Properties

Label 5077.2.a.c.1.2
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.71481 q^{2} +1.77107 q^{3} +5.37017 q^{4} +1.86347 q^{5} -4.80810 q^{6} +4.83883 q^{7} -9.14936 q^{8} +0.136673 q^{9} +O(q^{10})\) \(q-2.71481 q^{2} +1.77107 q^{3} +5.37017 q^{4} +1.86347 q^{5} -4.80810 q^{6} +4.83883 q^{7} -9.14936 q^{8} +0.136673 q^{9} -5.05896 q^{10} +3.13265 q^{11} +9.51093 q^{12} +1.94787 q^{13} -13.1365 q^{14} +3.30033 q^{15} +14.0984 q^{16} +5.73713 q^{17} -0.371041 q^{18} -6.55967 q^{19} +10.0072 q^{20} +8.56989 q^{21} -8.50453 q^{22} +0.545186 q^{23} -16.2041 q^{24} -1.52747 q^{25} -5.28810 q^{26} -5.07114 q^{27} +25.9854 q^{28} +5.56086 q^{29} -8.95976 q^{30} +1.85084 q^{31} -19.9757 q^{32} +5.54813 q^{33} -15.5752 q^{34} +9.01703 q^{35} +0.733958 q^{36} +1.35875 q^{37} +17.8082 q^{38} +3.44981 q^{39} -17.0496 q^{40} +6.54345 q^{41} -23.2656 q^{42} -9.17990 q^{43} +16.8229 q^{44} +0.254686 q^{45} -1.48007 q^{46} +7.16793 q^{47} +24.9692 q^{48} +16.4143 q^{49} +4.14679 q^{50} +10.1608 q^{51} +10.4604 q^{52} -7.86968 q^{53} +13.7672 q^{54} +5.83760 q^{55} -44.2722 q^{56} -11.6176 q^{57} -15.0967 q^{58} +1.74437 q^{59} +17.7233 q^{60} -7.92126 q^{61} -5.02468 q^{62} +0.661338 q^{63} +26.0334 q^{64} +3.62981 q^{65} -15.0621 q^{66} +4.79617 q^{67} +30.8094 q^{68} +0.965559 q^{69} -24.4795 q^{70} -7.79224 q^{71} -1.25047 q^{72} -12.2852 q^{73} -3.68875 q^{74} -2.70526 q^{75} -35.2265 q^{76} +15.1584 q^{77} -9.36557 q^{78} +4.36881 q^{79} +26.2720 q^{80} -9.39134 q^{81} -17.7642 q^{82} +0.938894 q^{83} +46.0218 q^{84} +10.6910 q^{85} +24.9216 q^{86} +9.84864 q^{87} -28.6617 q^{88} -0.422521 q^{89} -0.691424 q^{90} +9.42544 q^{91} +2.92774 q^{92} +3.27796 q^{93} -19.4595 q^{94} -12.2238 q^{95} -35.3783 q^{96} -2.43594 q^{97} -44.5617 q^{98} +0.428149 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71481 −1.91966 −0.959829 0.280586i \(-0.909471\pi\)
−0.959829 + 0.280586i \(0.909471\pi\)
\(3\) 1.77107 1.02253 0.511263 0.859425i \(-0.329178\pi\)
0.511263 + 0.859425i \(0.329178\pi\)
\(4\) 5.37017 2.68509
\(5\) 1.86347 0.833370 0.416685 0.909051i \(-0.363192\pi\)
0.416685 + 0.909051i \(0.363192\pi\)
\(6\) −4.80810 −1.96290
\(7\) 4.83883 1.82891 0.914454 0.404691i \(-0.132621\pi\)
0.914454 + 0.404691i \(0.132621\pi\)
\(8\) −9.14936 −3.23479
\(9\) 0.136673 0.0455577
\(10\) −5.05896 −1.59978
\(11\) 3.13265 0.944529 0.472264 0.881457i \(-0.343437\pi\)
0.472264 + 0.881457i \(0.343437\pi\)
\(12\) 9.51093 2.74557
\(13\) 1.94787 0.540243 0.270122 0.962826i \(-0.412936\pi\)
0.270122 + 0.962826i \(0.412936\pi\)
\(14\) −13.1365 −3.51088
\(15\) 3.30033 0.852142
\(16\) 14.0984 3.52460
\(17\) 5.73713 1.39146 0.695729 0.718304i \(-0.255081\pi\)
0.695729 + 0.718304i \(0.255081\pi\)
\(18\) −0.371041 −0.0874552
\(19\) −6.55967 −1.50489 −0.752445 0.658655i \(-0.771126\pi\)
−0.752445 + 0.658655i \(0.771126\pi\)
\(20\) 10.0072 2.23767
\(21\) 8.56989 1.87010
\(22\) −8.50453 −1.81317
\(23\) 0.545186 0.113679 0.0568395 0.998383i \(-0.481898\pi\)
0.0568395 + 0.998383i \(0.481898\pi\)
\(24\) −16.2041 −3.30765
\(25\) −1.52747 −0.305495
\(26\) −5.28810 −1.03708
\(27\) −5.07114 −0.975941
\(28\) 25.9854 4.91077
\(29\) 5.56086 1.03263 0.516313 0.856400i \(-0.327304\pi\)
0.516313 + 0.856400i \(0.327304\pi\)
\(30\) −8.95976 −1.63582
\(31\) 1.85084 0.332421 0.166211 0.986090i \(-0.446847\pi\)
0.166211 + 0.986090i \(0.446847\pi\)
\(32\) −19.9757 −3.53124
\(33\) 5.54813 0.965805
\(34\) −15.5752 −2.67112
\(35\) 9.01703 1.52416
\(36\) 0.733958 0.122326
\(37\) 1.35875 0.223378 0.111689 0.993743i \(-0.464374\pi\)
0.111689 + 0.993743i \(0.464374\pi\)
\(38\) 17.8082 2.88887
\(39\) 3.44981 0.552412
\(40\) −17.0496 −2.69578
\(41\) 6.54345 1.02191 0.510957 0.859606i \(-0.329291\pi\)
0.510957 + 0.859606i \(0.329291\pi\)
\(42\) −23.2656 −3.58996
\(43\) −9.17990 −1.39992 −0.699961 0.714181i \(-0.746799\pi\)
−0.699961 + 0.714181i \(0.746799\pi\)
\(44\) 16.8229 2.53614
\(45\) 0.254686 0.0379664
\(46\) −1.48007 −0.218225
\(47\) 7.16793 1.04555 0.522775 0.852471i \(-0.324897\pi\)
0.522775 + 0.852471i \(0.324897\pi\)
\(48\) 24.9692 3.60399
\(49\) 16.4143 2.34490
\(50\) 4.14679 0.586445
\(51\) 10.1608 1.42280
\(52\) 10.4604 1.45060
\(53\) −7.86968 −1.08098 −0.540492 0.841349i \(-0.681762\pi\)
−0.540492 + 0.841349i \(0.681762\pi\)
\(54\) 13.7672 1.87347
\(55\) 5.83760 0.787142
\(56\) −44.2722 −5.91613
\(57\) −11.6176 −1.53879
\(58\) −15.0967 −1.98229
\(59\) 1.74437 0.227097 0.113549 0.993532i \(-0.463778\pi\)
0.113549 + 0.993532i \(0.463778\pi\)
\(60\) 17.7233 2.28807
\(61\) −7.92126 −1.01421 −0.507107 0.861883i \(-0.669285\pi\)
−0.507107 + 0.861883i \(0.669285\pi\)
\(62\) −5.02468 −0.638135
\(63\) 0.661338 0.0833208
\(64\) 26.0334 3.25417
\(65\) 3.62981 0.450222
\(66\) −15.0621 −1.85401
\(67\) 4.79617 0.585946 0.292973 0.956121i \(-0.405355\pi\)
0.292973 + 0.956121i \(0.405355\pi\)
\(68\) 30.8094 3.73619
\(69\) 0.965559 0.116240
\(70\) −24.4795 −2.92586
\(71\) −7.79224 −0.924769 −0.462384 0.886680i \(-0.653006\pi\)
−0.462384 + 0.886680i \(0.653006\pi\)
\(72\) −1.25047 −0.147370
\(73\) −12.2852 −1.43787 −0.718936 0.695076i \(-0.755371\pi\)
−0.718936 + 0.695076i \(0.755371\pi\)
\(74\) −3.68875 −0.428809
\(75\) −2.70526 −0.312376
\(76\) −35.2265 −4.04076
\(77\) 15.1584 1.72746
\(78\) −9.36557 −1.06044
\(79\) 4.36881 0.491530 0.245765 0.969329i \(-0.420961\pi\)
0.245765 + 0.969329i \(0.420961\pi\)
\(80\) 26.2720 2.93730
\(81\) −9.39134 −1.04348
\(82\) −17.7642 −1.96173
\(83\) 0.938894 0.103057 0.0515285 0.998672i \(-0.483591\pi\)
0.0515285 + 0.998672i \(0.483591\pi\)
\(84\) 46.0218 5.02139
\(85\) 10.6910 1.15960
\(86\) 24.9216 2.68737
\(87\) 9.84864 1.05589
\(88\) −28.6617 −3.05535
\(89\) −0.422521 −0.0447871 −0.0223936 0.999749i \(-0.507129\pi\)
−0.0223936 + 0.999749i \(0.507129\pi\)
\(90\) −0.691424 −0.0728825
\(91\) 9.42544 0.988054
\(92\) 2.92774 0.305238
\(93\) 3.27796 0.339909
\(94\) −19.4595 −2.00710
\(95\) −12.2238 −1.25413
\(96\) −35.3783 −3.61078
\(97\) −2.43594 −0.247332 −0.123666 0.992324i \(-0.539465\pi\)
−0.123666 + 0.992324i \(0.539465\pi\)
\(98\) −44.5617 −4.50141
\(99\) 0.428149 0.0430306
\(100\) −8.20280 −0.820280
\(101\) 4.50717 0.448480 0.224240 0.974534i \(-0.428010\pi\)
0.224240 + 0.974534i \(0.428010\pi\)
\(102\) −27.5847 −2.73129
\(103\) 10.8445 1.06854 0.534268 0.845315i \(-0.320587\pi\)
0.534268 + 0.845315i \(0.320587\pi\)
\(104\) −17.8218 −1.74757
\(105\) 15.9697 1.55849
\(106\) 21.3646 2.07512
\(107\) 1.06109 0.102580 0.0512899 0.998684i \(-0.483667\pi\)
0.0512899 + 0.998684i \(0.483667\pi\)
\(108\) −27.2329 −2.62049
\(109\) 3.14990 0.301706 0.150853 0.988556i \(-0.451798\pi\)
0.150853 + 0.988556i \(0.451798\pi\)
\(110\) −15.8480 −1.51104
\(111\) 2.40644 0.228409
\(112\) 68.2198 6.44617
\(113\) 14.9772 1.40894 0.704469 0.709735i \(-0.251185\pi\)
0.704469 + 0.709735i \(0.251185\pi\)
\(114\) 31.5395 2.95395
\(115\) 1.01594 0.0947367
\(116\) 29.8628 2.77269
\(117\) 0.266222 0.0246122
\(118\) −4.73562 −0.435949
\(119\) 27.7610 2.54485
\(120\) −30.1959 −2.75650
\(121\) −1.18652 −0.107865
\(122\) 21.5047 1.94694
\(123\) 11.5889 1.04493
\(124\) 9.93934 0.892579
\(125\) −12.1638 −1.08796
\(126\) −1.79541 −0.159947
\(127\) 20.5485 1.82338 0.911692 0.410874i \(-0.134776\pi\)
0.911692 + 0.410874i \(0.134776\pi\)
\(128\) −30.7241 −2.71565
\(129\) −16.2582 −1.43145
\(130\) −9.85423 −0.864273
\(131\) 13.2404 1.15682 0.578411 0.815746i \(-0.303673\pi\)
0.578411 + 0.815746i \(0.303673\pi\)
\(132\) 29.7944 2.59327
\(133\) −31.7411 −2.75231
\(134\) −13.0207 −1.12482
\(135\) −9.44992 −0.813320
\(136\) −52.4911 −4.50107
\(137\) −6.65916 −0.568930 −0.284465 0.958686i \(-0.591816\pi\)
−0.284465 + 0.958686i \(0.591816\pi\)
\(138\) −2.62131 −0.223140
\(139\) −17.0027 −1.44215 −0.721076 0.692856i \(-0.756352\pi\)
−0.721076 + 0.692856i \(0.756352\pi\)
\(140\) 48.4230 4.09249
\(141\) 12.6949 1.06910
\(142\) 21.1544 1.77524
\(143\) 6.10200 0.510275
\(144\) 1.92687 0.160573
\(145\) 10.3625 0.860559
\(146\) 33.3519 2.76022
\(147\) 29.0708 2.39772
\(148\) 7.29674 0.599788
\(149\) 11.8891 0.973993 0.486996 0.873404i \(-0.338093\pi\)
0.486996 + 0.873404i \(0.338093\pi\)
\(150\) 7.34424 0.599655
\(151\) 6.92064 0.563193 0.281597 0.959533i \(-0.409136\pi\)
0.281597 + 0.959533i \(0.409136\pi\)
\(152\) 60.0168 4.86800
\(153\) 0.784111 0.0633916
\(154\) −41.1520 −3.31612
\(155\) 3.44899 0.277030
\(156\) 18.5261 1.48327
\(157\) −1.24263 −0.0991730 −0.0495865 0.998770i \(-0.515790\pi\)
−0.0495865 + 0.998770i \(0.515790\pi\)
\(158\) −11.8605 −0.943569
\(159\) −13.9377 −1.10533
\(160\) −37.2242 −2.94283
\(161\) 2.63806 0.207908
\(162\) 25.4957 2.00313
\(163\) −10.0515 −0.787292 −0.393646 0.919262i \(-0.628786\pi\)
−0.393646 + 0.919262i \(0.628786\pi\)
\(164\) 35.1394 2.74393
\(165\) 10.3388 0.804872
\(166\) −2.54892 −0.197834
\(167\) 3.29704 0.255133 0.127566 0.991830i \(-0.459283\pi\)
0.127566 + 0.991830i \(0.459283\pi\)
\(168\) −78.4090 −6.04939
\(169\) −9.20579 −0.708137
\(170\) −29.0239 −2.22603
\(171\) −0.896530 −0.0685594
\(172\) −49.2976 −3.75891
\(173\) 17.9537 1.36500 0.682499 0.730887i \(-0.260893\pi\)
0.682499 + 0.730887i \(0.260893\pi\)
\(174\) −26.7372 −2.02694
\(175\) −7.39119 −0.558721
\(176\) 44.1653 3.32909
\(177\) 3.08939 0.232213
\(178\) 1.14706 0.0859760
\(179\) 19.2278 1.43715 0.718576 0.695449i \(-0.244794\pi\)
0.718576 + 0.695449i \(0.244794\pi\)
\(180\) 1.36771 0.101943
\(181\) 9.25669 0.688045 0.344022 0.938961i \(-0.388210\pi\)
0.344022 + 0.938961i \(0.388210\pi\)
\(182\) −25.5882 −1.89673
\(183\) −14.0291 −1.03706
\(184\) −4.98810 −0.367728
\(185\) 2.53200 0.186156
\(186\) −8.89904 −0.652509
\(187\) 17.9724 1.31427
\(188\) 38.4930 2.80739
\(189\) −24.5384 −1.78491
\(190\) 33.1851 2.40750
\(191\) −6.85279 −0.495850 −0.247925 0.968779i \(-0.579749\pi\)
−0.247925 + 0.968779i \(0.579749\pi\)
\(192\) 46.1068 3.32747
\(193\) 6.25790 0.450453 0.225227 0.974306i \(-0.427688\pi\)
0.225227 + 0.974306i \(0.427688\pi\)
\(194\) 6.61310 0.474793
\(195\) 6.42863 0.460364
\(196\) 88.1477 6.29626
\(197\) −1.69869 −0.121027 −0.0605133 0.998167i \(-0.519274\pi\)
−0.0605133 + 0.998167i \(0.519274\pi\)
\(198\) −1.16234 −0.0826040
\(199\) 13.4152 0.950981 0.475491 0.879721i \(-0.342271\pi\)
0.475491 + 0.879721i \(0.342271\pi\)
\(200\) 13.9754 0.988211
\(201\) 8.49434 0.599144
\(202\) −12.2361 −0.860928
\(203\) 26.9081 1.88858
\(204\) 54.5654 3.82034
\(205\) 12.1935 0.851633
\(206\) −29.4406 −2.05122
\(207\) 0.0745122 0.00517896
\(208\) 27.4619 1.90414
\(209\) −20.5491 −1.42141
\(210\) −43.3548 −2.99176
\(211\) −23.2703 −1.60200 −0.800998 0.598667i \(-0.795697\pi\)
−0.800998 + 0.598667i \(0.795697\pi\)
\(212\) −42.2615 −2.90253
\(213\) −13.8006 −0.945599
\(214\) −2.88066 −0.196918
\(215\) −17.1065 −1.16665
\(216\) 46.3977 3.15696
\(217\) 8.95592 0.607967
\(218\) −8.55137 −0.579172
\(219\) −21.7579 −1.47026
\(220\) 31.3489 2.11354
\(221\) 11.1752 0.751726
\(222\) −6.53302 −0.438468
\(223\) −19.5494 −1.30912 −0.654561 0.756009i \(-0.727147\pi\)
−0.654561 + 0.756009i \(0.727147\pi\)
\(224\) −96.6591 −6.45831
\(225\) −0.208765 −0.0139176
\(226\) −40.6602 −2.70468
\(227\) −21.6602 −1.43764 −0.718819 0.695197i \(-0.755317\pi\)
−0.718819 + 0.695197i \(0.755317\pi\)
\(228\) −62.3885 −4.13178
\(229\) −11.2409 −0.742821 −0.371410 0.928469i \(-0.621126\pi\)
−0.371410 + 0.928469i \(0.621126\pi\)
\(230\) −2.75807 −0.181862
\(231\) 26.8465 1.76637
\(232\) −50.8783 −3.34032
\(233\) −29.0867 −1.90553 −0.952767 0.303702i \(-0.901777\pi\)
−0.952767 + 0.303702i \(0.901777\pi\)
\(234\) −0.722741 −0.0472471
\(235\) 13.3572 0.871329
\(236\) 9.36756 0.609776
\(237\) 7.73745 0.502602
\(238\) −75.3658 −4.88524
\(239\) −25.8779 −1.67390 −0.836950 0.547279i \(-0.815664\pi\)
−0.836950 + 0.547279i \(0.815664\pi\)
\(240\) 46.5294 3.00346
\(241\) −17.4017 −1.12094 −0.560470 0.828175i \(-0.689380\pi\)
−0.560470 + 0.828175i \(0.689380\pi\)
\(242\) 3.22116 0.207064
\(243\) −1.41926 −0.0910455
\(244\) −42.5386 −2.72325
\(245\) 30.5876 1.95417
\(246\) −31.4615 −2.00591
\(247\) −12.7774 −0.813007
\(248\) −16.9340 −1.07531
\(249\) 1.66284 0.105378
\(250\) 33.0223 2.08851
\(251\) 18.8223 1.18805 0.594027 0.804445i \(-0.297537\pi\)
0.594027 + 0.804445i \(0.297537\pi\)
\(252\) 3.55150 0.223724
\(253\) 1.70787 0.107373
\(254\) −55.7852 −3.50027
\(255\) 18.9344 1.18572
\(256\) 31.3433 1.95895
\(257\) −8.80268 −0.549096 −0.274548 0.961573i \(-0.588528\pi\)
−0.274548 + 0.961573i \(0.588528\pi\)
\(258\) 44.1379 2.74790
\(259\) 6.57478 0.408537
\(260\) 19.4927 1.20889
\(261\) 0.760020 0.0470440
\(262\) −35.9452 −2.22070
\(263\) −15.0573 −0.928475 −0.464237 0.885711i \(-0.653672\pi\)
−0.464237 + 0.885711i \(0.653672\pi\)
\(264\) −50.7618 −3.12417
\(265\) −14.6649 −0.900859
\(266\) 86.1710 5.28348
\(267\) −0.748312 −0.0457960
\(268\) 25.7563 1.57332
\(269\) −0.462306 −0.0281873 −0.0140937 0.999901i \(-0.504486\pi\)
−0.0140937 + 0.999901i \(0.504486\pi\)
\(270\) 25.6547 1.56130
\(271\) 23.9990 1.45784 0.728918 0.684601i \(-0.240024\pi\)
0.728918 + 0.684601i \(0.240024\pi\)
\(272\) 80.8844 4.90434
\(273\) 16.6931 1.01031
\(274\) 18.0783 1.09215
\(275\) −4.78504 −0.288549
\(276\) 5.18522 0.312114
\(277\) −17.0435 −1.02405 −0.512023 0.858972i \(-0.671104\pi\)
−0.512023 + 0.858972i \(0.671104\pi\)
\(278\) 46.1591 2.76844
\(279\) 0.252960 0.0151443
\(280\) −82.5001 −4.93032
\(281\) 21.7216 1.29580 0.647902 0.761724i \(-0.275647\pi\)
0.647902 + 0.761724i \(0.275647\pi\)
\(282\) −34.4641 −2.05231
\(283\) 3.11864 0.185384 0.0926919 0.995695i \(-0.470453\pi\)
0.0926919 + 0.995695i \(0.470453\pi\)
\(284\) −41.8457 −2.48308
\(285\) −21.6491 −1.28238
\(286\) −16.5658 −0.979554
\(287\) 31.6627 1.86899
\(288\) −2.73014 −0.160875
\(289\) 15.9147 0.936157
\(290\) −28.1322 −1.65198
\(291\) −4.31421 −0.252903
\(292\) −65.9735 −3.86081
\(293\) 8.97534 0.524345 0.262172 0.965021i \(-0.415561\pi\)
0.262172 + 0.965021i \(0.415561\pi\)
\(294\) −78.9216 −4.60280
\(295\) 3.25058 0.189256
\(296\) −12.4317 −0.722579
\(297\) −15.8861 −0.921805
\(298\) −32.2766 −1.86973
\(299\) 1.06195 0.0614143
\(300\) −14.5277 −0.838756
\(301\) −44.4200 −2.56033
\(302\) −18.7882 −1.08114
\(303\) 7.98248 0.458582
\(304\) −92.4808 −5.30414
\(305\) −14.7611 −0.845215
\(306\) −2.12871 −0.121690
\(307\) 11.5206 0.657513 0.328757 0.944415i \(-0.393370\pi\)
0.328757 + 0.944415i \(0.393370\pi\)
\(308\) 81.4030 4.63837
\(309\) 19.2063 1.09261
\(310\) −9.36335 −0.531802
\(311\) 10.4869 0.594655 0.297328 0.954776i \(-0.403905\pi\)
0.297328 + 0.954776i \(0.403905\pi\)
\(312\) −31.5636 −1.78694
\(313\) −22.6451 −1.27998 −0.639988 0.768385i \(-0.721061\pi\)
−0.639988 + 0.768385i \(0.721061\pi\)
\(314\) 3.37351 0.190378
\(315\) 1.23239 0.0694370
\(316\) 23.4613 1.31980
\(317\) 16.8636 0.947156 0.473578 0.880752i \(-0.342962\pi\)
0.473578 + 0.880752i \(0.342962\pi\)
\(318\) 37.8382 2.12186
\(319\) 17.4202 0.975345
\(320\) 48.5124 2.71193
\(321\) 1.87926 0.104890
\(322\) −7.16183 −0.399113
\(323\) −37.6337 −2.09399
\(324\) −50.4331 −2.80184
\(325\) −2.97533 −0.165041
\(326\) 27.2878 1.51133
\(327\) 5.57868 0.308502
\(328\) −59.8684 −3.30568
\(329\) 34.6844 1.91221
\(330\) −28.0678 −1.54508
\(331\) 12.9496 0.711776 0.355888 0.934529i \(-0.384178\pi\)
0.355888 + 0.934529i \(0.384178\pi\)
\(332\) 5.04202 0.276717
\(333\) 0.185705 0.0101766
\(334\) −8.95083 −0.489768
\(335\) 8.93753 0.488310
\(336\) 120.822 6.59137
\(337\) −19.5380 −1.06430 −0.532152 0.846649i \(-0.678616\pi\)
−0.532152 + 0.846649i \(0.678616\pi\)
\(338\) 24.9919 1.35938
\(339\) 26.5256 1.44067
\(340\) 57.4124 3.11362
\(341\) 5.79804 0.313981
\(342\) 2.43390 0.131610
\(343\) 45.5543 2.45970
\(344\) 83.9902 4.52845
\(345\) 1.79929 0.0968707
\(346\) −48.7409 −2.62033
\(347\) −27.9164 −1.49863 −0.749317 0.662212i \(-0.769618\pi\)
−0.749317 + 0.662212i \(0.769618\pi\)
\(348\) 52.8889 2.83514
\(349\) 6.40692 0.342955 0.171477 0.985188i \(-0.445146\pi\)
0.171477 + 0.985188i \(0.445146\pi\)
\(350\) 20.0656 1.07255
\(351\) −9.87794 −0.527246
\(352\) −62.5768 −3.33536
\(353\) −4.81923 −0.256502 −0.128251 0.991742i \(-0.540936\pi\)
−0.128251 + 0.991742i \(0.540936\pi\)
\(354\) −8.38710 −0.445769
\(355\) −14.5206 −0.770674
\(356\) −2.26901 −0.120257
\(357\) 49.1666 2.60217
\(358\) −52.1997 −2.75884
\(359\) −15.2860 −0.806764 −0.403382 0.915032i \(-0.632165\pi\)
−0.403382 + 0.915032i \(0.632165\pi\)
\(360\) −2.33022 −0.122813
\(361\) 24.0292 1.26470
\(362\) −25.1301 −1.32081
\(363\) −2.10140 −0.110295
\(364\) 50.6162 2.65301
\(365\) −22.8931 −1.19828
\(366\) 38.0862 1.99080
\(367\) −19.2143 −1.00298 −0.501490 0.865163i \(-0.667215\pi\)
−0.501490 + 0.865163i \(0.667215\pi\)
\(368\) 7.68625 0.400673
\(369\) 0.894313 0.0465561
\(370\) −6.87388 −0.357356
\(371\) −38.0800 −1.97702
\(372\) 17.6032 0.912685
\(373\) −30.5361 −1.58110 −0.790550 0.612397i \(-0.790205\pi\)
−0.790550 + 0.612397i \(0.790205\pi\)
\(374\) −48.7916 −2.52295
\(375\) −21.5428 −1.11247
\(376\) −65.5820 −3.38213
\(377\) 10.8319 0.557869
\(378\) 66.6170 3.42641
\(379\) −15.6478 −0.803775 −0.401888 0.915689i \(-0.631646\pi\)
−0.401888 + 0.915689i \(0.631646\pi\)
\(380\) −65.6436 −3.36745
\(381\) 36.3927 1.86446
\(382\) 18.6040 0.951863
\(383\) −12.6981 −0.648844 −0.324422 0.945912i \(-0.605170\pi\)
−0.324422 + 0.945912i \(0.605170\pi\)
\(384\) −54.4144 −2.77682
\(385\) 28.2472 1.43961
\(386\) −16.9890 −0.864716
\(387\) −1.25465 −0.0637772
\(388\) −13.0814 −0.664108
\(389\) 9.81419 0.497599 0.248800 0.968555i \(-0.419964\pi\)
0.248800 + 0.968555i \(0.419964\pi\)
\(390\) −17.4525 −0.883741
\(391\) 3.12780 0.158180
\(392\) −150.180 −7.58526
\(393\) 23.4497 1.18288
\(394\) 4.61161 0.232330
\(395\) 8.14116 0.409626
\(396\) 2.29923 0.115541
\(397\) 20.2262 1.01512 0.507562 0.861615i \(-0.330547\pi\)
0.507562 + 0.861615i \(0.330547\pi\)
\(398\) −36.4198 −1.82556
\(399\) −56.2156 −2.81430
\(400\) −21.5349 −1.07675
\(401\) −7.02651 −0.350887 −0.175444 0.984490i \(-0.556136\pi\)
−0.175444 + 0.984490i \(0.556136\pi\)
\(402\) −23.0605 −1.15015
\(403\) 3.60521 0.179588
\(404\) 24.2043 1.20421
\(405\) −17.5005 −0.869607
\(406\) −73.0502 −3.62542
\(407\) 4.25649 0.210987
\(408\) −92.9652 −4.60246
\(409\) −23.7931 −1.17649 −0.588246 0.808682i \(-0.700182\pi\)
−0.588246 + 0.808682i \(0.700182\pi\)
\(410\) −33.1031 −1.63484
\(411\) −11.7938 −0.581745
\(412\) 58.2366 2.86911
\(413\) 8.44071 0.415340
\(414\) −0.202286 −0.00994182
\(415\) 1.74960 0.0858846
\(416\) −38.9102 −1.90773
\(417\) −30.1129 −1.47464
\(418\) 55.7869 2.72863
\(419\) −28.1605 −1.37573 −0.687865 0.725839i \(-0.741452\pi\)
−0.687865 + 0.725839i \(0.741452\pi\)
\(420\) 85.7603 4.18467
\(421\) 36.9646 1.80155 0.900773 0.434290i \(-0.143001\pi\)
0.900773 + 0.434290i \(0.143001\pi\)
\(422\) 63.1745 3.07529
\(423\) 0.979663 0.0476328
\(424\) 72.0025 3.49675
\(425\) −8.76331 −0.425083
\(426\) 37.4659 1.81523
\(427\) −38.3297 −1.85490
\(428\) 5.69825 0.275435
\(429\) 10.8070 0.521769
\(430\) 46.4408 2.23957
\(431\) 18.7231 0.901858 0.450929 0.892560i \(-0.351093\pi\)
0.450929 + 0.892560i \(0.351093\pi\)
\(432\) −71.4950 −3.43980
\(433\) 7.51540 0.361167 0.180583 0.983560i \(-0.442201\pi\)
0.180583 + 0.983560i \(0.442201\pi\)
\(434\) −24.3136 −1.16709
\(435\) 18.3527 0.879943
\(436\) 16.9155 0.810106
\(437\) −3.57624 −0.171075
\(438\) 59.0684 2.82240
\(439\) −19.2646 −0.919451 −0.459726 0.888061i \(-0.652052\pi\)
−0.459726 + 0.888061i \(0.652052\pi\)
\(440\) −53.4103 −2.54624
\(441\) 2.24339 0.106828
\(442\) −30.3385 −1.44306
\(443\) 36.7261 1.74491 0.872454 0.488696i \(-0.162527\pi\)
0.872454 + 0.488696i \(0.162527\pi\)
\(444\) 12.9230 0.613298
\(445\) −0.787356 −0.0373242
\(446\) 53.0727 2.51307
\(447\) 21.0564 0.995932
\(448\) 125.971 5.95157
\(449\) −22.9828 −1.08462 −0.542312 0.840177i \(-0.682451\pi\)
−0.542312 + 0.840177i \(0.682451\pi\)
\(450\) 0.566755 0.0267171
\(451\) 20.4983 0.965228
\(452\) 80.4302 3.78312
\(453\) 12.2569 0.575880
\(454\) 58.8033 2.75977
\(455\) 17.5640 0.823415
\(456\) 106.294 4.97766
\(457\) −1.64189 −0.0768043 −0.0384021 0.999262i \(-0.512227\pi\)
−0.0384021 + 0.999262i \(0.512227\pi\)
\(458\) 30.5169 1.42596
\(459\) −29.0938 −1.35798
\(460\) 5.45576 0.254376
\(461\) −35.9968 −1.67654 −0.838269 0.545257i \(-0.816432\pi\)
−0.838269 + 0.545257i \(0.816432\pi\)
\(462\) −72.8829 −3.39082
\(463\) 0.0996890 0.00463294 0.00231647 0.999997i \(-0.499263\pi\)
0.00231647 + 0.999997i \(0.499263\pi\)
\(464\) 78.3992 3.63959
\(465\) 6.10839 0.283270
\(466\) 78.9648 3.65797
\(467\) 11.7359 0.543073 0.271537 0.962428i \(-0.412468\pi\)
0.271537 + 0.962428i \(0.412468\pi\)
\(468\) 1.42966 0.0660860
\(469\) 23.2079 1.07164
\(470\) −36.2623 −1.67265
\(471\) −2.20079 −0.101407
\(472\) −15.9599 −0.734612
\(473\) −28.7574 −1.32227
\(474\) −21.0057 −0.964823
\(475\) 10.0197 0.459736
\(476\) 149.081 6.83314
\(477\) −1.07557 −0.0492471
\(478\) 70.2534 3.21332
\(479\) −38.5412 −1.76099 −0.880497 0.474051i \(-0.842791\pi\)
−0.880497 + 0.474051i \(0.842791\pi\)
\(480\) −65.9264 −3.00912
\(481\) 2.64668 0.120678
\(482\) 47.2422 2.15182
\(483\) 4.67218 0.212592
\(484\) −6.37179 −0.289627
\(485\) −4.53930 −0.206119
\(486\) 3.85301 0.174776
\(487\) −6.23699 −0.282625 −0.141313 0.989965i \(-0.545132\pi\)
−0.141313 + 0.989965i \(0.545132\pi\)
\(488\) 72.4745 3.28077
\(489\) −17.8018 −0.805026
\(490\) −83.0394 −3.75134
\(491\) −37.9215 −1.71137 −0.855686 0.517495i \(-0.826865\pi\)
−0.855686 + 0.517495i \(0.826865\pi\)
\(492\) 62.2342 2.80574
\(493\) 31.9034 1.43686
\(494\) 34.6882 1.56069
\(495\) 0.797843 0.0358604
\(496\) 26.0939 1.17165
\(497\) −37.7054 −1.69132
\(498\) −4.51430 −0.202290
\(499\) 36.9368 1.65352 0.826759 0.562557i \(-0.190182\pi\)
0.826759 + 0.562557i \(0.190182\pi\)
\(500\) −65.3215 −2.92127
\(501\) 5.83928 0.260880
\(502\) −51.0990 −2.28066
\(503\) 19.5867 0.873329 0.436664 0.899624i \(-0.356160\pi\)
0.436664 + 0.899624i \(0.356160\pi\)
\(504\) −6.05082 −0.269525
\(505\) 8.39897 0.373749
\(506\) −4.63655 −0.206120
\(507\) −16.3041 −0.724088
\(508\) 110.349 4.89594
\(509\) 3.19049 0.141416 0.0707081 0.997497i \(-0.477474\pi\)
0.0707081 + 0.997497i \(0.477474\pi\)
\(510\) −51.4033 −2.27618
\(511\) −59.4459 −2.62973
\(512\) −23.6427 −1.04487
\(513\) 33.2650 1.46868
\(514\) 23.8976 1.05408
\(515\) 20.2083 0.890486
\(516\) −87.3093 −3.84358
\(517\) 22.4546 0.987552
\(518\) −17.8492 −0.784251
\(519\) 31.7972 1.39574
\(520\) −33.2104 −1.45637
\(521\) −2.21851 −0.0971945 −0.0485973 0.998818i \(-0.515475\pi\)
−0.0485973 + 0.998818i \(0.515475\pi\)
\(522\) −2.06331 −0.0903084
\(523\) −0.480417 −0.0210072 −0.0105036 0.999945i \(-0.503343\pi\)
−0.0105036 + 0.999945i \(0.503343\pi\)
\(524\) 71.1033 3.10616
\(525\) −13.0903 −0.571307
\(526\) 40.8777 1.78235
\(527\) 10.6185 0.462550
\(528\) 78.2197 3.40408
\(529\) −22.7028 −0.987077
\(530\) 39.8124 1.72934
\(531\) 0.238408 0.0103460
\(532\) −170.455 −7.39018
\(533\) 12.7458 0.552082
\(534\) 2.03152 0.0879126
\(535\) 1.97732 0.0854868
\(536\) −43.8819 −1.89541
\(537\) 34.0536 1.46952
\(538\) 1.25507 0.0541100
\(539\) 51.4203 2.21483
\(540\) −50.7477 −2.18383
\(541\) 40.3067 1.73292 0.866461 0.499245i \(-0.166389\pi\)
0.866461 + 0.499245i \(0.166389\pi\)
\(542\) −65.1526 −2.79854
\(543\) 16.3942 0.703543
\(544\) −114.603 −4.91357
\(545\) 5.86975 0.251432
\(546\) −45.3184 −1.93945
\(547\) −23.0346 −0.984888 −0.492444 0.870344i \(-0.663896\pi\)
−0.492444 + 0.870344i \(0.663896\pi\)
\(548\) −35.7608 −1.52763
\(549\) −1.08262 −0.0462053
\(550\) 12.9904 0.553915
\(551\) −36.4774 −1.55399
\(552\) −8.83425 −0.376011
\(553\) 21.1400 0.898962
\(554\) 46.2699 1.96582
\(555\) 4.48433 0.190349
\(556\) −91.3075 −3.87230
\(557\) −1.92300 −0.0814802 −0.0407401 0.999170i \(-0.512972\pi\)
−0.0407401 + 0.999170i \(0.512972\pi\)
\(558\) −0.686739 −0.0290720
\(559\) −17.8813 −0.756298
\(560\) 127.126 5.37204
\(561\) 31.8303 1.34388
\(562\) −58.9700 −2.48750
\(563\) −16.2179 −0.683505 −0.341752 0.939790i \(-0.611020\pi\)
−0.341752 + 0.939790i \(0.611020\pi\)
\(564\) 68.1736 2.87063
\(565\) 27.9096 1.17417
\(566\) −8.46650 −0.355873
\(567\) −45.4431 −1.90843
\(568\) 71.2940 2.99143
\(569\) 16.4625 0.690142 0.345071 0.938576i \(-0.387855\pi\)
0.345071 + 0.938576i \(0.387855\pi\)
\(570\) 58.7730 2.46173
\(571\) −4.89710 −0.204937 −0.102469 0.994736i \(-0.532674\pi\)
−0.102469 + 0.994736i \(0.532674\pi\)
\(572\) 32.7688 1.37013
\(573\) −12.1367 −0.507019
\(574\) −85.9580 −3.58782
\(575\) −0.832757 −0.0347284
\(576\) 3.55806 0.148252
\(577\) −33.8889 −1.41081 −0.705406 0.708804i \(-0.749235\pi\)
−0.705406 + 0.708804i \(0.749235\pi\)
\(578\) −43.2052 −1.79710
\(579\) 11.0831 0.460600
\(580\) 55.6484 2.31067
\(581\) 4.54315 0.188482
\(582\) 11.7122 0.485488
\(583\) −24.6529 −1.02102
\(584\) 112.402 4.65121
\(585\) 0.496097 0.0205111
\(586\) −24.3663 −1.00656
\(587\) 27.7584 1.14571 0.572855 0.819656i \(-0.305836\pi\)
0.572855 + 0.819656i \(0.305836\pi\)
\(588\) 156.115 6.43809
\(589\) −12.1409 −0.500258
\(590\) −8.82470 −0.363307
\(591\) −3.00849 −0.123753
\(592\) 19.1562 0.787317
\(593\) −20.0951 −0.825207 −0.412603 0.910911i \(-0.635380\pi\)
−0.412603 + 0.910911i \(0.635380\pi\)
\(594\) 43.1277 1.76955
\(595\) 51.7319 2.12080
\(596\) 63.8465 2.61525
\(597\) 23.7593 0.972402
\(598\) −2.88300 −0.117894
\(599\) 13.1037 0.535403 0.267701 0.963502i \(-0.413736\pi\)
0.267701 + 0.963502i \(0.413736\pi\)
\(600\) 24.7514 1.01047
\(601\) −37.5086 −1.53001 −0.765005 0.644025i \(-0.777263\pi\)
−0.765005 + 0.644025i \(0.777263\pi\)
\(602\) 120.592 4.91495
\(603\) 0.655508 0.0266943
\(604\) 37.1650 1.51222
\(605\) −2.21104 −0.0898915
\(606\) −21.6709 −0.880320
\(607\) 40.6738 1.65090 0.825449 0.564476i \(-0.190922\pi\)
0.825449 + 0.564476i \(0.190922\pi\)
\(608\) 131.034 5.31413
\(609\) 47.6559 1.93112
\(610\) 40.0734 1.62252
\(611\) 13.9622 0.564851
\(612\) 4.21081 0.170212
\(613\) 36.3755 1.46919 0.734597 0.678503i \(-0.237371\pi\)
0.734597 + 0.678503i \(0.237371\pi\)
\(614\) −31.2761 −1.26220
\(615\) 21.5955 0.870816
\(616\) −138.689 −5.58795
\(617\) −30.2481 −1.21774 −0.608871 0.793269i \(-0.708377\pi\)
−0.608871 + 0.793269i \(0.708377\pi\)
\(618\) −52.1413 −2.09743
\(619\) 29.2455 1.17547 0.587737 0.809052i \(-0.300019\pi\)
0.587737 + 0.809052i \(0.300019\pi\)
\(620\) 18.5217 0.743849
\(621\) −2.76471 −0.110944
\(622\) −28.4698 −1.14153
\(623\) −2.04451 −0.0819115
\(624\) 48.6369 1.94703
\(625\) −15.0295 −0.601178
\(626\) 61.4770 2.45712
\(627\) −36.3938 −1.45343
\(628\) −6.67316 −0.266288
\(629\) 7.79534 0.310821
\(630\) −3.34569 −0.133295
\(631\) −5.26560 −0.209620 −0.104810 0.994492i \(-0.533423\pi\)
−0.104810 + 0.994492i \(0.533423\pi\)
\(632\) −39.9719 −1.59000
\(633\) −41.2133 −1.63808
\(634\) −45.7815 −1.81821
\(635\) 38.2915 1.51955
\(636\) −74.8479 −2.96791
\(637\) 31.9730 1.26682
\(638\) −47.2925 −1.87233
\(639\) −1.06499 −0.0421303
\(640\) −57.2535 −2.26314
\(641\) −15.4626 −0.610735 −0.305368 0.952235i \(-0.598779\pi\)
−0.305368 + 0.952235i \(0.598779\pi\)
\(642\) −5.10184 −0.201354
\(643\) 2.49487 0.0983882 0.0491941 0.998789i \(-0.484335\pi\)
0.0491941 + 0.998789i \(0.484335\pi\)
\(644\) 14.1668 0.558252
\(645\) −30.2967 −1.19293
\(646\) 102.168 4.01975
\(647\) 34.0810 1.33986 0.669932 0.742423i \(-0.266323\pi\)
0.669932 + 0.742423i \(0.266323\pi\)
\(648\) 85.9248 3.37544
\(649\) 5.46449 0.214500
\(650\) 8.07743 0.316823
\(651\) 15.8615 0.621662
\(652\) −53.9781 −2.11395
\(653\) 36.3173 1.42121 0.710603 0.703594i \(-0.248422\pi\)
0.710603 + 0.703594i \(0.248422\pi\)
\(654\) −15.1450 −0.592218
\(655\) 24.6732 0.964060
\(656\) 92.2522 3.60184
\(657\) −1.67905 −0.0655061
\(658\) −94.1614 −3.67079
\(659\) −22.9519 −0.894078 −0.447039 0.894514i \(-0.647521\pi\)
−0.447039 + 0.894514i \(0.647521\pi\)
\(660\) 55.5210 2.16115
\(661\) 34.3123 1.33459 0.667297 0.744792i \(-0.267451\pi\)
0.667297 + 0.744792i \(0.267451\pi\)
\(662\) −35.1557 −1.36637
\(663\) 19.7920 0.768659
\(664\) −8.59028 −0.333368
\(665\) −59.1487 −2.29369
\(666\) −0.504153 −0.0195355
\(667\) 3.03170 0.117388
\(668\) 17.7057 0.685053
\(669\) −34.6232 −1.33861
\(670\) −24.2637 −0.937387
\(671\) −24.8145 −0.957955
\(672\) −171.190 −6.60378
\(673\) 41.1979 1.58806 0.794032 0.607877i \(-0.207978\pi\)
0.794032 + 0.607877i \(0.207978\pi\)
\(674\) 53.0419 2.04310
\(675\) 7.74603 0.298145
\(676\) −49.4367 −1.90141
\(677\) 8.77820 0.337374 0.168687 0.985670i \(-0.446047\pi\)
0.168687 + 0.985670i \(0.446047\pi\)
\(678\) −72.0120 −2.76560
\(679\) −11.7871 −0.452347
\(680\) −97.8157 −3.75106
\(681\) −38.3617 −1.47002
\(682\) −15.7406 −0.602737
\(683\) 12.5580 0.480518 0.240259 0.970709i \(-0.422768\pi\)
0.240259 + 0.970709i \(0.422768\pi\)
\(684\) −4.81452 −0.184088
\(685\) −12.4091 −0.474129
\(686\) −123.671 −4.72178
\(687\) −19.9084 −0.759553
\(688\) −129.422 −4.93416
\(689\) −15.3291 −0.583994
\(690\) −4.88473 −0.185959
\(691\) −49.5280 −1.88413 −0.942066 0.335426i \(-0.891120\pi\)
−0.942066 + 0.335426i \(0.891120\pi\)
\(692\) 96.4146 3.66513
\(693\) 2.07174 0.0786989
\(694\) 75.7877 2.87686
\(695\) −31.6841 −1.20185
\(696\) −90.1088 −3.41557
\(697\) 37.5406 1.42195
\(698\) −17.3935 −0.658355
\(699\) −51.5145 −1.94846
\(700\) −39.6920 −1.50022
\(701\) 42.3113 1.59807 0.799037 0.601281i \(-0.205343\pi\)
0.799037 + 0.601281i \(0.205343\pi\)
\(702\) 26.8167 1.01213
\(703\) −8.91297 −0.336159
\(704\) 81.5533 3.07366
\(705\) 23.6565 0.890956
\(706\) 13.0833 0.492395
\(707\) 21.8094 0.820228
\(708\) 16.5906 0.623511
\(709\) 32.8555 1.23391 0.616957 0.786997i \(-0.288365\pi\)
0.616957 + 0.786997i \(0.288365\pi\)
\(710\) 39.4207 1.47943
\(711\) 0.597099 0.0223930
\(712\) 3.86580 0.144877
\(713\) 1.00905 0.0377893
\(714\) −133.478 −4.99528
\(715\) 11.3709 0.425248
\(716\) 103.256 3.85887
\(717\) −45.8314 −1.71161
\(718\) 41.4985 1.54871
\(719\) −35.4464 −1.32193 −0.660964 0.750418i \(-0.729852\pi\)
−0.660964 + 0.750418i \(0.729852\pi\)
\(720\) 3.59067 0.133816
\(721\) 52.4745 1.95425
\(722\) −65.2347 −2.42778
\(723\) −30.8195 −1.14619
\(724\) 49.7100 1.84746
\(725\) −8.49406 −0.315462
\(726\) 5.70489 0.211728
\(727\) 46.2553 1.71552 0.857758 0.514054i \(-0.171857\pi\)
0.857758 + 0.514054i \(0.171857\pi\)
\(728\) −86.2368 −3.19615
\(729\) 25.6604 0.950386
\(730\) 62.1503 2.30029
\(731\) −52.6663 −1.94793
\(732\) −75.3386 −2.78459
\(733\) −38.8504 −1.43497 −0.717487 0.696572i \(-0.754708\pi\)
−0.717487 + 0.696572i \(0.754708\pi\)
\(734\) 52.1632 1.92538
\(735\) 54.1726 1.99819
\(736\) −10.8905 −0.401428
\(737\) 15.0247 0.553443
\(738\) −2.42789 −0.0893718
\(739\) −24.8497 −0.914112 −0.457056 0.889438i \(-0.651096\pi\)
−0.457056 + 0.889438i \(0.651096\pi\)
\(740\) 13.5973 0.499845
\(741\) −22.6296 −0.831320
\(742\) 103.380 3.79520
\(743\) 13.3748 0.490674 0.245337 0.969438i \(-0.421101\pi\)
0.245337 + 0.969438i \(0.421101\pi\)
\(744\) −29.9913 −1.09953
\(745\) 22.1550 0.811696
\(746\) 82.8996 3.03517
\(747\) 0.128322 0.00469504
\(748\) 96.5149 3.52894
\(749\) 5.13445 0.187609
\(750\) 58.4846 2.13555
\(751\) −30.6552 −1.11862 −0.559312 0.828958i \(-0.688934\pi\)
−0.559312 + 0.828958i \(0.688934\pi\)
\(752\) 101.056 3.68514
\(753\) 33.3356 1.21482
\(754\) −29.4064 −1.07092
\(755\) 12.8964 0.469348
\(756\) −131.775 −4.79263
\(757\) 45.2241 1.64370 0.821848 0.569706i \(-0.192943\pi\)
0.821848 + 0.569706i \(0.192943\pi\)
\(758\) 42.4808 1.54297
\(759\) 3.02476 0.109792
\(760\) 111.840 4.05685
\(761\) −14.3095 −0.518720 −0.259360 0.965781i \(-0.583512\pi\)
−0.259360 + 0.965781i \(0.583512\pi\)
\(762\) −98.7992 −3.57912
\(763\) 15.2418 0.551792
\(764\) −36.8006 −1.33140
\(765\) 1.46117 0.0528287
\(766\) 34.4729 1.24556
\(767\) 3.39781 0.122688
\(768\) 55.5110 2.00308
\(769\) −6.65959 −0.240151 −0.120075 0.992765i \(-0.538314\pi\)
−0.120075 + 0.992765i \(0.538314\pi\)
\(770\) −76.6856 −2.76356
\(771\) −15.5901 −0.561464
\(772\) 33.6060 1.20951
\(773\) 9.74075 0.350350 0.175175 0.984537i \(-0.443951\pi\)
0.175175 + 0.984537i \(0.443951\pi\)
\(774\) 3.40612 0.122430
\(775\) −2.82711 −0.101553
\(776\) 22.2873 0.800067
\(777\) 11.6444 0.417739
\(778\) −26.6436 −0.955220
\(779\) −42.9228 −1.53787
\(780\) 34.5228 1.23612
\(781\) −24.4103 −0.873471
\(782\) −8.49137 −0.303651
\(783\) −28.1999 −1.00778
\(784\) 231.416 8.26484
\(785\) −2.31561 −0.0826478
\(786\) −63.6613 −2.27072
\(787\) −38.0087 −1.35486 −0.677431 0.735586i \(-0.736907\pi\)
−0.677431 + 0.735586i \(0.736907\pi\)
\(788\) −9.12225 −0.324967
\(789\) −26.6675 −0.949389
\(790\) −22.1017 −0.786342
\(791\) 72.4723 2.57682
\(792\) −3.91729 −0.139195
\(793\) −15.4296 −0.547922
\(794\) −54.9102 −1.94869
\(795\) −25.9725 −0.921151
\(796\) 72.0421 2.55347
\(797\) 47.2815 1.67480 0.837398 0.546594i \(-0.184076\pi\)
0.837398 + 0.546594i \(0.184076\pi\)
\(798\) 152.615 5.40250
\(799\) 41.1233 1.45484
\(800\) 30.5124 1.07877
\(801\) −0.0577472 −0.00204040
\(802\) 19.0756 0.673583
\(803\) −38.4852 −1.35811
\(804\) 45.6161 1.60875
\(805\) 4.91595 0.173265
\(806\) −9.78744 −0.344748
\(807\) −0.818774 −0.0288222
\(808\) −41.2377 −1.45074
\(809\) −32.9644 −1.15897 −0.579484 0.814984i \(-0.696746\pi\)
−0.579484 + 0.814984i \(0.696746\pi\)
\(810\) 47.5104 1.66935
\(811\) 38.0375 1.33568 0.667839 0.744306i \(-0.267220\pi\)
0.667839 + 0.744306i \(0.267220\pi\)
\(812\) 144.501 5.07099
\(813\) 42.5038 1.49067
\(814\) −11.5556 −0.405022
\(815\) −18.7306 −0.656105
\(816\) 143.252 5.01481
\(817\) 60.2171 2.10673
\(818\) 64.5936 2.25846
\(819\) 1.28820 0.0450135
\(820\) 65.4813 2.28671
\(821\) −13.7396 −0.479514 −0.239757 0.970833i \(-0.577068\pi\)
−0.239757 + 0.970833i \(0.577068\pi\)
\(822\) 32.0179 1.11675
\(823\) −43.4574 −1.51483 −0.757414 0.652934i \(-0.773538\pi\)
−0.757414 + 0.652934i \(0.773538\pi\)
\(824\) −99.2199 −3.45649
\(825\) −8.47461 −0.295048
\(826\) −22.9149 −0.797311
\(827\) 24.5983 0.855366 0.427683 0.903929i \(-0.359330\pi\)
0.427683 + 0.903929i \(0.359330\pi\)
\(828\) 0.400143 0.0139059
\(829\) −25.9415 −0.900985 −0.450492 0.892780i \(-0.648752\pi\)
−0.450492 + 0.892780i \(0.648752\pi\)
\(830\) −4.74983 −0.164869
\(831\) −30.1852 −1.04711
\(832\) 50.7097 1.75804
\(833\) 94.1710 3.26283
\(834\) 81.7507 2.83080
\(835\) 6.14394 0.212620
\(836\) −110.352 −3.81662
\(837\) −9.38588 −0.324424
\(838\) 76.4503 2.64093
\(839\) 18.4066 0.635465 0.317732 0.948180i \(-0.397079\pi\)
0.317732 + 0.948180i \(0.397079\pi\)
\(840\) −146.113 −5.04138
\(841\) 1.92314 0.0663152
\(842\) −100.352 −3.45835
\(843\) 38.4704 1.32499
\(844\) −124.966 −4.30150
\(845\) −17.1547 −0.590140
\(846\) −2.65959 −0.0914387
\(847\) −5.74135 −0.197275
\(848\) −110.950 −3.81003
\(849\) 5.52331 0.189560
\(850\) 23.7907 0.816014
\(851\) 0.740773 0.0253934
\(852\) −74.1114 −2.53902
\(853\) 46.0794 1.57773 0.788864 0.614568i \(-0.210670\pi\)
0.788864 + 0.614568i \(0.210670\pi\)
\(854\) 104.058 3.56078
\(855\) −1.67066 −0.0571353
\(856\) −9.70832 −0.331824
\(857\) −17.8912 −0.611152 −0.305576 0.952168i \(-0.598849\pi\)
−0.305576 + 0.952168i \(0.598849\pi\)
\(858\) −29.3390 −1.00162
\(859\) 8.72940 0.297843 0.148922 0.988849i \(-0.452420\pi\)
0.148922 + 0.988849i \(0.452420\pi\)
\(860\) −91.8647 −3.13256
\(861\) 56.0766 1.91109
\(862\) −50.8295 −1.73126
\(863\) −56.1905 −1.91275 −0.956374 0.292144i \(-0.905631\pi\)
−0.956374 + 0.292144i \(0.905631\pi\)
\(864\) 101.300 3.44628
\(865\) 33.4563 1.13755
\(866\) −20.4028 −0.693317
\(867\) 28.1859 0.957244
\(868\) 48.0948 1.63244
\(869\) 13.6860 0.464264
\(870\) −49.8239 −1.68919
\(871\) 9.34234 0.316553
\(872\) −28.8196 −0.975954
\(873\) −0.332927 −0.0112679
\(874\) 9.70879 0.328405
\(875\) −58.8584 −1.98978
\(876\) −116.843 −3.94777
\(877\) 39.4851 1.33332 0.666659 0.745363i \(-0.267724\pi\)
0.666659 + 0.745363i \(0.267724\pi\)
\(878\) 52.2998 1.76503
\(879\) 15.8959 0.536156
\(880\) 82.3008 2.77436
\(881\) 14.4808 0.487872 0.243936 0.969791i \(-0.421561\pi\)
0.243936 + 0.969791i \(0.421561\pi\)
\(882\) −6.09038 −0.205074
\(883\) −12.5576 −0.422596 −0.211298 0.977422i \(-0.567769\pi\)
−0.211298 + 0.977422i \(0.567769\pi\)
\(884\) 60.0128 2.01845
\(885\) 5.75699 0.193519
\(886\) −99.7041 −3.34963
\(887\) 3.17216 0.106511 0.0532553 0.998581i \(-0.483040\pi\)
0.0532553 + 0.998581i \(0.483040\pi\)
\(888\) −22.0174 −0.738855
\(889\) 99.4308 3.33480
\(890\) 2.13752 0.0716498
\(891\) −29.4198 −0.985599
\(892\) −104.983 −3.51511
\(893\) −47.0192 −1.57344
\(894\) −57.1639 −1.91185
\(895\) 35.8304 1.19768
\(896\) −148.669 −4.96668
\(897\) 1.88079 0.0627977
\(898\) 62.3938 2.08211
\(899\) 10.2923 0.343267
\(900\) −1.12110 −0.0373700
\(901\) −45.1494 −1.50414
\(902\) −55.6490 −1.85291
\(903\) −78.6707 −2.61800
\(904\) −137.032 −4.55762
\(905\) 17.2496 0.573396
\(906\) −33.2751 −1.10549
\(907\) 43.8157 1.45488 0.727439 0.686173i \(-0.240711\pi\)
0.727439 + 0.686173i \(0.240711\pi\)
\(908\) −116.319 −3.86018
\(909\) 0.616008 0.0204317
\(910\) −47.6830 −1.58067
\(911\) 0.486012 0.0161023 0.00805115 0.999968i \(-0.497437\pi\)
0.00805115 + 0.999968i \(0.497437\pi\)
\(912\) −163.790 −5.42362
\(913\) 2.94122 0.0973403
\(914\) 4.45741 0.147438
\(915\) −26.1428 −0.864254
\(916\) −60.3657 −1.99454
\(917\) 64.0682 2.11572
\(918\) 78.9840 2.60686
\(919\) −13.6658 −0.450793 −0.225396 0.974267i \(-0.572368\pi\)
−0.225396 + 0.974267i \(0.572368\pi\)
\(920\) −9.29519 −0.306453
\(921\) 20.4037 0.672324
\(922\) 97.7243 3.21838
\(923\) −15.1783 −0.499600
\(924\) 144.170 4.74285
\(925\) −2.07546 −0.0682407
\(926\) −0.270636 −0.00889366
\(927\) 1.48215 0.0486801
\(928\) −111.082 −3.64645
\(929\) 4.45820 0.146269 0.0731344 0.997322i \(-0.476700\pi\)
0.0731344 + 0.997322i \(0.476700\pi\)
\(930\) −16.5831 −0.543781
\(931\) −107.672 −3.52882
\(932\) −156.201 −5.11652
\(933\) 18.5729 0.608050
\(934\) −31.8607 −1.04251
\(935\) 33.4911 1.09528
\(936\) −2.43576 −0.0796154
\(937\) 59.4901 1.94346 0.971728 0.236103i \(-0.0758704\pi\)
0.971728 + 0.236103i \(0.0758704\pi\)
\(938\) −63.0049 −2.05718
\(939\) −40.1059 −1.30881
\(940\) 71.7306 2.33959
\(941\) −19.4501 −0.634056 −0.317028 0.948416i \(-0.602685\pi\)
−0.317028 + 0.948416i \(0.602685\pi\)
\(942\) 5.97471 0.194666
\(943\) 3.56739 0.116170
\(944\) 24.5928 0.800428
\(945\) −45.7266 −1.48749
\(946\) 78.0707 2.53830
\(947\) 35.3764 1.14958 0.574789 0.818302i \(-0.305084\pi\)
0.574789 + 0.818302i \(0.305084\pi\)
\(948\) 41.5515 1.34953
\(949\) −23.9300 −0.776800
\(950\) −27.2016 −0.882536
\(951\) 29.8666 0.968490
\(952\) −253.996 −8.23205
\(953\) 27.7804 0.899894 0.449947 0.893055i \(-0.351443\pi\)
0.449947 + 0.893055i \(0.351443\pi\)
\(954\) 2.91997 0.0945376
\(955\) −12.7700 −0.413227
\(956\) −138.969 −4.49457
\(957\) 30.8523 0.997314
\(958\) 104.632 3.38051
\(959\) −32.2225 −1.04052
\(960\) 85.9187 2.77301
\(961\) −27.5744 −0.889496
\(962\) −7.18522 −0.231661
\(963\) 0.145023 0.00467330
\(964\) −93.4500 −3.00982
\(965\) 11.6614 0.375394
\(966\) −12.6841 −0.408103
\(967\) 54.3047 1.74632 0.873161 0.487432i \(-0.162066\pi\)
0.873161 + 0.487432i \(0.162066\pi\)
\(968\) 10.8559 0.348921
\(969\) −66.6517 −2.14116
\(970\) 12.3233 0.395678
\(971\) 4.35799 0.139854 0.0699272 0.997552i \(-0.477723\pi\)
0.0699272 + 0.997552i \(0.477723\pi\)
\(972\) −7.62167 −0.244465
\(973\) −82.2733 −2.63756
\(974\) 16.9322 0.542544
\(975\) −5.26950 −0.168759
\(976\) −111.677 −3.57470
\(977\) 39.7648 1.27219 0.636094 0.771612i \(-0.280549\pi\)
0.636094 + 0.771612i \(0.280549\pi\)
\(978\) 48.3285 1.54537
\(979\) −1.32361 −0.0423027
\(980\) 164.261 5.24711
\(981\) 0.430507 0.0137450
\(982\) 102.949 3.28525
\(983\) −43.1950 −1.37771 −0.688854 0.724900i \(-0.741886\pi\)
−0.688854 + 0.724900i \(0.741886\pi\)
\(984\) −106.031 −3.38014
\(985\) −3.16546 −0.100860
\(986\) −86.6115 −2.75827
\(987\) 61.4283 1.95529
\(988\) −68.6169 −2.18299
\(989\) −5.00475 −0.159142
\(990\) −2.16599 −0.0688396
\(991\) −34.3512 −1.09120 −0.545600 0.838045i \(-0.683698\pi\)
−0.545600 + 0.838045i \(0.683698\pi\)
\(992\) −36.9719 −1.17386
\(993\) 22.9347 0.727809
\(994\) 102.363 3.24675
\(995\) 24.9989 0.792519
\(996\) 8.92975 0.282950
\(997\) −23.7018 −0.750645 −0.375322 0.926894i \(-0.622468\pi\)
−0.375322 + 0.926894i \(0.622468\pi\)
\(998\) −100.276 −3.17419
\(999\) −6.89043 −0.218003
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 \(a_p\))