Properties

Label 10000.2.a.bj.1.5
Level 1000010000
Weight 22
Character 10000.1
Self dual yes
Analytic conductor 79.85079.850
Analytic rank 11
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [10000,2,Mod(1,10000)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10000, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("10000.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 10000=2454 10000 = 2^{4} \cdot 5^{4}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 10000.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: 79.850402021379.8504020213
Analytic rank: 11
Dimension: 88
Coefficient field: 8.8.14884000000.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x811x6+36x431x2+1 x^{8} - 11x^{6} + 36x^{4} - 31x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 25)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 2.30927-2.30927 of defining polynomial
Character χ\chi == 10000.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+0.474903q3+3.03582q72.77447q92.00000q11+1.42721q131.86025q170.903319q19+1.44172q213.32932q232.74231q27+3.96307q29+6.43997q310.949806q333.82022q37+0.677786q391.83422q413.59445q434.79995q47+2.21619q490.883436q51+9.50473q530.428989q5710.6456q59+14.2742q618.42278q6310.6902q671.58111q6912.4598q710.267631q736.07163q77+8.57176q79+7.02107q8112.6182q83+1.88207q874.76796q89+4.33275q91+3.05836q93+9.95805q97+5.54893q99+O(q100)q+0.474903 q^{3} +3.03582 q^{7} -2.77447 q^{9} -2.00000 q^{11} +1.42721 q^{13} -1.86025 q^{17} -0.903319 q^{19} +1.44172 q^{21} -3.32932 q^{23} -2.74231 q^{27} +3.96307 q^{29} +6.43997 q^{31} -0.949806 q^{33} -3.82022 q^{37} +0.677786 q^{39} -1.83422 q^{41} -3.59445 q^{43} -4.79995 q^{47} +2.21619 q^{49} -0.883436 q^{51} +9.50473 q^{53} -0.428989 q^{57} -10.6456 q^{59} +14.2742 q^{61} -8.42278 q^{63} -10.6902 q^{67} -1.58111 q^{69} -12.4598 q^{71} -0.267631 q^{73} -6.07163 q^{77} +8.57176 q^{79} +7.02107 q^{81} -12.6182 q^{83} +1.88207 q^{87} -4.76796 q^{89} +4.33275 q^{91} +3.05836 q^{93} +9.95805 q^{97} +5.54893 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+4q916q1110q19+6q21+20q2916q3118q39+26q4114q49+4q5130q59+6q61+8q6946q7110q7932q81+30q89+8q99+O(q100) 8 q + 4 q^{9} - 16 q^{11} - 10 q^{19} + 6 q^{21} + 20 q^{29} - 16 q^{31} - 18 q^{39} + 26 q^{41} - 14 q^{49} + 4 q^{51} - 30 q^{59} + 6 q^{61} + 8 q^{69} - 46 q^{71} - 10 q^{79} - 32 q^{81} + 30 q^{89}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.474903 0.274185 0.137093 0.990558i 0.456224π-0.456224\pi
0.137093 + 0.990558i 0.456224π0.456224\pi
44 0 0
55 0 0
66 0 0
77 3.03582 1.14743 0.573716 0.819055i 0.305502π-0.305502\pi
0.573716 + 0.819055i 0.305502π0.305502\pi
88 0 0
99 −2.77447 −0.924822
1010 0 0
1111 −2.00000 −0.603023 −0.301511 0.953463i 0.597491π-0.597491\pi
−0.301511 + 0.953463i 0.597491π0.597491\pi
1212 0 0
1313 1.42721 0.395837 0.197918 0.980218i 0.436582π-0.436582\pi
0.197918 + 0.980218i 0.436582π0.436582\pi
1414 0 0
1515 0 0
1616 0 0
1717 −1.86025 −0.451176 −0.225588 0.974223i 0.572430π-0.572430\pi
−0.225588 + 0.974223i 0.572430π0.572430\pi
1818 0 0
1919 −0.903319 −0.207236 −0.103618 0.994617i 0.533042π-0.533042\pi
−0.103618 + 0.994617i 0.533042π0.533042\pi
2020 0 0
2121 1.44172 0.314609
2222 0 0
2323 −3.32932 −0.694212 −0.347106 0.937826i 0.612836π-0.612836\pi
−0.347106 + 0.937826i 0.612836π0.612836\pi
2424 0 0
2525 0 0
2626 0 0
2727 −2.74231 −0.527758
2828 0 0
2929 3.96307 0.735924 0.367962 0.929841i 0.380056π-0.380056\pi
0.367962 + 0.929841i 0.380056π0.380056\pi
3030 0 0
3131 6.43997 1.15665 0.578326 0.815806i 0.303706π-0.303706\pi
0.578326 + 0.815806i 0.303706π0.303706\pi
3232 0 0
3333 −0.949806 −0.165340
3434 0 0
3535 0 0
3636 0 0
3737 −3.82022 −0.628040 −0.314020 0.949416i 0.601676π-0.601676\pi
−0.314020 + 0.949416i 0.601676π0.601676\pi
3838 0 0
3939 0.677786 0.108533
4040 0 0
4141 −1.83422 −0.286457 −0.143228 0.989690i 0.545748π-0.545748\pi
−0.143228 + 0.989690i 0.545748π0.545748\pi
4242 0 0
4343 −3.59445 −0.548149 −0.274074 0.961708i 0.588371π-0.588371\pi
−0.274074 + 0.961708i 0.588371π0.588371\pi
4444 0 0
4545 0 0
4646 0 0
4747 −4.79995 −0.700144 −0.350072 0.936723i 0.613843π-0.613843\pi
−0.350072 + 0.936723i 0.613843π0.613843\pi
4848 0 0
4949 2.21619 0.316598
5050 0 0
5151 −0.883436 −0.123706
5252 0 0
5353 9.50473 1.30558 0.652788 0.757541i 0.273599π-0.273599\pi
0.652788 + 0.757541i 0.273599π0.273599\pi
5454 0 0
5555 0 0
5656 0 0
5757 −0.428989 −0.0568209
5858 0 0
5959 −10.6456 −1.38594 −0.692971 0.720966i 0.743698π-0.743698\pi
−0.692971 + 0.720966i 0.743698π0.743698\pi
6060 0 0
6161 14.2742 1.82762 0.913811 0.406140i 0.133125π-0.133125\pi
0.913811 + 0.406140i 0.133125π0.133125\pi
6262 0 0
6363 −8.42278 −1.06117
6464 0 0
6565 0 0
6666 0 0
6767 −10.6902 −1.30601 −0.653007 0.757352i 0.726493π-0.726493\pi
−0.653007 + 0.757352i 0.726493π0.726493\pi
6868 0 0
6969 −1.58111 −0.190343
7070 0 0
7171 −12.4598 −1.47871 −0.739356 0.673315i 0.764870π-0.764870\pi
−0.739356 + 0.673315i 0.764870π0.764870\pi
7272 0 0
7373 −0.267631 −0.0313239 −0.0156619 0.999877i 0.504986π-0.504986\pi
−0.0156619 + 0.999877i 0.504986π0.504986\pi
7474 0 0
7575 0 0
7676 0 0
7777 −6.07163 −0.691927
7878 0 0
7979 8.57176 0.964398 0.482199 0.876062i 0.339838π-0.339838\pi
0.482199 + 0.876062i 0.339838π0.339838\pi
8080 0 0
8181 7.02107 0.780119
8282 0 0
8383 −12.6182 −1.38502 −0.692512 0.721406i 0.743496π-0.743496\pi
−0.692512 + 0.721406i 0.743496π0.743496\pi
8484 0 0
8585 0 0
8686 0 0
8787 1.88207 0.201779
8888 0 0
8989 −4.76796 −0.505402 −0.252701 0.967544i 0.581319π-0.581319\pi
−0.252701 + 0.967544i 0.581319π0.581319\pi
9090 0 0
9191 4.33275 0.454196
9292 0 0
9393 3.05836 0.317137
9494 0 0
9595 0 0
9696 0 0
9797 9.95805 1.01109 0.505543 0.862801i 0.331292π-0.331292\pi
0.505543 + 0.862801i 0.331292π0.331292\pi
9898 0 0
9999 5.54893 0.557689
100100 0 0
101101 9.34612 0.929974 0.464987 0.885318i 0.346059π-0.346059\pi
0.464987 + 0.885318i 0.346059π0.346059\pi
102102 0 0
103103 9.08408 0.895081 0.447540 0.894264i 0.352300π-0.352300\pi
0.447540 + 0.894264i 0.352300π0.352300\pi
104104 0 0
105105 0 0
106106 0 0
107107 5.62871 0.544148 0.272074 0.962276i 0.412290π-0.412290\pi
0.272074 + 0.962276i 0.412290π0.412290\pi
108108 0 0
109109 −10.1130 −0.968649 −0.484325 0.874888i 0.660935π-0.660935\pi
−0.484325 + 0.874888i 0.660935π0.660935\pi
110110 0 0
111111 −1.81423 −0.172199
112112 0 0
113113 −10.7120 −1.00770 −0.503851 0.863791i 0.668084π-0.668084\pi
−0.503851 + 0.863791i 0.668084π0.668084\pi
114114 0 0
115115 0 0
116116 0 0
117117 −3.95975 −0.366079
118118 0 0
119119 −5.64737 −0.517693
120120 0 0
121121 −7.00000 −0.636364
122122 0 0
123123 −0.871076 −0.0785423
124124 0 0
125125 0 0
126126 0 0
127127 −11.3609 −1.00812 −0.504060 0.863669i 0.668161π-0.668161\pi
−0.504060 + 0.863669i 0.668161π0.668161\pi
128128 0 0
129129 −1.70702 −0.150294
130130 0 0
131131 −7.98771 −0.697890 −0.348945 0.937143i 0.613460π-0.613460\pi
−0.348945 + 0.937143i 0.613460π0.613460\pi
132132 0 0
133133 −2.74231 −0.237789
134134 0 0
135135 0 0
136136 0 0
137137 −9.33726 −0.797736 −0.398868 0.917008i 0.630597π-0.630597\pi
−0.398868 + 0.917008i 0.630597π0.630597\pi
138138 0 0
139139 −17.9150 −1.51953 −0.759767 0.650195i 0.774687π-0.774687\pi
−0.759767 + 0.650195i 0.774687π0.774687\pi
140140 0 0
141141 −2.27951 −0.191969
142142 0 0
143143 −2.85442 −0.238699
144144 0 0
145145 0 0
146146 0 0
147147 1.05247 0.0868065
148148 0 0
149149 −6.31395 −0.517259 −0.258629 0.965977i 0.583271π-0.583271\pi
−0.258629 + 0.965977i 0.583271π0.583271\pi
150150 0 0
151151 −4.71947 −0.384065 −0.192033 0.981389i 0.561508π-0.561508\pi
−0.192033 + 0.981389i 0.561508π0.561508\pi
152152 0 0
153153 5.16119 0.417258
154154 0 0
155155 0 0
156156 0 0
157157 −1.46908 −0.117245 −0.0586225 0.998280i 0.518671π-0.518671\pi
−0.0586225 + 0.998280i 0.518671π0.518671\pi
158158 0 0
159159 4.51382 0.357969
160160 0 0
161161 −10.1072 −0.796560
162162 0 0
163163 4.45969 0.349310 0.174655 0.984630i 0.444119π-0.444119\pi
0.174655 + 0.984630i 0.444119π0.444119\pi
164164 0 0
165165 0 0
166166 0 0
167167 10.4337 0.807381 0.403691 0.914896i 0.367727π-0.367727\pi
0.403691 + 0.914896i 0.367727π0.367727\pi
168168 0 0
169169 −10.9631 −0.843313
170170 0 0
171171 2.50623 0.191656
172172 0 0
173173 7.67619 0.583610 0.291805 0.956478i 0.405744π-0.405744\pi
0.291805 + 0.956478i 0.405744π0.405744\pi
174174 0 0
175175 0 0
176176 0 0
177177 −5.05563 −0.380005
178178 0 0
179179 −15.5168 −1.15978 −0.579889 0.814696i 0.696904π-0.696904\pi
−0.579889 + 0.814696i 0.696904π0.696904\pi
180180 0 0
181181 −1.59056 −0.118225 −0.0591126 0.998251i 0.518827π-0.518827\pi
−0.0591126 + 0.998251i 0.518827π0.518827\pi
182182 0 0
183183 6.77885 0.501107
184184 0 0
185185 0 0
186186 0 0
187187 3.72049 0.272069
188188 0 0
189189 −8.32515 −0.605566
190190 0 0
191191 −19.6684 −1.42316 −0.711579 0.702606i 0.752020π-0.752020\pi
−0.711579 + 0.702606i 0.752020π0.752020\pi
192192 0 0
193193 −13.1100 −0.943680 −0.471840 0.881684i 0.656410π-0.656410\pi
−0.471840 + 0.881684i 0.656410π0.656410\pi
194194 0 0
195195 0 0
196196 0 0
197197 3.42949 0.244341 0.122170 0.992509i 0.461015π-0.461015\pi
0.122170 + 0.992509i 0.461015π0.461015\pi
198198 0 0
199199 −17.6959 −1.25443 −0.627215 0.778846i 0.715805π-0.715805\pi
−0.627215 + 0.778846i 0.715805π0.715805\pi
200200 0 0
201201 −5.07680 −0.358090
202202 0 0
203203 12.0312 0.844422
204204 0 0
205205 0 0
206206 0 0
207207 9.23710 0.642023
208208 0 0
209209 1.80664 0.124968
210210 0 0
211211 3.24366 0.223303 0.111651 0.993747i 0.464386π-0.464386\pi
0.111651 + 0.993747i 0.464386π0.464386\pi
212212 0 0
213213 −5.91722 −0.405441
214214 0 0
215215 0 0
216216 0 0
217217 19.5506 1.32718
218218 0 0
219219 −0.127099 −0.00858854
220220 0 0
221221 −2.65496 −0.178592
222222 0 0
223223 28.7148 1.92288 0.961441 0.275010i 0.0886812π-0.0886812\pi
0.961441 + 0.275010i 0.0886812π0.0886812\pi
224224 0 0
225225 0 0
226226 0 0
227227 11.7206 0.777926 0.388963 0.921253i 0.372833π-0.372833\pi
0.388963 + 0.921253i 0.372833π0.372833\pi
228228 0 0
229229 −16.4013 −1.08383 −0.541914 0.840434i 0.682300π-0.682300\pi
−0.541914 + 0.840434i 0.682300π0.682300\pi
230230 0 0
231231 −2.88344 −0.189716
232232 0 0
233233 −22.5146 −1.47498 −0.737490 0.675358i 0.763989π-0.763989\pi
−0.737490 + 0.675358i 0.763989π0.763989\pi
234234 0 0
235235 0 0
236236 0 0
237237 4.07075 0.264424
238238 0 0
239239 6.63333 0.429074 0.214537 0.976716i 0.431176π-0.431176\pi
0.214537 + 0.976716i 0.431176π0.431176\pi
240240 0 0
241241 26.2261 1.68937 0.844684 0.535265i 0.179788π-0.179788\pi
0.844684 + 0.535265i 0.179788π0.179788\pi
242242 0 0
243243 11.5613 0.741655
244244 0 0
245245 0 0
246246 0 0
247247 −1.28923 −0.0820315
248248 0 0
249249 −5.99241 −0.379753
250250 0 0
251251 10.9121 0.688766 0.344383 0.938829i 0.388088π-0.388088\pi
0.344383 + 0.938829i 0.388088π0.388088\pi
252252 0 0
253253 6.65865 0.418626
254254 0 0
255255 0 0
256256 0 0
257257 −6.58051 −0.410481 −0.205240 0.978712i 0.565798π-0.565798\pi
−0.205240 + 0.978712i 0.565798π0.565798\pi
258258 0 0
259259 −11.5975 −0.720632
260260 0 0
261261 −10.9954 −0.680599
262262 0 0
263263 −27.1073 −1.67151 −0.835753 0.549106i 0.814968π-0.814968\pi
−0.835753 + 0.549106i 0.814968π0.814968\pi
264264 0 0
265265 0 0
266266 0 0
267267 −2.26432 −0.138574
268268 0 0
269269 1.00945 0.0615474 0.0307737 0.999526i 0.490203π-0.490203\pi
0.0307737 + 0.999526i 0.490203π0.490203\pi
270270 0 0
271271 −6.25203 −0.379784 −0.189892 0.981805i 0.560814π-0.560814\pi
−0.189892 + 0.981805i 0.560814π0.560814\pi
272272 0 0
273273 2.05763 0.124534
274274 0 0
275275 0 0
276276 0 0
277277 24.6703 1.48230 0.741148 0.671342i 0.234282π-0.234282\pi
0.741148 + 0.671342i 0.234282π0.234282\pi
278278 0 0
279279 −17.8675 −1.06970
280280 0 0
281281 1.83891 0.109700 0.0548502 0.998495i 0.482532π-0.482532\pi
0.0548502 + 0.998495i 0.482532π0.482532\pi
282282 0 0
283283 −8.64116 −0.513664 −0.256832 0.966456i 0.582679π-0.582679\pi
−0.256832 + 0.966456i 0.582679π0.582679\pi
284284 0 0
285285 0 0
286286 0 0
287287 −5.56835 −0.328690
288288 0 0
289289 −13.5395 −0.796440
290290 0 0
291291 4.72910 0.277225
292292 0 0
293293 −6.29156 −0.367557 −0.183779 0.982968i 0.558833π-0.558833\pi
−0.183779 + 0.982968i 0.558833π0.558833\pi
294294 0 0
295295 0 0
296296 0 0
297297 5.48462 0.318250
298298 0 0
299299 −4.75164 −0.274795
300300 0 0
301301 −10.9121 −0.628963
302302 0 0
303303 4.43850 0.254985
304304 0 0
305305 0 0
306306 0 0
307307 −28.6661 −1.63606 −0.818030 0.575175i 0.804934π-0.804934\pi
−0.818030 + 0.575175i 0.804934π0.804934\pi
308308 0 0
309309 4.31405 0.245418
310310 0 0
311311 7.83649 0.444367 0.222183 0.975005i 0.428682π-0.428682\pi
0.222183 + 0.975005i 0.428682π0.428682\pi
312312 0 0
313313 −21.4093 −1.21012 −0.605061 0.796179i 0.706851π-0.706851\pi
−0.605061 + 0.796179i 0.706851π0.706851\pi
314314 0 0
315315 0 0
316316 0 0
317317 −4.01983 −0.225776 −0.112888 0.993608i 0.536010π-0.536010\pi
−0.112888 + 0.993608i 0.536010π0.536010\pi
318318 0 0
319319 −7.92614 −0.443779
320320 0 0
321321 2.67309 0.149197
322322 0 0
323323 1.68040 0.0934997
324324 0 0
325325 0 0
326326 0 0
327327 −4.80269 −0.265589
328328 0 0
329329 −14.5718 −0.803367
330330 0 0
331331 −11.6439 −0.640005 −0.320002 0.947417i 0.603684π-0.603684\pi
−0.320002 + 0.947417i 0.603684π0.603684\pi
332332 0 0
333333 10.5991 0.580825
334334 0 0
335335 0 0
336336 0 0
337337 21.5348 1.17307 0.586537 0.809922i 0.300491π-0.300491\pi
0.586537 + 0.809922i 0.300491π0.300491\pi
338338 0 0
339339 −5.08716 −0.276297
340340 0 0
341341 −12.8799 −0.697487
342342 0 0
343343 −14.5228 −0.784157
344344 0 0
345345 0 0
346346 0 0
347347 15.5972 0.837303 0.418652 0.908147i 0.362503π-0.362503\pi
0.418652 + 0.908147i 0.362503π0.362503\pi
348348 0 0
349349 5.56598 0.297940 0.148970 0.988842i 0.452404π-0.452404\pi
0.148970 + 0.988842i 0.452404π0.452404\pi
350350 0 0
351351 −3.91385 −0.208906
352352 0 0
353353 −8.02216 −0.426977 −0.213488 0.976946i 0.568483π-0.568483\pi
−0.213488 + 0.976946i 0.568483π0.568483\pi
354354 0 0
355355 0 0
356356 0 0
357357 −2.68195 −0.141944
358358 0 0
359359 12.3427 0.651424 0.325712 0.945469i 0.394396π-0.394396\pi
0.325712 + 0.945469i 0.394396π0.394396\pi
360360 0 0
361361 −18.1840 −0.957053
362362 0 0
363363 −3.32432 −0.174482
364364 0 0
365365 0 0
366366 0 0
367367 26.8749 1.40286 0.701430 0.712738i 0.252545π-0.252545\pi
0.701430 + 0.712738i 0.252545π0.252545\pi
368368 0 0
369369 5.08898 0.264922
370370 0 0
371371 28.8546 1.49806
372372 0 0
373373 27.6389 1.43109 0.715544 0.698567i 0.246179π-0.246179\pi
0.715544 + 0.698567i 0.246179π0.246179\pi
374374 0 0
375375 0 0
376376 0 0
377377 5.65614 0.291306
378378 0 0
379379 3.47462 0.178479 0.0892397 0.996010i 0.471556π-0.471556\pi
0.0892397 + 0.996010i 0.471556π0.471556\pi
380380 0 0
381381 −5.39534 −0.276412
382382 0 0
383383 27.3719 1.39864 0.699319 0.714810i 0.253487π-0.253487\pi
0.699319 + 0.714810i 0.253487π0.253487\pi
384384 0 0
385385 0 0
386386 0 0
387387 9.97269 0.506940
388388 0 0
389389 10.8845 0.551867 0.275934 0.961177i 0.411013π-0.411013\pi
0.275934 + 0.961177i 0.411013π0.411013\pi
390390 0 0
391391 6.19336 0.313212
392392 0 0
393393 −3.79339 −0.191351
394394 0 0
395395 0 0
396396 0 0
397397 −16.2212 −0.814120 −0.407060 0.913401i 0.633446π-0.633446\pi
−0.407060 + 0.913401i 0.633446π0.633446\pi
398398 0 0
399399 −1.30233 −0.0651981
400400 0 0
401401 3.78686 0.189107 0.0945534 0.995520i 0.469858π-0.469858\pi
0.0945534 + 0.995520i 0.469858π0.469858\pi
402402 0 0
403403 9.19118 0.457845
404404 0 0
405405 0 0
406406 0 0
407407 7.64044 0.378722
408408 0 0
409409 1.85585 0.0917661 0.0458831 0.998947i 0.485390π-0.485390\pi
0.0458831 + 0.998947i 0.485390π0.485390\pi
410410 0 0
411411 −4.43429 −0.218728
412412 0 0
413413 −32.3181 −1.59027
414414 0 0
415415 0 0
416416 0 0
417417 −8.50790 −0.416634
418418 0 0
419419 −14.3472 −0.700907 −0.350453 0.936580i 0.613972π-0.613972\pi
−0.350453 + 0.936580i 0.613972π0.613972\pi
420420 0 0
421421 15.4545 0.753207 0.376604 0.926374i 0.377092π-0.377092\pi
0.376604 + 0.926374i 0.377092π0.377092\pi
422422 0 0
423423 13.3173 0.647509
424424 0 0
425425 0 0
426426 0 0
427427 43.3338 2.09707
428428 0 0
429429 −1.35557 −0.0654477
430430 0 0
431431 −12.5043 −0.602311 −0.301156 0.953575i 0.597372π-0.597372\pi
−0.301156 + 0.953575i 0.597372π0.597372\pi
432432 0 0
433433 22.4951 1.08105 0.540524 0.841329i 0.318226π-0.318226\pi
0.540524 + 0.841329i 0.318226π0.318226\pi
434434 0 0
435435 0 0
436436 0 0
437437 3.00744 0.143865
438438 0 0
439439 −12.1776 −0.581204 −0.290602 0.956844i 0.593855π-0.593855\pi
−0.290602 + 0.956844i 0.593855π0.593855\pi
440440 0 0
441441 −6.14873 −0.292797
442442 0 0
443443 −20.7101 −0.983968 −0.491984 0.870604i 0.663728π-0.663728\pi
−0.491984 + 0.870604i 0.663728π0.663728\pi
444444 0 0
445445 0 0
446446 0 0
447447 −2.99851 −0.141825
448448 0 0
449449 −25.9539 −1.22484 −0.612420 0.790533i 0.709804π-0.709804\pi
−0.612420 + 0.790533i 0.709804π0.709804\pi
450450 0 0
451451 3.66844 0.172740
452452 0 0
453453 −2.24129 −0.105305
454454 0 0
455455 0 0
456456 0 0
457457 8.50150 0.397684 0.198842 0.980032i 0.436282π-0.436282\pi
0.198842 + 0.980032i 0.436282π0.436282\pi
458458 0 0
459459 5.10137 0.238112
460460 0 0
461461 14.7851 0.688609 0.344305 0.938858i 0.388115π-0.388115\pi
0.344305 + 0.938858i 0.388115π0.388115\pi
462462 0 0
463463 −22.1921 −1.03135 −0.515677 0.856783i 0.672460π-0.672460\pi
−0.515677 + 0.856783i 0.672460π0.672460\pi
464464 0 0
465465 0 0
466466 0 0
467467 −28.5014 −1.31889 −0.659443 0.751754i 0.729208π-0.729208\pi
−0.659443 + 0.751754i 0.729208π0.729208\pi
468468 0 0
469469 −32.4534 −1.49856
470470 0 0
471471 −0.697669 −0.0321469
472472 0 0
473473 7.18891 0.330546
474474 0 0
475475 0 0
476476 0 0
477477 −26.3706 −1.20743
478478 0 0
479479 −25.0569 −1.14488 −0.572440 0.819947i 0.694003π-0.694003\pi
−0.572440 + 0.819947i 0.694003π0.694003\pi
480480 0 0
481481 −5.45225 −0.248601
482482 0 0
483483 −4.79995 −0.218405
484484 0 0
485485 0 0
486486 0 0
487487 −1.46479 −0.0663758 −0.0331879 0.999449i 0.510566π-0.510566\pi
−0.0331879 + 0.999449i 0.510566π0.510566\pi
488488 0 0
489489 2.11792 0.0957757
490490 0 0
491491 20.0686 0.905685 0.452843 0.891591i 0.350410π-0.350410\pi
0.452843 + 0.891591i 0.350410π0.350410\pi
492492 0 0
493493 −7.37229 −0.332031
494494 0 0
495495 0 0
496496 0 0
497497 −37.8258 −1.69672
498498 0 0
499499 −0.624999 −0.0279788 −0.0139894 0.999902i 0.504453π-0.504453\pi
−0.0139894 + 0.999902i 0.504453π0.504453\pi
500500 0 0
501501 4.95498 0.221372
502502 0 0
503503 −19.3052 −0.860776 −0.430388 0.902644i 0.641623π-0.641623\pi
−0.430388 + 0.902644i 0.641623π0.641623\pi
504504 0 0
505505 0 0
506506 0 0
507507 −5.20639 −0.231224
508508 0 0
509509 −10.5202 −0.466298 −0.233149 0.972441i 0.574903π-0.574903\pi
−0.233149 + 0.972441i 0.574903π0.574903\pi
510510 0 0
511511 −0.812479 −0.0359420
512512 0 0
513513 2.47718 0.109370
514514 0 0
515515 0 0
516516 0 0
517517 9.59989 0.422203
518518 0 0
519519 3.64545 0.160017
520520 0 0
521521 −10.0070 −0.438413 −0.219207 0.975678i 0.570347π-0.570347\pi
−0.219207 + 0.975678i 0.570347π0.570347\pi
522522 0 0
523523 22.7830 0.996233 0.498117 0.867110i 0.334025π-0.334025\pi
0.498117 + 0.867110i 0.334025π0.334025\pi
524524 0 0
525525 0 0
526526 0 0
527527 −11.9799 −0.521854
528528 0 0
529529 −11.9156 −0.518070
530530 0 0
531531 29.5359 1.28175
532532 0 0
533533 −2.61782 −0.113390
534534 0 0
535535 0 0
536536 0 0
537537 −7.36896 −0.317994
538538 0 0
539539 −4.43237 −0.190916
540540 0 0
541541 3.25900 0.140115 0.0700576 0.997543i 0.477682π-0.477682\pi
0.0700576 + 0.997543i 0.477682π0.477682\pi
542542 0 0
543543 −0.755360 −0.0324156
544544 0 0
545545 0 0
546546 0 0
547547 −13.5883 −0.580993 −0.290497 0.956876i 0.593821π-0.593821\pi
−0.290497 + 0.956876i 0.593821π0.593821\pi
548548 0 0
549549 −39.6033 −1.69023
550550 0 0
551551 −3.57992 −0.152510
552552 0 0
553553 26.0223 1.10658
554554 0 0
555555 0 0
556556 0 0
557557 27.6399 1.17114 0.585571 0.810621i 0.300870π-0.300870\pi
0.585571 + 0.810621i 0.300870π0.300870\pi
558558 0 0
559559 −5.13004 −0.216978
560560 0 0
561561 1.76687 0.0745974
562562 0 0
563563 −1.65925 −0.0699291 −0.0349646 0.999389i 0.511132π-0.511132\pi
−0.0349646 + 0.999389i 0.511132π0.511132\pi
564564 0 0
565565 0 0
566566 0 0
567567 21.3147 0.895133
568568 0 0
569569 17.8828 0.749686 0.374843 0.927088i 0.377697π-0.377697\pi
0.374843 + 0.927088i 0.377697π0.377697\pi
570570 0 0
571571 36.8723 1.54306 0.771530 0.636193i 0.219492π-0.219492\pi
0.771530 + 0.636193i 0.219492π0.219492\pi
572572 0 0
573573 −9.34060 −0.390209
574574 0 0
575575 0 0
576576 0 0
577577 22.8137 0.949746 0.474873 0.880054i 0.342494π-0.342494\pi
0.474873 + 0.880054i 0.342494π0.342494\pi
578578 0 0
579579 −6.22599 −0.258743
580580 0 0
581581 −38.3065 −1.58922
582582 0 0
583583 −19.0095 −0.787291
584584 0 0
585585 0 0
586586 0 0
587587 −11.0855 −0.457546 −0.228773 0.973480i 0.573471π-0.573471\pi
−0.228773 + 0.973480i 0.573471π0.573471\pi
588588 0 0
589589 −5.81734 −0.239699
590590 0 0
591591 1.62867 0.0669947
592592 0 0
593593 −11.1321 −0.457139 −0.228570 0.973528i 0.573405π-0.573405\pi
−0.228570 + 0.973528i 0.573405π0.573405\pi
594594 0 0
595595 0 0
596596 0 0
597597 −8.40384 −0.343946
598598 0 0
599599 −36.2736 −1.48210 −0.741049 0.671451i 0.765671π-0.765671\pi
−0.741049 + 0.671451i 0.765671π0.765671\pi
600600 0 0
601601 −15.1051 −0.616150 −0.308075 0.951362i 0.599685π-0.599685\pi
−0.308075 + 0.951362i 0.599685π0.599685\pi
602602 0 0
603603 29.6596 1.20783
604604 0 0
605605 0 0
606606 0 0
607607 −33.5066 −1.35999 −0.679996 0.733216i 0.738018π-0.738018\pi
−0.679996 + 0.733216i 0.738018π0.738018\pi
608608 0 0
609609 5.71363 0.231528
610610 0 0
611611 −6.85053 −0.277143
612612 0 0
613613 28.0289 1.13208 0.566038 0.824379i 0.308476π-0.308476\pi
0.566038 + 0.824379i 0.308476π0.308476\pi
614614 0 0
615615 0 0
616616 0 0
617617 −30.5223 −1.22878 −0.614391 0.789002i 0.710598π-0.710598\pi
−0.614391 + 0.789002i 0.710598π0.710598\pi
618618 0 0
619619 21.6971 0.872080 0.436040 0.899927i 0.356381π-0.356381\pi
0.436040 + 0.899927i 0.356381π0.356381\pi
620620 0 0
621621 9.13004 0.366376
622622 0 0
623623 −14.4746 −0.579914
624624 0 0
625625 0 0
626626 0 0
627627 0.857977 0.0342643
628628 0 0
629629 7.10655 0.283357
630630 0 0
631631 16.2277 0.646015 0.323007 0.946396i 0.395306π-0.395306\pi
0.323007 + 0.946396i 0.395306π0.395306\pi
632632 0 0
633633 1.54042 0.0612264
634634 0 0
635635 0 0
636636 0 0
637637 3.16296 0.125321
638638 0 0
639639 34.5694 1.36755
640640 0 0
641641 −22.1774 −0.875956 −0.437978 0.898986i 0.644305π-0.644305\pi
−0.437978 + 0.898986i 0.644305π0.644305\pi
642642 0 0
643643 −13.2767 −0.523583 −0.261792 0.965124i 0.584313π-0.584313\pi
−0.261792 + 0.965124i 0.584313π0.584313\pi
644644 0 0
645645 0 0
646646 0 0
647647 −11.2853 −0.443671 −0.221835 0.975084i 0.571205π-0.571205\pi
−0.221835 + 0.975084i 0.571205π0.571205\pi
648648 0 0
649649 21.2912 0.835754
650650 0 0
651651 9.28462 0.363893
652652 0 0
653653 35.8134 1.40149 0.700743 0.713414i 0.252852π-0.252852\pi
0.700743 + 0.713414i 0.252852π0.252852\pi
654654 0 0
655655 0 0
656656 0 0
657657 0.742534 0.0289690
658658 0 0
659659 −39.7655 −1.54905 −0.774523 0.632546i 0.782010π-0.782010\pi
−0.774523 + 0.632546i 0.782010π0.782010\pi
660660 0 0
661661 −6.24734 −0.242993 −0.121497 0.992592i 0.538769π-0.538769\pi
−0.121497 + 0.992592i 0.538769π0.538769\pi
662662 0 0
663663 −1.26085 −0.0489673
664664 0 0
665665 0 0
666666 0 0
667667 −13.1943 −0.510887
668668 0 0
669669 13.6367 0.527226
670670 0 0
671671 −28.5484 −1.10210
672672 0 0
673673 41.4627 1.59827 0.799135 0.601151i 0.205291π-0.205291\pi
0.799135 + 0.601151i 0.205291π0.205291\pi
674674 0 0
675675 0 0
676676 0 0
677677 1.43915 0.0553112 0.0276556 0.999618i 0.491196π-0.491196\pi
0.0276556 + 0.999618i 0.491196π0.491196\pi
678678 0 0
679679 30.2308 1.16015
680680 0 0
681681 5.56616 0.213296
682682 0 0
683683 −8.48623 −0.324716 −0.162358 0.986732i 0.551910π-0.551910\pi
−0.162358 + 0.986732i 0.551910π0.551910\pi
684684 0 0
685685 0 0
686686 0 0
687687 −7.78902 −0.297170
688688 0 0
689689 13.5652 0.516795
690690 0 0
691691 43.7797 1.66546 0.832730 0.553679i 0.186777π-0.186777\pi
0.832730 + 0.553679i 0.186777π0.186777\pi
692692 0 0
693693 16.8456 0.639910
694694 0 0
695695 0 0
696696 0 0
697697 3.41210 0.129243
698698 0 0
699699 −10.6922 −0.404418
700700 0 0
701701 0.840795 0.0317564 0.0158782 0.999874i 0.494946π-0.494946\pi
0.0158782 + 0.999874i 0.494946π0.494946\pi
702702 0 0
703703 3.45087 0.130152
704704 0 0
705705 0 0
706706 0 0
707707 28.3731 1.06708
708708 0 0
709709 −13.3812 −0.502543 −0.251271 0.967917i 0.580849π-0.580849\pi
−0.251271 + 0.967917i 0.580849π0.580849\pi
710710 0 0
711711 −23.7821 −0.891897
712712 0 0
713713 −21.4407 −0.802962
714714 0 0
715715 0 0
716716 0 0
717717 3.15019 0.117646
718718 0 0
719719 −43.4148 −1.61910 −0.809550 0.587051i 0.800289π-0.800289\pi
−0.809550 + 0.587051i 0.800289π0.800289\pi
720720 0 0
721721 27.5776 1.02704
722722 0 0
723723 12.4548 0.463200
724724 0 0
725725 0 0
726726 0 0
727727 −32.0480 −1.18859 −0.594297 0.804245i 0.702570π-0.702570\pi
−0.594297 + 0.804245i 0.702570π0.702570\pi
728728 0 0
729729 −15.5727 −0.576768
730730 0 0
731731 6.68657 0.247312
732732 0 0
733733 −8.13928 −0.300631 −0.150316 0.988638i 0.548029π-0.548029\pi
−0.150316 + 0.988638i 0.548029π0.548029\pi
734734 0 0
735735 0 0
736736 0 0
737737 21.3804 0.787556
738738 0 0
739739 7.12714 0.262176 0.131088 0.991371i 0.458153π-0.458153\pi
0.131088 + 0.991371i 0.458153π0.458153\pi
740740 0 0
741741 −0.612257 −0.0224918
742742 0 0
743743 21.9040 0.803578 0.401789 0.915732i 0.368388π-0.368388\pi
0.401789 + 0.915732i 0.368388π0.368388\pi
744744 0 0
745745 0 0
746746 0 0
747747 35.0087 1.28090
748748 0 0
749749 17.0877 0.624373
750750 0 0
751751 −9.21909 −0.336409 −0.168205 0.985752i 0.553797π-0.553797\pi
−0.168205 + 0.985752i 0.553797π0.553797\pi
752752 0 0
753753 5.18219 0.188849
754754 0 0
755755 0 0
756756 0 0
757757 −45.6524 −1.65926 −0.829632 0.558311i 0.811450π-0.811450\pi
−0.829632 + 0.558311i 0.811450π0.811450\pi
758758 0 0
759759 3.16221 0.114781
760760 0 0
761761 39.9058 1.44658 0.723291 0.690543i 0.242628π-0.242628\pi
0.723291 + 0.690543i 0.242628π0.242628\pi
762762 0 0
763763 −30.7012 −1.11146
764764 0 0
765765 0 0
766766 0 0
767767 −15.1935 −0.548607
768768 0 0
769769 −44.3420 −1.59901 −0.799506 0.600658i 0.794906π-0.794906\pi
−0.799506 + 0.600658i 0.794906π0.794906\pi
770770 0 0
771771 −3.12510 −0.112548
772772 0 0
773773 38.4944 1.38455 0.692273 0.721635i 0.256609π-0.256609\pi
0.692273 + 0.721635i 0.256609π0.256609\pi
774774 0 0
775775 0 0
776776 0 0
777777 −5.50768 −0.197587
778778 0 0
779779 1.65689 0.0593641
780780 0 0
781781 24.9197 0.891697
782782 0 0
783783 −10.8680 −0.388390
784784 0 0
785785 0 0
786786 0 0
787787 −53.0202 −1.88997 −0.944983 0.327120i 0.893922π-0.893922\pi
−0.944983 + 0.327120i 0.893922π0.893922\pi
788788 0 0
789789 −12.8733 −0.458302
790790 0 0
791791 −32.5197 −1.15627
792792 0 0
793793 20.3723 0.723440
794794 0 0
795795 0 0
796796 0 0
797797 12.6769 0.449037 0.224519 0.974470i 0.427919π-0.427919\pi
0.224519 + 0.974470i 0.427919π0.427919\pi
798798 0 0
799799 8.92908 0.315888
800800 0 0
801801 13.2285 0.467407
802802 0 0
803803 0.535262 0.0188890
804804 0 0
805805 0 0
806806 0 0
807807 0.479392 0.0168754
808808 0 0
809809 −41.8935 −1.47290 −0.736449 0.676493i 0.763499π-0.763499\pi
−0.736449 + 0.676493i 0.763499π0.763499\pi
810810 0 0
811811 34.5486 1.21317 0.606583 0.795020i 0.292540π-0.292540\pi
0.606583 + 0.795020i 0.292540π0.292540\pi
812812 0 0
813813 −2.96911 −0.104131
814814 0 0
815815 0 0
816816 0 0
817817 3.24694 0.113596
818818 0 0
819819 −12.0211 −0.420050
820820 0 0
821821 −21.1349 −0.737612 −0.368806 0.929506i 0.620233π-0.620233\pi
−0.368806 + 0.929506i 0.620233π0.620233\pi
822822 0 0
823823 3.17714 0.110748 0.0553740 0.998466i 0.482365π-0.482365\pi
0.0553740 + 0.998466i 0.482365π0.482365\pi
824824 0 0
825825 0 0
826826 0 0
827827 9.74482 0.338860 0.169430 0.985542i 0.445807π-0.445807\pi
0.169430 + 0.985542i 0.445807π0.445807\pi
828828 0 0
829829 23.4352 0.813938 0.406969 0.913442i 0.366586π-0.366586\pi
0.406969 + 0.913442i 0.366586π0.366586\pi
830830 0 0
831831 11.7160 0.406424
832832 0 0
833833 −4.12265 −0.142841
834834 0 0
835835 0 0
836836 0 0
837837 −17.6604 −0.610432
838838 0 0
839839 −42.6819 −1.47354 −0.736771 0.676142i 0.763650π-0.763650\pi
−0.736771 + 0.676142i 0.763650π0.763650\pi
840840 0 0
841841 −13.2941 −0.458416
842842 0 0
843843 0.873305 0.0300782
844844 0 0
845845 0 0
846846 0 0
847847 −21.2507 −0.730183
848848 0 0
849849 −4.10371 −0.140839
850850 0 0
851851 12.7187 0.435993
852852 0 0
853853 −16.9610 −0.580733 −0.290367 0.956915i 0.593777π-0.593777\pi
−0.290367 + 0.956915i 0.593777π0.593777\pi
854854 0 0
855855 0 0
856856 0 0
857857 39.3176 1.34306 0.671531 0.740976i 0.265637π-0.265637\pi
0.671531 + 0.740976i 0.265637π0.265637\pi
858858 0 0
859859 −0.707056 −0.0241244 −0.0120622 0.999927i 0.503840π-0.503840\pi
−0.0120622 + 0.999927i 0.503840π0.503840\pi
860860 0 0
861861 −2.64443 −0.0901219
862862 0 0
863863 0.909409 0.0309567 0.0154783 0.999880i 0.495073π-0.495073\pi
0.0154783 + 0.999880i 0.495073π0.495073\pi
864864 0 0
865865 0 0
866866 0 0
867867 −6.42994 −0.218372
868868 0 0
869869 −17.1435 −0.581554
870870 0 0
871871 −15.2571 −0.516968
872872 0 0
873873 −27.6283 −0.935075
874874 0 0
875875 0 0
876876 0 0
877877 −33.6613 −1.13666 −0.568331 0.822800i 0.692411π-0.692411\pi
−0.568331 + 0.822800i 0.692411π0.692411\pi
878878 0 0
879879 −2.98788 −0.100779
880880 0 0
881881 −19.9283 −0.671402 −0.335701 0.941969i 0.608973π-0.608973\pi
−0.335701 + 0.941969i 0.608973π0.608973\pi
882882 0 0
883883 15.6081 0.525255 0.262627 0.964897i 0.415411π-0.415411\pi
0.262627 + 0.964897i 0.415411π0.415411\pi
884884 0 0
885885 0 0
886886 0 0
887887 46.8968 1.57464 0.787320 0.616544i 0.211468π-0.211468\pi
0.787320 + 0.616544i 0.211468π0.211468\pi
888888 0 0
889889 −34.4897 −1.15675
890890 0 0
891891 −14.0421 −0.470429
892892 0 0
893893 4.33588 0.145095
894894 0 0
895895 0 0
896896 0 0
897897 −2.25657 −0.0753447
898898 0 0
899899 25.5220 0.851208
900900 0 0
901901 −17.6811 −0.589044
902902 0 0
903903 −5.18219 −0.172452
904904 0 0
905905 0 0
906906 0 0
907907 1.43447 0.0476308 0.0238154 0.999716i 0.492419π-0.492419\pi
0.0238154 + 0.999716i 0.492419π0.492419\pi
908908 0 0
909909 −25.9305 −0.860061
910910 0 0
911911 2.81129 0.0931422 0.0465711 0.998915i 0.485171π-0.485171\pi
0.0465711 + 0.998915i 0.485171π0.485171\pi
912912 0 0
913913 25.2363 0.835201
914914 0 0
915915 0 0
916916 0 0
917917 −24.2492 −0.800780
918918 0 0
919919 −0.992236 −0.0327308 −0.0163654 0.999866i 0.505210π-0.505210\pi
−0.0163654 + 0.999866i 0.505210π0.505210\pi
920920 0 0
921921 −13.6136 −0.448584
922922 0 0
923923 −17.7828 −0.585329
924924 0 0
925925 0 0
926926 0 0
927927 −25.2035 −0.827791
928928 0 0
929929 33.3227 1.09328 0.546642 0.837367i 0.315906π-0.315906\pi
0.546642 + 0.837367i 0.315906π0.315906\pi
930930 0 0
931931 −2.00192 −0.0656104
932932 0 0
933933 3.72157 0.121839
934934 0 0
935935 0 0
936936 0 0
937937 −13.3675 −0.436698 −0.218349 0.975871i 0.570067π-0.570067\pi
−0.218349 + 0.975871i 0.570067π0.570067\pi
938938 0 0
939939 −10.1673 −0.331798
940940 0 0
941941 −2.14982 −0.0700820 −0.0350410 0.999386i 0.511156π-0.511156\pi
−0.0350410 + 0.999386i 0.511156π0.511156\pi
942942 0 0
943943 6.10671 0.198862
944944 0 0
945945 0 0
946946 0 0
947947 34.9183 1.13469 0.567346 0.823479i 0.307970π-0.307970\pi
0.567346 + 0.823479i 0.307970π0.307970\pi
948948 0 0
949949 −0.381966 −0.0123991
950950 0 0
951951 −1.90903 −0.0619046
952952 0 0
953953 8.27883 0.268178 0.134089 0.990969i 0.457189π-0.457189\pi
0.134089 + 0.990969i 0.457189π0.457189\pi
954954 0 0
955955 0 0
956956 0 0
957957 −3.76415 −0.121678
958958 0 0
959959 −28.3462 −0.915347
960960 0 0
961961 10.4732 0.337844
962962 0 0
963963 −15.6167 −0.503241
964964 0 0
965965 0 0
966966 0 0
967967 29.4871 0.948241 0.474121 0.880460i 0.342766π-0.342766\pi
0.474121 + 0.880460i 0.342766π0.342766\pi
968968 0 0
969969 0.798025 0.0256363
970970 0 0
971971 −21.8666 −0.701733 −0.350867 0.936425i 0.614113π-0.614113\pi
−0.350867 + 0.936425i 0.614113π0.614113\pi
972972 0 0
973973 −54.3868 −1.74356
974974 0 0
975975 0 0
976976 0 0
977977 −13.8482 −0.443043 −0.221521 0.975155i 0.571102π-0.571102\pi
−0.221521 + 0.975155i 0.571102π0.571102\pi
978978 0 0
979979 9.53591 0.304769
980980 0 0
981981 28.0582 0.895828
982982 0 0
983983 2.93538 0.0936241 0.0468120 0.998904i 0.485094π-0.485094\pi
0.0468120 + 0.998904i 0.485094π0.485094\pi
984984 0 0
985985 0 0
986986 0 0
987987 −6.92017 −0.220271
988988 0 0
989989 11.9671 0.380531
990990 0 0
991991 −31.6137 −1.00424 −0.502122 0.864797i 0.667447π-0.667447\pi
−0.502122 + 0.864797i 0.667447π0.667447\pi
992992 0 0
993993 −5.52970 −0.175480
994994 0 0
995995 0 0
996996 0 0
997997 12.0885 0.382845 0.191423 0.981508i 0.438690π-0.438690\pi
0.191423 + 0.981508i 0.438690π0.438690\pi
998998 0 0
999999 10.4762 0.331453
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 10000.2.a.bj.1.5 8
4.3 odd 2 625.2.a.f.1.1 8
5.4 even 2 inner 10000.2.a.bj.1.4 8
12.11 even 2 5625.2.a.x.1.8 8
20.3 even 4 625.2.b.c.624.8 8
20.7 even 4 625.2.b.c.624.1 8
20.19 odd 2 625.2.a.f.1.8 8
25.8 odd 20 400.2.y.c.289.1 8
25.22 odd 20 400.2.y.c.209.1 8
60.59 even 2 5625.2.a.x.1.1 8
100.3 even 20 125.2.e.b.49.2 8
100.11 odd 10 625.2.d.o.501.1 16
100.19 odd 10 125.2.d.b.51.1 16
100.23 even 20 625.2.e.a.124.2 8
100.27 even 20 625.2.e.i.124.1 8
100.31 odd 10 125.2.d.b.51.4 16
100.39 odd 10 625.2.d.o.501.4 16
100.47 even 20 25.2.e.a.9.1 8
100.59 odd 10 625.2.d.o.126.4 16
100.63 even 20 625.2.e.i.499.1 8
100.67 even 20 125.2.e.b.74.2 8
100.71 odd 10 125.2.d.b.76.4 16
100.79 odd 10 125.2.d.b.76.1 16
100.83 even 20 25.2.e.a.14.1 yes 8
100.87 even 20 625.2.e.a.499.2 8
100.91 odd 10 625.2.d.o.126.1 16
300.47 odd 20 225.2.m.a.109.2 8
300.83 odd 20 225.2.m.a.64.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.2.e.a.9.1 8 100.47 even 20
25.2.e.a.14.1 yes 8 100.83 even 20
125.2.d.b.51.1 16 100.19 odd 10
125.2.d.b.51.4 16 100.31 odd 10
125.2.d.b.76.1 16 100.79 odd 10
125.2.d.b.76.4 16 100.71 odd 10
125.2.e.b.49.2 8 100.3 even 20
125.2.e.b.74.2 8 100.67 even 20
225.2.m.a.64.2 8 300.83 odd 20
225.2.m.a.109.2 8 300.47 odd 20
400.2.y.c.209.1 8 25.22 odd 20
400.2.y.c.289.1 8 25.8 odd 20
625.2.a.f.1.1 8 4.3 odd 2
625.2.a.f.1.8 8 20.19 odd 2
625.2.b.c.624.1 8 20.7 even 4
625.2.b.c.624.8 8 20.3 even 4
625.2.d.o.126.1 16 100.91 odd 10
625.2.d.o.126.4 16 100.59 odd 10
625.2.d.o.501.1 16 100.11 odd 10
625.2.d.o.501.4 16 100.39 odd 10
625.2.e.a.124.2 8 100.23 even 20
625.2.e.a.499.2 8 100.87 even 20
625.2.e.i.124.1 8 100.27 even 20
625.2.e.i.499.1 8 100.63 even 20
5625.2.a.x.1.1 8 60.59 even 2
5625.2.a.x.1.8 8 12.11 even 2
10000.2.a.bj.1.4 8 5.4 even 2 inner
10000.2.a.bj.1.5 8 1.1 even 1 trivial