Properties

Label 8016.2.a.be.1.1
Level 8016
Weight 2
Character 8016.1
Self dual yes
Analytic conductor 64.008
Analytic rank 0
Dimension 11
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + 292 x^{2} - 5687 x + 242\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.54432\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.54432 q^{5} -0.525270 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.54432 q^{5} -0.525270 q^{7} +1.00000 q^{9} -5.59056 q^{11} +1.57904 q^{13} -2.54432 q^{15} +4.20935 q^{17} -3.78855 q^{19} -0.525270 q^{21} +2.45151 q^{23} +1.47356 q^{25} +1.00000 q^{27} -4.24006 q^{29} +5.76018 q^{31} -5.59056 q^{33} +1.33645 q^{35} -2.67489 q^{37} +1.57904 q^{39} +10.7672 q^{41} -8.36680 q^{43} -2.54432 q^{45} -4.77944 q^{47} -6.72409 q^{49} +4.20935 q^{51} -2.34459 q^{53} +14.2242 q^{55} -3.78855 q^{57} +5.25946 q^{59} -5.02359 q^{61} -0.525270 q^{63} -4.01758 q^{65} -8.91781 q^{67} +2.45151 q^{69} +5.10616 q^{71} -2.16373 q^{73} +1.47356 q^{75} +2.93655 q^{77} +2.52659 q^{79} +1.00000 q^{81} +4.01520 q^{83} -10.7099 q^{85} -4.24006 q^{87} +16.2275 q^{89} -0.829422 q^{91} +5.76018 q^{93} +9.63928 q^{95} -16.4673 q^{97} -5.59056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + O(q^{10}) \) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + q^{11} + 10q^{13} + 10q^{15} + 17q^{17} - 2q^{19} + q^{21} + 3q^{23} + 21q^{25} + 11q^{27} + 17q^{29} + 15q^{31} + q^{33} - 11q^{35} + 4q^{37} + 10q^{39} + 16q^{41} - 10q^{43} + 10q^{45} + 16q^{47} + 22q^{49} + 17q^{51} + 42q^{53} + 5q^{55} - 2q^{57} + 2q^{59} + 12q^{61} + q^{63} + 10q^{65} + q^{67} + 3q^{69} + 9q^{71} + 24q^{73} + 21q^{75} + 22q^{77} + 30q^{79} + 11q^{81} - 16q^{83} + 25q^{85} + 17q^{87} + 37q^{89} - q^{91} + 15q^{93} - 5q^{95} + 4q^{97} + q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −2.54432 −1.13785 −0.568927 0.822388i \(-0.692641\pi\)
−0.568927 + 0.822388i \(0.692641\pi\)
\(6\) 0 0
\(7\) −0.525270 −0.198533 −0.0992667 0.995061i \(-0.531650\pi\)
−0.0992667 + 0.995061i \(0.531650\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.59056 −1.68562 −0.842809 0.538213i \(-0.819100\pi\)
−0.842809 + 0.538213i \(0.819100\pi\)
\(12\) 0 0
\(13\) 1.57904 0.437947 0.218974 0.975731i \(-0.429729\pi\)
0.218974 + 0.975731i \(0.429729\pi\)
\(14\) 0 0
\(15\) −2.54432 −0.656940
\(16\) 0 0
\(17\) 4.20935 1.02092 0.510459 0.859902i \(-0.329476\pi\)
0.510459 + 0.859902i \(0.329476\pi\)
\(18\) 0 0
\(19\) −3.78855 −0.869153 −0.434577 0.900635i \(-0.643102\pi\)
−0.434577 + 0.900635i \(0.643102\pi\)
\(20\) 0 0
\(21\) −0.525270 −0.114623
\(22\) 0 0
\(23\) 2.45151 0.511174 0.255587 0.966786i \(-0.417731\pi\)
0.255587 + 0.966786i \(0.417731\pi\)
\(24\) 0 0
\(25\) 1.47356 0.294711
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.24006 −0.787359 −0.393679 0.919248i \(-0.628798\pi\)
−0.393679 + 0.919248i \(0.628798\pi\)
\(30\) 0 0
\(31\) 5.76018 1.03456 0.517279 0.855817i \(-0.326945\pi\)
0.517279 + 0.855817i \(0.326945\pi\)
\(32\) 0 0
\(33\) −5.59056 −0.973192
\(34\) 0 0
\(35\) 1.33645 0.225902
\(36\) 0 0
\(37\) −2.67489 −0.439749 −0.219874 0.975528i \(-0.570565\pi\)
−0.219874 + 0.975528i \(0.570565\pi\)
\(38\) 0 0
\(39\) 1.57904 0.252849
\(40\) 0 0
\(41\) 10.7672 1.68155 0.840774 0.541387i \(-0.182101\pi\)
0.840774 + 0.541387i \(0.182101\pi\)
\(42\) 0 0
\(43\) −8.36680 −1.27593 −0.637963 0.770067i \(-0.720223\pi\)
−0.637963 + 0.770067i \(0.720223\pi\)
\(44\) 0 0
\(45\) −2.54432 −0.379285
\(46\) 0 0
\(47\) −4.77944 −0.697153 −0.348577 0.937280i \(-0.613335\pi\)
−0.348577 + 0.937280i \(0.613335\pi\)
\(48\) 0 0
\(49\) −6.72409 −0.960585
\(50\) 0 0
\(51\) 4.20935 0.589427
\(52\) 0 0
\(53\) −2.34459 −0.322054 −0.161027 0.986950i \(-0.551481\pi\)
−0.161027 + 0.986950i \(0.551481\pi\)
\(54\) 0 0
\(55\) 14.2242 1.91799
\(56\) 0 0
\(57\) −3.78855 −0.501806
\(58\) 0 0
\(59\) 5.25946 0.684723 0.342362 0.939568i \(-0.388773\pi\)
0.342362 + 0.939568i \(0.388773\pi\)
\(60\) 0 0
\(61\) −5.02359 −0.643205 −0.321602 0.946875i \(-0.604221\pi\)
−0.321602 + 0.946875i \(0.604221\pi\)
\(62\) 0 0
\(63\) −0.525270 −0.0661778
\(64\) 0 0
\(65\) −4.01758 −0.498320
\(66\) 0 0
\(67\) −8.91781 −1.08948 −0.544742 0.838604i \(-0.683372\pi\)
−0.544742 + 0.838604i \(0.683372\pi\)
\(68\) 0 0
\(69\) 2.45151 0.295127
\(70\) 0 0
\(71\) 5.10616 0.605990 0.302995 0.952992i \(-0.402013\pi\)
0.302995 + 0.952992i \(0.402013\pi\)
\(72\) 0 0
\(73\) −2.16373 −0.253246 −0.126623 0.991951i \(-0.540414\pi\)
−0.126623 + 0.991951i \(0.540414\pi\)
\(74\) 0 0
\(75\) 1.47356 0.170151
\(76\) 0 0
\(77\) 2.93655 0.334651
\(78\) 0 0
\(79\) 2.52659 0.284263 0.142132 0.989848i \(-0.454604\pi\)
0.142132 + 0.989848i \(0.454604\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 4.01520 0.440726 0.220363 0.975418i \(-0.429276\pi\)
0.220363 + 0.975418i \(0.429276\pi\)
\(84\) 0 0
\(85\) −10.7099 −1.16165
\(86\) 0 0
\(87\) −4.24006 −0.454582
\(88\) 0 0
\(89\) 16.2275 1.72011 0.860055 0.510201i \(-0.170429\pi\)
0.860055 + 0.510201i \(0.170429\pi\)
\(90\) 0 0
\(91\) −0.829422 −0.0869471
\(92\) 0 0
\(93\) 5.76018 0.597303
\(94\) 0 0
\(95\) 9.63928 0.988969
\(96\) 0 0
\(97\) −16.4673 −1.67201 −0.836003 0.548725i \(-0.815113\pi\)
−0.836003 + 0.548725i \(0.815113\pi\)
\(98\) 0 0
\(99\) −5.59056 −0.561873
\(100\) 0 0
\(101\) −7.51102 −0.747374 −0.373687 0.927555i \(-0.621907\pi\)
−0.373687 + 0.927555i \(0.621907\pi\)
\(102\) 0 0
\(103\) −1.49723 −0.147527 −0.0737634 0.997276i \(-0.523501\pi\)
−0.0737634 + 0.997276i \(0.523501\pi\)
\(104\) 0 0
\(105\) 1.33645 0.130425
\(106\) 0 0
\(107\) 2.29357 0.221728 0.110864 0.993836i \(-0.464638\pi\)
0.110864 + 0.993836i \(0.464638\pi\)
\(108\) 0 0
\(109\) 13.3290 1.27669 0.638344 0.769751i \(-0.279620\pi\)
0.638344 + 0.769751i \(0.279620\pi\)
\(110\) 0 0
\(111\) −2.67489 −0.253889
\(112\) 0 0
\(113\) 18.9368 1.78142 0.890711 0.454570i \(-0.150207\pi\)
0.890711 + 0.454570i \(0.150207\pi\)
\(114\) 0 0
\(115\) −6.23741 −0.581642
\(116\) 0 0
\(117\) 1.57904 0.145982
\(118\) 0 0
\(119\) −2.21104 −0.202686
\(120\) 0 0
\(121\) 20.2544 1.84131
\(122\) 0 0
\(123\) 10.7672 0.970842
\(124\) 0 0
\(125\) 8.97240 0.802516
\(126\) 0 0
\(127\) 0.286281 0.0254034 0.0127017 0.999919i \(-0.495957\pi\)
0.0127017 + 0.999919i \(0.495957\pi\)
\(128\) 0 0
\(129\) −8.36680 −0.736656
\(130\) 0 0
\(131\) −12.5000 −1.09213 −0.546064 0.837744i \(-0.683874\pi\)
−0.546064 + 0.837744i \(0.683874\pi\)
\(132\) 0 0
\(133\) 1.99001 0.172556
\(134\) 0 0
\(135\) −2.54432 −0.218980
\(136\) 0 0
\(137\) 12.4508 1.06374 0.531872 0.846825i \(-0.321489\pi\)
0.531872 + 0.846825i \(0.321489\pi\)
\(138\) 0 0
\(139\) −13.8333 −1.17333 −0.586663 0.809831i \(-0.699559\pi\)
−0.586663 + 0.809831i \(0.699559\pi\)
\(140\) 0 0
\(141\) −4.77944 −0.402502
\(142\) 0 0
\(143\) −8.82773 −0.738212
\(144\) 0 0
\(145\) 10.7881 0.895899
\(146\) 0 0
\(147\) −6.72409 −0.554594
\(148\) 0 0
\(149\) 17.9274 1.46867 0.734335 0.678787i \(-0.237494\pi\)
0.734335 + 0.678787i \(0.237494\pi\)
\(150\) 0 0
\(151\) 5.27238 0.429061 0.214530 0.976717i \(-0.431178\pi\)
0.214530 + 0.976717i \(0.431178\pi\)
\(152\) 0 0
\(153\) 4.20935 0.340306
\(154\) 0 0
\(155\) −14.6557 −1.17718
\(156\) 0 0
\(157\) 23.2595 1.85631 0.928155 0.372195i \(-0.121395\pi\)
0.928155 + 0.372195i \(0.121395\pi\)
\(158\) 0 0
\(159\) −2.34459 −0.185938
\(160\) 0 0
\(161\) −1.28770 −0.101485
\(162\) 0 0
\(163\) 21.8496 1.71139 0.855696 0.517478i \(-0.173129\pi\)
0.855696 + 0.517478i \(0.173129\pi\)
\(164\) 0 0
\(165\) 14.2242 1.10735
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −10.5066 −0.808202
\(170\) 0 0
\(171\) −3.78855 −0.289718
\(172\) 0 0
\(173\) 10.0266 0.762310 0.381155 0.924511i \(-0.375526\pi\)
0.381155 + 0.924511i \(0.375526\pi\)
\(174\) 0 0
\(175\) −0.774014 −0.0585100
\(176\) 0 0
\(177\) 5.25946 0.395325
\(178\) 0 0
\(179\) −0.201597 −0.0150681 −0.00753404 0.999972i \(-0.502398\pi\)
−0.00753404 + 0.999972i \(0.502398\pi\)
\(180\) 0 0
\(181\) 11.7308 0.871946 0.435973 0.899960i \(-0.356404\pi\)
0.435973 + 0.899960i \(0.356404\pi\)
\(182\) 0 0
\(183\) −5.02359 −0.371354
\(184\) 0 0
\(185\) 6.80576 0.500370
\(186\) 0 0
\(187\) −23.5326 −1.72088
\(188\) 0 0
\(189\) −0.525270 −0.0382078
\(190\) 0 0
\(191\) 25.0393 1.81178 0.905891 0.423511i \(-0.139203\pi\)
0.905891 + 0.423511i \(0.139203\pi\)
\(192\) 0 0
\(193\) −10.7710 −0.775315 −0.387658 0.921803i \(-0.626716\pi\)
−0.387658 + 0.921803i \(0.626716\pi\)
\(194\) 0 0
\(195\) −4.01758 −0.287705
\(196\) 0 0
\(197\) 11.1738 0.796102 0.398051 0.917363i \(-0.369687\pi\)
0.398051 + 0.917363i \(0.369687\pi\)
\(198\) 0 0
\(199\) 23.0987 1.63742 0.818710 0.574207i \(-0.194690\pi\)
0.818710 + 0.574207i \(0.194690\pi\)
\(200\) 0 0
\(201\) −8.91781 −0.629014
\(202\) 0 0
\(203\) 2.22717 0.156317
\(204\) 0 0
\(205\) −27.3951 −1.91335
\(206\) 0 0
\(207\) 2.45151 0.170391
\(208\) 0 0
\(209\) 21.1801 1.46506
\(210\) 0 0
\(211\) 8.65386 0.595756 0.297878 0.954604i \(-0.403721\pi\)
0.297878 + 0.954604i \(0.403721\pi\)
\(212\) 0 0
\(213\) 5.10616 0.349868
\(214\) 0 0
\(215\) 21.2878 1.45182
\(216\) 0 0
\(217\) −3.02565 −0.205394
\(218\) 0 0
\(219\) −2.16373 −0.146212
\(220\) 0 0
\(221\) 6.64673 0.447108
\(222\) 0 0
\(223\) −3.47630 −0.232791 −0.116395 0.993203i \(-0.537134\pi\)
−0.116395 + 0.993203i \(0.537134\pi\)
\(224\) 0 0
\(225\) 1.47356 0.0982370
\(226\) 0 0
\(227\) −4.99391 −0.331458 −0.165729 0.986171i \(-0.552998\pi\)
−0.165729 + 0.986171i \(0.552998\pi\)
\(228\) 0 0
\(229\) −0.724364 −0.0478673 −0.0239337 0.999714i \(-0.507619\pi\)
−0.0239337 + 0.999714i \(0.507619\pi\)
\(230\) 0 0
\(231\) 2.93655 0.193211
\(232\) 0 0
\(233\) 3.07905 0.201716 0.100858 0.994901i \(-0.467841\pi\)
0.100858 + 0.994901i \(0.467841\pi\)
\(234\) 0 0
\(235\) 12.1604 0.793258
\(236\) 0 0
\(237\) 2.52659 0.164120
\(238\) 0 0
\(239\) −23.7125 −1.53383 −0.766916 0.641748i \(-0.778210\pi\)
−0.766916 + 0.641748i \(0.778210\pi\)
\(240\) 0 0
\(241\) 14.1304 0.910219 0.455109 0.890436i \(-0.349600\pi\)
0.455109 + 0.890436i \(0.349600\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 17.1082 1.09300
\(246\) 0 0
\(247\) −5.98227 −0.380643
\(248\) 0 0
\(249\) 4.01520 0.254453
\(250\) 0 0
\(251\) −0.523099 −0.0330177 −0.0165089 0.999864i \(-0.505255\pi\)
−0.0165089 + 0.999864i \(0.505255\pi\)
\(252\) 0 0
\(253\) −13.7053 −0.861645
\(254\) 0 0
\(255\) −10.7099 −0.670682
\(256\) 0 0
\(257\) 19.5504 1.21952 0.609761 0.792586i \(-0.291266\pi\)
0.609761 + 0.792586i \(0.291266\pi\)
\(258\) 0 0
\(259\) 1.40504 0.0873048
\(260\) 0 0
\(261\) −4.24006 −0.262453
\(262\) 0 0
\(263\) 2.94567 0.181638 0.0908189 0.995867i \(-0.471052\pi\)
0.0908189 + 0.995867i \(0.471052\pi\)
\(264\) 0 0
\(265\) 5.96539 0.366451
\(266\) 0 0
\(267\) 16.2275 0.993106
\(268\) 0 0
\(269\) 9.57622 0.583872 0.291936 0.956438i \(-0.405701\pi\)
0.291936 + 0.956438i \(0.405701\pi\)
\(270\) 0 0
\(271\) −24.1059 −1.46433 −0.732164 0.681128i \(-0.761490\pi\)
−0.732164 + 0.681128i \(0.761490\pi\)
\(272\) 0 0
\(273\) −0.829422 −0.0501989
\(274\) 0 0
\(275\) −8.23800 −0.496770
\(276\) 0 0
\(277\) −2.19302 −0.131766 −0.0658828 0.997827i \(-0.520986\pi\)
−0.0658828 + 0.997827i \(0.520986\pi\)
\(278\) 0 0
\(279\) 5.76018 0.344853
\(280\) 0 0
\(281\) 6.78076 0.404506 0.202253 0.979333i \(-0.435174\pi\)
0.202253 + 0.979333i \(0.435174\pi\)
\(282\) 0 0
\(283\) 4.02725 0.239395 0.119697 0.992810i \(-0.461808\pi\)
0.119697 + 0.992810i \(0.461808\pi\)
\(284\) 0 0
\(285\) 9.63928 0.570982
\(286\) 0 0
\(287\) −5.65566 −0.333843
\(288\) 0 0
\(289\) 0.718627 0.0422722
\(290\) 0 0
\(291\) −16.4673 −0.965333
\(292\) 0 0
\(293\) 22.8461 1.33468 0.667342 0.744751i \(-0.267432\pi\)
0.667342 + 0.744751i \(0.267432\pi\)
\(294\) 0 0
\(295\) −13.3817 −0.779115
\(296\) 0 0
\(297\) −5.59056 −0.324397
\(298\) 0 0
\(299\) 3.87103 0.223867
\(300\) 0 0
\(301\) 4.39483 0.253314
\(302\) 0 0
\(303\) −7.51102 −0.431497
\(304\) 0 0
\(305\) 12.7816 0.731873
\(306\) 0 0
\(307\) −2.74814 −0.156845 −0.0784223 0.996920i \(-0.524988\pi\)
−0.0784223 + 0.996920i \(0.524988\pi\)
\(308\) 0 0
\(309\) −1.49723 −0.0851746
\(310\) 0 0
\(311\) 3.22030 0.182606 0.0913032 0.995823i \(-0.470897\pi\)
0.0913032 + 0.995823i \(0.470897\pi\)
\(312\) 0 0
\(313\) −30.2753 −1.71126 −0.855629 0.517589i \(-0.826830\pi\)
−0.855629 + 0.517589i \(0.826830\pi\)
\(314\) 0 0
\(315\) 1.33645 0.0753006
\(316\) 0 0
\(317\) 13.1079 0.736214 0.368107 0.929783i \(-0.380006\pi\)
0.368107 + 0.929783i \(0.380006\pi\)
\(318\) 0 0
\(319\) 23.7043 1.32719
\(320\) 0 0
\(321\) 2.29357 0.128015
\(322\) 0 0
\(323\) −15.9473 −0.887333
\(324\) 0 0
\(325\) 2.32680 0.129068
\(326\) 0 0
\(327\) 13.3290 0.737096
\(328\) 0 0
\(329\) 2.51050 0.138408
\(330\) 0 0
\(331\) 22.4120 1.23188 0.615938 0.787795i \(-0.288777\pi\)
0.615938 + 0.787795i \(0.288777\pi\)
\(332\) 0 0
\(333\) −2.67489 −0.146583
\(334\) 0 0
\(335\) 22.6898 1.23967
\(336\) 0 0
\(337\) 1.50311 0.0818797 0.0409398 0.999162i \(-0.486965\pi\)
0.0409398 + 0.999162i \(0.486965\pi\)
\(338\) 0 0
\(339\) 18.9368 1.02850
\(340\) 0 0
\(341\) −32.2026 −1.74387
\(342\) 0 0
\(343\) 7.20885 0.389241
\(344\) 0 0
\(345\) −6.23741 −0.335811
\(346\) 0 0
\(347\) −29.4505 −1.58099 −0.790493 0.612471i \(-0.790175\pi\)
−0.790493 + 0.612471i \(0.790175\pi\)
\(348\) 0 0
\(349\) 5.58173 0.298783 0.149392 0.988778i \(-0.452268\pi\)
0.149392 + 0.988778i \(0.452268\pi\)
\(350\) 0 0
\(351\) 1.57904 0.0842829
\(352\) 0 0
\(353\) −9.27363 −0.493586 −0.246793 0.969068i \(-0.579377\pi\)
−0.246793 + 0.969068i \(0.579377\pi\)
\(354\) 0 0
\(355\) −12.9917 −0.689528
\(356\) 0 0
\(357\) −2.21104 −0.117021
\(358\) 0 0
\(359\) 32.7886 1.73052 0.865258 0.501326i \(-0.167154\pi\)
0.865258 + 0.501326i \(0.167154\pi\)
\(360\) 0 0
\(361\) −4.64689 −0.244573
\(362\) 0 0
\(363\) 20.2544 1.06308
\(364\) 0 0
\(365\) 5.50523 0.288157
\(366\) 0 0
\(367\) −4.93563 −0.257638 −0.128819 0.991668i \(-0.541119\pi\)
−0.128819 + 0.991668i \(0.541119\pi\)
\(368\) 0 0
\(369\) 10.7672 0.560516
\(370\) 0 0
\(371\) 1.23154 0.0639385
\(372\) 0 0
\(373\) 32.9187 1.70446 0.852232 0.523165i \(-0.175249\pi\)
0.852232 + 0.523165i \(0.175249\pi\)
\(374\) 0 0
\(375\) 8.97240 0.463333
\(376\) 0 0
\(377\) −6.69522 −0.344821
\(378\) 0 0
\(379\) 0.820431 0.0421427 0.0210714 0.999778i \(-0.493292\pi\)
0.0210714 + 0.999778i \(0.493292\pi\)
\(380\) 0 0
\(381\) 0.286281 0.0146666
\(382\) 0 0
\(383\) 1.99971 0.102180 0.0510901 0.998694i \(-0.483730\pi\)
0.0510901 + 0.998694i \(0.483730\pi\)
\(384\) 0 0
\(385\) −7.47153 −0.380784
\(386\) 0 0
\(387\) −8.36680 −0.425309
\(388\) 0 0
\(389\) −17.8177 −0.903395 −0.451698 0.892171i \(-0.649181\pi\)
−0.451698 + 0.892171i \(0.649181\pi\)
\(390\) 0 0
\(391\) 10.3192 0.521867
\(392\) 0 0
\(393\) −12.5000 −0.630540
\(394\) 0 0
\(395\) −6.42845 −0.323450
\(396\) 0 0
\(397\) 32.8025 1.64631 0.823156 0.567816i \(-0.192211\pi\)
0.823156 + 0.567816i \(0.192211\pi\)
\(398\) 0 0
\(399\) 1.99001 0.0996252
\(400\) 0 0
\(401\) −35.4145 −1.76852 −0.884258 0.466998i \(-0.845336\pi\)
−0.884258 + 0.466998i \(0.845336\pi\)
\(402\) 0 0
\(403\) 9.09555 0.453082
\(404\) 0 0
\(405\) −2.54432 −0.126428
\(406\) 0 0
\(407\) 14.9541 0.741248
\(408\) 0 0
\(409\) −26.5720 −1.31390 −0.656950 0.753934i \(-0.728154\pi\)
−0.656950 + 0.753934i \(0.728154\pi\)
\(410\) 0 0
\(411\) 12.4508 0.614153
\(412\) 0 0
\(413\) −2.76264 −0.135940
\(414\) 0 0
\(415\) −10.2160 −0.501482
\(416\) 0 0
\(417\) −13.8333 −0.677420
\(418\) 0 0
\(419\) −26.4006 −1.28975 −0.644876 0.764287i \(-0.723091\pi\)
−0.644876 + 0.764287i \(0.723091\pi\)
\(420\) 0 0
\(421\) 30.2066 1.47218 0.736090 0.676884i \(-0.236670\pi\)
0.736090 + 0.676884i \(0.236670\pi\)
\(422\) 0 0
\(423\) −4.77944 −0.232384
\(424\) 0 0
\(425\) 6.20271 0.300876
\(426\) 0 0
\(427\) 2.63874 0.127698
\(428\) 0 0
\(429\) −8.82773 −0.426207
\(430\) 0 0
\(431\) 26.0759 1.25603 0.628015 0.778201i \(-0.283868\pi\)
0.628015 + 0.778201i \(0.283868\pi\)
\(432\) 0 0
\(433\) 22.3412 1.07365 0.536825 0.843694i \(-0.319624\pi\)
0.536825 + 0.843694i \(0.319624\pi\)
\(434\) 0 0
\(435\) 10.7881 0.517248
\(436\) 0 0
\(437\) −9.28766 −0.444289
\(438\) 0 0
\(439\) −2.40123 −0.114604 −0.0573021 0.998357i \(-0.518250\pi\)
−0.0573021 + 0.998357i \(0.518250\pi\)
\(440\) 0 0
\(441\) −6.72409 −0.320195
\(442\) 0 0
\(443\) 6.06561 0.288186 0.144093 0.989564i \(-0.453974\pi\)
0.144093 + 0.989564i \(0.453974\pi\)
\(444\) 0 0
\(445\) −41.2879 −1.95723
\(446\) 0 0
\(447\) 17.9274 0.847937
\(448\) 0 0
\(449\) 40.4576 1.90931 0.954656 0.297713i \(-0.0962237\pi\)
0.954656 + 0.297713i \(0.0962237\pi\)
\(450\) 0 0
\(451\) −60.1945 −2.83445
\(452\) 0 0
\(453\) 5.27238 0.247718
\(454\) 0 0
\(455\) 2.11031 0.0989331
\(456\) 0 0
\(457\) 4.88373 0.228451 0.114226 0.993455i \(-0.463561\pi\)
0.114226 + 0.993455i \(0.463561\pi\)
\(458\) 0 0
\(459\) 4.20935 0.196476
\(460\) 0 0
\(461\) −12.2825 −0.572051 −0.286026 0.958222i \(-0.592334\pi\)
−0.286026 + 0.958222i \(0.592334\pi\)
\(462\) 0 0
\(463\) −20.0073 −0.929818 −0.464909 0.885359i \(-0.653913\pi\)
−0.464909 + 0.885359i \(0.653913\pi\)
\(464\) 0 0
\(465\) −14.6557 −0.679643
\(466\) 0 0
\(467\) −7.24777 −0.335387 −0.167693 0.985839i \(-0.553632\pi\)
−0.167693 + 0.985839i \(0.553632\pi\)
\(468\) 0 0
\(469\) 4.68426 0.216299
\(470\) 0 0
\(471\) 23.2595 1.07174
\(472\) 0 0
\(473\) 46.7752 2.15072
\(474\) 0 0
\(475\) −5.58264 −0.256149
\(476\) 0 0
\(477\) −2.34459 −0.107351
\(478\) 0 0
\(479\) 0.0521512 0.00238285 0.00119143 0.999999i \(-0.499621\pi\)
0.00119143 + 0.999999i \(0.499621\pi\)
\(480\) 0 0
\(481\) −4.22375 −0.192587
\(482\) 0 0
\(483\) −1.28770 −0.0585925
\(484\) 0 0
\(485\) 41.8982 1.90250
\(486\) 0 0
\(487\) −6.29237 −0.285135 −0.142567 0.989785i \(-0.545536\pi\)
−0.142567 + 0.989785i \(0.545536\pi\)
\(488\) 0 0
\(489\) 21.8496 0.988073
\(490\) 0 0
\(491\) −27.3974 −1.23643 −0.618214 0.786010i \(-0.712144\pi\)
−0.618214 + 0.786010i \(0.712144\pi\)
\(492\) 0 0
\(493\) −17.8479 −0.803828
\(494\) 0 0
\(495\) 14.2242 0.639329
\(496\) 0 0
\(497\) −2.68211 −0.120309
\(498\) 0 0
\(499\) 32.7237 1.46492 0.732458 0.680813i \(-0.238373\pi\)
0.732458 + 0.680813i \(0.238373\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −1.12421 −0.0501261 −0.0250630 0.999686i \(-0.507979\pi\)
−0.0250630 + 0.999686i \(0.507979\pi\)
\(504\) 0 0
\(505\) 19.1104 0.850402
\(506\) 0 0
\(507\) −10.5066 −0.466616
\(508\) 0 0
\(509\) −4.83949 −0.214506 −0.107253 0.994232i \(-0.534206\pi\)
−0.107253 + 0.994232i \(0.534206\pi\)
\(510\) 0 0
\(511\) 1.13654 0.0502778
\(512\) 0 0
\(513\) −3.78855 −0.167269
\(514\) 0 0
\(515\) 3.80944 0.167864
\(516\) 0 0
\(517\) 26.7198 1.17513
\(518\) 0 0
\(519\) 10.0266 0.440120
\(520\) 0 0
\(521\) −36.5789 −1.60255 −0.801275 0.598296i \(-0.795844\pi\)
−0.801275 + 0.598296i \(0.795844\pi\)
\(522\) 0 0
\(523\) 23.8955 1.04488 0.522439 0.852677i \(-0.325022\pi\)
0.522439 + 0.852677i \(0.325022\pi\)
\(524\) 0 0
\(525\) −0.774014 −0.0337807
\(526\) 0 0
\(527\) 24.2466 1.05620
\(528\) 0 0
\(529\) −16.9901 −0.738701
\(530\) 0 0
\(531\) 5.25946 0.228241
\(532\) 0 0
\(533\) 17.0018 0.736429
\(534\) 0 0
\(535\) −5.83558 −0.252294
\(536\) 0 0
\(537\) −0.201597 −0.00869956
\(538\) 0 0
\(539\) 37.5915 1.61918
\(540\) 0 0
\(541\) −31.0286 −1.33402 −0.667012 0.745047i \(-0.732427\pi\)
−0.667012 + 0.745047i \(0.732427\pi\)
\(542\) 0 0
\(543\) 11.7308 0.503418
\(544\) 0 0
\(545\) −33.9132 −1.45268
\(546\) 0 0
\(547\) −3.82578 −0.163578 −0.0817892 0.996650i \(-0.526063\pi\)
−0.0817892 + 0.996650i \(0.526063\pi\)
\(548\) 0 0
\(549\) −5.02359 −0.214402
\(550\) 0 0
\(551\) 16.0637 0.684335
\(552\) 0 0
\(553\) −1.32714 −0.0564358
\(554\) 0 0
\(555\) 6.80576 0.288889
\(556\) 0 0
\(557\) 24.6847 1.04592 0.522962 0.852356i \(-0.324827\pi\)
0.522962 + 0.852356i \(0.324827\pi\)
\(558\) 0 0
\(559\) −13.2115 −0.558788
\(560\) 0 0
\(561\) −23.5326 −0.993549
\(562\) 0 0
\(563\) −17.9996 −0.758592 −0.379296 0.925275i \(-0.623834\pi\)
−0.379296 + 0.925275i \(0.623834\pi\)
\(564\) 0 0
\(565\) −48.1812 −2.02700
\(566\) 0 0
\(567\) −0.525270 −0.0220593
\(568\) 0 0
\(569\) −21.9387 −0.919718 −0.459859 0.887992i \(-0.652100\pi\)
−0.459859 + 0.887992i \(0.652100\pi\)
\(570\) 0 0
\(571\) 19.4601 0.814378 0.407189 0.913344i \(-0.366509\pi\)
0.407189 + 0.913344i \(0.366509\pi\)
\(572\) 0 0
\(573\) 25.0393 1.04603
\(574\) 0 0
\(575\) 3.61243 0.150649
\(576\) 0 0
\(577\) 8.17908 0.340500 0.170250 0.985401i \(-0.445543\pi\)
0.170250 + 0.985401i \(0.445543\pi\)
\(578\) 0 0
\(579\) −10.7710 −0.447628
\(580\) 0 0
\(581\) −2.10907 −0.0874988
\(582\) 0 0
\(583\) 13.1076 0.542861
\(584\) 0 0
\(585\) −4.01758 −0.166107
\(586\) 0 0
\(587\) −7.61306 −0.314225 −0.157112 0.987581i \(-0.550218\pi\)
−0.157112 + 0.987581i \(0.550218\pi\)
\(588\) 0 0
\(589\) −21.8227 −0.899190
\(590\) 0 0
\(591\) 11.1738 0.459629
\(592\) 0 0
\(593\) −21.7438 −0.892912 −0.446456 0.894806i \(-0.647314\pi\)
−0.446456 + 0.894806i \(0.647314\pi\)
\(594\) 0 0
\(595\) 5.62560 0.230627
\(596\) 0 0
\(597\) 23.0987 0.945365
\(598\) 0 0
\(599\) −39.3506 −1.60782 −0.803911 0.594750i \(-0.797251\pi\)
−0.803911 + 0.594750i \(0.797251\pi\)
\(600\) 0 0
\(601\) 18.4627 0.753109 0.376555 0.926394i \(-0.377109\pi\)
0.376555 + 0.926394i \(0.377109\pi\)
\(602\) 0 0
\(603\) −8.91781 −0.363161
\(604\) 0 0
\(605\) −51.5336 −2.09514
\(606\) 0 0
\(607\) 6.84061 0.277652 0.138826 0.990317i \(-0.455667\pi\)
0.138826 + 0.990317i \(0.455667\pi\)
\(608\) 0 0
\(609\) 2.22717 0.0902496
\(610\) 0 0
\(611\) −7.54693 −0.305316
\(612\) 0 0
\(613\) 46.6604 1.88460 0.942298 0.334776i \(-0.108661\pi\)
0.942298 + 0.334776i \(0.108661\pi\)
\(614\) 0 0
\(615\) −27.3951 −1.10468
\(616\) 0 0
\(617\) 19.4605 0.783452 0.391726 0.920082i \(-0.371878\pi\)
0.391726 + 0.920082i \(0.371878\pi\)
\(618\) 0 0
\(619\) −22.6463 −0.910232 −0.455116 0.890432i \(-0.650402\pi\)
−0.455116 + 0.890432i \(0.650402\pi\)
\(620\) 0 0
\(621\) 2.45151 0.0983756
\(622\) 0 0
\(623\) −8.52381 −0.341499
\(624\) 0 0
\(625\) −30.1964 −1.20786
\(626\) 0 0
\(627\) 21.1801 0.845853
\(628\) 0 0
\(629\) −11.2595 −0.448947
\(630\) 0 0
\(631\) −41.4338 −1.64945 −0.824727 0.565531i \(-0.808671\pi\)
−0.824727 + 0.565531i \(0.808671\pi\)
\(632\) 0 0
\(633\) 8.65386 0.343960
\(634\) 0 0
\(635\) −0.728391 −0.0289053
\(636\) 0 0
\(637\) −10.6176 −0.420685
\(638\) 0 0
\(639\) 5.10616 0.201997
\(640\) 0 0
\(641\) −5.85111 −0.231105 −0.115552 0.993301i \(-0.536864\pi\)
−0.115552 + 0.993301i \(0.536864\pi\)
\(642\) 0 0
\(643\) −1.42749 −0.0562947 −0.0281473 0.999604i \(-0.508961\pi\)
−0.0281473 + 0.999604i \(0.508961\pi\)
\(644\) 0 0
\(645\) 21.2878 0.838207
\(646\) 0 0
\(647\) 10.5140 0.413349 0.206675 0.978410i \(-0.433736\pi\)
0.206675 + 0.978410i \(0.433736\pi\)
\(648\) 0 0
\(649\) −29.4033 −1.15418
\(650\) 0 0
\(651\) −3.02565 −0.118584
\(652\) 0 0
\(653\) 44.1836 1.72904 0.864519 0.502601i \(-0.167623\pi\)
0.864519 + 0.502601i \(0.167623\pi\)
\(654\) 0 0
\(655\) 31.8039 1.24268
\(656\) 0 0
\(657\) −2.16373 −0.0844153
\(658\) 0 0
\(659\) 9.39910 0.366137 0.183069 0.983100i \(-0.441397\pi\)
0.183069 + 0.983100i \(0.441397\pi\)
\(660\) 0 0
\(661\) 47.0872 1.83148 0.915739 0.401774i \(-0.131606\pi\)
0.915739 + 0.401774i \(0.131606\pi\)
\(662\) 0 0
\(663\) 6.64673 0.258138
\(664\) 0 0
\(665\) −5.06322 −0.196343
\(666\) 0 0
\(667\) −10.3945 −0.402478
\(668\) 0 0
\(669\) −3.47630 −0.134402
\(670\) 0 0
\(671\) 28.0847 1.08420
\(672\) 0 0
\(673\) −8.95242 −0.345091 −0.172545 0.985002i \(-0.555199\pi\)
−0.172545 + 0.985002i \(0.555199\pi\)
\(674\) 0 0
\(675\) 1.47356 0.0567172
\(676\) 0 0
\(677\) −8.00580 −0.307688 −0.153844 0.988095i \(-0.549165\pi\)
−0.153844 + 0.988095i \(0.549165\pi\)
\(678\) 0 0
\(679\) 8.64980 0.331949
\(680\) 0 0
\(681\) −4.99391 −0.191367
\(682\) 0 0
\(683\) −3.64312 −0.139400 −0.0697001 0.997568i \(-0.522204\pi\)
−0.0697001 + 0.997568i \(0.522204\pi\)
\(684\) 0 0
\(685\) −31.6788 −1.21038
\(686\) 0 0
\(687\) −0.724364 −0.0276362
\(688\) 0 0
\(689\) −3.70220 −0.141043
\(690\) 0 0
\(691\) −18.2229 −0.693230 −0.346615 0.938008i \(-0.612669\pi\)
−0.346615 + 0.938008i \(0.612669\pi\)
\(692\) 0 0
\(693\) 2.93655 0.111550
\(694\) 0 0
\(695\) 35.1964 1.33507
\(696\) 0 0
\(697\) 45.3227 1.71672
\(698\) 0 0
\(699\) 3.07905 0.116461
\(700\) 0 0
\(701\) −18.3239 −0.692085 −0.346043 0.938219i \(-0.612475\pi\)
−0.346043 + 0.938219i \(0.612475\pi\)
\(702\) 0 0
\(703\) 10.1339 0.382209
\(704\) 0 0
\(705\) 12.1604 0.457988
\(706\) 0 0
\(707\) 3.94531 0.148379
\(708\) 0 0
\(709\) 33.1399 1.24460 0.622298 0.782781i \(-0.286199\pi\)
0.622298 + 0.782781i \(0.286199\pi\)
\(710\) 0 0
\(711\) 2.52659 0.0947545
\(712\) 0 0
\(713\) 14.1211 0.528840
\(714\) 0 0
\(715\) 22.4605 0.839977
\(716\) 0 0
\(717\) −23.7125 −0.885558
\(718\) 0 0
\(719\) −10.6679 −0.397847 −0.198924 0.980015i \(-0.563745\pi\)
−0.198924 + 0.980015i \(0.563745\pi\)
\(720\) 0 0
\(721\) 0.786451 0.0292890
\(722\) 0 0
\(723\) 14.1304 0.525515
\(724\) 0 0
\(725\) −6.24796 −0.232043
\(726\) 0 0
\(727\) 16.3733 0.607254 0.303627 0.952791i \(-0.401802\pi\)
0.303627 + 0.952791i \(0.401802\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −35.2188 −1.30261
\(732\) 0 0
\(733\) 10.1931 0.376492 0.188246 0.982122i \(-0.439720\pi\)
0.188246 + 0.982122i \(0.439720\pi\)
\(734\) 0 0
\(735\) 17.1082 0.631047
\(736\) 0 0
\(737\) 49.8556 1.83645
\(738\) 0 0
\(739\) −14.0639 −0.517349 −0.258675 0.965964i \(-0.583286\pi\)
−0.258675 + 0.965964i \(0.583286\pi\)
\(740\) 0 0
\(741\) −5.98227 −0.219764
\(742\) 0 0
\(743\) 8.93010 0.327614 0.163807 0.986492i \(-0.447623\pi\)
0.163807 + 0.986492i \(0.447623\pi\)
\(744\) 0 0
\(745\) −45.6130 −1.67113
\(746\) 0 0
\(747\) 4.01520 0.146909
\(748\) 0 0
\(749\) −1.20475 −0.0440204
\(750\) 0 0
\(751\) 16.7755 0.612146 0.306073 0.952008i \(-0.400985\pi\)
0.306073 + 0.952008i \(0.400985\pi\)
\(752\) 0 0
\(753\) −0.523099 −0.0190628
\(754\) 0 0
\(755\) −13.4146 −0.488208
\(756\) 0 0
\(757\) −28.3838 −1.03163 −0.515814 0.856701i \(-0.672510\pi\)
−0.515814 + 0.856701i \(0.672510\pi\)
\(758\) 0 0
\(759\) −13.7053 −0.497471
\(760\) 0 0
\(761\) 41.5928 1.50774 0.753869 0.657025i \(-0.228185\pi\)
0.753869 + 0.657025i \(0.228185\pi\)
\(762\) 0 0
\(763\) −7.00133 −0.253465
\(764\) 0 0
\(765\) −10.7099 −0.387218
\(766\) 0 0
\(767\) 8.30490 0.299873
\(768\) 0 0
\(769\) −13.5540 −0.488770 −0.244385 0.969678i \(-0.578586\pi\)
−0.244385 + 0.969678i \(0.578586\pi\)
\(770\) 0 0
\(771\) 19.5504 0.704091
\(772\) 0 0
\(773\) −36.6981 −1.31994 −0.659970 0.751292i \(-0.729431\pi\)
−0.659970 + 0.751292i \(0.729431\pi\)
\(774\) 0 0
\(775\) 8.48794 0.304896
\(776\) 0 0
\(777\) 1.40504 0.0504054
\(778\) 0 0
\(779\) −40.7919 −1.46152
\(780\) 0 0
\(781\) −28.5463 −1.02147
\(782\) 0 0
\(783\) −4.24006 −0.151527
\(784\) 0 0
\(785\) −59.1795 −2.11221
\(786\) 0 0
\(787\) −20.9838 −0.747993 −0.373996 0.927430i \(-0.622013\pi\)
−0.373996 + 0.927430i \(0.622013\pi\)
\(788\) 0 0
\(789\) 2.94567 0.104869
\(790\) 0 0
\(791\) −9.94692 −0.353672
\(792\) 0 0
\(793\) −7.93245 −0.281690
\(794\) 0 0
\(795\) 5.96539 0.211570
\(796\) 0 0
\(797\) 8.30024 0.294010 0.147005 0.989136i \(-0.453037\pi\)
0.147005 + 0.989136i \(0.453037\pi\)
\(798\) 0 0
\(799\) −20.1183 −0.711736
\(800\) 0 0
\(801\) 16.2275 0.573370
\(802\) 0 0
\(803\) 12.0965 0.426876
\(804\) 0 0
\(805\) 3.27632 0.115475
\(806\) 0 0
\(807\) 9.57622 0.337099
\(808\) 0 0
\(809\) −40.2664 −1.41569 −0.707845 0.706368i \(-0.750333\pi\)
−0.707845 + 0.706368i \(0.750333\pi\)
\(810\) 0 0
\(811\) 11.0881 0.389357 0.194679 0.980867i \(-0.437634\pi\)
0.194679 + 0.980867i \(0.437634\pi\)
\(812\) 0 0
\(813\) −24.1059 −0.845430
\(814\) 0 0
\(815\) −55.5923 −1.94731
\(816\) 0 0
\(817\) 31.6981 1.10897
\(818\) 0 0
\(819\) −0.829422 −0.0289824
\(820\) 0 0
\(821\) 40.0645 1.39826 0.699130 0.714995i \(-0.253571\pi\)
0.699130 + 0.714995i \(0.253571\pi\)
\(822\) 0 0
\(823\) 30.7172 1.07073 0.535366 0.844620i \(-0.320174\pi\)
0.535366 + 0.844620i \(0.320174\pi\)
\(824\) 0 0
\(825\) −8.23800 −0.286810
\(826\) 0 0
\(827\) 26.1112 0.907977 0.453988 0.891008i \(-0.350001\pi\)
0.453988 + 0.891008i \(0.350001\pi\)
\(828\) 0 0
\(829\) −3.46592 −0.120376 −0.0601882 0.998187i \(-0.519170\pi\)
−0.0601882 + 0.998187i \(0.519170\pi\)
\(830\) 0 0
\(831\) −2.19302 −0.0760749
\(832\) 0 0
\(833\) −28.3041 −0.980677
\(834\) 0 0
\(835\) 2.54432 0.0880498
\(836\) 0 0
\(837\) 5.76018 0.199101
\(838\) 0 0
\(839\) −24.7905 −0.855864 −0.427932 0.903811i \(-0.640758\pi\)
−0.427932 + 0.903811i \(0.640758\pi\)
\(840\) 0 0
\(841\) −11.0219 −0.380066
\(842\) 0 0
\(843\) 6.78076 0.233542
\(844\) 0 0
\(845\) 26.7322 0.919616
\(846\) 0 0
\(847\) −10.6390 −0.365561
\(848\) 0 0
\(849\) 4.02725 0.138215
\(850\) 0 0
\(851\) −6.55750 −0.224788
\(852\) 0 0
\(853\) −35.4429 −1.21354 −0.606772 0.794876i \(-0.707536\pi\)
−0.606772 + 0.794876i \(0.707536\pi\)
\(854\) 0 0
\(855\) 9.63928 0.329656
\(856\) 0 0
\(857\) −19.6459 −0.671092 −0.335546 0.942024i \(-0.608921\pi\)
−0.335546 + 0.942024i \(0.608921\pi\)
\(858\) 0 0
\(859\) −4.37538 −0.149286 −0.0746430 0.997210i \(-0.523782\pi\)
−0.0746430 + 0.997210i \(0.523782\pi\)
\(860\) 0 0
\(861\) −5.65566 −0.192744
\(862\) 0 0
\(863\) 10.7669 0.366510 0.183255 0.983065i \(-0.441337\pi\)
0.183255 + 0.983065i \(0.441337\pi\)
\(864\) 0 0
\(865\) −25.5109 −0.867397
\(866\) 0 0
\(867\) 0.718627 0.0244059
\(868\) 0 0
\(869\) −14.1251 −0.479160
\(870\) 0 0
\(871\) −14.0816 −0.477136
\(872\) 0 0
\(873\) −16.4673 −0.557335
\(874\) 0 0
\(875\) −4.71293 −0.159326
\(876\) 0 0
\(877\) −36.0855 −1.21852 −0.609261 0.792970i \(-0.708534\pi\)
−0.609261 + 0.792970i \(0.708534\pi\)
\(878\) 0 0
\(879\) 22.8461 0.770580
\(880\) 0 0
\(881\) −10.9935 −0.370379 −0.185190 0.982703i \(-0.559290\pi\)
−0.185190 + 0.982703i \(0.559290\pi\)
\(882\) 0 0
\(883\) 53.8415 1.81191 0.905956 0.423372i \(-0.139154\pi\)
0.905956 + 0.423372i \(0.139154\pi\)
\(884\) 0 0
\(885\) −13.3817 −0.449822
\(886\) 0 0
\(887\) −50.4057 −1.69246 −0.846229 0.532820i \(-0.821132\pi\)
−0.846229 + 0.532820i \(0.821132\pi\)
\(888\) 0 0
\(889\) −0.150375 −0.00504342
\(890\) 0 0
\(891\) −5.59056 −0.187291
\(892\) 0 0
\(893\) 18.1072 0.605933
\(894\) 0 0
\(895\) 0.512927 0.0171453
\(896\) 0 0
\(897\) 3.87103 0.129250
\(898\) 0 0
\(899\) −24.4235 −0.814569
\(900\) 0 0
\(901\) −9.86921 −0.328791
\(902\) 0 0
\(903\) 4.39483 0.146251
\(904\) 0 0
\(905\) −29.8470 −0.992147
\(906\) 0 0
\(907\) 52.2807 1.73595 0.867976 0.496607i \(-0.165421\pi\)
0.867976 + 0.496607i \(0.165421\pi\)
\(908\) 0 0
\(909\) −7.51102 −0.249125
\(910\) 0 0
\(911\) −46.9594 −1.55584 −0.777918 0.628366i \(-0.783724\pi\)
−0.777918 + 0.628366i \(0.783724\pi\)
\(912\) 0 0
\(913\) −22.4473 −0.742896
\(914\) 0 0
\(915\) 12.7816 0.422547
\(916\) 0 0
\(917\) 6.56586 0.216824
\(918\) 0 0
\(919\) 40.3643 1.33150 0.665748 0.746177i \(-0.268113\pi\)
0.665748 + 0.746177i \(0.268113\pi\)
\(920\) 0 0
\(921\) −2.74814 −0.0905543
\(922\) 0 0
\(923\) 8.06283 0.265391
\(924\) 0 0
\(925\) −3.94159 −0.129599
\(926\) 0 0
\(927\) −1.49723 −0.0491756
\(928\) 0 0
\(929\) 24.0090 0.787710 0.393855 0.919173i \(-0.371141\pi\)
0.393855 + 0.919173i \(0.371141\pi\)
\(930\) 0 0
\(931\) 25.4746 0.834895
\(932\) 0 0
\(933\) 3.22030 0.105428
\(934\) 0 0
\(935\) 59.8745 1.95811
\(936\) 0 0
\(937\) 20.1221 0.657359 0.328680 0.944442i \(-0.393396\pi\)
0.328680 + 0.944442i \(0.393396\pi\)
\(938\) 0 0
\(939\) −30.2753 −0.987996
\(940\) 0 0
\(941\) −26.2819 −0.856766 −0.428383 0.903597i \(-0.640917\pi\)
−0.428383 + 0.903597i \(0.640917\pi\)
\(942\) 0 0
\(943\) 26.3958 0.859564
\(944\) 0 0
\(945\) 1.33645 0.0434748
\(946\) 0 0
\(947\) 6.14635 0.199730 0.0998648 0.995001i \(-0.468159\pi\)
0.0998648 + 0.995001i \(0.468159\pi\)
\(948\) 0 0
\(949\) −3.41662 −0.110908
\(950\) 0 0
\(951\) 13.1079 0.425054
\(952\) 0 0
\(953\) −31.2709 −1.01296 −0.506481 0.862251i \(-0.669054\pi\)
−0.506481 + 0.862251i \(0.669054\pi\)
\(954\) 0 0
\(955\) −63.7080 −2.06154
\(956\) 0 0
\(957\) 23.7043 0.766251
\(958\) 0 0
\(959\) −6.54003 −0.211189
\(960\) 0 0
\(961\) 2.17965 0.0703114
\(962\) 0 0
\(963\) 2.29357 0.0739094
\(964\) 0 0
\(965\) 27.4049 0.882195
\(966\) 0 0
\(967\) 11.5240 0.370585 0.185293 0.982683i \(-0.440677\pi\)
0.185293 + 0.982683i \(0.440677\pi\)
\(968\) 0 0
\(969\) −15.9473 −0.512302
\(970\) 0 0
\(971\) 5.19367 0.166673 0.0833365 0.996521i \(-0.473442\pi\)
0.0833365 + 0.996521i \(0.473442\pi\)
\(972\) 0 0
\(973\) 7.26622 0.232944
\(974\) 0 0
\(975\) 2.32680 0.0745173
\(976\) 0 0
\(977\) 23.7262 0.759067 0.379534 0.925178i \(-0.376084\pi\)
0.379534 + 0.925178i \(0.376084\pi\)
\(978\) 0 0
\(979\) −90.7208 −2.89945
\(980\) 0 0
\(981\) 13.3290 0.425562
\(982\) 0 0
\(983\) 15.9426 0.508490 0.254245 0.967140i \(-0.418173\pi\)
0.254245 + 0.967140i \(0.418173\pi\)
\(984\) 0 0
\(985\) −28.4297 −0.905847
\(986\) 0 0
\(987\) 2.51050 0.0799100
\(988\) 0 0
\(989\) −20.5113 −0.652221
\(990\) 0 0
\(991\) 40.7291 1.29380 0.646902 0.762573i \(-0.276064\pi\)
0.646902 + 0.762573i \(0.276064\pi\)
\(992\) 0 0
\(993\) 22.4120 0.711223
\(994\) 0 0
\(995\) −58.7703 −1.86314
\(996\) 0 0
\(997\) 45.1173 1.42888 0.714440 0.699697i \(-0.246681\pi\)
0.714440 + 0.699697i \(0.246681\pi\)
\(998\) 0 0
\(999\) −2.67489 −0.0846297
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8016.2.a.be.1.1 11
4.3 odd 2 4008.2.a.k.1.1 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.k.1.1 11 4.3 odd 2
8016.2.a.be.1.1 11 1.1 even 1 trivial