Properties

Label 1265.1.bi.b.747.1
Level $1265$
Weight $1$
Character 1265.747
Analytic conductor $0.631$
Analytic rank $0$
Dimension $20$
Projective image $D_{44}$
CM discriminant -11
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1265,1,Mod(43,1265)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1265, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([33, 22, 10]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1265.43");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1265 = 5 \cdot 11 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1265.bi (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: \(0.631317240981\)
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: \(\Z[a_1, \ldots, a_{4}]\)
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 747.1
Root \(-0.281733 - 0.959493i\) of defining polynomial
Character \(\chi\) \(=\) 1265.747
Dual form 1265.1.bi.b.1033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.19550 - 1.59700i) q^{3} +(0.909632 + 0.415415i) q^{4} +(0.755750 + 0.654861i) q^{5} +(-0.839462 + 2.85895i) q^{9} +O(q^{10})\) \(q+(-1.19550 - 1.59700i) q^{3} +(0.909632 + 0.415415i) q^{4} +(0.755750 + 0.654861i) q^{5} +(-0.839462 + 2.85895i) q^{9} +(0.540641 - 0.841254i) q^{11} +(-0.424047 - 1.94931i) q^{12} +(0.142315 - 1.98982i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.415415 + 0.909632i) q^{20} +(0.841254 + 0.540641i) q^{23} +(0.142315 + 0.989821i) q^{25} +(3.70020 - 1.38010i) q^{27} +(-0.0801894 - 0.557730i) q^{31} +(-1.98982 + 0.142315i) q^{33} +(-1.95125 + 2.25186i) q^{36} +(-0.613435 + 0.334961i) q^{37} +(0.841254 - 0.540641i) q^{44} +(-2.50664 + 1.61092i) q^{45} +(-0.677760 - 0.677760i) q^{47} +(0.424047 - 1.94931i) q^{48} +(0.989821 + 0.142315i) q^{49} +(0.133682 - 1.86912i) q^{53} +(0.959493 - 0.281733i) q^{55} +(-1.37491 - 1.19136i) q^{59} +(0.956056 - 1.75089i) q^{60} +(0.281733 + 0.959493i) q^{64} +(-0.0303285 + 0.139418i) q^{67} +(-0.142315 - 1.98982i) q^{69} +(-1.41542 + 0.909632i) q^{71} +(1.41061 - 1.41061i) q^{75} +1.00000i q^{80} +(-4.12099 - 2.64840i) q^{81} +(0.215109 - 1.49611i) q^{89} +(0.540641 + 0.841254i) q^{92} +(-0.794830 + 0.794830i) q^{93} +(-0.841254 + 1.54064i) q^{97} +(1.95125 + 2.25186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{3} - 2 q^{12} + 2 q^{15} + 2 q^{16} - 2 q^{20} - 2 q^{23} + 2 q^{25} - 20 q^{33} - 2 q^{36} + 2 q^{37} - 2 q^{44} + 2 q^{45} - 2 q^{47} + 2 q^{48} - 2 q^{53} + 2 q^{55} - 2 q^{60} + 2 q^{67} - 2 q^{69} - 18 q^{71} + 2 q^{75} - 2 q^{81} + 2 q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1265\mathbb{Z}\right)^\times\).

\(n\) \(166\) \(507\) \(1036\)
\(\chi(n)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(3\) −1.19550 1.59700i −1.19550 1.59700i −0.654861 0.755750i \(-0.727273\pi\)
−0.540641 0.841254i \(-0.681818\pi\)
\(4\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(5\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(6\) 0 0
\(7\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(8\) 0 0
\(9\) −0.839462 + 2.85895i −0.839462 + 2.85895i
\(10\) 0 0
\(11\) 0.540641 0.841254i 0.540641 0.841254i
\(12\) −0.424047 1.94931i −0.424047 1.94931i
\(13\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(14\) 0 0
\(15\) 0.142315 1.98982i 0.142315 1.98982i
\(16\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(17\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(18\) 0 0
\(19\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(20\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(21\) 0 0
\(22\) 0 0
\(23\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(24\) 0 0
\(25\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(26\) 0 0
\(27\) 3.70020 1.38010i 3.70020 1.38010i
\(28\) 0 0
\(29\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(30\) 0 0
\(31\) −0.0801894 0.557730i −0.0801894 0.557730i −0.989821 0.142315i \(-0.954545\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(32\) 0 0
\(33\) −1.98982 + 0.142315i −1.98982 + 0.142315i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.95125 + 2.25186i −1.95125 + 2.25186i
\(37\) −0.613435 + 0.334961i −0.613435 + 0.334961i −0.755750 0.654861i \(-0.772727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(42\) 0 0
\(43\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(44\) 0.841254 0.540641i 0.841254 0.540641i
\(45\) −2.50664 + 1.61092i −2.50664 + 1.61092i
\(46\) 0 0
\(47\) −0.677760 0.677760i −0.677760 0.677760i 0.281733 0.959493i \(-0.409091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(48\) 0.424047 1.94931i 0.424047 1.94931i
\(49\) 0.989821 + 0.142315i 0.989821 + 0.142315i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.133682 1.86912i 0.133682 1.86912i −0.281733 0.959493i \(-0.590909\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(54\) 0 0
\(55\) 0.959493 0.281733i 0.959493 0.281733i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.37491 1.19136i −1.37491 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(60\) 0.956056 1.75089i 0.956056 1.75089i
\(61\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.0303285 + 0.139418i −0.0303285 + 0.139418i −0.989821 0.142315i \(-0.954545\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(68\) 0 0
\(69\) −0.142315 1.98982i −0.142315 1.98982i
\(70\) 0 0
\(71\) −1.41542 + 0.909632i −1.41542 + 0.909632i −0.415415 + 0.909632i \(0.636364\pi\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(74\) 0 0
\(75\) 1.41061 1.41061i 1.41061 1.41061i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(80\) 1.00000i 1.00000i
\(81\) −4.12099 2.64840i −4.12099 2.64840i
\(82\) 0 0
\(83\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.215109 1.49611i 0.215109 1.49611i −0.540641 0.841254i \(-0.681818\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.540641 + 0.841254i 0.540641 + 0.841254i
\(93\) −0.794830 + 0.794830i −0.794830 + 0.794830i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.841254 + 1.54064i −0.841254 + 1.54064i 1.00000i \(0.5\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(98\) 0 0
\(99\) 1.95125 + 2.25186i 1.95125 + 2.25186i
\(100\) −0.281733 + 0.959493i −0.281733 + 0.959493i
\(101\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(102\) 0 0
\(103\) 0.254771 + 1.17116i 0.254771 + 1.17116i 0.909632 + 0.415415i \(0.136364\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(108\) 3.93914 + 0.281733i 3.93914 + 0.281733i
\(109\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(110\) 0 0
\(111\) 1.26830 + 0.579211i 1.26830 + 0.579211i
\(112\) 0 0
\(113\) 0.936593 + 0.203743i 0.936593 + 0.203743i 0.654861 0.755750i \(-0.272727\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(114\) 0 0
\(115\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.415415 0.909632i −0.415415 0.909632i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.158746 0.540641i 0.158746 0.540641i
\(125\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(126\) 0 0
\(127\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(132\) −1.86912 0.697148i −1.86912 0.697148i
\(133\) 0 0
\(134\) 0 0
\(135\) 3.70020 + 1.38010i 3.70020 + 1.38010i
\(136\) 0 0
\(137\) −1.13214 + 1.13214i −1.13214 + 1.13214i −0.142315 + 0.989821i \(0.545455\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −0.272122 + 1.89265i −0.272122 + 1.89265i
\(142\) 0 0
\(143\) 0 0
\(144\) −2.71038 + 1.23779i −2.71038 + 1.23779i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.956056 1.75089i −0.956056 1.75089i
\(148\) −0.697148 + 0.0498610i −0.697148 + 0.0498610i
\(149\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(150\) 0 0
\(151\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.304632 0.474017i 0.304632 0.474017i
\(156\) 0 0
\(157\) −0.494217 1.32505i −0.494217 1.32505i −0.909632 0.415415i \(-0.863636\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(158\) 0 0
\(159\) −3.14482 + 2.02105i −3.14482 + 2.02105i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.254771 + 1.17116i −0.254771 + 1.17116i 0.654861 + 0.755750i \(0.272727\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(164\) 0 0
\(165\) −1.59700 1.19550i −1.59700 1.19550i
\(166\) 0 0
\(167\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(168\) 0 0
\(169\) −0.989821 + 0.142315i −0.989821 + 0.142315i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.977147 0.212565i \(-0.0681818\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.989821 0.142315i 0.989821 0.142315i
\(177\) −0.258908 + 3.62001i −0.258908 + 3.62001i
\(178\) 0 0
\(179\) 0.0801894 + 0.273100i 0.0801894 + 0.273100i 0.989821 0.142315i \(-0.0454545\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(180\) −2.94931 + 0.424047i −2.94931 + 0.424047i
\(181\) 0.281733 + 0.0405070i 0.281733 + 0.0405070i 0.281733 0.959493i \(-0.409091\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.682956 0.148568i −0.682956 0.148568i
\(186\) 0 0
\(187\) 0 0
\(188\) −0.334961 0.898064i −0.334961 0.898064i
\(189\) 0 0
\(190\) 0 0
\(191\) 0.989821 0.857685i 0.989821 0.857685i 1.00000i \(-0.5\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(192\) 1.19550 1.59700i 1.19550 1.59700i
\(193\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(197\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(198\) 0 0
\(199\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(200\) 0 0
\(201\) 0.258908 0.118239i 0.258908 0.118239i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −2.25186 + 1.95125i −2.25186 + 1.95125i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(212\) 0.898064 1.64468i 0.898064 1.64468i
\(213\) 3.14482 + 1.17296i 3.14482 + 1.17296i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.989821 + 0.142315i 0.989821 + 0.142315i
\(221\) 0 0
\(222\) 0 0
\(223\) −1.59700 0.114220i −1.59700 0.114220i −0.755750 0.654861i \(-0.772727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(224\) 0 0
\(225\) −2.94931 0.424047i −2.94931 0.424047i
\(226\) 0 0
\(227\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(228\) 0 0
\(229\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(234\) 0 0
\(235\) −0.0683785 0.956056i −0.0683785 0.956056i
\(236\) −0.755750 1.65486i −0.755750 1.65486i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(240\) 1.59700 1.19550i 1.59700 1.19550i
\(241\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(242\) 0 0
\(243\) 0.415415 + 5.80826i 0.415415 + 5.80826i
\(244\) 0 0
\(245\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.983568 1.53046i −0.983568 1.53046i −0.841254 0.540641i \(-0.818182\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(252\) 0 0
\(253\) 0.909632 0.415415i 0.909632 0.415415i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(257\) −1.75575 + 0.654861i −1.75575 + 0.654861i −0.755750 + 0.654861i \(0.772727\pi\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(264\) 0 0
\(265\) 1.32505 1.32505i 1.32505 1.32505i
\(266\) 0 0
\(267\) −2.64646 + 1.44508i −2.64646 + 1.44508i
\(268\) −0.0855040 + 0.114220i −0.0855040 + 0.114220i
\(269\) −0.817178 + 0.708089i −0.817178 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(270\) 0 0
\(271\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(276\) 0.697148 1.86912i 0.697148 1.86912i
\(277\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(278\) 0 0
\(279\) 1.66184 + 0.238936i 1.66184 + 0.238936i
\(280\) 0 0
\(281\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(282\) 0 0
\(283\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(284\) −1.66538 + 0.239446i −1.66538 + 0.239446i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(290\) 0 0
\(291\) 3.46613 0.498354i 3.46613 0.498354i
\(292\) 0 0
\(293\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(294\) 0 0
\(295\) −0.258908 1.80075i −0.258908 1.80075i
\(296\) 0 0
\(297\) 0.839462 3.85895i 0.839462 3.85895i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.86912 0.697148i 1.86912 0.697148i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(308\) 0 0
\(309\) 1.56577 1.80700i 1.56577 1.80700i
\(310\) 0 0
\(311\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(312\) 0 0
\(313\) 0.203743 + 0.373128i 0.203743 + 0.373128i 0.959493 0.281733i \(-0.0909091\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.54064 + 0.841254i 1.54064 + 0.841254i 1.00000 \(0\)
0.540641 + 0.841254i \(0.318182\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −2.64840 4.12099i −2.64840 4.12099i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.03748 0.304632i −1.03748 0.304632i −0.281733 0.959493i \(-0.590909\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(332\) 0 0
\(333\) −0.442679 2.03496i −0.442679 2.03496i
\(334\) 0 0
\(335\) −0.114220 + 0.0855040i −0.114220 + 0.0855040i
\(336\) 0 0
\(337\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(338\) 0 0
\(339\) −0.794320 1.73932i −0.794320 1.73932i
\(340\) 0 0
\(341\) −0.512546 0.234072i −0.512546 0.234072i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.19550 1.59700i 1.19550 1.59700i
\(346\) 0 0
\(347\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(348\) 0 0
\(349\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.959493 0.718267i −0.959493 0.718267i 1.00000i \(-0.5\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(354\) 0 0
\(355\) −1.66538 0.239446i −1.66538 0.239446i
\(356\) 0.817178 1.27155i 0.817178 1.27155i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(360\) 0 0
\(361\) −0.654861 0.755750i −0.654861 0.755750i
\(362\) 0 0
\(363\) −0.956056 + 1.75089i −0.956056 + 1.75089i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.38189 1.38189i 1.38189 1.38189i 0.540641 0.841254i \(-0.318182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(368\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.05319 + 0.392818i −1.05319 + 0.392818i
\(373\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(374\) 0 0
\(375\) 1.98982 0.142315i 1.98982 0.142315i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.718267 0.959493i 0.718267 0.959493i −0.281733 0.959493i \(-0.590909\pi\)
1.00000 \(0\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −1.40524 + 1.05195i −1.40524 + 1.05195i
\(389\) −0.239446 + 0.153882i −0.239446 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0.839462 + 2.85895i 0.839462 + 2.85895i
\(397\) 0.148568 0.398326i 0.148568 0.398326i −0.841254 0.540641i \(-0.818182\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(401\) −1.45027 1.25667i −1.45027 1.25667i −0.909632 0.415415i \(-0.863636\pi\)
−0.540641 0.841254i \(-0.681818\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.38010 4.70020i −1.38010 4.70020i
\(406\) 0 0
\(407\) −0.0498610 + 0.697148i −0.0498610 + 0.697148i
\(408\) 0 0
\(409\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(410\) 0 0
\(411\) 3.16150 + 0.454554i 3.16150 + 0.454554i
\(412\) −0.254771 + 1.17116i −0.254771 + 1.17116i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.89945 0.557730i 1.89945 0.557730i 0.909632 0.415415i \(-0.136364\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(420\) 0 0
\(421\) −1.27155 + 1.10181i −1.27155 + 1.10181i −0.281733 + 0.959493i \(0.590909\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(422\) 0 0
\(423\) 2.50664 1.36873i 2.50664 1.36873i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(432\) 3.46613 + 1.89265i 3.46613 + 1.89265i
\(433\) 1.50013 0.559521i 1.50013 0.559521i 0.540641 0.841254i \(-0.318182\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(440\) 0 0
\(441\) −1.23779 + 2.71038i −1.23779 + 2.71038i
\(442\) 0 0
\(443\) 0.398326 + 0.148568i 0.398326 + 0.148568i 0.540641 0.841254i \(-0.318182\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(444\) 0.913069 + 1.05374i 0.913069 + 1.05374i
\(445\) 1.14231 0.989821i 1.14231 0.989821i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.03748 + 1.61435i −1.03748 + 1.61435i −0.281733 + 0.959493i \(0.590909\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0.767317 + 0.574406i 0.767317 + 0.574406i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.05195 1.40524i −1.05195 1.40524i −0.909632 0.415415i \(-0.863636\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(464\) 0 0
\(465\) −1.12119 + 0.0801894i −1.12119 + 0.0801894i
\(466\) 0 0
\(467\) −1.75089 0.125226i −1.75089 0.125226i −0.841254 0.540641i \(-0.818182\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.52527 + 2.37336i −1.52527 + 2.37336i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.23151 + 1.95125i 5.23151 + 1.95125i
\(478\) 0 0
\(479\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000i 1.00000i
\(485\) −1.64468 + 0.613435i −1.64468 + 0.613435i
\(486\) 0 0
\(487\) 0.133682 0.0498610i 0.133682 0.0498610i −0.281733 0.959493i \(-0.590909\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(488\) 0 0
\(489\) 2.17493 0.993259i 2.17493 0.993259i
\(490\) 0 0
\(491\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 2.97964i 2.97964i
\(496\) 0.368991 0.425839i 0.368991 0.425839i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.14231 + 0.989821i −1.14231 + 0.989821i −0.142315 + 0.989821i \(0.545455\pi\)
−1.00000 \(\pi\)
\(500\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.41061 + 1.41061i 1.41061 + 1.41061i
\(508\) 0 0
\(509\) 1.49611 + 0.215109i 1.49611 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.574406 + 1.05195i −0.574406 + 1.05195i
\(516\) 0 0
\(517\) −0.936593 + 0.203743i −0.936593 + 0.203743i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.822373 + 0.118239i −0.822373 + 0.118239i −0.540641 0.841254i \(-0.681818\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(522\) 0 0
\(523\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.41061 1.41061i −1.41061 1.41061i
\(529\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(530\) 0 0
\(531\) 4.56023 2.93068i 4.56023 2.93068i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.340275 0.454554i 0.340275 0.454554i
\(538\) 0 0
\(539\) 0.654861 0.755750i 0.654861 0.755750i
\(540\) 2.79250 + 2.79250i 2.79250 + 2.79250i
\(541\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(542\) 0 0
\(543\) −0.272122 0.498354i −0.272122 0.498354i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(548\) −1.50013 + 0.559521i −1.50013 + 0.559521i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.579211 + 1.26830i 0.579211 + 1.26830i
\(556\) 0 0
\(557\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(564\) −1.03377 + 1.60857i −1.03377 + 1.60857i
\(565\) 0.574406 + 0.767317i 0.574406 + 0.767317i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(570\) 0 0
\(571\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(572\) 0 0
\(573\) −2.55306 0.555384i −2.55306 0.555384i
\(574\) 0 0
\(575\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(576\) −2.97964 −2.97964
\(577\) −0.682956 0.148568i −0.682956 0.148568i −0.142315 0.989821i \(-0.545455\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.50013 1.12299i −1.50013 1.12299i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.0303285 0.139418i −0.0303285 0.139418i 0.959493 0.281733i \(-0.0909091\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(588\) −0.142315 1.98982i −0.142315 1.98982i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.654861 0.244250i −0.654861 0.244250i
\(593\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.84751 1.84751i 1.84751 1.84751i
\(598\) 0 0
\(599\) 1.30972i 1.30972i −0.755750 0.654861i \(-0.772727\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(600\) 0 0
\(601\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(602\) 0 0
\(603\) −0.373128 0.203743i −0.373128 0.203743i
\(604\) 0 0
\(605\) 0.281733 0.959493i 0.281733 0.959493i
\(606\) 0 0
\(607\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.0498610 + 0.133682i 0.0498610 + 0.133682i 0.959493 0.281733i \(-0.0909091\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(618\) 0 0
\(619\) −0.909632 + 0.584585i −0.909632 + 0.584585i −0.909632 0.415415i \(-0.863636\pi\)
1.00000i \(0.5\pi\)
\(620\) 0.474017 0.304632i 0.474017 0.304632i
\(621\) 3.85895 + 0.839462i 3.85895 + 0.839462i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.100889 1.41061i 0.100889 1.41061i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.425839 0.368991i −0.425839 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −3.70020 + 0.532008i −3.70020 + 0.532008i
\(637\) 0 0
\(638\) 0 0
\(639\) −1.41240 4.81020i −1.41240 4.81020i
\(640\) 0 0
\(641\) 0.822373 + 0.118239i 0.822373 + 0.118239i 0.540641 0.841254i \(-0.318182\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(642\) 0 0
\(643\) −0.677760 0.677760i −0.677760 0.677760i 0.281733 0.959493i \(-0.409091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.28173 + 0.959493i −1.28173 + 0.959493i −0.281733 + 0.959493i \(0.590909\pi\)
−1.00000 \(1.00000\pi\)
\(648\) 0 0
\(649\) −1.74557 + 0.512546i −1.74557 + 0.512546i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.718267 + 0.959493i −0.718267 + 0.959493i
\(653\) 1.40524 0.767317i 1.40524 0.767317i 0.415415 0.909632i \(-0.363636\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(660\) −0.956056 1.75089i −0.956056 1.75089i
\(661\) 1.80075 0.822373i 1.80075 0.822373i 0.841254 0.540641i \(-0.181818\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1.72681 + 2.68697i 1.72681 + 2.68697i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(674\) 0 0
\(675\) 1.89265 + 3.46613i 1.89265 + 3.46613i
\(676\) −0.959493 0.281733i −0.959493 0.281733i
\(677\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.59700 + 0.114220i 1.59700 + 0.114220i 0.841254 0.540641i \(-0.181818\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(684\) 0 0
\(685\) −1.59700 + 0.114220i −1.59700 + 0.114220i
\(686\) 0 0
\(687\) −2.29415 3.06463i −2.29415 3.06463i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(705\) −1.44508 + 1.25217i −1.44508 + 1.25217i
\(706\) 0 0
\(707\) 0 0
\(708\) −1.73932 + 3.18532i −1.73932 + 3.18532i
\(709\) 0.627899 1.37491i 0.627899 1.37491i −0.281733 0.959493i \(-0.590909\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.234072 0.512546i 0.234072 0.512546i
\(714\) 0 0
\(715\) 0 0
\(716\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(717\) 0 0
\(718\) 0 0
\(719\) −1.19136 + 0.544078i −1.19136 + 0.544078i −0.909632 0.415415i \(-0.863636\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(720\) −2.85895 0.839462i −2.85895 0.839462i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(725\) 0 0
\(726\) 0 0
\(727\) 1.64468 0.898064i 1.64468 0.898064i 0.654861 0.755750i \(-0.272727\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(728\) 0 0
\(729\) 5.07704 4.39928i 5.07704 4.39928i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(734\) 0 0
\(735\) 0.424047 1.94931i 0.424047 1.94931i
\(736\) 0 0
\(737\) 0.100889 + 0.100889i 0.100889 + 0.100889i
\(738\) 0 0
\(739\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(740\) −0.559521 0.418852i −0.559521 0.418852i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(752\) 0.0683785 0.956056i 0.0683785 0.956056i
\(753\) −1.26830 + 3.40043i −1.26830 + 3.40043i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.340335 1.56449i 0.340335 1.56449i −0.415415 0.909632i \(-0.636364\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(758\) 0 0
\(759\) −1.75089 0.956056i −1.75089 0.956056i
\(760\) 0 0
\(761\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.25667 0.368991i 1.25667 0.368991i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.75089 0.956056i 1.75089 0.956056i
\(769\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(770\) 0 0
\(771\) 3.14482 + 2.02105i 3.14482 + 2.02105i
\(772\) 0 0
\(773\) 0.841254 + 1.54064i 0.841254 + 1.54064i 0.841254 + 0.540641i \(0.181818\pi\)
1.00000i \(0.500000\pi\)
\(774\) 0 0
\(775\) 0.540641 0.158746i 0.540641 0.158746i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 1.68251i 1.68251i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.540641 + 0.841254i 0.540641 + 0.841254i
\(785\) 0.494217 1.32505i 0.494217 1.32505i
\(786\) 0 0
\(787\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −3.70020 0.532008i −3.70020 0.532008i
\(796\) −0.368991 + 1.25667i −0.368991 + 1.25667i
\(797\) 0.114220 + 0.0855040i 0.114220 + 0.0855040i 0.654861 0.755750i \(-0.272727\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 4.09673 + 1.87092i 4.09673 + 1.87092i
\(802\) 0 0
\(803\) 0 0
\(804\) 0.284630 0.284630
\(805\) 0 0
\(806\) 0 0
\(807\) 2.10776 + 0.458515i 2.10776 + 0.458515i
\(808\) 0 0
\(809\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(810\) 0 0
\(811\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −0.959493 + 0.718267i −0.959493 + 0.718267i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(822\) 0 0
\(823\) 0.898064 1.64468i 0.898064 1.64468i 0.142315 0.989821i \(-0.454545\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(824\) 0 0
\(825\) −0.424047 1.94931i −0.424047 1.94931i
\(826\) 0 0
\(827\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(828\) −2.85895 + 0.839462i −2.85895 + 0.839462i
\(829\) 0.284630i 0.284630i −0.989821 0.142315i \(-0.954545\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.06644 1.95304i −1.06644 1.95304i
\(838\) 0 0
\(839\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(840\) 0 0
\(841\) 0.654861 0.755750i 0.654861 0.755750i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.841254 0.540641i −0.841254 0.540641i
\(846\) 0 0
\(847\) 0 0
\(848\) 1.50013 1.12299i 1.50013 1.12299i
\(849\) 0 0
\(850\) 0 0
\(851\) −0.697148 0.0498610i −0.697148 0.0498610i
\(852\) 2.37336 + 2.37336i 2.37336 + 2.37336i
\(853\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(858\) 0 0
\(859\) −1.29639 + 0.186393i −1.29639 + 0.186393i −0.755750 0.654861i \(-0.772727\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −0.415415 + 0.0903680i −0.415415 + 0.0903680i −0.415415 0.909632i \(-0.636364\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0.142315 1.98982i 0.142315 1.98982i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −3.69841 3.69841i −3.69841 3.69841i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(881\) −1.49611 + 1.29639i −1.49611 + 1.29639i −0.654861 + 0.755750i \(0.727273\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(882\) 0 0
\(883\) −1.54064 + 0.841254i −1.54064 + 0.841254i −0.540641 + 0.841254i \(0.681818\pi\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) −2.56627 + 2.56627i −2.56627 + 2.56627i
\(886\) 0 0
\(887\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −4.45595 + 2.03496i −4.45595 + 2.03496i
\(892\) −1.40524 0.767317i −1.40524 0.767317i
\(893\) 0 0
\(894\) 0 0
\(895\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −2.50664 1.61092i −2.50664 1.61092i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(906\) 0 0
\(907\) 0.139418 + 1.94931i 0.139418 + 1.94931i 0.281733 + 0.959493i \(0.409091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.0801894 0.273100i 0.0801894 0.273100i −0.909632 0.415415i \(-0.863636\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.74557 + 0.797176i 1.74557 + 0.797176i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −0.418852 0.559521i −0.418852 0.559521i
\(926\) 0 0
\(927\) −3.56217 0.254771i −3.56217 0.254771i
\(928\) 0 0
\(929\) −0.425839 + 1.45027i −0.425839 + 1.45027i 0.415415 + 0.909632i \(0.363636\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0.118239 + 1.65320i 0.118239 + 1.65320i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(938\) 0 0
\(939\) 0.352311 0.771454i 0.352311 0.771454i
\(940\) 0.334961 0.898064i 0.334961 0.898064i
\(941\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 1.81926i 1.81926i
\(945\) 0 0
\(946\) 0 0
\(947\) 1.12299 0.418852i 1.12299 0.418852i 0.281733 0.959493i \(-0.409091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −0.498354 3.46613i −0.498354 3.46613i
\(952\) 0 0
\(953\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(954\) 0 0
\(955\) 1.30972 1.30972
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.94931 0.424047i 1.94931 0.424047i
\(961\) 0.654861 0.192284i 0.654861 0.192284i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0.0801894 + 0.273100i 0.0801894 + 0.273100i 0.989821 0.142315i \(-0.0454545\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(972\) −2.03496 + 5.45595i −2.03496 + 5.45595i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.17116 0.254771i 1.17116 0.254771i 0.415415 0.909632i \(-0.363636\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(978\) 0 0
\(979\) −1.14231 0.989821i −1.14231 0.989821i
\(980\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(981\) 0 0
\(982\) 0 0
\(983\) 0.244250 0.654861i 0.244250 0.654861i −0.755750 0.654861i \(-0.772727\pi\)
1.00000 \(0\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.909632 0.584585i 0.909632 0.584585i 1.00000i \(-0.5\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(992\) 0 0
\(993\) 0.753813 + 2.02105i 0.753813 + 2.02105i
\(994\) 0 0
\(995\) −0.708089 + 1.10181i −0.708089 + 1.10181i
\(996\) 0 0
\(997\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(998\) 0 0
\(999\) −1.80755 + 2.08602i −1.80755 + 2.08602i
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 1265.1.bi.b.747.1 yes 20
5.3 odd 4 1265.1.bi.a.1253.1 yes 20
11.10 odd 2 CM 1265.1.bi.b.747.1 yes 20
23.21 odd 22 1265.1.bi.a.527.1 20
55.43 even 4 1265.1.bi.a.1253.1 yes 20
115.113 even 44 inner 1265.1.bi.b.1033.1 yes 20
253.21 even 22 1265.1.bi.a.527.1 20
1265.1033 odd 44 inner 1265.1.bi.b.1033.1 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1265.1.bi.a.527.1 20 23.21 odd 22
1265.1.bi.a.527.1 20 253.21 even 22
1265.1.bi.a.1253.1 yes 20 5.3 odd 4
1265.1.bi.a.1253.1 yes 20 55.43 even 4
1265.1.bi.b.747.1 yes 20 1.1 even 1 trivial
1265.1.bi.b.747.1 yes 20 11.10 odd 2 CM
1265.1.bi.b.1033.1 yes 20 115.113 even 44 inner
1265.1.bi.b.1033.1 yes 20 1265.1033 odd 44 inner