Properties

Label 3267.1.be.a.1697.1
Level 32673267
Weight 11
Character 3267.1697
Analytic conductor 1.6301.630
Analytic rank 00
Dimension 2424
Projective image D18D_{18}
CM discriminant -11
Inner twists 1616

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3267,1,Mod(245,3267)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3267, base_ring=CyclotomicField(90))
 
chi = DirichletCharacter(H, H._module([5, 72]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3267.245");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 3267=33112 3267 = 3^{3} \cdot 11^{2}
Weight: k k == 1 1
Character orbit: [χ][\chi] == 3267.be (of order 9090, degree 2424, 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: 1.630445396271.63044539627
Analytic rank: 00
Dimension: 2424
Coefficient field: Q(ζ45)\Q(\zeta_{45})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x24x21+x15x12+x9x3+1 x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D18D_{18}
Projective field: Galois closure of Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots)

Embedding invariants

Embedding label 1697.1
Root 0.882948+0.469472i-0.882948 + 0.469472i of defining polynomial
Character χ\chi == 3267.1697
Dual form 3267.1.be.a.1775.1

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+(0.615661+0.788011i)q3+(0.8480480.529919i)q4+(0.893036+0.924765i)q5+(0.241922+0.970296i)q9+(0.939693+0.342020i)q12+(0.178917+1.27306i)q15+(0.4383710.898794i)q16+(1.24739+0.311009i)q20+(1.113341.32683i)q23+(0.0227790+0.652306i)q25+(0.913545+0.406737i)q27+(1.874810.131099i)q31+(0.309017+0.951057i)q36+(1.025171.13856i)q37+(1.11334+0.642788i)q45+(1.04374+1.67033i)q47+(0.9781480.207912i)q48+(0.7193400.694658i)q49+(0.402069+0.553400i)q53+(0.3211370.603972i)q59+(0.522891+1.17443i)q60+(0.1045280.994522i)q64+(1.76604+0.642788i)q67+(1.73100+0.0604477i)q69+(0.801115+1.79933i)q71+(0.528048+0.383650i)q75+(1.222650.397265i)q80+(0.8829480.469472i)q81+(1.50000+0.866025i)q89+(0.2410551.71519i)q92+(1.050941.55808i)q93+(0.2498240.241252i)q97+O(q100)q+(0.615661 + 0.788011i) q^{3} +(0.848048 - 0.529919i) q^{4} +(0.893036 + 0.924765i) q^{5} +(-0.241922 + 0.970296i) q^{9} +(0.939693 + 0.342020i) q^{12} +(-0.178917 + 1.27306i) q^{15} +(0.438371 - 0.898794i) q^{16} +(1.24739 + 0.311009i) q^{20} +(1.11334 - 1.32683i) q^{23} +(-0.0227790 + 0.652306i) q^{25} +(-0.913545 + 0.406737i) q^{27} +(-1.87481 - 0.131099i) q^{31} +(0.309017 + 0.951057i) q^{36} +(-1.02517 - 1.13856i) q^{37} +(-1.11334 + 0.642788i) q^{45} +(-1.04374 + 1.67033i) q^{47} +(0.978148 - 0.207912i) q^{48} +(0.719340 - 0.694658i) q^{49} +(0.402069 + 0.553400i) q^{53} +(0.321137 - 0.603972i) q^{59} +(0.522891 + 1.17443i) q^{60} +(-0.104528 - 0.994522i) q^{64} +(-1.76604 + 0.642788i) q^{67} +(1.73100 + 0.0604477i) q^{69} +(0.801115 + 1.79933i) q^{71} +(-0.528048 + 0.383650i) q^{75} +(1.22265 - 0.397265i) q^{80} +(-0.882948 - 0.469472i) q^{81} +(-1.50000 + 0.866025i) q^{89} +(0.241055 - 1.71519i) q^{92} +(-1.05094 - 1.55808i) q^{93} +(-0.249824 - 0.241252i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+3q5+3q15+6q20+3q253q273q316q363q473q483q59+3q6424q676q7536q896q936q97+O(q100) 24 q + 3 q^{5} + 3 q^{15} + 6 q^{20} + 3 q^{25} - 3 q^{27} - 3 q^{31} - 6 q^{36} - 3 q^{47} - 3 q^{48} - 3 q^{59} + 3 q^{64} - 24 q^{67} - 6 q^{75} - 36 q^{89} - 6 q^{93} - 6 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3267Z)×\left(\mathbb{Z}/3267\mathbb{Z}\right)^\times.

nn 244244 30263026
χ(n)\chi(n) e(45)e\left(\frac{4}{5}\right) e(1118)e\left(\frac{11}{18}\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 0 0.961262 0.275637i 0.0888889π-0.0888889\pi
−0.961262 + 0.275637i 0.911111π0.911111\pi
33 0.615661 + 0.788011i 0.615661 + 0.788011i
44 0.848048 0.529919i 0.848048 0.529919i
55 0.893036 + 0.924765i 0.893036 + 0.924765i 0.997564 0.0697565i 0.0222222π-0.0222222\pi
−0.104528 + 0.994522i 0.533333π0.533333\pi
66 0 0
77 0 0 0.927184 0.374607i 0.122222π-0.122222\pi
−0.927184 + 0.374607i 0.877778π0.877778\pi
88 0 0
99 −0.241922 + 0.970296i −0.241922 + 0.970296i
1010 0 0
1111 0 0
1212 0.939693 + 0.342020i 0.939693 + 0.342020i
1313 0 0 −0.829038 0.559193i 0.811111π-0.811111\pi
0.829038 + 0.559193i 0.188889π0.188889\pi
1414 0 0
1515 −0.178917 + 1.27306i −0.178917 + 1.27306i
1616 0.438371 0.898794i 0.438371 0.898794i
1717 0 0 0.913545 0.406737i 0.133333π-0.133333\pi
−0.913545 + 0.406737i 0.866667π0.866667\pi
1818 0 0
1919 0 0 −0.743145 0.669131i 0.766667π-0.766667\pi
0.743145 + 0.669131i 0.233333π0.233333\pi
2020 1.24739 + 0.311009i 1.24739 + 0.311009i
2121 0 0
2222 0 0
2323 1.11334 1.32683i 1.11334 1.32683i 0.173648 0.984808i 0.444444π-0.444444\pi
0.939693 0.342020i 0.111111π-0.111111\pi
2424 0 0
2525 −0.0227790 + 0.652306i −0.0227790 + 0.652306i
2626 0 0
2727 −0.913545 + 0.406737i −0.913545 + 0.406737i
2828 0 0
2929 0 0 0.615661 0.788011i 0.288889π-0.288889\pi
−0.615661 + 0.788011i 0.711111π0.711111\pi
3030 0 0
3131 −1.87481 0.131099i −1.87481 0.131099i −0.913545 0.406737i 0.866667π-0.866667\pi
−0.961262 + 0.275637i 0.911111π0.911111\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0.309017 + 0.951057i 0.309017 + 0.951057i
3737 −1.02517 1.13856i −1.02517 1.13856i −0.990268 0.139173i 0.955556π-0.955556\pi
−0.0348995 0.999391i 0.511111π-0.511111\pi
3838 0 0
3939 0 0
4040 0 0
4141 0 0 −0.615661 0.788011i 0.711111π-0.711111\pi
0.615661 + 0.788011i 0.288889π0.288889\pi
4242 0 0
4343 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
4444 0 0
4545 −1.11334 + 0.642788i −1.11334 + 0.642788i
4646 0 0
4747 −1.04374 + 1.67033i −1.04374 + 1.67033i −0.374607 + 0.927184i 0.622222π0.622222\pi
−0.669131 + 0.743145i 0.733333π0.733333\pi
4848 0.978148 0.207912i 0.978148 0.207912i
4949 0.719340 0.694658i 0.719340 0.694658i
5050 0 0
5151 0 0
5252 0 0
5353 0.402069 + 0.553400i 0.402069 + 0.553400i 0.961262 0.275637i 0.0888889π-0.0888889\pi
−0.559193 + 0.829038i 0.688889π0.688889\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 0.321137 0.603972i 0.321137 0.603972i −0.669131 0.743145i 0.733333π-0.733333\pi
0.990268 + 0.139173i 0.0444444π0.0444444\pi
6060 0.522891 + 1.17443i 0.522891 + 1.17443i
6161 0 0 −0.0697565 0.997564i 0.522222π-0.522222\pi
0.0697565 + 0.997564i 0.477778π0.477778\pi
6262 0 0
6363 0 0
6464 −0.104528 0.994522i −0.104528 0.994522i
6565 0 0
6666 0 0
6767 −1.76604 + 0.642788i −1.76604 + 0.642788i −0.766044 + 0.642788i 0.777778π0.777778\pi
−1.00000 1.00000π1.00000\pi
6868 0 0
6969 1.73100 + 0.0604477i 1.73100 + 0.0604477i
7070 0 0
7171 0.801115 + 1.79933i 0.801115 + 1.79933i 0.559193 + 0.829038i 0.311111π0.311111\pi
0.241922 + 0.970296i 0.422222π0.422222\pi
7272 0 0
7373 0 0 −0.207912 0.978148i 0.566667π-0.566667\pi
0.207912 + 0.978148i 0.433333π0.433333\pi
7474 0 0
7575 −0.528048 + 0.383650i −0.528048 + 0.383650i
7676 0 0
7777 0 0
7878 0 0
7979 0 0 −0.275637 0.961262i 0.588889π-0.588889\pi
0.275637 + 0.961262i 0.411111π0.411111\pi
8080 1.22265 0.397265i 1.22265 0.397265i
8181 −0.882948 0.469472i −0.882948 0.469472i
8282 0 0
8383 0 0 −0.559193 0.829038i 0.688889π-0.688889\pi
0.559193 + 0.829038i 0.311111π0.311111\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i 0.666667π0.666667\pi
−1.00000 π\pi
9090 0 0
9191 0 0
9292 0.241055 1.71519i 0.241055 1.71519i
9393 −1.05094 1.55808i −1.05094 1.55808i
9494 0 0
9595 0 0
9696 0 0
9797 −0.249824 0.241252i −0.249824 0.241252i 0.559193 0.829038i 0.311111π-0.311111\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
9898 0 0
9999 0 0
100100 0.326352 + 0.565258i 0.326352 + 0.565258i
101101 0 0 0.241922 0.970296i 0.422222π-0.422222\pi
−0.241922 + 0.970296i 0.577778π0.577778\pi
102102 0 0
103103 −1.35275 0.719272i −1.35275 0.719272i −0.374607 0.927184i 0.622222π-0.622222\pi
−0.978148 + 0.207912i 0.933333π0.933333\pi
104104 0 0
105105 0 0
106106 0 0
107107 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
108108 −0.559193 + 0.829038i −0.559193 + 0.829038i
109109 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
110110 0 0
111111 0.266044 1.50881i 0.266044 1.50881i
112112 0 0
113113 −0.274117 1.95045i −0.274117 1.95045i −0.309017 0.951057i 0.600000π-0.600000\pi
0.0348995 0.999391i 0.488889π-0.488889\pi
114114 0 0
115115 2.22126 0.155325i 2.22126 0.155325i
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 0 0
122122 0 0
123123 0 0
124124 −1.65940 + 0.882318i −1.65940 + 0.882318i
125125 0.331796 0.298750i 0.331796 0.298750i
126126 0 0
127127 0 0 −0.994522 0.104528i 0.966667π-0.966667\pi
0.994522 + 0.104528i 0.0333333π0.0333333\pi
128128 0 0
129129 0 0
130130 0 0
131131 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
132132 0 0
133133 0 0
134134 0 0
135135 −1.19196 0.481585i −1.19196 0.481585i
136136 0 0
137137 0.567095 0.382510i 0.567095 0.382510i −0.241922 0.970296i 0.577778π-0.577778\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
138138 0 0
139139 0 0 −0.529919 0.848048i 0.677778π-0.677778\pi
0.529919 + 0.848048i 0.322222π0.322222\pi
140140 0 0
141141 −1.95883 + 0.205881i −1.95883 + 0.205881i
142142 0 0
143143 0 0
144144 0.766044 + 0.642788i 0.766044 + 0.642788i
145145 0 0
146146 0 0
147147 0.990268 + 0.139173i 0.990268 + 0.139173i
148148 −1.47274 0.422301i −1.47274 0.422301i
149149 0 0 −0.961262 0.275637i 0.911111π-0.911111\pi
0.961262 + 0.275637i 0.0888889π0.0888889\pi
150150 0 0
151151 0 0 −0.469472 0.882948i 0.655556π-0.655556\pi
0.469472 + 0.882948i 0.344444π0.344444\pi
152152 0 0
153153 0 0
154154 0 0
155155 −1.55303 1.85083i −1.55303 1.85083i
156156 0 0
157157 1.86110 0.261560i 1.86110 0.261560i 0.882948 0.469472i 0.155556π-0.155556\pi
0.978148 + 0.207912i 0.0666667π0.0666667\pi
158158 0 0
159159 −0.188547 + 0.657542i −0.188547 + 0.657542i
160160 0 0
161161 0 0
162162 0 0
163163 −0.280969 + 0.204136i −0.280969 + 0.204136i −0.719340 0.694658i 0.755556π-0.755556\pi
0.438371 + 0.898794i 0.355556π0.355556\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 −0.438371 0.898794i 0.644444π-0.644444\pi
0.438371 + 0.898794i 0.355556π0.355556\pi
168168 0 0
169169 0.374607 + 0.927184i 0.374607 + 0.927184i
170170 0 0
171171 0 0
172172 0 0
173173 0 0 0.882948 0.469472i 0.155556π-0.155556\pi
−0.882948 + 0.469472i 0.844444π0.844444\pi
174174 0 0
175175 0 0
176176 0 0
177177 0.673648 0.118782i 0.673648 0.118782i
178178 0 0
179179 0.142220 0.669092i 0.142220 0.669092i −0.848048 0.529919i 0.822222π-0.822222\pi
0.990268 0.139173i 0.0444444π-0.0444444\pi
180180 −0.603541 + 1.13510i −0.603541 + 1.13510i
181181 −0.160147 + 1.52370i −0.160147 + 1.52370i 0.559193 + 0.829038i 0.311111π0.311111\pi
−0.719340 + 0.694658i 0.755556π0.755556\pi
182182 0 0
183183 0 0
184184 0 0
185185 0.137393 1.96482i 0.137393 1.96482i
186186 0 0
187187 0 0
188188 1.96962i 1.96962i
189189 0 0
190190 0 0
191191 1.55208 + 1.21262i 1.55208 + 1.21262i 0.882948 + 0.469472i 0.155556π0.155556\pi
0.669131 + 0.743145i 0.266667π0.266667\pi
192192 0.719340 0.694658i 0.719340 0.694658i
193193 0 0 0.970296 0.241922i 0.0777778π-0.0777778\pi
−0.970296 + 0.241922i 0.922222π0.922222\pi
194194 0 0
195195 0 0
196196 0.241922 0.970296i 0.241922 0.970296i
197197 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
198198 0 0
199199 0.173648 0.300767i 0.173648 0.300767i −0.766044 0.642788i 0.777778π-0.777778\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
200200 0 0
201201 −1.59381 0.995922i −1.59381 0.995922i
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 1.01807 + 1.40126i 1.01807 + 1.40126i
208208 0 0
209209 0 0
210210 0 0
211211 0 0 0.898794 0.438371i 0.144444π-0.144444\pi
−0.898794 + 0.438371i 0.855556π0.855556\pi
212212 0.634231 + 0.256246i 0.634231 + 0.256246i
213213 −0.924678 + 1.73907i −0.924678 + 1.73907i
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 −0.848048 0.529919i −0.848048 0.529919i 0.0348995 0.999391i 0.488889π-0.488889\pi
−0.882948 + 0.469472i 0.844444π0.844444\pi
224224 0 0
225225 −0.627419 0.179910i −0.627419 0.179910i
226226 0 0
227227 0 0 −0.990268 0.139173i 0.955556π-0.955556\pi
0.990268 + 0.139173i 0.0444444π0.0444444\pi
228228 0 0
229229 0.559193 0.829038i 0.559193 0.829038i −0.438371 0.898794i 0.644444π-0.644444\pi
0.997564 + 0.0697565i 0.0222222π0.0222222\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 −0.104528 0.994522i 0.533333π-0.533333\pi
0.104528 + 0.994522i 0.466667π0.466667\pi
234234 0 0
235235 −2.47676 + 0.526451i −2.47676 + 0.526451i
236236 −0.0477162 0.682374i −0.0477162 0.682374i
237237 0 0
238238 0 0
239239 0 0 0.374607 0.927184i 0.377778π-0.377778\pi
−0.374607 + 0.927184i 0.622222π0.622222\pi
240240 1.06579 + 0.718885i 1.06579 + 0.718885i
241241 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
242242 0 0
243243 −0.173648 0.984808i −0.173648 0.984808i
244244 0 0
245245 1.28479 + 0.0448659i 1.28479 + 0.0448659i
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 0 0
251251 0 0 −0.913545 0.406737i 0.866667π-0.866667\pi
0.913545 + 0.406737i 0.133333π0.133333\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 −0.615661 0.788011i −0.615661 0.788011i
257257 1.73100 0.0604477i 1.73100 0.0604477i 0.848048 0.529919i 0.177778π-0.177778\pi
0.882948 + 0.469472i 0.155556π0.155556\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
264264 0 0
265265 −0.152704 + 0.866025i −0.152704 + 0.866025i
266266 0 0
267267 −1.60593 0.648838i −1.60593 0.648838i
268268 −1.15707 + 1.48098i −1.15707 + 1.48098i
269269 −1.15771 + 1.59345i −1.15771 + 1.59345i −0.438371 + 0.898794i 0.644444π0.644444\pi
−0.719340 + 0.694658i 0.755556π0.755556\pi
270270 0 0
271271 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 1.50000 0.866025i 1.50000 0.866025i
277277 0 0 −0.970296 0.241922i 0.922222π-0.922222\pi
0.970296 + 0.241922i 0.0777778π0.0777778\pi
278278 0 0
279279 0.580762 1.78740i 0.580762 1.78740i
280280 0 0
281281 0 0 0.438371 0.898794i 0.355556π-0.355556\pi
−0.438371 + 0.898794i 0.644444π0.644444\pi
282282 0 0
283283 0 0 0.788011 0.615661i 0.211111π-0.211111\pi
−0.788011 + 0.615661i 0.788889π0.788889\pi
284284 1.63289 + 1.10140i 1.63289 + 1.10140i
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 0.669131 0.743145i 0.669131 0.743145i
290290 0 0
291291 0.0363024 0.345394i 0.0363024 0.345394i
292292 0 0
293293 0 0 0.848048 0.529919i 0.177778π-0.177778\pi
−0.848048 + 0.529919i 0.822222π0.822222\pi
294294 0 0
295295 0.845319 0.242391i 0.845319 0.242391i
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 −0.244507 + 0.605176i −0.244507 + 0.605176i
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 0 0
307307 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
308308 0 0
309309 −0.266044 1.50881i −0.266044 1.50881i
310310 0 0
311311 −0.539031 + 0.421137i −0.539031 + 0.421137i −0.848048 0.529919i 0.822222π-0.822222\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
312312 0 0
313313 0.438371 0.898794i 0.438371 0.898794i −0.559193 0.829038i 0.688889π-0.688889\pi
0.997564 0.0697565i 0.0222222π-0.0222222\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 0.241922 0.970296i 0.422222π-0.422222\pi
−0.241922 + 0.970296i 0.577778π0.577778\pi
318318 0 0
319319 0 0
320320 0.826352 0.984808i 0.826352 0.984808i
321321 0 0
322322 0 0
323323 0 0
324324 −0.997564 + 0.0697565i −0.997564 + 0.0697565i
325325 0 0
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 0.266044 0.223238i 0.266044 0.223238i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
332332 0 0
333333 1.35275 0.719272i 1.35275 0.719272i
334334 0 0
335335 −2.17157 1.05914i −2.17157 1.05914i
336336 0 0
337337 0 0 0.999391 0.0348995i 0.0111111π-0.0111111\pi
−0.999391 + 0.0348995i 0.988889π0.988889\pi
338338 0 0
339339 1.36821 1.41682i 1.36821 1.41682i
340340 0 0
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 1.48994 + 1.65475i 1.48994 + 1.65475i
346346 0 0
347347 0 0 −0.241922 0.970296i 0.577778π-0.577778\pi
0.241922 + 0.970296i 0.422222π0.422222\pi
348348 0 0
349349 0 0 −0.999391 0.0348995i 0.988889π-0.988889\pi
0.999391 + 0.0348995i 0.0111111π0.0111111\pi
350350 0 0
351351 0 0
352352 0 0
353353 −0.592396 + 1.62760i −0.592396 + 1.62760i 0.173648 + 0.984808i 0.444444π0.444444\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
354354 0 0
355355 −0.948537 + 2.34771i −0.948537 + 2.34771i
356356 −0.813149 + 1.52931i −0.813149 + 1.52931i
357357 0 0
358358 0 0
359359 0 0 0.978148 0.207912i 0.0666667π-0.0666667\pi
−0.978148 + 0.207912i 0.933333π0.933333\pi
360360 0 0
361361 0.104528 + 0.994522i 0.104528 + 0.994522i
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 0.343916 + 0.0483343i 0.343916 + 0.0483343i 0.309017 0.951057i 0.400000π-0.400000\pi
0.0348995 + 0.999391i 0.488889π0.488889\pi
368368 −0.704489 1.58231i −0.704489 1.58231i
369369 0 0
370370 0 0
371371 0 0
372372 −1.71690 0.764415i −1.71690 0.764415i
373373 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
374374 0 0
375375 0.439693 + 0.0775297i 0.439693 + 0.0775297i
376376 0 0
377377 0 0
378378 0 0
379379 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i 0.133333π-0.133333\pi
−0.104528 + 0.994522i 0.533333π0.533333\pi
380380 0 0
381381 0 0
382382 0 0
383383 −0.614811 + 0.299864i −0.614811 + 0.299864i −0.719340 0.694658i 0.755556π-0.755556\pi
0.104528 + 0.994522i 0.466667π0.466667\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 −0.339707 0.0722070i −0.339707 0.0722070i
389389 0.274117 1.95045i 0.274117 1.95045i −0.0348995 0.999391i 0.511111π-0.511111\pi
0.309017 0.951057i 0.400000π-0.400000\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i 0.222222π0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
398398 0 0
399399 0 0
400400 0.576303 + 0.306426i 0.576303 + 0.306426i
401401 1.24739 0.311009i 1.24739 0.311009i 0.438371 0.898794i 0.355556π-0.355556\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
402402 0 0
403403 0 0
404404 0 0
405405 −0.354353 1.23577i −0.354353 1.23577i
406406 0 0
407407 0 0
408408 0 0
409409 0 0 0.0697565 0.997564i 0.477778π-0.477778\pi
−0.0697565 + 0.997564i 0.522222π0.522222\pi
410410 0 0
411411 0.650561 + 0.211380i 0.650561 + 0.211380i
412412 −1.52836 + 0.106873i −1.52836 + 0.106873i
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 0.439693 + 1.20805i 0.439693 + 1.20805i 0.939693 + 0.342020i 0.111111π0.111111\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
420420 0 0
421421 1.35275 0.719272i 1.35275 0.719272i 0.374607 0.927184i 0.377778π-0.377778\pi
0.978148 + 0.207912i 0.0666667π0.0666667\pi
422422 0 0
423423 −1.36821 1.41682i −1.36821 1.41682i
424424 0 0
425425 0 0
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
432432 −0.0348995 + 0.999391i −0.0348995 + 0.999391i
433433 −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i 0.266667π0.266667\pi
−0.978148 + 0.207912i 0.933333π0.933333\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 0 0
439439 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
440440 0 0
441441 0.500000 + 0.866025i 0.500000 + 0.866025i
442442 0 0
443443 −0.603541 1.13510i −0.603541 1.13510i −0.978148 0.207912i 0.933333π-0.933333\pi
0.374607 0.927184i 0.377778π-0.377778\pi
444444 −0.573931 1.42053i −0.573931 1.42053i
445445 −2.14042 0.613757i −2.14042 0.613757i
446446 0 0
447447 0 0
448448 0 0
449449 1.27853 0.134379i 1.27853 0.134379i 0.559193 0.829038i 0.311111π-0.311111\pi
0.719340 + 0.694658i 0.244444π0.244444\pi
450450 0 0
451451 0 0
452452 −1.26604 1.50881i −1.26604 1.50881i
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 0 0 0.829038 0.559193i 0.188889π-0.188889\pi
−0.829038 + 0.559193i 0.811111π0.811111\pi
458458 0 0
459459 0 0
460460 1.80142 1.30881i 1.80142 1.30881i
461461 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
462462 0 0
463463 −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i 0.444444π-0.444444\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
464464 0 0
465465 0.502334 2.36329i 0.502334 2.36329i
466466 0 0
467467 −1.95883 0.205881i −1.95883 0.205881i −0.961262 0.275637i 0.911111π-0.911111\pi
−0.997564 + 0.0697565i 0.977778π0.977778\pi
468468 0 0
469469 0 0
470470 0 0
471471 1.35192 + 1.30553i 1.35192 + 1.30553i
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 −0.634231 + 0.256246i −0.634231 + 0.256246i
478478 0 0
479479 0 0 0.997564 0.0697565i 0.0222222π-0.0222222\pi
−0.997564 + 0.0697565i 0.977778π0.977778\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 0 0
485485 0.446476i 0.446476i
486486 0 0
487487 −0.473442 1.45710i −0.473442 1.45710i −0.848048 0.529919i 0.822222π-0.822222\pi
0.374607 0.927184i 0.377778π-0.377778\pi
488488 0 0
489489 −0.333843 0.0957278i −0.333843 0.0957278i
490490 0 0
491491 0 0 −0.882948 0.469472i 0.844444π-0.844444\pi
0.882948 + 0.469472i 0.155556π0.155556\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 −0.939693 + 1.62760i −0.939693 + 1.62760i
497497 0 0
498498 0 0
499499 −0.0534691 1.53116i −0.0534691 1.53116i −0.669131 0.743145i 0.733333π-0.733333\pi
0.615661 0.788011i 0.288889π-0.288889\pi
500500 0.123065 0.429180i 0.123065 0.429180i
501501 0 0
502502 0 0
503503 0 0 −0.978148 0.207912i 0.933333π-0.933333\pi
0.978148 + 0.207912i 0.0666667π0.0666667\pi
504504 0 0
505505 0 0
506506 0 0
507507 −0.500000 + 0.866025i −0.500000 + 0.866025i
508508 0 0
509509 −1.60593 0.648838i −1.60593 0.648838i −0.615661 0.788011i 0.711111π-0.711111\pi
−0.990268 + 0.139173i 0.955556π0.955556\pi
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 −0.542900 1.89332i −0.542900 1.89332i
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 −0.267286 1.25748i −0.267286 1.25748i −0.882948 0.469472i 0.844444π-0.844444\pi
0.615661 0.788011i 0.288889π-0.288889\pi
522522 0 0
523523 0 0 −0.406737 0.913545i 0.633333π-0.633333\pi
0.406737 + 0.913545i 0.366667π0.366667\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 −0.347296 1.96962i −0.347296 1.96962i
530530 0 0
531531 0.508341 + 0.457712i 0.508341 + 0.457712i
532532 0 0
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 0.614811 0.299864i 0.614811 0.299864i
538538 0 0
539539 0 0
540540 −1.26604 + 0.223238i −1.26604 + 0.223238i
541541 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
542542 0 0
543543 −1.29929 + 0.811883i −1.29929 + 0.811883i
544544 0 0
545545 0 0
546546 0 0
547547 0 0 0.529919 0.848048i 0.322222π-0.322222\pi
−0.529919 + 0.848048i 0.677778π0.677778\pi
548548 0.278224 0.624902i 0.278224 0.624902i
549549 0 0
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 1.63289 1.10140i 1.63289 1.10140i
556556 0 0
557557 0 0 −0.669131 0.743145i 0.733333π-0.733333\pi
0.669131 + 0.743145i 0.266667π0.266667\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 0 0 −0.997564 0.0697565i 0.977778π-0.977778\pi
0.997564 + 0.0697565i 0.0222222π0.0222222\pi
564564 −1.55208 + 1.21262i −1.55208 + 1.21262i
565565 1.55891 1.99531i 1.55891 1.99531i
566566 0 0
567567 0 0
568568 0 0
569569 0 0 0.0348995 0.999391i 0.488889π-0.488889\pi
−0.0348995 + 0.999391i 0.511111π0.511111\pi
570570 0 0
571571 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
572572 0 0
573573 1.96962i 1.96962i
574574 0 0
575575 0.840137 + 0.756463i 0.840137 + 0.756463i
576576 0.990268 + 0.139173i 0.990268 + 0.139173i
577577 −1.39963 + 0.623157i −1.39963 + 0.623157i −0.961262 0.275637i 0.911111π-0.911111\pi
−0.438371 + 0.898794i 0.644444π0.644444\pi
578578 0 0
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 −1.19196 + 0.481585i −1.19196 + 0.481585i −0.882948 0.469472i 0.844444π-0.844444\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
588588 0.913545 0.406737i 0.913545 0.406737i
589589 0 0
590590 0 0
591591 0 0
592592 −1.47274 + 0.422301i −1.47274 + 0.422301i
593593 0 0 1.00000 00
−1.00000 π\pi
594594 0 0
595595 0 0
596596 0 0
597597 0.343916 0.0483343i 0.343916 0.0483343i
598598 0 0
599599 1.20318 + 1.24593i 1.20318 + 1.24593i 0.961262 + 0.275637i 0.0888889π0.0888889\pi
0.241922 + 0.970296i 0.422222π0.422222\pi
600600 0 0
601601 0 0 0.927184 0.374607i 0.122222π-0.122222\pi
−0.927184 + 0.374607i 0.877778π0.877778\pi
602602 0 0
603603 −0.196449 1.86909i −0.196449 1.86909i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 −0.829038 0.559193i 0.811111π-0.811111\pi
0.829038 + 0.559193i 0.188889π0.188889\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 0 0 −0.743145 0.669131i 0.766667π-0.766667\pi
0.743145 + 0.669131i 0.233333π0.233333\pi
614614 0 0
615615 0 0
616616 0 0
617617 −0.439693 + 0.524005i −0.439693 + 0.524005i −0.939693 0.342020i 0.888889π-0.888889\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
618618 0 0
619619 0.0534691 1.53116i 0.0534691 1.53116i −0.615661 0.788011i 0.711111π-0.711111\pi
0.669131 0.743145i 0.266667π-0.266667\pi
620620 −2.29784 0.746613i −2.29784 0.746613i
621621 −0.477418 + 1.66495i −0.477418 + 1.66495i
622622 0 0
623623 0 0
624624 0 0
625625 1.22369 + 0.0855690i 1.22369 + 0.0855690i
626626 0 0
627627 0 0
628628 1.43969 1.20805i 1.43969 1.20805i
629629 0 0
630630 0 0
631631 1.25755 + 1.39666i 1.25755 + 1.39666i 0.882948 + 0.469472i 0.155556π0.155556\pi
0.374607 + 0.927184i 0.377778π0.377778\pi
632632 0 0
633633 0 0
634634 0 0
635635 0 0
636636 0.188547 + 0.657542i 0.188547 + 0.657542i
637637 0 0
638638 0 0
639639 −1.93969 + 0.342020i −1.93969 + 0.342020i
640640 0 0
641641 −0.917847 + 1.46886i −0.917847 + 1.46886i −0.0348995 + 0.999391i 0.511111π0.511111\pi
−0.882948 + 0.469472i 0.844444π0.844444\pi
642642 0 0
643643 0.719340 0.694658i 0.719340 0.694658i −0.241922 0.970296i 0.577778π-0.577778\pi
0.961262 + 0.275637i 0.0888889π0.0888889\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 −0.130100 + 0.322008i −0.130100 + 0.322008i
653653 −0.603541 + 1.13510i −0.603541 + 1.13510i 0.374607 + 0.927184i 0.377778π0.377778\pi
−0.978148 + 0.207912i 0.933333π0.933333\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
660660 0 0
661661 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
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −0.104528 0.994522i −0.104528 0.994522i
670670 0 0
671671 0 0
672672 0 0
673673 0 0 −0.275637 0.961262i 0.588889π-0.588889\pi
0.275637 + 0.961262i 0.411111π0.411111\pi
674674 0 0
675675 −0.244507 0.605176i −0.244507 0.605176i
676676 0.809017 + 0.587785i 0.809017 + 0.587785i
677677 0 0 −0.559193 0.829038i 0.688889π-0.688889\pi
0.559193 + 0.829038i 0.311111π0.311111\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 0 0
683683 1.70574 0.984808i 1.70574 0.984808i 0.766044 0.642788i 0.222222π-0.222222\pi
0.939693 0.342020i 0.111111π-0.111111\pi
684684 0 0
685685 0.860169 + 0.182834i 0.860169 + 0.182834i
686686 0 0
687687 0.997564 0.0697565i 0.997564 0.0697565i
688688 0 0
689689 0 0
690690 0 0
691691 −1.10209 1.06428i −1.10209 1.06428i −0.997564 0.0697565i 0.977778π-0.977778\pi
−0.104528 0.994522i 0.533333π-0.533333\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 0 0
701701 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
702702 0 0
703703 0 0
704704 0 0
705705 −1.93969 1.62760i −1.93969 1.62760i
706706 0 0
707707 0 0
708708 0.508341 0.457712i 0.508341 0.457712i
709709 1.52836 0.106873i 1.52836 0.106873i 0.719340 0.694658i 0.244444π-0.244444\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
710710 0 0
711711 0 0
712712 0 0
713713 −2.26125 + 2.34159i −2.26125 + 2.34159i
714714 0 0
715715 0 0
716716 −0.233956 0.642788i −0.233956 0.642788i
717717 0 0
718718 0 0
719719 −1.46371 + 1.31793i −1.46371 + 1.31793i −0.615661 + 0.788011i 0.711111π0.711111\pi
−0.848048 + 0.529919i 0.822222π0.822222\pi
720720 0.0896772 + 1.28244i 0.0896772 + 1.28244i
721721 0 0
722722 0 0
723723 0 0
724724 0.671624 + 1.37703i 0.671624 + 1.37703i
725725 0 0
726726 0 0
727727 0.326352 + 0.118782i 0.326352 + 0.118782i 0.500000 0.866025i 0.333333π-0.333333\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
728728 0 0
729729 0.669131 0.743145i 0.669131 0.743145i
730730 0 0
731731 0 0
732732 0 0
733733 0 0 −0.529919 0.848048i 0.677778π-0.677778\pi
0.529919 + 0.848048i 0.322222π0.322222\pi
734734 0 0
735735 0.755642 + 1.04005i 0.755642 + 1.04005i
736736 0 0
737737 0 0
738738 0 0
739739 0 0 0.994522 0.104528i 0.0333333π-0.0333333\pi
−0.994522 + 0.104528i 0.966667π0.966667\pi
740740 −0.924678 1.73907i −0.924678 1.73907i
741741 0 0
742742 0 0
743743 0 0 −0.961262 0.275637i 0.911111π-0.911111\pi
0.961262 + 0.275637i 0.0888889π0.0888889\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −0.343916 + 0.0483343i −0.343916 + 0.0483343i −0.309017 0.951057i 0.600000π-0.600000\pi
−0.0348995 + 0.999391i 0.511111π0.511111\pi
752752 1.04374 + 1.67033i 1.04374 + 1.67033i
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 −1.52045 + 1.10467i −1.52045 + 1.10467i −0.559193 + 0.829038i 0.688889π0.688889\pi
−0.961262 + 0.275637i 0.911111π0.911111\pi
758758 0 0
759759 0 0
760760 0 0
761761 0 0 −0.438371 0.898794i 0.644444π-0.644444\pi
0.438371 + 0.898794i 0.355556π0.355556\pi
762762 0 0
763763 0 0
764764 1.95883 + 0.205881i 1.95883 + 0.205881i
765765 0 0
766766 0 0
767767 0 0
768768 0.241922 0.970296i 0.241922 0.970296i
769769 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
770770 0 0
771771 1.11334 + 1.32683i 1.11334 + 1.32683i
772772 0 0
773773 0 0 −0.978148 0.207912i 0.933333π-0.933333\pi
0.978148 + 0.207912i 0.0666667π0.0666667\pi
774774 0 0
775775 0.128223 1.21996i 0.128223 1.21996i
776776 0 0
777777 0 0
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −0.309017 0.951057i −0.309017 0.951057i
785785 1.90391 + 1.48749i 1.90391 + 1.48749i
786786 0 0
787787 0 0 0.970296 0.241922i 0.0777778π-0.0777778\pi
−0.970296 + 0.241922i 0.922222π0.922222\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 −0.776451 + 0.412846i −0.776451 + 0.412846i
796796 −0.0121205 0.347085i −0.0121205 0.347085i
797797 0.354353 1.23577i 0.354353 1.23577i −0.559193 0.829038i 0.688889π-0.688889\pi
0.913545 0.406737i 0.133333π-0.133333\pi
798798 0 0
799799 0 0
800800 0 0
801801 −0.477418 1.66495i −0.477418 1.66495i
802802 0 0
803803 0 0
804804 −1.87939 −1.87939
805805 0 0
806806 0 0
807807 −1.96842 + 0.0687386i −1.96842 + 0.0687386i
808808 0 0
809809 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
810810 0 0
811811 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
812812 0 0
813813 0 0
814814 0 0
815815 −0.439693 0.0775297i −0.439693 0.0775297i
816816 0 0
817817 0 0
818818 0 0
819819 0 0
820820 0 0
821821 0 0 −0.990268 0.139173i 0.955556π-0.955556\pi
0.990268 + 0.139173i 0.0444444π0.0444444\pi
822822 0 0
823823 −0.559193 + 0.829038i −0.559193 + 0.829038i −0.997564 0.0697565i 0.977778π-0.977778\pi
0.438371 + 0.898794i 0.355556π0.355556\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 −0.104528 0.994522i 0.533333π-0.533333\pi
0.104528 + 0.994522i 0.466667π0.466667\pi
828828 1.60593 + 0.648838i 1.60593 + 0.648838i
829829 1.83832 0.390746i 1.83832 0.390746i 0.848048 0.529919i 0.177778π-0.177778\pi
0.990268 + 0.139173i 0.0444444π0.0444444\pi
830830 0 0
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 1.76604 0.642788i 1.76604 0.642788i
838838 0 0
839839 1.73100 + 0.0604477i 1.73100 + 0.0604477i 0.882948 0.469472i 0.155556π-0.155556\pi
0.848048 + 0.529919i 0.177778π0.177778\pi
840840 0 0
841841 −0.241922 0.970296i −0.241922 0.970296i
842842 0 0
843843 0 0
844844 0 0
845845 −0.522891 + 1.17443i −0.522891 + 1.17443i
846846 0 0
847847 0 0
848848 0.673648 0.118782i 0.673648 0.118782i
849849 0 0
850850 0 0
851851 −2.65204 + 0.0926113i −2.65204 + 0.0926113i
852852 0.137393 + 1.96482i 0.137393 + 1.96482i
853853 0 0 −0.898794 0.438371i 0.855556π-0.855556\pi
0.898794 + 0.438371i 0.144444π0.144444\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
858858 0 0
859859 0.0603074 0.342020i 0.0603074 0.342020i −0.939693 0.342020i 0.888889π-0.888889\pi
1.00000 00
860860 0 0
861861 0 0
862862 0 0
863863 −1.01807 + 1.40126i −1.01807 + 1.40126i −0.104528 + 0.994522i 0.533333π0.533333\pi
−0.913545 + 0.406737i 0.866667π0.866667\pi
864864 0 0
865865 0 0
866866 0 0
867867 0.997564 + 0.0697565i 0.997564 + 0.0697565i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 0.294524 0.184039i 0.294524 0.184039i
874874 0 0
875875 0 0
876876 0 0
877877 0 0 0.788011 0.615661i 0.211111π-0.211111\pi
−0.788011 + 0.615661i 0.788889π0.788889\pi
878878 0 0
879879 0 0
880880 0 0
881881 1.70574 + 0.984808i 1.70574 + 0.984808i 0.939693 + 0.342020i 0.111111π0.111111\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
882882 0 0
883883 −0.232387 + 0.258091i −0.232387 + 0.258091i −0.848048 0.529919i 0.822222π-0.822222\pi
0.615661 + 0.788011i 0.288889π0.288889\pi
884884 0 0
885885 0.711438 + 0.516890i 0.711438 + 0.516890i
886886 0 0
887887 0 0 0.848048 0.529919i 0.177778π-0.177778\pi
−0.848048 + 0.529919i 0.822222π0.822222\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 −1.00000 −1.00000
893893 0 0
894894 0 0
895895 0.745761 0.466003i 0.745761 0.466003i
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 −0.627419 + 0.179910i −0.627419 + 0.179910i
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 −1.55208 + 1.21262i −1.55208 + 1.21262i
906906 0 0
907907 −0.438371 + 0.898794i −0.438371 + 0.898794i 0.559193 + 0.829038i 0.311111π0.311111\pi
−0.997564 + 0.0697565i 0.977778π0.977778\pi
908908 0 0
909909 0 0
910910 0 0
911911 −1.24739 0.311009i −1.24739 0.311009i −0.438371 0.898794i 0.644444π-0.644444\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0.0348995 0.999391i 0.0348995 0.999391i
917917 0 0
918918 0 0
919919 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 0.766044 0.642788i 0.766044 0.642788i
926926 0 0
927927 1.02517 1.13856i 1.02517 1.13856i
928928 0 0
929929 0.614811 + 0.299864i 0.614811 + 0.299864i 0.719340 0.694658i 0.244444π-0.244444\pi
−0.104528 + 0.994522i 0.533333π0.533333\pi
930930 0 0
931931 0 0
932932 0 0
933933 −0.663721 0.165484i −0.663721 0.165484i
934934 0 0
935935 0 0
936936 0 0
937937 0 0 0.406737 0.913545i 0.366667π-0.366667\pi
−0.406737 + 0.913545i 0.633333π0.633333\pi
938938 0 0
939939 0.978148 0.207912i 0.978148 0.207912i
940940 −1.82143 + 1.75894i −1.82143 + 1.75894i
941941 0 0 −0.241922 0.970296i 0.577778π-0.577778\pi
0.241922 + 0.970296i 0.422222π0.422222\pi
942942 0 0
943943 0 0
944944 −0.402069 0.553400i −0.402069 0.553400i
945945 0 0
946946 0 0
947947 0.233956 0.642788i 0.233956 0.642788i −0.766044 0.642788i 0.777778π-0.777778\pi
1.00000 00
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 0 0 0.978148 0.207912i 0.0666667π-0.0666667\pi
−0.978148 + 0.207912i 0.933333π0.933333\pi
954954 0 0
955955 0.264675 + 2.51822i 0.264675 + 2.51822i
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 1.28479 + 0.0448659i 1.28479 + 0.0448659i
961961 2.50745 + 0.352399i 2.50745 + 0.352399i
962962 0 0
963963 0 0
964964 0 0
965965 0 0
966966 0 0
967967 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
968968 0 0
969969 0 0
970970 0 0
971971 −1.64728 + 0.535233i −1.64728 + 0.535233i −0.978148 0.207912i 0.933333π-0.933333\pi
−0.669131 + 0.743145i 0.733333π0.733333\pi
972972 −0.669131 0.743145i −0.669131 0.743145i
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 0 0 −0.438371 0.898794i 0.644444π-0.644444\pi
0.438371 + 0.898794i 0.355556π0.355556\pi
978978 0 0
979979 0 0
980980 1.11334 0.642788i 1.11334 0.642788i
981981 0 0
982982 0 0
983983 0.0952000 0.677383i 0.0952000 0.677383i −0.882948 0.469472i 0.844444π-0.844444\pi
0.978148 0.207912i 0.0666667π-0.0666667\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
−1.00000 π\pi
992992 0 0
993993 0.339707 + 0.0722070i 0.339707 + 0.0722070i
994994 0 0
995995 0.433213 0.108012i 0.433213 0.108012i
996996 0 0
997997 0 0 −0.788011 0.615661i 0.788889π-0.788889\pi
0.788011 + 0.615661i 0.211111π0.211111\pi
998998 0 0
999999 1.39963 + 0.623157i 1.39963 + 0.623157i
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 3267.1.be.a.1697.1 24
11.2 odd 10 3267.1.q.a.1211.1 6
11.3 even 5 inner 3267.1.be.a.995.1 24
11.4 even 5 inner 3267.1.be.a.1049.1 24
11.5 even 5 inner 3267.1.be.a.3155.1 24
11.6 odd 10 inner 3267.1.be.a.3155.1 24
11.7 odd 10 inner 3267.1.be.a.1049.1 24
11.8 odd 10 inner 3267.1.be.a.995.1 24
11.9 even 5 3267.1.q.a.1211.1 6
11.10 odd 2 CM 3267.1.be.a.1697.1 24
27.20 odd 18 inner 3267.1.be.a.2423.1 24
297.20 odd 90 3267.1.q.a.1937.1 yes 6
297.47 odd 90 inner 3267.1.be.a.1721.1 24
297.74 even 90 inner 3267.1.be.a.1721.1 24
297.101 even 90 3267.1.q.a.1937.1 yes 6
297.128 even 90 inner 3267.1.be.a.1775.1 24
297.182 even 90 inner 3267.1.be.a.614.1 24
297.236 odd 90 inner 3267.1.be.a.614.1 24
297.263 even 18 inner 3267.1.be.a.2423.1 24
297.290 odd 90 inner 3267.1.be.a.1775.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3267.1.q.a.1211.1 6 11.2 odd 10
3267.1.q.a.1211.1 6 11.9 even 5
3267.1.q.a.1937.1 yes 6 297.20 odd 90
3267.1.q.a.1937.1 yes 6 297.101 even 90
3267.1.be.a.614.1 24 297.182 even 90 inner
3267.1.be.a.614.1 24 297.236 odd 90 inner
3267.1.be.a.995.1 24 11.3 even 5 inner
3267.1.be.a.995.1 24 11.8 odd 10 inner
3267.1.be.a.1049.1 24 11.4 even 5 inner
3267.1.be.a.1049.1 24 11.7 odd 10 inner
3267.1.be.a.1697.1 24 1.1 even 1 trivial
3267.1.be.a.1697.1 24 11.10 odd 2 CM
3267.1.be.a.1721.1 24 297.47 odd 90 inner
3267.1.be.a.1721.1 24 297.74 even 90 inner
3267.1.be.a.1775.1 24 297.128 even 90 inner
3267.1.be.a.1775.1 24 297.290 odd 90 inner
3267.1.be.a.2423.1 24 27.20 odd 18 inner
3267.1.be.a.2423.1 24 297.263 even 18 inner
3267.1.be.a.3155.1 24 11.5 even 5 inner
3267.1.be.a.3155.1 24 11.6 odd 10 inner