Properties

Label 462.2.i.e.331.2
Level 462462
Weight 22
Character 462.331
Analytic conductor 3.6893.689
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [462,2,Mod(67,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 462=23711 462 = 2 \cdot 3 \cdot 7 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 462.i (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: 3.689088573383.68908857338
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(3,7)\Q(\sqrt{-3}, \sqrt{7})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+7x2+49 x^{4} + 7x^{2} + 49 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 331.2
Root 1.322882.29129i-1.32288 - 2.29129i of defining polynomial
Character χ\chi == 462.331
Dual form 462.2.i.e.67.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.5000000.866025i)q2+(0.500000+0.866025i)q3+(0.5000000.866025i)q4+(1.322882.29129i)q5+1.00000q6+(1.322882.29129i)q71.00000q8+(0.500000+0.866025i)q9+(1.322882.29129i)q10+(0.5000000.866025i)q11+(0.5000000.866025i)q124.00000q13+(1.322882.29129i)q14+2.64575q15+(0.500000+0.866025i)q16+(1.50000+2.59808i)q17+(0.500000+0.866025i)q18+(2.645754.58258i)q192.64575q20+2.64575q211.00000q22+(1.32288+2.29129i)q23+(0.5000000.866025i)q24+(1.000001.73205i)q25+(2.00000+3.46410i)q261.00000q272.64575q28+2.00000q29+(1.322882.29129i)q30+(2.00000+3.46410i)q31+(0.500000+0.866025i)q32+(0.5000000.866025i)q33+3.00000q34+(3.500006.06218i)q35+1.00000q36+(4.645758.04668i)q37+(2.645754.58258i)q38+(2.000003.46410i)q39+(1.32288+2.29129i)q40+9.00000q41+(1.322882.29129i)q421.29150q43+(0.500000+0.866025i)q44+(1.32288+2.29129i)q45+(1.32288+2.29129i)q46+(5.96863+10.3380i)q471.00000q48+(3.500006.06218i)q492.00000q50+(1.50000+2.59808i)q51+(2.00000+3.46410i)q52+(2.000003.46410i)q53+(0.500000+0.866025i)q542.64575q55+(1.32288+2.29129i)q56+5.29150q57+(1.000001.73205i)q58+(7.29150+12.6293i)q59+(1.322882.29129i)q60+(1.968633.40976i)q61+4.00000q62+(1.32288+2.29129i)q63+1.00000q64+(5.29150+9.16515i)q65+(0.5000000.866025i)q66+(6.79150+11.7632i)q67+(1.500002.59808i)q682.64575q697.00000q7013.2915q71+(0.5000000.866025i)q72+(2.35425+4.07768i)q73+(4.645758.04668i)q74+(1.000001.73205i)q755.29150q762.64575q774.00000q78+(2.67712+4.63692i)q79+(1.32288+2.29129i)q80+(0.5000000.866025i)q81+(4.500007.79423i)q825.58301q83+(1.322882.29129i)q84+7.93725q85+(0.645751+1.11847i)q86+(1.00000+1.73205i)q87+(0.500000+0.866025i)q88+(6.64575+11.5108i)q89+2.64575q90+(5.29150+9.16515i)q91+2.64575q92+(2.00000+3.46410i)q93+(5.96863+10.3380i)q94+(7.0000012.1244i)q95+(0.500000+0.866025i)q96+9.58301q977.00000q98+1.00000q99+O(q100)q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.32288 - 2.29129i) q^{5} +1.00000 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.32288 - 2.29129i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.00000 q^{13} +(-1.32288 - 2.29129i) q^{14} +2.64575 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.64575 - 4.58258i) q^{19} -2.64575 q^{20} +2.64575 q^{21} -1.00000 q^{22} +(-1.32288 + 2.29129i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-2.00000 + 3.46410i) q^{26} -1.00000 q^{27} -2.64575 q^{28} +2.00000 q^{29} +(1.32288 - 2.29129i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +3.00000 q^{34} +(-3.50000 - 6.06218i) q^{35} +1.00000 q^{36} +(4.64575 - 8.04668i) q^{37} +(-2.64575 - 4.58258i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(-1.32288 + 2.29129i) q^{40} +9.00000 q^{41} +(1.32288 - 2.29129i) q^{42} -1.29150 q^{43} +(-0.500000 + 0.866025i) q^{44} +(1.32288 + 2.29129i) q^{45} +(1.32288 + 2.29129i) q^{46} +(-5.96863 + 10.3380i) q^{47} -1.00000 q^{48} +(-3.50000 - 6.06218i) q^{49} -2.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} -2.64575 q^{55} +(-1.32288 + 2.29129i) q^{56} +5.29150 q^{57} +(1.00000 - 1.73205i) q^{58} +(7.29150 + 12.6293i) q^{59} +(-1.32288 - 2.29129i) q^{60} +(1.96863 - 3.40976i) q^{61} +4.00000 q^{62} +(1.32288 + 2.29129i) q^{63} +1.00000 q^{64} +(-5.29150 + 9.16515i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(6.79150 + 11.7632i) q^{67} +(1.50000 - 2.59808i) q^{68} -2.64575 q^{69} -7.00000 q^{70} -13.2915 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.35425 + 4.07768i) q^{73} +(-4.64575 - 8.04668i) q^{74} +(1.00000 - 1.73205i) q^{75} -5.29150 q^{76} -2.64575 q^{77} -4.00000 q^{78} +(-2.67712 + 4.63692i) q^{79} +(1.32288 + 2.29129i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} -5.58301 q^{83} +(-1.32288 - 2.29129i) q^{84} +7.93725 q^{85} +(-0.645751 + 1.11847i) q^{86} +(1.00000 + 1.73205i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-6.64575 + 11.5108i) q^{89} +2.64575 q^{90} +(-5.29150 + 9.16515i) q^{91} +2.64575 q^{92} +(-2.00000 + 3.46410i) q^{93} +(5.96863 + 10.3380i) q^{94} +(-7.00000 - 12.1244i) q^{95} +(-0.500000 + 0.866025i) q^{96} +9.58301 q^{97} -7.00000 q^{98} +1.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q2+2q32q4+4q64q82q92q11+2q1216q132q16+6q17+2q184q222q244q258q264q27+8q29+8q31++4q99+O(q100) 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{11} + 2 q^{12} - 16 q^{13} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{22} - 2 q^{24} - 4 q^{25} - 8 q^{26} - 4 q^{27} + 8 q^{29} + 8 q^{31}+ \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/462Z)×\left(\mathbb{Z}/462\mathbb{Z}\right)^\times.

nn 155155 199199 211211
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right) 11

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
44 −0.500000 0.866025i −0.250000 0.433013i
55 1.32288 2.29129i 0.591608 1.02470i −0.402408 0.915460i 0.631827π-0.631827\pi
0.994016 0.109235i 0.0348400π-0.0348400\pi
66 1.00000 0.408248
77 1.32288 2.29129i 0.500000 0.866025i
88 −1.00000 −0.353553
99 −0.500000 + 0.866025i −0.166667 + 0.288675i
1010 −1.32288 2.29129i −0.418330 0.724569i
1111 −0.500000 0.866025i −0.150756 0.261116i
1212 0.500000 0.866025i 0.144338 0.250000i
1313 −4.00000 −1.10940 −0.554700 0.832050i 0.687167π-0.687167\pi
−0.554700 + 0.832050i 0.687167π0.687167\pi
1414 −1.32288 2.29129i −0.353553 0.612372i
1515 2.64575 0.683130
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i 0.0481447π-0.0481447\pi
−0.624780 + 0.780801i 0.714811π0.714811\pi
1818 0.500000 + 0.866025i 0.117851 + 0.204124i
1919 2.64575 4.58258i 0.606977 1.05131i −0.384759 0.923017i 0.625715π-0.625715\pi
0.991736 0.128298i 0.0409513π-0.0409513\pi
2020 −2.64575 −0.591608
2121 2.64575 0.577350
2222 −1.00000 −0.213201
2323 −1.32288 + 2.29129i −0.275839 + 0.477767i −0.970346 0.241719i 0.922289π-0.922289\pi
0.694508 + 0.719485i 0.255622π0.255622\pi
2424 −0.500000 0.866025i −0.102062 0.176777i
2525 −1.00000 1.73205i −0.200000 0.346410i
2626 −2.00000 + 3.46410i −0.392232 + 0.679366i
2727 −1.00000 −0.192450
2828 −2.64575 −0.500000
2929 2.00000 0.371391 0.185695 0.982607i 0.440546π-0.440546\pi
0.185695 + 0.982607i 0.440546π0.440546\pi
3030 1.32288 2.29129i 0.241523 0.418330i
3131 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i 0.0497126π-0.0497126\pi
−0.628619 + 0.777714i 0.716379π0.716379\pi
3232 0.500000 + 0.866025i 0.0883883 + 0.153093i
3333 0.500000 0.866025i 0.0870388 0.150756i
3434 3.00000 0.514496
3535 −3.50000 6.06218i −0.591608 1.02470i
3636 1.00000 0.166667
3737 4.64575 8.04668i 0.763757 1.32287i −0.177145 0.984185i 0.556686π-0.556686\pi
0.940901 0.338681i 0.109981π-0.109981\pi
3838 −2.64575 4.58258i −0.429198 0.743392i
3939 −2.00000 3.46410i −0.320256 0.554700i
4040 −1.32288 + 2.29129i −0.209165 + 0.362284i
4141 9.00000 1.40556 0.702782 0.711405i 0.251941π-0.251941\pi
0.702782 + 0.711405i 0.251941π0.251941\pi
4242 1.32288 2.29129i 0.204124 0.353553i
4343 −1.29150 −0.196952 −0.0984762 0.995139i 0.531397π-0.531397\pi
−0.0984762 + 0.995139i 0.531397π0.531397\pi
4444 −0.500000 + 0.866025i −0.0753778 + 0.130558i
4545 1.32288 + 2.29129i 0.197203 + 0.341565i
4646 1.32288 + 2.29129i 0.195047 + 0.337832i
4747 −5.96863 + 10.3380i −0.870614 + 1.50795i −0.00925075 + 0.999957i 0.502945π0.502945\pi
−0.861363 + 0.507990i 0.830389π0.830389\pi
4848 −1.00000 −0.144338
4949 −3.50000 6.06218i −0.500000 0.866025i
5050 −2.00000 −0.282843
5151 −1.50000 + 2.59808i −0.210042 + 0.363803i
5252 2.00000 + 3.46410i 0.277350 + 0.480384i
5353 −2.00000 3.46410i −0.274721 0.475831i 0.695344 0.718677i 0.255252π-0.255252\pi
−0.970065 + 0.242846i 0.921919π0.921919\pi
5454 −0.500000 + 0.866025i −0.0680414 + 0.117851i
5555 −2.64575 −0.356753
5656 −1.32288 + 2.29129i −0.176777 + 0.306186i
5757 5.29150 0.700877
5858 1.00000 1.73205i 0.131306 0.227429i
5959 7.29150 + 12.6293i 0.949273 + 1.64419i 0.746961 + 0.664867i 0.231512π0.231512\pi
0.202311 + 0.979321i 0.435155π0.435155\pi
6060 −1.32288 2.29129i −0.170783 0.295804i
6161 1.96863 3.40976i 0.252057 0.436575i −0.712035 0.702144i 0.752226π-0.752226\pi
0.964092 + 0.265569i 0.0855597π0.0855597\pi
6262 4.00000 0.508001
6363 1.32288 + 2.29129i 0.166667 + 0.288675i
6464 1.00000 0.125000
6565 −5.29150 + 9.16515i −0.656330 + 1.13680i
6666 −0.500000 0.866025i −0.0615457 0.106600i
6767 6.79150 + 11.7632i 0.829714 + 1.43711i 0.898263 + 0.439459i 0.144830π0.144830\pi
−0.0685485 + 0.997648i 0.521837π0.521837\pi
6868 1.50000 2.59808i 0.181902 0.315063i
6969 −2.64575 −0.318511
7070 −7.00000 −0.836660
7171 −13.2915 −1.57741 −0.788706 0.614771i 0.789248π-0.789248\pi
−0.788706 + 0.614771i 0.789248π0.789248\pi
7272 0.500000 0.866025i 0.0589256 0.102062i
7373 2.35425 + 4.07768i 0.275544 + 0.477256i 0.970272 0.242016i 0.0778087π-0.0778087\pi
−0.694728 + 0.719272i 0.744475π0.744475\pi
7474 −4.64575 8.04668i −0.540058 0.935407i
7575 1.00000 1.73205i 0.115470 0.200000i
7676 −5.29150 −0.606977
7777 −2.64575 −0.301511
7878 −4.00000 −0.452911
7979 −2.67712 + 4.63692i −0.301200 + 0.521694i −0.976408 0.215934i 0.930721π-0.930721\pi
0.675208 + 0.737627i 0.264054π0.264054\pi
8080 1.32288 + 2.29129i 0.147902 + 0.256174i
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 4.50000 7.79423i 0.496942 0.860729i
8383 −5.58301 −0.612814 −0.306407 0.951901i 0.599127π-0.599127\pi
−0.306407 + 0.951901i 0.599127π0.599127\pi
8484 −1.32288 2.29129i −0.144338 0.250000i
8585 7.93725 0.860916
8686 −0.645751 + 1.11847i −0.0696332 + 0.120608i
8787 1.00000 + 1.73205i 0.107211 + 0.185695i
8888 0.500000 + 0.866025i 0.0533002 + 0.0923186i
8989 −6.64575 + 11.5108i −0.704448 + 1.22014i 0.262442 + 0.964948i 0.415472π0.415472\pi
−0.966890 + 0.255192i 0.917861π0.917861\pi
9090 2.64575 0.278887
9191 −5.29150 + 9.16515i −0.554700 + 0.960769i
9292 2.64575 0.275839
9393 −2.00000 + 3.46410i −0.207390 + 0.359211i
9494 5.96863 + 10.3380i 0.615617 + 1.06628i
9595 −7.00000 12.1244i −0.718185 1.24393i
9696 −0.500000 + 0.866025i −0.0510310 + 0.0883883i
9797 9.58301 0.973007 0.486503 0.873679i 0.338272π-0.338272\pi
0.486503 + 0.873679i 0.338272π0.338272\pi
9898 −7.00000 −0.707107
9999 1.00000 0.100504
100100 −1.00000 + 1.73205i −0.100000 + 0.173205i
101101 1.64575 + 2.85052i 0.163758 + 0.283638i 0.936214 0.351431i 0.114305π-0.114305\pi
−0.772455 + 0.635069i 0.780972π0.780972\pi
102102 1.50000 + 2.59808i 0.148522 + 0.257248i
103103 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i 0.669356π-0.669356\pi
0.999964 + 0.00844953i 0.00268960π0.00268960\pi
104104 4.00000 0.392232
105105 3.50000 6.06218i 0.341565 0.591608i
106106 −4.00000 −0.388514
107107 −4.50000 + 7.79423i −0.435031 + 0.753497i −0.997298 0.0734594i 0.976596π-0.976596\pi
0.562267 + 0.826956i 0.309929π0.309929\pi
108108 0.500000 + 0.866025i 0.0481125 + 0.0833333i
109109 −5.96863 10.3380i −0.571691 0.990197i −0.996393 0.0848642i 0.972954π-0.972954\pi
0.424702 0.905333i 0.360379π-0.360379\pi
110110 −1.32288 + 2.29129i −0.126131 + 0.218466i
111111 9.29150 0.881910
112112 1.32288 + 2.29129i 0.125000 + 0.216506i
113113 −8.58301 −0.807421 −0.403711 0.914887i 0.632280π-0.632280\pi
−0.403711 + 0.914887i 0.632280π0.632280\pi
114114 2.64575 4.58258i 0.247797 0.429198i
115115 3.50000 + 6.06218i 0.326377 + 0.565301i
116116 −1.00000 1.73205i −0.0928477 0.160817i
117117 2.00000 3.46410i 0.184900 0.320256i
118118 14.5830 1.34247
119119 7.93725 0.727607
120120 −2.64575 −0.241523
121121 −0.500000 + 0.866025i −0.0454545 + 0.0787296i
122122 −1.96863 3.40976i −0.178231 0.308705i
123123 4.50000 + 7.79423i 0.405751 + 0.702782i
124124 2.00000 3.46410i 0.179605 0.311086i
125125 7.93725 0.709930
126126 2.64575 0.235702
127127 −2.64575 −0.234772 −0.117386 0.993086i 0.537452π-0.537452\pi
−0.117386 + 0.993086i 0.537452π0.537452\pi
128128 0.500000 0.866025i 0.0441942 0.0765466i
129129 −0.645751 1.11847i −0.0568552 0.0984762i
130130 5.29150 + 9.16515i 0.464095 + 0.803837i
131131 −1.29150 + 2.23695i −0.112839 + 0.195443i −0.916914 0.399085i 0.869328π-0.869328\pi
0.804075 + 0.594528i 0.202661π0.202661\pi
132132 −1.00000 −0.0870388
133133 −7.00000 12.1244i −0.606977 1.05131i
134134 13.5830 1.17339
135135 −1.32288 + 2.29129i −0.113855 + 0.197203i
136136 −1.50000 2.59808i −0.128624 0.222783i
137137 1.35425 + 2.34563i 0.115701 + 0.200400i 0.918060 0.396442i 0.129755π-0.129755\pi
−0.802359 + 0.596842i 0.796422π0.796422\pi
138138 −1.32288 + 2.29129i −0.112611 + 0.195047i
139139 8.58301 0.728001 0.364001 0.931399i 0.381411π-0.381411\pi
0.364001 + 0.931399i 0.381411π0.381411\pi
140140 −3.50000 + 6.06218i −0.295804 + 0.512348i
141141 −11.9373 −1.00530
142142 −6.64575 + 11.5108i −0.557699 + 0.965963i
143143 2.00000 + 3.46410i 0.167248 + 0.289683i
144144 −0.500000 0.866025i −0.0416667 0.0721688i
145145 2.64575 4.58258i 0.219718 0.380562i
146146 4.70850 0.389678
147147 3.50000 6.06218i 0.288675 0.500000i
148148 −9.29150 −0.763757
149149 5.93725 10.2836i 0.486399 0.842467i −0.513479 0.858102i 0.671644π-0.671644\pi
0.999878 + 0.0156348i 0.00497690π0.00497690\pi
150150 −1.00000 1.73205i −0.0816497 0.141421i
151151 −8.67712 15.0292i −0.706134 1.22306i −0.966281 0.257491i 0.917104π-0.917104\pi
0.260146 0.965569i 0.416229π-0.416229\pi
152152 −2.64575 + 4.58258i −0.214599 + 0.371696i
153153 −3.00000 −0.242536
154154 −1.32288 + 2.29129i −0.106600 + 0.184637i
155155 10.5830 0.850047
156156 −2.00000 + 3.46410i −0.160128 + 0.277350i
157157 5.64575 + 9.77873i 0.450580 + 0.780427i 0.998422 0.0561543i 0.0178839π-0.0178839\pi
−0.547842 + 0.836582i 0.684551π0.684551\pi
158158 2.67712 + 4.63692i 0.212981 + 0.368893i
159159 2.00000 3.46410i 0.158610 0.274721i
160160 2.64575 0.209165
161161 3.50000 + 6.06218i 0.275839 + 0.477767i
162162 −1.00000 −0.0785674
163163 −7.79150 + 13.4953i −0.610278 + 1.05703i 0.380916 + 0.924610i 0.375609π0.375609\pi
−0.991193 + 0.132422i 0.957725π0.957725\pi
164164 −4.50000 7.79423i −0.351391 0.608627i
165165 −1.32288 2.29129i −0.102986 0.178377i
166166 −2.79150 + 4.83502i −0.216663 + 0.375271i
167167 19.2915 1.49282 0.746411 0.665486i 0.231776π-0.231776\pi
0.746411 + 0.665486i 0.231776π0.231776\pi
168168 −2.64575 −0.204124
169169 3.00000 0.230769
170170 3.96863 6.87386i 0.304380 0.527201i
171171 2.64575 + 4.58258i 0.202326 + 0.350438i
172172 0.645751 + 1.11847i 0.0492381 + 0.0852828i
173173 −2.00000 + 3.46410i −0.152057 + 0.263371i −0.931984 0.362500i 0.881923π-0.881923\pi
0.779926 + 0.625871i 0.215256π0.215256\pi
174174 2.00000 0.151620
175175 −5.29150 −0.400000
176176 1.00000 0.0753778
177177 −7.29150 + 12.6293i −0.548063 + 0.949273i
178178 6.64575 + 11.5108i 0.498120 + 0.862769i
179179 −7.64575 13.2428i −0.571470 0.989816i −0.996415 0.0845964i 0.973040π-0.973040\pi
0.424945 0.905219i 0.360293π-0.360293\pi
180180 1.32288 2.29129i 0.0986013 0.170783i
181181 5.29150 0.393314 0.196657 0.980472i 0.436991π-0.436991\pi
0.196657 + 0.980472i 0.436991π0.436991\pi
182182 5.29150 + 9.16515i 0.392232 + 0.679366i
183183 3.93725 0.291050
184184 1.32288 2.29129i 0.0975237 0.168916i
185185 −12.2915 21.2895i −0.903689 1.56524i
186186 2.00000 + 3.46410i 0.146647 + 0.254000i
187187 1.50000 2.59808i 0.109691 0.189990i
188188 11.9373 0.870614
189189 −1.32288 + 2.29129i −0.0962250 + 0.166667i
190190 −14.0000 −1.01567
191191 −8.64575 + 14.9749i −0.625585 + 1.08354i 0.362843 + 0.931850i 0.381806π0.381806\pi
−0.988428 + 0.151694i 0.951527π0.951527\pi
192192 0.500000 + 0.866025i 0.0360844 + 0.0625000i
193193 −7.93725 13.7477i −0.571336 0.989583i −0.996429 0.0844334i 0.973092π-0.973092\pi
0.425093 0.905150i 0.360241π-0.360241\pi
194194 4.79150 8.29913i 0.344010 0.595843i
195195 −10.5830 −0.757865
196196 −3.50000 + 6.06218i −0.250000 + 0.433013i
197197 −9.87451 −0.703530 −0.351765 0.936088i 0.614418π-0.614418\pi
−0.351765 + 0.936088i 0.614418π0.614418\pi
198198 0.500000 0.866025i 0.0355335 0.0615457i
199199 −11.5830 20.0624i −0.821097 1.42218i −0.904866 0.425697i 0.860029π-0.860029\pi
0.0837682 0.996485i 0.473304π-0.473304\pi
200200 1.00000 + 1.73205i 0.0707107 + 0.122474i
201201 −6.79150 + 11.7632i −0.479036 + 0.829714i
202202 3.29150 0.231589
203203 2.64575 4.58258i 0.185695 0.321634i
204204 3.00000 0.210042
205205 11.9059 20.6216i 0.831543 1.44027i
206206 −5.00000 8.66025i −0.348367 0.603388i
207207 −1.32288 2.29129i −0.0919462 0.159256i
208208 2.00000 3.46410i 0.138675 0.240192i
209209 −5.29150 −0.366021
210210 −3.50000 6.06218i −0.241523 0.418330i
211211 10.7085 0.737203 0.368602 0.929587i 0.379837π-0.379837\pi
0.368602 + 0.929587i 0.379837π0.379837\pi
212212 −2.00000 + 3.46410i −0.137361 + 0.237915i
213213 −6.64575 11.5108i −0.455359 0.788706i
214214 4.50000 + 7.79423i 0.307614 + 0.532803i
215215 −1.70850 + 2.95920i −0.116519 + 0.201816i
216216 1.00000 0.0680414
217217 10.5830 0.718421
218218 −11.9373 −0.808493
219219 −2.35425 + 4.07768i −0.159085 + 0.275544i
220220 1.32288 + 2.29129i 0.0891883 + 0.154479i
221221 −6.00000 10.3923i −0.403604 0.699062i
222222 4.64575 8.04668i 0.311802 0.540058i
223223 −24.4575 −1.63780 −0.818898 0.573939i 0.805415π-0.805415\pi
−0.818898 + 0.573939i 0.805415π0.805415\pi
224224 2.64575 0.176777
225225 2.00000 0.133333
226226 −4.29150 + 7.43310i −0.285467 + 0.494442i
227227 −11.7915 20.4235i −0.782630 1.35555i −0.930405 0.366533i 0.880545π-0.880545\pi
0.147775 0.989021i 0.452789π-0.452789\pi
228228 −2.64575 4.58258i −0.175219 0.303488i
229229 −8.64575 + 14.9749i −0.571327 + 0.989568i 0.425103 + 0.905145i 0.360238π0.360238\pi
−0.996430 + 0.0844228i 0.973095π0.973095\pi
230230 7.00000 0.461566
231231 −1.32288 2.29129i −0.0870388 0.150756i
232232 −2.00000 −0.131306
233233 11.0830 19.1963i 0.726072 1.25759i −0.232460 0.972606i 0.574677π-0.574677\pi
0.958531 0.284987i 0.0919894π-0.0919894\pi
234234 −2.00000 3.46410i −0.130744 0.226455i
235235 15.7915 + 27.3517i 1.03012 + 1.78423i
236236 7.29150 12.6293i 0.474636 0.822094i
237237 −5.35425 −0.347796
238238 3.96863 6.87386i 0.257248 0.445566i
239239 13.2915 0.859756 0.429878 0.902887i 0.358557π-0.358557\pi
0.429878 + 0.902887i 0.358557π0.358557\pi
240240 −1.32288 + 2.29129i −0.0853913 + 0.147902i
241241 −7.58301 13.1342i −0.488464 0.846045i 0.511448 0.859314i 0.329109π-0.329109\pi
−0.999912 + 0.0132694i 0.995776π0.995776\pi
242242 0.500000 + 0.866025i 0.0321412 + 0.0556702i
243243 0.500000 0.866025i 0.0320750 0.0555556i
244244 −3.93725 −0.252057
245245 −18.5203 −1.18322
246246 9.00000 0.573819
247247 −10.5830 + 18.3303i −0.673380 + 1.16633i
248248 −2.00000 3.46410i −0.127000 0.219971i
249249 −2.79150 4.83502i −0.176904 0.306407i
250250 3.96863 6.87386i 0.250998 0.434741i
251251 12.7085 0.802153 0.401077 0.916045i 0.368636π-0.368636\pi
0.401077 + 0.916045i 0.368636π0.368636\pi
252252 1.32288 2.29129i 0.0833333 0.144338i
253253 2.64575 0.166337
254254 −1.32288 + 2.29129i −0.0830046 + 0.143768i
255255 3.96863 + 6.87386i 0.248525 + 0.430458i
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 0.645751 1.11847i 0.0402809 0.0697685i −0.845182 0.534478i 0.820508π-0.820508\pi
0.885463 + 0.464710i 0.153841π0.153841\pi
258258 −1.29150 −0.0804054
259259 −12.2915 21.2895i −0.763757 1.32287i
260260 10.5830 0.656330
261261 −1.00000 + 1.73205i −0.0618984 + 0.107211i
262262 1.29150 + 2.23695i 0.0797893 + 0.138199i
263263 4.93725 + 8.55157i 0.304444 + 0.527313i 0.977137 0.212609i 0.0681960π-0.0681960\pi
−0.672693 + 0.739921i 0.734863π0.734863\pi
264264 −0.500000 + 0.866025i −0.0307729 + 0.0533002i
265265 −10.5830 −0.650109
266266 −14.0000 −0.858395
267267 −13.2915 −0.813427
268268 6.79150 11.7632i 0.414857 0.718553i
269269 2.67712 + 4.63692i 0.163227 + 0.282718i 0.936024 0.351935i 0.114476π-0.114476\pi
−0.772797 + 0.634653i 0.781143π0.781143\pi
270270 1.32288 + 2.29129i 0.0805076 + 0.139443i
271271 0.645751 1.11847i 0.0392266 0.0679425i −0.845746 0.533586i 0.820844π-0.820844\pi
0.884972 + 0.465644i 0.154177π0.154177\pi
272272 −3.00000 −0.181902
273273 −10.5830 −0.640513
274274 2.70850 0.163626
275275 −1.00000 + 1.73205i −0.0603023 + 0.104447i
276276 1.32288 + 2.29129i 0.0796278 + 0.137919i
277277 −12.5830 21.7944i −0.756040 1.30950i −0.944856 0.327486i 0.893798π-0.893798\pi
0.188816 0.982012i 0.439535π-0.439535\pi
278278 4.29150 7.43310i 0.257387 0.445808i
279279 −4.00000 −0.239474
280280 3.50000 + 6.06218i 0.209165 + 0.362284i
281281 −3.00000 −0.178965 −0.0894825 0.995988i 0.528521π-0.528521\pi
−0.0894825 + 0.995988i 0.528521π0.528521\pi
282282 −5.96863 + 10.3380i −0.355427 + 0.615617i
283283 11.2288 + 19.4488i 0.667480 + 1.15611i 0.978606 + 0.205741i 0.0659605π0.0659605\pi
−0.311126 + 0.950369i 0.600706π0.600706\pi
284284 6.64575 + 11.5108i 0.394353 + 0.683039i
285285 7.00000 12.1244i 0.414644 0.718185i
286286 4.00000 0.236525
287287 11.9059 20.6216i 0.702782 1.21725i
288288 −1.00000 −0.0589256
289289 4.00000 6.92820i 0.235294 0.407541i
290290 −2.64575 4.58258i −0.155364 0.269098i
291291 4.79150 + 8.29913i 0.280883 + 0.486503i
292292 2.35425 4.07768i 0.137772 0.238628i
293293 6.58301 0.384583 0.192292 0.981338i 0.438408π-0.438408\pi
0.192292 + 0.981338i 0.438408π0.438408\pi
294294 −3.50000 6.06218i −0.204124 0.353553i
295295 38.5830 2.24639
296296 −4.64575 + 8.04668i −0.270029 + 0.467704i
297297 0.500000 + 0.866025i 0.0290129 + 0.0502519i
298298 −5.93725 10.2836i −0.343936 0.595714i
299299 5.29150 9.16515i 0.306015 0.530034i
300300 −2.00000 −0.115470
301301 −1.70850 + 2.95920i −0.0984762 + 0.170566i
302302 −17.3542 −0.998625
303303 −1.64575 + 2.85052i −0.0945459 + 0.163758i
304304 2.64575 + 4.58258i 0.151744 + 0.262829i
305305 −5.20850 9.02138i −0.298238 0.516563i
306306 −1.50000 + 2.59808i −0.0857493 + 0.148522i
307307 −32.5830 −1.85961 −0.929805 0.368052i 0.880025π-0.880025\pi
−0.929805 + 0.368052i 0.880025π0.880025\pi
308308 1.32288 + 2.29129i 0.0753778 + 0.130558i
309309 10.0000 0.568880
310310 5.29150 9.16515i 0.300537 0.520546i
311311 7.26013 + 12.5749i 0.411684 + 0.713058i 0.995074 0.0991343i 0.0316074π-0.0316074\pi
−0.583390 + 0.812192i 0.698274π0.698274\pi
312312 2.00000 + 3.46410i 0.113228 + 0.196116i
313313 −0.291503 + 0.504897i −0.0164767 + 0.0285385i −0.874146 0.485663i 0.838578π-0.838578\pi
0.857669 + 0.514201i 0.171912π0.171912\pi
314314 11.2915 0.637216
315315 7.00000 0.394405
316316 5.35425 0.301200
317317 8.61438 14.9205i 0.483832 0.838021i −0.515996 0.856591i 0.672578π-0.672578\pi
0.999828 + 0.0185700i 0.00591136π0.00591136\pi
318318 −2.00000 3.46410i −0.112154 0.194257i
319319 −1.00000 1.73205i −0.0559893 0.0969762i
320320 1.32288 2.29129i 0.0739510 0.128087i
321321 −9.00000 −0.502331
322322 7.00000 0.390095
323323 15.8745 0.883281
324324 −0.500000 + 0.866025i −0.0277778 + 0.0481125i
325325 4.00000 + 6.92820i 0.221880 + 0.384308i
326326 7.79150 + 13.4953i 0.431531 + 0.747434i
327327 5.96863 10.3380i 0.330066 0.571691i
328328 −9.00000 −0.496942
329329 15.7915 + 27.3517i 0.870614 + 1.50795i
330330 −2.64575 −0.145644
331331 −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i 0.949627π-0.949627\pi
0.630232 + 0.776407i 0.282960π0.282960\pi
332332 2.79150 + 4.83502i 0.153204 + 0.265356i
333333 4.64575 + 8.04668i 0.254586 + 0.440955i
334334 9.64575 16.7069i 0.527792 0.914163i
335335 35.9373 1.96346
336336 −1.32288 + 2.29129i −0.0721688 + 0.125000i
337337 17.2915 0.941928 0.470964 0.882152i 0.343906π-0.343906\pi
0.470964 + 0.882152i 0.343906π0.343906\pi
338338 1.50000 2.59808i 0.0815892 0.141317i
339339 −4.29150 7.43310i −0.233082 0.403711i
340340 −3.96863 6.87386i −0.215229 0.372788i
341341 2.00000 3.46410i 0.108306 0.187592i
342342 5.29150 0.286132
343343 −18.5203 −1.00000
344344 1.29150 0.0696332
345345 −3.50000 + 6.06218i −0.188434 + 0.326377i
346346 2.00000 + 3.46410i 0.107521 + 0.186231i
347347 −4.20850 7.28933i −0.225924 0.391312i 0.730672 0.682728i 0.239207π-0.239207\pi
−0.956596 + 0.291417i 0.905873π0.905873\pi
348348 1.00000 1.73205i 0.0536056 0.0928477i
349349 13.2288 0.708119 0.354060 0.935223i 0.384801π-0.384801\pi
0.354060 + 0.935223i 0.384801π0.384801\pi
350350 −2.64575 + 4.58258i −0.141421 + 0.244949i
351351 4.00000 0.213504
352352 0.500000 0.866025i 0.0266501 0.0461593i
353353 6.35425 + 11.0059i 0.338203 + 0.585784i 0.984095 0.177645i 0.0568478π-0.0568478\pi
−0.645892 + 0.763429i 0.723514π0.723514\pi
354354 7.29150 + 12.6293i 0.387539 + 0.671237i
355355 −17.5830 + 30.4547i −0.933209 + 1.61637i
356356 13.2915 0.704448
357357 3.96863 + 6.87386i 0.210042 + 0.363803i
358358 −15.2915 −0.808181
359359 0.291503 0.504897i 0.0153849 0.0266475i −0.858230 0.513265i 0.828436π-0.828436\pi
0.873615 + 0.486617i 0.161769π0.161769\pi
360360 −1.32288 2.29129i −0.0697217 0.120761i
361361 −4.50000 7.79423i −0.236842 0.410223i
362362 2.64575 4.58258i 0.139058 0.240855i
363363 −1.00000 −0.0524864
364364 10.5830 0.554700
365365 12.4575 0.652056
366366 1.96863 3.40976i 0.102902 0.178231i
367367 −10.6458 18.4390i −0.555704 0.962507i −0.997848 0.0655633i 0.979116π-0.979116\pi
0.442145 0.896944i 0.354218π-0.354218\pi
368368 −1.32288 2.29129i −0.0689597 0.119442i
369369 −4.50000 + 7.79423i −0.234261 + 0.405751i
370370 −24.5830 −1.27801
371371 −10.5830 −0.549442
372372 4.00000 0.207390
373373 −15.9059 + 27.5498i −0.823575 + 1.42647i 0.0794280 + 0.996841i 0.474691π0.474691\pi
−0.903003 + 0.429634i 0.858643π0.858643\pi
374374 −1.50000 2.59808i −0.0775632 0.134343i
375375 3.96863 + 6.87386i 0.204939 + 0.354965i
376376 5.96863 10.3380i 0.307808 0.533140i
377377 −8.00000 −0.412021
378378 1.32288 + 2.29129i 0.0680414 + 0.117851i
379379 −6.41699 −0.329619 −0.164809 0.986325i 0.552701π-0.552701\pi
−0.164809 + 0.986325i 0.552701π0.552701\pi
380380 −7.00000 + 12.1244i −0.359092 + 0.621966i
381381 −1.32288 2.29129i −0.0677730 0.117386i
382382 8.64575 + 14.9749i 0.442355 + 0.766182i
383383 −14.6458 + 25.3672i −0.748363 + 1.29620i 0.200244 + 0.979746i 0.435826π0.435826\pi
−0.948607 + 0.316457i 0.897507π0.897507\pi
384384 1.00000 0.0510310
385385 −3.50000 + 6.06218i −0.178377 + 0.308957i
386386 −15.8745 −0.807991
387387 0.645751 1.11847i 0.0328254 0.0568552i
388388 −4.79150 8.29913i −0.243252 0.421324i
389389 −8.03137 13.9107i −0.407207 0.705303i 0.587369 0.809319i 0.300164π-0.300164\pi
−0.994576 + 0.104017i 0.966830π0.966830\pi
390390 −5.29150 + 9.16515i −0.267946 + 0.464095i
391391 −7.93725 −0.401404
392392 3.50000 + 6.06218i 0.176777 + 0.306186i
393393 −2.58301 −0.130295
394394 −4.93725 + 8.55157i −0.248735 + 0.430822i
395395 7.08301 + 12.2681i 0.356385 + 0.617276i
396396 −0.500000 0.866025i −0.0251259 0.0435194i
397397 −3.00000 + 5.19615i −0.150566 + 0.260787i −0.931436 0.363906i 0.881443π-0.881443\pi
0.780870 + 0.624694i 0.214776π0.214776\pi
398398 −23.1660 −1.16121
399399 7.00000 12.1244i 0.350438 0.606977i
400400 2.00000 0.100000
401401 2.06275 3.57278i 0.103009 0.178416i −0.809914 0.586548i 0.800486π-0.800486\pi
0.912923 + 0.408132i 0.133820π0.133820\pi
402402 6.79150 + 11.7632i 0.338729 + 0.586696i
403403 −8.00000 13.8564i −0.398508 0.690237i
404404 1.64575 2.85052i 0.0818792 0.141819i
405405 −2.64575 −0.131468
406406 −2.64575 4.58258i −0.131306 0.227429i
407407 −9.29150 −0.460563
408408 1.50000 2.59808i 0.0742611 0.128624i
409409 −2.06275 3.57278i −0.101996 0.176663i 0.810511 0.585724i 0.199190π-0.199190\pi
−0.912507 + 0.409061i 0.865856π0.865856\pi
410410 −11.9059 20.6216i −0.587990 1.01843i
411411 −1.35425 + 2.34563i −0.0668002 + 0.115701i
412412 −10.0000 −0.492665
413413 38.5830 1.89855
414414 −2.64575 −0.130032
415415 −7.38562 + 12.7923i −0.362546 + 0.627948i
416416 −2.00000 3.46410i −0.0980581 0.169842i
417417 4.29150 + 7.43310i 0.210156 + 0.364001i
418418 −2.64575 + 4.58258i −0.129408 + 0.224141i
419419 21.8745 1.06864 0.534320 0.845282i 0.320568π-0.320568\pi
0.534320 + 0.845282i 0.320568π0.320568\pi
420420 −7.00000 −0.341565
421421 37.8745 1.84589 0.922945 0.384931i 0.125775π-0.125775\pi
0.922945 + 0.384931i 0.125775π0.125775\pi
422422 5.35425 9.27383i 0.260641 0.451443i
423423 −5.96863 10.3380i −0.290205 0.502649i
424424 2.00000 + 3.46410i 0.0971286 + 0.168232i
425425 3.00000 5.19615i 0.145521 0.252050i
426426 −13.2915 −0.643975
427427 −5.20850 9.02138i −0.252057 0.436575i
428428 9.00000 0.435031
429429 −2.00000 + 3.46410i −0.0965609 + 0.167248i
430430 1.70850 + 2.95920i 0.0823911 + 0.142706i
431431 3.35425 + 5.80973i 0.161568 + 0.279845i 0.935431 0.353508i 0.115011π-0.115011\pi
−0.773863 + 0.633353i 0.781678π0.781678\pi
432432 0.500000 0.866025i 0.0240563 0.0416667i
433433 −19.5830 −0.941099 −0.470550 0.882374i 0.655944π-0.655944\pi
−0.470550 + 0.882374i 0.655944π0.655944\pi
434434 5.29150 9.16515i 0.254000 0.439941i
435435 5.29150 0.253708
436436 −5.96863 + 10.3380i −0.285845 + 0.495099i
437437 7.00000 + 12.1244i 0.334855 + 0.579987i
438438 2.35425 + 4.07768i 0.112490 + 0.194839i
439439 7.32288 12.6836i 0.349502 0.605355i −0.636659 0.771145i 0.719684π-0.719684\pi
0.986161 + 0.165790i 0.0530175π0.0530175\pi
440440 2.64575 0.126131
441441 7.00000 0.333333
442442 −12.0000 −0.570782
443443 −5.58301 + 9.67005i −0.265257 + 0.459438i −0.967631 0.252370i 0.918790π-0.918790\pi
0.702374 + 0.711808i 0.252123π0.252123\pi
444444 −4.64575 8.04668i −0.220478 0.381878i
445445 17.5830 + 30.4547i 0.833514 + 1.44369i
446446 −12.2288 + 21.1808i −0.579048 + 1.00294i
447447 11.8745 0.561645
448448 1.32288 2.29129i 0.0625000 0.108253i
449449 −22.4575 −1.05984 −0.529918 0.848049i 0.677777π-0.677777\pi
−0.529918 + 0.848049i 0.677777π0.677777\pi
450450 1.00000 1.73205i 0.0471405 0.0816497i
451451 −4.50000 7.79423i −0.211897 0.367016i
452452 4.29150 + 7.43310i 0.201855 + 0.349624i
453453 8.67712 15.0292i 0.407687 0.706134i
454454 −23.5830 −1.10681
455455 14.0000 + 24.2487i 0.656330 + 1.13680i
456456 −5.29150 −0.247797
457457 9.70850 16.8156i 0.454144 0.786601i −0.544494 0.838765i 0.683278π-0.683278\pi
0.998639 + 0.0521635i 0.0166117π0.0166117\pi
458458 8.64575 + 14.9749i 0.403989 + 0.699730i
459459 −1.50000 2.59808i −0.0700140 0.121268i
460460 3.50000 6.06218i 0.163188 0.282650i
461461 −3.41699 −0.159145 −0.0795727 0.996829i 0.525356π-0.525356\pi
−0.0795727 + 0.996829i 0.525356π0.525356\pi
462462 −2.64575 −0.123091
463463 −35.0405 −1.62847 −0.814235 0.580535i 0.802844π-0.802844\pi
−0.814235 + 0.580535i 0.802844π0.802844\pi
464464 −1.00000 + 1.73205i −0.0464238 + 0.0804084i
465465 5.29150 + 9.16515i 0.245388 + 0.425024i
466466 −11.0830 19.1963i −0.513410 0.889253i
467467 −4.00000 + 6.92820i −0.185098 + 0.320599i −0.943610 0.331061i 0.892594π-0.892594\pi
0.758512 + 0.651660i 0.225927π0.225927\pi
468468 −4.00000 −0.184900
469469 35.9373 1.65943
470470 31.5830 1.45682
471471 −5.64575 + 9.77873i −0.260142 + 0.450580i
472472 −7.29150 12.6293i −0.335619 0.581308i
473473 0.645751 + 1.11847i 0.0296917 + 0.0514275i
474474 −2.67712 + 4.63692i −0.122964 + 0.212981i
475475 −10.5830 −0.485582
476476 −3.96863 6.87386i −0.181902 0.315063i
477477 4.00000 0.183147
478478 6.64575 11.5108i 0.303970 0.526491i
479479 1.06275 + 1.84073i 0.0485581 + 0.0841051i 0.889283 0.457358i 0.151204π-0.151204\pi
−0.840725 + 0.541463i 0.817871π0.817871\pi
480480 1.32288 + 2.29129i 0.0603807 + 0.104583i
481481 −18.5830 + 32.1867i −0.847312 + 1.46759i
482482 −15.1660 −0.690793
483483 −3.50000 + 6.06218i −0.159256 + 0.275839i
484484 1.00000 0.0454545
485485 12.6771 21.9574i 0.575639 0.997035i
486486 −0.500000 0.866025i −0.0226805 0.0392837i
487487 4.93725 + 8.55157i 0.223728 + 0.387509i 0.955937 0.293571i 0.0948438π-0.0948438\pi
−0.732209 + 0.681080i 0.761510π0.761510\pi
488488 −1.96863 + 3.40976i −0.0891156 + 0.154353i
489489 −15.5830 −0.704688
490490 −9.26013 + 16.0390i −0.418330 + 0.724569i
491491 −1.00000 −0.0451294 −0.0225647 0.999745i 0.507183π-0.507183\pi
−0.0225647 + 0.999745i 0.507183π0.507183\pi
492492 4.50000 7.79423i 0.202876 0.351391i
493493 3.00000 + 5.19615i 0.135113 + 0.234023i
494494 10.5830 + 18.3303i 0.476152 + 0.824719i
495495 1.32288 2.29129i 0.0594588 0.102986i
496496 −4.00000 −0.179605
497497 −17.5830 + 30.4547i −0.788706 + 1.36608i
498498 −5.58301 −0.250180
499499 −1.29150 + 2.23695i −0.0578156 + 0.100140i −0.893485 0.449094i 0.851747π-0.851747\pi
0.835669 + 0.549233i 0.185080π0.185080\pi
500500 −3.96863 6.87386i −0.177482 0.307409i
501501 9.64575 + 16.7069i 0.430940 + 0.746411i
502502 6.35425 11.0059i 0.283604 0.491217i
503503 9.29150 0.414288 0.207144 0.978311i 0.433583π-0.433583\pi
0.207144 + 0.978311i 0.433583π0.433583\pi
504504 −1.32288 2.29129i −0.0589256 0.102062i
505505 8.70850 0.387523
506506 1.32288 2.29129i 0.0588090 0.101860i
507507 1.50000 + 2.59808i 0.0666173 + 0.115385i
508508 1.32288 + 2.29129i 0.0586931 + 0.101659i
509509 8.58301 14.8662i 0.380435 0.658933i −0.610689 0.791870i 0.709108π-0.709108\pi
0.991124 + 0.132937i 0.0424409π0.0424409\pi
510510 7.93725 0.351468
511511 12.4575 0.551088
512512 −1.00000 −0.0441942
513513 −2.64575 + 4.58258i −0.116813 + 0.202326i
514514 −0.645751 1.11847i −0.0284829 0.0493338i
515515 −13.2288 22.9129i −0.582929 1.00966i
516516 −0.645751 + 1.11847i −0.0284276 + 0.0492381i
517517 11.9373 0.525000
518518 −24.5830 −1.08012
519519 −4.00000 −0.175581
520520 5.29150 9.16515i 0.232048 0.401918i
521521 −21.0000 36.3731i −0.920027 1.59353i −0.799370 0.600839i 0.794833π-0.794833\pi
−0.120656 0.992694i 0.538500π-0.538500\pi
522522 1.00000 + 1.73205i 0.0437688 + 0.0758098i
523523 −6.64575 + 11.5108i −0.290598 + 0.503331i −0.973951 0.226757i 0.927188π-0.927188\pi
0.683353 + 0.730088i 0.260521π0.260521\pi
524524 2.58301 0.112839
525525 −2.64575 4.58258i −0.115470 0.200000i
526526 9.87451 0.430549
527527 −6.00000 + 10.3923i −0.261364 + 0.452696i
528528 0.500000 + 0.866025i 0.0217597 + 0.0376889i
529529 8.00000 + 13.8564i 0.347826 + 0.602452i
530530 −5.29150 + 9.16515i −0.229848 + 0.398109i
531531 −14.5830 −0.632849
532532 −7.00000 + 12.1244i −0.303488 + 0.525657i
533533 −36.0000 −1.55933
534534 −6.64575 + 11.5108i −0.287590 + 0.498120i
535535 11.9059 + 20.6216i 0.514736 + 0.891549i
536536 −6.79150 11.7632i −0.293348 0.508094i
537537 7.64575 13.2428i 0.329939 0.571470i
538538 5.35425 0.230838
539539 −3.50000 + 6.06218i −0.150756 + 0.261116i
540540 2.64575 0.113855
541541 21.9059 37.9421i 0.941807 1.63126i 0.179787 0.983706i 0.442459π-0.442459\pi
0.762021 0.647553i 0.224207π-0.224207\pi
542542 −0.645751 1.11847i −0.0277374 0.0480426i
543543 2.64575 + 4.58258i 0.113540 + 0.196657i
544544 −1.50000 + 2.59808i −0.0643120 + 0.111392i
545545 −31.5830 −1.35287
546546 −5.29150 + 9.16515i −0.226455 + 0.392232i
547547 25.2915 1.08139 0.540693 0.841220i 0.318162π-0.318162\pi
0.540693 + 0.841220i 0.318162π0.318162\pi
548548 1.35425 2.34563i 0.0578506 0.100200i
549549 1.96863 + 3.40976i 0.0840190 + 0.145525i
550550 1.00000 + 1.73205i 0.0426401 + 0.0738549i
551551 5.29150 9.16515i 0.225426 0.390449i
552552 2.64575 0.112611
553553 7.08301 + 12.2681i 0.301200 + 0.521694i
554554 −25.1660 −1.06920
555555 12.2915 21.2895i 0.521745 0.903689i
556556 −4.29150 7.43310i −0.182000 0.315234i
557557 4.35425 + 7.54178i 0.184495 + 0.319555i 0.943406 0.331639i 0.107602π-0.107602\pi
−0.758911 + 0.651194i 0.774268π0.774268\pi
558558 −2.00000 + 3.46410i −0.0846668 + 0.146647i
559559 5.16601 0.218499
560560 7.00000 0.295804
561561 3.00000 0.126660
562562 −1.50000 + 2.59808i −0.0632737 + 0.109593i
563563 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
564564 5.96863 + 10.3380i 0.251325 + 0.435307i
565565 −11.3542 + 19.6661i −0.477677 + 0.827361i
566566 22.4575 0.943960
567567 −2.64575 −0.111111
568568 13.2915 0.557699
569569 −13.5830 + 23.5265i −0.569429 + 0.986280i 0.427193 + 0.904160i 0.359502π0.359502\pi
−0.996622 + 0.0821200i 0.973831π0.973831\pi
570570 −7.00000 12.1244i −0.293198 0.507833i
571571 −16.8745 29.2275i −0.706176 1.22313i −0.966265 0.257548i 0.917085π-0.917085\pi
0.260089 0.965585i 0.416248π-0.416248\pi
572572 2.00000 3.46410i 0.0836242 0.144841i
573573 −17.2915 −0.722363
574574 −11.9059 20.6216i −0.496942 0.860729i
575575 5.29150 0.220671
576576 −0.500000 + 0.866025i −0.0208333 + 0.0360844i
577577 20.3745 + 35.2897i 0.848202 + 1.46913i 0.882811 + 0.469728i 0.155648π0.155648\pi
−0.0346094 + 0.999401i 0.511019π0.511019\pi
578578 −4.00000 6.92820i −0.166378 0.288175i
579579 7.93725 13.7477i 0.329861 0.571336i
580580 −5.29150 −0.219718
581581 −7.38562 + 12.7923i −0.306407 + 0.530713i
582582 9.58301 0.397228
583583 −2.00000 + 3.46410i −0.0828315 + 0.143468i
584584 −2.35425 4.07768i −0.0974195 0.168736i
585585 −5.29150 9.16515i −0.218777 0.378932i
586586 3.29150 5.70105i 0.135971 0.235508i
587587 −21.8745 −0.902858 −0.451429 0.892307i 0.649086π-0.649086\pi
−0.451429 + 0.892307i 0.649086π0.649086\pi
588588 −7.00000 −0.288675
589589 21.1660 0.872130
590590 19.2915 33.4139i 0.794219 1.37563i
591591 −4.93725 8.55157i −0.203091 0.351765i
592592 4.64575 + 8.04668i 0.190939 + 0.330716i
593593 −18.8745 + 32.6916i −0.775083 + 1.34248i 0.159665 + 0.987171i 0.448959π0.448959\pi
−0.934748 + 0.355312i 0.884375π0.884375\pi
594594 1.00000 0.0410305
595595 10.5000 18.1865i 0.430458 0.745575i
596596 −11.8745 −0.486399
597597 11.5830 20.0624i 0.474061 0.821097i
598598 −5.29150 9.16515i −0.216386 0.374791i
599599 −17.3229 30.0041i −0.707794 1.22593i −0.965674 0.259757i 0.916357π-0.916357\pi
0.257880 0.966177i 0.416976π-0.416976\pi
600600 −1.00000 + 1.73205i −0.0408248 + 0.0707107i
601601 −17.4170 −0.710454 −0.355227 0.934780i 0.615596π-0.615596\pi
−0.355227 + 0.934780i 0.615596π0.615596\pi
602602 1.70850 + 2.95920i 0.0696332 + 0.120608i
603603 −13.5830 −0.553143
604604 −8.67712 + 15.0292i −0.353067 + 0.611530i
605605 1.32288 + 2.29129i 0.0537825 + 0.0931541i
606606 1.64575 + 2.85052i 0.0668541 + 0.115795i
607607 −22.5516 + 39.0606i −0.915343 + 1.58542i −0.108943 + 0.994048i 0.534747π0.534747\pi
−0.806399 + 0.591372i 0.798587π0.798587\pi
608608 5.29150 0.214599
609609 5.29150 0.214423
610610 −10.4170 −0.421772
611611 23.8745 41.3519i 0.965859 1.67292i
612612 1.50000 + 2.59808i 0.0606339 + 0.105021i
613613 19.9059 + 34.4780i 0.803991 + 1.39255i 0.916970 + 0.398956i 0.130627π0.130627\pi
−0.112979 + 0.993597i 0.536039π0.536039\pi
614614 −16.2915 + 28.2177i −0.657472 + 1.13877i
615615 23.8118 0.960183
616616 2.64575 0.106600
617617 −25.2915 −1.01820 −0.509099 0.860708i 0.670021π-0.670021\pi
−0.509099 + 0.860708i 0.670021π0.670021\pi
618618 5.00000 8.66025i 0.201129 0.348367i
619619 20.5000 + 35.5070i 0.823965 + 1.42715i 0.902708 + 0.430254i 0.141576π0.141576\pi
−0.0787435 + 0.996895i 0.525091π0.525091\pi
620620 −5.29150 9.16515i −0.212512 0.368081i
621621 1.32288 2.29129i 0.0530852 0.0919462i
622622 14.5203 0.582209
623623 17.5830 + 30.4547i 0.704448 + 1.22014i
624624 4.00000 0.160128
625625 15.5000 26.8468i 0.620000 1.07387i
626626 0.291503 + 0.504897i 0.0116508 + 0.0201798i
627627 −2.64575 4.58258i −0.105661 0.183010i
628628 5.64575 9.77873i 0.225290 0.390214i
629629 27.8745 1.11143
630630 3.50000 6.06218i 0.139443 0.241523i
631631 10.1255 0.403089 0.201545 0.979479i 0.435404π-0.435404\pi
0.201545 + 0.979479i 0.435404π0.435404\pi
632632 2.67712 4.63692i 0.106490 0.184447i
633633 5.35425 + 9.27383i 0.212812 + 0.368602i
634634 −8.61438 14.9205i −0.342121 0.592570i
635635 −3.50000 + 6.06218i −0.138893 + 0.240570i
636636 −4.00000 −0.158610
637637 14.0000 + 24.2487i 0.554700 + 0.960769i
638638 −2.00000 −0.0791808
639639 6.64575 11.5108i 0.262902 0.455359i
640640 −1.32288 2.29129i −0.0522913 0.0905711i
641641 2.70850 + 4.69126i 0.106979 + 0.185293i 0.914545 0.404484i 0.132549π-0.132549\pi
−0.807566 + 0.589777i 0.799216π0.799216\pi
642642 −4.50000 + 7.79423i −0.177601 + 0.307614i
643643 41.1660 1.62343 0.811714 0.584054i 0.198535π-0.198535\pi
0.811714 + 0.584054i 0.198535π0.198535\pi
644644 3.50000 6.06218i 0.137919 0.238883i
645645 −3.41699 −0.134544
646646 7.93725 13.7477i 0.312287 0.540897i
647647 −21.1974 36.7149i −0.833355 1.44341i −0.895363 0.445338i 0.853084π-0.853084\pi
0.0620075 0.998076i 0.480250π-0.480250\pi
648648 0.500000 + 0.866025i 0.0196419 + 0.0340207i
649649 7.29150 12.6293i 0.286217 0.495742i
650650 8.00000 0.313786
651651 5.29150 + 9.16515i 0.207390 + 0.359211i
652652 15.5830 0.610278
653653 −6.55163 + 11.3478i −0.256385 + 0.444072i −0.965271 0.261251i 0.915865π-0.915865\pi
0.708886 + 0.705323i 0.249198π0.249198\pi
654654 −5.96863 10.3380i −0.233392 0.404246i
655655 3.41699 + 5.91841i 0.133513 + 0.231251i
656656 −4.50000 + 7.79423i −0.175695 + 0.304314i
657657 −4.70850 −0.183696
658658 31.5830 1.23123
659659 18.1660 0.707647 0.353824 0.935312i 0.384881π-0.384881\pi
0.353824 + 0.935312i 0.384881π0.384881\pi
660660 −1.32288 + 2.29129i −0.0514929 + 0.0891883i
661661 −15.6458 27.0992i −0.608549 1.05404i −0.991480 0.130261i 0.958418π-0.958418\pi
0.382931 0.923777i 0.374915π-0.374915\pi
662662 6.50000 + 11.2583i 0.252630 + 0.437567i
663663 6.00000 10.3923i 0.233021 0.403604i
664664 5.58301 0.216663
665665 −37.0405 −1.43637
666666 9.29150 0.360038
667667 −2.64575 + 4.58258i −0.102444 + 0.177438i
668668 −9.64575 16.7069i −0.373205 0.646411i
669669 −12.2288 21.1808i −0.472791 0.818898i
670670 17.9686 31.1226i 0.694189 1.20237i
671671 −3.93725 −0.151996
672672 1.32288 + 2.29129i 0.0510310 + 0.0883883i
673673 −40.5830 −1.56436 −0.782180 0.623053i 0.785892π-0.785892\pi
−0.782180 + 0.623053i 0.785892π0.785892\pi
674674 8.64575 14.9749i 0.333022 0.576811i
675675 1.00000 + 1.73205i 0.0384900 + 0.0666667i
676676 −1.50000 2.59808i −0.0576923 0.0999260i
677677 19.9373 34.5323i 0.766251 1.32719i −0.173332 0.984863i 0.555453π-0.555453\pi
0.939583 0.342322i 0.111213π-0.111213\pi
678678 −8.58301 −0.329628
679679 12.6771 21.9574i 0.486503 0.842649i
680680 −7.93725 −0.304380
681681 11.7915 20.4235i 0.451851 0.782630i
682682 −2.00000 3.46410i −0.0765840 0.132647i
683683 −12.5830 21.7944i −0.481475 0.833940i 0.518299 0.855200i 0.326566π-0.326566\pi
−0.999774 + 0.0212600i 0.993232π0.993232\pi
684684 2.64575 4.58258i 0.101163 0.175219i
685685 7.16601 0.273799
686686 −9.26013 + 16.0390i −0.353553 + 0.612372i
687687 −17.2915 −0.659712
688688 0.645751 1.11847i 0.0246190 0.0426414i
689689 8.00000 + 13.8564i 0.304776 + 0.527887i
690690 3.50000 + 6.06218i 0.133243 + 0.230783i
691691 14.0830 24.3925i 0.535743 0.927934i −0.463384 0.886157i 0.653365π-0.653365\pi
0.999127 0.0417762i 0.0133017π-0.0133017\pi
692692 4.00000 0.152057
693693 1.32288 2.29129i 0.0502519 0.0870388i
694694 −8.41699 −0.319505
695695 11.3542 19.6661i 0.430691 0.745979i
696696 −1.00000 1.73205i −0.0379049 0.0656532i
697697 13.5000 + 23.3827i 0.511349 + 0.885682i
698698 6.61438 11.4564i 0.250358 0.433633i
699699 22.1660 0.838396
700700 2.64575 + 4.58258i 0.100000 + 0.173205i
701701 −10.4575 −0.394975 −0.197487 0.980305i 0.563278π-0.563278\pi
−0.197487 + 0.980305i 0.563278π0.563278\pi
702702 2.00000 3.46410i 0.0754851 0.130744i
703703 −24.5830 42.5790i −0.927166 1.60590i
704704 −0.500000 0.866025i −0.0188445 0.0326396i
705705 −15.7915 + 27.3517i −0.594742 + 1.03012i
706706 12.7085 0.478291
707707 8.70850 0.327517
708708 14.5830 0.548063
709709 23.8745 41.3519i 0.896626 1.55300i 0.0648467 0.997895i 0.479344π-0.479344\pi
0.831779 0.555106i 0.187322π-0.187322\pi
710710 17.5830 + 30.4547i 0.659878 + 1.14294i
711711 −2.67712 4.63692i −0.100400 0.173898i
712712 6.64575 11.5108i 0.249060 0.431385i
713713 −10.5830 −0.396337
714714 7.93725 0.297044
715715 10.5830 0.395782
716716 −7.64575 + 13.2428i −0.285735 + 0.494908i
717717 6.64575 + 11.5108i 0.248190 + 0.429878i
718718 −0.291503 0.504897i −0.0108788 0.0188426i
719719 21.9686 38.0508i 0.819292 1.41905i −0.0869134 0.996216i 0.527700π-0.527700\pi
0.906205 0.422839i 0.138966π-0.138966\pi
720720 −2.64575 −0.0986013
721721 −13.2288 22.9129i −0.492665 0.853320i
722722 −9.00000 −0.334945
723723 7.58301 13.1342i 0.282015 0.488464i
724724 −2.64575 4.58258i −0.0983286 0.170310i
725725 −2.00000 3.46410i −0.0742781 0.128654i
726726 −0.500000 + 0.866025i −0.0185567 + 0.0321412i
727727 −2.00000 −0.0741759 −0.0370879 0.999312i 0.511808π-0.511808\pi
−0.0370879 + 0.999312i 0.511808π0.511808\pi
728728 5.29150 9.16515i 0.196116 0.339683i
729729 1.00000 0.0370370
730730 6.22876 10.7885i 0.230537 0.399301i
731731 −1.93725 3.35542i −0.0716519 0.124105i
732732 −1.96863 3.40976i −0.0727625 0.126028i
733733 1.96863 3.40976i 0.0727129 0.125942i −0.827377 0.561648i 0.810168π-0.810168\pi
0.900089 + 0.435705i 0.143501π0.143501\pi
734734 −21.2915 −0.785884
735735 −9.26013 16.0390i −0.341565 0.591608i
736736 −2.64575 −0.0975237
737737 6.79150 11.7632i 0.250168 0.433304i
738738 4.50000 + 7.79423i 0.165647 + 0.286910i
739739 1.70850 + 2.95920i 0.0628481 + 0.108856i 0.895737 0.444584i 0.146648π-0.146648\pi
−0.832889 + 0.553440i 0.813315π0.813315\pi
740740 −12.2915 + 21.2895i −0.451845 + 0.782618i
741741 −21.1660 −0.777553
742742 −5.29150 + 9.16515i −0.194257 + 0.336463i
743743 −29.2915 −1.07460 −0.537301 0.843391i 0.680556π-0.680556\pi
−0.537301 + 0.843391i 0.680556π0.680556\pi
744744 2.00000 3.46410i 0.0733236 0.127000i
745745 −15.7085 27.2079i −0.575515 0.996821i
746746 15.9059 + 27.5498i 0.582356 + 1.00867i
747747 2.79150 4.83502i 0.102136 0.176904i
748748 −3.00000 −0.109691
749749 11.9059 + 20.6216i 0.435031 + 0.753497i
750750 7.93725 0.289828
751751 9.35425 16.2020i 0.341341 0.591221i −0.643341 0.765580i 0.722452π-0.722452\pi
0.984682 + 0.174359i 0.0557854π0.0557854\pi
752752 −5.96863 10.3380i −0.217653 0.376987i
753753 6.35425 + 11.0059i 0.231562 + 0.401077i
754754 −4.00000 + 6.92820i −0.145671 + 0.252310i
755755 −45.9150 −1.67102
756756 2.64575 0.0962250
757757 −11.4170 −0.414958 −0.207479 0.978240i 0.566526π-0.566526\pi
−0.207479 + 0.978240i 0.566526π0.566526\pi
758758 −3.20850 + 5.55728i −0.116538 + 0.201850i
759759 1.32288 + 2.29129i 0.0480173 + 0.0831685i
760760 7.00000 + 12.1244i 0.253917 + 0.439797i
761761 −13.2085 + 22.8778i −0.478808 + 0.829319i −0.999705 0.0243003i 0.992264π-0.992264\pi
0.520897 + 0.853620i 0.325598π0.325598\pi
762762 −2.64575 −0.0958455
763763 −31.5830 −1.14338
764764 17.2915 0.625585
765765 −3.96863 + 6.87386i −0.143486 + 0.248525i
766766 14.6458 + 25.3672i 0.529173 + 0.916554i
767767 −29.1660 50.5170i −1.05312 1.82406i
768768 0.500000 0.866025i 0.0180422 0.0312500i
769769 −41.2915 −1.48901 −0.744505 0.667617i 0.767314π-0.767314\pi
−0.744505 + 0.667617i 0.767314π0.767314\pi
770770 3.50000 + 6.06218i 0.126131 + 0.218466i
771771 1.29150 0.0465123
772772 −7.93725 + 13.7477i −0.285668 + 0.494792i
773773 11.9686 + 20.7303i 0.430482 + 0.745616i 0.996915 0.0784917i 0.0250104π-0.0250104\pi
−0.566433 + 0.824108i 0.691677π0.691677\pi
774774 −0.645751 1.11847i −0.0232111 0.0402027i
775775 4.00000 6.92820i 0.143684 0.248868i
776776 −9.58301 −0.344010
777777 12.2915 21.2895i 0.440955 0.763757i
778778 −16.0627 −0.575877
779779 23.8118 41.2432i 0.853145 1.47769i
780780 5.29150 + 9.16515i 0.189466 + 0.328165i
781781 6.64575 + 11.5108i 0.237804 + 0.411888i
782782 −3.96863 + 6.87386i −0.141918 + 0.245809i
783783 −2.00000 −0.0714742
784784 7.00000 0.250000
785785 29.8745 1.06627
786786 −1.29150 + 2.23695i −0.0460664 + 0.0797893i
787787 0.645751 + 1.11847i 0.0230185 + 0.0398693i 0.877305 0.479933i 0.159339π-0.159339\pi
−0.854287 + 0.519802i 0.826006π0.826006\pi
788788 4.93725 + 8.55157i 0.175882 + 0.304637i
789789 −4.93725 + 8.55157i −0.175771 + 0.304444i
790790 14.1660 0.504004
791791 −11.3542 + 19.6661i −0.403711 + 0.699247i
792792 −1.00000 −0.0355335
793793 −7.87451 + 13.6390i −0.279632 + 0.484337i
794794 3.00000 + 5.19615i 0.106466 + 0.184405i
795795 −5.29150 9.16515i −0.187670 0.325054i
796796 −11.5830 + 20.0624i −0.410549 + 0.711091i
797797 −13.1033 −0.464141 −0.232071 0.972699i 0.574550π-0.574550\pi
−0.232071 + 0.972699i 0.574550π0.574550\pi
798798 −7.00000 12.1244i −0.247797 0.429198i
799799 −35.8118 −1.26693
800800 1.00000 1.73205i 0.0353553 0.0612372i
801801 −6.64575 11.5108i −0.234816 0.406713i
802802 −2.06275 3.57278i −0.0728381 0.126159i
803803 2.35425 4.07768i 0.0830796 0.143898i
804804 13.5830 0.479036
805805 18.5203 0.652753
806806 −16.0000 −0.563576
807807 −2.67712 + 4.63692i −0.0942392 + 0.163227i
808808 −1.64575 2.85052i −0.0578973 0.100281i
809809 19.6660 + 34.0625i 0.691420 + 1.19757i 0.971373 + 0.237561i 0.0763479π0.0763479\pi
−0.279953 + 0.960014i 0.590319π0.590319\pi
810810 −1.32288 + 2.29129i −0.0464811 + 0.0805076i
811811 −4.58301 −0.160931 −0.0804655 0.996757i 0.525641π-0.525641\pi
−0.0804655 + 0.996757i 0.525641π0.525641\pi
812812 −5.29150 −0.185695
813813 1.29150 0.0452950
814814 −4.64575 + 8.04668i −0.162833 + 0.282036i
815815 20.6144 + 35.7052i 0.722090 + 1.25070i
816816 −1.50000 2.59808i −0.0525105 0.0909509i
817817 −3.41699 + 5.91841i −0.119546 + 0.207059i
818818 −4.12549 −0.144244
819819 −5.29150 9.16515i −0.184900 0.320256i
820820 −23.8118 −0.831543
821821 −27.1660 + 47.0529i −0.948100 + 1.64216i −0.198679 + 0.980065i 0.563665π0.563665\pi
−0.749421 + 0.662093i 0.769668π0.769668\pi
822822 1.35425 + 2.34563i 0.0472348 + 0.0818132i
823823 21.9373 + 37.9964i 0.764685 + 1.32447i 0.940413 + 0.340034i 0.110439π0.110439\pi
−0.175729 + 0.984439i 0.556228π0.556228\pi
824824 −5.00000 + 8.66025i −0.174183 + 0.301694i
825825 −2.00000 −0.0696311
826826 19.2915 33.4139i 0.671237 1.16262i
827827 −49.3320 −1.71544 −0.857721 0.514115i 0.828120π-0.828120\pi
−0.857721 + 0.514115i 0.828120π0.828120\pi
828828 −1.32288 + 2.29129i −0.0459731 + 0.0796278i
829829 5.93725 + 10.2836i 0.206209 + 0.357165i 0.950517 0.310671i 0.100554π-0.100554\pi
−0.744308 + 0.667836i 0.767221π0.767221\pi
830830 7.38562 + 12.7923i 0.256359 + 0.444026i
831831 12.5830 21.7944i 0.436500 0.756040i
832832 −4.00000 −0.138675
833833 10.5000 18.1865i 0.363803 0.630126i
834834 8.58301 0.297205
835835 25.5203 44.2024i 0.883165 1.52969i
836836 2.64575 + 4.58258i 0.0915052 + 0.158492i
837837 −2.00000 3.46410i −0.0691301 0.119737i
838838 10.9373 18.9439i 0.377821 0.654405i
839839 21.1033 0.728566 0.364283 0.931288i 0.381314π-0.381314\pi
0.364283 + 0.931288i 0.381314π0.381314\pi
840840 −3.50000 + 6.06218i −0.120761 + 0.209165i
841841 −25.0000 −0.862069
842842 18.9373 32.8003i 0.652621 1.13037i
843843 −1.50000 2.59808i −0.0516627 0.0894825i
844844 −5.35425 9.27383i −0.184301 0.319218i
845845 3.96863 6.87386i 0.136525 0.236468i
846846 −11.9373 −0.410411
847847 1.32288 + 2.29129i 0.0454545 + 0.0787296i
848848 4.00000 0.137361
849849 −11.2288 + 19.4488i −0.385370 + 0.667480i
850850 −3.00000 5.19615i −0.102899 0.178227i
851851 12.2915 + 21.2895i 0.421347 + 0.729795i
852852 −6.64575 + 11.5108i −0.227680 + 0.394353i
853853 −22.5203 −0.771079 −0.385539 0.922691i 0.625985π-0.625985\pi
−0.385539 + 0.922691i 0.625985π0.625985\pi
854854 −10.4170 −0.356462
855855 14.0000 0.478790
856856 4.50000 7.79423i 0.153807 0.266401i
857857 −26.0830 45.1771i −0.890978 1.54322i −0.838704 0.544587i 0.816686π-0.816686\pi
−0.0522743 0.998633i 0.516647π-0.516647\pi
858858 2.00000 + 3.46410i 0.0682789 + 0.118262i
859859 7.37451 12.7730i 0.251615 0.435810i −0.712356 0.701819i 0.752372π-0.752372\pi
0.963971 + 0.266009i 0.0857050π0.0857050\pi
860860 3.41699 0.116519
861861 23.8118 0.811503
862862 6.70850 0.228492
863863 −12.5516 + 21.7401i −0.427263 + 0.740040i −0.996629 0.0820436i 0.973855π-0.973855\pi
0.569366 + 0.822084i 0.307189π0.307189\pi
864864 −0.500000 0.866025i −0.0170103 0.0294628i
865865 5.29150 + 9.16515i 0.179916 + 0.311624i
866866 −9.79150 + 16.9594i −0.332729 + 0.576303i
867867 8.00000 0.271694
868868 −5.29150 9.16515i −0.179605 0.311086i
869869 5.35425 0.181630
870870 2.64575 4.58258i 0.0896994 0.155364i
871871 −27.1660 47.0529i −0.920485 1.59433i
872872 5.96863 + 10.3380i 0.202123 + 0.350088i
873873 −4.79150 + 8.29913i −0.162168 + 0.280883i
874874 14.0000 0.473557
875875 10.5000 18.1865i 0.354965 0.614817i
876876 4.70850 0.159085
877877 −18.6144 + 32.2410i −0.628563 + 1.08870i 0.359277 + 0.933231i 0.383023π0.383023\pi
−0.987840 + 0.155472i 0.950310π0.950310\pi
878878 −7.32288 12.6836i −0.247135 0.428051i
879879 3.29150 + 5.70105i 0.111020 + 0.192292i
880880 1.32288 2.29129i 0.0445941 0.0772393i
881881 −19.1660 −0.645719 −0.322860 0.946447i 0.604644π-0.604644\pi
−0.322860 + 0.946447i 0.604644π0.604644\pi
882882 3.50000 6.06218i 0.117851 0.204124i
883883 −55.5830 −1.87052 −0.935259 0.353965i 0.884833π-0.884833\pi
−0.935259 + 0.353965i 0.884833π0.884833\pi
884884 −6.00000 + 10.3923i −0.201802 + 0.349531i
885885 19.2915 + 33.4139i 0.648477 + 1.12319i
886886 5.58301 + 9.67005i 0.187565 + 0.324872i
887887 −21.5203 + 37.2742i −0.722580 + 1.25154i 0.237383 + 0.971416i 0.423710π0.423710\pi
−0.959963 + 0.280128i 0.909623π0.909623\pi
888888 −9.29150 −0.311802
889889 −3.50000 + 6.06218i −0.117386 + 0.203319i
890890 35.1660 1.17877
891891 −0.500000 + 0.866025i −0.0167506 + 0.0290129i
892892 12.2288 + 21.1808i 0.409449 + 0.709187i
893893 31.5830 + 54.7034i 1.05688 + 1.83058i
894894 5.93725 10.2836i 0.198571 0.343936i
895895 −40.4575 −1.35235
896896 −1.32288 2.29129i −0.0441942 0.0765466i
897897 10.5830 0.353356
898898 −11.2288 + 19.4488i −0.374708 + 0.649014i
899899 4.00000 + 6.92820i 0.133407 + 0.231069i
900900 −1.00000 1.73205i −0.0333333 0.0577350i
901901 6.00000 10.3923i 0.199889 0.346218i
902902 −9.00000 −0.299667
903903 −3.41699 −0.113710
904904 8.58301 0.285467
905905 7.00000 12.1244i 0.232688 0.403027i
906906 −8.67712 15.0292i −0.288278 0.499312i
907907 29.0830 + 50.3732i 0.965685 + 1.67262i 0.707762 + 0.706451i 0.249705π0.249705\pi
0.257923 + 0.966165i 0.416962π0.416962\pi
908908 −11.7915 + 20.4235i −0.391315 + 0.677777i
909909 −3.29150 −0.109172
910910 28.0000 0.928191
911911 50.3948 1.66965 0.834827 0.550513i 0.185568π-0.185568\pi
0.834827 + 0.550513i 0.185568π0.185568\pi
912912 −2.64575 + 4.58258i −0.0876096 + 0.151744i
913913 2.79150 + 4.83502i 0.0923853 + 0.160016i
914914 −9.70850 16.8156i −0.321129 0.556211i
915915 5.20850 9.02138i 0.172188 0.298238i
916916 17.2915 0.571327
917917 3.41699 + 5.91841i 0.112839 + 0.195443i
918918 −3.00000 −0.0990148
919919 −7.32288 + 12.6836i −0.241559 + 0.418393i −0.961159 0.275996i 0.910992π-0.910992\pi
0.719599 + 0.694390i 0.244326π0.244326\pi
920920 −3.50000 6.06218i −0.115392 0.199864i
921921 −16.2915 28.2177i −0.536823 0.929805i
922922 −1.70850 + 2.95920i −0.0562664 + 0.0974562i
923923 53.1660 1.74998
924924 −1.32288 + 2.29129i −0.0435194 + 0.0753778i
925925 −18.5830 −0.611005
926926 −17.5203 + 30.3460i −0.575751 + 0.997231i
927927 5.00000 + 8.66025i 0.164222 + 0.284440i
928928 1.00000 + 1.73205i 0.0328266 + 0.0568574i
929929 −9.22876 + 15.9847i −0.302786 + 0.524440i −0.976766 0.214309i 0.931250π-0.931250\pi
0.673980 + 0.738749i 0.264583π0.264583\pi
930930 10.5830 0.347030
931931 −37.0405 −1.21395
932932 −22.1660 −0.726072
933933 −7.26013 + 12.5749i −0.237686 + 0.411684i
934934 4.00000 + 6.92820i 0.130884 + 0.226698i
935935 −3.96863 6.87386i −0.129788 0.224799i
936936 −2.00000 + 3.46410i −0.0653720 + 0.113228i
937937 50.0000 1.63343 0.816714 0.577042i 0.195793π-0.195793\pi
0.816714 + 0.577042i 0.195793π0.195793\pi
938938 17.9686 31.1226i 0.586696 1.01619i
939939 −0.583005 −0.0190257
940940 15.7915 27.3517i 0.515062 0.892114i
941941 −12.2915 21.2895i −0.400692 0.694018i 0.593118 0.805116i 0.297897π-0.297897\pi
−0.993810 + 0.111097i 0.964563π0.964563\pi
942942 5.64575 + 9.77873i 0.183949 + 0.318608i
943943 −11.9059 + 20.6216i −0.387709 + 0.671531i
944944 −14.5830 −0.474636
945945 3.50000 + 6.06218i 0.113855 + 0.197203i
946946 1.29150 0.0419904
947947 18.2915 31.6818i 0.594394 1.02952i −0.399238 0.916847i 0.630725π-0.630725\pi
0.993632 0.112673i 0.0359413π-0.0359413\pi
948948 2.67712 + 4.63692i 0.0869490 + 0.150600i
949949 −9.41699 16.3107i −0.305689 0.529468i
950950 −5.29150 + 9.16515i −0.171679 + 0.297357i
951951 17.2288 0.558681
952952 −7.93725 −0.257248
953953 −36.7490 −1.19042 −0.595209 0.803571i 0.702931π-0.702931\pi
−0.595209 + 0.803571i 0.702931π0.702931\pi
954954 2.00000 3.46410i 0.0647524 0.112154i
955955 22.8745 + 39.6198i 0.740202 + 1.28207i
956956 −6.64575 11.5108i −0.214939 0.372285i
957957 1.00000 1.73205i 0.0323254 0.0559893i
958958 2.12549 0.0686715
959959 7.16601 0.231403
960960 2.64575 0.0853913
961961 7.50000 12.9904i 0.241935 0.419045i
962962 18.5830 + 32.1867i 0.599140 + 1.03774i
963963 −4.50000 7.79423i −0.145010 0.251166i
964964 −7.58301 + 13.1342i −0.244232 + 0.423022i
965965 −42.0000 −1.35203
966966 3.50000 + 6.06218i 0.112611 + 0.195047i
967967 55.9373 1.79882 0.899410 0.437105i 0.143996π-0.143996\pi
0.899410 + 0.437105i 0.143996π0.143996\pi
968968 0.500000 0.866025i 0.0160706 0.0278351i
969969 7.93725 + 13.7477i 0.254981 + 0.441641i
970970 −12.6771 21.9574i −0.407038 0.705010i
971971 −3.00000 + 5.19615i −0.0962746 + 0.166752i −0.910140 0.414301i 0.864026π-0.864026\pi
0.813865 + 0.581054i 0.197359π0.197359\pi
972972 −1.00000 −0.0320750
973973 11.3542 19.6661i 0.364001 0.630467i
974974 9.87451 0.316400
975975 −4.00000 + 6.92820i −0.128103 + 0.221880i
976976 1.96863 + 3.40976i 0.0630142 + 0.109144i
977977 14.5830 + 25.2585i 0.466552 + 0.808091i 0.999270 0.0382014i 0.0121628π-0.0121628\pi
−0.532718 + 0.846293i 0.678830π0.678830\pi
978978 −7.79150 + 13.4953i −0.249145 + 0.431531i
979979 13.2915 0.424798
980980 9.26013 + 16.0390i 0.295804 + 0.512348i
981981 11.9373 0.381127
982982 −0.500000 + 0.866025i −0.0159556 + 0.0276360i
983983 −2.73987 4.74559i −0.0873883 0.151361i 0.819018 0.573768i 0.194519π-0.194519\pi
−0.906406 + 0.422407i 0.861185π0.861185\pi
984984 −4.50000 7.79423i −0.143455 0.248471i
985985 −13.0627 + 22.6253i −0.416214 + 0.720903i
986986 6.00000 0.191079
987987 −15.7915 + 27.3517i −0.502649 + 0.870614i
988988 21.1660 0.673380
989989 1.70850 2.95920i 0.0543271 0.0940972i
990990 −1.32288 2.29129i −0.0420437 0.0728219i
991991 6.06275 + 10.5010i 0.192589 + 0.333575i 0.946108 0.323852i 0.104978π-0.104978\pi
−0.753518 + 0.657427i 0.771645π0.771645\pi
992992 −2.00000 + 3.46410i −0.0635001 + 0.109985i
993993 −13.0000 −0.412543
994994 17.5830 + 30.4547i 0.557699 + 0.965963i
995995 −61.2915 −1.94307
996996 −2.79150 + 4.83502i −0.0884521 + 0.153204i
997997 −24.5830 42.5790i −0.778552 1.34849i −0.932777 0.360455i 0.882621π-0.882621\pi
0.154225 0.988036i 0.450712π-0.450712\pi
998998 1.29150 + 2.23695i 0.0408818 + 0.0708094i
999999 −4.64575 + 8.04668i −0.146985 + 0.254586i
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 462.2.i.e.331.2 yes 4
3.2 odd 2 1386.2.k.r.793.1 4
7.2 even 3 3234.2.a.w.1.1 2
7.4 even 3 inner 462.2.i.e.67.2 4
7.5 odd 6 3234.2.a.ba.1.2 2
21.2 odd 6 9702.2.a.db.1.2 2
21.5 even 6 9702.2.a.dm.1.1 2
21.11 odd 6 1386.2.k.r.991.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.i.e.67.2 4 7.4 even 3 inner
462.2.i.e.331.2 yes 4 1.1 even 1 trivial
1386.2.k.r.793.1 4 3.2 odd 2
1386.2.k.r.991.1 4 21.11 odd 6
3234.2.a.w.1.1 2 7.2 even 3
3234.2.a.ba.1.2 2 7.5 odd 6
9702.2.a.db.1.2 2 21.2 odd 6
9702.2.a.dm.1.1 2 21.5 even 6