Properties

Label 4016.2.a.m.1.5
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 23
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
Dimension: \(23\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 2008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.53334 q^{3} +1.50187 q^{5} -0.478852 q^{7} +3.41783 q^{9} +O(q^{10})\) \(q-2.53334 q^{3} +1.50187 q^{5} -0.478852 q^{7} +3.41783 q^{9} -4.20287 q^{11} +4.32908 q^{13} -3.80475 q^{15} +2.05558 q^{17} -0.535658 q^{19} +1.21310 q^{21} +6.64982 q^{23} -2.74440 q^{25} -1.05852 q^{27} +0.258982 q^{29} -4.57844 q^{31} +10.6473 q^{33} -0.719173 q^{35} -11.8796 q^{37} -10.9671 q^{39} -5.23725 q^{41} +8.69198 q^{43} +5.13313 q^{45} +11.5859 q^{47} -6.77070 q^{49} -5.20748 q^{51} +12.2460 q^{53} -6.31216 q^{55} +1.35701 q^{57} -3.96974 q^{59} +4.23862 q^{61} -1.63664 q^{63} +6.50171 q^{65} -14.8609 q^{67} -16.8463 q^{69} +16.3598 q^{71} +6.11513 q^{73} +6.95250 q^{75} +2.01256 q^{77} -10.5582 q^{79} -7.57191 q^{81} -12.1519 q^{83} +3.08720 q^{85} -0.656090 q^{87} +5.39741 q^{89} -2.07299 q^{91} +11.5988 q^{93} -0.804488 q^{95} +14.0202 q^{97} -14.3647 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) −2.53334 −1.46263 −0.731314 0.682041i \(-0.761092\pi\)
−0.731314 + 0.682041i \(0.761092\pi\)
\(4\) 0 0
\(5\) 1.50187 0.671655 0.335828 0.941923i \(-0.390984\pi\)
0.335828 + 0.941923i \(0.390984\pi\)
\(6\) 0 0
\(7\) −0.478852 −0.180989 −0.0904946 0.995897i \(-0.528845\pi\)
−0.0904946 + 0.995897i \(0.528845\pi\)
\(8\) 0 0
\(9\) 3.41783 1.13928
\(10\) 0 0
\(11\) −4.20287 −1.26721 −0.633607 0.773655i \(-0.718426\pi\)
−0.633607 + 0.773655i \(0.718426\pi\)
\(12\) 0 0
\(13\) 4.32908 1.20067 0.600336 0.799748i \(-0.295034\pi\)
0.600336 + 0.799748i \(0.295034\pi\)
\(14\) 0 0
\(15\) −3.80475 −0.982381
\(16\) 0 0
\(17\) 2.05558 0.498551 0.249275 0.968433i \(-0.419808\pi\)
0.249275 + 0.968433i \(0.419808\pi\)
\(18\) 0 0
\(19\) −0.535658 −0.122888 −0.0614442 0.998111i \(-0.519571\pi\)
−0.0614442 + 0.998111i \(0.519571\pi\)
\(20\) 0 0
\(21\) 1.21310 0.264720
\(22\) 0 0
\(23\) 6.64982 1.38658 0.693292 0.720657i \(-0.256160\pi\)
0.693292 + 0.720657i \(0.256160\pi\)
\(24\) 0 0
\(25\) −2.74440 −0.548879
\(26\) 0 0
\(27\) −1.05852 −0.203712
\(28\) 0 0
\(29\) 0.258982 0.0480917 0.0240459 0.999711i \(-0.492345\pi\)
0.0240459 + 0.999711i \(0.492345\pi\)
\(30\) 0 0
\(31\) −4.57844 −0.822311 −0.411156 0.911565i \(-0.634875\pi\)
−0.411156 + 0.911565i \(0.634875\pi\)
\(32\) 0 0
\(33\) 10.6473 1.85346
\(34\) 0 0
\(35\) −0.719173 −0.121562
\(36\) 0 0
\(37\) −11.8796 −1.95300 −0.976500 0.215518i \(-0.930856\pi\)
−0.976500 + 0.215518i \(0.930856\pi\)
\(38\) 0 0
\(39\) −10.9671 −1.75614
\(40\) 0 0
\(41\) −5.23725 −0.817921 −0.408961 0.912552i \(-0.634109\pi\)
−0.408961 + 0.912552i \(0.634109\pi\)
\(42\) 0 0
\(43\) 8.69198 1.32552 0.662758 0.748834i \(-0.269386\pi\)
0.662758 + 0.748834i \(0.269386\pi\)
\(44\) 0 0
\(45\) 5.13313 0.765202
\(46\) 0 0
\(47\) 11.5859 1.68998 0.844990 0.534783i \(-0.179607\pi\)
0.844990 + 0.534783i \(0.179607\pi\)
\(48\) 0 0
\(49\) −6.77070 −0.967243
\(50\) 0 0
\(51\) −5.20748 −0.729194
\(52\) 0 0
\(53\) 12.2460 1.68211 0.841056 0.540948i \(-0.181934\pi\)
0.841056 + 0.540948i \(0.181934\pi\)
\(54\) 0 0
\(55\) −6.31216 −0.851131
\(56\) 0 0
\(57\) 1.35701 0.179740
\(58\) 0 0
\(59\) −3.96974 −0.516816 −0.258408 0.966036i \(-0.583198\pi\)
−0.258408 + 0.966036i \(0.583198\pi\)
\(60\) 0 0
\(61\) 4.23862 0.542699 0.271350 0.962481i \(-0.412530\pi\)
0.271350 + 0.962481i \(0.412530\pi\)
\(62\) 0 0
\(63\) −1.63664 −0.206197
\(64\) 0 0
\(65\) 6.50171 0.806438
\(66\) 0 0
\(67\) −14.8609 −1.81555 −0.907773 0.419461i \(-0.862219\pi\)
−0.907773 + 0.419461i \(0.862219\pi\)
\(68\) 0 0
\(69\) −16.8463 −2.02805
\(70\) 0 0
\(71\) 16.3598 1.94155 0.970773 0.240001i \(-0.0771478\pi\)
0.970773 + 0.240001i \(0.0771478\pi\)
\(72\) 0 0
\(73\) 6.11513 0.715722 0.357861 0.933775i \(-0.383506\pi\)
0.357861 + 0.933775i \(0.383506\pi\)
\(74\) 0 0
\(75\) 6.95250 0.802805
\(76\) 0 0
\(77\) 2.01256 0.229352
\(78\) 0 0
\(79\) −10.5582 −1.18789 −0.593944 0.804506i \(-0.702430\pi\)
−0.593944 + 0.804506i \(0.702430\pi\)
\(80\) 0 0
\(81\) −7.57191 −0.841324
\(82\) 0 0
\(83\) −12.1519 −1.33384 −0.666920 0.745130i \(-0.732388\pi\)
−0.666920 + 0.745130i \(0.732388\pi\)
\(84\) 0 0
\(85\) 3.08720 0.334854
\(86\) 0 0
\(87\) −0.656090 −0.0703403
\(88\) 0 0
\(89\) 5.39741 0.572124 0.286062 0.958211i \(-0.407654\pi\)
0.286062 + 0.958211i \(0.407654\pi\)
\(90\) 0 0
\(91\) −2.07299 −0.217309
\(92\) 0 0
\(93\) 11.5988 1.20274
\(94\) 0 0
\(95\) −0.804488 −0.0825387
\(96\) 0 0
\(97\) 14.0202 1.42354 0.711768 0.702414i \(-0.247895\pi\)
0.711768 + 0.702414i \(0.247895\pi\)
\(98\) 0 0
\(99\) −14.3647 −1.44371
\(100\) 0 0
\(101\) −0.0962519 −0.00957742 −0.00478871 0.999989i \(-0.501524\pi\)
−0.00478871 + 0.999989i \(0.501524\pi\)
\(102\) 0 0
\(103\) 10.7390 1.05814 0.529072 0.848577i \(-0.322540\pi\)
0.529072 + 0.848577i \(0.322540\pi\)
\(104\) 0 0
\(105\) 1.82191 0.177800
\(106\) 0 0
\(107\) −19.4866 −1.88384 −0.941920 0.335836i \(-0.890981\pi\)
−0.941920 + 0.335836i \(0.890981\pi\)
\(108\) 0 0
\(109\) 0.0525721 0.00503549 0.00251775 0.999997i \(-0.499199\pi\)
0.00251775 + 0.999997i \(0.499199\pi\)
\(110\) 0 0
\(111\) 30.0952 2.85651
\(112\) 0 0
\(113\) 2.74548 0.258273 0.129136 0.991627i \(-0.458780\pi\)
0.129136 + 0.991627i \(0.458780\pi\)
\(114\) 0 0
\(115\) 9.98715 0.931306
\(116\) 0 0
\(117\) 14.7961 1.36790
\(118\) 0 0
\(119\) −0.984318 −0.0902323
\(120\) 0 0
\(121\) 6.66414 0.605831
\(122\) 0 0
\(123\) 13.2678 1.19631
\(124\) 0 0
\(125\) −11.6311 −1.04031
\(126\) 0 0
\(127\) 15.4193 1.36824 0.684122 0.729367i \(-0.260185\pi\)
0.684122 + 0.729367i \(0.260185\pi\)
\(128\) 0 0
\(129\) −22.0198 −1.93873
\(130\) 0 0
\(131\) −13.8641 −1.21131 −0.605656 0.795727i \(-0.707089\pi\)
−0.605656 + 0.795727i \(0.707089\pi\)
\(132\) 0 0
\(133\) 0.256501 0.0222415
\(134\) 0 0
\(135\) −1.58975 −0.136824
\(136\) 0 0
\(137\) −14.4346 −1.23323 −0.616613 0.787266i \(-0.711496\pi\)
−0.616613 + 0.787266i \(0.711496\pi\)
\(138\) 0 0
\(139\) 22.9011 1.94244 0.971221 0.238179i \(-0.0765505\pi\)
0.971221 + 0.238179i \(0.0765505\pi\)
\(140\) 0 0
\(141\) −29.3511 −2.47181
\(142\) 0 0
\(143\) −18.1946 −1.52151
\(144\) 0 0
\(145\) 0.388956 0.0323011
\(146\) 0 0
\(147\) 17.1525 1.41472
\(148\) 0 0
\(149\) −9.40542 −0.770522 −0.385261 0.922808i \(-0.625889\pi\)
−0.385261 + 0.922808i \(0.625889\pi\)
\(150\) 0 0
\(151\) 7.32090 0.595766 0.297883 0.954602i \(-0.403719\pi\)
0.297883 + 0.954602i \(0.403719\pi\)
\(152\) 0 0
\(153\) 7.02562 0.567988
\(154\) 0 0
\(155\) −6.87620 −0.552310
\(156\) 0 0
\(157\) 7.11074 0.567499 0.283749 0.958898i \(-0.408422\pi\)
0.283749 + 0.958898i \(0.408422\pi\)
\(158\) 0 0
\(159\) −31.0232 −2.46030
\(160\) 0 0
\(161\) −3.18428 −0.250957
\(162\) 0 0
\(163\) 6.35460 0.497730 0.248865 0.968538i \(-0.419942\pi\)
0.248865 + 0.968538i \(0.419942\pi\)
\(164\) 0 0
\(165\) 15.9909 1.24489
\(166\) 0 0
\(167\) 8.47308 0.655667 0.327833 0.944736i \(-0.393682\pi\)
0.327833 + 0.944736i \(0.393682\pi\)
\(168\) 0 0
\(169\) 5.74097 0.441613
\(170\) 0 0
\(171\) −1.83079 −0.140004
\(172\) 0 0
\(173\) 14.2270 1.08166 0.540828 0.841133i \(-0.318111\pi\)
0.540828 + 0.841133i \(0.318111\pi\)
\(174\) 0 0
\(175\) 1.31416 0.0993412
\(176\) 0 0
\(177\) 10.0567 0.755909
\(178\) 0 0
\(179\) 8.07057 0.603223 0.301611 0.953431i \(-0.402476\pi\)
0.301611 + 0.953431i \(0.402476\pi\)
\(180\) 0 0
\(181\) 17.9756 1.33612 0.668060 0.744108i \(-0.267125\pi\)
0.668060 + 0.744108i \(0.267125\pi\)
\(182\) 0 0
\(183\) −10.7379 −0.793766
\(184\) 0 0
\(185\) −17.8416 −1.31174
\(186\) 0 0
\(187\) −8.63933 −0.631770
\(188\) 0 0
\(189\) 0.506874 0.0368696
\(190\) 0 0
\(191\) 19.0431 1.37791 0.688954 0.724805i \(-0.258070\pi\)
0.688954 + 0.724805i \(0.258070\pi\)
\(192\) 0 0
\(193\) −2.70949 −0.195033 −0.0975166 0.995234i \(-0.531090\pi\)
−0.0975166 + 0.995234i \(0.531090\pi\)
\(194\) 0 0
\(195\) −16.4711 −1.17952
\(196\) 0 0
\(197\) −13.3153 −0.948674 −0.474337 0.880343i \(-0.657312\pi\)
−0.474337 + 0.880343i \(0.657312\pi\)
\(198\) 0 0
\(199\) −2.68736 −0.190502 −0.0952510 0.995453i \(-0.530365\pi\)
−0.0952510 + 0.995453i \(0.530365\pi\)
\(200\) 0 0
\(201\) 37.6477 2.65547
\(202\) 0 0
\(203\) −0.124014 −0.00870408
\(204\) 0 0
\(205\) −7.86566 −0.549361
\(206\) 0 0
\(207\) 22.7280 1.57970
\(208\) 0 0
\(209\) 2.25130 0.155726
\(210\) 0 0
\(211\) 9.55720 0.657945 0.328973 0.944339i \(-0.393298\pi\)
0.328973 + 0.944339i \(0.393298\pi\)
\(212\) 0 0
\(213\) −41.4449 −2.83976
\(214\) 0 0
\(215\) 13.0542 0.890289
\(216\) 0 0
\(217\) 2.19240 0.148829
\(218\) 0 0
\(219\) −15.4917 −1.04683
\(220\) 0 0
\(221\) 8.89876 0.598596
\(222\) 0 0
\(223\) −4.23789 −0.283790 −0.141895 0.989882i \(-0.545320\pi\)
−0.141895 + 0.989882i \(0.545320\pi\)
\(224\) 0 0
\(225\) −9.37989 −0.625326
\(226\) 0 0
\(227\) 2.23005 0.148013 0.0740067 0.997258i \(-0.476421\pi\)
0.0740067 + 0.997258i \(0.476421\pi\)
\(228\) 0 0
\(229\) 27.2320 1.79954 0.899769 0.436366i \(-0.143735\pi\)
0.899769 + 0.436366i \(0.143735\pi\)
\(230\) 0 0
\(231\) −5.09850 −0.335456
\(232\) 0 0
\(233\) 17.4212 1.14130 0.570649 0.821194i \(-0.306692\pi\)
0.570649 + 0.821194i \(0.306692\pi\)
\(234\) 0 0
\(235\) 17.4005 1.13508
\(236\) 0 0
\(237\) 26.7475 1.73744
\(238\) 0 0
\(239\) 29.2187 1.89000 0.945002 0.327066i \(-0.106060\pi\)
0.945002 + 0.327066i \(0.106060\pi\)
\(240\) 0 0
\(241\) −0.793095 −0.0510877 −0.0255439 0.999674i \(-0.508132\pi\)
−0.0255439 + 0.999674i \(0.508132\pi\)
\(242\) 0 0
\(243\) 22.3578 1.43425
\(244\) 0 0
\(245\) −10.1687 −0.649654
\(246\) 0 0
\(247\) −2.31891 −0.147549
\(248\) 0 0
\(249\) 30.7848 1.95091
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) −27.9484 −1.75710
\(254\) 0 0
\(255\) −7.82095 −0.489767
\(256\) 0 0
\(257\) −5.86990 −0.366154 −0.183077 0.983099i \(-0.558606\pi\)
−0.183077 + 0.983099i \(0.558606\pi\)
\(258\) 0 0
\(259\) 5.68859 0.353472
\(260\) 0 0
\(261\) 0.885157 0.0547898
\(262\) 0 0
\(263\) 16.2437 1.00163 0.500815 0.865554i \(-0.333034\pi\)
0.500815 + 0.865554i \(0.333034\pi\)
\(264\) 0 0
\(265\) 18.3918 1.12980
\(266\) 0 0
\(267\) −13.6735 −0.836804
\(268\) 0 0
\(269\) 20.6368 1.25825 0.629125 0.777304i \(-0.283413\pi\)
0.629125 + 0.777304i \(0.283413\pi\)
\(270\) 0 0
\(271\) 31.0148 1.88401 0.942007 0.335593i \(-0.108937\pi\)
0.942007 + 0.335593i \(0.108937\pi\)
\(272\) 0 0
\(273\) 5.25160 0.317841
\(274\) 0 0
\(275\) 11.5343 0.695547
\(276\) 0 0
\(277\) 4.90285 0.294584 0.147292 0.989093i \(-0.452944\pi\)
0.147292 + 0.989093i \(0.452944\pi\)
\(278\) 0 0
\(279\) −15.6483 −0.936841
\(280\) 0 0
\(281\) 15.7041 0.936827 0.468413 0.883509i \(-0.344826\pi\)
0.468413 + 0.883509i \(0.344826\pi\)
\(282\) 0 0
\(283\) −18.2286 −1.08358 −0.541790 0.840514i \(-0.682253\pi\)
−0.541790 + 0.840514i \(0.682253\pi\)
\(284\) 0 0
\(285\) 2.03804 0.120723
\(286\) 0 0
\(287\) 2.50787 0.148035
\(288\) 0 0
\(289\) −12.7746 −0.751447
\(290\) 0 0
\(291\) −35.5180 −2.08210
\(292\) 0 0
\(293\) −1.47789 −0.0863394 −0.0431697 0.999068i \(-0.513746\pi\)
−0.0431697 + 0.999068i \(0.513746\pi\)
\(294\) 0 0
\(295\) −5.96202 −0.347122
\(296\) 0 0
\(297\) 4.44882 0.258147
\(298\) 0 0
\(299\) 28.7876 1.66483
\(300\) 0 0
\(301\) −4.16218 −0.239904
\(302\) 0 0
\(303\) 0.243839 0.0140082
\(304\) 0 0
\(305\) 6.36584 0.364507
\(306\) 0 0
\(307\) 28.7263 1.63950 0.819748 0.572725i \(-0.194114\pi\)
0.819748 + 0.572725i \(0.194114\pi\)
\(308\) 0 0
\(309\) −27.2056 −1.54767
\(310\) 0 0
\(311\) −17.8515 −1.01227 −0.506133 0.862455i \(-0.668926\pi\)
−0.506133 + 0.862455i \(0.668926\pi\)
\(312\) 0 0
\(313\) −13.9352 −0.787662 −0.393831 0.919183i \(-0.628850\pi\)
−0.393831 + 0.919183i \(0.628850\pi\)
\(314\) 0 0
\(315\) −2.45801 −0.138493
\(316\) 0 0
\(317\) 17.6130 0.989247 0.494623 0.869107i \(-0.335306\pi\)
0.494623 + 0.869107i \(0.335306\pi\)
\(318\) 0 0
\(319\) −1.08847 −0.0609425
\(320\) 0 0
\(321\) 49.3663 2.75536
\(322\) 0 0
\(323\) −1.10109 −0.0612661
\(324\) 0 0
\(325\) −11.8807 −0.659024
\(326\) 0 0
\(327\) −0.133183 −0.00736505
\(328\) 0 0
\(329\) −5.54794 −0.305868
\(330\) 0 0
\(331\) 12.0310 0.661284 0.330642 0.943756i \(-0.392735\pi\)
0.330642 + 0.943756i \(0.392735\pi\)
\(332\) 0 0
\(333\) −40.6026 −2.22501
\(334\) 0 0
\(335\) −22.3191 −1.21942
\(336\) 0 0
\(337\) 17.3931 0.947463 0.473732 0.880669i \(-0.342907\pi\)
0.473732 + 0.880669i \(0.342907\pi\)
\(338\) 0 0
\(339\) −6.95524 −0.377757
\(340\) 0 0
\(341\) 19.2426 1.04204
\(342\) 0 0
\(343\) 6.59413 0.356050
\(344\) 0 0
\(345\) −25.3009 −1.36215
\(346\) 0 0
\(347\) −15.6671 −0.841054 −0.420527 0.907280i \(-0.638155\pi\)
−0.420527 + 0.907280i \(0.638155\pi\)
\(348\) 0 0
\(349\) 21.9367 1.17425 0.587123 0.809498i \(-0.300260\pi\)
0.587123 + 0.809498i \(0.300260\pi\)
\(350\) 0 0
\(351\) −4.58241 −0.244591
\(352\) 0 0
\(353\) 32.9804 1.75537 0.877686 0.479237i \(-0.159087\pi\)
0.877686 + 0.479237i \(0.159087\pi\)
\(354\) 0 0
\(355\) 24.5702 1.30405
\(356\) 0 0
\(357\) 2.49362 0.131976
\(358\) 0 0
\(359\) 17.6493 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(360\) 0 0
\(361\) −18.7131 −0.984898
\(362\) 0 0
\(363\) −16.8826 −0.886105
\(364\) 0 0
\(365\) 9.18411 0.480718
\(366\) 0 0
\(367\) 31.5782 1.64837 0.824183 0.566323i \(-0.191634\pi\)
0.824183 + 0.566323i \(0.191634\pi\)
\(368\) 0 0
\(369\) −17.9001 −0.931840
\(370\) 0 0
\(371\) −5.86401 −0.304444
\(372\) 0 0
\(373\) 14.7157 0.761949 0.380975 0.924585i \(-0.375589\pi\)
0.380975 + 0.924585i \(0.375589\pi\)
\(374\) 0 0
\(375\) 29.4655 1.52159
\(376\) 0 0
\(377\) 1.12115 0.0577424
\(378\) 0 0
\(379\) −25.6456 −1.31732 −0.658662 0.752439i \(-0.728877\pi\)
−0.658662 + 0.752439i \(0.728877\pi\)
\(380\) 0 0
\(381\) −39.0625 −2.00123
\(382\) 0 0
\(383\) −14.6100 −0.746537 −0.373268 0.927723i \(-0.621763\pi\)
−0.373268 + 0.927723i \(0.621763\pi\)
\(384\) 0 0
\(385\) 3.02259 0.154046
\(386\) 0 0
\(387\) 29.7078 1.51013
\(388\) 0 0
\(389\) −7.94533 −0.402844 −0.201422 0.979505i \(-0.564556\pi\)
−0.201422 + 0.979505i \(0.564556\pi\)
\(390\) 0 0
\(391\) 13.6692 0.691282
\(392\) 0 0
\(393\) 35.1225 1.77170
\(394\) 0 0
\(395\) −15.8570 −0.797852
\(396\) 0 0
\(397\) −6.55835 −0.329154 −0.164577 0.986364i \(-0.552626\pi\)
−0.164577 + 0.986364i \(0.552626\pi\)
\(398\) 0 0
\(399\) −0.649806 −0.0325310
\(400\) 0 0
\(401\) −5.20130 −0.259741 −0.129870 0.991531i \(-0.541456\pi\)
−0.129870 + 0.991531i \(0.541456\pi\)
\(402\) 0 0
\(403\) −19.8204 −0.987326
\(404\) 0 0
\(405\) −11.3720 −0.565079
\(406\) 0 0
\(407\) 49.9286 2.47487
\(408\) 0 0
\(409\) 14.7419 0.728939 0.364470 0.931215i \(-0.381250\pi\)
0.364470 + 0.931215i \(0.381250\pi\)
\(410\) 0 0
\(411\) 36.5677 1.80375
\(412\) 0 0
\(413\) 1.90092 0.0935382
\(414\) 0 0
\(415\) −18.2505 −0.895880
\(416\) 0 0
\(417\) −58.0163 −2.84107
\(418\) 0 0
\(419\) −29.9425 −1.46279 −0.731394 0.681955i \(-0.761130\pi\)
−0.731394 + 0.681955i \(0.761130\pi\)
\(420\) 0 0
\(421\) −0.851309 −0.0414903 −0.0207451 0.999785i \(-0.506604\pi\)
−0.0207451 + 0.999785i \(0.506604\pi\)
\(422\) 0 0
\(423\) 39.5987 1.92536
\(424\) 0 0
\(425\) −5.64132 −0.273644
\(426\) 0 0
\(427\) −2.02967 −0.0982227
\(428\) 0 0
\(429\) 46.0932 2.22540
\(430\) 0 0
\(431\) −12.5827 −0.606086 −0.303043 0.952977i \(-0.598003\pi\)
−0.303043 + 0.952977i \(0.598003\pi\)
\(432\) 0 0
\(433\) −10.9864 −0.527974 −0.263987 0.964526i \(-0.585038\pi\)
−0.263987 + 0.964526i \(0.585038\pi\)
\(434\) 0 0
\(435\) −0.985360 −0.0472444
\(436\) 0 0
\(437\) −3.56203 −0.170395
\(438\) 0 0
\(439\) 21.3714 1.02000 0.510000 0.860175i \(-0.329645\pi\)
0.510000 + 0.860175i \(0.329645\pi\)
\(440\) 0 0
\(441\) −23.1411 −1.10196
\(442\) 0 0
\(443\) −37.4243 −1.77808 −0.889040 0.457829i \(-0.848627\pi\)
−0.889040 + 0.457829i \(0.848627\pi\)
\(444\) 0 0
\(445\) 8.10618 0.384270
\(446\) 0 0
\(447\) 23.8272 1.12699
\(448\) 0 0
\(449\) 30.9688 1.46151 0.730755 0.682640i \(-0.239168\pi\)
0.730755 + 0.682640i \(0.239168\pi\)
\(450\) 0 0
\(451\) 22.0115 1.03648
\(452\) 0 0
\(453\) −18.5464 −0.871384
\(454\) 0 0
\(455\) −3.11336 −0.145957
\(456\) 0 0
\(457\) −9.39062 −0.439275 −0.219637 0.975582i \(-0.570487\pi\)
−0.219637 + 0.975582i \(0.570487\pi\)
\(458\) 0 0
\(459\) −2.17587 −0.101561
\(460\) 0 0
\(461\) −5.75111 −0.267856 −0.133928 0.990991i \(-0.542759\pi\)
−0.133928 + 0.990991i \(0.542759\pi\)
\(462\) 0 0
\(463\) 25.7631 1.19731 0.598656 0.801006i \(-0.295701\pi\)
0.598656 + 0.801006i \(0.295701\pi\)
\(464\) 0 0
\(465\) 17.4198 0.807823
\(466\) 0 0
\(467\) −29.5070 −1.36542 −0.682710 0.730689i \(-0.739199\pi\)
−0.682710 + 0.730689i \(0.739199\pi\)
\(468\) 0 0
\(469\) 7.11617 0.328594
\(470\) 0 0
\(471\) −18.0139 −0.830039
\(472\) 0 0
\(473\) −36.5313 −1.67971
\(474\) 0 0
\(475\) 1.47006 0.0674509
\(476\) 0 0
\(477\) 41.8547 1.91639
\(478\) 0 0
\(479\) −19.6959 −0.899927 −0.449963 0.893047i \(-0.648563\pi\)
−0.449963 + 0.893047i \(0.648563\pi\)
\(480\) 0 0
\(481\) −51.4279 −2.34491
\(482\) 0 0
\(483\) 8.06688 0.367056
\(484\) 0 0
\(485\) 21.0565 0.956126
\(486\) 0 0
\(487\) −10.1758 −0.461108 −0.230554 0.973060i \(-0.574054\pi\)
−0.230554 + 0.973060i \(0.574054\pi\)
\(488\) 0 0
\(489\) −16.0984 −0.727994
\(490\) 0 0
\(491\) 30.0822 1.35759 0.678796 0.734327i \(-0.262502\pi\)
0.678796 + 0.734327i \(0.262502\pi\)
\(492\) 0 0
\(493\) 0.532357 0.0239762
\(494\) 0 0
\(495\) −21.5739 −0.969675
\(496\) 0 0
\(497\) −7.83391 −0.351399
\(498\) 0 0
\(499\) 28.6262 1.28149 0.640743 0.767756i \(-0.278627\pi\)
0.640743 + 0.767756i \(0.278627\pi\)
\(500\) 0 0
\(501\) −21.4652 −0.958996
\(502\) 0 0
\(503\) 5.95326 0.265443 0.132721 0.991153i \(-0.457628\pi\)
0.132721 + 0.991153i \(0.457628\pi\)
\(504\) 0 0
\(505\) −0.144558 −0.00643273
\(506\) 0 0
\(507\) −14.5438 −0.645915
\(508\) 0 0
\(509\) −9.90797 −0.439163 −0.219582 0.975594i \(-0.570469\pi\)
−0.219582 + 0.975594i \(0.570469\pi\)
\(510\) 0 0
\(511\) −2.92824 −0.129538
\(512\) 0 0
\(513\) 0.567004 0.0250338
\(514\) 0 0
\(515\) 16.1285 0.710709
\(516\) 0 0
\(517\) −48.6941 −2.14157
\(518\) 0 0
\(519\) −36.0418 −1.58206
\(520\) 0 0
\(521\) 2.43628 0.106735 0.0533677 0.998575i \(-0.483004\pi\)
0.0533677 + 0.998575i \(0.483004\pi\)
\(522\) 0 0
\(523\) −31.7452 −1.38812 −0.694061 0.719916i \(-0.744180\pi\)
−0.694061 + 0.719916i \(0.744180\pi\)
\(524\) 0 0
\(525\) −3.32922 −0.145299
\(526\) 0 0
\(527\) −9.41133 −0.409964
\(528\) 0 0
\(529\) 21.2201 0.922614
\(530\) 0 0
\(531\) −13.5679 −0.588797
\(532\) 0 0
\(533\) −22.6725 −0.982055
\(534\) 0 0
\(535\) −29.2663 −1.26529
\(536\) 0 0
\(537\) −20.4455 −0.882290
\(538\) 0 0
\(539\) 28.4564 1.22570
\(540\) 0 0
\(541\) 0.211389 0.00908834 0.00454417 0.999990i \(-0.498554\pi\)
0.00454417 + 0.999990i \(0.498554\pi\)
\(542\) 0 0
\(543\) −45.5385 −1.95424
\(544\) 0 0
\(545\) 0.0789563 0.00338212
\(546\) 0 0
\(547\) 8.20570 0.350850 0.175425 0.984493i \(-0.443870\pi\)
0.175425 + 0.984493i \(0.443870\pi\)
\(548\) 0 0
\(549\) 14.4869 0.618285
\(550\) 0 0
\(551\) −0.138726 −0.00590992
\(552\) 0 0
\(553\) 5.05581 0.214995
\(554\) 0 0
\(555\) 45.1990 1.91859
\(556\) 0 0
\(557\) −39.8194 −1.68720 −0.843602 0.536970i \(-0.819569\pi\)
−0.843602 + 0.536970i \(0.819569\pi\)
\(558\) 0 0
\(559\) 37.6283 1.59151
\(560\) 0 0
\(561\) 21.8864 0.924044
\(562\) 0 0
\(563\) −5.24909 −0.221223 −0.110611 0.993864i \(-0.535281\pi\)
−0.110611 + 0.993864i \(0.535281\pi\)
\(564\) 0 0
\(565\) 4.12334 0.173470
\(566\) 0 0
\(567\) 3.62583 0.152270
\(568\) 0 0
\(569\) −8.91025 −0.373537 −0.186769 0.982404i \(-0.559801\pi\)
−0.186769 + 0.982404i \(0.559801\pi\)
\(570\) 0 0
\(571\) 14.0518 0.588051 0.294025 0.955798i \(-0.405005\pi\)
0.294025 + 0.955798i \(0.405005\pi\)
\(572\) 0 0
\(573\) −48.2426 −2.01536
\(574\) 0 0
\(575\) −18.2497 −0.761067
\(576\) 0 0
\(577\) 2.31977 0.0965735 0.0482867 0.998834i \(-0.484624\pi\)
0.0482867 + 0.998834i \(0.484624\pi\)
\(578\) 0 0
\(579\) 6.86407 0.285261
\(580\) 0 0
\(581\) 5.81894 0.241410
\(582\) 0 0
\(583\) −51.4682 −2.13160
\(584\) 0 0
\(585\) 22.2218 0.918757
\(586\) 0 0
\(587\) 7.53569 0.311031 0.155516 0.987833i \(-0.450296\pi\)
0.155516 + 0.987833i \(0.450296\pi\)
\(588\) 0 0
\(589\) 2.45248 0.101053
\(590\) 0 0
\(591\) 33.7322 1.38756
\(592\) 0 0
\(593\) 20.1818 0.828768 0.414384 0.910102i \(-0.363997\pi\)
0.414384 + 0.910102i \(0.363997\pi\)
\(594\) 0 0
\(595\) −1.47831 −0.0606050
\(596\) 0 0
\(597\) 6.80802 0.278634
\(598\) 0 0
\(599\) 11.2813 0.460943 0.230471 0.973079i \(-0.425973\pi\)
0.230471 + 0.973079i \(0.425973\pi\)
\(600\) 0 0
\(601\) −37.6425 −1.53547 −0.767734 0.640769i \(-0.778616\pi\)
−0.767734 + 0.640769i \(0.778616\pi\)
\(602\) 0 0
\(603\) −50.7921 −2.06841
\(604\) 0 0
\(605\) 10.0087 0.406910
\(606\) 0 0
\(607\) 38.9414 1.58058 0.790291 0.612732i \(-0.209929\pi\)
0.790291 + 0.612732i \(0.209929\pi\)
\(608\) 0 0
\(609\) 0.314170 0.0127308
\(610\) 0 0
\(611\) 50.1564 2.02911
\(612\) 0 0
\(613\) −33.6687 −1.35987 −0.679934 0.733274i \(-0.737991\pi\)
−0.679934 + 0.733274i \(0.737991\pi\)
\(614\) 0 0
\(615\) 19.9264 0.803511
\(616\) 0 0
\(617\) 6.86536 0.276389 0.138194 0.990405i \(-0.455870\pi\)
0.138194 + 0.990405i \(0.455870\pi\)
\(618\) 0 0
\(619\) 14.3773 0.577873 0.288936 0.957348i \(-0.406698\pi\)
0.288936 + 0.957348i \(0.406698\pi\)
\(620\) 0 0
\(621\) −7.03895 −0.282464
\(622\) 0 0
\(623\) −2.58456 −0.103548
\(624\) 0 0
\(625\) −3.74632 −0.149853
\(626\) 0 0
\(627\) −5.70333 −0.227769
\(628\) 0 0
\(629\) −24.4195 −0.973669
\(630\) 0 0
\(631\) −23.1422 −0.921278 −0.460639 0.887588i \(-0.652380\pi\)
−0.460639 + 0.887588i \(0.652380\pi\)
\(632\) 0 0
\(633\) −24.2117 −0.962328
\(634\) 0 0
\(635\) 23.1578 0.918989
\(636\) 0 0
\(637\) −29.3109 −1.16134
\(638\) 0 0
\(639\) 55.9149 2.21196
\(640\) 0 0
\(641\) 25.5776 1.01026 0.505128 0.863045i \(-0.331445\pi\)
0.505128 + 0.863045i \(0.331445\pi\)
\(642\) 0 0
\(643\) −2.45113 −0.0966633 −0.0483316 0.998831i \(-0.515390\pi\)
−0.0483316 + 0.998831i \(0.515390\pi\)
\(644\) 0 0
\(645\) −33.0708 −1.30216
\(646\) 0 0
\(647\) −43.9315 −1.72712 −0.863562 0.504243i \(-0.831772\pi\)
−0.863562 + 0.504243i \(0.831772\pi\)
\(648\) 0 0
\(649\) 16.6843 0.654917
\(650\) 0 0
\(651\) −5.55409 −0.217682
\(652\) 0 0
\(653\) 35.4190 1.38605 0.693025 0.720913i \(-0.256277\pi\)
0.693025 + 0.720913i \(0.256277\pi\)
\(654\) 0 0
\(655\) −20.8220 −0.813584
\(656\) 0 0
\(657\) 20.9005 0.815406
\(658\) 0 0
\(659\) −40.6085 −1.58188 −0.790940 0.611893i \(-0.790408\pi\)
−0.790940 + 0.611893i \(0.790408\pi\)
\(660\) 0 0
\(661\) 8.84140 0.343891 0.171945 0.985106i \(-0.444995\pi\)
0.171945 + 0.985106i \(0.444995\pi\)
\(662\) 0 0
\(663\) −22.5436 −0.875522
\(664\) 0 0
\(665\) 0.385231 0.0149386
\(666\) 0 0
\(667\) 1.72218 0.0666832
\(668\) 0 0
\(669\) 10.7360 0.415079
\(670\) 0 0
\(671\) −17.8144 −0.687716
\(672\) 0 0
\(673\) 43.8126 1.68885 0.844426 0.535672i \(-0.179942\pi\)
0.844426 + 0.535672i \(0.179942\pi\)
\(674\) 0 0
\(675\) 2.90499 0.111813
\(676\) 0 0
\(677\) −32.7378 −1.25822 −0.629109 0.777317i \(-0.716580\pi\)
−0.629109 + 0.777317i \(0.716580\pi\)
\(678\) 0 0
\(679\) −6.71361 −0.257645
\(680\) 0 0
\(681\) −5.64948 −0.216488
\(682\) 0 0
\(683\) 18.2997 0.700218 0.350109 0.936709i \(-0.386145\pi\)
0.350109 + 0.936709i \(0.386145\pi\)
\(684\) 0 0
\(685\) −21.6788 −0.828303
\(686\) 0 0
\(687\) −68.9879 −2.63205
\(688\) 0 0
\(689\) 53.0138 2.01966
\(690\) 0 0
\(691\) −19.0415 −0.724372 −0.362186 0.932106i \(-0.617969\pi\)
−0.362186 + 0.932106i \(0.617969\pi\)
\(692\) 0 0
\(693\) 6.87858 0.261296
\(694\) 0 0
\(695\) 34.3943 1.30465
\(696\) 0 0
\(697\) −10.7656 −0.407775
\(698\) 0 0
\(699\) −44.1338 −1.66929
\(700\) 0 0
\(701\) −42.8488 −1.61838 −0.809189 0.587549i \(-0.800093\pi\)
−0.809189 + 0.587549i \(0.800093\pi\)
\(702\) 0 0
\(703\) 6.36343 0.240001
\(704\) 0 0
\(705\) −44.0815 −1.66020
\(706\) 0 0
\(707\) 0.0460905 0.00173341
\(708\) 0 0
\(709\) −33.0324 −1.24056 −0.620279 0.784382i \(-0.712980\pi\)
−0.620279 + 0.784382i \(0.712980\pi\)
\(710\) 0 0
\(711\) −36.0861 −1.35334
\(712\) 0 0
\(713\) −30.4458 −1.14020
\(714\) 0 0
\(715\) −27.3259 −1.02193
\(716\) 0 0
\(717\) −74.0211 −2.76437
\(718\) 0 0
\(719\) −44.0194 −1.64165 −0.820824 0.571182i \(-0.806485\pi\)
−0.820824 + 0.571182i \(0.806485\pi\)
\(720\) 0 0
\(721\) −5.14239 −0.191513
\(722\) 0 0
\(723\) 2.00918 0.0747223
\(724\) 0 0
\(725\) −0.710749 −0.0263965
\(726\) 0 0
\(727\) 11.1168 0.412300 0.206150 0.978520i \(-0.433906\pi\)
0.206150 + 0.978520i \(0.433906\pi\)
\(728\) 0 0
\(729\) −33.9243 −1.25646
\(730\) 0 0
\(731\) 17.8670 0.660836
\(732\) 0 0
\(733\) −11.6867 −0.431659 −0.215829 0.976431i \(-0.569246\pi\)
−0.215829 + 0.976431i \(0.569246\pi\)
\(734\) 0 0
\(735\) 25.7608 0.950201
\(736\) 0 0
\(737\) 62.4584 2.30069
\(738\) 0 0
\(739\) 44.9919 1.65505 0.827527 0.561426i \(-0.189747\pi\)
0.827527 + 0.561426i \(0.189747\pi\)
\(740\) 0 0
\(741\) 5.87460 0.215809
\(742\) 0 0
\(743\) −26.7461 −0.981220 −0.490610 0.871379i \(-0.663226\pi\)
−0.490610 + 0.871379i \(0.663226\pi\)
\(744\) 0 0
\(745\) −14.1257 −0.517525
\(746\) 0 0
\(747\) −41.5330 −1.51961
\(748\) 0 0
\(749\) 9.33121 0.340955
\(750\) 0 0
\(751\) 12.7444 0.465049 0.232525 0.972591i \(-0.425301\pi\)
0.232525 + 0.972591i \(0.425301\pi\)
\(752\) 0 0
\(753\) −2.53334 −0.0923202
\(754\) 0 0
\(755\) 10.9950 0.400150
\(756\) 0 0
\(757\) 10.2279 0.371739 0.185870 0.982574i \(-0.440490\pi\)
0.185870 + 0.982574i \(0.440490\pi\)
\(758\) 0 0
\(759\) 70.8028 2.56998
\(760\) 0 0
\(761\) 22.1670 0.803555 0.401777 0.915737i \(-0.368393\pi\)
0.401777 + 0.915737i \(0.368393\pi\)
\(762\) 0 0
\(763\) −0.0251743 −0.000911370 0
\(764\) 0 0
\(765\) 10.5515 0.381492
\(766\) 0 0
\(767\) −17.1853 −0.620527
\(768\) 0 0
\(769\) 51.3208 1.85067 0.925337 0.379146i \(-0.123782\pi\)
0.925337 + 0.379146i \(0.123782\pi\)
\(770\) 0 0
\(771\) 14.8705 0.535547
\(772\) 0 0
\(773\) 6.17332 0.222039 0.111019 0.993818i \(-0.464588\pi\)
0.111019 + 0.993818i \(0.464588\pi\)
\(774\) 0 0
\(775\) 12.5650 0.451350
\(776\) 0 0
\(777\) −14.4112 −0.516997
\(778\) 0 0
\(779\) 2.80538 0.100513
\(780\) 0 0
\(781\) −68.7580 −2.46035
\(782\) 0 0
\(783\) −0.274137 −0.00979686
\(784\) 0 0
\(785\) 10.6794 0.381164
\(786\) 0 0
\(787\) −19.7681 −0.704658 −0.352329 0.935876i \(-0.614610\pi\)
−0.352329 + 0.935876i \(0.614610\pi\)
\(788\) 0 0
\(789\) −41.1509 −1.46501
\(790\) 0 0
\(791\) −1.31468 −0.0467446
\(792\) 0 0
\(793\) 18.3493 0.651604
\(794\) 0 0
\(795\) −46.5928 −1.65248
\(796\) 0 0
\(797\) −0.193962 −0.00687048 −0.00343524 0.999994i \(-0.501093\pi\)
−0.00343524 + 0.999994i \(0.501093\pi\)
\(798\) 0 0
\(799\) 23.8157 0.842540
\(800\) 0 0
\(801\) 18.4474 0.651808
\(802\) 0 0
\(803\) −25.7011 −0.906973
\(804\) 0 0
\(805\) −4.78237 −0.168556
\(806\) 0 0
\(807\) −52.2802 −1.84035
\(808\) 0 0
\(809\) −25.7244 −0.904422 −0.452211 0.891911i \(-0.649365\pi\)
−0.452211 + 0.891911i \(0.649365\pi\)
\(810\) 0 0
\(811\) −27.3805 −0.961459 −0.480730 0.876869i \(-0.659628\pi\)
−0.480730 + 0.876869i \(0.659628\pi\)
\(812\) 0 0
\(813\) −78.5711 −2.75561
\(814\) 0 0
\(815\) 9.54376 0.334303
\(816\) 0 0
\(817\) −4.65593 −0.162891
\(818\) 0 0
\(819\) −7.08514 −0.247575
\(820\) 0 0
\(821\) −22.8188 −0.796380 −0.398190 0.917303i \(-0.630362\pi\)
−0.398190 + 0.917303i \(0.630362\pi\)
\(822\) 0 0
\(823\) −34.9298 −1.21758 −0.608789 0.793332i \(-0.708344\pi\)
−0.608789 + 0.793332i \(0.708344\pi\)
\(824\) 0 0
\(825\) −29.2205 −1.01733
\(826\) 0 0
\(827\) −8.95134 −0.311269 −0.155634 0.987815i \(-0.549742\pi\)
−0.155634 + 0.987815i \(0.549742\pi\)
\(828\) 0 0
\(829\) 40.6186 1.41074 0.705372 0.708838i \(-0.250780\pi\)
0.705372 + 0.708838i \(0.250780\pi\)
\(830\) 0 0
\(831\) −12.4206 −0.430866
\(832\) 0 0
\(833\) −13.9177 −0.482220
\(834\) 0 0
\(835\) 12.7254 0.440382
\(836\) 0 0
\(837\) 4.84636 0.167515
\(838\) 0 0
\(839\) −23.2914 −0.804108 −0.402054 0.915616i \(-0.631704\pi\)
−0.402054 + 0.915616i \(0.631704\pi\)
\(840\) 0 0
\(841\) −28.9329 −0.997687
\(842\) 0 0
\(843\) −39.7838 −1.37023
\(844\) 0 0
\(845\) 8.62217 0.296612
\(846\) 0 0
\(847\) −3.19114 −0.109649
\(848\) 0 0
\(849\) 46.1794 1.58487
\(850\) 0 0
\(851\) −78.9974 −2.70800
\(852\) 0 0
\(853\) 5.70196 0.195231 0.0976157 0.995224i \(-0.468878\pi\)
0.0976157 + 0.995224i \(0.468878\pi\)
\(854\) 0 0
\(855\) −2.74961 −0.0940345
\(856\) 0 0
\(857\) 3.35878 0.114734 0.0573669 0.998353i \(-0.481730\pi\)
0.0573669 + 0.998353i \(0.481730\pi\)
\(858\) 0 0
\(859\) 9.73347 0.332102 0.166051 0.986117i \(-0.446898\pi\)
0.166051 + 0.986117i \(0.446898\pi\)
\(860\) 0 0
\(861\) −6.35330 −0.216520
\(862\) 0 0
\(863\) 9.75375 0.332022 0.166011 0.986124i \(-0.446911\pi\)
0.166011 + 0.986124i \(0.446911\pi\)
\(864\) 0 0
\(865\) 21.3670 0.726500
\(866\) 0 0
\(867\) 32.3625 1.09909
\(868\) 0 0
\(869\) 44.3747 1.50531
\(870\) 0 0
\(871\) −64.3340 −2.17988
\(872\) 0 0
\(873\) 47.9187 1.62180
\(874\) 0 0
\(875\) 5.56956 0.188285
\(876\) 0 0
\(877\) −11.7419 −0.396495 −0.198247 0.980152i \(-0.563525\pi\)
−0.198247 + 0.980152i \(0.563525\pi\)
\(878\) 0 0
\(879\) 3.74401 0.126282
\(880\) 0 0
\(881\) 37.1291 1.25091 0.625456 0.780259i \(-0.284913\pi\)
0.625456 + 0.780259i \(0.284913\pi\)
\(882\) 0 0
\(883\) 18.9646 0.638210 0.319105 0.947719i \(-0.396618\pi\)
0.319105 + 0.947719i \(0.396618\pi\)
\(884\) 0 0
\(885\) 15.1039 0.507711
\(886\) 0 0
\(887\) 23.0150 0.772770 0.386385 0.922338i \(-0.373724\pi\)
0.386385 + 0.922338i \(0.373724\pi\)
\(888\) 0 0
\(889\) −7.38359 −0.247638
\(890\) 0 0
\(891\) 31.8238 1.06614
\(892\) 0 0
\(893\) −6.20609 −0.207679
\(894\) 0 0
\(895\) 12.1209 0.405158
\(896\) 0 0
\(897\) −72.9290 −2.43503
\(898\) 0 0
\(899\) −1.18573 −0.0395464
\(900\) 0 0
\(901\) 25.1725 0.838618
\(902\) 0 0
\(903\) 10.5442 0.350890
\(904\) 0 0
\(905\) 26.9970 0.897411
\(906\) 0 0
\(907\) 23.5773 0.782873 0.391436 0.920205i \(-0.371978\pi\)
0.391436 + 0.920205i \(0.371978\pi\)
\(908\) 0 0
\(909\) −0.328973 −0.0109114
\(910\) 0 0
\(911\) 20.6900 0.685492 0.342746 0.939428i \(-0.388643\pi\)
0.342746 + 0.939428i \(0.388643\pi\)
\(912\) 0 0
\(913\) 51.0727 1.69026
\(914\) 0 0
\(915\) −16.1269 −0.533137
\(916\) 0 0
\(917\) 6.63886 0.219234
\(918\) 0 0
\(919\) −39.6254 −1.30712 −0.653560 0.756875i \(-0.726725\pi\)
−0.653560 + 0.756875i \(0.726725\pi\)
\(920\) 0 0
\(921\) −72.7736 −2.39797
\(922\) 0 0
\(923\) 70.8227 2.33116
\(924\) 0 0
\(925\) 32.6024 1.07196
\(926\) 0 0
\(927\) 36.7041 1.20552
\(928\) 0 0
\(929\) −8.16495 −0.267883 −0.133942 0.990989i \(-0.542763\pi\)
−0.133942 + 0.990989i \(0.542763\pi\)
\(930\) 0 0
\(931\) 3.62678 0.118863
\(932\) 0 0
\(933\) 45.2240 1.48057
\(934\) 0 0
\(935\) −12.9751 −0.424332
\(936\) 0 0
\(937\) −15.2089 −0.496853 −0.248426 0.968651i \(-0.579913\pi\)
−0.248426 + 0.968651i \(0.579913\pi\)
\(938\) 0 0
\(939\) 35.3026 1.15206
\(940\) 0 0
\(941\) 28.5538 0.930827 0.465414 0.885093i \(-0.345906\pi\)
0.465414 + 0.885093i \(0.345906\pi\)
\(942\) 0 0
\(943\) −34.8268 −1.13412
\(944\) 0 0
\(945\) 0.761257 0.0247637
\(946\) 0 0
\(947\) −15.8580 −0.515317 −0.257658 0.966236i \(-0.582951\pi\)
−0.257658 + 0.966236i \(0.582951\pi\)
\(948\) 0 0
\(949\) 26.4729 0.859347
\(950\) 0 0
\(951\) −44.6199 −1.44690
\(952\) 0 0
\(953\) −15.4793 −0.501423 −0.250711 0.968062i \(-0.580665\pi\)
−0.250711 + 0.968062i \(0.580665\pi\)
\(954\) 0 0
\(955\) 28.6001 0.925479
\(956\) 0 0
\(957\) 2.75746 0.0891361
\(958\) 0 0
\(959\) 6.91202 0.223201
\(960\) 0 0
\(961\) −10.0379 −0.323804
\(962\) 0 0
\(963\) −66.6020 −2.14622
\(964\) 0 0
\(965\) −4.06929 −0.130995
\(966\) 0 0
\(967\) 46.7818 1.50440 0.752201 0.658933i \(-0.228992\pi\)
0.752201 + 0.658933i \(0.228992\pi\)
\(968\) 0 0
\(969\) 2.78943 0.0896095
\(970\) 0 0
\(971\) −4.16808 −0.133760 −0.0668801 0.997761i \(-0.521304\pi\)
−0.0668801 + 0.997761i \(0.521304\pi\)
\(972\) 0 0
\(973\) −10.9662 −0.351561
\(974\) 0 0
\(975\) 30.0980 0.963906
\(976\) 0 0
\(977\) 10.8271 0.346389 0.173195 0.984888i \(-0.444591\pi\)
0.173195 + 0.984888i \(0.444591\pi\)
\(978\) 0 0
\(979\) −22.6846 −0.725003
\(980\) 0 0
\(981\) 0.179683 0.00573683
\(982\) 0 0
\(983\) −30.8392 −0.983616 −0.491808 0.870704i \(-0.663664\pi\)
−0.491808 + 0.870704i \(0.663664\pi\)
\(984\) 0 0
\(985\) −19.9978 −0.637182
\(986\) 0 0
\(987\) 14.0548 0.447371
\(988\) 0 0
\(989\) 57.8001 1.83794
\(990\) 0 0
\(991\) 22.0982 0.701973 0.350987 0.936380i \(-0.385846\pi\)
0.350987 + 0.936380i \(0.385846\pi\)
\(992\) 0 0
\(993\) −30.4787 −0.967212
\(994\) 0 0
\(995\) −4.03606 −0.127952
\(996\) 0 0
\(997\) 5.31981 0.168480 0.0842400 0.996445i \(-0.473154\pi\)
0.0842400 + 0.996445i \(0.473154\pi\)
\(998\) 0 0
\(999\) 12.5748 0.397849
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 4016.2.a.m.1.5 23
4.3 odd 2 2008.2.a.d.1.19 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.19 23 4.3 odd 2
4016.2.a.m.1.5 23 1.1 even 1 trivial