Properties

Label 63.2.h.a.25.1
Level 6363
Weight 22
Character 63.25
Analytic conductor 0.5030.503
Analytic rank 00
Dimension 22
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,2,Mod(25,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 63=327 63 = 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 63.h (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.5030575327340.503057532734
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 25.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 63.25
Dual form 63.2.h.a.58.1

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+1.00000q2+1.73205iq31.00000q4+(0.5000000.866025i)q5+1.73205iq6+(2.000001.73205i)q73.00000q83.00000q9+(0.5000000.866025i)q10+(2.500004.33013i)q111.73205iq12+(2.50000+4.33013i)q13+(2.000001.73205i)q14+(1.50000+0.866025i)q151.00000q16+(1.50000+2.59808i)q173.00000q18+(0.5000000.866025i)q19+(0.500000+0.866025i)q20+(3.00000+3.46410i)q21+(2.500004.33013i)q22+(1.50000+2.59808i)q235.19615iq24+(2.00000+3.46410i)q25+(2.50000+4.33013i)q265.19615iq27+(2.00000+1.73205i)q28+(0.5000000.866025i)q29+(1.50000+0.866025i)q30+5.00000q32+(7.500004.33013i)q33+(1.50000+2.59808i)q34+(0.5000002.59808i)q35+3.00000q36+(1.500002.59808i)q37+(0.5000000.866025i)q38+(7.50000+4.33013i)q39+(1.50000+2.59808i)q40+(2.50000+4.33013i)q41+(3.00000+3.46410i)q42+(0.5000000.866025i)q43+(2.50000+4.33013i)q44+(1.50000+2.59808i)q45+(1.50000+2.59808i)q461.73205iq48+(1.000006.92820i)q49+(2.00000+3.46410i)q50+(4.500002.59808i)q51+(2.500004.33013i)q52+(4.500007.79423i)q535.19615iq545.00000q55+(6.00000+5.19615i)q56+(1.500000.866025i)q57+(0.5000000.866025i)q58+(1.500000.866025i)q6014.0000q61+(6.00000+5.19615i)q63+7.00000q64+5.00000q65+(7.500004.33013i)q66+4.00000q67+(1.500002.59808i)q68+(4.500002.59808i)q69+(0.5000002.59808i)q7012.0000q71+9.00000q72+(1.50000+2.59808i)q73+(1.500002.59808i)q74+(6.00000+3.46410i)q75+(0.500000+0.866025i)q76+(12.50004.33013i)q77+(7.50000+4.33013i)q78+8.00000q79+(0.500000+0.866025i)q80+9.00000q81+(2.50000+4.33013i)q82+(4.500007.79423i)q83+(3.000003.46410i)q84+(1.50000+2.59808i)q85+(0.5000000.866025i)q86+(1.50000+0.866025i)q87+(7.50000+12.9904i)q88+(6.50000+11.2583i)q89+(1.50000+2.59808i)q90+(12.5000+4.33013i)q91+(1.500002.59808i)q921.00000q95+8.66025iq96+(4.500007.79423i)q97+(1.000006.92820i)q98+(7.50000+12.9904i)q99+O(q100)q+1.00000 q^{2} +1.73205i q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(2.00000 - 1.73205i) q^{7} -3.00000 q^{8} -3.00000 q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.50000 - 4.33013i) q^{11} -1.73205i q^{12} +(2.50000 + 4.33013i) q^{13} +(2.00000 - 1.73205i) q^{14} +(1.50000 + 0.866025i) q^{15} -1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(3.00000 + 3.46410i) q^{21} +(-2.50000 - 4.33013i) q^{22} +(-1.50000 + 2.59808i) q^{23} -5.19615i q^{24} +(2.00000 + 3.46410i) q^{25} +(2.50000 + 4.33013i) q^{26} -5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{29} +(1.50000 + 0.866025i) q^{30} +5.00000 q^{32} +(7.50000 - 4.33013i) q^{33} +(-1.50000 + 2.59808i) q^{34} +(-0.500000 - 2.59808i) q^{35} +3.00000 q^{36} +(-1.50000 - 2.59808i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-7.50000 + 4.33013i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(2.50000 + 4.33013i) q^{41} +(3.00000 + 3.46410i) q^{42} +(0.500000 - 0.866025i) q^{43} +(2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-1.50000 + 2.59808i) q^{46} -1.73205i q^{48} +(1.00000 - 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(4.50000 - 7.79423i) q^{53} -5.19615i q^{54} -5.00000 q^{55} +(-6.00000 + 5.19615i) q^{56} +(1.50000 - 0.866025i) q^{57} +(0.500000 - 0.866025i) q^{58} +(-1.50000 - 0.866025i) q^{60} -14.0000 q^{61} +(-6.00000 + 5.19615i) q^{63} +7.00000 q^{64} +5.00000 q^{65} +(7.50000 - 4.33013i) q^{66} +4.00000 q^{67} +(1.50000 - 2.59808i) q^{68} +(-4.50000 - 2.59808i) q^{69} +(-0.500000 - 2.59808i) q^{70} -12.0000 q^{71} +9.00000 q^{72} +(-1.50000 + 2.59808i) q^{73} +(-1.50000 - 2.59808i) q^{74} +(-6.00000 + 3.46410i) q^{75} +(0.500000 + 0.866025i) q^{76} +(-12.5000 - 4.33013i) q^{77} +(-7.50000 + 4.33013i) q^{78} +8.00000 q^{79} +(-0.500000 + 0.866025i) q^{80} +9.00000 q^{81} +(2.50000 + 4.33013i) q^{82} +(4.50000 - 7.79423i) q^{83} +(-3.00000 - 3.46410i) q^{84} +(1.50000 + 2.59808i) q^{85} +(0.500000 - 0.866025i) q^{86} +(1.50000 + 0.866025i) q^{87} +(7.50000 + 12.9904i) q^{88} +(6.50000 + 11.2583i) q^{89} +(-1.50000 + 2.59808i) q^{90} +(12.5000 + 4.33013i) q^{91} +(1.50000 - 2.59808i) q^{92} -1.00000 q^{95} +8.66025i q^{96} +(4.50000 - 7.79423i) q^{97} +(1.00000 - 6.92820i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q22q4+q5+4q76q86q9+q105q11+5q13+4q14+3q152q163q176q18q19q20+6q215q223q23++15q99+O(q100) 2 q + 2 q^{2} - 2 q^{4} + q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + q^{10} - 5 q^{11} + 5 q^{13} + 4 q^{14} + 3 q^{15} - 2 q^{16} - 3 q^{17} - 6 q^{18} - q^{19} - q^{20} + 6 q^{21} - 5 q^{22} - 3 q^{23}+ \cdots + 15 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/63Z)×\left(\mathbb{Z}/63\mathbb{Z}\right)^\times.

nn 1010 2929
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.00000 0.707107 0.353553 0.935414i 0.384973π-0.384973\pi
0.353553 + 0.935414i 0.384973π0.384973\pi
33 1.73205i 1.00000i
44 −1.00000 −0.500000
55 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i 0.761550π-0.761550\pi
0.955901 + 0.293691i 0.0948835π0.0948835\pi
66 1.73205i 0.707107i
77 2.00000 1.73205i 0.755929 0.654654i
88 −3.00000 −1.06066
99 −3.00000 −1.00000
1010 0.500000 0.866025i 0.158114 0.273861i
1111 −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i 0.894896π-0.894896\pi
0.192201 0.981356i 0.438437π-0.438437\pi
1212 1.73205i 0.500000i
1313 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i 0.0772105π0.0772105\pi
−0.277350 + 0.960769i 0.589456π0.589456\pi
1414 2.00000 1.73205i 0.534522 0.462910i
1515 1.50000 + 0.866025i 0.387298 + 0.223607i
1616 −1.00000 −0.250000
1717 −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i 0.951855π-0.951855\pi
0.624780 + 0.780801i 0.285189π0.285189\pi
1818 −3.00000 −0.707107
1919 −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i 0.203260π-0.203260\pi
−0.917663 + 0.397360i 0.869927π0.869927\pi
2020 −0.500000 + 0.866025i −0.111803 + 0.193649i
2121 3.00000 + 3.46410i 0.654654 + 0.755929i
2222 −2.50000 4.33013i −0.533002 0.923186i
2323 −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i 0.934591π-0.934591\pi
0.666190 + 0.745782i 0.267924π0.267924\pi
2424 5.19615i 1.06066i
2525 2.00000 + 3.46410i 0.400000 + 0.692820i
2626 2.50000 + 4.33013i 0.490290 + 0.849208i
2727 5.19615i 1.00000i
2828 −2.00000 + 1.73205i −0.377964 + 0.327327i
2929 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i 0.803736π-0.803736\pi
0.908708 + 0.417432i 0.137070π0.137070\pi
3030 1.50000 + 0.866025i 0.273861 + 0.158114i
3131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3232 5.00000 0.883883
3333 7.50000 4.33013i 1.30558 0.753778i
3434 −1.50000 + 2.59808i −0.257248 + 0.445566i
3535 −0.500000 2.59808i −0.0845154 0.439155i
3636 3.00000 0.500000
3737 −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i 0.245980π-0.245980\pi
−0.962580 + 0.270998i 0.912646π0.912646\pi
3838 −0.500000 0.866025i −0.0811107 0.140488i
3939 −7.50000 + 4.33013i −1.20096 + 0.693375i
4040 −1.50000 + 2.59808i −0.237171 + 0.410792i
4141 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i 0.0389915π-0.0389915\pi
−0.602072 + 0.798441i 0.705658π0.705658\pi
4242 3.00000 + 3.46410i 0.462910 + 0.534522i
4343 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i 0.809039π-0.809039\pi
0.901629 + 0.432511i 0.142372π0.142372\pi
4444 2.50000 + 4.33013i 0.376889 + 0.652791i
4545 −1.50000 + 2.59808i −0.223607 + 0.387298i
4646 −1.50000 + 2.59808i −0.221163 + 0.383065i
4747 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4848 1.73205i 0.250000i
4949 1.00000 6.92820i 0.142857 0.989743i
5050 2.00000 + 3.46410i 0.282843 + 0.489898i
5151 −4.50000 2.59808i −0.630126 0.363803i
5252 −2.50000 4.33013i −0.346688 0.600481i
5353 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i 0.621227π-0.621227\pi
0.989828 0.142269i 0.0454398π-0.0454398\pi
5454 5.19615i 0.707107i
5555 −5.00000 −0.674200
5656 −6.00000 + 5.19615i −0.801784 + 0.694365i
5757 1.50000 0.866025i 0.198680 0.114708i
5858 0.500000 0.866025i 0.0656532 0.113715i
5959 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6060 −1.50000 0.866025i −0.193649 0.111803i
6161 −14.0000 −1.79252 −0.896258 0.443533i 0.853725π-0.853725\pi
−0.896258 + 0.443533i 0.853725π0.853725\pi
6262 0 0
6363 −6.00000 + 5.19615i −0.755929 + 0.654654i
6464 7.00000 0.875000
6565 5.00000 0.620174
6666 7.50000 4.33013i 0.923186 0.533002i
6767 4.00000 0.488678 0.244339 0.969690i 0.421429π-0.421429\pi
0.244339 + 0.969690i 0.421429π0.421429\pi
6868 1.50000 2.59808i 0.181902 0.315063i
6969 −4.50000 2.59808i −0.541736 0.312772i
7070 −0.500000 2.59808i −0.0597614 0.310530i
7171 −12.0000 −1.42414 −0.712069 0.702109i 0.752242π-0.752242\pi
−0.712069 + 0.702109i 0.752242π0.752242\pi
7272 9.00000 1.06066
7373 −1.50000 + 2.59808i −0.175562 + 0.304082i −0.940356 0.340193i 0.889507π-0.889507\pi
0.764794 + 0.644275i 0.222841π0.222841\pi
7474 −1.50000 2.59808i −0.174371 0.302020i
7575 −6.00000 + 3.46410i −0.692820 + 0.400000i
7676 0.500000 + 0.866025i 0.0573539 + 0.0993399i
7777 −12.5000 4.33013i −1.42451 0.493464i
7878 −7.50000 + 4.33013i −0.849208 + 0.490290i
7979 8.00000 0.900070 0.450035 0.893011i 0.351411π-0.351411\pi
0.450035 + 0.893011i 0.351411π0.351411\pi
8080 −0.500000 + 0.866025i −0.0559017 + 0.0968246i
8181 9.00000 1.00000
8282 2.50000 + 4.33013i 0.276079 + 0.478183i
8383 4.50000 7.79423i 0.493939 0.855528i −0.506036 0.862512i 0.668890π-0.668890\pi
0.999976 + 0.00698436i 0.00222321π0.00222321\pi
8484 −3.00000 3.46410i −0.327327 0.377964i
8585 1.50000 + 2.59808i 0.162698 + 0.281801i
8686 0.500000 0.866025i 0.0539164 0.0933859i
8787 1.50000 + 0.866025i 0.160817 + 0.0928477i
8888 7.50000 + 12.9904i 0.799503 + 1.38478i
8989 6.50000 + 11.2583i 0.688999 + 1.19338i 0.972162 + 0.234309i 0.0752827π0.0752827\pi
−0.283164 + 0.959072i 0.591384π0.591384\pi
9090 −1.50000 + 2.59808i −0.158114 + 0.273861i
9191 12.5000 + 4.33013i 1.31036 + 0.453921i
9292 1.50000 2.59808i 0.156386 0.270868i
9393 0 0
9494 0 0
9595 −1.00000 −0.102598
9696 8.66025i 0.883883i
9797 4.50000 7.79423i 0.456906 0.791384i −0.541890 0.840450i 0.682291π-0.682291\pi
0.998796 + 0.0490655i 0.0156243π0.0156243\pi
9898 1.00000 6.92820i 0.101015 0.699854i
9999 7.50000 + 12.9904i 0.753778 + 1.30558i
100100 −2.00000 3.46410i −0.200000 0.346410i
101101 8.50000 + 14.7224i 0.845782 + 1.46494i 0.884941 + 0.465704i 0.154199π0.154199\pi
−0.0391591 + 0.999233i 0.512468π0.512468\pi
102102 −4.50000 2.59808i −0.445566 0.257248i
103103 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i 0.817645π-0.817645\pi
0.889607 + 0.456727i 0.150978π0.150978\pi
104104 −7.50000 12.9904i −0.735436 1.27381i
105105 4.50000 0.866025i 0.439155 0.0845154i
106106 4.50000 7.79423i 0.437079 0.757042i
107107 −8.50000 14.7224i −0.821726 1.42327i −0.904396 0.426694i 0.859678π-0.859678\pi
0.0826699 0.996577i 0.473655π-0.473655\pi
108108 5.19615i 0.500000i
109109 4.50000 7.79423i 0.431022 0.746552i −0.565940 0.824447i 0.691487π-0.691487\pi
0.996962 + 0.0778949i 0.0248199π0.0248199\pi
110110 −5.00000 −0.476731
111111 4.50000 2.59808i 0.427121 0.246598i
112112 −2.00000 + 1.73205i −0.188982 + 0.163663i
113113 0.500000 + 0.866025i 0.0470360 + 0.0814688i 0.888585 0.458712i 0.151689π-0.151689\pi
−0.841549 + 0.540181i 0.818356π0.818356\pi
114114 1.50000 0.866025i 0.140488 0.0811107i
115115 1.50000 + 2.59808i 0.139876 + 0.242272i
116116 −0.500000 + 0.866025i −0.0464238 + 0.0804084i
117117 −7.50000 12.9904i −0.693375 1.20096i
118118 0 0
119119 1.50000 + 7.79423i 0.137505 + 0.714496i
120120 −4.50000 2.59808i −0.410792 0.237171i
121121 −7.00000 + 12.1244i −0.636364 + 1.10221i
122122 −14.0000 −1.26750
123123 −7.50000 + 4.33013i −0.676252 + 0.390434i
124124 0 0
125125 9.00000 0.804984
126126 −6.00000 + 5.19615i −0.534522 + 0.462910i
127127 −12.0000 −1.06483 −0.532414 0.846484i 0.678715π-0.678715\pi
−0.532414 + 0.846484i 0.678715π0.678715\pi
128128 −3.00000 −0.265165
129129 1.50000 + 0.866025i 0.132068 + 0.0762493i
130130 5.00000 0.438529
131131 0.500000 0.866025i 0.0436852 0.0756650i −0.843356 0.537355i 0.819423π-0.819423\pi
0.887041 + 0.461690i 0.152757π0.152757\pi
132132 −7.50000 + 4.33013i −0.652791 + 0.376889i
133133 −2.50000 0.866025i −0.216777 0.0750939i
134134 4.00000 0.345547
135135 −4.50000 2.59808i −0.387298 0.223607i
136136 4.50000 7.79423i 0.385872 0.668350i
137137 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i 0.0410540π-0.0410540\pi
−0.607233 + 0.794524i 0.707721π0.707721\pi
138138 −4.50000 2.59808i −0.383065 0.221163i
139139 −4.50000 7.79423i −0.381685 0.661098i 0.609618 0.792695i 0.291323π-0.291323\pi
−0.991303 + 0.131597i 0.957989π0.957989\pi
140140 0.500000 + 2.59808i 0.0422577 + 0.219578i
141141 0 0
142142 −12.0000 −1.00702
143143 12.5000 21.6506i 1.04530 1.81052i
144144 3.00000 0.250000
145145 −0.500000 0.866025i −0.0415227 0.0719195i
146146 −1.50000 + 2.59808i −0.124141 + 0.215018i
147147 12.0000 + 1.73205i 0.989743 + 0.142857i
148148 1.50000 + 2.59808i 0.123299 + 0.213561i
149149 −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i 0.872548π-0.872548\pi
0.798019 + 0.602632i 0.205881π0.205881\pi
150150 −6.00000 + 3.46410i −0.489898 + 0.282843i
151151 −2.50000 4.33013i −0.203447 0.352381i 0.746190 0.665733i 0.231881π-0.231881\pi
−0.949637 + 0.313353i 0.898548π0.898548\pi
152152 1.50000 + 2.59808i 0.121666 + 0.210732i
153153 4.50000 7.79423i 0.363803 0.630126i
154154 −12.5000 4.33013i −1.00728 0.348932i
155155 0 0
156156 7.50000 4.33013i 0.600481 0.346688i
157157 −14.0000 −1.11732 −0.558661 0.829396i 0.688685π-0.688685\pi
−0.558661 + 0.829396i 0.688685π0.688685\pi
158158 8.00000 0.636446
159159 13.5000 + 7.79423i 1.07062 + 0.618123i
160160 2.50000 4.33013i 0.197642 0.342327i
161161 1.50000 + 7.79423i 0.118217 + 0.614271i
162162 9.00000 0.707107
163163 5.50000 + 9.52628i 0.430793 + 0.746156i 0.996942 0.0781474i 0.0249005π-0.0249005\pi
−0.566149 + 0.824303i 0.691567π0.691567\pi
164164 −2.50000 4.33013i −0.195217 0.338126i
165165 8.66025i 0.674200i
166166 4.50000 7.79423i 0.349268 0.604949i
167167 9.50000 + 16.4545i 0.735132 + 1.27329i 0.954665 + 0.297681i 0.0962132π0.0962132\pi
−0.219533 + 0.975605i 0.570453π0.570453\pi
168168 −9.00000 10.3923i −0.694365 0.801784i
169169 −6.00000 + 10.3923i −0.461538 + 0.799408i
170170 1.50000 + 2.59808i 0.115045 + 0.199263i
171171 1.50000 + 2.59808i 0.114708 + 0.198680i
172172 −0.500000 + 0.866025i −0.0381246 + 0.0660338i
173173 −14.0000 −1.06440 −0.532200 0.846619i 0.678635π-0.678635\pi
−0.532200 + 0.846619i 0.678635π0.678635\pi
174174 1.50000 + 0.866025i 0.113715 + 0.0656532i
175175 10.0000 + 3.46410i 0.755929 + 0.261861i
176176 2.50000 + 4.33013i 0.188445 + 0.326396i
177177 0 0
178178 6.50000 + 11.2583i 0.487196 + 0.843848i
179179 −9.50000 + 16.4545i −0.710063 + 1.22987i 0.254770 + 0.967002i 0.418000π0.418000\pi
−0.964833 + 0.262864i 0.915333π0.915333\pi
180180 1.50000 2.59808i 0.111803 0.193649i
181181 −14.0000 −1.04061 −0.520306 0.853980i 0.674182π-0.674182\pi
−0.520306 + 0.853980i 0.674182π0.674182\pi
182182 12.5000 + 4.33013i 0.926562 + 0.320970i
183183 24.2487i 1.79252i
184184 4.50000 7.79423i 0.331744 0.574598i
185185 −3.00000 −0.220564
186186 0 0
187187 15.0000 1.09691
188188 0 0
189189 −9.00000 10.3923i −0.654654 0.755929i
190190 −1.00000 −0.0725476
191191 8.00000 0.578860 0.289430 0.957199i 0.406534π-0.406534\pi
0.289430 + 0.957199i 0.406534π0.406534\pi
192192 12.1244i 0.875000i
193193 −10.0000 −0.719816 −0.359908 0.932988i 0.617192π-0.617192\pi
−0.359908 + 0.932988i 0.617192π0.617192\pi
194194 4.50000 7.79423i 0.323081 0.559593i
195195 8.66025i 0.620174i
196196 −1.00000 + 6.92820i −0.0714286 + 0.494872i
197197 2.00000 0.142494 0.0712470 0.997459i 0.477302π-0.477302\pi
0.0712470 + 0.997459i 0.477302π0.477302\pi
198198 7.50000 + 12.9904i 0.533002 + 0.923186i
199199 −1.50000 + 2.59808i −0.106332 + 0.184173i −0.914282 0.405079i 0.867244π-0.867244\pi
0.807950 + 0.589252i 0.200577π0.200577\pi
200200 −6.00000 10.3923i −0.424264 0.734847i
201201 6.92820i 0.488678i
202202 8.50000 + 14.7224i 0.598058 + 1.03587i
203203 −0.500000 2.59808i −0.0350931 0.182349i
204204 4.50000 + 2.59808i 0.315063 + 0.181902i
205205 5.00000 0.349215
206206 0.500000 0.866025i 0.0348367 0.0603388i
207207 4.50000 7.79423i 0.312772 0.541736i
208208 −2.50000 4.33013i −0.173344 0.300240i
209209 −2.50000 + 4.33013i −0.172929 + 0.299521i
210210 4.50000 0.866025i 0.310530 0.0597614i
211211 −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i 0.314345π-0.314345\pi
−0.998221 + 0.0596196i 0.981011π0.981011\pi
212212 −4.50000 + 7.79423i −0.309061 + 0.535310i
213213 20.7846i 1.42414i
214214 −8.50000 14.7224i −0.581048 1.00640i
215215 −0.500000 0.866025i −0.0340997 0.0590624i
216216 15.5885i 1.06066i
217217 0 0
218218 4.50000 7.79423i 0.304778 0.527892i
219219 −4.50000 2.59808i −0.304082 0.175562i
220220 5.00000 0.337100
221221 −15.0000 −1.00901
222222 4.50000 2.59808i 0.302020 0.174371i
223223 −9.50000 + 16.4545i −0.636167 + 1.10187i 0.350100 + 0.936713i 0.386148π0.386148\pi
−0.986267 + 0.165161i 0.947186π0.947186\pi
224224 10.0000 8.66025i 0.668153 0.578638i
225225 −6.00000 10.3923i −0.400000 0.692820i
226226 0.500000 + 0.866025i 0.0332595 + 0.0576072i
227227 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i 0.134924π-0.134924\pi
−0.811943 + 0.583736i 0.801590π0.801590\pi
228228 −1.50000 + 0.866025i −0.0993399 + 0.0573539i
229229 0.500000 0.866025i 0.0330409 0.0572286i −0.849032 0.528341i 0.822814π-0.822814\pi
0.882073 + 0.471113i 0.156147π0.156147\pi
230230 1.50000 + 2.59808i 0.0989071 + 0.171312i
231231 7.50000 21.6506i 0.493464 1.42451i
232232 −1.50000 + 2.59808i −0.0984798 + 0.170572i
233233 −1.50000 2.59808i −0.0982683 0.170206i 0.812700 0.582683i 0.197997π-0.197997\pi
−0.910968 + 0.412477i 0.864664π0.864664\pi
234234 −7.50000 12.9904i −0.490290 0.849208i
235235 0 0
236236 0 0
237237 13.8564i 0.900070i
238238 1.50000 + 7.79423i 0.0972306 + 0.505225i
239239 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i 0.00543724π-0.00543724\pi
−0.514719 + 0.857359i 0.672104π0.672104\pi
240240 −1.50000 0.866025i −0.0968246 0.0559017i
241241 −5.50000 9.52628i −0.354286 0.613642i 0.632709 0.774389i 0.281943π-0.281943\pi
−0.986996 + 0.160748i 0.948609π0.948609\pi
242242 −7.00000 + 12.1244i −0.449977 + 0.779383i
243243 15.5885i 1.00000i
244244 14.0000 0.896258
245245 −5.50000 4.33013i −0.351382 0.276642i
246246 −7.50000 + 4.33013i −0.478183 + 0.276079i
247247 2.50000 4.33013i 0.159071 0.275519i
248248 0 0
249249 13.5000 + 7.79423i 0.855528 + 0.493939i
250250 9.00000 0.569210
251251 −28.0000 −1.76734 −0.883672 0.468106i 0.844936π-0.844936\pi
−0.883672 + 0.468106i 0.844936π0.844936\pi
252252 6.00000 5.19615i 0.377964 0.327327i
253253 15.0000 0.943042
254254 −12.0000 −0.752947
255255 −4.50000 + 2.59808i −0.281801 + 0.162698i
256256 −17.0000 −1.06250
257257 14.5000 25.1147i 0.904485 1.56661i 0.0828783 0.996560i 0.473589π-0.473589\pi
0.821607 0.570055i 0.193078π-0.193078\pi
258258 1.50000 + 0.866025i 0.0933859 + 0.0539164i
259259 −7.50000 2.59808i −0.466027 0.161437i
260260 −5.00000 −0.310087
261261 −1.50000 + 2.59808i −0.0928477 + 0.160817i
262262 0.500000 0.866025i 0.0308901 0.0535032i
263263 −2.50000 4.33013i −0.154157 0.267007i 0.778595 0.627527i 0.215933π-0.215933\pi
−0.932752 + 0.360520i 0.882599π0.882599\pi
264264 −22.5000 + 12.9904i −1.38478 + 0.799503i
265265 −4.50000 7.79423i −0.276433 0.478796i
266266 −2.50000 0.866025i −0.153285 0.0530994i
267267 −19.5000 + 11.2583i −1.19338 + 0.688999i
268268 −4.00000 −0.244339
269269 −1.50000 + 2.59808i −0.0914566 + 0.158408i −0.908124 0.418701i 0.862486π-0.862486\pi
0.816668 + 0.577108i 0.195819π0.195819\pi
270270 −4.50000 2.59808i −0.273861 0.158114i
271271 −0.500000 0.866025i −0.0303728 0.0526073i 0.850439 0.526073i 0.176336π-0.176336\pi
−0.880812 + 0.473466i 0.843003π0.843003\pi
272272 1.50000 2.59808i 0.0909509 0.157532i
273273 −7.50000 + 21.6506i −0.453921 + 1.31036i
274274 4.50000 + 7.79423i 0.271855 + 0.470867i
275275 10.0000 17.3205i 0.603023 1.04447i
276276 4.50000 + 2.59808i 0.270868 + 0.156386i
277277 −9.50000 16.4545i −0.570800 0.988654i −0.996484 0.0837823i 0.973300π-0.973300\pi
0.425684 0.904872i 0.360033π-0.360033\pi
278278 −4.50000 7.79423i −0.269892 0.467467i
279279 0 0
280280 1.50000 + 7.79423i 0.0896421 + 0.465794i
281281 14.5000 25.1147i 0.864997 1.49822i −0.00205220 0.999998i 0.500653π-0.500653\pi
0.867050 0.498222i 0.166013π-0.166013\pi
282282 0 0
283283 28.0000 1.66443 0.832214 0.554455i 0.187073π-0.187073\pi
0.832214 + 0.554455i 0.187073π0.187073\pi
284284 12.0000 0.712069
285285 1.73205i 0.102598i
286286 12.5000 21.6506i 0.739140 1.28023i
287287 12.5000 + 4.33013i 0.737852 + 0.255599i
288288 −15.0000 −0.883883
289289 4.00000 + 6.92820i 0.235294 + 0.407541i
290290 −0.500000 0.866025i −0.0293610 0.0508548i
291291 13.5000 + 7.79423i 0.791384 + 0.456906i
292292 1.50000 2.59808i 0.0877809 0.152041i
293293 2.50000 + 4.33013i 0.146052 + 0.252969i 0.929765 0.368154i 0.120010π-0.120010\pi
−0.783713 + 0.621123i 0.786677π0.786677\pi
294294 12.0000 + 1.73205i 0.699854 + 0.101015i
295295 0 0
296296 4.50000 + 7.79423i 0.261557 + 0.453030i
297297 −22.5000 + 12.9904i −1.30558 + 0.753778i
298298 −1.50000 + 2.59808i −0.0868927 + 0.150503i
299299 −15.0000 −0.867472
300300 6.00000 3.46410i 0.346410 0.200000i
301301 −0.500000 2.59808i −0.0288195 0.149751i
302302 −2.50000 4.33013i −0.143859 0.249171i
303303 −25.5000 + 14.7224i −1.46494 + 0.845782i
304304 0.500000 + 0.866025i 0.0286770 + 0.0496700i
305305 −7.00000 + 12.1244i −0.400819 + 0.694239i
306306 4.50000 7.79423i 0.257248 0.445566i
307307 28.0000 1.59804 0.799022 0.601302i 0.205351π-0.205351\pi
0.799022 + 0.601302i 0.205351π0.205351\pi
308308 12.5000 + 4.33013i 0.712254 + 0.246732i
309309 1.50000 + 0.866025i 0.0853320 + 0.0492665i
310310 0 0
311311 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
312312 22.5000 12.9904i 1.27381 0.735436i
313313 14.0000 0.791327 0.395663 0.918396i 0.370515π-0.370515\pi
0.395663 + 0.918396i 0.370515π0.370515\pi
314314 −14.0000 −0.790066
315315 1.50000 + 7.79423i 0.0845154 + 0.439155i
316316 −8.00000 −0.450035
317317 −6.00000 −0.336994 −0.168497 0.985702i 0.553891π-0.553891\pi
−0.168497 + 0.985702i 0.553891π0.553891\pi
318318 13.5000 + 7.79423i 0.757042 + 0.437079i
319319 −5.00000 −0.279946
320320 3.50000 6.06218i 0.195656 0.338886i
321321 25.5000 14.7224i 1.42327 0.821726i
322322 1.50000 + 7.79423i 0.0835917 + 0.434355i
323323 3.00000 0.166924
324324 −9.00000 −0.500000
325325 −10.0000 + 17.3205i −0.554700 + 0.960769i
326326 5.50000 + 9.52628i 0.304617 + 0.527612i
327327 13.5000 + 7.79423i 0.746552 + 0.431022i
328328 −7.50000 12.9904i −0.414118 0.717274i
329329 0 0
330330 8.66025i 0.476731i
331331 8.00000 0.439720 0.219860 0.975531i 0.429440π-0.429440\pi
0.219860 + 0.975531i 0.429440π0.429440\pi
332332 −4.50000 + 7.79423i −0.246970 + 0.427764i
333333 4.50000 + 7.79423i 0.246598 + 0.427121i
334334 9.50000 + 16.4545i 0.519817 + 0.900349i
335335 2.00000 3.46410i 0.109272 0.189264i
336336 −3.00000 3.46410i −0.163663 0.188982i
337337 14.5000 + 25.1147i 0.789865 + 1.36809i 0.926049 + 0.377403i 0.123183π0.123183\pi
−0.136184 + 0.990684i 0.543484π0.543484\pi
338338 −6.00000 + 10.3923i −0.326357 + 0.565267i
339339 −1.50000 + 0.866025i −0.0814688 + 0.0470360i
340340 −1.50000 2.59808i −0.0813489 0.140900i
341341 0 0
342342 1.50000 + 2.59808i 0.0811107 + 0.140488i
343343 −10.0000 15.5885i −0.539949 0.841698i
344344 −1.50000 + 2.59808i −0.0808746 + 0.140079i
345345 −4.50000 + 2.59808i −0.242272 + 0.139876i
346346 −14.0000 −0.752645
347347 4.00000 0.214731 0.107366 0.994220i 0.465758π-0.465758\pi
0.107366 + 0.994220i 0.465758π0.465758\pi
348348 −1.50000 0.866025i −0.0804084 0.0464238i
349349 −9.50000 + 16.4545i −0.508523 + 0.880788i 0.491428 + 0.870918i 0.336475π0.336475\pi
−0.999951 + 0.00987003i 0.996858π0.996858\pi
350350 10.0000 + 3.46410i 0.534522 + 0.185164i
351351 22.5000 12.9904i 1.20096 0.693375i
352352 −12.5000 21.6506i −0.666252 1.15398i
353353 −5.50000 9.52628i −0.292735 0.507033i 0.681720 0.731613i 0.261232π-0.261232\pi
−0.974456 + 0.224580i 0.927899π0.927899\pi
354354 0 0
355355 −6.00000 + 10.3923i −0.318447 + 0.551566i
356356 −6.50000 11.2583i −0.344499 0.596690i
357357 −13.5000 + 2.59808i −0.714496 + 0.137505i
358358 −9.50000 + 16.4545i −0.502091 + 0.869646i
359359 5.50000 + 9.52628i 0.290279 + 0.502778i 0.973876 0.227082i 0.0729186π-0.0729186\pi
−0.683597 + 0.729860i 0.739585π0.739585\pi
360360 4.50000 7.79423i 0.237171 0.410792i
361361 9.00000 15.5885i 0.473684 0.820445i
362362 −14.0000 −0.735824
363363 −21.0000 12.1244i −1.10221 0.636364i
364364 −12.5000 4.33013i −0.655178 0.226960i
365365 1.50000 + 2.59808i 0.0785136 + 0.135990i
366366 24.2487i 1.26750i
367367 1.50000 + 2.59808i 0.0782994 + 0.135618i 0.902516 0.430656i 0.141718π-0.141718\pi
−0.824217 + 0.566274i 0.808384π0.808384\pi
368368 1.50000 2.59808i 0.0781929 0.135434i
369369 −7.50000 12.9904i −0.390434 0.676252i
370370 −3.00000 −0.155963
371371 −4.50000 23.3827i −0.233628 1.21397i
372372 0 0
373373 12.5000 21.6506i 0.647225 1.12103i −0.336557 0.941663i 0.609263π-0.609263\pi
0.983783 0.179364i 0.0574041π-0.0574041\pi
374374 15.0000 0.775632
375375 15.5885i 0.804984i
376376 0 0
377377 5.00000 0.257513
378378 −9.00000 10.3923i −0.462910 0.534522i
379379 −12.0000 −0.616399 −0.308199 0.951322i 0.599726π-0.599726\pi
−0.308199 + 0.951322i 0.599726π0.599726\pi
380380 1.00000 0.0512989
381381 20.7846i 1.06483i
382382 8.00000 0.409316
383383 −13.5000 + 23.3827i −0.689818 + 1.19480i 0.282079 + 0.959391i 0.408976π0.408976\pi
−0.971897 + 0.235408i 0.924357π0.924357\pi
384384 5.19615i 0.265165i
385385 −10.0000 + 8.66025i −0.509647 + 0.441367i
386386 −10.0000 −0.508987
387387 −1.50000 + 2.59808i −0.0762493 + 0.132068i
388388 −4.50000 + 7.79423i −0.228453 + 0.395692i
389389 4.50000 + 7.79423i 0.228159 + 0.395183i 0.957263 0.289220i 0.0933960π-0.0933960\pi
−0.729103 + 0.684403i 0.760063π0.760063\pi
390390 8.66025i 0.438529i
391391 −4.50000 7.79423i −0.227575 0.394171i
392392 −3.00000 + 20.7846i −0.151523 + 1.04978i
393393 1.50000 + 0.866025i 0.0756650 + 0.0436852i
394394 2.00000 0.100759
395395 4.00000 6.92820i 0.201262 0.348596i
396396 −7.50000 12.9904i −0.376889 0.652791i
397397 −7.50000 12.9904i −0.376414 0.651969i 0.614123 0.789210i 0.289510π-0.289510\pi
−0.990538 + 0.137241i 0.956176π0.956176\pi
398398 −1.50000 + 2.59808i −0.0751882 + 0.130230i
399399 1.50000 4.33013i 0.0750939 0.216777i
400400 −2.00000 3.46410i −0.100000 0.173205i
401401 −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i 0.857199π-0.857199\pi
0.826139 + 0.563466i 0.190532π0.190532\pi
402402 6.92820i 0.345547i
403403 0 0
404404 −8.50000 14.7224i −0.422891 0.732468i
405405 4.50000 7.79423i 0.223607 0.387298i
406406 −0.500000 2.59808i −0.0248146 0.128940i
407407 −7.50000 + 12.9904i −0.371761 + 0.643909i
408408 13.5000 + 7.79423i 0.668350 + 0.385872i
409409 14.0000 0.692255 0.346128 0.938187i 0.387496π-0.387496\pi
0.346128 + 0.938187i 0.387496π0.387496\pi
410410 5.00000 0.246932
411411 −13.5000 + 7.79423i −0.665906 + 0.384461i
412412 −0.500000 + 0.866025i −0.0246332 + 0.0426660i
413413 0 0
414414 4.50000 7.79423i 0.221163 0.383065i
415415 −4.50000 7.79423i −0.220896 0.382604i
416416 12.5000 + 21.6506i 0.612863 + 1.06151i
417417 13.5000 7.79423i 0.661098 0.381685i
418418 −2.50000 + 4.33013i −0.122279 + 0.211793i
419419 −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i 0.237220π-0.237220\pi
−0.954759 + 0.297382i 0.903887π0.903887\pi
420420 −4.50000 + 0.866025i −0.219578 + 0.0422577i
421421 0.500000 0.866025i 0.0243685 0.0422075i −0.853584 0.520955i 0.825576π-0.825576\pi
0.877952 + 0.478748i 0.158909π0.158909\pi
422422 −6.50000 11.2583i −0.316415 0.548047i
423423 0 0
424424 −13.5000 + 23.3827i −0.655618 + 1.13556i
425425 −12.0000 −0.582086
426426 20.7846i 1.00702i
427427 −28.0000 + 24.2487i −1.35501 + 1.17348i
428428 8.50000 + 14.7224i 0.410863 + 0.711636i
429429 37.5000 + 21.6506i 1.81052 + 1.04530i
430430 −0.500000 0.866025i −0.0241121 0.0417635i
431431 4.50000 7.79423i 0.216757 0.375435i −0.737057 0.675830i 0.763785π-0.763785\pi
0.953815 + 0.300395i 0.0971186π0.0971186\pi
432432 5.19615i 0.250000i
433433 −14.0000 −0.672797 −0.336399 0.941720i 0.609209π-0.609209\pi
−0.336399 + 0.941720i 0.609209π0.609209\pi
434434 0 0
435435 1.50000 0.866025i 0.0719195 0.0415227i
436436 −4.50000 + 7.79423i −0.215511 + 0.373276i
437437 3.00000 0.143509
438438 −4.50000 2.59808i −0.215018 0.124141i
439439 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
440440 15.0000 0.715097
441441 −3.00000 + 20.7846i −0.142857 + 0.989743i
442442 −15.0000 −0.713477
443443 36.0000 1.71041 0.855206 0.518289i 0.173431π-0.173431\pi
0.855206 + 0.518289i 0.173431π0.173431\pi
444444 −4.50000 + 2.59808i −0.213561 + 0.123299i
445445 13.0000 0.616259
446446 −9.50000 + 16.4545i −0.449838 + 0.779142i
447447 −4.50000 2.59808i −0.212843 0.122885i
448448 14.0000 12.1244i 0.661438 0.572822i
449449 30.0000 1.41579 0.707894 0.706319i 0.249646π-0.249646\pi
0.707894 + 0.706319i 0.249646π0.249646\pi
450450 −6.00000 10.3923i −0.282843 0.489898i
451451 12.5000 21.6506i 0.588602 1.01949i
452452 −0.500000 0.866025i −0.0235180 0.0407344i
453453 7.50000 4.33013i 0.352381 0.203447i
454454 1.50000 + 2.59808i 0.0703985 + 0.121934i
455455 10.0000 8.66025i 0.468807 0.405999i
456456 −4.50000 + 2.59808i −0.210732 + 0.121666i
457457 22.0000 1.02912 0.514558 0.857455i 0.327956π-0.327956\pi
0.514558 + 0.857455i 0.327956π0.327956\pi
458458 0.500000 0.866025i 0.0233635 0.0404667i
459459 13.5000 + 7.79423i 0.630126 + 0.363803i
460460 −1.50000 2.59808i −0.0699379 0.121136i
461461 −9.50000 + 16.4545i −0.442459 + 0.766362i −0.997871 0.0652135i 0.979227π-0.979227\pi
0.555412 + 0.831575i 0.312560π0.312560\pi
462462 7.50000 21.6506i 0.348932 1.00728i
463463 −6.50000 11.2583i −0.302081 0.523219i 0.674526 0.738251i 0.264348π-0.264348\pi
−0.976607 + 0.215032i 0.931015π0.931015\pi
464464 −0.500000 + 0.866025i −0.0232119 + 0.0402042i
465465 0 0
466466 −1.50000 2.59808i −0.0694862 0.120354i
467467 13.5000 + 23.3827i 0.624705 + 1.08202i 0.988598 + 0.150581i 0.0481143π0.0481143\pi
−0.363892 + 0.931441i 0.618552π0.618552\pi
468468 7.50000 + 12.9904i 0.346688 + 0.600481i
469469 8.00000 6.92820i 0.369406 0.319915i
470470 0 0
471471 24.2487i 1.11732i
472472 0 0
473473 −5.00000 −0.229900
474474 13.8564i 0.636446i
475475 2.00000 3.46410i 0.0917663 0.158944i
476476 −1.50000 7.79423i −0.0687524 0.357248i
477477 −13.5000 + 23.3827i −0.618123 + 1.07062i
478478 7.50000 + 12.9904i 0.343042 + 0.594166i
479479 −12.5000 21.6506i −0.571140 0.989243i −0.996449 0.0841949i 0.973168π-0.973168\pi
0.425310 0.905048i 0.360165π-0.360165\pi
480480 7.50000 + 4.33013i 0.342327 + 0.197642i
481481 7.50000 12.9904i 0.341971 0.592310i
482482 −5.50000 9.52628i −0.250518 0.433910i
483483 −13.5000 + 2.59808i −0.614271 + 0.118217i
484484 7.00000 12.1244i 0.318182 0.551107i
485485 −4.50000 7.79423i −0.204334 0.353918i
486486 15.5885i 0.707107i
487487 −9.50000 + 16.4545i −0.430486 + 0.745624i −0.996915 0.0784867i 0.974991π-0.974991\pi
0.566429 + 0.824110i 0.308325π0.308325\pi
488488 42.0000 1.90125
489489 −16.5000 + 9.52628i −0.746156 + 0.430793i
490490 −5.50000 4.33013i −0.248465 0.195615i
491491 −6.50000 11.2583i −0.293341 0.508081i 0.681257 0.732045i 0.261434π-0.261434\pi
−0.974598 + 0.223963i 0.928100π0.928100\pi
492492 7.50000 4.33013i 0.338126 0.195217i
493493 1.50000 + 2.59808i 0.0675566 + 0.117011i
494494 2.50000 4.33013i 0.112480 0.194822i
495495 15.0000 0.674200
496496 0 0
497497 −24.0000 + 20.7846i −1.07655 + 0.932317i
498498 13.5000 + 7.79423i 0.604949 + 0.349268i
499499 −15.5000 + 26.8468i −0.693875 + 1.20183i 0.276683 + 0.960961i 0.410765π0.410765\pi
−0.970558 + 0.240866i 0.922569π0.922569\pi
500500 −9.00000 −0.402492
501501 −28.5000 + 16.4545i −1.27329 + 0.735132i
502502 −28.0000 −1.24970
503503 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
504504 18.0000 15.5885i 0.801784 0.694365i
505505 17.0000 0.756490
506506 15.0000 0.666831
507507 −18.0000 10.3923i −0.799408 0.461538i
508508 12.0000 0.532414
509509 14.5000 25.1147i 0.642701 1.11319i −0.342126 0.939654i 0.611147π-0.611147\pi
0.984827 0.173537i 0.0555197π-0.0555197\pi
510510 −4.50000 + 2.59808i −0.199263 + 0.115045i
511511 1.50000 + 7.79423i 0.0663561 + 0.344796i
512512 −11.0000 −0.486136
513513 −4.50000 + 2.59808i −0.198680 + 0.114708i
514514 14.5000 25.1147i 0.639568 1.10776i
515515 −0.500000 0.866025i −0.0220326 0.0381616i
516516 −1.50000 0.866025i −0.0660338 0.0381246i
517517 0 0
518518 −7.50000 2.59808i −0.329531 0.114153i
519519 24.2487i 1.06440i
520520 −15.0000 −0.657794
521521 −1.50000 + 2.59808i −0.0657162 + 0.113824i −0.897011 0.442007i 0.854267π-0.854267\pi
0.831295 + 0.555831i 0.187600π0.187600\pi
522522 −1.50000 + 2.59808i −0.0656532 + 0.113715i
523523 −0.500000 0.866025i −0.0218635 0.0378686i 0.854887 0.518815i 0.173627π-0.173627\pi
−0.876750 + 0.480946i 0.840293π0.840293\pi
524524 −0.500000 + 0.866025i −0.0218426 + 0.0378325i
525525 −6.00000 + 17.3205i −0.261861 + 0.755929i
526526 −2.50000 4.33013i −0.109005 0.188803i
527527 0 0
528528 −7.50000 + 4.33013i −0.326396 + 0.188445i
529529 7.00000 + 12.1244i 0.304348 + 0.527146i
530530 −4.50000 7.79423i −0.195468 0.338560i
531531 0 0
532532 2.50000 + 0.866025i 0.108389 + 0.0375470i
533533 −12.5000 + 21.6506i −0.541435 + 0.937793i
534534 −19.5000 + 11.2583i −0.843848 + 0.487196i
535535 −17.0000 −0.734974
536536 −12.0000 −0.518321
537537 −28.5000 16.4545i −1.22987 0.710063i
538538 −1.50000 + 2.59808i −0.0646696 + 0.112011i
539539 −32.5000 + 12.9904i −1.39987 + 0.559535i
540540 4.50000 + 2.59808i 0.193649 + 0.111803i
541541 12.5000 + 21.6506i 0.537417 + 0.930834i 0.999042 + 0.0437584i 0.0139332π0.0139332\pi
−0.461625 + 0.887075i 0.652733π0.652733\pi
542542 −0.500000 0.866025i −0.0214768 0.0371990i
543543 24.2487i 1.04061i
544544 −7.50000 + 12.9904i −0.321560 + 0.556958i
545545 −4.50000 7.79423i −0.192759 0.333868i
546546 −7.50000 + 21.6506i −0.320970 + 0.926562i
547547 14.5000 25.1147i 0.619975 1.07383i −0.369514 0.929225i 0.620476π-0.620476\pi
0.989490 0.144604i 0.0461907π-0.0461907\pi
548548 −4.50000 7.79423i −0.192230 0.332953i
549549 42.0000 1.79252
550550 10.0000 17.3205i 0.426401 0.738549i
551551 −1.00000 −0.0426014
552552 13.5000 + 7.79423i 0.574598 + 0.331744i
553553 16.0000 13.8564i 0.680389 0.589234i
554554 −9.50000 16.4545i −0.403616 0.699084i
555555 5.19615i 0.220564i
556556 4.50000 + 7.79423i 0.190843 + 0.330549i
557557 18.5000 32.0429i 0.783870 1.35770i −0.145802 0.989314i 0.546576π-0.546576\pi
0.929672 0.368389i 0.120091π-0.120091\pi
558558 0 0
559559 5.00000 0.211477
560560 0.500000 + 2.59808i 0.0211289 + 0.109789i
561561 25.9808i 1.09691i
562562 14.5000 25.1147i 0.611646 1.05940i
563563 −28.0000 −1.18006 −0.590030 0.807382i 0.700884π-0.700884\pi
−0.590030 + 0.807382i 0.700884π0.700884\pi
564564 0 0
565565 1.00000 0.0420703
566566 28.0000 1.17693
567567 18.0000 15.5885i 0.755929 0.654654i
568568 36.0000 1.51053
569569 −34.0000 −1.42535 −0.712677 0.701492i 0.752517π-0.752517\pi
−0.712677 + 0.701492i 0.752517π0.752517\pi
570570 1.73205i 0.0725476i
571571 32.0000 1.33916 0.669579 0.742741i 0.266474π-0.266474\pi
0.669579 + 0.742741i 0.266474π0.266474\pi
572572 −12.5000 + 21.6506i −0.522651 + 0.905259i
573573 13.8564i 0.578860i
574574 12.5000 + 4.33013i 0.521740 + 0.180736i
575575 −12.0000 −0.500435
576576 −21.0000 −0.875000
577577 −15.5000 + 26.8468i −0.645273 + 1.11765i 0.338965 + 0.940799i 0.389923π0.389923\pi
−0.984238 + 0.176847i 0.943410π0.943410\pi
578578 4.00000 + 6.92820i 0.166378 + 0.288175i
579579 17.3205i 0.719816i
580580 0.500000 + 0.866025i 0.0207614 + 0.0359597i
581581 −4.50000 23.3827i −0.186691 0.970077i
582582 13.5000 + 7.79423i 0.559593 + 0.323081i
583583 −45.0000 −1.86371
584584 4.50000 7.79423i 0.186211 0.322527i
585585 −15.0000 −0.620174
586586 2.50000 + 4.33013i 0.103274 + 0.178876i
587587 18.5000 32.0429i 0.763577 1.32255i −0.177419 0.984135i 0.556775π-0.556775\pi
0.940996 0.338418i 0.109892π-0.109892\pi
588588 −12.0000 1.73205i −0.494872 0.0714286i
589589 0 0
590590 0 0
591591 3.46410i 0.142494i
592592 1.50000 + 2.59808i 0.0616496 + 0.106780i
593593 −7.50000 12.9904i −0.307988 0.533451i 0.669934 0.742421i 0.266322π-0.266322\pi
−0.977922 + 0.208970i 0.932989π0.932989\pi
594594 −22.5000 + 12.9904i −0.923186 + 0.533002i
595595 7.50000 + 2.59808i 0.307470 + 0.106511i
596596 1.50000 2.59808i 0.0614424 0.106421i
597597 −4.50000 2.59808i −0.184173 0.106332i
598598 −15.0000 −0.613396
599599 −24.0000 −0.980613 −0.490307 0.871550i 0.663115π-0.663115\pi
−0.490307 + 0.871550i 0.663115π0.663115\pi
600600 18.0000 10.3923i 0.734847 0.424264i
601601 4.50000 7.79423i 0.183559 0.317933i −0.759531 0.650471i 0.774572π-0.774572\pi
0.943090 + 0.332538i 0.107905π0.107905\pi
602602 −0.500000 2.59808i −0.0203785 0.105890i
603603 −12.0000 −0.488678
604604 2.50000 + 4.33013i 0.101724 + 0.176190i
605605 7.00000 + 12.1244i 0.284590 + 0.492925i
606606 −25.5000 + 14.7224i −1.03587 + 0.598058i
607607 0.500000 0.866025i 0.0202944 0.0351509i −0.855700 0.517472i 0.826873π-0.826873\pi
0.875994 + 0.482322i 0.160206π0.160206\pi
608608 −2.50000 4.33013i −0.101388 0.175610i
609609 4.50000 0.866025i 0.182349 0.0350931i
610610 −7.00000 + 12.1244i −0.283422 + 0.490901i
611611 0 0
612612 −4.50000 + 7.79423i −0.181902 + 0.315063i
613613 −9.50000 + 16.4545i −0.383701 + 0.664590i −0.991588 0.129433i 0.958684π-0.958684\pi
0.607887 + 0.794024i 0.292017π0.292017\pi
614614 28.0000 1.12999
615615 8.66025i 0.349215i
616616 37.5000 + 12.9904i 1.51092 + 0.523397i
617617 −13.5000 23.3827i −0.543490 0.941351i −0.998700 0.0509678i 0.983769π-0.983769\pi
0.455211 0.890384i 0.349564π-0.349564\pi
618618 1.50000 + 0.866025i 0.0603388 + 0.0348367i
619619 −12.5000 21.6506i −0.502417 0.870212i −0.999996 0.00279365i 0.999111π-0.999111\pi
0.497579 0.867419i 0.334223π-0.334223\pi
620620 0 0
621621 13.5000 + 7.79423i 0.541736 + 0.312772i
622622 0 0
623623 32.5000 + 11.2583i 1.30209 + 0.451055i
624624 7.50000 4.33013i 0.300240 0.173344i
625625 −5.50000 + 9.52628i −0.220000 + 0.381051i
626626 14.0000 0.559553
627627 −7.50000 4.33013i −0.299521 0.172929i
628628 14.0000 0.558661
629629 9.00000 0.358854
630630 1.50000 + 7.79423i 0.0597614 + 0.310530i
631631 −40.0000 −1.59237 −0.796187 0.605050i 0.793153π-0.793153\pi
−0.796187 + 0.605050i 0.793153π0.793153\pi
632632 −24.0000 −0.954669
633633 19.5000 11.2583i 0.775055 0.447478i
634634 −6.00000 −0.238290
635635 −6.00000 + 10.3923i −0.238103 + 0.412406i
636636 −13.5000 7.79423i −0.535310 0.309061i
637637 32.5000 12.9904i 1.28770 0.514698i
638638 −5.00000 −0.197952
639639 36.0000 1.42414
640640 −1.50000 + 2.59808i −0.0592927 + 0.102698i
641641 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i 0.109788π-0.109788\pi
−0.763367 + 0.645966i 0.776455π0.776455\pi
642642 25.5000 14.7224i 1.00640 0.581048i
643643 9.50000 + 16.4545i 0.374643 + 0.648901i 0.990274 0.139134i 0.0444318π-0.0444318\pi
−0.615630 + 0.788035i 0.711098π0.711098\pi
644644 −1.50000 7.79423i −0.0591083 0.307136i
645645 1.50000 0.866025i 0.0590624 0.0340997i
646646 3.00000 0.118033
647647 −15.5000 + 26.8468i −0.609368 + 1.05546i 0.381977 + 0.924172i 0.375243π0.375243\pi
−0.991345 + 0.131284i 0.958090π0.958090\pi
648648 −27.0000 −1.06066
649649 0 0
650650 −10.0000 + 17.3205i −0.392232 + 0.679366i
651651 0 0
652652 −5.50000 9.52628i −0.215397 0.373078i
653653 −1.50000 + 2.59808i −0.0586995 + 0.101671i −0.893882 0.448303i 0.852029π-0.852029\pi
0.835182 + 0.549973i 0.185362π0.185362\pi
654654 13.5000 + 7.79423i 0.527892 + 0.304778i
655655 −0.500000 0.866025i −0.0195366 0.0338384i
656656 −2.50000 4.33013i −0.0976086 0.169063i
657657 4.50000 7.79423i 0.175562 0.304082i
658658 0 0
659659 −13.5000 + 23.3827i −0.525885 + 0.910860i 0.473660 + 0.880708i 0.342933π0.342933\pi
−0.999545 + 0.0301523i 0.990401π0.990401\pi
660660 8.66025i 0.337100i
661661 −14.0000 −0.544537 −0.272268 0.962221i 0.587774π-0.587774\pi
−0.272268 + 0.962221i 0.587774π0.587774\pi
662662 8.00000 0.310929
663663 25.9808i 1.00901i
664664 −13.5000 + 23.3827i −0.523902 + 0.907424i
665665 −2.00000 + 1.73205i −0.0775567 + 0.0671660i
666666 4.50000 + 7.79423i 0.174371 + 0.302020i
667667 1.50000 + 2.59808i 0.0580802 + 0.100598i
668668 −9.50000 16.4545i −0.367566 0.636643i
669669 −28.5000 16.4545i −1.10187 0.636167i
670670 2.00000 3.46410i 0.0772667 0.133830i
671671 35.0000 + 60.6218i 1.35116 + 2.34028i
672672 15.0000 + 17.3205i 0.578638 + 0.668153i
673673 14.5000 25.1147i 0.558934 0.968102i −0.438652 0.898657i 0.644544π-0.644544\pi
0.997586 0.0694449i 0.0221228π-0.0221228\pi
674674 14.5000 + 25.1147i 0.558519 + 0.967384i
675675 18.0000 10.3923i 0.692820 0.400000i
676676 6.00000 10.3923i 0.230769 0.399704i
677677 42.0000 1.61419 0.807096 0.590421i 0.201038π-0.201038\pi
0.807096 + 0.590421i 0.201038π0.201038\pi
678678 −1.50000 + 0.866025i −0.0576072 + 0.0332595i
679679 −4.50000 23.3827i −0.172694 0.897345i
680680 −4.50000 7.79423i −0.172567 0.298895i
681681 −4.50000 + 2.59808i −0.172440 + 0.0995585i
682682 0 0
683683 4.50000 7.79423i 0.172188 0.298238i −0.766997 0.641651i 0.778250π-0.778250\pi
0.939184 + 0.343413i 0.111583π0.111583\pi
684684 −1.50000 2.59808i −0.0573539 0.0993399i
685685 9.00000 0.343872
686686 −10.0000 15.5885i −0.381802 0.595170i
687687 1.50000 + 0.866025i 0.0572286 + 0.0330409i
688688 −0.500000 + 0.866025i −0.0190623 + 0.0330169i
689689 45.0000 1.71436
690690 −4.50000 + 2.59808i −0.171312 + 0.0989071i
691691 −28.0000 −1.06517 −0.532585 0.846376i 0.678779π-0.678779\pi
−0.532585 + 0.846376i 0.678779π0.678779\pi
692692 14.0000 0.532200
693693 37.5000 + 12.9904i 1.42451 + 0.493464i
694694 4.00000 0.151838
695695 −9.00000 −0.341389
696696 −4.50000 2.59808i −0.170572 0.0984798i
697697 −15.0000 −0.568166
698698 −9.50000 + 16.4545i −0.359580 + 0.622811i
699699 4.50000 2.59808i 0.170206 0.0982683i
700700 −10.0000 3.46410i −0.377964 0.130931i
701701 30.0000 1.13308 0.566542 0.824033i 0.308281π-0.308281\pi
0.566542 + 0.824033i 0.308281π0.308281\pi
702702 22.5000 12.9904i 0.849208 0.490290i
703703 −1.50000 + 2.59808i −0.0565736 + 0.0979883i
704704 −17.5000 30.3109i −0.659556 1.14238i
705705 0 0
706706 −5.50000 9.52628i −0.206995 0.358526i
707707 42.5000 + 14.7224i 1.59838 + 0.553694i
708708 0 0
709709 −6.00000 −0.225335 −0.112667 0.993633i 0.535939π-0.535939\pi
−0.112667 + 0.993633i 0.535939π0.535939\pi
710710 −6.00000 + 10.3923i −0.225176 + 0.390016i
711711 −24.0000 −0.900070
712712 −19.5000 33.7750i −0.730793 1.26577i
713713 0 0
714714 −13.5000 + 2.59808i −0.505225 + 0.0972306i
715715 −12.5000 21.6506i −0.467473 0.809688i
716716 9.50000 16.4545i 0.355032 0.614933i
717717 −22.5000 + 12.9904i −0.840278 + 0.485135i
718718 5.50000 + 9.52628i 0.205258 + 0.355518i
719719 13.5000 + 23.3827i 0.503465 + 0.872027i 0.999992 + 0.00400572i 0.00127506π0.00127506\pi
−0.496527 + 0.868021i 0.665392π0.665392\pi
720720 1.50000 2.59808i 0.0559017 0.0968246i
721721 −0.500000 2.59808i −0.0186210 0.0967574i
722722 9.00000 15.5885i 0.334945 0.580142i
723723 16.5000 9.52628i 0.613642 0.354286i
724724 14.0000 0.520306
725725 4.00000 0.148556
726726 −21.0000 12.1244i −0.779383 0.449977i
727727 −23.5000 + 40.7032i −0.871567 + 1.50960i −0.0111912 + 0.999937i 0.503562π0.503562\pi
−0.860376 + 0.509661i 0.829771π0.829771\pi
728728 −37.5000 12.9904i −1.38984 0.481456i
729729 −27.0000 −1.00000
730730 1.50000 + 2.59808i 0.0555175 + 0.0961591i
731731 1.50000 + 2.59808i 0.0554795 + 0.0960933i
732732 24.2487i 0.896258i
733733 −13.5000 + 23.3827i −0.498634 + 0.863659i −0.999999 0.00157675i 0.999498π-0.999498\pi
0.501365 + 0.865236i 0.332831π0.332831\pi
734734 1.50000 + 2.59808i 0.0553660 + 0.0958967i
735735 7.50000 9.52628i 0.276642 0.351382i
736736 −7.50000 + 12.9904i −0.276454 + 0.478832i
737737 −10.0000 17.3205i −0.368355 0.638009i
738738 −7.50000 12.9904i −0.276079 0.478183i
739739 4.50000 7.79423i 0.165535 0.286715i −0.771310 0.636460i 0.780398π-0.780398\pi
0.936845 + 0.349744i 0.113732π0.113732\pi
740740 3.00000 0.110282
741741 7.50000 + 4.33013i 0.275519 + 0.159071i
742742 −4.50000 23.3827i −0.165200 0.858405i
743743 7.50000 + 12.9904i 0.275148 + 0.476571i 0.970173 0.242415i 0.0779397π-0.0779397\pi
−0.695024 + 0.718986i 0.744606π0.744606\pi
744744 0 0
745745 1.50000 + 2.59808i 0.0549557 + 0.0951861i
746746 12.5000 21.6506i 0.457658 0.792686i
747747 −13.5000 + 23.3827i −0.493939 + 0.855528i
748748 −15.0000 −0.548454
749749 −42.5000 14.7224i −1.55292 0.537946i
750750 15.5885i 0.569210i
751751 −15.5000 + 26.8468i −0.565603 + 0.979653i 0.431390 + 0.902165i 0.358023π0.358023\pi
−0.996993 + 0.0774878i 0.975310π0.975310\pi
752752 0 0
753753 48.4974i 1.76734i
754754 5.00000 0.182089
755755 −5.00000 −0.181969
756756 9.00000 + 10.3923i 0.327327 + 0.377964i
757757 2.00000 0.0726912 0.0363456 0.999339i 0.488428π-0.488428\pi
0.0363456 + 0.999339i 0.488428π0.488428\pi
758758 −12.0000 −0.435860
759759 25.9808i 0.943042i
760760 3.00000 0.108821
761761 −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i 0.996108π-0.996108\pi
0.510551 + 0.859848i 0.329442π0.329442\pi
762762 20.7846i 0.752947i
763763 −4.50000 23.3827i −0.162911 0.846510i
764764 −8.00000 −0.289430
765765 −4.50000 7.79423i −0.162698 0.281801i
766766 −13.5000 + 23.3827i −0.487775 + 0.844851i
767767 0 0
768768 29.4449i 1.06250i
769769 −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i 0.302780π-0.302780\pi
−0.995397 + 0.0958377i 0.969447π0.969447\pi
770770 −10.0000 + 8.66025i −0.360375 + 0.312094i
771771 43.5000 + 25.1147i 1.56661 + 0.904485i
772772 10.0000 0.359908
773773 −15.5000 + 26.8468i −0.557496 + 0.965612i 0.440208 + 0.897896i 0.354905π0.354905\pi
−0.997705 + 0.0677162i 0.978429π0.978429\pi
774774 −1.50000 + 2.59808i −0.0539164 + 0.0933859i
775775 0 0
776776 −13.5000 + 23.3827i −0.484622 + 0.839390i
777777 4.50000 12.9904i 0.161437 0.466027i
778778 4.50000 + 7.79423i 0.161333 + 0.279437i
779779 2.50000 4.33013i 0.0895718 0.155143i
780780 8.66025i 0.310087i
781781 30.0000 + 51.9615i 1.07348 + 1.85933i
782782 −4.50000 7.79423i −0.160920 0.278721i
783783 −4.50000 2.59808i −0.160817 0.0928477i
784784 −1.00000 + 6.92820i −0.0357143 + 0.247436i
785785 −7.00000 + 12.1244i −0.249841 + 0.432737i
786786 1.50000 + 0.866025i 0.0535032 + 0.0308901i
787787 28.0000 0.998092 0.499046 0.866575i 0.333684π-0.333684\pi
0.499046 + 0.866575i 0.333684π0.333684\pi
788788 −2.00000 −0.0712470
789789 7.50000 4.33013i 0.267007 0.154157i
790790 4.00000 6.92820i 0.142314 0.246494i
791791 2.50000 + 0.866025i 0.0888898 + 0.0307923i
792792 −22.5000 38.9711i −0.799503 1.38478i
793793 −35.0000 60.6218i −1.24289 2.15274i
794794 −7.50000 12.9904i −0.266165 0.461011i
795795 13.5000 7.79423i 0.478796 0.276433i
796796 1.50000 2.59808i 0.0531661 0.0920864i
797797 −11.5000 19.9186i −0.407351 0.705552i 0.587241 0.809412i 0.300214π-0.300214\pi
−0.994592 + 0.103860i 0.966881π0.966881\pi
798798 1.50000 4.33013i 0.0530994 0.153285i
799799 0 0
800800 10.0000 + 17.3205i 0.353553 + 0.612372i
801801 −19.5000 33.7750i −0.688999 1.19338i
802802 −1.50000 + 2.59808i −0.0529668 + 0.0917413i
803803 15.0000 0.529339
804804 6.92820i 0.244339i
805805 7.50000 + 2.59808i 0.264340 + 0.0915702i
806806 0 0
807807 −4.50000 2.59808i −0.158408 0.0914566i
808808 −25.5000 44.1673i −0.897087 1.55380i
809809 4.50000 7.79423i 0.158212 0.274030i −0.776012 0.630718i 0.782761π-0.782761\pi
0.934224 + 0.356687i 0.116094π0.116094\pi
810810 4.50000 7.79423i 0.158114 0.273861i
811811 −28.0000 −0.983213 −0.491606 0.870817i 0.663590π-0.663590\pi
−0.491606 + 0.870817i 0.663590π0.663590\pi
812812 0.500000 + 2.59808i 0.0175466 + 0.0911746i
813813 1.50000 0.866025i 0.0526073 0.0303728i
814814 −7.50000 + 12.9904i −0.262875 + 0.455313i
815815 11.0000 0.385313
816816 4.50000 + 2.59808i 0.157532 + 0.0909509i
817817 −1.00000 −0.0349856
818818 14.0000 0.489499
819819 −37.5000 12.9904i −1.31036 0.453921i
820820 −5.00000 −0.174608
821821 22.0000 0.767805 0.383903 0.923374i 0.374580π-0.374580\pi
0.383903 + 0.923374i 0.374580π0.374580\pi
822822 −13.5000 + 7.79423i −0.470867 + 0.271855i
823823 −24.0000 −0.836587 −0.418294 0.908312i 0.637372π-0.637372\pi
−0.418294 + 0.908312i 0.637372π0.637372\pi
824824 −1.50000 + 2.59808i −0.0522550 + 0.0905083i
825825 30.0000 + 17.3205i 1.04447 + 0.603023i
826826 0 0
827827 −12.0000 −0.417281 −0.208640 0.977992i 0.566904π-0.566904\pi
−0.208640 + 0.977992i 0.566904π0.566904\pi
828828 −4.50000 + 7.79423i −0.156386 + 0.270868i
829829 12.5000 21.6506i 0.434143 0.751958i −0.563082 0.826401i 0.690385π-0.690385\pi
0.997225 + 0.0744432i 0.0237179π0.0237179\pi
830830 −4.50000 7.79423i −0.156197 0.270542i
831831 28.5000 16.4545i 0.988654 0.570800i
832832 17.5000 + 30.3109i 0.606703 + 1.05084i
833833 16.5000 + 12.9904i 0.571691 + 0.450090i
834834 13.5000 7.79423i 0.467467 0.269892i
835835 19.0000 0.657522
836836 2.50000 4.33013i 0.0864643 0.149761i
837837 0 0
838838 −4.50000 7.79423i −0.155450 0.269247i
839839 18.5000 32.0429i 0.638691 1.10625i −0.347029 0.937854i 0.612810π-0.612810\pi
0.985720 0.168391i 0.0538571π-0.0538571\pi
840840 −13.5000 + 2.59808i −0.465794 + 0.0896421i
841841 14.0000 + 24.2487i 0.482759 + 0.836162i
842842 0.500000 0.866025i 0.0172311 0.0298452i
843843 43.5000 + 25.1147i 1.49822 + 0.864997i
844844 6.50000 + 11.2583i 0.223739 + 0.387528i
845845 6.00000 + 10.3923i 0.206406 + 0.357506i
846846 0 0
847847 7.00000 + 36.3731i 0.240523 + 1.24979i
848848 −4.50000 + 7.79423i −0.154531 + 0.267655i
849849 48.4974i 1.66443i
850850 −12.0000 −0.411597
851851 9.00000 0.308516
852852 20.7846i 0.712069i
853853 18.5000 32.0429i 0.633428 1.09713i −0.353418 0.935466i 0.614981π-0.614981\pi
0.986846 0.161664i 0.0516860π-0.0516860\pi
854854 −28.0000 + 24.2487i −0.958140 + 0.829774i
855855 3.00000 0.102598
856856 25.5000 + 44.1673i 0.871572 + 1.50961i
857857 −5.50000 9.52628i −0.187876 0.325412i 0.756666 0.653802i 0.226827π-0.226827\pi
−0.944542 + 0.328391i 0.893494π0.893494\pi
858858 37.5000 + 21.6506i 1.28023 + 0.739140i
859859 0.500000 0.866025i 0.0170598 0.0295484i −0.857369 0.514701i 0.827903π-0.827903\pi
0.874429 + 0.485153i 0.161236π0.161236\pi
860860 0.500000 + 0.866025i 0.0170499 + 0.0295312i
861861 −7.50000 + 21.6506i −0.255599 + 0.737852i
862862 4.50000 7.79423i 0.153271 0.265472i
863863 19.5000 + 33.7750i 0.663788 + 1.14971i 0.979612 + 0.200897i 0.0643855π0.0643855\pi
−0.315825 + 0.948818i 0.602281π0.602281\pi
864864 25.9808i 0.883883i
865865 −7.00000 + 12.1244i −0.238007 + 0.412240i
866866 −14.0000 −0.475739
867867 −12.0000 + 6.92820i −0.407541 + 0.235294i
868868 0 0
869869 −20.0000 34.6410i −0.678454 1.17512i
870870 1.50000 0.866025i 0.0508548 0.0293610i
871871 10.0000 + 17.3205i 0.338837 + 0.586883i
872872 −13.5000 + 23.3827i −0.457168 + 0.791838i
873873 −13.5000 + 23.3827i −0.456906 + 0.791384i
874874 3.00000 0.101477
875875 18.0000 15.5885i 0.608511 0.526986i
876876 4.50000 + 2.59808i 0.152041 + 0.0877809i
877877 26.5000 45.8993i 0.894841 1.54991i 0.0608407 0.998147i 0.480622π-0.480622\pi
0.834001 0.551763i 0.186045π-0.186045\pi
878878 0 0
879879 −7.50000 + 4.33013i −0.252969 + 0.146052i
880880 5.00000 0.168550
881881 −42.0000 −1.41502 −0.707508 0.706705i 0.750181π-0.750181\pi
−0.707508 + 0.706705i 0.750181π0.750181\pi
882882 −3.00000 + 20.7846i −0.101015 + 0.699854i
883883 44.0000 1.48072 0.740359 0.672212i 0.234656π-0.234656\pi
0.740359 + 0.672212i 0.234656π0.234656\pi
884884 15.0000 0.504505
885885 0 0
886886 36.0000 1.20944
887887 14.5000 25.1147i 0.486862 0.843270i −0.513024 0.858375i 0.671475π-0.671475\pi
0.999886 + 0.0151042i 0.00480800π0.00480800\pi
888888 −13.5000 + 7.79423i −0.453030 + 0.261557i
889889 −24.0000 + 20.7846i −0.804934 + 0.697093i
890890 13.0000 0.435761
891891 −22.5000 38.9711i −0.753778 1.30558i
892892 9.50000 16.4545i 0.318084 0.550937i
893893 0 0
894894 −4.50000 2.59808i −0.150503 0.0868927i
895895 9.50000 + 16.4545i 0.317550 + 0.550013i
896896 −6.00000 + 5.19615i −0.200446 + 0.173591i
897897 25.9808i 0.867472i
898898 30.0000 1.00111
899899 0 0
900900 6.00000 + 10.3923i 0.200000 + 0.346410i
901901 13.5000 + 23.3827i 0.449750 + 0.778990i
902902 12.5000 21.6506i 0.416204 0.720887i
903903 4.50000 0.866025i 0.149751 0.0288195i
904904 −1.50000 2.59808i −0.0498893 0.0864107i
905905 −7.00000 + 12.1244i −0.232688 + 0.403027i
906906 7.50000 4.33013i 0.249171 0.143859i
907907 −2.50000 4.33013i −0.0830111 0.143780i 0.821531 0.570164i 0.193120π-0.193120\pi
−0.904542 + 0.426385i 0.859787π0.859787\pi
908908 −1.50000 2.59808i −0.0497792 0.0862202i
909909 −25.5000 44.1673i −0.845782 1.46494i
910910 10.0000 8.66025i 0.331497 0.287085i
911911 −13.5000 + 23.3827i −0.447275 + 0.774703i −0.998208 0.0598468i 0.980939π-0.980939\pi
0.550933 + 0.834550i 0.314272π0.314272\pi
912912 −1.50000 + 0.866025i −0.0496700 + 0.0286770i
913913 −45.0000 −1.48928
914914 22.0000 0.727695
915915 −21.0000 12.1244i −0.694239 0.400819i
916916 −0.500000 + 0.866025i −0.0165205 + 0.0286143i
917917 −0.500000 2.59808i −0.0165115 0.0857960i
918918 13.5000 + 7.79423i 0.445566 + 0.257248i
919919 −8.50000 14.7224i −0.280389 0.485648i 0.691091 0.722767i 0.257130π-0.257130\pi
−0.971481 + 0.237119i 0.923797π0.923797\pi
920920 −4.50000 7.79423i −0.148361 0.256968i
921921 48.4974i 1.59804i
922922 −9.50000 + 16.4545i −0.312866 + 0.541900i
923923 −30.0000 51.9615i −0.987462 1.71033i
924924 −7.50000 + 21.6506i −0.246732 + 0.712254i
925925 6.00000 10.3923i 0.197279 0.341697i
926926 −6.50000 11.2583i −0.213603 0.369972i
927927 −1.50000 + 2.59808i −0.0492665 + 0.0853320i
928928 2.50000 4.33013i 0.0820665 0.142143i
929929 −14.0000 −0.459325 −0.229663 0.973270i 0.573762π-0.573762\pi
−0.229663 + 0.973270i 0.573762π0.573762\pi
930930 0 0
931931 −6.50000 + 2.59808i −0.213029 + 0.0851485i
932932 1.50000 + 2.59808i 0.0491341 + 0.0851028i
933933 0 0
934934 13.5000 + 23.3827i 0.441733 + 0.765105i
935935 7.50000 12.9904i 0.245276 0.424831i
936936 22.5000 + 38.9711i 0.735436 + 1.27381i
937937 42.0000 1.37208 0.686040 0.727564i 0.259347π-0.259347\pi
0.686040 + 0.727564i 0.259347π0.259347\pi
938938 8.00000 6.92820i 0.261209 0.226214i
939939 24.2487i 0.791327i
940940 0 0
941941 −14.0000 −0.456387 −0.228193 0.973616i 0.573282π-0.573282\pi
−0.228193 + 0.973616i 0.573282π0.573282\pi
942942 24.2487i 0.790066i
943943 −15.0000 −0.488467
944944 0 0
945945 −13.5000 + 2.59808i −0.439155 + 0.0845154i
946946 −5.00000 −0.162564
947947 −20.0000 −0.649913 −0.324956 0.945729i 0.605350π-0.605350\pi
−0.324956 + 0.945729i 0.605350π0.605350\pi
948948 13.8564i 0.450035i
949949 −15.0000 −0.486921
950950 2.00000 3.46410i 0.0648886 0.112390i
951951 10.3923i 0.336994i
952952 −4.50000 23.3827i −0.145846 0.757837i
953953 −26.0000 −0.842223 −0.421111 0.907009i 0.638360π-0.638360\pi
−0.421111 + 0.907009i 0.638360π0.638360\pi
954954 −13.5000 + 23.3827i −0.437079 + 0.757042i
955955 4.00000 6.92820i 0.129437 0.224191i
956956 −7.50000 12.9904i −0.242567 0.420139i
957957 8.66025i 0.279946i
958958 −12.5000 21.6506i −0.403857 0.699500i
959959 22.5000 + 7.79423i 0.726563 + 0.251689i
960960 10.5000 + 6.06218i 0.338886 + 0.195656i
961961 −31.0000 −1.00000
962962 7.50000 12.9904i 0.241810 0.418827i
963963 25.5000 + 44.1673i 0.821726 + 1.42327i
964964 5.50000 + 9.52628i 0.177143 + 0.306821i
965965 −5.00000 + 8.66025i −0.160956 + 0.278783i
966966 −13.5000 + 2.59808i −0.434355 + 0.0835917i
967967 −6.50000 11.2583i −0.209026 0.362043i 0.742382 0.669977i 0.233696π-0.233696\pi
−0.951408 + 0.307933i 0.900363π0.900363\pi
968968 21.0000 36.3731i 0.674966 1.16907i
969969 5.19615i 0.166924i
970970 −4.50000 7.79423i −0.144486 0.250258i
971971 −28.5000 49.3634i −0.914609 1.58415i −0.807473 0.589904i 0.799166π-0.799166\pi
−0.107135 0.994244i 0.534168π-0.534168\pi
972972 15.5885i 0.500000i
973973 −22.5000 7.79423i −0.721317 0.249871i
974974 −9.50000 + 16.4545i −0.304400 + 0.527236i
975975 −30.0000 17.3205i −0.960769 0.554700i
976976 14.0000 0.448129
977977 18.0000 0.575871 0.287936 0.957650i 0.407031π-0.407031\pi
0.287936 + 0.957650i 0.407031π0.407031\pi
978978 −16.5000 + 9.52628i −0.527612 + 0.304617i
979979 32.5000 56.2917i 1.03870 1.79909i
980980 5.50000 + 4.33013i 0.175691 + 0.138321i
981981 −13.5000 + 23.3827i −0.431022 + 0.746552i
982982 −6.50000 11.2583i −0.207423 0.359268i
983983 1.50000 + 2.59808i 0.0478426 + 0.0828658i 0.888955 0.457995i 0.151432π-0.151432\pi
−0.841112 + 0.540860i 0.818099π0.818099\pi
984984 22.5000 12.9904i 0.717274 0.414118i
985985 1.00000 1.73205i 0.0318626 0.0551877i
986986 1.50000 + 2.59808i 0.0477697 + 0.0827396i
987987 0 0
988988 −2.50000 + 4.33013i −0.0795356 + 0.137760i
989989 1.50000 + 2.59808i 0.0476972 + 0.0826140i
990990 15.0000 0.476731
991991 18.5000 32.0429i 0.587672 1.01788i −0.406865 0.913488i 0.633378π-0.633378\pi
0.994537 0.104389i 0.0332887π-0.0332887\pi
992992 0 0
993993 13.8564i 0.439720i
994994 −24.0000 + 20.7846i −0.761234 + 0.659248i
995995 1.50000 + 2.59808i 0.0475532 + 0.0823646i
996996 −13.5000 7.79423i −0.427764 0.246970i
997997 8.50000 + 14.7224i 0.269198 + 0.466264i 0.968655 0.248410i 0.0799082π-0.0799082\pi
−0.699457 + 0.714675i 0.746575π0.746575\pi
998998 −15.5000 + 26.8468i −0.490644 + 0.849820i
999999 −13.5000 + 7.79423i −0.427121 + 0.246598i
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 63.2.h.a.25.1 yes 2
3.2 odd 2 189.2.h.a.46.1 2
4.3 odd 2 1008.2.q.c.529.1 2
7.2 even 3 63.2.g.a.16.1 yes 2
7.3 odd 6 441.2.f.a.295.1 2
7.4 even 3 441.2.f.b.295.1 2
7.5 odd 6 441.2.g.a.79.1 2
7.6 odd 2 441.2.h.a.214.1 2
9.2 odd 6 567.2.e.b.487.1 2
9.4 even 3 63.2.g.a.4.1 2
9.5 odd 6 189.2.g.a.172.1 2
9.7 even 3 567.2.e.a.487.1 2
12.11 even 2 3024.2.q.b.2881.1 2
21.2 odd 6 189.2.g.a.100.1 2
21.5 even 6 1323.2.g.a.667.1 2
21.11 odd 6 1323.2.f.a.883.1 2
21.17 even 6 1323.2.f.b.883.1 2
21.20 even 2 1323.2.h.a.802.1 2
28.23 odd 6 1008.2.t.d.961.1 2
36.23 even 6 3024.2.t.d.1873.1 2
36.31 odd 6 1008.2.t.d.193.1 2
63.2 odd 6 567.2.e.b.163.1 2
63.4 even 3 441.2.f.b.148.1 2
63.5 even 6 1323.2.h.a.226.1 2
63.11 odd 6 3969.2.a.c.1.1 1
63.13 odd 6 441.2.g.a.67.1 2
63.16 even 3 567.2.e.a.163.1 2
63.23 odd 6 189.2.h.a.37.1 2
63.25 even 3 3969.2.a.d.1.1 1
63.31 odd 6 441.2.f.a.148.1 2
63.32 odd 6 1323.2.f.a.442.1 2
63.38 even 6 3969.2.a.a.1.1 1
63.40 odd 6 441.2.h.a.373.1 2
63.41 even 6 1323.2.g.a.361.1 2
63.52 odd 6 3969.2.a.f.1.1 1
63.58 even 3 inner 63.2.h.a.58.1 yes 2
63.59 even 6 1323.2.f.b.442.1 2
84.23 even 6 3024.2.t.d.289.1 2
252.23 even 6 3024.2.q.b.2305.1 2
252.247 odd 6 1008.2.q.c.625.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.a.4.1 2 9.4 even 3
63.2.g.a.16.1 yes 2 7.2 even 3
63.2.h.a.25.1 yes 2 1.1 even 1 trivial
63.2.h.a.58.1 yes 2 63.58 even 3 inner
189.2.g.a.100.1 2 21.2 odd 6
189.2.g.a.172.1 2 9.5 odd 6
189.2.h.a.37.1 2 63.23 odd 6
189.2.h.a.46.1 2 3.2 odd 2
441.2.f.a.148.1 2 63.31 odd 6
441.2.f.a.295.1 2 7.3 odd 6
441.2.f.b.148.1 2 63.4 even 3
441.2.f.b.295.1 2 7.4 even 3
441.2.g.a.67.1 2 63.13 odd 6
441.2.g.a.79.1 2 7.5 odd 6
441.2.h.a.214.1 2 7.6 odd 2
441.2.h.a.373.1 2 63.40 odd 6
567.2.e.a.163.1 2 63.16 even 3
567.2.e.a.487.1 2 9.7 even 3
567.2.e.b.163.1 2 63.2 odd 6
567.2.e.b.487.1 2 9.2 odd 6
1008.2.q.c.529.1 2 4.3 odd 2
1008.2.q.c.625.1 2 252.247 odd 6
1008.2.t.d.193.1 2 36.31 odd 6
1008.2.t.d.961.1 2 28.23 odd 6
1323.2.f.a.442.1 2 63.32 odd 6
1323.2.f.a.883.1 2 21.11 odd 6
1323.2.f.b.442.1 2 63.59 even 6
1323.2.f.b.883.1 2 21.17 even 6
1323.2.g.a.361.1 2 63.41 even 6
1323.2.g.a.667.1 2 21.5 even 6
1323.2.h.a.226.1 2 63.5 even 6
1323.2.h.a.802.1 2 21.20 even 2
3024.2.q.b.2305.1 2 252.23 even 6
3024.2.q.b.2881.1 2 12.11 even 2
3024.2.t.d.289.1 2 84.23 even 6
3024.2.t.d.1873.1 2 36.23 even 6
3969.2.a.a.1.1 1 63.38 even 6
3969.2.a.c.1.1 1 63.11 odd 6
3969.2.a.d.1.1 1 63.25 even 3
3969.2.a.f.1.1 1 63.52 odd 6