Properties

Label 117.2.x.a.2.5
Level 117117
Weight 22
Character 117.2
Analytic conductor 0.9340.934
Analytic rank 00
Dimension 4848
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [117,2,Mod(2,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 117=3213 117 = 3^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 117.x (of order 1212, degree 44, 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: 0.9342497036490.934249703649
Analytic rank: 00
Dimension: 4848
Relative dimension: 1212 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 2.5
Character χ\chi == 117.2
Dual form 117.2.x.a.59.5

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+(0.7540090.754009i)q2+(0.8613741.50268i)q30.862941iq4+(0.5954262.22216i)q5+(1.78251+0.483547i)q6+(1.34030+5.00206i)q7+(2.15868+2.15868i)q8+(1.516072.58873i)q9+(2.12448+1.22657i)q10+(1.936711.93671i)q11+(1.296720.743315i)q12+(3.421681.13671i)q13+(4.782202.76100i)q14+(2.826302.80884i)q15+1.52945q16+(0.07162420.124057i)q17+(0.808798+3.09506i)q18+(0.552200+2.06084i)q19+(1.917590.513817i)q20+(6.36198+6.32269i)q212.92060q22+(0.4218080.730594i)q23+(1.38437+5.10323i)q24+(0.2533290.146260i)q25+(3.437071.72289i)q26+(5.19593+0.0482913i)q27+(4.31649+1.15660i)q28+0.605036iq29+(0.0131630+4.24895i)q30+(3.38018+0.905716i)q31+(3.16415+3.16415i)q32+(1.242024.57849i)q33+(0.147545+0.0395346i)q34+(10.3173+5.95671i)q35+(2.23392+1.30828i)q36+(0.9730463.63146i)q37+(1.137531.97025i)q38+(1.239246.12081i)q39+(3.51160+6.08227i)q40+(7.55452+2.02423i)q41+(0.02962989.56435i)q42+(0.1875670.108292i)q43+(1.671271.67127i)q44+(6.65528+1.82755i)q45+(0.868921+0.232827i)q46+(2.72952+10.1867i)q47+(1.317432.29827i)q48+(17.16219.90853i)q49+(0.0807314+0.301294i)q50+(0.1247220.214487i)q51+(0.9809142.95271i)q52+8.00631iq53+(3.95419+3.88136i)q54+(3.150525.45686i)q55+(7.9045913.6912i)q56+(3.57242+0.945376i)q57+(0.4562030.456203i)q58+(5.265325.26532i)q59+(2.42386+2.43893i)q60+(0.675442+1.16990i)q61+(1.865773.23160i)q62+(14.98104.11380i)q637.83049iq64+(0.4885968.28034i)q65+(2.51573+4.38871i)q66+(1.98346+7.40238i)q67+(0.1070540.0618075i)q68+(0.7345101.26316i)q69+(3.2879412.2708i)q70+(7.04646+1.88809i)q71+(8.86096+2.31554i)q72+(3.767363.76736i)q73+(3.47184+2.00447i)q74+(0.437992+0.254687i)q75+(1.778380.476516i)q76+(7.09179+12.2833i)q77+(5.54954+3.68075i)q78+(1.626412.81703i)q79+(0.9106743.39868i)q80+(4.40307+7.84939i)q81+(7.22246+4.16989i)q82+(14.7099+3.94150i)q83+(5.456105.49002i)q84+(0.2330270.233027i)q85+(0.2230810.0597743i)q86+(0.909174+0.521163i)q87+8.36151iq88+(14.24313.81643i)q89+(6.39613+3.64015i)q90+(1.09983+18.6390i)q91+(0.6304590.363996i)q92+(4.272604.29915i)q93+(5.622799.73895i)q94+4.90830q95+(7.480202.02917i)q96+(0.525725+0.140868i)q97+(5.46924+20.4115i)q98+(7.949832.07744i)q99+O(q100)q+(-0.754009 - 0.754009i) q^{2} +(0.861374 - 1.50268i) q^{3} -0.862941i q^{4} +(0.595426 - 2.22216i) q^{5} +(-1.78251 + 0.483547i) q^{6} +(-1.34030 + 5.00206i) q^{7} +(-2.15868 + 2.15868i) q^{8} +(-1.51607 - 2.58873i) q^{9} +(-2.12448 + 1.22657i) q^{10} +(1.93671 - 1.93671i) q^{11} +(-1.29672 - 0.743315i) q^{12} +(3.42168 - 1.13671i) q^{13} +(4.78220 - 2.76100i) q^{14} +(-2.82630 - 2.80884i) q^{15} +1.52945 q^{16} +(0.0716242 - 0.124057i) q^{17} +(-0.808798 + 3.09506i) q^{18} +(0.552200 + 2.06084i) q^{19} +(-1.91759 - 0.513817i) q^{20} +(6.36198 + 6.32269i) q^{21} -2.92060 q^{22} +(0.421808 - 0.730594i) q^{23} +(1.38437 + 5.10323i) q^{24} +(-0.253329 - 0.146260i) q^{25} +(-3.43707 - 1.72289i) q^{26} +(-5.19593 + 0.0482913i) q^{27} +(4.31649 + 1.15660i) q^{28} +0.605036i q^{29} +(0.0131630 + 4.24895i) q^{30} +(3.38018 + 0.905716i) q^{31} +(3.16415 + 3.16415i) q^{32} +(-1.24202 - 4.57849i) q^{33} +(-0.147545 + 0.0395346i) q^{34} +(10.3173 + 5.95671i) q^{35} +(-2.23392 + 1.30828i) q^{36} +(0.973046 - 3.63146i) q^{37} +(1.13753 - 1.97025i) q^{38} +(1.23924 - 6.12081i) q^{39} +(3.51160 + 6.08227i) q^{40} +(-7.55452 + 2.02423i) q^{41} +(-0.0296298 - 9.56435i) q^{42} +(0.187567 - 0.108292i) q^{43} +(-1.67127 - 1.67127i) q^{44} +(-6.65528 + 1.82755i) q^{45} +(-0.868921 + 0.232827i) q^{46} +(2.72952 + 10.1867i) q^{47} +(1.31743 - 2.29827i) q^{48} +(-17.1621 - 9.90853i) q^{49} +(0.0807314 + 0.301294i) q^{50} +(-0.124722 - 0.214487i) q^{51} +(-0.980914 - 2.95271i) q^{52} +8.00631i q^{53} +(3.95419 + 3.88136i) q^{54} +(-3.15052 - 5.45686i) q^{55} +(-7.90459 - 13.6912i) q^{56} +(3.57242 + 0.945376i) q^{57} +(0.456203 - 0.456203i) q^{58} +(5.26532 - 5.26532i) q^{59} +(-2.42386 + 2.43893i) q^{60} +(0.675442 + 1.16990i) q^{61} +(-1.86577 - 3.23160i) q^{62} +(14.9810 - 4.11380i) q^{63} -7.83049i q^{64} +(-0.488596 - 8.28034i) q^{65} +(-2.51573 + 4.38871i) q^{66} +(1.98346 + 7.40238i) q^{67} +(-0.107054 - 0.0618075i) q^{68} +(-0.734510 - 1.26316i) q^{69} +(-3.28794 - 12.2708i) q^{70} +(-7.04646 + 1.88809i) q^{71} +(8.86096 + 2.31554i) q^{72} +(-3.76736 - 3.76736i) q^{73} +(-3.47184 + 2.00447i) q^{74} +(-0.437992 + 0.254687i) q^{75} +(1.77838 - 0.476516i) q^{76} +(7.09179 + 12.2833i) q^{77} +(-5.54954 + 3.68075i) q^{78} +(1.62641 - 2.81703i) q^{79} +(0.910674 - 3.39868i) q^{80} +(-4.40307 + 7.84939i) q^{81} +(7.22246 + 4.16989i) q^{82} +(-14.7099 + 3.94150i) q^{83} +(5.45610 - 5.49002i) q^{84} +(-0.233027 - 0.233027i) q^{85} +(-0.223081 - 0.0597743i) q^{86} +(0.909174 + 0.521163i) q^{87} +8.36151i q^{88} +(-14.2431 - 3.81643i) q^{89} +(6.39613 + 3.64015i) q^{90} +(1.09983 + 18.6390i) q^{91} +(-0.630459 - 0.363996i) q^{92} +(4.27260 - 4.29915i) q^{93} +(5.62279 - 9.73895i) q^{94} +4.90830 q^{95} +(7.48020 - 2.02917i) q^{96} +(0.525725 + 0.140868i) q^{97} +(5.46924 + 20.4115i) q^{98} +(-7.94983 - 2.07744i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q6q22q36q58q64q7+30q82q912q106q11+18q122q1312q1426q1528q1614q184q1918q208q21+8q99+O(q100) 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/117Z)×\left(\mathbb{Z}/117\mathbb{Z}\right)^\times.

nn 2828 9292
χ(n)\chi(n) e(112)e\left(\frac{1}{12}\right) e(16)e\left(\frac{1}{6}\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 −0.754009 0.754009i −0.533165 0.533165i 0.388348 0.921513i 0.373046π-0.373046\pi
−0.921513 + 0.388348i 0.873046π0.873046\pi
33 0.861374 1.50268i 0.497315 0.867570i
44 0.862941i 0.431471i
55 0.595426 2.22216i 0.266282 0.993779i −0.695178 0.718837i 0.744675π-0.744675\pi
0.961461 0.274942i 0.0886587π-0.0886587\pi
66 −1.78251 + 0.483547i −0.727709 + 0.197407i
77 −1.34030 + 5.00206i −0.506585 + 1.89060i −0.0547531 + 0.998500i 0.517437π0.517437\pi
−0.451832 + 0.892103i 0.649229π0.649229\pi
88 −2.15868 + 2.15868i −0.763210 + 0.763210i
99 −1.51607 2.58873i −0.505356 0.862911i
1010 −2.12448 + 1.22657i −0.671821 + 0.387876i
1111 1.93671 1.93671i 0.583941 0.583941i −0.352043 0.935984i 0.614513π-0.614513\pi
0.935984 + 0.352043i 0.114513π0.114513\pi
1212 −1.29672 0.743315i −0.374331 0.214577i
1313 3.42168 1.13671i 0.949003 0.315267i
1414 4.78220 2.76100i 1.27810 0.737909i
1515 −2.82630 2.80884i −0.729747 0.725240i
1616 1.52945 0.382363
1717 0.0716242 0.124057i 0.0173714 0.0300882i −0.857209 0.514969i 0.827804π-0.827804\pi
0.874580 + 0.484880i 0.161137π0.161137\pi
1818 −0.808798 + 3.09506i −0.190636 + 0.729512i
1919 0.552200 + 2.06084i 0.126683 + 0.472789i 0.999894 0.0145541i 0.00463288π-0.00463288\pi
−0.873211 + 0.487343i 0.837966π0.837966\pi
2020 −1.91759 0.513817i −0.428787 0.114893i
2121 6.36198 + 6.32269i 1.38830 + 1.37972i
2222 −2.92060 −0.622674
2323 0.421808 0.730594i 0.0879531 0.152339i −0.818693 0.574232i 0.805301π-0.805301\pi
0.906646 + 0.421893i 0.138634π0.138634\pi
2424 1.38437 + 5.10323i 0.282583 + 1.04169i
2525 −0.253329 0.146260i −0.0506658 0.0292519i
2626 −3.43707 1.72289i −0.674064 0.337886i
2727 −5.19593 + 0.0482913i −0.999957 + 0.00929366i
2828 4.31649 + 1.15660i 0.815739 + 0.218577i
2929 0.605036i 0.112352i 0.998421 + 0.0561762i 0.0178909π0.0178909\pi
−0.998421 + 0.0561762i 0.982109π0.982109\pi
3030 0.0131630 + 4.24895i 0.00240322 + 0.775748i
3131 3.38018 + 0.905716i 0.607098 + 0.162671i 0.549256 0.835654i 0.314911π-0.314911\pi
0.0578423 + 0.998326i 0.481578π0.481578\pi
3232 3.16415 + 3.16415i 0.559347 + 0.559347i
3333 −1.24202 4.57849i −0.216208 0.797013i
3434 −0.147545 + 0.0395346i −0.0253038 + 0.00678013i
3535 10.3173 + 5.95671i 1.74395 + 1.00687i
3636 −2.23392 + 1.30828i −0.372321 + 0.218046i
3737 0.973046 3.63146i 0.159968 0.597008i −0.838661 0.544654i 0.816661π-0.816661\pi
0.998629 0.0523539i 0.0166724π-0.0166724\pi
3838 1.13753 1.97025i 0.184531 0.319617i
3939 1.23924 6.12081i 0.198437 0.980114i
4040 3.51160 + 6.08227i 0.555233 + 0.961691i
4141 −7.55452 + 2.02423i −1.17982 + 0.316131i −0.794854 0.606801i 0.792453π-0.792453\pi
−0.384963 + 0.922932i 0.625786π0.625786\pi
4242 −0.0296298 9.56435i −0.00457198 1.47581i
4343 0.187567 0.108292i 0.0286038 0.0165144i −0.485630 0.874164i 0.661410π-0.661410\pi
0.514234 + 0.857650i 0.328076π0.328076\pi
4444 −1.67127 1.67127i −0.251953 0.251953i
4545 −6.65528 + 1.82755i −0.992111 + 0.272435i
4646 −0.868921 + 0.232827i −0.128115 + 0.0343284i
4747 2.72952 + 10.1867i 0.398141 + 1.48588i 0.816363 + 0.577539i 0.195987π0.195987\pi
−0.418222 + 0.908345i 0.637347π0.637347\pi
4848 1.31743 2.29827i 0.190155 0.331726i
4949 −17.1621 9.90853i −2.45172 1.41550i
5050 0.0807314 + 0.301294i 0.0114171 + 0.0426093i
5151 −0.124722 0.214487i −0.0174645 0.0300342i
5252 −0.980914 2.95271i −0.136028 0.409467i
5353 8.00631i 1.09975i 0.835246 + 0.549876i 0.185325π0.185325\pi
−0.835246 + 0.549876i 0.814675π0.814675\pi
5454 3.95419 + 3.88136i 0.538097 + 0.528187i
5555 −3.15052 5.45686i −0.424816 0.735802i
5656 −7.90459 13.6912i −1.05630 1.82956i
5757 3.57242 + 0.945376i 0.473179 + 0.125218i
5858 0.456203 0.456203i 0.0599024 0.0599024i
5959 5.26532 5.26532i 0.685487 0.685487i −0.275744 0.961231i 0.588924π-0.588924\pi
0.961231 + 0.275744i 0.0889243π0.0889243\pi
6060 −2.42386 + 2.43893i −0.312920 + 0.314864i
6161 0.675442 + 1.16990i 0.0864815 + 0.149790i 0.906022 0.423232i 0.139104π-0.139104\pi
−0.819540 + 0.573022i 0.805771π0.805771\pi
6262 −1.86577 3.23160i −0.236953 0.410414i
6363 14.9810 4.11380i 1.88743 0.518290i
6464 7.83049i 0.978811i
6565 −0.488596 8.28034i −0.0606028 1.02705i
6666 −2.51573 + 4.38871i −0.309665 + 0.540213i
6767 1.98346 + 7.40238i 0.242318 + 0.904345i 0.974712 + 0.223464i 0.0717364π0.0717364\pi
−0.732394 + 0.680881i 0.761597π0.761597\pi
6868 −0.107054 0.0618075i −0.0129822 0.00749526i
6969 −0.734510 1.26316i −0.0884246 0.152066i
7070 −3.28794 12.2708i −0.392985 1.46664i
7171 −7.04646 + 1.88809i −0.836261 + 0.224075i −0.651443 0.758697i 0.725836π-0.725836\pi
−0.184818 + 0.982773i 0.559169π0.559169\pi
7272 8.86096 + 2.31554i 1.04427 + 0.272889i
7373 −3.76736 3.76736i −0.440936 0.440936i 0.451391 0.892326i 0.350928π-0.350928\pi
−0.892326 + 0.451391i 0.850928π0.850928\pi
7474 −3.47184 + 2.00447i −0.403593 + 0.233014i
7575 −0.437992 + 0.254687i −0.0505750 + 0.0294088i
7676 1.77838 0.476516i 0.203994 0.0546601i
7777 7.09179 + 12.2833i 0.808185 + 1.39982i
7878 −5.54954 + 3.68075i −0.628362 + 0.416762i
7979 1.62641 2.81703i 0.182986 0.316941i −0.759910 0.650028i 0.774757π-0.774757\pi
0.942896 + 0.333087i 0.108090π0.108090\pi
8080 0.910674 3.39868i 0.101816 0.379984i
8181 −4.40307 + 7.84939i −0.489230 + 0.872155i
8282 7.22246 + 4.16989i 0.797587 + 0.460487i
8383 −14.7099 + 3.94150i −1.61462 + 0.432636i −0.949415 0.314025i 0.898323π-0.898323\pi
−0.665205 + 0.746661i 0.731656π0.731656\pi
8484 5.45610 5.49002i 0.595310 0.599010i
8585 −0.233027 0.233027i −0.0252753 0.0252753i
8686 −0.223081 0.0597743i −0.0240554 0.00644563i
8787 0.909174 + 0.521163i 0.0974736 + 0.0558745i
8888 8.36151i 0.891340i
8989 −14.2431 3.81643i −1.50977 0.404541i −0.593409 0.804901i 0.702218π-0.702218\pi
−0.916358 + 0.400361i 0.868885π0.868885\pi
9090 6.39613 + 3.64015i 0.674211 + 0.383706i
9191 1.09983 + 18.6390i 0.115293 + 1.95390i
9292 −0.630459 0.363996i −0.0657299 0.0379492i
9393 4.27260 4.29915i 0.443048 0.445801i
9494 5.62279 9.73895i 0.579946 1.00450i
9595 4.90830 0.503581
9696 7.48020 2.02917i 0.763445 0.207101i
9797 0.525725 + 0.140868i 0.0533793 + 0.0143029i 0.285410 0.958406i 0.407870π-0.407870\pi
−0.232031 + 0.972708i 0.574537π0.574537\pi
9898 5.46924 + 20.4115i 0.552476 + 2.06187i
9999 −7.94983 2.07744i −0.798988 0.208791i
100100 −0.126213 + 0.218608i −0.0126213 + 0.0218608i
101101 3.51090 0.349347 0.174674 0.984626i 0.444113π-0.444113\pi
0.174674 + 0.984626i 0.444113π0.444113\pi
102102 −0.0676839 + 0.255767i −0.00670171 + 0.0253247i
103103 0.661851 0.382120i 0.0652141 0.0376514i −0.467038 0.884237i 0.654679π-0.654679\pi
0.532253 + 0.846586i 0.321346π0.321346\pi
104104 −4.93252 + 9.84012i −0.483674 + 0.964903i
105105 17.8381 10.3726i 1.74082 1.01227i
106106 6.03683 6.03683i 0.586349 0.586349i
107107 5.29840 3.05903i 0.512216 0.295728i −0.221528 0.975154i 0.571104π-0.571104\pi
0.733744 + 0.679426i 0.237771π0.237771\pi
108108 0.0416725 + 4.48378i 0.00400994 + 0.431452i
109109 −3.64352 + 3.64352i −0.348986 + 0.348986i −0.859732 0.510746i 0.829369π-0.829369\pi
0.510746 + 0.859732i 0.329369π0.329369\pi
110110 −1.73900 + 6.49004i −0.165807 + 0.618801i
111111 −4.61875 4.59022i −0.438392 0.435684i
112112 −2.04992 + 7.65041i −0.193699 + 0.722896i
113113 9.31035i 0.875844i −0.899013 0.437922i 0.855715π-0.855715\pi
0.899013 0.437922i 0.144285π-0.144285\pi
114114 −1.98082 3.40646i −0.185520 0.319044i
115115 −1.37234 1.37234i −0.127971 0.127971i
116116 0.522111 0.0484768
117117 −8.13014 7.13448i −0.751632 0.659583i
118118 −7.94020 −0.730955
119119 0.524542 + 0.524542i 0.0480847 + 0.0480847i
120120 12.1645 0.0376848i 1.11046 0.00344014i
121121 3.49827i 0.318025i
122122 0.372826 1.39140i 0.0337541 0.125972i
123123 −3.46551 + 13.0956i −0.312475 + 1.18079i
124124 0.781580 2.91690i 0.0701879 0.261945i
125125 7.65781 7.65781i 0.684936 0.684936i
126126 −14.3976 8.19396i −1.28264 0.729976i
127127 0.310458 0.179243i 0.0275487 0.0159052i −0.486162 0.873868i 0.661604π-0.661604\pi
0.513711 + 0.857963i 0.328270π0.328270\pi
128128 0.424033 0.424033i 0.0374796 0.0374796i
129129 −0.00116214 0.375133i −0.000102321 0.0330286i
130130 −5.87504 + 6.61186i −0.515276 + 0.579898i
131131 −10.1169 + 5.84101i −0.883920 + 0.510331i −0.871949 0.489597i 0.837144π-0.837144\pi
−0.0119710 + 0.999928i 0.503811π0.503811\pi
132132 −3.95097 + 1.07179i −0.343888 + 0.0932872i
133133 −11.0486 −0.958032
134134 4.08591 7.07701i 0.352969 0.611361i
135135 −2.98648 + 11.5749i −0.257035 + 0.996211i
136136 0.113185 + 0.422413i 0.00970556 + 0.0362216i
137137 15.1873 + 4.06943i 1.29754 + 0.347675i 0.840520 0.541781i 0.182250π-0.182250\pi
0.457021 + 0.889456i 0.348916π0.348916\pi
138138 −0.398603 + 1.50626i −0.0339314 + 0.128221i
139139 13.7650 1.16753 0.583767 0.811922i 0.301578π-0.301578\pi
0.583767 + 0.811922i 0.301578π0.301578\pi
140140 5.14029 8.90325i 0.434434 0.752462i
141141 17.6585 + 4.67298i 1.48711 + 0.393536i
142142 6.73673 + 3.88945i 0.565334 + 0.326396i
143143 4.42533 8.82830i 0.370065 0.738260i
144144 −2.31875 3.95934i −0.193229 0.329945i
145145 1.34449 + 0.360254i 0.111654 + 0.0299175i
146146 5.68124i 0.470183i
147147 −29.6723 + 17.2541i −2.44733 + 1.42309i
148148 −3.13373 0.839681i −0.257591 0.0690214i
149149 −9.35362 9.35362i −0.766278 0.766278i 0.211171 0.977449i 0.432272π-0.432272\pi
−0.977449 + 0.211171i 0.932272π0.932272\pi
150150 0.522286 + 0.138213i 0.0426445 + 0.0112851i
151151 −11.1072 + 2.97615i −0.903888 + 0.242196i −0.680685 0.732576i 0.738318π-0.738318\pi
−0.223203 + 0.974772i 0.571651π0.571651\pi
152152 −5.64072 3.25667i −0.457523 0.264151i
153153 −0.429737 + 0.00266262i −0.0347422 + 0.000215260i
154154 3.91448 14.6090i 0.315438 1.17723i
155155 4.02529 6.97201i 0.323319 0.560005i
156156 −5.28190 1.06939i −0.422890 0.0856198i
157157 −4.68972 8.12283i −0.374280 0.648272i 0.615939 0.787794i 0.288777π-0.288777\pi
−0.990219 + 0.139522i 0.955443π0.955443\pi
158158 −3.35040 + 0.897737i −0.266543 + 0.0714201i
159159 12.0309 + 6.89643i 0.954112 + 0.546923i
160160 8.91525 5.14722i 0.704812 0.406924i
161161 3.08913 + 3.08913i 0.243457 + 0.243457i
162162 9.23847 2.59855i 0.725843 0.204162i
163163 −14.3617 + 3.84819i −1.12489 + 0.301414i −0.772861 0.634575i 0.781175π-0.781175\pi
−0.352030 + 0.935989i 0.614508π0.614508\pi
164164 1.74679 + 6.51910i 0.136401 + 0.509056i
165165 −10.9137 + 0.0338099i −0.849627 + 0.00263209i
166166 14.0633 + 8.11946i 1.09152 + 0.630192i
167167 −0.558665 2.08497i −0.0432308 0.161339i 0.940936 0.338585i 0.109948π-0.109948\pi
−0.984167 + 0.177245i 0.943281π0.943281\pi
168168 −27.3822 + 0.0848284i −2.11258 + 0.00654465i
169169 10.4158 7.77892i 0.801214 0.598378i
170170 0.351409i 0.0269518i
171171 4.49779 4.55387i 0.343954 0.348243i
172172 −0.0934497 0.161860i −0.00712547 0.0123417i
173173 6.04205 + 10.4651i 0.459369 + 0.795650i 0.998928 0.0462976i 0.0147423π-0.0147423\pi
−0.539559 + 0.841948i 0.681409π0.681409\pi
174174 −0.292564 1.07849i −0.0221792 0.0817598i
175175 1.07114 1.07114i 0.0809704 0.0809704i
176176 2.96211 2.96211i 0.223277 0.223277i
177177 −3.37666 12.4475i −0.253805 0.935610i
178178 7.86181 + 13.6171i 0.589267 + 1.02064i
179179 −1.54606 2.67786i −0.115558 0.200152i 0.802445 0.596727i 0.203532π-0.203532\pi
−0.918003 + 0.396574i 0.870199π0.870199\pi
180180 1.57706 + 5.74311i 0.117547 + 0.428066i
181181 20.3888i 1.51549i −0.652550 0.757745i 0.726301π-0.726301\pi
0.652550 0.757745i 0.273699π-0.273699\pi
182182 13.2247 14.8832i 0.980279 1.10322i
183183 2.33979 0.00724853i 0.172962 0.000535827i
184184 0.666569 + 2.48767i 0.0491401 + 0.183394i
185185 −7.49030 4.32453i −0.550698 0.317945i
186186 −6.46318 + 0.0200225i −0.473903 + 0.00146812i
187187 −0.101547 0.378978i −0.00742584 0.0277136i
188188 8.79053 2.35541i 0.641115 0.171786i
189189 6.72254 26.0551i 0.488993 1.89523i
190190 −3.70090 3.70090i −0.268492 0.268492i
191191 8.18928 4.72808i 0.592555 0.342112i −0.173552 0.984825i 0.555524π-0.555524\pi
0.766107 + 0.642713i 0.222191π0.222191\pi
192192 −11.7667 6.74498i −0.849188 0.486777i
193193 0.383474 0.102752i 0.0276031 0.00739622i −0.244991 0.969525i 0.578785π-0.578785\pi
0.272594 + 0.962129i 0.412118π0.412118\pi
194194 −0.290186 0.502617i −0.0208341 0.0360858i
195195 −12.8635 6.39827i −0.921176 0.458190i
196196 −8.55047 + 14.8099i −0.610748 + 1.05785i
197197 0.713601 2.66320i 0.0508420 0.189745i −0.935834 0.352440i 0.885352π-0.885352\pi
0.986676 + 0.162695i 0.0520187π0.0520187\pi
198198 4.42783 + 7.56065i 0.314672 + 0.537312i
199199 13.4785 + 7.78181i 0.955465 + 0.551638i 0.894774 0.446519i 0.147336π-0.147336\pi
0.0606908 + 0.998157i 0.480670π0.480670\pi
200200 0.862586 0.231129i 0.0609940 0.0163433i
201201 12.8319 + 3.39572i 0.905091 + 0.239516i
202202 −2.64725 2.64725i −0.186260 0.186260i
203203 −3.02643 0.810930i −0.212414 0.0569161i
204204 −0.185090 + 0.107628i −0.0129589 + 0.00753544i
205205 17.9926i 1.25666i
206206 −0.787163 0.210920i −0.0548443 0.0146955i
207207 −2.53080 + 0.0156807i −0.175903 + 0.00108988i
208208 5.23329 1.73854i 0.362863 0.120546i
209209 5.06071 + 2.92180i 0.350057 + 0.202105i
210210 −21.2711 5.62902i −1.46785 0.388439i
211211 −4.61191 + 7.98807i −0.317497 + 0.549921i −0.979965 0.199169i 0.936176π-0.936176\pi
0.662468 + 0.749090i 0.269509π0.269509\pi
212212 6.90898 0.474510
213213 −3.23245 + 12.2149i −0.221484 + 0.836951i
214214 −6.30158 1.68850i −0.430767 0.115424i
215215 −0.128960 0.481284i −0.00879498 0.0328233i
216216 11.1121 11.3206i 0.756084 0.770270i
217217 −9.06090 + 15.6939i −0.615094 + 1.06537i
218218 5.49449 0.372134
219219 −8.90622 + 2.41601i −0.601827 + 0.163259i
220220 −4.70894 + 2.71871i −0.317477 + 0.183295i
221221 0.104058 0.505898i 0.00699973 0.0340304i
222222 0.0215110 + 6.94364i 0.00144372 + 0.466027i
223223 1.36740 1.36740i 0.0915676 0.0915676i −0.659839 0.751407i 0.729376π-0.729376\pi
0.751407 + 0.659839i 0.229376π0.229376\pi
224224 −20.0682 + 11.5864i −1.34086 + 0.774146i
225225 0.00543719 + 0.877541i 0.000362480 + 0.0585027i
226226 −7.02009 + 7.02009i −0.466969 + 0.466969i
227227 4.96201 18.5185i 0.329340 1.22912i −0.580536 0.814235i 0.697157π-0.697157\pi
0.909876 0.414880i 0.136177π-0.136177\pi
228228 0.815804 3.08279i 0.0540279 0.204163i
229229 4.89219 18.2579i 0.323285 1.20652i −0.592739 0.805394i 0.701954π-0.701954\pi
0.916025 0.401122i 0.131380π-0.131380\pi
230230 2.06951i 0.136460i
231231 24.5666 0.0761058i 1.61636 0.00500739i
232232 −1.30608 1.30608i −0.0857485 0.0857485i
233233 −15.0092 −0.983286 −0.491643 0.870797i 0.663603π-0.663603\pi
−0.491643 + 0.870797i 0.663603π0.663603\pi
234234 0.750735 + 11.5097i 0.0490771 + 0.752410i
235235 24.2617 1.58266
236236 −4.54366 4.54366i −0.295767 0.295767i
237237 −2.83213 4.87049i −0.183967 0.316373i
238238 0.791019i 0.0512741i
239239 1.78174 6.64956i 0.115251 0.430124i −0.884054 0.467384i 0.845196π-0.845196\pi
0.999306 + 0.0372603i 0.0118631π0.0118631\pi
240240 −4.32268 4.29598i −0.279028 0.277305i
241241 0.264008 0.985292i 0.0170063 0.0634683i −0.956901 0.290413i 0.906207π-0.906207\pi
0.973908 + 0.226945i 0.0728738π0.0728738\pi
242242 2.63773 2.63773i 0.169560 0.169560i
243243 8.00240 + 13.3777i 0.513354 + 0.858177i
244244 1.00956 0.582867i 0.0646301 0.0373142i
245245 −32.2371 + 32.2371i −2.05955 + 2.05955i
246246 12.4872 7.26118i 0.796157 0.462956i
247247 4.23203 + 6.42384i 0.269277 + 0.408739i
248248 −9.25189 + 5.34158i −0.587496 + 0.339191i
249249 −6.74792 + 25.4993i −0.427632 + 1.61595i
250250 −11.5481 −0.730367
251251 14.6482 25.3714i 0.924586 1.60143i 0.132359 0.991202i 0.457745π-0.457745\pi
0.792226 0.610228i 0.208922π-0.208922\pi
252252 −3.54996 12.9277i −0.223627 0.814369i
253253 −0.598029 2.23187i −0.0375977 0.140317i
254254 −0.369239 0.0989372i −0.0231681 0.00620787i
255255 −0.550887 + 0.149440i −0.0344979 + 0.00935832i
256256 −16.3004 −1.01878
257257 −9.09224 + 15.7482i −0.567159 + 0.982347i 0.429687 + 0.902978i 0.358624π0.358624\pi
−0.996845 + 0.0793694i 0.974709π0.974709\pi
258258 −0.281977 + 0.283730i −0.0175551 + 0.0176642i
259259 16.8606 + 9.73448i 1.04767 + 0.604871i
260260 −7.14545 + 0.421629i −0.443142 + 0.0261483i
261261 1.56628 0.917277i 0.0969501 0.0567780i
262262 12.0324 + 3.22408i 0.743366 + 0.199184i
263263 19.5534i 1.20572i 0.797848 + 0.602858i 0.205971π0.205971\pi
−0.797848 + 0.602858i 0.794029π0.794029\pi
264264 12.5646 + 7.20239i 0.773300 + 0.443276i
265265 17.7913 + 4.76716i 1.09291 + 0.292845i
266266 8.33071 + 8.33071i 0.510789 + 0.510789i
267267 −18.0035 + 18.1154i −1.10180 + 1.10864i
268268 6.38782 1.71161i 0.390198 0.104553i
269269 23.9955 + 13.8538i 1.46303 + 0.844683i 0.999150 0.0412138i 0.0131225π-0.0131225\pi
0.463883 + 0.885896i 0.346456π0.346456\pi
270270 10.9794 6.47577i 0.668187 0.394103i
271271 2.16310 8.07278i 0.131399 0.490387i −0.868588 0.495535i 0.834972π-0.834972\pi
0.999987 + 0.00514827i 0.00163875π0.00163875\pi
272272 0.109546 0.189739i 0.00664218 0.0115046i
273273 28.9557 + 14.4025i 1.75248 + 0.871677i
274274 −8.38299 14.5198i −0.506435 0.877171i
275275 −0.773889 + 0.207363i −0.0466673 + 0.0125045i
276276 −1.09003 + 0.633839i −0.0656120 + 0.0381526i
277277 13.6565 7.88460i 0.820541 0.473740i −0.0300620 0.999548i 0.509570π-0.509570\pi
0.850603 + 0.525808i 0.176237π0.176237\pi
278278 −10.3789 10.3789i −0.622488 0.622488i
279279 −2.77993 10.1235i −0.166430 0.606079i
280280 −35.1305 + 9.41319i −2.09945 + 0.562546i
281281 3.53952 + 13.2097i 0.211150 + 0.788022i 0.987486 + 0.157704i 0.0504091π0.0504091\pi
−0.776337 + 0.630319i 0.782924π0.782924\pi
282282 −9.79116 16.8381i −0.583055 1.00269i
283283 −11.6559 6.72951i −0.692869 0.400028i 0.111817 0.993729i 0.464333π-0.464333\pi
−0.804686 + 0.593701i 0.797666π0.797666\pi
284284 1.62931 + 6.08068i 0.0966820 + 0.360822i
285285 4.22789 7.37559i 0.250438 0.436892i
286286 −9.99336 + 3.31988i −0.590920 + 0.196308i
287287 40.5013i 2.39071i
288288 3.39407 12.9882i 0.199997 0.765337i
289289 8.48974 + 14.7047i 0.499396 + 0.864980i
290290 −0.742120 1.28539i −0.0435788 0.0754807i
291291 0.664525 0.668655i 0.0389551 0.0391972i
292292 −3.25101 + 3.25101i −0.190251 + 0.190251i
293293 5.04007 5.04007i 0.294444 0.294444i −0.544389 0.838833i 0.683238π-0.683238\pi
0.838833 + 0.544389i 0.183238π0.183238\pi
294294 35.3829 + 9.36343i 2.06357 + 0.546086i
295295 −8.56527 14.8355i −0.498689 0.863756i
296296 5.73867 + 9.93966i 0.333553 + 0.577731i
297297 −9.96950 + 10.1566i −0.578489 + 0.589343i
298298 14.1054i 0.817105i
299299 0.612820 2.97933i 0.0354403 0.172299i
300300 0.219780 + 0.377961i 0.0126890 + 0.0218216i
301301 0.290288 + 1.08337i 0.0167319 + 0.0624443i
302302 10.6189 + 6.13085i 0.611051 + 0.352791i
303303 3.02420 5.27574i 0.173736 0.303083i
304304 0.844562 + 3.15195i 0.0484390 + 0.180777i
305305 3.00188 0.804351i 0.171887 0.0460570i
306306 0.326033 + 0.322018i 0.0186381 + 0.0184085i
307307 −8.37481 8.37481i −0.477976 0.477976i 0.426508 0.904484i 0.359744π-0.359744\pi
−0.904484 + 0.426508i 0.859744π0.859744\pi
308308 10.5998 6.11980i 0.603980 0.348708i
309309 −0.00410073 1.32370i −0.000233282 0.0753024i
310310 −8.29206 + 2.22185i −0.470957 + 0.126193i
311311 1.34766 + 2.33421i 0.0764186 + 0.132361i 0.901702 0.432357i 0.142318π-0.142318\pi
−0.825284 + 0.564718i 0.808985π0.808985\pi
312312 10.5378 + 15.8880i 0.596583 + 0.899481i
313313 1.67357 2.89871i 0.0945958 0.163845i −0.814844 0.579680i 0.803177π-0.803177\pi
0.909440 + 0.415836i 0.136511π0.136511\pi
314314 −2.58860 + 9.66077i −0.146083 + 0.545189i
315315 −0.221440 35.7396i −0.0124768 2.01370i
316316 −2.43093 1.40350i −0.136751 0.0789530i
317317 −3.08107 + 0.825569i −0.173050 + 0.0463686i −0.344304 0.938858i 0.611885π-0.611885\pi
0.171254 + 0.985227i 0.445218π0.445218\pi
318318 −3.87143 14.2714i −0.217099 0.800299i
319319 1.17178 + 1.17178i 0.0656072 + 0.0656072i
320320 −17.4006 4.66247i −0.972723 0.260640i
321321 −0.0328281 10.5968i −0.00183229 0.591453i
322322 4.65846i 0.259606i
323323 0.295212 + 0.0791017i 0.0164260 + 0.00440134i
324324 6.77356 + 3.79959i 0.376309 + 0.211088i
325325 −1.03307 0.212492i −0.0573042 0.0117869i
326326 13.7304 + 7.92724i 0.760456 + 0.439049i
327327 2.33659 + 8.61346i 0.129214 + 0.476325i
328328 11.9381 20.6775i 0.659174 1.14172i
329329 −54.6129 −3.01091
330330 8.25449 + 8.20350i 0.454395 + 0.451588i
331331 −29.7907 7.98241i −1.63745 0.438753i −0.681387 0.731923i 0.738623π-0.738623\pi
−0.956060 + 0.293170i 0.905290π0.905290\pi
332332 3.40128 + 12.6938i 0.186670 + 0.696661i
333333 −10.8761 + 2.98658i −0.596005 + 0.163664i
334334 −1.15084 + 1.99332i −0.0629714 + 0.109070i
335335 17.6303 0.963244
336336 9.73034 + 9.67024i 0.530833 + 0.527555i
337337 −4.37979 + 2.52867i −0.238582 + 0.137745i −0.614525 0.788897i 0.710652π-0.710652\pi
0.375943 + 0.926643i 0.377319π0.377319\pi
338338 −13.7190 1.98822i −0.746213 0.108145i
339339 −13.9904 8.01969i −0.759856 0.435570i
340340 −0.201088 + 0.201088i −0.0109056 + 0.0109056i
341341 8.30056 4.79233i 0.449500 0.259519i
342342 −6.82503 + 0.0422875i −0.369055 + 0.00228664i
343343 46.9330 46.9330i 2.53415 2.53415i
344344 −0.171130 + 0.638667i −0.00922672 + 0.0344346i
345345 −3.24428 + 0.880083i −0.174666 + 0.0473821i
346346 3.33505 12.4466i 0.179293 0.669132i
347347 9.93186i 0.533170i 0.963811 + 0.266585i 0.0858954π0.0858954\pi
−0.963811 + 0.266585i 0.914105π0.914105\pi
348348 0.449733 0.784563i 0.0241082 0.0420570i
349349 −16.7774 16.7774i −0.898073 0.898073i 0.0971927 0.995266i 0.469014π-0.469014\pi
−0.995266 + 0.0971927i 0.969014π0.969014\pi
350350 −1.61529 −0.0863411
351351 −17.7239 + 6.07150i −0.946032 + 0.324073i
352352 12.2561 0.653252
353353 −14.8488 14.8488i −0.790322 0.790322i 0.191225 0.981546i 0.438754π-0.438754\pi
−0.981546 + 0.191225i 0.938754π0.938754\pi
354354 −6.83949 + 11.9315i −0.363515 + 0.634155i
355355 16.7826i 0.890726i
356356 −3.29335 + 12.2910i −0.174547 + 0.651420i
357357 1.24004 0.336389i 0.0656301 0.0178036i
358358 −0.853384 + 3.18487i −0.0451027 + 0.168326i
359359 −8.32119 + 8.32119i −0.439175 + 0.439175i −0.891734 0.452559i 0.850511π-0.850511\pi
0.452559 + 0.891734i 0.350511π0.350511\pi
360360 10.4215 18.3117i 0.549264 0.965113i
361361 12.5124 7.22401i 0.658545 0.380211i
362362 −15.3734 + 15.3734i −0.808006 + 0.808006i
363363 5.25677 + 3.01332i 0.275909 + 0.158158i
364364 16.0844 0.949085i 0.843049 0.0497456i
365365 −10.6148 + 6.12849i −0.555607 + 0.320780i
366366 −1.76969 1.75876i −0.0925031 0.0919317i
367367 −5.67060 −0.296003 −0.148001 0.988987i 0.547284π-0.547284\pi
−0.148001 + 0.988987i 0.547284π0.547284\pi
368368 0.645135 1.11741i 0.0336300 0.0582489i
369369 16.6933 + 16.4878i 0.869021 + 0.858318i
370370 2.38702 + 8.90848i 0.124095 + 0.463130i
371371 −40.0481 10.7309i −2.07919 0.557118i
372372 −3.70992 3.68700i −0.192350 0.191162i
373373 −26.9106 −1.39338 −0.696690 0.717373i 0.745345π-0.745345\pi
−0.696690 + 0.717373i 0.745345π0.745345\pi
374374 −0.209186 + 0.362320i −0.0108167 + 0.0187351i
375375 −4.91097 18.1035i −0.253601 0.934858i
376376 −27.8820 16.0977i −1.43791 0.830176i
377377 0.687751 + 2.07024i 0.0354210 + 0.106623i
378378 −24.7146 + 14.5769i −1.27118 + 0.749756i
379379 −26.3773 7.06778i −1.35491 0.363047i −0.492966 0.870049i 0.664087π-0.664087\pi
−0.861945 + 0.507001i 0.830754π0.830754\pi
380380 4.23558i 0.217280i
381381 −0.00192355 0.620913i −9.85465e−5 0.0318103i
382382 −9.73981 2.60977i −0.498332 0.133528i
383383 11.8575 + 11.8575i 0.605891 + 0.605891i 0.941870 0.335978i 0.109067π-0.109067\pi
−0.335978 + 0.941870i 0.609067π0.609067\pi
384384 −0.271933 1.00244i −0.0138770 0.0511553i
385385 31.5182 8.44527i 1.60632 0.430411i
386386 −0.366619 0.211667i −0.0186604 0.0107736i
387387 −0.564704 0.321384i −0.0287055 0.0163368i
388388 0.121560 0.453670i 0.00617130 0.0230316i
389389 0.566623 0.981420i 0.0287289 0.0497600i −0.851303 0.524674i 0.824187π-0.824187\pi
0.880032 + 0.474914i 0.157521π0.157521\pi
390390 4.87486 + 14.5236i 0.246848 + 0.735430i
391391 −0.0604234 0.104656i −0.00305574 0.00529270i
392392 58.4368 15.6581i 2.95151 0.790854i
393393 0.0626830 + 20.2338i 0.00316194 + 1.02066i
394394 −2.54613 + 1.47001i −0.128272 + 0.0740581i
395395 −5.29148 5.29148i −0.266243 0.266243i
396396 −1.79271 + 6.86023i −0.0900872 + 0.344740i
397397 17.9346 4.80557i 0.900114 0.241185i 0.221049 0.975263i 0.429052π-0.429052\pi
0.679065 + 0.734078i 0.262385π0.262385\pi
398398 −4.29535 16.0305i −0.215306 0.803534i
399399 −9.51695 + 16.6024i −0.476443 + 0.831160i
400400 −0.387454 0.223697i −0.0193727 0.0111848i
401401 −4.50864 16.8265i −0.225151 0.840274i −0.982344 0.187083i 0.940097π-0.940097\pi
0.757193 0.653191i 0.226570π-0.226570\pi
402402 −7.11495 12.2358i −0.354861 0.610264i
403403 12.5954 0.743215i 0.627423 0.0370222i
404404 3.02970i 0.150733i
405405 14.8209 + 14.4581i 0.736456 + 0.718426i
406406 1.67051 + 2.89340i 0.0829059 + 0.143597i
407407 −5.14858 8.91761i −0.255206 0.442029i
408408 0.732245 + 0.193775i 0.0362515 + 0.00959330i
409409 21.9023 21.9023i 1.08300 1.08300i 0.0867723 0.996228i 0.472345π-0.472345\pi
0.996228 0.0867723i 0.0276553π-0.0276553\pi
410410 13.5666 13.5666i 0.670006 0.670006i
411411 19.1970 19.3163i 0.946918 0.952804i
412412 −0.329747 0.571138i −0.0162455 0.0281380i
413413 19.2804 + 33.3946i 0.948725 + 1.64324i
414414 1.92007 + 1.89642i 0.0943663 + 0.0932041i
415415 35.0346i 1.71978i
416416 14.4234 + 7.22998i 0.707166 + 0.354479i
417417 11.8568 20.6843i 0.580631 1.01292i
418418 −1.61276 6.01888i −0.0788824 0.294393i
419419 18.5952 + 10.7360i 0.908436 + 0.524486i 0.879928 0.475108i 0.157591π-0.157591\pi
0.0285086 + 0.999594i 0.490924π0.490924\pi
420420 −8.95098 15.3932i −0.436763 0.751112i
421421 6.14101 + 22.9186i 0.299295 + 1.11698i 0.937746 + 0.347321i 0.112908π0.112908\pi
−0.638452 + 0.769662i 0.720425π0.720425\pi
422422 9.50050 2.54565i 0.462477 0.123920i
423423 22.2325 22.5097i 1.08098 1.09446i
424424 −17.2831 17.2831i −0.839341 0.839341i
425425 −0.0362890 + 0.0209515i −0.00176027 + 0.00101630i
426426 11.6474 6.77285i 0.564320 0.328146i
427427 −6.75721 + 1.81059i −0.327004 + 0.0876206i
428428 −2.63977 4.57221i −0.127598 0.221006i
429429 −9.45420 14.2543i −0.456453 0.688205i
430430 −0.265656 + 0.460129i −0.0128111 + 0.0221894i
431431 −6.05706 + 22.6052i −0.291758 + 1.08886i 0.652000 + 0.758219i 0.273930π0.273930\pi
−0.943758 + 0.330637i 0.892736π0.892736\pi
432432 −7.94692 + 0.0738591i −0.382346 + 0.00355355i
433433 −23.0080 13.2837i −1.10569 0.638372i −0.167982 0.985790i 0.553725π-0.553725\pi
−0.937710 + 0.347418i 0.887058π0.887058\pi
434434 18.6654 5.00137i 0.895967 0.240074i
435435 1.69945 1.71001i 0.0814825 0.0819889i
436436 3.14414 + 3.14414i 0.150577 + 0.150577i
437437 1.73856 + 0.465845i 0.0831665 + 0.0222844i
438438 8.53707 + 4.89368i 0.407917 + 0.233829i
439439 0.426976i 0.0203784i −0.999948 0.0101892i 0.996757π-0.996757\pi
0.999948 0.0101892i 0.00324338π-0.00324338\pi
440440 18.5806 + 4.97865i 0.885795 + 0.237348i
441441 0.368349 + 59.4500i 0.0175404 + 2.83095i
442442 −0.459913 + 0.302991i −0.0218758 + 0.0144118i
443443 9.92611 + 5.73084i 0.471604 + 0.272281i 0.716911 0.697165i 0.245555π-0.245555\pi
−0.245307 + 0.969445i 0.578889π0.578889\pi
444444 −3.96109 + 3.98571i −0.187985 + 0.189153i
445445 −16.9614 + 29.3780i −0.804048 + 1.39265i
446446 −2.06206 −0.0976412
447447 −22.1124 + 5.99849i −1.04588 + 0.283719i
448448 39.1686 + 10.4952i 1.85054 + 0.495852i
449449 1.66954 + 6.23079i 0.0787903 + 0.294049i 0.994066 0.108779i 0.0346940π-0.0346940\pi
−0.915276 + 0.402828i 0.868027π0.868027\pi
450450 0.657574 0.665774i 0.0309983 0.0313849i
451451 −10.7106 + 18.5513i −0.504342 + 0.873546i
452452 −8.03428 −0.377901
453453 −5.09523 + 19.2540i −0.239395 + 0.904634i
454454 −17.7045 + 10.2217i −0.830914 + 0.479728i
455455 42.0737 + 8.65415i 1.97244 + 0.405713i
456456 −9.75249 + 5.67096i −0.456702 + 0.265567i
457457 7.68615 7.68615i 0.359543 0.359543i −0.504101 0.863644i 0.668176π-0.668176\pi
0.863644 + 0.504101i 0.168176π0.168176\pi
458458 −17.4554 + 10.0779i −0.815636 + 0.470908i
459459 −0.366163 + 0.648049i −0.0170910 + 0.0302483i
460460 −1.18425 + 1.18425i −0.0552158 + 0.0552158i
461461 −4.40054 + 16.4230i −0.204953 + 0.764896i 0.784510 + 0.620116i 0.212914π0.212914\pi
−0.989464 + 0.144781i 0.953752π0.953752\pi
462462 −18.5808 18.4660i −0.864457 0.859118i
463463 −10.0407 + 37.4724i −0.466630 + 1.74149i 0.184796 + 0.982777i 0.440838π0.440838\pi
−0.651427 + 0.758712i 0.725829π0.725829\pi
464464 0.925373i 0.0429594i
465465 −7.00938 12.0542i −0.325052 0.559001i
466466 11.3171 + 11.3171i 0.524253 + 0.524253i
467467 −37.7239 −1.74566 −0.872828 0.488028i 0.837716π-0.837716\pi
−0.872828 + 0.488028i 0.837716π0.837716\pi
468468 −6.15664 + 7.01583i −0.284591 + 0.324307i
469469 −39.6856 −1.83251
470470 −18.2935 18.2935i −0.843818 0.843818i
471471 −16.2456 + 0.0503278i −0.748557 + 0.00231898i
472472 22.7323i 1.04634i
473473 0.153534 0.572995i 0.00705948 0.0263463i
474474 −1.53694 + 5.80785i −0.0705940 + 0.266763i
475475 0.161529 0.602835i 0.00741147 0.0276600i
476476 0.452649 0.452649i 0.0207471 0.0207471i
477477 20.7262 12.1381i 0.948988 0.555766i
478478 −6.35728 + 3.67037i −0.290775 + 0.167879i
479479 14.7645 14.7645i 0.674607 0.674607i −0.284167 0.958775i 0.591717π-0.591717\pi
0.958775 + 0.284167i 0.0917171π0.0917171\pi
480480 −0.0552376 17.8304i −0.00252124 0.813843i
481481 −0.798464 13.5318i −0.0364068 0.616995i
482482 −0.941984 + 0.543855i −0.0429062 + 0.0247719i
483483 7.30285 1.98106i 0.332291 0.0901414i
484484 3.01880 0.137218
485485 0.626060 1.08437i 0.0284279 0.0492386i
486486 4.05299 16.1207i 0.183848 0.731252i
487487 4.59917 + 17.1643i 0.208408 + 0.777791i 0.988384 + 0.151980i 0.0485650π0.0485650\pi
−0.779975 + 0.625811i 0.784768π0.784768\pi
488488 −3.98351 1.06738i −0.180325 0.0483180i
489489 −6.58817 + 24.8956i −0.297927 + 1.12582i
490490 48.6141 2.19616
491491 7.29594 12.6369i 0.329261 0.570297i −0.653104 0.757268i 0.726534π-0.726534\pi
0.982365 + 0.186971i 0.0598670π0.0598670\pi
492492 11.3007 + 2.99053i 0.509477 + 0.134824i
493493 0.0750588 + 0.0433352i 0.00338048 + 0.00195172i
494494 1.65264 8.03462i 0.0743559 0.361494i
495495 −9.34994 + 16.4288i −0.420249 + 0.738420i
496496 5.16982 + 1.38525i 0.232132 + 0.0621995i
497497 37.7775i 1.69455i
498498 24.3147 14.1387i 1.08957 0.633571i
499499 11.5561 + 3.09645i 0.517323 + 0.138616i 0.508028 0.861341i 0.330375π-0.330375\pi
0.00929473 + 0.999957i 0.497041π0.497041\pi
500500 −6.60824 6.60824i −0.295530 0.295530i
501501 −3.61425 0.956444i −0.161473 0.0427308i
502502 −30.1751 + 8.08540i −1.34678 + 0.360869i
503503 −24.4849 14.1364i −1.09173 0.630310i −0.157693 0.987488i 0.550406π-0.550406\pi
−0.934036 + 0.357178i 0.883739π0.883739\pi
504504 −23.4588 + 41.2196i −1.04494 + 1.83607i
505505 2.09048 7.80177i 0.0930250 0.347174i
506506 −1.23193 + 2.13377i −0.0547661 + 0.0948577i
507507 −2.71731 22.3521i −0.120680 0.992691i
508508 −0.154676 0.267907i −0.00686264 0.0118864i
509509 8.79489 2.35658i 0.389827 0.104454i −0.0585816 0.998283i 0.518658π-0.518658\pi
0.448408 + 0.893829i 0.351991π0.351991\pi
510510 0.528053 + 0.302694i 0.0233826 + 0.0134035i
511511 23.8940 13.7952i 1.05701 0.610263i
512512 11.4426 + 11.4426i 0.505696 + 0.505696i
513513 −2.96871 10.6813i −0.131072 0.471591i
514514 18.7299 5.01867i 0.826142 0.221364i
515515 −0.455048 1.69826i −0.0200518 0.0748344i
516516 −0.323718 + 0.00100286i −0.0142509 + 4.41484e-5i
517517 25.0150 + 14.4424i 1.10016 + 0.635178i
518518 −5.37317 20.0529i −0.236083 0.881075i
519519 20.9302 0.0648405i 0.918733 0.00284618i
520520 18.9294 + 16.8199i 0.830107 + 0.737602i
521521 10.8148i 0.473806i −0.971533 0.236903i 0.923868π-0.923868\pi
0.971533 0.236903i 0.0761324π-0.0761324\pi
522522 −1.87262 0.489352i −0.0819624 0.0214184i
523523 −16.8346 29.1584i −0.736125 1.27501i −0.954228 0.299080i 0.903320π-0.903320\pi
0.218103 0.975926i 0.430013π-0.430013\pi
524524 5.04045 + 8.73031i 0.220193 + 0.381385i
525525 −0.686922 2.53222i −0.0299797 0.110515i
526526 14.7435 14.7435i 0.642845 0.642845i
527527 0.354463 0.354463i 0.0154406 0.0154406i
528528 −1.89960 7.00257i −0.0826697 0.304748i
529529 11.1442 + 19.3022i 0.484528 + 0.839228i
530530 −9.82031 17.0093i −0.426567 0.738836i
531531 −21.6131 5.64792i −0.937929 0.245099i
532532 9.53425i 0.413362i
533533 −23.5482 + 15.5136i −1.01998 + 0.671967i
534534 27.2340 0.0843692i 1.17853 0.00365101i
535535 −3.64285 13.5953i −0.157494 0.587777i
536536 −20.2611 11.6977i −0.875145 0.505265i
537537 −5.35569 + 0.0165916i −0.231115 + 0.000715980i
538538 −7.64694 28.5388i −0.329683 1.23039i
539539 −52.4280 + 14.0480i −2.25823 + 0.605092i
540540 9.98848 + 2.57715i 0.429836 + 0.110903i
541541 19.2044 + 19.2044i 0.825663 + 0.825663i 0.986914 0.161250i 0.0515526π-0.0515526\pi
−0.161250 + 0.986914i 0.551553π0.551553\pi
542542 −7.71794 + 4.45596i −0.331514 + 0.191400i
543543 −30.6378 17.5624i −1.31479 0.753676i
544544 0.619163 0.165904i 0.0265464 0.00711309i
545545 5.92703 + 10.2659i 0.253886 + 0.439744i
546546 −10.9733 32.6925i −0.469613 1.39911i
547547 −12.0347 + 20.8447i −0.514565 + 0.891253i 0.485292 + 0.874352i 0.338713π0.338713\pi
−0.999857 + 0.0169009i 0.994620π0.994620\pi
548548 3.51168 13.1058i 0.150011 0.559850i
549549 2.00454 3.52219i 0.0855518 0.150323i
550550 0.739873 + 0.427166i 0.0315483 + 0.0182144i
551551 −1.24688 + 0.334101i −0.0531190 + 0.0142332i
552552 4.31233 + 1.14118i 0.183545 + 0.0485718i
553553 11.9111 + 11.9111i 0.506511 + 0.506511i
554554 −16.2422 4.35208i −0.690065 0.184902i
555555 −12.9503 + 7.53045i −0.549710 + 0.319650i
556556 11.8784i 0.503756i
557557 25.0352 + 6.70816i 1.06078 + 0.284234i 0.746698 0.665163i 0.231638π-0.231638\pi
0.314078 + 0.949397i 0.398305π0.398305\pi
558558 −5.53713 + 9.72930i −0.234405 + 0.411874i
559559 0.518699 0.583750i 0.0219386 0.0246900i
560560 15.7798 + 9.11050i 0.666820 + 0.384989i
561561 −0.656951 0.173850i −0.0277365 0.00733995i
562562 7.29137 12.6290i 0.307568 0.532723i
563563 16.4516 0.693352 0.346676 0.937985i 0.387310π-0.387310\pi
0.346676 + 0.937985i 0.387310π0.387310\pi
564564 4.03251 15.2382i 0.169799 0.641644i
565565 −20.6891 5.54362i −0.870396 0.233222i
566566 3.71451 + 13.8627i 0.156132 + 0.582694i
567567 −33.3617 32.5450i −1.40106 1.36676i
568568 11.1353 19.2869i 0.467226 0.809259i
569569 14.2291 0.596516 0.298258 0.954485i 0.403594π-0.403594\pi
0.298258 + 0.954485i 0.403594π0.403594\pi
570570 −8.74912 + 2.37339i −0.366460 + 0.0994106i
571571 18.0451 10.4184i 0.755164 0.435994i −0.0723925 0.997376i 0.523063π-0.523063\pi
0.827557 + 0.561382i 0.189730π0.189730\pi
572572 −7.61830 3.81880i −0.318537 0.159672i
573573 −0.0507396 16.3785i −0.00211968 0.684221i
574574 −30.5383 + 30.5383i −1.27464 + 1.27464i
575575 −0.213713 + 0.123387i −0.00891244 + 0.00514560i
576576 −20.2710 + 11.8716i −0.844627 + 0.494648i
577577 −32.0720 + 32.0720i −1.33517 + 1.33517i −0.434505 + 0.900670i 0.643076π0.643076\pi
−0.900670 + 0.434505i 0.856924π0.856924\pi
578578 4.68611 17.4888i 0.194916 0.727438i
579579 0.175913 0.664745i 0.00731068 0.0276259i
580580 0.310878 1.16021i 0.0129085 0.0481752i
581581 78.8626i 3.27177i
582582 −1.00523 + 0.00311414i −0.0416681 + 0.000129085i
583583 15.5059 + 15.5059i 0.642191 + 0.642191i
584584 16.2651 0.673053
585585 −20.6948 + 13.8184i −0.855626 + 0.571321i
586586 −7.60051 −0.313974
587587 11.1721 + 11.1721i 0.461121 + 0.461121i 0.899023 0.437902i 0.144278π-0.144278\pi
−0.437902 + 0.899023i 0.644278π0.644278\pi
588588 14.8893 + 25.6054i 0.614022 + 1.05595i
589589 7.46614i 0.307637i
590590 −4.72780 + 17.6444i −0.194640 + 0.726408i
591591 −3.38724 3.36632i −0.139332 0.138472i
592592 1.48823 5.55414i 0.0611657 0.228274i
593593 25.1695 25.1695i 1.03359 1.03359i 0.0341707 0.999416i 0.489121π-0.489121\pi
0.999416 0.0341707i 0.0108790π-0.0108790\pi
594594 15.1752 0.141039i 0.622647 0.00578692i
595595 1.47794 0.853290i 0.0605897 0.0349815i
596596 −8.07162 + 8.07162i −0.330626 + 0.330626i
597597 23.3036 13.5508i 0.953752 0.554595i
598598 −2.70851 + 1.78437i −0.110759 + 0.0729683i
599599 −1.33423 + 0.770320i −0.0545153 + 0.0314744i −0.527010 0.849859i 0.676687π-0.676687\pi
0.472495 + 0.881334i 0.343354π0.343354\pi
600600 0.395697 1.49528i 0.0161543 0.0610444i
601601 29.3874 1.19874 0.599369 0.800473i 0.295418π-0.295418\pi
0.599369 + 0.800473i 0.295418π0.295418\pi
602602 0.597990 1.03575i 0.0243722 0.0422140i
603603 16.1557 16.3572i 0.657912 0.666115i
604604 2.56825 + 9.58482i 0.104500 + 0.390001i
605605 7.77372 + 2.08296i 0.316047 + 0.0846844i
606606 −6.25823 + 1.69768i −0.254223 + 0.0689637i
607607 −20.8526 −0.846382 −0.423191 0.906041i 0.639090π-0.639090\pi
−0.423191 + 0.906041i 0.639090π0.639090\pi
608608 −4.77355 + 8.26804i −0.193593 + 0.335313i
609609 −3.82546 + 3.84923i −0.155015 + 0.155979i
610610 −2.86993 1.65696i −0.116200 0.0670882i
611611 20.9189 + 31.7530i 0.846287 + 1.28459i
612612 0.00229769 + 0.370838i 9.28785e−5 + 0.0149902i
613613 −21.4484 5.74708i −0.866292 0.232122i −0.201809 0.979425i 0.564682π-0.564682\pi
−0.664484 + 0.747303i 0.731349π0.731349\pi
614614 12.6294i 0.509680i
615615 27.0371 + 15.4984i 1.09024 + 0.624955i
616616 −41.8248 11.2069i −1.68517 0.451540i
617617 8.58385 + 8.58385i 0.345573 + 0.345573i 0.858457 0.512885i 0.171423π-0.171423\pi
−0.512885 + 0.858457i 0.671423π0.671423\pi
618618 −0.994986 + 1.00117i −0.0400242 + 0.0402730i
619619 −5.57125 + 1.49281i −0.223928 + 0.0600012i −0.369038 0.929414i 0.620313π-0.620313\pi
0.145111 + 0.989415i 0.453646π0.453646\pi
620620 −6.01643 3.47359i −0.241626 0.139503i
621621 −2.15640 + 3.81648i −0.0865335 + 0.153150i
622622 0.743870 2.77616i 0.0298265 0.111314i
623623 38.1800 66.1298i 1.52965 2.64943i
624624 1.89536 9.36147i 0.0758749 0.374759i
625625 −13.1885 22.8432i −0.527541 0.913727i
626626 −3.44754 + 0.923765i −0.137791 + 0.0369211i
627627 8.74968 5.08784i 0.349429 0.203189i
628628 −7.00952 + 4.04695i −0.279710 + 0.161491i
629629 −0.380813 0.380813i −0.0151840 0.0151840i
630630 −26.7810 + 27.1149i −1.06698 + 1.08029i
631631 −0.701230 + 0.187894i −0.0279155 + 0.00747994i −0.272750 0.962085i 0.587933π-0.587933\pi
0.244834 + 0.969565i 0.421266π0.421266\pi
632632 2.57017 + 9.59200i 0.102236 + 0.381549i
633633 8.03089 + 13.8109i 0.319199 + 0.548935i
634634 2.94564 + 1.70066i 0.116986 + 0.0675420i
635635 −0.213452 0.796612i −0.00847057 0.0316126i
636636 5.95122 10.3820i 0.235981 0.411671i
637637 −69.9862 14.3955i −2.77296 0.570370i
638638 1.76707i 0.0699589i
639639 15.5707 + 15.3789i 0.615967 + 0.608381i
640640 −0.689789 1.19475i −0.0272663 0.0472266i
641641 −0.968362 1.67725i −0.0382480 0.0662475i 0.846268 0.532758i 0.178844π-0.178844\pi
−0.884516 + 0.466510i 0.845511π0.845511\pi
642642 −7.96529 + 8.01480i −0.314365 + 0.316319i
643643 3.83575 3.83575i 0.151267 0.151267i −0.627417 0.778684i 0.715888π-0.715888\pi
0.778684 + 0.627417i 0.215888π0.215888\pi
644644 2.66573 2.66573i 0.105045 0.105045i
645645 −0.834297 0.220781i −0.0328504 0.00869325i
646646 −0.162949 0.282236i −0.00641114 0.0111044i
647647 −5.52455 9.56880i −0.217192 0.376188i 0.736756 0.676159i 0.236357π-0.236357\pi
−0.953949 + 0.299970i 0.903023π0.903023\pi
648648 −7.43951 26.4492i −0.292252 1.03902i
649649 20.3949i 0.800568i
650650 0.618720 + 0.939162i 0.0242682 + 0.0368370i
651651 15.7781 + 27.1340i 0.618392 + 1.06346i
652652 3.32076 + 12.3933i 0.130051 + 0.485357i
653653 22.9231 + 13.2346i 0.897049 + 0.517912i 0.876242 0.481872i 0.160043π-0.160043\pi
0.0208076 + 0.999783i 0.493376π0.493376\pi
654654 4.73281 8.25644i 0.185068 0.322852i
655655 6.95577 + 25.9593i 0.271784 + 1.01431i
656656 −11.5543 + 3.09595i −0.451118 + 0.120877i
657657 −4.04111 + 15.4643i −0.157659 + 0.603318i
658658 41.1786 + 41.1786i 1.60531 + 1.60531i
659659 −38.2912 + 22.1074i −1.49161 + 0.861184i −0.999954 0.00960334i 0.996943π-0.996943\pi
−0.491660 + 0.870787i 0.663610π0.663610\pi
660660 0.0291759 + 9.41784i 0.00113567 + 0.366589i
661661 30.5589 8.18823i 1.18860 0.318485i 0.390270 0.920701i 0.372382π-0.372382\pi
0.798334 + 0.602215i 0.205715π0.205715\pi
662662 16.4437 + 28.4813i 0.639102 + 1.10696i
663663 −0.670568 0.592134i −0.0260427 0.0229966i
664664 23.2455 40.2624i 0.902102 1.56249i
665665 −6.57859 + 24.5516i −0.255107 + 0.952072i
666666 10.4526 + 5.94875i 0.405029 + 0.230509i
667667 0.442036 + 0.255209i 0.0171157 + 0.00988175i
668668 −1.79920 + 0.482095i −0.0696132 + 0.0186528i
669669 −0.876913 3.23259i −0.0339034 0.124979i
670670 −13.2934 13.2934i −0.513568 0.513568i
671671 3.57390 + 0.957624i 0.137969 + 0.0369687i
672672 0.124339 + 40.1361i 0.00479650 + 1.54829i
673673 18.3367i 0.706829i −0.935467 0.353414i 0.885021π-0.885021\pi
0.935467 0.353414i 0.114979π-0.114979\pi
674674 5.20904 + 1.39576i 0.200645 + 0.0537626i
675675 1.32334 + 0.747721i 0.0509355 + 0.0287798i
676676 −6.71275 8.98820i −0.258183 0.345700i
677677 16.0817 + 9.28475i 0.618068 + 0.356842i 0.776116 0.630590i 0.217187π-0.217187\pi
−0.158048 + 0.987431i 0.550520π0.550520\pi
678678 4.50199 + 16.5958i 0.172898 + 0.637359i
679679 −1.40926 + 2.44091i −0.0540824 + 0.0936734i
680680 1.00606 0.0385807
681681 −23.5531 23.4076i −0.902558 0.896983i
682682 −9.87215 2.64524i −0.378024 0.101291i
683683 6.10105 + 22.7694i 0.233450 + 0.871249i 0.978841 + 0.204621i 0.0655962π0.0655962\pi
−0.745391 + 0.666628i 0.767737π0.767737\pi
684684 −3.92972 3.88132i −0.150257 0.148406i
685685 18.0858 31.3256i 0.691024 1.19689i
686686 −70.7759 −2.70224
687687 −23.2217 23.0783i −0.885963 0.880491i
688688 0.286875 0.165627i 0.0109370 0.00631448i
689689 9.10086 + 27.3950i 0.346715 + 1.04367i
690690 3.10981 + 1.78262i 0.118388 + 0.0678634i
691691 30.5011 30.5011i 1.16032 1.16032i 0.175910 0.984406i 0.443713π-0.443713\pi
0.984406 0.175910i 0.0562867π-0.0562867\pi
692692 9.03080 5.21394i 0.343300 0.198204i
693693 21.0467 36.9812i 0.799496 1.40480i
694694 7.48871 7.48871i 0.284268 0.284268i
695695 8.19604 30.5880i 0.310893 1.16027i
696696 −3.08764 + 0.837592i −0.117037 + 0.0317488i
697697 −0.289967 + 1.08217i −0.0109833 + 0.0409902i
698698 25.3006i 0.957642i
699699 −12.9285 + 22.5540i −0.489003 + 0.853070i
700700 −0.924328 0.924328i −0.0349363 0.0349363i
701701 −16.2764 −0.614753 −0.307376 0.951588i 0.599451π-0.599451\pi
−0.307376 + 0.951588i 0.599451π0.599451\pi
702702 17.9420 + 8.78602i 0.677175 + 0.331607i
703703 8.02116 0.302524
704704 −15.1654 15.1654i −0.571568 0.571568i
705705 20.8984 36.4575i 0.787080 1.37307i
706706 22.3923i 0.842744i
707707 −4.70565 + 17.5617i −0.176974 + 0.660477i
708708 −10.7414 + 2.91386i −0.403688 + 0.109509i
709709 −1.26752 + 4.73044i −0.0476026 + 0.177655i −0.985634 0.168895i 0.945980π-0.945980\pi
0.938032 + 0.346550i 0.112647π0.112647\pi
710710 12.6542 12.6542i 0.474904 0.474904i
711711 −9.75830 + 0.0604619i −0.365965 + 0.00226750i
712712 38.9848 22.5079i 1.46102 0.843519i
713713 2.08750 2.08750i 0.0781774 0.0781774i
714714 −1.18864 0.681363i −0.0444839 0.0254994i
715715 −16.9829 15.0904i −0.635125 0.564348i
716716 −2.31083 + 1.33416i −0.0863599 + 0.0498599i
717717 −8.45738 8.40514i −0.315847 0.313896i
718718 12.5485 0.468306
719719 −17.2570 + 29.8900i −0.643577 + 1.11471i 0.341052 + 0.940045i 0.389217π0.389217\pi
−0.984628 + 0.174663i 0.944116π0.944116\pi
720720 −10.1789 + 2.79514i −0.379346 + 0.104169i
721721 1.02431 + 3.82278i 0.0381473 + 0.142368i
722722 −14.8814 3.98746i −0.553828 0.148398i
723723 −1.25316 1.24542i −0.0466057 0.0463178i
724724 −17.5944 −0.653890
725725 0.0884924 0.153273i 0.00328653 0.00569243i
726726 −1.69158 6.23573i −0.0627804 0.231429i
727727 6.05240 + 3.49435i 0.224471 + 0.129598i 0.608019 0.793923i 0.291965π-0.291965\pi
−0.383548 + 0.923521i 0.625298π0.625298\pi
728728 −42.6099 37.8615i −1.57923 1.40324i
729729 26.9953 0.501836i 0.999827 0.0185865i
730730 12.6246 + 3.38276i 0.467258 + 0.125201i
731731 0.0310253i 0.00114751i
732732 −0.00625505 2.01910i −0.000231193 0.0746281i
733733 −22.0147 5.89883i −0.813133 0.217878i −0.171791 0.985133i 0.554955π-0.554955\pi
−0.641342 + 0.767255i 0.721622π0.721622\pi
734734 4.27568 + 4.27568i 0.157818 + 0.157818i
735735 20.6737 + 76.2100i 0.762560 + 2.81105i
736736 3.64637 0.977042i 0.134407 0.0360142i
737737 18.1777 + 10.4949i 0.669584 + 0.386585i
738738 −0.155015 25.0189i −0.00570619 0.920957i
739739 −3.70607 + 13.8313i −0.136330 + 0.508791i 0.863659 + 0.504077i 0.168167π0.168167\pi
−0.999989 + 0.00471409i 0.998499π0.998499\pi
740740 −3.73181 + 6.46368i −0.137184 + 0.237610i
741741 13.2983 0.826037i 0.488525 0.0303452i
742742 22.1055 + 38.2878i 0.811517 + 1.40559i
743743 −6.00805 + 1.60985i −0.220414 + 0.0590598i −0.367336 0.930088i 0.619730π-0.619730\pi
0.146922 + 0.989148i 0.453063π0.453063\pi
744744 0.0573233 + 18.5037i 0.00210158 + 0.678378i
745745 −26.3546 + 15.2158i −0.965558 + 0.557465i
746746 20.2909 + 20.2909i 0.742901 + 0.742901i
747747 32.5047 + 32.1044i 1.18928 + 1.17464i
748748 −0.327036 + 0.0876290i −0.0119576 + 0.00320403i
749749 8.20004 + 30.6030i 0.299623 + 1.11821i
750750 −9.94725 + 17.3531i −0.363222 + 0.633645i
751751 −37.8087 21.8289i −1.37966 0.796547i −0.387542 0.921852i 0.626676π-0.626676\pi
−0.992118 + 0.125304i 0.960009π0.960009\pi
752752 4.17467 + 15.5801i 0.152234 + 0.568146i
753753 −25.5074 43.8658i −0.929542 1.59856i
754754 1.04241 2.07955i 0.0379623 0.0757328i
755755 26.4539i 0.962757i
756756 −22.4840 5.80116i −0.817736 0.210986i
757757 9.84349 + 17.0494i 0.357768 + 0.619672i 0.987588 0.157069i 0.0502046π-0.0502046\pi
−0.629820 + 0.776741i 0.716871π0.716871\pi
758758 14.5596 + 25.2179i 0.528827 + 0.915955i
759759 −3.86891 1.02384i −0.140432 0.0371629i
760760 −10.5955 + 10.5955i −0.384338 + 0.384338i
761761 6.11282 6.11282i 0.221590 0.221590i −0.587578 0.809168i 0.699918π-0.699918\pi
0.809168 + 0.587578i 0.199918π0.199918\pi
762762 −0.466723 + 0.469624i −0.0169076 + 0.0170127i
763763 −13.3417 23.1085i −0.483002 0.836585i
764764 −4.08006 7.06686i −0.147611 0.255670i
765765 −0.249960 + 0.956529i −0.00903731 + 0.0345834i
766766 17.8814i 0.646080i
767767 12.0311 24.0014i 0.434418 0.866640i
768768 −14.0408 + 24.4943i −0.506653 + 0.883861i
769769 −2.26984 8.47115i −0.0818524 0.305477i 0.912847 0.408301i 0.133879π-0.133879\pi
−0.994700 + 0.102824i 0.967212π0.967212\pi
770770 −30.1328 17.3972i −1.08591 0.626951i
771771 15.8327 + 27.2278i 0.570199 + 0.980586i
772772 −0.0886686 0.330916i −0.00319125 0.0119099i
773773 3.74962 1.00471i 0.134865 0.0361368i −0.190755 0.981638i 0.561094π-0.561094\pi
0.325620 + 0.945501i 0.394427π0.394427\pi
774774 0.183466 + 0.668118i 0.00659455 + 0.0240150i
775775 −0.723828 0.723828i −0.0260007 0.0260007i
776776 −1.43896 + 0.830785i −0.0516558 + 0.0298235i
777777 29.1511 16.9510i 1.04579 0.608114i
778778 −1.16724 + 0.312761i −0.0418475 + 0.0112130i
779779 −8.34321 14.4509i −0.298926 0.517756i
780780 −5.52133 + 11.1005i −0.197695 + 0.397460i
781781 −9.99028 + 17.3037i −0.357480 + 0.619174i
782782 −0.0333521 + 0.124472i −0.00119267 + 0.00445109i
783783 −0.0292180 3.14373i −0.00104417 0.112348i
784784 −26.2485 15.1546i −0.937448 0.541236i
785785 −20.8426 + 5.58475i −0.743904 + 0.199328i
786786 15.2092 15.3037i 0.542493 0.545865i
787787 3.03191 + 3.03191i 0.108076 + 0.108076i 0.759077 0.651001i 0.225651π-0.225651\pi
−0.651001 + 0.759077i 0.725651π0.725651\pi
788788 −2.29818 0.615796i −0.0818693 0.0219368i
789789 29.3825 + 16.8428i 1.04604 + 0.599620i
790790 7.97965i 0.283903i
791791 46.5710 + 12.4787i 1.65587 + 0.443690i
792792 21.6457 12.6766i 0.769147 0.450444i
793793 3.64099 + 3.23524i 0.129295 + 0.114887i
794794 −17.1463 9.89944i −0.608501 0.351318i
795795 22.4885 22.6282i 0.797584 0.802541i
796796 6.71525 11.6311i 0.238016 0.412255i
797797 10.9142 0.386603 0.193301 0.981139i 0.438081π-0.438081\pi
0.193301 + 0.981139i 0.438081π0.438081\pi
798798 19.6942 5.34250i 0.697168 0.189122i
799799 1.45923 + 0.390999i 0.0516238 + 0.0138326i
800800 −0.338784 1.26436i −0.0119778 0.0447018i
801801 11.7138 + 42.6576i 0.413887 + 1.50723i
802802 −9.28776 + 16.0869i −0.327962 + 0.568047i
803803 −14.5926 −0.514962
804804 2.93031 11.0732i 0.103344 0.390520i
805805 8.70387 5.02518i 0.306771 0.177114i
806806 −10.0575 8.93667i −0.354259 0.314781i
807807 41.4869 24.1242i 1.46041 0.849211i
808808 −7.57891 + 7.57891i −0.266625 + 0.266625i
809809 24.7010 14.2611i 0.868439 0.501394i 0.00160994 0.999999i 0.499488π-0.499488\pi
0.866829 + 0.498605i 0.166154π0.166154\pi
810810 −0.273581 22.0766i −0.00961265 0.775692i
811811 −14.4345 + 14.4345i −0.506862 + 0.506862i −0.913562 0.406700i 0.866680π-0.866680\pi
0.406700 + 0.913562i 0.366680π0.366680\pi
812812 −0.699785 + 2.61163i −0.0245576 + 0.0916503i
813813 −10.2675 10.2041i −0.360098 0.357874i
814814 −2.84188 + 10.6060i −0.0996078 + 0.371741i
815815 34.2052i 1.19815i
816816 −0.190756 0.328048i −0.00667779 0.0114840i
817817 0.326747 + 0.326747i 0.0114314 + 0.0114314i
818818 −33.0291 −1.15484
819819 46.5840 31.1051i 1.62778 1.08690i
820820 15.5266 0.542211
821821 15.7089 + 15.7089i 0.548243 + 0.548243i 0.925932 0.377689i 0.123281π-0.123281\pi
−0.377689 + 0.925932i 0.623281π0.623281\pi
822822 −29.0394 + 0.0899623i −1.01286 + 0.00313780i
823823 56.1423i 1.95700i −0.206255 0.978498i 0.566128π-0.566128\pi
0.206255 0.978498i 0.433872π-0.433872\pi
824824 −0.603851 + 2.25360i −0.0210361 + 0.0785080i
825825 −0.355009 + 1.34152i −0.0123598 + 0.0467058i
826826 10.6422 39.7174i 0.370291 1.38195i
827827 −7.73555 + 7.73555i −0.268991 + 0.268991i −0.828694 0.559702i 0.810915π-0.810915\pi
0.559702 + 0.828694i 0.310915π0.310915\pi
828828 0.0135315 + 2.18393i 0.000470253 + 0.0758969i
829829 −22.3717 + 12.9163i −0.777001 + 0.448602i −0.835366 0.549693i 0.814745π-0.814745\pi
0.0583652 + 0.998295i 0.481411π0.481411\pi
830830 26.4164 26.4164i 0.916926 0.916926i
831831 −0.0846138 27.3129i −0.00293522 0.947475i
832832 −8.90100 26.7934i −0.308587 0.928895i
833833 −2.45844 + 1.41938i −0.0851799 + 0.0491786i
834834 −24.5363 + 6.65603i −0.849624 + 0.230479i
835835 −4.96577 −0.171847
836836 2.52134 4.36709i 0.0872024 0.151039i
837837 −17.6069 4.54280i −0.608584 0.157022i
838838 −5.92596 22.1160i −0.204709 0.763984i
839839 −34.3643 9.20790i −1.18639 0.317892i −0.388931 0.921267i 0.627156π-0.627156\pi
−0.797458 + 0.603375i 0.793822π0.793822\pi
840840 −16.1155 + 60.8980i −0.556039 + 2.10118i
841841 28.6339 0.987377
842842 12.6504 21.9112i 0.435962 0.755109i
843843 22.8987 + 6.05971i 0.788673 + 0.208708i
844844 6.89323 + 3.97981i 0.237275 + 0.136991i
845845 −11.0842 27.7773i −0.381307 0.955567i
846846 −33.7361 + 0.209027i −1.15987 + 0.00718648i
847847 −17.4986 4.68873i −0.601259 0.161107i
848848 12.2453i 0.420504i
849849 −20.1523 + 11.7183i −0.691626 + 0.402172i
850850 0.0431598 + 0.0115646i 0.00148037 + 0.000396664i
851851 −2.24268 2.24268i −0.0768781 0.0768781i
852852 10.5407 + 2.78941i 0.361120 + 0.0955637i
853853 −11.9527 + 3.20271i −0.409252 + 0.109659i −0.457571 0.889173i 0.651280π-0.651280\pi
0.0483186 + 0.998832i 0.484614π0.484614\pi
854854 6.46020 + 3.72980i 0.221063 + 0.127631i
855855 −7.44132 12.7063i −0.254488 0.434546i
856856 −4.83409 + 18.0411i −0.165226 + 0.616630i
857857 −1.46053 + 2.52971i −0.0498907 + 0.0864132i −0.889892 0.456171i 0.849221π-0.849221\pi
0.840002 + 0.542584i 0.182554π0.182554\pi
858858 −3.61932 + 17.8764i −0.123562 + 0.610291i
859859 14.1298 + 24.4734i 0.482101 + 0.835023i 0.999789 0.0205462i 0.00654052π-0.00654052\pi
−0.517688 + 0.855569i 0.673207π0.673207\pi
860860 −0.415320 + 0.111285i −0.0141623 + 0.00379477i
861861 −60.8602 34.8867i −2.07411 1.18894i
862862 21.6116 12.4775i 0.736095 0.424985i
863863 −32.6894 32.6894i −1.11276 1.11276i −0.992776 0.119986i 0.961715π-0.961715\pi
−0.119986 0.992776i 0.538285π-0.538285\pi
864864 −16.5935 16.2879i −0.564522 0.554125i
865865 26.8528 7.19519i 0.913023 0.244644i
866866 7.33222 + 27.3642i 0.249159 + 0.929874i
867867 29.4092 0.0911079i 0.998788 0.00309419i
868868 13.5429 + 7.81903i 0.459678 + 0.265395i
869869 −2.30589 8.60569i −0.0782219 0.291928i
870870 −2.57077 + 0.00796408i −0.0871572 + 0.000270008i
871871 15.2011 + 23.0740i 0.515071 + 0.781831i
872872 15.7304i 0.532699i
873873 −0.432367 1.57453i −0.0146334 0.0532897i
874874 −0.959637 1.66214i −0.0324602 0.0562227i
875875 28.0411 + 48.5686i 0.947963 + 1.64192i
876876 2.08488 + 7.68555i 0.0704414 + 0.259671i
877877 −39.9952 + 39.9952i −1.35054 + 1.35054i −0.465486 + 0.885055i 0.654120π0.654120\pi
−0.885055 + 0.465486i 0.845880π0.845880\pi
878878 −0.321943 + 0.321943i −0.0108651 + 0.0108651i
879879 −3.23220 11.9150i −0.109019 0.401882i
880880 −4.81856 8.34599i −0.162434 0.281343i
881881 −14.1084 24.4364i −0.475323 0.823284i 0.524278 0.851547i 0.324335π-0.324335\pi
−0.999600 + 0.0282639i 0.991002π0.991002\pi
882882 44.5481 45.1036i 1.50001 1.51872i
883883 7.20265i 0.242388i −0.992629 0.121194i 0.961328π-0.961328\pi
0.992629 0.121194i 0.0386724π-0.0386724\pi
884884 −0.436560 0.0897963i −0.0146831 0.00302018i
885885 −29.6708 + 0.0919185i −0.997374 + 0.00308981i
886886 −3.16327 11.8055i −0.106272 0.396613i
887887 −27.3550 15.7934i −0.918490 0.530291i −0.0353373 0.999375i 0.511251π-0.511251\pi
−0.883153 + 0.469085i 0.844584π0.844584\pi
888888 19.8792 0.0615847i 0.667103 0.00206665i
889889 0.480478 + 1.79317i 0.0161147 + 0.0601410i
890890 34.9404 9.36224i 1.17120 0.313823i
891891 6.67453 + 23.7295i 0.223605 + 0.794969i
892892 −1.17998 1.17998i −0.0395087 0.0395087i
893893 −19.4859 + 11.2502i −0.652071 + 0.376473i
894894 21.1959 + 12.1501i 0.708896 + 0.406358i
895895 −6.87119 + 1.84113i −0.229678 + 0.0615421i
896896 1.55271 + 2.68937i 0.0518724 + 0.0898456i
897897 −3.94910 3.48719i −0.131857 0.116434i
898898 3.43923 5.95692i 0.114769 0.198785i
899899 −0.547991 + 2.04513i −0.0182765 + 0.0682090i
900900 0.757266 0.00469198i 0.0252422 0.000156399i
901901 0.993237 + 0.573446i 0.0330895 + 0.0191042i
902902 22.0637 5.91196i 0.734642 0.196847i
903903 1.87800 + 0.496977i 0.0624958 + 0.0165384i
904904 20.0981 + 20.0981i 0.668453 + 0.668453i
905905 −45.3072 12.1400i −1.50606 0.403549i
906906 18.3596 10.6759i 0.609956 0.354682i
907907 22.6161i 0.750954i 0.926832 + 0.375477i 0.122521π0.122521\pi
−0.926832 + 0.375477i 0.877479π0.877479\pi
908908 −15.9804 4.28192i −0.530327 0.142101i
909909 −5.32276 9.08877i −0.176545 0.301456i
910910 −25.1986 38.2492i −0.835326 1.26795i
911911 −20.2816 11.7096i −0.671958 0.387955i 0.124860 0.992174i 0.460152π-0.460152\pi
−0.796818 + 0.604219i 0.793485π0.793485\pi
912912 5.46384 + 1.44591i 0.180926 + 0.0478787i
913913 −20.8553 + 36.1224i −0.690209 + 1.19548i
914914 −11.5909 −0.383391
915915 1.37706 5.20370i 0.0455243 0.172029i
916916 −15.7555 4.22167i −0.520576 0.139488i
917917 −15.6574 58.4342i −0.517053 1.92967i
918918 0.764725 0.212544i 0.0252397 0.00701500i
919919 13.0969 22.6845i 0.432027 0.748293i −0.565020 0.825077i 0.691132π-0.691132\pi
0.997048 + 0.0767835i 0.0244650π0.0244650\pi
920920 5.92489 0.195338
921921 −19.7985 + 5.37078i −0.652382 + 0.176973i
922922 15.7012 9.06506i 0.517090 0.298542i
923923 −21.9645 + 14.4702i −0.722971 + 0.476294i
924924 −0.0656748 21.1995i −0.00216054 0.697413i
925925 −0.777637 + 0.777637i −0.0255685 + 0.0255685i
926926 35.8253 20.6837i 1.17729 0.679710i
927927 −1.99262 1.13404i −0.0654462 0.0372466i
928928 −1.91442 + 1.91442i −0.0628440 + 0.0628440i
929929 2.52294 9.41573i 0.0827749 0.308920i −0.912109 0.409949i 0.865547π-0.865547\pi
0.994884 + 0.101028i 0.0322133π0.0322133\pi
930930 −3.80385 + 14.3741i −0.124733 + 0.471346i
931931 10.9430 40.8397i 0.358642 1.33847i
932932 12.9521i 0.424259i
933933 4.66840 0.0144624i 0.152836 0.000473478i
934934 28.4442 + 28.4442i 0.930722 + 0.930722i
935935 −0.902613 −0.0295186
936936 32.9515 2.14931i 1.07705 0.0702524i
937937 38.7284 1.26520 0.632601 0.774478i 0.281987π-0.281987\pi
0.632601 + 0.774478i 0.281987π0.281987\pi
938938 29.9233 + 29.9233i 0.977031 + 0.977031i
939939 −2.91425 5.01171i −0.0951029 0.163551i
940940 20.9364i 0.682871i
941941 13.5986 50.7507i 0.443302 1.65442i −0.277080 0.960847i 0.589367π-0.589367\pi
0.720382 0.693578i 0.243967π-0.243967\pi
942942 12.2873 + 12.2114i 0.400341 + 0.397868i
943943 −1.70767 + 6.37312i −0.0556094 + 0.207537i
944944 8.05305 8.05305i 0.262104 0.262104i
945945 −53.8958 30.4524i −1.75323 0.990617i
946946 −0.547809 + 0.316278i −0.0178108 + 0.0102831i
947947 33.3193 33.3193i 1.08273 1.08273i 0.0864783 0.996254i 0.472439π-0.472439\pi
0.996254 0.0864783i 0.0275613π-0.0275613\pi
948948 −4.20295 + 2.44397i −0.136505 + 0.0793763i
949949 −17.1731 8.60830i −0.557462 0.279437i
950950 −0.576337 + 0.332749i −0.0186989 + 0.0107958i
951951 −1.41339 + 5.34097i −0.0458323 + 0.173193i
952952 −2.26464 −0.0733974
953953 −24.8010 + 42.9566i −0.803383 + 1.39150i 0.113994 + 0.993481i 0.463636π0.463636\pi
−0.917377 + 0.398019i 0.869698π0.869698\pi
954954 −24.7800 6.47549i −0.802282 0.209652i
955955 −5.63044 21.0131i −0.182197 0.679968i
956956 −5.73818 1.53754i −0.185586 0.0497276i
957957 2.77015 0.751466i 0.0895463 0.0242914i
958958 −22.2651 −0.719354
959959 −40.7111 + 70.5137i −1.31463 + 2.27701i
960960 −21.9946 + 22.1313i −0.709873 + 0.714285i
961961 −16.2415 9.37703i −0.523919 0.302485i
962962 −9.60101 + 10.8051i −0.309549 + 0.348371i
963963 −15.9518 9.07844i −0.514038 0.292549i
964964 −0.850249 0.227824i −0.0273847 0.00733770i
965965 0.913321i 0.0294009i
966966 −7.00015 4.01268i −0.225226 0.129106i
967967 57.2307 + 15.3349i 1.84042 + 0.493138i 0.998891 0.0470805i 0.0149917π-0.0149917\pi
0.841525 + 0.540218i 0.181658π0.181658\pi
968968 −7.55166 7.55166i −0.242720 0.242720i
969969 0.373152 0.375471i 0.0119874 0.0120619i
970970 −1.28968 + 0.345568i −0.0414091 + 0.0110955i
971971 19.4119 + 11.2075i 0.622957 + 0.359665i 0.778019 0.628240i 0.216224π-0.216224\pi
−0.155062 + 0.987905i 0.549558π0.549558\pi
972972 11.5441 6.90560i 0.370278 0.221497i
973973 −18.4492 + 68.8535i −0.591455 + 2.20734i
974974 9.47425 16.4099i 0.303575 0.525807i
975975 −1.20916 + 1.36933i −0.0387242 + 0.0438536i
976976 1.03306 + 1.78931i 0.0330673 + 0.0572743i
977977 −14.9916 + 4.01699i −0.479624 + 0.128515i −0.490528 0.871426i 0.663196π-0.663196\pi
0.0109035 + 0.999941i 0.496529π0.496529\pi
978978 23.7391 13.8040i 0.759092 0.441403i
979979 −34.9762 + 20.1935i −1.11784 + 0.645387i
980980 27.8187 + 27.8187i 0.888635 + 0.888635i
981981 14.9559 + 3.90827i 0.477506 + 0.124782i
982982 −15.0296 + 4.02716i −0.479613 + 0.128512i
983983 0.650655 + 2.42828i 0.0207527 + 0.0774500i 0.975526 0.219886i 0.0705685π-0.0705685\pi
−0.954773 + 0.297336i 0.903902π0.903902\pi
984984 −20.7883 35.7502i −0.662708 1.13967i
985985 −5.49315 3.17147i −0.175026 0.101051i
986986 −0.0239199 0.0892702i −0.000761764 0.00284294i
987987 −47.0422 + 82.0655i −1.49737 + 2.61217i
988988 5.54339 3.65199i 0.176359 0.116185i
989989 0.182714i 0.00580997i
990990 19.4374 5.33753i 0.617761 0.169638i
991991 15.2437 + 26.4028i 0.484231 + 0.838713i 0.999836 0.0181139i 0.00576614π-0.00576614\pi
−0.515605 + 0.856826i 0.672433π0.672433\pi
992992 7.82956 + 13.5612i 0.248589 + 0.430569i
993993 −37.6560 + 37.8900i −1.19498 + 1.20240i
994994 −28.4845 + 28.4845i −0.903475 + 0.903475i
995995 25.3179 25.3179i 0.802630 0.802630i
996996 22.0044 + 5.82306i 0.697236 + 0.184511i
997997 3.99304 + 6.91615i 0.126461 + 0.219037i 0.922303 0.386467i 0.126305π-0.126305\pi
−0.795842 + 0.605504i 0.792972π0.792972\pi
998998 −6.37866 11.0482i −0.201913 0.349723i
999999 −4.88051 + 18.9158i −0.154412 + 0.598469i
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 117.2.x.a.2.5 48
3.2 odd 2 351.2.ba.a.197.8 48
9.4 even 3 351.2.bf.a.314.8 48
9.5 odd 6 117.2.bc.a.41.5 yes 48
13.7 odd 12 117.2.bc.a.20.5 yes 48
39.20 even 12 351.2.bf.a.332.8 48
117.59 even 12 inner 117.2.x.a.59.5 yes 48
117.85 odd 12 351.2.ba.a.98.8 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.x.a.2.5 48 1.1 even 1 trivial
117.2.x.a.59.5 yes 48 117.59 even 12 inner
117.2.bc.a.20.5 yes 48 13.7 odd 12
117.2.bc.a.41.5 yes 48 9.5 odd 6
351.2.ba.a.98.8 48 117.85 odd 12
351.2.ba.a.197.8 48 3.2 odd 2
351.2.bf.a.314.8 48 9.4 even 3
351.2.bf.a.332.8 48 39.20 even 12