Properties

Label 8016.2.a.w.1.7
Level 8016
Weight 2
Character 8016.1
Self dual yes
Analytic conductor 64.008
Analytic rank 1
Dimension 7
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: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 2 x^{6} - 7 x^{5} + 11 x^{4} + 12 x^{3} - 14 x^{2} - 6 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.332704\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +3.61705 q^{5} -2.72774 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +3.61705 q^{5} -2.72774 q^{7} +1.00000 q^{9} -4.28246 q^{11} -0.0474194 q^{13} +3.61705 q^{15} +3.70725 q^{17} -0.502366 q^{19} -2.72774 q^{21} -2.97951 q^{23} +8.08304 q^{25} +1.00000 q^{27} -6.25576 q^{29} -5.93115 q^{31} -4.28246 q^{33} -9.86637 q^{35} +0.158358 q^{37} -0.0474194 q^{39} -3.89424 q^{41} -4.94980 q^{43} +3.61705 q^{45} -8.39628 q^{47} +0.440569 q^{49} +3.70725 q^{51} -10.7084 q^{53} -15.4899 q^{55} -0.502366 q^{57} +3.54507 q^{59} +3.62786 q^{61} -2.72774 q^{63} -0.171518 q^{65} -0.477808 q^{67} -2.97951 q^{69} -0.963732 q^{71} -12.5153 q^{73} +8.08304 q^{75} +11.6814 q^{77} +1.53153 q^{79} +1.00000 q^{81} +13.4089 q^{83} +13.4093 q^{85} -6.25576 q^{87} +1.01339 q^{89} +0.129348 q^{91} -5.93115 q^{93} -1.81708 q^{95} -1.19560 q^{97} -4.28246 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 7q^{3} - 3q^{5} - 8q^{7} + 7q^{9} + O(q^{10}) \) \( 7q + 7q^{3} - 3q^{5} - 8q^{7} + 7q^{9} - q^{11} - 2q^{13} - 3q^{15} + 11q^{17} - 2q^{19} - 8q^{21} - 17q^{23} + 4q^{25} + 7q^{27} - 7q^{29} - 10q^{31} - q^{33} - 10q^{35} - 21q^{37} - 2q^{39} + 8q^{41} + 12q^{43} - 3q^{45} - 25q^{47} - 7q^{49} + 11q^{51} - 7q^{53} - 15q^{55} - 2q^{57} - 3q^{59} - 14q^{61} - 8q^{63} + 4q^{65} - 4q^{67} - 17q^{69} - 27q^{71} - 12q^{73} + 4q^{75} + 16q^{77} - 8q^{79} + 7q^{81} - 15q^{83} - 3q^{85} - 7q^{87} + 14q^{89} + 3q^{91} - 10q^{93} - 37q^{95} + 3q^{97} - q^{99} + O(q^{100}) \)

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
\(5\) 3.61705 1.61759 0.808797 0.588088i \(-0.200119\pi\)
0.808797 + 0.588088i \(0.200119\pi\)
\(6\) 0 0
\(7\) −2.72774 −1.03099 −0.515495 0.856893i \(-0.672392\pi\)
−0.515495 + 0.856893i \(0.672392\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.28246 −1.29121 −0.645605 0.763672i \(-0.723395\pi\)
−0.645605 + 0.763672i \(0.723395\pi\)
\(12\) 0 0
\(13\) −0.0474194 −0.0131518 −0.00657589 0.999978i \(-0.502093\pi\)
−0.00657589 + 0.999978i \(0.502093\pi\)
\(14\) 0 0
\(15\) 3.61705 0.933918
\(16\) 0 0
\(17\) 3.70725 0.899140 0.449570 0.893245i \(-0.351577\pi\)
0.449570 + 0.893245i \(0.351577\pi\)
\(18\) 0 0
\(19\) −0.502366 −0.115251 −0.0576254 0.998338i \(-0.518353\pi\)
−0.0576254 + 0.998338i \(0.518353\pi\)
\(20\) 0 0
\(21\) −2.72774 −0.595242
\(22\) 0 0
\(23\) −2.97951 −0.621270 −0.310635 0.950529i \(-0.600542\pi\)
−0.310635 + 0.950529i \(0.600542\pi\)
\(24\) 0 0
\(25\) 8.08304 1.61661
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.25576 −1.16167 −0.580833 0.814023i \(-0.697273\pi\)
−0.580833 + 0.814023i \(0.697273\pi\)
\(30\) 0 0
\(31\) −5.93115 −1.06527 −0.532633 0.846346i \(-0.678797\pi\)
−0.532633 + 0.846346i \(0.678797\pi\)
\(32\) 0 0
\(33\) −4.28246 −0.745480
\(34\) 0 0
\(35\) −9.86637 −1.66772
\(36\) 0 0
\(37\) 0.158358 0.0260339 0.0130170 0.999915i \(-0.495856\pi\)
0.0130170 + 0.999915i \(0.495856\pi\)
\(38\) 0 0
\(39\) −0.0474194 −0.00759318
\(40\) 0 0
\(41\) −3.89424 −0.608178 −0.304089 0.952644i \(-0.598352\pi\)
−0.304089 + 0.952644i \(0.598352\pi\)
\(42\) 0 0
\(43\) −4.94980 −0.754838 −0.377419 0.926043i \(-0.623188\pi\)
−0.377419 + 0.926043i \(0.623188\pi\)
\(44\) 0 0
\(45\) 3.61705 0.539198
\(46\) 0 0
\(47\) −8.39628 −1.22472 −0.612362 0.790578i \(-0.709780\pi\)
−0.612362 + 0.790578i \(0.709780\pi\)
\(48\) 0 0
\(49\) 0.440569 0.0629384
\(50\) 0 0
\(51\) 3.70725 0.519119
\(52\) 0 0
\(53\) −10.7084 −1.47091 −0.735453 0.677576i \(-0.763031\pi\)
−0.735453 + 0.677576i \(0.763031\pi\)
\(54\) 0 0
\(55\) −15.4899 −2.08865
\(56\) 0 0
\(57\) −0.502366 −0.0665401
\(58\) 0 0
\(59\) 3.54507 0.461529 0.230764 0.973010i \(-0.425877\pi\)
0.230764 + 0.973010i \(0.425877\pi\)
\(60\) 0 0
\(61\) 3.62786 0.464500 0.232250 0.972656i \(-0.425391\pi\)
0.232250 + 0.972656i \(0.425391\pi\)
\(62\) 0 0
\(63\) −2.72774 −0.343663
\(64\) 0 0
\(65\) −0.171518 −0.0212742
\(66\) 0 0
\(67\) −0.477808 −0.0583736 −0.0291868 0.999574i \(-0.509292\pi\)
−0.0291868 + 0.999574i \(0.509292\pi\)
\(68\) 0 0
\(69\) −2.97951 −0.358691
\(70\) 0 0
\(71\) −0.963732 −0.114374 −0.0571870 0.998363i \(-0.518213\pi\)
−0.0571870 + 0.998363i \(0.518213\pi\)
\(72\) 0 0
\(73\) −12.5153 −1.46481 −0.732405 0.680870i \(-0.761602\pi\)
−0.732405 + 0.680870i \(0.761602\pi\)
\(74\) 0 0
\(75\) 8.08304 0.933349
\(76\) 0 0
\(77\) 11.6814 1.33122
\(78\) 0 0
\(79\) 1.53153 0.172311 0.0861554 0.996282i \(-0.472542\pi\)
0.0861554 + 0.996282i \(0.472542\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 13.4089 1.47182 0.735911 0.677078i \(-0.236754\pi\)
0.735911 + 0.677078i \(0.236754\pi\)
\(84\) 0 0
\(85\) 13.4093 1.45444
\(86\) 0 0
\(87\) −6.25576 −0.670688
\(88\) 0 0
\(89\) 1.01339 0.107419 0.0537095 0.998557i \(-0.482896\pi\)
0.0537095 + 0.998557i \(0.482896\pi\)
\(90\) 0 0
\(91\) 0.129348 0.0135593
\(92\) 0 0
\(93\) −5.93115 −0.615031
\(94\) 0 0
\(95\) −1.81708 −0.186429
\(96\) 0 0
\(97\) −1.19560 −0.121395 −0.0606973 0.998156i \(-0.519332\pi\)
−0.0606973 + 0.998156i \(0.519332\pi\)
\(98\) 0 0
\(99\) −4.28246 −0.430403
\(100\) 0 0
\(101\) 2.15983 0.214911 0.107456 0.994210i \(-0.465730\pi\)
0.107456 + 0.994210i \(0.465730\pi\)
\(102\) 0 0
\(103\) 13.6082 1.34086 0.670428 0.741975i \(-0.266111\pi\)
0.670428 + 0.741975i \(0.266111\pi\)
\(104\) 0 0
\(105\) −9.86637 −0.962859
\(106\) 0 0
\(107\) 3.76340 0.363821 0.181911 0.983315i \(-0.441772\pi\)
0.181911 + 0.983315i \(0.441772\pi\)
\(108\) 0 0
\(109\) −11.9192 −1.14165 −0.570824 0.821072i \(-0.693376\pi\)
−0.570824 + 0.821072i \(0.693376\pi\)
\(110\) 0 0
\(111\) 0.158358 0.0150307
\(112\) 0 0
\(113\) −5.99961 −0.564396 −0.282198 0.959356i \(-0.591063\pi\)
−0.282198 + 0.959356i \(0.591063\pi\)
\(114\) 0 0
\(115\) −10.7770 −1.00496
\(116\) 0 0
\(117\) −0.0474194 −0.00438393
\(118\) 0 0
\(119\) −10.1124 −0.927003
\(120\) 0 0
\(121\) 7.33944 0.667222
\(122\) 0 0
\(123\) −3.89424 −0.351132
\(124\) 0 0
\(125\) 11.1515 0.997421
\(126\) 0 0
\(127\) −3.12683 −0.277461 −0.138731 0.990330i \(-0.544302\pi\)
−0.138731 + 0.990330i \(0.544302\pi\)
\(128\) 0 0
\(129\) −4.94980 −0.435806
\(130\) 0 0
\(131\) 17.0808 1.49236 0.746180 0.665745i \(-0.231886\pi\)
0.746180 + 0.665745i \(0.231886\pi\)
\(132\) 0 0
\(133\) 1.37033 0.118822
\(134\) 0 0
\(135\) 3.61705 0.311306
\(136\) 0 0
\(137\) −5.91181 −0.505080 −0.252540 0.967586i \(-0.581266\pi\)
−0.252540 + 0.967586i \(0.581266\pi\)
\(138\) 0 0
\(139\) −19.2110 −1.62946 −0.814729 0.579842i \(-0.803114\pi\)
−0.814729 + 0.579842i \(0.803114\pi\)
\(140\) 0 0
\(141\) −8.39628 −0.707094
\(142\) 0 0
\(143\) 0.203072 0.0169817
\(144\) 0 0
\(145\) −22.6274 −1.87910
\(146\) 0 0
\(147\) 0.440569 0.0363375
\(148\) 0 0
\(149\) 12.4216 1.01762 0.508810 0.860879i \(-0.330086\pi\)
0.508810 + 0.860879i \(0.330086\pi\)
\(150\) 0 0
\(151\) 19.4910 1.58615 0.793076 0.609123i \(-0.208478\pi\)
0.793076 + 0.609123i \(0.208478\pi\)
\(152\) 0 0
\(153\) 3.70725 0.299713
\(154\) 0 0
\(155\) −21.4533 −1.72317
\(156\) 0 0
\(157\) −9.17743 −0.732439 −0.366219 0.930529i \(-0.619348\pi\)
−0.366219 + 0.930529i \(0.619348\pi\)
\(158\) 0 0
\(159\) −10.7084 −0.849228
\(160\) 0 0
\(161\) 8.12733 0.640523
\(162\) 0 0
\(163\) −4.11130 −0.322022 −0.161011 0.986953i \(-0.551475\pi\)
−0.161011 + 0.986953i \(0.551475\pi\)
\(164\) 0 0
\(165\) −15.4899 −1.20588
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −12.9978 −0.999827
\(170\) 0 0
\(171\) −0.502366 −0.0384169
\(172\) 0 0
\(173\) 1.79124 0.136185 0.0680925 0.997679i \(-0.478309\pi\)
0.0680925 + 0.997679i \(0.478309\pi\)
\(174\) 0 0
\(175\) −22.0484 −1.66670
\(176\) 0 0
\(177\) 3.54507 0.266464
\(178\) 0 0
\(179\) −8.69277 −0.649728 −0.324864 0.945761i \(-0.605319\pi\)
−0.324864 + 0.945761i \(0.605319\pi\)
\(180\) 0 0
\(181\) −11.5836 −0.861003 −0.430501 0.902590i \(-0.641663\pi\)
−0.430501 + 0.902590i \(0.641663\pi\)
\(182\) 0 0
\(183\) 3.62786 0.268179
\(184\) 0 0
\(185\) 0.572789 0.0421123
\(186\) 0 0
\(187\) −15.8761 −1.16098
\(188\) 0 0
\(189\) −2.72774 −0.198414
\(190\) 0 0
\(191\) −3.96251 −0.286717 −0.143359 0.989671i \(-0.545790\pi\)
−0.143359 + 0.989671i \(0.545790\pi\)
\(192\) 0 0
\(193\) 6.81160 0.490310 0.245155 0.969484i \(-0.421161\pi\)
0.245155 + 0.969484i \(0.421161\pi\)
\(194\) 0 0
\(195\) −0.171518 −0.0122827
\(196\) 0 0
\(197\) −7.39262 −0.526702 −0.263351 0.964700i \(-0.584828\pi\)
−0.263351 + 0.964700i \(0.584828\pi\)
\(198\) 0 0
\(199\) 16.2256 1.15020 0.575100 0.818083i \(-0.304963\pi\)
0.575100 + 0.818083i \(0.304963\pi\)
\(200\) 0 0
\(201\) −0.477808 −0.0337020
\(202\) 0 0
\(203\) 17.0641 1.19766
\(204\) 0 0
\(205\) −14.0856 −0.983784
\(206\) 0 0
\(207\) −2.97951 −0.207090
\(208\) 0 0
\(209\) 2.15136 0.148813
\(210\) 0 0
\(211\) −9.20559 −0.633739 −0.316869 0.948469i \(-0.602632\pi\)
−0.316869 + 0.948469i \(0.602632\pi\)
\(212\) 0 0
\(213\) −0.963732 −0.0660338
\(214\) 0 0
\(215\) −17.9037 −1.22102
\(216\) 0 0
\(217\) 16.1786 1.09828
\(218\) 0 0
\(219\) −12.5153 −0.845708
\(220\) 0 0
\(221\) −0.175796 −0.0118253
\(222\) 0 0
\(223\) 1.77142 0.118623 0.0593114 0.998240i \(-0.481109\pi\)
0.0593114 + 0.998240i \(0.481109\pi\)
\(224\) 0 0
\(225\) 8.08304 0.538869
\(226\) 0 0
\(227\) −3.39753 −0.225502 −0.112751 0.993623i \(-0.535966\pi\)
−0.112751 + 0.993623i \(0.535966\pi\)
\(228\) 0 0
\(229\) 11.6919 0.772622 0.386311 0.922369i \(-0.373749\pi\)
0.386311 + 0.922369i \(0.373749\pi\)
\(230\) 0 0
\(231\) 11.6814 0.768582
\(232\) 0 0
\(233\) 20.2352 1.32565 0.662825 0.748775i \(-0.269357\pi\)
0.662825 + 0.748775i \(0.269357\pi\)
\(234\) 0 0
\(235\) −30.3698 −1.98110
\(236\) 0 0
\(237\) 1.53153 0.0994837
\(238\) 0 0
\(239\) −8.35872 −0.540680 −0.270340 0.962765i \(-0.587136\pi\)
−0.270340 + 0.962765i \(0.587136\pi\)
\(240\) 0 0
\(241\) −7.49687 −0.482916 −0.241458 0.970411i \(-0.577626\pi\)
−0.241458 + 0.970411i \(0.577626\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 1.59356 0.101809
\(246\) 0 0
\(247\) 0.0238219 0.00151575
\(248\) 0 0
\(249\) 13.4089 0.849757
\(250\) 0 0
\(251\) −9.63798 −0.608344 −0.304172 0.952617i \(-0.598380\pi\)
−0.304172 + 0.952617i \(0.598380\pi\)
\(252\) 0 0
\(253\) 12.7596 0.802190
\(254\) 0 0
\(255\) 13.4093 0.839723
\(256\) 0 0
\(257\) 16.0721 1.00255 0.501275 0.865288i \(-0.332865\pi\)
0.501275 + 0.865288i \(0.332865\pi\)
\(258\) 0 0
\(259\) −0.431960 −0.0268407
\(260\) 0 0
\(261\) −6.25576 −0.387222
\(262\) 0 0
\(263\) −13.8779 −0.855745 −0.427872 0.903839i \(-0.640737\pi\)
−0.427872 + 0.903839i \(0.640737\pi\)
\(264\) 0 0
\(265\) −38.7327 −2.37933
\(266\) 0 0
\(267\) 1.01339 0.0620184
\(268\) 0 0
\(269\) −11.7466 −0.716202 −0.358101 0.933683i \(-0.616576\pi\)
−0.358101 + 0.933683i \(0.616576\pi\)
\(270\) 0 0
\(271\) −27.0126 −1.64090 −0.820450 0.571718i \(-0.806277\pi\)
−0.820450 + 0.571718i \(0.806277\pi\)
\(272\) 0 0
\(273\) 0.129348 0.00782849
\(274\) 0 0
\(275\) −34.6153 −2.08738
\(276\) 0 0
\(277\) −27.7942 −1.66999 −0.834997 0.550255i \(-0.814531\pi\)
−0.834997 + 0.550255i \(0.814531\pi\)
\(278\) 0 0
\(279\) −5.93115 −0.355089
\(280\) 0 0
\(281\) 16.0329 0.956443 0.478221 0.878239i \(-0.341282\pi\)
0.478221 + 0.878239i \(0.341282\pi\)
\(282\) 0 0
\(283\) 9.97967 0.593230 0.296615 0.954997i \(-0.404142\pi\)
0.296615 + 0.954997i \(0.404142\pi\)
\(284\) 0 0
\(285\) −1.81708 −0.107635
\(286\) 0 0
\(287\) 10.6225 0.627025
\(288\) 0 0
\(289\) −3.25630 −0.191547
\(290\) 0 0
\(291\) −1.19560 −0.0700872
\(292\) 0 0
\(293\) −6.84400 −0.399831 −0.199915 0.979813i \(-0.564067\pi\)
−0.199915 + 0.979813i \(0.564067\pi\)
\(294\) 0 0
\(295\) 12.8227 0.746566
\(296\) 0 0
\(297\) −4.28246 −0.248493
\(298\) 0 0
\(299\) 0.141287 0.00817081
\(300\) 0 0
\(301\) 13.5018 0.778230
\(302\) 0 0
\(303\) 2.15983 0.124079
\(304\) 0 0
\(305\) 13.1222 0.751373
\(306\) 0 0
\(307\) 1.88679 0.107685 0.0538424 0.998549i \(-0.482853\pi\)
0.0538424 + 0.998549i \(0.482853\pi\)
\(308\) 0 0
\(309\) 13.6082 0.774144
\(310\) 0 0
\(311\) −18.8665 −1.06982 −0.534910 0.844909i \(-0.679654\pi\)
−0.534910 + 0.844909i \(0.679654\pi\)
\(312\) 0 0
\(313\) 28.2178 1.59497 0.797483 0.603341i \(-0.206164\pi\)
0.797483 + 0.603341i \(0.206164\pi\)
\(314\) 0 0
\(315\) −9.86637 −0.555907
\(316\) 0 0
\(317\) −17.9184 −1.00640 −0.503198 0.864171i \(-0.667843\pi\)
−0.503198 + 0.864171i \(0.667843\pi\)
\(318\) 0 0
\(319\) 26.7900 1.49995
\(320\) 0 0
\(321\) 3.76340 0.210052
\(322\) 0 0
\(323\) −1.86240 −0.103627
\(324\) 0 0
\(325\) −0.383293 −0.0212613
\(326\) 0 0
\(327\) −11.9192 −0.659131
\(328\) 0 0
\(329\) 22.9029 1.26268
\(330\) 0 0
\(331\) −6.98539 −0.383952 −0.191976 0.981400i \(-0.561490\pi\)
−0.191976 + 0.981400i \(0.561490\pi\)
\(332\) 0 0
\(333\) 0.158358 0.00867797
\(334\) 0 0
\(335\) −1.72826 −0.0944247
\(336\) 0 0
\(337\) 11.8306 0.644455 0.322227 0.946662i \(-0.395568\pi\)
0.322227 + 0.946662i \(0.395568\pi\)
\(338\) 0 0
\(339\) −5.99961 −0.325854
\(340\) 0 0
\(341\) 25.3999 1.37548
\(342\) 0 0
\(343\) 17.8924 0.966100
\(344\) 0 0
\(345\) −10.7770 −0.580216
\(346\) 0 0
\(347\) −34.1259 −1.83197 −0.915987 0.401208i \(-0.868591\pi\)
−0.915987 + 0.401208i \(0.868591\pi\)
\(348\) 0 0
\(349\) 28.2829 1.51395 0.756975 0.653444i \(-0.226677\pi\)
0.756975 + 0.653444i \(0.226677\pi\)
\(350\) 0 0
\(351\) −0.0474194 −0.00253106
\(352\) 0 0
\(353\) −0.561669 −0.0298946 −0.0149473 0.999888i \(-0.504758\pi\)
−0.0149473 + 0.999888i \(0.504758\pi\)
\(354\) 0 0
\(355\) −3.48586 −0.185010
\(356\) 0 0
\(357\) −10.1124 −0.535206
\(358\) 0 0
\(359\) 1.11628 0.0589149 0.0294574 0.999566i \(-0.490622\pi\)
0.0294574 + 0.999566i \(0.490622\pi\)
\(360\) 0 0
\(361\) −18.7476 −0.986717
\(362\) 0 0
\(363\) 7.33944 0.385221
\(364\) 0 0
\(365\) −45.2686 −2.36947
\(366\) 0 0
\(367\) 6.04257 0.315420 0.157710 0.987485i \(-0.449589\pi\)
0.157710 + 0.987485i \(0.449589\pi\)
\(368\) 0 0
\(369\) −3.89424 −0.202726
\(370\) 0 0
\(371\) 29.2096 1.51649
\(372\) 0 0
\(373\) 29.5233 1.52866 0.764328 0.644828i \(-0.223071\pi\)
0.764328 + 0.644828i \(0.223071\pi\)
\(374\) 0 0
\(375\) 11.1515 0.575861
\(376\) 0 0
\(377\) 0.296644 0.0152780
\(378\) 0 0
\(379\) 30.8528 1.58480 0.792401 0.610000i \(-0.208831\pi\)
0.792401 + 0.610000i \(0.208831\pi\)
\(380\) 0 0
\(381\) −3.12683 −0.160192
\(382\) 0 0
\(383\) 11.1831 0.571427 0.285714 0.958315i \(-0.407769\pi\)
0.285714 + 0.958315i \(0.407769\pi\)
\(384\) 0 0
\(385\) 42.2523 2.15338
\(386\) 0 0
\(387\) −4.94980 −0.251613
\(388\) 0 0
\(389\) 24.2164 1.22782 0.613911 0.789375i \(-0.289595\pi\)
0.613911 + 0.789375i \(0.289595\pi\)
\(390\) 0 0
\(391\) −11.0458 −0.558609
\(392\) 0 0
\(393\) 17.0808 0.861614
\(394\) 0 0
\(395\) 5.53962 0.278729
\(396\) 0 0
\(397\) 0.297814 0.0149469 0.00747343 0.999972i \(-0.497621\pi\)
0.00747343 + 0.999972i \(0.497621\pi\)
\(398\) 0 0
\(399\) 1.37033 0.0686021
\(400\) 0 0
\(401\) 1.84713 0.0922413 0.0461207 0.998936i \(-0.485314\pi\)
0.0461207 + 0.998936i \(0.485314\pi\)
\(402\) 0 0
\(403\) 0.281252 0.0140101
\(404\) 0 0
\(405\) 3.61705 0.179733
\(406\) 0 0
\(407\) −0.678162 −0.0336152
\(408\) 0 0
\(409\) −28.7688 −1.42252 −0.711262 0.702927i \(-0.751876\pi\)
−0.711262 + 0.702927i \(0.751876\pi\)
\(410\) 0 0
\(411\) −5.91181 −0.291608
\(412\) 0 0
\(413\) −9.67003 −0.475831
\(414\) 0 0
\(415\) 48.5008 2.38081
\(416\) 0 0
\(417\) −19.2110 −0.940768
\(418\) 0 0
\(419\) 31.6216 1.54482 0.772408 0.635127i \(-0.219052\pi\)
0.772408 + 0.635127i \(0.219052\pi\)
\(420\) 0 0
\(421\) −4.86687 −0.237197 −0.118598 0.992942i \(-0.537840\pi\)
−0.118598 + 0.992942i \(0.537840\pi\)
\(422\) 0 0
\(423\) −8.39628 −0.408241
\(424\) 0 0
\(425\) 29.9658 1.45356
\(426\) 0 0
\(427\) −9.89587 −0.478895
\(428\) 0 0
\(429\) 0.203072 0.00980439
\(430\) 0 0
\(431\) 19.5696 0.942635 0.471317 0.881964i \(-0.343779\pi\)
0.471317 + 0.881964i \(0.343779\pi\)
\(432\) 0 0
\(433\) −20.2099 −0.971224 −0.485612 0.874174i \(-0.661403\pi\)
−0.485612 + 0.874174i \(0.661403\pi\)
\(434\) 0 0
\(435\) −22.6274 −1.08490
\(436\) 0 0
\(437\) 1.49681 0.0716019
\(438\) 0 0
\(439\) −24.6452 −1.17625 −0.588126 0.808769i \(-0.700134\pi\)
−0.588126 + 0.808769i \(0.700134\pi\)
\(440\) 0 0
\(441\) 0.440569 0.0209795
\(442\) 0 0
\(443\) −26.1398 −1.24194 −0.620969 0.783835i \(-0.713261\pi\)
−0.620969 + 0.783835i \(0.713261\pi\)
\(444\) 0 0
\(445\) 3.66548 0.173760
\(446\) 0 0
\(447\) 12.4216 0.587523
\(448\) 0 0
\(449\) −0.704072 −0.0332272 −0.0166136 0.999862i \(-0.505289\pi\)
−0.0166136 + 0.999862i \(0.505289\pi\)
\(450\) 0 0
\(451\) 16.6769 0.785285
\(452\) 0 0
\(453\) 19.4910 0.915765
\(454\) 0 0
\(455\) 0.467857 0.0219335
\(456\) 0 0
\(457\) 40.5289 1.89586 0.947931 0.318476i \(-0.103171\pi\)
0.947931 + 0.318476i \(0.103171\pi\)
\(458\) 0 0
\(459\) 3.70725 0.173040
\(460\) 0 0
\(461\) −15.2707 −0.711228 −0.355614 0.934633i \(-0.615728\pi\)
−0.355614 + 0.934633i \(0.615728\pi\)
\(462\) 0 0
\(463\) −22.1528 −1.02953 −0.514763 0.857333i \(-0.672120\pi\)
−0.514763 + 0.857333i \(0.672120\pi\)
\(464\) 0 0
\(465\) −21.4533 −0.994871
\(466\) 0 0
\(467\) −20.2118 −0.935291 −0.467646 0.883916i \(-0.654898\pi\)
−0.467646 + 0.883916i \(0.654898\pi\)
\(468\) 0 0
\(469\) 1.30334 0.0601825
\(470\) 0 0
\(471\) −9.17743 −0.422874
\(472\) 0 0
\(473\) 21.1973 0.974654
\(474\) 0 0
\(475\) −4.06065 −0.186315
\(476\) 0 0
\(477\) −10.7084 −0.490302
\(478\) 0 0
\(479\) −32.2890 −1.47532 −0.737661 0.675171i \(-0.764070\pi\)
−0.737661 + 0.675171i \(0.764070\pi\)
\(480\) 0 0
\(481\) −0.00750925 −0.000342392 0
\(482\) 0 0
\(483\) 8.12733 0.369806
\(484\) 0 0
\(485\) −4.32454 −0.196367
\(486\) 0 0
\(487\) −33.6362 −1.52420 −0.762101 0.647458i \(-0.775832\pi\)
−0.762101 + 0.647458i \(0.775832\pi\)
\(488\) 0 0
\(489\) −4.11130 −0.185919
\(490\) 0 0
\(491\) −0.820863 −0.0370450 −0.0185225 0.999828i \(-0.505896\pi\)
−0.0185225 + 0.999828i \(0.505896\pi\)
\(492\) 0 0
\(493\) −23.1917 −1.04450
\(494\) 0 0
\(495\) −15.4899 −0.696217
\(496\) 0 0
\(497\) 2.62881 0.117918
\(498\) 0 0
\(499\) 34.5903 1.54847 0.774237 0.632896i \(-0.218134\pi\)
0.774237 + 0.632896i \(0.218134\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 28.2747 1.26071 0.630354 0.776308i \(-0.282910\pi\)
0.630354 + 0.776308i \(0.282910\pi\)
\(504\) 0 0
\(505\) 7.81222 0.347639
\(506\) 0 0
\(507\) −12.9978 −0.577250
\(508\) 0 0
\(509\) −7.01436 −0.310906 −0.155453 0.987843i \(-0.549684\pi\)
−0.155453 + 0.987843i \(0.549684\pi\)
\(510\) 0 0
\(511\) 34.1386 1.51020
\(512\) 0 0
\(513\) −0.502366 −0.0221800
\(514\) 0 0
\(515\) 49.2215 2.16896
\(516\) 0 0
\(517\) 35.9567 1.58137
\(518\) 0 0
\(519\) 1.79124 0.0786265
\(520\) 0 0
\(521\) 23.4917 1.02919 0.514594 0.857434i \(-0.327943\pi\)
0.514594 + 0.857434i \(0.327943\pi\)
\(522\) 0 0
\(523\) −13.3081 −0.581924 −0.290962 0.956735i \(-0.593975\pi\)
−0.290962 + 0.956735i \(0.593975\pi\)
\(524\) 0 0
\(525\) −22.0484 −0.962273
\(526\) 0 0
\(527\) −21.9882 −0.957823
\(528\) 0 0
\(529\) −14.1225 −0.614023
\(530\) 0 0
\(531\) 3.54507 0.153843
\(532\) 0 0
\(533\) 0.184662 0.00799862
\(534\) 0 0
\(535\) 13.6124 0.588515
\(536\) 0 0
\(537\) −8.69277 −0.375121
\(538\) 0 0
\(539\) −1.88672 −0.0812666
\(540\) 0 0
\(541\) −1.93696 −0.0832765 −0.0416383 0.999133i \(-0.513258\pi\)
−0.0416383 + 0.999133i \(0.513258\pi\)
\(542\) 0 0
\(543\) −11.5836 −0.497100
\(544\) 0 0
\(545\) −43.1122 −1.84672
\(546\) 0 0
\(547\) 18.2239 0.779200 0.389600 0.920984i \(-0.372613\pi\)
0.389600 + 0.920984i \(0.372613\pi\)
\(548\) 0 0
\(549\) 3.62786 0.154833
\(550\) 0 0
\(551\) 3.14268 0.133883
\(552\) 0 0
\(553\) −4.17762 −0.177651
\(554\) 0 0
\(555\) 0.572789 0.0243135
\(556\) 0 0
\(557\) 4.50775 0.190999 0.0954997 0.995429i \(-0.469555\pi\)
0.0954997 + 0.995429i \(0.469555\pi\)
\(558\) 0 0
\(559\) 0.234717 0.00992746
\(560\) 0 0
\(561\) −15.8761 −0.670291
\(562\) 0 0
\(563\) 3.26172 0.137465 0.0687325 0.997635i \(-0.478104\pi\)
0.0687325 + 0.997635i \(0.478104\pi\)
\(564\) 0 0
\(565\) −21.7009 −0.912963
\(566\) 0 0
\(567\) −2.72774 −0.114554
\(568\) 0 0
\(569\) 18.6572 0.782151 0.391075 0.920359i \(-0.372103\pi\)
0.391075 + 0.920359i \(0.372103\pi\)
\(570\) 0 0
\(571\) 4.26021 0.178284 0.0891422 0.996019i \(-0.471587\pi\)
0.0891422 + 0.996019i \(0.471587\pi\)
\(572\) 0 0
\(573\) −3.96251 −0.165536
\(574\) 0 0
\(575\) −24.0835 −1.00435
\(576\) 0 0
\(577\) 9.98097 0.415513 0.207757 0.978181i \(-0.433384\pi\)
0.207757 + 0.978181i \(0.433384\pi\)
\(578\) 0 0
\(579\) 6.81160 0.283080
\(580\) 0 0
\(581\) −36.5761 −1.51743
\(582\) 0 0
\(583\) 45.8581 1.89925
\(584\) 0 0
\(585\) −0.171518 −0.00709141
\(586\) 0 0
\(587\) −36.1902 −1.49373 −0.746864 0.664977i \(-0.768441\pi\)
−0.746864 + 0.664977i \(0.768441\pi\)
\(588\) 0 0
\(589\) 2.97961 0.122773
\(590\) 0 0
\(591\) −7.39262 −0.304092
\(592\) 0 0
\(593\) −2.81631 −0.115652 −0.0578261 0.998327i \(-0.518417\pi\)
−0.0578261 + 0.998327i \(0.518417\pi\)
\(594\) 0 0
\(595\) −36.5771 −1.49951
\(596\) 0 0
\(597\) 16.2256 0.664069
\(598\) 0 0
\(599\) 12.4462 0.508537 0.254269 0.967134i \(-0.418165\pi\)
0.254269 + 0.967134i \(0.418165\pi\)
\(600\) 0 0
\(601\) 0.462497 0.0188657 0.00943283 0.999956i \(-0.496997\pi\)
0.00943283 + 0.999956i \(0.496997\pi\)
\(602\) 0 0
\(603\) −0.477808 −0.0194579
\(604\) 0 0
\(605\) 26.5471 1.07929
\(606\) 0 0
\(607\) −10.5665 −0.428883 −0.214441 0.976737i \(-0.568793\pi\)
−0.214441 + 0.976737i \(0.568793\pi\)
\(608\) 0 0
\(609\) 17.0641 0.691472
\(610\) 0 0
\(611\) 0.398147 0.0161073
\(612\) 0 0
\(613\) −48.6267 −1.96401 −0.982007 0.188846i \(-0.939525\pi\)
−0.982007 + 0.188846i \(0.939525\pi\)
\(614\) 0 0
\(615\) −14.0856 −0.567988
\(616\) 0 0
\(617\) 1.72932 0.0696197 0.0348098 0.999394i \(-0.488917\pi\)
0.0348098 + 0.999394i \(0.488917\pi\)
\(618\) 0 0
\(619\) 48.2593 1.93971 0.969853 0.243692i \(-0.0783587\pi\)
0.969853 + 0.243692i \(0.0783587\pi\)
\(620\) 0 0
\(621\) −2.97951 −0.119564
\(622\) 0 0
\(623\) −2.76426 −0.110748
\(624\) 0 0
\(625\) −0.0796737 −0.00318695
\(626\) 0 0
\(627\) 2.15136 0.0859172
\(628\) 0 0
\(629\) 0.587073 0.0234081
\(630\) 0 0
\(631\) −3.15911 −0.125762 −0.0628812 0.998021i \(-0.520029\pi\)
−0.0628812 + 0.998021i \(0.520029\pi\)
\(632\) 0 0
\(633\) −9.20559 −0.365889
\(634\) 0 0
\(635\) −11.3099 −0.448819
\(636\) 0 0
\(637\) −0.0208915 −0.000827752 0
\(638\) 0 0
\(639\) −0.963732 −0.0381246
\(640\) 0 0
\(641\) 30.2179 1.19353 0.596767 0.802415i \(-0.296452\pi\)
0.596767 + 0.802415i \(0.296452\pi\)
\(642\) 0 0
\(643\) 31.1151 1.22706 0.613531 0.789671i \(-0.289749\pi\)
0.613531 + 0.789671i \(0.289749\pi\)
\(644\) 0 0
\(645\) −17.9037 −0.704957
\(646\) 0 0
\(647\) 23.7860 0.935125 0.467563 0.883960i \(-0.345132\pi\)
0.467563 + 0.883960i \(0.345132\pi\)
\(648\) 0 0
\(649\) −15.1816 −0.595930
\(650\) 0 0
\(651\) 16.1786 0.634091
\(652\) 0 0
\(653\) −47.4018 −1.85497 −0.927487 0.373855i \(-0.878036\pi\)
−0.927487 + 0.373855i \(0.878036\pi\)
\(654\) 0 0
\(655\) 61.7822 2.41403
\(656\) 0 0
\(657\) −12.5153 −0.488270
\(658\) 0 0
\(659\) 5.52732 0.215314 0.107657 0.994188i \(-0.465665\pi\)
0.107657 + 0.994188i \(0.465665\pi\)
\(660\) 0 0
\(661\) −8.39078 −0.326363 −0.163182 0.986596i \(-0.552176\pi\)
−0.163182 + 0.986596i \(0.552176\pi\)
\(662\) 0 0
\(663\) −0.175796 −0.00682733
\(664\) 0 0
\(665\) 4.95653 0.192206
\(666\) 0 0
\(667\) 18.6391 0.721708
\(668\) 0 0
\(669\) 1.77142 0.0684869
\(670\) 0 0
\(671\) −15.5362 −0.599767
\(672\) 0 0
\(673\) −26.2165 −1.01057 −0.505286 0.862952i \(-0.668613\pi\)
−0.505286 + 0.862952i \(0.668613\pi\)
\(674\) 0 0
\(675\) 8.08304 0.311116
\(676\) 0 0
\(677\) 36.4778 1.40196 0.700978 0.713183i \(-0.252747\pi\)
0.700978 + 0.713183i \(0.252747\pi\)
\(678\) 0 0
\(679\) 3.26128 0.125156
\(680\) 0 0
\(681\) −3.39753 −0.130194
\(682\) 0 0
\(683\) −33.8618 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(684\) 0 0
\(685\) −21.3833 −0.817014
\(686\) 0 0
\(687\) 11.6919 0.446074
\(688\) 0 0
\(689\) 0.507784 0.0193450
\(690\) 0 0
\(691\) 13.0531 0.496562 0.248281 0.968688i \(-0.420134\pi\)
0.248281 + 0.968688i \(0.420134\pi\)
\(692\) 0 0
\(693\) 11.6814 0.443741
\(694\) 0 0
\(695\) −69.4872 −2.63580
\(696\) 0 0
\(697\) −14.4369 −0.546837
\(698\) 0 0
\(699\) 20.2352 0.765364
\(700\) 0 0
\(701\) 7.42917 0.280596 0.140298 0.990109i \(-0.455194\pi\)
0.140298 + 0.990109i \(0.455194\pi\)
\(702\) 0 0
\(703\) −0.0795538 −0.00300043
\(704\) 0 0
\(705\) −30.3698 −1.14379
\(706\) 0 0
\(707\) −5.89146 −0.221571
\(708\) 0 0
\(709\) −16.6979 −0.627104 −0.313552 0.949571i \(-0.601519\pi\)
−0.313552 + 0.949571i \(0.601519\pi\)
\(710\) 0 0
\(711\) 1.53153 0.0574369
\(712\) 0 0
\(713\) 17.6719 0.661818
\(714\) 0 0
\(715\) 0.734520 0.0274695
\(716\) 0 0
\(717\) −8.35872 −0.312162
\(718\) 0 0
\(719\) −25.5510 −0.952892 −0.476446 0.879204i \(-0.658075\pi\)
−0.476446 + 0.879204i \(0.658075\pi\)
\(720\) 0 0
\(721\) −37.1196 −1.38241
\(722\) 0 0
\(723\) −7.49687 −0.278811
\(724\) 0 0
\(725\) −50.5655 −1.87796
\(726\) 0 0
\(727\) 24.2347 0.898814 0.449407 0.893327i \(-0.351635\pi\)
0.449407 + 0.893327i \(0.351635\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −18.3502 −0.678705
\(732\) 0 0
\(733\) −41.0374 −1.51575 −0.757875 0.652400i \(-0.773762\pi\)
−0.757875 + 0.652400i \(0.773762\pi\)
\(734\) 0 0
\(735\) 1.59356 0.0587793
\(736\) 0 0
\(737\) 2.04619 0.0753725
\(738\) 0 0
\(739\) 31.7107 1.16650 0.583248 0.812294i \(-0.301782\pi\)
0.583248 + 0.812294i \(0.301782\pi\)
\(740\) 0 0
\(741\) 0.0238219 0.000875120 0
\(742\) 0 0
\(743\) −31.7721 −1.16560 −0.582802 0.812614i \(-0.698044\pi\)
−0.582802 + 0.812614i \(0.698044\pi\)
\(744\) 0 0
\(745\) 44.9297 1.64610
\(746\) 0 0
\(747\) 13.4089 0.490607
\(748\) 0 0
\(749\) −10.2656 −0.375096
\(750\) 0 0
\(751\) 23.5750 0.860264 0.430132 0.902766i \(-0.358467\pi\)
0.430132 + 0.902766i \(0.358467\pi\)
\(752\) 0 0
\(753\) −9.63798 −0.351227
\(754\) 0 0
\(755\) 70.4997 2.56575
\(756\) 0 0
\(757\) 20.9217 0.760411 0.380206 0.924902i \(-0.375853\pi\)
0.380206 + 0.924902i \(0.375853\pi\)
\(758\) 0 0
\(759\) 12.7596 0.463145
\(760\) 0 0
\(761\) −6.74661 −0.244564 −0.122282 0.992495i \(-0.539021\pi\)
−0.122282 + 0.992495i \(0.539021\pi\)
\(762\) 0 0
\(763\) 32.5124 1.17703
\(764\) 0 0
\(765\) 13.4093 0.484814
\(766\) 0 0
\(767\) −0.168105 −0.00606993
\(768\) 0 0
\(769\) 11.1193 0.400974 0.200487 0.979696i \(-0.435748\pi\)
0.200487 + 0.979696i \(0.435748\pi\)
\(770\) 0 0
\(771\) 16.0721 0.578822
\(772\) 0 0
\(773\) −42.9830 −1.54599 −0.772995 0.634412i \(-0.781242\pi\)
−0.772995 + 0.634412i \(0.781242\pi\)
\(774\) 0 0
\(775\) −47.9417 −1.72212
\(776\) 0 0
\(777\) −0.431960 −0.0154965
\(778\) 0 0
\(779\) 1.95633 0.0700930
\(780\) 0 0
\(781\) 4.12714 0.147681
\(782\) 0 0
\(783\) −6.25576 −0.223563
\(784\) 0 0
\(785\) −33.1952 −1.18479
\(786\) 0 0
\(787\) 3.90798 0.139304 0.0696522 0.997571i \(-0.477811\pi\)
0.0696522 + 0.997571i \(0.477811\pi\)
\(788\) 0 0
\(789\) −13.8779 −0.494065
\(790\) 0 0
\(791\) 16.3654 0.581886
\(792\) 0 0
\(793\) −0.172031 −0.00610901
\(794\) 0 0
\(795\) −38.7327 −1.37371
\(796\) 0 0
\(797\) 20.2466 0.717171 0.358586 0.933497i \(-0.383259\pi\)
0.358586 + 0.933497i \(0.383259\pi\)
\(798\) 0 0
\(799\) −31.1271 −1.10120
\(800\) 0 0
\(801\) 1.01339 0.0358063
\(802\) 0 0
\(803\) 53.5964 1.89138
\(804\) 0 0
\(805\) 29.3969 1.03611
\(806\) 0 0
\(807\) −11.7466 −0.413499
\(808\) 0 0
\(809\) −27.8278 −0.978372 −0.489186 0.872179i \(-0.662706\pi\)
−0.489186 + 0.872179i \(0.662706\pi\)
\(810\) 0 0
\(811\) 29.0208 1.01906 0.509529 0.860453i \(-0.329820\pi\)
0.509529 + 0.860453i \(0.329820\pi\)
\(812\) 0 0
\(813\) −27.0126 −0.947374
\(814\) 0 0
\(815\) −14.8708 −0.520900
\(816\) 0 0
\(817\) 2.48662 0.0869957
\(818\) 0 0
\(819\) 0.129348 0.00451978
\(820\) 0 0
\(821\) −44.3461 −1.54769 −0.773845 0.633374i \(-0.781669\pi\)
−0.773845 + 0.633374i \(0.781669\pi\)
\(822\) 0 0
\(823\) 25.6252 0.893239 0.446620 0.894724i \(-0.352628\pi\)
0.446620 + 0.894724i \(0.352628\pi\)
\(824\) 0 0
\(825\) −34.6153 −1.20515
\(826\) 0 0
\(827\) 14.0006 0.486848 0.243424 0.969920i \(-0.421729\pi\)
0.243424 + 0.969920i \(0.421729\pi\)
\(828\) 0 0
\(829\) −12.6296 −0.438643 −0.219321 0.975653i \(-0.570384\pi\)
−0.219321 + 0.975653i \(0.570384\pi\)
\(830\) 0 0
\(831\) −27.7942 −0.964171
\(832\) 0 0
\(833\) 1.63330 0.0565904
\(834\) 0 0
\(835\) 3.61705 0.125173
\(836\) 0 0
\(837\) −5.93115 −0.205010
\(838\) 0 0
\(839\) 37.8724 1.30750 0.653750 0.756710i \(-0.273195\pi\)
0.653750 + 0.756710i \(0.273195\pi\)
\(840\) 0 0
\(841\) 10.1345 0.349466
\(842\) 0 0
\(843\) 16.0329 0.552202
\(844\) 0 0
\(845\) −47.0135 −1.61731
\(846\) 0 0
\(847\) −20.0201 −0.687898
\(848\) 0 0
\(849\) 9.97967 0.342501
\(850\) 0 0
\(851\) −0.471829 −0.0161741
\(852\) 0 0
\(853\) 31.1052 1.06502 0.532512 0.846423i \(-0.321248\pi\)
0.532512 + 0.846423i \(0.321248\pi\)
\(854\) 0 0
\(855\) −1.81708 −0.0621430
\(856\) 0 0
\(857\) 47.6667 1.62826 0.814131 0.580681i \(-0.197214\pi\)
0.814131 + 0.580681i \(0.197214\pi\)
\(858\) 0 0
\(859\) −6.93685 −0.236682 −0.118341 0.992973i \(-0.537758\pi\)
−0.118341 + 0.992973i \(0.537758\pi\)
\(860\) 0 0
\(861\) 10.6225 0.362013
\(862\) 0 0
\(863\) −44.3736 −1.51050 −0.755248 0.655439i \(-0.772484\pi\)
−0.755248 + 0.655439i \(0.772484\pi\)
\(864\) 0 0
\(865\) 6.47898 0.220292
\(866\) 0 0
\(867\) −3.25630 −0.110590
\(868\) 0 0
\(869\) −6.55872 −0.222489
\(870\) 0 0
\(871\) 0.0226574 0.000767717 0
\(872\) 0 0
\(873\) −1.19560 −0.0404649
\(874\) 0 0
\(875\) −30.4184 −1.02833
\(876\) 0 0
\(877\) −15.2810 −0.516003 −0.258002 0.966144i \(-0.583064\pi\)
−0.258002 + 0.966144i \(0.583064\pi\)
\(878\) 0 0
\(879\) −6.84400 −0.230842
\(880\) 0 0
\(881\) 9.33130 0.314379 0.157190 0.987568i \(-0.449757\pi\)
0.157190 + 0.987568i \(0.449757\pi\)
\(882\) 0 0
\(883\) 14.6940 0.494492 0.247246 0.968953i \(-0.420474\pi\)
0.247246 + 0.968953i \(0.420474\pi\)
\(884\) 0 0
\(885\) 12.8227 0.431030
\(886\) 0 0
\(887\) −35.8669 −1.20429 −0.602147 0.798385i \(-0.705688\pi\)
−0.602147 + 0.798385i \(0.705688\pi\)
\(888\) 0 0
\(889\) 8.52918 0.286060
\(890\) 0 0
\(891\) −4.28246 −0.143468
\(892\) 0 0
\(893\) 4.21801 0.141150
\(894\) 0 0
\(895\) −31.4422 −1.05100
\(896\) 0 0
\(897\) 0.141287 0.00471742
\(898\) 0 0
\(899\) 37.1038 1.23748
\(900\) 0 0
\(901\) −39.6986 −1.32255
\(902\) 0 0
\(903\) 13.5018 0.449311
\(904\) 0 0
\(905\) −41.8985 −1.39275
\(906\) 0 0
\(907\) −10.0185 −0.332658 −0.166329 0.986070i \(-0.553191\pi\)
−0.166329 + 0.986070i \(0.553191\pi\)
\(908\) 0 0
\(909\) 2.15983 0.0716371
\(910\) 0 0
\(911\) −45.0288 −1.49187 −0.745936 0.666018i \(-0.767997\pi\)
−0.745936 + 0.666018i \(0.767997\pi\)
\(912\) 0 0
\(913\) −57.4232 −1.90043
\(914\) 0 0
\(915\) 13.1222 0.433805
\(916\) 0 0
\(917\) −46.5921 −1.53861
\(918\) 0 0
\(919\) 6.14537 0.202717 0.101359 0.994850i \(-0.467681\pi\)
0.101359 + 0.994850i \(0.467681\pi\)
\(920\) 0 0
\(921\) 1.88679 0.0621718
\(922\) 0 0
\(923\) 0.0456996 0.00150422
\(924\) 0 0
\(925\) 1.28002 0.0420866
\(926\) 0 0
\(927\) 13.6082 0.446952
\(928\) 0 0
\(929\) −24.0472 −0.788964 −0.394482 0.918904i \(-0.629076\pi\)
−0.394482 + 0.918904i \(0.629076\pi\)
\(930\) 0 0
\(931\) −0.221327 −0.00725370
\(932\) 0 0
\(933\) −18.8665 −0.617661
\(934\) 0 0
\(935\) −57.4247 −1.87799
\(936\) 0 0
\(937\) 10.2412 0.334567 0.167283 0.985909i \(-0.446501\pi\)
0.167283 + 0.985909i \(0.446501\pi\)
\(938\) 0 0
\(939\) 28.2178 0.920854
\(940\) 0 0
\(941\) 2.37486 0.0774183 0.0387092 0.999251i \(-0.487675\pi\)
0.0387092 + 0.999251i \(0.487675\pi\)
\(942\) 0 0
\(943\) 11.6029 0.377843
\(944\) 0 0
\(945\) −9.86637 −0.320953
\(946\) 0 0
\(947\) 10.4904 0.340891 0.170445 0.985367i \(-0.445479\pi\)
0.170445 + 0.985367i \(0.445479\pi\)
\(948\) 0 0
\(949\) 0.593470 0.0192648
\(950\) 0 0
\(951\) −17.9184 −0.581043
\(952\) 0 0
\(953\) 43.4610 1.40784 0.703920 0.710279i \(-0.251431\pi\)
0.703920 + 0.710279i \(0.251431\pi\)
\(954\) 0 0
\(955\) −14.3326 −0.463792
\(956\) 0 0
\(957\) 26.7900 0.865998
\(958\) 0 0
\(959\) 16.1259 0.520732
\(960\) 0 0
\(961\) 4.17852 0.134791
\(962\) 0 0
\(963\) 3.76340 0.121274
\(964\) 0 0
\(965\) 24.6379 0.793122
\(966\) 0 0
\(967\) −14.9457 −0.480623 −0.240311 0.970696i \(-0.577250\pi\)
−0.240311 + 0.970696i \(0.577250\pi\)
\(968\) 0 0
\(969\) −1.86240 −0.0598288
\(970\) 0 0
\(971\) −7.84860 −0.251873 −0.125937 0.992038i \(-0.540194\pi\)
−0.125937 + 0.992038i \(0.540194\pi\)
\(972\) 0 0
\(973\) 52.4027 1.67995
\(974\) 0 0
\(975\) −0.383293 −0.0122752
\(976\) 0 0
\(977\) −43.6046 −1.39503 −0.697517 0.716568i \(-0.745712\pi\)
−0.697517 + 0.716568i \(0.745712\pi\)
\(978\) 0 0
\(979\) −4.33979 −0.138700
\(980\) 0 0
\(981\) −11.9192 −0.380549
\(982\) 0 0
\(983\) −49.1287 −1.56696 −0.783481 0.621416i \(-0.786558\pi\)
−0.783481 + 0.621416i \(0.786558\pi\)
\(984\) 0 0
\(985\) −26.7395 −0.851990
\(986\) 0 0
\(987\) 22.9029 0.729007
\(988\) 0 0
\(989\) 14.7480 0.468959
\(990\) 0 0
\(991\) 4.17577 0.132648 0.0663239 0.997798i \(-0.478873\pi\)
0.0663239 + 0.997798i \(0.478873\pi\)
\(992\) 0 0
\(993\) −6.98539 −0.221675
\(994\) 0 0
\(995\) 58.6887 1.86056
\(996\) 0 0
\(997\) −4.40338 −0.139456 −0.0697282 0.997566i \(-0.522213\pi\)
−0.0697282 + 0.997566i \(0.522213\pi\)
\(998\) 0 0
\(999\) 0.158358 0.00501023
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.w.1.7 7
4.3 odd 2 4008.2.a.g.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.g.1.7 7 4.3 odd 2
8016.2.a.w.1.7 7 1.1 even 1 trivial