Properties

Label 4284.2.a.l.1.2
Level $4284$
Weight $2$
Character 4284.1
Self dual yes
Analytic conductor $34.208$
Analytic rank $0$
Dimension $2$
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] = [4284,2,Mod(1,4284)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4284, 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("4284.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4284.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: \(34.2079122259\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 476)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.30278\) of defining polynomial
Character \(\chi\) \(=\) 4284.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.30278 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+1.30278 q^{5} -1.00000 q^{7} -4.00000 q^{11} -4.60555 q^{13} +1.00000 q^{17} +8.60555 q^{19} -4.00000 q^{23} -3.30278 q^{25} -9.21110 q^{29} +7.30278 q^{31} -1.30278 q^{35} +9.81665 q^{37} +11.5139 q^{41} -4.30278 q^{43} +2.60555 q^{47} +1.00000 q^{49} -0.697224 q^{53} -5.21110 q^{55} +8.00000 q^{59} +15.5139 q^{61} -6.00000 q^{65} +2.69722 q^{67} +3.39445 q^{71} +7.51388 q^{73} +4.00000 q^{77} -2.60555 q^{79} -3.21110 q^{83} +1.30278 q^{85} -7.81665 q^{89} +4.60555 q^{91} +11.2111 q^{95} -13.3028 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{5} - 2 q^{7} - 8 q^{11} - 2 q^{13} + 2 q^{17} + 10 q^{19} - 8 q^{23} - 3 q^{25} - 4 q^{29} + 11 q^{31} + q^{35} - 2 q^{37} + 5 q^{41} - 5 q^{43} - 2 q^{47} + 2 q^{49} - 5 q^{53} + 4 q^{55} + 16 q^{59} + 13 q^{61} - 12 q^{65} + 9 q^{67} + 14 q^{71} - 3 q^{73} + 8 q^{77} + 2 q^{79} + 8 q^{83} - q^{85} + 6 q^{89} + 2 q^{91} + 8 q^{95} - 23 q^{97}+O(q^{100}) \) 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
\(5\) 1.30278 0.582619 0.291309 0.956629i \(-0.405909\pi\)
0.291309 + 0.956629i \(0.405909\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) −4.60555 −1.27735 −0.638675 0.769477i \(-0.720517\pi\)
−0.638675 + 0.769477i \(0.720517\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) 8.60555 1.97425 0.987124 0.159954i \(-0.0511347\pi\)
0.987124 + 0.159954i \(0.0511347\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −3.30278 −0.660555
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −9.21110 −1.71046 −0.855229 0.518250i \(-0.826584\pi\)
−0.855229 + 0.518250i \(0.826584\pi\)
\(30\) 0 0
\(31\) 7.30278 1.31162 0.655809 0.754927i \(-0.272328\pi\)
0.655809 + 0.754927i \(0.272328\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.30278 −0.220209
\(36\) 0 0
\(37\) 9.81665 1.61385 0.806924 0.590655i \(-0.201131\pi\)
0.806924 + 0.590655i \(0.201131\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 11.5139 1.79817 0.899083 0.437779i \(-0.144235\pi\)
0.899083 + 0.437779i \(0.144235\pi\)
\(42\) 0 0
\(43\) −4.30278 −0.656167 −0.328084 0.944649i \(-0.606403\pi\)
−0.328084 + 0.944649i \(0.606403\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.60555 0.380059 0.190029 0.981778i \(-0.439142\pi\)
0.190029 + 0.981778i \(0.439142\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.697224 −0.0957711 −0.0478856 0.998853i \(-0.515248\pi\)
−0.0478856 + 0.998853i \(0.515248\pi\)
\(54\) 0 0
\(55\) −5.21110 −0.702665
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) 15.5139 1.98635 0.993174 0.116640i \(-0.0372123\pi\)
0.993174 + 0.116640i \(0.0372123\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.00000 −0.744208
\(66\) 0 0
\(67\) 2.69722 0.329518 0.164759 0.986334i \(-0.447315\pi\)
0.164759 + 0.986334i \(0.447315\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.39445 0.402847 0.201423 0.979504i \(-0.435443\pi\)
0.201423 + 0.979504i \(0.435443\pi\)
\(72\) 0 0
\(73\) 7.51388 0.879433 0.439716 0.898137i \(-0.355079\pi\)
0.439716 + 0.898137i \(0.355079\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) −2.60555 −0.293147 −0.146574 0.989200i \(-0.546825\pi\)
−0.146574 + 0.989200i \(0.546825\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −3.21110 −0.352464 −0.176232 0.984349i \(-0.556391\pi\)
−0.176232 + 0.984349i \(0.556391\pi\)
\(84\) 0 0
\(85\) 1.30278 0.141306
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.81665 −0.828564 −0.414282 0.910149i \(-0.635967\pi\)
−0.414282 + 0.910149i \(0.635967\pi\)
\(90\) 0 0
\(91\) 4.60555 0.482793
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 11.2111 1.15023
\(96\) 0 0
\(97\) −13.3028 −1.35069 −0.675346 0.737501i \(-0.736006\pi\)
−0.675346 + 0.737501i \(0.736006\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.6056 1.25430 0.627150 0.778899i \(-0.284221\pi\)
0.627150 + 0.778899i \(0.284221\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.60555 0.445235 0.222618 0.974906i \(-0.428540\pi\)
0.222618 + 0.974906i \(0.428540\pi\)
\(108\) 0 0
\(109\) 4.78890 0.458693 0.229347 0.973345i \(-0.426341\pi\)
0.229347 + 0.973345i \(0.426341\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.39445 0.883755 0.441878 0.897075i \(-0.354313\pi\)
0.441878 + 0.897075i \(0.354313\pi\)
\(114\) 0 0
\(115\) −5.21110 −0.485938
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.00000 −0.0916698
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −10.8167 −0.967471
\(126\) 0 0
\(127\) 14.5139 1.28790 0.643949 0.765068i \(-0.277295\pi\)
0.643949 + 0.765068i \(0.277295\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.21110 0.804778 0.402389 0.915469i \(-0.368180\pi\)
0.402389 + 0.915469i \(0.368180\pi\)
\(132\) 0 0
\(133\) −8.60555 −0.746196
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.1194 −1.54805 −0.774024 0.633157i \(-0.781759\pi\)
−0.774024 + 0.633157i \(0.781759\pi\)
\(138\) 0 0
\(139\) 8.51388 0.722138 0.361069 0.932539i \(-0.382412\pi\)
0.361069 + 0.932539i \(0.382412\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 18.4222 1.54054
\(144\) 0 0
\(145\) −12.0000 −0.996546
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.30278 0.352497 0.176249 0.984346i \(-0.443604\pi\)
0.176249 + 0.984346i \(0.443604\pi\)
\(150\) 0 0
\(151\) 11.6972 0.951907 0.475953 0.879471i \(-0.342103\pi\)
0.475953 + 0.879471i \(0.342103\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 9.51388 0.764173
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.00000 0.315244
\(162\) 0 0
\(163\) 1.39445 0.109222 0.0546108 0.998508i \(-0.482608\pi\)
0.0546108 + 0.998508i \(0.482608\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.1194 −0.937830 −0.468915 0.883243i \(-0.655355\pi\)
−0.468915 + 0.883243i \(0.655355\pi\)
\(168\) 0 0
\(169\) 8.21110 0.631623
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −20.7250 −1.57569 −0.787846 0.615873i \(-0.788803\pi\)
−0.787846 + 0.615873i \(0.788803\pi\)
\(174\) 0 0
\(175\) 3.30278 0.249666
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.51388 −0.711101 −0.355550 0.934657i \(-0.615707\pi\)
−0.355550 + 0.934657i \(0.615707\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 12.7889 0.940258
\(186\) 0 0
\(187\) −4.00000 −0.292509
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.7250 0.848390 0.424195 0.905571i \(-0.360557\pi\)
0.424195 + 0.905571i \(0.360557\pi\)
\(192\) 0 0
\(193\) −15.0278 −1.08172 −0.540861 0.841112i \(-0.681901\pi\)
−0.540861 + 0.841112i \(0.681901\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.60555 0.470626 0.235313 0.971920i \(-0.424388\pi\)
0.235313 + 0.971920i \(0.424388\pi\)
\(198\) 0 0
\(199\) 9.69722 0.687418 0.343709 0.939076i \(-0.388317\pi\)
0.343709 + 0.939076i \(0.388317\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.21110 0.646493
\(204\) 0 0
\(205\) 15.0000 1.04765
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −34.4222 −2.38103
\(210\) 0 0
\(211\) 6.18335 0.425679 0.212840 0.977087i \(-0.431729\pi\)
0.212840 + 0.977087i \(0.431729\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −5.60555 −0.382295
\(216\) 0 0
\(217\) −7.30278 −0.495745
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.60555 −0.309803
\(222\) 0 0
\(223\) 13.8167 0.925232 0.462616 0.886559i \(-0.346911\pi\)
0.462616 + 0.886559i \(0.346911\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.09167 −0.138829 −0.0694146 0.997588i \(-0.522113\pi\)
−0.0694146 + 0.997588i \(0.522113\pi\)
\(228\) 0 0
\(229\) −1.21110 −0.0800319 −0.0400160 0.999199i \(-0.512741\pi\)
−0.0400160 + 0.999199i \(0.512741\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −26.6056 −1.74299 −0.871494 0.490407i \(-0.836848\pi\)
−0.871494 + 0.490407i \(0.836848\pi\)
\(234\) 0 0
\(235\) 3.39445 0.221429
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −18.1194 −1.17205 −0.586024 0.810294i \(-0.699308\pi\)
−0.586024 + 0.810294i \(0.699308\pi\)
\(240\) 0 0
\(241\) −26.5139 −1.70791 −0.853955 0.520348i \(-0.825802\pi\)
−0.853955 + 0.520348i \(0.825802\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.30278 0.0832313
\(246\) 0 0
\(247\) −39.6333 −2.52181
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.18335 0.137812 0.0689058 0.997623i \(-0.478049\pi\)
0.0689058 + 0.997623i \(0.478049\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.42221 0.275850 0.137925 0.990443i \(-0.455957\pi\)
0.137925 + 0.990443i \(0.455957\pi\)
\(258\) 0 0
\(259\) −9.81665 −0.609977
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 18.4222 1.13596 0.567981 0.823042i \(-0.307725\pi\)
0.567981 + 0.823042i \(0.307725\pi\)
\(264\) 0 0
\(265\) −0.908327 −0.0557981
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −12.7889 −0.779753 −0.389876 0.920867i \(-0.627482\pi\)
−0.389876 + 0.920867i \(0.627482\pi\)
\(270\) 0 0
\(271\) −10.4222 −0.633104 −0.316552 0.948575i \(-0.602525\pi\)
−0.316552 + 0.948575i \(0.602525\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 13.2111 0.796659
\(276\) 0 0
\(277\) 1.57779 0.0948005 0.0474003 0.998876i \(-0.484906\pi\)
0.0474003 + 0.998876i \(0.484906\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 19.1194 1.14057 0.570285 0.821447i \(-0.306833\pi\)
0.570285 + 0.821447i \(0.306833\pi\)
\(282\) 0 0
\(283\) 20.3305 1.20852 0.604262 0.796785i \(-0.293468\pi\)
0.604262 + 0.796785i \(0.293468\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.5139 −0.679643
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 11.2111 0.654960 0.327480 0.944858i \(-0.393801\pi\)
0.327480 + 0.944858i \(0.393801\pi\)
\(294\) 0 0
\(295\) 10.4222 0.606804
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 18.4222 1.06538
\(300\) 0 0
\(301\) 4.30278 0.248008
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 20.2111 1.15728
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 17.7250 1.00509 0.502546 0.864551i \(-0.332397\pi\)
0.502546 + 0.864551i \(0.332397\pi\)
\(312\) 0 0
\(313\) 3.90833 0.220912 0.110456 0.993881i \(-0.464769\pi\)
0.110456 + 0.993881i \(0.464769\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 33.6333 1.88903 0.944517 0.328461i \(-0.106530\pi\)
0.944517 + 0.328461i \(0.106530\pi\)
\(318\) 0 0
\(319\) 36.8444 2.06289
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.60555 0.478826
\(324\) 0 0
\(325\) 15.2111 0.843760
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.60555 −0.143649
\(330\) 0 0
\(331\) 3.72498 0.204743 0.102372 0.994746i \(-0.467357\pi\)
0.102372 + 0.994746i \(0.467357\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.51388 0.191984
\(336\) 0 0
\(337\) −14.4222 −0.785628 −0.392814 0.919618i \(-0.628498\pi\)
−0.392814 + 0.919618i \(0.628498\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −29.2111 −1.58187
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −26.8444 −1.44108 −0.720542 0.693412i \(-0.756107\pi\)
−0.720542 + 0.693412i \(0.756107\pi\)
\(348\) 0 0
\(349\) 18.4222 0.986118 0.493059 0.869996i \(-0.335879\pi\)
0.493059 + 0.869996i \(0.335879\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 16.0000 0.851594 0.425797 0.904819i \(-0.359994\pi\)
0.425797 + 0.904819i \(0.359994\pi\)
\(354\) 0 0
\(355\) 4.42221 0.234706
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.48612 0.0784345 0.0392173 0.999231i \(-0.487514\pi\)
0.0392173 + 0.999231i \(0.487514\pi\)
\(360\) 0 0
\(361\) 55.0555 2.89766
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.78890 0.512374
\(366\) 0 0
\(367\) 6.90833 0.360612 0.180306 0.983611i \(-0.442291\pi\)
0.180306 + 0.983611i \(0.442291\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.697224 0.0361981
\(372\) 0 0
\(373\) −15.3305 −0.793785 −0.396892 0.917865i \(-0.629911\pi\)
−0.396892 + 0.917865i \(0.629911\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 42.4222 2.18485
\(378\) 0 0
\(379\) 9.57779 0.491978 0.245989 0.969273i \(-0.420887\pi\)
0.245989 + 0.969273i \(0.420887\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.57779 0.0806216 0.0403108 0.999187i \(-0.487165\pi\)
0.0403108 + 0.999187i \(0.487165\pi\)
\(384\) 0 0
\(385\) 5.21110 0.265582
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 29.7250 1.50712 0.753558 0.657381i \(-0.228336\pi\)
0.753558 + 0.657381i \(0.228336\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.39445 −0.170793
\(396\) 0 0
\(397\) −12.0917 −0.606864 −0.303432 0.952853i \(-0.598132\pi\)
−0.303432 + 0.952853i \(0.598132\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.60555 −0.130115 −0.0650575 0.997882i \(-0.520723\pi\)
−0.0650575 + 0.997882i \(0.520723\pi\)
\(402\) 0 0
\(403\) −33.6333 −1.67539
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −39.2666 −1.94637
\(408\) 0 0
\(409\) −5.81665 −0.287615 −0.143808 0.989606i \(-0.545935\pi\)
−0.143808 + 0.989606i \(0.545935\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.00000 −0.393654
\(414\) 0 0
\(415\) −4.18335 −0.205352
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 8.51388 0.415930 0.207965 0.978136i \(-0.433316\pi\)
0.207965 + 0.978136i \(0.433316\pi\)
\(420\) 0 0
\(421\) 11.0917 0.540575 0.270288 0.962780i \(-0.412881\pi\)
0.270288 + 0.962780i \(0.412881\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.30278 −0.160208
\(426\) 0 0
\(427\) −15.5139 −0.750769
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 28.8444 1.38939 0.694693 0.719306i \(-0.255540\pi\)
0.694693 + 0.719306i \(0.255540\pi\)
\(432\) 0 0
\(433\) −7.39445 −0.355355 −0.177677 0.984089i \(-0.556858\pi\)
−0.177677 + 0.984089i \(0.556858\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −34.4222 −1.64664
\(438\) 0 0
\(439\) 21.0917 1.00665 0.503325 0.864097i \(-0.332110\pi\)
0.503325 + 0.864097i \(0.332110\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 33.2111 1.57791 0.788954 0.614453i \(-0.210623\pi\)
0.788954 + 0.614453i \(0.210623\pi\)
\(444\) 0 0
\(445\) −10.1833 −0.482737
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.02776 0.237274 0.118637 0.992938i \(-0.462147\pi\)
0.118637 + 0.992938i \(0.462147\pi\)
\(450\) 0 0
\(451\) −46.0555 −2.16867
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.00000 0.281284
\(456\) 0 0
\(457\) −13.9083 −0.650604 −0.325302 0.945610i \(-0.605466\pi\)
−0.325302 + 0.945610i \(0.605466\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −23.3944 −1.08959 −0.544794 0.838570i \(-0.683392\pi\)
−0.544794 + 0.838570i \(0.683392\pi\)
\(462\) 0 0
\(463\) −6.72498 −0.312536 −0.156268 0.987715i \(-0.549946\pi\)
−0.156268 + 0.987715i \(0.549946\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16.6056 0.768413 0.384207 0.923247i \(-0.374475\pi\)
0.384207 + 0.923247i \(0.374475\pi\)
\(468\) 0 0
\(469\) −2.69722 −0.124546
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 17.2111 0.791367
\(474\) 0 0
\(475\) −28.4222 −1.30410
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17.0917 −0.780938 −0.390469 0.920616i \(-0.627687\pi\)
−0.390469 + 0.920616i \(0.627687\pi\)
\(480\) 0 0
\(481\) −45.2111 −2.06145
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17.3305 −0.786939
\(486\) 0 0
\(487\) −28.0000 −1.26880 −0.634401 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 22.5139 1.01604 0.508019 0.861346i \(-0.330378\pi\)
0.508019 + 0.861346i \(0.330378\pi\)
\(492\) 0 0
\(493\) −9.21110 −0.414847
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.39445 −0.152262
\(498\) 0 0
\(499\) −29.2111 −1.30767 −0.653834 0.756638i \(-0.726841\pi\)
−0.653834 + 0.756638i \(0.726841\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 31.1194 1.38755 0.693773 0.720193i \(-0.255947\pi\)
0.693773 + 0.720193i \(0.255947\pi\)
\(504\) 0 0
\(505\) 16.4222 0.730779
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6.60555 −0.292786 −0.146393 0.989227i \(-0.546766\pi\)
−0.146393 + 0.989227i \(0.546766\pi\)
\(510\) 0 0
\(511\) −7.51388 −0.332394
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 18.2389 0.803700
\(516\) 0 0
\(517\) −10.4222 −0.458368
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.486122 0.0212974 0.0106487 0.999943i \(-0.496610\pi\)
0.0106487 + 0.999943i \(0.496610\pi\)
\(522\) 0 0
\(523\) 38.0555 1.66405 0.832026 0.554737i \(-0.187181\pi\)
0.832026 + 0.554737i \(0.187181\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7.30278 0.318114
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −53.0278 −2.29689
\(534\) 0 0
\(535\) 6.00000 0.259403
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.00000 −0.172292
\(540\) 0 0
\(541\) 4.00000 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 6.23886 0.267243
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −79.2666 −3.37687
\(552\) 0 0
\(553\) 2.60555 0.110799
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 20.7889 0.880854 0.440427 0.897788i \(-0.354827\pi\)
0.440427 + 0.897788i \(0.354827\pi\)
\(558\) 0 0
\(559\) 19.8167 0.838155
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) 12.2389 0.514893
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22.1194 −0.927295 −0.463647 0.886020i \(-0.653460\pi\)
−0.463647 + 0.886020i \(0.653460\pi\)
\(570\) 0 0
\(571\) −45.4500 −1.90202 −0.951011 0.309158i \(-0.899953\pi\)
−0.951011 + 0.309158i \(0.899953\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 13.2111 0.550941
\(576\) 0 0
\(577\) −8.18335 −0.340677 −0.170339 0.985386i \(-0.554486\pi\)
−0.170339 + 0.985386i \(0.554486\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.21110 0.133219
\(582\) 0 0
\(583\) 2.78890 0.115504
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.3944 0.470299 0.235150 0.971959i \(-0.424442\pi\)
0.235150 + 0.971959i \(0.424442\pi\)
\(588\) 0 0
\(589\) 62.8444 2.58946
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −22.1833 −0.910961 −0.455480 0.890246i \(-0.650532\pi\)
−0.455480 + 0.890246i \(0.650532\pi\)
\(594\) 0 0
\(595\) −1.30278 −0.0534086
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −26.7250 −1.09195 −0.545977 0.837800i \(-0.683841\pi\)
−0.545977 + 0.837800i \(0.683841\pi\)
\(600\) 0 0
\(601\) 45.2666 1.84646 0.923232 0.384243i \(-0.125538\pi\)
0.923232 + 0.384243i \(0.125538\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.51388 0.264827
\(606\) 0 0
\(607\) 0.330532 0.0134159 0.00670794 0.999978i \(-0.497865\pi\)
0.00670794 + 0.999978i \(0.497865\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.0000 −0.485468
\(612\) 0 0
\(613\) −21.7250 −0.877464 −0.438732 0.898618i \(-0.644572\pi\)
−0.438732 + 0.898618i \(0.644572\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.63331 −0.307305 −0.153653 0.988125i \(-0.549104\pi\)
−0.153653 + 0.988125i \(0.549104\pi\)
\(618\) 0 0
\(619\) 37.2111 1.49564 0.747820 0.663901i \(-0.231100\pi\)
0.747820 + 0.663901i \(0.231100\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.81665 0.313168
\(624\) 0 0
\(625\) 2.42221 0.0968882
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.81665 0.391416
\(630\) 0 0
\(631\) 9.11943 0.363039 0.181519 0.983387i \(-0.441898\pi\)
0.181519 + 0.983387i \(0.441898\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 18.9083 0.750354
\(636\) 0 0
\(637\) −4.60555 −0.182479
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −43.6333 −1.72341 −0.861706 0.507408i \(-0.830604\pi\)
−0.861706 + 0.507408i \(0.830604\pi\)
\(642\) 0 0
\(643\) 7.88057 0.310779 0.155390 0.987853i \(-0.450337\pi\)
0.155390 + 0.987853i \(0.450337\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 35.6333 1.40089 0.700445 0.713706i \(-0.252985\pi\)
0.700445 + 0.713706i \(0.252985\pi\)
\(648\) 0 0
\(649\) −32.0000 −1.25611
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −40.4222 −1.58184 −0.790922 0.611918i \(-0.790398\pi\)
−0.790922 + 0.611918i \(0.790398\pi\)
\(654\) 0 0
\(655\) 12.0000 0.468879
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −21.1194 −0.822696 −0.411348 0.911478i \(-0.634942\pi\)
−0.411348 + 0.911478i \(0.634942\pi\)
\(660\) 0 0
\(661\) −5.02776 −0.195557 −0.0977785 0.995208i \(-0.531174\pi\)
−0.0977785 + 0.995208i \(0.531174\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −11.2111 −0.434748
\(666\) 0 0
\(667\) 36.8444 1.42662
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −62.0555 −2.39563
\(672\) 0 0
\(673\) −7.02776 −0.270900 −0.135450 0.990784i \(-0.543248\pi\)
−0.135450 + 0.990784i \(0.543248\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 0 0
\(679\) 13.3028 0.510514
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −13.3944 −0.512524 −0.256262 0.966607i \(-0.582491\pi\)
−0.256262 + 0.966607i \(0.582491\pi\)
\(684\) 0 0
\(685\) −23.6056 −0.901922
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.21110 0.122333
\(690\) 0 0
\(691\) −1.93608 −0.0736521 −0.0368260 0.999322i \(-0.511725\pi\)
−0.0368260 + 0.999322i \(0.511725\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 11.0917 0.420731
\(696\) 0 0
\(697\) 11.5139 0.436119
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11.5778 0.437287 0.218644 0.975805i \(-0.429837\pi\)
0.218644 + 0.975805i \(0.429837\pi\)
\(702\) 0 0
\(703\) 84.4777 3.18614
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.6056 −0.474081
\(708\) 0 0
\(709\) −4.23886 −0.159194 −0.0795968 0.996827i \(-0.525363\pi\)
−0.0795968 + 0.996827i \(0.525363\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −29.2111 −1.09396
\(714\) 0 0
\(715\) 24.0000 0.897549
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9.69722 −0.361645 −0.180823 0.983516i \(-0.557876\pi\)
−0.180823 + 0.983516i \(0.557876\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 30.4222 1.12985
\(726\) 0 0
\(727\) −14.4222 −0.534890 −0.267445 0.963573i \(-0.586179\pi\)
−0.267445 + 0.963573i \(0.586179\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.30278 −0.159144
\(732\) 0 0
\(733\) 16.2389 0.599796 0.299898 0.953971i \(-0.403047\pi\)
0.299898 + 0.953971i \(0.403047\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −10.7889 −0.397414
\(738\) 0 0
\(739\) −23.3305 −0.858227 −0.429114 0.903250i \(-0.641174\pi\)
−0.429114 + 0.903250i \(0.641174\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 34.6056 1.26955 0.634777 0.772695i \(-0.281092\pi\)
0.634777 + 0.772695i \(0.281092\pi\)
\(744\) 0 0
\(745\) 5.60555 0.205372
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.60555 −0.168283
\(750\) 0 0
\(751\) 3.39445 0.123865 0.0619326 0.998080i \(-0.480274\pi\)
0.0619326 + 0.998080i \(0.480274\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 15.2389 0.554599
\(756\) 0 0
\(757\) −7.69722 −0.279760 −0.139880 0.990168i \(-0.544672\pi\)
−0.139880 + 0.990168i \(0.544672\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 50.2389 1.82116 0.910579 0.413336i \(-0.135636\pi\)
0.910579 + 0.413336i \(0.135636\pi\)
\(762\) 0 0
\(763\) −4.78890 −0.173370
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −36.8444 −1.33037
\(768\) 0 0
\(769\) −36.0555 −1.30020 −0.650098 0.759851i \(-0.725272\pi\)
−0.650098 + 0.759851i \(0.725272\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −17.0278 −0.612446 −0.306223 0.951960i \(-0.599065\pi\)
−0.306223 + 0.951960i \(0.599065\pi\)
\(774\) 0 0
\(775\) −24.1194 −0.866395
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 99.0833 3.55003
\(780\) 0 0
\(781\) −13.5778 −0.485852
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.60555 0.0929961
\(786\) 0 0
\(787\) 50.4222 1.79736 0.898679 0.438607i \(-0.144528\pi\)
0.898679 + 0.438607i \(0.144528\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.39445 −0.334028
\(792\) 0 0
\(793\) −71.4500 −2.53726
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −48.0555 −1.70221 −0.851107 0.524993i \(-0.824068\pi\)
−0.851107 + 0.524993i \(0.824068\pi\)
\(798\) 0 0
\(799\) 2.60555 0.0921778
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −30.0555 −1.06064
\(804\) 0 0
\(805\) 5.21110 0.183667
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 19.8167 0.696716 0.348358 0.937361i \(-0.386739\pi\)
0.348358 + 0.937361i \(0.386739\pi\)
\(810\) 0 0
\(811\) −4.48612 −0.157529 −0.0787645 0.996893i \(-0.525098\pi\)
−0.0787645 + 0.996893i \(0.525098\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.81665 0.0636346
\(816\) 0 0
\(817\) −37.0278 −1.29544
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 8.23886 0.287538 0.143769 0.989611i \(-0.454078\pi\)
0.143769 + 0.989611i \(0.454078\pi\)
\(822\) 0 0
\(823\) −38.6056 −1.34570 −0.672852 0.739777i \(-0.734931\pi\)
−0.672852 + 0.739777i \(0.734931\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −45.2111 −1.57214 −0.786072 0.618135i \(-0.787889\pi\)
−0.786072 + 0.618135i \(0.787889\pi\)
\(828\) 0 0
\(829\) −16.2389 −0.563999 −0.281999 0.959415i \(-0.590998\pi\)
−0.281999 + 0.959415i \(0.590998\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.00000 0.0346479
\(834\) 0 0
\(835\) −15.7889 −0.546397
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −18.4222 −0.636005 −0.318003 0.948090i \(-0.603012\pi\)
−0.318003 + 0.948090i \(0.603012\pi\)
\(840\) 0 0
\(841\) 55.8444 1.92567
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 10.6972 0.367996
\(846\) 0 0
\(847\) −5.00000 −0.171802
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −39.2666 −1.34604
\(852\) 0 0
\(853\) −10.0000 −0.342393 −0.171197 0.985237i \(-0.554763\pi\)
−0.171197 + 0.985237i \(0.554763\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 45.9638 1.57009 0.785047 0.619436i \(-0.212639\pi\)
0.785047 + 0.619436i \(0.212639\pi\)
\(858\) 0 0
\(859\) −54.6056 −1.86312 −0.931559 0.363591i \(-0.881551\pi\)
−0.931559 + 0.363591i \(0.881551\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −23.3583 −0.795125 −0.397563 0.917575i \(-0.630144\pi\)
−0.397563 + 0.917575i \(0.630144\pi\)
\(864\) 0 0
\(865\) −27.0000 −0.918028
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 10.4222 0.353549
\(870\) 0 0
\(871\) −12.4222 −0.420910
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 10.8167 0.365670
\(876\) 0 0
\(877\) −1.39445 −0.0470872 −0.0235436 0.999723i \(-0.507495\pi\)
−0.0235436 + 0.999723i \(0.507495\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 13.1194 0.442005 0.221002 0.975273i \(-0.429067\pi\)
0.221002 + 0.975273i \(0.429067\pi\)
\(882\) 0 0
\(883\) 12.0917 0.406917 0.203459 0.979084i \(-0.434782\pi\)
0.203459 + 0.979084i \(0.434782\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −55.7805 −1.87293 −0.936463 0.350767i \(-0.885921\pi\)
−0.936463 + 0.350767i \(0.885921\pi\)
\(888\) 0 0
\(889\) −14.5139 −0.486780
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 22.4222 0.750330
\(894\) 0 0
\(895\) −12.3944 −0.414301
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −67.2666 −2.24347
\(900\) 0 0
\(901\) −0.697224 −0.0232279
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.81665 −0.259834
\(906\) 0 0
\(907\) 27.2111 0.903530 0.451765 0.892137i \(-0.350795\pi\)
0.451765 + 0.892137i \(0.350795\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 15.8167 0.524029 0.262015 0.965064i \(-0.415613\pi\)
0.262015 + 0.965064i \(0.415613\pi\)
\(912\) 0 0
\(913\) 12.8444 0.425088
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −9.21110 −0.304177
\(918\) 0 0
\(919\) 26.3583 0.869480 0.434740 0.900556i \(-0.356840\pi\)
0.434740 + 0.900556i \(0.356840\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −15.6333 −0.514577
\(924\) 0 0
\(925\) −32.4222 −1.06604
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −36.0917 −1.18413 −0.592065 0.805890i \(-0.701687\pi\)
−0.592065 + 0.805890i \(0.701687\pi\)
\(930\) 0 0
\(931\) 8.60555 0.282036
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −5.21110 −0.170421
\(936\) 0 0
\(937\) −37.2111 −1.21563 −0.607817 0.794077i \(-0.707955\pi\)
−0.607817 + 0.794077i \(0.707955\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 33.6972 1.09850 0.549249 0.835659i \(-0.314914\pi\)
0.549249 + 0.835659i \(0.314914\pi\)
\(942\) 0 0
\(943\) −46.0555 −1.49977
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −24.8444 −0.807335 −0.403667 0.914906i \(-0.632265\pi\)
−0.403667 + 0.914906i \(0.632265\pi\)
\(948\) 0 0
\(949\) −34.6056 −1.12334
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 21.3583 0.691863 0.345931 0.938260i \(-0.387563\pi\)
0.345931 + 0.938260i \(0.387563\pi\)
\(954\) 0 0
\(955\) 15.2750 0.494288
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 18.1194 0.585107
\(960\) 0 0
\(961\) 22.3305 0.720340
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −19.5778 −0.630232
\(966\) 0 0
\(967\) −9.51388 −0.305946 −0.152973 0.988230i \(-0.548885\pi\)
−0.152973 + 0.988230i \(0.548885\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2.78890 −0.0895000 −0.0447500 0.998998i \(-0.514249\pi\)
−0.0447500 + 0.998998i \(0.514249\pi\)
\(972\) 0 0
\(973\) −8.51388 −0.272942
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 8.69722 0.278249 0.139124 0.990275i \(-0.455571\pi\)
0.139124 + 0.990275i \(0.455571\pi\)
\(978\) 0 0
\(979\) 31.2666 0.999285
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −47.7805 −1.52396 −0.761981 0.647600i \(-0.775773\pi\)
−0.761981 + 0.647600i \(0.775773\pi\)
\(984\) 0 0
\(985\) 8.60555 0.274196
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 17.2111 0.547281
\(990\) 0 0
\(991\) −11.2111 −0.356132 −0.178066 0.984019i \(-0.556984\pi\)
−0.178066 + 0.984019i \(0.556984\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 12.6333 0.400503
\(996\) 0 0
\(997\) −45.6972 −1.44725 −0.723623 0.690196i \(-0.757524\pi\)
−0.723623 + 0.690196i \(0.757524\pi\)
\(998\) 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 4284.2.a.l.1.2 2
3.2 odd 2 476.2.a.c.1.1 2
12.11 even 2 1904.2.a.k.1.2 2
21.20 even 2 3332.2.a.k.1.2 2
24.5 odd 2 7616.2.a.t.1.2 2
24.11 even 2 7616.2.a.o.1.1 2
51.50 odd 2 8092.2.a.l.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
476.2.a.c.1.1 2 3.2 odd 2
1904.2.a.k.1.2 2 12.11 even 2
3332.2.a.k.1.2 2 21.20 even 2
4284.2.a.l.1.2 2 1.1 even 1 trivial
7616.2.a.o.1.1 2 24.11 even 2
7616.2.a.t.1.2 2 24.5 odd 2
8092.2.a.l.1.2 2 51.50 odd 2