Properties

Label 605.2.m.c.233.2
Level $605$
Weight $2$
Character 605.233
Analytic conductor $4.831$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(112,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.112");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.m (of order \(20\), degree \(8\), 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 233.2
Character \(\chi\) \(=\) 605.233
Dual form 605.2.m.c.457.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.10335 + 0.562185i) q^{2} +(2.51281 + 0.397989i) q^{3} +(-0.274241 + 0.377461i) q^{4} +(1.89876 + 1.18097i) q^{5} +(-2.99625 + 0.973540i) q^{6} +(0.542552 + 3.42554i) q^{7} +(0.477813 - 3.01679i) q^{8} +(3.30263 + 1.07309i) q^{9} +O(q^{10})\) \(q+(-1.10335 + 0.562185i) q^{2} +(2.51281 + 0.397989i) q^{3} +(-0.274241 + 0.377461i) q^{4} +(1.89876 + 1.18097i) q^{5} +(-2.99625 + 0.973540i) q^{6} +(0.542552 + 3.42554i) q^{7} +(0.477813 - 3.01679i) q^{8} +(3.30263 + 1.07309i) q^{9} +(-2.75893 - 0.235572i) q^{10} +(-0.839340 + 0.839340i) q^{12} +(0.335770 + 0.658986i) q^{13} +(-2.52441 - 3.47455i) q^{14} +(4.30121 + 3.72325i) q^{15} +(0.880445 + 2.70973i) q^{16} +(-0.280240 + 0.550001i) q^{17} +(-4.24723 + 0.672695i) q^{18} +(2.54465 - 1.84880i) q^{19} +(-0.966490 + 0.392836i) q^{20} +8.82364i q^{21} +(-4.30752 - 4.30752i) q^{23} +(2.40130 - 7.39045i) q^{24} +(2.21060 + 4.48478i) q^{25} +(-0.740944 - 0.538327i) q^{26} +(1.07129 + 0.545847i) q^{27} +(-1.44180 - 0.734631i) q^{28} +(-2.34668 - 1.70497i) q^{29} +(-6.83889 - 1.68997i) q^{30} +(0.937993 - 2.88684i) q^{31} +(1.82476 + 1.82476i) q^{32} -0.764390i q^{34} +(-3.01529 + 7.14502i) q^{35} +(-1.31077 + 0.952327i) q^{36} +(-2.27244 + 0.359919i) q^{37} +(-1.76828 + 3.47044i) q^{38} +(0.581456 + 1.78954i) q^{39} +(4.47001 - 5.16389i) q^{40} +(-0.599732 - 0.825461i) q^{41} +(-4.96052 - 9.73556i) q^{42} +(4.07488 - 4.07488i) q^{43} +(5.00362 + 5.93786i) q^{45} +(7.17433 + 2.33108i) q^{46} +(-0.169785 + 1.07198i) q^{47} +(1.13394 + 7.15944i) q^{48} +(-4.78255 + 1.55394i) q^{49} +(-4.96034 - 3.70552i) q^{50} +(-0.923082 + 1.27051i) q^{51} +(-0.340823 - 0.0539811i) q^{52} +(3.82623 - 1.94956i) q^{53} -1.48887 q^{54} +10.5934 q^{56} +(7.13002 - 3.63293i) q^{57} +(3.54772 + 0.561903i) q^{58} +(4.35079 - 5.98835i) q^{59} +(-2.58495 + 0.602469i) q^{60} +(-3.56415 + 1.15806i) q^{61} +(0.588006 + 3.71253i) q^{62} +(-1.88406 + 11.8955i) q^{63} +(-8.45866 - 2.74839i) q^{64} +(-0.140698 + 1.64779i) q^{65} +(-9.39407 + 9.39407i) q^{67} +(-0.130751 - 0.256612i) q^{68} +(-9.10962 - 12.5383i) q^{69} +(-0.689900 - 9.57861i) q^{70} +(1.11688 + 3.43742i) q^{71} +(4.81533 - 9.45061i) q^{72} +(0.531022 - 0.0841057i) q^{73} +(2.30496 - 1.67465i) q^{74} +(3.76992 + 12.1492i) q^{75} +1.46752i q^{76} +(-1.64760 - 1.64760i) q^{78} +(-3.77215 + 11.6095i) q^{79} +(-1.52837 + 6.18492i) q^{80} +(-5.95346 - 4.32544i) q^{81} +(1.12578 + 0.573611i) q^{82} +(14.2813 + 7.27669i) q^{83} +(-3.33058 - 2.41981i) q^{84} +(-1.18165 + 0.713366i) q^{85} +(-2.20518 + 6.78685i) q^{86} +(-5.21820 - 5.21820i) q^{87} -14.6832i q^{89} +(-8.85892 - 3.73858i) q^{90} +(-2.07521 + 1.50773i) q^{91} +(2.80722 - 0.444620i) q^{92} +(3.50593 - 6.88077i) q^{93} +(-0.415320 - 1.27822i) q^{94} +(7.01507 - 0.505261i) q^{95} +(3.85903 + 5.31150i) q^{96} +(6.51518 + 12.7868i) q^{97} +(4.40322 - 4.40322i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 6 q^{3} - 2 q^{5} - 20 q^{7} + 20 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 6 q^{3} - 2 q^{5} - 20 q^{7} + 20 q^{8} + 12 q^{12} + 20 q^{13} + 4 q^{15} + 12 q^{16} - 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} + 20 q^{28} - 40 q^{30} + 32 q^{31} - 30 q^{35} - 36 q^{36} - 8 q^{37} + 10 q^{38} + 50 q^{40} - 20 q^{42} - 28 q^{45} - 20 q^{46} + 42 q^{47} + 26 q^{48} - 80 q^{50} + 100 q^{51} + 20 q^{52} - 34 q^{53} - 80 q^{56} + 40 q^{57} + 90 q^{58} - 86 q^{60} - 10 q^{62} + 10 q^{63} - 8 q^{67} + 70 q^{68} + 10 q^{70} - 36 q^{71} + 70 q^{72} - 30 q^{73} + 4 q^{75} + 60 q^{78} - 102 q^{80} + 8 q^{81} + 20 q^{82} + 60 q^{83} - 60 q^{85} - 80 q^{86} - 130 q^{90} - 60 q^{91} + 42 q^{92} - 8 q^{93} + 30 q^{95} - 38 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10335 + 0.562185i −0.780186 + 0.397525i −0.798261 0.602312i \(-0.794246\pi\)
0.0180746 + 0.999837i \(0.494246\pi\)
\(3\) 2.51281 + 0.397989i 1.45077 + 0.229779i 0.831555 0.555443i \(-0.187451\pi\)
0.619214 + 0.785222i \(0.287451\pi\)
\(4\) −0.274241 + 0.377461i −0.137121 + 0.188730i
\(5\) 1.89876 + 1.18097i 0.849153 + 0.528148i
\(6\) −2.99625 + 0.973540i −1.22321 + 0.397446i
\(7\) 0.542552 + 3.42554i 0.205065 + 1.29473i 0.848486 + 0.529218i \(0.177515\pi\)
−0.643420 + 0.765513i \(0.722485\pi\)
\(8\) 0.477813 3.01679i 0.168932 1.06660i
\(9\) 3.30263 + 1.07309i 1.10088 + 0.357697i
\(10\) −2.75893 0.235572i −0.872449 0.0744944i
\(11\) 0 0
\(12\) −0.839340 + 0.839340i −0.242297 + 0.242297i
\(13\) 0.335770 + 0.658986i 0.0931259 + 0.182770i 0.932871 0.360211i \(-0.117295\pi\)
−0.839745 + 0.542981i \(0.817295\pi\)
\(14\) −2.52441 3.47455i −0.674677 0.928613i
\(15\) 4.30121 + 3.72325i 1.11057 + 0.961338i
\(16\) 0.880445 + 2.70973i 0.220111 + 0.677433i
\(17\) −0.280240 + 0.550001i −0.0679681 + 0.133395i −0.922491 0.386019i \(-0.873850\pi\)
0.854523 + 0.519414i \(0.173850\pi\)
\(18\) −4.24723 + 0.672695i −1.00108 + 0.158556i
\(19\) 2.54465 1.84880i 0.583783 0.424143i −0.256303 0.966597i \(-0.582504\pi\)
0.840086 + 0.542453i \(0.182504\pi\)
\(20\) −0.966490 + 0.392836i −0.216114 + 0.0878409i
\(21\) 8.82364i 1.92548i
\(22\) 0 0
\(23\) −4.30752 4.30752i −0.898181 0.898181i 0.0970945 0.995275i \(-0.469045\pi\)
−0.995275 + 0.0970945i \(0.969045\pi\)
\(24\) 2.40130 7.39045i 0.490164 1.50857i
\(25\) 2.21060 + 4.48478i 0.442120 + 0.896956i
\(26\) −0.740944 0.538327i −0.145311 0.105575i
\(27\) 1.07129 + 0.545847i 0.206169 + 0.105048i
\(28\) −1.44180 0.734631i −0.272474 0.138832i
\(29\) −2.34668 1.70497i −0.435768 0.316604i 0.348183 0.937427i \(-0.386799\pi\)
−0.783951 + 0.620822i \(0.786799\pi\)
\(30\) −6.83889 1.68997i −1.24860 0.308545i
\(31\) 0.937993 2.88684i 0.168468 0.518493i −0.830807 0.556561i \(-0.812121\pi\)
0.999275 + 0.0380685i \(0.0121205\pi\)
\(32\) 1.82476 + 1.82476i 0.322575 + 0.322575i
\(33\) 0 0
\(34\) 0.764390i 0.131092i
\(35\) −3.01529 + 7.14502i −0.509678 + 1.20773i
\(36\) −1.31077 + 0.952327i −0.218461 + 0.158721i
\(37\) −2.27244 + 0.359919i −0.373587 + 0.0591704i −0.340405 0.940279i \(-0.610564\pi\)
−0.0331821 + 0.999449i \(0.510564\pi\)
\(38\) −1.76828 + 3.47044i −0.286852 + 0.562979i
\(39\) 0.581456 + 1.78954i 0.0931075 + 0.286555i
\(40\) 4.47001 5.16389i 0.706770 0.816482i
\(41\) −0.599732 0.825461i −0.0936624 0.128915i 0.759614 0.650374i \(-0.225388\pi\)
−0.853276 + 0.521459i \(0.825388\pi\)
\(42\) −4.96052 9.73556i −0.765424 1.50223i
\(43\) 4.07488 4.07488i 0.621413 0.621413i −0.324480 0.945893i \(-0.605189\pi\)
0.945893 + 0.324480i \(0.105189\pi\)
\(44\) 0 0
\(45\) 5.00362 + 5.93786i 0.745896 + 0.885164i
\(46\) 7.17433 + 2.33108i 1.05780 + 0.343699i
\(47\) −0.169785 + 1.07198i −0.0247658 + 0.156365i −0.996972 0.0777612i \(-0.975223\pi\)
0.972206 + 0.234126i \(0.0752228\pi\)
\(48\) 1.13394 + 7.15944i 0.163671 + 1.03338i
\(49\) −4.78255 + 1.55394i −0.683221 + 0.221992i
\(50\) −4.96034 3.70552i −0.701498 0.524039i
\(51\) −0.923082 + 1.27051i −0.129257 + 0.177908i
\(52\) −0.340823 0.0539811i −0.0472637 0.00748583i
\(53\) 3.82623 1.94956i 0.525573 0.267793i −0.171010 0.985269i \(-0.554703\pi\)
0.696583 + 0.717476i \(0.254703\pi\)
\(54\) −1.48887 −0.202609
\(55\) 0 0
\(56\) 10.5934 1.41560
\(57\) 7.13002 3.63293i 0.944394 0.481193i
\(58\) 3.54772 + 0.561903i 0.465838 + 0.0737815i
\(59\) 4.35079 5.98835i 0.566425 0.779617i −0.425701 0.904864i \(-0.639972\pi\)
0.992126 + 0.125247i \(0.0399724\pi\)
\(60\) −2.58495 + 0.602469i −0.333715 + 0.0777784i
\(61\) −3.56415 + 1.15806i −0.456342 + 0.148275i −0.528163 0.849143i \(-0.677119\pi\)
0.0718208 + 0.997418i \(0.477119\pi\)
\(62\) 0.588006 + 3.71253i 0.0746769 + 0.471491i
\(63\) −1.88406 + 11.8955i −0.237369 + 1.49869i
\(64\) −8.45866 2.74839i −1.05733 0.343548i
\(65\) −0.140698 + 1.64779i −0.0174514 + 0.204384i
\(66\) 0 0
\(67\) −9.39407 + 9.39407i −1.14767 + 1.14767i −0.160658 + 0.987010i \(0.551361\pi\)
−0.987010 + 0.160658i \(0.948639\pi\)
\(68\) −0.130751 0.256612i −0.0158558 0.0311188i
\(69\) −9.10962 12.5383i −1.09667 1.50944i
\(70\) −0.689900 9.57861i −0.0824588 1.14486i
\(71\) 1.11688 + 3.43742i 0.132550 + 0.407946i 0.995201 0.0978532i \(-0.0311976\pi\)
−0.862651 + 0.505799i \(0.831198\pi\)
\(72\) 4.81533 9.45061i 0.567492 1.11376i
\(73\) 0.531022 0.0841057i 0.0621515 0.00984382i −0.125281 0.992121i \(-0.539983\pi\)
0.187433 + 0.982277i \(0.439983\pi\)
\(74\) 2.30496 1.67465i 0.267946 0.194674i
\(75\) 3.76992 + 12.1492i 0.435312 + 1.40287i
\(76\) 1.46752i 0.168336i
\(77\) 0 0
\(78\) −1.64760 1.64760i −0.186554 0.186554i
\(79\) −3.77215 + 11.6095i −0.424400 + 1.30617i 0.479168 + 0.877723i \(0.340939\pi\)
−0.903568 + 0.428446i \(0.859061\pi\)
\(80\) −1.52837 + 6.18492i −0.170877 + 0.691495i
\(81\) −5.95346 4.32544i −0.661496 0.480605i
\(82\) 1.12578 + 0.573611i 0.124321 + 0.0633448i
\(83\) 14.2813 + 7.27669i 1.56758 + 0.798721i 0.999702 0.0243933i \(-0.00776541\pi\)
0.567876 + 0.823114i \(0.307765\pi\)
\(84\) −3.33058 2.41981i −0.363396 0.264022i
\(85\) −1.18165 + 0.713366i −0.128167 + 0.0773754i
\(86\) −2.20518 + 6.78685i −0.237791 + 0.731845i
\(87\) −5.21820 5.21820i −0.559450 0.559450i
\(88\) 0 0
\(89\) 14.6832i 1.55642i −0.628004 0.778210i \(-0.716128\pi\)
0.628004 0.778210i \(-0.283872\pi\)
\(90\) −8.85892 3.73858i −0.933812 0.394081i
\(91\) −2.07521 + 1.50773i −0.217541 + 0.158053i
\(92\) 2.80722 0.444620i 0.292673 0.0463548i
\(93\) 3.50593 6.88077i 0.363548 0.713503i
\(94\) −0.415320 1.27822i −0.0428370 0.131839i
\(95\) 7.01507 0.505261i 0.719731 0.0518387i
\(96\) 3.85903 + 5.31150i 0.393860 + 0.542102i
\(97\) 6.51518 + 12.7868i 0.661516 + 1.29830i 0.941084 + 0.338173i \(0.109809\pi\)
−0.279568 + 0.960126i \(0.590191\pi\)
\(98\) 4.40322 4.40322i 0.444792 0.444792i
\(99\) 0 0
\(100\) −2.29906 0.395497i −0.229906 0.0395497i
\(101\) −7.67156 2.49264i −0.763349 0.248027i −0.0986336 0.995124i \(-0.531447\pi\)
−0.664715 + 0.747097i \(0.731447\pi\)
\(102\) 0.304219 1.92076i 0.0301222 0.190184i
\(103\) −0.560316 3.53769i −0.0552095 0.348579i −0.999794 0.0203101i \(-0.993535\pi\)
0.944584 0.328269i \(-0.106465\pi\)
\(104\) 2.14846 0.698077i 0.210674 0.0684520i
\(105\) −10.4205 + 16.7540i −1.01694 + 1.63502i
\(106\) −3.12566 + 4.30210i −0.303591 + 0.417857i
\(107\) 6.51530 + 1.03192i 0.629858 + 0.0997598i 0.463198 0.886255i \(-0.346702\pi\)
0.166660 + 0.986014i \(0.446702\pi\)
\(108\) −0.499826 + 0.254674i −0.0480958 + 0.0245060i
\(109\) −7.21601 −0.691169 −0.345584 0.938388i \(-0.612319\pi\)
−0.345584 + 0.938388i \(0.612319\pi\)
\(110\) 0 0
\(111\) −5.85345 −0.555585
\(112\) −8.80460 + 4.48617i −0.831957 + 0.423903i
\(113\) 4.17124 + 0.660660i 0.392397 + 0.0621496i 0.349516 0.936931i \(-0.386346\pi\)
0.0428817 + 0.999080i \(0.486346\pi\)
\(114\) −5.82453 + 8.01678i −0.545517 + 0.750840i
\(115\) −3.09189 13.2660i −0.288320 1.23706i
\(116\) 1.28711 0.418209i 0.119506 0.0388297i
\(117\) 0.401774 + 2.53670i 0.0371440 + 0.234518i
\(118\) −1.43388 + 9.05319i −0.132000 + 0.833414i
\(119\) −2.03609 0.661567i −0.186648 0.0606458i
\(120\) 13.2874 11.1968i 1.21297 1.02213i
\(121\) 0 0
\(122\) 3.28146 3.28146i 0.297089 0.297089i
\(123\) −1.17849 2.31291i −0.106261 0.208548i
\(124\) 0.832434 + 1.14575i 0.0747548 + 0.102891i
\(125\) −1.09900 + 11.1262i −0.0982978 + 0.995157i
\(126\) −4.60869 14.1841i −0.410574 1.26362i
\(127\) 5.89508 11.5697i 0.523104 1.02665i −0.466728 0.884401i \(-0.654567\pi\)
0.989831 0.142247i \(-0.0454329\pi\)
\(128\) 5.78032 0.915512i 0.510913 0.0809206i
\(129\) 11.8611 8.61762i 1.04431 0.758739i
\(130\) −0.771126 1.89719i −0.0676323 0.166395i
\(131\) 17.2362i 1.50593i −0.658058 0.752967i \(-0.728622\pi\)
0.658058 0.752967i \(-0.271378\pi\)
\(132\) 0 0
\(133\) 7.71373 + 7.71373i 0.668866 + 0.668866i
\(134\) 5.08374 15.6461i 0.439168 1.35162i
\(135\) 1.38949 + 2.30159i 0.119588 + 0.198090i
\(136\) 1.52534 + 1.10822i 0.130797 + 0.0950292i
\(137\) 5.12484 + 2.61124i 0.437845 + 0.223093i 0.658996 0.752146i \(-0.270981\pi\)
−0.221151 + 0.975240i \(0.570981\pi\)
\(138\) 17.1000 + 8.71286i 1.45564 + 0.741688i
\(139\) 10.3683 + 7.53301i 0.879427 + 0.638941i 0.933100 0.359617i \(-0.117093\pi\)
−0.0536727 + 0.998559i \(0.517093\pi\)
\(140\) −1.87005 3.09761i −0.158048 0.261796i
\(141\) −0.853276 + 2.62611i −0.0718588 + 0.221159i
\(142\) −3.16478 3.16478i −0.265582 0.265582i
\(143\) 0 0
\(144\) 9.89404i 0.824503i
\(145\) −2.44228 6.00870i −0.202820 0.498995i
\(146\) −0.538621 + 0.391331i −0.0445766 + 0.0323868i
\(147\) −12.6361 + 2.00136i −1.04221 + 0.165069i
\(148\) 0.487341 0.956462i 0.0400592 0.0786207i
\(149\) −5.92654 18.2400i −0.485521 1.49428i −0.831225 0.555937i \(-0.812360\pi\)
0.345704 0.938344i \(-0.387640\pi\)
\(150\) −10.9896 11.2854i −0.897299 0.921449i
\(151\) −11.1225 15.3088i −0.905136 1.24581i −0.968801 0.247841i \(-0.920279\pi\)
0.0636652 0.997971i \(-0.479721\pi\)
\(152\) −4.36157 8.56007i −0.353770 0.694313i
\(153\) −1.51573 + 1.51573i −0.122539 + 0.122539i
\(154\) 0 0
\(155\) 5.19031 4.37369i 0.416896 0.351303i
\(156\) −0.834939 0.271288i −0.0668486 0.0217204i
\(157\) 1.92127 12.1304i 0.153334 0.968114i −0.784273 0.620416i \(-0.786964\pi\)
0.937607 0.347697i \(-0.113036\pi\)
\(158\) −2.36467 14.9300i −0.188123 1.18776i
\(159\) 10.3905 3.37607i 0.824019 0.267740i
\(160\) 1.30979 + 5.61977i 0.103548 + 0.444282i
\(161\) 12.4185 17.0926i 0.978717 1.34709i
\(162\) 9.00045 + 1.42553i 0.707142 + 0.112000i
\(163\) 8.64305 4.40385i 0.676976 0.344936i −0.0814671 0.996676i \(-0.525961\pi\)
0.758443 + 0.651740i \(0.225961\pi\)
\(164\) 0.476050 0.0371733
\(165\) 0 0
\(166\) −19.8481 −1.54051
\(167\) 10.1035 5.14798i 0.781830 0.398362i −0.0170486 0.999855i \(-0.505427\pi\)
0.798879 + 0.601492i \(0.205427\pi\)
\(168\) 26.6191 + 4.21605i 2.05371 + 0.325275i
\(169\) 7.31969 10.0747i 0.563053 0.774976i
\(170\) 0.902725 1.45140i 0.0692359 0.111317i
\(171\) 10.3880 3.37526i 0.794388 0.258112i
\(172\) 0.420606 + 2.65560i 0.0320709 + 0.202488i
\(173\) 0.718617 4.53717i 0.0546354 0.344954i −0.945194 0.326508i \(-0.894128\pi\)
0.999830 0.0184465i \(-0.00587202\pi\)
\(174\) 8.69110 + 2.82391i 0.658871 + 0.214080i
\(175\) −14.1634 + 10.0057i −1.07065 + 0.756361i
\(176\) 0 0
\(177\) 13.3160 13.3160i 1.00089 1.00089i
\(178\) 8.25470 + 16.2008i 0.618716 + 1.21430i
\(179\) 1.61687 + 2.22543i 0.120850 + 0.166336i 0.865156 0.501503i \(-0.167219\pi\)
−0.744306 + 0.667839i \(0.767219\pi\)
\(180\) −3.61351 + 0.260263i −0.269335 + 0.0193988i
\(181\) −2.20891 6.79832i −0.164187 0.505315i 0.834789 0.550571i \(-0.185590\pi\)
−0.998975 + 0.0452555i \(0.985590\pi\)
\(182\) 1.44206 2.83020i 0.106893 0.209789i
\(183\) −9.41691 + 1.49149i −0.696118 + 0.110254i
\(184\) −15.0531 + 10.9367i −1.10973 + 0.806265i
\(185\) −4.73988 2.00029i −0.348483 0.147064i
\(186\) 9.56288i 0.701184i
\(187\) 0 0
\(188\) −0.358069 0.358069i −0.0261149 0.0261149i
\(189\) −1.28859 + 3.96588i −0.0937312 + 0.288475i
\(190\) −7.45603 + 4.50125i −0.540917 + 0.326555i
\(191\) 2.81857 + 2.04781i 0.203945 + 0.148175i 0.685070 0.728477i \(-0.259772\pi\)
−0.481125 + 0.876652i \(0.659772\pi\)
\(192\) −20.1612 10.2726i −1.45501 0.741362i
\(193\) −9.67938 4.93189i −0.696737 0.355005i 0.0694834 0.997583i \(-0.477865\pi\)
−0.766220 + 0.642578i \(0.777865\pi\)
\(194\) −14.3771 10.4455i −1.03221 0.749946i
\(195\) −1.00935 + 4.08459i −0.0722811 + 0.292504i
\(196\) 0.725019 2.23138i 0.0517870 0.159384i
\(197\) 11.3729 + 11.3729i 0.810285 + 0.810285i 0.984676 0.174391i \(-0.0557958\pi\)
−0.174391 + 0.984676i \(0.555796\pi\)
\(198\) 0 0
\(199\) 27.7479i 1.96700i 0.180916 + 0.983499i \(0.442094\pi\)
−0.180916 + 0.983499i \(0.557906\pi\)
\(200\) 14.5859 4.52603i 1.03138 0.320039i
\(201\) −27.3442 + 19.8667i −1.92871 + 1.40129i
\(202\) 9.86574 1.56258i 0.694151 0.109943i
\(203\) 4.56722 8.96368i 0.320556 0.629127i
\(204\) −0.226422 0.696854i −0.0158527 0.0487896i
\(205\) −0.163902 2.27562i −0.0114474 0.158936i
\(206\) 2.60706 + 3.58831i 0.181643 + 0.250010i
\(207\) −9.60380 18.8485i −0.667510 1.31006i
\(208\) −1.49005 + 1.49005i −0.103316 + 0.103316i
\(209\) 0 0
\(210\) 2.07860 24.3438i 0.143437 1.67988i
\(211\) −19.5731 6.35970i −1.34747 0.437820i −0.455630 0.890169i \(-0.650586\pi\)
−0.891841 + 0.452349i \(0.850586\pi\)
\(212\) −0.313427 + 1.97890i −0.0215263 + 0.135911i
\(213\) 1.43846 + 9.08207i 0.0985615 + 0.622293i
\(214\) −7.76879 + 2.52423i −0.531064 + 0.172553i
\(215\) 12.5496 2.92490i 0.855872 0.199477i
\(216\) 2.15858 2.97103i 0.146873 0.202153i
\(217\) 10.3979 + 1.64687i 0.705856 + 0.111797i
\(218\) 7.96179 4.05673i 0.539240 0.274757i
\(219\) 1.36783 0.0924293
\(220\) 0 0
\(221\) −0.456539 −0.0307102
\(222\) 6.45840 3.29072i 0.433460 0.220859i
\(223\) 7.91412 + 1.25347i 0.529969 + 0.0839388i 0.415684 0.909509i \(-0.363542\pi\)
0.114285 + 0.993448i \(0.463542\pi\)
\(224\) −5.26075 + 7.24080i −0.351499 + 0.483796i
\(225\) 2.48823 + 17.1837i 0.165882 + 1.14558i
\(226\) −4.97375 + 1.61607i −0.330849 + 0.107499i
\(227\) −0.484764 3.06068i −0.0321749 0.203144i 0.966364 0.257177i \(-0.0827924\pi\)
−0.998539 + 0.0540329i \(0.982792\pi\)
\(228\) −0.584058 + 3.68760i −0.0386802 + 0.244217i
\(229\) −14.0003 4.54899i −0.925169 0.300606i −0.192583 0.981281i \(-0.561687\pi\)
−0.732586 + 0.680675i \(0.761687\pi\)
\(230\) 10.8694 + 12.8989i 0.716707 + 0.850526i
\(231\) 0 0
\(232\) −6.26480 + 6.26480i −0.411304 + 0.411304i
\(233\) 6.33106 + 12.4254i 0.414761 + 0.814015i 0.999995 + 0.00315044i \(0.00100282\pi\)
−0.585234 + 0.810865i \(0.698997\pi\)
\(234\) −1.86939 2.57300i −0.122206 0.168202i
\(235\) −1.58837 + 1.83493i −0.103614 + 0.119698i
\(236\) 1.06720 + 3.28450i 0.0694688 + 0.213803i
\(237\) −14.0991 + 27.6711i −0.915837 + 1.79743i
\(238\) 2.61845 0.414721i 0.169729 0.0268824i
\(239\) 2.60330 1.89141i 0.168393 0.122345i −0.500397 0.865796i \(-0.666812\pi\)
0.668790 + 0.743451i \(0.266812\pi\)
\(240\) −6.30202 + 14.9332i −0.406794 + 0.963936i
\(241\) 15.0738i 0.970989i −0.874240 0.485494i \(-0.838640\pi\)
0.874240 0.485494i \(-0.161360\pi\)
\(242\) 0 0
\(243\) −15.7890 15.7890i −1.01286 1.01286i
\(244\) 0.540313 1.66291i 0.0345900 0.106457i
\(245\) −10.9161 2.69749i −0.697403 0.172337i
\(246\) 2.60057 + 1.88942i 0.165806 + 0.120465i
\(247\) 2.07275 + 1.05612i 0.131886 + 0.0671993i
\(248\) −8.26082 4.20910i −0.524563 0.267278i
\(249\) 32.9901 + 23.9687i 2.09066 + 1.51896i
\(250\) −5.04239 12.8939i −0.318909 0.815484i
\(251\) −0.619073 + 1.90531i −0.0390755 + 0.120262i −0.968691 0.248268i \(-0.920139\pi\)
0.929616 + 0.368530i \(0.120139\pi\)
\(252\) −3.97339 3.97339i −0.250300 0.250300i
\(253\) 0 0
\(254\) 16.0796i 1.00892i
\(255\) −3.25316 + 1.32227i −0.203721 + 0.0828037i
\(256\) 8.52771 6.19575i 0.532982 0.387234i
\(257\) −3.76356 + 0.596089i −0.234764 + 0.0371830i −0.272708 0.962097i \(-0.587919\pi\)
0.0379437 + 0.999280i \(0.487919\pi\)
\(258\) −8.24229 + 16.1764i −0.513142 + 1.00710i
\(259\) −2.46583 7.58906i −0.153219 0.471561i
\(260\) −0.583392 0.505001i −0.0361805 0.0313188i
\(261\) −5.92065 8.14907i −0.366479 0.504415i
\(262\) 9.68993 + 19.0176i 0.598646 + 1.17491i
\(263\) −0.123512 + 0.123512i −0.00761605 + 0.00761605i −0.710905 0.703289i \(-0.751714\pi\)
0.703289 + 0.710905i \(0.251714\pi\)
\(264\) 0 0
\(265\) 9.56749 + 0.816924i 0.587726 + 0.0501832i
\(266\) −12.8475 4.17440i −0.787730 0.255949i
\(267\) 5.84378 36.8962i 0.357633 2.25801i
\(268\) −0.969650 6.12213i −0.0592308 0.373969i
\(269\) −6.58632 + 2.14003i −0.401575 + 0.130480i −0.502839 0.864380i \(-0.667711\pi\)
0.101264 + 0.994860i \(0.467711\pi\)
\(270\) −2.82701 1.75832i −0.172046 0.107008i
\(271\) −13.4374 + 18.4949i −0.816261 + 1.12349i 0.174066 + 0.984734i \(0.444309\pi\)
−0.990327 + 0.138753i \(0.955691\pi\)
\(272\) −1.73709 0.275128i −0.105327 0.0166821i
\(273\) −5.81466 + 2.96272i −0.351919 + 0.179312i
\(274\) −7.12249 −0.430285
\(275\) 0 0
\(276\) 7.23096 0.435252
\(277\) −3.30236 + 1.68264i −0.198420 + 0.101100i −0.550377 0.834916i \(-0.685516\pi\)
0.351958 + 0.936016i \(0.385516\pi\)
\(278\) −15.6748 2.48264i −0.940112 0.148899i
\(279\) 6.19569 8.52763i 0.370926 0.510536i
\(280\) 20.1143 + 12.5105i 1.20206 + 0.747645i
\(281\) 3.05555 0.992807i 0.182279 0.0592259i −0.216456 0.976292i \(-0.569450\pi\)
0.398734 + 0.917067i \(0.369450\pi\)
\(282\) −0.534899 3.37722i −0.0318528 0.201111i
\(283\) −3.30934 + 20.8944i −0.196720 + 1.24204i 0.669664 + 0.742664i \(0.266438\pi\)
−0.866384 + 0.499378i \(0.833562\pi\)
\(284\) −1.60378 0.521101i −0.0951671 0.0309217i
\(285\) 17.8286 + 1.52230i 1.05608 + 0.0901735i
\(286\) 0 0
\(287\) 2.50226 2.50226i 0.147704 0.147704i
\(288\) 4.06837 + 7.98463i 0.239731 + 0.470499i
\(289\) 9.76838 + 13.4450i 0.574611 + 0.790884i
\(290\) 6.07268 + 5.25669i 0.356600 + 0.308683i
\(291\) 11.2824 + 34.7236i 0.661386 + 2.03554i
\(292\) −0.113882 + 0.223505i −0.00666442 + 0.0130797i
\(293\) −28.3396 + 4.48855i −1.65561 + 0.262224i −0.913139 0.407649i \(-0.866349\pi\)
−0.742476 + 0.669872i \(0.766349\pi\)
\(294\) 12.8169 9.31200i 0.747495 0.543087i
\(295\) 15.3332 6.23228i 0.892734 0.362858i
\(296\) 7.02745i 0.408462i
\(297\) 0 0
\(298\) 16.7933 + 16.7933i 0.972810 + 0.972810i
\(299\) 1.39226 4.28494i 0.0805165 0.247804i
\(300\) −5.61970 1.90881i −0.324454 0.110205i
\(301\) 16.1695 + 11.7478i 0.931993 + 0.677133i
\(302\) 20.8784 + 10.6381i 1.20142 + 0.612152i
\(303\) −18.2851 9.31673i −1.05045 0.535232i
\(304\) 7.25018 + 5.26756i 0.415826 + 0.302115i
\(305\) −8.13511 2.01028i −0.465815 0.115108i
\(306\) 0.820259 2.52450i 0.0468911 0.144316i
\(307\) −13.1727 13.1727i −0.751808 0.751808i 0.223008 0.974817i \(-0.428412\pi\)
−0.974817 + 0.223008i \(0.928412\pi\)
\(308\) 0 0
\(309\) 9.11254i 0.518394i
\(310\) −3.26791 + 7.74363i −0.185605 + 0.439808i
\(311\) 13.7812 10.0126i 0.781461 0.567765i −0.123956 0.992288i \(-0.539558\pi\)
0.905417 + 0.424523i \(0.139558\pi\)
\(312\) 5.67649 0.899067i 0.321368 0.0508997i
\(313\) −7.16333 + 14.0588i −0.404895 + 0.794651i −0.999959 0.00902676i \(-0.997127\pi\)
0.595064 + 0.803678i \(0.297127\pi\)
\(314\) 4.69971 + 14.4642i 0.265220 + 0.816263i
\(315\) −17.6256 + 20.3617i −0.993093 + 1.14725i
\(316\) −3.34764 4.60764i −0.188320 0.259200i
\(317\) 3.01302 + 5.91339i 0.169228 + 0.332129i 0.960008 0.279971i \(-0.0903249\pi\)
−0.790780 + 0.612100i \(0.790325\pi\)
\(318\) −9.56636 + 9.56636i −0.536455 + 0.536455i
\(319\) 0 0
\(320\) −12.8152 15.2080i −0.716393 0.850153i
\(321\) 15.9610 + 5.18604i 0.890856 + 0.289457i
\(322\) −4.09276 + 25.8407i −0.228081 + 1.44004i
\(323\) 0.303729 + 1.91767i 0.0168999 + 0.106702i
\(324\) 3.26537 1.06098i 0.181409 0.0589435i
\(325\) −2.21315 + 2.96261i −0.122764 + 0.164336i
\(326\) −7.06053 + 9.71798i −0.391046 + 0.538229i
\(327\) −18.1324 2.87190i −1.00273 0.158816i
\(328\) −2.77680 + 1.41485i −0.153323 + 0.0781221i
\(329\) −3.76424 −0.207529
\(330\) 0 0
\(331\) 12.0774 0.663835 0.331918 0.943308i \(-0.392304\pi\)
0.331918 + 0.943308i \(0.392304\pi\)
\(332\) −6.66319 + 3.39506i −0.365690 + 0.186328i
\(333\) −7.89126 1.24985i −0.432438 0.0684915i
\(334\) −8.25355 + 11.3600i −0.451614 + 0.621594i
\(335\) −28.9313 + 6.74295i −1.58068 + 0.368407i
\(336\) −23.9097 + 7.76873i −1.30438 + 0.423819i
\(337\) −1.52334 9.61797i −0.0829815 0.523924i −0.993806 0.111130i \(-0.964553\pi\)
0.910824 0.412794i \(-0.135447\pi\)
\(338\) −2.41234 + 15.2309i −0.131214 + 0.828453i
\(339\) 10.2186 + 3.32022i 0.554997 + 0.180330i
\(340\) 0.0547883 0.641659i 0.00297131 0.0347988i
\(341\) 0 0
\(342\) −9.56405 + 9.56405i −0.517165 + 0.517165i
\(343\) 3.10396 + 6.09186i 0.167598 + 0.328929i
\(344\) −10.3460 14.2401i −0.557820 0.767774i
\(345\) −2.48958 34.5655i −0.134035 1.86095i
\(346\) 1.75784 + 5.41008i 0.0945021 + 0.290848i
\(347\) −11.0499 + 21.6867i −0.593192 + 1.16420i 0.377978 + 0.925815i \(0.376620\pi\)
−0.971170 + 0.238390i \(0.923380\pi\)
\(348\) 3.40071 0.538620i 0.182297 0.0288731i
\(349\) −15.2336 + 11.0678i −0.815434 + 0.592448i −0.915401 0.402543i \(-0.868126\pi\)
0.0999667 + 0.994991i \(0.468126\pi\)
\(350\) 10.0021 19.0023i 0.534637 1.01571i
\(351\) 0.889241i 0.0474642i
\(352\) 0 0
\(353\) −5.39206 5.39206i −0.286990 0.286990i 0.548899 0.835889i \(-0.315047\pi\)
−0.835889 + 0.548899i \(0.815047\pi\)
\(354\) −7.20615 + 22.1782i −0.383003 + 1.17876i
\(355\) −1.93880 + 7.84585i −0.102901 + 0.416414i
\(356\) 5.54235 + 4.02675i 0.293744 + 0.213417i
\(357\) −4.85301 2.47273i −0.256849 0.130871i
\(358\) −3.03508 1.54645i −0.160409 0.0817323i
\(359\) −12.3940 9.00475i −0.654129 0.475253i 0.210546 0.977584i \(-0.432476\pi\)
−0.864675 + 0.502331i \(0.832476\pi\)
\(360\) 20.3041 12.2577i 1.07012 0.646037i
\(361\) −2.81412 + 8.66097i −0.148112 + 0.455841i
\(362\) 6.25911 + 6.25911i 0.328971 + 0.328971i
\(363\) 0 0
\(364\) 1.19679i 0.0627289i
\(365\) 1.10761 + 0.467427i 0.0579751 + 0.0244662i
\(366\) 9.55165 6.93968i 0.499273 0.362743i
\(367\) −2.27206 + 0.359859i −0.118601 + 0.0187845i −0.215453 0.976514i \(-0.569123\pi\)
0.0968520 + 0.995299i \(0.469123\pi\)
\(368\) 7.87970 15.4648i 0.410758 0.806157i
\(369\) −1.09490 3.36976i −0.0569982 0.175423i
\(370\) 6.35428 0.457667i 0.330343 0.0237930i
\(371\) 8.75422 + 12.0492i 0.454497 + 0.625561i
\(372\) 1.63575 + 3.21034i 0.0848097 + 0.166448i
\(373\) −22.9215 + 22.9215i −1.18683 + 1.18683i −0.208889 + 0.977939i \(0.566985\pi\)
−0.977939 + 0.208889i \(0.933015\pi\)
\(374\) 0 0
\(375\) −7.18969 + 27.5206i −0.371274 + 1.42116i
\(376\) 3.15282 + 1.02441i 0.162594 + 0.0528301i
\(377\) 0.335602 2.11891i 0.0172844 0.109129i
\(378\) −0.807789 5.10018i −0.0415482 0.262325i
\(379\) 10.7802 3.50269i 0.553740 0.179921i −0.0187623 0.999824i \(-0.505973\pi\)
0.572503 + 0.819903i \(0.305973\pi\)
\(380\) −1.73311 + 2.78648i −0.0889065 + 0.142943i
\(381\) 19.4178 26.7263i 0.994805 1.36923i
\(382\) −4.26112 0.674895i −0.218018 0.0345306i
\(383\) 1.25676 0.640349i 0.0642172 0.0327203i −0.421587 0.906788i \(-0.638527\pi\)
0.485804 + 0.874068i \(0.338527\pi\)
\(384\) 14.8892 0.759810
\(385\) 0 0
\(386\) 13.4524 0.684708
\(387\) 17.8305 9.08510i 0.906376 0.461822i
\(388\) −6.61323 1.04743i −0.335736 0.0531753i
\(389\) −18.1326 + 24.9574i −0.919360 + 1.26539i 0.0445072 + 0.999009i \(0.485828\pi\)
−0.963868 + 0.266382i \(0.914172\pi\)
\(390\) −1.18263 5.07418i −0.0598847 0.256941i
\(391\) 3.57628 1.16200i 0.180860 0.0587651i
\(392\) 2.40276 + 15.1704i 0.121358 + 0.766223i
\(393\) 6.85983 43.3112i 0.346032 2.18476i
\(394\) −18.9419 6.15461i −0.954282 0.310065i
\(395\) −20.8729 + 17.5888i −1.05023 + 0.884991i
\(396\) 0 0
\(397\) 6.24852 6.24852i 0.313604 0.313604i −0.532700 0.846304i \(-0.678823\pi\)
0.846304 + 0.532700i \(0.178823\pi\)
\(398\) −15.5995 30.6157i −0.781930 1.53462i
\(399\) 16.3131 + 22.4531i 0.816678 + 1.12406i
\(400\) −10.2062 + 9.93874i −0.510312 + 0.496937i
\(401\) −4.14836 12.7673i −0.207159 0.637570i −0.999618 0.0276446i \(-0.991199\pi\)
0.792459 0.609926i \(-0.208801\pi\)
\(402\) 19.0015 37.2925i 0.947706 1.85998i
\(403\) 2.21734 0.351192i 0.110454 0.0174941i
\(404\) 3.04473 2.21213i 0.151481 0.110057i
\(405\) −6.19598 15.2439i −0.307881 0.757474i
\(406\) 12.4577i 0.618266i
\(407\) 0 0
\(408\) 3.39181 + 3.39181i 0.167920 + 0.167920i
\(409\) −0.385284 + 1.18578i −0.0190511 + 0.0586332i −0.960130 0.279554i \(-0.909814\pi\)
0.941079 + 0.338187i \(0.109814\pi\)
\(410\) 1.46016 + 2.41866i 0.0721122 + 0.119449i
\(411\) 11.8385 + 8.60117i 0.583950 + 0.424264i
\(412\) 1.48900 + 0.758684i 0.0733578 + 0.0373777i
\(413\) 22.8738 + 11.6548i 1.12555 + 0.573495i
\(414\) 21.1927 + 15.3974i 1.04156 + 0.756741i
\(415\) 18.5232 + 30.6826i 0.909270 + 1.50615i
\(416\) −0.589791 + 1.81519i −0.0289169 + 0.0889970i
\(417\) 23.0555 + 23.0555i 1.12903 + 1.12903i
\(418\) 0 0
\(419\) 20.5995i 1.00635i −0.864185 0.503175i \(-0.832165\pi\)
0.864185 0.503175i \(-0.167835\pi\)
\(420\) −3.46625 8.52796i −0.169136 0.416122i
\(421\) 6.41888 4.66359i 0.312837 0.227290i −0.420276 0.907396i \(-0.638067\pi\)
0.733113 + 0.680107i \(0.238067\pi\)
\(422\) 25.1714 3.98675i 1.22532 0.194072i
\(423\) −1.71107 + 3.35817i −0.0831952 + 0.163280i
\(424\) −4.05320 12.4745i −0.196841 0.605814i
\(425\) −3.08613 0.0409799i −0.149699 0.00198782i
\(426\) −6.69293 9.21202i −0.324273 0.446324i
\(427\) −5.90072 11.5808i −0.285556 0.560435i
\(428\) −2.17627 + 2.17627i −0.105194 + 0.105194i
\(429\) 0 0
\(430\) −12.2022 + 10.2824i −0.588443 + 0.495859i
\(431\) 28.3532 + 9.21253i 1.36573 + 0.443752i 0.897951 0.440095i \(-0.145055\pi\)
0.467776 + 0.883847i \(0.345055\pi\)
\(432\) −0.535891 + 3.38348i −0.0257831 + 0.162788i
\(433\) 1.60810 + 10.1532i 0.0772806 + 0.487930i 0.995724 + 0.0923781i \(0.0294468\pi\)
−0.918443 + 0.395552i \(0.870553\pi\)
\(434\) −12.3984 + 4.02847i −0.595141 + 0.193373i
\(435\) −3.74557 16.0707i −0.179586 0.770531i
\(436\) 1.97893 2.72376i 0.0947734 0.130444i
\(437\) −18.9249 2.99741i −0.905300 0.143386i
\(438\) −1.50919 + 0.768973i −0.0721121 + 0.0367430i
\(439\) 30.3973 1.45078 0.725392 0.688336i \(-0.241659\pi\)
0.725392 + 0.688336i \(0.241659\pi\)
\(440\) 0 0
\(441\) −17.4625 −0.831548
\(442\) 0.503723 0.256660i 0.0239596 0.0122080i
\(443\) 11.0949 + 1.75726i 0.527135 + 0.0834900i 0.414329 0.910127i \(-0.364016\pi\)
0.112806 + 0.993617i \(0.464016\pi\)
\(444\) 1.60526 2.20945i 0.0761821 0.104856i
\(445\) 17.3405 27.8800i 0.822020 1.32164i
\(446\) −9.43673 + 3.06618i −0.446842 + 0.145188i
\(447\) −7.63291 48.1923i −0.361024 2.27942i
\(448\) 4.82544 30.4666i 0.227980 1.43941i
\(449\) −18.5837 6.03822i −0.877021 0.284961i −0.164301 0.986410i \(-0.552537\pi\)
−0.712720 + 0.701449i \(0.752537\pi\)
\(450\) −12.4058 17.5608i −0.584816 0.827826i
\(451\) 0 0
\(452\) −1.39330 + 1.39330i −0.0655353 + 0.0655353i
\(453\) −21.8559 42.8947i −1.02688 2.01537i
\(454\) 2.25553 + 3.10447i 0.105857 + 0.145700i
\(455\) −5.72092 + 0.412049i −0.268201 + 0.0193172i
\(456\) −7.55297 23.2456i −0.353700 1.08858i
\(457\) 5.34479 10.4897i 0.250019 0.490690i −0.731553 0.681785i \(-0.761204\pi\)
0.981571 + 0.191095i \(0.0612040\pi\)
\(458\) 18.0047 2.85166i 0.841302 0.133249i
\(459\) −0.600433 + 0.436240i −0.0280258 + 0.0203619i
\(460\) 5.85533 + 2.47103i 0.273006 + 0.115212i
\(461\) 26.5631i 1.23717i −0.785719 0.618583i \(-0.787707\pi\)
0.785719 0.618583i \(-0.212293\pi\)
\(462\) 0 0
\(463\) −14.4258 14.4258i −0.670424 0.670424i 0.287390 0.957814i \(-0.407213\pi\)
−0.957814 + 0.287390i \(0.907213\pi\)
\(464\) 2.55387 7.86001i 0.118561 0.364892i
\(465\) 14.7829 8.92454i 0.685542 0.413866i
\(466\) −13.9707 10.1503i −0.647182 0.470206i
\(467\) −16.6421 8.47955i −0.770102 0.392387i 0.0243575 0.999703i \(-0.492246\pi\)
−0.794460 + 0.607316i \(0.792246\pi\)
\(468\) −1.06769 0.544014i −0.0493538 0.0251470i
\(469\) −37.2765 27.0830i −1.72127 1.25057i
\(470\) 0.720955 2.91752i 0.0332552 0.134575i
\(471\) 9.65556 29.7168i 0.444905 1.36928i
\(472\) −15.9867 15.9867i −0.735849 0.735849i
\(473\) 0 0
\(474\) 38.4572i 1.76640i
\(475\) 13.9167 + 7.32525i 0.638540 + 0.336106i
\(476\) 0.808096 0.587116i 0.0370390 0.0269104i
\(477\) 14.7287 2.33279i 0.674380 0.106811i
\(478\) −1.80903 + 3.55042i −0.0827431 + 0.162392i
\(479\) 2.25319 + 6.93461i 0.102951 + 0.316851i 0.989244 0.146274i \(-0.0467282\pi\)
−0.886293 + 0.463125i \(0.846728\pi\)
\(480\) 1.05464 + 14.6427i 0.0481375 + 0.668344i
\(481\) −1.00020 1.37666i −0.0456052 0.0627702i
\(482\) 8.47426 + 16.6317i 0.385992 + 0.757552i
\(483\) 38.0080 38.0080i 1.72943 1.72943i
\(484\) 0 0
\(485\) −2.73005 + 31.9733i −0.123965 + 1.45183i
\(486\) 26.2970 + 8.54443i 1.19286 + 0.387583i
\(487\) −4.27267 + 26.9766i −0.193613 + 1.22243i 0.679046 + 0.734096i \(0.262394\pi\)
−0.872659 + 0.488330i \(0.837606\pi\)
\(488\) 1.79064 + 11.3056i 0.0810582 + 0.511782i
\(489\) 23.4710 7.62619i 1.06139 0.344868i
\(490\) 13.5608 3.16058i 0.612612 0.142780i
\(491\) −9.04456 + 12.4488i −0.408175 + 0.561805i −0.962772 0.270314i \(-0.912872\pi\)
0.554597 + 0.832119i \(0.312872\pi\)
\(492\) 1.19622 + 0.189463i 0.0539298 + 0.00854165i
\(493\) 1.59537 0.812880i 0.0718517 0.0366103i
\(494\) −2.88070 −0.129609
\(495\) 0 0
\(496\) 8.64843 0.388326
\(497\) −11.1690 + 5.69090i −0.500999 + 0.255272i
\(498\) −49.8745 7.89935i −2.23493 0.353978i
\(499\) −1.34768 + 1.85492i −0.0603305 + 0.0830378i −0.838116 0.545492i \(-0.816343\pi\)
0.777786 + 0.628530i \(0.216343\pi\)
\(500\) −3.89831 3.46609i −0.174338 0.155008i
\(501\) 27.4369 8.91479i 1.22579 0.398283i
\(502\) −0.388083 2.45026i −0.0173210 0.109360i
\(503\) 4.09842 25.8764i 0.182740 1.15377i −0.710335 0.703864i \(-0.751456\pi\)
0.893075 0.449909i \(-0.148544\pi\)
\(504\) 34.9860 + 11.3676i 1.55840 + 0.506355i
\(505\) −11.6227 13.7929i −0.517205 0.613774i
\(506\) 0 0
\(507\) 22.4026 22.4026i 0.994933 0.994933i
\(508\) 2.75045 + 5.39806i 0.122031 + 0.239500i
\(509\) 17.2271 + 23.7111i 0.763580 + 1.05098i 0.996908 + 0.0785793i \(0.0250384\pi\)
−0.233328 + 0.972398i \(0.574962\pi\)
\(510\) 2.84601 3.28780i 0.126024 0.145586i
\(511\) 0.576214 + 1.77340i 0.0254902 + 0.0784508i
\(512\) −11.2397 + 22.0592i −0.496731 + 0.974889i
\(513\) 3.73521 0.591599i 0.164914 0.0261197i
\(514\) 3.81741 2.77351i 0.168379 0.122334i
\(515\) 3.11402 7.37896i 0.137220 0.325156i
\(516\) 6.84042i 0.301133i
\(517\) 0 0
\(518\) 6.98713 + 6.98713i 0.306997 + 0.306997i
\(519\) 3.61149 11.1150i 0.158527 0.487895i
\(520\) 4.90382 + 1.21179i 0.215047 + 0.0531406i
\(521\) −35.9304 26.1049i −1.57414 1.14368i −0.923053 0.384673i \(-0.874314\pi\)
−0.651085 0.759005i \(-0.725686\pi\)
\(522\) 11.1138 + 5.66278i 0.486439 + 0.247853i
\(523\) 23.7758 + 12.1144i 1.03964 + 0.529725i 0.888543 0.458793i \(-0.151718\pi\)
0.151101 + 0.988518i \(0.451718\pi\)
\(524\) 6.50599 + 4.72688i 0.284215 + 0.206495i
\(525\) −39.5721 + 19.5055i −1.72707 + 0.851292i
\(526\) 0.0668402 0.205713i 0.00291437 0.00896951i
\(527\) 1.32491 + 1.32491i 0.0577138 + 0.0577138i
\(528\) 0 0
\(529\) 14.1095i 0.613457i
\(530\) −11.0155 + 4.47734i −0.478485 + 0.194483i
\(531\) 20.7951 15.1085i 0.902430 0.655654i
\(532\) −5.02705 + 0.796207i −0.217950 + 0.0345200i
\(533\) 0.342595 0.672380i 0.0148394 0.0291240i
\(534\) 14.2947 + 43.9947i 0.618593 + 1.90383i
\(535\) 11.1523 + 9.65378i 0.482158 + 0.417369i
\(536\) 23.8513 + 32.8285i 1.03022 + 1.41798i
\(537\) 3.17718 + 6.23557i 0.137105 + 0.269085i
\(538\) 6.06393 6.06393i 0.261435 0.261435i
\(539\) 0 0
\(540\) −1.24982 0.106716i −0.0537835 0.00459232i
\(541\) −38.3849 12.4720i −1.65030 0.536214i −0.671492 0.741012i \(-0.734346\pi\)
−0.978804 + 0.204798i \(0.934346\pi\)
\(542\) 4.42853 27.9607i 0.190222 1.20101i
\(543\) −2.84490 17.9620i −0.122086 0.770822i
\(544\) −1.51499 + 0.492250i −0.0649546 + 0.0211050i
\(545\) −13.7015 8.52192i −0.586908 0.365039i
\(546\) 4.75001 6.53783i 0.203282 0.279793i
\(547\) 36.1217 + 5.72112i 1.54445 + 0.244617i 0.869758 0.493479i \(-0.164275\pi\)
0.674695 + 0.738097i \(0.264275\pi\)
\(548\) −2.39108 + 1.21832i −0.102142 + 0.0520439i
\(549\) −13.0138 −0.555414
\(550\) 0 0
\(551\) −9.12363 −0.388680
\(552\) −42.1782 + 21.4909i −1.79522 + 0.914712i
\(553\) −41.8153 6.62289i −1.77817 0.281634i
\(554\) 2.69771 3.71308i 0.114615 0.157754i
\(555\) −11.1143 6.91277i −0.471776 0.293431i
\(556\) −5.68683 + 1.84776i −0.241175 + 0.0783625i
\(557\) 5.08481 + 32.1043i 0.215451 + 1.36030i 0.823912 + 0.566718i \(0.191787\pi\)
−0.608462 + 0.793583i \(0.708213\pi\)
\(558\) −2.04191 + 12.8921i −0.0864407 + 0.545765i
\(559\) 4.05351 + 1.31707i 0.171445 + 0.0557059i
\(560\) −22.0159 1.87984i −0.930342 0.0794376i
\(561\) 0 0
\(562\) −2.81320 + 2.81320i −0.118667 + 0.118667i
\(563\) −1.30823 2.56754i −0.0551351 0.108209i 0.861795 0.507257i \(-0.169341\pi\)
−0.916930 + 0.399048i \(0.869341\pi\)
\(564\) −0.757251 1.04227i −0.0318860 0.0438873i
\(565\) 7.13998 + 6.18056i 0.300381 + 0.260018i
\(566\) −8.09514 24.9143i −0.340264 1.04722i
\(567\) 11.5869 22.7406i 0.486604 0.955015i
\(568\) 10.9036 1.72697i 0.457506 0.0724618i
\(569\) 0.151872 0.110341i 0.00636679 0.00462575i −0.584597 0.811324i \(-0.698747\pi\)
0.590964 + 0.806698i \(0.298747\pi\)
\(570\) −20.5270 + 8.34334i −0.859782 + 0.349464i
\(571\) 46.3235i 1.93858i 0.245922 + 0.969290i \(0.420909\pi\)
−0.245922 + 0.969290i \(0.579091\pi\)
\(572\) 0 0
\(573\) 6.26752 + 6.26752i 0.261829 + 0.261829i
\(574\) −1.35414 + 4.16760i −0.0565205 + 0.173952i
\(575\) 9.79608 28.8405i 0.408525 1.20273i
\(576\) −24.9866 18.1538i −1.04111 0.756409i
\(577\) −16.5846 8.45025i −0.690424 0.351789i 0.0733193 0.997309i \(-0.476641\pi\)
−0.763744 + 0.645520i \(0.776641\pi\)
\(578\) −18.3365 9.34293i −0.762699 0.388615i
\(579\) −22.3596 16.2452i −0.929232 0.675126i
\(580\) 2.93782 + 0.725969i 0.121986 + 0.0301442i
\(581\) −17.1782 + 52.8692i −0.712673 + 2.19338i
\(582\) −31.9695 31.9695i −1.32518 1.32518i
\(583\) 0 0
\(584\) 1.64217i 0.0679535i
\(585\) −2.23290 + 5.29107i −0.0923192 + 0.218759i
\(586\) 28.7451 20.8845i 1.18745 0.862731i
\(587\) −23.5088 + 3.72343i −0.970313 + 0.153683i −0.621418 0.783479i \(-0.713443\pi\)
−0.348895 + 0.937162i \(0.613443\pi\)
\(588\) 2.70990 5.31847i 0.111754 0.219330i
\(589\) −2.95033 9.08018i −0.121566 0.374142i
\(590\) −13.4142 + 15.4965i −0.552254 + 0.637980i
\(591\) 24.0516 + 33.1042i 0.989350 + 1.36172i
\(592\) −2.97605 5.84082i −0.122315 0.240056i
\(593\) 24.6819 24.6819i 1.01356 1.01356i 0.0136582 0.999907i \(-0.495652\pi\)
0.999907 0.0136582i \(-0.00434768\pi\)
\(594\) 0 0
\(595\) −3.08477 3.66073i −0.126463 0.150075i
\(596\) 8.51019 + 2.76513i 0.348591 + 0.113264i
\(597\) −11.0434 + 69.7251i −0.451975 + 2.85366i
\(598\) 0.872776 + 5.51049i 0.0356905 + 0.225341i
\(599\) −11.4862 + 3.73210i −0.469315 + 0.152490i −0.534121 0.845408i \(-0.679357\pi\)
0.0648060 + 0.997898i \(0.479357\pi\)
\(600\) 38.4528 5.56802i 1.56983 0.227313i
\(601\) 10.1245 13.9352i 0.412986 0.568427i −0.550957 0.834533i \(-0.685737\pi\)
0.963944 + 0.266107i \(0.0857373\pi\)
\(602\) −24.4450 3.87171i −0.996305 0.157799i
\(603\) −41.1058 + 20.9444i −1.67396 + 0.852924i
\(604\) 8.82871 0.359235
\(605\) 0 0
\(606\) 25.4126 1.03232
\(607\) −7.58037 + 3.86239i −0.307678 + 0.156770i −0.601011 0.799241i \(-0.705235\pi\)
0.293334 + 0.956010i \(0.405235\pi\)
\(608\) 8.01698 + 1.26977i 0.325132 + 0.0514958i
\(609\) 15.0440 20.7063i 0.609614 0.839061i
\(610\) 10.1060 2.35539i 0.409181 0.0953671i
\(611\) −0.763431 + 0.248054i −0.0308851 + 0.0100352i
\(612\) −0.156453 0.987803i −0.00632422 0.0399296i
\(613\) −5.08373 + 32.0974i −0.205330 + 1.29640i 0.642562 + 0.766234i \(0.277872\pi\)
−0.847892 + 0.530169i \(0.822128\pi\)
\(614\) 21.9397 + 7.12863i 0.885413 + 0.287688i
\(615\) 0.493820 5.78343i 0.0199128 0.233210i
\(616\) 0 0
\(617\) −22.2515 + 22.2515i −0.895812 + 0.895812i −0.995062 0.0992505i \(-0.968355\pi\)
0.0992505 + 0.995062i \(0.468355\pi\)
\(618\) 5.12293 + 10.0543i 0.206075 + 0.404444i
\(619\) −16.4164 22.5953i −0.659832 0.908180i 0.339644 0.940554i \(-0.389693\pi\)
−0.999476 + 0.0323737i \(0.989693\pi\)
\(620\) 0.227497 + 3.15858i 0.00913650 + 0.126852i
\(621\) −2.26334 6.96583i −0.0908246 0.279529i
\(622\) −9.57655 + 18.7950i −0.383985 + 0.753612i
\(623\) 50.2980 7.96642i 2.01515 0.319168i
\(624\) −4.33723 + 3.15118i −0.173628 + 0.126148i
\(625\) −15.2265 + 19.8281i −0.609060 + 0.793124i
\(626\) 19.5389i 0.780932i
\(627\) 0 0
\(628\) 4.05187 + 4.05187i 0.161687 + 0.161687i
\(629\) 0.438872 1.35071i 0.0174990 0.0538563i
\(630\) 8.00023 32.3749i 0.318737 1.28985i
\(631\) 23.4229 + 17.0177i 0.932450 + 0.677465i 0.946591 0.322435i \(-0.104501\pi\)
−0.0141414 + 0.999900i \(0.504501\pi\)
\(632\) 33.2210 + 16.9269i 1.32146 + 0.673318i
\(633\) −46.6524 23.7706i −1.85427 0.944797i
\(634\) −6.64884 4.83066i −0.264059 0.191850i
\(635\) 24.8569 15.0063i 0.986417 0.595505i
\(636\) −1.57516 + 4.84785i −0.0624593 + 0.192230i
\(637\) −2.62986 2.62986i −0.104199 0.104199i
\(638\) 0 0
\(639\) 12.5510i 0.496511i
\(640\) 12.0566 + 5.08806i 0.476581 + 0.201123i
\(641\) −34.3068 + 24.9253i −1.35504 + 0.984491i −0.356293 + 0.934374i \(0.615959\pi\)
−0.998743 + 0.0501167i \(0.984041\pi\)
\(642\) −20.5261 + 3.25101i −0.810100 + 0.128307i
\(643\) 1.36977 2.68833i 0.0540185 0.106017i −0.862419 0.506195i \(-0.831052\pi\)
0.916438 + 0.400178i \(0.131052\pi\)
\(644\) 3.04612 + 9.37501i 0.120034 + 0.369427i
\(645\) 32.6987 2.35512i 1.28751 0.0927328i
\(646\) −1.41320 1.94511i −0.0556017 0.0765292i
\(647\) 3.76262 + 7.38456i 0.147924 + 0.290317i 0.953065 0.302767i \(-0.0979103\pi\)
−0.805141 + 0.593084i \(0.797910\pi\)
\(648\) −15.8936 + 15.8936i −0.624360 + 0.624360i
\(649\) 0 0
\(650\) 0.776348 4.51300i 0.0304509 0.177014i
\(651\) 25.4725 + 8.27651i 0.998345 + 0.324382i
\(652\) −0.707998 + 4.47013i −0.0277274 + 0.175064i
\(653\) 2.08465 + 13.1620i 0.0815787 + 0.515067i 0.994312 + 0.106511i \(0.0339678\pi\)
−0.912733 + 0.408557i \(0.866032\pi\)
\(654\) 21.6210 7.02508i 0.845447 0.274702i
\(655\) 20.3555 32.7275i 0.795356 1.27877i
\(656\) 1.70875 2.35189i 0.0667153 0.0918258i
\(657\) 1.84402 + 0.292065i 0.0719422 + 0.0113945i
\(658\) 4.15327 2.11620i 0.161911 0.0824979i
\(659\) 12.1943 0.475023 0.237511 0.971385i \(-0.423668\pi\)
0.237511 + 0.971385i \(0.423668\pi\)
\(660\) 0 0
\(661\) 14.1589 0.550718 0.275359 0.961341i \(-0.411203\pi\)
0.275359 + 0.961341i \(0.411203\pi\)
\(662\) −13.3256 + 6.78975i −0.517915 + 0.263891i
\(663\) −1.14719 0.181698i −0.0445534 0.00705656i
\(664\) 28.7761 39.6069i 1.11673 1.53704i
\(665\) 5.53683 + 23.7563i 0.214709 + 0.921229i
\(666\) 9.40947 3.05732i 0.364609 0.118469i
\(667\) 2.76422 + 17.4526i 0.107031 + 0.675766i
\(668\) −0.827630 + 5.22545i −0.0320220 + 0.202179i
\(669\) 19.3878 + 6.29947i 0.749575 + 0.243552i
\(670\) 28.1305 23.7046i 1.08678 0.915787i
\(671\) 0 0
\(672\) −16.1010 + 16.1010i −0.621110 + 0.621110i
\(673\) −10.5343 20.6747i −0.406067 0.796952i 0.593904 0.804536i \(-0.297586\pi\)
−0.999971 + 0.00758420i \(0.997586\pi\)
\(674\) 7.08785 + 9.75559i 0.273014 + 0.375771i
\(675\) −0.0798202 + 6.01113i −0.00307228 + 0.231368i
\(676\) 1.79544 + 5.52579i 0.0690553 + 0.212530i
\(677\) −16.0179 + 31.4369i −0.615617 + 1.20822i 0.347131 + 0.937817i \(0.387156\pi\)
−0.962748 + 0.270400i \(0.912844\pi\)
\(678\) −13.1413 + 2.08137i −0.504687 + 0.0799345i
\(679\) −40.2667 + 29.2555i −1.54529 + 1.12272i
\(680\) 1.58747 + 3.90563i 0.0608767 + 0.149774i
\(681\) 7.88382i 0.302109i
\(682\) 0 0
\(683\) −7.64701 7.64701i −0.292605 0.292605i 0.545504 0.838108i \(-0.316338\pi\)
−0.838108 + 0.545504i \(0.816338\pi\)
\(684\) −1.57478 + 4.84668i −0.0602133 + 0.185318i
\(685\) 6.64706 + 11.0104i 0.253971 + 0.420687i
\(686\) −6.84950 4.97645i −0.261515 0.190002i
\(687\) −33.3697 17.0027i −1.27313 0.648694i
\(688\) 14.6295 + 7.45412i 0.557746 + 0.284186i
\(689\) 2.56947 + 1.86683i 0.0978890 + 0.0711205i
\(690\) 22.1791 + 36.7383i 0.844344 + 1.39860i
\(691\) 9.11894 28.0652i 0.346901 1.06765i −0.613657 0.789572i \(-0.710302\pi\)
0.960558 0.278079i \(-0.0896976\pi\)
\(692\) 1.51553 + 1.51553i 0.0576117 + 0.0576117i
\(693\) 0 0
\(694\) 30.1402i 1.14410i
\(695\) 10.7906 + 26.5481i 0.409312 + 1.00703i
\(696\) −18.2356 + 13.2489i −0.691217 + 0.502198i
\(697\) 0.622073 0.0985267i 0.0235627 0.00373196i
\(698\) 10.5858 20.7758i 0.400678 0.786375i
\(699\) 10.9635 + 33.7423i 0.414679 + 1.27625i
\(700\) 0.107426 8.09011i 0.00406034 0.305777i
\(701\) 4.33862 + 5.97160i 0.163867 + 0.225544i 0.883052 0.469275i \(-0.155485\pi\)
−0.719185 + 0.694819i \(0.755485\pi\)
\(702\) −0.499918 0.981144i −0.0188682 0.0370309i
\(703\) −5.11715 + 5.11715i −0.192997 + 0.192997i
\(704\) 0 0
\(705\) −4.72154 + 3.97867i −0.177823 + 0.149845i
\(706\) 8.98066 + 2.91799i 0.337992 + 0.109820i
\(707\) 4.37642 27.6316i 0.164592 1.03919i
\(708\) 1.37447 + 8.67805i 0.0516557 + 0.326141i
\(709\) −46.8212 + 15.2131i −1.75841 + 0.571341i −0.997033 0.0769719i \(-0.975475\pi\)
−0.761374 + 0.648313i \(0.775475\pi\)
\(710\) −2.27164 9.74668i −0.0852532 0.365786i
\(711\) −24.9160 + 34.2940i −0.934424 + 1.28612i
\(712\) −44.2963 7.01584i −1.66007 0.262930i
\(713\) −16.4756 + 8.39473i −0.617015 + 0.314385i
\(714\) 6.74471 0.252414
\(715\) 0 0
\(716\) −1.28342 −0.0479638
\(717\) 7.29435 3.71666i 0.272412 0.138801i
\(718\) 18.7372 + 2.96769i 0.699267 + 0.110753i
\(719\) −3.41704 + 4.70315i −0.127434 + 0.175398i −0.867967 0.496622i \(-0.834573\pi\)
0.740532 + 0.672021i \(0.234573\pi\)
\(720\) −11.6846 + 18.7864i −0.435460 + 0.700129i
\(721\) 11.8145 3.83876i 0.439995 0.142963i
\(722\) −1.76411 11.1381i −0.0656533 0.414519i
\(723\) 5.99921 37.8775i 0.223113 1.40868i
\(724\) 3.17187 + 1.03060i 0.117882 + 0.0383021i
\(725\) 2.45881 14.2934i 0.0913181 0.530842i
\(726\) 0 0
\(727\) 20.3755 20.3755i 0.755685 0.755685i −0.219849 0.975534i \(-0.570556\pi\)
0.975534 + 0.219849i \(0.0705565\pi\)
\(728\) 3.55694 + 6.98088i 0.131829 + 0.258729i
\(729\) −20.4144 28.0980i −0.756089 1.04067i
\(730\) −1.48486 + 0.106947i −0.0549573 + 0.00395830i
\(731\) 1.09925 + 3.38313i 0.0406571 + 0.125130i
\(732\) 2.01952 3.96354i 0.0746438 0.146497i
\(733\) −23.7224 + 3.75725i −0.876205 + 0.138777i −0.578306 0.815820i \(-0.696286\pi\)
−0.297899 + 0.954597i \(0.596286\pi\)
\(734\) 2.30457 1.67437i 0.0850632 0.0618021i
\(735\) −26.3564 11.1228i −0.972172 0.410269i
\(736\) 15.7204i 0.579461i
\(737\) 0 0
\(738\) 3.10248 + 3.10248i 0.114204 + 0.114204i
\(739\) 6.33611 19.5005i 0.233077 0.717339i −0.764293 0.644869i \(-0.776912\pi\)
0.997371 0.0724697i \(-0.0230881\pi\)
\(740\) 2.05490 1.24056i 0.0755397 0.0456037i
\(741\) 4.78810 + 3.47876i 0.175895 + 0.127795i
\(742\) −16.4328 8.37294i −0.603268 0.307380i
\(743\) −2.48142 1.26434i −0.0910343 0.0463843i 0.407881 0.913035i \(-0.366268\pi\)
−0.498915 + 0.866651i \(0.666268\pi\)
\(744\) −19.0827 13.8644i −0.699605 0.508293i
\(745\) 10.2879 41.6326i 0.376919 1.52530i
\(746\) 12.4043 38.1765i 0.454153 1.39774i
\(747\) 39.3574 + 39.3574i 1.44001 + 1.44001i
\(748\) 0 0
\(749\) 22.8783i 0.835955i
\(750\) −7.53891 34.4068i −0.275282 1.25636i
\(751\) 3.70291 2.69033i 0.135121 0.0981714i −0.518171 0.855277i \(-0.673387\pi\)
0.653293 + 0.757105i \(0.273387\pi\)
\(752\) −3.05427 + 0.483750i −0.111378 + 0.0176405i
\(753\) −2.31390 + 4.54129i −0.0843234 + 0.165494i
\(754\) 0.820932 + 2.52657i 0.0298966 + 0.0920122i
\(755\) −3.03968 42.2031i −0.110625 1.53593i
\(756\) −1.14358 1.57400i −0.0415915 0.0572458i
\(757\) −11.3069 22.1911i −0.410957 0.806548i 0.589042 0.808103i \(-0.299505\pi\)
−0.999999 + 0.00155412i \(0.999505\pi\)
\(758\) −9.92515 + 9.92515i −0.360498 + 0.360498i
\(759\) 0 0
\(760\) 1.82763 21.4044i 0.0662950 0.776420i
\(761\) −33.0432 10.7364i −1.19781 0.389193i −0.358857 0.933392i \(-0.616834\pi\)
−0.838956 + 0.544199i \(0.816834\pi\)
\(762\) −6.39951 + 40.4049i −0.231830 + 1.46372i
\(763\) −3.91506 24.7187i −0.141735 0.894878i
\(764\) −1.54594 + 0.502305i −0.0559300 + 0.0181728i
\(765\) −4.66804 + 1.08797i −0.168773 + 0.0393357i
\(766\) −1.02665 + 1.41306i −0.0370943 + 0.0510559i
\(767\) 5.40710 + 0.856401i 0.195239 + 0.0309229i
\(768\) 23.8943 12.1748i 0.862212 0.439319i
\(769\) −7.47240 −0.269462 −0.134731 0.990882i \(-0.543017\pi\)
−0.134731 + 0.990882i \(0.543017\pi\)
\(770\) 0 0
\(771\) −9.69432 −0.349133
\(772\) 4.51608 2.30106i 0.162537 0.0828168i
\(773\) −31.4308 4.97815i −1.13049 0.179052i −0.436959 0.899481i \(-0.643945\pi\)
−0.693528 + 0.720430i \(0.743945\pi\)
\(774\) −14.5658 + 20.0481i −0.523557 + 0.720614i
\(775\) 15.0204 2.17497i 0.539548 0.0781272i
\(776\) 41.6880 13.5453i 1.49651 0.486247i
\(777\) −3.17580 20.0512i −0.113931 0.719333i
\(778\) 5.97595 37.7306i 0.214248 1.35271i
\(779\) −3.05222 0.991726i −0.109357 0.0355323i
\(780\) −1.26497 1.50115i −0.0452931 0.0537499i
\(781\) 0 0
\(782\) −3.29263 + 3.29263i −0.117744 + 0.117744i
\(783\) −1.58332 3.10743i −0.0565831 0.111051i
\(784\) −8.42154 11.5913i −0.300769 0.413974i
\(785\) 17.9738 20.7638i 0.641511 0.741093i
\(786\) 16.7801 + 51.6439i 0.598528 + 1.84208i
\(787\) −5.78709 + 11.3578i −0.206287 + 0.404862i −0.970850 0.239688i \(-0.922955\pi\)
0.764563 + 0.644549i \(0.222955\pi\)
\(788\) −7.41173 + 1.17390i −0.264032 + 0.0418186i
\(789\) −0.359517 + 0.261204i −0.0127991 + 0.00929912i
\(790\) 13.1420 31.1411i 0.467570 1.10795i
\(791\) 14.6472i 0.520794i
\(792\) 0 0
\(793\) −1.95988 1.95988i −0.0695974 0.0695974i
\(794\) −3.38148 + 10.4071i −0.120004 + 0.369335i
\(795\) 23.7161 + 5.86053i 0.841124 + 0.207852i
\(796\) −10.4737 7.60962i −0.371232 0.269716i
\(797\) 23.5550 + 12.0019i 0.834362 + 0.425128i 0.818334 0.574743i \(-0.194898\pi\)
0.0160277 + 0.999872i \(0.494898\pi\)
\(798\) −30.6219 15.6026i −1.08400 0.552327i
\(799\) −0.542011 0.393794i −0.0191750 0.0139314i
\(800\) −4.14983 + 12.2174i −0.146718 + 0.431952i
\(801\) 15.7564 48.4933i 0.556726 1.71343i
\(802\) 11.7547 + 11.7547i 0.415073 + 0.415073i
\(803\) 0 0
\(804\) 15.7696i 0.556152i
\(805\) 43.7658 17.7889i 1.54254 0.626976i
\(806\) −2.24907 + 1.63404i −0.0792200 + 0.0575567i
\(807\) −17.4019 + 2.75618i −0.612575 + 0.0970223i
\(808\) −11.1853 + 21.9525i −0.393499 + 0.772286i
\(809\) −9.77565 30.0864i −0.343694 1.05778i −0.962279 0.272063i \(-0.912294\pi\)
0.618586 0.785717i \(-0.287706\pi\)
\(810\) 15.4062 + 13.3361i 0.541319 + 0.468581i
\(811\) −21.1123 29.0585i −0.741352 1.02038i −0.998540 0.0540218i \(-0.982796\pi\)
0.257188 0.966361i \(-0.417204\pi\)
\(812\) 2.13092 + 4.18216i 0.0747805 + 0.146765i
\(813\) −41.1263 + 41.1263i −1.44236 + 1.44236i
\(814\) 0 0
\(815\) 21.6119 + 1.84534i 0.757033 + 0.0646396i
\(816\) −4.25548 1.38269i −0.148971 0.0484038i
\(817\) 2.83552 17.9028i 0.0992023 0.626339i
\(818\) −0.241526 1.52493i −0.00844476 0.0533181i
\(819\) −8.47157 + 2.75258i −0.296021 + 0.0961830i
\(820\) 0.903906 + 0.562203i 0.0315658 + 0.0196330i
\(821\) −15.3322 + 21.1030i −0.535099 + 0.736500i −0.987897 0.155113i \(-0.950426\pi\)
0.452798 + 0.891613i \(0.350426\pi\)
\(822\) −17.8974 2.83468i −0.624245 0.0988707i
\(823\) −35.0517 + 17.8597i −1.22182 + 0.622550i −0.941389 0.337323i \(-0.890479\pi\)
−0.280435 + 0.959873i \(0.590479\pi\)
\(824\) −10.9402 −0.381120
\(825\) 0 0
\(826\) −31.7900 −1.10612
\(827\) 47.0611 23.9789i 1.63648 0.833826i 0.638542 0.769587i \(-0.279538\pi\)
0.997935 0.0642393i \(-0.0204621\pi\)
\(828\) 9.74833 + 1.54398i 0.338778 + 0.0536571i
\(829\) 4.58456 6.31010i 0.159228 0.219159i −0.721947 0.691948i \(-0.756753\pi\)
0.881176 + 0.472789i \(0.156753\pi\)
\(830\) −37.6869 23.4401i −1.30813 0.813619i
\(831\) −8.96787 + 2.91384i −0.311092 + 0.101080i
\(832\) −1.02902 6.49697i −0.0356748 0.225242i
\(833\) 0.485588 3.06588i 0.0168246 0.106227i
\(834\) −38.3997 12.4768i −1.32967 0.432037i
\(835\) 25.2637 + 2.15715i 0.874287 + 0.0746513i
\(836\) 0 0
\(837\) 2.58063 2.58063i 0.0891997 0.0891997i
\(838\) 11.5807 + 22.7284i 0.400049 + 0.785140i
\(839\) 15.5988 + 21.4699i 0.538531 + 0.741224i 0.988400 0.151870i \(-0.0485295\pi\)
−0.449869 + 0.893094i \(0.648529\pi\)
\(840\) 45.5643 + 39.4417i 1.57212 + 1.36087i
\(841\) −6.36148 19.5786i −0.219361 0.675125i
\(842\) −4.46047 + 8.75417i −0.153718 + 0.301689i
\(843\) 8.07312 1.27866i 0.278053 0.0440393i
\(844\) 7.76830 5.64400i 0.267396 0.194274i
\(845\) 25.7963 10.4851i 0.887419 0.360698i
\(846\) 4.66717i 0.160461i
\(847\) 0 0
\(848\) 8.65158 + 8.65158i 0.297096 + 0.297096i
\(849\) −16.6315 + 51.1864i −0.570791 + 1.75671i
\(850\) 3.42812 1.68976i 0.117584 0.0579583i
\(851\) 11.3390 + 8.23823i 0.388694 + 0.282403i
\(852\) −3.82261 1.94772i −0.130960 0.0667276i
\(853\) −45.2547 23.0584i −1.54949 0.789505i −0.550517 0.834824i \(-0.685570\pi\)
−0.998973 + 0.0453191i \(0.985570\pi\)
\(854\) 13.0211 + 9.46039i 0.445573 + 0.323728i
\(855\) 23.7104 + 5.85911i 0.810878 + 0.200377i
\(856\) 6.22619 19.1622i 0.212807 0.654952i
\(857\) 21.6116 + 21.6116i 0.738238 + 0.738238i 0.972237 0.233999i \(-0.0751812\pi\)
−0.233999 + 0.972237i \(0.575181\pi\)
\(858\) 0 0
\(859\) 14.1414i 0.482499i −0.970463 0.241250i \(-0.922443\pi\)
0.970463 0.241250i \(-0.0775572\pi\)
\(860\) −2.33757 + 5.53909i −0.0797104 + 0.188881i
\(861\) 7.28357 5.29182i 0.248223 0.180345i
\(862\) −36.4627 + 5.77512i −1.24192 + 0.196701i
\(863\) 18.1738 35.6682i 0.618644 1.21416i −0.342865 0.939385i \(-0.611397\pi\)
0.961509 0.274773i \(-0.0886028\pi\)
\(864\) 0.958797 + 2.95087i 0.0326189 + 0.100391i
\(865\) 6.72276 7.76634i 0.228581 0.264063i
\(866\) −7.48226 10.2985i −0.254258 0.349956i
\(867\) 19.1951 + 37.6725i 0.651899 + 1.27942i
\(868\) −3.47316 + 3.47316i −0.117887 + 0.117887i
\(869\) 0 0
\(870\) 13.1674 + 15.6259i 0.446416 + 0.529767i
\(871\) −9.34481 3.03631i −0.316637 0.102882i
\(872\) −3.44790 + 21.7692i −0.116761 + 0.737198i
\(873\) 7.79589 + 49.2213i 0.263851 + 1.66589i
\(874\) 22.5659 7.33210i 0.763302 0.248012i
\(875\) −38.7095 + 2.27186i −1.30862 + 0.0768030i
\(876\) −0.375115 + 0.516302i −0.0126740 + 0.0174442i
\(877\) 36.1778 + 5.73000i 1.22164 + 0.193488i 0.733751 0.679419i \(-0.237768\pi\)
0.487887 + 0.872907i \(0.337768\pi\)
\(878\) −33.5388 + 17.0889i −1.13188 + 0.576722i
\(879\) −72.9982 −2.46217
\(880\) 0 0
\(881\) −50.8785 −1.71414 −0.857069 0.515201i \(-0.827717\pi\)
−0.857069 + 0.515201i \(0.827717\pi\)
\(882\) 19.2673 9.81715i 0.648762 0.330561i
\(883\) −7.99304 1.26597i −0.268987 0.0426034i 0.0204837 0.999790i \(-0.493479\pi\)
−0.289471 + 0.957187i \(0.593479\pi\)
\(884\) 0.125202 0.172326i 0.00421099 0.00579594i
\(885\) 41.0098 9.55807i 1.37853 0.321291i
\(886\) −13.2295 + 4.29852i −0.444453 + 0.144412i
\(887\) 2.80215 + 17.6921i 0.0940870 + 0.594042i 0.989013 + 0.147828i \(0.0472281\pi\)
−0.894926 + 0.446214i \(0.852772\pi\)
\(888\) −2.79685 + 17.6586i −0.0938562 + 0.592585i
\(889\) 42.8310 + 13.9166i 1.43650 + 0.466749i
\(890\) −3.45896 + 40.5100i −0.115945 + 1.35790i
\(891\) 0 0
\(892\) −2.64351 + 2.64351i −0.0885114 + 0.0885114i
\(893\) 1.54984 + 3.04172i 0.0518633 + 0.101787i
\(894\) 35.5148 + 48.8819i 1.18779 + 1.63485i
\(895\) 0.441876 + 6.13504i 0.0147703 + 0.205072i
\(896\) 6.27224 + 19.3040i 0.209541 + 0.644900i
\(897\) 5.20384 10.2131i 0.173751 0.341006i
\(898\) 23.8990 3.78522i 0.797519 0.126315i
\(899\) −7.12314 + 5.17527i −0.237570 + 0.172605i
\(900\) −7.16856 3.77328i −0.238952 0.125776i
\(901\) 2.65078i 0.0883101i
\(902\) 0 0
\(903\) 35.9553 + 35.9553i 1.19652 + 1.19652i
\(904\) 3.98614 12.2681i 0.132577 0.408031i
\(905\) 3.83445 15.5171i 0.127461 0.515804i
\(906\) 48.2295 + 35.0408i 1.60232 + 1.16415i
\(907\) 46.8164 + 23.8541i 1.55451 + 0.792064i 0.999216 0.0395883i \(-0.0126046\pi\)
0.555297 + 0.831652i \(0.312605\pi\)
\(908\) 1.28823 + 0.656384i 0.0427513 + 0.0217829i
\(909\) −22.6615 16.4645i −0.751635 0.546094i
\(910\) 6.08053 3.67085i 0.201567 0.121687i
\(911\) −4.37040 + 13.4507i −0.144798 + 0.445642i −0.996985 0.0775954i \(-0.975276\pi\)
0.852187 + 0.523237i \(0.175276\pi\)
\(912\) 16.1219 + 16.1219i 0.533848 + 0.533848i
\(913\) 0 0
\(914\) 14.5786i 0.482218i
\(915\) −19.6419 8.28914i −0.649341 0.274030i
\(916\) 5.55654 4.03706i 0.183593 0.133388i
\(917\) 59.0432 9.35153i 1.94978 0.308815i
\(918\) 0.417240 0.818880i 0.0137710 0.0270271i
\(919\) 13.1640 + 40.5145i 0.434239 + 1.33645i 0.893864 + 0.448338i \(0.147984\pi\)
−0.459625 + 0.888113i \(0.652016\pi\)
\(920\) −41.4982 + 2.98891i −1.36816 + 0.0985414i
\(921\) −27.8579 38.3432i −0.917951 1.26345i
\(922\) 14.9334 + 29.3084i 0.491804 + 0.965221i
\(923\) −1.89019 + 1.89019i −0.0622165 + 0.0622165i
\(924\) 0 0
\(925\) −6.63762 9.39576i −0.218244 0.308931i
\(926\) 24.0267 + 7.80674i 0.789566 + 0.256546i
\(927\) 1.94575 12.2850i 0.0639067 0.403491i
\(928\) −1.17098 7.39328i −0.0384393 0.242696i
\(929\) −11.2714 + 3.66231i −0.369804 + 0.120157i −0.488023 0.872831i \(-0.662282\pi\)
0.118219 + 0.992988i \(0.462282\pi\)
\(930\) −11.2935 + 18.1576i −0.370329 + 0.595412i
\(931\) −9.29699 + 12.7962i −0.304697 + 0.419379i
\(932\) −6.42634 1.01783i −0.210502 0.0333402i
\(933\) 38.6144 19.6750i 1.26418 0.644132i
\(934\) 23.1291 0.756807
\(935\) 0 0
\(936\) 7.84466 0.256411
\(937\) −16.3614 + 8.33653i −0.534503 + 0.272343i −0.700339 0.713811i \(-0.746968\pi\)
0.165836 + 0.986153i \(0.446968\pi\)
\(938\) 56.3546 + 8.92570i 1.84004 + 0.291434i
\(939\) −23.5953 + 32.4762i −0.770004 + 1.05982i
\(940\) −0.257018 1.10276i −0.00838300 0.0359680i
\(941\) −2.61735 + 0.850427i −0.0853230 + 0.0277231i −0.351367 0.936238i \(-0.614283\pi\)
0.266044 + 0.963961i \(0.414283\pi\)
\(942\) 6.05285 + 38.2162i 0.197213 + 1.24515i
\(943\) −0.972330 + 6.13905i −0.0316634 + 0.199915i
\(944\) 20.0575 + 6.51706i 0.652815 + 0.212112i
\(945\) −7.13033 + 6.00847i −0.231950 + 0.195455i
\(946\) 0 0
\(947\) 16.3254 16.3254i 0.530503 0.530503i −0.390219 0.920722i \(-0.627601\pi\)
0.920722 + 0.390219i \(0.127601\pi\)
\(948\) −6.57819 12.9104i −0.213650 0.419311i
\(949\) 0.233726 + 0.321696i 0.00758707 + 0.0104427i
\(950\) −19.4731 0.258578i −0.631791 0.00838938i
\(951\) 5.21768 + 16.0584i 0.169195 + 0.520728i
\(952\) −2.96868 + 5.82637i −0.0962155 + 0.188834i
\(953\) 47.7643 7.56512i 1.54724 0.245058i 0.676365 0.736567i \(-0.263554\pi\)
0.870873 + 0.491508i \(0.163554\pi\)
\(954\) −14.9394 + 10.8541i −0.483682 + 0.351415i
\(955\) 2.93339 + 7.21697i 0.0949222 + 0.233536i
\(956\) 1.50134i 0.0485570i
\(957\) 0 0
\(958\) −6.38460 6.38460i −0.206277 0.206277i
\(959\) −6.16440 + 18.9721i −0.199059 + 0.612640i
\(960\) −26.1495 43.3151i −0.843973 1.39799i
\(961\) 17.6255 + 12.8057i 0.568564 + 0.413086i
\(962\) 1.87751 + 0.956637i 0.0605332 + 0.0308432i
\(963\) 20.4103 + 10.3996i 0.657713 + 0.335121i
\(964\) 5.68976 + 4.13386i 0.183255 + 0.133143i
\(965\) −12.5544 20.7956i −0.404141 0.669434i
\(966\) −20.5686 + 63.3037i −0.661785 + 2.03676i
\(967\) −14.7018 14.7018i −0.472778 0.472778i 0.430034 0.902813i \(-0.358501\pi\)
−0.902813 + 0.430034i \(0.858501\pi\)
\(968\) 0 0
\(969\) 4.93961i 0.158683i
\(970\) −14.9627 36.8125i −0.480423 1.18198i
\(971\) −21.6941 + 15.7617i −0.696198 + 0.505817i −0.878692 0.477390i \(-0.841583\pi\)
0.182494 + 0.983207i \(0.441583\pi\)
\(972\) 10.2897 1.62973i 0.330042 0.0522735i
\(973\) −20.1793 + 39.6040i −0.646917 + 1.26965i
\(974\) −10.4516 32.1666i −0.334890 1.03069i
\(975\) −6.74031 + 6.56365i −0.215863 + 0.210205i
\(976\) −6.27608 8.63828i −0.200892 0.276504i
\(977\) −20.3996 40.0365i −0.652641 1.28088i −0.945779 0.324810i \(-0.894699\pi\)
0.293138 0.956070i \(-0.405301\pi\)
\(978\) −21.6094 + 21.6094i −0.690992 + 0.690992i
\(979\) 0 0
\(980\) 4.01184 3.38063i 0.128153 0.107990i
\(981\) −23.8318 7.74343i −0.760891 0.247229i
\(982\) 2.98081 18.8201i 0.0951213 0.600572i
\(983\) −7.94660 50.1729i −0.253457 1.60027i −0.705793 0.708419i \(-0.749409\pi\)
0.452335 0.891848i \(-0.350591\pi\)
\(984\) −7.54066 + 2.45011i −0.240387 + 0.0781066i
\(985\) 8.16333 + 35.0255i 0.260105 + 1.11601i
\(986\) −1.30326 + 1.79378i −0.0415042 + 0.0571257i
\(987\) −9.45879 1.49813i −0.301077 0.0476859i
\(988\) −0.967077 + 0.492750i −0.0307668 + 0.0156765i
\(989\) −35.1053 −1.11628
\(990\) 0 0
\(991\) −13.2536 −0.421013 −0.210507 0.977592i \(-0.567511\pi\)
−0.210507 + 0.977592i \(0.567511\pi\)
\(992\) 6.97940 3.55618i 0.221596 0.112909i
\(993\) 30.3482 + 4.80669i 0.963072 + 0.152536i
\(994\) 9.12401 12.5581i 0.289396 0.398319i
\(995\) −32.7696 + 52.6867i −1.03886 + 1.67028i
\(996\) −18.0945 + 5.87926i −0.573346 + 0.186292i
\(997\) 2.87479 + 18.1507i 0.0910455 + 0.574839i 0.990466 + 0.137755i \(0.0439886\pi\)
−0.899421 + 0.437084i \(0.856011\pi\)
\(998\) 0.444154 2.80428i 0.0140594 0.0887678i
\(999\) −2.63089 0.854829i −0.0832378 0.0270456i
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 605.2.m.c.233.2 32
5.2 odd 4 inner 605.2.m.c.112.2 32
11.2 odd 10 55.2.l.a.8.2 yes 32
11.3 even 5 55.2.l.a.18.3 yes 32
11.4 even 5 605.2.e.b.483.5 32
11.5 even 5 605.2.m.d.578.3 32
11.6 odd 10 inner 605.2.m.c.578.2 32
11.7 odd 10 605.2.e.b.483.12 32
11.8 odd 10 605.2.m.e.403.2 32
11.9 even 5 605.2.m.e.118.3 32
11.10 odd 2 605.2.m.d.233.3 32
33.2 even 10 495.2.bj.a.118.3 32
33.14 odd 10 495.2.bj.a.73.2 32
44.3 odd 10 880.2.cm.a.513.4 32
44.35 even 10 880.2.cm.a.833.1 32
55.2 even 20 55.2.l.a.52.3 yes 32
55.3 odd 20 275.2.bm.b.7.3 32
55.7 even 20 605.2.e.b.362.5 32
55.13 even 20 275.2.bm.b.107.2 32
55.14 even 10 275.2.bm.b.18.2 32
55.17 even 20 inner 605.2.m.c.457.2 32
55.24 odd 10 275.2.bm.b.118.3 32
55.27 odd 20 605.2.m.d.457.3 32
55.32 even 4 605.2.m.d.112.3 32
55.37 odd 20 605.2.e.b.362.12 32
55.42 odd 20 605.2.m.e.602.2 32
55.47 odd 20 55.2.l.a.7.2 32
55.52 even 20 605.2.m.e.282.3 32
165.2 odd 20 495.2.bj.a.217.2 32
165.47 even 20 495.2.bj.a.172.3 32
220.47 even 20 880.2.cm.a.337.1 32
220.167 odd 20 880.2.cm.a.657.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.l.a.7.2 32 55.47 odd 20
55.2.l.a.8.2 yes 32 11.2 odd 10
55.2.l.a.18.3 yes 32 11.3 even 5
55.2.l.a.52.3 yes 32 55.2 even 20
275.2.bm.b.7.3 32 55.3 odd 20
275.2.bm.b.18.2 32 55.14 even 10
275.2.bm.b.107.2 32 55.13 even 20
275.2.bm.b.118.3 32 55.24 odd 10
495.2.bj.a.73.2 32 33.14 odd 10
495.2.bj.a.118.3 32 33.2 even 10
495.2.bj.a.172.3 32 165.47 even 20
495.2.bj.a.217.2 32 165.2 odd 20
605.2.e.b.362.5 32 55.7 even 20
605.2.e.b.362.12 32 55.37 odd 20
605.2.e.b.483.5 32 11.4 even 5
605.2.e.b.483.12 32 11.7 odd 10
605.2.m.c.112.2 32 5.2 odd 4 inner
605.2.m.c.233.2 32 1.1 even 1 trivial
605.2.m.c.457.2 32 55.17 even 20 inner
605.2.m.c.578.2 32 11.6 odd 10 inner
605.2.m.d.112.3 32 55.32 even 4
605.2.m.d.233.3 32 11.10 odd 2
605.2.m.d.457.3 32 55.27 odd 20
605.2.m.d.578.3 32 11.5 even 5
605.2.m.e.118.3 32 11.9 even 5
605.2.m.e.282.3 32 55.52 even 20
605.2.m.e.403.2 32 11.8 odd 10
605.2.m.e.602.2 32 55.42 odd 20
880.2.cm.a.337.1 32 220.47 even 20
880.2.cm.a.513.4 32 44.3 odd 10
880.2.cm.a.657.4 32 220.167 odd 20
880.2.cm.a.833.1 32 44.35 even 10