Properties

Label 3192.2.a.q.1.2
Level 31923192
Weight 22
Character 3192.1
Self dual yes
Analytic conductor 25.48825.488
Analytic rank 11
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [3192,2,Mod(1,3192)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3192, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3192.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 3192=233719 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3192.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,-2,0,2,0,2,0,2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 25.488248325225.4882483252
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ12)+\Q(\zeta_{12})^+
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x23 x^{2} - 3 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.732051.73205 of defining polynomial
Character χ\chi == 3192.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q1.00000q3+2.73205q5+1.00000q7+1.00000q95.46410q132.73205q151.26795q171.00000q191.00000q21+2.46410q251.00000q279.66025q29+2.00000q31+2.73205q3510.0000q37+5.46410q398.92820q41+4.92820q43+2.73205q4511.6603q47+1.00000q49+1.26795q516.73205q53+1.00000q57+8.00000q592.00000q61+1.00000q6314.9282q6513.4641q67+4.73205q71+10.3923q732.46410q75+4.00000q79+1.00000q81+10.1962q833.46410q85+9.66025q87+4.92820q895.46410q912.00000q932.73205q95+2.00000q97+O(q100)q-1.00000 q^{3} +2.73205 q^{5} +1.00000 q^{7} +1.00000 q^{9} -5.46410 q^{13} -2.73205 q^{15} -1.26795 q^{17} -1.00000 q^{19} -1.00000 q^{21} +2.46410 q^{25} -1.00000 q^{27} -9.66025 q^{29} +2.00000 q^{31} +2.73205 q^{35} -10.0000 q^{37} +5.46410 q^{39} -8.92820 q^{41} +4.92820 q^{43} +2.73205 q^{45} -11.6603 q^{47} +1.00000 q^{49} +1.26795 q^{51} -6.73205 q^{53} +1.00000 q^{57} +8.00000 q^{59} -2.00000 q^{61} +1.00000 q^{63} -14.9282 q^{65} -13.4641 q^{67} +4.73205 q^{71} +10.3923 q^{73} -2.46410 q^{75} +4.00000 q^{79} +1.00000 q^{81} +10.1962 q^{83} -3.46410 q^{85} +9.66025 q^{87} +4.92820 q^{89} -5.46410 q^{91} -2.00000 q^{93} -2.73205 q^{95} +2.00000 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q3+2q5+2q7+2q94q132q156q172q192q212q252q272q29+4q31+2q3520q37+4q394q414q43+2q45++4q97+O(q100) 2 q - 2 q^{3} + 2 q^{5} + 2 q^{7} + 2 q^{9} - 4 q^{13} - 2 q^{15} - 6 q^{17} - 2 q^{19} - 2 q^{21} - 2 q^{25} - 2 q^{27} - 2 q^{29} + 4 q^{31} + 2 q^{35} - 20 q^{37} + 4 q^{39} - 4 q^{41} - 4 q^{43} + 2 q^{45}+ \cdots + 4 q^{97}+O(q^{100}) Copy content Toggle raw display

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 −1.00000 −0.577350
44 0 0
55 2.73205 1.22181 0.610905 0.791704i 0.290806π-0.290806\pi
0.610905 + 0.791704i 0.290806π0.290806\pi
66 0 0
77 1.00000 0.377964
88 0 0
99 1.00000 0.333333
1010 0 0
1111 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1212 0 0
1313 −5.46410 −1.51547 −0.757735 0.652563i 0.773694π-0.773694\pi
−0.757735 + 0.652563i 0.773694π0.773694\pi
1414 0 0
1515 −2.73205 −0.705412
1616 0 0
1717 −1.26795 −0.307523 −0.153761 0.988108i 0.549139π-0.549139\pi
−0.153761 + 0.988108i 0.549139π0.549139\pi
1818 0 0
1919 −1.00000 −0.229416
2020 0 0
2121 −1.00000 −0.218218
2222 0 0
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 0 0
2525 2.46410 0.492820
2626 0 0
2727 −1.00000 −0.192450
2828 0 0
2929 −9.66025 −1.79386 −0.896932 0.442168i 0.854209π-0.854209\pi
−0.896932 + 0.442168i 0.854209π0.854209\pi
3030 0 0
3131 2.00000 0.359211 0.179605 0.983739i 0.442518π-0.442518\pi
0.179605 + 0.983739i 0.442518π0.442518\pi
3232 0 0
3333 0 0
3434 0 0
3535 2.73205 0.461801
3636 0 0
3737 −10.0000 −1.64399 −0.821995 0.569495i 0.807139π-0.807139\pi
−0.821995 + 0.569495i 0.807139π0.807139\pi
3838 0 0
3939 5.46410 0.874957
4040 0 0
4141 −8.92820 −1.39435 −0.697176 0.716900i 0.745560π-0.745560\pi
−0.697176 + 0.716900i 0.745560π0.745560\pi
4242 0 0
4343 4.92820 0.751544 0.375772 0.926712i 0.377378π-0.377378\pi
0.375772 + 0.926712i 0.377378π0.377378\pi
4444 0 0
4545 2.73205 0.407270
4646 0 0
4747 −11.6603 −1.70082 −0.850411 0.526118i 0.823647π-0.823647\pi
−0.850411 + 0.526118i 0.823647π0.823647\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 1.26795 0.177548
5252 0 0
5353 −6.73205 −0.924718 −0.462359 0.886693i 0.652997π-0.652997\pi
−0.462359 + 0.886693i 0.652997π0.652997\pi
5454 0 0
5555 0 0
5656 0 0
5757 1.00000 0.132453
5858 0 0
5959 8.00000 1.04151 0.520756 0.853706i 0.325650π-0.325650\pi
0.520756 + 0.853706i 0.325650π0.325650\pi
6060 0 0
6161 −2.00000 −0.256074 −0.128037 0.991769i 0.540868π-0.540868\pi
−0.128037 + 0.991769i 0.540868π0.540868\pi
6262 0 0
6363 1.00000 0.125988
6464 0 0
6565 −14.9282 −1.85162
6666 0 0
6767 −13.4641 −1.64490 −0.822451 0.568836i 0.807394π-0.807394\pi
−0.822451 + 0.568836i 0.807394π0.807394\pi
6868 0 0
6969 0 0
7070 0 0
7171 4.73205 0.561591 0.280796 0.959768i 0.409402π-0.409402\pi
0.280796 + 0.959768i 0.409402π0.409402\pi
7272 0 0
7373 10.3923 1.21633 0.608164 0.793812i 0.291906π-0.291906\pi
0.608164 + 0.793812i 0.291906π0.291906\pi
7474 0 0
7575 −2.46410 −0.284530
7676 0 0
7777 0 0
7878 0 0
7979 4.00000 0.450035 0.225018 0.974355i 0.427756π-0.427756\pi
0.225018 + 0.974355i 0.427756π0.427756\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 10.1962 1.11917 0.559587 0.828772i 0.310960π-0.310960\pi
0.559587 + 0.828772i 0.310960π0.310960\pi
8484 0 0
8585 −3.46410 −0.375735
8686 0 0
8787 9.66025 1.03569
8888 0 0
8989 4.92820 0.522388 0.261194 0.965286i 0.415884π-0.415884\pi
0.261194 + 0.965286i 0.415884π0.415884\pi
9090 0 0
9191 −5.46410 −0.572793
9292 0 0
9393 −2.00000 −0.207390
9494 0 0
9595 −2.73205 −0.280302
9696 0 0
9797 2.00000 0.203069 0.101535 0.994832i 0.467625π-0.467625\pi
0.101535 + 0.994832i 0.467625π0.467625\pi
9898 0 0
9999 0 0
100100 0 0
101101 1.26795 0.126166 0.0630828 0.998008i 0.479907π-0.479907\pi
0.0630828 + 0.998008i 0.479907π0.479907\pi
102102 0 0
103103 −2.92820 −0.288524 −0.144262 0.989539i 0.546081π-0.546081\pi
−0.144262 + 0.989539i 0.546081π0.546081\pi
104104 0 0
105105 −2.73205 −0.266621
106106 0 0
107107 −4.73205 −0.457465 −0.228732 0.973489i 0.573458π-0.573458\pi
−0.228732 + 0.973489i 0.573458π0.573458\pi
108108 0 0
109109 2.39230 0.229141 0.114571 0.993415i 0.463451π-0.463451\pi
0.114571 + 0.993415i 0.463451π0.463451\pi
110110 0 0
111111 10.0000 0.949158
112112 0 0
113113 0.196152 0.0184525 0.00922623 0.999957i 0.497063π-0.497063\pi
0.00922623 + 0.999957i 0.497063π0.497063\pi
114114 0 0
115115 0 0
116116 0 0
117117 −5.46410 −0.505156
118118 0 0
119119 −1.26795 −0.116233
120120 0 0
121121 −11.0000 −1.00000
122122 0 0
123123 8.92820 0.805029
124124 0 0
125125 −6.92820 −0.619677
126126 0 0
127127 20.3923 1.80952 0.904762 0.425917i 0.140048π-0.140048\pi
0.904762 + 0.425917i 0.140048π0.140048\pi
128128 0 0
129129 −4.92820 −0.433904
130130 0 0
131131 14.5885 1.27460 0.637300 0.770616i 0.280051π-0.280051\pi
0.637300 + 0.770616i 0.280051π0.280051\pi
132132 0 0
133133 −1.00000 −0.0867110
134134 0 0
135135 −2.73205 −0.235137
136136 0 0
137137 12.9282 1.10453 0.552265 0.833668i 0.313763π-0.313763\pi
0.552265 + 0.833668i 0.313763π0.313763\pi
138138 0 0
139139 −15.3205 −1.29947 −0.649734 0.760161i 0.725120π-0.725120\pi
−0.649734 + 0.760161i 0.725120π0.725120\pi
140140 0 0
141141 11.6603 0.981971
142142 0 0
143143 0 0
144144 0 0
145145 −26.3923 −2.19176
146146 0 0
147147 −1.00000 −0.0824786
148148 0 0
149149 14.3923 1.17906 0.589532 0.807745i 0.299312π-0.299312\pi
0.589532 + 0.807745i 0.299312π0.299312\pi
150150 0 0
151151 −2.53590 −0.206368 −0.103184 0.994662i 0.532903π-0.532903\pi
−0.103184 + 0.994662i 0.532903π0.532903\pi
152152 0 0
153153 −1.26795 −0.102508
154154 0 0
155155 5.46410 0.438887
156156 0 0
157157 −14.0000 −1.11732 −0.558661 0.829396i 0.688685π-0.688685\pi
−0.558661 + 0.829396i 0.688685π0.688685\pi
158158 0 0
159159 6.73205 0.533886
160160 0 0
161161 0 0
162162 0 0
163163 −7.07180 −0.553906 −0.276953 0.960883i 0.589325π-0.589325\pi
−0.276953 + 0.960883i 0.589325π0.589325\pi
164164 0 0
165165 0 0
166166 0 0
167167 11.3205 0.876007 0.438004 0.898973i 0.355686π-0.355686\pi
0.438004 + 0.898973i 0.355686π0.355686\pi
168168 0 0
169169 16.8564 1.29665
170170 0 0
171171 −1.00000 −0.0764719
172172 0 0
173173 −16.9282 −1.28703 −0.643514 0.765435i 0.722524π-0.722524\pi
−0.643514 + 0.765435i 0.722524π0.722524\pi
174174 0 0
175175 2.46410 0.186269
176176 0 0
177177 −8.00000 −0.601317
178178 0 0
179179 −14.1962 −1.06107 −0.530535 0.847663i 0.678009π-0.678009\pi
−0.530535 + 0.847663i 0.678009π0.678009\pi
180180 0 0
181181 4.92820 0.366310 0.183155 0.983084i 0.441369π-0.441369\pi
0.183155 + 0.983084i 0.441369π0.441369\pi
182182 0 0
183183 2.00000 0.147844
184184 0 0
185185 −27.3205 −2.00864
186186 0 0
187187 0 0
188188 0 0
189189 −1.00000 −0.0727393
190190 0 0
191191 −14.9282 −1.08017 −0.540083 0.841611i 0.681607π-0.681607\pi
−0.540083 + 0.841611i 0.681607π0.681607\pi
192192 0 0
193193 −23.8564 −1.71722 −0.858611 0.512628i 0.828672π-0.828672\pi
−0.858611 + 0.512628i 0.828672π0.828672\pi
194194 0 0
195195 14.9282 1.06903
196196 0 0
197197 −18.0000 −1.28245 −0.641223 0.767354i 0.721573π-0.721573\pi
−0.641223 + 0.767354i 0.721573π0.721573\pi
198198 0 0
199199 −12.3923 −0.878467 −0.439234 0.898373i 0.644750π-0.644750\pi
−0.439234 + 0.898373i 0.644750π0.644750\pi
200200 0 0
201201 13.4641 0.949685
202202 0 0
203203 −9.66025 −0.678017
204204 0 0
205205 −24.3923 −1.70363
206206 0 0
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 4.00000 0.275371 0.137686 0.990476i 0.456034π-0.456034\pi
0.137686 + 0.990476i 0.456034π0.456034\pi
212212 0 0
213213 −4.73205 −0.324235
214214 0 0
215215 13.4641 0.918244
216216 0 0
217217 2.00000 0.135769
218218 0 0
219219 −10.3923 −0.702247
220220 0 0
221221 6.92820 0.466041
222222 0 0
223223 −20.9282 −1.40146 −0.700728 0.713428i 0.747141π-0.747141\pi
−0.700728 + 0.713428i 0.747141π0.747141\pi
224224 0 0
225225 2.46410 0.164273
226226 0 0
227227 16.3923 1.08800 0.543998 0.839087i 0.316910π-0.316910\pi
0.543998 + 0.839087i 0.316910π0.316910\pi
228228 0 0
229229 28.2487 1.86673 0.933364 0.358932i 0.116859π-0.116859\pi
0.933364 + 0.358932i 0.116859π0.116859\pi
230230 0 0
231231 0 0
232232 0 0
233233 −2.39230 −0.156725 −0.0783626 0.996925i 0.524969π-0.524969\pi
−0.0783626 + 0.996925i 0.524969π0.524969\pi
234234 0 0
235235 −31.8564 −2.07808
236236 0 0
237237 −4.00000 −0.259828
238238 0 0
239239 −4.39230 −0.284115 −0.142057 0.989858i 0.545372π-0.545372\pi
−0.142057 + 0.989858i 0.545372π0.545372\pi
240240 0 0
241241 −12.9282 −0.832779 −0.416389 0.909186i 0.636705π-0.636705\pi
−0.416389 + 0.909186i 0.636705π0.636705\pi
242242 0 0
243243 −1.00000 −0.0641500
244244 0 0
245245 2.73205 0.174544
246246 0 0
247247 5.46410 0.347672
248248 0 0
249249 −10.1962 −0.646155
250250 0 0
251251 0.339746 0.0214446 0.0107223 0.999943i 0.496587π-0.496587\pi
0.0107223 + 0.999943i 0.496587π0.496587\pi
252252 0 0
253253 0 0
254254 0 0
255255 3.46410 0.216930
256256 0 0
257257 11.4641 0.715111 0.357556 0.933892i 0.383610π-0.383610\pi
0.357556 + 0.933892i 0.383610π0.383610\pi
258258 0 0
259259 −10.0000 −0.621370
260260 0 0
261261 −9.66025 −0.597955
262262 0 0
263263 −19.3205 −1.19135 −0.595677 0.803224i 0.703116π-0.703116\pi
−0.595677 + 0.803224i 0.703116π0.703116\pi
264264 0 0
265265 −18.3923 −1.12983
266266 0 0
267267 −4.92820 −0.301601
268268 0 0
269269 31.1769 1.90089 0.950445 0.310893i 0.100628π-0.100628\pi
0.950445 + 0.310893i 0.100628π0.100628\pi
270270 0 0
271271 −28.7846 −1.74854 −0.874270 0.485440i 0.838660π-0.838660\pi
−0.874270 + 0.485440i 0.838660π0.838660\pi
272272 0 0
273273 5.46410 0.330702
274274 0 0
275275 0 0
276276 0 0
277277 12.3923 0.744581 0.372291 0.928116i 0.378572π-0.378572\pi
0.372291 + 0.928116i 0.378572π0.378572\pi
278278 0 0
279279 2.00000 0.119737
280280 0 0
281281 −4.19615 −0.250321 −0.125161 0.992136i 0.539945π-0.539945\pi
−0.125161 + 0.992136i 0.539945π0.539945\pi
282282 0 0
283283 −20.3923 −1.21220 −0.606098 0.795390i 0.707266π-0.707266\pi
−0.606098 + 0.795390i 0.707266π0.707266\pi
284284 0 0
285285 2.73205 0.161833
286286 0 0
287287 −8.92820 −0.527015
288288 0 0
289289 −15.3923 −0.905430
290290 0 0
291291 −2.00000 −0.117242
292292 0 0
293293 −6.00000 −0.350524 −0.175262 0.984522i 0.556077π-0.556077\pi
−0.175262 + 0.984522i 0.556077π0.556077\pi
294294 0 0
295295 21.8564 1.27253
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 0 0
301301 4.92820 0.284057
302302 0 0
303303 −1.26795 −0.0728418
304304 0 0
305305 −5.46410 −0.312874
306306 0 0
307307 18.7846 1.07209 0.536047 0.844188i 0.319917π-0.319917\pi
0.536047 + 0.844188i 0.319917π0.319917\pi
308308 0 0
309309 2.92820 0.166580
310310 0 0
311311 18.5885 1.05405 0.527027 0.849848i 0.323307π-0.323307\pi
0.527027 + 0.849848i 0.323307π0.323307\pi
312312 0 0
313313 −2.00000 −0.113047 −0.0565233 0.998401i 0.518002π-0.518002\pi
−0.0565233 + 0.998401i 0.518002π0.518002\pi
314314 0 0
315315 2.73205 0.153934
316316 0 0
317317 12.1962 0.685004 0.342502 0.939517i 0.388726π-0.388726\pi
0.342502 + 0.939517i 0.388726π0.388726\pi
318318 0 0
319319 0 0
320320 0 0
321321 4.73205 0.264117
322322 0 0
323323 1.26795 0.0705506
324324 0 0
325325 −13.4641 −0.746854
326326 0 0
327327 −2.39230 −0.132295
328328 0 0
329329 −11.6603 −0.642851
330330 0 0
331331 22.2487 1.22290 0.611450 0.791283i 0.290587π-0.290587\pi
0.611450 + 0.791283i 0.290587π0.290587\pi
332332 0 0
333333 −10.0000 −0.547997
334334 0 0
335335 −36.7846 −2.00976
336336 0 0
337337 30.3923 1.65557 0.827787 0.561042i 0.189599π-0.189599\pi
0.827787 + 0.561042i 0.189599π0.189599\pi
338338 0 0
339339 −0.196152 −0.0106535
340340 0 0
341341 0 0
342342 0 0
343343 1.00000 0.0539949
344344 0 0
345345 0 0
346346 0 0
347347 −16.3923 −0.879985 −0.439993 0.898001i 0.645019π-0.645019\pi
−0.439993 + 0.898001i 0.645019π0.645019\pi
348348 0 0
349349 −19.0718 −1.02089 −0.510445 0.859910i 0.670519π-0.670519\pi
−0.510445 + 0.859910i 0.670519π0.670519\pi
350350 0 0
351351 5.46410 0.291652
352352 0 0
353353 16.1962 0.862034 0.431017 0.902344i 0.358155π-0.358155\pi
0.431017 + 0.902344i 0.358155π0.358155\pi
354354 0 0
355355 12.9282 0.686158
356356 0 0
357357 1.26795 0.0671070
358358 0 0
359359 30.9282 1.63233 0.816164 0.577820i 0.196097π-0.196097\pi
0.816164 + 0.577820i 0.196097π0.196097\pi
360360 0 0
361361 1.00000 0.0526316
362362 0 0
363363 11.0000 0.577350
364364 0 0
365365 28.3923 1.48612
366366 0 0
367367 18.5359 0.967566 0.483783 0.875188i 0.339262π-0.339262\pi
0.483783 + 0.875188i 0.339262π0.339262\pi
368368 0 0
369369 −8.92820 −0.464784
370370 0 0
371371 −6.73205 −0.349511
372372 0 0
373373 0.928203 0.0480605 0.0240303 0.999711i 0.492350π-0.492350\pi
0.0240303 + 0.999711i 0.492350π0.492350\pi
374374 0 0
375375 6.92820 0.357771
376376 0 0
377377 52.7846 2.71855
378378 0 0
379379 −15.3205 −0.786962 −0.393481 0.919333i 0.628729π-0.628729\pi
−0.393481 + 0.919333i 0.628729π0.628729\pi
380380 0 0
381381 −20.3923 −1.04473
382382 0 0
383383 −11.3205 −0.578451 −0.289225 0.957261i 0.593398π-0.593398\pi
−0.289225 + 0.957261i 0.593398π0.593398\pi
384384 0 0
385385 0 0
386386 0 0
387387 4.92820 0.250515
388388 0 0
389389 −20.5359 −1.04121 −0.520606 0.853797i 0.674294π-0.674294\pi
−0.520606 + 0.853797i 0.674294π0.674294\pi
390390 0 0
391391 0 0
392392 0 0
393393 −14.5885 −0.735890
394394 0 0
395395 10.9282 0.549858
396396 0 0
397397 −21.7128 −1.08973 −0.544867 0.838522i 0.683420π-0.683420\pi
−0.544867 + 0.838522i 0.683420π0.683420\pi
398398 0 0
399399 1.00000 0.0500626
400400 0 0
401401 0.196152 0.00979538 0.00489769 0.999988i 0.498441π-0.498441\pi
0.00489769 + 0.999988i 0.498441π0.498441\pi
402402 0 0
403403 −10.9282 −0.544373
404404 0 0
405405 2.73205 0.135757
406406 0 0
407407 0 0
408408 0 0
409409 −28.3923 −1.40391 −0.701955 0.712222i 0.747689π-0.747689\pi
−0.701955 + 0.712222i 0.747689π0.747689\pi
410410 0 0
411411 −12.9282 −0.637701
412412 0 0
413413 8.00000 0.393654
414414 0 0
415415 27.8564 1.36742
416416 0 0
417417 15.3205 0.750249
418418 0 0
419419 20.7321 1.01283 0.506413 0.862291i 0.330971π-0.330971\pi
0.506413 + 0.862291i 0.330971π0.330971\pi
420420 0 0
421421 −32.2487 −1.57171 −0.785853 0.618413i 0.787776π-0.787776\pi
−0.785853 + 0.618413i 0.787776π0.787776\pi
422422 0 0
423423 −11.6603 −0.566941
424424 0 0
425425 −3.12436 −0.151554
426426 0 0
427427 −2.00000 −0.0967868
428428 0 0
429429 0 0
430430 0 0
431431 0.0525589 0.00253167 0.00126584 0.999999i 0.499597π-0.499597\pi
0.00126584 + 0.999999i 0.499597π0.499597\pi
432432 0 0
433433 −15.8564 −0.762010 −0.381005 0.924573i 0.624422π-0.624422\pi
−0.381005 + 0.924573i 0.624422π0.624422\pi
434434 0 0
435435 26.3923 1.26541
436436 0 0
437437 0 0
438438 0 0
439439 35.8564 1.71133 0.855666 0.517528i 0.173148π-0.173148\pi
0.855666 + 0.517528i 0.173148π0.173148\pi
440440 0 0
441441 1.00000 0.0476190
442442 0 0
443443 −34.5359 −1.64085 −0.820425 0.571754i 0.806263π-0.806263\pi
−0.820425 + 0.571754i 0.806263π0.806263\pi
444444 0 0
445445 13.4641 0.638260
446446 0 0
447447 −14.3923 −0.680733
448448 0 0
449449 5.26795 0.248610 0.124305 0.992244i 0.460330π-0.460330\pi
0.124305 + 0.992244i 0.460330π0.460330\pi
450450 0 0
451451 0 0
452452 0 0
453453 2.53590 0.119147
454454 0 0
455455 −14.9282 −0.699845
456456 0 0
457457 −20.3923 −0.953912 −0.476956 0.878927i 0.658260π-0.658260\pi
−0.476956 + 0.878927i 0.658260π0.658260\pi
458458 0 0
459459 1.26795 0.0591828
460460 0 0
461461 14.3397 0.667869 0.333934 0.942596i 0.391624π-0.391624\pi
0.333934 + 0.942596i 0.391624π0.391624\pi
462462 0 0
463463 21.8564 1.01575 0.507877 0.861430i 0.330431π-0.330431\pi
0.507877 + 0.861430i 0.330431π0.330431\pi
464464 0 0
465465 −5.46410 −0.253392
466466 0 0
467467 −0.0525589 −0.00243214 −0.00121607 0.999999i 0.500387π-0.500387\pi
−0.00121607 + 0.999999i 0.500387π0.500387\pi
468468 0 0
469469 −13.4641 −0.621714
470470 0 0
471471 14.0000 0.645086
472472 0 0
473473 0 0
474474 0 0
475475 −2.46410 −0.113061
476476 0 0
477477 −6.73205 −0.308239
478478 0 0
479479 27.6603 1.26383 0.631915 0.775038i 0.282269π-0.282269\pi
0.631915 + 0.775038i 0.282269π0.282269\pi
480480 0 0
481481 54.6410 2.49142
482482 0 0
483483 0 0
484484 0 0
485485 5.46410 0.248112
486486 0 0
487487 25.8564 1.17167 0.585833 0.810432i 0.300768π-0.300768\pi
0.585833 + 0.810432i 0.300768π0.300768\pi
488488 0 0
489489 7.07180 0.319798
490490 0 0
491491 19.3205 0.871922 0.435961 0.899965i 0.356409π-0.356409\pi
0.435961 + 0.899965i 0.356409π0.356409\pi
492492 0 0
493493 12.2487 0.551654
494494 0 0
495495 0 0
496496 0 0
497497 4.73205 0.212261
498498 0 0
499499 −9.85641 −0.441233 −0.220617 0.975361i 0.570807π-0.570807\pi
−0.220617 + 0.975361i 0.570807π0.570807\pi
500500 0 0
501501 −11.3205 −0.505763
502502 0 0
503503 4.73205 0.210992 0.105496 0.994420i 0.466357π-0.466357\pi
0.105496 + 0.994420i 0.466357π0.466357\pi
504504 0 0
505505 3.46410 0.154150
506506 0 0
507507 −16.8564 −0.748619
508508 0 0
509509 −8.24871 −0.365618 −0.182809 0.983148i 0.558519π-0.558519\pi
−0.182809 + 0.983148i 0.558519π0.558519\pi
510510 0 0
511511 10.3923 0.459728
512512 0 0
513513 1.00000 0.0441511
514514 0 0
515515 −8.00000 −0.352522
516516 0 0
517517 0 0
518518 0 0
519519 16.9282 0.743066
520520 0 0
521521 36.2487 1.58808 0.794042 0.607862i 0.207973π-0.207973\pi
0.794042 + 0.607862i 0.207973π0.207973\pi
522522 0 0
523523 −22.0000 −0.961993 −0.480996 0.876723i 0.659725π-0.659725\pi
−0.480996 + 0.876723i 0.659725π0.659725\pi
524524 0 0
525525 −2.46410 −0.107542
526526 0 0
527527 −2.53590 −0.110465
528528 0 0
529529 −23.0000 −1.00000
530530 0 0
531531 8.00000 0.347170
532532 0 0
533533 48.7846 2.11310
534534 0 0
535535 −12.9282 −0.558935
536536 0 0
537537 14.1962 0.612609
538538 0 0
539539 0 0
540540 0 0
541541 −22.0000 −0.945854 −0.472927 0.881102i 0.656803π-0.656803\pi
−0.472927 + 0.881102i 0.656803π0.656803\pi
542542 0 0
543543 −4.92820 −0.211489
544544 0 0
545545 6.53590 0.279967
546546 0 0
547547 −11.7128 −0.500804 −0.250402 0.968142i 0.580563π-0.580563\pi
−0.250402 + 0.968142i 0.580563π0.580563\pi
548548 0 0
549549 −2.00000 −0.0853579
550550 0 0
551551 9.66025 0.411541
552552 0 0
553553 4.00000 0.170097
554554 0 0
555555 27.3205 1.15969
556556 0 0
557557 20.5359 0.870134 0.435067 0.900398i 0.356725π-0.356725\pi
0.435067 + 0.900398i 0.356725π0.356725\pi
558558 0 0
559559 −26.9282 −1.13894
560560 0 0
561561 0 0
562562 0 0
563563 −25.4641 −1.07318 −0.536592 0.843842i 0.680289π-0.680289\pi
−0.536592 + 0.843842i 0.680289π0.680289\pi
564564 0 0
565565 0.535898 0.0225454
566566 0 0
567567 1.00000 0.0419961
568568 0 0
569569 28.5885 1.19849 0.599245 0.800566i 0.295467π-0.295467\pi
0.599245 + 0.800566i 0.295467π0.295467\pi
570570 0 0
571571 −25.8564 −1.08206 −0.541028 0.841004i 0.681965π-0.681965\pi
−0.541028 + 0.841004i 0.681965π0.681965\pi
572572 0 0
573573 14.9282 0.623635
574574 0 0
575575 0 0
576576 0 0
577577 −10.0000 −0.416305 −0.208153 0.978096i 0.566745π-0.566745\pi
−0.208153 + 0.978096i 0.566745π0.566745\pi
578578 0 0
579579 23.8564 0.991438
580580 0 0
581581 10.1962 0.423008
582582 0 0
583583 0 0
584584 0 0
585585 −14.9282 −0.617205
586586 0 0
587587 25.9090 1.06938 0.534689 0.845049i 0.320429π-0.320429\pi
0.534689 + 0.845049i 0.320429π0.320429\pi
588588 0 0
589589 −2.00000 −0.0824086
590590 0 0
591591 18.0000 0.740421
592592 0 0
593593 27.8038 1.14177 0.570884 0.821031i 0.306601π-0.306601\pi
0.570884 + 0.821031i 0.306601π0.306601\pi
594594 0 0
595595 −3.46410 −0.142014
596596 0 0
597597 12.3923 0.507183
598598 0 0
599599 −7.26795 −0.296960 −0.148480 0.988915i 0.547438π-0.547438\pi
−0.148480 + 0.988915i 0.547438π0.547438\pi
600600 0 0
601601 34.0000 1.38689 0.693444 0.720510i 0.256092π-0.256092\pi
0.693444 + 0.720510i 0.256092π0.256092\pi
602602 0 0
603603 −13.4641 −0.548301
604604 0 0
605605 −30.0526 −1.22181
606606 0 0
607607 −13.0718 −0.530568 −0.265284 0.964170i 0.585466π-0.585466\pi
−0.265284 + 0.964170i 0.585466π0.585466\pi
608608 0 0
609609 9.66025 0.391453
610610 0 0
611611 63.7128 2.57754
612612 0 0
613613 −18.2487 −0.737059 −0.368529 0.929616i 0.620139π-0.620139\pi
−0.368529 + 0.929616i 0.620139π0.620139\pi
614614 0 0
615615 24.3923 0.983593
616616 0 0
617617 −24.6410 −0.992010 −0.496005 0.868320i 0.665200π-0.665200\pi
−0.496005 + 0.868320i 0.665200π0.665200\pi
618618 0 0
619619 −13.1769 −0.529625 −0.264812 0.964300i 0.585310π-0.585310\pi
−0.264812 + 0.964300i 0.585310π0.585310\pi
620620 0 0
621621 0 0
622622 0 0
623623 4.92820 0.197444
624624 0 0
625625 −31.2487 −1.24995
626626 0 0
627627 0 0
628628 0 0
629629 12.6795 0.505564
630630 0 0
631631 40.9282 1.62933 0.814663 0.579935i 0.196922π-0.196922\pi
0.814663 + 0.579935i 0.196922π0.196922\pi
632632 0 0
633633 −4.00000 −0.158986
634634 0 0
635635 55.7128 2.21090
636636 0 0
637637 −5.46410 −0.216496
638638 0 0
639639 4.73205 0.187197
640640 0 0
641641 −6.33975 −0.250405 −0.125202 0.992131i 0.539958π-0.539958\pi
−0.125202 + 0.992131i 0.539958π0.539958\pi
642642 0 0
643643 20.3923 0.804194 0.402097 0.915597i 0.368281π-0.368281\pi
0.402097 + 0.915597i 0.368281π0.368281\pi
644644 0 0
645645 −13.4641 −0.530148
646646 0 0
647647 −3.66025 −0.143899 −0.0719497 0.997408i 0.522922π-0.522922\pi
−0.0719497 + 0.997408i 0.522922π0.522922\pi
648648 0 0
649649 0 0
650650 0 0
651651 −2.00000 −0.0783862
652652 0 0
653653 −42.7846 −1.67429 −0.837146 0.546980i 0.815777π-0.815777\pi
−0.837146 + 0.546980i 0.815777π0.815777\pi
654654 0 0
655655 39.8564 1.55732
656656 0 0
657657 10.3923 0.405442
658658 0 0
659659 32.0526 1.24859 0.624295 0.781189i 0.285386π-0.285386\pi
0.624295 + 0.781189i 0.285386π0.285386\pi
660660 0 0
661661 −6.53590 −0.254217 −0.127108 0.991889i 0.540570π-0.540570\pi
−0.127108 + 0.991889i 0.540570π0.540570\pi
662662 0 0
663663 −6.92820 −0.269069
664664 0 0
665665 −2.73205 −0.105944
666666 0 0
667667 0 0
668668 0 0
669669 20.9282 0.809131
670670 0 0
671671 0 0
672672 0 0
673673 −7.07180 −0.272598 −0.136299 0.990668i 0.543521π-0.543521\pi
−0.136299 + 0.990668i 0.543521π0.543521\pi
674674 0 0
675675 −2.46410 −0.0948433
676676 0 0
677677 29.3205 1.12688 0.563439 0.826157i 0.309478π-0.309478\pi
0.563439 + 0.826157i 0.309478π0.309478\pi
678678 0 0
679679 2.00000 0.0767530
680680 0 0
681681 −16.3923 −0.628154
682682 0 0
683683 4.73205 0.181067 0.0905334 0.995893i 0.471143π-0.471143\pi
0.0905334 + 0.995893i 0.471143π0.471143\pi
684684 0 0
685685 35.3205 1.34953
686686 0 0
687687 −28.2487 −1.07776
688688 0 0
689689 36.7846 1.40138
690690 0 0
691691 −8.78461 −0.334182 −0.167091 0.985941i 0.553437π-0.553437\pi
−0.167091 + 0.985941i 0.553437π0.553437\pi
692692 0 0
693693 0 0
694694 0 0
695695 −41.8564 −1.58770
696696 0 0
697697 11.3205 0.428795
698698 0 0
699699 2.39230 0.0904853
700700 0 0
701701 2.00000 0.0755390 0.0377695 0.999286i 0.487975π-0.487975\pi
0.0377695 + 0.999286i 0.487975π0.487975\pi
702702 0 0
703703 10.0000 0.377157
704704 0 0
705705 31.8564 1.19978
706706 0 0
707707 1.26795 0.0476861
708708 0 0
709709 0.392305 0.0147333 0.00736666 0.999973i 0.497655π-0.497655\pi
0.00736666 + 0.999973i 0.497655π0.497655\pi
710710 0 0
711711 4.00000 0.150012
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 4.39230 0.164034
718718 0 0
719719 46.9808 1.75209 0.876043 0.482232i 0.160174π-0.160174\pi
0.876043 + 0.482232i 0.160174π0.160174\pi
720720 0 0
721721 −2.92820 −0.109052
722722 0 0
723723 12.9282 0.480805
724724 0 0
725725 −23.8038 −0.884053
726726 0 0
727727 18.9282 0.702008 0.351004 0.936374i 0.385840π-0.385840\pi
0.351004 + 0.936374i 0.385840π0.385840\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −6.24871 −0.231117
732732 0 0
733733 4.24871 0.156930 0.0784649 0.996917i 0.474998π-0.474998\pi
0.0784649 + 0.996917i 0.474998π0.474998\pi
734734 0 0
735735 −2.73205 −0.100773
736736 0 0
737737 0 0
738738 0 0
739739 −20.1436 −0.740994 −0.370497 0.928834i 0.620813π-0.620813\pi
−0.370497 + 0.928834i 0.620813π0.620813\pi
740740 0 0
741741 −5.46410 −0.200729
742742 0 0
743743 −8.73205 −0.320348 −0.160174 0.987089i 0.551206π-0.551206\pi
−0.160174 + 0.987089i 0.551206π0.551206\pi
744744 0 0
745745 39.3205 1.44059
746746 0 0
747747 10.1962 0.373058
748748 0 0
749749 −4.73205 −0.172905
750750 0 0
751751 −49.1769 −1.79449 −0.897246 0.441532i 0.854435π-0.854435\pi
−0.897246 + 0.441532i 0.854435π0.854435\pi
752752 0 0
753753 −0.339746 −0.0123810
754754 0 0
755755 −6.92820 −0.252143
756756 0 0
757757 −22.7846 −0.828121 −0.414060 0.910249i 0.635890π-0.635890\pi
−0.414060 + 0.910249i 0.635890π0.635890\pi
758758 0 0
759759 0 0
760760 0 0
761761 33.6603 1.22018 0.610092 0.792331i 0.291133π-0.291133\pi
0.610092 + 0.792331i 0.291133π0.291133\pi
762762 0 0
763763 2.39230 0.0866073
764764 0 0
765765 −3.46410 −0.125245
766766 0 0
767767 −43.7128 −1.57838
768768 0 0
769769 0.143594 0.00517812 0.00258906 0.999997i 0.499176π-0.499176\pi
0.00258906 + 0.999997i 0.499176π0.499176\pi
770770 0 0
771771 −11.4641 −0.412870
772772 0 0
773773 −14.0000 −0.503545 −0.251773 0.967786i 0.581013π-0.581013\pi
−0.251773 + 0.967786i 0.581013π0.581013\pi
774774 0 0
775775 4.92820 0.177026
776776 0 0
777777 10.0000 0.358748
778778 0 0
779779 8.92820 0.319886
780780 0 0
781781 0 0
782782 0 0
783783 9.66025 0.345229
784784 0 0
785785 −38.2487 −1.36516
786786 0 0
787787 27.8564 0.992974 0.496487 0.868044i 0.334623π-0.334623\pi
0.496487 + 0.868044i 0.334623π0.334623\pi
788788 0 0
789789 19.3205 0.687828
790790 0 0
791791 0.196152 0.00697438
792792 0 0
793793 10.9282 0.388072
794794 0 0
795795 18.3923 0.652308
796796 0 0
797797 −10.7846 −0.382010 −0.191005 0.981589i 0.561175π-0.561175\pi
−0.191005 + 0.981589i 0.561175π0.561175\pi
798798 0 0
799799 14.7846 0.523042
800800 0 0
801801 4.92820 0.174129
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 −31.1769 −1.09748
808808 0 0
809809 −10.7846 −0.379167 −0.189583 0.981865i 0.560714π-0.560714\pi
−0.189583 + 0.981865i 0.560714π0.560714\pi
810810 0 0
811811 4.00000 0.140459 0.0702295 0.997531i 0.477627π-0.477627\pi
0.0702295 + 0.997531i 0.477627π0.477627\pi
812812 0 0
813813 28.7846 1.00952
814814 0 0
815815 −19.3205 −0.676768
816816 0 0
817817 −4.92820 −0.172416
818818 0 0
819819 −5.46410 −0.190931
820820 0 0
821821 35.4641 1.23771 0.618853 0.785507i 0.287598π-0.287598\pi
0.618853 + 0.785507i 0.287598π0.287598\pi
822822 0 0
823823 20.6410 0.719501 0.359750 0.933049i 0.382862π-0.382862\pi
0.359750 + 0.933049i 0.382862π0.382862\pi
824824 0 0
825825 0 0
826826 0 0
827827 −53.9090 −1.87460 −0.937299 0.348526i 0.886682π-0.886682\pi
−0.937299 + 0.348526i 0.886682π0.886682\pi
828828 0 0
829829 −37.7128 −1.30982 −0.654910 0.755707i 0.727294π-0.727294\pi
−0.654910 + 0.755707i 0.727294π0.727294\pi
830830 0 0
831831 −12.3923 −0.429884
832832 0 0
833833 −1.26795 −0.0439318
834834 0 0
835835 30.9282 1.07031
836836 0 0
837837 −2.00000 −0.0691301
838838 0 0
839839 −28.7846 −0.993755 −0.496878 0.867821i 0.665520π-0.665520\pi
−0.496878 + 0.867821i 0.665520π0.665520\pi
840840 0 0
841841 64.3205 2.21795
842842 0 0
843843 4.19615 0.144523
844844 0 0
845845 46.0526 1.58426
846846 0 0
847847 −11.0000 −0.377964
848848 0 0
849849 20.3923 0.699862
850850 0 0
851851 0 0
852852 0 0
853853 −16.1436 −0.552746 −0.276373 0.961050i 0.589133π-0.589133\pi
−0.276373 + 0.961050i 0.589133π0.589133\pi
854854 0 0
855855 −2.73205 −0.0934342
856856 0 0
857857 16.9282 0.578256 0.289128 0.957290i 0.406635π-0.406635\pi
0.289128 + 0.957290i 0.406635π0.406635\pi
858858 0 0
859859 45.8564 1.56460 0.782300 0.622902i 0.214046π-0.214046\pi
0.782300 + 0.622902i 0.214046π0.214046\pi
860860 0 0
861861 8.92820 0.304272
862862 0 0
863863 −42.9808 −1.46308 −0.731541 0.681797i 0.761199π-0.761199\pi
−0.731541 + 0.681797i 0.761199π0.761199\pi
864864 0 0
865865 −46.2487 −1.57250
866866 0 0
867867 15.3923 0.522750
868868 0 0
869869 0 0
870870 0 0
871871 73.5692 2.49280
872872 0 0
873873 2.00000 0.0676897
874874 0 0
875875 −6.92820 −0.234216
876876 0 0
877877 −53.7128 −1.81375 −0.906876 0.421397i 0.861540π-0.861540\pi
−0.906876 + 0.421397i 0.861540π0.861540\pi
878878 0 0
879879 6.00000 0.202375
880880 0 0
881881 −2.73205 −0.0920451 −0.0460226 0.998940i 0.514655π-0.514655\pi
−0.0460226 + 0.998940i 0.514655π0.514655\pi
882882 0 0
883883 9.07180 0.305290 0.152645 0.988281i 0.451221π-0.451221\pi
0.152645 + 0.988281i 0.451221π0.451221\pi
884884 0 0
885885 −21.8564 −0.734695
886886 0 0
887887 42.2487 1.41857 0.709286 0.704920i 0.249017π-0.249017\pi
0.709286 + 0.704920i 0.249017π0.249017\pi
888888 0 0
889889 20.3923 0.683936
890890 0 0
891891 0 0
892892 0 0
893893 11.6603 0.390196
894894 0 0
895895 −38.7846 −1.29643
896896 0 0
897897 0 0
898898 0 0
899899 −19.3205 −0.644375
900900 0 0
901901 8.53590 0.284372
902902 0 0
903903 −4.92820 −0.164000
904904 0 0
905905 13.4641 0.447562
906906 0 0
907907 14.6410 0.486147 0.243073 0.970008i 0.421844π-0.421844\pi
0.243073 + 0.970008i 0.421844π0.421844\pi
908908 0 0
909909 1.26795 0.0420552
910910 0 0
911911 −12.7321 −0.421832 −0.210916 0.977504i 0.567645π-0.567645\pi
−0.210916 + 0.977504i 0.567645π0.567645\pi
912912 0 0
913913 0 0
914914 0 0
915915 5.46410 0.180638
916916 0 0
917917 14.5885 0.481753
918918 0 0
919919 −29.8564 −0.984872 −0.492436 0.870349i 0.663893π-0.663893\pi
−0.492436 + 0.870349i 0.663893π0.663893\pi
920920 0 0
921921 −18.7846 −0.618974
922922 0 0
923923 −25.8564 −0.851074
924924 0 0
925925 −24.6410 −0.810192
926926 0 0
927927 −2.92820 −0.0961748
928928 0 0
929929 −4.98076 −0.163414 −0.0817068 0.996656i 0.526037π-0.526037\pi
−0.0817068 + 0.996656i 0.526037π0.526037\pi
930930 0 0
931931 −1.00000 −0.0327737
932932 0 0
933933 −18.5885 −0.608559
934934 0 0
935935 0 0
936936 0 0
937937 48.6410 1.58903 0.794516 0.607243i 0.207724π-0.207724\pi
0.794516 + 0.607243i 0.207724π0.207724\pi
938938 0 0
939939 2.00000 0.0652675
940940 0 0
941941 −51.4641 −1.67768 −0.838841 0.544377i 0.816766π-0.816766\pi
−0.838841 + 0.544377i 0.816766π0.816766\pi
942942 0 0
943943 0 0
944944 0 0
945945 −2.73205 −0.0888736
946946 0 0
947947 9.07180 0.294794 0.147397 0.989077i 0.452911π-0.452911\pi
0.147397 + 0.989077i 0.452911π0.452911\pi
948948 0 0
949949 −56.7846 −1.84331
950950 0 0
951951 −12.1962 −0.395487
952952 0 0
953953 40.1962 1.30208 0.651041 0.759043i 0.274333π-0.274333\pi
0.651041 + 0.759043i 0.274333π0.274333\pi
954954 0 0
955955 −40.7846 −1.31976
956956 0 0
957957 0 0
958958 0 0
959959 12.9282 0.417473
960960 0 0
961961 −27.0000 −0.870968
962962 0 0
963963 −4.73205 −0.152488
964964 0 0
965965 −65.1769 −2.09812
966966 0 0
967967 −36.6410 −1.17830 −0.589148 0.808025i 0.700536π-0.700536\pi
−0.589148 + 0.808025i 0.700536π0.700536\pi
968968 0 0
969969 −1.26795 −0.0407324
970970 0 0
971971 4.28719 0.137582 0.0687912 0.997631i 0.478086π-0.478086\pi
0.0687912 + 0.997631i 0.478086π0.478086\pi
972972 0 0
973973 −15.3205 −0.491153
974974 0 0
975975 13.4641 0.431196
976976 0 0
977977 −28.3013 −0.905438 −0.452719 0.891653i 0.649546π-0.649546\pi
−0.452719 + 0.891653i 0.649546π0.649546\pi
978978 0 0
979979 0 0
980980 0 0
981981 2.39230 0.0763804
982982 0 0
983983 −24.0000 −0.765481 −0.382741 0.923856i 0.625020π-0.625020\pi
−0.382741 + 0.923856i 0.625020π0.625020\pi
984984 0 0
985985 −49.1769 −1.56691
986986 0 0
987987 11.6603 0.371150
988988 0 0
989989 0 0
990990 0 0
991991 −12.7846 −0.406117 −0.203058 0.979167i 0.565088π-0.565088\pi
−0.203058 + 0.979167i 0.565088π0.565088\pi
992992 0 0
993993 −22.2487 −0.706042
994994 0 0
995995 −33.8564 −1.07332
996996 0 0
997997 −19.8564 −0.628859 −0.314429 0.949281i 0.601813π-0.601813\pi
−0.314429 + 0.949281i 0.601813π0.601813\pi
998998 0 0
999999 10.0000 0.316386
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 3192.2.a.q.1.2 2
3.2 odd 2 9576.2.a.bj.1.1 2
4.3 odd 2 6384.2.a.bs.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3192.2.a.q.1.2 2 1.1 even 1 trivial
6384.2.a.bs.1.2 2 4.3 odd 2
9576.2.a.bj.1.1 2 3.2 odd 2