Properties

Label 722.2.c.f.653.1
Level 722722
Weight 22
Character 722.653
Analytic conductor 5.7655.765
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [722,2,Mod(429,722)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(722, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("722.429");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 722=2192 722 = 2 \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 722.c (of order 33, degree 22, not 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: 5.765199025945.76519902594
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,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 653.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 722.653
Dual form 722.2.c.f.429.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.500000+0.866025i)q2+(0.5000000.866025i)q3+(0.500000+0.866025i)q4+(2.00000+3.46410i)q5+(0.5000000.866025i)q6+3.00000q71.00000q8+(1.000001.73205i)q9+(2.00000+3.46410i)q10+2.00000q11+1.00000q12+(0.500000+0.866025i)q13+(1.50000+2.59808i)q14+(2.000003.46410i)q15+(0.5000000.866025i)q16+(1.500002.59808i)q17+2.00000q184.00000q20+(1.500002.59808i)q21+(1.00000+1.73205i)q22+(0.5000000.866025i)q23+(0.500000+0.866025i)q24+(5.50000+9.52628i)q251.00000q265.00000q27+(1.50000+2.59808i)q28+(2.50000+4.33013i)q29+4.00000q30+8.00000q31+(0.5000000.866025i)q32+(1.000001.73205i)q33+(1.500002.59808i)q34+(6.00000+10.3923i)q35+(1.00000+1.73205i)q36+2.00000q37+1.00000q39+(2.000003.46410i)q40+(4.000006.92820i)q41+(1.500002.59808i)q42+(2.000003.46410i)q43+(1.00000+1.73205i)q44+8.00000q45+1.00000q46+(4.00000+6.92820i)q47+(0.500000+0.866025i)q48+2.00000q4911.0000q50+(1.50000+2.59808i)q51+(0.5000000.866025i)q52+(0.500000+0.866025i)q53+(2.500004.33013i)q54+(4.00000+6.92820i)q553.00000q565.00000q58+(7.50000+12.9904i)q59+(2.00000+3.46410i)q60+(1.00000+1.73205i)q61+(4.00000+6.92820i)q62+(3.000005.19615i)q63+1.00000q644.00000q65+(1.000001.73205i)q66+(1.500002.59808i)q67+3.00000q681.00000q69+(6.00000+10.3923i)q70+(1.00000+1.73205i)q71+(1.00000+1.73205i)q72+(4.500007.79423i)q73+(1.00000+1.73205i)q74+11.0000q75+6.00000q77+(0.500000+0.866025i)q78+(5.000008.66025i)q79+(2.000003.46410i)q80+(0.5000000.866025i)q81+(4.000006.92820i)q826.00000q83+3.00000q84+(6.0000010.3923i)q85+(2.000003.46410i)q86+5.00000q872.00000q88+(4.00000+6.92820i)q90+(1.50000+2.59808i)q91+(0.500000+0.866025i)q92+(4.000006.92820i)q938.00000q941.00000q96+(1.000001.73205i)q97+(1.00000+1.73205i)q98+(2.000003.46410i)q99+O(q100)q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-2.00000 + 3.46410i) q^{10} +2.00000 q^{11} +1.00000 q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.50000 + 2.59808i) q^{14} +(2.00000 - 3.46410i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +2.00000 q^{18} -4.00000 q^{20} +(-1.50000 - 2.59808i) q^{21} +(1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} -1.00000 q^{26} -5.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} +(-2.50000 + 4.33013i) q^{29} +4.00000 q^{30} +8.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(1.50000 - 2.59808i) q^{34} +(6.00000 + 10.3923i) q^{35} +(1.00000 + 1.73205i) q^{36} +2.00000 q^{37} +1.00000 q^{39} +(-2.00000 - 3.46410i) q^{40} +(-4.00000 - 6.92820i) q^{41} +(1.50000 - 2.59808i) q^{42} +(-2.00000 - 3.46410i) q^{43} +(-1.00000 + 1.73205i) q^{44} +8.00000 q^{45} +1.00000 q^{46} +(-4.00000 + 6.92820i) q^{47} +(-0.500000 + 0.866025i) q^{48} +2.00000 q^{49} -11.0000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(-2.50000 - 4.33013i) q^{54} +(4.00000 + 6.92820i) q^{55} -3.00000 q^{56} -5.00000 q^{58} +(7.50000 + 12.9904i) q^{59} +(2.00000 + 3.46410i) q^{60} +(-1.00000 + 1.73205i) q^{61} +(4.00000 + 6.92820i) q^{62} +(3.00000 - 5.19615i) q^{63} +1.00000 q^{64} -4.00000 q^{65} +(1.00000 - 1.73205i) q^{66} +(1.50000 - 2.59808i) q^{67} +3.00000 q^{68} -1.00000 q^{69} +(-6.00000 + 10.3923i) q^{70} +(1.00000 + 1.73205i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(-4.50000 - 7.79423i) q^{73} +(1.00000 + 1.73205i) q^{74} +11.0000 q^{75} +6.00000 q^{77} +(0.500000 + 0.866025i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.00000 - 6.92820i) q^{82} -6.00000 q^{83} +3.00000 q^{84} +(6.00000 - 10.3923i) q^{85} +(2.00000 - 3.46410i) q^{86} +5.00000 q^{87} -2.00000 q^{88} +(4.00000 + 6.92820i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(0.500000 + 0.866025i) q^{92} +(-4.00000 - 6.92820i) q^{93} -8.00000 q^{94} -1.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(1.00000 + 1.73205i) q^{98} +(2.00000 - 3.46410i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q2q3q4+4q5+q6+6q72q8+2q94q10+4q11+2q12q13+3q14+4q15q163q17+4q188q203q21+2q22++4q99+O(q100) 2 q + q^{2} - q^{3} - q^{4} + 4 q^{5} + q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{11} + 2 q^{12} - q^{13} + 3 q^{14} + 4 q^{15} - q^{16} - 3 q^{17} + 4 q^{18} - 8 q^{20} - 3 q^{21} + 2 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/722Z)×\left(\mathbb{Z}/722\mathbb{Z}\right)^\times.

nn 363363
χ(n)\chi(n) e(13)e\left(\frac{1}{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 0.500000 + 0.866025i 0.353553 + 0.612372i
33 −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i 0.259881π-0.259881\pi
−0.973494 + 0.228714i 0.926548π0.926548\pi
44 −0.500000 + 0.866025i −0.250000 + 0.433013i
55 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i 0.185750π0.185750\pi
0.0599153 + 0.998203i 0.480917π0.480917\pi
66 0.500000 0.866025i 0.204124 0.353553i
77 3.00000 1.13389 0.566947 0.823754i 0.308125π-0.308125\pi
0.566947 + 0.823754i 0.308125π0.308125\pi
88 −1.00000 −0.353553
99 1.00000 1.73205i 0.333333 0.577350i
1010 −2.00000 + 3.46410i −0.632456 + 1.09545i
1111 2.00000 0.603023 0.301511 0.953463i 0.402509π-0.402509\pi
0.301511 + 0.953463i 0.402509π0.402509\pi
1212 1.00000 0.288675
1313 −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i 0.877618π-0.877618\pi
0.788320 + 0.615265i 0.210951π0.210951\pi
1414 1.50000 + 2.59808i 0.400892 + 0.694365i
1515 2.00000 3.46410i 0.516398 0.894427i
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i 0.285189π-0.285189\pi
−0.988583 + 0.150675i 0.951855π0.951855\pi
1818 2.00000 0.471405
1919 0 0
2020 −4.00000 −0.894427
2121 −1.50000 2.59808i −0.327327 0.566947i
2222 1.00000 + 1.73205i 0.213201 + 0.369274i
2323 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i 0.800087π-0.800087\pi
0.913434 + 0.406986i 0.133420π0.133420\pi
2424 0.500000 + 0.866025i 0.102062 + 0.176777i
2525 −5.50000 + 9.52628i −1.10000 + 1.90526i
2626 −1.00000 −0.196116
2727 −5.00000 −0.962250
2828 −1.50000 + 2.59808i −0.283473 + 0.490990i
2929 −2.50000 + 4.33013i −0.464238 + 0.804084i −0.999167 0.0408130i 0.987005π-0.987005\pi
0.534928 + 0.844897i 0.320339π0.320339\pi
3030 4.00000 0.730297
3131 8.00000 1.43684 0.718421 0.695608i 0.244865π-0.244865\pi
0.718421 + 0.695608i 0.244865π0.244865\pi
3232 0.500000 0.866025i 0.0883883 0.153093i
3333 −1.00000 1.73205i −0.174078 0.301511i
3434 1.50000 2.59808i 0.257248 0.445566i
3535 6.00000 + 10.3923i 1.01419 + 1.75662i
3636 1.00000 + 1.73205i 0.166667 + 0.288675i
3737 2.00000 0.328798 0.164399 0.986394i 0.447432π-0.447432\pi
0.164399 + 0.986394i 0.447432π0.447432\pi
3838 0 0
3939 1.00000 0.160128
4040 −2.00000 3.46410i −0.316228 0.547723i
4141 −4.00000 6.92820i −0.624695 1.08200i −0.988600 0.150567i 0.951890π-0.951890\pi
0.363905 0.931436i 0.381443π-0.381443\pi
4242 1.50000 2.59808i 0.231455 0.400892i
4343 −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i 0.265322π-0.265322\pi
−0.977261 + 0.212041i 0.931989π0.931989\pi
4444 −1.00000 + 1.73205i −0.150756 + 0.261116i
4545 8.00000 1.19257
4646 1.00000 0.147442
4747 −4.00000 + 6.92820i −0.583460 + 1.01058i 0.411606 + 0.911362i 0.364968π0.364968\pi
−0.995066 + 0.0992202i 0.968365π0.968365\pi
4848 −0.500000 + 0.866025i −0.0721688 + 0.125000i
4949 2.00000 0.285714
5050 −11.0000 −1.55563
5151 −1.50000 + 2.59808i −0.210042 + 0.363803i
5252 −0.500000 0.866025i −0.0693375 0.120096i
5353 −0.500000 + 0.866025i −0.0686803 + 0.118958i −0.898321 0.439340i 0.855212π-0.855212\pi
0.829640 + 0.558298i 0.188546π0.188546\pi
5454 −2.50000 4.33013i −0.340207 0.589256i
5555 4.00000 + 6.92820i 0.539360 + 0.934199i
5656 −3.00000 −0.400892
5757 0 0
5858 −5.00000 −0.656532
5959 7.50000 + 12.9904i 0.976417 + 1.69120i 0.675178 + 0.737655i 0.264067π0.264067\pi
0.301239 + 0.953549i 0.402600π0.402600\pi
6060 2.00000 + 3.46410i 0.258199 + 0.447214i
6161 −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i 0.874201π-0.874201\pi
0.794879 + 0.606768i 0.207534π0.207534\pi
6262 4.00000 + 6.92820i 0.508001 + 0.879883i
6363 3.00000 5.19615i 0.377964 0.654654i
6464 1.00000 0.125000
6565 −4.00000 −0.496139
6666 1.00000 1.73205i 0.123091 0.213201i
6767 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i 0.774670π-0.774670\pi
0.942987 + 0.332830i 0.108004π0.108004\pi
6868 3.00000 0.363803
6969 −1.00000 −0.120386
7070 −6.00000 + 10.3923i −0.717137 + 1.24212i
7171 1.00000 + 1.73205i 0.118678 + 0.205557i 0.919244 0.393688i 0.128801π-0.128801\pi
−0.800566 + 0.599245i 0.795468π0.795468\pi
7272 −1.00000 + 1.73205i −0.117851 + 0.204124i
7373 −4.50000 7.79423i −0.526685 0.912245i −0.999517 0.0310925i 0.990101π-0.990101\pi
0.472831 0.881153i 0.343232π-0.343232\pi
7474 1.00000 + 1.73205i 0.116248 + 0.201347i
7575 11.0000 1.27017
7676 0 0
7777 6.00000 0.683763
7878 0.500000 + 0.866025i 0.0566139 + 0.0980581i
7979 −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i 0.976489π-0.976489\pi
0.434730 0.900561i 0.356844π-0.356844\pi
8080 2.00000 3.46410i 0.223607 0.387298i
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 4.00000 6.92820i 0.441726 0.765092i
8383 −6.00000 −0.658586 −0.329293 0.944228i 0.606810π-0.606810\pi
−0.329293 + 0.944228i 0.606810π0.606810\pi
8484 3.00000 0.327327
8585 6.00000 10.3923i 0.650791 1.12720i
8686 2.00000 3.46410i 0.215666 0.373544i
8787 5.00000 0.536056
8888 −2.00000 −0.213201
8989 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
9090 4.00000 + 6.92820i 0.421637 + 0.730297i
9191 −1.50000 + 2.59808i −0.157243 + 0.272352i
9292 0.500000 + 0.866025i 0.0521286 + 0.0902894i
9393 −4.00000 6.92820i −0.414781 0.718421i
9494 −8.00000 −0.825137
9595 0 0
9696 −1.00000 −0.102062
9797 −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i 0.199042π-0.199042\pi
−0.912317 + 0.409484i 0.865709π0.865709\pi
9898 1.00000 + 1.73205i 0.101015 + 0.174964i
9999 2.00000 3.46410i 0.201008 0.348155i
100100 −5.50000 9.52628i −0.550000 0.952628i
101101 −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i 0.865059π-0.865059\pi
0.811976 + 0.583691i 0.198392π0.198392\pi
102102 −3.00000 −0.297044
103103 6.00000 0.591198 0.295599 0.955312i 0.404481π-0.404481\pi
0.295599 + 0.955312i 0.404481π0.404481\pi
104104 0.500000 0.866025i 0.0490290 0.0849208i
105105 6.00000 10.3923i 0.585540 1.01419i
106106 −1.00000 −0.0971286
107107 7.00000 0.676716 0.338358 0.941018i 0.390129π-0.390129\pi
0.338358 + 0.941018i 0.390129π0.390129\pi
108108 2.50000 4.33013i 0.240563 0.416667i
109109 −7.50000 12.9904i −0.718370 1.24425i −0.961645 0.274296i 0.911555π-0.911555\pi
0.243276 0.969957i 0.421778π-0.421778\pi
110110 −4.00000 + 6.92820i −0.381385 + 0.660578i
111111 −1.00000 1.73205i −0.0949158 0.164399i
112112 −1.50000 2.59808i −0.141737 0.245495i
113113 −14.0000 −1.31701 −0.658505 0.752577i 0.728811π-0.728811\pi
−0.658505 + 0.752577i 0.728811π0.728811\pi
114114 0 0
115115 4.00000 0.373002
116116 −2.50000 4.33013i −0.232119 0.402042i
117117 1.00000 + 1.73205i 0.0924500 + 0.160128i
118118 −7.50000 + 12.9904i −0.690431 + 1.19586i
119119 −4.50000 7.79423i −0.412514 0.714496i
120120 −2.00000 + 3.46410i −0.182574 + 0.316228i
121121 −7.00000 −0.636364
122122 −2.00000 −0.181071
123123 −4.00000 + 6.92820i −0.360668 + 0.624695i
124124 −4.00000 + 6.92820i −0.359211 + 0.622171i
125125 −24.0000 −2.14663
126126 6.00000 0.534522
127127 9.00000 15.5885i 0.798621 1.38325i −0.121894 0.992543i 0.538897π-0.538897\pi
0.920514 0.390709i 0.127770π-0.127770\pi
128128 0.500000 + 0.866025i 0.0441942 + 0.0765466i
129129 −2.00000 + 3.46410i −0.176090 + 0.304997i
130130 −2.00000 3.46410i −0.175412 0.303822i
131131 −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i 0.991023π-0.991023\pi
0.475380 0.879781i 0.342311π-0.342311\pi
132132 2.00000 0.174078
133133 0 0
134134 3.00000 0.259161
135135 −10.0000 17.3205i −0.860663 1.49071i
136136 1.50000 + 2.59808i 0.128624 + 0.222783i
137137 8.50000 14.7224i 0.726204 1.25782i −0.232273 0.972651i 0.574616π-0.574616\pi
0.958477 0.285171i 0.0920506π-0.0920506\pi
138138 −0.500000 0.866025i −0.0425628 0.0737210i
139139 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
140140 −12.0000 −1.01419
141141 8.00000 0.673722
142142 −1.00000 + 1.73205i −0.0839181 + 0.145350i
143143 −1.00000 + 1.73205i −0.0836242 + 0.144841i
144144 −2.00000 −0.166667
145145 −20.0000 −1.66091
146146 4.50000 7.79423i 0.372423 0.645055i
147147 −1.00000 1.73205i −0.0824786 0.142857i
148148 −1.00000 + 1.73205i −0.0821995 + 0.142374i
149149 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
150150 5.50000 + 9.52628i 0.449073 + 0.777817i
151151 −2.00000 −0.162758 −0.0813788 0.996683i 0.525932π-0.525932\pi
−0.0813788 + 0.996683i 0.525932π0.525932\pi
152152 0 0
153153 −6.00000 −0.485071
154154 3.00000 + 5.19615i 0.241747 + 0.418718i
155155 16.0000 + 27.7128i 1.28515 + 2.22595i
156156 −0.500000 + 0.866025i −0.0400320 + 0.0693375i
157157 1.00000 + 1.73205i 0.0798087 + 0.138233i 0.903167 0.429289i 0.141236π-0.141236\pi
−0.823359 + 0.567521i 0.807902π0.807902\pi
158158 5.00000 8.66025i 0.397779 0.688973i
159159 1.00000 0.0793052
160160 4.00000 0.316228
161161 1.50000 2.59808i 0.118217 0.204757i
162162 0.500000 0.866025i 0.0392837 0.0680414i
163163 −16.0000 −1.25322 −0.626608 0.779334i 0.715557π-0.715557\pi
−0.626608 + 0.779334i 0.715557π0.715557\pi
164164 8.00000 0.624695
165165 4.00000 6.92820i 0.311400 0.539360i
166166 −3.00000 5.19615i −0.232845 0.403300i
167167 −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i 0.987025π-0.987025\pi
0.534875 + 0.844931i 0.320359π0.320359\pi
168168 1.50000 + 2.59808i 0.115728 + 0.200446i
169169 6.00000 + 10.3923i 0.461538 + 0.799408i
170170 12.0000 0.920358
171171 0 0
172172 4.00000 0.304997
173173 −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i 0.239913π-0.239913\pi
−0.957241 + 0.289292i 0.906580π0.906580\pi
174174 2.50000 + 4.33013i 0.189525 + 0.328266i
175175 −16.5000 + 28.5788i −1.24728 + 2.16036i
176176 −1.00000 1.73205i −0.0753778 0.130558i
177177 7.50000 12.9904i 0.563735 0.976417i
178178 0 0
179179 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
180180 −4.00000 + 6.92820i −0.298142 + 0.516398i
181181 11.0000 19.0526i 0.817624 1.41617i −0.0898051 0.995959i 0.528624π-0.528624\pi
0.907429 0.420206i 0.138042π-0.138042\pi
182182 −3.00000 −0.222375
183183 2.00000 0.147844
184184 −0.500000 + 0.866025i −0.0368605 + 0.0638442i
185185 4.00000 + 6.92820i 0.294086 + 0.509372i
186186 4.00000 6.92820i 0.293294 0.508001i
187187 −3.00000 5.19615i −0.219382 0.379980i
188188 −4.00000 6.92820i −0.291730 0.505291i
189189 −15.0000 −1.09109
190190 0 0
191191 7.00000 0.506502 0.253251 0.967401i 0.418500π-0.418500\pi
0.253251 + 0.967401i 0.418500π0.418500\pi
192192 −0.500000 0.866025i −0.0360844 0.0625000i
193193 −3.00000 5.19615i −0.215945 0.374027i 0.737620 0.675216i 0.235950π-0.235950\pi
−0.953564 + 0.301189i 0.902616π0.902616\pi
194194 1.00000 1.73205i 0.0717958 0.124354i
195195 2.00000 + 3.46410i 0.143223 + 0.248069i
196196 −1.00000 + 1.73205i −0.0714286 + 0.123718i
197197 8.00000 0.569976 0.284988 0.958531i 0.408010π-0.408010\pi
0.284988 + 0.958531i 0.408010π0.408010\pi
198198 4.00000 0.284268
199199 12.5000 21.6506i 0.886102 1.53477i 0.0416556 0.999132i 0.486737π-0.486737\pi
0.844446 0.535641i 0.179930π-0.179930\pi
200200 5.50000 9.52628i 0.388909 0.673610i
201201 −3.00000 −0.211604
202202 −2.00000 −0.140720
203203 −7.50000 + 12.9904i −0.526397 + 0.911746i
204204 −1.50000 2.59808i −0.105021 0.181902i
205205 16.0000 27.7128i 1.11749 1.93555i
206206 3.00000 + 5.19615i 0.209020 + 0.362033i
207207 −1.00000 1.73205i −0.0695048 0.120386i
208208 1.00000 0.0693375
209209 0 0
210210 12.0000 0.828079
211211 13.5000 + 23.3827i 0.929378 + 1.60973i 0.784364 + 0.620301i 0.212990π0.212990\pi
0.145014 + 0.989430i 0.453677π0.453677\pi
212212 −0.500000 0.866025i −0.0343401 0.0594789i
213213 1.00000 1.73205i 0.0685189 0.118678i
214214 3.50000 + 6.06218i 0.239255 + 0.414402i
215215 8.00000 13.8564i 0.545595 0.944999i
216216 5.00000 0.340207
217217 24.0000 1.62923
218218 7.50000 12.9904i 0.507964 0.879820i
219219 −4.50000 + 7.79423i −0.304082 + 0.526685i
220220 −8.00000 −0.539360
221221 3.00000 0.201802
222222 1.00000 1.73205i 0.0671156 0.116248i
223223 7.00000 + 12.1244i 0.468755 + 0.811907i 0.999362 0.0357107i 0.0113695π-0.0113695\pi
−0.530607 + 0.847618i 0.678036π0.678036\pi
224224 1.50000 2.59808i 0.100223 0.173591i
225225 11.0000 + 19.0526i 0.733333 + 1.27017i
226226 −7.00000 12.1244i −0.465633 0.806500i
227227 17.0000 1.12833 0.564165 0.825662i 0.309198π-0.309198\pi
0.564165 + 0.825662i 0.309198π0.309198\pi
228228 0 0
229229 −10.0000 −0.660819 −0.330409 0.943838i 0.607187π-0.607187\pi
−0.330409 + 0.943838i 0.607187π0.607187\pi
230230 2.00000 + 3.46410i 0.131876 + 0.228416i
231231 −3.00000 5.19615i −0.197386 0.341882i
232232 2.50000 4.33013i 0.164133 0.284287i
233233 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i 0.103697π-0.103697\pi
−0.750867 + 0.660454i 0.770364π0.770364\pi
234234 −1.00000 + 1.73205i −0.0653720 + 0.113228i
235235 −32.0000 −2.08745
236236 −15.0000 −0.976417
237237 −5.00000 + 8.66025i −0.324785 + 0.562544i
238238 4.50000 7.79423i 0.291692 0.505225i
239239 15.0000 0.970269 0.485135 0.874439i 0.338771π-0.338771\pi
0.485135 + 0.874439i 0.338771π0.338771\pi
240240 −4.00000 −0.258199
241241 −4.00000 + 6.92820i −0.257663 + 0.446285i −0.965615 0.259975i 0.916286π-0.916286\pi
0.707953 + 0.706260i 0.249619π0.249619\pi
242242 −3.50000 6.06218i −0.224989 0.389692i
243243 −8.00000 + 13.8564i −0.513200 + 0.888889i
244244 −1.00000 1.73205i −0.0640184 0.110883i
245245 4.00000 + 6.92820i 0.255551 + 0.442627i
246246 −8.00000 −0.510061
247247 0 0
248248 −8.00000 −0.508001
249249 3.00000 + 5.19615i 0.190117 + 0.329293i
250250 −12.0000 20.7846i −0.758947 1.31453i
251251 −1.00000 + 1.73205i −0.0631194 + 0.109326i −0.895858 0.444340i 0.853438π-0.853438\pi
0.832739 + 0.553666i 0.186772π0.186772\pi
252252 3.00000 + 5.19615i 0.188982 + 0.327327i
253253 1.00000 1.73205i 0.0628695 0.108893i
254254 18.0000 1.12942
255255 −12.0000 −0.751469
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 4.00000 6.92820i 0.249513 0.432169i −0.713878 0.700270i 0.753063π-0.753063\pi
0.963391 + 0.268101i 0.0863961π0.0863961\pi
258258 −4.00000 −0.249029
259259 6.00000 0.372822
260260 2.00000 3.46410i 0.124035 0.214834i
261261 5.00000 + 8.66025i 0.309492 + 0.536056i
262262 6.00000 10.3923i 0.370681 0.642039i
263263 −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i 0.901515π-0.901515\pi
0.212565 0.977147i 0.431818π-0.431818\pi
264264 1.00000 + 1.73205i 0.0615457 + 0.106600i
265265 −4.00000 −0.245718
266266 0 0
267267 0 0
268268 1.50000 + 2.59808i 0.0916271 + 0.158703i
269269 15.0000 + 25.9808i 0.914566 + 1.58408i 0.807535 + 0.589819i 0.200801π0.200801\pi
0.107031 + 0.994256i 0.465866π0.465866\pi
270270 10.0000 17.3205i 0.608581 1.05409i
271271 −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i 0.234863π-0.234863\pi
−0.952531 + 0.304443i 0.901530π0.901530\pi
272272 −1.50000 + 2.59808i −0.0909509 + 0.157532i
273273 3.00000 0.181568
274274 17.0000 1.02701
275275 −11.0000 + 19.0526i −0.663325 + 1.14891i
276276 0.500000 0.866025i 0.0300965 0.0521286i
277277 28.0000 1.68236 0.841178 0.540758i 0.181862π-0.181862\pi
0.841178 + 0.540758i 0.181862π0.181862\pi
278278 0 0
279279 8.00000 13.8564i 0.478947 0.829561i
280280 −6.00000 10.3923i −0.358569 0.621059i
281281 −4.00000 + 6.92820i −0.238620 + 0.413302i −0.960319 0.278906i 0.910028π-0.910028\pi
0.721699 + 0.692207i 0.243362π0.243362\pi
282282 4.00000 + 6.92820i 0.238197 + 0.412568i
283283 3.00000 + 5.19615i 0.178331 + 0.308879i 0.941309 0.337546i 0.109597π-0.109597\pi
−0.762978 + 0.646425i 0.776263π0.776263\pi
284284 −2.00000 −0.118678
285285 0 0
286286 −2.00000 −0.118262
287287 −12.0000 20.7846i −0.708338 1.22688i
288288 −1.00000 1.73205i −0.0589256 0.102062i
289289 4.00000 6.92820i 0.235294 0.407541i
290290 −10.0000 17.3205i −0.587220 1.01710i
291291 −1.00000 + 1.73205i −0.0586210 + 0.101535i
292292 9.00000 0.526685
293293 −9.00000 −0.525786 −0.262893 0.964825i 0.584677π-0.584677\pi
−0.262893 + 0.964825i 0.584677π0.584677\pi
294294 1.00000 1.73205i 0.0583212 0.101015i
295295 −30.0000 + 51.9615i −1.74667 + 3.02532i
296296 −2.00000 −0.116248
297297 −10.0000 −0.580259
298298 0 0
299299 0.500000 + 0.866025i 0.0289157 + 0.0500835i
300300 −5.50000 + 9.52628i −0.317543 + 0.550000i
301301 −6.00000 10.3923i −0.345834 0.599002i
302302 −1.00000 1.73205i −0.0575435 0.0996683i
303303 2.00000 0.114897
304304 0 0
305305 −8.00000 −0.458079
306306 −3.00000 5.19615i −0.171499 0.297044i
307307 −6.00000 10.3923i −0.342438 0.593120i 0.642447 0.766330i 0.277919π-0.277919\pi
−0.984885 + 0.173210i 0.944586π0.944586\pi
308308 −3.00000 + 5.19615i −0.170941 + 0.296078i
309309 −3.00000 5.19615i −0.170664 0.295599i
310310 −16.0000 + 27.7128i −0.908739 + 1.57398i
311311 7.00000 0.396934 0.198467 0.980108i 0.436404π-0.436404\pi
0.198467 + 0.980108i 0.436404π0.436404\pi
312312 −1.00000 −0.0566139
313313 −14.5000 + 25.1147i −0.819588 + 1.41957i 0.0863973 + 0.996261i 0.472465π0.472465\pi
−0.905986 + 0.423308i 0.860869π0.860869\pi
314314 −1.00000 + 1.73205i −0.0564333 + 0.0977453i
315315 24.0000 1.35225
316316 10.0000 0.562544
317317 −13.5000 + 23.3827i −0.758236 + 1.31330i 0.185514 + 0.982642i 0.440605π0.440605\pi
−0.943750 + 0.330661i 0.892728π0.892728\pi
318318 0.500000 + 0.866025i 0.0280386 + 0.0485643i
319319 −5.00000 + 8.66025i −0.279946 + 0.484881i
320320 2.00000 + 3.46410i 0.111803 + 0.193649i
321321 −3.50000 6.06218i −0.195351 0.338358i
322322 3.00000 0.167183
323323 0 0
324324 1.00000 0.0555556
325325 −5.50000 9.52628i −0.305085 0.528423i
326326 −8.00000 13.8564i −0.443079 0.767435i
327327 −7.50000 + 12.9904i −0.414751 + 0.718370i
328328 4.00000 + 6.92820i 0.220863 + 0.382546i
329329 −12.0000 + 20.7846i −0.661581 + 1.14589i
330330 8.00000 0.440386
331331 −17.0000 −0.934405 −0.467202 0.884150i 0.654738π-0.654738\pi
−0.467202 + 0.884150i 0.654738π0.654738\pi
332332 3.00000 5.19615i 0.164646 0.285176i
333333 2.00000 3.46410i 0.109599 0.189832i
334334 −12.0000 −0.656611
335335 12.0000 0.655630
336336 −1.50000 + 2.59808i −0.0818317 + 0.141737i
337337 −16.0000 27.7128i −0.871576 1.50961i −0.860366 0.509676i 0.829765π-0.829765\pi
−0.0112091 0.999937i 0.503568π-0.503568\pi
338338 −6.00000 + 10.3923i −0.326357 + 0.565267i
339339 7.00000 + 12.1244i 0.380188 + 0.658505i
340340 6.00000 + 10.3923i 0.325396 + 0.563602i
341341 16.0000 0.866449
342342 0 0
343343 −15.0000 −0.809924
344344 2.00000 + 3.46410i 0.107833 + 0.186772i
345345 −2.00000 3.46410i −0.107676 0.186501i
346346 3.00000 5.19615i 0.161281 0.279347i
347347 1.00000 + 1.73205i 0.0536828 + 0.0929814i 0.891618 0.452788i 0.149571π-0.149571\pi
−0.837935 + 0.545770i 0.816237π0.816237\pi
348348 −2.50000 + 4.33013i −0.134014 + 0.232119i
349349 10.0000 0.535288 0.267644 0.963518i 0.413755π-0.413755\pi
0.267644 + 0.963518i 0.413755π0.413755\pi
350350 −33.0000 −1.76392
351351 2.50000 4.33013i 0.133440 0.231125i
352352 1.00000 1.73205i 0.0533002 0.0923186i
353353 9.00000 0.479022 0.239511 0.970894i 0.423013π-0.423013\pi
0.239511 + 0.970894i 0.423013π0.423013\pi
354354 15.0000 0.797241
355355 −4.00000 + 6.92820i −0.212298 + 0.367711i
356356 0 0
357357 −4.50000 + 7.79423i −0.238165 + 0.412514i
358358 0 0
359359 7.50000 + 12.9904i 0.395835 + 0.685606i 0.993207 0.116358i 0.0371219π-0.0371219\pi
−0.597372 + 0.801964i 0.703789π0.703789\pi
360360 −8.00000 −0.421637
361361 0 0
362362 22.0000 1.15629
363363 3.50000 + 6.06218i 0.183702 + 0.318182i
364364 −1.50000 2.59808i −0.0786214 0.136176i
365365 18.0000 31.1769i 0.942163 1.63187i
366366 1.00000 + 1.73205i 0.0522708 + 0.0905357i
367367 −14.0000 + 24.2487i −0.730794 + 1.26577i 0.225750 + 0.974185i 0.427517π0.427517\pi
−0.956544 + 0.291587i 0.905817π0.905817\pi
368368 −1.00000 −0.0521286
369369 −16.0000 −0.832927
370370 −4.00000 + 6.92820i −0.207950 + 0.360180i
371371 −1.50000 + 2.59808i −0.0778761 + 0.134885i
372372 8.00000 0.414781
373373 −29.0000 −1.50156 −0.750782 0.660551i 0.770323π-0.770323\pi
−0.750782 + 0.660551i 0.770323π0.770323\pi
374374 3.00000 5.19615i 0.155126 0.268687i
375375 12.0000 + 20.7846i 0.619677 + 1.07331i
376376 4.00000 6.92820i 0.206284 0.357295i
377377 −2.50000 4.33013i −0.128757 0.223013i
378378 −7.50000 12.9904i −0.385758 0.668153i
379379 −15.0000 −0.770498 −0.385249 0.922813i 0.625884π-0.625884\pi
−0.385249 + 0.922813i 0.625884π0.625884\pi
380380 0 0
381381 −18.0000 −0.922168
382382 3.50000 + 6.06218i 0.179076 + 0.310168i
383383 −13.0000 22.5167i −0.664269 1.15055i −0.979483 0.201527i 0.935410π-0.935410\pi
0.315214 0.949021i 0.397924π-0.397924\pi
384384 0.500000 0.866025i 0.0255155 0.0441942i
385385 12.0000 + 20.7846i 0.611577 + 1.05928i
386386 3.00000 5.19615i 0.152696 0.264477i
387387 −8.00000 −0.406663
388388 2.00000 0.101535
389389 15.0000 25.9808i 0.760530 1.31728i −0.182047 0.983290i 0.558272π-0.558272\pi
0.942578 0.333987i 0.108394π-0.108394\pi
390390 −2.00000 + 3.46410i −0.101274 + 0.175412i
391391 −3.00000 −0.151717
392392 −2.00000 −0.101015
393393 −6.00000 + 10.3923i −0.302660 + 0.524222i
394394 4.00000 + 6.92820i 0.201517 + 0.349038i
395395 20.0000 34.6410i 1.00631 1.74298i
396396 2.00000 + 3.46410i 0.100504 + 0.174078i
397397 −4.00000 6.92820i −0.200754 0.347717i 0.748017 0.663679i 0.231006π-0.231006\pi
−0.948772 + 0.315963i 0.897673π0.897673\pi
398398 25.0000 1.25314
399399 0 0
400400 11.0000 0.550000
401401 −4.00000 6.92820i −0.199750 0.345978i 0.748697 0.662912i 0.230680π-0.230680\pi
−0.948447 + 0.316934i 0.897346π0.897346\pi
402402 −1.50000 2.59808i −0.0748132 0.129580i
403403 −4.00000 + 6.92820i −0.199254 + 0.345118i
404404 −1.00000 1.73205i −0.0497519 0.0861727i
405405 2.00000 3.46410i 0.0993808 0.172133i
406406 −15.0000 −0.744438
407407 4.00000 0.198273
408408 1.50000 2.59808i 0.0742611 0.128624i
409409 −10.0000 + 17.3205i −0.494468 + 0.856444i −0.999980 0.00637586i 0.997970π-0.997970\pi
0.505511 + 0.862820i 0.331304π0.331304\pi
410410 32.0000 1.58037
411411 −17.0000 −0.838548
412412 −3.00000 + 5.19615i −0.147799 + 0.255996i
413413 22.5000 + 38.9711i 1.10715 + 1.91764i
414414 1.00000 1.73205i 0.0491473 0.0851257i
415415 −12.0000 20.7846i −0.589057 1.02028i
416416 0.500000 + 0.866025i 0.0245145 + 0.0424604i
417417 0 0
418418 0 0
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 6.00000 + 10.3923i 0.292770 + 0.507093i
421421 −6.50000 11.2583i −0.316791 0.548697i 0.663026 0.748596i 0.269272π-0.269272\pi
−0.979817 + 0.199899i 0.935939π0.935939\pi
422422 −13.5000 + 23.3827i −0.657170 + 1.13825i
423423 8.00000 + 13.8564i 0.388973 + 0.673722i
424424 0.500000 0.866025i 0.0242821 0.0420579i
425425 33.0000 1.60074
426426 2.00000 0.0969003
427427 −3.00000 + 5.19615i −0.145180 + 0.251459i
428428 −3.50000 + 6.06218i −0.169179 + 0.293026i
429429 2.00000 0.0965609
430430 16.0000 0.771589
431431 −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i 0.976060π-0.976060\pi
0.563658 + 0.826008i 0.309393π0.309393\pi
432432 2.50000 + 4.33013i 0.120281 + 0.208333i
433433 7.00000 12.1244i 0.336399 0.582659i −0.647354 0.762190i 0.724124π-0.724124\pi
0.983752 + 0.179530i 0.0574578π0.0574578\pi
434434 12.0000 + 20.7846i 0.576018 + 0.997693i
435435 10.0000 + 17.3205i 0.479463 + 0.830455i
436436 15.0000 0.718370
437437 0 0
438438 −9.00000 −0.430037
439439 10.0000 + 17.3205i 0.477274 + 0.826663i 0.999661 0.0260459i 0.00829161π-0.00829161\pi
−0.522387 + 0.852709i 0.674958π0.674958\pi
440440 −4.00000 6.92820i −0.190693 0.330289i
441441 2.00000 3.46410i 0.0952381 0.164957i
442442 1.50000 + 2.59808i 0.0713477 + 0.123578i
443443 13.0000 22.5167i 0.617649 1.06980i −0.372265 0.928126i 0.621419π-0.621419\pi
0.989914 0.141672i 0.0452479π-0.0452479\pi
444444 2.00000 0.0949158
445445 0 0
446446 −7.00000 + 12.1244i −0.331460 + 0.574105i
447447 0 0
448448 3.00000 0.141737
449449 −10.0000 −0.471929 −0.235965 0.971762i 0.575825π-0.575825\pi
−0.235965 + 0.971762i 0.575825π0.575825\pi
450450 −11.0000 + 19.0526i −0.518545 + 0.898146i
451451 −8.00000 13.8564i −0.376705 0.652473i
452452 7.00000 12.1244i 0.329252 0.570282i
453453 1.00000 + 1.73205i 0.0469841 + 0.0813788i
454454 8.50000 + 14.7224i 0.398925 + 0.690958i
455455 −12.0000 −0.562569
456456 0 0
457457 −7.00000 −0.327446 −0.163723 0.986506i 0.552350π-0.552350\pi
−0.163723 + 0.986506i 0.552350π0.552350\pi
458458 −5.00000 8.66025i −0.233635 0.404667i
459459 7.50000 + 12.9904i 0.350070 + 0.606339i
460460 −2.00000 + 3.46410i −0.0932505 + 0.161515i
461461 14.0000 + 24.2487i 0.652045 + 1.12938i 0.982626 + 0.185597i 0.0594220π0.0594220\pi
−0.330581 + 0.943778i 0.607245π0.607245\pi
462462 3.00000 5.19615i 0.139573 0.241747i
463463 4.00000 0.185896 0.0929479 0.995671i 0.470371π-0.470371\pi
0.0929479 + 0.995671i 0.470371π0.470371\pi
464464 5.00000 0.232119
465465 16.0000 27.7128i 0.741982 1.28515i
466466 −3.00000 + 5.19615i −0.138972 + 0.240707i
467467 −2.00000 −0.0925490 −0.0462745 0.998929i 0.514735π-0.514735\pi
−0.0462745 + 0.998929i 0.514735π0.514735\pi
468468 −2.00000 −0.0924500
469469 4.50000 7.79423i 0.207791 0.359904i
470470 −16.0000 27.7128i −0.738025 1.27830i
471471 1.00000 1.73205i 0.0460776 0.0798087i
472472 −7.50000 12.9904i −0.345215 0.597931i
473473 −4.00000 6.92820i −0.183920 0.318559i
474474 −10.0000 −0.459315
475475 0 0
476476 9.00000 0.412514
477477 1.00000 + 1.73205i 0.0457869 + 0.0793052i
478478 7.50000 + 12.9904i 0.343042 + 0.594166i
479479 10.0000 17.3205i 0.456912 0.791394i −0.541884 0.840453i 0.682289π-0.682289\pi
0.998796 + 0.0490589i 0.0156222π0.0156222\pi
480480 −2.00000 3.46410i −0.0912871 0.158114i
481481 −1.00000 + 1.73205i −0.0455961 + 0.0789747i
482482 −8.00000 −0.364390
483483 −3.00000 −0.136505
484484 3.50000 6.06218i 0.159091 0.275554i
485485 4.00000 6.92820i 0.181631 0.314594i
486486 −16.0000 −0.725775
487487 2.00000 0.0906287 0.0453143 0.998973i 0.485571π-0.485571\pi
0.0453143 + 0.998973i 0.485571π0.485571\pi
488488 1.00000 1.73205i 0.0452679 0.0784063i
489489 8.00000 + 13.8564i 0.361773 + 0.626608i
490490 −4.00000 + 6.92820i −0.180702 + 0.312984i
491491 14.0000 + 24.2487i 0.631811 + 1.09433i 0.987181 + 0.159603i 0.0510215π0.0510215\pi
−0.355370 + 0.934726i 0.615645π0.615645\pi
492492 −4.00000 6.92820i −0.180334 0.312348i
493493 15.0000 0.675566
494494 0 0
495495 16.0000 0.719147
496496 −4.00000 6.92820i −0.179605 0.311086i
497497 3.00000 + 5.19615i 0.134568 + 0.233079i
498498 −3.00000 + 5.19615i −0.134433 + 0.232845i
499499 −20.0000 34.6410i −0.895323 1.55074i −0.833404 0.552664i 0.813611π-0.813611\pi
−0.0619186 0.998081i 0.519722π-0.519722\pi
500500 12.0000 20.7846i 0.536656 0.929516i
501501 12.0000 0.536120
502502 −2.00000 −0.0892644
503503 −19.5000 + 33.7750i −0.869462 + 1.50595i −0.00691465 + 0.999976i 0.502201π0.502201\pi
−0.862547 + 0.505976i 0.831132π0.831132\pi
504504 −3.00000 + 5.19615i −0.133631 + 0.231455i
505505 −8.00000 −0.355995
506506 2.00000 0.0889108
507507 6.00000 10.3923i 0.266469 0.461538i
508508 9.00000 + 15.5885i 0.399310 + 0.691626i
509509 −15.0000 + 25.9808i −0.664863 + 1.15158i 0.314459 + 0.949271i 0.398177π0.398177\pi
−0.979322 + 0.202306i 0.935156π0.935156\pi
510510 −6.00000 10.3923i −0.265684 0.460179i
511511 −13.5000 23.3827i −0.597205 1.03439i
512512 −1.00000 −0.0441942
513513 0 0
514514 8.00000 0.352865
515515 12.0000 + 20.7846i 0.528783 + 0.915879i
516516 −2.00000 3.46410i −0.0880451 0.152499i
517517 −8.00000 + 13.8564i −0.351840 + 0.609404i
518518 3.00000 + 5.19615i 0.131812 + 0.228306i
519519 −3.00000 + 5.19615i −0.131685 + 0.228086i
520520 4.00000 0.175412
521521 28.0000 1.22670 0.613351 0.789810i 0.289821π-0.289821\pi
0.613351 + 0.789810i 0.289821π0.289821\pi
522522 −5.00000 + 8.66025i −0.218844 + 0.379049i
523523 14.5000 25.1147i 0.634041 1.09819i −0.352677 0.935745i 0.614728π-0.614728\pi
0.986718 0.162446i 0.0519382π-0.0519382\pi
524524 12.0000 0.524222
525525 33.0000 1.44024
526526 12.0000 20.7846i 0.523225 0.906252i
527527 −12.0000 20.7846i −0.522728 0.905392i
528528 −1.00000 + 1.73205i −0.0435194 + 0.0753778i
529529 11.0000 + 19.0526i 0.478261 + 0.828372i
530530 −2.00000 3.46410i −0.0868744 0.150471i
531531 30.0000 1.30189
532532 0 0
533533 8.00000 0.346518
534534 0 0
535535 14.0000 + 24.2487i 0.605273 + 1.04836i
536536 −1.50000 + 2.59808i −0.0647901 + 0.112220i
537537 0 0
538538 −15.0000 + 25.9808i −0.646696 + 1.12011i
539539 4.00000 0.172292
540540 20.0000 0.860663
541541 −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i 0.847023π-0.847023\pi
0.843728 + 0.536771i 0.180356π0.180356\pi
542542 3.50000 6.06218i 0.150338 0.260393i
543543 −22.0000 −0.944110
544544 −3.00000 −0.128624
545545 30.0000 51.9615i 1.28506 2.22579i
546546 1.50000 + 2.59808i 0.0641941 + 0.111187i
547547 14.0000 24.2487i 0.598597 1.03680i −0.394432 0.918925i 0.629059π-0.629059\pi
0.993028 0.117875i 0.0376081π-0.0376081\pi
548548 8.50000 + 14.7224i 0.363102 + 0.628911i
549549 2.00000 + 3.46410i 0.0853579 + 0.147844i
550550 −22.0000 −0.938083
551551 0 0
552552 1.00000 0.0425628
553553 −15.0000 25.9808i −0.637865 1.10481i
554554 14.0000 + 24.2487i 0.594803 + 1.03023i
555555 4.00000 6.92820i 0.169791 0.294086i
556556 0 0
557557 −14.0000 + 24.2487i −0.593199 + 1.02745i 0.400599 + 0.916253i 0.368802π0.368802\pi
−0.993798 + 0.111198i 0.964531π0.964531\pi
558558 16.0000 0.677334
559559 4.00000 0.169182
560560 6.00000 10.3923i 0.253546 0.439155i
561561 −3.00000 + 5.19615i −0.126660 + 0.219382i
562562 −8.00000 −0.337460
563563 36.0000 1.51722 0.758610 0.651546i 0.225879π-0.225879\pi
0.758610 + 0.651546i 0.225879π0.225879\pi
564564 −4.00000 + 6.92820i −0.168430 + 0.291730i
565565 −28.0000 48.4974i −1.17797 2.04030i
566566 −3.00000 + 5.19615i −0.126099 + 0.218411i
567567 −1.50000 2.59808i −0.0629941 0.109109i
568568 −1.00000 1.73205i −0.0419591 0.0726752i
569569 −40.0000 −1.67689 −0.838444 0.544988i 0.816534π-0.816534\pi
−0.838444 + 0.544988i 0.816534π0.816534\pi
570570 0 0
571571 −28.0000 −1.17176 −0.585882 0.810397i 0.699252π-0.699252\pi
−0.585882 + 0.810397i 0.699252π0.699252\pi
572572 −1.00000 1.73205i −0.0418121 0.0724207i
573573 −3.50000 6.06218i −0.146215 0.253251i
574574 12.0000 20.7846i 0.500870 0.867533i
575575 5.50000 + 9.52628i 0.229366 + 0.397273i
576576 1.00000 1.73205i 0.0416667 0.0721688i
577577 −37.0000 −1.54033 −0.770165 0.637845i 0.779826π-0.779826\pi
−0.770165 + 0.637845i 0.779826π0.779826\pi
578578 8.00000 0.332756
579579 −3.00000 + 5.19615i −0.124676 + 0.215945i
580580 10.0000 17.3205i 0.415227 0.719195i
581581 −18.0000 −0.746766
582582 −2.00000 −0.0829027
583583 −1.00000 + 1.73205i −0.0414158 + 0.0717342i
584584 4.50000 + 7.79423i 0.186211 + 0.322527i
585585 −4.00000 + 6.92820i −0.165380 + 0.286446i
586586 −4.50000 7.79423i −0.185893 0.321977i
587587 6.00000 + 10.3923i 0.247647 + 0.428936i 0.962872 0.269957i 0.0870095π-0.0870095\pi
−0.715226 + 0.698893i 0.753676π0.753676\pi
588588 2.00000 0.0824786
589589 0 0
590590 −60.0000 −2.47016
591591 −4.00000 6.92820i −0.164538 0.284988i
592592 −1.00000 1.73205i −0.0410997 0.0711868i
593593 −17.0000 + 29.4449i −0.698106 + 1.20916i 0.271016 + 0.962575i 0.412640π0.412640\pi
−0.969122 + 0.246581i 0.920693π0.920693\pi
594594 −5.00000 8.66025i −0.205152 0.355335i
595595 18.0000 31.1769i 0.737928 1.27813i
596596 0 0
597597 −25.0000 −1.02318
598598 −0.500000 + 0.866025i −0.0204465 + 0.0354144i
599599 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
600600 −11.0000 −0.449073
601601 8.00000 0.326327 0.163163 0.986599i 0.447830π-0.447830\pi
0.163163 + 0.986599i 0.447830π0.447830\pi
602602 6.00000 10.3923i 0.244542 0.423559i
603603 −3.00000 5.19615i −0.122169 0.211604i
604604 1.00000 1.73205i 0.0406894 0.0704761i
605605 −14.0000 24.2487i −0.569181 0.985850i
606606 1.00000 + 1.73205i 0.0406222 + 0.0703598i
607607 22.0000 0.892952 0.446476 0.894795i 0.352679π-0.352679\pi
0.446476 + 0.894795i 0.352679π0.352679\pi
608608 0 0
609609 15.0000 0.607831
610610 −4.00000 6.92820i −0.161955 0.280515i
611611 −4.00000 6.92820i −0.161823 0.280285i
612612 3.00000 5.19615i 0.121268 0.210042i
613613 −17.0000 29.4449i −0.686624 1.18927i −0.972924 0.231127i 0.925759π-0.925759\pi
0.286300 0.958140i 0.407575π-0.407575\pi
614614 6.00000 10.3923i 0.242140 0.419399i
615615 −32.0000 −1.29036
616616 −6.00000 −0.241747
617617 −9.00000 + 15.5885i −0.362326 + 0.627568i −0.988343 0.152242i 0.951351π-0.951351\pi
0.626017 + 0.779809i 0.284684π0.284684\pi
618618 3.00000 5.19615i 0.120678 0.209020i
619619 10.0000 0.401934 0.200967 0.979598i 0.435592π-0.435592\pi
0.200967 + 0.979598i 0.435592π0.435592\pi
620620 −32.0000 −1.28515
621621 −2.50000 + 4.33013i −0.100322 + 0.173762i
622622 3.50000 + 6.06218i 0.140337 + 0.243071i
623623 0 0
624624 −0.500000 0.866025i −0.0200160 0.0346688i
625625 −20.5000 35.5070i −0.820000 1.42028i
626626 −29.0000 −1.15907
627627 0 0
628628 −2.00000 −0.0798087
629629 −3.00000 5.19615i −0.119618 0.207184i
630630 12.0000 + 20.7846i 0.478091 + 0.828079i
631631 −16.0000 + 27.7128i −0.636950 + 1.10323i 0.349148 + 0.937067i 0.386471π0.386471\pi
−0.986098 + 0.166162i 0.946862π0.946862\pi
632632 5.00000 + 8.66025i 0.198889 + 0.344486i
633633 13.5000 23.3827i 0.536577 0.929378i
634634 −27.0000 −1.07231
635635 72.0000 2.85723
636636 −0.500000 + 0.866025i −0.0198263 + 0.0343401i
637637 −1.00000 + 1.73205i −0.0396214 + 0.0686264i
638638 −10.0000 −0.395904
639639 4.00000 0.158238
640640 −2.00000 + 3.46410i −0.0790569 + 0.136931i
641641 21.0000 + 36.3731i 0.829450 + 1.43665i 0.898470 + 0.439034i 0.144679π0.144679\pi
−0.0690201 + 0.997615i 0.521987π0.521987\pi
642642 3.50000 6.06218i 0.138134 0.239255i
643643 13.0000 + 22.5167i 0.512670 + 0.887970i 0.999892 + 0.0146923i 0.00467688π0.00467688\pi
−0.487222 + 0.873278i 0.661990π0.661990\pi
644644 1.50000 + 2.59808i 0.0591083 + 0.102379i
645645 −16.0000 −0.629999
646646 0 0
647647 23.0000 0.904223 0.452112 0.891961i 0.350671π-0.350671\pi
0.452112 + 0.891961i 0.350671π0.350671\pi
648648 0.500000 + 0.866025i 0.0196419 + 0.0340207i
649649 15.0000 + 25.9808i 0.588802 + 1.01983i
650650 5.50000 9.52628i 0.215728 0.373651i
651651 −12.0000 20.7846i −0.470317 0.814613i
652652 8.00000 13.8564i 0.313304 0.542659i
653653 −36.0000 −1.40879 −0.704394 0.709809i 0.748781π-0.748781\pi
−0.704394 + 0.709809i 0.748781π0.748781\pi
654654 −15.0000 −0.586546
655655 24.0000 41.5692i 0.937758 1.62424i
656656 −4.00000 + 6.92820i −0.156174 + 0.270501i
657657 −18.0000 −0.702247
658658 −24.0000 −0.935617
659659 2.50000 4.33013i 0.0973862 0.168678i −0.813216 0.581962i 0.802285π-0.802285\pi
0.910602 + 0.413284i 0.135618π0.135618\pi
660660 4.00000 + 6.92820i 0.155700 + 0.269680i
661661 −11.5000 + 19.9186i −0.447298 + 0.774743i −0.998209 0.0598209i 0.980947π-0.980947\pi
0.550911 + 0.834564i 0.314280π0.314280\pi
662662 −8.50000 14.7224i −0.330362 0.572204i
663663 −1.50000 2.59808i −0.0582552 0.100901i
664664 6.00000 0.232845
665665 0 0
666666 4.00000 0.154997
667667 2.50000 + 4.33013i 0.0968004 + 0.167663i
668668 −6.00000 10.3923i −0.232147 0.402090i
669669 7.00000 12.1244i 0.270636 0.468755i
670670 6.00000 + 10.3923i 0.231800 + 0.401490i
671671 −2.00000 + 3.46410i −0.0772091 + 0.133730i
672672 −3.00000 −0.115728
673673 −44.0000 −1.69608 −0.848038 0.529936i 0.822216π-0.822216\pi
−0.848038 + 0.529936i 0.822216π0.822216\pi
674674 16.0000 27.7128i 0.616297 1.06746i
675675 27.5000 47.6314i 1.05848 1.83333i
676676 −12.0000 −0.461538
677677 −13.0000 −0.499631 −0.249815 0.968294i 0.580370π-0.580370\pi
−0.249815 + 0.968294i 0.580370π0.580370\pi
678678 −7.00000 + 12.1244i −0.268833 + 0.465633i
679679 −3.00000 5.19615i −0.115129 0.199410i
680680 −6.00000 + 10.3923i −0.230089 + 0.398527i
681681 −8.50000 14.7224i −0.325721 0.564165i
682682 8.00000 + 13.8564i 0.306336 + 0.530589i
683683 −4.00000 −0.153056 −0.0765279 0.997067i 0.524383π-0.524383\pi
−0.0765279 + 0.997067i 0.524383π0.524383\pi
684684 0 0
685685 68.0000 2.59815
686686 −7.50000 12.9904i −0.286351 0.495975i
687687 5.00000 + 8.66025i 0.190762 + 0.330409i
688688 −2.00000 + 3.46410i −0.0762493 + 0.132068i
689689 −0.500000 0.866025i −0.0190485 0.0329929i
690690 2.00000 3.46410i 0.0761387 0.131876i
691691 42.0000 1.59776 0.798878 0.601494i 0.205427π-0.205427\pi
0.798878 + 0.601494i 0.205427π0.205427\pi
692692 6.00000 0.228086
693693 6.00000 10.3923i 0.227921 0.394771i
694694 −1.00000 + 1.73205i −0.0379595 + 0.0657477i
695695 0 0
696696 −5.00000 −0.189525
697697 −12.0000 + 20.7846i −0.454532 + 0.787273i
698698 5.00000 + 8.66025i 0.189253 + 0.327795i
699699 3.00000 5.19615i 0.113470 0.196537i
700700 −16.5000 28.5788i −0.623641 1.08018i
701701 14.0000 + 24.2487i 0.528773 + 0.915861i 0.999437 + 0.0335489i 0.0106809π0.0106809\pi
−0.470664 + 0.882312i 0.655986π0.655986\pi
702702 5.00000 0.188713
703703 0 0
704704 2.00000 0.0753778
705705 16.0000 + 27.7128i 0.602595 + 1.04372i
706706 4.50000 + 7.79423i 0.169360 + 0.293340i
707707 −3.00000 + 5.19615i −0.112827 + 0.195421i
708708 7.50000 + 12.9904i 0.281867 + 0.488208i
709709 15.0000 25.9808i 0.563337 0.975728i −0.433865 0.900978i 0.642851π-0.642851\pi
0.997202 0.0747503i 0.0238160π-0.0238160\pi
710710 −8.00000 −0.300235
711711 −20.0000 −0.750059
712712 0 0
713713 4.00000 6.92820i 0.149801 0.259463i
714714 −9.00000 −0.336817
715715 −8.00000 −0.299183
716716 0 0
717717 −7.50000 12.9904i −0.280093 0.485135i
718718 −7.50000 + 12.9904i −0.279898 + 0.484797i
719719 2.50000 + 4.33013i 0.0932343 + 0.161486i 0.908870 0.417079i 0.136946π-0.136946\pi
−0.815636 + 0.578565i 0.803613π0.803613\pi
720720 −4.00000 6.92820i −0.149071 0.258199i
721721 18.0000 0.670355
722722 0 0
723723 8.00000 0.297523
724724 11.0000 + 19.0526i 0.408812 + 0.708083i
725725 −27.5000 47.6314i −1.02132 1.76899i
726726 −3.50000 + 6.06218i −0.129897 + 0.224989i
727727 8.50000 + 14.7224i 0.315248 + 0.546025i 0.979490 0.201492i 0.0645791π-0.0645791\pi
−0.664243 + 0.747517i 0.731246π0.731246\pi
728728 1.50000 2.59808i 0.0555937 0.0962911i
729729 13.0000 0.481481
730730 36.0000 1.33242
731731 −6.00000 + 10.3923i −0.221918 + 0.384373i
732732 −1.00000 + 1.73205i −0.0369611 + 0.0640184i
733733 −36.0000 −1.32969 −0.664845 0.746981i 0.731502π-0.731502\pi
−0.664845 + 0.746981i 0.731502π0.731502\pi
734734 −28.0000 −1.03350
735735 4.00000 6.92820i 0.147542 0.255551i
736736 −0.500000 0.866025i −0.0184302 0.0319221i
737737 3.00000 5.19615i 0.110506 0.191403i
738738 −8.00000 13.8564i −0.294484 0.510061i
739739 20.0000 + 34.6410i 0.735712 + 1.27429i 0.954410 + 0.298498i 0.0964856π0.0964856\pi
−0.218698 + 0.975793i 0.570181π0.570181\pi
740740 −8.00000 −0.294086
741741 0 0
742742 −3.00000 −0.110133
743743 −8.00000 13.8564i −0.293492 0.508342i 0.681141 0.732152i 0.261484π-0.261484\pi
−0.974633 + 0.223810i 0.928151π0.928151\pi
744744 4.00000 + 6.92820i 0.146647 + 0.254000i
745745 0 0
746746 −14.5000 25.1147i −0.530883 0.919516i
747747 −6.00000 + 10.3923i −0.219529 + 0.380235i
748748 6.00000 0.219382
749749 21.0000 0.767323
750750 −12.0000 + 20.7846i −0.438178 + 0.758947i
751751 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i 0.634880π-0.634880\pi
0.995018 0.0996961i 0.0317870π-0.0317870\pi
752752 8.00000 0.291730
753753 2.00000 0.0728841
754754 2.50000 4.33013i 0.0910446 0.157694i
755755 −4.00000 6.92820i −0.145575 0.252143i
756756 7.50000 12.9904i 0.272772 0.472456i
757757 1.00000 + 1.73205i 0.0363456 + 0.0629525i 0.883626 0.468193i 0.155095π-0.155095\pi
−0.847280 + 0.531146i 0.821762π0.821762\pi
758758 −7.50000 12.9904i −0.272412 0.471832i
759759 −2.00000 −0.0725954
760760 0 0
761761 27.0000 0.978749 0.489375 0.872074i 0.337225π-0.337225\pi
0.489375 + 0.872074i 0.337225π0.337225\pi
762762 −9.00000 15.5885i −0.326036 0.564710i
763763 −22.5000 38.9711i −0.814555 1.41085i
764764 −3.50000 + 6.06218i −0.126626 + 0.219322i
765765 −12.0000 20.7846i −0.433861 0.751469i
766766 13.0000 22.5167i 0.469709 0.813560i
767767 −15.0000 −0.541619
768768 1.00000 0.0360844
769769 17.5000 30.3109i 0.631066 1.09304i −0.356268 0.934384i 0.615951π-0.615951\pi
0.987334 0.158655i 0.0507157π-0.0507157\pi
770770 −12.0000 + 20.7846i −0.432450 + 0.749025i
771771 −8.00000 −0.288113
772772 6.00000 0.215945
773773 4.50000 7.79423i 0.161854 0.280339i −0.773680 0.633577i 0.781586π-0.781586\pi
0.935534 + 0.353238i 0.114919π0.114919\pi
774774 −4.00000 6.92820i −0.143777 0.249029i
775775 −44.0000 + 76.2102i −1.58053 + 2.73755i
776776 1.00000 + 1.73205i 0.0358979 + 0.0621770i
777777 −3.00000 5.19615i −0.107624 0.186411i
778778 30.0000 1.07555
779779 0 0
780780 −4.00000 −0.143223
781781 2.00000 + 3.46410i 0.0715656 + 0.123955i
782782 −1.50000 2.59808i −0.0536399 0.0929070i
783783 12.5000 21.6506i 0.446714 0.773731i
784784 −1.00000 1.73205i −0.0357143 0.0618590i
785785 −4.00000 + 6.92820i −0.142766 + 0.247278i
786786 −12.0000 −0.428026
787787 17.0000 0.605985 0.302992 0.952993i 0.402014π-0.402014\pi
0.302992 + 0.952993i 0.402014π0.402014\pi
788788 −4.00000 + 6.92820i −0.142494 + 0.246807i
789789 −12.0000 + 20.7846i −0.427211 + 0.739952i
790790 40.0000 1.42314
791791 −42.0000 −1.49335
792792 −2.00000 + 3.46410i −0.0710669 + 0.123091i
793793 −1.00000 1.73205i −0.0355110 0.0615069i
794794 4.00000 6.92820i 0.141955 0.245873i
795795 2.00000 + 3.46410i 0.0709327 + 0.122859i
796796 12.5000 + 21.6506i 0.443051 + 0.767386i
797797 −3.00000 −0.106265 −0.0531327 0.998587i 0.516921π-0.516921\pi
−0.0531327 + 0.998587i 0.516921π0.516921\pi
798798 0 0
799799 24.0000 0.849059
800800 5.50000 + 9.52628i 0.194454 + 0.336805i
801801 0 0
802802 4.00000 6.92820i 0.141245 0.244643i
803803 −9.00000 15.5885i −0.317603 0.550105i
804804 1.50000 2.59808i 0.0529009 0.0916271i
805805 12.0000 0.422944
806806 −8.00000 −0.281788
807807 15.0000 25.9808i 0.528025 0.914566i
808808 1.00000 1.73205i 0.0351799 0.0609333i
809809 −15.0000 −0.527372 −0.263686 0.964609i 0.584938π-0.584938\pi
−0.263686 + 0.964609i 0.584938π0.584938\pi
810810 4.00000 0.140546
811811 −1.50000 + 2.59808i −0.0526721 + 0.0912308i −0.891159 0.453691i 0.850107π-0.850107\pi
0.838487 + 0.544921i 0.183440π0.183440\pi
812812 −7.50000 12.9904i −0.263198 0.455873i
813813 −3.50000 + 6.06218i −0.122750 + 0.212610i
814814 2.00000 + 3.46410i 0.0701000 + 0.121417i
815815 −32.0000 55.4256i −1.12091 1.94147i
816816 3.00000 0.105021
817817 0 0
818818 −20.0000 −0.699284
819819 3.00000 + 5.19615i 0.104828 + 0.181568i
820820 16.0000 + 27.7128i 0.558744 + 0.967773i
821821 −6.00000 + 10.3923i −0.209401 + 0.362694i −0.951526 0.307568i 0.900485π-0.900485\pi
0.742125 + 0.670262i 0.233818π0.233818\pi
822822 −8.50000 14.7224i −0.296472 0.513504i
823823 −14.5000 + 25.1147i −0.505438 + 0.875445i 0.494542 + 0.869154i 0.335336π0.335336\pi
−0.999980 + 0.00629095i 0.997998π0.997998\pi
824824 −6.00000 −0.209020
825825 22.0000 0.765942
826826 −22.5000 + 38.9711i −0.782875 + 1.35598i
827827 11.5000 19.9186i 0.399894 0.692637i −0.593818 0.804599i 0.702380π-0.702380\pi
0.993712 + 0.111962i 0.0357135π0.0357135\pi
828828 2.00000 0.0695048
829829 15.0000 0.520972 0.260486 0.965478i 0.416117π-0.416117\pi
0.260486 + 0.965478i 0.416117π0.416117\pi
830830 12.0000 20.7846i 0.416526 0.721444i
831831 −14.0000 24.2487i −0.485655 0.841178i
832832 −0.500000 + 0.866025i −0.0173344 + 0.0300240i
833833 −3.00000 5.19615i −0.103944 0.180036i
834834 0 0
835835 −48.0000 −1.66111
836836 0 0
837837 −40.0000 −1.38260
838838 0 0
839839 10.0000 + 17.3205i 0.345238 + 0.597970i 0.985397 0.170272i 0.0544647π-0.0544647\pi
−0.640159 + 0.768243i 0.721131π0.721131\pi
840840 −6.00000 + 10.3923i −0.207020 + 0.358569i
841841 2.00000 + 3.46410i 0.0689655 + 0.119452i
842842 6.50000 11.2583i 0.224005 0.387988i
843843 8.00000 0.275535
844844 −27.0000 −0.929378
845845 −24.0000 + 41.5692i −0.825625 + 1.43002i
846846 −8.00000 + 13.8564i −0.275046 + 0.476393i
847847 −21.0000 −0.721569
848848 1.00000 0.0343401
849849 3.00000 5.19615i 0.102960 0.178331i
850850 16.5000 + 28.5788i 0.565945 + 0.980246i
851851 1.00000 1.73205i 0.0342796 0.0593739i
852852 1.00000 + 1.73205i 0.0342594 + 0.0593391i
853853 3.00000 + 5.19615i 0.102718 + 0.177913i 0.912804 0.408399i 0.133913π-0.133913\pi
−0.810086 + 0.586312i 0.800579π0.800579\pi
854854 −6.00000 −0.205316
855855 0 0
856856 −7.00000 −0.239255
857857 −6.00000 10.3923i −0.204956 0.354994i 0.745163 0.666883i 0.232372π-0.232372\pi
−0.950119 + 0.311888i 0.899038π0.899038\pi
858858 1.00000 + 1.73205i 0.0341394 + 0.0591312i
859859 25.0000 43.3013i 0.852989 1.47742i −0.0255092 0.999675i 0.508121π-0.508121\pi
0.878498 0.477746i 0.158546π-0.158546\pi
860860 8.00000 + 13.8564i 0.272798 + 0.472500i
861861 −12.0000 + 20.7846i −0.408959 + 0.708338i
862862 −18.0000 −0.613082
863863 −54.0000 −1.83818 −0.919091 0.394046i 0.871075π-0.871075\pi
−0.919091 + 0.394046i 0.871075π0.871075\pi
864864 −2.50000 + 4.33013i −0.0850517 + 0.147314i
865865 12.0000 20.7846i 0.408012 0.706698i
866866 14.0000 0.475739
867867 −8.00000 −0.271694
868868 −12.0000 + 20.7846i −0.407307 + 0.705476i
869869 −10.0000 17.3205i −0.339227 0.587558i
870870 −10.0000 + 17.3205i −0.339032 + 0.587220i
871871 1.50000 + 2.59808i 0.0508256 + 0.0880325i
872872 7.50000 + 12.9904i 0.253982 + 0.439910i
873873 −4.00000 −0.135379
874874 0 0
875875 −72.0000 −2.43404
876876 −4.50000 7.79423i −0.152041 0.263343i
877877 6.50000 + 11.2583i 0.219489 + 0.380167i 0.954652 0.297724i 0.0962275π-0.0962275\pi
−0.735163 + 0.677891i 0.762894π0.762894\pi
878878 −10.0000 + 17.3205i −0.337484 + 0.584539i
879879 4.50000 + 7.79423i 0.151781 + 0.262893i
880880 4.00000 6.92820i 0.134840 0.233550i
881881 −18.0000 −0.606435 −0.303218 0.952921i 0.598061π-0.598061\pi
−0.303218 + 0.952921i 0.598061π0.598061\pi
882882 4.00000 0.134687
883883 −17.0000 + 29.4449i −0.572096 + 0.990899i 0.424255 + 0.905543i 0.360536π0.360536\pi
−0.996351 + 0.0853558i 0.972797π0.972797\pi
884884 −1.50000 + 2.59808i −0.0504505 + 0.0873828i
885885 60.0000 2.01688
886886 26.0000 0.873487
887887 −1.00000 + 1.73205i −0.0335767 + 0.0581566i −0.882325 0.470640i 0.844023π-0.844023\pi
0.848749 + 0.528796i 0.177356π0.177356\pi
888888 1.00000 + 1.73205i 0.0335578 + 0.0581238i
889889 27.0000 46.7654i 0.905551 1.56846i
890890 0 0
891891 −1.00000 1.73205i −0.0335013 0.0580259i
892892 −14.0000 −0.468755
893893 0 0
894894 0 0
895895 0 0
896896 1.50000 + 2.59808i 0.0501115 + 0.0867956i
897897 0.500000 0.866025i 0.0166945 0.0289157i
898898 −5.00000 8.66025i −0.166852 0.288996i
899899 −20.0000 + 34.6410i −0.667037 + 1.15534i
900900 −22.0000 −0.733333
901901 3.00000 0.0999445
902902 8.00000 13.8564i 0.266371 0.461368i
903903 −6.00000 + 10.3923i −0.199667 + 0.345834i
904904 14.0000 0.465633
905905 88.0000 2.92522
906906 −1.00000 + 1.73205i −0.0332228 + 0.0575435i
907907 26.5000 + 45.8993i 0.879918 + 1.52406i 0.851430 + 0.524469i 0.175736π0.175736\pi
0.0284883 + 0.999594i 0.490931π0.490931\pi
908908 −8.50000 + 14.7224i −0.282082 + 0.488581i
909909 2.00000 + 3.46410i 0.0663358 + 0.114897i
910910 −6.00000 10.3923i −0.198898 0.344502i
911911 −12.0000 −0.397578 −0.198789 0.980042i 0.563701π-0.563701\pi
−0.198789 + 0.980042i 0.563701π0.563701\pi
912912 0 0
913913 −12.0000 −0.397142
914914 −3.50000 6.06218i −0.115770 0.200519i
915915 4.00000 + 6.92820i 0.132236 + 0.229039i
916916 5.00000 8.66025i 0.165205 0.286143i
917917 −18.0000 31.1769i −0.594412 1.02955i
918918 −7.50000 + 12.9904i −0.247537 + 0.428746i
919919 5.00000 0.164935 0.0824674 0.996594i 0.473720π-0.473720\pi
0.0824674 + 0.996594i 0.473720π0.473720\pi
920920 −4.00000 −0.131876
921921 −6.00000 + 10.3923i −0.197707 + 0.342438i
922922 −14.0000 + 24.2487i −0.461065 + 0.798589i
923923 −2.00000 −0.0658308
924924 6.00000 0.197386
925925 −11.0000 + 19.0526i −0.361678 + 0.626444i
926926 2.00000 + 3.46410i 0.0657241 + 0.113837i
927927 6.00000 10.3923i 0.197066 0.341328i
928928 2.50000 + 4.33013i 0.0820665 + 0.142143i
929929 27.5000 + 47.6314i 0.902246 + 1.56274i 0.824572 + 0.565757i 0.191416π0.191416\pi
0.0776734 + 0.996979i 0.475251π0.475251\pi
930930 32.0000 1.04932
931931 0 0
932932 −6.00000 −0.196537
933933 −3.50000 6.06218i −0.114585 0.198467i
934934 −1.00000 1.73205i −0.0327210 0.0566744i
935935 12.0000 20.7846i 0.392442 0.679729i
936936 −1.00000 1.73205i −0.0326860 0.0566139i
937937 3.50000 6.06218i 0.114340 0.198043i −0.803176 0.595742i 0.796858π-0.796858\pi
0.917516 + 0.397699i 0.130191π0.130191\pi
938938 9.00000 0.293860
939939 29.0000 0.946379
940940 16.0000 27.7128i 0.521862 0.903892i
941941 3.50000 6.06218i 0.114097 0.197621i −0.803322 0.595545i 0.796936π-0.796936\pi
0.917418 + 0.397924i 0.130269π0.130269\pi
942942 2.00000 0.0651635
943943 −8.00000 −0.260516
944944 7.50000 12.9904i 0.244104 0.422801i
945945 −30.0000 51.9615i −0.975900 1.69031i
946946 4.00000 6.92820i 0.130051 0.225255i
947947 6.00000 + 10.3923i 0.194974 + 0.337705i 0.946892 0.321552i 0.104204π-0.104204\pi
−0.751918 + 0.659256i 0.770871π0.770871\pi
948948 −5.00000 8.66025i −0.162392 0.281272i
949949 9.00000 0.292152
950950 0 0
951951 27.0000 0.875535
952952 4.50000 + 7.79423i 0.145846 + 0.252612i
953953 −23.0000 39.8372i −0.745043 1.29045i −0.950175 0.311718i 0.899096π-0.899096\pi
0.205132 0.978734i 0.434238π-0.434238\pi
954954 −1.00000 + 1.73205i −0.0323762 + 0.0560772i
955955 14.0000 + 24.2487i 0.453029 + 0.784670i
956956 −7.50000 + 12.9904i −0.242567 + 0.420139i
957957 10.0000 0.323254
958958 20.0000 0.646171
959959 25.5000 44.1673i 0.823438 1.42624i
960960 2.00000 3.46410i 0.0645497 0.111803i
961961 33.0000 1.06452
962962 −2.00000 −0.0644826
963963 7.00000 12.1244i 0.225572 0.390702i
964964 −4.00000 6.92820i −0.128831 0.223142i
965965 12.0000 20.7846i 0.386294 0.669080i
966966 −1.50000 2.59808i −0.0482617 0.0835917i
967967 −24.0000 41.5692i −0.771788 1.33678i −0.936582 0.350448i 0.886029π-0.886029\pi
0.164794 0.986328i 0.447304π-0.447304\pi
968968 7.00000 0.224989
969969 0 0
970970 8.00000 0.256865
971971 −14.0000 24.2487i −0.449281 0.778178i 0.549058 0.835784i 0.314987π-0.314987\pi
−0.998339 + 0.0576061i 0.981653π0.981653\pi
972972 −8.00000 13.8564i −0.256600 0.444444i
973973 0 0
974974 1.00000 + 1.73205i 0.0320421 + 0.0554985i
975975 −5.50000 + 9.52628i −0.176141 + 0.305085i
976976 2.00000 0.0640184
977977 −8.00000 −0.255943 −0.127971 0.991778i 0.540847π-0.540847\pi
−0.127971 + 0.991778i 0.540847π0.540847\pi
978978 −8.00000 + 13.8564i −0.255812 + 0.443079i
979979 0 0
980980 −8.00000 −0.255551
981981 −30.0000 −0.957826
982982 −14.0000 + 24.2487i −0.446758 + 0.773807i
983983 −3.00000 5.19615i −0.0956851 0.165732i 0.814209 0.580572i 0.197171π-0.197171\pi
−0.909894 + 0.414840i 0.863838π0.863838\pi
984984 4.00000 6.92820i 0.127515 0.220863i
985985 16.0000 + 27.7128i 0.509802 + 0.883004i
986986 7.50000 + 12.9904i 0.238849 + 0.413698i
987987 24.0000 0.763928
988988 0 0
989989 −4.00000 −0.127193
990990 8.00000 + 13.8564i 0.254257 + 0.440386i
991991 −4.00000 6.92820i −0.127064 0.220082i 0.795474 0.605988i 0.207222π-0.207222\pi
−0.922538 + 0.385906i 0.873889π0.873889\pi
992992 4.00000 6.92820i 0.127000 0.219971i
993993 8.50000 + 14.7224i 0.269739 + 0.467202i
994994 −3.00000 + 5.19615i −0.0951542 + 0.164812i
995995 100.000 3.17021
996996 −6.00000 −0.190117
997997 −14.0000 + 24.2487i −0.443384 + 0.767964i −0.997938 0.0641836i 0.979556π-0.979556\pi
0.554554 + 0.832148i 0.312889π0.312889\pi
998998 20.0000 34.6410i 0.633089 1.09654i
999999 −10.0000 −0.316386
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 722.2.c.f.653.1 2
19.2 odd 18 722.2.e.c.389.1 6
19.3 odd 18 722.2.e.c.595.1 6
19.4 even 9 722.2.e.d.245.1 6
19.5 even 9 722.2.e.d.99.1 6
19.6 even 9 722.2.e.d.423.1 6
19.7 even 3 722.2.a.b.1.1 1
19.8 odd 6 722.2.c.d.429.1 2
19.9 even 9 722.2.e.d.415.1 6
19.10 odd 18 722.2.e.c.415.1 6
19.11 even 3 inner 722.2.c.f.429.1 2
19.12 odd 6 38.2.a.b.1.1 1
19.13 odd 18 722.2.e.c.423.1 6
19.14 odd 18 722.2.e.c.99.1 6
19.15 odd 18 722.2.e.c.245.1 6
19.16 even 9 722.2.e.d.595.1 6
19.17 even 9 722.2.e.d.389.1 6
19.18 odd 2 722.2.c.d.653.1 2
57.26 odd 6 6498.2.a.y.1.1 1
57.50 even 6 342.2.a.d.1.1 1
76.7 odd 6 5776.2.a.d.1.1 1
76.31 even 6 304.2.a.d.1.1 1
95.12 even 12 950.2.b.c.799.2 2
95.69 odd 6 950.2.a.b.1.1 1
95.88 even 12 950.2.b.c.799.1 2
133.69 even 6 1862.2.a.f.1.1 1
152.69 odd 6 1216.2.a.n.1.1 1
152.107 even 6 1216.2.a.g.1.1 1
209.164 even 6 4598.2.a.a.1.1 1
228.107 odd 6 2736.2.a.w.1.1 1
247.12 odd 6 6422.2.a.b.1.1 1
285.164 even 6 8550.2.a.u.1.1 1
380.259 even 6 7600.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.a.b.1.1 1 19.12 odd 6
304.2.a.d.1.1 1 76.31 even 6
342.2.a.d.1.1 1 57.50 even 6
722.2.a.b.1.1 1 19.7 even 3
722.2.c.d.429.1 2 19.8 odd 6
722.2.c.d.653.1 2 19.18 odd 2
722.2.c.f.429.1 2 19.11 even 3 inner
722.2.c.f.653.1 2 1.1 even 1 trivial
722.2.e.c.99.1 6 19.14 odd 18
722.2.e.c.245.1 6 19.15 odd 18
722.2.e.c.389.1 6 19.2 odd 18
722.2.e.c.415.1 6 19.10 odd 18
722.2.e.c.423.1 6 19.13 odd 18
722.2.e.c.595.1 6 19.3 odd 18
722.2.e.d.99.1 6 19.5 even 9
722.2.e.d.245.1 6 19.4 even 9
722.2.e.d.389.1 6 19.17 even 9
722.2.e.d.415.1 6 19.9 even 9
722.2.e.d.423.1 6 19.6 even 9
722.2.e.d.595.1 6 19.16 even 9
950.2.a.b.1.1 1 95.69 odd 6
950.2.b.c.799.1 2 95.88 even 12
950.2.b.c.799.2 2 95.12 even 12
1216.2.a.g.1.1 1 152.107 even 6
1216.2.a.n.1.1 1 152.69 odd 6
1862.2.a.f.1.1 1 133.69 even 6
2736.2.a.w.1.1 1 228.107 odd 6
4598.2.a.a.1.1 1 209.164 even 6
5776.2.a.d.1.1 1 76.7 odd 6
6422.2.a.b.1.1 1 247.12 odd 6
6498.2.a.y.1.1 1 57.26 odd 6
7600.2.a.h.1.1 1 380.259 even 6
8550.2.a.u.1.1 1 285.164 even 6