Properties

Label 324.4.a.c.1.3
Level 324324
Weight 44
Character 324.1
Self dual yes
Analytic conductor 19.11719.117
Analytic rank 11
Dimension 33
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,4,Mod(1,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("324.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 324=2234 324 = 2^{2} \cdot 3^{4}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 324.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: 19.116618841919.1166188419
Analytic rank: 11
Dimension: 33
Coefficient field: 3.3.1509.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x27x+4 x^{3} - x^{2} - 7x + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 232 2\cdot 3^{2}
Twist minimal: no (minimal twist has level 36)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 0.5519290.551929 of defining polynomial
Character χ\chi == 324.1

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+12.7419q514.0535q742.5491q1172.4632q1359.6114q17+105.570q190.225180q23+37.3563q25225.710q29+201.194q31179.068q35152.926q37489.648q417.58743q43+373.391q47145.500q4943.6780q53542.157q55671.899q59+74.0354q61923.320q65+420.871q67730.840q71+473.927q73+597.963q77529.622q79+26.1534q83759.563q85+415.949q89+1018.36q91+1345.17q95+927.485q97+O(q100)q+12.7419 q^{5} -14.0535 q^{7} -42.5491 q^{11} -72.4632 q^{13} -59.6114 q^{17} +105.570 q^{19} -0.225180 q^{23} +37.3563 q^{25} -225.710 q^{29} +201.194 q^{31} -179.068 q^{35} -152.926 q^{37} -489.648 q^{41} -7.58743 q^{43} +373.391 q^{47} -145.500 q^{49} -43.6780 q^{53} -542.157 q^{55} -671.899 q^{59} +74.0354 q^{61} -923.320 q^{65} +420.871 q^{67} -730.840 q^{71} +473.927 q^{73} +597.963 q^{77} -529.622 q^{79} +26.1534 q^{83} -759.563 q^{85} +415.949 q^{89} +1018.36 q^{91} +1345.17 q^{95} +927.485 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q6q5+6q751q1112q13111q17+15q19210q23+3q25456q2948q31552q3548q37897q41129q43522q47+225q491104q53+93q97+O(q100) 3 q - 6 q^{5} + 6 q^{7} - 51 q^{11} - 12 q^{13} - 111 q^{17} + 15 q^{19} - 210 q^{23} + 3 q^{25} - 456 q^{29} - 48 q^{31} - 552 q^{35} - 48 q^{37} - 897 q^{41} - 129 q^{43} - 522 q^{47} + 225 q^{49} - 1104 q^{53}+ \cdots - 93 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 12.7419 1.13967 0.569836 0.821759i 0.307007π-0.307007\pi
0.569836 + 0.821759i 0.307007π0.307007\pi
66 0 0
77 −14.0535 −0.758817 −0.379408 0.925229i 0.623872π-0.623872\pi
−0.379408 + 0.925229i 0.623872π0.623872\pi
88 0 0
99 0 0
1010 0 0
1111 −42.5491 −1.16628 −0.583138 0.812373i 0.698175π-0.698175\pi
−0.583138 + 0.812373i 0.698175π0.698175\pi
1212 0 0
1313 −72.4632 −1.54598 −0.772988 0.634421i 0.781239π-0.781239\pi
−0.772988 + 0.634421i 0.781239π0.781239\pi
1414 0 0
1515 0 0
1616 0 0
1717 −59.6114 −0.850464 −0.425232 0.905084i 0.639807π-0.639807\pi
−0.425232 + 0.905084i 0.639807π0.639807\pi
1818 0 0
1919 105.570 1.27471 0.637354 0.770571i 0.280029π-0.280029\pi
0.637354 + 0.770571i 0.280029π0.280029\pi
2020 0 0
2121 0 0
2222 0 0
2323 −0.225180 −0.00204144 −0.00102072 0.999999i 0.500325π-0.500325\pi
−0.00102072 + 0.999999i 0.500325π0.500325\pi
2424 0 0
2525 37.3563 0.298850
2626 0 0
2727 0 0
2828 0 0
2929 −225.710 −1.44528 −0.722642 0.691223i 0.757072π-0.757072\pi
−0.722642 + 0.691223i 0.757072π0.757072\pi
3030 0 0
3131 201.194 1.16566 0.582831 0.812594i 0.301945π-0.301945\pi
0.582831 + 0.812594i 0.301945π0.301945\pi
3232 0 0
3333 0 0
3434 0 0
3535 −179.068 −0.864802
3636 0 0
3737 −152.926 −0.679485 −0.339743 0.940518i 0.610340π-0.610340\pi
−0.339743 + 0.940518i 0.610340π0.610340\pi
3838 0 0
3939 0 0
4040 0 0
4141 −489.648 −1.86513 −0.932563 0.361008i 0.882433π-0.882433\pi
−0.932563 + 0.361008i 0.882433π0.882433\pi
4242 0 0
4343 −7.58743 −0.0269087 −0.0134543 0.999909i 0.504283π-0.504283\pi
−0.0134543 + 0.999909i 0.504283π0.504283\pi
4444 0 0
4545 0 0
4646 0 0
4747 373.391 1.15882 0.579412 0.815035i 0.303282π-0.303282\pi
0.579412 + 0.815035i 0.303282π0.303282\pi
4848 0 0
4949 −145.500 −0.424197
5050 0 0
5151 0 0
5252 0 0
5353 −43.6780 −0.113201 −0.0566003 0.998397i 0.518026π-0.518026\pi
−0.0566003 + 0.998397i 0.518026π0.518026\pi
5454 0 0
5555 −542.157 −1.32917
5656 0 0
5757 0 0
5858 0 0
5959 −671.899 −1.48261 −0.741303 0.671171i 0.765792π-0.765792\pi
−0.741303 + 0.671171i 0.765792π0.765792\pi
6060 0 0
6161 74.0354 0.155398 0.0776988 0.996977i 0.475243π-0.475243\pi
0.0776988 + 0.996977i 0.475243π0.475243\pi
6262 0 0
6363 0 0
6464 0 0
6565 −923.320 −1.76190
6666 0 0
6767 420.871 0.767427 0.383713 0.923452i 0.374645π-0.374645\pi
0.383713 + 0.923452i 0.374645π0.374645\pi
6868 0 0
6969 0 0
7070 0 0
7171 −730.840 −1.22162 −0.610808 0.791778i 0.709155π-0.709155\pi
−0.610808 + 0.791778i 0.709155π0.709155\pi
7272 0 0
7373 473.927 0.759849 0.379925 0.925017i 0.375950π-0.375950\pi
0.379925 + 0.925017i 0.375950π0.375950\pi
7474 0 0
7575 0 0
7676 0 0
7777 597.963 0.884990
7878 0 0
7979 −529.622 −0.754267 −0.377134 0.926159i 0.623090π-0.623090\pi
−0.377134 + 0.926159i 0.623090π0.623090\pi
8080 0 0
8181 0 0
8282 0 0
8383 26.1534 0.0345868 0.0172934 0.999850i 0.494495π-0.494495\pi
0.0172934 + 0.999850i 0.494495π0.494495\pi
8484 0 0
8585 −759.563 −0.969249
8686 0 0
8787 0 0
8888 0 0
8989 415.949 0.495399 0.247700 0.968837i 0.420325π-0.420325\pi
0.247700 + 0.968837i 0.420325π0.420325\pi
9090 0 0
9191 1018.36 1.17311
9292 0 0
9393 0 0
9494 0 0
9595 1345.17 1.45275
9696 0 0
9797 927.485 0.970844 0.485422 0.874280i 0.338666π-0.338666\pi
0.485422 + 0.874280i 0.338666π0.338666\pi
9898 0 0
9999 0 0
100100 0 0
101101 −90.1180 −0.0887829 −0.0443915 0.999014i 0.514135π-0.514135\pi
−0.0443915 + 0.999014i 0.514135π0.514135\pi
102102 0 0
103103 −325.652 −0.311529 −0.155765 0.987794i 0.549784π-0.549784\pi
−0.155765 + 0.987794i 0.549784π0.549784\pi
104104 0 0
105105 0 0
106106 0 0
107107 1073.49 0.969888 0.484944 0.874545i 0.338840π-0.338840\pi
0.484944 + 0.874545i 0.338840π0.338840\pi
108108 0 0
109109 601.488 0.528552 0.264276 0.964447i 0.414867π-0.414867\pi
0.264276 + 0.964447i 0.414867π0.414867\pi
110110 0 0
111111 0 0
112112 0 0
113113 −420.039 −0.349681 −0.174840 0.984597i 0.555941π-0.555941\pi
−0.174840 + 0.984597i 0.555941π0.555941\pi
114114 0 0
115115 −2.86922 −0.00232658
116116 0 0
117117 0 0
118118 0 0
119119 837.748 0.645346
120120 0 0
121121 479.425 0.360199
122122 0 0
123123 0 0
124124 0 0
125125 −1116.75 −0.799080
126126 0 0
127127 −980.264 −0.684916 −0.342458 0.939533i 0.611259π-0.611259\pi
−0.342458 + 0.939533i 0.611259π0.611259\pi
128128 0 0
129129 0 0
130130 0 0
131131 1355.39 0.903976 0.451988 0.892024i 0.350715π-0.350715\pi
0.451988 + 0.892024i 0.350715π0.350715\pi
132132 0 0
133133 −1483.63 −0.967271
134134 0 0
135135 0 0
136136 0 0
137137 906.522 0.565324 0.282662 0.959220i 0.408783π-0.408783\pi
0.282662 + 0.959220i 0.408783π0.408783\pi
138138 0 0
139139 −818.418 −0.499405 −0.249703 0.968323i 0.580333π-0.580333\pi
−0.249703 + 0.968323i 0.580333π0.580333\pi
140140 0 0
141141 0 0
142142 0 0
143143 3083.25 1.80303
144144 0 0
145145 −2875.97 −1.64715
146146 0 0
147147 0 0
148148 0 0
149149 −1159.50 −0.637514 −0.318757 0.947836i 0.603265π-0.603265\pi
−0.318757 + 0.947836i 0.603265π0.603265\pi
150150 0 0
151151 −637.973 −0.343825 −0.171912 0.985112i 0.554995π-0.554995\pi
−0.171912 + 0.985112i 0.554995π0.554995\pi
152152 0 0
153153 0 0
154154 0 0
155155 2563.59 1.32847
156156 0 0
157157 3291.72 1.67330 0.836649 0.547739i 0.184511π-0.184511\pi
0.836649 + 0.547739i 0.184511π0.184511\pi
158158 0 0
159159 0 0
160160 0 0
161161 3.16456 0.00154908
162162 0 0
163163 −1197.14 −0.575258 −0.287629 0.957742i 0.592867π-0.592867\pi
−0.287629 + 0.957742i 0.592867π0.592867\pi
164164 0 0
165165 0 0
166166 0 0
167167 838.838 0.388690 0.194345 0.980933i 0.437742π-0.437742\pi
0.194345 + 0.980933i 0.437742π0.437742\pi
168168 0 0
169169 3053.92 1.39004
170170 0 0
171171 0 0
172172 0 0
173173 2307.18 1.01394 0.506970 0.861964i 0.330765π-0.330765\pi
0.506970 + 0.861964i 0.330765π0.330765\pi
174174 0 0
175175 −524.986 −0.226773
176176 0 0
177177 0 0
178178 0 0
179179 3114.47 1.30048 0.650241 0.759728i 0.274668π-0.274668\pi
0.650241 + 0.759728i 0.274668π0.274668\pi
180180 0 0
181181 3902.75 1.60270 0.801350 0.598195i 0.204115π-0.204115\pi
0.801350 + 0.598195i 0.204115π0.204115\pi
182182 0 0
183183 0 0
184184 0 0
185185 −1948.58 −0.774390
186186 0 0
187187 2536.41 0.991875
188188 0 0
189189 0 0
190190 0 0
191191 105.739 0.0400578 0.0200289 0.999799i 0.493624π-0.493624\pi
0.0200289 + 0.999799i 0.493624π0.493624\pi
192192 0 0
193193 −1585.37 −0.591282 −0.295641 0.955299i 0.595533π-0.595533\pi
−0.295641 + 0.955299i 0.595533π0.595533\pi
194194 0 0
195195 0 0
196196 0 0
197197 −3905.37 −1.41242 −0.706208 0.708005i 0.749595π-0.749595\pi
−0.706208 + 0.708005i 0.749595π0.749595\pi
198198 0 0
199199 1538.77 0.548143 0.274072 0.961709i 0.411629π-0.411629\pi
0.274072 + 0.961709i 0.411629π0.411629\pi
200200 0 0
201201 0 0
202202 0 0
203203 3172.01 1.09671
204204 0 0
205205 −6239.05 −2.12563
206206 0 0
207207 0 0
208208 0 0
209209 −4491.92 −1.48666
210210 0 0
211211 941.467 0.307172 0.153586 0.988135i 0.450918π-0.450918\pi
0.153586 + 0.988135i 0.450918π0.450918\pi
212212 0 0
213213 0 0
214214 0 0
215215 −96.6784 −0.0306670
216216 0 0
217217 −2827.48 −0.884523
218218 0 0
219219 0 0
220220 0 0
221221 4319.63 1.31480
222222 0 0
223223 3321.57 0.997438 0.498719 0.866764i 0.333804π-0.333804\pi
0.498719 + 0.866764i 0.333804π0.333804\pi
224224 0 0
225225 0 0
226226 0 0
227227 −4211.84 −1.23150 −0.615749 0.787943i 0.711146π-0.711146\pi
−0.615749 + 0.787943i 0.711146π0.711146\pi
228228 0 0
229229 −354.145 −0.102195 −0.0510973 0.998694i 0.516272π-0.516272\pi
−0.0510973 + 0.998694i 0.516272π0.516272\pi
230230 0 0
231231 0 0
232232 0 0
233233 868.789 0.244276 0.122138 0.992513i 0.461025π-0.461025\pi
0.122138 + 0.992513i 0.461025π0.461025\pi
234234 0 0
235235 4757.72 1.32068
236236 0 0
237237 0 0
238238 0 0
239239 −1204.35 −0.325955 −0.162977 0.986630i 0.552110π-0.552110\pi
−0.162977 + 0.986630i 0.552110π0.552110\pi
240240 0 0
241241 −5087.40 −1.35979 −0.679893 0.733311i 0.737974π-0.737974\pi
−0.679893 + 0.733311i 0.737974π0.737974\pi
242242 0 0
243243 0 0
244244 0 0
245245 −1853.94 −0.483445
246246 0 0
247247 −7649.96 −1.97067
248248 0 0
249249 0 0
250250 0 0
251251 −5463.91 −1.37402 −0.687010 0.726648i 0.741077π-0.741077\pi
−0.687010 + 0.726648i 0.741077π0.741077\pi
252252 0 0
253253 9.58119 0.00238089
254254 0 0
255255 0 0
256256 0 0
257257 −7402.12 −1.79662 −0.898311 0.439361i 0.855205π-0.855205\pi
−0.898311 + 0.439361i 0.855205π0.855205\pi
258258 0 0
259259 2149.15 0.515605
260260 0 0
261261 0 0
262262 0 0
263263 −200.031 −0.0468989 −0.0234495 0.999725i 0.507465π-0.507465\pi
−0.0234495 + 0.999725i 0.507465π0.507465\pi
264264 0 0
265265 −556.541 −0.129011
266266 0 0
267267 0 0
268268 0 0
269269 −5493.50 −1.24515 −0.622574 0.782561i 0.713913π-0.713913\pi
−0.622574 + 0.782561i 0.713913π0.713913\pi
270270 0 0
271271 −1861.89 −0.417350 −0.208675 0.977985i 0.566915π-0.566915\pi
−0.208675 + 0.977985i 0.566915π0.566915\pi
272272 0 0
273273 0 0
274274 0 0
275275 −1589.48 −0.348542
276276 0 0
277277 5639.03 1.22316 0.611582 0.791181i 0.290533π-0.290533\pi
0.611582 + 0.791181i 0.290533π0.290533\pi
278278 0 0
279279 0 0
280280 0 0
281281 2558.04 0.543059 0.271530 0.962430i 0.412470π-0.412470\pi
0.271530 + 0.962430i 0.412470π0.412470\pi
282282 0 0
283283 7467.95 1.56863 0.784317 0.620360i 0.213014π-0.213014\pi
0.784317 + 0.620360i 0.213014π0.213014\pi
284284 0 0
285285 0 0
286286 0 0
287287 6881.26 1.41529
288288 0 0
289289 −1359.48 −0.276712
290290 0 0
291291 0 0
292292 0 0
293293 −3561.32 −0.710083 −0.355041 0.934851i 0.615533π-0.615533\pi
−0.355041 + 0.934851i 0.615533π0.615533\pi
294294 0 0
295295 −8561.27 −1.68968
296296 0 0
297297 0 0
298298 0 0
299299 16.3173 0.00315602
300300 0 0
301301 106.630 0.0204188
302302 0 0
303303 0 0
304304 0 0
305305 943.352 0.177102
306306 0 0
307307 −6101.93 −1.13438 −0.567192 0.823586i 0.691970π-0.691970\pi
−0.567192 + 0.823586i 0.691970π0.691970\pi
308308 0 0
309309 0 0
310310 0 0
311311 371.235 0.0676875 0.0338438 0.999427i 0.489225π-0.489225\pi
0.0338438 + 0.999427i 0.489225π0.489225\pi
312312 0 0
313313 9321.10 1.68326 0.841629 0.540056i 0.181597π-0.181597\pi
0.841629 + 0.540056i 0.181597π0.181597\pi
314314 0 0
315315 0 0
316316 0 0
317317 −6383.57 −1.13103 −0.565516 0.824737i 0.691323π-0.691323\pi
−0.565516 + 0.824737i 0.691323π0.691323\pi
318318 0 0
319319 9603.74 1.68560
320320 0 0
321321 0 0
322322 0 0
323323 −6293.19 −1.08409
324324 0 0
325325 −2706.96 −0.462015
326326 0 0
327327 0 0
328328 0 0
329329 −5247.45 −0.879335
330330 0 0
331331 −2529.42 −0.420028 −0.210014 0.977698i 0.567351π-0.567351\pi
−0.210014 + 0.977698i 0.567351π0.567351\pi
332332 0 0
333333 0 0
334334 0 0
335335 5362.70 0.874614
336336 0 0
337337 3599.81 0.581882 0.290941 0.956741i 0.406032π-0.406032\pi
0.290941 + 0.956741i 0.406032π0.406032\pi
338338 0 0
339339 0 0
340340 0 0
341341 −8560.62 −1.35948
342342 0 0
343343 6865.12 1.08070
344344 0 0
345345 0 0
346346 0 0
347347 −11373.2 −1.75950 −0.879748 0.475440i 0.842289π-0.842289\pi
−0.879748 + 0.475440i 0.842289π0.842289\pi
348348 0 0
349349 −1788.95 −0.274385 −0.137193 0.990544i 0.543808π-0.543808\pi
−0.137193 + 0.990544i 0.543808π0.543808\pi
350350 0 0
351351 0 0
352352 0 0
353353 −1110.37 −0.167419 −0.0837096 0.996490i 0.526677π-0.526677\pi
−0.0837096 + 0.996490i 0.526677π0.526677\pi
354354 0 0
355355 −9312.30 −1.39224
356356 0 0
357357 0 0
358358 0 0
359359 2250.71 0.330886 0.165443 0.986219i 0.447095π-0.447095\pi
0.165443 + 0.986219i 0.447095π0.447095\pi
360360 0 0
361361 4286.07 0.624883
362362 0 0
363363 0 0
364364 0 0
365365 6038.74 0.865978
366366 0 0
367367 2507.38 0.356632 0.178316 0.983973i 0.442935π-0.442935\pi
0.178316 + 0.983973i 0.442935π0.442935\pi
368368 0 0
369369 0 0
370370 0 0
371371 613.828 0.0858985
372372 0 0
373373 −4965.41 −0.689274 −0.344637 0.938736i 0.611998π-0.611998\pi
−0.344637 + 0.938736i 0.611998π0.611998\pi
374374 0 0
375375 0 0
376376 0 0
377377 16355.6 2.23437
378378 0 0
379379 −13541.7 −1.83534 −0.917668 0.397349i 0.869930π-0.869930\pi
−0.917668 + 0.397349i 0.869930π0.869930\pi
380380 0 0
381381 0 0
382382 0 0
383383 8350.08 1.11402 0.557009 0.830506i 0.311949π-0.311949\pi
0.557009 + 0.830506i 0.311949π0.311949\pi
384384 0 0
385385 7619.19 1.00860
386386 0 0
387387 0 0
388388 0 0
389389 −2324.62 −0.302989 −0.151495 0.988458i 0.548409π-0.548409\pi
−0.151495 + 0.988458i 0.548409π0.548409\pi
390390 0 0
391391 13.4233 0.00173617
392392 0 0
393393 0 0
394394 0 0
395395 −6748.39 −0.859617
396396 0 0
397397 13253.5 1.67550 0.837749 0.546056i 0.183871π-0.183871\pi
0.837749 + 0.546056i 0.183871π0.183871\pi
398398 0 0
399399 0 0
400400 0 0
401401 15580.6 1.94029 0.970144 0.242528i 0.0779767π-0.0779767\pi
0.970144 + 0.242528i 0.0779767π0.0779767\pi
402402 0 0
403403 −14579.2 −1.80208
404404 0 0
405405 0 0
406406 0 0
407407 6506.88 0.792467
408408 0 0
409409 −12239.2 −1.47968 −0.739840 0.672783i 0.765099π-0.765099\pi
−0.739840 + 0.672783i 0.765099π0.765099\pi
410410 0 0
411411 0 0
412412 0 0
413413 9442.52 1.12503
414414 0 0
415415 333.244 0.0394176
416416 0 0
417417 0 0
418418 0 0
419419 6393.00 0.745390 0.372695 0.927954i 0.378434π-0.378434\pi
0.372695 + 0.927954i 0.378434π0.378434\pi
420420 0 0
421421 −15832.6 −1.83286 −0.916431 0.400193i 0.868943π-0.868943\pi
−0.916431 + 0.400193i 0.868943π0.868943\pi
422422 0 0
423423 0 0
424424 0 0
425425 −2226.86 −0.254161
426426 0 0
427427 −1040.45 −0.117918
428428 0 0
429429 0 0
430430 0 0
431431 −9339.01 −1.04372 −0.521861 0.853030i 0.674762π-0.674762\pi
−0.521861 + 0.853030i 0.674762π0.674762\pi
432432 0 0
433433 −3379.19 −0.375043 −0.187522 0.982260i 0.560045π-0.560045\pi
−0.187522 + 0.982260i 0.560045π0.560045\pi
434434 0 0
435435 0 0
436436 0 0
437437 −23.7723 −0.00260225
438438 0 0
439439 14547.0 1.58153 0.790766 0.612119i 0.209683π-0.209683\pi
0.790766 + 0.612119i 0.209683π0.209683\pi
440440 0 0
441441 0 0
442442 0 0
443443 −5902.00 −0.632985 −0.316492 0.948595i 0.602505π-0.602505\pi
−0.316492 + 0.948595i 0.602505π0.602505\pi
444444 0 0
445445 5299.99 0.564592
446446 0 0
447447 0 0
448448 0 0
449449 2448.48 0.257352 0.128676 0.991687i 0.458927π-0.458927\pi
0.128676 + 0.991687i 0.458927π0.458927\pi
450450 0 0
451451 20834.1 2.17525
452452 0 0
453453 0 0
454454 0 0
455455 12975.9 1.33696
456456 0 0
457457 4473.74 0.457928 0.228964 0.973435i 0.426466π-0.426466\pi
0.228964 + 0.973435i 0.426466π0.426466\pi
458458 0 0
459459 0 0
460460 0 0
461461 502.213 0.0507384 0.0253692 0.999678i 0.491924π-0.491924\pi
0.0253692 + 0.999678i 0.491924π0.491924\pi
462462 0 0
463463 7086.74 0.711337 0.355668 0.934612i 0.384253π-0.384253\pi
0.355668 + 0.934612i 0.384253π0.384253\pi
464464 0 0
465465 0 0
466466 0 0
467467 8057.18 0.798376 0.399188 0.916869i 0.369292π-0.369292\pi
0.399188 + 0.916869i 0.369292π0.369292\pi
468468 0 0
469469 −5914.71 −0.582336
470470 0 0
471471 0 0
472472 0 0
473473 322.838 0.0313829
474474 0 0
475475 3943.71 0.380947
476476 0 0
477477 0 0
478478 0 0
479479 17160.9 1.63695 0.818477 0.574539i 0.194819π-0.194819\pi
0.818477 + 0.574539i 0.194819π0.194819\pi
480480 0 0
481481 11081.5 1.05047
482482 0 0
483483 0 0
484484 0 0
485485 11817.9 1.10644
486486 0 0
487487 −9909.84 −0.922090 −0.461045 0.887377i 0.652525π-0.652525\pi
−0.461045 + 0.887377i 0.652525π0.652525\pi
488488 0 0
489489 0 0
490490 0 0
491491 −19488.5 −1.79125 −0.895627 0.444806i 0.853273π-0.853273\pi
−0.895627 + 0.444806i 0.853273π0.853273\pi
492492 0 0
493493 13454.9 1.22916
494494 0 0
495495 0 0
496496 0 0
497497 10270.9 0.926984
498498 0 0
499499 −925.456 −0.0830242 −0.0415121 0.999138i 0.513218π-0.513218\pi
−0.0415121 + 0.999138i 0.513218π0.513218\pi
500500 0 0
501501 0 0
502502 0 0
503503 8723.45 0.773279 0.386640 0.922231i 0.373636π-0.373636\pi
0.386640 + 0.922231i 0.373636π0.373636\pi
504504 0 0
505505 −1148.28 −0.101183
506506 0 0
507507 0 0
508508 0 0
509509 3048.70 0.265484 0.132742 0.991151i 0.457622π-0.457622\pi
0.132742 + 0.991151i 0.457622π0.457622\pi
510510 0 0
511511 −6660.33 −0.576587
512512 0 0
513513 0 0
514514 0 0
515515 −4149.43 −0.355041
516516 0 0
517517 −15887.5 −1.35151
518518 0 0
519519 0 0
520520 0 0
521521 −15593.0 −1.31121 −0.655607 0.755103i 0.727587π-0.727587\pi
−0.655607 + 0.755103i 0.727587π0.727587\pi
522522 0 0
523523 −9052.67 −0.756875 −0.378438 0.925627i 0.623539π-0.623539\pi
−0.378438 + 0.925627i 0.623539π0.623539\pi
524524 0 0
525525 0 0
526526 0 0
527527 −11993.4 −0.991352
528528 0 0
529529 −12166.9 −0.999996
530530 0 0
531531 0 0
532532 0 0
533533 35481.5 2.88344
534534 0 0
535535 13678.3 1.10535
536536 0 0
537537 0 0
538538 0 0
539539 6190.87 0.494730
540540 0 0
541541 −11742.8 −0.933200 −0.466600 0.884469i 0.654521π-0.654521\pi
−0.466600 + 0.884469i 0.654521π0.654521\pi
542542 0 0
543543 0 0
544544 0 0
545545 7664.11 0.602375
546546 0 0
547547 3946.91 0.308515 0.154257 0.988031i 0.450701π-0.450701\pi
0.154257 + 0.988031i 0.450701π0.450701\pi
548548 0 0
549549 0 0
550550 0 0
551551 −23828.2 −1.84232
552552 0 0
553553 7443.03 0.572351
554554 0 0
555555 0 0
556556 0 0
557557 3129.69 0.238078 0.119039 0.992890i 0.462019π-0.462019\pi
0.119039 + 0.992890i 0.462019π0.462019\pi
558558 0 0
559559 549.810 0.0416001
560560 0 0
561561 0 0
562562 0 0
563563 −192.036 −0.0143754 −0.00718769 0.999974i 0.502288π-0.502288\pi
−0.00718769 + 0.999974i 0.502288π0.502288\pi
564564 0 0
565565 −5352.09 −0.398521
566566 0 0
567567 0 0
568568 0 0
569569 3261.01 0.240261 0.120131 0.992758i 0.461669π-0.461669\pi
0.120131 + 0.992758i 0.461669π0.461669\pi
570570 0 0
571571 −9414.44 −0.689986 −0.344993 0.938605i 0.612119π-0.612119\pi
−0.344993 + 0.938605i 0.612119π0.612119\pi
572572 0 0
573573 0 0
574574 0 0
575575 −8.41187 −0.000610086 0
576576 0 0
577577 −9739.86 −0.702731 −0.351366 0.936238i 0.614283π-0.614283\pi
−0.351366 + 0.936238i 0.614283π0.614283\pi
578578 0 0
579579 0 0
580580 0 0
581581 −367.546 −0.0262451
582582 0 0
583583 1858.46 0.132023
584584 0 0
585585 0 0
586586 0 0
587587 −25405.7 −1.78638 −0.893190 0.449680i 0.851538π-0.851538\pi
−0.893190 + 0.449680i 0.851538π0.851538\pi
588588 0 0
589589 21240.1 1.48588
590590 0 0
591591 0 0
592592 0 0
593593 2751.26 0.190524 0.0952620 0.995452i 0.469631π-0.469631\pi
0.0952620 + 0.995452i 0.469631π0.469631\pi
594594 0 0
595595 10674.5 0.735482
596596 0 0
597597 0 0
598598 0 0
599599 3316.22 0.226206 0.113103 0.993583i 0.463921π-0.463921\pi
0.113103 + 0.993583i 0.463921π0.463921\pi
600600 0 0
601601 −7919.69 −0.537522 −0.268761 0.963207i 0.586614π-0.586614\pi
−0.268761 + 0.963207i 0.586614π0.586614\pi
602602 0 0
603603 0 0
604604 0 0
605605 6108.79 0.410509
606606 0 0
607607 −9474.47 −0.633537 −0.316768 0.948503i 0.602598π-0.602598\pi
−0.316768 + 0.948503i 0.602598π0.602598\pi
608608 0 0
609609 0 0
610610 0 0
611611 −27057.2 −1.79151
612612 0 0
613613 −3165.90 −0.208596 −0.104298 0.994546i 0.533260π-0.533260\pi
−0.104298 + 0.994546i 0.533260π0.533260\pi
614614 0 0
615615 0 0
616616 0 0
617617 −630.345 −0.0411292 −0.0205646 0.999789i 0.506546π-0.506546\pi
−0.0205646 + 0.999789i 0.506546π0.506546\pi
618618 0 0
619619 1172.54 0.0761365 0.0380683 0.999275i 0.487880π-0.487880\pi
0.0380683 + 0.999275i 0.487880π0.487880\pi
620620 0 0
621621 0 0
622622 0 0
623623 −5845.54 −0.375918
624624 0 0
625625 −18899.0 −1.20954
626626 0 0
627627 0 0
628628 0 0
629629 9116.16 0.577878
630630 0 0
631631 17925.9 1.13093 0.565465 0.824772i 0.308697π-0.308697\pi
0.565465 + 0.824772i 0.308697π0.308697\pi
632632 0 0
633633 0 0
634634 0 0
635635 −12490.4 −0.780579
636636 0 0
637637 10543.4 0.655798
638638 0 0
639639 0 0
640640 0 0
641641 −6696.85 −0.412652 −0.206326 0.978483i 0.566151π-0.566151\pi
−0.206326 + 0.978483i 0.566151π0.566151\pi
642642 0 0
643643 −29691.0 −1.82100 −0.910498 0.413513i 0.864301π-0.864301\pi
−0.910498 + 0.413513i 0.864301π0.864301\pi
644644 0 0
645645 0 0
646646 0 0
647647 −12607.6 −0.766084 −0.383042 0.923731i 0.625124π-0.625124\pi
−0.383042 + 0.923731i 0.625124π0.625124\pi
648648 0 0
649649 28588.7 1.72913
650650 0 0
651651 0 0
652652 0 0
653653 −939.460 −0.0563000 −0.0281500 0.999604i 0.508962π-0.508962\pi
−0.0281500 + 0.999604i 0.508962π0.508962\pi
654654 0 0
655655 17270.2 1.03024
656656 0 0
657657 0 0
658658 0 0
659659 −13883.2 −0.820656 −0.410328 0.911938i 0.634586π-0.634586\pi
−0.410328 + 0.911938i 0.634586π0.634586\pi
660660 0 0
661661 8144.59 0.479256 0.239628 0.970865i 0.422975π-0.422975\pi
0.239628 + 0.970865i 0.422975π0.422975\pi
662662 0 0
663663 0 0
664664 0 0
665665 −18904.3 −1.10237
666666 0 0
667667 50.8252 0.00295047
668668 0 0
669669 0 0
670670 0 0
671671 −3150.14 −0.181236
672672 0 0
673673 −28922.4 −1.65658 −0.828290 0.560300i 0.810686π-0.810686\pi
−0.828290 + 0.560300i 0.810686π0.810686\pi
674674 0 0
675675 0 0
676676 0 0
677677 −27180.8 −1.54305 −0.771524 0.636200i 0.780505π-0.780505\pi
−0.771524 + 0.636200i 0.780505π0.780505\pi
678678 0 0
679679 −13034.4 −0.736693
680680 0 0
681681 0 0
682682 0 0
683683 −7985.87 −0.447395 −0.223697 0.974659i 0.571813π-0.571813\pi
−0.223697 + 0.974659i 0.571813π0.571813\pi
684684 0 0
685685 11550.8 0.644283
686686 0 0
687687 0 0
688688 0 0
689689 3165.05 0.175005
690690 0 0
691691 9250.05 0.509246 0.254623 0.967040i 0.418049π-0.418049\pi
0.254623 + 0.967040i 0.418049π0.418049\pi
692692 0 0
693693 0 0
694694 0 0
695695 −10428.2 −0.569158
696696 0 0
697697 29188.6 1.58622
698698 0 0
699699 0 0
700700 0 0
701701 −10267.4 −0.553201 −0.276601 0.960985i 0.589208π-0.589208\pi
−0.276601 + 0.960985i 0.589208π0.589208\pi
702702 0 0
703703 −16144.5 −0.866146
704704 0 0
705705 0 0
706706 0 0
707707 1266.47 0.0673700
708708 0 0
709709 13958.7 0.739392 0.369696 0.929153i 0.379462π-0.379462\pi
0.369696 + 0.929153i 0.379462π0.379462\pi
710710 0 0
711711 0 0
712712 0 0
713713 −45.3048 −0.00237963
714714 0 0
715715 39286.4 2.05487
716716 0 0
717717 0 0
718718 0 0
719719 26373.7 1.36798 0.683988 0.729493i 0.260244π-0.260244\pi
0.683988 + 0.729493i 0.260244π0.260244\pi
720720 0 0
721721 4576.55 0.236394
722722 0 0
723723 0 0
724724 0 0
725725 −8431.67 −0.431923
726726 0 0
727727 −8793.84 −0.448618 −0.224309 0.974518i 0.572013π-0.572013\pi
−0.224309 + 0.974518i 0.572013π0.572013\pi
728728 0 0
729729 0 0
730730 0 0
731731 452.297 0.0228848
732732 0 0
733733 −10674.0 −0.537862 −0.268931 0.963159i 0.586670π-0.586670\pi
−0.268931 + 0.963159i 0.586670π0.586670\pi
734734 0 0
735735 0 0
736736 0 0
737737 −17907.7 −0.895031
738738 0 0
739739 −12678.1 −0.631084 −0.315542 0.948912i 0.602186π-0.602186\pi
−0.315542 + 0.948912i 0.602186π0.602186\pi
740740 0 0
741741 0 0
742742 0 0
743743 22111.3 1.09177 0.545884 0.837861i 0.316194π-0.316194\pi
0.545884 + 0.837861i 0.316194π0.316194\pi
744744 0 0
745745 −14774.2 −0.726556
746746 0 0
747747 0 0
748748 0 0
749749 −15086.2 −0.735967
750750 0 0
751751 −22151.0 −1.07630 −0.538151 0.842848i 0.680877π-0.680877\pi
−0.538151 + 0.842848i 0.680877π0.680877\pi
752752 0 0
753753 0 0
754754 0 0
755755 −8129.00 −0.391847
756756 0 0
757757 −25282.2 −1.21387 −0.606933 0.794753i 0.707601π-0.707601\pi
−0.606933 + 0.794753i 0.707601π0.707601\pi
758758 0 0
759759 0 0
760760 0 0
761761 −10128.9 −0.482488 −0.241244 0.970464i 0.577555π-0.577555\pi
−0.241244 + 0.970464i 0.577555π0.577555\pi
762762 0 0
763763 −8453.01 −0.401074
764764 0 0
765765 0 0
766766 0 0
767767 48688.0 2.29207
768768 0 0
769769 −25234.5 −1.18333 −0.591663 0.806185i 0.701528π-0.701528\pi
−0.591663 + 0.806185i 0.701528π0.701528\pi
770770 0 0
771771 0 0
772772 0 0
773773 30384.6 1.41379 0.706895 0.707319i 0.250096π-0.250096\pi
0.706895 + 0.707319i 0.250096π0.250096\pi
774774 0 0
775775 7515.85 0.348358
776776 0 0
777777 0 0
778778 0 0
779779 −51692.2 −2.37749
780780 0 0
781781 31096.6 1.42474
782782 0 0
783783 0 0
784784 0 0
785785 41942.8 1.90701
786786 0 0
787787 30144.7 1.36536 0.682682 0.730716i 0.260814π-0.260814\pi
0.682682 + 0.730716i 0.260814π0.260814\pi
788788 0 0
789789 0 0
790790 0 0
791791 5903.01 0.265344
792792 0 0
793793 −5364.84 −0.240241
794794 0 0
795795 0 0
796796 0 0
797797 −16128.0 −0.716793 −0.358397 0.933569i 0.616676π-0.616676\pi
−0.358397 + 0.933569i 0.616676π0.616676\pi
798798 0 0
799799 −22258.4 −0.985538
800800 0 0
801801 0 0
802802 0 0
803803 −20165.2 −0.886194
804804 0 0
805805 40.3225 0.00176544
806806 0 0
807807 0 0
808808 0 0
809809 −23446.4 −1.01895 −0.509475 0.860485i 0.670160π-0.670160\pi
−0.509475 + 0.860485i 0.670160π0.670160\pi
810810 0 0
811811 −37762.1 −1.63503 −0.817513 0.575910i 0.804648π-0.804648\pi
−0.817513 + 0.575910i 0.804648π0.804648\pi
812812 0 0
813813 0 0
814814 0 0
815815 −15253.8 −0.655605
816816 0 0
817817 −801.007 −0.0343007
818818 0 0
819819 0 0
820820 0 0
821821 −11884.7 −0.505213 −0.252606 0.967569i 0.581288π-0.581288\pi
−0.252606 + 0.967569i 0.581288π0.581288\pi
822822 0 0
823823 −9064.05 −0.383904 −0.191952 0.981404i 0.561482π-0.561482\pi
−0.191952 + 0.981404i 0.561482π0.561482\pi
824824 0 0
825825 0 0
826826 0 0
827827 −36451.4 −1.53270 −0.766348 0.642426i 0.777928π-0.777928\pi
−0.766348 + 0.642426i 0.777928π0.777928\pi
828828 0 0
829829 −15293.4 −0.640725 −0.320362 0.947295i 0.603805π-0.603805\pi
−0.320362 + 0.947295i 0.603805π0.603805\pi
830830 0 0
831831 0 0
832832 0 0
833833 8673.43 0.360764
834834 0 0
835835 10688.4 0.442979
836836 0 0
837837 0 0
838838 0 0
839839 −353.539 −0.0145477 −0.00727385 0.999974i 0.502315π-0.502315\pi
−0.00727385 + 0.999974i 0.502315π0.502315\pi
840840 0 0
841841 26555.8 1.08884
842842 0 0
843843 0 0
844844 0 0
845845 38912.8 1.58419
846846 0 0
847847 −6737.59 −0.273325
848848 0 0
849849 0 0
850850 0 0
851851 34.4359 0.00138713
852852 0 0
853853 25692.7 1.03130 0.515651 0.856799i 0.327550π-0.327550\pi
0.515651 + 0.856799i 0.327550π0.327550\pi
854854 0 0
855855 0 0
856856 0 0
857857 −13018.0 −0.518886 −0.259443 0.965758i 0.583539π-0.583539\pi
−0.259443 + 0.965758i 0.583539π0.583539\pi
858858 0 0
859859 −2132.08 −0.0846862 −0.0423431 0.999103i 0.513482π-0.513482\pi
−0.0423431 + 0.999103i 0.513482π0.513482\pi
860860 0 0
861861 0 0
862862 0 0
863863 39300.5 1.55018 0.775090 0.631851i 0.217705π-0.217705\pi
0.775090 + 0.631851i 0.217705π0.217705\pi
864864 0 0
865865 29397.9 1.15556
866866 0 0
867867 0 0
868868 0 0
869869 22534.9 0.879684
870870 0 0
871871 −30497.7 −1.18642
872872 0 0
873873 0 0
874874 0 0
875875 15694.2 0.606356
876876 0 0
877877 −10608.5 −0.408463 −0.204232 0.978923i 0.565470π-0.565470\pi
−0.204232 + 0.978923i 0.565470π0.565470\pi
878878 0 0
879879 0 0
880880 0 0
881881 41310.4 1.57978 0.789888 0.613251i 0.210139π-0.210139\pi
0.789888 + 0.613251i 0.210139π0.210139\pi
882882 0 0
883883 47180.5 1.79813 0.899066 0.437814i 0.144247π-0.144247\pi
0.899066 + 0.437814i 0.144247π0.144247\pi
884884 0 0
885885 0 0
886886 0 0
887887 49777.7 1.88430 0.942148 0.335197i 0.108803π-0.108803\pi
0.942148 + 0.335197i 0.108803π0.108803\pi
888888 0 0
889889 13776.1 0.519726
890890 0 0
891891 0 0
892892 0 0
893893 39419.0 1.47716
894894 0 0
895895 39684.2 1.48212
896896 0 0
897897 0 0
898898 0 0
899899 −45411.4 −1.68471
900900 0 0
901901 2603.70 0.0962730
902902 0 0
903903 0 0
904904 0 0
905905 49728.4 1.82655
906906 0 0
907907 1036.51 0.0379456 0.0189728 0.999820i 0.493960π-0.493960\pi
0.0189728 + 0.999820i 0.493960π0.493960\pi
908908 0 0
909909 0 0
910910 0 0
911911 24780.9 0.901239 0.450620 0.892716i 0.351203π-0.351203\pi
0.450620 + 0.892716i 0.351203π0.351203\pi
912912 0 0
913913 −1112.80 −0.0403378
914914 0 0
915915 0 0
916916 0 0
917917 −19047.9 −0.685953
918918 0 0
919919 25210.4 0.904912 0.452456 0.891787i 0.350548π-0.350548\pi
0.452456 + 0.891787i 0.350548π0.350548\pi
920920 0 0
921921 0 0
922922 0 0
923923 52959.1 1.88859
924924 0 0
925925 −5712.76 −0.203064
926926 0 0
927927 0 0
928928 0 0
929929 −27878.6 −0.984570 −0.492285 0.870434i 0.663838π-0.663838\pi
−0.492285 + 0.870434i 0.663838π0.663838\pi
930930 0 0
931931 −15360.4 −0.540727
932932 0 0
933933 0 0
934934 0 0
935935 32318.7 1.13041
936936 0 0
937937 5091.76 0.177525 0.0887623 0.996053i 0.471709π-0.471709\pi
0.0887623 + 0.996053i 0.471709π0.471709\pi
938938 0 0
939939 0 0
940940 0 0
941941 −43099.4 −1.49309 −0.746547 0.665333i 0.768290π-0.768290\pi
−0.746547 + 0.665333i 0.768290π0.768290\pi
942942 0 0
943943 110.259 0.00380755
944944 0 0
945945 0 0
946946 0 0
947947 −24685.7 −0.847072 −0.423536 0.905879i 0.639211π-0.639211\pi
−0.423536 + 0.905879i 0.639211π0.639211\pi
948948 0 0
949949 −34342.3 −1.17471
950950 0 0
951951 0 0
952952 0 0
953953 9714.42 0.330200 0.165100 0.986277i 0.447205π-0.447205\pi
0.165100 + 0.986277i 0.447205π0.447205\pi
954954 0 0
955955 1347.32 0.0456527
956956 0 0
957957 0 0
958958 0 0
959959 −12739.8 −0.428977
960960 0 0
961961 10688.0 0.358766
962962 0 0
963963 0 0
964964 0 0
965965 −20200.6 −0.673867
966966 0 0
967967 −34368.2 −1.14292 −0.571461 0.820629i 0.693623π-0.693623\pi
−0.571461 + 0.820629i 0.693623π0.693623\pi
968968 0 0
969969 0 0
970970 0 0
971971 31313.7 1.03492 0.517458 0.855708i 0.326878π-0.326878\pi
0.517458 + 0.855708i 0.326878π0.326878\pi
972972 0 0
973973 11501.6 0.378957
974974 0 0
975975 0 0
976976 0 0
977977 25398.2 0.831688 0.415844 0.909436i 0.363486π-0.363486\pi
0.415844 + 0.909436i 0.363486π0.363486\pi
978978 0 0
979979 −17698.3 −0.577772
980980 0 0
981981 0 0
982982 0 0
983983 48894.2 1.58645 0.793227 0.608926i 0.208399π-0.208399\pi
0.793227 + 0.608926i 0.208399π0.208399\pi
984984 0 0
985985 −49761.8 −1.60969
986986 0 0
987987 0 0
988988 0 0
989989 1.70854 5.49325e−5 0
990990 0 0
991991 −46870.9 −1.50242 −0.751212 0.660061i 0.770530π-0.770530\pi
−0.751212 + 0.660061i 0.770530π0.770530\pi
992992 0 0
993993 0 0
994994 0 0
995995 19606.9 0.624703
996996 0 0
997997 −31408.2 −0.997702 −0.498851 0.866688i 0.666245π-0.666245\pi
−0.498851 + 0.866688i 0.666245π0.666245\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 324.4.a.c.1.3 3
3.2 odd 2 324.4.a.d.1.1 3
4.3 odd 2 1296.4.a.v.1.3 3
9.2 odd 6 108.4.e.a.37.3 6
9.4 even 3 36.4.e.a.25.2 yes 6
9.5 odd 6 108.4.e.a.73.3 6
9.7 even 3 36.4.e.a.13.2 6
12.11 even 2 1296.4.a.w.1.1 3
36.7 odd 6 144.4.i.d.49.2 6
36.11 even 6 432.4.i.d.145.3 6
36.23 even 6 432.4.i.d.289.3 6
36.31 odd 6 144.4.i.d.97.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.4.e.a.13.2 6 9.7 even 3
36.4.e.a.25.2 yes 6 9.4 even 3
108.4.e.a.37.3 6 9.2 odd 6
108.4.e.a.73.3 6 9.5 odd 6
144.4.i.d.49.2 6 36.7 odd 6
144.4.i.d.97.2 6 36.31 odd 6
324.4.a.c.1.3 3 1.1 even 1 trivial
324.4.a.d.1.1 3 3.2 odd 2
432.4.i.d.145.3 6 36.11 even 6
432.4.i.d.289.3 6 36.23 even 6
1296.4.a.v.1.3 3 4.3 odd 2
1296.4.a.w.1.1 3 12.11 even 2