Properties

Label 3800.1.cq.b.899.1
Level 38003800
Weight 11
Character 3800.899
Analytic conductor 1.8961.896
Analytic rank 00
Dimension 1212
Projective image D9D_{9}
CM discriminant -8
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3800,1,Mod(99,3800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3800, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 9, 2]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3800.99");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 3800=235219 3800 = 2^{3} \cdot 5^{2} \cdot 19
Weight: k k == 1 1
Character orbit: [χ][\chi] == 3800.cq (of order 1818, degree 66, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.896447048011.89644704801
Analytic rank: 00
Dimension: 1212
Relative dimension: 22 over Q(ζ18)\Q(\zeta_{18})
Coefficient field: Q(ζ36)\Q(\zeta_{36})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12x6+1 x^{12} - x^{6} + 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 152)
Projective image: D9D_{9}
Projective field: Galois closure of 9.1.69564674215936.1

Embedding invariants

Embedding label 899.1
Root 0.6427880.766044i-0.642788 - 0.766044i of defining polynomial
Character χ\chi == 3800.899
Dual form 3800.1.cq.b.1099.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.6427880.766044i)q2+(0.5240051.43969i)q3+(0.173648+0.984808i)q4+(1.43969+0.524005i)q6+(0.8660250.500000i)q8+(1.032090.866025i)q9+(0.939693+1.62760i)q11+(1.32683+0.766044i)q12+(0.9396930.342020i)q16+(0.642788+0.766044i)q17+1.34730iq18+(0.173648+0.984808i)q19+(0.6427881.76604i)q22+(0.2660441.50881i)q24+(0.460802+0.266044i)q27+(0.342020+0.939693i)q32+(2.835640.500000i)q33+(0.1736480.984808i)q34+(1.032090.866025i)q36+(0.8660250.500000i)q38+(0.3263520.118782i)q41+(0.9848080.173648i)q43+(1.76604+0.642788i)q44+(0.984808+1.17365i)q48+(0.500000+0.866025i)q49+(1.439690.524005i)q51+(0.500000+0.181985i)q54+(1.32683+0.766044i)q57+(1.439691.20805i)q59+(0.5000000.866025i)q64+(2.205741.85083i)q66+(0.2232380.266044i)q67+(0.866025+0.500000i)q68+(1.326830.233956i)q72+(0.642788+1.76604i)q73+(0.9396930.342020i)q76+(0.09239630.524005i)q81+(0.118782+0.326352i)q82+(0.3007670.173648i)q83+(0.7660440.642788i)q86+(1.62760+0.939693i)q88+(0.939693+0.342020i)q89+1.53209q96+(0.2232380.266044i)q97+(0.3420200.939693i)q98+(0.4396932.49362i)q99+O(q100)q+(-0.642788 - 0.766044i) q^{2} +(0.524005 - 1.43969i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.43969 + 0.524005i) q^{6} +(0.866025 - 0.500000i) q^{8} +(-1.03209 - 0.866025i) q^{9} +(0.939693 + 1.62760i) q^{11} +(1.32683 + 0.766044i) q^{12} +(-0.939693 - 0.342020i) q^{16} +(0.642788 + 0.766044i) q^{17} +1.34730i q^{18} +(-0.173648 + 0.984808i) q^{19} +(0.642788 - 1.76604i) q^{22} +(-0.266044 - 1.50881i) q^{24} +(-0.460802 + 0.266044i) q^{27} +(0.342020 + 0.939693i) q^{32} +(2.83564 - 0.500000i) q^{33} +(0.173648 - 0.984808i) q^{34} +(1.03209 - 0.866025i) q^{36} +(0.866025 - 0.500000i) q^{38} +(-0.326352 - 0.118782i) q^{41} +(0.984808 - 0.173648i) q^{43} +(-1.76604 + 0.642788i) q^{44} +(-0.984808 + 1.17365i) q^{48} +(0.500000 + 0.866025i) q^{49} +(1.43969 - 0.524005i) q^{51} +(0.500000 + 0.181985i) q^{54} +(1.32683 + 0.766044i) q^{57} +(1.43969 - 1.20805i) q^{59} +(0.500000 - 0.866025i) q^{64} +(-2.20574 - 1.85083i) q^{66} +(0.223238 - 0.266044i) q^{67} +(-0.866025 + 0.500000i) q^{68} +(-1.32683 - 0.233956i) q^{72} +(-0.642788 + 1.76604i) q^{73} +(-0.939693 - 0.342020i) q^{76} +(-0.0923963 - 0.524005i) q^{81} +(0.118782 + 0.326352i) q^{82} +(-0.300767 - 0.173648i) q^{83} +(-0.766044 - 0.642788i) q^{86} +(1.62760 + 0.939693i) q^{88} +(-0.939693 + 0.342020i) q^{89} +1.53209 q^{96} +(-0.223238 - 0.266044i) q^{97} +(0.342020 - 0.939693i) q^{98} +(0.439693 - 2.49362i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q6q6+6q9+6q246q366q4112q44+6q49+6q51+6q54+6q59+6q646q66+6q816q99+O(q100) 12 q - 6 q^{6} + 6 q^{9} + 6 q^{24} - 6 q^{36} - 6 q^{41} - 12 q^{44} + 6 q^{49} + 6 q^{51} + 6 q^{54} + 6 q^{59} + 6 q^{64} - 6 q^{66} + 6 q^{81} - 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3800Z)×\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times.

nn 401401 951951 19011901 19771977
χ(n)\chi(n) e(79)e\left(\frac{7}{9}\right) 1-1 1-1 1-1

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 −0.642788 0.766044i −0.642788 0.766044i
33 0.524005 1.43969i 0.524005 1.43969i −0.342020 0.939693i 0.611111π-0.611111\pi
0.866025 0.500000i 0.166667π-0.166667\pi
44 −0.173648 + 0.984808i −0.173648 + 0.984808i
55 0 0
66 −1.43969 + 0.524005i −1.43969 + 0.524005i
77 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
88 0.866025 0.500000i 0.866025 0.500000i
99 −1.03209 0.866025i −1.03209 0.866025i
1010 0 0
1111 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i 0.222222π0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
1212 1.32683 + 0.766044i 1.32683 + 0.766044i
1313 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
1414 0 0
1515 0 0
1616 −0.939693 0.342020i −0.939693 0.342020i
1717 0.642788 + 0.766044i 0.642788 + 0.766044i 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
1818 1.34730i 1.34730i
1919 −0.173648 + 0.984808i −0.173648 + 0.984808i
2020 0 0
2121 0 0
2222 0.642788 1.76604i 0.642788 1.76604i
2323 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
2424 −0.266044 1.50881i −0.266044 1.50881i
2525 0 0
2626 0 0
2727 −0.460802 + 0.266044i −0.460802 + 0.266044i
2828 0 0
2929 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
3030 0 0
3131 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
3232 0.342020 + 0.939693i 0.342020 + 0.939693i
3333 2.83564 0.500000i 2.83564 0.500000i
3434 0.173648 0.984808i 0.173648 0.984808i
3535 0 0
3636 1.03209 0.866025i 1.03209 0.866025i
3737 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3838 0.866025 0.500000i 0.866025 0.500000i
3939 0 0
4040 0 0
4141 −0.326352 0.118782i −0.326352 0.118782i 0.173648 0.984808i 0.444444π-0.444444\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
4242 0 0
4343 0.984808 0.173648i 0.984808 0.173648i 0.342020 0.939693i 0.388889π-0.388889\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
4444 −1.76604 + 0.642788i −1.76604 + 0.642788i
4545 0 0
4646 0 0
4747 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
4848 −0.984808 + 1.17365i −0.984808 + 1.17365i
4949 0.500000 + 0.866025i 0.500000 + 0.866025i
5050 0 0
5151 1.43969 0.524005i 1.43969 0.524005i
5252 0 0
5353 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
5454 0.500000 + 0.181985i 0.500000 + 0.181985i
5555 0 0
5656 0 0
5757 1.32683 + 0.766044i 1.32683 + 0.766044i
5858 0 0
5959 1.43969 1.20805i 1.43969 1.20805i 0.500000 0.866025i 0.333333π-0.333333\pi
0.939693 0.342020i 0.111111π-0.111111\pi
6060 0 0
6161 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
6262 0 0
6363 0 0
6464 0.500000 0.866025i 0.500000 0.866025i
6565 0 0
6666 −2.20574 1.85083i −2.20574 1.85083i
6767 0.223238 0.266044i 0.223238 0.266044i −0.642788 0.766044i 0.722222π-0.722222\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
6868 −0.866025 + 0.500000i −0.866025 + 0.500000i
6969 0 0
7070 0 0
7171 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
7272 −1.32683 0.233956i −1.32683 0.233956i
7373 −0.642788 + 1.76604i −0.642788 + 1.76604i 1.00000i 0.5π0.5\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
7474 0 0
7575 0 0
7676 −0.939693 0.342020i −0.939693 0.342020i
7777 0 0
7878 0 0
7979 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
8080 0 0
8181 −0.0923963 0.524005i −0.0923963 0.524005i
8282 0.118782 + 0.326352i 0.118782 + 0.326352i
8383 −0.300767 0.173648i −0.300767 0.173648i 0.342020 0.939693i 0.388889π-0.388889\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
8484 0 0
8585 0 0
8686 −0.766044 0.642788i −0.766044 0.642788i
8787 0 0
8888 1.62760 + 0.939693i 1.62760 + 0.939693i
8989 −0.939693 + 0.342020i −0.939693 + 0.342020i −0.766044 0.642788i 0.777778π-0.777778\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 1.53209 1.53209
9797 −0.223238 0.266044i −0.223238 0.266044i 0.642788 0.766044i 0.277778π-0.277778\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
9898 0.342020 0.939693i 0.342020 0.939693i
9999 0.439693 2.49362i 0.439693 2.49362i
100100 0 0
101101 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
102102 −1.32683 0.766044i −1.32683 0.766044i
103103 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
104104 0 0
105105 0 0
106106 0 0
107107 −0.866025 0.500000i −0.866025 0.500000i 1.00000i 0.5π-0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
108108 −0.181985 0.500000i −0.181985 0.500000i
109109 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
110110 0 0
111111 0 0
112112 0 0
113113 1.87939i 1.87939i −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 0.939693i 0.388889π-0.388889\pi
114114 −0.266044 1.50881i −0.266044 1.50881i
115115 0 0
116116 0 0
117117 0 0
118118 −1.85083 0.326352i −1.85083 0.326352i
119119 0 0
120120 0 0
121121 −1.26604 + 2.19285i −1.26604 + 2.19285i
122122 0 0
123123 −0.342020 + 0.407604i −0.342020 + 0.407604i
124124 0 0
125125 0 0
126126 0 0
127127 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
128128 −0.984808 + 0.173648i −0.984808 + 0.173648i
129129 0.266044 1.50881i 0.266044 1.50881i
130130 0 0
131131 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i 0.444444π-0.444444\pi
1.00000 00
132132 2.87939i 2.87939i
133133 0 0
134134 −0.347296 −0.347296
135135 0 0
136136 0.939693 + 0.342020i 0.939693 + 0.342020i
137137 −1.50881 0.266044i −1.50881 0.266044i −0.642788 0.766044i 0.722222π-0.722222\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
138138 0 0
139139 0.326352 0.118782i 0.326352 0.118782i −0.173648 0.984808i 0.555556π-0.555556\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 0.673648 + 1.16679i 0.673648 + 1.16679i
145145 0 0
146146 1.76604 0.642788i 1.76604 0.642788i
147147 1.50881 0.266044i 1.50881 0.266044i
148148 0 0
149149 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
150150 0 0
151151 0 0 1.00000 00
−1.00000 π\pi
152152 0.342020 + 0.939693i 0.342020 + 0.939693i
153153 1.34730i 1.34730i
154154 0 0
155155 0 0
156156 0 0
157157 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 −0.342020 + 0.407604i −0.342020 + 0.407604i
163163 1.32683 0.766044i 1.32683 0.766044i 0.342020 0.939693i 0.388889π-0.388889\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
164164 0.173648 0.300767i 0.173648 0.300767i
165165 0 0
166166 0.0603074 + 0.342020i 0.0603074 + 0.342020i
167167 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
168168 0 0
169169 −0.766044 + 0.642788i −0.766044 + 0.642788i
170170 0 0
171171 1.03209 0.866025i 1.03209 0.866025i
172172 1.00000i 1.00000i
173173 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
174174 0 0
175175 0 0
176176 −0.326352 1.85083i −0.326352 1.85083i
177177 −0.984808 2.70574i −0.984808 2.70574i
178178 0.866025 + 0.500000i 0.866025 + 0.500000i
179179 0.173648 + 0.300767i 0.173648 + 0.300767i 0.939693 0.342020i 0.111111π-0.111111\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
180180 0 0
181181 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 −0.642788 + 1.76604i −0.642788 + 1.76604i
188188 0 0
189189 0 0
190190 0 0
191191 0 0 1.00000 00
−1.00000 π\pi
192192 −0.984808 1.17365i −0.984808 1.17365i
193193 −0.342020 + 0.939693i −0.342020 + 0.939693i 0.642788 + 0.766044i 0.277778π0.277778\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
194194 −0.0603074 + 0.342020i −0.0603074 + 0.342020i
195195 0 0
196196 −0.939693 + 0.342020i −0.939693 + 0.342020i
197197 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
198198 −2.19285 + 1.26604i −2.19285 + 1.26604i
199199 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
200200 0 0
201201 −0.266044 0.460802i −0.266044 0.460802i
202202 0 0
203203 0 0
204204 0.266044 + 1.50881i 0.266044 + 1.50881i
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 −1.76604 + 0.642788i −1.76604 + 0.642788i
210210 0 0
211211 −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
212212 0 0
213213 0 0
214214 0.173648 + 0.984808i 0.173648 + 0.984808i
215215 0 0
216216 −0.266044 + 0.460802i −0.266044 + 0.460802i
217217 0 0
218218 0 0
219219 2.20574 + 1.85083i 2.20574 + 1.85083i
220220 0 0
221221 0 0
222222 0 0
223223 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
224224 0 0
225225 0 0
226226 −1.43969 + 1.20805i −1.43969 + 1.20805i
227227 0.347296i 0.347296i −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 0.173648i 0.0555556π-0.0555556\pi
228228 −0.984808 + 1.17365i −0.984808 + 1.17365i
229229 0 0 1.00000 00
−1.00000 π\pi
230230 0 0
231231 0 0
232232 0 0
233233 −1.50881 + 0.266044i −1.50881 + 0.266044i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
234234 0 0
235235 0 0
236236 0.939693 + 1.62760i 0.939693 + 1.62760i
237237 0 0
238238 0 0
239239 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
240240 0 0
241241 −1.43969 + 0.524005i −1.43969 + 0.524005i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
242242 2.49362 0.439693i 2.49362 0.439693i
243243 −1.32683 0.233956i −1.32683 0.233956i
244244 0 0
245245 0 0
246246 0.532089 0.532089
247247 0 0
248248 0 0
249249 −0.407604 + 0.342020i −0.407604 + 0.342020i
250250 0 0
251251 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 0.642788i 0.222222π-0.222222\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0.766044 + 0.642788i 0.766044 + 0.642788i
257257 0.984808 1.17365i 0.984808 1.17365i 1.00000i 0.5π-0.5\pi
0.984808 0.173648i 0.0555556π-0.0555556\pi
258258 −1.32683 + 0.766044i −1.32683 + 0.766044i
259259 0 0
260260 0 0
261261 0 0
262262 −1.50881 0.266044i −1.50881 0.266044i
263263 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
264264 2.20574 1.85083i 2.20574 1.85083i
265265 0 0
266266 0 0
267267 1.53209i 1.53209i
268268 0.223238 + 0.266044i 0.223238 + 0.266044i
269269 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
270270 0 0
271271 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
272272 −0.342020 0.939693i −0.342020 0.939693i
273273 0 0
274274 0.766044 + 1.32683i 0.766044 + 1.32683i
275275 0 0
276276 0 0
277277 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
278278 −0.300767 0.173648i −0.300767 0.173648i
279279 0 0
280280 0 0
281281 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 0.642788i 0.222222π-0.222222\pi
282282 0 0
283283 −1.20805 1.43969i −1.20805 1.43969i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.342020 0.939693i 0.611111π-0.611111\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0.460802 1.26604i 0.460802 1.26604i
289289 0 0
290290 0 0
291291 −0.500000 + 0.181985i −0.500000 + 0.181985i
292292 −1.62760 0.939693i −1.62760 0.939693i
293293 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
294294 −1.17365 0.984808i −1.17365 0.984808i
295295 0 0
296296 0 0
297297 −0.866025 0.500000i −0.866025 0.500000i
298298 0 0
299299 0 0
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0.500000 0.866025i 0.500000 0.866025i
305305 0 0
306306 −1.03209 + 0.866025i −1.03209 + 0.866025i
307307 0.642788 1.76604i 0.642788 1.76604i 1.00000i 0.5π-0.5\pi
0.642788 0.766044i 0.277778π-0.277778\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
312312 0 0
313313 −0.984808 + 1.17365i −0.984808 + 1.17365i 1.00000i 0.5π0.5\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
318318 0 0
319319 0 0
320320 0 0
321321 −1.17365 + 0.984808i −1.17365 + 0.984808i
322322 0 0
323323 −0.866025 + 0.500000i −0.866025 + 0.500000i
324324 0.532089 0.532089
325325 0 0
326326 −1.43969 0.524005i −1.43969 0.524005i
327327 0 0
328328 −0.342020 + 0.0603074i −0.342020 + 0.0603074i
329329 0 0
330330 0 0
331331 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i 0.222222π0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
332332 0.223238 0.266044i 0.223238 0.266044i
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 1.50881 0.266044i 1.50881 0.266044i 0.642788 0.766044i 0.277778π-0.277778\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
338338 0.984808 + 0.173648i 0.984808 + 0.173648i
339339 −2.70574 0.984808i −2.70574 0.984808i
340340 0 0
341341 0 0
342342 −1.32683 0.233956i −1.32683 0.233956i
343343 0 0
344344 0.766044 0.642788i 0.766044 0.642788i
345345 0 0
346346 0 0
347347 0.342020 0.0603074i 0.342020 0.0603074i 1.00000i 0.5π-0.5\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
348348 0 0
349349 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
350350 0 0
351351 0 0
352352 −1.20805 + 1.43969i −1.20805 + 1.43969i
353353 0.300767 0.173648i 0.300767 0.173648i −0.342020 0.939693i 0.611111π-0.611111\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
354354 −1.43969 + 2.49362i −1.43969 + 2.49362i
355355 0 0
356356 −0.173648 0.984808i −0.173648 0.984808i
357357 0 0
358358 0.118782 0.326352i 0.118782 0.326352i
359359 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
360360 0 0
361361 −0.939693 0.342020i −0.939693 0.342020i
362362 0 0
363363 2.49362 + 2.97178i 2.49362 + 2.97178i
364364 0 0
365365 0 0
366366 0 0
367367 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
368368 0 0
369369 0.233956 + 0.405223i 0.233956 + 0.405223i
370370 0 0
371371 0 0
372372 0 0
373373 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
374374 1.76604 0.642788i 1.76604 0.642788i
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 −2.00000 −2.00000 −1.00000 π\pi
−1.00000 π\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
384384 −0.266044 + 1.50881i −0.266044 + 1.50881i
385385 0 0
386386 0.939693 0.342020i 0.939693 0.342020i
387387 −1.16679 0.673648i −1.16679 0.673648i
388388 0.300767 0.173648i 0.300767 0.173648i
389389 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
390390 0 0
391391 0 0
392392 0.866025 + 0.500000i 0.866025 + 0.500000i
393393 −0.802823 2.20574i −0.802823 2.20574i
394394 0 0
395395 0 0
396396 2.37939 + 0.866025i 2.37939 + 0.866025i
397397 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
398398 0 0
399399 0 0
400400 0 0
401401 −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i 0.666667π0.666667\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
402402 −0.181985 + 0.500000i −0.181985 + 0.500000i
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0.984808 1.17365i 0.984808 1.17365i
409409 1.43969 + 1.20805i 1.43969 + 1.20805i 0.939693 + 0.342020i 0.111111π0.111111\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
410410 0 0
411411 −1.17365 + 2.03282i −1.17365 + 2.03282i
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 0.532089i 0.532089i
418418 1.62760 + 0.939693i 1.62760 + 0.939693i
419419 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
420420 0 0
421421 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
422422 0.984808 + 0.173648i 0.984808 + 0.173648i
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 0 0
428428 0.642788 0.766044i 0.642788 0.766044i
429429 0 0
430430 0 0
431431 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
432432 0.524005 0.0923963i 0.524005 0.0923963i
433433 1.96962 + 0.347296i 1.96962 + 0.347296i 0.984808 + 0.173648i 0.0555556π0.0555556\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 2.87939i 2.87939i
439439 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
440440 0 0
441441 0.233956 1.32683i 0.233956 1.32683i
442442 0 0
443443 −0.524005 1.43969i −0.524005 1.43969i −0.866025 0.500000i 0.833333π-0.833333\pi
0.342020 0.939693i 0.388889π-0.388889\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 0.766044 1.32683i 0.766044 1.32683i −0.173648 0.984808i 0.555556π-0.555556\pi
0.939693 0.342020i 0.111111π-0.111111\pi
450450 0 0
451451 −0.113341 0.642788i −0.113341 0.642788i
452452 1.85083 + 0.326352i 1.85083 + 0.326352i
453453 0 0
454454 −0.266044 + 0.223238i −0.266044 + 0.223238i
455455 0 0
456456 1.53209 1.53209
457457 0.347296i 0.347296i −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 0.173648i 0.0555556π-0.0555556\pi
458458 0 0
459459 −0.500000 0.181985i −0.500000 0.181985i
460460 0 0
461461 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
462462 0 0
463463 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
464464 0 0
465465 0 0
466466 1.17365 + 0.984808i 1.17365 + 0.984808i
467467 −0.300767 + 0.173648i −0.300767 + 0.173648i −0.642788 0.766044i 0.722222π-0.722222\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0.642788 1.76604i 0.642788 1.76604i
473473 1.20805 + 1.43969i 1.20805 + 1.43969i
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
480480 0 0
481481 0 0
482482 1.32683 + 0.766044i 1.32683 + 0.766044i
483483 0 0
484484 −1.93969 1.62760i −1.93969 1.62760i
485485 0 0
486486 0.673648 + 1.16679i 0.673648 + 1.16679i
487487 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
488488 0 0
489489 −0.407604 2.31164i −0.407604 2.31164i
490490 0 0
491491 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i 0.222222π-0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
492492 −0.342020 0.407604i −0.342020 0.407604i
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0.524005 + 0.0923963i 0.524005 + 0.0923963i
499499 0.326352 + 1.85083i 0.326352 + 1.85083i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
500500 0 0
501501 0 0
502502 −1.32683 + 0.766044i −1.32683 + 0.766044i
503503 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
504504 0 0
505505 0 0
506506 0 0
507507 0.524005 + 1.43969i 0.524005 + 1.43969i
508508 0 0
509509 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
510510 0 0
511511 0 0
512512 1.00000i 1.00000i
513513 −0.181985 0.500000i −0.181985 0.500000i
514514 −1.53209 −1.53209
515515 0 0
516516 1.43969 + 0.524005i 1.43969 + 0.524005i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 0.984808i 0.444444π-0.444444\pi
522522 0 0
523523 −1.28558 + 1.53209i −1.28558 + 1.53209i −0.642788 + 0.766044i 0.722222π0.722222\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
524524 0.766044 + 1.32683i 0.766044 + 1.32683i
525525 0 0
526526 0 0
527527 0 0
528528 −2.83564 0.500000i −2.83564 0.500000i
529529 0.939693 + 0.342020i 0.939693 + 0.342020i
530530 0 0
531531 −2.53209 −2.53209
532532 0 0
533533 0 0
534534 1.17365 0.984808i 1.17365 0.984808i
535535 0 0
536536 0.0603074 0.342020i 0.0603074 0.342020i
537537 0.524005 0.0923963i 0.524005 0.0923963i
538538 0 0
539539 −0.939693 + 1.62760i −0.939693 + 1.62760i
540540 0 0
541541 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
542542 0 0
543543 0 0
544544 −0.500000 + 0.866025i −0.500000 + 0.866025i
545545 0 0
546546 0 0
547547 0.984808 + 0.173648i 0.984808 + 0.173648i 0.642788 0.766044i 0.277778π-0.277778\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
548548 0.524005 1.43969i 0.524005 1.43969i
549549 0 0
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0.0603074 + 0.342020i 0.0603074 + 0.342020i
557557 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
558558 0 0
559559 0 0
560560 0 0
561561 2.20574 + 1.85083i 2.20574 + 1.85083i
562562 −1.32683 + 0.766044i −1.32683 + 0.766044i
563563 1.62760 + 0.939693i 1.62760 + 0.939693i 0.984808 + 0.173648i 0.0555556π0.0555556\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
564564 0 0
565565 0 0
566566 −0.326352 + 1.85083i −0.326352 + 1.85083i
567567 0 0
568568 0 0
569569 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
570570 0 0
571571 1.53209 1.53209 0.766044 0.642788i 0.222222π-0.222222\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 −1.26604 + 0.460802i −1.26604 + 0.460802i
577577 −1.62760 0.939693i −1.62760 0.939693i −0.984808 0.173648i 0.944444π-0.944444\pi
−0.642788 0.766044i 0.722222π-0.722222\pi
578578 0 0
579579 1.17365 + 0.984808i 1.17365 + 0.984808i
580580 0 0
581581 0 0
582582 0.460802 + 0.266044i 0.460802 + 0.266044i
583583 0 0
584584 0.326352 + 1.85083i 0.326352 + 1.85083i
585585 0 0
586586 0 0
587587 0.642788 + 0.766044i 0.642788 + 0.766044i 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
588588 1.53209i 1.53209i
589589 0 0
590590 0 0
591591 0 0
592592 0 0
593593 −1.85083 0.326352i −1.85083 0.326352i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
594594 0.173648 + 0.984808i 0.173648 + 0.984808i
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
600600 0 0
601601 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i 0.444444π-0.444444\pi
0.766044 0.642788i 0.222222π-0.222222\pi
602602 0 0
603603 −0.460802 + 0.0812519i −0.460802 + 0.0812519i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
608608 −0.984808 + 0.173648i −0.984808 + 0.173648i
609609 0 0
610610 0 0
611611 0 0
612612 1.32683 + 0.233956i 1.32683 + 0.233956i
613613 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
614614 −1.76604 + 0.642788i −1.76604 + 0.642788i
615615 0 0
616616 0 0
617617 −1.20805 + 1.43969i −1.20805 + 1.43969i −0.342020 + 0.939693i 0.611111π0.611111\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
618618 0 0
619619 −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
−1.00000 π\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 0 0
626626 1.53209 1.53209
627627 2.87939i 2.87939i
628628 0 0
629629 0 0
630630 0 0
631631 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
632632 0 0
633633 0.524005 + 1.43969i 0.524005 + 1.43969i
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 0.0603074 + 0.342020i 0.0603074 + 0.342020i 1.00000 00
−0.939693 + 0.342020i 0.888889π0.888889\pi
642642 1.50881 + 0.266044i 1.50881 + 0.266044i
643643 0.524005 1.43969i 0.524005 1.43969i −0.342020 0.939693i 0.611111π-0.611111\pi
0.866025 0.500000i 0.166667π-0.166667\pi
644644 0 0
645645 0 0
646646 0.939693 + 0.342020i 0.939693 + 0.342020i
647647 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
648648 −0.342020 0.407604i −0.342020 0.407604i
649649 3.31908 + 1.20805i 3.31908 + 1.20805i
650650 0 0
651651 0 0
652652 0.524005 + 1.43969i 0.524005 + 1.43969i
653653 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
654654 0 0
655655 0 0
656656 0.266044 + 0.223238i 0.266044 + 0.223238i
657657 2.19285 1.26604i 2.19285 1.26604i
658658 0 0
659659 −0.939693 + 0.342020i −0.939693 + 0.342020i −0.766044 0.642788i 0.777778π-0.777778\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
660660 0 0
661661 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
662662 0.642788 1.76604i 0.642788 1.76604i
663663 0 0
664664 −0.347296 −0.347296
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i 0.833333π-0.833333\pi
1.00000i 0.5π0.5\pi
674674 −1.17365 0.984808i −1.17365 0.984808i
675675 0 0
676676 −0.500000 0.866025i −0.500000 0.866025i
677677 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
678678 0.984808 + 2.70574i 0.984808 + 2.70574i
679679 0 0
680680 0 0
681681 −0.500000 0.181985i −0.500000 0.181985i
682682 0 0
683683 1.00000i 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
684684 0.673648 + 1.16679i 0.673648 + 1.16679i
685685 0 0
686686 0 0
687687 0 0
688688 −0.984808 0.173648i −0.984808 0.173648i
689689 0 0
690690 0 0
691691 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
692692 0 0
693693 0 0
694694 −0.266044 0.223238i −0.266044 0.223238i
695695 0 0
696696 0 0
697697 −0.118782 0.326352i −0.118782 0.326352i
698698 0 0
699699 −0.407604 + 2.31164i −0.407604 + 2.31164i
700700 0 0
701701 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
702702 0 0
703703 0 0
704704 1.87939 1.87939
705705 0 0
706706 −0.326352 0.118782i −0.326352 0.118782i
707707 0 0
708708 2.83564 0.500000i 2.83564 0.500000i
709709 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
710710 0 0
711711 0 0
712712 −0.642788 + 0.766044i −0.642788 + 0.766044i
713713 0 0
714714 0 0
715715 0 0
716716 −0.326352 + 0.118782i −0.326352 + 0.118782i
717717 0 0
718718 0 0
719719 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
720720 0 0
721721 0 0
722722 0.342020 + 0.939693i 0.342020 + 0.939693i
723723 2.34730i 2.34730i
724724 0 0
725725 0 0
726726 0.673648 3.82045i 0.673648 3.82045i
727727 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
728728 0 0
729729 −0.766044 + 1.32683i −0.766044 + 1.32683i
730730 0 0
731731 0.766044 + 0.642788i 0.766044 + 0.642788i
732732 0 0
733733 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
734734 0 0
735735 0 0
736736 0 0
737737 0.642788 + 0.113341i 0.642788 + 0.113341i
738738 0.160035 0.439693i 0.160035 0.439693i
739739 −0.266044 + 0.223238i −0.266044 + 0.223238i −0.766044 0.642788i 0.777778π-0.777778\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
740740 0 0
741741 0 0
742742 0 0
743743 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
744744 0 0
745745 0 0
746746 0 0
747747 0.160035 + 0.439693i 0.160035 + 0.439693i
748748 −1.62760 0.939693i −1.62760 0.939693i
749749 0 0
750750 0 0
751751 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
752752 0 0
753753 −2.03282 1.17365i −2.03282 1.17365i
754754 0 0
755755 0 0
756756 0 0
757757 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
758758 1.28558 + 1.53209i 1.28558 + 1.53209i
759759 0 0
760760 0 0
761761 1.53209 1.53209 0.766044 0.642788i 0.222222π-0.222222\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 1.32683 0.766044i 1.32683 0.766044i
769769 0.766044 + 0.642788i 0.766044 + 0.642788i 0.939693 0.342020i 0.111111π-0.111111\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
770770 0 0
771771 −1.17365 2.03282i −1.17365 2.03282i
772772 −0.866025 0.500000i −0.866025 0.500000i
773773 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
774774 0.233956 + 1.32683i 0.233956 + 1.32683i
775775 0 0
776776 −0.326352 0.118782i −0.326352 0.118782i
777777 0 0
778778 0 0
779779 0.173648 0.300767i 0.173648 0.300767i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −0.173648 0.984808i −0.173648 0.984808i
785785 0 0
786786 −1.17365 + 2.03282i −1.17365 + 2.03282i
787787 1.62760 0.939693i 1.62760 0.939693i 0.642788 0.766044i 0.277778π-0.277778\pi
0.984808 0.173648i 0.0555556π-0.0555556\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 −0.866025 2.37939i −0.866025 2.37939i
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
798798 0 0
799799 0 0
800800 0 0
801801 1.26604 + 0.460802i 1.26604 + 0.460802i
802802 1.85083 + 0.326352i 1.85083 + 0.326352i
803803 −3.47843 + 0.613341i −3.47843 + 0.613341i
804804 0.500000 0.181985i 0.500000 0.181985i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 −0.939693 1.62760i −0.939693 1.62760i −0.766044 0.642788i 0.777778π-0.777778\pi
−0.173648 0.984808i 0.555556π-0.555556\pi
810810 0 0
811811 −1.87939 + 0.684040i −1.87939 + 0.684040i −0.939693 + 0.342020i 0.888889π0.888889\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 −1.53209 −1.53209
817817 1.00000i 1.00000i
818818 1.87939i 1.87939i
819819 0 0
820820 0 0
821821 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
822822 2.31164 0.407604i 2.31164 0.407604i
823823 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
824824 0 0
825825 0 0
826826 0 0
827827 −1.20805 + 1.43969i −1.20805 + 1.43969i −0.342020 + 0.939693i 0.611111π0.611111\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
828828 0 0
829829 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
830830 0 0
831831 0 0
832832 0 0
833833 −0.342020 + 0.939693i −0.342020 + 0.939693i
834834 −0.407604 + 0.342020i −0.407604 + 0.342020i
835835 0 0
836836 −0.326352 1.85083i −0.326352 1.85083i
837837 0 0
838838 −0.642788 0.766044i −0.642788 0.766044i
839839 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
840840 0 0
841841 0.173648 + 0.984808i 0.173648 + 0.984808i
842842 0 0
843843 −2.03282 1.17365i −2.03282 1.17365i
844844 −0.500000 0.866025i −0.500000 0.866025i
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 −2.70574 + 0.984808i −2.70574 + 0.984808i
850850 0 0
851851 0 0
852852 0 0
853853 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
854854 0 0
855855 0 0
856856 −1.00000 −1.00000
857857 −0.984808 1.17365i −0.984808 1.17365i −0.984808 0.173648i 0.944444π-0.944444\pi
1.00000i 0.5π-0.5\pi
858858 0 0
859859 0.326352 1.85083i 0.326352 1.85083i −0.173648 0.984808i 0.555556π-0.555556\pi
0.500000 0.866025i 0.333333π-0.333333\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
864864 −0.407604 0.342020i −0.407604 0.342020i
865865 0 0
866866 −1.00000 1.73205i −1.00000 1.73205i
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 0.467911i 0.467911i
874874 0 0
875875 0 0
876876 −2.20574 + 1.85083i −2.20574 + 1.85083i
877877 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
878878 0 0
879879 0 0
880880 0 0
881881 −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i 0.888889π-0.888889\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
882882 −1.16679 + 0.673648i −1.16679 + 0.673648i
883883 −0.223238 + 0.266044i −0.223238 + 0.266044i −0.866025 0.500000i 0.833333π-0.833333\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
884884 0 0
885885 0 0
886886 −0.766044 + 1.32683i −0.766044 + 1.32683i
887887 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
888888 0 0
889889 0 0
890890 0 0
891891 0.766044 0.642788i 0.766044 0.642788i
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 −1.50881 + 0.266044i −1.50881 + 0.266044i
899899 0 0
900900 0 0
901901 0 0
902902 −0.419550 + 0.500000i −0.419550 + 0.500000i
903903 0 0
904904 −0.939693 1.62760i −0.939693 1.62760i
905905 0 0
906906 0 0
907907 −1.85083 + 0.326352i −1.85083 + 0.326352i −0.984808 0.173648i 0.944444π-0.944444\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
908908 0.342020 + 0.0603074i 0.342020 + 0.0603074i
909909 0 0
910910 0 0
911911 0 0 1.00000 00
−1.00000 π\pi
912912 −0.984808 1.17365i −0.984808 1.17365i
913913 0.652704i 0.652704i
914914 −0.266044 + 0.223238i −0.266044 + 0.223238i
915915 0 0
916916 0 0
917917 0 0
918918 0.181985 + 0.500000i 0.181985 + 0.500000i
919919 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
920920 0 0
921921 −2.20574 1.85083i −2.20574 1.85083i
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 1.43969 1.20805i 1.43969 1.20805i 0.500000 0.866025i 0.333333π-0.333333\pi
0.939693 0.342020i 0.111111π-0.111111\pi
930930 0 0
931931 −0.939693 + 0.342020i −0.939693 + 0.342020i
932932 1.53209i 1.53209i
933933 0 0
934934 0.326352 + 0.118782i 0.326352 + 0.118782i
935935 0 0
936936 0 0
937937 0.524005 + 1.43969i 0.524005 + 1.43969i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
938938 0 0
939939 1.17365 + 2.03282i 1.17365 + 2.03282i
940940 0 0
941941 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
942942 0 0
943943 0 0
944944 −1.76604 + 0.642788i −1.76604 + 0.642788i
945945 0 0
946946 0.326352 1.85083i 0.326352 1.85083i
947947 −0.684040 + 1.87939i −0.684040 + 1.87939i −0.342020 + 0.939693i 0.611111π0.611111\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 −0.642788 + 1.76604i −0.642788 + 1.76604i 1.00000i 0.5π0.5\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −0.500000 0.866025i −0.500000 0.866025i
962962 0 0
963963 0.460802 + 1.26604i 0.460802 + 1.26604i
964964 −0.266044 1.50881i −0.266044 1.50881i
965965 0 0
966966 0 0
967967 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
968968 2.53209i 2.53209i
969969 0.266044 + 1.50881i 0.266044 + 1.50881i
970970 0 0
971971 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i 0.444444π-0.444444\pi
1.00000 00
972972 0.460802 1.26604i 0.460802 1.26604i
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −1.32683 + 0.766044i −1.32683 + 0.766044i −0.984808 0.173648i 0.944444π-0.944444\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
978978 −1.50881 + 1.79813i −1.50881 + 1.79813i
979979 −1.43969 1.20805i −1.43969 1.20805i
980980 0 0
981981 0 0
982982 −0.342020 0.939693i −0.342020 0.939693i
983983 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
984984 −0.0923963 + 0.524005i −0.0923963 + 0.524005i
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
992992 0 0
993993 2.83564 0.500000i 2.83564 0.500000i
994994 0 0
995995 0 0
996996 −0.266044 0.460802i −0.266044 0.460802i
997997 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
998998 1.20805 1.43969i 1.20805 1.43969i
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 3800.1.cq.b.899.1 12
5.2 odd 4 152.1.u.a.139.1 yes 6
5.3 odd 4 3800.1.cv.c.1051.1 6
5.4 even 2 inner 3800.1.cq.b.899.2 12
8.3 odd 2 CM 3800.1.cq.b.899.1 12
15.2 even 4 1368.1.eh.a.595.1 6
19.16 even 9 inner 3800.1.cq.b.1099.2 12
20.7 even 4 608.1.bg.a.367.1 6
40.3 even 4 3800.1.cv.c.1051.1 6
40.19 odd 2 inner 3800.1.cq.b.899.2 12
40.27 even 4 152.1.u.a.139.1 yes 6
40.37 odd 4 608.1.bg.a.367.1 6
95.2 even 36 2888.1.u.f.1867.1 6
95.7 odd 12 2888.1.u.g.2555.1 6
95.12 even 12 2888.1.u.a.2555.1 6
95.17 odd 36 2888.1.u.b.1867.1 6
95.22 even 36 2888.1.u.e.1859.1 6
95.27 even 12 2888.1.u.f.99.1 6
95.32 even 36 2888.1.k.c.2819.3 6
95.37 even 4 2888.1.u.e.595.1 6
95.42 odd 36 2888.1.f.d.723.3 3
95.47 odd 36 2888.1.k.b.2595.1 6
95.52 even 36 2888.1.u.a.2411.1 6
95.54 even 18 inner 3800.1.cq.b.1099.1 12
95.62 odd 36 2888.1.u.g.2411.1 6
95.67 even 36 2888.1.k.c.2595.3 6
95.72 even 36 2888.1.f.c.723.1 3
95.73 odd 36 3800.1.cv.c.1251.1 6
95.82 odd 36 2888.1.k.b.2819.1 6
95.87 odd 12 2888.1.u.b.99.1 6
95.92 odd 36 152.1.u.a.35.1 6
120.107 odd 4 1368.1.eh.a.595.1 6
152.35 odd 18 inner 3800.1.cq.b.1099.2 12
285.92 even 36 1368.1.eh.a.1099.1 6
380.187 even 36 608.1.bg.a.111.1 6
760.27 odd 12 2888.1.u.f.99.1 6
760.67 odd 36 2888.1.k.c.2595.3 6
760.107 odd 12 2888.1.u.a.2555.1 6
760.147 odd 36 2888.1.u.a.2411.1 6
760.187 even 36 152.1.u.a.35.1 6
760.227 odd 4 2888.1.u.e.595.1 6
760.307 odd 36 2888.1.u.e.1859.1 6
760.339 odd 18 inner 3800.1.cq.b.1099.1 12
760.347 even 36 2888.1.u.g.2411.1 6
760.387 even 12 2888.1.u.g.2555.1 6
760.427 even 36 2888.1.k.b.2595.1 6
760.467 even 12 2888.1.u.b.99.1 6
760.507 odd 36 2888.1.k.c.2819.3 6
760.547 odd 36 2888.1.f.c.723.1 3
760.587 even 36 2888.1.u.b.1867.1 6
760.643 even 36 3800.1.cv.c.1251.1 6
760.667 odd 36 2888.1.u.f.1867.1 6
760.707 even 36 2888.1.f.d.723.3 3
760.747 even 36 2888.1.k.b.2819.1 6
760.757 odd 36 608.1.bg.a.111.1 6
2280.947 odd 36 1368.1.eh.a.1099.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.1.u.a.35.1 6 95.92 odd 36
152.1.u.a.35.1 6 760.187 even 36
152.1.u.a.139.1 yes 6 5.2 odd 4
152.1.u.a.139.1 yes 6 40.27 even 4
608.1.bg.a.111.1 6 380.187 even 36
608.1.bg.a.111.1 6 760.757 odd 36
608.1.bg.a.367.1 6 20.7 even 4
608.1.bg.a.367.1 6 40.37 odd 4
1368.1.eh.a.595.1 6 15.2 even 4
1368.1.eh.a.595.1 6 120.107 odd 4
1368.1.eh.a.1099.1 6 285.92 even 36
1368.1.eh.a.1099.1 6 2280.947 odd 36
2888.1.f.c.723.1 3 95.72 even 36
2888.1.f.c.723.1 3 760.547 odd 36
2888.1.f.d.723.3 3 95.42 odd 36
2888.1.f.d.723.3 3 760.707 even 36
2888.1.k.b.2595.1 6 95.47 odd 36
2888.1.k.b.2595.1 6 760.427 even 36
2888.1.k.b.2819.1 6 95.82 odd 36
2888.1.k.b.2819.1 6 760.747 even 36
2888.1.k.c.2595.3 6 95.67 even 36
2888.1.k.c.2595.3 6 760.67 odd 36
2888.1.k.c.2819.3 6 95.32 even 36
2888.1.k.c.2819.3 6 760.507 odd 36
2888.1.u.a.2411.1 6 95.52 even 36
2888.1.u.a.2411.1 6 760.147 odd 36
2888.1.u.a.2555.1 6 95.12 even 12
2888.1.u.a.2555.1 6 760.107 odd 12
2888.1.u.b.99.1 6 95.87 odd 12
2888.1.u.b.99.1 6 760.467 even 12
2888.1.u.b.1867.1 6 95.17 odd 36
2888.1.u.b.1867.1 6 760.587 even 36
2888.1.u.e.595.1 6 95.37 even 4
2888.1.u.e.595.1 6 760.227 odd 4
2888.1.u.e.1859.1 6 95.22 even 36
2888.1.u.e.1859.1 6 760.307 odd 36
2888.1.u.f.99.1 6 95.27 even 12
2888.1.u.f.99.1 6 760.27 odd 12
2888.1.u.f.1867.1 6 95.2 even 36
2888.1.u.f.1867.1 6 760.667 odd 36
2888.1.u.g.2411.1 6 95.62 odd 36
2888.1.u.g.2411.1 6 760.347 even 36
2888.1.u.g.2555.1 6 95.7 odd 12
2888.1.u.g.2555.1 6 760.387 even 12
3800.1.cq.b.899.1 12 1.1 even 1 trivial
3800.1.cq.b.899.1 12 8.3 odd 2 CM
3800.1.cq.b.899.2 12 5.4 even 2 inner
3800.1.cq.b.899.2 12 40.19 odd 2 inner
3800.1.cq.b.1099.1 12 95.54 even 18 inner
3800.1.cq.b.1099.1 12 760.339 odd 18 inner
3800.1.cq.b.1099.2 12 19.16 even 9 inner
3800.1.cq.b.1099.2 12 152.35 odd 18 inner
3800.1.cv.c.1051.1 6 5.3 odd 4
3800.1.cv.c.1051.1 6 40.3 even 4
3800.1.cv.c.1251.1 6 95.73 odd 36
3800.1.cv.c.1251.1 6 760.643 even 36