Properties

Label 1488.2.a.h.1.1
Level 14881488
Weight 22
Character 1488.1
Self dual yes
Analytic conductor 11.88211.882
Analytic rank 11
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1488,2,Mod(1,1488)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1488, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1488.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1488=24331 1488 = 2^{4} \cdot 3 \cdot 31
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1488.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,0,3,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 11.881739820811.8817398208
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 186)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 1488.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q1.00000q3+3.00000q5+2.00000q7+1.00000q95.00000q117.00000q133.00000q151.00000q177.00000q192.00000q214.00000q23+4.00000q251.00000q278.00000q29+1.00000q31+5.00000q33+6.00000q356.00000q37+7.00000q392.00000q41+10.0000q43+3.00000q45+1.00000q473.00000q49+1.00000q51+6.00000q5315.0000q55+7.00000q57+10.0000q59+1.00000q61+2.00000q6321.0000q65+3.00000q67+4.00000q693.00000q71+14.0000q734.00000q7510.0000q77+11.0000q79+1.00000q817.00000q833.00000q85+8.00000q876.00000q8914.0000q911.00000q9321.0000q953.00000q975.00000q99+O(q100)q-1.00000 q^{3} +3.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} -5.00000 q^{11} -7.00000 q^{13} -3.00000 q^{15} -1.00000 q^{17} -7.00000 q^{19} -2.00000 q^{21} -4.00000 q^{23} +4.00000 q^{25} -1.00000 q^{27} -8.00000 q^{29} +1.00000 q^{31} +5.00000 q^{33} +6.00000 q^{35} -6.00000 q^{37} +7.00000 q^{39} -2.00000 q^{41} +10.0000 q^{43} +3.00000 q^{45} +1.00000 q^{47} -3.00000 q^{49} +1.00000 q^{51} +6.00000 q^{53} -15.0000 q^{55} +7.00000 q^{57} +10.0000 q^{59} +1.00000 q^{61} +2.00000 q^{63} -21.0000 q^{65} +3.00000 q^{67} +4.00000 q^{69} -3.00000 q^{71} +14.0000 q^{73} -4.00000 q^{75} -10.0000 q^{77} +11.0000 q^{79} +1.00000 q^{81} -7.00000 q^{83} -3.00000 q^{85} +8.00000 q^{87} -6.00000 q^{89} -14.0000 q^{91} -1.00000 q^{93} -21.0000 q^{95} -3.00000 q^{97} -5.00000 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 −1.00000 −0.577350
44 0 0
55 3.00000 1.34164 0.670820 0.741620i 0.265942π-0.265942\pi
0.670820 + 0.741620i 0.265942π0.265942\pi
66 0 0
77 2.00000 0.755929 0.377964 0.925820i 0.376624π-0.376624\pi
0.377964 + 0.925820i 0.376624π0.376624\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 −5.00000 −1.50756 −0.753778 0.657129i 0.771771π-0.771771\pi
−0.753778 + 0.657129i 0.771771π0.771771\pi
1212 0 0
1313 −7.00000 −1.94145 −0.970725 0.240192i 0.922790π-0.922790\pi
−0.970725 + 0.240192i 0.922790π0.922790\pi
1414 0 0
1515 −3.00000 −0.774597
1616 0 0
1717 −1.00000 −0.242536 −0.121268 0.992620i 0.538696π-0.538696\pi
−0.121268 + 0.992620i 0.538696π0.538696\pi
1818 0 0
1919 −7.00000 −1.60591 −0.802955 0.596040i 0.796740π-0.796740\pi
−0.802955 + 0.596040i 0.796740π0.796740\pi
2020 0 0
2121 −2.00000 −0.436436
2222 0 0
2323 −4.00000 −0.834058 −0.417029 0.908893i 0.636929π-0.636929\pi
−0.417029 + 0.908893i 0.636929π0.636929\pi
2424 0 0
2525 4.00000 0.800000
2626 0 0
2727 −1.00000 −0.192450
2828 0 0
2929 −8.00000 −1.48556 −0.742781 0.669534i 0.766494π-0.766494\pi
−0.742781 + 0.669534i 0.766494π0.766494\pi
3030 0 0
3131 1.00000 0.179605
3232 0 0
3333 5.00000 0.870388
3434 0 0
3535 6.00000 1.01419
3636 0 0
3737 −6.00000 −0.986394 −0.493197 0.869918i 0.664172π-0.664172\pi
−0.493197 + 0.869918i 0.664172π0.664172\pi
3838 0 0
3939 7.00000 1.12090
4040 0 0
4141 −2.00000 −0.312348 −0.156174 0.987730i 0.549916π-0.549916\pi
−0.156174 + 0.987730i 0.549916π0.549916\pi
4242 0 0
4343 10.0000 1.52499 0.762493 0.646997i 0.223975π-0.223975\pi
0.762493 + 0.646997i 0.223975π0.223975\pi
4444 0 0
4545 3.00000 0.447214
4646 0 0
4747 1.00000 0.145865 0.0729325 0.997337i 0.476764π-0.476764\pi
0.0729325 + 0.997337i 0.476764π0.476764\pi
4848 0 0
4949 −3.00000 −0.428571
5050 0 0
5151 1.00000 0.140028
5252 0 0
5353 6.00000 0.824163 0.412082 0.911147i 0.364802π-0.364802\pi
0.412082 + 0.911147i 0.364802π0.364802\pi
5454 0 0
5555 −15.0000 −2.02260
5656 0 0
5757 7.00000 0.927173
5858 0 0
5959 10.0000 1.30189 0.650945 0.759125i 0.274373π-0.274373\pi
0.650945 + 0.759125i 0.274373π0.274373\pi
6060 0 0
6161 1.00000 0.128037 0.0640184 0.997949i 0.479608π-0.479608\pi
0.0640184 + 0.997949i 0.479608π0.479608\pi
6262 0 0
6363 2.00000 0.251976
6464 0 0
6565 −21.0000 −2.60473
6666 0 0
6767 3.00000 0.366508 0.183254 0.983066i 0.441337π-0.441337\pi
0.183254 + 0.983066i 0.441337π0.441337\pi
6868 0 0
6969 4.00000 0.481543
7070 0 0
7171 −3.00000 −0.356034 −0.178017 0.984027i 0.556968π-0.556968\pi
−0.178017 + 0.984027i 0.556968π0.556968\pi
7272 0 0
7373 14.0000 1.63858 0.819288 0.573382i 0.194369π-0.194369\pi
0.819288 + 0.573382i 0.194369π0.194369\pi
7474 0 0
7575 −4.00000 −0.461880
7676 0 0
7777 −10.0000 −1.13961
7878 0 0
7979 11.0000 1.23760 0.618798 0.785550i 0.287620π-0.287620\pi
0.618798 + 0.785550i 0.287620π0.287620\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 −7.00000 −0.768350 −0.384175 0.923260i 0.625514π-0.625514\pi
−0.384175 + 0.923260i 0.625514π0.625514\pi
8484 0 0
8585 −3.00000 −0.325396
8686 0 0
8787 8.00000 0.857690
8888 0 0
8989 −6.00000 −0.635999 −0.317999 0.948091i 0.603011π-0.603011\pi
−0.317999 + 0.948091i 0.603011π0.603011\pi
9090 0 0
9191 −14.0000 −1.46760
9292 0 0
9393 −1.00000 −0.103695
9494 0 0
9595 −21.0000 −2.15455
9696 0 0
9797 −3.00000 −0.304604 −0.152302 0.988334i 0.548669π-0.548669\pi
−0.152302 + 0.988334i 0.548669π0.548669\pi
9898 0 0
9999 −5.00000 −0.502519
100100 0 0
101101 6.00000 0.597022 0.298511 0.954406i 0.403510π-0.403510\pi
0.298511 + 0.954406i 0.403510π0.403510\pi
102102 0 0
103103 −10.0000 −0.985329 −0.492665 0.870219i 0.663977π-0.663977\pi
−0.492665 + 0.870219i 0.663977π0.663977\pi
104104 0 0
105105 −6.00000 −0.585540
106106 0 0
107107 −8.00000 −0.773389 −0.386695 0.922208i 0.626383π-0.626383\pi
−0.386695 + 0.922208i 0.626383π0.626383\pi
108108 0 0
109109 −6.00000 −0.574696 −0.287348 0.957826i 0.592774π-0.592774\pi
−0.287348 + 0.957826i 0.592774π0.592774\pi
110110 0 0
111111 6.00000 0.569495
112112 0 0
113113 6.00000 0.564433 0.282216 0.959351i 0.408930π-0.408930\pi
0.282216 + 0.959351i 0.408930π0.408930\pi
114114 0 0
115115 −12.0000 −1.11901
116116 0 0
117117 −7.00000 −0.647150
118118 0 0
119119 −2.00000 −0.183340
120120 0 0
121121 14.0000 1.27273
122122 0 0
123123 2.00000 0.180334
124124 0 0
125125 −3.00000 −0.268328
126126 0 0
127127 −4.00000 −0.354943 −0.177471 0.984126i 0.556792π-0.556792\pi
−0.177471 + 0.984126i 0.556792π0.556792\pi
128128 0 0
129129 −10.0000 −0.880451
130130 0 0
131131 −10.0000 −0.873704 −0.436852 0.899533i 0.643907π-0.643907\pi
−0.436852 + 0.899533i 0.643907π0.643907\pi
132132 0 0
133133 −14.0000 −1.21395
134134 0 0
135135 −3.00000 −0.258199
136136 0 0
137137 −18.0000 −1.53784 −0.768922 0.639343i 0.779207π-0.779207\pi
−0.768922 + 0.639343i 0.779207π0.779207\pi
138138 0 0
139139 8.00000 0.678551 0.339276 0.940687i 0.389818π-0.389818\pi
0.339276 + 0.940687i 0.389818π0.389818\pi
140140 0 0
141141 −1.00000 −0.0842152
142142 0 0
143143 35.0000 2.92685
144144 0 0
145145 −24.0000 −1.99309
146146 0 0
147147 3.00000 0.247436
148148 0 0
149149 15.0000 1.22885 0.614424 0.788976i 0.289388π-0.289388\pi
0.614424 + 0.788976i 0.289388π0.289388\pi
150150 0 0
151151 1.00000 0.0813788 0.0406894 0.999172i 0.487045π-0.487045\pi
0.0406894 + 0.999172i 0.487045π0.487045\pi
152152 0 0
153153 −1.00000 −0.0808452
154154 0 0
155155 3.00000 0.240966
156156 0 0
157157 −4.00000 −0.319235 −0.159617 0.987179i 0.551026π-0.551026\pi
−0.159617 + 0.987179i 0.551026π0.551026\pi
158158 0 0
159159 −6.00000 −0.475831
160160 0 0
161161 −8.00000 −0.630488
162162 0 0
163163 9.00000 0.704934 0.352467 0.935824i 0.385343π-0.385343\pi
0.352467 + 0.935824i 0.385343π0.385343\pi
164164 0 0
165165 15.0000 1.16775
166166 0 0
167167 −10.0000 −0.773823 −0.386912 0.922117i 0.626458π-0.626458\pi
−0.386912 + 0.922117i 0.626458π0.626458\pi
168168 0 0
169169 36.0000 2.76923
170170 0 0
171171 −7.00000 −0.535303
172172 0 0
173173 1.00000 0.0760286 0.0380143 0.999277i 0.487897π-0.487897\pi
0.0380143 + 0.999277i 0.487897π0.487897\pi
174174 0 0
175175 8.00000 0.604743
176176 0 0
177177 −10.0000 −0.751646
178178 0 0
179179 −19.0000 −1.42013 −0.710063 0.704138i 0.751334π-0.751334\pi
−0.710063 + 0.704138i 0.751334π0.751334\pi
180180 0 0
181181 18.0000 1.33793 0.668965 0.743294i 0.266738π-0.266738\pi
0.668965 + 0.743294i 0.266738π0.266738\pi
182182 0 0
183183 −1.00000 −0.0739221
184184 0 0
185185 −18.0000 −1.32339
186186 0 0
187187 5.00000 0.365636
188188 0 0
189189 −2.00000 −0.145479
190190 0 0
191191 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
192192 0 0
193193 19.0000 1.36765 0.683825 0.729646i 0.260315π-0.260315\pi
0.683825 + 0.729646i 0.260315π0.260315\pi
194194 0 0
195195 21.0000 1.50384
196196 0 0
197197 −2.00000 −0.142494 −0.0712470 0.997459i 0.522698π-0.522698\pi
−0.0712470 + 0.997459i 0.522698π0.522698\pi
198198 0 0
199199 11.0000 0.779769 0.389885 0.920864i 0.372515π-0.372515\pi
0.389885 + 0.920864i 0.372515π0.372515\pi
200200 0 0
201201 −3.00000 −0.211604
202202 0 0
203203 −16.0000 −1.12298
204204 0 0
205205 −6.00000 −0.419058
206206 0 0
207207 −4.00000 −0.278019
208208 0 0
209209 35.0000 2.42100
210210 0 0
211211 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
212212 0 0
213213 3.00000 0.205557
214214 0 0
215215 30.0000 2.04598
216216 0 0
217217 2.00000 0.135769
218218 0 0
219219 −14.0000 −0.946032
220220 0 0
221221 7.00000 0.470871
222222 0 0
223223 5.00000 0.334825 0.167412 0.985887i 0.446459π-0.446459\pi
0.167412 + 0.985887i 0.446459π0.446459\pi
224224 0 0
225225 4.00000 0.266667
226226 0 0
227227 −22.0000 −1.46019 −0.730096 0.683345i 0.760525π-0.760525\pi
−0.730096 + 0.683345i 0.760525π0.760525\pi
228228 0 0
229229 13.0000 0.859064 0.429532 0.903052i 0.358679π-0.358679\pi
0.429532 + 0.903052i 0.358679π0.358679\pi
230230 0 0
231231 10.0000 0.657952
232232 0 0
233233 20.0000 1.31024 0.655122 0.755523i 0.272617π-0.272617\pi
0.655122 + 0.755523i 0.272617π0.272617\pi
234234 0 0
235235 3.00000 0.195698
236236 0 0
237237 −11.0000 −0.714527
238238 0 0
239239 4.00000 0.258738 0.129369 0.991596i 0.458705π-0.458705\pi
0.129369 + 0.991596i 0.458705π0.458705\pi
240240 0 0
241241 −14.0000 −0.901819 −0.450910 0.892570i 0.648900π-0.648900\pi
−0.450910 + 0.892570i 0.648900π0.648900\pi
242242 0 0
243243 −1.00000 −0.0641500
244244 0 0
245245 −9.00000 −0.574989
246246 0 0
247247 49.0000 3.11780
248248 0 0
249249 7.00000 0.443607
250250 0 0
251251 −20.0000 −1.26239 −0.631194 0.775625i 0.717435π-0.717435\pi
−0.631194 + 0.775625i 0.717435π0.717435\pi
252252 0 0
253253 20.0000 1.25739
254254 0 0
255255 3.00000 0.187867
256256 0 0
257257 −12.0000 −0.748539 −0.374270 0.927320i 0.622107π-0.622107\pi
−0.374270 + 0.927320i 0.622107π0.622107\pi
258258 0 0
259259 −12.0000 −0.745644
260260 0 0
261261 −8.00000 −0.495188
262262 0 0
263263 −12.0000 −0.739952 −0.369976 0.929041i 0.620634π-0.620634\pi
−0.369976 + 0.929041i 0.620634π0.620634\pi
264264 0 0
265265 18.0000 1.10573
266266 0 0
267267 6.00000 0.367194
268268 0 0
269269 6.00000 0.365826 0.182913 0.983129i 0.441447π-0.441447\pi
0.182913 + 0.983129i 0.441447π0.441447\pi
270270 0 0
271271 19.0000 1.15417 0.577084 0.816685i 0.304191π-0.304191\pi
0.577084 + 0.816685i 0.304191π0.304191\pi
272272 0 0
273273 14.0000 0.847319
274274 0 0
275275 −20.0000 −1.20605
276276 0 0
277277 −7.00000 −0.420589 −0.210295 0.977638i 0.567442π-0.567442\pi
−0.210295 + 0.977638i 0.567442π0.567442\pi
278278 0 0
279279 1.00000 0.0598684
280280 0 0
281281 −30.0000 −1.78965 −0.894825 0.446417i 0.852700π-0.852700\pi
−0.894825 + 0.446417i 0.852700π0.852700\pi
282282 0 0
283283 −5.00000 −0.297219 −0.148610 0.988896i 0.547480π-0.547480\pi
−0.148610 + 0.988896i 0.547480π0.547480\pi
284284 0 0
285285 21.0000 1.24393
286286 0 0
287287 −4.00000 −0.236113
288288 0 0
289289 −16.0000 −0.941176
290290 0 0
291291 3.00000 0.175863
292292 0 0
293293 −6.00000 −0.350524 −0.175262 0.984522i 0.556077π-0.556077\pi
−0.175262 + 0.984522i 0.556077π0.556077\pi
294294 0 0
295295 30.0000 1.74667
296296 0 0
297297 5.00000 0.290129
298298 0 0
299299 28.0000 1.61928
300300 0 0
301301 20.0000 1.15278
302302 0 0
303303 −6.00000 −0.344691
304304 0 0
305305 3.00000 0.171780
306306 0 0
307307 −16.0000 −0.913168 −0.456584 0.889680i 0.650927π-0.650927\pi
−0.456584 + 0.889680i 0.650927π0.650927\pi
308308 0 0
309309 10.0000 0.568880
310310 0 0
311311 −21.0000 −1.19080 −0.595400 0.803429i 0.703007π-0.703007\pi
−0.595400 + 0.803429i 0.703007π0.703007\pi
312312 0 0
313313 2.00000 0.113047 0.0565233 0.998401i 0.481998π-0.481998\pi
0.0565233 + 0.998401i 0.481998π0.481998\pi
314314 0 0
315315 6.00000 0.338062
316316 0 0
317317 5.00000 0.280828 0.140414 0.990093i 0.455157π-0.455157\pi
0.140414 + 0.990093i 0.455157π0.455157\pi
318318 0 0
319319 40.0000 2.23957
320320 0 0
321321 8.00000 0.446516
322322 0 0
323323 7.00000 0.389490
324324 0 0
325325 −28.0000 −1.55316
326326 0 0
327327 6.00000 0.331801
328328 0 0
329329 2.00000 0.110264
330330 0 0
331331 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
332332 0 0
333333 −6.00000 −0.328798
334334 0 0
335335 9.00000 0.491723
336336 0 0
337337 −8.00000 −0.435788 −0.217894 0.975972i 0.569919π-0.569919\pi
−0.217894 + 0.975972i 0.569919π0.569919\pi
338338 0 0
339339 −6.00000 −0.325875
340340 0 0
341341 −5.00000 −0.270765
342342 0 0
343343 −20.0000 −1.07990
344344 0 0
345345 12.0000 0.646058
346346 0 0
347347 −17.0000 −0.912608 −0.456304 0.889824i 0.650827π-0.650827\pi
−0.456304 + 0.889824i 0.650827π0.650827\pi
348348 0 0
349349 24.0000 1.28469 0.642345 0.766415i 0.277962π-0.277962\pi
0.642345 + 0.766415i 0.277962π0.277962\pi
350350 0 0
351351 7.00000 0.373632
352352 0 0
353353 −11.0000 −0.585471 −0.292735 0.956193i 0.594566π-0.594566\pi
−0.292735 + 0.956193i 0.594566π0.594566\pi
354354 0 0
355355 −9.00000 −0.477670
356356 0 0
357357 2.00000 0.105851
358358 0 0
359359 17.0000 0.897226 0.448613 0.893726i 0.351918π-0.351918\pi
0.448613 + 0.893726i 0.351918π0.351918\pi
360360 0 0
361361 30.0000 1.57895
362362 0 0
363363 −14.0000 −0.734809
364364 0 0
365365 42.0000 2.19838
366366 0 0
367367 11.0000 0.574195 0.287098 0.957901i 0.407310π-0.407310\pi
0.287098 + 0.957901i 0.407310π0.407310\pi
368368 0 0
369369 −2.00000 −0.104116
370370 0 0
371371 12.0000 0.623009
372372 0 0
373373 −32.0000 −1.65690 −0.828449 0.560065i 0.810776π-0.810776\pi
−0.828449 + 0.560065i 0.810776π0.810776\pi
374374 0 0
375375 3.00000 0.154919
376376 0 0
377377 56.0000 2.88415
378378 0 0
379379 −1.00000 −0.0513665 −0.0256833 0.999670i 0.508176π-0.508176\pi
−0.0256833 + 0.999670i 0.508176π0.508176\pi
380380 0 0
381381 4.00000 0.204926
382382 0 0
383383 10.0000 0.510976 0.255488 0.966812i 0.417764π-0.417764\pi
0.255488 + 0.966812i 0.417764π0.417764\pi
384384 0 0
385385 −30.0000 −1.52894
386386 0 0
387387 10.0000 0.508329
388388 0 0
389389 −34.0000 −1.72387 −0.861934 0.507020i 0.830747π-0.830747\pi
−0.861934 + 0.507020i 0.830747π0.830747\pi
390390 0 0
391391 4.00000 0.202289
392392 0 0
393393 10.0000 0.504433
394394 0 0
395395 33.0000 1.66041
396396 0 0
397397 −22.0000 −1.10415 −0.552074 0.833795i 0.686163π-0.686163\pi
−0.552074 + 0.833795i 0.686163π0.686163\pi
398398 0 0
399399 14.0000 0.700877
400400 0 0
401401 −23.0000 −1.14857 −0.574283 0.818657i 0.694719π-0.694719\pi
−0.574283 + 0.818657i 0.694719π0.694719\pi
402402 0 0
403403 −7.00000 −0.348695
404404 0 0
405405 3.00000 0.149071
406406 0 0
407407 30.0000 1.48704
408408 0 0
409409 −30.0000 −1.48340 −0.741702 0.670729i 0.765981π-0.765981\pi
−0.741702 + 0.670729i 0.765981π0.765981\pi
410410 0 0
411411 18.0000 0.887875
412412 0 0
413413 20.0000 0.984136
414414 0 0
415415 −21.0000 −1.03085
416416 0 0
417417 −8.00000 −0.391762
418418 0 0
419419 4.00000 0.195413 0.0977064 0.995215i 0.468849π-0.468849\pi
0.0977064 + 0.995215i 0.468849π0.468849\pi
420420 0 0
421421 2.00000 0.0974740 0.0487370 0.998812i 0.484480π-0.484480\pi
0.0487370 + 0.998812i 0.484480π0.484480\pi
422422 0 0
423423 1.00000 0.0486217
424424 0 0
425425 −4.00000 −0.194029
426426 0 0
427427 2.00000 0.0967868
428428 0 0
429429 −35.0000 −1.68982
430430 0 0
431431 −24.0000 −1.15604 −0.578020 0.816023i 0.696174π-0.696174\pi
−0.578020 + 0.816023i 0.696174π0.696174\pi
432432 0 0
433433 28.0000 1.34559 0.672797 0.739827i 0.265093π-0.265093\pi
0.672797 + 0.739827i 0.265093π0.265093\pi
434434 0 0
435435 24.0000 1.15071
436436 0 0
437437 28.0000 1.33942
438438 0 0
439439 −32.0000 −1.52728 −0.763638 0.645644i 0.776589π-0.776589\pi
−0.763638 + 0.645644i 0.776589π0.776589\pi
440440 0 0
441441 −3.00000 −0.142857
442442 0 0
443443 14.0000 0.665160 0.332580 0.943075i 0.392081π-0.392081\pi
0.332580 + 0.943075i 0.392081π0.392081\pi
444444 0 0
445445 −18.0000 −0.853282
446446 0 0
447447 −15.0000 −0.709476
448448 0 0
449449 −11.0000 −0.519122 −0.259561 0.965727i 0.583578π-0.583578\pi
−0.259561 + 0.965727i 0.583578π0.583578\pi
450450 0 0
451451 10.0000 0.470882
452452 0 0
453453 −1.00000 −0.0469841
454454 0 0
455455 −42.0000 −1.96899
456456 0 0
457457 −42.0000 −1.96468 −0.982339 0.187112i 0.940087π-0.940087\pi
−0.982339 + 0.187112i 0.940087π0.940087\pi
458458 0 0
459459 1.00000 0.0466760
460460 0 0
461461 −34.0000 −1.58354 −0.791769 0.610821i 0.790840π-0.790840\pi
−0.791769 + 0.610821i 0.790840π0.790840\pi
462462 0 0
463463 −33.0000 −1.53364 −0.766820 0.641862i 0.778162π-0.778162\pi
−0.766820 + 0.641862i 0.778162π0.778162\pi
464464 0 0
465465 −3.00000 −0.139122
466466 0 0
467467 −24.0000 −1.11059 −0.555294 0.831654i 0.687394π-0.687394\pi
−0.555294 + 0.831654i 0.687394π0.687394\pi
468468 0 0
469469 6.00000 0.277054
470470 0 0
471471 4.00000 0.184310
472472 0 0
473473 −50.0000 −2.29900
474474 0 0
475475 −28.0000 −1.28473
476476 0 0
477477 6.00000 0.274721
478478 0 0
479479 −29.0000 −1.32504 −0.662522 0.749043i 0.730514π-0.730514\pi
−0.662522 + 0.749043i 0.730514π0.730514\pi
480480 0 0
481481 42.0000 1.91504
482482 0 0
483483 8.00000 0.364013
484484 0 0
485485 −9.00000 −0.408669
486486 0 0
487487 27.0000 1.22349 0.611743 0.791056i 0.290469π-0.290469\pi
0.611743 + 0.791056i 0.290469π0.290469\pi
488488 0 0
489489 −9.00000 −0.406994
490490 0 0
491491 20.0000 0.902587 0.451294 0.892375i 0.350963π-0.350963\pi
0.451294 + 0.892375i 0.350963π0.350963\pi
492492 0 0
493493 8.00000 0.360302
494494 0 0
495495 −15.0000 −0.674200
496496 0 0
497497 −6.00000 −0.269137
498498 0 0
499499 24.0000 1.07439 0.537194 0.843459i 0.319484π-0.319484\pi
0.537194 + 0.843459i 0.319484π0.319484\pi
500500 0 0
501501 10.0000 0.446767
502502 0 0
503503 33.0000 1.47140 0.735699 0.677309i 0.236854π-0.236854\pi
0.735699 + 0.677309i 0.236854π0.236854\pi
504504 0 0
505505 18.0000 0.800989
506506 0 0
507507 −36.0000 −1.59882
508508 0 0
509509 40.0000 1.77297 0.886484 0.462758i 0.153140π-0.153140\pi
0.886484 + 0.462758i 0.153140π0.153140\pi
510510 0 0
511511 28.0000 1.23865
512512 0 0
513513 7.00000 0.309058
514514 0 0
515515 −30.0000 −1.32196
516516 0 0
517517 −5.00000 −0.219900
518518 0 0
519519 −1.00000 −0.0438951
520520 0 0
521521 12.0000 0.525730 0.262865 0.964833i 0.415333π-0.415333\pi
0.262865 + 0.964833i 0.415333π0.415333\pi
522522 0 0
523523 −30.0000 −1.31181 −0.655904 0.754844i 0.727712π-0.727712\pi
−0.655904 + 0.754844i 0.727712π0.727712\pi
524524 0 0
525525 −8.00000 −0.349149
526526 0 0
527527 −1.00000 −0.0435607
528528 0 0
529529 −7.00000 −0.304348
530530 0 0
531531 10.0000 0.433963
532532 0 0
533533 14.0000 0.606407
534534 0 0
535535 −24.0000 −1.03761
536536 0 0
537537 19.0000 0.819911
538538 0 0
539539 15.0000 0.646096
540540 0 0
541541 44.0000 1.89171 0.945854 0.324593i 0.105227π-0.105227\pi
0.945854 + 0.324593i 0.105227π0.105227\pi
542542 0 0
543543 −18.0000 −0.772454
544544 0 0
545545 −18.0000 −0.771035
546546 0 0
547547 −32.0000 −1.36822 −0.684111 0.729378i 0.739809π-0.739809\pi
−0.684111 + 0.729378i 0.739809π0.739809\pi
548548 0 0
549549 1.00000 0.0426790
550550 0 0
551551 56.0000 2.38568
552552 0 0
553553 22.0000 0.935535
554554 0 0
555555 18.0000 0.764057
556556 0 0
557557 −24.0000 −1.01691 −0.508456 0.861088i 0.669784π-0.669784\pi
−0.508456 + 0.861088i 0.669784π0.669784\pi
558558 0 0
559559 −70.0000 −2.96068
560560 0 0
561561 −5.00000 −0.211100
562562 0 0
563563 24.0000 1.01148 0.505740 0.862686i 0.331220π-0.331220\pi
0.505740 + 0.862686i 0.331220π0.331220\pi
564564 0 0
565565 18.0000 0.757266
566566 0 0
567567 2.00000 0.0839921
568568 0 0
569569 26.0000 1.08998 0.544988 0.838444i 0.316534π-0.316534\pi
0.544988 + 0.838444i 0.316534π0.316534\pi
570570 0 0
571571 −12.0000 −0.502184 −0.251092 0.967963i 0.580790π-0.580790\pi
−0.251092 + 0.967963i 0.580790π0.580790\pi
572572 0 0
573573 0 0
574574 0 0
575575 −16.0000 −0.667246
576576 0 0
577577 27.0000 1.12402 0.562012 0.827129i 0.310027π-0.310027\pi
0.562012 + 0.827129i 0.310027π0.310027\pi
578578 0 0
579579 −19.0000 −0.789613
580580 0 0
581581 −14.0000 −0.580818
582582 0 0
583583 −30.0000 −1.24247
584584 0 0
585585 −21.0000 −0.868243
586586 0 0
587587 17.0000 0.701665 0.350833 0.936438i 0.385899π-0.385899\pi
0.350833 + 0.936438i 0.385899π0.385899\pi
588588 0 0
589589 −7.00000 −0.288430
590590 0 0
591591 2.00000 0.0822690
592592 0 0
593593 −30.0000 −1.23195 −0.615976 0.787765i 0.711238π-0.711238\pi
−0.615976 + 0.787765i 0.711238π0.711238\pi
594594 0 0
595595 −6.00000 −0.245976
596596 0 0
597597 −11.0000 −0.450200
598598 0 0
599599 39.0000 1.59350 0.796748 0.604311i 0.206552π-0.206552\pi
0.796748 + 0.604311i 0.206552π0.206552\pi
600600 0 0
601601 −2.00000 −0.0815817 −0.0407909 0.999168i 0.512988π-0.512988\pi
−0.0407909 + 0.999168i 0.512988π0.512988\pi
602602 0 0
603603 3.00000 0.122169
604604 0 0
605605 42.0000 1.70754
606606 0 0
607607 −10.0000 −0.405887 −0.202944 0.979190i 0.565051π-0.565051\pi
−0.202944 + 0.979190i 0.565051π0.565051\pi
608608 0 0
609609 16.0000 0.648353
610610 0 0
611611 −7.00000 −0.283190
612612 0 0
613613 5.00000 0.201948 0.100974 0.994889i 0.467804π-0.467804\pi
0.100974 + 0.994889i 0.467804π0.467804\pi
614614 0 0
615615 6.00000 0.241943
616616 0 0
617617 6.00000 0.241551 0.120775 0.992680i 0.461462π-0.461462\pi
0.120775 + 0.992680i 0.461462π0.461462\pi
618618 0 0
619619 8.00000 0.321547 0.160774 0.986991i 0.448601π-0.448601\pi
0.160774 + 0.986991i 0.448601π0.448601\pi
620620 0 0
621621 4.00000 0.160514
622622 0 0
623623 −12.0000 −0.480770
624624 0 0
625625 −29.0000 −1.16000
626626 0 0
627627 −35.0000 −1.39777
628628 0 0
629629 6.00000 0.239236
630630 0 0
631631 16.0000 0.636950 0.318475 0.947931i 0.396829π-0.396829\pi
0.318475 + 0.947931i 0.396829π0.396829\pi
632632 0 0
633633 0 0
634634 0 0
635635 −12.0000 −0.476205
636636 0 0
637637 21.0000 0.832050
638638 0 0
639639 −3.00000 −0.118678
640640 0 0
641641 23.0000 0.908445 0.454223 0.890888i 0.349917π-0.349917\pi
0.454223 + 0.890888i 0.349917π0.349917\pi
642642 0 0
643643 32.0000 1.26196 0.630978 0.775800i 0.282654π-0.282654\pi
0.630978 + 0.775800i 0.282654π0.282654\pi
644644 0 0
645645 −30.0000 −1.18125
646646 0 0
647647 −14.0000 −0.550397 −0.275198 0.961387i 0.588744π-0.588744\pi
−0.275198 + 0.961387i 0.588744π0.588744\pi
648648 0 0
649649 −50.0000 −1.96267
650650 0 0
651651 −2.00000 −0.0783862
652652 0 0
653653 27.0000 1.05659 0.528296 0.849060i 0.322831π-0.322831\pi
0.528296 + 0.849060i 0.322831π0.322831\pi
654654 0 0
655655 −30.0000 −1.17220
656656 0 0
657657 14.0000 0.546192
658658 0 0
659659 26.0000 1.01282 0.506408 0.862294i 0.330973π-0.330973\pi
0.506408 + 0.862294i 0.330973π0.330973\pi
660660 0 0
661661 4.00000 0.155582 0.0777910 0.996970i 0.475213π-0.475213\pi
0.0777910 + 0.996970i 0.475213π0.475213\pi
662662 0 0
663663 −7.00000 −0.271857
664664 0 0
665665 −42.0000 −1.62869
666666 0 0
667667 32.0000 1.23904
668668 0 0
669669 −5.00000 −0.193311
670670 0 0
671671 −5.00000 −0.193023
672672 0 0
673673 8.00000 0.308377 0.154189 0.988041i 0.450724π-0.450724\pi
0.154189 + 0.988041i 0.450724π0.450724\pi
674674 0 0
675675 −4.00000 −0.153960
676676 0 0
677677 36.0000 1.38359 0.691796 0.722093i 0.256820π-0.256820\pi
0.691796 + 0.722093i 0.256820π0.256820\pi
678678 0 0
679679 −6.00000 −0.230259
680680 0 0
681681 22.0000 0.843042
682682 0 0
683683 −16.0000 −0.612223 −0.306111 0.951996i 0.599028π-0.599028\pi
−0.306111 + 0.951996i 0.599028π0.599028\pi
684684 0 0
685685 −54.0000 −2.06323
686686 0 0
687687 −13.0000 −0.495981
688688 0 0
689689 −42.0000 −1.60007
690690 0 0
691691 −13.0000 −0.494543 −0.247272 0.968946i 0.579534π-0.579534\pi
−0.247272 + 0.968946i 0.579534π0.579534\pi
692692 0 0
693693 −10.0000 −0.379869
694694 0 0
695695 24.0000 0.910372
696696 0 0
697697 2.00000 0.0757554
698698 0 0
699699 −20.0000 −0.756469
700700 0 0
701701 35.0000 1.32193 0.660966 0.750416i 0.270147π-0.270147\pi
0.660966 + 0.750416i 0.270147π0.270147\pi
702702 0 0
703703 42.0000 1.58406
704704 0 0
705705 −3.00000 −0.112987
706706 0 0
707707 12.0000 0.451306
708708 0 0
709709 −21.0000 −0.788672 −0.394336 0.918966i 0.629025π-0.629025\pi
−0.394336 + 0.918966i 0.629025π0.629025\pi
710710 0 0
711711 11.0000 0.412532
712712 0 0
713713 −4.00000 −0.149801
714714 0 0
715715 105.000 3.92678
716716 0 0
717717 −4.00000 −0.149383
718718 0 0
719719 12.0000 0.447524 0.223762 0.974644i 0.428166π-0.428166\pi
0.223762 + 0.974644i 0.428166π0.428166\pi
720720 0 0
721721 −20.0000 −0.744839
722722 0 0
723723 14.0000 0.520666
724724 0 0
725725 −32.0000 −1.18845
726726 0 0
727727 −4.00000 −0.148352 −0.0741759 0.997245i 0.523633π-0.523633\pi
−0.0741759 + 0.997245i 0.523633π0.523633\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −10.0000 −0.369863
732732 0 0
733733 −30.0000 −1.10808 −0.554038 0.832492i 0.686914π-0.686914\pi
−0.554038 + 0.832492i 0.686914π0.686914\pi
734734 0 0
735735 9.00000 0.331970
736736 0 0
737737 −15.0000 −0.552532
738738 0 0
739739 16.0000 0.588570 0.294285 0.955718i 0.404919π-0.404919\pi
0.294285 + 0.955718i 0.404919π0.404919\pi
740740 0 0
741741 −49.0000 −1.80006
742742 0 0
743743 16.0000 0.586983 0.293492 0.955962i 0.405183π-0.405183\pi
0.293492 + 0.955962i 0.405183π0.405183\pi
744744 0 0
745745 45.0000 1.64867
746746 0 0
747747 −7.00000 −0.256117
748748 0 0
749749 −16.0000 −0.584627
750750 0 0
751751 38.0000 1.38664 0.693320 0.720630i 0.256147π-0.256147\pi
0.693320 + 0.720630i 0.256147π0.256147\pi
752752 0 0
753753 20.0000 0.728841
754754 0 0
755755 3.00000 0.109181
756756 0 0
757757 18.0000 0.654221 0.327111 0.944986i 0.393925π-0.393925\pi
0.327111 + 0.944986i 0.393925π0.393925\pi
758758 0 0
759759 −20.0000 −0.725954
760760 0 0
761761 1.00000 0.0362500 0.0181250 0.999836i 0.494230π-0.494230\pi
0.0181250 + 0.999836i 0.494230π0.494230\pi
762762 0 0
763763 −12.0000 −0.434429
764764 0 0
765765 −3.00000 −0.108465
766766 0 0
767767 −70.0000 −2.52755
768768 0 0
769769 −10.0000 −0.360609 −0.180305 0.983611i 0.557708π-0.557708\pi
−0.180305 + 0.983611i 0.557708π0.557708\pi
770770 0 0
771771 12.0000 0.432169
772772 0 0
773773 −16.0000 −0.575480 −0.287740 0.957709i 0.592904π-0.592904\pi
−0.287740 + 0.957709i 0.592904π0.592904\pi
774774 0 0
775775 4.00000 0.143684
776776 0 0
777777 12.0000 0.430498
778778 0 0
779779 14.0000 0.501602
780780 0 0
781781 15.0000 0.536742
782782 0 0
783783 8.00000 0.285897
784784 0 0
785785 −12.0000 −0.428298
786786 0 0
787787 −40.0000 −1.42585 −0.712923 0.701242i 0.752629π-0.752629\pi
−0.712923 + 0.701242i 0.752629π0.752629\pi
788788 0 0
789789 12.0000 0.427211
790790 0 0
791791 12.0000 0.426671
792792 0 0
793793 −7.00000 −0.248577
794794 0 0
795795 −18.0000 −0.638394
796796 0 0
797797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
798798 0 0
799799 −1.00000 −0.0353775
800800 0 0
801801 −6.00000 −0.212000
802802 0 0
803803 −70.0000 −2.47025
804804 0 0
805805 −24.0000 −0.845889
806806 0 0
807807 −6.00000 −0.211210
808808 0 0
809809 −29.0000 −1.01959 −0.509793 0.860297i 0.670278π-0.670278\pi
−0.509793 + 0.860297i 0.670278π0.670278\pi
810810 0 0
811811 −20.0000 −0.702295 −0.351147 0.936320i 0.614208π-0.614208\pi
−0.351147 + 0.936320i 0.614208π0.614208\pi
812812 0 0
813813 −19.0000 −0.666359
814814 0 0
815815 27.0000 0.945769
816816 0 0
817817 −70.0000 −2.44899
818818 0 0
819819 −14.0000 −0.489200
820820 0 0
821821 −10.0000 −0.349002 −0.174501 0.984657i 0.555831π-0.555831\pi
−0.174501 + 0.984657i 0.555831π0.555831\pi
822822 0 0
823823 −43.0000 −1.49889 −0.749443 0.662069i 0.769679π-0.769679\pi
−0.749443 + 0.662069i 0.769679π0.769679\pi
824824 0 0
825825 20.0000 0.696311
826826 0 0
827827 −27.0000 −0.938882 −0.469441 0.882964i 0.655545π-0.655545\pi
−0.469441 + 0.882964i 0.655545π0.655545\pi
828828 0 0
829829 26.0000 0.903017 0.451509 0.892267i 0.350886π-0.350886\pi
0.451509 + 0.892267i 0.350886π0.350886\pi
830830 0 0
831831 7.00000 0.242827
832832 0 0
833833 3.00000 0.103944
834834 0 0
835835 −30.0000 −1.03819
836836 0 0
837837 −1.00000 −0.0345651
838838 0 0
839839 −12.0000 −0.414286 −0.207143 0.978311i 0.566417π-0.566417\pi
−0.207143 + 0.978311i 0.566417π0.566417\pi
840840 0 0
841841 35.0000 1.20690
842842 0 0
843843 30.0000 1.03325
844844 0 0
845845 108.000 3.71531
846846 0 0
847847 28.0000 0.962091
848848 0 0
849849 5.00000 0.171600
850850 0 0
851851 24.0000 0.822709
852852 0 0
853853 −46.0000 −1.57501 −0.787505 0.616308i 0.788628π-0.788628\pi
−0.787505 + 0.616308i 0.788628π0.788628\pi
854854 0 0
855855 −21.0000 −0.718185
856856 0 0
857857 −8.00000 −0.273275 −0.136637 0.990621i 0.543630π-0.543630\pi
−0.136637 + 0.990621i 0.543630π0.543630\pi
858858 0 0
859859 26.0000 0.887109 0.443554 0.896248i 0.353717π-0.353717\pi
0.443554 + 0.896248i 0.353717π0.353717\pi
860860 0 0
861861 4.00000 0.136320
862862 0 0
863863 −10.0000 −0.340404 −0.170202 0.985409i 0.554442π-0.554442\pi
−0.170202 + 0.985409i 0.554442π0.554442\pi
864864 0 0
865865 3.00000 0.102003
866866 0 0
867867 16.0000 0.543388
868868 0 0
869869 −55.0000 −1.86575
870870 0 0
871871 −21.0000 −0.711558
872872 0 0
873873 −3.00000 −0.101535
874874 0 0
875875 −6.00000 −0.202837
876876 0 0
877877 28.0000 0.945493 0.472746 0.881199i 0.343263π-0.343263\pi
0.472746 + 0.881199i 0.343263π0.343263\pi
878878 0 0
879879 6.00000 0.202375
880880 0 0
881881 51.0000 1.71823 0.859117 0.511780i 0.171014π-0.171014\pi
0.859117 + 0.511780i 0.171014π0.171014\pi
882882 0 0
883883 46.0000 1.54802 0.774012 0.633171i 0.218247π-0.218247\pi
0.774012 + 0.633171i 0.218247π0.218247\pi
884884 0 0
885885 −30.0000 −1.00844
886886 0 0
887887 −16.0000 −0.537227 −0.268614 0.963248i 0.586566π-0.586566\pi
−0.268614 + 0.963248i 0.586566π0.586566\pi
888888 0 0
889889 −8.00000 −0.268311
890890 0 0
891891 −5.00000 −0.167506
892892 0 0
893893 −7.00000 −0.234246
894894 0 0
895895 −57.0000 −1.90530
896896 0 0
897897 −28.0000 −0.934893
898898 0 0
899899 −8.00000 −0.266815
900900 0 0
901901 −6.00000 −0.199889
902902 0 0
903903 −20.0000 −0.665558
904904 0 0
905905 54.0000 1.79502
906906 0 0
907907 1.00000 0.0332045 0.0166022 0.999862i 0.494715π-0.494715\pi
0.0166022 + 0.999862i 0.494715π0.494715\pi
908908 0 0
909909 6.00000 0.199007
910910 0 0
911911 24.0000 0.795155 0.397578 0.917568i 0.369851π-0.369851\pi
0.397578 + 0.917568i 0.369851π0.369851\pi
912912 0 0
913913 35.0000 1.15833
914914 0 0
915915 −3.00000 −0.0991769
916916 0 0
917917 −20.0000 −0.660458
918918 0 0
919919 −28.0000 −0.923635 −0.461817 0.886975i 0.652802π-0.652802\pi
−0.461817 + 0.886975i 0.652802π0.652802\pi
920920 0 0
921921 16.0000 0.527218
922922 0 0
923923 21.0000 0.691223
924924 0 0
925925 −24.0000 −0.789115
926926 0 0
927927 −10.0000 −0.328443
928928 0 0
929929 14.0000 0.459325 0.229663 0.973270i 0.426238π-0.426238\pi
0.229663 + 0.973270i 0.426238π0.426238\pi
930930 0 0
931931 21.0000 0.688247
932932 0 0
933933 21.0000 0.687509
934934 0 0
935935 15.0000 0.490552
936936 0 0
937937 1.00000 0.0326686 0.0163343 0.999867i 0.494800π-0.494800\pi
0.0163343 + 0.999867i 0.494800π0.494800\pi
938938 0 0
939939 −2.00000 −0.0652675
940940 0 0
941941 −48.0000 −1.56476 −0.782378 0.622804i 0.785993π-0.785993\pi
−0.782378 + 0.622804i 0.785993π0.785993\pi
942942 0 0
943943 8.00000 0.260516
944944 0 0
945945 −6.00000 −0.195180
946946 0 0
947947 5.00000 0.162478 0.0812391 0.996695i 0.474112π-0.474112\pi
0.0812391 + 0.996695i 0.474112π0.474112\pi
948948 0 0
949949 −98.0000 −3.18121
950950 0 0
951951 −5.00000 −0.162136
952952 0 0
953953 −5.00000 −0.161966 −0.0809829 0.996715i 0.525806π-0.525806\pi
−0.0809829 + 0.996715i 0.525806π0.525806\pi
954954 0 0
955955 0 0
956956 0 0
957957 −40.0000 −1.29302
958958 0 0
959959 −36.0000 −1.16250
960960 0 0
961961 1.00000 0.0322581
962962 0 0
963963 −8.00000 −0.257796
964964 0 0
965965 57.0000 1.83489
966966 0 0
967967 −33.0000 −1.06121 −0.530604 0.847620i 0.678035π-0.678035\pi
−0.530604 + 0.847620i 0.678035π0.678035\pi
968968 0 0
969969 −7.00000 −0.224872
970970 0 0
971971 −34.0000 −1.09111 −0.545556 0.838074i 0.683681π-0.683681\pi
−0.545556 + 0.838074i 0.683681π0.683681\pi
972972 0 0
973973 16.0000 0.512936
974974 0 0
975975 28.0000 0.896718
976976 0 0
977977 −22.0000 −0.703842 −0.351921 0.936030i 0.614471π-0.614471\pi
−0.351921 + 0.936030i 0.614471π0.614471\pi
978978 0 0
979979 30.0000 0.958804
980980 0 0
981981 −6.00000 −0.191565
982982 0 0
983983 −24.0000 −0.765481 −0.382741 0.923856i 0.625020π-0.625020\pi
−0.382741 + 0.923856i 0.625020π0.625020\pi
984984 0 0
985985 −6.00000 −0.191176
986986 0 0
987987 −2.00000 −0.0636607
988988 0 0
989989 −40.0000 −1.27193
990990 0 0
991991 20.0000 0.635321 0.317660 0.948205i 0.397103π-0.397103\pi
0.317660 + 0.948205i 0.397103π0.397103\pi
992992 0 0
993993 0 0
994994 0 0
995995 33.0000 1.04617
996996 0 0
997997 −42.0000 −1.33015 −0.665077 0.746775i 0.731601π-0.731601\pi
−0.665077 + 0.746775i 0.731601π0.731601\pi
998998 0 0
999999 6.00000 0.189832
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 1488.2.a.h.1.1 1
3.2 odd 2 4464.2.a.c.1.1 1
4.3 odd 2 186.2.a.b.1.1 1
8.3 odd 2 5952.2.a.b.1.1 1
8.5 even 2 5952.2.a.s.1.1 1
12.11 even 2 558.2.a.f.1.1 1
20.3 even 4 4650.2.d.k.3349.2 2
20.7 even 4 4650.2.d.k.3349.1 2
20.19 odd 2 4650.2.a.bh.1.1 1
28.27 even 2 9114.2.a.b.1.1 1
124.123 even 2 5766.2.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
186.2.a.b.1.1 1 4.3 odd 2
558.2.a.f.1.1 1 12.11 even 2
1488.2.a.h.1.1 1 1.1 even 1 trivial
4464.2.a.c.1.1 1 3.2 odd 2
4650.2.a.bh.1.1 1 20.19 odd 2
4650.2.d.k.3349.1 2 20.7 even 4
4650.2.d.k.3349.2 2 20.3 even 4
5766.2.a.c.1.1 1 124.123 even 2
5952.2.a.b.1.1 1 8.3 odd 2
5952.2.a.s.1.1 1 8.5 even 2
9114.2.a.b.1.1 1 28.27 even 2