Properties

Label 841.2.e.k.63.1
Level $841$
Weight $2$
Character 841.63
Analytic conductor $6.715$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $12$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [841,2,Mod(63,841)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(841, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("841.63");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 841.e (of order \(14\), degree \(6\), 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: \(6.71541880999\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{14})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 63.1
Character \(\chi\) \(=\) 841.63
Dual form 841.2.e.k.267.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.88751 + 1.50524i) q^{2} +(-2.35368 + 0.537213i) q^{3} +(0.851905 - 3.73244i) q^{4} +(0.623490 + 0.781831i) q^{5} +(3.63396 - 4.55685i) q^{6} +(0.629384 + 2.75751i) q^{7} +(1.91526 + 3.97707i) q^{8} +(2.54832 - 1.22721i) q^{9} +O(q^{10})\) \(q+(-1.88751 + 1.50524i) q^{2} +(-2.35368 + 0.537213i) q^{3} +(0.851905 - 3.73244i) q^{4} +(0.623490 + 0.781831i) q^{5} +(3.63396 - 4.55685i) q^{6} +(0.629384 + 2.75751i) q^{7} +(1.91526 + 3.97707i) q^{8} +(2.54832 - 1.22721i) q^{9} +(-2.35368 - 0.537213i) q^{10} +(0.179721 - 0.373194i) q^{11} +9.24264i q^{12} +(-3.44929 - 1.66109i) q^{13} +(-5.33868 - 4.25745i) q^{14} +(-1.88751 - 1.50524i) q^{15} +(-2.70291 - 1.30165i) q^{16} -0.828427i q^{17} +(-2.96274 + 6.15220i) q^{18} +(5.84957 + 1.33513i) q^{19} +(3.44929 - 1.66109i) q^{20} +(-2.96274 - 6.15220i) q^{21} +(0.222521 + 0.974928i) q^{22} +(2.28001 - 2.85904i) q^{23} +(-6.64444 - 8.33186i) q^{24} +(0.890084 - 3.89971i) q^{25} +(9.01091 - 2.05668i) q^{26} +(0.323845 - 0.258258i) q^{27} +10.8284 q^{28} +5.82843 q^{30} +(7.87388 - 6.27921i) q^{31} +(-1.54603 + 0.352871i) q^{32} +(-0.222521 + 0.974928i) q^{33} +(1.24698 + 1.56366i) q^{34} +(-1.76350 + 2.21135i) q^{35} +(-2.40955 - 10.5569i) q^{36} +(1.73553 + 3.60388i) q^{37} +(-13.0508 + 6.28493i) q^{38} +(9.01091 + 2.05668i) q^{39} +(-1.91526 + 3.97707i) q^{40} -4.48528i q^{41} +(14.8527 + 7.15270i) q^{42} +(-2.80348 - 2.23570i) q^{43} +(-1.23982 - 0.988722i) q^{44} +(2.54832 + 1.22721i) q^{45} +8.82843i q^{46} +(-1.40693 + 2.92152i) q^{47} +(7.06105 + 1.61164i) q^{48} +(-0.900969 + 0.433884i) q^{49} +(4.18995 + 8.70053i) q^{50} +(0.445042 + 1.94986i) q^{51} +(-9.13840 + 11.4592i) q^{52} +(5.91398 + 7.41589i) q^{53} +(-0.222521 + 0.974928i) q^{54} +(0.403828 - 0.0921712i) q^{55} +(-9.76139 + 7.78445i) q^{56} -14.4853 q^{57} -3.65685 q^{59} +(-7.22619 + 5.76269i) q^{60} +(4.70737 - 1.07443i) q^{61} +(-5.41031 + 23.7041i) q^{62} +(4.98792 + 6.25465i) q^{63} +(6.12792 - 7.68417i) q^{64} +(-0.851905 - 3.73244i) q^{65} +(-1.04749 - 2.17513i) q^{66} +(5.09665 - 2.45442i) q^{67} +(-3.09205 - 0.705741i) q^{68} +(-3.83051 + 7.95414i) q^{69} -6.82843i q^{70} +(-7.95414 - 3.83051i) q^{71} +(9.76139 + 7.78445i) q^{72} +(3.12733 + 2.49396i) q^{73} +(-8.70053 - 4.18995i) q^{74} +9.65685i q^{75} +(9.96655 - 20.6958i) q^{76} +(1.14220 + 0.260699i) q^{77} +(-20.1040 + 9.68156i) q^{78} +(-1.04749 - 2.17513i) q^{79} +(-0.667563 - 2.92478i) q^{80} +(-5.91398 + 7.41589i) q^{81} +(6.75141 + 8.46601i) q^{82} +(-1.70381 + 7.46488i) q^{83} +(-25.4867 + 5.81717i) q^{84} +(0.647690 - 0.516516i) q^{85} +8.65685 q^{86} +1.82843 q^{88} +(-9.76139 + 7.78445i) q^{89} +(-6.65722 + 1.51947i) q^{90} +(2.40955 - 10.5569i) q^{91} +(-8.72886 - 10.9456i) q^{92} +(-15.1593 + 19.0092i) q^{93} +(-1.74199 - 7.63215i) q^{94} +(2.60330 + 5.40581i) q^{95} +(3.44929 - 1.66109i) q^{96} +(-4.37283 - 0.998069i) q^{97} +(1.04749 - 2.17513i) q^{98} -1.17157i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/841\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{11}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88751 + 1.50524i −1.33467 + 1.06436i −0.342493 + 0.939520i \(0.611271\pi\)
−0.992176 + 0.124843i \(0.960157\pi\)
\(3\) −2.35368 + 0.537213i −1.35890 + 0.310160i −0.839030 0.544085i \(-0.816877\pi\)
−0.519870 + 0.854245i \(0.674020\pi\)
\(4\) 0.851905 3.73244i 0.425953 1.86622i
\(5\) 0.623490 + 0.781831i 0.278833 + 0.349646i 0.901452 0.432880i \(-0.142503\pi\)
−0.622619 + 0.782526i \(0.713931\pi\)
\(6\) 3.63396 4.55685i 1.48356 1.86033i
\(7\) 0.629384 + 2.75751i 0.237885 + 1.04224i 0.942907 + 0.333056i \(0.108080\pi\)
−0.705022 + 0.709185i \(0.749063\pi\)
\(8\) 1.91526 + 3.97707i 0.677145 + 1.40611i
\(9\) 2.54832 1.22721i 0.849442 0.409070i
\(10\) −2.35368 0.537213i −0.744300 0.169882i
\(11\) 0.179721 0.373194i 0.0541878 0.112522i −0.872117 0.489298i \(-0.837253\pi\)
0.926304 + 0.376776i \(0.122967\pi\)
\(12\) 9.24264i 2.66812i
\(13\) −3.44929 1.66109i −0.956662 0.460704i −0.110645 0.993860i \(-0.535292\pi\)
−0.846017 + 0.533156i \(0.821006\pi\)
\(14\) −5.33868 4.25745i −1.42682 1.13785i
\(15\) −1.88751 1.50524i −0.487353 0.388651i
\(16\) −2.70291 1.30165i −0.675727 0.325413i
\(17\) 0.828427i 0.200923i −0.994941 0.100462i \(-0.967968\pi\)
0.994941 0.100462i \(-0.0320319\pi\)
\(18\) −2.96274 + 6.15220i −0.698325 + 1.45009i
\(19\) 5.84957 + 1.33513i 1.34198 + 0.306299i 0.832425 0.554138i \(-0.186952\pi\)
0.509558 + 0.860436i \(0.329809\pi\)
\(20\) 3.44929 1.66109i 0.771286 0.371432i
\(21\) −2.96274 6.15220i −0.646524 1.34252i
\(22\) 0.222521 + 0.974928i 0.0474416 + 0.207855i
\(23\) 2.28001 2.85904i 0.475415 0.596152i −0.485073 0.874474i \(-0.661207\pi\)
0.960488 + 0.278322i \(0.0897783\pi\)
\(24\) −6.64444 8.33186i −1.35629 1.70073i
\(25\) 0.890084 3.89971i 0.178017 0.779942i
\(26\) 9.01091 2.05668i 1.76718 0.403348i
\(27\) 0.323845 0.258258i 0.0623240 0.0497018i
\(28\) 10.8284 2.04638
\(29\) 0 0
\(30\) 5.82843 1.06412
\(31\) 7.87388 6.27921i 1.41419 1.12778i 0.441072 0.897472i \(-0.354598\pi\)
0.973118 0.230307i \(-0.0739732\pi\)
\(32\) −1.54603 + 0.352871i −0.273302 + 0.0623793i
\(33\) −0.222521 + 0.974928i −0.0387359 + 0.169713i
\(34\) 1.24698 + 1.56366i 0.213855 + 0.268166i
\(35\) −1.76350 + 2.21135i −0.298085 + 0.373787i
\(36\) −2.40955 10.5569i −0.401592 1.75949i
\(37\) 1.73553 + 3.60388i 0.285320 + 0.592473i 0.993535 0.113523i \(-0.0362136\pi\)
−0.708215 + 0.705997i \(0.750499\pi\)
\(38\) −13.0508 + 6.28493i −2.11712 + 1.01955i
\(39\) 9.01091 + 2.05668i 1.44290 + 0.329333i
\(40\) −1.91526 + 3.97707i −0.302828 + 0.628830i
\(41\) 4.48528i 0.700483i −0.936659 0.350242i \(-0.886099\pi\)
0.936659 0.350242i \(-0.113901\pi\)
\(42\) 14.8527 + 7.15270i 2.29183 + 1.10368i
\(43\) −2.80348 2.23570i −0.427527 0.340941i 0.385969 0.922512i \(-0.373867\pi\)
−0.813496 + 0.581570i \(0.802438\pi\)
\(44\) −1.23982 0.988722i −0.186910 0.149055i
\(45\) 2.54832 + 1.22721i 0.379882 + 0.182941i
\(46\) 8.82843i 1.30168i
\(47\) −1.40693 + 2.92152i −0.205222 + 0.426147i −0.978022 0.208502i \(-0.933141\pi\)
0.772800 + 0.634649i \(0.218855\pi\)
\(48\) 7.06105 + 1.61164i 1.01918 + 0.232620i
\(49\) −0.900969 + 0.433884i −0.128710 + 0.0619834i
\(50\) 4.18995 + 8.70053i 0.592549 + 1.23044i
\(51\) 0.445042 + 1.94986i 0.0623183 + 0.273034i
\(52\) −9.13840 + 11.4592i −1.26727 + 1.58910i
\(53\) 5.91398 + 7.41589i 0.812347 + 1.01865i 0.999341 + 0.0362900i \(0.0115540\pi\)
−0.186994 + 0.982361i \(0.559875\pi\)
\(54\) −0.222521 + 0.974928i −0.0302813 + 0.132671i
\(55\) 0.403828 0.0921712i 0.0544522 0.0124284i
\(56\) −9.76139 + 7.78445i −1.30442 + 1.04024i
\(57\) −14.4853 −1.91862
\(58\) 0 0
\(59\) −3.65685 −0.476082 −0.238041 0.971255i \(-0.576505\pi\)
−0.238041 + 0.971255i \(0.576505\pi\)
\(60\) −7.22619 + 5.76269i −0.932897 + 0.743960i
\(61\) 4.70737 1.07443i 0.602717 0.137566i 0.0897350 0.995966i \(-0.471398\pi\)
0.512982 + 0.858400i \(0.328541\pi\)
\(62\) −5.41031 + 23.7041i −0.687110 + 3.01043i
\(63\) 4.98792 + 6.25465i 0.628419 + 0.788012i
\(64\) 6.12792 7.68417i 0.765991 0.960522i
\(65\) −0.851905 3.73244i −0.105666 0.462952i
\(66\) −1.04749 2.17513i −0.128937 0.267740i
\(67\) 5.09665 2.45442i 0.622655 0.299855i −0.0958296 0.995398i \(-0.530550\pi\)
0.718484 + 0.695543i \(0.244836\pi\)
\(68\) −3.09205 0.705741i −0.374967 0.0855837i
\(69\) −3.83051 + 7.95414i −0.461139 + 0.957566i
\(70\) 6.82843i 0.816153i
\(71\) −7.95414 3.83051i −0.943983 0.454598i −0.102410 0.994742i \(-0.532655\pi\)
−0.841572 + 0.540144i \(0.818370\pi\)
\(72\) 9.76139 + 7.78445i 1.15039 + 0.917406i
\(73\) 3.12733 + 2.49396i 0.366026 + 0.291896i 0.789180 0.614162i \(-0.210506\pi\)
−0.423154 + 0.906058i \(0.639077\pi\)
\(74\) −8.70053 4.18995i −1.01142 0.487072i
\(75\) 9.65685i 1.11508i
\(76\) 9.96655 20.6958i 1.14324 2.37397i
\(77\) 1.14220 + 0.260699i 0.130166 + 0.0297095i
\(78\) −20.1040 + 9.68156i −2.27632 + 1.09622i
\(79\) −1.04749 2.17513i −0.117852 0.244721i 0.833695 0.552224i \(-0.186221\pi\)
−0.951547 + 0.307503i \(0.900507\pi\)
\(80\) −0.667563 2.92478i −0.0746358 0.327001i
\(81\) −5.91398 + 7.41589i −0.657108 + 0.823988i
\(82\) 6.75141 + 8.46601i 0.745569 + 0.934914i
\(83\) −1.70381 + 7.46488i −0.187017 + 0.819377i 0.791161 + 0.611609i \(0.209477\pi\)
−0.978178 + 0.207769i \(0.933380\pi\)
\(84\) −25.4867 + 5.81717i −2.78083 + 0.634706i
\(85\) 0.647690 0.516516i 0.0702519 0.0560240i
\(86\) 8.65685 0.933493
\(87\) 0 0
\(88\) 1.82843 0.194911
\(89\) −9.76139 + 7.78445i −1.03470 + 0.825150i −0.984815 0.173605i \(-0.944458\pi\)
−0.0498895 + 0.998755i \(0.515887\pi\)
\(90\) −6.65722 + 1.51947i −0.701733 + 0.160166i
\(91\) 2.40955 10.5569i 0.252590 1.10667i
\(92\) −8.72886 10.9456i −0.910046 1.14116i
\(93\) −15.1593 + 19.0092i −1.57195 + 1.97116i
\(94\) −1.74199 7.63215i −0.179672 0.787196i
\(95\) 2.60330 + 5.40581i 0.267093 + 0.554625i
\(96\) 3.44929 1.66109i 0.352042 0.169535i
\(97\) −4.37283 0.998069i −0.443993 0.101339i −0.00532129 0.999986i \(-0.501694\pi\)
−0.438672 + 0.898647i \(0.644551\pi\)
\(98\) 1.04749 2.17513i 0.105812 0.219721i
\(99\) 1.17157i 0.117748i
\(100\) −13.7972 6.64437i −1.37972 0.664437i
\(101\) 1.83195 + 1.46093i 0.182285 + 0.145368i 0.710381 0.703817i \(-0.248522\pi\)
−0.528096 + 0.849185i \(0.677094\pi\)
\(102\) −3.77502 3.01048i −0.373782 0.298081i
\(103\) 4.35026 + 2.09498i 0.428644 + 0.206424i 0.635751 0.771894i \(-0.280691\pi\)
−0.207107 + 0.978318i \(0.566405\pi\)
\(104\) 16.8995i 1.65713i
\(105\) 2.96274 6.15220i 0.289134 0.600393i
\(106\) −22.3254 5.09562i −2.16843 0.494930i
\(107\) 13.3600 6.43381i 1.29156 0.621980i 0.343221 0.939255i \(-0.388482\pi\)
0.948334 + 0.317274i \(0.102768\pi\)
\(108\) −0.688047 1.42874i −0.0662073 0.137481i
\(109\) 2.81642 + 12.3395i 0.269764 + 1.18191i 0.910289 + 0.413974i \(0.135860\pi\)
−0.640525 + 0.767937i \(0.721283\pi\)
\(110\) −0.623490 + 0.781831i −0.0594474 + 0.0745447i
\(111\) −6.02095 7.55003i −0.571483 0.716617i
\(112\) 1.88815 8.27254i 0.178414 0.781681i
\(113\) −12.9799 + 2.96258i −1.22105 + 0.278696i −0.784010 0.620748i \(-0.786829\pi\)
−0.437037 + 0.899444i \(0.643972\pi\)
\(114\) 27.3411 21.8038i 2.56073 2.04211i
\(115\) 3.65685 0.341003
\(116\) 0 0
\(117\) −10.8284 −1.00109
\(118\) 6.90234 5.50443i 0.635412 0.506724i
\(119\) 2.28440 0.521399i 0.209410 0.0477966i
\(120\) 2.37137 10.3897i 0.216476 0.948442i
\(121\) 6.75141 + 8.46601i 0.613765 + 0.769637i
\(122\) −7.26793 + 9.11370i −0.658007 + 0.825115i
\(123\) 2.40955 + 10.5569i 0.217262 + 0.951887i
\(124\) −16.7290 34.7381i −1.50231 3.11957i
\(125\) 8.10872 3.90495i 0.725266 0.349270i
\(126\) −18.8295 4.29770i −1.67746 0.382870i
\(127\) 1.88442 3.91304i 0.167215 0.347226i −0.800476 0.599365i \(-0.795420\pi\)
0.967691 + 0.252139i \(0.0811340\pi\)
\(128\) 20.5563i 1.81694i
\(129\) 7.79956 + 3.75607i 0.686713 + 0.330703i
\(130\) 7.22619 + 5.76269i 0.633779 + 0.505422i
\(131\) 16.6637 + 13.2889i 1.45592 + 1.16105i 0.955395 + 0.295331i \(0.0954299\pi\)
0.500522 + 0.865724i \(0.333142\pi\)
\(132\) 3.44929 + 1.66109i 0.300222 + 0.144580i
\(133\) 16.9706i 1.47153i
\(134\) −5.92549 + 12.3044i −0.511884 + 1.06294i
\(135\) 0.403828 + 0.0921712i 0.0347560 + 0.00793283i
\(136\) 3.29471 1.58665i 0.282519 0.136054i
\(137\) 5.20660 + 10.8116i 0.444830 + 0.923700i 0.996004 + 0.0893090i \(0.0284659\pi\)
−0.551174 + 0.834391i \(0.685820\pi\)
\(138\) −4.74275 20.7793i −0.403729 1.76885i
\(139\) 8.72886 10.9456i 0.740372 0.928397i −0.258925 0.965898i \(-0.583368\pi\)
0.999297 + 0.0375004i \(0.0119395\pi\)
\(140\) 6.75141 + 8.46601i 0.570599 + 0.715508i
\(141\) 1.74199 7.63215i 0.146702 0.642743i
\(142\) 20.7793 4.74275i 1.74376 0.398002i
\(143\) −1.23982 + 0.988722i −0.103679 + 0.0826811i
\(144\) −8.48528 −0.707107
\(145\) 0 0
\(146\) −9.65685 −0.799207
\(147\) 1.88751 1.50524i 0.155679 0.124150i
\(148\) 14.9298 3.40762i 1.22722 0.280105i
\(149\) −1.74199 + 7.63215i −0.142709 + 0.625250i 0.852090 + 0.523395i \(0.175335\pi\)
−0.994799 + 0.101855i \(0.967522\pi\)
\(150\) −14.5359 18.2274i −1.18685 1.48826i
\(151\) 8.81748 11.0568i 0.717556 0.899787i −0.280641 0.959813i \(-0.590547\pi\)
0.998197 + 0.0600260i \(0.0191184\pi\)
\(152\) 5.89353 + 25.8212i 0.478028 + 2.09438i
\(153\) −1.01665 2.11110i −0.0821915 0.170672i
\(154\) −2.54832 + 1.22721i −0.205350 + 0.0988913i
\(155\) 9.81857 + 2.24102i 0.788646 + 0.180003i
\(156\) 15.3529 31.8806i 1.22921 2.55249i
\(157\) 8.48528i 0.677199i 0.940931 + 0.338600i \(0.109953\pi\)
−0.940931 + 0.338600i \(0.890047\pi\)
\(158\) 5.25123 + 2.52886i 0.417766 + 0.201185i
\(159\) −17.9035 14.2776i −1.41984 1.13229i
\(160\) −1.23982 0.988722i −0.0980162 0.0781653i
\(161\) 9.31885 + 4.48772i 0.734428 + 0.353682i
\(162\) 22.8995i 1.79915i
\(163\) 1.70470 3.53985i 0.133522 0.277262i −0.823478 0.567348i \(-0.807970\pi\)
0.957001 + 0.290086i \(0.0936838\pi\)
\(164\) −16.7410 3.82103i −1.30726 0.298373i
\(165\) −0.900969 + 0.433884i −0.0701403 + 0.0337778i
\(166\) −8.02046 16.6547i −0.622509 1.29265i
\(167\) −0.705741 3.09205i −0.0546119 0.239270i 0.940254 0.340474i \(-0.110588\pi\)
−0.994866 + 0.101204i \(0.967731\pi\)
\(168\) 18.7933 23.5661i 1.44994 1.81816i
\(169\) 1.03303 + 1.29538i 0.0794640 + 0.0996447i
\(170\) −0.445042 + 1.94986i −0.0341332 + 0.149547i
\(171\) 16.5451 3.77631i 1.26523 0.288781i
\(172\) −10.7329 + 8.55922i −0.818378 + 0.652634i
\(173\) −12.3431 −0.938432 −0.469216 0.883083i \(-0.655463\pi\)
−0.469216 + 0.883083i \(0.655463\pi\)
\(174\) 0 0
\(175\) 11.3137 0.855236
\(176\) −0.971536 + 0.774774i −0.0732323 + 0.0584008i
\(177\) 8.60708 1.96451i 0.646948 0.147662i
\(178\) 6.70726 29.3864i 0.502730 2.20260i
\(179\) 4.04351 + 5.07040i 0.302226 + 0.378979i 0.909634 0.415411i \(-0.136362\pi\)
−0.607408 + 0.794390i \(0.707791\pi\)
\(180\) 6.75141 8.46601i 0.503221 0.631019i
\(181\) −1.84997 8.10527i −0.137507 0.602460i −0.995978 0.0895969i \(-0.971442\pi\)
0.858471 0.512863i \(-0.171415\pi\)
\(182\) 11.3426 + 23.5533i 0.840773 + 1.74588i
\(183\) −10.5025 + 5.05772i −0.776364 + 0.373877i
\(184\) 15.7374 + 3.59196i 1.16018 + 0.264803i
\(185\) −1.73553 + 3.60388i −0.127599 + 0.264962i
\(186\) 58.6985i 4.30398i
\(187\) −0.309164 0.148885i −0.0226083 0.0108876i
\(188\) 9.70582 + 7.74014i 0.707870 + 0.564507i
\(189\) 0.915973 + 0.730464i 0.0666272 + 0.0531334i
\(190\) −13.0508 6.28493i −0.946804 0.455957i
\(191\) 25.3137i 1.83164i −0.401594 0.915818i \(-0.631544\pi\)
0.401594 0.915818i \(-0.368456\pi\)
\(192\) −10.2952 + 21.3781i −0.742989 + 1.54283i
\(193\) −5.04191 1.15078i −0.362925 0.0828352i 0.0371701 0.999309i \(-0.488166\pi\)
−0.400095 + 0.916474i \(0.631023\pi\)
\(194\) 9.75608 4.69828i 0.700445 0.337317i
\(195\) 4.01023 + 8.32733i 0.287179 + 0.596333i
\(196\) 0.851905 + 3.73244i 0.0608504 + 0.266603i
\(197\) 1.24698 1.56366i 0.0888436 0.111406i −0.735423 0.677609i \(-0.763016\pi\)
0.824266 + 0.566202i \(0.191588\pi\)
\(198\) 1.76350 + 2.21135i 0.125326 + 0.157154i
\(199\) 0.107985 0.473114i 0.00765487 0.0335382i −0.970956 0.239257i \(-0.923096\pi\)
0.978611 + 0.205719i \(0.0659533\pi\)
\(200\) 17.2142 3.92902i 1.21722 0.277824i
\(201\) −10.6774 + 8.51491i −0.753123 + 0.600595i
\(202\) −5.65685 −0.398015
\(203\) 0 0
\(204\) 7.65685 0.536087
\(205\) 3.50673 2.79653i 0.244921 0.195318i
\(206\) −11.3646 + 2.59389i −0.791809 + 0.180725i
\(207\) 2.30157 10.0838i 0.159970 0.700874i
\(208\) 7.16096 + 8.97955i 0.496523 + 0.622620i
\(209\) 1.54955 1.94307i 0.107184 0.134405i
\(210\) 3.66832 + 16.0720i 0.253138 + 1.10907i
\(211\) 8.41074 + 17.4651i 0.579019 + 1.20235i 0.960580 + 0.278002i \(0.0896722\pi\)
−0.381561 + 0.924344i \(0.624613\pi\)
\(212\) 32.7175 15.7559i 2.24705 1.08212i
\(213\) 20.7793 + 4.74275i 1.42378 + 0.324968i
\(214\) −15.5326 + 32.2538i −1.06179 + 2.20482i
\(215\) 3.58579i 0.244549i
\(216\) 1.64736 + 0.793325i 0.112088 + 0.0539789i
\(217\) 22.2707 + 17.7603i 1.51183 + 1.20565i
\(218\) −23.8899 19.0516i −1.61803 1.29034i
\(219\) −8.70053 4.18995i −0.587927 0.283131i
\(220\) 1.58579i 0.106914i
\(221\) −1.37609 + 2.85749i −0.0925661 + 0.192215i
\(222\) 22.7292 + 5.18779i 1.52548 + 0.348182i
\(223\) 2.85749 1.37609i 0.191352 0.0921501i −0.335755 0.941949i \(-0.608991\pi\)
0.527106 + 0.849799i \(0.323277\pi\)
\(224\) −1.94609 4.04110i −0.130029 0.270007i
\(225\) −2.51754 11.0301i −0.167836 0.735337i
\(226\) 20.0403 25.1297i 1.33306 1.67161i
\(227\) −5.07654 6.36578i −0.336942 0.422512i 0.584278 0.811553i \(-0.301378\pi\)
−0.921220 + 0.389042i \(0.872806\pi\)
\(228\) −12.3401 + 54.0655i −0.817242 + 3.58057i
\(229\) −3.42660 + 0.782098i −0.226436 + 0.0516825i −0.334233 0.942490i \(-0.608477\pi\)
0.107797 + 0.994173i \(0.465620\pi\)
\(230\) −6.90234 + 5.50443i −0.455127 + 0.362952i
\(231\) −2.82843 −0.186097
\(232\) 0 0
\(233\) 18.3137 1.19977 0.599885 0.800086i \(-0.295213\pi\)
0.599885 + 0.800086i \(0.295213\pi\)
\(234\) 20.4387 16.2994i 1.33612 1.06552i
\(235\) −3.16134 + 0.721555i −0.206223 + 0.0470691i
\(236\) −3.11529 + 13.6490i −0.202788 + 0.888474i
\(237\) 3.63396 + 4.55685i 0.236051 + 0.295999i
\(238\) −3.52699 + 4.42271i −0.228621 + 0.286681i
\(239\) 4.37406 + 19.1640i 0.282935 + 1.23962i 0.894011 + 0.448045i \(0.147880\pi\)
−0.611076 + 0.791572i \(0.709263\pi\)
\(240\) 3.14246 + 6.52539i 0.202845 + 0.421212i
\(241\) −16.5001 + 7.94602i −1.06286 + 0.511848i −0.881800 0.471623i \(-0.843668\pi\)
−0.181064 + 0.983471i \(0.557954\pi\)
\(242\) −25.4867 5.81717i −1.63835 0.373942i
\(243\) 9.39656 19.5122i 0.602789 1.25171i
\(244\) 18.4853i 1.18340i
\(245\) −0.900969 0.433884i −0.0575608 0.0277198i
\(246\) −20.4387 16.2994i −1.30313 1.03921i
\(247\) −17.9591 14.3219i −1.14271 0.911281i
\(248\) 40.0533 + 19.2887i 2.54339 + 1.22483i
\(249\) 18.4853i 1.17146i
\(250\) −9.42739 + 19.5762i −0.596241 + 1.23811i
\(251\) 19.5678 + 4.46623i 1.23511 + 0.281906i 0.789741 0.613440i \(-0.210215\pi\)
0.445370 + 0.895346i \(0.353072\pi\)
\(252\) 27.5943 13.2887i 1.73828 0.837112i
\(253\) −0.657212 1.36471i −0.0413186 0.0857989i
\(254\) 2.33319 + 10.2224i 0.146398 + 0.641410i
\(255\) −1.24698 + 1.56366i −0.0780889 + 0.0979204i
\(256\) −18.6863 23.4319i −1.16790 1.46450i
\(257\) 4.04356 17.7160i 0.252230 1.10509i −0.677114 0.735878i \(-0.736770\pi\)
0.929344 0.369214i \(-0.120373\pi\)
\(258\) −20.3755 + 4.65058i −1.26852 + 0.289532i
\(259\) −8.84541 + 7.05398i −0.549627 + 0.438313i
\(260\) −14.6569 −0.908980
\(261\) 0 0
\(262\) −51.4558 −3.17895
\(263\) 2.15579 1.71919i 0.132932 0.106010i −0.554767 0.832006i \(-0.687193\pi\)
0.687699 + 0.725996i \(0.258621\pi\)
\(264\) −4.30354 + 0.982255i −0.264865 + 0.0604536i
\(265\) −2.11067 + 9.24747i −0.129658 + 0.568067i
\(266\) −25.5447 32.0321i −1.56625 1.96401i
\(267\) 18.7933 23.5661i 1.15013 1.44222i
\(268\) −4.81910 21.1139i −0.294374 1.28973i
\(269\) −13.6482 28.3407i −0.832144 1.72797i −0.671570 0.740941i \(-0.734380\pi\)
−0.160575 0.987024i \(-0.551335\pi\)
\(270\) −0.900969 + 0.433884i −0.0548312 + 0.0264053i
\(271\) −16.1412 3.68413i −0.980511 0.223795i −0.297916 0.954592i \(-0.596292\pi\)
−0.682595 + 0.730797i \(0.739149\pi\)
\(272\) −1.07832 + 2.23916i −0.0653829 + 0.135769i
\(273\) 26.1421i 1.58219i
\(274\) −26.1016 12.5699i −1.57685 0.759373i
\(275\) −1.29538 1.03303i −0.0781144 0.0622942i
\(276\) 26.4251 + 21.0733i 1.59060 + 1.26847i
\(277\) 15.5991 + 7.51214i 0.937260 + 0.451361i 0.839202 0.543820i \(-0.183023\pi\)
0.0980580 + 0.995181i \(0.468737\pi\)
\(278\) 33.7990i 2.02713i
\(279\) 12.3593 25.6644i 0.739932 1.53648i
\(280\) −12.1722 2.77824i −0.727431 0.166031i
\(281\) −28.8045 + 13.8715i −1.71833 + 0.827505i −0.728536 + 0.685007i \(0.759799\pi\)
−0.989795 + 0.142497i \(0.954487\pi\)
\(282\) 8.20018 + 17.0279i 0.488314 + 1.01399i
\(283\) 2.59389 + 11.3646i 0.154191 + 0.675555i 0.991640 + 0.129039i \(0.0411892\pi\)
−0.837449 + 0.546516i \(0.815954\pi\)
\(284\) −21.0733 + 26.4251i −1.25047 + 1.56804i
\(285\) −9.03143 11.3250i −0.534975 0.670838i
\(286\) 0.851905 3.73244i 0.0503742 0.220704i
\(287\) 12.3682 2.82297i 0.730073 0.166634i
\(288\) −3.50673 + 2.79653i −0.206636 + 0.164787i
\(289\) 16.3137 0.959630
\(290\) 0 0
\(291\) 10.8284 0.634774
\(292\) 11.9727 9.54794i 0.700652 0.558751i
\(293\) −7.46488 + 1.70381i −0.436103 + 0.0995377i −0.434935 0.900462i \(-0.643229\pi\)
−0.00116759 + 0.999999i \(0.500372\pi\)
\(294\) −1.29695 + 5.68230i −0.0756395 + 0.331398i
\(295\) −2.28001 2.85904i −0.132747 0.166460i
\(296\) −11.0089 + 13.8047i −0.639877 + 0.802381i
\(297\) −0.0381786 0.167271i −0.00221534 0.00970606i
\(298\) −8.20018 17.0279i −0.475024 0.986397i
\(299\) −12.6136 + 6.07437i −0.729461 + 0.351290i
\(300\) 36.0436 + 8.22672i 2.08098 + 0.474970i
\(301\) 4.40051 9.13775i 0.253641 0.526691i
\(302\) 34.1421i 1.96466i
\(303\) −5.09665 2.45442i −0.292795 0.141003i
\(304\) −14.0730 11.2228i −0.807140 0.643673i
\(305\) 3.77502 + 3.01048i 0.216157 + 0.172379i
\(306\) 5.09665 + 2.45442i 0.291356 + 0.140310i
\(307\) 2.89949i 0.165483i −0.996571 0.0827415i \(-0.973632\pi\)
0.996571 0.0827415i \(-0.0263676\pi\)
\(308\) 1.94609 4.04110i 0.110889 0.230263i
\(309\) −11.3646 2.59389i −0.646509 0.147561i
\(310\) −21.9059 + 10.5493i −1.24417 + 0.599161i
\(311\) 1.16554 + 2.42027i 0.0660916 + 0.137241i 0.931398 0.364003i \(-0.118590\pi\)
−0.865306 + 0.501244i \(0.832876\pi\)
\(312\) 9.07863 + 39.7761i 0.513976 + 2.25188i
\(313\) 6.12792 7.68417i 0.346371 0.434335i −0.577880 0.816122i \(-0.696120\pi\)
0.924250 + 0.381787i \(0.124691\pi\)
\(314\) −12.7724 16.0160i −0.720786 0.903837i
\(315\) −1.78017 + 7.79942i −0.100301 + 0.439448i
\(316\) −9.01091 + 2.05668i −0.506903 + 0.115697i
\(317\) 24.5932 19.6124i 1.38129 1.10154i 0.398428 0.917200i \(-0.369556\pi\)
0.982862 0.184342i \(-0.0590155\pi\)
\(318\) 55.2843 3.10019
\(319\) 0 0
\(320\) 9.82843 0.549426
\(321\) −27.9888 + 22.3203i −1.56218 + 1.24580i
\(322\) −24.3445 + 5.55647i −1.35667 + 0.309650i
\(323\) 1.10605 4.84594i 0.0615425 0.269635i
\(324\) 22.6412 + 28.3912i 1.25785 + 1.57729i
\(325\) −9.54794 + 11.9727i −0.529624 + 0.664128i
\(326\) 2.11067 + 9.24747i 0.116899 + 0.512170i
\(327\) −13.2579 27.5303i −0.733164 1.52243i
\(328\) 17.8383 8.59046i 0.984954 0.474329i
\(329\) −8.94162 2.04087i −0.492968 0.112517i
\(330\) 1.04749 2.17513i 0.0576623 0.119737i
\(331\) 2.41421i 0.132697i −0.997797 0.0663486i \(-0.978865\pi\)
0.997797 0.0663486i \(-0.0211349\pi\)
\(332\) 26.4107 + 12.7187i 1.44948 + 0.698032i
\(333\) 8.84541 + 7.05398i 0.484726 + 0.386556i
\(334\) 5.98637 + 4.77397i 0.327560 + 0.261220i
\(335\) 5.09665 + 2.45442i 0.278460 + 0.134099i
\(336\) 20.4853i 1.11756i
\(337\) 9.45823 19.6402i 0.515222 1.06987i −0.467364 0.884065i \(-0.654796\pi\)
0.982587 0.185806i \(-0.0594894\pi\)
\(338\) −3.89971 0.890084i −0.212116 0.0484142i
\(339\) 28.9591 13.9459i 1.57284 0.757440i
\(340\) −1.37609 2.85749i −0.0746292 0.154969i
\(341\) −0.928262 4.06698i −0.0502682 0.220239i
\(342\) −25.5447 + 32.0321i −1.38130 + 1.73210i
\(343\) 10.5810 + 13.2681i 0.571319 + 0.716411i
\(344\) 3.52216 15.4316i 0.189902 0.832015i
\(345\) −8.60708 + 1.96451i −0.463390 + 0.105766i
\(346\) 23.2978 18.5794i 1.25250 0.998833i
\(347\) −2.48528 −0.133417 −0.0667084 0.997773i \(-0.521250\pi\)
−0.0667084 + 0.997773i \(0.521250\pi\)
\(348\) 0 0
\(349\) −5.14214 −0.275252 −0.137626 0.990484i \(-0.543947\pi\)
−0.137626 + 0.990484i \(0.543947\pi\)
\(350\) −21.3547 + 17.0298i −1.14146 + 0.910282i
\(351\) −1.54603 + 0.352871i −0.0825208 + 0.0188348i
\(352\) −0.146164 + 0.640386i −0.00779056 + 0.0341327i
\(353\) −16.8159 21.0864i −0.895018 1.12232i −0.991900 0.127022i \(-0.959458\pi\)
0.0968814 0.995296i \(-0.469113\pi\)
\(354\) −13.2889 + 16.6637i −0.706296 + 0.885667i
\(355\) −1.96451 8.60708i −0.104265 0.456816i
\(356\) 20.7392 + 43.0654i 1.09918 + 2.28246i
\(357\) −5.09665 + 2.45442i −0.269743 + 0.129902i
\(358\) −15.2643 3.48398i −0.806744 0.184134i
\(359\) −1.70470 + 3.53985i −0.0899706 + 0.186826i −0.941099 0.338132i \(-0.890205\pi\)
0.851128 + 0.524958i \(0.175919\pi\)
\(360\) 12.4853i 0.658032i
\(361\) 15.3165 + 7.37602i 0.806130 + 0.388212i
\(362\) 15.6922 + 12.5141i 0.824763 + 0.657727i
\(363\) −20.4387 16.2994i −1.07276 0.855494i
\(364\) −37.3504 17.9870i −1.95769 0.942776i
\(365\) 4.00000i 0.209370i
\(366\) 12.2104 25.3552i 0.638249 1.32534i
\(367\) 17.5487 + 4.00538i 0.916035 + 0.209079i 0.654453 0.756102i \(-0.272899\pi\)
0.261582 + 0.965181i \(0.415756\pi\)
\(368\) −9.88414 + 4.75995i −0.515246 + 0.248129i
\(369\) −5.50438 11.4300i −0.286546 0.595020i
\(370\) −2.14885 9.41474i −0.111714 0.489449i
\(371\) −16.7273 + 20.9753i −0.868436 + 1.08898i
\(372\) 58.0365 + 72.7754i 3.00905 + 3.77323i
\(373\) 5.85535 25.6540i 0.303179 1.32831i −0.562120 0.827056i \(-0.690014\pi\)
0.865299 0.501257i \(-0.167129\pi\)
\(374\) 0.807657 0.184342i 0.0417629 0.00953212i
\(375\) −16.9876 + 13.5471i −0.877235 + 0.699571i
\(376\) −14.3137 −0.738173
\(377\) 0 0
\(378\) −2.82843 −0.145479
\(379\) −5.44981 + 4.34607i −0.279938 + 0.223243i −0.753386 0.657579i \(-0.771581\pi\)
0.473448 + 0.880822i \(0.343009\pi\)
\(380\) 22.3946 5.11143i 1.14882 0.262211i
\(381\) −2.33319 + 10.2224i −0.119533 + 0.523709i
\(382\) 38.1031 + 47.7798i 1.94953 + 2.44463i
\(383\) 2.19139 2.74792i 0.111975 0.140412i −0.722686 0.691177i \(-0.757093\pi\)
0.834660 + 0.550765i \(0.185664\pi\)
\(384\) −11.0431 48.3832i −0.563543 2.46904i
\(385\) 0.508326 + 1.05555i 0.0259067 + 0.0537958i
\(386\) 11.2488 5.41716i 0.572551 0.275726i
\(387\) −9.88785 2.25684i −0.502628 0.114721i
\(388\) −7.45047 + 15.4711i −0.378240 + 0.785424i
\(389\) 3.02944i 0.153599i 0.997047 + 0.0767993i \(0.0244701\pi\)
−0.997047 + 0.0767993i \(0.975530\pi\)
\(390\) −20.1040 9.68156i −1.01800 0.490245i
\(391\) −2.36851 1.88882i −0.119781 0.0955219i
\(392\) −3.45117 2.75222i −0.174310 0.139008i
\(393\) −46.3601 22.3259i −2.33856 1.12619i
\(394\) 4.82843i 0.243253i
\(395\) 1.04749 2.17513i 0.0527048 0.109443i
\(396\) −4.37283 0.998069i −0.219743 0.0501549i
\(397\) −17.4276 + 8.39268i −0.874665 + 0.421216i −0.816673 0.577101i \(-0.804184\pi\)
−0.0579918 + 0.998317i \(0.518470\pi\)
\(398\) 0.508326 + 1.05555i 0.0254801 + 0.0529100i
\(399\) −9.11681 39.9433i −0.456411 1.99967i
\(400\) −7.48188 + 9.38198i −0.374094 + 0.469099i
\(401\) −11.6324 14.5865i −0.580892 0.728416i 0.401373 0.915915i \(-0.368533\pi\)
−0.982265 + 0.187499i \(0.939962\pi\)
\(402\) 7.33664 32.1439i 0.365918 1.60319i
\(403\) −37.5897 + 8.57959i −1.87247 + 0.427380i
\(404\) 7.01347 5.59305i 0.348933 0.278265i
\(405\) −9.48528 −0.471327
\(406\) 0 0
\(407\) 1.65685 0.0821272
\(408\) −6.90234 + 5.50443i −0.341717 + 0.272510i
\(409\) 18.4949 4.22135i 0.914515 0.208732i 0.260730 0.965412i \(-0.416037\pi\)
0.653786 + 0.756680i \(0.273180\pi\)
\(410\) −2.40955 + 10.5569i −0.118999 + 0.521370i
\(411\) −18.0629 22.6501i −0.890975 1.11725i
\(412\) 11.5254 14.4524i 0.567815 0.712017i
\(413\) −2.30157 10.0838i −0.113253 0.496192i
\(414\) 10.8343 + 22.4977i 0.532478 + 1.10570i
\(415\) −6.89859 + 3.32218i −0.338638 + 0.163080i
\(416\) 5.91885 + 1.35094i 0.290196 + 0.0662353i
\(417\) −14.6648 + 30.4518i −0.718140 + 1.49123i
\(418\) 6.00000i 0.293470i
\(419\) −8.57247 4.12828i −0.418792 0.201680i 0.212607 0.977138i \(-0.431805\pi\)
−0.631399 + 0.775458i \(0.717519\pi\)
\(420\) −20.4387 16.2994i −0.997309 0.795327i
\(421\) 29.0159 + 23.1394i 1.41415 + 1.12774i 0.973133 + 0.230245i \(0.0739527\pi\)
0.441015 + 0.897500i \(0.354619\pi\)
\(422\) −42.1644 20.3053i −2.05253 0.988448i
\(423\) 9.17157i 0.445937i
\(424\) −18.1667 + 37.7236i −0.882255 + 1.83202i
\(425\) −3.23063 0.737370i −0.156708 0.0357677i
\(426\) −46.3601 + 22.3259i −2.24615 + 1.08169i
\(427\) 5.92549 + 12.3044i 0.286754 + 0.595452i
\(428\) −12.6324 55.3462i −0.610611 2.67526i
\(429\) 2.38699 2.99318i 0.115245 0.144512i
\(430\) 5.39746 + 6.76820i 0.260289 + 0.326392i
\(431\) −4.37406 + 19.1640i −0.210691 + 0.923098i 0.753408 + 0.657554i \(0.228409\pi\)
−0.964099 + 0.265544i \(0.914448\pi\)
\(432\) −1.21149 + 0.276514i −0.0582876 + 0.0133038i
\(433\) −23.9455 + 19.0959i −1.15075 + 0.917690i −0.997512 0.0705003i \(-0.977540\pi\)
−0.153235 + 0.988190i \(0.548969\pi\)
\(434\) −68.7696 −3.30104
\(435\) 0 0
\(436\) 48.4558 2.32061
\(437\) 17.1543 13.6801i 0.820600 0.654406i
\(438\) 22.7292 5.18779i 1.08604 0.247882i
\(439\) −0.0763571 + 0.334542i −0.00364433 + 0.0159668i −0.976717 0.214530i \(-0.931178\pi\)
0.973073 + 0.230497i \(0.0740352\pi\)
\(440\) 1.14001 + 1.42952i 0.0543476 + 0.0681498i
\(441\) −1.76350 + 2.21135i −0.0839760 + 0.105303i
\(442\) −1.70381 7.46488i −0.0810420 0.355068i
\(443\) 10.5621 + 21.9324i 0.501820 + 1.04204i 0.985949 + 0.167044i \(0.0534222\pi\)
−0.484129 + 0.874997i \(0.660864\pi\)
\(444\) −33.3093 + 16.0409i −1.58079 + 0.761269i
\(445\) −12.1722 2.77824i −0.577020 0.131701i
\(446\) −3.32218 + 6.89859i −0.157310 + 0.326658i
\(447\) 18.8995i 0.893915i
\(448\) 25.0460 + 12.0615i 1.18331 + 0.569854i
\(449\) 27.3411 + 21.8038i 1.29031 + 1.02898i 0.997342 + 0.0728608i \(0.0232129\pi\)
0.292964 + 0.956124i \(0.405359\pi\)
\(450\) 21.3547 + 17.0298i 1.00667 + 0.802793i
\(451\) −1.67388 0.806097i −0.0788198 0.0379576i
\(452\) 50.9706i 2.39745i
\(453\) −14.8137 + 30.7610i −0.696009 + 1.44528i
\(454\) 19.1640 + 4.37406i 0.899412 + 0.205285i
\(455\) 9.75608 4.69828i 0.457372 0.220259i
\(456\) −27.7430 57.6090i −1.29919 2.69779i
\(457\) 0.229071 + 1.00363i 0.0107155 + 0.0469477i 0.980003 0.198983i \(-0.0637637\pi\)
−0.969288 + 0.245930i \(0.920907\pi\)
\(458\) 5.29049 6.63406i 0.247208 0.309989i
\(459\) −0.213948 0.268282i −0.00998623 0.0125223i
\(460\) 3.11529 13.6490i 0.145251 0.636387i
\(461\) 13.6490 3.11529i 0.635697 0.145094i 0.107486 0.994207i \(-0.465720\pi\)
0.528211 + 0.849113i \(0.322863\pi\)
\(462\) 5.33868 4.25745i 0.248378 0.198075i
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) 0 0
\(465\) −24.3137 −1.12752
\(466\) −34.5673 + 27.5665i −1.60130 + 1.27699i
\(467\) 37.3937 8.53487i 1.73037 0.394946i 0.762620 0.646846i \(-0.223913\pi\)
0.967753 + 0.251900i \(0.0810554\pi\)
\(468\) −9.22479 + 40.4165i −0.426416 + 1.86825i
\(469\) 9.97584 + 12.5093i 0.460641 + 0.577626i
\(470\) 4.88094 6.12051i 0.225141 0.282318i
\(471\) −4.55840 19.9717i −0.210040 0.920246i
\(472\) −7.00381 14.5436i −0.322376 0.669422i
\(473\) −1.33819 + 0.644439i −0.0615301 + 0.0296314i
\(474\) −13.7183 3.13111i −0.630101 0.143817i
\(475\) 10.4132 21.6233i 0.477791 0.992143i
\(476\) 8.97056i 0.411165i
\(477\) 24.1716 + 11.6404i 1.10674 + 0.532978i
\(478\) −37.1025 29.5882i −1.69703 1.35333i
\(479\) 5.39424 + 4.30176i 0.246469 + 0.196553i 0.738930 0.673782i \(-0.235331\pi\)
−0.492461 + 0.870334i \(0.663903\pi\)
\(480\) 3.44929 + 1.66109i 0.157438 + 0.0758181i
\(481\) 15.3137i 0.698245i
\(482\) 19.1834 39.8347i 0.873779 1.81442i
\(483\) −24.3445 5.55647i −1.10771 0.252828i
\(484\) 37.3504 17.9870i 1.69775 0.817592i
\(485\) −1.94609 4.04110i −0.0883674 0.183497i
\(486\) 11.6343 + 50.9734i 0.527745 + 2.31220i
\(487\) −7.17931 + 9.00257i −0.325326 + 0.407945i −0.917418 0.397925i \(-0.869731\pi\)
0.592093 + 0.805870i \(0.298302\pi\)
\(488\) 13.2889 + 16.6637i 0.601559 + 0.754332i
\(489\) −2.11067 + 9.24747i −0.0954480 + 0.418185i
\(490\) 2.35368 0.537213i 0.106329 0.0242688i
\(491\) 16.6082 13.2446i 0.749516 0.597719i −0.172437 0.985021i \(-0.555164\pi\)
0.921953 + 0.387301i \(0.126593\pi\)
\(492\) 41.4558 1.86897
\(493\) 0 0
\(494\) 55.4558 2.49508
\(495\) 0.915973 0.730464i 0.0411699 0.0328319i
\(496\) −29.4557 + 6.72307i −1.32260 + 0.301875i
\(497\) 5.55647 24.3445i 0.249242 1.09200i
\(498\) 27.8247 + 34.8911i 1.24686 + 1.56351i
\(499\) −11.8280 + 14.8318i −0.529492 + 0.663962i −0.972594 0.232509i \(-0.925306\pi\)
0.443102 + 0.896471i \(0.353878\pi\)
\(500\) −7.66715 33.5920i −0.342885 1.50228i
\(501\) 3.32218 + 6.89859i 0.148424 + 0.308206i
\(502\) −43.6572 + 21.0242i −1.94852 + 0.938356i
\(503\) −0.265256 0.0605430i −0.0118272 0.00269948i 0.216603 0.976260i \(-0.430502\pi\)
−0.228430 + 0.973560i \(0.573359\pi\)
\(504\) −15.3220 + 31.8166i −0.682498 + 1.41722i
\(505\) 2.34315i 0.104269i
\(506\) 3.29471 + 1.58665i 0.146468 + 0.0705352i
\(507\) −3.12733 2.49396i −0.138889 0.110761i
\(508\) −12.9998 10.3670i −0.576775 0.459962i
\(509\) 9.47343 + 4.56217i 0.419903 + 0.202214i 0.631890 0.775058i \(-0.282279\pi\)
−0.211988 + 0.977272i \(0.567994\pi\)
\(510\) 4.82843i 0.213806i
\(511\) −4.90883 + 10.1933i −0.217154 + 0.450925i
\(512\) 30.4593 + 6.95214i 1.34612 + 0.307244i
\(513\) 2.23916 1.07832i 0.0988614 0.0476091i
\(514\) 19.0345 + 39.5256i 0.839576 + 1.74340i
\(515\) 1.07443 + 4.70737i 0.0473449 + 0.207431i
\(516\) 20.6638 25.9116i 0.909672 1.14069i
\(517\) 0.837438 + 1.05011i 0.0368305 + 0.0461839i
\(518\) 6.07787 26.6289i 0.267046 1.17001i
\(519\) 29.0519 6.63090i 1.27524 0.291064i
\(520\) 13.2126 10.5367i 0.579409 0.462063i
\(521\) 29.1421 1.27674 0.638370 0.769730i \(-0.279609\pi\)
0.638370 + 0.769730i \(0.279609\pi\)
\(522\) 0 0
\(523\) 4.68629 0.204917 0.102459 0.994737i \(-0.467329\pi\)
0.102459 + 0.994737i \(0.467329\pi\)
\(524\) 63.7959 50.8755i 2.78694 2.22251i
\(525\) −26.6289 + 6.07787i −1.16218 + 0.265260i
\(526\) −1.48129 + 6.48995i −0.0645873 + 0.282975i
\(527\) −5.20187 6.52293i −0.226597 0.284143i
\(528\) 1.87047 2.34549i 0.0814017 0.102075i
\(529\) 2.14230 + 9.38604i 0.0931436 + 0.408089i
\(530\) −9.93572 20.6317i −0.431580 0.896185i
\(531\) −9.31885 + 4.48772i −0.404404 + 0.194751i
\(532\) 63.3416 + 14.4573i 2.74621 + 0.626804i
\(533\) −7.45047 + 15.4711i −0.322716 + 0.670126i
\(534\) 72.7696i 3.14905i
\(535\) 13.3600 + 6.43381i 0.577601 + 0.278158i
\(536\) 19.5228 + 15.5689i 0.843255 + 0.672474i
\(537\) −12.2410 9.76189i −0.528239 0.421257i
\(538\) 68.4206 + 32.9496i 2.94982 + 1.42056i
\(539\) 0.414214i 0.0178414i
\(540\) 0.688047 1.42874i 0.0296088 0.0614834i
\(541\) −10.0838 2.30157i −0.433537 0.0989521i 0.000182215 1.00000i \(-0.499942\pi\)
−0.433720 + 0.901048i \(0.642799\pi\)
\(542\) 36.0122 17.3426i 1.54686 0.744927i
\(543\) 8.70851 + 18.0834i 0.373718 + 0.776033i
\(544\) 0.292328 + 1.28077i 0.0125334 + 0.0549126i
\(545\) −7.89142 + 9.89553i −0.338031 + 0.423878i
\(546\) −39.3501 49.3435i −1.68403 2.11171i
\(547\) −7.96602 + 34.9014i −0.340603 + 1.49228i 0.457203 + 0.889362i \(0.348851\pi\)
−0.797805 + 0.602915i \(0.794006\pi\)
\(548\) 44.7893 10.2229i 1.91330 0.436699i
\(549\) 10.6774 8.51491i 0.455699 0.363407i
\(550\) 4.00000 0.170561
\(551\) 0 0
\(552\) −38.9706 −1.65870
\(553\) 5.33868 4.25745i 0.227024 0.181045i
\(554\) −40.7510 + 9.30115i −1.73134 + 0.395168i
\(555\) 2.14885 9.41474i 0.0912137 0.399633i
\(556\) −33.4178 41.9046i −1.41723 1.77715i
\(557\) 10.7949 13.5364i 0.457395 0.573556i −0.498639 0.866810i \(-0.666167\pi\)
0.956035 + 0.293254i \(0.0947381\pi\)
\(558\) 15.3027 + 67.0454i 0.647813 + 2.83826i
\(559\) 5.95632 + 12.3684i 0.251926 + 0.523129i
\(560\) 7.64497 3.68163i 0.323059 0.155577i
\(561\) 0.807657 + 0.184342i 0.0340993 + 0.00778294i
\(562\) 33.4888 69.5402i 1.41264 2.93338i
\(563\) 0.757359i 0.0319189i −0.999873 0.0159594i \(-0.994920\pi\)
0.999873 0.0159594i \(-0.00508026\pi\)
\(564\) −27.0025 13.0037i −1.13701 0.547556i
\(565\) −10.4091 8.30096i −0.437913 0.349224i
\(566\) −22.0024 17.5463i −0.924830 0.737527i
\(567\) −24.1716 11.6404i −1.01511 0.488852i
\(568\) 38.9706i 1.63517i
\(569\) −17.2065 + 35.7296i −0.721333 + 1.49786i 0.140180 + 0.990126i \(0.455232\pi\)
−0.861513 + 0.507736i \(0.830482\pi\)
\(570\) 34.0938 + 7.78168i 1.42803 + 0.325939i
\(571\) −13.1788 + 6.34660i −0.551518 + 0.265597i −0.688820 0.724932i \(-0.741871\pi\)
0.137303 + 0.990529i \(0.456157\pi\)
\(572\) 2.63414 + 5.46984i 0.110139 + 0.228706i
\(573\) 13.5989 + 59.5805i 0.568100 + 2.48901i
\(574\) −19.0959 + 23.9455i −0.797047 + 0.999465i
\(575\) −9.12005 11.4362i −0.380332 0.476921i
\(576\) 6.18586 27.1020i 0.257744 1.12925i
\(577\) −29.0519 + 6.63090i −1.20945 + 0.276048i −0.779265 0.626695i \(-0.784407\pi\)
−0.430180 + 0.902743i \(0.641550\pi\)
\(578\) −30.7923 + 24.5560i −1.28079 + 1.02140i
\(579\) 12.4853 0.518871
\(580\) 0 0
\(581\) −21.6569 −0.898478
\(582\) −20.4387 + 16.2994i −0.847213 + 0.675630i
\(583\) 3.83043 0.874270i 0.158640 0.0362085i
\(584\) −3.92902 + 17.2142i −0.162584 + 0.712327i
\(585\) −6.75141 8.46601i −0.279137 0.350026i
\(586\) 11.5254 14.4524i 0.476109 0.597022i
\(587\) −1.70381 7.46488i −0.0703238 0.308109i 0.927518 0.373780i \(-0.121938\pi\)
−0.997841 + 0.0656710i \(0.979081\pi\)
\(588\) −4.01023 8.32733i −0.165379 0.343413i
\(589\) 54.4423 26.2180i 2.24326 1.08030i
\(590\) 8.60708 + 1.96451i 0.354348 + 0.0808776i
\(591\) −2.09498 + 4.35026i −0.0861758 + 0.178946i
\(592\) 12.0000i 0.493197i
\(593\) −17.5556 8.45435i −0.720923 0.347178i 0.0371837 0.999308i \(-0.488161\pi\)
−0.758107 + 0.652130i \(0.773876\pi\)
\(594\) 0.323845 + 0.258258i 0.0132875 + 0.0105965i
\(595\) 1.83195 + 1.46093i 0.0751024 + 0.0598922i
\(596\) 27.0025 + 13.0037i 1.10607 + 0.532654i
\(597\) 1.17157i 0.0479493i
\(598\) 14.6648 30.4518i 0.599690 1.24527i
\(599\) 9.62259 + 2.19629i 0.393169 + 0.0897382i 0.414535 0.910034i \(-0.363944\pi\)
−0.0213660 + 0.999772i \(0.506802\pi\)
\(600\) −38.4060 + 18.4953i −1.56792 + 0.755069i
\(601\) −7.45047 15.4711i −0.303911 0.631077i 0.691952 0.721943i \(-0.256751\pi\)
−0.995863 + 0.0908658i \(0.971037\pi\)
\(602\) 5.44849 + 23.8714i 0.222064 + 0.972925i
\(603\) 9.97584 12.5093i 0.406247 0.509418i
\(604\) −33.7571 42.3300i −1.37356 1.72238i
\(605\) −2.40955 + 10.5569i −0.0979622 + 0.429200i
\(606\) 13.3144 3.03894i 0.540862 0.123448i
\(607\) 6.04193 4.81828i 0.245234 0.195568i −0.493157 0.869940i \(-0.664157\pi\)
0.738391 + 0.674372i \(0.235586\pi\)
\(608\) −9.51472 −0.385873
\(609\) 0 0
\(610\) −11.6569 −0.471972
\(611\) 9.70582 7.74014i 0.392656 0.313132i
\(612\) −8.74565 + 1.99614i −0.353522 + 0.0806891i
\(613\) −2.00269 + 8.77435i −0.0808878 + 0.354393i −0.999134 0.0416183i \(-0.986749\pi\)
0.918246 + 0.396011i \(0.129606\pi\)
\(614\) 4.36443 + 5.47282i 0.176134 + 0.220865i
\(615\) −6.75141 + 8.46601i −0.272243 + 0.341382i
\(616\) 1.15078 + 5.04191i 0.0463664 + 0.203144i
\(617\) −0.297771 0.618327i −0.0119878 0.0248929i 0.894889 0.446289i \(-0.147255\pi\)
−0.906877 + 0.421396i \(0.861540\pi\)
\(618\) 25.3552 12.2104i 1.01994 0.491175i
\(619\) −32.7437 7.47354i −1.31608 0.300387i −0.493853 0.869545i \(-0.664412\pi\)
−0.822228 + 0.569158i \(0.807269\pi\)
\(620\) 16.7290 34.7381i 0.671852 1.39511i
\(621\) 1.51472i 0.0607836i
\(622\) −5.84304 2.81386i −0.234284 0.112825i
\(623\) −27.6094 22.0177i −1.10615 0.882122i
\(624\) −21.6786 17.2881i −0.867837 0.692077i
\(625\) −9.91066 4.77272i −0.396426 0.190909i
\(626\) 23.7279i 0.948358i
\(627\) −2.60330 + 5.40581i −0.103966 + 0.215887i
\(628\) 31.6708 + 7.22866i 1.26380 + 0.288455i
\(629\) 2.98555 1.43776i 0.119042 0.0573274i
\(630\) −8.37990 17.4011i −0.333863 0.693274i
\(631\) −8.19510 35.9051i −0.326242 1.42936i −0.826233 0.563328i \(-0.809521\pi\)
0.499992 0.866030i \(-0.333336\pi\)
\(632\) 6.64444 8.33186i 0.264302 0.331424i
\(633\) −29.1787 36.5889i −1.15975 1.45428i
\(634\) −16.8985 + 74.0371i −0.671125 + 2.94039i
\(635\) 4.23425 0.966441i 0.168031 0.0383520i
\(636\) −68.5424 + 54.6608i −2.71788 + 2.16744i
\(637\) 3.82843 0.151688
\(638\) 0 0
\(639\) −24.9706 −0.987820
\(640\) −16.0716 + 12.8167i −0.635286 + 0.506624i
\(641\) −17.3527 + 3.96065i −0.685392 + 0.156436i −0.551017 0.834494i \(-0.685760\pi\)
−0.134375 + 0.990931i \(0.542903\pi\)
\(642\) 19.2317 84.2595i 0.759014 3.32546i
\(643\) −20.2542 25.3980i −0.798749 1.00160i −0.999758 0.0220105i \(-0.992993\pi\)
0.201008 0.979590i \(-0.435578\pi\)
\(644\) 24.6889 30.9589i 0.972880 1.21995i
\(645\) 1.92633 + 8.43981i 0.0758492 + 0.332317i
\(646\) 5.20660 + 10.8116i 0.204851 + 0.425378i
\(647\) 35.7296 17.2065i 1.40468 0.676456i 0.430571 0.902557i \(-0.358312\pi\)
0.974104 + 0.226101i \(0.0725978\pi\)
\(648\) −40.8203 9.31696i −1.60357 0.366005i
\(649\) −0.657212 + 1.36471i −0.0257978 + 0.0535697i
\(650\) 36.9706i 1.45010i
\(651\) −61.9592 29.8380i −2.42837 1.16944i
\(652\) −11.7600 9.37830i −0.460558 0.367283i
\(653\) −23.5661 18.7933i −0.922212 0.735439i 0.0424037 0.999101i \(-0.486498\pi\)
−0.964615 + 0.263661i \(0.915070\pi\)
\(654\) 66.4641 + 32.0074i 2.59895 + 1.25159i
\(655\) 21.3137i 0.832796i
\(656\) −5.83827 + 12.1233i −0.227946 + 0.473335i
\(657\) 11.0301 + 2.51754i 0.430323 + 0.0982185i
\(658\) 19.9494 9.60711i 0.777708 0.374524i
\(659\) 6.25409 + 12.9868i 0.243625 + 0.505892i 0.986545 0.163487i \(-0.0522743\pi\)
−0.742921 + 0.669380i \(0.766560\pi\)
\(660\) 0.851905 + 3.73244i 0.0331604 + 0.145285i
\(661\) 20.7708 26.0457i 0.807889 1.01306i −0.191612 0.981471i \(-0.561372\pi\)
0.999501 0.0315898i \(-0.0100570\pi\)
\(662\) 3.63396 + 4.55685i 0.141238 + 0.177107i
\(663\) 1.70381 7.46488i 0.0661705 0.289912i
\(664\) −32.9516 + 7.52098i −1.27877 + 0.291871i
\(665\) −13.2681 + 10.5810i −0.514516 + 0.410313i
\(666\) −27.3137 −1.05838
\(667\) 0 0
\(668\) −12.1421 −0.469793
\(669\) −5.98637 + 4.77397i −0.231446 + 0.184572i
\(670\) −13.3144 + 3.03894i −0.514382 + 0.117404i
\(671\) 0.445042 1.94986i 0.0171807 0.0752733i
\(672\) 6.75141 + 8.46601i 0.260441 + 0.326583i
\(673\) 13.4845 16.9090i 0.519788 0.651794i −0.450776 0.892637i \(-0.648853\pi\)
0.970564 + 0.240843i \(0.0774240\pi\)
\(674\) 11.7107 + 51.3079i 0.451079 + 1.97631i
\(675\) −0.718882 1.49277i −0.0276698 0.0574569i
\(676\) 5.71498 2.75219i 0.219807 0.105853i
\(677\) 21.4484 + 4.89546i 0.824330 + 0.188148i 0.613822 0.789444i \(-0.289631\pi\)
0.210507 + 0.977592i \(0.432488\pi\)
\(678\) −33.6685 + 69.9134i −1.29303 + 2.68501i
\(679\) 12.6863i 0.486855i
\(680\) 3.29471 + 1.58665i 0.126346 + 0.0608452i
\(681\) 15.3683 + 12.2558i 0.588916 + 0.469645i
\(682\) 7.87388 + 6.27921i 0.301506 + 0.240443i
\(683\) −18.8938 9.09879i −0.722952 0.348155i 0.0359558 0.999353i \(-0.488552\pi\)
−0.758908 + 0.651198i \(0.774267\pi\)
\(684\) 64.9706i 2.48421i
\(685\) −5.20660 + 10.8116i −0.198934 + 0.413091i
\(686\) −39.9433 9.11681i −1.52504 0.348081i
\(687\) 7.64497 3.68163i 0.291674 0.140463i
\(688\) 4.66744 + 9.69205i 0.177945 + 0.369506i
\(689\) −8.08056 35.4032i −0.307845 1.34876i
\(690\) 13.2889 16.6637i 0.505899 0.634377i
\(691\) 29.9275 + 37.5279i 1.13850 + 1.42763i 0.888198 + 0.459460i \(0.151957\pi\)
0.250298 + 0.968169i \(0.419471\pi\)
\(692\) −10.5152 + 46.0701i −0.399728 + 1.75132i
\(693\) 3.23063 0.737370i 0.122721 0.0280104i
\(694\) 4.69099 3.74094i 0.178068 0.142004i
\(695\) 14.0000 0.531050
\(696\) 0 0
\(697\) −3.71573 −0.140743
\(698\) 9.70582 7.74014i 0.367371 0.292968i
\(699\) −43.1047 + 9.83836i −1.63037 + 0.372121i
\(700\) 9.63821 42.2277i 0.364290 1.59606i
\(701\) 25.0099 + 31.3614i 0.944609 + 1.18450i 0.982696 + 0.185228i \(0.0593024\pi\)
−0.0380862 + 0.999274i \(0.512126\pi\)
\(702\) 2.38699 2.99318i 0.0900910 0.112970i
\(703\) 5.34050 + 23.3983i 0.201421 + 0.882482i
\(704\) −1.76637 3.66791i −0.0665726 0.138239i
\(705\) 7.05317 3.39663i 0.265638 0.127924i
\(706\) 63.4802 + 14.4889i 2.38911 + 0.545298i
\(707\) −2.87553 + 5.97110i −0.108145 + 0.224566i
\(708\) 33.7990i 1.27024i
\(709\) 26.2562 + 12.6443i 0.986071 + 0.474867i 0.856189 0.516663i \(-0.172826\pi\)
0.129882 + 0.991529i \(0.458540\pi\)
\(710\) 16.6637 + 13.2889i 0.625379 + 0.498723i
\(711\) −5.33868 4.25745i −0.200216 0.159667i
\(712\) −49.6548 23.9125i −1.86089 0.896159i
\(713\) 36.8284i 1.37924i
\(714\) 5.92549 12.3044i 0.221756 0.460481i
\(715\) −1.54603 0.352871i −0.0578181 0.0131966i
\(716\) 22.3696 10.7727i 0.835993 0.402593i
\(717\) −20.5903 42.7562i −0.768960 1.59676i
\(718\) −2.11067 9.24747i −0.0787696 0.345112i
\(719\) −12.5584 + 15.7478i −0.468350 + 0.587292i −0.958766 0.284196i \(-0.908273\pi\)
0.490416 + 0.871488i \(0.336845\pi\)
\(720\) −5.29049 6.63406i −0.197165 0.247237i
\(721\) −3.03894 + 13.3144i −0.113176 + 0.495856i
\(722\) −40.0126 + 9.13262i −1.48912 + 0.339881i
\(723\) 34.5673 27.5665i 1.28557 1.02521i
\(724\) −31.8284 −1.18289
\(725\) 0 0
\(726\) 63.1127 2.34233
\(727\) 1.02710 0.819084i 0.0380930 0.0303781i −0.604258 0.796789i \(-0.706530\pi\)
0.642351 + 0.766410i \(0.277959\pi\)
\(728\) 46.6006 10.6363i 1.72713 0.394207i
\(729\) −5.30232 + 23.2310i −0.196382 + 0.860407i
\(730\) −6.02095 7.55003i −0.222845 0.279439i
\(731\) −1.85212 + 2.32248i −0.0685030 + 0.0859000i
\(732\) 9.93053 + 43.5085i 0.367043 + 1.60812i
\(733\) 17.8998 + 37.1693i 0.661144 + 1.37288i 0.914134 + 0.405411i \(0.132872\pi\)
−0.252990 + 0.967469i \(0.581414\pi\)
\(734\) −39.1524 + 18.8548i −1.44514 + 0.695943i
\(735\) 2.35368 + 0.537213i 0.0868169 + 0.0198154i
\(736\) −2.51609 + 5.22471i −0.0927442 + 0.192585i
\(737\) 2.34315i 0.0863109i
\(738\) 27.5943 + 13.2887i 1.01576 + 0.489165i
\(739\) −3.18289 2.53827i −0.117084 0.0933717i 0.563197 0.826323i \(-0.309571\pi\)
−0.680282 + 0.732951i \(0.738143\pi\)
\(740\) 11.9727 + 9.54794i 0.440127 + 0.350989i
\(741\) 49.9640 + 24.0614i 1.83547 + 0.883917i
\(742\) 64.7696i 2.37777i
\(743\) 10.2643 21.3141i 0.376562 0.781938i −0.623438 0.781872i \(-0.714265\pi\)
1.00000 6.56698e-5i \(-2.09033e-5\pi\)
\(744\) −104.635 23.8823i −3.83611 0.875566i
\(745\) −7.05317 + 3.39663i −0.258408 + 0.124443i
\(746\) 27.5633 + 57.2358i 1.00916 + 2.09555i
\(747\) 4.81910 + 21.1139i 0.176322 + 0.772516i
\(748\) −0.819084 + 1.02710i −0.0299487 + 0.0375544i
\(749\) 26.1499 + 32.7909i 0.955495 + 1.19815i
\(750\) 11.6725 51.1407i 0.426220 1.86739i
\(751\) 24.6790 5.63283i 0.900551 0.205545i 0.252909 0.967490i \(-0.418613\pi\)
0.647642 + 0.761945i \(0.275755\pi\)
\(752\) 7.60560 6.06526i 0.277348 0.221177i
\(753\) −48.4558 −1.76583
\(754\) 0 0
\(755\) 14.1421 0.514685
\(756\) 3.50673 2.79653i 0.127539 0.101709i
\(757\) −24.8750 + 5.67756i −0.904098 + 0.206354i −0.649204 0.760615i \(-0.724898\pi\)
−0.254894 + 0.966969i \(0.582041\pi\)
\(758\) 3.74468 16.4065i 0.136013 0.595911i
\(759\) 2.28001 + 2.85904i 0.0827592 + 0.103777i
\(760\) −16.5133 + 20.7070i −0.599000 + 0.751123i
\(761\) −10.1465 44.4547i −0.367811 1.61148i −0.732781 0.680464i \(-0.761778\pi\)
0.364971 0.931019i \(-0.381079\pi\)
\(762\) −10.9832 22.8069i −0.397880 0.826205i
\(763\) −32.2538 + 15.5326i −1.16767 + 0.562318i
\(764\) −94.4819 21.5649i −3.41824 0.780190i
\(765\) 1.01665 2.11110i 0.0367572 0.0763270i
\(766\) 8.48528i 0.306586i
\(767\) 12.6136 + 6.07437i 0.455449 + 0.219333i
\(768\) 56.5697 + 45.1128i 2.04128 + 1.62787i
\(769\) −38.3979 30.6213i −1.38466 1.10423i −0.982000 0.188883i \(-0.939513\pi\)
−0.402662 0.915349i \(-0.631915\pi\)
\(770\) −2.54832 1.22721i −0.0918353 0.0442255i
\(771\) 43.8701i 1.57994i
\(772\) −8.59046 + 17.8383i −0.309177 + 0.642014i
\(773\) −19.0254 4.34243i −0.684298 0.156186i −0.133781 0.991011i \(-0.542712\pi\)
−0.550516 + 0.834824i \(0.685569\pi\)
\(774\) 22.0605 10.6238i 0.792947 0.381863i
\(775\) −17.4787 36.2949i −0.627853 1.30375i
\(776\) −4.40569 19.3026i −0.158155 0.692923i
\(777\) 17.0298 21.3547i 0.610941 0.766096i
\(778\) −4.56002 5.71809i −0.163485 0.205003i
\(779\) 5.98841 26.2370i 0.214557 0.940037i
\(780\) 34.4976 7.87385i 1.23521 0.281929i
\(781\) −2.85904 + 2.28001i −0.102305 + 0.0815852i
\(782\) 7.31371 0.261538
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) −6.63406 + 5.29049i −0.236780 + 0.188826i
\(786\) 121.111 27.6428i 4.31988 0.985984i
\(787\) −12.0347 + 52.7273i −0.428989 + 1.87952i 0.0449881 + 0.998988i \(0.485675\pi\)
−0.473977 + 0.880537i \(0.657182\pi\)
\(788\) −4.77397 5.98637i −0.170066 0.213256i
\(789\) −4.15048 + 5.20454i −0.147761 + 0.185286i
\(790\) 1.29695 + 5.68230i 0.0461433 + 0.202167i
\(791\) −16.3387 33.9277i −0.580937 1.20633i
\(792\) 4.65943 2.24386i 0.165565 0.0797321i
\(793\) −18.0218 4.11336i −0.639973 0.146070i
\(794\) 20.2617 42.0739i 0.719061 1.49315i
\(795\) 22.8995i 0.812161i
\(796\) −1.67388 0.806097i −0.0593290 0.0285714i
\(797\) −40.4521 32.2594i −1.43289 1.14269i −0.966054 0.258342i \(-0.916824\pi\)
−0.466832 0.884346i \(-0.654605\pi\)
\(798\) 77.3323 + 61.6704i 2.73753 + 2.18311i
\(799\) 2.42027 + 1.16554i 0.0856228 + 0.0412338i
\(800\) 6.34315i 0.224264i
\(801\) −15.3220 + 31.8166i −0.541378 + 1.12418i
\(802\) 43.9123 + 10.0227i 1.55060 + 0.353914i
\(803\) 1.49277 0.718882i 0.0526789 0.0253688i
\(804\) 22.6853 + 47.1065i 0.800049 + 1.66132i
\(805\) 2.30157 + 10.0838i 0.0811196 + 0.355408i
\(806\) 58.0365 72.7754i 2.04425 2.56340i
\(807\) 47.3485 + 59.3732i 1.66675 + 2.09003i
\(808\) −2.30157 + 10.0838i −0.0809688 + 0.354748i
\(809\) 35.3745 8.07401i 1.24370 0.283867i 0.450473 0.892790i \(-0.351255\pi\)
0.793230 + 0.608923i \(0.208398\pi\)
\(810\) 17.9035 14.2776i 0.629066 0.501664i
\(811\) −10.8284 −0.380238 −0.190119 0.981761i \(-0.560887\pi\)
−0.190119 + 0.981761i \(0.560887\pi\)
\(812\) 0 0
\(813\) 39.9706 1.40183
\(814\) −3.12733 + 2.49396i −0.109613 + 0.0874132i
\(815\) 3.83043 0.874270i 0.134174 0.0306243i
\(816\) 1.33513 5.84957i 0.0467387 0.204776i
\(817\) −13.4142 16.8209i −0.469304 0.588488i
\(818\) −28.5552 + 35.8071i −0.998409 + 1.25197i
\(819\) −6.81524 29.8595i −0.238144 1.04338i
\(820\) −7.45047 15.4711i −0.260182 0.540273i
\(821\) −1.33819 + 0.644439i −0.0467032 + 0.0224911i −0.457090 0.889421i \(-0.651108\pi\)
0.410386 + 0.911912i \(0.365394\pi\)
\(822\) 68.1876 + 15.5634i 2.37831 + 0.542835i
\(823\) 23.5531 48.9084i 0.821008 1.70484i 0.118744 0.992925i \(-0.462113\pi\)
0.702265 0.711916i \(-0.252172\pi\)
\(824\) 21.3137i 0.742498i
\(825\) 3.60388 + 1.73553i 0.125471 + 0.0604236i
\(826\) 19.5228 + 15.5689i 0.679284 + 0.541711i
\(827\) 25.7219 + 20.5125i 0.894437 + 0.713289i 0.958632 0.284648i \(-0.0918767\pi\)
−0.0641954 + 0.997937i \(0.520448\pi\)
\(828\) −35.6765 17.1809i −1.23985 0.597078i
\(829\) 29.7990i 1.03496i 0.855695 + 0.517481i \(0.173130\pi\)
−0.855695 + 0.517481i \(0.826870\pi\)
\(830\) 8.02046 16.6547i 0.278394 0.578092i
\(831\) −40.7510 9.30115i −1.41364 0.322653i
\(832\) −33.9011 + 16.3259i −1.17531 + 0.566000i
\(833\) 0.359441 + 0.746387i 0.0124539 + 0.0258608i
\(834\) −18.1573 79.5521i −0.628734 2.75467i
\(835\) 1.97744 2.47964i 0.0684322 0.0858113i
\(836\) −5.93233 7.43891i −0.205174 0.257280i
\(837\) 0.928262 4.06698i 0.0320854 0.140575i
\(838\) 22.3946 5.11143i 0.773610 0.176571i
\(839\) 6.19909 4.94361i 0.214016 0.170672i −0.510614 0.859810i \(-0.670582\pi\)
0.724630 + 0.689138i \(0.242010\pi\)
\(840\) 30.1421 1.04000
\(841\) 0 0
\(842\) −89.5980 −3.08775
\(843\) 60.3447 48.1233i 2.07838 1.65745i
\(844\) 72.3525 16.5140i 2.49048 0.568435i
\(845\) −0.368685 + 1.61531i −0.0126831 + 0.0555685i
\(846\) −13.8054 17.3114i −0.474639 0.595179i
\(847\) −19.0959 + 23.9455i −0.656142 + 0.822776i
\(848\) −6.33202 27.7424i −0.217442 0.952678i
\(849\) −12.2104 25.3552i −0.419060 0.870188i
\(850\) 7.20775 3.47107i 0.247224 0.119057i
\(851\) 14.2607 + 3.25491i 0.488850 + 0.111577i
\(852\) 35.4040 73.5172i 1.21292 2.51866i
\(853\) 22.9706i 0.786497i −0.919432 0.393249i \(-0.871351\pi\)
0.919432 0.393249i \(-0.128649\pi\)
\(854\) −29.7055 14.3054i −1.01650 0.489520i
\(855\) 13.2681 + 10.5810i 0.453760 + 0.361862i
\(856\) 51.1754 + 40.8111i 1.74914 + 1.39489i
\(857\) 5.56040 + 2.67775i 0.189939 + 0.0914700i 0.526436 0.850215i \(-0.323528\pi\)
−0.336497 + 0.941685i \(0.609242\pi\)
\(858\) 9.24264i 0.315539i
\(859\) 8.55962 17.7742i 0.292051 0.606449i −0.702385 0.711797i \(-0.747881\pi\)
0.994435 + 0.105348i \(0.0335957\pi\)
\(860\) −13.3837 3.05475i −0.456382 0.104166i
\(861\) −27.5943 + 13.2887i −0.940413 + 0.452879i
\(862\) −20.5903 42.7562i −0.701309 1.45628i
\(863\) 3.80793 + 16.6836i 0.129624 + 0.567918i 0.997470 + 0.0710858i \(0.0226464\pi\)
−0.867847 + 0.496832i \(0.834496\pi\)
\(864\) −0.409542 + 0.513549i −0.0139329 + 0.0174713i
\(865\) −7.69583 9.65026i −0.261666 0.328119i
\(866\) 16.4534 72.0873i 0.559111 2.44963i
\(867\) −38.3973 + 8.76394i −1.30404 + 0.297639i
\(868\) 85.2617 67.9939i 2.89397 2.30786i
\(869\) −1.00000 −0.0339227
\(870\) 0 0
\(871\) −21.6569 −0.733815
\(872\) −43.6810 + 34.8344i −1.47922 + 1.17964i
\(873\) −12.3682 + 2.82297i −0.418601 + 0.0955429i
\(874\) −11.7871 + 51.6425i −0.398703 + 1.74683i
\(875\) 15.8715 + 19.9022i 0.536553 + 0.672816i
\(876\) −23.0508 + 28.9047i −0.778813 + 0.976601i
\(877\) 8.26490 + 36.2109i 0.279086 + 1.22276i 0.898952 + 0.438048i \(0.144330\pi\)
−0.619866 + 0.784708i \(0.712813\pi\)
\(878\) −0.359441 0.746387i −0.0121305 0.0251893i
\(879\) 16.6547 8.02046i 0.561748 0.270524i
\(880\) −1.21149 0.276514i −0.0408392 0.00932127i
\(881\) −6.07437 + 12.6136i −0.204651 + 0.424962i −0.977881 0.209164i \(-0.932926\pi\)
0.773230 + 0.634126i \(0.218640\pi\)
\(882\) 6.82843i 0.229925i
\(883\) 34.6210 + 16.6726i 1.16509 + 0.561077i 0.913533 0.406765i \(-0.133343\pi\)
0.251557 + 0.967843i \(0.419058\pi\)
\(884\) 9.49310 + 7.57050i 0.319288 + 0.254623i
\(885\) 6.90234 + 5.50443i 0.232020 + 0.185030i
\(886\) −52.9495 25.4992i −1.77887 0.856661i
\(887\) 17.1005i 0.574179i −0.957904 0.287089i \(-0.907312\pi\)
0.957904 0.287089i \(-0.0926877\pi\)
\(888\) 18.4953 38.4060i 0.620663 1.28882i
\(889\) 11.9763 + 2.73351i 0.401672 + 0.0916789i
\(890\) 27.1571 13.0782i 0.910309 0.438382i
\(891\) 1.70470 + 3.53985i 0.0571096 + 0.118589i
\(892\) −2.70188 11.8377i −0.0904656 0.396356i
\(893\) −12.1305 + 15.2112i −0.405932 + 0.509023i
\(894\) 28.4482 + 35.6730i 0.951451 + 1.19308i
\(895\) −1.44311 + 6.32268i −0.0482379 + 0.211344i
\(896\) −56.6844 + 12.9378i −1.89369 + 0.432223i
\(897\) 26.4251 21.0733i 0.882309 0.703618i
\(898\) −84.4264 −2.81735
\(899\) 0 0
\(900\) −43.3137 −1.44379
\(901\) 6.14353 4.89930i 0.204671 0.163219i
\(902\) 4.37283 0.998069i 0.145599 0.0332321i
\(903\) −5.44849 + 23.8714i −0.181314 + 0.794390i
\(904\) −36.6422 45.9479i −1.21870 1.52820i
\(905\) 5.18351 6.49992i 0.172306 0.216065i
\(906\) −18.3416 80.3598i −0.609359 2.66978i
\(907\) −9.66878 20.0774i −0.321047 0.666660i 0.676517 0.736427i \(-0.263489\pi\)
−0.997563 + 0.0697671i \(0.977774\pi\)
\(908\) −28.0846 + 13.5248i −0.932021 + 0.448838i
\(909\) 6.46125 + 1.47474i 0.214306 + 0.0489140i
\(910\) −11.3426 + 23.5533i −0.376005 + 0.780783i
\(911\) 15.4437i 0.511671i −0.966720 0.255835i \(-0.917649\pi\)
0.966720 0.255835i \(-0.0823505\pi\)
\(912\) 39.1524 + 18.8548i 1.29646 + 0.624344i
\(913\) 2.47964 + 1.97744i 0.0820640 + 0.0654438i
\(914\) −1.94307 1.54955i −0.0642711 0.0512545i
\(915\) −10.5025 5.05772i −0.347201 0.167203i
\(916\) 13.4558i 0.444594i
\(917\) −26.1564 + 54.3143i −0.863759 + 1.79361i
\(918\) 0.807657 + 0.184342i 0.0266566 + 0.00608421i
\(919\) −7.33581 + 3.53274i −0.241986 + 0.116534i −0.550947 0.834541i \(-0.685733\pi\)
0.308960 + 0.951075i \(0.400019\pi\)
\(920\) 7.00381 + 14.5436i 0.230909 + 0.479487i
\(921\) 1.55765 + 6.82450i 0.0513262 + 0.224875i
\(922\) −21.0733 + 26.4251i −0.694013 + 0.870265i
\(923\) 21.0733 + 26.4251i 0.693637 + 0.869793i
\(924\) −2.40955 + 10.5569i −0.0792684 + 0.347298i
\(925\) 15.5988 3.56033i 0.512887 0.117063i
\(926\) −49.0752 + 39.1362i −1.61271 + 1.28609i
\(927\) 13.6569 0.448550
\(928\) 0 0
\(929\) 18.6863 0.613077 0.306539 0.951858i \(-0.400829\pi\)
0.306539 + 0.951858i \(0.400829\pi\)
\(930\) 45.8923 36.5979i 1.50487 1.20009i
\(931\) −5.84957 + 1.33513i −0.191712 + 0.0437570i
\(932\) 15.6015 68.3548i 0.511046 2.23904i
\(933\) −4.04351 5.07040i −0.132378 0.165997i
\(934\) −57.7339 + 72.3960i −1.88911 + 2.36887i
\(935\) −0.0763571 0.334542i −0.00249714 0.0109407i
\(936\) −20.7392 43.0654i −0.677882 1.40764i
\(937\) −14.9808 + 7.21437i −0.489401 + 0.235683i −0.662275 0.749261i \(-0.730409\pi\)
0.172874 + 0.984944i \(0.444695\pi\)
\(938\) −37.6589 8.59541i −1.22961 0.280650i
\(939\) −10.2952 + 21.3781i −0.335970 + 0.697649i
\(940\) 12.4142i 0.404907i
\(941\) −50.9930 24.5569i −1.66232 0.800533i −0.998619 0.0525400i \(-0.983268\pi\)
−0.663706 0.747994i \(-0.731017\pi\)
\(942\) 38.6661 + 30.8352i 1.25981 + 1.00467i
\(943\) −12.8236 10.2265i −0.417594 0.333020i
\(944\) 9.88414 + 4.75995i 0.321701 + 0.154923i
\(945\) 1.17157i 0.0381113i
\(946\) 1.55581 3.23068i 0.0505839 0.105039i
\(947\) 2.54965 + 0.581942i 0.0828526 + 0.0189106i 0.263746 0.964592i \(-0.415042\pi\)
−0.180894 + 0.983503i \(0.557899\pi\)
\(948\) 20.1040 9.68156i 0.652946 0.314442i
\(949\) −6.64437 13.7972i −0.215685 0.447875i
\(950\) 12.8931 + 56.4884i 0.418308 + 1.83273i
\(951\) −47.3485 + 59.3732i −1.53538 + 1.92531i
\(952\) 6.44885 + 8.08660i 0.209008 + 0.262088i
\(953\) 7.92785 34.7342i 0.256808 1.12515i −0.667833 0.744311i \(-0.732778\pi\)
0.924641 0.380839i \(-0.124365\pi\)
\(954\) −63.1456 + 14.4126i −2.04442 + 0.466625i
\(955\) 19.7911 15.7828i 0.640423 0.510721i
\(956\) 75.2548 2.43392
\(957\) 0 0
\(958\) −16.6569 −0.538159
\(959\) −26.5362 + 21.1619i −0.856900 + 0.683355i
\(960\) −23.1330 + 5.27996i −0.746615 + 0.170410i
\(961\) 15.6713 68.6607i 0.505527 2.21486i
\(962\) 23.0508 + 28.9047i 0.743187 + 0.931927i
\(963\) 26.1499 32.7909i 0.842668 1.05667i
\(964\) 15.6015 + 68.3548i 0.502492 + 2.20156i
\(965\) −2.24386 4.65943i −0.0722325 0.149992i
\(966\) 54.3143 26.1564i 1.74753 0.841567i
\(967\) 34.3590 + 7.84223i 1.10491 + 0.252189i 0.735802 0.677197i \(-0.236805\pi\)
0.369110 + 0.929386i \(0.379663\pi\)
\(968\) −20.7392 + 43.0654i −0.666583 + 1.38417i
\(969\) 12.0000i 0.385496i
\(970\) 9.75608 + 4.69828i 0.313249 + 0.150853i
\(971\) 12.2410 + 9.76189i 0.392833 + 0.313274i 0.799910 0.600120i \(-0.204880\pi\)
−0.407077 + 0.913394i \(0.633452\pi\)
\(972\) −64.8230 51.6946i −2.07920 1.65810i
\(973\) 35.6765 + 17.1809i 1.14374 + 0.550795i
\(974\) 27.7990i 0.890737i
\(975\) 16.0409 33.3093i 0.513721 1.06675i
\(976\) −14.1221 3.22328i −0.452038 0.103175i
\(977\) −32.5895 + 15.6943i −1.04263 + 0.502104i −0.875190 0.483779i \(-0.839264\pi\)
−0.167439 + 0.985882i \(0.553550\pi\)
\(978\) −9.93572 20.6317i −0.317709 0.659730i
\(979\) 1.15078 + 5.04191i 0.0367792 + 0.161140i
\(980\) −2.38699 + 2.99318i −0.0762494 + 0.0956138i
\(981\) 22.3203 + 27.9888i 0.712632 + 0.893613i
\(982\) −11.4118 + 49.9985i −0.364166 + 1.59552i
\(983\) −21.3217 + 4.86655i −0.680058 + 0.155219i −0.548577 0.836100i \(-0.684830\pi\)
−0.131481 + 0.991319i \(0.541973\pi\)
\(984\) −37.3708 + 29.8022i −1.19134 + 0.950059i
\(985\) 2.00000 0.0637253
\(986\) 0 0
\(987\) 22.1421 0.704792
\(988\) −68.7551 + 54.8304i −2.18739 + 1.74439i
\(989\) −12.7839 + 2.91785i −0.406506 + 0.0927822i
\(990\) −0.629384 + 2.75751i −0.0200031 + 0.0876395i
\(991\) 7.99839 + 10.0297i 0.254077 + 0.318603i 0.892469 0.451109i \(-0.148971\pi\)
−0.638392 + 0.769712i \(0.720400\pi\)
\(992\) −9.95748 + 12.4863i −0.316150 + 0.396440i
\(993\) 1.29695 + 5.68230i 0.0411574 + 0.180322i
\(994\) 26.1564 + 54.3143i 0.829630 + 1.72274i
\(995\) 0.437223 0.210556i 0.0138609 0.00667506i
\(996\) −68.9952 15.7477i −2.18620 0.498985i
\(997\) −12.2721 + 25.4832i −0.388661 + 0.807063i 0.611217 + 0.791463i \(0.290680\pi\)
−0.999878 + 0.0155999i \(0.995034\pi\)
\(998\) 45.7990i 1.44974i
\(999\) 1.49277 + 0.718882i 0.0472293 + 0.0227444i
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 841.2.e.k.63.1 24
29.2 odd 28 841.2.d.f.571.1 12
29.3 odd 28 841.2.d.f.190.1 12
29.4 even 14 inner 841.2.e.k.196.1 24
29.5 even 14 inner 841.2.e.k.270.4 24
29.6 even 14 inner 841.2.e.k.267.1 24
29.7 even 7 inner 841.2.e.k.651.4 24
29.8 odd 28 29.2.a.a.1.1 2
29.9 even 14 841.2.b.a.840.1 4
29.10 odd 28 841.2.d.j.645.2 12
29.11 odd 28 841.2.d.f.605.1 12
29.12 odd 4 841.2.d.j.778.1 12
29.13 even 14 inner 841.2.e.k.236.4 24
29.14 odd 28 841.2.d.f.574.2 12
29.15 odd 28 841.2.d.j.574.1 12
29.16 even 7 inner 841.2.e.k.236.1 24
29.17 odd 4 841.2.d.f.778.2 12
29.18 odd 28 841.2.d.j.605.2 12
29.19 odd 28 841.2.d.f.645.1 12
29.20 even 7 841.2.b.a.840.4 4
29.21 odd 28 841.2.a.d.1.2 2
29.22 even 14 inner 841.2.e.k.651.1 24
29.23 even 7 inner 841.2.e.k.267.4 24
29.24 even 7 inner 841.2.e.k.270.1 24
29.25 even 7 inner 841.2.e.k.196.4 24
29.26 odd 28 841.2.d.j.190.2 12
29.27 odd 28 841.2.d.j.571.2 12
29.28 even 2 inner 841.2.e.k.63.4 24
87.8 even 28 261.2.a.d.1.2 2
87.50 even 28 7569.2.a.c.1.1 2
116.95 even 28 464.2.a.h.1.1 2
145.8 even 28 725.2.b.b.349.4 4
145.37 even 28 725.2.b.b.349.1 4
145.124 odd 28 725.2.a.b.1.2 2
203.153 even 28 1421.2.a.j.1.1 2
232.37 odd 28 1856.2.a.r.1.1 2
232.211 even 28 1856.2.a.w.1.2 2
319.153 even 28 3509.2.a.j.1.2 2
348.95 odd 28 4176.2.a.bq.1.2 2
377.298 odd 28 4901.2.a.g.1.2 2
435.269 even 28 6525.2.a.o.1.1 2
493.356 odd 28 8381.2.a.e.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.2.a.a.1.1 2 29.8 odd 28
261.2.a.d.1.2 2 87.8 even 28
464.2.a.h.1.1 2 116.95 even 28
725.2.a.b.1.2 2 145.124 odd 28
725.2.b.b.349.1 4 145.37 even 28
725.2.b.b.349.4 4 145.8 even 28
841.2.a.d.1.2 2 29.21 odd 28
841.2.b.a.840.1 4 29.9 even 14
841.2.b.a.840.4 4 29.20 even 7
841.2.d.f.190.1 12 29.3 odd 28
841.2.d.f.571.1 12 29.2 odd 28
841.2.d.f.574.2 12 29.14 odd 28
841.2.d.f.605.1 12 29.11 odd 28
841.2.d.f.645.1 12 29.19 odd 28
841.2.d.f.778.2 12 29.17 odd 4
841.2.d.j.190.2 12 29.26 odd 28
841.2.d.j.571.2 12 29.27 odd 28
841.2.d.j.574.1 12 29.15 odd 28
841.2.d.j.605.2 12 29.18 odd 28
841.2.d.j.645.2 12 29.10 odd 28
841.2.d.j.778.1 12 29.12 odd 4
841.2.e.k.63.1 24 1.1 even 1 trivial
841.2.e.k.63.4 24 29.28 even 2 inner
841.2.e.k.196.1 24 29.4 even 14 inner
841.2.e.k.196.4 24 29.25 even 7 inner
841.2.e.k.236.1 24 29.16 even 7 inner
841.2.e.k.236.4 24 29.13 even 14 inner
841.2.e.k.267.1 24 29.6 even 14 inner
841.2.e.k.267.4 24 29.23 even 7 inner
841.2.e.k.270.1 24 29.24 even 7 inner
841.2.e.k.270.4 24 29.5 even 14 inner
841.2.e.k.651.1 24 29.22 even 14 inner
841.2.e.k.651.4 24 29.7 even 7 inner
1421.2.a.j.1.1 2 203.153 even 28
1856.2.a.r.1.1 2 232.37 odd 28
1856.2.a.w.1.2 2 232.211 even 28
3509.2.a.j.1.2 2 319.153 even 28
4176.2.a.bq.1.2 2 348.95 odd 28
4901.2.a.g.1.2 2 377.298 odd 28
6525.2.a.o.1.1 2 435.269 even 28
7569.2.a.c.1.1 2 87.50 even 28
8381.2.a.e.1.1 2 493.356 odd 28