Properties

Label 1632.2.a.r.1.3
Level 16321632
Weight 22
Character 1632.1
Self dual yes
Analytic conductor 13.03213.032
Analytic rank 00
Dimension 33
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] = [1632,2,Mod(1,1632)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1632, 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("1632.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1632=25317 1632 = 2^{5} \cdot 3 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1632.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: 13.031585609913.0315856099
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.316.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x24x+2 x^{3} - x^{2} - 4x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 0.4706830.470683 of defining polynomial
Character χ\chi == 1632.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.00000q3+3.77846q50.941367q7+1.00000q92.71982q110.719824q133.77846q15+1.00000q17+2.71982q19+0.941367q21+1.77846q23+9.27674q251.00000q27+8.61555q29+8.05520q31+2.71982q333.55691q35+2.94137q37+0.719824q398.27674q410.837090q43+3.77846q45+1.88273q476.11383q491.00000q511.55691q5310.2767q552.71982q57+0.443086q592.49828q610.941367q632.71982q65+12.9966q671.77846q696.61555q71+7.43965q739.27674q75+2.56035q772.82410q79+1.00000q81+17.2311q83+3.77846q858.61555q87+9.11383q89+0.677618q918.05520q93+10.2767q95+8.11727q972.71982q99+O(q100)q-1.00000 q^{3} +3.77846 q^{5} -0.941367 q^{7} +1.00000 q^{9} -2.71982 q^{11} -0.719824 q^{13} -3.77846 q^{15} +1.00000 q^{17} +2.71982 q^{19} +0.941367 q^{21} +1.77846 q^{23} +9.27674 q^{25} -1.00000 q^{27} +8.61555 q^{29} +8.05520 q^{31} +2.71982 q^{33} -3.55691 q^{35} +2.94137 q^{37} +0.719824 q^{39} -8.27674 q^{41} -0.837090 q^{43} +3.77846 q^{45} +1.88273 q^{47} -6.11383 q^{49} -1.00000 q^{51} -1.55691 q^{53} -10.2767 q^{55} -2.71982 q^{57} +0.443086 q^{59} -2.49828 q^{61} -0.941367 q^{63} -2.71982 q^{65} +12.9966 q^{67} -1.77846 q^{69} -6.61555 q^{71} +7.43965 q^{73} -9.27674 q^{75} +2.56035 q^{77} -2.82410 q^{79} +1.00000 q^{81} +17.2311 q^{83} +3.77846 q^{85} -8.61555 q^{87} +9.11383 q^{89} +0.677618 q^{91} -8.05520 q^{93} +10.2767 q^{95} +8.11727 q^{97} -2.71982 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q3q3+3q52q7+3q9+q11+7q133q15+3q17q19+2q213q23+2q253q27+10q2910q31q33+6q35+8q377q39++q99+O(q100) 3 q - 3 q^{3} + 3 q^{5} - 2 q^{7} + 3 q^{9} + q^{11} + 7 q^{13} - 3 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} - 3 q^{23} + 2 q^{25} - 3 q^{27} + 10 q^{29} - 10 q^{31} - q^{33} + 6 q^{35} + 8 q^{37} - 7 q^{39}+ \cdots + 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 3.77846 1.68978 0.844889 0.534942i 0.179667π-0.179667\pi
0.844889 + 0.534942i 0.179667π0.179667\pi
66 0 0
77 −0.941367 −0.355803 −0.177902 0.984048i 0.556931π-0.556931\pi
−0.177902 + 0.984048i 0.556931π0.556931\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 −2.71982 −0.820058 −0.410029 0.912073i 0.634481π-0.634481\pi
−0.410029 + 0.912073i 0.634481π0.634481\pi
1212 0 0
1313 −0.719824 −0.199643 −0.0998216 0.995005i 0.531827π-0.531827\pi
−0.0998216 + 0.995005i 0.531827π0.531827\pi
1414 0 0
1515 −3.77846 −0.975593
1616 0 0
1717 1.00000 0.242536
1818 0 0
1919 2.71982 0.623970 0.311985 0.950087i 0.399006π-0.399006\pi
0.311985 + 0.950087i 0.399006π0.399006\pi
2020 0 0
2121 0.941367 0.205423
2222 0 0
2323 1.77846 0.370834 0.185417 0.982660i 0.440636π-0.440636\pi
0.185417 + 0.982660i 0.440636π0.440636\pi
2424 0 0
2525 9.27674 1.85535
2626 0 0
2727 −1.00000 −0.192450
2828 0 0
2929 8.61555 1.59987 0.799933 0.600089i 0.204868π-0.204868\pi
0.799933 + 0.600089i 0.204868π0.204868\pi
3030 0 0
3131 8.05520 1.44676 0.723378 0.690452i 0.242588π-0.242588\pi
0.723378 + 0.690452i 0.242588π0.242588\pi
3232 0 0
3333 2.71982 0.473461
3434 0 0
3535 −3.55691 −0.601228
3636 0 0
3737 2.94137 0.483558 0.241779 0.970331i 0.422269π-0.422269\pi
0.241779 + 0.970331i 0.422269π0.422269\pi
3838 0 0
3939 0.719824 0.115264
4040 0 0
4141 −8.27674 −1.29261 −0.646305 0.763079i 0.723686π-0.723686\pi
−0.646305 + 0.763079i 0.723686π0.723686\pi
4242 0 0
4343 −0.837090 −0.127655 −0.0638275 0.997961i 0.520331π-0.520331\pi
−0.0638275 + 0.997961i 0.520331π0.520331\pi
4444 0 0
4545 3.77846 0.563259
4646 0 0
4747 1.88273 0.274625 0.137312 0.990528i 0.456154π-0.456154\pi
0.137312 + 0.990528i 0.456154π0.456154\pi
4848 0 0
4949 −6.11383 −0.873404
5050 0 0
5151 −1.00000 −0.140028
5252 0 0
5353 −1.55691 −0.213859 −0.106929 0.994267i 0.534102π-0.534102\pi
−0.106929 + 0.994267i 0.534102π0.534102\pi
5454 0 0
5555 −10.2767 −1.38572
5656 0 0
5757 −2.71982 −0.360249
5858 0 0
5959 0.443086 0.0576849 0.0288424 0.999584i 0.490818π-0.490818\pi
0.0288424 + 0.999584i 0.490818π0.490818\pi
6060 0 0
6161 −2.49828 −0.319872 −0.159936 0.987127i 0.551129π-0.551129\pi
−0.159936 + 0.987127i 0.551129π0.551129\pi
6262 0 0
6363 −0.941367 −0.118601
6464 0 0
6565 −2.71982 −0.337353
6666 0 0
6767 12.9966 1.58778 0.793891 0.608060i 0.208052π-0.208052\pi
0.793891 + 0.608060i 0.208052π0.208052\pi
6868 0 0
6969 −1.77846 −0.214101
7070 0 0
7171 −6.61555 −0.785121 −0.392561 0.919726i 0.628411π-0.628411\pi
−0.392561 + 0.919726i 0.628411π0.628411\pi
7272 0 0
7373 7.43965 0.870745 0.435372 0.900250i 0.356617π-0.356617\pi
0.435372 + 0.900250i 0.356617π0.356617\pi
7474 0 0
7575 −9.27674 −1.07119
7676 0 0
7777 2.56035 0.291779
7878 0 0
7979 −2.82410 −0.317736 −0.158868 0.987300i 0.550784π-0.550784\pi
−0.158868 + 0.987300i 0.550784π0.550784\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 17.2311 1.89136 0.945679 0.325101i 0.105398π-0.105398\pi
0.945679 + 0.325101i 0.105398π0.105398\pi
8484 0 0
8585 3.77846 0.409831
8686 0 0
8787 −8.61555 −0.923684
8888 0 0
8989 9.11383 0.966064 0.483032 0.875603i 0.339535π-0.339535\pi
0.483032 + 0.875603i 0.339535π0.339535\pi
9090 0 0
9191 0.677618 0.0710337
9292 0 0
9393 −8.05520 −0.835285
9494 0 0
9595 10.2767 1.05437
9696 0 0
9797 8.11727 0.824184 0.412092 0.911142i 0.364798π-0.364798\pi
0.412092 + 0.911142i 0.364798π0.364798\pi
9898 0 0
9999 −2.71982 −0.273353
100100 0 0
101101 9.32238 0.927612 0.463806 0.885937i 0.346484π-0.346484\pi
0.463806 + 0.885937i 0.346484π0.346484\pi
102102 0 0
103103 −10.7198 −1.05626 −0.528128 0.849165i 0.677106π-0.677106\pi
−0.528128 + 0.849165i 0.677106π0.677106\pi
104104 0 0
105105 3.55691 0.347119
106106 0 0
107107 16.1595 1.56220 0.781098 0.624409i 0.214660π-0.214660\pi
0.781098 + 0.624409i 0.214660π0.214660\pi
108108 0 0
109109 −3.17590 −0.304196 −0.152098 0.988365i 0.548603π-0.548603\pi
−0.152098 + 0.988365i 0.548603π0.548603\pi
110110 0 0
111111 −2.94137 −0.279182
112112 0 0
113113 −0.954357 −0.0897783 −0.0448892 0.998992i 0.514293π-0.514293\pi
−0.0448892 + 0.998992i 0.514293π0.514293\pi
114114 0 0
115115 6.71982 0.626627
116116 0 0
117117 −0.719824 −0.0665477
118118 0 0
119119 −0.941367 −0.0862950
120120 0 0
121121 −3.60256 −0.327505
122122 0 0
123123 8.27674 0.746288
124124 0 0
125125 16.1595 1.44535
126126 0 0
127127 4.60256 0.408411 0.204205 0.978928i 0.434539π-0.434539\pi
0.204205 + 0.978928i 0.434539π0.434539\pi
128128 0 0
129129 0.837090 0.0737017
130130 0 0
131131 −0.159472 −0.0139331 −0.00696656 0.999976i 0.502218π-0.502218\pi
−0.00696656 + 0.999976i 0.502218π0.502218\pi
132132 0 0
133133 −2.56035 −0.222011
134134 0 0
135135 −3.77846 −0.325198
136136 0 0
137137 −18.5535 −1.58513 −0.792565 0.609787i 0.791255π-0.791255\pi
−0.792565 + 0.609787i 0.791255π0.791255\pi
138138 0 0
139139 −2.11727 −0.179584 −0.0897921 0.995961i 0.528620π-0.528620\pi
−0.0897921 + 0.995961i 0.528620π0.528620\pi
140140 0 0
141141 −1.88273 −0.158555
142142 0 0
143143 1.95779 0.163719
144144 0 0
145145 32.5535 2.70342
146146 0 0
147147 6.11383 0.504260
148148 0 0
149149 −3.43965 −0.281787 −0.140893 0.990025i 0.544998π-0.544998\pi
−0.140893 + 0.990025i 0.544998π0.544998\pi
150150 0 0
151151 −20.0000 −1.62758 −0.813788 0.581161i 0.802599π-0.802599\pi
−0.813788 + 0.581161i 0.802599π0.802599\pi
152152 0 0
153153 1.00000 0.0808452
154154 0 0
155155 30.4362 2.44470
156156 0 0
157157 15.3906 1.22830 0.614150 0.789189i 0.289499π-0.289499\pi
0.614150 + 0.789189i 0.289499π0.289499\pi
158158 0 0
159159 1.55691 0.123471
160160 0 0
161161 −1.67418 −0.131944
162162 0 0
163163 −16.5535 −1.29657 −0.648284 0.761398i 0.724513π-0.724513\pi
−0.648284 + 0.761398i 0.724513π0.724513\pi
164164 0 0
165165 10.2767 0.800043
166166 0 0
167167 −20.4492 −1.58241 −0.791203 0.611553i 0.790545π-0.790545\pi
−0.791203 + 0.611553i 0.790545π0.790545\pi
168168 0 0
169169 −12.4819 −0.960143
170170 0 0
171171 2.71982 0.207990
172172 0 0
173173 18.8923 1.43635 0.718177 0.695861i 0.244977π-0.244977\pi
0.718177 + 0.695861i 0.244977π0.244977\pi
174174 0 0
175175 −8.73281 −0.660139
176176 0 0
177177 −0.443086 −0.0333044
178178 0 0
179179 24.5535 1.83521 0.917606 0.397490i 0.130119π-0.130119\pi
0.917606 + 0.397490i 0.130119π0.130119\pi
180180 0 0
181181 −15.9379 −1.18466 −0.592328 0.805697i 0.701791π-0.701791\pi
−0.592328 + 0.805697i 0.701791π0.701791\pi
182182 0 0
183183 2.49828 0.184678
184184 0 0
185185 11.1138 0.817105
186186 0 0
187187 −2.71982 −0.198893
188188 0 0
189189 0.941367 0.0684744
190190 0 0
191191 6.11727 0.442630 0.221315 0.975202i 0.428965π-0.428965\pi
0.221315 + 0.975202i 0.428965π0.428965\pi
192192 0 0
193193 15.2311 1.09636 0.548179 0.836361i 0.315321π-0.315321\pi
0.548179 + 0.836361i 0.315321π0.315321\pi
194194 0 0
195195 2.71982 0.194771
196196 0 0
197197 12.7750 0.910182 0.455091 0.890445i 0.349607π-0.349607\pi
0.455091 + 0.890445i 0.349607π0.349607\pi
198198 0 0
199199 −8.94137 −0.633837 −0.316918 0.948453i 0.602648π-0.602648\pi
−0.316918 + 0.948453i 0.602648π0.602648\pi
200200 0 0
201201 −12.9966 −0.916707
202202 0 0
203203 −8.11039 −0.569238
204204 0 0
205205 −31.2733 −2.18422
206206 0 0
207207 1.77846 0.123611
208208 0 0
209209 −7.39744 −0.511692
210210 0 0
211211 −7.55691 −0.520239 −0.260120 0.965576i 0.583762π-0.583762\pi
−0.260120 + 0.965576i 0.583762π0.583762\pi
212212 0 0
213213 6.61555 0.453290
214214 0 0
215215 −3.16291 −0.215709
216216 0 0
217217 −7.58289 −0.514760
218218 0 0
219219 −7.43965 −0.502725
220220 0 0
221221 −0.719824 −0.0484206
222222 0 0
223223 −19.5078 −1.30634 −0.653171 0.757211i 0.726562π-0.726562\pi
−0.653171 + 0.757211i 0.726562π0.726562\pi
224224 0 0
225225 9.27674 0.618449
226226 0 0
227227 1.72326 0.114377 0.0571885 0.998363i 0.481786π-0.481786\pi
0.0571885 + 0.998363i 0.481786π0.481786\pi
228228 0 0
229229 −20.8793 −1.37974 −0.689871 0.723932i 0.742333π-0.742333\pi
−0.689871 + 0.723932i 0.742333π0.742333\pi
230230 0 0
231231 −2.56035 −0.168459
232232 0 0
233233 11.5991 0.759884 0.379942 0.925010i 0.375944π-0.375944\pi
0.379942 + 0.925010i 0.375944π0.375944\pi
234234 0 0
235235 7.11383 0.464055
236236 0 0
237237 2.82410 0.183445
238238 0 0
239239 14.4362 0.933801 0.466900 0.884310i 0.345371π-0.345371\pi
0.466900 + 0.884310i 0.345371π0.345371\pi
240240 0 0
241241 11.8827 0.765434 0.382717 0.923866i 0.374988π-0.374988\pi
0.382717 + 0.923866i 0.374988π0.374988\pi
242242 0 0
243243 −1.00000 −0.0641500
244244 0 0
245245 −23.1008 −1.47586
246246 0 0
247247 −1.95779 −0.124571
248248 0 0
249249 −17.2311 −1.09198
250250 0 0
251251 27.1138 1.71141 0.855705 0.517464i 0.173124π-0.173124\pi
0.855705 + 0.517464i 0.173124π0.173124\pi
252252 0 0
253253 −4.83709 −0.304105
254254 0 0
255255 −3.77846 −0.236616
256256 0 0
257257 −24.8793 −1.55193 −0.775964 0.630777i 0.782736π-0.782736\pi
−0.775964 + 0.630777i 0.782736π0.782736\pi
258258 0 0
259259 −2.76891 −0.172051
260260 0 0
261261 8.61555 0.533289
262262 0 0
263263 24.9966 1.54135 0.770677 0.637226i 0.219918π-0.219918\pi
0.770677 + 0.637226i 0.219918π0.219918\pi
264264 0 0
265265 −5.88273 −0.361373
266266 0 0
267267 −9.11383 −0.557757
268268 0 0
269269 −21.8957 −1.33501 −0.667503 0.744607i 0.732637π-0.732637\pi
−0.667503 + 0.744607i 0.732637π0.732637\pi
270270 0 0
271271 4.60256 0.279585 0.139793 0.990181i 0.455356π-0.455356\pi
0.139793 + 0.990181i 0.455356π0.455356\pi
272272 0 0
273273 −0.677618 −0.0410113
274274 0 0
275275 −25.2311 −1.52149
276276 0 0
277277 −7.82754 −0.470311 −0.235156 0.971958i 0.575560π-0.575560\pi
−0.235156 + 0.971958i 0.575560π0.575560\pi
278278 0 0
279279 8.05520 0.482252
280280 0 0
281281 25.1138 1.49817 0.749083 0.662476i 0.230495π-0.230495\pi
0.749083 + 0.662476i 0.230495π0.230495\pi
282282 0 0
283283 −3.32238 −0.197495 −0.0987475 0.995113i 0.531484π-0.531484\pi
−0.0987475 + 0.995113i 0.531484π0.531484\pi
284284 0 0
285285 −10.2767 −0.608741
286286 0 0
287287 7.79145 0.459915
288288 0 0
289289 1.00000 0.0588235
290290 0 0
291291 −8.11727 −0.475843
292292 0 0
293293 −29.4328 −1.71948 −0.859740 0.510731i 0.829375π-0.829375\pi
−0.859740 + 0.510731i 0.829375π0.829375\pi
294294 0 0
295295 1.67418 0.0974746
296296 0 0
297297 2.71982 0.157820
298298 0 0
299299 −1.28018 −0.0740345
300300 0 0
301301 0.788009 0.0454201
302302 0 0
303303 −9.32238 −0.535557
304304 0 0
305305 −9.43965 −0.540513
306306 0 0
307307 −15.3484 −0.875977 −0.437989 0.898981i 0.644309π-0.644309\pi
−0.437989 + 0.898981i 0.644309π0.644309\pi
308308 0 0
309309 10.7198 0.609829
310310 0 0
311311 −31.6121 −1.79256 −0.896279 0.443490i 0.853740π-0.853740\pi
−0.896279 + 0.443490i 0.853740π0.853740\pi
312312 0 0
313313 −15.4656 −0.874169 −0.437084 0.899420i 0.643989π-0.643989\pi
−0.437084 + 0.899420i 0.643989π0.643989\pi
314314 0 0
315315 −3.55691 −0.200409
316316 0 0
317317 −22.6087 −1.26983 −0.634915 0.772582i 0.718965π-0.718965\pi
−0.634915 + 0.772582i 0.718965π0.718965\pi
318318 0 0
319319 −23.4328 −1.31198
320320 0 0
321321 −16.1595 −0.901934
322322 0 0
323323 2.71982 0.151335
324324 0 0
325325 −6.67762 −0.370408
326326 0 0
327327 3.17590 0.175628
328328 0 0
329329 −1.77234 −0.0977124
330330 0 0
331331 −29.3906 −1.61545 −0.807726 0.589558i 0.799302π-0.799302\pi
−0.807726 + 0.589558i 0.799302π0.799302\pi
332332 0 0
333333 2.94137 0.161186
334334 0 0
335335 49.1070 2.68300
336336 0 0
337337 −7.67418 −0.418039 −0.209020 0.977911i 0.567027π-0.567027\pi
−0.209020 + 0.977911i 0.567027π0.567027\pi
338338 0 0
339339 0.954357 0.0518335
340340 0 0
341341 −21.9087 −1.18642
342342 0 0
343343 12.3449 0.666563
344344 0 0
345345 −6.71982 −0.361783
346346 0 0
347347 −0.234533 −0.0125904 −0.00629519 0.999980i 0.502004π-0.502004\pi
−0.00629519 + 0.999980i 0.502004π0.502004\pi
348348 0 0
349349 8.48529 0.454207 0.227104 0.973871i 0.427074π-0.427074\pi
0.227104 + 0.973871i 0.427074π0.427074\pi
350350 0 0
351351 0.719824 0.0384214
352352 0 0
353353 −16.8793 −0.898394 −0.449197 0.893433i 0.648290π-0.648290\pi
−0.449197 + 0.893433i 0.648290π0.648290\pi
354354 0 0
355355 −24.9966 −1.32668
356356 0 0
357357 0.941367 0.0498224
358358 0 0
359359 30.2277 1.59535 0.797677 0.603084i 0.206062π-0.206062\pi
0.797677 + 0.603084i 0.206062π0.206062\pi
360360 0 0
361361 −11.6026 −0.610661
362362 0 0
363363 3.60256 0.189085
364364 0 0
365365 28.1104 1.47137
366366 0 0
367367 3.50172 0.182788 0.0913941 0.995815i 0.470868π-0.470868\pi
0.0913941 + 0.995815i 0.470868π0.470868\pi
368368 0 0
369369 −8.27674 −0.430870
370370 0 0
371371 1.46563 0.0760916
372372 0 0
373373 −22.7620 −1.17857 −0.589287 0.807924i 0.700591π-0.700591\pi
−0.589287 + 0.807924i 0.700591π0.700591\pi
374374 0 0
375375 −16.1595 −0.834472
376376 0 0
377377 −6.20168 −0.319403
378378 0 0
379379 28.7880 1.47874 0.739370 0.673299i 0.235123π-0.235123\pi
0.739370 + 0.673299i 0.235123π0.235123\pi
380380 0 0
381381 −4.60256 −0.235796
382382 0 0
383383 −28.6639 −1.46466 −0.732328 0.680952i 0.761566π-0.761566\pi
−0.732328 + 0.680952i 0.761566π0.761566\pi
384384 0 0
385385 9.67418 0.493042
386386 0 0
387387 −0.837090 −0.0425517
388388 0 0
389389 −22.7880 −1.15540 −0.577699 0.816250i 0.696049π-0.696049\pi
−0.577699 + 0.816250i 0.696049π0.696049\pi
390390 0 0
391391 1.77846 0.0899404
392392 0 0
393393 0.159472 0.00804429
394394 0 0
395395 −10.6707 −0.536903
396396 0 0
397397 −18.0812 −0.907468 −0.453734 0.891137i 0.649908π-0.649908\pi
−0.453734 + 0.891137i 0.649908π0.649908\pi
398398 0 0
399399 2.56035 0.128178
400400 0 0
401401 1.71639 0.0857122 0.0428561 0.999081i 0.486354π-0.486354\pi
0.0428561 + 0.999081i 0.486354π0.486354\pi
402402 0 0
403403 −5.79832 −0.288835
404404 0 0
405405 3.77846 0.187753
406406 0 0
407407 −8.00000 −0.396545
408408 0 0
409409 −25.1629 −1.24423 −0.622113 0.782928i 0.713726π-0.713726\pi
−0.622113 + 0.782928i 0.713726π0.713726\pi
410410 0 0
411411 18.5535 0.915175
412412 0 0
413413 −0.417106 −0.0205245
414414 0 0
415415 65.1070 3.19597
416416 0 0
417417 2.11727 0.103683
418418 0 0
419419 −12.0000 −0.586238 −0.293119 0.956076i 0.594693π-0.594693\pi
−0.293119 + 0.956076i 0.594693π0.594693\pi
420420 0 0
421421 21.5078 1.04823 0.524114 0.851648i 0.324397π-0.324397\pi
0.524114 + 0.851648i 0.324397π0.324397\pi
422422 0 0
423423 1.88273 0.0915416
424424 0 0
425425 9.27674 0.449988
426426 0 0
427427 2.35180 0.113812
428428 0 0
429429 −1.95779 −0.0945232
430430 0 0
431431 −4.73281 −0.227972 −0.113986 0.993482i 0.536362π-0.536362\pi
−0.113986 + 0.993482i 0.536362π0.536362\pi
432432 0 0
433433 10.2836 0.494199 0.247099 0.968990i 0.420523π-0.420523\pi
0.247099 + 0.968990i 0.420523π0.420523\pi
434434 0 0
435435 −32.5535 −1.56082
436436 0 0
437437 4.83709 0.231389
438438 0 0
439439 −25.7294 −1.22800 −0.613998 0.789308i 0.710440π-0.710440\pi
−0.613998 + 0.789308i 0.710440π0.710440\pi
440440 0 0
441441 −6.11383 −0.291135
442442 0 0
443443 23.3484 1.10931 0.554657 0.832079i 0.312849π-0.312849\pi
0.554657 + 0.832079i 0.312849π0.312849\pi
444444 0 0
445445 34.4362 1.63243
446446 0 0
447447 3.43965 0.162690
448448 0 0
449449 −28.6448 −1.35183 −0.675915 0.736980i 0.736251π-0.736251\pi
−0.675915 + 0.736980i 0.736251π0.736251\pi
450450 0 0
451451 22.5113 1.06001
452452 0 0
453453 20.0000 0.939682
454454 0 0
455455 2.56035 0.120031
456456 0 0
457457 17.7164 0.828738 0.414369 0.910109i 0.364002π-0.364002\pi
0.414369 + 0.910109i 0.364002π0.364002\pi
458458 0 0
459459 −1.00000 −0.0466760
460460 0 0
461461 13.8759 0.646263 0.323132 0.946354i 0.395264π-0.395264\pi
0.323132 + 0.946354i 0.395264π0.395264\pi
462462 0 0
463463 36.1104 1.67819 0.839096 0.543983i 0.183084π-0.183084\pi
0.839096 + 0.543983i 0.183084π0.183084\pi
464464 0 0
465465 −30.4362 −1.41145
466466 0 0
467467 −30.4622 −1.40962 −0.704811 0.709395i 0.748968π-0.748968\pi
−0.704811 + 0.709395i 0.748968π0.748968\pi
468468 0 0
469469 −12.2345 −0.564938
470470 0 0
471471 −15.3906 −0.709160
472472 0 0
473473 2.27674 0.104685
474474 0 0
475475 25.2311 1.15768
476476 0 0
477477 −1.55691 −0.0712862
478478 0 0
479479 −10.5665 −0.482794 −0.241397 0.970426i 0.577606π-0.577606\pi
−0.241397 + 0.970426i 0.577606π0.577606\pi
480480 0 0
481481 −2.11727 −0.0965390
482482 0 0
483483 1.67418 0.0761779
484484 0 0
485485 30.6707 1.39269
486486 0 0
487487 −5.28629 −0.239545 −0.119772 0.992801i 0.538216π-0.538216\pi
−0.119772 + 0.992801i 0.538216π0.538216\pi
488488 0 0
489489 16.5535 0.748574
490490 0 0
491491 −14.4622 −0.652669 −0.326335 0.945254i 0.605814π-0.605814\pi
−0.326335 + 0.945254i 0.605814π0.605814\pi
492492 0 0
493493 8.61555 0.388025
494494 0 0
495495 −10.2767 −0.461905
496496 0 0
497497 6.22766 0.279349
498498 0 0
499499 −1.23109 −0.0551114 −0.0275557 0.999620i 0.508772π-0.508772\pi
−0.0275557 + 0.999620i 0.508772π0.508772\pi
500500 0 0
501501 20.4492 0.913603
502502 0 0
503503 4.33881 0.193458 0.0967290 0.995311i 0.469162π-0.469162\pi
0.0967290 + 0.995311i 0.469162π0.469162\pi
504504 0 0
505505 35.2242 1.56746
506506 0 0
507507 12.4819 0.554339
508508 0 0
509509 14.9706 0.663559 0.331780 0.943357i 0.392351π-0.392351\pi
0.331780 + 0.943357i 0.392351π0.392351\pi
510510 0 0
511511 −7.00344 −0.309814
512512 0 0
513513 −2.71982 −0.120083
514514 0 0
515515 −40.5044 −1.78484
516516 0 0
517517 −5.12070 −0.225208
518518 0 0
519519 −18.8923 −0.829279
520520 0 0
521521 25.7164 1.12666 0.563328 0.826234i 0.309521π-0.309521\pi
0.563328 + 0.826234i 0.309521π0.309521\pi
522522 0 0
523523 28.9966 1.26793 0.633966 0.773361i 0.281426π-0.281426\pi
0.633966 + 0.773361i 0.281426π0.281426\pi
524524 0 0
525525 8.73281 0.381131
526526 0 0
527527 8.05520 0.350890
528528 0 0
529529 −19.8371 −0.862482
530530 0 0
531531 0.443086 0.0192283
532532 0 0
533533 5.95779 0.258061
534534 0 0
535535 61.0579 2.63976
536536 0 0
537537 −24.5535 −1.05956
538538 0 0
539539 16.6285 0.716242
540540 0 0
541541 −34.8172 −1.49691 −0.748455 0.663186i 0.769204π-0.769204\pi
−0.748455 + 0.663186i 0.769204π0.769204\pi
542542 0 0
543543 15.9379 0.683962
544544 0 0
545545 −12.0000 −0.514024
546546 0 0
547547 −24.4431 −1.04511 −0.522555 0.852605i 0.675021π-0.675021\pi
−0.522555 + 0.852605i 0.675021π0.675021\pi
548548 0 0
549549 −2.49828 −0.106624
550550 0 0
551551 23.4328 0.998270
552552 0 0
553553 2.65851 0.113052
554554 0 0
555555 −11.1138 −0.471756
556556 0 0
557557 1.00344 0.0425170 0.0212585 0.999774i 0.493233π-0.493233\pi
0.0212585 + 0.999774i 0.493233π0.493233\pi
558558 0 0
559559 0.602558 0.0254855
560560 0 0
561561 2.71982 0.114831
562562 0 0
563563 10.9053 0.459603 0.229801 0.973238i 0.426192π-0.426192\pi
0.229801 + 0.973238i 0.426192π0.426192\pi
564564 0 0
565565 −3.60600 −0.151705
566566 0 0
567567 −0.941367 −0.0395337
568568 0 0
569569 −1.34836 −0.0565262 −0.0282631 0.999601i 0.508998π-0.508998\pi
−0.0282631 + 0.999601i 0.508998π0.508998\pi
570570 0 0
571571 12.3189 0.515532 0.257766 0.966207i 0.417014π-0.417014\pi
0.257766 + 0.966207i 0.417014π0.417014\pi
572572 0 0
573573 −6.11727 −0.255552
574574 0 0
575575 16.4983 0.688026
576576 0 0
577577 33.2993 1.38627 0.693134 0.720809i 0.256230π-0.256230\pi
0.693134 + 0.720809i 0.256230π0.256230\pi
578578 0 0
579579 −15.2311 −0.632983
580580 0 0
581581 −16.2208 −0.672951
582582 0 0
583583 4.23453 0.175376
584584 0 0
585585 −2.71982 −0.112451
586586 0 0
587587 22.4622 0.927114 0.463557 0.886067i 0.346573π-0.346573\pi
0.463557 + 0.886067i 0.346573π0.346573\pi
588588 0 0
589589 21.9087 0.902733
590590 0 0
591591 −12.7750 −0.525494
592592 0 0
593593 1.21199 0.0497705 0.0248853 0.999690i 0.492078π-0.492078\pi
0.0248853 + 0.999690i 0.492078π0.492078\pi
594594 0 0
595595 −3.55691 −0.145819
596596 0 0
597597 8.94137 0.365946
598598 0 0
599599 −37.3415 −1.52573 −0.762866 0.646557i 0.776208π-0.776208\pi
−0.762866 + 0.646557i 0.776208π0.776208\pi
600600 0 0
601601 −20.2277 −0.825103 −0.412552 0.910934i 0.635362π-0.635362\pi
−0.412552 + 0.910934i 0.635362π0.635362\pi
602602 0 0
603603 12.9966 0.529261
604604 0 0
605605 −13.6121 −0.553411
606606 0 0
607607 −22.4914 −0.912898 −0.456449 0.889750i 0.650879π-0.650879\pi
−0.456449 + 0.889750i 0.650879π0.650879\pi
608608 0 0
609609 8.11039 0.328650
610610 0 0
611611 −1.35524 −0.0548270
612612 0 0
613613 3.62510 0.146416 0.0732082 0.997317i 0.476676π-0.476676\pi
0.0732082 + 0.997317i 0.476676π0.476676\pi
614614 0 0
615615 31.2733 1.26106
616616 0 0
617617 −9.23797 −0.371907 −0.185953 0.982559i 0.559537π-0.559537\pi
−0.185953 + 0.982559i 0.559537π0.559537\pi
618618 0 0
619619 −5.67418 −0.228065 −0.114032 0.993477i 0.536377π-0.536377\pi
−0.114032 + 0.993477i 0.536377π0.536377\pi
620620 0 0
621621 −1.77846 −0.0713670
622622 0 0
623623 −8.57946 −0.343729
624624 0 0
625625 14.6742 0.586967
626626 0 0
627627 7.39744 0.295425
628628 0 0
629629 2.94137 0.117280
630630 0 0
631631 −30.3871 −1.20969 −0.604846 0.796342i 0.706765π-0.706765\pi
−0.604846 + 0.796342i 0.706765π0.706765\pi
632632 0 0
633633 7.55691 0.300360
634634 0 0
635635 17.3906 0.690124
636636 0 0
637637 4.40088 0.174369
638638 0 0
639639 −6.61555 −0.261707
640640 0 0
641641 8.04221 0.317648 0.158824 0.987307i 0.449230π-0.449230\pi
0.158824 + 0.987307i 0.449230π0.449230\pi
642642 0 0
643643 −5.67418 −0.223768 −0.111884 0.993721i 0.535688π-0.535688\pi
−0.111884 + 0.993721i 0.535688π0.535688\pi
644644 0 0
645645 3.16291 0.124539
646646 0 0
647647 −2.76891 −0.108857 −0.0544284 0.998518i 0.517334π-0.517334\pi
−0.0544284 + 0.998518i 0.517334π0.517334\pi
648648 0 0
649649 −1.20512 −0.0473049
650650 0 0
651651 7.58289 0.297197
652652 0 0
653653 −18.4492 −0.721973 −0.360986 0.932571i 0.617560π-0.617560\pi
−0.360986 + 0.932571i 0.617560π0.617560\pi
654654 0 0
655655 −0.602558 −0.0235439
656656 0 0
657657 7.43965 0.290248
658658 0 0
659659 5.46563 0.212911 0.106455 0.994317i 0.466050π-0.466050\pi
0.106455 + 0.994317i 0.466050π0.466050\pi
660660 0 0
661661 −13.7424 −0.534516 −0.267258 0.963625i 0.586118π-0.586118\pi
−0.267258 + 0.963625i 0.586118π0.586118\pi
662662 0 0
663663 0.719824 0.0279556
664664 0 0
665665 −9.67418 −0.375149
666666 0 0
667667 15.3224 0.593285
668668 0 0
669669 19.5078 0.754216
670670 0 0
671671 6.79488 0.262314
672672 0 0
673673 32.4362 1.25032 0.625162 0.780495i 0.285033π-0.285033\pi
0.625162 + 0.780495i 0.285033π0.285033\pi
674674 0 0
675675 −9.27674 −0.357062
676676 0 0
677677 3.56990 0.137203 0.0686013 0.997644i 0.478146π-0.478146\pi
0.0686013 + 0.997644i 0.478146π0.478146\pi
678678 0 0
679679 −7.64133 −0.293247
680680 0 0
681681 −1.72326 −0.0660355
682682 0 0
683683 −36.9215 −1.41276 −0.706381 0.707832i 0.749673π-0.749673\pi
−0.706381 + 0.707832i 0.749673π0.749673\pi
684684 0 0
685685 −70.1035 −2.67852
686686 0 0
687687 20.8793 0.796595
688688 0 0
689689 1.12070 0.0426954
690690 0 0
691691 30.1035 1.14519 0.572596 0.819838i 0.305936π-0.305936\pi
0.572596 + 0.819838i 0.305936π0.305936\pi
692692 0 0
693693 2.56035 0.0972597
694694 0 0
695695 −8.00000 −0.303457
696696 0 0
697697 −8.27674 −0.313504
698698 0 0
699699 −11.5991 −0.438719
700700 0 0
701701 −5.79145 −0.218740 −0.109370 0.994001i 0.534883π-0.534883\pi
−0.109370 + 0.994001i 0.534883π0.534883\pi
702702 0 0
703703 8.00000 0.301726
704704 0 0
705705 −7.11383 −0.267922
706706 0 0
707707 −8.77578 −0.330047
708708 0 0
709709 −30.9414 −1.16203 −0.581014 0.813894i 0.697344π-0.697344\pi
−0.581014 + 0.813894i 0.697344π0.697344\pi
710710 0 0
711711 −2.82410 −0.105912
712712 0 0
713713 14.3258 0.536506
714714 0 0
715715 7.39744 0.276649
716716 0 0
717717 −14.4362 −0.539130
718718 0 0
719719 −47.5370 −1.77283 −0.886416 0.462889i 0.846813π-0.846813\pi
−0.886416 + 0.462889i 0.846813π0.846813\pi
720720 0 0
721721 10.0913 0.375819
722722 0 0
723723 −11.8827 −0.441924
724724 0 0
725725 79.9242 2.96831
726726 0 0
727727 −12.8862 −0.477922 −0.238961 0.971029i 0.576807π-0.576807\pi
−0.238961 + 0.971029i 0.576807π0.576807\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −0.837090 −0.0309609
732732 0 0
733733 9.23797 0.341212 0.170606 0.985339i 0.445427π-0.445427\pi
0.170606 + 0.985339i 0.445427π0.445427\pi
734734 0 0
735735 23.1008 0.852087
736736 0 0
737737 −35.3484 −1.30207
738738 0 0
739739 −35.9249 −1.32152 −0.660760 0.750597i 0.729766π-0.729766\pi
−0.660760 + 0.750597i 0.729766π0.729766\pi
740740 0 0
741741 1.95779 0.0719214
742742 0 0
743743 52.3741 1.92142 0.960710 0.277553i 0.0895233π-0.0895233\pi
0.960710 + 0.277553i 0.0895233π0.0895233\pi
744744 0 0
745745 −12.9966 −0.476157
746746 0 0
747747 17.2311 0.630453
748748 0 0
749749 −15.2120 −0.555834
750750 0 0
751751 −37.8138 −1.37984 −0.689922 0.723883i 0.742355π-0.742355\pi
−0.689922 + 0.723883i 0.742355π0.742355\pi
752752 0 0
753753 −27.1138 −0.988083
754754 0 0
755755 −75.5691 −2.75024
756756 0 0
757757 30.6026 1.11227 0.556134 0.831092i 0.312284π-0.312284\pi
0.556134 + 0.831092i 0.312284π0.312284\pi
758758 0 0
759759 4.83709 0.175575
760760 0 0
761761 14.6516 0.531121 0.265561 0.964094i 0.414443π-0.414443\pi
0.265561 + 0.964094i 0.414443π0.414443\pi
762762 0 0
763763 2.98969 0.108234
764764 0 0
765765 3.77846 0.136610
766766 0 0
767767 −0.318944 −0.0115164
768768 0 0
769769 −53.6182 −1.93352 −0.966761 0.255681i 0.917700π-0.917700\pi
−0.966761 + 0.255681i 0.917700π0.917700\pi
770770 0 0
771771 24.8793 0.896006
772772 0 0
773773 37.7655 1.35833 0.679165 0.733986i 0.262342π-0.262342\pi
0.679165 + 0.733986i 0.262342π0.262342\pi
774774 0 0
775775 74.7259 2.68423
776776 0 0
777777 2.76891 0.0993339
778778 0 0
779779 −22.5113 −0.806550
780780 0 0
781781 17.9931 0.643845
782782 0 0
783783 −8.61555 −0.307895
784784 0 0
785785 58.1526 2.07556
786786 0 0
787787 19.7914 0.705489 0.352744 0.935720i 0.385249π-0.385249\pi
0.352744 + 0.935720i 0.385249π0.385249\pi
788788 0 0
789789 −24.9966 −0.889901
790790 0 0
791791 0.898400 0.0319434
792792 0 0
793793 1.79832 0.0638603
794794 0 0
795795 5.88273 0.208639
796796 0 0
797797 50.0122 1.77152 0.885762 0.464140i 0.153636π-0.153636\pi
0.885762 + 0.464140i 0.153636π0.153636\pi
798798 0 0
799799 1.88273 0.0666063
800800 0 0
801801 9.11383 0.322021
802802 0 0
803803 −20.2345 −0.714061
804804 0 0
805805 −6.32582 −0.222956
806806 0 0
807807 21.8957 0.770766
808808 0 0
809809 −15.8077 −0.555768 −0.277884 0.960615i 0.589633π-0.589633\pi
−0.277884 + 0.960615i 0.589633π0.589633\pi
810810 0 0
811811 −44.6898 −1.56927 −0.784636 0.619956i 0.787150π-0.787150\pi
−0.784636 + 0.619956i 0.787150π0.787150\pi
812812 0 0
813813 −4.60256 −0.161419
814814 0 0
815815 −62.5466 −2.19091
816816 0 0
817817 −2.27674 −0.0796530
818818 0 0
819819 0.677618 0.0236779
820820 0 0
821821 −29.6872 −1.03609 −0.518045 0.855354i 0.673340π-0.673340\pi
−0.518045 + 0.855354i 0.673340π0.673340\pi
822822 0 0
823823 −7.84664 −0.273517 −0.136758 0.990604i 0.543668π-0.543668\pi
−0.136758 + 0.990604i 0.543668π0.543668\pi
824824 0 0
825825 25.2311 0.878434
826826 0 0
827827 −43.5078 −1.51292 −0.756458 0.654043i 0.773072π-0.773072\pi
−0.756458 + 0.654043i 0.773072π0.773072\pi
828828 0 0
829829 17.7655 0.617020 0.308510 0.951221i 0.400170π-0.400170\pi
0.308510 + 0.951221i 0.400170π0.400170\pi
830830 0 0
831831 7.82754 0.271534
832832 0 0
833833 −6.11383 −0.211832
834834 0 0
835835 −77.2664 −2.67391
836836 0 0
837837 −8.05520 −0.278428
838838 0 0
839839 1.98701 0.0685992 0.0342996 0.999412i 0.489080π-0.489080\pi
0.0342996 + 0.999412i 0.489080π0.489080\pi
840840 0 0
841841 45.2277 1.55957
842842 0 0
843843 −25.1138 −0.864966
844844 0 0
845845 −47.1621 −1.62243
846846 0 0
847847 3.39133 0.116527
848848 0 0
849849 3.32238 0.114024
850850 0 0
851851 5.23109 0.179320
852852 0 0
853853 53.1430 1.81958 0.909792 0.415065i 0.136241π-0.136241\pi
0.909792 + 0.415065i 0.136241π0.136241\pi
854854 0 0
855855 10.2767 0.351457
856856 0 0
857857 49.3346 1.68524 0.842619 0.538510i 0.181013π-0.181013\pi
0.842619 + 0.538510i 0.181013π0.181013\pi
858858 0 0
859859 5.77234 0.196950 0.0984749 0.995140i 0.468604π-0.468604\pi
0.0984749 + 0.995140i 0.468604π0.468604\pi
860860 0 0
861861 −7.79145 −0.265532
862862 0 0
863863 38.9637 1.32634 0.663170 0.748469i 0.269211π-0.269211\pi
0.663170 + 0.748469i 0.269211π0.269211\pi
864864 0 0
865865 71.3837 2.42712
866866 0 0
867867 −1.00000 −0.0339618
868868 0 0
869869 7.68106 0.260562
870870 0 0
871871 −9.35524 −0.316990
872872 0 0
873873 8.11727 0.274728
874874 0 0
875875 −15.2120 −0.514259
876876 0 0
877877 11.9379 0.403115 0.201558 0.979477i 0.435400π-0.435400\pi
0.201558 + 0.979477i 0.435400π0.435400\pi
878878 0 0
879879 29.4328 0.992743
880880 0 0
881881 −3.23109 −0.108858 −0.0544292 0.998518i 0.517334π-0.517334\pi
−0.0544292 + 0.998518i 0.517334π0.517334\pi
882882 0 0
883883 4.49217 0.151173 0.0755867 0.997139i 0.475917π-0.475917\pi
0.0755867 + 0.997139i 0.475917π0.475917\pi
884884 0 0
885885 −1.67418 −0.0562770
886886 0 0
887887 −0.671504 −0.0225469 −0.0112735 0.999936i 0.503589π-0.503589\pi
−0.0112735 + 0.999936i 0.503589π0.503589\pi
888888 0 0
889889 −4.33270 −0.145314
890890 0 0
891891 −2.71982 −0.0911175
892892 0 0
893893 5.12070 0.171358
894894 0 0
895895 92.7743 3.10110
896896 0 0
897897 1.28018 0.0427438
898898 0 0
899899 69.3999 2.31462
900900 0 0
901901 −1.55691 −0.0518683
902902 0 0
903903 −0.788009 −0.0262233
904904 0 0
905905 −60.2208 −2.00181
906906 0 0
907907 −13.4656 −0.447119 −0.223559 0.974690i 0.571768π-0.571768\pi
−0.223559 + 0.974690i 0.571768π0.571768\pi
908908 0 0
909909 9.32238 0.309204
910910 0 0
911911 45.2372 1.49878 0.749388 0.662131i 0.230348π-0.230348\pi
0.749388 + 0.662131i 0.230348π0.230348\pi
912912 0 0
913913 −46.8655 −1.55102
914914 0 0
915915 9.43965 0.312065
916916 0 0
917917 0.150122 0.00495745
918918 0 0
919919 −8.04908 −0.265515 −0.132757 0.991149i 0.542383π-0.542383\pi
−0.132757 + 0.991149i 0.542383π0.542383\pi
920920 0 0
921921 15.3484 0.505746
922922 0 0
923923 4.76203 0.156744
924924 0 0
925925 27.2863 0.897168
926926 0 0
927927 −10.7198 −0.352085
928928 0 0
929929 −8.59568 −0.282015 −0.141008 0.990009i 0.545034π-0.545034\pi
−0.141008 + 0.990009i 0.545034π0.545034\pi
930930 0 0
931931 −16.6285 −0.544978
932932 0 0
933933 31.6121 1.03493
934934 0 0
935935 −10.2767 −0.336085
936936 0 0
937937 19.9931 0.653147 0.326573 0.945172i 0.394106π-0.394106\pi
0.326573 + 0.945172i 0.394106π0.394106\pi
938938 0 0
939939 15.4656 0.504702
940940 0 0
941941 40.7259 1.32763 0.663814 0.747898i 0.268937π-0.268937\pi
0.663814 + 0.747898i 0.268937π0.268937\pi
942942 0 0
943943 −14.7198 −0.479343
944944 0 0
945945 3.55691 0.115706
946946 0 0
947947 0.344923 0.0112085 0.00560425 0.999984i 0.498216π-0.498216\pi
0.00560425 + 0.999984i 0.498216π0.498216\pi
948948 0 0
949949 −5.35524 −0.173838
950950 0 0
951951 22.6087 0.733136
952952 0 0
953953 39.0225 1.26406 0.632032 0.774942i 0.282221π-0.282221\pi
0.632032 + 0.774942i 0.282221π0.282221\pi
954954 0 0
955955 23.1138 0.747946
956956 0 0
957957 23.4328 0.757474
958958 0 0
959959 17.4656 0.563995
960960 0 0
961961 33.8862 1.09310
962962 0 0
963963 16.1595 0.520732
964964 0 0
965965 57.5500 1.85260
966966 0 0
967967 −51.4097 −1.65322 −0.826612 0.562773i 0.809735π-0.809735\pi
−0.826612 + 0.562773i 0.809735π0.809735\pi
968968 0 0
969969 −2.71982 −0.0873733
970970 0 0
971971 54.8915 1.76155 0.880776 0.473532i 0.157021π-0.157021\pi
0.880776 + 0.473532i 0.157021π0.157021\pi
972972 0 0
973973 1.99312 0.0638966
974974 0 0
975975 6.67762 0.213855
976976 0 0
977977 16.6967 0.534175 0.267088 0.963672i 0.413939π-0.413939\pi
0.267088 + 0.963672i 0.413939π0.413939\pi
978978 0 0
979979 −24.7880 −0.792228
980980 0 0
981981 −3.17590 −0.101399
982982 0 0
983983 −2.24752 −0.0716848 −0.0358424 0.999357i 0.511411π-0.511411\pi
−0.0358424 + 0.999357i 0.511411π0.511411\pi
984984 0 0
985985 48.2699 1.53801
986986 0 0
987987 1.77234 0.0564143
988988 0 0
989989 −1.48873 −0.0473388
990990 0 0
991991 7.05863 0.224225 0.112112 0.993696i 0.464238π-0.464238\pi
0.112112 + 0.993696i 0.464238π0.464238\pi
992992 0 0
993993 29.3906 0.932681
994994 0 0
995995 −33.7846 −1.07104
996996 0 0
997997 −1.61211 −0.0510560 −0.0255280 0.999674i 0.508127π-0.508127\pi
−0.0255280 + 0.999674i 0.508127π0.508127\pi
998998 0 0
999999 −2.94137 −0.0930607
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 1632.2.a.r.1.3 3
3.2 odd 2 4896.2.a.ba.1.1 3
4.3 odd 2 1632.2.a.t.1.3 yes 3
8.3 odd 2 3264.2.a.bq.1.1 3
8.5 even 2 3264.2.a.bs.1.1 3
12.11 even 2 4896.2.a.bb.1.1 3
24.5 odd 2 9792.2.a.dk.1.3 3
24.11 even 2 9792.2.a.dl.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1632.2.a.r.1.3 3 1.1 even 1 trivial
1632.2.a.t.1.3 yes 3 4.3 odd 2
3264.2.a.bq.1.1 3 8.3 odd 2
3264.2.a.bs.1.1 3 8.5 even 2
4896.2.a.ba.1.1 3 3.2 odd 2
4896.2.a.bb.1.1 3 12.11 even 2
9792.2.a.dk.1.3 3 24.5 odd 2
9792.2.a.dl.1.3 3 24.11 even 2