Properties

Label 900.1.bh.a.503.1
Level 900900
Weight 11
Character 900.503
Analytic conductor 0.4490.449
Analytic rank 00
Dimension 1616
Projective image D20D_{20}
CM discriminant -4
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [900,1,Mod(287,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 10, 9]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("900.287");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 900=223252 900 = 2^{2} \cdot 3^{2} \cdot 5^{2}
Weight: k k == 1 1
Character orbit: [χ][\chi] == 900.bh (of order 2020, degree 88, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.4491585113700.449158511370
Analytic rank: 00
Dimension: 1616
Relative dimension: 22 over Q(ζ20)\Q(\zeta_{20})
Coefficient field: Q(ζ40)\Q(\zeta_{40})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16x12+x8x4+1 x^{16} - x^{12} + x^{8} - x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D20D_{20}
Projective field: Galois closure of Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)

Embedding invariants

Embedding label 503.1
Root 0.453990+0.891007i0.453990 + 0.891007i of defining polynomial
Character χ\chi == 900.503
Dual form 900.1.bh.a.467.1

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+(0.891007+0.453990i)q2+(0.5877850.809017i)q4+(0.9876880.156434i)q5+(0.156434+0.987688i)q8+(0.9510570.309017i)q10+(0.896802+1.76007i)q13+(0.3090170.951057i)q16+(1.87869+0.297556i)q17+(0.707107+0.707107i)q20+(0.951057+0.309017i)q251.97538iq26+(1.44168+1.04744i)q29+(0.707107+0.707107i)q32+(1.80902+0.587785i)q34+(0.809017+0.412215i)q37+(0.3090170.951057i)q40+(0.297556+0.0966818i)q411.00000iq49+(0.987688+0.156434i)q50+(0.896802+1.76007i)q52+(1.16110+0.183900i)q53+(1.760070.278768i)q58+(0.363271+1.11803i)q61+(0.9510570.309017i)q64+(1.161101.59811i)q65+(1.345001.34500i)q68+(0.278768+0.142040i)q730.907981q74+(0.156434+0.987688i)q80+(0.2212320.221232i)q82+(1.809020.587785i)q85+(0.280582+0.863541i)q89+(1.76007+0.278768i)q97+(0.453990+0.891007i)q98+O(q100)q+(-0.891007 + 0.453990i) q^{2} +(0.587785 - 0.809017i) q^{4} +(-0.987688 - 0.156434i) q^{5} +(-0.156434 + 0.987688i) q^{8} +(0.951057 - 0.309017i) q^{10} +(-0.896802 + 1.76007i) q^{13} +(-0.309017 - 0.951057i) q^{16} +(1.87869 + 0.297556i) q^{17} +(-0.707107 + 0.707107i) q^{20} +(0.951057 + 0.309017i) q^{25} -1.97538i q^{26} +(1.44168 + 1.04744i) q^{29} +(0.707107 + 0.707107i) q^{32} +(-1.80902 + 0.587785i) q^{34} +(0.809017 + 0.412215i) q^{37} +(0.309017 - 0.951057i) q^{40} +(-0.297556 + 0.0966818i) q^{41} -1.00000i q^{49} +(-0.987688 + 0.156434i) q^{50} +(0.896802 + 1.76007i) q^{52} +(-1.16110 + 0.183900i) q^{53} +(-1.76007 - 0.278768i) q^{58} +(-0.363271 + 1.11803i) q^{61} +(-0.951057 - 0.309017i) q^{64} +(1.16110 - 1.59811i) q^{65} +(1.34500 - 1.34500i) q^{68} +(-0.278768 + 0.142040i) q^{73} -0.907981 q^{74} +(0.156434 + 0.987688i) q^{80} +(0.221232 - 0.221232i) q^{82} +(-1.80902 - 0.587785i) q^{85} +(-0.280582 + 0.863541i) q^{89} +(-1.76007 + 0.278768i) q^{97} +(0.453990 + 0.891007i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+4q13+4q1620q34+4q374q404q524q584q73+4q8220q854q97+O(q100) 16 q + 4 q^{13} + 4 q^{16} - 20 q^{34} + 4 q^{37} - 4 q^{40} - 4 q^{52} - 4 q^{58} - 4 q^{73} + 4 q^{82} - 20 q^{85} - 4 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/900Z)×\left(\mathbb{Z}/900\mathbb{Z}\right)^\times.

nn 101101 451451 577577
χ(n)\chi(n) 1-1 1-1 e(720)e\left(\frac{7}{20}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.891007 + 0.453990i −0.891007 + 0.453990i
33 0 0
44 0.587785 0.809017i 0.587785 0.809017i
55 −0.987688 0.156434i −0.987688 0.156434i
66 0 0
77 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
88 −0.156434 + 0.987688i −0.156434 + 0.987688i
99 0 0
1010 0.951057 0.309017i 0.951057 0.309017i
1111 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
1212 0 0
1313 −0.896802 + 1.76007i −0.896802 + 1.76007i −0.309017 + 0.951057i 0.600000π0.600000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
1414 0 0
1515 0 0
1616 −0.309017 0.951057i −0.309017 0.951057i
1717 1.87869 + 0.297556i 1.87869 + 0.297556i 0.987688 0.156434i 0.0500000π-0.0500000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
1818 0 0
1919 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
2020 −0.707107 + 0.707107i −0.707107 + 0.707107i
2121 0 0
2222 0 0
2323 0 0 −0.453990 0.891007i 0.650000π-0.650000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
2424 0 0
2525 0.951057 + 0.309017i 0.951057 + 0.309017i
2626 1.97538i 1.97538i
2727 0 0
2828 0 0
2929 1.44168 + 1.04744i 1.44168 + 1.04744i 0.987688 + 0.156434i 0.0500000π0.0500000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
3030 0 0
3131 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
3232 0.707107 + 0.707107i 0.707107 + 0.707107i
3333 0 0
3434 −1.80902 + 0.587785i −1.80902 + 0.587785i
3535 0 0
3636 0 0
3737 0.809017 + 0.412215i 0.809017 + 0.412215i 0.809017 0.587785i 0.200000π-0.200000\pi
1.00000i 0.5π0.5\pi
3838 0 0
3939 0 0
4040 0.309017 0.951057i 0.309017 0.951057i
4141 −0.297556 + 0.0966818i −0.297556 + 0.0966818i −0.453990 0.891007i 0.650000π-0.650000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
4242 0 0
4343 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
4444 0 0
4545 0 0
4646 0 0
4747 0 0 −0.156434 0.987688i 0.550000π-0.550000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
4848 0 0
4949 1.00000i 1.00000i
5050 −0.987688 + 0.156434i −0.987688 + 0.156434i
5151 0 0
5252 0.896802 + 1.76007i 0.896802 + 1.76007i
5353 −1.16110 + 0.183900i −1.16110 + 0.183900i −0.707107 0.707107i 0.750000π-0.750000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 −1.76007 0.278768i −1.76007 0.278768i
5959 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
6060 0 0
6161 −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i 0.300000π0.300000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
6262 0 0
6363 0 0
6464 −0.951057 0.309017i −0.951057 0.309017i
6565 1.16110 1.59811i 1.16110 1.59811i
6666 0 0
6767 0 0 0.156434 0.987688i 0.450000π-0.450000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
6868 1.34500 1.34500i 1.34500 1.34500i
6969 0 0
7070 0 0
7171 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
7272 0 0
7373 −0.278768 + 0.142040i −0.278768 + 0.142040i −0.587785 0.809017i 0.700000π-0.700000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
7474 −0.907981 −0.907981
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
8080 0.156434 + 0.987688i 0.156434 + 0.987688i
8181 0 0
8282 0.221232 0.221232i 0.221232 0.221232i
8383 0 0 0.156434 0.987688i 0.450000π-0.450000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
8484 0 0
8585 −1.80902 0.587785i −1.80902 0.587785i
8686 0 0
8787 0 0
8888 0 0
8989 −0.280582 + 0.863541i −0.280582 + 0.863541i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 −1.76007 + 0.278768i −1.76007 + 0.278768i −0.951057 0.309017i 0.900000π-0.900000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
9898 0.453990 + 0.891007i 0.453990 + 0.891007i
9999 0 0
100100 0.809017 0.587785i 0.809017 0.587785i
101101 0.907981i 0.907981i −0.891007 0.453990i 0.850000π-0.850000\pi
0.891007 0.453990i 0.150000π-0.150000\pi
102102 0 0
103103 0 0 −0.156434 0.987688i 0.550000π-0.550000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
104104 −1.59811 1.16110i −1.59811 1.16110i
105105 0 0
106106 0.951057 0.690983i 0.951057 0.690983i
107107 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
108108 0 0
109109 1.11803 0.363271i 1.11803 0.363271i 0.309017 0.951057i 0.400000π-0.400000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
110110 0 0
111111 0 0
112112 0 0
113113 −0.550672 0.280582i −0.550672 0.280582i 0.156434 0.987688i 0.450000π-0.450000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
114114 0 0
115115 0 0
116116 1.69480 0.550672i 1.69480 0.550672i
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 0.809017 + 0.587785i 0.809017 + 0.587785i
122122 −0.183900 1.16110i −0.183900 1.16110i
123123 0 0
124124 0 0
125125 −0.891007 0.453990i −0.891007 0.453990i
126126 0 0
127127 0 0 −0.453990 0.891007i 0.650000π-0.650000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
128128 0.987688 0.156434i 0.987688 0.156434i
129129 0 0
130130 −0.309017 + 1.95106i −0.309017 + 1.95106i
131131 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 −0.587785 + 1.80902i −0.587785 + 1.80902i
137137 0.734572 1.44168i 0.734572 1.44168i −0.156434 0.987688i 0.550000π-0.550000\pi
0.891007 0.453990i 0.150000π-0.150000\pi
138138 0 0
139139 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 0 0
145145 −1.26007 1.26007i −1.26007 1.26007i
146146 0.183900 0.253116i 0.183900 0.253116i
147147 0 0
148148 0.809017 0.412215i 0.809017 0.412215i
149149 −0.312869 −0.312869 −0.156434 0.987688i 0.550000π-0.550000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
150150 0 0
151151 0 0 1.00000 00
−1.00000 π\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 1.26007 1.26007i 1.26007 1.26007i 0.309017 0.951057i 0.400000π-0.400000\pi
0.951057 0.309017i 0.100000π-0.100000\pi
158158 0 0
159159 0 0
160160 −0.587785 0.809017i −0.587785 0.809017i
161161 0 0
162162 0 0
163163 0 0 0.453990 0.891007i 0.350000π-0.350000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
164164 −0.0966818 + 0.297556i −0.0966818 + 0.297556i
165165 0 0
166166 0 0
167167 0 0 −0.987688 0.156434i 0.950000π-0.950000\pi
0.987688 + 0.156434i 0.0500000π0.0500000\pi
168168 0 0
169169 −1.70582 2.34786i −1.70582 2.34786i
170170 1.87869 0.297556i 1.87869 0.297556i
171171 0 0
172172 0 0
173173 −0.280582 0.550672i −0.280582 0.550672i 0.707107 0.707107i 0.250000π-0.250000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 −0.142040 0.896802i −0.142040 0.896802i
179179 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
180180 0 0
181181 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i 0.300000π-0.300000\pi
0.951057 0.309017i 0.100000π-0.100000\pi
182182 0 0
183183 0 0
184184 0 0
185185 −0.734572 0.533698i −0.734572 0.533698i
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
192192 0 0
193193 −0.221232 0.221232i −0.221232 0.221232i 0.587785 0.809017i 0.300000π-0.300000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
194194 1.44168 1.04744i 1.44168 1.04744i
195195 0 0
196196 −0.809017 0.587785i −0.809017 0.587785i
197197 −0.253116 1.59811i −0.253116 1.59811i −0.707107 0.707107i 0.750000π-0.750000\pi
0.453990 0.891007i 0.350000π-0.350000\pi
198198 0 0
199199 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
200200 −0.453990 + 0.891007i −0.453990 + 0.891007i
201201 0 0
202202 0.412215 + 0.809017i 0.412215 + 0.809017i
203203 0 0
204204 0 0
205205 0.309017 0.0489435i 0.309017 0.0489435i
206206 0 0
207207 0 0
208208 1.95106 + 0.309017i 1.95106 + 0.309017i
209209 0 0
210210 0 0
211211 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
212212 −0.533698 + 1.04744i −0.533698 + 1.04744i
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 −0.831254 + 0.831254i −0.831254 + 0.831254i
219219 0 0
220220 0 0
221221 −2.20854 + 3.03979i −2.20854 + 3.03979i
222222 0 0
223223 0 0 0.891007 0.453990i 0.150000π-0.150000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
224224 0 0
225225 0 0
226226 0.618034 0.618034
227227 0 0 0.891007 0.453990i 0.150000π-0.150000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
228228 0 0
229229 −0.951057 + 1.30902i −0.951057 + 1.30902i 1.00000i 0.5π0.5\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
230230 0 0
231231 0 0
232232 −1.26007 + 1.26007i −1.26007 + 1.26007i
233233 −0.183900 + 1.16110i −0.183900 + 1.16110i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
234234 0 0
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
240240 0 0
241241 −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i 0.200000π-0.200000\pi
−1.00000 π\pi
242242 −0.987688 0.156434i −0.987688 0.156434i
243243 0 0
244244 0.690983 + 0.951057i 0.690983 + 0.951057i
245245 −0.156434 + 0.987688i −0.156434 + 0.987688i
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 1.00000 1.00000
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 −0.809017 + 0.587785i −0.809017 + 0.587785i
257257 1.14412 + 1.14412i 1.14412 + 1.14412i 0.987688 + 0.156434i 0.0500000π0.0500000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
258258 0 0
259259 0 0
260260 −0.610425 1.87869i −0.610425 1.87869i
261261 0 0
262262 0 0
263263 0 0 −0.891007 0.453990i 0.850000π-0.850000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
264264 0 0
265265 1.17557 1.17557
266266 0 0
267267 0 0
268268 0 0
269269 −1.59811 + 1.16110i −1.59811 + 1.16110i −0.707107 + 0.707107i 0.750000π0.750000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
270270 0 0
271271 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
272272 −0.297556 1.87869i −0.297556 1.87869i
273273 0 0
274274 1.61803i 1.61803i
275275 0 0
276276 0 0
277277 −0.412215 0.809017i −0.412215 0.809017i 0.587785 0.809017i 0.300000π-0.300000\pi
−1.00000 π\pi
278278 0 0
279279 0 0
280280 0 0
281281 1.16110 + 1.59811i 1.16110 + 1.59811i 0.707107 + 0.707107i 0.250000π0.250000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
282282 0 0
283283 0 0 −0.987688 0.156434i 0.950000π-0.950000\pi
0.987688 + 0.156434i 0.0500000π0.0500000\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 2.48990 + 0.809017i 2.48990 + 0.809017i
290290 1.69480 + 0.550672i 1.69480 + 0.550672i
291291 0 0
292292 −0.0489435 + 0.309017i −0.0489435 + 0.309017i
293293 0.437016 0.437016i 0.437016 0.437016i −0.453990 0.891007i 0.650000π-0.650000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
294294 0 0
295295 0 0
296296 −0.533698 + 0.734572i −0.533698 + 0.734572i
297297 0 0
298298 0.278768 0.142040i 0.278768 0.142040i
299299 0 0
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 0.533698 1.04744i 0.533698 1.04744i
306306 0 0
307307 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
312312 0 0
313313 0.642040 1.26007i 0.642040 1.26007i −0.309017 0.951057i 0.600000π-0.600000\pi
0.951057 0.309017i 0.100000π-0.100000\pi
314314 −0.550672 + 1.69480i −0.550672 + 1.69480i
315315 0 0
316316 0 0
317317 0 0 0.156434 0.987688i 0.450000π-0.450000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
318318 0 0
319319 0 0
320320 0.891007 + 0.453990i 0.891007 + 0.453990i
321321 0 0
322322 0 0
323323 0 0
324324 0 0
325325 −1.39680 + 1.39680i −1.39680 + 1.39680i
326326 0 0
327327 0 0
328328 −0.0489435 0.309017i −0.0489435 0.309017i
329329 0 0
330330 0 0
331331 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 −1.26007 0.642040i −1.26007 0.642040i −0.309017 0.951057i 0.600000π-0.600000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
338338 2.58580 + 1.31753i 2.58580 + 1.31753i
339339 0 0
340340 −1.53884 + 1.11803i −1.53884 + 1.11803i
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0.500000 + 0.363271i 0.500000 + 0.363271i
347347 0 0 −0.156434 0.987688i 0.550000π-0.550000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
348348 0 0
349349 1.90211i 1.90211i 0.309017 + 0.951057i 0.400000π0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
350350 0 0
351351 0 0
352352 0 0
353353 0 0 −0.156434 0.987688i 0.550000π-0.550000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
354354 0 0
355355 0 0
356356 0.533698 + 0.734572i 0.533698 + 0.734572i
357357 0 0
358358 0 0
359359 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
360360 0 0
361361 −0.309017 + 0.951057i −0.309017 + 0.951057i
362362 −0.863541 + 1.69480i −0.863541 + 1.69480i
363363 0 0
364364 0 0
365365 0.297556 0.0966818i 0.297556 0.0966818i
366366 0 0
367367 0 0 0.156434 0.987688i 0.450000π-0.450000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
368368 0 0
369369 0 0
370370 0.896802 + 0.142040i 0.896802 + 0.142040i
371371 0 0
372372 0 0
373373 1.26007 0.642040i 1.26007 0.642040i 0.309017 0.951057i 0.400000π-0.400000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
374374 0 0
375375 0 0
376376 0 0
377377 −3.13647 + 1.59811i −3.13647 + 1.59811i
378378 0 0
379379 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 0.156434 0.987688i 0.450000π-0.450000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
384384 0 0
385385 0 0
386386 0.297556 + 0.0966818i 0.297556 + 0.0966818i
387387 0 0
388388 −0.809017 + 1.58779i −0.809017 + 1.58779i
389389 0.610425 1.87869i 0.610425 1.87869i 0.156434 0.987688i 0.450000π-0.450000\pi
0.453990 0.891007i 0.350000π-0.350000\pi
390390 0 0
391391 0 0
392392 0.987688 + 0.156434i 0.987688 + 0.156434i
393393 0 0
394394 0.951057 + 1.30902i 0.951057 + 1.30902i
395395 0 0
396396 0 0
397397 −1.39680 + 0.221232i −1.39680 + 0.221232i −0.809017 0.587785i 0.800000π-0.800000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
398398 0 0
399399 0 0
400400 1.00000i 1.00000i
401401 0.312869i 0.312869i −0.987688 0.156434i 0.950000π-0.950000\pi
0.987688 0.156434i 0.0500000π-0.0500000\pi
402402 0 0
403403 0 0
404404 −0.734572 0.533698i −0.734572 0.533698i
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 1.80902 0.587785i 1.80902 0.587785i 0.809017 0.587785i 0.200000π-0.200000\pi
1.00000 00
410410 −0.253116 + 0.183900i −0.253116 + 0.183900i
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 −1.87869 + 0.610425i −1.87869 + 0.610425i
417417 0 0
418418 0 0
419419 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
420420 0 0
421421 −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i 0.400000π-0.400000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
422422 0 0
423423 0 0
424424 1.17557i 1.17557i
425425 1.69480 + 0.863541i 1.69480 + 0.863541i
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
432432 0 0
433433 −1.95106 0.309017i −1.95106 0.309017i −0.951057 0.309017i 0.900000π-0.900000\pi
−1.00000 π\pi
434434 0 0
435435 0 0
436436 0.363271 1.11803i 0.363271 1.11803i
437437 0 0
438438 0 0
439439 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
440440 0 0
441441 0 0
442442 0.587785 3.71113i 0.587785 3.71113i
443443 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
444444 0 0
445445 0.412215 0.809017i 0.412215 0.809017i
446446 0 0
447447 0 0
448448 0 0
449449 1.78201 1.78201 0.891007 0.453990i 0.150000π-0.150000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
450450 0 0
451451 0 0
452452 −0.550672 + 0.280582i −0.550672 + 0.280582i
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
458458 0.253116 1.59811i 0.253116 1.59811i
459459 0 0
460460 0 0
461461 −1.69480 0.550672i −1.69480 0.550672i −0.707107 0.707107i 0.750000π-0.750000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
462462 0 0
463463 0 0 0.453990 0.891007i 0.350000π-0.350000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
464464 0.550672 1.69480i 0.550672 1.69480i
465465 0 0
466466 −0.363271 1.11803i −0.363271 1.11803i
467467 0 0 −0.987688 0.156434i 0.950000π-0.950000\pi
0.987688 + 0.156434i 0.0500000π0.0500000\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
480480 0 0
481481 −1.45106 + 1.05425i −1.45106 + 1.05425i
482482 0.437016 + 0.437016i 0.437016 + 0.437016i
483483 0 0
484484 0.951057 0.309017i 0.951057 0.309017i
485485 1.78201 1.78201
486486 0 0
487487 0 0 −0.891007 0.453990i 0.850000π-0.850000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
488488 −1.04744 0.533698i −1.04744 0.533698i
489489 0 0
490490 −0.309017 0.951057i −0.309017 0.951057i
491491 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
492492 0 0
493493 2.39680 + 2.39680i 2.39680 + 2.39680i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
500500 −0.891007 + 0.453990i −0.891007 + 0.453990i
501501 0 0
502502 0 0
503503 0 0 0.987688 0.156434i 0.0500000π-0.0500000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
504504 0 0
505505 −0.142040 + 0.896802i −0.142040 + 0.896802i
506506 0 0
507507 0 0
508508 0 0
509509 −0.280582 0.863541i −0.280582 0.863541i −0.987688 0.156434i 0.950000π-0.950000\pi
0.707107 0.707107i 0.250000π-0.250000\pi
510510 0 0
511511 0 0
512512 0.453990 0.891007i 0.453990 0.891007i
513513 0 0
514514 −1.53884 0.500000i −1.53884 0.500000i
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 1.39680 + 1.39680i 1.39680 + 1.39680i
521521 1.16110 1.59811i 1.16110 1.59811i 0.453990 0.891007i 0.350000π-0.350000\pi
0.707107 0.707107i 0.250000π-0.250000\pi
522522 0 0
523523 0 0 0.891007 0.453990i 0.150000π-0.150000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 −0.587785 + 0.809017i −0.587785 + 0.809017i
530530 −1.04744 + 0.533698i −1.04744 + 0.533698i
531531 0 0
532532 0 0
533533 0.0966818 0.610425i 0.0966818 0.610425i
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0.896802 1.76007i 0.896802 1.76007i
539539 0 0
540540 0 0
541541 −0.587785 1.80902i −0.587785 1.80902i −0.587785 0.809017i 0.700000π-0.700000\pi
1.00000i 0.5π-0.5\pi
542542 0 0
543543 0 0
544544 1.11803 + 1.53884i 1.11803 + 1.53884i
545545 −1.16110 + 0.183900i −1.16110 + 0.183900i
546546 0 0
547547 0 0 0.987688 0.156434i 0.0500000π-0.0500000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
548548 −0.734572 1.44168i −0.734572 1.44168i
549549 0 0
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0.734572 + 0.533698i 0.734572 + 0.533698i
555555 0 0
556556 0 0
557557 −1.34500 1.34500i −1.34500 1.34500i −0.891007 0.453990i 0.850000π-0.850000\pi
−0.453990 0.891007i 0.650000π-0.650000\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 −1.76007 0.896802i −1.76007 0.896802i
563563 0 0 −0.891007 0.453990i 0.850000π-0.850000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
564564 0 0
565565 0.500000 + 0.363271i 0.500000 + 0.363271i
566566 0 0
567567 0 0
568568 0 0
569569 −0.734572 + 0.533698i −0.734572 + 0.533698i −0.891007 0.453990i 0.850000π-0.850000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
570570 0 0
571571 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0 0
577577 0.642040 + 1.26007i 0.642040 + 1.26007i 0.951057 + 0.309017i 0.100000π0.100000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
578578 −2.58580 + 0.409551i −2.58580 + 0.409551i
579579 0 0
580580 −1.76007 + 0.278768i −1.76007 + 0.278768i
581581 0 0
582582 0 0
583583 0 0
584584 −0.0966818 0.297556i −0.0966818 0.297556i
585585 0 0
586586 −0.190983 + 0.587785i −0.190983 + 0.587785i
587587 0 0 0.453990 0.891007i 0.350000π-0.350000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
588588 0 0
589589 0 0
590590 0 0
591591 0 0
592592 0.142040 0.896802i 0.142040 0.896802i
593593 −0.437016 + 0.437016i −0.437016 + 0.437016i −0.891007 0.453990i 0.850000π-0.850000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
594594 0 0
595595 0 0
596596 −0.183900 + 0.253116i −0.183900 + 0.253116i
597597 0 0
598598 0 0
599599 0 0 1.00000 00
−1.00000 π\pi
600600 0 0
601601 −1.17557 −1.17557 −0.587785 0.809017i 0.700000π-0.700000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
602602 0 0
603603 0 0
604604 0 0
605605 −0.707107 0.707107i −0.707107 0.707107i
606606 0 0
607607 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
608608 0 0
609609 0 0
610610 1.17557i 1.17557i
611611 0 0
612612 0 0
613613 0.809017 1.58779i 0.809017 1.58779i 1.00000i 0.5π-0.5\pi
0.809017 0.587785i 0.200000π-0.200000\pi
614614 0 0
615615 0 0
616616 0 0
617617 1.16110 + 0.183900i 1.16110 + 0.183900i 0.707107 0.707107i 0.250000π-0.250000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
618618 0 0
619619 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 0.809017 + 0.587785i 0.809017 + 0.587785i
626626 1.41421i 1.41421i
627627 0 0
628628 −0.278768 1.76007i −0.278768 1.76007i
629629 1.39724 + 1.01515i 1.39724 + 1.01515i
630630 0 0
631631 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
632632 0 0
633633 0 0
634634 0 0
635635 0 0
636636 0 0
637637 1.76007 + 0.896802i 1.76007 + 0.896802i
638638 0 0
639639 0 0
640640 −1.00000 −1.00000
641641 1.34500 0.437016i 1.34500 0.437016i 0.453990 0.891007i 0.350000π-0.350000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
642642 0 0
643643 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 −0.156434 0.987688i 0.550000π-0.550000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
648648 0 0
649649 0 0
650650 0.610425 1.87869i 0.610425 1.87869i
651651 0 0
652652 0 0
653653 1.87869 0.297556i 1.87869 0.297556i 0.891007 0.453990i 0.150000π-0.150000\pi
0.987688 + 0.156434i 0.0500000π0.0500000\pi
654654 0 0
655655 0 0
656656 0.183900 + 0.253116i 0.183900 + 0.253116i
657657 0 0
658658 0 0
659659 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
660660 0 0
661661 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
662662 0 0
663663 0 0
664664 0 0
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 −0.809017 + 0.412215i −0.809017 + 0.412215i −0.809017 0.587785i 0.800000π-0.800000\pi
1.00000i 0.5π0.5\pi
674674 1.41421 1.41421
675675 0 0
676676 −2.90211 −2.90211
677677 0 0 −0.453990 0.891007i 0.650000π-0.650000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
678678 0 0
679679 0 0
680680 0.863541 1.69480i 0.863541 1.69480i
681681 0 0
682682 0 0
683683 0 0 0.156434 0.987688i 0.450000π-0.450000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
684684 0 0
685685 −0.951057 + 1.30902i −0.951057 + 1.30902i
686686 0 0
687687 0 0
688688 0 0
689689 0.717598 2.20854i 0.717598 2.20854i
690690 0 0
691691 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
692692 −0.610425 0.0966818i −0.610425 0.0966818i
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 −0.587785 + 0.0930960i −0.587785 + 0.0930960i
698698 −0.863541 1.69480i −0.863541 1.69480i
699699 0 0
700700 0 0
701701 0.312869i 0.312869i 0.987688 + 0.156434i 0.0500000π0.0500000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 −1.53884 + 0.500000i −1.53884 + 0.500000i −0.951057 0.309017i 0.900000π-0.900000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
710710 0 0
711711 0 0
712712 −0.809017 0.412215i −0.809017 0.412215i
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
720720 0 0
721721 0 0
722722 −0.156434 0.987688i −0.156434 0.987688i
723723 0 0
724724 1.90211i 1.90211i
725725 1.04744 + 1.44168i 1.04744 + 1.44168i
726726 0 0
727727 0 0 −0.453990 0.891007i 0.650000π-0.650000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
728728 0 0
729729 0 0
730730 −0.221232 + 0.221232i −0.221232 + 0.221232i
731731 0 0
732732 0 0
733733 1.39680 + 0.221232i 1.39680 + 0.221232i 0.809017 0.587785i 0.200000π-0.200000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
740740 −0.863541 + 0.280582i −0.863541 + 0.280582i
741741 0 0
742742 0 0
743743 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
744744 0 0
745745 0.309017 + 0.0489435i 0.309017 + 0.0489435i
746746 −0.831254 + 1.14412i −0.831254 + 1.14412i
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 0 0 1.00000 00
−1.00000 π\pi
752752 0 0
753753 0 0
754754 2.06909 2.84786i 2.06909 2.84786i
755755 0 0
756756 0 0
757757 −0.221232 + 0.221232i −0.221232 + 0.221232i −0.809017 0.587785i 0.800000π-0.800000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
758758 0 0
759759 0 0
760760 0 0
761761 1.87869 + 0.610425i 1.87869 + 0.610425i 0.987688 + 0.156434i 0.0500000π0.0500000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
770770 0 0
771771 0 0
772772 −0.309017 + 0.0489435i −0.309017 + 0.0489435i
773773 −0.533698 1.04744i −0.533698 1.04744i −0.987688 0.156434i 0.950000π-0.950000\pi
0.453990 0.891007i 0.350000π-0.350000\pi
774774 0 0
775775 0 0
776776 1.78201i 1.78201i
777777 0 0
778778 0.309017 + 1.95106i 0.309017 + 1.95106i
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −0.951057 + 0.309017i −0.951057 + 0.309017i
785785 −1.44168 + 1.04744i −1.44168 + 1.04744i
786786 0 0
787787 0 0 −0.891007 0.453990i 0.850000π-0.850000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
788788 −1.44168 0.734572i −1.44168 0.734572i
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 −1.64204 1.64204i −1.64204 1.64204i
794794 1.14412 0.831254i 1.14412 0.831254i
795795 0 0
796796 0 0
797797 0.253116 + 1.59811i 0.253116 + 1.59811i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
798798 0 0
799799 0 0
800800 0.453990 + 0.891007i 0.453990 + 0.891007i
801801 0 0
802802 0.142040 + 0.278768i 0.142040 + 0.278768i
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0.896802 + 0.142040i 0.896802 + 0.142040i
809809 −0.550672 1.69480i −0.550672 1.69480i −0.707107 0.707107i 0.750000π-0.750000\pi
0.156434 0.987688i 0.450000π-0.450000\pi
810810 0 0
811811 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 −1.34500 + 1.34500i −1.34500 + 1.34500i
819819 0 0
820820 0.142040 0.278768i 0.142040 0.278768i
821821 0.831254 1.14412i 0.831254 1.14412i −0.156434 0.987688i 0.550000π-0.550000\pi
0.987688 0.156434i 0.0500000π-0.0500000\pi
822822 0 0
823823 0 0 0.891007 0.453990i 0.150000π-0.150000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 0.891007 0.453990i 0.150000π-0.150000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
828828 0 0
829829 −0.690983 + 0.951057i −0.690983 + 0.951057i 0.309017 + 0.951057i 0.400000π0.400000\pi
−1.00000 1.00000π1.00000\pi
830830 0 0
831831 0 0
832832 1.39680 1.39680i 1.39680 1.39680i
833833 0.297556 1.87869i 0.297556 1.87869i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
840840 0 0
841841 0.672288 + 2.06909i 0.672288 + 2.06909i
842842 0.610425 + 0.0966818i 0.610425 + 0.0966818i
843843 0 0
844844 0 0
845845 1.31753 + 2.58580i 1.31753 + 2.58580i
846846 0 0
847847 0 0
848848 0.533698 + 1.04744i 0.533698 + 1.04744i
849849 0 0
850850 −1.90211 −1.90211
851851 0 0
852852 0 0
853853 0.0489435 + 0.309017i 0.0489435 + 0.309017i 1.00000 00
−0.951057 + 0.309017i 0.900000π0.900000\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
858858 0 0
859859 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.891007 0.453990i 0.850000π-0.850000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
864864 0 0
865865 0.190983 + 0.587785i 0.190983 + 0.587785i
866866 1.87869 0.610425i 1.87869 0.610425i
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0.183900 + 1.16110i 0.183900 + 1.16110i
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 −0.896802 1.76007i −0.896802 1.76007i −0.587785 0.809017i 0.700000π-0.700000\pi
−0.309017 0.951057i 0.600000π-0.600000\pi
878878 0 0
879879 0 0
880880 0 0
881881 −0.831254 1.14412i −0.831254 1.14412i −0.987688 0.156434i 0.950000π-0.950000\pi
0.156434 0.987688i 0.450000π-0.450000\pi
882882 0 0
883883 0 0 −0.987688 0.156434i 0.950000π-0.950000\pi
0.987688 + 0.156434i 0.0500000π0.0500000\pi
884884 1.16110 + 3.57349i 1.16110 + 3.57349i
885885 0 0
886886 0 0
887887 0 0 0.453990 0.891007i 0.350000π-0.350000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
888888 0 0
889889 0 0
890890 0.907981i 0.907981i
891891 0 0
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 −1.58779 + 0.809017i −1.58779 + 0.809017i
899899 0 0
900900 0 0
901901 −2.23607 −2.23607
902902 0 0
903903 0 0
904904 0.363271 0.500000i 0.363271 0.500000i
905905 −1.69480 + 0.863541i −1.69480 + 0.863541i
906906 0 0
907907 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
908908 0 0
909909 0 0
910910 0 0
911911 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
912912 0 0
913913 0 0
914914 −0.437016 + 1.34500i −0.437016 + 1.34500i
915915 0 0
916916 0.500000 + 1.53884i 0.500000 + 1.53884i
917917 0 0
918918 0 0
919919 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
920920 0 0
921921 0 0
922922 1.76007 0.278768i 1.76007 0.278768i
923923 0 0
924924 0 0
925925 0.642040 + 0.642040i 0.642040 + 0.642040i
926926 0 0
927927 0 0
928928 0.278768 + 1.76007i 0.278768 + 1.76007i
929929 −1.44168 1.04744i −1.44168 1.04744i −0.987688 0.156434i 0.950000π-0.950000\pi
−0.453990 0.891007i 0.650000π-0.650000\pi
930930 0 0
931931 0 0
932932 0.831254 + 0.831254i 0.831254 + 0.831254i
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 1.58779 + 0.809017i 1.58779 + 0.809017i 1.00000 00
0.587785 + 0.809017i 0.300000π0.300000\pi
938938 0 0
939939 0 0
940940 0 0
941941 0.863541 0.280582i 0.863541 0.280582i 0.156434 0.987688i 0.450000π-0.450000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 −0.156434 0.987688i 0.550000π-0.550000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
948948 0 0
949949 0.618034i 0.618034i
950950 0 0
951951 0 0
952952 0 0
953953 −0.610425 + 0.0966818i −0.610425 + 0.0966818i −0.453990 0.891007i 0.650000π-0.650000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 0.309017 0.951057i 0.309017 0.951057i
962962 0.814279 1.59811i 0.814279 1.59811i
963963 0 0
964964 −0.587785 0.190983i −0.587785 0.190983i
965965 0.183900 + 0.253116i 0.183900 + 0.253116i
966966 0 0
967967 0 0 0.156434 0.987688i 0.450000π-0.450000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
968968 −0.707107 + 0.707107i −0.707107 + 0.707107i
969969 0 0
970970 −1.58779 + 0.809017i −1.58779 + 0.809017i
971971 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 1.17557 1.17557
977977 −1.04744 + 0.533698i −1.04744 + 0.533698i −0.891007 0.453990i 0.850000π-0.850000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
978978 0 0
979979 0 0
980980 0.707107 + 0.707107i 0.707107 + 0.707107i
981981 0 0
982982 0 0
983983 0 0 0.156434 0.987688i 0.450000π-0.450000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
984984 0 0
985985 1.61803i 1.61803i
986986 −3.22369 1.04744i −3.22369 1.04744i
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 1.39680 0.221232i 1.39680 0.221232i 0.587785 0.809017i 0.300000π-0.300000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
998998 0 0
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 900.1.bh.a.503.1 yes 16
3.2 odd 2 inner 900.1.bh.a.503.2 yes 16
4.3 odd 2 CM 900.1.bh.a.503.1 yes 16
12.11 even 2 inner 900.1.bh.a.503.2 yes 16
25.17 odd 20 inner 900.1.bh.a.467.2 yes 16
75.17 even 20 inner 900.1.bh.a.467.1 16
100.67 even 20 inner 900.1.bh.a.467.2 yes 16
300.167 odd 20 inner 900.1.bh.a.467.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
900.1.bh.a.467.1 16 75.17 even 20 inner
900.1.bh.a.467.1 16 300.167 odd 20 inner
900.1.bh.a.467.2 yes 16 25.17 odd 20 inner
900.1.bh.a.467.2 yes 16 100.67 even 20 inner
900.1.bh.a.503.1 yes 16 1.1 even 1 trivial
900.1.bh.a.503.1 yes 16 4.3 odd 2 CM
900.1.bh.a.503.2 yes 16 3.2 odd 2 inner
900.1.bh.a.503.2 yes 16 12.11 even 2 inner