Properties

Label 619.2.a.b.1.2
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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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 1.2
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.42956 q^{2} -3.02694 q^{3} +3.90276 q^{4} -0.0323024 q^{5} +7.35414 q^{6} -3.37580 q^{7} -4.62286 q^{8} +6.16239 q^{9} +O(q^{10})\) \(q-2.42956 q^{2} -3.02694 q^{3} +3.90276 q^{4} -0.0323024 q^{5} +7.35414 q^{6} -3.37580 q^{7} -4.62286 q^{8} +6.16239 q^{9} +0.0784807 q^{10} +0.333322 q^{11} -11.8134 q^{12} -1.65481 q^{13} +8.20170 q^{14} +0.0977777 q^{15} +3.42599 q^{16} -1.50147 q^{17} -14.9719 q^{18} -5.02748 q^{19} -0.126069 q^{20} +10.2184 q^{21} -0.809826 q^{22} -5.35036 q^{23} +13.9931 q^{24} -4.99896 q^{25} +4.02046 q^{26} -9.57238 q^{27} -13.1749 q^{28} +3.38998 q^{29} -0.237557 q^{30} -5.45120 q^{31} +0.922070 q^{32} -1.00895 q^{33} +3.64791 q^{34} +0.109047 q^{35} +24.0503 q^{36} -4.83972 q^{37} +12.2145 q^{38} +5.00902 q^{39} +0.149330 q^{40} +0.0826437 q^{41} -24.8261 q^{42} +1.78583 q^{43} +1.30087 q^{44} -0.199060 q^{45} +12.9990 q^{46} +7.93095 q^{47} -10.3703 q^{48} +4.39602 q^{49} +12.1453 q^{50} +4.54487 q^{51} -6.45832 q^{52} +11.6068 q^{53} +23.2567 q^{54} -0.0107671 q^{55} +15.6058 q^{56} +15.2179 q^{57} -8.23615 q^{58} -12.7123 q^{59} +0.381602 q^{60} -1.27687 q^{61} +13.2440 q^{62} -20.8030 q^{63} -9.09220 q^{64} +0.0534544 q^{65} +2.45130 q^{66} +11.1702 q^{67} -5.85987 q^{68} +16.1952 q^{69} -0.264935 q^{70} +9.44501 q^{71} -28.4879 q^{72} +16.0226 q^{73} +11.7584 q^{74} +15.1316 q^{75} -19.6210 q^{76} -1.12523 q^{77} -12.1697 q^{78} +2.17453 q^{79} -0.110668 q^{80} +10.4879 q^{81} -0.200788 q^{82} +0.893308 q^{83} +39.8797 q^{84} +0.0485011 q^{85} -4.33878 q^{86} -10.2613 q^{87} -1.54090 q^{88} +11.3541 q^{89} +0.483629 q^{90} +5.58631 q^{91} -20.8811 q^{92} +16.5005 q^{93} -19.2687 q^{94} +0.162400 q^{95} -2.79105 q^{96} -8.98396 q^{97} -10.6804 q^{98} +2.05406 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42956 −1.71796 −0.858979 0.512011i \(-0.828901\pi\)
−0.858979 + 0.512011i \(0.828901\pi\)
\(3\) −3.02694 −1.74761 −0.873804 0.486279i \(-0.838354\pi\)
−0.873804 + 0.486279i \(0.838354\pi\)
\(4\) 3.90276 1.95138
\(5\) −0.0323024 −0.0144461 −0.00722304 0.999974i \(-0.502299\pi\)
−0.00722304 + 0.999974i \(0.502299\pi\)
\(6\) 7.35414 3.00231
\(7\) −3.37580 −1.27593 −0.637966 0.770064i \(-0.720224\pi\)
−0.637966 + 0.770064i \(0.720224\pi\)
\(8\) −4.62286 −1.63443
\(9\) 6.16239 2.05413
\(10\) 0.0784807 0.0248178
\(11\) 0.333322 0.100500 0.0502502 0.998737i \(-0.483998\pi\)
0.0502502 + 0.998737i \(0.483998\pi\)
\(12\) −11.8134 −3.41024
\(13\) −1.65481 −0.458962 −0.229481 0.973313i \(-0.573703\pi\)
−0.229481 + 0.973313i \(0.573703\pi\)
\(14\) 8.20170 2.19200
\(15\) 0.0977777 0.0252461
\(16\) 3.42599 0.856497
\(17\) −1.50147 −0.364160 −0.182080 0.983284i \(-0.558283\pi\)
−0.182080 + 0.983284i \(0.558283\pi\)
\(18\) −14.9719 −3.52891
\(19\) −5.02748 −1.15338 −0.576691 0.816962i \(-0.695656\pi\)
−0.576691 + 0.816962i \(0.695656\pi\)
\(20\) −0.126069 −0.0281898
\(21\) 10.2184 2.22983
\(22\) −0.809826 −0.172655
\(23\) −5.35036 −1.11563 −0.557814 0.829966i \(-0.688360\pi\)
−0.557814 + 0.829966i \(0.688360\pi\)
\(24\) 13.9931 2.85634
\(25\) −4.99896 −0.999791
\(26\) 4.02046 0.788477
\(27\) −9.57238 −1.84221
\(28\) −13.1749 −2.48983
\(29\) 3.38998 0.629503 0.314752 0.949174i \(-0.398079\pi\)
0.314752 + 0.949174i \(0.398079\pi\)
\(30\) −0.237557 −0.0433717
\(31\) −5.45120 −0.979065 −0.489532 0.871985i \(-0.662832\pi\)
−0.489532 + 0.871985i \(0.662832\pi\)
\(32\) 0.922070 0.163000
\(33\) −1.00895 −0.175635
\(34\) 3.64791 0.625611
\(35\) 0.109047 0.0184322
\(36\) 24.0503 4.00838
\(37\) −4.83972 −0.795644 −0.397822 0.917463i \(-0.630234\pi\)
−0.397822 + 0.917463i \(0.630234\pi\)
\(38\) 12.2145 1.98146
\(39\) 5.00902 0.802085
\(40\) 0.149330 0.0236111
\(41\) 0.0826437 0.0129068 0.00645339 0.999979i \(-0.497946\pi\)
0.00645339 + 0.999979i \(0.497946\pi\)
\(42\) −24.8261 −3.83075
\(43\) 1.78583 0.272337 0.136168 0.990686i \(-0.456521\pi\)
0.136168 + 0.990686i \(0.456521\pi\)
\(44\) 1.30087 0.196114
\(45\) −0.199060 −0.0296742
\(46\) 12.9990 1.91660
\(47\) 7.93095 1.15685 0.578424 0.815736i \(-0.303668\pi\)
0.578424 + 0.815736i \(0.303668\pi\)
\(48\) −10.3703 −1.49682
\(49\) 4.39602 0.628003
\(50\) 12.1453 1.71760
\(51\) 4.54487 0.636409
\(52\) −6.45832 −0.895608
\(53\) 11.6068 1.59432 0.797161 0.603767i \(-0.206334\pi\)
0.797161 + 0.603767i \(0.206334\pi\)
\(54\) 23.2567 3.16483
\(55\) −0.0107671 −0.00145184
\(56\) 15.6058 2.08542
\(57\) 15.2179 2.01566
\(58\) −8.23615 −1.08146
\(59\) −12.7123 −1.65501 −0.827503 0.561461i \(-0.810240\pi\)
−0.827503 + 0.561461i \(0.810240\pi\)
\(60\) 0.381602 0.0492647
\(61\) −1.27687 −0.163486 −0.0817432 0.996653i \(-0.526049\pi\)
−0.0817432 + 0.996653i \(0.526049\pi\)
\(62\) 13.2440 1.68199
\(63\) −20.8030 −2.62093
\(64\) −9.09220 −1.13653
\(65\) 0.0534544 0.00663020
\(66\) 2.45130 0.301734
\(67\) 11.1702 1.36466 0.682329 0.731045i \(-0.260967\pi\)
0.682329 + 0.731045i \(0.260967\pi\)
\(68\) −5.85987 −0.710614
\(69\) 16.1952 1.94968
\(70\) −0.264935 −0.0316658
\(71\) 9.44501 1.12092 0.560458 0.828183i \(-0.310625\pi\)
0.560458 + 0.828183i \(0.310625\pi\)
\(72\) −28.4879 −3.35733
\(73\) 16.0226 1.87530 0.937651 0.347579i \(-0.112996\pi\)
0.937651 + 0.347579i \(0.112996\pi\)
\(74\) 11.7584 1.36688
\(75\) 15.1316 1.74724
\(76\) −19.6210 −2.25068
\(77\) −1.12523 −0.128232
\(78\) −12.1697 −1.37795
\(79\) 2.17453 0.244654 0.122327 0.992490i \(-0.460964\pi\)
0.122327 + 0.992490i \(0.460964\pi\)
\(80\) −0.110668 −0.0123730
\(81\) 10.4879 1.16532
\(82\) −0.200788 −0.0221733
\(83\) 0.893308 0.0980533 0.0490266 0.998797i \(-0.484388\pi\)
0.0490266 + 0.998797i \(0.484388\pi\)
\(84\) 39.8797 4.35124
\(85\) 0.0485011 0.00526069
\(86\) −4.33878 −0.467863
\(87\) −10.2613 −1.10012
\(88\) −1.54090 −0.164260
\(89\) 11.3541 1.20353 0.601767 0.798672i \(-0.294464\pi\)
0.601767 + 0.798672i \(0.294464\pi\)
\(90\) 0.483629 0.0509789
\(91\) 5.58631 0.585604
\(92\) −20.8811 −2.17701
\(93\) 16.5005 1.71102
\(94\) −19.2687 −1.98742
\(95\) 0.162400 0.0166619
\(96\) −2.79105 −0.284861
\(97\) −8.98396 −0.912183 −0.456091 0.889933i \(-0.650751\pi\)
−0.456091 + 0.889933i \(0.650751\pi\)
\(98\) −10.6804 −1.07888
\(99\) 2.05406 0.206441
\(100\) −19.5097 −1.95097
\(101\) −19.1212 −1.90263 −0.951315 0.308221i \(-0.900266\pi\)
−0.951315 + 0.308221i \(0.900266\pi\)
\(102\) −11.0420 −1.09332
\(103\) −19.7952 −1.95048 −0.975241 0.221143i \(-0.929021\pi\)
−0.975241 + 0.221143i \(0.929021\pi\)
\(104\) 7.64995 0.750139
\(105\) −0.330078 −0.0322123
\(106\) −28.1995 −2.73898
\(107\) −0.880564 −0.0851273 −0.0425637 0.999094i \(-0.513553\pi\)
−0.0425637 + 0.999094i \(0.513553\pi\)
\(108\) −37.3587 −3.59484
\(109\) 10.0304 0.960736 0.480368 0.877067i \(-0.340503\pi\)
0.480368 + 0.877067i \(0.340503\pi\)
\(110\) 0.0261593 0.00249420
\(111\) 14.6495 1.39047
\(112\) −11.5655 −1.09283
\(113\) 7.05601 0.663774 0.331887 0.943319i \(-0.392315\pi\)
0.331887 + 0.943319i \(0.392315\pi\)
\(114\) −36.9727 −3.46282
\(115\) 0.172830 0.0161165
\(116\) 13.2303 1.22840
\(117\) −10.1976 −0.942767
\(118\) 30.8854 2.84323
\(119\) 5.06866 0.464644
\(120\) −0.452012 −0.0412629
\(121\) −10.8889 −0.989900
\(122\) 3.10223 0.280863
\(123\) −0.250158 −0.0225560
\(124\) −21.2747 −1.91052
\(125\) 0.322991 0.0288892
\(126\) 50.5421 4.50265
\(127\) −3.23199 −0.286793 −0.143396 0.989665i \(-0.545802\pi\)
−0.143396 + 0.989665i \(0.545802\pi\)
\(128\) 20.2459 1.78950
\(129\) −5.40561 −0.475938
\(130\) −0.129871 −0.0113904
\(131\) 10.2444 0.895054 0.447527 0.894270i \(-0.352305\pi\)
0.447527 + 0.894270i \(0.352305\pi\)
\(132\) −3.93767 −0.342731
\(133\) 16.9717 1.47164
\(134\) −27.1387 −2.34442
\(135\) 0.309211 0.0266127
\(136\) 6.94108 0.595193
\(137\) −3.81470 −0.325912 −0.162956 0.986633i \(-0.552103\pi\)
−0.162956 + 0.986633i \(0.552103\pi\)
\(138\) −39.3473 −3.34946
\(139\) 14.8581 1.26025 0.630123 0.776496i \(-0.283005\pi\)
0.630123 + 0.776496i \(0.283005\pi\)
\(140\) 0.425582 0.0359682
\(141\) −24.0065 −2.02172
\(142\) −22.9472 −1.92569
\(143\) −0.551585 −0.0461258
\(144\) 21.1123 1.75936
\(145\) −0.109505 −0.00909386
\(146\) −38.9278 −3.22169
\(147\) −13.3065 −1.09750
\(148\) −18.8882 −1.55260
\(149\) −4.00235 −0.327885 −0.163943 0.986470i \(-0.552421\pi\)
−0.163943 + 0.986470i \(0.552421\pi\)
\(150\) −36.7630 −3.00169
\(151\) 4.75933 0.387309 0.193654 0.981070i \(-0.437966\pi\)
0.193654 + 0.981070i \(0.437966\pi\)
\(152\) 23.2413 1.88512
\(153\) −9.25265 −0.748032
\(154\) 2.73381 0.220297
\(155\) 0.176087 0.0141437
\(156\) 19.5490 1.56517
\(157\) 19.7896 1.57938 0.789690 0.613506i \(-0.210241\pi\)
0.789690 + 0.613506i \(0.210241\pi\)
\(158\) −5.28315 −0.420305
\(159\) −35.1333 −2.78625
\(160\) −0.0297851 −0.00235472
\(161\) 18.0617 1.42346
\(162\) −25.4810 −2.00197
\(163\) −6.82013 −0.534194 −0.267097 0.963670i \(-0.586064\pi\)
−0.267097 + 0.963670i \(0.586064\pi\)
\(164\) 0.322538 0.0251860
\(165\) 0.0325915 0.00253724
\(166\) −2.17034 −0.168451
\(167\) 13.2644 1.02643 0.513215 0.858260i \(-0.328454\pi\)
0.513215 + 0.858260i \(0.328454\pi\)
\(168\) −47.2380 −3.64449
\(169\) −10.2616 −0.789354
\(170\) −0.117836 −0.00903764
\(171\) −30.9813 −2.36920
\(172\) 6.96966 0.531432
\(173\) 14.2557 1.08384 0.541921 0.840429i \(-0.317697\pi\)
0.541921 + 0.840429i \(0.317697\pi\)
\(174\) 24.9304 1.88997
\(175\) 16.8755 1.27567
\(176\) 1.14196 0.0860783
\(177\) 38.4796 2.89230
\(178\) −27.5855 −2.06762
\(179\) 12.2721 0.917260 0.458630 0.888627i \(-0.348340\pi\)
0.458630 + 0.888627i \(0.348340\pi\)
\(180\) −0.776884 −0.0579055
\(181\) 5.03653 0.374362 0.187181 0.982325i \(-0.440065\pi\)
0.187181 + 0.982325i \(0.440065\pi\)
\(182\) −13.5723 −1.00604
\(183\) 3.86501 0.285710
\(184\) 24.7339 1.82341
\(185\) 0.156335 0.0114939
\(186\) −40.0889 −2.93946
\(187\) −0.500473 −0.0365982
\(188\) 30.9526 2.25745
\(189\) 32.3144 2.35053
\(190\) −0.394560 −0.0286244
\(191\) 6.68323 0.483581 0.241791 0.970328i \(-0.422265\pi\)
0.241791 + 0.970328i \(0.422265\pi\)
\(192\) 27.5216 1.98620
\(193\) −9.66090 −0.695407 −0.347703 0.937605i \(-0.613038\pi\)
−0.347703 + 0.937605i \(0.613038\pi\)
\(194\) 21.8271 1.56709
\(195\) −0.161804 −0.0115870
\(196\) 17.1566 1.22547
\(197\) 22.6726 1.61536 0.807678 0.589624i \(-0.200724\pi\)
0.807678 + 0.589624i \(0.200724\pi\)
\(198\) −4.99046 −0.354657
\(199\) −10.8711 −0.770633 −0.385316 0.922785i \(-0.625908\pi\)
−0.385316 + 0.922785i \(0.625908\pi\)
\(200\) 23.1095 1.63409
\(201\) −33.8116 −2.38489
\(202\) 46.4561 3.26864
\(203\) −11.4439 −0.803203
\(204\) 17.7375 1.24187
\(205\) −0.00266959 −0.000186452 0
\(206\) 48.0937 3.35085
\(207\) −32.9710 −2.29164
\(208\) −5.66936 −0.393100
\(209\) −1.67577 −0.115915
\(210\) 0.801943 0.0553394
\(211\) 22.4482 1.54540 0.772699 0.634773i \(-0.218906\pi\)
0.772699 + 0.634773i \(0.218906\pi\)
\(212\) 45.2987 3.11112
\(213\) −28.5895 −1.95892
\(214\) 2.13938 0.146245
\(215\) −0.0576867 −0.00393420
\(216\) 44.2518 3.01095
\(217\) 18.4022 1.24922
\(218\) −24.3694 −1.65050
\(219\) −48.4995 −3.27729
\(220\) −0.0420214 −0.00283308
\(221\) 2.48465 0.167136
\(222\) −35.5919 −2.38877
\(223\) 9.86150 0.660375 0.330187 0.943915i \(-0.392888\pi\)
0.330187 + 0.943915i \(0.392888\pi\)
\(224\) −3.11272 −0.207978
\(225\) −30.8055 −2.05370
\(226\) −17.1430 −1.14034
\(227\) −9.95777 −0.660920 −0.330460 0.943820i \(-0.607204\pi\)
−0.330460 + 0.943820i \(0.607204\pi\)
\(228\) 59.3917 3.93331
\(229\) 12.5539 0.829585 0.414792 0.909916i \(-0.363854\pi\)
0.414792 + 0.909916i \(0.363854\pi\)
\(230\) −0.419900 −0.0276874
\(231\) 3.40600 0.224099
\(232\) −15.6714 −1.02888
\(233\) −6.22700 −0.407944 −0.203972 0.978977i \(-0.565385\pi\)
−0.203972 + 0.978977i \(0.565385\pi\)
\(234\) 24.7756 1.61963
\(235\) −0.256189 −0.0167119
\(236\) −49.6132 −3.22954
\(237\) −6.58218 −0.427559
\(238\) −12.3146 −0.798238
\(239\) 2.13865 0.138338 0.0691688 0.997605i \(-0.477965\pi\)
0.0691688 + 0.997605i \(0.477965\pi\)
\(240\) 0.334985 0.0216232
\(241\) 23.6818 1.52548 0.762739 0.646706i \(-0.223854\pi\)
0.762739 + 0.646706i \(0.223854\pi\)
\(242\) 26.4552 1.70061
\(243\) −3.02913 −0.194319
\(244\) −4.98331 −0.319024
\(245\) −0.142002 −0.00907219
\(246\) 0.607773 0.0387502
\(247\) 8.31952 0.529358
\(248\) 25.2001 1.60021
\(249\) −2.70399 −0.171359
\(250\) −0.784725 −0.0496304
\(251\) −20.3919 −1.28713 −0.643563 0.765393i \(-0.722545\pi\)
−0.643563 + 0.765393i \(0.722545\pi\)
\(252\) −81.1890 −5.11443
\(253\) −1.78339 −0.112121
\(254\) 7.85231 0.492698
\(255\) −0.146810 −0.00919362
\(256\) −31.0042 −1.93776
\(257\) −30.6145 −1.90968 −0.954839 0.297125i \(-0.903972\pi\)
−0.954839 + 0.297125i \(0.903972\pi\)
\(258\) 13.1333 0.817641
\(259\) 16.3379 1.01519
\(260\) 0.208619 0.0129380
\(261\) 20.8904 1.29308
\(262\) −24.8893 −1.53766
\(263\) −24.3347 −1.50054 −0.750270 0.661132i \(-0.770076\pi\)
−0.750270 + 0.661132i \(0.770076\pi\)
\(264\) 4.66422 0.287063
\(265\) −0.374929 −0.0230317
\(266\) −41.2339 −2.52821
\(267\) −34.3683 −2.10331
\(268\) 43.5946 2.66296
\(269\) 12.3260 0.751528 0.375764 0.926715i \(-0.377380\pi\)
0.375764 + 0.926715i \(0.377380\pi\)
\(270\) −0.751247 −0.0457194
\(271\) −13.9583 −0.847906 −0.423953 0.905684i \(-0.639358\pi\)
−0.423953 + 0.905684i \(0.639358\pi\)
\(272\) −5.14402 −0.311902
\(273\) −16.9094 −1.02341
\(274\) 9.26804 0.559903
\(275\) −1.66626 −0.100479
\(276\) 63.2061 3.80456
\(277\) 1.93138 0.116046 0.0580228 0.998315i \(-0.481520\pi\)
0.0580228 + 0.998315i \(0.481520\pi\)
\(278\) −36.0986 −2.16505
\(279\) −33.5924 −2.01113
\(280\) −0.504107 −0.0301261
\(281\) 16.4329 0.980304 0.490152 0.871637i \(-0.336941\pi\)
0.490152 + 0.871637i \(0.336941\pi\)
\(282\) 58.3253 3.47322
\(283\) −29.2492 −1.73868 −0.869342 0.494210i \(-0.835457\pi\)
−0.869342 + 0.494210i \(0.835457\pi\)
\(284\) 36.8615 2.18733
\(285\) −0.491575 −0.0291184
\(286\) 1.34011 0.0792422
\(287\) −0.278988 −0.0164682
\(288\) 5.68215 0.334824
\(289\) −14.7456 −0.867387
\(290\) 0.266048 0.0156229
\(291\) 27.1939 1.59414
\(292\) 62.5322 3.65942
\(293\) 9.62737 0.562437 0.281218 0.959644i \(-0.409261\pi\)
0.281218 + 0.959644i \(0.409261\pi\)
\(294\) 32.3290 1.88546
\(295\) 0.410640 0.0239084
\(296\) 22.3733 1.30042
\(297\) −3.19069 −0.185142
\(298\) 9.72394 0.563293
\(299\) 8.85383 0.512030
\(300\) 59.0548 3.40953
\(301\) −6.02861 −0.347483
\(302\) −11.5631 −0.665380
\(303\) 57.8788 3.32505
\(304\) −17.2241 −0.987869
\(305\) 0.0412460 0.00236174
\(306\) 22.4799 1.28509
\(307\) 31.4085 1.79258 0.896288 0.443473i \(-0.146254\pi\)
0.896288 + 0.443473i \(0.146254\pi\)
\(308\) −4.39149 −0.250228
\(309\) 59.9191 3.40868
\(310\) −0.427814 −0.0242982
\(311\) −9.93124 −0.563149 −0.281575 0.959539i \(-0.590857\pi\)
−0.281575 + 0.959539i \(0.590857\pi\)
\(312\) −23.1560 −1.31095
\(313\) −17.6550 −0.997917 −0.498959 0.866626i \(-0.666284\pi\)
−0.498959 + 0.866626i \(0.666284\pi\)
\(314\) −48.0800 −2.71331
\(315\) 0.671988 0.0378622
\(316\) 8.48666 0.477412
\(317\) −22.9524 −1.28914 −0.644568 0.764547i \(-0.722963\pi\)
−0.644568 + 0.764547i \(0.722963\pi\)
\(318\) 85.3583 4.78666
\(319\) 1.12995 0.0632653
\(320\) 0.293700 0.0164183
\(321\) 2.66542 0.148769
\(322\) −43.8821 −2.44545
\(323\) 7.54860 0.420016
\(324\) 40.9317 2.27398
\(325\) 8.27232 0.458866
\(326\) 16.5699 0.917723
\(327\) −30.3614 −1.67899
\(328\) −0.382050 −0.0210952
\(329\) −26.7733 −1.47606
\(330\) −0.0791829 −0.00435887
\(331\) 12.6516 0.695396 0.347698 0.937606i \(-0.386963\pi\)
0.347698 + 0.937606i \(0.386963\pi\)
\(332\) 3.48636 0.191339
\(333\) −29.8242 −1.63436
\(334\) −32.2266 −1.76336
\(335\) −0.360825 −0.0197140
\(336\) 35.0080 1.90984
\(337\) 3.30965 0.180288 0.0901440 0.995929i \(-0.471267\pi\)
0.0901440 + 0.995929i \(0.471267\pi\)
\(338\) 24.9312 1.35608
\(339\) −21.3582 −1.16002
\(340\) 0.189288 0.0102656
\(341\) −1.81701 −0.0983964
\(342\) 75.2708 4.07018
\(343\) 8.79051 0.474643
\(344\) −8.25564 −0.445114
\(345\) −0.523146 −0.0281652
\(346\) −34.6351 −1.86199
\(347\) 17.1461 0.920450 0.460225 0.887802i \(-0.347769\pi\)
0.460225 + 0.887802i \(0.347769\pi\)
\(348\) −40.0473 −2.14676
\(349\) −13.5765 −0.726734 −0.363367 0.931646i \(-0.618373\pi\)
−0.363367 + 0.931646i \(0.618373\pi\)
\(350\) −41.0000 −2.19154
\(351\) 15.8405 0.845502
\(352\) 0.307346 0.0163816
\(353\) −35.8042 −1.90566 −0.952832 0.303499i \(-0.901845\pi\)
−0.952832 + 0.303499i \(0.901845\pi\)
\(354\) −93.4884 −4.96885
\(355\) −0.305097 −0.0161929
\(356\) 44.3124 2.34855
\(357\) −15.3426 −0.812014
\(358\) −29.8158 −1.57581
\(359\) 31.2324 1.64838 0.824191 0.566312i \(-0.191630\pi\)
0.824191 + 0.566312i \(0.191630\pi\)
\(360\) 0.920227 0.0485002
\(361\) 6.27551 0.330290
\(362\) −12.2365 −0.643138
\(363\) 32.9601 1.72996
\(364\) 21.8020 1.14273
\(365\) −0.517568 −0.0270908
\(366\) −9.39027 −0.490837
\(367\) 32.6644 1.70507 0.852534 0.522672i \(-0.175065\pi\)
0.852534 + 0.522672i \(0.175065\pi\)
\(368\) −18.3303 −0.955532
\(369\) 0.509283 0.0265122
\(370\) −0.379824 −0.0197461
\(371\) −39.1824 −2.03425
\(372\) 64.3973 3.33885
\(373\) 19.1389 0.990975 0.495487 0.868615i \(-0.334989\pi\)
0.495487 + 0.868615i \(0.334989\pi\)
\(374\) 1.21593 0.0628742
\(375\) −0.977675 −0.0504869
\(376\) −36.6636 −1.89078
\(377\) −5.60977 −0.288918
\(378\) −78.5098 −4.03811
\(379\) 22.0104 1.13060 0.565299 0.824886i \(-0.308761\pi\)
0.565299 + 0.824886i \(0.308761\pi\)
\(380\) 0.633806 0.0325136
\(381\) 9.78306 0.501201
\(382\) −16.2373 −0.830772
\(383\) −12.3848 −0.632833 −0.316416 0.948620i \(-0.602480\pi\)
−0.316416 + 0.948620i \(0.602480\pi\)
\(384\) −61.2832 −3.12735
\(385\) 0.0363476 0.00185245
\(386\) 23.4717 1.19468
\(387\) 11.0050 0.559415
\(388\) −35.0622 −1.78001
\(389\) 16.1516 0.818919 0.409460 0.912328i \(-0.365717\pi\)
0.409460 + 0.912328i \(0.365717\pi\)
\(390\) 0.393111 0.0199060
\(391\) 8.03341 0.406267
\(392\) −20.3222 −1.02642
\(393\) −31.0091 −1.56420
\(394\) −55.0844 −2.77511
\(395\) −0.0702426 −0.00353429
\(396\) 8.01650 0.402844
\(397\) −23.0393 −1.15631 −0.578155 0.815927i \(-0.696227\pi\)
−0.578155 + 0.815927i \(0.696227\pi\)
\(398\) 26.4120 1.32391
\(399\) −51.3725 −2.57184
\(400\) −17.1264 −0.856319
\(401\) −6.98825 −0.348977 −0.174488 0.984659i \(-0.555827\pi\)
−0.174488 + 0.984659i \(0.555827\pi\)
\(402\) 82.1472 4.09713
\(403\) 9.02070 0.449353
\(404\) −74.6253 −3.71275
\(405\) −0.338785 −0.0168343
\(406\) 27.8036 1.37987
\(407\) −1.61318 −0.0799626
\(408\) −21.0103 −1.04016
\(409\) −16.6359 −0.822591 −0.411296 0.911502i \(-0.634924\pi\)
−0.411296 + 0.911502i \(0.634924\pi\)
\(410\) 0.00648593 0.000320317 0
\(411\) 11.5469 0.569566
\(412\) −77.2560 −3.80613
\(413\) 42.9143 2.11168
\(414\) 80.1050 3.93695
\(415\) −0.0288560 −0.00141649
\(416\) −1.52585 −0.0748110
\(417\) −44.9746 −2.20241
\(418\) 4.07138 0.199138
\(419\) 16.2490 0.793815 0.396907 0.917859i \(-0.370083\pi\)
0.396907 + 0.917859i \(0.370083\pi\)
\(420\) −1.28821 −0.0628584
\(421\) −21.2631 −1.03630 −0.518150 0.855290i \(-0.673379\pi\)
−0.518150 + 0.855290i \(0.673379\pi\)
\(422\) −54.5392 −2.65493
\(423\) 48.8736 2.37632
\(424\) −53.6568 −2.60580
\(425\) 7.50578 0.364084
\(426\) 69.4599 3.36534
\(427\) 4.31045 0.208598
\(428\) −3.43663 −0.166116
\(429\) 1.66962 0.0806098
\(430\) 0.140153 0.00675879
\(431\) −12.5978 −0.606814 −0.303407 0.952861i \(-0.598124\pi\)
−0.303407 + 0.952861i \(0.598124\pi\)
\(432\) −32.7949 −1.57784
\(433\) 9.83400 0.472592 0.236296 0.971681i \(-0.424067\pi\)
0.236296 + 0.971681i \(0.424067\pi\)
\(434\) −44.7091 −2.14611
\(435\) 0.331464 0.0158925
\(436\) 39.1461 1.87476
\(437\) 26.8988 1.28674
\(438\) 117.832 5.63024
\(439\) −10.9426 −0.522259 −0.261130 0.965304i \(-0.584095\pi\)
−0.261130 + 0.965304i \(0.584095\pi\)
\(440\) 0.0497748 0.00237292
\(441\) 27.0900 1.29000
\(442\) −6.03660 −0.287132
\(443\) −9.86639 −0.468766 −0.234383 0.972144i \(-0.575307\pi\)
−0.234383 + 0.972144i \(0.575307\pi\)
\(444\) 57.1736 2.71334
\(445\) −0.366766 −0.0173864
\(446\) −23.9591 −1.13450
\(447\) 12.1149 0.573015
\(448\) 30.6934 1.45013
\(449\) 35.9120 1.69479 0.847397 0.530961i \(-0.178169\pi\)
0.847397 + 0.530961i \(0.178169\pi\)
\(450\) 74.8438 3.52817
\(451\) 0.0275470 0.00129714
\(452\) 27.5379 1.29527
\(453\) −14.4062 −0.676864
\(454\) 24.1930 1.13543
\(455\) −0.180451 −0.00845969
\(456\) −70.3501 −3.29445
\(457\) −24.8431 −1.16211 −0.581056 0.813864i \(-0.697360\pi\)
−0.581056 + 0.813864i \(0.697360\pi\)
\(458\) −30.5004 −1.42519
\(459\) 14.3726 0.670858
\(460\) 0.674512 0.0314493
\(461\) 32.2525 1.50215 0.751073 0.660219i \(-0.229536\pi\)
0.751073 + 0.660219i \(0.229536\pi\)
\(462\) −8.27509 −0.384992
\(463\) −10.2424 −0.476005 −0.238002 0.971265i \(-0.576493\pi\)
−0.238002 + 0.971265i \(0.576493\pi\)
\(464\) 11.6140 0.539168
\(465\) −0.533006 −0.0247176
\(466\) 15.1289 0.700830
\(467\) −12.5826 −0.582253 −0.291127 0.956685i \(-0.594030\pi\)
−0.291127 + 0.956685i \(0.594030\pi\)
\(468\) −39.7987 −1.83970
\(469\) −37.7084 −1.74121
\(470\) 0.622426 0.0287104
\(471\) −59.9020 −2.76014
\(472\) 58.7674 2.70499
\(473\) 0.595257 0.0273700
\(474\) 15.9918 0.734528
\(475\) 25.1321 1.15314
\(476\) 19.7817 0.906695
\(477\) 71.5259 3.27495
\(478\) −5.19597 −0.237658
\(479\) −5.02267 −0.229492 −0.114746 0.993395i \(-0.536605\pi\)
−0.114746 + 0.993395i \(0.536605\pi\)
\(480\) 0.0901578 0.00411512
\(481\) 8.00881 0.365170
\(482\) −57.5363 −2.62071
\(483\) −54.6719 −2.48766
\(484\) −42.4967 −1.93167
\(485\) 0.290204 0.0131775
\(486\) 7.35945 0.333831
\(487\) 14.1461 0.641019 0.320510 0.947245i \(-0.396146\pi\)
0.320510 + 0.947245i \(0.396146\pi\)
\(488\) 5.90278 0.267206
\(489\) 20.6442 0.933561
\(490\) 0.345003 0.0155856
\(491\) −2.94129 −0.132739 −0.0663693 0.997795i \(-0.521142\pi\)
−0.0663693 + 0.997795i \(0.521142\pi\)
\(492\) −0.976305 −0.0440152
\(493\) −5.08995 −0.229240
\(494\) −20.2128 −0.909415
\(495\) −0.0663512 −0.00298226
\(496\) −18.6758 −0.838566
\(497\) −31.8844 −1.43021
\(498\) 6.56951 0.294387
\(499\) 26.8514 1.20204 0.601018 0.799236i \(-0.294762\pi\)
0.601018 + 0.799236i \(0.294762\pi\)
\(500\) 1.26055 0.0563737
\(501\) −40.1506 −1.79380
\(502\) 49.5434 2.21123
\(503\) −22.6589 −1.01031 −0.505155 0.863029i \(-0.668565\pi\)
−0.505155 + 0.863029i \(0.668565\pi\)
\(504\) 96.1693 4.28372
\(505\) 0.617661 0.0274856
\(506\) 4.33286 0.192619
\(507\) 31.0613 1.37948
\(508\) −12.6137 −0.559641
\(509\) 4.59675 0.203747 0.101874 0.994797i \(-0.467516\pi\)
0.101874 + 0.994797i \(0.467516\pi\)
\(510\) 0.356684 0.0157942
\(511\) −54.0890 −2.39276
\(512\) 34.8347 1.53949
\(513\) 48.1249 2.12477
\(514\) 74.3796 3.28074
\(515\) 0.639434 0.0281768
\(516\) −21.0968 −0.928734
\(517\) 2.64356 0.116264
\(518\) −39.6939 −1.74405
\(519\) −43.1513 −1.89413
\(520\) −0.247112 −0.0108366
\(521\) −20.6840 −0.906182 −0.453091 0.891464i \(-0.649679\pi\)
−0.453091 + 0.891464i \(0.649679\pi\)
\(522\) −50.7544 −2.22146
\(523\) −33.1967 −1.45159 −0.725794 0.687912i \(-0.758528\pi\)
−0.725794 + 0.687912i \(0.758528\pi\)
\(524\) 39.9812 1.74659
\(525\) −51.0811 −2.22936
\(526\) 59.1225 2.57786
\(527\) 8.18482 0.356536
\(528\) −3.45664 −0.150431
\(529\) 5.62636 0.244624
\(530\) 0.910913 0.0395675
\(531\) −78.3385 −3.39960
\(532\) 66.2366 2.87172
\(533\) −0.136760 −0.00592372
\(534\) 83.4998 3.61339
\(535\) 0.0284444 0.00122976
\(536\) −51.6382 −2.23043
\(537\) −37.1470 −1.60301
\(538\) −29.9467 −1.29109
\(539\) 1.46529 0.0631146
\(540\) 1.20678 0.0519314
\(541\) 32.4624 1.39567 0.697833 0.716261i \(-0.254148\pi\)
0.697833 + 0.716261i \(0.254148\pi\)
\(542\) 33.9125 1.45667
\(543\) −15.2453 −0.654238
\(544\) −1.38446 −0.0593582
\(545\) −0.324006 −0.0138789
\(546\) 41.0825 1.75817
\(547\) 7.64787 0.326999 0.163500 0.986543i \(-0.447722\pi\)
0.163500 + 0.986543i \(0.447722\pi\)
\(548\) −14.8879 −0.635977
\(549\) −7.86857 −0.335822
\(550\) 4.04828 0.172619
\(551\) −17.0430 −0.726058
\(552\) −74.8683 −3.18661
\(553\) −7.34078 −0.312162
\(554\) −4.69241 −0.199361
\(555\) −0.473216 −0.0200869
\(556\) 57.9874 2.45921
\(557\) 11.5304 0.488559 0.244279 0.969705i \(-0.421449\pi\)
0.244279 + 0.969705i \(0.421449\pi\)
\(558\) 81.6148 3.45503
\(559\) −2.95521 −0.124992
\(560\) 0.373592 0.0157872
\(561\) 1.51490 0.0639593
\(562\) −39.9247 −1.68412
\(563\) −15.3958 −0.648858 −0.324429 0.945910i \(-0.605172\pi\)
−0.324429 + 0.945910i \(0.605172\pi\)
\(564\) −93.6917 −3.94513
\(565\) −0.227926 −0.00958894
\(566\) 71.0627 2.98699
\(567\) −35.4050 −1.48687
\(568\) −43.6629 −1.83205
\(569\) −44.9142 −1.88290 −0.941450 0.337153i \(-0.890536\pi\)
−0.941450 + 0.337153i \(0.890536\pi\)
\(570\) 1.19431 0.0500241
\(571\) −13.6202 −0.569988 −0.284994 0.958529i \(-0.591992\pi\)
−0.284994 + 0.958529i \(0.591992\pi\)
\(572\) −2.15270 −0.0900089
\(573\) −20.2298 −0.845110
\(574\) 0.677819 0.0282916
\(575\) 26.7462 1.11539
\(576\) −56.0297 −2.33457
\(577\) 25.4563 1.05976 0.529879 0.848073i \(-0.322237\pi\)
0.529879 + 0.848073i \(0.322237\pi\)
\(578\) 35.8253 1.49013
\(579\) 29.2430 1.21530
\(580\) −0.427370 −0.0177456
\(581\) −3.01563 −0.125109
\(582\) −66.0693 −2.73866
\(583\) 3.86882 0.160230
\(584\) −74.0701 −3.06504
\(585\) 0.329407 0.0136193
\(586\) −23.3903 −0.966242
\(587\) −0.0745162 −0.00307561 −0.00153781 0.999999i \(-0.500489\pi\)
−0.00153781 + 0.999999i \(0.500489\pi\)
\(588\) −51.9321 −2.14164
\(589\) 27.4058 1.12924
\(590\) −0.997674 −0.0410736
\(591\) −68.6287 −2.82301
\(592\) −16.5808 −0.681467
\(593\) 18.1883 0.746903 0.373452 0.927650i \(-0.378174\pi\)
0.373452 + 0.927650i \(0.378174\pi\)
\(594\) 7.75196 0.318067
\(595\) −0.163730 −0.00671228
\(596\) −15.6202 −0.639828
\(597\) 32.9062 1.34676
\(598\) −21.5109 −0.879646
\(599\) 10.8427 0.443021 0.221510 0.975158i \(-0.428901\pi\)
0.221510 + 0.975158i \(0.428901\pi\)
\(600\) −69.9510 −2.85574
\(601\) −10.7179 −0.437193 −0.218597 0.975815i \(-0.570148\pi\)
−0.218597 + 0.975815i \(0.570148\pi\)
\(602\) 14.6469 0.596961
\(603\) 68.8352 2.80318
\(604\) 18.5745 0.755786
\(605\) 0.351738 0.0143002
\(606\) −140.620 −5.71229
\(607\) 40.9798 1.66332 0.831660 0.555285i \(-0.187391\pi\)
0.831660 + 0.555285i \(0.187391\pi\)
\(608\) −4.63568 −0.188002
\(609\) 34.6400 1.40368
\(610\) −0.100210 −0.00405737
\(611\) −13.1242 −0.530949
\(612\) −36.1108 −1.45969
\(613\) −33.5595 −1.35546 −0.677728 0.735313i \(-0.737035\pi\)
−0.677728 + 0.735313i \(0.737035\pi\)
\(614\) −76.3087 −3.07957
\(615\) 0.00808071 0.000325846 0
\(616\) 5.20177 0.209585
\(617\) 37.5593 1.51208 0.756040 0.654526i \(-0.227132\pi\)
0.756040 + 0.654526i \(0.227132\pi\)
\(618\) −145.577 −5.85596
\(619\) 1.00000 0.0401934
\(620\) 0.687225 0.0275996
\(621\) 51.2157 2.05522
\(622\) 24.1285 0.967466
\(623\) −38.3292 −1.53563
\(624\) 17.1608 0.686984
\(625\) 24.9843 0.999374
\(626\) 42.8938 1.71438
\(627\) 5.07246 0.202574
\(628\) 77.2339 3.08197
\(629\) 7.26669 0.289742
\(630\) −1.63263 −0.0650457
\(631\) −33.2887 −1.32520 −0.662601 0.748973i \(-0.730547\pi\)
−0.662601 + 0.748973i \(0.730547\pi\)
\(632\) −10.0525 −0.399869
\(633\) −67.9494 −2.70075
\(634\) 55.7642 2.21468
\(635\) 0.104401 0.00414304
\(636\) −137.117 −5.43702
\(637\) −7.27458 −0.288229
\(638\) −2.74529 −0.108687
\(639\) 58.2038 2.30251
\(640\) −0.653992 −0.0258513
\(641\) −43.8778 −1.73307 −0.866535 0.499116i \(-0.833658\pi\)
−0.866535 + 0.499116i \(0.833658\pi\)
\(642\) −6.47579 −0.255579
\(643\) −16.4937 −0.650448 −0.325224 0.945637i \(-0.605440\pi\)
−0.325224 + 0.945637i \(0.605440\pi\)
\(644\) 70.4906 2.77772
\(645\) 0.174614 0.00687544
\(646\) −18.3398 −0.721569
\(647\) 16.1560 0.635160 0.317580 0.948232i \(-0.397130\pi\)
0.317580 + 0.948232i \(0.397130\pi\)
\(648\) −48.4840 −1.90463
\(649\) −4.23731 −0.166329
\(650\) −20.0981 −0.788312
\(651\) −55.7023 −2.18315
\(652\) −26.6173 −1.04241
\(653\) −14.2100 −0.556079 −0.278039 0.960570i \(-0.589685\pi\)
−0.278039 + 0.960570i \(0.589685\pi\)
\(654\) 73.7648 2.88443
\(655\) −0.330918 −0.0129300
\(656\) 0.283136 0.0110546
\(657\) 98.7374 3.85211
\(658\) 65.0473 2.53581
\(659\) 23.0308 0.897152 0.448576 0.893745i \(-0.351931\pi\)
0.448576 + 0.893745i \(0.351931\pi\)
\(660\) 0.127197 0.00495112
\(661\) −30.3656 −1.18109 −0.590543 0.807006i \(-0.701087\pi\)
−0.590543 + 0.807006i \(0.701087\pi\)
\(662\) −30.7379 −1.19466
\(663\) −7.52089 −0.292087
\(664\) −4.12963 −0.160261
\(665\) −0.548229 −0.0212594
\(666\) 72.4597 2.80776
\(667\) −18.1376 −0.702291
\(668\) 51.7677 2.00295
\(669\) −29.8502 −1.15408
\(670\) 0.876645 0.0338678
\(671\) −0.425609 −0.0164304
\(672\) 9.42204 0.363463
\(673\) −10.7264 −0.413474 −0.206737 0.978397i \(-0.566284\pi\)
−0.206737 + 0.978397i \(0.566284\pi\)
\(674\) −8.04099 −0.309727
\(675\) 47.8519 1.84182
\(676\) −40.0485 −1.54033
\(677\) 39.4288 1.51537 0.757687 0.652618i \(-0.226329\pi\)
0.757687 + 0.652618i \(0.226329\pi\)
\(678\) 51.8909 1.99286
\(679\) 30.3280 1.16388
\(680\) −0.224214 −0.00859821
\(681\) 30.1416 1.15503
\(682\) 4.41452 0.169041
\(683\) 13.3888 0.512308 0.256154 0.966636i \(-0.417545\pi\)
0.256154 + 0.966636i \(0.417545\pi\)
\(684\) −120.912 −4.62320
\(685\) 0.123224 0.00470815
\(686\) −21.3571 −0.815416
\(687\) −38.0000 −1.44979
\(688\) 6.11824 0.233256
\(689\) −19.2071 −0.731733
\(690\) 1.27101 0.0483867
\(691\) −10.3514 −0.393787 −0.196893 0.980425i \(-0.563085\pi\)
−0.196893 + 0.980425i \(0.563085\pi\)
\(692\) 55.6366 2.11499
\(693\) −6.93410 −0.263405
\(694\) −41.6574 −1.58129
\(695\) −0.479952 −0.0182056
\(696\) 47.4364 1.79807
\(697\) −0.124087 −0.00470013
\(698\) 32.9849 1.24850
\(699\) 18.8488 0.712926
\(700\) 65.8609 2.48931
\(701\) 1.46168 0.0552070 0.0276035 0.999619i \(-0.491212\pi\)
0.0276035 + 0.999619i \(0.491212\pi\)
\(702\) −38.4854 −1.45254
\(703\) 24.3315 0.917682
\(704\) −3.03063 −0.114221
\(705\) 0.775470 0.0292059
\(706\) 86.9883 3.27385
\(707\) 64.5493 2.42763
\(708\) 150.176 5.64397
\(709\) −2.10668 −0.0791180 −0.0395590 0.999217i \(-0.512595\pi\)
−0.0395590 + 0.999217i \(0.512595\pi\)
\(710\) 0.741250 0.0278186
\(711\) 13.4003 0.502551
\(712\) −52.4885 −1.96709
\(713\) 29.1659 1.09227
\(714\) 37.2756 1.39501
\(715\) 0.0178175 0.000666338 0
\(716\) 47.8950 1.78992
\(717\) −6.47356 −0.241760
\(718\) −75.8809 −2.83185
\(719\) −21.1806 −0.789903 −0.394952 0.918702i \(-0.629239\pi\)
−0.394952 + 0.918702i \(0.629239\pi\)
\(720\) −0.681978 −0.0254158
\(721\) 66.8248 2.48868
\(722\) −15.2467 −0.567424
\(723\) −71.6835 −2.66594
\(724\) 19.6563 0.730522
\(725\) −16.9464 −0.629372
\(726\) −80.0785 −2.97199
\(727\) 39.1371 1.45151 0.725757 0.687951i \(-0.241489\pi\)
0.725757 + 0.687951i \(0.241489\pi\)
\(728\) −25.8247 −0.957127
\(729\) −22.2947 −0.825729
\(730\) 1.25746 0.0465408
\(731\) −2.68137 −0.0991742
\(732\) 15.0842 0.557528
\(733\) −19.7887 −0.730914 −0.365457 0.930828i \(-0.619087\pi\)
−0.365457 + 0.930828i \(0.619087\pi\)
\(734\) −79.3601 −2.92923
\(735\) 0.429833 0.0158546
\(736\) −4.93341 −0.181848
\(737\) 3.72328 0.137149
\(738\) −1.23733 −0.0455468
\(739\) 34.3551 1.26377 0.631886 0.775061i \(-0.282281\pi\)
0.631886 + 0.775061i \(0.282281\pi\)
\(740\) 0.610136 0.0224290
\(741\) −25.1827 −0.925110
\(742\) 95.1959 3.49475
\(743\) 8.25712 0.302924 0.151462 0.988463i \(-0.451602\pi\)
0.151462 + 0.988463i \(0.451602\pi\)
\(744\) −76.2794 −2.79654
\(745\) 0.129286 0.00473666
\(746\) −46.4991 −1.70245
\(747\) 5.50491 0.201414
\(748\) −1.95322 −0.0714170
\(749\) 2.97261 0.108617
\(750\) 2.37532 0.0867344
\(751\) 12.9342 0.471975 0.235988 0.971756i \(-0.424167\pi\)
0.235988 + 0.971756i \(0.424167\pi\)
\(752\) 27.1713 0.990837
\(753\) 61.7252 2.24939
\(754\) 13.6293 0.496349
\(755\) −0.153738 −0.00559510
\(756\) 126.115 4.58677
\(757\) −9.35561 −0.340035 −0.170018 0.985441i \(-0.554382\pi\)
−0.170018 + 0.985441i \(0.554382\pi\)
\(758\) −53.4756 −1.94232
\(759\) 5.39823 0.195943
\(760\) −0.750750 −0.0272326
\(761\) −33.5186 −1.21505 −0.607524 0.794301i \(-0.707837\pi\)
−0.607524 + 0.794301i \(0.707837\pi\)
\(762\) −23.7685 −0.861042
\(763\) −33.8606 −1.22583
\(764\) 26.0830 0.943650
\(765\) 0.298883 0.0108061
\(766\) 30.0896 1.08718
\(767\) 21.0365 0.759585
\(768\) 93.8480 3.38645
\(769\) −11.1247 −0.401166 −0.200583 0.979677i \(-0.564284\pi\)
−0.200583 + 0.979677i \(0.564284\pi\)
\(770\) −0.0883087 −0.00318242
\(771\) 92.6682 3.33737
\(772\) −37.7041 −1.35700
\(773\) 16.8751 0.606953 0.303477 0.952839i \(-0.401853\pi\)
0.303477 + 0.952839i \(0.401853\pi\)
\(774\) −26.7373 −0.961052
\(775\) 27.2503 0.978860
\(776\) 41.5316 1.49090
\(777\) −49.4539 −1.77415
\(778\) −39.2413 −1.40687
\(779\) −0.415489 −0.0148864
\(780\) −0.631480 −0.0226106
\(781\) 3.14823 0.112652
\(782\) −19.5176 −0.697949
\(783\) −32.4502 −1.15967
\(784\) 15.0607 0.537883
\(785\) −0.639252 −0.0228159
\(786\) 75.3385 2.68723
\(787\) 10.5636 0.376553 0.188277 0.982116i \(-0.439710\pi\)
0.188277 + 0.982116i \(0.439710\pi\)
\(788\) 88.4856 3.15217
\(789\) 73.6596 2.62235
\(790\) 0.170659 0.00607176
\(791\) −23.8197 −0.846930
\(792\) −9.49563 −0.337413
\(793\) 2.11298 0.0750340
\(794\) 55.9753 1.98649
\(795\) 1.13489 0.0402504
\(796\) −42.4273 −1.50380
\(797\) 27.0776 0.959137 0.479568 0.877504i \(-0.340793\pi\)
0.479568 + 0.877504i \(0.340793\pi\)
\(798\) 124.813 4.41832
\(799\) −11.9081 −0.421278
\(800\) −4.60939 −0.162966
\(801\) 69.9685 2.47222
\(802\) 16.9784 0.599527
\(803\) 5.34068 0.188469
\(804\) −131.958 −4.65381
\(805\) −0.583438 −0.0205635
\(806\) −21.9163 −0.771970
\(807\) −37.3100 −1.31338
\(808\) 88.3945 3.10971
\(809\) 5.49991 0.193367 0.0966833 0.995315i \(-0.469177\pi\)
0.0966833 + 0.995315i \(0.469177\pi\)
\(810\) 0.823097 0.0289207
\(811\) 40.2347 1.41283 0.706415 0.707798i \(-0.250311\pi\)
0.706415 + 0.707798i \(0.250311\pi\)
\(812\) −44.6627 −1.56735
\(813\) 42.2510 1.48181
\(814\) 3.91933 0.137372
\(815\) 0.220307 0.00771701
\(816\) 15.5707 0.545082
\(817\) −8.97822 −0.314108
\(818\) 40.4179 1.41318
\(819\) 34.4250 1.20291
\(820\) −0.0104188 −0.000363839 0
\(821\) 22.0387 0.769157 0.384579 0.923092i \(-0.374347\pi\)
0.384579 + 0.923092i \(0.374347\pi\)
\(822\) −28.0539 −0.978490
\(823\) 1.67762 0.0584781 0.0292390 0.999572i \(-0.490692\pi\)
0.0292390 + 0.999572i \(0.490692\pi\)
\(824\) 91.5105 3.18792
\(825\) 5.04368 0.175599
\(826\) −104.263 −3.62777
\(827\) −3.15787 −0.109810 −0.0549049 0.998492i \(-0.517486\pi\)
−0.0549049 + 0.998492i \(0.517486\pi\)
\(828\) −128.678 −4.47186
\(829\) 24.1320 0.838138 0.419069 0.907954i \(-0.362357\pi\)
0.419069 + 0.907954i \(0.362357\pi\)
\(830\) 0.0701074 0.00243346
\(831\) −5.84619 −0.202802
\(832\) 15.0459 0.521622
\(833\) −6.60050 −0.228694
\(834\) 109.268 3.78365
\(835\) −0.428472 −0.0148279
\(836\) −6.54011 −0.226195
\(837\) 52.1810 1.80364
\(838\) −39.4778 −1.36374
\(839\) −54.9414 −1.89679 −0.948394 0.317095i \(-0.897293\pi\)
−0.948394 + 0.317095i \(0.897293\pi\)
\(840\) 1.52590 0.0526486
\(841\) −17.5080 −0.603726
\(842\) 51.6599 1.78032
\(843\) −49.7414 −1.71319
\(844\) 87.6098 3.01565
\(845\) 0.331475 0.0114031
\(846\) −118.741 −4.08241
\(847\) 36.7587 1.26304
\(848\) 39.7649 1.36553
\(849\) 88.5357 3.03854
\(850\) −18.2357 −0.625481
\(851\) 25.8942 0.887642
\(852\) −111.578 −3.82259
\(853\) −50.7022 −1.73601 −0.868006 0.496554i \(-0.834598\pi\)
−0.868006 + 0.496554i \(0.834598\pi\)
\(854\) −10.4725 −0.358362
\(855\) 1.00077 0.0342256
\(856\) 4.07072 0.139134
\(857\) 50.1517 1.71315 0.856575 0.516023i \(-0.172588\pi\)
0.856575 + 0.516023i \(0.172588\pi\)
\(858\) −4.05643 −0.138484
\(859\) −31.2237 −1.06534 −0.532669 0.846324i \(-0.678811\pi\)
−0.532669 + 0.846324i \(0.678811\pi\)
\(860\) −0.225137 −0.00767711
\(861\) 0.844483 0.0287799
\(862\) 30.6071 1.04248
\(863\) 55.4201 1.88652 0.943261 0.332053i \(-0.107741\pi\)
0.943261 + 0.332053i \(0.107741\pi\)
\(864\) −8.82641 −0.300280
\(865\) −0.460495 −0.0156573
\(866\) −23.8923 −0.811893
\(867\) 44.6341 1.51585
\(868\) 71.8191 2.43770
\(869\) 0.724819 0.0245878
\(870\) −0.805312 −0.0273026
\(871\) −18.4846 −0.626326
\(872\) −46.3690 −1.57025
\(873\) −55.3627 −1.87374
\(874\) −65.3522 −2.21057
\(875\) −1.09035 −0.0368606
\(876\) −189.282 −6.39523
\(877\) −49.2248 −1.66220 −0.831102 0.556120i \(-0.812289\pi\)
−0.831102 + 0.556120i \(0.812289\pi\)
\(878\) 26.5856 0.897220
\(879\) −29.1415 −0.982918
\(880\) −0.0368880 −0.00124350
\(881\) 14.1734 0.477515 0.238758 0.971079i \(-0.423260\pi\)
0.238758 + 0.971079i \(0.423260\pi\)
\(882\) −65.8168 −2.21617
\(883\) −44.5572 −1.49947 −0.749734 0.661739i \(-0.769819\pi\)
−0.749734 + 0.661739i \(0.769819\pi\)
\(884\) 9.69697 0.326145
\(885\) −1.24298 −0.0417824
\(886\) 23.9710 0.805321
\(887\) 43.2413 1.45190 0.725950 0.687748i \(-0.241401\pi\)
0.725950 + 0.687748i \(0.241401\pi\)
\(888\) −67.7228 −2.27263
\(889\) 10.9106 0.365928
\(890\) 0.891079 0.0298690
\(891\) 3.49585 0.117115
\(892\) 38.4870 1.28864
\(893\) −39.8726 −1.33429
\(894\) −29.4338 −0.984415
\(895\) −0.396419 −0.0132508
\(896\) −68.3461 −2.28328
\(897\) −26.8001 −0.894828
\(898\) −87.2504 −2.91158
\(899\) −18.4795 −0.616324
\(900\) −120.226 −4.00755
\(901\) −17.4273 −0.580588
\(902\) −0.0669270 −0.00222842
\(903\) 18.2483 0.607264
\(904\) −32.6189 −1.08489
\(905\) −0.162692 −0.00540807
\(906\) 35.0008 1.16282
\(907\) 0.447171 0.0148481 0.00742403 0.999972i \(-0.497637\pi\)
0.00742403 + 0.999972i \(0.497637\pi\)
\(908\) −38.8627 −1.28971
\(909\) −117.832 −3.90825
\(910\) 0.438417 0.0145334
\(911\) 10.6948 0.354335 0.177167 0.984181i \(-0.443307\pi\)
0.177167 + 0.984181i \(0.443307\pi\)
\(912\) 52.1363 1.72641
\(913\) 0.297759 0.00985439
\(914\) 60.3578 1.99646
\(915\) −0.124849 −0.00412739
\(916\) 48.9948 1.61883
\(917\) −34.5829 −1.14203
\(918\) −34.9192 −1.15251
\(919\) 30.0350 0.990762 0.495381 0.868676i \(-0.335028\pi\)
0.495381 + 0.868676i \(0.335028\pi\)
\(920\) −0.798967 −0.0263412
\(921\) −95.0716 −3.13272
\(922\) −78.3592 −2.58062
\(923\) −15.6297 −0.514458
\(924\) 13.2928 0.437301
\(925\) 24.1935 0.795478
\(926\) 24.8845 0.817756
\(927\) −121.986 −4.00655
\(928\) 3.12580 0.102609
\(929\) 57.2823 1.87937 0.939686 0.342038i \(-0.111117\pi\)
0.939686 + 0.342038i \(0.111117\pi\)
\(930\) 1.29497 0.0424637
\(931\) −22.1009 −0.724327
\(932\) −24.3024 −0.796053
\(933\) 30.0613 0.984163
\(934\) 30.5702 1.00029
\(935\) 0.0161665 0.000528701 0
\(936\) 47.1420 1.54088
\(937\) 1.22719 0.0400907 0.0200453 0.999799i \(-0.493619\pi\)
0.0200453 + 0.999799i \(0.493619\pi\)
\(938\) 91.6147 2.99133
\(939\) 53.4406 1.74397
\(940\) −0.999843 −0.0326113
\(941\) −38.6797 −1.26092 −0.630460 0.776221i \(-0.717134\pi\)
−0.630460 + 0.776221i \(0.717134\pi\)
\(942\) 145.535 4.74180
\(943\) −0.442173 −0.0143991
\(944\) −43.5524 −1.41751
\(945\) −1.04384 −0.0339560
\(946\) −1.44621 −0.0470204
\(947\) 26.2148 0.851867 0.425934 0.904754i \(-0.359946\pi\)
0.425934 + 0.904754i \(0.359946\pi\)
\(948\) −25.6887 −0.834329
\(949\) −26.5143 −0.860692
\(950\) −61.0600 −1.98105
\(951\) 69.4757 2.25290
\(952\) −23.4317 −0.759426
\(953\) −0.823051 −0.0266613 −0.0133306 0.999911i \(-0.504243\pi\)
−0.0133306 + 0.999911i \(0.504243\pi\)
\(954\) −173.776 −5.62622
\(955\) −0.215884 −0.00698586
\(956\) 8.34661 0.269949
\(957\) −3.42031 −0.110563
\(958\) 12.2029 0.394257
\(959\) 12.8777 0.415842
\(960\) −0.889014 −0.0286928
\(961\) −1.28441 −0.0414325
\(962\) −19.4579 −0.627347
\(963\) −5.42638 −0.174863
\(964\) 92.4242 2.97678
\(965\) 0.312071 0.0100459
\(966\) 132.829 4.27369
\(967\) −12.7952 −0.411466 −0.205733 0.978608i \(-0.565958\pi\)
−0.205733 + 0.978608i \(0.565958\pi\)
\(968\) 50.3378 1.61792
\(969\) −22.8492 −0.734022
\(970\) −0.705067 −0.0226383
\(971\) −25.3492 −0.813494 −0.406747 0.913541i \(-0.633337\pi\)
−0.406747 + 0.913541i \(0.633337\pi\)
\(972\) −11.8220 −0.379189
\(973\) −50.1579 −1.60799
\(974\) −34.3687 −1.10124
\(975\) −25.0399 −0.801917
\(976\) −4.37454 −0.140026
\(977\) 15.0049 0.480050 0.240025 0.970767i \(-0.422844\pi\)
0.240025 + 0.970767i \(0.422844\pi\)
\(978\) −50.1562 −1.60382
\(979\) 3.78458 0.120956
\(980\) −0.554200 −0.0177033
\(981\) 61.8112 1.97348
\(982\) 7.14604 0.228039
\(983\) −12.4298 −0.396451 −0.198225 0.980156i \(-0.563518\pi\)
−0.198225 + 0.980156i \(0.563518\pi\)
\(984\) 1.15644 0.0368661
\(985\) −0.732380 −0.0233356
\(986\) 12.3663 0.393824
\(987\) 81.0413 2.57957
\(988\) 32.4690 1.03298
\(989\) −9.55484 −0.303826
\(990\) 0.161204 0.00512340
\(991\) −26.4538 −0.840331 −0.420166 0.907447i \(-0.638028\pi\)
−0.420166 + 0.907447i \(0.638028\pi\)
\(992\) −5.02639 −0.159588
\(993\) −38.2958 −1.21528
\(994\) 77.4651 2.45704
\(995\) 0.351163 0.0111326
\(996\) −10.5530 −0.334385
\(997\) −33.4142 −1.05824 −0.529119 0.848547i \(-0.677478\pi\)
−0.529119 + 0.848547i \(0.677478\pi\)
\(998\) −65.2371 −2.06505
\(999\) 46.3276 1.46574
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 \(a_p\))