Properties

Label 4016.2.a.m.1.19
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 1.19
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.21536 q^{3} +3.09704 q^{5} +4.67984 q^{7} +1.90784 q^{9} +O(q^{10})\) \(q+2.21536 q^{3} +3.09704 q^{5} +4.67984 q^{7} +1.90784 q^{9} +4.76411 q^{11} -4.18229 q^{13} +6.86107 q^{15} -2.76575 q^{17} +4.43902 q^{19} +10.3676 q^{21} -8.88455 q^{23} +4.59165 q^{25} -2.41954 q^{27} +2.14992 q^{29} -7.46623 q^{31} +10.5542 q^{33} +14.4937 q^{35} +9.30620 q^{37} -9.26530 q^{39} -8.39778 q^{41} +3.77980 q^{43} +5.90865 q^{45} +3.41612 q^{47} +14.9009 q^{49} -6.12714 q^{51} +11.5655 q^{53} +14.7546 q^{55} +9.83404 q^{57} -0.620556 q^{59} -11.0665 q^{61} +8.92838 q^{63} -12.9527 q^{65} -3.88032 q^{67} -19.6825 q^{69} -5.36865 q^{71} +1.41033 q^{73} +10.1722 q^{75} +22.2953 q^{77} -6.15937 q^{79} -11.0837 q^{81} -4.20676 q^{83} -8.56563 q^{85} +4.76286 q^{87} -16.8333 q^{89} -19.5725 q^{91} -16.5404 q^{93} +13.7478 q^{95} +9.25212 q^{97} +9.08915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) 2.21536 1.27904 0.639520 0.768774i \(-0.279133\pi\)
0.639520 + 0.768774i \(0.279133\pi\)
\(4\) 0 0
\(5\) 3.09704 1.38504 0.692519 0.721400i \(-0.256501\pi\)
0.692519 + 0.721400i \(0.256501\pi\)
\(6\) 0 0
\(7\) 4.67984 1.76881 0.884407 0.466716i \(-0.154563\pi\)
0.884407 + 0.466716i \(0.154563\pi\)
\(8\) 0 0
\(9\) 1.90784 0.635946
\(10\) 0 0
\(11\) 4.76411 1.43643 0.718217 0.695819i \(-0.244959\pi\)
0.718217 + 0.695819i \(0.244959\pi\)
\(12\) 0 0
\(13\) −4.18229 −1.15996 −0.579980 0.814631i \(-0.696940\pi\)
−0.579980 + 0.814631i \(0.696940\pi\)
\(14\) 0 0
\(15\) 6.86107 1.77152
\(16\) 0 0
\(17\) −2.76575 −0.670792 −0.335396 0.942077i \(-0.608870\pi\)
−0.335396 + 0.942077i \(0.608870\pi\)
\(18\) 0 0
\(19\) 4.43902 1.01838 0.509190 0.860654i \(-0.329945\pi\)
0.509190 + 0.860654i \(0.329945\pi\)
\(20\) 0 0
\(21\) 10.3676 2.26239
\(22\) 0 0
\(23\) −8.88455 −1.85256 −0.926279 0.376840i \(-0.877011\pi\)
−0.926279 + 0.376840i \(0.877011\pi\)
\(24\) 0 0
\(25\) 4.59165 0.918331
\(26\) 0 0
\(27\) −2.41954 −0.465640
\(28\) 0 0
\(29\) 2.14992 0.399231 0.199615 0.979874i \(-0.436031\pi\)
0.199615 + 0.979874i \(0.436031\pi\)
\(30\) 0 0
\(31\) −7.46623 −1.34098 −0.670488 0.741921i \(-0.733915\pi\)
−0.670488 + 0.741921i \(0.733915\pi\)
\(32\) 0 0
\(33\) 10.5542 1.83726
\(34\) 0 0
\(35\) 14.4937 2.44988
\(36\) 0 0
\(37\) 9.30620 1.52993 0.764965 0.644072i \(-0.222756\pi\)
0.764965 + 0.644072i \(0.222756\pi\)
\(38\) 0 0
\(39\) −9.26530 −1.48364
\(40\) 0 0
\(41\) −8.39778 −1.31151 −0.655756 0.754973i \(-0.727650\pi\)
−0.655756 + 0.754973i \(0.727650\pi\)
\(42\) 0 0
\(43\) 3.77980 0.576413 0.288207 0.957568i \(-0.406941\pi\)
0.288207 + 0.957568i \(0.406941\pi\)
\(44\) 0 0
\(45\) 5.90865 0.880809
\(46\) 0 0
\(47\) 3.41612 0.498293 0.249146 0.968466i \(-0.419850\pi\)
0.249146 + 0.968466i \(0.419850\pi\)
\(48\) 0 0
\(49\) 14.9009 2.12870
\(50\) 0 0
\(51\) −6.12714 −0.857971
\(52\) 0 0
\(53\) 11.5655 1.58865 0.794323 0.607496i \(-0.207826\pi\)
0.794323 + 0.607496i \(0.207826\pi\)
\(54\) 0 0
\(55\) 14.7546 1.98952
\(56\) 0 0
\(57\) 9.83404 1.30255
\(58\) 0 0
\(59\) −0.620556 −0.0807895 −0.0403947 0.999184i \(-0.512862\pi\)
−0.0403947 + 0.999184i \(0.512862\pi\)
\(60\) 0 0
\(61\) −11.0665 −1.41692 −0.708460 0.705751i \(-0.750610\pi\)
−0.708460 + 0.705751i \(0.750610\pi\)
\(62\) 0 0
\(63\) 8.92838 1.12487
\(64\) 0 0
\(65\) −12.9527 −1.60659
\(66\) 0 0
\(67\) −3.88032 −0.474056 −0.237028 0.971503i \(-0.576173\pi\)
−0.237028 + 0.971503i \(0.576173\pi\)
\(68\) 0 0
\(69\) −19.6825 −2.36950
\(70\) 0 0
\(71\) −5.36865 −0.637142 −0.318571 0.947899i \(-0.603203\pi\)
−0.318571 + 0.947899i \(0.603203\pi\)
\(72\) 0 0
\(73\) 1.41033 0.165066 0.0825331 0.996588i \(-0.473699\pi\)
0.0825331 + 0.996588i \(0.473699\pi\)
\(74\) 0 0
\(75\) 10.1722 1.17458
\(76\) 0 0
\(77\) 22.2953 2.54078
\(78\) 0 0
\(79\) −6.15937 −0.692983 −0.346492 0.938053i \(-0.612627\pi\)
−0.346492 + 0.938053i \(0.612627\pi\)
\(80\) 0 0
\(81\) −11.0837 −1.23152
\(82\) 0 0
\(83\) −4.20676 −0.461752 −0.230876 0.972983i \(-0.574159\pi\)
−0.230876 + 0.972983i \(0.574159\pi\)
\(84\) 0 0
\(85\) −8.56563 −0.929073
\(86\) 0 0
\(87\) 4.76286 0.510632
\(88\) 0 0
\(89\) −16.8333 −1.78433 −0.892164 0.451712i \(-0.850814\pi\)
−0.892164 + 0.451712i \(0.850814\pi\)
\(90\) 0 0
\(91\) −19.5725 −2.05175
\(92\) 0 0
\(93\) −16.5404 −1.71516
\(94\) 0 0
\(95\) 13.7478 1.41050
\(96\) 0 0
\(97\) 9.25212 0.939411 0.469705 0.882823i \(-0.344360\pi\)
0.469705 + 0.882823i \(0.344360\pi\)
\(98\) 0 0
\(99\) 9.08915 0.913494
\(100\) 0 0
\(101\) 3.90761 0.388821 0.194411 0.980920i \(-0.437721\pi\)
0.194411 + 0.980920i \(0.437721\pi\)
\(102\) 0 0
\(103\) 0.244985 0.0241391 0.0120695 0.999927i \(-0.496158\pi\)
0.0120695 + 0.999927i \(0.496158\pi\)
\(104\) 0 0
\(105\) 32.1087 3.13349
\(106\) 0 0
\(107\) −2.64689 −0.255884 −0.127942 0.991782i \(-0.540837\pi\)
−0.127942 + 0.991782i \(0.540837\pi\)
\(108\) 0 0
\(109\) 19.7928 1.89581 0.947905 0.318554i \(-0.103197\pi\)
0.947905 + 0.318554i \(0.103197\pi\)
\(110\) 0 0
\(111\) 20.6166 1.95684
\(112\) 0 0
\(113\) 8.57936 0.807079 0.403539 0.914962i \(-0.367780\pi\)
0.403539 + 0.914962i \(0.367780\pi\)
\(114\) 0 0
\(115\) −27.5158 −2.56586
\(116\) 0 0
\(117\) −7.97914 −0.737671
\(118\) 0 0
\(119\) −12.9433 −1.18651
\(120\) 0 0
\(121\) 11.6968 1.06334
\(122\) 0 0
\(123\) −18.6041 −1.67748
\(124\) 0 0
\(125\) −1.26466 −0.113115
\(126\) 0 0
\(127\) 2.05904 0.182710 0.0913552 0.995818i \(-0.470880\pi\)
0.0913552 + 0.995818i \(0.470880\pi\)
\(128\) 0 0
\(129\) 8.37362 0.737256
\(130\) 0 0
\(131\) 8.45887 0.739055 0.369527 0.929220i \(-0.379520\pi\)
0.369527 + 0.929220i \(0.379520\pi\)
\(132\) 0 0
\(133\) 20.7739 1.80133
\(134\) 0 0
\(135\) −7.49341 −0.644930
\(136\) 0 0
\(137\) −11.8914 −1.01595 −0.507977 0.861370i \(-0.669607\pi\)
−0.507977 + 0.861370i \(0.669607\pi\)
\(138\) 0 0
\(139\) −17.0936 −1.44986 −0.724932 0.688821i \(-0.758129\pi\)
−0.724932 + 0.688821i \(0.758129\pi\)
\(140\) 0 0
\(141\) 7.56796 0.637337
\(142\) 0 0
\(143\) −19.9249 −1.66621
\(144\) 0 0
\(145\) 6.65840 0.552950
\(146\) 0 0
\(147\) 33.0110 2.72270
\(148\) 0 0
\(149\) −14.0639 −1.15216 −0.576079 0.817394i \(-0.695418\pi\)
−0.576079 + 0.817394i \(0.695418\pi\)
\(150\) 0 0
\(151\) −17.7621 −1.44546 −0.722731 0.691129i \(-0.757113\pi\)
−0.722731 + 0.691129i \(0.757113\pi\)
\(152\) 0 0
\(153\) −5.27659 −0.426587
\(154\) 0 0
\(155\) −23.1232 −1.85730
\(156\) 0 0
\(157\) −20.5184 −1.63755 −0.818774 0.574116i \(-0.805346\pi\)
−0.818774 + 0.574116i \(0.805346\pi\)
\(158\) 0 0
\(159\) 25.6218 2.03194
\(160\) 0 0
\(161\) −41.5783 −3.27683
\(162\) 0 0
\(163\) 8.63658 0.676469 0.338235 0.941062i \(-0.390170\pi\)
0.338235 + 0.941062i \(0.390170\pi\)
\(164\) 0 0
\(165\) 32.6869 2.54467
\(166\) 0 0
\(167\) −21.3671 −1.65344 −0.826719 0.562615i \(-0.809795\pi\)
−0.826719 + 0.562615i \(0.809795\pi\)
\(168\) 0 0
\(169\) 4.49159 0.345507
\(170\) 0 0
\(171\) 8.46892 0.647635
\(172\) 0 0
\(173\) 9.23508 0.702130 0.351065 0.936351i \(-0.385820\pi\)
0.351065 + 0.936351i \(0.385820\pi\)
\(174\) 0 0
\(175\) 21.4882 1.62436
\(176\) 0 0
\(177\) −1.37476 −0.103333
\(178\) 0 0
\(179\) 20.4876 1.53131 0.765657 0.643249i \(-0.222414\pi\)
0.765657 + 0.643249i \(0.222414\pi\)
\(180\) 0 0
\(181\) −8.31659 −0.618167 −0.309084 0.951035i \(-0.600022\pi\)
−0.309084 + 0.951035i \(0.600022\pi\)
\(182\) 0 0
\(183\) −24.5163 −1.81230
\(184\) 0 0
\(185\) 28.8217 2.11901
\(186\) 0 0
\(187\) −13.1763 −0.963548
\(188\) 0 0
\(189\) −11.3231 −0.823631
\(190\) 0 0
\(191\) 14.9096 1.07882 0.539411 0.842043i \(-0.318647\pi\)
0.539411 + 0.842043i \(0.318647\pi\)
\(192\) 0 0
\(193\) 25.6297 1.84486 0.922432 0.386159i \(-0.126198\pi\)
0.922432 + 0.386159i \(0.126198\pi\)
\(194\) 0 0
\(195\) −28.6950 −2.05489
\(196\) 0 0
\(197\) 5.72377 0.407802 0.203901 0.978992i \(-0.434638\pi\)
0.203901 + 0.978992i \(0.434638\pi\)
\(198\) 0 0
\(199\) −12.6418 −0.896154 −0.448077 0.893995i \(-0.647891\pi\)
−0.448077 + 0.893995i \(0.647891\pi\)
\(200\) 0 0
\(201\) −8.59631 −0.606337
\(202\) 0 0
\(203\) 10.0613 0.706165
\(204\) 0 0
\(205\) −26.0082 −1.81649
\(206\) 0 0
\(207\) −16.9503 −1.17813
\(208\) 0 0
\(209\) 21.1480 1.46284
\(210\) 0 0
\(211\) 16.1293 1.11039 0.555194 0.831721i \(-0.312644\pi\)
0.555194 + 0.831721i \(0.312644\pi\)
\(212\) 0 0
\(213\) −11.8935 −0.814930
\(214\) 0 0
\(215\) 11.7062 0.798355
\(216\) 0 0
\(217\) −34.9408 −2.37194
\(218\) 0 0
\(219\) 3.12439 0.211126
\(220\) 0 0
\(221\) 11.5672 0.778092
\(222\) 0 0
\(223\) −11.9175 −0.798053 −0.399026 0.916939i \(-0.630652\pi\)
−0.399026 + 0.916939i \(0.630652\pi\)
\(224\) 0 0
\(225\) 8.76013 0.584009
\(226\) 0 0
\(227\) 5.85776 0.388793 0.194397 0.980923i \(-0.437725\pi\)
0.194397 + 0.980923i \(0.437725\pi\)
\(228\) 0 0
\(229\) 4.73938 0.313187 0.156594 0.987663i \(-0.449949\pi\)
0.156594 + 0.987663i \(0.449949\pi\)
\(230\) 0 0
\(231\) 49.3922 3.24977
\(232\) 0 0
\(233\) 3.31495 0.217169 0.108585 0.994087i \(-0.465368\pi\)
0.108585 + 0.994087i \(0.465368\pi\)
\(234\) 0 0
\(235\) 10.5799 0.690155
\(236\) 0 0
\(237\) −13.6452 −0.886354
\(238\) 0 0
\(239\) 0.512422 0.0331458 0.0165729 0.999863i \(-0.494724\pi\)
0.0165729 + 0.999863i \(0.494724\pi\)
\(240\) 0 0
\(241\) −14.4997 −0.934011 −0.467005 0.884254i \(-0.654667\pi\)
−0.467005 + 0.884254i \(0.654667\pi\)
\(242\) 0 0
\(243\) −17.2957 −1.10952
\(244\) 0 0
\(245\) 46.1488 2.94834
\(246\) 0 0
\(247\) −18.5653 −1.18128
\(248\) 0 0
\(249\) −9.31951 −0.590600
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) −42.3270 −2.66108
\(254\) 0 0
\(255\) −18.9760 −1.18832
\(256\) 0 0
\(257\) 28.3085 1.76584 0.882918 0.469527i \(-0.155576\pi\)
0.882918 + 0.469527i \(0.155576\pi\)
\(258\) 0 0
\(259\) 43.5515 2.70616
\(260\) 0 0
\(261\) 4.10170 0.253889
\(262\) 0 0
\(263\) −15.7409 −0.970625 −0.485312 0.874341i \(-0.661294\pi\)
−0.485312 + 0.874341i \(0.661294\pi\)
\(264\) 0 0
\(265\) 35.8189 2.20033
\(266\) 0 0
\(267\) −37.2919 −2.28223
\(268\) 0 0
\(269\) 0.435839 0.0265736 0.0132868 0.999912i \(-0.495771\pi\)
0.0132868 + 0.999912i \(0.495771\pi\)
\(270\) 0 0
\(271\) −18.6737 −1.13434 −0.567172 0.823599i \(-0.691963\pi\)
−0.567172 + 0.823599i \(0.691963\pi\)
\(272\) 0 0
\(273\) −43.3602 −2.62428
\(274\) 0 0
\(275\) 21.8752 1.31912
\(276\) 0 0
\(277\) 20.9307 1.25761 0.628803 0.777564i \(-0.283545\pi\)
0.628803 + 0.777564i \(0.283545\pi\)
\(278\) 0 0
\(279\) −14.2444 −0.852787
\(280\) 0 0
\(281\) 28.1763 1.68086 0.840428 0.541924i \(-0.182304\pi\)
0.840428 + 0.541924i \(0.182304\pi\)
\(282\) 0 0
\(283\) 23.7841 1.41382 0.706910 0.707303i \(-0.250088\pi\)
0.706910 + 0.707303i \(0.250088\pi\)
\(284\) 0 0
\(285\) 30.4564 1.80408
\(286\) 0 0
\(287\) −39.3003 −2.31982
\(288\) 0 0
\(289\) −9.35064 −0.550038
\(290\) 0 0
\(291\) 20.4968 1.20154
\(292\) 0 0
\(293\) −16.0129 −0.935482 −0.467741 0.883866i \(-0.654932\pi\)
−0.467741 + 0.883866i \(0.654932\pi\)
\(294\) 0 0
\(295\) −1.92189 −0.111897
\(296\) 0 0
\(297\) −11.5270 −0.668862
\(298\) 0 0
\(299\) 37.1578 2.14889
\(300\) 0 0
\(301\) 17.6888 1.01957
\(302\) 0 0
\(303\) 8.65677 0.497319
\(304\) 0 0
\(305\) −34.2734 −1.96249
\(306\) 0 0
\(307\) 1.39255 0.0794772 0.0397386 0.999210i \(-0.487347\pi\)
0.0397386 + 0.999210i \(0.487347\pi\)
\(308\) 0 0
\(309\) 0.542731 0.0308749
\(310\) 0 0
\(311\) −29.9348 −1.69745 −0.848724 0.528836i \(-0.822629\pi\)
−0.848724 + 0.528836i \(0.822629\pi\)
\(312\) 0 0
\(313\) −2.51730 −0.142286 −0.0711432 0.997466i \(-0.522665\pi\)
−0.0711432 + 0.997466i \(0.522665\pi\)
\(314\) 0 0
\(315\) 27.6515 1.55799
\(316\) 0 0
\(317\) 2.00168 0.112425 0.0562127 0.998419i \(-0.482098\pi\)
0.0562127 + 0.998419i \(0.482098\pi\)
\(318\) 0 0
\(319\) 10.2425 0.573468
\(320\) 0 0
\(321\) −5.86382 −0.327286
\(322\) 0 0
\(323\) −12.2772 −0.683121
\(324\) 0 0
\(325\) −19.2036 −1.06523
\(326\) 0 0
\(327\) 43.8483 2.42482
\(328\) 0 0
\(329\) 15.9869 0.881388
\(330\) 0 0
\(331\) 4.32431 0.237686 0.118843 0.992913i \(-0.462082\pi\)
0.118843 + 0.992913i \(0.462082\pi\)
\(332\) 0 0
\(333\) 17.7547 0.972952
\(334\) 0 0
\(335\) −12.0175 −0.656586
\(336\) 0 0
\(337\) 7.56938 0.412330 0.206165 0.978517i \(-0.433902\pi\)
0.206165 + 0.978517i \(0.433902\pi\)
\(338\) 0 0
\(339\) 19.0064 1.03229
\(340\) 0 0
\(341\) −35.5700 −1.92622
\(342\) 0 0
\(343\) 36.9751 1.99647
\(344\) 0 0
\(345\) −60.9575 −3.28184
\(346\) 0 0
\(347\) −21.7995 −1.17026 −0.585128 0.810941i \(-0.698956\pi\)
−0.585128 + 0.810941i \(0.698956\pi\)
\(348\) 0 0
\(349\) 15.6011 0.835109 0.417554 0.908652i \(-0.362887\pi\)
0.417554 + 0.908652i \(0.362887\pi\)
\(350\) 0 0
\(351\) 10.1192 0.540124
\(352\) 0 0
\(353\) 7.89144 0.420019 0.210010 0.977699i \(-0.432650\pi\)
0.210010 + 0.977699i \(0.432650\pi\)
\(354\) 0 0
\(355\) −16.6269 −0.882466
\(356\) 0 0
\(357\) −28.6740 −1.51759
\(358\) 0 0
\(359\) −3.07626 −0.162359 −0.0811794 0.996700i \(-0.525869\pi\)
−0.0811794 + 0.996700i \(0.525869\pi\)
\(360\) 0 0
\(361\) 0.704867 0.0370982
\(362\) 0 0
\(363\) 25.9126 1.36006
\(364\) 0 0
\(365\) 4.36784 0.228623
\(366\) 0 0
\(367\) −9.13202 −0.476688 −0.238344 0.971181i \(-0.576605\pi\)
−0.238344 + 0.971181i \(0.576605\pi\)
\(368\) 0 0
\(369\) −16.0216 −0.834050
\(370\) 0 0
\(371\) 54.1248 2.81002
\(372\) 0 0
\(373\) −13.0955 −0.678060 −0.339030 0.940776i \(-0.610099\pi\)
−0.339030 + 0.940776i \(0.610099\pi\)
\(374\) 0 0
\(375\) −2.80169 −0.144679
\(376\) 0 0
\(377\) −8.99161 −0.463092
\(378\) 0 0
\(379\) 30.1576 1.54909 0.774547 0.632517i \(-0.217978\pi\)
0.774547 + 0.632517i \(0.217978\pi\)
\(380\) 0 0
\(381\) 4.56153 0.233694
\(382\) 0 0
\(383\) 11.8329 0.604635 0.302317 0.953207i \(-0.402240\pi\)
0.302317 + 0.953207i \(0.402240\pi\)
\(384\) 0 0
\(385\) 69.0494 3.51908
\(386\) 0 0
\(387\) 7.21123 0.366568
\(388\) 0 0
\(389\) −15.7765 −0.799901 −0.399951 0.916537i \(-0.630973\pi\)
−0.399951 + 0.916537i \(0.630973\pi\)
\(390\) 0 0
\(391\) 24.5724 1.24268
\(392\) 0 0
\(393\) 18.7395 0.945281
\(394\) 0 0
\(395\) −19.0758 −0.959808
\(396\) 0 0
\(397\) 20.2207 1.01485 0.507424 0.861697i \(-0.330598\pi\)
0.507424 + 0.861697i \(0.330598\pi\)
\(398\) 0 0
\(399\) 46.0217 2.30397
\(400\) 0 0
\(401\) 9.28020 0.463431 0.231716 0.972784i \(-0.425566\pi\)
0.231716 + 0.972784i \(0.425566\pi\)
\(402\) 0 0
\(403\) 31.2260 1.55548
\(404\) 0 0
\(405\) −34.3266 −1.70570
\(406\) 0 0
\(407\) 44.3358 2.19764
\(408\) 0 0
\(409\) 13.6673 0.675804 0.337902 0.941181i \(-0.390283\pi\)
0.337902 + 0.941181i \(0.390283\pi\)
\(410\) 0 0
\(411\) −26.3439 −1.29945
\(412\) 0 0
\(413\) −2.90410 −0.142902
\(414\) 0 0
\(415\) −13.0285 −0.639544
\(416\) 0 0
\(417\) −37.8686 −1.85443
\(418\) 0 0
\(419\) −10.3777 −0.506982 −0.253491 0.967338i \(-0.581579\pi\)
−0.253491 + 0.967338i \(0.581579\pi\)
\(420\) 0 0
\(421\) 14.2237 0.693222 0.346611 0.938009i \(-0.387332\pi\)
0.346611 + 0.938009i \(0.387332\pi\)
\(422\) 0 0
\(423\) 6.51741 0.316887
\(424\) 0 0
\(425\) −12.6994 −0.616009
\(426\) 0 0
\(427\) −51.7895 −2.50627
\(428\) 0 0
\(429\) −44.1409 −2.13114
\(430\) 0 0
\(431\) 10.0895 0.485994 0.242997 0.970027i \(-0.421869\pi\)
0.242997 + 0.970027i \(0.421869\pi\)
\(432\) 0 0
\(433\) −2.51477 −0.120852 −0.0604261 0.998173i \(-0.519246\pi\)
−0.0604261 + 0.998173i \(0.519246\pi\)
\(434\) 0 0
\(435\) 14.7508 0.707245
\(436\) 0 0
\(437\) −39.4387 −1.88661
\(438\) 0 0
\(439\) 6.73881 0.321626 0.160813 0.986985i \(-0.448588\pi\)
0.160813 + 0.986985i \(0.448588\pi\)
\(440\) 0 0
\(441\) 28.4285 1.35374
\(442\) 0 0
\(443\) −13.9799 −0.664204 −0.332102 0.943243i \(-0.607758\pi\)
−0.332102 + 0.943243i \(0.607758\pi\)
\(444\) 0 0
\(445\) −52.1334 −2.47136
\(446\) 0 0
\(447\) −31.1566 −1.47366
\(448\) 0 0
\(449\) 10.6552 0.502850 0.251425 0.967877i \(-0.419101\pi\)
0.251425 + 0.967877i \(0.419101\pi\)
\(450\) 0 0
\(451\) −40.0079 −1.88390
\(452\) 0 0
\(453\) −39.3496 −1.84881
\(454\) 0 0
\(455\) −60.6168 −2.84176
\(456\) 0 0
\(457\) −33.7899 −1.58062 −0.790312 0.612704i \(-0.790082\pi\)
−0.790312 + 0.612704i \(0.790082\pi\)
\(458\) 0 0
\(459\) 6.69183 0.312348
\(460\) 0 0
\(461\) 10.1644 0.473406 0.236703 0.971582i \(-0.423933\pi\)
0.236703 + 0.971582i \(0.423933\pi\)
\(462\) 0 0
\(463\) 16.8546 0.783299 0.391650 0.920114i \(-0.371905\pi\)
0.391650 + 0.920114i \(0.371905\pi\)
\(464\) 0 0
\(465\) −51.2263 −2.37556
\(466\) 0 0
\(467\) 6.51332 0.301401 0.150700 0.988579i \(-0.451847\pi\)
0.150700 + 0.988579i \(0.451847\pi\)
\(468\) 0 0
\(469\) −18.1593 −0.838517
\(470\) 0 0
\(471\) −45.4558 −2.09449
\(472\) 0 0
\(473\) 18.0074 0.827980
\(474\) 0 0
\(475\) 20.3824 0.935210
\(476\) 0 0
\(477\) 22.0651 1.01029
\(478\) 0 0
\(479\) 10.9557 0.500579 0.250290 0.968171i \(-0.419474\pi\)
0.250290 + 0.968171i \(0.419474\pi\)
\(480\) 0 0
\(481\) −38.9213 −1.77466
\(482\) 0 0
\(483\) −92.1111 −4.19120
\(484\) 0 0
\(485\) 28.6542 1.30112
\(486\) 0 0
\(487\) 7.58900 0.343891 0.171945 0.985106i \(-0.444995\pi\)
0.171945 + 0.985106i \(0.444995\pi\)
\(488\) 0 0
\(489\) 19.1332 0.865232
\(490\) 0 0
\(491\) 1.97891 0.0893070 0.0446535 0.999003i \(-0.485782\pi\)
0.0446535 + 0.999003i \(0.485782\pi\)
\(492\) 0 0
\(493\) −5.94614 −0.267801
\(494\) 0 0
\(495\) 28.1495 1.26522
\(496\) 0 0
\(497\) −25.1244 −1.12699
\(498\) 0 0
\(499\) 24.0373 1.07606 0.538029 0.842926i \(-0.319169\pi\)
0.538029 + 0.842926i \(0.319169\pi\)
\(500\) 0 0
\(501\) −47.3360 −2.11482
\(502\) 0 0
\(503\) 36.9120 1.64582 0.822912 0.568169i \(-0.192348\pi\)
0.822912 + 0.568169i \(0.192348\pi\)
\(504\) 0 0
\(505\) 12.1020 0.538533
\(506\) 0 0
\(507\) 9.95050 0.441917
\(508\) 0 0
\(509\) 1.19623 0.0530218 0.0265109 0.999649i \(-0.491560\pi\)
0.0265109 + 0.999649i \(0.491560\pi\)
\(510\) 0 0
\(511\) 6.60010 0.291971
\(512\) 0 0
\(513\) −10.7404 −0.474199
\(514\) 0 0
\(515\) 0.758728 0.0334335
\(516\) 0 0
\(517\) 16.2748 0.715765
\(518\) 0 0
\(519\) 20.4591 0.898053
\(520\) 0 0
\(521\) −42.0169 −1.84080 −0.920398 0.390984i \(-0.872135\pi\)
−0.920398 + 0.390984i \(0.872135\pi\)
\(522\) 0 0
\(523\) −35.1386 −1.53650 −0.768252 0.640148i \(-0.778873\pi\)
−0.768252 + 0.640148i \(0.778873\pi\)
\(524\) 0 0
\(525\) 47.6042 2.07762
\(526\) 0 0
\(527\) 20.6497 0.899516
\(528\) 0 0
\(529\) 55.9353 2.43197
\(530\) 0 0
\(531\) −1.18392 −0.0513777
\(532\) 0 0
\(533\) 35.1220 1.52130
\(534\) 0 0
\(535\) −8.19751 −0.354409
\(536\) 0 0
\(537\) 45.3875 1.95861
\(538\) 0 0
\(539\) 70.9897 3.05774
\(540\) 0 0
\(541\) 14.9408 0.642357 0.321179 0.947019i \(-0.395921\pi\)
0.321179 + 0.947019i \(0.395921\pi\)
\(542\) 0 0
\(543\) −18.4243 −0.790661
\(544\) 0 0
\(545\) 61.2992 2.62577
\(546\) 0 0
\(547\) 6.19872 0.265038 0.132519 0.991180i \(-0.457693\pi\)
0.132519 + 0.991180i \(0.457693\pi\)
\(548\) 0 0
\(549\) −21.1131 −0.901085
\(550\) 0 0
\(551\) 9.54354 0.406569
\(552\) 0 0
\(553\) −28.8249 −1.22576
\(554\) 0 0
\(555\) 63.8505 2.71030
\(556\) 0 0
\(557\) 14.9864 0.634993 0.317496 0.948259i \(-0.397158\pi\)
0.317496 + 0.948259i \(0.397158\pi\)
\(558\) 0 0
\(559\) −15.8082 −0.668616
\(560\) 0 0
\(561\) −29.1904 −1.23242
\(562\) 0 0
\(563\) −26.1225 −1.10093 −0.550466 0.834858i \(-0.685550\pi\)
−0.550466 + 0.834858i \(0.685550\pi\)
\(564\) 0 0
\(565\) 26.5706 1.11783
\(566\) 0 0
\(567\) −51.8698 −2.17833
\(568\) 0 0
\(569\) 28.5984 1.19891 0.599453 0.800410i \(-0.295385\pi\)
0.599453 + 0.800410i \(0.295385\pi\)
\(570\) 0 0
\(571\) 25.3749 1.06191 0.530953 0.847402i \(-0.321834\pi\)
0.530953 + 0.847402i \(0.321834\pi\)
\(572\) 0 0
\(573\) 33.0302 1.37986
\(574\) 0 0
\(575\) −40.7948 −1.70126
\(576\) 0 0
\(577\) 27.4355 1.14216 0.571078 0.820896i \(-0.306525\pi\)
0.571078 + 0.820896i \(0.306525\pi\)
\(578\) 0 0
\(579\) 56.7791 2.35966
\(580\) 0 0
\(581\) −19.6870 −0.816753
\(582\) 0 0
\(583\) 55.0994 2.28198
\(584\) 0 0
\(585\) −24.7117 −1.02170
\(586\) 0 0
\(587\) −26.4349 −1.09109 −0.545543 0.838083i \(-0.683676\pi\)
−0.545543 + 0.838083i \(0.683676\pi\)
\(588\) 0 0
\(589\) −33.1427 −1.36562
\(590\) 0 0
\(591\) 12.6802 0.521595
\(592\) 0 0
\(593\) −9.22666 −0.378893 −0.189447 0.981891i \(-0.560669\pi\)
−0.189447 + 0.981891i \(0.560669\pi\)
\(594\) 0 0
\(595\) −40.0858 −1.64336
\(596\) 0 0
\(597\) −28.0062 −1.14622
\(598\) 0 0
\(599\) −47.6451 −1.94673 −0.973363 0.229268i \(-0.926367\pi\)
−0.973363 + 0.229268i \(0.926367\pi\)
\(600\) 0 0
\(601\) −18.7911 −0.766506 −0.383253 0.923643i \(-0.625196\pi\)
−0.383253 + 0.923643i \(0.625196\pi\)
\(602\) 0 0
\(603\) −7.40301 −0.301474
\(604\) 0 0
\(605\) 36.2253 1.47277
\(606\) 0 0
\(607\) −9.16527 −0.372007 −0.186003 0.982549i \(-0.559554\pi\)
−0.186003 + 0.982549i \(0.559554\pi\)
\(608\) 0 0
\(609\) 22.2894 0.903214
\(610\) 0 0
\(611\) −14.2872 −0.578000
\(612\) 0 0
\(613\) 10.2067 0.412243 0.206122 0.978526i \(-0.433916\pi\)
0.206122 + 0.978526i \(0.433916\pi\)
\(614\) 0 0
\(615\) −57.6177 −2.32337
\(616\) 0 0
\(617\) 46.3435 1.86572 0.932860 0.360240i \(-0.117305\pi\)
0.932860 + 0.360240i \(0.117305\pi\)
\(618\) 0 0
\(619\) 20.6308 0.829221 0.414610 0.909999i \(-0.363918\pi\)
0.414610 + 0.909999i \(0.363918\pi\)
\(620\) 0 0
\(621\) 21.4965 0.862625
\(622\) 0 0
\(623\) −78.7773 −3.15614
\(624\) 0 0
\(625\) −26.8750 −1.07500
\(626\) 0 0
\(627\) 46.8504 1.87103
\(628\) 0 0
\(629\) −25.7386 −1.02626
\(630\) 0 0
\(631\) −0.503235 −0.0200335 −0.0100167 0.999950i \(-0.503188\pi\)
−0.0100167 + 0.999950i \(0.503188\pi\)
\(632\) 0 0
\(633\) 35.7323 1.42023
\(634\) 0 0
\(635\) 6.37693 0.253061
\(636\) 0 0
\(637\) −62.3201 −2.46921
\(638\) 0 0
\(639\) −10.2425 −0.405187
\(640\) 0 0
\(641\) 37.3295 1.47443 0.737214 0.675659i \(-0.236141\pi\)
0.737214 + 0.675659i \(0.236141\pi\)
\(642\) 0 0
\(643\) −0.106240 −0.00418969 −0.00209485 0.999998i \(-0.500667\pi\)
−0.00209485 + 0.999998i \(0.500667\pi\)
\(644\) 0 0
\(645\) 25.9334 1.02113
\(646\) 0 0
\(647\) −16.1931 −0.636616 −0.318308 0.947987i \(-0.603115\pi\)
−0.318308 + 0.947987i \(0.603115\pi\)
\(648\) 0 0
\(649\) −2.95640 −0.116049
\(650\) 0 0
\(651\) −77.4066 −3.03380
\(652\) 0 0
\(653\) −17.0952 −0.668989 −0.334494 0.942398i \(-0.608565\pi\)
−0.334494 + 0.942398i \(0.608565\pi\)
\(654\) 0 0
\(655\) 26.1975 1.02362
\(656\) 0 0
\(657\) 2.69067 0.104973
\(658\) 0 0
\(659\) 14.4895 0.564431 0.282216 0.959351i \(-0.408931\pi\)
0.282216 + 0.959351i \(0.408931\pi\)
\(660\) 0 0
\(661\) 10.1919 0.396418 0.198209 0.980160i \(-0.436487\pi\)
0.198209 + 0.980160i \(0.436487\pi\)
\(662\) 0 0
\(663\) 25.6255 0.995211
\(664\) 0 0
\(665\) 64.3376 2.49490
\(666\) 0 0
\(667\) −19.1011 −0.739598
\(668\) 0 0
\(669\) −26.4015 −1.02074
\(670\) 0 0
\(671\) −52.7221 −2.03531
\(672\) 0 0
\(673\) 38.0132 1.46530 0.732651 0.680604i \(-0.238283\pi\)
0.732651 + 0.680604i \(0.238283\pi\)
\(674\) 0 0
\(675\) −11.1097 −0.427612
\(676\) 0 0
\(677\) −42.3781 −1.62872 −0.814361 0.580358i \(-0.802913\pi\)
−0.814361 + 0.580358i \(0.802913\pi\)
\(678\) 0 0
\(679\) 43.2985 1.66164
\(680\) 0 0
\(681\) 12.9771 0.497282
\(682\) 0 0
\(683\) −36.7923 −1.40782 −0.703908 0.710291i \(-0.748563\pi\)
−0.703908 + 0.710291i \(0.748563\pi\)
\(684\) 0 0
\(685\) −36.8283 −1.40714
\(686\) 0 0
\(687\) 10.4995 0.400579
\(688\) 0 0
\(689\) −48.3704 −1.84277
\(690\) 0 0
\(691\) 1.24309 0.0472893 0.0236446 0.999720i \(-0.492473\pi\)
0.0236446 + 0.999720i \(0.492473\pi\)
\(692\) 0 0
\(693\) 42.5358 1.61580
\(694\) 0 0
\(695\) −52.9397 −2.00812
\(696\) 0 0
\(697\) 23.2261 0.879752
\(698\) 0 0
\(699\) 7.34382 0.277769
\(700\) 0 0
\(701\) 13.7481 0.519257 0.259629 0.965709i \(-0.416400\pi\)
0.259629 + 0.965709i \(0.416400\pi\)
\(702\) 0 0
\(703\) 41.3104 1.55805
\(704\) 0 0
\(705\) 23.4383 0.882736
\(706\) 0 0
\(707\) 18.2870 0.687753
\(708\) 0 0
\(709\) 40.7096 1.52888 0.764441 0.644694i \(-0.223015\pi\)
0.764441 + 0.644694i \(0.223015\pi\)
\(710\) 0 0
\(711\) −11.7511 −0.440700
\(712\) 0 0
\(713\) 66.3341 2.48423
\(714\) 0 0
\(715\) −61.7083 −2.30776
\(716\) 0 0
\(717\) 1.13520 0.0423948
\(718\) 0 0
\(719\) −21.7959 −0.812851 −0.406425 0.913684i \(-0.633225\pi\)
−0.406425 + 0.913684i \(0.633225\pi\)
\(720\) 0 0
\(721\) 1.14649 0.0426975
\(722\) 0 0
\(723\) −32.1222 −1.19464
\(724\) 0 0
\(725\) 9.87170 0.366626
\(726\) 0 0
\(727\) −44.6383 −1.65554 −0.827772 0.561064i \(-0.810392\pi\)
−0.827772 + 0.561064i \(0.810392\pi\)
\(728\) 0 0
\(729\) −5.06536 −0.187606
\(730\) 0 0
\(731\) −10.4540 −0.386654
\(732\) 0 0
\(733\) −24.1455 −0.891836 −0.445918 0.895074i \(-0.647123\pi\)
−0.445918 + 0.895074i \(0.647123\pi\)
\(734\) 0 0
\(735\) 102.236 3.77104
\(736\) 0 0
\(737\) −18.4863 −0.680950
\(738\) 0 0
\(739\) −0.696924 −0.0256368 −0.0128184 0.999918i \(-0.504080\pi\)
−0.0128184 + 0.999918i \(0.504080\pi\)
\(740\) 0 0
\(741\) −41.1288 −1.51091
\(742\) 0 0
\(743\) −11.1443 −0.408846 −0.204423 0.978883i \(-0.565532\pi\)
−0.204423 + 0.978883i \(0.565532\pi\)
\(744\) 0 0
\(745\) −43.5564 −1.59578
\(746\) 0 0
\(747\) −8.02581 −0.293649
\(748\) 0 0
\(749\) −12.3870 −0.452612
\(750\) 0 0
\(751\) 24.8606 0.907174 0.453587 0.891212i \(-0.350144\pi\)
0.453587 + 0.891212i \(0.350144\pi\)
\(752\) 0 0
\(753\) 2.21536 0.0807323
\(754\) 0 0
\(755\) −55.0100 −2.00202
\(756\) 0 0
\(757\) −11.6288 −0.422657 −0.211329 0.977415i \(-0.567779\pi\)
−0.211329 + 0.977415i \(0.567779\pi\)
\(758\) 0 0
\(759\) −93.7697 −3.40362
\(760\) 0 0
\(761\) 29.1632 1.05717 0.528583 0.848881i \(-0.322723\pi\)
0.528583 + 0.848881i \(0.322723\pi\)
\(762\) 0 0
\(763\) 92.6273 3.35333
\(764\) 0 0
\(765\) −16.3418 −0.590840
\(766\) 0 0
\(767\) 2.59535 0.0937126
\(768\) 0 0
\(769\) −24.3770 −0.879056 −0.439528 0.898229i \(-0.644854\pi\)
−0.439528 + 0.898229i \(0.644854\pi\)
\(770\) 0 0
\(771\) 62.7136 2.25858
\(772\) 0 0
\(773\) −41.2500 −1.48366 −0.741830 0.670588i \(-0.766042\pi\)
−0.741830 + 0.670588i \(0.766042\pi\)
\(774\) 0 0
\(775\) −34.2824 −1.23146
\(776\) 0 0
\(777\) 96.4825 3.46129
\(778\) 0 0
\(779\) −37.2779 −1.33562
\(780\) 0 0
\(781\) −25.5769 −0.915212
\(782\) 0 0
\(783\) −5.20182 −0.185898
\(784\) 0 0
\(785\) −63.5464 −2.26807
\(786\) 0 0
\(787\) 1.65386 0.0589537 0.0294769 0.999565i \(-0.490616\pi\)
0.0294769 + 0.999565i \(0.490616\pi\)
\(788\) 0 0
\(789\) −34.8718 −1.24147
\(790\) 0 0
\(791\) 40.1501 1.42757
\(792\) 0 0
\(793\) 46.2834 1.64357
\(794\) 0 0
\(795\) 79.3518 2.81432
\(796\) 0 0
\(797\) 2.53175 0.0896793 0.0448396 0.998994i \(-0.485722\pi\)
0.0448396 + 0.998994i \(0.485722\pi\)
\(798\) 0 0
\(799\) −9.44813 −0.334251
\(800\) 0 0
\(801\) −32.1152 −1.13474
\(802\) 0 0
\(803\) 6.71895 0.237107
\(804\) 0 0
\(805\) −128.770 −4.53853
\(806\) 0 0
\(807\) 0.965542 0.0339887
\(808\) 0 0
\(809\) 14.3444 0.504323 0.252161 0.967685i \(-0.418859\pi\)
0.252161 + 0.967685i \(0.418859\pi\)
\(810\) 0 0
\(811\) 25.5339 0.896618 0.448309 0.893879i \(-0.352026\pi\)
0.448309 + 0.893879i \(0.352026\pi\)
\(812\) 0 0
\(813\) −41.3690 −1.45087
\(814\) 0 0
\(815\) 26.7478 0.936935
\(816\) 0 0
\(817\) 16.7786 0.587008
\(818\) 0 0
\(819\) −37.3411 −1.30480
\(820\) 0 0
\(821\) −3.58307 −0.125050 −0.0625249 0.998043i \(-0.519915\pi\)
−0.0625249 + 0.998043i \(0.519915\pi\)
\(822\) 0 0
\(823\) 24.1716 0.842568 0.421284 0.906929i \(-0.361580\pi\)
0.421284 + 0.906929i \(0.361580\pi\)
\(824\) 0 0
\(825\) 48.4614 1.68721
\(826\) 0 0
\(827\) 4.63507 0.161177 0.0805885 0.996747i \(-0.474320\pi\)
0.0805885 + 0.996747i \(0.474320\pi\)
\(828\) 0 0
\(829\) −47.8954 −1.66348 −0.831738 0.555169i \(-0.812654\pi\)
−0.831738 + 0.555169i \(0.812654\pi\)
\(830\) 0 0
\(831\) 46.3692 1.60853
\(832\) 0 0
\(833\) −41.2122 −1.42792
\(834\) 0 0
\(835\) −66.1749 −2.29008
\(836\) 0 0
\(837\) 18.0648 0.624412
\(838\) 0 0
\(839\) −32.6951 −1.12876 −0.564380 0.825515i \(-0.690885\pi\)
−0.564380 + 0.825515i \(0.690885\pi\)
\(840\) 0 0
\(841\) −24.3778 −0.840615
\(842\) 0 0
\(843\) 62.4207 2.14988
\(844\) 0 0
\(845\) 13.9106 0.478540
\(846\) 0 0
\(847\) 54.7390 1.88085
\(848\) 0 0
\(849\) 52.6905 1.80833
\(850\) 0 0
\(851\) −82.6814 −2.83428
\(852\) 0 0
\(853\) 4.10625 0.140595 0.0702977 0.997526i \(-0.477605\pi\)
0.0702977 + 0.997526i \(0.477605\pi\)
\(854\) 0 0
\(855\) 26.2286 0.896999
\(856\) 0 0
\(857\) 14.0056 0.478424 0.239212 0.970967i \(-0.423111\pi\)
0.239212 + 0.970967i \(0.423111\pi\)
\(858\) 0 0
\(859\) 17.1442 0.584954 0.292477 0.956273i \(-0.405520\pi\)
0.292477 + 0.956273i \(0.405520\pi\)
\(860\) 0 0
\(861\) −87.0644 −2.96715
\(862\) 0 0
\(863\) 57.5292 1.95832 0.979158 0.203098i \(-0.0651010\pi\)
0.979158 + 0.203098i \(0.0651010\pi\)
\(864\) 0 0
\(865\) 28.6014 0.972477
\(866\) 0 0
\(867\) −20.7151 −0.703521
\(868\) 0 0
\(869\) −29.3439 −0.995425
\(870\) 0 0
\(871\) 16.2286 0.549886
\(872\) 0 0
\(873\) 17.6515 0.597414
\(874\) 0 0
\(875\) −5.91843 −0.200079
\(876\) 0 0
\(877\) 46.5128 1.57063 0.785313 0.619099i \(-0.212502\pi\)
0.785313 + 0.619099i \(0.212502\pi\)
\(878\) 0 0
\(879\) −35.4743 −1.19652
\(880\) 0 0
\(881\) −11.0699 −0.372954 −0.186477 0.982459i \(-0.559707\pi\)
−0.186477 + 0.982459i \(0.559707\pi\)
\(882\) 0 0
\(883\) −0.152523 −0.00513280 −0.00256640 0.999997i \(-0.500817\pi\)
−0.00256640 + 0.999997i \(0.500817\pi\)
\(884\) 0 0
\(885\) −4.25768 −0.143120
\(886\) 0 0
\(887\) −9.69157 −0.325411 −0.162706 0.986675i \(-0.552022\pi\)
−0.162706 + 0.986675i \(0.552022\pi\)
\(888\) 0 0
\(889\) 9.63599 0.323181
\(890\) 0 0
\(891\) −52.8038 −1.76900
\(892\) 0 0
\(893\) 15.1642 0.507452
\(894\) 0 0
\(895\) 63.4509 2.12093
\(896\) 0 0
\(897\) 82.3181 2.74852
\(898\) 0 0
\(899\) −16.0518 −0.535358
\(900\) 0 0
\(901\) −31.9873 −1.06565
\(902\) 0 0
\(903\) 39.1872 1.30407
\(904\) 0 0
\(905\) −25.7568 −0.856185
\(906\) 0 0
\(907\) 22.2135 0.737587 0.368793 0.929511i \(-0.379771\pi\)
0.368793 + 0.929511i \(0.379771\pi\)
\(908\) 0 0
\(909\) 7.45508 0.247269
\(910\) 0 0
\(911\) 31.3519 1.03873 0.519367 0.854551i \(-0.326168\pi\)
0.519367 + 0.854551i \(0.326168\pi\)
\(912\) 0 0
\(913\) −20.0415 −0.663276
\(914\) 0 0
\(915\) −75.9281 −2.51010
\(916\) 0 0
\(917\) 39.5862 1.30725
\(918\) 0 0
\(919\) −38.1544 −1.25860 −0.629299 0.777163i \(-0.716658\pi\)
−0.629299 + 0.777163i \(0.716658\pi\)
\(920\) 0 0
\(921\) 3.08501 0.101655
\(922\) 0 0
\(923\) 22.4533 0.739059
\(924\) 0 0
\(925\) 42.7308 1.40498
\(926\) 0 0
\(927\) 0.467391 0.0153511
\(928\) 0 0
\(929\) −10.3278 −0.338843 −0.169421 0.985544i \(-0.554190\pi\)
−0.169421 + 0.985544i \(0.554190\pi\)
\(930\) 0 0
\(931\) 66.1455 2.16783
\(932\) 0 0
\(933\) −66.3165 −2.17111
\(934\) 0 0
\(935\) −40.8076 −1.33455
\(936\) 0 0
\(937\) 8.05077 0.263007 0.131504 0.991316i \(-0.458020\pi\)
0.131504 + 0.991316i \(0.458020\pi\)
\(938\) 0 0
\(939\) −5.57674 −0.181990
\(940\) 0 0
\(941\) 28.8005 0.938870 0.469435 0.882967i \(-0.344458\pi\)
0.469435 + 0.882967i \(0.344458\pi\)
\(942\) 0 0
\(943\) 74.6105 2.42965
\(944\) 0 0
\(945\) −35.0680 −1.14076
\(946\) 0 0
\(947\) −19.4582 −0.632305 −0.316152 0.948708i \(-0.602391\pi\)
−0.316152 + 0.948708i \(0.602391\pi\)
\(948\) 0 0
\(949\) −5.89840 −0.191470
\(950\) 0 0
\(951\) 4.43444 0.143797
\(952\) 0 0
\(953\) −48.9075 −1.58427 −0.792135 0.610346i \(-0.791031\pi\)
−0.792135 + 0.610346i \(0.791031\pi\)
\(954\) 0 0
\(955\) 46.1757 1.49421
\(956\) 0 0
\(957\) 22.6908 0.733490
\(958\) 0 0
\(959\) −55.6501 −1.79704
\(960\) 0 0
\(961\) 24.7446 0.798214
\(962\) 0 0
\(963\) −5.04983 −0.162728
\(964\) 0 0
\(965\) 79.3761 2.55521
\(966\) 0 0
\(967\) −44.7258 −1.43828 −0.719142 0.694863i \(-0.755465\pi\)
−0.719142 + 0.694863i \(0.755465\pi\)
\(968\) 0 0
\(969\) −27.1985 −0.873740
\(970\) 0 0
\(971\) 2.73713 0.0878386 0.0439193 0.999035i \(-0.486016\pi\)
0.0439193 + 0.999035i \(0.486016\pi\)
\(972\) 0 0
\(973\) −79.9955 −2.56454
\(974\) 0 0
\(975\) −42.5431 −1.36247
\(976\) 0 0
\(977\) −14.8910 −0.476404 −0.238202 0.971216i \(-0.576558\pi\)
−0.238202 + 0.971216i \(0.576558\pi\)
\(978\) 0 0
\(979\) −80.1958 −2.56307
\(980\) 0 0
\(981\) 37.7615 1.20563
\(982\) 0 0
\(983\) 28.3312 0.903626 0.451813 0.892113i \(-0.350777\pi\)
0.451813 + 0.892113i \(0.350777\pi\)
\(984\) 0 0
\(985\) 17.7267 0.564821
\(986\) 0 0
\(987\) 35.4169 1.12733
\(988\) 0 0
\(989\) −33.5818 −1.06784
\(990\) 0 0
\(991\) −20.3125 −0.645248 −0.322624 0.946527i \(-0.604565\pi\)
−0.322624 + 0.946527i \(0.604565\pi\)
\(992\) 0 0
\(993\) 9.57992 0.304010
\(994\) 0 0
\(995\) −39.1522 −1.24121
\(996\) 0 0
\(997\) 24.2802 0.768961 0.384480 0.923133i \(-0.374381\pi\)
0.384480 + 0.923133i \(0.374381\pi\)
\(998\) 0 0
\(999\) −22.5167 −0.712397
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.1.19 23
4.3 odd 2 2008.2.a.d.1.5 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.5 23 4.3 odd 2
4016.2.a.m.1.19 23 1.1 even 1 trivial