Properties

Label 6019.2.a.c.1.17
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.20802 q^{2} -2.87685 q^{3} +2.87536 q^{4} +1.19118 q^{5} +6.35214 q^{6} -0.105056 q^{7} -1.93280 q^{8} +5.27625 q^{9} +O(q^{10})\) \(q-2.20802 q^{2} -2.87685 q^{3} +2.87536 q^{4} +1.19118 q^{5} +6.35214 q^{6} -0.105056 q^{7} -1.93280 q^{8} +5.27625 q^{9} -2.63016 q^{10} +2.37185 q^{11} -8.27196 q^{12} -1.00000 q^{13} +0.231966 q^{14} -3.42685 q^{15} -1.48304 q^{16} +7.30297 q^{17} -11.6501 q^{18} -3.69849 q^{19} +3.42508 q^{20} +0.302230 q^{21} -5.23709 q^{22} +5.61104 q^{23} +5.56038 q^{24} -3.58108 q^{25} +2.20802 q^{26} -6.54841 q^{27} -0.302073 q^{28} +2.61763 q^{29} +7.56656 q^{30} +3.62118 q^{31} +7.14019 q^{32} -6.82345 q^{33} -16.1251 q^{34} -0.125141 q^{35} +15.1711 q^{36} -3.01688 q^{37} +8.16635 q^{38} +2.87685 q^{39} -2.30233 q^{40} +3.21696 q^{41} -0.667330 q^{42} +5.89126 q^{43} +6.81991 q^{44} +6.28498 q^{45} -12.3893 q^{46} -13.1541 q^{47} +4.26648 q^{48} -6.98896 q^{49} +7.90710 q^{50} -21.0095 q^{51} -2.87536 q^{52} -2.12400 q^{53} +14.4590 q^{54} +2.82531 q^{55} +0.203053 q^{56} +10.6400 q^{57} -5.77979 q^{58} +6.88019 q^{59} -9.85343 q^{60} -7.18991 q^{61} -7.99565 q^{62} -0.554301 q^{63} -12.7996 q^{64} -1.19118 q^{65} +15.0663 q^{66} -0.729638 q^{67} +20.9986 q^{68} -16.1421 q^{69} +0.276314 q^{70} -10.2562 q^{71} -10.1980 q^{72} -10.5443 q^{73} +6.66134 q^{74} +10.3022 q^{75} -10.6345 q^{76} -0.249177 q^{77} -6.35214 q^{78} -1.19588 q^{79} -1.76657 q^{80} +3.01003 q^{81} -7.10312 q^{82} -6.45589 q^{83} +0.869019 q^{84} +8.69918 q^{85} -13.0080 q^{86} -7.53053 q^{87} -4.58432 q^{88} -8.93028 q^{89} -13.8774 q^{90} +0.105056 q^{91} +16.1337 q^{92} -10.4176 q^{93} +29.0446 q^{94} -4.40559 q^{95} -20.5412 q^{96} -1.92287 q^{97} +15.4318 q^{98} +12.5145 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108q - 11q^{2} + q^{3} + 95q^{4} - 40q^{5} - 10q^{6} - 8q^{7} - 33q^{8} + 79q^{9} + O(q^{10}) \) \( 108q - 11q^{2} + q^{3} + 95q^{4} - 40q^{5} - 10q^{6} - 8q^{7} - 33q^{8} + 79q^{9} - q^{10} - 45q^{11} - 6q^{12} - 108q^{13} - 31q^{14} - 39q^{15} + 73q^{16} + 21q^{17} - 35q^{18} - 19q^{19} - 79q^{20} - 72q^{21} - 26q^{23} - 23q^{24} + 92q^{25} + 11q^{26} + 7q^{27} - 21q^{28} - 94q^{29} - 24q^{30} - 36q^{31} - 77q^{32} - 32q^{33} - 58q^{34} - 10q^{35} + 17q^{36} - 54q^{37} - 12q^{38} - q^{39} - 4q^{40} - 68q^{41} - 11q^{42} - 32q^{43} - 151q^{44} - 121q^{45} - 33q^{46} - 51q^{47} - 27q^{48} + 72q^{49} - 45q^{50} - 24q^{51} - 95q^{52} - 81q^{53} - 29q^{54} + 4q^{55} - 68q^{56} - 45q^{57} - 30q^{58} - 94q^{59} - 108q^{60} - 39q^{61} - 9q^{62} - 52q^{63} + 31q^{64} + 40q^{65} - 40q^{66} - 47q^{67} + 24q^{68} - 60q^{69} - 66q^{70} - 86q^{71} - 91q^{72} - 51q^{73} - 110q^{74} - 7q^{75} - 51q^{76} - 96q^{77} + 10q^{78} - 18q^{79} - 136q^{80} - 24q^{81} - 33q^{82} - 77q^{83} - 113q^{84} - 95q^{85} - 137q^{86} + 23q^{87} + 19q^{88} - 112q^{89} - 19q^{90} + 8q^{91} - 111q^{92} - 124q^{93} - 20q^{94} - 73q^{95} - 77q^{96} - 41q^{97} - 80q^{98} - 154q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.20802 −1.56131 −0.780653 0.624964i \(-0.785113\pi\)
−0.780653 + 0.624964i \(0.785113\pi\)
\(3\) −2.87685 −1.66095 −0.830474 0.557057i \(-0.811930\pi\)
−0.830474 + 0.557057i \(0.811930\pi\)
\(4\) 2.87536 1.43768
\(5\) 1.19118 0.532714 0.266357 0.963874i \(-0.414180\pi\)
0.266357 + 0.963874i \(0.414180\pi\)
\(6\) 6.35214 2.59325
\(7\) −0.105056 −0.0397074 −0.0198537 0.999803i \(-0.506320\pi\)
−0.0198537 + 0.999803i \(0.506320\pi\)
\(8\) −1.93280 −0.683350
\(9\) 5.27625 1.75875
\(10\) −2.63016 −0.831729
\(11\) 2.37185 0.715140 0.357570 0.933886i \(-0.383605\pi\)
0.357570 + 0.933886i \(0.383605\pi\)
\(12\) −8.27196 −2.38791
\(13\) −1.00000 −0.277350
\(14\) 0.231966 0.0619955
\(15\) −3.42685 −0.884810
\(16\) −1.48304 −0.370760
\(17\) 7.30297 1.77123 0.885615 0.464421i \(-0.153737\pi\)
0.885615 + 0.464421i \(0.153737\pi\)
\(18\) −11.6501 −2.74595
\(19\) −3.69849 −0.848492 −0.424246 0.905547i \(-0.639461\pi\)
−0.424246 + 0.905547i \(0.639461\pi\)
\(20\) 3.42508 0.765871
\(21\) 0.302230 0.0659520
\(22\) −5.23709 −1.11655
\(23\) 5.61104 1.16998 0.584991 0.811040i \(-0.301098\pi\)
0.584991 + 0.811040i \(0.301098\pi\)
\(24\) 5.56038 1.13501
\(25\) −3.58108 −0.716216
\(26\) 2.20802 0.433029
\(27\) −6.54841 −1.26024
\(28\) −0.302073 −0.0570865
\(29\) 2.61763 0.486082 0.243041 0.970016i \(-0.421855\pi\)
0.243041 + 0.970016i \(0.421855\pi\)
\(30\) 7.56656 1.38146
\(31\) 3.62118 0.650384 0.325192 0.945648i \(-0.394571\pi\)
0.325192 + 0.945648i \(0.394571\pi\)
\(32\) 7.14019 1.26222
\(33\) −6.82345 −1.18781
\(34\) −16.1251 −2.76543
\(35\) −0.125141 −0.0211527
\(36\) 15.1711 2.52851
\(37\) −3.01688 −0.495973 −0.247986 0.968764i \(-0.579769\pi\)
−0.247986 + 0.968764i \(0.579769\pi\)
\(38\) 8.16635 1.32476
\(39\) 2.87685 0.460664
\(40\) −2.30233 −0.364030
\(41\) 3.21696 0.502405 0.251203 0.967935i \(-0.419174\pi\)
0.251203 + 0.967935i \(0.419174\pi\)
\(42\) −0.667330 −0.102971
\(43\) 5.89126 0.898409 0.449205 0.893429i \(-0.351707\pi\)
0.449205 + 0.893429i \(0.351707\pi\)
\(44\) 6.81991 1.02814
\(45\) 6.28498 0.936910
\(46\) −12.3893 −1.82670
\(47\) −13.1541 −1.91872 −0.959362 0.282178i \(-0.908943\pi\)
−0.959362 + 0.282178i \(0.908943\pi\)
\(48\) 4.26648 0.615813
\(49\) −6.98896 −0.998423
\(50\) 7.90710 1.11823
\(51\) −21.0095 −2.94192
\(52\) −2.87536 −0.398740
\(53\) −2.12400 −0.291753 −0.145877 0.989303i \(-0.546600\pi\)
−0.145877 + 0.989303i \(0.546600\pi\)
\(54\) 14.4590 1.96762
\(55\) 2.82531 0.380965
\(56\) 0.203053 0.0271341
\(57\) 10.6400 1.40930
\(58\) −5.77979 −0.758923
\(59\) 6.88019 0.895724 0.447862 0.894103i \(-0.352186\pi\)
0.447862 + 0.894103i \(0.352186\pi\)
\(60\) −9.85343 −1.27207
\(61\) −7.18991 −0.920574 −0.460287 0.887770i \(-0.652253\pi\)
−0.460287 + 0.887770i \(0.652253\pi\)
\(62\) −7.99565 −1.01545
\(63\) −0.554301 −0.0698354
\(64\) −12.7996 −1.59995
\(65\) −1.19118 −0.147748
\(66\) 15.0663 1.85454
\(67\) −0.729638 −0.0891394 −0.0445697 0.999006i \(-0.514192\pi\)
−0.0445697 + 0.999006i \(0.514192\pi\)
\(68\) 20.9986 2.54646
\(69\) −16.1421 −1.94328
\(70\) 0.276314 0.0330258
\(71\) −10.2562 −1.21719 −0.608595 0.793481i \(-0.708266\pi\)
−0.608595 + 0.793481i \(0.708266\pi\)
\(72\) −10.1980 −1.20184
\(73\) −10.5443 −1.23412 −0.617058 0.786918i \(-0.711676\pi\)
−0.617058 + 0.786918i \(0.711676\pi\)
\(74\) 6.66134 0.774366
\(75\) 10.3022 1.18960
\(76\) −10.6345 −1.21986
\(77\) −0.249177 −0.0283964
\(78\) −6.35214 −0.719238
\(79\) −1.19588 −0.134546 −0.0672732 0.997735i \(-0.521430\pi\)
−0.0672732 + 0.997735i \(0.521430\pi\)
\(80\) −1.76657 −0.197509
\(81\) 3.01003 0.334448
\(82\) −7.10312 −0.784409
\(83\) −6.45589 −0.708626 −0.354313 0.935127i \(-0.615285\pi\)
−0.354313 + 0.935127i \(0.615285\pi\)
\(84\) 0.869019 0.0948177
\(85\) 8.69918 0.943558
\(86\) −13.0080 −1.40269
\(87\) −7.53053 −0.807357
\(88\) −4.58432 −0.488691
\(89\) −8.93028 −0.946608 −0.473304 0.880899i \(-0.656939\pi\)
−0.473304 + 0.880899i \(0.656939\pi\)
\(90\) −13.8774 −1.46280
\(91\) 0.105056 0.0110129
\(92\) 16.1337 1.68206
\(93\) −10.4176 −1.08025
\(94\) 29.0446 2.99572
\(95\) −4.40559 −0.452003
\(96\) −20.5412 −2.09648
\(97\) −1.92287 −0.195238 −0.0976191 0.995224i \(-0.531123\pi\)
−0.0976191 + 0.995224i \(0.531123\pi\)
\(98\) 15.4318 1.55884
\(99\) 12.5145 1.25775
\(100\) −10.2969 −1.02969
\(101\) −17.5409 −1.74539 −0.872694 0.488268i \(-0.837629\pi\)
−0.872694 + 0.488268i \(0.837629\pi\)
\(102\) 46.3894 4.59324
\(103\) 18.8338 1.85575 0.927875 0.372890i \(-0.121633\pi\)
0.927875 + 0.372890i \(0.121633\pi\)
\(104\) 1.93280 0.189527
\(105\) 0.360012 0.0351335
\(106\) 4.68983 0.455517
\(107\) 8.51796 0.823462 0.411731 0.911305i \(-0.364924\pi\)
0.411731 + 0.911305i \(0.364924\pi\)
\(108\) −18.8290 −1.81182
\(109\) −20.0830 −1.92360 −0.961801 0.273751i \(-0.911736\pi\)
−0.961801 + 0.273751i \(0.911736\pi\)
\(110\) −6.23834 −0.594803
\(111\) 8.67911 0.823785
\(112\) 0.155802 0.0147219
\(113\) −0.599024 −0.0563514 −0.0281757 0.999603i \(-0.508970\pi\)
−0.0281757 + 0.999603i \(0.508970\pi\)
\(114\) −23.4933 −2.20035
\(115\) 6.68378 0.623265
\(116\) 7.52663 0.698830
\(117\) −5.27625 −0.487789
\(118\) −15.1916 −1.39850
\(119\) −0.767220 −0.0703310
\(120\) 6.62344 0.604635
\(121\) −5.37433 −0.488575
\(122\) 15.8755 1.43730
\(123\) −9.25471 −0.834469
\(124\) 10.4122 0.935042
\(125\) −10.2216 −0.914252
\(126\) 1.22391 0.109034
\(127\) −4.09597 −0.363459 −0.181729 0.983349i \(-0.558169\pi\)
−0.181729 + 0.983349i \(0.558169\pi\)
\(128\) 13.9814 1.23580
\(129\) −16.9483 −1.49221
\(130\) 2.63016 0.230680
\(131\) 17.5563 1.53390 0.766952 0.641705i \(-0.221773\pi\)
0.766952 + 0.641705i \(0.221773\pi\)
\(132\) −19.6198 −1.70769
\(133\) 0.388549 0.0336914
\(134\) 1.61106 0.139174
\(135\) −7.80036 −0.671348
\(136\) −14.1152 −1.21037
\(137\) 7.88424 0.673596 0.336798 0.941577i \(-0.390656\pi\)
0.336798 + 0.941577i \(0.390656\pi\)
\(138\) 35.6421 3.03405
\(139\) −6.14073 −0.520850 −0.260425 0.965494i \(-0.583863\pi\)
−0.260425 + 0.965494i \(0.583863\pi\)
\(140\) −0.359825 −0.0304108
\(141\) 37.8424 3.18690
\(142\) 22.6459 1.90041
\(143\) −2.37185 −0.198344
\(144\) −7.82488 −0.652073
\(145\) 3.11808 0.258943
\(146\) 23.2820 1.92683
\(147\) 20.1062 1.65833
\(148\) −8.67462 −0.713049
\(149\) −11.1779 −0.915727 −0.457864 0.889022i \(-0.651385\pi\)
−0.457864 + 0.889022i \(0.651385\pi\)
\(150\) −22.7475 −1.85733
\(151\) −10.0591 −0.818598 −0.409299 0.912400i \(-0.634227\pi\)
−0.409299 + 0.912400i \(0.634227\pi\)
\(152\) 7.14846 0.579817
\(153\) 38.5322 3.11515
\(154\) 0.550188 0.0443354
\(155\) 4.31350 0.346468
\(156\) 8.27196 0.662287
\(157\) 2.21286 0.176606 0.0883029 0.996094i \(-0.471856\pi\)
0.0883029 + 0.996094i \(0.471856\pi\)
\(158\) 2.64052 0.210068
\(159\) 6.11041 0.484587
\(160\) 8.50528 0.672402
\(161\) −0.589473 −0.0464570
\(162\) −6.64622 −0.522176
\(163\) −5.07204 −0.397273 −0.198637 0.980073i \(-0.563651\pi\)
−0.198637 + 0.980073i \(0.563651\pi\)
\(164\) 9.24992 0.722297
\(165\) −8.12798 −0.632763
\(166\) 14.2547 1.10638
\(167\) 12.9061 0.998704 0.499352 0.866399i \(-0.333571\pi\)
0.499352 + 0.866399i \(0.333571\pi\)
\(168\) −0.584151 −0.0450683
\(169\) 1.00000 0.0769231
\(170\) −19.2080 −1.47318
\(171\) −19.5142 −1.49228
\(172\) 16.9395 1.29162
\(173\) −12.3925 −0.942186 −0.471093 0.882084i \(-0.656140\pi\)
−0.471093 + 0.882084i \(0.656140\pi\)
\(174\) 16.6276 1.26053
\(175\) 0.376214 0.0284391
\(176\) −3.51755 −0.265145
\(177\) −19.7932 −1.48775
\(178\) 19.7182 1.47794
\(179\) 9.96551 0.744857 0.372429 0.928061i \(-0.378525\pi\)
0.372429 + 0.928061i \(0.378525\pi\)
\(180\) 18.0716 1.34697
\(181\) −11.2710 −0.837766 −0.418883 0.908040i \(-0.637578\pi\)
−0.418883 + 0.908040i \(0.637578\pi\)
\(182\) −0.231966 −0.0171944
\(183\) 20.6843 1.52903
\(184\) −10.8450 −0.799507
\(185\) −3.59367 −0.264212
\(186\) 23.0023 1.68661
\(187\) 17.3215 1.26668
\(188\) −37.8228 −2.75851
\(189\) 0.687950 0.0500410
\(190\) 9.72762 0.705716
\(191\) −15.5242 −1.12329 −0.561646 0.827378i \(-0.689832\pi\)
−0.561646 + 0.827378i \(0.689832\pi\)
\(192\) 36.8225 2.65744
\(193\) 2.38822 0.171908 0.0859538 0.996299i \(-0.472606\pi\)
0.0859538 + 0.996299i \(0.472606\pi\)
\(194\) 4.24575 0.304827
\(195\) 3.42685 0.245402
\(196\) −20.0958 −1.43541
\(197\) 8.53080 0.607794 0.303897 0.952705i \(-0.401712\pi\)
0.303897 + 0.952705i \(0.401712\pi\)
\(198\) −27.6322 −1.96373
\(199\) 4.11082 0.291408 0.145704 0.989328i \(-0.453455\pi\)
0.145704 + 0.989328i \(0.453455\pi\)
\(200\) 6.92153 0.489426
\(201\) 2.09906 0.148056
\(202\) 38.7307 2.72509
\(203\) −0.274998 −0.0193011
\(204\) −60.4098 −4.22953
\(205\) 3.83200 0.267638
\(206\) −41.5855 −2.89740
\(207\) 29.6052 2.05770
\(208\) 1.48304 0.102830
\(209\) −8.77227 −0.606791
\(210\) −0.794913 −0.0548542
\(211\) 24.8340 1.70964 0.854820 0.518925i \(-0.173668\pi\)
0.854820 + 0.518925i \(0.173668\pi\)
\(212\) −6.10725 −0.419448
\(213\) 29.5056 2.02169
\(214\) −18.8078 −1.28568
\(215\) 7.01758 0.478595
\(216\) 12.6568 0.861186
\(217\) −0.380427 −0.0258251
\(218\) 44.3437 3.00333
\(219\) 30.3343 2.04980
\(220\) 8.12377 0.547705
\(221\) −7.30297 −0.491251
\(222\) −19.1637 −1.28618
\(223\) 21.1415 1.41574 0.707869 0.706344i \(-0.249657\pi\)
0.707869 + 0.706344i \(0.249657\pi\)
\(224\) −0.750120 −0.0501195
\(225\) −18.8947 −1.25964
\(226\) 1.32266 0.0879819
\(227\) 5.67892 0.376923 0.188462 0.982081i \(-0.439650\pi\)
0.188462 + 0.982081i \(0.439650\pi\)
\(228\) 30.5938 2.02612
\(229\) −7.25286 −0.479282 −0.239641 0.970862i \(-0.577030\pi\)
−0.239641 + 0.970862i \(0.577030\pi\)
\(230\) −14.7579 −0.973108
\(231\) 0.716844 0.0471649
\(232\) −5.05937 −0.332164
\(233\) 0.139872 0.00916333 0.00458167 0.999990i \(-0.498542\pi\)
0.00458167 + 0.999990i \(0.498542\pi\)
\(234\) 11.6501 0.761588
\(235\) −15.6690 −1.02213
\(236\) 19.7830 1.28776
\(237\) 3.44035 0.223475
\(238\) 1.69404 0.109808
\(239\) −17.4169 −1.12661 −0.563304 0.826250i \(-0.690470\pi\)
−0.563304 + 0.826250i \(0.690470\pi\)
\(240\) 5.08216 0.328052
\(241\) 8.16718 0.526094 0.263047 0.964783i \(-0.415273\pi\)
0.263047 + 0.964783i \(0.415273\pi\)
\(242\) 11.8666 0.762816
\(243\) 10.9858 0.704741
\(244\) −20.6736 −1.32349
\(245\) −8.32514 −0.531874
\(246\) 20.4346 1.30286
\(247\) 3.69849 0.235329
\(248\) −6.99904 −0.444440
\(249\) 18.5726 1.17699
\(250\) 22.5696 1.42743
\(251\) 5.72186 0.361161 0.180580 0.983560i \(-0.442202\pi\)
0.180580 + 0.983560i \(0.442202\pi\)
\(252\) −1.59381 −0.100401
\(253\) 13.3085 0.836700
\(254\) 9.04399 0.567471
\(255\) −25.0262 −1.56720
\(256\) −5.27206 −0.329504
\(257\) −3.79970 −0.237019 −0.118510 0.992953i \(-0.537812\pi\)
−0.118510 + 0.992953i \(0.537812\pi\)
\(258\) 37.4221 2.32980
\(259\) 0.316942 0.0196938
\(260\) −3.42508 −0.212414
\(261\) 13.8113 0.854896
\(262\) −38.7647 −2.39489
\(263\) −8.50785 −0.524617 −0.262308 0.964984i \(-0.584484\pi\)
−0.262308 + 0.964984i \(0.584484\pi\)
\(264\) 13.1884 0.811690
\(265\) −2.53007 −0.155421
\(266\) −0.857924 −0.0526027
\(267\) 25.6910 1.57227
\(268\) −2.09797 −0.128154
\(269\) −14.7218 −0.897604 −0.448802 0.893631i \(-0.648149\pi\)
−0.448802 + 0.893631i \(0.648149\pi\)
\(270\) 17.2234 1.04818
\(271\) −19.3218 −1.17372 −0.586858 0.809690i \(-0.699636\pi\)
−0.586858 + 0.809690i \(0.699636\pi\)
\(272\) −10.8306 −0.656701
\(273\) −0.302230 −0.0182918
\(274\) −17.4086 −1.05169
\(275\) −8.49379 −0.512195
\(276\) −46.4143 −2.79381
\(277\) −16.0375 −0.963601 −0.481801 0.876281i \(-0.660017\pi\)
−0.481801 + 0.876281i \(0.660017\pi\)
\(278\) 13.5589 0.813207
\(279\) 19.1063 1.14386
\(280\) 0.241873 0.0144547
\(281\) 11.6575 0.695430 0.347715 0.937600i \(-0.386958\pi\)
0.347715 + 0.937600i \(0.386958\pi\)
\(282\) −83.5567 −4.97573
\(283\) 9.85784 0.585988 0.292994 0.956114i \(-0.405348\pi\)
0.292994 + 0.956114i \(0.405348\pi\)
\(284\) −29.4903 −1.74993
\(285\) 12.6742 0.750754
\(286\) 5.23709 0.309676
\(287\) −0.337961 −0.0199492
\(288\) 37.6734 2.21993
\(289\) 36.3333 2.13725
\(290\) −6.88479 −0.404289
\(291\) 5.53181 0.324281
\(292\) −30.3186 −1.77426
\(293\) 11.0214 0.643878 0.321939 0.946760i \(-0.395665\pi\)
0.321939 + 0.946760i \(0.395665\pi\)
\(294\) −44.3949 −2.58916
\(295\) 8.19557 0.477164
\(296\) 5.83105 0.338923
\(297\) −15.5318 −0.901249
\(298\) 24.6810 1.42973
\(299\) −5.61104 −0.324495
\(300\) 29.6225 1.71026
\(301\) −0.618912 −0.0356735
\(302\) 22.2107 1.27808
\(303\) 50.4626 2.89900
\(304\) 5.48501 0.314587
\(305\) −8.56451 −0.490402
\(306\) −85.0800 −4.86370
\(307\) 10.7776 0.615108 0.307554 0.951531i \(-0.400490\pi\)
0.307554 + 0.951531i \(0.400490\pi\)
\(308\) −0.716473 −0.0408248
\(309\) −54.1820 −3.08231
\(310\) −9.52429 −0.540943
\(311\) 5.26016 0.298276 0.149138 0.988816i \(-0.452350\pi\)
0.149138 + 0.988816i \(0.452350\pi\)
\(312\) −5.56038 −0.314795
\(313\) 23.2185 1.31239 0.656193 0.754593i \(-0.272166\pi\)
0.656193 + 0.754593i \(0.272166\pi\)
\(314\) −4.88605 −0.275736
\(315\) −0.660275 −0.0372023
\(316\) −3.43857 −0.193435
\(317\) −30.0776 −1.68933 −0.844664 0.535297i \(-0.820200\pi\)
−0.844664 + 0.535297i \(0.820200\pi\)
\(318\) −13.4919 −0.756589
\(319\) 6.20863 0.347617
\(320\) −15.2467 −0.852316
\(321\) −24.5049 −1.36773
\(322\) 1.30157 0.0725336
\(323\) −27.0100 −1.50287
\(324\) 8.65492 0.480829
\(325\) 3.58108 0.198643
\(326\) 11.1992 0.620265
\(327\) 57.7757 3.19500
\(328\) −6.21776 −0.343318
\(329\) 1.38192 0.0761876
\(330\) 17.9468 0.987937
\(331\) 7.74017 0.425438 0.212719 0.977113i \(-0.431768\pi\)
0.212719 + 0.977113i \(0.431768\pi\)
\(332\) −18.5630 −1.01878
\(333\) −15.9178 −0.872292
\(334\) −28.4969 −1.55928
\(335\) −0.869133 −0.0474858
\(336\) −0.448219 −0.0244523
\(337\) −9.43977 −0.514217 −0.257108 0.966383i \(-0.582770\pi\)
−0.257108 + 0.966383i \(0.582770\pi\)
\(338\) −2.20802 −0.120101
\(339\) 1.72330 0.0935968
\(340\) 25.0132 1.35653
\(341\) 8.58890 0.465115
\(342\) 43.0877 2.32991
\(343\) 1.46962 0.0793523
\(344\) −11.3867 −0.613928
\(345\) −19.2282 −1.03521
\(346\) 27.3629 1.47104
\(347\) −25.3195 −1.35922 −0.679611 0.733572i \(-0.737852\pi\)
−0.679611 + 0.733572i \(0.737852\pi\)
\(348\) −21.6529 −1.16072
\(349\) 12.8013 0.685236 0.342618 0.939475i \(-0.388686\pi\)
0.342618 + 0.939475i \(0.388686\pi\)
\(350\) −0.830688 −0.0444022
\(351\) 6.54841 0.349528
\(352\) 16.9355 0.902663
\(353\) 16.7519 0.891616 0.445808 0.895129i \(-0.352916\pi\)
0.445808 + 0.895129i \(0.352916\pi\)
\(354\) 43.7039 2.32284
\(355\) −12.2170 −0.648413
\(356\) −25.6777 −1.36092
\(357\) 2.20718 0.116816
\(358\) −22.0041 −1.16295
\(359\) −16.4037 −0.865752 −0.432876 0.901453i \(-0.642501\pi\)
−0.432876 + 0.901453i \(0.642501\pi\)
\(360\) −12.1476 −0.640237
\(361\) −5.32116 −0.280061
\(362\) 24.8866 1.30801
\(363\) 15.4611 0.811498
\(364\) 0.302073 0.0158329
\(365\) −12.5602 −0.657431
\(366\) −45.6713 −2.38728
\(367\) −25.9556 −1.35487 −0.677435 0.735583i \(-0.736908\pi\)
−0.677435 + 0.735583i \(0.736908\pi\)
\(368\) −8.32139 −0.433782
\(369\) 16.9735 0.883605
\(370\) 7.93489 0.412515
\(371\) 0.223139 0.0115848
\(372\) −29.9543 −1.55306
\(373\) 4.11030 0.212823 0.106412 0.994322i \(-0.466064\pi\)
0.106412 + 0.994322i \(0.466064\pi\)
\(374\) −38.2463 −1.97767
\(375\) 29.4061 1.51852
\(376\) 25.4243 1.31116
\(377\) −2.61763 −0.134815
\(378\) −1.51901 −0.0781293
\(379\) 13.3468 0.685578 0.342789 0.939412i \(-0.388628\pi\)
0.342789 + 0.939412i \(0.388628\pi\)
\(380\) −12.6676 −0.649836
\(381\) 11.7835 0.603686
\(382\) 34.2778 1.75380
\(383\) −2.69363 −0.137638 −0.0688191 0.997629i \(-0.521923\pi\)
−0.0688191 + 0.997629i \(0.521923\pi\)
\(384\) −40.2224 −2.05259
\(385\) −0.296816 −0.0151271
\(386\) −5.27323 −0.268401
\(387\) 31.0838 1.58008
\(388\) −5.52895 −0.280690
\(389\) 23.1966 1.17611 0.588056 0.808820i \(-0.299893\pi\)
0.588056 + 0.808820i \(0.299893\pi\)
\(390\) −7.56656 −0.383148
\(391\) 40.9772 2.07231
\(392\) 13.5083 0.682272
\(393\) −50.5068 −2.54773
\(394\) −18.8362 −0.948953
\(395\) −1.42451 −0.0716748
\(396\) 35.9835 1.80824
\(397\) −10.2639 −0.515130 −0.257565 0.966261i \(-0.582920\pi\)
−0.257565 + 0.966261i \(0.582920\pi\)
\(398\) −9.07677 −0.454977
\(399\) −1.11780 −0.0559597
\(400\) 5.31088 0.265544
\(401\) 5.67332 0.283312 0.141656 0.989916i \(-0.454757\pi\)
0.141656 + 0.989916i \(0.454757\pi\)
\(402\) −4.63476 −0.231161
\(403\) −3.62118 −0.180384
\(404\) −50.4364 −2.50931
\(405\) 3.58550 0.178165
\(406\) 0.607201 0.0301349
\(407\) −7.15560 −0.354690
\(408\) 40.6073 2.01036
\(409\) 18.4101 0.910322 0.455161 0.890409i \(-0.349582\pi\)
0.455161 + 0.890409i \(0.349582\pi\)
\(410\) −8.46113 −0.417865
\(411\) −22.6818 −1.11881
\(412\) 54.1539 2.66797
\(413\) −0.722805 −0.0355669
\(414\) −65.3689 −3.21271
\(415\) −7.69016 −0.377495
\(416\) −7.14019 −0.350077
\(417\) 17.6659 0.865105
\(418\) 19.3694 0.947386
\(419\) −13.9312 −0.680581 −0.340291 0.940320i \(-0.610525\pi\)
−0.340291 + 0.940320i \(0.610525\pi\)
\(420\) 1.03516 0.0505107
\(421\) −14.3201 −0.697918 −0.348959 0.937138i \(-0.613465\pi\)
−0.348959 + 0.937138i \(0.613465\pi\)
\(422\) −54.8339 −2.66927
\(423\) −69.4043 −3.37455
\(424\) 4.10527 0.199370
\(425\) −26.1525 −1.26858
\(426\) −65.1489 −3.15647
\(427\) 0.755343 0.0365536
\(428\) 24.4922 1.18387
\(429\) 6.82345 0.329439
\(430\) −15.4950 −0.747233
\(431\) 2.54093 0.122392 0.0611961 0.998126i \(-0.480509\pi\)
0.0611961 + 0.998126i \(0.480509\pi\)
\(432\) 9.71155 0.467247
\(433\) 4.33547 0.208349 0.104175 0.994559i \(-0.466780\pi\)
0.104175 + 0.994559i \(0.466780\pi\)
\(434\) 0.839991 0.0403208
\(435\) −8.97024 −0.430090
\(436\) −57.7457 −2.76552
\(437\) −20.7524 −0.992720
\(438\) −66.9788 −3.20037
\(439\) −2.47639 −0.118192 −0.0590958 0.998252i \(-0.518822\pi\)
−0.0590958 + 0.998252i \(0.518822\pi\)
\(440\) −5.46077 −0.260332
\(441\) −36.8755 −1.75598
\(442\) 16.1251 0.766993
\(443\) −30.8902 −1.46764 −0.733819 0.679345i \(-0.762264\pi\)
−0.733819 + 0.679345i \(0.762264\pi\)
\(444\) 24.9555 1.18434
\(445\) −10.6376 −0.504271
\(446\) −46.6808 −2.21040
\(447\) 32.1570 1.52098
\(448\) 1.34468 0.0635300
\(449\) −8.75400 −0.413127 −0.206563 0.978433i \(-0.566228\pi\)
−0.206563 + 0.978433i \(0.566228\pi\)
\(450\) 41.7198 1.96669
\(451\) 7.63016 0.359290
\(452\) −1.72241 −0.0810152
\(453\) 28.9385 1.35965
\(454\) −12.5392 −0.588492
\(455\) 0.125141 0.00586670
\(456\) −20.5650 −0.963046
\(457\) 28.6748 1.34135 0.670676 0.741750i \(-0.266004\pi\)
0.670676 + 0.741750i \(0.266004\pi\)
\(458\) 16.0145 0.748307
\(459\) −47.8228 −2.23218
\(460\) 19.2182 0.896055
\(461\) −12.8012 −0.596211 −0.298106 0.954533i \(-0.596355\pi\)
−0.298106 + 0.954533i \(0.596355\pi\)
\(462\) −1.58281 −0.0736388
\(463\) −1.00000 −0.0464739
\(464\) −3.88205 −0.180220
\(465\) −12.4093 −0.575466
\(466\) −0.308841 −0.0143068
\(467\) −28.4466 −1.31635 −0.658176 0.752864i \(-0.728672\pi\)
−0.658176 + 0.752864i \(0.728672\pi\)
\(468\) −15.1711 −0.701284
\(469\) 0.0766528 0.00353950
\(470\) 34.5974 1.59586
\(471\) −6.36607 −0.293333
\(472\) −13.2981 −0.612093
\(473\) 13.9732 0.642488
\(474\) −7.59636 −0.348913
\(475\) 13.2446 0.607704
\(476\) −2.20603 −0.101113
\(477\) −11.2067 −0.513121
\(478\) 38.4569 1.75898
\(479\) −3.10569 −0.141903 −0.0709514 0.997480i \(-0.522604\pi\)
−0.0709514 + 0.997480i \(0.522604\pi\)
\(480\) −24.4684 −1.11682
\(481\) 3.01688 0.137558
\(482\) −18.0333 −0.821394
\(483\) 1.69582 0.0771626
\(484\) −15.4531 −0.702414
\(485\) −2.29050 −0.104006
\(486\) −24.2569 −1.10032
\(487\) −16.5352 −0.749280 −0.374640 0.927170i \(-0.622234\pi\)
−0.374640 + 0.927170i \(0.622234\pi\)
\(488\) 13.8967 0.629074
\(489\) 14.5915 0.659850
\(490\) 18.3821 0.830418
\(491\) −39.3034 −1.77374 −0.886868 0.462023i \(-0.847124\pi\)
−0.886868 + 0.462023i \(0.847124\pi\)
\(492\) −26.6106 −1.19970
\(493\) 19.1165 0.860963
\(494\) −8.16635 −0.367421
\(495\) 14.9070 0.670021
\(496\) −5.37036 −0.241136
\(497\) 1.07748 0.0483315
\(498\) −41.0087 −1.83764
\(499\) −3.66199 −0.163933 −0.0819667 0.996635i \(-0.526120\pi\)
−0.0819667 + 0.996635i \(0.526120\pi\)
\(500\) −29.3909 −1.31440
\(501\) −37.1289 −1.65880
\(502\) −12.6340 −0.563883
\(503\) 8.07262 0.359940 0.179970 0.983672i \(-0.442400\pi\)
0.179970 + 0.983672i \(0.442400\pi\)
\(504\) 1.07136 0.0477220
\(505\) −20.8945 −0.929792
\(506\) −29.3855 −1.30635
\(507\) −2.87685 −0.127765
\(508\) −11.7774 −0.522537
\(509\) 13.7353 0.608809 0.304404 0.952543i \(-0.401543\pi\)
0.304404 + 0.952543i \(0.401543\pi\)
\(510\) 55.2584 2.44688
\(511\) 1.10774 0.0490036
\(512\) −16.3220 −0.721339
\(513\) 24.2192 1.06931
\(514\) 8.38983 0.370059
\(515\) 22.4345 0.988584
\(516\) −48.7323 −2.14532
\(517\) −31.1996 −1.37216
\(518\) −0.699814 −0.0307481
\(519\) 35.6514 1.56492
\(520\) 2.30233 0.100964
\(521\) 37.0344 1.62251 0.811254 0.584694i \(-0.198785\pi\)
0.811254 + 0.584694i \(0.198785\pi\)
\(522\) −30.4956 −1.33476
\(523\) −8.55393 −0.374037 −0.187019 0.982356i \(-0.559882\pi\)
−0.187019 + 0.982356i \(0.559882\pi\)
\(524\) 50.4807 2.20526
\(525\) −1.08231 −0.0472359
\(526\) 18.7855 0.819088
\(527\) 26.4454 1.15198
\(528\) 10.1194 0.440392
\(529\) 8.48372 0.368857
\(530\) 5.58645 0.242660
\(531\) 36.3015 1.57535
\(532\) 1.11722 0.0484375
\(533\) −3.21696 −0.139342
\(534\) −56.7264 −2.45479
\(535\) 10.1465 0.438670
\(536\) 1.41025 0.0609134
\(537\) −28.6692 −1.23717
\(538\) 32.5061 1.40144
\(539\) −16.5768 −0.714012
\(540\) −22.4288 −0.965183
\(541\) −29.5839 −1.27191 −0.635956 0.771725i \(-0.719394\pi\)
−0.635956 + 0.771725i \(0.719394\pi\)
\(542\) 42.6630 1.83253
\(543\) 32.4249 1.39149
\(544\) 52.1446 2.23568
\(545\) −23.9225 −1.02473
\(546\) 0.667330 0.0285591
\(547\) −38.3344 −1.63906 −0.819531 0.573035i \(-0.805766\pi\)
−0.819531 + 0.573035i \(0.805766\pi\)
\(548\) 22.6700 0.968414
\(549\) −37.9357 −1.61906
\(550\) 18.7545 0.799693
\(551\) −9.68129 −0.412437
\(552\) 31.1995 1.32794
\(553\) 0.125634 0.00534250
\(554\) 35.4112 1.50448
\(555\) 10.3384 0.438842
\(556\) −17.6568 −0.748815
\(557\) 24.9809 1.05847 0.529237 0.848474i \(-0.322478\pi\)
0.529237 + 0.848474i \(0.322478\pi\)
\(558\) −42.1870 −1.78592
\(559\) −5.89126 −0.249174
\(560\) 0.185589 0.00784257
\(561\) −49.8314 −2.10388
\(562\) −25.7401 −1.08578
\(563\) −39.2329 −1.65347 −0.826735 0.562592i \(-0.809804\pi\)
−0.826735 + 0.562592i \(0.809804\pi\)
\(564\) 108.810 4.58174
\(565\) −0.713548 −0.0300192
\(566\) −21.7663 −0.914907
\(567\) −0.316222 −0.0132801
\(568\) 19.8233 0.831766
\(569\) −6.80393 −0.285236 −0.142618 0.989778i \(-0.545552\pi\)
−0.142618 + 0.989778i \(0.545552\pi\)
\(570\) −27.9849 −1.17216
\(571\) −37.3818 −1.56438 −0.782191 0.623039i \(-0.785898\pi\)
−0.782191 + 0.623039i \(0.785898\pi\)
\(572\) −6.81991 −0.285155
\(573\) 44.6607 1.86573
\(574\) 0.746226 0.0311469
\(575\) −20.0936 −0.837960
\(576\) −67.5339 −2.81391
\(577\) −13.2988 −0.553634 −0.276817 0.960923i \(-0.589280\pi\)
−0.276817 + 0.960923i \(0.589280\pi\)
\(578\) −80.2247 −3.33691
\(579\) −6.87053 −0.285530
\(580\) 8.96560 0.372276
\(581\) 0.678230 0.0281377
\(582\) −12.2144 −0.506302
\(583\) −5.03780 −0.208644
\(584\) 20.3801 0.843333
\(585\) −6.28498 −0.259852
\(586\) −24.3355 −1.00529
\(587\) −4.35097 −0.179584 −0.0897918 0.995961i \(-0.528620\pi\)
−0.0897918 + 0.995961i \(0.528620\pi\)
\(588\) 57.8124 2.38414
\(589\) −13.3929 −0.551846
\(590\) −18.0960 −0.745000
\(591\) −24.5418 −1.00951
\(592\) 4.47416 0.183887
\(593\) 32.1475 1.32014 0.660071 0.751204i \(-0.270526\pi\)
0.660071 + 0.751204i \(0.270526\pi\)
\(594\) 34.2946 1.40713
\(595\) −0.913901 −0.0374663
\(596\) −32.1404 −1.31652
\(597\) −11.8262 −0.484014
\(598\) 12.3893 0.506635
\(599\) 47.8640 1.95567 0.977834 0.209381i \(-0.0671449\pi\)
0.977834 + 0.209381i \(0.0671449\pi\)
\(600\) −19.9122 −0.812911
\(601\) −17.4243 −0.710752 −0.355376 0.934723i \(-0.615647\pi\)
−0.355376 + 0.934723i \(0.615647\pi\)
\(602\) 1.36657 0.0556973
\(603\) −3.84975 −0.156774
\(604\) −28.9235 −1.17688
\(605\) −6.40181 −0.260271
\(606\) −111.422 −4.52623
\(607\) −18.7018 −0.759082 −0.379541 0.925175i \(-0.623918\pi\)
−0.379541 + 0.925175i \(0.623918\pi\)
\(608\) −26.4079 −1.07098
\(609\) 0.791127 0.0320581
\(610\) 18.9106 0.765668
\(611\) 13.1541 0.532158
\(612\) 110.794 4.47858
\(613\) −31.8360 −1.28584 −0.642922 0.765932i \(-0.722278\pi\)
−0.642922 + 0.765932i \(0.722278\pi\)
\(614\) −23.7971 −0.960372
\(615\) −11.0241 −0.444533
\(616\) 0.481611 0.0194046
\(617\) 4.24549 0.170917 0.0854584 0.996342i \(-0.472765\pi\)
0.0854584 + 0.996342i \(0.472765\pi\)
\(618\) 119.635 4.81242
\(619\) −1.45326 −0.0584113 −0.0292056 0.999573i \(-0.509298\pi\)
−0.0292056 + 0.999573i \(0.509298\pi\)
\(620\) 12.4028 0.498110
\(621\) −36.7434 −1.47446
\(622\) −11.6145 −0.465701
\(623\) 0.938179 0.0375874
\(624\) −4.26648 −0.170796
\(625\) 5.72954 0.229182
\(626\) −51.2669 −2.04904
\(627\) 25.2365 1.00785
\(628\) 6.36277 0.253902
\(629\) −22.0322 −0.878482
\(630\) 1.45790 0.0580841
\(631\) −3.33568 −0.132791 −0.0663957 0.997793i \(-0.521150\pi\)
−0.0663957 + 0.997793i \(0.521150\pi\)
\(632\) 2.31139 0.0919423
\(633\) −71.4435 −2.83962
\(634\) 66.4120 2.63756
\(635\) −4.87906 −0.193620
\(636\) 17.5696 0.696681
\(637\) 6.98896 0.276913
\(638\) −13.7088 −0.542736
\(639\) −54.1143 −2.14073
\(640\) 16.6545 0.658325
\(641\) 42.1391 1.66439 0.832197 0.554480i \(-0.187083\pi\)
0.832197 + 0.554480i \(0.187083\pi\)
\(642\) 54.1072 2.13544
\(643\) 16.7637 0.661097 0.330549 0.943789i \(-0.392766\pi\)
0.330549 + 0.943789i \(0.392766\pi\)
\(644\) −1.69494 −0.0667902
\(645\) −20.1885 −0.794921
\(646\) 59.6386 2.34645
\(647\) 18.9527 0.745107 0.372554 0.928011i \(-0.378482\pi\)
0.372554 + 0.928011i \(0.378482\pi\)
\(648\) −5.81781 −0.228545
\(649\) 16.3188 0.640568
\(650\) −7.90710 −0.310142
\(651\) 1.09443 0.0428941
\(652\) −14.5839 −0.571151
\(653\) 38.0324 1.48832 0.744162 0.667999i \(-0.232849\pi\)
0.744162 + 0.667999i \(0.232849\pi\)
\(654\) −127.570 −4.98838
\(655\) 20.9128 0.817131
\(656\) −4.77088 −0.186272
\(657\) −55.6343 −2.17050
\(658\) −3.05130 −0.118952
\(659\) −22.1117 −0.861348 −0.430674 0.902508i \(-0.641724\pi\)
−0.430674 + 0.902508i \(0.641724\pi\)
\(660\) −23.3708 −0.909709
\(661\) −30.8942 −1.20164 −0.600822 0.799383i \(-0.705160\pi\)
−0.600822 + 0.799383i \(0.705160\pi\)
\(662\) −17.0904 −0.664239
\(663\) 21.0095 0.815942
\(664\) 12.4780 0.484239
\(665\) 0.462833 0.0179479
\(666\) 35.1469 1.36191
\(667\) 14.6876 0.568707
\(668\) 37.1096 1.43582
\(669\) −60.8208 −2.35147
\(670\) 1.91906 0.0741399
\(671\) −17.0534 −0.658339
\(672\) 2.15798 0.0832459
\(673\) −13.2849 −0.512096 −0.256048 0.966664i \(-0.582421\pi\)
−0.256048 + 0.966664i \(0.582421\pi\)
\(674\) 20.8432 0.802850
\(675\) 23.4504 0.902606
\(676\) 2.87536 0.110591
\(677\) 26.6469 1.02413 0.512063 0.858948i \(-0.328882\pi\)
0.512063 + 0.858948i \(0.328882\pi\)
\(678\) −3.80508 −0.146133
\(679\) 0.202009 0.00775241
\(680\) −16.8138 −0.644780
\(681\) −16.3374 −0.626050
\(682\) −18.9645 −0.726188
\(683\) 2.34275 0.0896430 0.0448215 0.998995i \(-0.485728\pi\)
0.0448215 + 0.998995i \(0.485728\pi\)
\(684\) −56.1101 −2.14542
\(685\) 9.39158 0.358834
\(686\) −3.24496 −0.123893
\(687\) 20.8654 0.796063
\(688\) −8.73697 −0.333094
\(689\) 2.12400 0.0809178
\(690\) 42.4563 1.61628
\(691\) −35.5208 −1.35127 −0.675637 0.737234i \(-0.736132\pi\)
−0.675637 + 0.737234i \(0.736132\pi\)
\(692\) −35.6329 −1.35456
\(693\) −1.31472 −0.0499421
\(694\) 55.9060 2.12216
\(695\) −7.31474 −0.277464
\(696\) 14.5550 0.551707
\(697\) 23.4934 0.889875
\(698\) −28.2655 −1.06986
\(699\) −0.402391 −0.0152198
\(700\) 1.08175 0.0408863
\(701\) −37.1930 −1.40476 −0.702379 0.711803i \(-0.747879\pi\)
−0.702379 + 0.711803i \(0.747879\pi\)
\(702\) −14.4590 −0.545721
\(703\) 11.1579 0.420829
\(704\) −30.3588 −1.14419
\(705\) 45.0772 1.69771
\(706\) −36.9886 −1.39209
\(707\) 1.84278 0.0693049
\(708\) −56.9126 −2.13891
\(709\) 16.5083 0.619984 0.309992 0.950739i \(-0.399674\pi\)
0.309992 + 0.950739i \(0.399674\pi\)
\(710\) 26.9755 1.01237
\(711\) −6.30973 −0.236633
\(712\) 17.2605 0.646864
\(713\) 20.3186 0.760937
\(714\) −4.87349 −0.182386
\(715\) −2.82531 −0.105661
\(716\) 28.6544 1.07086
\(717\) 50.1058 1.87124
\(718\) 36.2196 1.35170
\(719\) 19.2968 0.719649 0.359824 0.933020i \(-0.382837\pi\)
0.359824 + 0.933020i \(0.382837\pi\)
\(720\) −9.32087 −0.347368
\(721\) −1.97860 −0.0736871
\(722\) 11.7492 0.437261
\(723\) −23.4957 −0.873815
\(724\) −32.4081 −1.20444
\(725\) −9.37395 −0.348140
\(726\) −34.1385 −1.26700
\(727\) 45.0506 1.67083 0.835416 0.549618i \(-0.185227\pi\)
0.835416 + 0.549618i \(0.185227\pi\)
\(728\) −0.203053 −0.00752563
\(729\) −40.6346 −1.50499
\(730\) 27.7332 1.02645
\(731\) 43.0237 1.59129
\(732\) 59.4746 2.19825
\(733\) −41.6143 −1.53706 −0.768529 0.639814i \(-0.779011\pi\)
−0.768529 + 0.639814i \(0.779011\pi\)
\(734\) 57.3104 2.11537
\(735\) 23.9502 0.883415
\(736\) 40.0639 1.47677
\(737\) −1.73059 −0.0637471
\(738\) −37.4778 −1.37958
\(739\) 34.8487 1.28193 0.640965 0.767570i \(-0.278534\pi\)
0.640965 + 0.767570i \(0.278534\pi\)
\(740\) −10.3331 −0.379851
\(741\) −10.6400 −0.390870
\(742\) −0.492695 −0.0180874
\(743\) −0.0612267 −0.00224619 −0.00112309 0.999999i \(-0.500357\pi\)
−0.00112309 + 0.999999i \(0.500357\pi\)
\(744\) 20.1352 0.738191
\(745\) −13.3149 −0.487820
\(746\) −9.07563 −0.332282
\(747\) −34.0629 −1.24630
\(748\) 49.8056 1.82107
\(749\) −0.894862 −0.0326976
\(750\) −64.9293 −2.37088
\(751\) −38.1465 −1.39199 −0.695993 0.718048i \(-0.745036\pi\)
−0.695993 + 0.718048i \(0.745036\pi\)
\(752\) 19.5081 0.711386
\(753\) −16.4609 −0.599869
\(754\) 5.77979 0.210487
\(755\) −11.9822 −0.436079
\(756\) 1.97810 0.0719428
\(757\) 7.44865 0.270726 0.135363 0.990796i \(-0.456780\pi\)
0.135363 + 0.990796i \(0.456780\pi\)
\(758\) −29.4700 −1.07040
\(759\) −38.2866 −1.38972
\(760\) 8.51514 0.308876
\(761\) −3.17691 −0.115163 −0.0575814 0.998341i \(-0.518339\pi\)
−0.0575814 + 0.998341i \(0.518339\pi\)
\(762\) −26.0182 −0.942539
\(763\) 2.10984 0.0763813
\(764\) −44.6376 −1.61493
\(765\) 45.8990 1.65948
\(766\) 5.94760 0.214896
\(767\) −6.88019 −0.248429
\(768\) 15.1669 0.547289
\(769\) −17.3781 −0.626672 −0.313336 0.949642i \(-0.601447\pi\)
−0.313336 + 0.949642i \(0.601447\pi\)
\(770\) 0.655375 0.0236181
\(771\) 10.9312 0.393676
\(772\) 6.86698 0.247148
\(773\) −5.90403 −0.212353 −0.106177 0.994347i \(-0.533861\pi\)
−0.106177 + 0.994347i \(0.533861\pi\)
\(774\) −68.6336 −2.46698
\(775\) −12.9677 −0.465815
\(776\) 3.71654 0.133416
\(777\) −0.911793 −0.0327104
\(778\) −51.2185 −1.83627
\(779\) −11.8979 −0.426287
\(780\) 9.85343 0.352809
\(781\) −24.3262 −0.870460
\(782\) −90.4785 −3.23551
\(783\) −17.1413 −0.612581
\(784\) 10.3649 0.370175
\(785\) 2.63593 0.0940803
\(786\) 111.520 3.97779
\(787\) 37.3092 1.32993 0.664965 0.746874i \(-0.268446\pi\)
0.664965 + 0.746874i \(0.268446\pi\)
\(788\) 24.5291 0.873813
\(789\) 24.4758 0.871361
\(790\) 3.14534 0.111906
\(791\) 0.0629311 0.00223757
\(792\) −24.1880 −0.859484
\(793\) 7.18991 0.255321
\(794\) 22.6629 0.804275
\(795\) 7.27863 0.258146
\(796\) 11.8201 0.418951
\(797\) −40.2900 −1.42714 −0.713572 0.700581i \(-0.752924\pi\)
−0.713572 + 0.700581i \(0.752924\pi\)
\(798\) 2.46811 0.0873703
\(799\) −96.0640 −3.39850
\(800\) −25.5696 −0.904022
\(801\) −47.1184 −1.66485
\(802\) −12.5268 −0.442337
\(803\) −25.0095 −0.882565
\(804\) 6.03553 0.212857
\(805\) −0.702171 −0.0247483
\(806\) 7.99565 0.281635
\(807\) 42.3524 1.49087
\(808\) 33.9032 1.19271
\(809\) −22.9719 −0.807650 −0.403825 0.914836i \(-0.632320\pi\)
−0.403825 + 0.914836i \(0.632320\pi\)
\(810\) −7.91687 −0.278170
\(811\) 0.123119 0.00432331 0.00216165 0.999998i \(-0.499312\pi\)
0.00216165 + 0.999998i \(0.499312\pi\)
\(812\) −0.790717 −0.0277487
\(813\) 55.5859 1.94948
\(814\) 15.7997 0.553780
\(815\) −6.04174 −0.211633
\(816\) 31.1579 1.09075
\(817\) −21.7888 −0.762293
\(818\) −40.6499 −1.42129
\(819\) 0.554301 0.0193689
\(820\) 11.0184 0.384778
\(821\) −43.9441 −1.53366 −0.766830 0.641850i \(-0.778167\pi\)
−0.766830 + 0.641850i \(0.778167\pi\)
\(822\) 50.0818 1.74680
\(823\) 33.3738 1.16334 0.581669 0.813426i \(-0.302400\pi\)
0.581669 + 0.813426i \(0.302400\pi\)
\(824\) −36.4021 −1.26813
\(825\) 24.4353 0.850729
\(826\) 1.59597 0.0555308
\(827\) 16.3648 0.569060 0.284530 0.958667i \(-0.408162\pi\)
0.284530 + 0.958667i \(0.408162\pi\)
\(828\) 85.1255 2.95832
\(829\) 28.0757 0.975110 0.487555 0.873092i \(-0.337889\pi\)
0.487555 + 0.873092i \(0.337889\pi\)
\(830\) 16.9800 0.589385
\(831\) 46.1375 1.60049
\(832\) 12.7996 0.443747
\(833\) −51.0402 −1.76844
\(834\) −39.0068 −1.35069
\(835\) 15.3735 0.532023
\(836\) −25.2234 −0.872369
\(837\) −23.7130 −0.819641
\(838\) 30.7603 1.06260
\(839\) −18.0586 −0.623452 −0.311726 0.950172i \(-0.600907\pi\)
−0.311726 + 0.950172i \(0.600907\pi\)
\(840\) −0.695832 −0.0240085
\(841\) −22.1480 −0.763724
\(842\) 31.6190 1.08966
\(843\) −33.5369 −1.15507
\(844\) 71.4065 2.45791
\(845\) 1.19118 0.0409780
\(846\) 153.246 5.26871
\(847\) 0.564605 0.0194001
\(848\) 3.14997 0.108170
\(849\) −28.3595 −0.973296
\(850\) 57.7453 1.98065
\(851\) −16.9278 −0.580279
\(852\) 84.8390 2.90654
\(853\) 12.4926 0.427738 0.213869 0.976862i \(-0.431393\pi\)
0.213869 + 0.976862i \(0.431393\pi\)
\(854\) −1.66781 −0.0570714
\(855\) −23.2450 −0.794961
\(856\) −16.4635 −0.562712
\(857\) −56.6674 −1.93572 −0.967861 0.251486i \(-0.919081\pi\)
−0.967861 + 0.251486i \(0.919081\pi\)
\(858\) −15.0663 −0.514356
\(859\) 15.7613 0.537769 0.268884 0.963172i \(-0.413345\pi\)
0.268884 + 0.963172i \(0.413345\pi\)
\(860\) 20.1780 0.688065
\(861\) 0.972263 0.0331346
\(862\) −5.61042 −0.191092
\(863\) −32.5158 −1.10685 −0.553426 0.832898i \(-0.686680\pi\)
−0.553426 + 0.832898i \(0.686680\pi\)
\(864\) −46.7569 −1.59070
\(865\) −14.7618 −0.501915
\(866\) −9.57280 −0.325297
\(867\) −104.525 −3.54987
\(868\) −1.09386 −0.0371281
\(869\) −2.83644 −0.0962195
\(870\) 19.8065 0.671503
\(871\) 0.729638 0.0247228
\(872\) 38.8165 1.31449
\(873\) −10.1456 −0.343375
\(874\) 45.8217 1.54994
\(875\) 1.07385 0.0363026
\(876\) 87.2219 2.94696
\(877\) −50.5255 −1.70613 −0.853063 0.521808i \(-0.825258\pi\)
−0.853063 + 0.521808i \(0.825258\pi\)
\(878\) 5.46792 0.184533
\(879\) −31.7069 −1.06945
\(880\) −4.19005 −0.141246
\(881\) 36.2660 1.22183 0.610916 0.791695i \(-0.290801\pi\)
0.610916 + 0.791695i \(0.290801\pi\)
\(882\) 81.4218 2.74162
\(883\) 6.20413 0.208786 0.104393 0.994536i \(-0.466710\pi\)
0.104393 + 0.994536i \(0.466710\pi\)
\(884\) −20.9986 −0.706260
\(885\) −23.5774 −0.792545
\(886\) 68.2062 2.29143
\(887\) −27.8846 −0.936273 −0.468137 0.883656i \(-0.655074\pi\)
−0.468137 + 0.883656i \(0.655074\pi\)
\(888\) −16.7750 −0.562933
\(889\) 0.430306 0.0144320
\(890\) 23.4881 0.787322
\(891\) 7.13935 0.239177
\(892\) 60.7893 2.03538
\(893\) 48.6504 1.62802
\(894\) −71.0034 −2.37471
\(895\) 11.8708 0.396796
\(896\) −1.46883 −0.0490703
\(897\) 16.1421 0.538969
\(898\) 19.3290 0.645017
\(899\) 9.47893 0.316140
\(900\) −54.3289 −1.81096
\(901\) −15.5115 −0.516762
\(902\) −16.8475 −0.560962
\(903\) 1.78052 0.0592519
\(904\) 1.15780 0.0385077
\(905\) −13.4258 −0.446290
\(906\) −63.8968 −2.12283
\(907\) 28.7486 0.954583 0.477291 0.878745i \(-0.341619\pi\)
0.477291 + 0.878745i \(0.341619\pi\)
\(908\) 16.3289 0.541894
\(909\) −92.5503 −3.06970
\(910\) −0.276314 −0.00915972
\(911\) −5.16514 −0.171129 −0.0855644 0.996333i \(-0.527269\pi\)
−0.0855644 + 0.996333i \(0.527269\pi\)
\(912\) −15.7795 −0.522512
\(913\) −15.3124 −0.506767
\(914\) −63.3146 −2.09426
\(915\) 24.6388 0.814533
\(916\) −20.8546 −0.689054
\(917\) −1.84440 −0.0609073
\(918\) 105.594 3.48511
\(919\) 7.43055 0.245111 0.122556 0.992462i \(-0.460891\pi\)
0.122556 + 0.992462i \(0.460891\pi\)
\(920\) −12.9184 −0.425908
\(921\) −31.0054 −1.02166
\(922\) 28.2653 0.930869
\(923\) 10.2562 0.337588
\(924\) 2.06118 0.0678079
\(925\) 10.8037 0.355224
\(926\) 2.20802 0.0725601
\(927\) 99.3718 3.26380
\(928\) 18.6904 0.613542
\(929\) −27.1034 −0.889235 −0.444618 0.895721i \(-0.646660\pi\)
−0.444618 + 0.895721i \(0.646660\pi\)
\(930\) 27.3999 0.898479
\(931\) 25.8486 0.847154
\(932\) 0.402182 0.0131739
\(933\) −15.1327 −0.495422
\(934\) 62.8107 2.05523
\(935\) 20.6331 0.674776
\(936\) 10.1980 0.333331
\(937\) 23.8466 0.779033 0.389516 0.921020i \(-0.372642\pi\)
0.389516 + 0.921020i \(0.372642\pi\)
\(938\) −0.169251 −0.00552624
\(939\) −66.7960 −2.17981
\(940\) −45.0539 −1.46950
\(941\) 34.7911 1.13416 0.567078 0.823664i \(-0.308074\pi\)
0.567078 + 0.823664i \(0.308074\pi\)
\(942\) 14.0564 0.457983
\(943\) 18.0505 0.587805
\(944\) −10.2036 −0.332098
\(945\) 0.819475 0.0266575
\(946\) −30.8531 −1.00312
\(947\) 37.3671 1.21427 0.607134 0.794599i \(-0.292319\pi\)
0.607134 + 0.794599i \(0.292319\pi\)
\(948\) 9.89223 0.321285
\(949\) 10.5443 0.342282
\(950\) −29.2443 −0.948812
\(951\) 86.5287 2.80589
\(952\) 1.48289 0.0480606
\(953\) 60.8631 1.97155 0.985775 0.168068i \(-0.0537529\pi\)
0.985775 + 0.168068i \(0.0537529\pi\)
\(954\) 24.7447 0.801139
\(955\) −18.4922 −0.598393
\(956\) −50.0799 −1.61970
\(957\) −17.8613 −0.577373
\(958\) 6.85744 0.221554
\(959\) −0.828287 −0.0267468
\(960\) 43.8624 1.41565
\(961\) −17.8870 −0.577001
\(962\) −6.66134 −0.214770
\(963\) 44.9428 1.44826
\(964\) 23.4835 0.756354
\(965\) 2.84481 0.0915776
\(966\) −3.74441 −0.120474
\(967\) 47.6342 1.53181 0.765907 0.642952i \(-0.222290\pi\)
0.765907 + 0.642952i \(0.222290\pi\)
\(968\) 10.3875 0.333868
\(969\) 77.7035 2.49620
\(970\) 5.05747 0.162385
\(971\) −11.7342 −0.376568 −0.188284 0.982115i \(-0.560293\pi\)
−0.188284 + 0.982115i \(0.560293\pi\)
\(972\) 31.5882 1.01319
\(973\) 0.645121 0.0206816
\(974\) 36.5100 1.16986
\(975\) −10.3022 −0.329935
\(976\) 10.6629 0.341312
\(977\) 42.9894 1.37535 0.687677 0.726017i \(-0.258631\pi\)
0.687677 + 0.726017i \(0.258631\pi\)
\(978\) −32.2183 −1.03023
\(979\) −21.1813 −0.676957
\(980\) −23.9377 −0.764663
\(981\) −105.963 −3.38313
\(982\) 86.7826 2.76934
\(983\) 3.78445 0.120705 0.0603526 0.998177i \(-0.480777\pi\)
0.0603526 + 0.998177i \(0.480777\pi\)
\(984\) 17.8875 0.570234
\(985\) 10.1618 0.323780
\(986\) −42.2096 −1.34423
\(987\) −3.97557 −0.126544
\(988\) 10.6345 0.338328
\(989\) 33.0561 1.05112
\(990\) −32.9150 −1.04611
\(991\) 21.4675 0.681938 0.340969 0.940075i \(-0.389245\pi\)
0.340969 + 0.940075i \(0.389245\pi\)
\(992\) 25.8559 0.820927
\(993\) −22.2673 −0.706630
\(994\) −2.37909 −0.0754602
\(995\) 4.89674 0.155237
\(996\) 53.4029 1.69213
\(997\) −38.0490 −1.20502 −0.602512 0.798110i \(-0.705833\pi\)
−0.602512 + 0.798110i \(0.705833\pi\)
\(998\) 8.08576 0.255950
\(999\) 19.7558 0.625046
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 \(a_p\))