Properties

Label 45.3.k.a.22.1
Level 4545
Weight 33
Character 45.22
Analytic conductor 1.2261.226
Analytic rank 00
Dimension 4040
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,3,Mod(7,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([8, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 45=325 45 = 3^{2} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 45.k (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: 1.226161189621.22616118962
Analytic rank: 00
Dimension: 4040
Relative dimension: 1010 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 22.1
Character χ\chi == 45.22
Dual form 45.3.k.a.43.1

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+(0.930497+3.47266i)q2+(0.635068+2.93201i)q3+(7.729474.46261i)q4+(4.999130.0933744i)q5+(10.77280.522853i)q6+(1.283234.78910i)q7+(12.520712.5207i)q8+(8.19338+3.72405i)q9+(4.32742+17.4472i)q10+(1.37764+2.38615i)q11+(8.1756925.4969i)q12+(2.45318+9.15539i)q13+(15.4369+8.91249i)q14+(3.44856+14.5982i)q15+(13.9793+24.2129i)q16+(9.17504+9.17504i)q17+(5.3084631.9181i)q1832.1912iq19+(39.057321.5874i)q20+(14.8566+0.721059i)q21+(9.56819+2.56379i)q22+(0.179412+0.669573i)q23+(44.6624+28.7594i)q24+(24.98260.933581i)q2534.0763q26+(16.122321.6581i)q27+(31.2906+31.2906i)q28+(30.1349+17.3984i)q29+(53.90351.60790i)q30+(12.848222.2537i)q31+(28.6765+7.68384i)q32+(6.12132+5.55463i)q33+(40.3992+23.3245i)q34+(5.9678824.0611i)q35+(79.9494+7.77893i)q36+(13.033113.0331i)q37+(111.789+29.9538i)q38+(25.2858+13.0070i)q39+(61.423663.7618i)q40+(20.213935.0116i)q41+(16.3280+50.9211i)q42+(3.68527+0.987466i)q4324.5915iq44+(40.6120+19.3821i)q452.49214q46+(0.9932313.70679i)q47+(62.1147+56.3644i)q48+(21.1465+12.2089i)q49+(20.0042+87.6247i)q50+(21.0745+32.7281i)q51+(21.895281.7139i)q52+(31.2240+31.2240i)q53+(90.212935.8346i)q54+(7.10982+11.8000i)q55+(43.895976.0300i)q56+(94.385020.4436i)q57+(32.3783120.837i)q58+(36.861121.2818i)q59+(38.4905128.226i)q60+(6.5699411.3795i)q61+(65.3243+65.3243i)q62+(7.32081+44.0177i)q63+5.10100iq64+(13.1186+45.5399i)q65+(13.593526.4259i)q66+(44.9977+12.0571i)q67+(29.9735111.863i)q68+(1.84926+0.951261i)q69+(78.0031+43.1133i)q70114.062q71+(55.9592+149.215i)q72+(18.7982+18.7982i)q73+(57.386733.1322i)q74+(18.6029+72.6563i)q75+(143.657+248.821i)q76+(13.19533.53568i)q77+(21.640799.9120i)q78+(18.3057+10.5688i)q79+(72.1453+119.738i)q80+(53.262961.0251i)q81+(102.774+102.774i)q82+(14.76883.95730i)q83+(111.61671.8727i)q84+(46.7239+45.0105i)q85+(6.85828+11.8789i)q86+(70.149977.3067i)q87+(47.1254+12.6272i)q8892.4405iq89+(29.5180159.067i)q90+46.9941q91+(1.601295.97609i)q92+(73.4075+23.5384i)q93+(11.9482+6.89832i)q94+(3.00583160.928i)q95+(40.740679.2000i)q96+(40.7091+151.928i)q97+(62.0742+62.0742i)q98+(20.173714.4202i)q99+O(q100)q+(-0.930497 + 3.47266i) q^{2} +(0.635068 + 2.93201i) q^{3} +(-7.72947 - 4.46261i) q^{4} +(4.99913 - 0.0933744i) q^{5} +(-10.7728 - 0.522853i) q^{6} +(1.28323 - 4.78910i) q^{7} +(12.5207 - 12.5207i) q^{8} +(-8.19338 + 3.72405i) q^{9} +(-4.32742 + 17.4472i) q^{10} +(1.37764 + 2.38615i) q^{11} +(8.17569 - 25.4969i) q^{12} +(2.45318 + 9.15539i) q^{13} +(15.4369 + 8.91249i) q^{14} +(3.44856 + 14.5982i) q^{15} +(13.9793 + 24.2129i) q^{16} +(9.17504 + 9.17504i) q^{17} +(-5.30846 - 31.9181i) q^{18} -32.1912i q^{19} +(-39.0573 - 21.5874i) q^{20} +(14.8566 + 0.721059i) q^{21} +(-9.56819 + 2.56379i) q^{22} +(0.179412 + 0.669573i) q^{23} +(44.6624 + 28.7594i) q^{24} +(24.9826 - 0.933581i) q^{25} -34.0763 q^{26} +(-16.1223 - 21.6581i) q^{27} +(-31.2906 + 31.2906i) q^{28} +(-30.1349 + 17.3984i) q^{29} +(-53.9035 - 1.60790i) q^{30} +(12.8482 - 22.2537i) q^{31} +(-28.6765 + 7.68384i) q^{32} +(-6.12132 + 5.55463i) q^{33} +(-40.3992 + 23.3245i) q^{34} +(5.96788 - 24.0611i) q^{35} +(79.9494 + 7.77893i) q^{36} +(-13.0331 - 13.0331i) q^{37} +(111.789 + 29.9538i) q^{38} +(-25.2858 + 13.0070i) q^{39} +(61.4236 - 63.7618i) q^{40} +(20.2139 - 35.0116i) q^{41} +(-16.3280 + 50.9211i) q^{42} +(3.68527 + 0.987466i) q^{43} -24.5915i q^{44} +(-40.6120 + 19.3821i) q^{45} -2.49214 q^{46} +(0.993231 - 3.70679i) q^{47} +(-62.1147 + 56.3644i) q^{48} +(21.1465 + 12.2089i) q^{49} +(-20.0042 + 87.6247i) q^{50} +(-21.0745 + 32.7281i) q^{51} +(21.8952 - 81.7139i) q^{52} +(-31.2240 + 31.2240i) q^{53} +(90.2129 - 35.8346i) q^{54} +(7.10982 + 11.8000i) q^{55} +(-43.8959 - 76.0300i) q^{56} +(94.3850 - 20.4436i) q^{57} +(-32.3783 - 120.837i) q^{58} +(-36.8611 - 21.2818i) q^{59} +(38.4905 - 128.226i) q^{60} +(-6.56994 - 11.3795i) q^{61} +(65.3243 + 65.3243i) q^{62} +(7.32081 + 44.0177i) q^{63} +5.10100i q^{64} +(13.1186 + 45.5399i) q^{65} +(-13.5935 - 26.4259i) q^{66} +(-44.9977 + 12.0571i) q^{67} +(-29.9735 - 111.863i) q^{68} +(-1.84926 + 0.951261i) q^{69} +(78.0031 + 43.1133i) q^{70} -114.062 q^{71} +(-55.9592 + 149.215i) q^{72} +(-18.7982 + 18.7982i) q^{73} +(57.3867 - 33.1322i) q^{74} +(18.6029 + 72.6563i) q^{75} +(-143.657 + 248.821i) q^{76} +(13.1953 - 3.53568i) q^{77} +(-21.6407 - 99.9120i) q^{78} +(-18.3057 + 10.5688i) q^{79} +(72.1453 + 119.738i) q^{80} +(53.2629 - 61.0251i) q^{81} +(102.774 + 102.774i) q^{82} +(-14.7688 - 3.95730i) q^{83} +(-111.616 - 71.8727i) q^{84} +(46.7239 + 45.0105i) q^{85} +(-6.85828 + 11.8789i) q^{86} +(-70.1499 - 77.3067i) q^{87} +(47.1254 + 12.6272i) q^{88} -92.4405i q^{89} +(-29.5180 - 159.067i) q^{90} +46.9941 q^{91} +(1.60129 - 5.97609i) q^{92} +(73.4075 + 23.5384i) q^{93} +(11.9482 + 6.89832i) q^{94} +(-3.00583 - 160.928i) q^{95} +(-40.7406 - 79.2000i) q^{96} +(-40.7091 + 151.928i) q^{97} +(-62.0742 + 62.0742i) q^{98} +(-20.1737 - 14.4202i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q2q26q32q524q62q724q88q10+8q1130q122q1330q15+28q16+28q17+48q18114q20+12q21+14q22+82q23+1876q98+O(q100) 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/45Z)×\left(\mathbb{Z}/45\mathbb{Z}\right)^\times.

nn 1111 3737
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\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 −0.930497 + 3.47266i −0.465249 + 1.73633i 0.190815 + 0.981626i 0.438887π0.438887\pi
−0.656063 + 0.754706i 0.727780π0.727780\pi
33 0.635068 + 2.93201i 0.211689 + 0.977337i
44 −7.72947 4.46261i −1.93237 1.11565i
55 4.99913 0.0933744i 0.999826 0.0186749i
66 −10.7728 0.522853i −1.79547 0.0871422i
77 1.28323 4.78910i 0.183319 0.684157i −0.811665 0.584123i 0.801438π-0.801438\pi
0.994984 0.100033i 0.0318950π-0.0318950\pi
88 12.5207 12.5207i 1.56509 1.56509i
99 −8.19338 + 3.72405i −0.910375 + 0.413783i
1010 −4.32742 + 17.4472i −0.432742 + 1.74472i
1111 1.37764 + 2.38615i 0.125240 + 0.216923i 0.921827 0.387602i 0.126696π-0.126696\pi
−0.796587 + 0.604525i 0.793363π0.793363\pi
1212 8.17569 25.4969i 0.681307 2.12474i
1313 2.45318 + 9.15539i 0.188706 + 0.704261i 0.993807 + 0.111123i 0.0354446π0.0354446\pi
−0.805101 + 0.593138i 0.797889π0.797889\pi
1414 15.4369 + 8.91249i 1.10263 + 0.636606i
1515 3.44856 + 14.5982i 0.229904 + 0.973213i
1616 13.9793 + 24.2129i 0.873708 + 1.51331i
1717 9.17504 + 9.17504i 0.539708 + 0.539708i 0.923443 0.383735i 0.125362π-0.125362\pi
−0.383735 + 0.923443i 0.625362π0.625362\pi
1818 −5.30846 31.9181i −0.294914 1.77323i
1919 32.1912i 1.69427i −0.531375 0.847137i 0.678324π-0.678324\pi
0.531375 0.847137i 0.321676π-0.321676\pi
2020 −39.0573 21.5874i −1.95286 1.07937i
2121 14.8566 + 0.721059i 0.707459 + 0.0343361i
2222 −9.56819 + 2.56379i −0.434918 + 0.116536i
2323 0.179412 + 0.669573i 0.00780050 + 0.0291119i 0.969716 0.244234i 0.0785364π-0.0785364\pi
−0.961916 + 0.273346i 0.911870π0.911870\pi
2424 44.6624 + 28.7594i 1.86093 + 1.19831i
2525 24.9826 0.933581i 0.999302 0.0373432i
2626 −34.0763 −1.31063
2727 −16.1223 21.6581i −0.597122 0.802150i
2828 −31.2906 + 31.2906i −1.11752 + 1.11752i
2929 −30.1349 + 17.3984i −1.03913 + 0.599944i −0.919588 0.392884i 0.871477π-0.871477\pi
−0.119546 + 0.992829i 0.538144π0.538144\pi
3030 −53.9035 1.60790i −1.79678 0.0535968i
3131 12.8482 22.2537i 0.414457 0.717860i −0.580914 0.813965i 0.697305π-0.697305\pi
0.995371 + 0.0961042i 0.0306382π0.0306382\pi
3232 −28.6765 + 7.68384i −0.896140 + 0.240120i
3333 −6.12132 + 5.55463i −0.185494 + 0.168322i
3434 −40.3992 + 23.3245i −1.18821 + 0.686014i
3535 5.96788 24.0611i 0.170511 0.687461i
3636 79.9494 + 7.77893i 2.22082 + 0.216081i
3737 −13.0331 13.0331i −0.352245 0.352245i 0.508699 0.860944i 0.330127π-0.330127\pi
−0.860944 + 0.508699i 0.830127π0.830127\pi
3838 111.789 + 29.9538i 2.94182 + 0.788259i
3939 −25.2858 + 13.0070i −0.648353 + 0.333514i
4040 61.4236 63.7618i 1.53559 1.59405i
4141 20.2139 35.0116i 0.493023 0.853941i −0.506945 0.861979i 0.669225π-0.669225\pi
0.999968 + 0.00803768i 0.00255850π0.00255850\pi
4242 −16.3280 + 50.9211i −0.388763 + 1.21241i
4343 3.68527 + 0.987466i 0.0857040 + 0.0229643i 0.301416 0.953493i 0.402541π-0.402541\pi
−0.215712 + 0.976457i 0.569207π0.569207\pi
4444 24.5915i 0.558899i
4545 −40.6120 + 19.3821i −0.902489 + 0.430712i
4646 −2.49214 −0.0541770
4747 0.993231 3.70679i 0.0211326 0.0788679i −0.954554 0.298037i 0.903668π-0.903668\pi
0.975687 + 0.219169i 0.0703347π0.0703347\pi
4848 −62.1147 + 56.3644i −1.29406 + 1.17426i
4949 21.1465 + 12.2089i 0.431561 + 0.249162i
5050 −20.0042 + 87.6247i −0.400084 + 1.75249i
5151 −21.0745 + 32.7281i −0.413226 + 0.641727i
5252 21.8952 81.7139i 0.421061 1.57142i
5353 −31.2240 + 31.2240i −0.589132 + 0.589132i −0.937396 0.348265i 0.886771π-0.886771\pi
0.348265 + 0.937396i 0.386771π0.386771\pi
5454 90.2129 35.8346i 1.67061 0.663603i
5555 7.10982 + 11.8000i 0.129269 + 0.214546i
5656 −43.8959 76.0300i −0.783856 1.35768i
5757 94.3850 20.4436i 1.65588 0.358659i
5858 −32.3783 120.837i −0.558247 2.08340i
5959 −36.8611 21.2818i −0.624765 0.360708i 0.153957 0.988078i 0.450798π-0.450798\pi
−0.778722 + 0.627369i 0.784132π0.784132\pi
6060 38.4905 128.226i 0.641509 2.13710i
6161 −6.56994 11.3795i −0.107704 0.186549i 0.807136 0.590366i 0.201017π-0.201017\pi
−0.914840 + 0.403817i 0.867683π0.867683\pi
6262 65.3243 + 65.3243i 1.05362 + 1.05362i
6363 7.32081 + 44.0177i 0.116203 + 0.698694i
6464 5.10100i 0.0797032i
6565 13.1186 + 45.5399i 0.201825 + 0.700614i
6666 −13.5935 26.4259i −0.205962 0.400392i
6767 −44.9977 + 12.0571i −0.671607 + 0.179957i −0.578479 0.815697i 0.696353π-0.696353\pi
−0.0931285 + 0.995654i 0.529687π0.529687\pi
6868 −29.9735 111.863i −0.440787 1.64504i
6969 −1.84926 + 0.951261i −0.0268008 + 0.0137864i
7070 78.0031 + 43.1133i 1.11433 + 0.615904i
7171 −114.062 −1.60651 −0.803254 0.595637i 0.796900π-0.796900\pi
−0.803254 + 0.595637i 0.796900π0.796900\pi
7272 −55.9592 + 149.215i −0.777212 + 2.07243i
7373 −18.7982 + 18.7982i −0.257510 + 0.257510i −0.824041 0.566531i 0.808285π-0.808285\pi
0.566531 + 0.824041i 0.308285π0.308285\pi
7474 57.3867 33.1322i 0.775496 0.447733i
7575 18.6029 + 72.6563i 0.248038 + 0.968750i
7676 −143.657 + 248.821i −1.89022 + 3.27396i
7777 13.1953 3.53568i 0.171368 0.0459179i
7878 −21.6407 99.9120i −0.277445 1.28092i
7979 −18.3057 + 10.5688i −0.231717 + 0.133782i −0.611364 0.791350i 0.709379π-0.709379\pi
0.379647 + 0.925132i 0.376046π0.376046\pi
8080 72.1453 + 119.738i 0.901816 + 1.49673i
8181 53.2629 61.0251i 0.657567 0.753396i
8282 102.774 + 102.774i 1.25335 + 1.25335i
8383 −14.7688 3.95730i −0.177938 0.0476783i 0.168750 0.985659i 0.446027π-0.446027\pi
−0.346688 + 0.937981i 0.612694π0.612694\pi
8484 −111.616 71.8727i −1.32876 0.855628i
8585 46.7239 + 45.0105i 0.549693 + 0.529535i
8686 −6.85828 + 11.8789i −0.0797474 + 0.138127i
8787 −70.1499 77.3067i −0.806321 0.888582i
8888 47.1254 + 12.6272i 0.535516 + 0.143491i
8989 92.4405i 1.03866i −0.854575 0.519329i 0.826182π-0.826182\pi
0.854575 0.519329i 0.173818π-0.173818\pi
9090 −29.5180 159.067i −0.327978 1.76741i
9191 46.9941 0.516418
9292 1.60129 5.97609i 0.0174053 0.0649574i
9393 73.4075 + 23.5384i 0.789328 + 0.253101i
9494 11.9482 + 6.89832i 0.127109 + 0.0733864i
9595 −3.00583 160.928i −0.0316404 1.69398i
9696 −40.7406 79.2000i −0.424382 0.825000i
9797 −40.7091 + 151.928i −0.419681 + 1.56627i 0.355590 + 0.934642i 0.384280π0.384280\pi
−0.775271 + 0.631629i 0.782387π0.782387\pi
9898 −62.0742 + 62.0742i −0.633411 + 0.633411i
9999 −20.1737 14.4202i −0.203775 0.145659i
100100 −197.268 104.271i −1.97268 1.04271i
101101 41.2983 + 71.5307i 0.408894 + 0.708225i 0.994766 0.102178i 0.0325813π-0.0325813\pi
−0.585872 + 0.810404i 0.699248π0.699248\pi
102102 −94.0438 103.638i −0.921998 1.01606i
103103 −12.9609 48.3706i −0.125834 0.469617i 0.874034 0.485864i 0.161495π-0.161495\pi
−0.999868 + 0.0162466i 0.994828π0.994828\pi
104104 145.348 + 83.9166i 1.39757 + 0.806890i
105105 74.3375 + 2.21744i 0.707976 + 0.0211184i
106106 −79.3765 137.484i −0.748835 1.29702i
107107 −57.4669 57.4669i −0.537074 0.537074i 0.385595 0.922668i 0.373996π-0.373996\pi
−0.922668 + 0.385595i 0.873996π0.873996\pi
108108 27.9654 + 239.353i 0.258939 + 2.21623i
109109 145.852i 1.33809i −0.743220 0.669047i 0.766702π-0.766702\pi
0.743220 0.669047i 0.233298π-0.233298\pi
110110 −47.5932 + 13.7101i −0.432665 + 0.124638i
111111 29.9362 46.4900i 0.269696 0.418829i
112112 133.897 35.8775i 1.19551 0.320335i
113113 14.0319 + 52.3679i 0.124176 + 0.463432i 0.999809 0.0195453i 0.00622185π-0.00622185\pi
−0.875633 + 0.482978i 0.839555π0.839555\pi
114114 −16.8313 + 346.790i −0.147643 + 3.04202i
115115 0.959422 + 3.33053i 0.00834280 + 0.0289611i
116116 310.569 2.67732
117117 −54.1950 65.8778i −0.463205 0.563058i
118118 108.204 108.204i 0.916980 0.916980i
119119 55.7139 32.1664i 0.468184 0.270306i
120120 225.959 + 139.602i 1.88299 + 1.16335i
121121 56.7042 98.2145i 0.468630 0.811690i
122122 45.6304 12.2266i 0.374019 0.100218i
123123 115.492 + 37.0328i 0.938956 + 0.301080i
124124 −198.619 + 114.673i −1.60177 + 0.924780i
125125 124.804 6.99982i 0.998431 0.0559986i
126126 −159.671 15.5357i −1.26723 0.123299i
127127 50.4054 + 50.4054i 0.396893 + 0.396893i 0.877136 0.480243i 0.159451π-0.159451\pi
−0.480243 + 0.877136i 0.659451π0.659451\pi
128128 −132.420 35.4818i −1.03453 0.277202i
129129 −0.554864 + 11.4324i −0.00430127 + 0.0886230i
130130 −170.352 + 3.18185i −1.31040 + 0.0244758i
131131 −89.6936 + 155.354i −0.684684 + 1.18591i 0.288852 + 0.957374i 0.406726π0.406726\pi
−0.973536 + 0.228534i 0.926607π0.926607\pi
132132 72.1027 15.6173i 0.546232 0.118313i
133133 −154.167 41.3089i −1.15915 0.310593i
134134 167.481i 1.24986i
135135 −82.6198 106.766i −0.611998 0.790859i
136136 229.756 1.68938
137137 −36.5154 + 136.277i −0.266536 + 0.994725i 0.694768 + 0.719234i 0.255507π0.255507\pi
−0.961304 + 0.275491i 0.911160π0.911160\pi
138138 −1.58268 7.30699i −0.0114687 0.0529492i
139139 236.063 + 136.291i 1.69829 + 0.980510i 0.947381 + 0.320108i 0.103719π0.103719\pi
0.750912 + 0.660402i 0.229614π0.229614\pi
140140 −153.504 + 159.347i −1.09646 + 1.13820i
141141 11.4991 + 0.558104i 0.0815540 + 0.00395818i
142142 106.134 396.099i 0.747426 2.78943i
143143 −18.4665 + 18.4665i −0.129137 + 0.129137i
144144 −204.708 146.326i −1.42158 1.01615i
145145 −149.024 + 89.7906i −1.02775 + 0.619245i
146146 −47.7882 82.7716i −0.327317 0.566929i
147147 −22.3673 + 69.7552i −0.152158 + 0.474525i
148148 42.5772 + 158.900i 0.287684 + 1.07365i
149149 174.004 + 100.461i 1.16781 + 0.674235i 0.953163 0.302457i 0.0978070π-0.0978070\pi
0.214646 + 0.976692i 0.431140π0.431140\pi
150150 −269.621 3.00491i −1.79747 0.0200327i
151151 58.6560 + 101.595i 0.388450 + 0.672816i 0.992241 0.124327i 0.0396771π-0.0396771\pi
−0.603791 + 0.797143i 0.706344π0.706344\pi
152152 −403.057 403.057i −2.65169 2.65169i
153153 −109.343 41.0063i −0.714659 0.268015i
154154 49.1129i 0.318915i
155155 62.1517 112.449i 0.400979 0.725475i
156156 253.491 + 12.3030i 1.62494 + 0.0788657i
157157 −205.058 + 54.9450i −1.30610 + 0.349968i −0.843753 0.536731i 0.819659π-0.819659\pi
−0.462346 + 0.886700i 0.652992π0.652992\pi
158158 −19.6684 73.4036i −0.124484 0.464580i
159159 −111.378 71.7197i −0.700493 0.451067i
160160 −142.640 + 41.0902i −0.891500 + 0.256814i
161161 3.43688 0.0213471
162162 162.359 + 241.748i 1.00221 + 1.49227i
163163 61.1545 61.1545i 0.375181 0.375181i −0.494179 0.869360i 0.664531π-0.664531\pi
0.869360 + 0.494179i 0.164531π0.164531\pi
164164 −312.486 + 180.414i −1.90540 + 1.10008i
165165 −30.0826 + 28.3399i −0.182319 + 0.171757i
166166 27.4847 47.6049i 0.165571 0.286777i
167167 234.945 62.9533i 1.40686 0.376966i 0.526054 0.850451i 0.323671π-0.323671\pi
0.880802 + 0.473486i 0.157004π0.157004\pi
168168 195.044 176.988i 1.16098 1.05350i
169169 68.5552 39.5803i 0.405652 0.234203i
170170 −199.783 + 120.374i −1.17519 + 0.708084i
171171 119.882 + 263.755i 0.701062 + 1.54243i
172172 −24.0785 24.0785i −0.139991 0.139991i
173173 −16.3284 4.37517i −0.0943835 0.0252900i 0.211318 0.977417i 0.432224π-0.432224\pi
−0.305702 + 0.952127i 0.598891π0.598891\pi
174174 333.734 171.673i 1.91801 0.986629i
175175 27.5875 120.842i 0.157643 0.690525i
176176 −38.5171 + 66.7135i −0.218847 + 0.379054i
177177 38.9891 121.593i 0.220277 0.686964i
178178 321.015 + 86.0157i 1.80345 + 0.483234i
179179 274.512i 1.53359i 0.641895 + 0.766793i 0.278149π0.278149\pi
−0.641895 + 0.766793i 0.721851π0.721851\pi
180180 400.404 + 31.4226i 2.22447 + 0.174570i
181181 −261.649 −1.44557 −0.722787 0.691070i 0.757139π-0.757139\pi
−0.722787 + 0.691070i 0.757139π0.757139\pi
182182 −43.7279 + 163.195i −0.240263 + 0.896674i
183183 29.1924 26.4899i 0.159521 0.144753i
184184 10.6299 + 6.13718i 0.0577712 + 0.0333542i
185185 −66.3709 63.9370i −0.358762 0.345606i
186186 −150.046 + 233.017i −0.806701 + 1.25278i
187187 −9.25307 + 34.5329i −0.0494817 + 0.184668i
188188 −24.2191 + 24.2191i −0.128825 + 0.128825i
189189 −124.411 + 49.4189i −0.658261 + 0.261476i
190190 561.646 + 139.305i 2.95603 + 0.733183i
191191 −89.7939 155.528i −0.470125 0.814280i 0.529291 0.848440i 0.322458π-0.322458\pi
−0.999416 + 0.0341597i 0.989125π0.989125\pi
192192 −14.9562 + 3.23948i −0.0778968 + 0.0168723i
193193 6.95596 + 25.9600i 0.0360412 + 0.134508i 0.981602 0.190937i 0.0611526π-0.0611526\pi
−0.945561 + 0.325445i 0.894486π0.894486\pi
194194 −489.716 282.738i −2.52431 1.45741i
195195 −125.192 + 67.3849i −0.642012 + 0.345564i
196196 −108.967 188.737i −0.555956 0.962944i
197197 118.588 + 118.588i 0.601967 + 0.601967i 0.940834 0.338867i 0.110044π-0.110044\pi
−0.338867 + 0.940834i 0.610044π0.610044\pi
198198 68.8481 56.6385i 0.347718 0.286053i
199199 23.9129i 0.120166i −0.998193 0.0600828i 0.980864π-0.980864\pi
0.998193 0.0600828i 0.0191365π-0.0191365\pi
200200 301.111 324.489i 1.50555 1.62244i
201201 −63.9281 124.277i −0.318050 0.618292i
202202 −286.830 + 76.8559i −1.41995 + 0.380475i
203203 44.6524 + 166.645i 0.219963 + 0.820912i
204204 308.948 158.923i 1.51445 0.779035i
205205 97.7829 176.915i 0.476990 0.862999i
206206 180.035 0.873956
207207 −3.96351 4.81793i −0.0191474 0.0232750i
208208 −187.385 + 187.385i −0.900889 + 0.900889i
209209 76.8130 44.3480i 0.367526 0.212191i
210210 −76.8713 + 256.086i −0.366054 + 1.21946i
211211 68.1081 117.967i 0.322787 0.559084i −0.658275 0.752778i 0.728713π-0.728713\pi
0.981062 + 0.193694i 0.0620468π0.0620468\pi
212212 380.685 102.004i 1.79568 0.481152i
213213 −72.4371 334.431i −0.340080 1.57010i
214214 253.036 146.090i 1.18241 0.682665i
215215 18.5154 + 4.59236i 0.0861180 + 0.0213598i
216216 −473.037 69.3116i −2.18999 0.320887i
217217 −90.0878 90.0878i −0.415151 0.415151i
218218 506.496 + 135.715i 2.32338 + 0.622547i
219219 −67.0548 43.1785i −0.306186 0.197162i
220220 −2.29622 122.936i −0.0104374 0.558801i
221221 −61.4931 + 106.509i −0.278249 + 0.481942i
222222 133.588 + 147.217i 0.601750 + 0.663141i
223223 −387.566 103.848i −1.73796 0.465686i −0.755970 0.654606i 0.772834π-0.772834\pi
−0.981992 + 0.188921i 0.939501π0.939501\pi
224224 147.195i 0.657119i
225225 −201.215 + 100.685i −0.894288 + 0.447491i
226226 −194.913 −0.862445
227227 48.9929 182.844i 0.215828 0.805480i −0.770046 0.637988i 0.779767π-0.779767\pi
0.985874 0.167491i 0.0535666π-0.0535666\pi
228228 −820.777 263.185i −3.59990 1.15432i
229229 −128.197 74.0143i −0.559810 0.323207i 0.193259 0.981148i 0.438094π-0.438094\pi
−0.753069 + 0.657941i 0.771428π0.771428\pi
230230 −12.4585 + 0.232702i −0.0541676 + 0.00101175i
231231 18.7466 + 36.4435i 0.0811541 + 0.157764i
232232 −159.470 + 595.151i −0.687372 + 2.56531i
233233 191.869 191.869i 0.823473 0.823473i −0.163131 0.986604i 0.552159π-0.552159\pi
0.986604 + 0.163131i 0.0521593π0.0521593\pi
234234 279.200 126.902i 1.19316 0.542315i
235235 4.61917 18.6235i 0.0196561 0.0792488i
236236 189.945 + 328.994i 0.804850 + 1.39404i
237237 −42.6131 46.9605i −0.179802 0.198146i
238238 59.8616 + 223.406i 0.251519 + 0.938682i
239239 −113.709 65.6499i −0.475770 0.274686i 0.242882 0.970056i 0.421907π-0.421907\pi
−0.718652 + 0.695370i 0.755240π0.755240\pi
240240 −305.256 + 287.573i −1.27190 + 1.19822i
241241 106.787 + 184.961i 0.443101 + 0.767473i 0.997918 0.0644993i 0.0205450π-0.0205450\pi
−0.554817 + 0.831972i 0.687212π0.687212\pi
242242 288.303 + 288.303i 1.19133 + 1.19133i
243243 212.752 + 117.412i 0.875522 + 0.483178i
244244 117.276i 0.480640i
245245 106.854 + 59.0594i 0.436139 + 0.241059i
246246 −236.067 + 366.604i −0.959622 + 1.49026i
247247 294.723 78.9708i 1.19321 0.319720i
248248 −117.764 439.501i −0.474854 1.77218i
249249 2.22363 45.8155i 0.00893025 0.183998i
250250 −91.8216 + 439.915i −0.367287 + 1.75966i
251251 48.4611 0.193072 0.0965360 0.995329i 0.469224π-0.469224\pi
0.0965360 + 0.995329i 0.469224π0.469224\pi
252252 139.848 372.903i 0.554952 1.47978i
253253 −1.35054 + 1.35054i −0.00533809 + 0.00533809i
254254 −221.943 + 128.139i −0.873792 + 0.504484i
255255 −102.298 + 165.580i −0.401170 + 0.649332i
256256 236.231 409.164i 0.922777 1.59830i
257257 −450.204 + 120.632i −1.75177 + 0.469385i −0.985002 0.172542i 0.944802π-0.944802\pi
−0.766766 + 0.641927i 0.778135π0.778135\pi
258258 −39.1845 12.5646i −0.151878 0.0487002i
259259 −79.1411 + 45.6921i −0.305564 + 0.176418i
260260 101.827 410.543i 0.391641 1.57901i
261261 182.114 254.775i 0.697755 0.976151i
262262 −456.032 456.032i −1.74058 1.74058i
263263 −104.698 28.0536i −0.398090 0.106668i 0.0542194 0.998529i 0.482733π-0.482733\pi
−0.452309 + 0.891861i 0.649400π0.649400\pi
264264 −7.09532 + 146.191i −0.0268762 + 0.553755i
265265 −153.177 + 159.008i −0.578027 + 0.600031i
266266 286.904 496.932i 1.07859 1.86816i
267267 271.037 58.7060i 1.01512 0.219873i
268268 401.614 + 107.612i 1.49856 + 0.401538i
269269 271.965i 1.01102i 0.862821 + 0.505510i 0.168696π0.168696\pi
−0.862821 + 0.505510i 0.831304π0.831304\pi
270270 447.640 187.565i 1.65793 0.694686i
271271 283.330 1.04550 0.522749 0.852487i 0.324907π-0.324907\pi
0.522749 + 0.852487i 0.324907π0.324907\pi
272272 −93.8935 + 350.415i −0.345197 + 1.28829i
273273 29.8444 + 137.787i 0.109320 + 0.504715i
274274 −439.268 253.611i −1.60317 0.925589i
275275 36.6447 + 58.3260i 0.133254 + 0.212094i
276276 18.5389 + 0.899774i 0.0671698 + 0.00326005i
277277 −38.5154 + 143.741i −0.139045 + 0.518922i 0.860904 + 0.508768i 0.169899π0.169899\pi
−0.999948 + 0.0101539i 0.996768π0.996768\pi
278278 −692.948 + 692.948i −2.49262 + 2.49262i
279279 −22.3961 + 230.180i −0.0802727 + 0.825018i
280280 −226.541 375.985i −0.809074 1.34280i
281281 −126.241 218.657i −0.449258 0.778137i 0.549080 0.835770i 0.314978π-0.314978\pi
−0.998338 + 0.0576326i 0.981645π0.981645\pi
282282 −12.6380 + 39.4133i −0.0448156 + 0.139763i
283283 124.137 + 463.286i 0.438647 + 1.63705i 0.732184 + 0.681107i 0.238501π0.238501\pi
−0.293537 + 0.955948i 0.594832π0.594832\pi
284284 881.639 + 509.015i 3.10436 + 1.79230i
285285 469.934 111.013i 1.64889 0.389520i
286286 −46.9450 81.3111i −0.164143 0.284304i
287287 −141.735 141.735i −0.493849 0.493849i
288288 206.342 169.749i 0.716467 0.589407i
289289 120.637i 0.417430i
290290 −173.146 601.059i −0.597056 2.07262i
291291 −471.308 22.8747i −1.61962 0.0786072i
292292 229.189 61.4111i 0.784895 0.210312i
293293 −52.5299 196.044i −0.179283 0.669093i −0.995782 0.0917468i 0.970755π-0.970755\pi
0.816499 0.577346i 0.195912π-0.195912\pi
294294 −221.424 142.581i −0.753142 0.484969i
295295 −186.261 102.948i −0.631392 0.348978i
296296 −326.367 −1.10259
297297 29.4685 68.3073i 0.0992207 0.229991i
298298 −510.777 + 510.777i −1.71402 + 1.71402i
299299 −5.69008 + 3.28517i −0.0190304 + 0.0109872i
300300 180.446 644.612i 0.601487 2.14871i
301301 9.45814 16.3820i 0.0314224 0.0544252i
302302 −407.385 + 109.159i −1.34896 + 0.361452i
303303 −183.502 + 166.514i −0.605616 + 0.549551i
304304 779.443 450.011i 2.56396 1.48030i
305305 −33.9065 56.2739i −0.111169 0.184505i
306306 244.144 341.555i 0.797857 1.11619i
307307 364.680 + 364.680i 1.18788 + 1.18788i 0.977652 + 0.210232i 0.0674220π0.0674220\pi
0.210232 + 0.977652i 0.432578π0.432578\pi
308308 −117.771 31.5567i −0.382374 0.102457i
309309 133.592 68.7200i 0.432337 0.222395i
310310 332.664 + 320.465i 1.07311 + 1.03376i
311311 −102.480 + 177.501i −0.329518 + 0.570743i −0.982416 0.186703i 0.940220π-0.940220\pi
0.652898 + 0.757446i 0.273553π0.273553\pi
312312 −153.739 + 479.454i −0.492752 + 1.53671i
313313 343.429 + 92.0214i 1.09722 + 0.293998i 0.761631 0.648011i 0.224399π-0.224399\pi
0.335586 + 0.942010i 0.391066π0.391066\pi
314314 763.222i 2.43064i
315315 40.7078 + 219.367i 0.129231 + 0.696402i
316316 188.657 0.597017
317317 −6.68768 + 24.9588i −0.0210968 + 0.0787343i −0.975672 0.219237i 0.929643π-0.929643\pi
0.954575 + 0.297971i 0.0963099π0.0963099\pi
318318 352.696 320.045i 1.10911 1.00643i
319319 −83.0303 47.9375i −0.260283 0.150274i
320320 0.476303 + 25.5006i 0.00148845 + 0.0796893i
321321 131.998 204.989i 0.411209 0.638595i
322322 −3.19801 + 11.9351i −0.00993169 + 0.0370656i
323323 295.356 295.356i 0.914414 0.914414i
324324 −684.025 + 234.000i −2.11119 + 0.722222i
325325 69.8340 + 226.435i 0.214874 + 0.696723i
326326 155.465 + 269.273i 0.476886 + 0.825992i
327327 427.640 92.6260i 1.30777 0.283260i
328328 −185.277 691.464i −0.564869 2.10812i
329329 −16.4776 9.51337i −0.0500840 0.0289160i
330330 −70.4231 130.837i −0.213403 0.396476i
331331 96.8582 + 167.763i 0.292623 + 0.506838i 0.974429 0.224695i 0.0721386π-0.0721386\pi
−0.681806 + 0.731533i 0.738805π0.738805\pi
332332 96.4953 + 96.4953i 0.290649 + 0.290649i
333333 155.321 + 58.2491i 0.466428 + 0.174922i
334334 874.462i 2.61815i
335335 −223.823 + 64.4766i −0.668129 + 0.192467i
336336 190.227 + 369.802i 0.566151 + 1.10060i
337337 88.6729 23.7598i 0.263124 0.0705039i −0.124845 0.992176i 0.539843π-0.539843\pi
0.387969 + 0.921672i 0.373177π0.373177\pi
338338 73.6588 + 274.898i 0.217925 + 0.813309i
339339 −144.632 + 74.3989i −0.426643 + 0.219466i
340340 −160.287 556.418i −0.471431 1.63652i
341341 70.8008 0.207627
342342 −1027.48 + 170.886i −3.00433 + 0.499665i
343343 257.393 257.393i 0.750417 0.750417i
344344 58.5061 33.7785i 0.170076 0.0981933i
345345 −9.15585 + 4.92815i −0.0265387 + 0.0142845i
346346 30.3870 52.6318i 0.0878236 0.152115i
347347 5.84253 1.56550i 0.0168372 0.00451153i −0.250391 0.968145i 0.580559π-0.580559\pi
0.267228 + 0.963633i 0.413892π0.413892\pi
348348 197.232 + 910.591i 0.566759 + 2.61664i
349349 67.8704 39.1850i 0.194471 0.112278i −0.399603 0.916688i 0.630852π-0.630852\pi
0.594074 + 0.804410i 0.297519π0.297519\pi
350350 393.973 + 208.245i 1.12564 + 0.594986i
351351 158.737 200.737i 0.452242 0.571901i
352352 −57.8408 57.8408i −0.164320 0.164320i
353353 38.2322 + 10.2443i 0.108307 + 0.0290207i 0.312565 0.949896i 0.398812π-0.398812\pi
−0.204259 + 0.978917i 0.565478π0.565478\pi
354354 385.971 + 248.538i 1.09031 + 0.702084i
355355 −570.211 + 10.6505i −1.60623 + 0.0300013i
356356 −412.526 + 714.516i −1.15878 + 2.00707i
357357 129.694 + 142.926i 0.363290 + 0.400353i
358358 −953.287 255.433i −2.66281 0.713499i
359359 116.601i 0.324795i −0.986725 0.162398i 0.948077π-0.948077\pi
0.986725 0.162398i 0.0519227π-0.0519227\pi
360360 −265.815 + 751.169i −0.738374 + 2.08658i
361361 −675.274 −1.87056
362362 243.464 908.619i 0.672552 2.51000i
363363 323.977 + 103.884i 0.892499 + 0.286183i
364364 −363.239 209.716i −0.997910 0.576144i
365365 −92.2195 + 95.7300i −0.252656 + 0.262274i
366366 64.8269 + 126.024i 0.177123 + 0.344328i
367367 112.479 419.779i 0.306483 1.14381i −0.625177 0.780483i 0.714973π-0.714973\pi
0.931661 0.363329i 0.118360π-0.118360\pi
368368 −13.7043 + 13.7043i −0.0372398 + 0.0372398i
369369 −35.2356 + 362.141i −0.0954895 + 0.981411i
370370 283.790 170.991i 0.766999 0.462137i
371371 109.467 + 189.602i 0.295059 + 0.511058i
372372 −462.358 509.528i −1.24290 1.36970i
373373 −167.428 624.849i −0.448868 1.67520i −0.705516 0.708694i 0.749285π-0.749285\pi
0.256647 0.966505i 0.417382π-0.417382\pi
374374 −111.311 64.2656i −0.297624 0.171833i
375375 99.7824 + 361.481i 0.266086 + 0.963949i
376376 −33.9757 58.8477i −0.0903610 0.156510i
377377 −233.215 233.215i −0.618608 0.618608i
378378 −55.8510 478.023i −0.147754 1.26461i
379379 297.836i 0.785846i −0.919571 0.392923i 0.871464π-0.871464\pi
0.919571 0.392923i 0.128536π-0.128536\pi
380380 −694.925 + 1257.30i −1.82875 + 3.30869i
381381 −115.778 + 179.800i −0.303880 + 0.471916i
382382 623.648 167.106i 1.63259 0.437450i
383383 −111.047 414.434i −0.289941 1.08207i −0.945153 0.326629i 0.894087π-0.894087\pi
0.655212 0.755445i 0.272579π-0.272579\pi
384384 19.9375 410.790i 0.0519206 1.06977i
385385 65.6351 18.9074i 0.170481 0.0491102i
386386 −96.6228 −0.250318
387387 −33.8722 + 5.63346i −0.0875251 + 0.0145567i
388388 992.656 992.656i 2.55839 2.55839i
389389 −197.682 + 114.132i −0.508181 + 0.293398i −0.732086 0.681213i 0.761453π-0.761453\pi
0.223905 + 0.974611i 0.428120π0.428120\pi
390390 −117.514 497.452i −0.301318 1.27552i
391391 −4.49725 + 7.78947i −0.0115019 + 0.0199219i
392392 417.634 111.905i 1.06539 0.285471i
393393 −512.461 164.322i −1.30397 0.418123i
394394 −522.160 + 301.469i −1.32528 + 0.765151i
395395 −90.5255 + 54.5440i −0.229178 + 0.138086i
396396 91.5801 + 201.488i 0.231263 + 0.508808i
397397 120.533 + 120.533i 0.303609 + 0.303609i 0.842424 0.538815i 0.181128π-0.181128\pi
−0.538815 + 0.842424i 0.681128π0.681128\pi
398398 83.0416 + 22.2509i 0.208647 + 0.0559069i
399399 23.2117 478.253i 0.0581748 1.19863i
400400 371.844 + 591.850i 0.929610 + 1.47962i
401401 226.669 392.602i 0.565259 0.979057i −0.431766 0.901985i 0.642110π-0.642110\pi
0.997026 0.0770720i 0.0245571π-0.0245571\pi
402402 491.056 106.362i 1.22153 0.264581i
403403 235.260 + 63.0377i 0.583772 + 0.156421i
404404 737.193i 1.82473i
405405 260.570 310.046i 0.643382 0.765545i
406406 −620.251 −1.52771
407407 13.1439 49.0538i 0.0322946 0.120525i
408408 145.911 + 673.648i 0.357624 + 1.65110i
409409 427.158 + 246.620i 1.04440 + 0.602982i 0.921075 0.389385i 0.127312π-0.127312\pi
0.123320 + 0.992367i 0.460646π0.460646\pi
410410 523.379 + 504.186i 1.27653 + 1.22972i
411411 −422.756 20.5183i −1.02860 0.0499228i
412412 −115.679 + 431.718i −0.280773 + 1.04786i
413413 −149.222 + 149.222i −0.361312 + 0.361312i
414414 20.4191 9.28087i 0.0493214 0.0224176i
415415 −74.2008 18.4040i −0.178797 0.0443470i
416416 −140.697 243.695i −0.338214 0.585805i
417417 −249.691 + 778.693i −0.598778 + 1.86737i
418418 82.5314 + 308.011i 0.197444 + 0.736870i
419419 −22.7963 13.1615i −0.0544066 0.0314116i 0.472550 0.881304i 0.343334π-0.343334\pi
−0.526957 + 0.849892i 0.676667π0.676667\pi
420420 −564.694 348.879i −1.34451 0.830664i
421421 243.419 + 421.613i 0.578192 + 1.00146i 0.995687 + 0.0927780i 0.0295747π0.0295747\pi
−0.417495 + 0.908679i 0.637092π0.637092\pi
422422 346.284 + 346.284i 0.820579 + 0.820579i
423423 5.66635 + 34.0700i 0.0133956 + 0.0805437i
424424 781.894i 1.84409i
425425 237.782 + 220.650i 0.559486 + 0.519177i
426426 1228.77 + 59.6377i 2.88444 + 0.139995i
427427 −62.9281 + 16.8615i −0.147373 + 0.0394884i
428428 187.736 + 700.641i 0.438636 + 1.63701i
429429 −65.8715 42.4166i −0.153547 0.0988731i
430430 −33.1762 + 60.0244i −0.0771540 + 0.139592i
431431 73.2818 0.170027 0.0850137 0.996380i 0.472907π-0.472907\pi
0.0850137 + 0.996380i 0.472907π0.472907\pi
432432 299.025 693.133i 0.692189 1.60447i
433433 79.7731 79.7731i 0.184234 0.184234i −0.608964 0.793198i 0.708415π-0.708415\pi
0.793198 + 0.608964i 0.208415π0.208415\pi
434434 396.671 229.018i 0.913989 0.527692i
435435 −357.907 379.916i −0.822775 0.873369i
436436 −650.882 + 1127.36i −1.49285 + 2.58569i
437437 21.5544 5.77547i 0.0493235 0.0132162i
438438 212.339 192.681i 0.484791 0.439911i
439439 −97.4363 + 56.2549i −0.221951 + 0.128143i −0.606853 0.794814i 0.707568π-0.707568\pi
0.384903 + 0.922957i 0.374235π0.374235\pi
440440 236.765 + 58.7248i 0.538102 + 0.133465i
441441 −218.728 21.2818i −0.495981 0.0482581i
442442 −312.651 312.651i −0.707356 0.707356i
443443 −154.045 41.2762i −0.347731 0.0931742i 0.0807263 0.996736i 0.474276π-0.474276\pi
−0.428457 + 0.903562i 0.640943π0.640943\pi
444444 −438.858 + 225.749i −0.988418 + 0.508444i
445445 −8.63158 462.122i −0.0193968 1.03848i
446446 721.258 1249.25i 1.61717 2.80102i
447447 −184.049 + 573.980i −0.411742 + 1.28407i
448448 24.4292 + 6.54578i 0.0545295 + 0.0146111i
449449 291.806i 0.649901i 0.945731 + 0.324951i 0.105348π0.105348\pi
−0.945731 + 0.324951i 0.894652π0.894652\pi
450450 −162.417 792.439i −0.360926 1.76098i
451451 111.390 0.246985
452452 125.238 467.395i 0.277075 1.03406i
453453 −260.628 + 236.500i −0.575337 + 0.522075i
454454 589.367 + 340.271i 1.29817 + 0.749497i
455455 234.929 4.38804i 0.516328 0.00964405i
456456 925.800 1437.74i 2.03026 3.15293i
457457 121.316 452.757i 0.265462 0.990716i −0.696506 0.717551i 0.745263π-0.745263\pi
0.961967 0.273165i 0.0880705π-0.0880705\pi
458458 376.313 376.313i 0.821645 0.821645i
459459 50.7907 346.636i 0.110655 0.755199i
460460 7.44703 30.0247i 0.0161892 0.0652712i
461461 −248.770 430.882i −0.539631 0.934668i −0.998924 0.0463832i 0.985230π-0.985230\pi
0.459293 0.888285i 0.348103π-0.348103\pi
462462 −144.000 + 31.1900i −0.311688 + 0.0675109i
463463 235.850 + 880.204i 0.509395 + 1.90109i 0.426391 + 0.904539i 0.359785π0.359785\pi
0.0830044 + 0.996549i 0.473548π0.473548\pi
464464 −842.531 486.435i −1.81580 1.04835i
465465 369.171 + 110.817i 0.793917 + 0.238316i
466466 487.764 + 844.831i 1.04670 + 1.81294i
467467 −204.884 204.884i −0.438724 0.438724i 0.452859 0.891582i 0.350404π-0.350404\pi
−0.891582 + 0.452859i 0.850404π0.850404\pi
468468 124.911 + 751.052i 0.266904 + 1.60481i
469469 230.970i 0.492474i
470470 60.3749 + 33.3699i 0.128457 + 0.0709998i
471471 −291.325 566.337i −0.618524 1.20241i
472472 −727.991 + 195.065i −1.54235 + 0.413273i
473473 2.72075 + 10.1540i 0.00575212 + 0.0214672i
474474 202.729 104.284i 0.427699 0.220009i
475475 −30.0531 804.219i −0.0632697 1.69309i
476476 −574.185 −1.20627
477477 139.550 372.109i 0.292558 0.780104i
478478 333.786 333.786i 0.698297 0.698297i
479479 −177.082 + 102.238i −0.369691 + 0.213441i −0.673324 0.739348i 0.735134π-0.735134\pi
0.303632 + 0.952789i 0.401801π0.401801\pi
480480 −211.063 392.127i −0.439714 0.816931i
481481 87.3504 151.295i 0.181602 0.314543i
482482 −741.673 + 198.731i −1.53874 + 0.412304i
483483 2.18265 + 10.0770i 0.00451894 + 0.0208633i
484484 −876.586 + 506.097i −1.81113 + 1.04566i
485485 −189.324 + 763.310i −0.390358 + 1.57384i
486486 −605.699 + 629.564i −1.24629 + 1.29540i
487487 −506.650 506.650i −1.04035 1.04035i −0.999151 0.0411985i 0.986882π-0.986882\pi
−0.0411985 0.999151i 0.513118π-0.513118\pi
488488 −224.740 60.2188i −0.460532 0.123399i
489489 218.143 + 140.469i 0.446100 + 0.287257i
490490 −304.521 + 316.113i −0.621471 + 0.645129i
491491 −104.633 + 181.229i −0.213101 + 0.369102i −0.952684 0.303964i 0.901690π-0.901690\pi
0.739582 + 0.673066i 0.235023π0.235023\pi
492492 −727.425 801.637i −1.47851 1.62934i
493493 −436.120 116.858i −0.884624 0.237034i
494494 1096.96i 2.22056i
495495 −102.197 70.2048i −0.206459 0.141828i
496496 718.435 1.44846
497497 −146.368 + 546.254i −0.294504 + 1.09910i
498498 157.033 + 50.3532i 0.315327 + 0.101111i
499499 −287.007 165.704i −0.575165 0.332072i 0.184044 0.982918i 0.441081π-0.441081\pi
−0.759210 + 0.650846i 0.774414π0.774414\pi
500500 −995.905 502.846i −1.99181 1.00569i
501501 333.786 + 648.881i 0.666239 + 1.29517i
502502 −45.0929 + 168.289i −0.0898265 + 0.335237i
503503 −278.209 + 278.209i −0.553100 + 0.553100i −0.927334 0.374234i 0.877906π-0.877906\pi
0.374234 + 0.927334i 0.377906π0.377906\pi
504504 642.796 + 459.472i 1.27539 + 0.911651i
505505 213.135 + 353.735i 0.422049 + 0.700466i
506506 −3.43329 5.94663i −0.00678515 0.0117522i
507507 159.587 + 175.868i 0.314768 + 0.346880i
508508 −164.667 614.546i −0.324148 1.20974i
509509 679.279 + 392.182i 1.33454 + 0.770495i 0.985991 0.166797i 0.0533423π-0.0533423\pi
0.348546 + 0.937292i 0.386676π0.386676\pi
510510 −479.814 509.319i −0.940812 0.998666i
511511 65.9040 + 114.149i 0.128971 + 0.223384i
512512 813.324 + 813.324i 1.58852 + 1.58852i
513513 −697.199 + 518.996i −1.35906 + 1.01169i
514514 1675.66i 3.26003i
515515 −69.3096 240.601i −0.134582 0.467186i
516516 55.3070 85.8900i 0.107184 0.166453i
517517 10.2133 2.73664i 0.0197549 0.00529330i
518518 −85.0329 317.347i −0.164156 0.612639i
519519 2.45844 50.6534i 0.00473687 0.0975981i
520520 734.448 + 405.938i 1.41240 + 0.780650i
521521 763.749 1.46593 0.732964 0.680267i 0.238136π-0.238136\pi
0.732964 + 0.680267i 0.238136π0.238136\pi
522522 715.292 + 869.489i 1.37029 + 1.66569i
523523 −284.699 + 284.699i −0.544358 + 0.544358i −0.924803 0.380445i 0.875771π-0.875771\pi
0.380445 + 0.924803i 0.375771π0.375771\pi
524524 1386.57 800.535i 2.64612 1.52774i
525525 371.830 + 4.14403i 0.708247 + 0.00789338i
526526 194.842 337.476i 0.370421 0.641589i
527527 322.061 86.2959i 0.611121 0.163749i
528528 −220.066 70.5649i −0.416791 0.133646i
529529 457.711 264.260i 0.865239 0.499546i
530530 −409.651 679.889i −0.772926 1.28281i
531531 381.272 + 37.0970i 0.718026 + 0.0698625i
532532 1007.28 + 1007.28i 1.89339 + 1.89339i
533533 370.133 + 99.1769i 0.694434 + 0.186073i
534534 −48.3328 + 995.845i −0.0905109 + 1.86488i
535535 −292.650 281.918i −0.547010 0.526950i
536536 −412.440 + 714.367i −0.769478 + 1.33277i
537537 −804.872 + 174.334i −1.49883 + 0.324643i
538538 −944.442 253.062i −1.75547 0.470376i
539539 67.2782i 0.124820i
540540 162.152 + 1193.94i 0.300281 + 2.21101i
541541 120.576 0.222876 0.111438 0.993771i 0.464454π-0.464454\pi
0.111438 + 0.993771i 0.464454π0.464454\pi
542542 −263.638 + 983.909i −0.486416 + 1.81533i
543543 −166.165 767.158i −0.306013 1.41281i
544544 −333.608 192.608i −0.613249 0.354060i
545545 −13.6189 729.134i −0.0249887 1.33786i
546546 −506.259 24.5710i −0.927214 0.0450018i
547547 59.6213 222.510i 0.108997 0.406782i −0.889771 0.456407i 0.849136π-0.849136\pi
0.998768 + 0.0496252i 0.0158027π0.0158027\pi
548548 890.397 890.397i 1.62481 1.62481i
549549 96.2077 + 68.7695i 0.175242 + 0.125263i
550550 −236.644 + 72.9827i −0.430262 + 0.132696i
551551 560.075 + 970.078i 1.01647 + 1.76058i
552552 −11.2436 + 35.0645i −0.0203688 + 0.0635227i
553553 27.1244 + 101.230i 0.0490496 + 0.183056i
554554 −463.327 267.502i −0.836330 0.482855i
555555 145.314 235.205i 0.261827 0.423792i
556556 −1216.43 2106.91i −2.18782 3.78941i
557557 −664.417 664.417i −1.19285 1.19285i −0.976264 0.216586i 0.930508π-0.930508\pi
−0.216586 0.976264i 0.569492π-0.569492\pi
558558 −778.498 291.956i −1.39516 0.523219i
559559 36.1626i 0.0646915i
560560 666.017 191.859i 1.18932 0.342605i
561561 −107.127 5.19937i −0.190958 0.00926803i
562562 876.788 234.935i 1.56012 0.418033i
563563 71.6752 + 267.496i 0.127309 + 0.475125i 0.999911 0.0133066i 0.00423574π-0.00423574\pi
−0.872602 + 0.488432i 0.837569π0.837569\pi
564564 −86.3915 55.6299i −0.153176 0.0986346i
565565 75.0372 + 260.483i 0.132809 + 0.461033i
566566 −1724.35 −3.04655
567567 −223.906 333.391i −0.394897 0.587991i
568568 −1428.14 + 1428.14i −2.51433 + 2.51433i
569569 830.591 479.542i 1.45974 0.842780i 0.460740 0.887535i 0.347584π-0.347584\pi
0.998998 + 0.0447548i 0.0142506π0.0142506\pi
570570 −51.7604 + 1735.22i −0.0908077 + 3.04424i
571571 −222.371 + 385.158i −0.389442 + 0.674533i −0.992375 0.123259i 0.960665π-0.960665\pi
0.602933 + 0.797792i 0.293999π0.293999\pi
572572 225.145 60.3275i 0.393611 0.105468i
573573 398.983 362.047i 0.696306 0.631845i
574574 624.080 360.313i 1.08725 0.627723i
575575 5.10726 + 16.5602i 0.00888219 + 0.0288003i
576576 −18.9964 41.7944i −0.0329798 0.0725598i
577577 670.378 + 670.378i 1.16183 + 1.16183i 0.984074 + 0.177761i 0.0568852π0.0568852\pi
0.177761 + 0.984074i 0.443115π0.443115\pi
578578 418.933 + 112.253i 0.724797 + 0.194209i
579579 −71.6975 + 36.8813i −0.123830 + 0.0636983i
580580 1552.57 28.9992i 2.67685 0.0499986i
581581 −37.9038 + 65.6513i −0.0652388 + 0.112997i
582582 517.987 1615.41i 0.890013 2.77562i
583583 −117.521 31.4895i −0.201579 0.0540129i
584584 470.735i 0.806053i
585585 −277.079 324.271i −0.473639 0.554310i
586586 729.675 1.24518
587587 −116.613 + 435.207i −0.198660 + 0.741410i 0.792629 + 0.609704i 0.208712π0.208712\pi
−0.991289 + 0.131705i 0.957955π0.957955\pi
588588 484.177 439.354i 0.823431 0.747201i
589589 −716.373 413.598i −1.21625 0.702204i
590590 530.820 551.027i 0.899696 0.933945i
591591 −272.389 + 423.011i −0.460895 + 0.715755i
592592 133.375 497.762i 0.225295 0.840814i
593593 292.884 292.884i 0.493902 0.493902i −0.415631 0.909533i 0.636439π-0.636439\pi
0.909533 + 0.415631i 0.136439π0.136439\pi
594594 209.788 + 165.894i 0.353178 + 0.279283i
595595 275.517 166.006i 0.463054 0.279002i
596596 −896.636 1553.02i −1.50442 2.60574i
597597 70.1130 15.1863i 0.117442 0.0254377i
598598 −6.11368 22.8166i −0.0102235 0.0381548i
599599 −434.899 251.089i −0.726042 0.419180i 0.0909308 0.995857i 0.471016π-0.471016\pi
−0.816972 + 0.576677i 0.804349π0.804349\pi
600600 1142.63 + 676.788i 1.90438 + 1.12798i
601601 −99.8075 172.872i −0.166069 0.287640i 0.770965 0.636877i 0.219774π-0.219774\pi
−0.937034 + 0.349237i 0.886441π0.886441\pi
602602 48.0883 + 48.0883i 0.0798810 + 0.0798810i
603603 323.782 266.362i 0.536952 0.441728i
604604 1047.04i 1.73350i
605605 274.301 496.282i 0.453390 0.820301i
606606 −407.499 792.180i −0.672440 1.30723i
607607 −837.927 + 224.522i −1.38044 + 0.369888i −0.871281 0.490785i 0.836710π-0.836710\pi
−0.509159 + 0.860672i 0.670043π0.670043\pi
608608 247.352 + 923.131i 0.406829 + 1.51831i
609609 −460.248 + 236.752i −0.755744 + 0.388756i
610610 226.970 65.3831i 0.372083 0.107185i
611611 36.3737 0.0595314
612612 662.167 + 804.911i 1.08197 + 1.31521i
613613 −31.6781 + 31.6781i −0.0516771 + 0.0516771i −0.732473 0.680796i 0.761634π-0.761634\pi
0.680796 + 0.732473i 0.261634π0.261634\pi
614614 −1605.75 + 927.078i −2.61522 + 1.50990i
615615 580.815 + 174.348i 0.944415 + 0.283492i
616616 120.946 209.485i 0.196341 0.340072i
617617 253.302 67.8722i 0.410539 0.110004i −0.0476380 0.998865i 0.515169π-0.515169\pi
0.458177 + 0.888861i 0.348503π0.348503\pi
618618 114.334 + 527.864i 0.185007 + 0.854149i
619619 −422.528 + 243.947i −0.682598 + 0.394098i −0.800833 0.598887i 0.795610π-0.795610\pi
0.118235 + 0.992986i 0.462276π0.462276\pi
620620 −982.214 + 591.809i −1.58422 + 0.954531i
621621 11.6091 14.6808i 0.0186942 0.0236405i
622622 −521.044 521.044i −0.837691 0.837691i
623623 −442.707 118.623i −0.710605 0.190406i
624624 −668.417 430.412i −1.07118 0.689764i
625625 623.257 46.6465i 0.997211 0.0746344i
626626 −639.119 + 1106.99i −1.02096 + 1.76835i
627627 178.810 + 197.053i 0.285184 + 0.314278i
628628 1830.18 + 490.396i 2.91431 + 0.780886i
629629 239.158i 0.380219i
630630 −799.665 62.7556i −1.26931 0.0996121i
631631 263.490 0.417576 0.208788 0.977961i 0.433048π-0.433048\pi
0.208788 + 0.977961i 0.433048π0.433048\pi
632632 −96.8714 + 361.529i −0.153277 + 0.572039i
633633 389.133 + 124.777i 0.614744 + 0.197120i
634634 −80.4505 46.4481i −0.126894 0.0732620i
635635 256.690 + 247.276i 0.404236 + 0.389412i
636636 540.838 + 1051.39i 0.850375 + 1.65313i
637637 −59.9014 + 223.555i −0.0940367 + 0.350950i
638638 243.730 243.730i 0.382023 0.382023i
639639 934.554 424.773i 1.46253 0.664746i
640640 −665.298 165.014i −1.03953 0.257834i
641641 −459.262 795.464i −0.716477 1.24097i −0.962387 0.271682i 0.912420π-0.912420\pi
0.245911 0.969293i 0.420913π-0.420913\pi
642642 589.034 + 649.127i 0.917498 + 1.01110i
643643 10.9456 + 40.8497i 0.0170228 + 0.0635298i 0.973915 0.226914i 0.0728637π-0.0728637\pi
−0.956892 + 0.290444i 0.906197π0.906197\pi
644644 −26.5652 15.3374i −0.0412504 0.0238159i
645645 −1.70635 + 57.2037i −0.00264550 + 0.0886879i
646646 750.843 + 1300.50i 1.16230 + 2.01316i
647647 −12.5734 12.5734i −0.0194334 0.0194334i 0.697323 0.716757i 0.254374π-0.254374\pi
−0.716757 + 0.697323i 0.754374π0.754374\pi
648648 −97.1884 1430.97i −0.149982 2.20829i
649649 117.275i 0.180701i
650650 −851.313 + 31.8130i −1.30971 + 0.0489430i
651651 206.927 321.350i 0.317860 0.493626i
652652 −745.601 + 199.783i −1.14356 + 0.306416i
653653 137.591 + 513.495i 0.210705 + 0.786363i 0.987634 + 0.156775i 0.0501096π0.0501096\pi
−0.776929 + 0.629588i 0.783224π0.783224\pi
654654 −76.2593 + 1571.24i −0.116604 + 2.40251i
655655 −433.884 + 785.009i −0.662418 + 1.19849i
656656 1130.31 1.72303
657657 84.0155 224.027i 0.127877 0.340984i
658658 48.3691 48.3691i 0.0735093 0.0735093i
659659 −64.8393 + 37.4350i −0.0983905 + 0.0568058i −0.548388 0.836224i 0.684758π-0.684758\pi
0.449997 + 0.893030i 0.351425π0.351425\pi
660660 358.992 84.8054i 0.543928 0.128493i
661661 11.3687 19.6912i 0.0171993 0.0297900i −0.857298 0.514821i 0.827858π-0.827858\pi
0.874497 + 0.485031i 0.161192π0.161192\pi
662662 −672.712 + 180.253i −1.01618 + 0.272285i
663663 −351.338 112.658i −0.529922 0.169921i
664664 −234.465 + 135.368i −0.353110 + 0.203868i
665665 −774.557 192.113i −1.16475 0.288892i
666666 −346.805 + 485.176i −0.520728 + 0.728492i
667667 −17.0560 17.0560i −0.0255713 0.0255713i
668668 −2096.93 561.872i −3.13912 0.841125i
669669 58.3528 1202.30i 0.0872240 1.79716i
670670 −15.6384 837.259i −0.0233409 1.24964i
671671 18.1021 31.3537i 0.0269777 0.0467268i
672672 −431.577 + 93.4786i −0.642227 + 0.139105i
673673 619.582 + 166.017i 0.920628 + 0.246681i 0.687854 0.725849i 0.258553π-0.258553\pi
0.232774 + 0.972531i 0.425220π0.425220\pi
674674 330.040i 0.489673i
675675 −422.996 526.022i −0.626661 0.779292i
676676 −706.526 −1.04516
677677 −150.613 + 562.095i −0.222471 + 0.830273i 0.760931 + 0.648833i 0.224742π0.224742\pi
−0.983402 + 0.181440i 0.941924π0.941924\pi
678678 −123.783 571.486i −0.182570 0.842900i
679679 675.360 + 389.919i 0.994639 + 0.574255i
680680 1148.58 21.4534i 1.68909 0.0315490i
681681 567.214 + 27.5294i 0.832913 + 0.0404250i
682682 −65.8799 + 245.867i −0.0965982 + 0.360509i
683683 599.384 599.384i 0.877576 0.877576i −0.115708 0.993283i 0.536914π-0.536914\pi
0.993283 + 0.115708i 0.0369136π0.0369136\pi
684684 250.413 2573.67i 0.366101 3.76267i
685685 −169.820 + 684.677i −0.247913 + 0.999529i
686686 654.336 + 1133.34i 0.953842 + 1.65210i
687687 135.597 422.878i 0.197376 0.615543i
688688 27.6082 + 103.035i 0.0401282 + 0.149761i
689689 −362.466 209.270i −0.526075 0.303730i
690690 −8.59430 36.3808i −0.0124555 0.0527258i
691691 −348.543 603.695i −0.504404 0.873654i −0.999987 0.00509303i 0.998379π-0.998379\pi
0.495583 0.868561i 0.334955π-0.334955\pi
692692 106.685 + 106.685i 0.154169 + 0.154169i
693693 −94.9474 + 78.1093i −0.137009 + 0.112712i
694694 21.7458i 0.0313340i
695695 1192.83 + 659.293i 1.71631 + 0.948624i
696696 −1846.26 89.6074i −2.65268 0.128746i
697697 506.696 135.769i 0.726967 0.194790i
698698 72.9231 + 272.153i 0.104474 + 0.389904i
699699 684.413 + 440.713i 0.979131 + 0.630491i
700700 −752.507 + 810.932i −1.07501 + 1.15847i
701701 −643.602 −0.918119 −0.459060 0.888405i 0.651814π-0.651814\pi
−0.459060 + 0.888405i 0.651814π0.651814\pi
702702 549.388 + 738.026i 0.782604 + 1.05132i
703703 −419.550 + 419.550i −0.596800 + 0.596800i
704704 −12.1718 + 7.02736i −0.0172894 + 0.00998205i
705705 57.5377 + 1.71631i 0.0816137 + 0.00243448i
706706 −71.1500 + 123.235i −0.100779 + 0.174554i
707707 395.563 105.991i 0.559495 0.149916i
708708 −843.985 + 765.853i −1.19207 + 1.08171i
709709 −1069.69 + 617.583i −1.50872 + 0.871062i −0.508775 + 0.860899i 0.669902π0.669902\pi
−0.999948 + 0.0101629i 0.996765π0.996765\pi
710710 493.594 1990.06i 0.695203 2.80290i
711711 110.627 154.765i 0.155593 0.217673i
712712 −1157.42 1157.42i −1.62559 1.62559i
713713 17.2056 + 4.61022i 0.0241312 + 0.00646594i
714714 −617.014 + 317.393i −0.864165 + 0.444528i
715715 −90.5922 + 94.0408i −0.126702 + 0.131526i
716716 1225.04 2121.83i 1.71095 2.96345i
717717 120.273 375.088i 0.167745 0.523135i
718718 404.918 + 108.497i 0.563952 + 0.151110i
719719 219.618i 0.305449i −0.988269 0.152724i 0.951195π-0.951195\pi
0.988269 0.152724i 0.0488047π-0.0488047\pi
720720 −1037.02 712.387i −1.44031 0.989426i
721721 −248.283 −0.344360
722722 628.340 2345.00i 0.870278 3.24792i
723723 −474.491 + 430.564i −0.656280 + 0.595525i
724724 2022.41 + 1167.64i 2.79338 + 1.61276i
725725 −736.604 + 462.789i −1.01601 + 0.638330i
726726 −662.216 + 1028.40i −0.912143 + 1.41653i
727727 73.8261 275.523i 0.101549 0.378986i −0.896382 0.443283i 0.853814π-0.853814\pi
0.997931 + 0.0642969i 0.0204805π0.0204805\pi
728728 588.400 588.400i 0.808242 0.808242i
729729 −209.143 + 698.355i −0.286890 + 0.957964i
730730 −246.628 409.324i −0.337847 0.560718i
731731 24.7525 + 42.8726i 0.0338611 + 0.0586492i
732732 −343.855 + 74.4783i −0.469748 + 0.101746i
733733 −181.709 678.149i −0.247898 0.925169i −0.971905 0.235375i 0.924368π-0.924368\pi
0.724006 0.689793i 0.242299π-0.242299\pi
734734 1353.09 + 781.206i 1.84345 + 1.06431i
735735 −105.303 + 350.804i −0.143270 + 0.477284i
736736 −10.2898 17.8224i −0.0139807 0.0242153i
737737 −90.7608 90.7608i −0.123149 0.123149i
738738 −1224.81 459.333i −1.65963 0.622402i
739739 1147.21i 1.55238i 0.630497 + 0.776192i 0.282851π0.282851\pi
−0.630497 + 0.776192i 0.717149π0.717149\pi
740740 227.686 + 790.387i 0.307684 + 1.06809i
741741 418.712 + 813.980i 0.565064 + 1.09849i
742742 −760.284 + 203.717i −1.02464 + 0.274552i
743743 226.953 + 847.001i 0.305455 + 1.13997i 0.932553 + 0.361034i 0.117576π0.117576\pi
−0.627098 + 0.778941i 0.715757π0.715757\pi
744744 1213.83 624.397i 1.63150 0.839244i
745745 879.246 + 485.970i 1.18020 + 0.652308i
746746 2325.68 3.11754
747747 135.744 22.5762i 0.181719 0.0302225i
748748 225.628 225.628i 0.301642 0.301642i
749749 −348.958 + 201.471i −0.465899 + 0.268987i
750750 −1348.15 + 10.1537i −1.79753 + 0.0135383i
751751 147.537 255.542i 0.196455 0.340269i −0.750922 0.660391i 0.770391π-0.770391\pi
0.947376 + 0.320122i 0.103724π0.103724\pi
752752 103.637 27.7694i 0.137815 0.0369274i
753753 30.7761 + 142.088i 0.0408713 + 0.188696i
754754 1026.88 592.872i 1.36192 0.786303i
755755 302.715 + 502.410i 0.400947 + 0.665444i
756756 1182.17 + 173.217i 1.56372 + 0.229123i
757757 89.6510 + 89.6510i 0.118429 + 0.118429i 0.763838 0.645408i 0.223313π-0.223313\pi
−0.645408 + 0.763838i 0.723313π0.723313\pi
758758 1034.28 + 277.135i 1.36449 + 0.365614i
759759 −4.81747 3.10210i −0.00634712 0.00408709i
760760 −2052.57 1977.30i −2.70075 2.60171i
761761 80.6635 139.713i 0.105997 0.183592i −0.808148 0.588979i 0.799530π-0.799530\pi
0.914145 + 0.405387i 0.132863π0.132863\pi
762762 −516.654 569.363i −0.678023 0.747195i
763763 −698.501 187.163i −0.915466 0.245298i
764764 1602.86i 2.09798i
765765 −550.448 194.786i −0.719540 0.254622i
766766 1542.52 2.01373
767767 104.416 389.686i 0.136136 0.508065i
768768 1349.70 + 432.785i 1.75742 + 0.563522i
769769 −129.486 74.7588i −0.168382 0.0972156i 0.413440 0.910531i 0.364327π-0.364327\pi
−0.581823 + 0.813316i 0.697660π0.697660\pi
770770 4.58589 + 245.522i 0.00595570 + 0.318859i
771771 −639.604 1243.40i −0.829578 1.61270i
772772 62.0835 231.699i 0.0804190 0.300128i
773773 −994.453 + 994.453i −1.28649 + 1.28649i −0.349578 + 0.936907i 0.613675π0.613675\pi
−0.936907 + 0.349578i 0.886325π0.886325\pi
774774 11.9549 122.869i 0.0154456 0.158745i
775775 300.204 567.949i 0.387361 0.732837i
776776 1392.55 + 2411.96i 1.79452 + 3.10819i
777777 −184.230 203.025i −0.237104 0.261294i
778778 −212.399 792.684i −0.273006 1.01887i
779779 −1127.06 650.711i −1.44681 0.835316i
780780 1268.38 + 37.8350i 1.62613 + 0.0485064i
781781 −157.137 272.169i −0.201200 0.348488i
782782 −22.8655 22.8655i −0.0292398 0.0292398i
783783 862.659 + 372.161i 1.10174 + 0.475301i
784784 682.690i 0.870778i
785785 −1019.98 + 293.824i −1.29934 + 0.374298i
786786 1047.48 1626.70i 1.33267 2.06960i
787787 −887.757 + 237.874i −1.12803 + 0.302254i −0.774128 0.633030i 0.781811π-0.781811\pi
−0.353899 + 0.935284i 0.615144π0.615144\pi
788788 −387.409 1445.83i −0.491635 1.83481i
789789 15.7635 324.790i 0.0199791 0.411648i
790790 −105.179 365.118i −0.133138 0.462174i
791791 268.801 0.339824
792792 −433.141 + 72.0378i −0.546895 + 0.0909569i
793793 88.0662 88.0662i 0.111055 0.111055i
794794 −530.725 + 306.414i −0.668420 + 0.385912i
795795 −563.492 348.136i −0.708794 0.437907i
796796 −106.714 + 184.834i −0.134063 + 0.232204i
797797 860.450 230.557i 1.07961 0.289281i 0.325175 0.945654i 0.394577π-0.394577\pi
0.754437 + 0.656373i 0.227910π0.227910\pi
798798 1639.21 + 525.620i 2.05415 + 0.658671i
799799 43.1229 24.8970i 0.0539711 0.0311602i
800800 −709.239 + 218.734i −0.886549 + 0.273417i
801801 344.253 + 757.400i 0.429779 + 0.945568i
802802 1152.46 + 1152.46i 1.43698 + 1.43698i
803803 −70.7526 18.9581i −0.0881104 0.0236091i
804804 −60.4680 + 1245.88i −0.0752090 + 1.54960i
805805 17.1814 0.320916i 0.0213433 0.000398654i
806806 −437.818 + 758.323i −0.543198 + 0.940847i
807807 −797.403 + 172.716i −0.988108 + 0.214022i
808808 1412.70 + 378.532i 1.74839 + 0.468480i
809809 1398.60i 1.72880i −0.502802 0.864402i 0.667698π-0.667698\pi
0.502802 0.864402i 0.332302π-0.332302\pi
810810 834.225 + 1193.37i 1.02991 + 1.47329i
811811 −347.451 −0.428423 −0.214211 0.976787i 0.568718π-0.568718\pi
−0.214211 + 0.976787i 0.568718π0.568718\pi
812812 398.533 1487.34i 0.490804 1.83170i
813813 179.934 + 830.726i 0.221321 + 1.02180i
814814 158.117 + 91.2888i 0.194247 + 0.112148i
815815 300.009 311.430i 0.368109 0.382122i
816816 −1087.05 52.7594i −1.33217 0.0646561i
817817 31.7877 118.633i 0.0389079 0.145206i
818818 −1253.90 + 1253.90i −1.53288 + 1.53288i
819819 −385.040 + 175.008i −0.470135 + 0.213685i
820820 −1545.31 + 931.090i −1.88453 + 1.13548i
821821 −493.294 854.410i −0.600845 1.04069i −0.992693 0.120665i 0.961497π-0.961497\pi
0.391848 0.920030i 0.371836π-0.371836\pi
822822 464.627 1449.00i 0.565239 1.76277i
823823 65.3381 + 243.845i 0.0793902 + 0.296288i 0.994193 0.107613i 0.0343207π-0.0343207\pi
−0.914803 + 0.403901i 0.867654π0.867654\pi
824824 −767.914 443.356i −0.931935 0.538053i
825825 −147.741 + 144.484i −0.179079 + 0.175132i
826826 −379.347 657.049i −0.459258 0.795458i
827827 1054.44 + 1054.44i 1.27502 + 1.27502i 0.943419 + 0.331604i 0.107590π0.107590\pi
0.331604 + 0.943419i 0.392410π0.392410\pi
828828 9.13529 + 54.9276i 0.0110330 + 0.0663377i
829829 819.644i 0.988714i −0.869259 0.494357i 0.835404π-0.835404\pi
0.869259 0.494357i 0.164596π-0.164596\pi
830830 132.955 240.550i 0.160186 0.289819i
831831 −445.911 21.6420i −0.536596 0.0260434i
832832 −46.7017 + 12.5137i −0.0561318 + 0.0150405i
833833 82.0024 + 306.037i 0.0984423 + 0.367392i
834834 −2471.80 1591.66i −2.96379 1.90847i
835835 1168.64 336.649i 1.39957 0.403173i
836836 −791.631 −0.946928
837837 −689.113 + 80.5143i −0.823313 + 0.0961939i
838838 66.9173 66.9173i 0.0798536 0.0798536i
839839 425.345 245.573i 0.506966 0.292697i −0.224619 0.974447i 0.572114π-0.572114\pi
0.731586 + 0.681749i 0.238781π0.238781\pi
840840 958.524 902.996i 1.14110 1.07499i
841841 184.907 320.269i 0.219866 0.380819i
842842 −1690.62 + 453.001i −2.00786 + 0.538006i
843843 560.932 509.003i 0.665399 0.603799i
844844 −1052.88 + 607.880i −1.24749 + 0.720237i
845845 339.020 204.268i 0.401207 0.241738i
846846 −123.586 12.0247i −0.146083 0.0142136i
847847 −397.594 397.594i −0.469415 0.469415i
848848 −1192.51 319.533i −1.40627 0.376808i
849849 −1279.53 + 658.190i −1.50710 + 0.775253i
850850 −987.500 + 620.421i −1.16176 + 0.729907i
851851 6.38831 11.0649i 0.00750682 0.0130022i
852852 −932.536 + 2908.23i −1.09453 + 3.41342i
853853 336.484 + 90.1607i 0.394472 + 0.105698i 0.450602 0.892725i 0.351209π-0.351209\pi
−0.0561301 + 0.998423i 0.517876π0.517876\pi
854854 234.218i 0.274260i
855855 623.932 + 1307.35i 0.729745 + 1.52906i
856856 −1439.05 −1.68114
857857 210.885 787.034i 0.246074 0.918359i −0.726767 0.686884i 0.758978π-0.758978\pi
0.972841 0.231475i 0.0743552π-0.0743552\pi
858858 208.592 189.281i 0.243114 0.220607i
859859 101.706 + 58.7201i 0.118401 + 0.0683587i 0.558031 0.829820i 0.311557π-0.311557\pi
−0.439630 + 0.898179i 0.644890π0.644890\pi
860860 −122.620 118.123i −0.142581 0.137353i
861861 325.556 505.579i 0.378114 0.587199i
862862 −68.1886 + 254.483i −0.0791051 + 0.295224i
863863 −148.570 + 148.570i −0.172155 + 0.172155i −0.787926 0.615770i 0.788845π-0.788845\pi
0.615770 + 0.787926i 0.288845π0.288845\pi
864864 628.748 + 497.196i 0.727718 + 0.575458i
865865 −82.0360 20.3474i −0.0948394 0.0235230i
866866 202.797 + 351.254i 0.234176 + 0.405605i
867867 353.710 76.6128i 0.407970 0.0883654i
868868 294.304 + 1098.36i 0.339060 + 1.26539i
869869 −50.4374 29.1200i −0.0580407 0.0335098i
870870 1652.35 889.380i 1.89925 1.02228i
871871 −220.775 382.393i −0.253473 0.439028i
872872 −1826.18 1826.18i −2.09424 2.09424i
873873 −232.244 1396.41i −0.266030 1.59955i
874874 80.2251i 0.0917907i
875875 126.630 606.680i 0.144720 0.693349i
876876 325.609 + 632.986i 0.371700 + 0.722587i
877877 480.790 128.827i 0.548221 0.146895i 0.0259318 0.999664i 0.491745π-0.491745\pi
0.522289 + 0.852768i 0.325078π0.325078\pi
878878 −104.690 390.709i −0.119237 0.444998i
879879 541.444 278.520i 0.615977 0.316860i
880880 −186.322 + 337.106i −0.211730 + 0.383075i
881881 306.447 0.347840 0.173920 0.984760i 0.444357π-0.444357\pi
0.173920 + 0.984760i 0.444357π0.444357\pi
882882 277.430 739.765i 0.314547 0.838736i
883883 930.058 930.058i 1.05329 1.05329i 0.0547963 0.998498i 0.482549π-0.482549\pi
0.998498 0.0547963i 0.0174509π-0.0174509\pi
884884 950.617 548.839i 1.07536 0.620859i
885885 183.558 611.498i 0.207410 0.690958i
886886 286.676 496.538i 0.323563 0.560427i
887887 −130.986 + 35.0975i −0.147673 + 0.0395688i −0.331898 0.943315i 0.607689π-0.607689\pi
0.184225 + 0.982884i 0.441022π0.441022\pi
888888 −207.265 956.911i −0.233407 1.07760i
889889 306.078 176.714i 0.344295 0.198779i
890890 1612.83 + 400.029i 1.81216 + 0.449471i
891891 218.992 + 43.0224i 0.245783 + 0.0482855i
892892 2532.24 + 2532.24i 2.83884 + 2.83884i
893893 −119.326 31.9733i −0.133624 0.0358044i
894894 −1821.98 1173.23i −2.03801 1.31233i
895895 25.6324 + 1372.32i 0.0286395 + 1.53332i
896896 −339.852 + 588.641i −0.379299 + 0.656965i
897897 −13.2457 14.5971i −0.0147667 0.0162732i
898898 −1013.34 271.524i −1.12844 0.302366i
899899 894.149i 0.994604i
900900 2004.60 + 119.698i 2.22734 + 0.132998i
901901 −572.962 −0.635918
902902 −103.649 + 386.822i −0.114910 + 0.428849i
903903 54.0387 + 17.3277i 0.0598435 + 0.0191891i
904904 831.374 + 479.994i 0.919661 + 0.530967i
905905 −1308.02 + 24.4313i −1.44532 + 0.0269959i
906906 −578.771 1125.14i −0.638820 1.24187i
907907 35.1572 131.208i 0.0387621 0.144662i −0.943833 0.330423i 0.892808π-0.892808\pi
0.982595 + 0.185761i 0.0594751π0.0594751\pi
908908 −1194.65 + 1194.65i −1.31569 + 1.31569i
909909 −604.757 432.282i −0.665299 0.475557i
910910 −203.363 + 819.914i −0.223476 + 0.901004i
911911 545.263 + 944.423i 0.598532 + 1.03669i 0.993038 + 0.117795i 0.0375826π0.0375826\pi
−0.394506 + 0.918894i 0.629084π0.629084\pi
912912 1814.44 + 1999.55i 1.98951 + 2.19249i
913913 −10.9035 40.6924i −0.0119425 0.0445700i
914914 1459.39 + 842.579i 1.59671 + 0.921859i
915915 143.463 135.152i 0.156790 0.147707i
916916 660.594 + 1144.18i 0.721173 + 1.24911i
917917 628.907 + 628.907i 0.685831 + 0.685831i
918918 1156.49 + 498.923i 1.25979 + 0.543489i
919919 367.996i 0.400431i −0.979752 0.200215i 0.935836π-0.935836\pi
0.979752 0.200215i 0.0641642π-0.0641642\pi
920920 53.7133 + 29.6880i 0.0583840 + 0.0322695i
921921 −837.650 + 1300.84i −0.909501 + 1.41242i
922922 1727.79 462.959i 1.87396 0.502125i
923923 −279.815 1044.28i −0.303158 1.13140i
924924 17.7319 365.347i 0.0191904 0.395398i
925925 −337.767 313.432i −0.365153 0.338845i
926926 −3276.11 −3.53792
927927 286.328 + 348.052i 0.308876 + 0.375460i
928928 730.476 730.476i 0.787151 0.787151i
929929 62.7337 36.2193i 0.0675282 0.0389874i −0.465856 0.884861i 0.654253π-0.654253\pi
0.533384 + 0.845873i 0.320920π0.320920\pi
930930 −728.343 + 1178.89i −0.783165 + 1.26763i
931931 393.020 680.731i 0.422148 0.731182i
932932 −2339.28 + 626.810i −2.50996 + 0.672542i
933933 −585.517 187.748i −0.627563 0.201231i
934934 902.137 520.849i 0.965886 0.557655i
935935 −43.0328 + 173.499i −0.0460244 + 0.185560i
936936 −1503.40 146.278i −1.60620 0.156280i
937937 −887.903 887.903i −0.947602 0.947602i 0.0510921 0.998694i 0.483730π-0.483730\pi
−0.998694 + 0.0510921i 0.983730π0.983730\pi
938938 −802.082 214.917i −0.855099 0.229123i
939939 −51.7075 + 1065.38i −0.0550666 + 1.13459i
940940 −118.813 + 123.336i −0.126397 + 0.131208i
941941 190.349 329.694i 0.202284 0.350366i −0.746980 0.664846i 0.768497π-0.768497\pi
0.949264 + 0.314480i 0.101830π0.101830\pi
942942 2237.78 484.698i 2.37556 0.514541i
943943 27.0694 + 7.25323i 0.0287056 + 0.00769165i
944944 1190.02i 1.26061i
945945 −617.333 + 258.668i −0.653263 + 0.273723i
946946 −37.7930 −0.0399504
947947 −139.605 + 521.012i −0.147418 + 0.550172i 0.852218 + 0.523187i 0.175257π0.175257\pi
−0.999636 + 0.0269844i 0.991410π0.991410\pi
948948 119.810 + 553.145i 0.126382 + 0.583487i
949949 −218.221 125.990i −0.229948 0.132761i
950950 2820.75 + 643.959i 2.96921 + 0.677852i
951951 −77.4265 3.75785i −0.0814159 0.00395148i
952952 294.831 1100.33i 0.309697 1.15580i
953953 −52.0743 + 52.0743i −0.0546425 + 0.0546425i −0.733900 0.679258i 0.762302π-0.762302\pi
0.679258 + 0.733900i 0.262302π0.262302\pi
954954 1162.36 + 830.858i 1.21841 + 0.870920i
955955 −463.413 769.118i −0.485250 0.805359i
956956 585.940 + 1014.88i 0.612908 + 1.06159i
957957 87.8236 273.889i 0.0917697 0.286196i
958958 −190.265 710.080i −0.198607 0.741210i
959959 605.788 + 349.752i 0.631687 + 0.364705i
960960 −74.4654 + 17.5911i −0.0775682 + 0.0183241i
961961 150.349 + 260.413i 0.156451 + 0.270981i
962962 444.118 + 444.118i 0.461662 + 0.461662i
963963 684.858 + 256.838i 0.711171 + 0.266707i
964964 1906.20i 1.97739i
965965 37.1977 + 129.128i 0.0385469 + 0.133811i
966966 −37.0249 1.79698i −0.0383280 0.00186023i
967967 278.265 74.5608i 0.287761 0.0771053i −0.112051 0.993702i 0.535742π-0.535742\pi
0.399812 + 0.916597i 0.369075π0.369075\pi
968968 −519.740 1939.70i −0.536921 2.00382i
969969 1053.56 + 678.415i 1.08726 + 0.700119i
970970 −2474.55 1367.72i −2.55109 1.41002i
971971 −227.938 −0.234745 −0.117373 0.993088i 0.537447π-0.537447\pi
−0.117373 + 0.993088i 0.537447π0.537447\pi
972972 −1120.49 1856.96i −1.15277 1.91046i
973973 955.634 955.634i 0.982152 0.982152i
974974 2230.86 1287.99i 2.29041 1.32237i
975975 −619.560 + 348.556i −0.635447 + 0.357493i
976976 183.687 318.155i 0.188203 0.325978i
977977 613.083 164.275i 0.627516 0.168142i 0.0689735 0.997618i 0.478028π-0.478028\pi
0.558542 + 0.829476i 0.311361π0.311361\pi
978978 −690.781 + 626.832i −0.706320 + 0.640932i
979979 220.577 127.350i 0.225308 0.130082i
980980 −562.365 933.345i −0.573842 0.952393i
981981 543.161 + 1195.02i 0.553681 + 1.21817i
982982 −531.988 531.988i −0.541739 0.541739i
983983 −1316.59 352.779i −1.33936 0.358880i −0.483163 0.875531i 0.660512π-0.660512\pi
−0.856196 + 0.516651i 0.827179π0.827179\pi
984984 1909.72 982.361i 1.94077 0.998334i
985985 603.908 + 581.761i 0.613104 + 0.590621i
986986 811.616 1405.76i 0.823140 1.42572i
987987 17.4289 54.3542i 0.0176584 0.0550701i
988988 −2630.47 704.832i −2.66242 0.713393i
989989 2.64472i 0.00267414i
990990 338.892 289.572i 0.342315 0.292497i
991991 1111.32 1.12141 0.560705 0.828016i 0.310530π-0.310530\pi
0.560705 + 0.828016i 0.310530π0.310530\pi
992992 −197.447 + 736.881i −0.199039 + 0.742823i
993993 −430.373 + 390.530i −0.433406 + 0.393283i
994994 −1760.76 1016.58i −1.77139 1.02271i
995995 −2.23286 119.544i −0.00224408 0.120145i
996996 −221.644 + 344.206i −0.222534 + 0.345589i
997997 −164.802 + 615.048i −0.165297 + 0.616898i 0.832705 + 0.553717i 0.186791π0.186791\pi
−0.998002 + 0.0631810i 0.979875π0.979875\pi
998998 842.493 842.493i 0.844182 0.844182i
999999 −72.1478 + 492.394i −0.0722200 + 0.492887i
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 45.3.k.a.22.1 yes 40
3.2 odd 2 135.3.l.a.37.10 40
5.2 odd 4 225.3.o.b.193.1 40
5.3 odd 4 inner 45.3.k.a.13.10 yes 40
5.4 even 2 225.3.o.b.157.10 40
9.2 odd 6 135.3.l.a.127.1 40
9.4 even 3 405.3.g.h.82.1 20
9.5 odd 6 405.3.g.g.82.10 20
9.7 even 3 inner 45.3.k.a.7.10 40
15.8 even 4 135.3.l.a.118.1 40
45.7 odd 12 225.3.o.b.43.10 40
45.13 odd 12 405.3.g.h.163.1 20
45.23 even 12 405.3.g.g.163.10 20
45.34 even 6 225.3.o.b.7.1 40
45.38 even 12 135.3.l.a.73.10 40
45.43 odd 12 inner 45.3.k.a.43.1 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.3.k.a.7.10 40 9.7 even 3 inner
45.3.k.a.13.10 yes 40 5.3 odd 4 inner
45.3.k.a.22.1 yes 40 1.1 even 1 trivial
45.3.k.a.43.1 yes 40 45.43 odd 12 inner
135.3.l.a.37.10 40 3.2 odd 2
135.3.l.a.73.10 40 45.38 even 12
135.3.l.a.118.1 40 15.8 even 4
135.3.l.a.127.1 40 9.2 odd 6
225.3.o.b.7.1 40 45.34 even 6
225.3.o.b.43.10 40 45.7 odd 12
225.3.o.b.157.10 40 5.4 even 2
225.3.o.b.193.1 40 5.2 odd 4
405.3.g.g.82.10 20 9.5 odd 6
405.3.g.g.163.10 20 45.23 even 12
405.3.g.h.82.1 20 9.4 even 3
405.3.g.h.163.1 20 45.13 odd 12