Properties

Label 4056.2.a.be.1.3
Level 40564056
Weight 22
Character 4056.1
Self dual yes
Analytic conductor 32.38732.387
Analytic rank 00
Dimension 44
CM no
Inner twists 11

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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] = [4056,2,Mod(1,4056)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4056, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 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("4056.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 4056=233132 4056 = 2^{3} \cdot 3 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4056.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,4,0,4,0,2,0,4,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 32.387323059832.3873230598
Analytic rank: 00
Dimension: 44
Coefficient field: 4.4.25488.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x49x26x+6 x^{4} - 9x^{2} - 6x + 6 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 312)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 2.28657-2.28657 of defining polynomial
Character χ\chi == 4056.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.00000q3+1.55452q5+2.96046q7+1.00000q92.24703q11+1.55452q151.01862q175.35607q19+2.96046q21+0.782926q232.58347q25+1.00000q27+2.69251q29+7.28657q312.24703q33+4.60209q35+7.80155q37+5.34474q41+3.12766q43+1.55452q45+7.13799q47+1.76430q491.01862q51+13.8388q533.49305q555.35607q57+4.35506q59+5.14528q61+2.96046q6312.9977q67+0.782926q69+13.8501q71+8.30519q732.58347q756.65223q77+1.23570q79+1.00000q81+7.67389q831.58347q85+2.69251q870.494055q89+7.28657q938.32611q9511.1057q972.24703q99+O(q100)q+1.00000 q^{3} +1.55452 q^{5} +2.96046 q^{7} +1.00000 q^{9} -2.24703 q^{11} +1.55452 q^{15} -1.01862 q^{17} -5.35607 q^{19} +2.96046 q^{21} +0.782926 q^{23} -2.58347 q^{25} +1.00000 q^{27} +2.69251 q^{29} +7.28657 q^{31} -2.24703 q^{33} +4.60209 q^{35} +7.80155 q^{37} +5.34474 q^{41} +3.12766 q^{43} +1.55452 q^{45} +7.13799 q^{47} +1.76430 q^{49} -1.01862 q^{51} +13.8388 q^{53} -3.49305 q^{55} -5.35607 q^{57} +4.35506 q^{59} +5.14528 q^{61} +2.96046 q^{63} -12.9977 q^{67} +0.782926 q^{69} +13.8501 q^{71} +8.30519 q^{73} -2.58347 q^{75} -6.65223 q^{77} +1.23570 q^{79} +1.00000 q^{81} +7.67389 q^{83} -1.58347 q^{85} +2.69251 q^{87} -0.494055 q^{89} +7.28657 q^{93} -8.32611 q^{95} -11.1057 q^{97} -2.24703 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q3+4q5+2q7+4q9+10q11+4q15+12q17+2q19+2q212q23+2q25+4q276q29+20q31+10q3310q35+10q37+6q41++10q99+O(q100) 4 q + 4 q^{3} + 4 q^{5} + 2 q^{7} + 4 q^{9} + 10 q^{11} + 4 q^{15} + 12 q^{17} + 2 q^{19} + 2 q^{21} - 2 q^{23} + 2 q^{25} + 4 q^{27} - 6 q^{29} + 20 q^{31} + 10 q^{33} - 10 q^{35} + 10 q^{37} + 6 q^{41}+ \cdots + 10 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 1.55452 0.695202 0.347601 0.937642i 0.386996π-0.386996\pi
0.347601 + 0.937642i 0.386996π0.386996\pi
66 0 0
77 2.96046 1.11895 0.559474 0.828848i 0.311003π-0.311003\pi
0.559474 + 0.828848i 0.311003π0.311003\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 −2.24703 −0.677504 −0.338752 0.940876i 0.610005π-0.610005\pi
−0.338752 + 0.940876i 0.610005π0.610005\pi
1212 0 0
1313 0 0
1414 0 0
1515 1.55452 0.401375
1616 0 0
1717 −1.01862 −0.247052 −0.123526 0.992341i 0.539420π-0.539420\pi
−0.123526 + 0.992341i 0.539420π0.539420\pi
1818 0 0
1919 −5.35607 −1.22877 −0.614383 0.789008i 0.710595π-0.710595\pi
−0.614383 + 0.789008i 0.710595π0.710595\pi
2020 0 0
2121 2.96046 0.646025
2222 0 0
2323 0.782926 0.163251 0.0816257 0.996663i 0.473989π-0.473989\pi
0.0816257 + 0.996663i 0.473989π0.473989\pi
2424 0 0
2525 −2.58347 −0.516694
2626 0 0
2727 1.00000 0.192450
2828 0 0
2929 2.69251 0.499986 0.249993 0.968248i 0.419572π-0.419572\pi
0.249993 + 0.968248i 0.419572π0.419572\pi
3030 0 0
3131 7.28657 1.30871 0.654353 0.756189i 0.272941π-0.272941\pi
0.654353 + 0.756189i 0.272941π0.272941\pi
3232 0 0
3333 −2.24703 −0.391157
3434 0 0
3535 4.60209 0.777895
3636 0 0
3737 7.80155 1.28257 0.641283 0.767304i 0.278402π-0.278402\pi
0.641283 + 0.767304i 0.278402π0.278402\pi
3838 0 0
3939 0 0
4040 0 0
4141 5.34474 0.834707 0.417354 0.908744i 0.362958π-0.362958\pi
0.417354 + 0.908744i 0.362958π0.362958\pi
4242 0 0
4343 3.12766 0.476964 0.238482 0.971147i 0.423350π-0.423350\pi
0.238482 + 0.971147i 0.423350π0.423350\pi
4444 0 0
4545 1.55452 0.231734
4646 0 0
4747 7.13799 1.04118 0.520591 0.853806i 0.325712π-0.325712\pi
0.520591 + 0.853806i 0.325712π0.325712\pi
4848 0 0
4949 1.76430 0.252043
5050 0 0
5151 −1.01862 −0.142636
5252 0 0
5353 13.8388 1.90090 0.950452 0.310871i 0.100621π-0.100621\pi
0.950452 + 0.310871i 0.100621π0.100621\pi
5454 0 0
5555 −3.49305 −0.471003
5656 0 0
5757 −5.35607 −0.709428
5858 0 0
5959 4.35506 0.566981 0.283490 0.958975i 0.408508π-0.408508\pi
0.283490 + 0.958975i 0.408508π0.408508\pi
6060 0 0
6161 5.14528 0.658785 0.329393 0.944193i 0.393156π-0.393156\pi
0.329393 + 0.944193i 0.393156π0.393156\pi
6262 0 0
6363 2.96046 0.372982
6464 0 0
6565 0 0
6666 0 0
6767 −12.9977 −1.58792 −0.793961 0.607969i 0.791985π-0.791985\pi
−0.793961 + 0.607969i 0.791985π0.791985\pi
6868 0 0
6969 0.782926 0.0942532
7070 0 0
7171 13.8501 1.64371 0.821854 0.569699i 0.192940π-0.192940\pi
0.821854 + 0.569699i 0.192940π0.192940\pi
7272 0 0
7373 8.30519 0.972049 0.486025 0.873945i 0.338447π-0.338447\pi
0.486025 + 0.873945i 0.338447π0.338447\pi
7474 0 0
7575 −2.58347 −0.298313
7676 0 0
7777 −6.65223 −0.758092
7878 0 0
7979 1.23570 0.139027 0.0695133 0.997581i 0.477855π-0.477855\pi
0.0695133 + 0.997581i 0.477855π0.477855\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 7.67389 0.842318 0.421159 0.906987i 0.361623π-0.361623\pi
0.421159 + 0.906987i 0.361623π0.361623\pi
8484 0 0
8585 −1.58347 −0.171751
8686 0 0
8787 2.69251 0.288667
8888 0 0
8989 −0.494055 −0.0523697 −0.0261849 0.999657i 0.508336π-0.508336\pi
−0.0261849 + 0.999657i 0.508336π0.508336\pi
9090 0 0
9191 0 0
9292 0 0
9393 7.28657 0.755582
9494 0 0
9595 −8.32611 −0.854241
9696 0 0
9797 −11.1057 −1.12762 −0.563808 0.825906i 0.690664π-0.690664\pi
−0.563808 + 0.825906i 0.690664π0.690664\pi
9898 0 0
9999 −2.24703 −0.225835
100100 0 0
101101 −15.1866 −1.51112 −0.755560 0.655080i 0.772635π-0.772635\pi
−0.755560 + 0.655080i 0.772635π0.772635\pi
102102 0 0
103103 −1.12766 −0.111112 −0.0555559 0.998456i 0.517693π-0.517693\pi
−0.0555559 + 0.998456i 0.517693π0.517693\pi
104104 0 0
105105 4.60209 0.449118
106106 0 0
107107 −17.0382 −1.64715 −0.823575 0.567208i 0.808024π-0.808024\pi
−0.823575 + 0.567208i 0.808024π0.808024\pi
108108 0 0
109109 15.2866 1.46419 0.732094 0.681204i 0.238543π-0.238543\pi
0.732094 + 0.681204i 0.238543π0.238543\pi
110110 0 0
111111 7.80155 0.740490
112112 0 0
113113 7.01862 0.660256 0.330128 0.943936i 0.392908π-0.392908\pi
0.330128 + 0.943936i 0.392908π0.392908\pi
114114 0 0
115115 1.21707 0.113493
116116 0 0
117117 0 0
118118 0 0
119119 −3.01559 −0.276438
120120 0 0
121121 −5.95087 −0.540988
122122 0 0
123123 5.34474 0.481919
124124 0 0
125125 −11.7887 −1.05441
126126 0 0
127127 −14.8015 −1.31342 −0.656712 0.754141i 0.728053π-0.728053\pi
−0.656712 + 0.754141i 0.728053π0.728053\pi
128128 0 0
129129 3.12766 0.275375
130130 0 0
131131 5.81916 0.508423 0.254211 0.967149i 0.418184π-0.418184\pi
0.254211 + 0.967149i 0.418184π0.418184\pi
132132 0 0
133133 −15.8564 −1.37492
134134 0 0
135135 1.55452 0.133792
136136 0 0
137137 17.3674 1.48380 0.741899 0.670512i 0.233926π-0.233926\pi
0.741899 + 0.670512i 0.233926π0.233926\pi
138138 0 0
139139 5.88792 0.499407 0.249704 0.968322i 0.419667π-0.419667\pi
0.249704 + 0.968322i 0.419667π0.419667\pi
140140 0 0
141141 7.13799 0.601127
142142 0 0
143143 0 0
144144 0 0
145145 4.18556 0.347592
146146 0 0
147147 1.76430 0.145517
148148 0 0
149149 −10.5845 −0.867114 −0.433557 0.901126i 0.642742π-0.642742\pi
−0.433557 + 0.901126i 0.642742π0.642742\pi
150150 0 0
151151 2.24703 0.182861 0.0914303 0.995811i 0.470856π-0.470856\pi
0.0914303 + 0.995811i 0.470856π0.470856\pi
152152 0 0
153153 −1.01862 −0.0823507
154154 0 0
155155 11.3271 0.909816
156156 0 0
157157 −8.45782 −0.675007 −0.337504 0.941324i 0.609583π-0.609583\pi
−0.337504 + 0.941324i 0.609583π0.609583\pi
158158 0 0
159159 13.8388 1.09749
160160 0 0
161161 2.31782 0.182670
162162 0 0
163163 −4.20019 −0.328985 −0.164492 0.986378i 0.552599π-0.552599\pi
−0.164492 + 0.986378i 0.552599π0.552599\pi
164164 0 0
165165 −3.49305 −0.271934
166166 0 0
167167 18.7121 1.44799 0.723994 0.689806i 0.242304π-0.242304\pi
0.723994 + 0.689806i 0.242304π0.242304\pi
168168 0 0
169169 0 0
170170 0 0
171171 −5.35607 −0.409589
172172 0 0
173173 2.89096 0.219796 0.109898 0.993943i 0.464948π-0.464948\pi
0.109898 + 0.993943i 0.464948π0.464948\pi
174174 0 0
175175 −7.64824 −0.578153
176176 0 0
177177 4.35506 0.327346
178178 0 0
179179 −22.8574 −1.70844 −0.854222 0.519909i 0.825966π-0.825966\pi
−0.854222 + 0.519909i 0.825966π0.825966\pi
180180 0 0
181181 −8.09042 −0.601356 −0.300678 0.953726i 0.597213π-0.597213\pi
−0.300678 + 0.953726i 0.597213π0.597213\pi
182182 0 0
183183 5.14528 0.380350
184184 0 0
185185 12.1277 0.891643
186186 0 0
187187 2.28887 0.167379
188188 0 0
189189 2.96046 0.215342
190190 0 0
191191 −15.3850 −1.11322 −0.556610 0.830774i 0.687898π-0.687898\pi
−0.556610 + 0.830774i 0.687898π0.687898\pi
192192 0 0
193193 −0.347036 −0.0249802 −0.0124901 0.999922i 0.503976π-0.503976\pi
−0.0124901 + 0.999922i 0.503976π0.503976\pi
194194 0 0
195195 0 0
196196 0 0
197197 25.8564 1.84219 0.921096 0.389335i 0.127295π-0.127295\pi
0.921096 + 0.389335i 0.127295π0.127295\pi
198198 0 0
199199 −7.34574 −0.520726 −0.260363 0.965511i 0.583842π-0.583842\pi
−0.260363 + 0.965511i 0.583842π0.583842\pi
200200 0 0
201201 −12.9977 −0.916787
202202 0 0
203203 7.97105 0.559458
204204 0 0
205205 8.30850 0.580291
206206 0 0
207207 0.782926 0.0544171
208208 0 0
209209 12.0352 0.832494
210210 0 0
211211 −28.6952 −1.97546 −0.987729 0.156175i 0.950084π-0.950084\pi
−0.987729 + 0.156175i 0.950084π0.950084\pi
212212 0 0
213213 13.8501 0.948995
214214 0 0
215215 4.86201 0.331586
216216 0 0
217217 21.5716 1.46437
218218 0 0
219219 8.30519 0.561213
220220 0 0
221221 0 0
222222 0 0
223223 −2.13698 −0.143103 −0.0715514 0.997437i 0.522795π-0.522795\pi
−0.0715514 + 0.997437i 0.522795π0.522795\pi
224224 0 0
225225 −2.58347 −0.172231
226226 0 0
227227 −18.3860 −1.22032 −0.610162 0.792277i 0.708895π-0.708895\pi
−0.610162 + 0.792277i 0.708895π0.708895\pi
228228 0 0
229229 1.74669 0.115424 0.0577122 0.998333i 0.481619π-0.481619\pi
0.0577122 + 0.998333i 0.481619π0.481619\pi
230230 0 0
231231 −6.65223 −0.437684
232232 0 0
233233 −26.3525 −1.72641 −0.863204 0.504855i 0.831546π-0.831546\pi
−0.863204 + 0.504855i 0.831546π0.831546\pi
234234 0 0
235235 11.0961 0.723833
236236 0 0
237237 1.23570 0.0802671
238238 0 0
239239 6.36336 0.411611 0.205806 0.978593i 0.434019π-0.434019\pi
0.205806 + 0.978593i 0.434019π0.434019\pi
240240 0 0
241241 −9.01862 −0.580940 −0.290470 0.956884i 0.593812π-0.593812\pi
−0.290470 + 0.956884i 0.593812π0.593812\pi
242242 0 0
243243 1.00000 0.0641500
244244 0 0
245245 2.74265 0.175221
246246 0 0
247247 0 0
248248 0 0
249249 7.67389 0.486313
250250 0 0
251251 −18.2760 −1.15357 −0.576785 0.816896i 0.695693π-0.695693\pi
−0.576785 + 0.816896i 0.695693π0.695693\pi
252252 0 0
253253 −1.75926 −0.110603
254254 0 0
255255 −1.58347 −0.0991606
256256 0 0
257257 26.4263 1.64843 0.824214 0.566279i 0.191617π-0.191617\pi
0.824214 + 0.566279i 0.191617π0.191617\pi
258258 0 0
259259 23.0961 1.43512
260260 0 0
261261 2.69251 0.166662
262262 0 0
263263 4.82017 0.297224 0.148612 0.988896i 0.452519π-0.452519\pi
0.148612 + 0.988896i 0.452519π0.452519\pi
264264 0 0
265265 21.5127 1.32151
266266 0 0
267267 −0.494055 −0.0302357
268268 0 0
269269 −1.64034 −0.100013 −0.0500066 0.998749i 0.515924π-0.515924\pi
−0.0500066 + 0.998749i 0.515924π0.515924\pi
270270 0 0
271271 −12.7300 −0.773294 −0.386647 0.922228i 0.626367π-0.626367\pi
−0.386647 + 0.922228i 0.626367π0.626367\pi
272272 0 0
273273 0 0
274274 0 0
275275 5.80512 0.350062
276276 0 0
277277 24.5008 1.47211 0.736055 0.676922i 0.236687π-0.236687\pi
0.736055 + 0.676922i 0.236687π0.236687\pi
278278 0 0
279279 7.28657 0.436236
280280 0 0
281281 1.93853 0.115643 0.0578215 0.998327i 0.481585π-0.481585\pi
0.0578215 + 0.998327i 0.481585π0.481585\pi
282282 0 0
283283 8.07853 0.480219 0.240109 0.970746i 0.422817π-0.422817\pi
0.240109 + 0.970746i 0.422817π0.422817\pi
284284 0 0
285285 −8.32611 −0.493196
286286 0 0
287287 15.8229 0.933994
288288 0 0
289289 −15.9624 −0.938965
290290 0 0
291291 −11.1057 −0.651030
292292 0 0
293293 −28.3411 −1.65571 −0.827854 0.560944i 0.810438π-0.810438\pi
−0.827854 + 0.560944i 0.810438π0.810438\pi
294294 0 0
295295 6.77003 0.394166
296296 0 0
297297 −2.24703 −0.130386
298298 0 0
299299 0 0
300300 0 0
301301 9.25931 0.533698
302302 0 0
303303 −15.1866 −0.872445
304304 0 0
305305 7.99844 0.457989
306306 0 0
307307 −30.7025 −1.75229 −0.876143 0.482051i 0.839892π-0.839892\pi
−0.876143 + 0.482051i 0.839892π0.839892\pi
308308 0 0
309309 −1.12766 −0.0641504
310310 0 0
311311 −13.7338 −0.778772 −0.389386 0.921075i 0.627313π-0.627313\pi
−0.389386 + 0.921075i 0.627313π0.627313\pi
312312 0 0
313313 32.1886 1.81941 0.909703 0.415260i 0.136309π-0.136309\pi
0.909703 + 0.415260i 0.136309π0.136309\pi
314314 0 0
315315 4.60209 0.259298
316316 0 0
317317 −4.54723 −0.255398 −0.127699 0.991813i 0.540759π-0.540759\pi
−0.127699 + 0.991813i 0.540759π0.540759\pi
318318 0 0
319319 −6.05014 −0.338743
320320 0 0
321321 −17.0382 −0.950982
322322 0 0
323323 5.45581 0.303569
324324 0 0
325325 0 0
326326 0 0
327327 15.2866 0.845349
328328 0 0
329329 21.1317 1.16503
330330 0 0
331331 14.7899 0.812928 0.406464 0.913667i 0.366762π-0.366762\pi
0.406464 + 0.913667i 0.366762π0.366762\pi
332332 0 0
333333 7.80155 0.427522
334334 0 0
335335 −20.2052 −1.10393
336336 0 0
337337 3.21808 0.175300 0.0876500 0.996151i 0.472064π-0.472064\pi
0.0876500 + 0.996151i 0.472064π0.472064\pi
338338 0 0
339339 7.01862 0.381199
340340 0 0
341341 −16.3731 −0.886654
342342 0 0
343343 −15.5001 −0.836924
344344 0 0
345345 1.21707 0.0655251
346346 0 0
347347 −4.30345 −0.231021 −0.115511 0.993306i 0.536850π-0.536850\pi
−0.115511 + 0.993306i 0.536850π0.536850\pi
348348 0 0
349349 −11.1284 −0.595689 −0.297845 0.954614i 0.596268π-0.596268\pi
−0.297845 + 0.954614i 0.596268π0.596268\pi
350350 0 0
351351 0 0
352352 0 0
353353 10.8295 0.576396 0.288198 0.957571i 0.406944π-0.406944\pi
0.288198 + 0.957571i 0.406944π0.406944\pi
354354 0 0
355355 21.5303 1.14271
356356 0 0
357357 −3.01559 −0.159602
358358 0 0
359359 32.0616 1.69215 0.846073 0.533067i 0.178961π-0.178961\pi
0.846073 + 0.533067i 0.178961π0.178961\pi
360360 0 0
361361 9.68746 0.509866
362362 0 0
363363 −5.95087 −0.312340
364364 0 0
365365 12.9106 0.675771
366366 0 0
367367 0.222122 0.0115947 0.00579734 0.999983i 0.498155π-0.498155\pi
0.00579734 + 0.999983i 0.498155π0.498155\pi
368368 0 0
369369 5.34474 0.278236
370370 0 0
371371 40.9691 2.12701
372372 0 0
373373 24.0961 1.24765 0.623826 0.781564i 0.285578π-0.285578\pi
0.623826 + 0.781564i 0.285578π0.285578\pi
374374 0 0
375375 −11.7887 −0.608763
376376 0 0
377377 0 0
378378 0 0
379379 −16.3518 −0.839933 −0.419967 0.907540i 0.637958π-0.637958\pi
−0.419967 + 0.907540i 0.637958π0.637958\pi
380380 0 0
381381 −14.8015 −0.758306
382382 0 0
383383 −19.4967 −0.996237 −0.498119 0.867109i 0.665976π-0.665976\pi
−0.498119 + 0.867109i 0.665976π0.665976\pi
384384 0 0
385385 −10.3410 −0.527027
386386 0 0
387387 3.12766 0.158988
388388 0 0
389389 29.6972 1.50571 0.752854 0.658187i 0.228677π-0.228677\pi
0.752854 + 0.658187i 0.228677π0.228677\pi
390390 0 0
391391 −0.797505 −0.0403316
392392 0 0
393393 5.81916 0.293538
394394 0 0
395395 1.92091 0.0966517
396396 0 0
397397 −15.8743 −0.796708 −0.398354 0.917232i 0.630418π-0.630418\pi
−0.398354 + 0.917232i 0.630418π0.630418\pi
398398 0 0
399399 −15.8564 −0.793813
400400 0 0
401401 −11.5402 −0.576288 −0.288144 0.957587i 0.593038π-0.593038\pi
−0.288144 + 0.957587i 0.593038π0.593038\pi
402402 0 0
403403 0 0
404404 0 0
405405 1.55452 0.0772447
406406 0 0
407407 −17.5303 −0.868944
408408 0 0
409409 −35.0979 −1.73548 −0.867739 0.497019i 0.834428π-0.834428\pi
−0.867739 + 0.497019i 0.834428π0.834428\pi
410410 0 0
411411 17.3674 0.856671
412412 0 0
413413 12.8930 0.634422
414414 0 0
415415 11.9292 0.585582
416416 0 0
417417 5.88792 0.288333
418418 0 0
419419 22.6284 1.10547 0.552736 0.833356i 0.313584π-0.313584\pi
0.552736 + 0.833356i 0.313584π0.313584\pi
420420 0 0
421421 13.3833 0.652261 0.326130 0.945325i 0.394255π-0.394255\pi
0.326130 + 0.945325i 0.394255π0.394255\pi
422422 0 0
423423 7.13799 0.347061
424424 0 0
425425 2.63158 0.127650
426426 0 0
427427 15.2324 0.737146
428428 0 0
429429 0 0
430430 0 0
431431 −20.0616 −0.966333 −0.483166 0.875529i 0.660513π-0.660513\pi
−0.483166 + 0.875529i 0.660513π0.660513\pi
432432 0 0
433433 37.8445 1.81869 0.909346 0.416041i 0.136583π-0.136583\pi
0.909346 + 0.416041i 0.136583π0.136583\pi
434434 0 0
435435 4.18556 0.200682
436436 0 0
437437 −4.19340 −0.200598
438438 0 0
439439 −25.6796 −1.22562 −0.612811 0.790230i 0.709961π-0.709961\pi
−0.612811 + 0.790230i 0.709961π0.709961\pi
440440 0 0
441441 1.76430 0.0840145
442442 0 0
443443 −37.4822 −1.78083 −0.890416 0.455148i 0.849586π-0.849586\pi
−0.890416 + 0.455148i 0.849586π0.849586\pi
444444 0 0
445445 −0.768019 −0.0364076
446446 0 0
447447 −10.5845 −0.500628
448448 0 0
449449 −5.92091 −0.279425 −0.139713 0.990192i 0.544618π-0.544618\pi
−0.139713 + 0.990192i 0.544618π0.544618\pi
450450 0 0
451451 −12.0098 −0.565518
452452 0 0
453453 2.24703 0.105575
454454 0 0
455455 0 0
456456 0 0
457457 −40.6184 −1.90005 −0.950025 0.312175i 0.898942π-0.898942\pi
−0.950025 + 0.312175i 0.898942π0.898942\pi
458458 0 0
459459 −1.01862 −0.0475452
460460 0 0
461461 7.86627 0.366369 0.183184 0.983079i 0.441360π-0.441360\pi
0.183184 + 0.983079i 0.441360π0.441360\pi
462462 0 0
463463 −3.96775 −0.184397 −0.0921984 0.995741i 0.529389π-0.529389\pi
−0.0921984 + 0.995741i 0.529389π0.529389\pi
464464 0 0
465465 11.3271 0.525283
466466 0 0
467467 −1.41249 −0.0653622 −0.0326811 0.999466i 0.510405π-0.510405\pi
−0.0326811 + 0.999466i 0.510405π0.510405\pi
468468 0 0
469469 −38.4791 −1.77680
470470 0 0
471471 −8.45782 −0.389716
472472 0 0
473473 −7.02794 −0.323145
474474 0 0
475475 13.8372 0.634896
476476 0 0
477477 13.8388 0.633635
478478 0 0
479479 21.4368 0.979474 0.489737 0.871870i 0.337093π-0.337093\pi
0.489737 + 0.871870i 0.337093π0.337093\pi
480480 0 0
481481 0 0
482482 0 0
483483 2.31782 0.105464
484484 0 0
485485 −17.2641 −0.783922
486486 0 0
487487 11.1898 0.507059 0.253529 0.967328i 0.418409π-0.418409\pi
0.253529 + 0.967328i 0.418409π0.418409\pi
488488 0 0
489489 −4.20019 −0.189939
490490 0 0
491491 19.9665 0.901073 0.450537 0.892758i 0.351233π-0.351233\pi
0.450537 + 0.892758i 0.351233π0.351233\pi
492492 0 0
493493 −2.74265 −0.123523
494494 0 0
495495 −3.49305 −0.157001
496496 0 0
497497 41.0027 1.83922
498498 0 0
499499 −4.15156 −0.185849 −0.0929247 0.995673i 0.529622π-0.529622\pi
−0.0929247 + 0.995673i 0.529622π0.529622\pi
500500 0 0
501501 18.7121 0.835997
502502 0 0
503503 −22.3488 −0.996483 −0.498241 0.867038i 0.666021π-0.666021\pi
−0.498241 + 0.867038i 0.666021π0.666021\pi
504504 0 0
505505 −23.6078 −1.05053
506506 0 0
507507 0 0
508508 0 0
509509 34.6523 1.53594 0.767969 0.640487i 0.221267π-0.221267\pi
0.767969 + 0.640487i 0.221267π0.221267\pi
510510 0 0
511511 24.5872 1.08767
512512 0 0
513513 −5.35607 −0.236476
514514 0 0
515515 −1.75297 −0.0772452
516516 0 0
517517 −16.0393 −0.705406
518518 0 0
519519 2.89096 0.126899
520520 0 0
521521 25.0186 1.09609 0.548043 0.836450i 0.315373π-0.315373\pi
0.548043 + 0.836450i 0.315373π0.315373\pi
522522 0 0
523523 −27.7484 −1.21335 −0.606676 0.794949i 0.707497π-0.707497\pi
−0.606676 + 0.794949i 0.707497π0.707497\pi
524524 0 0
525525 −7.64824 −0.333797
526526 0 0
527527 −7.42226 −0.323319
528528 0 0
529529 −22.3870 −0.973349
530530 0 0
531531 4.35506 0.188994
532532 0 0
533533 0 0
534534 0 0
535535 −26.4863 −1.14510
536536 0 0
537537 −22.8574 −0.986370
538538 0 0
539539 −3.96444 −0.170761
540540 0 0
541541 −31.4592 −1.35254 −0.676269 0.736655i 0.736404π-0.736404\pi
−0.676269 + 0.736655i 0.736404π0.736404\pi
542542 0 0
543543 −8.09042 −0.347193
544544 0 0
545545 23.7633 1.01791
546546 0 0
547547 −18.1510 −0.776081 −0.388040 0.921642i 0.626848π-0.626848\pi
−0.388040 + 0.921642i 0.626848π0.626848\pi
548548 0 0
549549 5.14528 0.219595
550550 0 0
551551 −14.4213 −0.614366
552552 0 0
553553 3.65822 0.155563
554554 0 0
555555 12.1277 0.514791
556556 0 0
557557 14.8977 0.631235 0.315618 0.948886i 0.397788π-0.397788\pi
0.315618 + 0.948886i 0.397788π0.397788\pi
558558 0 0
559559 0 0
560560 0 0
561561 2.28887 0.0966362
562562 0 0
563563 −6.23873 −0.262931 −0.131466 0.991321i 0.541968π-0.541968\pi
−0.131466 + 0.991321i 0.541968π0.541968\pi
564564 0 0
565565 10.9106 0.459012
566566 0 0
567567 2.96046 0.124327
568568 0 0
569569 −15.2268 −0.638342 −0.319171 0.947697i 0.603405π-0.603405\pi
−0.319171 + 0.947697i 0.603405π0.603405\pi
570570 0 0
571571 −14.8801 −0.622712 −0.311356 0.950293i 0.600783π-0.600783\pi
−0.311356 + 0.950293i 0.600783π0.600783\pi
572572 0 0
573573 −15.3850 −0.642718
574574 0 0
575575 −2.02266 −0.0843509
576576 0 0
577577 15.6078 0.649762 0.324881 0.945755i 0.394676π-0.394676\pi
0.324881 + 0.945755i 0.394676π0.394676\pi
578578 0 0
579579 −0.347036 −0.0144223
580580 0 0
581581 22.7182 0.942510
582582 0 0
583583 −31.0961 −1.28787
584584 0 0
585585 0 0
586586 0 0
587587 −40.2301 −1.66047 −0.830236 0.557411i 0.811795π-0.811795\pi
−0.830236 + 0.557411i 0.811795π0.811795\pi
588588 0 0
589589 −39.0274 −1.60809
590590 0 0
591591 25.8564 1.06359
592592 0 0
593593 37.7225 1.54908 0.774538 0.632527i 0.217982π-0.217982\pi
0.774538 + 0.632527i 0.217982π0.217982\pi
594594 0 0
595595 −4.68779 −0.192181
596596 0 0
597597 −7.34574 −0.300641
598598 0 0
599599 −30.0518 −1.22788 −0.613942 0.789351i 0.710417π-0.710417\pi
−0.613942 + 0.789351i 0.710417π0.710417\pi
600600 0 0
601601 −3.58347 −0.146173 −0.0730863 0.997326i 0.523285π-0.523285\pi
−0.0730863 + 0.997326i 0.523285π0.523285\pi
602602 0 0
603603 −12.9977 −0.529307
604604 0 0
605605 −9.25074 −0.376096
606606 0 0
607607 −23.5679 −0.956590 −0.478295 0.878199i 0.658745π-0.658745\pi
−0.478295 + 0.878199i 0.658745π0.658745\pi
608608 0 0
609609 7.97105 0.323003
610610 0 0
611611 0 0
612612 0 0
613613 −10.2390 −0.413549 −0.206775 0.978389i 0.566297π-0.566297\pi
−0.206775 + 0.978389i 0.566297π0.566297\pi
614614 0 0
615615 8.30850 0.335031
616616 0 0
617617 37.7804 1.52098 0.760490 0.649350i 0.224959π-0.224959\pi
0.760490 + 0.649350i 0.224959π0.224959\pi
618618 0 0
619619 20.1165 0.808551 0.404275 0.914637i 0.367524π-0.367524\pi
0.404275 + 0.914637i 0.367524π0.367524\pi
620620 0 0
621621 0.782926 0.0314177
622622 0 0
623623 −1.46263 −0.0585990
624624 0 0
625625 −5.40836 −0.216334
626626 0 0
627627 12.0352 0.480641
628628 0 0
629629 −7.94682 −0.316861
630630 0 0
631631 −23.6225 −0.940395 −0.470198 0.882561i 0.655817π-0.655817\pi
−0.470198 + 0.882561i 0.655817π0.655817\pi
632632 0 0
633633 −28.6952 −1.14053
634634 0 0
635635 −23.0093 −0.913096
636636 0 0
637637 0 0
638638 0 0
639639 13.8501 0.547902
640640 0 0
641641 3.57370 0.141153 0.0705763 0.997506i 0.477516π-0.477516\pi
0.0705763 + 0.997506i 0.477516π0.477516\pi
642642 0 0
643643 32.6876 1.28907 0.644537 0.764573i 0.277050π-0.277050\pi
0.644537 + 0.764573i 0.277050π0.277050\pi
644644 0 0
645645 4.86201 0.191442
646646 0 0
647647 37.0998 1.45855 0.729273 0.684223i 0.239859π-0.239859\pi
0.729273 + 0.684223i 0.239859π0.239859\pi
648648 0 0
649649 −9.78594 −0.384132
650650 0 0
651651 21.5716 0.845457
652652 0 0
653653 25.9143 1.01410 0.507052 0.861915i 0.330735π-0.330735\pi
0.507052 + 0.861915i 0.330735π0.330735\pi
654654 0 0
655655 9.04601 0.353457
656656 0 0
657657 8.30519 0.324016
658658 0 0
659659 −14.9861 −0.583776 −0.291888 0.956453i 0.594283π-0.594283\pi
−0.291888 + 0.956453i 0.594283π0.594283\pi
660660 0 0
661661 −12.1765 −0.473611 −0.236806 0.971557i 0.576100π-0.576100\pi
−0.236806 + 0.971557i 0.576100π0.576100\pi
662662 0 0
663663 0 0
664664 0 0
665665 −24.6491 −0.955851
666666 0 0
667667 2.10803 0.0816234
668668 0 0
669669 −2.13698 −0.0826205
670670 0 0
671671 −11.5616 −0.446330
672672 0 0
673673 38.8564 1.49780 0.748902 0.662681i 0.230581π-0.230581\pi
0.748902 + 0.662681i 0.230581π0.230581\pi
674674 0 0
675675 −2.58347 −0.0994377
676676 0 0
677677 −25.3624 −0.974754 −0.487377 0.873192i 0.662046π-0.662046\pi
−0.487377 + 0.873192i 0.662046π0.662046\pi
678678 0 0
679679 −32.8780 −1.26174
680680 0 0
681681 −18.3860 −0.704554
682682 0 0
683683 15.9189 0.609120 0.304560 0.952493i 0.401491π-0.401491\pi
0.304560 + 0.952493i 0.401491π0.401491\pi
684684 0 0
685685 26.9980 1.03154
686686 0 0
687687 1.74669 0.0666403
688688 0 0
689689 0 0
690690 0 0
691691 3.57084 0.135841 0.0679206 0.997691i 0.478364π-0.478364\pi
0.0679206 + 0.997691i 0.478364π0.478364\pi
692692 0 0
693693 −6.65223 −0.252697
694694 0 0
695695 9.15289 0.347189
696696 0 0
697697 −5.44426 −0.206216
698698 0 0
699699 −26.3525 −0.996742
700700 0 0
701701 −1.56585 −0.0591414 −0.0295707 0.999563i 0.509414π-0.509414\pi
−0.0295707 + 0.999563i 0.509414π0.509414\pi
702702 0 0
703703 −41.7856 −1.57597
704704 0 0
705705 11.0961 0.417905
706706 0 0
707707 −44.9592 −1.69086
708708 0 0
709709 −40.7930 −1.53201 −0.766006 0.642833i 0.777759π-0.777759\pi
−0.766006 + 0.642833i 0.777759π0.777759\pi
710710 0 0
711711 1.23570 0.0463422
712712 0 0
713713 5.70485 0.213648
714714 0 0
715715 0 0
716716 0 0
717717 6.36336 0.237644
718718 0 0
719719 −0.831053 −0.0309930 −0.0154965 0.999880i 0.504933π-0.504933\pi
−0.0154965 + 0.999880i 0.504933π0.504933\pi
720720 0 0
721721 −3.33839 −0.124328
722722 0 0
723723 −9.01862 −0.335406
724724 0 0
725725 −6.95601 −0.258340
726726 0 0
727727 −9.85844 −0.365629 −0.182815 0.983147i 0.558521π-0.558521\pi
−0.182815 + 0.983147i 0.558521π0.558521\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −3.18590 −0.117835
732732 0 0
733733 −11.6467 −0.430180 −0.215090 0.976594i 0.569004π-0.569004\pi
−0.215090 + 0.976594i 0.569004π0.569004\pi
734734 0 0
735735 2.74265 0.101164
736736 0 0
737737 29.2062 1.07582
738738 0 0
739739 28.1132 1.03416 0.517080 0.855937i 0.327019π-0.327019\pi
0.517080 + 0.855937i 0.327019π0.327019\pi
740740 0 0
741741 0 0
742742 0 0
743743 16.8078 0.616619 0.308309 0.951286i 0.400237π-0.400237\pi
0.308309 + 0.951286i 0.400237π0.400237\pi
744744 0 0
745745 −16.4538 −0.602820
746746 0 0
747747 7.67389 0.280773
748748 0 0
749749 −50.4410 −1.84307
750750 0 0
751751 18.4378 0.672806 0.336403 0.941718i 0.390789π-0.390789\pi
0.336403 + 0.941718i 0.390789π0.390789\pi
752752 0 0
753753 −18.2760 −0.666014
754754 0 0
755755 3.49305 0.127125
756756 0 0
757757 −1.44805 −0.0526303 −0.0263151 0.999654i 0.508377π-0.508377\pi
−0.0263151 + 0.999654i 0.508377π0.508377\pi
758758 0 0
759759 −1.75926 −0.0638570
760760 0 0
761761 −14.7121 −0.533314 −0.266657 0.963791i 0.585919π-0.585919\pi
−0.266657 + 0.963791i 0.585919π0.585919\pi
762762 0 0
763763 45.2552 1.63835
764764 0 0
765765 −1.58347 −0.0572504
766766 0 0
767767 0 0
768768 0 0
769769 −9.10703 −0.328408 −0.164204 0.986426i 0.552506π-0.552506\pi
−0.164204 + 0.986426i 0.552506π0.552506\pi
770770 0 0
771771 26.4263 0.951720
772772 0 0
773773 23.2027 0.834543 0.417272 0.908782i 0.362986π-0.362986\pi
0.417272 + 0.908782i 0.362986π0.362986\pi
774774 0 0
775775 −18.8246 −0.676200
776776 0 0
777777 23.0961 0.828570
778778 0 0
779779 −28.6268 −1.02566
780780 0 0
781781 −31.1216 −1.11362
782782 0 0
783783 2.69251 0.0962224
784784 0 0
785785 −13.1478 −0.469267
786786 0 0
787787 −12.7879 −0.455840 −0.227920 0.973680i 0.573192π-0.573192\pi
−0.227920 + 0.973680i 0.573192π0.573192\pi
788788 0 0
789789 4.82017 0.171603
790790 0 0
791791 20.7783 0.738792
792792 0 0
793793 0 0
794794 0 0
795795 21.5127 0.762976
796796 0 0
797797 40.4330 1.43221 0.716106 0.697992i 0.245923π-0.245923\pi
0.716106 + 0.697992i 0.245923π0.245923\pi
798798 0 0
799799 −7.27091 −0.257226
800800 0 0
801801 −0.494055 −0.0174566
802802 0 0
803803 −18.6620 −0.658568
804804 0 0
805805 3.60310 0.126992
806806 0 0
807807 −1.64034 −0.0577426
808808 0 0
809809 44.5607 1.56667 0.783335 0.621599i 0.213517π-0.213517\pi
0.783335 + 0.621599i 0.213517π0.213517\pi
810810 0 0
811811 −1.90102 −0.0667537 −0.0333769 0.999443i 0.510626π-0.510626\pi
−0.0333769 + 0.999443i 0.510626π0.510626\pi
812812 0 0
813813 −12.7300 −0.446461
814814 0 0
815815 −6.52929 −0.228711
816816 0 0
817817 −16.7520 −0.586077
818818 0 0
819819 0 0
820820 0 0
821821 43.0062 1.50093 0.750463 0.660913i 0.229831π-0.229831\pi
0.750463 + 0.660913i 0.229831π0.229831\pi
822822 0 0
823823 32.1490 1.12064 0.560321 0.828275i 0.310678π-0.310678\pi
0.560321 + 0.828275i 0.310678π0.310678\pi
824824 0 0
825825 5.80512 0.202108
826826 0 0
827827 −2.20149 −0.0765533 −0.0382766 0.999267i 0.512187π-0.512187\pi
−0.0382766 + 0.999267i 0.512187π0.512187\pi
828828 0 0
829829 37.7013 1.30942 0.654709 0.755881i 0.272791π-0.272791\pi
0.654709 + 0.755881i 0.272791π0.272791\pi
830830 0 0
831831 24.5008 0.849923
832832 0 0
833833 −1.79716 −0.0622679
834834 0 0
835835 29.0884 1.00665
836836 0 0
837837 7.28657 0.251861
838838 0 0
839839 −27.8776 −0.962442 −0.481221 0.876599i 0.659806π-0.659806\pi
−0.481221 + 0.876599i 0.659806π0.659806\pi
840840 0 0
841841 −21.7504 −0.750014
842842 0 0
843843 1.93853 0.0667665
844844 0 0
845845 0 0
846846 0 0
847847 −17.6173 −0.605337
848848 0 0
849849 8.07853 0.277254
850850 0 0
851851 6.10803 0.209381
852852 0 0
853853 3.38475 0.115891 0.0579457 0.998320i 0.481545π-0.481545\pi
0.0579457 + 0.998320i 0.481545π0.481545\pi
854854 0 0
855855 −8.32611 −0.284747
856856 0 0
857857 0.567882 0.0193985 0.00969925 0.999953i 0.496913π-0.496913\pi
0.00969925 + 0.999953i 0.496913π0.496913\pi
858858 0 0
859859 −43.1391 −1.47189 −0.735944 0.677043i 0.763261π-0.763261\pi
−0.735944 + 0.677043i 0.763261π0.763261\pi
860860 0 0
861861 15.8229 0.539242
862862 0 0
863863 21.6466 0.736860 0.368430 0.929656i 0.379895π-0.379895\pi
0.368430 + 0.929656i 0.379895π0.379895\pi
864864 0 0
865865 4.49406 0.152802
866866 0 0
867867 −15.9624 −0.542112
868868 0 0
869869 −2.77664 −0.0941911
870870 0 0
871871 0 0
872872 0 0
873873 −11.1057 −0.375872
874874 0 0
875875 −34.8998 −1.17983
876876 0 0
877877 −42.3494 −1.43004 −0.715019 0.699105i 0.753582π-0.753582\pi
−0.715019 + 0.699105i 0.753582π0.753582\pi
878878 0 0
879879 −28.3411 −0.955923
880880 0 0
881881 −29.1903 −0.983445 −0.491722 0.870752i 0.663633π-0.663633\pi
−0.491722 + 0.870752i 0.663633π0.663633\pi
882882 0 0
883883 41.6461 1.40150 0.700751 0.713406i 0.252848π-0.252848\pi
0.700751 + 0.713406i 0.252848π0.252848\pi
884884 0 0
885885 6.77003 0.227572
886886 0 0
887887 40.6471 1.36480 0.682398 0.730981i 0.260937π-0.260937\pi
0.682398 + 0.730981i 0.260937π0.260937\pi
888888 0 0
889889 −43.8193 −1.46965
890890 0 0
891891 −2.24703 −0.0752783
892892 0 0
893893 −38.2315 −1.27937
894894 0 0
895895 −35.5323 −1.18771
896896 0 0
897897 0 0
898898 0 0
899899 19.6191 0.654335
900900 0 0
901901 −14.0965 −0.469622
902902 0 0
903903 9.25931 0.308130
904904 0 0
905905 −12.5767 −0.418064
906906 0 0
907907 37.7561 1.25367 0.626836 0.779151i 0.284350π-0.284350\pi
0.626836 + 0.779151i 0.284350π0.284350\pi
908908 0 0
909909 −15.1866 −0.503706
910910 0 0
911911 −42.4249 −1.40560 −0.702801 0.711387i 0.748067π-0.748067\pi
−0.702801 + 0.711387i 0.748067π0.748067\pi
912912 0 0
913913 −17.2434 −0.570674
914914 0 0
915915 7.99844 0.264420
916916 0 0
917917 17.2274 0.568898
918918 0 0
919919 49.8346 1.64389 0.821947 0.569565i 0.192888π-0.192888\pi
0.821947 + 0.569565i 0.192888π0.192888\pi
920920 0 0
921921 −30.7025 −1.01168
922922 0 0
923923 0 0
924924 0 0
925925 −20.1550 −0.662694
926926 0 0
927927 −1.12766 −0.0370373
928928 0 0
929929 44.1893 1.44980 0.724901 0.688853i 0.241885π-0.241885\pi
0.724901 + 0.688853i 0.241885π0.241885\pi
930930 0 0
931931 −9.44973 −0.309703
932932 0 0
933933 −13.7338 −0.449624
934934 0 0
935935 3.55810 0.116362
936936 0 0
937937 −22.9644 −0.750215 −0.375107 0.926981i 0.622394π-0.622394\pi
−0.375107 + 0.926981i 0.622394π0.622394\pi
938938 0 0
939939 32.1886 1.05043
940940 0 0
941941 6.09255 0.198611 0.0993057 0.995057i 0.468338π-0.468338\pi
0.0993057 + 0.995057i 0.468338π0.468338\pi
942942 0 0
943943 4.18453 0.136267
944944 0 0
945945 4.60209 0.149706
946946 0 0
947947 −41.6982 −1.35501 −0.677505 0.735518i 0.736939π-0.736939\pi
−0.677505 + 0.735518i 0.736939π0.736939\pi
948948 0 0
949949 0 0
950950 0 0
951951 −4.54723 −0.147454
952952 0 0
953953 35.3850 1.14623 0.573117 0.819474i 0.305734π-0.305734\pi
0.573117 + 0.819474i 0.305734π0.305734\pi
954954 0 0
955955 −23.9163 −0.773914
956956 0 0
957957 −6.05014 −0.195573
958958 0 0
959959 51.4154 1.66029
960960 0 0
961961 22.0941 0.712713
962962 0 0
963963 −17.0382 −0.549050
964964 0 0
965965 −0.539474 −0.0173663
966966 0 0
967967 −4.08684 −0.131424 −0.0657120 0.997839i 0.520932π-0.520932\pi
−0.0657120 + 0.997839i 0.520932π0.520932\pi
968968 0 0
969969 5.45581 0.175266
970970 0 0
971971 −5.72402 −0.183693 −0.0918463 0.995773i 0.529277π-0.529277\pi
−0.0918463 + 0.995773i 0.529277π0.529277\pi
972972 0 0
973973 17.4309 0.558810
974974 0 0
975975 0 0
976976 0 0
977977 9.04498 0.289375 0.144687 0.989477i 0.453782π-0.453782\pi
0.144687 + 0.989477i 0.453782π0.453782\pi
978978 0 0
979979 1.11016 0.0354807
980980 0 0
981981 15.2866 0.488063
982982 0 0
983983 −7.05061 −0.224879 −0.112440 0.993659i 0.535867π-0.535867\pi
−0.112440 + 0.993659i 0.535867π0.535867\pi
984984 0 0
985985 40.1943 1.28070
986986 0 0
987987 21.1317 0.672630
988988 0 0
989989 2.44873 0.0778650
990990 0 0
991991 −19.9292 −0.633072 −0.316536 0.948580i 0.602520π-0.602520\pi
−0.316536 + 0.948580i 0.602520π0.602520\pi
992992 0 0
993993 14.7899 0.469344
994994 0 0
995995 −11.4191 −0.362010
996996 0 0
997997 −22.1395 −0.701164 −0.350582 0.936532i 0.614016π-0.614016\pi
−0.350582 + 0.936532i 0.614016π0.614016\pi
998998 0 0
999999 7.80155 0.246830
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 4056.2.a.be.1.3 4
4.3 odd 2 8112.2.a.cs.1.3 4
13.5 odd 4 4056.2.c.p.337.2 8
13.6 odd 12 312.2.bf.b.49.1 8
13.8 odd 4 4056.2.c.p.337.7 8
13.11 odd 12 312.2.bf.b.121.4 yes 8
13.12 even 2 4056.2.a.bd.1.2 4
39.11 even 12 936.2.bi.c.433.1 8
39.32 even 12 936.2.bi.c.361.4 8
52.11 even 12 624.2.bv.g.433.4 8
52.19 even 12 624.2.bv.g.49.1 8
52.51 odd 2 8112.2.a.cq.1.2 4
156.11 odd 12 1872.2.by.m.433.1 8
156.71 odd 12 1872.2.by.m.1297.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
312.2.bf.b.49.1 8 13.6 odd 12
312.2.bf.b.121.4 yes 8 13.11 odd 12
624.2.bv.g.49.1 8 52.19 even 12
624.2.bv.g.433.4 8 52.11 even 12
936.2.bi.c.361.4 8 39.32 even 12
936.2.bi.c.433.1 8 39.11 even 12
1872.2.by.m.433.1 8 156.11 odd 12
1872.2.by.m.1297.4 8 156.71 odd 12
4056.2.a.bd.1.2 4 13.12 even 2
4056.2.a.be.1.3 4 1.1 even 1 trivial
4056.2.c.p.337.2 8 13.5 odd 4
4056.2.c.p.337.7 8 13.8 odd 4
8112.2.a.cq.1.2 4 52.51 odd 2
8112.2.a.cs.1.3 4 4.3 odd 2