Properties

Label 3528.2.s.q.3313.1
Level 35283528
Weight 22
Character 3528.3313
Analytic conductor 28.17128.171
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [3528,2,Mod(361,3528)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3528, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) 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("3528.361"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 3528=233272 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3528.s (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,0,1,0,0,0,0,0,3,0,12,0,0,0,5,0,1,0,0,0,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 28.171221833128.1712218331
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 3313.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 3528.3313
Dual form 3528.2.s.q.361.1

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+(0.5000000.866025i)q5+(1.50000+2.59808i)q11+6.00000q13+(2.50000+4.33013i)q17+(0.5000000.866025i)q19+(3.50000+6.06218i)q23+(2.00000+3.46410i)q252.00000q29+(2.500004.33013i)q31+(1.50000+2.59808i)q372.00000q414.00000q43+(2.50000+4.33013i)q47+(0.5000000.866025i)q53+3.00000q55+(7.5000012.9904i)q59+(2.50000+4.33013i)q61+(3.000005.19615i)q65+(4.50000+7.79423i)q67+(3.50000+6.06218i)q73+(0.500000+0.866025i)q79+12.0000q83+5.00000q85+(3.50000+6.06218i)q89+(0.5000000.866025i)q95+2.00000q97+O(q100)q+(0.500000 - 0.866025i) q^{5} +(1.50000 + 2.59808i) q^{11} +6.00000 q^{13} +(2.50000 + 4.33013i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-3.50000 + 6.06218i) q^{23} +(2.00000 + 3.46410i) q^{25} -2.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-1.50000 + 2.59808i) q^{37} -2.00000 q^{41} -4.00000 q^{43} +(-2.50000 + 4.33013i) q^{47} +(-0.500000 - 0.866025i) q^{53} +3.00000 q^{55} +(-7.50000 - 12.9904i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(3.00000 - 5.19615i) q^{65} +(4.50000 + 7.79423i) q^{67} +(3.50000 + 6.06218i) q^{73} +(-0.500000 + 0.866025i) q^{79} +12.0000 q^{83} +5.00000 q^{85} +(-3.50000 + 6.06218i) q^{89} +(-0.500000 - 0.866025i) q^{95} +2.00000 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q5+3q11+12q13+5q17+q197q23+4q254q295q313q374q418q435q47q53+6q5515q595q61+6q65+9q67++4q97+O(q100) 2 q + q^{5} + 3 q^{11} + 12 q^{13} + 5 q^{17} + q^{19} - 7 q^{23} + 4 q^{25} - 4 q^{29} - 5 q^{31} - 3 q^{37} - 4 q^{41} - 8 q^{43} - 5 q^{47} - q^{53} + 6 q^{55} - 15 q^{59} - 5 q^{61} + 6 q^{65} + 9 q^{67}+ \cdots + 4 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3528Z)×\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times.

nn 785785 10811081 17651765 26472647
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right) 11 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0 0
44 0 0
55 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i 0.761550π-0.761550\pi
0.955901 + 0.293691i 0.0948835π0.0948835\pi
66 0 0
77 0 0
88 0 0
99 0 0
1010 0 0
1111 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i 0.0172821π-0.0172821\pi
−0.546259 + 0.837616i 0.683949π0.683949\pi
1212 0 0
1313 6.00000 1.66410 0.832050 0.554700i 0.187167π-0.187167\pi
0.832050 + 0.554700i 0.187167π0.187167\pi
1414 0 0
1515 0 0
1616 0 0
1717 2.50000 + 4.33013i 0.606339 + 1.05021i 0.991838 + 0.127502i 0.0406959π0.0406959\pi
−0.385499 + 0.922708i 0.625971π0.625971\pi
1818 0 0
1919 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i 0.796740π-0.796740\pi
0.917663 + 0.397360i 0.130073π0.130073\pi
2020 0 0
2121 0 0
2222 0 0
2323 −3.50000 + 6.06218i −0.729800 + 1.26405i 0.227167 + 0.973856i 0.427054π0.427054\pi
−0.956967 + 0.290196i 0.906280π0.906280\pi
2424 0 0
2525 2.00000 + 3.46410i 0.400000 + 0.692820i
2626 0 0
2727 0 0
2828 0 0
2929 −2.00000 −0.371391 −0.185695 0.982607i 0.559454π-0.559454\pi
−0.185695 + 0.982607i 0.559454π0.559454\pi
3030 0 0
3131 −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i 0.314891π-0.314891\pi
−0.998322 + 0.0579057i 0.981558π0.981558\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i 0.912646π-0.912646\pi
0.715981 + 0.698119i 0.245980π0.245980\pi
3838 0 0
3939 0 0
4040 0 0
4141 −2.00000 −0.312348 −0.156174 0.987730i 0.549916π-0.549916\pi
−0.156174 + 0.987730i 0.549916π0.549916\pi
4242 0 0
4343 −4.00000 −0.609994 −0.304997 0.952353i 0.598656π-0.598656\pi
−0.304997 + 0.952353i 0.598656π0.598656\pi
4444 0 0
4545 0 0
4646 0 0
4747 −2.50000 + 4.33013i −0.364662 + 0.631614i −0.988722 0.149763i 0.952149π-0.952149\pi
0.624059 + 0.781377i 0.285482π0.285482\pi
4848 0 0
4949 0 0
5050 0 0
5151 0 0
5252 0 0
5353 −0.500000 0.866025i −0.0686803 0.118958i 0.829640 0.558298i 0.188546π-0.188546\pi
−0.898321 + 0.439340i 0.855212π0.855212\pi
5454 0 0
5555 3.00000 0.404520
5656 0 0
5757 0 0
5858 0 0
5959 −7.50000 12.9904i −0.976417 1.69120i −0.675178 0.737655i 0.735933π-0.735933\pi
−0.301239 0.953549i 0.597400π-0.597400\pi
6060 0 0
6161 −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i 0.937047π-0.937047\pi
0.660415 + 0.750901i 0.270381π0.270381\pi
6262 0 0
6363 0 0
6464 0 0
6565 3.00000 5.19615i 0.372104 0.644503i
6666 0 0
6767 4.50000 + 7.79423i 0.549762 + 0.952217i 0.998290 + 0.0584478i 0.0186151π0.0186151\pi
−0.448528 + 0.893769i 0.648052π0.648052\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i 0.0323196π-0.0323196\pi
−0.585206 + 0.810885i 0.698986π0.698986\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i 0.851249π-0.851249\pi
0.836527 + 0.547926i 0.184582π0.184582\pi
8080 0 0
8181 0 0
8282 0 0
8383 12.0000 1.31717 0.658586 0.752506i 0.271155π-0.271155\pi
0.658586 + 0.752506i 0.271155π0.271155\pi
8484 0 0
8585 5.00000 0.542326
8686 0 0
8787 0 0
8888 0 0
8989 −3.50000 + 6.06218i −0.370999 + 0.642590i −0.989720 0.143022i 0.954318π-0.954318\pi
0.618720 + 0.785611i 0.287651π0.287651\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 −0.500000 0.866025i −0.0512989 0.0888523i
9696 0 0
9797 2.00000 0.203069 0.101535 0.994832i 0.467625π-0.467625\pi
0.101535 + 0.994832i 0.467625π0.467625\pi
9898 0 0
9999 0 0
100100 0 0
101101 −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i 0.214354π-0.214354\pi
−0.930953 + 0.365140i 0.881021π0.881021\pi
102102 0 0
103103 −7.50000 + 12.9904i −0.738997 + 1.27998i 0.213950 + 0.976845i 0.431367π0.431367\pi
−0.952947 + 0.303136i 0.901966π0.901966\pi
104104 0 0
105105 0 0
106106 0 0
107107 4.50000 7.79423i 0.435031 0.753497i −0.562267 0.826956i 0.690071π-0.690071\pi
0.997298 + 0.0734594i 0.0234039π0.0234039\pi
108108 0 0
109109 2.50000 + 4.33013i 0.239457 + 0.414751i 0.960558 0.278078i 0.0896974π-0.0896974\pi
−0.721102 + 0.692829i 0.756364π0.756364\pi
110110 0 0
111111 0 0
112112 0 0
113113 18.0000 1.69330 0.846649 0.532152i 0.178617π-0.178617\pi
0.846649 + 0.532152i 0.178617π0.178617\pi
114114 0 0
115115 3.50000 + 6.06218i 0.326377 + 0.565301i
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 1.00000 1.73205i 0.0909091 0.157459i
122122 0 0
123123 0 0
124124 0 0
125125 9.00000 0.804984
126126 0 0
127127 8.00000 0.709885 0.354943 0.934888i 0.384500π-0.384500\pi
0.354943 + 0.934888i 0.384500π0.384500\pi
128128 0 0
129129 0 0
130130 0 0
131131 −2.50000 + 4.33013i −0.218426 + 0.378325i −0.954327 0.298764i 0.903426π-0.903426\pi
0.735901 + 0.677089i 0.236759π0.236759\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0 0
137137 5.50000 + 9.52628i 0.469897 + 0.813885i 0.999408 0.0344182i 0.0109578π-0.0109578\pi
−0.529511 + 0.848303i 0.677624π0.677624\pi
138138 0 0
139139 12.0000 1.01783 0.508913 0.860818i 0.330047π-0.330047\pi
0.508913 + 0.860818i 0.330047π0.330047\pi
140140 0 0
141141 0 0
142142 0 0
143143 9.00000 + 15.5885i 0.752618 + 1.30357i
144144 0 0
145145 −1.00000 + 1.73205i −0.0830455 + 0.143839i
146146 0 0
147147 0 0
148148 0 0
149149 −8.50000 + 14.7224i −0.696347 + 1.20611i 0.273377 + 0.961907i 0.411859π0.411859\pi
−0.969724 + 0.244202i 0.921474π0.921474\pi
150150 0 0
151151 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i 0.101452π-0.101452\pi
−0.746190 + 0.665733i 0.768119π0.768119\pi
152152 0 0
153153 0 0
154154 0 0
155155 −5.00000 −0.401610
156156 0 0
157157 −4.50000 7.79423i −0.359139 0.622047i 0.628678 0.777666i 0.283596π-0.283596\pi
−0.987817 + 0.155618i 0.950263π0.950263\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 −6.50000 + 11.2583i −0.509119 + 0.881820i 0.490825 + 0.871258i 0.336695π0.336695\pi
−0.999944 + 0.0105623i 0.996638π0.996638\pi
164164 0 0
165165 0 0
166166 0 0
167167 −12.0000 −0.928588 −0.464294 0.885681i 0.653692π-0.653692\pi
−0.464294 + 0.885681i 0.653692π0.653692\pi
168168 0 0
169169 23.0000 1.76923
170170 0 0
171171 0 0
172172 0 0
173173 6.50000 11.2583i 0.494186 0.855955i −0.505792 0.862656i 0.668800π-0.668800\pi
0.999978 + 0.00670064i 0.00213290π0.00213290\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 −6.50000 11.2583i −0.485833 0.841487i 0.514035 0.857769i 0.328150π-0.328150\pi
−0.999867 + 0.0162823i 0.994817π0.994817\pi
180180 0 0
181181 10.0000 0.743294 0.371647 0.928374i 0.378793π-0.378793\pi
0.371647 + 0.928374i 0.378793π0.378793\pi
182182 0 0
183183 0 0
184184 0 0
185185 1.50000 + 2.59808i 0.110282 + 0.191014i
186186 0 0
187187 −7.50000 + 12.9904i −0.548454 + 0.949951i
188188 0 0
189189 0 0
190190 0 0
191191 −5.50000 + 9.52628i −0.397966 + 0.689297i −0.993475 0.114051i 0.963617π-0.963617\pi
0.595509 + 0.803349i 0.296950π0.296950\pi
192192 0 0
193193 −1.50000 2.59808i −0.107972 0.187014i 0.806976 0.590584i 0.201102π-0.201102\pi
−0.914949 + 0.403570i 0.867769π0.867769\pi
194194 0 0
195195 0 0
196196 0 0
197197 6.00000 0.427482 0.213741 0.976890i 0.431435π-0.431435\pi
0.213741 + 0.976890i 0.431435π0.431435\pi
198198 0 0
199199 −6.50000 11.2583i −0.460773 0.798082i 0.538227 0.842800i 0.319094π-0.319094\pi
−0.999000 + 0.0447181i 0.985761π0.985761\pi
200200 0 0
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 −1.00000 + 1.73205i −0.0698430 + 0.120972i
206206 0 0
207207 0 0
208208 0 0
209209 3.00000 0.207514
210210 0 0
211211 −4.00000 −0.275371 −0.137686 0.990476i 0.543966π-0.543966\pi
−0.137686 + 0.990476i 0.543966π0.543966\pi
212212 0 0
213213 0 0
214214 0 0
215215 −2.00000 + 3.46410i −0.136399 + 0.236250i
216216 0 0
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 15.0000 + 25.9808i 1.00901 + 1.74766i
222222 0 0
223223 24.0000 1.60716 0.803579 0.595198i 0.202926π-0.202926\pi
0.803579 + 0.595198i 0.202926π0.202926\pi
224224 0 0
225225 0 0
226226 0 0
227227 −5.50000 9.52628i −0.365048 0.632281i 0.623736 0.781635i 0.285614π-0.285614\pi
−0.988784 + 0.149354i 0.952281π0.952281\pi
228228 0 0
229229 11.5000 19.9186i 0.759941 1.31626i −0.182939 0.983124i 0.558561π-0.558561\pi
0.942880 0.333133i 0.108106π-0.108106\pi
230230 0 0
231231 0 0
232232 0 0
233233 5.50000 9.52628i 0.360317 0.624087i −0.627696 0.778459i 0.716002π-0.716002\pi
0.988013 + 0.154371i 0.0493352π0.0493352\pi
234234 0 0
235235 2.50000 + 4.33013i 0.163082 + 0.282466i
236236 0 0
237237 0 0
238238 0 0
239239 −20.0000 −1.29369 −0.646846 0.762620i 0.723912π-0.723912\pi
−0.646846 + 0.762620i 0.723912π0.723912\pi
240240 0 0
241241 −8.50000 14.7224i −0.547533 0.948355i −0.998443 0.0557856i 0.982234π-0.982234\pi
0.450910 0.892570i 0.351100π-0.351100\pi
242242 0 0
243243 0 0
244244 0 0
245245 0 0
246246 0 0
247247 3.00000 5.19615i 0.190885 0.330623i
248248 0 0
249249 0 0
250250 0 0
251251 16.0000 1.00991 0.504956 0.863145i 0.331509π-0.331509\pi
0.504956 + 0.863145i 0.331509π0.331509\pi
252252 0 0
253253 −21.0000 −1.32026
254254 0 0
255255 0 0
256256 0 0
257257 10.5000 18.1865i 0.654972 1.13444i −0.326929 0.945049i 0.606014π-0.606014\pi
0.981901 0.189396i 0.0606529π-0.0606529\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i 0.256167π-0.256167\pi
−0.970758 + 0.240059i 0.922833π0.922833\pi
264264 0 0
265265 −1.00000 −0.0614295
266266 0 0
267267 0 0
268268 0 0
269269 4.50000 + 7.79423i 0.274370 + 0.475223i 0.969976 0.243201i 0.0781974π-0.0781974\pi
−0.695606 + 0.718423i 0.744864π0.744864\pi
270270 0 0
271271 −3.50000 + 6.06218i −0.212610 + 0.368251i −0.952531 0.304443i 0.901530π-0.901530\pi
0.739921 + 0.672694i 0.234863π0.234863\pi
272272 0 0
273273 0 0
274274 0 0
275275 −6.00000 + 10.3923i −0.361814 + 0.626680i
276276 0 0
277277 8.50000 + 14.7224i 0.510716 + 0.884585i 0.999923 + 0.0124177i 0.00395278π0.00395278\pi
−0.489207 + 0.872167i 0.662714π0.662714\pi
278278 0 0
279279 0 0
280280 0 0
281281 −6.00000 −0.357930 −0.178965 0.983855i 0.557275π-0.557275\pi
−0.178965 + 0.983855i 0.557275π0.557275\pi
282282 0 0
283283 −6.50000 11.2583i −0.386385 0.669238i 0.605575 0.795788i 0.292943π-0.292943\pi
−0.991960 + 0.126550i 0.959610π0.959610\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −4.00000 + 6.92820i −0.235294 + 0.407541i
290290 0 0
291291 0 0
292292 0 0
293293 6.00000 0.350524 0.175262 0.984522i 0.443923π-0.443923\pi
0.175262 + 0.984522i 0.443923π0.443923\pi
294294 0 0
295295 −15.0000 −0.873334
296296 0 0
297297 0 0
298298 0 0
299299 −21.0000 + 36.3731i −1.21446 + 2.10351i
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 2.50000 + 4.33013i 0.143150 + 0.247942i
306306 0 0
307307 −4.00000 −0.228292 −0.114146 0.993464i 0.536413π-0.536413\pi
−0.114146 + 0.993464i 0.536413π0.536413\pi
308308 0 0
309309 0 0
310310 0 0
311311 −7.50000 12.9904i −0.425286 0.736617i 0.571161 0.820838i 0.306493π-0.306493\pi
−0.996447 + 0.0842210i 0.973160π0.973160\pi
312312 0 0
313313 −0.500000 + 0.866025i −0.0282617 + 0.0489506i −0.879810 0.475325i 0.842331π-0.842331\pi
0.851549 + 0.524276i 0.175664π0.175664\pi
314314 0 0
315315 0 0
316316 0 0
317317 1.50000 2.59808i 0.0842484 0.145922i −0.820822 0.571184i 0.806484π-0.806484\pi
0.905071 + 0.425261i 0.139818π0.139818\pi
318318 0 0
319319 −3.00000 5.19615i −0.167968 0.290929i
320320 0 0
321321 0 0
322322 0 0
323323 5.00000 0.278207
324324 0 0
325325 12.0000 + 20.7846i 0.665640 + 1.15292i
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 −14.5000 + 25.1147i −0.796992 + 1.38043i 0.124574 + 0.992210i 0.460243π0.460243\pi
−0.921567 + 0.388221i 0.873090π0.873090\pi
332332 0 0
333333 0 0
334334 0 0
335335 9.00000 0.491723
336336 0 0
337337 −10.0000 −0.544735 −0.272367 0.962193i 0.587807π-0.587807\pi
−0.272367 + 0.962193i 0.587807π0.587807\pi
338338 0 0
339339 0 0
340340 0 0
341341 7.50000 12.9904i 0.406148 0.703469i
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 7.50000 + 12.9904i 0.402621 + 0.697360i 0.994041 0.109003i 0.0347659π-0.0347659\pi
−0.591420 + 0.806363i 0.701433π0.701433\pi
348348 0 0
349349 −2.00000 −0.107058 −0.0535288 0.998566i 0.517047π-0.517047\pi
−0.0535288 + 0.998566i 0.517047π0.517047\pi
350350 0 0
351351 0 0
352352 0 0
353353 −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i 0.192107π-0.192107\pi
−0.903179 + 0.429263i 0.858773π0.858773\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 10.5000 18.1865i 0.554169 0.959849i −0.443799 0.896126i 0.646370π-0.646370\pi
0.997968 0.0637221i 0.0202971π-0.0202971\pi
360360 0 0
361361 9.00000 + 15.5885i 0.473684 + 0.820445i
362362 0 0
363363 0 0
364364 0 0
365365 7.00000 0.366397
366366 0 0
367367 11.5000 + 19.9186i 0.600295 + 1.03974i 0.992776 + 0.119982i 0.0382835π0.0382835\pi
−0.392481 + 0.919760i 0.628383π0.628383\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i 0.925254π-0.925254\pi
0.687776 + 0.725923i 0.258587π0.258587\pi
374374 0 0
375375 0 0
376376 0 0
377377 −12.0000 −0.618031
378378 0 0
379379 24.0000 1.23280 0.616399 0.787434i 0.288591π-0.288591\pi
0.616399 + 0.787434i 0.288591π0.288591\pi
380380 0 0
381381 0 0
382382 0 0
383383 1.50000 2.59808i 0.0766464 0.132755i −0.825155 0.564907i 0.808912π-0.808912\pi
0.901801 + 0.432151i 0.142245π0.142245\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 −14.5000 25.1147i −0.735179 1.27337i −0.954645 0.297747i 0.903765π-0.903765\pi
0.219465 0.975620i 0.429569π-0.429569\pi
390390 0 0
391391 −35.0000 −1.77003
392392 0 0
393393 0 0
394394 0 0
395395 0.500000 + 0.866025i 0.0251577 + 0.0435745i
396396 0 0
397397 −8.50000 + 14.7224i −0.426603 + 0.738898i −0.996569 0.0827707i 0.973623π-0.973623\pi
0.569966 + 0.821668i 0.306956π0.306956\pi
398398 0 0
399399 0 0
400400 0 0
401401 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i 0.597840π-0.597840\pi
0.976714 0.214544i 0.0688266π-0.0688266\pi
402402 0 0
403403 −15.0000 25.9808i −0.747203 1.29419i
404404 0 0
405405 0 0
406406 0 0
407407 −9.00000 −0.446113
408408 0 0
409409 13.5000 + 23.3827i 0.667532 + 1.15620i 0.978592 + 0.205809i 0.0659826π0.0659826\pi
−0.311060 + 0.950390i 0.600684π0.600684\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 6.00000 10.3923i 0.294528 0.510138i
416416 0 0
417417 0 0
418418 0 0
419419 20.0000 0.977064 0.488532 0.872546i 0.337533π-0.337533\pi
0.488532 + 0.872546i 0.337533π0.337533\pi
420420 0 0
421421 34.0000 1.65706 0.828529 0.559946i 0.189178π-0.189178\pi
0.828529 + 0.559946i 0.189178π0.189178\pi
422422 0 0
423423 0 0
424424 0 0
425425 −10.0000 + 17.3205i −0.485071 + 0.840168i
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 1.50000 + 2.59808i 0.0722525 + 0.125145i 0.899888 0.436121i 0.143648π-0.143648\pi
−0.827636 + 0.561266i 0.810315π0.810315\pi
432432 0 0
433433 2.00000 0.0961139 0.0480569 0.998845i 0.484697π-0.484697\pi
0.0480569 + 0.998845i 0.484697π0.484697\pi
434434 0 0
435435 0 0
436436 0 0
437437 3.50000 + 6.06218i 0.167428 + 0.289993i
438438 0 0
439439 10.5000 18.1865i 0.501138 0.867996i −0.498861 0.866682i 0.666248π-0.666248\pi
0.999999 0.00131415i 0.000418308π-0.000418308\pi
440440 0 0
441441 0 0
442442 0 0
443443 −15.5000 + 26.8468i −0.736427 + 1.27553i 0.217667 + 0.976023i 0.430155π0.430155\pi
−0.954094 + 0.299506i 0.903178π0.903178\pi
444444 0 0
445445 3.50000 + 6.06218i 0.165916 + 0.287375i
446446 0 0
447447 0 0
448448 0 0
449449 26.0000 1.22702 0.613508 0.789689i 0.289758π-0.289758\pi
0.613508 + 0.789689i 0.289758π0.289758\pi
450450 0 0
451451 −3.00000 5.19615i −0.141264 0.244677i
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 8.50000 14.7224i 0.397613 0.688686i −0.595818 0.803120i 0.703172π-0.703172\pi
0.993431 + 0.114433i 0.0365053π0.0365053\pi
458458 0 0
459459 0 0
460460 0 0
461461 −30.0000 −1.39724 −0.698620 0.715493i 0.746202π-0.746202\pi
−0.698620 + 0.715493i 0.746202π0.746202\pi
462462 0 0
463463 −16.0000 −0.743583 −0.371792 0.928316i 0.621256π-0.621256\pi
−0.371792 + 0.928316i 0.621256π0.621256\pi
464464 0 0
465465 0 0
466466 0 0
467467 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i 0.811221π-0.811221\pi
0.898642 + 0.438682i 0.144554π0.144554\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 −6.00000 10.3923i −0.275880 0.477839i
474474 0 0
475475 4.00000 0.183533
476476 0 0
477477 0 0
478478 0 0
479479 −15.5000 26.8468i −0.708213 1.22666i −0.965519 0.260331i 0.916168π-0.916168\pi
0.257306 0.966330i 0.417165π-0.417165\pi
480480 0 0
481481 −9.00000 + 15.5885i −0.410365 + 0.710772i
482482 0 0
483483 0 0
484484 0 0
485485 1.00000 1.73205i 0.0454077 0.0786484i
486486 0 0
487487 −3.50000 6.06218i −0.158600 0.274703i 0.775764 0.631023i 0.217365π-0.217365\pi
−0.934364 + 0.356320i 0.884031π0.884031\pi
488488 0 0
489489 0 0
490490 0 0
491491 24.0000 1.08310 0.541552 0.840667i 0.317837π-0.317837\pi
0.541552 + 0.840667i 0.317837π0.317837\pi
492492 0 0
493493 −5.00000 8.66025i −0.225189 0.390038i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 17.5000 30.3109i 0.783408 1.35690i −0.146538 0.989205i 0.546813π-0.546813\pi
0.929946 0.367697i 0.119854π-0.119854\pi
500500 0 0
501501 0 0
502502 0 0
503503 −32.0000 −1.42681 −0.713405 0.700752i 0.752848π-0.752848\pi
−0.713405 + 0.700752i 0.752848π0.752848\pi
504504 0 0
505505 −3.00000 −0.133498
506506 0 0
507507 0 0
508508 0 0
509509 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i 0.769415π-0.769415\pi
0.948353 + 0.317217i 0.102748π0.102748\pi
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 7.50000 + 12.9904i 0.330489 + 0.572425i
516516 0 0
517517 −15.0000 −0.659699
518518 0 0
519519 0 0
520520 0 0
521521 16.5000 + 28.5788i 0.722878 + 1.25206i 0.959841 + 0.280543i 0.0905145π0.0905145\pi
−0.236963 + 0.971519i 0.576152π0.576152\pi
522522 0 0
523523 −3.50000 + 6.06218i −0.153044 + 0.265081i −0.932345 0.361569i 0.882241π-0.882241\pi
0.779301 + 0.626650i 0.215574π0.215574\pi
524524 0 0
525525 0 0
526526 0 0
527527 12.5000 21.6506i 0.544509 0.943116i
528528 0 0
529529 −13.0000 22.5167i −0.565217 0.978985i
530530 0 0
531531 0 0
532532 0 0
533533 −12.0000 −0.519778
534534 0 0
535535 −4.50000 7.79423i −0.194552 0.336974i
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 20.5000 35.5070i 0.881364 1.52657i 0.0315385 0.999503i 0.489959π-0.489959\pi
0.849825 0.527064i 0.176707π-0.176707\pi
542542 0 0
543543 0 0
544544 0 0
545545 5.00000 0.214176
546546 0 0
547547 −8.00000 −0.342055 −0.171028 0.985266i 0.554709π-0.554709\pi
−0.171028 + 0.985266i 0.554709π0.554709\pi
548548 0 0
549549 0 0
550550 0 0
551551 −1.00000 + 1.73205i −0.0426014 + 0.0737878i
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 −2.50000 4.33013i −0.105928 0.183473i 0.808189 0.588924i 0.200448π-0.200448\pi
−0.914117 + 0.405450i 0.867115π0.867115\pi
558558 0 0
559559 −24.0000 −1.01509
560560 0 0
561561 0 0
562562 0 0
563563 20.5000 + 35.5070i 0.863972 + 1.49644i 0.868064 + 0.496452i 0.165364π0.165364\pi
−0.00409232 + 0.999992i 0.501303π0.501303\pi
564564 0 0
565565 9.00000 15.5885i 0.378633 0.655811i
566566 0 0
567567 0 0
568568 0 0
569569 −16.5000 + 28.5788i −0.691716 + 1.19809i 0.279559 + 0.960128i 0.409812π0.409812\pi
−0.971275 + 0.237959i 0.923522π0.923522\pi
570570 0 0
571571 6.50000 + 11.2583i 0.272017 + 0.471146i 0.969378 0.245573i 0.0789761π-0.0789761\pi
−0.697362 + 0.716720i 0.745643π0.745643\pi
572572 0 0
573573 0 0
574574 0 0
575575 −28.0000 −1.16768
576576 0 0
577577 −16.5000 28.5788i −0.686904 1.18975i −0.972834 0.231502i 0.925636π-0.925636\pi
0.285930 0.958250i 0.407697π-0.407697\pi
578578 0 0
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 1.50000 2.59808i 0.0621237 0.107601i
584584 0 0
585585 0 0
586586 0 0
587587 −20.0000 −0.825488 −0.412744 0.910847i 0.635430π-0.635430\pi
−0.412744 + 0.910847i 0.635430π0.635430\pi
588588 0 0
589589 −5.00000 −0.206021
590590 0 0
591591 0 0
592592 0 0
593593 22.5000 38.9711i 0.923964 1.60035i 0.130746 0.991416i 0.458263π-0.458263\pi
0.793219 0.608937i 0.208404π-0.208404\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 −8.50000 14.7224i −0.347301 0.601542i 0.638468 0.769648i 0.279568π-0.279568\pi
−0.985769 + 0.168106i 0.946235π0.946235\pi
600600 0 0
601601 −22.0000 −0.897399 −0.448699 0.893683i 0.648113π-0.648113\pi
−0.448699 + 0.893683i 0.648113π0.648113\pi
602602 0 0
603603 0 0
604604 0 0
605605 −1.00000 1.73205i −0.0406558 0.0704179i
606606 0 0
607607 6.50000 11.2583i 0.263827 0.456962i −0.703429 0.710766i 0.748349π-0.748349\pi
0.967256 + 0.253804i 0.0816819π0.0816819\pi
608608 0 0
609609 0 0
610610 0 0
611611 −15.0000 + 25.9808i −0.606835 + 1.05107i
612612 0 0
613613 −21.5000 37.2391i −0.868377 1.50407i −0.863655 0.504084i 0.831830π-0.831830\pi
−0.00472215 0.999989i 0.501503π-0.501503\pi
614614 0 0
615615 0 0
616616 0 0
617617 −30.0000 −1.20775 −0.603877 0.797077i 0.706378π-0.706378\pi
−0.603877 + 0.797077i 0.706378π0.706378\pi
618618 0 0
619619 −4.50000 7.79423i −0.180870 0.313276i 0.761307 0.648392i 0.224558π-0.224558\pi
−0.942177 + 0.335115i 0.891225π0.891225\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −5.50000 + 9.52628i −0.220000 + 0.381051i
626626 0 0
627627 0 0
628628 0 0
629629 −15.0000 −0.598089
630630 0 0
631631 −16.0000 −0.636950 −0.318475 0.947931i 0.603171π-0.603171\pi
−0.318475 + 0.947931i 0.603171π0.603171\pi
632632 0 0
633633 0 0
634634 0 0
635635 4.00000 6.92820i 0.158735 0.274937i
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 −8.50000 14.7224i −0.335730 0.581501i 0.647895 0.761730i 0.275650π-0.275650\pi
−0.983625 + 0.180229i 0.942316π0.942316\pi
642642 0 0
643643 44.0000 1.73519 0.867595 0.497271i 0.165665π-0.165665\pi
0.867595 + 0.497271i 0.165665π0.165665\pi
644644 0 0
645645 0 0
646646 0 0
647647 −7.50000 12.9904i −0.294855 0.510705i 0.680096 0.733123i 0.261938π-0.261938\pi
−0.974951 + 0.222419i 0.928605π0.928605\pi
648648 0 0
649649 22.5000 38.9711i 0.883202 1.52975i
650650 0 0
651651 0 0
652652 0 0
653653 17.5000 30.3109i 0.684828 1.18616i −0.288663 0.957431i 0.593211π-0.593211\pi
0.973491 0.228726i 0.0734560π-0.0734560\pi
654654 0 0
655655 2.50000 + 4.33013i 0.0976831 + 0.169192i
656656 0 0
657657 0 0
658658 0 0
659659 −44.0000 −1.71400 −0.856998 0.515319i 0.827673π-0.827673\pi
−0.856998 + 0.515319i 0.827673π0.827673\pi
660660 0 0
661661 11.5000 + 19.9186i 0.447298 + 0.774743i 0.998209 0.0598209i 0.0190530π-0.0190530\pi
−0.550911 + 0.834564i 0.685720π0.685720\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 7.00000 12.1244i 0.271041 0.469457i
668668 0 0
669669 0 0
670670 0 0
671671 −15.0000 −0.579069
672672 0 0
673673 −26.0000 −1.00223 −0.501113 0.865382i 0.667076π-0.667076\pi
−0.501113 + 0.865382i 0.667076π0.667076\pi
674674 0 0
675675 0 0
676676 0 0
677677 −19.5000 + 33.7750i −0.749446 + 1.29808i 0.198643 + 0.980072i 0.436347π0.436347\pi
−0.948089 + 0.318006i 0.896987π0.896987\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 0 0
683683 13.5000 + 23.3827i 0.516563 + 0.894714i 0.999815 + 0.0192323i 0.00612219π0.00612219\pi
−0.483252 + 0.875481i 0.660544π0.660544\pi
684684 0 0
685685 11.0000 0.420288
686686 0 0
687687 0 0
688688 0 0
689689 −3.00000 5.19615i −0.114291 0.197958i
690690 0 0
691691 2.50000 4.33013i 0.0951045 0.164726i −0.814548 0.580097i 0.803015π-0.803015\pi
0.909652 + 0.415371i 0.136348π0.136348\pi
692692 0 0
693693 0 0
694694 0 0
695695 6.00000 10.3923i 0.227593 0.394203i
696696 0 0
697697 −5.00000 8.66025i −0.189389 0.328031i
698698 0 0
699699 0 0
700700 0 0
701701 50.0000 1.88847 0.944237 0.329267i 0.106802π-0.106802\pi
0.944237 + 0.329267i 0.106802π0.106802\pi
702702 0 0
703703 1.50000 + 2.59808i 0.0565736 + 0.0979883i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 14.5000 25.1147i 0.544559 0.943204i −0.454076 0.890963i 0.650030π-0.650030\pi
0.998635 0.0522406i 0.0166363π-0.0166363\pi
710710 0 0
711711 0 0
712712 0 0
713713 35.0000 1.31076
714714 0 0
715715 18.0000 0.673162
716716 0 0
717717 0 0
718718 0 0
719719 19.5000 33.7750i 0.727227 1.25959i −0.230823 0.972996i 0.574142π-0.574142\pi
0.958051 0.286599i 0.0925247π-0.0925247\pi
720720 0 0
721721 0 0
722722 0 0
723723 0 0
724724 0 0
725725 −4.00000 6.92820i −0.148556 0.257307i
726726 0 0
727727 −32.0000 −1.18681 −0.593407 0.804902i 0.702218π-0.702218\pi
−0.593407 + 0.804902i 0.702218π0.702218\pi
728728 0 0
729729 0 0
730730 0 0
731731 −10.0000 17.3205i −0.369863 0.640622i
732732 0 0
733733 9.50000 16.4545i 0.350891 0.607760i −0.635515 0.772088i 0.719212π-0.719212\pi
0.986406 + 0.164328i 0.0525456π0.0525456\pi
734734 0 0
735735 0 0
736736 0 0
737737 −13.5000 + 23.3827i −0.497279 + 0.861312i
738738 0 0
739739 2.50000 + 4.33013i 0.0919640 + 0.159286i 0.908337 0.418238i 0.137352π-0.137352\pi
−0.816373 + 0.577524i 0.804019π0.804019\pi
740740 0 0
741741 0 0
742742 0 0
743743 16.0000 0.586983 0.293492 0.955962i 0.405183π-0.405183\pi
0.293492 + 0.955962i 0.405183π0.405183\pi
744744 0 0
745745 8.50000 + 14.7224i 0.311416 + 0.539388i
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −26.5000 + 45.8993i −0.966999 + 1.67489i −0.262852 + 0.964836i 0.584663π0.584663\pi
−0.704146 + 0.710055i 0.748670π0.748670\pi
752752 0 0
753753 0 0
754754 0 0
755755 5.00000 0.181969
756756 0 0
757757 10.0000 0.363456 0.181728 0.983349i 0.441831π-0.441831\pi
0.181728 + 0.983349i 0.441831π0.441831\pi
758758 0 0
759759 0 0
760760 0 0
761761 −1.50000 + 2.59808i −0.0543750 + 0.0941802i −0.891932 0.452170i 0.850650π-0.850650\pi
0.837557 + 0.546350i 0.183983π0.183983\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 −45.0000 77.9423i −1.62486 2.81433i
768768 0 0
769769 −22.0000 −0.793340 −0.396670 0.917961i 0.629834π-0.629834\pi
−0.396670 + 0.917961i 0.629834π0.629834\pi
770770 0 0
771771 0 0
772772 0 0
773773 −9.50000 16.4545i −0.341691 0.591827i 0.643056 0.765819i 0.277666π-0.277666\pi
−0.984747 + 0.173993i 0.944333π0.944333\pi
774774 0 0
775775 10.0000 17.3205i 0.359211 0.622171i
776776 0 0
777777 0 0
778778 0 0
779779 −1.00000 + 1.73205i −0.0358287 + 0.0620572i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0 0
785785 −9.00000 −0.321224
786786 0 0
787787 −8.50000 14.7224i −0.302992 0.524798i 0.673820 0.738896i 0.264652π-0.264652\pi
−0.976812 + 0.214097i 0.931319π0.931319\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 −15.0000 + 25.9808i −0.532666 + 0.922604i
794794 0 0
795795 0 0
796796 0 0
797797 18.0000 0.637593 0.318796 0.947823i 0.396721π-0.396721\pi
0.318796 + 0.947823i 0.396721π0.396721\pi
798798 0 0
799799 −25.0000 −0.884436
800800 0 0
801801 0 0
802802 0 0
803803 −10.5000 + 18.1865i −0.370537 + 0.641789i
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 19.5000 + 33.7750i 0.685583 + 1.18747i 0.973253 + 0.229736i 0.0737862π0.0737862\pi
−0.287670 + 0.957730i 0.592880π0.592880\pi
810810 0 0
811811 −12.0000 −0.421377 −0.210688 0.977553i 0.567571π-0.567571\pi
−0.210688 + 0.977553i 0.567571π0.567571\pi
812812 0 0
813813 0 0
814814 0 0
815815 6.50000 + 11.2583i 0.227685 + 0.394362i
816816 0 0
817817 −2.00000 + 3.46410i −0.0699711 + 0.121194i
818818 0 0
819819 0 0
820820 0 0
821821 −4.50000 + 7.79423i −0.157051 + 0.272020i −0.933804 0.357785i 0.883532π-0.883532\pi
0.776753 + 0.629805i 0.216865π0.216865\pi
822822 0 0
823823 −23.5000 40.7032i −0.819159 1.41882i −0.906303 0.422628i 0.861108π-0.861108\pi
0.0871445 0.996196i 0.472226π-0.472226\pi
824824 0 0
825825 0 0
826826 0 0
827827 36.0000 1.25184 0.625921 0.779886i 0.284723π-0.284723\pi
0.625921 + 0.779886i 0.284723π0.284723\pi
828828 0 0
829829 5.50000 + 9.52628i 0.191023 + 0.330861i 0.945589 0.325362i 0.105486π-0.105486\pi
−0.754567 + 0.656223i 0.772153π0.772153\pi
830830 0 0
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 −6.00000 + 10.3923i −0.207639 + 0.359641i
836836 0 0
837837 0 0
838838 0 0
839839 −24.0000 −0.828572 −0.414286 0.910147i 0.635969π-0.635969\pi
−0.414286 + 0.910147i 0.635969π0.635969\pi
840840 0 0
841841 −25.0000 −0.862069
842842 0 0
843843 0 0
844844 0 0
845845 11.5000 19.9186i 0.395612 0.685220i
846846 0 0
847847 0 0
848848 0 0
849849 0 0
850850 0 0
851851 −10.5000 18.1865i −0.359935 0.623426i
852852 0 0
853853 −34.0000 −1.16414 −0.582069 0.813139i 0.697757π-0.697757\pi
−0.582069 + 0.813139i 0.697757π0.697757\pi
854854 0 0
855855 0 0
856856 0 0
857857 −19.5000 33.7750i −0.666107 1.15373i −0.978984 0.203938i 0.934626π-0.934626\pi
0.312877 0.949794i 0.398707π-0.398707\pi
858858 0 0
859859 0.500000 0.866025i 0.0170598 0.0295484i −0.857369 0.514701i 0.827903π-0.827903\pi
0.874429 + 0.485153i 0.161236π0.161236\pi
860860 0 0
861861 0 0
862862 0 0
863863 8.50000 14.7224i 0.289343 0.501157i −0.684310 0.729191i 0.739896π-0.739896\pi
0.973653 + 0.228034i 0.0732297π0.0732297\pi
864864 0 0
865865 −6.50000 11.2583i −0.221007 0.382795i
866866 0 0
867867 0 0
868868 0 0
869869 −3.00000 −0.101768
870870 0 0
871871 27.0000 + 46.7654i 0.914860 + 1.58458i
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 −11.5000 + 19.9186i −0.388327 + 0.672603i −0.992225 0.124459i 0.960280π-0.960280\pi
0.603897 + 0.797062i 0.293614π0.293614\pi
878878 0 0
879879 0 0
880880 0 0
881881 −14.0000 −0.471672 −0.235836 0.971793i 0.575783π-0.575783\pi
−0.235836 + 0.971793i 0.575783π0.575783\pi
882882 0 0
883883 −20.0000 −0.673054 −0.336527 0.941674i 0.609252π-0.609252\pi
−0.336527 + 0.941674i 0.609252π0.609252\pi
884884 0 0
885885 0 0
886886 0 0
887887 1.50000 2.59808i 0.0503651 0.0872349i −0.839744 0.542983i 0.817295π-0.817295\pi
0.890109 + 0.455748i 0.150628π0.150628\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 2.50000 + 4.33013i 0.0836593 + 0.144902i
894894 0 0
895895 −13.0000 −0.434542
896896 0 0
897897 0 0
898898 0 0
899899 5.00000 + 8.66025i 0.166759 + 0.288836i
900900 0 0
901901 2.50000 4.33013i 0.0832871 0.144257i
902902 0 0
903903 0 0
904904 0 0
905905 5.00000 8.66025i 0.166206 0.287877i
906906 0 0
907907 0.500000 + 0.866025i 0.0166022 + 0.0287559i 0.874207 0.485553i 0.161382π-0.161382\pi
−0.857605 + 0.514309i 0.828048π0.828048\pi
908908 0 0
909909 0 0
910910 0 0
911911 −16.0000 −0.530104 −0.265052 0.964234i 0.585389π-0.585389\pi
−0.265052 + 0.964234i 0.585389π0.585389\pi
912912 0 0
913913 18.0000 + 31.1769i 0.595713 + 1.03181i
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 5.50000 9.52628i 0.181428 0.314243i −0.760939 0.648824i 0.775261π-0.775261\pi
0.942367 + 0.334581i 0.108595π0.108595\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 −12.0000 −0.394558
926926 0 0
927927 0 0
928928 0 0
929929 −3.50000 + 6.06218i −0.114831 + 0.198894i −0.917712 0.397246i 0.869966π-0.869966\pi
0.802881 + 0.596139i 0.203299π0.203299\pi
930930 0 0
931931 0 0
932932 0 0
933933 0 0
934934 0 0
935935 7.50000 + 12.9904i 0.245276 + 0.424831i
936936 0 0
937937 6.00000 0.196011 0.0980057 0.995186i 0.468754π-0.468754\pi
0.0980057 + 0.995186i 0.468754π0.468754\pi
938938 0 0
939939 0 0
940940 0 0
941941 16.5000 + 28.5788i 0.537885 + 0.931644i 0.999018 + 0.0443125i 0.0141097π0.0141097\pi
−0.461133 + 0.887331i 0.652557π0.652557\pi
942942 0 0
943943 7.00000 12.1244i 0.227951 0.394823i
944944 0 0
945945 0 0
946946 0 0
947947 18.5000 32.0429i 0.601169 1.04126i −0.391475 0.920189i 0.628035π-0.628035\pi
0.992644 0.121067i 0.0386316π-0.0386316\pi
948948 0 0
949949 21.0000 + 36.3731i 0.681689 + 1.18072i
950950 0 0
951951 0 0
952952 0 0
953953 −22.0000 −0.712650 −0.356325 0.934362i 0.615970π-0.615970\pi
−0.356325 + 0.934362i 0.615970π0.615970\pi
954954 0 0
955955 5.50000 + 9.52628i 0.177976 + 0.308263i
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 3.00000 5.19615i 0.0967742 0.167618i
962962 0 0
963963 0 0
964964 0 0
965965 −3.00000 −0.0965734
966966 0 0
967967 48.0000 1.54358 0.771788 0.635880i 0.219363π-0.219363\pi
0.771788 + 0.635880i 0.219363π0.219363\pi
968968 0 0
969969 0 0
970970 0 0
971971 17.5000 30.3109i 0.561602 0.972723i −0.435755 0.900065i 0.643519π-0.643519\pi
0.997357 0.0726575i 0.0231480π-0.0231480\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 1.50000 + 2.59808i 0.0479893 + 0.0831198i 0.889022 0.457864i 0.151385π-0.151385\pi
−0.841033 + 0.540984i 0.818052π0.818052\pi
978978 0 0
979979 −21.0000 −0.671163
980980 0 0
981981 0 0
982982 0 0
983983 10.5000 + 18.1865i 0.334898 + 0.580060i 0.983465 0.181097i 0.0579648π-0.0579648\pi
−0.648567 + 0.761157i 0.724631π0.724631\pi
984984 0 0
985985 3.00000 5.19615i 0.0955879 0.165563i
986986 0 0
987987 0 0
988988 0 0
989989 14.0000 24.2487i 0.445174 0.771064i
990990 0 0
991991 −7.50000 12.9904i −0.238245 0.412653i 0.721966 0.691929i 0.243239π-0.243239\pi
−0.960211 + 0.279276i 0.909906π0.909906\pi
992992 0 0
993993 0 0
994994 0 0
995995 −13.0000 −0.412128
996996 0 0
997997 −20.5000 35.5070i −0.649242 1.12452i −0.983304 0.181968i 0.941753π-0.941753\pi
0.334063 0.942551i 0.391580π-0.391580\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3528.2.s.q.3313.1 2
3.2 odd 2 392.2.i.b.177.1 2
7.2 even 3 3528.2.a.j.1.1 1
7.3 odd 6 504.2.s.c.361.1 2
7.4 even 3 inner 3528.2.s.q.361.1 2
7.5 odd 6 3528.2.a.p.1.1 1
7.6 odd 2 504.2.s.c.289.1 2
12.11 even 2 784.2.i.h.177.1 2
21.2 odd 6 392.2.a.e.1.1 1
21.5 even 6 392.2.a.c.1.1 1
21.11 odd 6 392.2.i.b.361.1 2
21.17 even 6 56.2.i.b.25.1 yes 2
21.20 even 2 56.2.i.b.9.1 2
28.3 even 6 1008.2.s.g.865.1 2
28.19 even 6 7056.2.a.bj.1.1 1
28.23 odd 6 7056.2.a.u.1.1 1
28.27 even 2 1008.2.s.g.289.1 2
84.11 even 6 784.2.i.h.753.1 2
84.23 even 6 784.2.a.c.1.1 1
84.47 odd 6 784.2.a.h.1.1 1
84.59 odd 6 112.2.i.a.81.1 2
84.83 odd 2 112.2.i.a.65.1 2
105.17 odd 12 1400.2.bh.a.249.1 4
105.38 odd 12 1400.2.bh.a.249.2 4
105.44 odd 6 9800.2.a.s.1.1 1
105.59 even 6 1400.2.q.d.1201.1 2
105.62 odd 4 1400.2.bh.a.849.2 4
105.83 odd 4 1400.2.bh.a.849.1 4
105.89 even 6 9800.2.a.be.1.1 1
105.104 even 2 1400.2.q.d.401.1 2
168.5 even 6 3136.2.a.u.1.1 1
168.59 odd 6 448.2.i.d.193.1 2
168.83 odd 2 448.2.i.d.65.1 2
168.101 even 6 448.2.i.b.193.1 2
168.107 even 6 3136.2.a.t.1.1 1
168.125 even 2 448.2.i.b.65.1 2
168.131 odd 6 3136.2.a.j.1.1 1
168.149 odd 6 3136.2.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.i.b.9.1 2 21.20 even 2
56.2.i.b.25.1 yes 2 21.17 even 6
112.2.i.a.65.1 2 84.83 odd 2
112.2.i.a.81.1 2 84.59 odd 6
392.2.a.c.1.1 1 21.5 even 6
392.2.a.e.1.1 1 21.2 odd 6
392.2.i.b.177.1 2 3.2 odd 2
392.2.i.b.361.1 2 21.11 odd 6
448.2.i.b.65.1 2 168.125 even 2
448.2.i.b.193.1 2 168.101 even 6
448.2.i.d.65.1 2 168.83 odd 2
448.2.i.d.193.1 2 168.59 odd 6
504.2.s.c.289.1 2 7.6 odd 2
504.2.s.c.361.1 2 7.3 odd 6
784.2.a.c.1.1 1 84.23 even 6
784.2.a.h.1.1 1 84.47 odd 6
784.2.i.h.177.1 2 12.11 even 2
784.2.i.h.753.1 2 84.11 even 6
1008.2.s.g.289.1 2 28.27 even 2
1008.2.s.g.865.1 2 28.3 even 6
1400.2.q.d.401.1 2 105.104 even 2
1400.2.q.d.1201.1 2 105.59 even 6
1400.2.bh.a.249.1 4 105.17 odd 12
1400.2.bh.a.249.2 4 105.38 odd 12
1400.2.bh.a.849.1 4 105.83 odd 4
1400.2.bh.a.849.2 4 105.62 odd 4
3136.2.a.i.1.1 1 168.149 odd 6
3136.2.a.j.1.1 1 168.131 odd 6
3136.2.a.t.1.1 1 168.107 even 6
3136.2.a.u.1.1 1 168.5 even 6
3528.2.a.j.1.1 1 7.2 even 3
3528.2.a.p.1.1 1 7.5 odd 6
3528.2.s.q.361.1 2 7.4 even 3 inner
3528.2.s.q.3313.1 2 1.1 even 1 trivial
7056.2.a.u.1.1 1 28.23 odd 6
7056.2.a.bj.1.1 1 28.19 even 6
9800.2.a.s.1.1 1 105.44 odd 6
9800.2.a.be.1.1 1 105.89 even 6