Properties

Label 4732.2.a.s.1.6
Level 47324732
Weight 22
Character 4732.1
Self dual yes
Analytic conductor 37.78537.785
Analytic rank 11
Dimension 88
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] = [4732,2,Mod(1,4732)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4732, 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("4732.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4732=227132 4732 = 2^{2} \cdot 7 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4732.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: 37.785210236537.7852102365
Analytic rank: 11
Dimension: 88
Coefficient field: Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x819x62x5+113x4+40x3232x2136x+52 x^{8} - 19x^{6} - 2x^{5} + 113x^{4} + 40x^{3} - 232x^{2} - 136x + 52 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 364)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.6
Root 1.75101-1.75101 of defining polynomial
Character χ\chi == 4732.1

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+1.75101q3+1.38536q51.00000q7+0.0660200q9+1.15290q11+2.42578q151.56249q178.38917q191.75101q212.22134q233.08077q255.13741q27+2.86981q296.65024q31+2.01874q331.38536q35+3.48068q3712.5583q416.15682q43+0.0914616q457.40432q47+1.00000q492.73593q51+11.2301q53+1.59719q5514.6895q578.05559q59+1.65841q610.0660200q63+3.71128q673.88958q69+9.93663q713.30200q735.39444q751.15290q77+4.64811q799.19370q811.82551q832.16462q85+5.02506q87+2.37681q8911.6446q9311.6220q957.54618q97+0.0761145q99+O(q100)q+1.75101 q^{3} +1.38536 q^{5} -1.00000 q^{7} +0.0660200 q^{9} +1.15290 q^{11} +2.42578 q^{15} -1.56249 q^{17} -8.38917 q^{19} -1.75101 q^{21} -2.22134 q^{23} -3.08077 q^{25} -5.13741 q^{27} +2.86981 q^{29} -6.65024 q^{31} +2.01874 q^{33} -1.38536 q^{35} +3.48068 q^{37} -12.5583 q^{41} -6.15682 q^{43} +0.0914616 q^{45} -7.40432 q^{47} +1.00000 q^{49} -2.73593 q^{51} +11.2301 q^{53} +1.59719 q^{55} -14.6895 q^{57} -8.05559 q^{59} +1.65841 q^{61} -0.0660200 q^{63} +3.71128 q^{67} -3.88958 q^{69} +9.93663 q^{71} -3.30200 q^{73} -5.39444 q^{75} -1.15290 q^{77} +4.64811 q^{79} -9.19370 q^{81} -1.82551 q^{83} -2.16462 q^{85} +5.02506 q^{87} +2.37681 q^{89} -11.6446 q^{93} -11.6220 q^{95} -7.54618 q^{97} +0.0761145 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q6q58q7+14q912q1112q15+2q176q19+22q256q27+22q2914q31+28q33+6q3512q374q41+6q4320q4542q47+80q99+O(q100) 8 q - 6 q^{5} - 8 q^{7} + 14 q^{9} - 12 q^{11} - 12 q^{15} + 2 q^{17} - 6 q^{19} + 22 q^{25} - 6 q^{27} + 22 q^{29} - 14 q^{31} + 28 q^{33} + 6 q^{35} - 12 q^{37} - 4 q^{41} + 6 q^{43} - 20 q^{45} - 42 q^{47}+ \cdots - 80 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 1.75101 1.01094 0.505472 0.862843i 0.331318π-0.331318\pi
0.505472 + 0.862843i 0.331318π0.331318\pi
44 0 0
55 1.38536 0.619553 0.309777 0.950809i 0.399746π-0.399746\pi
0.309777 + 0.950809i 0.399746π0.399746\pi
66 0 0
77 −1.00000 −0.377964
88 0 0
99 0.0660200 0.0220067
1010 0 0
1111 1.15290 0.347613 0.173806 0.984780i 0.444393π-0.444393\pi
0.173806 + 0.984780i 0.444393π0.444393\pi
1212 0 0
1313 0 0
1414 0 0
1515 2.42578 0.626333
1616 0 0
1717 −1.56249 −0.378960 −0.189480 0.981885i 0.560680π-0.560680\pi
−0.189480 + 0.981885i 0.560680π0.560680\pi
1818 0 0
1919 −8.38917 −1.92461 −0.962303 0.271978i 0.912322π-0.912322\pi
−0.962303 + 0.271978i 0.912322π0.912322\pi
2020 0 0
2121 −1.75101 −0.382101
2222 0 0
2323 −2.22134 −0.463182 −0.231591 0.972813i 0.574393π-0.574393\pi
−0.231591 + 0.972813i 0.574393π0.574393\pi
2424 0 0
2525 −3.08077 −0.616154
2626 0 0
2727 −5.13741 −0.988696
2828 0 0
2929 2.86981 0.532911 0.266455 0.963847i 0.414148π-0.414148\pi
0.266455 + 0.963847i 0.414148π0.414148\pi
3030 0 0
3131 −6.65024 −1.19442 −0.597209 0.802086i 0.703724π-0.703724\pi
−0.597209 + 0.802086i 0.703724π0.703724\pi
3232 0 0
3333 2.01874 0.351417
3434 0 0
3535 −1.38536 −0.234169
3636 0 0
3737 3.48068 0.572220 0.286110 0.958197i 0.407638π-0.407638\pi
0.286110 + 0.958197i 0.407638π0.407638\pi
3838 0 0
3939 0 0
4040 0 0
4141 −12.5583 −1.96128 −0.980641 0.195814i 0.937265π-0.937265\pi
−0.980641 + 0.195814i 0.937265π0.937265\pi
4242 0 0
4343 −6.15682 −0.938906 −0.469453 0.882958i 0.655549π-0.655549\pi
−0.469453 + 0.882958i 0.655549π0.655549\pi
4444 0 0
4545 0.0914616 0.0136343
4646 0 0
4747 −7.40432 −1.08003 −0.540015 0.841655i 0.681582π-0.681582\pi
−0.540015 + 0.841655i 0.681582π0.681582\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 −2.73593 −0.383107
5252 0 0
5353 11.2301 1.54257 0.771285 0.636490i 0.219614π-0.219614\pi
0.771285 + 0.636490i 0.219614π0.219614\pi
5454 0 0
5555 1.59719 0.215365
5656 0 0
5757 −14.6895 −1.94567
5858 0 0
5959 −8.05559 −1.04875 −0.524374 0.851488i 0.675701π-0.675701\pi
−0.524374 + 0.851488i 0.675701π0.675701\pi
6060 0 0
6161 1.65841 0.212338 0.106169 0.994348i 0.466142π-0.466142\pi
0.106169 + 0.994348i 0.466142π0.466142\pi
6262 0 0
6363 −0.0660200 −0.00831774
6464 0 0
6565 0 0
6666 0 0
6767 3.71128 0.453405 0.226702 0.973964i 0.427206π-0.427206\pi
0.226702 + 0.973964i 0.427206π0.427206\pi
6868 0 0
6969 −3.88958 −0.468251
7070 0 0
7171 9.93663 1.17926 0.589631 0.807673i 0.299273π-0.299273\pi
0.589631 + 0.807673i 0.299273π0.299273\pi
7272 0 0
7373 −3.30200 −0.386470 −0.193235 0.981153i 0.561898π-0.561898\pi
−0.193235 + 0.981153i 0.561898π0.561898\pi
7474 0 0
7575 −5.39444 −0.622897
7676 0 0
7777 −1.15290 −0.131385
7878 0 0
7979 4.64811 0.522953 0.261477 0.965210i 0.415791π-0.415791\pi
0.261477 + 0.965210i 0.415791π0.415791\pi
8080 0 0
8181 −9.19370 −1.02152
8282 0 0
8383 −1.82551 −0.200376 −0.100188 0.994969i 0.531944π-0.531944\pi
−0.100188 + 0.994969i 0.531944π0.531944\pi
8484 0 0
8585 −2.16462 −0.234786
8686 0 0
8787 5.02506 0.538743
8888 0 0
8989 2.37681 0.251941 0.125970 0.992034i 0.459796π-0.459796\pi
0.125970 + 0.992034i 0.459796π0.459796\pi
9090 0 0
9191 0 0
9292 0 0
9393 −11.6446 −1.20749
9494 0 0
9595 −11.6220 −1.19240
9696 0 0
9797 −7.54618 −0.766199 −0.383099 0.923707i 0.625143π-0.625143\pi
−0.383099 + 0.923707i 0.625143π0.625143\pi
9898 0 0
9999 0.0761145 0.00764980
100100 0 0
101101 13.2005 1.31350 0.656751 0.754108i 0.271930π-0.271930\pi
0.656751 + 0.754108i 0.271930π0.271930\pi
102102 0 0
103103 −5.90120 −0.581463 −0.290731 0.956805i 0.593899π-0.593899\pi
−0.290731 + 0.956805i 0.593899π0.593899\pi
104104 0 0
105105 −2.42578 −0.236732
106106 0 0
107107 10.1927 0.985363 0.492682 0.870210i 0.336017π-0.336017\pi
0.492682 + 0.870210i 0.336017π0.336017\pi
108108 0 0
109109 6.14856 0.588925 0.294463 0.955663i 0.404859π-0.404859\pi
0.294463 + 0.955663i 0.404859π0.404859\pi
110110 0 0
111111 6.09469 0.578482
112112 0 0
113113 14.5975 1.37322 0.686609 0.727027i 0.259098π-0.259098\pi
0.686609 + 0.727027i 0.259098π0.259098\pi
114114 0 0
115115 −3.07737 −0.286966
116116 0 0
117117 0 0
118118 0 0
119119 1.56249 0.143233
120120 0 0
121121 −9.67082 −0.879165
122122 0 0
123123 −21.9897 −1.98275
124124 0 0
125125 −11.1948 −1.00129
126126 0 0
127127 8.72229 0.773978 0.386989 0.922084i 0.373515π-0.373515\pi
0.386989 + 0.922084i 0.373515π0.373515\pi
128128 0 0
129129 −10.7806 −0.949180
130130 0 0
131131 19.4433 1.69877 0.849385 0.527773i 0.176973π-0.176973\pi
0.849385 + 0.527773i 0.176973π0.176973\pi
132132 0 0
133133 8.38917 0.727433
134134 0 0
135135 −7.11718 −0.612550
136136 0 0
137137 −3.35460 −0.286602 −0.143301 0.989679i 0.545772π-0.545772\pi
−0.143301 + 0.989679i 0.545772π0.545772\pi
138138 0 0
139139 −7.91259 −0.671137 −0.335568 0.942016i 0.608928π-0.608928\pi
−0.335568 + 0.942016i 0.608928π0.608928\pi
140140 0 0
141141 −12.9650 −1.09185
142142 0 0
143143 0 0
144144 0 0
145145 3.97573 0.330167
146146 0 0
147147 1.75101 0.144420
148148 0 0
149149 2.36432 0.193693 0.0968464 0.995299i 0.469124π-0.469124\pi
0.0968464 + 0.995299i 0.469124π0.469124\pi
150150 0 0
151151 −11.5883 −0.943041 −0.471520 0.881855i 0.656295π-0.656295\pi
−0.471520 + 0.881855i 0.656295π0.656295\pi
152152 0 0
153153 −0.103156 −0.00833965
154154 0 0
155155 −9.21299 −0.740005
156156 0 0
157157 −9.03642 −0.721184 −0.360592 0.932724i 0.617425π-0.617425\pi
−0.360592 + 0.932724i 0.617425π0.617425\pi
158158 0 0
159159 19.6639 1.55945
160160 0 0
161161 2.22134 0.175066
162162 0 0
163163 21.3556 1.67270 0.836351 0.548195i 0.184685π-0.184685\pi
0.836351 + 0.548195i 0.184685π0.184685\pi
164164 0 0
165165 2.79668 0.217721
166166 0 0
167167 −3.18129 −0.246176 −0.123088 0.992396i 0.539280π-0.539280\pi
−0.123088 + 0.992396i 0.539280π0.539280\pi
168168 0 0
169169 0 0
170170 0 0
171171 −0.553853 −0.0423542
172172 0 0
173173 5.33904 0.405920 0.202960 0.979187i 0.434944π-0.434944\pi
0.202960 + 0.979187i 0.434944π0.434944\pi
174174 0 0
175175 3.08077 0.232884
176176 0 0
177177 −14.1054 −1.06023
178178 0 0
179179 9.84558 0.735893 0.367947 0.929847i 0.380061π-0.380061\pi
0.367947 + 0.929847i 0.380061π0.380061\pi
180180 0 0
181181 −15.1253 −1.12425 −0.562127 0.827051i 0.690017π-0.690017\pi
−0.562127 + 0.827051i 0.690017π0.690017\pi
182182 0 0
183183 2.90389 0.214662
184184 0 0
185185 4.82200 0.354521
186186 0 0
187187 −1.80140 −0.131731
188188 0 0
189189 5.13741 0.373692
190190 0 0
191191 −22.1800 −1.60489 −0.802443 0.596729i 0.796467π-0.796467\pi
−0.802443 + 0.596729i 0.796467π0.796467\pi
192192 0 0
193193 −6.97186 −0.501846 −0.250923 0.968007i 0.580734π-0.580734\pi
−0.250923 + 0.968007i 0.580734π0.580734\pi
194194 0 0
195195 0 0
196196 0 0
197197 −19.7332 −1.40593 −0.702966 0.711223i 0.748141π-0.748141\pi
−0.702966 + 0.711223i 0.748141π0.748141\pi
198198 0 0
199199 −13.8039 −0.978529 −0.489265 0.872135i 0.662735π-0.662735\pi
−0.489265 + 0.872135i 0.662735π0.662735\pi
200200 0 0
201201 6.49847 0.458367
202202 0 0
203203 −2.86981 −0.201421
204204 0 0
205205 −17.3978 −1.21512
206206 0 0
207207 −0.146653 −0.0101931
208208 0 0
209209 −9.67188 −0.669018
210210 0 0
211211 −9.47437 −0.652242 −0.326121 0.945328i 0.605742π-0.605742\pi
−0.326121 + 0.945328i 0.605742π0.605742\pi
212212 0 0
213213 17.3991 1.19217
214214 0 0
215215 −8.52942 −0.581702
216216 0 0
217217 6.65024 0.451448
218218 0 0
219219 −5.78182 −0.390699
220220 0 0
221221 0 0
222222 0 0
223223 −14.5879 −0.976878 −0.488439 0.872598i 0.662434π-0.662434\pi
−0.488439 + 0.872598i 0.662434π0.662434\pi
224224 0 0
225225 −0.203392 −0.0135595
226226 0 0
227227 −7.16353 −0.475460 −0.237730 0.971331i 0.576403π-0.576403\pi
−0.237730 + 0.971331i 0.576403π0.576403\pi
228228 0 0
229229 −12.3005 −0.812839 −0.406420 0.913687i 0.633223π-0.633223\pi
−0.406420 + 0.913687i 0.633223π0.633223\pi
230230 0 0
231231 −2.01874 −0.132823
232232 0 0
233233 18.8037 1.23187 0.615936 0.787796i 0.288778π-0.288778\pi
0.615936 + 0.787796i 0.288778π0.288778\pi
234234 0 0
235235 −10.2577 −0.669136
236236 0 0
237237 8.13886 0.528676
238238 0 0
239239 1.60295 0.103686 0.0518432 0.998655i 0.483490π-0.483490\pi
0.0518432 + 0.998655i 0.483490π0.483490\pi
240240 0 0
241241 18.3657 1.18304 0.591519 0.806291i 0.298529π-0.298529\pi
0.591519 + 0.806291i 0.298529π0.298529\pi
242242 0 0
243243 −0.685976 −0.0440054
244244 0 0
245245 1.38536 0.0885076
246246 0 0
247247 0 0
248248 0 0
249249 −3.19649 −0.202569
250250 0 0
251251 −14.3646 −0.906683 −0.453341 0.891337i 0.649768π-0.649768\pi
−0.453341 + 0.891337i 0.649768π0.649768\pi
252252 0 0
253253 −2.56099 −0.161008
254254 0 0
255255 −3.79026 −0.237355
256256 0 0
257257 17.3657 1.08324 0.541620 0.840624i 0.317811π-0.317811\pi
0.541620 + 0.840624i 0.317811π0.317811\pi
258258 0 0
259259 −3.48068 −0.216279
260260 0 0
261261 0.189465 0.0117276
262262 0 0
263263 16.7419 1.03235 0.516175 0.856483i 0.327355π-0.327355\pi
0.516175 + 0.856483i 0.327355π0.327355\pi
264264 0 0
265265 15.5577 0.955704
266266 0 0
267267 4.16180 0.254698
268268 0 0
269269 24.7915 1.51156 0.755781 0.654824i 0.227257π-0.227257\pi
0.755781 + 0.654824i 0.227257π0.227257\pi
270270 0 0
271271 −20.2317 −1.22899 −0.614493 0.788922i 0.710639π-0.710639\pi
−0.614493 + 0.788922i 0.710639π0.710639\pi
272272 0 0
273273 0 0
274274 0 0
275275 −3.55182 −0.214183
276276 0 0
277277 11.0533 0.664127 0.332064 0.943257i 0.392255π-0.392255\pi
0.332064 + 0.943257i 0.392255π0.392255\pi
278278 0 0
279279 −0.439049 −0.0262852
280280 0 0
281281 3.18955 0.190273 0.0951363 0.995464i 0.469671π-0.469671\pi
0.0951363 + 0.995464i 0.469671π0.469671\pi
282282 0 0
283283 17.9296 1.06581 0.532903 0.846177i 0.321101π-0.321101\pi
0.532903 + 0.846177i 0.321101π0.321101\pi
284284 0 0
285285 −20.3503 −1.20545
286286 0 0
287287 12.5583 0.741295
288288 0 0
289289 −14.5586 −0.856389
290290 0 0
291291 −13.2134 −0.774584
292292 0 0
293293 16.9677 0.991264 0.495632 0.868533i 0.334936π-0.334936\pi
0.495632 + 0.868533i 0.334936π0.334936\pi
294294 0 0
295295 −11.1599 −0.649755
296296 0 0
297297 −5.92293 −0.343683
298298 0 0
299299 0 0
300300 0 0
301301 6.15682 0.354873
302302 0 0
303303 23.1142 1.32788
304304 0 0
305305 2.29750 0.131555
306306 0 0
307307 26.9884 1.54031 0.770155 0.637857i 0.220179π-0.220179\pi
0.770155 + 0.637857i 0.220179π0.220179\pi
308308 0 0
309309 −10.3330 −0.587826
310310 0 0
311311 −28.3781 −1.60918 −0.804588 0.593834i 0.797614π-0.797614\pi
−0.804588 + 0.593834i 0.797614π0.797614\pi
312312 0 0
313313 −16.6674 −0.942095 −0.471047 0.882108i 0.656124π-0.656124\pi
−0.471047 + 0.882108i 0.656124π0.656124\pi
314314 0 0
315315 −0.0914616 −0.00515328
316316 0 0
317317 −28.7427 −1.61435 −0.807175 0.590312i 0.799005π-0.799005\pi
−0.807175 + 0.590312i 0.799005π0.799005\pi
318318 0 0
319319 3.30861 0.185247
320320 0 0
321321 17.8474 0.996147
322322 0 0
323323 13.1080 0.729349
324324 0 0
325325 0 0
326326 0 0
327327 10.7662 0.595370
328328 0 0
329329 7.40432 0.408213
330330 0 0
331331 26.1917 1.43963 0.719814 0.694167i 0.244227π-0.244227\pi
0.719814 + 0.694167i 0.244227π0.244227\pi
332332 0 0
333333 0.229794 0.0125927
334334 0 0
335335 5.14147 0.280908
336336 0 0
337337 −4.47831 −0.243949 −0.121975 0.992533i 0.538923π-0.538923\pi
−0.121975 + 0.992533i 0.538923π0.538923\pi
338338 0 0
339339 25.5603 1.38825
340340 0 0
341341 −7.66707 −0.415195
342342 0 0
343343 −1.00000 −0.0539949
344344 0 0
345345 −5.38849 −0.290106
346346 0 0
347347 −26.9212 −1.44520 −0.722602 0.691264i 0.757054π-0.757054\pi
−0.722602 + 0.691264i 0.757054π0.757054\pi
348348 0 0
349349 20.7338 1.10986 0.554928 0.831898i 0.312746π-0.312746\pi
0.554928 + 0.831898i 0.312746π0.312746\pi
350350 0 0
351351 0 0
352352 0 0
353353 11.3041 0.601655 0.300828 0.953679i 0.402737π-0.402737\pi
0.300828 + 0.953679i 0.402737π0.402737\pi
354354 0 0
355355 13.7658 0.730615
356356 0 0
357357 2.73593 0.144801
358358 0 0
359359 −17.7453 −0.936559 −0.468279 0.883580i 0.655126π-0.655126\pi
−0.468279 + 0.883580i 0.655126π0.655126\pi
360360 0 0
361361 51.3781 2.70411
362362 0 0
363363 −16.9337 −0.888786
364364 0 0
365365 −4.57447 −0.239439
366366 0 0
367367 9.56310 0.499190 0.249595 0.968350i 0.419703π-0.419703\pi
0.249595 + 0.968350i 0.419703π0.419703\pi
368368 0 0
369369 −0.829101 −0.0431613
370370 0 0
371371 −11.2301 −0.583036
372372 0 0
373373 11.8835 0.615306 0.307653 0.951499i 0.400456π-0.400456\pi
0.307653 + 0.951499i 0.400456π0.400456\pi
374374 0 0
375375 −19.6022 −1.01225
376376 0 0
377377 0 0
378378 0 0
379379 17.2502 0.886085 0.443042 0.896501i 0.353899π-0.353899\pi
0.443042 + 0.896501i 0.353899π0.353899\pi
380380 0 0
381381 15.2728 0.782448
382382 0 0
383383 −13.0300 −0.665800 −0.332900 0.942962i 0.608027π-0.608027\pi
−0.332900 + 0.942962i 0.608027π0.608027\pi
384384 0 0
385385 −1.59719 −0.0814002
386386 0 0
387387 −0.406473 −0.0206622
388388 0 0
389389 −24.1585 −1.22488 −0.612442 0.790516i 0.709813π-0.709813\pi
−0.612442 + 0.790516i 0.709813π0.709813\pi
390390 0 0
391391 3.47083 0.175528
392392 0 0
393393 34.0454 1.71736
394394 0 0
395395 6.43932 0.323997
396396 0 0
397397 −4.81535 −0.241675 −0.120838 0.992672i 0.538558π-0.538558\pi
−0.120838 + 0.992672i 0.538558π0.538558\pi
398398 0 0
399399 14.6895 0.735394
400400 0 0
401401 −8.02173 −0.400586 −0.200293 0.979736i 0.564189π-0.564189\pi
−0.200293 + 0.979736i 0.564189π0.564189\pi
402402 0 0
403403 0 0
404404 0 0
405405 −12.7366 −0.632887
406406 0 0
407407 4.01288 0.198911
408408 0 0
409409 −9.96745 −0.492859 −0.246429 0.969161i 0.579257π-0.579257\pi
−0.246429 + 0.969161i 0.579257π0.579257\pi
410410 0 0
411411 −5.87391 −0.289739
412412 0 0
413413 8.05559 0.396390
414414 0 0
415415 −2.52900 −0.124144
416416 0 0
417417 −13.8550 −0.678481
418418 0 0
419419 −29.6884 −1.45037 −0.725187 0.688552i 0.758247π-0.758247\pi
−0.725187 + 0.688552i 0.758247π0.758247\pi
420420 0 0
421421 13.1380 0.640305 0.320152 0.947366i 0.396266π-0.396266\pi
0.320152 + 0.947366i 0.396266π0.396266\pi
422422 0 0
423423 −0.488833 −0.0237679
424424 0 0
425425 4.81368 0.233498
426426 0 0
427427 −1.65841 −0.0802562
428428 0 0
429429 0 0
430430 0 0
431431 14.4025 0.693745 0.346872 0.937912i 0.387244π-0.387244\pi
0.346872 + 0.937912i 0.387244π0.387244\pi
432432 0 0
433433 −36.3192 −1.74539 −0.872695 0.488266i 0.837630π-0.837630\pi
−0.872695 + 0.488266i 0.837630π0.837630\pi
434434 0 0
435435 6.96153 0.333780
436436 0 0
437437 18.6352 0.891443
438438 0 0
439439 20.5444 0.980532 0.490266 0.871573i 0.336900π-0.336900\pi
0.490266 + 0.871573i 0.336900π0.336900\pi
440440 0 0
441441 0.0660200 0.00314381
442442 0 0
443443 −25.3211 −1.20304 −0.601521 0.798857i 0.705439π-0.705439\pi
−0.601521 + 0.798857i 0.705439π0.705439\pi
444444 0 0
445445 3.29274 0.156091
446446 0 0
447447 4.13994 0.195812
448448 0 0
449449 33.6015 1.58575 0.792876 0.609383i 0.208583π-0.208583\pi
0.792876 + 0.609383i 0.208583π0.208583\pi
450450 0 0
451451 −14.4785 −0.681767
452452 0 0
453453 −20.2911 −0.953361
454454 0 0
455455 0 0
456456 0 0
457457 −37.9955 −1.77735 −0.888677 0.458534i 0.848375π-0.848375\pi
−0.888677 + 0.458534i 0.848375π0.848375\pi
458458 0 0
459459 8.02717 0.374676
460460 0 0
461461 −36.3513 −1.69305 −0.846525 0.532348i 0.821310π-0.821310\pi
−0.846525 + 0.532348i 0.821310π0.821310\pi
462462 0 0
463463 −35.3400 −1.64239 −0.821194 0.570649i 0.806692π-0.806692\pi
−0.821194 + 0.570649i 0.806692π0.806692\pi
464464 0 0
465465 −16.1320 −0.748104
466466 0 0
467467 29.5717 1.36842 0.684208 0.729287i 0.260148π-0.260148\pi
0.684208 + 0.729287i 0.260148π0.260148\pi
468468 0 0
469469 −3.71128 −0.171371
470470 0 0
471471 −15.8228 −0.729077
472472 0 0
473473 −7.09820 −0.326376
474474 0 0
475475 25.8451 1.18585
476476 0 0
477477 0.741409 0.0339468
478478 0 0
479479 21.7476 0.993672 0.496836 0.867845i 0.334495π-0.334495\pi
0.496836 + 0.867845i 0.334495π0.334495\pi
480480 0 0
481481 0 0
482482 0 0
483483 3.88958 0.176982
484484 0 0
485485 −10.4542 −0.474701
486486 0 0
487487 −30.0473 −1.36157 −0.680786 0.732482i 0.738362π-0.738362\pi
−0.680786 + 0.732482i 0.738362π0.738362\pi
488488 0 0
489489 37.3938 1.69101
490490 0 0
491491 −40.1797 −1.81329 −0.906643 0.421898i 0.861364π-0.861364\pi
−0.906643 + 0.421898i 0.861364π0.861364\pi
492492 0 0
493493 −4.48406 −0.201952
494494 0 0
495495 0.105446 0.00473946
496496 0 0
497497 −9.93663 −0.445719
498498 0 0
499499 −11.7400 −0.525554 −0.262777 0.964857i 0.584638π-0.584638\pi
−0.262777 + 0.964857i 0.584638π0.584638\pi
500500 0 0
501501 −5.57046 −0.248870
502502 0 0
503503 −33.3929 −1.48892 −0.744459 0.667669i 0.767292π-0.767292\pi
−0.744459 + 0.667669i 0.767292π0.767292\pi
504504 0 0
505505 18.2875 0.813784
506506 0 0
507507 0 0
508508 0 0
509509 20.7826 0.921172 0.460586 0.887615i 0.347639π-0.347639\pi
0.460586 + 0.887615i 0.347639π0.347639\pi
510510 0 0
511511 3.30200 0.146072
512512 0 0
513513 43.0986 1.90285
514514 0 0
515515 −8.17531 −0.360247
516516 0 0
517517 −8.53645 −0.375433
518518 0 0
519519 9.34869 0.410362
520520 0 0
521521 7.50239 0.328686 0.164343 0.986403i 0.447450π-0.447450\pi
0.164343 + 0.986403i 0.447450π0.447450\pi
522522 0 0
523523 7.32578 0.320334 0.160167 0.987090i 0.448797π-0.448797\pi
0.160167 + 0.987090i 0.448797π0.448797\pi
524524 0 0
525525 5.39444 0.235433
526526 0 0
527527 10.3909 0.452637
528528 0 0
529529 −18.0656 −0.785462
530530 0 0
531531 −0.531830 −0.0230794
532532 0 0
533533 0 0
534534 0 0
535535 14.1206 0.610485
536536 0 0
537537 17.2397 0.743947
538538 0 0
539539 1.15290 0.0496590
540540 0 0
541541 11.6924 0.502698 0.251349 0.967897i 0.419126π-0.419126\pi
0.251349 + 0.967897i 0.419126π0.419126\pi
542542 0 0
543543 −26.4844 −1.13656
544544 0 0
545545 8.51799 0.364871
546546 0 0
547547 5.10513 0.218280 0.109140 0.994026i 0.465190π-0.465190\pi
0.109140 + 0.994026i 0.465190π0.465190\pi
548548 0 0
549549 0.109488 0.00467285
550550 0 0
551551 −24.0753 −1.02564
552552 0 0
553553 −4.64811 −0.197658
554554 0 0
555555 8.44336 0.358401
556556 0 0
557557 12.5336 0.531065 0.265532 0.964102i 0.414452π-0.414452\pi
0.265532 + 0.964102i 0.414452π0.414452\pi
558558 0 0
559559 0 0
560560 0 0
561561 −3.15426 −0.133173
562562 0 0
563563 3.90630 0.164631 0.0823155 0.996606i 0.473768π-0.473768\pi
0.0823155 + 0.996606i 0.473768π0.473768\pi
564564 0 0
565565 20.2229 0.850782
566566 0 0
567567 9.19370 0.386099
568568 0 0
569569 −46.1329 −1.93399 −0.966996 0.254793i 0.917993π-0.917993\pi
−0.966996 + 0.254793i 0.917993π0.917993\pi
570570 0 0
571571 30.1160 1.26031 0.630157 0.776467i 0.282990π-0.282990\pi
0.630157 + 0.776467i 0.282990π0.282990\pi
572572 0 0
573573 −38.8372 −1.62245
574574 0 0
575575 6.84345 0.285391
576576 0 0
577577 25.6300 1.06699 0.533496 0.845803i 0.320878π-0.320878\pi
0.533496 + 0.845803i 0.320878π0.320878\pi
578578 0 0
579579 −12.2078 −0.507338
580580 0 0
581581 1.82551 0.0757351
582582 0 0
583583 12.9472 0.536217
584584 0 0
585585 0 0
586586 0 0
587587 −13.1805 −0.544018 −0.272009 0.962295i 0.587688π-0.587688\pi
−0.272009 + 0.962295i 0.587688π0.587688\pi
588588 0 0
589589 55.7900 2.29878
590590 0 0
591591 −34.5529 −1.42132
592592 0 0
593593 −6.53704 −0.268444 −0.134222 0.990951i 0.542854π-0.542854\pi
−0.134222 + 0.990951i 0.542854π0.542854\pi
594594 0 0
595595 2.16462 0.0887408
596596 0 0
597597 −24.1706 −0.989238
598598 0 0
599599 12.4244 0.507649 0.253824 0.967250i 0.418311π-0.418311\pi
0.253824 + 0.967250i 0.418311π0.418311\pi
600600 0 0
601601 −18.5404 −0.756278 −0.378139 0.925749i 0.623436π-0.623436\pi
−0.378139 + 0.925749i 0.623436π0.623436\pi
602602 0 0
603603 0.245018 0.00997792
604604 0 0
605605 −13.3976 −0.544690
606606 0 0
607607 15.7445 0.639050 0.319525 0.947578i 0.396477π-0.396477\pi
0.319525 + 0.947578i 0.396477π0.396477\pi
608608 0 0
609609 −5.02506 −0.203626
610610 0 0
611611 0 0
612612 0 0
613613 −19.2599 −0.777901 −0.388950 0.921259i 0.627162π-0.627162\pi
−0.388950 + 0.921259i 0.627162π0.627162\pi
614614 0 0
615615 −30.4637 −1.22842
616616 0 0
617617 43.4020 1.74730 0.873649 0.486557i 0.161748π-0.161748\pi
0.873649 + 0.486557i 0.161748π0.161748\pi
618618 0 0
619619 −13.3880 −0.538109 −0.269054 0.963125i 0.586711π-0.586711\pi
−0.269054 + 0.963125i 0.586711π0.586711\pi
620620 0 0
621621 11.4120 0.457946
622622 0 0
623623 −2.37681 −0.0952247
624624 0 0
625625 −0.105015 −0.00420059
626626 0 0
627627 −16.9355 −0.676339
628628 0 0
629629 −5.43854 −0.216849
630630 0 0
631631 −15.1921 −0.604789 −0.302394 0.953183i 0.597786π-0.597786\pi
−0.302394 + 0.953183i 0.597786π0.597786\pi
632632 0 0
633633 −16.5897 −0.659380
634634 0 0
635635 12.0835 0.479520
636636 0 0
637637 0 0
638638 0 0
639639 0.656016 0.0259516
640640 0 0
641641 −35.9342 −1.41932 −0.709658 0.704546i 0.751151π-0.751151\pi
−0.709658 + 0.704546i 0.751151π0.751151\pi
642642 0 0
643643 8.91979 0.351762 0.175881 0.984411i 0.443723π-0.443723\pi
0.175881 + 0.984411i 0.443723π0.443723\pi
644644 0 0
645645 −14.9351 −0.588068
646646 0 0
647647 9.76721 0.383989 0.191994 0.981396i 0.438505π-0.438505\pi
0.191994 + 0.981396i 0.438505π0.438505\pi
648648 0 0
649649 −9.28730 −0.364558
650650 0 0
651651 11.6446 0.456388
652652 0 0
653653 16.5372 0.647149 0.323575 0.946203i 0.395115π-0.395115\pi
0.323575 + 0.946203i 0.395115π0.395115\pi
654654 0 0
655655 26.9361 1.05248
656656 0 0
657657 −0.217998 −0.00850491
658658 0 0
659659 15.6402 0.609256 0.304628 0.952471i 0.401468π-0.401468\pi
0.304628 + 0.952471i 0.401468π0.401468\pi
660660 0 0
661661 −25.3249 −0.985024 −0.492512 0.870306i 0.663921π-0.663921\pi
−0.492512 + 0.870306i 0.663921π0.663921\pi
662662 0 0
663663 0 0
664664 0 0
665665 11.6220 0.450683
666666 0 0
667667 −6.37484 −0.246835
668668 0 0
669669 −25.5435 −0.987568
670670 0 0
671671 1.91199 0.0738114
672672 0 0
673673 −8.17838 −0.315253 −0.157627 0.987499i 0.550384π-0.550384\pi
−0.157627 + 0.987499i 0.550384π0.550384\pi
674674 0 0
675675 15.8272 0.609189
676676 0 0
677677 44.9616 1.72801 0.864007 0.503480i 0.167947π-0.167947\pi
0.864007 + 0.503480i 0.167947π0.167947\pi
678678 0 0
679679 7.54618 0.289596
680680 0 0
681681 −12.5434 −0.480663
682682 0 0
683683 −20.4486 −0.782444 −0.391222 0.920296i 0.627947π-0.627947\pi
−0.391222 + 0.920296i 0.627947π0.627947\pi
684684 0 0
685685 −4.64733 −0.177565
686686 0 0
687687 −21.5382 −0.821734
688688 0 0
689689 0 0
690690 0 0
691691 33.7107 1.28242 0.641208 0.767367i 0.278433π-0.278433\pi
0.641208 + 0.767367i 0.278433π0.278433\pi
692692 0 0
693693 −0.0761145 −0.00289135
694694 0 0
695695 −10.9618 −0.415805
696696 0 0
697697 19.6223 0.743248
698698 0 0
699699 32.9254 1.24535
700700 0 0
701701 29.6172 1.11862 0.559312 0.828957i 0.311065π-0.311065\pi
0.559312 + 0.828957i 0.311065π0.311065\pi
702702 0 0
703703 −29.2000 −1.10130
704704 0 0
705705 −17.9612 −0.676459
706706 0 0
707707 −13.2005 −0.496457
708708 0 0
709709 −9.92641 −0.372794 −0.186397 0.982474i 0.559681π-0.559681\pi
−0.186397 + 0.982474i 0.559681π0.559681\pi
710710 0 0
711711 0.306868 0.0115085
712712 0 0
713713 14.7725 0.553233
714714 0 0
715715 0 0
716716 0 0
717717 2.80678 0.104821
718718 0 0
719719 −20.6850 −0.771422 −0.385711 0.922620i 0.626044π-0.626044\pi
−0.385711 + 0.922620i 0.626044π0.626044\pi
720720 0 0
721721 5.90120 0.219772
722722 0 0
723723 32.1584 1.19598
724724 0 0
725725 −8.84123 −0.328355
726726 0 0
727727 −4.83449 −0.179301 −0.0896506 0.995973i 0.528575π-0.528575\pi
−0.0896506 + 0.995973i 0.528575π0.528575\pi
728728 0 0
729729 26.3800 0.977035
730730 0 0
731731 9.61998 0.355808
732732 0 0
733733 12.7037 0.469223 0.234612 0.972089i 0.424618π-0.424618\pi
0.234612 + 0.972089i 0.424618π0.424618\pi
734734 0 0
735735 2.42578 0.0894762
736736 0 0
737737 4.27874 0.157609
738738 0 0
739739 −2.58482 −0.0950840 −0.0475420 0.998869i 0.515139π-0.515139\pi
−0.0475420 + 0.998869i 0.515139π0.515139\pi
740740 0 0
741741 0 0
742742 0 0
743743 −11.5276 −0.422906 −0.211453 0.977388i 0.567820π-0.567820\pi
−0.211453 + 0.977388i 0.567820π0.567820\pi
744744 0 0
745745 3.27544 0.120003
746746 0 0
747747 −0.120520 −0.00440961
748748 0 0
749749 −10.1927 −0.372432
750750 0 0
751751 −7.00538 −0.255630 −0.127815 0.991798i 0.540796π-0.540796\pi
−0.127815 + 0.991798i 0.540796π0.540796\pi
752752 0 0
753753 −25.1524 −0.916605
754754 0 0
755755 −16.0540 −0.584264
756756 0 0
757757 −17.2018 −0.625211 −0.312605 0.949883i 0.601202π-0.601202\pi
−0.312605 + 0.949883i 0.601202π0.601202\pi
758758 0 0
759759 −4.48431 −0.162770
760760 0 0
761761 −34.5530 −1.25255 −0.626274 0.779603i 0.715421π-0.715421\pi
−0.626274 + 0.779603i 0.715421π0.715421\pi
762762 0 0
763763 −6.14856 −0.222593
764764 0 0
765765 −0.142908 −0.00516686
766766 0 0
767767 0 0
768768 0 0
769769 −10.9495 −0.394848 −0.197424 0.980318i 0.563258π-0.563258\pi
−0.197424 + 0.980318i 0.563258π0.563258\pi
770770 0 0
771771 30.4074 1.09509
772772 0 0
773773 22.0036 0.791413 0.395707 0.918377i 0.370500π-0.370500\pi
0.395707 + 0.918377i 0.370500π0.370500\pi
774774 0 0
775775 20.4878 0.735945
776776 0 0
777777 −6.09469 −0.218646
778778 0 0
779779 105.354 3.77470
780780 0 0
781781 11.4560 0.409926
782782 0 0
783783 −14.7434 −0.526887
784784 0 0
785785 −12.5187 −0.446812
786786 0 0
787787 −39.3231 −1.40172 −0.700859 0.713300i 0.747200π-0.747200\pi
−0.700859 + 0.713300i 0.747200π0.747200\pi
788788 0 0
789789 29.3152 1.04365
790790 0 0
791791 −14.5975 −0.519028
792792 0 0
793793 0 0
794794 0 0
795795 27.2417 0.966162
796796 0 0
797797 −54.5240 −1.93134 −0.965669 0.259775i 0.916352π-0.916352\pi
−0.965669 + 0.259775i 0.916352π0.916352\pi
798798 0 0
799799 11.5692 0.409289
800800 0 0
801801 0.156917 0.00554438
802802 0 0
803803 −3.80688 −0.134342
804804 0 0
805805 3.07737 0.108463
806806 0 0
807807 43.4100 1.52810
808808 0 0
809809 3.12637 0.109917 0.0549586 0.998489i 0.482497π-0.482497\pi
0.0549586 + 0.998489i 0.482497π0.482497\pi
810810 0 0
811811 −4.48741 −0.157574 −0.0787872 0.996891i 0.525105π-0.525105\pi
−0.0787872 + 0.996891i 0.525105π0.525105\pi
812812 0 0
813813 −35.4258 −1.24244
814814 0 0
815815 29.5853 1.03633
816816 0 0
817817 51.6506 1.80702
818818 0 0
819819 0 0
820820 0 0
821821 24.6872 0.861589 0.430795 0.902450i 0.358233π-0.358233\pi
0.430795 + 0.902450i 0.358233π0.358233\pi
822822 0 0
823823 −11.0134 −0.383904 −0.191952 0.981404i 0.561482π-0.561482\pi
−0.191952 + 0.981404i 0.561482π0.561482\pi
824824 0 0
825825 −6.21926 −0.216527
826826 0 0
827827 −23.8575 −0.829605 −0.414803 0.909911i 0.636149π-0.636149\pi
−0.414803 + 0.909911i 0.636149π0.636149\pi
828828 0 0
829829 20.4314 0.709611 0.354806 0.934940i 0.384547π-0.384547\pi
0.354806 + 0.934940i 0.384547π0.384547\pi
830830 0 0
831831 19.3544 0.671395
832832 0 0
833833 −1.56249 −0.0541372
834834 0 0
835835 −4.40725 −0.152519
836836 0 0
837837 34.1650 1.18092
838838 0 0
839839 −24.2579 −0.837477 −0.418738 0.908107i 0.637528π-0.637528\pi
−0.418738 + 0.908107i 0.637528π0.637528\pi
840840 0 0
841841 −20.7642 −0.716006
842842 0 0
843843 5.58492 0.192355
844844 0 0
845845 0 0
846846 0 0
847847 9.67082 0.332293
848848 0 0
849849 31.3949 1.07747
850850 0 0
851851 −7.73178 −0.265042
852852 0 0
853853 51.8470 1.77521 0.887604 0.460608i 0.152369π-0.152369\pi
0.887604 + 0.460608i 0.152369π0.152369\pi
854854 0 0
855855 −0.767287 −0.0262407
856856 0 0
857857 26.9054 0.919071 0.459536 0.888159i 0.348016π-0.348016\pi
0.459536 + 0.888159i 0.348016π0.348016\pi
858858 0 0
859859 33.4509 1.14133 0.570665 0.821183i 0.306685π-0.306685\pi
0.570665 + 0.821183i 0.306685π0.306685\pi
860860 0 0
861861 21.9897 0.749407
862862 0 0
863863 −5.94352 −0.202320 −0.101160 0.994870i 0.532255π-0.532255\pi
−0.101160 + 0.994870i 0.532255π0.532255\pi
864864 0 0
865865 7.39651 0.251489
866866 0 0
867867 −25.4922 −0.865761
868868 0 0
869869 5.35881 0.181785
870870 0 0
871871 0 0
872872 0 0
873873 −0.498199 −0.0168615
874874 0 0
875875 11.1948 0.378453
876876 0 0
877877 49.6605 1.67692 0.838458 0.544966i 0.183458π-0.183458\pi
0.838458 + 0.544966i 0.183458π0.183458\pi
878878 0 0
879879 29.7105 1.00211
880880 0 0
881881 −21.2905 −0.717294 −0.358647 0.933473i 0.616762π-0.616762\pi
−0.358647 + 0.933473i 0.616762π0.616762\pi
882882 0 0
883883 32.8053 1.10399 0.551993 0.833848i 0.313867π-0.313867\pi
0.551993 + 0.833848i 0.313867π0.313867\pi
884884 0 0
885885 −19.5411 −0.656866
886886 0 0
887887 −17.2358 −0.578721 −0.289361 0.957220i 0.593443π-0.593443\pi
−0.289361 + 0.957220i 0.593443π0.593443\pi
888888 0 0
889889 −8.72229 −0.292536
890890 0 0
891891 −10.5994 −0.355094
892892 0 0
893893 62.1161 2.07863
894894 0 0
895895 13.6397 0.455925
896896 0 0
897897 0 0
898898 0 0
899899 −19.0849 −0.636518
900900 0 0
901901 −17.5469 −0.584572
902902 0 0
903903 10.7806 0.358756
904904 0 0
905905 −20.9540 −0.696535
906906 0 0
907907 −34.6356 −1.15006 −0.575028 0.818134i 0.695009π-0.695009\pi
−0.575028 + 0.818134i 0.695009π0.695009\pi
908908 0 0
909909 0.871499 0.0289058
910910 0 0
911911 −7.85153 −0.260133 −0.130066 0.991505i 0.541519π-0.541519\pi
−0.130066 + 0.991505i 0.541519π0.541519\pi
912912 0 0
913913 −2.10464 −0.0696533
914914 0 0
915915 4.02294 0.132994
916916 0 0
917917 −19.4433 −0.642075
918918 0 0
919919 −36.7317 −1.21167 −0.605834 0.795591i 0.707160π-0.707160\pi
−0.605834 + 0.795591i 0.707160π0.707160\pi
920920 0 0
921921 47.2568 1.55717
922922 0 0
923923 0 0
924924 0 0
925925 −10.7232 −0.352576
926926 0 0
927927 −0.389597 −0.0127961
928928 0 0
929929 33.0655 1.08484 0.542421 0.840107i 0.317508π-0.317508\pi
0.542421 + 0.840107i 0.317508π0.317508\pi
930930 0 0
931931 −8.38917 −0.274944
932932 0 0
933933 −49.6902 −1.62679
934934 0 0
935935 −2.49559 −0.0816146
936936 0 0
937937 −45.8626 −1.49826 −0.749132 0.662421i 0.769529π-0.769529\pi
−0.749132 + 0.662421i 0.769529π0.769529\pi
938938 0 0
939939 −29.1846 −0.952404
940940 0 0
941941 −5.77729 −0.188334 −0.0941671 0.995556i 0.530019π-0.530019\pi
−0.0941671 + 0.995556i 0.530019π0.530019\pi
942942 0 0
943943 27.8964 0.908431
944944 0 0
945945 7.11718 0.231522
946946 0 0
947947 −0.0562941 −0.00182931 −0.000914656 1.00000i 0.500291π-0.500291\pi
−0.000914656 1.00000i 0.500291π0.500291\pi
948948 0 0
949949 0 0
950950 0 0
951951 −50.3286 −1.63202
952952 0 0
953953 −40.1557 −1.30077 −0.650385 0.759605i 0.725392π-0.725392\pi
−0.650385 + 0.759605i 0.725392π0.725392\pi
954954 0 0
955955 −30.7273 −0.994312
956956 0 0
957957 5.79339 0.187274
958958 0 0
959959 3.35460 0.108326
960960 0 0
961961 13.2257 0.426634
962962 0 0
963963 0.672920 0.0216846
964964 0 0
965965 −9.65856 −0.310920
966966 0 0
967967 −32.3647 −1.04078 −0.520390 0.853929i 0.674213π-0.674213\pi
−0.520390 + 0.853929i 0.674213π0.674213\pi
968968 0 0
969969 22.9522 0.737331
970970 0 0
971971 −30.6918 −0.984947 −0.492473 0.870328i 0.663907π-0.663907\pi
−0.492473 + 0.870328i 0.663907π0.663907\pi
972972 0 0
973973 7.91259 0.253666
974974 0 0
975975 0 0
976976 0 0
977977 −5.62992 −0.180117 −0.0900585 0.995936i 0.528705π-0.528705\pi
−0.0900585 + 0.995936i 0.528705π0.528705\pi
978978 0 0
979979 2.74022 0.0875779
980980 0 0
981981 0.405928 0.0129603
982982 0 0
983983 6.66363 0.212537 0.106268 0.994337i 0.466110π-0.466110\pi
0.106268 + 0.994337i 0.466110π0.466110\pi
984984 0 0
985985 −27.3376 −0.871050
986986 0 0
987987 12.9650 0.412681
988988 0 0
989989 13.6764 0.434884
990990 0 0
991991 −52.8312 −1.67824 −0.839120 0.543946i 0.816929π-0.816929\pi
−0.839120 + 0.543946i 0.816929π0.816929\pi
992992 0 0
993993 45.8618 1.45538
994994 0 0
995995 −19.1233 −0.606251
996996 0 0
997997 −14.6367 −0.463548 −0.231774 0.972770i 0.574453π-0.574453\pi
−0.231774 + 0.972770i 0.574453π0.574453\pi
998998 0 0
999999 −17.8817 −0.565752
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 4732.2.a.s.1.6 8
13.5 odd 4 4732.2.g.k.337.11 16
13.6 odd 12 364.2.u.a.309.3 yes 16
13.8 odd 4 4732.2.g.k.337.12 16
13.11 odd 12 364.2.u.a.225.3 16
13.12 even 2 4732.2.a.t.1.6 8
39.11 even 12 3276.2.cf.c.2773.3 16
39.32 even 12 3276.2.cf.c.1765.6 16
52.11 even 12 1456.2.cc.f.225.6 16
52.19 even 12 1456.2.cc.f.673.6 16
91.6 even 12 2548.2.u.c.1765.6 16
91.11 odd 12 2548.2.bq.e.1941.6 16
91.19 even 12 2548.2.bq.c.361.3 16
91.24 even 12 2548.2.bq.c.1941.3 16
91.32 odd 12 2548.2.bb.d.569.3 16
91.37 odd 12 2548.2.bb.d.1733.3 16
91.45 even 12 2548.2.bb.c.569.6 16
91.58 odd 12 2548.2.bq.e.361.6 16
91.76 even 12 2548.2.u.c.589.6 16
91.89 even 12 2548.2.bb.c.1733.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
364.2.u.a.225.3 16 13.11 odd 12
364.2.u.a.309.3 yes 16 13.6 odd 12
1456.2.cc.f.225.6 16 52.11 even 12
1456.2.cc.f.673.6 16 52.19 even 12
2548.2.u.c.589.6 16 91.76 even 12
2548.2.u.c.1765.6 16 91.6 even 12
2548.2.bb.c.569.6 16 91.45 even 12
2548.2.bb.c.1733.6 16 91.89 even 12
2548.2.bb.d.569.3 16 91.32 odd 12
2548.2.bb.d.1733.3 16 91.37 odd 12
2548.2.bq.c.361.3 16 91.19 even 12
2548.2.bq.c.1941.3 16 91.24 even 12
2548.2.bq.e.361.6 16 91.58 odd 12
2548.2.bq.e.1941.6 16 91.11 odd 12
3276.2.cf.c.1765.6 16 39.32 even 12
3276.2.cf.c.2773.3 16 39.11 even 12
4732.2.a.s.1.6 8 1.1 even 1 trivial
4732.2.a.t.1.6 8 13.12 even 2
4732.2.g.k.337.11 16 13.5 odd 4
4732.2.g.k.337.12 16 13.8 odd 4