Properties

Label 2160.3.c.q.1889.10
Level 21602160
Weight 33
Character 2160.1889
Analytic conductor 58.85658.856
Analytic rank 00
Dimension 2424
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2160,3,Mod(1889,2160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2160.1889");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 2160=24335 2160 = 2^{4} \cdot 3^{3} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 2160.c (of order 22, degree 11, 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: 58.855737101858.8557371018
Analytic rank: 00
Dimension: 2424
Twist minimal: no (minimal twist has level 1080)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1889.10
Character χ\chi == 2160.1889
Dual form 2160.3.c.q.1889.9

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+(1.72017+4.69478i)q513.6186iq71.59573iq11+17.2139iq13+21.0854q1711.6883q1924.4565q23+(19.082016.1517i)q25+40.5058iq29+38.6629q31+(63.9362+23.4263i)q3532.5152iq375.41815iq4115.7699iq43+32.8867q47136.465q49+97.5723q53+(7.49161+2.74493i)q55+88.1744iq59+9.07733q61+(80.815729.6110i)q6526.8943iq67109.861iq7129.0319iq7321.7316q77+18.3005q7923.3872q83+(36.2705+98.9912i)q85147.211iq89+234.429q91+(20.105854.8738i)q95+100.818iq97+O(q100)q+(-1.72017 + 4.69478i) q^{5} -13.6186i q^{7} -1.59573i q^{11} +17.2139i q^{13} +21.0854 q^{17} -11.6883 q^{19} -24.4565 q^{23} +(-19.0820 - 16.1517i) q^{25} +40.5058i q^{29} +38.6629 q^{31} +(63.9362 + 23.4263i) q^{35} -32.5152i q^{37} -5.41815i q^{41} -15.7699i q^{43} +32.8867 q^{47} -136.465 q^{49} +97.5723 q^{53} +(7.49161 + 2.74493i) q^{55} +88.1744i q^{59} +9.07733 q^{61} +(-80.8157 - 29.6110i) q^{65} -26.8943i q^{67} -109.861i q^{71} -29.0319i q^{73} -21.7316 q^{77} +18.3005 q^{79} -23.3872 q^{83} +(-36.2705 + 98.9912i) q^{85} -147.211i q^{89} +234.429 q^{91} +(20.1058 - 54.8738i) q^{95} +100.818i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q72q25+72q31408q49+168q55240q61+312q7996q85+O(q100) 24 q - 72 q^{25} + 72 q^{31} - 408 q^{49} + 168 q^{55} - 240 q^{61} + 312 q^{79} - 96 q^{85}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2160Z)×\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times.

nn 271271 12971297 16211621 20812081
χ(n)\chi(n) 11 1-1 11 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
33 0 0
44 0 0
55 −1.72017 + 4.69478i −0.344035 + 0.938957i
66 0 0
77 13.6186i 1.94551i −0.231838 0.972754i 0.574474π-0.574474\pi
0.231838 0.972754i 0.425526π-0.425526\pi
88 0 0
99 0 0
1010 0 0
1111 1.59573i 0.145066i −0.997366 0.0725332i 0.976892π-0.976892\pi
0.997366 0.0725332i 0.0231083π-0.0231083\pi
1212 0 0
1313 17.2139i 1.32415i 0.749438 + 0.662075i 0.230324π0.230324\pi
−0.749438 + 0.662075i 0.769676π0.769676\pi
1414 0 0
1515 0 0
1616 0 0
1717 21.0854 1.24031 0.620157 0.784477i 0.287069π-0.287069\pi
0.620157 + 0.784477i 0.287069π0.287069\pi
1818 0 0
1919 −11.6883 −0.615171 −0.307586 0.951520i 0.599521π-0.599521\pi
−0.307586 + 0.951520i 0.599521π0.599521\pi
2020 0 0
2121 0 0
2222 0 0
2323 −24.4565 −1.06333 −0.531663 0.846956i 0.678433π-0.678433\pi
−0.531663 + 0.846956i 0.678433π0.678433\pi
2424 0 0
2525 −19.0820 16.1517i −0.763280 0.646068i
2626 0 0
2727 0 0
2828 0 0
2929 40.5058i 1.39675i 0.715732 + 0.698375i 0.246093π0.246093\pi
−0.715732 + 0.698375i 0.753907π0.753907\pi
3030 0 0
3131 38.6629 1.24719 0.623595 0.781748i 0.285672π-0.285672\pi
0.623595 + 0.781748i 0.285672π0.285672\pi
3232 0 0
3333 0 0
3434 0 0
3535 63.9362 + 23.4263i 1.82675 + 0.669323i
3636 0 0
3737 32.5152i 0.878789i −0.898294 0.439394i 0.855193π-0.855193\pi
0.898294 0.439394i 0.144807π-0.144807\pi
3838 0 0
3939 0 0
4040 0 0
4141 5.41815i 0.132150i −0.997815 0.0660751i 0.978952π-0.978952\pi
0.997815 0.0660751i 0.0210477π-0.0210477\pi
4242 0 0
4343 15.7699i 0.366741i −0.983044 0.183371i 0.941299π-0.941299\pi
0.983044 0.183371i 0.0587008π-0.0587008\pi
4444 0 0
4545 0 0
4646 0 0
4747 32.8867 0.699717 0.349858 0.936803i 0.386230π-0.386230\pi
0.349858 + 0.936803i 0.386230π0.386230\pi
4848 0 0
4949 −136.465 −2.78501
5050 0 0
5151 0 0
5252 0 0
5353 97.5723 1.84099 0.920493 0.390759i 0.127787π-0.127787\pi
0.920493 + 0.390759i 0.127787π0.127787\pi
5454 0 0
5555 7.49161 + 2.74493i 0.136211 + 0.0499079i
5656 0 0
5757 0 0
5858 0 0
5959 88.1744i 1.49448i 0.664553 + 0.747241i 0.268622π0.268622\pi
−0.664553 + 0.747241i 0.731378π0.731378\pi
6060 0 0
6161 9.07733 0.148809 0.0744044 0.997228i 0.476294π-0.476294\pi
0.0744044 + 0.997228i 0.476294π0.476294\pi
6262 0 0
6363 0 0
6464 0 0
6565 −80.8157 29.6110i −1.24332 0.455553i
6666 0 0
6767 26.8943i 0.401408i −0.979652 0.200704i 0.935677π-0.935677\pi
0.979652 0.200704i 0.0643230π-0.0643230\pi
6868 0 0
6969 0 0
7070 0 0
7171 109.861i 1.54733i −0.633593 0.773666i 0.718421π-0.718421\pi
0.633593 0.773666i 0.281579π-0.281579\pi
7272 0 0
7373 29.0319i 0.397697i −0.980030 0.198848i 0.936280π-0.936280\pi
0.980030 0.198848i 0.0637202π-0.0637202\pi
7474 0 0
7575 0 0
7676 0 0
7777 −21.7316 −0.282228
7878 0 0
7979 18.3005 0.231652 0.115826 0.993269i 0.463048π-0.463048\pi
0.115826 + 0.993269i 0.463048π0.463048\pi
8080 0 0
8181 0 0
8282 0 0
8383 −23.3872 −0.281773 −0.140887 0.990026i 0.544995π-0.544995\pi
−0.140887 + 0.990026i 0.544995π0.544995\pi
8484 0 0
8585 −36.2705 + 98.9912i −0.426712 + 1.16460i
8686 0 0
8787 0 0
8888 0 0
8989 147.211i 1.65406i −0.562160 0.827028i 0.690030π-0.690030\pi
0.562160 0.827028i 0.309970π-0.309970\pi
9090 0 0
9191 234.429 2.57614
9292 0 0
9393 0 0
9494 0 0
9595 20.1058 54.8738i 0.211640 0.577619i
9696 0 0
9797 100.818i 1.03936i 0.854362 + 0.519678i 0.173948π0.173948\pi
−0.854362 + 0.519678i 0.826052π0.826052\pi
9898 0 0
9999 0 0
100100 0 0
101101 103.221i 1.02199i −0.859582 0.510997i 0.829276π-0.829276\pi
0.859582 0.510997i 0.170724π-0.170724\pi
102102 0 0
103103 42.0848i 0.408590i −0.978909 0.204295i 0.934510π-0.934510\pi
0.978909 0.204295i 0.0654902π-0.0654902\pi
104104 0 0
105105 0 0
106106 0 0
107107 151.752 1.41824 0.709121 0.705087i 0.249092π-0.249092\pi
0.709121 + 0.705087i 0.249092π0.249092\pi
108108 0 0
109109 −65.4958 −0.600879 −0.300439 0.953801i 0.597133π-0.597133\pi
−0.300439 + 0.953801i 0.597133π0.597133\pi
110110 0 0
111111 0 0
112112 0 0
113113 133.768 1.18379 0.591893 0.806016i 0.298381π-0.298381\pi
0.591893 + 0.806016i 0.298381π0.298381\pi
114114 0 0
115115 42.0694 114.818i 0.365821 0.998417i
116116 0 0
117117 0 0
118118 0 0
119119 287.152i 2.41304i
120120 0 0
121121 118.454 0.978956
122122 0 0
123123 0 0
124124 0 0
125125 108.653 61.8021i 0.869225 0.494417i
126126 0 0
127127 20.3722i 0.160411i −0.996778 0.0802054i 0.974442π-0.974442\pi
0.996778 0.0802054i 0.0255576π-0.0255576\pi
128128 0 0
129129 0 0
130130 0 0
131131 109.292i 0.834293i −0.908839 0.417146i 0.863030π-0.863030\pi
0.908839 0.417146i 0.136970π-0.136970\pi
132132 0 0
133133 159.177i 1.19682i
134134 0 0
135135 0 0
136136 0 0
137137 30.3772 0.221732 0.110866 0.993835i 0.464638π-0.464638\pi
0.110866 + 0.993835i 0.464638π0.464638\pi
138138 0 0
139139 −85.7921 −0.617210 −0.308605 0.951190i 0.599862π-0.599862\pi
−0.308605 + 0.951190i 0.599862π0.599862\pi
140140 0 0
141141 0 0
142142 0 0
143143 27.4688 0.192090
144144 0 0
145145 −190.166 69.6770i −1.31149 0.480531i
146146 0 0
147147 0 0
148148 0 0
149149 87.3174i 0.586023i −0.956109 0.293011i 0.905343π-0.905343\pi
0.956109 0.293011i 0.0946574π-0.0946574\pi
150150 0 0
151151 218.922 1.44982 0.724908 0.688846i 0.241882π-0.241882\pi
0.724908 + 0.688846i 0.241882π0.241882\pi
152152 0 0
153153 0 0
154154 0 0
155155 −66.5069 + 181.514i −0.429077 + 1.17106i
156156 0 0
157157 92.4742i 0.589008i 0.955650 + 0.294504i 0.0951544π0.0951544\pi
−0.955650 + 0.294504i 0.904846π0.904846\pi
158158 0 0
159159 0 0
160160 0 0
161161 333.062i 2.06871i
162162 0 0
163163 252.317i 1.54796i 0.633211 + 0.773979i 0.281737π0.281737\pi
−0.633211 + 0.773979i 0.718263π0.718263\pi
164164 0 0
165165 0 0
166166 0 0
167167 91.0894 0.545445 0.272723 0.962093i 0.412076π-0.412076\pi
0.272723 + 0.962093i 0.412076π0.412076\pi
168168 0 0
169169 −127.320 −0.753371
170170 0 0
171171 0 0
172172 0 0
173173 185.784 1.07390 0.536948 0.843616i 0.319577π-0.319577\pi
0.536948 + 0.843616i 0.319577π0.319577\pi
174174 0 0
175175 −219.963 + 259.869i −1.25693 + 1.48497i
176176 0 0
177177 0 0
178178 0 0
179179 150.913i 0.843088i 0.906808 + 0.421544i 0.138512π0.138512\pi
−0.906808 + 0.421544i 0.861488π0.861488\pi
180180 0 0
181181 16.5251 0.0912990 0.0456495 0.998958i 0.485464π-0.485464\pi
0.0456495 + 0.998958i 0.485464π0.485464\pi
182182 0 0
183183 0 0
184184 0 0
185185 152.652 + 55.9318i 0.825145 + 0.302334i
186186 0 0
187187 33.6465i 0.179928i
188188 0 0
189189 0 0
190190 0 0
191191 13.9230i 0.0728953i 0.999336 + 0.0364476i 0.0116042π0.0116042\pi
−0.999336 + 0.0364476i 0.988396π0.988396\pi
192192 0 0
193193 95.7140i 0.495928i −0.968769 0.247964i 0.920239π-0.920239\pi
0.968769 0.247964i 0.0797614π-0.0797614\pi
194194 0 0
195195 0 0
196196 0 0
197197 254.417 1.29145 0.645727 0.763568i 0.276554π-0.276554\pi
0.645727 + 0.763568i 0.276554π0.276554\pi
198198 0 0
199199 325.493 1.63564 0.817821 0.575472i 0.195182π-0.195182\pi
0.817821 + 0.575472i 0.195182π0.195182\pi
200200 0 0
201201 0 0
202202 0 0
203203 551.630 2.71739
204204 0 0
205205 25.4371 + 9.32017i 0.124083 + 0.0454642i
206206 0 0
207207 0 0
208208 0 0
209209 18.6513i 0.0892407i
210210 0 0
211211 93.0330 0.440915 0.220457 0.975397i 0.429245π-0.429245\pi
0.220457 + 0.975397i 0.429245π0.429245\pi
212212 0 0
213213 0 0
214214 0 0
215215 74.0361 + 27.1269i 0.344354 + 0.126172i
216216 0 0
217217 526.533i 2.42642i
218218 0 0
219219 0 0
220220 0 0
221221 362.962i 1.64236i
222222 0 0
223223 256.345i 1.14953i −0.818318 0.574765i 0.805093π-0.805093\pi
0.818318 0.574765i 0.194907π-0.194907\pi
224224 0 0
225225 0 0
226226 0 0
227227 30.2963 0.133464 0.0667319 0.997771i 0.478743π-0.478743\pi
0.0667319 + 0.997771i 0.478743π0.478743\pi
228228 0 0
229229 265.885 1.16107 0.580536 0.814235i 0.302843π-0.302843\pi
0.580536 + 0.814235i 0.302843π0.302843\pi
230230 0 0
231231 0 0
232232 0 0
233233 −405.182 −1.73898 −0.869488 0.493953i 0.835551π-0.835551\pi
−0.869488 + 0.493953i 0.835551π0.835551\pi
234234 0 0
235235 −56.5708 + 154.396i −0.240727 + 0.657004i
236236 0 0
237237 0 0
238238 0 0
239239 369.639i 1.54661i 0.634036 + 0.773303i 0.281397π0.281397\pi
−0.634036 + 0.773303i 0.718603π0.718603\pi
240240 0 0
241241 340.021 1.41088 0.705439 0.708771i 0.250750π-0.250750\pi
0.705439 + 0.708771i 0.250750π0.250750\pi
242242 0 0
243243 0 0
244244 0 0
245245 234.744 640.675i 0.958139 2.61500i
246246 0 0
247247 201.201i 0.814579i
248248 0 0
249249 0 0
250250 0 0
251251 103.390i 0.411914i −0.978561 0.205957i 0.933969π-0.933969\pi
0.978561 0.205957i 0.0660307π-0.0660307\pi
252252 0 0
253253 39.0260i 0.154253i
254254 0 0
255255 0 0
256256 0 0
257257 367.987 1.43185 0.715927 0.698175i 0.246004π-0.246004\pi
0.715927 + 0.698175i 0.246004π0.246004\pi
258258 0 0
259259 −442.810 −1.70969
260260 0 0
261261 0 0
262262 0 0
263263 356.509 1.35555 0.677774 0.735270i 0.262945π-0.262945\pi
0.677774 + 0.735270i 0.262945π0.262945\pi
264264 0 0
265265 −167.841 + 458.081i −0.633363 + 1.72861i
266266 0 0
267267 0 0
268268 0 0
269269 24.4804i 0.0910051i −0.998964 0.0455026i 0.985511π-0.985511\pi
0.998964 0.0455026i 0.0144889π-0.0144889\pi
270270 0 0
271271 −492.669 −1.81797 −0.908984 0.416831i 0.863141π-0.863141\pi
−0.908984 + 0.416831i 0.863141π0.863141\pi
272272 0 0
273273 0 0
274274 0 0
275275 −25.7738 + 30.4497i −0.0937227 + 0.110726i
276276 0 0
277277 54.0702i 0.195199i 0.995226 + 0.0975997i 0.0311165π0.0311165\pi
−0.995226 + 0.0975997i 0.968884π0.968884\pi
278278 0 0
279279 0 0
280280 0 0
281281 84.9003i 0.302136i −0.988523 0.151068i 0.951729π-0.951729\pi
0.988523 0.151068i 0.0482713π-0.0482713\pi
282282 0 0
283283 527.876i 1.86529i −0.360799 0.932644i 0.617496π-0.617496\pi
0.360799 0.932644i 0.382504π-0.382504\pi
284284 0 0
285285 0 0
286286 0 0
287287 −73.7875 −0.257099
288288 0 0
289289 155.592 0.538381
290290 0 0
291291 0 0
292292 0 0
293293 −296.974 −1.01356 −0.506781 0.862075i 0.669165π-0.669165\pi
−0.506781 + 0.862075i 0.669165π0.669165\pi
294294 0 0
295295 −413.960 151.675i −1.40325 0.514154i
296296 0 0
297297 0 0
298298 0 0
299299 420.993i 1.40800i
300300 0 0
301301 −214.763 −0.713498
302302 0 0
303303 0 0
304304 0 0
305305 −15.6146 + 42.6161i −0.0511954 + 0.139725i
306306 0 0
307307 39.8780i 0.129896i 0.997889 + 0.0649479i 0.0206881π0.0206881\pi
−0.997889 + 0.0649479i 0.979312π0.979312\pi
308308 0 0
309309 0 0
310310 0 0
311311 321.299i 1.03312i −0.856252 0.516558i 0.827213π-0.827213\pi
0.856252 0.516558i 0.172787π-0.172787\pi
312312 0 0
313313 79.9726i 0.255504i 0.991806 + 0.127752i 0.0407761π0.0407761\pi
−0.991806 + 0.127752i 0.959224π0.959224\pi
314314 0 0
315315 0 0
316316 0 0
317317 307.837 0.971095 0.485547 0.874210i 0.338620π-0.338620\pi
0.485547 + 0.874210i 0.338620π0.338620\pi
318318 0 0
319319 64.6363 0.202622
320320 0 0
321321 0 0
322322 0 0
323323 −246.451 −0.763006
324324 0 0
325325 278.034 328.476i 0.855490 1.01070i
326326 0 0
327327 0 0
328328 0 0
329329 447.870i 1.36131i
330330 0 0
331331 −445.730 −1.34662 −0.673308 0.739362i 0.735127π-0.735127\pi
−0.673308 + 0.739362i 0.735127π0.735127\pi
332332 0 0
333333 0 0
334334 0 0
335335 126.263 + 46.2630i 0.376905 + 0.138098i
336336 0 0
337337 252.981i 0.750685i −0.926886 0.375343i 0.877525π-0.877525\pi
0.926886 0.375343i 0.122475π-0.122475\pi
338338 0 0
339339 0 0
340340 0 0
341341 61.6955i 0.180925i
342342 0 0
343343 1191.15i 3.47274i
344344 0 0
345345 0 0
346346 0 0
347347 −240.422 −0.692858 −0.346429 0.938076i 0.612606π-0.612606\pi
−0.346429 + 0.938076i 0.612606π0.612606\pi
348348 0 0
349349 434.750 1.24570 0.622851 0.782340i 0.285974π-0.285974\pi
0.622851 + 0.782340i 0.285974π0.285974\pi
350350 0 0
351351 0 0
352352 0 0
353353 −121.782 −0.344992 −0.172496 0.985010i 0.555183π-0.555183\pi
−0.172496 + 0.985010i 0.555183π0.555183\pi
354354 0 0
355355 515.772 + 188.979i 1.45288 + 0.532336i
356356 0 0
357357 0 0
358358 0 0
359359 376.123i 1.04770i 0.851812 + 0.523848i 0.175504π0.175504\pi
−0.851812 + 0.523848i 0.824496π0.824496\pi
360360 0 0
361361 −224.385 −0.621564
362362 0 0
363363 0 0
364364 0 0
365365 136.298 + 49.9399i 0.373420 + 0.136822i
366366 0 0
367367 388.055i 1.05737i −0.848818 0.528685i 0.822685π-0.822685\pi
0.848818 0.528685i 0.177315π-0.177315\pi
368368 0 0
369369 0 0
370370 0 0
371371 1328.79i 3.58166i
372372 0 0
373373 498.003i 1.33513i −0.744552 0.667565i 0.767337π-0.767337\pi
0.744552 0.667565i 0.232663π-0.232663\pi
374374 0 0
375375 0 0
376376 0 0
377377 −697.264 −1.84951
378378 0 0
379379 −381.165 −1.00571 −0.502856 0.864370i 0.667717π-0.667717\pi
−0.502856 + 0.864370i 0.667717π0.667717\pi
380380 0 0
381381 0 0
382382 0 0
383383 83.2956 0.217482 0.108741 0.994070i 0.465318π-0.465318\pi
0.108741 + 0.994070i 0.465318π0.465318\pi
384384 0 0
385385 37.3821 102.025i 0.0970963 0.265000i
386386 0 0
387387 0 0
388388 0 0
389389 322.027i 0.827832i −0.910315 0.413916i 0.864161π-0.864161\pi
0.910315 0.413916i 0.135839π-0.135839\pi
390390 0 0
391391 −515.674 −1.31886
392392 0 0
393393 0 0
394394 0 0
395395 −31.4801 + 85.9171i −0.0796965 + 0.217512i
396396 0 0
397397 683.223i 1.72097i −0.509479 0.860483i 0.670162π-0.670162\pi
0.509479 0.860483i 0.329838π-0.329838\pi
398398 0 0
399399 0 0
400400 0 0
401401 673.555i 1.67969i 0.542828 + 0.839844i 0.317354π0.317354\pi
−0.542828 + 0.839844i 0.682646π0.682646\pi
402402 0 0
403403 665.540i 1.65146i
404404 0 0
405405 0 0
406406 0 0
407407 −51.8855 −0.127483
408408 0 0
409409 428.725 1.04823 0.524113 0.851648i 0.324397π-0.324397\pi
0.524113 + 0.851648i 0.324397π0.324397\pi
410410 0 0
411411 0 0
412412 0 0
413413 1200.81 2.90753
414414 0 0
415415 40.2301 109.798i 0.0969399 0.264573i
416416 0 0
417417 0 0
418418 0 0
419419 85.0394i 0.202958i 0.994838 + 0.101479i 0.0323575π0.0323575\pi
−0.994838 + 0.101479i 0.967643π0.967643\pi
420420 0 0
421421 −99.1071 −0.235409 −0.117704 0.993049i 0.537554π-0.537554\pi
−0.117704 + 0.993049i 0.537554π0.537554\pi
422422 0 0
423423 0 0
424424 0 0
425425 −402.351 340.564i −0.946708 0.801328i
426426 0 0
427427 123.620i 0.289509i
428428 0 0
429429 0 0
430430 0 0
431431 133.079i 0.308768i −0.988011 0.154384i 0.950661π-0.950661\pi
0.988011 0.154384i 0.0493393π-0.0493393\pi
432432 0 0
433433 305.104i 0.704628i 0.935882 + 0.352314i 0.114605π0.114605\pi
−0.935882 + 0.352314i 0.885395π0.885395\pi
434434 0 0
435435 0 0
436436 0 0
437437 285.854 0.654128
438438 0 0
439439 745.820 1.69891 0.849453 0.527664i 0.176932π-0.176932\pi
0.849453 + 0.527664i 0.176932π0.176932\pi
440440 0 0
441441 0 0
442442 0 0
443443 −477.301 −1.07743 −0.538715 0.842488i 0.681090π-0.681090\pi
−0.538715 + 0.842488i 0.681090π0.681090\pi
444444 0 0
445445 691.124 + 253.229i 1.55309 + 0.569053i
446446 0 0
447447 0 0
448448 0 0
449449 502.795i 1.11981i 0.828557 + 0.559905i 0.189163π0.189163\pi
−0.828557 + 0.559905i 0.810837π0.810837\pi
450450 0 0
451451 −8.64592 −0.0191705
452452 0 0
453453 0 0
454454 0 0
455455 −403.259 + 1100.59i −0.886283 + 2.41889i
456456 0 0
457457 352.233i 0.770750i 0.922760 + 0.385375i 0.125928π0.125928\pi
−0.922760 + 0.385375i 0.874072π0.874072\pi
458458 0 0
459459 0 0
460460 0 0
461461 159.782i 0.346598i 0.984869 + 0.173299i 0.0554427π0.0554427\pi
−0.984869 + 0.173299i 0.944557π0.944557\pi
462462 0 0
463463 486.215i 1.05014i −0.851059 0.525070i 0.824039π-0.824039\pi
0.851059 0.525070i 0.175961π-0.175961\pi
464464 0 0
465465 0 0
466466 0 0
467467 220.960 0.473147 0.236573 0.971614i 0.423976π-0.423976\pi
0.236573 + 0.971614i 0.423976π0.423976\pi
468468 0 0
469469 −366.262 −0.780943
470470 0 0
471471 0 0
472472 0 0
473473 −25.1645 −0.0532018
474474 0 0
475475 223.035 + 188.785i 0.469548 + 0.397442i
476476 0 0
477477 0 0
478478 0 0
479479 343.941i 0.718040i 0.933330 + 0.359020i 0.116889π0.116889\pi
−0.933330 + 0.359020i 0.883111π0.883111\pi
480480 0 0
481481 559.715 1.16365
482482 0 0
483483 0 0
484484 0 0
485485 −473.317 173.424i −0.975911 0.357575i
486486 0 0
487487 38.0395i 0.0781098i 0.999237 + 0.0390549i 0.0124347π0.0124347\pi
−0.999237 + 0.0390549i 0.987565π0.987565\pi
488488 0 0
489489 0 0
490490 0 0
491491 203.703i 0.414874i 0.978248 + 0.207437i 0.0665121π0.0665121\pi
−0.978248 + 0.207437i 0.933488π0.933488\pi
492492 0 0
493493 854.078i 1.73241i
494494 0 0
495495 0 0
496496 0 0
497497 −1496.14 −3.01035
498498 0 0
499499 −469.710 −0.941302 −0.470651 0.882319i 0.655981π-0.655981\pi
−0.470651 + 0.882319i 0.655981π0.655981\pi
500500 0 0
501501 0 0
502502 0 0
503503 −213.475 −0.424403 −0.212202 0.977226i 0.568063π-0.568063\pi
−0.212202 + 0.977226i 0.568063π0.568063\pi
504504 0 0
505505 484.603 + 177.559i 0.959609 + 0.351602i
506506 0 0
507507 0 0
508508 0 0
509509 535.595i 1.05225i 0.850407 + 0.526125i 0.176356π0.176356\pi
−0.850407 + 0.526125i 0.823644π0.823644\pi
510510 0 0
511511 −395.372 −0.773723
512512 0 0
513513 0 0
514514 0 0
515515 197.579 + 72.3931i 0.383648 + 0.140569i
516516 0 0
517517 52.4783i 0.101505i
518518 0 0
519519 0 0
520520 0 0
521521 503.822i 0.967029i 0.875336 + 0.483515i 0.160640π0.160640\pi
−0.875336 + 0.483515i 0.839360π0.839360\pi
522522 0 0
523523 370.237i 0.707911i −0.935262 0.353955i 0.884836π-0.884836\pi
0.935262 0.353955i 0.115164π-0.115164\pi
524524 0 0
525525 0 0
526526 0 0
527527 815.220 1.54691
528528 0 0
529529 69.1203 0.130662
530530 0 0
531531 0 0
532532 0 0
533533 93.2678 0.174986
534534 0 0
535535 −261.040 + 712.443i −0.487925 + 1.33167i
536536 0 0
537537 0 0
538538 0 0
539539 217.762i 0.404011i
540540 0 0
541541 −914.913 −1.69115 −0.845576 0.533856i 0.820743π-0.820743\pi
−0.845576 + 0.533856i 0.820743π0.820743\pi
542542 0 0
543543 0 0
544544 0 0
545545 112.664 307.489i 0.206723 0.564199i
546546 0 0
547547 513.322i 0.938431i −0.883084 0.469215i 0.844537π-0.844537\pi
0.883084 0.469215i 0.155463π-0.155463\pi
548548 0 0
549549 0 0
550550 0 0
551551 473.442i 0.859241i
552552 0 0
553553 249.227i 0.450682i
554554 0 0
555555 0 0
556556 0 0
557557 528.051 0.948028 0.474014 0.880517i 0.342805π-0.342805\pi
0.474014 + 0.880517i 0.342805π0.342805\pi
558558 0 0
559559 271.461 0.485620
560560 0 0
561561 0 0
562562 0 0
563563 −517.680 −0.919503 −0.459752 0.888048i 0.652062π-0.652062\pi
−0.459752 + 0.888048i 0.652062π0.652062\pi
564564 0 0
565565 −230.104 + 628.011i −0.407264 + 1.11152i
566566 0 0
567567 0 0
568568 0 0
569569 977.375i 1.71771i −0.512222 0.858853i 0.671177π-0.671177\pi
0.512222 0.858853i 0.328823π-0.328823\pi
570570 0 0
571571 299.724 0.524911 0.262456 0.964944i 0.415468π-0.415468\pi
0.262456 + 0.964944i 0.415468π0.415468\pi
572572 0 0
573573 0 0
574574 0 0
575575 466.679 + 395.014i 0.811615 + 0.686981i
576576 0 0
577577 117.212i 0.203140i 0.994828 + 0.101570i 0.0323866π0.0323866\pi
−0.994828 + 0.101570i 0.967613π0.967613\pi
578578 0 0
579579 0 0
580580 0 0
581581 318.500i 0.548193i
582582 0 0
583583 155.699i 0.267065i
584584 0 0
585585 0 0
586586 0 0
587587 −286.792 −0.488572 −0.244286 0.969703i 0.578554π-0.578554\pi
−0.244286 + 0.969703i 0.578554π0.578554\pi
588588 0 0
589589 −451.902 −0.767235
590590 0 0
591591 0 0
592592 0 0
593593 −57.1262 −0.0963343 −0.0481672 0.998839i 0.515338π-0.515338\pi
−0.0481672 + 0.998839i 0.515338π0.515338\pi
594594 0 0
595595 1348.12 + 493.952i 2.26574 + 0.830171i
596596 0 0
597597 0 0
598598 0 0
599599 407.955i 0.681060i 0.940234 + 0.340530i 0.110607π0.110607\pi
−0.940234 + 0.340530i 0.889393π0.889393\pi
600600 0 0
601601 −442.203 −0.735778 −0.367889 0.929870i 0.619919π-0.619919\pi
−0.367889 + 0.929870i 0.619919π0.619919\pi
602602 0 0
603603 0 0
604604 0 0
605605 −203.761 + 556.114i −0.336795 + 0.919197i
606606 0 0
607607 28.6479i 0.0471958i −0.999722 0.0235979i 0.992488π-0.992488\pi
0.999722 0.0235979i 0.00751215π-0.00751215\pi
608608 0 0
609609 0 0
610610 0 0
611611 566.110i 0.926529i
612612 0 0
613613 464.159i 0.757192i 0.925562 + 0.378596i 0.123593π0.123593\pi
−0.925562 + 0.378596i 0.876407π0.876407\pi
614614 0 0
615615 0 0
616616 0 0
617617 −593.277 −0.961551 −0.480776 0.876844i 0.659645π-0.659645\pi
−0.480776 + 0.876844i 0.659645π0.659645\pi
618618 0 0
619619 −794.099 −1.28287 −0.641437 0.767176i 0.721662π-0.721662\pi
−0.641437 + 0.767176i 0.721662π0.721662\pi
620620 0 0
621621 0 0
622622 0 0
623623 −2004.80 −3.21798
624624 0 0
625625 103.245 + 616.413i 0.165193 + 0.986261i
626626 0 0
627627 0 0
628628 0 0
629629 685.594i 1.08998i
630630 0 0
631631 −58.8087 −0.0931991 −0.0465996 0.998914i 0.514838π-0.514838\pi
−0.0465996 + 0.998914i 0.514838π0.514838\pi
632632 0 0
633633 0 0
634634 0 0
635635 95.6429 + 35.0437i 0.150619 + 0.0551869i
636636 0 0
637637 2349.10i 3.68776i
638638 0 0
639639 0 0
640640 0 0
641641 916.323i 1.42952i 0.699369 + 0.714760i 0.253464π0.253464\pi
−0.699369 + 0.714760i 0.746536π0.746536\pi
642642 0 0
643643 94.0391i 0.146251i 0.997323 + 0.0731253i 0.0232973π0.0232973\pi
−0.997323 + 0.0731253i 0.976703π0.976703\pi
644644 0 0
645645 0 0
646646 0 0
647647 −250.055 −0.386484 −0.193242 0.981151i 0.561900π-0.561900\pi
−0.193242 + 0.981151i 0.561900π0.561900\pi
648648 0 0
649649 140.703 0.216799
650650 0 0
651651 0 0
652652 0 0
653653 −716.952 −1.09794 −0.548968 0.835843i 0.684979π-0.684979\pi
−0.548968 + 0.835843i 0.684979π0.684979\pi
654654 0 0
655655 513.104 + 188.002i 0.783365 + 0.287026i
656656 0 0
657657 0 0
658658 0 0
659659 421.359i 0.639391i 0.947520 + 0.319696i 0.103581π0.103581\pi
−0.947520 + 0.319696i 0.896419π0.896419\pi
660660 0 0
661661 −426.618 −0.645413 −0.322707 0.946499i 0.604593π-0.604593\pi
−0.322707 + 0.946499i 0.604593π0.604593\pi
662662 0 0
663663 0 0
664664 0 0
665665 −747.303 273.813i −1.12376 0.411748i
666666 0 0
667667 990.629i 1.48520i
668668 0 0
669669 0 0
670670 0 0
671671 14.4850i 0.0215871i
672672 0 0
673673 8.65133i 0.0128549i −0.999979 0.00642744i 0.997954π-0.997954\pi
0.999979 0.00642744i 0.00204593π-0.00204593\pi
674674 0 0
675675 0 0
676676 0 0
677677 69.4880 0.102641 0.0513206 0.998682i 0.483657π-0.483657\pi
0.0513206 + 0.998682i 0.483657π0.483657\pi
678678 0 0
679679 1372.99 2.02208
680680 0 0
681681 0 0
682682 0 0
683683 217.382 0.318276 0.159138 0.987256i 0.449129π-0.449129\pi
0.159138 + 0.987256i 0.449129π0.449129\pi
684684 0 0
685685 −52.2541 + 142.615i −0.0762834 + 0.208196i
686686 0 0
687687 0 0
688688 0 0
689689 1679.60i 2.43774i
690690 0 0
691691 1063.94 1.53971 0.769853 0.638221i 0.220329π-0.220329\pi
0.769853 + 0.638221i 0.220329π0.220329\pi
692692 0 0
693693 0 0
694694 0 0
695695 147.577 402.776i 0.212342 0.579533i
696696 0 0
697697 114.244i 0.163908i
698698 0 0
699699 0 0
700700 0 0
701701 1095.79i 1.56318i 0.623795 + 0.781588i 0.285590π0.285590\pi
−0.623795 + 0.781588i 0.714410π0.714410\pi
702702 0 0
703703 380.046i 0.540606i
704704 0 0
705705 0 0
706706 0 0
707707 −1405.73 −1.98830
708708 0 0
709709 −784.926 −1.10709 −0.553545 0.832820i 0.686725π-0.686725\pi
−0.553545 + 0.832820i 0.686725π0.686725\pi
710710 0 0
711711 0 0
712712 0 0
713713 −945.558 −1.32617
714714 0 0
715715 −47.2511 + 128.960i −0.0660855 + 0.180364i
716716 0 0
717717 0 0
718718 0 0
719719 1086.25i 1.51078i −0.655274 0.755391i 0.727447π-0.727447\pi
0.655274 0.755391i 0.272553π-0.272553\pi
720720 0 0
721721 −573.134 −0.794915
722722 0 0
723723 0 0
724724 0 0
725725 654.237 772.931i 0.902396 1.06611i
726726 0 0
727727 790.496i 1.08734i −0.839299 0.543670i 0.817034π-0.817034\pi
0.839299 0.543670i 0.182966π-0.182966\pi
728728 0 0
729729 0 0
730730 0 0
731731 332.513i 0.454874i
732732 0 0
733733 82.0567i 0.111946i 0.998432 + 0.0559732i 0.0178261π0.0178261\pi
−0.998432 + 0.0559732i 0.982174π0.982174\pi
734734 0 0
735735 0 0
736736 0 0
737737 −42.9161 −0.0582309
738738 0 0
739739 −119.154 −0.161237 −0.0806186 0.996745i 0.525690π-0.525690\pi
−0.0806186 + 0.996745i 0.525690π0.525690\pi
740740 0 0
741741 0 0
742742 0 0
743743 1233.25 1.65982 0.829912 0.557894i 0.188391π-0.188391\pi
0.829912 + 0.557894i 0.188391π0.188391\pi
744744 0 0
745745 409.936 + 150.201i 0.550250 + 0.201612i
746746 0 0
747747 0 0
748748 0 0
749749 2066.64i 2.75920i
750750 0 0
751751 39.0008 0.0519318 0.0259659 0.999663i 0.491734π-0.491734\pi
0.0259659 + 0.999663i 0.491734π0.491734\pi
752752 0 0
753753 0 0
754754 0 0
755755 −376.584 + 1027.79i −0.498787 + 1.36131i
756756 0 0
757757 300.471i 0.396923i 0.980109 + 0.198461i 0.0635944π0.0635944\pi
−0.980109 + 0.198461i 0.936406π0.936406\pi
758758 0 0
759759 0 0
760760 0 0
761761 618.814i 0.813159i 0.913615 + 0.406579i 0.133279π0.133279\pi
−0.913615 + 0.406579i 0.866721π0.866721\pi
762762 0 0
763763 891.959i 1.16902i
764764 0 0
765765 0 0
766766 0 0
767767 −1517.83 −1.97892
768768 0 0
769769 −1333.56 −1.73414 −0.867072 0.498183i 0.834001π-0.834001\pi
−0.867072 + 0.498183i 0.834001π0.834001\pi
770770 0 0
771771 0 0
772772 0 0
773773 835.665 1.08107 0.540534 0.841322i 0.318222π-0.318222\pi
0.540534 + 0.841322i 0.318222π0.318222\pi
774774 0 0
775775 −737.765 624.471i −0.951955 0.805769i
776776 0 0
777777 0 0
778778 0 0
779779 63.3288i 0.0812950i
780780 0 0
781781 −175.308 −0.224466
782782 0 0
783783 0 0
784784 0 0
785785 −434.147 159.072i −0.553053 0.202639i
786786 0 0
787787 646.301i 0.821221i −0.911811 0.410610i 0.865316π-0.865316\pi
0.911811 0.410610i 0.134684π-0.134684\pi
788788 0 0
789789 0 0
790790 0 0
791791 1821.73i 2.30307i
792792 0 0
793793 156.257i 0.197045i
794794 0 0
795795 0 0
796796 0 0
797797 747.026 0.937297 0.468649 0.883385i 0.344741π-0.344741\pi
0.468649 + 0.883385i 0.344741π0.344741\pi
798798 0 0
799799 693.428 0.867869
800800 0 0
801801 0 0
802802 0 0
803803 −46.3271 −0.0576925
804804 0 0
805805 −1563.66 572.925i −1.94243 0.711708i
806806 0 0
807807 0 0
808808 0 0
809809 963.606i 1.19111i 0.803315 + 0.595554i 0.203067π0.203067\pi
−0.803315 + 0.595554i 0.796933π0.796933\pi
810810 0 0
811811 −862.849 −1.06393 −0.531966 0.846766i 0.678547π-0.678547\pi
−0.531966 + 0.846766i 0.678547π0.678547\pi
812812 0 0
813813 0 0
814814 0 0
815815 −1184.58 434.030i −1.45347 0.532552i
816816 0 0
817817 184.322i 0.225609i
818818 0 0
819819 0 0
820820 0 0
821821 1050.18i 1.27915i −0.768729 0.639575i 0.779111π-0.779111\pi
0.768729 0.639575i 0.220889π-0.220889\pi
822822 0 0
823823 216.916i 0.263567i −0.991278 0.131784i 0.957930π-0.957930\pi
0.991278 0.131784i 0.0420704π-0.0420704\pi
824824 0 0
825825 0 0
826826 0 0
827827 1051.87 1.27191 0.635955 0.771726i 0.280607π-0.280607\pi
0.635955 + 0.771726i 0.280607π0.280607\pi
828828 0 0
829829 647.285 0.780802 0.390401 0.920645i 0.372336π-0.372336\pi
0.390401 + 0.920645i 0.372336π0.372336\pi
830830 0 0
831831 0 0
832832 0 0
833833 −2877.42 −3.45428
834834 0 0
835835 −156.690 + 427.645i −0.187652 + 0.512150i
836836 0 0
837837 0 0
838838 0 0
839839 480.093i 0.572221i 0.958197 + 0.286110i 0.0923624π0.0923624\pi
−0.958197 + 0.286110i 0.907638π0.907638\pi
840840 0 0
841841 −799.718 −0.950913
842842 0 0
843843 0 0
844844 0 0
845845 219.012 597.738i 0.259186 0.707383i
846846 0 0
847847 1613.17i 1.90457i
848848 0 0
849849 0 0
850850 0 0
851851 795.208i 0.934439i
852852 0 0
853853 109.664i 0.128563i −0.997932 0.0642815i 0.979524π-0.979524\pi
0.997932 0.0642815i 0.0204756π-0.0204756\pi
854854 0 0
855855 0 0
856856 0 0
857857 434.234 0.506690 0.253345 0.967376i 0.418469π-0.418469\pi
0.253345 + 0.967376i 0.418469π0.418469\pi
858858 0 0
859859 −63.0244 −0.0733695 −0.0366848 0.999327i 0.511680π-0.511680\pi
−0.0366848 + 0.999327i 0.511680π0.511680\pi
860860 0 0
861861 0 0
862862 0 0
863863 −717.730 −0.831669 −0.415834 0.909440i 0.636510π-0.636510\pi
−0.415834 + 0.909440i 0.636510π0.636510\pi
864864 0 0
865865 −319.581 + 872.215i −0.369457 + 1.00834i
866866 0 0
867867 0 0
868868 0 0
869869 29.2027i 0.0336050i
870870 0 0
871871 462.958 0.531524
872872 0 0
873873 0 0
874874 0 0
875875 −841.656 1479.70i −0.961893 1.69108i
876876 0 0
877877 874.660i 0.997332i 0.866794 + 0.498666i 0.166176π0.166176\pi
−0.866794 + 0.498666i 0.833824π0.833824\pi
878878 0 0
879879 0 0
880880 0 0
881881 338.427i 0.384140i −0.981381 0.192070i 0.938480π-0.938480\pi
0.981381 0.192070i 0.0615200π-0.0615200\pi
882882 0 0
883883 1147.73i 1.29981i −0.760014 0.649906i 0.774808π-0.774808\pi
0.760014 0.649906i 0.225192π-0.225192\pi
884884 0 0
885885 0 0
886886 0 0
887887 −1090.15 −1.22903 −0.614516 0.788904i 0.710649π-0.710649\pi
−0.614516 + 0.788904i 0.710649π0.710649\pi
888888 0 0
889889 −277.440 −0.312081
890890 0 0
891891 0 0
892892 0 0
893893 −384.388 −0.430446
894894 0 0
895895 −708.502 259.596i −0.791623 0.290052i
896896 0 0
897897 0 0
898898 0 0
899899 1566.07i 1.74201i
900900 0 0
901901 2057.35 2.28340
902902 0 0
903903 0 0
904904 0 0
905905 −28.4261 + 77.5819i −0.0314100 + 0.0857258i
906906 0 0
907907 809.177i 0.892147i −0.894996 0.446073i 0.852822π-0.852822\pi
0.894996 0.446073i 0.147178π-0.147178\pi
908908 0 0
909909 0 0
910910 0 0
911911 80.7549i 0.0886442i −0.999017 0.0443221i 0.985887π-0.985887\pi
0.999017 0.0443221i 0.0141128π-0.0141128\pi
912912 0 0
913913 37.3197i 0.0408759i
914914 0 0
915915 0 0
916916 0 0
917917 −1488.40 −1.62312
918918 0 0
919919 473.589 0.515331 0.257665 0.966234i 0.417047π-0.417047\pi
0.257665 + 0.966234i 0.417047π0.417047\pi
920920 0 0
921921 0 0
922922 0 0
923923 1891.13 2.04890
924924 0 0
925925 −525.175 + 620.455i −0.567757 + 0.670762i
926926 0 0
927927 0 0
928928 0 0
929929 166.653i 0.179390i 0.995969 + 0.0896949i 0.0285892π0.0285892\pi
−0.995969 + 0.0896949i 0.971411π0.971411\pi
930930 0 0
931931 1595.04 1.71326
932932 0 0
933933 0 0
934934 0 0
935935 157.963 + 57.8779i 0.168945 + 0.0619015i
936936 0 0
937937 1128.54i 1.20442i −0.798338 0.602210i 0.794287π-0.794287\pi
0.798338 0.602210i 0.205713π-0.205713\pi
938938 0 0
939939 0 0
940940 0 0
941941 6.17302i 0.00656007i 0.999995 + 0.00328003i 0.00104407π0.00104407\pi
−0.999995 + 0.00328003i 0.998956π0.998956\pi
942942 0 0
943943 132.509i 0.140519i
944944 0 0
945945 0 0
946946 0 0
947947 1078.59 1.13895 0.569477 0.822007i 0.307146π-0.307146\pi
0.569477 + 0.822007i 0.307146π0.307146\pi
948948 0 0
949949 499.753 0.526610
950950 0 0
951951 0 0
952952 0 0
953953 −230.467 −0.241833 −0.120917 0.992663i 0.538583π-0.538583\pi
−0.120917 + 0.992663i 0.538583π0.538583\pi
954954 0 0
955955 −65.3655 23.9500i −0.0684455 0.0250785i
956956 0 0
957957 0 0
958958 0 0
959959 413.694i 0.431381i
960960 0 0
961961 533.817 0.555481
962962 0 0
963963 0 0
964964 0 0
965965 449.357 + 164.645i 0.465655 + 0.170616i
966966 0 0
967967 1452.71i 1.50229i 0.660140 + 0.751143i 0.270497π0.270497\pi
−0.660140 + 0.751143i 0.729503π0.729503\pi
968968 0 0
969969 0 0
970970 0 0
971971 1192.60i 1.22822i 0.789222 + 0.614108i 0.210484π0.210484\pi
−0.789222 + 0.614108i 0.789516π0.789516\pi
972972 0 0
973973 1168.37i 1.20079i
974974 0 0
975975 0 0
976976 0 0
977977 −540.885 −0.553619 −0.276809 0.960925i 0.589277π-0.589277\pi
−0.276809 + 0.960925i 0.589277π0.589277\pi
978978 0 0
979979 −234.909 −0.239948
980980 0 0
981981 0 0
982982 0 0
983983 1508.68 1.53477 0.767386 0.641186i 0.221557π-0.221557\pi
0.767386 + 0.641186i 0.221557π0.221557\pi
984984 0 0
985985 −437.641 + 1194.43i −0.444305 + 1.21262i
986986 0 0
987987 0 0
988988 0 0
989989 385.676i 0.389965i
990990 0 0
991991 483.637 0.488030 0.244015 0.969771i 0.421535π-0.421535\pi
0.244015 + 0.969771i 0.421535π0.421535\pi
992992 0 0
993993 0 0
994994 0 0
995995 −559.905 + 1528.12i −0.562718 + 1.53580i
996996 0 0
997997 1777.55i 1.78290i −0.453120 0.891450i 0.649689π-0.649689\pi
0.453120 0.891450i 0.350311π-0.350311\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2160.3.c.q.1889.10 24
3.2 odd 2 inner 2160.3.c.q.1889.15 24
4.3 odd 2 1080.3.c.c.809.10 yes 24
5.4 even 2 inner 2160.3.c.q.1889.16 24
12.11 even 2 1080.3.c.c.809.15 yes 24
15.14 odd 2 inner 2160.3.c.q.1889.9 24
20.19 odd 2 1080.3.c.c.809.16 yes 24
60.59 even 2 1080.3.c.c.809.9 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1080.3.c.c.809.9 24 60.59 even 2
1080.3.c.c.809.10 yes 24 4.3 odd 2
1080.3.c.c.809.15 yes 24 12.11 even 2
1080.3.c.c.809.16 yes 24 20.19 odd 2
2160.3.c.q.1889.9 24 15.14 odd 2 inner
2160.3.c.q.1889.10 24 1.1 even 1 trivial
2160.3.c.q.1889.15 24 3.2 odd 2 inner
2160.3.c.q.1889.16 24 5.4 even 2 inner