Properties

Label 644.1.r.b.559.1
Level $644$
Weight $1$
Character 644.559
Analytic conductor $0.321$
Analytic rank $0$
Dimension $10$
Projective image $D_{22}$
CM discriminant -7
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [644,1,Mod(83,644)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(644, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 21]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("644.83");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 644.r (of order \(22\), degree \(10\), 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: \(0.321397868136\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{22}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{22} - \cdots)\)

Embedding invariants

Embedding label 559.1
Root \(0.142315 - 0.989821i\) of defining polynomial
Character \(\chi\) \(=\) 644.559
Dual form 644.1.r.b.447.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.841254 + 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\) \(q+(0.841254 + 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-1.10181 - 1.27155i) q^{11} +(0.959493 + 0.281733i) q^{14} +(-0.654861 + 0.755750i) q^{16} +(-0.841254 + 0.540641i) q^{18} +(-0.239446 - 1.66538i) q^{22} +(-0.415415 - 0.909632i) q^{23} +(0.654861 - 0.755750i) q^{25} +(0.654861 + 0.755750i) q^{28} +(-0.186393 + 1.29639i) q^{29} +(-0.959493 + 0.281733i) q^{32} -1.00000 q^{36} +(-0.512546 - 0.234072i) q^{37} +(-0.698939 + 0.449181i) q^{43} +(0.698939 - 1.53046i) q^{44} +(0.142315 - 0.989821i) q^{46} +(0.841254 - 0.540641i) q^{49} +(0.959493 - 0.281733i) q^{50} +(-0.425839 - 1.45027i) q^{53} +(0.142315 + 0.989821i) q^{56} +(-0.857685 + 0.989821i) q^{58} +(-0.142315 + 0.989821i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.186393 - 0.215109i) q^{67} +(-0.817178 - 0.708089i) q^{71} +(-0.841254 - 0.540641i) q^{72} +(-0.304632 - 0.474017i) q^{74} +(-1.41542 - 0.909632i) q^{77} +(1.25667 + 0.368991i) q^{79} +(-0.654861 - 0.755750i) q^{81} -0.830830 q^{86} +(1.41542 - 0.909632i) q^{88} +(0.654861 - 0.755750i) q^{92} +1.00000 q^{98} +(1.61435 - 0.474017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} - q^{4} + q^{7} - q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - q^{2} - q^{4} + q^{7} - q^{8} + q^{9} - 2 q^{11} + q^{14} - q^{16} + q^{18} - 2 q^{22} + q^{23} + q^{25} + q^{28} + 2 q^{29} - q^{32} - 10 q^{36} + 2 q^{43} - 2 q^{44} + q^{46} - q^{49} + q^{50} + q^{56} - 9 q^{58} - q^{63} - q^{64} - 2 q^{67} + q^{72} - 9 q^{77} - 2 q^{79} - q^{81} + 2 q^{86} + 9 q^{88} + q^{92} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/644\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\) \(323\)
\(\chi(n)\) \(-1\) \(e\left(\frac{19}{22}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(3\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(4\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(5\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(6\) 0 0
\(7\) 0.959493 0.281733i 0.959493 0.281733i
\(8\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(9\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(10\) 0 0
\(11\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(12\) 0 0
\(13\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(14\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(15\) 0 0
\(16\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(17\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(18\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(19\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.239446 1.66538i −0.239446 1.66538i
\(23\) −0.415415 0.909632i −0.415415 0.909632i
\(24\) 0 0
\(25\) 0.654861 0.755750i 0.654861 0.755750i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(29\) −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(30\) 0 0
\(31\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(32\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −1.00000 −1.00000
\(37\) −0.512546 0.234072i −0.512546 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(42\) 0 0
\(43\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(44\) 0.698939 1.53046i 0.698939 1.53046i
\(45\) 0 0
\(46\) 0.142315 0.989821i 0.142315 0.989821i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 0.841254 0.540641i 0.841254 0.540641i
\(50\) 0.959493 0.281733i 0.959493 0.281733i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.425839 1.45027i −0.425839 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(57\) 0 0
\(58\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(59\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(60\) 0 0
\(61\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(62\) 0 0
\(63\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(64\) −0.959493 0.281733i −0.959493 0.281733i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.817178 0.708089i −0.817178 0.708089i 0.142315 0.989821i \(-0.454545\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(72\) −0.841254 0.540641i −0.841254 0.540641i
\(73\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(74\) −0.304632 0.474017i −0.304632 0.474017i
\(75\) 0 0
\(76\) 0 0
\(77\) −1.41542 0.909632i −1.41542 0.909632i
\(78\) 0 0
\(79\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(80\) 0 0
\(81\) −0.654861 0.755750i −0.654861 0.755750i
\(82\) 0 0
\(83\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.830830 −0.830830
\(87\) 0 0
\(88\) 1.41542 0.909632i 1.41542 0.909632i
\(89\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.654861 0.755750i 0.654861 0.755750i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(98\) 1.00000 1.00000
\(99\) 1.61435 0.474017i 1.61435 0.474017i
\(100\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(101\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(102\) 0 0
\(103\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.425839 1.45027i 0.425839 1.45027i
\(107\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(108\) 0 0
\(109\) −1.95949 0.281733i −1.95949 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(113\) 1.37491 + 1.19136i 1.37491 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.260554 + 1.81219i −0.260554 + 1.81219i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(127\) −1.37491 + 1.19136i −1.37491 + 1.19136i −0.415415 + 0.909632i \(0.636364\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(128\) −0.654861 0.755750i −0.654861 0.755750i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.273100 0.0801894i 0.273100 0.0801894i
\(135\) 0 0
\(136\) 0 0
\(137\) 1.97964i 1.97964i 0.142315 + 0.989821i \(0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.304632 1.03748i −0.304632 1.03748i
\(143\) 0 0
\(144\) −0.415415 0.909632i −0.415415 0.909632i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0.563465i 0.563465i
\(149\) 1.37491 1.19136i 1.37491 1.19136i 0.415415 0.909632i \(-0.363636\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(150\) 0 0
\(151\) −0.425839 + 1.45027i −0.425839 + 1.45027i 0.415415 + 0.909632i \(0.363636\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −0.698939 1.53046i −0.698939 1.53046i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(158\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.654861 0.755750i −0.654861 0.755750i
\(162\) −0.142315 0.989821i −0.142315 0.989821i
\(163\) 1.14231 + 0.989821i 1.14231 + 0.989821i 1.00000 \(0\)
0.142315 + 0.989821i \(0.454545\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(168\) 0 0
\(169\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.698939 0.449181i −0.698939 0.449181i
\(173\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(174\) 0 0
\(175\) 0.415415 0.909632i 0.415415 0.909632i
\(176\) 1.68251 1.68251
\(177\) 0 0
\(178\) 0 0
\(179\) −1.65486 + 0.755750i −1.65486 + 0.755750i −0.654861 + 0.755750i \(0.727273\pi\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.959493 0.281733i 0.959493 0.281733i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.84125 + 0.540641i −1.84125 + 0.540641i −0.841254 + 0.540641i \(0.818182\pi\)
−1.00000 \(1.00000\pi\)
\(192\) 0 0
\(193\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(197\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(198\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(199\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(200\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(201\) 0 0
\(202\) 0 0
\(203\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.00000 1.00000
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 1.07028 0.153882i 1.07028 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(212\) 1.14231 0.989821i 1.14231 0.989821i
\(213\) 0 0
\(214\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −1.49611 1.29639i −1.49611 1.29639i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(224\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(225\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(226\) 0.512546 + 1.74557i 0.512546 + 1.74557i
\(227\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.25667 0.368991i −1.25667 0.368991i
\(233\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.512546 0.234072i −0.512546 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(240\) 0 0
\(241\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(242\) −1.19894 + 1.38365i −1.19894 + 1.38365i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(252\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(253\) −0.698939 + 1.53046i −0.698939 + 1.53046i
\(254\) −1.80075 + 0.258908i −1.80075 + 0.258908i
\(255\) 0 0
\(256\) −0.142315 0.989821i −0.142315 0.989821i
\(257\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(258\) 0 0
\(259\) −0.557730 0.0801894i −0.557730 0.0801894i
\(260\) 0 0
\(261\) −1.10181 0.708089i −1.10181 0.708089i
\(262\) 0 0
\(263\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(269\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(270\) 0 0
\(271\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −1.07028 + 1.66538i −1.07028 + 1.66538i
\(275\) −1.68251 −1.68251
\(276\) 0 0
\(277\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.37491 + 0.627899i −1.37491 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(282\) 0 0
\(283\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(284\) 0.304632 1.03748i 0.304632 1.03748i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.142315 0.989821i 0.142315 0.989821i
\(289\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.304632 0.474017i 0.304632 0.474017i
\(297\) 0 0
\(298\) 1.80075 0.258908i 1.80075 0.258908i
\(299\) 0 0
\(300\) 0 0
\(301\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(302\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(308\) 0.239446 1.66538i 0.239446 1.66538i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(312\) 0 0
\(313\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(317\) 0.797176 + 1.74557i 0.797176 + 1.74557i 0.654861 + 0.755750i \(0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(318\) 0 0
\(319\) 1.85380 1.19136i 1.85380 1.19136i
\(320\) 0 0
\(321\) 0 0
\(322\) −0.142315 0.989821i −0.142315 0.989821i
\(323\) 0 0
\(324\) 0.415415 0.909632i 0.415415 0.909632i
\(325\) 0 0
\(326\) 0.425839 + 1.45027i 0.425839 + 1.45027i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.65486 0.755750i −1.65486 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0.425839 0.368991i 0.425839 0.368991i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.584585 0.909632i 0.584585 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
1.00000 \(0\)
\(338\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.654861 0.755750i 0.654861 0.755750i
\(344\) −0.345139 0.755750i −0.345139 0.755750i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.425839 + 0.368991i 0.425839 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(348\) 0 0
\(349\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(350\) 0.841254 0.540641i 0.841254 0.540641i
\(351\) 0 0
\(352\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(353\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −1.80075 0.258908i −1.80075 0.258908i
\(359\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(360\) 0 0
\(361\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.817178 1.27155i −0.817178 1.27155i
\(372\) 0 0
\(373\) −0.983568 + 0.449181i −0.983568 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.857685 + 0.989821i 0.857685 + 0.989821i 1.00000 \(0\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.84125 0.540641i −1.84125 0.540641i
\(383\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.41542 0.909632i 1.41542 0.909632i
\(387\) −0.118239 0.822373i −0.118239 0.822373i
\(388\) 0 0
\(389\) −0.817178 0.708089i −0.817178 0.708089i 0.142315 0.989821i \(-0.454545\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(393\) 0 0
\(394\) −0.544078 0.627899i −0.544078 0.627899i
\(395\) 0 0
\(396\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(397\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(401\) 0.158746 0.540641i 0.158746 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
1.00000 \(0\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(407\) 0.267092 + 0.909632i 0.267092 + 0.909632i
\(408\) 0 0
\(409\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(420\) 0 0
\(421\) −0.512546 1.74557i −0.512546 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(422\) 0.983568 + 0.449181i 0.983568 + 0.449181i
\(423\) 0 0
\(424\) 1.49611 0.215109i 1.49611 0.215109i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(429\) 0 0
\(430\) 0 0
\(431\) 0.118239 0.822373i 0.118239 0.822373i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(432\) 0 0
\(433\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.557730 1.89945i −0.557730 1.89945i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(440\) 0 0
\(441\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(442\) 0 0
\(443\) 1.07028 + 0.153882i 1.07028 + 0.153882i 0.654861 0.755750i \(-0.272727\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.00000 −1.00000
\(449\) −1.25667 1.45027i −1.25667 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(450\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(451\) 0 0
\(452\) −0.512546 + 1.74557i −0.512546 + 1.74557i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.817178 1.27155i −0.817178 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.07028 1.66538i −1.07028 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(464\) −0.857685 0.989821i −0.857685 0.989821i
\(465\) 0 0
\(466\) 1.91899 1.91899
\(467\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(468\) 0 0
\(469\) 0.118239 0.258908i 0.118239 0.258908i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.34125 + 0.393828i 1.34125 + 0.393828i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.49611 + 0.215109i 1.49611 + 0.215109i
\(478\) −0.304632 0.474017i −0.304632 0.474017i
\(479\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.75667 + 0.515804i −1.75667 + 0.515804i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.80075 0.258908i 1.80075 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.07028 1.66538i 1.07028 1.66538i 0.415415 0.909632i \(-0.363636\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.983568 0.449181i −0.983568 0.449181i
\(498\) 0 0
\(499\) −0.557730 1.89945i −0.557730 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(504\) −0.959493 0.281733i −0.959493 0.281733i
\(505\) 0 0
\(506\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(507\) 0 0
\(508\) −1.65486 0.755750i −1.65486 0.755750i
\(509\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.415415 0.909632i 0.415415 0.909632i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −0.425839 0.368991i −0.425839 0.368991i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(522\) −0.544078 1.19136i −0.544078 1.19136i
\(523\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(537\) 0 0
\(538\) 0 0
\(539\) −1.61435 0.474017i −1.61435 0.474017i
\(540\) 0 0
\(541\) −0.186393 0.215109i −0.186393 0.215109i 0.654861 0.755750i \(-0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.983568 + 0.449181i −0.983568 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(548\) −1.80075 + 0.822373i −1.80075 + 0.822373i
\(549\) 0 0
\(550\) −1.41542 0.909632i −1.41542 0.909632i
\(551\) 0 0
\(552\) 0 0
\(553\) 1.30972 1.30972
\(554\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.49611 0.215109i −1.49611 0.215109i
\(563\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.841254 0.540641i −0.841254 0.540641i
\(568\) 0.817178 0.708089i 0.817178 0.708089i
\(569\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(570\) 0 0
\(571\) −0.273100 1.89945i −0.273100 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.959493 0.281733i −0.959493 0.281733i
\(576\) 0.654861 0.755750i 0.654861 0.755750i
\(577\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(578\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.37491 + 2.13940i −1.37491 + 2.13940i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.512546 0.234072i 0.512546 0.234072i
\(593\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.65486 + 0.755750i 1.65486 + 0.755750i
\(597\) 0 0
\(598\) 0 0
\(599\) 1.97964i 1.97964i 0.142315 + 0.989821i \(0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(600\) 0 0
\(601\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(602\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(603\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(604\) −1.49611 + 0.215109i −1.49611 + 0.215109i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.07028 + 1.66538i −1.07028 + 1.66538i −0.415415 + 0.909632i \(0.636364\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 1.10181 1.27155i 1.10181 1.27155i
\(617\) −1.95949 + 0.281733i −1.95949 + 0.281733i −0.959493 + 0.281733i \(0.909091\pi\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.142315 0.989821i −0.142315 0.989821i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(632\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(633\) 0 0
\(634\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 2.20362 2.20362
\(639\) 0.983568 0.449181i 0.983568 0.449181i
\(640\) 0 0
\(641\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0.415415 0.909632i 0.415415 0.909632i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(648\) 0.841254 0.540641i 0.841254 0.540641i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.425839 + 1.45027i −0.425839 + 1.45027i
\(653\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(660\) 0 0
\(661\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(662\) −0.983568 1.53046i −0.983568 1.53046i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.557730 0.0801894i 0.557730 0.0801894i
\(667\) 1.25667 0.368991i 1.25667 0.368991i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i 0.959493 + 0.281733i \(0.0909091\pi\)
−1.00000 \(1.00000\pi\)
\(674\) 0.983568 0.449181i 0.983568 0.449181i
\(675\) 0 0
\(676\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(677\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.158746 + 0.540641i 0.158746 + 0.540641i 1.00000 \(0\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.959493 0.281733i 0.959493 0.281733i
\(687\) 0 0
\(688\) 0.118239 0.822373i 0.118239 0.822373i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 1.41542 0.909632i 1.41542 0.909632i
\(694\) 0.158746 + 0.540641i 0.158746 + 0.540641i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 1.00000 1.00000
\(701\) 1.49611 1.29639i 1.49611 1.29639i 0.654861 0.755750i \(-0.272727\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.07028 + 0.153882i −1.07028 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(710\) 0 0
\(711\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.37491 1.19136i −1.37491 1.19136i
\(717\) 0 0
\(718\) 0.698939 0.449181i 0.698939 0.449181i
\(719\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.959493 0.281733i −0.959493 0.281733i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(726\) 0 0
\(727\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(728\) 0 0
\(729\) 0.959493 0.281733i 0.959493 0.281733i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(737\) −0.478891 −0.478891
\(738\) 0 0
\(739\) 1.07028 + 1.66538i 1.07028 + 1.66538i 0.654861 + 0.755750i \(0.272727\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.51150i 1.51150i
\(743\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.07028 0.153882i −1.07028 0.153882i
\(747\) 0 0
\(748\) 0 0
\(749\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(750\) 0 0
\(751\) −1.10181 0.708089i −1.10181 0.708089i −0.142315 0.989821i \(-0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.817178 + 0.708089i 0.817178 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(758\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(762\) 0 0
\(763\) −1.95949 + 0.281733i −1.95949 + 0.281733i
\(764\) −1.25667 1.45027i −1.25667 1.45027i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.68251 1.68251
\(773\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(774\) 0.345139 0.755750i 0.345139 0.755750i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.304632 1.03748i −0.304632 1.03748i
\(779\) 0 0
\(780\) 0 0
\(781\) 1.81926i 1.81926i
\(782\) 0 0
\(783\) 0 0
\(784\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(788\) −0.118239 0.822373i −0.118239 0.822373i
\(789\) 0 0
\(790\) 0 0
\(791\) 1.65486 + 0.755750i 1.65486 + 0.755750i
\(792\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(801\) 0 0
\(802\) 0.425839 0.368991i 0.425839 0.368991i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(810\) 0 0
\(811\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(812\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(813\) 0 0
\(814\) −0.267092 + 0.909632i −0.267092 + 0.909632i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(822\) 0 0
\(823\) 1.37491 0.627899i 1.37491 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(828\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(840\) 0 0
\(841\) −0.686393 0.201543i −0.686393 0.201543i
\(842\) 0.512546 1.74557i 0.512546 1.74557i
\(843\) 0 0
\(844\) 0.584585 + 0.909632i 0.584585 + 0.909632i
\(845\) 0 0
\(846\) 0 0
\(847\) 0.260554 + 1.81219i 0.260554 + 1.81219i
\(848\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(849\) 0 0
\(850\) 0 0
\(851\) 0.563465i 0.563465i
\(852\) 0 0
\(853\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(857\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(858\) 0 0
\(859\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.544078 0.627899i 0.544078 0.627899i
\(863\) 0.817178 0.708089i 0.817178 0.708089i −0.142315 0.989821i \(-0.545455\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −0.915415 2.00448i −0.915415 2.00448i
\(870\) 0 0
\(871\) 0 0
\(872\) 0.557730 1.89945i 0.557730 1.89945i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −1.41542 + 0.909632i −1.41542 + 0.909632i −0.415415 + 0.909632i \(0.636364\pi\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(882\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(883\) 1.37491 + 0.627899i 1.37491 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.817178 + 0.708089i 0.817178 + 0.708089i
\(887\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(888\) 0 0
\(889\) −0.983568 + 1.53046i −0.983568 + 1.53046i
\(890\) 0 0
\(891\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −0.841254 0.540641i −0.841254 0.540641i
\(897\) 0 0
\(898\) −0.273100 1.89945i −0.273100 1.89945i
\(899\) 0 0
\(900\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −1.37491 + 1.19136i −1.37491 + 1.19136i
\(905\) 0 0
\(906\) 0 0
\(907\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 1.51150i 1.51150i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −0.512546 + 0.234072i −0.512546 + 0.234072i
\(926\) 1.97964i 1.97964i
\(927\) 0 0
\(928\) −0.186393 1.29639i −0.186393 1.29639i
\(929\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(938\) 0.239446 0.153882i 0.239446 0.153882i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0.915415 + 1.05645i 0.915415 + 1.05645i
\(947\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −0.158746 + 0.540641i −0.158746 + 0.540641i 0.841254 + 0.540641i \(0.181818\pi\)
−1.00000 \(\pi\)
\(954\) 1.14231 + 0.989821i 1.14231 + 0.989821i
\(955\) 0 0
\(956\) 0.563465i 0.563465i
\(957\) 0 0
\(958\) 0 0
\(959\) 0.557730 + 1.89945i 0.557730 + 1.89945i
\(960\) 0 0
\(961\) −0.415415 0.909632i −0.415415 0.909632i
\(962\) 0 0
\(963\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.08128i 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(968\) −1.75667 0.515804i −1.75667 0.515804i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 1.65486 + 0.755750i 1.65486 + 0.755750i
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1.07028 1.66538i 1.07028 1.66538i
\(982\) 1.80075 0.822373i 1.80075 0.822373i
\(983\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(990\) 0 0
\(991\) −1.49611 1.29639i −1.49611 1.29639i −0.841254 0.540641i \(-0.818182\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −0.584585 0.909632i −0.584585 0.909632i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(998\) 0.557730 1.89945i 0.557730 1.89945i
\(999\) 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 644.1.r.b.559.1 yes 10
4.3 odd 2 644.1.r.a.559.1 yes 10
7.6 odd 2 CM 644.1.r.b.559.1 yes 10
23.10 odd 22 644.1.r.a.447.1 10
28.27 even 2 644.1.r.a.559.1 yes 10
92.79 even 22 inner 644.1.r.b.447.1 yes 10
161.125 even 22 644.1.r.a.447.1 10
644.447 odd 22 inner 644.1.r.b.447.1 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
644.1.r.a.447.1 10 23.10 odd 22
644.1.r.a.447.1 10 161.125 even 22
644.1.r.a.559.1 yes 10 4.3 odd 2
644.1.r.a.559.1 yes 10 28.27 even 2
644.1.r.b.447.1 yes 10 92.79 even 22 inner
644.1.r.b.447.1 yes 10 644.447 odd 22 inner
644.1.r.b.559.1 yes 10 1.1 even 1 trivial
644.1.r.b.559.1 yes 10 7.6 odd 2 CM