Properties

Label 2592.2.d.g.1297.4
Level 25922592
Weight 22
Character 2592.1297
Analytic conductor 20.69720.697
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2592,2,Mod(1297,2592)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2592.1297"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2592, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 2592=2534 2592 = 2^{5} \cdot 3^{4}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2592.d (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,-8] 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: 20.697224203920.6972242039
Analytic rank: 00
Dimension: 44
Coefficient field: Q(ζ12)\Q(\zeta_{12})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 648)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1297.4
Root 0.866025+0.500000i0.866025 + 0.500000i of defining polynomial
Character χ\chi == 2592.1297
Dual form 2592.2.d.g.1297.1

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) == q+3.73205iq5+0.732051q74.73205iq11+2.46410iq133.73205q17+3.26795iq198.73205q238.92820q255.19615iq292.00000q31+2.73205iq35+5.00000iq37+4.53590q41+9.66025iq433.46410q476.46410q490.928203iq53+17.6603q558.39230iq599.00000iq619.19615q65+4.73205iq675.66025q71+9.00000q733.46410iq775.26795q79+14.0000iq8313.9282iq8511.7321q89+1.80385iq9112.1962q958.00000q97+O(q100)q+3.73205i q^{5} +0.732051 q^{7} -4.73205i q^{11} +2.46410i q^{13} -3.73205 q^{17} +3.26795i q^{19} -8.73205 q^{23} -8.92820 q^{25} -5.19615i q^{29} -2.00000 q^{31} +2.73205i q^{35} +5.00000i q^{37} +4.53590 q^{41} +9.66025i q^{43} -3.46410 q^{47} -6.46410 q^{49} -0.928203i q^{53} +17.6603 q^{55} -8.39230i q^{59} -9.00000i q^{61} -9.19615 q^{65} +4.73205i q^{67} -5.66025 q^{71} +9.00000 q^{73} -3.46410i q^{77} -5.26795 q^{79} +14.0000i q^{83} -13.9282i q^{85} -11.7321 q^{89} +1.80385i q^{91} -12.1962 q^{95} -8.00000 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q78q1728q238q258q31+32q4112q49+36q5516q65+12q71+36q7328q7940q8928q9532q97+O(q100) 4 q - 4 q^{7} - 8 q^{17} - 28 q^{23} - 8 q^{25} - 8 q^{31} + 32 q^{41} - 12 q^{49} + 36 q^{55} - 16 q^{65} + 12 q^{71} + 36 q^{73} - 28 q^{79} - 40 q^{89} - 28 q^{95} - 32 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2592Z)×\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times.

nn 325325 12171217 24312431
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 3.73205i 1.66902i 0.550990 + 0.834512i 0.314250π0.314250\pi
−0.550990 + 0.834512i 0.685750π0.685750\pi
66 0 0
77 0.732051 0.276689 0.138345 0.990384i 0.455822π-0.455822\pi
0.138345 + 0.990384i 0.455822π0.455822\pi
88 0 0
99 0 0
1010 0 0
1111 − 4.73205i − 1.42677i −0.700774 0.713384i 0.747162π-0.747162\pi
0.700774 0.713384i 0.252838π-0.252838\pi
1212 0 0
1313 2.46410i 0.683419i 0.939806 + 0.341709i 0.111006π0.111006\pi
−0.939806 + 0.341709i 0.888994π0.888994\pi
1414 0 0
1515 0 0
1616 0 0
1717 −3.73205 −0.905155 −0.452578 0.891725i 0.649495π-0.649495\pi
−0.452578 + 0.891725i 0.649495π0.649495\pi
1818 0 0
1919 3.26795i 0.749719i 0.927082 + 0.374859i 0.122309π0.122309\pi
−0.927082 + 0.374859i 0.877691π0.877691\pi
2020 0 0
2121 0 0
2222 0 0
2323 −8.73205 −1.82076 −0.910379 0.413775i 0.864210π-0.864210\pi
−0.910379 + 0.413775i 0.864210π0.864210\pi
2424 0 0
2525 −8.92820 −1.78564
2626 0 0
2727 0 0
2828 0 0
2929 − 5.19615i − 0.964901i −0.875923 0.482451i 0.839747π-0.839747\pi
0.875923 0.482451i 0.160253π-0.160253\pi
3030 0 0
3131 −2.00000 −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 2.73205i 0.461801i
3636 0 0
3737 5.00000i 0.821995i 0.911636 + 0.410997i 0.134819π0.134819\pi
−0.911636 + 0.410997i 0.865181π0.865181\pi
3838 0 0
3939 0 0
4040 0 0
4141 4.53590 0.708388 0.354194 0.935172i 0.384755π-0.384755\pi
0.354194 + 0.935172i 0.384755π0.384755\pi
4242 0 0
4343 9.66025i 1.47317i 0.676342 + 0.736587i 0.263564π0.263564\pi
−0.676342 + 0.736587i 0.736436π0.736436\pi
4444 0 0
4545 0 0
4646 0 0
4747 −3.46410 −0.505291 −0.252646 0.967559i 0.581301π-0.581301\pi
−0.252646 + 0.967559i 0.581301π0.581301\pi
4848 0 0
4949 −6.46410 −0.923443
5050 0 0
5151 0 0
5252 0 0
5353 − 0.928203i − 0.127499i −0.997966 0.0637493i 0.979694π-0.979694\pi
0.997966 0.0637493i 0.0203058π-0.0203058\pi
5454 0 0
5555 17.6603 2.38131
5656 0 0
5757 0 0
5858 0 0
5959 − 8.39230i − 1.09259i −0.837594 0.546293i 0.816039π-0.816039\pi
0.837594 0.546293i 0.183961π-0.183961\pi
6060 0 0
6161 − 9.00000i − 1.15233i −0.817333 0.576166i 0.804548π-0.804548\pi
0.817333 0.576166i 0.195452π-0.195452\pi
6262 0 0
6363 0 0
6464 0 0
6565 −9.19615 −1.14064
6666 0 0
6767 4.73205i 0.578112i 0.957312 + 0.289056i 0.0933414π0.0933414\pi
−0.957312 + 0.289056i 0.906659π0.906659\pi
6868 0 0
6969 0 0
7070 0 0
7171 −5.66025 −0.671749 −0.335874 0.941907i 0.609032π-0.609032\pi
−0.335874 + 0.941907i 0.609032π0.609032\pi
7272 0 0
7373 9.00000 1.05337 0.526685 0.850060i 0.323435π-0.323435\pi
0.526685 + 0.850060i 0.323435π0.323435\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 3.46410i − 0.394771i
7878 0 0
7979 −5.26795 −0.592691 −0.296345 0.955081i 0.595768π-0.595768\pi
−0.296345 + 0.955081i 0.595768π0.595768\pi
8080 0 0
8181 0 0
8282 0 0
8383 14.0000i 1.53670i 0.640030 + 0.768350i 0.278922π0.278922\pi
−0.640030 + 0.768350i 0.721078π0.721078\pi
8484 0 0
8585 − 13.9282i − 1.51073i
8686 0 0
8787 0 0
8888 0 0
8989 −11.7321 −1.24359 −0.621797 0.783178i 0.713597π-0.713597\pi
−0.621797 + 0.783178i 0.713597π0.713597\pi
9090 0 0
9191 1.80385i 0.189095i
9292 0 0
9393 0 0
9494 0 0
9595 −12.1962 −1.25130
9696 0 0
9797 −8.00000 −0.812277 −0.406138 0.913812i 0.633125π-0.633125\pi
−0.406138 + 0.913812i 0.633125π0.633125\pi
9898 0 0
9999 0 0
100100 0 0
101101 8.00000i 0.796030i 0.917379 + 0.398015i 0.130301π0.130301\pi
−0.917379 + 0.398015i 0.869699π0.869699\pi
102102 0 0
103103 3.46410 0.341328 0.170664 0.985329i 0.445409π-0.445409\pi
0.170664 + 0.985329i 0.445409π0.445409\pi
104104 0 0
105105 0 0
106106 0 0
107107 − 10.3923i − 1.00466i −0.864675 0.502331i 0.832476π-0.832476\pi
0.864675 0.502331i 0.167524π-0.167524\pi
108108 0 0
109109 − 12.8564i − 1.23142i −0.787973 0.615710i 0.788869π-0.788869\pi
0.787973 0.615710i 0.211131π-0.211131\pi
110110 0 0
111111 0 0
112112 0 0
113113 −7.73205 −0.727370 −0.363685 0.931522i 0.618482π-0.618482\pi
−0.363685 + 0.931522i 0.618482π0.618482\pi
114114 0 0
115115 − 32.5885i − 3.03889i
116116 0 0
117117 0 0
118118 0 0
119119 −2.73205 −0.250447
120120 0 0
121121 −11.3923 −1.03566
122122 0 0
123123 0 0
124124 0 0
125125 − 14.6603i − 1.31125i
126126 0 0
127127 13.6603 1.21215 0.606076 0.795407i 0.292743π-0.292743\pi
0.606076 + 0.795407i 0.292743π0.292743\pi
128128 0 0
129129 0 0
130130 0 0
131131 − 0.196152i − 0.0171379i −0.999963 0.00856896i 0.997272π-0.997272\pi
0.999963 0.00856896i 0.00272762π-0.00272762\pi
132132 0 0
133133 2.39230i 0.207439i
134134 0 0
135135 0 0
136136 0 0
137137 −17.1962 −1.46917 −0.734583 0.678519i 0.762622π-0.762622\pi
−0.734583 + 0.678519i 0.762622π0.762622\pi
138138 0 0
139139 − 19.4641i − 1.65092i −0.564458 0.825462i 0.690915π-0.690915\pi
0.564458 0.825462i 0.309085π-0.309085\pi
140140 0 0
141141 0 0
142142 0 0
143143 11.6603 0.975079
144144 0 0
145145 19.3923 1.61044
146146 0 0
147147 0 0
148148 0 0
149149 − 5.19615i − 0.425685i −0.977086 0.212843i 0.931728π-0.931728\pi
0.977086 0.212843i 0.0682722π-0.0682722\pi
150150 0 0
151151 −13.8564 −1.12762 −0.563809 0.825905i 0.690665π-0.690665\pi
−0.563809 + 0.825905i 0.690665π0.690665\pi
152152 0 0
153153 0 0
154154 0 0
155155 − 7.46410i − 0.599531i
156156 0 0
157157 2.46410i 0.196657i 0.995154 + 0.0983284i 0.0313495π0.0313495\pi
−0.995154 + 0.0983284i 0.968650π0.968650\pi
158158 0 0
159159 0 0
160160 0 0
161161 −6.39230 −0.503784
162162 0 0
163163 6.53590i 0.511931i 0.966686 + 0.255966i 0.0823934π0.0823934\pi
−0.966686 + 0.255966i 0.917607π0.917607\pi
164164 0 0
165165 0 0
166166 0 0
167167 14.7321 1.14000 0.570000 0.821645i 0.306943π-0.306943\pi
0.570000 + 0.821645i 0.306943π0.306943\pi
168168 0 0
169169 6.92820 0.532939
170170 0 0
171171 0 0
172172 0 0
173173 1.73205i 0.131685i 0.997830 + 0.0658427i 0.0209736π0.0209736\pi
−0.997830 + 0.0658427i 0.979026π0.979026\pi
174174 0 0
175175 −6.53590 −0.494067
176176 0 0
177177 0 0
178178 0 0
179179 14.0000i 1.04641i 0.852207 + 0.523205i 0.175264π0.175264\pi
−0.852207 + 0.523205i 0.824736π0.824736\pi
180180 0 0
181181 6.53590i 0.485810i 0.970050 + 0.242905i 0.0781002π0.0781002\pi
−0.970050 + 0.242905i 0.921900π0.921900\pi
182182 0 0
183183 0 0
184184 0 0
185185 −18.6603 −1.37193
186186 0 0
187187 17.6603i 1.29145i
188188 0 0
189189 0 0
190190 0 0
191191 −16.5885 −1.20030 −0.600149 0.799888i 0.704892π-0.704892\pi
−0.600149 + 0.799888i 0.704892π0.704892\pi
192192 0 0
193193 10.8564 0.781461 0.390731 0.920505i 0.372222π-0.372222\pi
0.390731 + 0.920505i 0.372222π0.372222\pi
194194 0 0
195195 0 0
196196 0 0
197197 4.12436i 0.293848i 0.989148 + 0.146924i 0.0469373π0.0469373\pi
−0.989148 + 0.146924i 0.953063π0.953063\pi
198198 0 0
199199 −2.39230 −0.169586 −0.0847930 0.996399i 0.527023π-0.527023\pi
−0.0847930 + 0.996399i 0.527023π0.527023\pi
200200 0 0
201201 0 0
202202 0 0
203203 − 3.80385i − 0.266978i
204204 0 0
205205 16.9282i 1.18232i
206206 0 0
207207 0 0
208208 0 0
209209 15.4641 1.06967
210210 0 0
211211 26.0526i 1.79353i 0.442505 + 0.896766i 0.354090π0.354090\pi
−0.442505 + 0.896766i 0.645910π0.645910\pi
212212 0 0
213213 0 0
214214 0 0
215215 −36.0526 −2.45876
216216 0 0
217217 −1.46410 −0.0993897
218218 0 0
219219 0 0
220220 0 0
221221 − 9.19615i − 0.618600i
222222 0 0
223223 −23.1244 −1.54852 −0.774261 0.632867i 0.781878π-0.781878\pi
−0.774261 + 0.632867i 0.781878π0.781878\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 6.73205i − 0.446822i −0.974724 0.223411i 0.928281π-0.928281\pi
0.974724 0.223411i 0.0717192π-0.0717192\pi
228228 0 0
229229 11.3923i 0.752825i 0.926452 + 0.376412i 0.122842π0.122842\pi
−0.926452 + 0.376412i 0.877158π0.877158\pi
230230 0 0
231231 0 0
232232 0 0
233233 3.73205 0.244495 0.122247 0.992500i 0.460990π-0.460990\pi
0.122247 + 0.992500i 0.460990π0.460990\pi
234234 0 0
235235 − 12.9282i − 0.843343i
236236 0 0
237237 0 0
238238 0 0
239239 −7.85641 −0.508189 −0.254094 0.967179i 0.581777π-0.581777\pi
−0.254094 + 0.967179i 0.581777π0.581777\pi
240240 0 0
241241 −4.46410 −0.287558 −0.143779 0.989610i 0.545925π-0.545925\pi
−0.143779 + 0.989610i 0.545925π0.545925\pi
242242 0 0
243243 0 0
244244 0 0
245245 − 24.1244i − 1.54125i
246246 0 0
247247 −8.05256 −0.512372
248248 0 0
249249 0 0
250250 0 0
251251 − 7.26795i − 0.458749i −0.973338 0.229374i 0.926332π-0.926332\pi
0.973338 0.229374i 0.0736680π-0.0736680\pi
252252 0 0
253253 41.3205i 2.59780i
254254 0 0
255255 0 0
256256 0 0
257257 −3.33975 −0.208328 −0.104164 0.994560i 0.533217π-0.533217\pi
−0.104164 + 0.994560i 0.533217π0.533217\pi
258258 0 0
259259 3.66025i 0.227437i
260260 0 0
261261 0 0
262262 0 0
263263 16.2487 1.00194 0.500969 0.865465i 0.332977π-0.332977\pi
0.500969 + 0.865465i 0.332977π0.332977\pi
264264 0 0
265265 3.46410 0.212798
266266 0 0
267267 0 0
268268 0 0
269269 25.7321i 1.56891i 0.620185 + 0.784455i 0.287057π0.287057\pi
−0.620185 + 0.784455i 0.712943π0.712943\pi
270270 0 0
271271 −10.7321 −0.651926 −0.325963 0.945383i 0.605688π-0.605688\pi
−0.325963 + 0.945383i 0.605688π0.605688\pi
272272 0 0
273273 0 0
274274 0 0
275275 42.2487i 2.54769i
276276 0 0
277277 − 9.85641i − 0.592214i −0.955155 0.296107i 0.904311π-0.904311\pi
0.955155 0.296107i 0.0956885π-0.0956885\pi
278278 0 0
279279 0 0
280280 0 0
281281 13.7321 0.819185 0.409593 0.912268i 0.365671π-0.365671\pi
0.409593 + 0.912268i 0.365671π0.365671\pi
282282 0 0
283283 − 6.39230i − 0.379983i −0.981786 0.189992i 0.939154π-0.939154\pi
0.981786 0.189992i 0.0608461π-0.0608461\pi
284284 0 0
285285 0 0
286286 0 0
287287 3.32051 0.196003
288288 0 0
289289 −3.07180 −0.180694
290290 0 0
291291 0 0
292292 0 0
293293 3.33975i 0.195110i 0.995230 + 0.0975550i 0.0311022π0.0311022\pi
−0.995230 + 0.0975550i 0.968898π0.968898\pi
294294 0 0
295295 31.3205 1.82355
296296 0 0
297297 0 0
298298 0 0
299299 − 21.5167i − 1.24434i
300300 0 0
301301 7.07180i 0.407612i
302302 0 0
303303 0 0
304304 0 0
305305 33.5885 1.92327
306306 0 0
307307 14.7846i 0.843802i 0.906642 + 0.421901i 0.138637π0.138637\pi
−0.906642 + 0.421901i 0.861363π0.861363\pi
308308 0 0
309309 0 0
310310 0 0
311311 19.3205 1.09557 0.547783 0.836621i 0.315472π-0.315472\pi
0.547783 + 0.836621i 0.315472π0.315472\pi
312312 0 0
313313 2.46410 0.139279 0.0696396 0.997572i 0.477815π-0.477815\pi
0.0696396 + 0.997572i 0.477815π0.477815\pi
314314 0 0
315315 0 0
316316 0 0
317317 1.19615i 0.0671826i 0.999436 + 0.0335913i 0.0106945π0.0106945\pi
−0.999436 + 0.0335913i 0.989306π0.989306\pi
318318 0 0
319319 −24.5885 −1.37669
320320 0 0
321321 0 0
322322 0 0
323323 − 12.1962i − 0.678612i
324324 0 0
325325 − 22.0000i − 1.22034i
326326 0 0
327327 0 0
328328 0 0
329329 −2.53590 −0.139809
330330 0 0
331331 13.1244i 0.721380i 0.932686 + 0.360690i 0.117459π0.117459\pi
−0.932686 + 0.360690i 0.882541π0.882541\pi
332332 0 0
333333 0 0
334334 0 0
335335 −17.6603 −0.964883
336336 0 0
337337 4.00000 0.217894 0.108947 0.994048i 0.465252π-0.465252\pi
0.108947 + 0.994048i 0.465252π0.465252\pi
338338 0 0
339339 0 0
340340 0 0
341341 9.46410i 0.512510i
342342 0 0
343343 −9.85641 −0.532196
344344 0 0
345345 0 0
346346 0 0
347347 − 6.73205i − 0.361395i −0.983539 0.180698i 0.942164π-0.942164\pi
0.983539 0.180698i 0.0578356π-0.0578356\pi
348348 0 0
349349 − 11.8564i − 0.634659i −0.948315 0.317329i 0.897214π-0.897214\pi
0.948315 0.317329i 0.102786π-0.102786\pi
350350 0 0
351351 0 0
352352 0 0
353353 −6.92820 −0.368751 −0.184376 0.982856i 0.559026π-0.559026\pi
−0.184376 + 0.982856i 0.559026π0.559026\pi
354354 0 0
355355 − 21.1244i − 1.12116i
356356 0 0
357357 0 0
358358 0 0
359359 −1.12436 −0.0593412 −0.0296706 0.999560i 0.509446π-0.509446\pi
−0.0296706 + 0.999560i 0.509446π0.509446\pi
360360 0 0
361361 8.32051 0.437921
362362 0 0
363363 0 0
364364 0 0
365365 33.5885i 1.75810i
366366 0 0
367367 −2.53590 −0.132373 −0.0661864 0.997807i 0.521083π-0.521083\pi
−0.0661864 + 0.997807i 0.521083π0.521083\pi
368368 0 0
369369 0 0
370370 0 0
371371 − 0.679492i − 0.0352775i
372372 0 0
373373 22.9282i 1.18718i 0.804769 + 0.593589i 0.202289π0.202289\pi
−0.804769 + 0.593589i 0.797711π0.797711\pi
374374 0 0
375375 0 0
376376 0 0
377377 12.8038 0.659432
378378 0 0
379379 − 10.0000i − 0.513665i −0.966456 0.256833i 0.917321π-0.917321\pi
0.966456 0.256833i 0.0826790π-0.0826790\pi
380380 0 0
381381 0 0
382382 0 0
383383 20.1962 1.03198 0.515988 0.856596i 0.327425π-0.327425\pi
0.515988 + 0.856596i 0.327425π0.327425\pi
384384 0 0
385385 12.9282 0.658882
386386 0 0
387387 0 0
388388 0 0
389389 16.9282i 0.858294i 0.903235 + 0.429147i 0.141186π0.141186\pi
−0.903235 + 0.429147i 0.858814π0.858814\pi
390390 0 0
391391 32.5885 1.64807
392392 0 0
393393 0 0
394394 0 0
395395 − 19.6603i − 0.989215i
396396 0 0
397397 − 32.4641i − 1.62933i −0.579934 0.814663i 0.696922π-0.696922\pi
0.579934 0.814663i 0.303078π-0.303078\pi
398398 0 0
399399 0 0
400400 0 0
401401 −9.58846 −0.478825 −0.239412 0.970918i 0.576955π-0.576955\pi
−0.239412 + 0.970918i 0.576955π0.576955\pi
402402 0 0
403403 − 4.92820i − 0.245491i
404404 0 0
405405 0 0
406406 0 0
407407 23.6603 1.17280
408408 0 0
409409 28.7128 1.41976 0.709879 0.704324i 0.248750π-0.248750\pi
0.709879 + 0.704324i 0.248750π0.248750\pi
410410 0 0
411411 0 0
412412 0 0
413413 − 6.14359i − 0.302306i
414414 0 0
415415 −52.2487 −2.56479
416416 0 0
417417 0 0
418418 0 0
419419 − 21.4641i − 1.04859i −0.851537 0.524295i 0.824329π-0.824329\pi
0.851537 0.524295i 0.175671π-0.175671\pi
420420 0 0
421421 13.0000i 0.633581i 0.948495 + 0.316791i 0.102605π0.102605\pi
−0.948495 + 0.316791i 0.897395π0.897395\pi
422422 0 0
423423 0 0
424424 0 0
425425 33.3205 1.61628
426426 0 0
427427 − 6.58846i − 0.318838i
428428 0 0
429429 0 0
430430 0 0
431431 21.7128 1.04587 0.522935 0.852373i 0.324837π-0.324837\pi
0.522935 + 0.852373i 0.324837π0.324837\pi
432432 0 0
433433 −21.7846 −1.04690 −0.523451 0.852056i 0.675356π-0.675356\pi
−0.523451 + 0.852056i 0.675356π0.675356\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 28.5359i − 1.36506i
438438 0 0
439439 30.0000 1.43182 0.715911 0.698192i 0.246012π-0.246012\pi
0.715911 + 0.698192i 0.246012π0.246012\pi
440440 0 0
441441 0 0
442442 0 0
443443 29.3205i 1.39306i 0.717528 + 0.696530i 0.245274π0.245274\pi
−0.717528 + 0.696530i 0.754726π0.754726\pi
444444 0 0
445445 − 43.7846i − 2.07559i
446446 0 0
447447 0 0
448448 0 0
449449 −24.9282 −1.17643 −0.588217 0.808703i 0.700170π-0.700170\pi
−0.588217 + 0.808703i 0.700170π0.700170\pi
450450 0 0
451451 − 21.4641i − 1.01071i
452452 0 0
453453 0 0
454454 0 0
455455 −6.73205 −0.315603
456456 0 0
457457 −6.32051 −0.295661 −0.147830 0.989013i 0.547229π-0.547229\pi
−0.147830 + 0.989013i 0.547229π0.547229\pi
458458 0 0
459459 0 0
460460 0 0
461461 41.3205i 1.92449i 0.272188 + 0.962244i 0.412253π0.412253\pi
−0.272188 + 0.962244i 0.587747π0.587747\pi
462462 0 0
463463 −13.4641 −0.625730 −0.312865 0.949798i 0.601289π-0.601289\pi
−0.312865 + 0.949798i 0.601289π0.601289\pi
464464 0 0
465465 0 0
466466 0 0
467467 24.7846i 1.14689i 0.819242 + 0.573447i 0.194394π0.194394\pi
−0.819242 + 0.573447i 0.805606π0.805606\pi
468468 0 0
469469 3.46410i 0.159957i
470470 0 0
471471 0 0
472472 0 0
473473 45.7128 2.10188
474474 0 0
475475 − 29.1769i − 1.33873i
476476 0 0
477477 0 0
478478 0 0
479479 −1.66025 −0.0758589 −0.0379295 0.999280i 0.512076π-0.512076\pi
−0.0379295 + 0.999280i 0.512076π0.512076\pi
480480 0 0
481481 −12.3205 −0.561767
482482 0 0
483483 0 0
484484 0 0
485485 − 29.8564i − 1.35571i
486486 0 0
487487 25.7128 1.16516 0.582579 0.812774i 0.302044π-0.302044\pi
0.582579 + 0.812774i 0.302044π0.302044\pi
488488 0 0
489489 0 0
490490 0 0
491491 − 13.8038i − 0.622959i −0.950253 0.311479i 0.899175π-0.899175\pi
0.950253 0.311479i 0.100825π-0.100825\pi
492492 0 0
493493 19.3923i 0.873385i
494494 0 0
495495 0 0
496496 0 0
497497 −4.14359 −0.185866
498498 0 0
499499 8.19615i 0.366910i 0.983028 + 0.183455i 0.0587282π0.0587282\pi
−0.983028 + 0.183455i 0.941272π0.941272\pi
500500 0 0
501501 0 0
502502 0 0
503503 0.679492 0.0302970 0.0151485 0.999885i 0.495178π-0.495178\pi
0.0151485 + 0.999885i 0.495178π0.495178\pi
504504 0 0
505505 −29.8564 −1.32859
506506 0 0
507507 0 0
508508 0 0
509509 − 29.3205i − 1.29961i −0.760102 0.649804i 0.774851π-0.774851\pi
0.760102 0.649804i 0.225149π-0.225149\pi
510510 0 0
511511 6.58846 0.291456
512512 0 0
513513 0 0
514514 0 0
515515 12.9282i 0.569685i
516516 0 0
517517 16.3923i 0.720933i
518518 0 0
519519 0 0
520520 0 0
521521 26.7846 1.17346 0.586728 0.809784i 0.300416π-0.300416\pi
0.586728 + 0.809784i 0.300416π0.300416\pi
522522 0 0
523523 − 13.2679i − 0.580167i −0.957001 0.290083i 0.906317π-0.906317\pi
0.957001 0.290083i 0.0936831π-0.0936831\pi
524524 0 0
525525 0 0
526526 0 0
527527 7.46410 0.325141
528528 0 0
529529 53.2487 2.31516
530530 0 0
531531 0 0
532532 0 0
533533 11.1769i 0.484126i
534534 0 0
535535 38.7846 1.67680
536536 0 0
537537 0 0
538538 0 0
539539 30.5885i 1.31754i
540540 0 0
541541 24.1769i 1.03945i 0.854335 + 0.519723i 0.173965π0.173965\pi
−0.854335 + 0.519723i 0.826035π0.826035\pi
542542 0 0
543543 0 0
544544 0 0
545545 47.9808 2.05527
546546 0 0
547547 26.0000i 1.11168i 0.831289 + 0.555840i 0.187603π0.187603\pi
−0.831289 + 0.555840i 0.812397π0.812397\pi
548548 0 0
549549 0 0
550550 0 0
551551 16.9808 0.723405
552552 0 0
553553 −3.85641 −0.163991
554554 0 0
555555 0 0
556556 0 0
557557 13.0526i 0.553055i 0.961006 + 0.276527i 0.0891836π0.0891836\pi
−0.961006 + 0.276527i 0.910816π0.910816\pi
558558 0 0
559559 −23.8038 −1.00680
560560 0 0
561561 0 0
562562 0 0
563563 − 24.2487i − 1.02196i −0.859592 0.510981i 0.829282π-0.829282\pi
0.859592 0.510981i 0.170718π-0.170718\pi
564564 0 0
565565 − 28.8564i − 1.21400i
566566 0 0
567567 0 0
568568 0 0
569569 −33.5885 −1.40810 −0.704051 0.710150i 0.748627π-0.748627\pi
−0.704051 + 0.710150i 0.748627π0.748627\pi
570570 0 0
571571 26.2487i 1.09847i 0.835667 + 0.549237i 0.185082π0.185082\pi
−0.835667 + 0.549237i 0.814918π0.814918\pi
572572 0 0
573573 0 0
574574 0 0
575575 77.9615 3.25122
576576 0 0
577577 −45.2487 −1.88373 −0.941864 0.335994i 0.890928π-0.890928\pi
−0.941864 + 0.335994i 0.890928π0.890928\pi
578578 0 0
579579 0 0
580580 0 0
581581 10.2487i 0.425188i
582582 0 0
583583 −4.39230 −0.181911
584584 0 0
585585 0 0
586586 0 0
587587 42.3013i 1.74596i 0.487756 + 0.872980i 0.337816π0.337816\pi
−0.487756 + 0.872980i 0.662184π0.662184\pi
588588 0 0
589589 − 6.53590i − 0.269307i
590590 0 0
591591 0 0
592592 0 0
593593 −14.4115 −0.591811 −0.295906 0.955217i 0.595621π-0.595621\pi
−0.295906 + 0.955217i 0.595621π0.595621\pi
594594 0 0
595595 − 10.1962i − 0.418001i
596596 0 0
597597 0 0
598598 0 0
599599 8.24871 0.337033 0.168517 0.985699i 0.446102π-0.446102\pi
0.168517 + 0.985699i 0.446102π0.446102\pi
600600 0 0
601601 17.2487 0.703590 0.351795 0.936077i 0.385571π-0.385571\pi
0.351795 + 0.936077i 0.385571π0.385571\pi
602602 0 0
603603 0 0
604604 0 0
605605 − 42.5167i − 1.72855i
606606 0 0
607607 25.9090 1.05161 0.525806 0.850604i 0.323764π-0.323764\pi
0.525806 + 0.850604i 0.323764π0.323764\pi
608608 0 0
609609 0 0
610610 0 0
611611 − 8.53590i − 0.345325i
612612 0 0
613613 − 24.3923i − 0.985196i −0.870257 0.492598i 0.836047π-0.836047\pi
0.870257 0.492598i 0.163953π-0.163953\pi
614614 0 0
615615 0 0
616616 0 0
617617 −26.1244 −1.05173 −0.525863 0.850569i 0.676258π-0.676258\pi
−0.525863 + 0.850569i 0.676258π0.676258\pi
618618 0 0
619619 − 6.24871i − 0.251157i −0.992084 0.125578i 0.959921π-0.959921\pi
0.992084 0.125578i 0.0400787π-0.0400787\pi
620620 0 0
621621 0 0
622622 0 0
623623 −8.58846 −0.344089
624624 0 0
625625 10.0718 0.402872
626626 0 0
627627 0 0
628628 0 0
629629 − 18.6603i − 0.744033i
630630 0 0
631631 −0.784610 −0.0312348 −0.0156174 0.999878i 0.504971π-0.504971\pi
−0.0156174 + 0.999878i 0.504971π0.504971\pi
632632 0 0
633633 0 0
634634 0 0
635635 50.9808i 2.02311i
636636 0 0
637637 − 15.9282i − 0.631098i
638638 0 0
639639 0 0
640640 0 0
641641 23.0526 0.910521 0.455261 0.890358i 0.349546π-0.349546\pi
0.455261 + 0.890358i 0.349546π0.349546\pi
642642 0 0
643643 − 6.39230i − 0.252088i −0.992025 0.126044i 0.959772π-0.959772\pi
0.992025 0.126044i 0.0402280π-0.0402280\pi
644644 0 0
645645 0 0
646646 0 0
647647 −49.7654 −1.95648 −0.978239 0.207480i 0.933474π-0.933474\pi
−0.978239 + 0.207480i 0.933474π0.933474\pi
648648 0 0
649649 −39.7128 −1.55886
650650 0 0
651651 0 0
652652 0 0
653653 35.5692i 1.39193i 0.718075 + 0.695966i 0.245023π0.245023\pi
−0.718075 + 0.695966i 0.754977π0.754977\pi
654654 0 0
655655 0.732051 0.0286036
656656 0 0
657657 0 0
658658 0 0
659659 − 10.0526i − 0.391592i −0.980645 0.195796i 0.937271π-0.937271\pi
0.980645 0.195796i 0.0627291π-0.0627291\pi
660660 0 0
661661 − 32.1769i − 1.25154i −0.780009 0.625768i 0.784785π-0.784785\pi
0.780009 0.625768i 0.215215π-0.215215\pi
662662 0 0
663663 0 0
664664 0 0
665665 −8.92820 −0.346221
666666 0 0
667667 45.3731i 1.75685i
668668 0 0
669669 0 0
670670 0 0
671671 −42.5885 −1.64411
672672 0 0
673673 −37.2487 −1.43583 −0.717916 0.696130i 0.754904π-0.754904\pi
−0.717916 + 0.696130i 0.754904π0.754904\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 29.3205i − 1.12688i −0.826157 0.563439i 0.809478π-0.809478\pi
0.826157 0.563439i 0.190522π-0.190522\pi
678678 0 0
679679 −5.85641 −0.224748
680680 0 0
681681 0 0
682682 0 0
683683 34.1051i 1.30500i 0.757790 + 0.652498i 0.226279π0.226279\pi
−0.757790 + 0.652498i 0.773721π0.773721\pi
684684 0 0
685685 − 64.1769i − 2.45207i
686686 0 0
687687 0 0
688688 0 0
689689 2.28719 0.0871349
690690 0 0
691691 12.7321i 0.484350i 0.970233 + 0.242175i 0.0778608π0.0778608\pi
−0.970233 + 0.242175i 0.922139π0.922139\pi
692692 0 0
693693 0 0
694694 0 0
695695 72.6410 2.75543
696696 0 0
697697 −16.9282 −0.641201
698698 0 0
699699 0 0
700700 0 0
701701 − 10.1244i − 0.382392i −0.981552 0.191196i 0.938763π-0.938763\pi
0.981552 0.191196i 0.0612365π-0.0612365\pi
702702 0 0
703703 −16.3397 −0.616265
704704 0 0
705705 0 0
706706 0 0
707707 5.85641i 0.220253i
708708 0 0
709709 47.3923i 1.77986i 0.456102 + 0.889928i 0.349245π0.349245\pi
−0.456102 + 0.889928i 0.650755π0.650755\pi
710710 0 0
711711 0 0
712712 0 0
713713 17.4641 0.654036
714714 0 0
715715 43.5167i 1.62743i
716716 0 0
717717 0 0
718718 0 0
719719 48.0526 1.79206 0.896029 0.443995i 0.146439π-0.146439\pi
0.896029 + 0.443995i 0.146439π0.146439\pi
720720 0 0
721721 2.53590 0.0944418
722722 0 0
723723 0 0
724724 0 0
725725 46.3923i 1.72297i
726726 0 0
727727 49.5167 1.83647 0.918236 0.396034i 0.129614π-0.129614\pi
0.918236 + 0.396034i 0.129614π0.129614\pi
728728 0 0
729729 0 0
730730 0 0
731731 − 36.0526i − 1.33345i
732732 0 0
733733 29.4641i 1.08828i 0.838994 + 0.544141i 0.183144π0.183144\pi
−0.838994 + 0.544141i 0.816856π0.816856\pi
734734 0 0
735735 0 0
736736 0 0
737737 22.3923 0.824831
738738 0 0
739739 − 9.60770i − 0.353425i −0.984263 0.176712i 0.943454π-0.943454\pi
0.984263 0.176712i 0.0565462π-0.0565462\pi
740740 0 0
741741 0 0
742742 0 0
743743 30.7846 1.12938 0.564689 0.825304i 0.308996π-0.308996\pi
0.564689 + 0.825304i 0.308996π0.308996\pi
744744 0 0
745745 19.3923 0.710479
746746 0 0
747747 0 0
748748 0 0
749749 − 7.60770i − 0.277979i
750750 0 0
751751 17.5167 0.639192 0.319596 0.947554i 0.396453π-0.396453\pi
0.319596 + 0.947554i 0.396453π0.396453\pi
752752 0 0
753753 0 0
754754 0 0
755755 − 51.7128i − 1.88202i
756756 0 0
757757 18.2487i 0.663261i 0.943409 + 0.331630i 0.107599π0.107599\pi
−0.943409 + 0.331630i 0.892401π0.892401\pi
758758 0 0
759759 0 0
760760 0 0
761761 35.9808 1.30430 0.652151 0.758089i 0.273867π-0.273867\pi
0.652151 + 0.758089i 0.273867π0.273867\pi
762762 0 0
763763 − 9.41154i − 0.340721i
764764 0 0
765765 0 0
766766 0 0
767767 20.6795 0.746693
768768 0 0
769769 −39.3923 −1.42052 −0.710261 0.703938i 0.751423π-0.751423\pi
−0.710261 + 0.703938i 0.751423π0.751423\pi
770770 0 0
771771 0 0
772772 0 0
773773 40.6603i 1.46245i 0.682138 + 0.731224i 0.261051π0.261051\pi
−0.682138 + 0.731224i 0.738949π0.738949\pi
774774 0 0
775775 17.8564 0.641421
776776 0 0
777777 0 0
778778 0 0
779779 14.8231i 0.531092i
780780 0 0
781781 26.7846i 0.958429i
782782 0 0
783783 0 0
784784 0 0
785785 −9.19615 −0.328225
786786 0 0
787787 − 14.4449i − 0.514904i −0.966291 0.257452i 0.917117π-0.917117\pi
0.966291 0.257452i 0.0828829π-0.0828829\pi
788788 0 0
789789 0 0
790790 0 0
791791 −5.66025 −0.201255
792792 0 0
793793 22.1769 0.787525
794794 0 0
795795 0 0
796796 0 0
797797 − 12.2679i − 0.434553i −0.976110 0.217277i 0.930283π-0.930283\pi
0.976110 0.217277i 0.0697173π-0.0697173\pi
798798 0 0
799799 12.9282 0.457367
800800 0 0
801801 0 0
802802 0 0
803803 − 42.5885i − 1.50291i
804804 0 0
805805 − 23.8564i − 0.840828i
806806 0 0
807807 0 0
808808 0 0
809809 −49.0526 −1.72460 −0.862298 0.506401i 0.830976π-0.830976\pi
−0.862298 + 0.506401i 0.830976π0.830976\pi
810810 0 0
811811 48.7846i 1.71306i 0.516098 + 0.856530i 0.327384π0.327384\pi
−0.516098 + 0.856530i 0.672616π0.672616\pi
812812 0 0
813813 0 0
814814 0 0
815815 −24.3923 −0.854425
816816 0 0
817817 −31.5692 −1.10447
818818 0 0
819819 0 0
820820 0 0
821821 − 1.58846i − 0.0554375i −0.999616 0.0277188i 0.991176π-0.991176\pi
0.999616 0.0277188i 0.00882429π-0.00882429\pi
822822 0 0
823823 17.6077 0.613766 0.306883 0.951747i 0.400714π-0.400714\pi
0.306883 + 0.951747i 0.400714π0.400714\pi
824824 0 0
825825 0 0
826826 0 0
827827 12.3397i 0.429095i 0.976714 + 0.214548i 0.0688277π0.0688277\pi
−0.976714 + 0.214548i 0.931172π0.931172\pi
828828 0 0
829829 53.1769i 1.84691i 0.383706 + 0.923455i 0.374648π0.374648\pi
−0.383706 + 0.923455i 0.625352π0.625352\pi
830830 0 0
831831 0 0
832832 0 0
833833 24.1244 0.835859
834834 0 0
835835 54.9808i 1.90269i
836836 0 0
837837 0 0
838838 0 0
839839 −41.8038 −1.44323 −0.721615 0.692295i 0.756600π-0.756600\pi
−0.721615 + 0.692295i 0.756600π0.756600\pi
840840 0 0
841841 2.00000 0.0689655
842842 0 0
843843 0 0
844844 0 0
845845 25.8564i 0.889487i
846846 0 0
847847 −8.33975 −0.286557
848848 0 0
849849 0 0
850850 0 0
851851 − 43.6603i − 1.49665i
852852 0 0
853853 − 5.07180i − 0.173655i −0.996223 0.0868275i 0.972327π-0.972327\pi
0.996223 0.0868275i 0.0276729π-0.0276729\pi
854854 0 0
855855 0 0
856856 0 0
857857 0.124356 0.00424791 0.00212395 0.999998i 0.499324π-0.499324\pi
0.00212395 + 0.999998i 0.499324π0.499324\pi
858858 0 0
859859 − 2.00000i − 0.0682391i −0.999418 0.0341196i 0.989137π-0.989137\pi
0.999418 0.0341196i 0.0108627π-0.0108627\pi
860860 0 0
861861 0 0
862862 0 0
863863 25.5167 0.868597 0.434299 0.900769i 0.356996π-0.356996\pi
0.434299 + 0.900769i 0.356996π0.356996\pi
864864 0 0
865865 −6.46410 −0.219786
866866 0 0
867867 0 0
868868 0 0
869869 24.9282i 0.845631i
870870 0 0
871871 −11.6603 −0.395093
872872 0 0
873873 0 0
874874 0 0
875875 − 10.7321i − 0.362810i
876876 0 0
877877 57.1051i 1.92830i 0.265353 + 0.964151i 0.414512π0.414512\pi
−0.265353 + 0.964151i 0.585488π0.585488\pi
878878 0 0
879879 0 0
880880 0 0
881881 27.8564 0.938506 0.469253 0.883064i 0.344523π-0.344523\pi
0.469253 + 0.883064i 0.344523π0.344523\pi
882882 0 0
883883 − 1.32051i − 0.0444386i −0.999753 0.0222193i 0.992927π-0.992927\pi
0.999753 0.0222193i 0.00707321π-0.00707321\pi
884884 0 0
885885 0 0
886886 0 0
887887 −2.19615 −0.0737396 −0.0368698 0.999320i 0.511739π-0.511739\pi
−0.0368698 + 0.999320i 0.511739π0.511739\pi
888888 0 0
889889 10.0000 0.335389
890890 0 0
891891 0 0
892892 0 0
893893 − 11.3205i − 0.378826i
894894 0 0
895895 −52.2487 −1.74648
896896 0 0
897897 0 0
898898 0 0
899899 10.3923i 0.346603i
900900 0 0
901901 3.46410i 0.115406i
902902 0 0
903903 0 0
904904 0 0
905905 −24.3923 −0.810828
906906 0 0
907907 − 32.3923i − 1.07557i −0.843082 0.537784i 0.819261π-0.819261\pi
0.843082 0.537784i 0.180739π-0.180739\pi
908908 0 0
909909 0 0
910910 0 0
911911 −16.7321 −0.554358 −0.277179 0.960818i 0.589399π-0.589399\pi
−0.277179 + 0.960818i 0.589399π0.589399\pi
912912 0 0
913913 66.2487 2.19251
914914 0 0
915915 0 0
916916 0 0
917917 − 0.143594i − 0.00474188i
918918 0 0
919919 −16.9808 −0.560144 −0.280072 0.959979i 0.590358π-0.590358\pi
−0.280072 + 0.959979i 0.590358π0.590358\pi
920920 0 0
921921 0 0
922922 0 0
923923 − 13.9474i − 0.459086i
924924 0 0
925925 − 44.6410i − 1.46779i
926926 0 0
927927 0 0
928928 0 0
929929 −0.516660 −0.0169511 −0.00847554 0.999964i 0.502698π-0.502698\pi
−0.00847554 + 0.999964i 0.502698π0.502698\pi
930930 0 0
931931 − 21.1244i − 0.692323i
932932 0 0
933933 0 0
934934 0 0
935935 −65.9090 −2.15545
936936 0 0
937937 −7.24871 −0.236805 −0.118403 0.992966i 0.537777π-0.537777\pi
−0.118403 + 0.992966i 0.537777π0.537777\pi
938938 0 0
939939 0 0
940940 0 0
941941 − 18.3731i − 0.598945i −0.954105 0.299472i 0.903189π-0.903189\pi
0.954105 0.299472i 0.0968107π-0.0968107\pi
942942 0 0
943943 −39.6077 −1.28980
944944 0 0
945945 0 0
946946 0 0
947947 20.1962i 0.656287i 0.944628 + 0.328143i 0.106423π0.106423\pi
−0.944628 + 0.328143i 0.893577π0.893577\pi
948948 0 0
949949 22.1769i 0.719893i
950950 0 0
951951 0 0
952952 0 0
953953 26.6603 0.863610 0.431805 0.901967i 0.357877π-0.357877\pi
0.431805 + 0.901967i 0.357877π0.357877\pi
954954 0 0
955955 − 61.9090i − 2.00333i
956956 0 0
957957 0 0
958958 0 0
959959 −12.5885 −0.406502
960960 0 0
961961 −27.0000 −0.870968
962962 0 0
963963 0 0
964964 0 0
965965 40.5167i 1.30428i
966966 0 0
967967 −10.1962 −0.327886 −0.163943 0.986470i 0.552421π-0.552421\pi
−0.163943 + 0.986470i 0.552421π0.552421\pi
968968 0 0
969969 0 0
970970 0 0
971971 51.1244i 1.64066i 0.571891 + 0.820329i 0.306210π0.306210\pi
−0.571891 + 0.820329i 0.693790π0.693790\pi
972972 0 0
973973 − 14.2487i − 0.456793i
974974 0 0
975975 0 0
976976 0 0
977977 −22.7846 −0.728944 −0.364472 0.931214i 0.618751π-0.618751\pi
−0.364472 + 0.931214i 0.618751π0.618751\pi
978978 0 0
979979 55.5167i 1.77432i
980980 0 0
981981 0 0
982982 0 0
983983 1.46410 0.0466976 0.0233488 0.999727i 0.492567π-0.492567\pi
0.0233488 + 0.999727i 0.492567π0.492567\pi
984984 0 0
985985 −15.3923 −0.490440
986986 0 0
987987 0 0
988988 0 0
989989 − 84.3538i − 2.68230i
990990 0 0
991991 −2.58846 −0.0822251 −0.0411125 0.999155i 0.513090π-0.513090\pi
−0.0411125 + 0.999155i 0.513090π0.513090\pi
992992 0 0
993993 0 0
994994 0 0
995995 − 8.92820i − 0.283043i
996996 0 0
997997 − 27.9282i − 0.884495i −0.896893 0.442248i 0.854181π-0.854181\pi
0.896893 0.442248i 0.145819π-0.145819\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 2592.2.d.g.1297.4 4
3.2 odd 2 2592.2.d.h.1297.1 4
4.3 odd 2 648.2.d.i.325.3 yes 4
8.3 odd 2 648.2.d.i.325.4 yes 4
8.5 even 2 inner 2592.2.d.g.1297.1 4
9.2 odd 6 2592.2.r.j.433.2 4
9.4 even 3 2592.2.r.k.2161.2 4
9.5 odd 6 2592.2.r.b.2161.1 4
9.7 even 3 2592.2.r.a.433.1 4
12.11 even 2 648.2.d.e.325.2 yes 4
24.5 odd 2 2592.2.d.h.1297.4 4
24.11 even 2 648.2.d.e.325.1 4
36.7 odd 6 648.2.n.a.109.1 4
36.11 even 6 648.2.n.m.109.2 4
36.23 even 6 648.2.n.b.541.2 4
36.31 odd 6 648.2.n.l.541.1 4
72.5 odd 6 2592.2.r.j.2161.2 4
72.11 even 6 648.2.n.b.109.2 4
72.13 even 6 2592.2.r.a.2161.1 4
72.29 odd 6 2592.2.r.b.433.1 4
72.43 odd 6 648.2.n.l.109.1 4
72.59 even 6 648.2.n.m.541.1 4
72.61 even 6 2592.2.r.k.433.2 4
72.67 odd 6 648.2.n.a.541.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
648.2.d.e.325.1 4 24.11 even 2
648.2.d.e.325.2 yes 4 12.11 even 2
648.2.d.i.325.3 yes 4 4.3 odd 2
648.2.d.i.325.4 yes 4 8.3 odd 2
648.2.n.a.109.1 4 36.7 odd 6
648.2.n.a.541.2 4 72.67 odd 6
648.2.n.b.109.2 4 72.11 even 6
648.2.n.b.541.2 4 36.23 even 6
648.2.n.l.109.1 4 72.43 odd 6
648.2.n.l.541.1 4 36.31 odd 6
648.2.n.m.109.2 4 36.11 even 6
648.2.n.m.541.1 4 72.59 even 6
2592.2.d.g.1297.1 4 8.5 even 2 inner
2592.2.d.g.1297.4 4 1.1 even 1 trivial
2592.2.d.h.1297.1 4 3.2 odd 2
2592.2.d.h.1297.4 4 24.5 odd 2
2592.2.r.a.433.1 4 9.7 even 3
2592.2.r.a.2161.1 4 72.13 even 6
2592.2.r.b.433.1 4 72.29 odd 6
2592.2.r.b.2161.1 4 9.5 odd 6
2592.2.r.j.433.2 4 9.2 odd 6
2592.2.r.j.2161.2 4 72.5 odd 6
2592.2.r.k.433.2 4 72.61 even 6
2592.2.r.k.2161.2 4 9.4 even 3