Properties

Label 1152.5.b.j.703.2
Level 11521152
Weight 55
Character 1152.703
Analytic conductor 119.082119.082
Analytic rank 00
Dimension 44
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1152,5,Mod(703,1152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1152, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 5, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1152.703"); S:= CuspForms(chi, 5); N := Newforms(S);
 
Level: N N == 1152=2732 1152 = 2^{7} \cdot 3^{2}
Weight: k k == 5 5
Character orbit: [χ][\chi] == 1152.b (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1352] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 119.082197473119.082197473
Analytic rank: 00
Dimension: 44
Coefficient field: Q(3,19)\Q(\sqrt{3}, \sqrt{-19})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x42x3+5x24x+61 x^{4} - 2x^{3} + 5x^{2} - 4x + 61 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 283 2^{8}\cdot 3
Twist minimal: no (minimal twist has level 384)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 703.2
Root 2.232052.17945i2.23205 - 2.17945i of defining polynomial
Character χ\chi == 1152.703
Dual form 1152.5.b.j.703.3

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q30.1993iq5+52.3068iq7+90.0666q11+60.3987iq13+338.000q176.92820q19732.295iq23287.000q25+1298.57iq291307.67iq31+1579.63q35+241.595iq37578.000q412029.96q43+2196.89iq47335.000q49+2446.15iq532719.95iq55+1198.58q59+6402.26iq61+1824.00q658265.35q674289.16iq71+8734.00q73+4711.10iq77+11246.0iq79+13198.2q8310207.4iq85910.000q893159.26q91+209.227iq95+5422.00q97+O(q100)q-30.1993i q^{5} +52.3068i q^{7} +90.0666 q^{11} +60.3987i q^{13} +338.000 q^{17} -6.92820 q^{19} -732.295i q^{23} -287.000 q^{25} +1298.57i q^{29} -1307.67i q^{31} +1579.63 q^{35} +241.595i q^{37} -578.000 q^{41} -2029.96 q^{43} +2196.89i q^{47} -335.000 q^{49} +2446.15i q^{53} -2719.95i q^{55} +1198.58 q^{59} +6402.26i q^{61} +1824.00 q^{65} -8265.35 q^{67} -4289.16i q^{71} +8734.00 q^{73} +4711.10i q^{77} +11246.0i q^{79} +13198.2 q^{83} -10207.4i q^{85} -910.000 q^{89} -3159.26 q^{91} +209.227i q^{95} +5422.00 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+1352q171148q252312q411340q49+7296q65+34936q733640q89+21688q97+O(q100) 4 q + 1352 q^{17} - 1148 q^{25} - 2312 q^{41} - 1340 q^{49} + 7296 q^{65} + 34936 q^{73} - 3640 q^{89} + 21688 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1152Z)×\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times.

nn 127127 641641 901901
χ(n)\chi(n) 1-1 11 1-1

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0 0
44 0 0
55 − 30.1993i − 1.20797i −0.796994 0.603987i 0.793578π-0.793578\pi
0.796994 0.603987i 0.206422π-0.206422\pi
66 0 0
77 52.3068i 1.06749i 0.845647 + 0.533743i 0.179215π0.179215\pi
−0.845647 + 0.533743i 0.820785π0.820785\pi
88 0 0
99 0 0
1010 0 0
1111 90.0666 0.744352 0.372176 0.928162i 0.378612π-0.378612\pi
0.372176 + 0.928162i 0.378612π0.378612\pi
1212 0 0
1313 60.3987i 0.357389i 0.983905 + 0.178694i 0.0571873π0.0571873\pi
−0.983905 + 0.178694i 0.942813π0.942813\pi
1414 0 0
1515 0 0
1616 0 0
1717 338.000 1.16955 0.584775 0.811195i 0.301183π-0.301183\pi
0.584775 + 0.811195i 0.301183π0.301183\pi
1818 0 0
1919 −6.92820 −0.0191917 −0.00959585 0.999954i 0.503055π-0.503055\pi
−0.00959585 + 0.999954i 0.503055π0.503055\pi
2020 0 0
2121 0 0
2222 0 0
2323 − 732.295i − 1.38430i −0.721753 0.692150i 0.756664π-0.756664\pi
0.721753 0.692150i 0.243336π-0.243336\pi
2424 0 0
2525 −287.000 −0.459200
2626 0 0
2727 0 0
2828 0 0
2929 1298.57i 1.54408i 0.635574 + 0.772040i 0.280764π0.280764\pi
−0.635574 + 0.772040i 0.719236π0.719236\pi
3030 0 0
3131 − 1307.67i − 1.36074i −0.732869 0.680369i 0.761819π-0.761819\pi
0.732869 0.680369i 0.238181π-0.238181\pi
3232 0 0
3333 0 0
3434 0 0
3535 1579.63 1.28949
3636 0 0
3737 241.595i 0.176475i 0.996099 + 0.0882377i 0.0281235π0.0281235\pi
−0.996099 + 0.0882377i 0.971877π0.971877\pi
3838 0 0
3939 0 0
4040 0 0
4141 −578.000 −0.343843 −0.171921 0.985111i 0.554998π-0.554998\pi
−0.171921 + 0.985111i 0.554998π0.554998\pi
4242 0 0
4343 −2029.96 −1.09787 −0.548936 0.835865i 0.684967π-0.684967\pi
−0.548936 + 0.835865i 0.684967π0.684967\pi
4444 0 0
4545 0 0
4646 0 0
4747 2196.89i 0.994516i 0.867603 + 0.497258i 0.165660π0.165660\pi
−0.867603 + 0.497258i 0.834340π0.834340\pi
4848 0 0
4949 −335.000 −0.139525
5050 0 0
5151 0 0
5252 0 0
5353 2446.15i 0.870825i 0.900231 + 0.435412i 0.143397π0.143397\pi
−0.900231 + 0.435412i 0.856603π0.856603\pi
5454 0 0
5555 − 2719.95i − 0.899158i
5656 0 0
5757 0 0
5858 0 0
5959 1198.58 0.344320 0.172160 0.985069i 0.444925π-0.444925\pi
0.172160 + 0.985069i 0.444925π0.444925\pi
6060 0 0
6161 6402.26i 1.72058i 0.509809 + 0.860288i 0.329716π0.329716\pi
−0.509809 + 0.860288i 0.670284π0.670284\pi
6262 0 0
6363 0 0
6464 0 0
6565 1824.00 0.431716
6666 0 0
6767 −8265.35 −1.84124 −0.920622 0.390454i 0.872318π-0.872318\pi
−0.920622 + 0.390454i 0.872318π0.872318\pi
6868 0 0
6969 0 0
7070 0 0
7171 − 4289.16i − 0.850854i −0.904993 0.425427i 0.860124π-0.860124\pi
0.904993 0.425427i 0.139876π-0.139876\pi
7272 0 0
7373 8734.00 1.63896 0.819478 0.573110i 0.194263π-0.194263\pi
0.819478 + 0.573110i 0.194263π0.194263\pi
7474 0 0
7575 0 0
7676 0 0
7777 4711.10i 0.794585i
7878 0 0
7979 11246.0i 1.80195i 0.433873 + 0.900974i 0.357147π0.357147\pi
−0.433873 + 0.900974i 0.642853π0.642853\pi
8080 0 0
8181 0 0
8282 0 0
8383 13198.2 1.91584 0.957920 0.287034i 0.0926693π-0.0926693\pi
0.957920 + 0.287034i 0.0926693π0.0926693\pi
8484 0 0
8585 − 10207.4i − 1.41279i
8686 0 0
8787 0 0
8888 0 0
8989 −910.000 −0.114884 −0.0574422 0.998349i 0.518295π-0.518295\pi
−0.0574422 + 0.998349i 0.518295π0.518295\pi
9090 0 0
9191 −3159.26 −0.381507
9292 0 0
9393 0 0
9494 0 0
9595 209.227i 0.0231831i
9696 0 0
9797 5422.00 0.576257 0.288128 0.957592i 0.406967π-0.406967\pi
0.288128 + 0.957592i 0.406967π0.406967\pi
9898 0 0
9999 0 0
100100 0 0
101101 − 10962.4i − 1.07464i −0.843380 0.537318i 0.819438π-0.819438\pi
0.843380 0.537318i 0.180562π-0.180562\pi
102102 0 0
103103 5387.60i 0.507833i 0.967226 + 0.253916i 0.0817188π0.0817188\pi
−0.967226 + 0.253916i 0.918281π0.918281\pi
104104 0 0
105105 0 0
106106 0 0
107107 6436.30 0.562171 0.281086 0.959683i 0.409305π-0.409305\pi
0.281086 + 0.959683i 0.409305π0.409305\pi
108108 0 0
109109 − 60.3987i − 0.00508364i −0.999997 0.00254182i 0.999191π-0.999191\pi
0.999997 0.00254182i 0.000809087π-0.000809087\pi
110110 0 0
111111 0 0
112112 0 0
113113 3166.00 0.247944 0.123972 0.992286i 0.460437π-0.460437\pi
0.123972 + 0.992286i 0.460437π0.460437\pi
114114 0 0
115115 −22114.8 −1.67220
116116 0 0
117117 0 0
118118 0 0
119119 17679.7i 1.24848i
120120 0 0
121121 −6529.00 −0.445939
122122 0 0
123123 0 0
124124 0 0
125125 − 10207.4i − 0.653272i
126126 0 0
127127 − 12919.8i − 0.801028i −0.916291 0.400514i 0.868832π-0.868832\pi
0.916291 0.400514i 0.131168π-0.131168\pi
128128 0 0
129129 0 0
130130 0 0
131131 22676.0 1.32137 0.660684 0.750664i 0.270266π-0.270266\pi
0.660684 + 0.750664i 0.270266π0.270266\pi
132132 0 0
133133 − 362.392i − 0.0204869i
134134 0 0
135135 0 0
136136 0 0
137137 15550.0 0.828494 0.414247 0.910165i 0.364045π-0.364045\pi
0.414247 + 0.910165i 0.364045π0.364045\pi
138138 0 0
139139 31502.5 1.63048 0.815241 0.579122i 0.196604π-0.196604\pi
0.815241 + 0.579122i 0.196604π0.196604\pi
140140 0 0
141141 0 0
142142 0 0
143143 5439.91i 0.266023i
144144 0 0
145145 39216.0 1.86521
146146 0 0
147147 0 0
148148 0 0
149149 − 22619.3i − 1.01884i −0.860518 0.509421i 0.829860π-0.829860\pi
0.860518 0.509421i 0.170140π-0.170140\pi
150150 0 0
151151 − 7689.10i − 0.337226i −0.985682 0.168613i 0.946071π-0.946071\pi
0.985682 0.168613i 0.0539289π-0.0539289\pi
152152 0 0
153153 0 0
154154 0 0
155155 −39490.8 −1.64374
156156 0 0
157157 1207.97i 0.0490070i 0.999700 + 0.0245035i 0.00780049π0.00780049\pi
−0.999700 + 0.0245035i 0.992200π0.992200\pi
158158 0 0
159159 0 0
160160 0 0
161161 38304.0 1.47772
162162 0 0
163163 −26749.8 −1.00680 −0.503402 0.864052i 0.667919π-0.667919\pi
−0.503402 + 0.864052i 0.667919π0.667919\pi
164164 0 0
165165 0 0
166166 0 0
167167 − 44983.8i − 1.61296i −0.591261 0.806480i 0.701370π-0.701370\pi
0.591261 0.806480i 0.298630π-0.298630\pi
168168 0 0
169169 24913.0 0.872273
170170 0 0
171171 0 0
172172 0 0
173173 − 4197.71i − 0.140256i −0.997538 0.0701278i 0.977659π-0.977659\pi
0.997538 0.0701278i 0.0223407π-0.0223407\pi
174174 0 0
175175 − 15012.0i − 0.490189i
176176 0 0
177177 0 0
178178 0 0
179179 −12491.6 −0.389861 −0.194931 0.980817i 0.562448π-0.562448\pi
−0.194931 + 0.980817i 0.562448π0.562448\pi
180180 0 0
181181 − 37870.0i − 1.15595i −0.816056 0.577973i 0.803844π-0.803844\pi
0.816056 0.577973i 0.196156π-0.196156\pi
182182 0 0
183183 0 0
184184 0 0
185185 7296.00 0.213178
186186 0 0
187187 30442.5 0.870557
188188 0 0
189189 0 0
190190 0 0
191191 − 32848.7i − 0.900432i −0.892920 0.450216i 0.851347π-0.851347\pi
0.892920 0.450216i 0.148653π-0.148653\pi
192192 0 0
193193 44830.0 1.20352 0.601761 0.798676i 0.294466π-0.294466\pi
0.601761 + 0.798676i 0.294466π0.294466\pi
194194 0 0
195195 0 0
196196 0 0
197197 42188.5i 1.08708i 0.839383 + 0.543540i 0.182916π0.182916\pi
−0.839383 + 0.543540i 0.817084π0.817084\pi
198198 0 0
199199 18778.1i 0.474183i 0.971487 + 0.237092i 0.0761942π0.0761942\pi
−0.971487 + 0.237092i 0.923806π0.923806\pi
200200 0 0
201201 0 0
202202 0 0
203203 −67924.1 −1.64828
204204 0 0
205205 17455.2i 0.415353i
206206 0 0
207207 0 0
208208 0 0
209209 −624.000 −0.0142854
210210 0 0
211211 63704.8 1.43089 0.715447 0.698667i 0.246223π-0.246223\pi
0.715447 + 0.698667i 0.246223π0.246223\pi
212212 0 0
213213 0 0
214214 0 0
215215 61303.6i 1.32620i
216216 0 0
217217 68400.0 1.45257
218218 0 0
219219 0 0
220220 0 0
221221 20414.8i 0.417984i
222222 0 0
223223 − 19405.8i − 0.390231i −0.980780 0.195116i 0.937492π-0.937492\pi
0.980780 0.195116i 0.0625082π-0.0625082\pi
224224 0 0
225225 0 0
226226 0 0
227227 12089.7 0.234620 0.117310 0.993095i 0.462573π-0.462573\pi
0.117310 + 0.993095i 0.462573π0.462573\pi
228228 0 0
229229 91020.8i 1.73568i 0.496844 + 0.867840i 0.334492π0.334492\pi
−0.496844 + 0.867840i 0.665508π0.665508\pi
230230 0 0
231231 0 0
232232 0 0
233233 −45166.0 −0.831955 −0.415977 0.909375i 0.636560π-0.636560\pi
−0.415977 + 0.909375i 0.636560π0.636560\pi
234234 0 0
235235 66344.5 1.20135
236236 0 0
237237 0 0
238238 0 0
239239 − 12135.2i − 0.212447i −0.994342 0.106223i 0.966124π-0.966124\pi
0.994342 0.106223i 0.0338759π-0.0338759\pi
240240 0 0
241241 85822.0 1.47763 0.738813 0.673910i 0.235387π-0.235387\pi
0.738813 + 0.673910i 0.235387π0.235387\pi
242242 0 0
243243 0 0
244244 0 0
245245 10116.8i 0.168543i
246246 0 0
247247 − 418.454i − 0.00685889i
248248 0 0
249249 0 0
250250 0 0
251251 −58190.0 −0.923636 −0.461818 0.886975i 0.652803π-0.652803\pi
−0.461818 + 0.886975i 0.652803π0.652803\pi
252252 0 0
253253 − 65955.4i − 1.03041i
254254 0 0
255255 0 0
256256 0 0
257257 121726. 1.84297 0.921483 0.388420i 0.126979π-0.126979\pi
0.921483 + 0.388420i 0.126979π0.126979\pi
258258 0 0
259259 −12637.0 −0.188385
260260 0 0
261261 0 0
262262 0 0
263263 97918.3i 1.41564i 0.706394 + 0.707819i 0.250321π0.250321\pi
−0.706394 + 0.707819i 0.749679π0.749679\pi
264264 0 0
265265 73872.0 1.05193
266266 0 0
267267 0 0
268268 0 0
269269 14465.5i 0.199907i 0.994992 + 0.0999536i 0.0318694π0.0318694\pi
−0.994992 + 0.0999536i 0.968131π0.968131\pi
270270 0 0
271271 55497.5i 0.755675i 0.925872 + 0.377837i 0.123332π0.123332\pi
−0.925872 + 0.377837i 0.876668π0.876668\pi
272272 0 0
273273 0 0
274274 0 0
275275 −25849.1 −0.341807
276276 0 0
277277 102013.i 1.32953i 0.747053 + 0.664764i 0.231468π0.231468\pi
−0.747053 + 0.664764i 0.768532π0.768532\pi
278278 0 0
279279 0 0
280280 0 0
281281 40082.0 0.507618 0.253809 0.967254i 0.418317π-0.418317\pi
0.253809 + 0.967254i 0.418317π0.418317\pi
282282 0 0
283283 48324.2 0.603381 0.301691 0.953406i 0.402449π-0.402449\pi
0.301691 + 0.953406i 0.402449π0.402449\pi
284284 0 0
285285 0 0
286286 0 0
287287 − 30233.3i − 0.367047i
288288 0 0
289289 30723.0 0.367848
290290 0 0
291291 0 0
292292 0 0
293293 127592.i 1.48624i 0.669158 + 0.743120i 0.266655π0.266655\pi
−0.669158 + 0.743120i 0.733345π0.733345\pi
294294 0 0
295295 − 36196.3i − 0.415930i
296296 0 0
297297 0 0
298298 0 0
299299 44229.6 0.494733
300300 0 0
301301 − 106181.i − 1.17196i
302302 0 0
303303 0 0
304304 0 0
305305 193344. 2.07841
306306 0 0
307307 39788.7 0.422165 0.211083 0.977468i 0.432301π-0.432301\pi
0.211083 + 0.977468i 0.432301π0.432301\pi
308308 0 0
309309 0 0
310310 0 0
311311 − 174705.i − 1.80627i −0.429352 0.903137i 0.641258π-0.641258\pi
0.429352 0.903137i 0.358742π-0.358742\pi
312312 0 0
313313 26930.0 0.274883 0.137441 0.990510i 0.456112π-0.456112\pi
0.137441 + 0.990510i 0.456112π0.456112\pi
314314 0 0
315315 0 0
316316 0 0
317317 10841.6i 0.107888i 0.998544 + 0.0539440i 0.0171793π0.0171793\pi
−0.998544 + 0.0539440i 0.982821π0.982821\pi
318318 0 0
319319 116958.i 1.14934i
320320 0 0
321321 0 0
322322 0 0
323323 −2341.73 −0.0224457
324324 0 0
325325 − 17334.4i − 0.164113i
326326 0 0
327327 0 0
328328 0 0
329329 −114912. −1.06163
330330 0 0
331331 −127597. −1.16462 −0.582309 0.812968i 0.697851π-0.697851\pi
−0.582309 + 0.812968i 0.697851π0.697851\pi
332332 0 0
333333 0 0
334334 0 0
335335 249608.i 2.22417i
336336 0 0
337337 186482. 1.64201 0.821007 0.570917i 0.193412π-0.193412\pi
0.821007 + 0.570917i 0.193412π0.193412\pi
338338 0 0
339339 0 0
340340 0 0
341341 − 117777.i − 1.01287i
342342 0 0
343343 108066.i 0.918544i
344344 0 0
345345 0 0
346346 0 0
347347 49224.9 0.408814 0.204407 0.978886i 0.434473π-0.434473\pi
0.204407 + 0.978886i 0.434473π0.434473\pi
348348 0 0
349349 209825.i 1.72269i 0.508023 + 0.861343i 0.330376π0.330376\pi
−0.508023 + 0.861343i 0.669624π0.669624\pi
350350 0 0
351351 0 0
352352 0 0
353353 67486.0 0.541582 0.270791 0.962638i 0.412715π-0.412715\pi
0.270791 + 0.962638i 0.412715π0.412715\pi
354354 0 0
355355 −129530. −1.02781
356356 0 0
357357 0 0
358358 0 0
359359 − 116016.i − 0.900183i −0.892983 0.450091i 0.851391π-0.851391\pi
0.892983 0.450091i 0.148609π-0.148609\pi
360360 0 0
361361 −130273. −0.999632
362362 0 0
363363 0 0
364364 0 0
365365 − 263761.i − 1.97982i
366366 0 0
367367 − 77884.8i − 0.578257i −0.957290 0.289128i 0.906635π-0.906635\pi
0.957290 0.289128i 0.0933654π-0.0933654\pi
368368 0 0
369369 0 0
370370 0 0
371371 −127950. −0.929593
372372 0 0
373373 − 259835.i − 1.86758i −0.357816 0.933792i 0.616479π-0.616479\pi
0.357816 0.933792i 0.383521π-0.383521\pi
374374 0 0
375375 0 0
376376 0 0
377377 −78432.0 −0.551837
378378 0 0
379379 −116761. −0.812867 −0.406433 0.913680i 0.633228π-0.633228\pi
−0.406433 + 0.913680i 0.633228π0.633228\pi
380380 0 0
381381 0 0
382382 0 0
383383 − 158803.i − 1.08259i −0.840834 0.541293i 0.817935π-0.817935\pi
0.840834 0.541293i 0.182065π-0.182065\pi
384384 0 0
385385 142272. 0.959838
386386 0 0
387387 0 0
388388 0 0
389389 − 121673.i − 0.804073i −0.915624 0.402037i 0.868302π-0.868302\pi
0.915624 0.402037i 0.131698π-0.131698\pi
390390 0 0
391391 − 247516.i − 1.61901i
392392 0 0
393393 0 0
394394 0 0
395395 339621. 2.17671
396396 0 0
397397 − 237850.i − 1.50911i −0.656234 0.754557i 0.727852π-0.727852\pi
0.656234 0.754557i 0.272148π-0.272148\pi
398398 0 0
399399 0 0
400400 0 0
401401 58130.0 0.361503 0.180751 0.983529i 0.442147π-0.442147\pi
0.180751 + 0.983529i 0.442147π0.442147\pi
402402 0 0
403403 78981.5 0.486312
404404 0 0
405405 0 0
406406 0 0
407407 21759.6i 0.131360i
408408 0 0
409409 65186.0 0.389680 0.194840 0.980835i 0.437581π-0.437581\pi
0.194840 + 0.980835i 0.437581π0.437581\pi
410410 0 0
411411 0 0
412412 0 0
413413 62693.8i 0.367557i
414414 0 0
415415 − 398578.i − 2.31428i
416416 0 0
417417 0 0
418418 0 0
419419 267519. 1.52379 0.761897 0.647698i 0.224268π-0.224268\pi
0.761897 + 0.647698i 0.224268π0.224268\pi
420420 0 0
421421 263399.i 1.48610i 0.669233 + 0.743052i 0.266623π0.266623\pi
−0.669233 + 0.743052i 0.733377π0.733377\pi
422422 0 0
423423 0 0
424424 0 0
425425 −97006.0 −0.537057
426426 0 0
427427 −334882. −1.83669
428428 0 0
429429 0 0
430430 0 0
431431 105346.i 0.567104i 0.958957 + 0.283552i 0.0915129π0.0915129\pi
−0.958957 + 0.283552i 0.908487π0.908487\pi
432432 0 0
433433 83758.0 0.446736 0.223368 0.974734i 0.428295π-0.428295\pi
0.223368 + 0.974734i 0.428295π0.428295\pi
434434 0 0
435435 0 0
436436 0 0
437437 5073.49i 0.0265671i
438438 0 0
439439 95983.0i 0.498041i 0.968498 + 0.249020i 0.0801087π0.0801087\pi
−0.968498 + 0.249020i 0.919891π0.919891\pi
440440 0 0
441441 0 0
442442 0 0
443443 222679. 1.13468 0.567339 0.823484i 0.307973π-0.307973\pi
0.567339 + 0.823484i 0.307973π0.307973\pi
444444 0 0
445445 27481.4i 0.138777i
446446 0 0
447447 0 0
448448 0 0
449449 88658.0 0.439770 0.219885 0.975526i 0.429432π-0.429432\pi
0.219885 + 0.975526i 0.429432π0.429432\pi
450450 0 0
451451 −52058.5 −0.255940
452452 0 0
453453 0 0
454454 0 0
455455 95407.6i 0.460851i
456456 0 0
457457 −29086.0 −0.139268 −0.0696340 0.997573i 0.522183π-0.522183\pi
−0.0696340 + 0.997573i 0.522183π0.522183\pi
458458 0 0
459459 0 0
460460 0 0
461461 277139.i 1.30406i 0.758195 + 0.652028i 0.226082π0.226082\pi
−0.758195 + 0.652028i 0.773918π0.773918\pi
462462 0 0
463463 279371.i 1.30322i 0.758553 + 0.651611i 0.225907π0.225907\pi
−0.758553 + 0.651611i 0.774093π0.774093\pi
464464 0 0
465465 0 0
466466 0 0
467467 −254702. −1.16788 −0.583939 0.811797i 0.698489π-0.698489\pi
−0.583939 + 0.811797i 0.698489π0.698489\pi
468468 0 0
469469 − 432334.i − 1.96550i
470470 0 0
471471 0 0
472472 0 0
473473 −182832. −0.817203
474474 0 0
475475 1988.39 0.00881283
476476 0 0
477477 0 0
478478 0 0
479479 − 52620.6i − 0.229343i −0.993403 0.114671i 0.963418π-0.963418\pi
0.993403 0.114671i 0.0365815π-0.0365815\pi
480480 0 0
481481 −14592.0 −0.0630703
482482 0 0
483483 0 0
484484 0 0
485485 − 163741.i − 0.696103i
486486 0 0
487487 147557.i 0.622162i 0.950383 + 0.311081i 0.100691π0.100691\pi
−0.950383 + 0.311081i 0.899309π0.899309\pi
488488 0 0
489489 0 0
490490 0 0
491491 78240.2 0.324539 0.162270 0.986746i 0.448119π-0.448119\pi
0.162270 + 0.986746i 0.448119π0.448119\pi
492492 0 0
493493 438917.i 1.80588i
494494 0 0
495495 0 0
496496 0 0
497497 224352. 0.908275
498498 0 0
499499 298044. 1.19696 0.598480 0.801138i 0.295771π-0.295771\pi
0.598480 + 0.801138i 0.295771π0.295771\pi
500500 0 0
501501 0 0
502502 0 0
503503 132964.i 0.525530i 0.964860 + 0.262765i 0.0846344π0.0846344\pi
−0.964860 + 0.262765i 0.915366π0.915366\pi
504504 0 0
505505 −331056. −1.29813
506506 0 0
507507 0 0
508508 0 0
509509 12411.9i 0.0479075i 0.999713 + 0.0239538i 0.00762545π0.00762545\pi
−0.999713 + 0.0239538i 0.992375π0.992375\pi
510510 0 0
511511 456847.i 1.74956i
512512 0 0
513513 0 0
514514 0 0
515515 162702. 0.613449
516516 0 0
517517 197866.i 0.740270i
518518 0 0
519519 0 0
520520 0 0
521521 −170018. −0.626353 −0.313177 0.949695i 0.601393π-0.601393\pi
−0.313177 + 0.949695i 0.601393π0.601393\pi
522522 0 0
523523 −401621. −1.46829 −0.734147 0.678991i 0.762418π-0.762418\pi
−0.734147 + 0.678991i 0.762418π0.762418\pi
524524 0 0
525525 0 0
526526 0 0
527527 − 441992.i − 1.59145i
528528 0 0
529529 −256415. −0.916288
530530 0 0
531531 0 0
532532 0 0
533533 − 34910.4i − 0.122886i
534534 0 0
535535 − 194372.i − 0.679088i
536536 0 0
537537 0 0
538538 0 0
539539 −30172.3 −0.103856
540540 0 0
541541 138857.i 0.474430i 0.971457 + 0.237215i 0.0762345π0.0762345\pi
−0.971457 + 0.237215i 0.923765π0.923765\pi
542542 0 0
543543 0 0
544544 0 0
545545 −1824.00 −0.00614090
546546 0 0
547547 99094.1 0.331187 0.165593 0.986194i 0.447046π-0.447046\pi
0.165593 + 0.986194i 0.447046π0.447046\pi
548548 0 0
549549 0 0
550550 0 0
551551 − 8996.77i − 0.0296335i
552552 0 0
553553 −588240. −1.92355
554554 0 0
555555 0 0
556556 0 0
557557 199104.i 0.641756i 0.947120 + 0.320878i 0.103978π0.103978\pi
−0.947120 + 0.320878i 0.896022π0.896022\pi
558558 0 0
559559 − 122607.i − 0.392367i
560560 0 0
561561 0 0
562562 0 0
563563 −572457. −1.80603 −0.903017 0.429605i 0.858653π-0.858653\pi
−0.903017 + 0.429605i 0.858653π0.858653\pi
564564 0 0
565565 − 95611.1i − 0.299510i
566566 0 0
567567 0 0
568568 0 0
569569 −563330. −1.73996 −0.869978 0.493090i 0.835867π-0.835867\pi
−0.869978 + 0.493090i 0.835867π0.835867\pi
570570 0 0
571571 113117. 0.346940 0.173470 0.984839i 0.444502π-0.444502\pi
0.173470 + 0.984839i 0.444502π0.444502\pi
572572 0 0
573573 0 0
574574 0 0
575575 210169.i 0.635671i
576576 0 0
577577 155858. 0.468142 0.234071 0.972220i 0.424795π-0.424795\pi
0.234071 + 0.972220i 0.424795π0.424795\pi
578578 0 0
579579 0 0
580580 0 0
581581 690357.i 2.04513i
582582 0 0
583583 220316.i 0.648200i
584584 0 0
585585 0 0
586586 0 0
587587 −270914. −0.786239 −0.393119 0.919487i 0.628604π-0.628604\pi
−0.393119 + 0.919487i 0.628604π0.628604\pi
588588 0 0
589589 9059.80i 0.0261149i
590590 0 0
591591 0 0
592592 0 0
593593 418078. 1.18891 0.594454 0.804130i 0.297368π-0.297368\pi
0.594454 + 0.804130i 0.297368π0.297368\pi
594594 0 0
595595 533915. 1.50813
596596 0 0
597597 0 0
598598 0 0
599599 539701.i 1.50418i 0.659060 + 0.752090i 0.270954π0.270954\pi
−0.659060 + 0.752090i 0.729046π0.729046\pi
600600 0 0
601601 −439490. −1.21675 −0.608373 0.793651i 0.708178π-0.708178\pi
−0.608373 + 0.793651i 0.708178π0.708178\pi
602602 0 0
603603 0 0
604604 0 0
605605 197171.i 0.538683i
606606 0 0
607607 − 256879.i − 0.697189i −0.937274 0.348595i 0.886659π-0.886659\pi
0.937274 0.348595i 0.113341π-0.113341\pi
608608 0 0
609609 0 0
610610 0 0
611611 −132689. −0.355429
612612 0 0
613613 − 222871.i − 0.593107i −0.955016 0.296553i 0.904163π-0.904163\pi
0.955016 0.296553i 0.0958373π-0.0958373\pi
614614 0 0
615615 0 0
616616 0 0
617617 −588718. −1.54645 −0.773227 0.634129i 0.781359π-0.781359\pi
−0.773227 + 0.634129i 0.781359π0.781359\pi
618618 0 0
619619 417570. 1.08980 0.544901 0.838500i 0.316567π-0.316567\pi
0.544901 + 0.838500i 0.316567π0.316567\pi
620620 0 0
621621 0 0
622622 0 0
623623 − 47599.2i − 0.122638i
624624 0 0
625625 −487631. −1.24834
626626 0 0
627627 0 0
628628 0 0
629629 81659.0i 0.206397i
630630 0 0
631631 204467.i 0.513529i 0.966474 + 0.256765i 0.0826565π0.0826565\pi
−0.966474 + 0.256765i 0.917344π0.917344\pi
632632 0 0
633633 0 0
634634 0 0
635635 −390169. −0.967620
636636 0 0
637637 − 20233.6i − 0.0498647i
638638 0 0
639639 0 0
640640 0 0
641641 270578. 0.658531 0.329266 0.944237i 0.393199π-0.393199\pi
0.329266 + 0.944237i 0.393199π0.393199\pi
642642 0 0
643643 −584969. −1.41485 −0.707426 0.706788i 0.750144π-0.750144\pi
−0.707426 + 0.706788i 0.750144π0.750144\pi
644644 0 0
645645 0 0
646646 0 0
647647 − 96976.8i − 0.231664i −0.993269 0.115832i 0.963047π-0.963047\pi
0.993269 0.115832i 0.0369535π-0.0369535\pi
648648 0 0
649649 107952. 0.256296
650650 0 0
651651 0 0
652652 0 0
653653 − 532082.i − 1.24782i −0.781496 0.623911i 0.785543π-0.785543\pi
0.781496 0.623911i 0.214457π-0.214457\pi
654654 0 0
655655 − 684800.i − 1.59618i
656656 0 0
657657 0 0
658658 0 0
659659 −253593. −0.583938 −0.291969 0.956428i 0.594310π-0.594310\pi
−0.291969 + 0.956428i 0.594310π0.594310\pi
660660 0 0
661661 339441.i 0.776892i 0.921471 + 0.388446i 0.126988π0.126988\pi
−0.921471 + 0.388446i 0.873012π0.873012\pi
662662 0 0
663663 0 0
664664 0 0
665665 −10944.0 −0.0247476
666666 0 0
667667 950937. 2.13747
668668 0 0
669669 0 0
670670 0 0
671671 576630.i 1.28071i
672672 0 0
673673 −191570. −0.422958 −0.211479 0.977383i 0.567828π-0.567828\pi
−0.211479 + 0.977383i 0.567828π0.567828\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 498923.i − 1.08857i −0.838900 0.544285i 0.816801π-0.816801\pi
0.838900 0.544285i 0.183199π-0.183199\pi
678678 0 0
679679 283607.i 0.615146i
680680 0 0
681681 0 0
682682 0 0
683683 96059.5 0.205920 0.102960 0.994685i 0.467169π-0.467169\pi
0.102960 + 0.994685i 0.467169π0.467169\pi
684684 0 0
685685 − 469600.i − 1.00080i
686686 0 0
687687 0 0
688688 0 0
689689 −147744. −0.311223
690690 0 0
691691 517474. 1.08376 0.541880 0.840456i 0.317713π-0.317713\pi
0.541880 + 0.840456i 0.317713π0.317713\pi
692692 0 0
693693 0 0
694694 0 0
695695 − 951356.i − 1.96958i
696696 0 0
697697 −195364. −0.402142
698698 0 0
699699 0 0
700700 0 0
701701 − 214204.i − 0.435904i −0.975959 0.217952i 0.930062π-0.930062\pi
0.975959 0.217952i 0.0699377π-0.0699377\pi
702702 0 0
703703 − 1673.82i − 0.00338686i
704704 0 0
705705 0 0
706706 0 0
707707 573406. 1.14716
708708 0 0
709709 413550.i 0.822688i 0.911480 + 0.411344i 0.134941π0.134941\pi
−0.911480 + 0.411344i 0.865059π0.865059\pi
710710 0 0
711711 0 0
712712 0 0
713713 −957600. −1.88367
714714 0 0
715715 164282. 0.321349
716716 0 0
717717 0 0
718718 0 0
719719 − 734073.i − 1.41998i −0.704213 0.709989i 0.748700π-0.748700\pi
0.704213 0.709989i 0.251300π-0.251300\pi
720720 0 0
721721 −281808. −0.542104
722722 0 0
723723 0 0
724724 0 0
725725 − 372690.i − 0.709042i
726726 0 0
727727 − 1.03479e6i − 1.95786i −0.204199 0.978929i 0.565459π-0.565459\pi
0.204199 0.978929i 0.434541π-0.434541\pi
728728 0 0
729729 0 0
730730 0 0
731731 −686128. −1.28402
732732 0 0
733733 − 200222.i − 0.372652i −0.982488 0.186326i 0.940342π-0.940342\pi
0.982488 0.186326i 0.0596580π-0.0596580\pi
734734 0 0
735735 0 0
736736 0 0
737737 −744432. −1.37053
738738 0 0
739739 −526855. −0.964722 −0.482361 0.875972i 0.660221π-0.660221\pi
−0.482361 + 0.875972i 0.660221π0.660221\pi
740740 0 0
741741 0 0
742742 0 0
743743 − 380375.i − 0.689024i −0.938782 0.344512i 0.888044π-0.888044\pi
0.938782 0.344512i 0.111956π-0.111956\pi
744744 0 0
745745 −683088. −1.23073
746746 0 0
747747 0 0
748748 0 0
749749 336662.i 0.600110i
750750 0 0
751751 591851.i 1.04938i 0.851293 + 0.524690i 0.175819π0.175819\pi
−0.851293 + 0.524690i 0.824181π0.824181\pi
752752 0 0
753753 0 0
754754 0 0
755755 −232206. −0.407360
756756 0 0
757757 373445.i 0.651681i 0.945425 + 0.325840i 0.105647π0.105647\pi
−0.945425 + 0.325840i 0.894353π0.894353\pi
758758 0 0
759759 0 0
760760 0 0
761761 −37154.0 −0.0641558 −0.0320779 0.999485i 0.510212π-0.510212\pi
−0.0320779 + 0.999485i 0.510212π0.510212\pi
762762 0 0
763763 3159.26 0.00542671
764764 0 0
765765 0 0
766766 0 0
767767 72392.6i 0.123056i
768768 0 0
769769 −455330. −0.769970 −0.384985 0.922923i 0.625793π-0.625793\pi
−0.384985 + 0.922923i 0.625793π0.625793\pi
770770 0 0
771771 0 0
772772 0 0
773773 57046.5i 0.0954708i 0.998860 + 0.0477354i 0.0152004π0.0152004\pi
−0.998860 + 0.0477354i 0.984800π0.984800\pi
774774 0 0
775775 375301.i 0.624851i
776776 0 0
777777 0 0
778778 0 0
779779 4004.50 0.00659893
780780 0 0
781781 − 386310.i − 0.633335i
782782 0 0
783783 0 0
784784 0 0
785785 36480.0 0.0591992
786786 0 0
787787 99953.2 0.161379 0.0806895 0.996739i 0.474288π-0.474288\pi
0.0806895 + 0.996739i 0.474288π0.474288\pi
788788 0 0
789789 0 0
790790 0 0
791791 165603.i 0.264677i
792792 0 0
793793 −386688. −0.614914
794794 0 0
795795 0 0
796796 0 0
797797 − 517345.i − 0.814448i −0.913328 0.407224i 0.866497π-0.866497\pi
0.913328 0.407224i 0.133503π-0.133503\pi
798798 0 0
799799 742547.i 1.16314i
800800 0 0
801801 0 0
802802 0 0
803803 786642. 1.21996
804804 0 0
805805 − 1.15676e6i − 1.78505i
806806 0 0
807807 0 0
808808 0 0
809809 570046. 0.870989 0.435495 0.900191i 0.356573π-0.356573\pi
0.435495 + 0.900191i 0.356573π0.356573\pi
810810 0 0
811811 174418. 0.265185 0.132592 0.991171i 0.457670π-0.457670\pi
0.132592 + 0.991171i 0.457670π0.457670\pi
812812 0 0
813813 0 0
814814 0 0
815815 807826.i 1.21619i
816816 0 0
817817 14064.0 0.0210700
818818 0 0
819819 0 0
820820 0 0
821821 − 438827.i − 0.651038i −0.945535 0.325519i 0.894461π-0.894461\pi
0.945535 0.325519i 0.105539π-0.105539\pi
822822 0 0
823823 − 608380.i − 0.898205i −0.893480 0.449102i 0.851744π-0.851744\pi
0.893480 0.449102i 0.148256π-0.148256\pi
824824 0 0
825825 0 0
826826 0 0
827827 −727898. −1.06429 −0.532144 0.846654i 0.678614π-0.678614\pi
−0.532144 + 0.846654i 0.678614π0.678614\pi
828828 0 0
829829 − 619509.i − 0.901444i −0.892664 0.450722i 0.851167π-0.851167\pi
0.892664 0.450722i 0.148833π-0.148833\pi
830830 0 0
831831 0 0
832832 0 0
833833 −113230. −0.163182
834834 0 0
835835 −1.35848e6 −1.94841
836836 0 0
837837 0 0
838838 0 0
839839 1.10064e6i 1.56358i 0.623539 + 0.781792i 0.285694π0.285694\pi
−0.623539 + 0.781792i 0.714306π0.714306\pi
840840 0 0
841841 −979007. −1.38418
842842 0 0
843843 0 0
844844 0 0
845845 − 752356.i − 1.05368i
846846 0 0
847847 − 341511.i − 0.476034i
848848 0 0
849849 0 0
850850 0 0
851851 176919. 0.244295
852852 0 0
853853 634911.i 0.872599i 0.899802 + 0.436299i 0.143711π0.143711\pi
−0.899802 + 0.436299i 0.856289π0.856289\pi
854854 0 0
855855 0 0
856856 0 0
857857 405310. 0.551856 0.275928 0.961178i 0.411015π-0.411015\pi
0.275928 + 0.961178i 0.411015π0.411015\pi
858858 0 0
859859 100230. 0.135835 0.0679177 0.997691i 0.478364π-0.478364\pi
0.0679177 + 0.997691i 0.478364π0.478364\pi
860860 0 0
861861 0 0
862862 0 0
863863 317816.i 0.426731i 0.976972 + 0.213366i 0.0684425π0.0684425\pi
−0.976972 + 0.213366i 0.931557π0.931557\pi
864864 0 0
865865 −126768. −0.169425
866866 0 0
867867 0 0
868868 0 0
869869 1.01289e6i 1.34128i
870870 0 0
871871 − 499216.i − 0.658040i
872872 0 0
873873 0 0
874874 0 0
875875 533915. 0.697358
876876 0 0
877877 323133.i 0.420128i 0.977688 + 0.210064i 0.0673673π0.0673673\pi
−0.977688 + 0.210064i 0.932633π0.932633\pi
878878 0 0
879879 0 0
880880 0 0
881881 1.10419e6 1.42263 0.711315 0.702873i 0.248100π-0.248100\pi
0.711315 + 0.702873i 0.248100π0.248100\pi
882882 0 0
883883 −813877. −1.04385 −0.521924 0.852992i 0.674786π-0.674786\pi
−0.521924 + 0.852992i 0.674786π0.674786\pi
884884 0 0
885885 0 0
886886 0 0
887887 221781.i 0.281888i 0.990018 + 0.140944i 0.0450138π0.0450138\pi
−0.990018 + 0.140944i 0.954986π0.954986\pi
888888 0 0
889889 675792. 0.855085
890890 0 0
891891 0 0
892892 0 0
893893 − 15220.5i − 0.0190864i
894894 0 0
895895 377237.i 0.470942i
896896 0 0
897897 0 0
898898 0 0
899899 1.69810e6 2.10109
900900 0 0
901901 826797.i 1.01847i
902902 0 0
903903 0 0
904904 0 0
905905 −1.14365e6 −1.39635
906906 0 0
907907 −577071. −0.701479 −0.350739 0.936473i 0.614070π-0.614070\pi
−0.350739 + 0.936473i 0.614070π0.614070\pi
908908 0 0
909909 0 0
910910 0 0
911911 − 922692.i − 1.11178i −0.831255 0.555891i 0.812377π-0.812377\pi
0.831255 0.555891i 0.187623π-0.187623\pi
912912 0 0
913913 1.18872e6 1.42606
914914 0 0
915915 0 0
916916 0 0
917917 1.18611e6i 1.41054i
918918 0 0
919919 1.47845e6i 1.75056i 0.483620 + 0.875278i 0.339322π0.339322\pi
−0.483620 + 0.875278i 0.660678π0.660678\pi
920920 0 0
921921 0 0
922922 0 0
923923 259059. 0.304086
924924 0 0
925925 − 69337.7i − 0.0810375i
926926 0 0
927927 0 0
928928 0 0
929929 −241006. −0.279252 −0.139626 0.990204i 0.544590π-0.544590\pi
−0.139626 + 0.990204i 0.544590π0.544590\pi
930930 0 0
931931 2320.95 0.00267773
932932 0 0
933933 0 0
934934 0 0
935935 − 919344.i − 1.05161i
936936 0 0
937937 −931058. −1.06047 −0.530234 0.847851i 0.677896π-0.677896\pi
−0.530234 + 0.847851i 0.677896π0.677896\pi
938938 0 0
939939 0 0
940940 0 0
941941 245490.i 0.277240i 0.990346 + 0.138620i 0.0442666π0.0442666\pi
−0.990346 + 0.138620i 0.955733π0.955733\pi
942942 0 0
943943 423267.i 0.475982i
944944 0 0
945945 0 0
946946 0 0
947947 207853. 0.231770 0.115885 0.993263i 0.463030π-0.463030\pi
0.115885 + 0.993263i 0.463030π0.463030\pi
948948 0 0
949949 527522.i 0.585744i
950950 0 0
951951 0 0
952952 0 0
953953 1.23446e6 1.35923 0.679613 0.733570i 0.262148π-0.262148\pi
0.679613 + 0.733570i 0.262148π0.262148\pi
954954 0 0
955955 −992008. −1.08770
956956 0 0
957957 0 0
958958 0 0
959959 813371.i 0.884405i
960960 0 0
961961 −786479. −0.851609
962962 0 0
963963 0 0
964964 0 0
965965 − 1.35384e6i − 1.45382i
966966 0 0
967967 − 181034.i − 0.193601i −0.995304 0.0968003i 0.969139π-0.969139\pi
0.995304 0.0968003i 0.0308608π-0.0308608\pi
968968 0 0
969969 0 0
970970 0 0
971971 −97708.5 −0.103632 −0.0518160 0.998657i 0.516501π-0.516501\pi
−0.0518160 + 0.998657i 0.516501π0.516501\pi
972972 0 0
973973 1.64780e6i 1.74052i
974974 0 0
975975 0 0
976976 0 0
977977 −1.67313e6 −1.75284 −0.876419 0.481550i 0.840074π-0.840074\pi
−0.876419 + 0.481550i 0.840074π0.840074\pi
978978 0 0
979979 −81960.6 −0.0855145
980980 0 0
981981 0 0
982982 0 0
983983 − 1.03358e6i − 1.06964i −0.844966 0.534820i 0.820379π-0.820379\pi
0.844966 0.534820i 0.179621π-0.179621\pi
984984 0 0
985985 1.27406e6 1.31316
986986 0 0
987987 0 0
988988 0 0
989989 1.48653e6i 1.51978i
990990 0 0
991991 − 907889.i − 0.924454i −0.886762 0.462227i 0.847050π-0.847050\pi
0.886762 0.462227i 0.152950π-0.152950\pi
992992 0 0
993993 0 0
994994 0 0
995995 567087. 0.572801
996996 0 0
997997 − 1.47844e6i − 1.48735i −0.668542 0.743675i 0.733081π-0.733081\pi
0.668542 0.743675i 0.266919π-0.266919\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1152.5.b.j.703.2 4
3.2 odd 2 384.5.b.a.319.4 yes 4
4.3 odd 2 inner 1152.5.b.j.703.1 4
8.3 odd 2 inner 1152.5.b.j.703.3 4
8.5 even 2 inner 1152.5.b.j.703.4 4
12.11 even 2 384.5.b.a.319.2 yes 4
24.5 odd 2 384.5.b.a.319.1 4
24.11 even 2 384.5.b.a.319.3 yes 4
48.5 odd 4 768.5.g.d.511.1 4
48.11 even 4 768.5.g.d.511.3 4
48.29 odd 4 768.5.g.d.511.4 4
48.35 even 4 768.5.g.d.511.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
384.5.b.a.319.1 4 24.5 odd 2
384.5.b.a.319.2 yes 4 12.11 even 2
384.5.b.a.319.3 yes 4 24.11 even 2
384.5.b.a.319.4 yes 4 3.2 odd 2
768.5.g.d.511.1 4 48.5 odd 4
768.5.g.d.511.2 4 48.35 even 4
768.5.g.d.511.3 4 48.11 even 4
768.5.g.d.511.4 4 48.29 odd 4
1152.5.b.j.703.1 4 4.3 odd 2 inner
1152.5.b.j.703.2 4 1.1 even 1 trivial
1152.5.b.j.703.3 4 8.3 odd 2 inner
1152.5.b.j.703.4 4 8.5 even 2 inner