Properties

Label 8046.2.a.h.1.8
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.0929510\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.96687 q^{5} -4.72097 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.96687 q^{5} -4.72097 q^{7} +1.00000 q^{8} +1.96687 q^{10} +2.36478 q^{11} -0.742721 q^{13} -4.72097 q^{14} +1.00000 q^{16} -1.40102 q^{17} -2.69068 q^{19} +1.96687 q^{20} +2.36478 q^{22} -3.63674 q^{23} -1.13141 q^{25} -0.742721 q^{26} -4.72097 q^{28} +0.980272 q^{29} +3.58715 q^{31} +1.00000 q^{32} -1.40102 q^{34} -9.28555 q^{35} +10.6294 q^{37} -2.69068 q^{38} +1.96687 q^{40} -6.88728 q^{41} -1.80326 q^{43} +2.36478 q^{44} -3.63674 q^{46} -2.73029 q^{47} +15.2876 q^{49} -1.13141 q^{50} -0.742721 q^{52} +1.45122 q^{53} +4.65123 q^{55} -4.72097 q^{56} +0.980272 q^{58} -2.49561 q^{59} -7.04971 q^{61} +3.58715 q^{62} +1.00000 q^{64} -1.46084 q^{65} -4.95825 q^{67} -1.40102 q^{68} -9.28555 q^{70} -14.3379 q^{71} -7.71974 q^{73} +10.6294 q^{74} -2.69068 q^{76} -11.1641 q^{77} +2.59929 q^{79} +1.96687 q^{80} -6.88728 q^{82} -10.3231 q^{83} -2.75562 q^{85} -1.80326 q^{86} +2.36478 q^{88} +1.95400 q^{89} +3.50637 q^{91} -3.63674 q^{92} -2.73029 q^{94} -5.29222 q^{95} +0.529108 q^{97} +15.2876 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} + O(q^{10}) \) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} - 4q^{10} - 4q^{11} - 8q^{13} - 4q^{14} + 9q^{16} - q^{17} - 10q^{19} - 4q^{20} - 4q^{22} - 8q^{23} - 3q^{25} - 8q^{26} - 4q^{28} - 4q^{29} - 17q^{31} + 9q^{32} - q^{34} - 10q^{35} - 11q^{37} - 10q^{38} - 4q^{40} - 16q^{43} - 4q^{44} - 8q^{46} - 7q^{47} - 5q^{49} - 3q^{50} - 8q^{52} - 12q^{53} - 23q^{55} - 4q^{56} - 4q^{58} - 6q^{59} - 13q^{61} - 17q^{62} + 9q^{64} + 24q^{65} - 14q^{67} - q^{68} - 10q^{70} - 30q^{71} - 12q^{73} - 11q^{74} - 10q^{76} - 12q^{77} - 35q^{79} - 4q^{80} - 5q^{83} - 27q^{85} - 16q^{86} - 4q^{88} - 23q^{89} - 28q^{91} - 8q^{92} - 7q^{94} - 32q^{95} - 21q^{97} - 5q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 1.96687 0.879612 0.439806 0.898093i \(-0.355047\pi\)
0.439806 + 0.898093i \(0.355047\pi\)
\(6\) 0 0
\(7\) −4.72097 −1.78436 −0.892180 0.451681i \(-0.850825\pi\)
−0.892180 + 0.451681i \(0.850825\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.96687 0.621980
\(11\) 2.36478 0.713009 0.356504 0.934294i \(-0.383968\pi\)
0.356504 + 0.934294i \(0.383968\pi\)
\(12\) 0 0
\(13\) −0.742721 −0.205994 −0.102997 0.994682i \(-0.532843\pi\)
−0.102997 + 0.994682i \(0.532843\pi\)
\(14\) −4.72097 −1.26173
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −1.40102 −0.339796 −0.169898 0.985462i \(-0.554344\pi\)
−0.169898 + 0.985462i \(0.554344\pi\)
\(18\) 0 0
\(19\) −2.69068 −0.617284 −0.308642 0.951178i \(-0.599874\pi\)
−0.308642 + 0.951178i \(0.599874\pi\)
\(20\) 1.96687 0.439806
\(21\) 0 0
\(22\) 2.36478 0.504173
\(23\) −3.63674 −0.758313 −0.379157 0.925333i \(-0.623786\pi\)
−0.379157 + 0.925333i \(0.623786\pi\)
\(24\) 0 0
\(25\) −1.13141 −0.226283
\(26\) −0.742721 −0.145660
\(27\) 0 0
\(28\) −4.72097 −0.892180
\(29\) 0.980272 0.182032 0.0910159 0.995849i \(-0.470989\pi\)
0.0910159 + 0.995849i \(0.470989\pi\)
\(30\) 0 0
\(31\) 3.58715 0.644271 0.322135 0.946694i \(-0.395599\pi\)
0.322135 + 0.946694i \(0.395599\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −1.40102 −0.240272
\(35\) −9.28555 −1.56954
\(36\) 0 0
\(37\) 10.6294 1.74747 0.873735 0.486403i \(-0.161691\pi\)
0.873735 + 0.486403i \(0.161691\pi\)
\(38\) −2.69068 −0.436486
\(39\) 0 0
\(40\) 1.96687 0.310990
\(41\) −6.88728 −1.07561 −0.537806 0.843069i \(-0.680747\pi\)
−0.537806 + 0.843069i \(0.680747\pi\)
\(42\) 0 0
\(43\) −1.80326 −0.274995 −0.137497 0.990502i \(-0.543906\pi\)
−0.137497 + 0.990502i \(0.543906\pi\)
\(44\) 2.36478 0.356504
\(45\) 0 0
\(46\) −3.63674 −0.536208
\(47\) −2.73029 −0.398254 −0.199127 0.979974i \(-0.563811\pi\)
−0.199127 + 0.979974i \(0.563811\pi\)
\(48\) 0 0
\(49\) 15.2876 2.18394
\(50\) −1.13141 −0.160006
\(51\) 0 0
\(52\) −0.742721 −0.102997
\(53\) 1.45122 0.199341 0.0996705 0.995020i \(-0.468221\pi\)
0.0996705 + 0.995020i \(0.468221\pi\)
\(54\) 0 0
\(55\) 4.65123 0.627171
\(56\) −4.72097 −0.630866
\(57\) 0 0
\(58\) 0.980272 0.128716
\(59\) −2.49561 −0.324900 −0.162450 0.986717i \(-0.551940\pi\)
−0.162450 + 0.986717i \(0.551940\pi\)
\(60\) 0 0
\(61\) −7.04971 −0.902623 −0.451311 0.892367i \(-0.649044\pi\)
−0.451311 + 0.892367i \(0.649044\pi\)
\(62\) 3.58715 0.455568
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.46084 −0.181195
\(66\) 0 0
\(67\) −4.95825 −0.605747 −0.302873 0.953031i \(-0.597946\pi\)
−0.302873 + 0.953031i \(0.597946\pi\)
\(68\) −1.40102 −0.169898
\(69\) 0 0
\(70\) −9.28555 −1.10983
\(71\) −14.3379 −1.70160 −0.850798 0.525493i \(-0.823881\pi\)
−0.850798 + 0.525493i \(0.823881\pi\)
\(72\) 0 0
\(73\) −7.71974 −0.903528 −0.451764 0.892138i \(-0.649205\pi\)
−0.451764 + 0.892138i \(0.649205\pi\)
\(74\) 10.6294 1.23565
\(75\) 0 0
\(76\) −2.69068 −0.308642
\(77\) −11.1641 −1.27226
\(78\) 0 0
\(79\) 2.59929 0.292443 0.146221 0.989252i \(-0.453289\pi\)
0.146221 + 0.989252i \(0.453289\pi\)
\(80\) 1.96687 0.219903
\(81\) 0 0
\(82\) −6.88728 −0.760572
\(83\) −10.3231 −1.13311 −0.566555 0.824024i \(-0.691724\pi\)
−0.566555 + 0.824024i \(0.691724\pi\)
\(84\) 0 0
\(85\) −2.75562 −0.298889
\(86\) −1.80326 −0.194451
\(87\) 0 0
\(88\) 2.36478 0.252087
\(89\) 1.95400 0.207123 0.103562 0.994623i \(-0.466976\pi\)
0.103562 + 0.994623i \(0.466976\pi\)
\(90\) 0 0
\(91\) 3.50637 0.367567
\(92\) −3.63674 −0.379157
\(93\) 0 0
\(94\) −2.73029 −0.281608
\(95\) −5.29222 −0.542970
\(96\) 0 0
\(97\) 0.529108 0.0537228 0.0268614 0.999639i \(-0.491449\pi\)
0.0268614 + 0.999639i \(0.491449\pi\)
\(98\) 15.2876 1.54428
\(99\) 0 0
\(100\) −1.13141 −0.113141
\(101\) 4.78364 0.475989 0.237995 0.971266i \(-0.423510\pi\)
0.237995 + 0.971266i \(0.423510\pi\)
\(102\) 0 0
\(103\) −1.60204 −0.157854 −0.0789268 0.996880i \(-0.525149\pi\)
−0.0789268 + 0.996880i \(0.525149\pi\)
\(104\) −0.742721 −0.0728298
\(105\) 0 0
\(106\) 1.45122 0.140955
\(107\) −14.1668 −1.36956 −0.684780 0.728750i \(-0.740102\pi\)
−0.684780 + 0.728750i \(0.740102\pi\)
\(108\) 0 0
\(109\) −14.8290 −1.42036 −0.710179 0.704021i \(-0.751386\pi\)
−0.710179 + 0.704021i \(0.751386\pi\)
\(110\) 4.65123 0.443477
\(111\) 0 0
\(112\) −4.72097 −0.446090
\(113\) 10.0435 0.944811 0.472405 0.881381i \(-0.343386\pi\)
0.472405 + 0.881381i \(0.343386\pi\)
\(114\) 0 0
\(115\) −7.15301 −0.667021
\(116\) 0.980272 0.0910159
\(117\) 0 0
\(118\) −2.49561 −0.229739
\(119\) 6.61415 0.606318
\(120\) 0 0
\(121\) −5.40780 −0.491618
\(122\) −7.04971 −0.638251
\(123\) 0 0
\(124\) 3.58715 0.322135
\(125\) −12.0597 −1.07865
\(126\) 0 0
\(127\) −10.1650 −0.901996 −0.450998 0.892525i \(-0.648932\pi\)
−0.450998 + 0.892525i \(0.648932\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −1.46084 −0.128124
\(131\) −14.2956 −1.24901 −0.624505 0.781021i \(-0.714699\pi\)
−0.624505 + 0.781021i \(0.714699\pi\)
\(132\) 0 0
\(133\) 12.7026 1.10146
\(134\) −4.95825 −0.428328
\(135\) 0 0
\(136\) −1.40102 −0.120136
\(137\) −2.27871 −0.194683 −0.0973417 0.995251i \(-0.531034\pi\)
−0.0973417 + 0.995251i \(0.531034\pi\)
\(138\) 0 0
\(139\) 2.63621 0.223601 0.111800 0.993731i \(-0.464338\pi\)
0.111800 + 0.993731i \(0.464338\pi\)
\(140\) −9.28555 −0.784772
\(141\) 0 0
\(142\) −14.3379 −1.20321
\(143\) −1.75638 −0.146875
\(144\) 0 0
\(145\) 1.92807 0.160117
\(146\) −7.71974 −0.638890
\(147\) 0 0
\(148\) 10.6294 0.873735
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) −8.80220 −0.716313 −0.358156 0.933662i \(-0.616595\pi\)
−0.358156 + 0.933662i \(0.616595\pi\)
\(152\) −2.69068 −0.218243
\(153\) 0 0
\(154\) −11.1641 −0.899627
\(155\) 7.05546 0.566708
\(156\) 0 0
\(157\) 23.7916 1.89878 0.949389 0.314102i \(-0.101703\pi\)
0.949389 + 0.314102i \(0.101703\pi\)
\(158\) 2.59929 0.206788
\(159\) 0 0
\(160\) 1.96687 0.155495
\(161\) 17.1690 1.35310
\(162\) 0 0
\(163\) 12.9127 1.01140 0.505699 0.862710i \(-0.331235\pi\)
0.505699 + 0.862710i \(0.331235\pi\)
\(164\) −6.88728 −0.537806
\(165\) 0 0
\(166\) −10.3231 −0.801230
\(167\) 12.1490 0.940119 0.470060 0.882635i \(-0.344232\pi\)
0.470060 + 0.882635i \(0.344232\pi\)
\(168\) 0 0
\(169\) −12.4484 −0.957567
\(170\) −2.75562 −0.211346
\(171\) 0 0
\(172\) −1.80326 −0.137497
\(173\) 4.61956 0.351219 0.175609 0.984460i \(-0.443810\pi\)
0.175609 + 0.984460i \(0.443810\pi\)
\(174\) 0 0
\(175\) 5.34137 0.403770
\(176\) 2.36478 0.178252
\(177\) 0 0
\(178\) 1.95400 0.146458
\(179\) 15.0982 1.12850 0.564248 0.825605i \(-0.309166\pi\)
0.564248 + 0.825605i \(0.309166\pi\)
\(180\) 0 0
\(181\) −18.5993 −1.38248 −0.691238 0.722627i \(-0.742934\pi\)
−0.691238 + 0.722627i \(0.742934\pi\)
\(182\) 3.50637 0.259909
\(183\) 0 0
\(184\) −3.63674 −0.268104
\(185\) 20.9067 1.53709
\(186\) 0 0
\(187\) −3.31310 −0.242278
\(188\) −2.73029 −0.199127
\(189\) 0 0
\(190\) −5.29222 −0.383938
\(191\) −16.7618 −1.21284 −0.606420 0.795145i \(-0.707395\pi\)
−0.606420 + 0.795145i \(0.707395\pi\)
\(192\) 0 0
\(193\) 9.50979 0.684530 0.342265 0.939604i \(-0.388806\pi\)
0.342265 + 0.939604i \(0.388806\pi\)
\(194\) 0.529108 0.0379878
\(195\) 0 0
\(196\) 15.2876 1.09197
\(197\) −3.67474 −0.261815 −0.130907 0.991395i \(-0.541789\pi\)
−0.130907 + 0.991395i \(0.541789\pi\)
\(198\) 0 0
\(199\) −3.86258 −0.273811 −0.136906 0.990584i \(-0.543716\pi\)
−0.136906 + 0.990584i \(0.543716\pi\)
\(200\) −1.13141 −0.0800031
\(201\) 0 0
\(202\) 4.78364 0.336575
\(203\) −4.62783 −0.324810
\(204\) 0 0
\(205\) −13.5464 −0.946121
\(206\) −1.60204 −0.111619
\(207\) 0 0
\(208\) −0.742721 −0.0514985
\(209\) −6.36287 −0.440129
\(210\) 0 0
\(211\) −2.33825 −0.160971 −0.0804857 0.996756i \(-0.525647\pi\)
−0.0804857 + 0.996756i \(0.525647\pi\)
\(212\) 1.45122 0.0996705
\(213\) 0 0
\(214\) −14.1668 −0.968425
\(215\) −3.54678 −0.241889
\(216\) 0 0
\(217\) −16.9348 −1.14961
\(218\) −14.8290 −1.00434
\(219\) 0 0
\(220\) 4.65123 0.313586
\(221\) 1.04056 0.0699959
\(222\) 0 0
\(223\) −0.0107588 −0.000720463 0 −0.000360232 1.00000i \(-0.500115\pi\)
−0.000360232 1.00000i \(0.500115\pi\)
\(224\) −4.72097 −0.315433
\(225\) 0 0
\(226\) 10.0435 0.668082
\(227\) −13.1054 −0.869839 −0.434919 0.900469i \(-0.643223\pi\)
−0.434919 + 0.900469i \(0.643223\pi\)
\(228\) 0 0
\(229\) −1.29209 −0.0853838 −0.0426919 0.999088i \(-0.513593\pi\)
−0.0426919 + 0.999088i \(0.513593\pi\)
\(230\) −7.15301 −0.471655
\(231\) 0 0
\(232\) 0.980272 0.0643580
\(233\) −15.7092 −1.02915 −0.514573 0.857447i \(-0.672050\pi\)
−0.514573 + 0.857447i \(0.672050\pi\)
\(234\) 0 0
\(235\) −5.37014 −0.350309
\(236\) −2.49561 −0.162450
\(237\) 0 0
\(238\) 6.61415 0.428732
\(239\) −17.2429 −1.11535 −0.557674 0.830060i \(-0.688306\pi\)
−0.557674 + 0.830060i \(0.688306\pi\)
\(240\) 0 0
\(241\) −14.6956 −0.946626 −0.473313 0.880894i \(-0.656942\pi\)
−0.473313 + 0.880894i \(0.656942\pi\)
\(242\) −5.40780 −0.347627
\(243\) 0 0
\(244\) −7.04971 −0.451311
\(245\) 30.0687 1.92102
\(246\) 0 0
\(247\) 1.99842 0.127157
\(248\) 3.58715 0.227784
\(249\) 0 0
\(250\) −12.0597 −0.762723
\(251\) 14.2238 0.897801 0.448901 0.893582i \(-0.351816\pi\)
0.448901 + 0.893582i \(0.351816\pi\)
\(252\) 0 0
\(253\) −8.60011 −0.540684
\(254\) −10.1650 −0.637807
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 17.3481 1.08215 0.541073 0.840976i \(-0.318018\pi\)
0.541073 + 0.840976i \(0.318018\pi\)
\(258\) 0 0
\(259\) −50.1813 −3.11811
\(260\) −1.46084 −0.0905973
\(261\) 0 0
\(262\) −14.2956 −0.883183
\(263\) 7.74953 0.477856 0.238928 0.971037i \(-0.423204\pi\)
0.238928 + 0.971037i \(0.423204\pi\)
\(264\) 0 0
\(265\) 2.85437 0.175343
\(266\) 12.7026 0.778847
\(267\) 0 0
\(268\) −4.95825 −0.302873
\(269\) 20.9413 1.27682 0.638408 0.769698i \(-0.279593\pi\)
0.638408 + 0.769698i \(0.279593\pi\)
\(270\) 0 0
\(271\) −12.6221 −0.766739 −0.383369 0.923595i \(-0.625236\pi\)
−0.383369 + 0.923595i \(0.625236\pi\)
\(272\) −1.40102 −0.0849490
\(273\) 0 0
\(274\) −2.27871 −0.137662
\(275\) −2.67555 −0.161342
\(276\) 0 0
\(277\) −23.0650 −1.38584 −0.692920 0.721014i \(-0.743676\pi\)
−0.692920 + 0.721014i \(0.743676\pi\)
\(278\) 2.63621 0.158109
\(279\) 0 0
\(280\) −9.28555 −0.554917
\(281\) 15.8213 0.943821 0.471911 0.881646i \(-0.343565\pi\)
0.471911 + 0.881646i \(0.343565\pi\)
\(282\) 0 0
\(283\) 8.98703 0.534224 0.267112 0.963666i \(-0.413931\pi\)
0.267112 + 0.963666i \(0.413931\pi\)
\(284\) −14.3379 −0.850798
\(285\) 0 0
\(286\) −1.75638 −0.103857
\(287\) 32.5146 1.91928
\(288\) 0 0
\(289\) −15.0372 −0.884539
\(290\) 1.92807 0.113220
\(291\) 0 0
\(292\) −7.71974 −0.451764
\(293\) 14.8801 0.869305 0.434652 0.900598i \(-0.356871\pi\)
0.434652 + 0.900598i \(0.356871\pi\)
\(294\) 0 0
\(295\) −4.90854 −0.285786
\(296\) 10.6294 0.617824
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 2.70109 0.156208
\(300\) 0 0
\(301\) 8.51314 0.490689
\(302\) −8.80220 −0.506510
\(303\) 0 0
\(304\) −2.69068 −0.154321
\(305\) −13.8659 −0.793958
\(306\) 0 0
\(307\) 19.0452 1.08697 0.543483 0.839420i \(-0.317105\pi\)
0.543483 + 0.839420i \(0.317105\pi\)
\(308\) −11.1641 −0.636132
\(309\) 0 0
\(310\) 7.05546 0.400723
\(311\) 4.29069 0.243303 0.121651 0.992573i \(-0.461181\pi\)
0.121651 + 0.992573i \(0.461181\pi\)
\(312\) 0 0
\(313\) 7.58104 0.428506 0.214253 0.976778i \(-0.431268\pi\)
0.214253 + 0.976778i \(0.431268\pi\)
\(314\) 23.7916 1.34264
\(315\) 0 0
\(316\) 2.59929 0.146221
\(317\) −9.19583 −0.516489 −0.258245 0.966080i \(-0.583144\pi\)
−0.258245 + 0.966080i \(0.583144\pi\)
\(318\) 0 0
\(319\) 2.31813 0.129790
\(320\) 1.96687 0.109951
\(321\) 0 0
\(322\) 17.1690 0.956788
\(323\) 3.76968 0.209751
\(324\) 0 0
\(325\) 0.840326 0.0466129
\(326\) 12.9127 0.715167
\(327\) 0 0
\(328\) −6.88728 −0.380286
\(329\) 12.8896 0.710629
\(330\) 0 0
\(331\) 17.4276 0.957907 0.478953 0.877840i \(-0.341016\pi\)
0.478953 + 0.877840i \(0.341016\pi\)
\(332\) −10.3231 −0.566555
\(333\) 0 0
\(334\) 12.1490 0.664765
\(335\) −9.75224 −0.532822
\(336\) 0 0
\(337\) −19.1104 −1.04101 −0.520504 0.853859i \(-0.674256\pi\)
−0.520504 + 0.853859i \(0.674256\pi\)
\(338\) −12.4484 −0.677102
\(339\) 0 0
\(340\) −2.75562 −0.149444
\(341\) 8.48283 0.459371
\(342\) 0 0
\(343\) −39.1254 −2.11257
\(344\) −1.80326 −0.0972253
\(345\) 0 0
\(346\) 4.61956 0.248349
\(347\) 2.29033 0.122951 0.0614756 0.998109i \(-0.480419\pi\)
0.0614756 + 0.998109i \(0.480419\pi\)
\(348\) 0 0
\(349\) 1.71719 0.0919192 0.0459596 0.998943i \(-0.485365\pi\)
0.0459596 + 0.998943i \(0.485365\pi\)
\(350\) 5.34137 0.285508
\(351\) 0 0
\(352\) 2.36478 0.126043
\(353\) 5.27408 0.280711 0.140356 0.990101i \(-0.455175\pi\)
0.140356 + 0.990101i \(0.455175\pi\)
\(354\) 0 0
\(355\) −28.2008 −1.49674
\(356\) 1.95400 0.103562
\(357\) 0 0
\(358\) 15.0982 0.797967
\(359\) −8.22530 −0.434115 −0.217057 0.976159i \(-0.569646\pi\)
−0.217057 + 0.976159i \(0.569646\pi\)
\(360\) 0 0
\(361\) −11.7603 −0.618961
\(362\) −18.5993 −0.977558
\(363\) 0 0
\(364\) 3.50637 0.183784
\(365\) −15.1837 −0.794754
\(366\) 0 0
\(367\) 10.6889 0.557957 0.278979 0.960297i \(-0.410004\pi\)
0.278979 + 0.960297i \(0.410004\pi\)
\(368\) −3.63674 −0.189578
\(369\) 0 0
\(370\) 20.9067 1.08689
\(371\) −6.85119 −0.355696
\(372\) 0 0
\(373\) 17.4257 0.902266 0.451133 0.892457i \(-0.351020\pi\)
0.451133 + 0.892457i \(0.351020\pi\)
\(374\) −3.31310 −0.171316
\(375\) 0 0
\(376\) −2.73029 −0.140804
\(377\) −0.728069 −0.0374974
\(378\) 0 0
\(379\) −26.0915 −1.34023 −0.670116 0.742257i \(-0.733756\pi\)
−0.670116 + 0.742257i \(0.733756\pi\)
\(380\) −5.29222 −0.271485
\(381\) 0 0
\(382\) −16.7618 −0.857607
\(383\) 25.7062 1.31352 0.656762 0.754098i \(-0.271926\pi\)
0.656762 + 0.754098i \(0.271926\pi\)
\(384\) 0 0
\(385\) −21.9583 −1.11910
\(386\) 9.50979 0.484036
\(387\) 0 0
\(388\) 0.529108 0.0268614
\(389\) −26.0895 −1.32279 −0.661396 0.750037i \(-0.730036\pi\)
−0.661396 + 0.750037i \(0.730036\pi\)
\(390\) 0 0
\(391\) 5.09513 0.257672
\(392\) 15.2876 0.772139
\(393\) 0 0
\(394\) −3.67474 −0.185131
\(395\) 5.11247 0.257236
\(396\) 0 0
\(397\) 33.2276 1.66765 0.833823 0.552033i \(-0.186148\pi\)
0.833823 + 0.552033i \(0.186148\pi\)
\(398\) −3.86258 −0.193614
\(399\) 0 0
\(400\) −1.13141 −0.0565707
\(401\) −9.03686 −0.451279 −0.225640 0.974211i \(-0.572447\pi\)
−0.225640 + 0.974211i \(0.572447\pi\)
\(402\) 0 0
\(403\) −2.66425 −0.132716
\(404\) 4.78364 0.237995
\(405\) 0 0
\(406\) −4.62783 −0.229676
\(407\) 25.1363 1.24596
\(408\) 0 0
\(409\) −0.663717 −0.0328187 −0.0164093 0.999865i \(-0.505223\pi\)
−0.0164093 + 0.999865i \(0.505223\pi\)
\(410\) −13.5464 −0.669008
\(411\) 0 0
\(412\) −1.60204 −0.0789268
\(413\) 11.7817 0.579739
\(414\) 0 0
\(415\) −20.3043 −0.996697
\(416\) −0.742721 −0.0364149
\(417\) 0 0
\(418\) −6.36287 −0.311218
\(419\) −23.3834 −1.14235 −0.571176 0.820827i \(-0.693513\pi\)
−0.571176 + 0.820827i \(0.693513\pi\)
\(420\) 0 0
\(421\) 8.86133 0.431875 0.215937 0.976407i \(-0.430719\pi\)
0.215937 + 0.976407i \(0.430719\pi\)
\(422\) −2.33825 −0.113824
\(423\) 0 0
\(424\) 1.45122 0.0704777
\(425\) 1.58513 0.0768900
\(426\) 0 0
\(427\) 33.2815 1.61060
\(428\) −14.1668 −0.684780
\(429\) 0 0
\(430\) −3.54678 −0.171041
\(431\) −11.0794 −0.533675 −0.266838 0.963741i \(-0.585979\pi\)
−0.266838 + 0.963741i \(0.585979\pi\)
\(432\) 0 0
\(433\) −4.17583 −0.200678 −0.100339 0.994953i \(-0.531993\pi\)
−0.100339 + 0.994953i \(0.531993\pi\)
\(434\) −16.9348 −0.812898
\(435\) 0 0
\(436\) −14.8290 −0.710179
\(437\) 9.78530 0.468095
\(438\) 0 0
\(439\) −2.56687 −0.122510 −0.0612550 0.998122i \(-0.519510\pi\)
−0.0612550 + 0.998122i \(0.519510\pi\)
\(440\) 4.65123 0.221738
\(441\) 0 0
\(442\) 1.04056 0.0494946
\(443\) 0.520689 0.0247387 0.0123693 0.999923i \(-0.496063\pi\)
0.0123693 + 0.999923i \(0.496063\pi\)
\(444\) 0 0
\(445\) 3.84326 0.182188
\(446\) −0.0107588 −0.000509444 0
\(447\) 0 0
\(448\) −4.72097 −0.223045
\(449\) −11.8948 −0.561348 −0.280674 0.959803i \(-0.590558\pi\)
−0.280674 + 0.959803i \(0.590558\pi\)
\(450\) 0 0
\(451\) −16.2869 −0.766921
\(452\) 10.0435 0.472405
\(453\) 0 0
\(454\) −13.1054 −0.615069
\(455\) 6.89657 0.323316
\(456\) 0 0
\(457\) −9.72256 −0.454802 −0.227401 0.973801i \(-0.573023\pi\)
−0.227401 + 0.973801i \(0.573023\pi\)
\(458\) −1.29209 −0.0603755
\(459\) 0 0
\(460\) −7.15301 −0.333511
\(461\) 21.1562 0.985341 0.492670 0.870216i \(-0.336021\pi\)
0.492670 + 0.870216i \(0.336021\pi\)
\(462\) 0 0
\(463\) −10.3735 −0.482098 −0.241049 0.970513i \(-0.577491\pi\)
−0.241049 + 0.970513i \(0.577491\pi\)
\(464\) 0.980272 0.0455080
\(465\) 0 0
\(466\) −15.7092 −0.727716
\(467\) −24.4398 −1.13094 −0.565470 0.824769i \(-0.691305\pi\)
−0.565470 + 0.824769i \(0.691305\pi\)
\(468\) 0 0
\(469\) 23.4078 1.08087
\(470\) −5.37014 −0.247706
\(471\) 0 0
\(472\) −2.49561 −0.114870
\(473\) −4.26432 −0.196074
\(474\) 0 0
\(475\) 3.04427 0.139681
\(476\) 6.61415 0.303159
\(477\) 0 0
\(478\) −17.2429 −0.788670
\(479\) −25.4413 −1.16244 −0.581222 0.813745i \(-0.697425\pi\)
−0.581222 + 0.813745i \(0.697425\pi\)
\(480\) 0 0
\(481\) −7.89471 −0.359968
\(482\) −14.6956 −0.669366
\(483\) 0 0
\(484\) −5.40780 −0.245809
\(485\) 1.04069 0.0472552
\(486\) 0 0
\(487\) 14.1757 0.642360 0.321180 0.947018i \(-0.395921\pi\)
0.321180 + 0.947018i \(0.395921\pi\)
\(488\) −7.04971 −0.319125
\(489\) 0 0
\(490\) 30.0687 1.35836
\(491\) 27.1441 1.22500 0.612499 0.790471i \(-0.290164\pi\)
0.612499 + 0.790471i \(0.290164\pi\)
\(492\) 0 0
\(493\) −1.37338 −0.0618537
\(494\) 1.99842 0.0899134
\(495\) 0 0
\(496\) 3.58715 0.161068
\(497\) 67.6888 3.03626
\(498\) 0 0
\(499\) 24.7065 1.10601 0.553007 0.833176i \(-0.313480\pi\)
0.553007 + 0.833176i \(0.313480\pi\)
\(500\) −12.0597 −0.539327
\(501\) 0 0
\(502\) 14.2238 0.634841
\(503\) 3.30721 0.147461 0.0737305 0.997278i \(-0.476510\pi\)
0.0737305 + 0.997278i \(0.476510\pi\)
\(504\) 0 0
\(505\) 9.40880 0.418686
\(506\) −8.60011 −0.382321
\(507\) 0 0
\(508\) −10.1650 −0.450998
\(509\) −10.6388 −0.471556 −0.235778 0.971807i \(-0.575764\pi\)
−0.235778 + 0.971807i \(0.575764\pi\)
\(510\) 0 0
\(511\) 36.4447 1.61222
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 17.3481 0.765193
\(515\) −3.15101 −0.138850
\(516\) 0 0
\(517\) −6.45656 −0.283959
\(518\) −50.1813 −2.20484
\(519\) 0 0
\(520\) −1.46084 −0.0640620
\(521\) 14.5721 0.638417 0.319209 0.947684i \(-0.396583\pi\)
0.319209 + 0.947684i \(0.396583\pi\)
\(522\) 0 0
\(523\) −16.0901 −0.703570 −0.351785 0.936081i \(-0.614425\pi\)
−0.351785 + 0.936081i \(0.614425\pi\)
\(524\) −14.2956 −0.624505
\(525\) 0 0
\(526\) 7.74953 0.337896
\(527\) −5.02565 −0.218921
\(528\) 0 0
\(529\) −9.77411 −0.424961
\(530\) 2.85437 0.123986
\(531\) 0 0
\(532\) 12.7026 0.550728
\(533\) 5.11533 0.221569
\(534\) 0 0
\(535\) −27.8643 −1.20468
\(536\) −4.95825 −0.214164
\(537\) 0 0
\(538\) 20.9413 0.902845
\(539\) 36.1518 1.55717
\(540\) 0 0
\(541\) 0.563076 0.0242085 0.0121043 0.999927i \(-0.496147\pi\)
0.0121043 + 0.999927i \(0.496147\pi\)
\(542\) −12.6221 −0.542166
\(543\) 0 0
\(544\) −1.40102 −0.0600680
\(545\) −29.1667 −1.24936
\(546\) 0 0
\(547\) 9.14176 0.390873 0.195437 0.980716i \(-0.437388\pi\)
0.195437 + 0.980716i \(0.437388\pi\)
\(548\) −2.27871 −0.0973417
\(549\) 0 0
\(550\) −2.67555 −0.114086
\(551\) −2.63760 −0.112365
\(552\) 0 0
\(553\) −12.2712 −0.521823
\(554\) −23.0650 −0.979937
\(555\) 0 0
\(556\) 2.63621 0.111800
\(557\) −14.7514 −0.625035 −0.312518 0.949912i \(-0.601172\pi\)
−0.312518 + 0.949912i \(0.601172\pi\)
\(558\) 0 0
\(559\) 1.33932 0.0566472
\(560\) −9.28555 −0.392386
\(561\) 0 0
\(562\) 15.8213 0.667382
\(563\) −2.58785 −0.109065 −0.0545324 0.998512i \(-0.517367\pi\)
−0.0545324 + 0.998512i \(0.517367\pi\)
\(564\) 0 0
\(565\) 19.7542 0.831067
\(566\) 8.98703 0.377753
\(567\) 0 0
\(568\) −14.3379 −0.601605
\(569\) 36.0992 1.51336 0.756678 0.653788i \(-0.226821\pi\)
0.756678 + 0.653788i \(0.226821\pi\)
\(570\) 0 0
\(571\) 11.7259 0.490714 0.245357 0.969433i \(-0.421095\pi\)
0.245357 + 0.969433i \(0.421095\pi\)
\(572\) −1.75638 −0.0734377
\(573\) 0 0
\(574\) 32.5146 1.35713
\(575\) 4.11466 0.171593
\(576\) 0 0
\(577\) 7.71463 0.321164 0.160582 0.987022i \(-0.448663\pi\)
0.160582 + 0.987022i \(0.448663\pi\)
\(578\) −15.0372 −0.625463
\(579\) 0 0
\(580\) 1.92807 0.0800587
\(581\) 48.7352 2.02188
\(582\) 0 0
\(583\) 3.43183 0.142132
\(584\) −7.71974 −0.319445
\(585\) 0 0
\(586\) 14.8801 0.614691
\(587\) 31.9581 1.31905 0.659526 0.751681i \(-0.270757\pi\)
0.659526 + 0.751681i \(0.270757\pi\)
\(588\) 0 0
\(589\) −9.65186 −0.397698
\(590\) −4.90854 −0.202081
\(591\) 0 0
\(592\) 10.6294 0.436867
\(593\) −9.78725 −0.401914 −0.200957 0.979600i \(-0.564405\pi\)
−0.200957 + 0.979600i \(0.564405\pi\)
\(594\) 0 0
\(595\) 13.0092 0.533325
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) 2.70109 0.110456
\(599\) 1.20677 0.0493071 0.0246535 0.999696i \(-0.492152\pi\)
0.0246535 + 0.999696i \(0.492152\pi\)
\(600\) 0 0
\(601\) −39.4430 −1.60891 −0.804456 0.594012i \(-0.797543\pi\)
−0.804456 + 0.594012i \(0.797543\pi\)
\(602\) 8.51314 0.346970
\(603\) 0 0
\(604\) −8.80220 −0.358156
\(605\) −10.6365 −0.432433
\(606\) 0 0
\(607\) −34.7465 −1.41032 −0.705159 0.709049i \(-0.749124\pi\)
−0.705159 + 0.709049i \(0.749124\pi\)
\(608\) −2.69068 −0.109121
\(609\) 0 0
\(610\) −13.8659 −0.561413
\(611\) 2.02785 0.0820380
\(612\) 0 0
\(613\) −7.46159 −0.301371 −0.150685 0.988582i \(-0.548148\pi\)
−0.150685 + 0.988582i \(0.548148\pi\)
\(614\) 19.0452 0.768600
\(615\) 0 0
\(616\) −11.1641 −0.449813
\(617\) 15.1694 0.610698 0.305349 0.952240i \(-0.401227\pi\)
0.305349 + 0.952240i \(0.401227\pi\)
\(618\) 0 0
\(619\) 29.1682 1.17237 0.586184 0.810178i \(-0.300630\pi\)
0.586184 + 0.810178i \(0.300630\pi\)
\(620\) 7.05546 0.283354
\(621\) 0 0
\(622\) 4.29069 0.172041
\(623\) −9.22476 −0.369582
\(624\) 0 0
\(625\) −18.0628 −0.722513
\(626\) 7.58104 0.302999
\(627\) 0 0
\(628\) 23.7916 0.949389
\(629\) −14.8920 −0.593783
\(630\) 0 0
\(631\) 23.2185 0.924314 0.462157 0.886798i \(-0.347076\pi\)
0.462157 + 0.886798i \(0.347076\pi\)
\(632\) 2.59929 0.103394
\(633\) 0 0
\(634\) −9.19583 −0.365213
\(635\) −19.9932 −0.793406
\(636\) 0 0
\(637\) −11.3544 −0.449878
\(638\) 2.31813 0.0917756
\(639\) 0 0
\(640\) 1.96687 0.0777474
\(641\) 45.2775 1.78835 0.894177 0.447714i \(-0.147762\pi\)
0.894177 + 0.447714i \(0.147762\pi\)
\(642\) 0 0
\(643\) 1.17400 0.0462980 0.0231490 0.999732i \(-0.492631\pi\)
0.0231490 + 0.999732i \(0.492631\pi\)
\(644\) 17.1690 0.676552
\(645\) 0 0
\(646\) 3.76968 0.148316
\(647\) −43.5948 −1.71389 −0.856945 0.515409i \(-0.827640\pi\)
−0.856945 + 0.515409i \(0.827640\pi\)
\(648\) 0 0
\(649\) −5.90157 −0.231657
\(650\) 0.840326 0.0329603
\(651\) 0 0
\(652\) 12.9127 0.505699
\(653\) 16.5167 0.646350 0.323175 0.946339i \(-0.395250\pi\)
0.323175 + 0.946339i \(0.395250\pi\)
\(654\) 0 0
\(655\) −28.1175 −1.09864
\(656\) −6.88728 −0.268903
\(657\) 0 0
\(658\) 12.8896 0.502491
\(659\) −30.3444 −1.18205 −0.591024 0.806654i \(-0.701276\pi\)
−0.591024 + 0.806654i \(0.701276\pi\)
\(660\) 0 0
\(661\) 45.5678 1.77238 0.886192 0.463319i \(-0.153341\pi\)
0.886192 + 0.463319i \(0.153341\pi\)
\(662\) 17.4276 0.677342
\(663\) 0 0
\(664\) −10.3231 −0.400615
\(665\) 24.9844 0.968854
\(666\) 0 0
\(667\) −3.56499 −0.138037
\(668\) 12.1490 0.470060
\(669\) 0 0
\(670\) −9.75224 −0.376762
\(671\) −16.6710 −0.643578
\(672\) 0 0
\(673\) 23.6770 0.912680 0.456340 0.889805i \(-0.349160\pi\)
0.456340 + 0.889805i \(0.349160\pi\)
\(674\) −19.1104 −0.736104
\(675\) 0 0
\(676\) −12.4484 −0.478783
\(677\) 31.7520 1.22033 0.610164 0.792276i \(-0.291104\pi\)
0.610164 + 0.792276i \(0.291104\pi\)
\(678\) 0 0
\(679\) −2.49790 −0.0958608
\(680\) −2.75562 −0.105673
\(681\) 0 0
\(682\) 8.48283 0.324824
\(683\) 19.1101 0.731228 0.365614 0.930767i \(-0.380859\pi\)
0.365614 + 0.930767i \(0.380859\pi\)
\(684\) 0 0
\(685\) −4.48193 −0.171246
\(686\) −39.1254 −1.49381
\(687\) 0 0
\(688\) −1.80326 −0.0687487
\(689\) −1.07786 −0.0410630
\(690\) 0 0
\(691\) −21.2510 −0.808426 −0.404213 0.914665i \(-0.632454\pi\)
−0.404213 + 0.914665i \(0.632454\pi\)
\(692\) 4.61956 0.175609
\(693\) 0 0
\(694\) 2.29033 0.0869396
\(695\) 5.18509 0.196682
\(696\) 0 0
\(697\) 9.64918 0.365489
\(698\) 1.71719 0.0649967
\(699\) 0 0
\(700\) 5.34137 0.201885
\(701\) 41.6697 1.57384 0.786922 0.617053i \(-0.211673\pi\)
0.786922 + 0.617053i \(0.211673\pi\)
\(702\) 0 0
\(703\) −28.6004 −1.07868
\(704\) 2.36478 0.0891261
\(705\) 0 0
\(706\) 5.27408 0.198493
\(707\) −22.5834 −0.849336
\(708\) 0 0
\(709\) 13.8554 0.520349 0.260174 0.965562i \(-0.416220\pi\)
0.260174 + 0.965562i \(0.416220\pi\)
\(710\) −28.2008 −1.05836
\(711\) 0 0
\(712\) 1.95400 0.0732291
\(713\) −13.0455 −0.488559
\(714\) 0 0
\(715\) −3.45456 −0.129193
\(716\) 15.0982 0.564248
\(717\) 0 0
\(718\) −8.22530 −0.306966
\(719\) 1.00407 0.0374455 0.0187228 0.999825i \(-0.494040\pi\)
0.0187228 + 0.999825i \(0.494040\pi\)
\(720\) 0 0
\(721\) 7.56318 0.281668
\(722\) −11.7603 −0.437671
\(723\) 0 0
\(724\) −18.5993 −0.691238
\(725\) −1.10909 −0.0411907
\(726\) 0 0
\(727\) 0.418696 0.0155286 0.00776429 0.999970i \(-0.497529\pi\)
0.00776429 + 0.999970i \(0.497529\pi\)
\(728\) 3.50637 0.129955
\(729\) 0 0
\(730\) −15.1837 −0.561976
\(731\) 2.52640 0.0934421
\(732\) 0 0
\(733\) −22.0840 −0.815690 −0.407845 0.913051i \(-0.633720\pi\)
−0.407845 + 0.913051i \(0.633720\pi\)
\(734\) 10.6889 0.394535
\(735\) 0 0
\(736\) −3.63674 −0.134052
\(737\) −11.7252 −0.431903
\(738\) 0 0
\(739\) −16.6984 −0.614259 −0.307130 0.951668i \(-0.599369\pi\)
−0.307130 + 0.951668i \(0.599369\pi\)
\(740\) 20.9067 0.768547
\(741\) 0 0
\(742\) −6.85119 −0.251515
\(743\) 15.4316 0.566132 0.283066 0.959100i \(-0.408648\pi\)
0.283066 + 0.959100i \(0.408648\pi\)
\(744\) 0 0
\(745\) −1.96687 −0.0720606
\(746\) 17.4257 0.637999
\(747\) 0 0
\(748\) −3.31310 −0.121139
\(749\) 66.8812 2.44379
\(750\) 0 0
\(751\) −24.8441 −0.906573 −0.453287 0.891365i \(-0.649749\pi\)
−0.453287 + 0.891365i \(0.649749\pi\)
\(752\) −2.73029 −0.0995636
\(753\) 0 0
\(754\) −0.728069 −0.0265147
\(755\) −17.3128 −0.630077
\(756\) 0 0
\(757\) −3.28099 −0.119250 −0.0596248 0.998221i \(-0.518990\pi\)
−0.0596248 + 0.998221i \(0.518990\pi\)
\(758\) −26.0915 −0.947687
\(759\) 0 0
\(760\) −5.29222 −0.191969
\(761\) 11.8041 0.427898 0.213949 0.976845i \(-0.431367\pi\)
0.213949 + 0.976845i \(0.431367\pi\)
\(762\) 0 0
\(763\) 70.0071 2.53443
\(764\) −16.7618 −0.606420
\(765\) 0 0
\(766\) 25.7062 0.928801
\(767\) 1.85354 0.0669275
\(768\) 0 0
\(769\) 45.5064 1.64100 0.820502 0.571644i \(-0.193694\pi\)
0.820502 + 0.571644i \(0.193694\pi\)
\(770\) −21.9583 −0.791322
\(771\) 0 0
\(772\) 9.50979 0.342265
\(773\) −32.3417 −1.16325 −0.581625 0.813457i \(-0.697583\pi\)
−0.581625 + 0.813457i \(0.697583\pi\)
\(774\) 0 0
\(775\) −4.05855 −0.145788
\(776\) 0.529108 0.0189939
\(777\) 0 0
\(778\) −26.0895 −0.935355
\(779\) 18.5314 0.663958
\(780\) 0 0
\(781\) −33.9060 −1.21325
\(782\) 5.09513 0.182201
\(783\) 0 0
\(784\) 15.2876 0.545985
\(785\) 46.7951 1.67019
\(786\) 0 0
\(787\) 26.6379 0.949538 0.474769 0.880110i \(-0.342532\pi\)
0.474769 + 0.880110i \(0.342532\pi\)
\(788\) −3.67474 −0.130907
\(789\) 0 0
\(790\) 5.11247 0.181893
\(791\) −47.4149 −1.68588
\(792\) 0 0
\(793\) 5.23597 0.185935
\(794\) 33.2276 1.17920
\(795\) 0 0
\(796\) −3.86258 −0.136906
\(797\) 24.6220 0.872156 0.436078 0.899909i \(-0.356367\pi\)
0.436078 + 0.899909i \(0.356367\pi\)
\(798\) 0 0
\(799\) 3.82518 0.135325
\(800\) −1.13141 −0.0400015
\(801\) 0 0
\(802\) −9.03686 −0.319103
\(803\) −18.2555 −0.644223
\(804\) 0 0
\(805\) 33.7691 1.19021
\(806\) −2.66425 −0.0938443
\(807\) 0 0
\(808\) 4.78364 0.168288
\(809\) −20.3222 −0.714492 −0.357246 0.934010i \(-0.616284\pi\)
−0.357246 + 0.934010i \(0.616284\pi\)
\(810\) 0 0
\(811\) −25.0866 −0.880910 −0.440455 0.897775i \(-0.645183\pi\)
−0.440455 + 0.897775i \(0.645183\pi\)
\(812\) −4.62783 −0.162405
\(813\) 0 0
\(814\) 25.1363 0.881028
\(815\) 25.3976 0.889638
\(816\) 0 0
\(817\) 4.85200 0.169750
\(818\) −0.663717 −0.0232063
\(819\) 0 0
\(820\) −13.5464 −0.473060
\(821\) 27.8602 0.972329 0.486165 0.873867i \(-0.338396\pi\)
0.486165 + 0.873867i \(0.338396\pi\)
\(822\) 0 0
\(823\) 2.46781 0.0860226 0.0430113 0.999075i \(-0.486305\pi\)
0.0430113 + 0.999075i \(0.486305\pi\)
\(824\) −1.60204 −0.0558097
\(825\) 0 0
\(826\) 11.7817 0.409937
\(827\) 29.2732 1.01793 0.508964 0.860788i \(-0.330028\pi\)
0.508964 + 0.860788i \(0.330028\pi\)
\(828\) 0 0
\(829\) −4.23609 −0.147125 −0.0735627 0.997291i \(-0.523437\pi\)
−0.0735627 + 0.997291i \(0.523437\pi\)
\(830\) −20.3043 −0.704771
\(831\) 0 0
\(832\) −0.742721 −0.0257492
\(833\) −21.4181 −0.742094
\(834\) 0 0
\(835\) 23.8956 0.826940
\(836\) −6.36287 −0.220064
\(837\) 0 0
\(838\) −23.3834 −0.807765
\(839\) −28.5329 −0.985066 −0.492533 0.870294i \(-0.663929\pi\)
−0.492533 + 0.870294i \(0.663929\pi\)
\(840\) 0 0
\(841\) −28.0391 −0.966864
\(842\) 8.86133 0.305381
\(843\) 0 0
\(844\) −2.33825 −0.0804857
\(845\) −24.4843 −0.842287
\(846\) 0 0
\(847\) 25.5301 0.877224
\(848\) 1.45122 0.0498352
\(849\) 0 0
\(850\) 1.58513 0.0543695
\(851\) −38.6565 −1.32513
\(852\) 0 0
\(853\) −11.3607 −0.388983 −0.194491 0.980904i \(-0.562306\pi\)
−0.194491 + 0.980904i \(0.562306\pi\)
\(854\) 33.2815 1.13887
\(855\) 0 0
\(856\) −14.1668 −0.484212
\(857\) 54.4857 1.86120 0.930599 0.366041i \(-0.119287\pi\)
0.930599 + 0.366041i \(0.119287\pi\)
\(858\) 0 0
\(859\) −44.3209 −1.51221 −0.756105 0.654450i \(-0.772900\pi\)
−0.756105 + 0.654450i \(0.772900\pi\)
\(860\) −3.54678 −0.120944
\(861\) 0 0
\(862\) −11.0794 −0.377366
\(863\) −39.7757 −1.35398 −0.676990 0.735992i \(-0.736716\pi\)
−0.676990 + 0.735992i \(0.736716\pi\)
\(864\) 0 0
\(865\) 9.08609 0.308936
\(866\) −4.17583 −0.141901
\(867\) 0 0
\(868\) −16.9348 −0.574805
\(869\) 6.14675 0.208514
\(870\) 0 0
\(871\) 3.68260 0.124780
\(872\) −14.8290 −0.502172
\(873\) 0 0
\(874\) 9.78530 0.330993
\(875\) 56.9335 1.92470
\(876\) 0 0
\(877\) 46.3619 1.56553 0.782765 0.622318i \(-0.213809\pi\)
0.782765 + 0.622318i \(0.213809\pi\)
\(878\) −2.56687 −0.0866276
\(879\) 0 0
\(880\) 4.65123 0.156793
\(881\) 14.5453 0.490045 0.245023 0.969517i \(-0.421205\pi\)
0.245023 + 0.969517i \(0.421205\pi\)
\(882\) 0 0
\(883\) −57.5300 −1.93604 −0.968019 0.250877i \(-0.919281\pi\)
−0.968019 + 0.250877i \(0.919281\pi\)
\(884\) 1.04056 0.0349980
\(885\) 0 0
\(886\) 0.520689 0.0174929
\(887\) 27.8500 0.935113 0.467556 0.883963i \(-0.345134\pi\)
0.467556 + 0.883963i \(0.345134\pi\)
\(888\) 0 0
\(889\) 47.9886 1.60948
\(890\) 3.84326 0.128826
\(891\) 0 0
\(892\) −0.0107588 −0.000360232 0
\(893\) 7.34635 0.245836
\(894\) 0 0
\(895\) 29.6963 0.992638
\(896\) −4.72097 −0.157717
\(897\) 0 0
\(898\) −11.8948 −0.396933
\(899\) 3.51638 0.117278
\(900\) 0 0
\(901\) −2.03319 −0.0677353
\(902\) −16.2869 −0.542295
\(903\) 0 0
\(904\) 10.0435 0.334041
\(905\) −36.5824 −1.21604
\(906\) 0 0
\(907\) 59.4138 1.97280 0.986401 0.164356i \(-0.0525547\pi\)
0.986401 + 0.164356i \(0.0525547\pi\)
\(908\) −13.1054 −0.434919
\(909\) 0 0
\(910\) 6.89657 0.228619
\(911\) −35.8757 −1.18861 −0.594307 0.804238i \(-0.702574\pi\)
−0.594307 + 0.804238i \(0.702574\pi\)
\(912\) 0 0
\(913\) −24.4119 −0.807917
\(914\) −9.72256 −0.321594
\(915\) 0 0
\(916\) −1.29209 −0.0426919
\(917\) 67.4889 2.22868
\(918\) 0 0
\(919\) −35.9219 −1.18495 −0.592477 0.805588i \(-0.701850\pi\)
−0.592477 + 0.805588i \(0.701850\pi\)
\(920\) −7.15301 −0.235828
\(921\) 0 0
\(922\) 21.1562 0.696741
\(923\) 10.6491 0.350518
\(924\) 0 0
\(925\) −12.0263 −0.395422
\(926\) −10.3735 −0.340895
\(927\) 0 0
\(928\) 0.980272 0.0321790
\(929\) 12.3339 0.404662 0.202331 0.979317i \(-0.435148\pi\)
0.202331 + 0.979317i \(0.435148\pi\)
\(930\) 0 0
\(931\) −41.1339 −1.34811
\(932\) −15.7092 −0.514573
\(933\) 0 0
\(934\) −24.4398 −0.799695
\(935\) −6.51644 −0.213110
\(936\) 0 0
\(937\) 12.2201 0.399212 0.199606 0.979876i \(-0.436034\pi\)
0.199606 + 0.979876i \(0.436034\pi\)
\(938\) 23.4078 0.764290
\(939\) 0 0
\(940\) −5.37014 −0.175155
\(941\) −43.5255 −1.41889 −0.709446 0.704760i \(-0.751055\pi\)
−0.709446 + 0.704760i \(0.751055\pi\)
\(942\) 0 0
\(943\) 25.0472 0.815651
\(944\) −2.49561 −0.0812251
\(945\) 0 0
\(946\) −4.26432 −0.138645
\(947\) 20.9375 0.680377 0.340188 0.940357i \(-0.389509\pi\)
0.340188 + 0.940357i \(0.389509\pi\)
\(948\) 0 0
\(949\) 5.73362 0.186121
\(950\) 3.04427 0.0987692
\(951\) 0 0
\(952\) 6.61415 0.214366
\(953\) −26.0035 −0.842336 −0.421168 0.906983i \(-0.638380\pi\)
−0.421168 + 0.906983i \(0.638380\pi\)
\(954\) 0 0
\(955\) −32.9683 −1.06683
\(956\) −17.2429 −0.557674
\(957\) 0 0
\(958\) −25.4413 −0.821973
\(959\) 10.7577 0.347385
\(960\) 0 0
\(961\) −18.1324 −0.584915
\(962\) −7.89471 −0.254536
\(963\) 0 0
\(964\) −14.6956 −0.473313
\(965\) 18.7045 0.602120
\(966\) 0 0
\(967\) −32.4654 −1.04402 −0.522008 0.852941i \(-0.674817\pi\)
−0.522008 + 0.852941i \(0.674817\pi\)
\(968\) −5.40780 −0.173813
\(969\) 0 0
\(970\) 1.04069 0.0334145
\(971\) 56.3554 1.80853 0.904265 0.426971i \(-0.140419\pi\)
0.904265 + 0.426971i \(0.140419\pi\)
\(972\) 0 0
\(973\) −12.4455 −0.398984
\(974\) 14.1757 0.454217
\(975\) 0 0
\(976\) −7.04971 −0.225656
\(977\) −22.5573 −0.721673 −0.360837 0.932629i \(-0.617509\pi\)
−0.360837 + 0.932629i \(0.617509\pi\)
\(978\) 0 0
\(979\) 4.62078 0.147681
\(980\) 30.0687 0.960509
\(981\) 0 0
\(982\) 27.1441 0.866204
\(983\) −2.66000 −0.0848407 −0.0424204 0.999100i \(-0.513507\pi\)
−0.0424204 + 0.999100i \(0.513507\pi\)
\(984\) 0 0
\(985\) −7.22775 −0.230295
\(986\) −1.37338 −0.0437372
\(987\) 0 0
\(988\) 1.99842 0.0635784
\(989\) 6.55800 0.208532
\(990\) 0 0
\(991\) −18.0611 −0.573730 −0.286865 0.957971i \(-0.592613\pi\)
−0.286865 + 0.957971i \(0.592613\pi\)
\(992\) 3.58715 0.113892
\(993\) 0 0
\(994\) 67.6888 2.14696
\(995\) −7.59721 −0.240848
\(996\) 0 0
\(997\) 48.9423 1.55002 0.775009 0.631950i \(-0.217745\pi\)
0.775009 + 0.631950i \(0.217745\pi\)
\(998\) 24.7065 0.782070
\(999\) 0 0
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 \(a_p\))