Properties

Label 3000.2.a.j.1.4
Level 30003000
Weight 22
Character 3000.1
Self dual yes
Analytic conductor 23.95523.955
Analytic rank 00
Dimension 44
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3000,2,Mod(1,3000)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3000, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3000.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3000=23353 3000 = 2^{3} \cdot 3 \cdot 5^{3}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3000.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 23.955120606423.9551206064
Analytic rank: 00
Dimension: 44
Coefficient field: 4.4.47025.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x322x2+13x+109 x^{4} - x^{3} - 22x^{2} + 13x + 109 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 2.35902-2.35902 of defining polynomial
Character χ\chi == 3000.1

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) == q1.00000q3+2.97706q7+1.00000q9+5.59509q11+6.43501q131.61803q173.07599q192.97706q21+3.59509q231.00000q27+7.19894q29+5.69402q315.59509q339.27493q376.43501q39+11.4492q410.145898q4312.9071q47+1.86287q49+1.61803q51+0.419089q53+3.07599q57+5.54379q5911.8471q61+2.97706q636.91525q673.59509q696.81698q713.33500q73+16.6569q776.30329q79+1.00000q818.45903q837.19894q872.31206q89+19.1574q915.69402q93+9.44919q97+5.59509q99+O(q100)q-1.00000 q^{3} +2.97706 q^{7} +1.00000 q^{9} +5.59509 q^{11} +6.43501 q^{13} -1.61803 q^{17} -3.07599 q^{19} -2.97706 q^{21} +3.59509 q^{23} -1.00000 q^{27} +7.19894 q^{29} +5.69402 q^{31} -5.59509 q^{33} -9.27493 q^{37} -6.43501 q^{39} +11.4492 q^{41} -0.145898 q^{43} -12.9071 q^{47} +1.86287 q^{49} +1.61803 q^{51} +0.419089 q^{53} +3.07599 q^{57} +5.54379 q^{59} -11.8471 q^{61} +2.97706 q^{63} -6.91525 q^{67} -3.59509 q^{69} -6.81698 q^{71} -3.33500 q^{73} +16.6569 q^{77} -6.30329 q^{79} +1.00000 q^{81} -8.45903 q^{83} -7.19894 q^{87} -2.31206 q^{89} +19.1574 q^{91} -5.69402 q^{93} +9.44919 q^{97} +5.59509 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q33q7+4q9+3q11+3q132q17+3q215q234q27+15q29+6q313q3311q373q39+13q4114q4311q47+19q49++3q99+O(q100) 4 q - 4 q^{3} - 3 q^{7} + 4 q^{9} + 3 q^{11} + 3 q^{13} - 2 q^{17} + 3 q^{21} - 5 q^{23} - 4 q^{27} + 15 q^{29} + 6 q^{31} - 3 q^{33} - 11 q^{37} - 3 q^{39} + 13 q^{41} - 14 q^{43} - 11 q^{47} + 19 q^{49}+ \cdots + 3 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −1.00000 −0.577350
44 0 0
55 0 0
66 0 0
77 2.97706 1.12522 0.562611 0.826722i 0.309797π-0.309797\pi
0.562611 + 0.826722i 0.309797π0.309797\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 5.59509 1.68698 0.843492 0.537142i 0.180496π-0.180496\pi
0.843492 + 0.537142i 0.180496π0.180496\pi
1212 0 0
1313 6.43501 1.78475 0.892376 0.451293i 0.149037π-0.149037\pi
0.892376 + 0.451293i 0.149037π0.149037\pi
1414 0 0
1515 0 0
1616 0 0
1717 −1.61803 −0.392431 −0.196215 0.980561i 0.562865π-0.562865\pi
−0.196215 + 0.980561i 0.562865π0.562865\pi
1818 0 0
1919 −3.07599 −0.705681 −0.352840 0.935684i 0.614784π-0.614784\pi
−0.352840 + 0.935684i 0.614784π0.614784\pi
2020 0 0
2121 −2.97706 −0.649647
2222 0 0
2323 3.59509 0.749628 0.374814 0.927100i 0.377707π-0.377707\pi
0.374814 + 0.927100i 0.377707π0.377707\pi
2424 0 0
2525 0 0
2626 0 0
2727 −1.00000 −0.192450
2828 0 0
2929 7.19894 1.33681 0.668405 0.743797i 0.266977π-0.266977\pi
0.668405 + 0.743797i 0.266977π0.266977\pi
3030 0 0
3131 5.69402 1.02268 0.511338 0.859379i 0.329150π-0.329150\pi
0.511338 + 0.859379i 0.329150π0.329150\pi
3232 0 0
3333 −5.59509 −0.973980
3434 0 0
3535 0 0
3636 0 0
3737 −9.27493 −1.52479 −0.762395 0.647112i 0.775977π-0.775977\pi
−0.762395 + 0.647112i 0.775977π0.775977\pi
3838 0 0
3939 −6.43501 −1.03043
4040 0 0
4141 11.4492 1.78806 0.894032 0.448004i 0.147865π-0.147865\pi
0.894032 + 0.448004i 0.147865π0.147865\pi
4242 0 0
4343 −0.145898 −0.0222492 −0.0111246 0.999938i 0.503541π-0.503541\pi
−0.0111246 + 0.999938i 0.503541π0.503541\pi
4444 0 0
4545 0 0
4646 0 0
4747 −12.9071 −1.88270 −0.941351 0.337430i 0.890442π-0.890442\pi
−0.941351 + 0.337430i 0.890442π0.890442\pi
4848 0 0
4949 1.86287 0.266124
5050 0 0
5151 1.61803 0.226570
5252 0 0
5353 0.419089 0.0575663 0.0287832 0.999586i 0.490837π-0.490837\pi
0.0287832 + 0.999586i 0.490837π0.490837\pi
5454 0 0
5555 0 0
5656 0 0
5757 3.07599 0.407425
5858 0 0
5959 5.54379 0.721740 0.360870 0.932616i 0.382480π-0.382480\pi
0.360870 + 0.932616i 0.382480π0.382480\pi
6060 0 0
6161 −11.8471 −1.51686 −0.758432 0.651753i 0.774034π-0.774034\pi
−0.758432 + 0.651753i 0.774034π0.774034\pi
6262 0 0
6363 2.97706 0.375074
6464 0 0
6565 0 0
6666 0 0
6767 −6.91525 −0.844832 −0.422416 0.906402i 0.638818π-0.638818\pi
−0.422416 + 0.906402i 0.638818π0.638818\pi
6868 0 0
6969 −3.59509 −0.432798
7070 0 0
7171 −6.81698 −0.809027 −0.404513 0.914532i 0.632559π-0.632559\pi
−0.404513 + 0.914532i 0.632559π0.632559\pi
7272 0 0
7373 −3.33500 −0.390332 −0.195166 0.980770i 0.562525π-0.562525\pi
−0.195166 + 0.980770i 0.562525π0.562525\pi
7474 0 0
7575 0 0
7676 0 0
7777 16.6569 1.89823
7878 0 0
7979 −6.30329 −0.709176 −0.354588 0.935023i 0.615379π-0.615379\pi
−0.354588 + 0.935023i 0.615379π0.615379\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 −8.45903 −0.928500 −0.464250 0.885704i 0.653676π-0.653676\pi
−0.464250 + 0.885704i 0.653676π0.653676\pi
8484 0 0
8585 0 0
8686 0 0
8787 −7.19894 −0.771808
8888 0 0
8989 −2.31206 −0.245078 −0.122539 0.992464i 0.539104π-0.539104\pi
−0.122539 + 0.992464i 0.539104π0.539104\pi
9090 0 0
9191 19.1574 2.00824
9292 0 0
9393 −5.69402 −0.590443
9494 0 0
9595 0 0
9696 0 0
9797 9.44919 0.959420 0.479710 0.877427i 0.340742π-0.340742\pi
0.479710 + 0.877427i 0.340742π0.340742\pi
9898 0 0
9999 5.59509 0.562328
100100 0 0
101101 16.2273 1.61468 0.807339 0.590089i 0.200907π-0.200907\pi
0.807339 + 0.590089i 0.200907π0.200907\pi
102102 0 0
103103 −10.2990 −1.01479 −0.507393 0.861715i 0.669391π-0.669391\pi
−0.507393 + 0.861715i 0.669391π0.669391\pi
104104 0 0
105105 0 0
106106 0 0
107107 1.10877 0.107189 0.0535946 0.998563i 0.482932π-0.482932\pi
0.0535946 + 0.998563i 0.482932π0.482932\pi
108108 0 0
109109 −15.1821 −1.45418 −0.727090 0.686542i 0.759128π-0.759128\pi
−0.727090 + 0.686542i 0.759128π0.759128\pi
110110 0 0
111111 9.27493 0.880338
112112 0 0
113113 5.48090 0.515600 0.257800 0.966198i 0.417002π-0.417002\pi
0.257800 + 0.966198i 0.417002π0.417002\pi
114114 0 0
115115 0 0
116116 0 0
117117 6.43501 0.594917
118118 0 0
119119 −4.81698 −0.441572
120120 0 0
121121 20.3050 1.84591
122122 0 0
123123 −11.4492 −1.03234
124124 0 0
125125 0 0
126126 0 0
127127 −3.39615 −0.301359 −0.150680 0.988583i 0.548146π-0.548146\pi
−0.150680 + 0.988583i 0.548146π0.548146\pi
128128 0 0
129129 0.145898 0.0128456
130130 0 0
131131 1.05130 0.0918528 0.0459264 0.998945i 0.485376π-0.485376\pi
0.0459264 + 0.998945i 0.485376π0.485376\pi
132132 0 0
133133 −9.15740 −0.794047
134134 0 0
135135 0 0
136136 0 0
137137 4.11311 0.351407 0.175703 0.984443i 0.443780π-0.443780\pi
0.175703 + 0.984443i 0.443780π0.443780\pi
138138 0 0
139139 20.9559 1.77745 0.888726 0.458438i 0.151591π-0.151591\pi
0.888726 + 0.458438i 0.151591π0.151591\pi
140140 0 0
141141 12.9071 1.08698
142142 0 0
143143 36.0045 3.01085
144144 0 0
145145 0 0
146146 0 0
147147 −1.86287 −0.153647
148148 0 0
149149 10.8781 0.891171 0.445585 0.895239i 0.352996π-0.352996\pi
0.445585 + 0.895239i 0.352996π0.352996\pi
150150 0 0
151151 15.9530 1.29824 0.649120 0.760686i 0.275137π-0.275137\pi
0.649120 + 0.760686i 0.275137π0.275137\pi
152152 0 0
153153 −1.61803 −0.130810
154154 0 0
155155 0 0
156156 0 0
157157 21.8744 1.74576 0.872882 0.487931i 0.162248π-0.162248\pi
0.872882 + 0.487931i 0.162248π0.162248\pi
158158 0 0
159159 −0.419089 −0.0332359
160160 0 0
161161 10.7028 0.843498
162162 0 0
163163 −18.1432 −1.42109 −0.710543 0.703654i 0.751551π-0.751551\pi
−0.710543 + 0.703654i 0.751551π0.751551\pi
164164 0 0
165165 0 0
166166 0 0
167167 −5.18910 −0.401545 −0.200772 0.979638i 0.564345π-0.564345\pi
−0.200772 + 0.979638i 0.564345π0.564345\pi
168168 0 0
169169 28.4094 2.18534
170170 0 0
171171 −3.07599 −0.235227
172172 0 0
173173 18.9771 1.44280 0.721399 0.692519i 0.243499π-0.243499\pi
0.721399 + 0.692519i 0.243499π0.243499\pi
174174 0 0
175175 0 0
176176 0 0
177177 −5.54379 −0.416697
178178 0 0
179179 −11.9744 −0.895007 −0.447503 0.894282i 0.647687π-0.647687\pi
−0.447503 + 0.894282i 0.647687π0.647687\pi
180180 0 0
181181 11.5881 0.861334 0.430667 0.902511i 0.358278π-0.358278\pi
0.430667 + 0.902511i 0.358278π0.358278\pi
182182 0 0
183183 11.8471 0.875761
184184 0 0
185185 0 0
186186 0 0
187187 −9.05305 −0.662024
188188 0 0
189189 −2.97706 −0.216549
190190 0 0
191191 −12.8322 −0.928508 −0.464254 0.885702i 0.653678π-0.653678\pi
−0.464254 + 0.885702i 0.653678π0.653678\pi
192192 0 0
193193 −9.15024 −0.658648 −0.329324 0.944217i 0.606821π-0.606821\pi
−0.329324 + 0.944217i 0.606821π0.606821\pi
194194 0 0
195195 0 0
196196 0 0
197197 8.45187 0.602171 0.301086 0.953597i 0.402651π-0.402651\pi
0.301086 + 0.953597i 0.402651π0.402651\pi
198198 0 0
199199 −18.0231 −1.27762 −0.638811 0.769364i 0.720574π-0.720574\pi
−0.638811 + 0.769364i 0.720574π0.720574\pi
200200 0 0
201201 6.91525 0.487764
202202 0 0
203203 21.4317 1.50421
204204 0 0
205205 0 0
206206 0 0
207207 3.59509 0.249876
208208 0 0
209209 −17.2104 −1.19047
210210 0 0
211211 7.11245 0.489641 0.244821 0.969568i 0.421271π-0.421271\pi
0.244821 + 0.969568i 0.421271π0.421271\pi
212212 0 0
213213 6.81698 0.467092
214214 0 0
215215 0 0
216216 0 0
217217 16.9514 1.15074
218218 0 0
219219 3.33500 0.225359
220220 0 0
221221 −10.4121 −0.700392
222222 0 0
223223 −24.7383 −1.65660 −0.828300 0.560285i 0.810692π-0.810692\pi
−0.828300 + 0.560285i 0.810692π0.810692\pi
224224 0 0
225225 0 0
226226 0 0
227227 −20.2581 −1.34458 −0.672288 0.740290i 0.734688π-0.734688\pi
−0.672288 + 0.740290i 0.734688π0.734688\pi
228228 0 0
229229 2.20002 0.145382 0.0726908 0.997355i 0.476841π-0.476841\pi
0.0726908 + 0.997355i 0.476841π0.476841\pi
230230 0 0
231231 −16.6569 −1.09594
232232 0 0
233233 1.55189 0.101667 0.0508337 0.998707i 0.483812π-0.483812\pi
0.0508337 + 0.998707i 0.483812π0.483812\pi
234234 0 0
235235 0 0
236236 0 0
237237 6.30329 0.409443
238238 0 0
239239 −5.98690 −0.387260 −0.193630 0.981075i 0.562026π-0.562026\pi
−0.193630 + 0.981075i 0.562026π0.562026\pi
240240 0 0
241241 −17.4368 −1.12320 −0.561600 0.827409i 0.689814π-0.689814\pi
−0.561600 + 0.827409i 0.689814π0.689814\pi
242242 0 0
243243 −1.00000 −0.0641500
244244 0 0
245245 0 0
246246 0 0
247247 −19.7940 −1.25946
248248 0 0
249249 8.45903 0.536069
250250 0 0
251251 15.4580 0.975698 0.487849 0.872928i 0.337782π-0.337782\pi
0.487849 + 0.872928i 0.337782π0.337782\pi
252252 0 0
253253 20.1149 1.26461
254254 0 0
255255 0 0
256256 0 0
257257 −9.74881 −0.608114 −0.304057 0.952654i 0.598341π-0.598341\pi
−0.304057 + 0.952654i 0.598341π0.598341\pi
258258 0 0
259259 −27.6120 −1.71573
260260 0 0
261261 7.19894 0.445603
262262 0 0
263263 7.81590 0.481949 0.240975 0.970531i 0.422533π-0.422533\pi
0.240975 + 0.970531i 0.422533π0.422533\pi
264264 0 0
265265 0 0
266266 0 0
267267 2.31206 0.141496
268268 0 0
269269 14.3640 0.875790 0.437895 0.899026i 0.355724π-0.355724\pi
0.437895 + 0.899026i 0.355724π0.355724\pi
270270 0 0
271271 −7.68418 −0.466781 −0.233390 0.972383i 0.574982π-0.574982\pi
−0.233390 + 0.972383i 0.574982π0.574982\pi
272272 0 0
273273 −19.1574 −1.15946
274274 0 0
275275 0 0
276276 0 0
277277 −4.92307 −0.295799 −0.147899 0.989002i 0.547251π-0.547251\pi
−0.147899 + 0.989002i 0.547251π0.547251\pi
278278 0 0
279279 5.69402 0.340892
280280 0 0
281281 −15.1371 −0.903006 −0.451503 0.892270i 0.649112π-0.649112\pi
−0.451503 + 0.892270i 0.649112π0.649112\pi
282282 0 0
283283 20.8914 1.24186 0.620931 0.783865i 0.286755π-0.286755\pi
0.620931 + 0.783865i 0.286755π0.286755\pi
284284 0 0
285285 0 0
286286 0 0
287287 34.0849 2.01197
288288 0 0
289289 −14.3820 −0.845998
290290 0 0
291291 −9.44919 −0.553921
292292 0 0
293293 13.2820 0.775940 0.387970 0.921672i 0.373176π-0.373176\pi
0.387970 + 0.921672i 0.373176π0.373176\pi
294294 0 0
295295 0 0
296296 0 0
297297 −5.59509 −0.324660
298298 0 0
299299 23.1345 1.33790
300300 0 0
301301 −0.434347 −0.0250353
302302 0 0
303303 −16.2273 −0.932234
304304 0 0
305305 0 0
306306 0 0
307307 −0.650819 −0.0371442 −0.0185721 0.999828i 0.505912π-0.505912\pi
−0.0185721 + 0.999828i 0.505912π0.505912\pi
308308 0 0
309309 10.2990 0.585887
310310 0 0
311311 25.6128 1.45237 0.726183 0.687501i 0.241292π-0.241292\pi
0.726183 + 0.687501i 0.241292π0.241292\pi
312312 0 0
313313 −18.8372 −1.06474 −0.532372 0.846511i 0.678699π-0.678699\pi
−0.532372 + 0.846511i 0.678699π0.678699\pi
314314 0 0
315315 0 0
316316 0 0
317317 −5.57649 −0.313207 −0.156603 0.987662i 0.550054π-0.550054\pi
−0.156603 + 0.987662i 0.550054π0.550054\pi
318318 0 0
319319 40.2787 2.25518
320320 0 0
321321 −1.10877 −0.0618858
322322 0 0
323323 4.97706 0.276931
324324 0 0
325325 0 0
326326 0 0
327327 15.1821 0.839571
328328 0 0
329329 −38.4253 −2.11846
330330 0 0
331331 −13.3088 −0.731518 −0.365759 0.930710i 0.619190π-0.619190\pi
−0.365759 + 0.930710i 0.619190π0.619190\pi
332332 0 0
333333 −9.27493 −0.508263
334334 0 0
335335 0 0
336336 0 0
337337 16.2122 0.883134 0.441567 0.897228i 0.354423π-0.354423\pi
0.441567 + 0.897228i 0.354423π0.354423\pi
338338 0 0
339339 −5.48090 −0.297682
340340 0 0
341341 31.8586 1.72524
342342 0 0
343343 −15.2935 −0.825774
344344 0 0
345345 0 0
346346 0 0
347347 7.18651 0.385792 0.192896 0.981219i 0.438212π-0.438212\pi
0.192896 + 0.981219i 0.438212π0.438212\pi
348348 0 0
349349 19.6390 1.05125 0.525625 0.850717i 0.323832π-0.323832\pi
0.525625 + 0.850717i 0.323832π0.323832\pi
350350 0 0
351351 −6.43501 −0.343476
352352 0 0
353353 10.6099 0.564710 0.282355 0.959310i 0.408884π-0.408884\pi
0.282355 + 0.959310i 0.408884π0.408884\pi
354354 0 0
355355 0 0
356356 0 0
357357 4.81698 0.254942
358358 0 0
359359 −30.3040 −1.59938 −0.799691 0.600412i 0.795003π-0.795003\pi
−0.799691 + 0.600412i 0.795003π0.795003\pi
360360 0 0
361361 −9.53828 −0.502015
362362 0 0
363363 −20.3050 −1.06574
364364 0 0
365365 0 0
366366 0 0
367367 1.16549 0.0608383 0.0304191 0.999537i 0.490316π-0.490316\pi
0.0304191 + 0.999537i 0.490316π0.490316\pi
368368 0 0
369369 11.4492 0.596021
370370 0 0
371371 1.24765 0.0647749
372372 0 0
373373 2.49400 0.129135 0.0645673 0.997913i 0.479433π-0.479433\pi
0.0645673 + 0.997913i 0.479433π0.479433\pi
374374 0 0
375375 0 0
376376 0 0
377377 46.3253 2.38587
378378 0 0
379379 1.83492 0.0942534 0.0471267 0.998889i 0.484994π-0.484994\pi
0.0471267 + 0.998889i 0.484994π0.484994\pi
380380 0 0
381381 3.39615 0.173990
382382 0 0
383383 −16.0646 −0.820864 −0.410432 0.911891i 0.634622π-0.634622\pi
−0.410432 + 0.911891i 0.634622π0.634622\pi
384384 0 0
385385 0 0
386386 0 0
387387 −0.145898 −0.00741641
388388 0 0
389389 −25.1203 −1.27365 −0.636824 0.771009i 0.719752π-0.719752\pi
−0.636824 + 0.771009i 0.719752π0.719752\pi
390390 0 0
391391 −5.81698 −0.294177
392392 0 0
393393 −1.05130 −0.0530312
394394 0 0
395395 0 0
396396 0 0
397397 17.6798 0.887326 0.443663 0.896194i 0.353679π-0.353679\pi
0.443663 + 0.896194i 0.353679π0.353679\pi
398398 0 0
399399 9.15740 0.458443
400400 0 0
401401 2.43219 0.121458 0.0607289 0.998154i 0.480657π-0.480657\pi
0.0607289 + 0.998154i 0.480657π0.480657\pi
402402 0 0
403403 36.6411 1.82522
404404 0 0
405405 0 0
406406 0 0
407407 −51.8941 −2.57230
408408 0 0
409409 −20.3509 −1.00629 −0.503144 0.864202i 0.667824π-0.667824\pi
−0.503144 + 0.864202i 0.667824π0.667824\pi
410410 0 0
411411 −4.11311 −0.202885
412412 0 0
413413 16.5042 0.812117
414414 0 0
415415 0 0
416416 0 0
417417 −20.9559 −1.02621
418418 0 0
419419 24.0158 1.17325 0.586625 0.809859i 0.300456π-0.300456\pi
0.586625 + 0.809859i 0.300456π0.300456\pi
420420 0 0
421421 −32.6241 −1.59000 −0.795001 0.606608i 0.792530π-0.792530\pi
−0.795001 + 0.606608i 0.792530π0.792530\pi
422422 0 0
423423 −12.9071 −0.627567
424424 0 0
425425 0 0
426426 0 0
427427 −35.2694 −1.70681
428428 0 0
429429 −36.0045 −1.73831
430430 0 0
431431 −8.72399 −0.420220 −0.210110 0.977678i 0.567382π-0.567382\pi
−0.210110 + 0.977678i 0.567382π0.567382\pi
432432 0 0
433433 −33.2307 −1.59697 −0.798483 0.602018i 0.794364π-0.794364\pi
−0.798483 + 0.602018i 0.794364π0.794364\pi
434434 0 0
435435 0 0
436436 0 0
437437 −11.0585 −0.528998
438438 0 0
439439 22.1581 1.05755 0.528773 0.848763i 0.322652π-0.322652\pi
0.528773 + 0.848763i 0.322652π0.322652\pi
440440 0 0
441441 1.86287 0.0887079
442442 0 0
443443 −2.95085 −0.140199 −0.0700996 0.997540i 0.522332π-0.522332\pi
−0.0700996 + 0.997540i 0.522332π0.522332\pi
444444 0 0
445445 0 0
446446 0 0
447447 −10.8781 −0.514518
448448 0 0
449449 7.48698 0.353333 0.176666 0.984271i 0.443469π-0.443469\pi
0.176666 + 0.984271i 0.443469π0.443469\pi
450450 0 0
451451 64.0593 3.01643
452452 0 0
453453 −15.9530 −0.749539
454454 0 0
455455 0 0
456456 0 0
457457 28.7258 1.34374 0.671868 0.740671i 0.265492π-0.265492\pi
0.671868 + 0.740671i 0.265492π0.265492\pi
458458 0 0
459459 1.61803 0.0755234
460460 0 0
461461 −16.0034 −0.745353 −0.372676 0.927961i 0.621560π-0.621560\pi
−0.372676 + 0.927961i 0.621560π0.621560\pi
462462 0 0
463463 −16.4852 −0.766134 −0.383067 0.923721i 0.625132π-0.625132\pi
−0.383067 + 0.923721i 0.625132π0.625132\pi
464464 0 0
465465 0 0
466466 0 0
467467 −7.68700 −0.355712 −0.177856 0.984057i 0.556916π-0.556916\pi
−0.177856 + 0.984057i 0.556916π0.556916\pi
468468 0 0
469469 −20.5871 −0.950623
470470 0 0
471471 −21.8744 −1.00792
472472 0 0
473473 −0.816313 −0.0375341
474474 0 0
475475 0 0
476476 0 0
477477 0.419089 0.0191888
478478 0 0
479479 16.0318 0.732514 0.366257 0.930514i 0.380639π-0.380639\pi
0.366257 + 0.930514i 0.380639π0.380639\pi
480480 0 0
481481 −59.6843 −2.72137
482482 0 0
483483 −10.7028 −0.486994
484484 0 0
485485 0 0
486486 0 0
487487 −18.6066 −0.843145 −0.421573 0.906795i 0.638522π-0.638522\pi
−0.421573 + 0.906795i 0.638522π0.638522\pi
488488 0 0
489489 18.1432 0.820465
490490 0 0
491491 3.62788 0.163724 0.0818619 0.996644i 0.473913π-0.473913\pi
0.0818619 + 0.996644i 0.473913π0.473913\pi
492492 0 0
493493 −11.6481 −0.524606
494494 0 0
495495 0 0
496496 0 0
497497 −20.2945 −0.910334
498498 0 0
499499 9.10435 0.407567 0.203783 0.979016i 0.434676π-0.434676\pi
0.203783 + 0.979016i 0.434676π0.434676\pi
500500 0 0
501501 5.18910 0.231832
502502 0 0
503503 1.80714 0.0805763 0.0402881 0.999188i 0.487172π-0.487172\pi
0.0402881 + 0.999188i 0.487172π0.487172\pi
504504 0 0
505505 0 0
506506 0 0
507507 −28.4094 −1.26171
508508 0 0
509509 25.9576 1.15055 0.575275 0.817960i 0.304895π-0.304895\pi
0.575275 + 0.817960i 0.304895π0.304895\pi
510510 0 0
511511 −9.92849 −0.439210
512512 0 0
513513 3.07599 0.135808
514514 0 0
515515 0 0
516516 0 0
517517 −72.2167 −3.17609
518518 0 0
519519 −18.9771 −0.833000
520520 0 0
521521 −35.4236 −1.55193 −0.775967 0.630773i 0.782738π-0.782738\pi
−0.775967 + 0.630773i 0.782738π0.782738\pi
522522 0 0
523523 23.7691 1.03935 0.519675 0.854364i 0.326053π-0.326053\pi
0.519675 + 0.854364i 0.326053π0.326053\pi
524524 0 0
525525 0 0
526526 0 0
527527 −9.21312 −0.401330
528528 0 0
529529 −10.0753 −0.438058
530530 0 0
531531 5.54379 0.240580
532532 0 0
533533 73.6757 3.19125
534534 0 0
535535 0 0
536536 0 0
537537 11.9744 0.516732
538538 0 0
539539 10.4229 0.448946
540540 0 0
541541 0.931170 0.0400341 0.0200171 0.999800i 0.493628π-0.493628\pi
0.0200171 + 0.999800i 0.493628π0.493628\pi
542542 0 0
543543 −11.5881 −0.497292
544544 0 0
545545 0 0
546546 0 0
547547 28.6968 1.22698 0.613492 0.789701i 0.289764π-0.289764\pi
0.613492 + 0.789701i 0.289764π0.289764\pi
548548 0 0
549549 −11.8471 −0.505621
550550 0 0
551551 −22.1439 −0.943361
552552 0 0
553553 −18.7653 −0.797980
554554 0 0
555555 0 0
556556 0 0
557557 28.5273 1.20874 0.604371 0.796703i 0.293424π-0.293424\pi
0.604371 + 0.796703i 0.293424π0.293424\pi
558558 0 0
559559 −0.938856 −0.0397094
560560 0 0
561561 9.05305 0.382220
562562 0 0
563563 35.6411 1.50209 0.751047 0.660249i 0.229549π-0.229549\pi
0.751047 + 0.660249i 0.229549π0.229549\pi
564564 0 0
565565 0 0
566566 0 0
567567 2.97706 0.125025
568568 0 0
569569 28.8728 1.21041 0.605205 0.796070i 0.293091π-0.293091\pi
0.605205 + 0.796070i 0.293091π0.293091\pi
570570 0 0
571571 −16.7217 −0.699782 −0.349891 0.936790i 0.613781π-0.613781\pi
−0.349891 + 0.936790i 0.613781π0.613781\pi
572572 0 0
573573 12.8322 0.536074
574574 0 0
575575 0 0
576576 0 0
577577 11.5022 0.478844 0.239422 0.970916i 0.423042π-0.423042\pi
0.239422 + 0.970916i 0.423042π0.423042\pi
578578 0 0
579579 9.15024 0.380271
580580 0 0
581581 −25.1830 −1.04477
582582 0 0
583583 2.34484 0.0971135
584584 0 0
585585 0 0
586586 0 0
587587 −22.5701 −0.931569 −0.465785 0.884898i 0.654228π-0.654228\pi
−0.465785 + 0.884898i 0.654228π0.654228\pi
588588 0 0
589589 −17.5148 −0.721683
590590 0 0
591591 −8.45187 −0.347664
592592 0 0
593593 −47.2237 −1.93924 −0.969622 0.244608i 0.921341π-0.921341\pi
−0.969622 + 0.244608i 0.921341π0.921341\pi
594594 0 0
595595 0 0
596596 0 0
597597 18.0231 0.737636
598598 0 0
599599 −2.79672 −0.114271 −0.0571354 0.998366i 0.518197π-0.518197\pi
−0.0571354 + 0.998366i 0.518197π0.518197\pi
600600 0 0
601601 −14.2935 −0.583042 −0.291521 0.956564i 0.594161π-0.594161\pi
−0.291521 + 0.956564i 0.594161π0.594161\pi
602602 0 0
603603 −6.91525 −0.281611
604604 0 0
605605 0 0
606606 0 0
607607 −12.8876 −0.523090 −0.261545 0.965191i 0.584232π-0.584232\pi
−0.261545 + 0.965191i 0.584232π0.584232\pi
608608 0 0
609609 −21.4317 −0.868455
610610 0 0
611611 −83.0577 −3.36015
612612 0 0
613613 14.1722 0.572411 0.286206 0.958168i 0.407606π-0.407606\pi
0.286206 + 0.958168i 0.407606π0.407606\pi
614614 0 0
615615 0 0
616616 0 0
617617 −10.7558 −0.433014 −0.216507 0.976281i 0.569466π-0.569466\pi
−0.216507 + 0.976281i 0.569466π0.569466\pi
618618 0 0
619619 −40.2143 −1.61635 −0.808175 0.588942i 0.799545π-0.799545\pi
−0.808175 + 0.588942i 0.799545π0.799545\pi
620620 0 0
621621 −3.59509 −0.144266
622622 0 0
623623 −6.88313 −0.275767
624624 0 0
625625 0 0
626626 0 0
627627 17.2104 0.687319
628628 0 0
629629 15.0072 0.598375
630630 0 0
631631 −3.16710 −0.126080 −0.0630401 0.998011i 0.520080π-0.520080\pi
−0.0630401 + 0.998011i 0.520080π0.520080\pi
632632 0 0
633633 −7.11245 −0.282694
634634 0 0
635635 0 0
636636 0 0
637637 11.9876 0.474965
638638 0 0
639639 −6.81698 −0.269676
640640 0 0
641641 −8.93559 −0.352935 −0.176467 0.984306i 0.556467π-0.556467\pi
−0.176467 + 0.984306i 0.556467π0.556467\pi
642642 0 0
643643 −17.5289 −0.691274 −0.345637 0.938368i 0.612337π-0.612337\pi
−0.345637 + 0.938368i 0.612337π0.612337\pi
644644 0 0
645645 0 0
646646 0 0
647647 −0.0600668 −0.00236147 −0.00118073 0.999999i 0.500376π-0.500376\pi
−0.00118073 + 0.999999i 0.500376π0.500376\pi
648648 0 0
649649 31.0180 1.21756
650650 0 0
651651 −16.9514 −0.664379
652652 0 0
653653 5.63396 0.220474 0.110237 0.993905i 0.464839π-0.464839\pi
0.110237 + 0.993905i 0.464839π0.464839\pi
654654 0 0
655655 0 0
656656 0 0
657657 −3.33500 −0.130111
658658 0 0
659659 −39.1355 −1.52450 −0.762252 0.647280i 0.775906π-0.775906\pi
−0.762252 + 0.647280i 0.775906π0.775906\pi
660660 0 0
661661 −13.8720 −0.539556 −0.269778 0.962922i 0.586950π-0.586950\pi
−0.269778 + 0.962922i 0.586950π0.586950\pi
662662 0 0
663663 10.4121 0.404371
664664 0 0
665665 0 0
666666 0 0
667667 25.8809 1.00211
668668 0 0
669669 24.7383 0.956438
670670 0 0
671671 −66.2855 −2.55892
672672 0 0
673673 18.5323 0.714369 0.357185 0.934034i 0.383737π-0.383737\pi
0.357185 + 0.934034i 0.383737π0.383737\pi
674674 0 0
675675 0 0
676676 0 0
677677 35.6361 1.36961 0.684804 0.728728i 0.259888π-0.259888\pi
0.684804 + 0.728728i 0.259888π0.259888\pi
678678 0 0
679679 28.1308 1.07956
680680 0 0
681681 20.2581 0.776291
682682 0 0
683683 30.4749 1.16609 0.583044 0.812440i 0.301861π-0.301861\pi
0.583044 + 0.812440i 0.301861π0.301861\pi
684684 0 0
685685 0 0
686686 0 0
687687 −2.20002 −0.0839361
688688 0 0
689689 2.69685 0.102742
690690 0 0
691691 16.5208 0.628479 0.314240 0.949344i 0.398250π-0.398250\pi
0.314240 + 0.949344i 0.398250π0.398250\pi
692692 0 0
693693 16.6569 0.632743
694694 0 0
695695 0 0
696696 0 0
697697 −18.5252 −0.701691
698698 0 0
699699 −1.55189 −0.0586977
700700 0 0
701701 6.68728 0.252575 0.126287 0.991994i 0.459694π-0.459694\pi
0.126287 + 0.991994i 0.459694π0.459694\pi
702702 0 0
703703 28.5296 1.07601
704704 0 0
705705 0 0
706706 0 0
707707 48.3096 1.81687
708708 0 0
709709 −4.84628 −0.182006 −0.0910029 0.995851i 0.529007π-0.529007\pi
−0.0910029 + 0.995851i 0.529007π0.529007\pi
710710 0 0
711711 −6.30329 −0.236392
712712 0 0
713713 20.4705 0.766627
714714 0 0
715715 0 0
716716 0 0
717717 5.98690 0.223585
718718 0 0
719719 36.6303 1.36608 0.683041 0.730380i 0.260657π-0.260657\pi
0.683041 + 0.730380i 0.260657π0.260657\pi
720720 0 0
721721 −30.6606 −1.14186
722722 0 0
723723 17.4368 0.648480
724724 0 0
725725 0 0
726726 0 0
727727 2.36143 0.0875807 0.0437903 0.999041i 0.486057π-0.486057\pi
0.0437903 + 0.999041i 0.486057π0.486057\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 0.236068 0.00873129
732732 0 0
733733 −3.19126 −0.117872 −0.0589359 0.998262i 0.518771π-0.518771\pi
−0.0589359 + 0.998262i 0.518771π0.518771\pi
734734 0 0
735735 0 0
736736 0 0
737737 −38.6914 −1.42522
738738 0 0
739739 −53.3412 −1.96219 −0.981094 0.193530i 0.938006π-0.938006\pi
−0.981094 + 0.193530i 0.938006π0.938006\pi
740740 0 0
741741 19.7940 0.727152
742742 0 0
743743 37.2497 1.36656 0.683280 0.730157i 0.260553π-0.260553\pi
0.683280 + 0.730157i 0.260553π0.260553\pi
744744 0 0
745745 0 0
746746 0 0
747747 −8.45903 −0.309500
748748 0 0
749749 3.30089 0.120612
750750 0 0
751751 39.5540 1.44334 0.721672 0.692235i 0.243374π-0.243374\pi
0.721672 + 0.692235i 0.243374π0.243374\pi
752752 0 0
753753 −15.4580 −0.563319
754754 0 0
755755 0 0
756756 0 0
757757 −17.0039 −0.618017 −0.309009 0.951059i 0.599997π-0.599997\pi
−0.309009 + 0.951059i 0.599997π0.599997\pi
758758 0 0
759759 −20.1149 −0.730123
760760 0 0
761761 40.6662 1.47415 0.737075 0.675811i 0.236207π-0.236207\pi
0.737075 + 0.675811i 0.236207π0.236207\pi
762762 0 0
763763 −45.1979 −1.63627
764764 0 0
765765 0 0
766766 0 0
767767 35.6743 1.28813
768768 0 0
769769 4.31197 0.155494 0.0777468 0.996973i 0.475227π-0.475227\pi
0.0777468 + 0.996973i 0.475227π0.475227\pi
770770 0 0
771771 9.74881 0.351095
772772 0 0
773773 21.1022 0.758993 0.379497 0.925193i 0.376097π-0.376097\pi
0.379497 + 0.925193i 0.376097π0.376097\pi
774774 0 0
775775 0 0
776776 0 0
777777 27.6120 0.990575
778778 0 0
779779 −35.2176 −1.26180
780780 0 0
781781 −38.1416 −1.36481
782782 0 0
783783 −7.19894 −0.257269
784784 0 0
785785 0 0
786786 0 0
787787 35.6296 1.27006 0.635029 0.772488i 0.280988π-0.280988\pi
0.635029 + 0.772488i 0.280988π0.280988\pi
788788 0 0
789789 −7.81590 −0.278253
790790 0 0
791791 16.3169 0.580164
792792 0 0
793793 −76.2361 −2.70722
794794 0 0
795795 0 0
796796 0 0
797797 −35.1353 −1.24455 −0.622277 0.782797i 0.713792π-0.713792\pi
−0.622277 + 0.782797i 0.713792π0.713792\pi
798798 0 0
799799 20.8842 0.738830
800800 0 0
801801 −2.31206 −0.0816926
802802 0 0
803803 −18.6596 −0.658484
804804 0 0
805805 0 0
806806 0 0
807807 −14.3640 −0.505638
808808 0 0
809809 −0.0908359 −0.00319362 −0.00159681 0.999999i 0.500508π-0.500508\pi
−0.00159681 + 0.999999i 0.500508π0.500508\pi
810810 0 0
811811 −3.09125 −0.108548 −0.0542742 0.998526i 0.517285π-0.517285\pi
−0.0542742 + 0.998526i 0.517285π0.517285\pi
812812 0 0
813813 7.68418 0.269496
814814 0 0
815815 0 0
816816 0 0
817817 0.448781 0.0157009
818818 0 0
819819 19.1574 0.669414
820820 0 0
821821 26.8171 0.935924 0.467962 0.883749i 0.344988π-0.344988\pi
0.467962 + 0.883749i 0.344988π0.344988\pi
822822 0 0
823823 −8.66133 −0.301915 −0.150957 0.988540i 0.548236π-0.548236\pi
−0.150957 + 0.988540i 0.548236π0.548236\pi
824824 0 0
825825 0 0
826826 0 0
827827 −54.9171 −1.90966 −0.954828 0.297160i 0.903961π-0.903961\pi
−0.954828 + 0.297160i 0.903961π0.903961\pi
828828 0 0
829829 27.2963 0.948039 0.474019 0.880514i 0.342803π-0.342803\pi
0.474019 + 0.880514i 0.342803π0.342803\pi
830830 0 0
831831 4.92307 0.170779
832832 0 0
833833 −3.01418 −0.104435
834834 0 0
835835 0 0
836836 0 0
837837 −5.69402 −0.196814
838838 0 0
839839 26.1547 0.902961 0.451481 0.892281i 0.350896π-0.350896\pi
0.451481 + 0.892281i 0.350896π0.350896\pi
840840 0 0
841841 22.8248 0.787062
842842 0 0
843843 15.1371 0.521351
844844 0 0
845845 0 0
846846 0 0
847847 60.4492 2.07706
848848 0 0
849849 −20.8914 −0.716990
850850 0 0
851851 −33.3442 −1.14303
852852 0 0
853853 −15.7614 −0.539660 −0.269830 0.962908i 0.586967π-0.586967\pi
−0.269830 + 0.962908i 0.586967π0.586967\pi
854854 0 0
855855 0 0
856856 0 0
857857 −8.76868 −0.299532 −0.149766 0.988721i 0.547852π-0.547852\pi
−0.149766 + 0.988721i 0.547852π0.547852\pi
858858 0 0
859859 −39.6170 −1.35171 −0.675857 0.737032i 0.736227π-0.736227\pi
−0.675857 + 0.737032i 0.736227π0.736227\pi
860860 0 0
861861 −34.0849 −1.16161
862862 0 0
863863 −15.7727 −0.536911 −0.268455 0.963292i 0.586513π-0.586513\pi
−0.268455 + 0.963292i 0.586513π0.586513\pi
864864 0 0
865865 0 0
866866 0 0
867867 14.3820 0.488437
868868 0 0
869869 −35.2675 −1.19637
870870 0 0
871871 −44.4997 −1.50781
872872 0 0
873873 9.44919 0.319807
874874 0 0
875875 0 0
876876 0 0
877877 −52.2422 −1.76409 −0.882047 0.471162i 0.843835π-0.843835\pi
−0.882047 + 0.471162i 0.843835π0.843835\pi
878878 0 0
879879 −13.2820 −0.447989
880880 0 0
881881 13.3902 0.451127 0.225564 0.974228i 0.427578π-0.427578\pi
0.225564 + 0.974228i 0.427578π0.427578\pi
882882 0 0
883883 −57.4075 −1.93192 −0.965958 0.258698i 0.916707π-0.916707\pi
−0.965958 + 0.258698i 0.916707π0.916707\pi
884884 0 0
885885 0 0
886886 0 0
887887 36.0967 1.21201 0.606004 0.795462i 0.292772π-0.292772\pi
0.606004 + 0.795462i 0.292772π0.292772\pi
888888 0 0
889889 −10.1105 −0.339096
890890 0 0
891891 5.59509 0.187443
892892 0 0
893893 39.7023 1.32859
894894 0 0
895895 0 0
896896 0 0
897897 −23.1345 −0.772437
898898 0 0
899899 40.9910 1.36713
900900 0 0
901901 −0.678101 −0.0225908
902902 0 0
903903 0.434347 0.0144542
904904 0 0
905905 0 0
906906 0 0
907907 7.07317 0.234861 0.117430 0.993081i 0.462534π-0.462534\pi
0.117430 + 0.993081i 0.462534π0.462534\pi
908908 0 0
909909 16.2273 0.538226
910910 0 0
911911 −15.6951 −0.520002 −0.260001 0.965608i 0.583723π-0.583723\pi
−0.260001 + 0.965608i 0.583723π0.583723\pi
912912 0 0
913913 −47.3291 −1.56636
914914 0 0
915915 0 0
916916 0 0
917917 3.12979 0.103355
918918 0 0
919919 20.4509 0.674614 0.337307 0.941395i 0.390484π-0.390484\pi
0.337307 + 0.941395i 0.390484π0.390484\pi
920920 0 0
921921 0.650819 0.0214452
922922 0 0
923923 −43.8673 −1.44391
924924 0 0
925925 0 0
926926 0 0
927927 −10.2990 −0.338262
928928 0 0
929929 20.3367 0.667227 0.333613 0.942710i 0.391732π-0.391732\pi
0.333613 + 0.942710i 0.391732π0.391732\pi
930930 0 0
931931 −5.73016 −0.187798
932932 0 0
933933 −25.6128 −0.838524
934934 0 0
935935 0 0
936936 0 0
937937 −60.3183 −1.97051 −0.985256 0.171086i 0.945273π-0.945273\pi
−0.985256 + 0.171086i 0.945273π0.945273\pi
938938 0 0
939939 18.8372 0.614730
940940 0 0
941941 −6.18625 −0.201666 −0.100833 0.994903i 0.532151π-0.532151\pi
−0.100833 + 0.994903i 0.532151π0.532151\pi
942942 0 0
943943 41.1609 1.34038
944944 0 0
945945 0 0
946946 0 0
947947 32.3809 1.05224 0.526120 0.850411i 0.323646π-0.323646\pi
0.526120 + 0.850411i 0.323646π0.323646\pi
948948 0 0
949949 −21.4608 −0.696646
950950 0 0
951951 5.57649 0.180830
952952 0 0
953953 −38.2037 −1.23754 −0.618770 0.785573i 0.712369π-0.712369\pi
−0.618770 + 0.785573i 0.712369π0.712369\pi
954954 0 0
955955 0 0
956956 0 0
957957 −40.2787 −1.30203
958958 0 0
959959 12.2450 0.395411
960960 0 0
961961 1.42191 0.0458681
962962 0 0
963963 1.10877 0.0357298
964964 0 0
965965 0 0
966966 0 0
967967 31.7778 1.02191 0.510953 0.859609i 0.329293π-0.329293\pi
0.510953 + 0.859609i 0.329293π0.329293\pi
968968 0 0
969969 −4.97706 −0.159886
970970 0 0
971971 0.870691 0.0279418 0.0139709 0.999902i 0.495553π-0.495553\pi
0.0139709 + 0.999902i 0.495553π0.495553\pi
972972 0 0
973973 62.3868 2.00003
974974 0 0
975975 0 0
976976 0 0
977977 −14.3197 −0.458128 −0.229064 0.973411i 0.573567π-0.573567\pi
−0.229064 + 0.973411i 0.573567π0.573567\pi
978978 0 0
979979 −12.9362 −0.413442
980980 0 0
981981 −15.1821 −0.484727
982982 0 0
983983 12.4302 0.396461 0.198231 0.980155i 0.436481π-0.436481\pi
0.198231 + 0.980155i 0.436481π0.436481\pi
984984 0 0
985985 0 0
986986 0 0
987987 38.4253 1.22309
988988 0 0
989989 −0.524517 −0.0166787
990990 0 0
991991 27.1963 0.863918 0.431959 0.901893i 0.357823π-0.357823\pi
0.431959 + 0.901893i 0.357823π0.357823\pi
992992 0 0
993993 13.3088 0.422342
994994 0 0
995995 0 0
996996 0 0
997997 47.1334 1.49273 0.746364 0.665537i 0.231798π-0.231798\pi
0.746364 + 0.665537i 0.231798π0.231798\pi
998998 0 0
999999 9.27493 0.293446
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 3000.2.a.j.1.4 4
3.2 odd 2 9000.2.a.t.1.4 4
4.3 odd 2 6000.2.a.bl.1.1 4
5.2 odd 4 3000.2.f.h.1249.8 8
5.3 odd 4 3000.2.f.h.1249.1 8
5.4 even 2 3000.2.a.o.1.1 yes 4
15.14 odd 2 9000.2.a.y.1.1 4
20.3 even 4 6000.2.f.p.1249.8 8
20.7 even 4 6000.2.f.p.1249.1 8
20.19 odd 2 6000.2.a.bc.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3000.2.a.j.1.4 4 1.1 even 1 trivial
3000.2.a.o.1.1 yes 4 5.4 even 2
3000.2.f.h.1249.1 8 5.3 odd 4
3000.2.f.h.1249.8 8 5.2 odd 4
6000.2.a.bc.1.4 4 20.19 odd 2
6000.2.a.bl.1.1 4 4.3 odd 2
6000.2.f.p.1249.1 8 20.7 even 4
6000.2.f.p.1249.8 8 20.3 even 4
9000.2.a.t.1.4 4 3.2 odd 2
9000.2.a.y.1.1 4 15.14 odd 2