Properties

Label 712.1.y.a.187.1
Level $712$
Weight $1$
Character 712.187
Analytic conductor $0.355$
Analytic rank $0$
Dimension $20$
Projective image $D_{44}$
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] = [712,1,Mod(99,712)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(712, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([22, 22, 43]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("712.99");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 712 = 2^{3} \cdot 89 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 712.y (of order \(44\), degree \(20\), 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: \(0.355334288995\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{44})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{44}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{44} - \cdots)\)

Embedding invariants

Embedding label 187.1
Root \(-0.540641 - 0.841254i\) of defining polynomial
Character \(\chi\) \(=\) 712.187
Dual form 712.1.y.a.99.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.415415 - 0.909632i) q^{2} +(-1.94931 - 0.139418i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.682956 + 1.83107i) q^{6} +(0.959493 + 0.281733i) q^{8} +(2.79057 + 0.401223i) q^{9} +O(q^{10})\) \(q+(-0.415415 - 0.909632i) q^{2} +(-1.94931 - 0.139418i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.682956 + 1.83107i) q^{6} +(0.959493 + 0.281733i) q^{8} +(2.79057 + 0.401223i) q^{9} +(-0.540641 + 0.158746i) q^{11} +(1.38189 - 1.38189i) q^{12} +(-0.142315 - 0.989821i) q^{16} +(-0.755750 - 0.345139i) q^{17} +(-0.794278 - 2.70506i) q^{18} +(1.40524 - 1.05195i) q^{19} +(0.368991 + 0.425839i) q^{22} +(-1.83107 - 0.682956i) q^{24} +(-0.841254 - 0.540641i) q^{25} +(-3.47412 - 0.755750i) q^{27} +(-0.841254 + 0.540641i) q^{32} +(1.07601 - 0.234072i) q^{33} +0.830830i q^{34} +(-2.13066 + 1.84623i) q^{36} +(-1.54064 - 0.841254i) q^{38} +(-0.100889 - 1.41061i) q^{41} +(0.898064 - 1.64468i) q^{43} +(0.234072 - 0.512546i) q^{44} +(0.139418 + 1.94931i) q^{48} +(0.540641 - 0.841254i) q^{49} +(-0.142315 + 0.989821i) q^{50} +(1.42508 + 0.778150i) q^{51} +(0.755750 + 3.47412i) q^{54} +(-2.88591 + 1.85466i) q^{57} +(0.697148 - 0.0498610i) q^{59} +(0.841254 + 0.540641i) q^{64} +(-0.659910 - 0.881537i) q^{66} +(1.29639 + 1.49611i) q^{67} +(0.755750 - 0.345139i) q^{68} +(2.56449 + 1.17116i) q^{72} +(-0.153882 - 1.07028i) q^{73} +(1.56449 + 1.17116i) q^{75} +(-0.125226 + 1.75089i) q^{76} +(3.96173 + 1.16327i) q^{81} +(-1.24123 + 0.677760i) q^{82} +(-0.697148 - 1.86912i) q^{83} +(-1.86912 - 0.133682i) q^{86} -0.563465 q^{88} +(-0.841254 + 0.540641i) q^{89} +(1.71524 - 0.936593i) q^{96} +(0.273100 + 0.0801894i) q^{97} +(-0.989821 - 0.142315i) q^{98} +(-1.57239 + 0.226075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8} - 2 q^{12} - 2 q^{16} - 2 q^{19} + 2 q^{24} + 2 q^{25} - 22 q^{27} + 2 q^{32} - 20 q^{38} + 2 q^{41} + 2 q^{43} - 2 q^{48} - 2 q^{50} + 4 q^{51} - 4 q^{57} - 2 q^{59} - 2 q^{64} + 22 q^{72} + 2 q^{75} - 2 q^{76} - 2 q^{81} - 2 q^{82} + 2 q^{83} - 2 q^{86} + 2 q^{89} + 2 q^{96} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/712\mathbb{Z}\right)^\times\).

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{44}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.415415 0.909632i −0.415415 0.909632i
\(3\) −1.94931 0.139418i −1.94931 0.139418i −0.959493 0.281733i \(-0.909091\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(4\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(5\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(6\) 0.682956 + 1.83107i 0.682956 + 1.83107i
\(7\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(8\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(9\) 2.79057 + 0.401223i 2.79057 + 0.401223i
\(10\) 0 0
\(11\) −0.540641 + 0.158746i −0.540641 + 0.158746i −0.540641 0.841254i \(-0.681818\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.38189 1.38189i 1.38189 1.38189i
\(13\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.142315 0.989821i −0.142315 0.989821i
\(17\) −0.755750 0.345139i −0.755750 0.345139i 1.00000i \(-0.5\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(18\) −0.794278 2.70506i −0.794278 2.70506i
\(19\) 1.40524 1.05195i 1.40524 1.05195i 0.415415 0.909632i \(-0.363636\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.368991 + 0.425839i 0.368991 + 0.425839i
\(23\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(24\) −1.83107 0.682956i −1.83107 0.682956i
\(25\) −0.841254 0.540641i −0.841254 0.540641i
\(26\) 0 0
\(27\) −3.47412 0.755750i −3.47412 0.755750i
\(28\) 0 0
\(29\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(30\) 0 0
\(31\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(32\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(33\) 1.07601 0.234072i 1.07601 0.234072i
\(34\) 0.830830i 0.830830i
\(35\) 0 0
\(36\) −2.13066 + 1.84623i −2.13066 + 1.84623i
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) −1.54064 0.841254i −1.54064 0.841254i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.100889 1.41061i −0.100889 1.41061i −0.755750 0.654861i \(-0.772727\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(42\) 0 0
\(43\) 0.898064 1.64468i 0.898064 1.64468i 0.142315 0.989821i \(-0.454545\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(44\) 0.234072 0.512546i 0.234072 0.512546i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(48\) 0.139418 + 1.94931i 0.139418 + 1.94931i
\(49\) 0.540641 0.841254i 0.540641 0.841254i
\(50\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(51\) 1.42508 + 0.778150i 1.42508 + 0.778150i
\(52\) 0 0
\(53\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(54\) 0.755750 + 3.47412i 0.755750 + 3.47412i
\(55\) 0 0
\(56\) 0 0
\(57\) −2.88591 + 1.85466i −2.88591 + 1.85466i
\(58\) 0 0
\(59\) 0.697148 0.0498610i 0.697148 0.0498610i 0.281733 0.959493i \(-0.409091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(60\) 0 0
\(61\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(65\) 0 0
\(66\) −0.659910 0.881537i −0.659910 0.881537i
\(67\) 1.29639 + 1.49611i 1.29639 + 1.49611i 0.755750 + 0.654861i \(0.227273\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(68\) 0.755750 0.345139i 0.755750 0.345139i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(72\) 2.56449 + 1.17116i 2.56449 + 1.17116i
\(73\) −0.153882 1.07028i −0.153882 1.07028i −0.909632 0.415415i \(-0.863636\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(74\) 0 0
\(75\) 1.56449 + 1.17116i 1.56449 + 1.17116i
\(76\) −0.125226 + 1.75089i −0.125226 + 1.75089i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(80\) 0 0
\(81\) 3.96173 + 1.16327i 3.96173 + 1.16327i
\(82\) −1.24123 + 0.677760i −1.24123 + 0.677760i
\(83\) −0.697148 1.86912i −0.697148 1.86912i −0.415415 0.909632i \(-0.636364\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.86912 0.133682i −1.86912 0.133682i
\(87\) 0 0
\(88\) −0.563465 −0.563465
\(89\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.71524 0.936593i 1.71524 0.936593i
\(97\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(98\) −0.989821 0.142315i −0.989821 0.142315i
\(99\) −1.57239 + 0.226075i −1.57239 + 0.226075i
\(100\) 0.959493 0.281733i 0.959493 0.281733i
\(101\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(102\) 0.115832 1.61955i 0.115832 1.61955i
\(103\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(108\) 2.84623 2.13066i 2.84623 2.13066i
\(109\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.86912 + 0.697148i 1.86912 + 0.697148i 0.959493 + 0.281733i \(0.0909091\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(114\) 2.88591 + 1.85466i 2.88591 + 1.85466i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.334961 0.613435i −0.334961 0.613435i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.574161 + 0.368991i −0.574161 + 0.368991i
\(122\) 0 0
\(123\) 2.76379i 2.76379i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(128\) 0.142315 0.989821i 0.142315 0.989821i
\(129\) −1.97991 + 3.08080i −1.97991 + 3.08080i
\(130\) 0 0
\(131\) −1.27155 1.10181i −1.27155 1.10181i −0.989821 0.142315i \(-0.954545\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(132\) −0.527738 + 0.966479i −0.527738 + 0.966479i
\(133\) 0 0
\(134\) 0.822373 1.80075i 0.822373 1.80075i
\(135\) 0 0
\(136\) −0.627899 0.544078i −0.627899 0.544078i
\(137\) −0.0498610 0.697148i −0.0498610 0.697148i −0.959493 0.281733i \(-0.909091\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(138\) 0 0
\(139\) −0.273100 + 1.89945i −0.273100 + 1.89945i 0.142315 + 0.989821i \(0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 2.81926i 2.81926i
\(145\) 0 0
\(146\) −0.909632 + 0.584585i −0.909632 + 0.584585i
\(147\) −1.17116 + 1.56449i −1.17116 + 1.56449i
\(148\) 0 0
\(149\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(150\) 0.415415 1.90963i 0.415415 1.90963i
\(151\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(152\) 1.64468 0.613435i 1.64468 0.613435i
\(153\) −1.97049 1.26636i −1.97049 1.26636i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.587616 4.08696i −0.587616 4.08696i
\(163\) 0.148568 0.398326i 0.148568 0.398326i −0.841254 0.540641i \(-0.818182\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(164\) 1.13214 + 0.847507i 1.13214 + 0.847507i
\(165\) 0 0
\(166\) −1.41061 + 1.41061i −1.41061 + 1.41061i
\(167\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(168\) 0 0
\(169\) −0.989821 0.142315i −0.989821 0.142315i
\(170\) 0 0
\(171\) 4.34347 2.37172i 4.34347 2.37172i
\(172\) 0.654861 + 1.75575i 0.654861 + 1.75575i
\(173\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.234072 + 0.512546i 0.234072 + 0.512546i
\(177\) −1.36591 −1.36591
\(178\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(179\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(180\) 0 0
\(181\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.463379 + 0.0666238i 0.463379 + 0.0666238i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(192\) −1.56449 1.17116i −1.56449 1.17116i
\(193\) −0.418852 + 1.12299i −0.418852 + 1.12299i 0.540641 + 0.841254i \(0.318182\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(194\) −0.0405070 0.281733i −0.0405070 0.281733i
\(195\) 0 0
\(196\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(197\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(198\) 0.858839 + 1.33638i 0.858839 + 1.33638i
\(199\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(200\) −0.654861 0.755750i −0.654861 0.755750i
\(201\) −2.31849 3.09714i −2.31849 3.09714i
\(202\) 0 0
\(203\) 0 0
\(204\) −1.52131 + 0.567420i −1.52131 + 0.567420i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.592735 + 0.791802i −0.592735 + 0.791802i
\(210\) 0 0
\(211\) 1.83107 0.398326i 1.83107 0.398326i 0.841254 0.540641i \(-0.181818\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) −3.12048 1.70391i −3.12048 1.70391i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.150750 + 2.10776i 0.150750 + 2.10776i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(224\) 0 0
\(225\) −2.13066 1.84623i −2.13066 1.84623i
\(226\) −0.142315 1.98982i −0.142315 1.98982i
\(227\) −0.584585 + 0.909632i −0.584585 + 0.909632i 0.415415 + 0.909632i \(0.363636\pi\)
−1.00000 \(1.00000\pi\)
\(228\) 0.488209 3.39557i 0.488209 3.39557i
\(229\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.30972i 1.30972i 0.755750 + 0.654861i \(0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.418852 + 0.559521i −0.418852 + 0.559521i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(240\) 0 0
\(241\) −0.133682 + 0.0498610i −0.133682 + 0.0498610i −0.415415 0.909632i \(-0.636364\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(242\) 0.574161 + 0.368991i 0.574161 + 0.368991i
\(243\) −4.22927 1.57744i −4.22927 1.57744i
\(244\) 0 0
\(245\) 0 0
\(246\) 2.51403 1.14812i 2.51403 1.14812i
\(247\) 0 0
\(248\) 0 0
\(249\) 1.09837 + 3.74071i 1.09837 + 3.74071i
\(250\) 0 0
\(251\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(257\) 1.89945 0.273100i 1.89945 0.273100i 0.909632 0.415415i \(-0.136364\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(258\) 3.62487 + 0.521178i 3.62487 + 0.521178i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.474017 + 1.61435i −0.474017 + 1.61435i
\(263\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(264\) 1.09837 + 0.0785570i 1.09837 + 0.0785570i
\(265\) 0 0
\(266\) 0 0
\(267\) 1.71524 0.936593i 1.71524 0.936593i
\(268\) −1.97964 −1.97964
\(269\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(270\) 0 0
\(271\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(272\) −0.234072 + 0.797176i −0.234072 + 0.797176i
\(273\) 0 0
\(274\) −0.613435 + 0.334961i −0.613435 + 0.334961i
\(275\) 0.540641 + 0.158746i 0.540641 + 0.158746i
\(276\) 0 0
\(277\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(278\) 1.84125 0.540641i 1.84125 0.540641i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.767317 0.574406i −0.767317 0.574406i 0.142315 0.989821i \(-0.454545\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(282\) 0 0
\(283\) −0.215109 1.49611i −0.215109 1.49611i −0.755750 0.654861i \(-0.772727\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −2.56449 + 1.17116i −2.56449 + 1.17116i
\(289\) −0.202824 0.234072i −0.202824 0.234072i
\(290\) 0 0
\(291\) −0.521178 0.194389i −0.521178 0.194389i
\(292\) 0.909632 + 0.584585i 0.909632 + 0.584585i
\(293\) 0 0 0.936950 0.349464i \(-0.113636\pi\)
−0.936950 + 0.349464i \(0.886364\pi\)
\(294\) 1.90963 + 0.415415i 1.90963 + 0.415415i
\(295\) 0 0
\(296\) 0 0
\(297\) 1.99823 0.142916i 1.99823 0.142916i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.90963 + 0.415415i −1.90963 + 0.415415i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.24123 1.24123i −1.24123 1.24123i
\(305\) 0 0
\(306\) −0.333348 + 2.31849i −0.333348 + 2.31849i
\(307\) −0.708089 + 1.10181i −0.708089 + 1.10181i 0.281733 + 0.959493i \(0.409091\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(312\) 0 0
\(313\) 0.574406 1.05195i 0.574406 1.05195i −0.415415 0.909632i \(-0.636364\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.42508 + 0.310006i −1.42508 + 0.310006i
\(324\) −3.47352 + 2.23230i −3.47352 + 2.23230i
\(325\) 0 0
\(326\) −0.424047 + 0.0303285i −0.424047 + 0.0303285i
\(327\) 0 0
\(328\) 0.300613 1.38189i 0.300613 1.38189i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(332\) 1.86912 + 0.697148i 1.86912 + 0.697148i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.767317 + 0.574406i −0.767317 + 0.574406i −0.909632 0.415415i \(-0.863636\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(338\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(339\) −3.54632 1.61955i −3.54632 1.61955i
\(340\) 0 0
\(341\) 0 0
\(342\) −3.96173 2.96572i −3.96173 2.96572i
\(343\) 0 0
\(344\) 1.32505 1.32505i 1.32505 1.32505i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.49611 + 0.215109i 1.49611 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(348\) 0 0
\(349\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.368991 0.425839i 0.368991 0.425839i
\(353\) 1.19550 + 0.0855040i 1.19550 + 0.0855040i 0.654861 0.755750i \(-0.272727\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(354\) 0.567420 + 1.24248i 0.567420 + 1.24248i
\(355\) 0 0
\(356\) 0.142315 0.989821i 0.142315 0.989821i
\(357\) 0 0
\(358\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(359\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(360\) 0 0
\(361\) 0.586365 1.99698i 0.586365 1.99698i
\(362\) 0 0
\(363\) 1.17067 0.639232i 1.17067 0.639232i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(368\) 0 0
\(369\) 0.284432 3.97688i 0.284432 3.97688i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(374\) −0.131891 0.449181i −0.131891 0.449181i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.959493 1.28173i −0.959493 1.28173i −0.959493 0.281733i \(-0.909091\pi\)
1.00000i \(-0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(384\) −0.415415 + 1.90963i −0.415415 + 1.90963i
\(385\) 0 0
\(386\) 1.19550 0.0855040i 1.19550 0.0855040i
\(387\) 3.16599 4.22927i 3.16599 4.22927i
\(388\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(389\) 0 0 0.977147 0.212565i \(-0.0681818\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.755750 0.654861i 0.755750 0.654861i
\(393\) 2.32505 + 2.32505i 2.32505 + 2.32505i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.858839 1.33638i 0.858839 1.33638i
\(397\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(401\) −0.822373 + 1.80075i −0.822373 + 1.80075i −0.281733 + 0.959493i \(0.590909\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(402\) −1.85412 + 3.39557i −1.85412 + 3.39557i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 1.14812 + 1.14812i 1.14812 + 1.14812i
\(409\) 0.215109 0.186393i 0.215109 0.186393i −0.540641 0.841254i \(-0.681818\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(410\) 0 0
\(411\) 1.36591i 1.36591i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.797176 3.66456i 0.797176 3.66456i
\(418\) 0.966479 + 0.210245i 0.966479 + 0.210245i
\(419\) −1.12299 + 0.418852i −1.12299 + 0.418852i −0.841254 0.540641i \(-0.818182\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(420\) 0 0
\(421\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(422\) −1.12299 1.50013i −1.12299 1.50013i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.449181 + 0.698939i 0.449181 + 0.698939i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(432\) −0.253638 + 3.54632i −0.253638 + 3.54632i
\(433\) 0.300613 0.300613i 0.300613 0.300613i −0.540641 0.841254i \(-0.681818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.85466 1.01272i 1.85466 1.01272i
\(439\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(440\) 0 0
\(441\) 1.84623 2.13066i 1.84623 2.13066i
\(442\) 0 0
\(443\) −0.627899 1.37491i −0.627899 1.37491i −0.909632 0.415415i \(-0.863636\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.989821 1.14231i 0.989821 1.14231i 1.00000i \(-0.5\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(450\) −0.794278 + 2.70506i −0.794278 + 2.70506i
\(451\) 0.278474 + 0.746618i 0.278474 + 0.746618i
\(452\) −1.75089 + 0.956056i −1.75089 + 0.956056i
\(453\) 0 0
\(454\) 1.07028 + 0.153882i 1.07028 + 0.153882i
\(455\) 0 0
\(456\) −3.29153 + 0.966479i −3.29153 + 0.966479i
\(457\) −1.13214 + 1.13214i −1.13214 + 1.13214i −0.142315 + 0.989821i \(0.545455\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(458\) 0 0
\(459\) 2.36473 + 1.77021i 2.36473 + 1.77021i
\(460\) 0 0
\(461\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(462\) 0 0
\(463\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.19136 0.544078i 1.19136 0.544078i
\(467\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.682956 + 0.148568i 0.682956 + 0.148568i
\(473\) −0.224443 + 1.03175i −0.224443 + 1.03175i
\(474\) 0 0
\(475\) −1.75089 + 0.125226i −1.75089 + 0.125226i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.100889 + 0.100889i 0.100889 + 0.100889i
\(483\) 0 0
\(484\) 0.0971309 0.675560i 0.0971309 0.675560i
\(485\) 0 0
\(486\) 0.322016 + 4.50237i 0.322016 + 4.50237i
\(487\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(488\) 0 0
\(489\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(490\) 0 0
\(491\) 0.459359 0.841254i 0.459359 0.841254i −0.540641 0.841254i \(-0.681818\pi\)
1.00000 \(0\)
\(492\) −2.08873 1.80990i −2.08873 1.80990i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 2.94639 2.55306i 2.94639 2.55306i
\(499\) 0.0303285 + 0.139418i 0.0303285 + 0.139418i 0.989821 0.142315i \(-0.0454545\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.10181 0.708089i 1.10181 0.708089i
\(503\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.90963 + 0.415415i 1.90963 + 0.415415i
\(508\) 0 0
\(509\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(513\) −5.67698 + 2.59259i −5.67698 + 2.59259i
\(514\) −1.03748 1.61435i −1.03748 1.61435i
\(515\) 0 0
\(516\) −1.03175 3.51381i −1.03175 3.51381i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.133682 + 1.86912i −0.133682 + 1.86912i 0.281733 + 0.959493i \(0.409091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(522\) 0 0
\(523\) −1.03748 + 0.304632i −1.03748 + 0.304632i −0.755750 0.654861i \(-0.772727\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(524\) 1.66538 0.239446i 1.66538 0.239446i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.384822 1.03175i −0.384822 1.03175i
\(529\) −0.281733 + 0.959493i −0.281733 + 0.959493i
\(530\) 0 0
\(531\) 1.96544 + 0.140571i 1.96544 + 0.140571i
\(532\) 0 0
\(533\) 0 0
\(534\) −1.56449 1.17116i −1.56449 1.17116i
\(535\) 0 0
\(536\) 0.822373 + 1.80075i 0.822373 + 1.80075i
\(537\) 0.554833 + 0.0396824i 0.554833 + 0.0396824i
\(538\) 0 0
\(539\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(540\) 0 0
\(541\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.822373 0.118239i 0.822373 0.118239i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.0683785 + 0.956056i −0.0683785 + 0.956056i 0.841254 + 0.540641i \(0.181818\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(548\) 0.559521 + 0.418852i 0.559521 + 0.418852i
\(549\) 0 0
\(550\) −0.0801894 0.557730i −0.0801894 0.557730i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.25667 1.45027i −1.25667 1.45027i
\(557\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.893982 0.194474i −0.893982 0.194474i
\(562\) −0.203743 + 0.936593i −0.203743 + 0.936593i
\(563\) 0.459359 + 0.841254i 0.459359 + 0.841254i 1.00000 \(0\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.27155 + 0.817178i −1.27155 + 0.817178i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.340335 1.56449i −0.340335 1.56449i −0.755750 0.654861i \(-0.772727\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(570\) 0 0
\(571\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 2.13066 + 1.84623i 2.13066 + 1.84623i
\(577\) −0.841254 + 1.54064i −0.841254 + 1.54064i 1.00000i \(0.5\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(578\) −0.128663 + 0.281733i −0.128663 + 0.281733i
\(579\) 0.973039 2.13066i 0.973039 2.13066i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.0396824 + 0.554833i 0.0396824 + 0.554833i
\(583\) 0 0
\(584\) 0.153882 1.07028i 0.153882 1.07028i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.45027 + 1.25667i −1.45027 + 1.25667i −0.540641 + 0.841254i \(0.681818\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(588\) −0.415415 1.90963i −0.415415 1.90963i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.59700 0.114220i 1.59700 0.114220i 0.755750 0.654861i \(-0.227273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(594\) −0.960094 1.75828i −0.960094 1.75828i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(600\) 1.17116 + 1.56449i 1.17116 + 1.56449i
\(601\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(602\) 0 0
\(603\) 3.01739 + 4.69515i 3.01739 + 4.69515i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(608\) −0.613435 + 1.64468i −0.613435 + 1.64468i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 2.24745 0.659910i 2.24745 0.659910i
\(613\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(614\) 1.29639 + 0.186393i 1.29639 + 0.186393i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.148568 0.398326i −0.148568 0.398326i 0.841254 0.540641i \(-0.181818\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(618\) 0 0
\(619\) 1.10181 1.27155i 1.10181 1.27155i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(626\) −1.19550 0.0855040i −1.19550 0.0855040i
\(627\) 1.26582 1.46083i 1.26582 1.46083i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(632\) 0 0
\(633\) −3.62487 + 0.521178i −3.62487 + 0.521178i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.474017 + 1.61435i 0.474017 + 1.61435i 0.755750 + 0.654861i \(0.227273\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(642\) 0 0
\(643\) 0.153882 + 0.239446i 0.153882 + 0.239446i 0.909632 0.415415i \(-0.136364\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.873989 + 1.16751i 0.873989 + 1.16751i
\(647\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(648\) 3.47352 + 2.23230i 3.47352 + 2.23230i
\(649\) −0.368991 + 0.137627i −0.368991 + 0.137627i
\(650\) 0 0
\(651\) 0 0
\(652\) 0.203743 + 0.373128i 0.203743 + 0.373128i
\(653\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.38189 + 0.300613i −1.38189 + 0.300613i
\(657\) 3.04842i 3.04842i
\(658\) 0 0
\(659\) −1.27155 + 1.10181i −1.27155 + 1.10181i −0.281733 + 0.959493i \(0.590909\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(660\) 0 0
\(661\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(662\) 0.273100 1.89945i 0.273100 1.89945i
\(663\) 0 0
\(664\) −0.142315 1.98982i −0.142315 1.98982i
\(665\) 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 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(674\) 0.841254 + 0.459359i 0.841254 + 0.459359i
\(675\) 2.51403 + 2.51403i 2.51403 + 2.51403i
\(676\) 0.755750 0.654861i 0.755750 0.654861i
\(677\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(678\) 3.89863i 3.89863i
\(679\) 0 0
\(680\) 0 0
\(681\) 1.26636 1.69166i 1.26636 1.69166i
\(682\) 0 0
\(683\) −0.203743 0.373128i −0.203743 0.373128i 0.755750 0.654861i \(-0.227273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(684\) −1.05195 + 4.83572i −1.05195 + 4.83572i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.75575 0.654861i −1.75575 0.654861i
\(689\) 0 0
\(690\) 0 0
\(691\) 1.19136 0.544078i 1.19136 0.544078i 0.281733 0.959493i \(-0.409091\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.425839 1.45027i −0.425839 1.45027i
\(695\) 0 0
\(696\) 0 0
\(697\) −0.410610 + 1.10089i −0.410610 + 1.10089i
\(698\) 0 0
\(699\) 0.182598 2.55306i 0.182598 2.55306i
\(700\) 0 0
\(701\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.540641 0.158746i −0.540641 0.158746i
\(705\) 0 0
\(706\) −0.418852 1.12299i −0.418852 1.12299i
\(707\) 0 0
\(708\) 0.894482 1.03229i 0.894482 1.03229i
\(709\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.186393 0.215109i 0.186393 0.215109i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −2.06010 + 0.296197i −2.06010 + 0.296197i
\(723\) 0.267541 0.0785570i 0.267541 0.0785570i
\(724\) 0 0
\(725\) 0 0
\(726\) −1.06778 0.799328i −1.06778 0.799328i
\(727\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(728\) 0 0
\(729\) 4.26840 + 1.94931i 4.26840 + 1.94931i
\(730\) 0 0
\(731\) −1.24636 + 0.933011i −1.24636 + 0.933011i
\(732\) 0 0
\(733\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.938384 0.603063i −0.938384 0.603063i
\(738\) −3.73566 + 1.39333i −3.73566 + 1.39333i
\(739\) −1.17116 0.254771i −1.17116 0.254771i −0.415415 0.909632i \(-0.636364\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.19550 5.49563i −1.19550 5.49563i
\(748\) −0.353799 + 0.306569i −0.353799 + 0.306569i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(752\) 0 0
\(753\) −0.182598 2.55306i −0.182598 2.55306i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(758\) −0.767317 + 1.40524i −0.767317 + 1.40524i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.304632 0.474017i 0.304632 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.90963 0.415415i 1.90963 0.415415i
\(769\) 1.27155 0.817178i 1.27155 0.817178i 0.281733 0.959493i \(-0.409091\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(770\) 0 0
\(771\) −3.74071 + 0.267541i −3.74071 + 0.267541i
\(772\) −0.574406 1.05195i −0.574406 1.05195i
\(773\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(774\) −5.16228 1.12299i −5.16228 1.12299i
\(775\) 0 0
\(776\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(777\) 0 0
\(778\) 0 0
\(779\) −1.62566 1.87611i −1.62566 1.87611i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.909632 0.415415i −0.909632 0.415415i
\(785\) 0 0
\(786\) 1.14908 3.08080i 1.14908 3.08080i
\(787\) 0.114220 + 0.0855040i 0.114220 + 0.0855040i 0.654861 0.755750i \(-0.272727\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −1.57239 0.226075i −1.57239 0.226075i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000 1.00000
\(801\) −2.56449 + 1.17116i −2.56449 + 1.17116i
\(802\) 1.97964 1.97964
\(803\) 0.253098 + 0.554206i 0.253098 + 0.554206i
\(804\) 3.85895 + 0.275997i 3.85895 + 0.275997i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(810\) 0 0
\(811\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0.567420 1.52131i 0.567420 1.52131i
\(817\) −0.468125 3.25588i −0.468125 3.25588i
\(818\) −0.258908 0.118239i −0.258908 0.118239i
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(822\) 1.24248 0.567420i 1.24248 0.567420i
\(823\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(824\) 0 0
\(825\) −1.03175 0.384822i −1.03175 0.384822i
\(826\) 0 0
\(827\) −0.133682 + 0.0498610i −0.133682 + 0.0498610i −0.415415 0.909632i \(-0.636364\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(828\) 0 0
\(829\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −0.698939 + 0.449181i −0.698939 + 0.449181i
\(834\) −3.66456 + 0.797176i −3.66456 + 0.797176i
\(835\) 0 0
\(836\) −0.210245 0.966479i −0.210245 0.966479i
\(837\) 0 0
\(838\) 0.847507 + 0.847507i 0.847507 + 0.847507i
\(839\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(840\) 0 0
\(841\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(842\) 0 0
\(843\) 1.41566 + 1.22668i 1.41566 + 1.22668i
\(844\) −0.898064 + 1.64468i −0.898064 + 1.64468i
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0.210730 + 2.94639i 0.210730 + 2.94639i
\(850\) 0.449181 0.698939i 0.449181 0.698939i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.71524 0.373128i 1.71524 0.373128i 0.755750 0.654861i \(-0.227273\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(858\) 0 0
\(859\) −1.19550 + 1.59700i −1.19550 + 1.59700i −0.540641 + 0.841254i \(0.681818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(864\) 3.33121 1.24248i 3.33121 1.24248i
\(865\) 0 0
\(866\) −0.398326 0.148568i −0.398326 0.148568i
\(867\) 0.362735 + 0.484557i 0.362735 + 0.484557i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0.729931 + 0.333348i 0.729931 + 0.333348i
\(874\) 0 0
\(875\) 0 0
\(876\) −1.69166 1.26636i −1.69166 1.26636i
\(877\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.80075 + 0.258908i 1.80075 + 0.258908i 0.959493 0.281733i \(-0.0909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(882\) −2.70506 0.794278i −2.70506 0.794278i
\(883\) 0.125226 0.0683785i 0.125226 0.0683785i −0.415415 0.909632i \(-0.636364\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −0.989821 + 1.14231i −0.989821 + 1.14231i
\(887\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −2.32654 −2.32654
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −1.45027 0.425839i −1.45027 0.425839i
\(899\) 0 0
\(900\) 2.79057 0.401223i 2.79057 0.401223i
\(901\) 0 0
\(902\) 0.563465 0.563465i 0.563465 0.563465i
\(903\) 0 0
\(904\) 1.59700 + 1.19550i 1.59700 + 1.19550i
\(905\) 0 0
\(906\) 0 0
\(907\) −1.65486 0.755750i −1.65486 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
−1.00000 \(\pi\)
\(908\) −0.304632 1.03748i −0.304632 1.03748i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(912\) 2.24649 + 2.59259i 2.24649 + 2.59259i
\(913\) 0.673623 + 0.899856i 0.673623 + 0.899856i
\(914\) 1.50013 + 0.559521i 1.50013 + 0.559521i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0.627899 2.88641i 0.627899 2.88641i
\(919\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(920\) 0 0
\(921\) 1.53390 2.04905i 1.53390 2.04905i
\(922\) 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 \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(930\) 0 0
\(931\) −0.125226 1.75089i −0.125226 1.75089i
\(932\) −0.989821 0.857685i −0.989821 0.857685i
\(933\) 0 0
\(934\) 0.345139 0.755750i 0.345139 0.755750i
\(935\) 0 0
\(936\) 0 0
\(937\) 1.37491 + 1.19136i 1.37491 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(938\) 0 0
\(939\) −1.26636 + 1.97049i −1.26636 + 1.97049i
\(940\) 0 0
\(941\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −0.148568 0.682956i −0.148568 0.682956i
\(945\) 0 0
\(946\) 1.03175 0.224443i 1.03175 0.224443i
\(947\) 1.66538 1.07028i 1.66538 1.07028i 0.755750 0.654861i \(-0.227273\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.841254 + 1.54064i 0.841254 + 1.54064i
\(951\) 0 0
\(952\) 0 0
\(953\) 0.398326 0.148568i 0.398326 0.148568i −0.142315 0.989821i \(-0.545455\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.281733 0.959493i −0.281733 0.959493i
\(962\) 0 0
\(963\) 0 0
\(964\) 0.0498610 0.133682i 0.0498610 0.133682i
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(968\) −0.654861 + 0.192284i −0.654861 + 0.192284i
\(969\) 2.82114 0.405619i 2.82114 0.405619i
\(970\) 0 0
\(971\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(972\) 3.96173 2.16327i 3.96173 2.16327i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −0.449181 0.983568i −0.449181 0.983568i −0.989821 0.142315i \(-0.954545\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(978\) 0.830830 0.830830
\(979\) 0.368991 0.425839i 0.368991 0.425839i
\(980\) 0 0
\(981\) 0 0
\(982\) −0.956056 0.0683785i −0.956056 0.0683785i
\(983\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(984\) −0.778649 + 2.65184i −0.778649 + 2.65184i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(992\) 0 0
\(993\) −3.00224 2.24745i −3.00224 2.24745i
\(994\) 0 0
\(995\) 0 0
\(996\) −3.54632 1.61955i −3.54632 1.61955i
\(997\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(998\) 0.114220 0.0855040i 0.114220 0.0855040i
\(999\) 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 712.1.y.a.187.1 yes 20
4.3 odd 2 2848.1.cc.a.1967.1 20
8.3 odd 2 CM 712.1.y.a.187.1 yes 20
8.5 even 2 2848.1.cc.a.1967.1 20
89.10 even 44 inner 712.1.y.a.99.1 20
356.99 odd 44 2848.1.cc.a.1167.1 20
712.99 odd 44 inner 712.1.y.a.99.1 20
712.277 even 44 2848.1.cc.a.1167.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
712.1.y.a.99.1 20 89.10 even 44 inner
712.1.y.a.99.1 20 712.99 odd 44 inner
712.1.y.a.187.1 yes 20 1.1 even 1 trivial
712.1.y.a.187.1 yes 20 8.3 odd 2 CM
2848.1.cc.a.1167.1 20 356.99 odd 44
2848.1.cc.a.1167.1 20 712.277 even 44
2848.1.cc.a.1967.1 20 4.3 odd 2
2848.1.cc.a.1967.1 20 8.5 even 2