Properties

Label 588.2.i.f.373.1
Level 588588
Weight 22
Character 588.373
Analytic conductor 4.6954.695
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,2,Mod(361,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 588=22372 588 = 2^{2} \cdot 3 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 588.i (of order 33, degree 22, not minimal)

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: no
Analytic conductor: 4.695203638854.69520363885
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
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,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 373.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 588.373
Dual form 588.2.i.f.361.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.500000+0.866025i)q3+(0.500000+0.866025i)q9+(3.00000+5.19615i)q112.00000q13+(2.00000+3.46410i)q19+(3.000005.19615i)q23+(2.50000+4.33013i)q251.00000q27+6.00000q29+(4.00000+6.92820i)q31+(3.00000+5.19615i)q33+(1.00000+1.73205i)q37+(1.000001.73205i)q3912.0000q414.00000q43+(6.0000010.3923i)q47+(3.00000+5.19615i)q534.00000q57+(5.00000+8.66025i)q61+(4.000006.92820i)q67+6.00000q69+6.00000q71+(5.000008.66025i)q73+(2.50000+4.33013i)q75+(2.000003.46410i)q79+(0.5000000.866025i)q81+12.0000q83+(3.00000+5.19615i)q87+(6.0000010.3923i)q89+(4.00000+6.92820i)q93+10.0000q976.00000q99+O(q100)q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{9} +(3.00000 + 5.19615i) q^{11} -2.00000 q^{13} +(-2.00000 + 3.46410i) q^{19} +(3.00000 - 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} -1.00000 q^{27} +6.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-3.00000 + 5.19615i) q^{33} +(-1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{39} -12.0000 q^{41} -4.00000 q^{43} +(6.00000 - 10.3923i) q^{47} +(3.00000 + 5.19615i) q^{53} -4.00000 q^{57} +(-5.00000 + 8.66025i) q^{61} +(-4.00000 - 6.92820i) q^{67} +6.00000 q^{69} +6.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(-2.50000 + 4.33013i) q^{75} +(2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(3.00000 + 5.19615i) q^{87} +(6.00000 - 10.3923i) q^{89} +(-4.00000 + 6.92820i) q^{93} +10.0000 q^{97} -6.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q3q9+6q114q134q19+6q23+5q252q27+12q29+8q316q332q372q3924q418q43+12q47+6q538q5710q61+12q99+O(q100) 2 q + q^{3} - q^{9} + 6 q^{11} - 4 q^{13} - 4 q^{19} + 6 q^{23} + 5 q^{25} - 2 q^{27} + 12 q^{29} + 8 q^{31} - 6 q^{33} - 2 q^{37} - 2 q^{39} - 24 q^{41} - 8 q^{43} + 12 q^{47} + 6 q^{53} - 8 q^{57} - 10 q^{61}+ \cdots - 12 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/588Z)×\left(\mathbb{Z}/588\mathbb{Z}\right)^\times.

nn 197197 295295 493493
χ(n)\chi(n) 11 11 e(13)e\left(\frac{1}{3}\right)

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 0.500000 + 0.866025i 0.288675 + 0.500000i
44 0 0
55 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
66 0 0
77 0 0
88 0 0
99 −0.500000 + 0.866025i −0.166667 + 0.288675i
1010 0 0
1111 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i 0.193114π0.193114\pi
0.0829925 + 0.996550i 0.473552π0.473552\pi
1212 0 0
1313 −2.00000 −0.554700 −0.277350 0.960769i 0.589456π-0.589456\pi
−0.277350 + 0.960769i 0.589456π0.589456\pi
1414 0 0
1515 0 0
1616 0 0
1717 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
1818 0 0
1919 −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i 0.985065π-0.985065\pi
0.540068 + 0.841621i 0.318398π0.318398\pi
2020 0 0
2121 0 0
2222 0 0
2323 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i 0.618211π-0.618211\pi
0.988436 0.151642i 0.0484560π-0.0484560\pi
2424 0 0
2525 2.50000 + 4.33013i 0.500000 + 0.866025i
2626 0 0
2727 −1.00000 −0.192450
2828 0 0
2929 6.00000 1.11417 0.557086 0.830455i 0.311919π-0.311919\pi
0.557086 + 0.830455i 0.311919π0.311919\pi
3030 0 0
3131 4.00000 + 6.92820i 0.718421 + 1.24434i 0.961625 + 0.274367i 0.0884683π0.0884683\pi
−0.243204 + 0.969975i 0.578198π0.578198\pi
3232 0 0
3333 −3.00000 + 5.19615i −0.522233 + 0.904534i
3434 0 0
3535 0 0
3636 0 0
3737 −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i 0.885902π-0.885902\pi
0.772043 + 0.635571i 0.219235π0.219235\pi
3838 0 0
3939 −1.00000 1.73205i −0.160128 0.277350i
4040 0 0
4141 −12.0000 −1.87409 −0.937043 0.349215i 0.886448π-0.886448\pi
−0.937043 + 0.349215i 0.886448π0.886448\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 6.00000 10.3923i 0.875190 1.51587i 0.0186297 0.999826i 0.494070π-0.494070\pi
0.856560 0.516047i 0.172597π-0.172597\pi
4848 0 0
4949 0 0
5050 0 0
5151 0 0
5252 0 0
5353 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i 0.0314685π-0.0314685\pi
−0.583036 + 0.812447i 0.698135π0.698135\pi
5454 0 0
5555 0 0
5656 0 0
5757 −4.00000 −0.529813
5858 0 0
5959 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
6060 0 0
6161 −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i 0.387809π0.387809\pi
−0.985391 + 0.170305i 0.945525π0.945525\pi
6262 0 0
6363 0 0
6464 0 0
6565 0 0
6666 0 0
6767 −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i 0.329187π-0.329187\pi
−0.999915 + 0.0130248i 0.995854π0.995854\pi
6868 0 0
6969 6.00000 0.722315
7070 0 0
7171 6.00000 0.712069 0.356034 0.934473i 0.384129π-0.384129\pi
0.356034 + 0.934473i 0.384129π0.384129\pi
7272 0 0
7373 −5.00000 8.66025i −0.585206 1.01361i −0.994850 0.101361i 0.967680π-0.967680\pi
0.409644 0.912245i 0.365653π-0.365653\pi
7474 0 0
7575 −2.50000 + 4.33013i −0.288675 + 0.500000i
7676 0 0
7777 0 0
7878 0 0
7979 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i 0.761089π-0.761089\pi
0.956325 + 0.292306i 0.0944227π0.0944227\pi
8080 0 0
8181 −0.500000 0.866025i −0.0555556 0.0962250i
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 0 0
8686 0 0
8787 3.00000 + 5.19615i 0.321634 + 0.557086i
8888 0 0
8989 6.00000 10.3923i 0.635999 1.10158i −0.350304 0.936636i 0.613922π-0.613922\pi
0.986303 0.164946i 0.0527450π-0.0527450\pi
9090 0 0
9191 0 0
9292 0 0
9393 −4.00000 + 6.92820i −0.414781 + 0.718421i
9494 0 0
9595 0 0
9696 0 0
9797 10.0000 1.01535 0.507673 0.861550i 0.330506π-0.330506\pi
0.507673 + 0.861550i 0.330506π0.330506\pi
9898 0 0
9999 −6.00000 −0.603023
100100 0 0
101101 −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i 0.963017π-0.963017\pi
0.396236 0.918149i 0.370316π-0.370316\pi
102102 0 0
103103 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i 0.704379π-0.704379\pi
0.992990 + 0.118199i 0.0377120π0.0377120\pi
104104 0 0
105105 0 0
106106 0 0
107107 3.00000 5.19615i 0.290021 0.502331i −0.683793 0.729676i 0.739671π-0.739671\pi
0.973814 + 0.227345i 0.0730044π0.0730044\pi
108108 0 0
109109 −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i 0.932756π-0.932756\pi
0.307290 0.951616i 0.400578π-0.400578\pi
110110 0 0
111111 −2.00000 −0.189832
112112 0 0
113113 −6.00000 −0.564433 −0.282216 0.959351i 0.591070π-0.591070\pi
−0.282216 + 0.959351i 0.591070π0.591070\pi
114114 0 0
115115 0 0
116116 0 0
117117 1.00000 1.73205i 0.0924500 0.160128i
118118 0 0
119119 0 0
120120 0 0
121121 −12.5000 + 21.6506i −1.13636 + 1.96824i
122122 0 0
123123 −6.00000 10.3923i −0.541002 0.937043i
124124 0 0
125125 0 0
126126 0 0
127127 −4.00000 −0.354943 −0.177471 0.984126i 0.556792π-0.556792\pi
−0.177471 + 0.984126i 0.556792π0.556792\pi
128128 0 0
129129 −2.00000 3.46410i −0.176090 0.304997i
130130 0 0
131131 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i 0.657689π-0.657689\pi
0.999602 0.0281993i 0.00897729π-0.00897729\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0 0
137137 −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i 0.249173π-0.249173\pi
−0.965250 + 0.261329i 0.915839π0.915839\pi
138138 0 0
139139 4.00000 0.339276 0.169638 0.985506i 0.445740π-0.445740\pi
0.169638 + 0.985506i 0.445740π0.445740\pi
140140 0 0
141141 12.0000 1.01058
142142 0 0
143143 −6.00000 10.3923i −0.501745 0.869048i
144144 0 0
145145 0 0
146146 0 0
147147 0 0
148148 0 0
149149 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i 0.754293π-0.754293\pi
0.962348 + 0.271821i 0.0876260π0.0876260\pi
150150 0 0
151151 −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i 0.272204π-0.272204\pi
−0.981617 + 0.190864i 0.938871π0.938871\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i 0.0220180π0.0220180\pi
−0.438948 + 0.898513i 0.644649π0.644649\pi
158158 0 0
159159 −3.00000 + 5.19615i −0.237915 + 0.412082i
160160 0 0
161161 0 0
162162 0 0
163163 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i 0.617776π-0.617776\pi
0.988227 0.152992i 0.0488907π-0.0488907\pi
164164 0 0
165165 0 0
166166 0 0
167167 12.0000 0.928588 0.464294 0.885681i 0.346308π-0.346308\pi
0.464294 + 0.885681i 0.346308π0.346308\pi
168168 0 0
169169 −9.00000 −0.692308
170170 0 0
171171 −2.00000 3.46410i −0.152944 0.264906i
172172 0 0
173173 −6.00000 + 10.3923i −0.456172 + 0.790112i −0.998755 0.0498898i 0.984113π-0.984113\pi
0.542583 + 0.840002i 0.317446π0.317446\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i 0.238654π-0.238654\pi
−0.956088 + 0.293079i 0.905320π0.905320\pi
180180 0 0
181181 −2.00000 −0.148659 −0.0743294 0.997234i 0.523682π-0.523682\pi
−0.0743294 + 0.997234i 0.523682π0.523682\pi
182182 0 0
183183 −10.0000 −0.739221
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i 0.902984π-0.902984\pi
0.736839 + 0.676068i 0.236317π0.236317\pi
192192 0 0
193193 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i 0.0494748π-0.0494748\pi
−0.628037 + 0.778183i 0.716141π0.716141\pi
194194 0 0
195195 0 0
196196 0 0
197197 −6.00000 −0.427482 −0.213741 0.976890i 0.568565π-0.568565\pi
−0.213741 + 0.976890i 0.568565π0.568565\pi
198198 0 0
199199 −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i 0.974730π-0.974730\pi
0.429745 0.902950i 0.358603π-0.358603\pi
200200 0 0
201201 4.00000 6.92820i 0.282138 0.488678i
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 3.00000 + 5.19615i 0.208514 + 0.361158i
208208 0 0
209209 −24.0000 −1.66011
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 3.00000 + 5.19615i 0.205557 + 0.356034i
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 0 0
219219 5.00000 8.66025i 0.337869 0.585206i
220220 0 0
221221 0 0
222222 0 0
223223 −8.00000 −0.535720 −0.267860 0.963458i 0.586316π-0.586316\pi
−0.267860 + 0.963458i 0.586316π0.586316\pi
224224 0 0
225225 −5.00000 −0.333333
226226 0 0
227227 12.0000 + 20.7846i 0.796468 + 1.37952i 0.921903 + 0.387421i 0.126634π0.126634\pi
−0.125435 + 0.992102i 0.540033π0.540033\pi
228228 0 0
229229 1.00000 1.73205i 0.0660819 0.114457i −0.831092 0.556136i 0.812283π-0.812283\pi
0.897173 + 0.441679i 0.145617π0.145617\pi
230230 0 0
231231 0 0
232232 0 0
233233 −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i 0.896303π-0.896303\pi
0.750867 + 0.660454i 0.229636π0.229636\pi
234234 0 0
235235 0 0
236236 0 0
237237 4.00000 0.259828
238238 0 0
239239 18.0000 1.16432 0.582162 0.813073i 0.302207π-0.302207\pi
0.582162 + 0.813073i 0.302207π0.302207\pi
240240 0 0
241241 −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i 0.271048π-0.271048\pi
−0.980917 + 0.194429i 0.937715π0.937715\pi
242242 0 0
243243 0.500000 0.866025i 0.0320750 0.0555556i
244244 0 0
245245 0 0
246246 0 0
247247 4.00000 6.92820i 0.254514 0.440831i
248248 0 0
249249 6.00000 + 10.3923i 0.380235 + 0.658586i
250250 0 0
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 36.0000 2.26330
254254 0 0
255255 0 0
256256 0 0
257257 −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i 0.955440π-0.955440\pi
0.615948 + 0.787787i 0.288773π0.288773\pi
258258 0 0
259259 0 0
260260 0 0
261261 −3.00000 + 5.19615i −0.185695 + 0.321634i
262262 0 0
263263 3.00000 + 5.19615i 0.184988 + 0.320408i 0.943572 0.331166i 0.107442π-0.107442\pi
−0.758585 + 0.651575i 0.774109π0.774109\pi
264264 0 0
265265 0 0
266266 0 0
267267 12.0000 0.734388
268268 0 0
269269 12.0000 + 20.7846i 0.731653 + 1.26726i 0.956176 + 0.292791i 0.0945841π0.0945841\pi
−0.224523 + 0.974469i 0.572083π0.572083\pi
270270 0 0
271271 −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i 0.994865π-0.994865\pi
0.513905 + 0.857847i 0.328199π0.328199\pi
272272 0 0
273273 0 0
274274 0 0
275275 −15.0000 + 25.9808i −0.904534 + 1.56670i
276276 0 0
277277 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i 0.0631696π0.0631696\pi
−0.319447 + 0.947604i 0.603497π0.603497\pi
278278 0 0
279279 −8.00000 −0.478947
280280 0 0
281281 −18.0000 −1.07379 −0.536895 0.843649i 0.680403π-0.680403\pi
−0.536895 + 0.843649i 0.680403π0.680403\pi
282282 0 0
283283 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i 0.0359589π0.0359589\pi
−0.399188 + 0.916869i 0.630708π0.630708\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 8.50000 14.7224i 0.500000 0.866025i
290290 0 0
291291 5.00000 + 8.66025i 0.293105 + 0.507673i
292292 0 0
293293 12.0000 0.701047 0.350524 0.936554i 0.386004π-0.386004\pi
0.350524 + 0.936554i 0.386004π0.386004\pi
294294 0 0
295295 0 0
296296 0 0
297297 −3.00000 5.19615i −0.174078 0.301511i
298298 0 0
299299 −6.00000 + 10.3923i −0.346989 + 0.601003i
300300 0 0
301301 0 0
302302 0 0
303303 6.00000 10.3923i 0.344691 0.597022i
304304 0 0
305305 0 0
306306 0 0
307307 −20.0000 −1.14146 −0.570730 0.821138i 0.693340π-0.693340\pi
−0.570730 + 0.821138i 0.693340π0.693340\pi
308308 0 0
309309 8.00000 0.455104
310310 0 0
311311 −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i 0.277171π-0.277171\pi
−0.984475 + 0.175525i 0.943838π0.943838\pi
312312 0 0
313313 13.0000 22.5167i 0.734803 1.27272i −0.220006 0.975499i 0.570608π-0.570608\pi
0.954810 0.297218i 0.0960589π-0.0960589\pi
314314 0 0
315315 0 0
316316 0 0
317317 15.0000 25.9808i 0.842484 1.45922i −0.0453045 0.998973i 0.514426π-0.514426\pi
0.887788 0.460252i 0.152241π-0.152241\pi
318318 0 0
319319 18.0000 + 31.1769i 1.00781 + 1.74557i
320320 0 0
321321 6.00000 0.334887
322322 0 0
323323 0 0
324324 0 0
325325 −5.00000 8.66025i −0.277350 0.480384i
326326 0 0
327327 7.00000 12.1244i 0.387101 0.670478i
328328 0 0
329329 0 0
330330 0 0
331331 −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i 0.351905π0.351905\pi
−0.998298 + 0.0583130i 0.981428π0.981428\pi
332332 0 0
333333 −1.00000 1.73205i −0.0547997 0.0949158i
334334 0 0
335335 0 0
336336 0 0
337337 −22.0000 −1.19842 −0.599208 0.800593i 0.704518π-0.704518\pi
−0.599208 + 0.800593i 0.704518π0.704518\pi
338338 0 0
339339 −3.00000 5.19615i −0.162938 0.282216i
340340 0 0
341341 −24.0000 + 41.5692i −1.29967 + 2.25110i
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 9.00000 + 15.5885i 0.483145 + 0.836832i 0.999813 0.0193540i 0.00616095π-0.00616095\pi
−0.516667 + 0.856186i 0.672828π0.672828\pi
348348 0 0
349349 10.0000 0.535288 0.267644 0.963518i 0.413755π-0.413755\pi
0.267644 + 0.963518i 0.413755π0.413755\pi
350350 0 0
351351 2.00000 0.106752
352352 0 0
353353 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 −3.00000 + 5.19615i −0.158334 + 0.274242i −0.934268 0.356572i 0.883946π-0.883946\pi
0.775934 + 0.630814i 0.217279π0.217279\pi
360360 0 0
361361 1.50000 + 2.59808i 0.0789474 + 0.136741i
362362 0 0
363363 −25.0000 −1.31216
364364 0 0
365365 0 0
366366 0 0
367367 16.0000 + 27.7128i 0.835193 + 1.44660i 0.893873 + 0.448320i 0.147978π0.147978\pi
−0.0586798 + 0.998277i 0.518689π0.518689\pi
368368 0 0
369369 6.00000 10.3923i 0.312348 0.541002i
370370 0 0
371371 0 0
372372 0 0
373373 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i 0.749977π-0.749977\pi
0.965945 + 0.258748i 0.0833099π0.0833099\pi
374374 0 0
375375 0 0
376376 0 0
377377 −12.0000 −0.618031
378378 0 0
379379 20.0000 1.02733 0.513665 0.857991i 0.328287π-0.328287\pi
0.513665 + 0.857991i 0.328287π0.328287\pi
380380 0 0
381381 −2.00000 3.46410i −0.102463 0.177471i
382382 0 0
383383 −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i 0.376773π0.376773\pi
−0.990702 + 0.136047i 0.956560π0.956560\pi
384384 0 0
385385 0 0
386386 0 0
387387 2.00000 3.46410i 0.101666 0.176090i
388388 0 0
389389 −15.0000 25.9808i −0.760530 1.31728i −0.942578 0.333987i 0.891606π-0.891606\pi
0.182047 0.983290i 0.441728π-0.441728\pi
390390 0 0
391391 0 0
392392 0 0
393393 12.0000 0.605320
394394 0 0
395395 0 0
396396 0 0
397397 7.00000 12.1244i 0.351320 0.608504i −0.635161 0.772380i 0.719066π-0.719066\pi
0.986481 + 0.163876i 0.0523996π0.0523996\pi
398398 0 0
399399 0 0
400400 0 0
401401 −3.00000 + 5.19615i −0.149813 + 0.259483i −0.931158 0.364615i 0.881200π-0.881200\pi
0.781345 + 0.624099i 0.214534π0.214534\pi
402402 0 0
403403 −8.00000 13.8564i −0.398508 0.690237i
404404 0 0
405405 0 0
406406 0 0
407407 −12.0000 −0.594818
408408 0 0
409409 7.00000 + 12.1244i 0.346128 + 0.599511i 0.985558 0.169338i 0.0541630π-0.0541630\pi
−0.639430 + 0.768849i 0.720830π0.720830\pi
410410 0 0
411411 3.00000 5.19615i 0.147979 0.256307i
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 2.00000 + 3.46410i 0.0979404 + 0.169638i
418418 0 0
419419 24.0000 1.17248 0.586238 0.810139i 0.300608π-0.300608\pi
0.586238 + 0.810139i 0.300608π0.300608\pi
420420 0 0
421421 26.0000 1.26716 0.633581 0.773676i 0.281584π-0.281584\pi
0.633581 + 0.773676i 0.281584π0.281584\pi
422422 0 0
423423 6.00000 + 10.3923i 0.291730 + 0.505291i
424424 0 0
425425 0 0
426426 0 0
427427 0 0
428428 0 0
429429 6.00000 10.3923i 0.289683 0.501745i
430430 0 0
431431 −3.00000 5.19615i −0.144505 0.250290i 0.784683 0.619897i 0.212826π-0.212826\pi
−0.929188 + 0.369607i 0.879492π0.879492\pi
432432 0 0
433433 −26.0000 −1.24948 −0.624740 0.780833i 0.714795π-0.714795\pi
−0.624740 + 0.780833i 0.714795π0.714795\pi
434434 0 0
435435 0 0
436436 0 0
437437 12.0000 + 20.7846i 0.574038 + 0.994263i
438438 0 0
439439 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i 0.772190π-0.772190\pi
0.945552 + 0.325471i 0.105523π0.105523\pi
440440 0 0
441441 0 0
442442 0 0
443443 −15.0000 + 25.9808i −0.712672 + 1.23438i 0.251179 + 0.967941i 0.419182π0.419182\pi
−0.963851 + 0.266443i 0.914152π0.914152\pi
444444 0 0
445445 0 0
446446 0 0
447447 6.00000 0.283790
448448 0 0
449449 −30.0000 −1.41579 −0.707894 0.706319i 0.750354π-0.750354\pi
−0.707894 + 0.706319i 0.750354π0.750354\pi
450450 0 0
451451 −36.0000 62.3538i −1.69517 2.93613i
452452 0 0
453453 4.00000 6.92820i 0.187936 0.325515i
454454 0 0
455455 0 0
456456 0 0
457457 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i 0.661289π-0.661289\pi
0.999857 0.0168929i 0.00537742π-0.00537742\pi
458458 0 0
459459 0 0
460460 0 0
461461 −12.0000 −0.558896 −0.279448 0.960161i 0.590151π-0.590151\pi
−0.279448 + 0.960161i 0.590151π0.590151\pi
462462 0 0
463463 −28.0000 −1.30127 −0.650635 0.759390i 0.725497π-0.725497\pi
−0.650635 + 0.759390i 0.725497π0.725497\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
468468 0 0
469469 0 0
470470 0 0
471471 −7.00000 + 12.1244i −0.322543 + 0.558661i
472472 0 0
473473 −12.0000 20.7846i −0.551761 0.955677i
474474 0 0
475475 −20.0000 −0.917663
476476 0 0
477477 −6.00000 −0.274721
478478 0 0
479479 −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i 0.255062π-0.255062\pi
−0.969920 + 0.243426i 0.921729π0.921729\pi
480480 0 0
481481 2.00000 3.46410i 0.0911922 0.157949i
482482 0 0
483483 0 0
484484 0 0
485485 0 0
486486 0 0
487487 −16.0000 27.7128i −0.725029 1.25579i −0.958962 0.283535i 0.908493π-0.908493\pi
0.233933 0.972253i 0.424840π-0.424840\pi
488488 0 0
489489 16.0000 0.723545
490490 0 0
491491 −18.0000 −0.812329 −0.406164 0.913800i 0.633134π-0.633134\pi
−0.406164 + 0.913800i 0.633134π0.633134\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i 0.804796π-0.804796\pi
0.907314 + 0.420455i 0.138129π0.138129\pi
500500 0 0
501501 6.00000 + 10.3923i 0.268060 + 0.464294i
502502 0 0
503503 24.0000 1.07011 0.535054 0.844818i 0.320291π-0.320291\pi
0.535054 + 0.844818i 0.320291π0.320291\pi
504504 0 0
505505 0 0
506506 0 0
507507 −4.50000 7.79423i −0.199852 0.346154i
508508 0 0
509509 12.0000 20.7846i 0.531891 0.921262i −0.467416 0.884037i 0.654815π-0.654815\pi
0.999307 0.0372243i 0.0118516π-0.0118516\pi
510510 0 0
511511 0 0
512512 0 0
513513 2.00000 3.46410i 0.0883022 0.152944i
514514 0 0
515515 0 0
516516 0 0
517517 72.0000 3.16656
518518 0 0
519519 −12.0000 −0.526742
520520 0 0
521521 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
522522 0 0
523523 −2.00000 + 3.46410i −0.0874539 + 0.151475i −0.906434 0.422347i 0.861206π-0.861206\pi
0.818980 + 0.573822i 0.194540π0.194540\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 −6.50000 11.2583i −0.282609 0.489493i
530530 0 0
531531 0 0
532532 0 0
533533 24.0000 1.03956
534534 0 0
535535 0 0
536536 0 0
537537 3.00000 5.19615i 0.129460 0.224231i
538538 0 0
539539 0 0
540540 0 0
541541 −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i 0.847023π-0.847023\pi
0.843728 + 0.536771i 0.180356π0.180356\pi
542542 0 0
543543 −1.00000 1.73205i −0.0429141 0.0743294i
544544 0 0
545545 0 0
546546 0 0
547547 8.00000 0.342055 0.171028 0.985266i 0.445291π-0.445291\pi
0.171028 + 0.985266i 0.445291π0.445291\pi
548548 0 0
549549 −5.00000 8.66025i −0.213395 0.369611i
550550 0 0
551551 −12.0000 + 20.7846i −0.511217 + 0.885454i
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 −21.0000 36.3731i −0.889799 1.54118i −0.840113 0.542411i 0.817511π-0.817511\pi
−0.0496855 0.998765i 0.515822π-0.515822\pi
558558 0 0
559559 8.00000 0.338364
560560 0 0
561561 0 0
562562 0 0
563563 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
564564 0 0
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i 0.873472π-0.873472\pi
0.796266 + 0.604947i 0.206806π0.206806\pi
570570 0 0
571571 20.0000 + 34.6410i 0.836974 + 1.44968i 0.892413 + 0.451219i 0.149011π0.149011\pi
−0.0554391 + 0.998462i 0.517656π0.517656\pi
572572 0 0
573573 −6.00000 −0.250654
574574 0 0
575575 30.0000 1.25109
576576 0 0
577577 −11.0000 19.0526i −0.457936 0.793168i 0.540916 0.841077i 0.318078π-0.318078\pi
−0.998852 + 0.0479084i 0.984744π0.984744\pi
578578 0 0
579579 −5.00000 + 8.66025i −0.207793 + 0.359908i
580580 0 0
581581 0 0
582582 0 0
583583 −18.0000 + 31.1769i −0.745484 + 1.29122i
584584 0 0
585585 0 0
586586 0 0
587587 24.0000 0.990586 0.495293 0.868726i 0.335061π-0.335061\pi
0.495293 + 0.868726i 0.335061π0.335061\pi
588588 0 0
589589 −32.0000 −1.31854
590590 0 0
591591 −3.00000 5.19615i −0.123404 0.213741i
592592 0 0
593593 24.0000 41.5692i 0.985562 1.70704i 0.346149 0.938179i 0.387489π-0.387489\pi
0.639413 0.768864i 0.279178π-0.279178\pi
594594 0 0
595595 0 0
596596 0 0
597597 8.00000 13.8564i 0.327418 0.567105i
598598 0 0
599599 −15.0000 25.9808i −0.612883 1.06155i −0.990752 0.135686i 0.956676π-0.956676\pi
0.377869 0.925859i 0.376657π-0.376657\pi
600600 0 0
601601 −2.00000 −0.0815817 −0.0407909 0.999168i 0.512988π-0.512988\pi
−0.0407909 + 0.999168i 0.512988π0.512988\pi
602602 0 0
603603 8.00000 0.325785
604604 0 0
605605 0 0
606606 0 0
607607 16.0000 27.7128i 0.649420 1.12483i −0.333842 0.942629i 0.608345π-0.608345\pi
0.983262 0.182199i 0.0583216π-0.0583216\pi
608608 0 0
609609 0 0
610610 0 0
611611 −12.0000 + 20.7846i −0.485468 + 0.840855i
612612 0 0
613613 −19.0000 32.9090i −0.767403 1.32918i −0.938967 0.344008i 0.888215π-0.888215\pi
0.171564 0.985173i 0.445118π-0.445118\pi
614614 0 0
615615 0 0
616616 0 0
617617 −18.0000 −0.724653 −0.362326 0.932051i 0.618017π-0.618017\pi
−0.362326 + 0.932051i 0.618017π0.618017\pi
618618 0 0
619619 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i 0.0350048π-0.0350048\pi
−0.592025 + 0.805919i 0.701671π0.701671\pi
620620 0 0
621621 −3.00000 + 5.19615i −0.120386 + 0.208514i
622622 0 0
623623 0 0
624624 0 0
625625 −12.5000 + 21.6506i −0.500000 + 0.866025i
626626 0 0
627627 −12.0000 20.7846i −0.479234 0.830057i
628628 0 0
629629 0 0
630630 0 0
631631 20.0000 0.796187 0.398094 0.917345i 0.369672π-0.369672\pi
0.398094 + 0.917345i 0.369672π0.369672\pi
632632 0 0
633633 −2.00000 3.46410i −0.0794929 0.137686i
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 −3.00000 + 5.19615i −0.118678 + 0.205557i
640640 0 0
641641 9.00000 + 15.5885i 0.355479 + 0.615707i 0.987200 0.159489i 0.0509845π-0.0509845\pi
−0.631721 + 0.775196i 0.717651π0.717651\pi
642642 0 0
643643 4.00000 0.157745 0.0788723 0.996885i 0.474868π-0.474868\pi
0.0788723 + 0.996885i 0.474868π0.474868\pi
644644 0 0
645645 0 0
646646 0 0
647647 −18.0000 31.1769i −0.707653 1.22569i −0.965726 0.259565i 0.916421π-0.916421\pi
0.258073 0.966126i 0.416913π-0.416913\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i 0.718768π-0.718768\pi
0.986634 + 0.162951i 0.0521013π0.0521013\pi
654654 0 0
655655 0 0
656656 0 0
657657 10.0000 0.390137
658658 0 0
659659 −6.00000 −0.233727 −0.116863 0.993148i 0.537284π-0.537284\pi
−0.116863 + 0.993148i 0.537284π0.537284\pi
660660 0 0
661661 19.0000 + 32.9090i 0.739014 + 1.28001i 0.952940 + 0.303160i 0.0980418π0.0980418\pi
−0.213925 + 0.976850i 0.568625π0.568625\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 18.0000 31.1769i 0.696963 1.20717i
668668 0 0
669669 −4.00000 6.92820i −0.154649 0.267860i
670670 0 0
671671 −60.0000 −2.31627
672672 0 0
673673 −34.0000 −1.31060 −0.655302 0.755367i 0.727459π-0.727459\pi
−0.655302 + 0.755367i 0.727459π0.727459\pi
674674 0 0
675675 −2.50000 4.33013i −0.0962250 0.166667i
676676 0 0
677677 6.00000 10.3923i 0.230599 0.399409i −0.727386 0.686229i 0.759265π-0.759265\pi
0.957984 + 0.286820i 0.0925982π0.0925982\pi
678678 0 0
679679 0 0
680680 0 0
681681 −12.0000 + 20.7846i −0.459841 + 0.796468i
682682 0 0
683683 21.0000 + 36.3731i 0.803543 + 1.39178i 0.917270 + 0.398265i 0.130387π0.130387\pi
−0.113728 + 0.993512i 0.536279π0.536279\pi
684684 0 0
685685 0 0
686686 0 0
687687 2.00000 0.0763048
688688 0 0
689689 −6.00000 10.3923i −0.228582 0.395915i
690690 0 0
691691 −2.00000 + 3.46410i −0.0760836 + 0.131781i −0.901557 0.432660i 0.857575π-0.857575\pi
0.825473 + 0.564441i 0.190908π0.190908\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 −6.00000 −0.226941
700700 0 0
701701 6.00000 0.226617 0.113308 0.993560i 0.463855π-0.463855\pi
0.113308 + 0.993560i 0.463855π0.463855\pi
702702 0 0
703703 −4.00000 6.92820i −0.150863 0.261302i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i 0.773204π-0.773204\pi
0.944509 + 0.328484i 0.106538π0.106538\pi
710710 0 0
711711 2.00000 + 3.46410i 0.0750059 + 0.129914i
712712 0 0
713713 48.0000 1.79761
714714 0 0
715715 0 0
716716 0 0
717717 9.00000 + 15.5885i 0.336111 + 0.582162i
718718 0 0
719719 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
720720 0 0
721721 0 0
722722 0 0
723723 5.00000 8.66025i 0.185952 0.322078i
724724 0 0
725725 15.0000 + 25.9808i 0.557086 + 0.964901i
726726 0 0
727727 −8.00000 −0.296704 −0.148352 0.988935i 0.547397π-0.547397\pi
−0.148352 + 0.988935i 0.547397π0.547397\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 0 0
732732 0 0
733733 −23.0000 + 39.8372i −0.849524 + 1.47142i 0.0321090 + 0.999484i 0.489778π0.489778\pi
−0.881633 + 0.471935i 0.843556π0.843556\pi
734734 0 0
735735 0 0
736736 0 0
737737 24.0000 41.5692i 0.884051 1.53122i
738738 0 0
739739 −16.0000 27.7128i −0.588570 1.01943i −0.994420 0.105493i 0.966358π-0.966358\pi
0.405851 0.913939i 0.366975π-0.366975\pi
740740 0 0
741741 8.00000 0.293887
742742 0 0
743743 6.00000 0.220119 0.110059 0.993925i 0.464896π-0.464896\pi
0.110059 + 0.993925i 0.464896π0.464896\pi
744744 0 0
745745 0 0
746746 0 0
747747 −6.00000 + 10.3923i −0.219529 + 0.380235i
748748 0 0
749749 0 0
750750 0 0
751751 −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i 0.365120π0.365120\pi
−0.995018 + 0.0996961i 0.968213π0.968213\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 38.0000 1.38113 0.690567 0.723269i 0.257361π-0.257361\pi
0.690567 + 0.723269i 0.257361π0.257361\pi
758758 0 0
759759 18.0000 + 31.1769i 0.653359 + 1.13165i
760760 0 0
761761 −18.0000 + 31.1769i −0.652499 + 1.13016i 0.330015 + 0.943976i 0.392946π0.392946\pi
−0.982514 + 0.186187i 0.940387π0.940387\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 −26.0000 −0.937584 −0.468792 0.883309i 0.655311π-0.655311\pi
−0.468792 + 0.883309i 0.655311π0.655311\pi
770770 0 0
771771 −12.0000 −0.432169
772772 0 0
773773 6.00000 + 10.3923i 0.215805 + 0.373785i 0.953521 0.301326i 0.0974291π-0.0974291\pi
−0.737716 + 0.675111i 0.764096π0.764096\pi
774774 0 0
775775 −20.0000 + 34.6410i −0.718421 + 1.24434i
776776 0 0
777777 0 0
778778 0 0
779779 24.0000 41.5692i 0.859889 1.48937i
780780 0 0
781781 18.0000 + 31.1769i 0.644091 + 1.11560i
782782 0 0
783783 −6.00000 −0.214423
784784 0 0
785785 0 0
786786 0 0
787787 −2.00000 3.46410i −0.0712923 0.123482i 0.828176 0.560469i 0.189379π-0.189379\pi
−0.899468 + 0.436987i 0.856046π0.856046\pi
788788 0 0
789789 −3.00000 + 5.19615i −0.106803 + 0.184988i
790790 0 0
791791 0 0
792792 0 0
793793 10.0000 17.3205i 0.355110 0.615069i
794794 0 0
795795 0 0
796796 0 0
797797 −36.0000 −1.27519 −0.637593 0.770374i 0.720070π-0.720070\pi
−0.637593 + 0.770374i 0.720070π0.720070\pi
798798 0 0
799799 0 0
800800 0 0
801801 6.00000 + 10.3923i 0.212000 + 0.367194i
802802 0 0
803803 30.0000 51.9615i 1.05868 1.83368i
804804 0 0
805805 0 0
806806 0 0
807807 −12.0000 + 20.7846i −0.422420 + 0.731653i
808808 0 0
809809 27.0000 + 46.7654i 0.949269 + 1.64418i 0.746968 + 0.664860i 0.231509π0.231509\pi
0.202301 + 0.979323i 0.435158π0.435158\pi
810810 0 0
811811 −20.0000 −0.702295 −0.351147 0.936320i 0.614208π-0.614208\pi
−0.351147 + 0.936320i 0.614208π0.614208\pi
812812 0 0
813813 −16.0000 −0.561144
814814 0 0
815815 0 0
816816 0 0
817817 8.00000 13.8564i 0.279885 0.484774i
818818 0 0
819819 0 0
820820 0 0
821821 −9.00000 + 15.5885i −0.314102 + 0.544041i −0.979246 0.202674i 0.935037π-0.935037\pi
0.665144 + 0.746715i 0.268370π0.268370\pi
822822 0 0
823823 2.00000 + 3.46410i 0.0697156 + 0.120751i 0.898776 0.438408i 0.144457π-0.144457\pi
−0.829060 + 0.559159i 0.811124π0.811124\pi
824824 0 0
825825 −30.0000 −1.04447
826826 0 0
827827 −6.00000 −0.208640 −0.104320 0.994544i 0.533267π-0.533267\pi
−0.104320 + 0.994544i 0.533267π0.533267\pi
828828 0 0
829829 −11.0000 19.0526i −0.382046 0.661723i 0.609309 0.792933i 0.291447π-0.291447\pi
−0.991355 + 0.131210i 0.958114π0.958114\pi
830830 0 0
831831 −11.0000 + 19.0526i −0.381586 + 0.660926i
832832 0 0
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 −4.00000 6.92820i −0.138260 0.239474i
838838 0 0
839839 −12.0000 −0.414286 −0.207143 0.978311i 0.566417π-0.566417\pi
−0.207143 + 0.978311i 0.566417π0.566417\pi
840840 0 0
841841 7.00000 0.241379
842842 0 0
843843 −9.00000 15.5885i −0.309976 0.536895i
844844 0 0
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 −10.0000 + 17.3205i −0.343199 + 0.594438i
850850 0 0
851851 6.00000 + 10.3923i 0.205677 + 0.356244i
852852 0 0
853853 −14.0000 −0.479351 −0.239675 0.970853i 0.577041π-0.577041\pi
−0.239675 + 0.970853i 0.577041π0.577041\pi
854854 0 0
855855 0 0
856856 0 0
857857 6.00000 + 10.3923i 0.204956 + 0.354994i 0.950119 0.311888i 0.100962π-0.100962\pi
−0.745163 + 0.666883i 0.767628π0.767628\pi
858858 0 0
859859 −2.00000 + 3.46410i −0.0682391 + 0.118194i −0.898126 0.439738i 0.855071π-0.855071\pi
0.829887 + 0.557931i 0.188405π0.188405\pi
860860 0 0
861861 0 0
862862 0 0
863863 3.00000 5.19615i 0.102121 0.176879i −0.810437 0.585826i 0.800770π-0.800770\pi
0.912558 + 0.408946i 0.134104π0.134104\pi
864864 0 0
865865 0 0
866866 0 0
867867 17.0000 0.577350
868868 0 0
869869 24.0000 0.814144
870870 0 0
871871 8.00000 + 13.8564i 0.271070 + 0.469506i
872872 0 0
873873 −5.00000 + 8.66025i −0.169224 + 0.293105i
874874 0 0
875875 0 0
876876 0 0
877877 −7.00000 + 12.1244i −0.236373 + 0.409410i −0.959671 0.281126i 0.909292π-0.909292\pi
0.723298 + 0.690536i 0.242625π0.242625\pi
878878 0 0
879879 6.00000 + 10.3923i 0.202375 + 0.350524i
880880 0 0
881881 −24.0000 −0.808581 −0.404290 0.914631i 0.632481π-0.632481\pi
−0.404290 + 0.914631i 0.632481π0.632481\pi
882882 0 0
883883 −4.00000 −0.134611 −0.0673054 0.997732i 0.521440π-0.521440\pi
−0.0673054 + 0.997732i 0.521440π0.521440\pi
884884 0 0
885885 0 0
886886 0 0
887887 18.0000 31.1769i 0.604381 1.04682i −0.387768 0.921757i 0.626754π-0.626754\pi
0.992149 0.125061i 0.0399128π-0.0399128\pi
888888 0 0
889889 0 0
890890 0 0
891891 3.00000 5.19615i 0.100504 0.174078i
892892 0 0
893893 24.0000 + 41.5692i 0.803129 + 1.39106i
894894 0 0
895895 0 0
896896 0 0
897897 −12.0000 −0.400668
898898 0 0
899899 24.0000 + 41.5692i 0.800445 + 1.38641i
900900 0 0
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 2.00000 + 3.46410i 0.0664089 + 0.115024i 0.897318 0.441384i 0.145512π-0.145512\pi
−0.830909 + 0.556408i 0.812179π0.812179\pi
908908 0 0
909909 12.0000 0.398015
910910 0 0
911911 54.0000 1.78910 0.894550 0.446968i 0.147496π-0.147496\pi
0.894550 + 0.446968i 0.147496π0.147496\pi
912912 0 0
913913 36.0000 + 62.3538i 1.19143 + 2.06361i
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 8.00000 13.8564i 0.263896 0.457081i −0.703378 0.710816i 0.748326π-0.748326\pi
0.967274 + 0.253735i 0.0816592π0.0816592\pi
920920 0 0
921921 −10.0000 17.3205i −0.329511 0.570730i
922922 0 0
923923 −12.0000 −0.394985
924924 0 0
925925 −10.0000 −0.328798
926926 0 0
927927 4.00000 + 6.92820i 0.131377 + 0.227552i
928928 0 0
929929 6.00000 10.3923i 0.196854 0.340960i −0.750653 0.660697i 0.770261π-0.770261\pi
0.947507 + 0.319736i 0.103594π0.103594\pi
930930 0 0
931931 0 0
932932 0 0
933933 6.00000 10.3923i 0.196431 0.340229i
934934 0 0
935935 0 0
936936 0 0
937937 −2.00000 −0.0653372 −0.0326686 0.999466i 0.510401π-0.510401\pi
−0.0326686 + 0.999466i 0.510401π0.510401\pi
938938 0 0
939939 26.0000 0.848478
940940 0 0
941941 −12.0000 20.7846i −0.391189 0.677559i 0.601418 0.798935i 0.294603π-0.294603\pi
−0.992607 + 0.121376i 0.961269π0.961269\pi
942942 0 0
943943 −36.0000 + 62.3538i −1.17232 + 2.03052i
944944 0 0
945945 0 0
946946 0 0
947947 15.0000 25.9808i 0.487435 0.844261i −0.512461 0.858710i 0.671266π-0.671266\pi
0.999896 + 0.0144491i 0.00459946π0.00459946\pi
948948 0 0
949949 10.0000 + 17.3205i 0.324614 + 0.562247i
950950 0 0
951951 30.0000 0.972817
952952 0 0
953953 42.0000 1.36051 0.680257 0.732974i 0.261868π-0.261868\pi
0.680257 + 0.732974i 0.261868π0.261868\pi
954954 0 0
955955 0 0
956956 0 0
957957 −18.0000 + 31.1769i −0.581857 + 1.00781i
958958 0 0
959959 0 0
960960 0 0
961961 −16.5000 + 28.5788i −0.532258 + 0.921898i
962962 0 0
963963 3.00000 + 5.19615i 0.0966736 + 0.167444i
964964 0 0
965965 0 0
966966 0 0
967967 −28.0000 −0.900419 −0.450210 0.892923i 0.648651π-0.648651\pi
−0.450210 + 0.892923i 0.648651π0.648651\pi
968968 0 0
969969 0 0
970970 0 0
971971 6.00000 10.3923i 0.192549 0.333505i −0.753545 0.657396i 0.771658π-0.771658\pi
0.946094 + 0.323891i 0.104991π0.104991\pi
972972 0 0
973973 0 0
974974 0 0
975975 5.00000 8.66025i 0.160128 0.277350i
976976 0 0
977977 −3.00000 5.19615i −0.0959785 0.166240i 0.814038 0.580812i 0.197265π-0.197265\pi
−0.910017 + 0.414572i 0.863931π0.863931\pi
978978 0 0
979979 72.0000 2.30113
980980 0 0
981981 14.0000 0.446986
982982 0 0
983983 −24.0000 41.5692i −0.765481 1.32585i −0.939992 0.341197i 0.889168π-0.889168\pi
0.174511 0.984655i 0.444166π-0.444166\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 −12.0000 + 20.7846i −0.381578 + 0.660912i
990990 0 0
991991 20.0000 + 34.6410i 0.635321 + 1.10041i 0.986447 + 0.164080i 0.0524655π0.0524655\pi
−0.351126 + 0.936328i 0.614201π0.614201\pi
992992 0 0
993993 −20.0000 −0.634681
994994 0 0
995995 0 0
996996 0 0
997997 −5.00000 8.66025i −0.158352 0.274273i 0.775923 0.630828i 0.217285π-0.217285\pi
−0.934274 + 0.356555i 0.883951π0.883951\pi
998998 0 0
999999 1.00000 1.73205i 0.0316386 0.0547997i
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 588.2.i.f.373.1 2
3.2 odd 2 1764.2.k.d.1549.1 2
4.3 odd 2 2352.2.q.g.961.1 2
7.2 even 3 588.2.a.c.1.1 1
7.3 odd 6 588.2.i.c.361.1 2
7.4 even 3 inner 588.2.i.f.361.1 2
7.5 odd 6 84.2.a.b.1.1 1
7.6 odd 2 588.2.i.c.373.1 2
21.2 odd 6 1764.2.a.g.1.1 1
21.5 even 6 252.2.a.b.1.1 1
21.11 odd 6 1764.2.k.d.361.1 2
21.17 even 6 1764.2.k.e.361.1 2
21.20 even 2 1764.2.k.e.1549.1 2
28.3 even 6 2352.2.q.s.1537.1 2
28.11 odd 6 2352.2.q.g.1537.1 2
28.19 even 6 336.2.a.b.1.1 1
28.23 odd 6 2352.2.a.s.1.1 1
28.27 even 2 2352.2.q.s.961.1 2
35.12 even 12 2100.2.k.a.1849.1 2
35.19 odd 6 2100.2.a.a.1.1 1
35.33 even 12 2100.2.k.a.1849.2 2
56.5 odd 6 1344.2.a.f.1.1 1
56.19 even 6 1344.2.a.o.1.1 1
56.37 even 6 9408.2.a.co.1.1 1
56.51 odd 6 9408.2.a.r.1.1 1
63.5 even 6 2268.2.j.f.1513.1 2
63.40 odd 6 2268.2.j.i.1513.1 2
63.47 even 6 2268.2.j.f.757.1 2
63.61 odd 6 2268.2.j.i.757.1 2
84.23 even 6 7056.2.a.x.1.1 1
84.47 odd 6 1008.2.a.g.1.1 1
105.47 odd 12 6300.2.k.r.6049.2 2
105.68 odd 12 6300.2.k.r.6049.1 2
105.89 even 6 6300.2.a.p.1.1 1
112.5 odd 12 5376.2.c.i.2689.1 2
112.19 even 12 5376.2.c.x.2689.1 2
112.61 odd 12 5376.2.c.i.2689.2 2
112.75 even 12 5376.2.c.x.2689.2 2
140.19 even 6 8400.2.a.ct.1.1 1
168.5 even 6 4032.2.a.u.1.1 1
168.131 odd 6 4032.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.2.a.b.1.1 1 7.5 odd 6
252.2.a.b.1.1 1 21.5 even 6
336.2.a.b.1.1 1 28.19 even 6
588.2.a.c.1.1 1 7.2 even 3
588.2.i.c.361.1 2 7.3 odd 6
588.2.i.c.373.1 2 7.6 odd 2
588.2.i.f.361.1 2 7.4 even 3 inner
588.2.i.f.373.1 2 1.1 even 1 trivial
1008.2.a.g.1.1 1 84.47 odd 6
1344.2.a.f.1.1 1 56.5 odd 6
1344.2.a.o.1.1 1 56.19 even 6
1764.2.a.g.1.1 1 21.2 odd 6
1764.2.k.d.361.1 2 21.11 odd 6
1764.2.k.d.1549.1 2 3.2 odd 2
1764.2.k.e.361.1 2 21.17 even 6
1764.2.k.e.1549.1 2 21.20 even 2
2100.2.a.a.1.1 1 35.19 odd 6
2100.2.k.a.1849.1 2 35.12 even 12
2100.2.k.a.1849.2 2 35.33 even 12
2268.2.j.f.757.1 2 63.47 even 6
2268.2.j.f.1513.1 2 63.5 even 6
2268.2.j.i.757.1 2 63.61 odd 6
2268.2.j.i.1513.1 2 63.40 odd 6
2352.2.a.s.1.1 1 28.23 odd 6
2352.2.q.g.961.1 2 4.3 odd 2
2352.2.q.g.1537.1 2 28.11 odd 6
2352.2.q.s.961.1 2 28.27 even 2
2352.2.q.s.1537.1 2 28.3 even 6
4032.2.a.t.1.1 1 168.131 odd 6
4032.2.a.u.1.1 1 168.5 even 6
5376.2.c.i.2689.1 2 112.5 odd 12
5376.2.c.i.2689.2 2 112.61 odd 12
5376.2.c.x.2689.1 2 112.19 even 12
5376.2.c.x.2689.2 2 112.75 even 12
6300.2.a.p.1.1 1 105.89 even 6
6300.2.k.r.6049.1 2 105.68 odd 12
6300.2.k.r.6049.2 2 105.47 odd 12
7056.2.a.x.1.1 1 84.23 even 6
8400.2.a.ct.1.1 1 140.19 even 6
9408.2.a.r.1.1 1 56.51 odd 6
9408.2.a.co.1.1 1 56.37 even 6