Properties

Label 1521.2.a.k.1.1
Level 15211521
Weight 22
Character 1521.1
Self dual yes
Analytic conductor 12.14512.145
Analytic rank 11
Dimension 22
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] = [1521,2,Mod(1,1521)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1521, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1521.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1521=32132 1521 = 3^{2} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1521.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,2,0,0,0,0,0,-6,0,0,0,0,0,-10,-6,0,0,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 12.145246147412.1452461474
Analytic rank: 11
Dimension: 22
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: x23 x^{2} - 3 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 13)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.73205-1.73205 of defining polynomial
Character χ\chi == 1521.1

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) == q1.73205q2+1.00000q4+1.73205q5+1.73205q83.00000q105.00000q163.00000q173.46410q19+1.73205q206.00000q232.00000q253.00000q29+3.46410q31+5.19615q32+5.19615q34+8.66025q37+6.00000q38+3.00000q405.19615q418.00000q43+10.3923q463.46410q477.00000q49+3.46410q50+3.00000q53+5.19615q58+6.92820q59+1.00000q616.00000q62+1.00000q643.46410q673.00000q683.46410q711.73205q7315.0000q743.46410q76+4.00000q798.66025q80+9.00000q8213.8564q835.19615q85+13.8564q86+6.92820q896.00000q92+6.00000q946.00000q95+6.92820q97+12.1244q98+O(q100)q-1.73205 q^{2} +1.00000 q^{4} +1.73205 q^{5} +1.73205 q^{8} -3.00000 q^{10} -5.00000 q^{16} -3.00000 q^{17} -3.46410 q^{19} +1.73205 q^{20} -6.00000 q^{23} -2.00000 q^{25} -3.00000 q^{29} +3.46410 q^{31} +5.19615 q^{32} +5.19615 q^{34} +8.66025 q^{37} +6.00000 q^{38} +3.00000 q^{40} -5.19615 q^{41} -8.00000 q^{43} +10.3923 q^{46} -3.46410 q^{47} -7.00000 q^{49} +3.46410 q^{50} +3.00000 q^{53} +5.19615 q^{58} +6.92820 q^{59} +1.00000 q^{61} -6.00000 q^{62} +1.00000 q^{64} -3.46410 q^{67} -3.00000 q^{68} -3.46410 q^{71} -1.73205 q^{73} -15.0000 q^{74} -3.46410 q^{76} +4.00000 q^{79} -8.66025 q^{80} +9.00000 q^{82} -13.8564 q^{83} -5.19615 q^{85} +13.8564 q^{86} +6.92820 q^{89} -6.00000 q^{92} +6.00000 q^{94} -6.00000 q^{95} +6.92820 q^{97} +12.1244 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q46q1010q166q1712q234q256q29+12q38+6q4016q4314q49+6q53+2q6112q62+2q646q6830q74+8q79+12q95+O(q100) 2 q + 2 q^{4} - 6 q^{10} - 10 q^{16} - 6 q^{17} - 12 q^{23} - 4 q^{25} - 6 q^{29} + 12 q^{38} + 6 q^{40} - 16 q^{43} - 14 q^{49} + 6 q^{53} + 2 q^{61} - 12 q^{62} + 2 q^{64} - 6 q^{68} - 30 q^{74} + 8 q^{79}+ \cdots - 12 q^{95}+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 −1.73205 −1.22474 −0.612372 0.790569i 0.709785π-0.709785\pi
−0.612372 + 0.790569i 0.709785π0.709785\pi
33 0 0
44 1.00000 0.500000
55 1.73205 0.774597 0.387298 0.921954i 0.373408π-0.373408\pi
0.387298 + 0.921954i 0.373408π0.373408\pi
66 0 0
77 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
88 1.73205 0.612372
99 0 0
1010 −3.00000 −0.948683
1111 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1212 0 0
1313 0 0
1414 0 0
1515 0 0
1616 −5.00000 −1.25000
1717 −3.00000 −0.727607 −0.363803 0.931476i 0.618522π-0.618522\pi
−0.363803 + 0.931476i 0.618522π0.618522\pi
1818 0 0
1919 −3.46410 −0.794719 −0.397360 0.917663i 0.630073π-0.630073\pi
−0.397360 + 0.917663i 0.630073π0.630073\pi
2020 1.73205 0.387298
2121 0 0
2222 0 0
2323 −6.00000 −1.25109 −0.625543 0.780189i 0.715123π-0.715123\pi
−0.625543 + 0.780189i 0.715123π0.715123\pi
2424 0 0
2525 −2.00000 −0.400000
2626 0 0
2727 0 0
2828 0 0
2929 −3.00000 −0.557086 −0.278543 0.960424i 0.589851π-0.589851\pi
−0.278543 + 0.960424i 0.589851π0.589851\pi
3030 0 0
3131 3.46410 0.622171 0.311086 0.950382i 0.399307π-0.399307\pi
0.311086 + 0.950382i 0.399307π0.399307\pi
3232 5.19615 0.918559
3333 0 0
3434 5.19615 0.891133
3535 0 0
3636 0 0
3737 8.66025 1.42374 0.711868 0.702313i 0.247849π-0.247849\pi
0.711868 + 0.702313i 0.247849π0.247849\pi
3838 6.00000 0.973329
3939 0 0
4040 3.00000 0.474342
4141 −5.19615 −0.811503 −0.405751 0.913984i 0.632990π-0.632990\pi
−0.405751 + 0.913984i 0.632990π0.632990\pi
4242 0 0
4343 −8.00000 −1.21999 −0.609994 0.792406i 0.708828π-0.708828\pi
−0.609994 + 0.792406i 0.708828π0.708828\pi
4444 0 0
4545 0 0
4646 10.3923 1.53226
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 −7.00000 −1.00000
5050 3.46410 0.489898
5151 0 0
5252 0 0
5353 3.00000 0.412082 0.206041 0.978543i 0.433942π-0.433942\pi
0.206041 + 0.978543i 0.433942π0.433942\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 5.19615 0.682288
5959 6.92820 0.901975 0.450988 0.892530i 0.351072π-0.351072\pi
0.450988 + 0.892530i 0.351072π0.351072\pi
6060 0 0
6161 1.00000 0.128037 0.0640184 0.997949i 0.479608π-0.479608\pi
0.0640184 + 0.997949i 0.479608π0.479608\pi
6262 −6.00000 −0.762001
6363 0 0
6464 1.00000 0.125000
6565 0 0
6666 0 0
6767 −3.46410 −0.423207 −0.211604 0.977356i 0.567869π-0.567869\pi
−0.211604 + 0.977356i 0.567869π0.567869\pi
6868 −3.00000 −0.363803
6969 0 0
7070 0 0
7171 −3.46410 −0.411113 −0.205557 0.978645i 0.565900π-0.565900\pi
−0.205557 + 0.978645i 0.565900π0.565900\pi
7272 0 0
7373 −1.73205 −0.202721 −0.101361 0.994850i 0.532320π-0.532320\pi
−0.101361 + 0.994850i 0.532320π0.532320\pi
7474 −15.0000 −1.74371
7575 0 0
7676 −3.46410 −0.397360
7777 0 0
7878 0 0
7979 4.00000 0.450035 0.225018 0.974355i 0.427756π-0.427756\pi
0.225018 + 0.974355i 0.427756π0.427756\pi
8080 −8.66025 −0.968246
8181 0 0
8282 9.00000 0.993884
8383 −13.8564 −1.52094 −0.760469 0.649374i 0.775031π-0.775031\pi
−0.760469 + 0.649374i 0.775031π0.775031\pi
8484 0 0
8585 −5.19615 −0.563602
8686 13.8564 1.49417
8787 0 0
8888 0 0
8989 6.92820 0.734388 0.367194 0.930144i 0.380318π-0.380318\pi
0.367194 + 0.930144i 0.380318π0.380318\pi
9090 0 0
9191 0 0
9292 −6.00000 −0.625543
9393 0 0
9494 6.00000 0.618853
9595 −6.00000 −0.615587
9696 0 0
9797 6.92820 0.703452 0.351726 0.936103i 0.385595π-0.385595\pi
0.351726 + 0.936103i 0.385595π0.385595\pi
9898 12.1244 1.22474
9999 0 0
100100 −2.00000 −0.200000
101101 −3.00000 −0.298511 −0.149256 0.988799i 0.547688π-0.547688\pi
−0.149256 + 0.988799i 0.547688π0.547688\pi
102102 0 0
103103 10.0000 0.985329 0.492665 0.870219i 0.336023π-0.336023\pi
0.492665 + 0.870219i 0.336023π0.336023\pi
104104 0 0
105105 0 0
106106 −5.19615 −0.504695
107107 −6.00000 −0.580042 −0.290021 0.957020i 0.593662π-0.593662\pi
−0.290021 + 0.957020i 0.593662π0.593662\pi
108108 0 0
109109 −13.8564 −1.32720 −0.663602 0.748086i 0.730973π-0.730973\pi
−0.663602 + 0.748086i 0.730973π0.730973\pi
110110 0 0
111111 0 0
112112 0 0
113113 15.0000 1.41108 0.705541 0.708669i 0.250704π-0.250704\pi
0.705541 + 0.708669i 0.250704π0.250704\pi
114114 0 0
115115 −10.3923 −0.969087
116116 −3.00000 −0.278543
117117 0 0
118118 −12.0000 −1.10469
119119 0 0
120120 0 0
121121 −11.0000 −1.00000
122122 −1.73205 −0.156813
123123 0 0
124124 3.46410 0.311086
125125 −12.1244 −1.08444
126126 0 0
127127 2.00000 0.177471 0.0887357 0.996055i 0.471717π-0.471717\pi
0.0887357 + 0.996055i 0.471717π0.471717\pi
128128 −12.1244 −1.07165
129129 0 0
130130 0 0
131131 −18.0000 −1.57267 −0.786334 0.617802i 0.788023π-0.788023\pi
−0.786334 + 0.617802i 0.788023π0.788023\pi
132132 0 0
133133 0 0
134134 6.00000 0.518321
135135 0 0
136136 −5.19615 −0.445566
137137 −15.5885 −1.33181 −0.665906 0.746036i 0.731955π-0.731955\pi
−0.665906 + 0.746036i 0.731955π0.731955\pi
138138 0 0
139139 −4.00000 −0.339276 −0.169638 0.985506i 0.554260π-0.554260\pi
−0.169638 + 0.985506i 0.554260π0.554260\pi
140140 0 0
141141 0 0
142142 6.00000 0.503509
143143 0 0
144144 0 0
145145 −5.19615 −0.431517
146146 3.00000 0.248282
147147 0 0
148148 8.66025 0.711868
149149 19.0526 1.56085 0.780423 0.625252i 0.215004π-0.215004\pi
0.780423 + 0.625252i 0.215004π0.215004\pi
150150 0 0
151151 −17.3205 −1.40952 −0.704761 0.709444i 0.748946π-0.748946\pi
−0.704761 + 0.709444i 0.748946π0.748946\pi
152152 −6.00000 −0.486664
153153 0 0
154154 0 0
155155 6.00000 0.481932
156156 0 0
157157 −13.0000 −1.03751 −0.518756 0.854922i 0.673605π-0.673605\pi
−0.518756 + 0.854922i 0.673605π0.673605\pi
158158 −6.92820 −0.551178
159159 0 0
160160 9.00000 0.711512
161161 0 0
162162 0 0
163163 −20.7846 −1.62798 −0.813988 0.580881i 0.802708π-0.802708\pi
−0.813988 + 0.580881i 0.802708π0.802708\pi
164164 −5.19615 −0.405751
165165 0 0
166166 24.0000 1.86276
167167 13.8564 1.07224 0.536120 0.844141i 0.319889π-0.319889\pi
0.536120 + 0.844141i 0.319889π0.319889\pi
168168 0 0
169169 0 0
170170 9.00000 0.690268
171171 0 0
172172 −8.00000 −0.609994
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 0 0
176176 0 0
177177 0 0
178178 −12.0000 −0.899438
179179 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
180180 0 0
181181 −11.0000 −0.817624 −0.408812 0.912619i 0.634057π-0.634057\pi
−0.408812 + 0.912619i 0.634057π0.634057\pi
182182 0 0
183183 0 0
184184 −10.3923 −0.766131
185185 15.0000 1.10282
186186 0 0
187187 0 0
188188 −3.46410 −0.252646
189189 0 0
190190 10.3923 0.753937
191191 −18.0000 −1.30243 −0.651217 0.758891i 0.725741π-0.725741\pi
−0.651217 + 0.758891i 0.725741π0.725741\pi
192192 0 0
193193 −5.19615 −0.374027 −0.187014 0.982357i 0.559881π-0.559881\pi
−0.187014 + 0.982357i 0.559881π0.559881\pi
194194 −12.0000 −0.861550
195195 0 0
196196 −7.00000 −0.500000
197197 13.8564 0.987228 0.493614 0.869681i 0.335676π-0.335676\pi
0.493614 + 0.869681i 0.335676π0.335676\pi
198198 0 0
199199 2.00000 0.141776 0.0708881 0.997484i 0.477417π-0.477417\pi
0.0708881 + 0.997484i 0.477417π0.477417\pi
200200 −3.46410 −0.244949
201201 0 0
202202 5.19615 0.365600
203203 0 0
204204 0 0
205205 −9.00000 −0.628587
206206 −17.3205 −1.20678
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 10.0000 0.688428 0.344214 0.938891i 0.388145π-0.388145\pi
0.344214 + 0.938891i 0.388145π0.388145\pi
212212 3.00000 0.206041
213213 0 0
214214 10.3923 0.710403
215215 −13.8564 −0.944999
216216 0 0
217217 0 0
218218 24.0000 1.62549
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 10.3923 0.695920 0.347960 0.937509i 0.386874π-0.386874\pi
0.347960 + 0.937509i 0.386874π0.386874\pi
224224 0 0
225225 0 0
226226 −25.9808 −1.72821
227227 −24.2487 −1.60944 −0.804722 0.593652i 0.797686π-0.797686\pi
−0.804722 + 0.593652i 0.797686π0.797686\pi
228228 0 0
229229 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
230230 18.0000 1.18688
231231 0 0
232232 −5.19615 −0.341144
233233 6.00000 0.393073 0.196537 0.980497i 0.437031π-0.437031\pi
0.196537 + 0.980497i 0.437031π0.437031\pi
234234 0 0
235235 −6.00000 −0.391397
236236 6.92820 0.450988
237237 0 0
238238 0 0
239239 20.7846 1.34444 0.672222 0.740349i 0.265340π-0.265340\pi
0.672222 + 0.740349i 0.265340π0.265340\pi
240240 0 0
241241 1.73205 0.111571 0.0557856 0.998443i 0.482234π-0.482234\pi
0.0557856 + 0.998443i 0.482234π0.482234\pi
242242 19.0526 1.22474
243243 0 0
244244 1.00000 0.0640184
245245 −12.1244 −0.774597
246246 0 0
247247 0 0
248248 6.00000 0.381000
249249 0 0
250250 21.0000 1.32816
251251 −18.0000 −1.13615 −0.568075 0.822977i 0.692312π-0.692312\pi
−0.568075 + 0.822977i 0.692312π0.692312\pi
252252 0 0
253253 0 0
254254 −3.46410 −0.217357
255255 0 0
256256 19.0000 1.18750
257257 3.00000 0.187135 0.0935674 0.995613i 0.470173π-0.470173\pi
0.0935674 + 0.995613i 0.470173π0.470173\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 31.1769 1.92612
263263 −12.0000 −0.739952 −0.369976 0.929041i 0.620634π-0.620634\pi
−0.369976 + 0.929041i 0.620634π0.620634\pi
264264 0 0
265265 5.19615 0.319197
266266 0 0
267267 0 0
268268 −3.46410 −0.211604
269269 6.00000 0.365826 0.182913 0.983129i 0.441447π-0.441447\pi
0.182913 + 0.983129i 0.441447π0.441447\pi
270270 0 0
271271 20.7846 1.26258 0.631288 0.775549i 0.282527π-0.282527\pi
0.631288 + 0.775549i 0.282527π0.282527\pi
272272 15.0000 0.909509
273273 0 0
274274 27.0000 1.63113
275275 0 0
276276 0 0
277277 7.00000 0.420589 0.210295 0.977638i 0.432558π-0.432558\pi
0.210295 + 0.977638i 0.432558π0.432558\pi
278278 6.92820 0.415526
279279 0 0
280280 0 0
281281 −22.5167 −1.34323 −0.671616 0.740900i 0.734399π-0.734399\pi
−0.671616 + 0.740900i 0.734399π0.734399\pi
282282 0 0
283283 −4.00000 −0.237775 −0.118888 0.992908i 0.537933π-0.537933\pi
−0.118888 + 0.992908i 0.537933π0.537933\pi
284284 −3.46410 −0.205557
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −8.00000 −0.470588
290290 9.00000 0.528498
291291 0 0
292292 −1.73205 −0.101361
293293 5.19615 0.303562 0.151781 0.988414i 0.451499π-0.451499\pi
0.151781 + 0.988414i 0.451499π0.451499\pi
294294 0 0
295295 12.0000 0.698667
296296 15.0000 0.871857
297297 0 0
298298 −33.0000 −1.91164
299299 0 0
300300 0 0
301301 0 0
302302 30.0000 1.72631
303303 0 0
304304 17.3205 0.993399
305305 1.73205 0.0991769
306306 0 0
307307 17.3205 0.988534 0.494267 0.869310i 0.335437π-0.335437\pi
0.494267 + 0.869310i 0.335437π0.335437\pi
308308 0 0
309309 0 0
310310 −10.3923 −0.590243
311311 −30.0000 −1.70114 −0.850572 0.525859i 0.823744π-0.823744\pi
−0.850572 + 0.525859i 0.823744π0.823744\pi
312312 0 0
313313 10.0000 0.565233 0.282617 0.959233i 0.408798π-0.408798\pi
0.282617 + 0.959233i 0.408798π0.408798\pi
314314 22.5167 1.27069
315315 0 0
316316 4.00000 0.225018
317317 5.19615 0.291845 0.145922 0.989296i 0.453385π-0.453385\pi
0.145922 + 0.989296i 0.453385π0.453385\pi
318318 0 0
319319 0 0
320320 1.73205 0.0968246
321321 0 0
322322 0 0
323323 10.3923 0.578243
324324 0 0
325325 0 0
326326 36.0000 1.99386
327327 0 0
328328 −9.00000 −0.496942
329329 0 0
330330 0 0
331331 −27.7128 −1.52323 −0.761617 0.648027i 0.775594π-0.775594\pi
−0.761617 + 0.648027i 0.775594π0.775594\pi
332332 −13.8564 −0.760469
333333 0 0
334334 −24.0000 −1.31322
335335 −6.00000 −0.327815
336336 0 0
337337 23.0000 1.25289 0.626445 0.779466i 0.284509π-0.284509\pi
0.626445 + 0.779466i 0.284509π0.284509\pi
338338 0 0
339339 0 0
340340 −5.19615 −0.281801
341341 0 0
342342 0 0
343343 0 0
344344 −13.8564 −0.747087
345345 0 0
346346 −10.3923 −0.558694
347347 30.0000 1.61048 0.805242 0.592946i 0.202035π-0.202035\pi
0.805242 + 0.592946i 0.202035π0.202035\pi
348348 0 0
349349 13.8564 0.741716 0.370858 0.928689i 0.379064π-0.379064\pi
0.370858 + 0.928689i 0.379064π0.379064\pi
350350 0 0
351351 0 0
352352 0 0
353353 32.9090 1.75157 0.875784 0.482704i 0.160345π-0.160345\pi
0.875784 + 0.482704i 0.160345π0.160345\pi
354354 0 0
355355 −6.00000 −0.318447
356356 6.92820 0.367194
357357 0 0
358358 0 0
359359 −6.92820 −0.365657 −0.182828 0.983145i 0.558525π-0.558525\pi
−0.182828 + 0.983145i 0.558525π0.558525\pi
360360 0 0
361361 −7.00000 −0.368421
362362 19.0526 1.00138
363363 0 0
364364 0 0
365365 −3.00000 −0.157027
366366 0 0
367367 −22.0000 −1.14839 −0.574195 0.818718i 0.694685π-0.694685\pi
−0.574195 + 0.818718i 0.694685π0.694685\pi
368368 30.0000 1.56386
369369 0 0
370370 −25.9808 −1.35068
371371 0 0
372372 0 0
373373 19.0000 0.983783 0.491891 0.870657i 0.336306π-0.336306\pi
0.491891 + 0.870657i 0.336306π0.336306\pi
374374 0 0
375375 0 0
376376 −6.00000 −0.309426
377377 0 0
378378 0 0
379379 24.2487 1.24557 0.622786 0.782392i 0.286001π-0.286001\pi
0.622786 + 0.782392i 0.286001π0.286001\pi
380380 −6.00000 −0.307794
381381 0 0
382382 31.1769 1.59515
383383 20.7846 1.06204 0.531022 0.847358i 0.321808π-0.321808\pi
0.531022 + 0.847358i 0.321808π0.321808\pi
384384 0 0
385385 0 0
386386 9.00000 0.458088
387387 0 0
388388 6.92820 0.351726
389389 −9.00000 −0.456318 −0.228159 0.973624i 0.573271π-0.573271\pi
−0.228159 + 0.973624i 0.573271π0.573271\pi
390390 0 0
391391 18.0000 0.910299
392392 −12.1244 −0.612372
393393 0 0
394394 −24.0000 −1.20910
395395 6.92820 0.348596
396396 0 0
397397 13.8564 0.695433 0.347717 0.937600i 0.386957π-0.386957\pi
0.347717 + 0.937600i 0.386957π0.386957\pi
398398 −3.46410 −0.173640
399399 0 0
400400 10.0000 0.500000
401401 1.73205 0.0864945 0.0432472 0.999064i 0.486230π-0.486230\pi
0.0432472 + 0.999064i 0.486230π0.486230\pi
402402 0 0
403403 0 0
404404 −3.00000 −0.149256
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 15.5885 0.770800 0.385400 0.922750i 0.374064π-0.374064\pi
0.385400 + 0.922750i 0.374064π0.374064\pi
410410 15.5885 0.769859
411411 0 0
412412 10.0000 0.492665
413413 0 0
414414 0 0
415415 −24.0000 −1.17811
416416 0 0
417417 0 0
418418 0 0
419419 −18.0000 −0.879358 −0.439679 0.898155i 0.644908π-0.644908\pi
−0.439679 + 0.898155i 0.644908π0.644908\pi
420420 0 0
421421 15.5885 0.759735 0.379867 0.925041i 0.375970π-0.375970\pi
0.379867 + 0.925041i 0.375970π0.375970\pi
422422 −17.3205 −0.843149
423423 0 0
424424 5.19615 0.252347
425425 6.00000 0.291043
426426 0 0
427427 0 0
428428 −6.00000 −0.290021
429429 0 0
430430 24.0000 1.15738
431431 −6.92820 −0.333720 −0.166860 0.985981i 0.553363π-0.553363\pi
−0.166860 + 0.985981i 0.553363π0.553363\pi
432432 0 0
433433 17.0000 0.816968 0.408484 0.912766i 0.366058π-0.366058\pi
0.408484 + 0.912766i 0.366058π0.366058\pi
434434 0 0
435435 0 0
436436 −13.8564 −0.663602
437437 20.7846 0.994263
438438 0 0
439439 28.0000 1.33637 0.668184 0.743996i 0.267072π-0.267072\pi
0.668184 + 0.743996i 0.267072π0.267072\pi
440440 0 0
441441 0 0
442442 0 0
443443 12.0000 0.570137 0.285069 0.958507i 0.407984π-0.407984\pi
0.285069 + 0.958507i 0.407984π0.407984\pi
444444 0 0
445445 12.0000 0.568855
446446 −18.0000 −0.852325
447447 0 0
448448 0 0
449449 −6.92820 −0.326962 −0.163481 0.986546i 0.552272π-0.552272\pi
−0.163481 + 0.986546i 0.552272π0.552272\pi
450450 0 0
451451 0 0
452452 15.0000 0.705541
453453 0 0
454454 42.0000 1.97116
455455 0 0
456456 0 0
457457 −1.73205 −0.0810219 −0.0405110 0.999179i 0.512899π-0.512899\pi
−0.0405110 + 0.999179i 0.512899π0.512899\pi
458458 0 0
459459 0 0
460460 −10.3923 −0.484544
461461 −22.5167 −1.04871 −0.524353 0.851501i 0.675693π-0.675693\pi
−0.524353 + 0.851501i 0.675693π0.675693\pi
462462 0 0
463463 −13.8564 −0.643962 −0.321981 0.946746i 0.604349π-0.604349\pi
−0.321981 + 0.946746i 0.604349π0.604349\pi
464464 15.0000 0.696358
465465 0 0
466466 −10.3923 −0.481414
467467 12.0000 0.555294 0.277647 0.960683i 0.410445π-0.410445\pi
0.277647 + 0.960683i 0.410445π0.410445\pi
468468 0 0
469469 0 0
470470 10.3923 0.479361
471471 0 0
472472 12.0000 0.552345
473473 0 0
474474 0 0
475475 6.92820 0.317888
476476 0 0
477477 0 0
478478 −36.0000 −1.64660
479479 −24.2487 −1.10795 −0.553976 0.832533i 0.686890π-0.686890\pi
−0.553976 + 0.832533i 0.686890π0.686890\pi
480480 0 0
481481 0 0
482482 −3.00000 −0.136646
483483 0 0
484484 −11.0000 −0.500000
485485 12.0000 0.544892
486486 0 0
487487 −6.92820 −0.313947 −0.156973 0.987603i 0.550174π-0.550174\pi
−0.156973 + 0.987603i 0.550174π0.550174\pi
488488 1.73205 0.0784063
489489 0 0
490490 21.0000 0.948683
491491 12.0000 0.541552 0.270776 0.962642i 0.412720π-0.412720\pi
0.270776 + 0.962642i 0.412720π0.412720\pi
492492 0 0
493493 9.00000 0.405340
494494 0 0
495495 0 0
496496 −17.3205 −0.777714
497497 0 0
498498 0 0
499499 31.1769 1.39567 0.697835 0.716258i 0.254147π-0.254147\pi
0.697835 + 0.716258i 0.254147π0.254147\pi
500500 −12.1244 −0.542218
501501 0 0
502502 31.1769 1.39149
503503 −36.0000 −1.60516 −0.802580 0.596544i 0.796540π-0.796540\pi
−0.802580 + 0.596544i 0.796540π0.796540\pi
504504 0 0
505505 −5.19615 −0.231226
506506 0 0
507507 0 0
508508 2.00000 0.0887357
509509 19.0526 0.844490 0.422245 0.906482i 0.361242π-0.361242\pi
0.422245 + 0.906482i 0.361242π0.361242\pi
510510 0 0
511511 0 0
512512 −8.66025 −0.382733
513513 0 0
514514 −5.19615 −0.229192
515515 17.3205 0.763233
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 −9.00000 −0.394297 −0.197149 0.980374i 0.563168π-0.563168\pi
−0.197149 + 0.980374i 0.563168π0.563168\pi
522522 0 0
523523 −16.0000 −0.699631 −0.349816 0.936819i 0.613756π-0.613756\pi
−0.349816 + 0.936819i 0.613756π0.613756\pi
524524 −18.0000 −0.786334
525525 0 0
526526 20.7846 0.906252
527527 −10.3923 −0.452696
528528 0 0
529529 13.0000 0.565217
530530 −9.00000 −0.390935
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 −10.3923 −0.449299
536536 −6.00000 −0.259161
537537 0 0
538538 −10.3923 −0.448044
539539 0 0
540540 0 0
541541 −29.4449 −1.26593 −0.632967 0.774179i 0.718163π-0.718163\pi
−0.632967 + 0.774179i 0.718163π0.718163\pi
542542 −36.0000 −1.54633
543543 0 0
544544 −15.5885 −0.668350
545545 −24.0000 −1.02805
546546 0 0
547547 −22.0000 −0.940652 −0.470326 0.882493i 0.655864π-0.655864\pi
−0.470326 + 0.882493i 0.655864π0.655864\pi
548548 −15.5885 −0.665906
549549 0 0
550550 0 0
551551 10.3923 0.442727
552552 0 0
553553 0 0
554554 −12.1244 −0.515115
555555 0 0
556556 −4.00000 −0.169638
557557 15.5885 0.660504 0.330252 0.943893i 0.392866π-0.392866\pi
0.330252 + 0.943893i 0.392866π0.392866\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 39.0000 1.64512
563563 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
564564 0 0
565565 25.9808 1.09302
566566 6.92820 0.291214
567567 0 0
568568 −6.00000 −0.251754
569569 −42.0000 −1.76073 −0.880366 0.474295i 0.842703π-0.842703\pi
−0.880366 + 0.474295i 0.842703π0.842703\pi
570570 0 0
571571 −40.0000 −1.67395 −0.836974 0.547243i 0.815677π-0.815677\pi
−0.836974 + 0.547243i 0.815677π0.815677\pi
572572 0 0
573573 0 0
574574 0 0
575575 12.0000 0.500435
576576 0 0
577577 −19.0526 −0.793168 −0.396584 0.917998i 0.629805π-0.629805\pi
−0.396584 + 0.917998i 0.629805π0.629805\pi
578578 13.8564 0.576351
579579 0 0
580580 −5.19615 −0.215758
581581 0 0
582582 0 0
583583 0 0
584584 −3.00000 −0.124141
585585 0 0
586586 −9.00000 −0.371787
587587 −20.7846 −0.857873 −0.428936 0.903335i 0.641112π-0.641112\pi
−0.428936 + 0.903335i 0.641112π0.641112\pi
588588 0 0
589589 −12.0000 −0.494451
590590 −20.7846 −0.855689
591591 0 0
592592 −43.3013 −1.77967
593593 −25.9808 −1.06690 −0.533451 0.845831i 0.679105π-0.679105\pi
−0.533451 + 0.845831i 0.679105π0.679105\pi
594594 0 0
595595 0 0
596596 19.0526 0.780423
597597 0 0
598598 0 0
599599 −30.0000 −1.22577 −0.612883 0.790173i 0.709990π-0.709990\pi
−0.612883 + 0.790173i 0.709990π0.709990\pi
600600 0 0
601601 25.0000 1.01977 0.509886 0.860242i 0.329688π-0.329688\pi
0.509886 + 0.860242i 0.329688π0.329688\pi
602602 0 0
603603 0 0
604604 −17.3205 −0.704761
605605 −19.0526 −0.774597
606606 0 0
607607 −34.0000 −1.38002 −0.690009 0.723801i 0.742393π-0.742393\pi
−0.690009 + 0.723801i 0.742393π0.742393\pi
608608 −18.0000 −0.729996
609609 0 0
610610 −3.00000 −0.121466
611611 0 0
612612 0 0
613613 12.1244 0.489698 0.244849 0.969561i 0.421262π-0.421262\pi
0.244849 + 0.969561i 0.421262π0.421262\pi
614614 −30.0000 −1.21070
615615 0 0
616616 0 0
617617 22.5167 0.906487 0.453243 0.891387i 0.350267π-0.350267\pi
0.453243 + 0.891387i 0.350267π0.350267\pi
618618 0 0
619619 20.7846 0.835404 0.417702 0.908584i 0.362836π-0.362836\pi
0.417702 + 0.908584i 0.362836π0.362836\pi
620620 6.00000 0.240966
621621 0 0
622622 51.9615 2.08347
623623 0 0
624624 0 0
625625 −11.0000 −0.440000
626626 −17.3205 −0.692267
627627 0 0
628628 −13.0000 −0.518756
629629 −25.9808 −1.03592
630630 0 0
631631 48.4974 1.93065 0.965326 0.261048i 0.0840679π-0.0840679\pi
0.965326 + 0.261048i 0.0840679π0.0840679\pi
632632 6.92820 0.275589
633633 0 0
634634 −9.00000 −0.357436
635635 3.46410 0.137469
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 −21.0000 −0.830098
641641 33.0000 1.30342 0.651711 0.758468i 0.274052π-0.274052\pi
0.651711 + 0.758468i 0.274052π0.274052\pi
642642 0 0
643643 13.8564 0.546443 0.273222 0.961951i 0.411911π-0.411911\pi
0.273222 + 0.961951i 0.411911π0.411911\pi
644644 0 0
645645 0 0
646646 −18.0000 −0.708201
647647 18.0000 0.707653 0.353827 0.935311i 0.384880π-0.384880\pi
0.353827 + 0.935311i 0.384880π0.384880\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 −20.7846 −0.813988
653653 30.0000 1.17399 0.586995 0.809590i 0.300311π-0.300311\pi
0.586995 + 0.809590i 0.300311π0.300311\pi
654654 0 0
655655 −31.1769 −1.21818
656656 25.9808 1.01438
657657 0 0
658658 0 0
659659 12.0000 0.467454 0.233727 0.972302i 0.424908π-0.424908\pi
0.233727 + 0.972302i 0.424908π0.424908\pi
660660 0 0
661661 −46.7654 −1.81896 −0.909481 0.415745i 0.863521π-0.863521\pi
−0.909481 + 0.415745i 0.863521π0.863521\pi
662662 48.0000 1.86557
663663 0 0
664664 −24.0000 −0.931381
665665 0 0
666666 0 0
667667 18.0000 0.696963
668668 13.8564 0.536120
669669 0 0
670670 10.3923 0.401490
671671 0 0
672672 0 0
673673 19.0000 0.732396 0.366198 0.930537i 0.380659π-0.380659\pi
0.366198 + 0.930537i 0.380659π0.380659\pi
674674 −39.8372 −1.53447
675675 0 0
676676 0 0
677677 6.00000 0.230599 0.115299 0.993331i 0.463217π-0.463217\pi
0.115299 + 0.993331i 0.463217π0.463217\pi
678678 0 0
679679 0 0
680680 −9.00000 −0.345134
681681 0 0
682682 0 0
683683 24.2487 0.927851 0.463926 0.885874i 0.346441π-0.346441\pi
0.463926 + 0.885874i 0.346441π0.346441\pi
684684 0 0
685685 −27.0000 −1.03162
686686 0 0
687687 0 0
688688 40.0000 1.52499
689689 0 0
690690 0 0
691691 −13.8564 −0.527123 −0.263561 0.964643i 0.584897π-0.584897\pi
−0.263561 + 0.964643i 0.584897π0.584897\pi
692692 6.00000 0.228086
693693 0 0
694694 −51.9615 −1.97243
695695 −6.92820 −0.262802
696696 0 0
697697 15.5885 0.590455
698698 −24.0000 −0.908413
699699 0 0
700700 0 0
701701 18.0000 0.679851 0.339925 0.940452i 0.389598π-0.389598\pi
0.339925 + 0.940452i 0.389598π0.389598\pi
702702 0 0
703703 −30.0000 −1.13147
704704 0 0
705705 0 0
706706 −57.0000 −2.14522
707707 0 0
708708 0 0
709709 5.19615 0.195146 0.0975728 0.995228i 0.468892π-0.468892\pi
0.0975728 + 0.995228i 0.468892π0.468892\pi
710710 10.3923 0.390016
711711 0 0
712712 12.0000 0.449719
713713 −20.7846 −0.778390
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 12.0000 0.447836
719719 −48.0000 −1.79010 −0.895049 0.445968i 0.852860π-0.852860\pi
−0.895049 + 0.445968i 0.852860π0.852860\pi
720720 0 0
721721 0 0
722722 12.1244 0.451222
723723 0 0
724724 −11.0000 −0.408812
725725 6.00000 0.222834
726726 0 0
727727 32.0000 1.18681 0.593407 0.804902i 0.297782π-0.297782\pi
0.593407 + 0.804902i 0.297782π0.297782\pi
728728 0 0
729729 0 0
730730 5.19615 0.192318
731731 24.0000 0.887672
732732 0 0
733733 12.1244 0.447823 0.223912 0.974609i 0.428117π-0.428117\pi
0.223912 + 0.974609i 0.428117π0.428117\pi
734734 38.1051 1.40649
735735 0 0
736736 −31.1769 −1.14920
737737 0 0
738738 0 0
739739 −20.7846 −0.764574 −0.382287 0.924044i 0.624863π-0.624863\pi
−0.382287 + 0.924044i 0.624863π0.624863\pi
740740 15.0000 0.551411
741741 0 0
742742 0 0
743743 −34.6410 −1.27086 −0.635428 0.772160i 0.719176π-0.719176\pi
−0.635428 + 0.772160i 0.719176π0.719176\pi
744744 0 0
745745 33.0000 1.20903
746746 −32.9090 −1.20488
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 16.0000 0.583848 0.291924 0.956441i 0.405705π-0.405705\pi
0.291924 + 0.956441i 0.405705π0.405705\pi
752752 17.3205 0.631614
753753 0 0
754754 0 0
755755 −30.0000 −1.09181
756756 0 0
757757 −26.0000 −0.944986 −0.472493 0.881334i 0.656646π-0.656646\pi
−0.472493 + 0.881334i 0.656646π0.656646\pi
758758 −42.0000 −1.52551
759759 0 0
760760 −10.3923 −0.376969
761761 34.6410 1.25574 0.627868 0.778320i 0.283928π-0.283928\pi
0.627868 + 0.778320i 0.283928π0.283928\pi
762762 0 0
763763 0 0
764764 −18.0000 −0.651217
765765 0 0
766766 −36.0000 −1.30073
767767 0 0
768768 0 0
769769 −6.92820 −0.249837 −0.124919 0.992167i 0.539867π-0.539867\pi
−0.124919 + 0.992167i 0.539867π0.539867\pi
770770 0 0
771771 0 0
772772 −5.19615 −0.187014
773773 34.6410 1.24595 0.622975 0.782241i 0.285924π-0.285924\pi
0.622975 + 0.782241i 0.285924π0.285924\pi
774774 0 0
775775 −6.92820 −0.248868
776776 12.0000 0.430775
777777 0 0
778778 15.5885 0.558873
779779 18.0000 0.644917
780780 0 0
781781 0 0
782782 −31.1769 −1.11488
783783 0 0
784784 35.0000 1.25000
785785 −22.5167 −0.803654
786786 0 0
787787 −38.1051 −1.35830 −0.679150 0.733999i 0.737652π-0.737652\pi
−0.679150 + 0.733999i 0.737652π0.737652\pi
788788 13.8564 0.493614
789789 0 0
790790 −12.0000 −0.426941
791791 0 0
792792 0 0
793793 0 0
794794 −24.0000 −0.851728
795795 0 0
796796 2.00000 0.0708881
797797 42.0000 1.48772 0.743858 0.668338i 0.232994π-0.232994\pi
0.743858 + 0.668338i 0.232994π0.232994\pi
798798 0 0
799799 10.3923 0.367653
800800 −10.3923 −0.367423
801801 0 0
802802 −3.00000 −0.105934
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 −5.19615 −0.182800
809809 −33.0000 −1.16022 −0.580109 0.814539i 0.696990π-0.696990\pi
−0.580109 + 0.814539i 0.696990π0.696990\pi
810810 0 0
811811 −38.1051 −1.33805 −0.669026 0.743239i 0.733288π-0.733288\pi
−0.669026 + 0.743239i 0.733288π0.733288\pi
812812 0 0
813813 0 0
814814 0 0
815815 −36.0000 −1.26102
816816 0 0
817817 27.7128 0.969549
818818 −27.0000 −0.944033
819819 0 0
820820 −9.00000 −0.314294
821821 −41.5692 −1.45078 −0.725388 0.688340i 0.758340π-0.758340\pi
−0.725388 + 0.688340i 0.758340π0.758340\pi
822822 0 0
823823 4.00000 0.139431 0.0697156 0.997567i 0.477791π-0.477791\pi
0.0697156 + 0.997567i 0.477791π0.477791\pi
824824 17.3205 0.603388
825825 0 0
826826 0 0
827827 20.7846 0.722752 0.361376 0.932420i 0.382307π-0.382307\pi
0.361376 + 0.932420i 0.382307π0.382307\pi
828828 0 0
829829 −25.0000 −0.868286 −0.434143 0.900844i 0.642949π-0.642949\pi
−0.434143 + 0.900844i 0.642949π0.642949\pi
830830 41.5692 1.44289
831831 0 0
832832 0 0
833833 21.0000 0.727607
834834 0 0
835835 24.0000 0.830554
836836 0 0
837837 0 0
838838 31.1769 1.07699
839839 45.0333 1.55472 0.777361 0.629054i 0.216558π-0.216558\pi
0.777361 + 0.629054i 0.216558π0.216558\pi
840840 0 0
841841 −20.0000 −0.689655
842842 −27.0000 −0.930481
843843 0 0
844844 10.0000 0.344214
845845 0 0
846846 0 0
847847 0 0
848848 −15.0000 −0.515102
849849 0 0
850850 −10.3923 −0.356453
851851 −51.9615 −1.78122
852852 0 0
853853 −25.9808 −0.889564 −0.444782 0.895639i 0.646719π-0.646719\pi
−0.444782 + 0.895639i 0.646719π0.646719\pi
854854 0 0
855855 0 0
856856 −10.3923 −0.355202
857857 3.00000 0.102478 0.0512390 0.998686i 0.483683π-0.483683\pi
0.0512390 + 0.998686i 0.483683π0.483683\pi
858858 0 0
859859 −14.0000 −0.477674 −0.238837 0.971060i 0.576766π-0.576766\pi
−0.238837 + 0.971060i 0.576766π0.576766\pi
860860 −13.8564 −0.472500
861861 0 0
862862 12.0000 0.408722
863863 27.7128 0.943355 0.471678 0.881771i 0.343649π-0.343649\pi
0.471678 + 0.881771i 0.343649π0.343649\pi
864864 0 0
865865 10.3923 0.353349
866866 −29.4449 −1.00058
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 −24.0000 −0.812743
873873 0 0
874874 −36.0000 −1.21772
875875 0 0
876876 0 0
877877 12.1244 0.409410 0.204705 0.978824i 0.434376π-0.434376\pi
0.204705 + 0.978824i 0.434376π0.434376\pi
878878 −48.4974 −1.63671
879879 0 0
880880 0 0
881881 27.0000 0.909653 0.454827 0.890580i 0.349701π-0.349701\pi
0.454827 + 0.890580i 0.349701π0.349701\pi
882882 0 0
883883 −10.0000 −0.336527 −0.168263 0.985742i 0.553816π-0.553816\pi
−0.168263 + 0.985742i 0.553816π0.553816\pi
884884 0 0
885885 0 0
886886 −20.7846 −0.698273
887887 −36.0000 −1.20876 −0.604381 0.796696i 0.706579π-0.706579\pi
−0.604381 + 0.796696i 0.706579π0.706579\pi
888888 0 0
889889 0 0
890890 −20.7846 −0.696702
891891 0 0
892892 10.3923 0.347960
893893 12.0000 0.401565
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 12.0000 0.400445
899899 −10.3923 −0.346603
900900 0 0
901901 −9.00000 −0.299833
902902 0 0
903903 0 0
904904 25.9808 0.864107
905905 −19.0526 −0.633328
906906 0 0
907907 −28.0000 −0.929725 −0.464862 0.885383i 0.653896π-0.653896\pi
−0.464862 + 0.885383i 0.653896π0.653896\pi
908908 −24.2487 −0.804722
909909 0 0
910910 0 0
911911 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
912912 0 0
913913 0 0
914914 3.00000 0.0992312
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 22.0000 0.725713 0.362857 0.931845i 0.381802π-0.381802\pi
0.362857 + 0.931845i 0.381802π0.381802\pi
920920 −18.0000 −0.593442
921921 0 0
922922 39.0000 1.28440
923923 0 0
924924 0 0
925925 −17.3205 −0.569495
926926 24.0000 0.788689
927927 0 0
928928 −15.5885 −0.511716
929929 46.7654 1.53432 0.767161 0.641455i 0.221669π-0.221669\pi
0.767161 + 0.641455i 0.221669π0.221669\pi
930930 0 0
931931 24.2487 0.794719
932932 6.00000 0.196537
933933 0 0
934934 −20.7846 −0.680093
935935 0 0
936936 0 0
937937 7.00000 0.228680 0.114340 0.993442i 0.463525π-0.463525\pi
0.114340 + 0.993442i 0.463525π0.463525\pi
938938 0 0
939939 0 0
940940 −6.00000 −0.195698
941941 −20.7846 −0.677559 −0.338779 0.940866i 0.610014π-0.610014\pi
−0.338779 + 0.940866i 0.610014π0.610014\pi
942942 0 0
943943 31.1769 1.01526
944944 −34.6410 −1.12747
945945 0 0
946946 0 0
947947 17.3205 0.562841 0.281420 0.959585i 0.409194π-0.409194\pi
0.281420 + 0.959585i 0.409194π0.409194\pi
948948 0 0
949949 0 0
950950 −12.0000 −0.389331
951951 0 0
952952 0 0
953953 −6.00000 −0.194359 −0.0971795 0.995267i 0.530982π-0.530982\pi
−0.0971795 + 0.995267i 0.530982π0.530982\pi
954954 0 0
955955 −31.1769 −1.00886
956956 20.7846 0.672222
957957 0 0
958958 42.0000 1.35696
959959 0 0
960960 0 0
961961 −19.0000 −0.612903
962962 0 0
963963 0 0
964964 1.73205 0.0557856
965965 −9.00000 −0.289720
966966 0 0
967967 58.8897 1.89377 0.946883 0.321578i 0.104213π-0.104213\pi
0.946883 + 0.321578i 0.104213π0.104213\pi
968968 −19.0526 −0.612372
969969 0 0
970970 −20.7846 −0.667354
971971 −6.00000 −0.192549 −0.0962746 0.995355i 0.530693π-0.530693\pi
−0.0962746 + 0.995355i 0.530693π0.530693\pi
972972 0 0
973973 0 0
974974 12.0000 0.384505
975975 0 0
976976 −5.00000 −0.160046
977977 43.3013 1.38533 0.692665 0.721259i 0.256436π-0.256436\pi
0.692665 + 0.721259i 0.256436π0.256436\pi
978978 0 0
979979 0 0
980980 −12.1244 −0.387298
981981 0 0
982982 −20.7846 −0.663264
983983 51.9615 1.65732 0.828658 0.559756i 0.189105π-0.189105\pi
0.828658 + 0.559756i 0.189105π0.189105\pi
984984 0 0
985985 24.0000 0.764704
986986 −15.5885 −0.496438
987987 0 0
988988 0 0
989989 48.0000 1.52631
990990 0 0
991991 2.00000 0.0635321 0.0317660 0.999495i 0.489887π-0.489887\pi
0.0317660 + 0.999495i 0.489887π0.489887\pi
992992 18.0000 0.571501
993993 0 0
994994 0 0
995995 3.46410 0.109819
996996 0 0
997997 17.0000 0.538395 0.269198 0.963085i 0.413241π-0.413241\pi
0.269198 + 0.963085i 0.413241π0.413241\pi
998998 −54.0000 −1.70934
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 1521.2.a.k.1.1 2
3.2 odd 2 169.2.a.a.1.2 2
12.11 even 2 2704.2.a.o.1.1 2
13.5 odd 4 1521.2.b.a.1351.2 2
13.6 odd 12 117.2.q.c.10.1 2
13.8 odd 4 1521.2.b.a.1351.1 2
13.11 odd 12 117.2.q.c.82.1 2
13.12 even 2 inner 1521.2.a.k.1.2 2
15.14 odd 2 4225.2.a.v.1.1 2
21.20 even 2 8281.2.a.q.1.2 2
39.2 even 12 169.2.e.a.147.1 2
39.5 even 4 169.2.b.a.168.1 2
39.8 even 4 169.2.b.a.168.2 2
39.11 even 12 13.2.e.a.4.1 2
39.17 odd 6 169.2.c.a.146.2 4
39.20 even 12 169.2.e.a.23.1 2
39.23 odd 6 169.2.c.a.22.2 4
39.29 odd 6 169.2.c.a.22.1 4
39.32 even 12 13.2.e.a.10.1 yes 2
39.35 odd 6 169.2.c.a.146.1 4
39.38 odd 2 169.2.a.a.1.1 2
52.11 even 12 1872.2.by.d.433.1 2
52.19 even 12 1872.2.by.d.1297.1 2
156.11 odd 12 208.2.w.b.17.1 2
156.47 odd 4 2704.2.f.b.337.1 2
156.71 odd 12 208.2.w.b.49.1 2
156.83 odd 4 2704.2.f.b.337.2 2
156.155 even 2 2704.2.a.o.1.2 2
195.32 odd 12 325.2.m.a.49.1 4
195.89 even 12 325.2.n.a.251.1 2
195.128 odd 12 325.2.m.a.199.1 4
195.149 even 12 325.2.n.a.101.1 2
195.167 odd 12 325.2.m.a.199.2 4
195.188 odd 12 325.2.m.a.49.2 4
195.194 odd 2 4225.2.a.v.1.2 2
273.11 even 12 637.2.u.c.30.1 2
273.32 even 12 637.2.k.a.569.1 2
273.89 odd 12 637.2.k.c.459.1 2
273.110 odd 12 637.2.u.b.361.1 2
273.128 even 12 637.2.k.a.459.1 2
273.149 even 12 637.2.u.c.361.1 2
273.167 odd 12 637.2.q.a.589.1 2
273.188 odd 12 637.2.q.a.491.1 2
273.206 odd 12 637.2.u.b.30.1 2
273.227 odd 12 637.2.k.c.569.1 2
273.272 even 2 8281.2.a.q.1.1 2
312.11 odd 12 832.2.w.a.641.1 2
312.149 even 12 832.2.w.d.257.1 2
312.227 odd 12 832.2.w.a.257.1 2
312.245 even 12 832.2.w.d.641.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.2.e.a.4.1 2 39.11 even 12
13.2.e.a.10.1 yes 2 39.32 even 12
117.2.q.c.10.1 2 13.6 odd 12
117.2.q.c.82.1 2 13.11 odd 12
169.2.a.a.1.1 2 39.38 odd 2
169.2.a.a.1.2 2 3.2 odd 2
169.2.b.a.168.1 2 39.5 even 4
169.2.b.a.168.2 2 39.8 even 4
169.2.c.a.22.1 4 39.29 odd 6
169.2.c.a.22.2 4 39.23 odd 6
169.2.c.a.146.1 4 39.35 odd 6
169.2.c.a.146.2 4 39.17 odd 6
169.2.e.a.23.1 2 39.20 even 12
169.2.e.a.147.1 2 39.2 even 12
208.2.w.b.17.1 2 156.11 odd 12
208.2.w.b.49.1 2 156.71 odd 12
325.2.m.a.49.1 4 195.32 odd 12
325.2.m.a.49.2 4 195.188 odd 12
325.2.m.a.199.1 4 195.128 odd 12
325.2.m.a.199.2 4 195.167 odd 12
325.2.n.a.101.1 2 195.149 even 12
325.2.n.a.251.1 2 195.89 even 12
637.2.k.a.459.1 2 273.128 even 12
637.2.k.a.569.1 2 273.32 even 12
637.2.k.c.459.1 2 273.89 odd 12
637.2.k.c.569.1 2 273.227 odd 12
637.2.q.a.491.1 2 273.188 odd 12
637.2.q.a.589.1 2 273.167 odd 12
637.2.u.b.30.1 2 273.206 odd 12
637.2.u.b.361.1 2 273.110 odd 12
637.2.u.c.30.1 2 273.11 even 12
637.2.u.c.361.1 2 273.149 even 12
832.2.w.a.257.1 2 312.227 odd 12
832.2.w.a.641.1 2 312.11 odd 12
832.2.w.d.257.1 2 312.149 even 12
832.2.w.d.641.1 2 312.245 even 12
1521.2.a.k.1.1 2 1.1 even 1 trivial
1521.2.a.k.1.2 2 13.12 even 2 inner
1521.2.b.a.1351.1 2 13.8 odd 4
1521.2.b.a.1351.2 2 13.5 odd 4
1872.2.by.d.433.1 2 52.11 even 12
1872.2.by.d.1297.1 2 52.19 even 12
2704.2.a.o.1.1 2 12.11 even 2
2704.2.a.o.1.2 2 156.155 even 2
2704.2.f.b.337.1 2 156.47 odd 4
2704.2.f.b.337.2 2 156.83 odd 4
4225.2.a.v.1.1 2 15.14 odd 2
4225.2.a.v.1.2 2 195.194 odd 2
8281.2.a.q.1.1 2 273.272 even 2
8281.2.a.q.1.2 2 21.20 even 2