Properties

Label 4896.2.a.bj.1.4
Level 48964896
Weight 22
Character 4896.1
Self dual yes
Analytic conductor 39.09539.095
Analytic rank 00
Dimension 44
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] = [4896,2,Mod(1,4896)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4896, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4896.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4896=253217 4896 = 2^{5} \cdot 3^{2} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4896.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: 39.094756829639.0947568296
Analytic rank: 00
Dimension: 44
Coefficient field: 4.4.13768.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x35x2+2x+2 x^{4} - x^{3} - 5x^{2} + 2x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 1.89761-1.89761 of defining polynomial
Character χ\chi == 4896.1

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+3.49854q5+4.74127q7+2.44459q11+1.24272q131.00000q170.444588q190.188768q23+7.23981q254.84918q292.84918q31+16.5875q35+4.84918q370.865188q410.552500q43+6.99709q47+15.4796q49+4.10791q53+8.55250q550.107912q5913.9542q61+4.34772q65+13.2129q6712.3317q719.59045q73+11.5904q77+6.25582q79+11.4825q833.49854q856.88918q89+5.89209q911.55541q95+14.1021q97+O(q100)q+3.49854 q^{5} +4.74127 q^{7} +2.44459 q^{11} +1.24272 q^{13} -1.00000 q^{17} -0.444588 q^{19} -0.188768 q^{23} +7.23981 q^{25} -4.84918 q^{29} -2.84918 q^{31} +16.5875 q^{35} +4.84918 q^{37} -0.865188 q^{41} -0.552500 q^{43} +6.99709 q^{47} +15.4796 q^{49} +4.10791 q^{53} +8.55250 q^{55} -0.107912 q^{59} -13.9542 q^{61} +4.34772 q^{65} +13.2129 q^{67} -12.3317 q^{71} -9.59045 q^{73} +11.5904 q^{77} +6.25582 q^{79} +11.4825 q^{83} -3.49854 q^{85} -6.88918 q^{89} +5.89209 q^{91} -1.55541 q^{95} +14.1021 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q5+4q7+2q134q17+8q19+2q25+8q31+8q352q41+12q43+4q47+8q49+12q53+20q55+4q598q6114q65+20q67++4q97+O(q100) 4 q + 2 q^{5} + 4 q^{7} + 2 q^{13} - 4 q^{17} + 8 q^{19} + 2 q^{25} + 8 q^{31} + 8 q^{35} - 2 q^{41} + 12 q^{43} + 4 q^{47} + 8 q^{49} + 12 q^{53} + 20 q^{55} + 4 q^{59} - 8 q^{61} - 14 q^{65} + 20 q^{67}+ \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 0 0
44 0 0
55 3.49854 1.56460 0.782298 0.622904i 0.214047π-0.214047\pi
0.782298 + 0.622904i 0.214047π0.214047\pi
66 0 0
77 4.74127 1.79203 0.896015 0.444023i 0.146449π-0.146449\pi
0.896015 + 0.444023i 0.146449π0.146449\pi
88 0 0
99 0 0
1010 0 0
1111 2.44459 0.737071 0.368536 0.929614i 0.379859π-0.379859\pi
0.368536 + 0.929614i 0.379859π0.379859\pi
1212 0 0
1313 1.24272 0.344670 0.172335 0.985038i 0.444869π-0.444869\pi
0.172335 + 0.985038i 0.444869π0.444869\pi
1414 0 0
1515 0 0
1616 0 0
1717 −1.00000 −0.242536
1818 0 0
1919 −0.444588 −0.101996 −0.0509978 0.998699i 0.516240π-0.516240\pi
−0.0509978 + 0.998699i 0.516240π0.516240\pi
2020 0 0
2121 0 0
2222 0 0
2323 −0.188768 −0.0393608 −0.0196804 0.999806i 0.506265π-0.506265\pi
−0.0196804 + 0.999806i 0.506265π0.506265\pi
2424 0 0
2525 7.23981 1.44796
2626 0 0
2727 0 0
2828 0 0
2929 −4.84918 −0.900470 −0.450235 0.892910i 0.648660π-0.648660\pi
−0.450235 + 0.892910i 0.648660π0.648660\pi
3030 0 0
3131 −2.84918 −0.511728 −0.255864 0.966713i 0.582360π-0.582360\pi
−0.255864 + 0.966713i 0.582360π0.582360\pi
3232 0 0
3333 0 0
3434 0 0
3535 16.5875 2.80381
3636 0 0
3737 4.84918 0.797200 0.398600 0.917125i 0.369496π-0.369496\pi
0.398600 + 0.917125i 0.369496π0.369496\pi
3838 0 0
3939 0 0
4040 0 0
4141 −0.865188 −0.135120 −0.0675599 0.997715i 0.521521π-0.521521\pi
−0.0675599 + 0.997715i 0.521521π0.521521\pi
4242 0 0
4343 −0.552500 −0.0842555 −0.0421278 0.999112i 0.513414π-0.513414\pi
−0.0421278 + 0.999112i 0.513414π0.513414\pi
4444 0 0
4545 0 0
4646 0 0
4747 6.99709 1.02063 0.510315 0.859987i 0.329529π-0.329529\pi
0.510315 + 0.859987i 0.329529π0.329529\pi
4848 0 0
4949 15.4796 2.21138
5050 0 0
5151 0 0
5252 0 0
5353 4.10791 0.564265 0.282133 0.959375i 0.408958π-0.408958\pi
0.282133 + 0.959375i 0.408958π0.408958\pi
5454 0 0
5555 8.55250 1.15322
5656 0 0
5757 0 0
5858 0 0
5959 −0.107912 −0.0140490 −0.00702449 0.999975i 0.502236π-0.502236\pi
−0.00702449 + 0.999975i 0.502236π0.502236\pi
6060 0 0
6161 −13.9542 −1.78665 −0.893325 0.449411i 0.851634π-0.851634\pi
−0.893325 + 0.449411i 0.851634π0.851634\pi
6262 0 0
6363 0 0
6464 0 0
6565 4.34772 0.539269
6666 0 0
6767 13.2129 1.61421 0.807107 0.590405i 0.201032π-0.201032\pi
0.807107 + 0.590405i 0.201032π0.201032\pi
6868 0 0
6969 0 0
7070 0 0
7171 −12.3317 −1.46351 −0.731753 0.681570i 0.761297π-0.761297\pi
−0.731753 + 0.681570i 0.761297π0.761297\pi
7272 0 0
7373 −9.59045 −1.12248 −0.561239 0.827654i 0.689675π-0.689675\pi
−0.561239 + 0.827654i 0.689675π0.689675\pi
7474 0 0
7575 0 0
7676 0 0
7777 11.5904 1.32085
7878 0 0
7979 6.25582 0.703835 0.351917 0.936031i 0.385530π-0.385530\pi
0.351917 + 0.936031i 0.385530π0.385530\pi
8080 0 0
8181 0 0
8282 0 0
8383 11.4825 1.26037 0.630186 0.776444i 0.282979π-0.282979\pi
0.630186 + 0.776444i 0.282979π0.282979\pi
8484 0 0
8585 −3.49854 −0.379470
8686 0 0
8787 0 0
8888 0 0
8989 −6.88918 −0.730251 −0.365126 0.930958i 0.618974π-0.618974\pi
−0.365126 + 0.930958i 0.618974π0.618974\pi
9090 0 0
9191 5.89209 0.617659
9292 0 0
9393 0 0
9494 0 0
9595 −1.55541 −0.159582
9696 0 0
9797 14.1021 1.43185 0.715925 0.698177i 0.246005π-0.246005\pi
0.715925 + 0.698177i 0.246005π0.246005\pi
9898 0 0
9999 0 0
100100 0 0
101101 −15.9622 −1.58829 −0.794147 0.607725i 0.792082π-0.792082\pi
−0.794147 + 0.607725i 0.792082π0.792082\pi
102102 0 0
103103 −6.03504 −0.594650 −0.297325 0.954776i 0.596094π-0.596094\pi
−0.297325 + 0.954776i 0.596094π0.596094\pi
104104 0 0
105105 0 0
106106 0 0
107107 2.66041 0.257192 0.128596 0.991697i 0.458953π-0.458953\pi
0.128596 + 0.991697i 0.458953π0.458953\pi
108108 0 0
109109 −17.1130 −1.63913 −0.819563 0.572989i 0.805784π-0.805784\pi
−0.819563 + 0.572989i 0.805784π0.805784\pi
110110 0 0
111111 0 0
112112 0 0
113113 −16.8332 −1.58353 −0.791766 0.610825i 0.790838π-0.790838\pi
−0.791766 + 0.610825i 0.790838π0.790838\pi
114114 0 0
115115 −0.660413 −0.0615838
116116 0 0
117117 0 0
118118 0 0
119119 −4.74127 −0.434631
120120 0 0
121121 −5.02399 −0.456726
122122 0 0
123123 0 0
124124 0 0
125125 7.83608 0.700881
126126 0 0
127127 12.5525 1.11385 0.556927 0.830561i 0.311980π-0.311980\pi
0.556927 + 0.830561i 0.311980π0.311980\pi
128128 0 0
129129 0 0
130130 0 0
131131 −12.4388 −1.08678 −0.543390 0.839480i 0.682860π-0.682860\pi
−0.543390 + 0.839480i 0.682860π0.682860\pi
132132 0 0
133133 −2.10791 −0.182779
134134 0 0
135135 0 0
136136 0 0
137137 −11.3746 −0.971800 −0.485900 0.874014i 0.661508π-0.661508\pi
−0.485900 + 0.874014i 0.661508π0.661508\pi
138138 0 0
139139 19.8863 1.68673 0.843366 0.537340i 0.180571π-0.180571\pi
0.843366 + 0.537340i 0.180571π0.180571\pi
140140 0 0
141141 0 0
142142 0 0
143143 3.03795 0.254046
144144 0 0
145145 −16.9651 −1.40887
146146 0 0
147147 0 0
148148 0 0
149149 6.67335 0.546702 0.273351 0.961914i 0.411868π-0.411868\pi
0.273351 + 0.961914i 0.411868π0.411868\pi
150150 0 0
151151 13.1867 1.07312 0.536560 0.843862i 0.319723π-0.319723\pi
0.536560 + 0.843862i 0.319723π0.319723\pi
152152 0 0
153153 0 0
154154 0 0
155155 −9.96798 −0.800648
156156 0 0
157157 0.946908 0.0755715 0.0377857 0.999286i 0.487970π-0.487970\pi
0.0377857 + 0.999286i 0.487970π0.487970\pi
158158 0 0
159159 0 0
160160 0 0
161161 −0.894999 −0.0705358
162162 0 0
163163 −1.99418 −0.156196 −0.0780980 0.996946i 0.524885π-0.524885\pi
−0.0780980 + 0.996946i 0.524885π0.524885\pi
164164 0 0
165165 0 0
166166 0 0
167167 −18.6946 −1.44663 −0.723315 0.690518i 0.757383π-0.757383\pi
−0.723315 + 0.690518i 0.757383π0.757383\pi
168168 0 0
169169 −11.4556 −0.881203
170170 0 0
171171 0 0
172172 0 0
173173 16.9811 1.29105 0.645524 0.763740i 0.276639π-0.276639\pi
0.645524 + 0.763740i 0.276639π0.276639\pi
174174 0 0
175175 34.3259 2.59479
176176 0 0
177177 0 0
178178 0 0
179179 −3.24493 −0.242537 −0.121269 0.992620i 0.538696π-0.538696\pi
−0.121269 + 0.992620i 0.538696π0.538696\pi
180180 0 0
181181 −14.7093 −1.09333 −0.546665 0.837351i 0.684103π-0.684103\pi
−0.546665 + 0.837351i 0.684103π0.684103\pi
182182 0 0
183183 0 0
184184 0 0
185185 16.9651 1.24730
186186 0 0
187187 −2.44459 −0.178766
188188 0 0
189189 0 0
190190 0 0
191191 21.0730 1.52479 0.762394 0.647113i 0.224024π-0.224024\pi
0.762394 + 0.647113i 0.224024π0.224024\pi
192192 0 0
193193 14.7754 1.06356 0.531780 0.846883i 0.321523π-0.321523\pi
0.531780 + 0.846883i 0.321523π0.321523\pi
194194 0 0
195195 0 0
196196 0 0
197197 1.50437 0.107182 0.0535909 0.998563i 0.482933π-0.482933\pi
0.0535909 + 0.998563i 0.482933π0.482933\pi
198198 0 0
199199 −21.3230 −1.51155 −0.755773 0.654834i 0.772739π-0.772739\pi
−0.755773 + 0.654834i 0.772739π0.772739\pi
200200 0 0
201201 0 0
202202 0 0
203203 −22.9913 −1.61367
204204 0 0
205205 −3.02690 −0.211408
206206 0 0
207207 0 0
208208 0 0
209209 −1.08684 −0.0751780
210210 0 0
211211 2.51746 0.173309 0.0866547 0.996238i 0.472382π-0.472382\pi
0.0866547 + 0.996238i 0.472382π0.472382\pi
212212 0 0
213213 0 0
214214 0 0
215215 −1.93295 −0.131826
216216 0 0
217217 −13.5087 −0.917032
218218 0 0
219219 0 0
220220 0 0
221221 −1.24272 −0.0835947
222222 0 0
223223 −9.95332 −0.666523 −0.333262 0.942834i 0.608149π-0.608149\pi
−0.333262 + 0.942834i 0.608149π0.608149\pi
224224 0 0
225225 0 0
226226 0 0
227227 −17.1138 −1.13589 −0.567943 0.823068i 0.692261π-0.692261\pi
−0.567943 + 0.823068i 0.692261π0.692261\pi
228228 0 0
229229 11.7784 0.778335 0.389168 0.921167i 0.372763π-0.372763\pi
0.389168 + 0.921167i 0.372763π0.372763\pi
230230 0 0
231231 0 0
232232 0 0
233233 −19.3186 −1.26560 −0.632802 0.774313i 0.718095π-0.718095\pi
−0.632802 + 0.774313i 0.718095π0.718095\pi
234234 0 0
235235 24.4796 1.59687
236236 0 0
237237 0 0
238238 0 0
239239 −21.2071 −1.37177 −0.685886 0.727709i 0.740585π-0.740585\pi
−0.685886 + 0.727709i 0.740585π0.740585\pi
240240 0 0
241241 −8.37171 −0.539269 −0.269635 0.962963i 0.586903π-0.586903\pi
−0.269635 + 0.962963i 0.586903π0.586903\pi
242242 0 0
243243 0 0
244244 0 0
245245 54.1562 3.45991
246246 0 0
247247 −0.552500 −0.0351548
248248 0 0
249249 0 0
250250 0 0
251251 −24.0701 −1.51929 −0.759645 0.650338i 0.774627π-0.774627\pi
−0.759645 + 0.650338i 0.774627π0.774627\pi
252252 0 0
253253 −0.461460 −0.0290117
254254 0 0
255255 0 0
256256 0 0
257257 −29.5846 −1.84544 −0.922719 0.385473i 0.874038π-0.874038\pi
−0.922719 + 0.385473i 0.874038π0.874038\pi
258258 0 0
259259 22.9913 1.42861
260260 0 0
261261 0 0
262262 0 0
263263 12.8092 0.789848 0.394924 0.918714i 0.370771π-0.370771\pi
0.394924 + 0.918714i 0.370771π0.370771\pi
264264 0 0
265265 14.3717 0.882847
266266 0 0
267267 0 0
268268 0 0
269269 5.76817 0.351691 0.175846 0.984418i 0.443734π-0.443734\pi
0.175846 + 0.984418i 0.443734π0.443734\pi
270270 0 0
271271 22.1150 1.34339 0.671696 0.740827i 0.265566π-0.265566\pi
0.671696 + 0.740827i 0.265566π0.265566\pi
272272 0 0
273273 0 0
274274 0 0
275275 17.6984 1.06725
276276 0 0
277277 31.7005 1.90470 0.952350 0.305008i 0.0986591π-0.0986591\pi
0.952350 + 0.305008i 0.0986591π0.0986591\pi
278278 0 0
279279 0 0
280280 0 0
281281 3.86007 0.230273 0.115136 0.993350i 0.463270π-0.463270\pi
0.115136 + 0.993350i 0.463270π0.463270\pi
282282 0 0
283283 26.5875 1.58047 0.790233 0.612807i 0.209960π-0.209960\pi
0.790233 + 0.612807i 0.209960π0.209960\pi
284284 0 0
285285 0 0
286286 0 0
287287 −4.10209 −0.242139
288288 0 0
289289 1.00000 0.0588235
290290 0 0
291291 0 0
292292 0 0
293293 9.02910 0.527486 0.263743 0.964593i 0.415043π-0.415043\pi
0.263743 + 0.964593i 0.415043π0.415043\pi
294294 0 0
295295 −0.377536 −0.0219810
296296 0 0
297297 0 0
298298 0 0
299299 −0.234586 −0.0135665
300300 0 0
301301 −2.61955 −0.150989
302302 0 0
303303 0 0
304304 0 0
305305 −48.8193 −2.79539
306306 0 0
307307 8.97090 0.511996 0.255998 0.966677i 0.417596π-0.417596\pi
0.255998 + 0.966677i 0.417596π0.417596\pi
308308 0 0
309309 0 0
310310 0 0
311311 −5.58247 −0.316553 −0.158276 0.987395i 0.550594π-0.550594\pi
−0.158276 + 0.987395i 0.550594π0.550594\pi
312312 0 0
313313 5.29463 0.299270 0.149635 0.988741i 0.452190π-0.452190\pi
0.149635 + 0.988741i 0.452190π0.452190\pi
314314 0 0
315315 0 0
316316 0 0
317317 −15.5984 −0.876095 −0.438048 0.898952i 0.644330π-0.644330\pi
−0.438048 + 0.898952i 0.644330π0.644330\pi
318318 0 0
319319 −11.8542 −0.663711
320320 0 0
321321 0 0
322322 0 0
323323 0.444588 0.0247376
324324 0 0
325325 8.99709 0.499069
326326 0 0
327327 0 0
328328 0 0
329329 33.1751 1.82900
330330 0 0
331331 14.5467 0.799558 0.399779 0.916612i 0.369087π-0.369087\pi
0.399779 + 0.916612i 0.369087π0.369087\pi
332332 0 0
333333 0 0
334334 0 0
335335 46.2260 2.52559
336336 0 0
337337 11.8601 0.646059 0.323030 0.946389i 0.395299π-0.395299\pi
0.323030 + 0.946389i 0.395299π0.395299\pi
338338 0 0
339339 0 0
340340 0 0
341341 −6.96507 −0.377180
342342 0 0
343343 40.2042 2.17082
344344 0 0
345345 0 0
346346 0 0
347347 −36.9593 −1.98408 −0.992038 0.125937i 0.959806π-0.959806\pi
−0.992038 + 0.125937i 0.959806π0.959806\pi
348348 0 0
349349 7.94400 0.425232 0.212616 0.977136i 0.431802π-0.431802\pi
0.212616 + 0.977136i 0.431802π0.431802\pi
350350 0 0
351351 0 0
352352 0 0
353353 1.18090 0.0628528 0.0314264 0.999506i 0.489995π-0.489995\pi
0.0314264 + 0.999506i 0.489995π0.489995\pi
354354 0 0
355355 −43.1431 −2.28980
356356 0 0
357357 0 0
358358 0 0
359359 −5.86007 −0.309283 −0.154641 0.987971i 0.549422π-0.549422\pi
−0.154641 + 0.987971i 0.549422π0.549422\pi
360360 0 0
361361 −18.8023 −0.989597
362362 0 0
363363 0 0
364364 0 0
365365 −33.5526 −1.75622
366366 0 0
367367 −19.9542 −1.04160 −0.520800 0.853679i 0.674366π-0.674366\pi
−0.520800 + 0.853679i 0.674366π0.674366\pi
368368 0 0
369369 0 0
370370 0 0
371371 19.4767 1.01118
372372 0 0
373373 25.4767 1.31913 0.659567 0.751646i 0.270740π-0.270740\pi
0.659567 + 0.751646i 0.270740π0.270740\pi
374374 0 0
375375 0 0
376376 0 0
377377 −6.02619 −0.310365
378378 0 0
379379 3.65448 0.187718 0.0938590 0.995585i 0.470080π-0.470080\pi
0.0938590 + 0.995585i 0.470080π0.470080\pi
380380 0 0
381381 0 0
382382 0 0
383383 4.39963 0.224811 0.112405 0.993662i 0.464144π-0.464144\pi
0.112405 + 0.993662i 0.464144π0.464144\pi
384384 0 0
385385 40.5497 2.06660
386386 0 0
387387 0 0
388388 0 0
389389 22.9709 1.16467 0.582335 0.812949i 0.302139π-0.302139\pi
0.582335 + 0.812949i 0.302139π0.302139\pi
390390 0 0
391391 0.188768 0.00954640
392392 0 0
393393 0 0
394394 0 0
395395 21.8863 1.10122
396396 0 0
397397 20.5196 1.02985 0.514925 0.857235i 0.327820π-0.327820\pi
0.514925 + 0.857235i 0.327820π0.327820\pi
398398 0 0
399399 0 0
400400 0 0
401401 24.5257 1.22476 0.612378 0.790565i 0.290213π-0.290213\pi
0.612378 + 0.790565i 0.290213π0.290213\pi
402402 0 0
403403 −3.54074 −0.176377
404404 0 0
405405 0 0
406406 0 0
407407 11.8542 0.587593
408408 0 0
409409 −7.26309 −0.359137 −0.179568 0.983745i 0.557470π-0.557470\pi
−0.179568 + 0.983745i 0.557470π0.557470\pi
410410 0 0
411411 0 0
412412 0 0
413413 −0.511641 −0.0251762
414414 0 0
415415 40.1722 1.97197
416416 0 0
417417 0 0
418418 0 0
419419 −3.78418 −0.184869 −0.0924345 0.995719i 0.529465π-0.529465\pi
−0.0924345 + 0.995719i 0.529465π0.529465\pi
420420 0 0
421421 8.48765 0.413663 0.206831 0.978377i 0.433685π-0.433685\pi
0.206831 + 0.978377i 0.433685π0.433685\pi
422422 0 0
423423 0 0
424424 0 0
425425 −7.23981 −0.351182
426426 0 0
427427 −66.1605 −3.20173
428428 0 0
429429 0 0
430430 0 0
431431 15.3608 0.739905 0.369952 0.929051i 0.379374π-0.379374\pi
0.369952 + 0.929051i 0.379374π0.379374\pi
432432 0 0
433433 −30.9353 −1.48665 −0.743327 0.668928i 0.766753π-0.766753\pi
−0.743327 + 0.668928i 0.766753π0.766753\pi
434434 0 0
435435 0 0
436436 0 0
437437 0.0839240 0.00401463
438438 0 0
439439 −7.38843 −0.352630 −0.176315 0.984334i 0.556418π-0.556418\pi
−0.176315 + 0.984334i 0.556418π0.556418\pi
440440 0 0
441441 0 0
442442 0 0
443443 −17.6663 −0.839353 −0.419677 0.907674i 0.637857π-0.637857\pi
−0.419677 + 0.907674i 0.637857π0.637857\pi
444444 0 0
445445 −24.1021 −1.14255
446446 0 0
447447 0 0
448448 0 0
449449 9.93597 0.468907 0.234454 0.972127i 0.424670π-0.424670\pi
0.234454 + 0.972127i 0.424670π0.424670\pi
450450 0 0
451451 −2.11503 −0.0995928
452452 0 0
453453 0 0
454454 0 0
455455 20.6137 0.966387
456456 0 0
457457 −20.6656 −0.966698 −0.483349 0.875428i 0.660580π-0.660580\pi
−0.483349 + 0.875428i 0.660580π0.660580\pi
458458 0 0
459459 0 0
460460 0 0
461461 10.5116 0.489576 0.244788 0.969577i 0.421282π-0.421282\pi
0.244788 + 0.969577i 0.421282π0.421282\pi
462462 0 0
463463 27.2609 1.26692 0.633460 0.773775i 0.281634π-0.281634\pi
0.633460 + 0.773775i 0.281634π0.281634\pi
464464 0 0
465465 0 0
466466 0 0
467467 25.1530 1.16394 0.581970 0.813210i 0.302282π-0.302282\pi
0.581970 + 0.813210i 0.302282π0.302282\pi
468468 0 0
469469 62.6460 2.89272
470470 0 0
471471 0 0
472472 0 0
473473 −1.35064 −0.0621023
474474 0 0
475475 −3.21874 −0.147686
476476 0 0
477477 0 0
478478 0 0
479479 26.3171 1.20246 0.601228 0.799077i 0.294678π-0.294678\pi
0.601228 + 0.799077i 0.294678π0.294678\pi
480480 0 0
481481 6.02619 0.274771
482482 0 0
483483 0 0
484484 0 0
485485 49.3368 2.24027
486486 0 0
487487 11.8183 0.535541 0.267770 0.963483i 0.413713π-0.413713\pi
0.267770 + 0.963483i 0.413713π0.413713\pi
488488 0 0
489489 0 0
490490 0 0
491491 8.70709 0.392946 0.196473 0.980509i 0.437051π-0.437051\pi
0.196473 + 0.980509i 0.437051π0.437051\pi
492492 0 0
493493 4.84918 0.218396
494494 0 0
495495 0 0
496496 0 0
497497 −58.4680 −2.62265
498498 0 0
499499 35.9563 1.60963 0.804813 0.593528i 0.202265π-0.202265\pi
0.804813 + 0.593528i 0.202265π0.202265\pi
500500 0 0
501501 0 0
502502 0 0
503503 −24.9980 −1.11460 −0.557302 0.830310i 0.688163π-0.688163\pi
−0.557302 + 0.830310i 0.688163π0.688163\pi
504504 0 0
505505 −55.8443 −2.48504
506506 0 0
507507 0 0
508508 0 0
509509 −27.2347 −1.20716 −0.603578 0.797304i 0.706259π-0.706259\pi
−0.603578 + 0.797304i 0.706259π0.706259\pi
510510 0 0
511511 −45.4709 −2.01151
512512 0 0
513513 0 0
514514 0 0
515515 −21.1138 −0.930387
516516 0 0
517517 17.1050 0.752277
518518 0 0
519519 0 0
520520 0 0
521521 −24.8012 −1.08656 −0.543279 0.839552i 0.682817π-0.682817\pi
−0.543279 + 0.839552i 0.682817π0.682817\pi
522522 0 0
523523 33.3647 1.45894 0.729468 0.684015i 0.239768π-0.239768\pi
0.729468 + 0.684015i 0.239768π0.239768\pi
524524 0 0
525525 0 0
526526 0 0
527527 2.84918 0.124112
528528 0 0
529529 −22.9644 −0.998451
530530 0 0
531531 0 0
532532 0 0
533533 −1.07519 −0.0465717
534534 0 0
535535 9.30757 0.402401
536536 0 0
537537 0 0
538538 0 0
539539 37.8413 1.62994
540540 0 0
541541 −13.6043 −0.584892 −0.292446 0.956282i 0.594469π-0.594469\pi
−0.292446 + 0.956282i 0.594469π0.594469\pi
542542 0 0
543543 0 0
544544 0 0
545545 −59.8705 −2.56457
546546 0 0
547547 23.8746 1.02081 0.510403 0.859936i 0.329496π-0.329496\pi
0.510403 + 0.859936i 0.329496π0.329496\pi
548548 0 0
549549 0 0
550550 0 0
551551 2.15589 0.0918439
552552 0 0
553553 29.6605 1.26129
554554 0 0
555555 0 0
556556 0 0
557557 29.9084 1.26726 0.633629 0.773637i 0.281565π-0.281565\pi
0.633629 + 0.773637i 0.281565π0.281565\pi
558558 0 0
559559 −0.686606 −0.0290403
560560 0 0
561561 0 0
562562 0 0
563563 37.7405 1.59057 0.795287 0.606234i 0.207320π-0.207320\pi
0.795287 + 0.606234i 0.207320π0.207320\pi
564564 0 0
565565 −58.8916 −2.47759
566566 0 0
567567 0 0
568568 0 0
569569 −19.4784 −0.816579 −0.408289 0.912853i 0.633875π-0.633875\pi
−0.408289 + 0.912853i 0.633875π0.633875\pi
570570 0 0
571571 −21.0713 −0.881805 −0.440902 0.897555i 0.645341π-0.645341\pi
−0.440902 + 0.897555i 0.645341π0.645341\pi
572572 0 0
573573 0 0
574574 0 0
575575 −1.36664 −0.0569930
576576 0 0
577577 23.6365 0.984002 0.492001 0.870595i 0.336266π-0.336266\pi
0.492001 + 0.870595i 0.336266π0.336266\pi
578578 0 0
579579 0 0
580580 0 0
581581 54.4418 2.25863
582582 0 0
583583 10.0422 0.415904
584584 0 0
585585 0 0
586586 0 0
587587 12.9593 0.534886 0.267443 0.963574i 0.413821π-0.413821\pi
0.267443 + 0.963574i 0.413821π0.413821\pi
588588 0 0
589589 1.26671 0.0521940
590590 0 0
591591 0 0
592592 0 0
593593 36.0584 1.48074 0.740371 0.672198i 0.234650π-0.234650\pi
0.740371 + 0.672198i 0.234650π0.234650\pi
594594 0 0
595595 −16.5875 −0.680023
596596 0 0
597597 0 0
598598 0 0
599599 −42.7597 −1.74711 −0.873557 0.486722i 0.838193π-0.838193\pi
−0.873557 + 0.486722i 0.838193π0.838193\pi
600600 0 0
601601 −31.6663 −1.29170 −0.645849 0.763466i 0.723496π-0.723496\pi
−0.645849 + 0.763466i 0.723496π0.723496\pi
602602 0 0
603603 0 0
604604 0 0
605605 −17.5766 −0.714592
606606 0 0
607607 −40.2980 −1.63564 −0.817822 0.575471i 0.804819π-0.804819\pi
−0.817822 + 0.575471i 0.804819π0.804819\pi
608608 0 0
609609 0 0
610610 0 0
611611 8.69545 0.351780
612612 0 0
613613 −7.43236 −0.300190 −0.150095 0.988672i 0.547958π-0.547958\pi
−0.150095 + 0.988672i 0.547958π0.547958\pi
614614 0 0
615615 0 0
616616 0 0
617617 38.1242 1.53482 0.767411 0.641155i 0.221545π-0.221545\pi
0.767411 + 0.641155i 0.221545π0.221545\pi
618618 0 0
619619 −37.0410 −1.48880 −0.744401 0.667733i 0.767265π-0.767265\pi
−0.744401 + 0.667733i 0.767265π0.767265\pi
620620 0 0
621621 0 0
622622 0 0
623623 −32.6634 −1.30863
624624 0 0
625625 −8.78418 −0.351367
626626 0 0
627627 0 0
628628 0 0
629629 −4.84918 −0.193349
630630 0 0
631631 −28.1633 −1.12116 −0.560582 0.828099i 0.689423π-0.689423\pi
−0.560582 + 0.828099i 0.689423π0.689423\pi
632632 0 0
633633 0 0
634634 0 0
635635 43.9155 1.74273
636636 0 0
637637 19.2369 0.762194
638638 0 0
639639 0 0
640640 0 0
641641 −29.1290 −1.15053 −0.575263 0.817969i 0.695100π-0.695100\pi
−0.575263 + 0.817969i 0.695100π0.695100\pi
642642 0 0
643643 36.4156 1.43609 0.718045 0.695996i 0.245037π-0.245037\pi
0.718045 + 0.695996i 0.245037π0.245037\pi
644644 0 0
645645 0 0
646646 0 0
647647 43.4988 1.71011 0.855057 0.518533i 0.173522π-0.173522\pi
0.855057 + 0.518533i 0.173522π0.173522\pi
648648 0 0
649649 −0.263801 −0.0103551
650650 0 0
651651 0 0
652652 0 0
653653 27.5145 1.07673 0.538363 0.842713i 0.319043π-0.319043\pi
0.538363 + 0.842713i 0.319043π0.319043\pi
654654 0 0
655655 −43.5176 −1.70037
656656 0 0
657657 0 0
658658 0 0
659659 19.9959 0.778930 0.389465 0.921041i 0.372660π-0.372660\pi
0.389465 + 0.921041i 0.372660π0.372660\pi
660660 0 0
661661 −38.9570 −1.51525 −0.757627 0.652688i 0.773641π-0.773641\pi
−0.757627 + 0.652688i 0.773641π0.773641\pi
662662 0 0
663663 0 0
664664 0 0
665665 −7.37462 −0.285976
666666 0 0
667667 0.915369 0.0354432
668668 0 0
669669 0 0
670670 0 0
671671 −34.1122 −1.31689
672672 0 0
673673 −11.8281 −0.455938 −0.227969 0.973668i 0.573209π-0.573209\pi
−0.227969 + 0.973668i 0.573209π0.573209\pi
674674 0 0
675675 0 0
676676 0 0
677677 15.2347 0.585519 0.292759 0.956186i 0.405427π-0.405427\pi
0.292759 + 0.956186i 0.405427π0.405427\pi
678678 0 0
679679 66.8618 2.56592
680680 0 0
681681 0 0
682682 0 0
683683 4.82795 0.184736 0.0923681 0.995725i 0.470556π-0.470556\pi
0.0923681 + 0.995725i 0.470556π0.470556\pi
684684 0 0
685685 −39.7946 −1.52047
686686 0 0
687687 0 0
688688 0 0
689689 5.10500 0.194485
690690 0 0
691691 21.6867 0.825002 0.412501 0.910957i 0.364655π-0.364655\pi
0.412501 + 0.910957i 0.364655π0.364655\pi
692692 0 0
693693 0 0
694694 0 0
695695 69.5730 2.63905
696696 0 0
697697 0.865188 0.0327713
698698 0 0
699699 0 0
700700 0 0
701701 38.7638 1.46409 0.732044 0.681257i 0.238566π-0.238566\pi
0.732044 + 0.681257i 0.238566π0.238566\pi
702702 0 0
703703 −2.15589 −0.0813109
704704 0 0
705705 0 0
706706 0 0
707707 −75.6809 −2.84627
708708 0 0
709709 21.4105 0.804089 0.402045 0.915620i 0.368300π-0.368300\pi
0.402045 + 0.915620i 0.368300π0.368300\pi
710710 0 0
711711 0 0
712712 0 0
713713 0.537834 0.0201420
714714 0 0
715715 10.6284 0.397480
716716 0 0
717717 0 0
718718 0 0
719719 −16.8621 −0.628851 −0.314425 0.949282i 0.601812π-0.601812\pi
−0.314425 + 0.949282i 0.601812π0.601812\pi
720720 0 0
721721 −28.6137 −1.06563
722722 0 0
723723 0 0
724724 0 0
725725 −35.1072 −1.30385
726726 0 0
727727 −45.9942 −1.70583 −0.852915 0.522050i 0.825167π-0.825167\pi
−0.852915 + 0.522050i 0.825167π0.825167\pi
728728 0 0
729729 0 0
730730 0 0
731731 0.552500 0.0204350
732732 0 0
733733 −17.0451 −0.629574 −0.314787 0.949162i 0.601933π-0.601933\pi
−0.314787 + 0.949162i 0.601933π0.601933\pi
734734 0 0
735735 0 0
736736 0 0
737737 32.3001 1.18979
738738 0 0
739739 −20.8122 −0.765589 −0.382795 0.923833i 0.625038π-0.625038\pi
−0.382795 + 0.923833i 0.625038π0.625038\pi
740740 0 0
741741 0 0
742742 0 0
743743 −42.9893 −1.57713 −0.788563 0.614954i 0.789174π-0.789174\pi
−0.788563 + 0.614954i 0.789174π0.789174\pi
744744 0 0
745745 23.3470 0.855369
746746 0 0
747747 0 0
748748 0 0
749749 12.6137 0.460896
750750 0 0
751751 2.38993 0.0872096 0.0436048 0.999049i 0.486116π-0.486116\pi
0.0436048 + 0.999049i 0.486116π0.486116\pi
752752 0 0
753753 0 0
754754 0 0
755755 46.1343 1.67900
756756 0 0
757757 22.9891 0.835552 0.417776 0.908550i 0.362810π-0.362810\pi
0.417776 + 0.908550i 0.362810π0.362810\pi
758758 0 0
759759 0 0
760760 0 0
761761 −7.01746 −0.254383 −0.127191 0.991878i 0.540596π-0.540596\pi
−0.127191 + 0.991878i 0.540596π0.540596\pi
762762 0 0
763763 −81.1372 −2.93737
764764 0 0
765765 0 0
766766 0 0
767767 −0.134105 −0.00484225
768768 0 0
769769 12.0764 0.435485 0.217743 0.976006i 0.430131π-0.430131\pi
0.217743 + 0.976006i 0.430131π0.430131\pi
770770 0 0
771771 0 0
772772 0 0
773773 −4.39208 −0.157972 −0.0789861 0.996876i 0.525168π-0.525168\pi
−0.0789861 + 0.996876i 0.525168π0.525168\pi
774774 0 0
775775 −20.6275 −0.740963
776776 0 0
777777 0 0
778778 0 0
779779 0.384653 0.0137816
780780 0 0
781781 −30.1460 −1.07871
782782 0 0
783783 0 0
784784 0 0
785785 3.31280 0.118239
786786 0 0
787787 −4.19545 −0.149552 −0.0747759 0.997200i 0.523824π-0.523824\pi
−0.0747759 + 0.997200i 0.523824π0.523824\pi
788788 0 0
789789 0 0
790790 0 0
791791 −79.8106 −2.83774
792792 0 0
793793 −17.3412 −0.615804
794794 0 0
795795 0 0
796796 0 0
797797 −11.0553 −0.391599 −0.195799 0.980644i 0.562730π-0.562730\pi
−0.195799 + 0.980644i 0.562730π0.562730\pi
798798 0 0
799799 −6.99709 −0.247539
800800 0 0
801801 0 0
802802 0 0
803803 −23.4447 −0.827345
804804 0 0
805805 −3.13119 −0.110360
806806 0 0
807807 0 0
808808 0 0
809809 15.9423 0.560500 0.280250 0.959927i 0.409583π-0.409583\pi
0.280250 + 0.959927i 0.409583π0.409583\pi
810810 0 0
811811 −19.7246 −0.692623 −0.346311 0.938120i 0.612566π-0.612566\pi
−0.346311 + 0.938120i 0.612566π0.612566\pi
812812 0 0
813813 0 0
814814 0 0
815815 −6.97672 −0.244384
816816 0 0
817817 0.245635 0.00859369
818818 0 0
819819 0 0
820820 0 0
821821 −4.48981 −0.156695 −0.0783477 0.996926i 0.524964π-0.524964\pi
−0.0783477 + 0.996926i 0.524964π0.524964\pi
822822 0 0
823823 −20.3858 −0.710605 −0.355303 0.934751i 0.615622π-0.615622\pi
−0.355303 + 0.934751i 0.615622π0.615622\pi
824824 0 0
825825 0 0
826826 0 0
827827 −42.6488 −1.48304 −0.741521 0.670929i 0.765895π-0.765895\pi
−0.741521 + 0.670929i 0.765895π0.765895\pi
828828 0 0
829829 −23.9301 −0.831128 −0.415564 0.909564i 0.636416π-0.636416\pi
−0.415564 + 0.909564i 0.636416π0.636416\pi
830830 0 0
831831 0 0
832832 0 0
833833 −15.4796 −0.536337
834834 0 0
835835 −65.4038 −2.26339
836836 0 0
837837 0 0
838838 0 0
839839 −43.5721 −1.50428 −0.752138 0.659005i 0.770977π-0.770977\pi
−0.752138 + 0.659005i 0.770977π0.770977\pi
840840 0 0
841841 −5.48545 −0.189153
842842 0 0
843843 0 0
844844 0 0
845845 −40.0781 −1.37873
846846 0 0
847847 −23.8201 −0.818468
848848 0 0
849849 0 0
850850 0 0
851851 −0.915369 −0.0313785
852852 0 0
853853 −19.8783 −0.680620 −0.340310 0.940313i 0.610532π-0.610532\pi
−0.340310 + 0.940313i 0.610532π0.610532\pi
854854 0 0
855855 0 0
856856 0 0
857857 −12.5858 −0.429923 −0.214962 0.976623i 0.568963π-0.568963\pi
−0.214962 + 0.976623i 0.568963π0.568963\pi
858858 0 0
859859 11.5043 0.392522 0.196261 0.980552i 0.437120π-0.437120\pi
0.196261 + 0.980552i 0.437120π0.437120\pi
860860 0 0
861861 0 0
862862 0 0
863863 −26.2321 −0.892951 −0.446476 0.894796i 0.647321π-0.647321\pi
−0.446476 + 0.894796i 0.647321π0.647321\pi
864864 0 0
865865 59.4091 2.01997
866866 0 0
867867 0 0
868868 0 0
869869 15.2929 0.518776
870870 0 0
871871 16.4200 0.556371
872872 0 0
873873 0 0
874874 0 0
875875 37.1530 1.25600
876876 0 0
877877 −37.5109 −1.26665 −0.633326 0.773885i 0.718311π-0.718311\pi
−0.633326 + 0.773885i 0.718311π0.718311\pi
878878 0 0
879879 0 0
880880 0 0
881881 10.2318 0.344718 0.172359 0.985034i 0.444861π-0.444861\pi
0.172359 + 0.985034i 0.444861π0.444861\pi
882882 0 0
883883 −21.5673 −0.725797 −0.362898 0.931829i 0.618213π-0.618213\pi
−0.362898 + 0.931829i 0.618213π0.618213\pi
884884 0 0
885885 0 0
886886 0 0
887887 49.6073 1.66565 0.832825 0.553537i 0.186722π-0.186722\pi
0.832825 + 0.553537i 0.186722π0.186722\pi
888888 0 0
889889 59.5148 1.99606
890890 0 0
891891 0 0
892892 0 0
893893 −3.11082 −0.104100
894894 0 0
895895 −11.3525 −0.379473
896896 0 0
897897 0 0
898898 0 0
899899 13.8162 0.460796
900900 0 0
901901 −4.10791 −0.136854
902902 0 0
903903 0 0
904904 0 0
905905 −51.4610 −1.71062
906906 0 0
907907 −16.7054 −0.554693 −0.277346 0.960770i 0.589455π-0.589455\pi
−0.277346 + 0.960770i 0.589455π0.589455\pi
908908 0 0
909909 0 0
910910 0 0
911911 −44.7004 −1.48099 −0.740495 0.672062i 0.765409π-0.765409\pi
−0.740495 + 0.672062i 0.765409π0.765409\pi
912912 0 0
913913 28.0701 0.928984
914914 0 0
915915 0 0
916916 0 0
917917 −58.9755 −1.94754
918918 0 0
919919 −43.1560 −1.42359 −0.711793 0.702390i 0.752116π-0.752116\pi
−0.711793 + 0.702390i 0.752116π0.752116\pi
920920 0 0
921921 0 0
922922 0 0
923923 −15.3249 −0.504426
924924 0 0
925925 35.1072 1.15432
926926 0 0
927927 0 0
928928 0 0
929929 −30.6915 −1.00696 −0.503478 0.864008i 0.667947π-0.667947\pi
−0.503478 + 0.864008i 0.667947π0.667947\pi
930930 0 0
931931 −6.88206 −0.225550
932932 0 0
933933 0 0
934934 0 0
935935 −8.55250 −0.279697
936936 0 0
937937 37.0072 1.20897 0.604487 0.796615i 0.293378π-0.293378\pi
0.604487 + 0.796615i 0.293378π0.293378\pi
938938 0 0
939939 0 0
940940 0 0
941941 −39.4350 −1.28554 −0.642772 0.766058i 0.722216π-0.722216\pi
−0.642772 + 0.766058i 0.722216π0.722216\pi
942942 0 0
943943 0.163320 0.00531842
944944 0 0
945945 0 0
946946 0 0
947947 −28.4360 −0.924045 −0.462022 0.886868i 0.652876π-0.652876\pi
−0.462022 + 0.886868i 0.652876π0.652876\pi
948948 0 0
949949 −11.9183 −0.386884
950950 0 0
951951 0 0
952952 0 0
953953 22.9113 0.742169 0.371084 0.928599i 0.378986π-0.378986\pi
0.371084 + 0.928599i 0.378986π0.378986\pi
954954 0 0
955955 73.7248 2.38568
956956 0 0
957957 0 0
958958 0 0
959959 −53.9301 −1.74150
960960 0 0
961961 −22.8822 −0.738135
962962 0 0
963963 0 0
964964 0 0
965965 51.6925 1.66404
966966 0 0
967967 16.8660 0.542374 0.271187 0.962527i 0.412584π-0.412584\pi
0.271187 + 0.962527i 0.412584π0.412584\pi
968968 0 0
969969 0 0
970970 0 0
971971 −6.77544 −0.217434 −0.108717 0.994073i 0.534674π-0.534674\pi
−0.108717 + 0.994073i 0.534674π0.534674\pi
972972 0 0
973973 94.2861 3.02267
974974 0 0
975975 0 0
976976 0 0
977977 6.16203 0.197141 0.0985703 0.995130i 0.468573π-0.468573\pi
0.0985703 + 0.995130i 0.468573π0.468573\pi
978978 0 0
979979 −16.8412 −0.538247
980980 0 0
981981 0 0
982982 0 0
983983 34.0113 1.08479 0.542396 0.840123i 0.317517π-0.317517\pi
0.542396 + 0.840123i 0.317517π0.317517\pi
984984 0 0
985985 5.26309 0.167696
986986 0 0
987987 0 0
988988 0 0
989989 0.104294 0.00331637
990990 0 0
991991 57.0431 1.81203 0.906017 0.423241i 0.139107π-0.139107\pi
0.906017 + 0.423241i 0.139107π0.139107\pi
992992 0 0
993993 0 0
994994 0 0
995995 −74.5994 −2.36496
996996 0 0
997997 −8.63336 −0.273421 −0.136711 0.990611i 0.543653π-0.543653\pi
−0.136711 + 0.990611i 0.543653π0.543653\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 4896.2.a.bj.1.4 yes 4
3.2 odd 2 4896.2.a.bh.1.1 yes 4
4.3 odd 2 4896.2.a.bi.1.4 yes 4
8.3 odd 2 9792.2.a.dm.1.1 4
8.5 even 2 9792.2.a.dn.1.1 4
12.11 even 2 4896.2.a.bg.1.1 4
24.5 odd 2 9792.2.a.dp.1.4 4
24.11 even 2 9792.2.a.do.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4896.2.a.bg.1.1 4 12.11 even 2
4896.2.a.bh.1.1 yes 4 3.2 odd 2
4896.2.a.bi.1.4 yes 4 4.3 odd 2
4896.2.a.bj.1.4 yes 4 1.1 even 1 trivial
9792.2.a.dm.1.1 4 8.3 odd 2
9792.2.a.dn.1.1 4 8.5 even 2
9792.2.a.do.1.4 4 24.11 even 2
9792.2.a.dp.1.4 4 24.5 odd 2