Properties

Label 1176.2.a.k.1.2
Level 11761176
Weight 22
Character 1176.1
Self dual yes
Analytic conductor 9.3909.390
Analytic rank 00
Dimension 22
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] = [1176,2,Mod(1,1176)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1176, 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("1176.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1176=23372 1176 = 2^{3} \cdot 3 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1176.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: 9.390407277709.39040727770
Analytic rank: 00
Dimension: 22
Coefficient field: Q(57)\Q(\sqrt{57})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x14 x^{2} - x - 14 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 168)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 3.27492-3.27492 of defining polynomial
Character χ\chi == 1176.1

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+3.27492q5+1.00000q9+3.27492q11+6.27492q133.27492q154.00000q176.27492q19+4.00000q23+5.72508q251.00000q27+5.27492q291.00000q313.27492q332.27492q376.27492q394.54983q41+0.274917q43+3.27492q456.00000q47+4.00000q51+9.27492q53+10.7251q55+6.27492q571.27492q59+10.0000q61+20.5498q650.274917q674.00000q69+2.00000q714.27492q735.72508q75+11.5498q79+1.00000q81+7.27492q8313.0997q855.27492q8710.5498q89+1.00000q9320.5498q95+8.72508q97+3.27492q99+O(q100)q-1.00000 q^{3} +3.27492 q^{5} +1.00000 q^{9} +3.27492 q^{11} +6.27492 q^{13} -3.27492 q^{15} -4.00000 q^{17} -6.27492 q^{19} +4.00000 q^{23} +5.72508 q^{25} -1.00000 q^{27} +5.27492 q^{29} -1.00000 q^{31} -3.27492 q^{33} -2.27492 q^{37} -6.27492 q^{39} -4.54983 q^{41} +0.274917 q^{43} +3.27492 q^{45} -6.00000 q^{47} +4.00000 q^{51} +9.27492 q^{53} +10.7251 q^{55} +6.27492 q^{57} -1.27492 q^{59} +10.0000 q^{61} +20.5498 q^{65} -0.274917 q^{67} -4.00000 q^{69} +2.00000 q^{71} -4.27492 q^{73} -5.72508 q^{75} +11.5498 q^{79} +1.00000 q^{81} +7.27492 q^{83} -13.0997 q^{85} -5.27492 q^{87} -10.5498 q^{89} +1.00000 q^{93} -20.5498 q^{95} +8.72508 q^{97} +3.27492 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q3q5+2q9q11+5q13+q158q175q19+8q23+19q252q27+3q292q31+q33+3q375q39+6q417q43q45+q99+O(q100) 2 q - 2 q^{3} - q^{5} + 2 q^{9} - q^{11} + 5 q^{13} + q^{15} - 8 q^{17} - 5 q^{19} + 8 q^{23} + 19 q^{25} - 2 q^{27} + 3 q^{29} - 2 q^{31} + q^{33} + 3 q^{37} - 5 q^{39} + 6 q^{41} - 7 q^{43} - q^{45}+ \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 3.27492 1.46459 0.732294 0.680989i 0.238450π-0.238450\pi
0.732294 + 0.680989i 0.238450π0.238450\pi
66 0 0
77 0 0
88 0 0
99 1.00000 0.333333
1010 0 0
1111 3.27492 0.987425 0.493712 0.869625i 0.335640π-0.335640\pi
0.493712 + 0.869625i 0.335640π0.335640\pi
1212 0 0
1313 6.27492 1.74035 0.870174 0.492744i 0.164006π-0.164006\pi
0.870174 + 0.492744i 0.164006π0.164006\pi
1414 0 0
1515 −3.27492 −0.845580
1616 0 0
1717 −4.00000 −0.970143 −0.485071 0.874475i 0.661206π-0.661206\pi
−0.485071 + 0.874475i 0.661206π0.661206\pi
1818 0 0
1919 −6.27492 −1.43956 −0.719782 0.694200i 0.755758π-0.755758\pi
−0.719782 + 0.694200i 0.755758π0.755758\pi
2020 0 0
2121 0 0
2222 0 0
2323 4.00000 0.834058 0.417029 0.908893i 0.363071π-0.363071\pi
0.417029 + 0.908893i 0.363071π0.363071\pi
2424 0 0
2525 5.72508 1.14502
2626 0 0
2727 −1.00000 −0.192450
2828 0 0
2929 5.27492 0.979528 0.489764 0.871855i 0.337083π-0.337083\pi
0.489764 + 0.871855i 0.337083π0.337083\pi
3030 0 0
3131 −1.00000 −0.179605 −0.0898027 0.995960i 0.528624π-0.528624\pi
−0.0898027 + 0.995960i 0.528624π0.528624\pi
3232 0 0
3333 −3.27492 −0.570090
3434 0 0
3535 0 0
3636 0 0
3737 −2.27492 −0.373994 −0.186997 0.982360i 0.559875π-0.559875\pi
−0.186997 + 0.982360i 0.559875π0.559875\pi
3838 0 0
3939 −6.27492 −1.00479
4040 0 0
4141 −4.54983 −0.710565 −0.355282 0.934759i 0.615615π-0.615615\pi
−0.355282 + 0.934759i 0.615615π0.615615\pi
4242 0 0
4343 0.274917 0.0419245 0.0209622 0.999780i 0.493327π-0.493327\pi
0.0209622 + 0.999780i 0.493327π0.493327\pi
4444 0 0
4545 3.27492 0.488196
4646 0 0
4747 −6.00000 −0.875190 −0.437595 0.899172i 0.644170π-0.644170\pi
−0.437595 + 0.899172i 0.644170π0.644170\pi
4848 0 0
4949 0 0
5050 0 0
5151 4.00000 0.560112
5252 0 0
5353 9.27492 1.27401 0.637004 0.770861i 0.280173π-0.280173\pi
0.637004 + 0.770861i 0.280173π0.280173\pi
5454 0 0
5555 10.7251 1.44617
5656 0 0
5757 6.27492 0.831133
5858 0 0
5959 −1.27492 −0.165980 −0.0829900 0.996550i 0.526447π-0.526447\pi
−0.0829900 + 0.996550i 0.526447π0.526447\pi
6060 0 0
6161 10.0000 1.28037 0.640184 0.768221i 0.278858π-0.278858\pi
0.640184 + 0.768221i 0.278858π0.278858\pi
6262 0 0
6363 0 0
6464 0 0
6565 20.5498 2.54889
6666 0 0
6767 −0.274917 −0.0335865 −0.0167932 0.999859i 0.505346π-0.505346\pi
−0.0167932 + 0.999859i 0.505346π0.505346\pi
6868 0 0
6969 −4.00000 −0.481543
7070 0 0
7171 2.00000 0.237356 0.118678 0.992933i 0.462134π-0.462134\pi
0.118678 + 0.992933i 0.462134π0.462134\pi
7272 0 0
7373 −4.27492 −0.500341 −0.250171 0.968202i 0.580487π-0.580487\pi
−0.250171 + 0.968202i 0.580487π0.580487\pi
7474 0 0
7575 −5.72508 −0.661076
7676 0 0
7777 0 0
7878 0 0
7979 11.5498 1.29946 0.649729 0.760166i 0.274882π-0.274882\pi
0.649729 + 0.760166i 0.274882π0.274882\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 7.27492 0.798526 0.399263 0.916836i 0.369266π-0.369266\pi
0.399263 + 0.916836i 0.369266π0.369266\pi
8484 0 0
8585 −13.0997 −1.42086
8686 0 0
8787 −5.27492 −0.565530
8888 0 0
8989 −10.5498 −1.11828 −0.559140 0.829073i 0.688869π-0.688869\pi
−0.559140 + 0.829073i 0.688869π0.688869\pi
9090 0 0
9191 0 0
9292 0 0
9393 1.00000 0.103695
9494 0 0
9595 −20.5498 −2.10837
9696 0 0
9797 8.72508 0.885898 0.442949 0.896547i 0.353932π-0.353932\pi
0.442949 + 0.896547i 0.353932π0.353932\pi
9898 0 0
9999 3.27492 0.329142
100100 0 0
101101 −6.00000 −0.597022 −0.298511 0.954406i 0.596490π-0.596490\pi
−0.298511 + 0.954406i 0.596490π0.596490\pi
102102 0 0
103103 10.8248 1.06659 0.533297 0.845928i 0.320953π-0.320953\pi
0.533297 + 0.845928i 0.320953π0.320953\pi
104104 0 0
105105 0 0
106106 0 0
107107 −15.8248 −1.52984 −0.764918 0.644127i 0.777221π-0.777221\pi
−0.764918 + 0.644127i 0.777221π0.777221\pi
108108 0 0
109109 16.8248 1.61152 0.805759 0.592243i 0.201757π-0.201757\pi
0.805759 + 0.592243i 0.201757π0.201757\pi
110110 0 0
111111 2.27492 0.215926
112112 0 0
113113 −4.54983 −0.428012 −0.214006 0.976832i 0.568651π-0.568651\pi
−0.214006 + 0.976832i 0.568651π0.568651\pi
114114 0 0
115115 13.0997 1.22155
116116 0 0
117117 6.27492 0.580116
118118 0 0
119119 0 0
120120 0 0
121121 −0.274917 −0.0249925
122122 0 0
123123 4.54983 0.410245
124124 0 0
125125 2.37459 0.212389
126126 0 0
127127 −6.45017 −0.572360 −0.286180 0.958176i 0.592385π-0.592385\pi
−0.286180 + 0.958176i 0.592385π0.592385\pi
128128 0 0
129129 −0.274917 −0.0242051
130130 0 0
131131 7.27492 0.635612 0.317806 0.948156i 0.397054π-0.397054\pi
0.317806 + 0.948156i 0.397054π0.397054\pi
132132 0 0
133133 0 0
134134 0 0
135135 −3.27492 −0.281860
136136 0 0
137137 1.45017 0.123896 0.0619480 0.998079i 0.480269π-0.480269\pi
0.0619480 + 0.998079i 0.480269π0.480269\pi
138138 0 0
139139 8.27492 0.701869 0.350935 0.936400i 0.385864π-0.385864\pi
0.350935 + 0.936400i 0.385864π0.385864\pi
140140 0 0
141141 6.00000 0.505291
142142 0 0
143143 20.5498 1.71846
144144 0 0
145145 17.2749 1.43460
146146 0 0
147147 0 0
148148 0 0
149149 −14.5498 −1.19197 −0.595984 0.802996i 0.703238π-0.703238\pi
−0.595984 + 0.802996i 0.703238π0.703238\pi
150150 0 0
151151 22.3746 1.82082 0.910409 0.413709i 0.135767π-0.135767\pi
0.910409 + 0.413709i 0.135767π0.135767\pi
152152 0 0
153153 −4.00000 −0.323381
154154 0 0
155155 −3.27492 −0.263048
156156 0 0
157157 −0.549834 −0.0438816 −0.0219408 0.999759i 0.506985π-0.506985\pi
−0.0219408 + 0.999759i 0.506985π0.506985\pi
158158 0 0
159159 −9.27492 −0.735549
160160 0 0
161161 0 0
162162 0 0
163163 −12.0000 −0.939913 −0.469956 0.882690i 0.655730π-0.655730\pi
−0.469956 + 0.882690i 0.655730π0.655730\pi
164164 0 0
165165 −10.7251 −0.834947
166166 0 0
167167 −6.00000 −0.464294 −0.232147 0.972681i 0.574575π-0.574575\pi
−0.232147 + 0.972681i 0.574575π0.574575\pi
168168 0 0
169169 26.3746 2.02881
170170 0 0
171171 −6.27492 −0.479855
172172 0 0
173173 −22.5498 −1.71443 −0.857216 0.514957i 0.827808π-0.827808\pi
−0.857216 + 0.514957i 0.827808π0.827808\pi
174174 0 0
175175 0 0
176176 0 0
177177 1.27492 0.0958286
178178 0 0
179179 −16.5498 −1.23699 −0.618496 0.785788i 0.712258π-0.712258\pi
−0.618496 + 0.785788i 0.712258π0.712258\pi
180180 0 0
181181 −18.8248 −1.39923 −0.699616 0.714519i 0.746646π-0.746646\pi
−0.699616 + 0.714519i 0.746646π0.746646\pi
182182 0 0
183183 −10.0000 −0.739221
184184 0 0
185185 −7.45017 −0.547747
186186 0 0
187187 −13.0997 −0.957943
188188 0 0
189189 0 0
190190 0 0
191191 4.54983 0.329214 0.164607 0.986359i 0.447364π-0.447364\pi
0.164607 + 0.986359i 0.447364π0.447364\pi
192192 0 0
193193 0.450166 0.0324036 0.0162018 0.999869i 0.494843π-0.494843\pi
0.0162018 + 0.999869i 0.494843π0.494843\pi
194194 0 0
195195 −20.5498 −1.47160
196196 0 0
197197 −1.45017 −0.103320 −0.0516600 0.998665i 0.516451π-0.516451\pi
−0.0516600 + 0.998665i 0.516451π0.516451\pi
198198 0 0
199199 −5.09967 −0.361506 −0.180753 0.983529i 0.557853π-0.557853\pi
−0.180753 + 0.983529i 0.557853π0.557853\pi
200200 0 0
201201 0.274917 0.0193912
202202 0 0
203203 0 0
204204 0 0
205205 −14.9003 −1.04068
206206 0 0
207207 4.00000 0.278019
208208 0 0
209209 −20.5498 −1.42146
210210 0 0
211211 −27.6495 −1.90347 −0.951735 0.306921i 0.900701π-0.900701\pi
−0.951735 + 0.306921i 0.900701π0.900701\pi
212212 0 0
213213 −2.00000 −0.137038
214214 0 0
215215 0.900331 0.0614021
216216 0 0
217217 0 0
218218 0 0
219219 4.27492 0.288872
220220 0 0
221221 −25.0997 −1.68839
222222 0 0
223223 −1.27492 −0.0853748 −0.0426874 0.999088i 0.513592π-0.513592\pi
−0.0426874 + 0.999088i 0.513592π0.513592\pi
224224 0 0
225225 5.72508 0.381672
226226 0 0
227227 −11.2749 −0.748343 −0.374171 0.927360i 0.622073π-0.622073\pi
−0.374171 + 0.927360i 0.622073π0.622073\pi
228228 0 0
229229 18.2749 1.20764 0.603820 0.797121i 0.293644π-0.293644\pi
0.603820 + 0.797121i 0.293644π0.293644\pi
230230 0 0
231231 0 0
232232 0 0
233233 −0.549834 −0.0360209 −0.0180104 0.999838i 0.505733π-0.505733\pi
−0.0180104 + 0.999838i 0.505733π0.505733\pi
234234 0 0
235235 −19.6495 −1.28179
236236 0 0
237237 −11.5498 −0.750242
238238 0 0
239239 15.4502 0.999388 0.499694 0.866202i 0.333446π-0.333446\pi
0.499694 + 0.866202i 0.333446π0.333446\pi
240240 0 0
241241 9.82475 0.632868 0.316434 0.948615i 0.397514π-0.397514\pi
0.316434 + 0.948615i 0.397514π0.397514\pi
242242 0 0
243243 −1.00000 −0.0641500
244244 0 0
245245 0 0
246246 0 0
247247 −39.3746 −2.50534
248248 0 0
249249 −7.27492 −0.461029
250250 0 0
251251 −18.3746 −1.15979 −0.579897 0.814690i 0.696907π-0.696907\pi
−0.579897 + 0.814690i 0.696907π0.696907\pi
252252 0 0
253253 13.0997 0.823569
254254 0 0
255255 13.0997 0.820333
256256 0 0
257257 11.0997 0.692378 0.346189 0.938165i 0.387476π-0.387476\pi
0.346189 + 0.938165i 0.387476π0.387476\pi
258258 0 0
259259 0 0
260260 0 0
261261 5.27492 0.326509
262262 0 0
263263 −9.45017 −0.582722 −0.291361 0.956613i 0.594108π-0.594108\pi
−0.291361 + 0.956613i 0.594108π0.594108\pi
264264 0 0
265265 30.3746 1.86590
266266 0 0
267267 10.5498 0.645639
268268 0 0
269269 20.7251 1.26363 0.631815 0.775119i 0.282310π-0.282310\pi
0.631815 + 0.775119i 0.282310π0.282310\pi
270270 0 0
271271 1.27492 0.0774457 0.0387229 0.999250i 0.487671π-0.487671\pi
0.0387229 + 0.999250i 0.487671π0.487671\pi
272272 0 0
273273 0 0
274274 0 0
275275 18.7492 1.13062
276276 0 0
277277 −26.8248 −1.61174 −0.805872 0.592090i 0.798303π-0.798303\pi
−0.805872 + 0.592090i 0.798303π0.798303\pi
278278 0 0
279279 −1.00000 −0.0598684
280280 0 0
281281 −26.5498 −1.58383 −0.791915 0.610631i 0.790916π-0.790916\pi
−0.791915 + 0.610631i 0.790916π0.790916\pi
282282 0 0
283283 −25.9244 −1.54105 −0.770523 0.637412i 0.780005π-0.780005\pi
−0.770523 + 0.637412i 0.780005π0.780005\pi
284284 0 0
285285 20.5498 1.21727
286286 0 0
287287 0 0
288288 0 0
289289 −1.00000 −0.0588235
290290 0 0
291291 −8.72508 −0.511473
292292 0 0
293293 −27.8248 −1.62554 −0.812770 0.582585i 0.802041π-0.802041\pi
−0.812770 + 0.582585i 0.802041π0.802041\pi
294294 0 0
295295 −4.17525 −0.243092
296296 0 0
297297 −3.27492 −0.190030
298298 0 0
299299 25.0997 1.45155
300300 0 0
301301 0 0
302302 0 0
303303 6.00000 0.344691
304304 0 0
305305 32.7492 1.87521
306306 0 0
307307 11.3746 0.649182 0.324591 0.945854i 0.394773π-0.394773\pi
0.324591 + 0.945854i 0.394773π0.394773\pi
308308 0 0
309309 −10.8248 −0.615799
310310 0 0
311311 −4.54983 −0.257997 −0.128999 0.991645i 0.541176π-0.541176\pi
−0.128999 + 0.991645i 0.541176π0.541176\pi
312312 0 0
313313 −19.5498 −1.10502 −0.552511 0.833506i 0.686330π-0.686330\pi
−0.552511 + 0.833506i 0.686330π0.686330\pi
314314 0 0
315315 0 0
316316 0 0
317317 −27.8248 −1.56279 −0.781397 0.624034i 0.785493π-0.785493\pi
−0.781397 + 0.624034i 0.785493π0.785493\pi
318318 0 0
319319 17.2749 0.967210
320320 0 0
321321 15.8248 0.883252
322322 0 0
323323 25.0997 1.39658
324324 0 0
325325 35.9244 1.99273
326326 0 0
327327 −16.8248 −0.930411
328328 0 0
329329 0 0
330330 0 0
331331 1.17525 0.0645975 0.0322987 0.999478i 0.489717π-0.489717\pi
0.0322987 + 0.999478i 0.489717π0.489717\pi
332332 0 0
333333 −2.27492 −0.124665
334334 0 0
335335 −0.900331 −0.0491903
336336 0 0
337337 −24.0997 −1.31279 −0.656396 0.754416i 0.727920π-0.727920\pi
−0.656396 + 0.754416i 0.727920π0.727920\pi
338338 0 0
339339 4.54983 0.247113
340340 0 0
341341 −3.27492 −0.177347
342342 0 0
343343 0 0
344344 0 0
345345 −13.0997 −0.705262
346346 0 0
347347 30.1993 1.62119 0.810593 0.585610i 0.199145π-0.199145\pi
0.810593 + 0.585610i 0.199145π0.199145\pi
348348 0 0
349349 −6.00000 −0.321173 −0.160586 0.987022i 0.551338π-0.551338\pi
−0.160586 + 0.987022i 0.551338π0.551338\pi
350350 0 0
351351 −6.27492 −0.334930
352352 0 0
353353 −20.5498 −1.09376 −0.546879 0.837212i 0.684184π-0.684184\pi
−0.546879 + 0.837212i 0.684184π0.684184\pi
354354 0 0
355355 6.54983 0.347629
356356 0 0
357357 0 0
358358 0 0
359359 −19.6495 −1.03706 −0.518531 0.855059i 0.673521π-0.673521\pi
−0.518531 + 0.855059i 0.673521π0.673521\pi
360360 0 0
361361 20.3746 1.07235
362362 0 0
363363 0.274917 0.0144294
364364 0 0
365365 −14.0000 −0.732793
366366 0 0
367367 22.0997 1.15359 0.576797 0.816888i 0.304302π-0.304302\pi
0.576797 + 0.816888i 0.304302π0.304302\pi
368368 0 0
369369 −4.54983 −0.236855
370370 0 0
371371 0 0
372372 0 0
373373 −6.27492 −0.324903 −0.162451 0.986717i 0.551940π-0.551940\pi
−0.162451 + 0.986717i 0.551940π0.551940\pi
374374 0 0
375375 −2.37459 −0.122623
376376 0 0
377377 33.0997 1.70472
378378 0 0
379379 13.1752 0.676767 0.338384 0.941008i 0.390120π-0.390120\pi
0.338384 + 0.941008i 0.390120π0.390120\pi
380380 0 0
381381 6.45017 0.330452
382382 0 0
383383 10.5498 0.539071 0.269536 0.962990i 0.413130π-0.413130\pi
0.269536 + 0.962990i 0.413130π0.413130\pi
384384 0 0
385385 0 0
386386 0 0
387387 0.274917 0.0139748
388388 0 0
389389 −2.00000 −0.101404 −0.0507020 0.998714i 0.516146π-0.516146\pi
−0.0507020 + 0.998714i 0.516146π0.516146\pi
390390 0 0
391391 −16.0000 −0.809155
392392 0 0
393393 −7.27492 −0.366971
394394 0 0
395395 37.8248 1.90317
396396 0 0
397397 −3.37459 −0.169366 −0.0846828 0.996408i 0.526988π-0.526988\pi
−0.0846828 + 0.996408i 0.526988π0.526988\pi
398398 0 0
399399 0 0
400400 0 0
401401 24.0000 1.19850 0.599251 0.800561i 0.295465π-0.295465\pi
0.599251 + 0.800561i 0.295465π0.295465\pi
402402 0 0
403403 −6.27492 −0.312576
404404 0 0
405405 3.27492 0.162732
406406 0 0
407407 −7.45017 −0.369291
408408 0 0
409409 10.4502 0.516727 0.258364 0.966048i 0.416817π-0.416817\pi
0.258364 + 0.966048i 0.416817π0.416817\pi
410410 0 0
411411 −1.45017 −0.0715314
412412 0 0
413413 0 0
414414 0 0
415415 23.8248 1.16951
416416 0 0
417417 −8.27492 −0.405224
418418 0 0
419419 28.5498 1.39475 0.697375 0.716706i 0.254351π-0.254351\pi
0.697375 + 0.716706i 0.254351π0.254351\pi
420420 0 0
421421 8.82475 0.430092 0.215046 0.976604i 0.431010π-0.431010\pi
0.215046 + 0.976604i 0.431010π0.431010\pi
422422 0 0
423423 −6.00000 −0.291730
424424 0 0
425425 −22.9003 −1.11083
426426 0 0
427427 0 0
428428 0 0
429429 −20.5498 −0.992155
430430 0 0
431431 −17.6495 −0.850147 −0.425073 0.905159i 0.639752π-0.639752\pi
−0.425073 + 0.905159i 0.639752π0.639752\pi
432432 0 0
433433 3.17525 0.152593 0.0762963 0.997085i 0.475690π-0.475690\pi
0.0762963 + 0.997085i 0.475690π0.475690\pi
434434 0 0
435435 −17.2749 −0.828269
436436 0 0
437437 −25.0997 −1.20068
438438 0 0
439439 17.2749 0.824487 0.412243 0.911074i 0.364745π-0.364745\pi
0.412243 + 0.911074i 0.364745π0.364745\pi
440440 0 0
441441 0 0
442442 0 0
443443 −6.37459 −0.302866 −0.151433 0.988468i 0.548389π-0.548389\pi
−0.151433 + 0.988468i 0.548389π0.548389\pi
444444 0 0
445445 −34.5498 −1.63782
446446 0 0
447447 14.5498 0.688184
448448 0 0
449449 20.5498 0.969807 0.484903 0.874568i 0.338855π-0.338855\pi
0.484903 + 0.874568i 0.338855π0.338855\pi
450450 0 0
451451 −14.9003 −0.701629
452452 0 0
453453 −22.3746 −1.05125
454454 0 0
455455 0 0
456456 0 0
457457 36.6495 1.71439 0.857196 0.514991i 0.172205π-0.172205\pi
0.857196 + 0.514991i 0.172205π0.172205\pi
458458 0 0
459459 4.00000 0.186704
460460 0 0
461461 −3.64950 −0.169974 −0.0849872 0.996382i 0.527085π-0.527085\pi
−0.0849872 + 0.996382i 0.527085π0.527085\pi
462462 0 0
463463 13.1752 0.612306 0.306153 0.951982i 0.400958π-0.400958\pi
0.306153 + 0.951982i 0.400958π0.400958\pi
464464 0 0
465465 3.27492 0.151871
466466 0 0
467467 40.5498 1.87642 0.938211 0.346063i 0.112482π-0.112482\pi
0.938211 + 0.346063i 0.112482π0.112482\pi
468468 0 0
469469 0 0
470470 0 0
471471 0.549834 0.0253350
472472 0 0
473473 0.900331 0.0413973
474474 0 0
475475 −35.9244 −1.64833
476476 0 0
477477 9.27492 0.424669
478478 0 0
479479 −5.45017 −0.249024 −0.124512 0.992218i 0.539737π-0.539737\pi
−0.124512 + 0.992218i 0.539737π0.539737\pi
480480 0 0
481481 −14.2749 −0.650880
482482 0 0
483483 0 0
484484 0 0
485485 28.5739 1.29748
486486 0 0
487487 1.00000 0.0453143 0.0226572 0.999743i 0.492787π-0.492787\pi
0.0226572 + 0.999743i 0.492787π0.492787\pi
488488 0 0
489489 12.0000 0.542659
490490 0 0
491491 36.9244 1.66638 0.833188 0.552990i 0.186513π-0.186513\pi
0.833188 + 0.552990i 0.186513π0.186513\pi
492492 0 0
493493 −21.0997 −0.950281
494494 0 0
495495 10.7251 0.482057
496496 0 0
497497 0 0
498498 0 0
499499 32.2749 1.44482 0.722412 0.691463i 0.243034π-0.243034\pi
0.722412 + 0.691463i 0.243034π0.243034\pi
500500 0 0
501501 6.00000 0.268060
502502 0 0
503503 −37.6495 −1.67871 −0.839354 0.543585i 0.817067π-0.817067\pi
−0.839354 + 0.543585i 0.817067π0.817067\pi
504504 0 0
505505 −19.6495 −0.874391
506506 0 0
507507 −26.3746 −1.17134
508508 0 0
509509 −11.2749 −0.499752 −0.249876 0.968278i 0.580390π-0.580390\pi
−0.249876 + 0.968278i 0.580390π0.580390\pi
510510 0 0
511511 0 0
512512 0 0
513513 6.27492 0.277044
514514 0 0
515515 35.4502 1.56212
516516 0 0
517517 −19.6495 −0.864184
518518 0 0
519519 22.5498 0.989828
520520 0 0
521521 −14.5498 −0.637440 −0.318720 0.947849i 0.603253π-0.603253\pi
−0.318720 + 0.947849i 0.603253π0.603253\pi
522522 0 0
523523 −17.7251 −0.775064 −0.387532 0.921856i 0.626672π-0.626672\pi
−0.387532 + 0.921856i 0.626672π0.626672\pi
524524 0 0
525525 0 0
526526 0 0
527527 4.00000 0.174243
528528 0 0
529529 −7.00000 −0.304348
530530 0 0
531531 −1.27492 −0.0553267
532532 0 0
533533 −28.5498 −1.23663
534534 0 0
535535 −51.8248 −2.24058
536536 0 0
537537 16.5498 0.714178
538538 0 0
539539 0 0
540540 0 0
541541 −8.27492 −0.355766 −0.177883 0.984052i 0.556925π-0.556925\pi
−0.177883 + 0.984052i 0.556925π0.556925\pi
542542 0 0
543543 18.8248 0.807847
544544 0 0
545545 55.0997 2.36021
546546 0 0
547547 −28.0000 −1.19719 −0.598597 0.801050i 0.704275π-0.704275\pi
−0.598597 + 0.801050i 0.704275π0.704275\pi
548548 0 0
549549 10.0000 0.426790
550550 0 0
551551 −33.0997 −1.41009
552552 0 0
553553 0 0
554554 0 0
555555 7.45017 0.316242
556556 0 0
557557 −29.8248 −1.26372 −0.631858 0.775084i 0.717707π-0.717707\pi
−0.631858 + 0.775084i 0.717707π0.717707\pi
558558 0 0
559559 1.72508 0.0729632
560560 0 0
561561 13.0997 0.553068
562562 0 0
563563 15.2749 0.643761 0.321881 0.946780i 0.395685π-0.395685\pi
0.321881 + 0.946780i 0.395685π0.395685\pi
564564 0 0
565565 −14.9003 −0.626862
566566 0 0
567567 0 0
568568 0 0
569569 11.4502 0.480016 0.240008 0.970771i 0.422850π-0.422850\pi
0.240008 + 0.970771i 0.422850π0.422850\pi
570570 0 0
571571 8.27492 0.346295 0.173147 0.984896i 0.444606π-0.444606\pi
0.173147 + 0.984896i 0.444606π0.444606\pi
572572 0 0
573573 −4.54983 −0.190072
574574 0 0
575575 22.9003 0.955010
576576 0 0
577577 −25.0000 −1.04076 −0.520382 0.853934i 0.674210π-0.674210\pi
−0.520382 + 0.853934i 0.674210π0.674210\pi
578578 0 0
579579 −0.450166 −0.0187082
580580 0 0
581581 0 0
582582 0 0
583583 30.3746 1.25799
584584 0 0
585585 20.5498 0.849631
586586 0 0
587587 9.27492 0.382817 0.191408 0.981510i 0.438695π-0.438695\pi
0.191408 + 0.981510i 0.438695π0.438695\pi
588588 0 0
589589 6.27492 0.258553
590590 0 0
591591 1.45017 0.0596518
592592 0 0
593593 −0.549834 −0.0225790 −0.0112895 0.999936i 0.503594π-0.503594\pi
−0.0112895 + 0.999936i 0.503594π0.503594\pi
594594 0 0
595595 0 0
596596 0 0
597597 5.09967 0.208716
598598 0 0
599599 22.5498 0.921361 0.460681 0.887566i 0.347605π-0.347605\pi
0.460681 + 0.887566i 0.347605π0.347605\pi
600600 0 0
601601 4.09967 0.167229 0.0836145 0.996498i 0.473354π-0.473354\pi
0.0836145 + 0.996498i 0.473354π0.473354\pi
602602 0 0
603603 −0.274917 −0.0111955
604604 0 0
605605 −0.900331 −0.0366037
606606 0 0
607607 −7.00000 −0.284121 −0.142061 0.989858i 0.545373π-0.545373\pi
−0.142061 + 0.989858i 0.545373π0.545373\pi
608608 0 0
609609 0 0
610610 0 0
611611 −37.6495 −1.52314
612612 0 0
613613 −8.54983 −0.345325 −0.172662 0.984981i 0.555237π-0.555237\pi
−0.172662 + 0.984981i 0.555237π0.555237\pi
614614 0 0
615615 14.9003 0.600839
616616 0 0
617617 −6.00000 −0.241551 −0.120775 0.992680i 0.538538π-0.538538\pi
−0.120775 + 0.992680i 0.538538π0.538538\pi
618618 0 0
619619 28.8248 1.15856 0.579282 0.815127i 0.303333π-0.303333\pi
0.579282 + 0.815127i 0.303333π0.303333\pi
620620 0 0
621621 −4.00000 −0.160514
622622 0 0
623623 0 0
624624 0 0
625625 −20.8488 −0.833954
626626 0 0
627627 20.5498 0.820681
628628 0 0
629629 9.09967 0.362828
630630 0 0
631631 19.8248 0.789211 0.394605 0.918851i 0.370881π-0.370881\pi
0.394605 + 0.918851i 0.370881π0.370881\pi
632632 0 0
633633 27.6495 1.09897
634634 0 0
635635 −21.1238 −0.838271
636636 0 0
637637 0 0
638638 0 0
639639 2.00000 0.0791188
640640 0 0
641641 −3.64950 −0.144147 −0.0720734 0.997399i 0.522962π-0.522962\pi
−0.0720734 + 0.997399i 0.522962π0.522962\pi
642642 0 0
643643 5.37459 0.211953 0.105976 0.994369i 0.466203π-0.466203\pi
0.105976 + 0.994369i 0.466203π0.466203\pi
644644 0 0
645645 −0.900331 −0.0354505
646646 0 0
647647 −34.0000 −1.33668 −0.668339 0.743857i 0.732994π-0.732994\pi
−0.668339 + 0.743857i 0.732994π0.732994\pi
648648 0 0
649649 −4.17525 −0.163893
650650 0 0
651651 0 0
652652 0 0
653653 −6.92442 −0.270974 −0.135487 0.990779i 0.543260π-0.543260\pi
−0.135487 + 0.990779i 0.543260π0.543260\pi
654654 0 0
655655 23.8248 0.930910
656656 0 0
657657 −4.27492 −0.166780
658658 0 0
659659 −42.1993 −1.64385 −0.821926 0.569594i 0.807101π-0.807101\pi
−0.821926 + 0.569594i 0.807101π0.807101\pi
660660 0 0
661661 7.17525 0.279085 0.139542 0.990216i 0.455437π-0.455437\pi
0.139542 + 0.990216i 0.455437π0.455437\pi
662662 0 0
663663 25.0997 0.974790
664664 0 0
665665 0 0
666666 0 0
667667 21.0997 0.816982
668668 0 0
669669 1.27492 0.0492911
670670 0 0
671671 32.7492 1.26427
672672 0 0
673673 41.5498 1.60163 0.800814 0.598913i 0.204400π-0.204400\pi
0.800814 + 0.598913i 0.204400π0.204400\pi
674674 0 0
675675 −5.72508 −0.220359
676676 0 0
677677 −13.2749 −0.510197 −0.255098 0.966915i 0.582108π-0.582108\pi
−0.255098 + 0.966915i 0.582108π0.582108\pi
678678 0 0
679679 0 0
680680 0 0
681681 11.2749 0.432056
682682 0 0
683683 12.1752 0.465873 0.232936 0.972492i 0.425167π-0.425167\pi
0.232936 + 0.972492i 0.425167π0.425167\pi
684684 0 0
685685 4.74917 0.181457
686686 0 0
687687 −18.2749 −0.697232
688688 0 0
689689 58.1993 2.21722
690690 0 0
691691 −10.8248 −0.411793 −0.205896 0.978574i 0.566011π-0.566011\pi
−0.205896 + 0.978574i 0.566011π0.566011\pi
692692 0 0
693693 0 0
694694 0 0
695695 27.0997 1.02795
696696 0 0
697697 18.1993 0.689349
698698 0 0
699699 0.549834 0.0207966
700700 0 0
701701 −12.9244 −0.488149 −0.244074 0.969757i 0.578484π-0.578484\pi
−0.244074 + 0.969757i 0.578484π0.578484\pi
702702 0 0
703703 14.2749 0.538389
704704 0 0
705705 19.6495 0.740043
706706 0 0
707707 0 0
708708 0 0
709709 −28.1993 −1.05905 −0.529524 0.848295i 0.677630π-0.677630\pi
−0.529524 + 0.848295i 0.677630π0.677630\pi
710710 0 0
711711 11.5498 0.433153
712712 0 0
713713 −4.00000 −0.149801
714714 0 0
715715 67.2990 2.51684
716716 0 0
717717 −15.4502 −0.576997
718718 0 0
719719 28.1993 1.05166 0.525829 0.850590i 0.323755π-0.323755\pi
0.525829 + 0.850590i 0.323755π0.323755\pi
720720 0 0
721721 0 0
722722 0 0
723723 −9.82475 −0.365386
724724 0 0
725725 30.1993 1.12158
726726 0 0
727727 31.5498 1.17012 0.585059 0.810991i 0.301071π-0.301071\pi
0.585059 + 0.810991i 0.301071π0.301071\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −1.09967 −0.0406727
732732 0 0
733733 5.92442 0.218823 0.109412 0.993997i 0.465103π-0.465103\pi
0.109412 + 0.993997i 0.465103π0.465103\pi
734734 0 0
735735 0 0
736736 0 0
737737 −0.900331 −0.0331641
738738 0 0
739739 1.37459 0.0505650 0.0252825 0.999680i 0.491951π-0.491951\pi
0.0252825 + 0.999680i 0.491951π0.491951\pi
740740 0 0
741741 39.3746 1.44646
742742 0 0
743743 −44.1993 −1.62152 −0.810758 0.585381i 0.800945π-0.800945\pi
−0.810758 + 0.585381i 0.800945π0.800945\pi
744744 0 0
745745 −47.6495 −1.74574
746746 0 0
747747 7.27492 0.266175
748748 0 0
749749 0 0
750750 0 0
751751 −10.4502 −0.381332 −0.190666 0.981655i 0.561065π-0.561065\pi
−0.190666 + 0.981655i 0.561065π0.561065\pi
752752 0 0
753753 18.3746 0.669607
754754 0 0
755755 73.2749 2.66675
756756 0 0
757757 −22.0000 −0.799604 −0.399802 0.916602i 0.630921π-0.630921\pi
−0.399802 + 0.916602i 0.630921π0.630921\pi
758758 0 0
759759 −13.0997 −0.475488
760760 0 0
761761 −25.0997 −0.909862 −0.454931 0.890527i 0.650336π-0.650336\pi
−0.454931 + 0.890527i 0.650336π0.650336\pi
762762 0 0
763763 0 0
764764 0 0
765765 −13.0997 −0.473620
766766 0 0
767767 −8.00000 −0.288863
768768 0 0
769769 −32.6495 −1.17737 −0.588686 0.808362i 0.700354π-0.700354\pi
−0.588686 + 0.808362i 0.700354π0.700354\pi
770770 0 0
771771 −11.0997 −0.399745
772772 0 0
773773 3.09967 0.111487 0.0557437 0.998445i 0.482247π-0.482247\pi
0.0557437 + 0.998445i 0.482247π0.482247\pi
774774 0 0
775775 −5.72508 −0.205651
776776 0 0
777777 0 0
778778 0 0
779779 28.5498 1.02290
780780 0 0
781781 6.54983 0.234372
782782 0 0
783783 −5.27492 −0.188510
784784 0 0
785785 −1.80066 −0.0642684
786786 0 0
787787 2.54983 0.0908918 0.0454459 0.998967i 0.485529π-0.485529\pi
0.0454459 + 0.998967i 0.485529π0.485529\pi
788788 0 0
789789 9.45017 0.336435
790790 0 0
791791 0 0
792792 0 0
793793 62.7492 2.22829
794794 0 0
795795 −30.3746 −1.07728
796796 0 0
797797 −31.4743 −1.11488 −0.557438 0.830219i 0.688215π-0.688215\pi
−0.557438 + 0.830219i 0.688215π0.688215\pi
798798 0 0
799799 24.0000 0.849059
800800 0 0
801801 −10.5498 −0.372760
802802 0 0
803803 −14.0000 −0.494049
804804 0 0
805805 0 0
806806 0 0
807807 −20.7251 −0.729557
808808 0 0
809809 −29.6495 −1.04242 −0.521211 0.853428i 0.674519π-0.674519\pi
−0.521211 + 0.853428i 0.674519π0.674519\pi
810810 0 0
811811 −42.5498 −1.49413 −0.747063 0.664753i 0.768537π-0.768537\pi
−0.747063 + 0.664753i 0.768537π0.768537\pi
812812 0 0
813813 −1.27492 −0.0447133
814814 0 0
815815 −39.2990 −1.37658
816816 0 0
817817 −1.72508 −0.0603530
818818 0 0
819819 0 0
820820 0 0
821821 12.7251 0.444108 0.222054 0.975034i 0.428724π-0.428724\pi
0.222054 + 0.975034i 0.428724π0.428724\pi
822822 0 0
823823 −34.1993 −1.19211 −0.596057 0.802942i 0.703267π-0.703267\pi
−0.596057 + 0.802942i 0.703267π0.703267\pi
824824 0 0
825825 −18.7492 −0.652762
826826 0 0
827827 −44.0241 −1.53087 −0.765434 0.643515i 0.777476π-0.777476\pi
−0.765434 + 0.643515i 0.777476π0.777476\pi
828828 0 0
829829 30.2749 1.05149 0.525746 0.850642i 0.323786π-0.323786\pi
0.525746 + 0.850642i 0.323786π0.323786\pi
830830 0 0
831831 26.8248 0.930540
832832 0 0
833833 0 0
834834 0 0
835835 −19.6495 −0.679999
836836 0 0
837837 1.00000 0.0345651
838838 0 0
839839 −30.1993 −1.04260 −0.521298 0.853374i 0.674552π-0.674552\pi
−0.521298 + 0.853374i 0.674552π0.674552\pi
840840 0 0
841841 −1.17525 −0.0405258
842842 0 0
843843 26.5498 0.914425
844844 0 0
845845 86.3746 2.97138
846846 0 0
847847 0 0
848848 0 0
849849 25.9244 0.889724
850850 0 0
851851 −9.09967 −0.311933
852852 0 0
853853 13.3746 0.457937 0.228969 0.973434i 0.426465π-0.426465\pi
0.228969 + 0.973434i 0.426465π0.426465\pi
854854 0 0
855855 −20.5498 −0.702790
856856 0 0
857857 −13.4502 −0.459449 −0.229724 0.973256i 0.573782π-0.573782\pi
−0.229724 + 0.973256i 0.573782π0.573782\pi
858858 0 0
859859 −55.6495 −1.89874 −0.949368 0.314165i 0.898275π-0.898275\pi
−0.949368 + 0.314165i 0.898275π0.898275\pi
860860 0 0
861861 0 0
862862 0 0
863863 19.0997 0.650160 0.325080 0.945686i 0.394609π-0.394609\pi
0.325080 + 0.945686i 0.394609π0.394609\pi
864864 0 0
865865 −73.8488 −2.51094
866866 0 0
867867 1.00000 0.0339618
868868 0 0
869869 37.8248 1.28312
870870 0 0
871871 −1.72508 −0.0584522
872872 0 0
873873 8.72508 0.295299
874874 0 0
875875 0 0
876876 0 0
877877 46.7492 1.57861 0.789304 0.614003i 0.210442π-0.210442\pi
0.789304 + 0.614003i 0.210442π0.210442\pi
878878 0 0
879879 27.8248 0.938506
880880 0 0
881881 9.45017 0.318384 0.159192 0.987248i 0.449111π-0.449111\pi
0.159192 + 0.987248i 0.449111π0.449111\pi
882882 0 0
883883 7.37459 0.248175 0.124087 0.992271i 0.460400π-0.460400\pi
0.124087 + 0.992271i 0.460400π0.460400\pi
884884 0 0
885885 4.17525 0.140349
886886 0 0
887887 33.6495 1.12984 0.564920 0.825146i 0.308907π-0.308907\pi
0.564920 + 0.825146i 0.308907π0.308907\pi
888888 0 0
889889 0 0
890890 0 0
891891 3.27492 0.109714
892892 0 0
893893 37.6495 1.25989
894894 0 0
895895 −54.1993 −1.81168
896896 0 0
897897 −25.0997 −0.838054
898898 0 0
899899 −5.27492 −0.175928
900900 0 0
901901 −37.0997 −1.23597
902902 0 0
903903 0 0
904904 0 0
905905 −61.6495 −2.04930
906906 0 0
907907 −29.7251 −0.987005 −0.493503 0.869744i 0.664284π-0.664284\pi
−0.493503 + 0.869744i 0.664284π0.664284\pi
908908 0 0
909909 −6.00000 −0.199007
910910 0 0
911911 53.8488 1.78409 0.892046 0.451945i 0.149270π-0.149270\pi
0.892046 + 0.451945i 0.149270π0.149270\pi
912912 0 0
913913 23.8248 0.788484
914914 0 0
915915 −32.7492 −1.08265
916916 0 0
917917 0 0
918918 0 0
919919 −2.82475 −0.0931800 −0.0465900 0.998914i 0.514835π-0.514835\pi
−0.0465900 + 0.998914i 0.514835π0.514835\pi
920920 0 0
921921 −11.3746 −0.374805
922922 0 0
923923 12.5498 0.413083
924924 0 0
925925 −13.0241 −0.428229
926926 0 0
927927 10.8248 0.355531
928928 0 0
929929 −40.1993 −1.31890 −0.659449 0.751750i 0.729210π-0.729210\pi
−0.659449 + 0.751750i 0.729210π0.729210\pi
930930 0 0
931931 0 0
932932 0 0
933933 4.54983 0.148955
934934 0 0
935935 −42.9003 −1.40299
936936 0 0
937937 −6.09967 −0.199267 −0.0996337 0.995024i 0.531767π-0.531767\pi
−0.0996337 + 0.995024i 0.531767π0.531767\pi
938938 0 0
939939 19.5498 0.637985
940940 0 0
941941 51.8248 1.68944 0.844719 0.535210i 0.179767π-0.179767\pi
0.844719 + 0.535210i 0.179767π0.179767\pi
942942 0 0
943943 −18.1993 −0.592652
944944 0 0
945945 0 0
946946 0 0
947947 −19.4502 −0.632045 −0.316023 0.948752i 0.602348π-0.602348\pi
−0.316023 + 0.948752i 0.602348π0.602348\pi
948948 0 0
949949 −26.8248 −0.870768
950950 0 0
951951 27.8248 0.902279
952952 0 0
953953 55.6495 1.80266 0.901332 0.433129i 0.142590π-0.142590\pi
0.901332 + 0.433129i 0.142590π0.142590\pi
954954 0 0
955955 14.9003 0.482163
956956 0 0
957957 −17.2749 −0.558419
958958 0 0
959959 0 0
960960 0 0
961961 −30.0000 −0.967742
962962 0 0
963963 −15.8248 −0.509945
964964 0 0
965965 1.47425 0.0474579
966966 0 0
967967 −53.5498 −1.72205 −0.861023 0.508566i 0.830176π-0.830176\pi
−0.861023 + 0.508566i 0.830176π0.830176\pi
968968 0 0
969969 −25.0997 −0.806318
970970 0 0
971971 56.5739 1.81554 0.907772 0.419464i 0.137782π-0.137782\pi
0.907772 + 0.419464i 0.137782π0.137782\pi
972972 0 0
973973 0 0
974974 0 0
975975 −35.9244 −1.15050
976976 0 0
977977 8.90033 0.284747 0.142373 0.989813i 0.454527π-0.454527\pi
0.142373 + 0.989813i 0.454527π0.454527\pi
978978 0 0
979979 −34.5498 −1.10422
980980 0 0
981981 16.8248 0.537173
982982 0 0
983983 39.2990 1.25344 0.626722 0.779243i 0.284396π-0.284396\pi
0.626722 + 0.779243i 0.284396π0.284396\pi
984984 0 0
985985 −4.74917 −0.151321
986986 0 0
987987 0 0
988988 0 0
989989 1.09967 0.0349674
990990 0 0
991991 −14.0997 −0.447891 −0.223945 0.974602i 0.571894π-0.571894\pi
−0.223945 + 0.974602i 0.571894π0.571894\pi
992992 0 0
993993 −1.17525 −0.0372954
994994 0 0
995995 −16.7010 −0.529457
996996 0 0
997997 −44.8248 −1.41961 −0.709807 0.704396i 0.751218π-0.751218\pi
−0.709807 + 0.704396i 0.751218π0.751218\pi
998998 0 0
999999 2.27492 0.0719752
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 1176.2.a.k.1.2 2
3.2 odd 2 3528.2.a.bk.1.1 2
4.3 odd 2 2352.2.a.bf.1.2 2
7.2 even 3 168.2.q.c.25.1 4
7.3 odd 6 1176.2.q.l.961.2 4
7.4 even 3 168.2.q.c.121.1 yes 4
7.5 odd 6 1176.2.q.l.361.2 4
7.6 odd 2 1176.2.a.n.1.1 2
8.3 odd 2 9408.2.a.dp.1.1 2
8.5 even 2 9408.2.a.ec.1.1 2
12.11 even 2 7056.2.a.cu.1.1 2
21.2 odd 6 504.2.s.i.361.2 4
21.5 even 6 3528.2.s.bk.361.1 4
21.11 odd 6 504.2.s.i.289.2 4
21.17 even 6 3528.2.s.bk.3313.1 4
21.20 even 2 3528.2.a.bd.1.2 2
28.3 even 6 2352.2.q.bf.961.2 4
28.11 odd 6 336.2.q.g.289.1 4
28.19 even 6 2352.2.q.bf.1537.2 4
28.23 odd 6 336.2.q.g.193.1 4
28.27 even 2 2352.2.a.ba.1.1 2
56.11 odd 6 1344.2.q.x.961.2 4
56.13 odd 2 9408.2.a.dj.1.2 2
56.27 even 2 9408.2.a.dw.1.2 2
56.37 even 6 1344.2.q.w.193.2 4
56.51 odd 6 1344.2.q.x.193.2 4
56.53 even 6 1344.2.q.w.961.2 4
84.11 even 6 1008.2.s.r.289.2 4
84.23 even 6 1008.2.s.r.865.2 4
84.83 odd 2 7056.2.a.ch.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.2.q.c.25.1 4 7.2 even 3
168.2.q.c.121.1 yes 4 7.4 even 3
336.2.q.g.193.1 4 28.23 odd 6
336.2.q.g.289.1 4 28.11 odd 6
504.2.s.i.289.2 4 21.11 odd 6
504.2.s.i.361.2 4 21.2 odd 6
1008.2.s.r.289.2 4 84.11 even 6
1008.2.s.r.865.2 4 84.23 even 6
1176.2.a.k.1.2 2 1.1 even 1 trivial
1176.2.a.n.1.1 2 7.6 odd 2
1176.2.q.l.361.2 4 7.5 odd 6
1176.2.q.l.961.2 4 7.3 odd 6
1344.2.q.w.193.2 4 56.37 even 6
1344.2.q.w.961.2 4 56.53 even 6
1344.2.q.x.193.2 4 56.51 odd 6
1344.2.q.x.961.2 4 56.11 odd 6
2352.2.a.ba.1.1 2 28.27 even 2
2352.2.a.bf.1.2 2 4.3 odd 2
2352.2.q.bf.961.2 4 28.3 even 6
2352.2.q.bf.1537.2 4 28.19 even 6
3528.2.a.bd.1.2 2 21.20 even 2
3528.2.a.bk.1.1 2 3.2 odd 2
3528.2.s.bk.361.1 4 21.5 even 6
3528.2.s.bk.3313.1 4 21.17 even 6
7056.2.a.ch.1.2 2 84.83 odd 2
7056.2.a.cu.1.1 2 12.11 even 2
9408.2.a.dj.1.2 2 56.13 odd 2
9408.2.a.dp.1.1 2 8.3 odd 2
9408.2.a.dw.1.2 2 56.27 even 2
9408.2.a.ec.1.1 2 8.5 even 2