572
\(322\) −9.90795 −0.552149
\(323\) 12.3932 0.689575
\(324\) 12.8545 0.714137
\(325\) 3.43732 0.190668
\(326\) 12.7840 0.708038
\(327\) −7.78727 −0.430637
\(328\) −46.6258 −2.57448
\(329\) −6.30676 −0.347703
\(330\) −53.9094 −2.96762
\(331\) 30.1696 1.65827 0.829136 0.559047i \(-0.188833\pi\)
0.829136 + 0.559047i \(0.188833\pi\)
\(332\) −6.34704 −0.348339
\(333\) −9.91437 −0.543304
\(334\) −44.5135 −2.43567
\(335\) 1.53952 0.0841132
\(336\) −12.8340 −0.700150
\(337\) −31.4116 −1.71110 −0.855549 0.517721i \(-0.826780\pi\)
−0.855549 + 0.517721i \(0.826780\pi\)
\(338\) 34.8232 1.89413
\(339\) −10.9266 −0.593449
\(340\) −80.2486 −4.35209
\(341\) 0.520155 0.0281680
\(342\) −17.7995 −0.962485
\(343\) 1.00000 0.0539949
\(344\) −103.306 −5.56990
\(345\) −11.7463 −0.632400
\(346\) 0.405659 0.0218084
\(347\) −0.429830 −0.0230745 −0.0115372 0.999933i \(-0.503673\pi\)
−0.0115372 + 0.999933i \(0.503673\pi\)
\(348\) 36.2293 1.94209
\(349\) 23.7478 1.27119 0.635595 0.772023i \(-0.280755\pi\)
0.635595 + 0.772023i \(0.280755\pi\)
\(350\) −21.3805 −1.14284
\(351\) 2.03943 0.108857
\(352\) 125.439 6.68590
\(353\) −1.83516 −0.0976759 −0.0488379 0.998807i \(-0.515552\pi\)
−0.0488379 + 0.998807i \(0.515552\pi\)
\(354\) 2.63721 0.140166
\(355\) 49.1184 2.60694
\(356\) −75.5657 −4.00497
\(357\) 3.72943 0.197383
\(358\) 22.3425 1.18084
\(359\) 16.7364 0.883311 0.441656 0.897185i \(-0.354391\pi\)
0.441656 + 0.897185i \(0.354391\pi\)
\(360\) 72.4979 3.82097
\(361\) −10.0827 −0.530667
\(362\) −57.8774 −3.04197
\(363\) −24.1289 −1.26644
\(364\) 2.35632 0.123505
\(365\) −47.6719 −2.49526
\(366\) −13.1685 −0.688330
\(367\) 31.3254 1.63517 0.817586 0.575807i \(-0.195312\pi\)
0.817586 + 0.575807i \(0.195312\pi\)
\(368\) 52.0490 2.71324
\(369\) −11.0883 −0.577235
\(370\) −44.0940 −2.29234
\(371\) −10.0023 −0.519296
\(372\) 0.409591 0.0212363
\(373\) −5.13661 −0.265964 −0.132982 0.991118i \(-0.542455\pi\)
−0.132982 + 0.991118i \(0.542455\pi\)
\(374\) −69.4158 −3.58941
\(375\) −9.23211 −0.476744
\(376\) 58.1436 2.99853
\(377\) −3.26859 −0.168341
\(378\) −12.6855 −0.652471
\(379\) −2.11173 −0.108472 −0.0542361 0.998528i \(-0.517272\pi\)
−0.0542361 + 0.998528i \(0.517272\pi\)
\(380\) −57.7417 −2.96208
\(381\) 10.7156 0.548978
\(382\) −52.3180 −2.67682
\(383\) 19.5018 0.996494 0.498247 0.867035i \(-0.333977\pi\)
0.498247 + 0.867035i \(0.333977\pi\)
\(384\) 28.9929 1.47954
\(385\) −22.0665 −1.12461
\(386\) −4.63922 −0.236130
\(387\) −24.5678 −1.24885
\(388\) 15.2734 0.775390
\(389\) −13.7410 −0.696695 −0.348348 0.937365i \(-0.613257\pi\)
−0.348348 + 0.937365i \(0.613257\pi\)
\(390\) 3.82986 0.193932
\(391\) −15.1250 −0.764903
\(392\) −9.21926 −0.465643
\(393\) −9.44321 −0.476347
\(394\) 30.9851 1.56101
\(395\) 14.7118 0.740229
\(396\) 72.7195 3.65429
\(397\) 30.6331 1.53743 0.768715 0.639592i \(-0.220897\pi\)
0.768715 + 0.639592i \(0.220897\pi\)
\(398\) −50.0213 −2.50734
\(399\) 2.68346 0.134341
\(400\) 112.317 5.61587
\(401\) 9.37442 0.468136 0.234068 0.972220i \(-0.424796\pi\)
0.234068 + 0.972220i \(0.424796\pi\)
\(402\) 1.04864 0.0523012
\(403\) −0.0369531 −0.00184077
\(404\) 55.4714 2.75981
\(405\) 8.55205 0.424955
\(406\) 20.3310 1.00901
\(407\) −27.8207 −1.37902
\(408\) −34.3826 −1.70219
\(409\) 16.3209 0.807014 0.403507 0.914977i \(-0.367791\pi\)
0.403507 + 0.914977i \(0.367791\pi\)
\(410\) −49.3151 −2.43550
\(411\) −4.39083 −0.216584
\(412\) 33.9446 1.67233
\(413\) 1.07947 0.0531175
\(414\) 21.7230 1.06763
\(415\) −4.22268 −0.207283
\(416\) −8.91146 −0.436920
\(417\) 14.4467 0.707459
\(418\) −49.9471 −2.44299
\(419\) 17.9286 0.875867 0.437934 0.899007i \(-0.355711\pi\)
0.437934 + 0.899007i \(0.355711\pi\)
\(420\) −17.3760 −0.847862
\(421\) −9.07939 −0.442502 −0.221251 0.975217i \(-0.571014\pi\)
−0.221251 + 0.975217i \(0.571014\pi\)
\(422\) −15.9560 −0.776725
\(423\) 13.8274 0.672312
\(424\) 92.2142 4.47832
\(425\) −32.6384 −1.58320
\(426\) 33.4567 1.62098
\(427\) −5.39020 −0.260850
\(428\) −74.8719 −3.61907
\(429\) 2.41642 0.116666
\(430\) −109.265 −5.26921
\(431\) 26.7123 1.28669 0.643344 0.765577i \(-0.277547\pi\)
0.643344 + 0.765577i \(0.277547\pi\)
\(432\) 66.6401 3.20622
\(433\) −25.7496 −1.23745 −0.618723 0.785609i \(-0.712350\pi\)
−0.618723 + 0.785609i \(0.712350\pi\)
\(434\) 0.229853 0.0110333
\(435\) 24.1033 1.15566
\(436\) 46.7181 2.23739
\(437\) −10.8829 −0.520602
\(438\) −32.4714 −1.55154
\(439\) 18.0350 0.860763 0.430381 0.902647i \(-0.358379\pi\)
0.430381 + 0.902647i \(0.358379\pi\)
\(440\) 203.436 9.69845
\(441\) −2.19248 −0.104404
\(442\) 4.93147 0.234566
\(443\) 33.9536 1.61318 0.806592 0.591109i \(-0.201310\pi\)
0.806592 + 0.591109i \(0.201310\pi\)
\(444\) −21.9071 −1.03967
\(445\) −50.2737 −2.38320
\(446\) 0.649411 0.0307505
\(447\) −14.6261 −0.691789
\(448\) 26.8667 1.26933
\(449\) 35.9164 1.69500 0.847500 0.530795i \(-0.178107\pi\)
0.847500 + 0.530795i \(0.178107\pi\)
\(450\) 46.8763 2.20977
\(451\) −31.1149 −1.46514
\(452\) 65.5516 3.08329
\(453\) 11.2249 0.527390
\(454\) 63.4222 2.97655
\(455\) 1.56766 0.0734928
\(456\) −24.7395 −1.15853
\(457\) 15.7647 0.737441 0.368721 0.929540i \(-0.379796\pi\)
0.368721 + 0.929540i \(0.379796\pi\)
\(458\) 61.6280 2.87969
\(459\) −19.3650 −0.903881
\(460\) 70.4695 3.28566
\(461\) −1.11400 −0.0518843 −0.0259421 0.999663i \(-0.508259\pi\)
−0.0259421 + 0.999663i \(0.508259\pi\)
\(462\) −15.0304 −0.699278
\(463\) −9.68434 −0.450069 −0.225035 0.974351i \(-0.572250\pi\)
−0.225035 + 0.974351i \(0.572250\pi\)
\(464\) −106.804 −4.95825
\(465\) 0.272500 0.0126369
\(466\) 31.9061 1.47802
\(467\) −16.2219 −0.750659 −0.375329 0.926891i \(-0.622470\pi\)
−0.375329 + 0.926891i \(0.622470\pi\)
\(468\) −5.16617 −0.238807
\(469\) 0.429232 0.0198201
\(470\) 61.4971 2.83665
\(471\) −17.2615 −0.795368
\(472\) −9.95196 −0.458076
\(473\) −68.9396 −3.16985
\(474\) 10.0208 0.460271
\(475\) −23.4845 −1.07754
\(476\) −22.3740 −1.02551
\(477\) 21.9299 1.00410
\(478\) −69.1458 −3.16266
\(479\) 24.4008 1.11490 0.557450 0.830211i \(-0.311780\pi\)
0.557450 + 0.830211i \(0.311780\pi\)
\(480\) 65.7150 2.99947
\(481\) 1.97645 0.0901185
\(482\) 13.0938 0.596407
\(483\) −3.27497 −0.149016
\(484\) 144.756 6.57983
\(485\) 10.1614 0.461404
\(486\) 43.8816 1.99051
\(487\) −16.0977 −0.729454 −0.364727 0.931114i \(-0.618838\pi\)
−0.364727 + 0.931114i \(0.618838\pi\)
\(488\) 49.6937 2.24953
\(489\) 4.22560 0.191088
\(490\) −9.75100 −0.440505
\(491\) 1.04602 0.0472063 0.0236031 0.999721i \(-0.492486\pi\)
0.0236031 + 0.999721i \(0.492486\pi\)
\(492\) −24.5011 −1.10460
\(493\) 31.0363 1.39780
\(494\) 3.54836 0.159648
\(495\) 48.3802 2.17453
\(496\) −1.20747 −0.0542172
\(497\) 13.6946 0.614288
\(498\) −2.87625 −0.128888
\(499\) 18.8517 0.843919 0.421959 0.906615i \(-0.361342\pi\)
0.421959 + 0.906615i \(0.361342\pi\)
\(500\) 55.3861 2.47694
\(501\) −14.7135 −0.657349
\(502\) −49.5114 −2.20980
\(503\) −9.67865 −0.431550 −0.215775 0.976443i \(-0.569228\pi\)
−0.215775 + 0.976443i \(0.569228\pi\)
\(504\) 20.2130 0.900359
\(505\) 36.9050 1.64225
\(506\) 60.9568 2.70986
\(507\) 11.5104 0.511196
\(508\) −64.2862 −2.85224
\(509\) 14.5048 0.642913 0.321457 0.946924i \(-0.395828\pi\)
0.321457 + 0.946924i \(0.395828\pi\)
\(510\) −36.3657 −1.61030
\(511\) −13.2913 −0.587974
\(512\) −27.8543 −1.23100
\(513\) −13.9338 −0.615192
\(514\) 5.03950 0.222283
\(515\) 22.5833 0.995139
\(516\) −54.2858 −2.38980
\(517\) 38.8011 1.70647
\(518\) −12.2938 −0.540157
\(519\) 0.134086 0.00588573
\(520\) −14.4526 −0.633789
\(521\) −18.4533 −0.808453 −0.404226 0.914659i \(-0.632459\pi\)
−0.404226 + 0.914659i \(0.632459\pi\)
\(522\) −44.5753 −1.95101
\(523\) 27.7331 1.21268 0.606342 0.795204i \(-0.292636\pi\)
0.606342 + 0.795204i \(0.292636\pi\)
\(524\) 56.6526 2.47488
\(525\) −7.06710 −0.308434
\(526\) 41.8667 1.82548
\(527\) 0.350881 0.0152846
\(528\) 78.9585 3.43623
\(529\) −9.71815 −0.422528
\(530\) 97.5328 4.23656
\(531\) −2.36672 −0.102707
\(532\) −16.0989 −0.697974
\(533\) 2.21048 0.0957466
\(534\) −34.2436 −1.48186
\(535\) −49.8121 −2.15357
\(536\) −3.95720 −0.170925
\(537\) 7.38508 0.318690
\(538\) 50.1972 2.16416
\(539\) −6.15231 −0.264999
\(540\) 90.2244 3.88264
\(541\) −22.1720 −0.953249 −0.476625 0.879107i \(-0.658140\pi\)
−0.476625 + 0.879107i \(0.658140\pi\)
\(542\) −5.42135 −0.232867
\(543\) −19.1307 −0.820979
\(544\) 84.6171 3.62793
\(545\) 31.0815 1.33138
\(546\) 1.06780 0.0456975
\(547\) 45.5619 1.94809 0.974043 0.226364i \(-0.0726838\pi\)
0.974043 + 0.226364i \(0.0726838\pi\)
\(548\) 26.3419 1.12527
\(549\) 11.8179 0.504375
\(550\) 131.540 5.60887
\(551\) 22.3317 0.951362
\(552\) 30.1928 1.28509
\(553\) 4.10176 0.174425
\(554\) −74.1527 −3.15045
\(555\) −14.5748 −0.618665
\(556\) −86.6701 −3.67563
\(557\) −20.2511 −0.858066 −0.429033 0.903289i \(-0.641146\pi\)
−0.429033 + 0.903289i \(0.641146\pi\)
\(558\) −0.503947 −0.0213338
\(559\) 4.89764 0.207148
\(560\) 51.2245 2.16463
\(561\) −22.9446 −0.968723
\(562\) −59.1945 −2.49697
\(563\) −3.17345 −0.133745 −0.0668724 0.997762i \(-0.521302\pi\)
−0.0668724 + 0.997762i \(0.521302\pi\)
\(564\) 30.5535 1.28654
\(565\) 43.6114 1.83474
\(566\) −42.3040 −1.77817
\(567\) 2.38438 0.100135
\(568\) −126.254 −5.29752
\(569\) −13.8716 −0.581529 −0.290764 0.956795i \(-0.593910\pi\)
−0.290764 + 0.956795i \(0.593910\pi\)
\(570\) −26.1664 −1.09599
\(571\) −24.4837 −1.02461 −0.512305 0.858803i \(-0.671208\pi\)
−0.512305 + 0.858803i \(0.671208\pi\)
\(572\) −14.4968 −0.606142
\(573\) −17.2932 −0.722432
\(574\) −13.7494 −0.573891
\(575\) 28.6611 1.19525
\(576\) −58.9046 −2.45436
\(577\) −43.9290 −1.82879 −0.914393 0.404827i \(-0.867332\pi\)
−0.914393 + 0.404827i \(0.867332\pi\)
\(578\) −0.608630 −0.0253157
\(579\) −1.53344 −0.0637277
\(580\) −144.603 −6.00430
\(581\) −1.17732 −0.0488434
\(582\) 6.92135 0.286899
\(583\) 61.5375 2.54862
\(584\) 122.536 5.07058
\(585\) −3.43705 −0.142104
\(586\) 55.3699 2.28731
\(587\) −15.8458 −0.654027 −0.327014 0.945020i \(-0.606042\pi\)
−0.327014 + 0.945020i \(0.606042\pi\)
\(588\) −4.84457 −0.199787
\(589\) 0.252471 0.0104029
\(590\) −10.5260 −0.433347
\(591\) 10.2418 0.421290
\(592\) 64.5823 2.65432
\(593\) 26.0204 1.06853 0.534264 0.845317i \(-0.320589\pi\)
0.534264 + 0.845317i \(0.320589\pi\)
\(594\) 78.0450 3.20223
\(595\) −14.8854 −0.610241
\(596\) 87.7460 3.59422
\(597\) −16.5340 −0.676691
\(598\) −4.33052 −0.177088
\(599\) 16.7520 0.684466 0.342233 0.939615i \(-0.388817\pi\)
0.342233 + 0.939615i \(0.388817\pi\)
\(600\) 65.1535 2.65988
\(601\) −36.0258 −1.46952 −0.734762 0.678325i \(-0.762706\pi\)
−0.734762 + 0.678325i \(0.762706\pi\)
\(602\) −30.4639 −1.24162
\(603\) −0.941082 −0.0383238
\(604\) −67.3413 −2.74008
\(605\) 96.3061 3.91540
\(606\) 25.1376 1.02114
\(607\) 30.4832 1.23728 0.618638 0.785676i \(-0.287685\pi\)
0.618638 + 0.785676i \(0.287685\pi\)
\(608\) 60.8849 2.46921
\(609\) 6.72020 0.272316
\(610\) 52.5598 2.12809
\(611\) −2.75653 −0.111517
\(612\) 49.0544 1.98291
\(613\) −16.4618 −0.664886 −0.332443 0.943123i \(-0.607873\pi\)
−0.332443 + 0.943123i \(0.607873\pi\)
\(614\) −61.3334 −2.47521
\(615\) −16.3006 −0.657302
\(616\) 56.7198 2.28530
\(617\) −41.2887 −1.66222 −0.831110 0.556107i \(-0.812294\pi\)
−0.831110 + 0.556107i \(0.812294\pi\)
\(618\) 15.3824 0.618773
\(619\) −21.8387 −0.877772 −0.438886 0.898543i \(-0.644627\pi\)
−0.438886 + 0.898543i \(0.644627\pi\)
\(620\) −1.63481 −0.0656555
\(621\) 17.0052 0.682395
\(622\) −32.5590 −1.30550
\(623\) −14.0167 −0.561568
\(624\) −5.60941 −0.224556
\(625\) −2.47354 −0.0989416
\(626\) −65.5274 −2.61900
\(627\) −16.5095 −0.659324
\(628\) 103.557 4.13237
\(629\) −18.7670 −0.748291
\(630\) 21.3788 0.851753
\(631\) −8.38874 −0.333951 −0.166975 0.985961i \(-0.553400\pi\)
−0.166975 + 0.985961i \(0.553400\pi\)
\(632\) −37.8152 −1.50421
\(633\) −5.27407 −0.209626
\(634\) −18.6933 −0.742405
\(635\) −42.7695 −1.69725
\(636\) 48.4571 1.92145
\(637\) 0.437075 0.0173176
\(638\) −125.083 −4.95207
\(639\) −30.0252 −1.18778
\(640\) −115.720 −4.57424
\(641\) 32.6795 1.29076 0.645382 0.763860i \(-0.276698\pi\)
0.645382 + 0.763860i \(0.276698\pi\)
\(642\) −33.9291 −1.33908
\(643\) 14.7099 0.580100 0.290050 0.957012i \(-0.406328\pi\)
0.290050 + 0.957012i \(0.406328\pi\)
\(644\) 19.6475 0.774220
\(645\) −36.1162 −1.42207
\(646\) −33.6928 −1.32563
\(647\) 8.99013 0.353438 0.176719 0.984261i \(-0.443452\pi\)
0.176719 + 0.984261i \(0.443452\pi\)
\(648\) −21.9823 −0.863545
\(649\) −6.64126 −0.260692
\(650\) −9.34490 −0.366537
\(651\) 0.0759753 0.00297771
\(652\) −25.3506 −0.992807
\(653\) 14.7857 0.578610 0.289305 0.957237i \(-0.406576\pi\)
0.289305 + 0.957237i \(0.406576\pi\)
\(654\) 21.1709 0.827849
\(655\) 37.6909 1.47271
\(656\) 72.2294 2.82008
\(657\) 29.1409 1.13690
\(658\) 17.1459 0.668417
\(659\) 20.1464 0.784794 0.392397 0.919796i \(-0.371646\pi\)
0.392397 + 0.919796i \(0.371646\pi\)
\(660\) 106.903 4.16118
\(661\) 7.15641 0.278352 0.139176 0.990268i \(-0.455555\pi\)
0.139176 + 0.990268i \(0.455555\pi\)
\(662\) −82.0209 −3.18783
\(663\) 1.63004 0.0633056
\(664\) 10.8540 0.421217
\(665\) −10.7105 −0.415337
\(666\) 26.9538 1.04444
\(667\) −27.2542 −1.05529
\(668\) 88.2704 3.41528
\(669\) 0.214656 0.00829907
\(670\) −4.18544 −0.161698
\(671\) 33.1622 1.28021
\(672\) 18.3219 0.706782
\(673\) 5.64587 0.217632 0.108816 0.994062i \(-0.465294\pi\)
0.108816 + 0.994062i \(0.465294\pi\)
\(674\) 85.3974 3.28939
\(675\) 36.6958 1.41242
\(676\) −69.0545 −2.65594
\(677\) −35.2244 −1.35378 −0.676892 0.736083i \(-0.736673\pi\)
−0.676892 + 0.736083i \(0.736673\pi\)
\(678\) 29.7056 1.14084
\(679\) 2.83308 0.108724
\(680\) 137.232 5.26261
\(681\) 20.9635 0.803323
\(682\) −1.41412 −0.0541496
\(683\) −14.2553 −0.545463 −0.272732 0.962090i \(-0.587927\pi\)
−0.272732 + 0.962090i \(0.587927\pi\)
\(684\) 35.2964 1.34959
\(685\) 17.5252 0.669604
\(686\) −2.71866 −0.103799
\(687\) 20.3705 0.777182
\(688\) 160.035 6.10126
\(689\) −4.37178 −0.166551
\(690\) 31.9342 1.21571
\(691\) 2.85379 0.108563 0.0542817 0.998526i \(-0.482713\pi\)
0.0542817 + 0.998526i \(0.482713\pi\)
\(692\) −0.804422 −0.0305795
\(693\) 13.4888 0.512397
\(694\) 1.16856 0.0443580
\(695\) −57.6615 −2.18722
\(696\) −61.9552 −2.34841
\(697\) −20.9892 −0.795023
\(698\) −64.5621 −2.44371
\(699\) 10.5462 0.398894
\(700\) 42.3976 1.60248
\(701\) −4.62937 −0.174849 −0.0874245 0.996171i \(-0.527864\pi\)
−0.0874245 + 0.996171i \(0.527864\pi\)
\(702\) −5.54451 −0.209264
\(703\) −13.5035 −0.509295
\(704\) −165.292 −6.22969
\(705\) 20.3272 0.765567
\(706\) 4.98918 0.187770
\(707\) 10.2894 0.386974
\(708\) −5.22959 −0.196540
\(709\) −12.1823 −0.457515 −0.228758 0.973483i \(-0.573466\pi\)
−0.228758 + 0.973483i \(0.573466\pi\)
\(710\) −133.536 −5.01153
\(711\) −8.99301 −0.337264
\(712\) 129.224 4.84287
\(713\) −0.308123 −0.0115393
\(714\) −10.1391 −0.379445
\(715\) −9.64470 −0.360691
\(716\) −44.3053 −1.65577
\(717\) −22.8554 −0.853550
\(718\) −45.5004 −1.69806
\(719\) −17.4261 −0.649882 −0.324941 0.945734i \(-0.605344\pi\)
−0.324941 + 0.945734i \(0.605344\pi\)
\(720\) −112.308 −4.18549
\(721\) 6.29641 0.234491
\(722\) 27.4114 1.02015
\(723\) 4.32802 0.160961
\(724\) 114.771 4.26543
\(725\) −58.8123 −2.18423
\(726\) 65.5982 2.43458
\(727\) −0.430594 −0.0159698 −0.00798492 0.999968i \(-0.502542\pi\)
−0.00798492 + 0.999968i \(0.502542\pi\)
\(728\) −4.02951 −0.149344
\(729\) 7.35143 0.272275
\(730\) 129.604 4.79685
\(731\) −46.5046 −1.72003
\(732\) 26.1132 0.965173
\(733\) −15.5938 −0.575969 −0.287984 0.957635i \(-0.592985\pi\)
−0.287984 + 0.957635i \(0.592985\pi\)
\(734\) −85.1630 −3.14342
\(735\) −3.22309 −0.118885
\(736\) −74.3057 −2.73894
\(737\) −2.64077 −0.0972740
\(738\) 30.1453 1.10967
\(739\) −22.4872 −0.827206 −0.413603 0.910457i \(-0.635730\pi\)
−0.413603 + 0.910457i \(0.635730\pi\)
\(740\) 87.4384 3.21430
\(741\) 1.17287 0.0430866
\(742\) 27.1930 0.998285
\(743\) −31.3730 −1.15096 −0.575481 0.817815i \(-0.695185\pi\)
−0.575481 + 0.817815i \(0.695185\pi\)
\(744\) −0.700436 −0.0256792
\(745\) 58.3773 2.13878
\(746\) 13.9647 0.511284
\(747\) 2.58124 0.0944427
\(748\) 137.652 5.03304
\(749\) −13.8880 −0.507458
\(750\) 25.0990 0.916484
\(751\) 47.3544 1.72799 0.863993 0.503505i \(-0.167956\pi\)
0.863993 + 0.503505i \(0.167956\pi\)
\(752\) −90.0719 −3.28458
\(753\) −16.3655 −0.596391
\(754\) 8.88618 0.323616
\(755\) −44.8020 −1.63051
\(756\) 25.1553 0.914890
\(757\) 32.1157 1.16726 0.583632 0.812018i \(-0.301631\pi\)
0.583632 + 0.812018i \(0.301631\pi\)
\(758\) 5.74107 0.208525
\(759\) 20.1486 0.731348
\(760\) 98.7433 3.58179
\(761\) 41.6987 1.51158 0.755788 0.654816i \(-0.227254\pi\)
0.755788 + 0.654816i \(0.227254\pi\)
\(762\) −29.1321 −1.05535
\(763\) 8.66578 0.313722
\(764\) 103.747 3.75343
\(765\) 32.6358 1.17995
\(766\) −53.0186 −1.91564
\(767\) 0.471812 0.0170361
\(768\) −30.5358 −1.10186
\(769\) 32.8642 1.18511 0.592556 0.805529i \(-0.298119\pi\)
0.592556 + 0.805529i \(0.298119\pi\)
\(770\) 59.9912 2.16193
\(771\) 1.66575 0.0599906
\(772\) 9.19958 0.331100
\(773\) −22.3320 −0.803227 −0.401613 0.915809i \(-0.631550\pi\)
−0.401613 + 0.915809i \(0.631550\pi\)
\(774\) 66.7913 2.40077
\(775\) −0.664904 −0.0238840
\(776\) −26.1189 −0.937613
\(777\) −4.06357 −0.145780
\(778\) 37.3570 1.33931
\(779\) −15.1025 −0.541102
\(780\) −7.59462 −0.271931
\(781\) −84.2536 −3.01483
\(782\) 41.1196 1.47044
\(783\) −34.8945 −1.24703
\(784\) 14.2818 0.510065
\(785\) 68.8962 2.45901
\(786\) 25.6729 0.915721
\(787\) −21.2017 −0.755758 −0.377879 0.925855i \(-0.623346\pi\)
−0.377879 + 0.925855i \(0.623346\pi\)
\(788\) −61.4435 −2.18883
\(789\) 13.8386 0.492667
\(790\) −39.9962 −1.42300
\(791\) 12.1592 0.432332
\(792\) −124.357 −4.41882
\(793\) −2.35592 −0.0836613
\(794\) −83.2809 −2.95553
\(795\) 32.2384 1.14338
\(796\) 99.1923 3.51578
\(797\) 35.2053 1.24704 0.623518 0.781809i \(-0.285703\pi\)
0.623518 + 0.781809i \(0.285703\pi\)
\(798\) −7.29540 −0.258255
\(799\) 26.1741 0.925972
\(800\) −160.345 −5.66907
\(801\) 30.7313 1.08584
\(802\) −25.4859 −0.899937
\(803\) 81.7724 2.88568
\(804\) −2.07945 −0.0733364
\(805\) 13.0714 0.460708
\(806\) 0.100463 0.00353865
\(807\) 16.5921 0.584071
\(808\) −94.8609 −3.33720
\(809\) 6.41510 0.225543 0.112771 0.993621i \(-0.464027\pi\)
0.112771 + 0.993621i \(0.464027\pi\)
\(810\) −23.2501 −0.816926
\(811\) 12.0851 0.424366 0.212183 0.977230i \(-0.431943\pi\)
0.212183 + 0.977230i \(0.431943\pi\)
\(812\) −40.3164 −1.41483
\(813\) −1.79197 −0.0628471
\(814\) 75.6351 2.65101
\(815\) −16.8657 −0.590780
\(816\) 53.2631 1.86458
\(817\) −33.4617 −1.17068
\(818\) −44.3708 −1.55139
\(819\) −0.958277 −0.0334849
\(820\) 97.7918 3.41504
\(821\) −7.47828 −0.260994 −0.130497 0.991449i \(-0.541657\pi\)
−0.130497 + 0.991449i \(0.541657\pi\)
\(822\) 11.9372 0.416356
\(823\) 46.6206 1.62509 0.812547 0.582896i \(-0.198080\pi\)
0.812547 + 0.582896i \(0.198080\pi\)
\(824\) −58.0482 −2.02221
\(825\) 43.4790 1.51375
\(826\) −2.93472 −0.102112
\(827\) −19.7120 −0.685454 −0.342727 0.939435i \(-0.611351\pi\)
−0.342727 + 0.939435i \(0.611351\pi\)
\(828\) −43.0767 −1.49702
\(829\) 10.1066 0.351017 0.175508 0.984478i \(-0.443843\pi\)
0.175508 + 0.984478i \(0.443843\pi\)
\(830\) 11.4800 0.398477
\(831\) −24.5104 −0.850255
\(832\) 11.7428 0.407108
\(833\) −4.15017 −0.143795
\(834\) −39.2757 −1.36001
\(835\) 58.7261 2.03230
\(836\) 99.0452 3.42555
\(837\) −0.394500 −0.0136359
\(838\) −48.7416 −1.68375
\(839\) 7.33493 0.253230 0.126615 0.991952i \(-0.459589\pi\)
0.126615 + 0.991952i \(0.459589\pi\)
\(840\) 29.7145 1.02525
\(841\) 26.9254 0.928460
\(842\) 24.6838 0.850659
\(843\) −19.5661 −0.673892
\(844\) 31.6407 1.08912
\(845\) −45.9418 −1.58045
\(846\) −37.5920 −1.29244
\(847\) 26.8509 0.922609
\(848\) −142.852 −4.90554
\(849\) −13.9831 −0.479900
\(850\) 88.7328 3.04351
\(851\) 16.4801 0.564930
\(852\) −66.3446 −2.27293
\(853\) −27.7324 −0.949539 −0.474770 0.880110i \(-0.657469\pi\)
−0.474770 + 0.880110i \(0.657469\pi\)
\(854\) 14.6541 0.501454
\(855\) 23.4826 0.803088
\(856\) 128.037 4.37623
\(857\) −49.5757 −1.69347 −0.846737 0.532012i \(-0.821436\pi\)
−0.846737 + 0.532012i \(0.821436\pi\)
\(858\) −6.56942 −0.224276
\(859\) 5.67823 0.193739 0.0968694 0.995297i \(-0.469117\pi\)
0.0968694 + 0.995297i \(0.469117\pi\)
\(860\) 216.672 7.38845
\(861\) −4.54473 −0.154884
\(862\) −72.6217 −2.47351
\(863\) −1.00000 −0.0340404
\(864\) −95.1360 −3.23659
\(865\) −0.535181 −0.0181967
\(866\) 70.0044 2.37885
\(867\) −0.201176 −0.00683230
\(868\) −0.455798 −0.0154708
\(869\) −25.2353 −0.856049
\(870\) −65.5286 −2.22163
\(871\) 0.187607 0.00635681
\(872\) −79.8921 −2.70549
\(873\) −6.21146 −0.210226
\(874\) 29.5870 1.00080
\(875\) 10.2736 0.347312
\(876\) 64.3908 2.17556
\(877\) −47.0585 −1.58905 −0.794527 0.607229i \(-0.792281\pi\)
−0.794527 + 0.607229i \(0.792281\pi\)
\(878\) −49.0310 −1.65472
\(879\) 18.3019 0.617308
\(880\) −315.149 −10.6237
\(881\) 39.7337 1.33866 0.669331 0.742964i \(-0.266581\pi\)
0.669331 + 0.742964i \(0.266581\pi\)
\(882\) 5.96060 0.200704
\(883\) −2.08887 −0.0702961 −0.0351481 0.999382i \(-0.511190\pi\)
−0.0351481 + 0.999382i \(0.511190\pi\)
\(884\) −9.77911 −0.328907
\(885\) −3.47924 −0.116953
\(886\) −92.3082 −3.10116
\(887\) −25.1053 −0.842955 −0.421477 0.906839i \(-0.638488\pi\)
−0.421477 + 0.906839i \(0.638488\pi\)
\(888\) 37.4631 1.25718
\(889\) −11.9245 −0.399934
\(890\) 136.677 4.58142
\(891\) −14.6695 −0.491446
\(892\) −1.28778 −0.0431182
\(893\) 18.8332 0.630228
\(894\) 39.7632 1.32988
\(895\) −29.4762 −0.985282
\(896\) −32.2637 −1.07786
\(897\) −1.43141 −0.0477933
\(898\) −97.6445 −3.25844
\(899\) 0.632265 0.0210872
\(900\) −92.9559 −3.09853
\(901\) 41.5114 1.38294
\(902\) 84.5909 2.81657
\(903\) −10.0695 −0.335092
\(904\) −112.099 −3.72836
\(905\) 76.3569 2.53819
\(906\) −30.5166 −1.01385
\(907\) 3.58011 0.118876 0.0594378 0.998232i \(-0.481069\pi\)
0.0594378 + 0.998232i \(0.481069\pi\)
\(908\) −125.766 −4.17370
\(909\) −22.5593 −0.748246
\(910\) −4.26192 −0.141281
\(911\) −36.1281 −1.19698 −0.598489 0.801131i \(-0.704232\pi\)
−0.598489 + 0.801131i \(0.704232\pi\)
\(912\) 38.3246 1.26906
\(913\) 7.24322 0.239716
\(914\) −42.8588 −1.41764
\(915\) 17.3731 0.574336
\(916\) −122.208 −4.03788
\(917\) 10.5085 0.347022
\(918\) 52.6468 1.73760
\(919\) 33.8793 1.11757 0.558787 0.829311i \(-0.311267\pi\)
0.558787 + 0.829311i \(0.311267\pi\)
\(920\) −120.509 −3.97307
\(921\) −20.2731 −0.668021
\(922\) 3.02859 0.0997414
\(923\) 5.98558 0.197018
\(924\) 29.8053 0.980523
\(925\) 35.5627 1.16929
\(926\) 26.3284 0.865205
\(927\) −13.8047 −0.453407
\(928\) 152.474 5.00522
\(929\) 35.1702 1.15390 0.576949 0.816780i \(-0.304243\pi\)
0.576949 + 0.816780i \(0.304243\pi\)
\(930\) −0.740835 −0.0242929
\(931\) −2.98619 −0.0978684
\(932\) −63.2699 −2.07247
\(933\) −10.7620 −0.352333
\(934\) 44.1017 1.44305
\(935\) 91.5794 2.99497
\(936\) 8.83461 0.288768
\(937\) 7.59282 0.248047 0.124023 0.992279i \(-0.460420\pi\)
0.124023 + 0.992279i \(0.460420\pi\)
\(938\) −1.16694 −0.0381018
\(939\) −21.6594 −0.706827
\(940\) −121.949 −3.97754
\(941\) −38.4311 −1.25282 −0.626408 0.779495i \(-0.715476\pi\)
−0.626408 + 0.779495i \(0.715476\pi\)
\(942\) 46.9281 1.52900
\(943\) 18.4315 0.600211
\(944\) 15.4169 0.501776
\(945\) 16.7358 0.544415
\(946\) 187.423 6.09366
\(947\) −23.8402 −0.774703 −0.387351 0.921932i \(-0.626610\pi\)
−0.387351 + 0.921932i \(0.626610\pi\)
\(948\) −19.8713 −0.645389
\(949\) −5.80931 −0.188578
\(950\) 63.8463 2.07145
\(951\) −6.17886 −0.200363
\(952\) 38.2615 1.24006
\(953\) −19.7189 −0.638758 −0.319379 0.947627i \(-0.603474\pi\)
−0.319379 + 0.947627i \(0.603474\pi\)
\(954\) −59.6199 −1.93027
\(955\) 69.0225 2.23352
\(956\) 137.116 4.43466
\(957\) −41.3447 −1.33649
\(958\) −66.3373 −2.14326
\(959\) 4.88617 0.157783
\(960\) −86.5937 −2.79480
\(961\) −30.9929 −0.999769
\(962\) −5.37330 −0.173242
\(963\) 30.4492 0.981211
\(964\) −25.9650 −0.836278
\(965\) 6.12047 0.197025
\(966\) 8.90352 0.286466
\(967\) 35.2356 1.13310 0.566550 0.824027i \(-0.308278\pi\)
0.566550 + 0.824027i \(0.308278\pi\)
\(968\) −247.546 −7.95642
\(969\) −11.1368 −0.357765
\(970\) −27.6253 −0.886996
\(971\) 2.30692 0.0740326 0.0370163 0.999315i \(-0.488215\pi\)
0.0370163 + 0.999315i \(0.488215\pi\)
\(972\) −87.0173 −2.79108
\(973\) −16.0765 −0.515389
\(974\) 43.7640 1.40229
\(975\) −3.08886 −0.0989226
\(976\) −76.9819 −2.46413
\(977\) 29.8815 0.955995 0.477997 0.878361i \(-0.341363\pi\)
0.477997 + 0.878361i \(0.341363\pi\)
\(978\) −11.4880 −0.367344
\(979\) 86.2353 2.75609
\(980\) 19.3362 0.617674
\(981\) −18.9995 −0.606608
\(982\) −2.84377 −0.0907485
\(983\) −49.1865 −1.56881 −0.784403 0.620252i \(-0.787030\pi\)
−0.784403 + 0.620252i \(0.787030\pi\)
\(984\) 41.8990 1.33569
\(985\) −40.8782 −1.30249
\(986\) −84.3771 −2.68711
\(987\) 5.66740 0.180395
\(988\) −7.03641 −0.223858
\(989\) 40.8376 1.29856
\(990\) −131.529 −4.18027
\(991\) −27.9441 −0.887675 −0.443837 0.896107i \(-0.646383\pi\)
−0.443837 + 0.896107i \(0.646383\pi\)
\(992\) 1.72380 0.0547308
\(993\) −27.1111 −0.860345
\(994\) −37.2310 −1.18090
\(995\) 65.9925 2.09210
\(996\) 5.70360 0.180725
\(997\) 58.9359 1.86652 0.933259 0.359205i \(-0.116952\pi\)
0.933259 + 0.359205i \(0.116952\pi\)
\(998\) −51.2514 −1.62233
\(999\) 21.1000 0.667574
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 \(a_p\))