Properties

Label 2209.1.d.a.2007.1
Level $2209$
Weight $1$
Character 2209.2007
Analytic conductor $1.102$
Analytic rank $0$
Dimension $44$
Projective image $D_{5}$
CM discriminant -47
Inner twists $44$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2209,1,Mod(67,2209)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2209, base_ring=CyclotomicField(46))
 
chi = DirichletCharacter(H, H._module([37]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2209.67");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2209 = 47^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2209.d (of order \(46\), degree \(22\), 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: \(1.10243461291\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(2\) over \(\Q(\zeta_{46})\)
Coefficient field: 44.0.3714575655453538975253519356486345582985254755453847127268314361572265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{44} - x^{43} + 2 x^{42} - 3 x^{41} + 5 x^{40} - 8 x^{39} + 13 x^{38} - 21 x^{37} + 34 x^{36} - 55 x^{35} + 89 x^{34} - 144 x^{33} + 233 x^{32} - 377 x^{31} + 610 x^{30} - 987 x^{29} + 1597 x^{28} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 47)
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.2209.1

Embedding invariants

Embedding label 2007.1
Root \(-0.329199 + 1.58419i\) of defining polynomial
Character \(\chi\) \(=\) 2209.2007
Dual form 2209.1.d.a.339.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.329199 + 1.58419i) q^{2} +(0.421841 - 0.451681i) q^{3} +(-1.48408 - 0.644627i) q^{4} +(0.576680 + 0.816970i) q^{6} +(1.25513 - 1.02112i) q^{7} +(0.576680 - 0.816970i) q^{8} +(0.0421761 + 0.616593i) q^{9} +O(q^{10})\) \(q+(-0.329199 + 1.58419i) q^{2} +(0.421841 - 0.451681i) q^{3} +(-1.48408 - 0.644627i) q^{4} +(0.576680 + 0.816970i) q^{6} +(1.25513 - 1.02112i) q^{7} +(0.576680 - 0.816970i) q^{8} +(0.0421761 + 0.616593i) q^{9} +(-0.917211 + 0.398401i) q^{12} +(1.20447 + 2.32451i) q^{14} +(-0.206967 - 0.582349i) q^{17} +(-0.990686 - 0.136167i) q^{18} +(0.0682424 - 0.997669i) q^{21} +(-0.125743 - 0.605107i) q^{24} +(0.854419 + 0.519584i) q^{25} +(0.775711 + 0.631088i) q^{27} +(-2.52095 + 0.706337i) q^{28} +(0.854419 - 0.519584i) q^{32} +(0.990686 - 0.136167i) q^{34} +(0.334880 - 0.942261i) q^{36} +(0.284336 - 0.548743i) q^{37} +(1.55803 + 0.436540i) q^{42} +(0.329199 - 1.58419i) q^{49} +(-1.10439 + 1.18252i) q^{50} +(-0.350344 - 0.152176i) q^{51} +(0.933088 + 1.32189i) q^{53} +(-1.25513 + 1.02112i) q^{54} +(-0.110419 - 1.61426i) q^{56} +(1.48408 - 0.644627i) q^{59} +(-0.744401 - 1.43663i) q^{61} +(0.682553 + 0.730836i) q^{63} +(0.541847 + 1.52461i) q^{64} +(-0.0682424 + 0.997669i) q^{68} +(0.125743 + 0.605107i) q^{71} +(0.528060 + 0.321121i) q^{72} +(0.775711 + 0.631088i) q^{74} +(0.595116 - 0.166744i) q^{75} +(0.528060 - 0.321121i) q^{79} +(-0.669759 + 1.88452i) q^{83} +(-0.744401 + 1.43663i) q^{84} +(-1.55803 - 0.436540i) q^{89} +(0.125743 - 0.605107i) q^{96} +(-1.10439 + 1.18252i) q^{97} +(2.40129 + 1.04303i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + q^{2} + q^{3} - q^{4} + 2 q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + q^{2} + q^{3} - q^{4} + 2 q^{6} + q^{7} + 2 q^{8} - q^{9} - 2 q^{12} - 3 q^{14} + q^{17} - 2 q^{18} + 2 q^{21} - q^{24} - 2 q^{25} + 2 q^{27} + 3 q^{28} - 2 q^{32} + 2 q^{34} + 2 q^{36} + q^{37} - q^{42} - q^{49} + q^{50} - 3 q^{51} + q^{53} - q^{54} - q^{56} + q^{59} + q^{61} - 2 q^{63} + q^{64} - 2 q^{68} + q^{71} + q^{72} + 2 q^{74} + q^{75} + q^{79} - 4 q^{83} + q^{84} + q^{89} + q^{96} + q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2209\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{27}{46}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.329199 + 1.58419i −0.329199 + 1.58419i 0.410892 + 0.911684i \(0.365217\pi\)
−0.740091 + 0.672507i \(0.765217\pi\)
\(3\) 0.421841 0.451681i 0.421841 0.451681i −0.484146 0.874987i \(-0.660870\pi\)
0.905987 + 0.423306i \(0.139130\pi\)
\(4\) −1.48408 0.644627i −1.48408 0.644627i
\(5\) 0 0 −0.962917 0.269797i \(-0.913043\pi\)
0.962917 + 0.269797i \(0.0869565\pi\)
\(6\) 0.576680 + 0.816970i 0.576680 + 0.816970i
\(7\) 1.25513 1.02112i 1.25513 1.02112i 0.256619 0.966513i \(-0.417391\pi\)
0.998508 0.0546092i \(-0.0173913\pi\)
\(8\) 0.576680 0.816970i 0.576680 0.816970i
\(9\) 0.0421761 + 0.616593i 0.0421761 + 0.616593i
\(10\) 0 0
\(11\) 0 0 0.334880 0.942261i \(-0.391304\pi\)
−0.334880 + 0.942261i \(0.608696\pi\)
\(12\) −0.917211 + 0.398401i −0.917211 + 0.398401i
\(13\) 0 0 0.990686 0.136167i \(-0.0434783\pi\)
−0.990686 + 0.136167i \(0.956522\pi\)
\(14\) 1.20447 + 2.32451i 1.20447 + 2.32451i
\(15\) 0 0
\(16\) 0 0
\(17\) −0.206967 0.582349i −0.206967 0.582349i 0.792660 0.609664i \(-0.208696\pi\)
−0.999627 + 0.0273148i \(0.991304\pi\)
\(18\) −0.990686 0.136167i −0.990686 0.136167i
\(19\) 0 0 0.962917 0.269797i \(-0.0869565\pi\)
−0.962917 + 0.269797i \(0.913043\pi\)
\(20\) 0 0
\(21\) 0.0682424 0.997669i 0.0682424 0.997669i
\(22\) 0 0
\(23\) 0 0 −0.203456 0.979084i \(-0.565217\pi\)
0.203456 + 0.979084i \(0.434783\pi\)
\(24\) −0.125743 0.605107i −0.125743 0.605107i
\(25\) 0.854419 + 0.519584i 0.854419 + 0.519584i
\(26\) 0 0
\(27\) 0.775711 + 0.631088i 0.775711 + 0.631088i
\(28\) −2.52095 + 0.706337i −2.52095 + 0.706337i
\(29\) 0 0 −0.990686 0.136167i \(-0.956522\pi\)
0.990686 + 0.136167i \(0.0434783\pi\)
\(30\) 0 0
\(31\) 0 0 −0.682553 0.730836i \(-0.739130\pi\)
0.682553 + 0.730836i \(0.260870\pi\)
\(32\) 0.854419 0.519584i 0.854419 0.519584i
\(33\) 0 0
\(34\) 0.990686 0.136167i 0.990686 0.136167i
\(35\) 0 0
\(36\) 0.334880 0.942261i 0.334880 0.942261i
\(37\) 0.284336 0.548743i 0.284336 0.548743i −0.702261 0.711919i \(-0.747826\pi\)
0.986597 + 0.163176i \(0.0521739\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.576680 0.816970i \(-0.695652\pi\)
0.576680 + 0.816970i \(0.304348\pi\)
\(42\) 1.55803 + 0.436540i 1.55803 + 0.436540i
\(43\) 0 0 −0.917211 0.398401i \(-0.869565\pi\)
0.917211 + 0.398401i \(0.130435\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0
\(48\) 0 0
\(49\) 0.329199 1.58419i 0.329199 1.58419i
\(50\) −1.10439 + 1.18252i −1.10439 + 1.18252i
\(51\) −0.350344 0.152176i −0.350344 0.152176i
\(52\) 0 0
\(53\) 0.933088 + 1.32189i 0.933088 + 1.32189i 0.946747 + 0.321978i \(0.104348\pi\)
−0.0136587 + 0.999907i \(0.504348\pi\)
\(54\) −1.25513 + 1.02112i −1.25513 + 1.02112i
\(55\) 0 0
\(56\) −0.110419 1.61426i −0.110419 1.61426i
\(57\) 0 0
\(58\) 0 0
\(59\) 1.48408 0.644627i 1.48408 0.644627i 0.507865 0.861437i \(-0.330435\pi\)
0.976214 + 0.216810i \(0.0695652\pi\)
\(60\) 0 0
\(61\) −0.744401 1.43663i −0.744401 1.43663i −0.894086 0.447895i \(-0.852174\pi\)
0.149685 0.988734i \(-0.452174\pi\)
\(62\) 0 0
\(63\) 0.682553 + 0.730836i 0.682553 + 0.730836i
\(64\) 0.541847 + 1.52461i 0.541847 + 1.52461i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.775711 0.631088i \(-0.782609\pi\)
0.775711 + 0.631088i \(0.217391\pi\)
\(68\) −0.0682424 + 0.997669i −0.0682424 + 0.997669i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.125743 + 0.605107i 0.125743 + 0.605107i 0.994036 + 0.109055i \(0.0347826\pi\)
−0.868293 + 0.496052i \(0.834783\pi\)
\(72\) 0.528060 + 0.321121i 0.528060 + 0.321121i
\(73\) 0 0 0.0682424 0.997669i \(-0.478261\pi\)
−0.0682424 + 0.997669i \(0.521739\pi\)
\(74\) 0.775711 + 0.631088i 0.775711 + 0.631088i
\(75\) 0.595116 0.166744i 0.595116 0.166744i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.528060 0.321121i 0.528060 0.321121i −0.230124 0.973161i \(-0.573913\pi\)
0.758184 + 0.652041i \(0.226087\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.669759 + 1.88452i −0.669759 + 1.88452i −0.334880 + 0.942261i \(0.608696\pi\)
−0.334880 + 0.942261i \(0.608696\pi\)
\(84\) −0.744401 + 1.43663i −0.744401 + 1.43663i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.55803 0.436540i −1.55803 0.436540i −0.620434 0.784259i \(-0.713043\pi\)
−0.937599 + 0.347718i \(0.886957\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.125743 0.605107i 0.125743 0.605107i
\(97\) −1.10439 + 1.18252i −1.10439 + 1.18252i −0.122622 + 0.992453i \(0.539130\pi\)
−0.981772 + 0.190064i \(0.939130\pi\)
\(98\) 2.40129 + 1.04303i 2.40129 + 1.04303i
\(99\) 0 0
\(100\) −0.933088 1.32189i −0.933088 1.32189i
\(101\) −0.479416 + 0.390034i −0.479416 + 0.390034i −0.839908 0.542728i \(-0.817391\pi\)
0.360492 + 0.932762i \(0.382609\pi\)
\(102\) 0.356408 0.504915i 0.356408 0.504915i
\(103\) −0.0421761 0.616593i −0.0421761 0.616593i −0.969927 0.243394i \(-0.921739\pi\)
0.927751 0.373199i \(-0.121739\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.40129 + 1.04303i −2.40129 + 1.04303i
\(107\) 0 0 0.990686 0.136167i \(-0.0434783\pi\)
−0.990686 + 0.136167i \(0.956522\pi\)
\(108\) −0.744401 1.43663i −0.744401 1.43663i
\(109\) 0 0 0.854419 0.519584i \(-0.173913\pi\)
−0.854419 + 0.519584i \(0.826087\pi\)
\(110\) 0 0
\(111\) −0.127913 0.359912i −0.127913 0.359912i
\(112\) 0 0
\(113\) 0 0 0.962917 0.269797i \(-0.0869565\pi\)
−0.962917 + 0.269797i \(0.913043\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.532655 + 2.56328i 0.532655 + 2.56328i
\(119\) −0.854419 0.519584i −0.854419 0.519584i
\(120\) 0 0
\(121\) −0.775711 0.631088i −0.775711 0.631088i
\(122\) 2.52095 0.706337i 2.52095 0.706337i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −1.38248 + 0.840704i −1.38248 + 0.840704i
\(127\) 0 0 −0.460065 0.887885i \(-0.652174\pi\)
0.460065 + 0.887885i \(0.347826\pi\)
\(128\) −1.60296 + 0.220322i −1.60296 + 0.220322i
\(129\) 0 0
\(130\) 0 0
\(131\) −0.744401 + 1.43663i −0.744401 + 1.43663i 0.149685 + 0.988734i \(0.452174\pi\)
−0.894086 + 0.447895i \(0.852174\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.595116 0.166744i −0.595116 0.166744i
\(137\) 0 0 −0.917211 0.398401i \(-0.869565\pi\)
0.917211 + 0.398401i \(0.130435\pi\)
\(138\) 0 0
\(139\) 0 0 0.203456 0.979084i \(-0.434783\pi\)
−0.203456 + 0.979084i \(0.565217\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.00000 −1.00000
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.576680 0.816970i −0.576680 0.816970i
\(148\) −0.775711 + 0.631088i −0.775711 + 0.631088i
\(149\) −0.356408 + 0.504915i −0.356408 + 0.504915i −0.955189 0.295998i \(-0.904348\pi\)
0.598781 + 0.800913i \(0.295652\pi\)
\(150\) 0.0682424 + 0.997669i 0.0682424 + 0.997669i
\(151\) 0 0 0.460065 0.887885i \(-0.347826\pi\)
−0.460065 + 0.887885i \(0.652174\pi\)
\(152\) 0 0
\(153\) 0.350344 0.152176i 0.350344 0.152176i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.10439 1.18252i −1.10439 1.18252i −0.981772 0.190064i \(-0.939130\pi\)
−0.122622 0.992453i \(-0.539130\pi\)
\(158\) 0.334880 + 0.942261i 0.334880 + 0.942261i
\(159\) 0.990686 + 0.136167i 0.990686 + 0.136167i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 −0.854419 0.519584i \(-0.826087\pi\)
0.854419 + 0.519584i \(0.173913\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −2.76496 1.68141i −2.76496 1.68141i
\(167\) 0 0 0.0682424 0.997669i \(-0.478261\pi\)
−0.0682424 + 0.997669i \(0.521739\pi\)
\(168\) −0.775711 0.631088i −0.775711 0.631088i
\(169\) 0.962917 0.269797i 0.962917 0.269797i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.38248 + 0.840704i −1.38248 + 0.840704i −0.996644 0.0818629i \(-0.973913\pi\)
−0.385836 + 0.922567i \(0.626087\pi\)
\(174\) 0 0
\(175\) 1.60296 0.220322i 1.60296 0.220322i
\(176\) 0 0
\(177\) 0.334880 0.942261i 0.334880 0.942261i
\(178\) 1.20447 2.32451i 1.20447 2.32451i
\(179\) 0 0 −0.0682424 0.997669i \(-0.521739\pi\)
0.0682424 + 0.997669i \(0.478261\pi\)
\(180\) 0 0
\(181\) 0 0 0.775711 0.631088i \(-0.217391\pi\)
−0.775711 + 0.631088i \(0.782609\pi\)
\(182\) 0 0
\(183\) −0.962917 0.269797i −0.962917 0.269797i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.61803 1.61803
\(190\) 0 0
\(191\) 1.36511 1.46167i 1.36511 1.46167i 0.682553 0.730836i \(-0.260870\pi\)
0.682553 0.730836i \(-0.260870\pi\)
\(192\) 0.917211 + 0.398401i 0.917211 + 0.398401i
\(193\) 0 0 −0.962917 0.269797i \(-0.913043\pi\)
0.962917 + 0.269797i \(0.0869565\pi\)
\(194\) −1.50977 2.13885i −1.50977 2.13885i
\(195\) 0 0
\(196\) −1.50977 + 2.13885i −1.50977 + 2.13885i
\(197\) −0.136485 1.99534i −0.136485 1.99534i −0.0682424 0.997669i \(-0.521739\pi\)
−0.0682424 0.997669i \(-0.521739\pi\)
\(198\) 0 0
\(199\) 0 0 0.334880 0.942261i \(-0.391304\pi\)
−0.334880 + 0.942261i \(0.608696\pi\)
\(200\) 0.917211 0.398401i 0.917211 0.398401i
\(201\) 0 0
\(202\) −0.460065 0.887885i −0.460065 0.887885i
\(203\) 0 0
\(204\) 0.421841 + 0.451681i 0.421841 + 0.451681i
\(205\) 0 0
\(206\) 0.990686 + 0.136167i 0.990686 + 0.136167i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.203456 0.979084i \(-0.565217\pi\)
0.203456 + 0.979084i \(0.434783\pi\)
\(212\) −0.532655 2.56328i −0.532655 2.56328i
\(213\) 0.326359 + 0.198463i 0.326359 + 0.198463i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.962917 0.269797i 0.962917 0.269797i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0.612278 0.0841556i 0.612278 0.0841556i
\(223\) 0 0 0.917211 0.398401i \(-0.130435\pi\)
−0.917211 + 0.398401i \(0.869565\pi\)
\(224\) 0.541847 1.52461i 0.541847 1.52461i
\(225\) −0.284336 + 0.548743i −0.284336 + 0.548743i
\(226\) 0 0
\(227\) 0 0 0.576680 0.816970i \(-0.304348\pi\)
−0.576680 + 0.816970i \(0.695652\pi\)
\(228\) 0 0
\(229\) 0 0 −0.576680 0.816970i \(-0.695652\pi\)
0.576680 + 0.816970i \(0.304348\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.203456 0.979084i \(-0.434783\pi\)
−0.203456 + 0.979084i \(0.565217\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −2.61803 −2.61803
\(237\) 0.0777133 0.373977i 0.0777133 0.373977i
\(238\) 1.10439 1.18252i 1.10439 1.18252i
\(239\) −0.566868 0.246225i −0.566868 0.246225i 0.0954681 0.995432i \(-0.469565\pi\)
−0.662336 + 0.749207i \(0.730435\pi\)
\(240\) 0 0
\(241\) −0.356408 0.504915i −0.356408 0.504915i 0.598781 0.800913i \(-0.295652\pi\)
−0.955189 + 0.295998i \(0.904348\pi\)
\(242\) 1.25513 1.02112i 1.25513 1.02112i
\(243\) −0.576680 + 0.816970i −0.576680 + 0.816970i
\(244\) 0.178661 + 2.61193i 0.178661 + 2.61193i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0.568672 + 1.09749i 0.568672 + 1.09749i
\(250\) 0 0
\(251\) 0.421841 + 0.451681i 0.421841 + 0.451681i 0.905987 0.423306i \(-0.139130\pi\)
−0.484146 + 0.874987i \(0.660870\pi\)
\(252\) −0.541847 1.52461i −0.541847 1.52461i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.0682424 0.997669i 0.0682424 0.997669i
\(257\) 0 0 −0.854419 0.519584i \(-0.826087\pi\)
0.854419 + 0.519584i \(0.173913\pi\)
\(258\) 0 0
\(259\) −0.203456 0.979084i −0.203456 0.979084i
\(260\) 0 0
\(261\) 0 0
\(262\) −2.03084 1.65221i −2.03084 1.65221i
\(263\) −1.55803 + 0.436540i −1.55803 + 0.436540i −0.937599 0.347718i \(-0.886957\pi\)
−0.620434 + 0.784259i \(0.713043\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.854419 + 0.519584i −0.854419 + 0.519584i
\(268\) 0 0
\(269\) −1.98137 + 0.272333i −1.98137 + 0.272333i −0.990686 + 0.136167i \(0.956522\pi\)
−0.990686 + 0.136167i \(0.956522\pi\)
\(270\) 0 0
\(271\) −0.206967 + 0.582349i −0.206967 + 0.582349i −0.999627 0.0273148i \(-0.991304\pi\)
0.792660 + 0.609664i \(0.208696\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.595116 + 0.166744i 0.595116 + 0.166744i 0.554150 0.832417i \(-0.313043\pi\)
0.0409658 + 0.999161i \(0.486957\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(284\) 0.203456 0.979084i 0.203456 0.979084i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.356408 + 0.504915i 0.356408 + 0.504915i
\(289\) 0.479416 0.390034i 0.479416 0.390034i
\(290\) 0 0
\(291\) 0.0682424 + 0.997669i 0.0682424 + 0.997669i
\(292\) 0 0
\(293\) 0 0 0.334880 0.942261i \(-0.391304\pi\)
−0.334880 + 0.942261i \(0.608696\pi\)
\(294\) 1.48408 0.644627i 1.48408 0.644627i
\(295\) 0 0
\(296\) −0.284336 0.548743i −0.284336 0.548743i
\(297\) 0 0
\(298\) −0.682553 0.730836i −0.682553 0.730836i
\(299\) 0 0
\(300\) −0.990686 0.136167i −0.990686 0.136167i
\(301\) 0 0
\(302\) 0 0
\(303\) −0.0260663 + 0.381076i −0.0260663 + 0.381076i
\(304\) 0 0
\(305\) 0 0
\(306\) 0.125743 + 0.605107i 0.125743 + 0.605107i
\(307\) 0.528060 + 0.321121i 0.528060 + 0.321121i 0.758184 0.652041i \(-0.226087\pi\)
−0.230124 + 0.973161i \(0.573913\pi\)
\(308\) 0 0
\(309\) −0.296295 0.241054i −0.296295 0.241054i
\(310\) 0 0
\(311\) 0 0 −0.990686 0.136167i \(-0.956522\pi\)
0.990686 + 0.136167i \(0.0434783\pi\)
\(312\) 0 0
\(313\) 0 0 −0.682553 0.730836i \(-0.739130\pi\)
0.682553 + 0.730836i \(0.260870\pi\)
\(314\) 2.23690 1.36029i 2.23690 1.36029i
\(315\) 0 0
\(316\) −0.990686 + 0.136167i −0.990686 + 0.136167i
\(317\) 0 0 0.917211 0.398401i \(-0.130435\pi\)
−0.917211 + 0.398401i \(0.869565\pi\)
\(318\) −0.541847 + 1.52461i −0.541847 + 1.52461i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.329199 + 1.58419i −0.329199 + 1.58419i 0.410892 + 0.911684i \(0.365217\pi\)
−0.740091 + 0.672507i \(0.765217\pi\)
\(332\) 2.20879 2.36503i 2.20879 2.36503i
\(333\) 0.350344 + 0.152176i 0.350344 + 0.152176i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.933088 1.32189i 0.933088 1.32189i −0.0136587 0.999907i \(-0.504348\pi\)
0.946747 0.321978i \(-0.104348\pi\)
\(338\) 0.110419 + 1.61426i 0.110419 + 1.61426i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.460065 0.887885i −0.460065 0.887885i
\(344\) 0 0
\(345\) 0 0
\(346\) −0.876726 2.46687i −0.876726 2.46687i
\(347\) −0.612278 0.0841556i −0.612278 0.0841556i −0.176637 0.984276i \(-0.556522\pi\)
−0.435641 + 0.900121i \(0.643478\pi\)
\(348\) 0 0
\(349\) 0 0 −0.775711 0.631088i \(-0.782609\pi\)
0.775711 + 0.631088i \(0.217391\pi\)
\(350\) −0.178661 + 2.61193i −0.178661 + 2.61193i
\(351\) 0 0
\(352\) 0 0
\(353\) −0.329199 1.58419i −0.329199 1.58419i −0.740091 0.672507i \(-0.765217\pi\)
0.410892 0.911684i \(-0.365217\pi\)
\(354\) 1.38248 + 0.840704i 1.38248 + 0.840704i
\(355\) 0 0
\(356\) 2.03084 + 1.65221i 2.03084 + 1.65221i
\(357\) −0.595116 + 0.166744i −0.595116 + 0.166744i
\(358\) 0 0
\(359\) 0 0 −0.334880 0.942261i \(-0.608696\pi\)
0.334880 + 0.942261i \(0.391304\pi\)
\(360\) 0 0
\(361\) 0.854419 0.519584i 0.854419 0.519584i
\(362\) 0 0
\(363\) −0.612278 + 0.0841556i −0.612278 + 0.0841556i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.744401 1.43663i 0.744401 1.43663i
\(367\) 0 0 −0.0682424 0.997669i \(-0.521739\pi\)
0.0682424 + 0.997669i \(0.478261\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.52095 + 0.706337i 2.52095 + 0.706337i
\(372\) 0 0
\(373\) 0 0 0.682553 0.730836i \(-0.260870\pi\)
−0.682553 + 0.730836i \(0.739130\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) −0.532655 + 2.56328i −0.532655 + 2.56328i
\(379\) −1.10439 + 1.18252i −1.10439 + 1.18252i −0.122622 + 0.992453i \(0.539130\pi\)
−0.981772 + 0.190064i \(0.939130\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.86618 + 2.64377i 1.86618 + 2.64377i
\(383\) −0.479416 + 0.390034i −0.479416 + 0.390034i −0.839908 0.542728i \(-0.817391\pi\)
0.360492 + 0.932762i \(0.382609\pi\)
\(384\) −0.576680 + 0.816970i −0.576680 + 0.816970i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 2.40129 1.04303i 2.40129 1.04303i
\(389\) 0 0 0.990686 0.136167i \(-0.0434783\pi\)
−0.990686 + 0.136167i \(0.956522\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.10439 1.18252i −1.10439 1.18252i
\(393\) 0.334880 + 0.942261i 0.334880 + 0.942261i
\(394\) 3.20593 + 0.440645i 3.20593 + 0.440645i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.0421761 + 0.616593i −0.0421761 + 0.616593i 0.927751 + 0.373199i \(0.121739\pi\)
−0.969927 + 0.243394i \(0.921739\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.528060 + 0.321121i 0.528060 + 0.321121i 0.758184 0.652041i \(-0.226087\pi\)
−0.230124 + 0.973161i \(0.573913\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.962917 0.269797i 0.962917 0.269797i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.326359 + 0.198463i −0.326359 + 0.198463i
\(409\) 0 0 −0.460065 0.887885i \(-0.652174\pi\)
0.460065 + 0.887885i \(0.347826\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.334880 + 0.942261i −0.334880 + 0.942261i
\(413\) 1.20447 2.32451i 1.20447 2.32451i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.917211 0.398401i \(-0.869565\pi\)
0.917211 + 0.398401i \(0.130435\pi\)
\(420\) 0 0
\(421\) 0 0 0.203456 0.979084i \(-0.434783\pi\)
−0.203456 + 0.979084i \(0.565217\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 1.61803 1.61803
\(425\) 0.125743 0.605107i 0.125743 0.605107i
\(426\) −0.421841 + 0.451681i −0.421841 + 0.451681i
\(427\) −2.40129 1.04303i −2.40129 1.04303i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.933088 1.32189i 0.933088 1.32189i −0.0136587 0.999907i \(-0.504348\pi\)
0.946747 0.321978i \(-0.104348\pi\)
\(432\) 0 0
\(433\) 0 0 0.460065 0.887885i \(-0.347826\pi\)
−0.460065 + 0.887885i \(0.652174\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 1.36511 + 1.46167i 1.36511 + 1.46167i 0.682553 + 0.730836i \(0.260870\pi\)
0.682553 + 0.730836i \(0.260870\pi\)
\(440\) 0 0
\(441\) 0.990686 + 0.136167i 0.990686 + 0.136167i
\(442\) 0 0
\(443\) 0 0 −0.775711 0.631088i \(-0.782609\pi\)
0.775711 + 0.631088i \(0.217391\pi\)
\(444\) −0.0421761 + 0.616593i −0.0421761 + 0.616593i
\(445\) 0 0
\(446\) 0 0
\(447\) 0.0777133 + 0.373977i 0.0777133 + 0.373977i
\(448\) 2.23690 + 1.36029i 2.23690 + 1.36029i
\(449\) 0 0 0.0682424 0.997669i \(-0.478261\pi\)
−0.0682424 + 0.997669i \(0.521739\pi\)
\(450\) −0.775711 0.631088i −0.775711 0.631088i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.612278 + 0.0841556i −0.612278 + 0.0841556i −0.435641 0.900121i \(-0.643478\pi\)
−0.176637 + 0.984276i \(0.556522\pi\)
\(458\) 0 0
\(459\) 0.206967 0.582349i 0.206967 0.582349i
\(460\) 0 0
\(461\) 0 0 −0.0682424 0.997669i \(-0.521739\pi\)
0.0682424 + 0.997669i \(0.478261\pi\)
\(462\) 0 0
\(463\) 0 0 0.775711 0.631088i \(-0.217391\pi\)
−0.775711 + 0.631088i \(0.782609\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.682553 0.730836i \(-0.260870\pi\)
−0.682553 + 0.730836i \(0.739130\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 −1.00000
\(472\) 0.329199 1.58419i 0.329199 1.58419i
\(473\) 0 0
\(474\) 0.566868 + 0.246225i 0.566868 + 0.246225i
\(475\) 0 0
\(476\) 0.933088 + 1.32189i 0.933088 + 1.32189i
\(477\) −0.775711 + 0.631088i −0.775711 + 0.631088i
\(478\) 0.576680 0.816970i 0.576680 0.816970i
\(479\) 0.110419 + 1.61426i 0.110419 + 1.61426i 0.641624 + 0.767019i \(0.278261\pi\)
−0.531206 + 0.847243i \(0.678261\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.917211 0.398401i 0.917211 0.398401i
\(483\) 0 0
\(484\) 0.744401 + 1.43663i 0.744401 + 1.43663i
\(485\) 0 0
\(486\) −1.10439 1.18252i −1.10439 1.18252i
\(487\) −0.669759 1.88452i −0.669759 1.88452i −0.334880 0.942261i \(-0.608696\pi\)
−0.334880 0.942261i \(-0.608696\pi\)
\(488\) −1.60296 0.220322i −1.60296 0.220322i
\(489\) 0 0
\(490\) 0 0
\(491\) 0.110419 1.61426i 0.110419 1.61426i −0.531206 0.847243i \(-0.678261\pi\)
0.641624 0.767019i \(-0.278261\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.775711 + 0.631088i 0.775711 + 0.631088i
\(498\) −1.92583 + 0.539594i −1.92583 + 0.539594i
\(499\) 0 0 −0.990686 0.136167i \(-0.956522\pi\)
0.990686 + 0.136167i \(0.0434783\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.854419 + 0.519584i −0.854419 + 0.519584i
\(503\) 0 0 −0.460065 0.887885i \(-0.652174\pi\)
0.460065 + 0.887885i \(0.347826\pi\)
\(504\) 0.990686 0.136167i 0.990686 0.136167i
\(505\) 0 0
\(506\) 0 0
\(507\) 0.284336 0.548743i 0.284336 0.548743i
\(508\) 0 0
\(509\) 0 0 0.576680 0.816970i \(-0.304348\pi\)
−0.576680 + 0.816970i \(0.695652\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.61803 1.61803
\(519\) −0.203456 + 0.979084i −0.203456 + 0.979084i
\(520\) 0 0
\(521\) 1.48408 + 0.644627i 1.48408 + 0.644627i 0.976214 0.216810i \(-0.0695652\pi\)
0.507865 + 0.861437i \(0.330435\pi\)
\(522\) 0 0
\(523\) −1.15336 1.63394i −1.15336 1.63394i −0.576680 0.816970i \(-0.695652\pi\)
−0.576680 0.816970i \(-0.695652\pi\)
\(524\) 2.03084 1.65221i 2.03084 1.65221i
\(525\) 0.576680 0.816970i 0.576680 0.816970i
\(526\) −0.178661 2.61193i −0.178661 2.61193i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.917211 + 0.398401i −0.917211 + 0.398401i
\(530\) 0 0
\(531\) 0.460065 + 0.887885i 0.460065 + 0.887885i
\(532\) 0 0
\(533\) 0 0
\(534\) −0.541847 1.52461i −0.541847 1.52461i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0.220837 3.22852i 0.220837 3.22852i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.329199 1.58419i −0.329199 1.58419i −0.740091 0.672507i \(-0.765217\pi\)
0.410892 0.911684i \(-0.365217\pi\)
\(542\) −0.854419 0.519584i −0.854419 0.519584i
\(543\) 0 0
\(544\) −0.479416 0.390034i −0.479416 0.390034i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.334880 0.942261i \(-0.608696\pi\)
0.334880 + 0.942261i \(0.391304\pi\)
\(548\) 0 0
\(549\) 0.854419 0.519584i 0.854419 0.519584i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0.334880 0.942261i 0.334880 0.942261i
\(554\) −0.460065 + 0.887885i −0.460065 + 0.887885i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.775711 0.631088i \(-0.217391\pi\)
−0.775711 + 0.631088i \(0.782609\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.532655 2.56328i 0.532655 2.56328i
\(567\) 0 0
\(568\) 0.566868 + 0.246225i 0.566868 + 0.246225i
\(569\) 0 0 −0.962917 0.269797i \(-0.913043\pi\)
0.962917 + 0.269797i \(0.0869565\pi\)
\(570\) 0 0
\(571\) −0.479416 + 0.390034i −0.479416 + 0.390034i −0.839908 0.542728i \(-0.817391\pi\)
0.360492 + 0.932762i \(0.382609\pi\)
\(572\) 0 0
\(573\) −0.0843523 1.23319i −0.0843523 1.23319i
\(574\) 0 0
\(575\) 0 0
\(576\) −0.917211 + 0.398401i −0.917211 + 0.398401i
\(577\) 0 0 0.990686 0.136167i \(-0.0434783\pi\)
−0.990686 + 0.136167i \(0.956522\pi\)
\(578\) 0.460065 + 0.887885i 0.460065 + 0.887885i
\(579\) 0 0
\(580\) 0 0
\(581\) 1.08369 + 3.04922i 1.08369 + 3.04922i
\(582\) −1.60296 0.220322i −1.60296 0.220322i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.203456 0.979084i \(-0.565217\pi\)
0.203456 + 0.979084i \(0.434783\pi\)
\(588\) 0.329199 + 1.58419i 0.329199 + 1.58419i
\(589\) 0 0
\(590\) 0 0
\(591\) −0.958832 0.780068i −0.958832 0.780068i
\(592\) 0 0
\(593\) 0 0 −0.990686 0.136167i \(-0.956522\pi\)
0.990686 + 0.136167i \(0.0434783\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.854419 0.519584i 0.854419 0.519584i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.917211 0.398401i \(-0.130435\pi\)
−0.917211 + 0.398401i \(0.869565\pi\)
\(600\) 0.206967 0.582349i 0.206967 0.582349i
\(601\) −0.744401 + 1.43663i −0.744401 + 1.43663i 0.149685 + 0.988734i \(0.452174\pi\)
−0.894086 + 0.447895i \(0.852174\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −0.595116 0.166744i −0.595116 0.166744i
\(607\) 0 0 −0.917211 0.398401i \(-0.869565\pi\)
0.917211 + 0.398401i \(0.130435\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.618034 −0.618034
\(613\) −0.329199 + 1.58419i −0.329199 + 1.58419i 0.410892 + 0.911684i \(0.365217\pi\)
−0.740091 + 0.672507i \(0.765217\pi\)
\(614\) −0.682553 + 0.730836i −0.682553 + 0.730836i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.356408 0.504915i −0.356408 0.504915i 0.598781 0.800913i \(-0.295652\pi\)
−0.955189 + 0.295998i \(0.904348\pi\)
\(618\) 0.479416 0.390034i 0.479416 0.390034i
\(619\) −1.15336 + 1.63394i −1.15336 + 1.63394i −0.576680 + 0.816970i \(0.695652\pi\)
−0.576680 + 0.816970i \(0.695652\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.40129 + 1.04303i −2.40129 + 1.04303i
\(624\) 0 0
\(625\) 0.460065 + 0.887885i 0.460065 + 0.887885i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.876726 + 2.46687i 0.876726 + 2.46687i
\(629\) −0.378408 0.0520110i −0.378408 0.0520110i
\(630\) 0 0
\(631\) 0 0 −0.775711 0.631088i \(-0.782609\pi\)
0.775711 + 0.631088i \(0.217391\pi\)
\(632\) 0.0421761 0.616593i 0.0421761 0.616593i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −1.38248 0.840704i −1.38248 0.840704i
\(637\) 0 0
\(638\) 0 0
\(639\) −0.367802 + 0.103053i −0.367802 + 0.103053i
\(640\) 0 0
\(641\) 0 0 −0.334880 0.942261i \(-0.608696\pi\)
0.334880 + 0.942261i \(0.391304\pi\)
\(642\) 0 0
\(643\) −1.38248 + 0.840704i −1.38248 + 0.840704i −0.996644 0.0818629i \(-0.973913\pi\)
−0.385836 + 0.922567i \(0.626087\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.541847 1.52461i 0.541847 1.52461i −0.282924 0.959142i \(-0.591304\pi\)
0.824770 0.565468i \(-0.191304\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.595116 + 0.166744i 0.595116 + 0.166744i 0.554150 0.832417i \(-0.313043\pi\)
0.0409658 + 0.999161i \(0.486957\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(660\) 0 0
\(661\) 0.421841 0.451681i 0.421841 0.451681i −0.484146 0.874987i \(-0.660870\pi\)
0.905987 + 0.423306i \(0.139130\pi\)
\(662\) −2.40129 1.04303i −2.40129 1.04303i
\(663\) 0 0
\(664\) 1.15336 + 1.63394i 1.15336 + 1.63394i
\(665\) 0 0
\(666\) −0.356408 + 0.504915i −0.356408 + 0.504915i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.460065 0.887885i −0.460065 0.887885i
\(673\) 0 0 0.854419 0.519584i \(-0.173913\pi\)
−0.854419 + 0.519584i \(0.826087\pi\)
\(674\) 1.78695 + 1.91335i 1.78695 + 1.91335i
\(675\) 0.334880 + 0.942261i 0.334880 + 0.942261i
\(676\) −1.60296 0.220322i −1.60296 0.220322i
\(677\) 0 0 0.962917 0.269797i \(-0.0869565\pi\)
−0.962917 + 0.269797i \(0.913043\pi\)
\(678\) 0 0
\(679\) −0.178661 + 2.61193i −0.178661 + 2.61193i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.38248 0.840704i −1.38248 0.840704i −0.385836 0.922567i \(-0.626087\pi\)
−0.996644 + 0.0818629i \(0.973913\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.55803 0.436540i 1.55803 0.436540i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.460065 0.887885i \(-0.652174\pi\)
0.460065 + 0.887885i \(0.347826\pi\)
\(692\) 2.59365 0.356489i 2.59365 0.356489i
\(693\) 0 0
\(694\) 0.334880 0.942261i 0.334880 0.942261i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −2.52095 0.706337i −2.52095 0.706337i
\(701\) 0 0 −0.917211 0.398401i \(-0.869565\pi\)
0.917211 + 0.398401i \(0.130435\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 2.61803 2.61803
\(707\) −0.203456 + 0.979084i −0.203456 + 0.979084i
\(708\) −1.10439 + 1.18252i −1.10439 + 1.18252i
\(709\) 1.48408 + 0.644627i 1.48408 + 0.644627i 0.976214 0.216810i \(-0.0695652\pi\)
0.507865 + 0.861437i \(0.330435\pi\)
\(710\) 0 0
\(711\) 0.220272 + 0.312055i 0.220272 + 0.312055i
\(712\) −1.25513 + 1.02112i −1.25513 + 1.02112i
\(713\) 0 0
\(714\) −0.0682424 0.997669i −0.0682424 0.997669i
\(715\) 0 0
\(716\) 0 0
\(717\) −0.350344 + 0.152176i −0.350344 + 0.152176i
\(718\) 0 0
\(719\) −0.744401 1.43663i −0.744401 1.43663i −0.894086 0.447895i \(-0.852174\pi\)
0.149685 0.988734i \(-0.452174\pi\)
\(720\) 0 0
\(721\) −0.682553 0.730836i −0.682553 0.730836i
\(722\) 0.541847 + 1.52461i 0.541847 + 1.52461i
\(723\) −0.378408 0.0520110i −0.378408 0.0520110i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.0682424 0.997669i 0.0682424 0.997669i
\(727\) 0 0 −0.854419 0.519584i \(-0.826087\pi\)
0.854419 + 0.519584i \(0.173913\pi\)
\(728\) 0 0
\(729\) 0.125743 + 0.605107i 0.125743 + 0.605107i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.25513 + 1.02112i 1.25513 + 1.02112i
\(733\) 0.595116 0.166744i 0.595116 0.166744i 0.0409658 0.999161i \(-0.486957\pi\)
0.554150 + 0.832417i \(0.313043\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.60296 0.220322i 1.60296 0.220322i 0.721445 0.692472i \(-0.243478\pi\)
0.881519 + 0.472149i \(0.156522\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.94887 + 3.76114i −1.94887 + 3.76114i
\(743\) 0 0 −0.0682424 0.997669i \(-0.521739\pi\)
0.0682424 + 0.997669i \(0.478261\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.19023 0.333487i −1.19023 0.333487i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0.381966 0.381966
\(754\) 0 0
\(755\) 0 0
\(756\) −2.40129 1.04303i −2.40129 1.04303i
\(757\) 0 0 −0.962917 0.269797i \(-0.913043\pi\)
0.962917 + 0.269797i \(0.0869565\pi\)
\(758\) −1.50977 2.13885i −1.50977 2.13885i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.136485 1.99534i −0.136485 1.99534i −0.0682424 0.997669i \(-0.521739\pi\)
−0.0682424 0.997669i \(-0.521739\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2.96816 + 1.28925i −2.96816 + 1.28925i
\(765\) 0 0
\(766\) −0.460065 0.887885i −0.460065 0.887885i
\(767\) 0 0
\(768\) −0.421841 0.451681i −0.421841 0.451681i
\(769\) −0.206967 0.582349i −0.206967 0.582349i 0.792660 0.609664i \(-0.208696\pi\)
−0.999627 + 0.0273148i \(0.991304\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.0421761 + 0.616593i −0.0421761 + 0.616593i 0.927751 + 0.373199i \(0.121739\pi\)
−0.969927 + 0.243394i \(0.921739\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0.329199 + 1.58419i 0.329199 + 1.58419i
\(777\) −0.528060 0.321121i −0.528060 0.321121i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) −1.60296 + 0.220322i −1.60296 + 0.220322i
\(787\) 0 0 0.917211 0.398401i \(-0.130435\pi\)
−0.917211 + 0.398401i \(0.869565\pi\)
\(788\) −1.08369 + 3.04922i −1.08369 + 3.04922i
\(789\) −0.460065 + 0.887885i −0.460065 + 0.887885i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −0.962917 0.269797i −0.962917 0.269797i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.203456 0.979084i \(-0.434783\pi\)
−0.203456 + 0.979084i \(0.565217\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000 1.00000
\(801\) 0.203456 0.979084i 0.203456 0.979084i
\(802\) −0.682553 + 0.730836i −0.682553 + 0.730836i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −0.712816 + 1.00983i −0.712816 + 1.00983i
\(808\) 0.0421761 + 0.616593i 0.0421761 + 0.616593i
\(809\) 0 0 0.460065 0.887885i \(-0.347826\pi\)
−0.460065 + 0.887885i \(0.652174\pi\)
\(810\) 0 0
\(811\) −0.566868 + 0.246225i −0.566868 + 0.246225i −0.662336 0.749207i \(-0.730435\pi\)
0.0954681 + 0.995432i \(0.469565\pi\)
\(812\) 0 0
\(813\) 0.175729 + 0.339142i 0.175729 + 0.339142i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.854419 0.519584i \(-0.826087\pi\)
0.854419 + 0.519584i \(0.173913\pi\)
\(822\) 0 0
\(823\) 0.406912 + 1.95817i 0.406912 + 1.95817i 0.203456 + 0.979084i \(0.434783\pi\)
0.203456 + 0.979084i \(0.434783\pi\)
\(824\) −0.528060 0.321121i −0.528060 0.321121i
\(825\) 0 0
\(826\) 3.28597 + 2.67333i 3.28597 + 2.67333i
\(827\) −1.55803 + 0.436540i −1.55803 + 0.436540i −0.937599 0.347718i \(-0.886957\pi\)
−0.620434 + 0.784259i \(0.713043\pi\)
\(828\) 0 0
\(829\) 0 0 −0.334880 0.942261i \(-0.608696\pi\)
0.334880 + 0.942261i \(0.391304\pi\)
\(830\) 0 0
\(831\) 0.326359 0.198463i 0.326359 0.198463i
\(832\) 0 0
\(833\) −0.990686 + 0.136167i −0.990686 + 0.136167i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.775711 0.631088i \(-0.217391\pi\)
−0.775711 + 0.631088i \(0.782609\pi\)
\(840\) 0 0
\(841\) 0.962917 + 0.269797i 0.962917 + 0.269797i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1.61803 −1.61803
\(848\) 0 0
\(849\) −0.682553 + 0.730836i −0.682553 + 0.730836i
\(850\) 0.917211 + 0.398401i 0.917211 + 0.398401i
\(851\) 0 0
\(852\) −0.356408 0.504915i −0.356408 0.504915i
\(853\) −0.479416 + 0.390034i −0.479416 + 0.390034i −0.839908 0.542728i \(-0.817391\pi\)
0.360492 + 0.932762i \(0.382609\pi\)
\(854\) 2.44286 3.46074i 2.44286 3.46074i
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.334880 0.942261i \(-0.391304\pi\)
−0.334880 + 0.942261i \(0.608696\pi\)
\(858\) 0 0
\(859\) 0 0 0.990686 0.136167i \(-0.0434783\pi\)
−0.990686 + 0.136167i \(0.956522\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.78695 + 1.91335i 1.78695 + 1.91335i
\(863\) −0.206967 0.582349i −0.206967 0.582349i 0.792660 0.609664i \(-0.208696\pi\)
−0.999627 + 0.0273148i \(0.991304\pi\)
\(864\) 0.990686 + 0.136167i 0.990686 + 0.136167i
\(865\) 0 0
\(866\) 0 0
\(867\) 0.0260663 0.381076i 0.0260663 0.381076i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.775711 0.631088i −0.775711 0.631088i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.682553 0.730836i \(-0.739130\pi\)
0.682553 + 0.730836i \(0.260870\pi\)
\(878\) −2.76496 + 1.68141i −2.76496 + 1.68141i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.917211 0.398401i \(-0.130435\pi\)
−0.917211 + 0.398401i \(0.869565\pi\)
\(882\) −0.541847 + 1.52461i −0.541847 + 1.52461i
\(883\) −0.744401 + 1.43663i −0.744401 + 1.43663i 0.149685 + 0.988734i \(0.452174\pi\)
−0.894086 + 0.447895i \(0.852174\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.576680 0.816970i \(-0.695652\pi\)
0.576680 + 0.816970i \(0.304348\pi\)
\(888\) −0.367802 0.103053i −0.367802 0.103053i
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) −0.618034 −0.618034
\(895\) 0 0
\(896\) −1.78695 + 1.91335i −1.78695 + 1.91335i
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0.775711 0.631088i 0.775711 0.631088i
\(901\) 0.576680 0.816970i 0.576680 0.816970i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0.920130 + 1.77577i 0.920130 + 1.77577i 0.460065 + 0.887885i \(0.347826\pi\)
0.460065 + 0.887885i \(0.347826\pi\)
\(908\) 0 0
\(909\) −0.260712 0.279154i −0.260712 0.279154i
\(910\) 0 0
\(911\) 1.60296 + 0.220322i 1.60296 + 0.220322i 0.881519 0.472149i \(-0.156522\pi\)
0.721445 + 0.692472i \(0.243478\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.0682424 0.997669i 0.0682424 0.997669i
\(915\) 0 0
\(916\) 0 0
\(917\) 0.532655 + 2.56328i 0.532655 + 2.56328i
\(918\) 0.854419 + 0.519584i 0.854419 + 0.519584i
\(919\) 0 0 0.0682424 0.997669i \(-0.478261\pi\)
−0.0682424 + 0.997669i \(0.521739\pi\)
\(920\) 0 0
\(921\) 0.367802 0.103053i 0.367802 0.103053i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0.528060 0.321121i 0.528060 0.321121i
\(926\) 0 0
\(927\) 0.378408 0.0520110i 0.378408 0.0520110i
\(928\) 0 0
\(929\) −0.206967 + 0.582349i −0.206967 + 0.582349i −0.999627 0.0273148i \(-0.991304\pi\)
0.792660 + 0.609664i \(0.208696\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.682553 0.730836i \(-0.260870\pi\)
−0.682553 + 0.730836i \(0.739130\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(942\) 0.329199 1.58419i 0.329199 1.58419i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.55142 + 1.26218i −1.55142 + 1.26218i −0.775711 + 0.631088i \(0.782609\pi\)
−0.775711 + 0.631088i \(0.782609\pi\)
\(948\) −0.356408 + 0.504915i −0.356408 + 0.504915i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) −0.917211 + 0.398401i −0.917211 + 0.398401i
\(953\) 0 0 0.990686 0.136167i \(-0.0434783\pi\)
−0.990686 + 0.136167i \(0.956522\pi\)
\(954\) −0.744401 1.43663i −0.744401 1.43663i
\(955\) 0 0
\(956\) 0.682553 + 0.730836i 0.682553 + 0.730836i
\(957\) 0 0
\(958\) −2.59365 0.356489i −2.59365 0.356489i
\(959\) 0 0
\(960\) 0 0
\(961\) −0.0682424 + 0.997669i −0.0682424 + 0.997669i
\(962\) 0 0
\(963\) 0 0
\(964\) 0.203456 + 0.979084i 0.203456 + 0.979084i
\(965\) 0 0
\(966\) 0 0
\(967\) 1.25513 + 1.02112i 1.25513 + 1.02112i 0.998508 + 0.0546092i \(0.0173913\pi\)
0.256619 + 0.966513i \(0.417391\pi\)
\(968\) −0.962917 + 0.269797i −0.962917 + 0.269797i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.682553 0.730836i \(-0.739130\pi\)
0.682553 + 0.730836i \(0.260870\pi\)
\(972\) 1.38248 0.840704i 1.38248 0.840704i
\(973\) 0 0
\(974\) 3.20593 0.440645i 3.20593 0.440645i
\(975\) 0 0
\(976\) 0 0
\(977\) 0.920130 1.77577i 0.920130 1.77577i 0.460065 0.887885i \(-0.347826\pi\)
0.460065 0.887885i \(-0.347826\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 2.52095 + 0.706337i 2.52095 + 0.706337i
\(983\) 0 0 −0.917211 0.398401i \(-0.869565\pi\)
0.917211 + 0.398401i \(0.130435\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.48408 + 0.644627i 1.48408 + 0.644627i 0.976214 0.216810i \(-0.0695652\pi\)
0.507865 + 0.861437i \(0.330435\pi\)
\(992\) 0 0
\(993\) 0.576680 + 0.816970i 0.576680 + 0.816970i
\(994\) −1.25513 + 1.02112i −1.25513 + 1.02112i
\(995\) 0 0
\(996\) −0.136485 1.99534i −0.136485 1.99534i
\(997\) 0 0 0.460065 0.887885i \(-0.347826\pi\)
−0.460065 + 0.887885i \(0.652174\pi\)
\(998\) 0 0
\(999\) 0.566868 0.246225i 0.566868 0.246225i
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 2209.1.d.a.2007.1 44
47.2 even 23 inner 2209.1.d.a.1730.1 44
47.3 even 23 inner 2209.1.d.a.438.2 44
47.4 even 23 inner 2209.1.d.a.1609.1 44
47.5 odd 46 inner 2209.1.d.a.1342.1 44
47.6 even 23 inner 2209.1.d.a.295.2 44
47.7 even 23 inner 2209.1.d.a.1335.2 44
47.8 even 23 inner 2209.1.d.a.655.1 44
47.9 even 23 inner 2209.1.d.a.2156.2 44
47.10 odd 46 inner 2209.1.d.a.339.1 44
47.11 odd 46 inner 2209.1.d.a.280.2 44
47.12 even 23 inner 2209.1.d.a.1979.2 44
47.13 odd 46 inner 2209.1.d.a.172.1 44
47.14 even 23 inner 2209.1.d.a.1580.2 44
47.15 odd 46 47.1.b.a.46.1 2
47.16 even 23 inner 2209.1.d.a.1586.1 44
47.17 even 23 inner 2209.1.d.a.1124.1 44
47.18 even 23 inner 2209.1.d.a.2138.2 44
47.19 odd 46 inner 2209.1.d.a.116.2 44
47.20 odd 46 inner 2209.1.d.a.1121.2 44
47.21 even 23 inner 2209.1.d.a.1064.1 44
47.22 odd 46 inner 2209.1.d.a.1167.2 44
47.23 odd 46 inner 2209.1.d.a.67.2 44
47.24 even 23 inner 2209.1.d.a.67.2 44
47.25 even 23 inner 2209.1.d.a.1167.2 44
47.26 odd 46 inner 2209.1.d.a.1064.1 44
47.27 even 23 inner 2209.1.d.a.1121.2 44
47.28 even 23 inner 2209.1.d.a.116.2 44
47.29 odd 46 inner 2209.1.d.a.2138.2 44
47.30 odd 46 inner 2209.1.d.a.1124.1 44
47.31 odd 46 inner 2209.1.d.a.1586.1 44
47.32 even 23 47.1.b.a.46.1 2
47.33 odd 46 inner 2209.1.d.a.1580.2 44
47.34 even 23 inner 2209.1.d.a.172.1 44
47.35 odd 46 inner 2209.1.d.a.1979.2 44
47.36 even 23 inner 2209.1.d.a.280.2 44
47.37 even 23 inner 2209.1.d.a.339.1 44
47.38 odd 46 inner 2209.1.d.a.2156.2 44
47.39 odd 46 inner 2209.1.d.a.655.1 44
47.40 odd 46 inner 2209.1.d.a.1335.2 44
47.41 odd 46 inner 2209.1.d.a.295.2 44
47.42 even 23 inner 2209.1.d.a.1342.1 44
47.43 odd 46 inner 2209.1.d.a.1609.1 44
47.44 odd 46 inner 2209.1.d.a.438.2 44
47.45 odd 46 inner 2209.1.d.a.1730.1 44
47.46 odd 2 CM 2209.1.d.a.2007.1 44
141.32 odd 46 423.1.d.a.46.2 2
141.62 even 46 423.1.d.a.46.2 2
188.15 even 46 752.1.g.a.657.1 2
188.79 odd 46 752.1.g.a.657.1 2
235.32 odd 92 1175.1.b.b.1174.1 4
235.62 even 92 1175.1.b.b.1174.1 4
235.79 even 46 1175.1.d.c.751.2 2
235.109 odd 46 1175.1.d.c.751.2 2
235.173 odd 92 1175.1.b.b.1174.4 4
235.203 even 92 1175.1.b.b.1174.4 4
329.32 even 69 2303.1.f.c.422.2 4
329.62 even 46 2303.1.d.c.2255.1 2
329.79 even 69 2303.1.f.c.704.2 4
329.109 odd 138 2303.1.f.c.422.2 4
329.156 odd 138 2303.1.f.c.704.2 4
329.173 odd 138 2303.1.f.b.704.2 4
329.220 odd 138 2303.1.f.b.422.2 4
329.250 even 138 2303.1.f.b.704.2 4
329.297 even 138 2303.1.f.b.422.2 4
329.314 odd 46 2303.1.d.c.2255.1 2
376.109 odd 46 3008.1.g.b.1409.1 2
376.173 even 46 3008.1.g.b.1409.1 2
376.203 even 46 3008.1.g.a.1409.2 2
376.267 odd 46 3008.1.g.a.1409.2 2
423.32 odd 138 3807.1.f.a.2161.1 4
423.79 even 69 3807.1.f.b.3430.2 4
423.173 odd 138 3807.1.f.a.3430.1 4
423.203 even 138 3807.1.f.a.2161.1 4
423.220 even 69 3807.1.f.b.2161.2 4
423.250 odd 138 3807.1.f.b.3430.2 4
423.344 even 138 3807.1.f.a.3430.1 4
423.391 odd 138 3807.1.f.b.2161.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
47.1.b.a.46.1 2 47.15 odd 46
47.1.b.a.46.1 2 47.32 even 23
423.1.d.a.46.2 2 141.32 odd 46
423.1.d.a.46.2 2 141.62 even 46
752.1.g.a.657.1 2 188.15 even 46
752.1.g.a.657.1 2 188.79 odd 46
1175.1.b.b.1174.1 4 235.32 odd 92
1175.1.b.b.1174.1 4 235.62 even 92
1175.1.b.b.1174.4 4 235.173 odd 92
1175.1.b.b.1174.4 4 235.203 even 92
1175.1.d.c.751.2 2 235.79 even 46
1175.1.d.c.751.2 2 235.109 odd 46
2209.1.d.a.67.2 44 47.23 odd 46 inner
2209.1.d.a.67.2 44 47.24 even 23 inner
2209.1.d.a.116.2 44 47.19 odd 46 inner
2209.1.d.a.116.2 44 47.28 even 23 inner
2209.1.d.a.172.1 44 47.13 odd 46 inner
2209.1.d.a.172.1 44 47.34 even 23 inner
2209.1.d.a.280.2 44 47.11 odd 46 inner
2209.1.d.a.280.2 44 47.36 even 23 inner
2209.1.d.a.295.2 44 47.6 even 23 inner
2209.1.d.a.295.2 44 47.41 odd 46 inner
2209.1.d.a.339.1 44 47.10 odd 46 inner
2209.1.d.a.339.1 44 47.37 even 23 inner
2209.1.d.a.438.2 44 47.3 even 23 inner
2209.1.d.a.438.2 44 47.44 odd 46 inner
2209.1.d.a.655.1 44 47.8 even 23 inner
2209.1.d.a.655.1 44 47.39 odd 46 inner
2209.1.d.a.1064.1 44 47.21 even 23 inner
2209.1.d.a.1064.1 44 47.26 odd 46 inner
2209.1.d.a.1121.2 44 47.20 odd 46 inner
2209.1.d.a.1121.2 44 47.27 even 23 inner
2209.1.d.a.1124.1 44 47.17 even 23 inner
2209.1.d.a.1124.1 44 47.30 odd 46 inner
2209.1.d.a.1167.2 44 47.22 odd 46 inner
2209.1.d.a.1167.2 44 47.25 even 23 inner
2209.1.d.a.1335.2 44 47.7 even 23 inner
2209.1.d.a.1335.2 44 47.40 odd 46 inner
2209.1.d.a.1342.1 44 47.5 odd 46 inner
2209.1.d.a.1342.1 44 47.42 even 23 inner
2209.1.d.a.1580.2 44 47.14 even 23 inner
2209.1.d.a.1580.2 44 47.33 odd 46 inner
2209.1.d.a.1586.1 44 47.16 even 23 inner
2209.1.d.a.1586.1 44 47.31 odd 46 inner
2209.1.d.a.1609.1 44 47.4 even 23 inner
2209.1.d.a.1609.1 44 47.43 odd 46 inner
2209.1.d.a.1730.1 44 47.2 even 23 inner
2209.1.d.a.1730.1 44 47.45 odd 46 inner
2209.1.d.a.1979.2 44 47.12 even 23 inner
2209.1.d.a.1979.2 44 47.35 odd 46 inner
2209.1.d.a.2007.1 44 1.1 even 1 trivial
2209.1.d.a.2007.1 44 47.46 odd 2 CM
2209.1.d.a.2138.2 44 47.18 even 23 inner
2209.1.d.a.2138.2 44 47.29 odd 46 inner
2209.1.d.a.2156.2 44 47.9 even 23 inner
2209.1.d.a.2156.2 44 47.38 odd 46 inner
2303.1.d.c.2255.1 2 329.62 even 46
2303.1.d.c.2255.1 2 329.314 odd 46
2303.1.f.b.422.2 4 329.220 odd 138
2303.1.f.b.422.2 4 329.297 even 138
2303.1.f.b.704.2 4 329.173 odd 138
2303.1.f.b.704.2 4 329.250 even 138
2303.1.f.c.422.2 4 329.32 even 69
2303.1.f.c.422.2 4 329.109 odd 138
2303.1.f.c.704.2 4 329.79 even 69
2303.1.f.c.704.2 4 329.156 odd 138
3008.1.g.a.1409.2 2 376.203 even 46
3008.1.g.a.1409.2 2 376.267 odd 46
3008.1.g.b.1409.1 2 376.109 odd 46
3008.1.g.b.1409.1 2 376.173 even 46
3807.1.f.a.2161.1 4 423.32 odd 138
3807.1.f.a.2161.1 4 423.203 even 138
3807.1.f.a.3430.1 4 423.173 odd 138
3807.1.f.a.3430.1 4 423.344 even 138
3807.1.f.b.2161.2 4 423.220 even 69
3807.1.f.b.2161.2 4 423.391 odd 138
3807.1.f.b.3430.2 4 423.79 even 69
3807.1.f.b.3430.2 4 423.250 odd 138