Properties

Label 980.2.q.e.949.2
Level 980980
Weight 22
Character 980.949
Analytic conductor 7.8257.825
Analytic rank 00
Dimension 44
Inner twists 44

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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] = [980,2,Mod(569,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) 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("980.569"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 980=22572 980 = 2^{2} \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 980.q (of order 66, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.825339398097.82533939809
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(ζ12)\Q(\zeta_{12})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 949.2
Root 0.8660250.500000i-0.866025 - 0.500000i of defining polynomial
Character χ\chi == 980.949
Dual form 980.2.q.e.569.2

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+(2.232050.133975i)q5+(1.500002.59808i)q94.00000iq13+(3.464102.00000i)q17+(2.000003.46410i)q19+(6.928204.00000i)q23+(4.964100.598076i)q252.00000q29+(4.00000+6.92820i)q31+(6.928204.00000i)q376.00000q41+8.00000iq43+(3.696155.59808i)q45+(6.928204.00000i)q47+(2.000003.46410i)q59+(3.000005.19615i)q61+(0.5358988.92820i)q65+(6.92820+4.00000i)q67+12.0000q71+(3.464102.00000i)q73+(2.000003.46410i)q79+(4.50000+7.79423i)q81+(8.000004.00000i)q85+(5.00000+8.66025i)q89+(4.928207.46410i)q9512.0000iq97+O(q100)q+(2.23205 - 0.133975i) q^{5} +(-1.50000 - 2.59808i) q^{9} -4.00000i q^{13} +(-3.46410 - 2.00000i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(6.92820 - 4.00000i) q^{23} +(4.96410 - 0.598076i) q^{25} -2.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(6.92820 - 4.00000i) q^{37} -6.00000 q^{41} +8.00000i q^{43} +(-3.69615 - 5.59808i) q^{45} +(6.92820 - 4.00000i) q^{47} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(-0.535898 - 8.92820i) q^{65} +(6.92820 + 4.00000i) q^{67} +12.0000 q^{71} +(-3.46410 - 2.00000i) q^{73} +(-2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-8.00000 - 4.00000i) q^{85} +(5.00000 + 8.66025i) q^{89} +(-4.92820 - 7.46410i) q^{95} -12.0000i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q56q98q19+6q258q2916q3124q41+6q45+8q5912q6116q65+48q718q7918q8132q85+20q89+8q95+O(q100) 4 q + 2 q^{5} - 6 q^{9} - 8 q^{19} + 6 q^{25} - 8 q^{29} - 16 q^{31} - 24 q^{41} + 6 q^{45} + 8 q^{59} - 12 q^{61} - 16 q^{65} + 48 q^{71} - 8 q^{79} - 18 q^{81} - 32 q^{85} + 20 q^{89} + 8 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/980Z)×\left(\mathbb{Z}/980\mathbb{Z}\right)^\times.

nn 101101 197197 491491
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 1-1 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 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
44 0 0
55 2.23205 0.133975i 0.998203 0.0599153i
66 0 0
77 0 0
88 0 0
99 −1.50000 2.59808i −0.500000 0.866025i
1010 0 0
1111 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
1212 0 0
1313 4.00000i 1.10940i −0.832050 0.554700i 0.812833π-0.812833\pi
0.832050 0.554700i 0.187167π-0.187167\pi
1414 0 0
1515 0 0
1616 0 0
1717 −3.46410 2.00000i −0.840168 0.485071i 0.0171533 0.999853i 0.494540π-0.494540\pi
−0.857321 + 0.514782i 0.827873π0.827873\pi
1818 0 0
1919 −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i 0.318398π-0.318398\pi
−0.998899 + 0.0469020i 0.985065π0.985065\pi
2020 0 0
2121 0 0
2222 0 0
2323 6.92820 4.00000i 1.44463 0.834058i 0.446476 0.894795i 0.352679π-0.352679\pi
0.998154 + 0.0607377i 0.0193453π0.0193453\pi
2424 0 0
2525 4.96410 0.598076i 0.992820 0.119615i
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 −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i 0.421802π0.421802\pi
−0.961625 + 0.274367i 0.911532π0.911532\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 6.92820 4.00000i 1.13899 0.657596i 0.192809 0.981236i 0.438240π-0.438240\pi
0.946180 + 0.323640i 0.104907π0.104907\pi
3838 0 0
3939 0 0
4040 0 0
4141 −6.00000 −0.937043 −0.468521 0.883452i 0.655213π-0.655213\pi
−0.468521 + 0.883452i 0.655213π0.655213\pi
4242 0 0
4343 8.00000i 1.21999i 0.792406 + 0.609994i 0.208828π0.208828\pi
−0.792406 + 0.609994i 0.791172π0.791172\pi
4444 0 0
4545 −3.69615 5.59808i −0.550990 0.834512i
4646 0 0
4747 6.92820 4.00000i 1.01058 0.583460i 0.0992202 0.995066i 0.468365π-0.468365\pi
0.911362 + 0.411606i 0.135032π0.135032\pi
4848 0 0
4949 0 0
5050 0 0
5151 0 0
5252 0 0
5353 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i 0.749486π-0.749486\pi
0.966342 + 0.257260i 0.0828195π0.0828195\pi
6060 0 0
6161 −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i 0.292159π-0.292159\pi
−0.991645 + 0.128994i 0.958825π0.958825\pi
6262 0 0
6363 0 0
6464 0 0
6565 −0.535898 8.92820i −0.0664700 1.10741i
6666 0 0
6767 6.92820 + 4.00000i 0.846415 + 0.488678i 0.859440 0.511237i 0.170813π-0.170813\pi
−0.0130248 + 0.999915i 0.504146π0.504146\pi
6868 0 0
6969 0 0
7070 0 0
7171 12.0000 1.42414 0.712069 0.702109i 0.247758π-0.247758\pi
0.712069 + 0.702109i 0.247758π0.247758\pi
7272 0 0
7373 −3.46410 2.00000i −0.405442 0.234082i 0.283387 0.959006i 0.408542π-0.408542\pi
−0.688830 + 0.724923i 0.741875π0.741875\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i 0.238911π-0.238911\pi
−0.956325 + 0.292306i 0.905577π0.905577\pi
8080 0 0
8181 −4.50000 + 7.79423i −0.500000 + 0.866025i
8282 0 0
8383 0 0 1.00000 00
−1.00000 π\pi
8484 0 0
8585 −8.00000 4.00000i −0.867722 0.433861i
8686 0 0
8787 0 0
8888 0 0
8989 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i 0.0111410π0.0111410\pi
−0.469389 + 0.882992i 0.655526π0.655526\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 −4.92820 7.46410i −0.505623 0.765801i
9696 0 0
9797 12.0000i 1.21842i −0.793011 0.609208i 0.791488π-0.791488\pi
0.793011 0.609208i 0.208512π-0.208512\pi
9898 0 0
9999 0 0
100100 0 0
101101 −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i 0.519872π0.519872\pi
−0.833143 + 0.553058i 0.813461π0.813461\pi
102102 0 0
103103 6.92820 4.00000i 0.682656 0.394132i −0.118199 0.992990i 0.537712π-0.537712\pi
0.800855 + 0.598858i 0.204379π0.204379\pi
104104 0 0
105105 0 0
106106 0 0
107107 −6.92820 + 4.00000i −0.669775 + 0.386695i −0.795991 0.605308i 0.793050π-0.793050\pi
0.126217 + 0.992003i 0.459717π0.459717\pi
108108 0 0
109109 7.00000 12.1244i 0.670478 1.16130i −0.307290 0.951616i 0.599422π-0.599422\pi
0.977769 0.209687i 0.0672444π-0.0672444\pi
110110 0 0
111111 0 0
112112 0 0
113113 16.0000i 1.50515i −0.658505 0.752577i 0.728811π-0.728811\pi
0.658505 0.752577i 0.271189π-0.271189\pi
114114 0 0
115115 14.9282 9.85641i 1.39206 0.919115i
116116 0 0
117117 −10.3923 + 6.00000i −0.960769 + 0.554700i
118118 0 0
119119 0 0
120120 0 0
121121 5.50000 + 9.52628i 0.500000 + 0.866025i
122122 0 0
123123 0 0
124124 0 0
125125 11.0000 2.00000i 0.983870 0.178885i
126126 0 0
127127 8.00000i 0.709885i 0.934888 + 0.354943i 0.115500π0.115500\pi
−0.934888 + 0.354943i 0.884500π0.884500\pi
128128 0 0
129129 0 0
130130 0 0
131131 −2.00000 3.46410i −0.174741 0.302660i 0.765331 0.643637i 0.222575π-0.222575\pi
−0.940072 + 0.340977i 0.889242π0.889242\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0 0
137137 −6.92820 4.00000i −0.591916 0.341743i 0.173939 0.984757i 0.444351π-0.444351\pi
−0.765855 + 0.643013i 0.777684π0.777684\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 0 0
142142 0 0
143143 0 0
144144 0 0
145145 −4.46410 + 0.267949i −0.370723 + 0.0222520i
146146 0 0
147147 0 0
148148 0 0
149149 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i 0.0876260π-0.0876260\pi
−0.716578 + 0.697507i 0.754293π0.754293\pi
150150 0 0
151151 −6.00000 + 10.3923i −0.488273 + 0.845714i −0.999909 0.0134886i 0.995706π-0.995706\pi
0.511636 + 0.859202i 0.329040π0.329040\pi
152152 0 0
153153 12.0000i 0.970143i
154154 0 0
155155 −8.00000 + 16.0000i −0.642575 + 1.28515i
156156 0 0
157157 10.3923 + 6.00000i 0.829396 + 0.478852i 0.853646 0.520854i 0.174386π-0.174386\pi
−0.0242497 + 0.999706i 0.507720π0.507720\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 −20.7846 + 12.0000i −1.62798 + 0.939913i −0.643280 + 0.765631i 0.722427π0.722427\pi
−0.984696 + 0.174282i 0.944240π0.944240\pi
164164 0 0
165165 0 0
166166 0 0
167167 24.0000i 1.85718i 0.371113 + 0.928588i 0.378976π0.378976\pi
−0.371113 + 0.928588i 0.621024π0.621024\pi
168168 0 0
169169 −3.00000 −0.230769
170170 0 0
171171 −6.00000 + 10.3923i −0.458831 + 0.794719i
172172 0 0
173173 −10.3923 + 6.00000i −0.790112 + 0.456172i −0.840002 0.542583i 0.817446π-0.817446\pi
0.0498898 + 0.998755i 0.484113π0.484113\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 −4.00000 + 6.92820i −0.298974 + 0.517838i −0.975901 0.218212i 0.929978π-0.929978\pi
0.676927 + 0.736050i 0.263311π0.263311\pi
180180 0 0
181181 −14.0000 −1.04061 −0.520306 0.853980i 0.674182π-0.674182\pi
−0.520306 + 0.853980i 0.674182π0.674182\pi
182182 0 0
183183 0 0
184184 0 0
185185 14.9282 9.85641i 1.09754 0.724657i
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 10.0000 + 17.3205i 0.723575 + 1.25327i 0.959558 + 0.281511i 0.0908356π0.0908356\pi
−0.235983 + 0.971757i 0.575831π0.575831\pi
192192 0 0
193193 13.8564 + 8.00000i 0.997406 + 0.575853i 0.907480 0.420096i 0.138004π-0.138004\pi
0.0899262 + 0.995948i 0.471337π0.471337\pi
194194 0 0
195195 0 0
196196 0 0
197197 16.0000i 1.13995i −0.821661 0.569976i 0.806952π-0.806952\pi
0.821661 0.569976i 0.193048π-0.193048\pi
198198 0 0
199199 12.0000 20.7846i 0.850657 1.47338i −0.0299585 0.999551i 0.509538π-0.509538\pi
0.880616 0.473831i 0.157129π-0.157129\pi
200200 0 0
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 −13.3923 + 0.803848i −0.935359 + 0.0561432i
206206 0 0
207207 −20.7846 12.0000i −1.44463 0.834058i
208208 0 0
209209 0 0
210210 0 0
211211 24.0000 1.65223 0.826114 0.563503i 0.190547π-0.190547\pi
0.826114 + 0.563503i 0.190547π0.190547\pi
212212 0 0
213213 0 0
214214 0 0
215215 1.07180 + 17.8564i 0.0730959 + 1.21780i
216216 0 0
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 −8.00000 + 13.8564i −0.538138 + 0.932083i
222222 0 0
223223 8.00000i 0.535720i 0.963458 + 0.267860i 0.0863164π0.0863164\pi
−0.963458 + 0.267860i 0.913684π0.913684\pi
224224 0 0
225225 −9.00000 12.0000i −0.600000 0.800000i
226226 0 0
227227 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
228228 0 0
229229 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i 0.0135930π-0.0135930\pi
−0.536515 + 0.843891i 0.680260π0.680260\pi
230230 0 0
231231 0 0
232232 0 0
233233 −6.92820 + 4.00000i −0.453882 + 0.262049i −0.709468 0.704737i 0.751065π-0.751065\pi
0.255586 + 0.966786i 0.417731π0.417731\pi
234234 0 0
235235 14.9282 9.85641i 0.973809 0.642961i
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 −9.00000 + 15.5885i −0.579741 + 1.00414i 0.415768 + 0.909471i 0.363513π0.363513\pi
−0.995509 + 0.0946700i 0.969820π0.969820\pi
242242 0 0
243243 0 0
244244 0 0
245245 0 0
246246 0 0
247247 −13.8564 + 8.00000i −0.881662 + 0.509028i
248248 0 0
249249 0 0
250250 0 0
251251 4.00000 0.252478 0.126239 0.992000i 0.459709π-0.459709\pi
0.126239 + 0.992000i 0.459709π0.459709\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0 0
257257 −10.3923 + 6.00000i −0.648254 + 0.374270i −0.787787 0.615948i 0.788773π-0.788773\pi
0.139533 + 0.990217i 0.455440π0.455440\pi
258258 0 0
259259 0 0
260260 0 0
261261 3.00000 + 5.19615i 0.185695 + 0.321634i
262262 0 0
263263 −20.7846 12.0000i −1.28163 0.739952i −0.304487 0.952517i 0.598485π-0.598485\pi
−0.977147 + 0.212565i 0.931818π0.931818\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 0 0
269269 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i 0.734725π-0.734725\pi
0.977229 + 0.212187i 0.0680585π0.0680585\pi
270270 0 0
271271 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 13.8564 + 8.00000i 0.832551 + 0.480673i 0.854725 0.519081i 0.173726π-0.173726\pi
−0.0221745 + 0.999754i 0.507059π0.507059\pi
278278 0 0
279279 24.0000 1.43684
280280 0 0
281281 6.00000 0.357930 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
282282 0 0
283283 27.7128 + 16.0000i 1.64736 + 0.951101i 0.978117 + 0.208053i 0.0667128π0.0667128\pi
0.669238 + 0.743048i 0.266621π0.266621\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −0.500000 0.866025i −0.0294118 0.0509427i
290290 0 0
291291 0 0
292292 0 0
293293 12.0000i 0.701047i −0.936554 0.350524i 0.886004π-0.886004\pi
0.936554 0.350524i 0.113996π-0.113996\pi
294294 0 0
295295 4.00000 8.00000i 0.232889 0.465778i
296296 0 0
297297 0 0
298298 0 0
299299 −16.0000 27.7128i −0.925304 1.60267i
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 −7.39230 11.1962i −0.423282 0.641090i
306306 0 0
307307 16.0000i 0.913168i −0.889680 0.456584i 0.849073π-0.849073\pi
0.889680 0.456584i 0.150927π-0.150927\pi
308308 0 0
309309 0 0
310310 0 0
311311 −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i 0.404886π0.404886\pi
−0.974841 + 0.222900i 0.928448π0.928448\pi
312312 0 0
313313 3.46410 2.00000i 0.195803 0.113047i −0.398894 0.916997i 0.630606π-0.630606\pi
0.594696 + 0.803951i 0.297272π0.297272\pi
314314 0 0
315315 0 0
316316 0 0
317317 −13.8564 + 8.00000i −0.778253 + 0.449325i −0.835811 0.549017i 0.815002π-0.815002\pi
0.0575576 + 0.998342i 0.481669π0.481669\pi
318318 0 0
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 16.0000i 0.890264i
324324 0 0
325325 −2.39230 19.8564i −0.132701 1.10144i
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 8.00000 + 13.8564i 0.439720 + 0.761617i 0.997668 0.0682590i 0.0217444π-0.0217444\pi
−0.557948 + 0.829876i 0.688411π0.688411\pi
332332 0 0
333333 −20.7846 12.0000i −1.13899 0.657596i
334334 0 0
335335 16.0000 + 8.00000i 0.874173 + 0.437087i
336336 0 0
337337 8.00000i 0.435788i 0.975972 + 0.217894i 0.0699187π0.0699187\pi
−0.975972 + 0.217894i 0.930081π0.930081\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 20.7846 + 12.0000i 1.11578 + 0.644194i 0.940319 0.340293i 0.110526π-0.110526\pi
0.175457 + 0.984487i 0.443860π0.443860\pi
348348 0 0
349349 −6.00000 −0.321173 −0.160586 0.987022i 0.551338π-0.551338\pi
−0.160586 + 0.987022i 0.551338π0.551338\pi
350350 0 0
351351 0 0
352352 0 0
353353 −10.3923 6.00000i −0.553127 0.319348i 0.197256 0.980352i 0.436797π-0.436797\pi
−0.750382 + 0.661004i 0.770130π0.770130\pi
354354 0 0
355355 26.7846 1.60770i 1.42158 0.0853276i
356356 0 0
357357 0 0
358358 0 0
359359 −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i 0.989691π-0.989691\pi
0.471696 0.881761i 0.343642π-0.343642\pi
360360 0 0
361361 1.50000 2.59808i 0.0789474 0.136741i
362362 0 0
363363 0 0
364364 0 0
365365 −8.00000 4.00000i −0.418739 0.209370i
366366 0 0
367367 6.92820 + 4.00000i 0.361649 + 0.208798i 0.669804 0.742538i 0.266378π-0.266378\pi
−0.308155 + 0.951336i 0.599711π0.599711\pi
368368 0 0
369369 9.00000 + 15.5885i 0.468521 + 0.811503i
370370 0 0
371371 0 0
372372 0 0
373373 27.7128 16.0000i 1.43492 0.828449i 0.437425 0.899255i 0.355891π-0.355891\pi
0.997490 + 0.0708063i 0.0225572π0.0225572\pi
374374 0 0
375375 0 0
376376 0 0
377377 8.00000i 0.412021i
378378 0 0
379379 8.00000 0.410932 0.205466 0.978664i 0.434129π-0.434129\pi
0.205466 + 0.978664i 0.434129π0.434129\pi
380380 0 0
381381 0 0
382382 0 0
383383 −20.7846 + 12.0000i −1.06204 + 0.613171i −0.925997 0.377531i 0.876773π-0.876773\pi
−0.136047 + 0.990702i 0.543440π0.543440\pi
384384 0 0
385385 0 0
386386 0 0
387387 20.7846 12.0000i 1.05654 0.609994i
388388 0 0
389389 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i 0.784728π-0.784728\pi
0.932002 + 0.362454i 0.118061π0.118061\pi
390390 0 0
391391 −32.0000 −1.61831
392392 0 0
393393 0 0
394394 0 0
395395 −4.92820 7.46410i −0.247965 0.375560i
396396 0 0
397397 24.2487 14.0000i 1.21701 0.702640i 0.252731 0.967537i 0.418671π-0.418671\pi
0.964277 + 0.264897i 0.0853379π0.0853379\pi
398398 0 0
399399 0 0
400400 0 0
401401 −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i 0.315043π-0.315043\pi
−0.998350 + 0.0574304i 0.981709π0.981709\pi
402402 0 0
403403 27.7128 + 16.0000i 1.38047 + 0.797017i
404404 0 0
405405 −9.00000 + 18.0000i −0.447214 + 0.894427i
406406 0 0
407407 0 0
408408 0 0
409409 −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i 0.912855π-0.912855\pi
0.715523 + 0.698589i 0.246188π0.246188\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 −28.0000 −1.36789 −0.683945 0.729534i 0.739737π-0.739737\pi
−0.683945 + 0.729534i 0.739737π0.739737\pi
420420 0 0
421421 10.0000 0.487370 0.243685 0.969854i 0.421644π-0.421644\pi
0.243685 + 0.969854i 0.421644π0.421644\pi
422422 0 0
423423 −20.7846 12.0000i −1.01058 0.583460i
424424 0 0
425425 −18.3923 7.85641i −0.892158 0.381092i
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 −10.0000 + 17.3205i −0.481683 + 0.834300i −0.999779 0.0210230i 0.993308π-0.993308\pi
0.518096 + 0.855323i 0.326641π0.326641\pi
432432 0 0
433433 28.0000i 1.34559i −0.739827 0.672797i 0.765093π-0.765093\pi
0.739827 0.672797i 0.234907π-0.234907\pi
434434 0 0
435435 0 0
436436 0 0
437437 −27.7128 16.0000i −1.32568 0.765384i
438438 0 0
439439 −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i 0.227810π-0.227810\pi
−0.945552 + 0.325471i 0.894477π0.894477\pi
440440 0 0
441441 0 0
442442 0 0
443443 20.7846 12.0000i 0.987507 0.570137i 0.0829786 0.996551i 0.473557π-0.473557\pi
0.904528 + 0.426414i 0.140223π0.140223\pi
444444 0 0
445445 12.3205 + 18.6603i 0.584048 + 0.884581i
446446 0 0
447447 0 0
448448 0 0
449449 −2.00000 −0.0943858 −0.0471929 0.998886i 0.515028π-0.515028\pi
−0.0471929 + 0.998886i 0.515028π0.515028\pi
450450 0 0
451451 0 0
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 13.8564 8.00000i 0.648175 0.374224i −0.139581 0.990211i 0.544576π-0.544576\pi
0.787757 + 0.615986i 0.211242π0.211242\pi
458458 0 0
459459 0 0
460460 0 0
461461 26.0000 1.21094 0.605470 0.795868i 0.292985π-0.292985\pi
0.605470 + 0.795868i 0.292985π0.292985\pi
462462 0 0
463463 8.00000i 0.371792i −0.982569 0.185896i 0.940481π-0.940481\pi
0.982569 0.185896i 0.0595187π-0.0595187\pi
464464 0 0
465465 0 0
466466 0 0
467467 13.8564 8.00000i 0.641198 0.370196i −0.143878 0.989595i 0.545957π-0.545957\pi
0.785076 + 0.619400i 0.212624π0.212624\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 −12.0000 16.0000i −0.550598 0.734130i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
480480 0 0
481481 −16.0000 27.7128i −0.729537 1.26360i
482482 0 0
483483 0 0
484484 0 0
485485 −1.60770 26.7846i −0.0730017 1.21623i
486486 0 0
487487 −6.92820 4.00000i −0.313947 0.181257i 0.334744 0.942309i 0.391350π-0.391350\pi
−0.648691 + 0.761052i 0.724683π0.724683\pi
488488 0 0
489489 0 0
490490 0 0
491491 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
492492 0 0
493493 6.92820 + 4.00000i 0.312031 + 0.180151i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 −4.00000 6.92820i −0.179065 0.310149i 0.762496 0.646993i 0.223974π-0.223974\pi
−0.941560 + 0.336844i 0.890640π0.890640\pi
500500 0 0
501501 0 0
502502 0 0
503503 8.00000i 0.356702i 0.983967 + 0.178351i 0.0570763π0.0570763\pi
−0.983967 + 0.178351i 0.942924π0.942924\pi
504504 0 0
505505 −18.0000 + 36.0000i −0.800989 + 1.60198i
506506 0 0
507507 0 0
508508 0 0
509509 11.0000 + 19.0526i 0.487566 + 0.844490i 0.999898 0.0142980i 0.00455136π-0.00455136\pi
−0.512331 + 0.858788i 0.671218π0.671218\pi
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 14.9282 9.85641i 0.657815 0.434325i
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 −3.00000 + 5.19615i −0.131432 + 0.227648i −0.924229 0.381839i 0.875291π-0.875291\pi
0.792797 + 0.609486i 0.208624π0.208624\pi
522522 0 0
523523 27.7128 16.0000i 1.21180 0.699631i 0.248646 0.968594i 0.420014π-0.420014\pi
0.963150 + 0.268963i 0.0866810π0.0866810\pi
524524 0 0
525525 0 0
526526 0 0
527527 27.7128 16.0000i 1.20719 0.696971i
528528 0 0
529529 20.5000 35.5070i 0.891304 1.54378i
530530 0 0
531531 −12.0000 −0.520756
532532 0 0
533533 24.0000i 1.03956i
534534 0 0
535535 −14.9282 + 9.85641i −0.645403 + 0.426130i
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 −7.00000 12.1244i −0.300954 0.521267i 0.675399 0.737453i 0.263972π-0.263972\pi
−0.976352 + 0.216186i 0.930638π0.930638\pi
542542 0 0
543543 0 0
544544 0 0
545545 14.0000 28.0000i 0.599694 1.19939i
546546 0 0
547547 8.00000i 0.342055i 0.985266 + 0.171028i 0.0547087π0.0547087\pi
−0.985266 + 0.171028i 0.945291π0.945291\pi
548548 0 0
549549 −9.00000 + 15.5885i −0.384111 + 0.665299i
550550 0 0
551551 4.00000 + 6.92820i 0.170406 + 0.295151i
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 −13.8564 8.00000i −0.587115 0.338971i 0.176841 0.984239i 0.443412π-0.443412\pi
−0.763956 + 0.645269i 0.776745π0.776745\pi
558558 0 0
559559 32.0000 1.35346
560560 0 0
561561 0 0
562562 0 0
563563 −13.8564 8.00000i −0.583978 0.337160i 0.178735 0.983897i 0.442800π-0.442800\pi
−0.762713 + 0.646737i 0.776133π0.776133\pi
564564 0 0
565565 −2.14359 35.7128i −0.0901817 1.50245i
566566 0 0
567567 0 0
568568 0 0
569569 21.0000 + 36.3731i 0.880366 + 1.52484i 0.850935 + 0.525271i 0.176036π0.176036\pi
0.0294311 + 0.999567i 0.490630π0.490630\pi
570570 0 0
571571 20.0000 34.6410i 0.836974 1.44968i −0.0554391 0.998462i 0.517656π-0.517656\pi
0.892413 0.451219i 0.149011π-0.149011\pi
572572 0 0
573573 0 0
574574 0 0
575575 32.0000 24.0000i 1.33449 1.00087i
576576 0 0
577577 3.46410 + 2.00000i 0.144212 + 0.0832611i 0.570370 0.821388i 0.306800π-0.306800\pi
−0.426158 + 0.904649i 0.640133π0.640133\pi
578578 0 0
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 −22.3923 + 14.7846i −0.925808 + 0.611268i
586586 0 0
587587 32.0000i 1.32078i −0.750922 0.660391i 0.770391π-0.770391\pi
0.750922 0.660391i 0.229609π-0.229609\pi
588588 0 0
589589 32.0000 1.31854
590590 0 0
591591 0 0
592592 0 0
593593 31.1769 18.0000i 1.28028 0.739171i 0.303383 0.952869i 0.401884π-0.401884\pi
0.976900 + 0.213697i 0.0685507π0.0685507\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 −18.0000 + 31.1769i −0.735460 + 1.27385i 0.219061 + 0.975711i 0.429701π0.429701\pi
−0.954521 + 0.298143i 0.903633π0.903633\pi
600600 0 0
601601 10.0000 0.407909 0.203954 0.978980i 0.434621π-0.434621\pi
0.203954 + 0.978980i 0.434621π0.434621\pi
602602 0 0
603603 24.0000i 0.977356i
604604 0 0
605605 13.5526 + 20.5263i 0.550990 + 0.834512i
606606 0 0
607607 −34.6410 + 20.0000i −1.40604 + 0.811775i −0.995003 0.0998457i 0.968165π-0.968165\pi
−0.411033 + 0.911621i 0.634832π0.634832\pi
608608 0 0
609609 0 0
610610 0 0
611611 −16.0000 27.7128i −0.647291 1.12114i
612612 0 0
613613 20.7846 + 12.0000i 0.839482 + 0.484675i 0.857088 0.515170i 0.172271π-0.172271\pi
−0.0176058 + 0.999845i 0.505604π0.505604\pi
614614 0 0
615615 0 0
616616 0 0
617617 8.00000i 0.322068i −0.986949 0.161034i 0.948517π-0.948517\pi
0.986949 0.161034i 0.0514829π-0.0514829\pi
618618 0 0
619619 −2.00000 + 3.46410i −0.0803868 + 0.139234i −0.903416 0.428765i 0.858949π-0.858949\pi
0.823029 + 0.567999i 0.192282π0.192282\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 24.2846 5.93782i 0.971384 0.237513i
626626 0 0
627627 0 0
628628 0 0
629629 −32.0000 −1.27592
630630 0 0
631631 −36.0000 −1.43314 −0.716569 0.697517i 0.754288π-0.754288\pi
−0.716569 + 0.697517i 0.754288π0.754288\pi
632632 0 0
633633 0 0
634634 0 0
635635 1.07180 + 17.8564i 0.0425330 + 0.708610i
636636 0 0
637637 0 0
638638 0 0
639639 −18.0000 31.1769i −0.712069 1.23334i
640640 0 0
641641 1.00000 1.73205i 0.0394976 0.0684119i −0.845601 0.533816i 0.820758π-0.820758\pi
0.885098 + 0.465404i 0.154091π0.154091\pi
642642 0 0
643643 16.0000i 0.630978i −0.948929 0.315489i 0.897831π-0.897831\pi
0.948929 0.315489i 0.102169π-0.102169\pi
644644 0 0
645645 0 0
646646 0 0
647647 −20.7846 12.0000i −0.817127 0.471769i 0.0322975 0.999478i 0.489718π-0.489718\pi
−0.849425 + 0.527710i 0.823051π0.823051\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 −20.7846 + 12.0000i −0.813365 + 0.469596i −0.848123 0.529799i 0.822267π-0.822267\pi
0.0347583 + 0.999396i 0.488934π0.488934\pi
654654 0 0
655655 −4.92820 7.46410i −0.192561 0.291647i
656656 0 0
657657 12.0000i 0.468165i
658658 0 0
659659 −24.0000 −0.934907 −0.467454 0.884018i 0.654829π-0.654829\pi
−0.467454 + 0.884018i 0.654829π0.654829\pi
660660 0 0
661661 17.0000 29.4449i 0.661223 1.14527i −0.319071 0.947731i 0.603371π-0.603371\pi
0.980294 0.197542i 0.0632958π-0.0632958\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 −13.8564 + 8.00000i −0.536522 + 0.309761i
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 8.00000i 0.308377i 0.988041 + 0.154189i 0.0492764π0.0492764\pi
−0.988041 + 0.154189i 0.950724π0.950724\pi
674674 0 0
675675 0 0
676676 0 0
677677 3.46410 2.00000i 0.133136 0.0768662i −0.431953 0.901896i 0.642175π-0.642175\pi
0.565089 + 0.825030i 0.308842π0.308842\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 0 0
683683 6.92820 + 4.00000i 0.265100 + 0.153056i 0.626659 0.779294i 0.284422π-0.284422\pi
−0.361559 + 0.932349i 0.617755π0.617755\pi
684684 0 0
685685 −16.0000 8.00000i −0.611329 0.305664i
686686 0 0
687687 0 0
688688 0 0
689689 0 0
690690 0 0
691691 14.0000 + 24.2487i 0.532585 + 0.922464i 0.999276 + 0.0380440i 0.0121127π0.0121127\pi
−0.466691 + 0.884420i 0.654554π0.654554\pi
692692 0 0
693693 0 0
694694 0 0
695695 8.92820 0.535898i 0.338666 0.0203278i
696696 0 0
697697 20.7846 + 12.0000i 0.787273 + 0.454532i
698698 0 0
699699 0 0
700700 0 0
701701 2.00000 0.0755390 0.0377695 0.999286i 0.487975π-0.487975\pi
0.0377695 + 0.999286i 0.487975π0.487975\pi
702702 0 0
703703 −27.7128 16.0000i −1.04521 0.603451i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 −3.00000 5.19615i −0.112667 0.195146i 0.804178 0.594389i 0.202606π-0.202606\pi
−0.916845 + 0.399244i 0.869273π0.869273\pi
710710 0 0
711711 −6.00000 + 10.3923i −0.225018 + 0.389742i
712712 0 0
713713 64.0000i 2.39682i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 −16.0000 27.7128i −0.596699 1.03351i −0.993305 0.115524i 0.963145π-0.963145\pi
0.396605 0.917989i 0.370188π-0.370188\pi
720720 0 0
721721 0 0
722722 0 0
723723 0 0
724724 0 0
725725 −9.92820 + 1.19615i −0.368724 + 0.0444240i
726726 0 0
727727 8.00000i 0.296704i −0.988935 0.148352i 0.952603π-0.952603\pi
0.988935 0.148352i 0.0473968π-0.0473968\pi
728728 0 0
729729 27.0000 1.00000
730730 0 0
731731 16.0000 27.7128i 0.591781 1.02500i
732732 0 0
733733 −17.3205 + 10.0000i −0.639748 + 0.369358i −0.784517 0.620107i 0.787089π-0.787089\pi
0.144770 + 0.989465i 0.453756π0.453756\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 −4.00000 + 6.92820i −0.147142 + 0.254858i −0.930170 0.367129i 0.880341π-0.880341\pi
0.783028 + 0.621987i 0.213674π0.213674\pi
740740 0 0
741741 0 0
742742 0 0
743743 24.0000i 0.880475i −0.897881 0.440237i 0.854894π-0.854894\pi
0.897881 0.440237i 0.145106π-0.145106\pi
744744 0 0
745745 7.39230 + 11.1962i 0.270833 + 0.410195i
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 10.0000 + 17.3205i 0.364905 + 0.632034i 0.988761 0.149505i 0.0477681π-0.0477681\pi
−0.623856 + 0.781540i 0.714435π0.714435\pi
752752 0 0
753753 0 0
754754 0 0
755755 −12.0000 + 24.0000i −0.436725 + 0.873449i
756756 0 0
757757 24.0000i 0.872295i 0.899875 + 0.436147i 0.143657π0.143657\pi
−0.899875 + 0.436147i 0.856343π0.856343\pi
758758 0 0
759759 0 0
760760 0 0
761761 5.00000 + 8.66025i 0.181250 + 0.313934i 0.942306 0.334752i 0.108652π-0.108652\pi
−0.761057 + 0.648686i 0.775319π0.775319\pi
762762 0 0
763763 0 0
764764 0 0
765765 1.60770 + 26.7846i 0.0581263 + 0.968400i
766766 0 0
767767 −13.8564 8.00000i −0.500326 0.288863i
768768 0 0
769769 −2.00000 −0.0721218 −0.0360609 0.999350i 0.511481π-0.511481\pi
−0.0360609 + 0.999350i 0.511481π0.511481\pi
770770 0 0
771771 0 0
772772 0 0
773773 31.1769 + 18.0000i 1.12136 + 0.647415i 0.941747 0.336323i 0.109183π-0.109183\pi
0.179609 + 0.983738i 0.442517π0.442517\pi
774774 0 0
775775 −15.7128 + 36.7846i −0.564421 + 1.32134i
776776 0 0
777777 0 0
778778 0 0
779779 12.0000 + 20.7846i 0.429945 + 0.744686i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0 0
785785 24.0000 + 12.0000i 0.856597 + 0.428298i
786786 0 0
787787 41.5692 + 24.0000i 1.48178 + 0.855508i 0.999786 0.0206657i 0.00657856π-0.00657856\pi
0.481996 + 0.876173i 0.339912π0.339912\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 −20.7846 + 12.0000i −0.738083 + 0.426132i
794794 0 0
795795 0 0
796796 0 0
797797 28.0000i 0.991811i 0.868377 + 0.495905i 0.165164π0.165164\pi
−0.868377 + 0.495905i 0.834836π0.834836\pi
798798 0 0
799799 −32.0000 −1.13208
800800 0 0
801801 15.0000 25.9808i 0.529999 0.917985i
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 −13.0000 + 22.5167i −0.457056 + 0.791644i −0.998804 0.0488972i 0.984429π-0.984429\pi
0.541748 + 0.840541i 0.317763π0.317763\pi
810810 0 0
811811 36.0000 1.26413 0.632065 0.774915i 0.282207π-0.282207\pi
0.632065 + 0.774915i 0.282207π0.282207\pi
812812 0 0
813813 0 0
814814 0 0
815815 −44.7846 + 29.5692i −1.56874 + 1.03576i
816816 0 0
817817 27.7128 16.0000i 0.969549 0.559769i
818818 0 0
819819 0 0
820820 0 0
821821 3.00000 + 5.19615i 0.104701 + 0.181347i 0.913616 0.406578i 0.133278π-0.133278\pi
−0.808915 + 0.587925i 0.799945π0.799945\pi
822822 0 0
823823 −20.7846 12.0000i −0.724506 0.418294i 0.0919029 0.995768i 0.470705π-0.470705\pi
−0.816409 + 0.577474i 0.804038π0.804038\pi
824824 0 0
825825 0 0
826826 0 0
827827 8.00000i 0.278187i −0.990279 0.139094i 0.955581π-0.955581\pi
0.990279 0.139094i 0.0444189π-0.0444189\pi
828828 0 0
829829 −11.0000 + 19.0526i −0.382046 + 0.661723i −0.991355 0.131210i 0.958114π-0.958114\pi
0.609309 + 0.792933i 0.291447π0.291447\pi
830830 0 0
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 3.21539 + 53.5692i 0.111273 + 1.85384i
836836 0 0
837837 0 0
838838 0 0
839839 −16.0000 −0.552381 −0.276191 0.961103i 0.589072π-0.589072\pi
−0.276191 + 0.961103i 0.589072π0.589072\pi
840840 0 0
841841 −25.0000 −0.862069
842842 0 0
843843 0 0
844844 0 0
845845 −6.69615 + 0.401924i −0.230355 + 0.0138266i
846846 0 0
847847 0 0
848848 0 0
849849 0 0
850850 0 0
851851 32.0000 55.4256i 1.09695 1.89997i
852852 0 0
853853 4.00000i 0.136957i 0.997653 + 0.0684787i 0.0218145π0.0218145\pi
−0.997653 + 0.0684787i 0.978185π0.978185\pi
854854 0 0
855855 −12.0000 + 24.0000i −0.410391 + 0.820783i
856856 0 0
857857 45.0333 + 26.0000i 1.53831 + 0.888143i 0.998938 + 0.0460748i 0.0146713π0.0146713\pi
0.539371 + 0.842068i 0.318662π0.318662\pi
858858 0 0
859859 −18.0000 31.1769i −0.614152 1.06374i −0.990533 0.137277i 0.956165π-0.956165\pi
0.376381 0.926465i 0.377169π-0.377169\pi
860860 0 0
861861 0 0
862862 0 0
863863 −6.92820 + 4.00000i −0.235839 + 0.136162i −0.613263 0.789879i 0.710143π-0.710143\pi
0.377424 + 0.926041i 0.376810π0.376810\pi
864864 0 0
865865 −22.3923 + 14.7846i −0.761361 + 0.502692i
866866 0 0
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 16.0000 27.7128i 0.542139 0.939013i
872872 0 0
873873 −31.1769 + 18.0000i −1.05518 + 0.609208i
874874 0 0
875875 0 0
876876 0 0
877877 −34.6410 + 20.0000i −1.16974 + 0.675352i −0.953620 0.301014i 0.902675π-0.902675\pi
−0.216124 + 0.976366i 0.569342π0.569342\pi
878878 0 0
879879 0 0
880880 0 0
881881 18.0000 0.606435 0.303218 0.952921i 0.401939π-0.401939\pi
0.303218 + 0.952921i 0.401939π0.401939\pi
882882 0 0
883883 8.00000i 0.269221i −0.990899 0.134611i 0.957022π-0.957022\pi
0.990899 0.134611i 0.0429784π-0.0429784\pi
884884 0 0
885885 0 0
886886 0 0
887887 −20.7846 + 12.0000i −0.697879 + 0.402921i −0.806557 0.591156i 0.798672π-0.798672\pi
0.108678 + 0.994077i 0.465338π0.465338\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 −27.7128 16.0000i −0.927374 0.535420i
894894 0 0
895895 −8.00000 + 16.0000i −0.267411 + 0.534821i
896896 0 0
897897 0 0
898898 0 0
899899 8.00000 13.8564i 0.266815 0.462137i
900900 0 0
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 −31.2487 + 1.87564i −1.03874 + 0.0623485i
906906 0 0
907907 6.92820 + 4.00000i 0.230047 + 0.132818i 0.610594 0.791944i 0.290931π-0.290931\pi
−0.380547 + 0.924762i 0.624264π0.624264\pi
908908 0 0
909909 54.0000 1.79107
910910 0 0
911911 −28.0000 −0.927681 −0.463841 0.885919i 0.653529π-0.653529\pi
−0.463841 + 0.885919i 0.653529π0.653529\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 −2.00000 3.46410i −0.0659739 0.114270i 0.831152 0.556046i 0.187682π-0.187682\pi
−0.897126 + 0.441776i 0.854349π0.854349\pi
920920 0 0
921921 0 0
922922 0 0
923923 48.0000i 1.57994i
924924 0 0
925925 32.0000 24.0000i 1.05215 0.789115i
926926 0 0
927927 −20.7846 12.0000i −0.682656 0.394132i
928928 0 0
929929 15.0000 + 25.9808i 0.492134 + 0.852401i 0.999959 0.00905914i 0.00288365π-0.00288365\pi
−0.507825 + 0.861460i 0.669550π0.669550\pi
930930 0 0
931931 0 0
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 4.00000i 0.130674i 0.997863 + 0.0653372i 0.0208123π0.0208123\pi
−0.997863 + 0.0653372i 0.979188π0.979188\pi
938938 0 0
939939 0 0
940940 0 0
941941 19.0000 32.9090i 0.619382 1.07280i −0.370216 0.928946i 0.620716π-0.620716\pi
0.989599 0.143856i 0.0459502π-0.0459502\pi
942942 0 0
943943 −41.5692 + 24.0000i −1.35368 + 0.781548i
944944 0 0
945945 0 0
946946 0 0
947947 −20.7846 + 12.0000i −0.675409 + 0.389948i −0.798123 0.602494i 0.794174π-0.794174\pi
0.122714 + 0.992442i 0.460840π0.460840\pi
948948 0 0
949949 −8.00000 + 13.8564i −0.259691 + 0.449798i
950950 0 0
951951 0 0
952952 0 0
953953 0 0 1.00000 00
−1.00000 π\pi
954954 0 0
955955 24.6410 + 37.3205i 0.797365 + 1.20766i
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −16.5000 28.5788i −0.532258 0.921898i
962962 0 0
963963 20.7846 + 12.0000i 0.669775 + 0.386695i
964964 0 0
965965 32.0000 + 16.0000i 1.03012 + 0.515058i
966966 0 0
967967 56.0000i 1.80084i −0.435023 0.900419i 0.643260π-0.643260\pi
0.435023 0.900419i 0.356740π-0.356740\pi
968968 0 0
969969 0 0
970970 0 0
971971 30.0000 + 51.9615i 0.962746 + 1.66752i 0.715553 + 0.698558i 0.246175π0.246175\pi
0.247193 + 0.968966i 0.420492π0.420492\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −20.7846 12.0000i −0.664959 0.383914i 0.129205 0.991618i 0.458757π-0.458757\pi
−0.794164 + 0.607704i 0.792091π0.792091\pi
978978 0 0
979979 0 0
980980 0 0
981981 −42.0000 −1.34096
982982 0 0
983983 34.6410 + 20.0000i 1.10488 + 0.637901i 0.937498 0.347992i 0.113136π-0.113136\pi
0.167379 + 0.985893i 0.446470π0.446470\pi
984984 0 0
985985 −2.14359 35.7128i −0.0683006 1.13790i
986986 0 0
987987 0 0
988988 0 0
989989 32.0000 + 55.4256i 1.01754 + 1.76243i
990990 0 0
991991 −2.00000 + 3.46410i −0.0635321 + 0.110041i −0.896042 0.443969i 0.853570π-0.853570\pi
0.832510 + 0.554010i 0.186903π0.186903\pi
992992 0 0
993993 0 0
994994 0 0
995995 24.0000 48.0000i 0.760851 1.52170i
996996 0 0
997997 −24.2487 14.0000i −0.767964 0.443384i 0.0641836 0.997938i 0.479556π-0.479556\pi
−0.832148 + 0.554554i 0.812889π0.812889\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 980.2.q.e.949.2 4
5.4 even 2 inner 980.2.q.e.949.1 4
7.2 even 3 inner 980.2.q.e.569.1 4
7.3 odd 6 140.2.e.b.29.1 2
7.4 even 3 980.2.e.a.589.2 2
7.5 odd 6 980.2.q.d.569.2 4
7.6 odd 2 980.2.q.d.949.1 4
21.17 even 6 1260.2.k.b.1009.2 2
28.3 even 6 560.2.g.c.449.1 2
35.3 even 12 700.2.a.f.1.1 1
35.4 even 6 980.2.e.a.589.1 2
35.9 even 6 inner 980.2.q.e.569.2 4
35.17 even 12 700.2.a.h.1.1 1
35.18 odd 12 4900.2.a.m.1.1 1
35.19 odd 6 980.2.q.d.569.1 4
35.24 odd 6 140.2.e.b.29.2 yes 2
35.32 odd 12 4900.2.a.l.1.1 1
35.34 odd 2 980.2.q.d.949.2 4
56.3 even 6 2240.2.g.c.449.2 2
56.45 odd 6 2240.2.g.d.449.2 2
84.59 odd 6 5040.2.t.g.1009.2 2
105.17 odd 12 6300.2.a.y.1.1 1
105.38 odd 12 6300.2.a.g.1.1 1
105.59 even 6 1260.2.k.b.1009.1 2
140.3 odd 12 2800.2.a.s.1.1 1
140.59 even 6 560.2.g.c.449.2 2
140.87 odd 12 2800.2.a.o.1.1 1
280.59 even 6 2240.2.g.c.449.1 2
280.269 odd 6 2240.2.g.d.449.1 2
420.59 odd 6 5040.2.t.g.1009.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.e.b.29.1 2 7.3 odd 6
140.2.e.b.29.2 yes 2 35.24 odd 6
560.2.g.c.449.1 2 28.3 even 6
560.2.g.c.449.2 2 140.59 even 6
700.2.a.f.1.1 1 35.3 even 12
700.2.a.h.1.1 1 35.17 even 12
980.2.e.a.589.1 2 35.4 even 6
980.2.e.a.589.2 2 7.4 even 3
980.2.q.d.569.1 4 35.19 odd 6
980.2.q.d.569.2 4 7.5 odd 6
980.2.q.d.949.1 4 7.6 odd 2
980.2.q.d.949.2 4 35.34 odd 2
980.2.q.e.569.1 4 7.2 even 3 inner
980.2.q.e.569.2 4 35.9 even 6 inner
980.2.q.e.949.1 4 5.4 even 2 inner
980.2.q.e.949.2 4 1.1 even 1 trivial
1260.2.k.b.1009.1 2 105.59 even 6
1260.2.k.b.1009.2 2 21.17 even 6
2240.2.g.c.449.1 2 280.59 even 6
2240.2.g.c.449.2 2 56.3 even 6
2240.2.g.d.449.1 2 280.269 odd 6
2240.2.g.d.449.2 2 56.45 odd 6
2800.2.a.o.1.1 1 140.87 odd 12
2800.2.a.s.1.1 1 140.3 odd 12
4900.2.a.l.1.1 1 35.32 odd 12
4900.2.a.m.1.1 1 35.18 odd 12
5040.2.t.g.1009.1 2 420.59 odd 6
5040.2.t.g.1009.2 2 84.59 odd 6
6300.2.a.g.1.1 1 105.38 odd 12
6300.2.a.y.1.1 1 105.17 odd 12