Properties

Label 288.4.d.c.145.4
Level 288288
Weight 44
Character 288.145
Analytic conductor 16.99316.993
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,4,Mod(145,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.145");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 288=2532 288 = 2^{5} \cdot 3^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 288.d (of order 22, degree 11, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 16.992550081716.9925500817
Analytic rank: 00
Dimension: 44
Coefficient field: Q(10,22)\Q(\sqrt{-10}, \sqrt{22})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x46x2+64 x^{4} - 6x^{2} + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 210 2^{10}
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 145.4
Root 2.34521+1.58114i2.34521 + 1.58114i of defining polynomial
Character χ\chi == 288.145
Dual form 288.4.d.c.145.1

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+6.32456iq510.0000q737.9473iq11+59.3296iq1375.0467q17118.659iq19150.093q23+85.0000q25246.658iq2962.0000q3163.2456iq35+59.3296iq37375.233q41+118.659iq43450.280q47243.000q49132.816iq53+240.000q55733.648iq59533.966iq61375.233q65+711.955iq67+30.0000q73+379.473iq7794.0000q79+670.403iq83474.637iq85+750.467q89593.296iq91+750.467q95+130.000q97+O(q100)q+6.32456i q^{5} -10.0000 q^{7} -37.9473i q^{11} +59.3296i q^{13} -75.0467 q^{17} -118.659i q^{19} -150.093 q^{23} +85.0000 q^{25} -246.658i q^{29} -62.0000 q^{31} -63.2456i q^{35} +59.3296i q^{37} -375.233 q^{41} +118.659i q^{43} -450.280 q^{47} -243.000 q^{49} -132.816i q^{53} +240.000 q^{55} -733.648i q^{59} -533.966i q^{61} -375.233 q^{65} +711.955i q^{67} +30.0000 q^{73} +379.473i q^{77} -94.0000 q^{79} +670.403i q^{83} -474.637i q^{85} +750.467 q^{89} -593.296i q^{91} +750.467 q^{95} +130.000 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q40q7+340q25248q31972q49+960q55+120q73376q79+520q97+O(q100) 4 q - 40 q^{7} + 340 q^{25} - 248 q^{31} - 972 q^{49} + 960 q^{55} + 120 q^{73} - 376 q^{79} + 520 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/288Z)×\left(\mathbb{Z}/288\mathbb{Z}\right)^\times.

nn 3737 6565 127127
χ(n)\chi(n) 1-1 11 11

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 6.32456i 0.565685i 0.959166 + 0.282843i 0.0912774π0.0912774\pi
−0.959166 + 0.282843i 0.908723π0.908723\pi
66 0 0
77 −10.0000 −0.539949 −0.269975 0.962867i 0.587015π-0.587015\pi
−0.269975 + 0.962867i 0.587015π0.587015\pi
88 0 0
99 0 0
1010 0 0
1111 − 37.9473i − 1.04014i −0.854123 0.520071i 0.825906π-0.825906\pi
0.854123 0.520071i 0.174094π-0.174094\pi
1212 0 0
1313 59.3296i 1.26577i 0.774244 + 0.632887i 0.218130π0.218130\pi
−0.774244 + 0.632887i 0.781870π0.781870\pi
1414 0 0
1515 0 0
1616 0 0
1717 −75.0467 −1.07068 −0.535338 0.844638i 0.679816π-0.679816\pi
−0.535338 + 0.844638i 0.679816π0.679816\pi
1818 0 0
1919 − 118.659i − 1.43275i −0.697715 0.716376i 0.745800π-0.745800\pi
0.697715 0.716376i 0.254200π-0.254200\pi
2020 0 0
2121 0 0
2222 0 0
2323 −150.093 −1.36072 −0.680361 0.732877i 0.738177π-0.738177\pi
−0.680361 + 0.732877i 0.738177π0.738177\pi
2424 0 0
2525 85.0000 0.680000
2626 0 0
2727 0 0
2828 0 0
2929 − 246.658i − 1.57942i −0.613480 0.789710i 0.710231π-0.710231\pi
0.613480 0.789710i 0.289769π-0.289769\pi
3030 0 0
3131 −62.0000 −0.359211 −0.179605 0.983739i 0.557482π-0.557482\pi
−0.179605 + 0.983739i 0.557482π0.557482\pi
3232 0 0
3333 0 0
3434 0 0
3535 − 63.2456i − 0.305441i
3636 0 0
3737 59.3296i 0.263614i 0.991275 + 0.131807i 0.0420779π0.0420779\pi
−0.991275 + 0.131807i 0.957922π0.957922\pi
3838 0 0
3939 0 0
4040 0 0
4141 −375.233 −1.42931 −0.714654 0.699479i 0.753416π-0.753416\pi
−0.714654 + 0.699479i 0.753416π0.753416\pi
4242 0 0
4343 118.659i 0.420822i 0.977613 + 0.210411i 0.0674802π0.0674802\pi
−0.977613 + 0.210411i 0.932520π0.932520\pi
4444 0 0
4545 0 0
4646 0 0
4747 −450.280 −1.39745 −0.698724 0.715391i 0.746249π-0.746249\pi
−0.698724 + 0.715391i 0.746249π0.746249\pi
4848 0 0
4949 −243.000 −0.708455
5050 0 0
5151 0 0
5252 0 0
5353 − 132.816i − 0.344220i −0.985078 0.172110i 0.944942π-0.944942\pi
0.985078 0.172110i 0.0550584π-0.0550584\pi
5454 0 0
5555 240.000 0.588393
5656 0 0
5757 0 0
5858 0 0
5959 − 733.648i − 1.61886i −0.587215 0.809431i 0.699776π-0.699776\pi
0.587215 0.809431i 0.300224π-0.300224\pi
6060 0 0
6161 − 533.966i − 1.12078i −0.828230 0.560388i 0.810652π-0.810652\pi
0.828230 0.560388i 0.189348π-0.189348\pi
6262 0 0
6363 0 0
6464 0 0
6565 −375.233 −0.716030
6666 0 0
6767 711.955i 1.29820i 0.760705 + 0.649098i 0.224854π0.224854\pi
−0.760705 + 0.649098i 0.775146π0.775146\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 30.0000 0.0480991 0.0240496 0.999711i 0.492344π-0.492344\pi
0.0240496 + 0.999711i 0.492344π0.492344\pi
7474 0 0
7575 0 0
7676 0 0
7777 379.473i 0.561623i
7878 0 0
7979 −94.0000 −0.133871 −0.0669356 0.997757i 0.521322π-0.521322\pi
−0.0669356 + 0.997757i 0.521322π0.521322\pi
8080 0 0
8181 0 0
8282 0 0
8383 670.403i 0.886582i 0.896378 + 0.443291i 0.146189π0.146189\pi
−0.896378 + 0.443291i 0.853811π0.853811\pi
8484 0 0
8585 − 474.637i − 0.605666i
8686 0 0
8787 0 0
8888 0 0
8989 750.467 0.893812 0.446906 0.894581i 0.352526π-0.352526\pi
0.446906 + 0.894581i 0.352526π0.352526\pi
9090 0 0
9191 − 593.296i − 0.683454i
9292 0 0
9393 0 0
9494 0 0
9595 750.467 0.810487
9696 0 0
9797 130.000 0.136077 0.0680387 0.997683i 0.478326π-0.478326\pi
0.0680387 + 0.997683i 0.478326π0.478326\pi
9898 0 0
9999 0 0
100100 0 0
101101 − 562.885i − 0.554546i −0.960791 0.277273i 0.910569π-0.910569\pi
0.960791 0.277273i 0.0894307π-0.0894307\pi
102102 0 0
103103 570.000 0.545279 0.272640 0.962116i 0.412103π-0.412103\pi
0.272640 + 0.962116i 0.412103π0.412103\pi
104104 0 0
105105 0 0
106106 0 0
107107 1290.21i 1.16569i 0.812582 + 0.582847i 0.198061π0.198061\pi
−0.812582 + 0.582847i 0.801939π0.801939\pi
108108 0 0
109109 1720.56i 1.51192i 0.654616 + 0.755961i 0.272830π0.272830\pi
−0.654616 + 0.755961i 0.727170π0.727170\pi
110110 0 0
111111 0 0
112112 0 0
113113 1350.84 1.12457 0.562285 0.826944i 0.309923π-0.309923\pi
0.562285 + 0.826944i 0.309923π0.309923\pi
114114 0 0
115115 − 949.273i − 0.769741i
116116 0 0
117117 0 0
118118 0 0
119119 750.467 0.578111
120120 0 0
121121 −109.000 −0.0818933
122122 0 0
123123 0 0
124124 0 0
125125 1328.16i 0.950352i
126126 0 0
127127 −2530.00 −1.76773 −0.883863 0.467746i 0.845066π-0.845066\pi
−0.883863 + 0.467746i 0.845066π0.845066\pi
128128 0 0
129129 0 0
130130 0 0
131131 252.982i 0.168726i 0.996435 + 0.0843632i 0.0268856π0.0268856\pi
−0.996435 + 0.0843632i 0.973114π0.973114\pi
132132 0 0
133133 1186.59i 0.773613i
134134 0 0
135135 0 0
136136 0 0
137137 675.420 0.421204 0.210602 0.977572i 0.432458π-0.432458\pi
0.210602 + 0.977572i 0.432458π0.432458\pi
138138 0 0
139139 237.318i 0.144814i 0.997375 + 0.0724068i 0.0230680π0.0230680\pi
−0.997375 + 0.0724068i 0.976932π0.976932\pi
140140 0 0
141141 0 0
142142 0 0
143143 2251.40 1.31658
144144 0 0
145145 1560.00 0.893455
146146 0 0
147147 0 0
148148 0 0
149149 2940.92i 1.61698i 0.588513 + 0.808488i 0.299714π0.299714\pi
−0.588513 + 0.808488i 0.700286π0.700286\pi
150150 0 0
151151 2262.00 1.21907 0.609533 0.792761i 0.291357π-0.291357\pi
0.609533 + 0.792761i 0.291357π0.291357\pi
152152 0 0
153153 0 0
154154 0 0
155155 − 392.122i − 0.203200i
156156 0 0
157157 − 1720.56i − 0.874621i −0.899311 0.437310i 0.855931π-0.855931\pi
0.899311 0.437310i 0.144069π-0.144069\pi
158158 0 0
159159 0 0
160160 0 0
161161 1500.93 0.734721
162162 0 0
163163 − 2017.21i − 0.969324i −0.874702 0.484662i 0.838943π-0.838943\pi
0.874702 0.484662i 0.161057π-0.161057\pi
164164 0 0
165165 0 0
166166 0 0
167167 1050.65 0.486838 0.243419 0.969921i 0.421731π-0.421731\pi
0.243419 + 0.969921i 0.421731π0.421731\pi
168168 0 0
169169 −1323.00 −0.602185
170170 0 0
171171 0 0
172172 0 0
173173 − 1423.02i − 0.625379i −0.949855 0.312690i 0.898770π-0.898770\pi
0.949855 0.312690i 0.101230π-0.101230\pi
174174 0 0
175175 −850.000 −0.367165
176176 0 0
177177 0 0
178178 0 0
179179 − 126.491i − 0.0528178i −0.999651 0.0264089i 0.991593π-0.991593\pi
0.999651 0.0264089i 0.00840719π-0.00840719\pi
180180 0 0
181181 − 59.3296i − 0.0243643i −0.999926 0.0121821i 0.996122π-0.996122\pi
0.999926 0.0121821i 0.00387779π-0.00387779\pi
182182 0 0
183183 0 0
184184 0 0
185185 −375.233 −0.149123
186186 0 0
187187 2847.82i 1.11365i
188188 0 0
189189 0 0
190190 0 0
191191 −3752.33 −1.42151 −0.710757 0.703437i 0.751648π-0.751648\pi
−0.710757 + 0.703437i 0.751648π0.751648\pi
192192 0 0
193193 −1350.00 −0.503498 −0.251749 0.967793i 0.581006π-0.581006\pi
−0.251749 + 0.967793i 0.581006π0.581006\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 1448.32i − 0.523801i −0.965095 0.261900i 0.915651π-0.915651\pi
0.965095 0.261900i 0.0843492π-0.0843492\pi
198198 0 0
199199 3194.00 1.13777 0.568886 0.822416i 0.307375π-0.307375\pi
0.568886 + 0.822416i 0.307375π0.307375\pi
200200 0 0
201201 0 0
202202 0 0
203203 2466.58i 0.852807i
204204 0 0
205205 − 2373.18i − 0.808538i
206206 0 0
207207 0 0
208208 0 0
209209 −4502.80 −1.49026
210210 0 0
211211 5458.32i 1.78088i 0.455097 + 0.890442i 0.349604π0.349604\pi
−0.455097 + 0.890442i 0.650396π0.650396\pi
212212 0 0
213213 0 0
214214 0 0
215215 −750.467 −0.238053
216216 0 0
217217 620.000 0.193955
218218 0 0
219219 0 0
220220 0 0
221221 − 4452.49i − 1.35523i
222222 0 0
223223 −5330.00 −1.60055 −0.800276 0.599632i 0.795314π-0.795314\pi
−0.800276 + 0.599632i 0.795314π0.795314\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 4768.71i − 1.39432i −0.716915 0.697160i 0.754447π-0.754447\pi
0.716915 0.697160i 0.245553π-0.245553\pi
228228 0 0
229229 − 3619.10i − 1.04435i −0.852837 0.522177i 0.825120π-0.825120\pi
0.852837 0.522177i 0.174880π-0.174880\pi
230230 0 0
231231 0 0
232232 0 0
233233 −150.093 −0.0422015 −0.0211007 0.999777i 0.506717π-0.506717\pi
−0.0211007 + 0.999777i 0.506717π0.506717\pi
234234 0 0
235235 − 2847.82i − 0.790516i
236236 0 0
237237 0 0
238238 0 0
239239 −2251.40 −0.609334 −0.304667 0.952459i 0.598545π-0.598545\pi
−0.304667 + 0.952459i 0.598545π0.598545\pi
240240 0 0
241241 −1162.00 −0.310585 −0.155293 0.987869i 0.549632π-0.549632\pi
−0.155293 + 0.987869i 0.549632π0.549632\pi
242242 0 0
243243 0 0
244244 0 0
245245 − 1536.87i − 0.400763i
246246 0 0
247247 7040.00 1.81354
248248 0 0
249249 0 0
250250 0 0
251251 − 645.105i − 0.162226i −0.996705 0.0811128i 0.974153π-0.974153\pi
0.996705 0.0811128i 0.0258474π-0.0258474\pi
252252 0 0
253253 5695.64i 1.41534i
254254 0 0
255255 0 0
256256 0 0
257257 −1801.12 −0.437162 −0.218581 0.975819i 0.570143π-0.570143\pi
−0.218581 + 0.975819i 0.570143π0.570143\pi
258258 0 0
259259 − 593.296i − 0.142338i
260260 0 0
261261 0 0
262262 0 0
263263 −6604.11 −1.54839 −0.774195 0.632947i 0.781845π-0.781845\pi
−0.774195 + 0.632947i 0.781845π0.781845\pi
264264 0 0
265265 840.000 0.194720
266266 0 0
267267 0 0
268268 0 0
269269 6052.60i 1.37187i 0.727662 + 0.685936i 0.240607π0.240607\pi
−0.727662 + 0.685936i 0.759393π0.759393\pi
270270 0 0
271271 −6402.00 −1.43503 −0.717516 0.696542i 0.754721π-0.754721\pi
−0.717516 + 0.696542i 0.754721π0.754721\pi
272272 0 0
273273 0 0
274274 0 0
275275 − 3225.52i − 0.707296i
276276 0 0
277277 2076.54i 0.450422i 0.974310 + 0.225211i 0.0723072π0.0723072\pi
−0.974310 + 0.225211i 0.927693π0.927693\pi
278278 0 0
279279 0 0
280280 0 0
281281 −9005.60 −1.91185 −0.955923 0.293616i 0.905141π-0.905141\pi
−0.955923 + 0.293616i 0.905141π0.905141\pi
282282 0 0
283283 − 5221.00i − 1.09667i −0.836260 0.548333i 0.815263π-0.815263\pi
0.836260 0.548333i 0.184737π-0.184737\pi
284284 0 0
285285 0 0
286286 0 0
287287 3752.33 0.771753
288288 0 0
289289 719.000 0.146346
290290 0 0
291291 0 0
292292 0 0
293293 − 5293.65i − 1.05549i −0.849403 0.527745i 0.823038π-0.823038\pi
0.849403 0.527745i 0.176962π-0.176962\pi
294294 0 0
295295 4640.00 0.915767
296296 0 0
297297 0 0
298298 0 0
299299 − 8904.97i − 1.72237i
300300 0 0
301301 − 1186.59i − 0.227223i
302302 0 0
303303 0 0
304304 0 0
305305 3377.10 0.634007
306306 0 0
307307 − 4983.69i − 0.926495i −0.886229 0.463247i 0.846684π-0.846684\pi
0.886229 0.463247i 0.153316π-0.153316\pi
308308 0 0
309309 0 0
310310 0 0
311311 −1500.93 −0.273666 −0.136833 0.990594i 0.543692π-0.543692\pi
−0.136833 + 0.990594i 0.543692π0.543692\pi
312312 0 0
313313 6350.00 1.14672 0.573360 0.819304i 0.305640π-0.305640\pi
0.573360 + 0.819304i 0.305640π0.305640\pi
314314 0 0
315315 0 0
316316 0 0
317317 − 1739.25i − 0.308158i −0.988059 0.154079i 0.950759π-0.950759\pi
0.988059 0.154079i 0.0492411π-0.0492411\pi
318318 0 0
319319 −9360.00 −1.64282
320320 0 0
321321 0 0
322322 0 0
323323 8904.97i 1.53401i
324324 0 0
325325 5043.01i 0.860727i
326326 0 0
327327 0 0
328328 0 0
329329 4502.80 0.754551
330330 0 0
331331 3322.46i 0.551718i 0.961198 + 0.275859i 0.0889623π0.0889623\pi
−0.961198 + 0.275859i 0.911038π0.911038\pi
332332 0 0
333333 0 0
334334 0 0
335335 −4502.80 −0.734371
336336 0 0
337337 −1430.00 −0.231149 −0.115574 0.993299i 0.536871π-0.536871\pi
−0.115574 + 0.993299i 0.536871π0.536871\pi
338338 0 0
339339 0 0
340340 0 0
341341 2352.73i 0.373630i
342342 0 0
343343 5860.00 0.922479
344344 0 0
345345 0 0
346346 0 0
347347 10106.6i 1.56355i 0.623559 + 0.781776i 0.285686π0.285686\pi
−0.623559 + 0.781776i 0.714314π0.714314\pi
348348 0 0
349349 1127.26i 0.172897i 0.996256 + 0.0864484i 0.0275518π0.0275518\pi
−0.996256 + 0.0864484i 0.972448π0.972448\pi
350350 0 0
351351 0 0
352352 0 0
353353 −1350.84 −0.203677 −0.101838 0.994801i 0.532472π-0.532472\pi
−0.101838 + 0.994801i 0.532472π0.532472\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 12007.5 1.76526 0.882632 0.470065i 0.155769π-0.155769\pi
0.882632 + 0.470065i 0.155769π0.155769\pi
360360 0 0
361361 −7221.00 −1.05278
362362 0 0
363363 0 0
364364 0 0
365365 189.737i 0.0272090i
366366 0 0
367367 −5070.00 −0.721122 −0.360561 0.932736i 0.617415π-0.617415\pi
−0.360561 + 0.932736i 0.617415π0.617415\pi
368368 0 0
369369 0 0
370370 0 0
371371 1328.16i 0.185861i
372372 0 0
373373 2432.51i 0.337670i 0.985644 + 0.168835i 0.0540004π0.0540004\pi
−0.985644 + 0.168835i 0.946000π0.946000\pi
374374 0 0
375375 0 0
376376 0 0
377377 14634.1 1.99919
378378 0 0
379379 7712.85i 1.04534i 0.852536 + 0.522668i 0.175063π0.175063\pi
−0.852536 + 0.522668i 0.824937π0.824937\pi
380380 0 0
381381 0 0
382382 0 0
383383 5853.64 0.780958 0.390479 0.920612i 0.372309π-0.372309\pi
0.390479 + 0.920612i 0.372309π0.372309\pi
384384 0 0
385385 −2400.00 −0.317702
386386 0 0
387387 0 0
388388 0 0
389389 2156.67i 0.281099i 0.990074 + 0.140550i 0.0448870π0.0448870\pi
−0.990074 + 0.140550i 0.955113π0.955113\pi
390390 0 0
391391 11264.0 1.45689
392392 0 0
393393 0 0
394394 0 0
395395 − 594.508i − 0.0757290i
396396 0 0
397397 − 12162.6i − 1.53759i −0.639498 0.768793i 0.720858π-0.720858\pi
0.639498 0.768793i 0.279142π-0.279142\pi
398398 0 0
399399 0 0
400400 0 0
401401 3377.10 0.420559 0.210280 0.977641i 0.432563π-0.432563\pi
0.210280 + 0.977641i 0.432563π0.432563\pi
402402 0 0
403403 − 3678.43i − 0.454680i
404404 0 0
405405 0 0
406406 0 0
407407 2251.40 0.274196
408408 0 0
409409 3526.00 0.426282 0.213141 0.977021i 0.431631π-0.431631\pi
0.213141 + 0.977021i 0.431631π0.431631\pi
410410 0 0
411411 0 0
412412 0 0
413413 7336.48i 0.874104i
414414 0 0
415415 −4240.00 −0.501526
416416 0 0
417417 0 0
418418 0 0
419419 2466.58i 0.287590i 0.989608 + 0.143795i 0.0459306π0.0459306\pi
−0.989608 + 0.143795i 0.954069π0.954069\pi
420420 0 0
421421 − 13586.5i − 1.57284i −0.617694 0.786418i 0.711933π-0.711933\pi
0.617694 0.786418i 0.288067π-0.288067\pi
422422 0 0
423423 0 0
424424 0 0
425425 −6378.97 −0.728059
426426 0 0
427427 5339.66i 0.605163i
428428 0 0
429429 0 0
430430 0 0
431431 6754.20 0.754845 0.377423 0.926041i 0.376810π-0.376810\pi
0.377423 + 0.926041i 0.376810π0.376810\pi
432432 0 0
433433 7790.00 0.864581 0.432290 0.901734i 0.357706π-0.357706\pi
0.432290 + 0.901734i 0.357706π0.357706\pi
434434 0 0
435435 0 0
436436 0 0
437437 17809.9i 1.94958i
438438 0 0
439439 9354.00 1.01695 0.508476 0.861076i 0.330209π-0.330209\pi
0.508476 + 0.861076i 0.330209π0.330209\pi
440440 0 0
441441 0 0
442442 0 0
443443 − 6488.99i − 0.695940i −0.937506 0.347970i 0.886871π-0.886871\pi
0.937506 0.347970i 0.113129π-0.113129\pi
444444 0 0
445445 4746.37i 0.505617i
446446 0 0
447447 0 0
448448 0 0
449449 10131.3 1.06487 0.532434 0.846472i 0.321278π-0.321278\pi
0.532434 + 0.846472i 0.321278π0.321278\pi
450450 0 0
451451 14239.1i 1.48668i
452452 0 0
453453 0 0
454454 0 0
455455 3752.33 0.386620
456456 0 0
457457 −12010.0 −1.22933 −0.614665 0.788788i 0.710709π-0.710709\pi
−0.614665 + 0.788788i 0.710709π0.710709\pi
458458 0 0
459459 0 0
460460 0 0
461461 − 9316.07i − 0.941199i −0.882347 0.470599i 0.844038π-0.844038\pi
0.882347 0.470599i 0.155962π-0.155962\pi
462462 0 0
463463 −14770.0 −1.48255 −0.741274 0.671202i 0.765778π-0.765778\pi
−0.741274 + 0.671202i 0.765778π0.765778\pi
464464 0 0
465465 0 0
466466 0 0
467467 8740.54i 0.866089i 0.901372 + 0.433045i 0.142561π0.142561\pi
−0.901372 + 0.433045i 0.857439π0.857439\pi
468468 0 0
469469 − 7119.55i − 0.700960i
470470 0 0
471471 0 0
472472 0 0
473473 4502.80 0.437714
474474 0 0
475475 − 10086.0i − 0.974271i
476476 0 0
477477 0 0
478478 0 0
479479 −3001.87 −0.286344 −0.143172 0.989698i 0.545730π-0.545730\pi
−0.143172 + 0.989698i 0.545730π0.545730\pi
480480 0 0
481481 −3520.00 −0.333676
482482 0 0
483483 0 0
484484 0 0
485485 822.192i 0.0769770i
486486 0 0
487487 9910.00 0.922105 0.461052 0.887373i 0.347472π-0.347472\pi
0.461052 + 0.887373i 0.347472π0.347472\pi
488488 0 0
489489 0 0
490490 0 0
491491 − 3389.96i − 0.311582i −0.987790 0.155791i 0.950207π-0.950207\pi
0.987790 0.155791i 0.0497927π-0.0497927\pi
492492 0 0
493493 18510.8i 1.69105i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 − 4271.73i − 0.383224i −0.981471 0.191612i 0.938628π-0.938628\pi
0.981471 0.191612i 0.0613716π-0.0613716\pi
500500 0 0
501501 0 0
502502 0 0
503503 900.560 0.0798290 0.0399145 0.999203i 0.487291π-0.487291\pi
0.0399145 + 0.999203i 0.487291π0.487291\pi
504504 0 0
505505 3560.00 0.313699
506506 0 0
507507 0 0
508508 0 0
509509 − 853.815i − 0.0743510i −0.999309 0.0371755i 0.988164π-0.988164\pi
0.999309 0.0371755i 0.0118361π-0.0118361\pi
510510 0 0
511511 −300.000 −0.0259711
512512 0 0
513513 0 0
514514 0 0
515515 3605.00i 0.308457i
516516 0 0
517517 17086.9i 1.45354i
518518 0 0
519519 0 0
520520 0 0
521521 −7879.90 −0.662619 −0.331310 0.943522i 0.607490π-0.607490\pi
−0.331310 + 0.943522i 0.607490π0.607490\pi
522522 0 0
523523 − 10323.3i − 0.863114i −0.902086 0.431557i 0.857964π-0.857964\pi
0.902086 0.431557i 0.142036π-0.142036\pi
524524 0 0
525525 0 0
526526 0 0
527527 4652.89 0.384598
528528 0 0
529529 10361.0 0.851566
530530 0 0
531531 0 0
532532 0 0
533533 − 22262.4i − 1.80918i
534534 0 0
535535 −8160.00 −0.659416
536536 0 0
537537 0 0
538538 0 0
539539 9221.20i 0.736893i
540540 0 0
541541 − 15603.7i − 1.24003i −0.784591 0.620014i 0.787127π-0.787127\pi
0.784591 0.620014i 0.212873π-0.212873\pi
542542 0 0
543543 0 0
544544 0 0
545545 −10881.8 −0.855273
546546 0 0
547547 − 2254.52i − 0.176228i −0.996110 0.0881138i 0.971916π-0.971916\pi
0.996110 0.0881138i 0.0280839π-0.0280839\pi
548548 0 0
549549 0 0
550550 0 0
551551 −29268.2 −2.26292
552552 0 0
553553 940.000 0.0722837
554554 0 0
555555 0 0
556556 0 0
557557 − 284.605i − 0.0216501i −0.999941 0.0108250i 0.996554π-0.996554\pi
0.999941 0.0108250i 0.00344579π-0.00344579\pi
558558 0 0
559559 −7040.00 −0.532666
560560 0 0
561561 0 0
562562 0 0
563563 − 18328.6i − 1.37204i −0.727584 0.686018i 0.759357π-0.759357\pi
0.727584 0.686018i 0.240643π-0.240643\pi
564564 0 0
565565 8543.46i 0.636152i
566566 0 0
567567 0 0
568568 0 0
569569 −7879.90 −0.580567 −0.290283 0.956941i 0.593750π-0.593750\pi
−0.290283 + 0.956941i 0.593750π0.593750\pi
570570 0 0
571571 − 8306.14i − 0.608759i −0.952551 0.304379i 0.901551π-0.901551\pi
0.952551 0.304379i 0.0984491π-0.0984491\pi
572572 0 0
573573 0 0
574574 0 0
575575 −12757.9 −0.925291
576576 0 0
577577 −6330.00 −0.456709 −0.228355 0.973578i 0.573335π-0.573335\pi
−0.228355 + 0.973578i 0.573335π0.573335\pi
578578 0 0
579579 0 0
580580 0 0
581581 − 6704.03i − 0.478709i
582582 0 0
583583 −5040.00 −0.358037
584584 0 0
585585 0 0
586586 0 0
587587 1922.66i 0.135191i 0.997713 + 0.0675953i 0.0215327π0.0215327\pi
−0.997713 + 0.0675953i 0.978467π0.978467\pi
588588 0 0
589589 7356.87i 0.514660i
590590 0 0
591591 0 0
592592 0 0
593593 −10356.4 −0.717180 −0.358590 0.933495i 0.616742π-0.616742\pi
−0.358590 + 0.933495i 0.616742π0.616742\pi
594594 0 0
595595 4746.37i 0.327029i
596596 0 0
597597 0 0
598598 0 0
599599 750.467 0.0511907 0.0255954 0.999672i 0.491852π-0.491852\pi
0.0255954 + 0.999672i 0.491852π0.491852\pi
600600 0 0
601601 18578.0 1.26092 0.630460 0.776222i 0.282866π-0.282866\pi
0.630460 + 0.776222i 0.282866π0.282866\pi
602602 0 0
603603 0 0
604604 0 0
605605 − 689.377i − 0.0463259i
606606 0 0
607607 8030.00 0.536948 0.268474 0.963287i 0.413481π-0.413481\pi
0.268474 + 0.963287i 0.413481π0.413481\pi
608608 0 0
609609 0 0
610610 0 0
611611 − 26714.9i − 1.76885i
612612 0 0
613613 3856.42i 0.254094i 0.991897 + 0.127047i 0.0405499π0.0405499\pi
−0.991897 + 0.127047i 0.959450π0.959450\pi
614614 0 0
615615 0 0
616616 0 0
617617 −300.187 −0.0195868 −0.00979340 0.999952i 0.503117π-0.503117\pi
−0.00979340 + 0.999952i 0.503117π0.503117\pi
618618 0 0
619619 1423.91i 0.0924584i 0.998931 + 0.0462292i 0.0147205π0.0147205\pi
−0.998931 + 0.0462292i 0.985280π0.985280\pi
620620 0 0
621621 0 0
622622 0 0
623623 −7504.67 −0.482613
624624 0 0
625625 2225.00 0.142400
626626 0 0
627627 0 0
628628 0 0
629629 − 4452.49i − 0.282245i
630630 0 0
631631 12902.0 0.813979 0.406989 0.913433i 0.366579π-0.366579\pi
0.406989 + 0.913433i 0.366579π0.366579\pi
632632 0 0
633633 0 0
634634 0 0
635635 − 16001.1i − 0.999977i
636636 0 0
637637 − 14417.1i − 0.896744i
638638 0 0
639639 0 0
640640 0 0
641641 −19887.4 −1.22543 −0.612717 0.790302i 0.709924π-0.709924\pi
−0.612717 + 0.790302i 0.709924π0.709924\pi
642642 0 0
643643 − 29783.5i − 1.82666i −0.407216 0.913332i 0.633500π-0.633500\pi
0.407216 0.913332i 0.366500π-0.366500\pi
644644 0 0
645645 0 0
646646 0 0
647647 13958.7 0.848180 0.424090 0.905620i 0.360594π-0.360594\pi
0.424090 + 0.905620i 0.360594π0.360594\pi
648648 0 0
649649 −27840.0 −1.68385
650650 0 0
651651 0 0
652652 0 0
653653 18461.4i 1.10635i 0.833064 + 0.553177i 0.186585π0.186585\pi
−0.833064 + 0.553177i 0.813415π0.813415\pi
654654 0 0
655655 −1600.00 −0.0954461
656656 0 0
657657 0 0
658658 0 0
659659 5160.84i 0.305065i 0.988298 + 0.152532i 0.0487428π0.0487428\pi
−0.988298 + 0.152532i 0.951257π0.951257\pi
660660 0 0
661661 − 13467.8i − 0.792492i −0.918144 0.396246i 0.870313π-0.870313\pi
0.918144 0.396246i 0.129687π-0.129687\pi
662662 0 0
663663 0 0
664664 0 0
665665 −7504.67 −0.437622
666666 0 0
667667 37021.7i 2.14915i
668668 0 0
669669 0 0
670670 0 0
671671 −20262.6 −1.16577
672672 0 0
673673 −15010.0 −0.859722 −0.429861 0.902895i 0.641437π-0.641437\pi
−0.429861 + 0.902895i 0.641437π0.641437\pi
674674 0 0
675675 0 0
676676 0 0
677677 6280.28i 0.356530i 0.983983 + 0.178265i 0.0570485π0.0570485\pi
−0.983983 + 0.178265i 0.942952π0.942952\pi
678678 0 0
679679 −1300.00 −0.0734748
680680 0 0
681681 0 0
682682 0 0
683683 12510.0i 0.700850i 0.936591 + 0.350425i 0.113963π0.113963\pi
−0.936591 + 0.350425i 0.886037π0.886037\pi
684684 0 0
685685 4271.73i 0.238269i
686686 0 0
687687 0 0
688688 0 0
689689 7879.90 0.435704
690690 0 0
691691 28359.5i 1.56128i 0.624978 + 0.780642i 0.285108π0.285108\pi
−0.624978 + 0.780642i 0.714892π0.714892\pi
692692 0 0
693693 0 0
694694 0 0
695695 −1500.93 −0.0819189
696696 0 0
697697 28160.0 1.53032
698698 0 0
699699 0 0
700700 0 0
701701 − 19802.2i − 1.06693i −0.845822 0.533465i 0.820890π-0.820890\pi
0.845822 0.533465i 0.179110π-0.179110\pi
702702 0 0
703703 7040.00 0.377694
704704 0 0
705705 0 0
706706 0 0
707707 5628.85i 0.299427i
708708 0 0
709709 − 12874.5i − 0.681964i −0.940070 0.340982i 0.889240π-0.889240\pi
0.940070 0.340982i 0.110760π-0.110760\pi
710710 0 0
711711 0 0
712712 0 0
713713 9305.78 0.488786
714714 0 0
715715 14239.1i 0.744772i
716716 0 0
717717 0 0
718718 0 0
719719 −1500.93 −0.0778517 −0.0389258 0.999242i 0.512394π-0.512394\pi
−0.0389258 + 0.999242i 0.512394π0.512394\pi
720720 0 0
721721 −5700.00 −0.294423
722722 0 0
723723 0 0
724724 0 0
725725 − 20965.9i − 1.07401i
726726 0 0
727727 −23850.0 −1.21671 −0.608355 0.793665i 0.708170π-0.708170\pi
−0.608355 + 0.793665i 0.708170π0.708170\pi
728728 0 0
729729 0 0
730730 0 0
731731 − 8904.97i − 0.450564i
732732 0 0
733733 2195.19i 0.110616i 0.998469 + 0.0553079i 0.0176140π0.0176140\pi
−0.998469 + 0.0553079i 0.982386π0.982386\pi
734734 0 0
735735 0 0
736736 0 0
737737 27016.8 1.35031
738738 0 0
739739 2610.50i 0.129944i 0.997887 + 0.0649722i 0.0206959π0.0206959\pi
−0.997887 + 0.0649722i 0.979304π0.979304\pi
740740 0 0
741741 0 0
742742 0 0
743743 2851.77 0.140809 0.0704047 0.997519i 0.477571π-0.477571\pi
0.0704047 + 0.997519i 0.477571π0.477571\pi
744744 0 0
745745 −18600.0 −0.914700
746746 0 0
747747 0 0
748748 0 0
749749 − 12902.1i − 0.629416i
750750 0 0
751751 20578.0 0.999869 0.499935 0.866063i 0.333357π-0.333357\pi
0.499935 + 0.866063i 0.333357π0.333357\pi
752752 0 0
753753 0 0
754754 0 0
755755 14306.1i 0.689608i
756756 0 0
757757 − 20468.7i − 0.982758i −0.870946 0.491379i 0.836493π-0.836493\pi
0.870946 0.491379i 0.163507π-0.163507\pi
758758 0 0
759759 0 0
760760 0 0
761761 −22138.8 −1.05457 −0.527286 0.849688i 0.676790π-0.676790\pi
−0.527286 + 0.849688i 0.676790π0.676790\pi
762762 0 0
763763 − 17205.6i − 0.816362i
764764 0 0
765765 0 0
766766 0 0
767767 43527.1 2.04911
768768 0 0
769769 −6854.00 −0.321406 −0.160703 0.987003i 0.551376π-0.551376\pi
−0.160703 + 0.987003i 0.551376π0.551376\pi
770770 0 0
771771 0 0
772772 0 0
773773 38902.3i 1.81012i 0.425288 + 0.905058i 0.360173π0.360173\pi
−0.425288 + 0.905058i 0.639827π0.639827\pi
774774 0 0
775775 −5270.00 −0.244263
776776 0 0
777777 0 0
778778 0 0
779779 44524.9i 2.04784i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0 0
785785 10881.8 0.494760
786786 0 0
787787 − 13171.2i − 0.596571i −0.954477 0.298286i 0.903585π-0.903585\pi
0.954477 0.298286i 0.0964148π-0.0964148\pi
788788 0 0
789789 0 0
790790 0 0
791791 −13508.4 −0.607210
792792 0 0
793793 31680.0 1.41865
794794 0 0
795795 0 0
796796 0 0
797797 13730.6i 0.610242i 0.952314 + 0.305121i 0.0986970π0.0986970\pi
−0.952314 + 0.305121i 0.901303π0.901303\pi
798798 0 0
799799 33792.0 1.49621
800800 0 0
801801 0 0
802802 0 0
803803 − 1138.42i − 0.0500298i
804804 0 0
805805 9492.73i 0.415621i
806806 0 0
807807 0 0
808808 0 0
809809 30393.9 1.32088 0.660440 0.750879i 0.270370π-0.270370\pi
0.660440 + 0.750879i 0.270370π0.270370\pi
810810 0 0
811811 − 27647.6i − 1.19709i −0.801090 0.598544i 0.795746π-0.795746\pi
0.801090 0.598544i 0.204254π-0.204254\pi
812812 0 0
813813 0 0
814814 0 0
815815 12757.9 0.548332
816816 0 0
817817 14080.0 0.602934
818818 0 0
819819 0 0
820820 0 0
821821 26303.8i 1.11816i 0.829114 + 0.559080i 0.188846π0.188846\pi
−0.829114 + 0.559080i 0.811154π0.811154\pi
822822 0 0
823823 −22970.0 −0.972884 −0.486442 0.873713i 0.661706π-0.661706\pi
−0.486442 + 0.873713i 0.661706π0.661706\pi
824824 0 0
825825 0 0
826826 0 0
827827 − 7665.36i − 0.322310i −0.986929 0.161155i 0.948478π-0.948478\pi
0.986929 0.161155i 0.0515220π-0.0515220\pi
828828 0 0
829829 17383.6i 0.728295i 0.931341 + 0.364147i 0.118640π0.118640\pi
−0.931341 + 0.364147i 0.881360π0.881360\pi
830830 0 0
831831 0 0
832832 0 0
833833 18236.3 0.758525
834834 0 0
835835 6644.91i 0.275397i
836836 0 0
837837 0 0
838838 0 0
839839 33020.5 1.35875 0.679377 0.733789i 0.262250π-0.262250\pi
0.679377 + 0.733789i 0.262250π0.262250\pi
840840 0 0
841841 −36451.0 −1.49457
842842 0 0
843843 0 0
844844 0 0
845845 − 8367.39i − 0.340647i
846846 0 0
847847 1090.00 0.0442182
848848 0 0
849849 0 0
850850 0 0
851851 − 8904.97i − 0.358706i
852852 0 0
853853 46099.1i 1.85041i 0.379463 + 0.925207i 0.376109π0.376109\pi
−0.379463 + 0.925207i 0.623891π0.623891\pi
854854 0 0
855855 0 0
856856 0 0
857857 44352.6 1.76786 0.883929 0.467620i 0.154889π-0.154889\pi
0.883929 + 0.467620i 0.154889π0.154889\pi
858858 0 0
859859 − 7712.85i − 0.306355i −0.988199 0.153177i 0.951049π-0.951049\pi
0.988199 0.153177i 0.0489506π-0.0489506\pi
860860 0 0
861861 0 0
862862 0 0
863863 21163.2 0.834765 0.417383 0.908731i 0.362948π-0.362948\pi
0.417383 + 0.908731i 0.362948π0.362948\pi
864864 0 0
865865 9000.00 0.353768
866866 0 0
867867 0 0
868868 0 0
869869 3567.05i 0.139245i
870870 0 0
871871 −42240.0 −1.64322
872872 0 0
873873 0 0
874874 0 0
875875 − 13281.6i − 0.513142i
876876 0 0
877877 − 17146.3i − 0.660191i −0.943947 0.330096i 0.892919π-0.892919\pi
0.943947 0.330096i 0.107081π-0.107081\pi
878878 0 0
879879 0 0
880880 0 0
881881 −42026.1 −1.60715 −0.803573 0.595206i 0.797071π-0.797071\pi
−0.803573 + 0.595206i 0.797071π0.797071\pi
882882 0 0
883883 − 4865.03i − 0.185415i −0.995693 0.0927073i 0.970448π-0.970448\pi
0.995693 0.0927073i 0.0295521π-0.0295521\pi
884884 0 0
885885 0 0
886886 0 0
887887 11707.3 0.443170 0.221585 0.975141i 0.428877π-0.428877\pi
0.221585 + 0.975141i 0.428877π0.428877\pi
888888 0 0
889889 25300.0 0.954482
890890 0 0
891891 0 0
892892 0 0
893893 53429.8i 2.00220i
894894 0 0
895895 800.000 0.0298783
896896 0 0
897897 0 0
898898 0 0
899899 15292.8i 0.567344i
900900 0 0
901901 9967.37i 0.368547i
902902 0 0
903903 0 0
904904 0 0
905905 375.233 0.0137825
906906 0 0
907907 − 12933.9i − 0.473497i −0.971571 0.236748i 0.923918π-0.923918\pi
0.971571 0.236748i 0.0760817π-0.0760817\pi
908908 0 0
909909 0 0
910910 0 0
911911 −20262.6 −0.736915 −0.368458 0.929645i 0.620114π-0.620114\pi
−0.368458 + 0.929645i 0.620114π0.620114\pi
912912 0 0
913913 25440.0 0.922170
914914 0 0
915915 0 0
916916 0 0
917917 − 2529.82i − 0.0911037i
918918 0 0
919919 −22746.0 −0.816454 −0.408227 0.912880i 0.633853π-0.633853\pi
−0.408227 + 0.912880i 0.633853π0.633853\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 5043.01i 0.179258i
926926 0 0
927927 0 0
928928 0 0
929929 13883.6 0.490320 0.245160 0.969483i 0.421160π-0.421160\pi
0.245160 + 0.969483i 0.421160π0.421160\pi
930930 0 0
931931 28834.2i 1.01504i
932932 0 0
933933 0 0
934934 0 0
935935 −18011.2 −0.629978
936936 0 0
937937 −27850.0 −0.970992 −0.485496 0.874239i 0.661361π-0.661361\pi
−0.485496 + 0.874239i 0.661361π0.661361\pi
938938 0 0
939939 0 0
940940 0 0
941941 − 36789.9i − 1.27451i −0.770651 0.637257i 0.780069π-0.780069\pi
0.770651 0.637257i 0.219931π-0.219931\pi
942942 0 0
943943 56320.0 1.94489
944944 0 0
945945 0 0
946946 0 0
947947 42728.7i 1.46620i 0.680118 + 0.733102i 0.261928π0.261928\pi
−0.680118 + 0.733102i 0.738072π0.738072\pi
948948 0 0
949949 1779.89i 0.0608826i
950950 0 0
951951 0 0
952952 0 0
953953 −24990.5 −0.849447 −0.424723 0.905323i 0.639629π-0.639629\pi
−0.424723 + 0.905323i 0.639629π0.639629\pi
954954 0 0
955955 − 23731.8i − 0.804130i
956956 0 0
957957 0 0
958958 0 0
959959 −6754.20 −0.227429
960960 0 0
961961 −25947.0 −0.870968
962962 0 0
963963 0 0
964964 0 0
965965 − 8538.15i − 0.284822i
966966 0 0
967967 −10550.0 −0.350843 −0.175421 0.984493i 0.556129π-0.556129\pi
−0.175421 + 0.984493i 0.556129π0.556129\pi
968968 0 0
969969 0 0
970970 0 0
971971 − 53012.4i − 1.75206i −0.482257 0.876030i 0.660183π-0.660183\pi
0.482257 0.876030i 0.339817π-0.339817\pi
972972 0 0
973973 − 2373.18i − 0.0781920i
974974 0 0
975975 0 0
976976 0 0
977977 34596.5 1.13290 0.566448 0.824097i 0.308317π-0.308317\pi
0.566448 + 0.824097i 0.308317π0.308317\pi
978978 0 0
979979 − 28478.2i − 0.929691i
980980 0 0
981981 0 0
982982 0 0
983983 33921.1 1.10063 0.550313 0.834959i 0.314509π-0.314509\pi
0.550313 + 0.834959i 0.314509π0.314509\pi
984984 0 0
985985 9160.00 0.296306
986986 0 0
987987 0 0
988988 0 0
989989 − 17809.9i − 0.572622i
990990 0 0
991991 8818.00 0.282657 0.141328 0.989963i 0.454863π-0.454863\pi
0.141328 + 0.989963i 0.454863π0.454863\pi
992992 0 0
993993 0 0
994994 0 0
995995 20200.6i 0.643621i
996996 0 0
997997 − 25096.4i − 0.797203i −0.917124 0.398602i 0.869496π-0.869496\pi
0.917124 0.398602i 0.130504π-0.130504\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 288.4.d.c.145.4 4
3.2 odd 2 inner 288.4.d.c.145.2 4
4.3 odd 2 72.4.d.c.37.2 yes 4
8.3 odd 2 72.4.d.c.37.1 4
8.5 even 2 inner 288.4.d.c.145.1 4
12.11 even 2 72.4.d.c.37.3 yes 4
16.3 odd 4 2304.4.a.bx.1.3 4
16.5 even 4 2304.4.a.cc.1.2 4
16.11 odd 4 2304.4.a.bx.1.2 4
16.13 even 4 2304.4.a.cc.1.3 4
24.5 odd 2 inner 288.4.d.c.145.3 4
24.11 even 2 72.4.d.c.37.4 yes 4
48.5 odd 4 2304.4.a.cc.1.4 4
48.11 even 4 2304.4.a.bx.1.4 4
48.29 odd 4 2304.4.a.cc.1.1 4
48.35 even 4 2304.4.a.bx.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.4.d.c.37.1 4 8.3 odd 2
72.4.d.c.37.2 yes 4 4.3 odd 2
72.4.d.c.37.3 yes 4 12.11 even 2
72.4.d.c.37.4 yes 4 24.11 even 2
288.4.d.c.145.1 4 8.5 even 2 inner
288.4.d.c.145.2 4 3.2 odd 2 inner
288.4.d.c.145.3 4 24.5 odd 2 inner
288.4.d.c.145.4 4 1.1 even 1 trivial
2304.4.a.bx.1.1 4 48.35 even 4
2304.4.a.bx.1.2 4 16.11 odd 4
2304.4.a.bx.1.3 4 16.3 odd 4
2304.4.a.bx.1.4 4 48.11 even 4
2304.4.a.cc.1.1 4 48.29 odd 4
2304.4.a.cc.1.2 4 16.5 even 4
2304.4.a.cc.1.3 4 16.13 even 4
2304.4.a.cc.1.4 4 48.5 odd 4