Properties

Label 1872.1.fi.b.1633.1
Level 18721872
Weight 11
Character 1872.1633
Analytic conductor 0.9340.934
Analytic rank 00
Dimension 44
Projective image S4S_{4}
CM/RM no
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1872,1,Mod(385,1872)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1872, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 8, 3]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1872.385");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 1872=243213 1872 = 2^{4} \cdot 3^{2} \cdot 13
Weight: k k == 1 1
Character orbit: [χ][\chi] == 1872.fi (of order 1212, degree 44, 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: 0.9342497036490.934249703649
Analytic rank: 00
Dimension: 44
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 936)
Projective image: S4S_{4}
Projective field: Galois closure of 4.0.2847312.2

Embedding invariants

Embedding label 1633.1
Root 0.8660250.500000i0.866025 - 0.500000i of defining polynomial
Character χ\chi == 1872.1633
Dual form 1872.1.fi.b.1825.1

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+(0.5000000.866025i)q3+(1.36603+0.366025i)q7+(0.5000000.866025i)q9+(1.36603+0.366025i)q11+(0.8660250.500000i)q13+1.00000iq17+(1.00000+1.00000i)q19+(1.000001.00000i)q21+(0.8660250.500000i)q23+(0.866025+0.500000i)q251.00000q27+(1.000001.00000i)q33+(1.000001.00000i)q37+(0.866025+0.500000i)q39+(1.36603+0.366025i)q41+(0.8660250.500000i)q43+(1.366030.366025i)q47+(0.866025+0.500000i)q49+(0.866025+0.500000i)q511.00000q53+(1.366030.366025i)q57+(0.5000000.866025i)q61+(0.3660251.36603i)q63+(0.866025+0.500000i)q69+1.00000iq75+(1.73205+1.00000i)q77+(0.500000+0.866025i)q79+(0.500000+0.866025i)q81+(0.3660251.36603i)q83+(1.00000+1.00000i)q89+(1.000001.00000i)q91+(0.3660251.36603i)q99+O(q100)q+(0.500000 - 0.866025i) q^{3} +(1.36603 + 0.366025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.36603 + 0.366025i) q^{11} +(-0.866025 - 0.500000i) q^{13} +1.00000i q^{17} +(1.00000 + 1.00000i) q^{19} +(1.00000 - 1.00000i) q^{21} +(-0.866025 - 0.500000i) q^{23} +(-0.866025 + 0.500000i) q^{25} -1.00000 q^{27} +(1.00000 - 1.00000i) q^{33} +(1.00000 - 1.00000i) q^{37} +(-0.866025 + 0.500000i) q^{39} +(-1.36603 + 0.366025i) q^{41} +(0.866025 - 0.500000i) q^{43} +(-1.36603 - 0.366025i) q^{47} +(0.866025 + 0.500000i) q^{49} +(0.866025 + 0.500000i) q^{51} -1.00000 q^{53} +(1.36603 - 0.366025i) q^{57} +(-0.500000 - 0.866025i) q^{61} +(-0.366025 - 1.36603i) q^{63} +(-0.866025 + 0.500000i) q^{69} +1.00000i q^{75} +(1.73205 + 1.00000i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(0.366025 - 1.36603i) q^{83} +(-1.00000 + 1.00000i) q^{89} +(-1.00000 - 1.00000i) q^{91} +(-0.366025 - 1.36603i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q3+2q72q9+2q11+4q19+4q214q27+4q33+4q372q412q474q53+2q572q61+2q63+2q792q812q834q89++2q99+O(q100) 4 q + 2 q^{3} + 2 q^{7} - 2 q^{9} + 2 q^{11} + 4 q^{19} + 4 q^{21} - 4 q^{27} + 4 q^{33} + 4 q^{37} - 2 q^{41} - 2 q^{47} - 4 q^{53} + 2 q^{57} - 2 q^{61} + 2 q^{63} + 2 q^{79} - 2 q^{81} - 2 q^{83} - 4 q^{89}+ \cdots + 2 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1872Z)×\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times.

nn 145145 209209 469469 703703
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right) e(13)e\left(\frac{1}{3}\right) 11 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.500000 0.866025i 0.500000 0.866025i
44 0 0
55 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
66 0 0
77 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i 0.166667π-0.166667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
88 0 0
99 −0.500000 0.866025i −0.500000 0.866025i
1010 0 0
1111 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i 0.166667π-0.166667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
1212 0 0
1313 −0.866025 0.500000i −0.866025 0.500000i
1414 0 0
1515 0 0
1616 0 0
1717 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
1818 0 0
1919 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
2020 0 0
2121 1.00000 1.00000i 1.00000 1.00000i
2222 0 0
2323 −0.866025 0.500000i −0.866025 0.500000i 1.00000i 0.5π-0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
2424 0 0
2525 −0.866025 + 0.500000i −0.866025 + 0.500000i
2626 0 0
2727 −1.00000 −1.00000
2828 0 0
2929 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
3030 0 0
3131 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
3232 0 0
3333 1.00000 1.00000i 1.00000 1.00000i
3434 0 0
3535 0 0
3636 0 0
3737 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
3838 0 0
3939 −0.866025 + 0.500000i −0.866025 + 0.500000i
4040 0 0
4141 −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
4242 0 0
4343 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
4444 0 0
4545 0 0
4646 0 0
4747 −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
4848 0 0
4949 0.866025 + 0.500000i 0.866025 + 0.500000i
5050 0 0
5151 0.866025 + 0.500000i 0.866025 + 0.500000i
5252 0 0
5353 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
5454 0 0
5555 0 0
5656 0 0
5757 1.36603 0.366025i 1.36603 0.366025i
5858 0 0
5959 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
6060 0 0
6161 −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
−1.00000 π\pi
6262 0 0
6363 −0.366025 1.36603i −0.366025 1.36603i
6464 0 0
6565 0 0
6666 0 0
6767 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
6868 0 0
6969 −0.866025 + 0.500000i −0.866025 + 0.500000i
7070 0 0
7171 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
7272 0 0
7373 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
7474 0 0
7575 1.00000i 1.00000i
7676 0 0
7777 1.73205 + 1.00000i 1.73205 + 1.00000i
7878 0 0
7979 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
8080 0 0
8181 −0.500000 + 0.866025i −0.500000 + 0.866025i
8282 0 0
8383 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i 0.666667π-0.666667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
9090 0 0
9191 −1.00000 1.00000i −1.00000 1.00000i
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
9898 0 0
9999 −0.366025 1.36603i −0.366025 1.36603i
100100 0 0
101101 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
102102 0 0
103103 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
104104 0 0
105105 0 0
106106 0 0
107107 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
108108 0 0
109109 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
110110 0 0
111111 −0.366025 1.36603i −0.366025 1.36603i
112112 0 0
113113 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
114114 0 0
115115 0 0
116116 0 0
117117 1.00000i 1.00000i
118118 0 0
119119 −0.366025 + 1.36603i −0.366025 + 1.36603i
120120 0 0
121121 0.866025 + 0.500000i 0.866025 + 0.500000i
122122 0 0
123123 −0.366025 + 1.36603i −0.366025 + 1.36603i
124124 0 0
125125 0 0
126126 0 0
127127 0 0 1.00000 00
−1.00000 π\pi
128128 0 0
129129 1.00000i 1.00000i
130130 0 0
131131 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
132132 0 0
133133 1.00000 + 1.73205i 1.00000 + 1.73205i
134134 0 0
135135 0 0
136136 0 0
137137 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
138138 0 0
139139 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
140140 0 0
141141 −1.00000 + 1.00000i −1.00000 + 1.00000i
142142 0 0
143143 −1.00000 1.00000i −1.00000 1.00000i
144144 0 0
145145 0 0
146146 0 0
147147 0.866025 0.500000i 0.866025 0.500000i
148148 0 0
149149 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
150150 0 0
151151 −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
152152 0 0
153153 0.866025 0.500000i 0.866025 0.500000i
154154 0 0
155155 0 0
156156 0 0
157157 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
158158 0 0
159159 −0.500000 + 0.866025i −0.500000 + 0.866025i
160160 0 0
161161 −1.00000 1.00000i −1.00000 1.00000i
162162 0 0
163163 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
164164 0 0
165165 0 0
166166 0 0
167167 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
168168 0 0
169169 0.500000 + 0.866025i 0.500000 + 0.866025i
170170 0 0
171171 0.366025 1.36603i 0.366025 1.36603i
172172 0 0
173173 −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i 0.833333π-0.833333\pi
1.00000i 0.5π0.5\pi
174174 0 0
175175 −1.36603 + 0.366025i −1.36603 + 0.366025i
176176 0 0
177177 0 0
178178 0 0
179179 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
180180 0 0
181181 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
182182 0 0
183183 −1.00000 −1.00000
184184 0 0
185185 0 0
186186 0 0
187187 −0.366025 + 1.36603i −0.366025 + 1.36603i
188188 0 0
189189 −1.36603 0.366025i −1.36603 0.366025i
190190 0 0
191191 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
192192 0 0
193193 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
194194 0 0
195195 0 0
196196 0 0
197197 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
198198 0 0
199199 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
200200 0 0
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 1.00000i 1.00000i
208208 0 0
209209 1.00000 + 1.73205i 1.00000 + 1.73205i
210210 0 0
211211 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 0.500000 0.866025i 0.500000 0.866025i
222222 0 0
223223 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
224224 0 0
225225 0.866025 + 0.500000i 0.866025 + 0.500000i
226226 0 0
227227 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
228228 0 0
229229 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
230230 0 0
231231 1.73205 1.00000i 1.73205 1.00000i
232232 0 0
233233 1.00000i 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
234234 0 0
235235 0 0
236236 0 0
237237 1.00000 1.00000
238238 0 0
239239 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i 0.333333π-0.333333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
240240 0 0
241241 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
242242 0 0
243243 0.500000 + 0.866025i 0.500000 + 0.866025i
244244 0 0
245245 0 0
246246 0 0
247247 −0.366025 1.36603i −0.366025 1.36603i
248248 0 0
249249 −1.00000 1.00000i −1.00000 1.00000i
250250 0 0
251251 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
252252 0 0
253253 −1.00000 1.00000i −1.00000 1.00000i
254254 0 0
255255 0 0
256256 0 0
257257 −0.866025 0.500000i −0.866025 0.500000i 1.00000i 0.5π-0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
258258 0 0
259259 1.73205 1.00000i 1.73205 1.00000i
260260 0 0
261261 0 0
262262 0 0
263263 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
264264 0 0
265265 0 0
266266 0 0
267267 0.366025 + 1.36603i 0.366025 + 1.36603i
268268 0 0
269269 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
270270 0 0
271271 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
272272 0 0
273273 −1.36603 + 0.366025i −1.36603 + 0.366025i
274274 0 0
275275 −1.36603 + 0.366025i −1.36603 + 0.366025i
276276 0 0
277277 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
278278 0 0
279279 0 0
280280 0 0
281281 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
282282 0 0
283283 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i 0.166667π-0.166667\pi
1.00000i 0.5π0.5\pi
284284 0 0
285285 0 0
286286 0 0
287287 −2.00000 −2.00000
288288 0 0
289289 0 0
290290 0 0
291291 0 0
292292 0 0
293293 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
294294 0 0
295295 0 0
296296 0 0
297297 −1.36603 0.366025i −1.36603 0.366025i
298298 0 0
299299 0.500000 + 0.866025i 0.500000 + 0.866025i
300300 0 0
301301 1.36603 0.366025i 1.36603 0.366025i
302302 0 0
303303 1.00000i 1.00000i
304304 0 0
305305 0 0
306306 0 0
307307 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\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 −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
318318 0 0
319319 0 0
320320 0 0
321321 −0.500000 + 0.866025i −0.500000 + 0.866025i
322322 0 0
323323 −1.00000 + 1.00000i −1.00000 + 1.00000i
324324 0 0
325325 1.00000 1.00000
326326 0 0
327327 −1.36603 + 0.366025i −1.36603 + 0.366025i
328328 0 0
329329 −1.73205 1.00000i −1.73205 1.00000i
330330 0 0
331331 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
332332 0 0
333333 −1.36603 0.366025i −1.36603 0.366025i
334334 0 0
335335 0 0
336336 0 0
337337 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i 0.166667π-0.166667\pi
1.00000i 0.5π0.5\pi
338338 0 0
339339 −0.500000 0.866025i −0.500000 0.866025i
340340 0 0
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
348348 0 0
349349 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
350350 0 0
351351 0.866025 + 0.500000i 0.866025 + 0.500000i
352352 0 0
353353 −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
354354 0 0
355355 0 0
356356 0 0
357357 1.00000 + 1.00000i 1.00000 + 1.00000i
358358 0 0
359359 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
360360 0 0
361361 1.00000i 1.00000i
362362 0 0
363363 0.866025 0.500000i 0.866025 0.500000i
364364 0 0
365365 0 0
366366 0 0
367367 −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
−1.00000 π\pi
368368 0 0
369369 1.00000 + 1.00000i 1.00000 + 1.00000i
370370 0 0
371371 −1.36603 0.366025i −1.36603 0.366025i
372372 0 0
373373 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
380380 0 0
381381 0 0
382382 0 0
383383 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i 0.333333π-0.333333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
384384 0 0
385385 0 0
386386 0 0
387387 −0.866025 0.500000i −0.866025 0.500000i
388388 0 0
389389 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
390390 0 0
391391 0.500000 0.866025i 0.500000 0.866025i
392392 0 0
393393 −0.500000 0.866025i −0.500000 0.866025i
394394 0 0
395395 0 0
396396 0 0
397397 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
398398 0 0
399399 2.00000 2.00000
400400 0 0
401401 −0.366025 1.36603i −0.366025 1.36603i −0.866025 0.500000i 0.833333π-0.833333\pi
0.500000 0.866025i 0.333333π-0.333333\pi
402402 0 0
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 1.73205 1.00000i 1.73205 1.00000i
408408 0 0
409409 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 −0.500000 0.866025i −0.500000 0.866025i
418418 0 0
419419 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
420420 0 0
421421 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i 0.666667π-0.666667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
422422 0 0
423423 0.366025 + 1.36603i 0.366025 + 1.36603i
424424 0 0
425425 −0.500000 0.866025i −0.500000 0.866025i
426426 0 0
427427 −0.366025 1.36603i −0.366025 1.36603i
428428 0 0
429429 −1.36603 + 0.366025i −1.36603 + 0.366025i
430430 0 0
431431 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
432432 0 0
433433 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
434434 0 0
435435 0 0
436436 0 0
437437 −0.366025 1.36603i −0.366025 1.36603i
438438 0 0
439439 −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i 0.833333π-0.833333\pi
1.00000i 0.5π0.5\pi
440440 0 0
441441 1.00000i 1.00000i
442442 0 0
443443 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
450450 0 0
451451 −2.00000 −2.00000
452452 0 0
453453 −1.00000 + 1.00000i −1.00000 + 1.00000i
454454 0 0
455455 0 0
456456 0 0
457457 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
458458 0 0
459459 1.00000i 1.00000i
460460 0 0
461461 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i 0.666667π-0.666667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
462462 0 0
463463 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
464464 0 0
465465 0 0
466466 0 0
467467 1.00000i 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
468468 0 0
469469 0 0
470470 0 0
471471 0.500000 + 0.866025i 0.500000 + 0.866025i
472472 0 0
473473 1.36603 0.366025i 1.36603 0.366025i
474474 0 0
475475 −1.36603 0.366025i −1.36603 0.366025i
476476 0 0
477477 0.500000 + 0.866025i 0.500000 + 0.866025i
478478 0 0
479479 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
480480 0 0
481481 −1.36603 + 0.366025i −1.36603 + 0.366025i
482482 0 0
483483 −1.36603 + 0.366025i −1.36603 + 0.366025i
484484 0 0
485485 0 0
486486 0 0
487487 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
488488 0 0
489489 0 0
490490 0 0
491491 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
500500 0 0
501501 1.36603 + 0.366025i 1.36603 + 0.366025i
502502 0 0
503503 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
504504 0 0
505505 0 0
506506 0 0
507507 1.00000 1.00000
508508 0 0
509509 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
510510 0 0
511511 0 0
512512 0 0
513513 −1.00000 1.00000i −1.00000 1.00000i
514514 0 0
515515 0 0
516516 0 0
517517 −1.73205 1.00000i −1.73205 1.00000i
518518 0 0
519519 1.00000i 1.00000i
520520 0 0
521521 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
522522 0 0
523523 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
524524 0 0
525525 −0.366025 + 1.36603i −0.366025 + 1.36603i
526526 0 0
527527 0 0
528528 0 0
529529 0 0
530530 0 0
531531 0 0
532532 0 0
533533 1.36603 + 0.366025i 1.36603 + 0.366025i
534534 0 0
535535 0 0
536536 0 0
537537 0.866025 + 0.500000i 0.866025 + 0.500000i
538538 0 0
539539 1.00000 + 1.00000i 1.00000 + 1.00000i
540540 0 0
541541 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
542542 0 0
543543 0.866025 + 0.500000i 0.866025 + 0.500000i
544544 0 0
545545 0 0
546546 0 0
547547 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
548548 0 0
549549 −0.500000 + 0.866025i −0.500000 + 0.866025i
550550 0 0
551551 0 0
552552 0 0
553553 0.366025 + 1.36603i 0.366025 + 1.36603i
554554 0 0
555555 0 0
556556 0 0
557557 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
558558 0 0
559559 −1.00000 −1.00000
560560 0 0
561561 1.00000 + 1.00000i 1.00000 + 1.00000i
562562 0 0
563563 −0.866025 0.500000i −0.866025 0.500000i 1.00000i 0.5π-0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
564564 0 0
565565 0 0
566566 0 0
567567 −1.00000 + 1.00000i −1.00000 + 1.00000i
568568 0 0
569569 −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i 0.833333π0.833333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
570570 0 0
571571 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
572572 0 0
573573 1.00000 1.00000
574574 0 0
575575 1.00000 1.00000
576576 0 0
577577 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
578578 0 0
579579 0 0
580580 0 0
581581 1.00000 1.73205i 1.00000 1.73205i
582582 0 0
583583 −1.36603 0.366025i −1.36603 0.366025i
584584 0 0
585585 0 0
586586 0 0
587587 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i 0.666667π-0.666667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
588588 0 0
589589 0 0
590590 0 0
591591 0 0
592592 0 0
593593 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
594594 0 0
595595 0 0
596596 0 0
597597 0.866025 + 0.500000i 0.866025 + 0.500000i
598598 0 0
599599 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
600600 0 0
601601 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
602602 0 0
603603 0 0
604604 0 0
605605 0 0
606606 0 0
607607 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
608608 0 0
609609 0 0
610610 0 0
611611 1.00000 + 1.00000i 1.00000 + 1.00000i
612612 0 0
613613 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
614614 0 0
615615 0 0
616616 0 0
617617 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
618618 0 0
619619 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
620620 0 0
621621 0.866025 + 0.500000i 0.866025 + 0.500000i
622622 0 0
623623 −1.73205 + 1.00000i −1.73205 + 1.00000i
624624 0 0
625625 0.500000 0.866025i 0.500000 0.866025i
626626 0 0
627627 2.00000 2.00000
628628 0 0
629629 1.00000 + 1.00000i 1.00000 + 1.00000i
630630 0 0
631631 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
632632 0 0
633633 0.500000 + 0.866025i 0.500000 + 0.866025i
634634 0 0
635635 0 0
636636 0 0
637637 −0.500000 0.866025i −0.500000 0.866025i
638638 0 0
639639 0 0
640640 0 0
641641 1.73205 1.00000i 1.73205 1.00000i 0.866025 0.500000i 0.166667π-0.166667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
642642 0 0
643643 −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
644644 0 0
645645 0 0
646646 0 0
647647 1.00000i 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 0 0
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 0
657657 0 0
658658 0 0
659659 −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
660660 0 0
661661 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
662662 0 0
663663 −0.500000 0.866025i −0.500000 0.866025i
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 −0.366025 1.36603i −0.366025 1.36603i
672672 0 0
673673 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
674674 0 0
675675 0.866025 0.500000i 0.866025 0.500000i
676676 0 0
677677 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i 0.333333π0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 0 0
683683 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
684684 0 0
685685 0 0
686686 0 0
687687 0 0
688688 0 0
689689 0.866025 + 0.500000i 0.866025 + 0.500000i
690690 0 0
691691 −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
692692 0 0
693693 2.00000i 2.00000i
694694 0 0
695695 0 0
696696 0 0
697697 −0.366025 1.36603i −0.366025 1.36603i
698698 0 0
699699 −0.866025 0.500000i −0.866025 0.500000i
700700 0 0
701701 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
702702 0 0
703703 2.00000 2.00000
704704 0 0
705705 0 0
706706 0 0
707707 1.36603 0.366025i 1.36603 0.366025i
708708 0 0
709709 −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
710710 0 0
711711 0.500000 0.866025i 0.500000 0.866025i
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0.366025 1.36603i 0.366025 1.36603i
718718 0 0
719719 0 0 1.00000 00
−1.00000 π\pi
720720 0 0
721721 0 0
722722 0 0
723723 0 0
724724 0 0
725725 0 0
726726 0 0
727727 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
728728 0 0
729729 1.00000 1.00000
730730 0 0
731731 0.500000 + 0.866025i 0.500000 + 0.866025i
732732 0 0
733733 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i 0.333333π-0.333333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
740740 0 0
741741 −1.36603 0.366025i −1.36603 0.366025i
742742 0 0
743743 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i 0.333333π-0.333333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
744744 0 0
745745 0 0
746746 0 0
747747 −1.36603 + 0.366025i −1.36603 + 0.366025i
748748 0 0
749749 −1.36603 0.366025i −1.36603 0.366025i
750750 0 0
751751 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
752752 0 0
753753 0.866025 + 0.500000i 0.866025 + 0.500000i
754754 0 0
755755 0 0
756756 0 0
757757 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
758758 0 0
759759 −1.36603 + 0.366025i −1.36603 + 0.366025i
760760 0 0
761761 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
762762 0 0
763763 −1.00000 1.73205i −1.00000 1.73205i
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
770770 0 0
771771 −0.866025 + 0.500000i −0.866025 + 0.500000i
772772 0 0
773773 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
774774 0 0
775775 0 0
776776 0 0
777777 2.00000i 2.00000i
778778 0 0
779779 −1.73205 1.00000i −1.73205 1.00000i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0 0
785785 0 0
786786 0 0
787787 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
788788 0 0
789789 1.00000 1.00000
790790 0 0
791791 1.00000 1.00000i 1.00000 1.00000i
792792 0 0
793793 1.00000i 1.00000i
794794 0 0
795795 0 0
796796 0 0
797797 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
798798 0 0
799799 0.366025 1.36603i 0.366025 1.36603i
800800 0 0
801801 1.36603 + 0.366025i 1.36603 + 0.366025i
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
810810 0 0
811811 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 1.36603 + 0.366025i 1.36603 + 0.366025i
818818 0 0
819819 −0.366025 + 1.36603i −0.366025 + 1.36603i
820820 0 0
821821 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
822822 0 0
823823 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i 0.166667π-0.166667\pi
1.00000i 0.5π0.5\pi
824824 0 0
825825 −0.366025 + 1.36603i −0.366025 + 1.36603i
826826 0 0
827827 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
828828 0 0
829829 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
830830 0 0
831831 0 0
832832 0 0
833833 −0.500000 + 0.866025i −0.500000 + 0.866025i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
840840 0 0
841841 0.500000 0.866025i 0.500000 0.866025i
842842 0 0
843843 0 0
844844 0 0
845845 0 0
846846 0 0
847847 1.00000 + 1.00000i 1.00000 + 1.00000i
848848 0 0
849849 0.866025 0.500000i 0.866025 0.500000i
850850 0 0
851851 −1.36603 + 0.366025i −1.36603 + 0.366025i
852852 0 0
853853 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
858858 0 0
859859 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
860860 0 0
861861 −1.00000 + 1.73205i −1.00000 + 1.73205i
862862 0 0
863863 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
864864 0 0
865865 0 0
866866 0 0
867867 0 0
868868 0 0
869869 0.366025 + 1.36603i 0.366025 + 1.36603i
870870 0 0
871871 0 0
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
878878 0 0
879879 1.36603 + 0.366025i 1.36603 + 0.366025i
880880 0 0
881881 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
882882 0 0
883883 0 0 1.00000 00
−1.00000 π\pi
884884 0 0
885885 0 0
886886 0 0
887887 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
888888 0 0
889889 0 0
890890 0 0
891891 −1.00000 + 1.00000i −1.00000 + 1.00000i
892892 0 0
893893 −1.00000 1.73205i −1.00000 1.73205i
894894 0 0
895895 0 0
896896 0 0
897897 1.00000 1.00000
898898 0 0
899899 0 0
900900 0 0
901901 1.00000i 1.00000i
902902 0 0
903903 0.366025 1.36603i 0.366025 1.36603i
904904 0 0
905905 0 0
906906 0 0
907907 −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i 0.833333π-0.833333\pi
1.00000i 0.5π0.5\pi
908908 0 0
909909 −0.866025 0.500000i −0.866025 0.500000i
910910 0 0
911911 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
912912 0 0
913913 1.00000 1.73205i 1.00000 1.73205i
914914 0 0
915915 0 0
916916 0 0
917917 1.00000 1.00000i 1.00000 1.00000i
918918 0 0
919919 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 −0.366025 + 1.36603i −0.366025 + 1.36603i
926926 0 0
927927 0 0
928928 0 0
929929 −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
930930 0 0
931931 0.366025 + 1.36603i 0.366025 + 1.36603i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
938938 0 0
939939 −2.00000 −2.00000
940940 0 0
941941 −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
942942 0 0
943943 1.36603 + 0.366025i 1.36603 + 0.366025i
944944 0 0
945945 0 0
946946 0 0
947947 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i 0.166667π-0.166667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 0 0 1.00000 00
−1.00000 π\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −0.866025 + 0.500000i −0.866025 + 0.500000i
962962 0 0
963963 0.500000 + 0.866025i 0.500000 + 0.866025i
964964 0 0
965965 0 0
966966 0 0
967967 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
968968 0 0
969969 0.366025 + 1.36603i 0.366025 + 1.36603i
970970 0 0
971971 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
972972 0 0
973973 1.00000 1.00000i 1.00000 1.00000i
974974 0 0
975975 0.500000 0.866025i 0.500000 0.866025i
976976 0 0
977977 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
978978 0 0
979979 −1.73205 + 1.00000i −1.73205 + 1.00000i
980980 0 0
981981 −0.366025 + 1.36603i −0.366025 + 1.36603i
982982 0 0
983983 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
984984 0 0
985985 0 0
986986 0 0
987987 −1.73205 + 1.00000i −1.73205 + 1.00000i
988988 0 0
989989 −1.00000 −1.00000
990990 0 0
991991 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
998998 0 0
999999 −1.00000 + 1.00000i −1.00000 + 1.00000i
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 1872.1.fi.b.1633.1 4
4.3 odd 2 936.1.dm.a.697.1 yes 4
9.7 even 3 inner 1872.1.fi.b.385.1 4
12.11 even 2 2808.1.dp.b.1009.1 4
13.5 odd 4 inner 1872.1.fi.b.1201.1 4
36.7 odd 6 936.1.dm.a.385.1 yes 4
36.11 even 6 2808.1.dp.b.73.1 4
52.31 even 4 936.1.dm.a.265.1 4
117.70 odd 12 inner 1872.1.fi.b.1825.1 4
156.83 odd 4 2808.1.dp.b.577.1 4
468.83 odd 12 2808.1.dp.b.2449.1 4
468.187 even 12 936.1.dm.a.889.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
936.1.dm.a.265.1 4 52.31 even 4
936.1.dm.a.385.1 yes 4 36.7 odd 6
936.1.dm.a.697.1 yes 4 4.3 odd 2
936.1.dm.a.889.1 yes 4 468.187 even 12
1872.1.fi.b.385.1 4 9.7 even 3 inner
1872.1.fi.b.1201.1 4 13.5 odd 4 inner
1872.1.fi.b.1633.1 4 1.1 even 1 trivial
1872.1.fi.b.1825.1 4 117.70 odd 12 inner
2808.1.dp.b.73.1 4 36.11 even 6
2808.1.dp.b.577.1 4 156.83 odd 4
2808.1.dp.b.1009.1 4 12.11 even 2
2808.1.dp.b.2449.1 4 468.83 odd 12