Properties

Label 845.2.t.g.427.2
Level 845845
Weight 22
Character 845.427
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(188,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.188");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 845=5132 845 = 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 845.t (of order 1212, degree 44, 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: 6.747358970806.74735897080
Analytic rank: 00
Dimension: 2020
Relative dimension: 55 over Q(ζ12)\Q(\zeta_{12})
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20+26x18+279x16+1604x14+5353x12+10466x10+11441x8+6176x6++1 x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 427.2
Root 1.58474i1.58474i of defining polynomial
Character χ\chi == 845.427
Dual form 845.2.t.g.188.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.37242+0.792369i)q2+(0.190588+0.0510678i)q3+(0.2556970.442881i)q4+(2.235060.0672627i)q5+(0.302032+0.0809291i)q6+(0.274164+0.474866i)q72.35905iq8+(2.564361.48053i)q9+(3.01415+1.86330i)q10+(0.1479280.0396372i)q11+(0.07134970.0713497i)q120.868956iq14+(0.429409+0.101320i)q15+(2.38063+4.12338i)q16+(0.813499+3.03602i)q17+4.69252q18+(1.18079+4.40678i)q19+(0.5417091.00706i)q20+(0.0765027+0.0765027i)q21+(0.2344270.0628146i)q22+(0.916011+3.41860i)q23+(0.1204720.449606i)q24+(4.990950.300672i)q25+(0.8316880.831688i)q27+(0.140206+0.242844i)q28+(2.028781.17132i)q29+(0.669614+0.201197i)q30+(6.61000+6.61000i)q31+(2.448481.41363i)q32+(0.02616910.0151087i)q33+(3.522113.52211i)q34+(0.580831+1.07979i)q35+(1.31140+0.757137i)q36+(3.403175.89447i)q37+(5.112345.11234i)q38+(0.1586765.27261i)q40+(0.926064+3.45612i)q41+(0.04437570.165612i)q42+(6.867841.84023i)q43+(0.0553794+0.0553794i)q44+(5.831073.13659i)q45+(1.451645.41759i)q46+9.13956q47+(0.243147+0.907439i)q48+(3.34967+5.80180i)q49+(6.61146+4.36732i)q50+0.620172iq51+(3.70952+3.70952i)q53+(1.80043+0.482424i)q54+(0.3332940.0786414i)q55+(1.12023+0.646766i)q56+0.900179iq57+(1.85623+3.21508i)q58+(3.677280.985325i)q59+(0.1546720.164270i)q60+(3.92486+6.79805i)q61+(14.30933.83416i)q62+(1.406110.811818i)q635.04207q64+0.0478868q66+(4.23514+2.44516i)q67+(1.55261+0.416019i)q68+(0.349161+0.604765i)q69+(0.05844831.94217i)q70+(15.10454.04725i)q71+(3.49265+6.04945i)q72+3.91807iq73+(9.34119+5.39314i)q74+(0.966569+0.197573i)q75+(2.25360+0.603851i)q76+(0.05937890.0593789i)q77+11.1394iq79+(5.59820+9.05585i)q80+(4.32557+7.49210i)q81+(1.467575.47704i)q8213.4251q83+(0.0143200+0.0534431i)q84+(2.02243+6.73096i)q85+(7.96744+7.96744i)q86+(0.4464770.119633i)q87+(0.0935062+0.348970i)q88+(2.35372+8.78419i)q89+(10.48800.315631i)q90+(1.27981+1.27981i)q92+(0.922226+1.59734i)q93+(12.5433+7.24190i)q94+(2.93555+9.76998i)q95+(0.3944590.394459i)q96+(6.556683.78550i)q97+(9.194335.30835i)q98+(0.320657+0.320657i)q99+O(q100)q+(-1.37242 + 0.792369i) q^{2} +(0.190588 + 0.0510678i) q^{3} +(0.255697 - 0.442881i) q^{4} +(2.23506 - 0.0672627i) q^{5} +(-0.302032 + 0.0809291i) q^{6} +(-0.274164 + 0.474866i) q^{7} -2.35905i q^{8} +(-2.56436 - 1.48053i) q^{9} +(-3.01415 + 1.86330i) q^{10} +(-0.147928 - 0.0396372i) q^{11} +(0.0713497 - 0.0713497i) q^{12} -0.868956i q^{14} +(0.429409 + 0.101320i) q^{15} +(2.38063 + 4.12338i) q^{16} +(0.813499 + 3.03602i) q^{17} +4.69252 q^{18} +(1.18079 + 4.40678i) q^{19} +(0.541709 - 1.00706i) q^{20} +(-0.0765027 + 0.0765027i) q^{21} +(0.234427 - 0.0628146i) q^{22} +(-0.916011 + 3.41860i) q^{23} +(0.120472 - 0.449606i) q^{24} +(4.99095 - 0.300672i) q^{25} +(-0.831688 - 0.831688i) q^{27} +(0.140206 + 0.242844i) q^{28} +(2.02878 - 1.17132i) q^{29} +(-0.669614 + 0.201197i) q^{30} +(6.61000 + 6.61000i) q^{31} +(-2.44848 - 1.41363i) q^{32} +(-0.0261691 - 0.0151087i) q^{33} +(-3.52211 - 3.52211i) q^{34} +(-0.580831 + 1.07979i) q^{35} +(-1.31140 + 0.757137i) q^{36} +(-3.40317 - 5.89447i) q^{37} +(-5.11234 - 5.11234i) q^{38} +(-0.158676 - 5.27261i) q^{40} +(-0.926064 + 3.45612i) q^{41} +(0.0443757 - 0.165612i) q^{42} +(6.86784 - 1.84023i) q^{43} +(-0.0553794 + 0.0553794i) q^{44} +(-5.83107 - 3.13659i) q^{45} +(-1.45164 - 5.41759i) q^{46} +9.13956 q^{47} +(0.243147 + 0.907439i) q^{48} +(3.34967 + 5.80180i) q^{49} +(-6.61146 + 4.36732i) q^{50} +0.620172i q^{51} +(-3.70952 + 3.70952i) q^{53} +(1.80043 + 0.482424i) q^{54} +(-0.333294 - 0.0786414i) q^{55} +(1.12023 + 0.646766i) q^{56} +0.900179i q^{57} +(-1.85623 + 3.21508i) q^{58} +(3.67728 - 0.985325i) q^{59} +(0.154672 - 0.164270i) q^{60} +(-3.92486 + 6.79805i) q^{61} +(-14.3093 - 3.83416i) q^{62} +(1.40611 - 0.811818i) q^{63} -5.04207 q^{64} +0.0478868 q^{66} +(-4.23514 + 2.44516i) q^{67} +(1.55261 + 0.416019i) q^{68} +(-0.349161 + 0.604765i) q^{69} +(-0.0584483 - 1.94217i) q^{70} +(15.1045 - 4.04725i) q^{71} +(-3.49265 + 6.04945i) q^{72} +3.91807i q^{73} +(9.34119 + 5.39314i) q^{74} +(0.966569 + 0.197573i) q^{75} +(2.25360 + 0.603851i) q^{76} +(0.0593789 - 0.0593789i) q^{77} +11.1394i q^{79} +(5.59820 + 9.05585i) q^{80} +(4.32557 + 7.49210i) q^{81} +(-1.46757 - 5.47704i) q^{82} -13.4251 q^{83} +(0.0143200 + 0.0534431i) q^{84} +(2.02243 + 6.73096i) q^{85} +(-7.96744 + 7.96744i) q^{86} +(0.446477 - 0.119633i) q^{87} +(-0.0935062 + 0.348970i) q^{88} +(-2.35372 + 8.78419i) q^{89} +(10.4880 - 0.315631i) q^{90} +(1.27981 + 1.27981i) q^{92} +(0.922226 + 1.59734i) q^{93} +(-12.5433 + 7.24190i) q^{94} +(2.93555 + 9.76998i) q^{95} +(-0.394459 - 0.394459i) q^{96} +(-6.55668 - 3.78550i) q^{97} +(-9.19433 - 5.30835i) q^{98} +(0.320657 + 0.320657i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+6q22q3+6q4+8q6+2q7+12q92q10+16q1124q12+20q152q16+4q17+20q194q21+16q2210q2332q24+18q25+60q99+O(q100) 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 8 q^{6} + 2 q^{7} + 12 q^{9} - 2 q^{10} + 16 q^{11} - 24 q^{12} + 20 q^{15} - 2 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{21} + 16 q^{22} - 10 q^{23} - 32 q^{24} + 18 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/845Z)×\left(\mathbb{Z}/845\mathbb{Z}\right)^\times.

nn 171171 677677
χ(n)\chi(n) e(712)e\left(\frac{7}{12}\right) e(14)e\left(\frac{1}{4}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.37242 + 0.792369i −0.970450 + 0.560290i −0.899373 0.437181i 0.855977π-0.855977\pi
−0.0710765 + 0.997471i 0.522643π0.522643\pi
33 0.190588 + 0.0510678i 0.110036 + 0.0294840i 0.313417 0.949616i 0.398526π-0.398526\pi
−0.203381 + 0.979100i 0.565193π0.565193\pi
44 0.255697 0.442881i 0.127849 0.221440i
55 2.23506 0.0672627i 0.999547 0.0300808i
66 −0.302032 + 0.0809291i −0.123304 + 0.0330392i
77 −0.274164 + 0.474866i −0.103624 + 0.179482i −0.913175 0.407567i 0.866377π-0.866377\pi
0.809551 + 0.587049i 0.199711π0.199711\pi
88 2.35905i 0.834050i
99 −2.56436 1.48053i −0.854787 0.493511i
1010 −3.01415 + 1.86330i −0.953157 + 0.589228i
1111 −0.147928 0.0396372i −0.0446020 0.0119511i 0.236449 0.971644i 0.424016π-0.424016\pi
−0.281051 + 0.959693i 0.590683π0.590683\pi
1212 0.0713497 0.0713497i 0.0205969 0.0205969i
1313 0 0
1414 0.868956i 0.232238i
1515 0.429409 + 0.101320i 0.110873 + 0.0261607i
1616 2.38063 + 4.12338i 0.595158 + 1.03084i
1717 0.813499 + 3.03602i 0.197303 + 0.736343i 0.991659 + 0.128891i 0.0411417π0.0411417\pi
−0.794356 + 0.607452i 0.792192π0.792192\pi
1818 4.69252 1.10604
1919 1.18079 + 4.40678i 0.270893 + 1.01098i 0.958544 + 0.284944i 0.0919750π0.0919750\pi
−0.687652 + 0.726041i 0.741358π0.741358\pi
2020 0.541709 1.00706i 0.121130 0.225186i
2121 −0.0765027 + 0.0765027i −0.0166942 + 0.0166942i
2222 0.234427 0.0628146i 0.0499801 0.0133921i
2323 −0.916011 + 3.41860i −0.191002 + 0.712828i 0.802264 + 0.596969i 0.203629π0.203629\pi
−0.993266 + 0.115858i 0.963038π0.963038\pi
2424 0.120472 0.449606i 0.0245912 0.0917754i
2525 4.99095 0.300672i 0.998190 0.0601343i
2626 0 0
2727 −0.831688 0.831688i −0.160058 0.160058i
2828 0.140206 + 0.242844i 0.0264964 + 0.0458932i
2929 2.02878 1.17132i 0.376735 0.217508i −0.299662 0.954045i 0.596874π-0.596874\pi
0.676397 + 0.736538i 0.263541π0.263541\pi
3030 −0.669614 + 0.201197i −0.122254 + 0.0367333i
3131 6.61000 + 6.61000i 1.18719 + 1.18719i 0.977841 + 0.209350i 0.0671347π0.0671347\pi
0.209350 + 0.977841i 0.432865π0.432865\pi
3232 −2.44848 1.41363i −0.432834 0.249897i
3333 −0.0261691 0.0151087i −0.00455546 0.00263009i
3434 −3.52211 3.52211i −0.604038 0.604038i
3535 −0.580831 + 1.07979i −0.0981784 + 0.182518i
3636 −1.31140 + 0.757137i −0.218567 + 0.126190i
3737 −3.40317 5.89447i −0.559478 0.969045i −0.997540 0.0700997i 0.977668π-0.977668\pi
0.438062 0.898945i 0.355665π-0.355665\pi
3838 −5.11234 5.11234i −0.829332 0.829332i
3939 0 0
4040 −0.158676 5.27261i −0.0250889 0.833672i
4141 −0.926064 + 3.45612i −0.144627 + 0.539755i 0.855145 + 0.518389i 0.173468π0.173468\pi
−0.999772 + 0.0213659i 0.993199π0.993199\pi
4242 0.0443757 0.165612i 0.00684732 0.0255545i
4343 6.86784 1.84023i 1.04734 0.280633i 0.306185 0.951972i 0.400947π-0.400947\pi
0.741150 + 0.671339i 0.234281π0.234281\pi
4444 −0.0553794 + 0.0553794i −0.00834876 + 0.00834876i
4545 −5.83107 3.13659i −0.869245 0.467575i
4646 −1.45164 5.41759i −0.214032 0.798780i
4747 9.13956 1.33314 0.666571 0.745442i 0.267761π-0.267761\pi
0.666571 + 0.745442i 0.267761π0.267761\pi
4848 0.243147 + 0.907439i 0.0350953 + 0.130978i
4949 3.34967 + 5.80180i 0.478524 + 0.828828i
5050 −6.61146 + 4.36732i −0.935001 + 0.617633i
5151 0.620172i 0.0868415i
5252 0 0
5353 −3.70952 + 3.70952i −0.509541 + 0.509541i −0.914386 0.404844i 0.867326π-0.867326\pi
0.404844 + 0.914386i 0.367326π0.367326\pi
5454 1.80043 + 0.482424i 0.245008 + 0.0656496i
5555 −0.333294 0.0786414i −0.0449413 0.0106040i
5656 1.12023 + 0.646766i 0.149697 + 0.0864278i
5757 0.900179i 0.119232i
5858 −1.85623 + 3.21508i −0.243735 + 0.422161i
5959 3.67728 0.985325i 0.478742 0.128278i −0.0113750 0.999935i 0.503621π-0.503621\pi
0.490117 + 0.871657i 0.336954π0.336954\pi
6060 0.154672 0.164270i 0.0199680 0.0212071i
6161 −3.92486 + 6.79805i −0.502526 + 0.870401i 0.497470 + 0.867481i 0.334263π0.334263\pi
−0.999996 + 0.00291945i 0.999071π0.999071\pi
6262 −14.3093 3.83416i −1.81728 0.486939i
6363 1.40611 0.811818i 0.177153 0.102279i
6464 −5.04207 −0.630258
6565 0 0
6666 0.0478868 0.00589446
6767 −4.23514 + 2.44516i −0.517405 + 0.298724i −0.735872 0.677120i 0.763228π-0.763228\pi
0.218467 + 0.975844i 0.429894π0.429894\pi
6868 1.55261 + 0.416019i 0.188281 + 0.0504497i
6969 −0.349161 + 0.604765i −0.0420341 + 0.0728051i
7070 −0.0584483 1.94217i −0.00698591 0.232133i
7171 15.1045 4.04725i 1.79258 0.480320i 0.799799 0.600267i 0.204939π-0.204939\pi
0.992780 + 0.119947i 0.0382725π0.0382725\pi
7272 −3.49265 + 6.04945i −0.411613 + 0.712935i
7373 3.91807i 0.458575i 0.973359 + 0.229288i 0.0736396π0.0736396\pi
−0.973359 + 0.229288i 0.926360π0.926360\pi
7474 9.34119 + 5.39314i 1.08589 + 0.626939i
7575 0.966569 + 0.197573i 0.111610 + 0.0228137i
7676 2.25360 + 0.603851i 0.258506 + 0.0692665i
7777 0.0593789 0.0593789i 0.00676686 0.00676686i
7878 0 0
7979 11.1394i 1.25328i 0.779309 + 0.626640i 0.215570π0.215570\pi
−0.779309 + 0.626640i 0.784430π0.784430\pi
8080 5.59820 + 9.05585i 0.625897 + 1.01247i
8181 4.32557 + 7.49210i 0.480618 + 0.832455i
8282 −1.46757 5.47704i −0.162066 0.604838i
8383 −13.4251 −1.47360 −0.736798 0.676113i 0.763663π-0.763663\pi
−0.736798 + 0.676113i 0.763663π0.763663\pi
8484 0.0143200 + 0.0534431i 0.00156244 + 0.00583112i
8585 2.02243 + 6.73096i 0.219363 + 0.730075i
8686 −7.96744 + 7.96744i −0.859151 + 0.859151i
8787 0.446477 0.119633i 0.0478673 0.0128260i
8888 −0.0935062 + 0.348970i −0.00996779 + 0.0372003i
8989 −2.35372 + 8.78419i −0.249493 + 0.931122i 0.721578 + 0.692333i 0.243417π0.243417\pi
−0.971071 + 0.238789i 0.923250π0.923250\pi
9090 10.4880 0.315631i 1.10554 0.0332705i
9191 0 0
9292 1.27981 + 1.27981i 0.133430 + 0.133430i
9393 0.922226 + 1.59734i 0.0956304 + 0.165637i
9494 −12.5433 + 7.24190i −1.29375 + 0.746945i
9595 2.93555 + 9.76998i 0.301181 + 1.00238i
9696 −0.394459 0.394459i −0.0402593 0.0402593i
9797 −6.55668 3.78550i −0.665730 0.384360i 0.128727 0.991680i 0.458911π-0.458911\pi
−0.794457 + 0.607321i 0.792244π0.792244\pi
9898 −9.19433 5.30835i −0.928767 0.536224i
9999 0.320657 + 0.320657i 0.0322272 + 0.0322272i
100100 1.14301 2.28728i 0.114301 0.228728i
101101 11.7218 6.76758i 1.16636 0.673400i 0.213542 0.976934i 0.431500π-0.431500\pi
0.952821 + 0.303534i 0.0981667π0.0981667\pi
102102 −0.491405 0.851139i −0.0486564 0.0842753i
103103 −10.3566 10.3566i −1.02046 1.02046i −0.999786 0.0206759i 0.993418π-0.993418\pi
−0.0206759 0.999786i 0.506582π-0.506582\pi
104104 0 0
105105 −0.165842 + 0.176134i −0.0161845 + 0.0171889i
106106 2.15172 8.03034i 0.208994 0.779975i
107107 4.16078 15.5283i 0.402238 1.50117i −0.406855 0.913493i 0.633375π-0.633375\pi
0.809093 0.587680i 0.199959π-0.199959\pi
108108 −0.580999 + 0.155678i −0.0559066 + 0.0149801i
109109 −8.20821 + 8.20821i −0.786203 + 0.786203i −0.980870 0.194666i 0.937638π-0.937638\pi
0.194666 + 0.980870i 0.437638π0.437638\pi
110110 0.519733 0.156162i 0.0495546 0.0148895i
111111 −0.347585 1.29721i −0.0329913 0.123125i
112112 −2.61073 −0.246691
113113 1.17964 + 4.40249i 0.110972 + 0.414151i 0.998954 0.0457259i 0.0145601π-0.0145601\pi
−0.887982 + 0.459877i 0.847893π0.847893\pi
114114 −0.713274 1.23543i −0.0668042 0.115708i
115115 −1.81739 + 7.70238i −0.169473 + 0.718251i
116116 1.19801i 0.111232i
117117 0 0
118118 −4.26605 + 4.26605i −0.392722 + 0.392722i
119119 −1.66473 0.446064i −0.152606 0.0408907i
120120 0.239019 1.01300i 0.0218193 0.0924736i
121121 −9.50597 5.48827i −0.864179 0.498934i
122122 12.4397i 1.12624i
123123 −0.352993 + 0.611402i −0.0318283 + 0.0551283i
124124 4.61760 1.23728i 0.414673 0.111111i
125125 11.1348 1.00772i 0.995930 0.0901335i
126126 −1.28652 + 2.22832i −0.114612 + 0.198514i
127127 2.34945 + 0.629533i 0.208480 + 0.0558620i 0.361547 0.932354i 0.382249π-0.382249\pi
−0.153068 + 0.988216i 0.548915π0.548915\pi
128128 11.8168 6.82244i 1.04447 0.603024i
129129 1.40290 0.123519
130130 0 0
131131 6.60705 0.577260 0.288630 0.957441i 0.406800π-0.406800\pi
0.288630 + 0.957441i 0.406800π0.406800\pi
132132 −0.0133827 + 0.00772653i −0.00116482 + 0.000672508i
133133 −2.41636 0.647462i −0.209525 0.0561421i
134134 3.87494 6.71159i 0.334744 0.579793i
135135 −1.91481 1.80293i −0.164801 0.155171i
136136 7.16212 1.91909i 0.614147 0.164560i
137137 2.02775 3.51216i 0.173242 0.300064i −0.766309 0.642472i 0.777909π-0.777909\pi
0.939552 + 0.342408i 0.111242π0.111242\pi
138138 1.10666i 0.0942050i
139139 −11.1052 6.41160i −0.941932 0.543825i −0.0513668 0.998680i 0.516358π-0.516358\pi
−0.890566 + 0.454855i 0.849691π0.849691\pi
140140 0.329703 + 0.533339i 0.0278650 + 0.0450754i
141141 1.74189 + 0.466737i 0.146693 + 0.0393064i
142142 −17.5229 + 17.5229i −1.47049 + 1.47049i
143143 0 0
144144 14.0984i 1.17487i
145145 4.45565 2.75442i 0.370021 0.228742i
146146 −3.10455 5.37725i −0.256935 0.445024i
147147 0.342121 + 1.27681i 0.0282176 + 0.105310i
148148 −3.48073 −0.286114
149149 1.10123 + 4.10983i 0.0902159 + 0.336690i 0.996251 0.0865128i 0.0275723π-0.0275723\pi
−0.906035 + 0.423203i 0.860906π0.860906\pi
150150 −1.48309 + 0.494726i −0.121094 + 0.0403942i
151151 −4.89430 + 4.89430i −0.398293 + 0.398293i −0.877630 0.479338i 0.840877π-0.840877\pi
0.479338 + 0.877630i 0.340877π0.340877\pi
152152 10.3958 2.78555i 0.843212 0.225938i
153153 2.40883 8.98987i 0.194742 0.726788i
154154 −0.0344430 + 0.128543i −0.00277550 + 0.0103583i
155155 15.2183 + 14.3291i 1.22236 + 1.15094i
156156 0 0
157157 2.29887 + 2.29887i 0.183470 + 0.183470i 0.792866 0.609396i 0.208588π-0.208588\pi
−0.609396 + 0.792866i 0.708588π0.708588\pi
158158 −8.82651 15.2880i −0.702199 1.21625i
159159 −0.896426 + 0.517552i −0.0710912 + 0.0410445i
160160 −5.56757 2.99485i −0.440155 0.236764i
161161 −1.37224 1.37224i −0.108148 0.108148i
162162 −11.8730 6.85489i −0.932832 0.538571i
163163 9.41236 + 5.43423i 0.737233 + 0.425642i 0.821062 0.570839i 0.193382π-0.193382\pi
−0.0838295 + 0.996480i 0.526715π0.526715\pi
164164 1.29386 + 1.29386i 0.101033 + 0.101033i
165165 −0.0595057 0.0320087i −0.00463251 0.00249187i
166166 18.4249 10.6376i 1.43005 0.825640i
167167 −8.17941 14.1672i −0.632942 1.09629i −0.986947 0.161044i 0.948514π-0.948514\pi
0.354005 0.935243i 0.384819π-0.384819\pi
168168 0.180474 + 0.180474i 0.0139238 + 0.0139238i
169169 0 0
170170 −8.10903 7.63522i −0.621934 0.585594i
171171 3.49641 13.0488i 0.267377 0.997865i
172172 0.941085 3.51218i 0.0717570 0.267801i
173173 −6.60091 + 1.76871i −0.501858 + 0.134472i −0.500862 0.865527i 0.666984π-0.666984\pi
−0.000995657 1.00000i 0.500317π0.500317\pi
174174 −0.517961 + 0.517961i −0.0392666 + 0.0392666i
175175 −1.22556 + 2.45247i −0.0926436 + 0.185389i
176176 −0.188723 0.704325i −0.0142256 0.0530905i
177177 0.751164 0.0564609
178178 −3.73002 13.9206i −0.279577 1.04340i
179179 2.83696 + 4.91376i 0.212044 + 0.367272i 0.952354 0.304994i 0.0986545π-0.0986545\pi
−0.740310 + 0.672266i 0.765321π0.765321\pi
180180 −2.88013 + 1.78045i −0.214672 + 0.132707i
181181 3.59115i 0.266928i 0.991054 + 0.133464i 0.0426101π0.0426101\pi
−0.991054 + 0.133464i 0.957390π0.957390\pi
182182 0 0
183183 −1.09519 + 1.09519i −0.0809588 + 0.0809588i
184184 8.06465 + 2.16092i 0.594534 + 0.159305i
185185 −8.00276 12.9456i −0.588375 0.951777i
186186 −2.53137 1.46149i −0.185609 0.107161i
187187 0.481358i 0.0352004i
188188 2.33696 4.04773i 0.170440 0.295211i
189189 0.622959 0.166921i 0.0453136 0.0121417i
190190 −11.7702 11.0825i −0.853903 0.804009i
191191 11.7411 20.3361i 0.849553 1.47147i −0.0320553 0.999486i 0.510205π-0.510205\pi
0.881608 0.471982i 0.156461π-0.156461\pi
192192 −0.960956 0.257487i −0.0693510 0.0185825i
193193 13.7160 7.91891i 0.987296 0.570016i 0.0828311 0.996564i 0.473604π-0.473604\pi
0.904465 + 0.426548i 0.140270π0.140270\pi
194194 11.9981 0.861411
195195 0 0
196196 3.42601 0.244715
197197 −4.94741 + 2.85639i −0.352488 + 0.203509i −0.665781 0.746148i 0.731901π-0.731901\pi
0.313292 + 0.949657i 0.398568π0.398568\pi
198198 −0.694156 0.185998i −0.0493315 0.0132183i
199199 −4.65156 + 8.05674i −0.329740 + 0.571127i −0.982460 0.186472i 0.940295π-0.940295\pi
0.652720 + 0.757599i 0.273628π0.273628\pi
200200 −0.709299 11.7739i −0.0501550 0.832541i
201201 −0.932035 + 0.249738i −0.0657407 + 0.0176152i
202202 −10.7248 + 18.5760i −0.754597 + 1.30700i
203203 1.28453i 0.0901563i
204204 0.274662 + 0.158576i 0.0192302 + 0.0111026i
205205 −1.83734 + 7.78691i −0.128325 + 0.543861i
206206 22.4198 + 6.00737i 1.56206 + 0.418553i
207207 7.41034 7.41034i 0.515054 0.515054i
208208 0 0
209209 0.698690i 0.0483294i
210210 0.0880427 0.373138i 0.00607552 0.0257490i
211211 2.73779 + 4.74199i 0.188477 + 0.326452i 0.944743 0.327813i 0.106311π-0.106311\pi
−0.756265 + 0.654265i 0.772978π0.772978\pi
212212 0.694360 + 2.59139i 0.0476889 + 0.177977i
213213 3.08543 0.211410
214214 6.59375 + 24.6082i 0.450739 + 1.68218i
215215 15.2262 4.57497i 1.03842 0.312010i
216216 −1.96199 + 1.96199i −0.133497 + 0.133497i
217217 −4.95108 + 1.32664i −0.336102 + 0.0900581i
218218 4.76121 17.7691i 0.322470 1.20347i
219219 −0.200087 + 0.746736i −0.0135206 + 0.0504597i
220220 −0.120051 + 0.127501i −0.00809385 + 0.00859612i
221221 0 0
222222 1.50490 + 1.50490i 0.101002 + 0.101002i
223223 −9.28408 16.0805i −0.621708 1.07683i −0.989168 0.146790i 0.953106π-0.953106\pi
0.367460 0.930039i 0.380227π-0.380227\pi
224224 1.34257 0.775132i 0.0897041 0.0517907i
225225 −13.2438 6.61824i −0.882917 0.441216i
226226 −5.10737 5.10737i −0.339737 0.339737i
227227 5.53101 + 3.19333i 0.367106 + 0.211949i 0.672193 0.740376i 0.265352π-0.265352\pi
−0.305087 + 0.952324i 0.598686π0.598686\pi
228228 0.398672 + 0.230173i 0.0264027 + 0.0152436i
229229 −11.1149 11.1149i −0.734491 0.734491i 0.237015 0.971506i 0.423831π-0.423831\pi
−0.971506 + 0.237015i 0.923831π0.923831\pi
230230 −3.60889 12.0110i −0.237963 0.791980i
231231 0.0143493 0.00828454i 0.000944111 0.000545083i
232232 −2.76319 4.78599i −0.181412 0.314215i
233233 5.85956 + 5.85956i 0.383873 + 0.383873i 0.872495 0.488623i 0.162500π-0.162500\pi
−0.488623 + 0.872495i 0.662500π0.662500\pi
234234 0 0
235235 20.4274 0.614751i 1.33254 0.0401019i
236236 0.503890 1.88054i 0.0328004 0.122413i
237237 −0.568865 + 2.12303i −0.0369517 + 0.137906i
238238 2.63817 0.706895i 0.171007 0.0458212i
239239 13.8081 13.8081i 0.893170 0.893170i −0.101650 0.994820i 0.532412π-0.532412\pi
0.994820 + 0.101650i 0.0324123π0.0324123\pi
240240 0.604485 + 2.01182i 0.0390193 + 0.129863i
241241 −4.43437 16.5493i −0.285643 1.06603i −0.948368 0.317172i 0.897267π-0.897267\pi
0.662725 0.748863i 0.269400π-0.269400\pi
242242 17.3950 1.11819
243243 1.35505 + 5.05712i 0.0869266 + 0.324414i
244244 2.00715 + 3.47649i 0.128495 + 0.222559i
245245 7.87694 + 12.7420i 0.503239 + 0.814058i
246246 1.11880i 0.0713323i
247247 0 0
248248 15.5933 15.5933i 0.990176 0.990176i
249249 −2.55866 0.685590i −0.162148 0.0434475i
250250 −14.4832 + 10.2059i −0.915999 + 0.645479i
251251 8.61959 + 4.97652i 0.544063 + 0.314115i 0.746724 0.665134i 0.231626π-0.231626\pi
−0.202661 + 0.979249i 0.564959π0.564959\pi
252252 0.830319i 0.0523052i
253253 0.271008 0.469399i 0.0170381 0.0295109i
254254 −3.72326 + 0.997644i −0.233618 + 0.0625978i
255255 0.0417144 + 1.38612i 0.00261226 + 0.0868022i
256256 −5.76971 + 9.99343i −0.360607 + 0.624589i
257257 −2.65761 0.712105i −0.165777 0.0444199i 0.174976 0.984573i 0.444015π-0.444015\pi
−0.340753 + 0.940153i 0.610682π0.610682\pi
258258 −1.92538 + 1.11162i −0.119869 + 0.0692062i
259259 3.73211 0.231902
260260 0 0
261261 −6.93669 −0.429370
262262 −9.06767 + 5.23522i −0.560202 + 0.323433i
263263 5.96686 + 1.59881i 0.367932 + 0.0985871i 0.438048 0.898952i 0.355670π-0.355670\pi
−0.0701155 + 0.997539i 0.522337π0.522337\pi
264264 −0.0356423 + 0.0617342i −0.00219363 + 0.00379948i
265265 −8.04147 + 8.54049i −0.493983 + 0.524638i
266266 3.82930 1.02606i 0.234789 0.0629116i
267267 −0.897179 + 1.55396i −0.0549065 + 0.0951008i
268268 2.50088i 0.152766i
269269 −18.3796 10.6115i −1.12063 0.646994i −0.179066 0.983837i 0.557308π-0.557308\pi
−0.941561 + 0.336843i 0.890641π0.890641\pi
270270 4.05651 + 0.957143i 0.246872 + 0.0582499i
271271 12.4458 + 3.33484i 0.756027 + 0.202577i 0.616190 0.787598i 0.288675π-0.288675\pi
0.139837 + 0.990174i 0.455342π0.455342\pi
272272 −10.5820 + 10.5820i −0.641629 + 0.641629i
273273 0 0
274274 6.42690i 0.388263i
275275 −0.750220 0.153350i −0.0452400 0.00924733i
276276 0.178559 + 0.309274i 0.0107480 + 0.0186161i
277277 −5.50674 20.5514i −0.330868 1.23482i −0.908280 0.418363i 0.862604π-0.862604\pi
0.577412 0.816453i 0.304063π-0.304063\pi
278278 20.3214 1.21880
279279 −7.16409 26.7367i −0.428903 1.60069i
280280 2.54728 + 1.37021i 0.152229 + 0.0818857i
281281 4.22655 4.22655i 0.252135 0.252135i −0.569711 0.821845i 0.692945π-0.692945\pi
0.821845 + 0.569711i 0.192945π0.192945\pi
282282 −2.76044 + 0.739656i −0.164382 + 0.0440459i
283283 −0.398044 + 1.48552i −0.0236613 + 0.0883050i −0.976747 0.214396i 0.931222π-0.931222\pi
0.953086 + 0.302701i 0.0978884π0.0978884\pi
284284 2.06974 7.72438i 0.122817 0.458358i
285285 0.0605484 + 2.01195i 0.00358658 + 0.119178i
286286 0 0
287287 −1.38730 1.38730i −0.0818897 0.0818897i
288288 4.18585 + 7.25011i 0.246654 + 0.427217i
289289 6.16679 3.56040i 0.362752 0.209435i
290290 −3.93252 + 7.31074i −0.230925 + 0.429301i
291291 −1.05631 1.05631i −0.0619218 0.0619218i
292292 1.73524 + 1.00184i 0.101547 + 0.0586282i
293293 −2.41782 1.39593i −0.141251 0.0815512i 0.427709 0.903916i 0.359321π-0.359321\pi
−0.568960 + 0.822365i 0.692654π0.692654\pi
294294 −1.48124 1.48124i −0.0863877 0.0863877i
295295 8.15266 2.44960i 0.474666 0.142621i
296296 −13.9053 + 8.02825i −0.808232 + 0.466633i
297297 0.0900642 + 0.155996i 0.00522606 + 0.00905180i
298298 −4.76785 4.76785i −0.276194 0.276194i
299299 0 0
300300 0.334650 0.377556i 0.0193210 0.0217982i
301301 −1.00905 + 3.76583i −0.0581607 + 0.217059i
302302 2.83896 10.5951i 0.163364 0.609682i
303303 2.57964 0.691212i 0.148196 0.0397091i
304304 −15.3598 + 15.3598i −0.880944 + 0.880944i
305305 −8.31502 + 15.4580i −0.476116 + 0.885123i
306306 3.81736 + 14.2466i 0.218224 + 0.814423i
307307 −2.12112 −0.121058 −0.0605292 0.998166i 0.519279π-0.519279\pi
−0.0605292 + 0.998166i 0.519279π0.519279\pi
308308 −0.0111148 0.0414808i −0.000633322 0.00236359i
309309 −1.44495 2.50272i −0.0822001 0.142375i
310310 −32.2399 7.60708i −1.83110 0.432053i
311311 21.2656i 1.20586i −0.797794 0.602931i 0.794000π-0.794000\pi
0.797794 0.602931i 0.206000π-0.206000\pi
312312 0 0
313313 −14.3666 + 14.3666i −0.812050 + 0.812050i −0.984941 0.172891i 0.944689π-0.944689\pi
0.172891 + 0.984941i 0.444689π0.444689\pi
314314 −4.97657 1.33347i −0.280844 0.0752519i
315315 3.08813 1.90904i 0.173996 0.107562i
316316 4.93342 + 2.84831i 0.277527 + 0.160230i
317317 8.78989i 0.493689i −0.969055 0.246845i 0.920606π-0.920606\pi
0.969055 0.246845i 0.0793937π-0.0793937\pi
318318 0.820184 1.42060i 0.0459936 0.0796633i
319319 −0.346541 + 0.0928554i −0.0194026 + 0.00519890i
320320 −11.2693 + 0.339143i −0.629973 + 0.0189587i
321321 1.58599 2.74701i 0.0885212 0.153323i
322322 2.97061 + 0.795974i 0.165546 + 0.0443579i
323323 −12.4185 + 7.16982i −0.690984 + 0.398940i
324324 4.42414 0.245786
325325 0 0
326326 −17.2237 −0.953930
327327 −1.98356 + 1.14521i −0.109691 + 0.0633302i
328328 8.15316 + 2.18463i 0.450183 + 0.120626i
329329 −2.50574 + 4.34006i −0.138146 + 0.239275i
330330 0.107030 0.00322099i 0.00589179 0.000177310i
331331 −17.5522 + 4.70310i −0.964756 + 0.258506i −0.706612 0.707601i 0.749777π-0.749777\pi
−0.258144 + 0.966107i 0.583111π0.583111\pi
332332 −3.43276 + 5.94572i −0.188397 + 0.326314i
333333 20.1541i 1.10444i
334334 22.4512 + 12.9622i 1.22848 + 0.709261i
335335 −9.30131 + 5.74994i −0.508185 + 0.314153i
336336 −0.497574 0.133325i −0.0271449 0.00727345i
337337 −17.2522 + 17.2522i −0.939788 + 0.939788i −0.998287 0.0584999i 0.981368π-0.981368\pi
0.0584999 + 0.998287i 0.481368π0.481368\pi
338338 0 0
339339 0.899302i 0.0488434i
340340 3.49814 + 0.825394i 0.189713 + 0.0447633i
341341 −0.715803 1.23981i −0.0387629 0.0671393i
342342 5.54089 + 20.6789i 0.299617 + 1.11819i
343343 −7.51173 −0.405595
344344 −4.34120 16.2016i −0.234062 0.873530i
345345 −0.739717 + 1.37517i −0.0398250 + 0.0740366i
346346 7.65777 7.65777i 0.411684 0.411684i
347347 7.50674 2.01142i 0.402983 0.107979i −0.0516340 0.998666i 0.516443π-0.516443\pi
0.454617 + 0.890687i 0.349776π0.349776\pi
348348 0.0611797 0.228326i 0.00327958 0.0122395i
349349 −1.31241 + 4.89796i −0.0702515 + 0.262182i −0.992115 0.125333i 0.960000π-0.960000\pi
0.921863 + 0.387515i 0.126667π0.126667\pi
350350 −0.261271 4.33692i −0.0139655 0.231818i
351351 0 0
352352 0.306166 + 0.306166i 0.0163187 + 0.0163187i
353353 12.8089 + 22.1857i 0.681749 + 1.18082i 0.974447 + 0.224618i 0.0721136π0.0721136\pi
−0.292698 + 0.956205i 0.594553π0.594553\pi
354354 −1.03091 + 0.595199i −0.0547925 + 0.0316345i
355355 33.4873 10.0618i 1.77732 0.534025i
356356 3.28851 + 3.28851i 0.174291 + 0.174291i
357357 −0.294499 0.170029i −0.0155865 0.00899888i
358358 −7.78702 4.49584i −0.411557 0.237613i
359359 10.0443 + 10.0443i 0.530117 + 0.530117i 0.920607 0.390490i 0.127694π-0.127694\pi
−0.390490 + 0.920607i 0.627694π0.627694\pi
360360 −7.39937 + 13.7558i −0.389981 + 0.724994i
361361 −1.57095 + 0.906990i −0.0826817 + 0.0477363i
362362 −2.84552 4.92858i −0.149557 0.259040i
363363 −1.53145 1.53145i −0.0803801 0.0803801i
364364 0 0
365365 0.263540 + 8.75710i 0.0137943 + 0.458368i
366366 0.635270 2.37086i 0.0332061 0.123927i
367367 −5.20802 + 19.4366i −0.271857 + 1.01458i 0.686062 + 0.727543i 0.259338π0.259338\pi
−0.957919 + 0.287040i 0.907329π0.907329\pi
368368 −16.2769 + 4.36137i −0.848490 + 0.227352i
369369 7.49167 7.49167i 0.390001 0.390001i
370370 21.2408 + 11.4257i 1.10426 + 0.593991i
371371 −0.744507 2.77854i −0.0386529 0.144255i
372372 0.943243 0.0489049
373373 6.78245 + 25.3125i 0.351182 + 1.31063i 0.885221 + 0.465170i 0.154007π0.154007\pi
−0.534039 + 0.845460i 0.679327π0.679327\pi
374374 0.381413 + 0.660627i 0.0197224 + 0.0341602i
375375 2.17362 + 0.376572i 0.112246 + 0.0194461i
376376 21.5607i 1.11191i
377377 0 0
378378 −0.722700 + 0.722700i −0.0371717 + 0.0371717i
379379 21.7627 + 5.83130i 1.11787 + 0.299534i 0.770023 0.638016i 0.220245π-0.220245\pi
0.347852 + 0.937550i 0.386911π0.386911\pi
380380 5.07755 + 1.19806i 0.260473 + 0.0614591i
381381 0.415627 + 0.239962i 0.0212932 + 0.0122936i
382382 37.2130i 1.90398i
383383 12.0630 20.8938i 0.616392 1.06762i −0.373747 0.927531i 0.621927π-0.621927\pi
0.990139 0.140091i 0.0447396π-0.0447396\pi
384384 2.60055 0.696814i 0.132709 0.0355591i
385385 0.128721 0.136709i 0.00656024 0.00696735i
386386 −12.5494 + 21.7362i −0.638748 + 1.10634i
387387 −20.3361 5.44905i −1.03374 0.276991i
388388 −3.35305 + 1.93589i −0.170225 + 0.0982797i
389389 14.3262 0.726365 0.363183 0.931718i 0.381690π-0.381690\pi
0.363183 + 0.931718i 0.381690π0.381690\pi
390390 0 0
391391 −11.1241 −0.562571
392392 13.6867 7.90203i 0.691284 0.399113i
393393 1.25922 + 0.337408i 0.0635194 + 0.0170200i
394394 4.52662 7.84034i 0.228048 0.394991i
395395 0.749265 + 24.8972i 0.0376996 + 1.25271i
396396 0.224004 0.0600217i 0.0112566 0.00301620i
397397 16.7465 29.0058i 0.840484 1.45576i −0.0490017 0.998799i 0.515604π-0.515604\pi
0.889486 0.456963i 0.151063π-0.151063\pi
398398 14.7430i 0.739000i
399399 −0.427464 0.246797i −0.0214000 0.0123553i
400400 13.1214 + 19.8638i 0.656070 + 0.993189i
401401 −17.9170 4.80084i −0.894731 0.239743i −0.217979 0.975953i 0.569946π-0.569946\pi
−0.676752 + 0.736211i 0.736613π0.736613\pi
402402 1.08126 1.08126i 0.0539285 0.0539285i
403403 0 0
404404 6.92181i 0.344373i
405405 10.1718 + 16.4543i 0.505442 + 0.817621i
406406 −1.01782 1.76292i −0.0505136 0.0874922i
407407 0.269785 + 1.00685i 0.0133727 + 0.0499077i
408408 1.46302 0.0724301
409409 1.33873 + 4.99622i 0.0661960 + 0.247047i 0.991093 0.133171i 0.0425158π-0.0425158\pi
−0.924897 + 0.380218i 0.875849π0.875849\pi
410410 −3.64850 12.1428i −0.180187 0.599690i
411411 0.565822 0.565822i 0.0279099 0.0279099i
412412 −7.23487 + 1.93858i −0.356436 + 0.0955068i
413413 −0.540281 + 2.01636i −0.0265855 + 0.0992184i
414414 −4.29840 + 16.0418i −0.211255 + 0.788414i
415415 −30.0058 + 0.903008i −1.47293 + 0.0443269i
416416 0 0
417417 −1.78909 1.78909i −0.0876122 0.0876122i
418418 0.553620 + 0.958899i 0.0270785 + 0.0469013i
419419 −0.872048 + 0.503477i −0.0426023 + 0.0245965i −0.521150 0.853465i 0.674497π-0.674497\pi
0.478548 + 0.878062i 0.341163π0.341163\pi
420420 0.0356008 + 0.118485i 0.00173714 + 0.00578148i
421421 −0.294746 0.294746i −0.0143650 0.0143650i 0.699888 0.714253i 0.253233π-0.253233\pi
−0.714253 + 0.699888i 0.753233π0.753233\pi
422422 −7.51482 4.33868i −0.365816 0.211204i
423423 −23.4371 13.5314i −1.13955 0.657920i
424424 8.75094 + 8.75094i 0.424983 + 0.424983i
425425 4.97298 + 14.9080i 0.241225 + 0.723146i
426426 −4.23451 + 2.44480i −0.205163 + 0.118451i
427427 −2.15211 3.72756i −0.104148 0.180389i
428428 −5.81326 5.81326i −0.280995 0.280995i
429429 0 0
430430 −17.2718 + 18.3436i −0.832918 + 0.884606i
431431 1.07449 4.01004i 0.0517562 0.193157i −0.935207 0.354100i 0.884787π-0.884787\pi
0.986964 + 0.160944i 0.0514538π0.0514538\pi
432432 1.44942 5.40930i 0.0697352 0.260255i
433433 14.4842 3.88103i 0.696067 0.186511i 0.106599 0.994302i 0.466004π-0.466004\pi
0.589468 + 0.807792i 0.299337π0.299337\pi
434434 5.74380 5.74380i 0.275711 0.275711i
435435 0.989854 0.297418i 0.0474598 0.0142601i
436436 1.53644 + 5.73407i 0.0735821 + 0.274612i
437437 −16.1466 −0.772399
438438 −0.317086 1.18338i −0.0151509 0.0565441i
439439 −6.94098 12.0221i −0.331275 0.573785i 0.651487 0.758660i 0.274145π-0.274145\pi
−0.982762 + 0.184875i 0.940812π0.940812\pi
440440 −0.185519 + 0.786257i −0.00884427 + 0.0374833i
441441 19.8372i 0.944628i
442442 0 0
443443 10.0594 10.0594i 0.477938 0.477938i −0.426533 0.904472i 0.640265π-0.640265\pi
0.904472 + 0.426533i 0.140265π0.140265\pi
444444 −0.663384 0.177753i −0.0314828 0.00843580i
445445 −4.66984 + 19.7915i −0.221372 + 0.938206i
446446 25.4834 + 14.7128i 1.20667 + 0.696673i
447447 0.839520i 0.0397079i
448448 1.38235 2.39430i 0.0653100 0.113120i
449449 −6.42946 + 1.72277i −0.303425 + 0.0813024i −0.407319 0.913286i 0.633536π-0.633536\pi
0.103894 + 0.994588i 0.466870π0.466870\pi
450450 23.4201 1.41091i 1.10404 0.0665108i
451451 0.273982 0.474551i 0.0129013 0.0223457i
452452 2.25141 + 0.603263i 0.105897 + 0.0283751i
453453 −1.18274 + 0.682853i −0.0555698 + 0.0320832i
454454 −10.1212 −0.475011
455455 0 0
456456 2.12357 0.0994451
457457 −32.0071 + 18.4793i −1.49723 + 0.864426i −0.999995 0.00318917i 0.998985π-0.998985\pi
−0.497236 + 0.867616i 0.665652π0.665652\pi
458458 24.0614 + 6.44722i 1.12431 + 0.301259i
459459 1.84844 3.20160i 0.0862780 0.149438i
460460 2.94653 + 2.77437i 0.137383 + 0.129355i
461461 −24.8502 + 6.65860i −1.15739 + 0.310122i −0.785923 0.618324i 0.787812π-0.787812\pi
−0.371468 + 0.928446i 0.621145π0.621145\pi
462462 −0.0131288 + 0.0227398i −0.000610809 + 0.00105795i
463463 15.9580i 0.741632i 0.928706 + 0.370816i 0.120922π0.120922\pi
−0.928706 + 0.370816i 0.879078π0.879078\pi
464464 9.65955 + 5.57694i 0.448433 + 0.258903i
465465 2.16867 + 3.50812i 0.100570 + 0.162685i
466466 −12.6847 3.39887i −0.587609 0.157449i
467467 18.6259 18.6259i 0.861902 0.861902i −0.129657 0.991559i 0.541388π-0.541388\pi
0.991559 + 0.129657i 0.0413877π0.0413877\pi
468468 0 0
469469 2.68150i 0.123820i
470470 −27.5480 + 17.0298i −1.27069 + 0.785524i
471471 0.320738 + 0.555534i 0.0147788 + 0.0255976i
472472 −2.32443 8.67489i −0.106991 0.399294i
473473 −1.08889 −0.0500671
474474 −0.901501 3.36445i −0.0414073 0.154534i
475475 7.21827 + 21.6390i 0.331197 + 0.992865i
476476 −0.623222 + 0.623222i −0.0285653 + 0.0285653i
477477 15.0046 4.02047i 0.687014 0.184085i
478478 −8.00943 + 29.8916i −0.366343 + 1.36721i
479479 −4.29638 + 16.0343i −0.196307 + 0.732627i 0.795618 + 0.605799i 0.207146π0.207146\pi
−0.991925 + 0.126828i 0.959520π0.959520\pi
480480 −0.908170 0.855105i −0.0414521 0.0390300i
481481 0 0
482482 19.1990 + 19.1990i 0.874490 + 0.874490i
483483 −0.191455 0.331609i −0.00871149 0.0150888i
484484 −4.86130 + 2.80667i −0.220968 + 0.127576i
485485 −14.9092 8.01979i −0.676991 0.364160i
486486 −5.86681 5.86681i −0.266124 0.266124i
487487 22.7590 + 13.1399i 1.03131 + 0.595425i 0.917359 0.398062i 0.130317π-0.130317\pi
0.113948 + 0.993487i 0.463650π0.463650\pi
488488 16.0369 + 9.25893i 0.725958 + 0.419132i
489489 1.51637 + 1.51637i 0.0685724 + 0.0685724i
490490 −20.9069 11.2460i −0.944477 0.508043i
491491 −36.0301 + 20.8020i −1.62602 + 0.938781i −0.640752 + 0.767748i 0.721377π0.721377\pi
−0.985265 + 0.171034i 0.945289π0.945289\pi
492492 0.180519 + 0.312668i 0.00813842 + 0.0140961i
493493 5.20655 + 5.20655i 0.234491 + 0.234491i
494494 0 0
495495 0.738254 + 0.695118i 0.0331821 + 0.0312432i
496496 −11.5195 + 42.9915i −0.517242 + 1.93037i
497497 −2.21922 + 8.28224i −0.0995456 + 0.371509i
498498 4.05480 1.08648i 0.181700 0.0486864i
499499 8.31651 8.31651i 0.372298 0.372298i −0.496015 0.868314i 0.665204π-0.665204\pi
0.868314 + 0.496015i 0.165204π0.165204\pi
500500 2.40085 5.18908i 0.107369 0.232063i
501501 −0.835410 3.11779i −0.0373234 0.139293i
502502 −15.7730 −0.703982
503503 2.76277 + 10.3108i 0.123186 + 0.459736i 0.999769 0.0215156i 0.00684916π-0.00684916\pi
−0.876583 + 0.481251i 0.840182π0.840182\pi
504504 −1.91512 3.31708i −0.0853062 0.147755i
505505 25.7437 15.9144i 1.14558 0.708180i
506506 0.858953i 0.0381851i
507507 0 0
508508 0.879556 0.879556i 0.0390240 0.0390240i
509509 −2.91197 0.780260i −0.129071 0.0345844i 0.193705 0.981060i 0.437949π-0.437949\pi
−0.322776 + 0.946475i 0.604616π0.604616\pi
510510 −1.15557 1.86929i −0.0511694 0.0827735i
511511 −1.86056 1.07419i −0.0823062 0.0475195i
512512 9.00279i 0.397871i
513513 2.68301 4.64712i 0.118458 0.205175i
514514 4.21162 1.12850i 0.185767 0.0497760i
515515 −23.8441 22.4509i −1.05070 0.989304i
516516 0.358718 0.621318i 0.0157917 0.0273520i
517517 −1.35200 0.362267i −0.0594608 0.0159325i
518518 −5.12203 + 2.95721i −0.225049 + 0.129932i
519519 −1.34838 −0.0591871
520520 0 0
521521 −5.84796 −0.256204 −0.128102 0.991761i 0.540888π-0.540888\pi
−0.128102 + 0.991761i 0.540888π0.540888\pi
522522 9.52007 5.49642i 0.416682 0.240572i
523523 −2.86434 0.767497i −0.125249 0.0335603i 0.195650 0.980674i 0.437318π-0.437318\pi
−0.320899 + 0.947113i 0.603985π0.603985\pi
524524 1.68940 2.92613i 0.0738020 0.127829i
525525 −0.358819 + 0.404823i −0.0156601 + 0.0176679i
526526 −9.45590 + 2.53370i −0.412297 + 0.110475i
527527 −14.6909 + 25.4453i −0.639944 + 1.10842i
528528 0.143873i 0.00626129i
529529 9.07083 + 5.23704i 0.394384 + 0.227698i
530530 4.26908 18.0930i 0.185437 0.785909i
531531 −10.8887 2.91762i −0.472529 0.126614i
532532 −0.904605 + 0.904605i −0.0392196 + 0.0392196i
533533 0 0
534534 2.84359i 0.123054i
535535 8.25511 34.9864i 0.356900 1.51259i
536536 5.76825 + 9.99091i 0.249151 + 0.431542i
537537 0.289755 + 1.08138i 0.0125038 + 0.0466650i
538538 33.6329 1.45002
539539 −0.265543 0.991021i −0.0114378 0.0426863i
540540 −1.28809 + 0.387029i −0.0554307 + 0.0166551i
541541 15.4678 15.4678i 0.665013 0.665013i −0.291544 0.956557i 0.594169π-0.594169\pi
0.956557 + 0.291544i 0.0941691π0.0941691\pi
542542 −19.7233 + 5.28484i −0.847188 + 0.227003i
543543 −0.183392 + 0.684429i −0.00787011 + 0.0293717i
544544 2.29997 8.58362i 0.0986105 0.368020i
545545 −17.7937 + 18.8979i −0.762198 + 0.809497i
546546 0 0
547547 1.76989 + 1.76989i 0.0756751 + 0.0756751i 0.743931 0.668256i 0.232959π-0.232959\pi
−0.668256 + 0.743931i 0.732959π0.732959\pi
548548 −1.03698 1.79610i −0.0442976 0.0767256i
549549 20.1295 11.6218i 0.859106 0.496005i
550550 1.15113 0.383990i 0.0490843 0.0163734i
551551 7.55729 + 7.55729i 0.321952 + 0.321952i
552552 1.42667 + 0.823688i 0.0607231 + 0.0350585i
553553 −5.28972 3.05402i −0.224942 0.129870i
554554 23.8419 + 23.8419i 1.01295 + 1.01295i
555555 −0.864126 2.87595i −0.0366801 0.122077i
556556 −5.67915 + 3.27886i −0.240850 + 0.139055i
557557 −4.71734 8.17068i −0.199880 0.346203i 0.748609 0.663012i 0.230722π-0.230722\pi
−0.948489 + 0.316809i 0.897389π0.897389\pi
558558 31.0175 + 31.0175i 1.31308 + 1.31308i
559559 0 0
560560 −5.83514 + 0.175605i −0.246580 + 0.00742067i
561561 0.0245819 0.0917409i 0.00103785 0.00387330i
562562 −2.45163 + 9.14960i −0.103416 + 0.385953i
563563 −9.45863 + 2.53443i −0.398634 + 0.106814i −0.452566 0.891731i 0.649491π-0.649491\pi
0.0539320 + 0.998545i 0.482825π0.482825\pi
564564 0.652105 0.652105i 0.0274586 0.0274586i
565565 2.93269 + 9.76047i 0.123379 + 0.410626i
566566 −0.630795 2.35416i −0.0265143 0.0989527i
567567 −4.74366 −0.199215
568568 −9.54766 35.6324i −0.400611 1.49510i
569569 −3.20931 5.55868i −0.134541 0.233032i 0.790881 0.611970i 0.209623π-0.209623\pi
−0.925422 + 0.378938i 0.876289π0.876289\pi
570570 −1.67731 2.71327i −0.0702546 0.113646i
571571 1.72174i 0.0720527i −0.999351 0.0360264i 0.988530π-0.988530\pi
0.999351 0.0360264i 0.0114700π-0.0114700\pi
572572 0 0
573573 3.27622 3.27622i 0.136866 0.136866i
574574 3.00322 + 0.804709i 0.125352 + 0.0335879i
575575 −3.54389 + 17.3375i −0.147791 + 0.723023i
576576 12.9297 + 7.46495i 0.538736 + 0.311040i
577577 24.8642i 1.03511i −0.855650 0.517554i 0.826843π-0.826843\pi
0.855650 0.517554i 0.173157π-0.173157\pi
578578 −5.64230 + 9.77275i −0.234689 + 0.406493i
579579 3.01849 0.808803i 0.125444 0.0336127i
580580 −0.0805813 2.67762i −0.00334596 0.111182i
581581 3.68068 6.37512i 0.152700 0.264484i
582582 2.28668 + 0.612715i 0.0947861 + 0.0253979i
583583 0.695777 0.401707i 0.0288161 0.0166370i
584584 9.24291 0.382474
585585 0 0
586586 4.42437 0.182769
587587 23.1811 13.3836i 0.956785 0.552400i 0.0616029 0.998101i 0.480379π-0.480379\pi
0.895182 + 0.445701i 0.147045π0.147045\pi
588588 0.652955 + 0.174959i 0.0269274 + 0.00721517i
589589 −21.3238 + 36.9338i −0.878630 + 1.52183i
590590 −9.24791 + 9.82180i −0.380731 + 0.404357i
591591 −1.08878 + 0.291739i −0.0447866 + 0.0120005i
592592 16.2034 28.0651i 0.665956 1.15347i
593593 19.8452i 0.814944i −0.913218 0.407472i 0.866410π-0.866410\pi
0.913218 0.407472i 0.133590π-0.133590\pi
594594 −0.247213 0.142728i −0.0101433 0.00585621i
595595 −3.75078 0.885004i −0.153767 0.0362816i
596596 2.10174 + 0.563161i 0.0860908 + 0.0230680i
597597 −1.29797 + 1.29797i −0.0531224 + 0.0531224i
598598 0 0
599599 36.5285i 1.49252i −0.665657 0.746258i 0.731849π-0.731849\pi
0.665657 0.746258i 0.268151π-0.268151\pi
600600 0.466084 2.28018i 0.0190278 0.0930881i
601601 −14.9478 25.8903i −0.609732 1.05609i −0.991284 0.131740i 0.957944π-0.957944\pi
0.381552 0.924347i 0.375390π-0.375390\pi
602602 −1.59908 5.96785i −0.0651736 0.243231i
603603 14.4806 0.589695
604604 0.916132 + 3.41905i 0.0372769 + 0.139119i
605605 −21.6155 11.6272i −0.878796 0.472713i
606606 −2.99266 + 2.99266i −0.121568 + 0.121568i
607607 −17.2598 + 4.62475i −0.700553 + 0.187713i −0.591478 0.806321i 0.701456π-0.701456\pi
−0.109075 + 0.994034i 0.534789π0.534789\pi
608608 3.33841 12.4591i 0.135390 0.505283i
609609 −0.0655981 + 0.244816i −0.00265817 + 0.00992043i
610610 −0.836730 27.8035i −0.0338782 1.12573i
611611 0 0
612612 −3.36551 3.36551i −0.136043 0.136043i
613613 7.68729 + 13.3148i 0.310487 + 0.537779i 0.978468 0.206399i 0.0661746π-0.0661746\pi
−0.667981 + 0.744178i 0.732841π0.732841\pi
614614 2.91107 1.68071i 0.117481 0.0678278i
615615 −0.747835 + 1.39026i −0.0301556 + 0.0560607i
616616 −0.140078 0.140078i −0.00564390 0.00564390i
617617 1.07707 + 0.621849i 0.0433614 + 0.0250347i 0.521524 0.853237i 0.325364π-0.325364\pi
−0.478163 + 0.878271i 0.658697π0.658697\pi
618618 3.96616 + 2.28986i 0.159542 + 0.0921117i
619619 −28.7865 28.7865i −1.15703 1.15703i −0.985112 0.171915i 0.945005π-0.945005\pi
−0.171915 0.985112i 0.554995π-0.554995\pi
620620 10.2374 3.07599i 0.411143 0.123535i
621621 3.60504 2.08137i 0.144665 0.0835226i
622622 16.8502 + 29.1854i 0.675631 + 1.17023i
623623 −3.52601 3.52601i −0.141266 0.141266i
624624 0 0
625625 24.8192 3.00128i 0.992768 0.120051i
626626 8.33343 31.1008i 0.333071 1.24304i
627627 0.0356806 0.133162i 0.00142495 0.00531797i
628628 1.60594 0.430310i 0.0640839 0.0171712i
629629 15.1272 15.1272i 0.603163 0.603163i
630630 −2.72556 + 5.06695i −0.108589 + 0.201872i
631631 5.36381 + 20.0180i 0.213530 + 0.796904i 0.986679 + 0.162680i 0.0520137π0.0520137\pi
−0.773149 + 0.634224i 0.781320π0.781320\pi
632632 26.2784 1.04530
633633 0.279626 + 1.04358i 0.0111141 + 0.0414785i
634634 6.96483 + 12.0634i 0.276609 + 0.479101i
635635 5.29349 + 1.24901i 0.210066 + 0.0495655i
636636 0.529346i 0.0209899i
637637 0 0
638638 0.402025 0.402025i 0.0159163 0.0159163i
639639 −44.7256 11.9842i −1.76932 0.474087i
640640 25.9523 16.0434i 1.02586 0.634169i
641641 −15.3071 8.83753i −0.604592 0.349061i 0.166254 0.986083i 0.446833π-0.446833\pi
−0.770846 + 0.637022i 0.780166π0.780166\pi
642642 5.02675i 0.198390i
643643 −1.33452 + 2.31145i −0.0526282 + 0.0911547i −0.891139 0.453730i 0.850093π-0.850093\pi
0.838511 + 0.544884i 0.183426π0.183426\pi
644644 −0.958617 + 0.256861i −0.0377748 + 0.0101217i
645645 3.13556 0.0943630i 0.123463 0.00371554i
646646 11.3623 19.6801i 0.447043 0.774302i
647647 40.7326 + 10.9143i 1.60136 + 0.429084i 0.945454 0.325755i 0.105619π-0.105619\pi
0.655910 + 0.754839i 0.272285π0.272285\pi
648648 17.6742 10.2042i 0.694309 0.400860i
649649 −0.583029 −0.0228859
650650 0 0
651651 −1.01136 −0.0396385
652652 4.81343 2.77904i 0.188508 0.108835i
653653 −24.4045 6.53917i −0.955023 0.255898i −0.252531 0.967589i 0.581263π-0.581263\pi
−0.702492 + 0.711691i 0.747930π0.747930\pi
654654 1.81485 3.14342i 0.0709664 0.122917i
655655 14.7671 0.444408i 0.576999 0.0173644i
656656 −16.4555 + 4.40924i −0.642479 + 0.172152i
657657 5.80083 10.0473i 0.226312 0.391984i
658658 7.94187i 0.309606i
659659 −32.7551 18.9112i −1.27596 0.736675i −0.299856 0.953985i 0.596939π-0.596939\pi
−0.976103 + 0.217310i 0.930272π0.930272\pi
660660 −0.0293915 + 0.0181694i −0.00114406 + 0.000707243i
661661 16.6205 + 4.45346i 0.646463 + 0.173219i 0.567129 0.823629i 0.308054π-0.308054\pi
0.0793341 + 0.996848i 0.474721π0.474721\pi
662662 20.3625 20.3625i 0.791409 0.791409i
663663 0 0
664664 31.6705i 1.22905i
665665 −5.44425 1.28458i −0.211119 0.0498140i
666666 −15.9694 27.6599i −0.618804 1.07180i
667667 2.14588 + 8.00852i 0.0830887 + 0.310091i
668668 −8.36582 −0.323683
669669 −0.948235 3.53886i −0.0366609 0.136820i
670670 8.20927 15.2614i 0.317152 0.589600i
671671 0.850052 0.850052i 0.0328159 0.0328159i
672672 0.295461 0.0791687i 0.0113977 0.00305400i
673673 8.14322 30.3909i 0.313898 1.17148i −0.611113 0.791543i 0.709278π-0.709278\pi
0.925011 0.379940i 0.124055π-0.124055\pi
674674 10.0072 37.3474i 0.385464 1.43857i
675675 −4.40098 3.90085i −0.169394 0.150144i
676676 0 0
677677 −28.8731 28.8731i −1.10968 1.10968i −0.993191 0.116494i 0.962835π-0.962835\pi
−0.116494 0.993191i 0.537165π-0.537165\pi
678678 −0.712579 1.23422i −0.0273664 0.0474001i
679679 3.59521 2.07570i 0.137972 0.0796579i
680680 15.8787 4.77101i 0.608919 0.182960i
681681 0.891066 + 0.891066i 0.0341457 + 0.0341457i
682682 1.96477 + 1.13436i 0.0752349 + 0.0434369i
683683 27.5215 + 15.8896i 1.05308 + 0.607998i 0.923511 0.383572i 0.125306π-0.125306\pi
0.129572 + 0.991570i 0.458640π0.458640\pi
684684 −4.88503 4.88503i −0.186784 0.186784i
685685 4.29589 7.98627i 0.164138 0.305140i
686686 10.3093 5.95206i 0.393610 0.227251i
687687 −1.55074 2.68597i −0.0591646 0.102476i
688688 23.9378 + 23.9378i 0.912619 + 0.912619i
689689 0 0
690690 −0.0744368 2.47344i −0.00283376 0.0941623i
691691 6.94735 25.9278i 0.264289 0.986342i −0.698394 0.715713i 0.746102π-0.746102\pi
0.962684 0.270629i 0.0872315π-0.0872315\pi
692692 −0.904508 + 3.37567i −0.0343842 + 0.128324i
693693 −0.240182 + 0.0643565i −0.00912374 + 0.00244470i
694694 −8.70863 + 8.70863i −0.330575 + 0.330575i
695695 −25.2520 13.5833i −0.957865 0.515245i
696696 −0.282220 1.05326i −0.0106975 0.0399237i
697697 −11.2462 −0.425980
698698 −2.07982 7.76199i −0.0787223 0.293796i
699699 0.817526 + 1.41600i 0.0309217 + 0.0535579i
700700 0.772778 + 1.16987i 0.0292082 + 0.0442168i
701701 39.3253i 1.48530i 0.669681 + 0.742649i 0.266431π0.266431\pi
−0.669681 + 0.742649i 0.733569π0.733569\pi
702702 0 0
703703 21.9572 21.9572i 0.828131 0.828131i
704704 0.745863 + 0.199854i 0.0281108 + 0.00753226i
705705 3.92461 + 0.926020i 0.147809 + 0.0348759i
706706 −35.1585 20.2987i −1.32321 0.763953i
707707 7.42171i 0.279122i
708708 0.192071 0.332676i 0.00721845 0.0125027i
709709 −36.2309 + 9.70804i −1.36068 + 0.364593i −0.864066 0.503378i 0.832090π-0.832090\pi
−0.496614 + 0.867972i 0.665424π0.665424\pi
710710 −37.9861 + 40.3433i −1.42559 + 1.51406i
711711 16.4923 28.5654i 0.618508 1.07129i
712712 20.7223 + 5.55253i 0.776602 + 0.208090i
713713 −28.6518 + 16.5421i −1.07302 + 0.619507i
714714 0.538902 0.0201679
715715 0 0
716716 2.90161 0.108438
717717 3.33680 1.92650i 0.124615 0.0719465i
718718 −21.7438 5.82623i −0.811471 0.217433i
719719 14.5578 25.2148i 0.542913 0.940353i −0.455822 0.890071i 0.650655π-0.650655\pi
0.998735 0.0502820i 0.0160120π-0.0160120\pi
720720 −0.948298 31.5108i −0.0353410 1.17434i
721721 7.75737 2.07858i 0.288900 0.0774104i
722722 1.43734 2.48955i 0.0534923 0.0926514i
723723 3.38055i 0.125724i
724724 1.59045 + 0.918247i 0.0591086 + 0.0341264i
725725 9.77335 6.45597i 0.362973 0.239769i
726726 3.31526 + 0.888322i 0.123041 + 0.0329687i
727727 −15.6053 + 15.6053i −0.578768 + 0.578768i −0.934564 0.355796i 0.884210π-0.884210\pi
0.355796 + 0.934564i 0.384210π0.384210\pi
728728 0 0
729729 24.9204i 0.922977i
730730 −7.30054 11.8096i −0.270205 0.437094i
731731 11.1740 + 19.3539i 0.413284 + 0.715829i
732732 0.205002 + 0.765076i 0.00757708 + 0.0282780i
733733 −34.8651 −1.28777 −0.643886 0.765121i 0.722679π-0.722679\pi
−0.643886 + 0.765121i 0.722679π0.722679\pi
734734 −8.25335 30.8019i −0.304637 1.13692i
735735 0.850540 + 2.83073i 0.0313727 + 0.104413i
736736 7.07547 7.07547i 0.260805 0.260805i
737737 0.723416 0.193839i 0.0266474 0.00714014i
738738 −4.34557 + 16.2179i −0.159963 + 0.596989i
739739 8.85631 33.0522i 0.325785 1.21584i −0.587736 0.809053i 0.699981π-0.699981\pi
0.913521 0.406792i 0.133353π-0.133353\pi
740740 −7.77962 + 0.234123i −0.285985 + 0.00860654i
741741 0 0
742742 3.22341 + 3.22341i 0.118335 + 0.118335i
743743 −1.56456 2.70989i −0.0573980 0.0994162i 0.835899 0.548884i 0.184947π-0.184947\pi
−0.893297 + 0.449468i 0.851614π0.851614\pi
744744 3.76821 2.17558i 0.138149 0.0797605i
745745 2.73774 + 9.11163i 0.100303 + 0.333824i
746746 −29.3652 29.3652i −1.07514 1.07514i
747747 34.4268 + 19.8763i 1.25961 + 0.727236i
748748 −0.213184 0.123082i −0.00779478 0.00450032i
749749 6.23310 + 6.23310i 0.227753 + 0.227753i
750750 −3.28152 + 1.20550i −0.119824 + 0.0440185i
751751 6.28199 3.62691i 0.229233 0.132348i −0.380985 0.924581i 0.624415π-0.624415\pi
0.610218 + 0.792233i 0.291082π0.291082\pi
752752 21.7579 + 37.6858i 0.793430 + 1.37426i
753753 1.38865 + 1.38865i 0.0506051 + 0.0506051i
754754 0 0
755755 −10.6098 + 11.2682i −0.386131 + 0.410093i
756756 0.0853627 0.318578i 0.00310461 0.0115866i
757757 4.28134 15.9782i 0.155608 0.580737i −0.843445 0.537216i 0.819476π-0.819476\pi
0.999053 0.0435205i 0.0138574π-0.0138574\pi
758758 −34.4882 + 9.24108i −1.25267 + 0.335651i
759759 0.0756220 0.0756220i 0.00274490 0.00274490i
760760 23.0479 6.92511i 0.836034 0.251200i
761761 5.99332 + 22.3674i 0.217258 + 0.810817i 0.985360 + 0.170489i 0.0545348π0.0545348\pi
−0.768102 + 0.640328i 0.778799π0.778799\pi
762762 −0.760555 −0.0275520
763763 −1.64740 6.14819i −0.0596400 0.222579i
764764 −6.00431 10.3998i −0.217228 0.376251i
765765 4.77918 20.2549i 0.172792 0.732317i
766766 38.2335i 1.38143i
767767 0 0
768768 −1.60998 + 1.60998i −0.0580951 + 0.0580951i
769769 5.69177 + 1.52511i 0.205251 + 0.0549967i 0.359979 0.932960i 0.382784π-0.382784\pi
−0.154729 + 0.987957i 0.549450π0.549450\pi
770770 −0.0683359 + 0.289618i −0.00246266 + 0.0104371i
771771 −0.470143 0.271437i −0.0169318 0.00977557i
772772 8.09938i 0.291503i
773773 −4.04499 + 7.00612i −0.145488 + 0.251993i −0.929555 0.368684i 0.879809π-0.879809\pi
0.784067 + 0.620676i 0.213142π0.213142\pi
774774 32.2274 8.63532i 1.15839 0.310390i
775775 34.9776 + 31.0027i 1.25643 + 1.11365i
776776 −8.93019 + 15.4675i −0.320575 + 0.555252i
777777 0.711294 + 0.190591i 0.0255175 + 0.00683740i
778778 −19.6616 + 11.3516i −0.704901 + 0.406975i
779779 −16.3238 −0.584863
780780 0 0
781781 −2.39481 −0.0856930
782782 15.2670 8.81441i 0.545947 0.315203i
783783 −2.66148 0.713141i −0.0951135 0.0254856i
784784 −15.9487 + 27.6239i −0.569595 + 0.986567i
785785 5.29272 + 4.98347i 0.188905 + 0.177868i
786786 −1.99554 + 0.534703i −0.0711785 + 0.0190722i
787787 −8.10582 + 14.0397i −0.288941 + 0.500461i −0.973557 0.228443i 0.926637π-0.926637\pi
0.684616 + 0.728904i 0.259970π0.259970\pi
788788 2.92148i 0.104073i
789789 1.05556 + 0.609429i 0.0375790 + 0.0216962i
790790 −20.7561 33.5758i −0.738467 1.19457i
791791 −2.41401 0.646831i −0.0858322 0.0229987i
792792 0.756445 0.756445i 0.0268791 0.0268791i
793793 0 0
794794 53.0777i 1.88366i
795795 −1.96875 + 1.21705i −0.0698244 + 0.0431644i
796796 2.37878 + 4.12017i 0.0843137 + 0.146036i
797797 −4.31449 16.1019i −0.152827 0.570358i −0.999282 0.0378972i 0.987934π-0.987934\pi
0.846455 0.532461i 0.178733π-0.178733\pi
798798 0.782216 0.0276901
799799 7.43502 + 27.7479i 0.263032 + 0.981649i
800800 −12.6453 6.31917i −0.447078 0.223416i
801801 19.0411 19.0411i 0.672783 0.672783i
802802 28.3937 7.60807i 1.00262 0.268650i
803803 0.155301 0.579592i 0.00548047 0.0204534i
804804 −0.127715 + 0.476638i −0.00450415 + 0.0168097i
805805 −3.15933 2.97473i −0.111352 0.104846i
806806 0 0
807807 −2.96103 2.96103i −0.104233 0.104233i
808808 −15.9651 27.6523i −0.561649 0.972804i
809809 −20.8943 + 12.0633i −0.734603 + 0.424123i −0.820104 0.572215i 0.806084π-0.806084\pi
0.0855005 + 0.996338i 0.472751π0.472751\pi
810810 −26.9979 14.5224i −0.948611 0.510267i
811811 −17.7808 17.7808i −0.624369 0.624369i 0.322276 0.946646i 0.395552π-0.395552\pi
−0.946646 + 0.322276i 0.895552π0.895552\pi
812812 0.568894 + 0.328451i 0.0199642 + 0.0115264i
813813 2.20171 + 1.27116i 0.0772173 + 0.0445815i
814814 −1.16806 1.16806i −0.0409403 0.0409403i
815815 21.4027 + 11.5127i 0.749703 + 0.403272i
816816 −2.55720 + 1.47640i −0.0895200 + 0.0516844i
817817 16.2190 + 28.0921i 0.567431 + 0.982819i
818818 −5.79615 5.79615i −0.202658 0.202658i
819819 0 0
820820 2.97887 + 2.80481i 0.104027 + 0.0979484i
821821 −10.2562 + 38.2768i −0.357945 + 1.33587i 0.518792 + 0.854901i 0.326382π0.326382\pi
−0.876737 + 0.480970i 0.840285π0.840285\pi
822822 −0.328208 + 1.22489i −0.0114476 + 0.0427229i
823823 38.5831 10.3383i 1.34492 0.360371i 0.486664 0.873589i 0.338214π-0.338214\pi
0.858258 + 0.513219i 0.171547π0.171547\pi
824824 −24.4316 + 24.4316i −0.851116 + 0.851116i
825825 −0.135152 0.0675387i −0.00470537 0.00235140i
826826 −0.856204 3.19540i −0.0297912 0.111182i
827827 −25.6019 −0.890264 −0.445132 0.895465i 0.646843π-0.646843\pi
−0.445132 + 0.895465i 0.646843π0.646843\pi
828828 −1.38709 5.17670i −0.0482048 0.179903i
829829 −9.41684 16.3104i −0.327060 0.566485i 0.654867 0.755744i 0.272725π-0.272725\pi
−0.981927 + 0.189259i 0.939391π0.939391\pi
830830 40.4652 25.0150i 1.40457 0.868283i
831831 4.19807i 0.145629i
832832 0 0
833833 −14.8894 + 14.8894i −0.515888 + 0.515888i
834834 3.87301 + 1.03777i 0.134111 + 0.0359351i
835835 −19.2344 31.1142i −0.665633 1.07675i
836836 −0.309436 0.178653i −0.0107021 0.00617885i
837837 10.9949i 0.380040i
838838 0.797879 1.38197i 0.0275623 0.0477393i
839839 −24.0857 + 6.45374i −0.831530 + 0.222808i −0.649381 0.760463i 0.724972π-0.724972\pi
−0.182149 + 0.983271i 0.558305π0.558305\pi
840840 0.415508 + 0.391229i 0.0143364 + 0.0134987i
841841 −11.7560 + 20.3621i −0.405381 + 0.702140i
842842 0.638063 + 0.170969i 0.0219891 + 0.00589196i
843843 1.02137 0.589688i 0.0351778 0.0203099i
844844 2.80018 0.0963863
845845 0 0
846846 42.8875 1.47450
847847 5.21239 3.00937i 0.179100 0.103403i
848848 −24.1267 6.46474i −0.828516 0.222000i
849849 −0.151725 + 0.262795i −0.00520717 + 0.00901909i
850850 −18.6377 16.5197i −0.639268 0.566621i
851851 23.2682 6.23469i 0.797623 0.213722i
852852 0.788935 1.36648i 0.0270285 0.0468147i
853853 2.14143i 0.0733210i 0.999328 + 0.0366605i 0.0116720π0.0116720\pi
−0.999328 + 0.0366605i 0.988328π0.988328\pi
854854 5.90721 + 3.41053i 0.202140 + 0.116706i
855855 6.93697 29.3999i 0.237240 1.00546i
856856 −36.6319 9.81549i −1.25205 0.335487i
857857 36.4384 36.4384i 1.24471 1.24471i 0.286686 0.958025i 0.407446π-0.407446\pi
0.958025 0.286686i 0.0925537π-0.0925537\pi
858858 0 0
859859 4.40721i 0.150372i 0.997170 + 0.0751861i 0.0239551π0.0239551\pi
−0.997170 + 0.0751861i 0.976045π0.976045\pi
860860 1.86714 7.91321i 0.0636689 0.269838i
861861 −0.193556 0.335249i −0.00659637 0.0114252i
862862 1.70278 + 6.35486i 0.0579969 + 0.216447i
863863 −53.8912 −1.83448 −0.917239 0.398338i 0.869587π-0.869587\pi
−0.917239 + 0.398338i 0.869587π0.869587\pi
864864 0.860671 + 3.21207i 0.0292806 + 0.109277i
865865 −14.6344 + 4.39716i −0.497586 + 0.149508i
866866 −16.8033 + 16.8033i −0.570998 + 0.570998i
867867 1.35714 0.363644i 0.0460908 0.0123500i
868868 −0.678436 + 2.53196i −0.0230276 + 0.0859403i
869869 0.441535 1.64783i 0.0149780 0.0558988i
870870 −1.12283 + 1.19251i −0.0380676 + 0.0404300i
871871 0 0
872872 19.3636 + 19.3636i 0.655733 + 0.655733i
873873 11.2091 + 19.4148i 0.379372 + 0.657091i
874874 22.1600 12.7941i 0.749574 0.432767i
875875 −2.57424 + 5.56383i −0.0870251 + 0.188092i
876876 0.279553 + 0.279553i 0.00944522 + 0.00944522i
877877 −11.3743 6.56696i −0.384083 0.221750i 0.295510 0.955340i 0.404510π-0.404510\pi
−0.679593 + 0.733589i 0.737844π0.737844\pi
878878 19.0519 + 10.9996i 0.642971 + 0.371220i
879879 −0.389521 0.389521i −0.0131382 0.0131382i
880880 −0.469182 1.56151i −0.0158161 0.0526386i
881881 31.7049 18.3049i 1.06817 0.616706i 0.140486 0.990083i 0.455133π-0.455133\pi
0.927680 + 0.373376i 0.121800π0.121800\pi
882882 15.7184 + 27.2250i 0.529265 + 0.916714i
883883 −7.40474 7.40474i −0.249189 0.249189i 0.571449 0.820638i 0.306382π-0.306382\pi
−0.820638 + 0.571449i 0.806382π0.806382\pi
884884 0 0
885885 1.67889 0.0505253i 0.0564354 0.00169839i
886886 −5.83502 + 21.7766i −0.196031 + 0.731599i
887887 −14.1308 + 52.7370i −0.474467 + 1.77074i 0.148948 + 0.988845i 0.452411π0.452411\pi
−0.623416 + 0.781891i 0.714255π0.714255\pi
888888 −3.06017 + 0.819971i −0.102693 + 0.0275164i
889889 −0.943078 + 0.943078i −0.0316298 + 0.0316298i
890890 −9.27315 30.8625i −0.310837 1.03451i
891891 −0.342907 1.27975i −0.0114878 0.0428731i
892892 −9.49566 −0.317938
893893 10.7919 + 40.2760i 0.361138 + 1.34779i
894894 −0.665210 1.15218i −0.0222479 0.0385346i
895895 6.67128 + 10.7917i 0.222996 + 0.360727i
896896 7.48186i 0.249951i
897897 0 0
898898 7.45887 7.45887i 0.248906 0.248906i
899899 21.1526 + 5.66782i 0.705479 + 0.189032i
900900 −6.31749 + 4.17314i −0.210583 + 0.139105i
901901 −14.2799 8.24448i −0.475731 0.274664i
902902 0.868379i 0.0289139i
903903 −0.384625 + 0.666190i −0.0127995 + 0.0221694i
904904 10.3857 2.78284i 0.345423 0.0925558i
905905 0.241550 + 8.02642i 0.00802940 + 0.266807i
906906 1.08214 1.87433i 0.0359518 0.0622703i
907907 39.5809 + 10.6057i 1.31426 + 0.352155i 0.846825 0.531871i 0.178511π-0.178511\pi
0.467437 + 0.884027i 0.345178π0.345178\pi
908908 2.82853 1.63305i 0.0938680 0.0541947i
909909 −40.0785 −1.32932
910910 0 0
911911 24.2232 0.802551 0.401276 0.915957i 0.368567π-0.368567\pi
0.401276 + 0.915957i 0.368567π0.368567\pi
912912 −3.71178 + 2.14299i −0.122909 + 0.0709616i
913913 1.98595 + 0.532133i 0.0657253 + 0.0176110i
914914 29.2849 50.7229i 0.968658 1.67777i
915915 −2.37415 + 2.52148i −0.0784869 + 0.0833575i
916916 −7.76460 + 2.08052i −0.256550 + 0.0687423i
917917 −1.81141 + 3.13746i −0.0598182 + 0.103608i
918918 5.85860i 0.193363i
919919 30.2077 + 17.4404i 0.996460 + 0.575307i 0.907199 0.420702i 0.138216π-0.138216\pi
0.0892612 + 0.996008i 0.471549π0.471549\pi
920920 18.1703 + 4.28732i 0.599057 + 0.141349i
921921 −0.404259 0.108321i −0.0133208 0.00356929i
922922 28.8290 28.8290i 0.949432 0.949432i
923923 0 0
924924 0.00847334i 0.000278753i
925925 −18.7574 28.3958i −0.616739 0.933647i
926926 −12.6446 21.9012i −0.415529 0.719717i
927927 11.2247 + 41.8912i 0.368668 + 1.37589i
928928 −6.62322 −0.217418
929929 2.24604 + 8.38235i 0.0736903 + 0.275016i 0.992933 0.118675i 0.0378647π-0.0378647\pi
−0.919243 + 0.393691i 0.871198π0.871198\pi
930930 −5.75606 3.09624i −0.188749 0.101530i
931931 −21.6120 + 21.6120i −0.708304 + 0.708304i
932932 4.09336 1.09681i 0.134083 0.0359273i
933933 1.08599 4.05296i 0.0355536 0.132688i
934934 −10.8040 + 40.3211i −0.353518 + 1.31935i
935935 −0.0323774 1.07586i −0.00105885 0.0351844i
936936 0 0
937937 −25.8920 25.8920i −0.845856 0.845856i 0.143757 0.989613i 0.454082π-0.454082\pi
−0.989613 + 0.143757i 0.954082π0.954082\pi
938938 2.12474 + 3.68015i 0.0693751 + 0.120161i
939939 −3.47178 + 2.00443i −0.113297 + 0.0654122i
940940 4.95098 9.20410i 0.161483 0.300205i
941941 20.9205 + 20.9205i 0.681989 + 0.681989i 0.960448 0.278459i 0.0898236π-0.0898236\pi
−0.278459 + 0.960448i 0.589824π0.589824\pi
942942 −0.880376 0.508285i −0.0286842 0.0165608i
943943 −10.9668 6.33169i −0.357128 0.206188i
944944 12.8171 + 12.8171i 0.417162 + 0.417162i
945945 1.38112 0.414980i 0.0449279 0.0134993i
946946 1.49442 0.862801i 0.0485876 0.0280521i
947947 −13.8023 23.9064i −0.448516 0.776852i 0.549774 0.835314i 0.314714π-0.314714\pi
−0.998290 + 0.0584612i 0.981381π0.981381\pi
948948 0.794793 + 0.794793i 0.0258137 + 0.0258137i
949949 0 0
950950 −27.0526 23.9783i −0.877702 0.777960i
951951 0.448880 1.67524i 0.0145559 0.0543235i
952952 −1.05229 + 3.92719i −0.0341048 + 0.127281i
953953 −27.9135 + 7.47941i −0.904208 + 0.242282i −0.680822 0.732448i 0.738377π-0.738377\pi
−0.223385 + 0.974730i 0.571711π0.571711\pi
954954 −17.4070 + 17.4070i −0.563572 + 0.563572i
955955 24.8740 46.2421i 0.804905 1.49636i
956956 −2.58464 9.64602i −0.0835933 0.311974i
957957 −0.0707884 −0.00228826
958958 −6.80864 25.4102i −0.219977 0.820966i
959959 1.11187 + 1.92582i 0.0359042 + 0.0621878i
960960 −2.16511 0.510862i −0.0698786 0.0164880i
961961 56.3841i 1.81884i
962962 0 0
963963 −33.6599 + 33.6599i −1.08467 + 1.08467i
964964 −8.46323 2.26771i −0.272582 0.0730382i
965965 30.1233 18.6218i 0.969703 0.599456i
966966 0.525514 + 0.303406i 0.0169081 + 0.00976192i
967967 4.31688i 0.138822i −0.997588 0.0694108i 0.977888π-0.977888\pi
0.997588 0.0694108i 0.0221119π-0.0221119\pi
968968 −12.9471 + 22.4250i −0.416136 + 0.720768i
969969 −2.73296 + 0.732295i −0.0877954 + 0.0235247i
970970 26.8163 0.807022i 0.861021 0.0259119i
971971 6.77930 11.7421i 0.217558 0.376822i −0.736503 0.676435i 0.763524π-0.763524\pi
0.954061 + 0.299613i 0.0968575π0.0968575\pi
972972 2.58618 + 0.692966i 0.0829519 + 0.0222269i
973973 6.08930 3.51566i 0.195214 0.112707i
974974 −41.6466 −1.33444
975975 0 0
976976 −37.3745 −1.19633
977977 41.2668 23.8254i 1.32024 0.762242i 0.336475 0.941692i 0.390765π-0.390765\pi
0.983767 + 0.179450i 0.0574318π0.0574318\pi
978978 −3.28262 0.879575i −0.104967 0.0281257i
979979 0.696362 1.20613i 0.0222558 0.0385482i
980980 7.65731 0.230442i 0.244604 0.00736121i
981981 33.2013 8.89627i 1.06004 0.284036i
982982 32.9657 57.0983i 1.05198 1.82208i
983983 7.39039i 0.235717i 0.993030 + 0.117858i 0.0376029π0.0376029\pi
−0.993030 + 0.117858i 0.962397π0.962397\pi
984984 1.44233 + 0.832728i 0.0459797 + 0.0265464i
985985 −10.8656 + 6.71696i −0.346207 + 0.214020i
986986 −11.2711 3.02008i −0.358945 0.0961789i
987987 −0.699200 + 0.699200i −0.0222558 + 0.0222558i
988988 0 0
989989 25.1641i 0.800171i
990990 −1.56399 0.369026i −0.0497068 0.0117284i
991991 −10.0052 17.3296i −0.317827 0.550493i 0.662207 0.749321i 0.269620π-0.269620\pi
−0.980034 + 0.198828i 0.936287π0.936287\pi
992992 −6.84035 25.5285i −0.217181 0.810531i
993993 −3.58541 −0.113780
994994 −3.51688 13.1252i −0.111549 0.416306i
995995 −9.85458 + 18.3201i −0.312411 + 0.580787i
996996 −0.957877 + 0.957877i −0.0303515 + 0.0303515i
997997 −32.6705 + 8.75402i −1.03468 + 0.277243i −0.735909 0.677081i 0.763245π-0.763245\pi
−0.298775 + 0.954324i 0.596578π0.596578\pi
998998 −4.82403 + 18.0035i −0.152702 + 0.569892i
999999 −2.07198 + 7.73273i −0.0655545 + 0.244653i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 845.2.t.g.427.2 20
5.3 odd 4 845.2.o.g.258.4 20
13.2 odd 12 845.2.k.d.577.4 20
13.3 even 3 845.2.f.d.437.4 20
13.4 even 6 845.2.t.f.657.2 20
13.5 odd 4 845.2.o.f.587.4 20
13.6 odd 12 845.2.o.g.357.4 20
13.7 odd 12 65.2.o.a.32.2 20
13.8 odd 4 845.2.o.e.587.2 20
13.9 even 3 845.2.t.e.657.4 20
13.10 even 6 845.2.f.e.437.7 20
13.11 odd 12 845.2.k.e.577.7 20
13.12 even 2 65.2.t.a.37.4 yes 20
39.20 even 12 585.2.cf.a.487.4 20
39.38 odd 2 585.2.dp.a.37.2 20
65.3 odd 12 845.2.k.d.268.4 20
65.7 even 12 325.2.x.b.318.2 20
65.8 even 4 845.2.t.f.418.2 20
65.12 odd 4 325.2.s.b.193.4 20
65.18 even 4 845.2.t.e.418.4 20
65.23 odd 12 845.2.k.e.268.7 20
65.28 even 12 845.2.f.d.408.7 20
65.33 even 12 65.2.t.a.58.4 yes 20
65.38 odd 4 65.2.o.a.63.2 yes 20
65.43 odd 12 845.2.o.e.488.2 20
65.48 odd 12 845.2.o.f.488.4 20
65.58 even 12 inner 845.2.t.g.188.2 20
65.59 odd 12 325.2.s.b.32.4 20
65.63 even 12 845.2.f.e.408.4 20
65.64 even 2 325.2.x.b.232.2 20
195.38 even 4 585.2.cf.a.388.4 20
195.98 odd 12 585.2.dp.a.253.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.32.2 20 13.7 odd 12
65.2.o.a.63.2 yes 20 65.38 odd 4
65.2.t.a.37.4 yes 20 13.12 even 2
65.2.t.a.58.4 yes 20 65.33 even 12
325.2.s.b.32.4 20 65.59 odd 12
325.2.s.b.193.4 20 65.12 odd 4
325.2.x.b.232.2 20 65.64 even 2
325.2.x.b.318.2 20 65.7 even 12
585.2.cf.a.388.4 20 195.38 even 4
585.2.cf.a.487.4 20 39.20 even 12
585.2.dp.a.37.2 20 39.38 odd 2
585.2.dp.a.253.2 20 195.98 odd 12
845.2.f.d.408.7 20 65.28 even 12
845.2.f.d.437.4 20 13.3 even 3
845.2.f.e.408.4 20 65.63 even 12
845.2.f.e.437.7 20 13.10 even 6
845.2.k.d.268.4 20 65.3 odd 12
845.2.k.d.577.4 20 13.2 odd 12
845.2.k.e.268.7 20 65.23 odd 12
845.2.k.e.577.7 20 13.11 odd 12
845.2.o.e.488.2 20 65.43 odd 12
845.2.o.e.587.2 20 13.8 odd 4
845.2.o.f.488.4 20 65.48 odd 12
845.2.o.f.587.4 20 13.5 odd 4
845.2.o.g.258.4 20 5.3 odd 4
845.2.o.g.357.4 20 13.6 odd 12
845.2.t.e.418.4 20 65.18 even 4
845.2.t.e.657.4 20 13.9 even 3
845.2.t.f.418.2 20 65.8 even 4
845.2.t.f.657.2 20 13.4 even 6
845.2.t.g.188.2 20 65.58 even 12 inner
845.2.t.g.427.2 20 1.1 even 1 trivial