Properties

Label 8820.2.a.bq.1.1
Level $8820$
Weight $2$
Character 8820.1
Self dual yes
Analytic conductor $70.428$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8820,2,Mod(1,8820)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8820, 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("8820.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8820.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: \(70.4280545828\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.404.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 5x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 1260)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.86620\) of defining polynomial
Character \(\chi\) \(=\) 8820.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} +O(q^{10})\) \(q+1.00000 q^{5} -2.38350 q^{11} +1.38350 q^{13} +0.831590 q^{17} -4.21509 q^{19} +5.59859 q^{23} +1.00000 q^{25} -10.0467 q^{29} -1.00000 q^{31} +4.59859 q^{37} -8.81369 q^{41} -1.83159 q^{43} +12.4302 q^{47} +1.66318 q^{53} -2.38350 q^{55} -8.38350 q^{59} +5.21509 q^{61} +1.38350 q^{65} +1.38350 q^{67} -3.61650 q^{71} -12.5986 q^{73} -11.8783 q^{79} +3.93541 q^{83} +0.831590 q^{85} +0.720322 q^{89} -4.21509 q^{95} -2.44809 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{5} + 2 q^{11} - 5 q^{13} - 2 q^{17} + q^{19} - 6 q^{23} + 3 q^{25} - 12 q^{29} - 3 q^{31} - 9 q^{37} + 10 q^{41} - q^{43} + 10 q^{47} - 4 q^{53} + 2 q^{55} - 16 q^{59} + 2 q^{61} - 5 q^{65} - 5 q^{67} - 20 q^{71} - 15 q^{73} - 13 q^{79} - 2 q^{83} - 2 q^{85} + 2 q^{89} + q^{95} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.38350 −0.718653 −0.359326 0.933212i \(-0.616994\pi\)
−0.359326 + 0.933212i \(0.616994\pi\)
\(12\) 0 0
\(13\) 1.38350 0.383715 0.191857 0.981423i \(-0.438549\pi\)
0.191857 + 0.981423i \(0.438549\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.831590 0.201690 0.100845 0.994902i \(-0.467845\pi\)
0.100845 + 0.994902i \(0.467845\pi\)
\(18\) 0 0
\(19\) −4.21509 −0.967009 −0.483504 0.875342i \(-0.660636\pi\)
−0.483504 + 0.875342i \(0.660636\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.59859 1.16739 0.583694 0.811974i \(-0.301607\pi\)
0.583694 + 0.811974i \(0.301607\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −10.0467 −1.86562 −0.932811 0.360366i \(-0.882652\pi\)
−0.932811 + 0.360366i \(0.882652\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605 −0.0898027 0.995960i \(-0.528624\pi\)
−0.0898027 + 0.995960i \(0.528624\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.59859 0.756004 0.378002 0.925805i \(-0.376611\pi\)
0.378002 + 0.925805i \(0.376611\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.81369 −1.37647 −0.688233 0.725489i \(-0.741613\pi\)
−0.688233 + 0.725489i \(0.741613\pi\)
\(42\) 0 0
\(43\) −1.83159 −0.279315 −0.139657 0.990200i \(-0.544600\pi\)
−0.139657 + 0.990200i \(0.544600\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.4302 1.81313 0.906564 0.422067i \(-0.138695\pi\)
0.906564 + 0.422067i \(0.138695\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.66318 0.228455 0.114228 0.993455i \(-0.463561\pi\)
0.114228 + 0.993455i \(0.463561\pi\)
\(54\) 0 0
\(55\) −2.38350 −0.321391
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.38350 −1.09144 −0.545720 0.837968i \(-0.683744\pi\)
−0.545720 + 0.837968i \(0.683744\pi\)
\(60\) 0 0
\(61\) 5.21509 0.667724 0.333862 0.942622i \(-0.391648\pi\)
0.333862 + 0.942622i \(0.391648\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.38350 0.171602
\(66\) 0 0
\(67\) 1.38350 0.169022 0.0845109 0.996423i \(-0.473067\pi\)
0.0845109 + 0.996423i \(0.473067\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.61650 −0.429199 −0.214600 0.976702i \(-0.568845\pi\)
−0.214600 + 0.976702i \(0.568845\pi\)
\(72\) 0 0
\(73\) −12.5986 −1.47455 −0.737277 0.675591i \(-0.763889\pi\)
−0.737277 + 0.675591i \(0.763889\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −11.8783 −1.33641 −0.668205 0.743977i \(-0.732937\pi\)
−0.668205 + 0.743977i \(0.732937\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.93541 0.431968 0.215984 0.976397i \(-0.430704\pi\)
0.215984 + 0.976397i \(0.430704\pi\)
\(84\) 0 0
\(85\) 0.831590 0.0901986
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.720322 0.0763540 0.0381770 0.999271i \(-0.487845\pi\)
0.0381770 + 0.999271i \(0.487845\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.21509 −0.432459
\(96\) 0 0
\(97\) −2.44809 −0.248566 −0.124283 0.992247i \(-0.539663\pi\)
−0.124283 + 0.992247i \(0.539663\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −13.1505 −1.30852 −0.654262 0.756268i \(-0.727021\pi\)
−0.654262 + 0.756268i \(0.727021\pi\)
\(102\) 0 0
\(103\) 6.26178 0.616991 0.308496 0.951226i \(-0.400175\pi\)
0.308496 + 0.951226i \(0.400175\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.5986 −1.12128 −0.560639 0.828060i \(-0.689445\pi\)
−0.560639 + 0.828060i \(0.689445\pi\)
\(108\) 0 0
\(109\) 12.9821 1.24346 0.621730 0.783232i \(-0.286430\pi\)
0.621730 + 0.783232i \(0.286430\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −16.7670 −1.57731 −0.788654 0.614838i \(-0.789221\pi\)
−0.788654 + 0.614838i \(0.789221\pi\)
\(114\) 0 0
\(115\) 5.59859 0.522072
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −5.31892 −0.483538
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 13.8137 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.23300 0.107727 0.0538637 0.998548i \(-0.482846\pi\)
0.0538637 + 0.998548i \(0.482846\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.401405 −0.0342944 −0.0171472 0.999853i \(-0.505458\pi\)
−0.0171472 + 0.999853i \(0.505458\pi\)
\(138\) 0 0
\(139\) −0.888732 −0.0753812 −0.0376906 0.999289i \(-0.512000\pi\)
−0.0376906 + 0.999289i \(0.512000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.29758 −0.275758
\(144\) 0 0
\(145\) −10.0467 −0.834332
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) −16.7491 −1.36302 −0.681511 0.731808i \(-0.738677\pi\)
−0.681511 + 0.731808i \(0.738677\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 0 0
\(157\) 3.66318 0.292354 0.146177 0.989258i \(-0.453303\pi\)
0.146177 + 0.989258i \(0.453303\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 16.0934 1.26053 0.630265 0.776380i \(-0.282946\pi\)
0.630265 + 0.776380i \(0.282946\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 11.5986 0.897526 0.448763 0.893651i \(-0.351865\pi\)
0.448763 + 0.893651i \(0.351865\pi\)
\(168\) 0 0
\(169\) −11.0859 −0.852763
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.4302 0.945049 0.472525 0.881317i \(-0.343343\pi\)
0.472525 + 0.881317i \(0.343343\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.10382 0.231991 0.115995 0.993250i \(-0.462994\pi\)
0.115995 + 0.993250i \(0.462994\pi\)
\(180\) 0 0
\(181\) −2.98210 −0.221658 −0.110829 0.993840i \(-0.535351\pi\)
−0.110829 + 0.993840i \(0.535351\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.59859 0.338095
\(186\) 0 0
\(187\) −1.98210 −0.144945
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −15.1038 −1.09287 −0.546437 0.837500i \(-0.684016\pi\)
−0.546437 + 0.837500i \(0.684016\pi\)
\(192\) 0 0
\(193\) −17.7958 −1.28097 −0.640484 0.767971i \(-0.721266\pi\)
−0.640484 + 0.767971i \(0.721266\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −17.1684 −1.22320 −0.611599 0.791168i \(-0.709474\pi\)
−0.611599 + 0.791168i \(0.709474\pi\)
\(198\) 0 0
\(199\) 20.7491 1.47086 0.735432 0.677598i \(-0.236979\pi\)
0.735432 + 0.677598i \(0.236979\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −8.81369 −0.615575
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 10.0467 0.694944
\(210\) 0 0
\(211\) 3.12173 0.214909 0.107454 0.994210i \(-0.465730\pi\)
0.107454 + 0.994210i \(0.465730\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.83159 −0.124913
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.15051 0.0773915
\(222\) 0 0
\(223\) −7.32636 −0.490609 −0.245305 0.969446i \(-0.578888\pi\)
−0.245305 + 0.969446i \(0.578888\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −25.2618 −1.67668 −0.838341 0.545145i \(-0.816474\pi\)
−0.838341 + 0.545145i \(0.816474\pi\)
\(228\) 0 0
\(229\) −10.3264 −0.682385 −0.341193 0.939993i \(-0.610831\pi\)
−0.341193 + 0.939993i \(0.610831\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −26.0934 −1.70943 −0.854717 0.519095i \(-0.826269\pi\)
−0.854717 + 0.519095i \(0.826269\pi\)
\(234\) 0 0
\(235\) 12.4302 0.810856
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.86037 0.443760 0.221880 0.975074i \(-0.428781\pi\)
0.221880 + 0.975074i \(0.428781\pi\)
\(240\) 0 0
\(241\) −2.87827 −0.185406 −0.0927029 0.995694i \(-0.529551\pi\)
−0.0927029 + 0.995694i \(0.529551\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −5.83159 −0.371055
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 24.1400 1.52371 0.761853 0.647750i \(-0.224290\pi\)
0.761853 + 0.647750i \(0.224290\pi\)
\(252\) 0 0
\(253\) −13.3443 −0.838947
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −24.4590 −1.52571 −0.762854 0.646571i \(-0.776203\pi\)
−0.762854 + 0.646571i \(0.776203\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −18.8604 −1.16298 −0.581490 0.813553i \(-0.697530\pi\)
−0.581490 + 0.813553i \(0.697530\pi\)
\(264\) 0 0
\(265\) 1.66318 0.102168
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5.19719 0.316878 0.158439 0.987369i \(-0.449354\pi\)
0.158439 + 0.987369i \(0.449354\pi\)
\(270\) 0 0
\(271\) 27.9821 1.69979 0.849896 0.526951i \(-0.176665\pi\)
0.849896 + 0.526951i \(0.176665\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.38350 −0.143731
\(276\) 0 0
\(277\) −6.16841 −0.370624 −0.185312 0.982680i \(-0.559330\pi\)
−0.185312 + 0.982680i \(0.559330\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −11.5698 −0.690197 −0.345099 0.938566i \(-0.612155\pi\)
−0.345099 + 0.938566i \(0.612155\pi\)
\(282\) 0 0
\(283\) −29.7958 −1.77118 −0.885588 0.464472i \(-0.846244\pi\)
−0.885588 + 0.464472i \(0.846244\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.3085 −0.959321
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 19.6632 1.14874 0.574368 0.818597i \(-0.305248\pi\)
0.574368 + 0.818597i \(0.305248\pi\)
\(294\) 0 0
\(295\) −8.38350 −0.488106
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.74567 0.447944
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 5.21509 0.298615
\(306\) 0 0
\(307\) 19.8137 1.13083 0.565413 0.824808i \(-0.308717\pi\)
0.565413 + 0.824808i \(0.308717\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −22.0467 −1.25015 −0.625076 0.780564i \(-0.714932\pi\)
−0.625076 + 0.780564i \(0.714932\pi\)
\(312\) 0 0
\(313\) −10.5052 −0.593791 −0.296895 0.954910i \(-0.595951\pi\)
−0.296895 + 0.954910i \(0.595951\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.73822 −0.266125 −0.133063 0.991108i \(-0.542481\pi\)
−0.133063 + 0.991108i \(0.542481\pi\)
\(318\) 0 0
\(319\) 23.9463 1.34073
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.50523 −0.195036
\(324\) 0 0
\(325\) 1.38350 0.0767429
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 17.8604 0.981695 0.490847 0.871246i \(-0.336687\pi\)
0.490847 + 0.871246i \(0.336687\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.38350 0.0755888
\(336\) 0 0
\(337\) −11.4769 −0.625185 −0.312592 0.949887i \(-0.601197\pi\)
−0.312592 + 0.949887i \(0.601197\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.38350 0.129074
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5.56982 0.299003 0.149502 0.988761i \(-0.452233\pi\)
0.149502 + 0.988761i \(0.452233\pi\)
\(348\) 0 0
\(349\) 3.66318 0.196086 0.0980428 0.995182i \(-0.468742\pi\)
0.0980428 + 0.995182i \(0.468742\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.401405 −0.0213646 −0.0106823 0.999943i \(-0.503400\pi\)
−0.0106823 + 0.999943i \(0.503400\pi\)
\(354\) 0 0
\(355\) −3.61650 −0.191944
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −26.8137 −1.41517 −0.707586 0.706627i \(-0.750216\pi\)
−0.707586 + 0.706627i \(0.750216\pi\)
\(360\) 0 0
\(361\) −1.23300 −0.0648945
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12.5986 −0.659441
\(366\) 0 0
\(367\) 0.523132 0.0273073 0.0136536 0.999907i \(-0.495654\pi\)
0.0136536 + 0.999907i \(0.495654\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 32.2439 1.66952 0.834762 0.550611i \(-0.185605\pi\)
0.834762 + 0.550611i \(0.185605\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −13.8996 −0.715866
\(378\) 0 0
\(379\) 19.5236 1.00286 0.501429 0.865199i \(-0.332808\pi\)
0.501429 + 0.865199i \(0.332808\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.802810 0.0410217 0.0205108 0.999790i \(-0.493471\pi\)
0.0205108 + 0.999790i \(0.493471\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −29.9175 −1.51688 −0.758439 0.651744i \(-0.774038\pi\)
−0.758439 + 0.651744i \(0.774038\pi\)
\(390\) 0 0
\(391\) 4.65574 0.235451
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −11.8783 −0.597661
\(396\) 0 0
\(397\) 29.4590 1.47850 0.739252 0.673429i \(-0.235179\pi\)
0.739252 + 0.673429i \(0.235179\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −26.5236 −1.32452 −0.662261 0.749273i \(-0.730403\pi\)
−0.662261 + 0.749273i \(0.730403\pi\)
\(402\) 0 0
\(403\) −1.38350 −0.0689172
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.9608 −0.543305
\(408\) 0 0
\(409\) 31.5236 1.55874 0.779370 0.626564i \(-0.215539\pi\)
0.779370 + 0.626564i \(0.215539\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 3.93541 0.193182
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.802810 0.0392199 0.0196099 0.999808i \(-0.493758\pi\)
0.0196099 + 0.999808i \(0.493758\pi\)
\(420\) 0 0
\(421\) 37.8425 1.84433 0.922164 0.386798i \(-0.126419\pi\)
0.922164 + 0.386798i \(0.126419\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.831590 0.0403380
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 17.1972 0.828359 0.414180 0.910195i \(-0.364068\pi\)
0.414180 + 0.910195i \(0.364068\pi\)
\(432\) 0 0
\(433\) 12.1505 0.583916 0.291958 0.956431i \(-0.405693\pi\)
0.291958 + 0.956431i \(0.405693\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −23.5986 −1.12887
\(438\) 0 0
\(439\) −31.2727 −1.49256 −0.746281 0.665631i \(-0.768163\pi\)
−0.746281 + 0.665631i \(0.768163\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.86037 0.325946 0.162973 0.986631i \(-0.447892\pi\)
0.162973 + 0.986631i \(0.447892\pi\)
\(444\) 0 0
\(445\) 0.720322 0.0341465
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −27.1038 −1.27911 −0.639554 0.768746i \(-0.720881\pi\)
−0.639554 + 0.768746i \(0.720881\pi\)
\(450\) 0 0
\(451\) 21.0074 0.989202
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 19.8137 0.926845 0.463423 0.886137i \(-0.346621\pi\)
0.463423 + 0.886137i \(0.346621\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.82415 0.178108 0.0890541 0.996027i \(-0.471616\pi\)
0.0890541 + 0.996027i \(0.471616\pi\)
\(462\) 0 0
\(463\) −8.95332 −0.416096 −0.208048 0.978119i \(-0.566711\pi\)
−0.208048 + 0.978119i \(0.566711\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10.3368 0.478331 0.239165 0.970979i \(-0.423126\pi\)
0.239165 + 0.970979i \(0.423126\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.36560 0.200730
\(474\) 0 0
\(475\) −4.21509 −0.193402
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −40.3944 −1.84567 −0.922833 0.385200i \(-0.874132\pi\)
−0.922833 + 0.385200i \(0.874132\pi\)
\(480\) 0 0
\(481\) 6.36217 0.290090
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.44809 −0.111162
\(486\) 0 0
\(487\) −13.1400 −0.595432 −0.297716 0.954654i \(-0.596225\pi\)
−0.297716 + 0.954654i \(0.596225\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −17.1972 −0.776098 −0.388049 0.921639i \(-0.626851\pi\)
−0.388049 + 0.921639i \(0.626851\pi\)
\(492\) 0 0
\(493\) −8.35472 −0.376278
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2.66318 −0.119220 −0.0596102 0.998222i \(-0.518986\pi\)
−0.0596102 + 0.998222i \(0.518986\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −13.1505 −0.585190
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 24.0576 1.06633 0.533166 0.846010i \(-0.321002\pi\)
0.533166 + 0.846010i \(0.321002\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.26178 0.275927
\(516\) 0 0
\(517\) −29.6274 −1.30301
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.6274 0.772269 0.386135 0.922442i \(-0.373810\pi\)
0.386135 + 0.922442i \(0.373810\pi\)
\(522\) 0 0
\(523\) −16.1863 −0.707778 −0.353889 0.935287i \(-0.615141\pi\)
−0.353889 + 0.935287i \(0.615141\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.831590 −0.0362246
\(528\) 0 0
\(529\) 8.34426 0.362794
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12.1938 −0.528170
\(534\) 0 0
\(535\) −11.5986 −0.501451
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −17.5594 −0.754936 −0.377468 0.926023i \(-0.623205\pi\)
−0.377468 + 0.926023i \(0.623205\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12.9821 0.556092
\(546\) 0 0
\(547\) −7.96419 −0.340524 −0.170262 0.985399i \(-0.554461\pi\)
−0.170262 + 0.985399i \(0.554461\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 42.3477 1.80407
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −27.5340 −1.16665 −0.583327 0.812238i \(-0.698249\pi\)
−0.583327 + 0.812238i \(0.698249\pi\)
\(558\) 0 0
\(559\) −2.53401 −0.107177
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22.9747 −0.968266 −0.484133 0.874994i \(-0.660865\pi\)
−0.484133 + 0.874994i \(0.660865\pi\)
\(564\) 0 0
\(565\) −16.7670 −0.705393
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.24387 0.135990 0.0679951 0.997686i \(-0.478340\pi\)
0.0679951 + 0.997686i \(0.478340\pi\)
\(570\) 0 0
\(571\) −28.2151 −1.18076 −0.590382 0.807124i \(-0.701023\pi\)
−0.590382 + 0.807124i \(0.701023\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.59859 0.233478
\(576\) 0 0
\(577\) −17.4769 −0.727572 −0.363786 0.931483i \(-0.618516\pi\)
−0.363786 + 0.931483i \(0.618516\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −3.96419 −0.164180
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.1580 −0.419264 −0.209632 0.977780i \(-0.567227\pi\)
−0.209632 + 0.977780i \(0.567227\pi\)
\(588\) 0 0
\(589\) 4.21509 0.173680
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5.39095 −0.221380 −0.110690 0.993855i \(-0.535306\pi\)
−0.110690 + 0.993855i \(0.535306\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 22.9895 0.939327 0.469664 0.882845i \(-0.344375\pi\)
0.469664 + 0.882845i \(0.344375\pi\)
\(600\) 0 0
\(601\) 38.2727 1.56117 0.780587 0.625047i \(-0.214920\pi\)
0.780587 + 0.625047i \(0.214920\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5.31892 −0.216245
\(606\) 0 0
\(607\) 11.7203 0.475713 0.237857 0.971300i \(-0.423555\pi\)
0.237857 + 0.971300i \(0.423555\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 17.1972 0.695724
\(612\) 0 0
\(613\) 27.9821 1.13019 0.565093 0.825027i \(-0.308840\pi\)
0.565093 + 0.825027i \(0.308840\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −31.0680 −1.25075 −0.625376 0.780324i \(-0.715054\pi\)
−0.625376 + 0.780324i \(0.715054\pi\)
\(618\) 0 0
\(619\) 7.30101 0.293453 0.146726 0.989177i \(-0.453126\pi\)
0.146726 + 0.989177i \(0.453126\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.82415 0.152479
\(630\) 0 0
\(631\) −22.4877 −0.895223 −0.447611 0.894228i \(-0.647725\pi\)
−0.447611 + 0.894228i \(0.647725\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 13.8137 0.548179
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −44.0109 −1.73833 −0.869163 0.494526i \(-0.835341\pi\)
−0.869163 + 0.494526i \(0.835341\pi\)
\(642\) 0 0
\(643\) −10.1863 −0.401709 −0.200854 0.979621i \(-0.564372\pi\)
−0.200854 + 0.979621i \(0.564372\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32.5523 1.27976 0.639882 0.768473i \(-0.278983\pi\)
0.639882 + 0.768473i \(0.278983\pi\)
\(648\) 0 0
\(649\) 19.9821 0.784366
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 20.9250 0.818857 0.409428 0.912342i \(-0.365728\pi\)
0.409428 + 0.912342i \(0.365728\pi\)
\(654\) 0 0
\(655\) 1.23300 0.0481771
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −37.7207 −1.46939 −0.734696 0.678397i \(-0.762675\pi\)
−0.734696 + 0.678397i \(0.762675\pi\)
\(660\) 0 0
\(661\) 9.22555 0.358832 0.179416 0.983773i \(-0.442579\pi\)
0.179416 + 0.983773i \(0.442579\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −56.2473 −2.17790
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −12.4302 −0.479862
\(672\) 0 0
\(673\) −30.2797 −1.16720 −0.583598 0.812043i \(-0.698356\pi\)
−0.583598 + 0.812043i \(0.698356\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33.7853 1.29848 0.649238 0.760586i \(-0.275088\pi\)
0.649238 + 0.760586i \(0.275088\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 33.1326 1.26778 0.633892 0.773422i \(-0.281456\pi\)
0.633892 + 0.773422i \(0.281456\pi\)
\(684\) 0 0
\(685\) −0.401405 −0.0153369
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.30101 0.0876616
\(690\) 0 0
\(691\) 44.9642 1.71052 0.855259 0.518200i \(-0.173398\pi\)
0.855259 + 0.518200i \(0.173398\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.888732 −0.0337115
\(696\) 0 0
\(697\) −7.32938 −0.277620
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −42.5702 −1.60786 −0.803928 0.594727i \(-0.797260\pi\)
−0.803928 + 0.594727i \(0.797260\pi\)
\(702\) 0 0
\(703\) −19.3835 −0.731063
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 10.2046 0.383243 0.191622 0.981469i \(-0.438625\pi\)
0.191622 + 0.981469i \(0.438625\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −5.59859 −0.209669
\(714\) 0 0
\(715\) −3.29758 −0.123323
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.09337 −0.0780694 −0.0390347 0.999238i \(-0.512428\pi\)
−0.0390347 + 0.999238i \(0.512428\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −10.0467 −0.373124
\(726\) 0 0
\(727\) 34.8211 1.29144 0.645722 0.763572i \(-0.276556\pi\)
0.645722 + 0.763572i \(0.276556\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.52313 −0.0563351
\(732\) 0 0
\(733\) −47.4769 −1.75360 −0.876799 0.480857i \(-0.840326\pi\)
−0.876799 + 0.480857i \(0.840326\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.29758 −0.121468
\(738\) 0 0
\(739\) −40.2727 −1.48145 −0.740727 0.671806i \(-0.765519\pi\)
−0.740727 + 0.671806i \(0.765519\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −27.7853 −1.01934 −0.509672 0.860369i \(-0.670233\pi\)
−0.509672 + 0.860369i \(0.670233\pi\)
\(744\) 0 0
\(745\) −6.00000 −0.219823
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.80281 −0.0657855 −0.0328927 0.999459i \(-0.510472\pi\)
−0.0328927 + 0.999459i \(0.510472\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −16.7491 −0.609562
\(756\) 0 0
\(757\) 21.8708 0.794909 0.397454 0.917622i \(-0.369894\pi\)
0.397454 + 0.917622i \(0.369894\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −22.0467 −0.799192 −0.399596 0.916691i \(-0.630850\pi\)
−0.399596 + 0.916691i \(0.630850\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −11.5986 −0.418801
\(768\) 0 0
\(769\) −28.2727 −1.01954 −0.509769 0.860311i \(-0.670269\pi\)
−0.509769 + 0.860311i \(0.670269\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −39.9930 −1.43845 −0.719224 0.694779i \(-0.755502\pi\)
−0.719224 + 0.694779i \(0.755502\pi\)
\(774\) 0 0
\(775\) −1.00000 −0.0359211
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 37.1505 1.33106
\(780\) 0 0
\(781\) 8.61993 0.308445
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.66318 0.130745
\(786\) 0 0
\(787\) 35.1614 1.25337 0.626684 0.779273i \(-0.284412\pi\)
0.626684 + 0.779273i \(0.284412\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 7.21509 0.256215
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 49.0968 1.73910 0.869549 0.493847i \(-0.164410\pi\)
0.869549 + 0.493847i \(0.164410\pi\)
\(798\) 0 0
\(799\) 10.3368 0.365690
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 30.0288 1.05969
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 13.2906 0.467271 0.233636 0.972324i \(-0.424938\pi\)
0.233636 + 0.972324i \(0.424938\pi\)
\(810\) 0 0
\(811\) −44.9358 −1.57791 −0.788955 0.614451i \(-0.789378\pi\)
−0.788955 + 0.614451i \(0.789378\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 16.0934 0.563726
\(816\) 0 0
\(817\) 7.72032 0.270100
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 14.4411 0.503997 0.251998 0.967728i \(-0.418912\pi\)
0.251998 + 0.967728i \(0.418912\pi\)
\(822\) 0 0
\(823\) 26.1113 0.910182 0.455091 0.890445i \(-0.349607\pi\)
0.455091 + 0.890445i \(0.349607\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 32.5236 1.13095 0.565477 0.824764i \(-0.308692\pi\)
0.565477 + 0.824764i \(0.308692\pi\)
\(828\) 0 0
\(829\) −39.0397 −1.35590 −0.677952 0.735106i \(-0.737132\pi\)
−0.677952 + 0.735106i \(0.737132\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 11.5986 0.401386
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −35.7099 −1.23284 −0.616421 0.787417i \(-0.711418\pi\)
−0.616421 + 0.787417i \(0.711418\pi\)
\(840\) 0 0
\(841\) 71.9358 2.48055
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −11.0859 −0.381367
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 25.7457 0.882550
\(852\) 0 0
\(853\) −44.0968 −1.50985 −0.754923 0.655814i \(-0.772326\pi\)
−0.754923 + 0.655814i \(0.772326\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 4.30804 0.147160 0.0735799 0.997289i \(-0.476558\pi\)
0.0735799 + 0.997289i \(0.476558\pi\)
\(858\) 0 0
\(859\) 23.2727 0.794053 0.397026 0.917807i \(-0.370042\pi\)
0.397026 + 0.917807i \(0.370042\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −54.9179 −1.86943 −0.934714 0.355401i \(-0.884344\pi\)
−0.934714 + 0.355401i \(0.884344\pi\)
\(864\) 0 0
\(865\) 12.4302 0.422639
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 28.3119 0.960415
\(870\) 0 0
\(871\) 1.91408 0.0648561
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −6.09337 −0.205758 −0.102879 0.994694i \(-0.532805\pi\)
−0.102879 + 0.994694i \(0.532805\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 21.3264 0.718503 0.359252 0.933241i \(-0.383032\pi\)
0.359252 + 0.933241i \(0.383032\pi\)
\(882\) 0 0
\(883\) −24.3761 −0.820320 −0.410160 0.912014i \(-0.634527\pi\)
−0.410160 + 0.912014i \(0.634527\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 44.3298 1.48845 0.744224 0.667930i \(-0.232819\pi\)
0.744224 + 0.667930i \(0.232819\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −52.3944 −1.75331
\(894\) 0 0
\(895\) 3.10382 0.103749
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 10.0467 0.335076
\(900\) 0 0
\(901\) 1.38308 0.0460772
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.98210 −0.0991283
\(906\) 0 0
\(907\) 10.5986 0.351921 0.175960 0.984397i \(-0.443697\pi\)
0.175960 + 0.984397i \(0.443697\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 24.1400 0.799795 0.399898 0.916560i \(-0.369046\pi\)
0.399898 + 0.916560i \(0.369046\pi\)
\(912\) 0 0
\(913\) −9.38007 −0.310435
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 9.98954 0.329525 0.164762 0.986333i \(-0.447314\pi\)
0.164762 + 0.986333i \(0.447314\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −5.00343 −0.164690
\(924\) 0 0
\(925\) 4.59859 0.151201
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −45.6741 −1.49852 −0.749259 0.662278i \(-0.769590\pi\)
−0.749259 + 0.662278i \(0.769590\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.98210 −0.0648215
\(936\) 0 0
\(937\) −15.4948 −0.506192 −0.253096 0.967441i \(-0.581449\pi\)
−0.253096 + 0.967441i \(0.581449\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −19.8032 −0.645567 −0.322783 0.946473i \(-0.604619\pi\)
−0.322783 + 0.946473i \(0.604619\pi\)
\(942\) 0 0
\(943\) −49.3443 −1.60687
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −10.1580 −0.330089 −0.165045 0.986286i \(-0.552777\pi\)
−0.165045 + 0.986286i \(0.552777\pi\)
\(948\) 0 0
\(949\) −17.4302 −0.565808
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 8.09337 0.262170 0.131085 0.991371i \(-0.458154\pi\)
0.131085 + 0.991371i \(0.458154\pi\)
\(954\) 0 0
\(955\) −15.1038 −0.488748
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −30.0000 −0.967742
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −17.7958 −0.572867
\(966\) 0 0
\(967\) 29.2513 0.940659 0.470329 0.882491i \(-0.344135\pi\)
0.470329 + 0.882491i \(0.344135\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −16.3944 −0.526121 −0.263060 0.964779i \(-0.584732\pi\)
−0.263060 + 0.964779i \(0.584732\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 31.0968 0.994875 0.497437 0.867500i \(-0.334274\pi\)
0.497437 + 0.867500i \(0.334274\pi\)
\(978\) 0 0
\(979\) −1.71689 −0.0548720
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4.36560 −0.139241 −0.0696205 0.997574i \(-0.522179\pi\)
−0.0696205 + 0.997574i \(0.522179\pi\)
\(984\) 0 0
\(985\) −17.1684 −0.547031
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −10.2543 −0.326069
\(990\) 0 0
\(991\) 27.2980 0.867150 0.433575 0.901118i \(-0.357252\pi\)
0.433575 + 0.901118i \(0.357252\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 20.7491 0.657791
\(996\) 0 0
\(997\) 30.4843 0.965448 0.482724 0.875773i \(-0.339647\pi\)
0.482724 + 0.875773i \(0.339647\pi\)
\(998\) 0 0
\(999\) 0 0
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 8820.2.a.bq.1.1 3
3.2 odd 2 8820.2.a.bn.1.3 3
7.2 even 3 1260.2.s.g.361.1 6
7.4 even 3 1260.2.s.g.541.1 yes 6
7.6 odd 2 8820.2.a.bo.1.1 3
21.2 odd 6 1260.2.s.h.361.1 yes 6
21.11 odd 6 1260.2.s.h.541.1 yes 6
21.20 even 2 8820.2.a.bp.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1260.2.s.g.361.1 6 7.2 even 3
1260.2.s.g.541.1 yes 6 7.4 even 3
1260.2.s.h.361.1 yes 6 21.2 odd 6
1260.2.s.h.541.1 yes 6 21.11 odd 6
8820.2.a.bn.1.3 3 3.2 odd 2
8820.2.a.bo.1.1 3 7.6 odd 2
8820.2.a.bp.1.3 3 21.20 even 2
8820.2.a.bq.1.1 3 1.1 even 1 trivial