Properties

Label 5202.2.a.bt.1.3
Level 52025202
Weight 22
Character 5202.1
Self dual yes
Analytic conductor 41.53841.538
Analytic rank 11
Dimension 44
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] = [5202,2,Mod(1,5202)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5202, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("5202.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 5202=232172 5202 = 2 \cdot 3^{2} \cdot 17^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 5202.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: 41.538179131541.5381791315
Analytic rank: 11
Dimension: 44
Coefficient field: Q(ζ16)+\Q(\zeta_{16})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x44x2+2 x^{4} - 4x^{2} + 2 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 102)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 0.7653670.765367 of defining polynomial
Character χ\chi == 5202.1

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) == q1.00000q2+1.00000q40.433546q5+3.41421q71.00000q8+0.433546q10+1.69552q110.331821q133.41421q14+1.00000q16+2.14386q190.433546q201.69552q221.88348q234.81204q25+0.331821q26+3.41421q288.53874q29+2.58579q311.00000q321.48022q3510.6143q372.14386q38+0.433546q4012.1177q4110.0933q43+1.69552q44+1.88348q462.38009q47+4.65685q49+4.81204q500.331821q52+3.13066q530.735084q553.41421q56+8.53874q58+7.67459q59+8.03988q612.58579q62+1.00000q64+0.143860q6515.7711q67+1.48022q700.226626q7112.1387q73+10.6143q74+2.14386q76+5.78886q77+12.5394q790.433546q80+12.1177q82+1.04373q83+10.0933q861.69552q8813.8281q891.13291q911.88348q92+2.38009q940.929461q953.75539q974.65685q98+O(q100)q-1.00000 q^{2} +1.00000 q^{4} -0.433546 q^{5} +3.41421 q^{7} -1.00000 q^{8} +0.433546 q^{10} +1.69552 q^{11} -0.331821 q^{13} -3.41421 q^{14} +1.00000 q^{16} +2.14386 q^{19} -0.433546 q^{20} -1.69552 q^{22} -1.88348 q^{23} -4.81204 q^{25} +0.331821 q^{26} +3.41421 q^{28} -8.53874 q^{29} +2.58579 q^{31} -1.00000 q^{32} -1.48022 q^{35} -10.6143 q^{37} -2.14386 q^{38} +0.433546 q^{40} -12.1177 q^{41} -10.0933 q^{43} +1.69552 q^{44} +1.88348 q^{46} -2.38009 q^{47} +4.65685 q^{49} +4.81204 q^{50} -0.331821 q^{52} +3.13066 q^{53} -0.735084 q^{55} -3.41421 q^{56} +8.53874 q^{58} +7.67459 q^{59} +8.03988 q^{61} -2.58579 q^{62} +1.00000 q^{64} +0.143860 q^{65} -15.7711 q^{67} +1.48022 q^{70} -0.226626 q^{71} -12.1387 q^{73} +10.6143 q^{74} +2.14386 q^{76} +5.78886 q^{77} +12.5394 q^{79} -0.433546 q^{80} +12.1177 q^{82} +1.04373 q^{83} +10.0933 q^{86} -1.69552 q^{88} -13.8281 q^{89} -1.13291 q^{91} -1.88348 q^{92} +2.38009 q^{94} -0.929461 q^{95} -3.75539 q^{97} -4.65685 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q2+4q4+8q74q88q118q14+4q168q19+8q228q234q25+8q288q29+16q314q32+8q35+8q37+8q388q41++4q98+O(q100) 4 q - 4 q^{2} + 4 q^{4} + 8 q^{7} - 4 q^{8} - 8 q^{11} - 8 q^{14} + 4 q^{16} - 8 q^{19} + 8 q^{22} - 8 q^{23} - 4 q^{25} + 8 q^{28} - 8 q^{29} + 16 q^{31} - 4 q^{32} + 8 q^{35} + 8 q^{37} + 8 q^{38} - 8 q^{41}+ \cdots + 4 q^{98}+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 −1.00000 −0.707107
33 0 0
44 1.00000 0.500000
55 −0.433546 −0.193887 −0.0969437 0.995290i 0.530907π-0.530907\pi
−0.0969437 + 0.995290i 0.530907π0.530907\pi
66 0 0
77 3.41421 1.29045 0.645226 0.763992i 0.276763π-0.276763\pi
0.645226 + 0.763992i 0.276763π0.276763\pi
88 −1.00000 −0.353553
99 0 0
1010 0.433546 0.137099
1111 1.69552 0.511218 0.255609 0.966780i 0.417724π-0.417724\pi
0.255609 + 0.966780i 0.417724π0.417724\pi
1212 0 0
1313 −0.331821 −0.0920307 −0.0460153 0.998941i 0.514652π-0.514652\pi
−0.0460153 + 0.998941i 0.514652π0.514652\pi
1414 −3.41421 −0.912487
1515 0 0
1616 1.00000 0.250000
1717 0 0
1818 0 0
1919 2.14386 0.491835 0.245918 0.969291i 0.420911π-0.420911\pi
0.245918 + 0.969291i 0.420911π0.420911\pi
2020 −0.433546 −0.0969437
2121 0 0
2222 −1.69552 −0.361486
2323 −1.88348 −0.392733 −0.196366 0.980531i 0.562914π-0.562914\pi
−0.196366 + 0.980531i 0.562914π0.562914\pi
2424 0 0
2525 −4.81204 −0.962408
2626 0.331821 0.0650755
2727 0 0
2828 3.41421 0.645226
2929 −8.53874 −1.58560 −0.792802 0.609479i 0.791379π-0.791379\pi
−0.792802 + 0.609479i 0.791379π0.791379\pi
3030 0 0
3131 2.58579 0.464421 0.232210 0.972666i 0.425404π-0.425404\pi
0.232210 + 0.972666i 0.425404π0.425404\pi
3232 −1.00000 −0.176777
3333 0 0
3434 0 0
3535 −1.48022 −0.250202
3636 0 0
3737 −10.6143 −1.74499 −0.872494 0.488625i 0.837499π-0.837499\pi
−0.872494 + 0.488625i 0.837499π0.837499\pi
3838 −2.14386 −0.347780
3939 0 0
4040 0.433546 0.0685496
4141 −12.1177 −1.89247 −0.946236 0.323476i 0.895149π-0.895149\pi
−0.946236 + 0.323476i 0.895149π0.895149\pi
4242 0 0
4343 −10.0933 −1.53922 −0.769610 0.638514i 0.779549π-0.779549\pi
−0.769610 + 0.638514i 0.779549π0.779549\pi
4444 1.69552 0.255609
4545 0 0
4646 1.88348 0.277704
4747 −2.38009 −0.347171 −0.173586 0.984819i 0.555535π-0.555535\pi
−0.173586 + 0.984819i 0.555535π0.555535\pi
4848 0 0
4949 4.65685 0.665265
5050 4.81204 0.680525
5151 0 0
5252 −0.331821 −0.0460153
5353 3.13066 0.430029 0.215014 0.976611i 0.431020π-0.431020\pi
0.215014 + 0.976611i 0.431020π0.431020\pi
5454 0 0
5555 −0.735084 −0.0991187
5656 −3.41421 −0.456243
5757 0 0
5858 8.53874 1.12119
5959 7.67459 0.999147 0.499573 0.866272i 0.333490π-0.333490\pi
0.499573 + 0.866272i 0.333490π0.333490\pi
6060 0 0
6161 8.03988 1.02940 0.514701 0.857370i 0.327903π-0.327903\pi
0.514701 + 0.857370i 0.327903π0.327903\pi
6262 −2.58579 −0.328395
6363 0 0
6464 1.00000 0.125000
6565 0.143860 0.0178436
6666 0 0
6767 −15.7711 −1.92675 −0.963375 0.268159i 0.913585π-0.913585\pi
−0.963375 + 0.268159i 0.913585π0.913585\pi
6868 0 0
6969 0 0
7070 1.48022 0.176920
7171 −0.226626 −0.0268955 −0.0134478 0.999910i 0.504281π-0.504281\pi
−0.0134478 + 0.999910i 0.504281π0.504281\pi
7272 0 0
7373 −12.1387 −1.42072 −0.710362 0.703837i 0.751469π-0.751469\pi
−0.710362 + 0.703837i 0.751469π0.751469\pi
7474 10.6143 1.23389
7575 0 0
7676 2.14386 0.245918
7777 5.78886 0.659702
7878 0 0
7979 12.5394 1.41080 0.705398 0.708811i 0.250768π-0.250768\pi
0.705398 + 0.708811i 0.250768π0.250768\pi
8080 −0.433546 −0.0484719
8181 0 0
8282 12.1177 1.33818
8383 1.04373 0.114564 0.0572820 0.998358i 0.481757π-0.481757\pi
0.0572820 + 0.998358i 0.481757π0.481757\pi
8484 0 0
8585 0 0
8686 10.0933 1.08839
8787 0 0
8888 −1.69552 −0.180743
8989 −13.8281 −1.46577 −0.732885 0.680352i 0.761827π-0.761827\pi
−0.732885 + 0.680352i 0.761827π0.761827\pi
9090 0 0
9191 −1.13291 −0.118761
9292 −1.88348 −0.196366
9393 0 0
9494 2.38009 0.245487
9595 −0.929461 −0.0953607
9696 0 0
9797 −3.75539 −0.381302 −0.190651 0.981658i 0.561060π-0.561060\pi
−0.190651 + 0.981658i 0.561060π0.561060\pi
9898 −4.65685 −0.470413
9999 0 0
100100 −4.81204 −0.481204
101101 −0.636303 −0.0633145 −0.0316573 0.999499i 0.510079π-0.510079\pi
−0.0316573 + 0.999499i 0.510079π0.510079\pi
102102 0 0
103103 8.59955 0.847339 0.423669 0.905817i 0.360742π-0.360742\pi
0.423669 + 0.905817i 0.360742π0.360742\pi
104104 0.331821 0.0325378
105105 0 0
106106 −3.13066 −0.304076
107107 −2.16478 −0.209278 −0.104639 0.994510i 0.533369π-0.533369\pi
−0.104639 + 0.994510i 0.533369π0.533369\pi
108108 0 0
109109 −7.91376 −0.758001 −0.379000 0.925396i 0.623732π-0.623732\pi
−0.379000 + 0.925396i 0.623732π0.623732\pi
110110 0.735084 0.0700875
111111 0 0
112112 3.41421 0.322613
113113 9.18828 0.864361 0.432180 0.901787i 0.357744π-0.357744\pi
0.432180 + 0.901787i 0.357744π0.357744\pi
114114 0 0
115115 0.816574 0.0761459
116116 −8.53874 −0.792802
117117 0 0
118118 −7.67459 −0.706504
119119 0 0
120120 0 0
121121 −8.12522 −0.738656
122122 −8.03988 −0.727897
123123 0 0
124124 2.58579 0.232210
125125 4.25397 0.380486
126126 0 0
127127 −12.0843 −1.07231 −0.536153 0.844121i 0.680123π-0.680123\pi
−0.536153 + 0.844121i 0.680123π0.680123\pi
128128 −1.00000 −0.0883883
129129 0 0
130130 −0.143860 −0.0126173
131131 −0.896683 −0.0783436 −0.0391718 0.999232i 0.512472π-0.512472\pi
−0.0391718 + 0.999232i 0.512472π0.512472\pi
132132 0 0
133133 7.31959 0.634689
134134 15.7711 1.36242
135135 0 0
136136 0 0
137137 −12.6109 −1.07742 −0.538710 0.842491i 0.681088π-0.681088\pi
−0.538710 + 0.842491i 0.681088π0.681088\pi
138138 0 0
139139 17.0447 1.44571 0.722857 0.690998i 0.242829π-0.242829\pi
0.722857 + 0.690998i 0.242829π0.242829\pi
140140 −1.48022 −0.125101
141141 0 0
142142 0.226626 0.0190180
143143 −0.562609 −0.0470477
144144 0 0
145145 3.70193 0.307429
146146 12.1387 1.00460
147147 0 0
148148 −10.6143 −0.872494
149149 −17.5004 −1.43369 −0.716844 0.697234i 0.754414π-0.754414\pi
−0.716844 + 0.697234i 0.754414π0.754414\pi
150150 0 0
151151 9.64009 0.784500 0.392250 0.919859i 0.371697π-0.371697\pi
0.392250 + 0.919859i 0.371697π0.371697\pi
152152 −2.14386 −0.173890
153153 0 0
154154 −5.78886 −0.466480
155155 −1.12106 −0.0900454
156156 0 0
157157 −4.78976 −0.382265 −0.191132 0.981564i 0.561216π-0.561216\pi
−0.191132 + 0.981564i 0.561216π0.561216\pi
158158 −12.5394 −0.997584
159159 0 0
160160 0.433546 0.0342748
161161 −6.43060 −0.506802
162162 0 0
163163 17.8049 1.39459 0.697293 0.716786i 0.254388π-0.254388\pi
0.697293 + 0.716786i 0.254388π0.254388\pi
164164 −12.1177 −0.946236
165165 0 0
166166 −1.04373 −0.0810090
167167 17.5950 1.36154 0.680771 0.732496i 0.261645π-0.261645\pi
0.680771 + 0.732496i 0.261645π0.261645\pi
168168 0 0
169169 −12.8899 −0.991530
170170 0 0
171171 0 0
172172 −10.0933 −0.769610
173173 19.3462 1.47087 0.735434 0.677597i 0.236978π-0.236978\pi
0.735434 + 0.677597i 0.236978π0.236978\pi
174174 0 0
175175 −16.4293 −1.24194
176176 1.69552 0.127804
177177 0 0
178178 13.8281 1.03646
179179 9.11933 0.681611 0.340805 0.940134i 0.389300π-0.389300\pi
0.340805 + 0.940134i 0.389300π0.389300\pi
180180 0 0
181181 −0.776691 −0.0577310 −0.0288655 0.999583i 0.509189π-0.509189\pi
−0.0288655 + 0.999583i 0.509189π0.509189\pi
182182 1.13291 0.0839768
183183 0 0
184184 1.88348 0.138852
185185 4.60180 0.338331
186186 0 0
187187 0 0
188188 −2.38009 −0.173586
189189 0 0
190190 0.929461 0.0674302
191191 13.4248 0.971384 0.485692 0.874130i 0.338568π-0.338568\pi
0.485692 + 0.874130i 0.338568π0.338568\pi
192192 0 0
193193 5.08905 0.366318 0.183159 0.983083i 0.441368π-0.441368\pi
0.183159 + 0.983083i 0.441368π0.441368\pi
194194 3.75539 0.269621
195195 0 0
196196 4.65685 0.332632
197197 4.15449 0.295995 0.147998 0.988988i 0.452717π-0.452717\pi
0.147998 + 0.988988i 0.452717π0.452717\pi
198198 0 0
199199 −10.7087 −0.759121 −0.379561 0.925167i 0.623925π-0.623925\pi
−0.379561 + 0.925167i 0.623925π0.623925\pi
200200 4.81204 0.340262
201201 0 0
202202 0.636303 0.0447701
203203 −29.1531 −2.04615
204204 0 0
205205 5.25359 0.366927
206206 −8.59955 −0.599159
207207 0 0
208208 −0.331821 −0.0230077
209209 3.63495 0.251435
210210 0 0
211211 −4.72151 −0.325042 −0.162521 0.986705i 0.551963π-0.551963\pi
−0.162521 + 0.986705i 0.551963π0.551963\pi
212212 3.13066 0.215014
213213 0 0
214214 2.16478 0.147982
215215 4.37592 0.298435
216216 0 0
217217 8.82843 0.599313
218218 7.91376 0.535988
219219 0 0
220220 −0.735084 −0.0495594
221221 0 0
222222 0 0
223223 −15.6359 −1.04706 −0.523530 0.852007i 0.675385π-0.675385\pi
−0.523530 + 0.852007i 0.675385π0.675385\pi
224224 −3.41421 −0.228122
225225 0 0
226226 −9.18828 −0.611195
227227 11.0615 0.734175 0.367088 0.930186i 0.380355π-0.380355\pi
0.367088 + 0.930186i 0.380355π0.380355\pi
228228 0 0
229229 −15.3852 −1.01668 −0.508340 0.861157i 0.669741π-0.669741\pi
−0.508340 + 0.861157i 0.669741π0.669741\pi
230230 −0.816574 −0.0538433
231231 0 0
232232 8.53874 0.560596
233233 −10.3776 −0.679859 −0.339929 0.940451i 0.610403π-0.610403\pi
−0.339929 + 0.940451i 0.610403π0.610403\pi
234234 0 0
235235 1.03188 0.0673121
236236 7.67459 0.499573
237237 0 0
238238 0 0
239239 24.7803 1.60291 0.801454 0.598057i 0.204060π-0.204060\pi
0.801454 + 0.598057i 0.204060π0.204060\pi
240240 0 0
241241 −4.30517 −0.277321 −0.138660 0.990340i 0.544280π-0.544280\pi
−0.138660 + 0.990340i 0.544280π0.544280\pi
242242 8.12522 0.522309
243243 0 0
244244 8.03988 0.514701
245245 −2.01896 −0.128987
246246 0 0
247247 −0.711378 −0.0452639
248248 −2.58579 −0.164198
249249 0 0
250250 −4.25397 −0.269044
251251 19.0639 1.20330 0.601652 0.798759i 0.294510π-0.294510\pi
0.601652 + 0.798759i 0.294510π0.294510\pi
252252 0 0
253253 −3.19347 −0.200772
254254 12.0843 0.758235
255255 0 0
256256 1.00000 0.0625000
257257 26.7594 1.66921 0.834603 0.550851i 0.185697π-0.185697\pi
0.834603 + 0.550851i 0.185697π0.185697\pi
258258 0 0
259259 −36.2396 −2.25182
260260 0.143860 0.00892180
261261 0 0
262262 0.896683 0.0553973
263263 −27.5122 −1.69648 −0.848239 0.529614i 0.822337π-0.822337\pi
−0.848239 + 0.529614i 0.822337π0.822337\pi
264264 0 0
265265 −1.35728 −0.0833772
266266 −7.31959 −0.448793
267267 0 0
268268 −15.7711 −0.963375
269269 10.0148 0.610613 0.305306 0.952254i 0.401241π-0.401241\pi
0.305306 + 0.952254i 0.401241π0.401241\pi
270270 0 0
271271 9.20949 0.559437 0.279718 0.960082i 0.409759π-0.409759\pi
0.279718 + 0.960082i 0.409759π0.409759\pi
272272 0 0
273273 0 0
274274 12.6109 0.761851
275275 −8.15890 −0.492000
276276 0 0
277277 −8.36529 −0.502622 −0.251311 0.967906i 0.580862π-0.580862\pi
−0.251311 + 0.967906i 0.580862π0.580862\pi
278278 −17.0447 −1.02227
279279 0 0
280280 1.48022 0.0884599
281281 −10.9996 −0.656183 −0.328091 0.944646i 0.606405π-0.606405\pi
−0.328091 + 0.944646i 0.606405π0.606405\pi
282282 0 0
283283 −21.1380 −1.25653 −0.628263 0.778001i 0.716234π-0.716234\pi
−0.628263 + 0.778001i 0.716234π0.716234\pi
284284 −0.226626 −0.0134478
285285 0 0
286286 0.562609 0.0332678
287287 −41.3725 −2.44214
288288 0 0
289289 0 0
290290 −3.70193 −0.217385
291291 0 0
292292 −12.1387 −0.710362
293293 −25.1277 −1.46797 −0.733987 0.679164i 0.762343π-0.762343\pi
−0.733987 + 0.679164i 0.762343π0.762343\pi
294294 0 0
295295 −3.32729 −0.193722
296296 10.6143 0.616946
297297 0 0
298298 17.5004 1.01377
299299 0.624979 0.0361435
300300 0 0
301301 −34.4608 −1.98629
302302 −9.64009 −0.554725
303303 0 0
304304 2.14386 0.122959
305305 −3.48566 −0.199588
306306 0 0
307307 15.3433 0.875688 0.437844 0.899051i 0.355742π-0.355742\pi
0.437844 + 0.899051i 0.355742π0.355742\pi
308308 5.78886 0.329851
309309 0 0
310310 1.12106 0.0636717
311311 −21.6825 −1.22950 −0.614750 0.788722i 0.710743π-0.710743\pi
−0.614750 + 0.788722i 0.710743π0.710743\pi
312312 0 0
313313 −8.38847 −0.474144 −0.237072 0.971492i 0.576188π-0.576188\pi
−0.237072 + 0.971492i 0.576188π0.576188\pi
314314 4.78976 0.270302
315315 0 0
316316 12.5394 0.705398
317317 23.9803 1.34687 0.673434 0.739248i 0.264819π-0.264819\pi
0.673434 + 0.739248i 0.264819π0.264819\pi
318318 0 0
319319 −14.4776 −0.810589
320320 −0.433546 −0.0242359
321321 0 0
322322 6.43060 0.358363
323323 0 0
324324 0 0
325325 1.59674 0.0885710
326326 −17.8049 −0.986121
327327 0 0
328328 12.1177 0.669090
329329 −8.12612 −0.448008
330330 0 0
331331 −4.07733 −0.224110 −0.112055 0.993702i 0.535743π-0.535743\pi
−0.112055 + 0.993702i 0.535743π0.535743\pi
332332 1.04373 0.0572820
333333 0 0
334334 −17.5950 −0.962756
335335 6.83750 0.373572
336336 0 0
337337 10.0167 0.545645 0.272822 0.962064i 0.412043π-0.412043\pi
0.272822 + 0.962064i 0.412043π0.412043\pi
338338 12.8899 0.701118
339339 0 0
340340 0 0
341341 4.38425 0.237420
342342 0 0
343343 −8.00000 −0.431959
344344 10.0933 0.544197
345345 0 0
346346 −19.3462 −1.04006
347347 8.64418 0.464044 0.232022 0.972711i 0.425466π-0.425466\pi
0.232022 + 0.972711i 0.425466π0.425466\pi
348348 0 0
349349 20.8126 1.11407 0.557036 0.830488i 0.311938π-0.311938\pi
0.557036 + 0.830488i 0.311938π0.311938\pi
350350 16.4293 0.878184
351351 0 0
352352 −1.69552 −0.0903714
353353 20.1049 1.07007 0.535037 0.844829i 0.320298π-0.320298\pi
0.535037 + 0.844829i 0.320298π0.320298\pi
354354 0 0
355355 0.0982525 0.00521470
356356 −13.8281 −0.732885
357357 0 0
358358 −9.11933 −0.481972
359359 −25.3001 −1.33529 −0.667645 0.744480i 0.732698π-0.732698\pi
−0.667645 + 0.744480i 0.732698π0.732698\pi
360360 0 0
361361 −14.4039 −0.758098
362362 0.776691 0.0408220
363363 0 0
364364 −1.13291 −0.0593806
365365 5.26266 0.275460
366366 0 0
367367 10.3200 0.538698 0.269349 0.963043i 0.413191π-0.413191\pi
0.269349 + 0.963043i 0.413191π0.413191\pi
368368 −1.88348 −0.0981832
369369 0 0
370370 −4.60180 −0.239236
371371 10.6887 0.554931
372372 0 0
373373 18.2719 0.946083 0.473041 0.881040i 0.343156π-0.343156\pi
0.473041 + 0.881040i 0.343156π0.343156\pi
374374 0 0
375375 0 0
376376 2.38009 0.122744
377377 2.83334 0.145924
378378 0 0
379379 20.9319 1.07520 0.537600 0.843200i 0.319331π-0.319331\pi
0.537600 + 0.843200i 0.319331π0.319331\pi
380380 −0.929461 −0.0476803
381381 0 0
382382 −13.4248 −0.686872
383383 −22.9974 −1.17511 −0.587555 0.809184i 0.699910π-0.699910\pi
−0.587555 + 0.809184i 0.699910π0.699910\pi
384384 0 0
385385 −2.50973 −0.127908
386386 −5.08905 −0.259026
387387 0 0
388388 −3.75539 −0.190651
389389 9.07748 0.460247 0.230123 0.973161i 0.426087π-0.426087\pi
0.230123 + 0.973161i 0.426087π0.426087\pi
390390 0 0
391391 0 0
392392 −4.65685 −0.235207
393393 0 0
394394 −4.15449 −0.209300
395395 −5.43641 −0.273536
396396 0 0
397397 −7.80857 −0.391901 −0.195950 0.980614i 0.562779π-0.562779\pi
−0.195950 + 0.980614i 0.562779π0.562779\pi
398398 10.7087 0.536780
399399 0 0
400400 −4.81204 −0.240602
401401 −17.3608 −0.866955 −0.433477 0.901164i 0.642714π-0.642714\pi
−0.433477 + 0.901164i 0.642714π0.642714\pi
402402 0 0
403403 −0.858019 −0.0427410
404404 −0.636303 −0.0316573
405405 0 0
406406 29.1531 1.44684
407407 −17.9968 −0.892069
408408 0 0
409409 4.42153 0.218631 0.109315 0.994007i 0.465134π-0.465134\pi
0.109315 + 0.994007i 0.465134π0.465134\pi
410410 −5.25359 −0.259456
411411 0 0
412412 8.59955 0.423669
413413 26.2027 1.28935
414414 0 0
415415 −0.452504 −0.0222125
416416 0.331821 0.0162689
417417 0 0
418418 −3.63495 −0.177791
419419 23.1663 1.13175 0.565874 0.824491i 0.308539π-0.308539\pi
0.565874 + 0.824491i 0.308539π0.308539\pi
420420 0 0
421421 −20.0524 −0.977295 −0.488648 0.872481i 0.662510π-0.662510\pi
−0.488648 + 0.872481i 0.662510π0.662510\pi
422422 4.72151 0.229839
423423 0 0
424424 −3.13066 −0.152038
425425 0 0
426426 0 0
427427 27.4499 1.32839
428428 −2.16478 −0.104639
429429 0 0
430430 −4.37592 −0.211026
431431 −40.1467 −1.93380 −0.966900 0.255154i 0.917874π-0.917874\pi
−0.966900 + 0.255154i 0.917874π0.917874\pi
432432 0 0
433433 −21.8499 −1.05004 −0.525020 0.851090i 0.675942π-0.675942\pi
−0.525020 + 0.851090i 0.675942π0.675942\pi
434434 −8.82843 −0.423778
435435 0 0
436436 −7.91376 −0.379000
437437 −4.03792 −0.193160
438438 0 0
439439 −0.838775 −0.0400325 −0.0200163 0.999800i 0.506372π-0.506372\pi
−0.0200163 + 0.999800i 0.506372π0.506372\pi
440440 0.735084 0.0350438
441441 0 0
442442 0 0
443443 3.21267 0.152639 0.0763194 0.997083i 0.475683π-0.475683\pi
0.0763194 + 0.997083i 0.475683π0.475683\pi
444444 0 0
445445 5.99509 0.284195
446446 15.6359 0.740383
447447 0 0
448448 3.41421 0.161306
449449 28.7483 1.35671 0.678357 0.734732i 0.262692π-0.262692\pi
0.678357 + 0.734732i 0.262692π0.262692\pi
450450 0 0
451451 −20.5458 −0.967466
452452 9.18828 0.432180
453453 0 0
454454 −11.0615 −0.519140
455455 0.491168 0.0230263
456456 0 0
457457 −7.45097 −0.348542 −0.174271 0.984698i 0.555757π-0.555757\pi
−0.174271 + 0.984698i 0.555757π0.555757\pi
458458 15.3852 0.718901
459459 0 0
460460 0.816574 0.0380730
461461 −25.6378 −1.19407 −0.597037 0.802214i 0.703655π-0.703655\pi
−0.597037 + 0.802214i 0.703655π0.703655\pi
462462 0 0
463463 −10.7747 −0.500744 −0.250372 0.968150i 0.580553π-0.580553\pi
−0.250372 + 0.968150i 0.580553π0.580553\pi
464464 −8.53874 −0.396401
465465 0 0
466466 10.3776 0.480733
467467 −35.6492 −1.64965 −0.824823 0.565391i 0.808725π-0.808725\pi
−0.824823 + 0.565391i 0.808725π0.808725\pi
468468 0 0
469469 −53.8460 −2.48638
470470 −1.03188 −0.0475969
471471 0 0
472472 −7.67459 −0.353252
473473 −17.1134 −0.786877
474474 0 0
475475 −10.3163 −0.473346
476476 0 0
477477 0 0
478478 −24.7803 −1.13343
479479 14.0702 0.642882 0.321441 0.946930i 0.395833π-0.395833\pi
0.321441 + 0.946930i 0.395833π0.395833\pi
480480 0 0
481481 3.52207 0.160592
482482 4.30517 0.196095
483483 0 0
484484 −8.12522 −0.369328
485485 1.62813 0.0739297
486486 0 0
487487 24.1325 1.09355 0.546775 0.837280i 0.315855π-0.315855\pi
0.546775 + 0.837280i 0.315855π0.315855\pi
488488 −8.03988 −0.363948
489489 0 0
490490 2.01896 0.0912072
491491 −26.5200 −1.19683 −0.598416 0.801186i 0.704203π-0.704203\pi
−0.598416 + 0.801186i 0.704203π0.704203\pi
492492 0 0
493493 0 0
494494 0.711378 0.0320064
495495 0 0
496496 2.58579 0.116105
497497 −0.773748 −0.0347073
498498 0 0
499499 −4.53996 −0.203237 −0.101618 0.994823i 0.532402π-0.532402\pi
−0.101618 + 0.994823i 0.532402π0.532402\pi
500500 4.25397 0.190243
501501 0 0
502502 −19.0639 −0.850864
503503 3.99734 0.178233 0.0891164 0.996021i 0.471596π-0.471596\pi
0.0891164 + 0.996021i 0.471596π0.471596\pi
504504 0 0
505505 0.275866 0.0122759
506506 3.19347 0.141967
507507 0 0
508508 −12.0843 −0.536153
509509 22.9751 1.01835 0.509176 0.860662i 0.329950π-0.329950\pi
0.509176 + 0.860662i 0.329950π0.329950\pi
510510 0 0
511511 −41.4440 −1.83337
512512 −1.00000 −0.0441942
513513 0 0
514514 −26.7594 −1.18031
515515 −3.72830 −0.164288
516516 0 0
517517 −4.03548 −0.177480
518518 36.2396 1.59228
519519 0 0
520520 −0.143860 −0.00630866
521521 −16.8828 −0.739650 −0.369825 0.929101i 0.620582π-0.620582\pi
−0.369825 + 0.929101i 0.620582π0.620582\pi
522522 0 0
523523 −15.5903 −0.681717 −0.340859 0.940115i 0.610718π-0.610718\pi
−0.340859 + 0.940115i 0.610718π0.610718\pi
524524 −0.896683 −0.0391718
525525 0 0
526526 27.5122 1.19959
527527 0 0
528528 0 0
529529 −19.4525 −0.845761
530530 1.35728 0.0589566
531531 0 0
532532 7.31959 0.317345
533533 4.02092 0.174166
534534 0 0
535535 0.938533 0.0405763
536536 15.7711 0.681209
537537 0 0
538538 −10.0148 −0.431769
539539 7.89578 0.340095
540540 0 0
541541 −15.1306 −0.650515 −0.325258 0.945625i 0.605451π-0.605451\pi
−0.325258 + 0.945625i 0.605451π0.605451\pi
542542 −9.20949 −0.395581
543543 0 0
544544 0 0
545545 3.43098 0.146967
546546 0 0
547547 −2.64688 −0.113172 −0.0565862 0.998398i 0.518022π-0.518022\pi
−0.0565862 + 0.998398i 0.518022π0.518022\pi
548548 −12.6109 −0.538710
549549 0 0
550550 8.15890 0.347897
551551 −18.3059 −0.779856
552552 0 0
553553 42.8123 1.82056
554554 8.36529 0.355407
555555 0 0
556556 17.0447 0.722857
557557 12.4900 0.529217 0.264609 0.964356i 0.414757π-0.414757\pi
0.264609 + 0.964356i 0.414757π0.414757\pi
558558 0 0
559559 3.34919 0.141656
560560 −1.48022 −0.0625506
561561 0 0
562562 10.9996 0.463991
563563 −1.98226 −0.0835423 −0.0417712 0.999127i 0.513300π-0.513300\pi
−0.0417712 + 0.999127i 0.513300π0.513300\pi
564564 0 0
565565 −3.98354 −0.167589
566566 21.1380 0.888498
567567 0 0
568568 0.226626 0.00950900
569569 −16.7666 −0.702892 −0.351446 0.936208i 0.614310π-0.614310\pi
−0.351446 + 0.936208i 0.614310π0.614310\pi
570570 0 0
571571 30.1229 1.26061 0.630303 0.776349i 0.282931π-0.282931\pi
0.630303 + 0.776349i 0.282931π0.282931\pi
572572 −0.562609 −0.0235239
573573 0 0
574574 41.3725 1.72686
575575 9.06338 0.377969
576576 0 0
577577 −19.8204 −0.825132 −0.412566 0.910928i 0.635367π-0.635367\pi
−0.412566 + 0.910928i 0.635367π0.635367\pi
578578 0 0
579579 0 0
580580 3.70193 0.153714
581581 3.56351 0.147839
582582 0 0
583583 5.30808 0.219838
584584 12.1387 0.502301
585585 0 0
586586 25.1277 1.03801
587587 −12.8612 −0.530839 −0.265419 0.964133i 0.585510π-0.585510\pi
−0.265419 + 0.964133i 0.585510π0.585510\pi
588588 0 0
589589 5.54356 0.228419
590590 3.32729 0.136982
591591 0 0
592592 −10.6143 −0.436247
593593 35.8300 1.47136 0.735681 0.677328i 0.236862π-0.236862\pi
0.735681 + 0.677328i 0.236862π0.236862\pi
594594 0 0
595595 0 0
596596 −17.5004 −0.716844
597597 0 0
598598 −0.624979 −0.0255573
599599 21.1148 0.862728 0.431364 0.902178i 0.358032π-0.358032\pi
0.431364 + 0.902178i 0.358032π0.358032\pi
600600 0 0
601601 15.2346 0.621434 0.310717 0.950503i 0.399431π-0.399431\pi
0.310717 + 0.950503i 0.399431π0.399431\pi
602602 34.4608 1.40452
603603 0 0
604604 9.64009 0.392250
605605 3.52265 0.143216
606606 0 0
607607 38.3848 1.55799 0.778995 0.627030i 0.215730π-0.215730\pi
0.778995 + 0.627030i 0.215730π0.215730\pi
608608 −2.14386 −0.0869450
609609 0 0
610610 3.48566 0.141130
611611 0.789763 0.0319504
612612 0 0
613613 −1.39554 −0.0563654 −0.0281827 0.999603i 0.508972π-0.508972\pi
−0.0281827 + 0.999603i 0.508972π0.508972\pi
614614 −15.3433 −0.619205
615615 0 0
616616 −5.78886 −0.233240
617617 −8.41487 −0.338770 −0.169385 0.985550i 0.554178π-0.554178\pi
−0.169385 + 0.985550i 0.554178π0.554178\pi
618618 0 0
619619 −5.34330 −0.214765 −0.107383 0.994218i 0.534247π-0.534247\pi
−0.107383 + 0.994218i 0.534247π0.534247\pi
620620 −1.12106 −0.0450227
621621 0 0
622622 21.6825 0.869388
623623 −47.2119 −1.89151
624624 0 0
625625 22.2159 0.888636
626626 8.38847 0.335271
627627 0 0
628628 −4.78976 −0.191132
629629 0 0
630630 0 0
631631 −1.46282 −0.0582340 −0.0291170 0.999576i 0.509270π-0.509270\pi
−0.0291170 + 0.999576i 0.509270π0.509270\pi
632632 −12.5394 −0.498792
633633 0 0
634634 −23.9803 −0.952379
635635 5.23908 0.207907
636636 0 0
637637 −1.54524 −0.0612248
638638 14.4776 0.573173
639639 0 0
640640 0.433546 0.0171374
641641 −0.479372 −0.0189340 −0.00946702 0.999955i 0.503013π-0.503013\pi
−0.00946702 + 0.999955i 0.503013π0.503013\pi
642642 0 0
643643 32.1049 1.26609 0.633046 0.774114i 0.281804π-0.281804\pi
0.633046 + 0.774114i 0.281804π0.281804\pi
644644 −6.43060 −0.253401
645645 0 0
646646 0 0
647647 −23.4802 −0.923103 −0.461551 0.887114i 0.652707π-0.652707\pi
−0.461551 + 0.887114i 0.652707π0.652707\pi
648648 0 0
649649 13.0124 0.510782
650650 −1.59674 −0.0626292
651651 0 0
652652 17.8049 0.697293
653653 −45.3689 −1.77542 −0.887710 0.460402i 0.847705π-0.847705\pi
−0.887710 + 0.460402i 0.847705π0.847705\pi
654654 0 0
655655 0.388753 0.0151898
656656 −12.1177 −0.473118
657657 0 0
658658 8.12612 0.316789
659659 −12.8417 −0.500240 −0.250120 0.968215i 0.580470π-0.580470\pi
−0.250120 + 0.968215i 0.580470π0.580470\pi
660660 0 0
661661 −27.1878 −1.05748 −0.528741 0.848783i 0.677336π-0.677336\pi
−0.528741 + 0.848783i 0.677336π0.677336\pi
662662 4.07733 0.158470
663663 0 0
664664 −1.04373 −0.0405045
665665 −3.17338 −0.123058
666666 0 0
667667 16.0825 0.622719
668668 17.5950 0.680771
669669 0 0
670670 −6.83750 −0.264156
671671 13.6318 0.526249
672672 0 0
673673 −16.6772 −0.642857 −0.321429 0.946934i 0.604163π-0.604163\pi
−0.321429 + 0.946934i 0.604163π0.604163\pi
674674 −10.0167 −0.385829
675675 0 0
676676 −12.8899 −0.495765
677677 2.60284 0.100035 0.0500175 0.998748i 0.484072π-0.484072\pi
0.0500175 + 0.998748i 0.484072π0.484072\pi
678678 0 0
679679 −12.8217 −0.492052
680680 0 0
681681 0 0
682682 −4.38425 −0.167882
683683 −12.2427 −0.468453 −0.234227 0.972182i 0.575256π-0.575256\pi
−0.234227 + 0.972182i 0.575256π0.575256\pi
684684 0 0
685685 5.46739 0.208898
686686 8.00000 0.305441
687687 0 0
688688 −10.0933 −0.384805
689689 −1.03882 −0.0395758
690690 0 0
691691 15.6736 0.596252 0.298126 0.954526i 0.403638π-0.403638\pi
0.298126 + 0.954526i 0.403638π0.403638\pi
692692 19.3462 0.735434
693693 0 0
694694 −8.64418 −0.328129
695695 −7.38966 −0.280306
696696 0 0
697697 0 0
698698 −20.8126 −0.787768
699699 0 0
700700 −16.4293 −0.620970
701701 −30.8222 −1.16414 −0.582070 0.813139i 0.697757π-0.697757\pi
−0.582070 + 0.813139i 0.697757π0.697757\pi
702702 0 0
703703 −22.7557 −0.858246
704704 1.69552 0.0639022
705705 0 0
706706 −20.1049 −0.756656
707707 −2.17248 −0.0817043
708708 0 0
709709 −0.394882 −0.0148301 −0.00741505 0.999973i 0.502360π-0.502360\pi
−0.00741505 + 0.999973i 0.502360π0.502360\pi
710710 −0.0982525 −0.00368735
711711 0 0
712712 13.8281 0.518228
713713 −4.87028 −0.182393
714714 0 0
715715 0.243917 0.00912197
716716 9.11933 0.340805
717717 0 0
718718 25.3001 0.944193
719719 11.0962 0.413817 0.206908 0.978360i 0.433660π-0.433660\pi
0.206908 + 0.978360i 0.433660π0.433660\pi
720720 0 0
721721 29.3607 1.09345
722722 14.4039 0.536056
723723 0 0
724724 −0.776691 −0.0288655
725725 41.0888 1.52600
726726 0 0
727727 27.2866 1.01200 0.506001 0.862533i 0.331123π-0.331123\pi
0.506001 + 0.862533i 0.331123π0.331123\pi
728728 1.13291 0.0419884
729729 0 0
730730 −5.26266 −0.194780
731731 0 0
732732 0 0
733733 −29.2870 −1.08174 −0.540870 0.841106i 0.681905π-0.681905\pi
−0.540870 + 0.841106i 0.681905π0.681905\pi
734734 −10.3200 −0.380917
735735 0 0
736736 1.88348 0.0694260
737737 −26.7402 −0.984989
738738 0 0
739739 37.0534 1.36303 0.681516 0.731803i 0.261321π-0.261321\pi
0.681516 + 0.731803i 0.261321π0.261321\pi
740740 4.60180 0.169166
741741 0 0
742742 −10.6887 −0.392396
743743 14.4872 0.531483 0.265742 0.964044i 0.414383π-0.414383\pi
0.265742 + 0.964044i 0.414383π0.414383\pi
744744 0 0
745745 7.58722 0.277974
746746 −18.2719 −0.668981
747747 0 0
748748 0 0
749749 −7.39104 −0.270063
750750 0 0
751751 43.9632 1.60424 0.802121 0.597162i 0.203705π-0.203705\pi
0.802121 + 0.597162i 0.203705π0.203705\pi
752752 −2.38009 −0.0867928
753753 0 0
754754 −2.83334 −0.103184
755755 −4.17942 −0.152105
756756 0 0
757757 −37.8588 −1.37600 −0.688001 0.725710i 0.741511π-0.741511\pi
−0.688001 + 0.725710i 0.741511π0.741511\pi
758758 −20.9319 −0.760281
759759 0 0
760760 0.929461 0.0337151
761761 9.82880 0.356294 0.178147 0.984004i 0.442990π-0.442990\pi
0.178147 + 0.984004i 0.442990π0.442990\pi
762762 0 0
763763 −27.0193 −0.978163
764764 13.4248 0.485692
765765 0 0
766766 22.9974 0.830929
767767 −2.54659 −0.0919522
768768 0 0
769769 41.1522 1.48398 0.741992 0.670408i 0.233881π-0.233881\pi
0.741992 + 0.670408i 0.233881π0.233881\pi
770770 2.50973 0.0904446
771771 0 0
772772 5.08905 0.183159
773773 −21.7456 −0.782136 −0.391068 0.920362i 0.627894π-0.627894\pi
−0.391068 + 0.920362i 0.627894π0.627894\pi
774774 0 0
775775 −12.4429 −0.446962
776776 3.75539 0.134811
777777 0 0
778778 −9.07748 −0.325444
779779 −25.9787 −0.930785
780780 0 0
781781 −0.384248 −0.0137495
782782 0 0
783783 0 0
784784 4.65685 0.166316
785785 2.07658 0.0741163
786786 0 0
787787 47.6021 1.69683 0.848415 0.529331i 0.177557π-0.177557\pi
0.848415 + 0.529331i 0.177557π0.177557\pi
788788 4.15449 0.147998
789789 0 0
790790 5.43641 0.193419
791791 31.3707 1.11542
792792 0 0
793793 −2.66780 −0.0947365
794794 7.80857 0.277116
795795 0 0
796796 −10.7087 −0.379561
797797 37.8984 1.34243 0.671215 0.741263i 0.265773π-0.265773\pi
0.671215 + 0.741263i 0.265773π0.265773\pi
798798 0 0
799799 0 0
800800 4.81204 0.170131
801801 0 0
802802 17.3608 0.613030
803803 −20.5813 −0.726299
804804 0 0
805805 2.78796 0.0982626
806806 0.858019 0.0302224
807807 0 0
808808 0.636303 0.0223851
809809 −38.5731 −1.35616 −0.678079 0.734989i 0.737187π-0.737187\pi
−0.678079 + 0.734989i 0.737187π0.737187\pi
810810 0 0
811811 19.4393 0.682608 0.341304 0.939953i 0.389131π-0.389131\pi
0.341304 + 0.939953i 0.389131π0.389131\pi
812812 −29.1531 −1.02307
813813 0 0
814814 17.9968 0.630788
815815 −7.71922 −0.270393
816816 0 0
817817 −21.6387 −0.757043
818818 −4.42153 −0.154595
819819 0 0
820820 5.25359 0.183463
821821 −0.231821 −0.00809062 −0.00404531 0.999992i 0.501288π-0.501288\pi
−0.00404531 + 0.999992i 0.501288π0.501288\pi
822822 0 0
823823 −22.4931 −0.784059 −0.392030 0.919953i 0.628227π-0.628227\pi
−0.392030 + 0.919953i 0.628227π0.628227\pi
824824 −8.59955 −0.299579
825825 0 0
826826 −26.2027 −0.911709
827827 −52.3121 −1.81907 −0.909534 0.415629i 0.863561π-0.863561\pi
−0.909534 + 0.415629i 0.863561π0.863561\pi
828828 0 0
829829 23.3260 0.810144 0.405072 0.914285i 0.367246π-0.367246\pi
0.405072 + 0.914285i 0.367246π0.367246\pi
830830 0.452504 0.0157066
831831 0 0
832832 −0.331821 −0.0115038
833833 0 0
834834 0 0
835835 −7.62824 −0.263986
836836 3.63495 0.125717
837837 0 0
838838 −23.1663 −0.800267
839839 13.4212 0.463350 0.231675 0.972793i 0.425579π-0.425579\pi
0.231675 + 0.972793i 0.425579π0.425579\pi
840840 0 0
841841 43.9101 1.51414
842842 20.0524 0.691052
843843 0 0
844844 −4.72151 −0.162521
845845 5.58836 0.192245
846846 0 0
847847 −27.7412 −0.953200
848848 3.13066 0.107507
849849 0 0
850850 0 0
851851 19.9919 0.685314
852852 0 0
853853 −49.9350 −1.70974 −0.854871 0.518841i 0.826364π-0.826364\pi
−0.854871 + 0.518841i 0.826364π0.826364\pi
854854 −27.4499 −0.939315
855855 0 0
856856 2.16478 0.0739908
857857 −17.1760 −0.586722 −0.293361 0.956002i 0.594774π-0.594774\pi
−0.293361 + 0.956002i 0.594774π0.594774\pi
858858 0 0
859859 8.76362 0.299011 0.149505 0.988761i 0.452232π-0.452232\pi
0.149505 + 0.988761i 0.452232π0.452232\pi
860860 4.37592 0.149218
861861 0 0
862862 40.1467 1.36740
863863 −35.9177 −1.22265 −0.611326 0.791379i 0.709364π-0.709364\pi
−0.611326 + 0.791379i 0.709364π0.709364\pi
864864 0 0
865865 −8.38748 −0.285183
866866 21.8499 0.742490
867867 0 0
868868 8.82843 0.299656
869869 21.2608 0.721224
870870 0 0
871871 5.23320 0.177320
872872 7.91376 0.267994
873873 0 0
874874 4.03792 0.136585
875875 14.5239 0.490999
876876 0 0
877877 4.22519 0.142674 0.0713372 0.997452i 0.477273π-0.477273\pi
0.0713372 + 0.997452i 0.477273π0.477273\pi
878878 0.838775 0.0283073
879879 0 0
880880 −0.735084 −0.0247797
881881 −29.9958 −1.01058 −0.505292 0.862949i 0.668615π-0.668615\pi
−0.505292 + 0.862949i 0.668615π0.668615\pi
882882 0 0
883883 13.9714 0.470175 0.235087 0.971974i 0.424462π-0.424462\pi
0.235087 + 0.971974i 0.424462π0.424462\pi
884884 0 0
885885 0 0
886886 −3.21267 −0.107932
887887 22.0276 0.739613 0.369807 0.929109i 0.379424π-0.379424\pi
0.369807 + 0.929109i 0.379424π0.379424\pi
888888 0 0
889889 −41.2583 −1.38376
890890 −5.99509 −0.200956
891891 0 0
892892 −15.6359 −0.523530
893893 −5.10257 −0.170751
894894 0 0
895895 −3.95365 −0.132156
896896 −3.41421 −0.114061
897897 0 0
898898 −28.7483 −0.959342
899899 −22.0794 −0.736388
900900 0 0
901901 0 0
902902 20.5458 0.684102
903903 0 0
904904 −9.18828 −0.305598
905905 0.336731 0.0111933
906906 0 0
907907 −26.9106 −0.893553 −0.446776 0.894646i 0.647428π-0.647428\pi
−0.446776 + 0.894646i 0.647428π0.647428\pi
908908 11.0615 0.367088
909909 0 0
910910 −0.491168 −0.0162820
911911 −35.4849 −1.17567 −0.587834 0.808982i 0.700019π-0.700019\pi
−0.587834 + 0.808982i 0.700019π0.700019\pi
912912 0 0
913913 1.76966 0.0585672
914914 7.45097 0.246456
915915 0 0
916916 −15.3852 −0.508340
917917 −3.06147 −0.101099
918918 0 0
919919 −38.6107 −1.27365 −0.636824 0.771009i 0.719752π-0.719752\pi
−0.636824 + 0.771009i 0.719752π0.719752\pi
920920 −0.816574 −0.0269217
921921 0 0
922922 25.6378 0.844337
923923 0.0751992 0.00247521
924924 0 0
925925 51.0766 1.67939
926926 10.7747 0.354079
927927 0 0
928928 8.53874 0.280298
929929 22.8949 0.751157 0.375579 0.926791i 0.377444π-0.377444\pi
0.375579 + 0.926791i 0.377444π0.377444\pi
930930 0 0
931931 9.98364 0.327201
932932 −10.3776 −0.339929
933933 0 0
934934 35.6492 1.16648
935935 0 0
936936 0 0
937937 39.6793 1.29627 0.648133 0.761527i 0.275550π-0.275550\pi
0.648133 + 0.761527i 0.275550π0.275550\pi
938938 53.8460 1.75813
939939 0 0
940940 1.03188 0.0336561
941941 52.6651 1.71683 0.858416 0.512953i 0.171449π-0.171449\pi
0.858416 + 0.512953i 0.171449π0.171449\pi
942942 0 0
943943 22.8235 0.743236
944944 7.67459 0.249787
945945 0 0
946946 17.1134 0.556406
947947 −1.52698 −0.0496201 −0.0248100 0.999692i 0.507898π-0.507898\pi
−0.0248100 + 0.999692i 0.507898π0.507898\pi
948948 0 0
949949 4.02787 0.130750
950950 10.3163 0.334706
951951 0 0
952952 0 0
953953 −9.95360 −0.322429 −0.161214 0.986919i 0.551541π-0.551541\pi
−0.161214 + 0.986919i 0.551541π0.551541\pi
954954 0 0
955955 −5.82026 −0.188339
956956 24.7803 0.801454
957957 0 0
958958 −14.0702 −0.454586
959959 −43.0562 −1.39036
960960 0 0
961961 −24.3137 −0.784313
962962 −3.52207 −0.113556
963963 0 0
964964 −4.30517 −0.138660
965965 −2.20633 −0.0710244
966966 0 0
967967 5.88843 0.189359 0.0946796 0.995508i 0.469817π-0.469817\pi
0.0946796 + 0.995508i 0.469817π0.469817\pi
968968 8.12522 0.261154
969969 0 0
970970 −1.62813 −0.0522762
971971 −18.9670 −0.608681 −0.304341 0.952563i 0.598436π-0.598436\pi
−0.304341 + 0.952563i 0.598436π0.598436\pi
972972 0 0
973973 58.1943 1.86562
974974 −24.1325 −0.773256
975975 0 0
976976 8.03988 0.257350
977977 −32.3172 −1.03392 −0.516959 0.856010i 0.672936π-0.672936\pi
−0.516959 + 0.856010i 0.672936π0.672936\pi
978978 0 0
979979 −23.4457 −0.749328
980980 −2.01896 −0.0644933
981981 0 0
982982 26.5200 0.846288
983983 −32.4363 −1.03456 −0.517278 0.855817i 0.673055π-0.673055\pi
−0.517278 + 0.855817i 0.673055π0.673055\pi
984984 0 0
985985 −1.80116 −0.0573898
986986 0 0
987987 0 0
988988 −0.711378 −0.0226320
989989 19.0106 0.604502
990990 0 0
991991 46.9010 1.48986 0.744930 0.667142i 0.232483π-0.232483\pi
0.744930 + 0.667142i 0.232483π0.232483\pi
992992 −2.58579 −0.0820988
993993 0 0
994994 0.773748 0.0245418
995995 4.64272 0.147184
996996 0 0
997997 47.4571 1.50298 0.751490 0.659744i 0.229335π-0.229335\pi
0.751490 + 0.659744i 0.229335π0.229335\pi
998998 4.53996 0.143710
999999 0 0
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 5202.2.a.bt.1.3 4
3.2 odd 2 1734.2.a.w.1.2 4
17.10 odd 16 306.2.l.d.253.2 8
17.12 odd 16 306.2.l.d.127.2 8
17.16 even 2 5202.2.a.br.1.2 4
51.2 odd 8 1734.2.f.m.1483.3 8
51.8 odd 8 1734.2.f.j.829.2 8
51.26 odd 8 1734.2.f.m.829.3 8
51.29 even 16 102.2.h.a.25.2 8
51.32 odd 8 1734.2.f.j.1483.2 8
51.38 odd 4 1734.2.b.k.577.3 8
51.44 even 16 102.2.h.a.49.2 yes 8
51.47 odd 4 1734.2.b.k.577.6 8
51.50 odd 2 1734.2.a.v.1.3 4
204.95 odd 16 816.2.bq.b.49.1 8
204.131 odd 16 816.2.bq.b.433.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
102.2.h.a.25.2 8 51.29 even 16
102.2.h.a.49.2 yes 8 51.44 even 16
306.2.l.d.127.2 8 17.12 odd 16
306.2.l.d.253.2 8 17.10 odd 16
816.2.bq.b.49.1 8 204.95 odd 16
816.2.bq.b.433.1 8 204.131 odd 16
1734.2.a.v.1.3 4 51.50 odd 2
1734.2.a.w.1.2 4 3.2 odd 2
1734.2.b.k.577.3 8 51.38 odd 4
1734.2.b.k.577.6 8 51.47 odd 4
1734.2.f.j.829.2 8 51.8 odd 8
1734.2.f.j.1483.2 8 51.32 odd 8
1734.2.f.m.829.3 8 51.26 odd 8
1734.2.f.m.1483.3 8 51.2 odd 8
5202.2.a.br.1.2 4 17.16 even 2
5202.2.a.bt.1.3 4 1.1 even 1 trivial