Properties

Label 1152.4.a.r.1.2
Level 11521152
Weight 44
Character 1152.1
Self dual yes
Analytic conductor 67.97067.970
Analytic rank 00
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1152,4,Mod(1,1152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1152.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 1152=2732 1152 = 2^{7} \cdot 3^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1152.a (trivial)

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: yes
Analytic conductor: 67.970200326667.9702003266
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ12)+\Q(\zeta_{12})^+
comment: defining polynomial
 
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,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 128)
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 == 1152.1

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+11.8564q59.85641q7+39.0718q11+91.5692q13+37.1384q17+46.4974q19120.708q23+15.5744q25+27.2820q29+81.1487q31116.862q35+10.9948q37+205.426q41115.359q43312.841q47245.851q4990.9948q53+463.251q55550.631q59+630.974q61+1085.68q65+661.041q67+494.985q71+566.267q73385.108q7749.4153q79+564.067q83+440.328q851089.67q89902.543q91+551.292q95+464.605q97+O(q100)q+11.8564 q^{5} -9.85641 q^{7} +39.0718 q^{11} +91.5692 q^{13} +37.1384 q^{17} +46.4974 q^{19} -120.708 q^{23} +15.5744 q^{25} +27.2820 q^{29} +81.1487 q^{31} -116.862 q^{35} +10.9948 q^{37} +205.426 q^{41} -115.359 q^{43} -312.841 q^{47} -245.851 q^{49} -90.9948 q^{53} +463.251 q^{55} -550.631 q^{59} +630.974 q^{61} +1085.68 q^{65} +661.041 q^{67} +494.985 q^{71} +566.267 q^{73} -385.108 q^{77} -49.4153 q^{79} +564.067 q^{83} +440.328 q^{85} -1089.67 q^{89} -902.543 q^{91} +551.292 q^{95} +464.605 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q4q5+8q7+92q11+100q1392q174q19+8q23+142q2584q29+384q31400q35172q37+300q41300q4316q47270q49+12q53++2204q97+O(q100) 2 q - 4 q^{5} + 8 q^{7} + 92 q^{11} + 100 q^{13} - 92 q^{17} - 4 q^{19} + 8 q^{23} + 142 q^{25} - 84 q^{29} + 384 q^{31} - 400 q^{35} - 172 q^{37} + 300 q^{41} - 300 q^{43} - 16 q^{47} - 270 q^{49} + 12 q^{53}+ \cdots + 2204 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 0 0
44 0 0
55 11.8564 1.06047 0.530235 0.847851i 0.322104π-0.322104\pi
0.530235 + 0.847851i 0.322104π0.322104\pi
66 0 0
77 −9.85641 −0.532196 −0.266098 0.963946i 0.585734π-0.585734\pi
−0.266098 + 0.963946i 0.585734π0.585734\pi
88 0 0
99 0 0
1010 0 0
1111 39.0718 1.07096 0.535481 0.844547i 0.320130π-0.320130\pi
0.535481 + 0.844547i 0.320130π0.320130\pi
1212 0 0
1313 91.5692 1.95359 0.976797 0.214166i 0.0687032π-0.0687032\pi
0.976797 + 0.214166i 0.0687032π0.0687032\pi
1414 0 0
1515 0 0
1616 0 0
1717 37.1384 0.529847 0.264923 0.964269i 0.414653π-0.414653\pi
0.264923 + 0.964269i 0.414653π0.414653\pi
1818 0 0
1919 46.4974 0.561434 0.280717 0.959791i 0.409428π-0.409428\pi
0.280717 + 0.959791i 0.409428π0.409428\pi
2020 0 0
2121 0 0
2222 0 0
2323 −120.708 −1.09432 −0.547158 0.837029i 0.684290π-0.684290\pi
−0.547158 + 0.837029i 0.684290π0.684290\pi
2424 0 0
2525 15.5744 0.124595
2626 0 0
2727 0 0
2828 0 0
2929 27.2820 0.174695 0.0873473 0.996178i 0.472161π-0.472161\pi
0.0873473 + 0.996178i 0.472161π0.472161\pi
3030 0 0
3131 81.1487 0.470153 0.235077 0.971977i 0.424466π-0.424466\pi
0.235077 + 0.971977i 0.424466π0.424466\pi
3232 0 0
3333 0 0
3434 0 0
3535 −116.862 −0.564377
3636 0 0
3737 10.9948 0.0488525 0.0244262 0.999702i 0.492224π-0.492224\pi
0.0244262 + 0.999702i 0.492224π0.492224\pi
3838 0 0
3939 0 0
4040 0 0
4141 205.426 0.782490 0.391245 0.920287i 0.372044π-0.372044\pi
0.391245 + 0.920287i 0.372044π0.372044\pi
4242 0 0
4343 −115.359 −0.409118 −0.204559 0.978854i 0.565576π-0.565576\pi
−0.204559 + 0.978854i 0.565576π0.565576\pi
4444 0 0
4545 0 0
4646 0 0
4747 −312.841 −0.970905 −0.485453 0.874263i 0.661345π-0.661345\pi
−0.485453 + 0.874263i 0.661345π0.661345\pi
4848 0 0
4949 −245.851 −0.716767
5050 0 0
5151 0 0
5252 0 0
5353 −90.9948 −0.235832 −0.117916 0.993024i 0.537621π-0.537621\pi
−0.117916 + 0.993024i 0.537621π0.537621\pi
5454 0 0
5555 463.251 1.13572
5656 0 0
5757 0 0
5858 0 0
5959 −550.631 −1.21502 −0.607509 0.794313i 0.707831π-0.707831\pi
−0.607509 + 0.794313i 0.707831π0.707831\pi
6060 0 0
6161 630.974 1.32439 0.662196 0.749330i 0.269624π-0.269624\pi
0.662196 + 0.749330i 0.269624π0.269624\pi
6262 0 0
6363 0 0
6464 0 0
6565 1085.68 2.07173
6666 0 0
6767 661.041 1.20536 0.602679 0.797984i 0.294100π-0.294100\pi
0.602679 + 0.797984i 0.294100π0.294100\pi
6868 0 0
6969 0 0
7070 0 0
7171 494.985 0.827378 0.413689 0.910418i 0.364240π-0.364240\pi
0.413689 + 0.910418i 0.364240π0.364240\pi
7272 0 0
7373 566.267 0.907897 0.453949 0.891028i 0.350015π-0.350015\pi
0.453949 + 0.891028i 0.350015π0.350015\pi
7474 0 0
7575 0 0
7676 0 0
7777 −385.108 −0.569962
7878 0 0
7979 −49.4153 −0.0703754 −0.0351877 0.999381i 0.511203π-0.511203\pi
−0.0351877 + 0.999381i 0.511203π0.511203\pi
8080 0 0
8181 0 0
8282 0 0
8383 564.067 0.745956 0.372978 0.927840i 0.378337π-0.378337\pi
0.372978 + 0.927840i 0.378337π0.378337\pi
8484 0 0
8585 440.328 0.561886
8686 0 0
8787 0 0
8888 0 0
8989 −1089.67 −1.29781 −0.648904 0.760870i 0.724772π-0.724772\pi
−0.648904 + 0.760870i 0.724772π0.724772\pi
9090 0 0
9191 −902.543 −1.03970
9292 0 0
9393 0 0
9494 0 0
9595 551.292 0.595383
9696 0 0
9797 464.605 0.486325 0.243162 0.969986i 0.421815π-0.421815\pi
0.243162 + 0.969986i 0.421815π0.421815\pi
9898 0 0
9999 0 0
100100 0 0
101101 965.005 0.950709 0.475354 0.879794i 0.342320π-0.342320\pi
0.475354 + 0.879794i 0.342320π0.342320\pi
102102 0 0
103103 1828.99 1.74967 0.874836 0.484419i 0.160969π-0.160969\pi
0.874836 + 0.484419i 0.160969π0.160969\pi
104104 0 0
105105 0 0
106106 0 0
107107 −1726.59 −1.55996 −0.779980 0.625805i 0.784771π-0.784771\pi
−0.779980 + 0.625805i 0.784771π0.784771\pi
108108 0 0
109109 423.015 0.371720 0.185860 0.982576i 0.440493π-0.440493\pi
0.185860 + 0.982576i 0.440493π0.440493\pi
110110 0 0
111111 0 0
112112 0 0
113113 −763.108 −0.635284 −0.317642 0.948211i 0.602891π-0.602891\pi
−0.317642 + 0.948211i 0.602891π0.602891\pi
114114 0 0
115115 −1431.16 −1.16049
116116 0 0
117117 0 0
118118 0 0
119119 −366.052 −0.281982
120120 0 0
121121 195.605 0.146961
122122 0 0
123123 0 0
124124 0 0
125125 −1297.39 −0.928340
126126 0 0
127127 2159.38 1.50877 0.754387 0.656430i 0.227934π-0.227934\pi
0.754387 + 0.656430i 0.227934π0.227934\pi
128128 0 0
129129 0 0
130130 0 0
131131 −710.723 −0.474016 −0.237008 0.971508i 0.576167π-0.576167\pi
−0.237008 + 0.971508i 0.576167π0.576167\pi
132132 0 0
133133 −458.297 −0.298793
134134 0 0
135135 0 0
136136 0 0
137137 987.128 0.615592 0.307796 0.951452i 0.400409π-0.400409\pi
0.307796 + 0.951452i 0.400409π0.400409\pi
138138 0 0
139139 −2334.15 −1.42432 −0.712158 0.702019i 0.752282π-0.752282\pi
−0.712158 + 0.702019i 0.752282π0.752282\pi
140140 0 0
141141 0 0
142142 0 0
143143 3577.77 2.09223
144144 0 0
145145 323.467 0.185258
146146 0 0
147147 0 0
148148 0 0
149149 1792.29 0.985435 0.492718 0.870189i 0.336004π-0.336004\pi
0.492718 + 0.870189i 0.336004π0.336004\pi
150150 0 0
151151 −2864.32 −1.54367 −0.771837 0.635820i 0.780662π-0.780662\pi
−0.771837 + 0.635820i 0.780662π0.780662\pi
152152 0 0
153153 0 0
154154 0 0
155155 962.133 0.498583
156156 0 0
157157 2123.57 1.07949 0.539743 0.841830i 0.318521π-0.318521\pi
0.539743 + 0.841830i 0.318521π0.318521\pi
158158 0 0
159159 0 0
160160 0 0
161161 1189.74 0.582391
162162 0 0
163163 −3164.21 −1.52049 −0.760245 0.649636i 0.774921π-0.774921\pi
−0.760245 + 0.649636i 0.774921π0.774921\pi
164164 0 0
165165 0 0
166166 0 0
167167 −1340.34 −0.621069 −0.310534 0.950562i 0.600508π-0.600508\pi
−0.310534 + 0.950562i 0.600508π0.600508\pi
168168 0 0
169169 6187.92 2.81653
170170 0 0
171171 0 0
172172 0 0
173173 2802.13 1.23146 0.615729 0.787958i 0.288862π-0.288862\pi
0.615729 + 0.787958i 0.288862π0.288862\pi
174174 0 0
175175 −153.507 −0.0663089
176176 0 0
177177 0 0
178178 0 0
179179 1074.84 0.448810 0.224405 0.974496i 0.427956π-0.427956\pi
0.224405 + 0.974496i 0.427956π0.427956\pi
180180 0 0
181181 571.036 0.234502 0.117251 0.993102i 0.462592π-0.462592\pi
0.117251 + 0.993102i 0.462592π0.462592\pi
182182 0 0
183183 0 0
184184 0 0
185185 130.359 0.0518065
186186 0 0
187187 1451.07 0.567446
188188 0 0
189189 0 0
190190 0 0
191191 872.657 0.330593 0.165296 0.986244i 0.447142π-0.447142\pi
0.165296 + 0.986244i 0.447142π0.447142\pi
192192 0 0
193193 672.523 0.250825 0.125413 0.992105i 0.459975π-0.459975\pi
0.125413 + 0.992105i 0.459975π0.459975\pi
194194 0 0
195195 0 0
196196 0 0
197197 3129.56 1.13184 0.565918 0.824461i 0.308522π-0.308522\pi
0.565918 + 0.824461i 0.308522π0.308522\pi
198198 0 0
199199 −1502.37 −0.535176 −0.267588 0.963533i 0.586227π-0.586227\pi
−0.267588 + 0.963533i 0.586227π0.586227\pi
200200 0 0
201201 0 0
202202 0 0
203203 −268.903 −0.0929718
204204 0 0
205205 2435.61 0.829807
206206 0 0
207207 0 0
208208 0 0
209209 1816.74 0.601275
210210 0 0
211211 1773.70 0.578703 0.289352 0.957223i 0.406560π-0.406560\pi
0.289352 + 0.957223i 0.406560π0.406560\pi
212212 0 0
213213 0 0
214214 0 0
215215 −1367.74 −0.433857
216216 0 0
217217 −799.835 −0.250214
218218 0 0
219219 0 0
220220 0 0
221221 3400.74 1.03511
222222 0 0
223223 5413.66 1.62568 0.812838 0.582490i 0.197922π-0.197922\pi
0.812838 + 0.582490i 0.197922π0.197922\pi
224224 0 0
225225 0 0
226226 0 0
227227 3744.27 1.09478 0.547392 0.836876i 0.315621π-0.315621\pi
0.547392 + 0.836876i 0.315621π0.315621\pi
228228 0 0
229229 680.739 0.196439 0.0982194 0.995165i 0.468685π-0.468685\pi
0.0982194 + 0.995165i 0.468685π0.468685\pi
230230 0 0
231231 0 0
232232 0 0
233233 679.271 0.190989 0.0954947 0.995430i 0.469557π-0.469557\pi
0.0954947 + 0.995430i 0.469557π0.469557\pi
234234 0 0
235235 −3709.17 −1.02962
236236 0 0
237237 0 0
238238 0 0
239239 3901.27 1.05587 0.527934 0.849286i 0.322967π-0.322967\pi
0.527934 + 0.849286i 0.322967π0.322967\pi
240240 0 0
241241 5859.72 1.56622 0.783108 0.621886i 0.213633π-0.213633\pi
0.783108 + 0.621886i 0.213633π0.213633\pi
242242 0 0
243243 0 0
244244 0 0
245245 −2914.91 −0.760110
246246 0 0
247247 4257.73 1.09681
248248 0 0
249249 0 0
250250 0 0
251251 −3381.48 −0.850348 −0.425174 0.905112i 0.639787π-0.639787\pi
−0.425174 + 0.905112i 0.639787π0.639787\pi
252252 0 0
253253 −4716.27 −1.17197
254254 0 0
255255 0 0
256256 0 0
257257 −3652.22 −0.886455 −0.443227 0.896409i 0.646167π-0.646167\pi
−0.443227 + 0.896409i 0.646167π0.646167\pi
258258 0 0
259259 −108.370 −0.0259991
260260 0 0
261261 0 0
262262 0 0
263263 2462.74 0.577410 0.288705 0.957418i 0.406775π-0.406775\pi
0.288705 + 0.957418i 0.406775π0.406775\pi
264264 0 0
265265 −1078.87 −0.250093
266266 0 0
267267 0 0
268268 0 0
269269 −482.503 −0.109363 −0.0546816 0.998504i 0.517414π-0.517414\pi
−0.0546816 + 0.998504i 0.517414π0.517414\pi
270270 0 0
271271 3602.48 0.807510 0.403755 0.914867i 0.367705π-0.367705\pi
0.403755 + 0.914867i 0.367705π0.367705\pi
272272 0 0
273273 0 0
274274 0 0
275275 608.519 0.133437
276276 0 0
277277 6177.72 1.34001 0.670006 0.742356i 0.266291π-0.266291\pi
0.670006 + 0.742356i 0.266291π0.266291\pi
278278 0 0
279279 0 0
280280 0 0
281281 543.477 0.115378 0.0576888 0.998335i 0.481627π-0.481627\pi
0.0576888 + 0.998335i 0.481627π0.481627\pi
282282 0 0
283283 −6582.11 −1.38256 −0.691282 0.722585i 0.742954π-0.742954\pi
−0.691282 + 0.722585i 0.742954π0.742954\pi
284284 0 0
285285 0 0
286286 0 0
287287 −2024.76 −0.416438
288288 0 0
289289 −3533.74 −0.719262
290290 0 0
291291 0 0
292292 0 0
293293 −6753.68 −1.34660 −0.673301 0.739369i 0.735124π-0.735124\pi
−0.673301 + 0.739369i 0.735124π0.735124\pi
294294 0 0
295295 −6528.50 −1.28849
296296 0 0
297297 0 0
298298 0 0
299299 −11053.1 −2.13785
300300 0 0
301301 1137.03 0.217731
302302 0 0
303303 0 0
304304 0 0
305305 7481.09 1.40448
306306 0 0
307307 1821.88 0.338698 0.169349 0.985556i 0.445833π-0.445833\pi
0.169349 + 0.985556i 0.445833π0.445833\pi
308308 0 0
309309 0 0
310310 0 0
311311 −10598.2 −1.93237 −0.966184 0.257852i 0.916985π-0.916985\pi
−0.966184 + 0.257852i 0.916985π0.916985\pi
312312 0 0
313313 −7969.69 −1.43921 −0.719606 0.694382i 0.755678π-0.755678\pi
−0.719606 + 0.694382i 0.755678π0.755678\pi
314314 0 0
315315 0 0
316316 0 0
317317 −7773.66 −1.37733 −0.688663 0.725082i 0.741802π-0.741802\pi
−0.688663 + 0.725082i 0.741802π0.741802\pi
318318 0 0
319319 1065.96 0.187092
320320 0 0
321321 0 0
322322 0 0
323323 1726.84 0.297474
324324 0 0
325325 1426.13 0.243408
326326 0 0
327327 0 0
328328 0 0
329329 3083.49 0.516712
330330 0 0
331331 8212.87 1.36381 0.681903 0.731442i 0.261152π-0.261152\pi
0.681903 + 0.731442i 0.261152π0.261152\pi
332332 0 0
333333 0 0
334334 0 0
335335 7837.57 1.27825
336336 0 0
337337 5260.17 0.850267 0.425133 0.905131i 0.360227π-0.360227\pi
0.425133 + 0.905131i 0.360227π0.360227\pi
338338 0 0
339339 0 0
340340 0 0
341341 3170.63 0.503516
342342 0 0
343343 5803.96 0.913657
344344 0 0
345345 0 0
346346 0 0
347347 −2162.12 −0.334492 −0.167246 0.985915i 0.553487π-0.553487\pi
−0.167246 + 0.985915i 0.553487π0.553487\pi
348348 0 0
349349 2888.90 0.443093 0.221546 0.975150i 0.428890π-0.428890\pi
0.221546 + 0.975150i 0.428890π0.428890\pi
350350 0 0
351351 0 0
352352 0 0
353353 −11550.2 −1.74152 −0.870760 0.491709i 0.836372π-0.836372\pi
−0.870760 + 0.491709i 0.836372π0.836372\pi
354354 0 0
355355 5868.74 0.877409
356356 0 0
357357 0 0
358358 0 0
359359 −6523.97 −0.959114 −0.479557 0.877511i 0.659203π-0.659203\pi
−0.479557 + 0.877511i 0.659203π0.659203\pi
360360 0 0
361361 −4696.99 −0.684792
362362 0 0
363363 0 0
364364 0 0
365365 6713.89 0.962797
366366 0 0
367367 −6856.96 −0.975287 −0.487644 0.873043i 0.662143π-0.662143\pi
−0.487644 + 0.873043i 0.662143π0.662143\pi
368368 0 0
369369 0 0
370370 0 0
371371 896.882 0.125509
372372 0 0
373373 −5001.68 −0.694309 −0.347155 0.937808i 0.612852π-0.612852\pi
−0.347155 + 0.937808i 0.612852π0.612852\pi
374374 0 0
375375 0 0
376376 0 0
377377 2498.19 0.341283
378378 0 0
379379 −84.9775 −0.0115172 −0.00575858 0.999983i 0.501833π-0.501833\pi
−0.00575858 + 0.999983i 0.501833π0.501833\pi
380380 0 0
381381 0 0
382382 0 0
383383 2596.76 0.346444 0.173222 0.984883i 0.444582π-0.444582\pi
0.173222 + 0.984883i 0.444582π0.444582\pi
384384 0 0
385385 −4565.99 −0.604427
386386 0 0
387387 0 0
388388 0 0
389389 −9213.21 −1.20084 −0.600422 0.799683i 0.705001π-0.705001\pi
−0.600422 + 0.799683i 0.705001π0.705001\pi
390390 0 0
391391 −4482.89 −0.579820
392392 0 0
393393 0 0
394394 0 0
395395 −585.888 −0.0746310
396396 0 0
397397 −6614.19 −0.836163 −0.418082 0.908409i 0.637297π-0.637297\pi
−0.418082 + 0.908409i 0.637297π0.637297\pi
398398 0 0
399399 0 0
400400 0 0
401401 −3434.94 −0.427763 −0.213881 0.976860i 0.568611π-0.568611\pi
−0.213881 + 0.976860i 0.568611π0.568611\pi
402402 0 0
403403 7430.73 0.918489
404404 0 0
405405 0 0
406406 0 0
407407 429.588 0.0523192
408408 0 0
409409 −6435.82 −0.778071 −0.389035 0.921223i 0.627192π-0.627192\pi
−0.389035 + 0.921223i 0.627192π0.627192\pi
410410 0 0
411411 0 0
412412 0 0
413413 5427.24 0.646627
414414 0 0
415415 6687.80 0.791064
416416 0 0
417417 0 0
418418 0 0
419419 4222.04 0.492267 0.246134 0.969236i 0.420840π-0.420840\pi
0.246134 + 0.969236i 0.420840π0.420840\pi
420420 0 0
421421 5164.92 0.597917 0.298958 0.954266i 0.403361π-0.403361\pi
0.298958 + 0.954266i 0.403361π0.403361\pi
422422 0 0
423423 0 0
424424 0 0
425425 578.408 0.0660163
426426 0 0
427427 −6219.14 −0.704837
428428 0 0
429429 0 0
430430 0 0
431431 7476.41 0.835559 0.417780 0.908548i 0.362808π-0.362808\pi
0.417780 + 0.908548i 0.362808π0.362808\pi
432432 0 0
433433 −11289.7 −1.25299 −0.626497 0.779424i 0.715512π-0.715512\pi
−0.626497 + 0.779424i 0.715512π0.715512\pi
434434 0 0
435435 0 0
436436 0 0
437437 −5612.59 −0.614386
438438 0 0
439439 1800.79 0.195779 0.0978895 0.995197i 0.468791π-0.468791\pi
0.0978895 + 0.995197i 0.468791π0.468791\pi
440440 0 0
441441 0 0
442442 0 0
443443 −7020.76 −0.752972 −0.376486 0.926422i 0.622868π-0.622868\pi
−0.376486 + 0.926422i 0.622868π0.622868\pi
444444 0 0
445445 −12919.6 −1.37629
446446 0 0
447447 0 0
448448 0 0
449449 3318.29 0.348774 0.174387 0.984677i 0.444206π-0.444206\pi
0.174387 + 0.984677i 0.444206π0.444206\pi
450450 0 0
451451 8026.35 0.838018
452452 0 0
453453 0 0
454454 0 0
455455 −10700.9 −1.10256
456456 0 0
457457 4468.38 0.457378 0.228689 0.973500i 0.426556π-0.426556\pi
0.228689 + 0.973500i 0.426556π0.426556\pi
458458 0 0
459459 0 0
460460 0 0
461461 −1179.45 −0.119159 −0.0595795 0.998224i 0.518976π-0.518976\pi
−0.0595795 + 0.998224i 0.518976π0.518976\pi
462462 0 0
463463 −13763.1 −1.38148 −0.690742 0.723101i 0.742716π-0.742716\pi
−0.690742 + 0.723101i 0.742716π0.742716\pi
464464 0 0
465465 0 0
466466 0 0
467467 17014.1 1.68591 0.842955 0.537984i 0.180814π-0.180814\pi
0.842955 + 0.537984i 0.180814π0.180814\pi
468468 0 0
469469 −6515.49 −0.641487
470470 0 0
471471 0 0
472472 0 0
473473 −4507.28 −0.438150
474474 0 0
475475 724.168 0.0699518
476476 0 0
477477 0 0
478478 0 0
479479 −18976.7 −1.81017 −0.905083 0.425236i 0.860191π-0.860191\pi
−0.905083 + 0.425236i 0.860191π0.860191\pi
480480 0 0
481481 1006.79 0.0954379
482482 0 0
483483 0 0
484484 0 0
485485 5508.55 0.515733
486486 0 0
487487 −10579.6 −0.984408 −0.492204 0.870480i 0.663809π-0.663809\pi
−0.492204 + 0.870480i 0.663809π0.663809\pi
488488 0 0
489489 0 0
490490 0 0
491491 15200.9 1.39716 0.698579 0.715533i 0.253816π-0.253816\pi
0.698579 + 0.715533i 0.253816π0.253816\pi
492492 0 0
493493 1013.21 0.0925614
494494 0 0
495495 0 0
496496 0 0
497497 −4878.77 −0.440327
498498 0 0
499499 2553.92 0.229117 0.114558 0.993417i 0.463455π-0.463455\pi
0.114558 + 0.993417i 0.463455π0.463455\pi
500500 0 0
501501 0 0
502502 0 0
503503 4863.70 0.431137 0.215568 0.976489i 0.430840π-0.430840\pi
0.215568 + 0.976489i 0.430840π0.430840\pi
504504 0 0
505505 11441.5 1.00820
506506 0 0
507507 0 0
508508 0 0
509509 −17659.5 −1.53781 −0.768903 0.639366i 0.779197π-0.779197\pi
−0.768903 + 0.639366i 0.779197π0.779197\pi
510510 0 0
511511 −5581.35 −0.483179
512512 0 0
513513 0 0
514514 0 0
515515 21685.3 1.85547
516516 0 0
517517 −12223.3 −1.03980
518518 0 0
519519 0 0
520520 0 0
521521 3778.19 0.317707 0.158853 0.987302i 0.449220π-0.449220\pi
0.158853 + 0.987302i 0.449220π0.449220\pi
522522 0 0
523523 −2792.67 −0.233489 −0.116745 0.993162i 0.537246π-0.537246\pi
−0.116745 + 0.993162i 0.537246π0.537246\pi
524524 0 0
525525 0 0
526526 0 0
527527 3013.74 0.249109
528528 0 0
529529 2403.34 0.197529
530530 0 0
531531 0 0
532532 0 0
533533 18810.7 1.52867
534534 0 0
535535 −20471.1 −1.65429
536536 0 0
537537 0 0
538538 0 0
539539 −9605.85 −0.767631
540540 0 0
541541 −2062.12 −0.163877 −0.0819383 0.996637i 0.526111π-0.526111\pi
−0.0819383 + 0.996637i 0.526111π0.526111\pi
542542 0 0
543543 0 0
544544 0 0
545545 5015.44 0.394198
546546 0 0
547547 16562.0 1.29459 0.647296 0.762239i 0.275900π-0.275900\pi
0.647296 + 0.762239i 0.275900π0.275900\pi
548548 0 0
549549 0 0
550550 0 0
551551 1268.54 0.0980795
552552 0 0
553553 487.057 0.0374535
554554 0 0
555555 0 0
556556 0 0
557557 9272.94 0.705399 0.352699 0.935737i 0.385264π-0.385264\pi
0.352699 + 0.935737i 0.385264π0.385264\pi
558558 0 0
559559 −10563.3 −0.799251
560560 0 0
561561 0 0
562562 0 0
563563 62.0181 0.00464254 0.00232127 0.999997i 0.499261π-0.499261\pi
0.00232127 + 0.999997i 0.499261π0.499261\pi
564564 0 0
565565 −9047.71 −0.673699
566566 0 0
567567 0 0
568568 0 0
569569 −10015.9 −0.737938 −0.368969 0.929442i 0.620289π-0.620289\pi
−0.368969 + 0.929442i 0.620289π0.620289\pi
570570 0 0
571571 15543.3 1.13917 0.569587 0.821931i 0.307103π-0.307103\pi
0.569587 + 0.821931i 0.307103π0.307103\pi
572572 0 0
573573 0 0
574574 0 0
575575 −1879.95 −0.136346
576576 0 0
577577 3776.77 0.272494 0.136247 0.990675i 0.456496π-0.456496\pi
0.136247 + 0.990675i 0.456496π0.456496\pi
578578 0 0
579579 0 0
580580 0 0
581581 −5559.67 −0.396995
582582 0 0
583583 −3555.33 −0.252567
584584 0 0
585585 0 0
586586 0 0
587587 596.285 0.0419273 0.0209637 0.999780i 0.493327π-0.493327\pi
0.0209637 + 0.999780i 0.493327π0.493327\pi
588588 0 0
589589 3773.21 0.263960
590590 0 0
591591 0 0
592592 0 0
593593 −20179.6 −1.39743 −0.698717 0.715398i 0.746245π-0.746245\pi
−0.698717 + 0.715398i 0.746245π0.746245\pi
594594 0 0
595595 −4340.06 −0.299034
596596 0 0
597597 0 0
598598 0 0
599599 −13076.3 −0.891960 −0.445980 0.895043i 0.647145π-0.647145\pi
−0.445980 + 0.895043i 0.647145π0.647145\pi
600600 0 0
601601 −16866.9 −1.14479 −0.572393 0.819980i 0.693985π-0.693985\pi
−0.572393 + 0.819980i 0.693985π0.693985\pi
602602 0 0
603603 0 0
604604 0 0
605605 2319.18 0.155848
606606 0 0
607607 19953.0 1.33421 0.667107 0.744962i 0.267532π-0.267532\pi
0.667107 + 0.744962i 0.267532π0.267532\pi
608608 0 0
609609 0 0
610610 0 0
611611 −28646.6 −1.89676
612612 0 0
613613 −7214.32 −0.475340 −0.237670 0.971346i 0.576384π-0.576384\pi
−0.237670 + 0.971346i 0.576384π0.576384\pi
614614 0 0
615615 0 0
616616 0 0
617617 −22212.9 −1.44936 −0.724681 0.689084i 0.758013π-0.758013\pi
−0.724681 + 0.689084i 0.758013π0.758013\pi
618618 0 0
619619 −4349.02 −0.282394 −0.141197 0.989982i 0.545095π-0.545095\pi
−0.141197 + 0.989982i 0.545095π0.545095\pi
620620 0 0
621621 0 0
622622 0 0
623623 10740.2 0.690688
624624 0 0
625625 −17329.2 −1.10907
626626 0 0
627627 0 0
628628 0 0
629629 408.331 0.0258843
630630 0 0
631631 −10127.9 −0.638966 −0.319483 0.947592i 0.603509π-0.603509\pi
−0.319483 + 0.947592i 0.603509π0.603509\pi
632632 0 0
633633 0 0
634634 0 0
635635 25602.5 1.60001
636636 0 0
637637 −22512.4 −1.40027
638638 0 0
639639 0 0
640640 0 0
641641 17624.6 1.08601 0.543003 0.839731i 0.317287π-0.317287\pi
0.543003 + 0.839731i 0.317287π0.317287\pi
642642 0 0
643643 −27238.1 −1.67055 −0.835277 0.549829i 0.814693π-0.814693\pi
−0.835277 + 0.549829i 0.814693π0.814693\pi
644644 0 0
645645 0 0
646646 0 0
647647 28702.1 1.74404 0.872021 0.489469i 0.162809π-0.162809\pi
0.872021 + 0.489469i 0.162809π0.162809\pi
648648 0 0
649649 −21514.1 −1.30124
650650 0 0
651651 0 0
652652 0 0
653653 −7937.84 −0.475700 −0.237850 0.971302i 0.576443π-0.576443\pi
−0.237850 + 0.971302i 0.576443π0.576443\pi
654654 0 0
655655 −8426.62 −0.502680
656656 0 0
657657 0 0
658658 0 0
659659 3675.29 0.217252 0.108626 0.994083i 0.465355π-0.465355\pi
0.108626 + 0.994083i 0.465355π0.465355\pi
660660 0 0
661661 −4205.49 −0.247466 −0.123733 0.992316i 0.539487π-0.539487\pi
−0.123733 + 0.992316i 0.539487π0.539487\pi
662662 0 0
663663 0 0
664664 0 0
665665 −5433.76 −0.316860
666666 0 0
667667 −3293.15 −0.191171
668668 0 0
669669 0 0
670670 0 0
671671 24653.3 1.41838
672672 0 0
673673 −4634.55 −0.265452 −0.132726 0.991153i 0.542373π-0.542373\pi
−0.132726 + 0.991153i 0.542373π0.542373\pi
674674 0 0
675675 0 0
676676 0 0
677677 −5327.42 −0.302437 −0.151218 0.988500i 0.548320π-0.548320\pi
−0.151218 + 0.988500i 0.548320π0.548320\pi
678678 0 0
679679 −4579.34 −0.258820
680680 0 0
681681 0 0
682682 0 0
683683 −2816.05 −0.157764 −0.0788822 0.996884i 0.525135π-0.525135\pi
−0.0788822 + 0.996884i 0.525135π0.525135\pi
684684 0 0
685685 11703.8 0.652816
686686 0 0
687687 0 0
688688 0 0
689689 −8332.33 −0.460720
690690 0 0
691691 −16910.1 −0.930955 −0.465477 0.885060i 0.654117π-0.654117\pi
−0.465477 + 0.885060i 0.654117π0.654117\pi
692692 0 0
693693 0 0
694694 0 0
695695 −27674.6 −1.51044
696696 0 0
697697 7629.19 0.414600
698698 0 0
699699 0 0
700700 0 0
701701 −30588.4 −1.64808 −0.824042 0.566528i 0.808286π-0.808286\pi
−0.824042 + 0.566528i 0.808286π0.808286\pi
702702 0 0
703703 511.232 0.0274274
704704 0 0
705705 0 0
706706 0 0
707707 −9511.48 −0.505963
708708 0 0
709709 −21242.9 −1.12524 −0.562619 0.826716i 0.690206π-0.690206\pi
−0.562619 + 0.826716i 0.690206π0.690206\pi
710710 0 0
711711 0 0
712712 0 0
713713 −9795.28 −0.514496
714714 0 0
715715 42419.5 2.21874
716716 0 0
717717 0 0
718718 0 0
719719 12452.7 0.645907 0.322954 0.946415i 0.395324π-0.395324\pi
0.322954 + 0.946415i 0.395324π0.395324\pi
720720 0 0
721721 −18027.3 −0.931168
722722 0 0
723723 0 0
724724 0 0
725725 424.901 0.0217661
726726 0 0
727727 27178.3 1.38650 0.693251 0.720696i 0.256178π-0.256178\pi
0.693251 + 0.720696i 0.256178π0.256178\pi
728728 0 0
729729 0 0
730730 0 0
731731 −4284.25 −0.216770
732732 0 0
733733 21999.7 1.10856 0.554282 0.832329i 0.312993π-0.312993\pi
0.554282 + 0.832329i 0.312993π0.312993\pi
734734 0 0
735735 0 0
736736 0 0
737737 25828.1 1.29089
738738 0 0
739739 13644.0 0.679166 0.339583 0.940576i 0.389714π-0.389714\pi
0.339583 + 0.940576i 0.389714π0.389714\pi
740740 0 0
741741 0 0
742742 0 0
743743 −13980.2 −0.690286 −0.345143 0.938550i 0.612170π-0.612170\pi
−0.345143 + 0.938550i 0.612170π0.612170\pi
744744 0 0
745745 21250.1 1.04502
746746 0 0
747747 0 0
748748 0 0
749749 17018.0 0.830204
750750 0 0
751751 21138.7 1.02711 0.513557 0.858055i 0.328327π-0.328327\pi
0.513557 + 0.858055i 0.328327π0.328327\pi
752752 0 0
753753 0 0
754754 0 0
755755 −33960.5 −1.63702
756756 0 0
757757 28328.1 1.36011 0.680054 0.733162i 0.261956π-0.261956\pi
0.680054 + 0.733162i 0.261956π0.261956\pi
758758 0 0
759759 0 0
760760 0 0
761761 1093.79 0.0521023 0.0260512 0.999661i 0.491707π-0.491707\pi
0.0260512 + 0.999661i 0.491707π0.491707\pi
762762 0 0
763763 −4169.41 −0.197828
764764 0 0
765765 0 0
766766 0 0
767767 −50420.8 −2.37365
768768 0 0
769769 −1659.21 −0.0778059 −0.0389029 0.999243i 0.512386π-0.512386\pi
−0.0389029 + 0.999243i 0.512386π0.512386\pi
770770 0 0
771771 0 0
772772 0 0
773773 −7537.89 −0.350736 −0.175368 0.984503i 0.556112π-0.556112\pi
−0.175368 + 0.984503i 0.556112π0.556112\pi
774774 0 0
775775 1263.84 0.0585787
776776 0 0
777777 0 0
778778 0 0
779779 9551.76 0.439316
780780 0 0
781781 19339.9 0.886091
782782 0 0
783783 0 0
784784 0 0
785785 25177.9 1.14476
786786 0 0
787787 9304.20 0.421422 0.210711 0.977548i 0.432422π-0.432422\pi
0.210711 + 0.977548i 0.432422π0.432422\pi
788788 0 0
789789 0 0
790790 0 0
791791 7521.50 0.338096
792792 0 0
793793 57777.8 2.58733
794794 0 0
795795 0 0
796796 0 0
797797 −38619.5 −1.71640 −0.858201 0.513314i 0.828418π-0.828418\pi
−0.858201 + 0.513314i 0.828418π0.828418\pi
798798 0 0
799799 −11618.4 −0.514431
800800 0 0
801801 0 0
802802 0 0
803803 22125.1 0.972324
804804 0 0
805805 14106.1 0.617608
806806 0 0
807807 0 0
808808 0 0
809809 18550.5 0.806179 0.403090 0.915160i 0.367936π-0.367936\pi
0.403090 + 0.915160i 0.367936π0.367936\pi
810810 0 0
811811 3704.80 0.160411 0.0802054 0.996778i 0.474442π-0.474442\pi
0.0802054 + 0.996778i 0.474442π0.474442\pi
812812 0 0
813813 0 0
814814 0 0
815815 −37516.2 −1.61243
816816 0 0
817817 −5363.90 −0.229693
818818 0 0
819819 0 0
820820 0 0
821821 5544.86 0.235709 0.117854 0.993031i 0.462398π-0.462398\pi
0.117854 + 0.993031i 0.462398π0.462398\pi
822822 0 0
823823 −3915.39 −0.165835 −0.0829174 0.996556i 0.526424π-0.526424\pi
−0.0829174 + 0.996556i 0.526424π0.526424\pi
824824 0 0
825825 0 0
826826 0 0
827827 −35091.2 −1.47550 −0.737751 0.675073i 0.764112π-0.764112\pi
−0.737751 + 0.675073i 0.764112π0.764112\pi
828828 0 0
829829 −3532.71 −0.148005 −0.0740025 0.997258i 0.523577π-0.523577\pi
−0.0740025 + 0.997258i 0.523577π0.523577\pi
830830 0 0
831831 0 0
832832 0 0
833833 −9130.53 −0.379777
834834 0 0
835835 −15891.6 −0.658624
836836 0 0
837837 0 0
838838 0 0
839839 30081.1 1.23780 0.618900 0.785470i 0.287579π-0.287579\pi
0.618900 + 0.785470i 0.287579π0.287579\pi
840840 0 0
841841 −23644.7 −0.969482
842842 0 0
843843 0 0
844844 0 0
845845 73366.5 2.98685
846846 0 0
847847 −1927.97 −0.0782121
848848 0 0
849849 0 0
850850 0 0
851851 −1327.16 −0.0534601
852852 0 0
853853 −11222.1 −0.450453 −0.225226 0.974306i 0.572312π-0.572312\pi
−0.225226 + 0.974306i 0.572312π0.572312\pi
854854 0 0
855855 0 0
856856 0 0
857857 27486.0 1.09557 0.547785 0.836619i 0.315471π-0.315471\pi
0.547785 + 0.836619i 0.315471π0.315471\pi
858858 0 0
859859 −14976.2 −0.594855 −0.297427 0.954744i 0.596129π-0.596129\pi
−0.297427 + 0.954744i 0.596129π0.596129\pi
860860 0 0
861861 0 0
862862 0 0
863863 9419.49 0.371545 0.185772 0.982593i 0.440521π-0.440521\pi
0.185772 + 0.982593i 0.440521π0.440521\pi
864864 0 0
865865 33223.2 1.30592
866866 0 0
867867 0 0
868868 0 0
869869 −1930.75 −0.0753694
870870 0 0
871871 60531.0 2.35478
872872 0 0
873873 0 0
874874 0 0
875875 12787.6 0.494059
876876 0 0
877877 21069.8 0.811263 0.405631 0.914037i 0.367052π-0.367052\pi
0.405631 + 0.914037i 0.367052π0.367052\pi
878878 0 0
879879 0 0
880880 0 0
881881 14511.7 0.554952 0.277476 0.960733i 0.410502π-0.410502\pi
0.277476 + 0.960733i 0.410502π0.410502\pi
882882 0 0
883883 26515.9 1.01057 0.505284 0.862953i 0.331388π-0.331388\pi
0.505284 + 0.862953i 0.331388π0.331388\pi
884884 0 0
885885 0 0
886886 0 0
887887 29223.6 1.10624 0.553119 0.833102i 0.313437π-0.313437\pi
0.553119 + 0.833102i 0.313437π0.313437\pi
888888 0 0
889889 −21283.8 −0.802964
890890 0 0
891891 0 0
892892 0 0
893893 −14546.3 −0.545099
894894 0 0
895895 12743.7 0.475949
896896 0 0
897897 0 0
898898 0 0
899899 2213.90 0.0821332
900900 0 0
901901 −3379.41 −0.124955
902902 0 0
903903 0 0
904904 0 0
905905 6770.44 0.248682
906906 0 0
907907 −32139.3 −1.17659 −0.588296 0.808646i 0.700201π-0.700201\pi
−0.588296 + 0.808646i 0.700201π0.700201\pi
908908 0 0
909909 0 0
910910 0 0
911911 −21430.7 −0.779396 −0.389698 0.920943i 0.627421π-0.627421\pi
−0.389698 + 0.920943i 0.627421π0.627421\pi
912912 0 0
913913 22039.1 0.798891
914914 0 0
915915 0 0
916916 0 0
917917 7005.17 0.252270
918918 0 0
919919 11676.1 0.419106 0.209553 0.977797i 0.432799π-0.432799\pi
0.209553 + 0.977797i 0.432799π0.432799\pi
920920 0 0
921921 0 0
922922 0 0
923923 45325.3 1.61636
924924 0 0
925925 171.238 0.00608677
926926 0 0
927927 0 0
928928 0 0
929929 −41969.7 −1.48222 −0.741110 0.671383i 0.765700π-0.765700\pi
−0.741110 + 0.671383i 0.765700π0.765700\pi
930930 0 0
931931 −11431.4 −0.402417
932932 0 0
933933 0 0
934934 0 0
935935 17204.4 0.601759
936936 0 0
937937 −45948.6 −1.60200 −0.801001 0.598663i 0.795699π-0.795699\pi
−0.801001 + 0.598663i 0.795699π0.795699\pi
938938 0 0
939939 0 0
940940 0 0
941941 −15000.1 −0.519648 −0.259824 0.965656i 0.583665π-0.583665\pi
−0.259824 + 0.965656i 0.583665π0.583665\pi
942942 0 0
943943 −24796.4 −0.856292
944944 0 0
945945 0 0
946946 0 0
947947 −37423.2 −1.28415 −0.642075 0.766642i 0.721926π-0.721926\pi
−0.642075 + 0.766642i 0.721926π0.721926\pi
948948 0 0
949949 51852.6 1.77366
950950 0 0
951951 0 0
952952 0 0
953953 55403.0 1.88319 0.941594 0.336750i 0.109328π-0.109328\pi
0.941594 + 0.336750i 0.109328π0.109328\pi
954954 0 0
955955 10346.6 0.350584
956956 0 0
957957 0 0
958958 0 0
959959 −9729.54 −0.327615
960960 0 0
961961 −23205.9 −0.778956
962962 0 0
963963 0 0
964964 0 0
965965 7973.70 0.265992
966966 0 0
967967 31440.5 1.04556 0.522780 0.852467i 0.324895π-0.324895\pi
0.522780 + 0.852467i 0.324895π0.324895\pi
968968 0 0
969969 0 0
970970 0 0
971971 −19010.3 −0.628290 −0.314145 0.949375i 0.601718π-0.601718\pi
−0.314145 + 0.949375i 0.601718π0.601718\pi
972972 0 0
973973 23006.3 0.758015
974974 0 0
975975 0 0
976976 0 0
977977 8504.01 0.278472 0.139236 0.990259i 0.455535π-0.455535\pi
0.139236 + 0.990259i 0.455535π0.455535\pi
978978 0 0
979979 −42575.4 −1.38990
980980 0 0
981981 0 0
982982 0 0
983983 52828.3 1.71410 0.857051 0.515232i 0.172294π-0.172294\pi
0.857051 + 0.515232i 0.172294π0.172294\pi
984984 0 0
985985 37105.3 1.20028
986986 0 0
987987 0 0
988988 0 0
989989 13924.7 0.447705
990990 0 0
991991 −13275.5 −0.425541 −0.212770 0.977102i 0.568249π-0.568249\pi
−0.212770 + 0.977102i 0.568249π0.568249\pi
992992 0 0
993993 0 0
994994 0 0
995995 −17812.7 −0.567538
996996 0 0
997997 20858.1 0.662570 0.331285 0.943531i 0.392518π-0.392518\pi
0.331285 + 0.943531i 0.392518π0.392518\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 1152.4.a.r.1.2 2
3.2 odd 2 128.4.a.f.1.1 yes 2
4.3 odd 2 1152.4.a.q.1.2 2
8.3 odd 2 1152.4.a.s.1.1 2
8.5 even 2 1152.4.a.t.1.1 2
12.11 even 2 128.4.a.h.1.2 yes 2
24.5 odd 2 128.4.a.g.1.2 yes 2
24.11 even 2 128.4.a.e.1.1 2
48.5 odd 4 256.4.b.h.129.4 4
48.11 even 4 256.4.b.i.129.1 4
48.29 odd 4 256.4.b.h.129.1 4
48.35 even 4 256.4.b.i.129.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.4.a.e.1.1 2 24.11 even 2
128.4.a.f.1.1 yes 2 3.2 odd 2
128.4.a.g.1.2 yes 2 24.5 odd 2
128.4.a.h.1.2 yes 2 12.11 even 2
256.4.b.h.129.1 4 48.29 odd 4
256.4.b.h.129.4 4 48.5 odd 4
256.4.b.i.129.1 4 48.11 even 4
256.4.b.i.129.4 4 48.35 even 4
1152.4.a.q.1.2 2 4.3 odd 2
1152.4.a.r.1.2 2 1.1 even 1 trivial
1152.4.a.s.1.1 2 8.3 odd 2
1152.4.a.t.1.1 2 8.5 even 2