Properties

Label 3703.1.l.i.3044.1
Level $3703$
Weight $1$
Character 3703.3044
Analytic conductor $1.848$
Analytic rank $0$
Dimension $10$
Projective image $D_{11}$
CM discriminant -7
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3703,1,Mod(118,3703)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3703, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 16]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3703.118");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3703 = 7 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3703.l (of order \(22\), degree \(10\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.84803774178\)
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: no (minimal twist has level 161)
Projective image: \(D_{11}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{11} - \cdots)\)

Embedding invariants

Embedding label 3044.1
Root \(-0.415415 + 0.909632i\) of defining polynomial
Character \(\chi\) \(=\) 3703.3044
Dual form 3703.1.l.i.118.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0405070 - 0.281733i) q^{2} +(0.881761 + 0.258908i) q^{4} +(-0.841254 - 0.540641i) q^{7} +(0.226900 - 0.496841i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.239446 + 1.66538i) q^{11} +(-0.186393 + 0.215109i) q^{14} +(0.642315 + 0.412791i) q^{16} +(0.186393 + 0.215109i) q^{18} +0.478891 q^{22} +(-0.142315 + 0.989821i) q^{25} +(-0.601808 - 0.694523i) q^{28} +(1.25667 - 0.368991i) q^{29} +(0.500000 - 0.577031i) q^{32} +(-0.773100 + 0.496841i) q^{36} +(-1.25667 + 1.45027i) q^{37} +(-0.345139 - 0.755750i) q^{43} +(-0.220047 + 1.53046i) q^{44} +(0.415415 + 0.909632i) q^{49} +(0.273100 + 0.0801894i) q^{50} +(1.10181 + 0.708089i) q^{53} +(-0.459493 + 0.295298i) q^{56} +(-0.0530529 - 0.368991i) q^{58} +(0.959493 - 0.281733i) q^{63} +(0.357685 + 0.412791i) q^{64} +(-0.0405070 + 0.281733i) q^{67} +(-0.239446 + 1.66538i) q^{71} +(0.226900 + 0.496841i) q^{72} +(0.357685 + 0.412791i) q^{74} +(0.698939 - 1.53046i) q^{77} +(1.10181 - 0.708089i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-0.226900 + 0.0666238i) q^{86} +(0.881761 + 0.258908i) q^{88} +(0.273100 - 0.0801894i) q^{98} +(-1.41542 - 0.909632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 9 q^{2} + 8 q^{4} + q^{7} + 7 q^{8} - q^{9} + 2 q^{11} + 2 q^{14} + 6 q^{16} - 2 q^{18} + 4 q^{22} - q^{25} + 3 q^{28} - 2 q^{29} + 5 q^{32} - 3 q^{36} + 2 q^{37} - 9 q^{43} + 6 q^{44} - q^{49}+ \cdots - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3703\mathbb{Z}\right)^\times\).

\(n\) \(2117\) \(3179\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(3\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(4\) 0.881761 + 0.258908i 0.881761 + 0.258908i
\(5\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(6\) 0 0
\(7\) −0.841254 0.540641i −0.841254 0.540641i
\(8\) 0.226900 0.496841i 0.226900 0.496841i
\(9\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(10\) 0 0
\(11\) 0.239446 + 1.66538i 0.239446 + 1.66538i 0.654861 + 0.755750i \(0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(12\) 0 0
\(13\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(14\) −0.186393 + 0.215109i −0.186393 + 0.215109i
\(15\) 0 0
\(16\) 0.642315 + 0.412791i 0.642315 + 0.412791i
\(17\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(18\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(19\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.478891 0.478891
\(23\) 0 0
\(24\) 0 0
\(25\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(26\) 0 0
\(27\) 0 0
\(28\) −0.601808 0.694523i −0.601808 0.694523i
\(29\) 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(30\) 0 0
\(31\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(32\) 0.500000 0.577031i 0.500000 0.577031i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.773100 + 0.496841i −0.773100 + 0.496841i
\(37\) −1.25667 + 1.45027i −1.25667 + 1.45027i −0.415415 + 0.909632i \(0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(42\) 0 0
\(43\) −0.345139 0.755750i −0.345139 0.755750i 0.654861 0.755750i \(-0.272727\pi\)
−1.00000 \(\pi\)
\(44\) −0.220047 + 1.53046i −0.220047 + 1.53046i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(50\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(51\) 0 0
\(52\) 0 0
\(53\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.459493 + 0.295298i −0.459493 + 0.295298i
\(57\) 0 0
\(58\) −0.0530529 0.368991i −0.0530529 0.368991i
\(59\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(60\) 0 0
\(61\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(62\) 0 0
\(63\) 0.959493 0.281733i 0.959493 0.281733i
\(64\) 0.357685 + 0.412791i 0.357685 + 0.412791i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i 0.959493 + 0.281733i \(0.0909091\pi\)
−1.00000 \(1.00000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(72\) 0.226900 + 0.496841i 0.226900 + 0.496841i
\(73\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(74\) 0.357685 + 0.412791i 0.357685 + 0.412791i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.698939 1.53046i 0.698939 1.53046i
\(78\) 0 0
\(79\) 1.10181 0.708089i 1.10181 0.708089i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(80\) 0 0
\(81\) −0.142315 0.989821i −0.142315 0.989821i
\(82\) 0 0
\(83\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.226900 + 0.0666238i −0.226900 + 0.0666238i
\(87\) 0 0
\(88\) 0.881761 + 0.258908i 0.881761 + 0.258908i
\(89\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(98\) 0.273100 0.0801894i 0.273100 0.0801894i
\(99\) −1.41542 0.909632i −1.41542 0.909632i
\(100\) −0.381761 + 0.835939i −0.381761 + 0.835939i
\(101\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(102\) 0 0
\(103\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.244123 0.281733i 0.244123 0.281733i
\(107\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(108\) 0 0
\(109\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.317178 0.694523i −0.317178 0.694523i
\(113\) 0.118239 0.822373i 0.118239 0.822373i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.20362 1.20362
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.75667 + 0.515804i −1.75667 + 0.515804i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.0405070 0.281733i −0.0405070 0.281733i
\(127\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(128\) 0.773100 0.496841i 0.773100 0.496841i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.0777324 + 0.0228243i 0.0777324 + 0.0228243i
\(135\) 0 0
\(136\) 0 0
\(137\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.459493 + 0.134919i 0.459493 + 0.134919i
\(143\) 0 0
\(144\) −0.732593 + 0.215109i −0.732593 + 0.215109i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −1.48357 + 0.953431i −1.48357 + 0.953431i
\(149\) 0.118239 + 0.822373i 0.118239 + 0.822373i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(150\) 0 0
\(151\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −0.402869 0.258908i −0.402869 0.258908i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(158\) −0.154861 0.339098i −0.154861 0.339098i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.284630 −0.284630
\(163\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(168\) 0 0
\(169\) 0.415415 0.909632i 0.415415 0.909632i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.108660 0.755750i −0.108660 0.755750i
\(173\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(174\) 0 0
\(175\) 0.654861 0.755750i 0.654861 0.755750i
\(176\) −0.533654 + 1.16854i −0.533654 + 1.16854i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(180\) 0 0
\(181\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(192\) 0 0
\(193\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.130785 + 0.909632i 0.130785 + 0.909632i
\(197\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(198\) −0.313607 + 0.361922i −0.313607 + 0.361922i
\(199\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(200\) 0.459493 + 0.295298i 0.459493 + 0.295298i
\(201\) 0 0
\(202\) 0 0
\(203\) −1.25667 0.368991i −1.25667 0.368991i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(212\) 0.788201 + 0.909632i 0.788201 + 0.909632i
\(213\) 0 0
\(214\) −0.459493 0.295298i −0.459493 0.295298i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.0115295 + 0.0801894i 0.0115295 + 0.0801894i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(224\) −0.732593 + 0.215109i −0.732593 + 0.215109i
\(225\) −0.654861 0.755750i −0.654861 0.755750i
\(226\) −0.226900 0.0666238i −0.226900 0.0666238i
\(227\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.101808 0.708089i 0.101808 0.708089i
\(233\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(240\) 0 0
\(241\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(242\) 0.0741615 + 0.515804i 0.0741615 + 0.515804i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(252\) 0.918986 0.918986
\(253\) 0 0
\(254\) −0.236479 −0.236479
\(255\) 0 0
\(256\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(257\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(258\) 0 0
\(259\) 1.84125 0.540641i 1.84125 0.540641i
\(260\) 0 0
\(261\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(262\) 0 0
\(263\) 0.239446 0.153882i 0.239446 0.153882i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.108660 + 0.237933i −0.108660 + 0.237933i
\(269\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(270\) 0 0
\(271\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0.0115295 0.0801894i 0.0115295 0.0801894i
\(275\) −1.68251 −1.68251
\(276\) 0 0
\(277\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.857685 0.989821i −0.857685 0.989821i 0.142315 0.989821i \(-0.454545\pi\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(284\) −0.642315 + 1.40647i −0.642315 + 1.40647i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.108660 + 0.755750i 0.108660 + 0.755750i
\(289\) 0.841254 0.540641i 0.841254 0.540641i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.435418 + 0.953431i 0.435418 + 0.953431i
\(297\) 0 0
\(298\) 0.236479 0.236479
\(299\) 0 0
\(300\) 0 0
\(301\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(302\) 0.154861 + 0.339098i 0.154861 + 0.339098i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(308\) 1.01255 1.16854i 1.01255 1.16854i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(312\) 0 0
\(313\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.15486 0.339098i 1.15486 0.339098i
\(317\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(318\) 0 0
\(319\) 0.915415 + 2.00448i 0.915415 + 2.00448i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.130785 0.909632i 0.130785 0.909632i
\(325\) 0 0
\(326\) −0.357685 0.105026i −0.357685 0.105026i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(332\) 0 0
\(333\) −0.273100 1.89945i −0.273100 1.89945i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(338\) −0.239446 0.153882i −0.239446 0.153882i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.142315 0.989821i 0.142315 0.989821i
\(344\) −0.453800 −0.453800
\(345\) 0 0
\(346\) 0 0
\(347\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(348\) 0 0
\(349\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(350\) −0.186393 0.215109i −0.186393 0.215109i
\(351\) 0 0
\(352\) 1.08070 + 0.694523i 1.08070 + 0.694523i
\(353\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.198939 + 0.127850i −0.198939 + 0.127850i
\(359\) 0.544078 0.627899i 0.544078 0.627899i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(360\) 0 0
\(361\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.544078 1.19136i −0.544078 1.19136i
\(372\) 0 0
\(373\) 1.10181 + 1.27155i 1.10181 + 1.27155i 0.959493 + 0.281733i \(0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.186393 1.29639i −0.186393 1.29639i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.357685 0.412791i 0.357685 0.412791i
\(383\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.313607 + 0.361922i 0.313607 + 0.361922i
\(387\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(388\) 0 0
\(389\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.546200 0.546200
\(393\) 0 0
\(394\) −0.0982369 0.215109i −0.0982369 0.215109i
\(395\) 0 0
\(396\) −1.01255 1.16854i −1.01255 1.16854i
\(397\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.500000 + 0.577031i −0.500000 + 0.577031i
\(401\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −0.154861 + 0.339098i −0.154861 + 0.339098i
\(407\) −2.71616 1.74557i −2.71616 1.74557i
\(408\) 0 0
\(409\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(420\) 0 0
\(421\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(422\) −0.198939 + 0.435615i −0.198939 + 0.435615i
\(423\) 0 0
\(424\) 0.601808 0.386758i 0.601808 0.386758i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 1.15486 1.33278i 1.15486 1.33278i
\(429\) 0 0
\(430\) 0 0
\(431\) 0.797176 0.234072i 0.797176 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(432\) 0 0
\(433\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.261571 −0.261571
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(440\) 0 0
\(441\) −0.959493 0.281733i −0.959493 0.281733i
\(442\) 0 0
\(443\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.0777324 0.540641i −0.0777324 0.540641i
\(449\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(450\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(451\) 0 0
\(452\) 0.317178 0.694523i 0.317178 0.694523i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(464\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(465\) 0 0
\(466\) −0.524075 + 0.153882i −0.524075 + 0.153882i
\(467\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(468\) 0 0
\(469\) 0.186393 0.215109i 0.186393 0.215109i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.17597 0.755750i 1.17597 0.755750i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(478\) −0.357685 0.412791i −0.357685 0.412791i
\(479\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.68251 −1.68251
\(485\) 0 0
\(486\) 0 0
\(487\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.10181 1.27155i 1.10181 1.27155i
\(498\) 0 0
\(499\) −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(504\) 0.0777324 0.540641i 0.0777324 0.540641i
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0.108660 0.755750i 0.108660 0.755750i
\(509\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.959493 0.281733i 0.959493 0.281733i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −0.0777324 0.540641i −0.0777324 0.540641i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(522\) 0.313607 + 0.201543i 0.313607 + 0.201543i
\(523\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −0.0336545 0.0736930i −0.0336545 0.0736930i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.130785 + 0.0840506i 0.130785 + 0.0840506i
\(537\) 0 0
\(538\) 0 0
\(539\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(540\) 0 0
\(541\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(548\) 0.250975 + 0.0736930i 0.250975 + 0.0736930i
\(549\) 0 0
\(550\) −0.0681534 + 0.474017i −0.0681534 + 0.474017i
\(551\) 0 0
\(552\) 0 0
\(553\) −1.30972 −1.30972
\(554\) −0.0777324 + 0.540641i −0.0777324 + 0.540641i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.30972 + 1.51150i 1.30972 + 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.313607 + 0.201543i −0.313607 + 0.201543i
\(563\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(568\) 0.773100 + 0.496841i 0.773100 + 0.496841i
\(569\) −1.84125 + 0.540641i −1.84125 + 0.540641i −0.841254 + 0.540641i \(0.818182\pi\)
−1.00000 \(1.00000\pi\)
\(570\) 0 0
\(571\) −1.84125 0.540641i −1.84125 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.546200 −0.546200
\(577\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(578\) −0.118239 0.258908i −0.118239 0.258908i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.915415 + 2.00448i −0.915415 + 2.00448i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.40584 + 0.412791i −1.40584 + 0.412791i
\(593\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.108660 + 0.755750i −0.108660 + 0.755750i
\(597\) 0 0
\(598\) 0 0
\(599\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(600\) 0 0
\(601\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(602\) 0.226900 + 0.0666238i 0.226900 + 0.0666238i
\(603\) −0.186393 0.215109i −0.186393 0.215109i
\(604\) −1.15486 + 0.339098i −1.15486 + 0.339098i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.118239 0.258908i 0.118239 0.258908i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.601808 0.694523i −0.601808 0.694523i
\(617\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(618\) 0 0
\(619\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 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 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(632\) −0.101808 0.708089i −0.101808 0.708089i
\(633\) 0 0
\(634\) 0.459493 0.295298i 0.459493 0.295298i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0.601808 0.176707i 0.601808 0.176707i
\(639\) −1.10181 1.27155i −1.10181 1.27155i
\(640\) 0 0
\(641\) −0.830830 1.81926i −0.830830 1.81926i −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(648\) −0.524075 0.153882i −0.524075 0.153882i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.500000 1.09485i 0.500000 1.09485i
\(653\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.544078 1.19136i 0.544078 1.19136i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(660\) 0 0
\(661\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(662\) 0.154861 + 0.178719i 0.154861 + 0.178719i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.546200 −0.546200
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(674\) 0.402869 + 0.258908i 0.402869 + 0.258908i
\(675\) 0 0
\(676\) 0.601808 0.694523i 0.601808 0.694523i
\(677\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.273100 0.0801894i −0.273100 0.0801894i
\(687\) 0 0
\(688\) 0.0902783 0.627899i 0.0902783 0.627899i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(694\) −0.524075 0.153882i −0.524075 0.153882i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.773100 0.496841i 0.773100 0.496841i
\(701\) −0.0405070 0.281733i −0.0405070 0.281733i 0.959493 0.281733i \(-0.0909091\pi\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.601808 + 0.694523i −0.601808 + 0.694523i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.61435 + 0.474017i 1.61435 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(710\) 0 0
\(711\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.317178 0.694523i −0.317178 0.694523i
\(717\) 0 0
\(718\) −0.154861 0.178719i −0.154861 0.178719i
\(719\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.186393 0.215109i 0.186393 0.215109i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(726\) 0 0
\(727\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(728\) 0 0
\(729\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.478891 −0.478891
\(738\) 0 0
\(739\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.357685 + 0.105026i −0.357685 + 0.105026i
\(743\) 0.239446 + 0.153882i 0.239446 + 0.153882i 0.654861 0.755750i \(-0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.402869 0.258908i 0.402869 0.258908i
\(747\) 0 0
\(748\) 0 0
\(749\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(750\) 0 0
\(751\) 0.544078 1.19136i 0.544078 1.19136i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(758\) −0.372786 −0.372786
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(762\) 0 0
\(763\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(764\) 1.15486 + 1.33278i 1.15486 + 1.33278i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.30075 + 0.835939i −1.30075 + 0.835939i
\(773\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(774\) 0.0982369 0.215109i 0.0982369 0.215109i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.459493 0.134919i −0.459493 0.134919i
\(779\) 0 0
\(780\) 0 0
\(781\) −2.83083 −2.83083
\(782\) 0 0
\(783\) 0 0
\(784\) −0.108660 + 0.755750i −0.108660 + 0.755750i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(788\) 0.732593 0.215109i 0.732593 0.215109i
\(789\) 0 0
\(790\) 0 0
\(791\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(792\) −0.773100 + 0.496841i −0.773100 + 0.496841i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.500000 + 0.577031i 0.500000 + 0.577031i
\(801\) 0 0
\(802\) −0.226900 0.496841i −0.226900 0.496841i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(810\) 0 0
\(811\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(812\) −1.01255 0.650724i −1.01255 0.650724i
\(813\) 0 0
\(814\) −0.601808 + 0.694523i −0.601808 + 0.694523i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 \(0\)
0.415415 + 0.909632i \(0.363636\pi\)
\(822\) 0 0
\(823\) 0.857685 + 0.989821i 0.857685 + 0.989821i 1.00000 \(0\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(840\) 0 0
\(841\) 0.601808 0.386758i 0.601808 0.386758i
\(842\) −0.154861 + 0.178719i −0.154861 + 0.178719i
\(843\) 0 0
\(844\) −1.30075 0.835939i −1.30075 0.835939i
\(845\) 0 0
\(846\) 0 0
\(847\) 1.75667 + 0.515804i 1.75667 + 0.515804i
\(848\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −0.686393 0.792140i −0.686393 0.792140i
\(857\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(858\) 0 0
\(859\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −0.0336545 0.234072i −0.0336545 0.234072i
\(863\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.44306 + 1.66538i 1.44306 + 1.66538i
\(870\) 0 0
\(871\) 0 0
\(872\) −0.0221250 + 0.153882i −0.0221250 + 0.153882i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(882\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(883\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.0681534 + 0.474017i 0.0681534 + 0.474017i
\(887\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(888\) 0 0
\(889\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(890\) 0 0
\(891\) 1.61435 0.474017i 1.61435 0.474017i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −0.918986 −0.918986
\(897\) 0 0
\(898\) 0.546200 0.546200
\(899\) 0 0
\(900\) −0.381761 0.835939i −0.381761 0.835939i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −0.381761 0.245343i −0.381761 0.245343i
\(905\) 0 0
\(906\) 0 0
\(907\) 0.239446 0.153882i 0.239446 0.153882i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.357685 0.105026i 0.357685 0.105026i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1.25667 1.45027i −1.25667 1.45027i
\(926\) −0.0777324 + 0.0228243i −0.0777324 + 0.0228243i
\(927\) 0 0
\(928\) 0.415415 0.909632i 0.415415 0.909632i
\(929\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −0.250975 1.74557i −0.250975 1.74557i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(938\) −0.0530529 0.0612263i −0.0530529 0.0612263i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −0.165284 0.361922i −0.165284 0.361922i
\(947\) 1.84125 + 0.540641i 1.84125 + 0.540641i 1.00000 \(0\)
0.841254 + 0.540641i \(0.181818\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(954\) 0.0530529 + 0.368991i 0.0530529 + 0.368991i
\(955\) 0 0
\(956\) 1.48357 0.953431i 1.48357 0.953431i
\(957\) 0 0
\(958\) 0 0
\(959\) −0.239446 0.153882i −0.239446 0.153882i
\(960\) 0 0
\(961\) −0.654861 0.755750i −0.654861 0.755750i
\(962\) 0 0
\(963\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(968\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −0.0982369 + 0.215109i −0.0982369 + 0.215109i
\(975\) 0 0
\(976\) 0 0
\(977\) 0.284630 + 1.97964i 0.284630 + 1.97964i 0.142315 + 0.989821i \(0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0.118239 0.258908i 0.118239 0.258908i
\(982\) 0.0681534 + 0.0437995i 0.0681534 + 0.0437995i
\(983\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(992\) 0 0
\(993\) 0 0
\(994\) −0.313607 0.361922i −0.313607 0.361922i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(998\) −0.0530529 + 0.0612263i −0.0530529 + 0.0612263i
\(999\) 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 3703.1.l.i.3044.1 10
7.6 odd 2 CM 3703.1.l.i.3044.1 10
23.2 even 11 3703.1.l.d.699.1 10
23.3 even 11 inner 3703.1.l.i.118.1 10
23.4 even 11 3703.1.l.f.2911.1 10
23.5 odd 22 161.1.l.a.62.1 yes 10
23.6 even 11 3703.1.l.g.1392.1 10
23.7 odd 22 3703.1.b.c.1588.3 5
23.8 even 11 3703.1.l.e.2582.1 10
23.9 even 11 3703.1.l.e.2603.1 10
23.10 odd 22 3703.1.l.b.2617.1 10
23.11 odd 22 3703.1.l.c.3429.1 10
23.12 even 11 3703.1.l.g.3429.1 10
23.13 even 11 3703.1.l.d.2617.1 10
23.14 odd 22 3703.1.l.a.2603.1 10
23.15 odd 22 3703.1.l.a.2582.1 10
23.16 even 11 3703.1.b.b.1588.3 5
23.17 odd 22 3703.1.l.c.1392.1 10
23.18 even 11 3703.1.l.f.706.1 10
23.19 odd 22 161.1.l.a.13.1 10
23.20 odd 22 3703.1.l.h.118.1 10
23.21 odd 22 3703.1.l.b.699.1 10
23.22 odd 2 3703.1.l.h.3044.1 10
69.5 even 22 1449.1.bq.a.1189.1 10
69.65 even 22 1449.1.bq.a.496.1 10
92.19 even 22 2576.1.cj.a.657.1 10
92.51 even 22 2576.1.cj.a.545.1 10
161.5 even 66 1127.1.v.a.913.1 20
161.6 odd 22 3703.1.l.g.1392.1 10
161.13 odd 22 3703.1.l.d.2617.1 10
161.19 even 66 1127.1.v.a.864.1 20
161.20 even 22 3703.1.l.h.118.1 10
161.27 odd 22 3703.1.l.f.2911.1 10
161.34 even 22 3703.1.l.c.3429.1 10
161.41 odd 22 3703.1.l.f.706.1 10
161.48 odd 22 3703.1.l.d.699.1 10
161.51 odd 66 1127.1.v.a.913.1 20
161.55 odd 22 3703.1.l.e.2603.1 10
161.62 odd 22 3703.1.b.b.1588.3 5
161.65 odd 66 1127.1.v.a.864.1 20
161.74 odd 66 1127.1.v.a.1097.1 20
161.76 even 22 3703.1.b.c.1588.3 5
161.83 even 22 3703.1.l.a.2603.1 10
161.88 odd 66 1127.1.v.a.1048.1 20
161.90 even 22 3703.1.l.b.699.1 10
161.97 even 22 161.1.l.a.62.1 yes 10
161.104 odd 22 3703.1.l.g.3429.1 10
161.111 even 22 161.1.l.a.13.1 10
161.118 odd 22 inner 3703.1.l.i.118.1 10
161.125 even 22 3703.1.l.b.2617.1 10
161.132 even 22 3703.1.l.c.1392.1 10
161.143 even 66 1127.1.v.a.1097.1 20
161.146 odd 22 3703.1.l.e.2582.1 10
161.153 even 22 3703.1.l.a.2582.1 10
161.157 even 66 1127.1.v.a.1048.1 20
161.160 even 2 3703.1.l.h.3044.1 10
483.272 odd 22 1449.1.bq.a.496.1 10
483.419 odd 22 1449.1.bq.a.1189.1 10
644.111 odd 22 2576.1.cj.a.657.1 10
644.419 odd 22 2576.1.cj.a.545.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
161.1.l.a.13.1 10 23.19 odd 22
161.1.l.a.13.1 10 161.111 even 22
161.1.l.a.62.1 yes 10 23.5 odd 22
161.1.l.a.62.1 yes 10 161.97 even 22
1127.1.v.a.864.1 20 161.19 even 66
1127.1.v.a.864.1 20 161.65 odd 66
1127.1.v.a.913.1 20 161.5 even 66
1127.1.v.a.913.1 20 161.51 odd 66
1127.1.v.a.1048.1 20 161.88 odd 66
1127.1.v.a.1048.1 20 161.157 even 66
1127.1.v.a.1097.1 20 161.74 odd 66
1127.1.v.a.1097.1 20 161.143 even 66
1449.1.bq.a.496.1 10 69.65 even 22
1449.1.bq.a.496.1 10 483.272 odd 22
1449.1.bq.a.1189.1 10 69.5 even 22
1449.1.bq.a.1189.1 10 483.419 odd 22
2576.1.cj.a.545.1 10 92.51 even 22
2576.1.cj.a.545.1 10 644.419 odd 22
2576.1.cj.a.657.1 10 92.19 even 22
2576.1.cj.a.657.1 10 644.111 odd 22
3703.1.b.b.1588.3 5 23.16 even 11
3703.1.b.b.1588.3 5 161.62 odd 22
3703.1.b.c.1588.3 5 23.7 odd 22
3703.1.b.c.1588.3 5 161.76 even 22
3703.1.l.a.2582.1 10 23.15 odd 22
3703.1.l.a.2582.1 10 161.153 even 22
3703.1.l.a.2603.1 10 23.14 odd 22
3703.1.l.a.2603.1 10 161.83 even 22
3703.1.l.b.699.1 10 23.21 odd 22
3703.1.l.b.699.1 10 161.90 even 22
3703.1.l.b.2617.1 10 23.10 odd 22
3703.1.l.b.2617.1 10 161.125 even 22
3703.1.l.c.1392.1 10 23.17 odd 22
3703.1.l.c.1392.1 10 161.132 even 22
3703.1.l.c.3429.1 10 23.11 odd 22
3703.1.l.c.3429.1 10 161.34 even 22
3703.1.l.d.699.1 10 23.2 even 11
3703.1.l.d.699.1 10 161.48 odd 22
3703.1.l.d.2617.1 10 23.13 even 11
3703.1.l.d.2617.1 10 161.13 odd 22
3703.1.l.e.2582.1 10 23.8 even 11
3703.1.l.e.2582.1 10 161.146 odd 22
3703.1.l.e.2603.1 10 23.9 even 11
3703.1.l.e.2603.1 10 161.55 odd 22
3703.1.l.f.706.1 10 23.18 even 11
3703.1.l.f.706.1 10 161.41 odd 22
3703.1.l.f.2911.1 10 23.4 even 11
3703.1.l.f.2911.1 10 161.27 odd 22
3703.1.l.g.1392.1 10 23.6 even 11
3703.1.l.g.1392.1 10 161.6 odd 22
3703.1.l.g.3429.1 10 23.12 even 11
3703.1.l.g.3429.1 10 161.104 odd 22
3703.1.l.h.118.1 10 23.20 odd 22
3703.1.l.h.118.1 10 161.20 even 22
3703.1.l.h.3044.1 10 23.22 odd 2
3703.1.l.h.3044.1 10 161.160 even 2
3703.1.l.i.118.1 10 23.3 even 11 inner
3703.1.l.i.118.1 10 161.118 odd 22 inner
3703.1.l.i.3044.1 10 1.1 even 1 trivial
3703.1.l.i.3044.1 10 7.6 odd 2 CM