Properties

Label 8016.2.a.ba.1.7
Level $8016$
Weight $2$
Character 8016.1
Self dual yes
Analytic conductor $64.008$
Analytic rank $0$
Dimension $9$
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: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - 3 x^{8} - 16 x^{7} + 45 x^{6} + 67 x^{5} - 166 x^{4} - 83 x^{3} + 152 x^{2} + 51 x - 10\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.58856\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +0.588564 q^{5} +1.23518 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +0.588564 q^{5} +1.23518 q^{7} +1.00000 q^{9} +5.01763 q^{11} +4.86230 q^{13} -0.588564 q^{15} -6.70724 q^{17} +1.72560 q^{19} -1.23518 q^{21} -3.90691 q^{23} -4.65359 q^{25} -1.00000 q^{27} +8.98846 q^{29} +5.36898 q^{31} -5.01763 q^{33} +0.726984 q^{35} +1.07031 q^{37} -4.86230 q^{39} +6.22415 q^{41} +9.74169 q^{43} +0.588564 q^{45} -3.85840 q^{47} -5.47432 q^{49} +6.70724 q^{51} -7.57769 q^{53} +2.95320 q^{55} -1.72560 q^{57} +8.99297 q^{59} -4.59852 q^{61} +1.23518 q^{63} +2.86177 q^{65} +15.2918 q^{67} +3.90691 q^{69} +6.37962 q^{71} +8.12499 q^{73} +4.65359 q^{75} +6.19770 q^{77} +6.10983 q^{79} +1.00000 q^{81} -3.46966 q^{83} -3.94764 q^{85} -8.98846 q^{87} +5.15759 q^{89} +6.00583 q^{91} -5.36898 q^{93} +1.01563 q^{95} -13.6764 q^{97} +5.01763 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 9q^{3} - 6q^{5} + 11q^{7} + 9q^{9} + O(q^{10}) \) \( 9q - 9q^{3} - 6q^{5} + 11q^{7} + 9q^{9} - q^{11} - 4q^{13} + 6q^{15} - 9q^{17} + 8q^{19} - 11q^{21} + 7q^{23} - q^{25} - 9q^{27} - 9q^{29} + 25q^{31} + q^{33} - 5q^{35} - 6q^{37} + 4q^{39} - 4q^{41} + 24q^{43} - 6q^{45} + 16q^{47} + 4q^{49} + 9q^{51} - 26q^{53} + 29q^{55} - 8q^{57} + 4q^{59} - 20q^{61} + 11q^{63} - 8q^{65} + 25q^{67} - 7q^{69} + 15q^{71} - 10q^{73} + q^{75} - 20q^{77} + 34q^{79} + 9q^{81} + 4q^{83} - 13q^{85} + 9q^{87} + 13q^{89} + 21q^{91} - 25q^{93} + 7q^{95} - 4q^{97} - q^{99} + O(q^{100}) \)

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
\(5\) 0.588564 0.263214 0.131607 0.991302i \(-0.457986\pi\)
0.131607 + 0.991302i \(0.457986\pi\)
\(6\) 0 0
\(7\) 1.23518 0.466855 0.233428 0.972374i \(-0.425006\pi\)
0.233428 + 0.972374i \(0.425006\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.01763 1.51287 0.756437 0.654067i \(-0.226939\pi\)
0.756437 + 0.654067i \(0.226939\pi\)
\(12\) 0 0
\(13\) 4.86230 1.34856 0.674280 0.738476i \(-0.264454\pi\)
0.674280 + 0.738476i \(0.264454\pi\)
\(14\) 0 0
\(15\) −0.588564 −0.151966
\(16\) 0 0
\(17\) −6.70724 −1.62675 −0.813373 0.581743i \(-0.802371\pi\)
−0.813373 + 0.581743i \(0.802371\pi\)
\(18\) 0 0
\(19\) 1.72560 0.395880 0.197940 0.980214i \(-0.436575\pi\)
0.197940 + 0.980214i \(0.436575\pi\)
\(20\) 0 0
\(21\) −1.23518 −0.269539
\(22\) 0 0
\(23\) −3.90691 −0.814648 −0.407324 0.913284i \(-0.633538\pi\)
−0.407324 + 0.913284i \(0.633538\pi\)
\(24\) 0 0
\(25\) −4.65359 −0.930719
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 8.98846 1.66912 0.834558 0.550920i \(-0.185723\pi\)
0.834558 + 0.550920i \(0.185723\pi\)
\(30\) 0 0
\(31\) 5.36898 0.964297 0.482149 0.876089i \(-0.339856\pi\)
0.482149 + 0.876089i \(0.339856\pi\)
\(32\) 0 0
\(33\) −5.01763 −0.873458
\(34\) 0 0
\(35\) 0.726984 0.122883
\(36\) 0 0
\(37\) 1.07031 0.175957 0.0879786 0.996122i \(-0.471959\pi\)
0.0879786 + 0.996122i \(0.471959\pi\)
\(38\) 0 0
\(39\) −4.86230 −0.778591
\(40\) 0 0
\(41\) 6.22415 0.972050 0.486025 0.873945i \(-0.338446\pi\)
0.486025 + 0.873945i \(0.338446\pi\)
\(42\) 0 0
\(43\) 9.74169 1.48559 0.742797 0.669517i \(-0.233499\pi\)
0.742797 + 0.669517i \(0.233499\pi\)
\(44\) 0 0
\(45\) 0.588564 0.0877379
\(46\) 0 0
\(47\) −3.85840 −0.562806 −0.281403 0.959590i \(-0.590800\pi\)
−0.281403 + 0.959590i \(0.590800\pi\)
\(48\) 0 0
\(49\) −5.47432 −0.782046
\(50\) 0 0
\(51\) 6.70724 0.939202
\(52\) 0 0
\(53\) −7.57769 −1.04088 −0.520438 0.853900i \(-0.674231\pi\)
−0.520438 + 0.853900i \(0.674231\pi\)
\(54\) 0 0
\(55\) 2.95320 0.398209
\(56\) 0 0
\(57\) −1.72560 −0.228562
\(58\) 0 0
\(59\) 8.99297 1.17079 0.585393 0.810750i \(-0.300940\pi\)
0.585393 + 0.810750i \(0.300940\pi\)
\(60\) 0 0
\(61\) −4.59852 −0.588780 −0.294390 0.955685i \(-0.595116\pi\)
−0.294390 + 0.955685i \(0.595116\pi\)
\(62\) 0 0
\(63\) 1.23518 0.155618
\(64\) 0 0
\(65\) 2.86177 0.354959
\(66\) 0 0
\(67\) 15.2918 1.86819 0.934093 0.357029i \(-0.116210\pi\)
0.934093 + 0.357029i \(0.116210\pi\)
\(68\) 0 0
\(69\) 3.90691 0.470337
\(70\) 0 0
\(71\) 6.37962 0.757122 0.378561 0.925576i \(-0.376419\pi\)
0.378561 + 0.925576i \(0.376419\pi\)
\(72\) 0 0
\(73\) 8.12499 0.950959 0.475479 0.879727i \(-0.342275\pi\)
0.475479 + 0.879727i \(0.342275\pi\)
\(74\) 0 0
\(75\) 4.65359 0.537351
\(76\) 0 0
\(77\) 6.19770 0.706293
\(78\) 0 0
\(79\) 6.10983 0.687410 0.343705 0.939078i \(-0.388318\pi\)
0.343705 + 0.939078i \(0.388318\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −3.46966 −0.380844 −0.190422 0.981702i \(-0.560986\pi\)
−0.190422 + 0.981702i \(0.560986\pi\)
\(84\) 0 0
\(85\) −3.94764 −0.428182
\(86\) 0 0
\(87\) −8.98846 −0.963664
\(88\) 0 0
\(89\) 5.15759 0.546703 0.273351 0.961914i \(-0.411868\pi\)
0.273351 + 0.961914i \(0.411868\pi\)
\(90\) 0 0
\(91\) 6.00583 0.629582
\(92\) 0 0
\(93\) −5.36898 −0.556737
\(94\) 0 0
\(95\) 1.01563 0.104201
\(96\) 0 0
\(97\) −13.6764 −1.38863 −0.694315 0.719671i \(-0.744293\pi\)
−0.694315 + 0.719671i \(0.744293\pi\)
\(98\) 0 0
\(99\) 5.01763 0.504291
\(100\) 0 0
\(101\) −3.33213 −0.331559 −0.165780 0.986163i \(-0.553014\pi\)
−0.165780 + 0.986163i \(0.553014\pi\)
\(102\) 0 0
\(103\) 1.59690 0.157347 0.0786737 0.996900i \(-0.474931\pi\)
0.0786737 + 0.996900i \(0.474931\pi\)
\(104\) 0 0
\(105\) −0.726984 −0.0709464
\(106\) 0 0
\(107\) −12.8858 −1.24571 −0.622857 0.782335i \(-0.714028\pi\)
−0.622857 + 0.782335i \(0.714028\pi\)
\(108\) 0 0
\(109\) −1.41783 −0.135804 −0.0679018 0.997692i \(-0.521630\pi\)
−0.0679018 + 0.997692i \(0.521630\pi\)
\(110\) 0 0
\(111\) −1.07031 −0.101589
\(112\) 0 0
\(113\) −18.0186 −1.69505 −0.847524 0.530757i \(-0.821908\pi\)
−0.847524 + 0.530757i \(0.821908\pi\)
\(114\) 0 0
\(115\) −2.29947 −0.214426
\(116\) 0 0
\(117\) 4.86230 0.449520
\(118\) 0 0
\(119\) −8.28468 −0.759455
\(120\) 0 0
\(121\) 14.1766 1.28879
\(122\) 0 0
\(123\) −6.22415 −0.561213
\(124\) 0 0
\(125\) −5.68175 −0.508191
\(126\) 0 0
\(127\) −19.7958 −1.75659 −0.878295 0.478120i \(-0.841318\pi\)
−0.878295 + 0.478120i \(0.841318\pi\)
\(128\) 0 0
\(129\) −9.74169 −0.857708
\(130\) 0 0
\(131\) 1.29378 0.113038 0.0565191 0.998402i \(-0.482000\pi\)
0.0565191 + 0.998402i \(0.482000\pi\)
\(132\) 0 0
\(133\) 2.13144 0.184819
\(134\) 0 0
\(135\) −0.588564 −0.0506555
\(136\) 0 0
\(137\) 15.2142 1.29983 0.649917 0.760005i \(-0.274804\pi\)
0.649917 + 0.760005i \(0.274804\pi\)
\(138\) 0 0
\(139\) 15.1674 1.28649 0.643243 0.765662i \(-0.277589\pi\)
0.643243 + 0.765662i \(0.277589\pi\)
\(140\) 0 0
\(141\) 3.85840 0.324936
\(142\) 0 0
\(143\) 24.3972 2.04020
\(144\) 0 0
\(145\) 5.29028 0.439334
\(146\) 0 0
\(147\) 5.47432 0.451514
\(148\) 0 0
\(149\) −14.4870 −1.18682 −0.593412 0.804899i \(-0.702220\pi\)
−0.593412 + 0.804899i \(0.702220\pi\)
\(150\) 0 0
\(151\) 4.68695 0.381419 0.190709 0.981647i \(-0.438921\pi\)
0.190709 + 0.981647i \(0.438921\pi\)
\(152\) 0 0
\(153\) −6.70724 −0.542249
\(154\) 0 0
\(155\) 3.15999 0.253816
\(156\) 0 0
\(157\) −22.2647 −1.77692 −0.888458 0.458958i \(-0.848223\pi\)
−0.888458 + 0.458958i \(0.848223\pi\)
\(158\) 0 0
\(159\) 7.57769 0.600950
\(160\) 0 0
\(161\) −4.82576 −0.380323
\(162\) 0 0
\(163\) 18.8338 1.47517 0.737587 0.675252i \(-0.235965\pi\)
0.737587 + 0.675252i \(0.235965\pi\)
\(164\) 0 0
\(165\) −2.95320 −0.229906
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 10.6420 0.818612
\(170\) 0 0
\(171\) 1.72560 0.131960
\(172\) 0 0
\(173\) −0.471351 −0.0358362 −0.0179181 0.999839i \(-0.505704\pi\)
−0.0179181 + 0.999839i \(0.505704\pi\)
\(174\) 0 0
\(175\) −5.74804 −0.434511
\(176\) 0 0
\(177\) −8.99297 −0.675953
\(178\) 0 0
\(179\) −15.7303 −1.17574 −0.587868 0.808957i \(-0.700033\pi\)
−0.587868 + 0.808957i \(0.700033\pi\)
\(180\) 0 0
\(181\) 13.6079 1.01147 0.505735 0.862689i \(-0.331221\pi\)
0.505735 + 0.862689i \(0.331221\pi\)
\(182\) 0 0
\(183\) 4.59852 0.339932
\(184\) 0 0
\(185\) 0.629943 0.0463143
\(186\) 0 0
\(187\) −33.6545 −2.46106
\(188\) 0 0
\(189\) −1.23518 −0.0898464
\(190\) 0 0
\(191\) 9.61701 0.695862 0.347931 0.937520i \(-0.386884\pi\)
0.347931 + 0.937520i \(0.386884\pi\)
\(192\) 0 0
\(193\) 3.01313 0.216890 0.108445 0.994102i \(-0.465413\pi\)
0.108445 + 0.994102i \(0.465413\pi\)
\(194\) 0 0
\(195\) −2.86177 −0.204936
\(196\) 0 0
\(197\) 2.78043 0.198097 0.0990486 0.995083i \(-0.468420\pi\)
0.0990486 + 0.995083i \(0.468420\pi\)
\(198\) 0 0
\(199\) −12.7220 −0.901835 −0.450918 0.892566i \(-0.648903\pi\)
−0.450918 + 0.892566i \(0.648903\pi\)
\(200\) 0 0
\(201\) −15.2918 −1.07860
\(202\) 0 0
\(203\) 11.1024 0.779236
\(204\) 0 0
\(205\) 3.66331 0.255857
\(206\) 0 0
\(207\) −3.90691 −0.271549
\(208\) 0 0
\(209\) 8.65844 0.598917
\(210\) 0 0
\(211\) −7.37467 −0.507693 −0.253847 0.967244i \(-0.581696\pi\)
−0.253847 + 0.967244i \(0.581696\pi\)
\(212\) 0 0
\(213\) −6.37962 −0.437124
\(214\) 0 0
\(215\) 5.73360 0.391028
\(216\) 0 0
\(217\) 6.63168 0.450187
\(218\) 0 0
\(219\) −8.12499 −0.549036
\(220\) 0 0
\(221\) −32.6126 −2.19376
\(222\) 0 0
\(223\) −6.83212 −0.457513 −0.228756 0.973484i \(-0.573466\pi\)
−0.228756 + 0.973484i \(0.573466\pi\)
\(224\) 0 0
\(225\) −4.65359 −0.310240
\(226\) 0 0
\(227\) −6.63738 −0.440538 −0.220269 0.975439i \(-0.570694\pi\)
−0.220269 + 0.975439i \(0.570694\pi\)
\(228\) 0 0
\(229\) 22.4406 1.48292 0.741458 0.670999i \(-0.234135\pi\)
0.741458 + 0.670999i \(0.234135\pi\)
\(230\) 0 0
\(231\) −6.19770 −0.407779
\(232\) 0 0
\(233\) −26.1458 −1.71287 −0.856435 0.516255i \(-0.827326\pi\)
−0.856435 + 0.516255i \(0.827326\pi\)
\(234\) 0 0
\(235\) −2.27091 −0.148138
\(236\) 0 0
\(237\) −6.10983 −0.396876
\(238\) 0 0
\(239\) 20.5154 1.32703 0.663517 0.748161i \(-0.269063\pi\)
0.663517 + 0.748161i \(0.269063\pi\)
\(240\) 0 0
\(241\) −20.5369 −1.32290 −0.661449 0.749990i \(-0.730058\pi\)
−0.661449 + 0.749990i \(0.730058\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −3.22199 −0.205845
\(246\) 0 0
\(247\) 8.39040 0.533868
\(248\) 0 0
\(249\) 3.46966 0.219881
\(250\) 0 0
\(251\) −5.12657 −0.323586 −0.161793 0.986825i \(-0.551728\pi\)
−0.161793 + 0.986825i \(0.551728\pi\)
\(252\) 0 0
\(253\) −19.6035 −1.23246
\(254\) 0 0
\(255\) 3.94764 0.247211
\(256\) 0 0
\(257\) 26.5939 1.65888 0.829442 0.558593i \(-0.188659\pi\)
0.829442 + 0.558593i \(0.188659\pi\)
\(258\) 0 0
\(259\) 1.32202 0.0821466
\(260\) 0 0
\(261\) 8.98846 0.556372
\(262\) 0 0
\(263\) −10.5800 −0.652393 −0.326196 0.945302i \(-0.605767\pi\)
−0.326196 + 0.945302i \(0.605767\pi\)
\(264\) 0 0
\(265\) −4.45995 −0.273973
\(266\) 0 0
\(267\) −5.15759 −0.315639
\(268\) 0 0
\(269\) 10.0877 0.615056 0.307528 0.951539i \(-0.400498\pi\)
0.307528 + 0.951539i \(0.400498\pi\)
\(270\) 0 0
\(271\) 20.1257 1.22255 0.611275 0.791418i \(-0.290657\pi\)
0.611275 + 0.791418i \(0.290657\pi\)
\(272\) 0 0
\(273\) −6.00583 −0.363489
\(274\) 0 0
\(275\) −23.3500 −1.40806
\(276\) 0 0
\(277\) −4.99188 −0.299933 −0.149966 0.988691i \(-0.547917\pi\)
−0.149966 + 0.988691i \(0.547917\pi\)
\(278\) 0 0
\(279\) 5.36898 0.321432
\(280\) 0 0
\(281\) 22.7616 1.35784 0.678922 0.734210i \(-0.262447\pi\)
0.678922 + 0.734210i \(0.262447\pi\)
\(282\) 0 0
\(283\) 23.4891 1.39628 0.698141 0.715961i \(-0.254011\pi\)
0.698141 + 0.715961i \(0.254011\pi\)
\(284\) 0 0
\(285\) −1.01563 −0.0601605
\(286\) 0 0
\(287\) 7.68797 0.453807
\(288\) 0 0
\(289\) 27.9871 1.64630
\(290\) 0 0
\(291\) 13.6764 0.801726
\(292\) 0 0
\(293\) 28.5327 1.66690 0.833450 0.552595i \(-0.186363\pi\)
0.833450 + 0.552595i \(0.186363\pi\)
\(294\) 0 0
\(295\) 5.29294 0.308167
\(296\) 0 0
\(297\) −5.01763 −0.291153
\(298\) 0 0
\(299\) −18.9966 −1.09860
\(300\) 0 0
\(301\) 12.0328 0.693557
\(302\) 0 0
\(303\) 3.33213 0.191426
\(304\) 0 0
\(305\) −2.70652 −0.154975
\(306\) 0 0
\(307\) −1.14107 −0.0651242 −0.0325621 0.999470i \(-0.510367\pi\)
−0.0325621 + 0.999470i \(0.510367\pi\)
\(308\) 0 0
\(309\) −1.59690 −0.0908445
\(310\) 0 0
\(311\) 27.8320 1.57821 0.789103 0.614261i \(-0.210546\pi\)
0.789103 + 0.614261i \(0.210546\pi\)
\(312\) 0 0
\(313\) 9.27809 0.524428 0.262214 0.965010i \(-0.415547\pi\)
0.262214 + 0.965010i \(0.415547\pi\)
\(314\) 0 0
\(315\) 0.726984 0.0409609
\(316\) 0 0
\(317\) 11.0846 0.622572 0.311286 0.950316i \(-0.399240\pi\)
0.311286 + 0.950316i \(0.399240\pi\)
\(318\) 0 0
\(319\) 45.1008 2.52516
\(320\) 0 0
\(321\) 12.8858 0.719214
\(322\) 0 0
\(323\) −11.5740 −0.643997
\(324\) 0 0
\(325\) −22.6272 −1.25513
\(326\) 0 0
\(327\) 1.41783 0.0784063
\(328\) 0 0
\(329\) −4.76583 −0.262749
\(330\) 0 0
\(331\) −28.7641 −1.58102 −0.790510 0.612449i \(-0.790184\pi\)
−0.790510 + 0.612449i \(0.790184\pi\)
\(332\) 0 0
\(333\) 1.07031 0.0586524
\(334\) 0 0
\(335\) 9.00018 0.491732
\(336\) 0 0
\(337\) 4.07043 0.221730 0.110865 0.993835i \(-0.464638\pi\)
0.110865 + 0.993835i \(0.464638\pi\)
\(338\) 0 0
\(339\) 18.0186 0.978636
\(340\) 0 0
\(341\) 26.9396 1.45886
\(342\) 0 0
\(343\) −15.4081 −0.831958
\(344\) 0 0
\(345\) 2.29947 0.123799
\(346\) 0 0
\(347\) 2.34196 0.125723 0.0628615 0.998022i \(-0.479977\pi\)
0.0628615 + 0.998022i \(0.479977\pi\)
\(348\) 0 0
\(349\) 20.0906 1.07542 0.537711 0.843129i \(-0.319289\pi\)
0.537711 + 0.843129i \(0.319289\pi\)
\(350\) 0 0
\(351\) −4.86230 −0.259530
\(352\) 0 0
\(353\) 1.08213 0.0575960 0.0287980 0.999585i \(-0.490832\pi\)
0.0287980 + 0.999585i \(0.490832\pi\)
\(354\) 0 0
\(355\) 3.75481 0.199285
\(356\) 0 0
\(357\) 8.28468 0.438472
\(358\) 0 0
\(359\) 4.25451 0.224545 0.112272 0.993677i \(-0.464187\pi\)
0.112272 + 0.993677i \(0.464187\pi\)
\(360\) 0 0
\(361\) −16.0223 −0.843279
\(362\) 0 0
\(363\) −14.1766 −0.744081
\(364\) 0 0
\(365\) 4.78208 0.250305
\(366\) 0 0
\(367\) 21.5891 1.12694 0.563472 0.826135i \(-0.309465\pi\)
0.563472 + 0.826135i \(0.309465\pi\)
\(368\) 0 0
\(369\) 6.22415 0.324017
\(370\) 0 0
\(371\) −9.35983 −0.485938
\(372\) 0 0
\(373\) −2.46856 −0.127817 −0.0639087 0.997956i \(-0.520357\pi\)
−0.0639087 + 0.997956i \(0.520357\pi\)
\(374\) 0 0
\(375\) 5.68175 0.293404
\(376\) 0 0
\(377\) 43.7046 2.25090
\(378\) 0 0
\(379\) 20.7402 1.06535 0.532675 0.846320i \(-0.321187\pi\)
0.532675 + 0.846320i \(0.321187\pi\)
\(380\) 0 0
\(381\) 19.7958 1.01417
\(382\) 0 0
\(383\) 12.1308 0.619855 0.309928 0.950760i \(-0.399695\pi\)
0.309928 + 0.950760i \(0.399695\pi\)
\(384\) 0 0
\(385\) 3.64774 0.185906
\(386\) 0 0
\(387\) 9.74169 0.495198
\(388\) 0 0
\(389\) −26.2089 −1.32884 −0.664422 0.747358i \(-0.731322\pi\)
−0.664422 + 0.747358i \(0.731322\pi\)
\(390\) 0 0
\(391\) 26.2046 1.32523
\(392\) 0 0
\(393\) −1.29378 −0.0652626
\(394\) 0 0
\(395\) 3.59602 0.180936
\(396\) 0 0
\(397\) 19.9952 1.00353 0.501766 0.865003i \(-0.332684\pi\)
0.501766 + 0.865003i \(0.332684\pi\)
\(398\) 0 0
\(399\) −2.13144 −0.106705
\(400\) 0 0
\(401\) 19.4819 0.972878 0.486439 0.873715i \(-0.338296\pi\)
0.486439 + 0.873715i \(0.338296\pi\)
\(402\) 0 0
\(403\) 26.1056 1.30041
\(404\) 0 0
\(405\) 0.588564 0.0292460
\(406\) 0 0
\(407\) 5.37040 0.266201
\(408\) 0 0
\(409\) −10.9296 −0.540433 −0.270217 0.962800i \(-0.587095\pi\)
−0.270217 + 0.962800i \(0.587095\pi\)
\(410\) 0 0
\(411\) −15.2142 −0.750460
\(412\) 0 0
\(413\) 11.1080 0.546588
\(414\) 0 0
\(415\) −2.04211 −0.100243
\(416\) 0 0
\(417\) −15.1674 −0.742753
\(418\) 0 0
\(419\) 4.80239 0.234612 0.117306 0.993096i \(-0.462574\pi\)
0.117306 + 0.993096i \(0.462574\pi\)
\(420\) 0 0
\(421\) −12.5947 −0.613829 −0.306915 0.951737i \(-0.599297\pi\)
−0.306915 + 0.951737i \(0.599297\pi\)
\(422\) 0 0
\(423\) −3.85840 −0.187602
\(424\) 0 0
\(425\) 31.2128 1.51404
\(426\) 0 0
\(427\) −5.68002 −0.274875
\(428\) 0 0
\(429\) −24.3972 −1.17791
\(430\) 0 0
\(431\) −38.3341 −1.84649 −0.923243 0.384216i \(-0.874472\pi\)
−0.923243 + 0.384216i \(0.874472\pi\)
\(432\) 0 0
\(433\) −21.6211 −1.03904 −0.519521 0.854458i \(-0.673890\pi\)
−0.519521 + 0.854458i \(0.673890\pi\)
\(434\) 0 0
\(435\) −5.29028 −0.253650
\(436\) 0 0
\(437\) −6.74178 −0.322503
\(438\) 0 0
\(439\) 11.0736 0.528512 0.264256 0.964453i \(-0.414874\pi\)
0.264256 + 0.964453i \(0.414874\pi\)
\(440\) 0 0
\(441\) −5.47432 −0.260682
\(442\) 0 0
\(443\) 22.7154 1.07924 0.539620 0.841909i \(-0.318568\pi\)
0.539620 + 0.841909i \(0.318568\pi\)
\(444\) 0 0
\(445\) 3.03557 0.143900
\(446\) 0 0
\(447\) 14.4870 0.685213
\(448\) 0 0
\(449\) −4.64041 −0.218994 −0.109497 0.993987i \(-0.534924\pi\)
−0.109497 + 0.993987i \(0.534924\pi\)
\(450\) 0 0
\(451\) 31.2305 1.47059
\(452\) 0 0
\(453\) −4.68695 −0.220212
\(454\) 0 0
\(455\) 3.53481 0.165715
\(456\) 0 0
\(457\) 7.63494 0.357147 0.178574 0.983927i \(-0.442852\pi\)
0.178574 + 0.983927i \(0.442852\pi\)
\(458\) 0 0
\(459\) 6.70724 0.313067
\(460\) 0 0
\(461\) −1.87870 −0.0874999 −0.0437500 0.999043i \(-0.513930\pi\)
−0.0437500 + 0.999043i \(0.513930\pi\)
\(462\) 0 0
\(463\) 10.1989 0.473985 0.236993 0.971511i \(-0.423838\pi\)
0.236993 + 0.971511i \(0.423838\pi\)
\(464\) 0 0
\(465\) −3.15999 −0.146541
\(466\) 0 0
\(467\) −27.4879 −1.27199 −0.635995 0.771694i \(-0.719410\pi\)
−0.635995 + 0.771694i \(0.719410\pi\)
\(468\) 0 0
\(469\) 18.8881 0.872173
\(470\) 0 0
\(471\) 22.2647 1.02590
\(472\) 0 0
\(473\) 48.8802 2.24752
\(474\) 0 0
\(475\) −8.03025 −0.368453
\(476\) 0 0
\(477\) −7.57769 −0.346958
\(478\) 0 0
\(479\) −4.84027 −0.221158 −0.110579 0.993867i \(-0.535270\pi\)
−0.110579 + 0.993867i \(0.535270\pi\)
\(480\) 0 0
\(481\) 5.20415 0.237289
\(482\) 0 0
\(483\) 4.82576 0.219580
\(484\) 0 0
\(485\) −8.04944 −0.365506
\(486\) 0 0
\(487\) −5.00720 −0.226898 −0.113449 0.993544i \(-0.536190\pi\)
−0.113449 + 0.993544i \(0.536190\pi\)
\(488\) 0 0
\(489\) −18.8338 −0.851692
\(490\) 0 0
\(491\) 1.70630 0.0770041 0.0385021 0.999259i \(-0.487741\pi\)
0.0385021 + 0.999259i \(0.487741\pi\)
\(492\) 0 0
\(493\) −60.2878 −2.71523
\(494\) 0 0
\(495\) 2.95320 0.132736
\(496\) 0 0
\(497\) 7.88000 0.353466
\(498\) 0 0
\(499\) 22.2962 0.998114 0.499057 0.866569i \(-0.333680\pi\)
0.499057 + 0.866569i \(0.333680\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 1.40579 0.0626811 0.0313406 0.999509i \(-0.490022\pi\)
0.0313406 + 0.999509i \(0.490022\pi\)
\(504\) 0 0
\(505\) −1.96117 −0.0872709
\(506\) 0 0
\(507\) −10.6420 −0.472626
\(508\) 0 0
\(509\) −43.1248 −1.91147 −0.955737 0.294223i \(-0.904939\pi\)
−0.955737 + 0.294223i \(0.904939\pi\)
\(510\) 0 0
\(511\) 10.0359 0.443960
\(512\) 0 0
\(513\) −1.72560 −0.0761872
\(514\) 0 0
\(515\) 0.939878 0.0414160
\(516\) 0 0
\(517\) −19.3600 −0.851454
\(518\) 0 0
\(519\) 0.471351 0.0206900
\(520\) 0 0
\(521\) 18.5381 0.812169 0.406085 0.913836i \(-0.366894\pi\)
0.406085 + 0.913836i \(0.366894\pi\)
\(522\) 0 0
\(523\) 24.6425 1.07754 0.538771 0.842452i \(-0.318889\pi\)
0.538771 + 0.842452i \(0.318889\pi\)
\(524\) 0 0
\(525\) 5.74804 0.250865
\(526\) 0 0
\(527\) −36.0111 −1.56867
\(528\) 0 0
\(529\) −7.73602 −0.336349
\(530\) 0 0
\(531\) 8.99297 0.390262
\(532\) 0 0
\(533\) 30.2637 1.31087
\(534\) 0 0
\(535\) −7.58410 −0.327889
\(536\) 0 0
\(537\) 15.7303 0.678812
\(538\) 0 0
\(539\) −27.4681 −1.18314
\(540\) 0 0
\(541\) 41.0312 1.76407 0.882034 0.471186i \(-0.156174\pi\)
0.882034 + 0.471186i \(0.156174\pi\)
\(542\) 0 0
\(543\) −13.6079 −0.583973
\(544\) 0 0
\(545\) −0.834484 −0.0357454
\(546\) 0 0
\(547\) −33.5441 −1.43424 −0.717121 0.696948i \(-0.754541\pi\)
−0.717121 + 0.696948i \(0.754541\pi\)
\(548\) 0 0
\(549\) −4.59852 −0.196260
\(550\) 0 0
\(551\) 15.5105 0.660770
\(552\) 0 0
\(553\) 7.54676 0.320921
\(554\) 0 0
\(555\) −0.629943 −0.0267396
\(556\) 0 0
\(557\) −4.42968 −0.187692 −0.0938458 0.995587i \(-0.529916\pi\)
−0.0938458 + 0.995587i \(0.529916\pi\)
\(558\) 0 0
\(559\) 47.3670 2.00341
\(560\) 0 0
\(561\) 33.6545 1.42089
\(562\) 0 0
\(563\) −4.13466 −0.174255 −0.0871276 0.996197i \(-0.527769\pi\)
−0.0871276 + 0.996197i \(0.527769\pi\)
\(564\) 0 0
\(565\) −10.6051 −0.446160
\(566\) 0 0
\(567\) 1.23518 0.0518728
\(568\) 0 0
\(569\) 35.5937 1.49217 0.746083 0.665852i \(-0.231932\pi\)
0.746083 + 0.665852i \(0.231932\pi\)
\(570\) 0 0
\(571\) 39.2825 1.64392 0.821962 0.569543i \(-0.192880\pi\)
0.821962 + 0.569543i \(0.192880\pi\)
\(572\) 0 0
\(573\) −9.61701 −0.401756
\(574\) 0 0
\(575\) 18.1812 0.758208
\(576\) 0 0
\(577\) 25.1884 1.04860 0.524302 0.851532i \(-0.324326\pi\)
0.524302 + 0.851532i \(0.324326\pi\)
\(578\) 0 0
\(579\) −3.01313 −0.125222
\(580\) 0 0
\(581\) −4.28566 −0.177799
\(582\) 0 0
\(583\) −38.0221 −1.57471
\(584\) 0 0
\(585\) 2.86177 0.118320
\(586\) 0 0
\(587\) −30.6309 −1.26427 −0.632136 0.774857i \(-0.717822\pi\)
−0.632136 + 0.774857i \(0.717822\pi\)
\(588\) 0 0
\(589\) 9.26473 0.381746
\(590\) 0 0
\(591\) −2.78043 −0.114371
\(592\) 0 0
\(593\) −16.8460 −0.691781 −0.345890 0.938275i \(-0.612423\pi\)
−0.345890 + 0.938275i \(0.612423\pi\)
\(594\) 0 0
\(595\) −4.87606 −0.199899
\(596\) 0 0
\(597\) 12.7220 0.520675
\(598\) 0 0
\(599\) −12.4465 −0.508549 −0.254275 0.967132i \(-0.581837\pi\)
−0.254275 + 0.967132i \(0.581837\pi\)
\(600\) 0 0
\(601\) 3.96091 0.161569 0.0807844 0.996732i \(-0.474257\pi\)
0.0807844 + 0.996732i \(0.474257\pi\)
\(602\) 0 0
\(603\) 15.2918 0.622729
\(604\) 0 0
\(605\) 8.34386 0.339226
\(606\) 0 0
\(607\) 5.93264 0.240799 0.120399 0.992726i \(-0.461583\pi\)
0.120399 + 0.992726i \(0.461583\pi\)
\(608\) 0 0
\(609\) −11.1024 −0.449892
\(610\) 0 0
\(611\) −18.7607 −0.758977
\(612\) 0 0
\(613\) 13.9450 0.563232 0.281616 0.959527i \(-0.409130\pi\)
0.281616 + 0.959527i \(0.409130\pi\)
\(614\) 0 0
\(615\) −3.66331 −0.147719
\(616\) 0 0
\(617\) −24.0063 −0.966457 −0.483229 0.875494i \(-0.660536\pi\)
−0.483229 + 0.875494i \(0.660536\pi\)
\(618\) 0 0
\(619\) −45.8501 −1.84287 −0.921435 0.388533i \(-0.872982\pi\)
−0.921435 + 0.388533i \(0.872982\pi\)
\(620\) 0 0
\(621\) 3.90691 0.156779
\(622\) 0 0
\(623\) 6.37056 0.255231
\(624\) 0 0
\(625\) 19.9239 0.796956
\(626\) 0 0
\(627\) −8.65844 −0.345785
\(628\) 0 0
\(629\) −7.17880 −0.286238
\(630\) 0 0
\(631\) 19.7197 0.785030 0.392515 0.919746i \(-0.371605\pi\)
0.392515 + 0.919746i \(0.371605\pi\)
\(632\) 0 0
\(633\) 7.37467 0.293117
\(634\) 0 0
\(635\) −11.6511 −0.462358
\(636\) 0 0
\(637\) −26.6178 −1.05464
\(638\) 0 0
\(639\) 6.37962 0.252374
\(640\) 0 0
\(641\) −34.2968 −1.35464 −0.677322 0.735687i \(-0.736859\pi\)
−0.677322 + 0.735687i \(0.736859\pi\)
\(642\) 0 0
\(643\) 12.4494 0.490957 0.245478 0.969402i \(-0.421055\pi\)
0.245478 + 0.969402i \(0.421055\pi\)
\(644\) 0 0
\(645\) −5.73360 −0.225760
\(646\) 0 0
\(647\) −38.4089 −1.51001 −0.755005 0.655719i \(-0.772365\pi\)
−0.755005 + 0.655719i \(0.772365\pi\)
\(648\) 0 0
\(649\) 45.1234 1.77125
\(650\) 0 0
\(651\) −6.63168 −0.259916
\(652\) 0 0
\(653\) 18.6064 0.728125 0.364062 0.931375i \(-0.381390\pi\)
0.364062 + 0.931375i \(0.381390\pi\)
\(654\) 0 0
\(655\) 0.761472 0.0297532
\(656\) 0 0
\(657\) 8.12499 0.316986
\(658\) 0 0
\(659\) −13.7868 −0.537059 −0.268530 0.963271i \(-0.586538\pi\)
−0.268530 + 0.963271i \(0.586538\pi\)
\(660\) 0 0
\(661\) −15.0955 −0.587149 −0.293574 0.955936i \(-0.594845\pi\)
−0.293574 + 0.955936i \(0.594845\pi\)
\(662\) 0 0
\(663\) 32.6126 1.26657
\(664\) 0 0
\(665\) 1.25449 0.0486468
\(666\) 0 0
\(667\) −35.1172 −1.35974
\(668\) 0 0
\(669\) 6.83212 0.264145
\(670\) 0 0
\(671\) −23.0737 −0.890750
\(672\) 0 0
\(673\) 25.1028 0.967642 0.483821 0.875167i \(-0.339249\pi\)
0.483821 + 0.875167i \(0.339249\pi\)
\(674\) 0 0
\(675\) 4.65359 0.179117
\(676\) 0 0
\(677\) −9.75143 −0.374778 −0.187389 0.982286i \(-0.560002\pi\)
−0.187389 + 0.982286i \(0.560002\pi\)
\(678\) 0 0
\(679\) −16.8929 −0.648289
\(680\) 0 0
\(681\) 6.63738 0.254345
\(682\) 0 0
\(683\) −13.0994 −0.501233 −0.250616 0.968086i \(-0.580633\pi\)
−0.250616 + 0.968086i \(0.580633\pi\)
\(684\) 0 0
\(685\) 8.95450 0.342134
\(686\) 0 0
\(687\) −22.4406 −0.856162
\(688\) 0 0
\(689\) −36.8450 −1.40368
\(690\) 0 0
\(691\) 12.4983 0.475459 0.237729 0.971331i \(-0.423597\pi\)
0.237729 + 0.971331i \(0.423597\pi\)
\(692\) 0 0
\(693\) 6.19770 0.235431
\(694\) 0 0
\(695\) 8.92700 0.338621
\(696\) 0 0
\(697\) −41.7469 −1.58128
\(698\) 0 0
\(699\) 26.1458 0.988926
\(700\) 0 0
\(701\) 8.26205 0.312053 0.156027 0.987753i \(-0.450131\pi\)
0.156027 + 0.987753i \(0.450131\pi\)
\(702\) 0 0
\(703\) 1.84692 0.0696580
\(704\) 0 0
\(705\) 2.27091 0.0855276
\(706\) 0 0
\(707\) −4.11579 −0.154790
\(708\) 0 0
\(709\) −16.6255 −0.624382 −0.312191 0.950019i \(-0.601063\pi\)
−0.312191 + 0.950019i \(0.601063\pi\)
\(710\) 0 0
\(711\) 6.10983 0.229137
\(712\) 0 0
\(713\) −20.9761 −0.785563
\(714\) 0 0
\(715\) 14.3593 0.537008
\(716\) 0 0
\(717\) −20.5154 −0.766163
\(718\) 0 0
\(719\) −15.7611 −0.587788 −0.293894 0.955838i \(-0.594951\pi\)
−0.293894 + 0.955838i \(0.594951\pi\)
\(720\) 0 0
\(721\) 1.97247 0.0734585
\(722\) 0 0
\(723\) 20.5369 0.763775
\(724\) 0 0
\(725\) −41.8287 −1.55348
\(726\) 0 0
\(727\) −5.66621 −0.210148 −0.105074 0.994464i \(-0.533508\pi\)
−0.105074 + 0.994464i \(0.533508\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −65.3399 −2.41668
\(732\) 0 0
\(733\) 16.3946 0.605549 0.302775 0.953062i \(-0.402087\pi\)
0.302775 + 0.953062i \(0.402087\pi\)
\(734\) 0 0
\(735\) 3.22199 0.118845
\(736\) 0 0
\(737\) 76.7285 2.82633
\(738\) 0 0
\(739\) −14.6648 −0.539453 −0.269726 0.962937i \(-0.586933\pi\)
−0.269726 + 0.962937i \(0.586933\pi\)
\(740\) 0 0
\(741\) −8.39040 −0.308229
\(742\) 0 0
\(743\) 4.63935 0.170201 0.0851006 0.996372i \(-0.472879\pi\)
0.0851006 + 0.996372i \(0.472879\pi\)
\(744\) 0 0
\(745\) −8.52654 −0.312388
\(746\) 0 0
\(747\) −3.46966 −0.126948
\(748\) 0 0
\(749\) −15.9163 −0.581569
\(750\) 0 0
\(751\) −7.52507 −0.274594 −0.137297 0.990530i \(-0.543841\pi\)
−0.137297 + 0.990530i \(0.543841\pi\)
\(752\) 0 0
\(753\) 5.12657 0.186823
\(754\) 0 0
\(755\) 2.75857 0.100395
\(756\) 0 0
\(757\) 49.4148 1.79601 0.898006 0.439984i \(-0.145016\pi\)
0.898006 + 0.439984i \(0.145016\pi\)
\(758\) 0 0
\(759\) 19.6035 0.711561
\(760\) 0 0
\(761\) −35.2793 −1.27887 −0.639437 0.768843i \(-0.720833\pi\)
−0.639437 + 0.768843i \(0.720833\pi\)
\(762\) 0 0
\(763\) −1.75128 −0.0634007
\(764\) 0 0
\(765\) −3.94764 −0.142727
\(766\) 0 0
\(767\) 43.7265 1.57887
\(768\) 0 0
\(769\) 27.7698 1.00140 0.500702 0.865620i \(-0.333075\pi\)
0.500702 + 0.865620i \(0.333075\pi\)
\(770\) 0 0
\(771\) −26.5939 −0.957757
\(772\) 0 0
\(773\) −3.62922 −0.130534 −0.0652669 0.997868i \(-0.520790\pi\)
−0.0652669 + 0.997868i \(0.520790\pi\)
\(774\) 0 0
\(775\) −24.9851 −0.897490
\(776\) 0 0
\(777\) −1.32202 −0.0474274
\(778\) 0 0
\(779\) 10.7404 0.384815
\(780\) 0 0
\(781\) 32.0106 1.14543
\(782\) 0 0
\(783\) −8.98846 −0.321221
\(784\) 0 0
\(785\) −13.1042 −0.467709
\(786\) 0 0
\(787\) 38.3837 1.36823 0.684116 0.729374i \(-0.260188\pi\)
0.684116 + 0.729374i \(0.260188\pi\)
\(788\) 0 0
\(789\) 10.5800 0.376659
\(790\) 0 0
\(791\) −22.2563 −0.791342
\(792\) 0 0
\(793\) −22.3594 −0.794005
\(794\) 0 0
\(795\) 4.45995 0.158178
\(796\) 0 0
\(797\) 32.6530 1.15663 0.578315 0.815814i \(-0.303711\pi\)
0.578315 + 0.815814i \(0.303711\pi\)
\(798\) 0 0
\(799\) 25.8792 0.915542
\(800\) 0 0
\(801\) 5.15759 0.182234
\(802\) 0 0
\(803\) 40.7682 1.43868
\(804\) 0 0
\(805\) −2.84026 −0.100106
\(806\) 0 0
\(807\) −10.0877 −0.355103
\(808\) 0 0
\(809\) −27.3338 −0.961007 −0.480503 0.876993i \(-0.659546\pi\)
−0.480503 + 0.876993i \(0.659546\pi\)
\(810\) 0 0
\(811\) 36.5168 1.28228 0.641140 0.767424i \(-0.278462\pi\)
0.641140 + 0.767424i \(0.278462\pi\)
\(812\) 0 0
\(813\) −20.1257 −0.705839
\(814\) 0 0
\(815\) 11.0849 0.388286
\(816\) 0 0
\(817\) 16.8103 0.588117
\(818\) 0 0
\(819\) 6.00583 0.209861
\(820\) 0 0
\(821\) −34.8331 −1.21568 −0.607842 0.794058i \(-0.707964\pi\)
−0.607842 + 0.794058i \(0.707964\pi\)
\(822\) 0 0
\(823\) −27.8026 −0.969139 −0.484570 0.874753i \(-0.661024\pi\)
−0.484570 + 0.874753i \(0.661024\pi\)
\(824\) 0 0
\(825\) 23.3500 0.812944
\(826\) 0 0
\(827\) 8.08198 0.281038 0.140519 0.990078i \(-0.455123\pi\)
0.140519 + 0.990078i \(0.455123\pi\)
\(828\) 0 0
\(829\) 8.93224 0.310229 0.155115 0.987896i \(-0.450425\pi\)
0.155115 + 0.987896i \(0.450425\pi\)
\(830\) 0 0
\(831\) 4.99188 0.173166
\(832\) 0 0
\(833\) 36.7176 1.27219
\(834\) 0 0
\(835\) 0.588564 0.0203681
\(836\) 0 0
\(837\) −5.36898 −0.185579
\(838\) 0 0
\(839\) 6.89723 0.238119 0.119059 0.992887i \(-0.462012\pi\)
0.119059 + 0.992887i \(0.462012\pi\)
\(840\) 0 0
\(841\) 51.7925 1.78595
\(842\) 0 0
\(843\) −22.7616 −0.783952
\(844\) 0 0
\(845\) 6.26347 0.215470
\(846\) 0 0
\(847\) 17.5108 0.601677
\(848\) 0 0
\(849\) −23.4891 −0.806143
\(850\) 0 0
\(851\) −4.18159 −0.143343
\(852\) 0 0
\(853\) 34.7250 1.18896 0.594481 0.804109i \(-0.297357\pi\)
0.594481 + 0.804109i \(0.297357\pi\)
\(854\) 0 0
\(855\) 1.01563 0.0347337
\(856\) 0 0
\(857\) −35.9067 −1.22655 −0.613276 0.789869i \(-0.710148\pi\)
−0.613276 + 0.789869i \(0.710148\pi\)
\(858\) 0 0
\(859\) −56.0190 −1.91134 −0.955671 0.294436i \(-0.904868\pi\)
−0.955671 + 0.294436i \(0.904868\pi\)
\(860\) 0 0
\(861\) −7.68797 −0.262005
\(862\) 0 0
\(863\) 3.47561 0.118311 0.0591556 0.998249i \(-0.481159\pi\)
0.0591556 + 0.998249i \(0.481159\pi\)
\(864\) 0 0
\(865\) −0.277420 −0.00943257
\(866\) 0 0
\(867\) −27.9871 −0.950492
\(868\) 0 0
\(869\) 30.6569 1.03996
\(870\) 0 0
\(871\) 74.3532 2.51936
\(872\) 0 0
\(873\) −13.6764 −0.462877
\(874\) 0 0
\(875\) −7.01801 −0.237252
\(876\) 0 0
\(877\) −5.27529 −0.178134 −0.0890670 0.996026i \(-0.528389\pi\)
−0.0890670 + 0.996026i \(0.528389\pi\)
\(878\) 0 0
\(879\) −28.5327 −0.962385
\(880\) 0 0
\(881\) 10.5890 0.356751 0.178376 0.983962i \(-0.442916\pi\)
0.178376 + 0.983962i \(0.442916\pi\)
\(882\) 0 0
\(883\) 28.3144 0.952855 0.476427 0.879214i \(-0.341932\pi\)
0.476427 + 0.879214i \(0.341932\pi\)
\(884\) 0 0
\(885\) −5.29294 −0.177920
\(886\) 0 0
\(887\) 32.9274 1.10560 0.552798 0.833316i \(-0.313560\pi\)
0.552798 + 0.833316i \(0.313560\pi\)
\(888\) 0 0
\(889\) −24.4514 −0.820073
\(890\) 0 0
\(891\) 5.01763 0.168097
\(892\) 0 0
\(893\) −6.65807 −0.222804
\(894\) 0 0
\(895\) −9.25827 −0.309470
\(896\) 0 0
\(897\) 18.9966 0.634278
\(898\) 0 0
\(899\) 48.2589 1.60952
\(900\) 0 0
\(901\) 50.8254 1.69324
\(902\) 0 0
\(903\) −12.0328 −0.400426
\(904\) 0 0
\(905\) 8.00914 0.266233
\(906\) 0 0
\(907\) −30.3164 −1.00664 −0.503320 0.864100i \(-0.667888\pi\)
−0.503320 + 0.864100i \(0.667888\pi\)
\(908\) 0 0
\(909\) −3.33213 −0.110520
\(910\) 0 0
\(911\) −57.0150 −1.88899 −0.944496 0.328524i \(-0.893449\pi\)
−0.944496 + 0.328524i \(0.893449\pi\)
\(912\) 0 0
\(913\) −17.4095 −0.576169
\(914\) 0 0
\(915\) 2.70652 0.0894748
\(916\) 0 0
\(917\) 1.59806 0.0527725
\(918\) 0 0
\(919\) 39.9071 1.31641 0.658206 0.752838i \(-0.271315\pi\)
0.658206 + 0.752838i \(0.271315\pi\)
\(920\) 0 0
\(921\) 1.14107 0.0375995
\(922\) 0 0
\(923\) 31.0196 1.02102
\(924\) 0 0
\(925\) −4.98077 −0.163767
\(926\) 0 0
\(927\) 1.59690 0.0524491
\(928\) 0 0
\(929\) 13.0857 0.429327 0.214663 0.976688i \(-0.431135\pi\)
0.214663 + 0.976688i \(0.431135\pi\)
\(930\) 0 0
\(931\) −9.44650 −0.309597
\(932\) 0 0
\(933\) −27.8320 −0.911178
\(934\) 0 0
\(935\) −19.8078 −0.647785
\(936\) 0 0
\(937\) −25.4531 −0.831516 −0.415758 0.909475i \(-0.636484\pi\)
−0.415758 + 0.909475i \(0.636484\pi\)
\(938\) 0 0
\(939\) −9.27809 −0.302779
\(940\) 0 0
\(941\) 46.6123 1.51952 0.759759 0.650205i \(-0.225317\pi\)
0.759759 + 0.650205i \(0.225317\pi\)
\(942\) 0 0
\(943\) −24.3172 −0.791878
\(944\) 0 0
\(945\) −0.726984 −0.0236488
\(946\) 0 0
\(947\) −28.4433 −0.924284 −0.462142 0.886806i \(-0.652919\pi\)
−0.462142 + 0.886806i \(0.652919\pi\)
\(948\) 0 0
\(949\) 39.5062 1.28242
\(950\) 0 0
\(951\) −11.0846 −0.359442
\(952\) 0 0
\(953\) 25.2469 0.817829 0.408914 0.912573i \(-0.365908\pi\)
0.408914 + 0.912573i \(0.365908\pi\)
\(954\) 0 0
\(955\) 5.66022 0.183160
\(956\) 0 0
\(957\) −45.1008 −1.45790
\(958\) 0 0
\(959\) 18.7923 0.606835
\(960\) 0 0
\(961\) −2.17405 −0.0701305
\(962\) 0 0
\(963\) −12.8858 −0.415238
\(964\) 0 0
\(965\) 1.77342 0.0570884
\(966\) 0 0
\(967\) −9.76071 −0.313883 −0.156942 0.987608i \(-0.550163\pi\)
−0.156942 + 0.987608i \(0.550163\pi\)
\(968\) 0 0
\(969\) 11.5740 0.371812
\(970\) 0 0
\(971\) −47.6643 −1.52962 −0.764810 0.644256i \(-0.777167\pi\)
−0.764810 + 0.644256i \(0.777167\pi\)
\(972\) 0 0
\(973\) 18.7346 0.600603
\(974\) 0 0
\(975\) 22.6272 0.724649
\(976\) 0 0
\(977\) −42.6661 −1.36501 −0.682505 0.730881i \(-0.739110\pi\)
−0.682505 + 0.730881i \(0.739110\pi\)
\(978\) 0 0
\(979\) 25.8789 0.827092
\(980\) 0 0
\(981\) −1.41783 −0.0452679
\(982\) 0 0
\(983\) −14.1240 −0.450486 −0.225243 0.974303i \(-0.572318\pi\)
−0.225243 + 0.974303i \(0.572318\pi\)
\(984\) 0 0
\(985\) 1.63646 0.0521419
\(986\) 0 0
\(987\) 4.76583 0.151698
\(988\) 0 0
\(989\) −38.0599 −1.21024
\(990\) 0 0
\(991\) −10.5986 −0.336677 −0.168339 0.985729i \(-0.553840\pi\)
−0.168339 + 0.985729i \(0.553840\pi\)
\(992\) 0 0
\(993\) 28.7641 0.912802
\(994\) 0 0
\(995\) −7.48768 −0.237375
\(996\) 0 0
\(997\) −26.7128 −0.846002 −0.423001 0.906129i \(-0.639023\pi\)
−0.423001 + 0.906129i \(0.639023\pi\)
\(998\) 0 0
\(999\) −1.07031 −0.0338630
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.ba.1.7 9
4.3 odd 2 4008.2.a.i.1.7 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.i.1.7 9 4.3 odd 2
8016.2.a.ba.1.7 9 1.1 even 1 trivial