Properties

Label 536.1.t.a.59.1
Level $536$
Weight $1$
Character 536.59
Analytic conductor $0.267$
Analytic rank $0$
Dimension $10$
Projective image $D_{11}$
CM discriminant -8
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [536,1,Mod(59,536)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(536, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 12]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("536.59");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 536 = 2^{3} \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 536.t (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: \(0.267498846771\)
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: \(D_{11}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{11} - \cdots)\)

Embedding invariants

Embedding label 59.1
Root \(-0.415415 - 0.909632i\) of defining polynomial
Character \(\chi\) \(=\) 536.59
Dual form 536.1.t.a.427.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.142315 + 0.989821i) q^{2} +(-0.544078 - 0.627899i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.698939 - 0.449181i) q^{6} +(0.415415 - 0.909632i) q^{8} +(0.0440780 - 0.306569i) q^{9} +O(q^{10})\) \(q+(-0.142315 + 0.989821i) q^{2} +(-0.544078 - 0.627899i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.698939 - 0.449181i) q^{6} +(0.415415 - 0.909632i) q^{8} +(0.0440780 - 0.306569i) q^{9} +(0.698939 + 0.449181i) q^{11} +(0.345139 + 0.755750i) q^{12} +(0.841254 + 0.540641i) q^{16} +(1.84125 - 0.540641i) q^{17} +(0.297176 + 0.0872586i) q^{18} +(-0.239446 - 1.66538i) q^{19} +(-0.544078 + 0.627899i) q^{22} +(-0.797176 + 0.234072i) q^{24} +(0.415415 + 0.909632i) q^{25} +(-0.915415 + 0.588302i) q^{27} +(-0.654861 + 0.755750i) q^{32} +(-0.0982369 - 0.683252i) q^{33} +(0.273100 + 1.89945i) q^{34} +(-0.128663 + 0.281733i) q^{36} +1.68251 q^{38} +(0.273100 - 0.0801894i) q^{41} +(-1.61435 + 0.474017i) q^{43} +(-0.544078 - 0.627899i) q^{44} +(-0.118239 - 0.822373i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-0.959493 + 0.281733i) q^{50} +(-1.34125 - 0.861971i) q^{51} +(-0.452036 - 0.989821i) q^{54} +(-0.915415 + 1.05645i) q^{57} +(0.345139 - 0.755750i) q^{59} +(-0.654861 - 0.755750i) q^{64} +0.690279 q^{66} +(0.841254 + 0.540641i) q^{67} -1.91899 q^{68} +(-0.260554 - 0.167448i) q^{72} +(-1.61435 + 1.03748i) q^{73} +(0.345139 - 0.755750i) q^{75} +(-0.239446 + 1.66538i) q^{76} +(0.570276 + 0.167448i) q^{81} +(0.0405070 + 0.281733i) q^{82} +(1.41542 + 0.909632i) q^{83} +(-0.239446 - 1.66538i) q^{86} +(0.698939 - 0.449181i) q^{88} +(0.186393 - 0.215109i) q^{89} +0.830830 q^{96} -1.91899 q^{97} +(0.415415 - 0.909632i) q^{98} +(0.168513 - 0.194474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} + 9 q^{12} - q^{16} + 9 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{22} - 2 q^{24} - q^{25} - 4 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} - 2 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} + 7 q^{54} - 4 q^{57} + 9 q^{59} - q^{64} + 18 q^{66} - q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} + 9 q^{75} - 2 q^{76} - 5 q^{81} + 9 q^{82} + 9 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/536\mathbb{Z}\right)^\times\).

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{6}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(3\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(4\) −0.959493 0.281733i −0.959493 0.281733i
\(5\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(6\) 0.698939 0.449181i 0.698939 0.449181i
\(7\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(8\) 0.415415 0.909632i 0.415415 0.909632i
\(9\) 0.0440780 0.306569i 0.0440780 0.306569i
\(10\) 0 0
\(11\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(12\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(13\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(17\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(18\) 0.297176 + 0.0872586i 0.297176 + 0.0872586i
\(19\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(23\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(24\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(25\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(26\) 0 0
\(27\) −0.915415 + 0.588302i −0.915415 + 0.588302i
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(32\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(33\) −0.0982369 0.683252i −0.0982369 0.683252i
\(34\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(35\) 0 0
\(36\) −0.128663 + 0.281733i −0.128663 + 0.281733i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 1.68251 1.68251
\(39\) 0 0
\(40\) 0 0
\(41\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(42\) 0 0
\(43\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(44\) −0.544078 0.627899i −0.544078 0.627899i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(48\) −0.118239 0.822373i −0.118239 0.822373i
\(49\) −0.959493 0.281733i −0.959493 0.281733i
\(50\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(51\) −1.34125 0.861971i −1.34125 0.861971i
\(52\) 0 0
\(53\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(54\) −0.452036 0.989821i −0.452036 0.989821i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.915415 + 1.05645i −0.915415 + 1.05645i
\(58\) 0 0
\(59\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(60\) 0 0
\(61\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) 0.690279 0.690279
\(67\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(68\) −1.91899 −1.91899
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(72\) −0.260554 0.167448i −0.260554 0.167448i
\(73\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(74\) 0 0
\(75\) 0.345139 0.755750i 0.345139 0.755750i
\(76\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(80\) 0 0
\(81\) 0.570276 + 0.167448i 0.570276 + 0.167448i
\(82\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(83\) 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 \(0\)
0.415415 + 0.909632i \(0.363636\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.239446 1.66538i −0.239446 1.66538i
\(87\) 0 0
\(88\) 0.698939 0.449181i 0.698939 0.449181i
\(89\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.830830 0.830830
\(97\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(98\) 0.415415 0.909632i 0.415415 0.909632i
\(99\) 0.168513 0.194474i 0.168513 0.194474i
\(100\) −0.142315 0.989821i −0.142315 0.989821i
\(101\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(102\) 1.04408 1.20493i 1.04408 1.20493i
\(103\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(108\) 1.04408 0.306569i 1.04408 0.306569i
\(109\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(114\) −0.915415 1.05645i −0.915415 1.05645i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.128663 0.281733i −0.128663 0.281733i
\(122\) 0 0
\(123\) −0.198939 0.127850i −0.198939 0.127850i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(128\) 0.841254 0.540641i 0.841254 0.540641i
\(129\) 1.17597 + 0.755750i 1.17597 + 0.755750i
\(130\) 0 0
\(131\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(132\) −0.0982369 + 0.683252i −0.0982369 + 0.683252i
\(133\) 0 0
\(134\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(135\) 0 0
\(136\) 0.273100 1.89945i 0.273100 1.89945i
\(137\) 0.857685 + 0.989821i 0.857685 + 0.989821i 1.00000 \(0\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(138\) 0 0
\(139\) 1.68251 + 1.08128i 1.68251 + 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.202824 0.234072i 0.202824 0.234072i
\(145\) 0 0
\(146\) −0.797176 1.74557i −0.797176 1.74557i
\(147\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(148\) 0 0
\(149\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(150\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(151\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(152\) −1.61435 0.474017i −1.61435 0.474017i
\(153\) −0.0845850 0.588302i −0.0845850 0.588302i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.246902 + 0.540641i −0.246902 + 0.540641i
\(163\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(164\) −0.284630 −0.284630
\(165\) 0 0
\(166\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(167\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(168\) 0 0
\(169\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(170\) 0 0
\(171\) −0.521109 −0.521109
\(172\) 1.68251 1.68251
\(173\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(177\) −0.662317 + 0.194474i −0.662317 + 0.194474i
\(178\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(179\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(180\) 0 0
\(181\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.52977 + 0.449181i 1.52977 + 0.449181i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(192\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(193\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(194\) 0.273100 1.89945i 0.273100 1.89945i
\(195\) 0 0
\(196\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(197\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(198\) 0.168513 + 0.194474i 0.168513 + 0.194474i
\(199\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(200\) 1.00000 1.00000
\(201\) −0.118239 0.822373i −0.118239 0.822373i
\(202\) 0 0
\(203\) 0 0
\(204\) 1.04408 + 1.20493i 1.04408 + 1.20493i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.580699 1.27155i 0.580699 1.27155i
\(210\) 0 0
\(211\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.544078 1.19136i −0.544078 1.19136i
\(215\) 0 0
\(216\) 0.154861 + 1.07708i 0.154861 + 1.07708i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.52977 + 0.449181i 1.52977 + 0.449181i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(224\) 0 0
\(225\) 0.297176 0.0872586i 0.297176 0.0872586i
\(226\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(227\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(228\) 1.17597 0.755750i 1.17597 0.755750i
\(229\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.30972 + 1.51150i −1.30972 + 1.51150i −0.654861 + 0.755750i \(0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(242\) 0.297176 0.0872586i 0.297176 0.0872586i
\(243\) 0.246902 + 0.540641i 0.246902 + 0.540641i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.154861 0.178719i 0.154861 0.178719i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.198939 1.38365i −0.198939 1.38365i
\(250\) 0 0
\(251\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(257\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(258\) −0.915415 + 1.05645i −0.915415 + 1.05645i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(263\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(264\) −0.662317 0.194474i −0.662317 0.194474i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.236479 −0.236479
\(268\) −0.654861 0.755750i −0.654861 0.755750i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(272\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(273\) 0 0
\(274\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(275\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(276\) 0 0
\(277\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(278\) −1.30972 + 1.51150i −1.30972 + 1.51150i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(282\) 0 0
\(283\) −0.284630 1.97964i −0.284630 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.202824 + 0.234072i 0.202824 + 0.234072i
\(289\) 2.25667 1.45027i 2.25667 1.45027i
\(290\) 0 0
\(291\) 1.04408 + 1.20493i 1.04408 + 1.20493i
\(292\) 1.84125 0.540641i 1.84125 0.540641i
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.904073 −0.904073
\(298\) 0 0
\(299\) 0 0
\(300\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.698939 1.53046i 0.698939 1.53046i
\(305\) 0 0
\(306\) 0.594351 0.594351
\(307\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(312\) 0 0
\(313\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 1.04408 + 0.306569i 1.04408 + 0.306569i
\(322\) 0 0
\(323\) −1.34125 2.93694i −1.34125 2.93694i
\(324\) −0.500000 0.321330i −0.500000 0.321330i
\(325\) 0 0
\(326\) 0.0405070 0.281733i 0.0405070 0.281733i
\(327\) 0 0
\(328\) 0.0405070 0.281733i 0.0405070 0.281733i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(332\) −1.10181 1.27155i −1.10181 1.27155i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(338\) −0.654861 0.755750i −0.654861 0.755750i
\(339\) −0.662317 0.194474i −0.662317 0.194474i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.0741615 0.515804i 0.0741615 0.515804i
\(343\) 0 0
\(344\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.830830 + 1.81926i 0.830830 + 1.81926i 0.415415 + 0.909632i \(0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(348\) 0 0
\(349\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(353\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(354\) −0.0982369 0.683252i −0.0982369 0.683252i
\(355\) 0 0
\(356\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(357\) 0 0
\(358\) −1.10181 1.27155i −1.10181 1.27155i
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) 0 0
\(361\) −1.75667 + 0.515804i −1.75667 + 0.515804i
\(362\) 0 0
\(363\) −0.106897 + 0.234072i −0.106897 + 0.234072i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(368\) 0 0
\(369\) −0.0125459 0.0872586i −0.0125459 0.0872586i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −0.662317 + 1.45027i −0.662317 + 1.45027i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(384\) −0.797176 0.234072i −0.797176 0.234072i
\(385\) 0 0
\(386\) −1.61435 1.03748i −1.61435 1.03748i
\(387\) 0.0741615 + 0.515804i 0.0741615 + 0.515804i
\(388\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(389\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(393\) 0.0336545 0.234072i 0.0336545 0.234072i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.216476 + 0.139121i −0.216476 + 0.139121i
\(397\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(401\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(402\) 0.830830 0.830830
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −1.34125 + 0.861971i −1.34125 + 0.861971i
\(409\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(410\) 0 0
\(411\) 0.154861 1.07708i 0.154861 1.07708i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.236479 1.64475i −0.236479 1.64475i
\(418\) 1.17597 + 0.755750i 1.17597 + 0.755750i
\(419\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(422\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(423\) 0 0
\(424\) 0 0
\(425\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.25667 0.368991i 1.25667 0.368991i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −1.08816 −1.08816
\(433\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.662317 + 1.45027i −0.662317 + 1.45027i
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −0.128663 + 0.281733i −0.128663 + 0.281733i
\(442\) 0 0
\(443\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(450\) 0.0440780 + 0.306569i 0.0440780 + 0.306569i
\(451\) 0.226900 + 0.0666238i 0.226900 + 0.0666238i
\(452\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(453\) 0 0
\(454\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(455\) 0 0
\(456\) 0.580699 + 1.27155i 0.580699 + 1.27155i
\(457\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(458\) 0 0
\(459\) −1.36745 + 1.57812i −1.36745 + 1.57812i
\(460\) 0 0
\(461\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(462\) 0 0
\(463\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.30972 1.51150i −1.30972 1.51150i
\(467\) −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i \(0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.544078 0.627899i −0.544078 0.627899i
\(473\) −1.34125 0.393828i −1.34125 0.393828i
\(474\) 0 0
\(475\) 1.41542 0.909632i 1.41542 0.909632i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(483\) 0 0
\(484\) 0.0440780 + 0.306569i 0.0440780 + 0.306569i
\(485\) 0 0
\(486\) −0.570276 + 0.167448i −0.570276 + 0.167448i
\(487\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(488\) 0 0
\(489\) 0.154861 + 0.178719i 0.154861 + 0.178719i
\(490\) 0 0
\(491\) −1.30972 + 1.51150i −1.30972 + 1.51150i −0.654861 + 0.755750i \(0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(492\) 0.154861 + 0.178719i 0.154861 + 0.178719i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.39788 1.39788
\(499\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(503\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.830830 0.830830
\(508\) 0 0
\(509\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(513\) 1.19894 + 1.38365i 1.19894 + 1.38365i
\(514\) 1.25667 1.45027i 1.25667 1.45027i
\(515\) 0 0
\(516\) −0.915415 1.05645i −0.915415 1.05645i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(522\) 0 0
\(523\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(524\) −0.118239 0.258908i −0.118239 0.258908i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.286752 0.627899i 0.286752 0.627899i
\(529\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(530\) 0 0
\(531\) −0.216476 0.139121i −0.216476 0.139121i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.0336545 0.234072i 0.0336545 0.234072i
\(535\) 0 0
\(536\) 0.841254 0.540641i 0.841254 0.540641i
\(537\) 1.39788 1.39788
\(538\) 0 0
\(539\) −0.544078 0.627899i −0.544078 0.627899i
\(540\) 0 0
\(541\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(545\) 0 0
\(546\) 0 0
\(547\) 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 \(0\)
0.415415 + 0.909632i \(0.363636\pi\)
\(548\) −0.544078 1.19136i −0.544078 1.19136i
\(549\) 0 0
\(550\) −0.797176 0.234072i −0.797176 0.234072i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.30972 1.51150i −1.30972 1.51150i
\(557\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.550273 1.20493i −0.550273 1.20493i
\(562\) 1.84125 0.540641i 1.84125 0.540641i
\(563\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2.00000 2.00000
\(567\) 0 0
\(568\) 0 0
\(569\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(570\) 0 0
\(571\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.260554 + 0.167448i −0.260554 + 0.167448i
\(577\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(578\) 1.11435 + 2.44009i 1.11435 + 2.44009i
\(579\) 1.52977 0.449181i 1.52977 0.449181i
\(580\) 0 0
\(581\) 0 0
\(582\) −1.34125 + 0.861971i −1.34125 + 0.861971i
\(583\) 0 0
\(584\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(588\) −0.118239 0.822373i −0.118239 0.822373i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(594\) 0.128663 0.894870i 0.128663 0.894870i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(600\) −0.544078 0.627899i −0.544078 0.627899i
\(601\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(602\) 0 0
\(603\) 0.202824 0.234072i 0.202824 0.234072i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(608\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.0845850 + 0.588302i −0.0845850 + 0.588302i
\(613\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(614\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(618\) 0 0
\(619\) −1.10181 0.708089i −1.10181 0.708089i −0.142315 0.989821i \(-0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(626\) −1.10181 1.27155i −1.10181 1.27155i
\(627\) −1.11435 + 0.327204i −1.11435 + 0.327204i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(632\) 0 0
\(633\) −0.236479 −0.236479
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(642\) −0.452036 + 0.989821i −0.452036 + 0.989821i
\(643\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3.09792 0.909632i 3.09792 0.909632i
\(647\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(648\) 0.389217 0.449181i 0.389217 0.449181i
\(649\) 0.580699 0.373193i 0.580699 0.373193i
\(650\) 0 0
\(651\) 0 0
\(652\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(653\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(657\) 0.246902 + 0.540641i 0.246902 + 0.540641i
\(658\) 0 0
\(659\) 1.68251 + 1.08128i 1.68251 + 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(660\) 0 0
\(661\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(662\) 0.698939 1.53046i 0.698939 1.53046i
\(663\) 0 0
\(664\) 1.41542 0.909632i 1.41542 0.909632i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.857685 + 0.989821i 0.857685 + 0.989821i 1.00000 \(0\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(674\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(675\) −0.915415 0.588302i −0.915415 0.588302i
\(676\) 0.841254 0.540641i 0.841254 0.540641i
\(677\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(678\) 0.286752 0.627899i 0.286752 0.627899i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.198939 0.127850i −0.198939 0.127850i
\(682\) 0 0
\(683\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(684\) 0.500000 + 0.146813i 0.500000 + 0.146813i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.61435 0.474017i −1.61435 0.474017i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.91899 + 0.563465i −1.91899 + 0.563465i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.459493 0.295298i 0.459493 0.295298i
\(698\) 0 0
\(699\) 1.66166 1.66166
\(700\) 0 0
\(701\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.118239 0.822373i −0.118239 0.822373i
\(705\) 0 0
\(706\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(707\) 0 0
\(708\) 0.690279 0.690279
\(709\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.118239 0.258908i −0.118239 0.258908i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.41542 0.909632i 1.41542 0.909632i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.260554 1.81219i −0.260554 1.81219i
\(723\) −1.34125 0.393828i −1.34125 0.393828i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.216476 0.139121i −0.216476 0.139121i
\(727\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(728\) 0 0
\(729\) 0.452036 0.989821i 0.452036 0.989821i
\(730\) 0 0
\(731\) −2.71616 + 1.74557i −2.71616 + 1.74557i
\(732\) 0 0
\(733\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(738\) 0.0881559 0.0881559
\(739\) −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i \(0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.341254 0.393828i 0.341254 0.393828i
\(748\) −1.34125 0.861971i −1.34125 0.861971i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(752\) 0 0
\(753\) −0.198939 0.127850i −0.198939 0.127850i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(758\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(759\) 0 0
\(760\) 0 0
\(761\) 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.345139 0.755750i 0.345139 0.755750i
\(769\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(770\) 0 0
\(771\) 0.226900 + 1.57812i 0.226900 + 1.57812i
\(772\) 1.25667 1.45027i 1.25667 1.45027i
\(773\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(774\) −0.521109 −0.521109
\(775\) 0 0
\(776\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.198939 0.435615i −0.198939 0.435615i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.654861 0.755750i −0.654861 0.755750i
\(785\) 0 0
\(786\) 0.226900 + 0.0666238i 0.226900 + 0.0666238i
\(787\) 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.106897 0.234072i −0.106897 0.234072i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.959493 0.281733i −0.959493 0.281733i
\(801\) −0.0577299 0.0666238i −0.0577299 0.0666238i
\(802\) 0.273100 1.89945i 0.273100 1.89945i
\(803\) −1.59435 −1.59435
\(804\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 \(0\)
0.415415 + 0.909632i \(0.363636\pi\)
\(810\) 0 0
\(811\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −0.662317 1.45027i −0.662317 1.45027i
\(817\) 1.17597 + 2.57501i 1.17597 + 2.57501i
\(818\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(822\) 1.04408 + 0.306569i 1.04408 + 0.306569i
\(823\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(824\) 0 0
\(825\) 0.580699 0.373193i 0.580699 0.373193i
\(826\) 0 0
\(827\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(828\) 0 0
\(829\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.91899 −1.91899
\(834\) 1.66166 1.66166
\(835\) 0 0
\(836\) −0.915415 + 1.05645i −0.915415 + 1.05645i
\(837\) 0 0
\(838\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(839\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) −0.662317 + 1.45027i −0.662317 + 1.45027i
\(844\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −1.08816 + 1.25580i −1.08816 + 1.25580i
\(850\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(857\) 1.84125 + 0.540641i 1.84125 + 0.540641i 1.00000 \(0\)
0.841254 + 0.540641i \(0.181818\pi\)
\(858\) 0 0
\(859\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(864\) 0.154861 1.07708i 0.154861 1.07708i
\(865\) 0 0
\(866\) −1.10181 0.708089i −1.10181 0.708089i
\(867\) −2.13843 0.627899i −2.13843 0.627899i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.0845850 + 0.588302i −0.0845850 + 0.588302i
\(874\) 0 0
\(875\) 0 0
\(876\) −1.34125 0.861971i −1.34125 0.861971i
\(877\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(882\) −0.260554 0.167448i −0.260554 0.167448i
\(883\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(887\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.323373 + 0.373193i 0.323373 + 0.373193i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0.698939 0.449181i 0.698939 0.449181i
\(899\) 0 0
\(900\) −0.309721 −0.309721
\(901\) 0 0
\(902\) −0.0982369 + 0.215109i −0.0982369 + 0.215109i
\(903\) 0 0
\(904\) −0.118239 0.822373i −0.118239 0.822373i
\(905\) 0 0
\(906\) 0 0
\(907\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(908\) −0.284630 −0.284630
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(912\) −1.34125 + 0.393828i −1.34125 + 0.393828i
\(913\) 0.580699 + 1.27155i 0.580699 + 1.27155i
\(914\) 0.273100 0.0801894i 0.273100 0.0801894i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) −1.36745 1.57812i −1.36745 1.57812i
\(919\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(920\) 0 0
\(921\) −1.34125 + 0.393828i −1.34125 + 0.393828i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(930\) 0 0
\(931\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(932\) 1.68251 1.08128i 1.68251 1.08128i
\(933\) 0 0
\(934\) −0.797176 0.234072i −0.797176 0.234072i
\(935\) 0 0
\(936\) 0 0
\(937\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(938\) 0 0
\(939\) 1.39788 1.39788
\(940\) 0 0
\(941\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0.698939 0.449181i 0.698939 0.449181i
\(945\) 0 0
\(946\) 0.580699 1.27155i 0.580699 1.27155i
\(947\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(951\) 0 0
\(952\) 0 0
\(953\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.654861 0.755750i −0.654861 0.755750i
\(962\) 0 0
\(963\) 0.168513 + 0.368991i 0.168513 + 0.368991i
\(964\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −0.309721 −0.309721
\(969\) −1.11435 + 2.44009i −1.11435 + 2.44009i
\(970\) 0 0
\(971\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(972\) −0.0845850 0.588302i −0.0845850 0.588302i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(978\) −0.198939 + 0.127850i −0.198939 + 0.127850i
\(979\) 0.226900 0.0666238i 0.226900 0.0666238i
\(980\) 0 0
\(981\) 0 0
\(982\) −1.30972 1.51150i −1.30972 1.51150i
\(983\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(984\) −0.198939 + 0.127850i −0.198939 + 0.127850i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(992\) 0 0
\(993\) 0.580699 + 1.27155i 0.580699 + 1.27155i
\(994\) 0 0
\(995\) 0 0
\(996\) −0.198939 + 1.38365i −0.198939 + 1.38365i
\(997\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(998\) 0.186393 1.29639i 0.186393 1.29639i
\(999\) 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 536.1.t.a.59.1 10
4.3 odd 2 2144.1.bf.a.1935.1 10
8.3 odd 2 CM 536.1.t.a.59.1 10
8.5 even 2 2144.1.bf.a.1935.1 10
67.25 even 11 inner 536.1.t.a.427.1 yes 10
268.159 odd 22 2144.1.bf.a.1231.1 10
536.293 even 22 2144.1.bf.a.1231.1 10
536.427 odd 22 inner 536.1.t.a.427.1 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
536.1.t.a.59.1 10 1.1 even 1 trivial
536.1.t.a.59.1 10 8.3 odd 2 CM
536.1.t.a.427.1 yes 10 67.25 even 11 inner
536.1.t.a.427.1 yes 10 536.427 odd 22 inner
2144.1.bf.a.1231.1 10 268.159 odd 22
2144.1.bf.a.1231.1 10 536.293 even 22
2144.1.bf.a.1935.1 10 4.3 odd 2
2144.1.bf.a.1935.1 10 8.5 even 2