Properties

Label 3808.2.a.l.1.4
Level 38083808
Weight 22
Character 3808.1
Self dual yes
Analytic conductor 30.40730.407
Analytic rank 00
Dimension 66
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3808,2,Mod(1,3808)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3808, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3808.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3808=25717 3808 = 2^{5} \cdot 7 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3808.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: 30.407033089730.4070330897
Analytic rank: 00
Dimension: 66
Coefficient field: 6.6.93059344.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x613x4+41x28x20 x^{6} - 13x^{4} + 41x^{2} - 8x - 20 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 0.644180-0.644180 of defining polynomial
Character χ\chi == 3808.1

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) == q+0.644180q32.53164q5+1.00000q72.58503q92.23245q115.25278q131.63083q151.00000q17+2.57420q19+0.644180q21+3.02032q23+1.40921q253.59777q270.232452q29+6.24195q311.43810q332.53164q35+3.26418q373.38373q396.47116q414.37614q43+6.54438q45+10.1380q47+1.00000q490.644180q51+6.27501q53+5.65177q55+1.65825q57+1.13610q591.14215q612.58503q63+13.2981q659.62799q67+1.94563q69+7.88135q71+1.67627q73+0.907785q752.23245q77+3.38373q79+5.43749q81+15.6628q83+2.53164q850.149741q87+16.8164q895.25278q91+4.02094q936.51696q950.616763q97+5.77096q99+O(q100)q+0.644180 q^{3} -2.53164 q^{5} +1.00000 q^{7} -2.58503 q^{9} -2.23245 q^{11} -5.25278 q^{13} -1.63083 q^{15} -1.00000 q^{17} +2.57420 q^{19} +0.644180 q^{21} +3.02032 q^{23} +1.40921 q^{25} -3.59777 q^{27} -0.232452 q^{29} +6.24195 q^{31} -1.43810 q^{33} -2.53164 q^{35} +3.26418 q^{37} -3.38373 q^{39} -6.47116 q^{41} -4.37614 q^{43} +6.54438 q^{45} +10.1380 q^{47} +1.00000 q^{49} -0.644180 q^{51} +6.27501 q^{53} +5.65177 q^{55} +1.65825 q^{57} +1.13610 q^{59} -1.14215 q^{61} -2.58503 q^{63} +13.2981 q^{65} -9.62799 q^{67} +1.94563 q^{69} +7.88135 q^{71} +1.67627 q^{73} +0.907785 q^{75} -2.23245 q^{77} +3.38373 q^{79} +5.43749 q^{81} +15.6628 q^{83} +2.53164 q^{85} -0.149741 q^{87} +16.8164 q^{89} -5.25278 q^{91} +4.02094 q^{93} -6.51696 q^{95} -0.616763 q^{97} +5.77096 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+4q5+6q7+8q94q114q132q156q176q19+8q25+8q29+12q31+28q33+4q35+10q37+14q39+14q4112q43+22q45+26q99+O(q100) 6 q + 4 q^{5} + 6 q^{7} + 8 q^{9} - 4 q^{11} - 4 q^{13} - 2 q^{15} - 6 q^{17} - 6 q^{19} + 8 q^{25} + 8 q^{29} + 12 q^{31} + 28 q^{33} + 4 q^{35} + 10 q^{37} + 14 q^{39} + 14 q^{41} - 12 q^{43} + 22 q^{45}+ \cdots - 26 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 0.644180 0.371917 0.185959 0.982558i 0.440461π-0.440461\pi
0.185959 + 0.982558i 0.440461π0.440461\pi
44 0 0
55 −2.53164 −1.13218 −0.566092 0.824342i 0.691545π-0.691545\pi
−0.566092 + 0.824342i 0.691545π0.691545\pi
66 0 0
77 1.00000 0.377964
88 0 0
99 −2.58503 −0.861677
1010 0 0
1111 −2.23245 −0.673110 −0.336555 0.941664i 0.609262π-0.609262\pi
−0.336555 + 0.941664i 0.609262π0.609262\pi
1212 0 0
1313 −5.25278 −1.45686 −0.728429 0.685121i 0.759749π-0.759749\pi
−0.728429 + 0.685121i 0.759749π0.759749\pi
1414 0 0
1515 −1.63083 −0.421079
1616 0 0
1717 −1.00000 −0.242536
1818 0 0
1919 2.57420 0.590563 0.295281 0.955410i 0.404587π-0.404587\pi
0.295281 + 0.955410i 0.404587π0.404587\pi
2020 0 0
2121 0.644180 0.140572
2222 0 0
2323 3.02032 0.629781 0.314890 0.949128i 0.398032π-0.398032\pi
0.314890 + 0.949128i 0.398032π0.398032\pi
2424 0 0
2525 1.40921 0.281842
2626 0 0
2727 −3.59777 −0.692390
2828 0 0
2929 −0.232452 −0.0431653 −0.0215826 0.999767i 0.506871π-0.506871\pi
−0.0215826 + 0.999767i 0.506871π0.506871\pi
3030 0 0
3131 6.24195 1.12109 0.560543 0.828125i 0.310592π-0.310592\pi
0.560543 + 0.828125i 0.310592π0.310592\pi
3232 0 0
3333 −1.43810 −0.250341
3434 0 0
3535 −2.53164 −0.427926
3636 0 0
3737 3.26418 0.536628 0.268314 0.963331i 0.413533π-0.413533\pi
0.268314 + 0.963331i 0.413533π0.413533\pi
3838 0 0
3939 −3.38373 −0.541831
4040 0 0
4141 −6.47116 −1.01063 −0.505313 0.862936i 0.668623π-0.668623\pi
−0.505313 + 0.862936i 0.668623π0.668623\pi
4242 0 0
4343 −4.37614 −0.667356 −0.333678 0.942687i 0.608290π-0.608290\pi
−0.333678 + 0.942687i 0.608290π0.608290\pi
4444 0 0
4545 6.54438 0.975578
4646 0 0
4747 10.1380 1.47878 0.739388 0.673280i 0.235115π-0.235115\pi
0.739388 + 0.673280i 0.235115π0.235115\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 −0.644180 −0.0902032
5252 0 0
5353 6.27501 0.861939 0.430970 0.902366i 0.358172π-0.358172\pi
0.430970 + 0.902366i 0.358172π0.358172\pi
5454 0 0
5555 5.65177 0.762084
5656 0 0
5757 1.65825 0.219641
5858 0 0
5959 1.13610 0.147908 0.0739539 0.997262i 0.476438π-0.476438\pi
0.0739539 + 0.997262i 0.476438π0.476438\pi
6060 0 0
6161 −1.14215 −0.146238 −0.0731188 0.997323i 0.523295π-0.523295\pi
−0.0731188 + 0.997323i 0.523295π0.523295\pi
6262 0 0
6363 −2.58503 −0.325683
6464 0 0
6565 13.2981 1.64943
6666 0 0
6767 −9.62799 −1.17625 −0.588123 0.808771i 0.700133π-0.700133\pi
−0.588123 + 0.808771i 0.700133π0.700133\pi
6868 0 0
6969 1.94563 0.234227
7070 0 0
7171 7.88135 0.935344 0.467672 0.883902i 0.345093π-0.345093\pi
0.467672 + 0.883902i 0.345093π0.345093\pi
7272 0 0
7373 1.67627 0.196192 0.0980962 0.995177i 0.468725π-0.468725\pi
0.0980962 + 0.995177i 0.468725π0.468725\pi
7474 0 0
7575 0.907785 0.104822
7676 0 0
7777 −2.23245 −0.254412
7878 0 0
7979 3.38373 0.380700 0.190350 0.981716i 0.439038π-0.439038\pi
0.190350 + 0.981716i 0.439038π0.439038\pi
8080 0 0
8181 5.43749 0.604165
8282 0 0
8383 15.6628 1.71922 0.859610 0.510950i 0.170706π-0.170706\pi
0.859610 + 0.510950i 0.170706π0.170706\pi
8484 0 0
8585 2.53164 0.274595
8686 0 0
8787 −0.149741 −0.0160539
8888 0 0
8989 16.8164 1.78254 0.891270 0.453474i 0.149815π-0.149815\pi
0.891270 + 0.453474i 0.149815π0.149815\pi
9090 0 0
9191 −5.25278 −0.550640
9292 0 0
9393 4.02094 0.416952
9494 0 0
9595 −6.51696 −0.668626
9696 0 0
9797 −0.616763 −0.0626228 −0.0313114 0.999510i 0.509968π-0.509968\pi
−0.0313114 + 0.999510i 0.509968π0.509968\pi
9898 0 0
9999 5.77096 0.580003
100100 0 0
101101 13.6375 1.35698 0.678490 0.734609i 0.262635π-0.262635\pi
0.678490 + 0.734609i 0.262635π0.262635\pi
102102 0 0
103103 −8.02119 −0.790352 −0.395176 0.918605i 0.629316π-0.629316\pi
−0.395176 + 0.918605i 0.629316π0.629316\pi
104104 0 0
105105 −1.63083 −0.159153
106106 0 0
107107 8.22058 0.794713 0.397357 0.917664i 0.369928π-0.369928\pi
0.397357 + 0.917664i 0.369928π0.369928\pi
108108 0 0
109109 −5.59453 −0.535858 −0.267929 0.963439i 0.586339π-0.586339\pi
−0.267929 + 0.963439i 0.586339π0.586339\pi
110110 0 0
111111 2.10272 0.199581
112112 0 0
113113 5.17017 0.486369 0.243184 0.969980i 0.421808π-0.421808\pi
0.243184 + 0.969980i 0.421808π0.421808\pi
114114 0 0
115115 −7.64638 −0.713028
116116 0 0
117117 13.5786 1.25534
118118 0 0
119119 −1.00000 −0.0916698
120120 0 0
121121 −6.01616 −0.546923
122122 0 0
123123 −4.16859 −0.375869
124124 0 0
125125 9.09059 0.813087
126126 0 0
127127 7.13639 0.633253 0.316626 0.948550i 0.397450π-0.397450\pi
0.316626 + 0.948550i 0.397450π0.397450\pi
128128 0 0
129129 −2.81902 −0.248201
130130 0 0
131131 −10.5435 −0.921194 −0.460597 0.887609i 0.652365π-0.652365\pi
−0.460597 + 0.887609i 0.652365π0.652365\pi
132132 0 0
133133 2.57420 0.223212
134134 0 0
135135 9.10825 0.783914
136136 0 0
137137 3.58575 0.306352 0.153176 0.988199i 0.451050π-0.451050\pi
0.153176 + 0.988199i 0.451050π0.451050\pi
138138 0 0
139139 −8.90646 −0.755436 −0.377718 0.925921i 0.623291π-0.623291\pi
−0.377718 + 0.925921i 0.623291π0.623291\pi
140140 0 0
141141 6.53068 0.549983
142142 0 0
143143 11.7266 0.980625
144144 0 0
145145 0.588486 0.0488711
146146 0 0
147147 0.644180 0.0531311
148148 0 0
149149 −15.3248 −1.25546 −0.627730 0.778431i 0.716016π-0.716016\pi
−0.627730 + 0.778431i 0.716016π0.716016\pi
150150 0 0
151151 −6.17776 −0.502739 −0.251370 0.967891i 0.580881π-0.580881\pi
−0.251370 + 0.967891i 0.580881π0.580881\pi
152152 0 0
153153 2.58503 0.208987
154154 0 0
155155 −15.8024 −1.26928
156156 0 0
157157 3.03309 0.242067 0.121034 0.992648i 0.461379π-0.461379\pi
0.121034 + 0.992648i 0.461379π0.461379\pi
158158 0 0
159159 4.04224 0.320570
160160 0 0
161161 3.02032 0.238035
162162 0 0
163163 −18.3161 −1.43462 −0.717312 0.696752i 0.754628π-0.754628\pi
−0.717312 + 0.696752i 0.754628π0.754628\pi
164164 0 0
165165 3.64076 0.283433
166166 0 0
167167 −5.61198 −0.434268 −0.217134 0.976142i 0.569671π-0.569671\pi
−0.217134 + 0.976142i 0.569671π0.569671\pi
168168 0 0
169169 14.5917 1.12243
170170 0 0
171171 −6.65440 −0.508874
172172 0 0
173173 −23.3613 −1.77613 −0.888064 0.459720i 0.847950π-0.847950\pi
−0.888064 + 0.459720i 0.847950π0.847950\pi
174174 0 0
175175 1.40921 0.106526
176176 0 0
177177 0.731854 0.0550095
178178 0 0
179179 −5.84203 −0.436654 −0.218327 0.975876i 0.570060π-0.570060\pi
−0.218327 + 0.975876i 0.570060π0.570060\pi
180180 0 0
181181 24.1189 1.79274 0.896370 0.443306i 0.146194π-0.146194\pi
0.896370 + 0.443306i 0.146194π0.146194\pi
182182 0 0
183183 −0.735751 −0.0543883
184184 0 0
185185 −8.26374 −0.607562
186186 0 0
187187 2.23245 0.163253
188188 0 0
189189 −3.59777 −0.261699
190190 0 0
191191 −10.9353 −0.791253 −0.395627 0.918411i 0.629473π-0.629473\pi
−0.395627 + 0.918411i 0.629473π0.629473\pi
192192 0 0
193193 5.38605 0.387696 0.193848 0.981032i 0.437903π-0.437903\pi
0.193848 + 0.981032i 0.437903π0.437903\pi
194194 0 0
195195 8.56640 0.613453
196196 0 0
197197 20.2473 1.44256 0.721279 0.692644i 0.243554π-0.243554\pi
0.721279 + 0.692644i 0.243554π0.243554\pi
198198 0 0
199199 4.73197 0.335441 0.167720 0.985835i 0.446359π-0.446359\pi
0.167720 + 0.985835i 0.446359π0.446359\pi
200200 0 0
201201 −6.20216 −0.437467
202202 0 0
203203 −0.232452 −0.0163149
204204 0 0
205205 16.3827 1.14421
206206 0 0
207207 −7.80763 −0.542668
208208 0 0
209209 −5.74678 −0.397513
210210 0 0
211211 12.0289 0.828106 0.414053 0.910253i 0.364113π-0.364113\pi
0.414053 + 0.910253i 0.364113π0.364113\pi
212212 0 0
213213 5.07701 0.347871
214214 0 0
215215 11.0788 0.755570
216216 0 0
217217 6.24195 0.423731
218218 0 0
219219 1.07982 0.0729674
220220 0 0
221221 5.25278 0.353340
222222 0 0
223223 26.3066 1.76162 0.880810 0.473470i 0.156999π-0.156999\pi
0.880810 + 0.473470i 0.156999π0.156999\pi
224224 0 0
225225 −3.64285 −0.242857
226226 0 0
227227 −12.9452 −0.859205 −0.429603 0.903018i 0.641346π-0.641346\pi
−0.429603 + 0.903018i 0.641346π0.641346\pi
228228 0 0
229229 11.9309 0.788415 0.394207 0.919021i 0.371019π-0.371019\pi
0.394207 + 0.919021i 0.371019π0.371019\pi
230230 0 0
231231 −1.43810 −0.0946201
232232 0 0
233233 17.9552 1.17628 0.588141 0.808758i 0.299860π-0.299860\pi
0.588141 + 0.808758i 0.299860π0.299860\pi
234234 0 0
235235 −25.6657 −1.67425
236236 0 0
237237 2.17973 0.141589
238238 0 0
239239 19.0273 1.23077 0.615386 0.788226i 0.289000π-0.289000\pi
0.615386 + 0.788226i 0.289000π0.289000\pi
240240 0 0
241241 −24.8273 −1.59927 −0.799633 0.600489i 0.794973π-0.794973\pi
−0.799633 + 0.600489i 0.794973π0.794973\pi
242242 0 0
243243 14.2960 0.917090
244244 0 0
245245 −2.53164 −0.161741
246246 0 0
247247 −13.5217 −0.860366
248248 0 0
249249 10.0897 0.639408
250250 0 0
251251 10.6601 0.672861 0.336431 0.941708i 0.390780π-0.390780\pi
0.336431 + 0.941708i 0.390780π0.390780\pi
252252 0 0
253253 −6.74273 −0.423912
254254 0 0
255255 1.63083 0.102127
256256 0 0
257257 20.0555 1.25103 0.625513 0.780214i 0.284890π-0.284890\pi
0.625513 + 0.780214i 0.284890π0.284890\pi
258258 0 0
259259 3.26418 0.202826
260260 0 0
261261 0.600897 0.0371946
262262 0 0
263263 −14.8216 −0.913938 −0.456969 0.889483i 0.651065π-0.651065\pi
−0.456969 + 0.889483i 0.651065π0.651065\pi
264264 0 0
265265 −15.8861 −0.975874
266266 0 0
267267 10.8328 0.662957
268268 0 0
269269 27.1783 1.65709 0.828546 0.559921i 0.189168π-0.189168\pi
0.828546 + 0.559921i 0.189168π0.189168\pi
270270 0 0
271271 18.4417 1.12026 0.560128 0.828406i 0.310752π-0.310752\pi
0.560128 + 0.828406i 0.310752π0.310752\pi
272272 0 0
273273 −3.38373 −0.204793
274274 0 0
275275 −3.14599 −0.189711
276276 0 0
277277 −9.25080 −0.555826 −0.277913 0.960606i 0.589643π-0.589643\pi
−0.277913 + 0.960606i 0.589643π0.589643\pi
278278 0 0
279279 −16.1356 −0.966015
280280 0 0
281281 2.18341 0.130251 0.0651257 0.997877i 0.479255π-0.479255\pi
0.0651257 + 0.997877i 0.479255π0.479255\pi
282282 0 0
283283 −9.32228 −0.554152 −0.277076 0.960848i 0.589365π-0.589365\pi
−0.277076 + 0.960848i 0.589365π0.589365\pi
284284 0 0
285285 −4.19809 −0.248674
286286 0 0
287287 −6.47116 −0.381980
288288 0 0
289289 1.00000 0.0588235
290290 0 0
291291 −0.397307 −0.0232905
292292 0 0
293293 5.03911 0.294388 0.147194 0.989108i 0.452976π-0.452976\pi
0.147194 + 0.989108i 0.452976π0.452976\pi
294294 0 0
295295 −2.87620 −0.167459
296296 0 0
297297 8.03184 0.466055
298298 0 0
299299 −15.8651 −0.917501
300300 0 0
301301 −4.37614 −0.252237
302302 0 0
303303 8.78500 0.504685
304304 0 0
305305 2.89152 0.165568
306306 0 0
307307 −8.14430 −0.464820 −0.232410 0.972618i 0.574661π-0.574661\pi
−0.232410 + 0.972618i 0.574661π0.574661\pi
308308 0 0
309309 −5.16709 −0.293946
310310 0 0
311311 2.13704 0.121180 0.0605901 0.998163i 0.480702π-0.480702\pi
0.0605901 + 0.998163i 0.480702π0.480702\pi
312312 0 0
313313 −8.04392 −0.454669 −0.227335 0.973817i 0.573001π-0.573001\pi
−0.227335 + 0.973817i 0.573001π0.573001\pi
314314 0 0
315315 6.54438 0.368734
316316 0 0
317317 26.3395 1.47938 0.739688 0.672950i 0.234973π-0.234973\pi
0.739688 + 0.672950i 0.234973π0.234973\pi
318318 0 0
319319 0.518939 0.0290550
320320 0 0
321321 5.29553 0.295568
322322 0 0
323323 −2.57420 −0.143232
324324 0 0
325325 −7.40227 −0.410604
326326 0 0
327327 −3.60388 −0.199295
328328 0 0
329329 10.1380 0.558925
330330 0 0
331331 15.9085 0.874408 0.437204 0.899362i 0.355969π-0.355969\pi
0.437204 + 0.899362i 0.355969π0.355969\pi
332332 0 0
333333 −8.43802 −0.462401
334334 0 0
335335 24.3746 1.33173
336336 0 0
337337 12.0768 0.657864 0.328932 0.944354i 0.393311π-0.393311\pi
0.328932 + 0.944354i 0.393311π0.393311\pi
338338 0 0
339339 3.33052 0.180889
340340 0 0
341341 −13.9348 −0.754614
342342 0 0
343343 1.00000 0.0539949
344344 0 0
345345 −4.92564 −0.265188
346346 0 0
347347 −4.40403 −0.236421 −0.118210 0.992989i 0.537716π-0.537716\pi
−0.118210 + 0.992989i 0.537716π0.537716\pi
348348 0 0
349349 −16.9043 −0.904866 −0.452433 0.891798i 0.649444π-0.649444\pi
−0.452433 + 0.891798i 0.649444π0.649444\pi
350350 0 0
351351 18.8983 1.00871
352352 0 0
353353 −11.8874 −0.632704 −0.316352 0.948642i 0.602458π-0.602458\pi
−0.316352 + 0.948642i 0.602458π0.602458\pi
354354 0 0
355355 −19.9527 −1.05898
356356 0 0
357357 −0.644180 −0.0340936
358358 0 0
359359 −19.0842 −1.00723 −0.503613 0.863929i 0.667996π-0.667996\pi
−0.503613 + 0.863929i 0.667996π0.667996\pi
360360 0 0
361361 −12.3735 −0.651236
362362 0 0
363363 −3.87549 −0.203410
364364 0 0
365365 −4.24371 −0.222126
366366 0 0
367367 22.6353 1.18155 0.590777 0.806835i 0.298821π-0.298821\pi
0.590777 + 0.806835i 0.298821π0.298821\pi
368368 0 0
369369 16.7282 0.870833
370370 0 0
371371 6.27501 0.325782
372372 0 0
373373 −36.7066 −1.90059 −0.950297 0.311343i 0.899221π-0.899221\pi
−0.950297 + 0.311343i 0.899221π0.899221\pi
374374 0 0
375375 5.85598 0.302401
376376 0 0
377377 1.22102 0.0628857
378378 0 0
379379 18.0207 0.925660 0.462830 0.886447i 0.346834π-0.346834\pi
0.462830 + 0.886447i 0.346834π0.346834\pi
380380 0 0
381381 4.59712 0.235518
382382 0 0
383383 21.0899 1.07764 0.538821 0.842421i 0.318870π-0.318870\pi
0.538821 + 0.842421i 0.318870π0.318870\pi
384384 0 0
385385 5.65177 0.288041
386386 0 0
387387 11.3125 0.575045
388388 0 0
389389 1.72499 0.0874603 0.0437302 0.999043i 0.486076π-0.486076\pi
0.0437302 + 0.999043i 0.486076π0.486076\pi
390390 0 0
391391 −3.02032 −0.152744
392392 0 0
393393 −6.79194 −0.342608
394394 0 0
395395 −8.56640 −0.431022
396396 0 0
397397 25.7157 1.29063 0.645316 0.763916i 0.276726π-0.276726\pi
0.645316 + 0.763916i 0.276726π0.276726\pi
398398 0 0
399399 1.65825 0.0830163
400400 0 0
401401 −3.46437 −0.173002 −0.0865011 0.996252i 0.527569π-0.527569\pi
−0.0865011 + 0.996252i 0.527569π0.527569\pi
402402 0 0
403403 −32.7875 −1.63326
404404 0 0
405405 −13.7658 −0.684027
406406 0 0
407407 −7.28713 −0.361210
408408 0 0
409409 −24.0357 −1.18849 −0.594244 0.804285i 0.702549π-0.702549\pi
−0.594244 + 0.804285i 0.702549π0.702549\pi
410410 0 0
411411 2.30987 0.113938
412412 0 0
413413 1.13610 0.0559039
414414 0 0
415415 −39.6527 −1.94648
416416 0 0
417417 −5.73736 −0.280960
418418 0 0
419419 2.87998 0.140696 0.0703481 0.997523i 0.477589π-0.477589\pi
0.0703481 + 0.997523i 0.477589π0.477589\pi
420420 0 0
421421 −17.1075 −0.833767 −0.416883 0.908960i 0.636878π-0.636878\pi
−0.416883 + 0.908960i 0.636878π0.636878\pi
422422 0 0
423423 −26.2070 −1.27423
424424 0 0
425425 −1.40921 −0.0683567
426426 0 0
427427 −1.14215 −0.0552726
428428 0 0
429429 7.55402 0.364712
430430 0 0
431431 −9.13203 −0.439874 −0.219937 0.975514i 0.570585π-0.570585\pi
−0.219937 + 0.975514i 0.570585π0.570585\pi
432432 0 0
433433 23.5045 1.12955 0.564776 0.825244i 0.308962π-0.308962\pi
0.564776 + 0.825244i 0.308962π0.308962\pi
434434 0 0
435435 0.379091 0.0181760
436436 0 0
437437 7.77492 0.371925
438438 0 0
439439 4.41378 0.210658 0.105329 0.994437i 0.466410π-0.466410\pi
0.105329 + 0.994437i 0.466410π0.466410\pi
440440 0 0
441441 −2.58503 −0.123097
442442 0 0
443443 −39.7219 −1.88724 −0.943622 0.331026i 0.892605π-0.892605\pi
−0.943622 + 0.331026i 0.892605π0.892605\pi
444444 0 0
445445 −42.5732 −2.01816
446446 0 0
447447 −9.87195 −0.466927
448448 0 0
449449 18.3900 0.867876 0.433938 0.900943i 0.357124π-0.357124\pi
0.433938 + 0.900943i 0.357124π0.357124\pi
450450 0 0
451451 14.4466 0.680262
452452 0 0
453453 −3.97959 −0.186977
454454 0 0
455455 13.2981 0.623427
456456 0 0
457457 30.5510 1.42911 0.714557 0.699577i 0.246628π-0.246628\pi
0.714557 + 0.699577i 0.246628π0.246628\pi
458458 0 0
459459 3.59777 0.167929
460460 0 0
461461 −32.9266 −1.53354 −0.766772 0.641920i 0.778138π-0.778138\pi
−0.766772 + 0.641920i 0.778138π0.778138\pi
462462 0 0
463463 27.9500 1.29895 0.649474 0.760384i 0.274989π-0.274989\pi
0.649474 + 0.760384i 0.274989π0.274989\pi
464464 0 0
465465 −10.1796 −0.472066
466466 0 0
467467 −23.5747 −1.09091 −0.545453 0.838141i 0.683643π-0.683643\pi
−0.545453 + 0.838141i 0.683643π0.683643\pi
468468 0 0
469469 −9.62799 −0.444579
470470 0 0
471471 1.95386 0.0900290
472472 0 0
473473 9.76953 0.449204
474474 0 0
475475 3.62759 0.166445
476476 0 0
477477 −16.2211 −0.742714
478478 0 0
479479 −16.8208 −0.768563 −0.384281 0.923216i 0.625551π-0.625551\pi
−0.384281 + 0.923216i 0.625551π0.625551\pi
480480 0 0
481481 −17.1460 −0.781791
482482 0 0
483483 1.94563 0.0885293
484484 0 0
485485 1.56142 0.0709006
486486 0 0
487487 −26.3615 −1.19456 −0.597278 0.802035i 0.703751π-0.703751\pi
−0.597278 + 0.802035i 0.703751π0.703751\pi
488488 0 0
489489 −11.7988 −0.533562
490490 0 0
491491 14.1855 0.640182 0.320091 0.947387i 0.396286π-0.396286\pi
0.320091 + 0.947387i 0.396286π0.396286\pi
492492 0 0
493493 0.232452 0.0104691
494494 0 0
495495 −14.6100 −0.656671
496496 0 0
497497 7.88135 0.353527
498498 0 0
499499 17.3945 0.778683 0.389341 0.921094i 0.372703π-0.372703\pi
0.389341 + 0.921094i 0.372703π0.372703\pi
500500 0 0
501501 −3.61513 −0.161512
502502 0 0
503503 37.3654 1.66604 0.833021 0.553241i 0.186609π-0.186609\pi
0.833021 + 0.553241i 0.186609π0.186609\pi
504504 0 0
505505 −34.5252 −1.53635
506506 0 0
507507 9.39965 0.417453
508508 0 0
509509 18.1939 0.806430 0.403215 0.915105i 0.367893π-0.367893\pi
0.403215 + 0.915105i 0.367893π0.367893\pi
510510 0 0
511511 1.67627 0.0741538
512512 0 0
513513 −9.26138 −0.408900
514514 0 0
515515 20.3068 0.894824
516516 0 0
517517 −22.6325 −0.995378
518518 0 0
519519 −15.0489 −0.660573
520520 0 0
521521 6.70351 0.293686 0.146843 0.989160i 0.453089π-0.453089\pi
0.146843 + 0.989160i 0.453089π0.453089\pi
522522 0 0
523523 4.02474 0.175990 0.0879948 0.996121i 0.471954π-0.471954\pi
0.0879948 + 0.996121i 0.471954π0.471954\pi
524524 0 0
525525 0.907785 0.0396190
526526 0 0
527527 −6.24195 −0.271903
528528 0 0
529529 −13.8776 −0.603376
530530 0 0
531531 −2.93686 −0.127449
532532 0 0
533533 33.9915 1.47234
534534 0 0
535535 −20.8116 −0.899762
536536 0 0
537537 −3.76332 −0.162399
538538 0 0
539539 −2.23245 −0.0961585
540540 0 0
541541 −13.9857 −0.601291 −0.300646 0.953736i 0.597202π-0.597202\pi
−0.300646 + 0.953736i 0.597202π0.597202\pi
542542 0 0
543543 15.5369 0.666752
544544 0 0
545545 14.1633 0.606691
546546 0 0
547547 −36.1152 −1.54418 −0.772088 0.635516i 0.780788π-0.780788\pi
−0.772088 + 0.635516i 0.780788π0.780788\pi
548548 0 0
549549 2.95250 0.126010
550550 0 0
551551 −0.598379 −0.0254918
552552 0 0
553553 3.38373 0.143891
554554 0 0
555555 −5.32334 −0.225963
556556 0 0
557557 4.42618 0.187543 0.0937716 0.995594i 0.470108π-0.470108\pi
0.0937716 + 0.995594i 0.470108π0.470108\pi
558558 0 0
559559 22.9869 0.972242
560560 0 0
561561 1.43810 0.0607167
562562 0 0
563563 29.1911 1.23026 0.615129 0.788426i 0.289104π-0.289104\pi
0.615129 + 0.788426i 0.289104π0.289104\pi
564564 0 0
565565 −13.0890 −0.550659
566566 0 0
567567 5.43749 0.228353
568568 0 0
569569 −2.84863 −0.119421 −0.0597103 0.998216i 0.519018π-0.519018\pi
−0.0597103 + 0.998216i 0.519018π0.519018\pi
570570 0 0
571571 2.68846 0.112508 0.0562542 0.998416i 0.482084π-0.482084\pi
0.0562542 + 0.998416i 0.482084π0.482084\pi
572572 0 0
573573 −7.04433 −0.294281
574574 0 0
575575 4.25627 0.177499
576576 0 0
577577 −8.47099 −0.352652 −0.176326 0.984332i 0.556421π-0.556421\pi
−0.176326 + 0.984332i 0.556421π0.556421\pi
578578 0 0
579579 3.46958 0.144191
580580 0 0
581581 15.6628 0.649804
582582 0 0
583583 −14.0087 −0.580180
584584 0 0
585585 −34.3761 −1.42128
586586 0 0
587587 22.1521 0.914316 0.457158 0.889385i 0.348867π-0.348867\pi
0.457158 + 0.889385i 0.348867π0.348867\pi
588588 0 0
589589 16.0680 0.662072
590590 0 0
591591 13.0429 0.536513
592592 0 0
593593 40.7679 1.67414 0.837068 0.547099i 0.184268π-0.184268\pi
0.837068 + 0.547099i 0.184268π0.184268\pi
594594 0 0
595595 2.53164 0.103787
596596 0 0
597597 3.04824 0.124756
598598 0 0
599599 −8.20893 −0.335408 −0.167704 0.985837i 0.553635π-0.553635\pi
−0.167704 + 0.985837i 0.553635π0.553635\pi
600600 0 0
601601 17.1112 0.697981 0.348990 0.937126i 0.386525π-0.386525\pi
0.348990 + 0.937126i 0.386525π0.386525\pi
602602 0 0
603603 24.8887 1.01355
604604 0 0
605605 15.2308 0.619218
606606 0 0
607607 7.07815 0.287293 0.143647 0.989629i 0.454117π-0.454117\pi
0.143647 + 0.989629i 0.454117π0.454117\pi
608608 0 0
609609 −0.149741 −0.00606781
610610 0 0
611611 −53.2525 −2.15437
612612 0 0
613613 −12.7724 −0.515871 −0.257935 0.966162i 0.583042π-0.583042\pi
−0.257935 + 0.966162i 0.583042π0.583042\pi
614614 0 0
615615 10.5534 0.425553
616616 0 0
617617 −14.2332 −0.573009 −0.286504 0.958079i 0.592493π-0.592493\pi
−0.286504 + 0.958079i 0.592493π0.592493\pi
618618 0 0
619619 23.6954 0.952399 0.476199 0.879337i 0.342014π-0.342014\pi
0.476199 + 0.879337i 0.342014π0.342014\pi
620620 0 0
621621 −10.8664 −0.436054
622622 0 0
623623 16.8164 0.673736
624624 0 0
625625 −30.0602 −1.20241
626626 0 0
627627 −3.70196 −0.147842
628628 0 0
629629 −3.26418 −0.130152
630630 0 0
631631 22.3675 0.890435 0.445217 0.895423i 0.353126π-0.353126\pi
0.445217 + 0.895423i 0.353126π0.353126\pi
632632 0 0
633633 7.74879 0.307987
634634 0 0
635635 −18.0668 −0.716959
636636 0 0
637637 −5.25278 −0.208123
638638 0 0
639639 −20.3735 −0.805965
640640 0 0
641641 11.4522 0.452333 0.226167 0.974089i 0.427381π-0.427381\pi
0.226167 + 0.974089i 0.427381π0.427381\pi
642642 0 0
643643 2.27858 0.0898586 0.0449293 0.998990i 0.485694π-0.485694\pi
0.0449293 + 0.998990i 0.485694π0.485694\pi
644644 0 0
645645 7.13676 0.281010
646646 0 0
647647 −5.52484 −0.217204 −0.108602 0.994085i 0.534637π-0.534637\pi
−0.108602 + 0.994085i 0.534637π0.534637\pi
648648 0 0
649649 −2.53629 −0.0995582
650650 0 0
651651 4.02094 0.157593
652652 0 0
653653 9.20106 0.360065 0.180033 0.983661i 0.442380π-0.442380\pi
0.180033 + 0.983661i 0.442380π0.442380\pi
654654 0 0
655655 26.6925 1.04296
656656 0 0
657657 −4.33321 −0.169055
658658 0 0
659659 2.93917 0.114494 0.0572469 0.998360i 0.481768π-0.481768\pi
0.0572469 + 0.998360i 0.481768π0.481768\pi
660660 0 0
661661 5.41241 0.210518 0.105259 0.994445i 0.466433π-0.466433\pi
0.105259 + 0.994445i 0.466433π0.466433\pi
662662 0 0
663663 3.38373 0.131413
664664 0 0
665665 −6.51696 −0.252717
666666 0 0
667667 −0.702081 −0.0271847
668668 0 0
669669 16.9462 0.655177
670670 0 0
671671 2.54980 0.0984339
672672 0 0
673673 −44.8633 −1.72935 −0.864677 0.502328i 0.832477π-0.832477\pi
−0.864677 + 0.502328i 0.832477π0.832477\pi
674674 0 0
675675 −5.07001 −0.195145
676676 0 0
677677 7.92315 0.304511 0.152256 0.988341i 0.451346π-0.451346\pi
0.152256 + 0.988341i 0.451346π0.451346\pi
678678 0 0
679679 −0.616763 −0.0236692
680680 0 0
681681 −8.33906 −0.319553
682682 0 0
683683 −39.8206 −1.52369 −0.761847 0.647757i 0.775707π-0.775707\pi
−0.761847 + 0.647757i 0.775707π0.775707\pi
684684 0 0
685685 −9.07785 −0.346847
686686 0 0
687687 7.68564 0.293225
688688 0 0
689689 −32.9612 −1.25572
690690 0 0
691691 8.92588 0.339557 0.169778 0.985482i 0.445695π-0.445695\pi
0.169778 + 0.985482i 0.445695π0.445695\pi
692692 0 0
693693 5.77096 0.219221
694694 0 0
695695 22.5480 0.855293
696696 0 0
697697 6.47116 0.245113
698698 0 0
699699 11.5664 0.437480
700700 0 0
701701 −41.1490 −1.55418 −0.777088 0.629392i 0.783304π-0.783304\pi
−0.777088 + 0.629392i 0.783304π0.783304\pi
702702 0 0
703703 8.40267 0.316913
704704 0 0
705705 −16.5333 −0.622682
706706 0 0
707707 13.6375 0.512890
708708 0 0
709709 −0.447742 −0.0168153 −0.00840766 0.999965i 0.502676π-0.502676\pi
−0.00840766 + 0.999965i 0.502676π0.502676\pi
710710 0 0
711711 −8.74706 −0.328040
712712 0 0
713713 18.8527 0.706039
714714 0 0
715715 −29.6875 −1.11025
716716 0 0
717717 12.2570 0.457746
718718 0 0
719719 −23.5887 −0.879712 −0.439856 0.898068i 0.644970π-0.644970\pi
−0.439856 + 0.898068i 0.644970π0.644970\pi
720720 0 0
721721 −8.02119 −0.298725
722722 0 0
723723 −15.9932 −0.594795
724724 0 0
725725 −0.327574 −0.0121658
726726 0 0
727727 −22.0040 −0.816082 −0.408041 0.912964i 0.633788π-0.633788\pi
−0.408041 + 0.912964i 0.633788π0.633788\pi
728728 0 0
729729 −7.10325 −0.263083
730730 0 0
731731 4.37614 0.161858
732732 0 0
733733 −25.7809 −0.952238 −0.476119 0.879381i 0.657957π-0.657957\pi
−0.476119 + 0.879381i 0.657957π0.657957\pi
734734 0 0
735735 −1.63083 −0.0601542
736736 0 0
737737 21.4940 0.791743
738738 0 0
739739 −25.3808 −0.933647 −0.466823 0.884351i 0.654602π-0.654602\pi
−0.466823 + 0.884351i 0.654602π0.654602\pi
740740 0 0
741741 −8.71041 −0.319985
742742 0 0
743743 14.4501 0.530122 0.265061 0.964232i 0.414608π-0.414608\pi
0.265061 + 0.964232i 0.414608π0.414608\pi
744744 0 0
745745 38.7970 1.42141
746746 0 0
747747 −40.4890 −1.48141
748748 0 0
749749 8.22058 0.300373
750750 0 0
751751 49.9082 1.82118 0.910588 0.413316i 0.135630π-0.135630\pi
0.910588 + 0.413316i 0.135630π0.135630\pi
752752 0 0
753753 6.86704 0.250249
754754 0 0
755755 15.6399 0.569193
756756 0 0
757757 29.6587 1.07796 0.538982 0.842317i 0.318809π-0.318809\pi
0.538982 + 0.842317i 0.318809π0.318809\pi
758758 0 0
759759 −4.34353 −0.157660
760760 0 0
761761 5.59792 0.202924 0.101462 0.994839i 0.467648π-0.467648\pi
0.101462 + 0.994839i 0.467648π0.467648\pi
762762 0 0
763763 −5.59453 −0.202535
764764 0 0
765765 −6.54438 −0.236612
766766 0 0
767767 −5.96769 −0.215481
768768 0 0
769769 13.5885 0.490014 0.245007 0.969521i 0.421210π-0.421210\pi
0.245007 + 0.969521i 0.421210π0.421210\pi
770770 0 0
771771 12.9193 0.465278
772772 0 0
773773 −20.2316 −0.727679 −0.363840 0.931462i 0.618534π-0.618534\pi
−0.363840 + 0.931462i 0.618534π0.618534\pi
774774 0 0
775775 8.79621 0.315969
776776 0 0
777777 2.10272 0.0754347
778778 0 0
779779 −16.6581 −0.596837
780780 0 0
781781 −17.5947 −0.629589
782782 0 0
783783 0.836309 0.0298872
784784 0 0
785785 −7.67870 −0.274065
786786 0 0
787787 42.0470 1.49882 0.749408 0.662109i 0.230338π-0.230338\pi
0.749408 + 0.662109i 0.230338π0.230338\pi
788788 0 0
789789 −9.54777 −0.339910
790790 0 0
791791 5.17017 0.183830
792792 0 0
793793 5.99947 0.213047
794794 0 0
795795 −10.2335 −0.362945
796796 0 0
797797 7.91996 0.280539 0.140270 0.990113i 0.455203π-0.455203\pi
0.140270 + 0.990113i 0.455203π0.455203\pi
798798 0 0
799799 −10.1380 −0.358656
800800 0 0
801801 −43.4710 −1.53597
802802 0 0
803803 −3.74219 −0.132059
804804 0 0
805805 −7.64638 −0.269499
806806 0 0
807807 17.5077 0.616302
808808 0 0
809809 54.6264 1.92056 0.960281 0.279036i 0.0900148π-0.0900148\pi
0.960281 + 0.279036i 0.0900148π0.0900148\pi
810810 0 0
811811 −37.4955 −1.31664 −0.658322 0.752736i 0.728734π-0.728734\pi
−0.658322 + 0.752736i 0.728734π0.728734\pi
812812 0 0
813813 11.8798 0.416643
814814 0 0
815815 46.3697 1.62426
816816 0 0
817817 −11.2651 −0.394115
818818 0 0
819819 13.5786 0.474474
820820 0 0
821821 12.0468 0.420435 0.210217 0.977655i 0.432583π-0.432583\pi
0.210217 + 0.977655i 0.432583π0.432583\pi
822822 0 0
823823 −19.9529 −0.695513 −0.347756 0.937585i 0.613056π-0.613056\pi
−0.347756 + 0.937585i 0.613056π0.613056\pi
824824 0 0
825825 −2.02659 −0.0705567
826826 0 0
827827 −12.6415 −0.439589 −0.219794 0.975546i 0.570539π-0.570539\pi
−0.219794 + 0.975546i 0.570539π0.570539\pi
828828 0 0
829829 −10.1202 −0.351489 −0.175744 0.984436i 0.556233π-0.556233\pi
−0.175744 + 0.984436i 0.556233π0.556233\pi
830830 0 0
831831 −5.95918 −0.206722
832832 0 0
833833 −1.00000 −0.0346479
834834 0 0
835835 14.2075 0.491672
836836 0 0
837837 −22.4571 −0.776230
838838 0 0
839839 44.0050 1.51922 0.759610 0.650379i 0.225390π-0.225390\pi
0.759610 + 0.650379i 0.225390π0.225390\pi
840840 0 0
841841 −28.9460 −0.998137
842842 0 0
843843 1.40651 0.0484428
844844 0 0
845845 −36.9408 −1.27080
846846 0 0
847847 −6.01616 −0.206718
848848 0 0
849849 −6.00523 −0.206099
850850 0 0
851851 9.85889 0.337958
852852 0 0
853853 −25.7767 −0.882576 −0.441288 0.897365i 0.645478π-0.645478\pi
−0.441288 + 0.897365i 0.645478π0.645478\pi
854854 0 0
855855 16.8465 0.576140
856856 0 0
857857 −19.8662 −0.678616 −0.339308 0.940675i 0.610193π-0.610193\pi
−0.339308 + 0.940675i 0.610193π0.610193\pi
858858 0 0
859859 14.2553 0.486385 0.243193 0.969978i 0.421805π-0.421805\pi
0.243193 + 0.969978i 0.421805π0.421805\pi
860860 0 0
861861 −4.16859 −0.142065
862862 0 0
863863 3.41168 0.116135 0.0580674 0.998313i 0.481506π-0.481506\pi
0.0580674 + 0.998313i 0.481506π0.481506\pi
864864 0 0
865865 59.1425 2.01090
866866 0 0
867867 0.644180 0.0218775
868868 0 0
869869 −7.55402 −0.256253
870870 0 0
871871 50.5737 1.71362
872872 0 0
873873 1.59435 0.0539607
874874 0 0
875875 9.09059 0.307318
876876 0 0
877877 20.4852 0.691738 0.345869 0.938283i 0.387584π-0.387584\pi
0.345869 + 0.938283i 0.387584π0.387584\pi
878878 0 0
879879 3.24609 0.109488
880880 0 0
881881 4.91501 0.165591 0.0827955 0.996567i 0.473615π-0.473615\pi
0.0827955 + 0.996567i 0.473615π0.473615\pi
882882 0 0
883883 −22.5908 −0.760241 −0.380121 0.924937i 0.624118π-0.624118\pi
−0.380121 + 0.924937i 0.624118π0.624118\pi
884884 0 0
885885 −1.85279 −0.0622809
886886 0 0
887887 −32.9356 −1.10587 −0.552934 0.833225i 0.686492π-0.686492\pi
−0.552934 + 0.833225i 0.686492π0.686492\pi
888888 0 0
889889 7.13639 0.239347
890890 0 0
891891 −12.1389 −0.406670
892892 0 0
893893 26.0972 0.873310
894894 0 0
895895 14.7899 0.494372
896896 0 0
897897 −10.2200 −0.341235
898898 0 0
899899 −1.45095 −0.0483920
900900 0 0
901901 −6.27501 −0.209051
902902 0 0
903903 −2.81902 −0.0938112
904904 0 0
905905 −61.0603 −2.02971
906906 0 0
907907 −13.4000 −0.444939 −0.222469 0.974940i 0.571412π-0.571412\pi
−0.222469 + 0.974940i 0.571412π0.571412\pi
908908 0 0
909909 −35.2533 −1.16928
910910 0 0
911911 −28.1036 −0.931113 −0.465557 0.885018i 0.654146π-0.654146\pi
−0.465557 + 0.885018i 0.654146π0.654146\pi
912912 0 0
913913 −34.9666 −1.15722
914914 0 0
915915 1.86266 0.0615776
916916 0 0
917917 −10.5435 −0.348179
918918 0 0
919919 49.2243 1.62376 0.811881 0.583823i 0.198444π-0.198444\pi
0.811881 + 0.583823i 0.198444π0.198444\pi
920920 0 0
921921 −5.24640 −0.172875
922922 0 0
923923 −41.3989 −1.36266
924924 0 0
925925 4.59992 0.151244
926926 0 0
927927 20.7350 0.681028
928928 0 0
929929 6.33709 0.207913 0.103957 0.994582i 0.466850π-0.466850\pi
0.103957 + 0.994582i 0.466850π0.466850\pi
930930 0 0
931931 2.57420 0.0843661
932932 0 0
933933 1.37664 0.0450691
934934 0 0
935935 −5.65177 −0.184833
936936 0 0
937937 −1.88941 −0.0617244 −0.0308622 0.999524i 0.509825π-0.509825\pi
−0.0308622 + 0.999524i 0.509825π0.509825\pi
938938 0 0
939939 −5.18173 −0.169099
940940 0 0
941941 12.7804 0.416630 0.208315 0.978062i 0.433202π-0.433202\pi
0.208315 + 0.978062i 0.433202π0.433202\pi
942942 0 0
943943 −19.5450 −0.636472
944944 0 0
945945 9.10825 0.296292
946946 0 0
947947 59.9664 1.94865 0.974323 0.225153i 0.0722884π-0.0722884\pi
0.974323 + 0.225153i 0.0722884π0.0722884\pi
948948 0 0
949949 −8.80507 −0.285825
950950 0 0
951951 16.9674 0.550206
952952 0 0
953953 −42.4980 −1.37664 −0.688322 0.725405i 0.741653π-0.741653\pi
−0.688322 + 0.725405i 0.741653π0.741653\pi
954954 0 0
955955 27.6844 0.895845
956956 0 0
957957 0.334290 0.0108061
958958 0 0
959959 3.58575 0.115790
960960 0 0
961961 7.96189 0.256835
962962 0 0
963963 −21.2505 −0.684787
964964 0 0
965965 −13.6355 −0.438944
966966 0 0
967967 −5.63019 −0.181055 −0.0905273 0.995894i 0.528855π-0.528855\pi
−0.0905273 + 0.995894i 0.528855π0.528855\pi
968968 0 0
969969 −1.65825 −0.0532707
970970 0 0
971971 −33.7682 −1.08367 −0.541836 0.840484i 0.682271π-0.682271\pi
−0.541836 + 0.840484i 0.682271π0.682271\pi
972972 0 0
973973 −8.90646 −0.285528
974974 0 0
975975 −4.76839 −0.152711
976976 0 0
977977 −41.3432 −1.32269 −0.661344 0.750083i 0.730013π-0.730013\pi
−0.661344 + 0.750083i 0.730013π0.730013\pi
978978 0 0
979979 −37.5419 −1.19984
980980 0 0
981981 14.4620 0.461737
982982 0 0
983983 9.91633 0.316282 0.158141 0.987417i 0.449450π-0.449450\pi
0.158141 + 0.987417i 0.449450π0.449450\pi
984984 0 0
985985 −51.2588 −1.63324
986986 0 0
987987 6.53068 0.207874
988988 0 0
989989 −13.2174 −0.420288
990990 0 0
991991 −59.2450 −1.88198 −0.940990 0.338434i 0.890103π-0.890103\pi
−0.940990 + 0.338434i 0.890103π0.890103\pi
992992 0 0
993993 10.2479 0.325208
994994 0 0
995995 −11.9797 −0.379781
996996 0 0
997997 15.0270 0.475911 0.237956 0.971276i 0.423523π-0.423523\pi
0.237956 + 0.971276i 0.423523π0.423523\pi
998998 0 0
999999 −11.7438 −0.371556
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 3808.2.a.l.1.4 yes 6
4.3 odd 2 3808.2.a.k.1.3 6
8.3 odd 2 7616.2.a.by.1.4 6
8.5 even 2 7616.2.a.bz.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3808.2.a.k.1.3 6 4.3 odd 2
3808.2.a.l.1.4 yes 6 1.1 even 1 trivial
7616.2.a.by.1.4 6 8.3 odd 2
7616.2.a.bz.1.3 6 8.5 even 2