Properties

Label 8036.2.a.p.1.4
Level $8036$
Weight $2$
Character 8036.1
Self dual yes
Analytic conductor $64.168$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8036.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} - 18 x^{8} + 32 x^{7} + 110 x^{6} - 154 x^{5} - 282 x^{4} + 256 x^{3} + 253 x^{2} - 126 x - 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.05099\) of defining polynomial
Character \(\chi\) \(=\) 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.05099 q^{3} -1.02904 q^{5} -1.89542 q^{9} +O(q^{10})\) \(q-1.05099 q^{3} -1.02904 q^{5} -1.89542 q^{9} -1.28502 q^{11} -2.29756 q^{13} +1.08151 q^{15} +4.44667 q^{17} -2.95049 q^{19} +4.81352 q^{23} -3.94108 q^{25} +5.14504 q^{27} +0.100729 q^{29} +0.925502 q^{31} +1.35054 q^{33} -7.07815 q^{37} +2.41471 q^{39} +1.00000 q^{41} -5.47396 q^{43} +1.95046 q^{45} -2.99968 q^{47} -4.67341 q^{51} -1.46189 q^{53} +1.32233 q^{55} +3.10094 q^{57} +4.37678 q^{59} -5.39476 q^{61} +2.36428 q^{65} -5.18998 q^{67} -5.05896 q^{69} -14.2892 q^{71} -9.89202 q^{73} +4.14203 q^{75} -7.39997 q^{79} +0.278885 q^{81} +16.1355 q^{83} -4.57580 q^{85} -0.105865 q^{87} -15.7712 q^{89} -0.972693 q^{93} +3.03617 q^{95} +3.20703 q^{97} +2.43565 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) −1.05099 −0.606789 −0.303395 0.952865i \(-0.598120\pi\)
−0.303395 + 0.952865i \(0.598120\pi\)
\(4\) 0 0
\(5\) −1.02904 −0.460200 −0.230100 0.973167i \(-0.573905\pi\)
−0.230100 + 0.973167i \(0.573905\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.89542 −0.631807
\(10\) 0 0
\(11\) −1.28502 −0.387448 −0.193724 0.981056i \(-0.562057\pi\)
−0.193724 + 0.981056i \(0.562057\pi\)
\(12\) 0 0
\(13\) −2.29756 −0.637228 −0.318614 0.947885i \(-0.603217\pi\)
−0.318614 + 0.947885i \(0.603217\pi\)
\(14\) 0 0
\(15\) 1.08151 0.279244
\(16\) 0 0
\(17\) 4.44667 1.07848 0.539239 0.842153i \(-0.318712\pi\)
0.539239 + 0.842153i \(0.318712\pi\)
\(18\) 0 0
\(19\) −2.95049 −0.676889 −0.338445 0.940986i \(-0.609901\pi\)
−0.338445 + 0.940986i \(0.609901\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.81352 1.00369 0.501844 0.864958i \(-0.332655\pi\)
0.501844 + 0.864958i \(0.332655\pi\)
\(24\) 0 0
\(25\) −3.94108 −0.788216
\(26\) 0 0
\(27\) 5.14504 0.990163
\(28\) 0 0
\(29\) 0.100729 0.0187050 0.00935248 0.999956i \(-0.497023\pi\)
0.00935248 + 0.999956i \(0.497023\pi\)
\(30\) 0 0
\(31\) 0.925502 0.166225 0.0831125 0.996540i \(-0.473514\pi\)
0.0831125 + 0.996540i \(0.473514\pi\)
\(32\) 0 0
\(33\) 1.35054 0.235099
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.07815 −1.16364 −0.581821 0.813317i \(-0.697659\pi\)
−0.581821 + 0.813317i \(0.697659\pi\)
\(38\) 0 0
\(39\) 2.41471 0.386663
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −5.47396 −0.834770 −0.417385 0.908730i \(-0.637053\pi\)
−0.417385 + 0.908730i \(0.637053\pi\)
\(44\) 0 0
\(45\) 1.95046 0.290758
\(46\) 0 0
\(47\) −2.99968 −0.437549 −0.218774 0.975775i \(-0.570206\pi\)
−0.218774 + 0.975775i \(0.570206\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −4.67341 −0.654408
\(52\) 0 0
\(53\) −1.46189 −0.200806 −0.100403 0.994947i \(-0.532013\pi\)
−0.100403 + 0.994947i \(0.532013\pi\)
\(54\) 0 0
\(55\) 1.32233 0.178304
\(56\) 0 0
\(57\) 3.10094 0.410729
\(58\) 0 0
\(59\) 4.37678 0.569808 0.284904 0.958556i \(-0.408038\pi\)
0.284904 + 0.958556i \(0.408038\pi\)
\(60\) 0 0
\(61\) −5.39476 −0.690729 −0.345364 0.938469i \(-0.612245\pi\)
−0.345364 + 0.938469i \(0.612245\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.36428 0.293252
\(66\) 0 0
\(67\) −5.18998 −0.634056 −0.317028 0.948416i \(-0.602685\pi\)
−0.317028 + 0.948416i \(0.602685\pi\)
\(68\) 0 0
\(69\) −5.05896 −0.609027
\(70\) 0 0
\(71\) −14.2892 −1.69581 −0.847905 0.530148i \(-0.822137\pi\)
−0.847905 + 0.530148i \(0.822137\pi\)
\(72\) 0 0
\(73\) −9.89202 −1.15777 −0.578887 0.815408i \(-0.696513\pi\)
−0.578887 + 0.815408i \(0.696513\pi\)
\(74\) 0 0
\(75\) 4.14203 0.478281
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −7.39997 −0.832562 −0.416281 0.909236i \(-0.636667\pi\)
−0.416281 + 0.909236i \(0.636667\pi\)
\(80\) 0 0
\(81\) 0.278885 0.0309872
\(82\) 0 0
\(83\) 16.1355 1.77110 0.885548 0.464547i \(-0.153783\pi\)
0.885548 + 0.464547i \(0.153783\pi\)
\(84\) 0 0
\(85\) −4.57580 −0.496315
\(86\) 0 0
\(87\) −0.105865 −0.0113500
\(88\) 0 0
\(89\) −15.7712 −1.67175 −0.835874 0.548922i \(-0.815039\pi\)
−0.835874 + 0.548922i \(0.815039\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −0.972693 −0.100864
\(94\) 0 0
\(95\) 3.03617 0.311505
\(96\) 0 0
\(97\) 3.20703 0.325625 0.162812 0.986657i \(-0.447943\pi\)
0.162812 + 0.986657i \(0.447943\pi\)
\(98\) 0 0
\(99\) 2.43565 0.244792
\(100\) 0 0
\(101\) 12.6500 1.25872 0.629361 0.777113i \(-0.283316\pi\)
0.629361 + 0.777113i \(0.283316\pi\)
\(102\) 0 0
\(103\) 4.93576 0.486335 0.243168 0.969984i \(-0.421814\pi\)
0.243168 + 0.969984i \(0.421814\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.41487 0.233455 0.116727 0.993164i \(-0.462760\pi\)
0.116727 + 0.993164i \(0.462760\pi\)
\(108\) 0 0
\(109\) 16.3593 1.56694 0.783470 0.621430i \(-0.213448\pi\)
0.783470 + 0.621430i \(0.213448\pi\)
\(110\) 0 0
\(111\) 7.43907 0.706085
\(112\) 0 0
\(113\) 8.11756 0.763636 0.381818 0.924238i \(-0.375298\pi\)
0.381818 + 0.924238i \(0.375298\pi\)
\(114\) 0 0
\(115\) −4.95330 −0.461897
\(116\) 0 0
\(117\) 4.35484 0.402605
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −9.34873 −0.849884
\(122\) 0 0
\(123\) −1.05099 −0.0947645
\(124\) 0 0
\(125\) 9.20072 0.822937
\(126\) 0 0
\(127\) −9.43718 −0.837415 −0.418707 0.908121i \(-0.637517\pi\)
−0.418707 + 0.908121i \(0.637517\pi\)
\(128\) 0 0
\(129\) 5.75307 0.506530
\(130\) 0 0
\(131\) −0.192974 −0.0168602 −0.00843009 0.999964i \(-0.502683\pi\)
−0.00843009 + 0.999964i \(0.502683\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −5.29444 −0.455673
\(136\) 0 0
\(137\) 14.8617 1.26972 0.634861 0.772626i \(-0.281057\pi\)
0.634861 + 0.772626i \(0.281057\pi\)
\(138\) 0 0
\(139\) −2.89568 −0.245608 −0.122804 0.992431i \(-0.539189\pi\)
−0.122804 + 0.992431i \(0.539189\pi\)
\(140\) 0 0
\(141\) 3.15263 0.265500
\(142\) 0 0
\(143\) 2.95240 0.246892
\(144\) 0 0
\(145\) −0.103654 −0.00860802
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −16.5174 −1.35316 −0.676578 0.736371i \(-0.736538\pi\)
−0.676578 + 0.736371i \(0.736538\pi\)
\(150\) 0 0
\(151\) −8.66936 −0.705503 −0.352751 0.935717i \(-0.614754\pi\)
−0.352751 + 0.935717i \(0.614754\pi\)
\(152\) 0 0
\(153\) −8.42832 −0.681389
\(154\) 0 0
\(155\) −0.952377 −0.0764968
\(156\) 0 0
\(157\) 20.4555 1.63253 0.816263 0.577681i \(-0.196042\pi\)
0.816263 + 0.577681i \(0.196042\pi\)
\(158\) 0 0
\(159\) 1.53643 0.121847
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 15.5478 1.21780 0.608898 0.793249i \(-0.291612\pi\)
0.608898 + 0.793249i \(0.291612\pi\)
\(164\) 0 0
\(165\) −1.38976 −0.108193
\(166\) 0 0
\(167\) −13.6387 −1.05539 −0.527695 0.849434i \(-0.676944\pi\)
−0.527695 + 0.849434i \(0.676944\pi\)
\(168\) 0 0
\(169\) −7.72123 −0.593941
\(170\) 0 0
\(171\) 5.59242 0.427663
\(172\) 0 0
\(173\) 3.02896 0.230288 0.115144 0.993349i \(-0.463267\pi\)
0.115144 + 0.993349i \(0.463267\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.59995 −0.345753
\(178\) 0 0
\(179\) 14.8778 1.11202 0.556010 0.831175i \(-0.312332\pi\)
0.556010 + 0.831175i \(0.312332\pi\)
\(180\) 0 0
\(181\) 18.7524 1.39386 0.696928 0.717141i \(-0.254550\pi\)
0.696928 + 0.717141i \(0.254550\pi\)
\(182\) 0 0
\(183\) 5.66984 0.419127
\(184\) 0 0
\(185\) 7.28370 0.535508
\(186\) 0 0
\(187\) −5.71406 −0.417854
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.07373 −0.367122 −0.183561 0.983008i \(-0.558762\pi\)
−0.183561 + 0.983008i \(0.558762\pi\)
\(192\) 0 0
\(193\) −2.47971 −0.178494 −0.0892468 0.996010i \(-0.528446\pi\)
−0.0892468 + 0.996010i \(0.528446\pi\)
\(194\) 0 0
\(195\) −2.48483 −0.177942
\(196\) 0 0
\(197\) −8.51382 −0.606584 −0.303292 0.952898i \(-0.598086\pi\)
−0.303292 + 0.952898i \(0.598086\pi\)
\(198\) 0 0
\(199\) 18.8343 1.33513 0.667563 0.744554i \(-0.267338\pi\)
0.667563 + 0.744554i \(0.267338\pi\)
\(200\) 0 0
\(201\) 5.45461 0.384738
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1.02904 −0.0718712
\(206\) 0 0
\(207\) −9.12365 −0.634137
\(208\) 0 0
\(209\) 3.79144 0.262259
\(210\) 0 0
\(211\) 11.1392 0.766854 0.383427 0.923571i \(-0.374744\pi\)
0.383427 + 0.923571i \(0.374744\pi\)
\(212\) 0 0
\(213\) 15.0178 1.02900
\(214\) 0 0
\(215\) 5.63291 0.384162
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 10.3964 0.702525
\(220\) 0 0
\(221\) −10.2165 −0.687235
\(222\) 0 0
\(223\) 14.7176 0.985565 0.492782 0.870153i \(-0.335980\pi\)
0.492782 + 0.870153i \(0.335980\pi\)
\(224\) 0 0
\(225\) 7.47000 0.498000
\(226\) 0 0
\(227\) 14.2238 0.944064 0.472032 0.881581i \(-0.343521\pi\)
0.472032 + 0.881581i \(0.343521\pi\)
\(228\) 0 0
\(229\) 8.34259 0.551294 0.275647 0.961259i \(-0.411108\pi\)
0.275647 + 0.961259i \(0.411108\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.97617 0.194976 0.0974878 0.995237i \(-0.468919\pi\)
0.0974878 + 0.995237i \(0.468919\pi\)
\(234\) 0 0
\(235\) 3.08679 0.201360
\(236\) 0 0
\(237\) 7.77730 0.505190
\(238\) 0 0
\(239\) 5.63303 0.364370 0.182185 0.983264i \(-0.441683\pi\)
0.182185 + 0.983264i \(0.441683\pi\)
\(240\) 0 0
\(241\) 7.29302 0.469784 0.234892 0.972021i \(-0.424526\pi\)
0.234892 + 0.972021i \(0.424526\pi\)
\(242\) 0 0
\(243\) −15.7282 −1.00897
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.77892 0.431332
\(248\) 0 0
\(249\) −16.9582 −1.07468
\(250\) 0 0
\(251\) 10.7087 0.675926 0.337963 0.941159i \(-0.390262\pi\)
0.337963 + 0.941159i \(0.390262\pi\)
\(252\) 0 0
\(253\) −6.18546 −0.388877
\(254\) 0 0
\(255\) 4.80912 0.301159
\(256\) 0 0
\(257\) 6.63688 0.413997 0.206999 0.978341i \(-0.433630\pi\)
0.206999 + 0.978341i \(0.433630\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.190924 −0.0118179
\(262\) 0 0
\(263\) −19.9365 −1.22934 −0.614669 0.788785i \(-0.710710\pi\)
−0.614669 + 0.788785i \(0.710710\pi\)
\(264\) 0 0
\(265\) 1.50434 0.0924111
\(266\) 0 0
\(267\) 16.5754 1.01440
\(268\) 0 0
\(269\) 5.10946 0.311529 0.155765 0.987794i \(-0.450216\pi\)
0.155765 + 0.987794i \(0.450216\pi\)
\(270\) 0 0
\(271\) −17.5747 −1.06759 −0.533793 0.845615i \(-0.679234\pi\)
−0.533793 + 0.845615i \(0.679234\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.06436 0.305393
\(276\) 0 0
\(277\) 18.5799 1.11636 0.558178 0.829721i \(-0.311501\pi\)
0.558178 + 0.829721i \(0.311501\pi\)
\(278\) 0 0
\(279\) −1.75422 −0.105022
\(280\) 0 0
\(281\) −11.5655 −0.689942 −0.344971 0.938613i \(-0.612111\pi\)
−0.344971 + 0.938613i \(0.612111\pi\)
\(282\) 0 0
\(283\) −12.6487 −0.751887 −0.375944 0.926643i \(-0.622681\pi\)
−0.375944 + 0.926643i \(0.622681\pi\)
\(284\) 0 0
\(285\) −3.19098 −0.189018
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.77292 0.163113
\(290\) 0 0
\(291\) −3.37056 −0.197586
\(292\) 0 0
\(293\) 22.3710 1.30693 0.653463 0.756958i \(-0.273315\pi\)
0.653463 + 0.756958i \(0.273315\pi\)
\(294\) 0 0
\(295\) −4.50388 −0.262226
\(296\) 0 0
\(297\) −6.61147 −0.383636
\(298\) 0 0
\(299\) −11.0593 −0.639578
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −13.2950 −0.763779
\(304\) 0 0
\(305\) 5.55142 0.317874
\(306\) 0 0
\(307\) 8.60090 0.490879 0.245440 0.969412i \(-0.421068\pi\)
0.245440 + 0.969412i \(0.421068\pi\)
\(308\) 0 0
\(309\) −5.18743 −0.295103
\(310\) 0 0
\(311\) −16.7875 −0.951933 −0.475966 0.879464i \(-0.657902\pi\)
−0.475966 + 0.879464i \(0.657902\pi\)
\(312\) 0 0
\(313\) −3.21817 −0.181902 −0.0909509 0.995855i \(-0.528991\pi\)
−0.0909509 + 0.995855i \(0.528991\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 26.9450 1.51338 0.756692 0.653772i \(-0.226814\pi\)
0.756692 + 0.653772i \(0.226814\pi\)
\(318\) 0 0
\(319\) −0.129439 −0.00724719
\(320\) 0 0
\(321\) −2.53801 −0.141658
\(322\) 0 0
\(323\) −13.1199 −0.730010
\(324\) 0 0
\(325\) 9.05485 0.502273
\(326\) 0 0
\(327\) −17.1935 −0.950802
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7.99110 −0.439230 −0.219615 0.975587i \(-0.570480\pi\)
−0.219615 + 0.975587i \(0.570480\pi\)
\(332\) 0 0
\(333\) 13.4161 0.735197
\(334\) 0 0
\(335\) 5.34069 0.291793
\(336\) 0 0
\(337\) −14.1652 −0.771628 −0.385814 0.922577i \(-0.626079\pi\)
−0.385814 + 0.922577i \(0.626079\pi\)
\(338\) 0 0
\(339\) −8.53147 −0.463366
\(340\) 0 0
\(341\) −1.18929 −0.0644035
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 5.20586 0.280274
\(346\) 0 0
\(347\) 10.1687 0.545885 0.272942 0.962030i \(-0.412003\pi\)
0.272942 + 0.962030i \(0.412003\pi\)
\(348\) 0 0
\(349\) 2.71487 0.145324 0.0726618 0.997357i \(-0.476851\pi\)
0.0726618 + 0.997357i \(0.476851\pi\)
\(350\) 0 0
\(351\) −11.8210 −0.630959
\(352\) 0 0
\(353\) 25.2164 1.34213 0.671066 0.741398i \(-0.265837\pi\)
0.671066 + 0.741398i \(0.265837\pi\)
\(354\) 0 0
\(355\) 14.7041 0.780413
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 25.9355 1.36882 0.684412 0.729095i \(-0.260059\pi\)
0.684412 + 0.729095i \(0.260059\pi\)
\(360\) 0 0
\(361\) −10.2946 −0.541821
\(362\) 0 0
\(363\) 9.82541 0.515700
\(364\) 0 0
\(365\) 10.1793 0.532808
\(366\) 0 0
\(367\) 11.6145 0.606274 0.303137 0.952947i \(-0.401966\pi\)
0.303137 + 0.952947i \(0.401966\pi\)
\(368\) 0 0
\(369\) −1.89542 −0.0986717
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.376334 −0.0194858 −0.00974291 0.999953i \(-0.503101\pi\)
−0.00974291 + 0.999953i \(0.503101\pi\)
\(374\) 0 0
\(375\) −9.66986 −0.499349
\(376\) 0 0
\(377\) −0.231431 −0.0119193
\(378\) 0 0
\(379\) −5.39565 −0.277156 −0.138578 0.990352i \(-0.544253\pi\)
−0.138578 + 0.990352i \(0.544253\pi\)
\(380\) 0 0
\(381\) 9.91838 0.508134
\(382\) 0 0
\(383\) −29.9041 −1.52803 −0.764014 0.645200i \(-0.776774\pi\)
−0.764014 + 0.645200i \(0.776774\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 10.3755 0.527414
\(388\) 0 0
\(389\) 10.2180 0.518071 0.259036 0.965868i \(-0.416595\pi\)
0.259036 + 0.965868i \(0.416595\pi\)
\(390\) 0 0
\(391\) 21.4042 1.08245
\(392\) 0 0
\(393\) 0.202813 0.0102306
\(394\) 0 0
\(395\) 7.61486 0.383145
\(396\) 0 0
\(397\) −1.21654 −0.0610566 −0.0305283 0.999534i \(-0.509719\pi\)
−0.0305283 + 0.999534i \(0.509719\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 25.5983 1.27832 0.639159 0.769075i \(-0.279283\pi\)
0.639159 + 0.769075i \(0.279283\pi\)
\(402\) 0 0
\(403\) −2.12639 −0.105923
\(404\) 0 0
\(405\) −0.286983 −0.0142603
\(406\) 0 0
\(407\) 9.09556 0.450850
\(408\) 0 0
\(409\) 38.4482 1.90114 0.950570 0.310510i \(-0.100500\pi\)
0.950570 + 0.310510i \(0.100500\pi\)
\(410\) 0 0
\(411\) −15.6195 −0.770454
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −16.6040 −0.815059
\(416\) 0 0
\(417\) 3.04333 0.149032
\(418\) 0 0
\(419\) −6.49022 −0.317068 −0.158534 0.987354i \(-0.550677\pi\)
−0.158534 + 0.987354i \(0.550677\pi\)
\(420\) 0 0
\(421\) 11.3180 0.551605 0.275803 0.961214i \(-0.411056\pi\)
0.275803 + 0.961214i \(0.411056\pi\)
\(422\) 0 0
\(423\) 5.68566 0.276446
\(424\) 0 0
\(425\) −17.5247 −0.850073
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −3.10295 −0.149812
\(430\) 0 0
\(431\) −23.3926 −1.12678 −0.563391 0.826191i \(-0.690503\pi\)
−0.563391 + 0.826191i \(0.690503\pi\)
\(432\) 0 0
\(433\) 2.82451 0.135737 0.0678687 0.997694i \(-0.478380\pi\)
0.0678687 + 0.997694i \(0.478380\pi\)
\(434\) 0 0
\(435\) 0.108940 0.00522325
\(436\) 0 0
\(437\) −14.2022 −0.679386
\(438\) 0 0
\(439\) 9.09712 0.434182 0.217091 0.976151i \(-0.430343\pi\)
0.217091 + 0.976151i \(0.430343\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.12057 0.195774 0.0978870 0.995198i \(-0.468792\pi\)
0.0978870 + 0.995198i \(0.468792\pi\)
\(444\) 0 0
\(445\) 16.2292 0.769339
\(446\) 0 0
\(447\) 17.3596 0.821080
\(448\) 0 0
\(449\) 9.26797 0.437382 0.218691 0.975794i \(-0.429821\pi\)
0.218691 + 0.975794i \(0.429821\pi\)
\(450\) 0 0
\(451\) −1.28502 −0.0605092
\(452\) 0 0
\(453\) 9.11141 0.428091
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −33.1586 −1.55109 −0.775547 0.631290i \(-0.782526\pi\)
−0.775547 + 0.631290i \(0.782526\pi\)
\(458\) 0 0
\(459\) 22.8783 1.06787
\(460\) 0 0
\(461\) −9.75466 −0.454320 −0.227160 0.973857i \(-0.572944\pi\)
−0.227160 + 0.973857i \(0.572944\pi\)
\(462\) 0 0
\(463\) 32.6665 1.51814 0.759069 0.651010i \(-0.225654\pi\)
0.759069 + 0.651010i \(0.225654\pi\)
\(464\) 0 0
\(465\) 1.00094 0.0464174
\(466\) 0 0
\(467\) −34.7311 −1.60716 −0.803582 0.595194i \(-0.797075\pi\)
−0.803582 + 0.595194i \(0.797075\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −21.4985 −0.990599
\(472\) 0 0
\(473\) 7.03414 0.323430
\(474\) 0 0
\(475\) 11.6281 0.533535
\(476\) 0 0
\(477\) 2.77090 0.126871
\(478\) 0 0
\(479\) 23.9080 1.09239 0.546193 0.837659i \(-0.316076\pi\)
0.546193 + 0.837659i \(0.316076\pi\)
\(480\) 0 0
\(481\) 16.2625 0.741504
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.30016 −0.149853
\(486\) 0 0
\(487\) 21.4037 0.969893 0.484947 0.874544i \(-0.338839\pi\)
0.484947 + 0.874544i \(0.338839\pi\)
\(488\) 0 0
\(489\) −16.3405 −0.738945
\(490\) 0 0
\(491\) −15.8929 −0.717235 −0.358618 0.933485i \(-0.616752\pi\)
−0.358618 + 0.933485i \(0.616752\pi\)
\(492\) 0 0
\(493\) 0.447910 0.0201729
\(494\) 0 0
\(495\) −2.50638 −0.112653
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 28.7109 1.28527 0.642637 0.766170i \(-0.277840\pi\)
0.642637 + 0.766170i \(0.277840\pi\)
\(500\) 0 0
\(501\) 14.3341 0.640400
\(502\) 0 0
\(503\) −3.02608 −0.134926 −0.0674631 0.997722i \(-0.521490\pi\)
−0.0674631 + 0.997722i \(0.521490\pi\)
\(504\) 0 0
\(505\) −13.0174 −0.579265
\(506\) 0 0
\(507\) 8.11494 0.360397
\(508\) 0 0
\(509\) 0.818528 0.0362806 0.0181403 0.999835i \(-0.494225\pi\)
0.0181403 + 0.999835i \(0.494225\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −15.1804 −0.670230
\(514\) 0 0
\(515\) −5.07909 −0.223812
\(516\) 0 0
\(517\) 3.85465 0.169527
\(518\) 0 0
\(519\) −3.18341 −0.139736
\(520\) 0 0
\(521\) −12.3960 −0.543078 −0.271539 0.962427i \(-0.587533\pi\)
−0.271539 + 0.962427i \(0.587533\pi\)
\(522\) 0 0
\(523\) 24.5318 1.07270 0.536351 0.843995i \(-0.319802\pi\)
0.536351 + 0.843995i \(0.319802\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.11541 0.179270
\(528\) 0 0
\(529\) 0.169962 0.00738967
\(530\) 0 0
\(531\) −8.29584 −0.360009
\(532\) 0 0
\(533\) −2.29756 −0.0995182
\(534\) 0 0
\(535\) −2.48500 −0.107436
\(536\) 0 0
\(537\) −15.6364 −0.674762
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 39.6480 1.70460 0.852301 0.523051i \(-0.175206\pi\)
0.852301 + 0.523051i \(0.175206\pi\)
\(542\) 0 0
\(543\) −19.7086 −0.845777
\(544\) 0 0
\(545\) −16.8344 −0.721106
\(546\) 0 0
\(547\) 19.1807 0.820107 0.410053 0.912062i \(-0.365510\pi\)
0.410053 + 0.912062i \(0.365510\pi\)
\(548\) 0 0
\(549\) 10.2253 0.436407
\(550\) 0 0
\(551\) −0.297201 −0.0126612
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −7.65509 −0.324940
\(556\) 0 0
\(557\) −4.90164 −0.207689 −0.103845 0.994594i \(-0.533114\pi\)
−0.103845 + 0.994594i \(0.533114\pi\)
\(558\) 0 0
\(559\) 12.5767 0.531939
\(560\) 0 0
\(561\) 6.00542 0.253549
\(562\) 0 0
\(563\) −0.494864 −0.0208560 −0.0104280 0.999946i \(-0.503319\pi\)
−0.0104280 + 0.999946i \(0.503319\pi\)
\(564\) 0 0
\(565\) −8.35329 −0.351425
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.10516 −0.130175 −0.0650875 0.997880i \(-0.520733\pi\)
−0.0650875 + 0.997880i \(0.520733\pi\)
\(570\) 0 0
\(571\) −24.7565 −1.03603 −0.518013 0.855373i \(-0.673328\pi\)
−0.518013 + 0.855373i \(0.673328\pi\)
\(572\) 0 0
\(573\) 5.33243 0.222766
\(574\) 0 0
\(575\) −18.9705 −0.791123
\(576\) 0 0
\(577\) −6.90679 −0.287534 −0.143767 0.989612i \(-0.545922\pi\)
−0.143767 + 0.989612i \(0.545922\pi\)
\(578\) 0 0
\(579\) 2.60615 0.108308
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.87856 0.0778020
\(584\) 0 0
\(585\) −4.48130 −0.185279
\(586\) 0 0
\(587\) 2.53709 0.104717 0.0523585 0.998628i \(-0.483326\pi\)
0.0523585 + 0.998628i \(0.483326\pi\)
\(588\) 0 0
\(589\) −2.73069 −0.112516
\(590\) 0 0
\(591\) 8.94793 0.368069
\(592\) 0 0
\(593\) 36.6188 1.50375 0.751877 0.659304i \(-0.229149\pi\)
0.751877 + 0.659304i \(0.229149\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −19.7946 −0.810139
\(598\) 0 0
\(599\) 16.8939 0.690264 0.345132 0.938554i \(-0.387834\pi\)
0.345132 + 0.938554i \(0.387834\pi\)
\(600\) 0 0
\(601\) 33.0537 1.34829 0.674145 0.738599i \(-0.264512\pi\)
0.674145 + 0.738599i \(0.264512\pi\)
\(602\) 0 0
\(603\) 9.83719 0.400601
\(604\) 0 0
\(605\) 9.62020 0.391117
\(606\) 0 0
\(607\) −32.3474 −1.31294 −0.656469 0.754353i \(-0.727951\pi\)
−0.656469 + 0.754353i \(0.727951\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.89194 0.278818
\(612\) 0 0
\(613\) −17.4200 −0.703587 −0.351794 0.936078i \(-0.614428\pi\)
−0.351794 + 0.936078i \(0.614428\pi\)
\(614\) 0 0
\(615\) 1.08151 0.0436107
\(616\) 0 0
\(617\) 30.1475 1.21369 0.606846 0.794819i \(-0.292434\pi\)
0.606846 + 0.794819i \(0.292434\pi\)
\(618\) 0 0
\(619\) −35.3433 −1.42057 −0.710283 0.703916i \(-0.751433\pi\)
−0.710283 + 0.703916i \(0.751433\pi\)
\(620\) 0 0
\(621\) 24.7657 0.993814
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 10.2375 0.409500
\(626\) 0 0
\(627\) −3.98476 −0.159136
\(628\) 0 0
\(629\) −31.4743 −1.25496
\(630\) 0 0
\(631\) 23.1762 0.922630 0.461315 0.887236i \(-0.347378\pi\)
0.461315 + 0.887236i \(0.347378\pi\)
\(632\) 0 0
\(633\) −11.7072 −0.465319
\(634\) 0 0
\(635\) 9.71123 0.385378
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 27.0840 1.07143
\(640\) 0 0
\(641\) −36.8733 −1.45641 −0.728204 0.685361i \(-0.759644\pi\)
−0.728204 + 0.685361i \(0.759644\pi\)
\(642\) 0 0
\(643\) 48.0696 1.89568 0.947841 0.318744i \(-0.103261\pi\)
0.947841 + 0.318744i \(0.103261\pi\)
\(644\) 0 0
\(645\) −5.92013 −0.233105
\(646\) 0 0
\(647\) 22.5246 0.885532 0.442766 0.896637i \(-0.353997\pi\)
0.442766 + 0.896637i \(0.353997\pi\)
\(648\) 0 0
\(649\) −5.62425 −0.220771
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −29.3035 −1.14674 −0.573368 0.819298i \(-0.694363\pi\)
−0.573368 + 0.819298i \(0.694363\pi\)
\(654\) 0 0
\(655\) 0.198577 0.00775906
\(656\) 0 0
\(657\) 18.7496 0.731490
\(658\) 0 0
\(659\) 25.4909 0.992983 0.496491 0.868042i \(-0.334621\pi\)
0.496491 + 0.868042i \(0.334621\pi\)
\(660\) 0 0
\(661\) 42.6069 1.65722 0.828608 0.559830i \(-0.189134\pi\)
0.828608 + 0.559830i \(0.189134\pi\)
\(662\) 0 0
\(663\) 10.7374 0.417007
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.484862 0.0187739
\(668\) 0 0
\(669\) −15.4681 −0.598030
\(670\) 0 0
\(671\) 6.93237 0.267621
\(672\) 0 0
\(673\) 20.2833 0.781864 0.390932 0.920420i \(-0.372153\pi\)
0.390932 + 0.920420i \(0.372153\pi\)
\(674\) 0 0
\(675\) −20.2770 −0.780462
\(676\) 0 0
\(677\) −12.9561 −0.497944 −0.248972 0.968511i \(-0.580093\pi\)
−0.248972 + 0.968511i \(0.580093\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −14.9490 −0.572848
\(682\) 0 0
\(683\) −18.5814 −0.710997 −0.355499 0.934677i \(-0.615689\pi\)
−0.355499 + 0.934677i \(0.615689\pi\)
\(684\) 0 0
\(685\) −15.2933 −0.584326
\(686\) 0 0
\(687\) −8.76798 −0.334519
\(688\) 0 0
\(689\) 3.35878 0.127959
\(690\) 0 0
\(691\) −16.2571 −0.618449 −0.309225 0.950989i \(-0.600069\pi\)
−0.309225 + 0.950989i \(0.600069\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.97977 0.113029
\(696\) 0 0
\(697\) 4.44667 0.168430
\(698\) 0 0
\(699\) −3.12793 −0.118309
\(700\) 0 0
\(701\) 14.4286 0.544961 0.272480 0.962161i \(-0.412156\pi\)
0.272480 + 0.962161i \(0.412156\pi\)
\(702\) 0 0
\(703\) 20.8840 0.787656
\(704\) 0 0
\(705\) −3.24418 −0.122183
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 28.2187 1.05978 0.529889 0.848067i \(-0.322234\pi\)
0.529889 + 0.848067i \(0.322234\pi\)
\(710\) 0 0
\(711\) 14.0261 0.526019
\(712\) 0 0
\(713\) 4.45492 0.166838
\(714\) 0 0
\(715\) −3.03814 −0.113620
\(716\) 0 0
\(717\) −5.92025 −0.221096
\(718\) 0 0
\(719\) −49.0294 −1.82849 −0.914243 0.405165i \(-0.867214\pi\)
−0.914243 + 0.405165i \(0.867214\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −7.66488 −0.285060
\(724\) 0 0
\(725\) −0.396982 −0.0147435
\(726\) 0 0
\(727\) 24.0066 0.890355 0.445178 0.895442i \(-0.353140\pi\)
0.445178 + 0.895442i \(0.353140\pi\)
\(728\) 0 0
\(729\) 15.6935 0.581242
\(730\) 0 0
\(731\) −24.3409 −0.900281
\(732\) 0 0
\(733\) 27.9928 1.03394 0.516969 0.856004i \(-0.327060\pi\)
0.516969 + 0.856004i \(0.327060\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.66922 0.245664
\(738\) 0 0
\(739\) 18.3985 0.676801 0.338401 0.941002i \(-0.390114\pi\)
0.338401 + 0.941002i \(0.390114\pi\)
\(740\) 0 0
\(741\) −7.12458 −0.261728
\(742\) 0 0
\(743\) 7.49198 0.274854 0.137427 0.990512i \(-0.456117\pi\)
0.137427 + 0.990512i \(0.456117\pi\)
\(744\) 0 0
\(745\) 16.9970 0.622723
\(746\) 0 0
\(747\) −30.5835 −1.11899
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −10.2250 −0.373116 −0.186558 0.982444i \(-0.559733\pi\)
−0.186558 + 0.982444i \(0.559733\pi\)
\(752\) 0 0
\(753\) −11.2547 −0.410144
\(754\) 0 0
\(755\) 8.92111 0.324672
\(756\) 0 0
\(757\) 13.8559 0.503602 0.251801 0.967779i \(-0.418977\pi\)
0.251801 + 0.967779i \(0.418977\pi\)
\(758\) 0 0
\(759\) 6.50086 0.235966
\(760\) 0 0
\(761\) 24.0153 0.870554 0.435277 0.900297i \(-0.356650\pi\)
0.435277 + 0.900297i \(0.356650\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 8.67307 0.313576
\(766\) 0 0
\(767\) −10.0559 −0.363098
\(768\) 0 0
\(769\) 50.6700 1.82721 0.913604 0.406606i \(-0.133288\pi\)
0.913604 + 0.406606i \(0.133288\pi\)
\(770\) 0 0
\(771\) −6.97529 −0.251209
\(772\) 0 0
\(773\) −16.1315 −0.580208 −0.290104 0.956995i \(-0.593690\pi\)
−0.290104 + 0.956995i \(0.593690\pi\)
\(774\) 0 0
\(775\) −3.64748 −0.131021
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.95049 −0.105712
\(780\) 0 0
\(781\) 18.3618 0.657038
\(782\) 0 0
\(783\) 0.518256 0.0185209
\(784\) 0 0
\(785\) −21.0495 −0.751289
\(786\) 0 0
\(787\) −19.9563 −0.711366 −0.355683 0.934607i \(-0.615752\pi\)
−0.355683 + 0.934607i \(0.615752\pi\)
\(788\) 0 0
\(789\) 20.9531 0.745949
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 12.3948 0.440151
\(794\) 0 0
\(795\) −1.58105 −0.0560740
\(796\) 0 0
\(797\) 45.4738 1.61077 0.805383 0.592755i \(-0.201960\pi\)
0.805383 + 0.592755i \(0.201960\pi\)
\(798\) 0 0
\(799\) −13.3386 −0.471886
\(800\) 0 0
\(801\) 29.8931 1.05622
\(802\) 0 0
\(803\) 12.7114 0.448577
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −5.36999 −0.189033
\(808\) 0 0
\(809\) 18.5341 0.651623 0.325812 0.945435i \(-0.394363\pi\)
0.325812 + 0.945435i \(0.394363\pi\)
\(810\) 0 0
\(811\) −45.3402 −1.59211 −0.796055 0.605224i \(-0.793084\pi\)
−0.796055 + 0.605224i \(0.793084\pi\)
\(812\) 0 0
\(813\) 18.4708 0.647800
\(814\) 0 0
\(815\) −15.9993 −0.560430
\(816\) 0 0
\(817\) 16.1509 0.565047
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.18741 −0.0414410 −0.0207205 0.999785i \(-0.506596\pi\)
−0.0207205 + 0.999785i \(0.506596\pi\)
\(822\) 0 0
\(823\) −3.43355 −0.119686 −0.0598431 0.998208i \(-0.519060\pi\)
−0.0598431 + 0.998208i \(0.519060\pi\)
\(824\) 0 0
\(825\) −5.32259 −0.185309
\(826\) 0 0
\(827\) −9.25662 −0.321884 −0.160942 0.986964i \(-0.551453\pi\)
−0.160942 + 0.986964i \(0.551453\pi\)
\(828\) 0 0
\(829\) −3.46216 −0.120246 −0.0601229 0.998191i \(-0.519149\pi\)
−0.0601229 + 0.998191i \(0.519149\pi\)
\(830\) 0 0
\(831\) −19.5272 −0.677393
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 14.0347 0.485691
\(836\) 0 0
\(837\) 4.76174 0.164590
\(838\) 0 0
\(839\) −29.6017 −1.02196 −0.510982 0.859591i \(-0.670718\pi\)
−0.510982 + 0.859591i \(0.670718\pi\)
\(840\) 0 0
\(841\) −28.9899 −0.999650
\(842\) 0 0
\(843\) 12.1553 0.418649
\(844\) 0 0
\(845\) 7.94545 0.273332
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 13.2937 0.456237
\(850\) 0 0
\(851\) −34.0708 −1.16793
\(852\) 0 0
\(853\) −57.9438 −1.98396 −0.991978 0.126409i \(-0.959655\pi\)
−0.991978 + 0.126409i \(0.959655\pi\)
\(854\) 0 0
\(855\) −5.75482 −0.196811
\(856\) 0 0
\(857\) 9.91912 0.338831 0.169415 0.985545i \(-0.445812\pi\)
0.169415 + 0.985545i \(0.445812\pi\)
\(858\) 0 0
\(859\) 47.6228 1.62487 0.812435 0.583052i \(-0.198142\pi\)
0.812435 + 0.583052i \(0.198142\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0.0647289 0.00220340 0.00110170 0.999999i \(-0.499649\pi\)
0.00110170 + 0.999999i \(0.499649\pi\)
\(864\) 0 0
\(865\) −3.11692 −0.105978
\(866\) 0 0
\(867\) −2.91431 −0.0989751
\(868\) 0 0
\(869\) 9.50911 0.322574
\(870\) 0 0
\(871\) 11.9243 0.404038
\(872\) 0 0
\(873\) −6.07868 −0.205732
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 12.5643 0.424266 0.212133 0.977241i \(-0.431959\pi\)
0.212133 + 0.977241i \(0.431959\pi\)
\(878\) 0 0
\(879\) −23.5117 −0.793029
\(880\) 0 0
\(881\) −42.1898 −1.42141 −0.710705 0.703490i \(-0.751624\pi\)
−0.710705 + 0.703490i \(0.751624\pi\)
\(882\) 0 0
\(883\) 8.61356 0.289869 0.144935 0.989441i \(-0.453703\pi\)
0.144935 + 0.989441i \(0.453703\pi\)
\(884\) 0 0
\(885\) 4.73353 0.159116
\(886\) 0 0
\(887\) −5.96189 −0.200181 −0.100090 0.994978i \(-0.531913\pi\)
−0.100090 + 0.994978i \(0.531913\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.358372 −0.0120059
\(892\) 0 0
\(893\) 8.85054 0.296172
\(894\) 0 0
\(895\) −15.3099 −0.511752
\(896\) 0 0
\(897\) 11.6232 0.388089
\(898\) 0 0
\(899\) 0.0932251 0.00310923
\(900\) 0 0
\(901\) −6.50056 −0.216565
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −19.2970 −0.641453
\(906\) 0 0
\(907\) −15.7086 −0.521595 −0.260797 0.965394i \(-0.583985\pi\)
−0.260797 + 0.965394i \(0.583985\pi\)
\(908\) 0 0
\(909\) −23.9771 −0.795270
\(910\) 0 0
\(911\) −45.8006 −1.51744 −0.758720 0.651417i \(-0.774175\pi\)
−0.758720 + 0.651417i \(0.774175\pi\)
\(912\) 0 0
\(913\) −20.7344 −0.686208
\(914\) 0 0
\(915\) −5.83449 −0.192882
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −45.2558 −1.49285 −0.746426 0.665469i \(-0.768232\pi\)
−0.746426 + 0.665469i \(0.768232\pi\)
\(920\) 0 0
\(921\) −9.03946 −0.297860
\(922\) 0 0
\(923\) 32.8301 1.08062
\(924\) 0 0
\(925\) 27.8956 0.917201
\(926\) 0 0
\(927\) −9.35535 −0.307270
\(928\) 0 0
\(929\) 23.9841 0.786892 0.393446 0.919348i \(-0.371283\pi\)
0.393446 + 0.919348i \(0.371283\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 17.6435 0.577622
\(934\) 0 0
\(935\) 5.87999 0.192296
\(936\) 0 0
\(937\) −18.6293 −0.608594 −0.304297 0.952577i \(-0.598422\pi\)
−0.304297 + 0.952577i \(0.598422\pi\)
\(938\) 0 0
\(939\) 3.38226 0.110376
\(940\) 0 0
\(941\) −9.62697 −0.313830 −0.156915 0.987612i \(-0.550155\pi\)
−0.156915 + 0.987612i \(0.550155\pi\)
\(942\) 0 0
\(943\) 4.81352 0.156750
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −25.0283 −0.813310 −0.406655 0.913582i \(-0.633305\pi\)
−0.406655 + 0.913582i \(0.633305\pi\)
\(948\) 0 0
\(949\) 22.7275 0.737765
\(950\) 0 0
\(951\) −28.3189 −0.918305
\(952\) 0 0
\(953\) 30.8050 0.997873 0.498936 0.866639i \(-0.333724\pi\)
0.498936 + 0.866639i \(0.333724\pi\)
\(954\) 0 0
\(955\) 5.22106 0.168950
\(956\) 0 0
\(957\) 0.136039 0.00439752
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −30.1434 −0.972369
\(962\) 0 0
\(963\) −4.57720 −0.147498
\(964\) 0 0
\(965\) 2.55172 0.0821428
\(966\) 0 0
\(967\) −26.7377 −0.859827 −0.429913 0.902870i \(-0.641456\pi\)
−0.429913 + 0.902870i \(0.641456\pi\)
\(968\) 0 0
\(969\) 13.7889 0.442962
\(970\) 0 0
\(971\) 2.65019 0.0850486 0.0425243 0.999095i \(-0.486460\pi\)
0.0425243 + 0.999095i \(0.486460\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −9.51655 −0.304774
\(976\) 0 0
\(977\) −2.38400 −0.0762710 −0.0381355 0.999273i \(-0.512142\pi\)
−0.0381355 + 0.999273i \(0.512142\pi\)
\(978\) 0 0
\(979\) 20.2663 0.647715
\(980\) 0 0
\(981\) −31.0078 −0.990004
\(982\) 0 0
\(983\) 27.5555 0.878882 0.439441 0.898271i \(-0.355176\pi\)
0.439441 + 0.898271i \(0.355176\pi\)
\(984\) 0 0
\(985\) 8.76105 0.279150
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −26.3490 −0.837849
\(990\) 0 0
\(991\) 17.8527 0.567109 0.283554 0.958956i \(-0.408486\pi\)
0.283554 + 0.958956i \(0.408486\pi\)
\(992\) 0 0
\(993\) 8.39856 0.266520
\(994\) 0 0
\(995\) −19.3812 −0.614425
\(996\) 0 0
\(997\) 16.4836 0.522042 0.261021 0.965333i \(-0.415941\pi\)
0.261021 + 0.965333i \(0.415941\pi\)
\(998\) 0 0
\(999\) −36.4174 −1.15219
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 8036.2.a.p.1.4 yes 10
7.6 odd 2 8036.2.a.o.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8036.2.a.o.1.7 10 7.6 odd 2
8036.2.a.p.1.4 yes 10 1.1 even 1 trivial