Properties

Label 1216.2.a.g.1.1
Level 12161216
Weight 22
Character 1216.1
Self dual yes
Analytic conductor 9.7109.710
Analytic rank 00
Dimension 11
CM no
Inner twists 11

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1216,2,Mod(1,1216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1216.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1216=2619 1216 = 2^{6} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1216.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: 9.709808885799.70980888579
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 38)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 1216.1

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+4.00000q53.00000q72.00000q9+2.00000q11+1.00000q134.00000q15+3.00000q171.00000q19+3.00000q21+1.00000q23+11.0000q25+5.00000q27+5.00000q29+8.00000q312.00000q3312.0000q35+2.00000q371.00000q398.00000q41+4.00000q438.00000q458.00000q47+2.00000q493.00000q51+1.00000q53+8.00000q55+1.00000q57+15.0000q592.00000q61+6.00000q63+4.00000q65+3.00000q671.00000q692.00000q71+9.00000q7311.0000q756.00000q77+10.0000q79+1.00000q816.00000q83+12.0000q855.00000q873.00000q918.00000q934.00000q952.00000q974.00000q99+O(q100)q-1.00000 q^{3} +4.00000 q^{5} -3.00000 q^{7} -2.00000 q^{9} +2.00000 q^{11} +1.00000 q^{13} -4.00000 q^{15} +3.00000 q^{17} -1.00000 q^{19} +3.00000 q^{21} +1.00000 q^{23} +11.0000 q^{25} +5.00000 q^{27} +5.00000 q^{29} +8.00000 q^{31} -2.00000 q^{33} -12.0000 q^{35} +2.00000 q^{37} -1.00000 q^{39} -8.00000 q^{41} +4.00000 q^{43} -8.00000 q^{45} -8.00000 q^{47} +2.00000 q^{49} -3.00000 q^{51} +1.00000 q^{53} +8.00000 q^{55} +1.00000 q^{57} +15.0000 q^{59} -2.00000 q^{61} +6.00000 q^{63} +4.00000 q^{65} +3.00000 q^{67} -1.00000 q^{69} -2.00000 q^{71} +9.00000 q^{73} -11.0000 q^{75} -6.00000 q^{77} +10.0000 q^{79} +1.00000 q^{81} -6.00000 q^{83} +12.0000 q^{85} -5.00000 q^{87} -3.00000 q^{91} -8.00000 q^{93} -4.00000 q^{95} -2.00000 q^{97} -4.00000 q^{99} +O(q^{100})

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 −0.288675 0.957427i 0.593215π-0.593215\pi
−0.288675 + 0.957427i 0.593215π0.593215\pi
44 0 0
55 4.00000 1.78885 0.894427 0.447214i 0.147584π-0.147584\pi
0.894427 + 0.447214i 0.147584π0.147584\pi
66 0 0
77 −3.00000 −1.13389 −0.566947 0.823754i 0.691875π-0.691875\pi
−0.566947 + 0.823754i 0.691875π0.691875\pi
88 0 0
99 −2.00000 −0.666667
1010 0 0
1111 2.00000 0.603023 0.301511 0.953463i 0.402509π-0.402509\pi
0.301511 + 0.953463i 0.402509π0.402509\pi
1212 0 0
1313 1.00000 0.277350 0.138675 0.990338i 0.455716π-0.455716\pi
0.138675 + 0.990338i 0.455716π0.455716\pi
1414 0 0
1515 −4.00000 −1.03280
1616 0 0
1717 3.00000 0.727607 0.363803 0.931476i 0.381478π-0.381478\pi
0.363803 + 0.931476i 0.381478π0.381478\pi
1818 0 0
1919 −1.00000 −0.229416
2020 0 0
2121 3.00000 0.654654
2222 0 0
2323 1.00000 0.208514 0.104257 0.994550i 0.466753π-0.466753\pi
0.104257 + 0.994550i 0.466753π0.466753\pi
2424 0 0
2525 11.0000 2.20000
2626 0 0
2727 5.00000 0.962250
2828 0 0
2929 5.00000 0.928477 0.464238 0.885710i 0.346328π-0.346328\pi
0.464238 + 0.885710i 0.346328π0.346328\pi
3030 0 0
3131 8.00000 1.43684 0.718421 0.695608i 0.244865π-0.244865\pi
0.718421 + 0.695608i 0.244865π0.244865\pi
3232 0 0
3333 −2.00000 −0.348155
3434 0 0
3535 −12.0000 −2.02837
3636 0 0
3737 2.00000 0.328798 0.164399 0.986394i 0.447432π-0.447432\pi
0.164399 + 0.986394i 0.447432π0.447432\pi
3838 0 0
3939 −1.00000 −0.160128
4040 0 0
4141 −8.00000 −1.24939 −0.624695 0.780869i 0.714777π-0.714777\pi
−0.624695 + 0.780869i 0.714777π0.714777\pi
4242 0 0
4343 4.00000 0.609994 0.304997 0.952353i 0.401344π-0.401344\pi
0.304997 + 0.952353i 0.401344π0.401344\pi
4444 0 0
4545 −8.00000 −1.19257
4646 0 0
4747 −8.00000 −1.16692 −0.583460 0.812142i 0.698301π-0.698301\pi
−0.583460 + 0.812142i 0.698301π0.698301\pi
4848 0 0
4949 2.00000 0.285714
5050 0 0
5151 −3.00000 −0.420084
5252 0 0
5353 1.00000 0.137361 0.0686803 0.997639i 0.478121π-0.478121\pi
0.0686803 + 0.997639i 0.478121π0.478121\pi
5454 0 0
5555 8.00000 1.07872
5656 0 0
5757 1.00000 0.132453
5858 0 0
5959 15.0000 1.95283 0.976417 0.215894i 0.0692665π-0.0692665\pi
0.976417 + 0.215894i 0.0692665π0.0692665\pi
6060 0 0
6161 −2.00000 −0.256074 −0.128037 0.991769i 0.540868π-0.540868\pi
−0.128037 + 0.991769i 0.540868π0.540868\pi
6262 0 0
6363 6.00000 0.755929
6464 0 0
6565 4.00000 0.496139
6666 0 0
6767 3.00000 0.366508 0.183254 0.983066i 0.441337π-0.441337\pi
0.183254 + 0.983066i 0.441337π0.441337\pi
6868 0 0
6969 −1.00000 −0.120386
7070 0 0
7171 −2.00000 −0.237356 −0.118678 0.992933i 0.537866π-0.537866\pi
−0.118678 + 0.992933i 0.537866π0.537866\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 −11.0000 −1.27017
7676 0 0
7777 −6.00000 −0.683763
7878 0 0
7979 10.0000 1.12509 0.562544 0.826767i 0.309823π-0.309823\pi
0.562544 + 0.826767i 0.309823π0.309823\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 −6.00000 −0.658586 −0.329293 0.944228i 0.606810π-0.606810\pi
−0.329293 + 0.944228i 0.606810π0.606810\pi
8484 0 0
8585 12.0000 1.30158
8686 0 0
8787 −5.00000 −0.536056
8888 0 0
8989 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
9090 0 0
9191 −3.00000 −0.314485
9292 0 0
9393 −8.00000 −0.829561
9494 0 0
9595 −4.00000 −0.410391
9696 0 0
9797 −2.00000 −0.203069 −0.101535 0.994832i 0.532375π-0.532375\pi
−0.101535 + 0.994832i 0.532375π0.532375\pi
9898 0 0
9999 −4.00000 −0.402015
100100 0 0
101101 −2.00000 −0.199007 −0.0995037 0.995037i 0.531726π-0.531726\pi
−0.0995037 + 0.995037i 0.531726π0.531726\pi
102102 0 0
103103 6.00000 0.591198 0.295599 0.955312i 0.404481π-0.404481\pi
0.295599 + 0.955312i 0.404481π0.404481\pi
104104 0 0
105105 12.0000 1.17108
106106 0 0
107107 −7.00000 −0.676716 −0.338358 0.941018i 0.609871π-0.609871\pi
−0.338358 + 0.941018i 0.609871π0.609871\pi
108108 0 0
109109 15.0000 1.43674 0.718370 0.695662i 0.244889π-0.244889\pi
0.718370 + 0.695662i 0.244889π0.244889\pi
110110 0 0
111111 −2.00000 −0.189832
112112 0 0
113113 14.0000 1.31701 0.658505 0.752577i 0.271189π-0.271189\pi
0.658505 + 0.752577i 0.271189π0.271189\pi
114114 0 0
115115 4.00000 0.373002
116116 0 0
117117 −2.00000 −0.184900
118118 0 0
119119 −9.00000 −0.825029
120120 0 0
121121 −7.00000 −0.636364
122122 0 0
123123 8.00000 0.721336
124124 0 0
125125 24.0000 2.14663
126126 0 0
127127 −18.0000 −1.59724 −0.798621 0.601834i 0.794437π-0.794437\pi
−0.798621 + 0.601834i 0.794437π0.794437\pi
128128 0 0
129129 −4.00000 −0.352180
130130 0 0
131131 12.0000 1.04844 0.524222 0.851581i 0.324356π-0.324356\pi
0.524222 + 0.851581i 0.324356π0.324356\pi
132132 0 0
133133 3.00000 0.260133
134134 0 0
135135 20.0000 1.72133
136136 0 0
137137 −17.0000 −1.45241 −0.726204 0.687479i 0.758717π-0.758717\pi
−0.726204 + 0.687479i 0.758717π0.758717\pi
138138 0 0
139139 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
140140 0 0
141141 8.00000 0.673722
142142 0 0
143143 2.00000 0.167248
144144 0 0
145145 20.0000 1.66091
146146 0 0
147147 −2.00000 −0.164957
148148 0 0
149149 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
150150 0 0
151151 −2.00000 −0.162758 −0.0813788 0.996683i 0.525932π-0.525932\pi
−0.0813788 + 0.996683i 0.525932π0.525932\pi
152152 0 0
153153 −6.00000 −0.485071
154154 0 0
155155 32.0000 2.57030
156156 0 0
157157 2.00000 0.159617 0.0798087 0.996810i 0.474569π-0.474569\pi
0.0798087 + 0.996810i 0.474569π0.474569\pi
158158 0 0
159159 −1.00000 −0.0793052
160160 0 0
161161 −3.00000 −0.236433
162162 0 0
163163 −16.0000 −1.25322 −0.626608 0.779334i 0.715557π-0.715557\pi
−0.626608 + 0.779334i 0.715557π0.715557\pi
164164 0 0
165165 −8.00000 −0.622799
166166 0 0
167167 12.0000 0.928588 0.464294 0.885681i 0.346308π-0.346308\pi
0.464294 + 0.885681i 0.346308π0.346308\pi
168168 0 0
169169 −12.0000 −0.923077
170170 0 0
171171 2.00000 0.152944
172172 0 0
173173 6.00000 0.456172 0.228086 0.973641i 0.426753π-0.426753\pi
0.228086 + 0.973641i 0.426753π0.426753\pi
174174 0 0
175175 −33.0000 −2.49457
176176 0 0
177177 −15.0000 −1.12747
178178 0 0
179179 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
180180 0 0
181181 −22.0000 −1.63525 −0.817624 0.575753i 0.804709π-0.804709\pi
−0.817624 + 0.575753i 0.804709π0.804709\pi
182182 0 0
183183 2.00000 0.147844
184184 0 0
185185 8.00000 0.588172
186186 0 0
187187 6.00000 0.438763
188188 0 0
189189 −15.0000 −1.09109
190190 0 0
191191 −7.00000 −0.506502 −0.253251 0.967401i 0.581500π-0.581500\pi
−0.253251 + 0.967401i 0.581500π0.581500\pi
192192 0 0
193193 −6.00000 −0.431889 −0.215945 0.976406i 0.569283π-0.569283\pi
−0.215945 + 0.976406i 0.569283π0.569283\pi
194194 0 0
195195 −4.00000 −0.286446
196196 0 0
197197 −8.00000 −0.569976 −0.284988 0.958531i 0.591990π-0.591990\pi
−0.284988 + 0.958531i 0.591990π0.591990\pi
198198 0 0
199199 25.0000 1.77220 0.886102 0.463491i 0.153403π-0.153403\pi
0.886102 + 0.463491i 0.153403π0.153403\pi
200200 0 0
201201 −3.00000 −0.211604
202202 0 0
203203 −15.0000 −1.05279
204204 0 0
205205 −32.0000 −2.23498
206206 0 0
207207 −2.00000 −0.139010
208208 0 0
209209 −2.00000 −0.138343
210210 0 0
211211 27.0000 1.85876 0.929378 0.369129i 0.120344π-0.120344\pi
0.929378 + 0.369129i 0.120344π0.120344\pi
212212 0 0
213213 2.00000 0.137038
214214 0 0
215215 16.0000 1.09119
216216 0 0
217217 −24.0000 −1.62923
218218 0 0
219219 −9.00000 −0.608164
220220 0 0
221221 3.00000 0.201802
222222 0 0
223223 −14.0000 −0.937509 −0.468755 0.883328i 0.655297π-0.655297\pi
−0.468755 + 0.883328i 0.655297π0.655297\pi
224224 0 0
225225 −22.0000 −1.46667
226226 0 0
227227 −17.0000 −1.12833 −0.564165 0.825662i 0.690802π-0.690802\pi
−0.564165 + 0.825662i 0.690802π0.690802\pi
228228 0 0
229229 10.0000 0.660819 0.330409 0.943838i 0.392813π-0.392813\pi
0.330409 + 0.943838i 0.392813π0.392813\pi
230230 0 0
231231 6.00000 0.394771
232232 0 0
233233 −6.00000 −0.393073 −0.196537 0.980497i 0.562969π-0.562969\pi
−0.196537 + 0.980497i 0.562969π0.562969\pi
234234 0 0
235235 −32.0000 −2.08745
236236 0 0
237237 −10.0000 −0.649570
238238 0 0
239239 −15.0000 −0.970269 −0.485135 0.874439i 0.661229π-0.661229\pi
−0.485135 + 0.874439i 0.661229π0.661229\pi
240240 0 0
241241 −8.00000 −0.515325 −0.257663 0.966235i 0.582952π-0.582952\pi
−0.257663 + 0.966235i 0.582952π0.582952\pi
242242 0 0
243243 −16.0000 −1.02640
244244 0 0
245245 8.00000 0.511101
246246 0 0
247247 −1.00000 −0.0636285
248248 0 0
249249 6.00000 0.380235
250250 0 0
251251 2.00000 0.126239 0.0631194 0.998006i 0.479895π-0.479895\pi
0.0631194 + 0.998006i 0.479895π0.479895\pi
252252 0 0
253253 2.00000 0.125739
254254 0 0
255255 −12.0000 −0.751469
256256 0 0
257257 8.00000 0.499026 0.249513 0.968371i 0.419729π-0.419729\pi
0.249513 + 0.968371i 0.419729π0.419729\pi
258258 0 0
259259 −6.00000 −0.372822
260260 0 0
261261 −10.0000 −0.618984
262262 0 0
263263 −24.0000 −1.47990 −0.739952 0.672660i 0.765152π-0.765152\pi
−0.739952 + 0.672660i 0.765152π0.765152\pi
264264 0 0
265265 4.00000 0.245718
266266 0 0
267267 0 0
268268 0 0
269269 −30.0000 −1.82913 −0.914566 0.404436i 0.867468π-0.867468\pi
−0.914566 + 0.404436i 0.867468π0.867468\pi
270270 0 0
271271 −7.00000 −0.425220 −0.212610 0.977137i 0.568196π-0.568196\pi
−0.212610 + 0.977137i 0.568196π0.568196\pi
272272 0 0
273273 3.00000 0.181568
274274 0 0
275275 22.0000 1.32665
276276 0 0
277277 −28.0000 −1.68236 −0.841178 0.540758i 0.818138π-0.818138\pi
−0.841178 + 0.540758i 0.818138π0.818138\pi
278278 0 0
279279 −16.0000 −0.957895
280280 0 0
281281 −8.00000 −0.477240 −0.238620 0.971113i 0.576695π-0.576695\pi
−0.238620 + 0.971113i 0.576695π0.576695\pi
282282 0 0
283283 −6.00000 −0.356663 −0.178331 0.983970i 0.557070π-0.557070\pi
−0.178331 + 0.983970i 0.557070π0.557070\pi
284284 0 0
285285 4.00000 0.236940
286286 0 0
287287 24.0000 1.41668
288288 0 0
289289 −8.00000 −0.470588
290290 0 0
291291 2.00000 0.117242
292292 0 0
293293 −9.00000 −0.525786 −0.262893 0.964825i 0.584677π-0.584677\pi
−0.262893 + 0.964825i 0.584677π0.584677\pi
294294 0 0
295295 60.0000 3.49334
296296 0 0
297297 10.0000 0.580259
298298 0 0
299299 1.00000 0.0578315
300300 0 0
301301 −12.0000 −0.691669
302302 0 0
303303 2.00000 0.114897
304304 0 0
305305 −8.00000 −0.458079
306306 0 0
307307 −12.0000 −0.684876 −0.342438 0.939540i 0.611253π-0.611253\pi
−0.342438 + 0.939540i 0.611253π0.611253\pi
308308 0 0
309309 −6.00000 −0.341328
310310 0 0
311311 −7.00000 −0.396934 −0.198467 0.980108i 0.563596π-0.563596\pi
−0.198467 + 0.980108i 0.563596π0.563596\pi
312312 0 0
313313 29.0000 1.63918 0.819588 0.572953i 0.194202π-0.194202\pi
0.819588 + 0.572953i 0.194202π0.194202\pi
314314 0 0
315315 24.0000 1.35225
316316 0 0
317317 27.0000 1.51647 0.758236 0.651981i 0.226062π-0.226062\pi
0.758236 + 0.651981i 0.226062π0.226062\pi
318318 0 0
319319 10.0000 0.559893
320320 0 0
321321 7.00000 0.390702
322322 0 0
323323 −3.00000 −0.166924
324324 0 0
325325 11.0000 0.610170
326326 0 0
327327 −15.0000 −0.829502
328328 0 0
329329 24.0000 1.32316
330330 0 0
331331 17.0000 0.934405 0.467202 0.884150i 0.345262π-0.345262\pi
0.467202 + 0.884150i 0.345262π0.345262\pi
332332 0 0
333333 −4.00000 −0.219199
334334 0 0
335335 12.0000 0.655630
336336 0 0
337337 −32.0000 −1.74315 −0.871576 0.490261i 0.836901π-0.836901\pi
−0.871576 + 0.490261i 0.836901π0.836901\pi
338338 0 0
339339 −14.0000 −0.760376
340340 0 0
341341 16.0000 0.866449
342342 0 0
343343 15.0000 0.809924
344344 0 0
345345 −4.00000 −0.215353
346346 0 0
347347 −2.00000 −0.107366 −0.0536828 0.998558i 0.517096π-0.517096\pi
−0.0536828 + 0.998558i 0.517096π0.517096\pi
348348 0 0
349349 −10.0000 −0.535288 −0.267644 0.963518i 0.586245π-0.586245\pi
−0.267644 + 0.963518i 0.586245π0.586245\pi
350350 0 0
351351 5.00000 0.266880
352352 0 0
353353 9.00000 0.479022 0.239511 0.970894i 0.423013π-0.423013\pi
0.239511 + 0.970894i 0.423013π0.423013\pi
354354 0 0
355355 −8.00000 −0.424596
356356 0 0
357357 9.00000 0.476331
358358 0 0
359359 15.0000 0.791670 0.395835 0.918322i 0.370455π-0.370455\pi
0.395835 + 0.918322i 0.370455π0.370455\pi
360360 0 0
361361 1.00000 0.0526316
362362 0 0
363363 7.00000 0.367405
364364 0 0
365365 36.0000 1.88433
366366 0 0
367367 −28.0000 −1.46159 −0.730794 0.682598i 0.760850π-0.760850\pi
−0.730794 + 0.682598i 0.760850π0.760850\pi
368368 0 0
369369 16.0000 0.832927
370370 0 0
371371 −3.00000 −0.155752
372372 0 0
373373 −29.0000 −1.50156 −0.750782 0.660551i 0.770323π-0.770323\pi
−0.750782 + 0.660551i 0.770323π0.770323\pi
374374 0 0
375375 −24.0000 −1.23935
376376 0 0
377377 5.00000 0.257513
378378 0 0
379379 15.0000 0.770498 0.385249 0.922813i 0.374116π-0.374116\pi
0.385249 + 0.922813i 0.374116π0.374116\pi
380380 0 0
381381 18.0000 0.922168
382382 0 0
383383 26.0000 1.32854 0.664269 0.747494i 0.268743π-0.268743\pi
0.664269 + 0.747494i 0.268743π0.268743\pi
384384 0 0
385385 −24.0000 −1.22315
386386 0 0
387387 −8.00000 −0.406663
388388 0 0
389389 30.0000 1.52106 0.760530 0.649303i 0.224939π-0.224939\pi
0.760530 + 0.649303i 0.224939π0.224939\pi
390390 0 0
391391 3.00000 0.151717
392392 0 0
393393 −12.0000 −0.605320
394394 0 0
395395 40.0000 2.01262
396396 0 0
397397 −8.00000 −0.401508 −0.200754 0.979642i 0.564339π-0.564339\pi
−0.200754 + 0.979642i 0.564339π0.564339\pi
398398 0 0
399399 −3.00000 −0.150188
400400 0 0
401401 −8.00000 −0.399501 −0.199750 0.979847i 0.564013π-0.564013\pi
−0.199750 + 0.979847i 0.564013π0.564013\pi
402402 0 0
403403 8.00000 0.398508
404404 0 0
405405 4.00000 0.198762
406406 0 0
407407 4.00000 0.198273
408408 0 0
409409 −20.0000 −0.988936 −0.494468 0.869196i 0.664637π-0.664637\pi
−0.494468 + 0.869196i 0.664637π0.664637\pi
410410 0 0
411411 17.0000 0.838548
412412 0 0
413413 −45.0000 −2.21431
414414 0 0
415415 −24.0000 −1.17811
416416 0 0
417417 0 0
418418 0 0
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 0 0
421421 13.0000 0.633581 0.316791 0.948495i 0.397395π-0.397395\pi
0.316791 + 0.948495i 0.397395π0.397395\pi
422422 0 0
423423 16.0000 0.777947
424424 0 0
425425 33.0000 1.60074
426426 0 0
427427 6.00000 0.290360
428428 0 0
429429 −2.00000 −0.0965609
430430 0 0
431431 18.0000 0.867029 0.433515 0.901146i 0.357273π-0.357273\pi
0.433515 + 0.901146i 0.357273π0.357273\pi
432432 0 0
433433 14.0000 0.672797 0.336399 0.941720i 0.390791π-0.390791\pi
0.336399 + 0.941720i 0.390791π0.390791\pi
434434 0 0
435435 −20.0000 −0.958927
436436 0 0
437437 −1.00000 −0.0478365
438438 0 0
439439 −20.0000 −0.954548 −0.477274 0.878755i 0.658375π-0.658375\pi
−0.477274 + 0.878755i 0.658375π0.658375\pi
440440 0 0
441441 −4.00000 −0.190476
442442 0 0
443443 −26.0000 −1.23530 −0.617649 0.786454i 0.711915π-0.711915\pi
−0.617649 + 0.786454i 0.711915π0.711915\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 10.0000 0.471929 0.235965 0.971762i 0.424175π-0.424175\pi
0.235965 + 0.971762i 0.424175π0.424175\pi
450450 0 0
451451 −16.0000 −0.753411
452452 0 0
453453 2.00000 0.0939682
454454 0 0
455455 −12.0000 −0.562569
456456 0 0
457457 −7.00000 −0.327446 −0.163723 0.986506i 0.552350π-0.552350\pi
−0.163723 + 0.986506i 0.552350π0.552350\pi
458458 0 0
459459 15.0000 0.700140
460460 0 0
461461 28.0000 1.30409 0.652045 0.758180i 0.273911π-0.273911\pi
0.652045 + 0.758180i 0.273911π0.273911\pi
462462 0 0
463463 −4.00000 −0.185896 −0.0929479 0.995671i 0.529629π-0.529629\pi
−0.0929479 + 0.995671i 0.529629π0.529629\pi
464464 0 0
465465 −32.0000 −1.48396
466466 0 0
467467 −2.00000 −0.0925490 −0.0462745 0.998929i 0.514735π-0.514735\pi
−0.0462745 + 0.998929i 0.514735π0.514735\pi
468468 0 0
469469 −9.00000 −0.415581
470470 0 0
471471 −2.00000 −0.0921551
472472 0 0
473473 8.00000 0.367840
474474 0 0
475475 −11.0000 −0.504715
476476 0 0
477477 −2.00000 −0.0915737
478478 0 0
479479 20.0000 0.913823 0.456912 0.889512i 0.348956π-0.348956\pi
0.456912 + 0.889512i 0.348956π0.348956\pi
480480 0 0
481481 2.00000 0.0911922
482482 0 0
483483 3.00000 0.136505
484484 0 0
485485 −8.00000 −0.363261
486486 0 0
487487 2.00000 0.0906287 0.0453143 0.998973i 0.485571π-0.485571\pi
0.0453143 + 0.998973i 0.485571π0.485571\pi
488488 0 0
489489 16.0000 0.723545
490490 0 0
491491 −28.0000 −1.26362 −0.631811 0.775122i 0.717688π-0.717688\pi
−0.631811 + 0.775122i 0.717688π0.717688\pi
492492 0 0
493493 15.0000 0.675566
494494 0 0
495495 −16.0000 −0.719147
496496 0 0
497497 6.00000 0.269137
498498 0 0
499499 40.0000 1.79065 0.895323 0.445418i 0.146945π-0.146945\pi
0.895323 + 0.445418i 0.146945π0.146945\pi
500500 0 0
501501 −12.0000 −0.536120
502502 0 0
503503 −39.0000 −1.73892 −0.869462 0.494000i 0.835534π-0.835534\pi
−0.869462 + 0.494000i 0.835534π0.835534\pi
504504 0 0
505505 −8.00000 −0.355995
506506 0 0
507507 12.0000 0.532939
508508 0 0
509509 30.0000 1.32973 0.664863 0.746965i 0.268490π-0.268490\pi
0.664863 + 0.746965i 0.268490π0.268490\pi
510510 0 0
511511 −27.0000 −1.19441
512512 0 0
513513 −5.00000 −0.220755
514514 0 0
515515 24.0000 1.05757
516516 0 0
517517 −16.0000 −0.703679
518518 0 0
519519 −6.00000 −0.263371
520520 0 0
521521 −28.0000 −1.22670 −0.613351 0.789810i 0.710179π-0.710179\pi
−0.613351 + 0.789810i 0.710179π0.710179\pi
522522 0 0
523523 29.0000 1.26808 0.634041 0.773300i 0.281395π-0.281395\pi
0.634041 + 0.773300i 0.281395π0.281395\pi
524524 0 0
525525 33.0000 1.44024
526526 0 0
527527 24.0000 1.04546
528528 0 0
529529 −22.0000 −0.956522
530530 0 0
531531 −30.0000 −1.30189
532532 0 0
533533 −8.00000 −0.346518
534534 0 0
535535 −28.0000 −1.21055
536536 0 0
537537 0 0
538538 0 0
539539 4.00000 0.172292
540540 0 0
541541 −2.00000 −0.0859867 −0.0429934 0.999075i 0.513689π-0.513689\pi
−0.0429934 + 0.999075i 0.513689π0.513689\pi
542542 0 0
543543 22.0000 0.944110
544544 0 0
545545 60.0000 2.57012
546546 0 0
547547 28.0000 1.19719 0.598597 0.801050i 0.295725π-0.295725\pi
0.598597 + 0.801050i 0.295725π0.295725\pi
548548 0 0
549549 4.00000 0.170716
550550 0 0
551551 −5.00000 −0.213007
552552 0 0
553553 −30.0000 −1.27573
554554 0 0
555555 −8.00000 −0.339581
556556 0 0
557557 −28.0000 −1.18640 −0.593199 0.805056i 0.702135π-0.702135\pi
−0.593199 + 0.805056i 0.702135π0.702135\pi
558558 0 0
559559 4.00000 0.169182
560560 0 0
561561 −6.00000 −0.253320
562562 0 0
563563 −36.0000 −1.51722 −0.758610 0.651546i 0.774121π-0.774121\pi
−0.758610 + 0.651546i 0.774121π0.774121\pi
564564 0 0
565565 56.0000 2.35594
566566 0 0
567567 −3.00000 −0.125988
568568 0 0
569569 40.0000 1.67689 0.838444 0.544988i 0.183466π-0.183466\pi
0.838444 + 0.544988i 0.183466π0.183466\pi
570570 0 0
571571 −28.0000 −1.17176 −0.585882 0.810397i 0.699252π-0.699252\pi
−0.585882 + 0.810397i 0.699252π0.699252\pi
572572 0 0
573573 7.00000 0.292429
574574 0 0
575575 11.0000 0.458732
576576 0 0
577577 −37.0000 −1.54033 −0.770165 0.637845i 0.779826π-0.779826\pi
−0.770165 + 0.637845i 0.779826π0.779826\pi
578578 0 0
579579 6.00000 0.249351
580580 0 0
581581 18.0000 0.746766
582582 0 0
583583 2.00000 0.0828315
584584 0 0
585585 −8.00000 −0.330759
586586 0 0
587587 −12.0000 −0.495293 −0.247647 0.968850i 0.579657π-0.579657\pi
−0.247647 + 0.968850i 0.579657π0.579657\pi
588588 0 0
589589 −8.00000 −0.329634
590590 0 0
591591 8.00000 0.329076
592592 0 0
593593 34.0000 1.39621 0.698106 0.715994i 0.254026π-0.254026\pi
0.698106 + 0.715994i 0.254026π0.254026\pi
594594 0 0
595595 −36.0000 −1.47586
596596 0 0
597597 −25.0000 −1.02318
598598 0 0
599599 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
600600 0 0
601601 −8.00000 −0.326327 −0.163163 0.986599i 0.552170π-0.552170\pi
−0.163163 + 0.986599i 0.552170π0.552170\pi
602602 0 0
603603 −6.00000 −0.244339
604604 0 0
605605 −28.0000 −1.13836
606606 0 0
607607 22.0000 0.892952 0.446476 0.894795i 0.352679π-0.352679\pi
0.446476 + 0.894795i 0.352679π0.352679\pi
608608 0 0
609609 15.0000 0.607831
610610 0 0
611611 −8.00000 −0.323645
612612 0 0
613613 −34.0000 −1.37325 −0.686624 0.727013i 0.740908π-0.740908\pi
−0.686624 + 0.727013i 0.740908π0.740908\pi
614614 0 0
615615 32.0000 1.29036
616616 0 0
617617 18.0000 0.724653 0.362326 0.932051i 0.381983π-0.381983\pi
0.362326 + 0.932051i 0.381983π0.381983\pi
618618 0 0
619619 10.0000 0.401934 0.200967 0.979598i 0.435592π-0.435592\pi
0.200967 + 0.979598i 0.435592π0.435592\pi
620620 0 0
621621 5.00000 0.200643
622622 0 0
623623 0 0
624624 0 0
625625 41.0000 1.64000
626626 0 0
627627 2.00000 0.0798723
628628 0 0
629629 6.00000 0.239236
630630 0 0
631631 −32.0000 −1.27390 −0.636950 0.770905i 0.719804π-0.719804\pi
−0.636950 + 0.770905i 0.719804π0.719804\pi
632632 0 0
633633 −27.0000 −1.07315
634634 0 0
635635 −72.0000 −2.85723
636636 0 0
637637 2.00000 0.0792429
638638 0 0
639639 4.00000 0.158238
640640 0 0
641641 42.0000 1.65890 0.829450 0.558581i 0.188654π-0.188654\pi
0.829450 + 0.558581i 0.188654π0.188654\pi
642642 0 0
643643 −26.0000 −1.02534 −0.512670 0.858586i 0.671344π-0.671344\pi
−0.512670 + 0.858586i 0.671344π0.671344\pi
644644 0 0
645645 −16.0000 −0.629999
646646 0 0
647647 −23.0000 −0.904223 −0.452112 0.891961i 0.649329π-0.649329\pi
−0.452112 + 0.891961i 0.649329π0.649329\pi
648648 0 0
649649 30.0000 1.17760
650650 0 0
651651 24.0000 0.940634
652652 0 0
653653 36.0000 1.40879 0.704394 0.709809i 0.251219π-0.251219\pi
0.704394 + 0.709809i 0.251219π0.251219\pi
654654 0 0
655655 48.0000 1.87552
656656 0 0
657657 −18.0000 −0.702247
658658 0 0
659659 5.00000 0.194772 0.0973862 0.995247i 0.468952π-0.468952\pi
0.0973862 + 0.995247i 0.468952π0.468952\pi
660660 0 0
661661 23.0000 0.894596 0.447298 0.894385i 0.352386π-0.352386\pi
0.447298 + 0.894385i 0.352386π0.352386\pi
662662 0 0
663663 −3.00000 −0.116510
664664 0 0
665665 12.0000 0.465340
666666 0 0
667667 5.00000 0.193601
668668 0 0
669669 14.0000 0.541271
670670 0 0
671671 −4.00000 −0.154418
672672 0 0
673673 44.0000 1.69608 0.848038 0.529936i 0.177784π-0.177784\pi
0.848038 + 0.529936i 0.177784π0.177784\pi
674674 0 0
675675 55.0000 2.11695
676676 0 0
677677 −13.0000 −0.499631 −0.249815 0.968294i 0.580370π-0.580370\pi
−0.249815 + 0.968294i 0.580370π0.580370\pi
678678 0 0
679679 6.00000 0.230259
680680 0 0
681681 17.0000 0.651441
682682 0 0
683683 4.00000 0.153056 0.0765279 0.997067i 0.475617π-0.475617\pi
0.0765279 + 0.997067i 0.475617π0.475617\pi
684684 0 0
685685 −68.0000 −2.59815
686686 0 0
687687 −10.0000 −0.381524
688688 0 0
689689 1.00000 0.0380970
690690 0 0
691691 42.0000 1.59776 0.798878 0.601494i 0.205427π-0.205427\pi
0.798878 + 0.601494i 0.205427π0.205427\pi
692692 0 0
693693 12.0000 0.455842
694694 0 0
695695 0 0
696696 0 0
697697 −24.0000 −0.909065
698698 0 0
699699 6.00000 0.226941
700700 0 0
701701 28.0000 1.05755 0.528773 0.848763i 0.322652π-0.322652\pi
0.528773 + 0.848763i 0.322652π0.322652\pi
702702 0 0
703703 −2.00000 −0.0754314
704704 0 0
705705 32.0000 1.20519
706706 0 0
707707 6.00000 0.225653
708708 0 0
709709 30.0000 1.12667 0.563337 0.826227i 0.309517π-0.309517\pi
0.563337 + 0.826227i 0.309517π0.309517\pi
710710 0 0
711711 −20.0000 −0.750059
712712 0 0
713713 8.00000 0.299602
714714 0 0
715715 8.00000 0.299183
716716 0 0
717717 15.0000 0.560185
718718 0 0
719719 5.00000 0.186469 0.0932343 0.995644i 0.470279π-0.470279\pi
0.0932343 + 0.995644i 0.470279π0.470279\pi
720720 0 0
721721 −18.0000 −0.670355
722722 0 0
723723 8.00000 0.297523
724724 0 0
725725 55.0000 2.04265
726726 0 0
727727 17.0000 0.630495 0.315248 0.949009i 0.397912π-0.397912\pi
0.315248 + 0.949009i 0.397912π0.397912\pi
728728 0 0
729729 13.0000 0.481481
730730 0 0
731731 12.0000 0.443836
732732 0 0
733733 36.0000 1.32969 0.664845 0.746981i 0.268498π-0.268498\pi
0.664845 + 0.746981i 0.268498π0.268498\pi
734734 0 0
735735 −8.00000 −0.295084
736736 0 0
737737 6.00000 0.221013
738738 0 0
739739 −40.0000 −1.47142 −0.735712 0.677295i 0.763152π-0.763152\pi
−0.735712 + 0.677295i 0.763152π0.763152\pi
740740 0 0
741741 1.00000 0.0367359
742742 0 0
743743 16.0000 0.586983 0.293492 0.955962i 0.405183π-0.405183\pi
0.293492 + 0.955962i 0.405183π0.405183\pi
744744 0 0
745745 0 0
746746 0 0
747747 12.0000 0.439057
748748 0 0
749749 21.0000 0.767323
750750 0 0
751751 −32.0000 −1.16770 −0.583848 0.811863i 0.698454π-0.698454\pi
−0.583848 + 0.811863i 0.698454π0.698454\pi
752752 0 0
753753 −2.00000 −0.0728841
754754 0 0
755755 −8.00000 −0.291150
756756 0 0
757757 2.00000 0.0726912 0.0363456 0.999339i 0.488428π-0.488428\pi
0.0363456 + 0.999339i 0.488428π0.488428\pi
758758 0 0
759759 −2.00000 −0.0725954
760760 0 0
761761 27.0000 0.978749 0.489375 0.872074i 0.337225π-0.337225\pi
0.489375 + 0.872074i 0.337225π0.337225\pi
762762 0 0
763763 −45.0000 −1.62911
764764 0 0
765765 −24.0000 −0.867722
766766 0 0
767767 15.0000 0.541619
768768 0 0
769769 −35.0000 −1.26213 −0.631066 0.775729i 0.717382π-0.717382\pi
−0.631066 + 0.775729i 0.717382π0.717382\pi
770770 0 0
771771 −8.00000 −0.288113
772772 0 0
773773 −9.00000 −0.323708 −0.161854 0.986815i 0.551747π-0.551747\pi
−0.161854 + 0.986815i 0.551747π0.551747\pi
774774 0 0
775775 88.0000 3.16105
776776 0 0
777777 6.00000 0.215249
778778 0 0
779779 8.00000 0.286630
780780 0 0
781781 −4.00000 −0.143131
782782 0 0
783783 25.0000 0.893427
784784 0 0
785785 8.00000 0.285532
786786 0 0
787787 −17.0000 −0.605985 −0.302992 0.952993i 0.597986π-0.597986\pi
−0.302992 + 0.952993i 0.597986π0.597986\pi
788788 0 0
789789 24.0000 0.854423
790790 0 0
791791 −42.0000 −1.49335
792792 0 0
793793 −2.00000 −0.0710221
794794 0 0
795795 −4.00000 −0.141865
796796 0 0
797797 −3.00000 −0.106265 −0.0531327 0.998587i 0.516921π-0.516921\pi
−0.0531327 + 0.998587i 0.516921π0.516921\pi
798798 0 0
799799 −24.0000 −0.849059
800800 0 0
801801 0 0
802802 0 0
803803 18.0000 0.635206
804804 0 0
805805 −12.0000 −0.422944
806806 0 0
807807 30.0000 1.05605
808808 0 0
809809 −15.0000 −0.527372 −0.263686 0.964609i 0.584938π-0.584938\pi
−0.263686 + 0.964609i 0.584938π0.584938\pi
810810 0 0
811811 −3.00000 −0.105344 −0.0526721 0.998612i 0.516774π-0.516774\pi
−0.0526721 + 0.998612i 0.516774π0.516774\pi
812812 0 0
813813 7.00000 0.245501
814814 0 0
815815 −64.0000 −2.24182
816816 0 0
817817 −4.00000 −0.139942
818818 0 0
819819 6.00000 0.209657
820820 0 0
821821 −12.0000 −0.418803 −0.209401 0.977830i 0.567152π-0.567152\pi
−0.209401 + 0.977830i 0.567152π0.567152\pi
822822 0 0
823823 −29.0000 −1.01088 −0.505438 0.862863i 0.668669π-0.668669\pi
−0.505438 + 0.862863i 0.668669π0.668669\pi
824824 0 0
825825 −22.0000 −0.765942
826826 0 0
827827 23.0000 0.799788 0.399894 0.916561i 0.369047π-0.369047\pi
0.399894 + 0.916561i 0.369047π0.369047\pi
828828 0 0
829829 15.0000 0.520972 0.260486 0.965478i 0.416117π-0.416117\pi
0.260486 + 0.965478i 0.416117π0.416117\pi
830830 0 0
831831 28.0000 0.971309
832832 0 0
833833 6.00000 0.207888
834834 0 0
835835 48.0000 1.66111
836836 0 0
837837 40.0000 1.38260
838838 0 0
839839 −20.0000 −0.690477 −0.345238 0.938515i 0.612202π-0.612202\pi
−0.345238 + 0.938515i 0.612202π0.612202\pi
840840 0 0
841841 −4.00000 −0.137931
842842 0 0
843843 8.00000 0.275535
844844 0 0
845845 −48.0000 −1.65125
846846 0 0
847847 21.0000 0.721569
848848 0 0
849849 6.00000 0.205919
850850 0 0
851851 2.00000 0.0685591
852852 0 0
853853 6.00000 0.205436 0.102718 0.994711i 0.467246π-0.467246\pi
0.102718 + 0.994711i 0.467246π0.467246\pi
854854 0 0
855855 8.00000 0.273594
856856 0 0
857857 −12.0000 −0.409912 −0.204956 0.978771i 0.565705π-0.565705\pi
−0.204956 + 0.978771i 0.565705π0.565705\pi
858858 0 0
859859 −50.0000 −1.70598 −0.852989 0.521929i 0.825213π-0.825213\pi
−0.852989 + 0.521929i 0.825213π0.825213\pi
860860 0 0
861861 −24.0000 −0.817918
862862 0 0
863863 −54.0000 −1.83818 −0.919091 0.394046i 0.871075π-0.871075\pi
−0.919091 + 0.394046i 0.871075π0.871075\pi
864864 0 0
865865 24.0000 0.816024
866866 0 0
867867 8.00000 0.271694
868868 0 0
869869 20.0000 0.678454
870870 0 0
871871 3.00000 0.101651
872872 0 0
873873 4.00000 0.135379
874874 0 0
875875 −72.0000 −2.43404
876876 0 0
877877 −13.0000 −0.438979 −0.219489 0.975615i 0.570439π-0.570439\pi
−0.219489 + 0.975615i 0.570439π0.570439\pi
878878 0 0
879879 9.00000 0.303562
880880 0 0
881881 −18.0000 −0.606435 −0.303218 0.952921i 0.598061π-0.598061\pi
−0.303218 + 0.952921i 0.598061π0.598061\pi
882882 0 0
883883 34.0000 1.14419 0.572096 0.820187i 0.306131π-0.306131\pi
0.572096 + 0.820187i 0.306131π0.306131\pi
884884 0 0
885885 −60.0000 −2.01688
886886 0 0
887887 2.00000 0.0671534 0.0335767 0.999436i 0.489310π-0.489310\pi
0.0335767 + 0.999436i 0.489310π0.489310\pi
888888 0 0
889889 54.0000 1.81110
890890 0 0
891891 2.00000 0.0670025
892892 0 0
893893 8.00000 0.267710
894894 0 0
895895 0 0
896896 0 0
897897 −1.00000 −0.0333890
898898 0 0
899899 40.0000 1.33407
900900 0 0
901901 3.00000 0.0999445
902902 0 0
903903 12.0000 0.399335
904904 0 0
905905 −88.0000 −2.92522
906906 0 0
907907 53.0000 1.75984 0.879918 0.475125i 0.157597π-0.157597\pi
0.879918 + 0.475125i 0.157597π0.157597\pi
908908 0 0
909909 4.00000 0.132672
910910 0 0
911911 −12.0000 −0.397578 −0.198789 0.980042i 0.563701π-0.563701\pi
−0.198789 + 0.980042i 0.563701π0.563701\pi
912912 0 0
913913 −12.0000 −0.397142
914914 0 0
915915 8.00000 0.264472
916916 0 0
917917 −36.0000 −1.18882
918918 0 0
919919 −5.00000 −0.164935 −0.0824674 0.996594i 0.526280π-0.526280\pi
−0.0824674 + 0.996594i 0.526280π0.526280\pi
920920 0 0
921921 12.0000 0.395413
922922 0 0
923923 −2.00000 −0.0658308
924924 0 0
925925 22.0000 0.723356
926926 0 0
927927 −12.0000 −0.394132
928928 0 0
929929 −55.0000 −1.80449 −0.902246 0.431222i 0.858082π-0.858082\pi
−0.902246 + 0.431222i 0.858082π0.858082\pi
930930 0 0
931931 −2.00000 −0.0655474
932932 0 0
933933 7.00000 0.229170
934934 0 0
935935 24.0000 0.784884
936936 0 0
937937 −7.00000 −0.228680 −0.114340 0.993442i 0.536475π-0.536475\pi
−0.114340 + 0.993442i 0.536475π0.536475\pi
938938 0 0
939939 −29.0000 −0.946379
940940 0 0
941941 −7.00000 −0.228193 −0.114097 0.993470i 0.536397π-0.536397\pi
−0.114097 + 0.993470i 0.536397π0.536397\pi
942942 0 0
943943 −8.00000 −0.260516
944944 0 0
945945 −60.0000 −1.95180
946946 0 0
947947 −12.0000 −0.389948 −0.194974 0.980808i 0.562462π-0.562462\pi
−0.194974 + 0.980808i 0.562462π0.562462\pi
948948 0 0
949949 9.00000 0.292152
950950 0 0
951951 −27.0000 −0.875535
952952 0 0
953953 −46.0000 −1.49009 −0.745043 0.667016i 0.767571π-0.767571\pi
−0.745043 + 0.667016i 0.767571π0.767571\pi
954954 0 0
955955 −28.0000 −0.906059
956956 0 0
957957 −10.0000 −0.323254
958958 0 0
959959 51.0000 1.64688
960960 0 0
961961 33.0000 1.06452
962962 0 0
963963 14.0000 0.451144
964964 0 0
965965 −24.0000 −0.772587
966966 0 0
967967 −48.0000 −1.54358 −0.771788 0.635880i 0.780637π-0.780637\pi
−0.771788 + 0.635880i 0.780637π0.780637\pi
968968 0 0
969969 3.00000 0.0963739
970970 0 0
971971 −28.0000 −0.898563 −0.449281 0.893390i 0.648320π-0.648320\pi
−0.449281 + 0.893390i 0.648320π0.648320\pi
972972 0 0
973973 0 0
974974 0 0
975975 −11.0000 −0.352282
976976 0 0
977977 8.00000 0.255943 0.127971 0.991778i 0.459153π-0.459153\pi
0.127971 + 0.991778i 0.459153π0.459153\pi
978978 0 0
979979 0 0
980980 0 0
981981 −30.0000 −0.957826
982982 0 0
983983 6.00000 0.191370 0.0956851 0.995412i 0.469496π-0.469496\pi
0.0956851 + 0.995412i 0.469496π0.469496\pi
984984 0 0
985985 −32.0000 −1.01960
986986 0 0
987987 −24.0000 −0.763928
988988 0 0
989989 4.00000 0.127193
990990 0 0
991991 8.00000 0.254128 0.127064 0.991894i 0.459445π-0.459445\pi
0.127064 + 0.991894i 0.459445π0.459445\pi
992992 0 0
993993 −17.0000 −0.539479
994994 0 0
995995 100.000 3.17021
996996 0 0
997997 −28.0000 −0.886769 −0.443384 0.896332i 0.646222π-0.646222\pi
−0.443384 + 0.896332i 0.646222π0.646222\pi
998998 0 0
999999 10.0000 0.316386
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 1216.2.a.g.1.1 1
4.3 odd 2 1216.2.a.n.1.1 1
8.3 odd 2 38.2.a.b.1.1 1
8.5 even 2 304.2.a.d.1.1 1
24.5 odd 2 2736.2.a.w.1.1 1
24.11 even 2 342.2.a.d.1.1 1
40.3 even 4 950.2.b.c.799.1 2
40.19 odd 2 950.2.a.b.1.1 1
40.27 even 4 950.2.b.c.799.2 2
40.29 even 2 7600.2.a.h.1.1 1
56.27 even 2 1862.2.a.f.1.1 1
88.43 even 2 4598.2.a.a.1.1 1
104.51 odd 2 6422.2.a.b.1.1 1
120.59 even 2 8550.2.a.u.1.1 1
152.3 even 18 722.2.e.d.389.1 6
152.11 odd 6 722.2.c.d.653.1 2
152.27 even 6 722.2.c.f.653.1 2
152.35 odd 18 722.2.e.c.389.1 6
152.37 odd 2 5776.2.a.d.1.1 1
152.43 odd 18 722.2.e.c.595.1 6
152.51 even 18 722.2.e.d.245.1 6
152.59 even 18 722.2.e.d.99.1 6
152.67 even 18 722.2.e.d.423.1 6
152.75 even 2 722.2.a.b.1.1 1
152.83 odd 6 722.2.c.d.429.1 2
152.91 even 18 722.2.e.d.415.1 6
152.99 odd 18 722.2.e.c.415.1 6
152.107 even 6 722.2.c.f.429.1 2
152.123 odd 18 722.2.e.c.423.1 6
152.131 odd 18 722.2.e.c.99.1 6
152.139 odd 18 722.2.e.c.245.1 6
152.147 even 18 722.2.e.d.595.1 6
456.227 odd 2 6498.2.a.y.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.a.b.1.1 1 8.3 odd 2
304.2.a.d.1.1 1 8.5 even 2
342.2.a.d.1.1 1 24.11 even 2
722.2.a.b.1.1 1 152.75 even 2
722.2.c.d.429.1 2 152.83 odd 6
722.2.c.d.653.1 2 152.11 odd 6
722.2.c.f.429.1 2 152.107 even 6
722.2.c.f.653.1 2 152.27 even 6
722.2.e.c.99.1 6 152.131 odd 18
722.2.e.c.245.1 6 152.139 odd 18
722.2.e.c.389.1 6 152.35 odd 18
722.2.e.c.415.1 6 152.99 odd 18
722.2.e.c.423.1 6 152.123 odd 18
722.2.e.c.595.1 6 152.43 odd 18
722.2.e.d.99.1 6 152.59 even 18
722.2.e.d.245.1 6 152.51 even 18
722.2.e.d.389.1 6 152.3 even 18
722.2.e.d.415.1 6 152.91 even 18
722.2.e.d.423.1 6 152.67 even 18
722.2.e.d.595.1 6 152.147 even 18
950.2.a.b.1.1 1 40.19 odd 2
950.2.b.c.799.1 2 40.3 even 4
950.2.b.c.799.2 2 40.27 even 4
1216.2.a.g.1.1 1 1.1 even 1 trivial
1216.2.a.n.1.1 1 4.3 odd 2
1862.2.a.f.1.1 1 56.27 even 2
2736.2.a.w.1.1 1 24.5 odd 2
4598.2.a.a.1.1 1 88.43 even 2
5776.2.a.d.1.1 1 152.37 odd 2
6422.2.a.b.1.1 1 104.51 odd 2
6498.2.a.y.1.1 1 456.227 odd 2
7600.2.a.h.1.1 1 40.29 even 2
8550.2.a.u.1.1 1 120.59 even 2