Properties

Label 975.2.bp.d.149.1
Level 975975
Weight 22
Character 975.149
Analytic conductor 7.7857.785
Analytic rank 00
Dimension 44
CM discriminant -3
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [975,2,Mod(149,975)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(975, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("975.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 975=35213 975 = 3 \cdot 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 975.bp (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: 7.785414197077.78541419707
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 39)
Sato-Tate group: U(1)[D12]\mathrm{U}(1)[D_{12}]

Embedding invariants

Embedding label 149.1
Root 0.866025+0.500000i-0.866025 + 0.500000i of defining polynomial
Character χ\chi == 975.149
Dual form 975.2.bp.d.674.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.50000+0.866025i)q3+(1.732051.00000i)q4+(2.86603+0.767949i)q7+(1.50000+2.59808i)q9+3.46410q12+(2.500002.59808i)q13+(2.000003.46410i)q16+(7.830132.09808i)q19+(3.63397+3.63397i)q21+5.19615iq27+(5.732051.53590i)q28+(7.83013+7.83013i)q31+(5.19615+3.00000i)q36+(0.5621782.09808i)q37+(6.000001.73205i)q39+(0.8660251.50000i)q43+(6.000003.46410i)q48+(1.56218+0.901924i)q49+(1.732057.00000i)q52+(9.928209.92820i)q57+(4.33013+7.50000i)q61+(2.30385+8.59808i)q638.00000iq64+(0.7679490.205771i)q67+(9.366039.36603i)q73+(15.6603+4.19615i)q7612.1244q79+(4.50000+7.79423i)q81+(9.92820+2.66025i)q84+(9.160255.52628i)q91+(18.5263+4.96410i)q93+(4.40192+16.4282i)q97+O(q100)q+(1.50000 + 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.86603 + 0.767949i) q^{7} +(1.50000 + 2.59808i) q^{9} +3.46410 q^{12} +(2.50000 - 2.59808i) q^{13} +(2.00000 - 3.46410i) q^{16} +(-7.83013 - 2.09808i) q^{19} +(3.63397 + 3.63397i) q^{21} +5.19615i q^{27} +(5.73205 - 1.53590i) q^{28} +(-7.83013 + 7.83013i) q^{31} +(5.19615 + 3.00000i) q^{36} +(-0.562178 - 2.09808i) q^{37} +(6.00000 - 1.73205i) q^{39} +(-0.866025 - 1.50000i) q^{43} +(6.00000 - 3.46410i) q^{48} +(1.56218 + 0.901924i) q^{49} +(1.73205 - 7.00000i) q^{52} +(-9.92820 - 9.92820i) q^{57} +(4.33013 + 7.50000i) q^{61} +(2.30385 + 8.59808i) q^{63} -8.00000i q^{64} +(0.767949 - 0.205771i) q^{67} +(9.36603 - 9.36603i) q^{73} +(-15.6603 + 4.19615i) q^{76} -12.1244 q^{79} +(-4.50000 + 7.79423i) q^{81} +(9.92820 + 2.66025i) q^{84} +(9.16025 - 5.52628i) q^{91} +(-18.5263 + 4.96410i) q^{93} +(-4.40192 + 16.4282i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+6q3+8q7+6q9+10q13+8q1614q19+18q21+16q2814q31+22q37+24q39+24q4818q4912q57+30q63+10q67+34q7328q76+28q97+O(q100) 4 q + 6 q^{3} + 8 q^{7} + 6 q^{9} + 10 q^{13} + 8 q^{16} - 14 q^{19} + 18 q^{21} + 16 q^{28} - 14 q^{31} + 22 q^{37} + 24 q^{39} + 24 q^{48} - 18 q^{49} - 12 q^{57} + 30 q^{63} + 10 q^{67} + 34 q^{73} - 28 q^{76}+ \cdots - 28 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/975Z)×\left(\mathbb{Z}/975\mathbb{Z}\right)^\times.

nn 301301 326326 352352
χ(n)\chi(n) e(512)e\left(\frac{5}{12}\right) 1-1 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
33 1.50000 + 0.866025i 0.866025 + 0.500000i
44 1.73205 1.00000i 0.866025 0.500000i
55 0 0
66 0 0
77 2.86603 + 0.767949i 1.08326 + 0.290258i 0.755929 0.654654i 0.227186π-0.227186\pi
0.327327 + 0.944911i 0.393852π0.393852\pi
88 0 0
99 1.50000 + 2.59808i 0.500000 + 0.866025i
1010 0 0
1111 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
1212 3.46410 1.00000
1313 2.50000 2.59808i 0.693375 0.720577i
1414 0 0
1515 0 0
1616 2.00000 3.46410i 0.500000 0.866025i
1717 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
1818 0 0
1919 −7.83013 2.09808i −1.79635 0.481332i −0.802955 0.596040i 0.796740π-0.796740\pi
−0.993399 + 0.114708i 0.963407π0.963407\pi
2020 0 0
2121 3.63397 + 3.63397i 0.792998 + 0.792998i
2222 0 0
2323 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
2424 0 0
2525 0 0
2626 0 0
2727 5.19615i 1.00000i
2828 5.73205 1.53590i 1.08326 0.290258i
2929 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
3030 0 0
3131 −7.83013 + 7.83013i −1.40633 + 1.40633i −0.628619 + 0.777714i 0.716379π0.716379\pi
−0.777714 + 0.628619i 0.783621π0.783621\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 5.19615 + 3.00000i 0.866025 + 0.500000i
3737 −0.562178 2.09808i −0.0924215 0.344922i 0.904194 0.427121i 0.140472π-0.140472\pi
−0.996616 + 0.0821995i 0.973806π0.973806\pi
3838 0 0
3939 6.00000 1.73205i 0.960769 0.277350i
4040 0 0
4141 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
4242 0 0
4343 −0.866025 1.50000i −0.132068 0.228748i 0.792406 0.609994i 0.208828π-0.208828\pi
−0.924473 + 0.381246i 0.875495π0.875495\pi
4444 0 0
4545 0 0
4646 0 0
4747 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
4848 6.00000 3.46410i 0.866025 0.500000i
4949 1.56218 + 0.901924i 0.223168 + 0.128846i
5050 0 0
5151 0 0
5252 1.73205 7.00000i 0.240192 0.970725i
5353 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
5454 0 0
5555 0 0
5656 0 0
5757 −9.92820 9.92820i −1.31502 1.31502i
5858 0 0
5959 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
6060 0 0
6161 4.33013 + 7.50000i 0.554416 + 0.960277i 0.997949 + 0.0640184i 0.0203916π0.0203916\pi
−0.443533 + 0.896258i 0.646275π0.646275\pi
6262 0 0
6363 2.30385 + 8.59808i 0.290258 + 1.08326i
6464 8.00000i 1.00000i
6565 0 0
6666 0 0
6767 0.767949 0.205771i 0.0938199 0.0251390i −0.211604 0.977356i 0.567869π-0.567869\pi
0.305424 + 0.952217i 0.401202π0.401202\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
7272 0 0
7373 9.36603 9.36603i 1.09621 1.09621i 0.101361 0.994850i 0.467680π-0.467680\pi
0.994850 0.101361i 0.0323196π-0.0323196\pi
7474 0 0
7575 0 0
7676 −15.6603 + 4.19615i −1.79635 + 0.481332i
7777 0 0
7878 0 0
7979 −12.1244 −1.36410 −0.682048 0.731307i 0.738911π-0.738911\pi
−0.682048 + 0.731307i 0.738911π0.738911\pi
8080 0 0
8181 −4.50000 + 7.79423i −0.500000 + 0.866025i
8282 0 0
8383 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
8484 9.92820 + 2.66025i 1.08326 + 0.290258i
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
9090 0 0
9191 9.16025 5.52628i 0.960256 0.579311i
9292 0 0
9393 −18.5263 + 4.96410i −1.92109 + 0.514753i
9494 0 0
9595 0 0
9696 0 0
9797 −4.40192 + 16.4282i −0.446948 + 1.66803i 0.263795 + 0.964579i 0.415026π0.415026\pi
−0.710742 + 0.703452i 0.751641π0.751641\pi
9898 0 0
9999 0 0
100100 0 0
101101 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
102102 0 0
103103 15.5885 1.53598 0.767988 0.640464i 0.221258π-0.221258\pi
0.767988 + 0.640464i 0.221258π0.221258\pi
104104 0 0
105105 0 0
106106 0 0
107107 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
108108 5.19615 + 9.00000i 0.500000 + 0.866025i
109109 −5.16987 + 5.16987i −0.495184 + 0.495184i −0.909935 0.414751i 0.863869π-0.863869\pi
0.414751 + 0.909935i 0.363869π0.363869\pi
110110 0 0
111111 0.973721 3.63397i 0.0924215 0.344922i
112112 8.39230 8.39230i 0.792998 0.792998i
113113 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
114114 0 0
115115 0 0
116116 0 0
117117 10.5000 + 2.59808i 0.970725 + 0.240192i
118118 0 0
119119 0 0
120120 0 0
121121 9.52628 5.50000i 0.866025 0.500000i
122122 0 0
123123 0 0
124124 −5.73205 + 21.3923i −0.514753 + 1.92109i
125125 0 0
126126 0 0
127127 −0.500000 + 0.866025i −0.0443678 + 0.0768473i −0.887357 0.461084i 0.847461π-0.847461\pi
0.842989 + 0.537931i 0.180794π0.180794\pi
128128 0 0
129129 3.00000i 0.264135i
130130 0 0
131131 0 0 1.00000 00
−1.00000 π\pi
132132 0 0
133133 −20.8301 12.0263i −1.80620 1.04281i
134134 0 0
135135 0 0
136136 0 0
137137 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
138138 0 0
139139 −3.50000 6.06218i −0.296866 0.514187i 0.678551 0.734553i 0.262608π-0.262608\pi
−0.975417 + 0.220366i 0.929275π0.929275\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 12.0000 1.00000
145145 0 0
146146 0 0
147147 1.56218 + 2.70577i 0.128846 + 0.223168i
148148 −3.07180 3.07180i −0.252500 0.252500i
149149 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
150150 0 0
151151 −14.1244 14.1244i −1.14942 1.14942i −0.986666 0.162758i 0.947961π-0.947961\pi
−0.162758 0.986666i 0.552039π-0.552039\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 8.66025 9.00000i 0.693375 0.720577i
157157 11.0000i 0.877896i 0.898513 + 0.438948i 0.144649π0.144649\pi
−0.898513 + 0.438948i 0.855351π0.855351\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 −20.6244 5.52628i −1.61542 0.432852i −0.665771 0.746156i 0.731897π-0.731897\pi
−0.949653 + 0.313304i 0.898564π0.898564\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
168168 0 0
169169 −0.500000 12.9904i −0.0384615 0.999260i
170170 0 0
171171 −6.29423 23.4904i −0.481332 1.79635i
172172 −3.00000 1.73205i −0.228748 0.132068i
173173 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
180180 0 0
181181 6.92820i 0.514969i 0.966282 + 0.257485i 0.0828937π0.0828937\pi
−0.966282 + 0.257485i 0.917106π0.917106\pi
182182 0 0
183183 15.0000i 1.10883i
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 −3.99038 + 14.8923i −0.290258 + 1.08326i
190190 0 0
191191 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
192192 6.92820 12.0000i 0.500000 0.866025i
193193 7.06218 + 26.3564i 0.508347 + 1.89718i 0.436365 + 0.899770i 0.356266π0.356266\pi
0.0719816 + 0.997406i 0.477068π0.477068\pi
194194 0 0
195195 0 0
196196 3.60770 0.257693
197197 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
198198 0 0
199199 14.7224 8.50000i 1.04365 0.602549i 0.122782 0.992434i 0.460818π-0.460818\pi
0.920864 + 0.389885i 0.127485π0.127485\pi
200200 0 0
201201 1.33013 + 0.356406i 0.0938199 + 0.0251390i
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 −4.00000 13.8564i −0.277350 0.960769i
209209 0 0
210210 0 0
211211 12.9904 22.5000i 0.894295 1.54896i 0.0596196 0.998221i 0.481011π-0.481011\pi
0.834675 0.550743i 0.185655π-0.185655\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 −28.4545 + 16.4282i −1.93162 + 1.11522i
218218 0 0
219219 22.1603 5.93782i 1.49745 0.401241i
220220 0 0
221221 0 0
222222 0 0
223223 −12.0263 + 3.22243i −0.805339 + 0.215790i −0.637927 0.770097i 0.720208π-0.720208\pi
−0.167412 + 0.985887i 0.553541π0.553541\pi
224224 0 0
225225 0 0
226226 0 0
227227 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
228228 −27.1244 7.26795i −1.79635 0.481332i
229229 −21.3923 21.3923i −1.41364 1.41364i −0.726900 0.686743i 0.759040π-0.759040\pi
−0.686743 0.726900i 0.740960π-0.740960\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 1.00000 00
−1.00000 π\pi
234234 0 0
235235 0 0
236236 0 0
237237 −18.1865 10.5000i −1.18134 0.682048i
238238 0 0
239239 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
240240 0 0
241241 −2.50962 + 9.36603i −0.161659 + 0.603319i 0.836784 + 0.547533i 0.184433π0.184433\pi
−0.998443 + 0.0557856i 0.982234π0.982234\pi
242242 0 0
243243 −13.5000 + 7.79423i −0.866025 + 0.500000i
244244 15.0000 + 8.66025i 0.960277 + 0.554416i
245245 0 0
246246 0 0
247247 −25.0263 + 15.0981i −1.59238 + 0.960668i
248248 0 0
249249 0 0
250250 0 0
251251 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
252252 12.5885 + 12.5885i 0.792998 + 0.792998i
253253 0 0
254254 0 0
255255 0 0
256256 −8.00000 13.8564i −0.500000 0.866025i
257257 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
258258 0 0
259259 6.44486i 0.400464i
260260 0 0
261261 0 0
262262 0 0
263263 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 1.12436 1.12436i 0.0686810 0.0686810i
269269 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
270270 0 0
271271 −9.16025 + 2.45448i −0.556446 + 0.149099i −0.526073 0.850439i 0.676336π-0.676336\pi
−0.0303728 + 0.999539i 0.509669π0.509669\pi
272272 0 0
273273 18.5263 0.356406i 1.12126 0.0215707i
274274 0 0
275275 0 0
276276 0 0
277277 −10.3923 18.0000i −0.624413 1.08152i −0.988654 0.150210i 0.952005π-0.952005\pi
0.364241 0.931305i 0.381328π-0.381328\pi
278278 0 0
279279 −32.0885 8.59808i −1.92109 0.514753i
280280 0 0
281281 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
282282 0 0
283283 −12.5000 + 21.6506i −0.743048 + 1.28700i 0.208053 + 0.978117i 0.433287π0.433287\pi
−0.951101 + 0.308879i 0.900046π0.900046\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −8.50000 + 14.7224i −0.500000 + 0.866025i
290290 0 0
291291 −20.8301 + 20.8301i −1.22108 + 1.22108i
292292 6.85641 25.5885i 0.401241 1.49745i
293293 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 0 0
301301 −1.33013 4.96410i −0.0766672 0.286126i
302302 0 0
303303 0 0
304304 −22.9282 + 22.9282i −1.31502 + 1.31502i
305305 0 0
306306 0 0
307307 16.6340 16.6340i 0.949351 0.949351i −0.0494267 0.998778i 0.515739π-0.515739\pi
0.998778 + 0.0494267i 0.0157394π0.0157394\pi
308308 0 0
309309 23.3827 + 13.5000i 1.33019 + 0.767988i
310310 0 0
311311 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
312312 0 0
313313 32.9090i 1.86012i −0.367402 0.930062i 0.619753π-0.619753\pi
0.367402 0.930062i 0.380247π-0.380247\pi
314314 0 0
315315 0 0
316316 −21.0000 + 12.1244i −1.18134 + 0.682048i
317317 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
318318 0 0
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 0 0
324324 18.0000i 1.00000i
325325 0 0
326326 0 0
327327 −12.2321 + 3.27757i −0.676434 + 0.181250i
328328 0 0
329329 0 0
330330 0 0
331331 −34.1865 9.16025i −1.87906 0.503493i −0.999622 0.0274825i 0.991251π-0.991251\pi
−0.879440 0.476011i 0.842082π-0.842082\pi
332332 0 0
333333 4.60770 4.60770i 0.252500 0.252500i
334334 0 0
335335 0 0
336336 19.8564 5.32051i 1.08326 0.290258i
337337 29.0000 1.57973 0.789865 0.613280i 0.210150π-0.210150\pi
0.789865 + 0.613280i 0.210150π0.210150\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 −10.9019 10.9019i −0.588649 0.588649i
344344 0 0
345345 0 0
346346 0 0
347347 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
348348 0 0
349349 4.40192 1.17949i 0.235630 0.0631368i −0.139072 0.990282i 0.544412π-0.544412\pi
0.374701 + 0.927146i 0.377745π0.377745\pi
350350 0 0
351351 13.5000 + 12.9904i 0.720577 + 0.693375i
352352 0 0
353353 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
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 40.4545 + 23.3564i 2.12918 + 1.22928i
362362 0 0
363363 19.0526 1.00000
364364 10.3397 18.7321i 0.541950 0.981826i
365365 0 0
366366 0 0
367367 26.8468 + 15.5000i 1.40139 + 0.809093i 0.994535 0.104399i 0.0332919π-0.0332919\pi
0.406855 + 0.913493i 0.366625π0.366625\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 −27.1244 + 27.1244i −1.40633 + 1.40633i
373373 31.5000 18.1865i 1.63101 0.941663i 0.647225 0.762299i 0.275929π-0.275929\pi
0.983783 0.179364i 0.0574041π-0.0574041\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 4.55256 + 16.9904i 0.233849 + 0.872737i 0.978664 + 0.205466i 0.0658711π0.0658711\pi
−0.744815 + 0.667271i 0.767462π0.767462\pi
380380 0 0
381381 −1.50000 + 0.866025i −0.0768473 + 0.0443678i
382382 0 0
383383 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
384384 0 0
385385 0 0
386386 0 0
387387 2.59808 4.50000i 0.132068 0.228748i
388388 8.80385 + 32.8564i 0.446948 + 1.66803i
389389 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 −27.8923 7.47372i −1.39987 0.375095i −0.521575 0.853206i 0.674655π-0.674655\pi
−0.878300 + 0.478110i 0.841322π0.841322\pi
398398 0 0
399399 −20.8301 36.0788i −1.04281 1.80620i
400400 0 0
401401 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
402402 0 0
403403 0.767949 + 39.9186i 0.0382543 + 1.98849i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 3.42820 + 0.918584i 0.169514 + 0.0454211i 0.342578 0.939490i 0.388700π-0.388700\pi
−0.173064 + 0.984911i 0.555367π0.555367\pi
410410 0 0
411411 0 0
412412 27.0000 15.5885i 1.33019 0.767988i
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 12.1244i 0.593732i
418418 0 0
419419 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
420420 0 0
421421 27.6865 27.6865i 1.34936 1.34936i 0.463002 0.886357i 0.346772π-0.346772\pi
0.886357 0.463002i 0.153228π-0.153228\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 6.65064 + 24.8205i 0.321847 + 1.20115i
428428 0 0
429429 0 0
430430 0 0
431431 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
432432 18.0000 + 10.3923i 0.866025 + 0.500000i
433433 17.5000 + 30.3109i 0.840996 + 1.45665i 0.889053 + 0.457804i 0.151364π0.151364\pi
−0.0480569 + 0.998845i 0.515303π0.515303\pi
434434 0 0
435435 0 0
436436 −3.78461 + 14.1244i −0.181250 + 0.676434i
437437 0 0
438438 0 0
439439 34.5000 + 19.9186i 1.64660 + 0.950662i 0.978412 + 0.206666i 0.0662612π0.0662612\pi
0.668184 + 0.743996i 0.267072π0.267072\pi
440440 0 0
441441 5.41154i 0.257693i
442442 0 0
443443 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
444444 −1.94744 7.26795i −0.0924215 0.344922i
445445 0 0
446446 0 0
447447 0 0
448448 6.14359 22.9282i 0.290258 1.08326i
449449 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
450450 0 0
451451 0 0
452452 0 0
453453 −8.95448 33.4186i −0.420718 1.57014i
454454 0 0
455455 0 0
456456 0 0
457457 36.2846 9.72243i 1.69732 0.454796i 0.725059 0.688686i 0.241812π-0.241812\pi
0.972263 + 0.233890i 0.0751456π0.0751456\pi
458458 0 0
459459 0 0
460460 0 0
461461 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
462462 0 0
463463 22.3660 22.3660i 1.03944 1.03944i 0.0402476 0.999190i 0.487185π-0.487185\pi
0.999190 0.0402476i 0.0128147π-0.0128147\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 1.00000 00
−1.00000 π\pi
468468 20.7846 6.00000i 0.960769 0.277350i
469469 2.35898 0.108928
470470 0 0
471471 −9.52628 + 16.5000i −0.438948 + 0.760280i
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
480480 0 0
481481 −6.85641 3.78461i −0.312625 0.172563i
482482 0 0
483483 0 0
484484 11.0000 19.0526i 0.500000 0.866025i
485485 0 0
486486 0 0
487487 −7.41858 + 27.6865i −0.336168 + 1.25460i 0.566429 + 0.824110i 0.308325π0.308325\pi
−0.902597 + 0.430486i 0.858342π0.858342\pi
488488 0 0
489489 −26.1506 26.1506i −1.18257 1.18257i
490490 0 0
491491 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 11.4641 + 42.7846i 0.514753 + 1.92109i
497497 0 0
498498 0 0
499499 −0.411543 + 0.411543i −0.0184232 + 0.0184232i −0.716258 0.697835i 0.754147π-0.754147\pi
0.697835 + 0.716258i 0.254147π0.254147\pi
500500 0 0
501501 0 0
502502 0 0
503503 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
504504 0 0
505505 0 0
506506 0 0
507507 10.5000 19.9186i 0.466321 0.884615i
508508 2.00000i 0.0887357i
509509 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
510510 0 0
511511 34.0359 19.6506i 1.50566 0.869293i
512512 0 0
513513 10.9019 40.6865i 0.481332 1.79635i
514514 0 0
515515 0 0
516516 −3.00000 5.19615i −0.132068 0.228748i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0 0 1.00000 00
−1.00000 π\pi
522522 0 0
523523 6.92820 + 4.00000i 0.302949 + 0.174908i 0.643767 0.765222i 0.277371π-0.277371\pi
−0.340818 + 0.940129i 0.610704π0.610704\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 −11.5000 19.9186i −0.500000 0.866025i
530530 0 0
531531 0 0
532532 −48.1051 −2.08562
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 13.1506 + 13.1506i 0.565390 + 0.565390i 0.930834 0.365444i 0.119083π-0.119083\pi
−0.365444 + 0.930834i 0.619083π0.619083\pi
542542 0 0
543543 −6.00000 + 10.3923i −0.257485 + 0.445976i
544544 0 0
545545 0 0
546546 0 0
547547 41.0000i 1.75303i −0.481371 0.876517i 0.659861π-0.659861\pi
0.481371 0.876517i 0.340139π-0.340139\pi
548548 0 0
549549 −12.9904 + 22.5000i −0.554416 + 0.960277i
550550 0 0
551551 0 0
552552 0 0
553553 −34.7487 9.31089i −1.47767 0.395939i
554554 0 0
555555 0 0
556556 −12.1244 7.00000i −0.514187 0.296866i
557557 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
558558 0 0
559559 −6.06218 1.50000i −0.256403 0.0634432i
560560 0 0
561561 0 0
562562 0 0
563563 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
564564 0 0
565565 0 0
566566 0 0
567567 −18.8827 + 18.8827i −0.792998 + 0.792998i
568568 0 0
569569 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
570570 0 0
571571 16.0000i 0.669579i 0.942293 + 0.334790i 0.108665π0.108665\pi
−0.942293 + 0.334790i 0.891335π0.891335\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 20.7846 12.0000i 0.866025 0.500000i
577577 16.0718 + 16.0718i 0.669078 + 0.669078i 0.957503 0.288425i 0.0931316π-0.0931316\pi
−0.288425 + 0.957503i 0.593132π0.593132\pi
578578 0 0
579579 −12.2321 + 45.6506i −0.508347 + 1.89718i
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
588588 5.41154 + 3.12436i 0.223168 + 0.128846i
589589 77.7391 44.8827i 3.20318 1.84936i
590590 0 0
591591 0 0
592592 −8.39230 2.24871i −0.344922 0.0924215i
593593 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
594594 0 0
595595 0 0
596596 0 0
597597 29.4449 1.20510
598598 0 0
599599 0 0 1.00000 00
−1.00000 π\pi
600600 0 0
601601 −20.7846 + 36.0000i −0.847822 + 1.46847i 0.0353259 + 0.999376i 0.488753π0.488753\pi
−0.883148 + 0.469095i 0.844580π0.844580\pi
602602 0 0
603603 1.68653 + 1.68653i 0.0686810 + 0.0686810i
604604 −38.5885 10.3397i −1.57014 0.420718i
605605 0 0
606606 0 0
607607 17.3205 10.0000i 0.703018 0.405887i −0.105453 0.994424i 0.533629π-0.533629\pi
0.808470 + 0.588537i 0.200296π0.200296\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 47.7487 12.7942i 1.92855 0.516754i 0.949156 0.314806i 0.101939π-0.101939\pi
0.979396 0.201948i 0.0647272π-0.0647272\pi
614614 0 0
615615 0 0
616616 0 0
617617 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
618618 0 0
619619 31.8827 + 31.8827i 1.28147 + 1.28147i 0.939829 + 0.341644i 0.110984π0.110984\pi
0.341644 + 0.939829i 0.389016π0.389016\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 6.00000 24.2487i 0.240192 0.970725i
625625 0 0
626626 0 0
627627 0 0
628628 11.0000 + 19.0526i 0.438948 + 0.760280i
629629 0 0
630630 0 0
631631 −9.00962 + 33.6244i −0.358667 + 1.33856i 0.517139 + 0.855901i 0.326997π0.326997\pi
−0.875806 + 0.482663i 0.839670π0.839670\pi
632632 0 0
633633 38.9711 22.5000i 1.54896 0.894295i
634634 0 0
635635 0 0
636636 0 0
637637 6.24871 1.80385i 0.247583 0.0714710i
638638 0 0
639639 0 0
640640 0 0
641641 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
642642 0 0
643643 −5.11474 + 19.0885i −0.201706 + 0.752775i 0.788723 + 0.614749i 0.210743π0.210743\pi
−0.990429 + 0.138027i 0.955924π0.955924\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
648648 0 0
649649 0 0
650650 0 0
651651 −56.9090 −2.23044
652652 −41.2487 + 11.0526i −1.61542 + 0.432852i
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 38.3827 + 10.2846i 1.49745 + 0.401241i
658658 0 0
659659 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
660660 0 0
661661 44.1147 11.8205i 1.71586 0.459764i 0.739014 0.673690i 0.235292π-0.235292\pi
0.976850 + 0.213925i 0.0686249π0.0686249\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −20.8301 5.58142i −0.805339 0.215790i
670670 0 0
671671 0 0
672672 0 0
673673 −25.1147 + 43.5000i −0.968102 + 1.67680i −0.267063 + 0.963679i 0.586053π0.586053\pi
−0.701039 + 0.713123i 0.747280π0.747280\pi
674674 0 0
675675 0 0
676676 −13.8564 22.0000i −0.532939 0.846154i
677677 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
678678 0 0
679679 −25.2321 + 43.7032i −0.968317 + 1.67717i
680680 0 0
681681 0 0
682682 0 0
683683 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
684684 −34.3923 34.3923i −1.31502 1.31502i
685685 0 0
686686 0 0
687687 −13.5622 50.6147i −0.517429 1.93107i
688688 −6.92820 −0.264135
689689 0 0
690690 0 0
691691 1.48076 + 5.52628i 0.0563308 + 0.210230i 0.988355 0.152167i 0.0486252π-0.0486252\pi
−0.932024 + 0.362397i 0.881959π0.881959\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 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
702702 0 0
703703 17.6077i 0.664087i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 −8.74871 + 32.6506i −0.328565 + 1.22622i 0.582115 + 0.813107i 0.302225π0.302225\pi
−0.910679 + 0.413114i 0.864441π0.864441\pi
710710 0 0
711711 −18.1865 31.5000i −0.682048 1.18134i
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
720720 0 0
721721 44.6769 + 11.9711i 1.66386 + 0.445829i
722722 0 0
723723 −11.8756 + 11.8756i −0.441660 + 0.441660i
724724 6.92820 + 12.0000i 0.257485 + 0.445976i
725725 0 0
726726 0 0
727727 −49.0000 −1.81731 −0.908655 0.417548i 0.862889π-0.862889\pi
−0.908655 + 0.417548i 0.862889π0.862889\pi
728728 0 0
729729 −27.0000 −1.00000
730730 0 0
731731 0 0
732732 15.0000 + 25.9808i 0.554416 + 0.960277i
733733 −30.3468 30.3468i −1.12088 1.12088i −0.991609 0.129275i 0.958735π-0.958735\pi
−0.129275 0.991609i 0.541265π-0.541265\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 46.4186 12.4378i 1.70754 0.457533i 0.732717 0.680534i 0.238252π-0.238252\pi
0.974818 + 0.223001i 0.0715853π0.0715853\pi
740740 0 0
741741 −50.6147 + 0.973721i −1.85938 + 0.0357705i
742742 0 0
743743 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −15.0000 8.66025i −0.547358 0.316017i 0.200698 0.979653i 0.435679π-0.435679\pi
−0.748056 + 0.663636i 0.769012π0.769012\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 7.98076 + 29.7846i 0.290258 + 1.08326i
757757 −42.0000 24.2487i −1.52652 0.881334i −0.999505 0.0314762i 0.989979π-0.989979\pi
−0.527011 0.849858i 0.676688π-0.676688\pi
758758 0 0
759759 0 0
760760 0 0
761761 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
762762 0 0
763763 −18.7872 + 10.8468i −0.680142 + 0.392680i
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 27.7128i 1.00000i
769769 9.77757 + 36.4904i 0.352588 + 1.31588i 0.883493 + 0.468445i 0.155186π0.155186\pi
−0.530904 + 0.847432i 0.678148π0.678148\pi
770770 0 0
771771 0 0
772772 38.5885 + 38.5885i 1.38883 + 1.38883i
773773 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
774774 0 0
775775 0 0
776776 0 0
777777 5.58142 9.66730i 0.200232 0.346812i
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 6.24871 3.60770i 0.223168 0.128846i
785785 0 0
786786 0 0
787787 51.3827 + 13.7679i 1.83159 + 0.490774i 0.998092 0.0617409i 0.0196653π-0.0196653\pi
0.833503 + 0.552515i 0.186332π0.186332\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 30.3109 + 7.50000i 1.07637 + 0.266333i
794794 0 0
795795 0 0
796796 17.0000 29.4449i 0.602549 1.04365i
797797 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
798798 0 0
799799 0 0
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 2.66025 0.712813i 0.0938199 0.0251390i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
810810 0 0
811811 −17.3468 + 17.3468i −0.609128 + 0.609128i −0.942718 0.333590i 0.891740π-0.891740\pi
0.333590 + 0.942718i 0.391740π0.391740\pi
812812 0 0
813813 −15.8660 4.25129i −0.556446 0.149099i
814814 0 0
815815 0 0
816816 0 0
817817 3.63397 + 13.5622i 0.127137 + 0.474481i
818818 0 0
819819 28.0981 + 15.5096i 0.981826 + 0.541950i
820820 0 0
821821 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
822822 0 0
823823 −12.1244 21.0000i −0.422628 0.732014i 0.573567 0.819159i 0.305559π-0.305559\pi
−0.996196 + 0.0871445i 0.972226π0.972226\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
828828 0 0
829829 45.8993 + 26.5000i 1.59415 + 0.920383i 0.992584 + 0.121560i 0.0387897π0.0387897\pi
0.601566 + 0.798823i 0.294544π0.294544\pi
830830 0 0
831831 36.0000i 1.24883i
832832 −20.7846 20.0000i −0.720577 0.693375i
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 −40.6865 40.6865i −1.40633 1.40633i
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 −14.5000 25.1147i −0.500000 0.866025i
842842 0 0
843843 0 0
844844 51.9615i 1.78859i
845845 0 0
846846 0 0
847847 31.5263 8.44744i 1.08326 0.290258i
848848 0 0
849849 −37.5000 + 21.6506i −1.28700 + 0.743048i
850850 0 0
851851 0 0
852852 0 0
853853 5.88269 5.88269i 0.201419 0.201419i −0.599189 0.800608i 0.704510π-0.704510\pi
0.800608 + 0.599189i 0.204510π0.204510\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 1.00000 00
−1.00000 π\pi
858858 0 0
859859 −57.1577 −1.95019 −0.975097 0.221777i 0.928814π-0.928814\pi
−0.975097 + 0.221777i 0.928814π0.928814\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
864864 0 0
865865 0 0
866866 0 0
867867 −25.5000 + 14.7224i −0.866025 + 0.500000i
868868 −32.8564 + 56.9090i −1.11522 + 1.93162i
869869 0 0
870870 0 0
871871 1.38526 2.50962i 0.0469379 0.0850352i
872872 0 0
873873 −49.2846 + 13.2058i −1.66803 + 0.446948i
874874 0 0
875875 0 0
876876 32.4449 32.4449i 1.09621 1.09621i
877877 15.0981 56.3468i 0.509826 1.90270i 0.0877308 0.996144i 0.472038π-0.472038\pi
0.422095 0.906552i 0.361295π-0.361295\pi
878878 0 0
879879 0 0
880880 0 0
881881 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
882882 0 0
883883 −55.0000 −1.85090 −0.925449 0.378873i 0.876312π-0.876312\pi
−0.925449 + 0.378873i 0.876312π0.876312\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
888888 0 0
889889 −2.09808 + 2.09808i −0.0703672 + 0.0703672i
890890 0 0
891891 0 0
892892 −17.6077 + 17.6077i −0.589549 + 0.589549i
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 0 0
901901 0 0
902902 0 0
903903 2.30385 8.59808i 0.0766672 0.286126i
904904 0 0
905905 0 0
906906 0 0
907907 −20.0000 + 34.6410i −0.664089 + 1.15024i 0.315442 + 0.948945i 0.397847π0.397847\pi
−0.979531 + 0.201291i 0.935486π0.935486\pi
908908 0 0
909909 0 0
910910 0 0
911911 0 0 1.00000 00
−1.00000 π\pi
912912 −54.2487 + 14.5359i −1.79635 + 0.481332i
913913 0 0
914914 0 0
915915 0 0
916916 −58.4449 15.6603i −1.93107 0.517429i
917917 0 0
918918 0 0
919919 −15.5885 27.0000i −0.514216 0.890648i −0.999864 0.0164935i 0.994750π-0.994750\pi
0.485648 0.874154i 0.338584π-0.338584\pi
920920 0 0
921921 39.3564 10.5455i 1.29684 0.347487i
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 23.3827 + 40.5000i 0.767988 + 1.33019i
928928 0 0
929929 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
930930 0 0
931931 −10.3397 10.3397i −0.338871 0.338871i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 55.4256i 1.81068i 0.424691 + 0.905338i 0.360383π0.360383\pi
−0.424691 + 0.905338i 0.639617π0.639617\pi
938938 0 0
939939 28.5000 49.3634i 0.930062 1.61092i
940940 0 0
941941 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
948948 −42.0000 −1.36410
949949 −0.918584 47.7487i −0.0298185 1.54999i
950950 0 0
951951 0 0
952952 0 0
953953 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 91.6218i 2.95554i
962962 0 0
963963 0 0
964964 5.01924 + 18.7321i 0.161659 + 0.603319i
965965 0 0
966966 0 0
967967 −19.4449 19.4449i −0.625305 0.625305i 0.321578 0.946883i 0.395787π-0.395787\pi
−0.946883 + 0.321578i 0.895787π0.895787\pi
968968 0 0
969969 0 0
970970 0 0
971971 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
972972 −15.5885 + 27.0000i −0.500000 + 0.866025i
973973 −5.37564 20.0622i −0.172335 0.643164i
974974 0 0
975975 0 0
976976 34.6410 1.10883
977977 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
978978 0 0
979979 0 0
980980 0 0
981981 −21.1865 5.67691i −0.676434 0.181250i
982982 0 0
983983 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 −28.2487 + 51.1769i −0.898711 + 1.62815i
989989 0 0
990990 0 0
991991 −22.0000 + 38.1051i −0.698853 + 1.21045i 0.270011 + 0.962857i 0.412973π0.412973\pi
−0.968864 + 0.247592i 0.920361π0.920361\pi
992992 0 0
993993 −43.3468 43.3468i −1.37557 1.37557i
994994 0 0
995995 0 0
996996 0 0
997997 51.0955 29.5000i 1.61821 0.934274i 0.630828 0.775923i 0.282715π-0.282715\pi
0.987383 0.158352i 0.0506179π-0.0506179\pi
998998 0 0
999999 10.9019 2.92116i 0.344922 0.0924215i
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 975.2.bp.d.149.1 4
3.2 odd 2 CM 975.2.bp.d.149.1 4
5.2 odd 4 39.2.k.a.32.1 yes 4
5.3 odd 4 975.2.bo.c.851.1 4
5.4 even 2 975.2.bp.a.149.1 4
13.11 odd 12 975.2.bp.a.674.1 4
15.2 even 4 39.2.k.a.32.1 yes 4
15.8 even 4 975.2.bo.c.851.1 4
15.14 odd 2 975.2.bp.a.149.1 4
20.7 even 4 624.2.cn.b.305.1 4
39.11 even 12 975.2.bp.a.674.1 4
60.47 odd 4 624.2.cn.b.305.1 4
65.2 even 12 507.2.k.c.89.1 4
65.7 even 12 507.2.f.c.437.1 4
65.12 odd 4 507.2.k.c.188.1 4
65.17 odd 12 507.2.f.b.239.1 4
65.22 odd 12 507.2.f.c.239.1 4
65.24 odd 12 inner 975.2.bp.d.674.1 4
65.32 even 12 507.2.f.b.437.1 4
65.37 even 12 39.2.k.a.11.1 4
65.42 odd 12 507.2.k.b.80.1 4
65.47 even 4 507.2.k.b.488.1 4
65.57 even 4 507.2.k.a.488.1 4
65.62 odd 12 507.2.k.a.80.1 4
65.63 even 12 975.2.bo.c.401.1 4
195.2 odd 12 507.2.k.c.89.1 4
195.17 even 12 507.2.f.b.239.1 4
195.32 odd 12 507.2.f.b.437.1 4
195.47 odd 4 507.2.k.b.488.1 4
195.62 even 12 507.2.k.a.80.1 4
195.77 even 4 507.2.k.c.188.1 4
195.89 even 12 inner 975.2.bp.d.674.1 4
195.107 even 12 507.2.k.b.80.1 4
195.122 odd 4 507.2.k.a.488.1 4
195.128 odd 12 975.2.bo.c.401.1 4
195.137 odd 12 507.2.f.c.437.1 4
195.152 even 12 507.2.f.c.239.1 4
195.167 odd 12 39.2.k.a.11.1 4
260.167 odd 12 624.2.cn.b.401.1 4
780.167 even 12 624.2.cn.b.401.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.k.a.11.1 4 65.37 even 12
39.2.k.a.11.1 4 195.167 odd 12
39.2.k.a.32.1 yes 4 5.2 odd 4
39.2.k.a.32.1 yes 4 15.2 even 4
507.2.f.b.239.1 4 65.17 odd 12
507.2.f.b.239.1 4 195.17 even 12
507.2.f.b.437.1 4 65.32 even 12
507.2.f.b.437.1 4 195.32 odd 12
507.2.f.c.239.1 4 65.22 odd 12
507.2.f.c.239.1 4 195.152 even 12
507.2.f.c.437.1 4 65.7 even 12
507.2.f.c.437.1 4 195.137 odd 12
507.2.k.a.80.1 4 65.62 odd 12
507.2.k.a.80.1 4 195.62 even 12
507.2.k.a.488.1 4 65.57 even 4
507.2.k.a.488.1 4 195.122 odd 4
507.2.k.b.80.1 4 65.42 odd 12
507.2.k.b.80.1 4 195.107 even 12
507.2.k.b.488.1 4 65.47 even 4
507.2.k.b.488.1 4 195.47 odd 4
507.2.k.c.89.1 4 65.2 even 12
507.2.k.c.89.1 4 195.2 odd 12
507.2.k.c.188.1 4 65.12 odd 4
507.2.k.c.188.1 4 195.77 even 4
624.2.cn.b.305.1 4 20.7 even 4
624.2.cn.b.305.1 4 60.47 odd 4
624.2.cn.b.401.1 4 260.167 odd 12
624.2.cn.b.401.1 4 780.167 even 12
975.2.bo.c.401.1 4 65.63 even 12
975.2.bo.c.401.1 4 195.128 odd 12
975.2.bo.c.851.1 4 5.3 odd 4
975.2.bo.c.851.1 4 15.8 even 4
975.2.bp.a.149.1 4 5.4 even 2
975.2.bp.a.149.1 4 15.14 odd 2
975.2.bp.a.674.1 4 13.11 odd 12
975.2.bp.a.674.1 4 39.11 even 12
975.2.bp.d.149.1 4 1.1 even 1 trivial
975.2.bp.d.149.1 4 3.2 odd 2 CM
975.2.bp.d.674.1 4 65.24 odd 12 inner
975.2.bp.d.674.1 4 195.89 even 12 inner