Properties

Label 80.16.a.b.1.1
Level 8080
Weight 1616
Character 80.1
Self dual yes
Analytic conductor 114.155114.155
Analytic rank 11
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [80,16,Mod(1,80)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(80, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 16, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("80.1");
 
S:= CuspForms(chi, 16);
 
N := Newforms(S);
 
Level: N N == 80=245 80 = 2^{4} \cdot 5
Weight: k k == 16 16
Character orbit: [χ][\chi] == 80.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: 114.154804080114.154804080
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 10)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 80.1

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+1302.00q378125.0q5+90706.0q71.26537e7q9+6.94116e7q113.70575e7q131.01719e8q151.37203e9q17+5.06876e9q19+1.18099e8q21+1.23426e10q23+6.10352e9q253.51574e10q27+5.78257e10q292.33728e11q31+9.03740e10q337.08641e9q35+7.42248e11q374.82488e10q397.72700e11q41+4.05994e11q43+9.88571e11q451.62301e12q474.73933e12q491.78638e12q515.36560e12q535.42278e12q55+6.59953e12q579.24016e12q59+9.44308e11q611.14777e12q63+2.89511e12q65+7.05676e13q67+1.60701e13q69+8.25347e13q711.78432e14q73+7.94678e12q75+6.29605e12q773.07261e14q79+1.35792e14q814.31597e13q83+1.07190e14q85+7.52891e13q87+6.81678e14q893.36133e12q913.04314e14q933.95997e14q952.36520e14q978.78314e14q99+O(q100)q+1302.00 q^{3} -78125.0 q^{5} +90706.0 q^{7} -1.26537e7 q^{9} +6.94116e7 q^{11} -3.70575e7 q^{13} -1.01719e8 q^{15} -1.37203e9 q^{17} +5.06876e9 q^{19} +1.18099e8 q^{21} +1.23426e10 q^{23} +6.10352e9 q^{25} -3.51574e10 q^{27} +5.78257e10 q^{29} -2.33728e11 q^{31} +9.03740e10 q^{33} -7.08641e9 q^{35} +7.42248e11 q^{37} -4.82488e10 q^{39} -7.72700e11 q^{41} +4.05994e11 q^{43} +9.88571e11 q^{45} -1.62301e12 q^{47} -4.73933e12 q^{49} -1.78638e12 q^{51} -5.36560e12 q^{53} -5.42278e12 q^{55} +6.59953e12 q^{57} -9.24016e12 q^{59} +9.44308e11 q^{61} -1.14777e12 q^{63} +2.89511e12 q^{65} +7.05676e13 q^{67} +1.60701e13 q^{69} +8.25347e13 q^{71} -1.78432e14 q^{73} +7.94678e12 q^{75} +6.29605e12 q^{77} -3.07261e14 q^{79} +1.35792e14 q^{81} -4.31597e13 q^{83} +1.07190e14 q^{85} +7.52891e13 q^{87} +6.81678e14 q^{89} -3.36133e12 q^{91} -3.04314e14 q^{93} -3.95997e14 q^{95} -2.36520e14 q^{97} -8.78314e14 q^{99} +O(q^{100})

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 1302.00 0.343717 0.171859 0.985122i 0.445023π-0.445023\pi
0.171859 + 0.985122i 0.445023π0.445023\pi
44 0 0
55 −78125.0 −0.447214
66 0 0
77 90706.0 0.0416295 0.0208147 0.999783i 0.493374π-0.493374\pi
0.0208147 + 0.999783i 0.493374π0.493374\pi
88 0 0
99 −1.26537e7 −0.881858
1010 0 0
1111 6.94116e7 1.07396 0.536979 0.843596i 0.319565π-0.319565\pi
0.536979 + 0.843596i 0.319565π0.319565\pi
1212 0 0
1313 −3.70575e7 −0.163795 −0.0818975 0.996641i 0.526098π-0.526098\pi
−0.0818975 + 0.996641i 0.526098π0.526098\pi
1414 0 0
1515 −1.01719e8 −0.153715
1616 0 0
1717 −1.37203e9 −0.810954 −0.405477 0.914105i 0.632894π-0.632894\pi
−0.405477 + 0.914105i 0.632894π0.632894\pi
1818 0 0
1919 5.06876e9 1.30092 0.650459 0.759542i 0.274577π-0.274577\pi
0.650459 + 0.759542i 0.274577π0.274577\pi
2020 0 0
2121 1.18099e8 0.0143088
2222 0 0
2323 1.23426e10 0.755873 0.377937 0.925831i 0.376634π-0.376634\pi
0.377937 + 0.925831i 0.376634π0.376634\pi
2424 0 0
2525 6.10352e9 0.200000
2626 0 0
2727 −3.51574e10 −0.646828
2828 0 0
2929 5.78257e10 0.622495 0.311248 0.950329i 0.399253π-0.399253\pi
0.311248 + 0.950329i 0.399253π0.399253\pi
3030 0 0
3131 −2.33728e11 −1.52580 −0.762901 0.646516i 0.776225π-0.776225\pi
−0.762901 + 0.646516i 0.776225π0.776225\pi
3232 0 0
3333 9.03740e10 0.369138
3434 0 0
3535 −7.08641e9 −0.0186173
3636 0 0
3737 7.42248e11 1.28539 0.642696 0.766121i 0.277816π-0.277816\pi
0.642696 + 0.766121i 0.277816π0.277816\pi
3838 0 0
3939 −4.82488e10 −0.0562992
4040 0 0
4141 −7.72700e11 −0.619629 −0.309815 0.950797i 0.600267π-0.600267\pi
−0.309815 + 0.950797i 0.600267π0.600267\pi
4242 0 0
4343 4.05994e11 0.227775 0.113888 0.993494i 0.463670π-0.463670\pi
0.113888 + 0.993494i 0.463670π0.463670\pi
4444 0 0
4545 9.88571e11 0.394379
4646 0 0
4747 −1.62301e12 −0.467291 −0.233646 0.972322i 0.575066π-0.575066\pi
−0.233646 + 0.972322i 0.575066π0.575066\pi
4848 0 0
4949 −4.73933e12 −0.998267
5050 0 0
5151 −1.78638e12 −0.278739
5252 0 0
5353 −5.36560e12 −0.627407 −0.313703 0.949521i 0.601570π-0.601570\pi
−0.313703 + 0.949521i 0.601570π0.601570\pi
5454 0 0
5555 −5.42278e12 −0.480289
5656 0 0
5757 6.59953e12 0.447148
5858 0 0
5959 −9.24016e12 −0.483381 −0.241690 0.970353i 0.577702π-0.577702\pi
−0.241690 + 0.970353i 0.577702π0.577702\pi
6060 0 0
6161 9.44308e11 0.0384716 0.0192358 0.999815i 0.493877π-0.493877\pi
0.0192358 + 0.999815i 0.493877π0.493877\pi
6262 0 0
6363 −1.14777e12 −0.0367113
6464 0 0
6565 2.89511e12 0.0732513
6666 0 0
6767 7.05676e13 1.42247 0.711237 0.702953i 0.248135π-0.248135\pi
0.711237 + 0.702953i 0.248135π0.248135\pi
6868 0 0
6969 1.60701e13 0.259807
7070 0 0
7171 8.25347e13 1.07696 0.538479 0.842639i 0.318999π-0.318999\pi
0.538479 + 0.842639i 0.318999π0.318999\pi
7272 0 0
7373 −1.78432e14 −1.89039 −0.945197 0.326502i 0.894130π-0.894130\pi
−0.945197 + 0.326502i 0.894130π0.894130\pi
7474 0 0
7575 7.94678e12 0.0687435
7676 0 0
7777 6.29605e12 0.0447083
7878 0 0
7979 −3.07261e14 −1.80013 −0.900067 0.435752i 0.856482π-0.856482\pi
−0.900067 + 0.435752i 0.856482π0.856482\pi
8080 0 0
8181 1.35792e14 0.659532
8282 0 0
8383 −4.31597e13 −0.174579 −0.0872897 0.996183i 0.527821π-0.527821\pi
−0.0872897 + 0.996183i 0.527821π0.527821\pi
8484 0 0
8585 1.07190e14 0.362669
8686 0 0
8787 7.52891e13 0.213962
8888 0 0
8989 6.81678e14 1.63363 0.816816 0.576899i 0.195737π-0.195737\pi
0.816816 + 0.576899i 0.195737π0.195737\pi
9090 0 0
9191 −3.36133e12 −0.00681869
9292 0 0
9393 −3.04314e14 −0.524445
9494 0 0
9595 −3.95997e14 −0.581788
9696 0 0
9797 −2.36520e14 −0.297222 −0.148611 0.988896i 0.547480π-0.547480\pi
−0.148611 + 0.988896i 0.547480π0.547480\pi
9898 0 0
9999 −8.78314e14 −0.947079
100100 0 0
101101 −1.39643e15 −1.29601 −0.648005 0.761636i 0.724397π-0.724397\pi
−0.648005 + 0.761636i 0.724397π0.724397\pi
102102 0 0
103103 1.46886e15 1.17680 0.588398 0.808572i 0.299759π-0.299759\pi
0.588398 + 0.808572i 0.299759π0.299759\pi
104104 0 0
105105 −9.22650e12 −0.00639908
106106 0 0
107107 −1.19960e15 −0.722203 −0.361102 0.932526i 0.617599π-0.617599\pi
−0.361102 + 0.932526i 0.617599π0.617599\pi
108108 0 0
109109 2.63914e14 0.138281 0.0691407 0.997607i 0.477974π-0.477974\pi
0.0691407 + 0.997607i 0.477974π0.477974\pi
110110 0 0
111111 9.66406e14 0.441812
112112 0 0
113113 −4.67332e15 −1.86869 −0.934346 0.356368i 0.884015π-0.884015\pi
−0.934346 + 0.356368i 0.884015π0.884015\pi
114114 0 0
115115 −9.64268e14 −0.338037
116116 0 0
117117 4.68914e14 0.144444
118118 0 0
119119 −1.24451e14 −0.0337596
120120 0 0
121121 6.40729e14 0.153385
122122 0 0
123123 −1.00606e15 −0.212977
124124 0 0
125125 −4.76837e14 −0.0894427
126126 0 0
127127 −5.53712e15 −0.922053 −0.461027 0.887386i 0.652519π-0.652519\pi
−0.461027 + 0.887386i 0.652519π0.652519\pi
128128 0 0
129129 5.28605e14 0.0782903
130130 0 0
131131 −7.83095e15 −1.03343 −0.516714 0.856158i 0.672845π-0.672845\pi
−0.516714 + 0.856158i 0.672845π0.672845\pi
132132 0 0
133133 4.59767e14 0.0541565
134134 0 0
135135 2.74667e15 0.289270
136136 0 0
137137 −1.88872e16 −1.78140 −0.890702 0.454587i 0.849787π-0.849787\pi
−0.890702 + 0.454587i 0.849787π0.849787\pi
138138 0 0
139139 −6.08888e15 −0.515142 −0.257571 0.966259i 0.582922π-0.582922\pi
−0.257571 + 0.966259i 0.582922π0.582922\pi
140140 0 0
141141 −2.11316e15 −0.160616
142142 0 0
143143 −2.57222e15 −0.175909
144144 0 0
145145 −4.51763e15 −0.278388
146146 0 0
147147 −6.17061e15 −0.343122
148148 0 0
149149 −2.97847e16 −1.49657 −0.748285 0.663378i 0.769122π-0.769122\pi
−0.748285 + 0.663378i 0.769122π0.769122\pi
150150 0 0
151151 −3.43750e16 −1.56284 −0.781421 0.624004i 0.785505π-0.785505\pi
−0.781421 + 0.624004i 0.785505π0.785505\pi
152152 0 0
153153 1.73612e16 0.715146
154154 0 0
155155 1.82600e16 0.682359
156156 0 0
157157 3.24674e16 1.10205 0.551024 0.834490i 0.314237π-0.314237\pi
0.551024 + 0.834490i 0.314237π0.314237\pi
158158 0 0
159159 −6.98601e15 −0.215651
160160 0 0
161161 1.11955e15 0.0314666
162162 0 0
163163 −2.42386e16 −0.621013 −0.310506 0.950571i 0.600499π-0.600499\pi
−0.310506 + 0.950571i 0.600499π0.600499\pi
164164 0 0
165165 −7.06047e15 −0.165084
166166 0 0
167167 −3.26384e15 −0.0697196 −0.0348598 0.999392i 0.511098π-0.511098\pi
−0.0348598 + 0.999392i 0.511098π0.511098\pi
168168 0 0
169169 −4.98126e16 −0.973171
170170 0 0
171171 −6.41386e16 −1.14722
172172 0 0
173173 −9.54205e16 −1.56421 −0.782106 0.623145i 0.785855π-0.785855\pi
−0.782106 + 0.623145i 0.785855π0.785855\pi
174174 0 0
175175 5.53625e14 0.00832589
176176 0 0
177177 −1.20307e16 −0.166146
178178 0 0
179179 1.08211e17 1.37365 0.686823 0.726824i 0.259005π-0.259005\pi
0.686823 + 0.726824i 0.259005π0.259005\pi
180180 0 0
181181 2.21984e16 0.259258 0.129629 0.991563i 0.458621π-0.458621\pi
0.129629 + 0.991563i 0.458621π0.458621\pi
182182 0 0
183183 1.22949e15 0.0132234
184184 0 0
185185 −5.79881e16 −0.574845
186186 0 0
187187 −9.52347e16 −0.870930
188188 0 0
189189 −3.18899e15 −0.0269271
190190 0 0
191191 3.42389e16 0.267159 0.133580 0.991038i 0.457353π-0.457353\pi
0.133580 + 0.991038i 0.457353π0.457353\pi
192192 0 0
193193 −2.27131e17 −1.63907 −0.819533 0.573031i 0.805767π-0.805767\pi
−0.819533 + 0.573031i 0.805767π0.805767\pi
194194 0 0
195195 3.76944e15 0.0251778
196196 0 0
197197 2.63870e16 0.163265 0.0816325 0.996662i 0.473987π-0.473987\pi
0.0816325 + 0.996662i 0.473987π0.473987\pi
198198 0 0
199199 −1.99493e17 −1.14427 −0.572137 0.820158i 0.693885π-0.693885\pi
−0.572137 + 0.820158i 0.693885π0.693885\pi
200200 0 0
201201 9.18790e16 0.488929
202202 0 0
203203 5.24514e15 0.0259141
204204 0 0
205205 6.03672e16 0.277107
206206 0 0
207207 −1.56180e17 −0.666573
208208 0 0
209209 3.51831e17 1.39713
210210 0 0
211211 −6.45604e16 −0.238697 −0.119349 0.992852i 0.538081π-0.538081\pi
−0.119349 + 0.992852i 0.538081π0.538081\pi
212212 0 0
213213 1.07460e17 0.370170
214214 0 0
215215 −3.17183e16 −0.101864
216216 0 0
217217 −2.12005e16 −0.0635183
218218 0 0
219219 −2.32319e17 −0.649761
220220 0 0
221221 5.08439e16 0.132830
222222 0 0
223223 6.71970e17 1.64083 0.820415 0.571769i 0.193743π-0.193743\pi
0.820415 + 0.571769i 0.193743π0.193743\pi
224224 0 0
225225 −7.72321e16 −0.176372
226226 0 0
227227 5.40955e17 1.15602 0.578012 0.816028i 0.303829π-0.303829\pi
0.578012 + 0.816028i 0.303829π0.303829\pi
228228 0 0
229229 7.52317e17 1.50534 0.752671 0.658397i 0.228765π-0.228765\pi
0.752671 + 0.658397i 0.228765π0.228765\pi
230230 0 0
231231 8.19746e15 0.0153670
232232 0 0
233233 −7.64780e17 −1.34390 −0.671951 0.740596i 0.734543π-0.734543\pi
−0.671951 + 0.740596i 0.734543π0.734543\pi
234234 0 0
235235 1.26798e17 0.208979
236236 0 0
237237 −4.00054e17 −0.618737
238238 0 0
239239 6.74103e17 0.978908 0.489454 0.872029i 0.337196π-0.337196\pi
0.489454 + 0.872029i 0.337196π0.337196\pi
240240 0 0
241241 3.16938e17 0.432361 0.216180 0.976353i 0.430640π-0.430640\pi
0.216180 + 0.976353i 0.430640π0.430640\pi
242242 0 0
243243 6.81271e17 0.873520
244244 0 0
245245 3.70260e17 0.446439
246246 0 0
247247 −1.87835e17 −0.213084
248248 0 0
249249 −5.61940e16 −0.0600060
250250 0 0
251251 1.54964e17 0.155840 0.0779200 0.996960i 0.475172π-0.475172\pi
0.0779200 + 0.996960i 0.475172π0.475172\pi
252252 0 0
253253 8.56722e17 0.811776
254254 0 0
255255 1.39561e17 0.124656
256256 0 0
257257 2.25253e18 1.89746 0.948731 0.316086i 0.102369π-0.102369\pi
0.948731 + 0.316086i 0.102369π0.102369\pi
258258 0 0
259259 6.73263e16 0.0535102
260260 0 0
261261 −7.31710e17 −0.548953
262262 0 0
263263 −1.00925e18 −0.715044 −0.357522 0.933905i 0.616378π-0.616378\pi
−0.357522 + 0.933905i 0.616378π0.616378\pi
264264 0 0
265265 4.19187e17 0.280585
266266 0 0
267267 8.87544e17 0.561508
268268 0 0
269269 −9.29818e17 −0.556232 −0.278116 0.960548i 0.589710π-0.589710\pi
−0.278116 + 0.960548i 0.589710π0.589710\pi
270270 0 0
271271 6.51376e16 0.0368606 0.0184303 0.999830i 0.494133π-0.494133\pi
0.0184303 + 0.999830i 0.494133π0.494133\pi
272272 0 0
273273 −4.37646e15 −0.00234370
274274 0 0
275275 4.23655e17 0.214792
276276 0 0
277277 −8.74228e16 −0.0419784 −0.0209892 0.999780i 0.506682π-0.506682\pi
−0.0209892 + 0.999780i 0.506682π0.506682\pi
278278 0 0
279279 2.95752e18 1.34554
280280 0 0
281281 1.10585e18 0.476867 0.238433 0.971159i 0.423366π-0.423366\pi
0.238433 + 0.971159i 0.423366π0.423366\pi
282282 0 0
283283 −2.15159e18 −0.879756 −0.439878 0.898058i 0.644978π-0.644978\pi
−0.439878 + 0.898058i 0.644978π0.644978\pi
284284 0 0
285285 −5.15588e17 −0.199971
286286 0 0
287287 −7.00885e16 −0.0257948
288288 0 0
289289 −9.79963e17 −0.342354
290290 0 0
291291 −3.07949e17 −0.102160
292292 0 0
293293 5.52332e18 1.74058 0.870288 0.492543i 0.163933π-0.163933\pi
0.870288 + 0.492543i 0.163933π0.163933\pi
294294 0 0
295295 7.21887e17 0.216174
296296 0 0
297297 −2.44033e18 −0.694665
298298 0 0
299299 −4.57387e17 −0.123808
300300 0 0
301301 3.68261e16 0.00948216
302302 0 0
303303 −1.81815e18 −0.445461
304304 0 0
305305 −7.37741e16 −0.0172050
306306 0 0
307307 −9.87586e17 −0.219299 −0.109650 0.993970i 0.534973π-0.534973\pi
−0.109650 + 0.993970i 0.534973π0.534973\pi
308308 0 0
309309 1.91245e18 0.404485
310310 0 0
311311 3.09644e18 0.623965 0.311982 0.950088i 0.399007π-0.399007\pi
0.311982 + 0.950088i 0.399007π0.399007\pi
312312 0 0
313313 1.19355e18 0.229224 0.114612 0.993410i 0.463438π-0.463438\pi
0.114612 + 0.993410i 0.463438π0.463438\pi
314314 0 0
315315 8.96693e16 0.0164178
316316 0 0
317317 −2.70108e18 −0.471621 −0.235811 0.971799i 0.575774π-0.575774\pi
−0.235811 + 0.971799i 0.575774π0.575774\pi
318318 0 0
319319 4.01378e18 0.668534
320320 0 0
321321 −1.56188e18 −0.248234
322322 0 0
323323 −6.95448e18 −1.05498
324324 0 0
325325 −2.26181e17 −0.0327590
326326 0 0
327327 3.43616e17 0.0475297
328328 0 0
329329 −1.47217e17 −0.0194531
330330 0 0
331331 9.04958e17 0.114266 0.0571332 0.998367i 0.481804π-0.481804\pi
0.0571332 + 0.998367i 0.481804π0.481804\pi
332332 0 0
333333 −9.39218e18 −1.13353
334334 0 0
335335 −5.51309e18 −0.636150
336336 0 0
337337 −6.84140e17 −0.0754955 −0.0377477 0.999287i 0.512018π-0.512018\pi
−0.0377477 + 0.999287i 0.512018π0.512018\pi
338338 0 0
339339 −6.08467e18 −0.642302
340340 0 0
341341 −1.62234e19 −1.63865
342342 0 0
343343 −8.60518e17 −0.0831868
344344 0 0
345345 −1.25548e18 −0.116189
346346 0 0
347347 1.18426e19 1.04948 0.524742 0.851261i 0.324162π-0.324162\pi
0.524742 + 0.851261i 0.324162π0.324162\pi
348348 0 0
349349 −4.67865e18 −0.397127 −0.198564 0.980088i 0.563628π-0.563628\pi
−0.198564 + 0.980088i 0.563628π0.563628\pi
350350 0 0
351351 1.30284e18 0.105947
352352 0 0
353353 −6.21571e18 −0.484374 −0.242187 0.970230i 0.577865π-0.577865\pi
−0.242187 + 0.970230i 0.577865π0.577865\pi
354354 0 0
355355 −6.44803e18 −0.481631
356356 0 0
357357 −1.62035e17 −0.0116037
358358 0 0
359359 −8.67422e18 −0.595693 −0.297846 0.954614i 0.596268π-0.596268\pi
−0.297846 + 0.954614i 0.596268π0.596268\pi
360360 0 0
361361 1.05112e19 0.692386
362362 0 0
363363 8.34229e17 0.0527212
364364 0 0
365365 1.39400e19 0.845410
366366 0 0
367367 −2.60076e19 −1.51393 −0.756964 0.653457i 0.773318π-0.773318\pi
−0.756964 + 0.653457i 0.773318π0.773318\pi
368368 0 0
369369 9.77751e18 0.546425
370370 0 0
371371 −4.86692e17 −0.0261186
372372 0 0
373373 3.24522e18 0.167274 0.0836369 0.996496i 0.473346π-0.473346\pi
0.0836369 + 0.996496i 0.473346π0.473346\pi
374374 0 0
375375 −6.20842e17 −0.0307430
376376 0 0
377377 −2.14287e18 −0.101962
378378 0 0
379379 −3.97275e19 −1.81676 −0.908379 0.418148i 0.862679π-0.862679\pi
−0.908379 + 0.418148i 0.862679π0.862679\pi
380380 0 0
381381 −7.20933e18 −0.316926
382382 0 0
383383 1.39053e19 0.587747 0.293874 0.955844i 0.405056π-0.405056\pi
0.293874 + 0.955844i 0.405056π0.405056\pi
384384 0 0
385385 −4.91879e17 −0.0199941
386386 0 0
387387 −5.13733e18 −0.200866
388388 0 0
389389 −2.40519e19 −0.904749 −0.452374 0.891828i 0.649423π-0.649423\pi
−0.452374 + 0.891828i 0.649423π0.649423\pi
390390 0 0
391391 −1.69344e19 −0.612978
392392 0 0
393393 −1.01959e19 −0.355207
394394 0 0
395395 2.40048e19 0.805044
396396 0 0
397397 4.68747e17 0.0151359 0.00756797 0.999971i 0.497591π-0.497591\pi
0.00756797 + 0.999971i 0.497591π0.497591\pi
398398 0 0
399399 5.98617e17 0.0186145
400400 0 0
401401 −4.59281e19 −1.37561 −0.687806 0.725894i 0.741426π-0.741426\pi
−0.687806 + 0.725894i 0.741426π0.741426\pi
402402 0 0
403403 8.66137e18 0.249919
404404 0 0
405405 −1.06087e19 −0.294952
406406 0 0
407407 5.15206e19 1.38046
408408 0 0
409409 −2.87071e18 −0.0741421 −0.0370710 0.999313i 0.511803π-0.511803\pi
−0.0370710 + 0.999313i 0.511803π0.511803\pi
410410 0 0
411411 −2.45911e19 −0.612300
412412 0 0
413413 −8.38138e17 −0.0201229
414414 0 0
415415 3.37185e18 0.0780743
416416 0 0
417417 −7.92773e18 −0.177063
418418 0 0
419419 1.95181e19 0.420563 0.210282 0.977641i 0.432562π-0.432562\pi
0.210282 + 0.977641i 0.432562π0.432562\pi
420420 0 0
421421 7.84258e19 1.63058 0.815292 0.579049i 0.196576π-0.196576\pi
0.815292 + 0.579049i 0.196576π0.196576\pi
422422 0 0
423423 2.05371e19 0.412084
424424 0 0
425425 −8.37419e18 −0.162191
426426 0 0
427427 8.56544e16 0.00160155
428428 0 0
429429 −3.34903e18 −0.0604629
430430 0 0
431431 5.24106e19 0.913776 0.456888 0.889524i 0.348964π-0.348964\pi
0.456888 + 0.889524i 0.348964π0.348964\pi
432432 0 0
433433 6.72089e19 1.13179 0.565897 0.824476i 0.308530π-0.308530\pi
0.565897 + 0.824476i 0.308530π0.308530\pi
434434 0 0
435435 −5.88196e18 −0.0956869
436436 0 0
437437 6.25618e19 0.983329
438438 0 0
439439 6.41938e19 0.975010 0.487505 0.873120i 0.337907π-0.337907\pi
0.487505 + 0.873120i 0.337907π0.337907\pi
440440 0 0
441441 5.99701e19 0.880330
442442 0 0
443443 −8.09420e19 −1.14854 −0.574270 0.818666i 0.694714π-0.694714\pi
−0.574270 + 0.818666i 0.694714π0.694714\pi
444444 0 0
445445 −5.32561e19 −0.730582
446446 0 0
447447 −3.87797e19 −0.514397
448448 0 0
449449 −5.63441e19 −0.722771 −0.361386 0.932416i 0.617696π-0.617696\pi
−0.361386 + 0.932416i 0.617696π0.617696\pi
450450 0 0
451451 −5.36344e19 −0.665456
452452 0 0
453453 −4.47562e19 −0.537176
454454 0 0
455455 2.62604e17 0.00304941
456456 0 0
457457 8.12666e19 0.913147 0.456573 0.889686i 0.349077π-0.349077\pi
0.456573 + 0.889686i 0.349077π0.349077\pi
458458 0 0
459459 4.82369e19 0.524547
460460 0 0
461461 1.12727e20 1.18651 0.593255 0.805015i 0.297843π-0.297843\pi
0.593255 + 0.805015i 0.297843π0.297843\pi
462462 0 0
463463 1.79852e20 1.83256 0.916278 0.400542i 0.131178π-0.131178\pi
0.916278 + 0.400542i 0.131178π0.131178\pi
464464 0 0
465465 2.37745e19 0.234539
466466 0 0
467467 −3.50796e19 −0.335103 −0.167552 0.985863i 0.553586π-0.553586\pi
−0.167552 + 0.985863i 0.553586π0.553586\pi
468468 0 0
469469 6.40090e18 0.0592168
470470 0 0
471471 4.22726e19 0.378793
472472 0 0
473473 2.81807e19 0.244621
474474 0 0
475475 3.09373e19 0.260184
476476 0 0
477477 6.78947e19 0.553284
478478 0 0
479479 −1.32716e19 −0.104811 −0.0524053 0.998626i 0.516689π-0.516689\pi
−0.0524053 + 0.998626i 0.516689π0.516689\pi
480480 0 0
481481 −2.75058e19 −0.210541
482482 0 0
483483 1.45766e18 0.0108156
484484 0 0
485485 1.84781e19 0.132922
486486 0 0
487487 2.27726e20 1.58835 0.794173 0.607692i 0.207904π-0.207904\pi
0.794173 + 0.607692i 0.207904π0.207904\pi
488488 0 0
489489 −3.15587e19 −0.213453
490490 0 0
491491 −2.06518e19 −0.135471 −0.0677356 0.997703i 0.521577π-0.521577\pi
−0.0677356 + 0.997703i 0.521577π0.521577\pi
492492 0 0
493493 −7.93385e19 −0.504815
494494 0 0
495495 6.86183e19 0.423546
496496 0 0
497497 7.48639e18 0.0448332
498498 0 0
499499 −2.08538e20 −1.21180 −0.605901 0.795540i 0.707187π-0.707187\pi
−0.605901 + 0.795540i 0.707187π0.707187\pi
500500 0 0
501501 −4.24952e18 −0.0239638
502502 0 0
503503 −1.61975e20 −0.886516 −0.443258 0.896394i 0.646178π-0.646178\pi
−0.443258 + 0.896394i 0.646178π0.646178\pi
504504 0 0
505505 1.09096e20 0.579594
506506 0 0
507507 −6.48561e19 −0.334496
508508 0 0
509509 1.84945e20 0.926102 0.463051 0.886332i 0.346755π-0.346755\pi
0.463051 + 0.886332i 0.346755π0.346755\pi
510510 0 0
511511 −1.61849e19 −0.0786960
512512 0 0
513513 −1.78204e20 −0.841469
514514 0 0
515515 −1.14755e20 −0.526279
516516 0 0
517517 −1.12656e20 −0.501851
518518 0 0
519519 −1.24237e20 −0.537647
520520 0 0
521521 −1.19106e20 −0.500785 −0.250392 0.968144i 0.580560π-0.580560\pi
−0.250392 + 0.968144i 0.580560π0.580560\pi
522522 0 0
523523 2.07240e20 0.846663 0.423331 0.905975i 0.360861π-0.360861\pi
0.423331 + 0.905975i 0.360861π0.360861\pi
524524 0 0
525525 7.20820e17 0.00286175
526526 0 0
527527 3.20681e20 1.23735
528528 0 0
529529 −1.14295e20 −0.428656
530530 0 0
531531 1.16922e20 0.426273
532532 0 0
533533 2.86343e19 0.101492
534534 0 0
535535 9.37190e19 0.322979
536536 0 0
537537 1.40891e20 0.472146
538538 0 0
539539 −3.28965e20 −1.07210
540540 0 0
541541 −4.26438e20 −1.35169 −0.675844 0.737045i 0.736221π-0.736221\pi
−0.675844 + 0.737045i 0.736221π0.736221\pi
542542 0 0
543543 2.89023e19 0.0891114
544544 0 0
545545 −2.06183e19 −0.0618413
546546 0 0
547547 1.46134e20 0.426427 0.213214 0.977006i 0.431607π-0.431607\pi
0.213214 + 0.977006i 0.431607π0.431607\pi
548548 0 0
549549 −1.19490e19 −0.0339265
550550 0 0
551551 2.93105e20 0.809815
552552 0 0
553553 −2.78704e19 −0.0749386
554554 0 0
555555 −7.55005e19 −0.197584
556556 0 0
557557 3.01056e20 0.766891 0.383445 0.923564i 0.374737π-0.374737\pi
0.383445 + 0.923564i 0.374737π0.374737\pi
558558 0 0
559559 −1.50451e19 −0.0373084
560560 0 0
561561 −1.23996e20 −0.299354
562562 0 0
563563 −5.43653e20 −1.27793 −0.638967 0.769234i 0.720638π-0.720638\pi
−0.638967 + 0.769234i 0.720638π0.720638\pi
564564 0 0
565565 3.65103e20 0.835704
566566 0 0
567567 1.23171e19 0.0274560
568568 0 0
569569 2.77606e19 0.0602681 0.0301340 0.999546i 0.490407π-0.490407\pi
0.0301340 + 0.999546i 0.490407π0.490407\pi
570570 0 0
571571 −7.86073e20 −1.66223 −0.831116 0.556098i 0.812298π-0.812298\pi
−0.831116 + 0.556098i 0.812298π0.812298\pi
572572 0 0
573573 4.45791e19 0.0918272
574574 0 0
575575 7.53334e19 0.151175
576576 0 0
577577 −9.30552e19 −0.181937 −0.0909687 0.995854i 0.528996π-0.528996\pi
−0.0909687 + 0.995854i 0.528996π0.528996\pi
578578 0 0
579579 −2.95725e20 −0.563376
580580 0 0
581581 −3.91485e18 −0.00726765
582582 0 0
583583 −3.72435e20 −0.673808
584584 0 0
585585 −3.66339e19 −0.0645973
586586 0 0
587587 −9.75604e20 −1.67682 −0.838412 0.545036i 0.816516π-0.816516\pi
−0.838412 + 0.545036i 0.816516π0.816516\pi
588588 0 0
589589 −1.18471e21 −1.98494
590590 0 0
591591 3.43559e19 0.0561171
592592 0 0
593593 1.11954e20 0.178292 0.0891459 0.996019i 0.471586π-0.471586\pi
0.0891459 + 0.996019i 0.471586π0.471586\pi
594594 0 0
595595 9.72275e18 0.0150977
596596 0 0
597597 −2.59740e20 −0.393307
598598 0 0
599599 7.49099e20 1.10621 0.553106 0.833111i 0.313442π-0.313442\pi
0.553106 + 0.833111i 0.313442π0.313442\pi
600600 0 0
601601 −1.59205e20 −0.229297 −0.114649 0.993406i 0.536574π-0.536574\pi
−0.114649 + 0.993406i 0.536574π0.536574\pi
602602 0 0
603603 −8.92941e20 −1.25442
604604 0 0
605605 −5.00569e19 −0.0685960
606606 0 0
607607 8.11583e20 1.08497 0.542485 0.840065i 0.317483π-0.317483\pi
0.542485 + 0.840065i 0.317483π0.317483\pi
608608 0 0
609609 6.82917e18 0.00890714
610610 0 0
611611 6.01447e19 0.0765399
612612 0 0
613613 5.55939e19 0.0690357 0.0345179 0.999404i 0.489010π-0.489010\pi
0.0345179 + 0.999404i 0.489010π0.489010\pi
614614 0 0
615615 7.85981e19 0.0952464
616616 0 0
617617 −6.97947e19 −0.0825437 −0.0412718 0.999148i 0.513141π-0.513141\pi
−0.0412718 + 0.999148i 0.513141π0.513141\pi
618618 0 0
619619 6.03520e20 0.696646 0.348323 0.937375i 0.386751π-0.386751\pi
0.348323 + 0.937375i 0.386751π0.386751\pi
620620 0 0
621621 −4.33935e20 −0.488920
622622 0 0
623623 6.18323e19 0.0680072
624624 0 0
625625 3.72529e19 0.0400000
626626 0 0
627627 4.58084e20 0.480218
628628 0 0
629629 −1.01838e21 −1.04239
630630 0 0
631631 3.64878e20 0.364693 0.182346 0.983234i 0.441631π-0.441631\pi
0.182346 + 0.983234i 0.441631π0.441631\pi
632632 0 0
633633 −8.40576e19 −0.0820445
634634 0 0
635635 4.32587e20 0.412355
636636 0 0
637637 1.75628e20 0.163511
638638 0 0
639639 −1.04437e21 −0.949725
640640 0 0
641641 2.06269e20 0.183231 0.0916156 0.995794i 0.470797π-0.470797\pi
0.0916156 + 0.995794i 0.470797π0.470797\pi
642642 0 0
643643 −2.11836e21 −1.83830 −0.919152 0.393903i 0.871125π-0.871125\pi
−0.919152 + 0.393903i 0.871125π0.871125\pi
644644 0 0
645645 −4.12972e19 −0.0350125
646646 0 0
647647 2.29485e21 1.90096 0.950480 0.310787i 0.100593π-0.100593\pi
0.950480 + 0.310787i 0.100593π0.100593\pi
648648 0 0
649649 −6.41375e20 −0.519130
650650 0 0
651651 −2.76031e19 −0.0218323
652652 0 0
653653 −5.84612e20 −0.451876 −0.225938 0.974142i 0.572545π-0.572545\pi
−0.225938 + 0.974142i 0.572545π0.572545\pi
654654 0 0
655655 6.11793e20 0.462163
656656 0 0
657657 2.25783e21 1.66706
658658 0 0
659659 −1.79922e21 −1.29850 −0.649252 0.760573i 0.724918π-0.724918\pi
−0.649252 + 0.760573i 0.724918π0.724918\pi
660660 0 0
661661 1.48620e21 1.04849 0.524247 0.851566i 0.324347π-0.324347\pi
0.524247 + 0.851566i 0.324347π0.324347\pi
662662 0 0
663663 6.61987e19 0.0456560
664664 0 0
665665 −3.59193e19 −0.0242195
666666 0 0
667667 7.13722e20 0.470528
668668 0 0
669669 8.74905e20 0.563982
670670 0 0
671671 6.55460e19 0.0413168
672672 0 0
673673 −1.01586e21 −0.626214 −0.313107 0.949718i 0.601370π-0.601370\pi
−0.313107 + 0.949718i 0.601370π0.601370\pi
674674 0 0
675675 −2.14584e20 −0.129366
676676 0 0
677677 2.64661e21 1.56054 0.780269 0.625445i 0.215082π-0.215082\pi
0.780269 + 0.625445i 0.215082π0.215082\pi
678678 0 0
679679 −2.14538e19 −0.0123732
680680 0 0
681681 7.04323e20 0.397346
682682 0 0
683683 1.97807e21 1.09166 0.545830 0.837896i 0.316214π-0.316214\pi
0.545830 + 0.837896i 0.316214π0.316214\pi
684684 0 0
685685 1.47556e21 0.796668
686686 0 0
687687 9.79517e20 0.517412
688688 0 0
689689 1.98835e20 0.102766
690690 0 0
691691 −2.52634e21 −1.27763 −0.638817 0.769359i 0.720576π-0.720576\pi
−0.638817 + 0.769359i 0.720576π0.720576\pi
692692 0 0
693693 −7.96684e19 −0.0394264
694694 0 0
695695 4.75694e20 0.230378
696696 0 0
697697 1.06017e21 0.502491
698698 0 0
699699 −9.95744e20 −0.461922
700700 0 0
701701 −2.18514e21 −0.992190 −0.496095 0.868268i 0.665233π-0.665233\pi
−0.496095 + 0.868268i 0.665233π0.665233\pi
702702 0 0
703703 3.76228e21 1.67219
704704 0 0
705705 1.65091e20 0.0718297
706706 0 0
707707 −1.26664e20 −0.0539522
708708 0 0
709709 −2.66228e19 −0.0111021 −0.00555107 0.999985i 0.501767π-0.501767\pi
−0.00555107 + 0.999985i 0.501767π0.501767\pi
710710 0 0
711711 3.88799e21 1.58746
712712 0 0
713713 −2.88482e21 −1.15331
714714 0 0
715715 2.00955e20 0.0786688
716716 0 0
717717 8.77682e20 0.336468
718718 0 0
719719 −9.86146e20 −0.370233 −0.185116 0.982717i 0.559266π-0.559266\pi
−0.185116 + 0.982717i 0.559266π0.559266\pi
720720 0 0
721721 1.33234e20 0.0489894
722722 0 0
723723 4.12653e20 0.148610
724724 0 0
725725 3.52940e20 0.124499
726726 0 0
727727 2.40230e21 0.830078 0.415039 0.909804i 0.363768π-0.363768\pi
0.415039 + 0.909804i 0.363768π0.363768\pi
728728 0 0
729729 −1.06145e21 −0.359288
730730 0 0
731731 −5.57036e20 −0.184715
732732 0 0
733733 1.87874e21 0.610361 0.305181 0.952295i 0.401283π-0.401283\pi
0.305181 + 0.952295i 0.401283π0.401283\pi
734734 0 0
735735 4.82079e20 0.153449
736736 0 0
737737 4.89821e21 1.52768
738738 0 0
739739 −5.37988e21 −1.64414 −0.822072 0.569384i 0.807182π-0.807182\pi
−0.822072 + 0.569384i 0.807182π0.807182\pi
740740 0 0
741741 −2.44562e20 −0.0732406
742742 0 0
743743 2.67434e21 0.784876 0.392438 0.919778i 0.371632π-0.371632\pi
0.392438 + 0.919778i 0.371632π0.371632\pi
744744 0 0
745745 2.32693e21 0.669286
746746 0 0
747747 5.46130e20 0.153954
748748 0 0
749749 −1.08811e20 −0.0300649
750750 0 0
751751 −4.11797e21 −1.11528 −0.557640 0.830083i 0.688293π-0.688293\pi
−0.557640 + 0.830083i 0.688293π0.688293\pi
752752 0 0
753753 2.01764e20 0.0535649
754754 0 0
755755 2.68554e21 0.698924
756756 0 0
757757 −3.83231e21 −0.977781 −0.488890 0.872345i 0.662598π-0.662598\pi
−0.488890 + 0.872345i 0.662598π0.662598\pi
758758 0 0
759759 1.11545e21 0.279022
760760 0 0
761761 3.19772e21 0.784253 0.392126 0.919911i 0.371740π-0.371740\pi
0.392126 + 0.919911i 0.371740π0.371740\pi
762762 0 0
763763 2.39386e19 0.00575658
764764 0 0
765765 −1.35635e21 −0.319823
766766 0 0
767767 3.42417e20 0.0791753
768768 0 0
769769 −5.42196e21 −1.22944 −0.614722 0.788744i 0.710732π-0.710732\pi
−0.614722 + 0.788744i 0.710732π0.710732\pi
770770 0 0
771771 2.93280e21 0.652191
772772 0 0
773773 −4.69088e21 −1.02308 −0.511538 0.859261i 0.670924π-0.670924\pi
−0.511538 + 0.859261i 0.670924π0.670924\pi
774774 0 0
775775 −1.42656e21 −0.305160
776776 0 0
777777 8.76589e19 0.0183924
778778 0 0
779779 −3.91663e21 −0.806087
780780 0 0
781781 5.72887e21 1.15661
782782 0 0
783783 −2.03300e21 −0.402647
784784 0 0
785785 −2.53652e21 −0.492851
786786 0 0
787787 9.27131e21 1.76738 0.883691 0.468070i 0.155051π-0.155051\pi
0.883691 + 0.468070i 0.155051π0.155051\pi
788788 0 0
789789 −1.31405e21 −0.245773
790790 0 0
791791 −4.23899e20 −0.0777926
792792 0 0
793793 −3.49937e19 −0.00630145
794794 0 0
795795 5.45782e20 0.0964419
796796 0 0
797797 8.35314e21 1.44848 0.724240 0.689548i 0.242191π-0.242191\pi
0.724240 + 0.689548i 0.242191π0.242191\pi
798798 0 0
799799 2.22682e21 0.378951
800800 0 0
801801 −8.62575e21 −1.44063
802802 0 0
803803 −1.23853e22 −2.03020
804804 0 0
805805 −8.74649e19 −0.0140723
806806 0 0
807807 −1.21062e21 −0.191187
808808 0 0
809809 −5.86882e21 −0.909781 −0.454890 0.890547i 0.650322π-0.650322\pi
−0.454890 + 0.890547i 0.650322π0.650322\pi
810810 0 0
811811 −9.20718e21 −1.40110 −0.700552 0.713602i 0.747063π-0.747063\pi
−0.700552 + 0.713602i 0.747063π0.747063\pi
812812 0 0
813813 8.48091e19 0.0126696
814814 0 0
815815 1.89364e21 0.277725
816816 0 0
817817 2.05789e21 0.296317
818818 0 0
819819 4.25333e19 0.00601312
820820 0 0
821821 2.78078e21 0.386005 0.193003 0.981198i 0.438177π-0.438177\pi
0.193003 + 0.981198i 0.438177π0.438177\pi
822822 0 0
823823 −1.08620e22 −1.48051 −0.740257 0.672324i 0.765296π-0.765296\pi
−0.740257 + 0.672324i 0.765296π0.765296\pi
824824 0 0
825825 5.51599e20 0.0738276
826826 0 0
827827 4.48033e21 0.588869 0.294435 0.955672i 0.404869π-0.404869\pi
0.294435 + 0.955672i 0.404869π0.404869\pi
828828 0 0
829829 −1.15562e22 −1.49161 −0.745807 0.666163i 0.767936π-0.767936\pi
−0.745807 + 0.666163i 0.767936π0.767936\pi
830830 0 0
831831 −1.13824e20 −0.0144287
832832 0 0
833833 6.50250e21 0.809548
834834 0 0
835835 2.54987e20 0.0311796
836836 0 0
837837 8.21727e21 0.986930
838838 0 0
839839 −1.16410e22 −1.37333 −0.686666 0.726973i 0.740926π-0.740926\pi
−0.686666 + 0.726973i 0.740926π0.740926\pi
840840 0 0
841841 −5.28537e21 −0.612500
842842 0 0
843843 1.43981e21 0.163907
844844 0 0
845845 3.89161e21 0.435215
846846 0 0
847847 5.81179e19 0.00638535
848848 0 0
849849 −2.80138e21 −0.302387
850850 0 0
851851 9.16129e21 0.971594
852852 0 0
853853 −8.05337e21 −0.839189 −0.419595 0.907712i 0.637828π-0.637828\pi
−0.419595 + 0.907712i 0.637828π0.637828\pi
854854 0 0
855855 5.01083e21 0.513055
856856 0 0
857857 3.51278e21 0.353423 0.176712 0.984263i 0.443454π-0.443454\pi
0.176712 + 0.984263i 0.443454π0.443454\pi
858858 0 0
859859 −4.79620e21 −0.474186 −0.237093 0.971487i 0.576195π-0.576195\pi
−0.237093 + 0.971487i 0.576195π0.576195\pi
860860 0 0
861861 −9.12552e19 −0.00886613
862862 0 0
863863 −6.27772e21 −0.599406 −0.299703 0.954033i 0.596888π-0.596888\pi
−0.299703 + 0.954033i 0.596888π0.596888\pi
864864 0 0
865865 7.45472e21 0.699537
866866 0 0
867867 −1.27591e21 −0.117673
868868 0 0
869869 −2.13275e22 −1.93327
870870 0 0
871871 −2.61506e21 −0.232994
872872 0 0
873873 2.99286e21 0.262107
874874 0 0
875875 −4.32520e19 −0.00372345
876876 0 0
877877 −4.69963e21 −0.397711 −0.198855 0.980029i 0.563722π-0.563722\pi
−0.198855 + 0.980029i 0.563722π0.563722\pi
878878 0 0
879879 7.19136e21 0.598266
880880 0 0
881881 −1.89876e22 −1.55293 −0.776465 0.630161i 0.782989π-0.782989\pi
−0.776465 + 0.630161i 0.782989π0.782989\pi
882882 0 0
883883 5.43744e21 0.437209 0.218605 0.975814i 0.429849π-0.429849\pi
0.218605 + 0.975814i 0.429849π0.429849\pi
884884 0 0
885885 9.39897e20 0.0743029
886886 0 0
887887 1.43529e22 1.11561 0.557807 0.829971i 0.311643π-0.311643\pi
0.557807 + 0.829971i 0.311643π0.311643\pi
888888 0 0
889889 −5.02250e20 −0.0383846
890890 0 0
891891 9.42554e21 0.708310
892892 0 0
893893 −8.22665e21 −0.607907
894894 0 0
895895 −8.45401e21 −0.614314
896896 0 0
897897 −5.95517e20 −0.0425551
898898 0 0
899899 −1.35155e22 −0.949804
900900 0 0
901901 7.36175e21 0.508798
902902 0 0
903903 4.79476e19 0.00325918
904904 0 0
905905 −1.73425e21 −0.115944
906906 0 0
907907 1.44404e22 0.949564 0.474782 0.880103i 0.342527π-0.342527\pi
0.474782 + 0.880103i 0.342527π0.342527\pi
908908 0 0
909909 1.76700e22 1.14290
910910 0 0
911911 6.00661e21 0.382157 0.191078 0.981575i 0.438802π-0.438802\pi
0.191078 + 0.981575i 0.438802π0.438802\pi
912912 0 0
913913 −2.99579e21 −0.187491
914914 0 0
915915 −9.60538e19 −0.00591366
916916 0 0
917917 −7.10315e20 −0.0430210
918918 0 0
919919 −2.25875e22 −1.34586 −0.672932 0.739704i 0.734966π-0.734966\pi
−0.672932 + 0.739704i 0.734966π0.734966\pi
920920 0 0
921921 −1.28584e21 −0.0753770
922922 0 0
923923 −3.05853e21 −0.176400
924924 0 0
925925 4.53032e21 0.257079
926926 0 0
927927 −1.85865e22 −1.03777
928928 0 0
929929 3.26962e22 1.79630 0.898151 0.439686i 0.144910π-0.144910\pi
0.898151 + 0.439686i 0.144910π0.144910\pi
930930 0 0
931931 −2.40225e22 −1.29866
932932 0 0
933933 4.03157e21 0.214468
934934 0 0
935935 7.44021e21 0.389492
936936 0 0
937937 2.67083e21 0.137594 0.0687970 0.997631i 0.478084π-0.478084\pi
0.0687970 + 0.997631i 0.478084π0.478084\pi
938938 0 0
939939 1.55401e21 0.0787881
940940 0 0
941941 −2.61162e22 −1.30313 −0.651565 0.758593i 0.725887π-0.725887\pi
−0.651565 + 0.758593i 0.725887π0.725887\pi
942942 0 0
943943 −9.53715e21 −0.468361
944944 0 0
945945 2.49140e20 0.0120422
946946 0 0
947947 1.03859e22 0.494105 0.247053 0.969002i 0.420538π-0.420538\pi
0.247053 + 0.969002i 0.420538π0.420538\pi
948948 0 0
949949 6.61225e21 0.309637
950950 0 0
951951 −3.51681e21 −0.162104
952952 0 0
953953 1.16131e20 0.00526929 0.00263464 0.999997i 0.499161π-0.499161\pi
0.00263464 + 0.999997i 0.499161π0.499161\pi
954954 0 0
955955 −2.67492e21 −0.119477
956956 0 0
957957 5.22594e21 0.229787
958958 0 0
959959 −1.71318e21 −0.0741589
960960 0 0
961961 3.11635e22 1.32807
962962 0 0
963963 1.51794e22 0.636881
964964 0 0
965965 1.77446e22 0.733013
966966 0 0
967967 3.55619e22 1.44639 0.723197 0.690642i 0.242672π-0.242672\pi
0.723197 + 0.690642i 0.242672π0.242672\pi
968968 0 0
969969 −9.05473e21 −0.362616
970970 0 0
971971 4.08883e22 1.61233 0.806166 0.591690i 0.201539π-0.201539\pi
0.806166 + 0.591690i 0.201539π0.201539\pi
972972 0 0
973973 −5.52298e20 −0.0214451
974974 0 0
975975 −2.94487e20 −0.0112598
976976 0 0
977977 1.47056e22 0.553700 0.276850 0.960913i 0.410709π-0.410709\pi
0.276850 + 0.960913i 0.410709π0.410709\pi
978978 0 0
979979 4.73164e22 1.75445
980980 0 0
981981 −3.33949e21 −0.121945
982982 0 0
983983 2.02443e22 0.728034 0.364017 0.931392i 0.381405π-0.381405\pi
0.364017 + 0.931392i 0.381405π0.381405\pi
984984 0 0
985985 −2.06148e21 −0.0730144
986986 0 0
987987 −1.91676e20 −0.00668636
988988 0 0
989989 5.01104e21 0.172169
990990 0 0
991991 −1.99356e22 −0.674649 −0.337324 0.941389i 0.609522π-0.609522\pi
−0.337324 + 0.941389i 0.609522π0.609522\pi
992992 0 0
993993 1.17825e21 0.0392753
994994 0 0
995995 1.55854e22 0.511735
996996 0 0
997997 −4.00115e21 −0.129411 −0.0647056 0.997904i 0.520611π-0.520611\pi
−0.0647056 + 0.997904i 0.520611π0.520611\pi
998998 0 0
999999 −2.60955e22 −0.831427
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 80.16.a.b.1.1 1
4.3 odd 2 10.16.a.c.1.1 1
12.11 even 2 90.16.a.d.1.1 1
20.3 even 4 50.16.b.b.49.1 2
20.7 even 4 50.16.b.b.49.2 2
20.19 odd 2 50.16.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.16.a.c.1.1 1 4.3 odd 2
50.16.a.a.1.1 1 20.19 odd 2
50.16.b.b.49.1 2 20.3 even 4
50.16.b.b.49.2 2 20.7 even 4
80.16.a.b.1.1 1 1.1 even 1 trivial
90.16.a.d.1.1 1 12.11 even 2