Properties

Label 637.2.q.c.589.1
Level 637637
Weight 22
Character 637.589
Analytic conductor 5.0865.086
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] = [637,2,Mod(491,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.491");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 637=7213 637 = 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 637.q (of order 66, 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: 5.086470608765.08647060876
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 91)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 589.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 637.589
Dual form 637.2.q.c.491.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.50000+0.866025i)q2+(0.5000000.866025i)q3+(0.500000+0.866025i)q4+1.73205iq5+(1.500000.866025i)q61.73205iq8+(1.00000+1.73205i)q9+(1.50000+2.59808i)q10+(4.50000+2.59808i)q11+1.00000q12+(1.00000+3.46410i)q13+(1.50000+0.866025i)q15+(2.500004.33013i)q16+(3.000005.19615i)q17+3.46410iq18+(1.500000.866025i)q19+(1.50000+0.866025i)q20+(4.50000+7.79423i)q22+(1.500000.866025i)q24+2.00000q25+(4.50000+4.33013i)q26+5.00000q27+(1.50000+2.59808i)q29+(1.50000+2.59808i)q30+1.73205iq31+(4.500002.59808i)q32+(4.500002.59808i)q3310.3923iq34+(1.00000+1.73205i)q36+3.00000q38+(2.50000+2.59808i)q39+3.00000q40+(4.500002.59808i)q41+(5.500009.52628i)q43+5.19615iq44+(3.00000+1.73205i)q45+8.66025iq47+(2.500004.33013i)q48+(3.00000+1.73205i)q506.00000q51+(3.50000+0.866025i)q529.00000q53+(7.50000+4.33013i)q54+(4.50000+7.79423i)q551.73205iq57+(4.50000+2.59808i)q58+(3.000001.73205i)q59+1.73205iq60+(3.500006.06218i)q61+(1.50000+2.59808i)q621.00000q64+(6.000001.73205i)q65+9.00000q66+(7.500004.33013i)q67+(3.000005.19615i)q68+(1.500000.866025i)q71+(3.000001.73205i)q728.66025iq73+(1.000001.73205i)q75+(1.50000+0.866025i)q76+(1.50000+6.06218i)q785.00000q79+(7.50000+4.33013i)q80+(0.500000+0.866025i)q81+(4.500007.79423i)q823.46410iq83+(9.000005.19615i)q8519.0526iq86+(1.50000+2.59808i)q87+(4.500007.79423i)q88+(6.00000+3.46410i)q896.00000q90+(1.50000+0.866025i)q93+(7.50000+12.9904i)q94+(1.50000+2.59808i)q955.19615iq96+(4.50000+2.59808i)q97+10.3923iq99+O(q100)q+(1.50000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.73205i q^{5} +(1.50000 - 0.866025i) q^{6} -1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(4.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} +(1.50000 + 0.866025i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-3.00000 - 5.19615i) q^{17} +3.46410i q^{18} +(1.50000 - 0.866025i) q^{19} +(-1.50000 + 0.866025i) q^{20} +(4.50000 + 7.79423i) q^{22} +(-1.50000 - 0.866025i) q^{24} +2.00000 q^{25} +(-4.50000 + 4.33013i) q^{26} +5.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} +(1.50000 + 2.59808i) q^{30} +1.73205i q^{31} +(4.50000 - 2.59808i) q^{32} +(4.50000 - 2.59808i) q^{33} -10.3923i q^{34} +(-1.00000 + 1.73205i) q^{36} +3.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +3.00000 q^{40} +(-4.50000 - 2.59808i) q^{41} +(-5.50000 - 9.52628i) q^{43} +5.19615i q^{44} +(-3.00000 + 1.73205i) q^{45} +8.66025i q^{47} +(-2.50000 - 4.33013i) q^{48} +(3.00000 + 1.73205i) q^{50} -6.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} -9.00000 q^{53} +(7.50000 + 4.33013i) q^{54} +(-4.50000 + 7.79423i) q^{55} -1.73205i q^{57} +(-4.50000 + 2.59808i) q^{58} +(3.00000 - 1.73205i) q^{59} +1.73205i q^{60} +(-3.50000 - 6.06218i) q^{61} +(-1.50000 + 2.59808i) q^{62} -1.00000 q^{64} +(-6.00000 - 1.73205i) q^{65} +9.00000 q^{66} +(-7.50000 - 4.33013i) q^{67} +(3.00000 - 5.19615i) q^{68} +(1.50000 - 0.866025i) q^{71} +(3.00000 - 1.73205i) q^{72} -8.66025i q^{73} +(1.00000 - 1.73205i) q^{75} +(1.50000 + 0.866025i) q^{76} +(1.50000 + 6.06218i) q^{78} -5.00000 q^{79} +(7.50000 + 4.33013i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{82} -3.46410i q^{83} +(9.00000 - 5.19615i) q^{85} -19.0526i q^{86} +(1.50000 + 2.59808i) q^{87} +(4.50000 - 7.79423i) q^{88} +(6.00000 + 3.46410i) q^{89} -6.00000 q^{90} +(1.50000 + 0.866025i) q^{93} +(-7.50000 + 12.9904i) q^{94} +(1.50000 + 2.59808i) q^{95} -5.19615i q^{96} +(-4.50000 + 2.59808i) q^{97} +10.3923i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+3q2+q3+q4+3q6+2q93q10+9q11+2q122q13+3q15+5q166q17+3q193q20+9q223q24+4q259q26+10q27+9q97+O(q100) 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} + 2 q^{9} - 3 q^{10} + 9 q^{11} + 2 q^{12} - 2 q^{13} + 3 q^{15} + 5 q^{16} - 6 q^{17} + 3 q^{19} - 3 q^{20} + 9 q^{22} - 3 q^{24} + 4 q^{25} - 9 q^{26} + 10 q^{27}+ \cdots - 9 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/637Z)×\left(\mathbb{Z}/637\mathbb{Z}\right)^\times.

nn 197197 248248
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\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 1.50000 + 0.866025i 1.06066 + 0.612372i 0.925615 0.378467i 0.123549π-0.123549\pi
0.135045 + 0.990839i 0.456882π0.456882\pi
33 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i 0.740119π-0.740119\pi
0.973494 + 0.228714i 0.0734519π0.0734519\pi
44 0.500000 + 0.866025i 0.250000 + 0.433013i
55 1.73205i 0.774597i 0.921954 + 0.387298i 0.126592π0.126592\pi
−0.921954 + 0.387298i 0.873408π0.873408\pi
66 1.50000 0.866025i 0.612372 0.353553i
77 0 0
88 1.73205i 0.612372i
99 1.00000 + 1.73205i 0.333333 + 0.577350i
1010 −1.50000 + 2.59808i −0.474342 + 0.821584i
1111 4.50000 + 2.59808i 1.35680 + 0.783349i 0.989191 0.146631i 0.0468429π-0.0468429\pi
0.367610 + 0.929980i 0.380176π0.380176\pi
1212 1.00000 0.288675
1313 −1.00000 + 3.46410i −0.277350 + 0.960769i
1414 0 0
1515 1.50000 + 0.866025i 0.387298 + 0.223607i
1616 2.50000 4.33013i 0.625000 1.08253i
1717 −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i 0.907299π-0.907299\pi
0.230285 0.973123i 0.426034π-0.426034\pi
1818 3.46410i 0.816497i
1919 1.50000 0.866025i 0.344124 0.198680i −0.317970 0.948101i 0.603001π-0.603001\pi
0.662094 + 0.749421i 0.269668π0.269668\pi
2020 −1.50000 + 0.866025i −0.335410 + 0.193649i
2121 0 0
2222 4.50000 + 7.79423i 0.959403 + 1.66174i
2323 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
2424 −1.50000 0.866025i −0.306186 0.176777i
2525 2.00000 0.400000
2626 −4.50000 + 4.33013i −0.882523 + 0.849208i
2727 5.00000 0.962250
2828 0 0
2929 −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i 0.923185π-0.923185\pi
0.692480 + 0.721437i 0.256518π0.256518\pi
3030 1.50000 + 2.59808i 0.273861 + 0.474342i
3131 1.73205i 0.311086i 0.987829 + 0.155543i 0.0497126π0.0497126\pi
−0.987829 + 0.155543i 0.950287π0.950287\pi
3232 4.50000 2.59808i 0.795495 0.459279i
3333 4.50000 2.59808i 0.783349 0.452267i
3434 10.3923i 1.78227i
3535 0 0
3636 −1.00000 + 1.73205i −0.166667 + 0.288675i
3737 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
3838 3.00000 0.486664
3939 2.50000 + 2.59808i 0.400320 + 0.416025i
4040 3.00000 0.474342
4141 −4.50000 2.59808i −0.702782 0.405751i 0.105601 0.994409i 0.466323π-0.466323\pi
−0.808383 + 0.588657i 0.799657π0.799657\pi
4242 0 0
4343 −5.50000 9.52628i −0.838742 1.45274i −0.890947 0.454108i 0.849958π-0.849958\pi
0.0522047 0.998636i 0.483375π-0.483375\pi
4444 5.19615i 0.783349i
4545 −3.00000 + 1.73205i −0.447214 + 0.258199i
4646 0 0
4747 8.66025i 1.26323i 0.775283 + 0.631614i 0.217607π0.217607\pi
−0.775283 + 0.631614i 0.782393π0.782393\pi
4848 −2.50000 4.33013i −0.360844 0.625000i
4949 0 0
5050 3.00000 + 1.73205i 0.424264 + 0.244949i
5151 −6.00000 −0.840168
5252 −3.50000 + 0.866025i −0.485363 + 0.120096i
5353 −9.00000 −1.23625 −0.618123 0.786082i 0.712106π-0.712106\pi
−0.618123 + 0.786082i 0.712106π0.712106\pi
5454 7.50000 + 4.33013i 1.02062 + 0.589256i
5555 −4.50000 + 7.79423i −0.606780 + 1.05097i
5656 0 0
5757 1.73205i 0.229416i
5858 −4.50000 + 2.59808i −0.590879 + 0.341144i
5959 3.00000 1.73205i 0.390567 0.225494i −0.291839 0.956467i 0.594267π-0.594267\pi
0.682406 + 0.730974i 0.260934π0.260934\pi
6060 1.73205i 0.223607i
6161 −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i 0.314576π-0.314576\pi
−0.998264 + 0.0588933i 0.981243π0.981243\pi
6262 −1.50000 + 2.59808i −0.190500 + 0.329956i
6363 0 0
6464 −1.00000 −0.125000
6565 −6.00000 1.73205i −0.744208 0.214834i
6666 9.00000 1.10782
6767 −7.50000 4.33013i −0.916271 0.529009i −0.0338274 0.999428i 0.510770π-0.510770\pi
−0.882443 + 0.470418i 0.844103π0.844103\pi
6868 3.00000 5.19615i 0.363803 0.630126i
6969 0 0
7070 0 0
7171 1.50000 0.866025i 0.178017 0.102778i −0.408344 0.912828i 0.633893π-0.633893\pi
0.586361 + 0.810050i 0.300560π0.300560\pi
7272 3.00000 1.73205i 0.353553 0.204124i
7373 8.66025i 1.01361i −0.862062 0.506803i 0.830827π-0.830827\pi
0.862062 0.506803i 0.169173π-0.169173\pi
7474 0 0
7575 1.00000 1.73205i 0.115470 0.200000i
7676 1.50000 + 0.866025i 0.172062 + 0.0993399i
7777 0 0
7878 1.50000 + 6.06218i 0.169842 + 0.686406i
7979 −5.00000 −0.562544 −0.281272 0.959628i 0.590756π-0.590756\pi
−0.281272 + 0.959628i 0.590756π0.590756\pi
8080 7.50000 + 4.33013i 0.838525 + 0.484123i
8181 −0.500000 + 0.866025i −0.0555556 + 0.0962250i
8282 −4.50000 7.79423i −0.496942 0.860729i
8383 3.46410i 0.380235i −0.981761 0.190117i 0.939113π-0.939113\pi
0.981761 0.190117i 0.0608868π-0.0608868\pi
8484 0 0
8585 9.00000 5.19615i 0.976187 0.563602i
8686 19.0526i 2.05449i
8787 1.50000 + 2.59808i 0.160817 + 0.278543i
8888 4.50000 7.79423i 0.479702 0.830868i
8989 6.00000 + 3.46410i 0.635999 + 0.367194i 0.783072 0.621932i 0.213652π-0.213652\pi
−0.147073 + 0.989126i 0.546985π0.546985\pi
9090 −6.00000 −0.632456
9191 0 0
9292 0 0
9393 1.50000 + 0.866025i 0.155543 + 0.0898027i
9494 −7.50000 + 12.9904i −0.773566 + 1.33986i
9595 1.50000 + 2.59808i 0.153897 + 0.266557i
9696 5.19615i 0.530330i
9797 −4.50000 + 2.59808i −0.456906 + 0.263795i −0.710742 0.703452i 0.751641π-0.751641\pi
0.253837 + 0.967247i 0.418307π0.418307\pi
9898 0 0
9999 10.3923i 1.04447i
100100 1.00000 + 1.73205i 0.100000 + 0.173205i
101101 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i 0.685553π-0.685553\pi
0.998240 + 0.0592978i 0.0188862π0.0188862\pi
102102 −9.00000 5.19615i −0.891133 0.514496i
103103 −13.0000 −1.28093 −0.640464 0.767988i 0.721258π-0.721258\pi
−0.640464 + 0.767988i 0.721258π0.721258\pi
104104 6.00000 + 1.73205i 0.588348 + 0.169842i
105105 0 0
106106 −13.5000 7.79423i −1.31124 0.757042i
107107 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
108108 2.50000 + 4.33013i 0.240563 + 0.416667i
109109 5.19615i 0.497701i 0.968542 + 0.248851i 0.0800528π0.0800528\pi
−0.968542 + 0.248851i 0.919947π0.919947\pi
110110 −13.5000 + 7.79423i −1.28717 + 0.743151i
111111 0 0
112112 0 0
113113 −7.50000 12.9904i −0.705541 1.22203i −0.966496 0.256681i 0.917371π-0.917371\pi
0.260955 0.965351i 0.415962π-0.415962\pi
114114 1.50000 2.59808i 0.140488 0.243332i
115115 0 0
116116 −3.00000 −0.278543
117117 −7.00000 + 1.73205i −0.647150 + 0.160128i
118118 6.00000 0.552345
119119 0 0
120120 1.50000 2.59808i 0.136931 0.237171i
121121 8.00000 + 13.8564i 0.727273 + 1.25967i
122122 12.1244i 1.09769i
123123 −4.50000 + 2.59808i −0.405751 + 0.234261i
124124 −1.50000 + 0.866025i −0.134704 + 0.0777714i
125125 12.1244i 1.08444i
126126 0 0
127127 −6.50000 + 11.2583i −0.576782 + 0.999015i 0.419064 + 0.907957i 0.362358π0.362358\pi
−0.995846 + 0.0910585i 0.970975π0.970975\pi
128128 −10.5000 6.06218i −0.928078 0.535826i
129129 −11.0000 −0.968496
130130 −7.50000 7.79423i −0.657794 0.683599i
131131 15.0000 1.31056 0.655278 0.755388i 0.272551π-0.272551\pi
0.655278 + 0.755388i 0.272551π0.272551\pi
132132 4.50000 + 2.59808i 0.391675 + 0.226134i
133133 0 0
134134 −7.50000 12.9904i −0.647901 1.12220i
135135 8.66025i 0.745356i
136136 −9.00000 + 5.19615i −0.771744 + 0.445566i
137137 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
138138 0 0
139139 6.50000 + 11.2583i 0.551323 + 0.954919i 0.998179 + 0.0603135i 0.0192101π0.0192101\pi
−0.446857 + 0.894606i 0.647457π0.647457\pi
140140 0 0
141141 7.50000 + 4.33013i 0.631614 + 0.364662i
142142 3.00000 0.251754
143143 −13.5000 + 12.9904i −1.12893 + 1.08631i
144144 10.0000 0.833333
145145 −4.50000 2.59808i −0.373705 0.215758i
146146 7.50000 12.9904i 0.620704 1.07509i
147147 0 0
148148 0 0
149149 16.5000 9.52628i 1.35173 0.780423i 0.363241 0.931695i 0.381670π-0.381670\pi
0.988492 + 0.151272i 0.0483370π0.0483370\pi
150150 3.00000 1.73205i 0.244949 0.141421i
151151 12.1244i 0.986666i −0.869841 0.493333i 0.835778π-0.835778\pi
0.869841 0.493333i 0.164222π-0.164222\pi
152152 −1.50000 2.59808i −0.121666 0.210732i
153153 6.00000 10.3923i 0.485071 0.840168i
154154 0 0
155155 −3.00000 −0.240966
156156 −1.00000 + 3.46410i −0.0800641 + 0.277350i
157157 23.0000 1.83560 0.917800 0.397043i 0.129964π-0.129964\pi
0.917800 + 0.397043i 0.129964π0.129964\pi
158158 −7.50000 4.33013i −0.596668 0.344486i
159159 −4.50000 + 7.79423i −0.356873 + 0.618123i
160160 4.50000 + 7.79423i 0.355756 + 0.616188i
161161 0 0
162162 −1.50000 + 0.866025i −0.117851 + 0.0680414i
163163 −10.5000 + 6.06218i −0.822423 + 0.474826i −0.851251 0.524758i 0.824156π-0.824156\pi
0.0288280 + 0.999584i 0.490822π0.490822\pi
164164 5.19615i 0.405751i
165165 4.50000 + 7.79423i 0.350325 + 0.606780i
166166 3.00000 5.19615i 0.232845 0.403300i
167167 −1.50000 0.866025i −0.116073 0.0670151i 0.440839 0.897586i 0.354681π-0.354681\pi
−0.556913 + 0.830571i 0.688014π0.688014\pi
168168 0 0
169169 −11.0000 6.92820i −0.846154 0.532939i
170170 18.0000 1.38054
171171 3.00000 + 1.73205i 0.229416 + 0.132453i
172172 5.50000 9.52628i 0.419371 0.726372i
173173 −7.50000 12.9904i −0.570214 0.987640i −0.996544 0.0830722i 0.973527π-0.973527\pi
0.426329 0.904568i 0.359807π-0.359807\pi
174174 5.19615i 0.393919i
175175 0 0
176176 22.5000 12.9904i 1.69600 0.979187i
177177 3.46410i 0.260378i
178178 6.00000 + 10.3923i 0.449719 + 0.778936i
179179 −1.50000 + 2.59808i −0.112115 + 0.194189i −0.916623 0.399753i 0.869096π-0.869096\pi
0.804508 + 0.593942i 0.202429π0.202429\pi
180180 −3.00000 1.73205i −0.223607 0.129099i
181181 2.00000 0.148659 0.0743294 0.997234i 0.476318π-0.476318\pi
0.0743294 + 0.997234i 0.476318π0.476318\pi
182182 0 0
183183 −7.00000 −0.517455
184184 0 0
185185 0 0
186186 1.50000 + 2.59808i 0.109985 + 0.190500i
187187 31.1769i 2.27988i
188188 −7.50000 + 4.33013i −0.546994 + 0.315807i
189189 0 0
190190 5.19615i 0.376969i
191191 7.50000 + 12.9904i 0.542681 + 0.939951i 0.998749 + 0.0500060i 0.0159241π0.0159241\pi
−0.456068 + 0.889945i 0.650743π0.650743\pi
192192 −0.500000 + 0.866025i −0.0360844 + 0.0625000i
193193 −1.50000 0.866025i −0.107972 0.0623379i 0.445041 0.895510i 0.353189π-0.353189\pi
−0.553014 + 0.833172i 0.686522π0.686522\pi
194194 −9.00000 −0.646162
195195 −4.50000 + 4.33013i −0.322252 + 0.310087i
196196 0 0
197197 19.5000 + 11.2583i 1.38932 + 0.802123i 0.993238 0.116094i 0.0370372π-0.0370372\pi
0.396079 + 0.918216i 0.370371π0.370371\pi
198198 −9.00000 + 15.5885i −0.639602 + 1.10782i
199199 −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i 0.211948π-0.211948\pi
−0.928166 + 0.372168i 0.878615π0.878615\pi
200200 3.46410i 0.244949i
201201 −7.50000 + 4.33013i −0.529009 + 0.305424i
202202 13.5000 7.79423i 0.949857 0.548400i
203203 0 0
204204 −3.00000 5.19615i −0.210042 0.363803i
205205 4.50000 7.79423i 0.314294 0.544373i
206206 −19.5000 11.2583i −1.35863 0.784405i
207207 0 0
208208 12.5000 + 12.9904i 0.866719 + 0.900721i
209209 9.00000 0.622543
210210 0 0
211211 −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i 0.981011π-0.981011\pi
0.550743 + 0.834675i 0.314345π0.314345\pi
212212 −4.50000 7.79423i −0.309061 0.535310i
213213 1.73205i 0.118678i
214214 0 0
215215 16.5000 9.52628i 1.12529 0.649687i
216216 8.66025i 0.589256i
217217 0 0
218218 −4.50000 + 7.79423i −0.304778 + 0.527892i
219219 −7.50000 4.33013i −0.506803 0.292603i
220220 −9.00000 −0.606780
221221 21.0000 5.19615i 1.41261 0.349531i
222222 0 0
223223 4.50000 + 2.59808i 0.301342 + 0.173980i 0.643046 0.765828i 0.277671π-0.277671\pi
−0.341703 + 0.939808i 0.611004π0.611004\pi
224224 0 0
225225 2.00000 + 3.46410i 0.133333 + 0.230940i
226226 25.9808i 1.72821i
227227 15.0000 8.66025i 0.995585 0.574801i 0.0886460 0.996063i 0.471746π-0.471746\pi
0.906939 + 0.421262i 0.138413π0.138413\pi
228228 1.50000 0.866025i 0.0993399 0.0573539i
229229 12.1244i 0.801200i −0.916253 0.400600i 0.868802π-0.868802\pi
0.916253 0.400600i 0.131198π-0.131198\pi
230230 0 0
231231 0 0
232232 4.50000 + 2.59808i 0.295439 + 0.170572i
233233 3.00000 0.196537 0.0982683 0.995160i 0.468670π-0.468670\pi
0.0982683 + 0.995160i 0.468670π0.468670\pi
234234 −12.0000 3.46410i −0.784465 0.226455i
235235 −15.0000 −0.978492
236236 3.00000 + 1.73205i 0.195283 + 0.112747i
237237 −2.50000 + 4.33013i −0.162392 + 0.281272i
238238 0 0
239239 10.3923i 0.672222i −0.941822 0.336111i 0.890888π-0.890888\pi
0.941822 0.336111i 0.109112π-0.109112\pi
240240 7.50000 4.33013i 0.484123 0.279508i
241241 6.00000 3.46410i 0.386494 0.223142i −0.294146 0.955761i 0.595035π-0.595035\pi
0.680640 + 0.732618i 0.261702π0.261702\pi
242242 27.7128i 1.78145i
243243 8.00000 + 13.8564i 0.513200 + 0.888889i
244244 3.50000 6.06218i 0.224065 0.388091i
245245 0 0
246246 −9.00000 −0.573819
247247 1.50000 + 6.06218i 0.0954427 + 0.385727i
248248 3.00000 0.190500
249249 −3.00000 1.73205i −0.190117 0.109764i
250250 −10.5000 + 18.1865i −0.664078 + 1.15022i
251251 −1.50000 2.59808i −0.0946792 0.163989i 0.814795 0.579748i 0.196849π-0.196849\pi
−0.909475 + 0.415759i 0.863516π0.863516\pi
252252 0 0
253253 0 0
254254 −19.5000 + 11.2583i −1.22354 + 0.706410i
255255 10.3923i 0.650791i
256256 −9.50000 16.4545i −0.593750 1.02841i
257257 −15.0000 + 25.9808i −0.935674 + 1.62064i −0.162247 + 0.986750i 0.551874π0.551874\pi
−0.773427 + 0.633885i 0.781459π0.781459\pi
258258 −16.5000 9.52628i −1.02725 0.593080i
259259 0 0
260260 −1.50000 6.06218i −0.0930261 0.375960i
261261 −6.00000 −0.371391
262262 22.5000 + 12.9904i 1.39005 + 0.802548i
263263 −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i 0.862817π-0.862817\pi
0.816066 + 0.577959i 0.196151π0.196151\pi
264264 −4.50000 7.79423i −0.276956 0.479702i
265265 15.5885i 0.957591i
266266 0 0
267267 6.00000 3.46410i 0.367194 0.212000i
268268 8.66025i 0.529009i
269269 3.00000 + 5.19615i 0.182913 + 0.316815i 0.942871 0.333157i 0.108114π-0.108114\pi
−0.759958 + 0.649972i 0.774781π0.774781\pi
270270 −7.50000 + 12.9904i −0.456435 + 0.790569i
271271 15.0000 + 8.66025i 0.911185 + 0.526073i 0.880812 0.473466i 0.156997π-0.156997\pi
0.0303728 + 0.999539i 0.490331π0.490331\pi
272272 −30.0000 −1.81902
273273 0 0
274274 0 0
275275 9.00000 + 5.19615i 0.542720 + 0.313340i
276276 0 0
277277 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i 0.0695395π-0.0695395\pi
−0.675810 + 0.737075i 0.736206π0.736206\pi
278278 22.5167i 1.35046i
279279 −3.00000 + 1.73205i −0.179605 + 0.103695i
280280 0 0
281281 6.92820i 0.413302i 0.978415 + 0.206651i 0.0662565π0.0662565\pi
−0.978415 + 0.206651i 0.933744π0.933744\pi
282282 7.50000 + 12.9904i 0.446619 + 0.773566i
283283 −9.50000 + 16.4545i −0.564716 + 0.978117i 0.432360 + 0.901701i 0.357681π0.357681\pi
−0.997076 + 0.0764162i 0.975652π0.975652\pi
284284 1.50000 + 0.866025i 0.0890086 + 0.0513892i
285285 3.00000 0.177705
286286 −31.5000 + 7.79423i −1.86263 + 0.460882i
287287 0 0
288288 9.00000 + 5.19615i 0.530330 + 0.306186i
289289 −9.50000 + 16.4545i −0.558824 + 0.967911i
290290 −4.50000 7.79423i −0.264249 0.457693i
291291 5.19615i 0.304604i
292292 7.50000 4.33013i 0.438904 0.253402i
293293 −22.5000 + 12.9904i −1.31446 + 0.758906i −0.982832 0.184503i 0.940933π-0.940933\pi
−0.331632 + 0.943409i 0.607599π0.607599\pi
294294 0 0
295295 3.00000 + 5.19615i 0.174667 + 0.302532i
296296 0 0
297297 22.5000 + 12.9904i 1.30558 + 0.753778i
298298 33.0000 1.91164
299299 0 0
300300 2.00000 0.115470
301301 0 0
302302 10.5000 18.1865i 0.604207 1.04652i
303303 −4.50000 7.79423i −0.258518 0.447767i
304304 8.66025i 0.496700i
305305 10.5000 6.06218i 0.601228 0.347119i
306306 18.0000 10.3923i 1.02899 0.594089i
307307 24.2487i 1.38395i −0.721923 0.691974i 0.756741π-0.756741\pi
0.721923 0.691974i 0.243259π-0.243259\pi
308308 0 0
309309 −6.50000 + 11.2583i −0.369772 + 0.640464i
310310 −4.50000 2.59808i −0.255583 0.147561i
311311 −15.0000 −0.850572 −0.425286 0.905059i 0.639826π-0.639826\pi
−0.425286 + 0.905059i 0.639826π0.639826\pi
312312 4.50000 4.33013i 0.254762 0.245145i
313313 19.0000 1.07394 0.536972 0.843600i 0.319568π-0.319568\pi
0.536972 + 0.843600i 0.319568π0.319568\pi
314314 34.5000 + 19.9186i 1.94695 + 1.12407i
315315 0 0
316316 −2.50000 4.33013i −0.140636 0.243589i
317317 5.19615i 0.291845i −0.989296 0.145922i 0.953385π-0.953385\pi
0.989296 0.145922i 0.0466150π-0.0466150\pi
318318 −13.5000 + 7.79423i −0.757042 + 0.437079i
319319 −13.5000 + 7.79423i −0.755855 + 0.436393i
320320 1.73205i 0.0968246i
321321 0 0
322322 0 0
323323 −9.00000 5.19615i −0.500773 0.289122i
324324 −1.00000 −0.0555556
325325 −2.00000 + 6.92820i −0.110940 + 0.384308i
326326 −21.0000 −1.16308
327327 4.50000 + 2.59808i 0.248851 + 0.143674i
328328 −4.50000 + 7.79423i −0.248471 + 0.430364i
329329 0 0
330330 15.5885i 0.858116i
331331 −28.5000 + 16.4545i −1.56650 + 0.904420i −0.569929 + 0.821694i 0.693029π0.693029\pi
−0.996572 + 0.0827265i 0.973637π0.973637\pi
332332 3.00000 1.73205i 0.164646 0.0950586i
333333 0 0
334334 −1.50000 2.59808i −0.0820763 0.142160i
335335 7.50000 12.9904i 0.409769 0.709740i
336336 0 0
337337 22.0000 1.19842 0.599208 0.800593i 0.295482π-0.295482\pi
0.599208 + 0.800593i 0.295482π0.295482\pi
338338 −10.5000 19.9186i −0.571125 1.08343i
339339 −15.0000 −0.814688
340340 9.00000 + 5.19615i 0.488094 + 0.281801i
341341 −4.50000 + 7.79423i −0.243689 + 0.422081i
342342 3.00000 + 5.19615i 0.162221 + 0.280976i
343343 0 0
344344 −16.5000 + 9.52628i −0.889620 + 0.513623i
345345 0 0
346346 25.9808i 1.39673i
347347 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
348348 −1.50000 + 2.59808i −0.0804084 + 0.139272i
349349 −4.50000 2.59808i −0.240879 0.139072i 0.374701 0.927146i 0.377745π-0.377745\pi
−0.615581 + 0.788074i 0.711079π0.711079\pi
350350 0 0
351351 −5.00000 + 17.3205i −0.266880 + 0.924500i
352352 27.0000 1.43910
353353 −1.50000 0.866025i −0.0798369 0.0460939i 0.459550 0.888152i 0.348011π-0.348011\pi
−0.539387 + 0.842058i 0.681344π0.681344\pi
354354 3.00000 5.19615i 0.159448 0.276172i
355355 1.50000 + 2.59808i 0.0796117 + 0.137892i
356356 6.92820i 0.367194i
357357 0 0
358358 −4.50000 + 2.59808i −0.237832 + 0.137313i
359359 19.0526i 1.00556i −0.864416 0.502778i 0.832311π-0.832311\pi
0.864416 0.502778i 0.167689π-0.167689\pi
360360 3.00000 + 5.19615i 0.158114 + 0.273861i
361361 −8.00000 + 13.8564i −0.421053 + 0.729285i
362362 3.00000 + 1.73205i 0.157676 + 0.0910346i
363363 16.0000 0.839782
364364 0 0
365365 15.0000 0.785136
366366 −10.5000 6.06218i −0.548844 0.316875i
367367 −11.5000 + 19.9186i −0.600295 + 1.03974i 0.392481 + 0.919760i 0.371617π0.371617\pi
−0.992776 + 0.119982i 0.961716π0.961716\pi
368368 0 0
369369 10.3923i 0.541002i
370370 0 0
371371 0 0
372372 1.73205i 0.0898027i
373373 −9.50000 16.4545i −0.491891 0.851981i 0.508065 0.861319i 0.330361π-0.330361\pi
−0.999956 + 0.00933789i 0.997028π0.997028\pi
374374 27.0000 46.7654i 1.39614 2.41818i
375375 10.5000 + 6.06218i 0.542218 + 0.313050i
376376 15.0000 0.773566
377377 −7.50000 7.79423i −0.386270 0.401423i
378378 0 0
379379 −1.50000 0.866025i −0.0770498 0.0444847i 0.460980 0.887410i 0.347498π-0.347498\pi
−0.538030 + 0.842926i 0.680831π0.680831\pi
380380 −1.50000 + 2.59808i −0.0769484 + 0.133278i
381381 6.50000 + 11.2583i 0.333005 + 0.576782i
382382 25.9808i 1.32929i
383383 13.5000 7.79423i 0.689818 0.398266i −0.113726 0.993512i 0.536279π-0.536279\pi
0.803544 + 0.595246i 0.202945π0.202945\pi
384384 −10.5000 + 6.06218i −0.535826 + 0.309359i
385385 0 0
386386 −1.50000 2.59808i −0.0763480 0.132239i
387387 11.0000 19.0526i 0.559161 0.968496i
388388 −4.50000 2.59808i −0.228453 0.131897i
389389 3.00000 0.152106 0.0760530 0.997104i 0.475768π-0.475768\pi
0.0760530 + 0.997104i 0.475768π0.475768\pi
390390 −10.5000 + 2.59808i −0.531688 + 0.131559i
391391 0 0
392392 0 0
393393 7.50000 12.9904i 0.378325 0.655278i
394394 19.5000 + 33.7750i 0.982396 + 1.70156i
395395 8.66025i 0.435745i
396396 −9.00000 + 5.19615i −0.452267 + 0.261116i
397397 −31.5000 + 18.1865i −1.58094 + 0.912756i −0.586217 + 0.810154i 0.699383π0.699383\pi
−0.994722 + 0.102602i 0.967283π0.967283\pi
398398 6.92820i 0.347279i
399399 0 0
400400 5.00000 8.66025i 0.250000 0.433013i
401401 6.00000 + 3.46410i 0.299626 + 0.172989i 0.642275 0.766475i 0.277991π-0.277991\pi
−0.342649 + 0.939463i 0.611324π0.611324\pi
402402 −15.0000 −0.748132
403403 −6.00000 1.73205i −0.298881 0.0862796i
404404 9.00000 0.447767
405405 −1.50000 0.866025i −0.0745356 0.0430331i
406406 0 0
407407 0 0
408408 10.3923i 0.514496i
409409 −6.00000 + 3.46410i −0.296681 + 0.171289i −0.640951 0.767582i 0.721460π-0.721460\pi
0.344270 + 0.938871i 0.388126π0.388126\pi
410410 13.5000 7.79423i 0.666717 0.384930i
411411 0 0
412412 −6.50000 11.2583i −0.320232 0.554658i
413413 0 0
414414 0 0
415415 6.00000 0.294528
416416 4.50000 + 18.1865i 0.220631 + 0.891668i
417417 13.0000 0.636613
418418 13.5000 + 7.79423i 0.660307 + 0.381228i
419419 −10.5000 + 18.1865i −0.512959 + 0.888470i 0.486928 + 0.873442i 0.338117π0.338117\pi
−0.999887 + 0.0150285i 0.995216π0.995216\pi
420420 0 0
421421 0 0 1.00000 00
−1.00000 π\pi
422422 −19.5000 + 11.2583i −0.949245 + 0.548047i
423423 −15.0000 + 8.66025i −0.729325 + 0.421076i
424424 15.5885i 0.757042i
425425 −6.00000 10.3923i −0.291043 0.504101i
426426 1.50000 2.59808i 0.0726752 0.125877i
427427 0 0
428428 0 0
429429 4.50000 + 18.1865i 0.217262 + 0.878054i
430430 33.0000 1.59140
431431 28.5000 + 16.4545i 1.37280 + 0.792585i 0.991279 0.131777i 0.0420683π-0.0420683\pi
0.381517 + 0.924362i 0.375402π0.375402\pi
432432 12.5000 21.6506i 0.601407 1.04167i
433433 −9.50000 16.4545i −0.456541 0.790752i 0.542234 0.840227i 0.317578π-0.317578\pi
−0.998775 + 0.0494752i 0.984245π0.984245\pi
434434 0 0
435435 −4.50000 + 2.59808i −0.215758 + 0.124568i
436436 −4.50000 + 2.59808i −0.215511 + 0.124425i
437437 0 0
438438 −7.50000 12.9904i −0.358364 0.620704i
439439 −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i 0.894477π-0.894477\pi
0.754642 + 0.656136i 0.227810π0.227810\pi
440440 13.5000 + 7.79423i 0.643587 + 0.371575i
441441 0 0
442442 36.0000 + 10.3923i 1.71235 + 0.494312i
443443 15.0000 0.712672 0.356336 0.934358i 0.384026π-0.384026\pi
0.356336 + 0.934358i 0.384026π0.384026\pi
444444 0 0
445445 −6.00000 + 10.3923i −0.284427 + 0.492642i
446446 4.50000 + 7.79423i 0.213081 + 0.369067i
447447 19.0526i 0.901155i
448448 0 0
449449 1.50000 0.866025i 0.0707894 0.0408703i −0.464188 0.885737i 0.653654π-0.653654\pi
0.534977 + 0.844867i 0.320320π0.320320\pi
450450 6.92820i 0.326599i
451451 −13.5000 23.3827i −0.635690 1.10105i
452452 7.50000 12.9904i 0.352770 0.611016i
453453 −10.5000 6.06218i −0.493333 0.284826i
454454 30.0000 1.40797
455455 0 0
456456 −3.00000 −0.140488
457457 30.0000 + 17.3205i 1.40334 + 0.810219i 0.994734 0.102491i 0.0326814π-0.0326814\pi
0.408607 + 0.912710i 0.366015π0.366015\pi
458458 10.5000 18.1865i 0.490633 0.849801i
459459 −15.0000 25.9808i −0.700140 1.21268i
460460 0 0
461461 25.5000 14.7224i 1.18765 0.685692i 0.229881 0.973219i 0.426166π-0.426166\pi
0.957773 + 0.287527i 0.0928330π0.0928330\pi
462462 0 0
463463 24.2487i 1.12693i 0.826139 + 0.563467i 0.190533π0.190533\pi
−0.826139 + 0.563467i 0.809467π0.809467\pi
464464 7.50000 + 12.9904i 0.348179 + 0.603063i
465465 −1.50000 + 2.59808i −0.0695608 + 0.120483i
466466 4.50000 + 2.59808i 0.208458 + 0.120354i
467467 −21.0000 −0.971764 −0.485882 0.874024i 0.661502π-0.661502\pi
−0.485882 + 0.874024i 0.661502π0.661502\pi
468468 −5.00000 5.19615i −0.231125 0.240192i
469469 0 0
470470 −22.5000 12.9904i −1.03785 0.599202i
471471 11.5000 19.9186i 0.529892 0.917800i
472472 −3.00000 5.19615i −0.138086 0.239172i
473473 57.1577i 2.62811i
474474 −7.50000 + 4.33013i −0.344486 + 0.198889i
475475 3.00000 1.73205i 0.137649 0.0794719i
476476 0 0
477477 −9.00000 15.5885i −0.412082 0.713746i
478478 9.00000 15.5885i 0.411650 0.712999i
479479 −25.5000 14.7224i −1.16512 0.672685i −0.212598 0.977140i 0.568192π-0.568192\pi
−0.952527 + 0.304455i 0.901526π0.901526\pi
480480 9.00000 0.410792
481481 0 0
482482 12.0000 0.546585
483483 0 0
484484 −8.00000 + 13.8564i −0.363636 + 0.629837i
485485 −4.50000 7.79423i −0.204334 0.353918i
486486 27.7128i 1.25708i
487487 21.0000 12.1244i 0.951601 0.549407i 0.0580230 0.998315i 0.481520π-0.481520\pi
0.893578 + 0.448908i 0.148187π0.148187\pi
488488 −10.5000 + 6.06218i −0.475313 + 0.274422i
489489 12.1244i 0.548282i
490490 0 0
491491 13.5000 23.3827i 0.609246 1.05525i −0.382118 0.924113i 0.624805π-0.624805\pi
0.991365 0.131132i 0.0418613π-0.0418613\pi
492492 −4.50000 2.59808i −0.202876 0.117130i
493493 18.0000 0.810679
494494 −3.00000 + 10.3923i −0.134976 + 0.467572i
495495 −18.0000 −0.809040
496496 7.50000 + 4.33013i 0.336760 + 0.194428i
497497 0 0
498498 −3.00000 5.19615i −0.134433 0.232845i
499499 1.73205i 0.0775372i 0.999248 + 0.0387686i 0.0123435π0.0123435\pi
−0.999248 + 0.0387686i 0.987656π0.987656\pi
500500 −10.5000 + 6.06218i −0.469574 + 0.271109i
501501 −1.50000 + 0.866025i −0.0670151 + 0.0386912i
502502 5.19615i 0.231916i
503503 4.50000 + 7.79423i 0.200645 + 0.347527i 0.948736 0.316068i 0.102363π-0.102363\pi
−0.748091 + 0.663596i 0.769030π0.769030\pi
504504 0 0
505505 13.5000 + 7.79423i 0.600742 + 0.346839i
506506 0 0
507507 −11.5000 + 6.06218i −0.510733 + 0.269231i
508508 −13.0000 −0.576782
509509 6.00000 + 3.46410i 0.265945 + 0.153544i 0.627044 0.778984i 0.284265π-0.284265\pi
−0.361098 + 0.932528i 0.617598π0.617598\pi
510510 9.00000 15.5885i 0.398527 0.690268i
511511 0 0
512512 8.66025i 0.382733i
513513 7.50000 4.33013i 0.331133 0.191180i
514514 −45.0000 + 25.9808i −1.98486 + 1.14596i
515515 22.5167i 0.992203i
516516 −5.50000 9.52628i −0.242124 0.419371i
517517 −22.5000 + 38.9711i −0.989549 + 1.71395i
518518 0 0
519519 −15.0000 −0.658427
520520 −3.00000 + 10.3923i −0.131559 + 0.455733i
521521 39.0000 1.70862 0.854311 0.519763i 0.173980π-0.173980\pi
0.854311 + 0.519763i 0.173980π0.173980\pi
522522 −9.00000 5.19615i −0.393919 0.227429i
523523 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i 0.805460π-0.805460\pi
0.906434 + 0.422347i 0.138794π0.138794\pi
524524 7.50000 + 12.9904i 0.327639 + 0.567487i
525525 0 0
526526 −4.50000 + 2.59808i −0.196209 + 0.113282i
527527 9.00000 5.19615i 0.392046 0.226348i
528528 25.9808i 1.13067i
529529 11.5000 + 19.9186i 0.500000 + 0.866025i
530530 13.5000 23.3827i 0.586403 1.01568i
531531 6.00000 + 3.46410i 0.260378 + 0.150329i
532532 0 0
533533 13.5000 12.9904i 0.584750 0.562676i
534534 12.0000 0.519291
535535 0 0
536536 −7.50000 + 12.9904i −0.323951 + 0.561099i
537537 1.50000 + 2.59808i 0.0647298 + 0.112115i
538538 10.3923i 0.448044i
539539 0 0
540540 −7.50000 + 4.33013i −0.322749 + 0.186339i
541541 12.1244i 0.521267i −0.965438 0.260633i 0.916069π-0.916069\pi
0.965438 0.260633i 0.0839314π-0.0839314\pi
542542 15.0000 + 25.9808i 0.644305 + 1.11597i
543543 1.00000 1.73205i 0.0429141 0.0743294i
544544 −27.0000 15.5885i −1.15762 0.668350i
545545 −9.00000 −0.385518
546546 0 0
547547 −28.0000 −1.19719 −0.598597 0.801050i 0.704275π-0.704275\pi
−0.598597 + 0.801050i 0.704275π0.704275\pi
548548 0 0
549549 7.00000 12.1244i 0.298753 0.517455i
550550 9.00000 + 15.5885i 0.383761 + 0.664694i
551551 5.19615i 0.221364i
552552 0 0
553553 0 0
554554 17.3205i 0.735878i
555555 0 0
556556 −6.50000 + 11.2583i −0.275661 + 0.477460i
557557 −13.5000 7.79423i −0.572013 0.330252i 0.185940 0.982561i 0.440467π-0.440467\pi
−0.757953 + 0.652309i 0.773800π0.773800\pi
558558 −6.00000 −0.254000
559559 38.5000 9.52628i 1.62838 0.402919i
560560 0 0
561561 −27.0000 15.5885i −1.13994 0.658145i
562562 −6.00000 + 10.3923i −0.253095 + 0.438373i
563563 18.0000 + 31.1769i 0.758610 + 1.31395i 0.943560 + 0.331202i 0.107454π0.107454\pi
−0.184950 + 0.982748i 0.559212π0.559212\pi
564564 8.66025i 0.364662i
565565 22.5000 12.9904i 0.946582 0.546509i
566566 −28.5000 + 16.4545i −1.19794 + 0.691633i
567567 0 0
568568 −1.50000 2.59808i −0.0629386 0.109013i
569569 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i 0.793194π-0.793194\pi
0.922032 + 0.387113i 0.126528π0.126528\pi
570570 4.50000 + 2.59808i 0.188484 + 0.108821i
571571 −23.0000 −0.962520 −0.481260 0.876578i 0.659821π-0.659821\pi
−0.481260 + 0.876578i 0.659821π0.659821\pi
572572 −18.0000 5.19615i −0.752618 0.217262i
573573 15.0000 0.626634
574574 0 0
575575 0 0
576576 −1.00000 1.73205i −0.0416667 0.0721688i
577577 15.5885i 0.648956i −0.945893 0.324478i 0.894811π-0.894811\pi
0.945893 0.324478i 0.105189π-0.105189\pi
578578 −28.5000 + 16.4545i −1.18544 + 0.684416i
579579 −1.50000 + 0.866025i −0.0623379 + 0.0359908i
580580 5.19615i 0.215758i
581581 0 0
582582 −4.50000 + 7.79423i −0.186531 + 0.323081i
583583 −40.5000 23.3827i −1.67734 0.968412i
584584 −15.0000 −0.620704
585585 −3.00000 12.1244i −0.124035 0.501280i
586586 −45.0000 −1.85893
587587 −13.5000 7.79423i −0.557205 0.321702i 0.194818 0.980839i 0.437588π-0.437588\pi
−0.752023 + 0.659137i 0.770922π0.770922\pi
588588 0 0
589589 1.50000 + 2.59808i 0.0618064 + 0.107052i
590590 10.3923i 0.427844i
591591 19.5000 11.2583i 0.802123 0.463106i
592592 0 0
593593 5.19615i 0.213380i −0.994292 0.106690i 0.965975π-0.965975\pi
0.994292 0.106690i 0.0340253π-0.0340253\pi
594594 22.5000 + 38.9711i 0.923186 + 1.59901i
595595 0 0
596596 16.5000 + 9.52628i 0.675866 + 0.390212i
597597 −4.00000 −0.163709
598598 0 0
599599 9.00000 0.367730 0.183865 0.982952i 0.441139π-0.441139\pi
0.183865 + 0.982952i 0.441139π0.441139\pi
600600 −3.00000 1.73205i −0.122474 0.0707107i
601601 −9.50000 + 16.4545i −0.387513 + 0.671192i −0.992114 0.125336i 0.959999π-0.959999\pi
0.604601 + 0.796528i 0.293332π0.293332\pi
602602 0 0
603603 17.3205i 0.705346i
604604 10.5000 6.06218i 0.427239 0.246667i
605605 −24.0000 + 13.8564i −0.975739 + 0.563343i
606606 15.5885i 0.633238i
607607 21.5000 + 37.2391i 0.872658 + 1.51149i 0.859237 + 0.511578i 0.170939π0.170939\pi
0.0134214 + 0.999910i 0.495728π0.495728\pi
608608 4.50000 7.79423i 0.182499 0.316098i
609609 0 0
610610 21.0000 0.850265
611611 −30.0000 8.66025i −1.21367 0.350356i
612612 12.0000 0.485071
613613 −31.5000 18.1865i −1.27227 0.734547i −0.296858 0.954922i 0.595939π-0.595939\pi
−0.975415 + 0.220375i 0.929272π0.929272\pi
614614 21.0000 36.3731i 0.847491 1.46790i
615615 −4.50000 7.79423i −0.181458 0.314294i
616616 0 0
617617 37.5000 21.6506i 1.50969 0.871622i 0.509757 0.860318i 0.329735π-0.329735\pi
0.999936 0.0113033i 0.00359804π-0.00359804\pi
618618 −19.5000 + 11.2583i −0.784405 + 0.452876i
619619 19.0526i 0.765787i −0.923792 0.382893i 0.874928π-0.874928\pi
0.923792 0.382893i 0.125072π-0.125072\pi
620620 −1.50000 2.59808i −0.0602414 0.104341i
621621 0 0
622622 −22.5000 12.9904i −0.902168 0.520867i
623623 0 0
624624 17.5000 4.33013i 0.700561 0.173344i
625625 −11.0000 −0.440000
626626 28.5000 + 16.4545i 1.13909 + 0.657653i
627627 4.50000 7.79423i 0.179713 0.311272i
628628 11.5000 + 19.9186i 0.458900 + 0.794838i
629629 0 0
630630 0 0
631631 −40.5000 + 23.3827i −1.61228 + 0.930850i −0.623439 + 0.781872i 0.714265π0.714265\pi
−0.988841 + 0.148978i 0.952402π0.952402\pi
632632 8.66025i 0.344486i
633633 6.50000 + 11.2583i 0.258352 + 0.447478i
634634 4.50000 7.79423i 0.178718 0.309548i
635635 −19.5000 11.2583i −0.773834 0.446773i
636636 −9.00000 −0.356873
637637 0 0
638638 −27.0000 −1.06894
639639 3.00000 + 1.73205i 0.118678 + 0.0685189i
640640 10.5000 18.1865i 0.415049 0.718886i
641641 −15.0000 25.9808i −0.592464 1.02618i −0.993899 0.110291i 0.964822π-0.964822\pi
0.401435 0.915888i 0.368512π-0.368512\pi
642642 0 0
643643 −4.50000 + 2.59808i −0.177463 + 0.102458i −0.586100 0.810239i 0.699337π-0.699337\pi
0.408637 + 0.912697i 0.366004π0.366004\pi
644644 0 0
645645 19.0526i 0.750194i
646646 −9.00000 15.5885i −0.354100 0.613320i
647647 4.50000 7.79423i 0.176913 0.306423i −0.763908 0.645325i 0.776722π-0.776722\pi
0.940822 + 0.338902i 0.110055π0.110055\pi
648648 1.50000 + 0.866025i 0.0589256 + 0.0340207i
649649 18.0000 0.706562
650650 −9.00000 + 8.66025i −0.353009 + 0.339683i
651651 0 0
652652 −10.5000 6.06218i −0.411212 0.237413i
653653 15.0000 25.9808i 0.586995 1.01671i −0.407628 0.913148i 0.633644π-0.633644\pi
0.994623 0.103558i 0.0330227π-0.0330227\pi
654654 4.50000 + 7.79423i 0.175964 + 0.304778i
655655 25.9808i 1.01515i
656656 −22.5000 + 12.9904i −0.878477 + 0.507189i
657657 15.0000 8.66025i 0.585206 0.337869i
658658 0 0
659659 −7.50000 12.9904i −0.292159 0.506033i 0.682161 0.731202i 0.261040π-0.261040\pi
−0.974320 + 0.225168i 0.927707π0.927707\pi
660660 −4.50000 + 7.79423i −0.175162 + 0.303390i
661661 −31.5000 18.1865i −1.22521 0.707374i −0.259184 0.965828i 0.583454π-0.583454\pi
−0.966024 + 0.258454i 0.916787π0.916787\pi
662662 −57.0000 −2.21537
663663 6.00000 20.7846i 0.233021 0.807207i
664664 −6.00000 −0.232845
665665 0 0
666666 0 0
667667 0 0
668668 1.73205i 0.0670151i
669669 4.50000 2.59808i 0.173980 0.100447i
670670 22.5000 12.9904i 0.869251 0.501862i
671671 36.3731i 1.40417i
672672 0 0
673673 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i 0.827198π-0.827198\pi
0.875501 + 0.483216i 0.160531π0.160531\pi
674674 33.0000 + 19.0526i 1.27111 + 0.733877i
675675 10.0000 0.384900
676676 0.500000 12.9904i 0.0192308 0.499630i
677677 27.0000 1.03769 0.518847 0.854867i 0.326361π-0.326361\pi
0.518847 + 0.854867i 0.326361π0.326361\pi
678678 −22.5000 12.9904i −0.864107 0.498893i
679679 0 0
680680 −9.00000 15.5885i −0.345134 0.597790i
681681 17.3205i 0.663723i
682682 −13.5000 + 7.79423i −0.516942 + 0.298456i
683683 −21.0000 + 12.1244i −0.803543 + 0.463926i −0.844708 0.535227i 0.820226π-0.820226\pi
0.0411658 + 0.999152i 0.486893π0.486893\pi
684684 3.46410i 0.132453i
685685 0 0
686686 0 0
687687 −10.5000 6.06218i −0.400600 0.231287i
688688 −55.0000 −2.09686
689689 9.00000 31.1769i 0.342873 1.18775i
690690 0 0
691691 −27.0000 15.5885i −1.02713 0.593013i −0.110968 0.993824i 0.535395π-0.535395\pi
−0.916161 + 0.400811i 0.868728π0.868728\pi
692692 7.50000 12.9904i 0.285107 0.493820i
693693 0 0
694694 0 0
695695 −19.5000 + 11.2583i −0.739677 + 0.427053i
696696 4.50000 2.59808i 0.170572 0.0984798i
697697 31.1769i 1.18091i
698698 −4.50000 7.79423i −0.170328 0.295016i
699699 1.50000 2.59808i 0.0567352 0.0982683i
700700 0 0
701701 −6.00000 −0.226617 −0.113308 0.993560i 0.536145π-0.536145\pi
−0.113308 + 0.993560i 0.536145π0.536145\pi
702702 −22.5000 + 21.6506i −0.849208 + 0.817151i
703703 0 0
704704 −4.50000 2.59808i −0.169600 0.0979187i
705705 −7.50000 + 12.9904i −0.282466 + 0.489246i
706706 −1.50000 2.59808i −0.0564532 0.0977799i
707707 0 0
708708 3.00000 1.73205i 0.112747 0.0650945i
709709 10.5000 6.06218i 0.394336 0.227670i −0.289701 0.957117i 0.593556π-0.593556\pi
0.684037 + 0.729447i 0.260223π0.260223\pi
710710 5.19615i 0.195008i
711711 −5.00000 8.66025i −0.187515 0.324785i
712712 6.00000 10.3923i 0.224860 0.389468i
713713 0 0
714714 0 0
715715 −22.5000 23.3827i −0.841452 0.874463i
716716 −3.00000 −0.112115
717717 −9.00000 5.19615i −0.336111 0.194054i
718718 16.5000 28.5788i 0.615775 1.06655i
719719 7.50000 + 12.9904i 0.279703 + 0.484459i 0.971311 0.237814i 0.0764307π-0.0764307\pi
−0.691608 + 0.722273i 0.743097π0.743097\pi
720720 17.3205i 0.645497i
721721 0 0
722722 −24.0000 + 13.8564i −0.893188 + 0.515682i
723723 6.92820i 0.257663i
724724 1.00000 + 1.73205i 0.0371647 + 0.0643712i
725725 −3.00000 + 5.19615i −0.111417 + 0.192980i
726726 24.0000 + 13.8564i 0.890724 + 0.514259i
727727 −32.0000 −1.18681 −0.593407 0.804902i 0.702218π-0.702218\pi
−0.593407 + 0.804902i 0.702218π0.702218\pi
728728 0 0
729729 13.0000 0.481481
730730 22.5000 + 12.9904i 0.832762 + 0.480796i
731731 −33.0000 + 57.1577i −1.22055 + 2.11405i
732732 −3.50000 6.06218i −0.129364 0.224065i
733733 50.2295i 1.85527i 0.373491 + 0.927634i 0.378161π0.378161\pi
−0.373491 + 0.927634i 0.621839π0.621839\pi
734734 −34.5000 + 19.9186i −1.27342 + 0.735208i
735735 0 0
736736 0 0
737737 −22.5000 38.9711i −0.828798 1.43552i
738738 9.00000 15.5885i 0.331295 0.573819i
739739 34.5000 + 19.9186i 1.26910 + 0.732717i 0.974818 0.223001i 0.0715853π-0.0715853\pi
0.294285 + 0.955718i 0.404919π0.404919\pi
740740 0 0
741741 6.00000 + 1.73205i 0.220416 + 0.0636285i
742742 0 0
743743 −1.50000 0.866025i −0.0550297 0.0317714i 0.472233 0.881474i 0.343448π-0.343448\pi
−0.527262 + 0.849703i 0.676782π0.676782\pi
744744 1.50000 2.59808i 0.0549927 0.0952501i
745745 16.5000 + 28.5788i 0.604513 + 1.04705i
746746 32.9090i 1.20488i
747747 6.00000 3.46410i 0.219529 0.126745i
748748 27.0000 15.5885i 0.987218 0.569970i
749749 0 0
750750 10.5000 + 18.1865i 0.383406 + 0.664078i
751751 −10.0000 + 17.3205i −0.364905 + 0.632034i −0.988761 0.149505i 0.952232π-0.952232\pi
0.623856 + 0.781540i 0.285565π0.285565\pi
752752 37.5000 + 21.6506i 1.36748 + 0.789517i
753753 −3.00000 −0.109326
754754 −4.50000 18.1865i −0.163880 0.662314i
755755 21.0000 0.764268
756756 0 0
757757 8.50000 14.7224i 0.308938 0.535096i −0.669193 0.743089i 0.733360π-0.733360\pi
0.978130 + 0.207993i 0.0666932π0.0666932\pi
758758 −1.50000 2.59808i −0.0544825 0.0943664i
759759 0 0
760760 4.50000 2.59808i 0.163232 0.0942421i
761761 −25.5000 + 14.7224i −0.924374 + 0.533688i −0.885028 0.465538i 0.845861π-0.845861\pi
−0.0393463 + 0.999226i 0.512528π0.512528\pi
762762 22.5167i 0.815693i
763763 0 0
764764 −7.50000 + 12.9904i −0.271340 + 0.469975i
765765 18.0000 + 10.3923i 0.650791 + 0.375735i
766766 27.0000 0.975550
767767 3.00000 + 12.1244i 0.108324 + 0.437785i
768768 −19.0000 −0.685603
769769 −16.5000 9.52628i −0.595005 0.343526i 0.172069 0.985085i 0.444955π-0.444955\pi
−0.767074 + 0.641558i 0.778288π0.778288\pi
770770 0 0
771771 15.0000 + 25.9808i 0.540212 + 0.935674i
772772 1.73205i 0.0623379i
773773 12.0000 6.92820i 0.431610 0.249190i −0.268422 0.963301i 0.586502π-0.586502\pi
0.700032 + 0.714111i 0.253169π0.253169\pi
774774 33.0000 19.0526i 1.18616 0.684830i
775775 3.46410i 0.124434i
776776 4.50000 + 7.79423i 0.161541 + 0.279797i
777777 0 0
778778 4.50000 + 2.59808i 0.161333 + 0.0931455i
779779 −9.00000 −0.322458
780780 −6.00000 1.73205i −0.214834 0.0620174i
781781 9.00000 0.322045
782782 0 0
783783 −7.50000 + 12.9904i −0.268028 + 0.464238i
784784 0 0
785785 39.8372i 1.42185i
786786 22.5000 12.9904i 0.802548 0.463352i
787787 27.0000 15.5885i 0.962446 0.555668i 0.0655211 0.997851i 0.479129π-0.479129\pi
0.896925 + 0.442183i 0.145796π0.145796\pi
788788 22.5167i 0.802123i
789789 1.50000 + 2.59808i 0.0534014 + 0.0924940i
790790 7.50000 12.9904i 0.266838 0.462177i
791791 0 0
792792 18.0000 0.639602
793793 24.5000 6.06218i 0.870021 0.215274i
794794 −63.0000 −2.23579
795795 −13.5000 7.79423i −0.478796 0.276433i
796796 2.00000 3.46410i 0.0708881 0.122782i
797797 16.5000 + 28.5788i 0.584460 + 1.01231i 0.994943 + 0.100446i 0.0320269π0.0320269\pi
−0.410483 + 0.911868i 0.634640π0.634640\pi
798798 0 0
799799 45.0000 25.9808i 1.59199 0.919133i
800800 9.00000 5.19615i 0.318198 0.183712i
801801 13.8564i 0.489592i
802802 6.00000 + 10.3923i 0.211867 + 0.366965i
803803 22.5000 38.9711i 0.794008 1.37526i
804804 −7.50000 4.33013i −0.264505 0.152712i
805805 0 0
806806 −7.50000 7.79423i −0.264176 0.274540i
807807 6.00000 0.211210
808808 −13.5000 7.79423i −0.474928 0.274200i
809809 10.5000 18.1865i 0.369160 0.639404i −0.620274 0.784385i 0.712979π-0.712979\pi
0.989434 + 0.144981i 0.0463120π0.0463120\pi
810810 −1.50000 2.59808i −0.0527046 0.0912871i
811811 3.46410i 0.121641i 0.998149 + 0.0608205i 0.0193717π0.0193717\pi
−0.998149 + 0.0608205i 0.980628π0.980628\pi
812812 0 0
813813 15.0000 8.66025i 0.526073 0.303728i
814814 0 0
815815 −10.5000 18.1865i −0.367799 0.637046i
816816 −15.0000 + 25.9808i −0.525105 + 0.909509i
817817 −16.5000 9.52628i −0.577262 0.333282i
818818 −12.0000 −0.419570
819819 0 0
820820 9.00000 0.314294
821821 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
822822 0 0
823823 −16.0000 27.7128i −0.557725 0.966008i −0.997686 0.0679910i 0.978341π-0.978341\pi
0.439961 0.898017i 0.354992π-0.354992\pi
824824 22.5167i 0.784405i
825825 9.00000 5.19615i 0.313340 0.180907i
826826 0 0
827827 10.3923i 0.361376i −0.983540 0.180688i 0.942168π-0.942168\pi
0.983540 0.180688i 0.0578324π-0.0578324\pi
828828 0 0
829829 −3.50000 + 6.06218i −0.121560 + 0.210548i −0.920383 0.391018i 0.872123π-0.872123\pi
0.798823 + 0.601566i 0.205456π0.205456\pi
830830 9.00000 + 5.19615i 0.312395 + 0.180361i
831831 10.0000 0.346896
832832 1.00000 3.46410i 0.0346688 0.120096i
833833 0 0
834834 19.5000 + 11.2583i 0.675230 + 0.389844i
835835 1.50000 2.59808i 0.0519096 0.0899101i
836836 4.50000 + 7.79423i 0.155636 + 0.269569i
837837 8.66025i 0.299342i
838838 −31.5000 + 18.1865i −1.08815 + 0.628243i
839839 1.50000 0.866025i 0.0517858 0.0298985i −0.473884 0.880587i 0.657148π-0.657148\pi
0.525669 + 0.850689i 0.323815π0.323815\pi
840840 0 0
841841 10.0000 + 17.3205i 0.344828 + 0.597259i
842842 0 0
843843 6.00000 + 3.46410i 0.206651 + 0.119310i
844844 −13.0000 −0.447478
845845 12.0000 19.0526i 0.412813 0.655428i
846846 −30.0000 −1.03142
847847 0 0
848848 −22.5000 + 38.9711i −0.772653 + 1.33827i
849849 9.50000 + 16.4545i 0.326039 + 0.564716i
850850 20.7846i 0.712906i
851851 0 0
852852 1.50000 0.866025i 0.0513892 0.0296695i
853853 41.5692i 1.42330i −0.702533 0.711651i 0.747948π-0.747948\pi
0.702533 0.711651i 0.252052π-0.252052\pi
854854 0 0
855855 −3.00000 + 5.19615i −0.102598 + 0.177705i
856856 0 0
857857 −33.0000 −1.12726 −0.563629 0.826028i 0.690595π-0.690595\pi
−0.563629 + 0.826028i 0.690595π0.690595\pi
858858 −9.00000 + 31.1769i −0.307255 + 1.06436i
859859 −29.0000 −0.989467 −0.494734 0.869045i 0.664734π-0.664734\pi
−0.494734 + 0.869045i 0.664734π0.664734\pi
860860 16.5000 + 9.52628i 0.562645 + 0.324843i
861861 0 0
862862 28.5000 + 49.3634i 0.970714 + 1.68133i
863863 1.73205i 0.0589597i 0.999565 + 0.0294798i 0.00938509π0.00938509\pi
−0.999565 + 0.0294798i 0.990615π0.990615\pi
864864 22.5000 12.9904i 0.765466 0.441942i
865865 22.5000 12.9904i 0.765023 0.441686i
866866 32.9090i 1.11829i
867867 9.50000 + 16.4545i 0.322637 + 0.558824i
868868 0 0
869869 −22.5000 12.9904i −0.763260 0.440668i
870870 −9.00000 −0.305129
871871 22.5000 21.6506i 0.762383 0.733604i
872872 9.00000 0.304778
873873 −9.00000 5.19615i −0.304604 0.175863i
874874 0 0
875875 0 0
876876 8.66025i 0.292603i
877877 −1.50000 + 0.866025i −0.0506514 + 0.0292436i −0.525112 0.851033i 0.675977π-0.675977\pi
0.474460 + 0.880277i 0.342643π0.342643\pi
878878 −12.0000 + 6.92820i −0.404980 + 0.233816i
879879 25.9808i 0.876309i
880880 22.5000 + 38.9711i 0.758475 + 1.31372i
881881 16.5000 28.5788i 0.555899 0.962846i −0.441934 0.897048i 0.645707π-0.645707\pi
0.997833 0.0657979i 0.0209593π-0.0209593\pi
882882 0 0
883883 −44.0000 −1.48072 −0.740359 0.672212i 0.765344π-0.765344\pi
−0.740359 + 0.672212i 0.765344π0.765344\pi
884884 15.0000 + 15.5885i 0.504505 + 0.524297i
885885 6.00000 0.201688
886886 22.5000 + 12.9904i 0.755902 + 0.436420i
887887 −12.0000 + 20.7846i −0.402921 + 0.697879i −0.994077 0.108678i 0.965338π-0.965338\pi
0.591156 + 0.806557i 0.298672π0.298672\pi
888888 0 0
889889 0 0
890890 −18.0000 + 10.3923i −0.603361 + 0.348351i
891891 −4.50000 + 2.59808i −0.150756 + 0.0870388i
892892 5.19615i 0.173980i
893893 7.50000 + 12.9904i 0.250978 + 0.434707i
894894 16.5000 28.5788i 0.551843 0.955819i
895895 −4.50000 2.59808i −0.150418 0.0868441i
896896 0 0
897897 0 0
898898 3.00000 0.100111
899899 −4.50000 2.59808i −0.150083 0.0866507i
900900 −2.00000 + 3.46410i −0.0666667 + 0.115470i
901901 27.0000 + 46.7654i 0.899500 + 1.55798i
902902 46.7654i 1.55712i
903903 0 0
904904 −22.5000 + 12.9904i −0.748339 + 0.432054i
905905 3.46410i 0.115151i
906906 −10.5000 18.1865i −0.348839 0.604207i
907907 14.5000 25.1147i 0.481465 0.833921i −0.518309 0.855193i 0.673438π-0.673438\pi
0.999774 + 0.0212722i 0.00677166π0.00677166\pi
908908 15.0000 + 8.66025i 0.497792 + 0.287401i
909909 18.0000 0.597022
910910 0 0
911911 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
912912 −7.50000 4.33013i −0.248350 0.143385i
913913 9.00000 15.5885i 0.297857 0.515903i
914914 30.0000 + 51.9615i 0.992312 + 1.71873i
915915 12.1244i 0.400819i
916916 10.5000 6.06218i 0.346930 0.200300i
917917 0 0
918918 51.9615i 1.71499i
919919 23.5000 + 40.7032i 0.775193 + 1.34267i 0.934686 + 0.355475i 0.115681π0.115681\pi
−0.159492 + 0.987199i 0.550986π0.550986\pi
920920 0 0
921921 −21.0000 12.1244i −0.691974 0.399511i
922922 51.0000 1.67960
923923 1.50000 + 6.06218i 0.0493731 + 0.199539i
924924 0 0
925925 0 0
926926 −21.0000 + 36.3731i −0.690103 + 1.19529i
927927 −13.0000 22.5167i −0.426976 0.739544i
928928 15.5885i 0.511716i
929929 40.5000 23.3827i 1.32876 0.767161i 0.343654 0.939096i 0.388335π-0.388335\pi
0.985108 + 0.171935i 0.0550020π0.0550020\pi
930930 −4.50000 + 2.59808i −0.147561 + 0.0851943i
931931 0 0
932932 1.50000 + 2.59808i 0.0491341 + 0.0851028i
933933 −7.50000 + 12.9904i −0.245539 + 0.425286i
934934 −31.5000 18.1865i −1.03071 0.595082i
935935 54.0000 1.76599
936936 3.00000 + 12.1244i 0.0980581 + 0.396297i
937937 22.0000 0.718709 0.359354 0.933201i 0.382997π-0.382997\pi
0.359354 + 0.933201i 0.382997π0.382997\pi
938938 0 0
939939 9.50000 16.4545i 0.310021 0.536972i
940940 −7.50000 12.9904i −0.244623 0.423700i
941941 5.19615i 0.169390i 0.996407 + 0.0846949i 0.0269915π0.0269915\pi
−0.996407 + 0.0846949i 0.973008π0.973008\pi
942942 34.5000 19.9186i 1.12407 0.648983i
943943 0 0
944944 17.3205i 0.563735i
945945 0 0
946946 49.5000 85.7365i 1.60938 2.78753i
947947 33.0000 + 19.0526i 1.07236 + 0.619125i 0.928824 0.370521i 0.120821π-0.120821\pi
0.143532 + 0.989646i 0.454154π0.454154\pi
948948 −5.00000 −0.162392
949949 30.0000 + 8.66025i 0.973841 + 0.281124i
950950 6.00000 0.194666
951951 −4.50000 2.59808i −0.145922 0.0842484i
952952 0 0
953953 28.5000 + 49.3634i 0.923206 + 1.59904i 0.794422 + 0.607366i 0.207774π0.207774\pi
0.128784 + 0.991673i 0.458893π0.458893\pi
954954 31.1769i 1.00939i
955955 −22.5000 + 12.9904i −0.728083 + 0.420359i
956956 9.00000 5.19615i 0.291081 0.168056i
957957 15.5885i 0.503903i
958958 −25.5000 44.1673i −0.823868 1.42698i
959959 0 0
960960 −1.50000 0.866025i −0.0484123 0.0279508i
961961 28.0000 0.903226
962962 0 0
963963 0 0
964964 6.00000 + 3.46410i 0.193247 + 0.111571i
965965 1.50000 2.59808i 0.0482867 0.0836350i
966966 0 0
967967 10.3923i 0.334194i 0.985940 + 0.167097i 0.0534393π0.0534393\pi
−0.985940 + 0.167097i 0.946561π0.946561\pi
968968 24.0000 13.8564i 0.771389 0.445362i
969969 −9.00000 + 5.19615i −0.289122 + 0.166924i
970970 15.5885i 0.500515i
971971 −10.5000 18.1865i −0.336961 0.583634i 0.646899 0.762576i 0.276066π-0.276066\pi
−0.983860 + 0.178942i 0.942732π0.942732\pi
972972 −8.00000 + 13.8564i −0.256600 + 0.444444i
973973 0 0
974974 42.0000 1.34577
975975 5.00000 + 5.19615i 0.160128 + 0.166410i
976976 −35.0000 −1.12032
977977 16.5000 + 9.52628i 0.527882 + 0.304773i 0.740153 0.672438i 0.234753π-0.234753\pi
−0.212272 + 0.977211i 0.568086π0.568086\pi
978978 −10.5000 + 18.1865i −0.335753 + 0.581541i
979979 18.0000 + 31.1769i 0.575282 + 0.996419i
980980 0 0
981981 −9.00000 + 5.19615i −0.287348 + 0.165900i
982982 40.5000 23.3827i 1.29241 0.746171i
983983 36.3731i 1.16012i 0.814574 + 0.580060i 0.196971π0.196971\pi
−0.814574 + 0.580060i 0.803029π0.803029\pi
984984 4.50000 + 7.79423i 0.143455 + 0.248471i
985985 −19.5000 + 33.7750i −0.621322 + 1.07616i
986986 27.0000 + 15.5885i 0.859855 + 0.496438i
987987 0 0
988988 −4.50000 + 4.33013i −0.143164 + 0.137760i
989989 0 0
990990 −27.0000 15.5885i −0.858116 0.495434i
991991 −29.5000 + 51.0955i −0.937098 + 1.62310i −0.166250 + 0.986084i 0.553166π0.553166\pi
−0.770849 + 0.637018i 0.780168π0.780168\pi
992992 4.50000 + 7.79423i 0.142875 + 0.247467i
993993 32.9090i 1.04433i
994994 0 0
995995 6.00000 3.46410i 0.190213 0.109819i
996996 3.46410i 0.109764i
997997 −1.00000 1.73205i −0.0316703 0.0548546i 0.849756 0.527176i 0.176749π-0.176749\pi
−0.881426 + 0.472322i 0.843416π0.843416\pi
998998 −1.50000 + 2.59808i −0.0474817 + 0.0822407i
999999 0 0
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 637.2.q.c.589.1 2
7.2 even 3 91.2.k.a.4.1 2
7.3 odd 6 637.2.u.a.30.1 2
7.4 even 3 91.2.u.a.30.1 yes 2
7.5 odd 6 637.2.k.b.459.1 2
7.6 odd 2 637.2.q.b.589.1 2
13.6 odd 12 8281.2.a.s.1.1 2
13.7 odd 12 8281.2.a.s.1.2 2
13.10 even 6 inner 637.2.q.c.491.1 2
21.2 odd 6 819.2.bm.a.550.1 2
21.11 odd 6 819.2.do.c.667.1 2
91.6 even 12 8281.2.a.w.1.1 2
91.10 odd 6 637.2.k.b.569.1 2
91.20 even 12 8281.2.a.w.1.2 2
91.23 even 6 91.2.u.a.88.1 yes 2
91.32 odd 12 1183.2.e.e.170.2 4
91.46 odd 12 1183.2.e.e.170.1 4
91.58 odd 12 1183.2.e.e.508.2 4
91.62 odd 6 637.2.q.b.491.1 2
91.72 odd 12 1183.2.e.e.508.1 4
91.75 odd 6 637.2.u.a.361.1 2
91.88 even 6 91.2.k.a.23.1 yes 2
273.23 odd 6 819.2.do.c.361.1 2
273.179 odd 6 819.2.bm.a.478.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.k.a.4.1 2 7.2 even 3
91.2.k.a.23.1 yes 2 91.88 even 6
91.2.u.a.30.1 yes 2 7.4 even 3
91.2.u.a.88.1 yes 2 91.23 even 6
637.2.k.b.459.1 2 7.5 odd 6
637.2.k.b.569.1 2 91.10 odd 6
637.2.q.b.491.1 2 91.62 odd 6
637.2.q.b.589.1 2 7.6 odd 2
637.2.q.c.491.1 2 13.10 even 6 inner
637.2.q.c.589.1 2 1.1 even 1 trivial
637.2.u.a.30.1 2 7.3 odd 6
637.2.u.a.361.1 2 91.75 odd 6
819.2.bm.a.478.1 2 273.179 odd 6
819.2.bm.a.550.1 2 21.2 odd 6
819.2.do.c.361.1 2 273.23 odd 6
819.2.do.c.667.1 2 21.11 odd 6
1183.2.e.e.170.1 4 91.46 odd 12
1183.2.e.e.170.2 4 91.32 odd 12
1183.2.e.e.508.1 4 91.72 odd 12
1183.2.e.e.508.2 4 91.58 odd 12
8281.2.a.s.1.1 2 13.6 odd 12
8281.2.a.s.1.2 2 13.7 odd 12
8281.2.a.w.1.1 2 91.6 even 12
8281.2.a.w.1.2 2 91.20 even 12