Properties

Label 507.2.p.a.64.1
Level 507507
Weight 22
Character 507.64
Analytic conductor 4.0484.048
Analytic rank 00
Dimension 168168
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(25,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(26))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 507=3132 507 = 3 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 507.p (of order 2626, degree 1212, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.048415382484.04841538248
Analytic rank: 00
Dimension: 168168
Relative dimension: 1414 over Q(ζ26)\Q(\zeta_{26})
Twist minimal: yes
Sato-Tate group: SU(2)[C26]\mathrm{SU}(2)[C_{26}]

Embedding invariants

Embedding label 64.1
Character χ\chi == 507.64
Dual form 507.2.p.a.103.1

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+(2.322860.282046i)q2+(0.748511+0.663123i)q3+(3.37425+0.831678i)q4+(0.09186250.175029i)q5+(1.925721.32923i)q6+(0.06429640.0243844i)q7+(3.227621.22407i)q8+(0.1205370.992709i)q9+(0.164018+0.432479i)q10+(4.19756+0.509676i)q11+(3.07717+1.61502i)q12+(2.619652.47739i)q13+(0.142474+0.0747762i)q14+(0.184826+0.0700953i)q15+(0.997726+0.523647i)q16+(0.724665+1.91078i)q17+(0.559980+2.27193i)q18+4.20632iq19+(0.1643990.666994i)q20+(0.06429640.0243844i)q21+9.89410q220.481984q23+(3.227621.22407i)q24+(2.818134.08276i)q25+(6.78382+5.01576i)q26+(0.568065+0.822984i)q27+(0.1966720.135753i)q28+(0.5766134.74884i)q29+(0.4095550.214951i)q30+(4.78369+3.30194i)q31+(3.51189+2.42408i)q32+(2.803943.16499i)q33+(2.222234.23410i)q34+(0.00163844+0.0134938i)q35+(1.232343.24940i)q36+(2.82811+1.95210i)q37+(1.186389.77070i)q38+(0.318025+3.59150i)q39+(0.0822482+0.677375i)q40+(8.142409.19087i)q41+(0.156229+0.0385070i)q42+(3.157324.57417i)q43+(14.58751.77124i)q44+(0.184826+0.0700953i)q45+(1.11958+0.135942i)q46+(1.617326.56173i)q47+(1.09405+0.269659i)q48+(5.236044.63872i)q49+(7.69765+8.68885i)q50+(0.7246651.91078i)q51+(10.89976.18062i)q52+(0.2426810.639897i)q53+(1.087422.07190i)q54+(0.474807+0.687876i)q55+(0.177676+0.157407i)q56+(2.789313.14848i)q57+(2.67879+10.8683i)q58+(2.043963.89444i)q59+(0.565353+0.390235i)q60+(2.135255.63019i)q61+(12.04316.32073i)q62+(0.0319567+0.0608884i)q63+(9.160778.11573i)q64+(0.6742630.230937i)q65+(7.40584+6.56100i)q66+(2.417019.80618i)q67+(4.03436+5.84478i)q68+(0.3607700.319614i)q690.0318063iq70+(0.9548641.07782i)q71+(1.60420+3.05654i)q72+(5.40032+0.655717i)q73+(7.119883.73680i)q74+(0.597974+4.92476i)q75+(3.49831+14.1932i)q76+(0.282316+0.0695846i)q77+(1.751708.25286i)q78+(6.75332+1.66454i)q790.222735iq80+(0.9709420.239316i)q81+(16.3214+23.6457i)q82+(0.7974760.900164i)q83+(0.2372320.0288052i)q84+(0.4010130.0486918i)q85+(8.62415+9.73465i)q86+(2.71746+3.93692i)q87+(14.1720+3.49308i)q88+5.70975iq89+(0.4490960.110692i)q90+(0.228844+0.0954084i)q91+(1.626330.400855i)q92+(1.391055.64371i)q93+(1.90610+15.6981i)q94+(0.7362300.386403i)q95+(4.23615+0.514362i)q96+(4.548248.66595i)q97+(10.8543+12.2519i)q98+4.22839iq99+O(q100)q+(-2.32286 - 0.282046i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(3.37425 + 0.831678i) q^{4} +(-0.0918625 - 0.175029i) q^{5} +(1.92572 - 1.32923i) q^{6} +(-0.0642964 - 0.0243844i) q^{7} +(-3.22762 - 1.22407i) q^{8} +(0.120537 - 0.992709i) q^{9} +(0.164018 + 0.432479i) q^{10} +(-4.19756 + 0.509676i) q^{11} +(-3.07717 + 1.61502i) q^{12} +(2.61965 - 2.47739i) q^{13} +(0.142474 + 0.0747762i) q^{14} +(0.184826 + 0.0700953i) q^{15} +(0.997726 + 0.523647i) q^{16} +(-0.724665 + 1.91078i) q^{17} +(-0.559980 + 2.27193i) q^{18} +4.20632i q^{19} +(-0.164399 - 0.666994i) q^{20} +(0.0642964 - 0.0243844i) q^{21} +9.89410 q^{22} -0.481984 q^{23} +(3.22762 - 1.22407i) q^{24} +(2.81813 - 4.08276i) q^{25} +(-6.78382 + 5.01576i) q^{26} +(0.568065 + 0.822984i) q^{27} +(-0.196672 - 0.135753i) q^{28} +(0.576613 - 4.74884i) q^{29} +(-0.409555 - 0.214951i) q^{30} +(-4.78369 + 3.30194i) q^{31} +(3.51189 + 2.42408i) q^{32} +(2.80394 - 3.16499i) q^{33} +(2.22223 - 4.23410i) q^{34} +(0.00163844 + 0.0134938i) q^{35} +(1.23234 - 3.24940i) q^{36} +(-2.82811 + 1.95210i) q^{37} +(1.18638 - 9.77070i) q^{38} +(-0.318025 + 3.59150i) q^{39} +(0.0822482 + 0.677375i) q^{40} +(-8.14240 - 9.19087i) q^{41} +(-0.156229 + 0.0385070i) q^{42} +(3.15732 - 4.57417i) q^{43} +(-14.5875 - 1.77124i) q^{44} +(-0.184826 + 0.0700953i) q^{45} +(1.11958 + 0.135942i) q^{46} +(-1.61732 - 6.56173i) q^{47} +(-1.09405 + 0.269659i) q^{48} +(-5.23604 - 4.63872i) q^{49} +(-7.69765 + 8.68885i) q^{50} +(-0.724665 - 1.91078i) q^{51} +(10.8997 - 6.18062i) q^{52} +(0.242681 - 0.639897i) q^{53} +(-1.08742 - 2.07190i) q^{54} +(0.474807 + 0.687876i) q^{55} +(0.177676 + 0.157407i) q^{56} +(-2.78931 - 3.14848i) q^{57} +(-2.67879 + 10.8683i) q^{58} +(-2.04396 - 3.89444i) q^{59} +(0.565353 + 0.390235i) q^{60} +(-2.13525 - 5.63019i) q^{61} +(12.0431 - 6.32073i) q^{62} +(-0.0319567 + 0.0608884i) q^{63} +(-9.16077 - 8.11573i) q^{64} +(-0.674263 - 0.230937i) q^{65} +(-7.40584 + 6.56100i) q^{66} +(-2.41701 - 9.80618i) q^{67} +(-4.03436 + 5.84478i) q^{68} +(0.360770 - 0.319614i) q^{69} -0.0318063i q^{70} +(-0.954864 - 1.07782i) q^{71} +(-1.60420 + 3.05654i) q^{72} +(-5.40032 + 0.655717i) q^{73} +(7.11988 - 3.73680i) q^{74} +(0.597974 + 4.92476i) q^{75} +(-3.49831 + 14.1932i) q^{76} +(0.282316 + 0.0695846i) q^{77} +(1.75170 - 8.25286i) q^{78} +(-6.75332 + 1.66454i) q^{79} -0.222735i q^{80} +(-0.970942 - 0.239316i) q^{81} +(16.3214 + 23.6457i) q^{82} +(0.797476 - 0.900164i) q^{83} +(0.237232 - 0.0288052i) q^{84} +(0.401013 - 0.0486918i) q^{85} +(-8.62415 + 9.73465i) q^{86} +(2.71746 + 3.93692i) q^{87} +(14.1720 + 3.49308i) q^{88} +5.70975i q^{89} +(0.449096 - 0.110692i) q^{90} +(-0.228844 + 0.0954084i) q^{91} +(-1.62633 - 0.400855i) q^{92} +(1.39105 - 5.64371i) q^{93} +(1.90610 + 15.6981i) q^{94} +(0.736230 - 0.386403i) q^{95} +(-4.23615 + 0.514362i) q^{96} +(4.54824 - 8.66595i) q^{97} +(10.8543 + 12.2519i) q^{98} +4.22839i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 168q14q3+12q414q94q10+12q12+13q13+2q148q164q1772q22+48q2344q2539q2614q27+45q294q3026q31+104q98+O(q100) 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/507Z)×\left(\mathbb{Z}/507\mathbb{Z}\right)^\times.

nn 170170 340340
χ(n)\chi(n) 11 e(126)e\left(\frac{1}{26}\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 −2.32286 0.282046i −1.64251 0.199437i −0.753541 0.657401i 0.771656π-0.771656\pi
−0.888971 + 0.457964i 0.848579π0.848579\pi
33 −0.748511 + 0.663123i −0.432153 + 0.382854i
44 3.37425 + 0.831678i 1.68713 + 0.415839i
55 −0.0918625 0.175029i −0.0410822 0.0782756i 0.864050 0.503407i 0.167920π-0.167920\pi
−0.905132 + 0.425131i 0.860228π0.860228\pi
66 1.92572 1.32923i 0.786171 0.542655i
77 −0.0642964 0.0243844i −0.0243018 0.00921644i 0.342424 0.939546i 0.388752π-0.388752\pi
−0.366726 + 0.930329i 0.619521π0.619521\pi
88 −3.22762 1.22407i −1.14114 0.432776i
99 0.120537 0.992709i 0.0401789 0.330903i
1010 0.164018 + 0.432479i 0.0518669 + 0.136762i
1111 −4.19756 + 0.509676i −1.26561 + 0.153673i −0.725678 0.688035i 0.758474π-0.758474\pi
−0.539933 + 0.841708i 0.681551π0.681551\pi
1212 −3.07717 + 1.61502i −0.888302 + 0.466217i
1313 2.61965 2.47739i 0.726560 0.687103i
1414 0.142474 + 0.0747762i 0.0380778 + 0.0199848i
1515 0.184826 + 0.0700953i 0.0477219 + 0.0180985i
1616 0.997726 + 0.523647i 0.249432 + 0.130912i
1717 −0.724665 + 1.91078i −0.175757 + 0.463433i −0.993728 0.111827i 0.964330π-0.964330\pi
0.817971 + 0.575260i 0.195099π0.195099\pi
1818 −0.559980 + 2.27193i −0.131989 + 0.535499i
1919 4.20632i 0.964996i 0.875897 + 0.482498i 0.160270π0.160270\pi
−0.875897 + 0.482498i 0.839730π0.839730\pi
2020 −0.164399 0.666994i −0.0367608 0.149144i
2121 0.0642964 0.0243844i 0.0140306 0.00532111i
2222 9.89410 2.10943
2323 −0.481984 −0.100501 −0.0502503 0.998737i 0.516002π-0.516002\pi
−0.0502503 + 0.998737i 0.516002π0.516002\pi
2424 3.22762 1.22407i 0.658835 0.249863i
2525 2.81813 4.08276i 0.563625 0.816552i
2626 −6.78382 + 5.01576i −1.33042 + 0.983672i
2727 0.568065 + 0.822984i 0.109324 + 0.158383i
2828 −0.196672 0.135753i −0.0371676 0.0256549i
2929 0.576613 4.74884i 0.107074 0.881837i −0.835879 0.548913i 0.815042π-0.815042\pi
0.942954 0.332924i 0.108035π-0.108035\pi
3030 −0.409555 0.214951i −0.0747742 0.0392445i
3131 −4.78369 + 3.30194i −0.859175 + 0.593046i −0.914120 0.405443i 0.867117π-0.867117\pi
0.0549447 + 0.998489i 0.482502π0.482502\pi
3232 3.51189 + 2.42408i 0.620820 + 0.428521i
3333 2.80394 3.16499i 0.488103 0.550955i
3434 2.22223 4.23410i 0.381109 0.726142i
3535 0.00163844 + 0.0134938i 0.000276947 + 0.00228086i
3636 1.23234 3.24940i 0.205389 0.541567i
3737 −2.82811 + 1.95210i −0.464938 + 0.320923i −0.777400 0.629007i 0.783462π-0.783462\pi
0.312462 + 0.949930i 0.398846π0.398846\pi
3838 1.18638 9.77070i 0.192456 1.58502i
3939 −0.318025 + 3.59150i −0.0509247 + 0.575100i
4040 0.0822482 + 0.677375i 0.0130046 + 0.107102i
4141 −8.14240 9.19087i −1.27163 1.43537i −0.848404 0.529349i 0.822436π-0.822436\pi
−0.423225 0.906024i 0.639102π-0.639102\pi
4242 −0.156229 + 0.0385070i −0.0241067 + 0.00594176i
4343 3.15732 4.57417i 0.481487 0.697554i −0.504681 0.863306i 0.668390π-0.668390\pi
0.986167 + 0.165752i 0.0530051π0.0530051\pi
4444 −14.5875 1.77124i −2.19915 0.267025i
4545 −0.184826 + 0.0700953i −0.0275522 + 0.0104492i
4646 1.11958 + 0.135942i 0.165073 + 0.0200435i
4747 −1.61732 6.56173i −0.235910 0.957126i −0.962766 0.270336i 0.912865π-0.912865\pi
0.726856 0.686790i 0.240981π-0.240981\pi
4848 −1.09405 + 0.269659i −0.157913 + 0.0389220i
4949 −5.23604 4.63872i −0.748005 0.662675i
5050 −7.69765 + 8.68885i −1.08861 + 1.22879i
5151 −0.724665 1.91078i −0.101473 0.267563i
5252 10.8997 6.18062i 1.51152 0.857098i
5353 0.242681 0.639897i 0.0333348 0.0878966i −0.917315 0.398161i 0.869648π-0.869648\pi
0.950650 + 0.310265i 0.100418π0.100418\pi
5454 −1.08742 2.07190i −0.147979 0.281950i
5555 0.474807 + 0.687876i 0.0640229 + 0.0927532i
5656 0.177676 + 0.157407i 0.0237429 + 0.0210344i
5757 −2.78931 3.14848i −0.369453 0.417026i
5858 −2.67879 + 10.8683i −0.351742 + 1.42707i
5959 −2.04396 3.89444i −0.266101 0.507012i 0.715340 0.698776i 0.246272π-0.246272\pi
−0.981441 + 0.191764i 0.938579π0.938579\pi
6060 0.565353 + 0.390235i 0.0729868 + 0.0503791i
6161 −2.13525 5.63019i −0.273391 0.720873i −0.999447 0.0332376i 0.989418π-0.989418\pi
0.726057 0.687635i 0.241351π-0.241351\pi
6262 12.0431 6.32073i 1.52948 0.802733i
6363 −0.0319567 + 0.0608884i −0.00402617 + 0.00767122i
6464 −9.16077 8.11573i −1.14510 1.01447i
6565 −0.674263 0.230937i −0.0836320 0.0286442i
6666 −7.40584 + 6.56100i −0.911596 + 0.807603i
6767 −2.41701 9.80618i −0.295284 1.19802i −0.911787 0.410663i 0.865297π-0.865297\pi
0.616503 0.787353i 0.288549π-0.288549\pi
6868 −4.03436 + 5.84478i −0.489238 + 0.708784i
6969 0.360770 0.319614i 0.0434316 0.0384770i
7070 0.0318063i 0.00380158i
7171 −0.954864 1.07782i −0.113321 0.127914i 0.689113 0.724654i 0.258001π-0.258001\pi
−0.802434 + 0.596741i 0.796462π0.796462\pi
7272 −1.60420 + 3.05654i −0.189056 + 0.360217i
7373 −5.40032 + 0.655717i −0.632059 + 0.0767459i −0.430295 0.902688i 0.641590π-0.641590\pi
−0.201764 + 0.979434i 0.564667π0.564667\pi
7474 7.11988 3.73680i 0.827670 0.434395i
7575 0.597974 + 4.92476i 0.0690480 + 0.568662i
7676 −3.49831 + 14.1932i −0.401283 + 1.62807i
7777 0.282316 + 0.0695846i 0.0321729 + 0.00792991i
7878 1.75170 8.25286i 0.198341 0.934452i
7979 −6.75332 + 1.66454i −0.759808 + 0.187276i −0.600140 0.799895i 0.704889π-0.704889\pi
−0.159668 + 0.987171i 0.551042π0.551042\pi
8080 0.222735i 0.0249025i
8181 −0.970942 0.239316i −0.107882 0.0265906i
8282 16.3214 + 23.6457i 1.80240 + 2.61123i
8383 0.797476 0.900164i 0.0875343 0.0988058i −0.703111 0.711080i 0.748207π-0.748207\pi
0.790646 + 0.612274i 0.209745π0.209745\pi
8484 0.237232 0.0288052i 0.0258842 0.00314291i
8585 0.401013 0.0486918i 0.0434960 0.00528137i
8686 −8.62415 + 9.73465i −0.929966 + 1.04971i
8787 2.71746 + 3.93692i 0.291342 + 0.422082i
8888 14.1720 + 3.49308i 1.51074 + 0.372364i
8989 5.70975i 0.605233i 0.953112 + 0.302616i 0.0978601π0.0978601\pi
−0.953112 + 0.302616i 0.902140π0.902140\pi
9090 0.449096 0.110692i 0.0473388 0.0116680i
9191 −0.228844 + 0.0954084i −0.0239893 + 0.0100015i
9292 −1.62633 0.400855i −0.169557 0.0417921i
9393 1.39105 5.64371i 0.144245 0.585225i
9494 1.90610 + 15.6981i 0.196599 + 1.61914i
9595 0.736230 0.386403i 0.0755356 0.0396441i
9696 −4.23615 + 0.514362i −0.432351 + 0.0524969i
9797 4.54824 8.66595i 0.461804 0.879894i −0.537524 0.843248i 0.680640π-0.680640\pi
0.999328 0.0366456i 0.0116673π-0.0116673\pi
9898 10.8543 + 12.2519i 1.09644 + 1.23763i
9999 4.22839i 0.424969i
100100 12.9046 11.4325i 1.29046 1.14325i
101101 0.729670 1.05711i 0.0726049 0.105186i −0.784999 0.619497i 0.787337π-0.787337\pi
0.857604 + 0.514310i 0.171952π0.171952\pi
102102 1.14437 + 4.64288i 0.113309 + 0.459713i
103103 2.91392 2.58151i 0.287117 0.254364i −0.507253 0.861797i 0.669339π-0.669339\pi
0.794371 + 0.607433i 0.207801π0.207801\pi
104104 −11.4877 + 4.78941i −1.12646 + 0.469640i
105105 −0.0101744 0.00901375i −0.000992922 0.000879652i
106106 −0.744195 + 1.41795i −0.0722826 + 0.137723i
107107 13.9084 7.29968i 1.34457 0.705686i 0.369848 0.929092i 0.379410π-0.379410\pi
0.974725 + 0.223406i 0.0717176π0.0717176\pi
108108 1.23234 + 3.24940i 0.118582 + 0.312674i
109109 −3.72877 2.57378i −0.357151 0.246524i 0.375955 0.926638i 0.377315π-0.377315\pi
−0.733106 + 0.680114i 0.761930π0.761930\pi
110110 −0.908897 1.73176i −0.0866599 0.165117i
111111 0.822386 3.33655i 0.0780574 0.316691i
112112 −0.0513814 0.0579976i −0.00485508 0.00548026i
113113 14.0359 + 12.4347i 1.32038 + 1.16976i 0.972679 + 0.232155i 0.0745776π0.0745776\pi
0.347706 + 0.937604i 0.386961π0.386961\pi
114114 5.59116 + 8.10019i 0.523660 + 0.758652i
115115 0.0442762 + 0.0843613i 0.00412878 + 0.00786673i
116116 5.89515 15.5442i 0.547351 1.44324i
117117 −2.14356 2.89916i −0.198172 0.268028i
118118 3.64942 + 9.62273i 0.335956 + 0.885844i
119119 0.0931867 0.105186i 0.00854241 0.00964239i
120120 −0.510746 0.452482i −0.0466245 0.0413057i
121121 6.67936 1.64631i 0.607215 0.149665i
122122 3.37192 + 13.6804i 0.305279 + 1.23857i
123123 12.1894 + 1.48006i 1.09908 + 0.133452i
124124 −18.8875 + 7.16309i −1.69615 + 0.643264i
125125 −1.95464 0.237336i −0.174828 0.0212280i
126126 0.0914043 0.132422i 0.00814295 0.0117971i
127127 −7.73057 + 1.90541i −0.685977 + 0.169078i −0.566875 0.823804i 0.691848π-0.691848\pi
−0.119102 + 0.992882i 0.538002π0.538002\pi
128128 13.3307 + 15.0473i 1.17828 + 1.33001i
129129 0.669946 + 5.51750i 0.0589855 + 0.485789i
130130 1.50108 + 0.726608i 0.131654 + 0.0637277i
131131 −0.822178 + 6.77124i −0.0718340 + 0.591606i 0.911697 + 0.410864i 0.134773π0.134773\pi
−0.983531 + 0.180742i 0.942150π0.942150\pi
132132 12.0935 8.34751i 1.05260 0.726557i
133133 0.102569 0.270451i 0.00889383 0.0234511i
134134 2.84857 + 23.4601i 0.246079 + 2.02664i
135135 0.0918625 0.175029i 0.00790627 0.0150641i
136136 4.67788 5.28024i 0.401125 0.452777i
137137 13.1937 + 9.10696i 1.12721 + 0.778060i 0.977556 0.210678i 0.0675672π-0.0675672\pi
0.149659 + 0.988738i 0.452183π0.452183\pi
138138 −0.928165 + 0.640666i −0.0790106 + 0.0545371i
139139 −11.8853 6.23788i −1.00810 0.529090i −0.121971 0.992534i 0.538921π-0.538921\pi
−0.886127 + 0.463443i 0.846614π0.846614\pi
140140 −0.00569397 + 0.0468941i −0.000481228 + 0.00396327i
141141 5.56181 + 3.83904i 0.468389 + 0.323306i
142142 1.91402 + 2.77294i 0.160621 + 0.232700i
143143 −9.73346 + 11.7341i −0.813953 + 0.981258i
144144 0.640092 0.927333i 0.0533410 0.0772777i
145145 −0.884156 + 0.335316i −0.0734252 + 0.0278465i
146146 12.7291 1.05347
147147 6.99527 0.576960
148148 −11.1663 + 4.23481i −0.917861 + 0.348099i
149149 −5.37870 21.8223i −0.440641 1.78775i −0.599419 0.800435i 0.704602π-0.704602\pi
0.158779 0.987314i 0.449244π-0.449244\pi
150150 11.6082i 0.947804i
151151 −5.10116 + 20.6962i −0.415127 + 1.68423i 0.275724 + 0.961237i 0.411083π0.411083\pi
−0.690850 + 0.722998i 0.742764π0.742764\pi
152152 5.14885 13.5764i 0.417627 1.10119i
153153 1.80950 + 0.949701i 0.146290 + 0.0767788i
154154 −0.636155 0.241262i −0.0512628 0.0194414i
155155 1.01738 + 0.533961i 0.0817178 + 0.0428888i
156156 −4.06007 + 11.8541i −0.325066 + 0.949090i
157157 −1.97830 + 1.03829i −0.157885 + 0.0828646i −0.541815 0.840498i 0.682263π-0.682263\pi
0.383930 + 0.923362i 0.374570π0.374570\pi
158158 16.1565 1.96176i 1.28534 0.156069i
159159 0.242681 + 0.639897i 0.0192459 + 0.0507471i
160160 0.101675 0.837367i 0.00803809 0.0661997i
161161 0.0309898 + 0.0117529i 0.00244234 + 0.000926257i
162162 2.18787 + 0.829748i 0.171895 + 0.0651911i
163163 −9.80318 + 6.76664i −0.767844 + 0.530004i −0.886387 0.462944i 0.846793π-0.846793\pi
0.118543 + 0.992949i 0.462178π0.462178\pi
164164 −19.8307 37.7842i −1.54852 2.95045i
165165 −0.811544 0.200028i −0.0631786 0.0155721i
166166 −2.10631 + 1.86603i −0.163482 + 0.144832i
167167 −2.19108 0.266045i −0.169551 0.0205872i 0.0353209 0.999376i 0.488755π-0.488755\pi
−0.204872 + 0.978789i 0.565678π0.565678\pi
168168 −0.237373 −0.0183137
169169 0.725120 12.9798i 0.0557784 0.998443i
170170 −0.945231 −0.0724959
171171 4.17565 + 0.507016i 0.319320 + 0.0387725i
172172 14.4578 12.8085i 1.10240 0.976641i
173173 −11.3306 2.79274i −0.861448 0.212328i −0.216245 0.976339i 0.569381π-0.569381\pi
−0.645203 + 0.764011i 0.723227π0.723227\pi
174174 −5.20189 9.91138i −0.394354 0.751380i
175175 −0.280751 + 0.193789i −0.0212228 + 0.0146490i
176176 −4.45490 1.68952i −0.335801 0.127353i
177177 4.11241 + 1.55963i 0.309108 + 0.117229i
178178 1.61042 13.2630i 0.120706 0.994102i
179179 3.50296 + 9.23655i 0.261824 + 0.690372i 0.999878 + 0.0156308i 0.00497564π0.00497564\pi
−0.738054 + 0.674741i 0.764255π0.764255\pi
180180 −0.681947 + 0.0828033i −0.0508293 + 0.00617179i
181181 −3.35898 + 1.76293i −0.249671 + 0.131037i −0.584917 0.811093i 0.698873π-0.698873\pi
0.335246 + 0.942131i 0.391181π0.391181\pi
182182 0.558482 0.157076i 0.0413974 0.0116432i
183183 5.33177 + 2.79833i 0.394136 + 0.206858i
184184 1.55566 + 0.589984i 0.114685 + 0.0434942i
185185 0.601472 + 0.315677i 0.0442211 + 0.0232090i
186186 −4.82300 + 12.7172i −0.353640 + 0.932471i
187187 2.06794 8.38997i 0.151223 0.613535i
188188 23.4860i 1.71289i
189189 −0.0164565 0.0667668i −0.00119704 0.00485657i
190190 −1.81914 + 0.689910i −0.131975 + 0.0500514i
191191 −9.65314 −0.698477 −0.349238 0.937034i 0.613560π-0.613560\pi
−0.349238 + 0.937034i 0.613560π0.613560\pi
192192 12.2387 0.883249
193193 −17.6326 + 6.68716i −1.26922 + 0.481352i −0.895033 0.446000i 0.852848π-0.852848\pi
−0.374189 + 0.927353i 0.622079π0.622079\pi
194194 −13.0091 + 18.8470i −0.934001 + 1.35313i
195195 0.657833 0.274261i 0.0471084 0.0196402i
196196 −13.8098 20.0069i −0.986413 1.42907i
197197 −2.93237 2.02407i −0.208922 0.144209i 0.459009 0.888432i 0.348205π-0.348205\pi
−0.667931 + 0.744223i 0.732820π0.732820\pi
198198 1.19260 9.82196i 0.0847545 0.698016i
199199 15.3512 + 8.05692i 1.08822 + 0.571140i 0.910738 0.412985i 0.135514π-0.135514\pi
0.177478 + 0.984125i 0.443206π0.443206\pi
200200 −14.0934 + 9.72800i −0.996557 + 0.687873i
201201 8.31185 + 5.73726i 0.586273 + 0.404675i
202202 −1.99308 + 2.24972i −0.140232 + 0.158290i
203203 −0.152872 + 0.291273i −0.0107295 + 0.0204434i
204204 −0.856044 7.05016i −0.0599351 0.493610i
205205 −0.860692 + 2.26946i −0.0601133 + 0.158506i
206206 −7.49675 + 5.17463i −0.522323 + 0.360534i
207207 −0.0580967 + 0.478469i −0.00403800 + 0.0332559i
208208 3.91097 1.09998i 0.271177 0.0762700i
209209 −2.14386 17.6563i −0.148294 1.22131i
210210 0.0210915 + 0.0238074i 0.00145545 + 0.00164286i
211211 9.74571 2.40210i 0.670922 0.165367i 0.110883 0.993833i 0.464632π-0.464632\pi
0.560039 + 0.828466i 0.310786π0.310786\pi
212212 1.35106 1.95734i 0.0927909 0.134431i
213213 1.42945 + 0.173567i 0.0979444 + 0.0118926i
214214 −34.3661 + 13.0333i −2.34922 + 0.890940i
215215 −1.09065 0.132429i −0.0743820 0.00903161i
216216 −0.826103 3.35163i −0.0562092 0.228050i
217217 0.388090 0.0956555i 0.0263452 0.00649352i
218218 7.93548 + 7.03022i 0.537459 + 0.476147i
219219 3.60737 4.07188i 0.243764 0.275152i
220220 1.03003 + 2.71595i 0.0694443 + 0.183110i
221221 2.83538 + 6.80086i 0.190728 + 0.457475i
222222 −2.85135 + 7.51839i −0.191370 + 0.504602i
223223 −9.64284 18.3729i −0.645732 1.23034i −0.959732 0.280917i 0.909361π-0.909361\pi
0.314000 0.949423i 0.398331π-0.398331\pi
224224 −0.166692 0.241495i −0.0111376 0.0161356i
225225 −3.71331 3.28970i −0.247554 0.219313i
226226 −29.0962 32.8429i −1.93545 2.18468i
227227 3.62063 14.6895i 0.240310 0.974975i −0.719538 0.694453i 0.755646π-0.755646\pi
0.959848 0.280522i 0.0905075π-0.0905075\pi
228228 −6.79330 12.9436i −0.449897 0.857208i
229229 11.1555 + 7.70009i 0.737177 + 0.508836i 0.876495 0.481411i 0.159876π-0.159876\pi
−0.139318 + 0.990248i 0.544491π0.544491\pi
230230 −0.0790538 0.208448i −0.00521265 0.0137446i
231231 −0.257460 + 0.135125i −0.0169396 + 0.00889059i
232232 −7.67402 + 14.6216i −0.503824 + 0.959956i
233233 −14.1473 12.5334i −0.926820 0.821091i 0.0573432 0.998355i 0.481737π-0.481737\pi
−0.984163 + 0.177263i 0.943276π0.943276\pi
234234 4.16149 + 7.33894i 0.272045 + 0.479762i
235235 −0.999924 + 0.885855i −0.0652279 + 0.0577868i
236236 −3.65791 14.8407i −0.238110 0.966049i
237237 3.95114 5.72421i 0.256654 0.371828i
238238 −0.246127 + 0.218050i −0.0159541 + 0.0141341i
239239 21.4743i 1.38906i 0.719464 + 0.694530i 0.244388π0.244388\pi
−0.719464 + 0.694530i 0.755612π0.755612\pi
240240 0.147701 + 0.166720i 0.00953404 + 0.0107617i
241241 −1.19543 + 2.27770i −0.0770045 + 0.146720i −0.920914 0.389766i 0.872556π-0.872556\pi
0.843910 + 0.536485i 0.180248π0.180248\pi
242242 −15.9796 + 1.94027i −1.02721 + 0.124725i
243243 0.885456 0.464723i 0.0568020 0.0298120i
244244 −2.52236 20.7735i −0.161478 1.32989i
245245 −0.330918 + 1.34259i −0.0211415 + 0.0857746i
246246 −27.8967 6.87593i −1.77863 0.438393i
247247 10.4207 + 11.0191i 0.663052 + 0.701127i
248248 19.4817 4.80182i 1.23709 0.304916i
249249 1.20261i 0.0762121i
250250 4.47341 + 1.10260i 0.282923 + 0.0697343i
251251 −11.0635 16.0283i −0.698325 1.01170i −0.998330 0.0577605i 0.981604π-0.981604\pi
0.300006 0.953937i 0.403011π-0.403011\pi
252252 −0.158470 + 0.178875i −0.00998264 + 0.0112681i
253253 2.02315 0.245655i 0.127195 0.0154442i
254254 18.4945 2.24563i 1.16045 0.140904i
255255 −0.267874 + 0.302367i −0.0167749 + 0.0189350i
256256 −12.8167 18.5682i −0.801045 1.16051i
257257 18.7692 + 4.62619i 1.17079 + 0.288574i 0.776323 0.630336i 0.217083π-0.217083\pi
0.394468 + 0.918910i 0.370929π0.370929\pi
258258 13.0054i 0.809678i
259259 0.229438 0.0565514i 0.0142566 0.00351393i
260260 −2.08307 1.34001i −0.129186 0.0831038i
261261 −4.64471 1.14482i −0.287500 0.0708625i
262262 3.81961 15.4968i 0.235976 0.957393i
263263 0.740989 + 6.10260i 0.0456914 + 0.376302i 0.997561 + 0.0697992i 0.0222359π0.0222359\pi
−0.951870 + 0.306503i 0.900841π0.900841\pi
264264 −12.9242 + 6.78316i −0.795431 + 0.417475i
265265 −0.134294 + 0.0163063i −0.00824962 + 0.00100169i
266266 −0.314533 + 0.599292i −0.0192852 + 0.0367449i
267267 −3.78627 4.27381i −0.231716 0.261553i
268268 35.0987i 2.14399i
269269 −4.05177 + 3.58956i −0.247041 + 0.218859i −0.777552 0.628819i 0.783539π-0.783539\pi
0.530511 + 0.847678i 0.322000π0.322000\pi
270270 −0.262750 + 0.380660i −0.0159905 + 0.0231662i
271271 3.26557 + 13.2489i 0.198369 + 0.804816i 0.982811 + 0.184614i 0.0591034π0.0591034\pi
−0.784442 + 0.620202i 0.787050π0.787050\pi
272272 −1.72359 + 1.52697i −0.104508 + 0.0925862i
273273 0.108024 0.223166i 0.00653793 0.0135066i
274274 −28.0786 24.8754i −1.69629 1.50278i
275275 −9.74837 + 18.5740i −0.587849 + 1.12005i
276276 1.48314 0.778414i 0.0892748 0.0468550i
277277 3.86275 + 10.1852i 0.232090 + 0.611971i 0.999577 0.0290939i 0.00926218π-0.00926218\pi
−0.767487 + 0.641065i 0.778493π0.778493\pi
278278 25.8485 + 17.8419i 1.55029 + 1.07009i
279279 2.70126 + 5.14681i 0.161720 + 0.308132i
280280 0.0112291 0.0455583i 0.000671068 0.00272263i
281281 −2.61998 2.95735i −0.156295 0.176421i 0.665147 0.746712i 0.268369π-0.268369\pi
−0.821442 + 0.570291i 0.806830π0.806830\pi
282282 −11.8365 10.4862i −0.704855 0.624447i
283283 15.1804 + 21.9926i 0.902380 + 1.30732i 0.951219 + 0.308517i 0.0998326π0.0998326\pi
−0.0488387 + 0.998807i 0.515552π0.515552\pi
284284 −2.32555 4.43097i −0.137996 0.262930i
285285 −0.294843 + 0.777438i −0.0174650 + 0.0460514i
286286 25.9191 24.5115i 1.53263 1.44940i
287287 0.299413 + 0.789488i 0.0176738 + 0.0466020i
288288 2.82972 3.19409i 0.166743 0.188214i
289289 9.59873 + 8.50373i 0.564631 + 0.500219i
290290 2.14835 0.529520i 0.126155 0.0310945i
291291 2.34218 + 9.50260i 0.137301 + 0.557052i
292292 −18.7674 2.27877i −1.09828 0.133355i
293293 −9.72343 + 3.68761i −0.568049 + 0.215433i −0.621873 0.783118i 0.713628π-0.713628\pi
0.0538243 + 0.998550i 0.482859π0.482859\pi
294294 −16.2490 1.97299i −0.947664 0.115067i
295295 −0.493878 + 0.715506i −0.0287547 + 0.0416584i
296296 11.5176 2.83882i 0.669445 0.165003i
297297 −2.80394 3.16499i −0.162701 0.183652i
298298 6.33909 + 52.2071i 0.367214 + 3.02428i
299299 −1.26263 + 1.19406i −0.0730197 + 0.0690542i
300300 −2.07810 + 17.1147i −0.119979 + 0.988117i
301301 −0.314543 + 0.217113i −0.0181299 + 0.0125142i
302302 17.6866 46.6357i 1.01775 2.68358i
303303 0.154827 + 1.27512i 0.00889461 + 0.0732537i
304304 −2.20263 + 4.19676i −0.126329 + 0.240700i
305305 −0.789300 + 0.890936i −0.0451952 + 0.0510148i
306306 −3.93537 2.71639i −0.224970 0.155286i
307307 18.8657 13.0220i 1.07672 0.743206i 0.108699 0.994075i 0.465332π-0.465332\pi
0.968021 + 0.250869i 0.0807163π0.0807163\pi
308308 0.894733 + 0.469592i 0.0509822 + 0.0267575i
309309 −0.469245 + 3.86458i −0.0266944 + 0.219848i
310310 −2.21263 1.52727i −0.125669 0.0867429i
311311 1.17733 + 1.70566i 0.0667604 + 0.0967191i 0.854942 0.518724i 0.173593π-0.173593\pi
−0.788182 + 0.615443i 0.788977π0.788977\pi
312312 5.42272 11.2027i 0.307001 0.634228i
313313 0.542882 0.786501i 0.0306855 0.0444556i −0.807341 0.590085i 0.799094π-0.799094\pi
0.838026 + 0.545630i 0.183709π0.183709\pi
314314 4.88816 1.85383i 0.275855 0.104618i
315315 0.0135929 0.000765872
316316 −24.1718 −1.35977
317317 16.7707 6.36029i 0.941937 0.357230i 0.164633 0.986355i 0.447356π-0.447356\pi
0.777304 + 0.629125i 0.216587π0.216587\pi
318318 −0.383234 1.55484i −0.0214907 0.0871911i
319319 20.2274i 1.13252i
320320 −0.578961 + 2.34894i −0.0323649 + 0.131310i
321321 −5.56999 + 14.6868i −0.310886 + 0.819740i
322322 −0.0686702 0.0360409i −0.00382684 0.00200848i
323323 −8.03737 3.04817i −0.447211 0.169605i
324324 −3.07717 1.61502i −0.170954 0.0897235i
325325 −2.73207 17.6770i −0.151548 0.980543i
326326 24.6799 12.9530i 1.36689 0.717402i
327327 4.49775 0.546126i 0.248726 0.0302008i
328328 15.0303 + 39.6315i 0.829907 + 2.18829i
329329 −0.0560159 + 0.461333i −0.00308826 + 0.0254341i
330330 1.82869 + 0.693530i 0.100666 + 0.0381776i
331331 15.4842 + 5.87238i 0.851088 + 0.322775i 0.741295 0.671180i 0.234212π-0.234212\pi
0.109793 + 0.993955i 0.464981π0.464981\pi
332332 3.43953 2.37414i 0.188769 0.130298i
333333 1.59698 + 3.04279i 0.0875138 + 0.166744i
334334 5.01454 + 1.23597i 0.274383 + 0.0676294i
335335 −1.49434 + 1.32387i −0.0816444 + 0.0723306i
336336 0.0769190 + 0.00933966i 0.00419628 + 0.000509520i
337337 −18.4016 −1.00240 −0.501200 0.865331i 0.667108π-0.667108\pi
−0.501200 + 0.865331i 0.667108π0.667108\pi
338338 −5.34525 + 29.9457i −0.290743 + 1.62883i
339339 −18.7517 −1.01845
340340 1.39362 + 0.169216i 0.0755794 + 0.00917700i
341341 18.3969 16.2982i 0.996247 0.882598i
342342 −9.55646 2.35546i −0.516754 0.127368i
343343 0.447243 + 0.852150i 0.0241488 + 0.0460118i
344344 −15.7897 + 10.8989i −0.851326 + 0.587628i
345345 −0.0890832 0.0337848i −0.00479608 0.00181891i
346346 25.5317 + 9.68290i 1.37259 + 0.520556i
347347 −3.76309 + 30.9919i −0.202013 + 1.66373i 0.440723 + 0.897643i 0.354722π0.354722\pi
−0.642737 + 0.766087i 0.722201π0.722201\pi
348348 5.89515 + 15.5442i 0.316013 + 0.833258i
349349 −7.35668 + 0.893263i −0.393794 + 0.0478152i −0.315039 0.949079i 0.602018π-0.602018\pi
−0.0787551 + 0.996894i 0.525094π0.525094\pi
350350 0.706803 0.370959i 0.0377802 0.0198286i
351351 3.52698 + 0.748613i 0.188256 + 0.0399580i
352352 −15.9769 8.38530i −0.851570 0.446938i
353353 10.1295 + 3.84161i 0.539139 + 0.204468i 0.609117 0.793080i 0.291524π-0.291524\pi
−0.0699785 + 0.997549i 0.522293π0.522293\pi
354354 −9.11268 4.78270i −0.484333 0.254198i
355355 −0.100934 + 0.266140i −0.00535701 + 0.0141253i
356356 −4.74868 + 19.2662i −0.251680 + 1.02110i
357357 0.140527i 0.00743748i
358358 −5.53176 22.4432i −0.292363 1.18616i
359359 28.3545 10.7534i 1.49649 0.567544i 0.535600 0.844472i 0.320085π-0.320085\pi
0.960891 + 0.276927i 0.0893161π0.0893161\pi
360360 0.682350 0.0359630
361361 1.30687 0.0687827
362362 8.29966 3.14765i 0.436221 0.165437i
363363 −3.90786 + 5.66152i −0.205110 + 0.297153i
364364 −0.851525 + 0.131608i −0.0446320 + 0.00689812i
365365 0.610857 + 0.884979i 0.0319737 + 0.0463219i
366366 −11.5957 8.00393i −0.606117 0.418372i
367367 0.251891 2.07451i 0.0131486 0.108288i −0.984657 0.174501i 0.944169π-0.944169\pi
0.997806 + 0.0662131i 0.0210917π0.0210917\pi
368368 −0.480888 0.252389i −0.0250680 0.0131567i
369369 −10.1053 + 6.97520i −0.526062 + 0.363114i
370370 −1.30810 0.902917i −0.0680049 0.0469404i
371371 −0.0312070 + 0.0352255i −0.00162019 + 0.00182881i
372372 9.38750 17.8864i 0.486719 0.927366i
373373 −4.28547 35.2940i −0.221893 1.82746i −0.498983 0.866612i 0.666293π-0.666293\pi
0.277089 0.960844i 0.410630π-0.410630\pi
374374 −7.16991 + 18.9055i −0.370747 + 0.977579i
375375 1.62045 1.11851i 0.0836796 0.0577599i
376376 −2.81195 + 23.1585i −0.145015 + 1.19431i
377377 −10.2542 13.8688i −0.528117 0.714279i
378378 0.0193949 + 0.159732i 0.000997567 + 0.00821571i
379379 −10.1631 11.4718i −0.522044 0.589265i 0.427062 0.904222i 0.359548π-0.359548\pi
−0.949106 + 0.314957i 0.898010π0.898010\pi
380380 2.80559 0.691515i 0.143924 0.0354740i
381381 4.52289 6.55254i 0.231715 0.335697i
382382 22.4229 + 2.72263i 1.14726 + 0.139302i
383383 −29.7898 + 11.2978i −1.52219 + 0.577289i −0.967076 0.254487i 0.918093π-0.918093\pi
−0.555111 + 0.831776i 0.687324π0.687324\pi
384384 −19.9564 2.42315i −1.01840 0.123656i
385385 −0.0137549 0.0558058i −0.000701015 0.00284413i
386386 42.8442 10.5601i 2.18071 0.537497i
387387 −4.16024 3.68566i −0.211477 0.187352i
388388 22.5542 25.4584i 1.14502 1.29246i
389389 −3.20617 8.45397i −0.162559 0.428633i 0.828843 0.559481i 0.188999π-0.188999\pi
−0.991403 + 0.130847i 0.958230π0.958230\pi
390390 −1.60541 + 0.451530i −0.0812930 + 0.0228641i
391391 0.349277 0.920967i 0.0176637 0.0465753i
392392 11.2218 + 21.3813i 0.566786 + 1.07992i
393393 −3.87476 5.61355i −0.195456 0.283166i
394394 6.24060 + 5.52869i 0.314397 + 0.278531i
395395 0.911722 + 1.02912i 0.0458737 + 0.0517807i
396396 −3.51666 + 14.2676i −0.176719 + 0.716976i
397397 9.16829 + 17.4687i 0.460144 + 0.876730i 0.999402 + 0.0345897i 0.0110124π0.0110124\pi
−0.539258 + 0.842141i 0.681295π0.681295\pi
398398 −33.3862 23.0449i −1.67350 1.15513i
399399 0.102569 + 0.270451i 0.00513485 + 0.0135395i
400400 4.94965 2.59777i 0.247482 0.129889i
401401 4.34390 8.27661i 0.216924 0.413314i −0.752540 0.658546i 0.771172π-0.771172\pi
0.969464 + 0.245232i 0.0788641π0.0788641\pi
402402 −17.6891 15.6712i −0.882253 0.781608i
403403 −4.35140 + 20.5010i −0.216759 + 1.02123i
404404 3.34127 2.96010i 0.166234 0.147271i
405405 0.0473059 + 0.191928i 0.00235065 + 0.00953696i
406406 0.437253 0.633470i 0.0217005 0.0314386i
407407 10.8762 9.63547i 0.539113 0.477613i
408408 7.05433i 0.349241i
409409 −20.8841 23.5733i −1.03265 1.16562i −0.986006 0.166712i 0.946685π-0.946685\pi
−0.0466467 0.998911i 0.514854π-0.514854\pi
410410 2.63936 5.02888i 0.130349 0.248359i
411411 −15.9147 + 1.93239i −0.785012 + 0.0953177i
412412 11.9793 6.28722i 0.590178 0.309749i
413413 0.0364556 + 0.300239i 0.00179386 + 0.0147738i
414414 0.269901 1.09503i 0.0132649 0.0538179i
415415 −0.230813 0.0568904i −0.0113302 0.00279264i
416416 15.2053 2.35006i 0.745502 0.115221i
417417 13.0327 3.21228i 0.638216 0.157306i
418418 41.6177i 2.03559i
419419 −2.50456 0.617319i −0.122356 0.0301580i 0.177662 0.984092i 0.443147π-0.443147\pi
−0.300018 + 0.953934i 0.596993π0.596993\pi
420420 −0.0268345 0.0388765i −0.00130939 0.00189698i
421421 15.8941 17.9408i 0.774632 0.874379i −0.220248 0.975444i 0.570687π-0.570687\pi
0.994880 + 0.101065i 0.0322250π0.0322250\pi
422422 −23.3154 + 2.83101i −1.13498 + 0.137811i
423423 −6.70883 + 0.814599i −0.326194 + 0.0396072i
424424 −1.56656 + 1.76828i −0.0760790 + 0.0858755i
425425 5.75908 + 8.34347i 0.279356 + 0.404718i
426426 −3.27146 0.806344i −0.158503 0.0390675i
427427 0.414068i 0.0200382i
428428 53.0013 13.0637i 2.56192 0.631456i
429429 −0.495573 15.2376i −0.0239265 0.735679i
430430 2.49609 + 0.615230i 0.120372 + 0.0296690i
431431 −2.75449 + 11.1754i −0.132679 + 0.538301i 0.866552 + 0.499088i 0.166331π0.166331\pi
−0.999231 + 0.0392136i 0.987515π0.987515\pi
432432 0.135820 + 1.11858i 0.00653464 + 0.0538176i
433433 8.92619 4.68483i 0.428965 0.225138i −0.236401 0.971656i 0.575968π-0.575968\pi
0.665366 + 0.746517i 0.268275π0.268275\pi
434434 −0.928458 + 0.112735i −0.0445674 + 0.00541146i
435435 0.439445 0.837292i 0.0210698 0.0401451i
436436 −10.4412 11.7857i −0.500045 0.564434i
437437 2.02738i 0.0969826i
438438 −9.52789 + 8.44097i −0.455260 + 0.403325i
439439 −17.8007 + 25.7887i −0.849580 + 1.23083i 0.121623 + 0.992576i 0.461190π0.461190\pi
−0.971203 + 0.238253i 0.923425π0.923425\pi
440440 −0.690483 2.80140i −0.0329175 0.133551i
441441 −5.23604 + 4.63872i −0.249335 + 0.220892i
442442 −4.66804 16.5972i −0.222036 0.789447i
443443 −10.3861 9.20127i −0.493458 0.437166i 0.379333 0.925260i 0.376154π-0.376154\pi
−0.872791 + 0.488095i 0.837692π0.837692\pi
444444 5.54987 10.5744i 0.263385 0.501839i
445445 0.999375 0.524513i 0.0473749 0.0248643i
446446 17.2170 + 45.3974i 0.815247 + 2.14963i
447447 18.4969 + 12.7675i 0.874871 + 0.603880i
448448 0.391107 + 0.745192i 0.0184781 + 0.0352070i
449449 −3.32231 + 13.4792i −0.156790 + 0.636121i 0.838974 + 0.544171i 0.183156π0.183156\pi
−0.995764 + 0.0919492i 0.970690π0.970690\pi
450450 7.69765 + 8.68885i 0.362871 + 0.409596i
451451 38.8626 + 34.4292i 1.82997 + 1.62121i
452452 37.0189 + 53.6312i 1.74122 + 2.52260i
453453 −9.90586 18.8740i −0.465418 0.886780i
454454 −12.5533 + 33.1004i −0.589158 + 1.55348i
455455 0.0377214 + 0.0312899i 0.00176841 + 0.00146689i
456456 5.14885 + 13.5764i 0.241117 + 0.635773i
457457 −15.6246 + 17.6365i −0.730888 + 0.825002i −0.990033 0.140837i 0.955021π-0.955021\pi
0.259145 + 0.965838i 0.416559π0.416559\pi
458458 −23.7409 21.0326i −1.10934 0.982790i
459459 −1.98420 + 0.489062i −0.0926146 + 0.0228274i
460460 0.0792377 + 0.321480i 0.00369448 + 0.0149891i
461461 38.5908 + 4.68578i 1.79735 + 0.218238i 0.949884 0.312604i 0.101201π-0.101201\pi
0.847471 + 0.530842i 0.178124π0.178124\pi
462462 0.636155 0.241262i 0.0295966 0.0112245i
463463 39.3621 + 4.77942i 1.82931 + 0.222119i 0.961506 0.274784i 0.0886065π-0.0886065\pi
0.867806 + 0.496903i 0.165530π0.165530\pi
464464 3.06202 4.43610i 0.142151 0.205941i
465465 −1.11560 + 0.274971i −0.0517347 + 0.0127515i
466466 29.3272 + 33.1036i 1.35856 + 1.53349i
467467 2.35441 + 19.3903i 0.108949 + 0.897275i 0.940022 + 0.341113i 0.110804π0.110804\pi
−0.831073 + 0.556163i 0.812273π0.812273\pi
468468 −4.82174 11.5653i −0.222885 0.534604i
469469 −0.0837131 + 0.689439i −0.00386551 + 0.0318353i
470470 2.57254 1.77569i 0.118662 0.0819067i
471471 0.792263 2.08902i 0.0365055 0.0962572i
472472 1.83004 + 15.0717i 0.0842343 + 0.693732i
473473 −10.9217 + 20.8095i −0.502180 + 0.956824i
474474 −10.7924 + 12.1821i −0.495713 + 0.559545i
475475 17.1734 + 11.8539i 0.787970 + 0.543896i
476476 0.401916 0.277423i 0.0184218 0.0127157i
477477 −0.605980 0.318043i −0.0277459 0.0145622i
478478 6.05676 49.8819i 0.277030 2.28155i
479479 −27.5215 18.9967i −1.25749 0.867983i −0.262209 0.965011i 0.584451π-0.584451\pi
−0.995282 + 0.0970282i 0.969066π0.969066\pi
480480 0.479172 + 0.694201i 0.0218711 + 0.0316858i
481481 −2.57254 + 12.1201i −0.117298 + 0.552630i
482482 3.41924 4.95362i 0.155742 0.225631i
483483 −0.0309898 + 0.0117529i −0.00141009 + 0.000534775i
484484 23.9070 1.08668
485485 −1.93461 −0.0878461
486486 −2.18787 + 0.829748i −0.0992436 + 0.0376381i
487487 −4.77549 19.3749i −0.216398 0.877962i −0.974238 0.225522i 0.927591π-0.927591\pi
0.757840 0.652441i 0.226255π-0.226255\pi
488488 20.7858i 0.940930i
489489 2.85067 11.5656i 0.128912 0.523015i
490490 1.14735 3.02531i 0.0518319 0.136669i
491491 −13.5186 7.09513i −0.610088 0.320199i 0.131231 0.991352i 0.458107π-0.458107\pi
−0.741319 + 0.671153i 0.765799π0.765799\pi
492492 39.8990 + 15.1317i 1.79879 + 0.682190i
493493 8.65616 + 4.54310i 0.389854 + 0.204611i
494494 −21.0979 28.5349i −0.949239 1.28385i
495495 0.740092 0.388430i 0.0332647 0.0174586i
496496 −6.50186 + 0.789469i −0.291942 + 0.0354482i
497497 0.0351123 + 0.0925836i 0.00157500 + 0.00415294i
498498 0.339191 2.79349i 0.0151995 0.125179i
499499 25.3234 + 9.60389i 1.13363 + 0.429929i 0.848834 0.528659i 0.177305π-0.177305\pi
0.284796 + 0.958588i 0.408074π0.408074\pi
500500 −6.39805 2.42646i −0.286129 0.108515i
501501 1.81647 1.25382i 0.0811538 0.0560164i
502502 21.1784 + 40.3520i 0.945236 + 1.80100i
503503 −32.0225 7.89283i −1.42781 0.351924i −0.551705 0.834040i 0.686022π-0.686022\pi
−0.876108 + 0.482116i 0.839869π0.839869\pi
504504 0.177676 0.157407i 0.00791431 0.00701147i
505505 −0.252055 0.0306050i −0.0112163 0.00136190i
506506 −4.76879 −0.211999
507507 8.06441 + 10.1963i 0.358153 + 0.452835i
508508 −27.6696 −1.22764
509509 −15.7390 1.91106i −0.697618 0.0847061i −0.235958 0.971763i 0.575823π-0.575823\pi
−0.461660 + 0.887057i 0.652746π0.652746\pi
510510 0.707516 0.626804i 0.0313293 0.0277554i
511511 0.363210 + 0.0895233i 0.0160675 + 0.00396028i
512512 5.84974 + 11.1457i 0.258524 + 0.492577i
513513 −3.46173 + 2.38946i −0.152839 + 0.105497i
514514 −42.2934 16.0398i −1.86548 0.707485i
515515 −0.719521 0.272878i −0.0317059 0.0120245i
516516 −2.32822 + 19.1746i −0.102494 + 0.844116i
517517 10.1331 + 26.7189i 0.445655 + 1.17510i
518518 −0.548903 + 0.0666488i −0.0241174 + 0.00292838i
519519 10.3330 5.42317i 0.453568 0.238051i
520520 1.89358 + 1.57072i 0.0830390 + 0.0688808i
521521 12.3809 + 6.49797i 0.542415 + 0.284681i 0.713595 0.700558i 0.247066π-0.247066\pi
−0.171180 + 0.985240i 0.554758π0.554758\pi
522522 10.4661 + 3.96928i 0.458090 + 0.173731i
523523 −26.5778 13.9491i −1.16217 0.609952i −0.230431 0.973089i 0.574014π-0.574014\pi
−0.931736 + 0.363136i 0.881706π0.881706\pi
524524 −8.40573 + 22.1641i −0.367206 + 0.968243i
525525 0.0816397 0.331225i 0.00356305 0.0144559i
526526 14.3845i 0.627193i
527527 −2.84273 11.5334i −0.123831 0.502402i
528528 4.45490 1.68952i 0.193875 0.0735270i
529529 −22.7677 −0.989900
530530 0.316546 0.0137499
531531 −4.11241 + 1.55963i −0.178464 + 0.0676823i
532532 0.571021 0.827267i 0.0247569 0.0358666i
533533 −44.0996 3.90499i −1.91016 0.169144i
534534 7.58956 + 10.9954i 0.328432 + 0.475817i
535535 −2.55532 1.76381i −0.110476 0.0762561i
536536 −4.20232 + 34.6092i −0.181512 + 1.49489i
537537 −8.74697 4.59076i −0.377460 0.198106i
538538 10.4241 7.19526i 0.449416 0.310210i
539539 24.3428 + 16.8026i 1.04852 + 0.723740i
540540 0.455536 0.514193i 0.0196031 0.0221274i
541541 17.8839 34.0749i 0.768888 1.46499i −0.113030 0.993592i 0.536056π-0.536056\pi
0.881918 0.471403i 0.156252π-0.156252\pi
542542 −3.84865 31.6965i −0.165314 1.36148i
543543 1.34519 3.54698i 0.0577278 0.152216i
544544 −7.17684 + 4.95382i −0.307705 + 0.212393i
545545 −0.107954 + 0.889078i −0.00462422 + 0.0380839i
546546 −0.313869 + 0.487915i −0.0134323 + 0.0208808i
547547 −0.926892 7.63365i −0.0396311 0.326391i −0.999018 0.0442988i 0.985895π-0.985895\pi
0.959387 0.282092i 0.0910284π-0.0910284\pi
548548 36.9448 + 41.7021i 1.57820 + 1.78142i
549549 −5.84652 + 1.44104i −0.249523 + 0.0615020i
550550 27.8828 40.3952i 1.18893 1.72246i
551551 19.9751 + 2.42542i 0.850970 + 0.103326i
552552 −1.55566 + 0.589984i −0.0662132 + 0.0251114i
553553 0.474803 + 0.0576516i 0.0201907 + 0.00245159i
554554 −6.09992 24.7483i −0.259161 1.05146i
555555 −0.659541 + 0.162562i −0.0279960 + 0.00690038i
556556 −34.9161 30.9329i −1.48077 1.31185i
557557 −1.59064 + 1.79546i −0.0673977 + 0.0760763i −0.781242 0.624228i 0.785414π-0.785414\pi
0.713845 + 0.700304i 0.246952π0.246952\pi
558558 −4.82300 12.7172i −0.204174 0.538363i
559559 −3.06091 19.8046i −0.129463 0.837646i
560560 −0.00543126 + 0.0143211i −0.000229513 + 0.000605175i
561561 4.01570 + 7.65128i 0.169543 + 0.323037i
562562 5.25175 + 7.60847i 0.221532 + 0.320944i
563563 −14.9089 13.2081i −0.628333 0.556655i 0.287718 0.957715i 0.407103π-0.407103\pi
−0.916052 + 0.401060i 0.868642π0.868642\pi
564564 15.5741 + 17.5795i 0.655788 + 0.740232i
565565 0.887068 3.59898i 0.0373192 0.151410i
566566 −29.0590 55.3673i −1.22144 2.32726i
567567 0.0565925 + 0.0390630i 0.00237666 + 0.00164049i
568568 1.76261 + 4.64761i 0.0739573 + 0.195009i
569569 −1.51734 + 0.796363i −0.0636104 + 0.0333853i −0.496228 0.868192i 0.665282π-0.665282\pi
0.432618 + 0.901577i 0.357590π0.357590\pi
570570 0.904154 1.72272i 0.0378708 0.0721568i
571571 −21.1962 18.7782i −0.887033 0.785843i 0.0906596 0.995882i 0.471102π-0.471102\pi
−0.977693 + 0.210039i 0.932641π0.932641\pi
572572 −42.6022 + 31.4988i −1.78129 + 1.31703i
573573 7.22548 6.40122i 0.301849 0.267415i
574574 −0.472823 1.91832i −0.0197353 0.0800691i
575575 −1.35829 + 1.96782i −0.0566447 + 0.0820639i
576576 −9.16077 + 8.11573i −0.381699 + 0.338155i
577577 12.0587i 0.502009i 0.967986 + 0.251004i 0.0807608π0.0807608\pi
−0.967986 + 0.251004i 0.919239π0.919239\pi
578578 −19.8981 22.4603i −0.827650 0.934224i
579579 8.76378 16.6980i 0.364210 0.693944i
580580 −3.26224 + 0.396108i −0.135457 + 0.0164475i
581581 −0.0732248 + 0.0384313i −0.00303788 + 0.00159440i
582582 −2.76039 22.7338i −0.114422 0.942347i
583583 −0.692527 + 2.80969i −0.0286816 + 0.116366i
584584 18.2328 + 4.49398i 0.754479 + 0.185962i
585585 −0.310526 + 0.641511i −0.0128387 + 0.0265232i
586586 23.6263 5.82335i 0.975992 0.240560i
587587 37.6765i 1.55508i −0.628835 0.777539i 0.716468π-0.716468\pi
0.628835 0.777539i 0.283532π-0.283532\pi
588588 23.6038 + 5.81782i 0.973405 + 0.239923i
589589 −13.8890 20.1217i −0.572287 0.829101i
590590 1.34902 1.52272i 0.0555381 0.0626896i
591591 3.53711 0.429483i 0.145497 0.0176666i
592592 −3.84389 + 0.466733i −0.157983 + 0.0191826i
593593 −30.3397 + 34.2465i −1.24590 + 1.40633i −0.366390 + 0.930461i 0.619406π0.619406\pi
−0.879514 + 0.475873i 0.842132π0.842132\pi
594594 5.62049 + 8.14268i 0.230611 + 0.334098i
595595 −0.0269710 0.00664776i −0.00110570 0.000272532i
596596 78.1072i 3.19939i
597597 −16.8332 + 4.14902i −0.688939 + 0.169808i
598598 3.26969 2.41751i 0.133708 0.0988595i
599599 −18.3400 4.52040i −0.749351 0.184698i −0.153896 0.988087i 0.549182π-0.549182\pi
−0.595455 + 0.803389i 0.703028π0.703028\pi
600600 4.09823 16.6272i 0.167310 0.678802i
601601 3.13577 + 25.8254i 0.127911 + 1.05344i 0.905405 + 0.424550i 0.139568π0.139568\pi
−0.777494 + 0.628890i 0.783509π0.783509\pi
602602 0.791875 0.415608i 0.0322744 0.0169389i
603603 −10.0260 + 1.21738i −0.408291 + 0.0495755i
604604 −34.4252 + 65.5917i −1.40074 + 2.66889i
605605 −0.901737 1.01785i −0.0366608 0.0413815i
606606 3.00559i 0.122094i
607607 6.58296 5.83199i 0.267194 0.236713i −0.518878 0.854848i 0.673650π-0.673650\pi
0.786072 + 0.618135i 0.212112π0.212112\pi
608608 −10.1965 + 14.7721i −0.413521 + 0.599089i
609609 −0.0787235 0.319394i −0.00319004 0.0129425i
610610 2.08472 1.84690i 0.0844079 0.0747789i
611611 −20.4927 13.1827i −0.829047 0.533315i
612612 5.31588 + 4.70946i 0.214882 + 0.190368i
613613 20.9560 39.9283i 0.846405 1.61269i 0.0573602 0.998354i 0.481732π-0.481732\pi
0.789045 0.614336i 0.210576π-0.210576\pi
614614 −47.4951 + 24.9274i −1.91675 + 1.00599i
615615 −0.860692 2.26946i −0.0347064 0.0915134i
616616 −0.826031 0.570168i −0.0332818 0.0229727i
617617 12.7264 + 24.2481i 0.512346 + 0.976194i 0.994952 + 0.100356i 0.0319981π0.0319981\pi
−0.482606 + 0.875838i 0.660310π0.660310\pi
618618 2.17998 8.84453i 0.0876917 0.355779i
619619 19.5554 + 22.0735i 0.786000 + 0.887210i 0.995895 0.0905137i 0.0288509π-0.0288509\pi
−0.209896 + 0.977724i 0.567312π0.567312\pi
620620 2.98881 + 2.64785i 0.120033 + 0.106340i
621621 −0.273798 0.396665i −0.0109871 0.0159176i
622622 −2.25370 4.29407i −0.0903653 0.172177i
623623 0.139229 0.367117i 0.00557809 0.0147082i
624624 −2.19798 + 3.41680i −0.0879896 + 0.136781i
625625 −8.65783 22.8288i −0.346313 0.913152i
626626 −1.48287 + 1.67381i −0.0592674 + 0.0668991i
627627 13.3130 + 11.7943i 0.531669 + 0.471018i
628628 −7.53880 + 1.85815i −0.300831 + 0.0741481i
629629 −1.68061 6.81852i −0.0670105 0.271872i
630630 −0.0315744 0.00383383i −0.00125795 0.000152743i
631631 24.2203 9.18556i 0.964196 0.365671i 0.178263 0.983983i 0.442952π-0.442952\pi
0.785933 + 0.618312i 0.212183π0.212183\pi
632632 23.8347 + 2.89405i 0.948092 + 0.115119i
633633 −5.70188 + 8.26060i −0.226629 + 0.328329i
634634 −40.7499 + 10.0440i −1.61839 + 0.398897i
635635 1.04365 + 1.17804i 0.0414161 + 0.0467491i
636636 0.286678 + 2.36101i 0.0113675 + 0.0936200i
637637 −25.2085 + 0.819856i −0.998796 + 0.0324839i
638638 5.70507 46.9855i 0.225866 1.86017i
639639 −1.18506 + 0.817985i −0.0468801 + 0.0323590i
640640 1.40912 3.71555i 0.0557005 0.146870i
641641 −4.57322 37.6639i −0.180631 1.48763i −0.747741 0.663991i 0.768862π-0.768862\pi
0.567110 0.823642i 0.308062π-0.308062\pi
642642 17.0807 32.5445i 0.674121 1.28443i
643643 −8.54875 + 9.64954i −0.337130 + 0.380541i −0.892489 0.451070i 0.851042π-0.851042\pi
0.555359 + 0.831611i 0.312581π0.312581\pi
644644 0.0947928 + 0.0654308i 0.00373536 + 0.00257833i
645645 0.904183 0.624112i 0.0356022 0.0245744i
646646 17.8100 + 9.34740i 0.700724 + 0.367768i
647647 4.11819 33.9163i 0.161903 1.33339i −0.654568 0.756003i 0.727150π-0.727150\pi
0.816471 0.577386i 0.195927π-0.195927\pi
648648 2.84089 + 1.96092i 0.111601 + 0.0770324i
649649 10.5645 + 15.3054i 0.414694 + 0.600788i
650650 1.36049 + 41.8318i 0.0533630 + 1.64078i
651651 −0.227058 + 0.328950i −0.00889910 + 0.0128926i
652652 −38.7061 + 14.6793i −1.51585 + 0.574885i
653653 −1.05235 −0.0411816 −0.0205908 0.999788i 0.506555π-0.506555\pi
−0.0205908 + 0.999788i 0.506555π0.506555\pi
654654 −10.6017 −0.414559
655655 1.26069 0.478118i 0.0492594 0.0186816i
656656 −3.31111 13.4337i −0.129277 0.524499i
657657 5.43998i 0.212234i
658658 0.260235 1.05581i 0.0101450 0.0411599i
659659 12.8798 33.9613i 0.501727 1.32295i −0.409976 0.912096i 0.634463π-0.634463\pi
0.911703 0.410849i 0.134768π-0.134768\pi
660660 −2.57200 1.34989i −0.100115 0.0525443i
661661 26.0770 + 9.88968i 1.01428 + 0.384664i 0.805052 0.593204i 0.202137π-0.202137\pi
0.209224 + 0.977868i 0.432906π0.432906\pi
662662 −34.3113 18.0080i −1.33355 0.699900i
663663 −6.63212 3.21031i −0.257570 0.124678i
664664 −3.67581 + 1.92922i −0.142649 + 0.0748681i
665665 −0.0567592 + 0.00689181i −0.00220103 + 0.000267253i
666666 −2.85135 7.51839i −0.110488 0.291332i
667667 −0.277918 + 2.28886i −0.0107610 + 0.0886251i
668668 −7.17199 2.71998i −0.277493 0.105239i
669669 19.4012 + 7.35792i 0.750096 + 0.284474i
670670 3.84453 2.65369i 0.148527 0.102521i
671671 11.8324 + 22.5448i 0.456785 + 0.870332i
672672 0.284912 + 0.0702245i 0.0109907 + 0.00270897i
673673 8.20573 7.26965i 0.316308 0.280224i −0.489998 0.871724i 0.663002π-0.663002\pi
0.806305 + 0.591500i 0.201464π0.201464\pi
674674 42.7444 + 5.19011i 1.64645 + 0.199916i
675675 4.96093 0.190946
676676 13.2417 43.1939i 0.509297 1.66130i
677677 7.93325 0.304899 0.152450 0.988311i 0.451284π-0.451284\pi
0.152450 + 0.988311i 0.451284π0.451284\pi
678678 43.5577 + 5.28886i 1.67282 + 0.203118i
679679 −0.503750 + 0.446283i −0.0193321 + 0.0171268i
680680 −1.35392 0.333711i −0.0519204 0.0127972i
681681 7.03085 + 13.3962i 0.269423 + 0.513342i
682682 −47.3303 + 32.6697i −1.81237 + 1.25099i
683683 7.37288 + 2.79616i 0.282115 + 0.106992i 0.491604 0.870819i 0.336411π-0.336411\pi
−0.209489 + 0.977811i 0.567180π0.567180\pi
684684 13.6680 + 5.18360i 0.522610 + 0.198200i
685685 0.381978 3.14587i 0.0145946 0.120198i
686686 −0.798537 2.10557i −0.0304883 0.0803910i
687687 −13.4561 + 1.63387i −0.513383 + 0.0623360i
688688 5.54539 2.91045i 0.211416 0.110960i
689689 −0.949533 2.27752i −0.0361743 0.0867666i
690690 0.197399 + 0.103603i 0.00751485 + 0.00394410i
691691 −21.0629 7.98812i −0.801272 0.303883i −0.0802325 0.996776i 0.525566π-0.525566\pi
−0.721040 + 0.692894i 0.756336π0.756336\pi
692692 −35.9096 18.8468i −1.36508 0.716448i
693693 0.103107 0.271870i 0.00391670 0.0103275i
694694 17.4823 70.9284i 0.663619 2.69241i
695695 2.65330i 0.100646i
696696 −3.95184 16.0333i −0.149794 0.607739i
697697 23.4623 8.89807i 0.888698 0.337039i
698698 17.3405 0.656347
699699 18.9006 0.714886
700700 −1.10849 + 0.420397i −0.0418972 + 0.0158895i
701701 −21.6932 + 31.4281i −0.819342 + 1.18702i 0.160458 + 0.987043i 0.448703π0.448703\pi
−0.979800 + 0.199979i 0.935913π0.935913\pi
702702 −7.98154 2.73370i −0.301244 0.103177i
703703 −8.21116 11.8959i −0.309690 0.448663i
704704 42.5892 + 29.3972i 1.60514 + 1.10795i
705705 0.161023 1.32614i 0.00606448 0.0499455i
706706 −22.4459 11.7805i −0.844763 0.443366i
707707 −0.0726922 + 0.0501758i −0.00273387 + 0.00188705i
708708 12.5792 + 8.68280i 0.472756 + 0.326320i
709709 −1.72013 + 1.94163i −0.0646009 + 0.0729194i −0.779923 0.625876i 0.784742π-0.784742\pi
0.715322 + 0.698795i 0.246280π0.246280\pi
710710 0.309519 0.589739i 0.0116160 0.0221325i
711711 0.838385 + 6.90472i 0.0314419 + 0.258947i
712712 6.98916 18.4289i 0.261930 0.690652i
713713 2.30566 1.59148i 0.0863476 0.0596014i
714714 0.0396352 0.326425i 0.00148331 0.0122161i
715715 2.94796 + 0.625715i 0.110247 + 0.0234004i
716716 4.13804 + 34.0798i 0.154646 + 1.27362i
717717 −14.2401 16.0738i −0.531807 0.600286i
718718 −68.8965 + 16.9815i −2.57119 + 0.633742i
719719 13.4791 19.5278i 0.502684 0.728263i −0.486703 0.873567i 0.661801π-0.661801\pi
0.989387 + 0.145304i 0.0464161π0.0464161\pi
720720 −0.221111 0.0268477i −0.00824032 0.00100056i
721721 −0.250303 + 0.0949276i −0.00932179 + 0.00353529i
722722 −3.03568 0.368598i −0.112976 0.0137178i
723723 −0.615604 2.49760i −0.0228945 0.0928868i
724724 −12.8002 + 3.15497i −0.475716 + 0.117254i
725725 −17.7634 15.7370i −0.659717 0.584458i
726726 10.6742 12.0487i 0.396158 0.447170i
727727 16.7801 + 44.2454i 0.622338 + 1.64097i 0.759565 + 0.650432i 0.225412π0.225412\pi
−0.137226 + 0.990540i 0.543819π0.543819\pi
728728 0.855407 0.0278204i 0.0317035 0.00103109i
729729 −0.354605 + 0.935016i −0.0131335 + 0.0346302i
730730 −1.16933 2.22797i −0.0432789 0.0824610i
731731 6.45225 + 9.34770i 0.238645 + 0.345737i
732732 15.6634 + 13.8766i 0.578937 + 0.512893i
733733 5.67846 + 6.40966i 0.209739 + 0.236746i 0.843961 0.536405i 0.180218π-0.180218\pi
−0.634222 + 0.773151i 0.718679π0.718679\pi
734734 −1.17021 + 4.74775i −0.0431934 + 0.175243i
735735 −0.642603 1.22438i −0.0237028 0.0451619i
736736 −1.69267 1.16837i −0.0623928 0.0430666i
737737 15.1435 + 39.9301i 0.557818 + 1.47084i
738738 25.4406 13.3523i 0.936481 0.491503i
739739 −22.4114 + 42.7013i −0.824416 + 1.57079i −0.00332522 + 0.999994i 0.501058π0.501058\pi
−0.821090 + 0.570798i 0.806634π0.806634\pi
740740 1.76698 + 1.56541i 0.0649554 + 0.0575454i
741741 −15.1070 1.33771i −0.554969 0.0491421i
742742 0.0824248 0.0730220i 0.00302591 0.00268072i
743743 −5.75270 23.3396i −0.211046 0.856247i −0.976980 0.213329i 0.931569π-0.931569\pi
0.765934 0.642919i 0.222277π-0.222277\pi
744744 −11.3981 + 16.5130i −0.417874 + 0.605395i
745745 −3.32544 + 2.94608i −0.121835 + 0.107936i
746746 83.1919i 3.04587i
747747 −0.797476 0.900164i −0.0291781 0.0329353i
748748 13.9555 26.5900i 0.510264 0.972227i
749749 −1.07226 + 0.130196i −0.0391794 + 0.00475724i
750750 −4.07955 + 2.14111i −0.148964 + 0.0781824i
751751 −5.00061 41.1837i −0.182475 1.50282i −0.739973 0.672637i 0.765162π-0.765162\pi
0.557498 0.830178i 0.311762π-0.311762\pi
752752 1.82239 7.39371i 0.0664556 0.269621i
753753 18.9099 + 4.66088i 0.689116 + 0.169852i
754754 19.9074 + 35.1074i 0.724985 + 1.27854i
755755 4.09105 1.00835i 0.148889 0.0366978i
756756 0.238975i 0.00869142i
757757 −29.2857 7.21827i −1.06441 0.262353i −0.332041 0.943265i 0.607737π-0.607737\pi
−0.732365 + 0.680912i 0.761584π0.761584\pi
758758 20.3719 + 29.5138i 0.739941 + 1.07199i
759759 −1.35145 + 1.52547i −0.0490546 + 0.0553712i
760760 −2.84926 + 0.345962i −0.103353 + 0.0125494i
761761 22.2285 2.69903i 0.805782 0.0978396i 0.292728 0.956196i 0.405437π-0.405437\pi
0.513054 + 0.858356i 0.328514π0.328514\pi
762762 −12.3542 + 13.9450i −0.447544 + 0.505173i
763763 0.176986 + 0.256409i 0.00640733 + 0.00928262i
764764 −32.5721 8.02831i −1.17842 0.290454i
765765 0.403958i 0.0146051i
766766 72.3840 17.8411i 2.61534 0.644624i
767767 −15.0025 5.13838i −0.541708 0.185536i
768768 21.9065 + 5.39946i 0.790482 + 0.194836i
769769 −2.53791 + 10.2967i −0.0915195 + 0.371309i −0.998787 0.0492455i 0.984318π-0.984318\pi
0.907267 + 0.420555i 0.138164π0.138164\pi
770770 0.0162109 + 0.133509i 0.000584200 + 0.00481132i
771771 −17.1167 + 8.98353i −0.616442 + 0.323534i
772772 −65.0584 + 7.89952i −2.34150 + 0.284310i
773773 8.05247 15.3427i 0.289627 0.551839i −0.696555 0.717504i 0.745285π-0.745285\pi
0.986182 + 0.165665i 0.0529770π0.0529770\pi
774774 8.62415 + 9.73465i 0.309989 + 0.349905i
775775 28.8359i 1.03582i
776776 −25.2877 + 22.4030i −0.907777 + 0.804220i
777777 −0.134236 + 0.194475i −0.00481570 + 0.00697674i
778778 5.06307 + 20.5417i 0.181520 + 0.736456i
779779 38.6598 34.2496i 1.38513 1.22712i
780780 2.44779 0.378319i 0.0876449 0.0135460i
781781 4.55743 + 4.03753i 0.163078 + 0.144474i
782782 −1.07108 + 2.04077i −0.0383016 + 0.0729776i
783783 4.23577 2.22310i 0.151374 0.0794473i
784784 −2.79508 7.37001i −0.0998242 0.263215i
785785 0.363463 + 0.250880i 0.0129725 + 0.00895430i
786786 7.41724 + 14.1324i 0.264564 + 0.504085i
787787 −7.61330 + 30.8884i −0.271385 + 1.10105i 0.664088 + 0.747654i 0.268820π0.268820\pi
−0.935473 + 0.353398i 0.885026π0.885026\pi
788788 −8.21117 9.26849i −0.292511 0.330176i
789789 −4.60141 4.07649i −0.163814 0.145127i
790790 −1.82754 2.64765i −0.0650211 0.0941993i
791791 −0.599244 1.14176i −0.0213067 0.0405964i
792792 5.17586 13.6476i 0.183916 0.484947i
793793 −19.5418 9.45929i −0.693949 0.335909i
794794 −16.3697 43.1633i −0.580938 1.53181i
795795 0.0897076 0.101259i 0.00318160 0.00359128i
796796 45.0980 + 39.9533i 1.59846 + 1.41611i
797797 32.1959 7.93558i 1.14044 0.281093i 0.376522 0.926408i 0.377120π-0.377120\pi
0.763917 + 0.645315i 0.223274π0.223274\pi
798798 −0.161973 0.657150i −0.00573378 0.0232629i
799799 13.7101 + 1.66470i 0.485027 + 0.0588929i
800800 19.7939 7.50684i 0.699820 0.265407i
801801 5.66812 + 0.688235i 0.200273 + 0.0243176i
802802 −12.4247 + 18.0002i −0.438730 + 0.635610i
803803 22.3339 5.50482i 0.788147 0.194261i
804804 23.2747 + 26.2717i 0.820837 + 0.926533i
805805 −0.000789702 0.00650378i −2.78333e−5 0.000229228i
806806 15.8899 46.3936i 0.559699 1.63414i
807807 0.652479 5.37365i 0.0229683 0.189161i
808808 −3.64908 + 2.51878i −0.128374 + 0.0886102i
809809 −5.87141 + 15.4816i −0.206428 + 0.544305i −0.997746 0.0670990i 0.978626π-0.978626\pi
0.791319 + 0.611404i 0.209395π0.209395\pi
810810 −0.0557526 0.459164i −0.00195895 0.0161334i
811811 20.4442 38.9531i 0.717892 1.36783i −0.203454 0.979085i 0.565217π-0.565217\pi
0.921346 0.388744i 0.127091π-0.127091\pi
812812 −0.758073 + 0.855688i −0.0266032 + 0.0300288i
813813 −11.2300 7.75150i −0.393853 0.271857i
814814 −27.9816 + 19.3143i −0.980753 + 0.676965i
815815 2.08491 + 1.09424i 0.0730311 + 0.0383297i
816816 0.277560 2.28591i 0.00971653 0.0800228i
817817 19.2404 + 13.2807i 0.673137 + 0.464633i
818818 41.8621 + 60.6477i 1.46367 + 2.12050i
819819 0.0671287 + 0.238675i 0.00234567 + 0.00833999i
820820 −4.79165 + 6.94190i −0.167332 + 0.242422i
821821 46.8980 17.7861i 1.63675 0.620738i 0.646866 0.762604i 0.276079π-0.276079\pi
0.989886 + 0.141866i 0.0453101π0.0453101\pi
822822 37.5126 1.30840
823823 21.8796 0.762674 0.381337 0.924436i 0.375464π-0.375464\pi
0.381337 + 0.924436i 0.375464π0.375464\pi
824824 −12.5650 + 4.76527i −0.437722 + 0.166006i
825825 −5.02006 20.3672i −0.174776 0.709094i
826826 0.707696i 0.0246239i
827827 −4.03767 + 16.3815i −0.140404 + 0.569640i 0.858025 + 0.513607i 0.171691π0.171691\pi
−0.998429 + 0.0560323i 0.982155π0.982155\pi
828828 −0.593966 + 1.56616i −0.0206417 + 0.0544278i
829829 −49.3909 25.9223i −1.71542 0.900319i −0.973137 0.230228i 0.926053π-0.926053\pi
−0.742279 0.670092i 0.766255π-0.766255\pi
830830 0.520102 + 0.197249i 0.0180530 + 0.00684660i
831831 −9.64536 5.06228i −0.334594 0.175608i
832832 −44.1038 + 1.43439i −1.52902 + 0.0497284i
833833 12.6580 6.64342i 0.438573 0.230181i
834834 −31.1793 + 3.78585i −1.07965 + 0.131093i
835835 0.154712 + 0.407943i 0.00535405 + 0.0141175i
836836 7.45042 61.3597i 0.257678 2.12217i
837837 −5.43489 2.06118i −0.187857 0.0712448i
838838 5.64364 + 2.14035i 0.194956 + 0.0739372i
839839 −14.0309 + 9.68481i −0.484399 + 0.334357i −0.785108 0.619359i 0.787392π-0.787392\pi
0.300708 + 0.953716i 0.402777π0.402777\pi
840840 0.0218056 + 0.0415472i 0.000752366 + 0.00143351i
841841 5.93832 + 1.46366i 0.204770 + 0.0504712i
842842 −41.9800 + 37.1910i −1.44673 + 1.28169i
843843 3.92217 + 0.476238i 0.135087 + 0.0164025i
844844 34.8822 1.20070
845845 −2.33845 + 1.06544i −0.0804452 + 0.0366521i
846846 15.8134 0.543677
847847 −0.469603 0.0570202i −0.0161358 0.00195924i
848848 0.577209 0.511363i 0.0198215 0.0175603i
849849 −25.9465 6.39523i −0.890480 0.219484i
850850 −11.0243 21.0050i −0.378130 0.720467i
851851 1.36310 0.940881i 0.0467265 0.0322530i
852852 4.67898 + 1.77450i 0.160299 + 0.0607935i
853853 −16.2695 6.17019i −0.557056 0.211263i 0.0599785 0.998200i 0.480897π-0.480897\pi
−0.617034 + 0.786936i 0.711666π0.711666\pi
854854 0.116786 0.961823i 0.00399635 0.0329129i
855855 −0.294843 0.777438i −0.0100834 0.0265878i
856856 −53.8263 + 6.53569i −1.83974 + 0.223385i
857857 −33.2507 + 17.4513i −1.13582 + 0.596125i −0.924459 0.381283i 0.875482π-0.875482\pi
−0.211363 + 0.977408i 0.567790π0.567790\pi
858858 −3.14657 + 35.5346i −0.107422 + 1.21313i
859859 32.5474 + 17.0822i 1.11050 + 0.582836i 0.917250 0.398313i 0.130404π-0.130404\pi
0.193252 + 0.981149i 0.438096π0.438096\pi
860860 −3.57000 1.35392i −0.121736 0.0461684i
861861 −0.747641 0.392392i −0.0254795 0.0133727i
862862 9.55030 25.1821i 0.325284 0.857705i
863863 −9.13311 + 37.0545i −0.310895 + 1.26135i 0.582779 + 0.812631i 0.301965π0.301965\pi
−0.893673 + 0.448718i 0.851881π0.851881\pi
864864 4.26727i 0.145175i
865865 0.552045 + 2.23973i 0.0187701 + 0.0761533i
866866 −22.0557 + 8.36461i −0.749482 + 0.284241i
867867 −12.8238 −0.435518
868868 1.38907 0.0471480
869869 27.4991 10.4290i 0.932843 0.353781i
870870 −1.25692 + 1.82097i −0.0426137 + 0.0617366i
871871 −30.6254 19.7009i −1.03770 0.667539i
872872 8.88453 + 12.8715i 0.300868 + 0.435883i
873873 −8.05453 5.55964i −0.272605 0.188165i
874874 −0.571815 + 4.70932i −0.0193419 + 0.159295i
875875 0.119889 + 0.0629225i 0.00405298 + 0.00212717i
876876 15.5587 10.7394i 0.525679 0.362850i
877877 22.4922 + 15.5252i 0.759506 + 0.524249i 0.883726 0.468006i 0.155027π-0.155027\pi
−0.124219 + 0.992255i 0.539643π0.539643\pi
878878 48.6221 54.8830i 1.64092 1.85221i
879879 4.83276 9.20805i 0.163005 0.310580i
880880 0.113523 + 0.934943i 0.00382685 + 0.0315169i
881881 −16.7025 + 44.0409i −0.562722 + 1.48378i 0.287724 + 0.957713i 0.407102π0.407102\pi
−0.850446 + 0.526063i 0.823668π0.823668\pi
882882 13.4709 9.29831i 0.453590 0.313090i
883883 1.67735 13.8142i 0.0564473 0.464886i −0.936888 0.349629i 0.886308π-0.886308\pi
0.993336 0.115257i 0.0367691π-0.0367691\pi
884884 3.91117 + 25.3059i 0.131547 + 0.851131i
885885 −0.104795 0.863065i −0.00352265 0.0290116i
886886 21.5303 + 24.3026i 0.723323 + 0.816463i
887887 −26.5006 + 6.53182i −0.889804 + 0.219317i −0.657615 0.753354i 0.728435π-0.728435\pi
−0.232188 + 0.972671i 0.574589π0.574589\pi
888888 −6.73853 + 9.76245i −0.226130 + 0.327606i
889889 0.543510 + 0.0659941i 0.0182287 + 0.00221337i
890890 −2.46935 + 0.936500i −0.0827727 + 0.0313915i
891891 4.19756 + 0.509676i 0.140623 + 0.0170748i
892892 −17.2570 70.0145i −0.577808 2.34426i
893893 27.6007 6.80297i 0.923623 0.227653i
894894 −39.3646 34.8740i −1.31655 1.16636i
895895 1.29488 1.46161i 0.0432830 0.0488564i
896896 −0.490199 1.29255i −0.0163764 0.0431810i
897897 0.153283 1.73104i 0.00511796 0.0577979i
898898 11.5190 30.3732i 0.384395 1.01357i
899899 12.9220 + 24.6209i 0.430974 + 0.821153i
900900 −9.79366 14.1886i −0.326455 0.472952i
901901 1.04684 + 0.927422i 0.0348754 + 0.0308969i
902902 −80.5617 90.9354i −2.68241 3.02782i
903903 0.0914660 0.371092i 0.00304380 0.0123492i
904904 −30.0815 57.3154i −1.00049 1.90628i
905905 0.617128 + 0.425973i 0.0205140 + 0.0141598i
906906 17.6866 + 46.6357i 0.587597 + 1.54937i
907907 −5.99795 + 3.14797i −0.199159 + 0.104527i −0.561354 0.827576i 0.689720π-0.689720\pi
0.362196 + 0.932102i 0.382027π0.382027\pi
908908 24.4338 46.5548i 0.810866 1.54498i
909909 −0.961450 0.851771i −0.0318893 0.0282515i
910910 −0.0787965 0.0833213i −0.00261208 0.00276208i
911911 −1.24754 + 1.10523i −0.0413330 + 0.0366178i −0.683536 0.729916i 0.739559π-0.739559\pi
0.642203 + 0.766534i 0.278020π0.278020\pi
912912 −1.13427 4.60193i −0.0375596 0.152385i
913913 −2.88866 + 4.18494i −0.0956006 + 0.138501i
914914 41.2681 36.5603i 1.36503 1.20931i
915915 1.19028i 0.0393494i
916916 31.2375 + 35.2599i 1.03212 + 1.16502i
917917 0.217976 0.415318i 0.00719820 0.0137150i
918918 4.74696 0.576386i 0.156673 0.0190236i
919919 −36.9217 + 19.3780i −1.21793 + 0.639221i −0.946334 0.323190i 0.895245π-0.895245\pi
−0.271599 + 0.962411i 0.587552π0.587552\pi
920920 −0.0396423 0.326484i −0.00130697 0.0107638i
921921 −5.48595 + 22.2574i −0.180768 + 0.733405i
922922 −88.3196 21.7688i −2.90865 0.716918i
923923 −5.17158 0.457940i −0.170225 0.0150733i
924924 −0.981115 + 0.241823i −0.0322763 + 0.00795539i
925925 17.0478i 0.560527i
926926 −90.0847 22.2039i −2.96037 0.729665i
927927 −2.21145 3.20385i −0.0726337 0.105228i
928928 13.5366 15.2796i 0.444360 0.501579i
929929 22.6958 2.75577i 0.744626 0.0904140i 0.260575 0.965454i 0.416088π-0.416088\pi
0.484051 + 0.875040i 0.339165π0.339165\pi
930930 2.66894 0.324068i 0.0875180 0.0106266i
931931 19.5120 22.0244i 0.639478 0.721822i
932932 −37.3128 54.0569i −1.22222 1.77069i
933933 −2.01231 0.495989i −0.0658800 0.0162380i
934934 45.7050i 1.49551i
935935 −1.65846 + 0.408773i −0.0542374 + 0.0133683i
936936 3.36980 + 11.9813i 0.110145 + 0.391620i
937937 41.8097 + 10.3052i 1.36586 + 0.336655i 0.853043 0.521841i 0.174754π-0.174754\pi
0.512821 + 0.858496i 0.328601π0.328601\pi
938938 0.388908 1.57786i 0.0126983 0.0515190i
939939 0.115193 + 0.948702i 0.00375919 + 0.0309597i
940940 −4.11074 + 2.15748i −0.134078 + 0.0703694i
941941 −41.6368 + 5.05562i −1.35732 + 0.164809i −0.766630 0.642090i 0.778068π-0.778068\pi
−0.590691 + 0.806898i 0.701145π0.701145\pi
942942 −2.42952 + 4.62906i −0.0791580 + 0.150823i
943943 3.92450 + 4.42985i 0.127799 + 0.144256i
944944 4.95589i 0.161301i
945945 −0.0101744 + 0.00901375i −0.000330974 + 0.000293217i
946946 31.2388 45.2573i 1.01566 1.47144i
947947 1.31415 + 5.33170i 0.0427040 + 0.173257i 0.988422 0.151733i 0.0484853π-0.0484853\pi
−0.945718 + 0.324990i 0.894639π0.894639\pi
948948 18.0928 16.0289i 0.587628 0.520593i
949949 −12.5225 + 15.0964i −0.406496 + 0.490050i
950950 −36.5481 32.3788i −1.18578 1.05051i
951951 −8.33541 + 15.8818i −0.270294 + 0.515002i
952952 −0.429527 + 0.225433i −0.0139210 + 0.00730632i
953953 5.23347 + 13.7995i 0.169529 + 0.447010i 0.992674 0.120820i 0.0385523π-0.0385523\pi
−0.823146 + 0.567830i 0.807783π0.807783\pi
954954 1.31790 + 0.909683i 0.0426687 + 0.0294521i
955955 0.886762 + 1.68958i 0.0286949 + 0.0546737i
956956 −17.8597 + 72.4598i −0.577625 + 2.34352i
957957 −13.4133 15.1404i −0.433589 0.489421i
958958 58.5707 + 51.8891i 1.89233 + 1.67646i
959959 −0.626240 0.907265i −0.0202223 0.0292971i
960960 −1.12427 2.14213i −0.0362858 0.0691368i
961961 0.988093 2.60539i 0.0318740 0.0840447i
962962 9.39409 27.4278i 0.302878 0.884308i
963963 −5.56999 14.6868i −0.179490 0.473277i
964964 −5.92800 + 6.69133i −0.190928 + 0.215513i
965965 2.79022 + 2.47192i 0.0898205 + 0.0795740i
966966 0.0752999 0.0185598i 0.00242273 0.000597150i
967967 2.33597 + 9.47738i 0.0751196 + 0.304772i 0.996469 0.0839638i 0.0267580π-0.0267580\pi
−0.921349 + 0.388736i 0.872912π0.872912\pi
968968 −23.5736 2.86236i −0.757685 0.0919996i
969969 8.03737 3.04817i 0.258198 0.0979214i
970970 4.49383 + 0.545650i 0.144288 + 0.0175198i
971971 −24.0299 + 34.8133i −0.771155 + 1.11721i 0.218792 + 0.975772i 0.429788π0.429788\pi
−0.989947 + 0.141440i 0.954827π0.954827\pi
972972 3.37425 0.831678i 0.108229 0.0266761i
973973 0.612074 + 0.690889i 0.0196222 + 0.0221489i
974974 5.62818 + 46.3522i 0.180338 + 1.48522i
975975 13.7670 + 11.4197i 0.440897 + 0.365724i
976976 0.817839 6.73551i 0.0261784 0.215598i
977977 16.4213 11.3348i 0.525365 0.362633i −0.275669 0.961253i 0.588899π-0.588899\pi
0.801033 + 0.598620i 0.204284π0.204284\pi
978978 −9.88375 + 26.0613i −0.316047 + 0.833348i
979979 −2.91012 23.9670i −0.0930080 0.765989i
980980 −2.23320 + 4.25500i −0.0713369 + 0.135921i
981981 −3.00447 + 3.39134i −0.0959253 + 0.108277i
982982 29.4008 + 20.2939i 0.938217 + 0.647604i
983983 −46.3377 + 31.9846i −1.47794 + 1.02015i −0.488928 + 0.872324i 0.662612π0.662612\pi
−0.989013 + 0.147825i 0.952773π0.952773\pi
984984 −37.5309 19.6977i −1.19644 0.627940i
985985 −0.0848966 + 0.699186i −0.00270503 + 0.0222779i
986986 −18.8257 12.9944i −0.599532 0.413827i
987987 −0.263992 0.382458i −0.00840295 0.0121738i
988988 25.9977 + 45.8478i 0.827096 + 1.45861i
989989 −1.52178 + 2.20467i −0.0483897 + 0.0701046i
990990 −1.82869 + 0.693530i −0.0581195 + 0.0220418i
991991 16.1346 0.512532 0.256266 0.966606i 0.417508π-0.417508\pi
0.256266 + 0.966606i 0.417508π0.417508\pi
992992 −24.8040 −0.787527
993993 −15.4842 + 5.87238i −0.491376 + 0.186354i
994994 −0.0554482 0.224962i −0.00175871 0.00713537i
995995 3.42704i 0.108644i
996996 −1.00018 + 4.05790i −0.0316920 + 0.128579i
997997 −5.40213 + 14.2442i −0.171087 + 0.451120i −0.992945 0.118572i 0.962168π-0.962168\pi
0.821858 + 0.569692i 0.192938π0.192938\pi
998998 −56.1140 29.4509i −1.77626 0.932251i
999999 −3.21310 1.21857i −0.101658 0.0385537i
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 507.2.p.a.64.1 168
169.103 even 26 inner 507.2.p.a.103.1 yes 168
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.p.a.64.1 168 1.1 even 1 trivial
507.2.p.a.103.1 yes 168 169.103 even 26 inner