Properties

Label 5200.2.a.cb.1.2
Level 52005200
Weight 22
Character 5200.1
Self dual yes
Analytic conductor 41.52241.522
Analytic rank 11
Dimension 33
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] = [5200,2,Mod(1,5200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5200.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 5200=245213 5200 = 2^{4} \cdot 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 5200.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: 41.522209051141.5222090511
Analytic rank: 11
Dimension: 33
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x23x+1 x^{3} - x^{2} - 3x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 65)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 0.3111080.311108 of defining polynomial
Character χ\chi == 5200.1

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) == q1.31111q32.90321q71.28100q90.214320q111.00000q13+6.42864q172.21432q19+3.80642q214.68889q23+5.61285q27+8.70964q29+5.59210q31+0.280996q33+2.28100q37+1.31111q39+3.05086q416.36196q431.09679q47+1.42864q498.42864q516.23506q53+2.90321q57+9.26517q590.280996q61+3.71900q63+7.76049q67+6.14764q69+6.08097q7110.2810q73+0.622216q77+14.2351q793.51606q819.52543q8311.4193q875.61285q89+2.90321q917.33185q9318.0415q97+0.274543q99+O(q100)q-1.31111 q^{3} -2.90321 q^{7} -1.28100 q^{9} -0.214320 q^{11} -1.00000 q^{13} +6.42864 q^{17} -2.21432 q^{19} +3.80642 q^{21} -4.68889 q^{23} +5.61285 q^{27} +8.70964 q^{29} +5.59210 q^{31} +0.280996 q^{33} +2.28100 q^{37} +1.31111 q^{39} +3.05086 q^{41} -6.36196 q^{43} -1.09679 q^{47} +1.42864 q^{49} -8.42864 q^{51} -6.23506 q^{53} +2.90321 q^{57} +9.26517 q^{59} -0.280996 q^{61} +3.71900 q^{63} +7.76049 q^{67} +6.14764 q^{69} +6.08097 q^{71} -10.2810 q^{73} +0.622216 q^{77} +14.2351 q^{79} -3.51606 q^{81} -9.52543 q^{83} -11.4193 q^{87} -5.61285 q^{89} +2.90321 q^{91} -7.33185 q^{93} -18.0415 q^{97} +0.274543 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q4q32q7+3q9+6q113q13+6q172q2114q2310q27+6q29+10q316q33+4q394q416q4310q479q4912q51++8q99+O(q100) 3 q - 4 q^{3} - 2 q^{7} + 3 q^{9} + 6 q^{11} - 3 q^{13} + 6 q^{17} - 2 q^{21} - 14 q^{23} - 10 q^{27} + 6 q^{29} + 10 q^{31} - 6 q^{33} + 4 q^{39} - 4 q^{41} - 6 q^{43} - 10 q^{47} - 9 q^{49} - 12 q^{51}+ \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 −1.31111 −0.756968 −0.378484 0.925608i 0.623555π-0.623555\pi
−0.378484 + 0.925608i 0.623555π0.623555\pi
44 0 0
55 0 0
66 0 0
77 −2.90321 −1.09731 −0.548655 0.836049i 0.684860π-0.684860\pi
−0.548655 + 0.836049i 0.684860π0.684860\pi
88 0 0
99 −1.28100 −0.426999
1010 0 0
1111 −0.214320 −0.0646198 −0.0323099 0.999478i 0.510286π-0.510286\pi
−0.0323099 + 0.999478i 0.510286π0.510286\pi
1212 0 0
1313 −1.00000 −0.277350
1414 0 0
1515 0 0
1616 0 0
1717 6.42864 1.55917 0.779587 0.626294i 0.215429π-0.215429\pi
0.779587 + 0.626294i 0.215429π0.215429\pi
1818 0 0
1919 −2.21432 −0.508000 −0.254000 0.967204i 0.581746π-0.581746\pi
−0.254000 + 0.967204i 0.581746π0.581746\pi
2020 0 0
2121 3.80642 0.830630
2222 0 0
2323 −4.68889 −0.977702 −0.488851 0.872367i 0.662584π-0.662584\pi
−0.488851 + 0.872367i 0.662584π0.662584\pi
2424 0 0
2525 0 0
2626 0 0
2727 5.61285 1.08019
2828 0 0
2929 8.70964 1.61734 0.808669 0.588263i 0.200188π-0.200188\pi
0.808669 + 0.588263i 0.200188π0.200188\pi
3030 0 0
3131 5.59210 1.00437 0.502186 0.864760i 0.332529π-0.332529\pi
0.502186 + 0.864760i 0.332529π0.332529\pi
3232 0 0
3333 0.280996 0.0489152
3434 0 0
3535 0 0
3636 0 0
3737 2.28100 0.374993 0.187497 0.982265i 0.439963π-0.439963\pi
0.187497 + 0.982265i 0.439963π0.439963\pi
3838 0 0
3939 1.31111 0.209945
4040 0 0
4141 3.05086 0.476464 0.238232 0.971208i 0.423432π-0.423432\pi
0.238232 + 0.971208i 0.423432π0.423432\pi
4242 0 0
4343 −6.36196 −0.970190 −0.485095 0.874461i 0.661215π-0.661215\pi
−0.485095 + 0.874461i 0.661215π0.661215\pi
4444 0 0
4545 0 0
4646 0 0
4747 −1.09679 −0.159983 −0.0799915 0.996796i 0.525489π-0.525489\pi
−0.0799915 + 0.996796i 0.525489π0.525489\pi
4848 0 0
4949 1.42864 0.204091
5050 0 0
5151 −8.42864 −1.18025
5252 0 0
5353 −6.23506 −0.856452 −0.428226 0.903672i 0.640861π-0.640861\pi
−0.428226 + 0.903672i 0.640861π0.640861\pi
5454 0 0
5555 0 0
5656 0 0
5757 2.90321 0.384540
5858 0 0
5959 9.26517 1.20622 0.603112 0.797657i 0.293927π-0.293927\pi
0.603112 + 0.797657i 0.293927π0.293927\pi
6060 0 0
6161 −0.280996 −0.0359779 −0.0179889 0.999838i 0.505726π-0.505726\pi
−0.0179889 + 0.999838i 0.505726π0.505726\pi
6262 0 0
6363 3.71900 0.468550
6464 0 0
6565 0 0
6666 0 0
6767 7.76049 0.948095 0.474047 0.880499i 0.342793π-0.342793\pi
0.474047 + 0.880499i 0.342793π0.342793\pi
6868 0 0
6969 6.14764 0.740089
7070 0 0
7171 6.08097 0.721678 0.360839 0.932628i 0.382490π-0.382490\pi
0.360839 + 0.932628i 0.382490π0.382490\pi
7272 0 0
7373 −10.2810 −1.20330 −0.601650 0.798760i 0.705490π-0.705490\pi
−0.601650 + 0.798760i 0.705490π0.705490\pi
7474 0 0
7575 0 0
7676 0 0
7777 0.622216 0.0709081
7878 0 0
7979 14.2351 1.60157 0.800785 0.598952i 0.204416π-0.204416\pi
0.800785 + 0.598952i 0.204416π0.204416\pi
8080 0 0
8181 −3.51606 −0.390673
8282 0 0
8383 −9.52543 −1.04555 −0.522776 0.852470i 0.675103π-0.675103\pi
−0.522776 + 0.852470i 0.675103π0.675103\pi
8484 0 0
8585 0 0
8686 0 0
8787 −11.4193 −1.22427
8888 0 0
8989 −5.61285 −0.594961 −0.297480 0.954728i 0.596146π-0.596146\pi
−0.297480 + 0.954728i 0.596146π0.596146\pi
9090 0 0
9191 2.90321 0.304339
9292 0 0
9393 −7.33185 −0.760278
9494 0 0
9595 0 0
9696 0 0
9797 −18.0415 −1.83184 −0.915918 0.401366i 0.868536π-0.868536\pi
−0.915918 + 0.401366i 0.868536π0.868536\pi
9898 0 0
9999 0.274543 0.0275926
100100 0 0
101101 3.93978 0.392022 0.196011 0.980602i 0.437201π-0.437201\pi
0.196011 + 0.980602i 0.437201π0.437201\pi
102102 0 0
103103 −2.82225 −0.278084 −0.139042 0.990286i 0.544402π-0.544402\pi
−0.139042 + 0.990286i 0.544402π0.544402\pi
104104 0 0
105105 0 0
106106 0 0
107107 −17.1175 −1.65481 −0.827407 0.561603i 0.810185π-0.810185\pi
−0.827407 + 0.561603i 0.810185π0.810185\pi
108108 0 0
109109 −16.7239 −1.60186 −0.800931 0.598757i 0.795662π-0.795662\pi
−0.800931 + 0.598757i 0.795662π0.795662\pi
110110 0 0
111111 −2.99063 −0.283858
112112 0 0
113113 1.18421 0.111401 0.0557005 0.998448i 0.482261π-0.482261\pi
0.0557005 + 0.998448i 0.482261π0.482261\pi
114114 0 0
115115 0 0
116116 0 0
117117 1.28100 0.118428
118118 0 0
119119 −18.6637 −1.71090
120120 0 0
121121 −10.9541 −0.995824
122122 0 0
123123 −4.00000 −0.360668
124124 0 0
125125 0 0
126126 0 0
127127 −2.30174 −0.204246 −0.102123 0.994772i 0.532564π-0.532564\pi
−0.102123 + 0.994772i 0.532564π0.532564\pi
128128 0 0
129129 8.34122 0.734403
130130 0 0
131131 13.4193 1.17245 0.586224 0.810149i 0.300614π-0.300614\pi
0.586224 + 0.810149i 0.300614π0.300614\pi
132132 0 0
133133 6.42864 0.557434
134134 0 0
135135 0 0
136136 0 0
137137 19.1526 1.63631 0.818157 0.574995i 0.194996π-0.194996\pi
0.818157 + 0.574995i 0.194996π0.194996\pi
138138 0 0
139139 −19.0923 −1.61939 −0.809696 0.586850i 0.800368π-0.800368\pi
−0.809696 + 0.586850i 0.800368π0.800368\pi
140140 0 0
141141 1.43801 0.121102
142142 0 0
143143 0.214320 0.0179223
144144 0 0
145145 0 0
146146 0 0
147147 −1.87310 −0.154491
148148 0 0
149149 −3.57136 −0.292577 −0.146289 0.989242i 0.546733π-0.546733\pi
−0.146289 + 0.989242i 0.546733π0.546733\pi
150150 0 0
151151 1.26517 0.102958 0.0514792 0.998674i 0.483606π-0.483606\pi
0.0514792 + 0.998674i 0.483606π0.483606\pi
152152 0 0
153153 −8.23506 −0.665765
154154 0 0
155155 0 0
156156 0 0
157157 −5.61285 −0.447954 −0.223977 0.974594i 0.571904π-0.571904\pi
−0.223977 + 0.974594i 0.571904π0.571904\pi
158158 0 0
159159 8.17484 0.648307
160160 0 0
161161 13.6128 1.07284
162162 0 0
163163 −3.71900 −0.291295 −0.145647 0.989337i 0.546527π-0.546527\pi
−0.145647 + 0.989337i 0.546527π0.546527\pi
164164 0 0
165165 0 0
166166 0 0
167167 7.03657 0.544506 0.272253 0.962226i 0.412231π-0.412231\pi
0.272253 + 0.962226i 0.412231π0.412231\pi
168168 0 0
169169 1.00000 0.0769231
170170 0 0
171171 2.83654 0.216915
172172 0 0
173173 0.723926 0.0550391 0.0275195 0.999621i 0.491239π-0.491239\pi
0.0275195 + 0.999621i 0.491239π0.491239\pi
174174 0 0
175175 0 0
176176 0 0
177177 −12.1476 −0.913073
178178 0 0
179179 4.04149 0.302075 0.151037 0.988528i 0.451739π-0.451739\pi
0.151037 + 0.988528i 0.451739π0.451739\pi
180180 0 0
181181 2.34122 0.174021 0.0870107 0.996207i 0.472269π-0.472269\pi
0.0870107 + 0.996207i 0.472269π0.472269\pi
182182 0 0
183183 0.368416 0.0272341
184184 0 0
185185 0 0
186186 0 0
187187 −1.37778 −0.100754
188188 0 0
189189 −16.2953 −1.18531
190190 0 0
191191 2.10171 0.152074 0.0760372 0.997105i 0.475773π-0.475773\pi
0.0760372 + 0.997105i 0.475773π0.475773\pi
192192 0 0
193193 13.5210 0.973262 0.486631 0.873608i 0.338226π-0.338226\pi
0.486631 + 0.873608i 0.338226π0.338226\pi
194194 0 0
195195 0 0
196196 0 0
197197 2.00000 0.142494 0.0712470 0.997459i 0.477302π-0.477302\pi
0.0712470 + 0.997459i 0.477302π0.477302\pi
198198 0 0
199199 −22.1432 −1.56969 −0.784845 0.619692i 0.787257π-0.787257\pi
−0.784845 + 0.619692i 0.787257π0.787257\pi
200200 0 0
201201 −10.1748 −0.717678
202202 0 0
203203 −25.2859 −1.77472
204204 0 0
205205 0 0
206206 0 0
207207 6.00645 0.417477
208208 0 0
209209 0.474572 0.0328269
210210 0 0
211211 −19.6543 −1.35306 −0.676530 0.736415i 0.736517π-0.736517\pi
−0.676530 + 0.736415i 0.736517π0.736517\pi
212212 0 0
213213 −7.97280 −0.546287
214214 0 0
215215 0 0
216216 0 0
217217 −16.2351 −1.10211
218218 0 0
219219 13.4795 0.910860
220220 0 0
221221 −6.42864 −0.432437
222222 0 0
223223 19.6686 1.31711 0.658554 0.752533i 0.271168π-0.271168\pi
0.658554 + 0.752533i 0.271168π0.271168\pi
224224 0 0
225225 0 0
226226 0 0
227227 −13.2716 −0.880869 −0.440434 0.897785i 0.645176π-0.645176\pi
−0.440434 + 0.897785i 0.645176π0.645176\pi
228228 0 0
229229 −2.42864 −0.160489 −0.0802445 0.996775i 0.525570π-0.525570\pi
−0.0802445 + 0.996775i 0.525570π0.525570\pi
230230 0 0
231231 −0.815792 −0.0536752
232232 0 0
233233 −16.1748 −1.05965 −0.529825 0.848107i 0.677742π-0.677742\pi
−0.529825 + 0.848107i 0.677742π0.677742\pi
234234 0 0
235235 0 0
236236 0 0
237237 −18.6637 −1.21234
238238 0 0
239239 12.7763 0.826431 0.413215 0.910633i 0.364406π-0.364406\pi
0.413215 + 0.910633i 0.364406π0.364406\pi
240240 0 0
241241 −5.89829 −0.379942 −0.189971 0.981790i 0.560839π-0.560839\pi
−0.189971 + 0.981790i 0.560839π0.560839\pi
242242 0 0
243243 −12.2286 −0.784466
244244 0 0
245245 0 0
246246 0 0
247247 2.21432 0.140894
248248 0 0
249249 12.4889 0.791450
250250 0 0
251251 2.07313 0.130855 0.0654274 0.997857i 0.479159π-0.479159\pi
0.0654274 + 0.997857i 0.479159π0.479159\pi
252252 0 0
253253 1.00492 0.0631789
254254 0 0
255255 0 0
256256 0 0
257257 −18.3970 −1.14757 −0.573787 0.819005i 0.694526π-0.694526\pi
−0.573787 + 0.819005i 0.694526π0.694526\pi
258258 0 0
259259 −6.62222 −0.411484
260260 0 0
261261 −11.1570 −0.690602
262262 0 0
263263 11.0257 0.679872 0.339936 0.940449i 0.389595π-0.389595\pi
0.339936 + 0.940449i 0.389595π0.389595\pi
264264 0 0
265265 0 0
266266 0 0
267267 7.35905 0.450366
268268 0 0
269269 −16.1432 −0.984268 −0.492134 0.870519i 0.663783π-0.663783\pi
−0.492134 + 0.870519i 0.663783π0.663783\pi
270270 0 0
271271 −13.0114 −0.790385 −0.395192 0.918598i 0.629322π-0.629322\pi
−0.395192 + 0.918598i 0.629322π0.629322\pi
272272 0 0
273273 −3.80642 −0.230375
274274 0 0
275275 0 0
276276 0 0
277277 −7.57136 −0.454919 −0.227459 0.973788i 0.573042π-0.573042\pi
−0.227459 + 0.973788i 0.573042π0.573042\pi
278278 0 0
279279 −7.16346 −0.428865
280280 0 0
281281 6.75557 0.403003 0.201502 0.979488i 0.435418π-0.435418\pi
0.201502 + 0.979488i 0.435418π0.435418\pi
282282 0 0
283283 19.0859 1.13454 0.567269 0.823532i 0.308000π-0.308000\pi
0.567269 + 0.823532i 0.308000π0.308000\pi
284284 0 0
285285 0 0
286286 0 0
287287 −8.85728 −0.522829
288288 0 0
289289 24.3274 1.43102
290290 0 0
291291 23.6543 1.38664
292292 0 0
293293 8.08742 0.472472 0.236236 0.971696i 0.424086π-0.424086\pi
0.236236 + 0.971696i 0.424086π0.424086\pi
294294 0 0
295295 0 0
296296 0 0
297297 −1.20294 −0.0698019
298298 0 0
299299 4.68889 0.271166
300300 0 0
301301 18.4701 1.06460
302302 0 0
303303 −5.16547 −0.296749
304304 0 0
305305 0 0
306306 0 0
307307 −13.4336 −0.766694 −0.383347 0.923604i 0.625229π-0.625229\pi
−0.383347 + 0.923604i 0.625229π0.625229\pi
308308 0 0
309309 3.70027 0.210501
310310 0 0
311311 −20.2034 −1.14563 −0.572815 0.819684i 0.694149π-0.694149\pi
−0.572815 + 0.819684i 0.694149π0.694149\pi
312312 0 0
313313 −15.1111 −0.854129 −0.427064 0.904221i 0.640452π-0.640452\pi
−0.427064 + 0.904221i 0.640452π0.640452\pi
314314 0 0
315315 0 0
316316 0 0
317317 −22.2810 −1.25143 −0.625713 0.780054i 0.715192π-0.715192\pi
−0.625713 + 0.780054i 0.715192π0.715192\pi
318318 0 0
319319 −1.86665 −0.104512
320320 0 0
321321 22.4429 1.25264
322322 0 0
323323 −14.2351 −0.792060
324324 0 0
325325 0 0
326326 0 0
327327 21.9269 1.21256
328328 0 0
329329 3.18421 0.175551
330330 0 0
331331 −8.25581 −0.453780 −0.226890 0.973920i 0.572856π-0.572856\pi
−0.226890 + 0.973920i 0.572856π0.572856\pi
332332 0 0
333333 −2.92195 −0.160122
334334 0 0
335335 0 0
336336 0 0
337337 13.7462 0.748803 0.374402 0.927267i 0.377848π-0.377848\pi
0.374402 + 0.927267i 0.377848π0.377848\pi
338338 0 0
339339 −1.55262 −0.0843270
340340 0 0
341341 −1.19850 −0.0649023
342342 0 0
343343 16.1748 0.873359
344344 0 0
345345 0 0
346346 0 0
347347 1.21924 0.0654523 0.0327262 0.999464i 0.489581π-0.489581\pi
0.0327262 + 0.999464i 0.489581π0.489581\pi
348348 0 0
349349 22.5116 1.20502 0.602510 0.798112i 0.294168π-0.294168\pi
0.602510 + 0.798112i 0.294168π0.294168\pi
350350 0 0
351351 −5.61285 −0.299592
352352 0 0
353353 14.2810 0.760101 0.380050 0.924966i 0.375907π-0.375907\pi
0.380050 + 0.924966i 0.375907π0.375907\pi
354354 0 0
355355 0 0
356356 0 0
357357 24.4701 1.29510
358358 0 0
359359 12.1541 0.641469 0.320734 0.947169i 0.396070π-0.396070\pi
0.320734 + 0.947169i 0.396070π0.396070\pi
360360 0 0
361361 −14.0968 −0.741936
362362 0 0
363363 14.3620 0.753808
364364 0 0
365365 0 0
366366 0 0
367367 −4.65725 −0.243106 −0.121553 0.992585i 0.538788π-0.538788\pi
−0.121553 + 0.992585i 0.538788π0.538788\pi
368368 0 0
369369 −3.90813 −0.203449
370370 0 0
371371 18.1017 0.939794
372372 0 0
373373 −34.9403 −1.80914 −0.904569 0.426328i 0.859807π-0.859807\pi
−0.904569 + 0.426328i 0.859807π0.859807\pi
374374 0 0
375375 0 0
376376 0 0
377377 −8.70964 −0.448569
378378 0 0
379379 17.4717 0.897459 0.448729 0.893668i 0.351877π-0.351877\pi
0.448729 + 0.893668i 0.351877π0.351877\pi
380380 0 0
381381 3.01783 0.154608
382382 0 0
383383 −18.6780 −0.954401 −0.477200 0.878794i 0.658348π-0.658348\pi
−0.477200 + 0.878794i 0.658348π0.658348\pi
384384 0 0
385385 0 0
386386 0 0
387387 8.14965 0.414270
388388 0 0
389389 1.61285 0.0817746 0.0408873 0.999164i 0.486982π-0.486982\pi
0.0408873 + 0.999164i 0.486982π0.486982\pi
390390 0 0
391391 −30.1432 −1.52441
392392 0 0
393393 −17.5941 −0.887506
394394 0 0
395395 0 0
396396 0 0
397397 −6.57628 −0.330054 −0.165027 0.986289i 0.552771π-0.552771\pi
−0.165027 + 0.986289i 0.552771π0.552771\pi
398398 0 0
399399 −8.42864 −0.421960
400400 0 0
401401 −21.9081 −1.09404 −0.547020 0.837120i 0.684238π-0.684238\pi
−0.547020 + 0.837120i 0.684238π0.684238\pi
402402 0 0
403403 −5.59210 −0.278563
404404 0 0
405405 0 0
406406 0 0
407407 −0.488863 −0.0242320
408408 0 0
409409 −10.1936 −0.504040 −0.252020 0.967722i 0.581095π-0.581095\pi
−0.252020 + 0.967722i 0.581095π0.581095\pi
410410 0 0
411411 −25.1111 −1.23864
412412 0 0
413413 −26.8988 −1.32360
414414 0 0
415415 0 0
416416 0 0
417417 25.0321 1.22583
418418 0 0
419419 −7.31756 −0.357486 −0.178743 0.983896i 0.557203π-0.557203\pi
−0.178743 + 0.983896i 0.557203π0.557203\pi
420420 0 0
421421 −7.86665 −0.383397 −0.191698 0.981454i 0.561400π-0.561400\pi
−0.191698 + 0.981454i 0.561400π0.561400\pi
422422 0 0
423423 1.40498 0.0683125
424424 0 0
425425 0 0
426426 0 0
427427 0.815792 0.0394789
428428 0 0
429429 −0.280996 −0.0135666
430430 0 0
431431 38.9195 1.87469 0.937343 0.348407i 0.113277π-0.113277\pi
0.937343 + 0.348407i 0.113277π0.113277\pi
432432 0 0
433433 20.2034 0.970914 0.485457 0.874260i 0.338653π-0.338653\pi
0.485457 + 0.874260i 0.338653π0.338653\pi
434434 0 0
435435 0 0
436436 0 0
437437 10.3827 0.496672
438438 0 0
439439 −10.8889 −0.519700 −0.259850 0.965649i 0.583673π-0.583673\pi
−0.259850 + 0.965649i 0.583673π0.583673\pi
440440 0 0
441441 −1.83008 −0.0871468
442442 0 0
443443 −28.6287 −1.36019 −0.680095 0.733124i 0.738061π-0.738061\pi
−0.680095 + 0.733124i 0.738061π0.738061\pi
444444 0 0
445445 0 0
446446 0 0
447447 4.68244 0.221472
448448 0 0
449449 −10.9304 −0.515838 −0.257919 0.966167i 0.583037π-0.583037\pi
−0.257919 + 0.966167i 0.583037π0.583037\pi
450450 0 0
451451 −0.653858 −0.0307890
452452 0 0
453453 −1.65878 −0.0779363
454454 0 0
455455 0 0
456456 0 0
457457 11.4064 0.533567 0.266784 0.963756i 0.414039π-0.414039\pi
0.266784 + 0.963756i 0.414039π0.414039\pi
458458 0 0
459459 36.0830 1.68421
460460 0 0
461461 −26.1334 −1.21715 −0.608576 0.793496i 0.708259π-0.708259\pi
−0.608576 + 0.793496i 0.708259π0.708259\pi
462462 0 0
463463 −7.92242 −0.368186 −0.184093 0.982909i 0.558935π-0.558935\pi
−0.184093 + 0.982909i 0.558935π0.558935\pi
464464 0 0
465465 0 0
466466 0 0
467467 10.8923 0.504036 0.252018 0.967723i 0.418906π-0.418906\pi
0.252018 + 0.967723i 0.418906π0.418906\pi
468468 0 0
469469 −22.5303 −1.04035
470470 0 0
471471 7.35905 0.339087
472472 0 0
473473 1.36349 0.0626935
474474 0 0
475475 0 0
476476 0 0
477477 7.98709 0.365704
478478 0 0
479479 9.13182 0.417244 0.208622 0.977996i 0.433102π-0.433102\pi
0.208622 + 0.977996i 0.433102π0.433102\pi
480480 0 0
481481 −2.28100 −0.104004
482482 0 0
483483 −17.8479 −0.812108
484484 0 0
485485 0 0
486486 0 0
487487 −16.1891 −0.733600 −0.366800 0.930300i 0.619547π-0.619547\pi
−0.366800 + 0.930300i 0.619547π0.619547\pi
488488 0 0
489489 4.87601 0.220501
490490 0 0
491491 −26.2636 −1.18526 −0.592631 0.805474i 0.701911π-0.701911\pi
−0.592631 + 0.805474i 0.701911π0.701911\pi
492492 0 0
493493 55.9911 2.52171
494494 0 0
495495 0 0
496496 0 0
497497 −17.6543 −0.791905
498498 0 0
499499 −30.0306 −1.34435 −0.672177 0.740391i 0.734641π-0.734641\pi
−0.672177 + 0.740391i 0.734641π0.734641\pi
500500 0 0
501501 −9.22570 −0.412174
502502 0 0
503503 −16.7304 −0.745971 −0.372985 0.927837i 0.621666π-0.621666\pi
−0.372985 + 0.927837i 0.621666π0.621666\pi
504504 0 0
505505 0 0
506506 0 0
507507 −1.31111 −0.0582283
508508 0 0
509509 −11.9684 −0.530488 −0.265244 0.964181i 0.585453π-0.585453\pi
−0.265244 + 0.964181i 0.585453π0.585453\pi
510510 0 0
511511 29.8479 1.32039
512512 0 0
513513 −12.4286 −0.548738
514514 0 0
515515 0 0
516516 0 0
517517 0.235063 0.0103381
518518 0 0
519519 −0.949145 −0.0416628
520520 0 0
521521 5.75065 0.251940 0.125970 0.992034i 0.459796π-0.459796\pi
0.125970 + 0.992034i 0.459796π0.459796\pi
522522 0 0
523523 −20.8035 −0.909674 −0.454837 0.890575i 0.650302π-0.650302\pi
−0.454837 + 0.890575i 0.650302π0.650302\pi
524524 0 0
525525 0 0
526526 0 0
527527 35.9496 1.56599
528528 0 0
529529 −1.01429 −0.0440996
530530 0 0
531531 −11.8687 −0.515056
532532 0 0
533533 −3.05086 −0.132147
534534 0 0
535535 0 0
536536 0 0
537537 −5.29883 −0.228661
538538 0 0
539539 −0.306186 −0.0131883
540540 0 0
541541 16.6222 0.714645 0.357322 0.933981i 0.383690π-0.383690\pi
0.357322 + 0.933981i 0.383690π0.383690\pi
542542 0 0
543543 −3.06959 −0.131729
544544 0 0
545545 0 0
546546 0 0
547547 −29.9748 −1.28163 −0.640815 0.767695i 0.721404π-0.721404\pi
−0.640815 + 0.767695i 0.721404π0.721404\pi
548548 0 0
549549 0.359955 0.0153625
550550 0 0
551551 −19.2859 −0.821608
552552 0 0
553553 −41.3274 −1.75742
554554 0 0
555555 0 0
556556 0 0
557557 5.03657 0.213406 0.106703 0.994291i 0.465971π-0.465971\pi
0.106703 + 0.994291i 0.465971π0.465971\pi
558558 0 0
559559 6.36196 0.269082
560560 0 0
561561 1.80642 0.0762673
562562 0 0
563563 2.88247 0.121482 0.0607408 0.998154i 0.480654π-0.480654\pi
0.0607408 + 0.998154i 0.480654π0.480654\pi
564564 0 0
565565 0 0
566566 0 0
567567 10.2079 0.428690
568568 0 0
569569 −4.37286 −0.183320 −0.0916600 0.995790i 0.529217π-0.529217\pi
−0.0916600 + 0.995790i 0.529217π0.529217\pi
570570 0 0
571571 1.58120 0.0661714 0.0330857 0.999453i 0.489467π-0.489467\pi
0.0330857 + 0.999453i 0.489467π0.489467\pi
572572 0 0
573573 −2.75557 −0.115116
574574 0 0
575575 0 0
576576 0 0
577577 7.61729 0.317112 0.158556 0.987350i 0.449316π-0.449316\pi
0.158556 + 0.987350i 0.449316π0.449316\pi
578578 0 0
579579 −17.7275 −0.736728
580580 0 0
581581 27.6543 1.14730
582582 0 0
583583 1.33630 0.0553438
584584 0 0
585585 0 0
586586 0 0
587587 −46.8243 −1.93264 −0.966322 0.257336i 0.917155π-0.917155\pi
−0.966322 + 0.257336i 0.917155π0.917155\pi
588588 0 0
589589 −12.3827 −0.510221
590590 0 0
591591 −2.62222 −0.107864
592592 0 0
593593 15.9398 0.654568 0.327284 0.944926i 0.393867π-0.393867\pi
0.327284 + 0.944926i 0.393867π0.393867\pi
594594 0 0
595595 0 0
596596 0 0
597597 29.0321 1.18821
598598 0 0
599599 −18.4889 −0.755434 −0.377717 0.925921i 0.623291π-0.623291\pi
−0.377717 + 0.925921i 0.623291π0.623291\pi
600600 0 0
601601 20.7556 0.846637 0.423319 0.905981i 0.360865π-0.360865\pi
0.423319 + 0.905981i 0.360865π0.360865\pi
602602 0 0
603603 −9.94116 −0.404835
604604 0 0
605605 0 0
606606 0 0
607607 36.0765 1.46430 0.732150 0.681143i 0.238517π-0.238517\pi
0.732150 + 0.681143i 0.238517π0.238517\pi
608608 0 0
609609 33.1526 1.34341
610610 0 0
611611 1.09679 0.0443713
612612 0 0
613613 −9.94962 −0.401861 −0.200931 0.979605i 0.564397π-0.564397\pi
−0.200931 + 0.979605i 0.564397π0.564397\pi
614614 0 0
615615 0 0
616616 0 0
617617 −2.09187 −0.0842154 −0.0421077 0.999113i 0.513407π-0.513407\pi
−0.0421077 + 0.999113i 0.513407π0.513407\pi
618618 0 0
619619 −18.4681 −0.742296 −0.371148 0.928574i 0.621036π-0.621036\pi
−0.371148 + 0.928574i 0.621036π0.621036\pi
620620 0 0
621621 −26.3180 −1.05611
622622 0 0
623623 16.2953 0.652857
624624 0 0
625625 0 0
626626 0 0
627627 −0.622216 −0.0248489
628628 0 0
629629 14.6637 0.584680
630630 0 0
631631 38.6657 1.53926 0.769629 0.638492i 0.220441π-0.220441\pi
0.769629 + 0.638492i 0.220441π0.220441\pi
632632 0 0
633633 25.7690 1.02422
634634 0 0
635635 0 0
636636 0 0
637637 −1.42864 −0.0566048
638638 0 0
639639 −7.78970 −0.308156
640640 0 0
641641 24.5718 0.970529 0.485265 0.874367i 0.338723π-0.338723\pi
0.485265 + 0.874367i 0.338723π0.338723\pi
642642 0 0
643643 27.4938 1.08425 0.542125 0.840298i 0.317620π-0.317620\pi
0.542125 + 0.840298i 0.317620π0.317620\pi
644644 0 0
645645 0 0
646646 0 0
647647 13.7812 0.541796 0.270898 0.962608i 0.412679π-0.412679\pi
0.270898 + 0.962608i 0.412679π0.412679\pi
648648 0 0
649649 −1.98571 −0.0779459
650650 0 0
651651 21.2859 0.834261
652652 0 0
653653 2.12045 0.0829795 0.0414897 0.999139i 0.486790π-0.486790\pi
0.0414897 + 0.999139i 0.486790π0.486790\pi
654654 0 0
655655 0 0
656656 0 0
657657 13.1699 0.513807
658658 0 0
659659 −33.8894 −1.32014 −0.660072 0.751203i 0.729474π-0.729474\pi
−0.660072 + 0.751203i 0.729474π0.729474\pi
660660 0 0
661661 −37.3689 −1.45348 −0.726741 0.686912i 0.758966π-0.758966\pi
−0.726741 + 0.686912i 0.758966π0.758966\pi
662662 0 0
663663 8.42864 0.327341
664664 0 0
665665 0 0
666666 0 0
667667 −40.8385 −1.58127
668668 0 0
669669 −25.7877 −0.997010
670670 0 0
671671 0.0602231 0.00232489
672672 0 0
673673 35.4608 1.36691 0.683456 0.729992i 0.260476π-0.260476\pi
0.683456 + 0.729992i 0.260476π0.260476\pi
674674 0 0
675675 0 0
676676 0 0
677677 −15.3047 −0.588206 −0.294103 0.955774i 0.595021π-0.595021\pi
−0.294103 + 0.955774i 0.595021π0.595021\pi
678678 0 0
679679 52.3783 2.01009
680680 0 0
681681 17.4005 0.666790
682682 0 0
683683 −13.0968 −0.501135 −0.250567 0.968099i 0.580617π-0.580617\pi
−0.250567 + 0.968099i 0.580617π0.580617\pi
684684 0 0
685685 0 0
686686 0 0
687687 3.18421 0.121485
688688 0 0
689689 6.23506 0.237537
690690 0 0
691691 18.4079 0.700269 0.350135 0.936699i 0.386136π-0.386136\pi
0.350135 + 0.936699i 0.386136π0.386136\pi
692692 0 0
693693 −0.797056 −0.0302777
694694 0 0
695695 0 0
696696 0 0
697697 19.6128 0.742890
698698 0 0
699699 21.2070 0.802121
700700 0 0
701701 −31.3689 −1.18479 −0.592393 0.805649i 0.701817π-0.701817\pi
−0.592393 + 0.805649i 0.701817π0.701817\pi
702702 0 0
703703 −5.05086 −0.190497
704704 0 0
705705 0 0
706706 0 0
707707 −11.4380 −0.430171
708708 0 0
709709 9.47949 0.356010 0.178005 0.984030i 0.443036π-0.443036\pi
0.178005 + 0.984030i 0.443036π0.443036\pi
710710 0 0
711711 −18.2351 −0.683868
712712 0 0
713713 −26.2208 −0.981976
714714 0 0
715715 0 0
716716 0 0
717717 −16.7511 −0.625582
718718 0 0
719719 29.6227 1.10474 0.552370 0.833599i 0.313724π-0.313724\pi
0.552370 + 0.833599i 0.313724π0.313724\pi
720720 0 0
721721 8.19358 0.305145
722722 0 0
723723 7.73329 0.287604
724724 0 0
725725 0 0
726726 0 0
727727 42.6702 1.58255 0.791274 0.611461i 0.209418π-0.209418\pi
0.791274 + 0.611461i 0.209418π0.209418\pi
728728 0 0
729729 26.5812 0.984489
730730 0 0
731731 −40.8988 −1.51270
732732 0 0
733733 −26.0830 −0.963397 −0.481698 0.876337i 0.659980π-0.659980\pi
−0.481698 + 0.876337i 0.659980π0.659980\pi
734734 0 0
735735 0 0
736736 0 0
737737 −1.66323 −0.0612657
738738 0 0
739739 28.2687 1.03988 0.519941 0.854202i 0.325954π-0.325954\pi
0.519941 + 0.854202i 0.325954π0.325954\pi
740740 0 0
741741 −2.90321 −0.106652
742742 0 0
743743 20.6681 0.758241 0.379120 0.925347i 0.376227π-0.376227\pi
0.379120 + 0.925347i 0.376227π0.376227\pi
744744 0 0
745745 0 0
746746 0 0
747747 12.2020 0.446449
748748 0 0
749749 49.6958 1.81585
750750 0 0
751751 −2.46028 −0.0897770 −0.0448885 0.998992i 0.514293π-0.514293\pi
−0.0448885 + 0.998992i 0.514293π0.514293\pi
752752 0 0
753753 −2.71810 −0.0990530
754754 0 0
755755 0 0
756756 0 0
757757 48.6035 1.76652 0.883262 0.468880i 0.155342π-0.155342\pi
0.883262 + 0.468880i 0.155342π0.155342\pi
758758 0 0
759759 −1.31756 −0.0478244
760760 0 0
761761 −13.8252 −0.501162 −0.250581 0.968096i 0.580622π-0.580622\pi
−0.250581 + 0.968096i 0.580622π0.580622\pi
762762 0 0
763763 48.5531 1.75774
764764 0 0
765765 0 0
766766 0 0
767767 −9.26517 −0.334546
768768 0 0
769769 −38.9688 −1.40525 −0.702626 0.711559i 0.747989π-0.747989\pi
−0.702626 + 0.711559i 0.747989π0.747989\pi
770770 0 0
771771 24.1204 0.868677
772772 0 0
773773 0.445992 0.0160412 0.00802061 0.999968i 0.497447π-0.497447\pi
0.00802061 + 0.999968i 0.497447π0.497447\pi
774774 0 0
775775 0 0
776776 0 0
777777 8.68244 0.311481
778778 0 0
779779 −6.75557 −0.242043
780780 0 0
781781 −1.30327 −0.0466347
782782 0 0
783783 48.8859 1.74704
784784 0 0
785785 0 0
786786 0 0
787787 −33.9037 −1.20854 −0.604268 0.796781i 0.706534π-0.706534\pi
−0.604268 + 0.796781i 0.706534π0.706534\pi
788788 0 0
789789 −14.4558 −0.514641
790790 0 0
791791 −3.43801 −0.122241
792792 0 0
793793 0.280996 0.00997847
794794 0 0
795795 0 0
796796 0 0
797797 −10.2953 −0.364678 −0.182339 0.983236i 0.558367π-0.558367\pi
−0.182339 + 0.983236i 0.558367π0.558367\pi
798798 0 0
799799 −7.05086 −0.249441
800800 0 0
801801 7.19004 0.254047
802802 0 0
803803 2.20342 0.0777570
804804 0 0
805805 0 0
806806 0 0
807807 21.1655 0.745060
808808 0 0
809809 7.94422 0.279304 0.139652 0.990201i 0.455402π-0.455402\pi
0.139652 + 0.990201i 0.455402π0.455402\pi
810810 0 0
811811 8.12245 0.285218 0.142609 0.989779i 0.454451π-0.454451\pi
0.142609 + 0.989779i 0.454451π0.454451\pi
812812 0 0
813813 17.0593 0.598296
814814 0 0
815815 0 0
816816 0 0
817817 14.0874 0.492856
818818 0 0
819819 −3.71900 −0.129953
820820 0 0
821821 −22.2065 −0.775012 −0.387506 0.921867i 0.626663π-0.626663\pi
−0.387506 + 0.921867i 0.626663π0.626663\pi
822822 0 0
823823 −11.1175 −0.387533 −0.193766 0.981048i 0.562070π-0.562070\pi
−0.193766 + 0.981048i 0.562070π0.562070\pi
824824 0 0
825825 0 0
826826 0 0
827827 −23.1570 −0.805248 −0.402624 0.915365i 0.631902π-0.631902\pi
−0.402624 + 0.915365i 0.631902π0.631902\pi
828828 0 0
829829 −27.1195 −0.941901 −0.470950 0.882160i 0.656089π-0.656089\pi
−0.470950 + 0.882160i 0.656089π0.656089\pi
830830 0 0
831831 9.92687 0.344359
832832 0 0
833833 9.18421 0.318214
834834 0 0
835835 0 0
836836 0 0
837837 31.3876 1.08492
838838 0 0
839839 −25.3955 −0.876749 −0.438374 0.898792i 0.644446π-0.644446\pi
−0.438374 + 0.898792i 0.644446π0.644446\pi
840840 0 0
841841 46.8578 1.61578
842842 0 0
843843 −8.85728 −0.305061
844844 0 0
845845 0 0
846846 0 0
847847 31.8020 1.09273
848848 0 0
849849 −25.0237 −0.858810
850850 0 0
851851 −10.6953 −0.366632
852852 0 0
853853 25.0651 0.858214 0.429107 0.903254i 0.358828π-0.358828\pi
0.429107 + 0.903254i 0.358828π0.358828\pi
854854 0 0
855855 0 0
856856 0 0
857857 7.61285 0.260050 0.130025 0.991511i 0.458494π-0.458494\pi
0.130025 + 0.991511i 0.458494π0.458494\pi
858858 0 0
859859 −42.1432 −1.43791 −0.718954 0.695058i 0.755379π-0.755379\pi
−0.718954 + 0.695058i 0.755379π0.755379\pi
860860 0 0
861861 11.6128 0.395765
862862 0 0
863863 −51.5768 −1.75569 −0.877847 0.478942i 0.841020π-0.841020\pi
−0.877847 + 0.478942i 0.841020π0.841020\pi
864864 0 0
865865 0 0
866866 0 0
867867 −31.8959 −1.08324
868868 0 0
869869 −3.05086 −0.103493
870870 0 0
871871 −7.76049 −0.262954
872872 0 0
873873 23.1111 0.782191
874874 0 0
875875 0 0
876876 0 0
877877 −34.0701 −1.15046 −0.575232 0.817990i 0.695088π-0.695088\pi
−0.575232 + 0.817990i 0.695088π0.695088\pi
878878 0 0
879879 −10.6035 −0.357646
880880 0 0
881881 3.71900 0.125296 0.0626482 0.998036i 0.480045π-0.480045\pi
0.0626482 + 0.998036i 0.480045π0.480045\pi
882882 0 0
883883 42.0163 1.41396 0.706981 0.707233i 0.250057π-0.250057\pi
0.706981 + 0.707233i 0.250057π0.250057\pi
884884 0 0
885885 0 0
886886 0 0
887887 40.3116 1.35353 0.676765 0.736199i 0.263381π-0.263381\pi
0.676765 + 0.736199i 0.263381π0.263381\pi
888888 0 0
889889 6.68244 0.224122
890890 0 0
891891 0.753561 0.0252452
892892 0 0
893893 2.42864 0.0812713
894894 0 0
895895 0 0
896896 0 0
897897 −6.14764 −0.205264
898898 0 0
899899 48.7052 1.62441
900900 0 0
901901 −40.0830 −1.33536
902902 0 0
903903 −24.2163 −0.805869
904904 0 0
905905 0 0
906906 0 0
907907 −34.8419 −1.15691 −0.578454 0.815715i 0.696344π-0.696344\pi
−0.578454 + 0.815715i 0.696344π0.696344\pi
908908 0 0
909909 −5.04684 −0.167393
910910 0 0
911911 −23.2672 −0.770876 −0.385438 0.922734i 0.625950π-0.625950\pi
−0.385438 + 0.922734i 0.625950π0.625950\pi
912912 0 0
913913 2.04149 0.0675634
914914 0 0
915915 0 0
916916 0 0
917917 −38.9590 −1.28654
918918 0 0
919919 3.22570 0.106406 0.0532029 0.998584i 0.483057π-0.483057\pi
0.0532029 + 0.998584i 0.483057π0.483057\pi
920920 0 0
921921 17.6128 0.580363
922922 0 0
923923 −6.08097 −0.200157
924924 0 0
925925 0 0
926926 0 0
927927 3.61529 0.118742
928928 0 0
929929 −39.3461 −1.29091 −0.645453 0.763800i 0.723331π-0.723331\pi
−0.645453 + 0.763800i 0.723331π0.723331\pi
930930 0 0
931931 −3.16346 −0.103678
932932 0 0
933933 26.4889 0.867206
934934 0 0
935935 0 0
936936 0 0
937937 −51.6040 −1.68583 −0.842914 0.538048i 0.819162π-0.819162\pi
−0.842914 + 0.538048i 0.819162π0.819162\pi
938938 0 0
939939 19.8123 0.646548
940940 0 0
941941 37.5081 1.22273 0.611364 0.791349i 0.290621π-0.290621\pi
0.611364 + 0.791349i 0.290621π0.290621\pi
942942 0 0
943943 −14.3051 −0.465839
944944 0 0
945945 0 0
946946 0 0
947947 −38.1160 −1.23860 −0.619302 0.785153i 0.712584π-0.712584\pi
−0.619302 + 0.785153i 0.712584π0.712584\pi
948948 0 0
949949 10.2810 0.333735
950950 0 0
951951 29.2128 0.947290
952952 0 0
953953 28.7368 0.930877 0.465439 0.885080i 0.345897π-0.345897\pi
0.465439 + 0.885080i 0.345897π0.345897\pi
954954 0 0
955955 0 0
956956 0 0
957957 2.44738 0.0791124
958958 0 0
959959 −55.6040 −1.79555
960960 0 0
961961 0.271628 0.00876221
962962 0 0
963963 21.9275 0.706604
964964 0 0
965965 0 0
966966 0 0
967967 29.0593 0.934485 0.467242 0.884129i 0.345248π-0.345248\pi
0.467242 + 0.884129i 0.345248π0.345248\pi
968968 0 0
969969 18.6637 0.599565
970970 0 0
971971 39.8578 1.27910 0.639548 0.768751i 0.279121π-0.279121\pi
0.639548 + 0.768751i 0.279121π0.279121\pi
972972 0 0
973973 55.4291 1.77698
974974 0 0
975975 0 0
976976 0 0
977977 12.8617 0.411483 0.205742 0.978606i 0.434039π-0.434039\pi
0.205742 + 0.978606i 0.434039π0.434039\pi
978978 0 0
979979 1.20294 0.0384463
980980 0 0
981981 21.4233 0.683993
982982 0 0
983983 45.4880 1.45084 0.725420 0.688306i 0.241645π-0.241645\pi
0.725420 + 0.688306i 0.241645π0.241645\pi
984984 0 0
985985 0 0
986986 0 0
987987 −4.17484 −0.132887
988988 0 0
989989 29.8306 0.948557
990990 0 0
991991 −8.07007 −0.256354 −0.128177 0.991751i 0.540913π-0.540913\pi
−0.128177 + 0.991751i 0.540913π0.540913\pi
992992 0 0
993993 10.8243 0.343497
994994 0 0
995995 0 0
996996 0 0
997997 32.8158 1.03929 0.519643 0.854383i 0.326065π-0.326065\pi
0.519643 + 0.854383i 0.326065π0.326065\pi
998998 0 0
999999 12.8029 0.405065
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 5200.2.a.cb.1.2 3
4.3 odd 2 325.2.a.k.1.1 3
5.2 odd 4 1040.2.d.c.209.5 6
5.3 odd 4 1040.2.d.c.209.2 6
5.4 even 2 5200.2.a.cj.1.2 3
12.11 even 2 2925.2.a.bf.1.3 3
20.3 even 4 65.2.b.a.14.4 yes 6
20.7 even 4 65.2.b.a.14.3 6
20.19 odd 2 325.2.a.j.1.3 3
52.51 odd 2 4225.2.a.ba.1.3 3
60.23 odd 4 585.2.c.b.469.3 6
60.47 odd 4 585.2.c.b.469.4 6
60.59 even 2 2925.2.a.bj.1.1 3
260.3 even 12 845.2.n.f.529.3 12
260.7 odd 12 845.2.l.e.699.1 12
260.23 even 12 845.2.n.g.529.4 12
260.43 even 12 845.2.n.g.484.3 12
260.47 odd 4 845.2.d.a.844.5 6
260.63 odd 12 845.2.l.d.654.5 12
260.67 odd 12 845.2.l.d.654.6 12
260.83 odd 4 845.2.d.a.844.6 6
260.87 even 12 845.2.n.f.484.3 12
260.103 even 4 845.2.b.c.339.3 6
260.107 even 12 845.2.n.f.529.4 12
260.123 odd 12 845.2.l.e.699.2 12
260.127 even 12 845.2.n.g.529.3 12
260.147 even 12 845.2.n.g.484.4 12
260.163 odd 12 845.2.l.d.699.6 12
260.167 odd 12 845.2.l.e.654.2 12
260.187 odd 4 845.2.d.b.844.1 6
260.203 odd 4 845.2.d.b.844.2 6
260.207 even 4 845.2.b.c.339.4 6
260.223 odd 12 845.2.l.e.654.1 12
260.227 odd 12 845.2.l.d.699.5 12
260.243 even 12 845.2.n.f.484.4 12
260.259 odd 2 4225.2.a.bh.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.b.a.14.3 6 20.7 even 4
65.2.b.a.14.4 yes 6 20.3 even 4
325.2.a.j.1.3 3 20.19 odd 2
325.2.a.k.1.1 3 4.3 odd 2
585.2.c.b.469.3 6 60.23 odd 4
585.2.c.b.469.4 6 60.47 odd 4
845.2.b.c.339.3 6 260.103 even 4
845.2.b.c.339.4 6 260.207 even 4
845.2.d.a.844.5 6 260.47 odd 4
845.2.d.a.844.6 6 260.83 odd 4
845.2.d.b.844.1 6 260.187 odd 4
845.2.d.b.844.2 6 260.203 odd 4
845.2.l.d.654.5 12 260.63 odd 12
845.2.l.d.654.6 12 260.67 odd 12
845.2.l.d.699.5 12 260.227 odd 12
845.2.l.d.699.6 12 260.163 odd 12
845.2.l.e.654.1 12 260.223 odd 12
845.2.l.e.654.2 12 260.167 odd 12
845.2.l.e.699.1 12 260.7 odd 12
845.2.l.e.699.2 12 260.123 odd 12
845.2.n.f.484.3 12 260.87 even 12
845.2.n.f.484.4 12 260.243 even 12
845.2.n.f.529.3 12 260.3 even 12
845.2.n.f.529.4 12 260.107 even 12
845.2.n.g.484.3 12 260.43 even 12
845.2.n.g.484.4 12 260.147 even 12
845.2.n.g.529.3 12 260.127 even 12
845.2.n.g.529.4 12 260.23 even 12
1040.2.d.c.209.2 6 5.3 odd 4
1040.2.d.c.209.5 6 5.2 odd 4
2925.2.a.bf.1.3 3 12.11 even 2
2925.2.a.bj.1.1 3 60.59 even 2
4225.2.a.ba.1.3 3 52.51 odd 2
4225.2.a.bh.1.1 3 260.259 odd 2
5200.2.a.cb.1.2 3 1.1 even 1 trivial
5200.2.a.cj.1.2 3 5.4 even 2