Properties

Label 619.2.a.b.1.14
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.258847 q^{2} +2.67579 q^{3} -1.93300 q^{4} -2.46163 q^{5} +0.692619 q^{6} +1.88069 q^{7} -1.01804 q^{8} +4.15985 q^{9} +O(q^{10})\) \(q+0.258847 q^{2} +2.67579 q^{3} -1.93300 q^{4} -2.46163 q^{5} +0.692619 q^{6} +1.88069 q^{7} -1.01804 q^{8} +4.15985 q^{9} -0.637185 q^{10} +2.17477 q^{11} -5.17230 q^{12} +5.79098 q^{13} +0.486810 q^{14} -6.58682 q^{15} +3.60248 q^{16} +5.77460 q^{17} +1.07676 q^{18} -2.25742 q^{19} +4.75833 q^{20} +5.03233 q^{21} +0.562932 q^{22} -2.33879 q^{23} -2.72407 q^{24} +1.05964 q^{25} +1.49897 q^{26} +3.10353 q^{27} -3.63537 q^{28} +10.0750 q^{29} -1.70497 q^{30} -9.67907 q^{31} +2.96858 q^{32} +5.81923 q^{33} +1.49474 q^{34} -4.62957 q^{35} -8.04099 q^{36} +8.94849 q^{37} -0.584325 q^{38} +15.4954 q^{39} +2.50605 q^{40} -1.23360 q^{41} +1.30260 q^{42} -11.2529 q^{43} -4.20383 q^{44} -10.2400 q^{45} -0.605388 q^{46} +6.19029 q^{47} +9.63948 q^{48} -3.46301 q^{49} +0.274285 q^{50} +15.4516 q^{51} -11.1940 q^{52} -0.0669552 q^{53} +0.803338 q^{54} -5.35349 q^{55} -1.91462 q^{56} -6.04038 q^{57} +2.60789 q^{58} -8.20161 q^{59} +12.7323 q^{60} -10.3312 q^{61} -2.50539 q^{62} +7.82339 q^{63} -6.43655 q^{64} -14.2553 q^{65} +1.50629 q^{66} +0.238391 q^{67} -11.1623 q^{68} -6.25812 q^{69} -1.19835 q^{70} +2.25584 q^{71} -4.23491 q^{72} -9.40009 q^{73} +2.31629 q^{74} +2.83538 q^{75} +4.36359 q^{76} +4.09007 q^{77} +4.01094 q^{78} +1.71495 q^{79} -8.86799 q^{80} -4.17517 q^{81} -0.319314 q^{82} -1.43433 q^{83} -9.72748 q^{84} -14.2150 q^{85} -2.91278 q^{86} +26.9587 q^{87} -2.21401 q^{88} +15.0519 q^{89} -2.65060 q^{90} +10.8910 q^{91} +4.52088 q^{92} -25.8992 q^{93} +1.60233 q^{94} +5.55694 q^{95} +7.94329 q^{96} +9.35744 q^{97} -0.896388 q^{98} +9.04673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258847 0.183032 0.0915161 0.995804i \(-0.470829\pi\)
0.0915161 + 0.995804i \(0.470829\pi\)
\(3\) 2.67579 1.54487 0.772434 0.635095i \(-0.219039\pi\)
0.772434 + 0.635095i \(0.219039\pi\)
\(4\) −1.93300 −0.966499
\(5\) −2.46163 −1.10088 −0.550438 0.834876i \(-0.685539\pi\)
−0.550438 + 0.834876i \(0.685539\pi\)
\(6\) 0.692619 0.282761
\(7\) 1.88069 0.710834 0.355417 0.934708i \(-0.384339\pi\)
0.355417 + 0.934708i \(0.384339\pi\)
\(8\) −1.01804 −0.359933
\(9\) 4.15985 1.38662
\(10\) −0.637185 −0.201496
\(11\) 2.17477 0.655718 0.327859 0.944727i \(-0.393673\pi\)
0.327859 + 0.944727i \(0.393673\pi\)
\(12\) −5.17230 −1.49311
\(13\) 5.79098 1.60613 0.803064 0.595893i \(-0.203202\pi\)
0.803064 + 0.595893i \(0.203202\pi\)
\(14\) 0.486810 0.130105
\(15\) −6.58682 −1.70071
\(16\) 3.60248 0.900620
\(17\) 5.77460 1.40055 0.700273 0.713875i \(-0.253061\pi\)
0.700273 + 0.713875i \(0.253061\pi\)
\(18\) 1.07676 0.253796
\(19\) −2.25742 −0.517887 −0.258944 0.965892i \(-0.583374\pi\)
−0.258944 + 0.965892i \(0.583374\pi\)
\(20\) 4.75833 1.06400
\(21\) 5.03233 1.09814
\(22\) 0.562932 0.120017
\(23\) −2.33879 −0.487672 −0.243836 0.969816i \(-0.578406\pi\)
−0.243836 + 0.969816i \(0.578406\pi\)
\(24\) −2.72407 −0.556048
\(25\) 1.05964 0.211928
\(26\) 1.49897 0.293973
\(27\) 3.10353 0.597274
\(28\) −3.63537 −0.687020
\(29\) 10.0750 1.87089 0.935443 0.353478i \(-0.115001\pi\)
0.935443 + 0.353478i \(0.115001\pi\)
\(30\) −1.70497 −0.311284
\(31\) −9.67907 −1.73841 −0.869207 0.494449i \(-0.835370\pi\)
−0.869207 + 0.494449i \(0.835370\pi\)
\(32\) 2.96858 0.524775
\(33\) 5.81923 1.01300
\(34\) 1.49474 0.256345
\(35\) −4.62957 −0.782540
\(36\) −8.04099 −1.34017
\(37\) 8.94849 1.47112 0.735561 0.677458i \(-0.236918\pi\)
0.735561 + 0.677458i \(0.236918\pi\)
\(38\) −0.584325 −0.0947900
\(39\) 15.4954 2.48126
\(40\) 2.50605 0.396241
\(41\) −1.23360 −0.192657 −0.0963283 0.995350i \(-0.530710\pi\)
−0.0963283 + 0.995350i \(0.530710\pi\)
\(42\) 1.30260 0.200996
\(43\) −11.2529 −1.71605 −0.858026 0.513606i \(-0.828309\pi\)
−0.858026 + 0.513606i \(0.828309\pi\)
\(44\) −4.20383 −0.633751
\(45\) −10.2400 −1.52650
\(46\) −0.605388 −0.0892596
\(47\) 6.19029 0.902946 0.451473 0.892285i \(-0.350899\pi\)
0.451473 + 0.892285i \(0.350899\pi\)
\(48\) 9.63948 1.39134
\(49\) −3.46301 −0.494716
\(50\) 0.274285 0.0387897
\(51\) 15.4516 2.16366
\(52\) −11.1940 −1.55232
\(53\) −0.0669552 −0.00919700 −0.00459850 0.999989i \(-0.501464\pi\)
−0.00459850 + 0.999989i \(0.501464\pi\)
\(54\) 0.803338 0.109320
\(55\) −5.35349 −0.721864
\(56\) −1.91462 −0.255852
\(57\) −6.04038 −0.800068
\(58\) 2.60789 0.342432
\(59\) −8.20161 −1.06776 −0.533879 0.845561i \(-0.679266\pi\)
−0.533879 + 0.845561i \(0.679266\pi\)
\(60\) 12.7323 1.64373
\(61\) −10.3312 −1.32278 −0.661388 0.750044i \(-0.730032\pi\)
−0.661388 + 0.750044i \(0.730032\pi\)
\(62\) −2.50539 −0.318185
\(63\) 7.82339 0.985655
\(64\) −6.43655 −0.804569
\(65\) −14.2553 −1.76815
\(66\) 1.50629 0.185411
\(67\) 0.238391 0.0291241 0.0145621 0.999894i \(-0.495365\pi\)
0.0145621 + 0.999894i \(0.495365\pi\)
\(68\) −11.1623 −1.35363
\(69\) −6.25812 −0.753389
\(70\) −1.19835 −0.143230
\(71\) 2.25584 0.267718 0.133859 0.991000i \(-0.457263\pi\)
0.133859 + 0.991000i \(0.457263\pi\)
\(72\) −4.23491 −0.499089
\(73\) −9.40009 −1.10020 −0.550099 0.835100i \(-0.685410\pi\)
−0.550099 + 0.835100i \(0.685410\pi\)
\(74\) 2.31629 0.269263
\(75\) 2.83538 0.327402
\(76\) 4.36359 0.500538
\(77\) 4.09007 0.466106
\(78\) 4.01094 0.454150
\(79\) 1.71495 0.192947 0.0964733 0.995336i \(-0.469244\pi\)
0.0964733 + 0.995336i \(0.469244\pi\)
\(80\) −8.86799 −0.991471
\(81\) −4.17517 −0.463908
\(82\) −0.319314 −0.0352623
\(83\) −1.43433 −0.157438 −0.0787192 0.996897i \(-0.525083\pi\)
−0.0787192 + 0.996897i \(0.525083\pi\)
\(84\) −9.72748 −1.06136
\(85\) −14.2150 −1.54183
\(86\) −2.91278 −0.314093
\(87\) 26.9587 2.89027
\(88\) −2.21401 −0.236014
\(89\) 15.0519 1.59550 0.797749 0.602989i \(-0.206024\pi\)
0.797749 + 0.602989i \(0.206024\pi\)
\(90\) −2.65060 −0.279398
\(91\) 10.8910 1.14169
\(92\) 4.52088 0.471335
\(93\) −25.8992 −2.68562
\(94\) 1.60233 0.165268
\(95\) 5.55694 0.570130
\(96\) 7.94329 0.810708
\(97\) 9.35744 0.950104 0.475052 0.879958i \(-0.342429\pi\)
0.475052 + 0.879958i \(0.342429\pi\)
\(98\) −0.896388 −0.0905489
\(99\) 9.04673 0.909231
\(100\) −2.04829 −0.204829
\(101\) −0.733101 −0.0729463 −0.0364731 0.999335i \(-0.511612\pi\)
−0.0364731 + 0.999335i \(0.511612\pi\)
\(102\) 3.99960 0.396019
\(103\) −4.03656 −0.397734 −0.198867 0.980026i \(-0.563726\pi\)
−0.198867 + 0.980026i \(0.563726\pi\)
\(104\) −5.89546 −0.578098
\(105\) −12.3878 −1.20892
\(106\) −0.0173311 −0.00168335
\(107\) −13.2306 −1.27905 −0.639527 0.768768i \(-0.720870\pi\)
−0.639527 + 0.768768i \(0.720870\pi\)
\(108\) −5.99912 −0.577265
\(109\) 5.99549 0.574264 0.287132 0.957891i \(-0.407298\pi\)
0.287132 + 0.957891i \(0.407298\pi\)
\(110\) −1.38573 −0.132124
\(111\) 23.9443 2.27269
\(112\) 6.77514 0.640191
\(113\) 9.71932 0.914317 0.457158 0.889385i \(-0.348867\pi\)
0.457158 + 0.889385i \(0.348867\pi\)
\(114\) −1.56353 −0.146438
\(115\) 5.75725 0.536866
\(116\) −19.4750 −1.80821
\(117\) 24.0896 2.22709
\(118\) −2.12296 −0.195434
\(119\) 10.8602 0.995556
\(120\) 6.70566 0.612140
\(121\) −6.27037 −0.570034
\(122\) −2.67420 −0.242110
\(123\) −3.30087 −0.297629
\(124\) 18.7096 1.68018
\(125\) 9.69972 0.867569
\(126\) 2.02506 0.180406
\(127\) 12.9505 1.14917 0.574585 0.818445i \(-0.305163\pi\)
0.574585 + 0.818445i \(0.305163\pi\)
\(128\) −7.60323 −0.672037
\(129\) −30.1104 −2.65108
\(130\) −3.68993 −0.323628
\(131\) −21.0455 −1.83875 −0.919376 0.393380i \(-0.871306\pi\)
−0.919376 + 0.393380i \(0.871306\pi\)
\(132\) −11.2486 −0.979062
\(133\) −4.24550 −0.368132
\(134\) 0.0617067 0.00533065
\(135\) −7.63975 −0.657525
\(136\) −5.87879 −0.504102
\(137\) 17.4982 1.49497 0.747485 0.664279i \(-0.231261\pi\)
0.747485 + 0.664279i \(0.231261\pi\)
\(138\) −1.61989 −0.137894
\(139\) 5.41721 0.459482 0.229741 0.973252i \(-0.426212\pi\)
0.229741 + 0.973252i \(0.426212\pi\)
\(140\) 8.94895 0.756324
\(141\) 16.5639 1.39493
\(142\) 0.583915 0.0490011
\(143\) 12.5940 1.05317
\(144\) 14.9858 1.24882
\(145\) −24.8010 −2.05961
\(146\) −2.43318 −0.201372
\(147\) −9.26629 −0.764271
\(148\) −17.2974 −1.42184
\(149\) −20.6900 −1.69499 −0.847495 0.530804i \(-0.821890\pi\)
−0.847495 + 0.530804i \(0.821890\pi\)
\(150\) 0.733928 0.0599250
\(151\) −8.11163 −0.660115 −0.330057 0.943961i \(-0.607068\pi\)
−0.330057 + 0.943961i \(0.607068\pi\)
\(152\) 2.29815 0.186405
\(153\) 24.0215 1.94202
\(154\) 1.05870 0.0853124
\(155\) 23.8263 1.91378
\(156\) −29.9527 −2.39813
\(157\) −0.536449 −0.0428133 −0.0214067 0.999771i \(-0.506814\pi\)
−0.0214067 + 0.999771i \(0.506814\pi\)
\(158\) 0.443908 0.0353154
\(159\) −0.179158 −0.0142082
\(160\) −7.30755 −0.577712
\(161\) −4.39854 −0.346654
\(162\) −1.08073 −0.0849101
\(163\) 7.37372 0.577554 0.288777 0.957396i \(-0.406751\pi\)
0.288777 + 0.957396i \(0.406751\pi\)
\(164\) 2.38455 0.186202
\(165\) −14.3248 −1.11519
\(166\) −0.371272 −0.0288163
\(167\) −4.57561 −0.354071 −0.177036 0.984204i \(-0.556651\pi\)
−0.177036 + 0.984204i \(0.556651\pi\)
\(168\) −5.12313 −0.395258
\(169\) 20.5354 1.57965
\(170\) −3.67949 −0.282204
\(171\) −9.39053 −0.718112
\(172\) 21.7519 1.65856
\(173\) 10.2956 0.782759 0.391379 0.920229i \(-0.371998\pi\)
0.391379 + 0.920229i \(0.371998\pi\)
\(174\) 6.97816 0.529013
\(175\) 1.99286 0.150646
\(176\) 7.83457 0.590553
\(177\) −21.9458 −1.64955
\(178\) 3.89613 0.292028
\(179\) −12.4323 −0.929233 −0.464616 0.885512i \(-0.653808\pi\)
−0.464616 + 0.885512i \(0.653808\pi\)
\(180\) 19.7940 1.47536
\(181\) −4.14942 −0.308424 −0.154212 0.988038i \(-0.549284\pi\)
−0.154212 + 0.988038i \(0.549284\pi\)
\(182\) 2.81910 0.208966
\(183\) −27.6442 −2.04351
\(184\) 2.38099 0.175529
\(185\) −22.0279 −1.61952
\(186\) −6.70391 −0.491555
\(187\) 12.5584 0.918364
\(188\) −11.9658 −0.872697
\(189\) 5.83677 0.424563
\(190\) 1.43839 0.104352
\(191\) −4.07924 −0.295163 −0.147582 0.989050i \(-0.547149\pi\)
−0.147582 + 0.989050i \(0.547149\pi\)
\(192\) −17.2229 −1.24295
\(193\) −26.6618 −1.91916 −0.959581 0.281433i \(-0.909190\pi\)
−0.959581 + 0.281433i \(0.909190\pi\)
\(194\) 2.42214 0.173900
\(195\) −38.1441 −2.73156
\(196\) 6.69399 0.478142
\(197\) 1.35535 0.0965644 0.0482822 0.998834i \(-0.484625\pi\)
0.0482822 + 0.998834i \(0.484625\pi\)
\(198\) 2.34171 0.166418
\(199\) −15.3182 −1.08588 −0.542940 0.839771i \(-0.682689\pi\)
−0.542940 + 0.839771i \(0.682689\pi\)
\(200\) −1.07876 −0.0762799
\(201\) 0.637885 0.0449929
\(202\) −0.189761 −0.0133515
\(203\) 18.9480 1.32989
\(204\) −29.8680 −2.09118
\(205\) 3.03668 0.212091
\(206\) −1.04485 −0.0727981
\(207\) −9.72904 −0.676215
\(208\) 20.8619 1.44651
\(209\) −4.90937 −0.339588
\(210\) −3.20653 −0.221271
\(211\) −16.1659 −1.11291 −0.556453 0.830879i \(-0.687838\pi\)
−0.556453 + 0.830879i \(0.687838\pi\)
\(212\) 0.129424 0.00888890
\(213\) 6.03614 0.413590
\(214\) −3.42471 −0.234108
\(215\) 27.7005 1.88916
\(216\) −3.15953 −0.214978
\(217\) −18.2033 −1.23572
\(218\) 1.55191 0.105109
\(219\) −25.1527 −1.69966
\(220\) 10.3483 0.697681
\(221\) 33.4406 2.24946
\(222\) 6.19789 0.415975
\(223\) 20.8221 1.39435 0.697177 0.716899i \(-0.254439\pi\)
0.697177 + 0.716899i \(0.254439\pi\)
\(224\) 5.58297 0.373028
\(225\) 4.40796 0.293864
\(226\) 2.51581 0.167349
\(227\) 6.06934 0.402836 0.201418 0.979505i \(-0.435445\pi\)
0.201418 + 0.979505i \(0.435445\pi\)
\(228\) 11.6760 0.773265
\(229\) −10.2583 −0.677886 −0.338943 0.940807i \(-0.610069\pi\)
−0.338943 + 0.940807i \(0.610069\pi\)
\(230\) 1.49024 0.0982638
\(231\) 10.9442 0.720073
\(232\) −10.2568 −0.673393
\(233\) 19.2229 1.25933 0.629666 0.776866i \(-0.283192\pi\)
0.629666 + 0.776866i \(0.283192\pi\)
\(234\) 6.23552 0.407628
\(235\) −15.2382 −0.994032
\(236\) 15.8537 1.03199
\(237\) 4.58884 0.298077
\(238\) 2.81113 0.182219
\(239\) 10.2594 0.663625 0.331812 0.943345i \(-0.392340\pi\)
0.331812 + 0.943345i \(0.392340\pi\)
\(240\) −23.7289 −1.53169
\(241\) −26.1029 −1.68143 −0.840717 0.541475i \(-0.817866\pi\)
−0.840717 + 0.541475i \(0.817866\pi\)
\(242\) −1.62306 −0.104335
\(243\) −20.4825 −1.31395
\(244\) 19.9702 1.27846
\(245\) 8.52466 0.544621
\(246\) −0.854417 −0.0544757
\(247\) −13.0727 −0.831793
\(248\) 9.85371 0.625711
\(249\) −3.83797 −0.243222
\(250\) 2.51074 0.158793
\(251\) −23.2207 −1.46568 −0.732838 0.680403i \(-0.761805\pi\)
−0.732838 + 0.680403i \(0.761805\pi\)
\(252\) −15.1226 −0.952635
\(253\) −5.08634 −0.319775
\(254\) 3.35219 0.210335
\(255\) −38.0363 −2.38192
\(256\) 10.9050 0.681565
\(257\) −25.0242 −1.56097 −0.780483 0.625178i \(-0.785027\pi\)
−0.780483 + 0.625178i \(0.785027\pi\)
\(258\) −7.79398 −0.485232
\(259\) 16.8293 1.04572
\(260\) 27.5554 1.70891
\(261\) 41.9107 2.59420
\(262\) −5.44755 −0.336551
\(263\) 6.34438 0.391211 0.195606 0.980683i \(-0.437333\pi\)
0.195606 + 0.980683i \(0.437333\pi\)
\(264\) −5.92423 −0.364611
\(265\) 0.164819 0.0101248
\(266\) −1.09893 −0.0673799
\(267\) 40.2757 2.46484
\(268\) −0.460810 −0.0281484
\(269\) −12.3186 −0.751075 −0.375538 0.926807i \(-0.622542\pi\)
−0.375538 + 0.926807i \(0.622542\pi\)
\(270\) −1.97752 −0.120348
\(271\) 16.4188 0.997371 0.498685 0.866783i \(-0.333816\pi\)
0.498685 + 0.866783i \(0.333816\pi\)
\(272\) 20.8029 1.26136
\(273\) 29.1421 1.76376
\(274\) 4.52934 0.273627
\(275\) 2.30448 0.138965
\(276\) 12.0969 0.728150
\(277\) 2.50362 0.150428 0.0752141 0.997167i \(-0.476036\pi\)
0.0752141 + 0.997167i \(0.476036\pi\)
\(278\) 1.40223 0.0841000
\(279\) −40.2635 −2.41052
\(280\) 4.71310 0.281661
\(281\) −5.07121 −0.302523 −0.151262 0.988494i \(-0.548334\pi\)
−0.151262 + 0.988494i \(0.548334\pi\)
\(282\) 4.28751 0.255317
\(283\) −1.32526 −0.0787788 −0.0393894 0.999224i \(-0.512541\pi\)
−0.0393894 + 0.999224i \(0.512541\pi\)
\(284\) −4.36053 −0.258750
\(285\) 14.8692 0.880776
\(286\) 3.25993 0.192763
\(287\) −2.32002 −0.136947
\(288\) 12.3488 0.727663
\(289\) 16.3460 0.961532
\(290\) −6.41966 −0.376975
\(291\) 25.0386 1.46779
\(292\) 18.1704 1.06334
\(293\) 25.1442 1.46894 0.734469 0.678642i \(-0.237431\pi\)
0.734469 + 0.678642i \(0.237431\pi\)
\(294\) −2.39855 −0.139886
\(295\) 20.1894 1.17547
\(296\) −9.10995 −0.529505
\(297\) 6.74946 0.391644
\(298\) −5.35553 −0.310237
\(299\) −13.5439 −0.783264
\(300\) −5.48079 −0.316433
\(301\) −21.1632 −1.21983
\(302\) −2.09967 −0.120822
\(303\) −1.96163 −0.112692
\(304\) −8.13231 −0.466420
\(305\) 25.4317 1.45621
\(306\) 6.21788 0.355453
\(307\) 18.8588 1.07633 0.538166 0.842839i \(-0.319117\pi\)
0.538166 + 0.842839i \(0.319117\pi\)
\(308\) −7.90609 −0.450491
\(309\) −10.8010 −0.614447
\(310\) 6.16736 0.350283
\(311\) 17.9045 1.01527 0.507636 0.861572i \(-0.330519\pi\)
0.507636 + 0.861572i \(0.330519\pi\)
\(312\) −15.7750 −0.893085
\(313\) 5.73725 0.324288 0.162144 0.986767i \(-0.448159\pi\)
0.162144 + 0.986767i \(0.448159\pi\)
\(314\) −0.138858 −0.00783621
\(315\) −19.2583 −1.08508
\(316\) −3.31499 −0.186483
\(317\) 13.5902 0.763300 0.381650 0.924307i \(-0.375356\pi\)
0.381650 + 0.924307i \(0.375356\pi\)
\(318\) −0.0463744 −0.00260055
\(319\) 21.9109 1.22677
\(320\) 15.8444 0.885731
\(321\) −35.4024 −1.97597
\(322\) −1.13855 −0.0634487
\(323\) −13.0357 −0.725326
\(324\) 8.07060 0.448367
\(325\) 6.13636 0.340384
\(326\) 1.90866 0.105711
\(327\) 16.0427 0.887162
\(328\) 1.25586 0.0693434
\(329\) 11.6420 0.641844
\(330\) −3.70793 −0.204115
\(331\) −1.90596 −0.104761 −0.0523805 0.998627i \(-0.516681\pi\)
−0.0523805 + 0.998627i \(0.516681\pi\)
\(332\) 2.77256 0.152164
\(333\) 37.2244 2.03989
\(334\) −1.18438 −0.0648064
\(335\) −0.586832 −0.0320620
\(336\) 18.1289 0.989011
\(337\) −0.393425 −0.0214312 −0.0107156 0.999943i \(-0.503411\pi\)
−0.0107156 + 0.999943i \(0.503411\pi\)
\(338\) 5.31552 0.289126
\(339\) 26.0069 1.41250
\(340\) 27.4775 1.49018
\(341\) −21.0498 −1.13991
\(342\) −2.43071 −0.131438
\(343\) −19.6777 −1.06249
\(344\) 11.4559 0.617663
\(345\) 15.4052 0.829388
\(346\) 2.66498 0.143270
\(347\) 23.1336 1.24187 0.620937 0.783860i \(-0.286752\pi\)
0.620937 + 0.783860i \(0.286752\pi\)
\(348\) −52.1111 −2.79345
\(349\) 11.9490 0.639613 0.319806 0.947483i \(-0.396382\pi\)
0.319806 + 0.947483i \(0.396382\pi\)
\(350\) 0.515844 0.0275730
\(351\) 17.9725 0.959299
\(352\) 6.45597 0.344104
\(353\) −7.64497 −0.406901 −0.203450 0.979085i \(-0.565216\pi\)
−0.203450 + 0.979085i \(0.565216\pi\)
\(354\) −5.68059 −0.301920
\(355\) −5.55304 −0.294725
\(356\) −29.0953 −1.54205
\(357\) 29.0597 1.53800
\(358\) −3.21805 −0.170079
\(359\) −16.3685 −0.863895 −0.431948 0.901899i \(-0.642173\pi\)
−0.431948 + 0.901899i \(0.642173\pi\)
\(360\) 10.4248 0.549435
\(361\) −13.9041 −0.731793
\(362\) −1.07406 −0.0564515
\(363\) −16.7782 −0.880627
\(364\) −21.0523 −1.10344
\(365\) 23.1396 1.21118
\(366\) −7.15559 −0.374029
\(367\) −17.2762 −0.901811 −0.450905 0.892572i \(-0.648899\pi\)
−0.450905 + 0.892572i \(0.648899\pi\)
\(368\) −8.42545 −0.439207
\(369\) −5.13161 −0.267141
\(370\) −5.70185 −0.296425
\(371\) −0.125922 −0.00653754
\(372\) 50.0631 2.59565
\(373\) 19.8177 1.02612 0.513062 0.858352i \(-0.328511\pi\)
0.513062 + 0.858352i \(0.328511\pi\)
\(374\) 3.25071 0.168090
\(375\) 25.9544 1.34028
\(376\) −6.30198 −0.325000
\(377\) 58.3443 3.00488
\(378\) 1.51083 0.0777086
\(379\) −31.6560 −1.62606 −0.813030 0.582222i \(-0.802184\pi\)
−0.813030 + 0.582222i \(0.802184\pi\)
\(380\) −10.7416 −0.551030
\(381\) 34.6528 1.77532
\(382\) −1.05590 −0.0540243
\(383\) −7.55621 −0.386104 −0.193052 0.981188i \(-0.561839\pi\)
−0.193052 + 0.981188i \(0.561839\pi\)
\(384\) −20.3447 −1.03821
\(385\) −10.0682 −0.513125
\(386\) −6.90133 −0.351268
\(387\) −46.8105 −2.37951
\(388\) −18.0879 −0.918275
\(389\) −21.8357 −1.10711 −0.553556 0.832812i \(-0.686730\pi\)
−0.553556 + 0.832812i \(0.686730\pi\)
\(390\) −9.87347 −0.499963
\(391\) −13.5056 −0.683007
\(392\) 3.52549 0.178064
\(393\) −56.3133 −2.84063
\(394\) 0.350826 0.0176744
\(395\) −4.22157 −0.212410
\(396\) −17.4873 −0.878771
\(397\) 21.7604 1.09212 0.546062 0.837745i \(-0.316126\pi\)
0.546062 + 0.837745i \(0.316126\pi\)
\(398\) −3.96507 −0.198751
\(399\) −11.3601 −0.568715
\(400\) 3.81734 0.190867
\(401\) −11.9702 −0.597762 −0.298881 0.954290i \(-0.596613\pi\)
−0.298881 + 0.954290i \(0.596613\pi\)
\(402\) 0.165114 0.00823515
\(403\) −56.0513 −2.79211
\(404\) 1.41708 0.0705025
\(405\) 10.2777 0.510705
\(406\) 4.90462 0.243412
\(407\) 19.4609 0.964642
\(408\) −15.7304 −0.778772
\(409\) 37.2651 1.84264 0.921320 0.388804i \(-0.127112\pi\)
0.921320 + 0.388804i \(0.127112\pi\)
\(410\) 0.786034 0.0388195
\(411\) 46.8214 2.30953
\(412\) 7.80266 0.384410
\(413\) −15.4247 −0.758999
\(414\) −2.51833 −0.123769
\(415\) 3.53080 0.173320
\(416\) 17.1910 0.842856
\(417\) 14.4953 0.709839
\(418\) −1.27077 −0.0621555
\(419\) −5.31688 −0.259746 −0.129873 0.991531i \(-0.541457\pi\)
−0.129873 + 0.991531i \(0.541457\pi\)
\(420\) 23.9455 1.16842
\(421\) −0.0885710 −0.00431668 −0.00215834 0.999998i \(-0.500687\pi\)
−0.00215834 + 0.999998i \(0.500687\pi\)
\(422\) −4.18449 −0.203698
\(423\) 25.7507 1.25204
\(424\) 0.0681633 0.00331030
\(425\) 6.11901 0.296816
\(426\) 1.56243 0.0757002
\(427\) −19.4298 −0.940273
\(428\) 25.5748 1.23621
\(429\) 33.6990 1.62700
\(430\) 7.17019 0.345777
\(431\) −12.4923 −0.601732 −0.300866 0.953666i \(-0.597276\pi\)
−0.300866 + 0.953666i \(0.597276\pi\)
\(432\) 11.1804 0.537917
\(433\) −32.3933 −1.55672 −0.778361 0.627817i \(-0.783949\pi\)
−0.778361 + 0.627817i \(0.783949\pi\)
\(434\) −4.71187 −0.226177
\(435\) −66.3624 −3.18183
\(436\) −11.5893 −0.555025
\(437\) 5.27963 0.252559
\(438\) −6.51068 −0.311092
\(439\) −37.7205 −1.80030 −0.900150 0.435579i \(-0.856544\pi\)
−0.900150 + 0.435579i \(0.856544\pi\)
\(440\) 5.45008 0.259822
\(441\) −14.4056 −0.685982
\(442\) 8.65598 0.411723
\(443\) 23.3690 1.11030 0.555148 0.831751i \(-0.312662\pi\)
0.555148 + 0.831751i \(0.312662\pi\)
\(444\) −46.2843 −2.19655
\(445\) −37.0523 −1.75645
\(446\) 5.38974 0.255211
\(447\) −55.3621 −2.61854
\(448\) −12.1052 −0.571915
\(449\) 21.2211 1.00148 0.500742 0.865597i \(-0.333061\pi\)
0.500742 + 0.865597i \(0.333061\pi\)
\(450\) 1.14098 0.0537865
\(451\) −2.68281 −0.126328
\(452\) −18.7874 −0.883687
\(453\) −21.7050 −1.01979
\(454\) 1.57103 0.0737320
\(455\) −26.8097 −1.25686
\(456\) 6.14937 0.287970
\(457\) −11.7688 −0.550523 −0.275262 0.961369i \(-0.588764\pi\)
−0.275262 + 0.961369i \(0.588764\pi\)
\(458\) −2.65532 −0.124075
\(459\) 17.9216 0.836511
\(460\) −11.1288 −0.518881
\(461\) 27.8579 1.29747 0.648736 0.761014i \(-0.275298\pi\)
0.648736 + 0.761014i \(0.275298\pi\)
\(462\) 2.83286 0.131796
\(463\) −20.3394 −0.945252 −0.472626 0.881263i \(-0.656694\pi\)
−0.472626 + 0.881263i \(0.656694\pi\)
\(464\) 36.2951 1.68496
\(465\) 63.7543 2.95653
\(466\) 4.97578 0.230498
\(467\) 32.2678 1.49318 0.746588 0.665287i \(-0.231691\pi\)
0.746588 + 0.665287i \(0.231691\pi\)
\(468\) −46.5652 −2.15248
\(469\) 0.448339 0.0207024
\(470\) −3.94436 −0.181940
\(471\) −1.43543 −0.0661409
\(472\) 8.34959 0.384321
\(473\) −24.4725 −1.12525
\(474\) 1.18781 0.0545577
\(475\) −2.39206 −0.109755
\(476\) −20.9928 −0.962204
\(477\) −0.278524 −0.0127527
\(478\) 2.65561 0.121465
\(479\) −14.2539 −0.651277 −0.325639 0.945494i \(-0.605579\pi\)
−0.325639 + 0.945494i \(0.605579\pi\)
\(480\) −19.5535 −0.892489
\(481\) 51.8205 2.36281
\(482\) −6.75664 −0.307756
\(483\) −11.7696 −0.535534
\(484\) 12.1206 0.550937
\(485\) −23.0346 −1.04595
\(486\) −5.30182 −0.240495
\(487\) 16.3122 0.739178 0.369589 0.929195i \(-0.379499\pi\)
0.369589 + 0.929195i \(0.379499\pi\)
\(488\) 10.5176 0.476110
\(489\) 19.7305 0.892245
\(490\) 2.20658 0.0996831
\(491\) 13.8481 0.624956 0.312478 0.949925i \(-0.398841\pi\)
0.312478 + 0.949925i \(0.398841\pi\)
\(492\) 6.38057 0.287658
\(493\) 58.1793 2.62026
\(494\) −3.38381 −0.152245
\(495\) −22.2697 −1.00095
\(496\) −34.8687 −1.56565
\(497\) 4.24252 0.190303
\(498\) −0.993446 −0.0445174
\(499\) 22.0707 0.988019 0.494010 0.869456i \(-0.335531\pi\)
0.494010 + 0.869456i \(0.335531\pi\)
\(500\) −18.7495 −0.838505
\(501\) −12.2434 −0.546994
\(502\) −6.01059 −0.268266
\(503\) 9.78331 0.436216 0.218108 0.975925i \(-0.430011\pi\)
0.218108 + 0.975925i \(0.430011\pi\)
\(504\) −7.96455 −0.354769
\(505\) 1.80463 0.0803048
\(506\) −1.31658 −0.0585291
\(507\) 54.9485 2.44035
\(508\) −25.0333 −1.11067
\(509\) 10.7054 0.474507 0.237254 0.971448i \(-0.423753\pi\)
0.237254 + 0.971448i \(0.423753\pi\)
\(510\) −9.84555 −0.435968
\(511\) −17.6786 −0.782057
\(512\) 18.0292 0.796785
\(513\) −7.00596 −0.309321
\(514\) −6.47742 −0.285707
\(515\) 9.93653 0.437856
\(516\) 58.2034 2.56226
\(517\) 13.4625 0.592078
\(518\) 4.35621 0.191401
\(519\) 27.5488 1.20926
\(520\) 14.5125 0.636414
\(521\) −1.36329 −0.0597267 −0.0298634 0.999554i \(-0.509507\pi\)
−0.0298634 + 0.999554i \(0.509507\pi\)
\(522\) 10.8484 0.474823
\(523\) 1.14893 0.0502394 0.0251197 0.999684i \(-0.492003\pi\)
0.0251197 + 0.999684i \(0.492003\pi\)
\(524\) 40.6809 1.77715
\(525\) 5.33247 0.232728
\(526\) 1.64222 0.0716042
\(527\) −55.8928 −2.43473
\(528\) 20.9637 0.912326
\(529\) −17.5300 −0.762176
\(530\) 0.0426629 0.00185316
\(531\) −34.1175 −1.48057
\(532\) 8.20655 0.355799
\(533\) −7.14377 −0.309431
\(534\) 10.4252 0.451144
\(535\) 32.5690 1.40808
\(536\) −0.242692 −0.0104827
\(537\) −33.2662 −1.43554
\(538\) −3.18861 −0.137471
\(539\) −7.53125 −0.324394
\(540\) 14.7676 0.635498
\(541\) −12.4480 −0.535181 −0.267591 0.963533i \(-0.586227\pi\)
−0.267591 + 0.963533i \(0.586227\pi\)
\(542\) 4.24995 0.182551
\(543\) −11.1030 −0.476475
\(544\) 17.1423 0.734972
\(545\) −14.7587 −0.632193
\(546\) 7.54333 0.322825
\(547\) 38.3171 1.63832 0.819159 0.573566i \(-0.194440\pi\)
0.819159 + 0.573566i \(0.194440\pi\)
\(548\) −33.8239 −1.44489
\(549\) −42.9763 −1.83419
\(550\) 0.596506 0.0254351
\(551\) −22.7436 −0.968908
\(552\) 6.37103 0.271169
\(553\) 3.22528 0.137153
\(554\) 0.648054 0.0275332
\(555\) −58.9421 −2.50195
\(556\) −10.4715 −0.444089
\(557\) 4.02221 0.170426 0.0852132 0.996363i \(-0.472843\pi\)
0.0852132 + 0.996363i \(0.472843\pi\)
\(558\) −10.4221 −0.441202
\(559\) −65.1653 −2.75620
\(560\) −16.6779 −0.704771
\(561\) 33.6037 1.41875
\(562\) −1.31267 −0.0553714
\(563\) 25.4776 1.07375 0.536877 0.843661i \(-0.319604\pi\)
0.536877 + 0.843661i \(0.319604\pi\)
\(564\) −32.0180 −1.34820
\(565\) −23.9254 −1.00655
\(566\) −0.343040 −0.0144191
\(567\) −7.85220 −0.329761
\(568\) −2.29654 −0.0963605
\(569\) −21.0793 −0.883691 −0.441846 0.897091i \(-0.645676\pi\)
−0.441846 + 0.897091i \(0.645676\pi\)
\(570\) 3.84884 0.161210
\(571\) 23.7934 0.995722 0.497861 0.867257i \(-0.334119\pi\)
0.497861 + 0.867257i \(0.334119\pi\)
\(572\) −24.3443 −1.01789
\(573\) −10.9152 −0.455988
\(574\) −0.600530 −0.0250657
\(575\) −2.47828 −0.103352
\(576\) −26.7751 −1.11563
\(577\) −10.8946 −0.453549 −0.226774 0.973947i \(-0.572818\pi\)
−0.226774 + 0.973947i \(0.572818\pi\)
\(578\) 4.23111 0.175991
\(579\) −71.3415 −2.96485
\(580\) 47.9404 1.99061
\(581\) −2.69753 −0.111912
\(582\) 6.48114 0.268652
\(583\) −0.145612 −0.00603064
\(584\) 9.56970 0.395997
\(585\) −59.2998 −2.45175
\(586\) 6.50848 0.268863
\(587\) 7.49991 0.309555 0.154777 0.987949i \(-0.450534\pi\)
0.154777 + 0.987949i \(0.450534\pi\)
\(588\) 17.9117 0.738667
\(589\) 21.8497 0.900302
\(590\) 5.22594 0.215149
\(591\) 3.62662 0.149179
\(592\) 32.2368 1.32492
\(593\) 25.7995 1.05946 0.529730 0.848166i \(-0.322293\pi\)
0.529730 + 0.848166i \(0.322293\pi\)
\(594\) 1.74708 0.0716834
\(595\) −26.7339 −1.09598
\(596\) 39.9937 1.63821
\(597\) −40.9884 −1.67754
\(598\) −3.50579 −0.143362
\(599\) 5.48616 0.224159 0.112079 0.993699i \(-0.464249\pi\)
0.112079 + 0.993699i \(0.464249\pi\)
\(600\) −2.88654 −0.117842
\(601\) −5.96910 −0.243485 −0.121742 0.992562i \(-0.538848\pi\)
−0.121742 + 0.992562i \(0.538848\pi\)
\(602\) −5.47803 −0.223268
\(603\) 0.991672 0.0403840
\(604\) 15.6798 0.638001
\(605\) 15.4354 0.627537
\(606\) −0.507760 −0.0206263
\(607\) −7.03534 −0.285556 −0.142778 0.989755i \(-0.545603\pi\)
−0.142778 + 0.989755i \(0.545603\pi\)
\(608\) −6.70132 −0.271774
\(609\) 50.7009 2.05450
\(610\) 6.58290 0.266534
\(611\) 35.8478 1.45025
\(612\) −46.4335 −1.87696
\(613\) −0.971359 −0.0392328 −0.0196164 0.999808i \(-0.506244\pi\)
−0.0196164 + 0.999808i \(0.506244\pi\)
\(614\) 4.88155 0.197003
\(615\) 8.12552 0.327653
\(616\) −4.16386 −0.167767
\(617\) 17.1413 0.690084 0.345042 0.938587i \(-0.387865\pi\)
0.345042 + 0.938587i \(0.387865\pi\)
\(618\) −2.79580 −0.112463
\(619\) 1.00000 0.0401934
\(620\) −46.0563 −1.84966
\(621\) −7.25851 −0.291274
\(622\) 4.63452 0.185827
\(623\) 28.3079 1.13413
\(624\) 55.8220 2.23467
\(625\) −29.1754 −1.16701
\(626\) 1.48507 0.0593552
\(627\) −13.1364 −0.524619
\(628\) 1.03696 0.0413790
\(629\) 51.6740 2.06038
\(630\) −4.98495 −0.198605
\(631\) 6.18468 0.246208 0.123104 0.992394i \(-0.460715\pi\)
0.123104 + 0.992394i \(0.460715\pi\)
\(632\) −1.74589 −0.0694478
\(633\) −43.2566 −1.71929
\(634\) 3.51777 0.139708
\(635\) −31.8794 −1.26509
\(636\) 0.346312 0.0137322
\(637\) −20.0542 −0.794577
\(638\) 5.67155 0.224539
\(639\) 9.38395 0.371223
\(640\) 18.7164 0.739829
\(641\) −20.5842 −0.813028 −0.406514 0.913644i \(-0.633256\pi\)
−0.406514 + 0.913644i \(0.633256\pi\)
\(642\) −9.16380 −0.361666
\(643\) 42.6168 1.68064 0.840322 0.542088i \(-0.182366\pi\)
0.840322 + 0.542088i \(0.182366\pi\)
\(644\) 8.50237 0.335040
\(645\) 74.1209 2.91851
\(646\) −3.37424 −0.132758
\(647\) −10.3100 −0.405328 −0.202664 0.979248i \(-0.564960\pi\)
−0.202664 + 0.979248i \(0.564960\pi\)
\(648\) 4.25050 0.166976
\(649\) −17.8366 −0.700148
\(650\) 1.58838 0.0623012
\(651\) −48.7083 −1.90903
\(652\) −14.2534 −0.558206
\(653\) −8.69444 −0.340240 −0.170120 0.985423i \(-0.554415\pi\)
−0.170120 + 0.985423i \(0.554415\pi\)
\(654\) 4.15259 0.162379
\(655\) 51.8063 2.02424
\(656\) −4.44403 −0.173510
\(657\) −39.1030 −1.52555
\(658\) 3.01349 0.117478
\(659\) −19.8991 −0.775157 −0.387579 0.921837i \(-0.626688\pi\)
−0.387579 + 0.921837i \(0.626688\pi\)
\(660\) 27.6898 1.07783
\(661\) 24.9324 0.969756 0.484878 0.874582i \(-0.338864\pi\)
0.484878 + 0.874582i \(0.338864\pi\)
\(662\) −0.493351 −0.0191746
\(663\) 89.4800 3.47512
\(664\) 1.46021 0.0566672
\(665\) 10.4509 0.405267
\(666\) 9.63541 0.373365
\(667\) −23.5634 −0.912378
\(668\) 8.84465 0.342210
\(669\) 55.7157 2.15409
\(670\) −0.151899 −0.00586838
\(671\) −22.4680 −0.867368
\(672\) 14.9388 0.576279
\(673\) −21.1947 −0.816996 −0.408498 0.912759i \(-0.633947\pi\)
−0.408498 + 0.912759i \(0.633947\pi\)
\(674\) −0.101837 −0.00392260
\(675\) 3.28863 0.126579
\(676\) −39.6949 −1.52673
\(677\) −21.4905 −0.825949 −0.412974 0.910743i \(-0.635510\pi\)
−0.412974 + 0.910743i \(0.635510\pi\)
\(678\) 6.73179 0.258533
\(679\) 17.5984 0.675366
\(680\) 14.4714 0.554954
\(681\) 16.2403 0.622329
\(682\) −5.44866 −0.208640
\(683\) 24.6755 0.944181 0.472090 0.881550i \(-0.343500\pi\)
0.472090 + 0.881550i \(0.343500\pi\)
\(684\) 18.1519 0.694055
\(685\) −43.0741 −1.64578
\(686\) −5.09349 −0.194471
\(687\) −27.4490 −1.04724
\(688\) −40.5384 −1.54551
\(689\) −0.387736 −0.0147716
\(690\) 3.98758 0.151805
\(691\) 22.4535 0.854170 0.427085 0.904211i \(-0.359540\pi\)
0.427085 + 0.904211i \(0.359540\pi\)
\(692\) −19.9013 −0.756536
\(693\) 17.0141 0.646312
\(694\) 5.98804 0.227303
\(695\) −13.3352 −0.505833
\(696\) −27.4451 −1.04030
\(697\) −7.12357 −0.269825
\(698\) 3.09295 0.117070
\(699\) 51.4364 1.94550
\(700\) −3.85219 −0.145599
\(701\) 28.3393 1.07036 0.535181 0.844738i \(-0.320244\pi\)
0.535181 + 0.844738i \(0.320244\pi\)
\(702\) 4.65211 0.175583
\(703\) −20.2005 −0.761876
\(704\) −13.9980 −0.527571
\(705\) −40.7743 −1.53565
\(706\) −1.97887 −0.0744759
\(707\) −1.37874 −0.0518527
\(708\) 42.4212 1.59429
\(709\) 25.3207 0.950938 0.475469 0.879732i \(-0.342278\pi\)
0.475469 + 0.879732i \(0.342278\pi\)
\(710\) −1.43739 −0.0539441
\(711\) 7.13393 0.267543
\(712\) −15.3235 −0.574272
\(713\) 22.6373 0.847775
\(714\) 7.52200 0.281504
\(715\) −31.0019 −1.15941
\(716\) 24.0316 0.898103
\(717\) 27.4520 1.02521
\(718\) −4.23692 −0.158121
\(719\) 9.71575 0.362336 0.181168 0.983452i \(-0.442012\pi\)
0.181168 + 0.983452i \(0.442012\pi\)
\(720\) −36.8895 −1.37479
\(721\) −7.59151 −0.282723
\(722\) −3.59902 −0.133942
\(723\) −69.8458 −2.59759
\(724\) 8.02083 0.298092
\(725\) 10.6759 0.396494
\(726\) −4.34298 −0.161183
\(727\) −11.6133 −0.430714 −0.215357 0.976535i \(-0.569092\pi\)
−0.215357 + 0.976535i \(0.569092\pi\)
\(728\) −11.0875 −0.410931
\(729\) −42.2813 −1.56597
\(730\) 5.98960 0.221685
\(731\) −64.9811 −2.40341
\(732\) 53.4361 1.97506
\(733\) −35.2914 −1.30352 −0.651759 0.758426i \(-0.725969\pi\)
−0.651759 + 0.758426i \(0.725969\pi\)
\(734\) −4.47189 −0.165060
\(735\) 22.8102 0.841367
\(736\) −6.94288 −0.255918
\(737\) 0.518446 0.0190972
\(738\) −1.32830 −0.0488954
\(739\) −45.6431 −1.67901 −0.839504 0.543353i \(-0.817155\pi\)
−0.839504 + 0.543353i \(0.817155\pi\)
\(740\) 42.5799 1.56527
\(741\) −34.9797 −1.28501
\(742\) −0.0325944 −0.00119658
\(743\) −21.4039 −0.785232 −0.392616 0.919702i \(-0.628430\pi\)
−0.392616 + 0.919702i \(0.628430\pi\)
\(744\) 26.3665 0.966642
\(745\) 50.9312 1.86597
\(746\) 5.12975 0.187814
\(747\) −5.96661 −0.218307
\(748\) −24.2754 −0.887598
\(749\) −24.8827 −0.909195
\(750\) 6.71821 0.245314
\(751\) 11.8967 0.434119 0.217059 0.976158i \(-0.430354\pi\)
0.217059 + 0.976158i \(0.430354\pi\)
\(752\) 22.3004 0.813211
\(753\) −62.1337 −2.26428
\(754\) 15.1022 0.549990
\(755\) 19.9679 0.726705
\(756\) −11.2825 −0.410340
\(757\) −7.01284 −0.254886 −0.127443 0.991846i \(-0.540677\pi\)
−0.127443 + 0.991846i \(0.540677\pi\)
\(758\) −8.19405 −0.297621
\(759\) −13.6100 −0.494011
\(760\) −5.65720 −0.205208
\(761\) −40.4600 −1.46667 −0.733337 0.679866i \(-0.762038\pi\)
−0.733337 + 0.679866i \(0.762038\pi\)
\(762\) 8.96976 0.324940
\(763\) 11.2756 0.408206
\(764\) 7.88516 0.285275
\(765\) −59.1322 −2.13793
\(766\) −1.95590 −0.0706695
\(767\) −47.4953 −1.71496
\(768\) 29.1796 1.05293
\(769\) −23.1438 −0.834586 −0.417293 0.908772i \(-0.637021\pi\)
−0.417293 + 0.908772i \(0.637021\pi\)
\(770\) −2.60613 −0.0939184
\(771\) −66.9594 −2.41149
\(772\) 51.5373 1.85487
\(773\) −4.39037 −0.157910 −0.0789552 0.996878i \(-0.525158\pi\)
−0.0789552 + 0.996878i \(0.525158\pi\)
\(774\) −12.1167 −0.435527
\(775\) −10.2564 −0.368419
\(776\) −9.52628 −0.341973
\(777\) 45.0317 1.61550
\(778\) −5.65209 −0.202637
\(779\) 2.78476 0.0997744
\(780\) 73.7325 2.64005
\(781\) 4.90592 0.175548
\(782\) −3.49588 −0.125012
\(783\) 31.2681 1.11743
\(784\) −12.4754 −0.445551
\(785\) 1.32054 0.0471321
\(786\) −14.5765 −0.519926
\(787\) −24.8822 −0.886955 −0.443478 0.896285i \(-0.646255\pi\)
−0.443478 + 0.896285i \(0.646255\pi\)
\(788\) −2.61988 −0.0933294
\(789\) 16.9762 0.604370
\(790\) −1.09274 −0.0388779
\(791\) 18.2790 0.649927
\(792\) −9.20996 −0.327262
\(793\) −59.8278 −2.12455
\(794\) 5.63260 0.199894
\(795\) 0.441022 0.0156414
\(796\) 29.6101 1.04950
\(797\) −55.2621 −1.95748 −0.978742 0.205098i \(-0.934249\pi\)
−0.978742 + 0.205098i \(0.934249\pi\)
\(798\) −2.94052 −0.104093
\(799\) 35.7464 1.26462
\(800\) 3.14563 0.111215
\(801\) 62.6137 2.21235
\(802\) −3.09844 −0.109410
\(803\) −20.4430 −0.721419
\(804\) −1.23303 −0.0434856
\(805\) 10.8276 0.381623
\(806\) −14.5087 −0.511047
\(807\) −32.9619 −1.16031
\(808\) 0.746328 0.0262557
\(809\) 15.3727 0.540474 0.270237 0.962794i \(-0.412898\pi\)
0.270237 + 0.962794i \(0.412898\pi\)
\(810\) 2.66036 0.0934755
\(811\) 28.4653 0.999552 0.499776 0.866155i \(-0.333416\pi\)
0.499776 + 0.866155i \(0.333416\pi\)
\(812\) −36.6264 −1.28534
\(813\) 43.9333 1.54081
\(814\) 5.03739 0.176560
\(815\) −18.1514 −0.635815
\(816\) 55.6642 1.94864
\(817\) 25.4025 0.888722
\(818\) 9.64594 0.337262
\(819\) 45.3051 1.58309
\(820\) −5.86990 −0.204986
\(821\) 39.8830 1.39193 0.695963 0.718078i \(-0.254978\pi\)
0.695963 + 0.718078i \(0.254978\pi\)
\(822\) 12.1196 0.422718
\(823\) 33.8559 1.18014 0.590071 0.807351i \(-0.299100\pi\)
0.590071 + 0.807351i \(0.299100\pi\)
\(824\) 4.10939 0.143157
\(825\) 6.16630 0.214683
\(826\) −3.99262 −0.138921
\(827\) −31.1589 −1.08350 −0.541750 0.840540i \(-0.682238\pi\)
−0.541750 + 0.840540i \(0.682238\pi\)
\(828\) 18.8062 0.653561
\(829\) 21.9578 0.762625 0.381312 0.924446i \(-0.375472\pi\)
0.381312 + 0.924446i \(0.375472\pi\)
\(830\) 0.913935 0.0317232
\(831\) 6.69917 0.232392
\(832\) −37.2739 −1.29224
\(833\) −19.9975 −0.692873
\(834\) 3.75207 0.129923
\(835\) 11.2635 0.389789
\(836\) 9.48980 0.328212
\(837\) −30.0393 −1.03831
\(838\) −1.37626 −0.0475419
\(839\) −13.3272 −0.460106 −0.230053 0.973178i \(-0.573890\pi\)
−0.230053 + 0.973178i \(0.573890\pi\)
\(840\) 12.6113 0.435130
\(841\) 72.5062 2.50021
\(842\) −0.0229263 −0.000790092 0
\(843\) −13.5695 −0.467358
\(844\) 31.2487 1.07562
\(845\) −50.5507 −1.73900
\(846\) 6.66548 0.229164
\(847\) −11.7926 −0.405199
\(848\) −0.241205 −0.00828301
\(849\) −3.54613 −0.121703
\(850\) 1.58388 0.0543268
\(851\) −20.9287 −0.717425
\(852\) −11.6679 −0.399734
\(853\) −11.1545 −0.381923 −0.190962 0.981597i \(-0.561161\pi\)
−0.190962 + 0.981597i \(0.561161\pi\)
\(854\) −5.02933 −0.172100
\(855\) 23.1161 0.790553
\(856\) 13.4694 0.460373
\(857\) 22.5934 0.771777 0.385889 0.922545i \(-0.373895\pi\)
0.385889 + 0.922545i \(0.373895\pi\)
\(858\) 8.72288 0.297794
\(859\) 14.0664 0.479941 0.239970 0.970780i \(-0.422862\pi\)
0.239970 + 0.970780i \(0.422862\pi\)
\(860\) −53.5451 −1.82587
\(861\) −6.20790 −0.211565
\(862\) −3.23358 −0.110136
\(863\) −49.7257 −1.69268 −0.846342 0.532640i \(-0.821200\pi\)
−0.846342 + 0.532640i \(0.821200\pi\)
\(864\) 9.21306 0.313435
\(865\) −25.3440 −0.861720
\(866\) −8.38489 −0.284930
\(867\) 43.7386 1.48544
\(868\) 35.1870 1.19432
\(869\) 3.72962 0.126519
\(870\) −17.1777 −0.582377
\(871\) 1.38052 0.0467770
\(872\) −6.10366 −0.206696
\(873\) 38.9256 1.31743
\(874\) 1.36661 0.0462264
\(875\) 18.2422 0.616697
\(876\) 48.6201 1.64272
\(877\) −0.725108 −0.0244852 −0.0122426 0.999925i \(-0.503897\pi\)
−0.0122426 + 0.999925i \(0.503897\pi\)
\(878\) −9.76382 −0.329513
\(879\) 67.2805 2.26932
\(880\) −19.2858 −0.650125
\(881\) 37.1950 1.25313 0.626566 0.779368i \(-0.284460\pi\)
0.626566 + 0.779368i \(0.284460\pi\)
\(882\) −3.72884 −0.125557
\(883\) −57.5237 −1.93583 −0.967913 0.251285i \(-0.919147\pi\)
−0.967913 + 0.251285i \(0.919147\pi\)
\(884\) −64.6406 −2.17410
\(885\) 54.0225 1.81595
\(886\) 6.04899 0.203220
\(887\) −34.2813 −1.15105 −0.575527 0.817782i \(-0.695203\pi\)
−0.575527 + 0.817782i \(0.695203\pi\)
\(888\) −24.3763 −0.818015
\(889\) 24.3558 0.816869
\(890\) −9.59085 −0.321486
\(891\) −9.08004 −0.304193
\(892\) −40.2492 −1.34764
\(893\) −13.9741 −0.467624
\(894\) −14.3303 −0.479276
\(895\) 30.6037 1.02297
\(896\) −14.2993 −0.477706
\(897\) −36.2406 −1.21004
\(898\) 5.49300 0.183304
\(899\) −97.5169 −3.25237
\(900\) −8.52058 −0.284019
\(901\) −0.386640 −0.0128808
\(902\) −0.694435 −0.0231221
\(903\) −56.6283 −1.88447
\(904\) −9.89469 −0.329092
\(905\) 10.2144 0.339537
\(906\) −5.61827 −0.186654
\(907\) 21.9477 0.728761 0.364380 0.931250i \(-0.381281\pi\)
0.364380 + 0.931250i \(0.381281\pi\)
\(908\) −11.7320 −0.389341
\(909\) −3.04959 −0.101149
\(910\) −6.93960 −0.230046
\(911\) 10.9369 0.362357 0.181179 0.983450i \(-0.442009\pi\)
0.181179 + 0.983450i \(0.442009\pi\)
\(912\) −21.7603 −0.720557
\(913\) −3.11934 −0.103235
\(914\) −3.04632 −0.100763
\(915\) 68.0498 2.24966
\(916\) 19.8292 0.655176
\(917\) −39.5800 −1.30705
\(918\) 4.63896 0.153108
\(919\) −15.1849 −0.500905 −0.250452 0.968129i \(-0.580579\pi\)
−0.250452 + 0.968129i \(0.580579\pi\)
\(920\) −5.86113 −0.193236
\(921\) 50.4623 1.66279
\(922\) 7.21092 0.237479
\(923\) 13.0635 0.429990
\(924\) −21.1550 −0.695950
\(925\) 9.48220 0.311773
\(926\) −5.26478 −0.173011
\(927\) −16.7915 −0.551505
\(928\) 29.9085 0.981794
\(929\) 18.6029 0.610341 0.305171 0.952298i \(-0.401286\pi\)
0.305171 + 0.952298i \(0.401286\pi\)
\(930\) 16.5026 0.541141
\(931\) 7.81746 0.256207
\(932\) −37.1578 −1.21714
\(933\) 47.9088 1.56846
\(934\) 8.35241 0.273299
\(935\) −30.9143 −1.01100
\(936\) −24.5243 −0.801601
\(937\) 39.8655 1.30235 0.651175 0.758928i \(-0.274277\pi\)
0.651175 + 0.758928i \(0.274277\pi\)
\(938\) 0.116051 0.00378920
\(939\) 15.3517 0.500983
\(940\) 29.4555 0.960731
\(941\) −5.14348 −0.167673 −0.0838364 0.996480i \(-0.526717\pi\)
−0.0838364 + 0.996480i \(0.526717\pi\)
\(942\) −0.371555 −0.0121059
\(943\) 2.88514 0.0939532
\(944\) −29.5461 −0.961645
\(945\) −14.3680 −0.467391
\(946\) −6.33462 −0.205956
\(947\) 6.13580 0.199387 0.0996933 0.995018i \(-0.468214\pi\)
0.0996933 + 0.995018i \(0.468214\pi\)
\(948\) −8.87022 −0.288091
\(949\) −54.4357 −1.76706
\(950\) −0.619175 −0.0200887
\(951\) 36.3645 1.17920
\(952\) −11.0562 −0.358333
\(953\) 37.8521 1.22615 0.613075 0.790025i \(-0.289932\pi\)
0.613075 + 0.790025i \(0.289932\pi\)
\(954\) −0.0720949 −0.00233416
\(955\) 10.0416 0.324938
\(956\) −19.8314 −0.641393
\(957\) 58.6289 1.89520
\(958\) −3.68957 −0.119205
\(959\) 32.9086 1.06267
\(960\) 42.3964 1.36834
\(961\) 62.6845 2.02208
\(962\) 13.4136 0.432470
\(963\) −55.0376 −1.77356
\(964\) 50.4568 1.62510
\(965\) 65.6317 2.11276
\(966\) −3.04651 −0.0980200
\(967\) 33.1631 1.06645 0.533226 0.845973i \(-0.320980\pi\)
0.533226 + 0.845973i \(0.320980\pi\)
\(968\) 6.38351 0.205174
\(969\) −34.8808 −1.12053
\(970\) −5.96243 −0.191442
\(971\) 17.8174 0.571788 0.285894 0.958261i \(-0.407710\pi\)
0.285894 + 0.958261i \(0.407710\pi\)
\(972\) 39.5926 1.26993
\(973\) 10.1881 0.326615
\(974\) 4.22236 0.135293
\(975\) 16.4196 0.525849
\(976\) −37.2180 −1.19132
\(977\) 2.19389 0.0701887 0.0350943 0.999384i \(-0.488827\pi\)
0.0350943 + 0.999384i \(0.488827\pi\)
\(978\) 5.10718 0.163309
\(979\) 32.7344 1.04620
\(980\) −16.4782 −0.526376
\(981\) 24.9404 0.796284
\(982\) 3.58453 0.114387
\(983\) 17.3296 0.552729 0.276364 0.961053i \(-0.410870\pi\)
0.276364 + 0.961053i \(0.410870\pi\)
\(984\) 3.36042 0.107126
\(985\) −3.33636 −0.106305
\(986\) 15.0595 0.479592
\(987\) 31.1516 0.991565
\(988\) 25.2694 0.803928
\(989\) 26.3182 0.836871
\(990\) −5.76444 −0.183206
\(991\) 45.9501 1.45965 0.729826 0.683633i \(-0.239601\pi\)
0.729826 + 0.683633i \(0.239601\pi\)
\(992\) −28.7331 −0.912276
\(993\) −5.09995 −0.161842
\(994\) 1.09816 0.0348316
\(995\) 37.7079 1.19542
\(996\) 7.41879 0.235073
\(997\) −24.6533 −0.780779 −0.390389 0.920650i \(-0.627660\pi\)
−0.390389 + 0.920650i \(0.627660\pi\)
\(998\) 5.71292 0.180839
\(999\) 27.7719 0.878664
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 \(a_p\))