Properties

Label 8016.2.a.be.1.10
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 1.10
Root \(-2.83671\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +3.83671 q^{5} -4.48179 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +3.83671 q^{5} -4.48179 q^{7} +1.00000 q^{9} -1.10612 q^{11} -5.67402 q^{13} +3.83671 q^{15} -0.581232 q^{17} +4.72213 q^{19} -4.48179 q^{21} +3.33676 q^{23} +9.72035 q^{25} +1.00000 q^{27} +3.38537 q^{29} -2.78132 q^{31} -1.10612 q^{33} -17.1953 q^{35} +4.43128 q^{37} -5.67402 q^{39} +5.90332 q^{41} -10.0030 q^{43} +3.83671 q^{45} +12.4032 q^{47} +13.0864 q^{49} -0.581232 q^{51} +5.10414 q^{53} -4.24388 q^{55} +4.72213 q^{57} +2.77902 q^{59} +9.42616 q^{61} -4.48179 q^{63} -21.7696 q^{65} -9.07361 q^{67} +3.33676 q^{69} -13.8081 q^{71} +9.14053 q^{73} +9.72035 q^{75} +4.95742 q^{77} +17.4215 q^{79} +1.00000 q^{81} -16.9891 q^{83} -2.23002 q^{85} +3.38537 q^{87} -1.50452 q^{89} +25.4298 q^{91} -2.78132 q^{93} +18.1174 q^{95} +0.761888 q^{97} -1.10612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + O(q^{10}) \) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + q^{11} + 10q^{13} + 10q^{15} + 17q^{17} - 2q^{19} + q^{21} + 3q^{23} + 21q^{25} + 11q^{27} + 17q^{29} + 15q^{31} + q^{33} - 11q^{35} + 4q^{37} + 10q^{39} + 16q^{41} - 10q^{43} + 10q^{45} + 16q^{47} + 22q^{49} + 17q^{51} + 42q^{53} + 5q^{55} - 2q^{57} + 2q^{59} + 12q^{61} + q^{63} + 10q^{65} + q^{67} + 3q^{69} + 9q^{71} + 24q^{73} + 21q^{75} + 22q^{77} + 30q^{79} + 11q^{81} - 16q^{83} + 25q^{85} + 17q^{87} + 37q^{89} - q^{91} + 15q^{93} - 5q^{95} + 4q^{97} + q^{99} + O(q^{100}) \)

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
\(5\) 3.83671 1.71583 0.857915 0.513792i \(-0.171760\pi\)
0.857915 + 0.513792i \(0.171760\pi\)
\(6\) 0 0
\(7\) −4.48179 −1.69396 −0.846979 0.531627i \(-0.821581\pi\)
−0.846979 + 0.531627i \(0.821581\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.10612 −0.333509 −0.166755 0.985998i \(-0.553329\pi\)
−0.166755 + 0.985998i \(0.553329\pi\)
\(12\) 0 0
\(13\) −5.67402 −1.57369 −0.786845 0.617151i \(-0.788287\pi\)
−0.786845 + 0.617151i \(0.788287\pi\)
\(14\) 0 0
\(15\) 3.83671 0.990635
\(16\) 0 0
\(17\) −0.581232 −0.140969 −0.0704847 0.997513i \(-0.522455\pi\)
−0.0704847 + 0.997513i \(0.522455\pi\)
\(18\) 0 0
\(19\) 4.72213 1.08333 0.541665 0.840594i \(-0.317794\pi\)
0.541665 + 0.840594i \(0.317794\pi\)
\(20\) 0 0
\(21\) −4.48179 −0.978007
\(22\) 0 0
\(23\) 3.33676 0.695762 0.347881 0.937539i \(-0.386901\pi\)
0.347881 + 0.937539i \(0.386901\pi\)
\(24\) 0 0
\(25\) 9.72035 1.94407
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 3.38537 0.628648 0.314324 0.949316i \(-0.398222\pi\)
0.314324 + 0.949316i \(0.398222\pi\)
\(30\) 0 0
\(31\) −2.78132 −0.499540 −0.249770 0.968305i \(-0.580355\pi\)
−0.249770 + 0.968305i \(0.580355\pi\)
\(32\) 0 0
\(33\) −1.10612 −0.192552
\(34\) 0 0
\(35\) −17.1953 −2.90654
\(36\) 0 0
\(37\) 4.43128 0.728498 0.364249 0.931302i \(-0.381326\pi\)
0.364249 + 0.931302i \(0.381326\pi\)
\(38\) 0 0
\(39\) −5.67402 −0.908570
\(40\) 0 0
\(41\) 5.90332 0.921944 0.460972 0.887415i \(-0.347501\pi\)
0.460972 + 0.887415i \(0.347501\pi\)
\(42\) 0 0
\(43\) −10.0030 −1.52544 −0.762722 0.646727i \(-0.776137\pi\)
−0.762722 + 0.646727i \(0.776137\pi\)
\(44\) 0 0
\(45\) 3.83671 0.571943
\(46\) 0 0
\(47\) 12.4032 1.80920 0.904598 0.426266i \(-0.140171\pi\)
0.904598 + 0.426266i \(0.140171\pi\)
\(48\) 0 0
\(49\) 13.0864 1.86949
\(50\) 0 0
\(51\) −0.581232 −0.0813887
\(52\) 0 0
\(53\) 5.10414 0.701108 0.350554 0.936543i \(-0.385993\pi\)
0.350554 + 0.936543i \(0.385993\pi\)
\(54\) 0 0
\(55\) −4.24388 −0.572245
\(56\) 0 0
\(57\) 4.72213 0.625461
\(58\) 0 0
\(59\) 2.77902 0.361798 0.180899 0.983502i \(-0.442099\pi\)
0.180899 + 0.983502i \(0.442099\pi\)
\(60\) 0 0
\(61\) 9.42616 1.20690 0.603448 0.797402i \(-0.293793\pi\)
0.603448 + 0.797402i \(0.293793\pi\)
\(62\) 0 0
\(63\) −4.48179 −0.564652
\(64\) 0 0
\(65\) −21.7696 −2.70018
\(66\) 0 0
\(67\) −9.07361 −1.10852 −0.554259 0.832344i \(-0.686998\pi\)
−0.554259 + 0.832344i \(0.686998\pi\)
\(68\) 0 0
\(69\) 3.33676 0.401698
\(70\) 0 0
\(71\) −13.8081 −1.63872 −0.819359 0.573281i \(-0.805670\pi\)
−0.819359 + 0.573281i \(0.805670\pi\)
\(72\) 0 0
\(73\) 9.14053 1.06982 0.534909 0.844910i \(-0.320346\pi\)
0.534909 + 0.844910i \(0.320346\pi\)
\(74\) 0 0
\(75\) 9.72035 1.12241
\(76\) 0 0
\(77\) 4.95742 0.564950
\(78\) 0 0
\(79\) 17.4215 1.96007 0.980034 0.198831i \(-0.0637144\pi\)
0.980034 + 0.198831i \(0.0637144\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −16.9891 −1.86479 −0.932397 0.361435i \(-0.882287\pi\)
−0.932397 + 0.361435i \(0.882287\pi\)
\(84\) 0 0
\(85\) −2.23002 −0.241879
\(86\) 0 0
\(87\) 3.38537 0.362950
\(88\) 0 0
\(89\) −1.50452 −0.159478 −0.0797391 0.996816i \(-0.525409\pi\)
−0.0797391 + 0.996816i \(0.525409\pi\)
\(90\) 0 0
\(91\) 25.4298 2.66576
\(92\) 0 0
\(93\) −2.78132 −0.288410
\(94\) 0 0
\(95\) 18.1174 1.85881
\(96\) 0 0
\(97\) 0.761888 0.0773580 0.0386790 0.999252i \(-0.487685\pi\)
0.0386790 + 0.999252i \(0.487685\pi\)
\(98\) 0 0
\(99\) −1.10612 −0.111170
\(100\) 0 0
\(101\) −1.37489 −0.136807 −0.0684034 0.997658i \(-0.521790\pi\)
−0.0684034 + 0.997658i \(0.521790\pi\)
\(102\) 0 0
\(103\) 0.0629727 0.00620488 0.00310244 0.999995i \(-0.499012\pi\)
0.00310244 + 0.999995i \(0.499012\pi\)
\(104\) 0 0
\(105\) −17.1953 −1.67809
\(106\) 0 0
\(107\) −10.0437 −0.970959 −0.485480 0.874248i \(-0.661355\pi\)
−0.485480 + 0.874248i \(0.661355\pi\)
\(108\) 0 0
\(109\) 1.87839 0.179917 0.0899584 0.995946i \(-0.471327\pi\)
0.0899584 + 0.995946i \(0.471327\pi\)
\(110\) 0 0
\(111\) 4.43128 0.420598
\(112\) 0 0
\(113\) 4.11228 0.386851 0.193425 0.981115i \(-0.438040\pi\)
0.193425 + 0.981115i \(0.438040\pi\)
\(114\) 0 0
\(115\) 12.8022 1.19381
\(116\) 0 0
\(117\) −5.67402 −0.524563
\(118\) 0 0
\(119\) 2.60496 0.238796
\(120\) 0 0
\(121\) −9.77649 −0.888772
\(122\) 0 0
\(123\) 5.90332 0.532284
\(124\) 0 0
\(125\) 18.1106 1.61986
\(126\) 0 0
\(127\) 19.9118 1.76689 0.883445 0.468536i \(-0.155218\pi\)
0.883445 + 0.468536i \(0.155218\pi\)
\(128\) 0 0
\(129\) −10.0030 −0.880715
\(130\) 0 0
\(131\) 6.42577 0.561422 0.280711 0.959792i \(-0.409430\pi\)
0.280711 + 0.959792i \(0.409430\pi\)
\(132\) 0 0
\(133\) −21.1636 −1.83512
\(134\) 0 0
\(135\) 3.83671 0.330212
\(136\) 0 0
\(137\) −1.42007 −0.121325 −0.0606625 0.998158i \(-0.519321\pi\)
−0.0606625 + 0.998158i \(0.519321\pi\)
\(138\) 0 0
\(139\) −9.43659 −0.800401 −0.400200 0.916428i \(-0.631059\pi\)
−0.400200 + 0.916428i \(0.631059\pi\)
\(140\) 0 0
\(141\) 12.4032 1.04454
\(142\) 0 0
\(143\) 6.27617 0.524840
\(144\) 0 0
\(145\) 12.9887 1.07865
\(146\) 0 0
\(147\) 13.0864 1.07935
\(148\) 0 0
\(149\) 7.81076 0.639882 0.319941 0.947437i \(-0.396337\pi\)
0.319941 + 0.947437i \(0.396337\pi\)
\(150\) 0 0
\(151\) −0.614618 −0.0500169 −0.0250085 0.999687i \(-0.507961\pi\)
−0.0250085 + 0.999687i \(0.507961\pi\)
\(152\) 0 0
\(153\) −0.581232 −0.0469898
\(154\) 0 0
\(155\) −10.6711 −0.857126
\(156\) 0 0
\(157\) 18.5892 1.48358 0.741792 0.670631i \(-0.233976\pi\)
0.741792 + 0.670631i \(0.233976\pi\)
\(158\) 0 0
\(159\) 5.10414 0.404785
\(160\) 0 0
\(161\) −14.9547 −1.17859
\(162\) 0 0
\(163\) 17.6487 1.38235 0.691175 0.722687i \(-0.257093\pi\)
0.691175 + 0.722687i \(0.257093\pi\)
\(164\) 0 0
\(165\) −4.24388 −0.330386
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) 19.1945 1.47650
\(170\) 0 0
\(171\) 4.72213 0.361110
\(172\) 0 0
\(173\) 4.79962 0.364909 0.182454 0.983214i \(-0.441596\pi\)
0.182454 + 0.983214i \(0.441596\pi\)
\(174\) 0 0
\(175\) −43.5646 −3.29317
\(176\) 0 0
\(177\) 2.77902 0.208884
\(178\) 0 0
\(179\) 20.6389 1.54262 0.771310 0.636459i \(-0.219602\pi\)
0.771310 + 0.636459i \(0.219602\pi\)
\(180\) 0 0
\(181\) 10.9125 0.811123 0.405562 0.914068i \(-0.367076\pi\)
0.405562 + 0.914068i \(0.367076\pi\)
\(182\) 0 0
\(183\) 9.42616 0.696802
\(184\) 0 0
\(185\) 17.0015 1.24998
\(186\) 0 0
\(187\) 0.642915 0.0470146
\(188\) 0 0
\(189\) −4.48179 −0.326002
\(190\) 0 0
\(191\) 10.4748 0.757931 0.378965 0.925411i \(-0.376280\pi\)
0.378965 + 0.925411i \(0.376280\pi\)
\(192\) 0 0
\(193\) −8.30352 −0.597701 −0.298850 0.954300i \(-0.596603\pi\)
−0.298850 + 0.954300i \(0.596603\pi\)
\(194\) 0 0
\(195\) −21.7696 −1.55895
\(196\) 0 0
\(197\) 24.7450 1.76301 0.881503 0.472179i \(-0.156533\pi\)
0.881503 + 0.472179i \(0.156533\pi\)
\(198\) 0 0
\(199\) 20.9627 1.48601 0.743003 0.669288i \(-0.233401\pi\)
0.743003 + 0.669288i \(0.233401\pi\)
\(200\) 0 0
\(201\) −9.07361 −0.640003
\(202\) 0 0
\(203\) −15.1725 −1.06490
\(204\) 0 0
\(205\) 22.6493 1.58190
\(206\) 0 0
\(207\) 3.33676 0.231921
\(208\) 0 0
\(209\) −5.22326 −0.361301
\(210\) 0 0
\(211\) 13.3764 0.920866 0.460433 0.887694i \(-0.347694\pi\)
0.460433 + 0.887694i \(0.347694\pi\)
\(212\) 0 0
\(213\) −13.8081 −0.946114
\(214\) 0 0
\(215\) −38.3786 −2.61740
\(216\) 0 0
\(217\) 12.4653 0.846200
\(218\) 0 0
\(219\) 9.14053 0.617660
\(220\) 0 0
\(221\) 3.29792 0.221842
\(222\) 0 0
\(223\) 7.31317 0.489726 0.244863 0.969558i \(-0.421257\pi\)
0.244863 + 0.969558i \(0.421257\pi\)
\(224\) 0 0
\(225\) 9.72035 0.648024
\(226\) 0 0
\(227\) −2.35302 −0.156175 −0.0780875 0.996947i \(-0.524881\pi\)
−0.0780875 + 0.996947i \(0.524881\pi\)
\(228\) 0 0
\(229\) 16.3540 1.08070 0.540350 0.841440i \(-0.318292\pi\)
0.540350 + 0.841440i \(0.318292\pi\)
\(230\) 0 0
\(231\) 4.95742 0.326174
\(232\) 0 0
\(233\) −24.5380 −1.60753 −0.803767 0.594944i \(-0.797174\pi\)
−0.803767 + 0.594944i \(0.797174\pi\)
\(234\) 0 0
\(235\) 47.5876 3.10427
\(236\) 0 0
\(237\) 17.4215 1.13165
\(238\) 0 0
\(239\) 16.5560 1.07092 0.535460 0.844561i \(-0.320138\pi\)
0.535460 + 0.844561i \(0.320138\pi\)
\(240\) 0 0
\(241\) 13.4248 0.864765 0.432383 0.901690i \(-0.357673\pi\)
0.432383 + 0.901690i \(0.357673\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 50.2089 3.20773
\(246\) 0 0
\(247\) −26.7935 −1.70483
\(248\) 0 0
\(249\) −16.9891 −1.07664
\(250\) 0 0
\(251\) −7.08588 −0.447257 −0.223628 0.974674i \(-0.571790\pi\)
−0.223628 + 0.974674i \(0.571790\pi\)
\(252\) 0 0
\(253\) −3.69087 −0.232043
\(254\) 0 0
\(255\) −2.23002 −0.139649
\(256\) 0 0
\(257\) 9.32571 0.581722 0.290861 0.956765i \(-0.406058\pi\)
0.290861 + 0.956765i \(0.406058\pi\)
\(258\) 0 0
\(259\) −19.8601 −1.23404
\(260\) 0 0
\(261\) 3.38537 0.209549
\(262\) 0 0
\(263\) −1.03494 −0.0638170 −0.0319085 0.999491i \(-0.510159\pi\)
−0.0319085 + 0.999491i \(0.510159\pi\)
\(264\) 0 0
\(265\) 19.5831 1.20298
\(266\) 0 0
\(267\) −1.50452 −0.0920748
\(268\) 0 0
\(269\) −13.2297 −0.806630 −0.403315 0.915061i \(-0.632142\pi\)
−0.403315 + 0.915061i \(0.632142\pi\)
\(270\) 0 0
\(271\) −15.6279 −0.949330 −0.474665 0.880166i \(-0.657431\pi\)
−0.474665 + 0.880166i \(0.657431\pi\)
\(272\) 0 0
\(273\) 25.4298 1.53908
\(274\) 0 0
\(275\) −10.7519 −0.648365
\(276\) 0 0
\(277\) −0.591123 −0.0355171 −0.0177586 0.999842i \(-0.505653\pi\)
−0.0177586 + 0.999842i \(0.505653\pi\)
\(278\) 0 0
\(279\) −2.78132 −0.166513
\(280\) 0 0
\(281\) −4.64950 −0.277366 −0.138683 0.990337i \(-0.544287\pi\)
−0.138683 + 0.990337i \(0.544287\pi\)
\(282\) 0 0
\(283\) 23.7408 1.41124 0.705621 0.708590i \(-0.250668\pi\)
0.705621 + 0.708590i \(0.250668\pi\)
\(284\) 0 0
\(285\) 18.1174 1.07319
\(286\) 0 0
\(287\) −26.4574 −1.56173
\(288\) 0 0
\(289\) −16.6622 −0.980128
\(290\) 0 0
\(291\) 0.761888 0.0446627
\(292\) 0 0
\(293\) −27.7554 −1.62149 −0.810743 0.585402i \(-0.800937\pi\)
−0.810743 + 0.585402i \(0.800937\pi\)
\(294\) 0 0
\(295\) 10.6623 0.620783
\(296\) 0 0
\(297\) −1.10612 −0.0641839
\(298\) 0 0
\(299\) −18.9328 −1.09491
\(300\) 0 0
\(301\) 44.8314 2.58404
\(302\) 0 0
\(303\) −1.37489 −0.0789854
\(304\) 0 0
\(305\) 36.1654 2.07083
\(306\) 0 0
\(307\) −1.47952 −0.0844405 −0.0422202 0.999108i \(-0.513443\pi\)
−0.0422202 + 0.999108i \(0.513443\pi\)
\(308\) 0 0
\(309\) 0.0629727 0.00358239
\(310\) 0 0
\(311\) −19.6599 −1.11481 −0.557404 0.830241i \(-0.688203\pi\)
−0.557404 + 0.830241i \(0.688203\pi\)
\(312\) 0 0
\(313\) −13.0409 −0.737116 −0.368558 0.929605i \(-0.620148\pi\)
−0.368558 + 0.929605i \(0.620148\pi\)
\(314\) 0 0
\(315\) −17.1953 −0.968847
\(316\) 0 0
\(317\) 13.2143 0.742191 0.371096 0.928595i \(-0.378982\pi\)
0.371096 + 0.928595i \(0.378982\pi\)
\(318\) 0 0
\(319\) −3.74464 −0.209660
\(320\) 0 0
\(321\) −10.0437 −0.560584
\(322\) 0 0
\(323\) −2.74465 −0.152717
\(324\) 0 0
\(325\) −55.1535 −3.05936
\(326\) 0 0
\(327\) 1.87839 0.103875
\(328\) 0 0
\(329\) −55.5886 −3.06470
\(330\) 0 0
\(331\) 27.4467 1.50860 0.754302 0.656527i \(-0.227975\pi\)
0.754302 + 0.656527i \(0.227975\pi\)
\(332\) 0 0
\(333\) 4.43128 0.242833
\(334\) 0 0
\(335\) −34.8128 −1.90203
\(336\) 0 0
\(337\) −28.0032 −1.52543 −0.762716 0.646733i \(-0.776135\pi\)
−0.762716 + 0.646733i \(0.776135\pi\)
\(338\) 0 0
\(339\) 4.11228 0.223348
\(340\) 0 0
\(341\) 3.07649 0.166601
\(342\) 0 0
\(343\) −27.2782 −1.47288
\(344\) 0 0
\(345\) 12.8022 0.689246
\(346\) 0 0
\(347\) −31.7281 −1.70325 −0.851627 0.524148i \(-0.824384\pi\)
−0.851627 + 0.524148i \(0.824384\pi\)
\(348\) 0 0
\(349\) −22.0742 −1.18160 −0.590802 0.806817i \(-0.701189\pi\)
−0.590802 + 0.806817i \(0.701189\pi\)
\(350\) 0 0
\(351\) −5.67402 −0.302857
\(352\) 0 0
\(353\) 24.7084 1.31509 0.657547 0.753413i \(-0.271594\pi\)
0.657547 + 0.753413i \(0.271594\pi\)
\(354\) 0 0
\(355\) −52.9776 −2.81176
\(356\) 0 0
\(357\) 2.60496 0.137869
\(358\) 0 0
\(359\) 26.1424 1.37975 0.689873 0.723931i \(-0.257666\pi\)
0.689873 + 0.723931i \(0.257666\pi\)
\(360\) 0 0
\(361\) 3.29851 0.173606
\(362\) 0 0
\(363\) −9.77649 −0.513133
\(364\) 0 0
\(365\) 35.0696 1.83563
\(366\) 0 0
\(367\) −10.7397 −0.560607 −0.280303 0.959911i \(-0.590435\pi\)
−0.280303 + 0.959911i \(0.590435\pi\)
\(368\) 0 0
\(369\) 5.90332 0.307315
\(370\) 0 0
\(371\) −22.8757 −1.18765
\(372\) 0 0
\(373\) −32.2357 −1.66910 −0.834551 0.550930i \(-0.814273\pi\)
−0.834551 + 0.550930i \(0.814273\pi\)
\(374\) 0 0
\(375\) 18.1106 0.935229
\(376\) 0 0
\(377\) −19.2087 −0.989296
\(378\) 0 0
\(379\) 25.1380 1.29125 0.645626 0.763654i \(-0.276597\pi\)
0.645626 + 0.763654i \(0.276597\pi\)
\(380\) 0 0
\(381\) 19.9118 1.02011
\(382\) 0 0
\(383\) −25.2766 −1.29157 −0.645787 0.763518i \(-0.723470\pi\)
−0.645787 + 0.763518i \(0.723470\pi\)
\(384\) 0 0
\(385\) 19.0202 0.969358
\(386\) 0 0
\(387\) −10.0030 −0.508481
\(388\) 0 0
\(389\) −2.01440 −0.102134 −0.0510670 0.998695i \(-0.516262\pi\)
−0.0510670 + 0.998695i \(0.516262\pi\)
\(390\) 0 0
\(391\) −1.93943 −0.0980812
\(392\) 0 0
\(393\) 6.42577 0.324137
\(394\) 0 0
\(395\) 66.8411 3.36314
\(396\) 0 0
\(397\) −29.6705 −1.48912 −0.744561 0.667555i \(-0.767341\pi\)
−0.744561 + 0.667555i \(0.767341\pi\)
\(398\) 0 0
\(399\) −21.1636 −1.05950
\(400\) 0 0
\(401\) −11.0918 −0.553900 −0.276950 0.960884i \(-0.589324\pi\)
−0.276950 + 0.960884i \(0.589324\pi\)
\(402\) 0 0
\(403\) 15.7813 0.786121
\(404\) 0 0
\(405\) 3.83671 0.190648
\(406\) 0 0
\(407\) −4.90155 −0.242961
\(408\) 0 0
\(409\) 21.5517 1.06566 0.532831 0.846221i \(-0.321128\pi\)
0.532831 + 0.846221i \(0.321128\pi\)
\(410\) 0 0
\(411\) −1.42007 −0.0700470
\(412\) 0 0
\(413\) −12.4550 −0.612870
\(414\) 0 0
\(415\) −65.1822 −3.19967
\(416\) 0 0
\(417\) −9.43659 −0.462112
\(418\) 0 0
\(419\) −2.34797 −0.114706 −0.0573530 0.998354i \(-0.518266\pi\)
−0.0573530 + 0.998354i \(0.518266\pi\)
\(420\) 0 0
\(421\) −24.1533 −1.17716 −0.588581 0.808439i \(-0.700313\pi\)
−0.588581 + 0.808439i \(0.700313\pi\)
\(422\) 0 0
\(423\) 12.4032 0.603065
\(424\) 0 0
\(425\) −5.64978 −0.274055
\(426\) 0 0
\(427\) −42.2461 −2.04443
\(428\) 0 0
\(429\) 6.27617 0.303016
\(430\) 0 0
\(431\) 14.9384 0.719558 0.359779 0.933038i \(-0.382852\pi\)
0.359779 + 0.933038i \(0.382852\pi\)
\(432\) 0 0
\(433\) −10.2775 −0.493907 −0.246954 0.969027i \(-0.579430\pi\)
−0.246954 + 0.969027i \(0.579430\pi\)
\(434\) 0 0
\(435\) 12.9887 0.622760
\(436\) 0 0
\(437\) 15.7566 0.753741
\(438\) 0 0
\(439\) −2.86030 −0.136514 −0.0682572 0.997668i \(-0.521744\pi\)
−0.0682572 + 0.997668i \(0.521744\pi\)
\(440\) 0 0
\(441\) 13.0864 0.623164
\(442\) 0 0
\(443\) 25.8556 1.22844 0.614219 0.789136i \(-0.289471\pi\)
0.614219 + 0.789136i \(0.289471\pi\)
\(444\) 0 0
\(445\) −5.77239 −0.273638
\(446\) 0 0
\(447\) 7.81076 0.369436
\(448\) 0 0
\(449\) −7.46562 −0.352325 −0.176162 0.984361i \(-0.556368\pi\)
−0.176162 + 0.984361i \(0.556368\pi\)
\(450\) 0 0
\(451\) −6.52981 −0.307477
\(452\) 0 0
\(453\) −0.614618 −0.0288773
\(454\) 0 0
\(455\) 97.5667 4.57400
\(456\) 0 0
\(457\) 40.6342 1.90079 0.950393 0.311052i \(-0.100681\pi\)
0.950393 + 0.311052i \(0.100681\pi\)
\(458\) 0 0
\(459\) −0.581232 −0.0271296
\(460\) 0 0
\(461\) 0.791635 0.0368701 0.0184351 0.999830i \(-0.494132\pi\)
0.0184351 + 0.999830i \(0.494132\pi\)
\(462\) 0 0
\(463\) 35.1065 1.63154 0.815769 0.578377i \(-0.196314\pi\)
0.815769 + 0.578377i \(0.196314\pi\)
\(464\) 0 0
\(465\) −10.6711 −0.494862
\(466\) 0 0
\(467\) 37.1756 1.72028 0.860141 0.510056i \(-0.170375\pi\)
0.860141 + 0.510056i \(0.170375\pi\)
\(468\) 0 0
\(469\) 40.6660 1.87778
\(470\) 0 0
\(471\) 18.5892 0.856547
\(472\) 0 0
\(473\) 11.0646 0.508749
\(474\) 0 0
\(475\) 45.9008 2.10607
\(476\) 0 0
\(477\) 5.10414 0.233703
\(478\) 0 0
\(479\) −19.1213 −0.873675 −0.436838 0.899540i \(-0.643902\pi\)
−0.436838 + 0.899540i \(0.643902\pi\)
\(480\) 0 0
\(481\) −25.1432 −1.14643
\(482\) 0 0
\(483\) −14.9547 −0.680460
\(484\) 0 0
\(485\) 2.92315 0.132733
\(486\) 0 0
\(487\) 9.51757 0.431282 0.215641 0.976473i \(-0.430816\pi\)
0.215641 + 0.976473i \(0.430816\pi\)
\(488\) 0 0
\(489\) 17.6487 0.798100
\(490\) 0 0
\(491\) −2.94043 −0.132700 −0.0663499 0.997796i \(-0.521135\pi\)
−0.0663499 + 0.997796i \(0.521135\pi\)
\(492\) 0 0
\(493\) −1.96769 −0.0886201
\(494\) 0 0
\(495\) −4.24388 −0.190748
\(496\) 0 0
\(497\) 61.8849 2.77592
\(498\) 0 0
\(499\) −28.1976 −1.26230 −0.631149 0.775662i \(-0.717416\pi\)
−0.631149 + 0.775662i \(0.717416\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −4.54162 −0.202501 −0.101250 0.994861i \(-0.532284\pi\)
−0.101250 + 0.994861i \(0.532284\pi\)
\(504\) 0 0
\(505\) −5.27506 −0.234737
\(506\) 0 0
\(507\) 19.1945 0.852457
\(508\) 0 0
\(509\) 23.0856 1.02325 0.511625 0.859209i \(-0.329044\pi\)
0.511625 + 0.859209i \(0.329044\pi\)
\(510\) 0 0
\(511\) −40.9659 −1.81223
\(512\) 0 0
\(513\) 4.72213 0.208487
\(514\) 0 0
\(515\) 0.241608 0.0106465
\(516\) 0 0
\(517\) −13.7195 −0.603383
\(518\) 0 0
\(519\) 4.79962 0.210680
\(520\) 0 0
\(521\) 7.64748 0.335042 0.167521 0.985868i \(-0.446424\pi\)
0.167521 + 0.985868i \(0.446424\pi\)
\(522\) 0 0
\(523\) −31.1172 −1.36066 −0.680329 0.732906i \(-0.738163\pi\)
−0.680329 + 0.732906i \(0.738163\pi\)
\(524\) 0 0
\(525\) −43.5646 −1.90131
\(526\) 0 0
\(527\) 1.61659 0.0704199
\(528\) 0 0
\(529\) −11.8660 −0.515915
\(530\) 0 0
\(531\) 2.77902 0.120599
\(532\) 0 0
\(533\) −33.4955 −1.45085
\(534\) 0 0
\(535\) −38.5347 −1.66600
\(536\) 0 0
\(537\) 20.6389 0.890633
\(538\) 0 0
\(539\) −14.4752 −0.623493
\(540\) 0 0
\(541\) −25.3270 −1.08889 −0.544447 0.838795i \(-0.683260\pi\)
−0.544447 + 0.838795i \(0.683260\pi\)
\(542\) 0 0
\(543\) 10.9125 0.468302
\(544\) 0 0
\(545\) 7.20683 0.308707
\(546\) 0 0
\(547\) 27.8497 1.19077 0.595383 0.803442i \(-0.297000\pi\)
0.595383 + 0.803442i \(0.297000\pi\)
\(548\) 0 0
\(549\) 9.42616 0.402299
\(550\) 0 0
\(551\) 15.9862 0.681034
\(552\) 0 0
\(553\) −78.0793 −3.32027
\(554\) 0 0
\(555\) 17.0015 0.721675
\(556\) 0 0
\(557\) 9.21977 0.390654 0.195327 0.980738i \(-0.437423\pi\)
0.195327 + 0.980738i \(0.437423\pi\)
\(558\) 0 0
\(559\) 56.7572 2.40057
\(560\) 0 0
\(561\) 0.642915 0.0271439
\(562\) 0 0
\(563\) 16.8905 0.711851 0.355926 0.934514i \(-0.384166\pi\)
0.355926 + 0.934514i \(0.384166\pi\)
\(564\) 0 0
\(565\) 15.7776 0.663770
\(566\) 0 0
\(567\) −4.48179 −0.188217
\(568\) 0 0
\(569\) −38.5370 −1.61556 −0.807778 0.589487i \(-0.799330\pi\)
−0.807778 + 0.589487i \(0.799330\pi\)
\(570\) 0 0
\(571\) −13.6738 −0.572232 −0.286116 0.958195i \(-0.592364\pi\)
−0.286116 + 0.958195i \(0.592364\pi\)
\(572\) 0 0
\(573\) 10.4748 0.437592
\(574\) 0 0
\(575\) 32.4345 1.35261
\(576\) 0 0
\(577\) −0.888543 −0.0369905 −0.0184953 0.999829i \(-0.505888\pi\)
−0.0184953 + 0.999829i \(0.505888\pi\)
\(578\) 0 0
\(579\) −8.30352 −0.345083
\(580\) 0 0
\(581\) 76.1415 3.15888
\(582\) 0 0
\(583\) −5.64582 −0.233826
\(584\) 0 0
\(585\) −21.7696 −0.900061
\(586\) 0 0
\(587\) −24.2849 −1.00234 −0.501172 0.865348i \(-0.667098\pi\)
−0.501172 + 0.865348i \(0.667098\pi\)
\(588\) 0 0
\(589\) −13.1338 −0.541167
\(590\) 0 0
\(591\) 24.7450 1.01787
\(592\) 0 0
\(593\) −6.05351 −0.248588 −0.124294 0.992245i \(-0.539667\pi\)
−0.124294 + 0.992245i \(0.539667\pi\)
\(594\) 0 0
\(595\) 9.99448 0.409734
\(596\) 0 0
\(597\) 20.9627 0.857946
\(598\) 0 0
\(599\) −29.9256 −1.22273 −0.611364 0.791349i \(-0.709379\pi\)
−0.611364 + 0.791349i \(0.709379\pi\)
\(600\) 0 0
\(601\) −45.2604 −1.84621 −0.923105 0.384548i \(-0.874357\pi\)
−0.923105 + 0.384548i \(0.874357\pi\)
\(602\) 0 0
\(603\) −9.07361 −0.369506
\(604\) 0 0
\(605\) −37.5096 −1.52498
\(606\) 0 0
\(607\) −3.72389 −0.151148 −0.0755740 0.997140i \(-0.524079\pi\)
−0.0755740 + 0.997140i \(0.524079\pi\)
\(608\) 0 0
\(609\) −15.1725 −0.614822
\(610\) 0 0
\(611\) −70.3761 −2.84711
\(612\) 0 0
\(613\) −35.3721 −1.42867 −0.714333 0.699806i \(-0.753270\pi\)
−0.714333 + 0.699806i \(0.753270\pi\)
\(614\) 0 0
\(615\) 22.6493 0.913309
\(616\) 0 0
\(617\) −7.32100 −0.294732 −0.147366 0.989082i \(-0.547080\pi\)
−0.147366 + 0.989082i \(0.547080\pi\)
\(618\) 0 0
\(619\) 15.2901 0.614559 0.307280 0.951619i \(-0.400581\pi\)
0.307280 + 0.951619i \(0.400581\pi\)
\(620\) 0 0
\(621\) 3.33676 0.133899
\(622\) 0 0
\(623\) 6.74292 0.270149
\(624\) 0 0
\(625\) 20.8835 0.835341
\(626\) 0 0
\(627\) −5.22326 −0.208597
\(628\) 0 0
\(629\) −2.57560 −0.102696
\(630\) 0 0
\(631\) 13.2764 0.528524 0.264262 0.964451i \(-0.414872\pi\)
0.264262 + 0.964451i \(0.414872\pi\)
\(632\) 0 0
\(633\) 13.3764 0.531662
\(634\) 0 0
\(635\) 76.3959 3.03168
\(636\) 0 0
\(637\) −74.2527 −2.94200
\(638\) 0 0
\(639\) −13.8081 −0.546239
\(640\) 0 0
\(641\) 6.17423 0.243867 0.121934 0.992538i \(-0.461090\pi\)
0.121934 + 0.992538i \(0.461090\pi\)
\(642\) 0 0
\(643\) −0.865911 −0.0341482 −0.0170741 0.999854i \(-0.505435\pi\)
−0.0170741 + 0.999854i \(0.505435\pi\)
\(644\) 0 0
\(645\) −38.3786 −1.51116
\(646\) 0 0
\(647\) −34.3420 −1.35012 −0.675062 0.737761i \(-0.735883\pi\)
−0.675062 + 0.737761i \(0.735883\pi\)
\(648\) 0 0
\(649\) −3.07394 −0.120663
\(650\) 0 0
\(651\) 12.4653 0.488554
\(652\) 0 0
\(653\) 17.1698 0.671908 0.335954 0.941878i \(-0.390941\pi\)
0.335954 + 0.941878i \(0.390941\pi\)
\(654\) 0 0
\(655\) 24.6538 0.963305
\(656\) 0 0
\(657\) 9.14053 0.356606
\(658\) 0 0
\(659\) −36.8878 −1.43695 −0.718473 0.695555i \(-0.755159\pi\)
−0.718473 + 0.695555i \(0.755159\pi\)
\(660\) 0 0
\(661\) 26.5260 1.03174 0.515871 0.856666i \(-0.327468\pi\)
0.515871 + 0.856666i \(0.327468\pi\)
\(662\) 0 0
\(663\) 3.29792 0.128081
\(664\) 0 0
\(665\) −81.1986 −3.14875
\(666\) 0 0
\(667\) 11.2962 0.437389
\(668\) 0 0
\(669\) 7.31317 0.282744
\(670\) 0 0
\(671\) −10.4265 −0.402511
\(672\) 0 0
\(673\) −27.2730 −1.05130 −0.525648 0.850702i \(-0.676177\pi\)
−0.525648 + 0.850702i \(0.676177\pi\)
\(674\) 0 0
\(675\) 9.72035 0.374137
\(676\) 0 0
\(677\) 12.4893 0.480004 0.240002 0.970772i \(-0.422852\pi\)
0.240002 + 0.970772i \(0.422852\pi\)
\(678\) 0 0
\(679\) −3.41462 −0.131041
\(680\) 0 0
\(681\) −2.35302 −0.0901677
\(682\) 0 0
\(683\) 29.6433 1.13427 0.567134 0.823626i \(-0.308052\pi\)
0.567134 + 0.823626i \(0.308052\pi\)
\(684\) 0 0
\(685\) −5.44841 −0.208173
\(686\) 0 0
\(687\) 16.3540 0.623943
\(688\) 0 0
\(689\) −28.9610 −1.10333
\(690\) 0 0
\(691\) −1.78092 −0.0677493 −0.0338747 0.999426i \(-0.510785\pi\)
−0.0338747 + 0.999426i \(0.510785\pi\)
\(692\) 0 0
\(693\) 4.95742 0.188317
\(694\) 0 0
\(695\) −36.2055 −1.37335
\(696\) 0 0
\(697\) −3.43120 −0.129966
\(698\) 0 0
\(699\) −24.5380 −0.928111
\(700\) 0 0
\(701\) 19.8886 0.751182 0.375591 0.926785i \(-0.377440\pi\)
0.375591 + 0.926785i \(0.377440\pi\)
\(702\) 0 0
\(703\) 20.9251 0.789204
\(704\) 0 0
\(705\) 47.5876 1.79225
\(706\) 0 0
\(707\) 6.16197 0.231745
\(708\) 0 0
\(709\) −41.6852 −1.56552 −0.782760 0.622323i \(-0.786189\pi\)
−0.782760 + 0.622323i \(0.786189\pi\)
\(710\) 0 0
\(711\) 17.4215 0.653356
\(712\) 0 0
\(713\) −9.28060 −0.347561
\(714\) 0 0
\(715\) 24.0799 0.900536
\(716\) 0 0
\(717\) 16.5560 0.618296
\(718\) 0 0
\(719\) −16.0390 −0.598153 −0.299076 0.954229i \(-0.596679\pi\)
−0.299076 + 0.954229i \(0.596679\pi\)
\(720\) 0 0
\(721\) −0.282230 −0.0105108
\(722\) 0 0
\(723\) 13.4248 0.499272
\(724\) 0 0
\(725\) 32.9070 1.22214
\(726\) 0 0
\(727\) −4.28104 −0.158775 −0.0793874 0.996844i \(-0.525296\pi\)
−0.0793874 + 0.996844i \(0.525296\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 5.81406 0.215041
\(732\) 0 0
\(733\) −14.9604 −0.552574 −0.276287 0.961075i \(-0.589104\pi\)
−0.276287 + 0.961075i \(0.589104\pi\)
\(734\) 0 0
\(735\) 50.2089 1.85198
\(736\) 0 0
\(737\) 10.0365 0.369701
\(738\) 0 0
\(739\) −7.78573 −0.286403 −0.143201 0.989694i \(-0.545740\pi\)
−0.143201 + 0.989694i \(0.545740\pi\)
\(740\) 0 0
\(741\) −26.7935 −0.984282
\(742\) 0 0
\(743\) 4.23167 0.155245 0.0776224 0.996983i \(-0.475267\pi\)
0.0776224 + 0.996983i \(0.475267\pi\)
\(744\) 0 0
\(745\) 29.9676 1.09793
\(746\) 0 0
\(747\) −16.9891 −0.621598
\(748\) 0 0
\(749\) 45.0137 1.64476
\(750\) 0 0
\(751\) 49.4751 1.80537 0.902686 0.430301i \(-0.141592\pi\)
0.902686 + 0.430301i \(0.141592\pi\)
\(752\) 0 0
\(753\) −7.08588 −0.258224
\(754\) 0 0
\(755\) −2.35811 −0.0858205
\(756\) 0 0
\(757\) −13.6590 −0.496444 −0.248222 0.968703i \(-0.579846\pi\)
−0.248222 + 0.968703i \(0.579846\pi\)
\(758\) 0 0
\(759\) −3.69087 −0.133970
\(760\) 0 0
\(761\) 7.48874 0.271467 0.135733 0.990745i \(-0.456661\pi\)
0.135733 + 0.990745i \(0.456661\pi\)
\(762\) 0 0
\(763\) −8.41853 −0.304771
\(764\) 0 0
\(765\) −2.23002 −0.0806265
\(766\) 0 0
\(767\) −15.7682 −0.569357
\(768\) 0 0
\(769\) 51.7046 1.86452 0.932258 0.361795i \(-0.117836\pi\)
0.932258 + 0.361795i \(0.117836\pi\)
\(770\) 0 0
\(771\) 9.32571 0.335857
\(772\) 0 0
\(773\) 17.9350 0.645078 0.322539 0.946556i \(-0.395464\pi\)
0.322539 + 0.946556i \(0.395464\pi\)
\(774\) 0 0
\(775\) −27.0354 −0.971142
\(776\) 0 0
\(777\) −19.8601 −0.712476
\(778\) 0 0
\(779\) 27.8762 0.998770
\(780\) 0 0
\(781\) 15.2735 0.546527
\(782\) 0 0
\(783\) 3.38537 0.120983
\(784\) 0 0
\(785\) 71.3216 2.54558
\(786\) 0 0
\(787\) −10.1192 −0.360711 −0.180356 0.983601i \(-0.557725\pi\)
−0.180356 + 0.983601i \(0.557725\pi\)
\(788\) 0 0
\(789\) −1.03494 −0.0368448
\(790\) 0 0
\(791\) −18.4304 −0.655309
\(792\) 0 0
\(793\) −53.4842 −1.89928
\(794\) 0 0
\(795\) 19.5831 0.694542
\(796\) 0 0
\(797\) 2.51921 0.0892351 0.0446175 0.999004i \(-0.485793\pi\)
0.0446175 + 0.999004i \(0.485793\pi\)
\(798\) 0 0
\(799\) −7.20915 −0.255041
\(800\) 0 0
\(801\) −1.50452 −0.0531594
\(802\) 0 0
\(803\) −10.1106 −0.356794
\(804\) 0 0
\(805\) −57.3767 −2.02226
\(806\) 0 0
\(807\) −13.2297 −0.465708
\(808\) 0 0
\(809\) 3.10619 0.109208 0.0546039 0.998508i \(-0.482610\pi\)
0.0546039 + 0.998508i \(0.482610\pi\)
\(810\) 0 0
\(811\) 21.4811 0.754303 0.377152 0.926152i \(-0.376904\pi\)
0.377152 + 0.926152i \(0.376904\pi\)
\(812\) 0 0
\(813\) −15.6279 −0.548096
\(814\) 0 0
\(815\) 67.7128 2.37188
\(816\) 0 0
\(817\) −47.2355 −1.65256
\(818\) 0 0
\(819\) 25.4298 0.888588
\(820\) 0 0
\(821\) 15.2130 0.530936 0.265468 0.964120i \(-0.414473\pi\)
0.265468 + 0.964120i \(0.414473\pi\)
\(822\) 0 0
\(823\) −11.0861 −0.386439 −0.193219 0.981156i \(-0.561893\pi\)
−0.193219 + 0.981156i \(0.561893\pi\)
\(824\) 0 0
\(825\) −10.7519 −0.374334
\(826\) 0 0
\(827\) −1.19279 −0.0414773 −0.0207387 0.999785i \(-0.506602\pi\)
−0.0207387 + 0.999785i \(0.506602\pi\)
\(828\) 0 0
\(829\) 35.5477 1.23462 0.617311 0.786719i \(-0.288222\pi\)
0.617311 + 0.786719i \(0.288222\pi\)
\(830\) 0 0
\(831\) −0.591123 −0.0205058
\(832\) 0 0
\(833\) −7.60626 −0.263541
\(834\) 0 0
\(835\) −3.83671 −0.132775
\(836\) 0 0
\(837\) −2.78132 −0.0961366
\(838\) 0 0
\(839\) 6.12432 0.211435 0.105718 0.994396i \(-0.466286\pi\)
0.105718 + 0.994396i \(0.466286\pi\)
\(840\) 0 0
\(841\) −17.5393 −0.604802
\(842\) 0 0
\(843\) −4.64950 −0.160137
\(844\) 0 0
\(845\) 73.6437 2.53342
\(846\) 0 0
\(847\) 43.8162 1.50554
\(848\) 0 0
\(849\) 23.7408 0.814781
\(850\) 0 0
\(851\) 14.7861 0.506861
\(852\) 0 0
\(853\) −16.7670 −0.574091 −0.287046 0.957917i \(-0.592673\pi\)
−0.287046 + 0.957917i \(0.592673\pi\)
\(854\) 0 0
\(855\) 18.1174 0.619604
\(856\) 0 0
\(857\) −11.0064 −0.375972 −0.187986 0.982172i \(-0.560196\pi\)
−0.187986 + 0.982172i \(0.560196\pi\)
\(858\) 0 0
\(859\) −30.9158 −1.05483 −0.527416 0.849607i \(-0.676839\pi\)
−0.527416 + 0.849607i \(0.676839\pi\)
\(860\) 0 0
\(861\) −26.4574 −0.901667
\(862\) 0 0
\(863\) 18.7791 0.639247 0.319624 0.947545i \(-0.396444\pi\)
0.319624 + 0.947545i \(0.396444\pi\)
\(864\) 0 0
\(865\) 18.4148 0.626121
\(866\) 0 0
\(867\) −16.6622 −0.565877
\(868\) 0 0
\(869\) −19.2703 −0.653700
\(870\) 0 0
\(871\) 51.4838 1.74446
\(872\) 0 0
\(873\) 0.761888 0.0257860
\(874\) 0 0
\(875\) −81.1681 −2.74398
\(876\) 0 0
\(877\) −8.89364 −0.300317 −0.150158 0.988662i \(-0.547978\pi\)
−0.150158 + 0.988662i \(0.547978\pi\)
\(878\) 0 0
\(879\) −27.7554 −0.936166
\(880\) 0 0
\(881\) 14.0530 0.473457 0.236728 0.971576i \(-0.423925\pi\)
0.236728 + 0.971576i \(0.423925\pi\)
\(882\) 0 0
\(883\) −31.0318 −1.04430 −0.522151 0.852853i \(-0.674870\pi\)
−0.522151 + 0.852853i \(0.674870\pi\)
\(884\) 0 0
\(885\) 10.6623 0.358409
\(886\) 0 0
\(887\) 17.0309 0.571842 0.285921 0.958253i \(-0.407700\pi\)
0.285921 + 0.958253i \(0.407700\pi\)
\(888\) 0 0
\(889\) −89.2406 −2.99304
\(890\) 0 0
\(891\) −1.10612 −0.0370566
\(892\) 0 0
\(893\) 58.5696 1.95996
\(894\) 0 0
\(895\) 79.1854 2.64687
\(896\) 0 0
\(897\) −18.9328 −0.632149
\(898\) 0 0
\(899\) −9.41581 −0.314035
\(900\) 0 0
\(901\) −2.96669 −0.0988348
\(902\) 0 0
\(903\) 44.8314 1.49189
\(904\) 0 0
\(905\) 41.8683 1.39175
\(906\) 0 0
\(907\) −56.3207 −1.87010 −0.935049 0.354520i \(-0.884644\pi\)
−0.935049 + 0.354520i \(0.884644\pi\)
\(908\) 0 0
\(909\) −1.37489 −0.0456023
\(910\) 0 0
\(911\) 57.9696 1.92062 0.960309 0.278937i \(-0.0899821\pi\)
0.960309 + 0.278937i \(0.0899821\pi\)
\(912\) 0 0
\(913\) 18.7920 0.621926
\(914\) 0 0
\(915\) 36.1654 1.19559
\(916\) 0 0
\(917\) −28.7990 −0.951026
\(918\) 0 0
\(919\) 7.93192 0.261650 0.130825 0.991405i \(-0.458237\pi\)
0.130825 + 0.991405i \(0.458237\pi\)
\(920\) 0 0
\(921\) −1.47952 −0.0487517
\(922\) 0 0
\(923\) 78.3473 2.57883
\(924\) 0 0
\(925\) 43.0736 1.41625
\(926\) 0 0
\(927\) 0.0629727 0.00206829
\(928\) 0 0
\(929\) 11.1314 0.365209 0.182604 0.983186i \(-0.441547\pi\)
0.182604 + 0.983186i \(0.441547\pi\)
\(930\) 0 0
\(931\) 61.7959 2.02528
\(932\) 0 0
\(933\) −19.6599 −0.643635
\(934\) 0 0
\(935\) 2.46668 0.0806690
\(936\) 0 0
\(937\) 4.29223 0.140221 0.0701105 0.997539i \(-0.477665\pi\)
0.0701105 + 0.997539i \(0.477665\pi\)
\(938\) 0 0
\(939\) −13.0409 −0.425574
\(940\) 0 0
\(941\) −39.4909 −1.28737 −0.643683 0.765292i \(-0.722595\pi\)
−0.643683 + 0.765292i \(0.722595\pi\)
\(942\) 0 0
\(943\) 19.6979 0.641453
\(944\) 0 0
\(945\) −17.1953 −0.559364
\(946\) 0 0
\(947\) −39.0910 −1.27029 −0.635144 0.772394i \(-0.719059\pi\)
−0.635144 + 0.772394i \(0.719059\pi\)
\(948\) 0 0
\(949\) −51.8635 −1.68356
\(950\) 0 0
\(951\) 13.2143 0.428504
\(952\) 0 0
\(953\) 33.7855 1.09442 0.547210 0.836995i \(-0.315690\pi\)
0.547210 + 0.836995i \(0.315690\pi\)
\(954\) 0 0
\(955\) 40.1888 1.30048
\(956\) 0 0
\(957\) −3.74464 −0.121047
\(958\) 0 0
\(959\) 6.36447 0.205519
\(960\) 0 0
\(961\) −23.2642 −0.750459
\(962\) 0 0
\(963\) −10.0437 −0.323653
\(964\) 0 0
\(965\) −31.8582 −1.02555
\(966\) 0 0
\(967\) 5.47656 0.176114 0.0880572 0.996115i \(-0.471934\pi\)
0.0880572 + 0.996115i \(0.471934\pi\)
\(968\) 0 0
\(969\) −2.74465 −0.0881709
\(970\) 0 0
\(971\) −23.8330 −0.764836 −0.382418 0.923989i \(-0.624909\pi\)
−0.382418 + 0.923989i \(0.624909\pi\)
\(972\) 0 0
\(973\) 42.2928 1.35584
\(974\) 0 0
\(975\) −55.1535 −1.76632
\(976\) 0 0
\(977\) −31.9054 −1.02075 −0.510373 0.859953i \(-0.670493\pi\)
−0.510373 + 0.859953i \(0.670493\pi\)
\(978\) 0 0
\(979\) 1.66418 0.0531875
\(980\) 0 0
\(981\) 1.87839 0.0599723
\(982\) 0 0
\(983\) −23.5991 −0.752696 −0.376348 0.926478i \(-0.622820\pi\)
−0.376348 + 0.926478i \(0.622820\pi\)
\(984\) 0 0
\(985\) 94.9393 3.02502
\(986\) 0 0
\(987\) −55.5886 −1.76941
\(988\) 0 0
\(989\) −33.3776 −1.06135
\(990\) 0 0
\(991\) 35.7794 1.13657 0.568285 0.822832i \(-0.307607\pi\)
0.568285 + 0.822832i \(0.307607\pi\)
\(992\) 0 0
\(993\) 27.4467 0.870993
\(994\) 0 0
\(995\) 80.4278 2.54973
\(996\) 0 0
\(997\) −35.1383 −1.11284 −0.556420 0.830901i \(-0.687825\pi\)
−0.556420 + 0.830901i \(0.687825\pi\)
\(998\) 0 0
\(999\) 4.43128 0.140199
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.1.10 11
4.3 odd 2 4008.2.a.k.1.10 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.k.1.10 11 4.3 odd 2
8016.2.a.be.1.10 11 1.1 even 1 trivial