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Properties

Label 7448.2.a.b.1.1
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7448,2,Mod(1,7448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7448, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7448.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(59.4725794254\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1064)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7448.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{3} -1.00000 q^{5} +1.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{3} -1.00000 q^{5} +1.00000 q^{9} -1.00000 q^{11} +2.00000 q^{13} +2.00000 q^{15} -2.00000 q^{17} +1.00000 q^{19} -3.00000 q^{23} -4.00000 q^{25} +4.00000 q^{27} +4.00000 q^{29} +4.00000 q^{31} +2.00000 q^{33} -10.0000 q^{37} -4.00000 q^{39} +10.0000 q^{41} +1.00000 q^{43} -1.00000 q^{45} +1.00000 q^{47} +4.00000 q^{51} -4.00000 q^{53} +1.00000 q^{55} -2.00000 q^{57} +8.00000 q^{59} +3.00000 q^{61} -2.00000 q^{65} -4.00000 q^{67} +6.00000 q^{69} -4.00000 q^{71} -3.00000 q^{73} +8.00000 q^{75} +14.0000 q^{79} -11.0000 q^{81} -9.00000 q^{83} +2.00000 q^{85} -8.00000 q^{87} +6.00000 q^{89} -8.00000 q^{93} -1.00000 q^{95} -14.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(3\) −2.00000 −1.15470 −0.577350 − 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214 −0.223607 − 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.00000 −0.301511 −0.150756 − 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 −0.625543 −0.312772 − 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 − 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 − 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 2.00000 0.348155
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.0000 −1.64399 −0.821995 − 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 − 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 − 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 1.00000 0.145865 0.0729325 − 0.997337i \(-0.476764\pi\)
0.0729325 + 0.997337i \(0.476764\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) 0 0
\(53\) −4.00000 −0.549442 −0.274721 − 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) 8.00000 1.04151 0.520756 − 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) 3.00000 0.384111 0.192055 − 0.981384i \(-0.438485\pi\)
0.192055 + 0.981384i \(0.438485\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 − 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) −3.00000 −0.351123 −0.175562 − 0.984468i \(-0.556174\pi\)
−0.175562 + 0.984468i \(0.556174\pi\)
\(74\) 0 0
\(75\) 8.00000 0.923760
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 14.0000 1.57512 0.787562 − 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) −9.00000 −0.987878 −0.493939 − 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) −8.00000 −0.857690
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 − 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −8.00000 −0.829561
\(94\) 0 0
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 − 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) −3.00000 −0.298511 −0.149256 − 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 0 0
\(103\) 10.0000 0.985329 0.492665 − 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.00000 0.193347 0.0966736 − 0.995316i \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) 0 0
\(109\) 16.0000 1.53252 0.766261 − 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 0 0
\(111\) 20.0000 1.89832
\(112\) 0 0
\(113\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 3.00000 0.279751
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 0 0
\(123\) −20.0000 −1.80334
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 − 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0 0
\(129\) −2.00000 −0.176090
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −4.00000 −0.344265
\(136\) 0 0
\(137\) 13.0000 1.11066 0.555332 − 0.831628i \(-0.312591\pi\)
0.555332 + 0.831628i \(0.312591\pi\)
\(138\) 0 0
\(139\) −1.00000 −0.0848189 −0.0424094 − 0.999100i \(-0.513503\pi\)
−0.0424094 + 0.999100i \(0.513503\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 0 0
\(143\) −2.00000 −0.167248
\(144\) 0 0
\(145\) −4.00000 −0.332182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −15.0000 −1.22885 −0.614424 − 0.788976i \(-0.710612\pi\)
−0.614424 + 0.788976i \(0.710612\pi\)
\(150\) 0 0
\(151\) 10.0000 0.813788 0.406894 − 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) 5.00000 0.399043 0.199522 − 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) 0 0
\(159\) 8.00000 0.634441
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 9.00000 0.704934 0.352467 − 0.935824i \(-0.385343\pi\)
0.352467 + 0.935824i \(0.385343\pi\)
\(164\) 0 0
\(165\) −2.00000 −0.155700
\(166\) 0 0
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 1.00000 0.0764719
\(172\) 0 0
\(173\) −16.0000 −1.21646 −0.608229 − 0.793762i \(-0.708120\pi\)
−0.608229 + 0.793762i \(0.708120\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −16.0000 −1.20263
\(178\) 0 0
\(179\) 14.0000 1.04641 0.523205 − 0.852207i \(-0.324736\pi\)
0.523205 + 0.852207i \(0.324736\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 − 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) −6.00000 −0.443533
\(184\) 0 0
\(185\) 10.0000 0.735215
\(186\) 0 0
\(187\) 2.00000 0.146254
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.00000 −0.217072 −0.108536 − 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 0 0
\(193\) −10.0000 −0.719816 −0.359908 − 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) 0 0
\(195\) 4.00000 0.286446
\(196\) 0 0
\(197\) 3.00000 0.213741 0.106871 − 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) −19.0000 −1.34687 −0.673437 − 0.739244i \(-0.735183\pi\)
−0.673437 + 0.739244i \(0.735183\pi\)
\(200\) 0 0
\(201\) 8.00000 0.564276
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −10.0000 −0.698430
\(206\) 0 0
\(207\) −3.00000 −0.208514
\(208\) 0 0
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 − 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 0 0
\(213\) 8.00000 0.548151
\(214\) 0 0
\(215\) −1.00000 −0.0681994
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 6.00000 0.405442
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 − 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) 0 0
\(227\) 22.0000 1.46019 0.730096 − 0.683345i \(-0.239475\pi\)
0.730096 + 0.683345i \(0.239475\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 − 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 − 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) −1.00000 −0.0652328
\(236\) 0 0
\(237\) −28.0000 −1.81880
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 − 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 − 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 0 0
\(243\) 10.0000 0.641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.00000 0.127257
\(248\) 0 0
\(249\) 18.0000 1.14070
\(250\) 0 0
\(251\) 19.0000 1.19927 0.599635 − 0.800274i \(-0.295313\pi\)
0.599635 + 0.800274i \(0.295313\pi\)
\(252\) 0 0
\(253\) 3.00000 0.188608
\(254\) 0 0
\(255\) −4.00000 −0.250490
\(256\) 0 0
\(257\) 22.0000 1.37232 0.686161 − 0.727450i \(-0.259294\pi\)
0.686161 + 0.727450i \(0.259294\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 4.00000 0.247594
\(262\) 0 0
\(263\) −12.0000 −0.739952 −0.369976 − 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) 0 0
\(269\) −12.0000 −0.731653 −0.365826 − 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) 0 0
\(271\) −13.0000 −0.789694 −0.394847 − 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.00000 0.241209
\(276\) 0 0
\(277\) −23.0000 −1.38194 −0.690968 − 0.722885i \(-0.742815\pi\)
−0.690968 + 0.722885i \(0.742815\pi\)
\(278\) 0 0
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 − 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) −7.00000 −0.416107 −0.208053 − 0.978117i \(-0.566713\pi\)
−0.208053 + 0.978117i \(0.566713\pi\)
\(284\) 0 0
\(285\) 2.00000 0.118470
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 28.0000 1.64139
\(292\) 0 0
\(293\) −14.0000 −0.817889 −0.408944 − 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) −4.00000 −0.232104
\(298\) 0 0
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 6.00000 0.344691
\(304\) 0 0
\(305\) −3.00000 −0.171780
\(306\) 0 0
\(307\) −26.0000 −1.48390 −0.741949 − 0.670456i \(-0.766098\pi\)
−0.741949 + 0.670456i \(0.766098\pi\)
\(308\) 0 0
\(309\) −20.0000 −1.13776
\(310\) 0 0
\(311\) −4.00000 −0.226819 −0.113410 − 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) 0 0
\(313\) 11.0000 0.621757 0.310878 − 0.950450i \(-0.399377\pi\)
0.310878 + 0.950450i \(0.399377\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 12.0000 0.673987 0.336994 − 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 0 0
\(319\) −4.00000 −0.223957
\(320\) 0 0
\(321\) −4.00000 −0.223258
\(322\) 0 0
\(323\) −2.00000 −0.111283
\(324\) 0 0
\(325\) −8.00000 −0.443760
\(326\) 0 0
\(327\) −32.0000 −1.76960
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 −0.109930 −0.0549650 − 0.998488i \(-0.517505\pi\)
−0.0549650 + 0.998488i \(0.517505\pi\)
\(332\) 0 0
\(333\) −10.0000 −0.547997
\(334\) 0 0
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) −36.0000 −1.96104 −0.980522 − 0.196407i \(-0.937073\pi\)
−0.980522 + 0.196407i \(0.937073\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.00000 −0.216612
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −6.00000 −0.323029
\(346\) 0 0
\(347\) 23.0000 1.23470 0.617352 − 0.786687i \(-0.288205\pi\)
0.617352 + 0.786687i \(0.288205\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 − 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 8.00000 0.427008
\(352\) 0 0
\(353\) −30.0000 −1.59674 −0.798369 − 0.602168i \(-0.794304\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) 0 0
\(355\) 4.00000 0.212298
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.00000 −0.263890 −0.131945 − 0.991257i \(-0.542122\pi\)
−0.131945 + 0.991257i \(0.542122\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 20.0000 1.04973
\(364\) 0 0
\(365\) 3.00000 0.157027
\(366\) 0 0
\(367\) −16.0000 −0.835193 −0.417597 − 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 0 0
\(369\) 10.0000 0.520579
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 4.00000 0.207112 0.103556 − 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) −18.0000 −0.929516
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) −26.0000 −1.33553 −0.667765 − 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 0 0
\(381\) −4.00000 −0.204926
\(382\) 0 0
\(383\) −6.00000 −0.306586 −0.153293 − 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.00000 0.0508329
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 − 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) 0 0
\(393\) −24.0000 −1.21064
\(394\) 0 0
\(395\) −14.0000 −0.704416
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 − 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12.0000 −0.599251 −0.299626 − 0.954057i \(-0.596862\pi\)
−0.299626 + 0.954057i \(0.596862\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 0 0
\(405\) 11.0000 0.546594
\(406\) 0 0
\(407\) 10.0000 0.495682
\(408\) 0 0
\(409\) −6.00000 −0.296681 −0.148340 − 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) 0 0
\(411\) −26.0000 −1.28249
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 9.00000 0.441793
\(416\) 0 0
\(417\) 2.00000 0.0979404
\(418\) 0 0
\(419\) 15.0000 0.732798 0.366399 − 0.930458i \(-0.380591\pi\)
0.366399 + 0.930458i \(0.380591\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 − 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 0 0
\(423\) 1.00000 0.0486217
\(424\) 0 0
\(425\) 8.00000 0.388057
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 4.00000 0.193122
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 − 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 0 0
\(433\) 4.00000 0.192228 0.0961139 − 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) 0 0
\(437\) −3.00000 −0.143509
\(438\) 0 0
\(439\) −20.0000 −0.954548 −0.477274 − 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0000 −0.570137 −0.285069 − 0.958507i \(-0.592016\pi\)
−0.285069 + 0.958507i \(0.592016\pi\)
\(444\) 0 0
\(445\) −6.00000 −0.284427
\(446\) 0 0
\(447\) 30.0000 1.41895
\(448\) 0 0
\(449\) 8.00000 0.377543 0.188772 − 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) 0 0
\(451\) −10.0000 −0.470882
\(452\) 0 0
\(453\) −20.0000 −0.939682
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.00000 0.140334 0.0701670 − 0.997535i \(-0.477647\pi\)
0.0701670 + 0.997535i \(0.477647\pi\)
\(458\) 0 0
\(459\) −8.00000 −0.373408
\(460\) 0 0
\(461\) 9.00000 0.419172 0.209586 − 0.977790i \(-0.432788\pi\)
0.209586 + 0.977790i \(0.432788\pi\)
\(462\) 0 0
\(463\) −31.0000 −1.44069 −0.720346 − 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) 0 0
\(465\) 8.00000 0.370991
\(466\) 0 0
\(467\) −15.0000 −0.694117 −0.347059 − 0.937843i \(-0.612820\pi\)
−0.347059 + 0.937843i \(0.612820\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −10.0000 −0.460776
\(472\) 0 0
\(473\) −1.00000 −0.0459800
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) −4.00000 −0.183147
\(478\) 0 0
\(479\) −21.0000 −0.959514 −0.479757 − 0.877401i \(-0.659275\pi\)
−0.479757 + 0.877401i \(0.659275\pi\)
\(480\) 0 0
\(481\) −20.0000 −0.911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 14.0000 0.635707
\(486\) 0 0
\(487\) −38.0000 −1.72194 −0.860972 − 0.508652i \(-0.830144\pi\)
−0.860972 + 0.508652i \(0.830144\pi\)
\(488\) 0 0
\(489\) −18.0000 −0.813988
\(490\) 0 0
\(491\) 15.0000 0.676941 0.338470 − 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) 0 0
\(493\) −8.00000 −0.360302
\(494\) 0 0
\(495\) 1.00000 0.0449467
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.00000 0.134298 0.0671492 − 0.997743i \(-0.478610\pi\)
0.0671492 + 0.997743i \(0.478610\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 21.0000 0.936344 0.468172 − 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 0 0
\(505\) 3.00000 0.133498
\(506\) 0 0
\(507\) 18.0000 0.799408
\(508\) 0 0
\(509\) −18.0000 −0.797836 −0.398918 − 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 4.00000 0.176604
\(514\) 0 0
\(515\) −10.0000 −0.440653
\(516\) 0 0
\(517\) −1.00000 −0.0439799
\(518\) 0 0
\(519\) 32.0000 1.40464
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 − 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 0 0
\(523\) 38.0000 1.66162 0.830812 − 0.556553i \(-0.187876\pi\)
0.830812 + 0.556553i \(0.187876\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.00000 −0.348485
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) 8.00000 0.347170
\(532\) 0 0
\(533\) 20.0000 0.866296
\(534\) 0 0
\(535\) −2.00000 −0.0864675
\(536\) 0 0
\(537\) −28.0000 −1.20829
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −25.0000 −1.07483 −0.537417 − 0.843317i \(-0.680600\pi\)
−0.537417 + 0.843317i \(0.680600\pi\)
\(542\) 0 0
\(543\) 16.0000 0.686626
\(544\) 0 0
\(545\) −16.0000 −0.685365
\(546\) 0 0
\(547\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 3.00000 0.128037
\(550\) 0 0
\(551\) 4.00000 0.170406
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −20.0000 −0.848953
\(556\) 0 0
\(557\) 21.0000 0.889799 0.444899 − 0.895581i \(-0.353239\pi\)
0.444899 + 0.895581i \(0.353239\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 0 0
\(563\) 6.00000 0.252870 0.126435 − 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −46.0000 −1.92842 −0.964210 − 0.265139i \(-0.914582\pi\)
−0.964210 + 0.265139i \(0.914582\pi\)
\(570\) 0 0
\(571\) 23.0000 0.962520 0.481260 − 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) −9.00000 −0.374675 −0.187337 − 0.982296i \(-0.559986\pi\)
−0.187337 + 0.982296i \(0.559986\pi\)
\(578\) 0 0
\(579\) 20.0000 0.831172
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.00000 0.165663
\(584\) 0 0
\(585\) −2.00000 −0.0826898
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 − 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) −6.00000 −0.246807
\(592\) 0 0
\(593\) 3.00000 0.123195 0.0615976 − 0.998101i \(-0.480380\pi\)
0.0615976 + 0.998101i \(0.480380\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 38.0000 1.55524
\(598\) 0 0
\(599\) 44.0000 1.79779 0.898896 − 0.438163i \(-0.144371\pi\)
0.898896 + 0.438163i \(0.144371\pi\)
\(600\) 0 0
\(601\) 6.00000 0.244745 0.122373 − 0.992484i \(-0.460950\pi\)
0.122373 + 0.992484i \(0.460950\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0 0
\(605\) 10.0000 0.406558
\(606\) 0 0
\(607\) −22.0000 −0.892952 −0.446476 − 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.00000 0.0809113
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 − 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) 0 0
\(615\) 20.0000 0.806478
\(616\) 0 0
\(617\) −43.0000 −1.73111 −0.865557 − 0.500810i \(-0.833036\pi\)
−0.865557 + 0.500810i \(0.833036\pi\)
\(618\) 0 0
\(619\) −25.0000 −1.00483 −0.502417 − 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 0 0
\(621\) −12.0000 −0.481543
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 2.00000 0.0798723
\(628\) 0 0
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) 25.0000 0.995234 0.497617 − 0.867397i \(-0.334208\pi\)
0.497617 + 0.867397i \(0.334208\pi\)
\(632\) 0 0
\(633\) 16.0000 0.635943
\(634\) 0 0
\(635\) −2.00000 −0.0793676
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −4.00000 −0.158238
\(640\) 0 0
\(641\) −40.0000 −1.57991 −0.789953 − 0.613168i \(-0.789895\pi\)
−0.789953 + 0.613168i \(0.789895\pi\)
\(642\) 0 0
\(643\) −4.00000 −0.157745 −0.0788723 − 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 2.00000 0.0787499
\(646\) 0 0
\(647\) −47.0000 −1.84776 −0.923880 − 0.382682i \(-0.875001\pi\)
−0.923880 + 0.382682i \(0.875001\pi\)
\(648\) 0 0
\(649\) −8.00000 −0.314027
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 30.0000 1.17399 0.586995 − 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) 0 0
\(655\) −12.0000 −0.468879
\(656\) 0 0
\(657\) −3.00000 −0.117041
\(658\) 0 0
\(659\) 4.00000 0.155818 0.0779089 − 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 − 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 0 0
\(663\) 8.00000 0.310694
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −12.0000 −0.464642
\(668\) 0 0
\(669\) −8.00000 −0.309298
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) −12.0000 −0.462566 −0.231283 − 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(674\) 0 0
\(675\) −16.0000 −0.615840
\(676\) 0 0
\(677\) 16.0000 0.614930 0.307465 − 0.951559i \(-0.400519\pi\)
0.307465 + 0.951559i \(0.400519\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −44.0000 −1.68608
\(682\) 0 0
\(683\) −6.00000 −0.229584 −0.114792 − 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(684\) 0 0
\(685\) −13.0000 −0.496704
\(686\) 0 0
\(687\) −44.0000 −1.67870
\(688\) 0 0
\(689\) −8.00000 −0.304776
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 − 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.00000 0.0379322
\(696\) 0 0
\(697\) −20.0000 −0.757554
\(698\) 0 0
\(699\) 36.0000 1.36165
\(700\) 0 0
\(701\) −23.0000 −0.868698 −0.434349 − 0.900745i \(-0.643022\pi\)
−0.434349 + 0.900745i \(0.643022\pi\)
\(702\) 0 0
\(703\) −10.0000 −0.377157
\(704\) 0 0
\(705\) 2.00000 0.0753244
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −23.0000 −0.863783 −0.431892 − 0.901926i \(-0.642154\pi\)
−0.431892 + 0.901926i \(0.642154\pi\)
\(710\) 0 0
\(711\) 14.0000 0.525041
\(712\) 0 0
\(713\) −12.0000 −0.449404
\(714\) 0 0
\(715\) 2.00000 0.0747958
\(716\) 0 0
\(717\) 48.0000 1.79259
\(718\) 0 0
\(719\) −36.0000 −1.34257 −0.671287 − 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 44.0000 1.63638
\(724\) 0 0
\(725\) −16.0000 −0.594225
\(726\) 0 0
\(727\) −29.0000 −1.07555 −0.537775 − 0.843088i \(-0.680735\pi\)
−0.537775 + 0.843088i \(0.680735\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −2.00000 −0.0739727
\(732\) 0 0
\(733\) 26.0000 0.960332 0.480166 − 0.877178i \(-0.340576\pi\)
0.480166 + 0.877178i \(0.340576\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.00000 0.147342
\(738\) 0 0
\(739\) −16.0000 −0.588570 −0.294285 − 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 0 0
\(741\) −4.00000 −0.146944
\(742\) 0 0
\(743\) −18.0000 −0.660356 −0.330178 − 0.943919i \(-0.607109\pi\)
−0.330178 + 0.943919i \(0.607109\pi\)
\(744\) 0 0
\(745\) 15.0000 0.549557
\(746\) 0 0
\(747\) −9.00000 −0.329293
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 − 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) 0 0
\(753\) −38.0000 −1.38480
\(754\) 0 0
\(755\) −10.0000 −0.363937
\(756\) 0 0
\(757\) −21.0000 −0.763258 −0.381629 − 0.924316i \(-0.624637\pi\)
−0.381629 + 0.924316i \(0.624637\pi\)
\(758\) 0 0
\(759\) −6.00000 −0.217786
\(760\) 0 0
\(761\) −3.00000 −0.108750 −0.0543750 − 0.998521i \(-0.517317\pi\)
−0.0543750 + 0.998521i \(0.517317\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2.00000 0.0723102
\(766\) 0 0
\(767\) 16.0000 0.577727
\(768\) 0 0
\(769\) −1.00000 −0.0360609 −0.0180305 − 0.999837i \(-0.505740\pi\)
−0.0180305 + 0.999837i \(0.505740\pi\)
\(770\) 0 0
\(771\) −44.0000 −1.58462
\(772\) 0 0
\(773\) −50.0000 −1.79838 −0.899188 − 0.437564i \(-0.855842\pi\)
−0.899188 + 0.437564i \(0.855842\pi\)
\(774\) 0 0
\(775\) −16.0000 −0.574737
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10.0000 0.358287
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 16.0000 0.571793
\(784\) 0 0
\(785\) −5.00000 −0.178458
\(786\) 0 0
\(787\) 42.0000 1.49714 0.748569 − 0.663057i \(-0.230741\pi\)
0.748569 + 0.663057i \(0.230741\pi\)
\(788\) 0 0
\(789\) 24.0000 0.854423
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.00000 0.213066
\(794\) 0 0
\(795\) −8.00000 −0.283731
\(796\) 0 0
\(797\) −18.0000 −0.637593 −0.318796 − 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 0 0
\(799\) −2.00000 −0.0707549
\(800\) 0 0
\(801\) 6.00000 0.212000
\(802\) 0 0
\(803\) 3.00000 0.105868
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 24.0000 0.844840
\(808\) 0 0
\(809\) −5.00000 −0.175791 −0.0878953 − 0.996130i \(-0.528014\pi\)
−0.0878953 + 0.996130i \(0.528014\pi\)
\(810\) 0 0
\(811\) −30.0000 −1.05344 −0.526721 − 0.850038i \(-0.676579\pi\)
−0.526721 + 0.850038i \(0.676579\pi\)
\(812\) 0 0
\(813\) 26.0000 0.911860
\(814\) 0 0
\(815\) −9.00000 −0.315256
\(816\) 0 0
\(817\) 1.00000 0.0349856
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15.0000 −0.523504 −0.261752 − 0.965135i \(-0.584300\pi\)
−0.261752 + 0.965135i \(0.584300\pi\)
\(822\) 0 0
\(823\) −1.00000 −0.0348578 −0.0174289 − 0.999848i \(-0.505548\pi\)
−0.0174289 + 0.999848i \(0.505548\pi\)
\(824\) 0 0
\(825\) −8.00000 −0.278524
\(826\) 0 0
\(827\) 36.0000 1.25184 0.625921 − 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) 48.0000 1.66711 0.833554 − 0.552437i \(-0.186302\pi\)
0.833554 + 0.552437i \(0.186302\pi\)
\(830\) 0 0
\(831\) 46.0000 1.59572
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 16.0000 0.553041
\(838\) 0 0
\(839\) −4.00000 −0.138095 −0.0690477 − 0.997613i \(-0.521996\pi\)
−0.0690477 + 0.997613i \(0.521996\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 0 0
\(843\) −24.0000 −0.826604
\(844\) 0 0
\(845\) 9.00000 0.309609
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 14.0000 0.480479
\(850\) 0 0
\(851\) 30.0000 1.02839
\(852\) 0 0
\(853\) −17.0000 −0.582069 −0.291034 − 0.956713i \(-0.593999\pi\)
−0.291034 + 0.956713i \(0.593999\pi\)
\(854\) 0 0
\(855\) −1.00000 −0.0341993
\(856\) 0 0
\(857\) −12.0000 −0.409912 −0.204956 − 0.978771i \(-0.565705\pi\)
−0.204956 + 0.978771i \(0.565705\pi\)
\(858\) 0 0
\(859\) −15.0000 −0.511793 −0.255897 − 0.966704i \(-0.582371\pi\)
−0.255897 + 0.966704i \(0.582371\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 52.0000 1.77010 0.885050 − 0.465495i \(-0.154124\pi\)
0.885050 + 0.465495i \(0.154124\pi\)
\(864\) 0 0
\(865\) 16.0000 0.544016
\(866\) 0 0
\(867\) 26.0000 0.883006
\(868\) 0 0
\(869\) −14.0000 −0.474917
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) 0 0
\(873\) −14.0000 −0.473828
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −6.00000 −0.202606 −0.101303 − 0.994856i \(-0.532301\pi\)
−0.101303 + 0.994856i \(0.532301\pi\)
\(878\) 0 0
\(879\) 28.0000 0.944417
\(880\) 0 0
\(881\) −2.00000 −0.0673817 −0.0336909 − 0.999432i \(-0.510726\pi\)
−0.0336909 + 0.999432i \(0.510726\pi\)
\(882\) 0 0
\(883\) 28.0000 0.942275 0.471138 − 0.882060i \(-0.343844\pi\)
0.471138 + 0.882060i \(0.343844\pi\)
\(884\) 0 0
\(885\) 16.0000 0.537834
\(886\) 0 0
\(887\) −50.0000 −1.67884 −0.839418 − 0.543487i \(-0.817104\pi\)
−0.839418 + 0.543487i \(0.817104\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 11.0000 0.368514
\(892\) 0 0
\(893\) 1.00000 0.0334637
\(894\) 0 0
\(895\) −14.0000 −0.467968
\(896\) 0 0
\(897\) 12.0000 0.400668
\(898\) 0 0
\(899\) 16.0000 0.533630
\(900\) 0 0
\(901\) 8.00000 0.266519
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8.00000 0.265929
\(906\) 0 0
\(907\) −48.0000 −1.59381 −0.796907 − 0.604102i \(-0.793532\pi\)
−0.796907 + 0.604102i \(0.793532\pi\)
\(908\) 0 0
\(909\) −3.00000 −0.0995037
\(910\) 0 0
\(911\) −8.00000 −0.265052 −0.132526 − 0.991180i \(-0.542309\pi\)
−0.132526 + 0.991180i \(0.542309\pi\)
\(912\) 0 0
\(913\) 9.00000 0.297857
\(914\) 0 0
\(915\) 6.00000 0.198354
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 27.0000 0.890648 0.445324 − 0.895370i \(-0.353089\pi\)
0.445324 + 0.895370i \(0.353089\pi\)
\(920\) 0 0
\(921\) 52.0000 1.71346
\(922\) 0 0
\(923\) −8.00000 −0.263323
\(924\) 0 0
\(925\) 40.0000 1.31519
\(926\) 0 0
\(927\) 10.0000 0.328443
\(928\) 0 0
\(929\) −1.00000 −0.0328089 −0.0164045 − 0.999865i \(-0.505222\pi\)
−0.0164045 + 0.999865i \(0.505222\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 8.00000 0.261908
\(934\) 0 0
\(935\) −2.00000 −0.0654070
\(936\) 0 0
\(937\) −23.0000 −0.751377 −0.375689 − 0.926746i \(-0.622594\pi\)
−0.375689 + 0.926746i \(0.622594\pi\)
\(938\) 0 0
\(939\) −22.0000 −0.717943
\(940\) 0 0
\(941\) 44.0000 1.43436 0.717180 − 0.696888i \(-0.245433\pi\)
0.717180 + 0.696888i \(0.245433\pi\)
\(942\) 0 0
\(943\) −30.0000 −0.976934
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −36.0000 −1.16984 −0.584921 − 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 0 0
\(949\) −6.00000 −0.194768
\(950\) 0 0
\(951\) −24.0000 −0.778253
\(952\) 0 0
\(953\) −50.0000 −1.61966 −0.809829 − 0.586665i \(-0.800440\pi\)
−0.809829 + 0.586665i \(0.800440\pi\)
\(954\) 0 0
\(955\) 3.00000 0.0970777
\(956\) 0 0
\(957\) 8.00000 0.258603
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 2.00000 0.0644491
\(964\) 0 0
\(965\) 10.0000 0.321911
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 − 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) 0 0
\(969\) 4.00000 0.128499
\(970\) 0 0
\(971\) 42.0000 1.34784 0.673922 − 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 16.0000 0.512410
\(976\) 0 0
\(977\) −12.0000 −0.383914 −0.191957 − 0.981403i \(-0.561483\pi\)
−0.191957 + 0.981403i \(0.561483\pi\)
\(978\) 0 0
\(979\) −6.00000 −0.191761
\(980\) 0 0
\(981\) 16.0000 0.510841
\(982\) 0 0
\(983\) −18.0000 −0.574111 −0.287055 − 0.957914i \(-0.592676\pi\)
−0.287055 + 0.957914i \(0.592676\pi\)
\(984\) 0 0
\(985\) −3.00000 −0.0955879
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3.00000 −0.0953945
\(990\) 0 0
\(991\) 4.00000 0.127064 0.0635321 − 0.997980i \(-0.479763\pi\)
0.0635321 + 0.997980i \(0.479763\pi\)
\(992\) 0 0
\(993\) 4.00000 0.126936
\(994\) 0 0
\(995\) 19.0000 0.602340
\(996\) 0 0
\(997\) 46.0000 1.45683 0.728417 − 0.685134i \(-0.240256\pi\)
0.728417 + 0.685134i \(0.240256\pi\)
\(998\) 0 0
\(999\) −40.0000 −1.26554
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 7448.2.a.b.1.1 1
7.2 even 3 1064.2.q.i.305.1 ✓ 2
7.4 even 3 1064.2.q.i.457.1 yes 2
7.6 odd 2 7448.2.a.u.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.q.i.305.1 ✓ 2 7.2 even 3
1064.2.q.i.457.1 yes 2 7.4 even 3
7448.2.a.b.1.1 1 1.1 even 1 trivial
7448.2.a.u.1.1 1 7.6 odd 2