Properties

Label 325.2.s.b.193.2
Level 325325
Weight 22
Character 325.193
Analytic conductor 2.5952.595
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [325,2,Mod(32,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.32");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 325=5213 325 = 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 325.s (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: 2.595138065692.59513806569
Analytic rank: 00
Dimension: 2020
Relative dimension: 55 over Q(ζ12)\Q(\zeta_{12})
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20+26x18+279x16+1604x14+5353x12+10466x10+11441x8+6176x6++1 x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 193.2
Root 1.02262i1.02262i of defining polynomial
Character χ\chi == 325.193
Dual form 325.2.s.b.32.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.5113090.885613i)q2+(0.7213002.69193i)q3+(0.4771260.826407i)q4+(2.75281+0.737614i)q6+(0.8344790.481787i)q73.02107q8+(4.128122.38337i)q9+(1.60661+0.430490i)q11+(1.880481.88048i)q12+(1.82127+3.11175i)q13+0.985368iq14+(0.590448+1.02269i)q16+(7.003421.87656i)q17+4.87456iq18+(0.7074962.64041i)q19+(1.89884+1.89884i)q21+(0.4402261.64295i)q22+(3.72214+0.997344i)q23+(2.17910+8.13250i)q24+(3.68704+0.0218799i)q26+(3.48159+3.48159i)q27+(0.796304+0.459747i)q28+(0.2531070.146132i)q29+(0.1256490.125649i)q31+(2.41727+4.18683i)q32+(2.317694.01436i)q33+(5.242825.24282i)q34+(3.93927+2.27434i)q36+(3.53443+2.04061i)q37+(1.97663+1.97663i)q38+(7.06291+7.14724i)q39+(1.79277+6.69071i)q41+(2.65254+0.710745i)q42+(2.057067.67707i)q43+(1.122321.12232i)q44+(1.019903.80633i)q467.84582iq47+(3.178880.851780i)q48+(3.035765.25810i)q4920.2063iq51+(1.70259+2.98981i)q52+(1.99855+1.99855i)q53+(4.86351+1.30317i)q54+(2.52102+1.45551i)q567.61811q57+(0.2588320.149437i)q58+(4.879241.30739i)q59+(1.04169+1.80425i)q61+(0.0470311+0.175522i)q62+(2.29655+3.97775i)q63+7.30568q644.74023q66+(3.64915+6.32050i)q67+(1.790716.68304i)q68+(5.369569.30034i)q69+(12.60823.37837i)q71+(12.4713+7.20034i)q723.22747q73+(3.61437+2.08676i)q74+(2.519620.675130i)q76+(1.133281.13328i)q77+(2.718369.90945i)q78+13.5845iq79+(0.2891960.500902i)q81+(6.842041.83332i)q82+8.56854iq83+(0.663230+2.47521i)q84+(5.74712+5.74712i)q86+(0.2108090.786751i)q87+(4.853681.30054i)q88+(0.1342070.500868i)q89+(3.019011.71922i)q91+(2.600142.60014i)q92+(0.428870+0.247608i)q93+(6.94836+4.01164i)q94+(9.52707+9.52707i)q96+(3.756606.50662i)q97+(3.10442+5.37702i)q98+(5.606265.60626i)q99+O(q100)q+(-0.511309 - 0.885613i) q^{2} +(0.721300 - 2.69193i) q^{3} +(0.477126 - 0.826407i) q^{4} +(-2.75281 + 0.737614i) q^{6} +(-0.834479 - 0.481787i) q^{7} -3.02107 q^{8} +(-4.12812 - 2.38337i) q^{9} +(1.60661 + 0.430490i) q^{11} +(-1.88048 - 1.88048i) q^{12} +(-1.82127 + 3.11175i) q^{13} +0.985368i q^{14} +(0.590448 + 1.02269i) q^{16} +(7.00342 - 1.87656i) q^{17} +4.87456i q^{18} +(-0.707496 - 2.64041i) q^{19} +(-1.89884 + 1.89884i) q^{21} +(-0.440226 - 1.64295i) q^{22} +(3.72214 + 0.997344i) q^{23} +(-2.17910 + 8.13250i) q^{24} +(3.68704 + 0.0218799i) q^{26} +(-3.48159 + 3.48159i) q^{27} +(-0.796304 + 0.459747i) q^{28} +(0.253107 - 0.146132i) q^{29} +(-0.125649 - 0.125649i) q^{31} +(-2.41727 + 4.18683i) q^{32} +(2.31769 - 4.01436i) q^{33} +(-5.24282 - 5.24282i) q^{34} +(-3.93927 + 2.27434i) q^{36} +(-3.53443 + 2.04061i) q^{37} +(-1.97663 + 1.97663i) q^{38} +(7.06291 + 7.14724i) q^{39} +(-1.79277 + 6.69071i) q^{41} +(2.65254 + 0.710745i) q^{42} +(-2.05706 - 7.67707i) q^{43} +(1.12232 - 1.12232i) q^{44} +(-1.01990 - 3.80633i) q^{46} -7.84582i q^{47} +(3.17888 - 0.851780i) q^{48} +(-3.03576 - 5.25810i) q^{49} -20.2063i q^{51} +(1.70259 + 2.98981i) q^{52} +(1.99855 + 1.99855i) q^{53} +(4.86351 + 1.30317i) q^{54} +(2.52102 + 1.45551i) q^{56} -7.61811 q^{57} +(-0.258832 - 0.149437i) q^{58} +(4.87924 - 1.30739i) q^{59} +(-1.04169 + 1.80425i) q^{61} +(-0.0470311 + 0.175522i) q^{62} +(2.29655 + 3.97775i) q^{63} +7.30568 q^{64} -4.74023 q^{66} +(3.64915 + 6.32050i) q^{67} +(1.79071 - 6.68304i) q^{68} +(5.36956 - 9.30034i) q^{69} +(12.6082 - 3.37837i) q^{71} +(12.4713 + 7.20034i) q^{72} -3.22747 q^{73} +(3.61437 + 2.08676i) q^{74} +(-2.51962 - 0.675130i) q^{76} +(-1.13328 - 1.13328i) q^{77} +(2.71836 - 9.90945i) q^{78} +13.5845i q^{79} +(-0.289196 - 0.500902i) q^{81} +(6.84204 - 1.83332i) q^{82} +8.56854i q^{83} +(0.663230 + 2.47521i) q^{84} +(-5.74712 + 5.74712i) q^{86} +(-0.210809 - 0.786751i) q^{87} +(-4.85368 - 1.30054i) q^{88} +(0.134207 - 0.500868i) q^{89} +(3.01901 - 1.71922i) q^{91} +(2.60014 - 2.60014i) q^{92} +(-0.428870 + 0.247608i) q^{93} +(-6.94836 + 4.01164i) q^{94} +(9.52707 + 9.52707i) q^{96} +(3.75660 - 6.50662i) q^{97} +(-3.10442 + 5.37702i) q^{98} +(-5.60626 - 5.60626i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+4q2+2q36q48q6+6q712q812q916q1124q122q132q16+10q17+20q19+4q2116q22+2q2332q2424q26+60q99+O(q100) 20 q + 4 q^{2} + 2 q^{3} - 6 q^{4} - 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 16 q^{11} - 24 q^{12} - 2 q^{13} - 2 q^{16} + 10 q^{17} + 20 q^{19} + 4 q^{21} - 16 q^{22} + 2 q^{23} - 32 q^{24} - 24 q^{26}+ \cdots - 60 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/325Z)×\left(\mathbb{Z}/325\mathbb{Z}\right)^\times.

nn 2727 301301
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) e(712)e\left(\frac{7}{12}\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 −0.511309 0.885613i −0.361550 0.626223i 0.626666 0.779288i 0.284419π-0.284419\pi
−0.988216 + 0.153065i 0.951086π0.951086\pi
33 0.721300 2.69193i 0.416443 1.55418i −0.365486 0.930817i 0.619097π-0.619097\pi
0.781929 0.623368i 0.214236π-0.214236\pi
44 0.477126 0.826407i 0.238563 0.413204i
55 0 0
66 −2.75281 + 0.737614i −1.12383 + 0.301130i
77 −0.834479 0.481787i −0.315404 0.182098i 0.333938 0.942595i 0.391622π-0.391622\pi
−0.649342 + 0.760497i 0.724956π0.724956\pi
88 −3.02107 −1.06811
99 −4.12812 2.38337i −1.37604 0.794457i
1010 0 0
1111 1.60661 + 0.430490i 0.484411 + 0.129797i 0.492756 0.870168i 0.335990π-0.335990\pi
−0.00834492 + 0.999965i 0.502656π0.502656\pi
1212 −1.88048 1.88048i −0.542847 0.542847i
1313 −1.82127 + 3.11175i −0.505130 + 0.863043i
1414 0.985368i 0.263351i
1515 0 0
1616 0.590448 + 1.02269i 0.147612 + 0.255671i
1717 7.00342 1.87656i 1.69858 0.455133i 0.725998 0.687697i 0.241378π-0.241378\pi
0.972581 + 0.232564i 0.0747114π0.0747114\pi
1818 4.87456i 1.14894i
1919 −0.707496 2.64041i −0.162311 0.605752i −0.998368 0.0571095i 0.981812π-0.981812\pi
0.836057 0.548642i 0.184855π-0.184855\pi
2020 0 0
2121 −1.89884 + 1.89884i −0.414362 + 0.414362i
2222 −0.440226 1.64295i −0.0938565 0.350277i
2323 3.72214 + 0.997344i 0.776120 + 0.207961i 0.625073 0.780566i 0.285069π-0.285069\pi
0.151046 + 0.988527i 0.451736π0.451736\pi
2424 −2.17910 + 8.13250i −0.444806 + 1.66004i
2525 0 0
2626 3.68704 + 0.0218799i 0.723087 + 0.00429099i
2727 −3.48159 + 3.48159i −0.670033 + 0.670033i
2828 −0.796304 + 0.459747i −0.150487 + 0.0868839i
2929 0.253107 0.146132i 0.0470008 0.0271360i −0.476315 0.879274i 0.658028π-0.658028\pi
0.523316 + 0.852139i 0.324695π0.324695\pi
3030 0 0
3131 −0.125649 0.125649i −0.0225673 0.0225673i 0.695733 0.718300i 0.255080π-0.255080\pi
−0.718300 + 0.695733i 0.755080π0.755080\pi
3232 −2.41727 + 4.18683i −0.427317 + 0.740134i
3333 2.31769 4.01436i 0.403458 0.698811i
3434 −5.24282 5.24282i −0.899136 0.899136i
3535 0 0
3636 −3.93927 + 2.27434i −0.656545 + 0.379057i
3737 −3.53443 + 2.04061i −0.581057 + 0.335474i −0.761553 0.648102i 0.775563π-0.775563\pi
0.180496 + 0.983576i 0.442230π0.442230\pi
3838 −1.97663 + 1.97663i −0.320652 + 0.320652i
3939 7.06291 + 7.14724i 1.13097 + 1.14447i
4040 0 0
4141 −1.79277 + 6.69071i −0.279984 + 1.04491i 0.672444 + 0.740148i 0.265245π0.265245\pi
−0.952427 + 0.304765i 0.901422π0.901422\pi
4242 2.65254 + 0.710745i 0.409295 + 0.109670i
4343 −2.05706 7.67707i −0.313699 1.17074i −0.925194 0.379494i 0.876098π-0.876098\pi
0.611495 0.791248i 0.290568π-0.290568\pi
4444 1.12232 1.12232i 0.169195 0.169195i
4545 0 0
4646 −1.01990 3.80633i −0.150376 0.561212i
4747 7.84582i 1.14443i −0.820103 0.572215i 0.806084π-0.806084\pi
0.820103 0.572215i 0.193916π-0.193916\pi
4848 3.17888 0.851780i 0.458832 0.122944i
4949 −3.03576 5.25810i −0.433680 0.751156i
5050 0 0
5151 20.2063i 2.82944i
5252 1.70259 + 2.98981i 0.236107 + 0.414612i
5353 1.99855 + 1.99855i 0.274522 + 0.274522i 0.830918 0.556395i 0.187816π-0.187816\pi
−0.556395 + 0.830918i 0.687816π0.687816\pi
5454 4.86351 + 1.30317i 0.661840 + 0.177339i
5555 0 0
5656 2.52102 + 1.45551i 0.336886 + 0.194501i
5757 −7.61811 −1.00904
5858 −0.258832 0.149437i −0.0339863 0.0196220i
5959 4.87924 1.30739i 0.635223 0.170207i 0.0731843 0.997318i 0.476684π-0.476684\pi
0.562039 + 0.827111i 0.310017π0.310017\pi
6060 0 0
6161 −1.04169 + 1.80425i −0.133374 + 0.231011i −0.924975 0.380027i 0.875915π-0.875915\pi
0.791601 + 0.611038i 0.209248π0.209248\pi
6262 −0.0470311 + 0.175522i −0.00597296 + 0.0222914i
6363 2.29655 + 3.97775i 0.289339 + 0.501149i
6464 7.30568 0.913209
6565 0 0
6666 −4.74023 −0.583482
6767 3.64915 + 6.32050i 0.445814 + 0.772173i 0.998109 0.0614765i 0.0195809π-0.0195809\pi
−0.552294 + 0.833649i 0.686248π0.686248\pi
6868 1.79071 6.68304i 0.217156 0.810437i
6969 5.36956 9.30034i 0.646419 1.11963i
7070 0 0
7171 12.6082 3.37837i 1.49632 0.400939i 0.584457 0.811425i 0.301308π-0.301308\pi
0.911867 + 0.410486i 0.134641π0.134641\pi
7272 12.4713 + 7.20034i 1.46976 + 0.848568i
7373 −3.22747 −0.377746 −0.188873 0.982001i 0.560483π-0.560483\pi
−0.188873 + 0.982001i 0.560483π0.560483\pi
7474 3.61437 + 2.08676i 0.420163 + 0.242581i
7575 0 0
7676 −2.51962 0.675130i −0.289020 0.0774427i
7777 −1.13328 1.13328i −0.129149 0.129149i
7878 2.71836 9.90945i 0.307793 1.12202i
7979 13.5845i 1.52838i 0.644992 + 0.764190i 0.276861π0.276861\pi
−0.644992 + 0.764190i 0.723139π0.723139\pi
8080 0 0
8181 −0.289196 0.500902i −0.0321329 0.0556558i
8282 6.84204 1.83332i 0.755577 0.202456i
8383 8.56854i 0.940519i 0.882528 + 0.470260i 0.155840π0.155840\pi
−0.882528 + 0.470260i 0.844160π0.844160\pi
8484 0.663230 + 2.47521i 0.0723643 + 0.270067i
8585 0 0
8686 −5.74712 + 5.74712i −0.619728 + 0.619728i
8787 −0.210809 0.786751i −0.0226011 0.0843486i
8888 −4.85368 1.30054i −0.517404 0.138638i
8989 0.134207 0.500868i 0.0142259 0.0530919i −0.958448 0.285267i 0.907918π-0.907918\pi
0.972674 + 0.232175i 0.0745843π0.0745843\pi
9090 0 0
9191 3.01901 1.71922i 0.316479 0.180223i
9292 2.60014 2.60014i 0.271084 0.271084i
9393 −0.428870 + 0.247608i −0.0444718 + 0.0256758i
9494 −6.94836 + 4.01164i −0.716669 + 0.413769i
9595 0 0
9696 9.52707 + 9.52707i 0.972353 + 0.972353i
9797 3.75660 6.50662i 0.381425 0.660648i −0.609841 0.792524i 0.708767π-0.708767\pi
0.991266 + 0.131876i 0.0421001π0.0421001\pi
9898 −3.10442 + 5.37702i −0.313594 + 0.543161i
9999 −5.60626 5.60626i −0.563450 0.563450i
100100 0 0
101101 8.44685 4.87679i 0.840493 0.485259i −0.0169388 0.999857i 0.505392π-0.505392\pi
0.857432 + 0.514598i 0.172059π0.172059\pi
102102 −17.8949 + 10.3316i −1.77186 + 1.02298i
103103 2.52321 2.52321i 0.248619 0.248619i −0.571784 0.820404i 0.693749π-0.693749\pi
0.820404 + 0.571784i 0.193749π0.193749\pi
104104 5.50220 9.40081i 0.539535 0.921825i
105105 0 0
106106 0.748066 2.79182i 0.0726586 0.271166i
107107 −0.429359 0.115046i −0.0415077 0.0111220i 0.238005 0.971264i 0.423506π-0.423506\pi
−0.279513 + 0.960142i 0.590173π0.590173\pi
108108 1.21605 + 4.53837i 0.117015 + 0.436705i
109109 −6.42134 + 6.42134i −0.615053 + 0.615053i −0.944258 0.329206i 0.893219π-0.893219\pi
0.329206 + 0.944258i 0.393219π0.393219\pi
110110 0 0
111111 2.94378 + 10.9863i 0.279411 + 1.04278i
112112 1.13788i 0.107520i
113113 1.86865 0.500704i 0.175788 0.0471023i −0.169851 0.985470i 0.554329π-0.554329\pi
0.345639 + 0.938367i 0.387662π0.387662\pi
114114 3.89521 + 6.74670i 0.364820 + 0.631886i
115115 0 0
116116 0.278893i 0.0258946i
117117 14.9349 8.50489i 1.38073 0.786277i
118118 −3.65264 3.65264i −0.336253 0.336253i
119119 −6.74831 1.80821i −0.618617 0.165758i
120120 0 0
121121 −7.13041 4.11674i −0.648219 0.374249i
122122 2.13050 0.192886
123123 16.7178 + 9.65202i 1.50739 + 0.870293i
124124 −0.163788 + 0.0438869i −0.0147086 + 0.00394116i
125125 0 0
126126 2.34850 4.06772i 0.209221 0.362381i
127127 0.562967 2.10102i 0.0499553 0.186436i −0.936440 0.350829i 0.885900π-0.885900\pi
0.986395 + 0.164393i 0.0525666π0.0525666\pi
128128 1.09908 + 1.90366i 0.0971460 + 0.168262i
129129 −22.1499 −1.95019
130130 0 0
131131 −0.0622493 −0.00543874 −0.00271937 0.999996i 0.500866π-0.500866\pi
−0.00271937 + 0.999996i 0.500866π0.500866\pi
132132 −2.21166 3.83072i −0.192501 0.333421i
133133 −0.681725 + 2.54423i −0.0591130 + 0.220613i
134134 3.73168 6.46346i 0.322368 0.558358i
135135 0 0
136136 −21.1578 + 5.66923i −1.81427 + 0.486132i
137137 3.82564 + 2.20873i 0.326846 + 0.188705i 0.654440 0.756114i 0.272904π-0.272904\pi
−0.327594 + 0.944819i 0.606238π0.606238\pi
138138 −10.9820 −0.934850
139139 11.9066 + 6.87430i 1.00991 + 0.583070i 0.911165 0.412043i 0.135184π-0.135184\pi
0.0987430 + 0.995113i 0.468518π0.468518\pi
140140 0 0
141141 −21.1204 5.65919i −1.77866 0.476590i
142142 −9.43864 9.43864i −0.792073 0.792073i
143143 −4.26565 + 4.21532i −0.356711 + 0.352503i
144144 5.62903i 0.469085i
145145 0 0
146146 1.65023 + 2.85829i 0.136574 + 0.236553i
147147 −16.3441 + 4.37939i −1.34804 + 0.361206i
148148 3.89451i 0.320127i
149149 −1.12129 4.18471i −0.0918596 0.342825i 0.904665 0.426124i 0.140121π-0.140121\pi
−0.996525 + 0.0832987i 0.973454π0.973454\pi
150150 0 0
151151 4.74990 4.74990i 0.386542 0.386542i −0.486910 0.873452i 0.661876π-0.661876\pi
0.873452 + 0.486910i 0.161876π0.161876\pi
152152 2.13740 + 7.97687i 0.173366 + 0.647010i
153153 −33.3835 8.94508i −2.69890 0.723167i
154154 −0.424190 + 1.58310i −0.0341822 + 0.127570i
155155 0 0
156156 9.27643 2.42670i 0.742709 0.194292i
157157 −14.4488 + 14.4488i −1.15314 + 1.15314i −0.167218 + 0.985920i 0.553478π0.553478\pi
−0.985920 + 0.167218i 0.946522π0.946522\pi
158158 12.0306 6.94589i 0.957106 0.552586i
159159 6.82151 3.93840i 0.540981 0.312336i
160160 0 0
161161 −2.62554 2.62554i −0.206922 0.206922i
162162 −0.295737 + 0.512231i −0.0232353 + 0.0402447i
163163 10.6926 18.5201i 0.837508 1.45061i −0.0544633 0.998516i 0.517345π-0.517345\pi
0.891972 0.452091i 0.149322π-0.149322\pi
164164 4.67387 + 4.67387i 0.364968 + 0.364968i
165165 0 0
166166 7.58841 4.38117i 0.588975 0.340045i
167167 −1.48475 + 0.857220i −0.114893 + 0.0663337i −0.556345 0.830951i 0.687797π-0.687797\pi
0.441452 + 0.897285i 0.354464π0.354464\pi
168168 5.73655 5.73655i 0.442584 0.442584i
169169 −6.36593 11.3347i −0.489687 0.871898i
170170 0 0
171171 −3.37245 + 12.5862i −0.257898 + 0.962488i
172172 −7.32587 1.96296i −0.558592 0.149674i
173173 3.92804 + 14.6596i 0.298643 + 1.11455i 0.938281 + 0.345875i 0.112418π0.112418\pi
−0.639638 + 0.768677i 0.720916π0.720916\pi
174174 −0.588968 + 0.588968i −0.0446496 + 0.0446496i
175175 0 0
176176 0.508363 + 1.89724i 0.0383193 + 0.143010i
177177 14.0776i 1.05814i
178178 −0.512196 + 0.137243i −0.0383907 + 0.0102868i
179179 1.37961 + 2.38956i 0.103117 + 0.178604i 0.912967 0.408033i 0.133785π-0.133785\pi
−0.809850 + 0.586637i 0.800452π0.800452\pi
180180 0 0
181181 10.3568i 0.769818i 0.922954 + 0.384909i 0.125767π0.125767\pi
−0.922954 + 0.384909i 0.874233π0.874233\pi
182182 −3.06621 1.79462i −0.227283 0.133026i
183183 4.10555 + 4.10555i 0.303491 + 0.303491i
184184 −11.2449 3.01305i −0.828981 0.222125i
185185 0 0
186186 0.438570 + 0.253209i 0.0321575 + 0.0185662i
187187 12.0596 0.881885
188188 −6.48384 3.74345i −0.472883 0.273019i
189189 4.58270 1.22793i 0.333342 0.0893188i
190190 0 0
191191 −9.28983 + 16.0905i −0.672189 + 1.16427i 0.305093 + 0.952322i 0.401312π0.401312\pi
−0.977282 + 0.211943i 0.932021π0.932021\pi
192192 5.26958 19.6663i 0.380299 1.41930i
193193 6.28576 + 10.8872i 0.452459 + 0.783681i 0.998538 0.0540520i 0.0172137π-0.0172137\pi
−0.546079 + 0.837733i 0.683880π0.683880\pi
194194 −7.68313 −0.551617
195195 0 0
196196 −5.79377 −0.413841
197197 7.14308 + 12.3722i 0.508924 + 0.881481i 0.999947 + 0.0103349i 0.00328975π0.00328975\pi
−0.491023 + 0.871147i 0.663377π0.663377\pi
198198 −2.09845 + 7.83150i −0.149130 + 0.556561i
199199 −7.36781 + 12.7614i −0.522291 + 0.904634i 0.477373 + 0.878701i 0.341589π0.341589\pi
−0.999664 + 0.0259331i 0.991744π0.991744\pi
200200 0 0
201201 19.6465 5.26425i 1.38575 0.371312i
202202 −8.63790 4.98709i −0.607760 0.350891i
203203 −0.281617 −0.0197656
204204 −16.6986 9.64094i −1.16914 0.675001i
205205 0 0
206206 −3.52473 0.944449i −0.245580 0.0658029i
207207 −12.9884 12.9884i −0.902756 0.902756i
208208 −4.25770 0.0252664i −0.295219 0.00175191i
209209 4.54668i 0.314500i
210210 0 0
211211 4.26604 + 7.38900i 0.293686 + 0.508680i 0.974678 0.223611i 0.0717845π-0.0717845\pi
−0.680992 + 0.732291i 0.738451π0.738451\pi
212212 2.60518 0.698056i 0.178925 0.0479427i
213213 36.3773i 2.49253i
214214 0.117649 + 0.439070i 0.00804229 + 0.0300142i
215215 0 0
216216 10.5181 10.5181i 0.715669 0.715669i
217217 0.0443156 + 0.165388i 0.00300834 + 0.0112273i
218218 8.97011 + 2.40353i 0.607532 + 0.162788i
219219 −2.32797 + 8.68810i −0.157310 + 0.587087i
220220 0 0
221221 −6.91576 + 25.2106i −0.465205 + 1.69585i
222222 8.22445 8.22445i 0.551989 0.551989i
223223 −6.11483 + 3.53040i −0.409479 + 0.236413i −0.690566 0.723269i 0.742638π-0.742638\pi
0.281087 + 0.959682i 0.409305π0.409305\pi
224224 4.03432 2.32922i 0.269555 0.155627i
225225 0 0
226226 −1.39889 1.39889i −0.0930527 0.0930527i
227227 −8.58775 + 14.8744i −0.569989 + 0.987249i 0.426578 + 0.904451i 0.359719π0.359719\pi
−0.996566 + 0.0827985i 0.973614π0.973614\pi
228228 −3.63480 + 6.29566i −0.240721 + 0.416940i
229229 8.90647 + 8.90647i 0.588556 + 0.588556i 0.937240 0.348684i 0.113371π-0.113371\pi
−0.348684 + 0.937240i 0.613371π0.613371\pi
230230 0 0
231231 −3.86813 + 2.23327i −0.254504 + 0.146938i
232232 −0.764655 + 0.441474i −0.0502021 + 0.0289842i
233233 −17.5822 + 17.5822i −1.15185 + 1.15185i −0.165666 + 0.986182i 0.552977π0.552977\pi
−0.986182 + 0.165666i 0.947023π0.947023\pi
234234 −15.1684 8.87790i −0.991588 0.580366i
235235 0 0
236236 1.24758 4.65603i 0.0812105 0.303082i
237237 36.5686 + 9.79852i 2.37538 + 0.636482i
238238 1.84910 + 6.90095i 0.119860 + 0.447322i
239239 2.23488 2.23488i 0.144562 0.144562i −0.631122 0.775684i 0.717405π-0.717405\pi
0.775684 + 0.631122i 0.217405π0.217405\pi
240240 0 0
241241 −4.66361 17.4048i −0.300409 1.12114i −0.936825 0.349797i 0.886250π-0.886250\pi
0.636416 0.771346i 0.280416π-0.280416\pi
242242 8.41971i 0.541239i
243243 −15.8248 + 4.24025i −1.01516 + 0.272012i
244244 0.994033 + 1.72172i 0.0636364 + 0.110222i
245245 0 0
246246 19.7406i 1.25862i
247247 9.50483 + 2.60736i 0.604778 + 0.165902i
248248 0.379596 + 0.379596i 0.0241044 + 0.0241044i
249249 23.0659 + 6.18048i 1.46174 + 0.391672i
250250 0 0
251251 12.1009 + 6.98644i 0.763800 + 0.440980i 0.830658 0.556782i 0.187964π-0.187964\pi
−0.0668586 + 0.997762i 0.521298π0.521298\pi
252252 4.38299 0.276102
253253 5.55068 + 3.20468i 0.348968 + 0.201477i
254254 −2.14854 + 0.575700i −0.134812 + 0.0361227i
255255 0 0
256256 8.42962 14.6005i 0.526851 0.912533i
257257 5.99887 22.3881i 0.374199 1.39653i −0.480312 0.877098i 0.659476π-0.659476\pi
0.854511 0.519433i 0.173857π-0.173857\pi
258258 11.3254 + 19.6162i 0.705090 + 1.22125i
259259 3.93255 0.244357
260260 0 0
261261 −1.39314 −0.0862334
262262 0.0318286 + 0.0551288i 0.00196638 + 0.00340587i
263263 −0.336737 + 1.25672i −0.0207641 + 0.0774926i −0.975530 0.219864i 0.929438π-0.929438\pi
0.954766 + 0.297357i 0.0961052π0.0961052\pi
264264 −7.00191 + 12.1277i −0.430938 + 0.746407i
265265 0 0
266266 2.60178 0.697144i 0.159525 0.0427446i
267267 −1.25150 0.722551i −0.0765903 0.0442194i
268268 6.96441 0.425419
269269 6.87429 + 3.96887i 0.419133 + 0.241986i 0.694706 0.719294i 0.255534π-0.255534\pi
−0.275574 + 0.961280i 0.588868π0.588868\pi
270270 0 0
271271 −0.865041 0.231787i −0.0525475 0.0140801i 0.232450 0.972608i 0.425326π-0.425326\pi
−0.284997 + 0.958528i 0.591993π0.591993\pi
272272 6.05429 + 6.05429i 0.367095 + 0.367095i
273273 −2.45041 9.36704i −0.148305 0.566919i
274274 4.51738i 0.272905i
275275 0 0
276276 −5.12391 8.87488i −0.308423 0.534205i
277277 −9.22930 + 2.47298i −0.554535 + 0.148587i −0.525194 0.850982i 0.676007π-0.676007\pi
−0.0293404 + 0.999569i 0.509341π0.509341\pi
278278 14.0596i 0.843236i
279279 0.219227 + 0.818165i 0.0131248 + 0.0489823i
280280 0 0
281281 5.58408 5.58408i 0.333118 0.333118i −0.520651 0.853769i 0.674311π-0.674311\pi
0.853769 + 0.520651i 0.174311π0.174311\pi
282282 5.78719 + 21.5981i 0.344622 + 1.28615i
283283 20.3851 + 5.46218i 1.21177 + 0.324693i 0.807457 0.589927i 0.200843π-0.200843\pi
0.404314 + 0.914620i 0.367510π0.367510\pi
284284 3.22382 12.0315i 0.191298 0.713936i
285285 0 0
286286 5.91420 + 1.62238i 0.349714 + 0.0959335i
287287 4.71953 4.71953i 0.278585 0.278585i
288288 19.9576 11.5225i 1.17601 0.678970i
289289 30.8040 17.7847i 1.81200 1.04616i
290290 0 0
291291 −14.8057 14.8057i −0.867927 0.867927i
292292 −1.53991 + 2.66720i −0.0901164 + 0.156086i
293293 2.01079 3.48280i 0.117472 0.203467i −0.801293 0.598272i 0.795854π-0.795854\pi
0.918765 + 0.394805i 0.129188π0.129188\pi
294294 12.2353 + 12.2353i 0.713579 + 0.713579i
295295 0 0
296296 10.6778 6.16482i 0.620633 0.358323i
297297 −7.09234 + 4.09477i −0.411539 + 0.237602i
298298 −3.13271 + 3.13271i −0.181473 + 0.181473i
299299 −9.88252 + 9.76592i −0.571521 + 0.564778i
300300 0 0
301301 −1.98213 + 7.39742i −0.114248 + 0.426380i
302302 −6.63524 1.77791i −0.381815 0.102307i
303303 −7.03525 26.2559i −0.404165 1.50836i
304304 2.28257 2.28257i 0.130914 0.130914i
305305 0 0
306306 9.14740 + 34.1386i 0.522922 + 1.95157i
307307 24.2191i 1.38226i 0.722732 + 0.691128i 0.242886π0.242886\pi
−0.722732 + 0.691128i 0.757114π0.757114\pi
308308 −1.47727 + 0.395832i −0.0841750 + 0.0225546i
309309 −4.97231 8.61229i −0.282865 0.489936i
310310 0 0
311311 7.87243i 0.446405i −0.974772 0.223202i 0.928349π-0.928349\pi
0.974772 0.223202i 0.0716511π-0.0716511\pi
312312 −21.3376 21.5923i −1.20800 1.22242i
313313 −3.39121 3.39121i −0.191683 0.191683i 0.604740 0.796423i 0.293277π-0.293277\pi
−0.796423 + 0.604740i 0.793277π0.793277\pi
314314 20.1838 + 5.40824i 1.13904 + 0.305204i
315315 0 0
316316 11.2264 + 6.48154i 0.631532 + 0.364615i
317317 −22.9255 −1.28762 −0.643812 0.765184i 0.722648π-0.722648\pi
−0.643812 + 0.765184i 0.722648π0.722648\pi
318318 −6.97580 4.02748i −0.391183 0.225850i
319319 0.469553 0.125816i 0.0262899 0.00704436i
320320 0 0
321321 −0.619393 + 1.07282i −0.0345712 + 0.0598790i
322322 −0.982751 + 3.66768i −0.0547666 + 0.204392i
323323 −9.90979 17.1643i −0.551395 0.955044i
324324 −0.551932 −0.0306629
325325 0 0
326326 −21.8689 −1.21120
327327 12.6541 + 21.9175i 0.699771 + 1.21204i
328328 5.41609 20.2131i 0.299053 1.11608i
329329 −3.78001 + 6.54718i −0.208399 + 0.360958i
330330 0 0
331331 −32.4118 + 8.68470i −1.78151 + 0.477354i −0.990858 0.134910i 0.956925π-0.956925\pi
−0.790653 + 0.612264i 0.790259π0.790259\pi
332332 7.08110 + 4.08828i 0.388626 + 0.224373i
333333 19.4541 1.06608
334334 1.51833 + 0.876609i 0.0830794 + 0.0479659i
335335 0 0
336336 −3.06309 0.820752i −0.167105 0.0447757i
337337 −14.5544 14.5544i −0.792826 0.792826i 0.189126 0.981953i 0.439434π-0.439434\pi
−0.981953 + 0.189126i 0.939434π0.939434\pi
338338 −6.78318 + 11.4333i −0.368957 + 0.621888i
339339 5.39143i 0.292822i
340340 0 0
341341 −0.147779 0.255960i −0.00800267 0.0138610i
342342 12.8708 3.44873i 0.695975 0.186486i
343343 12.5954i 0.680087i
344344 6.21454 + 23.1930i 0.335065 + 1.25048i
345345 0 0
346346 10.9743 10.9743i 0.589983 0.589983i
347347 −5.90442 22.0356i −0.316966 1.18293i −0.922145 0.386844i 0.873565π-0.873565\pi
0.605179 0.796089i 0.293101π-0.293101\pi
348348 −0.750759 0.201165i −0.0402449 0.0107836i
349349 2.68798 10.0317i 0.143884 0.536983i −0.855918 0.517111i 0.827008π-0.827008\pi
0.999803 0.0198718i 0.00632581π-0.00632581\pi
350350 0 0
351351 −4.49290 17.1748i −0.239813 0.916721i
352352 −5.68599 + 5.68599i −0.303064 + 0.303064i
353353 −3.72420 + 2.15017i −0.198219 + 0.114442i −0.595825 0.803115i 0.703175π-0.703175\pi
0.397605 + 0.917556i 0.369841π0.369841\pi
354354 −12.4673 + 7.19799i −0.662629 + 0.382569i
355355 0 0
356356 −0.349887 0.349887i −0.0185440 0.0185440i
357357 −9.73511 + 16.8617i −0.515237 + 0.892416i
358358 1.41082 2.44361i 0.0745640 0.129149i
359359 10.4273 + 10.4273i 0.550333 + 0.550333i 0.926537 0.376204i 0.122771π-0.122771\pi
−0.376204 + 0.926537i 0.622771π0.622771\pi
360360 0 0
361361 9.98326 5.76384i 0.525435 0.303360i
362362 9.17216 5.29555i 0.482078 0.278328i
363363 −16.2251 + 16.2251i −0.851599 + 0.851599i
364364 0.0196734 3.31522i 0.00103117 0.173765i
365365 0 0
366366 1.53673 5.73514i 0.0803259 0.299780i
367367 11.0341 + 2.95657i 0.575973 + 0.154331i 0.535034 0.844830i 0.320299π-0.320299\pi
0.0409383 + 0.999162i 0.486965π0.486965\pi
368368 1.17776 + 4.39546i 0.0613950 + 0.229129i
369369 23.3472 23.3472i 1.21541 1.21541i
370370 0 0
371371 −0.704874 2.63063i −0.0365953 0.136575i
372372 0.472562i 0.0245012i
373373 27.1975 7.28755i 1.40823 0.377335i 0.526939 0.849903i 0.323339π-0.323339\pi
0.881294 + 0.472568i 0.156673π0.156673\pi
374374 −6.16618 10.6801i −0.318846 0.552257i
375375 0 0
376376 23.7028i 1.22238i
377377 −0.00625324 + 1.05375i −0.000322058 + 0.0542709i
378378 −3.43065 3.43065i −0.176453 0.176453i
379379 −16.3551 4.38232i −0.840103 0.225105i −0.186987 0.982362i 0.559872π-0.559872\pi
−0.653116 + 0.757258i 0.726539π0.726539\pi
380380 0 0
381381 −5.24973 3.03093i −0.268952 0.155279i
382382 18.9999 0.972119
383383 5.71918 + 3.30197i 0.292236 + 0.168723i 0.638950 0.769248i 0.279369π-0.279369\pi
−0.346714 + 0.937971i 0.612702π0.612702\pi
384384 5.91729 1.58553i 0.301966 0.0809114i
385385 0 0
386386 6.42793 11.1335i 0.327173 0.566680i
387387 −9.80550 + 36.5946i −0.498441 + 1.86021i
388388 −3.58475 6.20897i −0.181988 0.315212i
389389 −33.6949 −1.70840 −0.854199 0.519946i 0.825952π-0.825952\pi
−0.854199 + 0.519946i 0.825952π0.825952\pi
390390 0 0
391391 27.9393 1.41295
392392 9.17126 + 15.8851i 0.463218 + 0.802318i
393393 −0.0449004 + 0.167570i −0.00226492 + 0.00845281i
394394 7.30464 12.6520i 0.368003 0.637399i
395395 0 0
396396 −7.30795 + 1.95816i −0.367238 + 0.0984012i
397397 −5.04104 2.91045i −0.253002 0.146071i 0.368136 0.929772i 0.379996π-0.379996\pi
−0.621138 + 0.783701i 0.713329π0.713329\pi
398398 15.0689 0.755337
399399 6.35716 + 3.67031i 0.318256 + 0.183745i
400400 0 0
401401 0.255004 + 0.0683280i 0.0127343 + 0.00341214i 0.265181 0.964199i 0.414568π-0.414568\pi
−0.252446 + 0.967611i 0.581235π0.581235\pi
402402 −14.7075 14.7075i −0.733544 0.733544i
403403 0.619831 0.162147i 0.0308760 0.00807713i
404404 9.30738i 0.463060i
405405 0 0
406406 0.143993 + 0.249404i 0.00714627 + 0.0123777i
407407 −6.55691 + 1.75692i −0.325014 + 0.0870872i
408408 61.0446i 3.02216i
409409 9.61872 + 35.8975i 0.475615 + 1.77502i 0.619042 + 0.785358i 0.287521π0.287521\pi
−0.143427 + 0.989661i 0.545812π0.545812\pi
410410 0 0
411411 8.70518 8.70518i 0.429395 0.429395i
412412 −0.881310 3.28909i −0.0434190 0.162042i
413413 −4.70151 1.25977i −0.231346 0.0619890i
414414 −4.86161 + 18.1438i −0.238935 + 0.891718i
415415 0 0
416416 −8.62585 15.1473i −0.422917 0.742657i
417417 27.0934 27.0934i 1.32677 1.32677i
418418 −4.02660 + 2.32476i −0.196947 + 0.113708i
419419 −29.3721 + 16.9580i −1.43492 + 0.828451i −0.997490 0.0708027i 0.977444π-0.977444\pi
−0.437428 + 0.899253i 0.644111π0.644111\pi
420420 0 0
421421 −21.5599 21.5599i −1.05076 1.05076i −0.998641 0.0521230i 0.983401π-0.983401\pi
−0.0521230 0.998641i 0.516599π-0.516599\pi
422422 4.36253 7.55613i 0.212365 0.367826i
423423 −18.6995 + 32.3885i −0.909201 + 1.57478i
424424 −6.03777 6.03777i −0.293220 0.293220i
425425 0 0
426426 −32.2162 + 18.6000i −1.56088 + 0.901175i
427427 1.73853 1.00374i 0.0841335 0.0485745i
428428 −0.299934 + 0.299934i −0.0144979 + 0.0144979i
429429 8.27052 + 14.5233i 0.399305 + 0.701192i
430430 0 0
431431 1.19014 4.44167i 0.0573271 0.213948i −0.931320 0.364201i 0.881342π-0.881342\pi
0.988648 + 0.150253i 0.0480089π0.0480089\pi
432432 −5.61627 1.50488i −0.270213 0.0724033i
433433 1.03596 + 3.86627i 0.0497853 + 0.185801i 0.986341 0.164719i 0.0526716π-0.0526716\pi
−0.936555 + 0.350520i 0.886005π0.886005\pi
434434 0.123811 0.123811i 0.00594311 0.00594311i
435435 0 0
436436 2.24285 + 8.37043i 0.107413 + 0.400871i
437437 10.5336i 0.503890i
438438 8.88461 2.38062i 0.424523 0.113751i
439439 −11.3618 19.6793i −0.542271 0.939242i −0.998773 0.0495192i 0.984231π-0.984231\pi
0.456502 0.889723i 0.349102π-0.349102\pi
440440 0 0
441441 28.9414i 1.37816i
442442 25.8629 6.76571i 1.23017 0.321812i
443443 −1.84874 1.84874i −0.0878361 0.0878361i 0.661824 0.749660i 0.269783π-0.269783\pi
−0.749660 + 0.661824i 0.769783π0.769783\pi
444444 10.4837 + 2.80911i 0.497536 + 0.133314i
445445 0 0
446446 6.25313 + 3.61025i 0.296094 + 0.170950i
447447 −12.0737 −0.571067
448448 −6.09644 3.51978i −0.288030 0.166294i
449449 −31.0770 + 8.32705i −1.46661 + 0.392978i −0.901769 0.432219i 0.857731π-0.857731\pi
−0.564845 + 0.825197i 0.691064π0.691064\pi
450450 0 0
451451 −5.76056 + 9.97759i −0.271254 + 0.469826i
452452 0.477798 1.78317i 0.0224737 0.0838731i
453453 −9.36029 16.2125i −0.439785 0.761729i
454454 17.5640 0.824318
455455 0 0
456456 23.0149 1.07777
457457 −14.1837 24.5669i −0.663486 1.14919i −0.979693 0.200501i 0.935743π-0.935743\pi
0.316208 0.948690i 0.397590π-0.397590\pi
458458 3.33373 12.4416i 0.155775 0.581360i
459459 −17.8496 + 30.9165i −0.833149 + 1.44306i
460460 0 0
461461 −11.1174 + 2.97890i −0.517790 + 0.138741i −0.508244 0.861213i 0.669705π-0.669705\pi
−0.00954570 + 0.999954i 0.503039π0.503039\pi
462462 3.95562 + 2.28378i 0.184032 + 0.106251i
463463 −29.9456 −1.39169 −0.695845 0.718192i 0.744970π-0.744970\pi
−0.695845 + 0.718192i 0.744970π0.744970\pi
464464 0.298893 + 0.172566i 0.0138758 + 0.00801118i
465465 0 0
466466 24.5609 + 6.58109i 1.13776 + 0.304863i
467467 16.1332 + 16.1332i 0.746557 + 0.746557i 0.973831 0.227274i 0.0729812π-0.0729812\pi
−0.227274 + 0.973831i 0.572981π0.572981\pi
468468 0.0973232 16.4002i 0.00449877 0.758100i
469469 7.03244i 0.324728i
470470 0 0
471471 28.4732 + 49.3170i 1.31197 + 2.27241i
472472 −14.7405 + 3.94971i −0.678488 + 0.181800i
473473 13.2196i 0.607837i
474474 −10.0201 37.3957i −0.460240 1.71764i
475475 0 0
476476 −4.71411 + 4.71411i −0.216071 + 0.216071i
477477 −3.48697 13.0136i −0.159657 0.595850i
478478 −3.12195 0.836524i −0.142795 0.0382617i
479479 10.0493 37.5043i 0.459162 1.71362i −0.216393 0.976306i 0.569429π-0.569429\pi
0.675555 0.737309i 0.263904π-0.263904\pi
480480 0 0
481481 0.0873213 14.7148i 0.00398151 0.670935i
482482 −13.0294 + 13.0294i −0.593473 + 0.593473i
483483 −8.96157 + 5.17396i −0.407765 + 0.235424i
484484 −6.80421 + 3.92841i −0.309282 + 0.178564i
485485 0 0
486486 11.8466 + 11.8466i 0.537372 + 0.537372i
487487 14.4718 25.0660i 0.655782 1.13585i −0.325916 0.945399i 0.605673π-0.605673\pi
0.981697 0.190448i 0.0609941π-0.0609941\pi
488488 3.14701 5.45078i 0.142458 0.246745i
489489 −42.1422 42.1422i −1.90574 1.90574i
490490 0 0
491491 6.30003 3.63733i 0.284317 0.164150i −0.351059 0.936353i 0.614178π-0.614178\pi
0.635376 + 0.772203i 0.280845π0.280845\pi
492492 15.9530 9.21046i 0.719216 0.415240i
493493 1.49839 1.49839i 0.0674842 0.0674842i
494494 −2.55079 9.75077i −0.114766 0.438708i
495495 0 0
496496 0.0543104 0.202689i 0.00243861 0.00910102i
497497 −12.1490 3.25531i −0.544956 0.146021i
498498 −6.32027 23.5876i −0.283218 1.05698i
499499 −4.24201 + 4.24201i −0.189899 + 0.189899i −0.795652 0.605754i 0.792872π-0.792872\pi
0.605754 + 0.795652i 0.292872π0.292872\pi
500500 0 0
501501 1.23663 + 4.61515i 0.0552483 + 0.206190i
502502 14.2889i 0.637745i
503503 3.50677 0.939636i 0.156359 0.0418963i −0.179790 0.983705i 0.557542π-0.557542\pi
0.336149 + 0.941809i 0.390875π0.390875\pi
504504 −6.93805 12.0171i −0.309046 0.535283i
505505 0 0
506506 6.55433i 0.291376i
507507 −35.1039 + 8.96091i −1.55902 + 0.397968i
508508 −1.46769 1.46769i −0.0651184 0.0651184i
509509 22.5037 + 6.02986i 0.997460 + 0.267269i 0.720381 0.693578i 0.243967π-0.243967\pi
0.277079 + 0.960847i 0.410634π0.410634\pi
510510 0 0
511511 2.69325 + 1.55495i 0.119143 + 0.0687870i
512512 −12.8442 −0.567640
513513 11.6560 + 6.72962i 0.514627 + 0.297120i
514514 −22.8945 + 6.13455i −1.00983 + 0.270584i
515515 0 0
516516 −10.5683 + 18.3048i −0.465243 + 0.805824i
517517 3.37754 12.6052i 0.148544 0.554375i
518518 −2.01075 3.48272i −0.0883472 0.153022i
519519 42.2960 1.85659
520520 0 0
521521 −13.0530 −0.571862 −0.285931 0.958250i 0.592303π-0.592303\pi
−0.285931 + 0.958250i 0.592303π0.592303\pi
522522 0.712327 + 1.23379i 0.0311777 + 0.0540013i
523523 −4.40520 + 16.4404i −0.192626 + 0.718890i 0.800243 + 0.599677i 0.204704π0.204704\pi
−0.992869 + 0.119214i 0.961963π0.961963\pi
524524 −0.0297008 + 0.0514432i −0.00129748 + 0.00224731i
525525 0 0
526526 1.28514 0.344353i 0.0560349 0.0150145i
527527 −1.11577 0.644187i −0.0486035 0.0280612i
528528 5.47391 0.238221
529529 −7.05896 4.07549i −0.306911 0.177195i
530530 0 0
531531 −23.2581 6.23198i −1.00931 0.270445i
532532 1.77730 + 1.77730i 0.0770558 + 0.0770558i
533533 −17.5547 17.7643i −0.760377 0.769456i
534534 1.47779i 0.0639501i
535535 0 0
536536 −11.0243 19.0947i −0.476178 0.824765i
537537 7.42764 1.99023i 0.320526 0.0858847i
538538 8.11728i 0.349961i
539539 −2.61373 9.75457i −0.112581 0.420159i
540540 0 0
541541 −10.9728 + 10.9728i −0.471756 + 0.471756i −0.902483 0.430727i 0.858257π-0.858257\pi
0.430727 + 0.902483i 0.358257π0.358257\pi
542542 0.237029 + 0.884606i 0.0101813 + 0.0379971i
543543 27.8799 + 7.47039i 1.19644 + 0.320585i
544544 −9.07231 + 33.8583i −0.388972 + 1.45166i
545545 0 0
546546 −7.04266 + 6.95956i −0.301398 + 0.297842i
547547 20.4450 20.4450i 0.874167 0.874167i −0.118756 0.992923i 0.537891π-0.537891\pi
0.992923 + 0.118756i 0.0378908π0.0378908\pi
548548 3.65063 2.10769i 0.155947 0.0900361i
549549 8.60042 4.96545i 0.367057 0.211920i
550550 0 0
551551 −0.564920 0.564920i −0.0240664 0.0240664i
552552 −16.2218 + 28.0970i −0.690446 + 1.19589i
553553 6.54485 11.3360i 0.278315 0.482056i
554554 6.90913 + 6.90913i 0.293541 + 0.293541i
555555 0 0
556556 11.3619 6.55982i 0.481854 0.278198i
557557 −11.7609 + 6.79015i −0.498324 + 0.287708i −0.728021 0.685555i 0.759560π-0.759560\pi
0.229697 + 0.973262i 0.426226π0.426226\pi
558558 0.612485 0.612485i 0.0259286 0.0259286i
559559 27.6356 + 7.58098i 1.16886 + 0.320641i
560560 0 0
561561 8.69858 32.4636i 0.367254 1.37061i
562562 −7.80052 2.09014i −0.329045 0.0881673i
563563 −1.25538 4.68514i −0.0529080 0.197455i 0.934413 0.356191i 0.115925π-0.115925\pi
−0.987321 + 0.158736i 0.949258π0.949258\pi
564564 −14.7539 + 14.7539i −0.621251 + 0.621251i
565565 0 0
566566 −5.58573 20.8462i −0.234786 0.876232i
567567 0.557323i 0.0234054i
568568 −38.0904 + 10.2063i −1.59824 + 0.428247i
569569 −0.124396 0.215461i −0.00521497 0.00903259i 0.863406 0.504509i 0.168327π-0.168327\pi
−0.868621 + 0.495477i 0.834993π0.834993\pi
570570 0 0
571571 7.72842i 0.323424i −0.986838 0.161712i 0.948298π-0.948298\pi
0.986838 0.161712i 0.0517016π-0.0517016\pi
572572 1.44832 + 5.53640i 0.0605572 + 0.231489i
573573 36.6136 + 36.6136i 1.52955 + 1.52955i
574574 −6.59281 1.76654i −0.275179 0.0737339i
575575 0 0
576576 −30.1587 17.4121i −1.25661 0.725506i
577577 12.1339 0.505141 0.252570 0.967578i 0.418724π-0.418724\pi
0.252570 + 0.967578i 0.418724π0.418724\pi
578578 −31.5007 18.1869i −1.31026 0.756477i
579579 33.8416 9.06783i 1.40641 0.376846i
580580 0 0
581581 4.12821 7.15027i 0.171267 0.296643i
582582 −5.54184 + 20.6824i −0.229717 + 0.857315i
583583 2.35054 + 4.07125i 0.0973492 + 0.168614i
584584 9.75040 0.403475
585585 0 0
586586 −4.11255 −0.169888
587587 −18.2647 31.6354i −0.753865 1.30573i −0.945937 0.324351i 0.894854π-0.894854\pi
0.192072 0.981381i 0.438479π-0.438479\pi
588588 −4.17904 + 15.5964i −0.172341 + 0.643185i
589589 −0.242870 + 0.420663i −0.0100073 + 0.0173331i
590590 0 0
591591 38.4573 10.3046i 1.58192 0.423875i
592592 −4.17380 2.40974i −0.171542 0.0990398i
593593 16.6936 0.685525 0.342762 0.939422i 0.388637π-0.388637\pi
0.342762 + 0.939422i 0.388637π0.388637\pi
594594 7.25276 + 4.18738i 0.297584 + 0.171810i
595595 0 0
596596 −3.99327 1.06999i −0.163571 0.0438287i
597597 29.0384 + 29.0384i 1.18846 + 1.18846i
598598 13.7018 + 3.75868i 0.560310 + 0.153704i
599599 13.2549i 0.541579i 0.962639 + 0.270789i 0.0872847π0.0872847\pi
−0.962639 + 0.270789i 0.912715π0.912715\pi
600600 0 0
601601 −0.546605 0.946748i −0.0222965 0.0386187i 0.854662 0.519185i 0.173764π-0.173764\pi
−0.876958 + 0.480566i 0.840431π0.840431\pi
602602 7.56474 2.02696i 0.308316 0.0826129i
603603 34.7891i 1.41672i
604604 −1.65905 6.19166i −0.0675058 0.251935i
605605 0 0
606606 −19.6554 + 19.6554i −0.798446 + 0.798446i
607607 10.8348 + 40.4361i 0.439771 + 1.64125i 0.729384 + 0.684105i 0.239807π0.239807\pi
−0.289612 + 0.957144i 0.593526π0.593526\pi
608608 12.7652 + 3.42042i 0.517696 + 0.138716i
609609 −0.203130 + 0.758093i −0.00823126 + 0.0307195i
610610 0 0
611611 24.4142 + 14.2894i 0.987693 + 0.578087i
612612 −23.3204 + 23.3204i −0.942673 + 0.942673i
613613 −24.1705 + 13.9548i −0.976235 + 0.563630i −0.901131 0.433546i 0.857262π-0.857262\pi
−0.0751039 + 0.997176i 0.523929π0.523929\pi
614614 21.4487 12.3834i 0.865601 0.499755i
615615 0 0
616616 3.42371 + 3.42371i 0.137945 + 0.137945i
617617 2.19132 3.79548i 0.0882193 0.152800i −0.818539 0.574451i 0.805216π-0.805216\pi
0.906758 + 0.421650i 0.138549π0.138549\pi
618618 −5.08477 + 8.80708i −0.204540 + 0.354273i
619619 −8.67268 8.67268i −0.348584 0.348584i 0.510998 0.859582i 0.329276π-0.329276\pi
−0.859582 + 0.510998i 0.829276π0.829276\pi
620620 0 0
621621 −16.4313 + 9.48662i −0.659366 + 0.380685i
622622 −6.97193 + 4.02525i −0.279549 + 0.161398i
623623 −0.353304 + 0.353304i −0.0141548 + 0.0141548i
624624 −3.13910 + 11.4432i −0.125664 + 0.458095i
625625 0 0
626626 −1.26934 + 4.73726i −0.0507332 + 0.189339i
627627 −12.2393 3.27952i −0.488791 0.130971i
628628 5.04668 + 18.8345i 0.201385 + 0.751577i
629629 −20.9238 + 20.9238i −0.834287 + 0.834287i
630630 0 0
631631 −6.55800 24.4748i −0.261070 0.974326i −0.964612 0.263673i 0.915066π-0.915066\pi
0.703542 0.710653i 0.251601π-0.251601\pi
632632 41.0398i 1.63248i
633633 22.9677 6.15419i 0.912886 0.244607i
634634 11.7220 + 20.3031i 0.465540 + 0.806340i
635635 0 0
636636 7.51646i 0.298047i
637637 21.8908 + 0.129906i 0.867345 + 0.00514706i
638638 −0.351511 0.351511i −0.0139164 0.0139164i
639639 −60.1003 16.1038i −2.37753 0.637057i
640640 0 0
641641 −1.41675 0.817961i −0.0559582 0.0323075i 0.471760 0.881727i 0.343619π-0.343619\pi
−0.527718 + 0.849420i 0.676952π0.676952\pi
642642 1.26681 0.0499968
643643 −34.3541 19.8344i −1.35479 0.782191i −0.365878 0.930663i 0.619231π-0.619231\pi
−0.988917 + 0.148472i 0.952565π0.952565\pi
644644 −3.42248 + 0.917051i −0.134865 + 0.0361369i
645645 0 0
646646 −10.1339 + 17.5525i −0.398714 + 0.690593i
647647 3.84742 14.3588i 0.151258 0.564501i −0.848139 0.529773i 0.822277π-0.822277\pi
0.999397 0.0347277i 0.0110564π-0.0110564\pi
648648 0.873682 + 1.51326i 0.0343215 + 0.0594465i
649649 8.40185 0.329801
650650 0 0
651651 0.477178 0.0187021
652652 −10.2034 17.6729i −0.399597 0.692123i
653653 −3.32718 + 12.4172i −0.130203 + 0.485922i −0.999972 0.00753655i 0.997601π-0.997601\pi
0.869769 + 0.493459i 0.164268π0.164268\pi
654654 12.9403 22.4132i 0.506005 0.876426i
655655 0 0
656656 −7.90103 + 2.11708i −0.308483 + 0.0826579i
657657 13.3234 + 7.69225i 0.519794 + 0.300103i
658658 7.73102 0.301387
659659 −20.8742 12.0517i −0.813144 0.469469i 0.0349025 0.999391i 0.488888π-0.488888\pi
−0.848047 + 0.529922i 0.822221π0.822221\pi
660660 0 0
661661 37.8150 + 10.1325i 1.47083 + 0.394108i 0.903217 0.429185i 0.141199π-0.141199\pi
0.567616 + 0.823293i 0.307866π0.307866\pi
662662 24.2637 + 24.2637i 0.943036 + 0.943036i
663663 62.8768 + 36.8011i 2.44193 + 1.42924i
664664 25.8862i 1.00458i
665665 0 0
666666 −9.94705 17.2288i −0.385440 0.667602i
667667 1.08784 0.291487i 0.0421215 0.0112864i
668668 1.63601i 0.0632991i
669669 5.09295 + 19.0071i 0.196905 + 0.734858i
670670 0 0
671671 −2.45030 + 2.45030i −0.0945926 + 0.0945926i
672672 −3.36013 12.5402i −0.129620 0.483747i
673673 9.87723 + 2.64660i 0.380739 + 0.102019i 0.444112 0.895971i 0.353519π-0.353519\pi
−0.0633730 + 0.997990i 0.520186π0.520186\pi
674674 −5.44776 + 20.3313i −0.209840 + 0.783132i
675675 0 0
676676 −12.4044 0.147227i −0.477093 0.00566259i
677677 −29.8933 + 29.8933i −1.14889 + 1.14889i −0.162121 + 0.986771i 0.551833π0.551833\pi
−0.986771 + 0.162121i 0.948167π0.948167\pi
678678 −4.77472 + 2.75669i −0.183372 + 0.105870i
679679 −6.26961 + 3.61976i −0.240606 + 0.138914i
680680 0 0
681681 33.8465 + 33.8465i 1.29700 + 1.29700i
682682 −0.151121 + 0.261750i −0.00578673 + 0.0100229i
683683 10.0103 17.3384i 0.383035 0.663436i −0.608459 0.793585i 0.708212π-0.708212\pi
0.991494 + 0.130149i 0.0415455π0.0415455\pi
684684 8.79221 + 8.79221i 0.336178 + 0.336178i
685685 0 0
686686 11.1546 6.44013i 0.425886 0.245885i
687687 30.3998 17.5513i 1.15983 0.669625i
688688 6.63664 6.63664i 0.253019 0.253019i
689689 −9.85890 + 2.57908i −0.375594 + 0.0982550i
690690 0 0
691691 −9.15886 + 34.1813i −0.348420 + 1.30032i 0.540147 + 0.841571i 0.318369π0.318369\pi
−0.888566 + 0.458749i 0.848298π0.848298\pi
692692 13.9890 + 3.74834i 0.531782 + 0.142491i
693693 1.97729 + 7.37933i 0.0751109 + 0.280318i
694694 −16.4960 + 16.4960i −0.626181 + 0.626181i
695695 0 0
696696 0.636870 + 2.37683i 0.0241405 + 0.0900935i
697697 50.2221i 1.90230i
698698 −10.2586 + 2.74877i −0.388292 + 0.104043i
699699 34.6479 + 60.0120i 1.31051 + 2.26986i
700700 0 0
701701 37.1781i 1.40420i 0.712080 + 0.702098i 0.247753π0.247753\pi
−0.712080 + 0.702098i 0.752247π0.752247\pi
702702 −12.9129 + 12.7606i −0.487367 + 0.481617i
703703 7.88864 + 7.88864i 0.297526 + 0.297526i
704704 11.7374 + 3.14502i 0.442368 + 0.118532i
705705 0 0
706706 3.80843 + 2.19880i 0.143332 + 0.0827529i
707707 −9.39830 −0.353459
708708 −11.6338 6.71678i −0.437225 0.252432i
709709 46.5506 12.4732i 1.74824 0.468440i 0.763994 0.645224i 0.223236π-0.223236\pi
0.984250 + 0.176783i 0.0565692π0.0565692\pi
710710 0 0
711711 32.3770 56.0786i 1.21423 2.10311i
712712 −0.405449 + 1.51316i −0.0151948 + 0.0567079i
713713 −0.342369 0.593001i −0.0128218 0.0222080i
714714 19.9106 0.745135
715715 0 0
716716 2.63300 0.0983998
717717 −4.40411 7.62814i −0.164474 0.284878i
718718 3.90299 14.5662i 0.145658 0.543604i
719719 16.6992 28.9239i 0.622777 1.07868i −0.366190 0.930540i 0.619338π-0.619338\pi
0.988966 0.148141i 0.0473288π-0.0473288\pi
720720 0 0
721721 −3.32122 + 0.889918i −0.123689 + 0.0331423i
722722 −10.2091 5.89421i −0.379942 0.219360i
723723 −50.2164 −1.86757
724724 8.55897 + 4.94153i 0.318092 + 0.183650i
725725 0 0
726726 22.6652 + 6.07313i 0.841186 + 0.225395i
727727 23.6487 + 23.6487i 0.877083 + 0.877083i 0.993232 0.116149i 0.0370549π-0.0370549\pi
−0.116149 + 0.993232i 0.537055π0.537055\pi
728728 −9.12066 + 5.19389i −0.338034 + 0.192499i
729729 43.9226i 1.62676i
730730 0 0
731731 −28.8130 49.9055i −1.06569 1.84582i
732732 5.35173 1.43399i 0.197806 0.0530018i
733733 14.7049i 0.543138i 0.962419 + 0.271569i 0.0875424π0.0875424\pi
−0.962419 + 0.271569i 0.912458π0.912458\pi
734734 −3.02344 11.2836i −0.111597 0.416486i
735735 0 0
736736 −13.1731 + 13.1731i −0.485568 + 0.485568i
737737 3.14184 + 11.7255i 0.115731 + 0.431914i
738738 −32.6142 8.73896i −1.20055 0.321686i
739739 5.32432 19.8706i 0.195858 0.730953i −0.796185 0.605054i 0.793152π-0.793152\pi
0.992043 0.125900i 0.0401817π-0.0401817\pi
740740 0 0
741741 13.8747 23.7056i 0.509698 0.870848i
742742 −1.96931 + 1.96931i −0.0722956 + 0.0722956i
743743 38.6601 22.3204i 1.41830 0.818856i 0.422151 0.906526i 0.361275π-0.361275\pi
0.996150 + 0.0876692i 0.0279419π0.0279419\pi
744744 1.29565 0.748042i 0.0475007 0.0274246i
745745 0 0
746746 −20.3603 20.3603i −0.745443 0.745443i
747747 20.4220 35.3720i 0.747202 1.29419i
748748 5.75395 9.96614i 0.210385 0.364398i
749749 0.302864 + 0.302864i 0.0110664 + 0.0110664i
750750 0 0
751751 15.2247 8.78996i 0.555555 0.320750i −0.195804 0.980643i 0.562732π-0.562732\pi
0.751360 + 0.659893i 0.229398π0.229398\pi
752752 8.02381 4.63255i 0.292598 0.168932i
753753 27.5353 27.5353i 1.00344 1.00344i
754754 0.936413 0.533254i 0.0341022 0.0194200i
755755 0 0
756756 1.17176 4.37306i 0.0426164 0.159047i
757757 −33.9933 9.10848i −1.23551 0.331053i −0.418786 0.908085i 0.637544π-0.637544\pi
−0.816722 + 0.577032i 0.804211π0.804211\pi
758758 4.48144 + 16.7250i 0.162773 + 0.607478i
759759 12.6305 12.6305i 0.458457 0.458457i
760760 0 0
761761 −3.03122 11.3127i −0.109882 0.410084i 0.888972 0.457962i 0.151421π-0.151421\pi
−0.998853 + 0.0478787i 0.984754π0.984754\pi
762762 6.19897i 0.224565i
763763 8.45219 2.26476i 0.305990 0.0819897i
764764 8.86485 + 15.3544i 0.320719 + 0.555502i
765765 0 0
766766 6.75331i 0.244007i
767767 −4.81817 + 17.5641i −0.173974 + 0.634202i
768768 −33.2233 33.2233i −1.19884 1.19884i
769769 −18.3227 4.90954i −0.660732 0.177043i −0.0871555 0.996195i 0.527778π-0.527778\pi
−0.573576 + 0.819152i 0.694444π0.694444\pi
770770 0 0
771771 −55.9401 32.2971i −2.01463 1.16315i
772772 11.9964 0.431760
773773 14.2114 + 8.20497i 0.511149 + 0.295112i 0.733306 0.679899i 0.237976π-0.237976\pi
−0.222157 + 0.975011i 0.571310π0.571310\pi
774774 37.4223 10.0273i 1.34512 0.360423i
775775 0 0
776776 −11.3490 + 19.6570i −0.407404 + 0.705644i
777777 2.83655 10.5861i 0.101761 0.379775i
778778 17.2285 + 29.8406i 0.617671 + 1.06984i
779779 18.9346 0.678403
780780 0 0
781781 21.7109 0.776876
782782 −14.2856 24.7434i −0.510852 0.884822i
783783 −0.372446 + 1.38999i −0.0133101 + 0.0496741i
784784 3.58492 6.20926i 0.128033 0.221759i
785785 0 0
786786 0.171361 0.0459159i 0.00611223 0.00163777i
787787 11.7781 + 6.80008i 0.419844 + 0.242397i 0.695010 0.719000i 0.255400π-0.255400\pi
−0.275167 + 0.961396i 0.588733π0.588733\pi
788788 13.6326 0.485642
789789 3.14011 + 1.81294i 0.111791 + 0.0645424i
790790 0 0
791791 −1.80058 0.482465i −0.0640214 0.0171545i
792792 16.9369 + 16.9369i 0.601827 + 0.601827i
793793 −3.71719 6.52751i −0.132001 0.231799i
794794 5.95255i 0.211248i
795795 0 0
796796 7.03076 + 12.1776i 0.249199 + 0.431625i
797797 28.9148 7.74769i 1.02421 0.274437i 0.292657 0.956218i 0.405461π-0.405461\pi
0.731557 + 0.681780i 0.238794π0.238794\pi
798798 7.50664i 0.265732i
799799 −14.7232 54.9476i −0.520868 1.94391i
800800 0 0
801801 −1.74778 + 1.74778i −0.0617546 + 0.0617546i
802802 −0.0698734 0.260771i −0.00246732 0.00920815i
803803 −5.18527 1.38939i −0.182984 0.0490305i
804804 5.02343 18.7477i 0.177163 0.661180i
805805 0 0
806806 −0.460525 0.466023i −0.0162213 0.0164150i
807807 15.6423 15.6423i 0.550636 0.550636i
808808 −25.5185 + 14.7331i −0.897739 + 0.518310i
809809 2.54661 1.47029i 0.0895342 0.0516926i −0.454564 0.890714i 0.650205π-0.650205\pi
0.544099 + 0.839021i 0.316872π0.316872\pi
810810 0 0
811811 16.3366 + 16.3366i 0.573657 + 0.573657i 0.933148 0.359492i 0.117050π-0.117050\pi
−0.359492 + 0.933148i 0.617050π0.617050\pi
812812 −0.134367 + 0.232730i −0.00471536 + 0.00816724i
813813 −1.24791 + 2.16144i −0.0437660 + 0.0758050i
814814 4.90856 + 4.90856i 0.172045 + 0.172045i
815815 0 0
816816 20.6647 11.9307i 0.723408 0.417660i
817817 −18.8153 + 10.8630i −0.658262 + 0.380048i
818818 26.8732 26.8732i 0.939599 0.939599i
819819 −16.5604 0.0982738i −0.578667 0.00343397i
820820 0 0
821821 11.8735 44.3125i 0.414388 1.54652i −0.371672 0.928364i 0.621215π-0.621215\pi
0.786059 0.618151i 0.212118π-0.212118\pi
822822 −12.1605 3.25838i −0.424145 0.113649i
823823 4.58752 + 17.1209i 0.159911 + 0.596796i 0.998635 + 0.0522385i 0.0166356π0.0166356\pi
−0.838724 + 0.544557i 0.816698π0.816698\pi
824824 −7.62280 + 7.62280i −0.265553 + 0.265553i
825825 0 0
826826 1.28826 + 4.80785i 0.0448242 + 0.167286i
827827 5.79276i 0.201434i 0.994915 + 0.100717i 0.0321137π0.0321137\pi
−0.994915 + 0.100717i 0.967886π0.967886\pi
828828 −16.9308 + 4.53660i −0.588387 + 0.157658i
829829 −16.8799 29.2368i −0.586262 1.01544i −0.994717 0.102657i 0.967265π-0.967265\pi
0.408454 0.912779i 0.366068π-0.366068\pi
830830 0 0
831831 26.6284i 0.923727i
832832 −13.3056 + 22.7334i −0.461290 + 0.788139i
833833 −31.1279 31.1279i −1.07852 1.07852i
834834 −37.8473 10.1412i −1.31055 0.351160i
835835 0 0
836836 −3.75741 2.16934i −0.129953 0.0750282i
837837 0.874920 0.0302417
838838 30.0364 + 17.3415i 1.03759 + 0.599053i
839839 −37.8626 + 10.1452i −1.30716 + 0.350253i −0.844154 0.536101i 0.819897π-0.819897\pi
−0.463008 + 0.886354i 0.653230π0.653230\pi
840840 0 0
841841 −14.4573 + 25.0408i −0.498527 + 0.863475i
842842 −8.06995 + 30.1175i −0.278109 + 1.03792i
843843 −11.0041 19.0597i −0.379002 0.656451i
844844 8.14177 0.280251
845845 0 0
846846 38.2449 1.31489
847847 3.96679 + 6.87068i 0.136300 + 0.236079i
848848 −0.863850 + 3.22393i −0.0296647 + 0.110710i
849849 29.4076 50.9354i 1.00927 1.74810i
850850 0 0
851851 −15.1908 + 4.07037i −0.520735 + 0.139531i
852852 −30.0625 17.3566i −1.02992 0.594626i
853853 −40.6417 −1.39154 −0.695772 0.718262i 0.744938π-0.744938\pi
−0.695772 + 0.718262i 0.744938π0.744938\pi
854854 −1.77785 1.02644i −0.0608369 0.0351242i
855855 0 0
856856 1.29713 + 0.347564i 0.0443348 + 0.0118795i
857857 −27.2327 27.2327i −0.930252 0.930252i 0.0674695 0.997721i 0.478507π-0.478507\pi
−0.997721 + 0.0674695i 0.978507π0.978507\pi
858858 8.63325 14.7504i 0.294734 0.503570i
859859 44.5502i 1.52003i 0.649904 + 0.760016i 0.274809π0.274809\pi
−0.649904 + 0.760016i 0.725191π0.725191\pi
860860 0 0
861861 −9.30043 16.1088i −0.316958 0.548987i
862862 −4.54213 + 1.21706i −0.154706 + 0.0414532i
863863 55.4497i 1.88753i −0.330615 0.943766i 0.607256π-0.607256\pi
0.330615 0.943766i 0.392744π-0.392744\pi
864864 −6.16090 22.9928i −0.209598 0.782230i
865865 0 0
866866 2.89432 2.89432i 0.0983531 0.0983531i
867867 −25.6562 95.7502i −0.871330 3.25185i
868868 0.157822 + 0.0422883i 0.00535683 + 0.00143536i
869869 −5.84800 + 21.8250i −0.198380 + 0.740363i
870870 0 0
871871 −26.3139 0.156154i −0.891612 0.00529107i
872872 19.3993 19.3993i 0.656944 0.656944i
873873 −31.0154 + 17.9068i −1.04971 + 0.606052i
874874 −9.32869 + 5.38592i −0.315548 + 0.182181i
875875 0 0
876876 6.06917 + 6.06917i 0.205058 + 0.205058i
877877 2.68849 4.65661i 0.0907839 0.157242i −0.817057 0.576557i 0.804396π-0.804396\pi
0.907841 + 0.419314i 0.137729π0.137729\pi
878878 −11.6188 + 20.1244i −0.392116 + 0.679166i
879879 −7.92505 7.92505i −0.267305 0.267305i
880880 0 0
881881 −37.0890 + 21.4133i −1.24956 + 0.721434i −0.971022 0.238992i 0.923183π-0.923183\pi
−0.278538 + 0.960425i 0.589850π0.589850\pi
882882 25.6309 14.7980i 0.863037 0.498274i
883883 32.9568 32.9568i 1.10908 1.10908i 0.115813 0.993271i 0.463053π-0.463053\pi
0.993271 0.115813i 0.0369473π-0.0369473\pi
884884 17.5345 + 17.7439i 0.589750 + 0.596791i
885885 0 0
886886 −0.691990 + 2.58254i −0.0232478 + 0.0867622i
887887 −20.4194 5.47136i −0.685616 0.183710i −0.100837 0.994903i 0.532152π-0.532152\pi
−0.584779 + 0.811193i 0.698819π0.698819\pi
888888 −8.89336 33.1905i −0.298442 1.11380i
889889 −1.48203 + 1.48203i −0.0497057 + 0.0497057i
890890 0 0
891891 −0.248992 0.929249i −0.00834153 0.0311310i
892892 6.73778i 0.225598i
893893 −20.7162 + 5.55089i −0.693241 + 0.185753i
894894 6.17340 + 10.6926i 0.206469 + 0.357616i
895895 0 0
896896 2.11809i 0.0707605i
897897 19.1609 + 33.6472i 0.639763 + 1.12345i
898898 23.2645 + 23.2645i 0.776346 + 0.776346i
899899 −0.0501642 0.0134414i −0.00167307 0.000448297i
900900 0 0
901901 17.7471 + 10.2463i 0.591242 + 0.341354i
902902 11.7817 0.392288
903903 18.4836 + 10.6715i 0.615096 + 0.355126i
904904 −5.64533 + 1.51266i −0.187761 + 0.0503104i
905905 0 0
906906 −9.57200 + 16.5792i −0.318008 + 0.550807i
907907 −2.86355 + 10.6869i −0.0950825 + 0.354853i −0.997032 0.0769889i 0.975469π-0.975469\pi
0.901949 + 0.431842i 0.142136π0.142136\pi
908908 8.19488 + 14.1940i 0.271957 + 0.471043i
909909 −46.4928 −1.54207
910910 0 0
911911 −15.0479 −0.498560 −0.249280 0.968431i 0.580194π-0.580194\pi
−0.249280 + 0.968431i 0.580194π0.580194\pi
912912 −4.49810 7.79093i −0.148947 0.257983i
913913 −3.68867 + 13.7663i −0.122077 + 0.455598i
914914 −14.5045 + 25.1226i −0.479767 + 0.830980i
915915 0 0
916916 11.6099 3.11086i 0.383602 0.102786i
917917 0.0519457 + 0.0299909i 0.00171540 + 0.000990386i
918918 36.5067 1.20490
919919 10.8342 + 6.25513i 0.357388 + 0.206338i 0.667934 0.744220i 0.267179π-0.267179\pi
−0.310547 + 0.950558i 0.600512π0.600512\pi
920920 0 0
921921 65.1960 + 17.4692i 2.14828 + 0.575630i
922922 8.32259 + 8.32259i 0.274090 + 0.274090i
923923 −12.4504 + 45.3866i −0.409811 + 1.49392i
924924 4.26220i 0.140216i
925925 0 0
926926 15.3114 + 26.5202i 0.503165 + 0.871508i
927927 −16.4299 + 4.40237i −0.539628 + 0.144593i
928928 1.41296i 0.0463826i
929929 12.6170 + 47.0874i 0.413952 + 1.54489i 0.786926 + 0.617047i 0.211671π0.211671\pi
−0.372975 + 0.927841i 0.621662π0.621662\pi
930930 0 0
931931 −11.7357 + 11.7357i −0.384623 + 0.384623i
932932 6.14112 + 22.9190i 0.201159 + 0.750736i
933933 −21.1920 5.67838i −0.693795 0.185902i
934934 6.03874 22.5369i 0.197594 0.737429i
935935 0 0
936936 −45.1193 + 25.6939i −1.47477 + 0.839831i
937937 −7.38027 + 7.38027i −0.241103 + 0.241103i −0.817306 0.576203i 0.804534π-0.804534\pi
0.576203 + 0.817306i 0.304534π0.304534\pi
938938 −6.22802 + 3.59575i −0.203352 + 0.117405i
939939 −11.5750 + 6.68281i −0.377735 + 0.218085i
940940 0 0
941941 −1.54410 1.54410i −0.0503363 0.0503363i 0.681491 0.731827i 0.261332π-0.261332\pi
−0.731827 + 0.681491i 0.761332π0.761332\pi
942942 29.1172 50.4324i 0.948688 1.64318i
943943 −13.3459 + 23.1158i −0.434602 + 0.752753i
944944 4.21798 + 4.21798i 0.137284 + 0.137284i
945945 0 0
946946 −11.7074 + 6.75929i −0.380642 + 0.219764i
947947 −5.81670 + 3.35827i −0.189017 + 0.109129i −0.591522 0.806289i 0.701473π-0.701473\pi
0.402505 + 0.915418i 0.368140π0.368140\pi
948948 25.5454 25.5454i 0.829676 0.829676i
949949 5.87810 10.0431i 0.190811 0.326011i
950950 0 0
951951 −16.5361 + 61.7137i −0.536221 + 2.00121i
952952 20.3871 + 5.46272i 0.660751 + 0.177048i
953953 4.67309 + 17.4402i 0.151376 + 0.564944i 0.999388 + 0.0349673i 0.0111327π0.0111327\pi
−0.848012 + 0.529977i 0.822201π0.822201\pi
954954 −9.74205 + 9.74205i −0.315411 + 0.315411i
955955 0 0
956956 −0.780600 2.91324i −0.0252464 0.0942208i
957957 1.35475i 0.0437929i
958958 −38.3526 + 10.2765i −1.23912 + 0.332020i
959959 −2.12828 3.68629i −0.0687257 0.119036i
960960 0 0
961961 30.9684i 0.998981i
962962 −13.0762 + 7.44646i −0.421595 + 0.240083i
963963 1.49825 + 1.49825i 0.0482804 + 0.0482804i
964964 −16.6086 4.45026i −0.534927 0.143333i
965965 0 0
966966 9.16426 + 5.29099i 0.294855 + 0.170235i
967967 −60.0570 −1.93130 −0.965651 0.259841i 0.916330π-0.916330\pi
−0.965651 + 0.259841i 0.916330π0.916330\pi
968968 21.5415 + 12.4370i 0.692369 + 0.399740i
969969 −53.3528 + 14.2958i −1.71394 + 0.459249i
970970 0 0
971971 20.4589 35.4359i 0.656558 1.13719i −0.324942 0.945734i 0.605345π-0.605345\pi
0.981501 0.191459i 0.0613218π-0.0613218\pi
972972 −4.04627 + 15.1009i −0.129784 + 0.484361i
973973 −6.62390 11.4729i −0.212352 0.367805i
974974 −29.5983 −0.948391
975975 0 0
976976 −2.46025 −0.0787506
977977 18.7479 + 32.4724i 0.599800 + 1.03888i 0.992850 + 0.119367i 0.0380865π0.0380865\pi
−0.393050 + 0.919517i 0.628580π0.628580\pi
978978 −15.7740 + 58.8694i −0.504397 + 1.88244i
979979 0.431236 0.746923i 0.0137824 0.0238718i
980980 0 0
981981 41.8125 11.2036i 1.33497 0.357704i
982982 −6.44253 3.71959i −0.205589 0.118697i
983983 46.1176 1.47092 0.735461 0.677567i 0.236966π-0.236966\pi
0.735461 + 0.677567i 0.236966π0.236966\pi
984984 −50.5056 29.1594i −1.61006 0.929569i
985985 0 0
986986 −2.09314 0.560854i −0.0666591 0.0178612i
987987 14.8980 + 14.8980i 0.474208 + 0.474208i
988988 6.68975 6.61082i 0.212829 0.210318i
989989 30.6267i 0.973873i
990990 0 0
991991 −0.401099 0.694724i −0.0127413 0.0220686i 0.859584 0.510994i 0.170722π-0.170722\pi
−0.872326 + 0.488925i 0.837389π0.837389\pi
992992 0.829802 0.222345i 0.0263462 0.00705945i
993993 93.5143i 2.96759i
994994 3.32894 + 12.4238i 0.105587 + 0.394058i
995995 0 0
996996 16.1129 16.1129i 0.510558 0.510558i
997997 −4.04012 15.0779i −0.127952 0.477522i 0.871976 0.489549i 0.162838π-0.162838\pi
−0.999928 + 0.0120264i 0.996172π0.996172\pi
998998 5.92576 + 1.58780i 0.187577 + 0.0502610i
999999 5.20090 19.4100i 0.164549 0.614106i
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 325.2.s.b.193.2 20
5.2 odd 4 325.2.x.b.232.4 20
5.3 odd 4 65.2.t.a.37.2 yes 20
5.4 even 2 65.2.o.a.63.4 yes 20
13.6 odd 12 325.2.x.b.318.4 20
15.8 even 4 585.2.dp.a.37.4 20
15.14 odd 2 585.2.cf.a.388.2 20
65.3 odd 12 845.2.f.e.437.3 20
65.4 even 6 845.2.o.f.488.2 20
65.8 even 4 845.2.o.f.587.2 20
65.9 even 6 845.2.o.e.488.4 20
65.18 even 4 845.2.o.e.587.4 20
65.19 odd 12 65.2.t.a.58.2 yes 20
65.23 odd 12 845.2.f.d.437.8 20
65.24 odd 12 845.2.f.d.408.3 20
65.28 even 12 845.2.k.e.577.3 20
65.29 even 6 845.2.k.e.268.3 20
65.32 even 12 inner 325.2.s.b.32.2 20
65.33 even 12 845.2.o.g.357.2 20
65.34 odd 4 845.2.t.e.418.2 20
65.38 odd 4 845.2.t.g.427.4 20
65.43 odd 12 845.2.t.e.657.2 20
65.44 odd 4 845.2.t.f.418.4 20
65.48 odd 12 845.2.t.f.657.4 20
65.49 even 6 845.2.k.d.268.8 20
65.54 odd 12 845.2.f.e.408.8 20
65.58 even 12 65.2.o.a.32.4 20
65.59 odd 12 845.2.t.g.188.4 20
65.63 even 12 845.2.k.d.577.8 20
65.64 even 2 845.2.o.g.258.2 20
195.149 even 12 585.2.dp.a.253.4 20
195.188 odd 12 585.2.cf.a.487.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.32.4 20 65.58 even 12
65.2.o.a.63.4 yes 20 5.4 even 2
65.2.t.a.37.2 yes 20 5.3 odd 4
65.2.t.a.58.2 yes 20 65.19 odd 12
325.2.s.b.32.2 20 65.32 even 12 inner
325.2.s.b.193.2 20 1.1 even 1 trivial
325.2.x.b.232.4 20 5.2 odd 4
325.2.x.b.318.4 20 13.6 odd 12
585.2.cf.a.388.2 20 15.14 odd 2
585.2.cf.a.487.2 20 195.188 odd 12
585.2.dp.a.37.4 20 15.8 even 4
585.2.dp.a.253.4 20 195.149 even 12
845.2.f.d.408.3 20 65.24 odd 12
845.2.f.d.437.8 20 65.23 odd 12
845.2.f.e.408.8 20 65.54 odd 12
845.2.f.e.437.3 20 65.3 odd 12
845.2.k.d.268.8 20 65.49 even 6
845.2.k.d.577.8 20 65.63 even 12
845.2.k.e.268.3 20 65.29 even 6
845.2.k.e.577.3 20 65.28 even 12
845.2.o.e.488.4 20 65.9 even 6
845.2.o.e.587.4 20 65.18 even 4
845.2.o.f.488.2 20 65.4 even 6
845.2.o.f.587.2 20 65.8 even 4
845.2.o.g.258.2 20 65.64 even 2
845.2.o.g.357.2 20 65.33 even 12
845.2.t.e.418.2 20 65.34 odd 4
845.2.t.e.657.2 20 65.43 odd 12
845.2.t.f.418.4 20 65.44 odd 4
845.2.t.f.657.4 20 65.48 odd 12
845.2.t.g.188.4 20 65.59 odd 12
845.2.t.g.427.4 20 65.38 odd 4