Properties

Label 4732.2.a.s.1.5
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

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [4732,2,Mod(1,4732)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage: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")
 
Copy content magma://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

Copy content comment:select newform
 
Copy content sage:traces = [8,0,0,0,-6,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content 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)
Copy content comment:defining polynomial
 
Copy content 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 1.5
Root 1.17707-1.17707 of defining polynomial
Character χ\chi == 4732.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.17707q3+1.46614q51.00000q71.61452q92.75012q11+1.72574q15+4.79948q17+1.97179q191.17707q212.93781q232.85043q255.43159q275.46889q293.90020q313.23707q331.46614q352.16723q379.44655q41+11.6086q432.36711q4510.3753q47+1.00000q49+5.64930q51+1.24369q534.03207q55+2.32092q57+4.56755q59+8.39800q61+1.61452q633.75711q673.45799q699.90743q715.93768q733.35514q75+2.75012q7712.8697q791.54979q81+0.811244q83+7.03671q856.43725q87+9.67958q894.59079q93+2.89092q95+9.51440q97+4.44012q99+O(q100)q+1.17707 q^{3} +1.46614 q^{5} -1.00000 q^{7} -1.61452 q^{9} -2.75012 q^{11} +1.72574 q^{15} +4.79948 q^{17} +1.97179 q^{19} -1.17707 q^{21} -2.93781 q^{23} -2.85043 q^{25} -5.43159 q^{27} -5.46889 q^{29} -3.90020 q^{31} -3.23707 q^{33} -1.46614 q^{35} -2.16723 q^{37} -9.44655 q^{41} +11.6086 q^{43} -2.36711 q^{45} -10.3753 q^{47} +1.00000 q^{49} +5.64930 q^{51} +1.24369 q^{53} -4.03207 q^{55} +2.32092 q^{57} +4.56755 q^{59} +8.39800 q^{61} +1.61452 q^{63} -3.75711 q^{67} -3.45799 q^{69} -9.90743 q^{71} -5.93768 q^{73} -3.35514 q^{75} +2.75012 q^{77} -12.8697 q^{79} -1.54979 q^{81} +0.811244 q^{83} +7.03671 q^{85} -6.43725 q^{87} +9.67958 q^{89} -4.59079 q^{93} +2.89092 q^{95} +9.51440 q^{97} +4.44012 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 1.17707 0.679579 0.339790 0.940501i 0.389644π-0.389644\pi
0.339790 + 0.940501i 0.389644π0.389644\pi
44 0 0
55 1.46614 0.655678 0.327839 0.944734i 0.393680π-0.393680\pi
0.327839 + 0.944734i 0.393680π0.393680\pi
66 0 0
77 −1.00000 −0.377964
88 0 0
99 −1.61452 −0.538172
1010 0 0
1111 −2.75012 −0.829193 −0.414597 0.910005i 0.636077π-0.636077\pi
−0.414597 + 0.910005i 0.636077π0.636077\pi
1212 0 0
1313 0 0
1414 0 0
1515 1.72574 0.445585
1616 0 0
1717 4.79948 1.16404 0.582022 0.813173i 0.302262π-0.302262\pi
0.582022 + 0.813173i 0.302262π0.302262\pi
1818 0 0
1919 1.97179 0.452359 0.226179 0.974086i 0.427376π-0.427376\pi
0.226179 + 0.974086i 0.427376π0.427376\pi
2020 0 0
2121 −1.17707 −0.256857
2222 0 0
2323 −2.93781 −0.612575 −0.306288 0.951939i 0.599087π-0.599087\pi
−0.306288 + 0.951939i 0.599087π0.599087\pi
2424 0 0
2525 −2.85043 −0.570086
2626 0 0
2727 −5.43159 −1.04531
2828 0 0
2929 −5.46889 −1.01555 −0.507774 0.861490i 0.669531π-0.669531\pi
−0.507774 + 0.861490i 0.669531π0.669531\pi
3030 0 0
3131 −3.90020 −0.700497 −0.350248 0.936657i 0.613903π-0.613903\pi
−0.350248 + 0.936657i 0.613903π0.613903\pi
3232 0 0
3333 −3.23707 −0.563502
3434 0 0
3535 −1.46614 −0.247823
3636 0 0
3737 −2.16723 −0.356290 −0.178145 0.984004i 0.557010π-0.557010\pi
−0.178145 + 0.984004i 0.557010π0.557010\pi
3838 0 0
3939 0 0
4040 0 0
4141 −9.44655 −1.47530 −0.737652 0.675181i 0.764065π-0.764065\pi
−0.737652 + 0.675181i 0.764065π0.764065\pi
4242 0 0
4343 11.6086 1.77029 0.885144 0.465316i 0.154059π-0.154059\pi
0.885144 + 0.465316i 0.154059π0.154059\pi
4444 0 0
4545 −2.36711 −0.352868
4646 0 0
4747 −10.3753 −1.51339 −0.756693 0.653770i 0.773186π-0.773186\pi
−0.756693 + 0.653770i 0.773186π0.773186\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 5.64930 0.791061
5252 0 0
5353 1.24369 0.170835 0.0854173 0.996345i 0.472778π-0.472778\pi
0.0854173 + 0.996345i 0.472778π0.472778\pi
5454 0 0
5555 −4.03207 −0.543684
5656 0 0
5757 2.32092 0.307414
5858 0 0
5959 4.56755 0.594644 0.297322 0.954777i 0.403906π-0.403906\pi
0.297322 + 0.954777i 0.403906π0.403906\pi
6060 0 0
6161 8.39800 1.07525 0.537627 0.843183i 0.319321π-0.319321\pi
0.537627 + 0.843183i 0.319321π0.319321\pi
6262 0 0
6363 1.61452 0.203410
6464 0 0
6565 0 0
6666 0 0
6767 −3.75711 −0.459005 −0.229502 0.973308i 0.573710π-0.573710\pi
−0.229502 + 0.973308i 0.573710π0.573710\pi
6868 0 0
6969 −3.45799 −0.416293
7070 0 0
7171 −9.90743 −1.17580 −0.587898 0.808935i 0.700044π-0.700044\pi
−0.587898 + 0.808935i 0.700044π0.700044\pi
7272 0 0
7373 −5.93768 −0.694953 −0.347477 0.937689i 0.612961π-0.612961\pi
−0.347477 + 0.937689i 0.612961π0.612961\pi
7474 0 0
7575 −3.35514 −0.387419
7676 0 0
7777 2.75012 0.313406
7878 0 0
7979 −12.8697 −1.44795 −0.723975 0.689826i 0.757687π-0.757687\pi
−0.723975 + 0.689826i 0.757687π0.757687\pi
8080 0 0
8181 −1.54979 −0.172199
8282 0 0
8383 0.811244 0.0890456 0.0445228 0.999008i 0.485823π-0.485823\pi
0.0445228 + 0.999008i 0.485823π0.485823\pi
8484 0 0
8585 7.03671 0.763239
8686 0 0
8787 −6.43725 −0.690145
8888 0 0
8989 9.67958 1.02603 0.513017 0.858379i 0.328528π-0.328528\pi
0.513017 + 0.858379i 0.328528π0.328528\pi
9090 0 0
9191 0 0
9292 0 0
9393 −4.59079 −0.476043
9494 0 0
9595 2.89092 0.296602
9696 0 0
9797 9.51440 0.966041 0.483020 0.875609i 0.339540π-0.339540\pi
0.483020 + 0.875609i 0.339540π0.339540\pi
9898 0 0
9999 4.44012 0.446249
100100 0 0
101101 10.3663 1.03148 0.515742 0.856744i 0.327516π-0.327516\pi
0.515742 + 0.856744i 0.327516π0.327516\pi
102102 0 0
103103 7.81778 0.770309 0.385155 0.922852i 0.374148π-0.374148\pi
0.385155 + 0.922852i 0.374148π0.374148\pi
104104 0 0
105105 −1.72574 −0.168415
106106 0 0
107107 −9.76845 −0.944351 −0.472176 0.881505i 0.656531π-0.656531\pi
−0.472176 + 0.881505i 0.656531π0.656531\pi
108108 0 0
109109 −12.9827 −1.24352 −0.621758 0.783209i 0.713581π-0.713581\pi
−0.621758 + 0.783209i 0.713581π0.713581\pi
110110 0 0
111111 −2.55097 −0.242127
112112 0 0
113113 −11.0423 −1.03877 −0.519386 0.854540i 0.673839π-0.673839\pi
−0.519386 + 0.854540i 0.673839π0.673839\pi
114114 0 0
115115 −4.30724 −0.401652
116116 0 0
117117 0 0
118118 0 0
119119 −4.79948 −0.439968
120120 0 0
121121 −3.43683 −0.312439
122122 0 0
123123 −11.1192 −1.00259
124124 0 0
125125 −11.5098 −1.02947
126126 0 0
127127 −15.6532 −1.38899 −0.694497 0.719496i 0.744373π-0.744373\pi
−0.694497 + 0.719496i 0.744373π0.744373\pi
128128 0 0
129129 13.6640 1.20305
130130 0 0
131131 −3.84949 −0.336332 −0.168166 0.985759i 0.553784π-0.553784\pi
−0.168166 + 0.985759i 0.553784π0.553784\pi
132132 0 0
133133 −1.97179 −0.170976
134134 0 0
135135 −7.96348 −0.685387
136136 0 0
137137 −6.34437 −0.542036 −0.271018 0.962574i 0.587360π-0.587360\pi
−0.271018 + 0.962574i 0.587360π0.587360\pi
138138 0 0
139139 −10.2971 −0.873386 −0.436693 0.899611i 0.643850π-0.643850\pi
−0.436693 + 0.899611i 0.643850π0.643850\pi
140140 0 0
141141 −12.2124 −1.02847
142142 0 0
143143 0 0
144144 0 0
145145 −8.01817 −0.665873
146146 0 0
147147 1.17707 0.0970827
148148 0 0
149149 −20.4015 −1.67136 −0.835678 0.549220i 0.814925π-0.814925\pi
−0.835678 + 0.549220i 0.814925π0.814925\pi
150150 0 0
151151 −22.8050 −1.85584 −0.927922 0.372774i 0.878407π-0.878407\pi
−0.927922 + 0.372774i 0.878407π0.878407\pi
152152 0 0
153153 −7.74884 −0.626456
154154 0 0
155155 −5.71824 −0.459300
156156 0 0
157157 14.6229 1.16703 0.583516 0.812102i 0.301677π-0.301677\pi
0.583516 + 0.812102i 0.301677π0.301677\pi
158158 0 0
159159 1.46391 0.116096
160160 0 0
161161 2.93781 0.231532
162162 0 0
163163 −0.858968 −0.0672795 −0.0336398 0.999434i 0.510710π-0.510710\pi
−0.0336398 + 0.999434i 0.510710π0.510710\pi
164164 0 0
165165 −4.74601 −0.369476
166166 0 0
167167 5.24059 0.405529 0.202764 0.979228i 0.435007π-0.435007\pi
0.202764 + 0.979228i 0.435007π0.435007\pi
168168 0 0
169169 0 0
170170 0 0
171171 −3.18348 −0.243447
172172 0 0
173173 19.3657 1.47235 0.736174 0.676792i 0.236630π-0.236630\pi
0.736174 + 0.676792i 0.236630π0.236630\pi
174174 0 0
175175 2.85043 0.215472
176176 0 0
177177 5.37631 0.404108
178178 0 0
179179 7.91929 0.591916 0.295958 0.955201i 0.404361π-0.404361\pi
0.295958 + 0.955201i 0.404361π0.404361\pi
180180 0 0
181181 18.5469 1.37858 0.689288 0.724487i 0.257923π-0.257923\pi
0.689288 + 0.724487i 0.257923π0.257923\pi
182182 0 0
183183 9.88499 0.730720
184184 0 0
185185 −3.17746 −0.233612
186186 0 0
187187 −13.1992 −0.965218
188188 0 0
189189 5.43159 0.395090
190190 0 0
191191 15.9759 1.15598 0.577989 0.816045i 0.303838π-0.303838\pi
0.577989 + 0.816045i 0.303838π0.303838\pi
192192 0 0
193193 −13.5305 −0.973945 −0.486972 0.873417i 0.661899π-0.661899\pi
−0.486972 + 0.873417i 0.661899π0.661899\pi
194194 0 0
195195 0 0
196196 0 0
197197 −1.27550 −0.0908753 −0.0454377 0.998967i 0.514468π-0.514468\pi
−0.0454377 + 0.998967i 0.514468π0.514468\pi
198198 0 0
199199 −1.69720 −0.120311 −0.0601555 0.998189i 0.519160π-0.519160\pi
−0.0601555 + 0.998189i 0.519160π0.519160\pi
200200 0 0
201201 −4.42237 −0.311930
202202 0 0
203203 5.46889 0.383841
204204 0 0
205205 −13.8500 −0.967325
206206 0 0
207207 4.74314 0.329671
208208 0 0
209209 −5.42266 −0.375093
210210 0 0
211211 0.0338871 0.00233289 0.00116644 0.999999i 0.499629π-0.499629\pi
0.00116644 + 0.999999i 0.499629π0.499629\pi
212212 0 0
213213 −11.6617 −0.799046
214214 0 0
215215 17.0198 1.16074
216216 0 0
217217 3.90020 0.264763
218218 0 0
219219 −6.98904 −0.472276
220220 0 0
221221 0 0
222222 0 0
223223 22.1213 1.48135 0.740676 0.671862i 0.234505π-0.234505\pi
0.740676 + 0.671862i 0.234505π0.234505\pi
224224 0 0
225225 4.60207 0.306804
226226 0 0
227227 2.07867 0.137966 0.0689832 0.997618i 0.478025π-0.478025\pi
0.0689832 + 0.997618i 0.478025π0.478025\pi
228228 0 0
229229 4.60929 0.304591 0.152295 0.988335i 0.451333π-0.451333\pi
0.152295 + 0.988335i 0.451333π0.451333\pi
230230 0 0
231231 3.23707 0.212984
232232 0 0
233233 27.6690 1.81266 0.906328 0.422576i 0.138874π-0.138874\pi
0.906328 + 0.422576i 0.138874π0.138874\pi
234234 0 0
235235 −15.2116 −0.992295
236236 0 0
237237 −15.1484 −0.983997
238238 0 0
239239 −4.72236 −0.305464 −0.152732 0.988268i 0.548807π-0.548807\pi
−0.152732 + 0.988268i 0.548807π0.548807\pi
240240 0 0
241241 6.16812 0.397323 0.198662 0.980068i 0.436341π-0.436341\pi
0.198662 + 0.980068i 0.436341π0.436341\pi
242242 0 0
243243 14.4706 0.928287
244244 0 0
245245 1.46614 0.0936683
246246 0 0
247247 0 0
248248 0 0
249249 0.954887 0.0605135
250250 0 0
251251 −9.50340 −0.599850 −0.299925 0.953963i 0.596962π-0.596962\pi
−0.299925 + 0.953963i 0.596962π0.596962\pi
252252 0 0
253253 8.07933 0.507943
254254 0 0
255255 8.28267 0.518681
256256 0 0
257257 −16.9509 −1.05737 −0.528684 0.848818i 0.677315π-0.677315\pi
−0.528684 + 0.848818i 0.677315π0.677315\pi
258258 0 0
259259 2.16723 0.134665
260260 0 0
261261 8.82962 0.546539
262262 0 0
263263 −7.66825 −0.472845 −0.236422 0.971650i 0.575975π-0.575975\pi
−0.236422 + 0.971650i 0.575975π0.575975\pi
264264 0 0
265265 1.82343 0.112013
266266 0 0
267267 11.3935 0.697271
268268 0 0
269269 −8.12363 −0.495307 −0.247653 0.968849i 0.579659π-0.579659\pi
−0.247653 + 0.968849i 0.579659π0.579659\pi
270270 0 0
271271 2.10302 0.127749 0.0638746 0.997958i 0.479654π-0.479654\pi
0.0638746 + 0.997958i 0.479654π0.479654\pi
272272 0 0
273273 0 0
274274 0 0
275275 7.83903 0.472711
276276 0 0
277277 −6.14676 −0.369323 −0.184661 0.982802i 0.559119π-0.559119\pi
−0.184661 + 0.982802i 0.559119π0.559119\pi
278278 0 0
279279 6.29694 0.376988
280280 0 0
281281 −17.5826 −1.04889 −0.524445 0.851444i 0.675727π-0.675727\pi
−0.524445 + 0.851444i 0.675727π0.675727\pi
282282 0 0
283283 0.349504 0.0207759 0.0103879 0.999946i 0.496693π-0.496693\pi
0.0103879 + 0.999946i 0.496693π0.496693\pi
284284 0 0
285285 3.40280 0.201565
286286 0 0
287287 9.44655 0.557612
288288 0 0
289289 6.03500 0.355000
290290 0 0
291291 11.1991 0.656501
292292 0 0
293293 1.68707 0.0985595 0.0492798 0.998785i 0.484307π-0.484307\pi
0.0492798 + 0.998785i 0.484307π0.484307\pi
294294 0 0
295295 6.69667 0.389895
296296 0 0
297297 14.9375 0.866764
298298 0 0
299299 0 0
300300 0 0
301301 −11.6086 −0.669106
302302 0 0
303303 12.2018 0.700975
304304 0 0
305305 12.3126 0.705020
306306 0 0
307307 −15.8850 −0.906606 −0.453303 0.891357i 0.649754π-0.649754\pi
−0.453303 + 0.891357i 0.649754π0.649754\pi
308308 0 0
309309 9.20205 0.523486
310310 0 0
311311 5.73424 0.325159 0.162579 0.986695i 0.448019π-0.448019\pi
0.162579 + 0.986695i 0.448019π0.448019\pi
312312 0 0
313313 10.3701 0.586155 0.293078 0.956089i 0.405321π-0.405321\pi
0.293078 + 0.956089i 0.405321π0.405321\pi
314314 0 0
315315 2.36711 0.133371
316316 0 0
317317 20.0766 1.12761 0.563807 0.825907i 0.309336π-0.309336\pi
0.563807 + 0.825907i 0.309336π0.309336\pi
318318 0 0
319319 15.0401 0.842085
320320 0 0
321321 −11.4981 −0.641761
322322 0 0
323323 9.46355 0.526566
324324 0 0
325325 0 0
326326 0 0
327327 −15.2815 −0.845068
328328 0 0
329329 10.3753 0.572006
330330 0 0
331331 −22.6980 −1.24759 −0.623797 0.781586i 0.714411π-0.714411\pi
−0.623797 + 0.781586i 0.714411π0.714411\pi
332332 0 0
333333 3.49902 0.191745
334334 0 0
335335 −5.50846 −0.300959
336336 0 0
337337 31.8134 1.73299 0.866493 0.499189i 0.166369π-0.166369\pi
0.866493 + 0.499189i 0.166369π0.166369\pi
338338 0 0
339339 −12.9975 −0.705927
340340 0 0
341341 10.7260 0.580847
342342 0 0
343343 −1.00000 −0.0539949
344344 0 0
345345 −5.06990 −0.272954
346346 0 0
347347 33.5527 1.80121 0.900603 0.434644i 0.143126π-0.143126\pi
0.900603 + 0.434644i 0.143126π0.143126\pi
348348 0 0
349349 −22.4496 −1.20170 −0.600850 0.799362i 0.705171π-0.705171\pi
−0.600850 + 0.799362i 0.705171π0.705171\pi
350350 0 0
351351 0 0
352352 0 0
353353 −20.3207 −1.08156 −0.540782 0.841163i 0.681871π-0.681871\pi
−0.540782 + 0.841163i 0.681871π0.681871\pi
354354 0 0
355355 −14.5257 −0.770944
356356 0 0
357357 −5.64930 −0.298993
358358 0 0
359359 −32.5948 −1.72029 −0.860144 0.510052i 0.829626π-0.829626\pi
−0.860144 + 0.510052i 0.829626π0.829626\pi
360360 0 0
361361 −15.1121 −0.795371
362362 0 0
363363 −4.04537 −0.212327
364364 0 0
365365 −8.70548 −0.455666
366366 0 0
367367 −15.1385 −0.790222 −0.395111 0.918633i 0.629294π-0.629294\pi
−0.395111 + 0.918633i 0.629294π0.629294\pi
368368 0 0
369369 15.2516 0.793967
370370 0 0
371371 −1.24369 −0.0645694
372372 0 0
373373 −33.0340 −1.71043 −0.855217 0.518270i 0.826576π-0.826576\pi
−0.855217 + 0.518270i 0.826576π0.826576\pi
374374 0 0
375375 −13.5478 −0.699607
376376 0 0
377377 0 0
378378 0 0
379379 −12.9858 −0.667033 −0.333517 0.942744i 0.608235π-0.608235\pi
−0.333517 + 0.942744i 0.608235π0.608235\pi
380380 0 0
381381 −18.4248 −0.943931
382382 0 0
383383 −22.6435 −1.15703 −0.578514 0.815673i 0.696367π-0.696367\pi
−0.578514 + 0.815673i 0.696367π0.696367\pi
384384 0 0
385385 4.03207 0.205493
386386 0 0
387387 −18.7422 −0.952720
388388 0 0
389389 −3.51171 −0.178051 −0.0890254 0.996029i 0.528375π-0.528375\pi
−0.0890254 + 0.996029i 0.528375π0.528375\pi
390390 0 0
391391 −14.0999 −0.713065
392392 0 0
393393 −4.53110 −0.228564
394394 0 0
395395 −18.8687 −0.949389
396396 0 0
397397 17.9590 0.901334 0.450667 0.892692i 0.351186π-0.351186\pi
0.450667 + 0.892692i 0.351186π0.351186\pi
398398 0 0
399399 −2.32092 −0.116191
400400 0 0
401401 9.18476 0.458665 0.229333 0.973348i 0.426346π-0.426346\pi
0.229333 + 0.973348i 0.426346π0.426346\pi
402402 0 0
403403 0 0
404404 0 0
405405 −2.27221 −0.112907
406406 0 0
407407 5.96014 0.295433
408408 0 0
409409 33.1849 1.64089 0.820444 0.571727i 0.193727π-0.193727\pi
0.820444 + 0.571727i 0.193727π0.193727\pi
410410 0 0
411411 −7.46773 −0.368356
412412 0 0
413413 −4.56755 −0.224754
414414 0 0
415415 1.18940 0.0583853
416416 0 0
417417 −12.1203 −0.593535
418418 0 0
419419 −14.7409 −0.720142 −0.360071 0.932925i 0.617248π-0.617248\pi
−0.360071 + 0.932925i 0.617248π0.617248\pi
420420 0 0
421421 26.7288 1.30268 0.651341 0.758785i 0.274207π-0.274207\pi
0.651341 + 0.758785i 0.274207π0.274207\pi
422422 0 0
423423 16.7510 0.814463
424424 0 0
425425 −13.6806 −0.663606
426426 0 0
427427 −8.39800 −0.406408
428428 0 0
429429 0 0
430430 0 0
431431 10.1684 0.489793 0.244897 0.969549i 0.421246π-0.421246\pi
0.244897 + 0.969549i 0.421246π0.421246\pi
432432 0 0
433433 −13.0280 −0.626085 −0.313043 0.949739i 0.601348π-0.601348\pi
−0.313043 + 0.949739i 0.601348π0.601348\pi
434434 0 0
435435 −9.43791 −0.452513
436436 0 0
437437 −5.79273 −0.277104
438438 0 0
439439 21.6571 1.03364 0.516819 0.856095i 0.327116π-0.327116\pi
0.516819 + 0.856095i 0.327116π0.327116\pi
440440 0 0
441441 −1.61452 −0.0768817
442442 0 0
443443 26.2812 1.24866 0.624330 0.781161i 0.285372π-0.285372\pi
0.624330 + 0.781161i 0.285372π0.285372\pi
444444 0 0
445445 14.1916 0.672748
446446 0 0
447447 −24.0139 −1.13582
448448 0 0
449449 −15.1500 −0.714975 −0.357487 0.933918i 0.616366π-0.616366\pi
−0.357487 + 0.933918i 0.616366π0.616366\pi
450450 0 0
451451 25.9792 1.22331
452452 0 0
453453 −26.8430 −1.26119
454454 0 0
455455 0 0
456456 0 0
457457 30.4632 1.42501 0.712505 0.701667i 0.247560π-0.247560\pi
0.712505 + 0.701667i 0.247560π0.247560\pi
458458 0 0
459459 −26.0688 −1.21679
460460 0 0
461461 30.4655 1.41892 0.709461 0.704745i 0.248939π-0.248939\pi
0.709461 + 0.704745i 0.248939π0.248939\pi
462462 0 0
463463 10.4617 0.486197 0.243099 0.970002i 0.421836π-0.421836\pi
0.243099 + 0.970002i 0.421836π0.421836\pi
464464 0 0
465465 −6.73075 −0.312131
466466 0 0
467467 −15.2825 −0.707190 −0.353595 0.935399i 0.615041π-0.615041\pi
−0.353595 + 0.935399i 0.615041π0.615041\pi
468468 0 0
469469 3.75711 0.173487
470470 0 0
471471 17.2121 0.793090
472472 0 0
473473 −31.9250 −1.46791
474474 0 0
475475 −5.62044 −0.257884
476476 0 0
477477 −2.00797 −0.0919384
478478 0 0
479479 −19.5909 −0.895129 −0.447564 0.894252i 0.647708π-0.647708\pi
−0.447564 + 0.894252i 0.647708π0.647708\pi
480480 0 0
481481 0 0
482482 0 0
483483 3.45799 0.157344
484484 0 0
485485 13.9494 0.633412
486486 0 0
487487 6.39343 0.289714 0.144857 0.989453i 0.453728π-0.453728\pi
0.144857 + 0.989453i 0.453728π0.453728\pi
488488 0 0
489489 −1.01106 −0.0457218
490490 0 0
491491 −22.2520 −1.00422 −0.502109 0.864805i 0.667442π-0.667442\pi
−0.502109 + 0.864805i 0.667442π0.667442\pi
492492 0 0
493493 −26.2478 −1.18214
494494 0 0
495495 6.50984 0.292595
496496 0 0
497497 9.90743 0.444409
498498 0 0
499499 30.0165 1.34372 0.671862 0.740677i 0.265495π-0.265495\pi
0.671862 + 0.740677i 0.265495π0.265495\pi
500500 0 0
501501 6.16852 0.275589
502502 0 0
503503 −35.0031 −1.56071 −0.780356 0.625336i 0.784962π-0.784962\pi
−0.780356 + 0.625336i 0.784962π0.784962\pi
504504 0 0
505505 15.1984 0.676322
506506 0 0
507507 0 0
508508 0 0
509509 −9.95401 −0.441204 −0.220602 0.975364i 0.570802π-0.570802\pi
−0.220602 + 0.975364i 0.570802π0.570802\pi
510510 0 0
511511 5.93768 0.262668
512512 0 0
513513 −10.7099 −0.472855
514514 0 0
515515 11.4620 0.505075
516516 0 0
517517 28.5332 1.25489
518518 0 0
519519 22.7947 1.00058
520520 0 0
521521 −7.75549 −0.339774 −0.169887 0.985464i 0.554340π-0.554340\pi
−0.169887 + 0.985464i 0.554340π0.554340\pi
522522 0 0
523523 4.84825 0.211999 0.105999 0.994366i 0.466196π-0.466196\pi
0.105999 + 0.994366i 0.466196π0.466196\pi
524524 0 0
525525 3.35514 0.146430
526526 0 0
527527 −18.7189 −0.815409
528528 0 0
529529 −14.3693 −0.624752
530530 0 0
531531 −7.37438 −0.320021
532532 0 0
533533 0 0
534534 0 0
535535 −14.3219 −0.619191
536536 0 0
537537 9.32153 0.402254
538538 0 0
539539 −2.75012 −0.118456
540540 0 0
541541 28.2030 1.21254 0.606271 0.795258i 0.292665π-0.292665\pi
0.606271 + 0.795258i 0.292665π0.292665\pi
542542 0 0
543543 21.8309 0.936852
544544 0 0
545545 −19.0345 −0.815346
546546 0 0
547547 −1.10083 −0.0470680 −0.0235340 0.999723i 0.507492π-0.507492\pi
−0.0235340 + 0.999723i 0.507492π0.507492\pi
548548 0 0
549549 −13.5587 −0.578671
550550 0 0
551551 −10.7835 −0.459392
552552 0 0
553553 12.8697 0.547274
554554 0 0
555555 −3.74008 −0.158758
556556 0 0
557557 20.7862 0.880738 0.440369 0.897817i 0.354848π-0.354848\pi
0.440369 + 0.897817i 0.354848π0.354848\pi
558558 0 0
559559 0 0
560560 0 0
561561 −15.5363 −0.655942
562562 0 0
563563 33.5659 1.41463 0.707316 0.706897i 0.249906π-0.249906\pi
0.707316 + 0.706897i 0.249906π0.249906\pi
564564 0 0
565565 −16.1896 −0.681100
566566 0 0
567567 1.54979 0.0650850
568568 0 0
569569 −8.90865 −0.373470 −0.186735 0.982410i 0.559791π-0.559791\pi
−0.186735 + 0.982410i 0.559791π0.559791\pi
570570 0 0
571571 −29.3722 −1.22919 −0.614594 0.788844i 0.710680π-0.710680\pi
−0.614594 + 0.788844i 0.710680π0.710680\pi
572572 0 0
573573 18.8047 0.785578
574574 0 0
575575 8.37401 0.349221
576576 0 0
577577 34.5820 1.43967 0.719834 0.694146i 0.244218π-0.244218\pi
0.719834 + 0.694146i 0.244218π0.244218\pi
578578 0 0
579579 −15.9263 −0.661873
580580 0 0
581581 −0.811244 −0.0336561
582582 0 0
583583 −3.42031 −0.141655
584584 0 0
585585 0 0
586586 0 0
587587 38.2900 1.58040 0.790199 0.612850i 0.209977π-0.209977\pi
0.790199 + 0.612850i 0.209977π0.209977\pi
588588 0 0
589589 −7.69036 −0.316876
590590 0 0
591591 −1.50134 −0.0617570
592592 0 0
593593 44.1937 1.81482 0.907408 0.420250i 0.138058π-0.138058\pi
0.907408 + 0.420250i 0.138058π0.138058\pi
594594 0 0
595595 −7.03671 −0.288477
596596 0 0
597597 −1.99771 −0.0817608
598598 0 0
599599 −18.1168 −0.740232 −0.370116 0.928986i 0.620682π-0.620682\pi
−0.370116 + 0.928986i 0.620682π0.620682\pi
600600 0 0
601601 −34.7627 −1.41800 −0.709001 0.705208i 0.750854π-0.750854\pi
−0.709001 + 0.705208i 0.750854π0.750854\pi
602602 0 0
603603 6.06592 0.247023
604604 0 0
605605 −5.03887 −0.204859
606606 0 0
607607 17.6284 0.715514 0.357757 0.933815i 0.383542π-0.383542\pi
0.357757 + 0.933815i 0.383542π0.383542\pi
608608 0 0
609609 6.43725 0.260850
610610 0 0
611611 0 0
612612 0 0
613613 −7.00516 −0.282936 −0.141468 0.989943i 0.545182π-0.545182\pi
−0.141468 + 0.989943i 0.545182π0.545182\pi
614614 0 0
615615 −16.3023 −0.657374
616616 0 0
617617 −25.1516 −1.01257 −0.506283 0.862367i 0.668981π-0.668981\pi
−0.506283 + 0.862367i 0.668981π0.668981\pi
618618 0 0
619619 5.30877 0.213377 0.106689 0.994292i 0.465975π-0.465975\pi
0.106689 + 0.994292i 0.465975π0.465975\pi
620620 0 0
621621 15.9570 0.640331
622622 0 0
623623 −9.67958 −0.387804
624624 0 0
625625 −2.62289 −0.104916
626626 0 0
627627 −6.38282 −0.254905
628628 0 0
629629 −10.4016 −0.414738
630630 0 0
631631 −21.9584 −0.874151 −0.437076 0.899425i 0.643986π-0.643986\pi
−0.437076 + 0.899425i 0.643986π0.643986\pi
632632 0 0
633633 0.0398874 0.00158538
634634 0 0
635635 −22.9497 −0.910732
636636 0 0
637637 0 0
638638 0 0
639639 15.9957 0.632780
640640 0 0
641641 29.2954 1.15710 0.578549 0.815648i 0.303619π-0.303619\pi
0.578549 + 0.815648i 0.303619π0.303619\pi
642642 0 0
643643 44.3931 1.75069 0.875346 0.483496i 0.160633π-0.160633\pi
0.875346 + 0.483496i 0.160633π0.160633\pi
644644 0 0
645645 20.0334 0.788815
646646 0 0
647647 2.88866 0.113565 0.0567824 0.998387i 0.481916π-0.481916\pi
0.0567824 + 0.998387i 0.481916π0.481916\pi
648648 0 0
649649 −12.5613 −0.493075
650650 0 0
651651 4.59079 0.179927
652652 0 0
653653 −18.8390 −0.737229 −0.368614 0.929582i 0.620168π-0.620168\pi
−0.368614 + 0.929582i 0.620168π0.620168\pi
654654 0 0
655655 −5.64390 −0.220525
656656 0 0
657657 9.58649 0.374004
658658 0 0
659659 26.2632 1.02307 0.511535 0.859263i 0.329077π-0.329077\pi
0.511535 + 0.859263i 0.329077π0.329077\pi
660660 0 0
661661 33.0289 1.28468 0.642338 0.766421i 0.277964π-0.277964\pi
0.642338 + 0.766421i 0.277964π0.277964\pi
662662 0 0
663663 0 0
664664 0 0
665665 −2.89092 −0.112105
666666 0 0
667667 16.0665 0.622099
668668 0 0
669669 26.0382 1.00670
670670 0 0
671671 −23.0955 −0.891592
672672 0 0
673673 −4.60997 −0.177701 −0.0888507 0.996045i 0.528319π-0.528319\pi
−0.0888507 + 0.996045i 0.528319π0.528319\pi
674674 0 0
675675 15.4824 0.595917
676676 0 0
677677 −0.757520 −0.0291138 −0.0145569 0.999894i 0.504634π-0.504634\pi
−0.0145569 + 0.999894i 0.504634π0.504634\pi
678678 0 0
679679 −9.51440 −0.365129
680680 0 0
681681 2.44674 0.0937591
682682 0 0
683683 −40.0568 −1.53273 −0.766366 0.642405i 0.777937π-0.777937\pi
−0.766366 + 0.642405i 0.777937π0.777937\pi
684684 0 0
685685 −9.30173 −0.355401
686686 0 0
687687 5.42544 0.206994
688688 0 0
689689 0 0
690690 0 0
691691 15.3280 0.583106 0.291553 0.956555i 0.405828π-0.405828\pi
0.291553 + 0.956555i 0.405828π0.405828\pi
692692 0 0
693693 −4.44012 −0.168666
694694 0 0
695695 −15.0970 −0.572660
696696 0 0
697697 −45.3385 −1.71732
698698 0 0
699699 32.5682 1.23184
700700 0 0
701701 15.1453 0.572032 0.286016 0.958225i 0.407669π-0.407669\pi
0.286016 + 0.958225i 0.407669π0.407669\pi
702702 0 0
703703 −4.27331 −0.161171
704704 0 0
705705 −17.9050 −0.674343
706706 0 0
707707 −10.3663 −0.389864
708708 0 0
709709 11.0785 0.416063 0.208032 0.978122i 0.433294π-0.433294\pi
0.208032 + 0.978122i 0.433294π0.433294\pi
710710 0 0
711711 20.7783 0.779246
712712 0 0
713713 11.4580 0.429107
714714 0 0
715715 0 0
716716 0 0
717717 −5.55853 −0.207587
718718 0 0
719719 34.5299 1.28775 0.643874 0.765132i 0.277326π-0.277326\pi
0.643874 + 0.765132i 0.277326π0.277326\pi
720720 0 0
721721 −7.81778 −0.291149
722722 0 0
723723 7.26028 0.270013
724724 0 0
725725 15.5887 0.578950
726726 0 0
727727 −13.5521 −0.502621 −0.251311 0.967907i 0.580862π-0.580862\pi
−0.251311 + 0.967907i 0.580862π0.580862\pi
728728 0 0
729729 21.6822 0.803043
730730 0 0
731731 55.7150 2.06070
732732 0 0
733733 −12.5720 −0.464357 −0.232179 0.972673i 0.574585π-0.574585\pi
−0.232179 + 0.972673i 0.574585π0.574585\pi
734734 0 0
735735 1.72574 0.0636550
736736 0 0
737737 10.3325 0.380603
738738 0 0
739739 51.2157 1.88400 0.942000 0.335614i 0.108944π-0.108944\pi
0.942000 + 0.335614i 0.108944π0.108944\pi
740740 0 0
741741 0 0
742742 0 0
743743 −23.6367 −0.867148 −0.433574 0.901118i 0.642748π-0.642748\pi
−0.433574 + 0.901118i 0.642748π0.642748\pi
744744 0 0
745745 −29.9115 −1.09587
746746 0 0
747747 −1.30977 −0.0479218
748748 0 0
749749 9.76845 0.356931
750750 0 0
751751 −50.3119 −1.83591 −0.917954 0.396686i 0.870160π-0.870160\pi
−0.917954 + 0.396686i 0.870160π0.870160\pi
752752 0 0
753753 −11.1861 −0.407645
754754 0 0
755755 −33.4353 −1.21684
756756 0 0
757757 33.7267 1.22582 0.612909 0.790153i 0.289999π-0.289999\pi
0.612909 + 0.790153i 0.289999π0.289999\pi
758758 0 0
759759 9.50990 0.345188
760760 0 0
761761 −27.8570 −1.00982 −0.504908 0.863173i 0.668474π-0.668474\pi
−0.504908 + 0.863173i 0.668474π0.668474\pi
762762 0 0
763763 12.9827 0.470005
764764 0 0
765765 −11.3609 −0.410754
766766 0 0
767767 0 0
768768 0 0
769769 45.9195 1.65590 0.827950 0.560801i 0.189507π-0.189507\pi
0.827950 + 0.560801i 0.189507π0.189507\pi
770770 0 0
771771 −19.9523 −0.718566
772772 0 0
773773 29.5683 1.06350 0.531748 0.846902i 0.321535π-0.321535\pi
0.531748 + 0.846902i 0.321535π0.321535\pi
774774 0 0
775775 11.1172 0.399343
776776 0 0
777777 2.55097 0.0915155
778778 0 0
779779 −18.6266 −0.667367
780780 0 0
781781 27.2466 0.974962
782782 0 0
783783 29.7048 1.06156
784784 0 0
785785 21.4392 0.765197
786786 0 0
787787 −26.5408 −0.946076 −0.473038 0.881042i 0.656843π-0.656843\pi
−0.473038 + 0.881042i 0.656843π0.656843\pi
788788 0 0
789789 −9.02604 −0.321335
790790 0 0
791791 11.0423 0.392619
792792 0 0
793793 0 0
794794 0 0
795795 2.14630 0.0761214
796796 0 0
797797 −50.4099 −1.78561 −0.892806 0.450442i 0.851267π-0.851267\pi
−0.892806 + 0.450442i 0.851267π0.851267\pi
798798 0 0
799799 −49.7958 −1.76165
800800 0 0
801801 −15.6278 −0.552183
802802 0 0
803803 16.3294 0.576250
804804 0 0
805805 4.30724 0.151810
806806 0 0
807807 −9.56205 −0.336600
808808 0 0
809809 11.1822 0.393146 0.196573 0.980489i 0.437019π-0.437019\pi
0.196573 + 0.980489i 0.437019π0.437019\pi
810810 0 0
811811 −22.8117 −0.801027 −0.400513 0.916291i 0.631168π-0.631168\pi
−0.400513 + 0.916291i 0.631168π0.631168\pi
812812 0 0
813813 2.47539 0.0868157
814814 0 0
815815 −1.25937 −0.0441137
816816 0 0
817817 22.8896 0.800806
818818 0 0
819819 0 0
820820 0 0
821821 −45.7200 −1.59564 −0.797819 0.602897i 0.794013π-0.794013\pi
−0.797819 + 0.602897i 0.794013π0.794013\pi
822822 0 0
823823 −48.8445 −1.70261 −0.851306 0.524669i 0.824189π-0.824189\pi
−0.851306 + 0.524669i 0.824189π0.824189\pi
824824 0 0
825825 9.22706 0.321245
826826 0 0
827827 39.2720 1.36562 0.682810 0.730596i 0.260757π-0.260757\pi
0.682810 + 0.730596i 0.260757π0.260757\pi
828828 0 0
829829 37.8209 1.31358 0.656788 0.754075i 0.271915π-0.271915\pi
0.656788 + 0.754075i 0.271915π0.271915\pi
830830 0 0
831831 −7.23514 −0.250984
832832 0 0
833833 4.79948 0.166292
834834 0 0
835835 7.68344 0.265897
836836 0 0
837837 21.1843 0.732236
838838 0 0
839839 −43.5636 −1.50398 −0.751991 0.659174i 0.770906π-0.770906\pi
−0.751991 + 0.659174i 0.770906π0.770906\pi
840840 0 0
841841 0.908780 0.0313372
842842 0 0
843843 −20.6959 −0.712804
844844 0 0
845845 0 0
846846 0 0
847847 3.43683 0.118091
848848 0 0
849849 0.411389 0.0141188
850850 0 0
851851 6.36690 0.218254
852852 0 0
853853 −3.80505 −0.130282 −0.0651412 0.997876i 0.520750π-0.520750\pi
−0.0651412 + 0.997876i 0.520750π0.520750\pi
854854 0 0
855855 −4.66743 −0.159623
856856 0 0
857857 −48.9717 −1.67284 −0.836420 0.548089i 0.815355π-0.815355\pi
−0.836420 + 0.548089i 0.815355π0.815355\pi
858858 0 0
859859 11.2339 0.383296 0.191648 0.981464i 0.438617π-0.438617\pi
0.191648 + 0.981464i 0.438617π0.438617\pi
860860 0 0
861861 11.1192 0.378942
862862 0 0
863863 21.5744 0.734400 0.367200 0.930142i 0.380316π-0.380316\pi
0.367200 + 0.930142i 0.380316π0.380316\pi
864864 0 0
865865 28.3929 0.965387
866866 0 0
867867 7.10359 0.241251
868868 0 0
869869 35.3931 1.20063
870870 0 0
871871 0 0
872872 0 0
873873 −15.3611 −0.519896
874874 0 0
875875 11.5098 0.389104
876876 0 0
877877 −20.1323 −0.679821 −0.339911 0.940458i 0.610397π-0.610397\pi
−0.339911 + 0.940458i 0.610397π0.610397\pi
878878 0 0
879879 1.98579 0.0669790
880880 0 0
881881 22.4408 0.756050 0.378025 0.925795i 0.376603π-0.376603\pi
0.378025 + 0.925795i 0.376603π0.376603\pi
882882 0 0
883883 −28.8016 −0.969251 −0.484625 0.874722i 0.661044π-0.661044\pi
−0.484625 + 0.874722i 0.661044π0.661044\pi
884884 0 0
885885 7.88242 0.264965
886886 0 0
887887 25.0780 0.842037 0.421018 0.907052i 0.361673π-0.361673\pi
0.421018 + 0.907052i 0.361673π0.361673\pi
888888 0 0
889889 15.6532 0.524990
890890 0 0
891891 4.26211 0.142786
892892 0 0
893893 −20.4578 −0.684594
894894 0 0
895895 11.6108 0.388106
896896 0 0
897897 0 0
898898 0 0
899899 21.3298 0.711388
900900 0 0
901901 5.96909 0.198859
902902 0 0
903903 −13.6640 −0.454711
904904 0 0
905905 27.1923 0.903903
906906 0 0
907907 1.14981 0.0381788 0.0190894 0.999818i 0.493923π-0.493923\pi
0.0190894 + 0.999818i 0.493923π0.493923\pi
908908 0 0
909909 −16.7365 −0.555116
910910 0 0
911911 −12.7197 −0.421423 −0.210712 0.977548i 0.567578π-0.567578\pi
−0.210712 + 0.977548i 0.567578π0.567578\pi
912912 0 0
913913 −2.23102 −0.0738360
914914 0 0
915915 14.4928 0.479117
916916 0 0
917917 3.84949 0.127121
918918 0 0
919919 44.9476 1.48268 0.741342 0.671127i 0.234190π-0.234190\pi
0.741342 + 0.671127i 0.234190π0.234190\pi
920920 0 0
921921 −18.6977 −0.616111
922922 0 0
923923 0 0
924924 0 0
925925 6.17753 0.203116
926926 0 0
927927 −12.6219 −0.414559
928928 0 0
929929 25.6144 0.840381 0.420190 0.907436i 0.361963π-0.361963\pi
0.420190 + 0.907436i 0.361963π0.361963\pi
930930 0 0
931931 1.97179 0.0646227
932932 0 0
933933 6.74957 0.220971
934934 0 0
935935 −19.3518 −0.632872
936936 0 0
937937 −33.0018 −1.07812 −0.539061 0.842267i 0.681221π-0.681221\pi
−0.539061 + 0.842267i 0.681221π0.681221\pi
938938 0 0
939939 12.2063 0.398339
940940 0 0
941941 −34.2701 −1.11717 −0.558587 0.829446i 0.688656π-0.688656\pi
−0.558587 + 0.829446i 0.688656π0.688656\pi
942942 0 0
943943 27.7522 0.903734
944944 0 0
945945 7.96348 0.259052
946946 0 0
947947 26.7901 0.870560 0.435280 0.900295i 0.356649π-0.356649\pi
0.435280 + 0.900295i 0.356649π0.356649\pi
948948 0 0
949949 0 0
950950 0 0
951951 23.6315 0.766303
952952 0 0
953953 59.5224 1.92812 0.964061 0.265682i 0.0855973π-0.0855973\pi
0.964061 + 0.265682i 0.0855973π0.0855973\pi
954954 0 0
955955 23.4230 0.757949
956956 0 0
957957 17.7032 0.572264
958958 0 0
959959 6.34437 0.204870
960960 0 0
961961 −15.7884 −0.509304
962962 0 0
963963 15.7713 0.508223
964964 0 0
965965 −19.8376 −0.638594
966966 0 0
967967 −22.3740 −0.719501 −0.359750 0.933049i 0.617138π-0.617138\pi
−0.359750 + 0.933049i 0.617138π0.617138\pi
968968 0 0
969969 11.1392 0.357843
970970 0 0
971971 −24.0032 −0.770301 −0.385150 0.922854i 0.625850π-0.625850\pi
−0.385150 + 0.922854i 0.625850π0.625850\pi
972972 0 0
973973 10.2971 0.330109
974974 0 0
975975 0 0
976976 0 0
977977 26.7043 0.854347 0.427174 0.904170i 0.359509π-0.359509\pi
0.427174 + 0.904170i 0.359509π0.359509\pi
978978 0 0
979979 −26.6200 −0.850780
980980 0 0
981981 20.9608 0.669226
982982 0 0
983983 −25.3231 −0.807682 −0.403841 0.914829i 0.632325π-0.632325\pi
−0.403841 + 0.914829i 0.632325π0.632325\pi
984984 0 0
985985 −1.87006 −0.0595850
986986 0 0
987987 12.2124 0.388724
988988 0 0
989989 −34.1037 −1.08443
990990 0 0
991991 −14.2634 −0.453092 −0.226546 0.974000i 0.572743π-0.572743\pi
−0.226546 + 0.974000i 0.572743π0.572743\pi
992992 0 0
993993 −26.7170 −0.847839
994994 0 0
995995 −2.48833 −0.0788853
996996 0 0
997997 −28.9565 −0.917062 −0.458531 0.888678i 0.651624π-0.651624\pi
−0.458531 + 0.888678i 0.651624π0.651624\pi
998998 0 0
999999 11.7715 0.372434
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.1.5 8
13.2 odd 12 364.2.u.a.225.4 16
13.5 odd 4 4732.2.g.k.337.9 16
13.7 odd 12 364.2.u.a.309.4 yes 16
13.8 odd 4 4732.2.g.k.337.10 16
13.12 even 2 4732.2.a.t.1.5 8
39.2 even 12 3276.2.cf.c.2773.6 16
39.20 even 12 3276.2.cf.c.1765.3 16
52.7 even 12 1456.2.cc.f.673.5 16
52.15 even 12 1456.2.cc.f.225.5 16
91.2 odd 12 2548.2.bb.d.1733.4 16
91.20 even 12 2548.2.u.c.1765.5 16
91.33 even 12 2548.2.bq.c.361.4 16
91.41 even 12 2548.2.u.c.589.5 16
91.46 odd 12 2548.2.bb.d.569.4 16
91.54 even 12 2548.2.bb.c.1733.5 16
91.59 even 12 2548.2.bb.c.569.5 16
91.67 odd 12 2548.2.bq.e.1941.5 16
91.72 odd 12 2548.2.bq.e.361.5 16
91.80 even 12 2548.2.bq.c.1941.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
364.2.u.a.225.4 16 13.2 odd 12
364.2.u.a.309.4 yes 16 13.7 odd 12
1456.2.cc.f.225.5 16 52.15 even 12
1456.2.cc.f.673.5 16 52.7 even 12
2548.2.u.c.589.5 16 91.41 even 12
2548.2.u.c.1765.5 16 91.20 even 12
2548.2.bb.c.569.5 16 91.59 even 12
2548.2.bb.c.1733.5 16 91.54 even 12
2548.2.bb.d.569.4 16 91.46 odd 12
2548.2.bb.d.1733.4 16 91.2 odd 12
2548.2.bq.c.361.4 16 91.33 even 12
2548.2.bq.c.1941.4 16 91.80 even 12
2548.2.bq.e.361.5 16 91.72 odd 12
2548.2.bq.e.1941.5 16 91.67 odd 12
3276.2.cf.c.1765.3 16 39.20 even 12
3276.2.cf.c.2773.6 16 39.2 even 12
4732.2.a.s.1.5 8 1.1 even 1 trivial
4732.2.a.t.1.5 8 13.12 even 2
4732.2.g.k.337.9 16 13.5 odd 4
4732.2.g.k.337.10 16 13.8 odd 4