Properties

Label 3549.1.dd.a.2447.1
Level $3549$
Weight $1$
Character 3549.2447
Analytic conductor $1.771$
Analytic rank $0$
Dimension $24$
Projective image $D_{39}$
CM discriminant -3
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3549,1,Mod(263,3549)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3549, base_ring=CyclotomicField(78))
 
chi = DirichletCharacter(H, H._module([39, 52, 32]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3549.263");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3549.dd (of order \(78\), degree \(24\), minimal)

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: no
Analytic conductor: \(1.77118172983\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient field: \(\Q(\zeta_{39})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{24} - x^{23} + x^{21} - x^{20} + x^{18} - x^{17} + x^{15} - x^{14} + x^{12} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{39}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{39} - \cdots)\)

Embedding invariants

Embedding label 2447.1
Root \(0.987050 + 0.160411i\) of defining polynomial
Character \(\chi\) \(=\) 3549.2447
Dual form 3549.1.dd.a.2921.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.970942 + 0.239316i) q^{3} +(-0.996757 - 0.0804666i) q^{4} +(-0.919979 - 0.391967i) q^{7} +(0.885456 - 0.464723i) q^{9} +O(q^{10})\) \(q+(-0.970942 + 0.239316i) q^{3} +(-0.996757 - 0.0804666i) q^{4} +(-0.919979 - 0.391967i) q^{7} +(0.885456 - 0.464723i) q^{9} +(0.987050 - 0.160411i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.987050 + 0.160411i) q^{16} -0.0805319 q^{19} +(0.987050 + 0.160411i) q^{21} +(0.948536 - 0.316668i) q^{25} +(-0.748511 + 0.663123i) q^{27} +(0.885456 + 0.464723i) q^{28} +(-0.227255 - 1.11317i) q^{31} +(-0.919979 + 0.391967i) q^{36} +(0.368039 + 1.80277i) q^{37} +(0.692724 + 0.721202i) q^{39} +(-1.74527 + 0.582656i) q^{43} +(-0.996757 + 0.0804666i) q^{48} +(0.692724 + 0.721202i) q^{49} +(0.428693 + 0.903450i) q^{52} +(0.0781918 - 0.0192725i) q^{57} +(-0.240292 - 1.97898i) q^{61} +(-0.996757 + 0.0804666i) q^{63} +(-0.970942 - 0.239316i) q^{64} +(-0.850405 - 1.23202i) q^{67} +(-1.66849 + 1.05509i) q^{73} +(-0.845190 + 0.534466i) q^{75} +(0.0802707 + 0.00648012i) q^{76} +(-0.832471 + 1.75440i) q^{79} +(0.568065 - 0.822984i) q^{81} +(-0.970942 - 0.239316i) q^{84} +(0.120537 + 0.992709i) q^{91} +(0.487050 + 1.02644i) q^{93} +(-0.987050 - 0.160411i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{3} + q^{4} + q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{3} + q^{4} + q^{7} - 2 q^{9} + q^{12} - 12 q^{13} + q^{16} + 2 q^{19} + q^{21} + q^{25} - 2 q^{27} - 2 q^{28} + 2 q^{31} + q^{36} - q^{37} + q^{39} - q^{43} + q^{48} + q^{49} + q^{52} + 2 q^{57} + 2 q^{61} + q^{63} - 2 q^{64} - 4 q^{67} - q^{73} + q^{75} - q^{76} + 2 q^{79} - 2 q^{81} - 2 q^{84} - 2 q^{91} - 11 q^{93} - q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3549\mathbb{Z}\right)^\times\).

\(n\) \(1184\) \(1522\) \(3382\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{39}\right)\)

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 0.0402659 0.999189i \(-0.487179\pi\)
−0.0402659 + 0.999189i \(0.512821\pi\)
\(3\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(4\) −0.996757 0.0804666i −0.996757 0.0804666i
\(5\) 0 0 0.987050 0.160411i \(-0.0512821\pi\)
−0.987050 + 0.160411i \(0.948718\pi\)
\(6\) 0 0
\(7\) −0.919979 0.391967i −0.919979 0.391967i
\(8\) 0 0
\(9\) 0.885456 0.464723i 0.885456 0.464723i
\(10\) 0 0
\(11\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(12\) 0.987050 0.160411i 0.987050 0.160411i
\(13\) −0.500000 0.866025i −0.500000 0.866025i
\(14\) 0 0
\(15\) 0 0
\(16\) 0.987050 + 0.160411i 0.987050 + 0.160411i
\(17\) 0 0 0.919979 0.391967i \(-0.128205\pi\)
−0.919979 + 0.391967i \(0.871795\pi\)
\(18\) 0 0
\(19\) −0.0805319 −0.0805319 −0.0402659 0.999189i \(-0.512821\pi\)
−0.0402659 + 0.999189i \(0.512821\pi\)
\(20\) 0 0
\(21\) 0.987050 + 0.160411i 0.987050 + 0.160411i
\(22\) 0 0
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) 0.948536 0.316668i 0.948536 0.316668i
\(26\) 0 0
\(27\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(28\) 0.885456 + 0.464723i 0.885456 + 0.464723i
\(29\) 0 0 −0.845190 0.534466i \(-0.820513\pi\)
0.845190 + 0.534466i \(0.179487\pi\)
\(30\) 0 0
\(31\) −0.227255 1.11317i −0.227255 1.11317i −0.919979 0.391967i \(-0.871795\pi\)
0.692724 0.721202i \(-0.256410\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.919979 + 0.391967i −0.919979 + 0.391967i
\(37\) 0.368039 + 1.80277i 0.368039 + 1.80277i 0.568065 + 0.822984i \(0.307692\pi\)
−0.200026 + 0.979791i \(0.564103\pi\)
\(38\) 0 0
\(39\) 0.692724 + 0.721202i 0.692724 + 0.721202i
\(40\) 0 0
\(41\) 0 0 −0.692724 0.721202i \(-0.743590\pi\)
0.692724 + 0.721202i \(0.256410\pi\)
\(42\) 0 0
\(43\) −1.74527 + 0.582656i −1.74527 + 0.582656i −0.996757 0.0804666i \(-0.974359\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.428693 0.903450i \(-0.358974\pi\)
−0.428693 + 0.903450i \(0.641026\pi\)
\(48\) −0.996757 + 0.0804666i −0.996757 + 0.0804666i
\(49\) 0.692724 + 0.721202i 0.692724 + 0.721202i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.428693 + 0.903450i 0.428693 + 0.903450i
\(53\) 0 0 −0.799443 0.600742i \(-0.794872\pi\)
0.799443 + 0.600742i \(0.205128\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.0781918 0.0192725i 0.0781918 0.0192725i
\(58\) 0 0
\(59\) 0 0 0.987050 0.160411i \(-0.0512821\pi\)
−0.987050 + 0.160411i \(0.948718\pi\)
\(60\) 0 0
\(61\) −0.240292 1.97898i −0.240292 1.97898i −0.200026 0.979791i \(-0.564103\pi\)
−0.0402659 0.999189i \(-0.512821\pi\)
\(62\) 0 0
\(63\) −0.996757 + 0.0804666i −0.996757 + 0.0804666i
\(64\) −0.970942 0.239316i −0.970942 0.239316i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.850405 1.23202i −0.850405 1.23202i −0.970942 0.239316i \(-0.923077\pi\)
0.120537 0.992709i \(-0.461538\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.278217 0.960518i \(-0.410256\pi\)
−0.278217 + 0.960518i \(0.589744\pi\)
\(72\) 0 0
\(73\) −1.66849 + 1.05509i −1.66849 + 1.05509i −0.748511 + 0.663123i \(0.769231\pi\)
−0.919979 + 0.391967i \(0.871795\pi\)
\(74\) 0 0
\(75\) −0.845190 + 0.534466i −0.845190 + 0.534466i
\(76\) 0.0802707 + 0.00648012i 0.0802707 + 0.00648012i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.832471 + 1.75440i −0.832471 + 1.75440i −0.200026 + 0.979791i \(0.564103\pi\)
−0.632445 + 0.774605i \(0.717949\pi\)
\(80\) 0 0
\(81\) 0.568065 0.822984i 0.568065 0.822984i
\(82\) 0 0
\(83\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(84\) −0.970942 0.239316i −0.970942 0.239316i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) 0 0
\(91\) 0.120537 + 0.992709i 0.120537 + 0.992709i
\(92\) 0 0
\(93\) 0.487050 + 1.02644i 0.487050 + 1.02644i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.987050 0.160411i −0.987050 0.160411i −0.354605 0.935016i \(-0.615385\pi\)
−0.632445 + 0.774605i \(0.717949\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(101\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(102\) 0 0
\(103\) 1.36751 + 1.42373i 1.36751 + 1.42373i 0.799443 + 0.600742i \(0.205128\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.632445 0.774605i \(-0.717949\pi\)
0.632445 + 0.774605i \(0.282051\pi\)
\(108\) 0.799443 0.600742i 0.799443 0.600742i
\(109\) −1.19979 + 0.400550i −1.19979 + 0.400550i −0.845190 0.534466i \(-0.820513\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(110\) 0 0
\(111\) −0.788777 1.66231i −0.788777 1.66231i
\(112\) −0.845190 0.534466i −0.845190 0.534466i
\(113\) 0 0 0.692724 0.721202i \(-0.256410\pi\)
−0.692724 + 0.721202i \(0.743590\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.845190 0.534466i −0.845190 0.534466i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.136945 + 1.12785i 0.136945 + 1.12785i
\(125\) 0 0
\(126\) 0 0
\(127\) −0.542249 + 1.14277i −0.542249 + 1.14277i 0.428693 + 0.903450i \(0.358974\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(128\) 0 0
\(129\) 1.55512 0.983395i 1.55512 0.983395i
\(130\) 0 0
\(131\) 0 0 −0.845190 0.534466i \(-0.820513\pi\)
0.845190 + 0.534466i \(0.179487\pi\)
\(132\) 0 0
\(133\) 0.0740877 + 0.0315658i 0.0740877 + 0.0315658i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.200026 0.979791i \(-0.435897\pi\)
−0.200026 + 0.979791i \(0.564103\pi\)
\(138\) 0 0
\(139\) −1.47764 0.240139i −1.47764 0.240139i −0.632445 0.774605i \(-0.717949\pi\)
−0.845190 + 0.534466i \(0.820513\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.948536 0.316668i 0.948536 0.316668i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.845190 0.534466i −0.845190 0.534466i
\(148\) −0.221783 1.82654i −0.221783 1.82654i
\(149\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(150\) 0 0
\(151\) −0.641762 1.35248i −0.641762 1.35248i −0.919979 0.391967i \(-0.871795\pi\)
0.278217 0.960518i \(-0.410256\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.632445 0.774605i −0.632445 0.774605i
\(157\) −0.542249 0.664135i −0.542249 0.664135i 0.428693 0.903450i \(-0.358974\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.41998 + 1.25799i −1.41998 + 1.25799i −0.500000 + 0.866025i \(0.666667\pi\)
−0.919979 + 0.391967i \(0.871795\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.845190 0.534466i \(-0.820513\pi\)
0.845190 + 0.534466i \(0.179487\pi\)
\(168\) 0 0
\(169\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(170\) 0 0
\(171\) −0.0713074 + 0.0374250i −0.0713074 + 0.0374250i
\(172\) 1.78649 0.440331i 1.78649 0.440331i
\(173\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(174\) 0 0
\(175\) −0.996757 0.0804666i −0.996757 0.0804666i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(180\) 0 0
\(181\) −0.672711 + 1.77379i −0.672711 + 1.77379i −0.0402659 + 0.999189i \(0.512821\pi\)
−0.632445 + 0.774605i \(0.717949\pi\)
\(182\) 0 0
\(183\) 0.706910 + 1.86397i 0.706910 + 1.86397i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.948536 0.316668i 0.948536 0.316668i
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 1.00000 1.00000
\(193\) 0.192724 + 1.58723i 0.192724 + 1.58723i 0.692724 + 0.721202i \(0.256410\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.632445 0.774605i −0.632445 0.774605i
\(197\) 0 0 0.200026 0.979791i \(-0.435897\pi\)
−0.200026 + 0.979791i \(0.564103\pi\)
\(198\) 0 0
\(199\) 0.0509320 0.0623804i 0.0509320 0.0623804i −0.748511 0.663123i \(-0.769231\pi\)
0.799443 + 0.600742i \(0.205128\pi\)
\(200\) 0 0
\(201\) 1.12054 + 0.992709i 1.12054 + 0.992709i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.354605 0.935016i −0.354605 0.935016i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.813261 1.71391i 0.813261 1.71391i 0.120537 0.992709i \(-0.461538\pi\)
0.692724 0.721202i \(-0.256410\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.227255 + 1.11317i −0.227255 + 1.11317i
\(218\) 0 0
\(219\) 1.36751 1.42373i 1.36751 1.42373i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.97410 0.320823i 1.97410 0.320823i 0.987050 0.160411i \(-0.0512821\pi\)
0.987050 0.160411i \(-0.0512821\pi\)
\(224\) 0 0
\(225\) 0.692724 0.721202i 0.692724 0.721202i
\(226\) 0 0
\(227\) 0 0 −0.996757 0.0804666i \(-0.974359\pi\)
0.996757 + 0.0804666i \(0.0256410\pi\)
\(228\) −0.0794890 + 0.0129182i −0.0794890 + 0.0129182i
\(229\) 0.253011 1.23933i 0.253011 1.23933i −0.632445 0.774605i \(-0.717949\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.278217 0.960518i \(-0.589744\pi\)
0.278217 + 0.960518i \(0.410256\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.388427 1.90264i 0.388427 1.90264i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −0.718540 + 0.880052i −0.718540 + 0.880052i −0.996757 0.0804666i \(-0.974359\pi\)
0.278217 + 0.960518i \(0.410256\pi\)
\(242\) 0 0
\(243\) −0.354605 + 0.935016i −0.354605 + 0.935016i
\(244\) 0.0802707 + 1.99190i 0.0802707 + 1.99190i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.0402659 + 0.0697427i 0.0402659 + 0.0697427i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.200026 0.979791i \(-0.564103\pi\)
0.200026 + 0.979791i \(0.435897\pi\)
\(252\) 1.00000 1.00000
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.948536 + 0.316668i 0.948536 + 0.316668i
\(257\) 0 0 −0.428693 0.903450i \(-0.641026\pi\)
0.428693 + 0.903450i \(0.358974\pi\)
\(258\) 0 0
\(259\) 0.368039 1.80277i 0.368039 1.80277i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.748511 + 1.29646i 0.748511 + 1.29646i
\(269\) 0 0 −0.692724 0.721202i \(-0.743590\pi\)
0.692724 + 0.721202i \(0.256410\pi\)
\(270\) 0 0
\(271\) −0.854605 + 0.0689908i −0.854605 + 0.0689908i −0.500000 0.866025i \(-0.666667\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(272\) 0 0
\(273\) −0.354605 0.935016i −0.354605 0.935016i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.444838 0.334274i 0.444838 0.334274i −0.354605 0.935016i \(-0.615385\pi\)
0.799443 + 0.600742i \(0.205128\pi\)
\(278\) 0 0
\(279\) −0.718540 0.880052i −0.718540 0.880052i
\(280\) 0 0
\(281\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(282\) 0 0
\(283\) −1.47764 + 1.30907i −1.47764 + 1.30907i −0.632445 + 0.774605i \(0.717949\pi\)
−0.845190 + 0.534466i \(0.820513\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.692724 0.721202i 0.692724 0.721202i
\(290\) 0 0
\(291\) 0.996757 0.0804666i 0.996757 0.0804666i
\(292\) 1.74798 0.917410i 1.74798 0.917410i
\(293\) 0 0 −0.919979 0.391967i \(-0.871795\pi\)
0.919979 + 0.391967i \(0.128205\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0.885456 0.464723i 0.885456 0.464723i
\(301\) 1.83399 + 0.148055i 1.83399 + 0.148055i
\(302\) 0 0
\(303\) 0 0
\(304\) −0.0794890 0.0129182i −0.0794890 0.0129182i
\(305\) 0 0
\(306\) 0 0
\(307\) −0.180446 + 0.159861i −0.180446 + 0.159861i −0.748511 0.663123i \(-0.769231\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(308\) 0 0
\(309\) −1.66849 1.05509i −1.66849 1.05509i
\(310\) 0 0
\(311\) 0 0 −0.200026 0.979791i \(-0.564103\pi\)
0.200026 + 0.979791i \(0.435897\pi\)
\(312\) 0 0
\(313\) −0.111301 + 0.545190i −0.111301 + 0.545190i 0.885456 + 0.464723i \(0.153846\pi\)
−0.996757 + 0.0804666i \(0.974359\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.970942 1.68172i 0.970942 1.68172i
\(317\) 0 0 0.799443 0.600742i \(-0.205128\pi\)
−0.799443 + 0.600742i \(0.794872\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.632445 + 0.774605i −0.632445 + 0.774605i
\(325\) −0.748511 0.663123i −0.748511 0.663123i
\(326\) 0 0
\(327\) 1.06907 0.676041i 1.06907 0.676041i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.0482209 + 0.397135i −0.0482209 + 0.397135i 0.948536 + 0.316668i \(0.102564\pi\)
−0.996757 + 0.0804666i \(0.974359\pi\)
\(332\) 0 0
\(333\) 1.16367 + 1.42524i 1.16367 + 1.42524i
\(334\) 0 0
\(335\) 0 0
\(336\) 0.948536 + 0.316668i 0.948536 + 0.316668i
\(337\) 1.59889 1.59889 0.799443 0.600742i \(-0.205128\pi\)
0.799443 + 0.600742i \(0.205128\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.354605 0.935016i −0.354605 0.935016i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.845190 0.534466i \(-0.820513\pi\)
0.845190 + 0.534466i \(0.179487\pi\)
\(348\) 0 0
\(349\) 0.0402659 + 0.999189i 0.0402659 + 0.999189i 0.885456 + 0.464723i \(0.153846\pi\)
−0.845190 + 0.534466i \(0.820513\pi\)
\(350\) 0 0
\(351\) 0.948536 + 0.316668i 0.948536 + 0.316668i
\(352\) 0 0
\(353\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.799443 0.600742i \(-0.205128\pi\)
−0.799443 + 0.600742i \(0.794872\pi\)
\(360\) 0 0
\(361\) −0.993515 −0.993515
\(362\) 0 0
\(363\) −0.748511 0.663123i −0.748511 0.663123i
\(364\) −0.0402659 0.999189i −0.0402659 0.999189i
\(365\) 0 0
\(366\) 0 0
\(367\) 1.22675 0.643850i 1.22675 0.643850i 0.278217 0.960518i \(-0.410256\pi\)
0.948536 + 0.316668i \(0.102564\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −0.402877 1.06230i −0.402877 1.06230i
\(373\) 1.00599 + 0.527986i 1.00599 + 0.527986i 0.885456 0.464723i \(-0.153846\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.22675 + 1.27719i 1.22675 + 1.27719i 0.948536 + 0.316668i \(0.102564\pi\)
0.278217 + 0.960518i \(0.410256\pi\)
\(380\) 0 0
\(381\) 0.253011 1.23933i 0.253011 1.23933i
\(382\) 0 0
\(383\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.27458 + 1.32698i −1.27458 + 1.32698i
\(388\) 0.970942 + 0.239316i 0.970942 + 0.239316i
\(389\) 0 0 −0.919979 0.391967i \(-0.871795\pi\)
0.919979 + 0.391967i \(0.128205\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.706910 1.86397i 0.706910 1.86397i 0.278217 0.960518i \(-0.410256\pi\)
0.428693 0.903450i \(-0.358974\pi\)
\(398\) 0 0
\(399\) −0.0794890 0.0129182i −0.0794890 0.0129182i
\(400\) 0.987050 0.160411i 0.987050 0.160411i
\(401\) 0 0 −0.987050 0.160411i \(-0.948718\pi\)
0.987050 + 0.160411i \(0.0512821\pi\)
\(402\) 0 0
\(403\) −0.850405 + 0.753393i −0.850405 + 0.753393i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.17097 1.21911i −1.17097 1.21911i −0.970942 0.239316i \(-0.923077\pi\)
−0.200026 0.979791i \(-0.564103\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.24851 1.52915i −1.24851 1.52915i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.49217 0.120460i 1.49217 0.120460i
\(418\) 0 0
\(419\) 0 0 −0.996757 0.0804666i \(-0.974359\pi\)
0.996757 + 0.0804666i \(0.0256410\pi\)
\(420\) 0 0
\(421\) 0.688601 + 0.169725i 0.688601 + 0.169725i 0.568065 0.822984i \(-0.307692\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.554631 + 1.91481i −0.554631 + 1.91481i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(432\) −0.845190 + 0.534466i −0.845190 + 0.534466i
\(433\) −1.12001 1.37176i −1.12001 1.37176i −0.919979 0.391967i \(-0.871795\pi\)
−0.200026 0.979791i \(-0.564103\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.22814 0.302708i 1.22814 0.302708i
\(437\) 0 0
\(438\) 0 0
\(439\) −0.0763874 + 0.0255019i −0.0763874 + 0.0255019i −0.354605 0.935016i \(-0.615385\pi\)
0.278217 + 0.960518i \(0.410256\pi\)
\(440\) 0 0
\(441\) 0.948536 + 0.316668i 0.948536 + 0.316668i
\(442\) 0 0
\(443\) 0 0 −0.278217 0.960518i \(-0.589744\pi\)
0.278217 + 0.960518i \(0.410256\pi\)
\(444\) 0.652458 + 1.72039i 0.652458 + 1.72039i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.799443 + 0.600742i 0.799443 + 0.600742i
\(449\) 0 0 −0.428693 0.903450i \(-0.641026\pi\)
0.428693 + 0.903450i \(0.358974\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0.946784 + 1.15960i 0.946784 + 1.15960i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.491287 + 0.511484i −0.491287 + 0.511484i −0.919979 0.391967i \(-0.871795\pi\)
0.428693 + 0.903450i \(0.358974\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.0402659 0.999189i \(-0.487179\pi\)
−0.0402659 + 0.999189i \(0.512821\pi\)
\(462\) 0 0
\(463\) −1.49676 + 0.785559i −1.49676 + 0.785559i −0.996757 0.0804666i \(-0.974359\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.0402659 0.999189i \(-0.512821\pi\)
0.0402659 + 0.999189i \(0.487179\pi\)
\(468\) 0.799443 + 0.600742i 0.799443 + 0.600742i
\(469\) 0.299443 + 1.46677i 0.299443 + 1.46677i
\(470\) 0 0
\(471\) 0.685430 + 0.515067i 0.685430 + 0.515067i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.0763874 + 0.0255019i −0.0763874 + 0.0255019i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(480\) 0 0
\(481\) 1.37723 1.22012i 1.37723 1.22012i
\(482\) 0 0
\(483\) 0 0
\(484\) −0.500000 0.866025i −0.500000 0.866025i
\(485\) 0 0
\(486\) 0 0
\(487\) 0.367555 0.774605i 0.367555 0.774605i −0.632445 0.774605i \(-0.717949\pi\)
1.00000 \(0\)
\(488\) 0 0
\(489\) 1.07766 1.56126i 1.07766 1.56126i
\(490\) 0 0
\(491\) 0 0 0.632445 0.774605i \(-0.282051\pi\)
−0.632445 + 0.774605i \(0.717949\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.0457473 1.13521i −0.0457473 1.13521i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.81613 + 0.773781i −1.81613 + 0.773781i −0.845190 + 0.534466i \(0.820513\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.428693 0.903450i \(-0.641026\pi\)
0.428693 + 0.903450i \(0.358974\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.278217 0.960518i 0.278217 0.960518i
\(508\) 0.632445 1.09543i 0.632445 1.09543i
\(509\) 0 0 0.0402659 0.999189i \(-0.487179\pi\)
−0.0402659 + 0.999189i \(0.512821\pi\)
\(510\) 0 0
\(511\) 1.94854 0.316668i 1.94854 0.316668i
\(512\) 0 0
\(513\) 0.0602790 0.0534025i 0.0602790 0.0534025i
\(514\) 0 0
\(515\) 0 0
\(516\) −1.62920 + 0.855072i −1.62920 + 0.855072i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.987050 0.160411i \(-0.948718\pi\)
0.987050 + 0.160411i \(0.0512821\pi\)
\(522\) 0 0
\(523\) −1.66849 0.271156i −1.66849 0.271156i −0.748511 0.663123i \(-0.769231\pi\)
−0.919979 + 0.391967i \(0.871795\pi\)
\(524\) 0 0
\(525\) 0.987050 0.160411i 0.987050 0.160411i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.500000 0.866025i −0.500000 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.0713074 0.0374250i −0.0713074 0.0374250i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0.253011 0.309882i 0.253011 0.309882i −0.632445 0.774605i \(-0.717949\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(542\) 0 0
\(543\) 0.228667 1.88324i 0.228667 1.88324i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.759177 + 0.398447i 0.759177 + 0.398447i 0.799443 0.600742i \(-0.205128\pi\)
−0.0402659 + 0.999189i \(0.512821\pi\)
\(548\) 0 0
\(549\) −1.13245 1.64063i −1.13245 1.64063i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.45352 1.28771i 1.45352 1.28771i
\(554\) 0 0
\(555\) 0 0
\(556\) 1.45352 + 0.358261i 1.45352 + 0.358261i
\(557\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(558\) 0 0
\(559\) 1.37723 + 1.22012i 1.37723 + 1.22012i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.278217 0.960518i \(-0.589744\pi\)
0.278217 + 0.960518i \(0.410256\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.845190 + 0.534466i −0.845190 + 0.534466i
\(568\) 0 0
\(569\) 0 0 −0.632445 0.774605i \(-0.717949\pi\)
0.632445 + 0.774605i \(0.282051\pi\)
\(570\) 0 0
\(571\) 0.959734 0.999189i 0.959734 0.999189i −0.0402659 0.999189i \(-0.512821\pi\)
1.00000 \(0\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(577\) −0.948536 + 1.64291i −0.948536 + 1.64291i −0.200026 + 0.979791i \(0.564103\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(578\) 0 0
\(579\) −0.566973 1.49498i −0.566973 1.49498i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 0.799443 + 0.600742i 0.799443 + 0.600742i
\(589\) 0.0183013 + 0.0896456i 0.0183013 + 0.0896456i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.0740877 + 1.83847i 0.0740877 + 1.83847i
\(593\) 0 0 −0.278217 0.960518i \(-0.589744\pi\)
0.278217 + 0.960518i \(0.410256\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.0345234 + 0.0727566i −0.0345234 + 0.0727566i
\(598\) 0 0
\(599\) 0 0 −0.428693 0.903450i \(-0.641026\pi\)
0.428693 + 0.903450i \(0.358974\pi\)
\(600\) 0 0
\(601\) 0.0740877 + 1.83847i 0.0740877 + 1.83847i 0.428693 + 0.903450i \(0.358974\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(602\) 0 0
\(603\) −1.32555 0.695701i −1.32555 0.695701i
\(604\) 0.530851 + 1.39974i 0.530851 + 1.39974i
\(605\) 0 0
\(606\) 0 0
\(607\) −1.55242 + 0.382638i −1.55242 + 0.382638i −0.919979 0.391967i \(-0.871795\pi\)
−0.632445 + 0.774605i \(0.717949\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.566973 1.49498i −0.566973 1.49498i −0.845190 0.534466i \(-0.820513\pi\)
0.278217 0.960518i \(-0.410256\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.632445 0.774605i \(-0.717949\pi\)
0.632445 + 0.774605i \(0.282051\pi\)
\(618\) 0 0
\(619\) −0.511909 + 1.76731i −0.511909 + 1.76731i 0.120537 + 0.992709i \(0.461538\pi\)
−0.632445 + 0.774605i \(0.717949\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(625\) 0.799443 0.600742i 0.799443 0.600742i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.487050 + 0.705614i 0.487050 + 0.705614i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.69272 + 0.721202i 1.69272 + 0.721202i 1.00000 \(0\)
0.692724 + 0.721202i \(0.256410\pi\)
\(632\) 0 0
\(633\) −0.379463 + 1.85873i −0.379463 + 1.85873i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0.278217 0.960518i 0.278217 0.960518i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.0402659 0.999189i \(-0.512821\pi\)
0.0402659 + 0.999189i \(0.487179\pi\)
\(642\) 0 0
\(643\) 1.10759 1.15312i 1.10759 1.15312i 0.120537 0.992709i \(-0.461538\pi\)
0.987050 0.160411i \(-0.0512821\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −0.0457473 1.13521i −0.0457473 1.13521i
\(652\) 1.51660 1.13965i 1.51660 1.13965i
\(653\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.987050 + 1.70962i −0.987050 + 1.70962i
\(658\) 0 0
\(659\) 0 0 −0.799443 0.600742i \(-0.794872\pi\)
0.799443 + 0.600742i \(0.205128\pi\)
\(660\) 0 0
\(661\) 0.213460 1.75800i 0.213460 1.75800i −0.354605 0.935016i \(-0.615385\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −1.83996 + 0.783933i −1.83996 + 0.783933i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.17097 1.21911i −1.17097 1.21911i −0.970942 0.239316i \(-0.923077\pi\)
−0.200026 0.979791i \(-0.564103\pi\)
\(674\) 0 0
\(675\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(676\) 0.568065 0.822984i 0.568065 0.822984i
\(677\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(678\) 0 0
\(679\) 0.845190 + 0.534466i 0.845190 + 0.534466i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.919979 0.391967i \(-0.128205\pi\)
−0.919979 + 0.391967i \(0.871795\pi\)
\(684\) 0.0740877 0.0315658i 0.0740877 0.0315658i
\(685\) 0 0
\(686\) 0 0
\(687\) 0.0509320 + 1.26386i 0.0509320 + 1.26386i
\(688\) −1.81613 + 0.295150i −1.81613 + 0.295150i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.59370 1.19759i −1.59370 1.19759i −0.845190 0.534466i \(-0.820513\pi\)
−0.748511 0.663123i \(-0.769231\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.987050 + 0.160411i 0.987050 + 0.160411i
\(701\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(702\) 0 0
\(703\) −0.0296389 0.145181i −0.0296389 0.145181i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.84195 0.453999i −1.84195 0.453999i −0.845190 0.534466i \(-0.820513\pi\)
−0.996757 + 0.0804666i \(0.974359\pi\)
\(710\) 0 0
\(711\) 0.0781918 + 1.94031i 0.0781918 + 1.94031i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(720\) 0 0
\(721\) −0.700026 1.84582i −0.700026 1.84582i
\(722\) 0 0
\(723\) 0.487050 1.02644i 0.487050 1.02644i
\(724\) 0.813261 1.71391i 0.813261 1.71391i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.0290582 + 0.239316i 0.0290582 + 0.239316i 1.00000 \(0\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(728\) 0 0
\(729\) 0.120537 0.992709i 0.120537 0.992709i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.554631 1.91481i −0.554631 1.91481i
\(733\) 0.166997 + 0.173863i 0.166997 + 0.173863i 0.799443 0.600742i \(-0.205128\pi\)
−0.632445 + 0.774605i \(0.717949\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.706910 + 1.86397i 0.706910 + 1.86397i 0.428693 + 0.903450i \(0.358974\pi\)
0.278217 + 0.960518i \(0.410256\pi\)
\(740\) 0 0
\(741\) −0.0557864 0.0580798i −0.0557864 0.0580798i
\(742\) 0 0
\(743\) 0 0 0.428693 0.903450i \(-0.358974\pi\)
−0.428693 + 0.903450i \(0.641026\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.06907 0.676041i 1.06907 0.676041i 0.120537 0.992709i \(-0.461538\pi\)
0.948536 + 0.316668i \(0.102564\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(757\) −0.240292 0.0193983i −0.240292 0.0193983i −0.0402659 0.999189i \(-0.512821\pi\)
−0.200026 + 0.979791i \(0.564103\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(762\) 0 0
\(763\) 1.26079 + 0.101781i 1.26079 + 0.101781i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.996757 0.0804666i −0.996757 0.0804666i
\(769\) 0.398754 + 0.0321908i 0.398754 + 0.0321908i 0.278217 0.960518i \(-0.410256\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.0643806 1.59759i −0.0643806 1.59759i
\(773\) 0 0 0.632445 0.774605i \(-0.282051\pi\)
−0.632445 + 0.774605i \(0.717949\pi\)
\(774\) 0 0
\(775\) −0.568065 0.983917i −0.568065 0.983917i
\(776\) 0 0
\(777\) 0.0740877 + 1.83847i 0.0740877 + 1.83847i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.96770 0.158849i −1.96770 0.158849i −0.970942 0.239316i \(-0.923077\pi\)
−0.996757 + 0.0804666i \(0.974359\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −1.59370 + 1.19759i −1.59370 + 1.19759i
\(794\) 0 0
\(795\) 0 0
\(796\) −0.0557864 + 0.0580798i −0.0557864 + 0.0580798i
\(797\) 0 0 0.996757 0.0804666i \(-0.0256410\pi\)
−0.996757 + 0.0804666i \(0.974359\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) −1.03702 1.07966i −1.03702 1.07966i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(810\) 0 0
\(811\) 0.0285570 + 0.0752986i 0.0285570 + 0.0752986i 0.948536 0.316668i \(-0.102564\pi\)
−0.919979 + 0.391967i \(0.871795\pi\)
\(812\) 0 0
\(813\) 0.813261 0.271506i 0.813261 0.271506i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0.140550 0.0469224i 0.140550 0.0469224i
\(818\) 0 0
\(819\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(820\) 0 0
\(821\) 0 0 −0.919979 0.391967i \(-0.871795\pi\)
0.919979 + 0.391967i \(0.128205\pi\)
\(822\) 0 0
\(823\) −0.885456 1.53365i −0.885456 1.53365i −0.845190 0.534466i \(-0.820513\pi\)
−0.0402659 0.999189i \(-0.512821\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(828\) 0 0
\(829\) 0.448536 + 1.18269i 0.448536 + 1.18269i 0.948536 + 0.316668i \(0.102564\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) −0.351915 + 0.431017i −0.351915 + 0.431017i
\(832\) 0.278217 + 0.960518i 0.278217 + 0.960518i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0.908271 + 0.682521i 0.908271 + 0.682521i
\(838\) 0 0
\(839\) 0 0 −0.200026 0.979791i \(-0.564103\pi\)
0.200026 + 0.979791i \(0.435897\pi\)
\(840\) 0 0
\(841\) 0.428693 + 0.903450i 0.428693 + 0.903450i
\(842\) 0 0
\(843\) 0 0
\(844\) −0.948536 + 1.64291i −0.948536 + 1.64291i
\(845\) 0 0
\(846\) 0 0
\(847\) −0.200026 0.979791i −0.200026 0.979791i
\(848\) 0 0
\(849\) 1.12142 1.62465i 1.12142 1.62465i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −0.0854858 + 0.704039i −0.0854858 + 0.704039i 0.885456 + 0.464723i \(0.153846\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.632445 0.774605i \(-0.717949\pi\)
0.632445 + 0.774605i \(0.282051\pi\)
\(858\) 0 0
\(859\) −0.876221 + 1.07318i −0.876221 + 1.07318i 0.120537 + 0.992709i \(0.461538\pi\)
−0.996757 + 0.0804666i \(0.974359\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.996757 0.0804666i \(-0.974359\pi\)
0.996757 + 0.0804666i \(0.0256410\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(868\) 0.316091 1.09127i 0.316091 1.09127i
\(869\) 0 0
\(870\) 0 0
\(871\) −0.641762 + 1.35248i −0.641762 + 1.35248i
\(872\) 0 0
\(873\) −0.948536 + 0.316668i −0.948536 + 0.316668i
\(874\) 0 0
\(875\) 0 0
\(876\) −1.47764 + 1.30907i −1.47764 + 1.30907i
\(877\) −0.180446 0.159861i −0.180446 0.159861i 0.568065 0.822984i \(-0.307692\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.919979 0.391967i \(-0.128205\pi\)
−0.919979 + 0.391967i \(0.871795\pi\)
\(882\) 0 0
\(883\) −1.62920 + 0.855072i −1.62920 + 0.855072i −0.632445 + 0.774605i \(0.717949\pi\)
−0.996757 + 0.0804666i \(0.974359\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.996757 0.0804666i \(-0.0256410\pi\)
−0.996757 + 0.0804666i \(0.974359\pi\)
\(888\) 0 0
\(889\) 0.946784 0.838778i 0.946784 0.838778i
\(890\) 0 0
\(891\) 0 0
\(892\) −1.99351 + 0.160933i −1.99351 + 0.160933i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(901\) 0 0
\(902\) 0 0
\(903\) −1.81613 + 0.295150i −1.81613 + 0.295150i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0.141860 0.374055i 0.141860 0.374055i −0.845190 0.534466i \(-0.820513\pi\)
0.987050 + 0.160411i \(0.0512821\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(912\) 0.0802707 0.00648012i 0.0802707 0.00648012i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.351915 + 1.21495i −0.351915 + 1.21495i
\(917\) 0 0
\(918\) 0 0
\(919\) 0.141860 0.374055i 0.141860 0.374055i −0.845190 0.534466i \(-0.820513\pi\)
0.987050 + 0.160411i \(0.0512821\pi\)
\(920\) 0 0
\(921\) 0.136945 0.198399i 0.136945 0.198399i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0.919979 + 1.59345i 0.919979 + 1.59345i
\(926\) 0 0
\(927\) 1.87251 + 0.625134i 1.87251 + 0.625134i
\(928\) 0 0
\(929\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(930\) 0 0
\(931\) −0.0557864 0.0580798i −0.0557864 0.0580798i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −0.960245 + 1.39116i −0.960245 + 1.39116i −0.0402659 + 0.999189i \(0.512821\pi\)
−0.919979 + 0.391967i \(0.871795\pi\)
\(938\) 0 0
\(939\) −0.0224054 0.555984i −0.0224054 0.555984i
\(940\) 0 0
\(941\) 0 0 0.845190 0.534466i \(-0.179487\pi\)
−0.845190 + 0.534466i \(0.820513\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 0.996757 0.0804666i \(-0.0256410\pi\)
−0.996757 + 0.0804666i \(0.974359\pi\)
\(948\) −0.540266 + 1.86521i −0.540266 + 1.86521i
\(949\) 1.74798 + 0.917410i 1.74798 + 0.917410i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.919979 0.391967i \(-0.871795\pi\)
0.919979 + 0.391967i \(0.128205\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.267521 + 0.113980i −0.267521 + 0.113980i
\(962\) 0 0
\(963\) 0 0
\(964\) 0.787025 0.819379i 0.787025 0.819379i
\(965\) 0 0
\(966\) 0 0
\(967\) −1.13245 1.64063i −1.13245 1.64063i −0.632445 0.774605i \(-0.717949\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(972\) 0.428693 0.903450i 0.428693 0.903450i
\(973\) 1.26527 + 0.800107i 1.26527 + 0.800107i
\(974\) 0 0
\(975\) 0.885456 + 0.464723i 0.885456 + 0.464723i
\(976\) 0.0802707 1.99190i 0.0802707 1.99190i
\(977\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −0.876221 + 0.912242i −0.876221 + 0.912242i
\(982\) 0 0
\(983\) 0 0 −0.200026 0.979791i \(-0.564103\pi\)
0.200026 + 0.979791i \(0.435897\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −0.0345234 0.0727566i −0.0345234 0.0727566i
\(989\) 0 0
\(990\) 0 0
\(991\) −0.0805319 −0.0805319 −0.0402659 0.999189i \(-0.512821\pi\)
−0.0402659 + 0.999189i \(0.512821\pi\)
\(992\) 0 0
\(993\) −0.0482209 0.397135i −0.0482209 0.397135i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0.368039 0.156807i 0.368039 0.156807i −0.200026 0.979791i \(-0.564103\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(998\) 0 0
\(999\) −1.47094 1.10534i −1.47094 1.10534i
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 3549.1.dd.a.2447.1 24
3.2 odd 2 CM 3549.1.dd.a.2447.1 24
7.2 even 3 3549.1.dx.a.926.1 yes 24
21.2 odd 6 3549.1.dx.a.926.1 yes 24
169.48 even 39 3549.1.dx.a.893.1 yes 24
507.386 odd 78 3549.1.dx.a.893.1 yes 24
1183.555 even 39 inner 3549.1.dd.a.2921.1 yes 24
3549.2921 odd 78 inner 3549.1.dd.a.2921.1 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.1.dd.a.2447.1 24 1.1 even 1 trivial
3549.1.dd.a.2447.1 24 3.2 odd 2 CM
3549.1.dd.a.2921.1 yes 24 1183.555 even 39 inner
3549.1.dd.a.2921.1 yes 24 3549.2921 odd 78 inner
3549.1.dx.a.893.1 yes 24 169.48 even 39
3549.1.dx.a.893.1 yes 24 507.386 odd 78
3549.1.dx.a.926.1 yes 24 7.2 even 3
3549.1.dx.a.926.1 yes 24 21.2 odd 6