Properties

Label 676.2.f.e.99.1
Level 676676
Weight 22
Character 676.99
Analytic conductor 5.3985.398
Analytic rank 00
Dimension 44
CM discriminant -4
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] = [676,2,Mod(99,676)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(676, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) 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("676.99"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 676=22132 676 = 2^{2} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 676.f (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,4,0,0,6] 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: 5.397887176645.39788717664
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(i)\Q(i)
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,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 52)
Sato-Tate group: U(1)[D4]\mathrm{U}(1)[D_{4}]

Embedding invariants

Embedding label 99.1
Root 0.8660250.500000i0.866025 - 0.500000i of defining polynomial
Character χ\chi == 676.99
Dual form 676.2.f.e.239.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.00000+1.00000i)q2+2.00000iq4+(0.633975+0.633975i)q5+(2.00000+2.00000i)q8+3.00000q9+1.26795iq104.00000q16+7.92820iq17+(3.00000+3.00000i)q18+(1.26795+1.26795i)q204.19615iq25+6.66025q29+(4.000004.00000i)q32+(7.92820+7.92820i)q34+6.00000iq36+(8.56218+8.56218i)q372.53590q40+(7.294237.29423i)q41+(1.90192+1.90192i)q457.00000iq49+(4.196154.19615i)q50+10.4641q53+(6.66025+6.66025i)q58+5.39230q618.00000iq6415.8564q68+(6.00000+6.00000i)q72+(9.830139.83013i)q7317.1244q74+(2.535902.53590i)q80+9.00000q8114.5885iq82+(5.02628+5.02628i)q85+(3.000003.00000i)q89+3.80385iq90+(5.00000+5.00000i)q97+(7.000007.00000i)q98+O(q100)q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(0.633975 + 0.633975i) q^{5} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +1.26795i q^{10} -4.00000 q^{16} +7.92820i q^{17} +(3.00000 + 3.00000i) q^{18} +(-1.26795 + 1.26795i) q^{20} -4.19615i q^{25} +6.66025 q^{29} +(-4.00000 - 4.00000i) q^{32} +(-7.92820 + 7.92820i) q^{34} +6.00000i q^{36} +(-8.56218 + 8.56218i) q^{37} -2.53590 q^{40} +(-7.29423 - 7.29423i) q^{41} +(1.90192 + 1.90192i) q^{45} -7.00000i q^{49} +(4.19615 - 4.19615i) q^{50} +10.4641 q^{53} +(6.66025 + 6.66025i) q^{58} +5.39230 q^{61} -8.00000i q^{64} -15.8564 q^{68} +(-6.00000 + 6.00000i) q^{72} +(9.83013 - 9.83013i) q^{73} -17.1244 q^{74} +(-2.53590 - 2.53590i) q^{80} +9.00000 q^{81} -14.5885i q^{82} +(-5.02628 + 5.02628i) q^{85} +(3.00000 - 3.00000i) q^{89} +3.80385i q^{90} +(5.00000 + 5.00000i) q^{97} +(7.00000 - 7.00000i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q2+6q58q8+12q916q16+12q1812q208q2916q324q3410q3724q40+2q41+18q454q50+28q538q5820q61++28q98+O(q100) 4 q + 4 q^{2} + 6 q^{5} - 8 q^{8} + 12 q^{9} - 16 q^{16} + 12 q^{18} - 12 q^{20} - 8 q^{29} - 16 q^{32} - 4 q^{34} - 10 q^{37} - 24 q^{40} + 2 q^{41} + 18 q^{45} - 4 q^{50} + 28 q^{53} - 8 q^{58} - 20 q^{61}+ \cdots + 28 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/676Z)×\left(\mathbb{Z}/676\mathbb{Z}\right)^\times.

nn 339339 509509
χ(n)\chi(n) 1-1 e(14)e\left(\frac{1}{4}\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 1.00000 + 1.00000i 0.707107 + 0.707107i
33 0 0 1.00000 00
−1.00000 π\pi
44 2.00000i 1.00000i
55 0.633975 + 0.633975i 0.283522 + 0.283522i 0.834512 0.550990i 0.185750π-0.185750\pi
−0.550990 + 0.834512i 0.685750π0.685750\pi
66 0 0
77 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
88 −2.00000 + 2.00000i −0.707107 + 0.707107i
99 3.00000 1.00000
1010 1.26795i 0.400961i
1111 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
1212 0 0
1313 0 0
1414 0 0
1515 0 0
1616 −4.00000 −1.00000
1717 7.92820i 1.92287i 0.275029 + 0.961436i 0.411312π0.411312\pi
−0.275029 + 0.961436i 0.588688π0.588688\pi
1818 3.00000 + 3.00000i 0.707107 + 0.707107i
1919 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
2020 −1.26795 + 1.26795i −0.283522 + 0.283522i
2121 0 0
2222 0 0
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 0 0
2525 4.19615i 0.839230i
2626 0 0
2727 0 0
2828 0 0
2929 6.66025 1.23678 0.618389 0.785872i 0.287786π-0.287786\pi
0.618389 + 0.785872i 0.287786π0.287786\pi
3030 0 0
3131 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
3232 −4.00000 4.00000i −0.707107 0.707107i
3333 0 0
3434 −7.92820 + 7.92820i −1.35968 + 1.35968i
3535 0 0
3636 6.00000i 1.00000i
3737 −8.56218 + 8.56218i −1.40761 + 1.40761i −0.635571 + 0.772043i 0.719235π0.719235\pi
−0.772043 + 0.635571i 0.780765π0.780765\pi
3838 0 0
3939 0 0
4040 −2.53590 −0.400961
4141 −7.29423 7.29423i −1.13917 1.13917i −0.988600 0.150567i 0.951890π-0.951890\pi
−0.150567 0.988600i 0.548110π-0.548110\pi
4242 0 0
4343 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4444 0 0
4545 1.90192 + 1.90192i 0.283522 + 0.283522i
4646 0 0
4747 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
4848 0 0
4949 7.00000i 1.00000i
5050 4.19615 4.19615i 0.593426 0.593426i
5151 0 0
5252 0 0
5353 10.4641 1.43735 0.718677 0.695344i 0.244748π-0.244748\pi
0.718677 + 0.695344i 0.244748π0.244748\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 6.66025 + 6.66025i 0.874534 + 0.874534i
5959 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
6060 0 0
6161 5.39230 0.690414 0.345207 0.938527i 0.387809π-0.387809\pi
0.345207 + 0.938527i 0.387809π0.387809\pi
6262 0 0
6363 0 0
6464 8.00000i 1.00000i
6565 0 0
6666 0 0
6767 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
6868 −15.8564 −1.92287
6969 0 0
7070 0 0
7171 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
7272 −6.00000 + 6.00000i −0.707107 + 0.707107i
7373 9.83013 9.83013i 1.15053 1.15053i 0.164083 0.986447i 0.447534π-0.447534\pi
0.986447 0.164083i 0.0524664π-0.0524664\pi
7474 −17.1244 −1.99067
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 0 0 1.00000 00
−1.00000 π\pi
8080 −2.53590 2.53590i −0.283522 0.283522i
8181 9.00000 1.00000
8282 14.5885i 1.61103i
8383 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
8484 0 0
8585 −5.02628 + 5.02628i −0.545177 + 0.545177i
8686 0 0
8787 0 0
8888 0 0
8989 3.00000 3.00000i 0.317999 0.317999i −0.529999 0.847998i 0.677808π-0.677808\pi
0.847998 + 0.529999i 0.177808π0.177808\pi
9090 3.80385i 0.400961i
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 5.00000 + 5.00000i 0.507673 + 0.507673i 0.913812 0.406138i 0.133125π-0.133125\pi
−0.406138 + 0.913812i 0.633125π0.633125\pi
9898 7.00000 7.00000i 0.707107 0.707107i
9999 0 0
100100 8.39230 0.839230
101101 11.7321i 1.16738i −0.811976 0.583691i 0.801608π-0.801608\pi
0.811976 0.583691i 0.198392π-0.198392\pi
102102 0 0
103103 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
104104 0 0
105105 0 0
106106 10.4641 + 10.4641i 1.01636 + 1.01636i
107107 0 0 1.00000 00
−1.00000 π\pi
108108 0 0
109109 −7.00000 7.00000i −0.670478 0.670478i 0.287348 0.957826i 0.407226π-0.407226\pi
−0.957826 + 0.287348i 0.907226π0.907226\pi
110110 0 0
111111 0 0
112112 0 0
113113 −4.12436 −0.387987 −0.193993 0.981003i 0.562144π-0.562144\pi
−0.193993 + 0.981003i 0.562144π0.562144\pi
114114 0 0
115115 0 0
116116 13.3205i 1.23678i
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 11.0000i 1.00000i
122122 5.39230 + 5.39230i 0.488196 + 0.488196i
123123 0 0
124124 0 0
125125 5.83013 5.83013i 0.521462 0.521462i
126126 0 0
127127 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
128128 8.00000 8.00000i 0.707107 0.707107i
129129 0 0
130130 0 0
131131 0 0 1.00000 00
−1.00000 π\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 −15.8564 15.8564i −1.35968 1.35968i
137137 16.4904 16.4904i 1.40887 1.40887i 0.643013 0.765855i 0.277684π-0.277684\pi
0.765855 0.643013i 0.222316π-0.222316\pi
138138 0 0
139139 0 0 1.00000 00
−1.00000 π\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 −12.0000 −1.00000
145145 4.22243 + 4.22243i 0.350654 + 0.350654i
146146 19.6603 1.62709
147147 0 0
148148 −17.1244 17.1244i −1.40761 1.40761i
149149 −11.0981 11.0981i −0.909190 0.909190i 0.0870170 0.996207i 0.472267π-0.472267\pi
−0.996207 + 0.0870170i 0.972267π0.972267\pi
150150 0 0
151151 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
152152 0 0
153153 23.7846i 1.92287i
154154 0 0
155155 0 0
156156 0 0
157157 −25.0526 −1.99941 −0.999706 0.0242497i 0.992280π-0.992280\pi
−0.999706 + 0.0242497i 0.992280π0.992280\pi
158158 0 0
159159 0 0
160160 5.07180i 0.400961i
161161 0 0
162162 9.00000 + 9.00000i 0.707107 + 0.707107i
163163 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
164164 14.5885 14.5885i 1.13917 1.13917i
165165 0 0
166166 0 0
167167 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
168168 0 0
169169 0 0
170170 −10.0526 −0.770996
171171 0 0
172172 0 0
173173 4.00000i 0.304114i 0.988372 + 0.152057i 0.0485898π0.0485898\pi
−0.988372 + 0.152057i 0.951410π0.951410\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 6.00000 0.449719
179179 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
180180 −3.80385 + 3.80385i −0.283522 + 0.283522i
181181 26.3205i 1.95639i 0.207693 + 0.978194i 0.433404π0.433404\pi
−0.207693 + 0.978194i 0.566596π0.566596\pi
182182 0 0
183183 0 0
184184 0 0
185185 −10.8564 −0.798179
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 0 0 1.00000 00
−1.00000 π\pi
192192 0 0
193193 13.9545 13.9545i 1.00447 1.00447i 0.00447566 0.999990i 0.498575π-0.498575\pi
0.999990 0.00447566i 0.00142465π-0.00142465\pi
194194 10.0000i 0.717958i
195195 0 0
196196 14.0000 1.00000
197197 15.0000 + 15.0000i 1.06871 + 1.06871i 0.997459 + 0.0712470i 0.0226979π0.0226979\pi
0.0712470 + 0.997459i 0.477302π0.477302\pi
198198 0 0
199199 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
200200 8.39230 + 8.39230i 0.593426 + 0.593426i
201201 0 0
202202 11.7321 11.7321i 0.825464 0.825464i
203203 0 0
204204 0 0
205205 9.24871i 0.645958i
206206 0 0
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 0 0 1.00000 00
−1.00000 π\pi
212212 20.9282i 1.43735i
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 14.0000i 0.948200i
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
224224 0 0
225225 12.5885i 0.839230i
226226 −4.12436 4.12436i −0.274348 0.274348i
227227 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
228228 0 0
229229 −17.0000 + 17.0000i −1.12339 + 1.12339i −0.132164 + 0.991228i 0.542192π0.542192\pi
−0.991228 + 0.132164i 0.957808π0.957808\pi
230230 0 0
231231 0 0
232232 −13.3205 + 13.3205i −0.874534 + 0.874534i
233233 16.0000i 1.04819i −0.851658 0.524097i 0.824403π-0.824403\pi
0.851658 0.524097i 0.175597π-0.175597\pi
234234 0 0
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
240240 0 0
241241 −19.0263 + 19.0263i −1.22559 + 1.22559i −0.259975 + 0.965615i 0.583714π0.583714\pi
−0.965615 + 0.259975i 0.916286π0.916286\pi
242242 11.0000 11.0000i 0.707107 0.707107i
243243 0 0
244244 10.7846i 0.690414i
245245 4.43782 4.43782i 0.283522 0.283522i
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 11.6603 0.737459
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 16.0000 1.00000
257257 14.2679i 0.890010i 0.895528 + 0.445005i 0.146798π0.146798\pi
−0.895528 + 0.445005i 0.853202π0.853202\pi
258258 0 0
259259 0 0
260260 0 0
261261 19.9808 1.23678
262262 0 0
263263 0 0 1.00000 00
−1.00000 π\pi
264264 0 0
265265 6.63397 + 6.63397i 0.407522 + 0.407522i
266266 0 0
267267 0 0
268268 0 0
269269 −20.0000 −1.21942 −0.609711 0.792624i 0.708714π-0.708714\pi
−0.609711 + 0.792624i 0.708714π0.708714\pi
270270 0 0
271271 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
272272 31.7128i 1.92287i
273273 0 0
274274 32.9808 1.99244
275275 0 0
276276 0 0
277277 1.58846i 0.0954411i −0.998861 0.0477206i 0.984804π-0.984804\pi
0.998861 0.0477206i 0.0151957π-0.0151957\pi
278278 0 0
279279 0 0
280280 0 0
281281 −12.6865 + 12.6865i −0.756815 + 0.756815i −0.975741 0.218926i 0.929745π-0.929745\pi
0.218926 + 0.975741i 0.429745π0.429745\pi
282282 0 0
283283 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 −12.0000 12.0000i −0.707107 0.707107i
289289 −45.8564 −2.69744
290290 8.44486i 0.495899i
291291 0 0
292292 19.6603 + 19.6603i 1.15053 + 1.15053i
293293 3.49038 3.49038i 0.203910 0.203910i −0.597763 0.801673i 0.703944π-0.703944\pi
0.801673 + 0.597763i 0.203944π0.203944\pi
294294 0 0
295295 0 0
296296 34.2487i 1.99067i
297297 0 0
298298 22.1962i 1.28579i
299299 0 0
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 3.41858 + 3.41858i 0.195748 + 0.195748i
306306 −23.7846 + 23.7846i −1.35968 + 1.35968i
307307 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
312312 0 0
313313 −24.0000 −1.35656 −0.678280 0.734803i 0.737274π-0.737274\pi
−0.678280 + 0.734803i 0.737274π0.737274\pi
314314 −25.0526 25.0526i −1.41380 1.41380i
315315 0 0
316316 0 0
317317 23.1506 + 23.1506i 1.30027 + 1.30027i 0.928208 + 0.372061i 0.121349π0.121349\pi
0.372061 + 0.928208i 0.378651π0.378651\pi
318318 0 0
319319 0 0
320320 5.07180 5.07180i 0.283522 0.283522i
321321 0 0
322322 0 0
323323 0 0
324324 18.0000i 1.00000i
325325 0 0
326326 0 0
327327 0 0
328328 29.1769 1.61103
329329 0 0
330330 0 0
331331 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
332332 0 0
333333 −25.6865 + 25.6865i −1.40761 + 1.40761i
334334 0 0
335335 0 0
336336 0 0
337337 18.7128i 1.01935i −0.860366 0.509676i 0.829765π-0.829765\pi
0.860366 0.509676i 0.170235π-0.170235\pi
338338 0 0
339339 0 0
340340 −10.0526 10.0526i −0.545177 0.545177i
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 −4.00000 + 4.00000i −0.215041 + 0.215041i
347347 0 0 1.00000 00
−1.00000 π\pi
348348 0 0
349349 −23.0000 + 23.0000i −1.23116 + 1.23116i −0.267644 + 0.963518i 0.586245π0.586245\pi
−0.963518 + 0.267644i 0.913755π0.913755\pi
350350 0 0
351351 0 0
352352 0 0
353353 −20.2942 20.2942i −1.08015 1.08015i −0.996495 0.0836583i 0.973340π-0.973340\pi
−0.0836583 0.996495i 0.526660π-0.526660\pi
354354 0 0
355355 0 0
356356 6.00000 + 6.00000i 0.317999 + 0.317999i
357357 0 0
358358 0 0
359359 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
360360 −7.60770 −0.400961
361361 19.0000i 1.00000i
362362 −26.3205 + 26.3205i −1.38338 + 1.38338i
363363 0 0
364364 0 0
365365 12.4641 0.652401
366366 0 0
367367 0 0 1.00000 00
−1.00000 π\pi
368368 0 0
369369 −21.8827 21.8827i −1.13917 1.13917i
370370 −10.8564 10.8564i −0.564398 0.564398i
371371 0 0
372372 0 0
373373 −30.1244 −1.55978 −0.779890 0.625917i 0.784725π-0.784725\pi
−0.779890 + 0.625917i 0.784725π0.784725\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
384384 0 0
385385 0 0
386386 27.9090 1.42053
387387 0 0
388388 −10.0000 + 10.0000i −0.507673 + 0.507673i
389389 0.320508i 0.0162504i 0.999967 + 0.00812520i 0.00258636π0.00258636\pi
−0.999967 + 0.00812520i 0.997414π0.997414\pi
390390 0 0
391391 0 0
392392 14.0000 + 14.0000i 0.707107 + 0.707107i
393393 0 0
394394 30.0000i 1.51138i
395395 0 0
396396 0 0
397397 −25.0000 + 25.0000i −1.25471 + 1.25471i −0.301131 + 0.953583i 0.597364π0.597364\pi
−0.953583 + 0.301131i 0.902636π0.902636\pi
398398 0 0
399399 0 0
400400 16.7846i 0.839230i
401401 26.9545 26.9545i 1.34604 1.34604i 0.456129 0.889914i 0.349236π-0.349236\pi
0.889914 0.456129i 0.150764π-0.150764\pi
402402 0 0
403403 0 0
404404 23.4641 1.16738
405405 5.70577 + 5.70577i 0.283522 + 0.283522i
406406 0 0
407407 0 0
408408 0 0
409409 11.4186 + 11.4186i 0.564613 + 0.564613i 0.930614 0.366002i 0.119274π-0.119274\pi
−0.366002 + 0.930614i 0.619274π0.619274\pi
410410 9.24871 9.24871i 0.456761 0.456761i
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 0 0 1.00000 00
−1.00000 π\pi
420420 0 0
421421 13.6340 + 13.6340i 0.664479 + 0.664479i 0.956433 0.291953i 0.0943052π-0.0943052\pi
−0.291953 + 0.956433i 0.594305π0.594305\pi
422422 0 0
423423 0 0
424424 −20.9282 + 20.9282i −1.01636 + 1.01636i
425425 33.2679 1.61373
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
432432 0 0
433433 17.4449i 0.838347i 0.907906 + 0.419173i 0.137680π0.137680\pi
−0.907906 + 0.419173i 0.862320π0.862320\pi
434434 0 0
435435 0 0
436436 14.0000 14.0000i 0.670478 0.670478i
437437 0 0
438438 0 0
439439 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
440440 0 0
441441 21.0000i 1.00000i
442442 0 0
443443 0 0 1.00000 00
−1.00000 π\pi
444444 0 0
445445 3.80385 0.180320
446446 0 0
447447 0 0
448448 0 0
449449 27.0000 27.0000i 1.27421 1.27421i 0.330350 0.943858i 0.392833π-0.392833\pi
0.943858 0.330350i 0.107167π-0.107167\pi
450450 12.5885 12.5885i 0.593426 0.593426i
451451 0 0
452452 8.24871i 0.387987i
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 2.22243 + 2.22243i 0.103961 + 0.103961i 0.757174 0.653213i 0.226579π-0.226579\pi
−0.653213 + 0.757174i 0.726579π0.726579\pi
458458 −34.0000 −1.58872
459459 0 0
460460 0 0
461461 −20.6147 20.6147i −0.960124 0.960124i 0.0391109 0.999235i 0.487547π-0.487547\pi
−0.999235 + 0.0391109i 0.987547π0.987547\pi
462462 0 0
463463 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
464464 −26.6410 −1.23678
465465 0 0
466466 16.0000 16.0000i 0.741186 0.741186i
467467 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 31.3923 1.43735
478478 0 0
479479 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
480480 0 0
481481 0 0
482482 −38.0526 −1.73325
483483 0 0
484484 22.0000 1.00000
485485 6.33975i 0.287873i
486486 0 0
487487 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
488488 −10.7846 + 10.7846i −0.488196 + 0.488196i
489489 0 0
490490 8.87564 0.400961
491491 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
492492 0 0
493493 52.8038i 2.37817i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
500500 11.6603 + 11.6603i 0.521462 + 0.521462i
501501 0 0
502502 0 0
503503 0 0 1.00000 00
−1.00000 π\pi
504504 0 0
505505 7.43782 7.43782i 0.330979 0.330979i
506506 0 0
507507 0 0
508508 0 0
509509 28.2224 + 28.2224i 1.25094 + 1.25094i 0.955300 + 0.295637i 0.0955319π0.0955319\pi
0.295637 + 0.955300i 0.404468π0.404468\pi
510510 0 0
511511 0 0
512512 16.0000 + 16.0000i 0.707107 + 0.707107i
513513 0 0
514514 −14.2679 + 14.2679i −0.629332 + 0.629332i
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0.947441 0.0415081 0.0207541 0.999785i 0.493393π-0.493393\pi
0.0207541 + 0.999785i 0.493393π0.493393\pi
522522 19.9808 + 19.9808i 0.874534 + 0.874534i
523523 0 0 1.00000 00
−1.00000 π\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 −23.0000 −1.00000
530530 13.2679i 0.576323i
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 −20.0000 20.0000i −0.862261 0.862261i
539539 0 0
540540 0 0
541541 32.3468 32.3468i 1.39070 1.39070i 0.566933 0.823764i 0.308130π-0.308130\pi
0.823764 0.566933i 0.191870π-0.191870\pi
542542 0 0
543543 0 0
544544 31.7128 31.7128i 1.35968 1.35968i
545545 8.87564i 0.380191i
546546 0 0
547547 0 0 1.00000 00
−1.00000 π\pi
548548 32.9808 + 32.9808i 1.40887 + 1.40887i
549549 16.1769 0.690414
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 1.58846 1.58846i 0.0674871 0.0674871i
555555 0 0
556556 0 0
557557 −31.0788 + 31.0788i −1.31685 + 1.31685i −0.400599 + 0.916253i 0.631198π0.631198\pi
−0.916253 + 0.400599i 0.868802π0.868802\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 −25.3731 −1.07030
563563 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
564564 0 0
565565 −2.61474 2.61474i −0.110003 0.110003i
566566 0 0
567567 0 0
568568 0 0
569569 40.0000i 1.67689i −0.544988 0.838444i 0.683466π-0.683466\pi
0.544988 0.838444i 0.316534π-0.316534\pi
570570 0 0
571571 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 24.0000i 1.00000i
577577 10.1506 + 10.1506i 0.422576 + 0.422576i 0.886090 0.463513i 0.153411π-0.153411\pi
−0.463513 + 0.886090i 0.653411π0.653411\pi
578578 −45.8564 45.8564i −1.90738 1.90738i
579579 0 0
580580 −8.44486 + 8.44486i −0.350654 + 0.350654i
581581 0 0
582582 0 0
583583 0 0
584584 39.3205i 1.62709i
585585 0 0
586586 6.98076 0.288373
587587 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
588588 0 0
589589 0 0
590590 0 0
591591 0 0
592592 34.2487 34.2487i 1.40761 1.40761i
593593 19.3468 19.3468i 0.794477 0.794477i −0.187741 0.982219i 0.560117π-0.560117\pi
0.982219 + 0.187741i 0.0601166π0.0601166\pi
594594 0 0
595595 0 0
596596 22.1962 22.1962i 0.909190 0.909190i
597597 0 0
598598 0 0
599599 0 0 1.00000 00
−1.00000 π\pi
600600 0 0
601601 32.6603 1.33224 0.666120 0.745845i 0.267954π-0.267954\pi
0.666120 + 0.745845i 0.267954π0.267954\pi
602602 0 0
603603 0 0
604604 0 0
605605 6.97372 6.97372i 0.283522 0.283522i
606606 0 0
607607 0 0 1.00000 00
−1.00000 π\pi
608608 0 0
609609 0 0
610610 6.83717i 0.276829i
611611 0 0
612612 −47.5692 −1.92287
613613 −29.8109 29.8109i −1.20405 1.20405i −0.972924 0.231127i 0.925759π-0.925759\pi
−0.231127 0.972924i 0.574241π-0.574241\pi
614614 0 0
615615 0 0
616616 0 0
617617 14.9019 + 14.9019i 0.599929 + 0.599929i 0.940294 0.340365i 0.110551π-0.110551\pi
−0.340365 + 0.940294i 0.610551π0.610551\pi
618618 0 0
619619 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −13.5885 −0.543538
626626 −24.0000 24.0000i −0.959233 0.959233i
627627 0 0
628628 50.1051i 1.99941i
629629 −67.8827 67.8827i −2.70666 2.70666i
630630 0 0
631631 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
632632 0 0
633633 0 0
634634 46.3013i 1.83886i
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 10.1436 0.400961
641641 18.0718i 0.713793i −0.934144 0.356897i 0.883835π-0.883835\pi
0.934144 0.356897i 0.116165π-0.116165\pi
642642 0 0
643643 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
648648 −18.0000 + 18.0000i −0.707107 + 0.707107i
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 44.0000 1.72185 0.860927 0.508729i 0.169885π-0.169885\pi
0.860927 + 0.508729i 0.169885π0.169885\pi
654654 0 0
655655 0 0
656656 29.1769 + 29.1769i 1.13917 + 1.13917i
657657 29.4904 29.4904i 1.15053 1.15053i
658658 0 0
659659 0 0 1.00000 00
−1.00000 π\pi
660660 0 0
661661 0.954483 0.954483i 0.0371251 0.0371251i −0.688301 0.725426i 0.741643π-0.741643\pi
0.725426 + 0.688301i 0.241643π0.241643\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 −51.3731 −1.99067
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 2.21539i 0.0853970i −0.999088 0.0426985i 0.986405π-0.986405\pi
0.999088 0.0426985i 0.0135955π-0.0135955\pi
674674 18.7128 18.7128i 0.720791 0.720791i
675675 0 0
676676 0 0
677677 2.00000 0.0768662 0.0384331 0.999261i 0.487763π-0.487763\pi
0.0384331 + 0.999261i 0.487763π0.487763\pi
678678 0 0
679679 0 0
680680 20.1051i 0.770996i
681681 0 0
682682 0 0
683683 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
684684 0 0
685685 20.9090 0.798891
686686 0 0
687687 0 0
688688 0 0
689689 0 0
690690 0 0
691691 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
692692 −8.00000 −0.304114
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 57.8301 57.8301i 2.19047 2.19047i
698698 −46.0000 −1.74113
699699 0 0
700700 0 0
701701 10.0000i 0.377695i 0.982006 + 0.188847i 0.0604752π0.0604752\pi
−0.982006 + 0.188847i 0.939525π0.939525\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 40.5885i 1.52757i
707707 0 0
708708 0 0
709709 −28.5429 + 28.5429i −1.07195 + 1.07195i −0.0747503 + 0.997202i 0.523816π0.523816\pi
−0.997202 + 0.0747503i 0.976184π0.976184\pi
710710 0 0
711711 0 0
712712 12.0000i 0.449719i
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
720720 −7.60770 7.60770i −0.283522 0.283522i
721721 0 0
722722 −19.0000 + 19.0000i −0.707107 + 0.707107i
723723 0 0
724724 −52.6410 −1.95639
725725 27.9474i 1.03794i
726726 0 0
727727 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
728728 0 0
729729 27.0000 1.00000
730730 12.4641 + 12.4641i 0.461317 + 0.461317i
731731 0 0
732732 0 0
733733 36.1506 + 36.1506i 1.33525 + 1.33525i 0.900595 + 0.434659i 0.143131π0.143131\pi
0.434659 + 0.900595i 0.356869π0.356869\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 43.7654i 1.61103i
739739 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
740740 21.7128i 0.798179i
741741 0 0
742742 0 0
743743 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
744744 0 0
745745 14.0718i 0.515551i
746746 −30.1244 30.1244i −1.10293 1.10293i
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 18.0000 0.654221 0.327111 0.944986i 0.393925π-0.393925\pi
0.327111 + 0.944986i 0.393925π0.393925\pi
758758 0 0
759759 0 0
760760 0 0
761761 1.00000 1.00000i 0.0362500 0.0362500i −0.688749 0.724999i 0.741840π-0.741840\pi
0.724999 + 0.688749i 0.241840π0.241840\pi
762762 0 0
763763 0 0
764764 0 0
765765 −15.0788 + 15.0788i −0.545177 + 0.545177i
766766 0 0
767767 0 0
768768 0 0
769769 −37.0000 37.0000i −1.33425 1.33425i −0.901523 0.432731i 0.857550π-0.857550\pi
−0.432731 0.901523i 0.642450π-0.642450\pi
770770 0 0
771771 0 0
772772 27.9090 + 27.9090i 1.00447 + 1.00447i
773773 5.00000 + 5.00000i 0.179838 + 0.179838i 0.791285 0.611448i 0.209412π-0.209412\pi
−0.611448 + 0.791285i 0.709412π0.709412\pi
774774 0 0
775775 0 0
776776 −20.0000 −0.717958
777777 0 0
778778 −0.320508 + 0.320508i −0.0114908 + 0.0114908i
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 28.0000i 1.00000i
785785 −15.8827 15.8827i −0.566877 0.566877i
786786 0 0
787787 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
788788 −30.0000 + 30.0000i −1.06871 + 1.06871i
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 −50.0000 −1.77443
795795 0 0
796796 0 0
797797 22.0000i 0.779280i −0.920967 0.389640i 0.872599π-0.872599\pi
0.920967 0.389640i 0.127401π-0.127401\pi
798798 0 0
799799 0 0
800800 −16.7846 + 16.7846i −0.593426 + 0.593426i
801801 9.00000 9.00000i 0.317999 0.317999i
802802 53.9090 1.90359
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 23.4641 + 23.4641i 0.825464 + 0.825464i
809809 −19.3397 −0.679949 −0.339975 0.940435i 0.610418π-0.610418\pi
−0.339975 + 0.940435i 0.610418π0.610418\pi
810810 11.4115i 0.400961i
811811 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 22.8372i 0.798483i
819819 0 0
820820 18.4974 0.645958
821821 −11.0000 11.0000i −0.383903 0.383903i 0.488603 0.872506i 0.337507π-0.337507\pi
−0.872506 + 0.488603i 0.837507π0.837507\pi
822822 0 0
823823 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
828828 0 0
829829 56.7654i 1.97154i −0.168091 0.985771i 0.553760π-0.553760\pi
0.168091 0.985771i 0.446240π-0.446240\pi
830830 0 0
831831 0 0
832832 0 0
833833 55.4974 1.92287
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
840840 0 0
841841 15.3590 0.529620
842842 27.2679i 0.939716i
843843 0 0
844844 0 0
845845 0 0
846846 0 0
847847 0 0
848848 −41.8564 −1.43735
849849 0 0
850850 33.2679 + 33.2679i 1.14108 + 1.14108i
851851 0 0
852852 0 0
853853 −16.1699 + 16.1699i −0.553646 + 0.553646i −0.927491 0.373845i 0.878039π-0.878039\pi
0.373845 + 0.927491i 0.378039π0.378039\pi
854854 0 0
855855 0 0
856856 0 0
857857 54.2295i 1.85244i −0.376979 0.926222i 0.623037π-0.623037\pi
0.376979 0.926222i 0.376963π-0.376963\pi
858858 0 0
859859 0 0 1.00000 00
−1.00000 π\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
864864 0 0
865865 −2.53590 + 2.53590i −0.0862231 + 0.0862231i
866866 −17.4449 + 17.4449i −0.592801 + 0.592801i
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 28.0000 0.948200
873873 15.0000 + 15.0000i 0.507673 + 0.507673i
874874 0 0
875875 0 0
876876 0 0
877877 37.4186 + 37.4186i 1.26354 + 1.26354i 0.949367 + 0.314169i 0.101726π0.101726\pi
0.314169 + 0.949367i 0.398274π0.398274\pi
878878 0 0
879879 0 0
880880 0 0
881881 59.3013i 1.99791i 0.0456985 + 0.998955i 0.485449π0.485449\pi
−0.0456985 + 0.998955i 0.514551π0.514551\pi
882882 21.0000 21.0000i 0.707107 0.707107i
883883 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 1.00000 00
−1.00000 π\pi
888888 0 0
889889 0 0
890890 3.80385 + 3.80385i 0.127505 + 0.127505i
891891 0 0
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 54.0000 1.80200
899899 0 0
900900 25.1769 0.839230
901901 82.9615i 2.76385i
902902 0 0
903903 0 0
904904 8.24871 8.24871i 0.274348 0.274348i
905905 −16.6865 + 16.6865i −0.554679 + 0.554679i
906906 0 0
907907 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
908908 0 0
909909 35.1962i 1.16738i
910910 0 0
911911 0 0 1.00000 00
−1.00000 π\pi
912912 0 0
913913 0 0
914914 4.44486i 0.147023i
915915 0 0
916916 −34.0000 34.0000i −1.12339 1.12339i
917917 0 0
918918 0 0
919919 0 0 1.00000 00
−1.00000 π\pi
920920 0 0
921921 0 0
922922 41.2295i 1.35782i
923923 0 0
924924 0 0
925925 35.9282 + 35.9282i 1.18131 + 1.18131i
926926 0 0
927927 0 0
928928 −26.6410 26.6410i −0.874534 0.874534i
929929 −24.0981 24.0981i −0.790632 0.790632i 0.190965 0.981597i 0.438838π-0.438838\pi
−0.981597 + 0.190965i 0.938838π0.938838\pi
930930 0 0
931931 0 0
932932 32.0000 1.04819
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 −60.5692 −1.97871 −0.989355 0.145522i 0.953514π-0.953514\pi
−0.989355 + 0.145522i 0.953514π0.953514\pi
938938 0 0
939939 0 0
940940 0 0
941941 19.0000 + 19.0000i 0.619382 + 0.619382i 0.945373 0.325991i 0.105698π-0.105698\pi
−0.325991 + 0.945373i 0.605698π0.605698\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 56.0000i 1.81402i 0.421111 + 0.907009i 0.361640π0.361640\pi
−0.421111 + 0.907009i 0.638360π0.638360\pi
954954 31.3923 + 31.3923i 1.01636 + 1.01636i
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 31.0000i 1.00000i
962962 0 0
963963 0 0
964964 −38.0526 38.0526i −1.22559 1.22559i
965965 17.6936 0.569576
966966 0 0
967967 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
968968 22.0000 + 22.0000i 0.707107 + 0.707107i
969969 0 0
970970 −6.33975 + 6.33975i −0.203557 + 0.203557i
971971 0 0 1.00000 00
−1.00000 π\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 −21.5692 −0.690414
977977 −16.8109 16.8109i −0.537828 0.537828i 0.385063 0.922890i 0.374180π-0.374180\pi
−0.922890 + 0.385063i 0.874180π0.874180\pi
978978 0 0
979979 0 0
980980 8.87564 + 8.87564i 0.283522 + 0.283522i
981981 −21.0000 21.0000i −0.670478 0.670478i
982982 0 0
983983 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
984984 0 0
985985 19.0192i 0.606003i
986986 −52.8038 + 52.8038i −1.68162 + 1.68162i
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 1.00000 00
−1.00000 π\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 −20.6077 −0.652652 −0.326326 0.945257i 0.605811π-0.605811\pi
−0.326326 + 0.945257i 0.605811π0.605811\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 676.2.f.e.99.1 4
4.3 odd 2 CM 676.2.f.e.99.1 4
13.2 odd 12 52.2.l.a.19.1 yes 4
13.3 even 3 676.2.l.c.319.1 4
13.4 even 6 676.2.l.d.427.1 4
13.5 odd 4 inner 676.2.f.e.239.1 4
13.6 odd 12 676.2.l.c.587.1 4
13.7 odd 12 676.2.l.e.587.1 4
13.8 odd 4 676.2.f.d.239.2 4
13.9 even 3 52.2.l.a.11.1 4
13.10 even 6 676.2.l.e.319.1 4
13.11 odd 12 676.2.l.d.19.1 4
13.12 even 2 676.2.f.d.99.2 4
39.2 even 12 468.2.cb.d.19.1 4
39.35 odd 6 468.2.cb.d.271.1 4
52.3 odd 6 676.2.l.c.319.1 4
52.7 even 12 676.2.l.e.587.1 4
52.11 even 12 676.2.l.d.19.1 4
52.15 even 12 52.2.l.a.19.1 yes 4
52.19 even 12 676.2.l.c.587.1 4
52.23 odd 6 676.2.l.e.319.1 4
52.31 even 4 inner 676.2.f.e.239.1 4
52.35 odd 6 52.2.l.a.11.1 4
52.43 odd 6 676.2.l.d.427.1 4
52.47 even 4 676.2.f.d.239.2 4
52.51 odd 2 676.2.f.d.99.2 4
104.35 odd 6 832.2.bu.d.63.1 4
104.61 even 6 832.2.bu.d.63.1 4
104.67 even 12 832.2.bu.d.383.1 4
104.93 odd 12 832.2.bu.d.383.1 4
156.35 even 6 468.2.cb.d.271.1 4
156.119 odd 12 468.2.cb.d.19.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
52.2.l.a.11.1 4 13.9 even 3
52.2.l.a.11.1 4 52.35 odd 6
52.2.l.a.19.1 yes 4 13.2 odd 12
52.2.l.a.19.1 yes 4 52.15 even 12
468.2.cb.d.19.1 4 39.2 even 12
468.2.cb.d.19.1 4 156.119 odd 12
468.2.cb.d.271.1 4 39.35 odd 6
468.2.cb.d.271.1 4 156.35 even 6
676.2.f.d.99.2 4 13.12 even 2
676.2.f.d.99.2 4 52.51 odd 2
676.2.f.d.239.2 4 13.8 odd 4
676.2.f.d.239.2 4 52.47 even 4
676.2.f.e.99.1 4 1.1 even 1 trivial
676.2.f.e.99.1 4 4.3 odd 2 CM
676.2.f.e.239.1 4 13.5 odd 4 inner
676.2.f.e.239.1 4 52.31 even 4 inner
676.2.l.c.319.1 4 13.3 even 3
676.2.l.c.319.1 4 52.3 odd 6
676.2.l.c.587.1 4 13.6 odd 12
676.2.l.c.587.1 4 52.19 even 12
676.2.l.d.19.1 4 13.11 odd 12
676.2.l.d.19.1 4 52.11 even 12
676.2.l.d.427.1 4 13.4 even 6
676.2.l.d.427.1 4 52.43 odd 6
676.2.l.e.319.1 4 13.10 even 6
676.2.l.e.319.1 4 52.23 odd 6
676.2.l.e.587.1 4 13.7 odd 12
676.2.l.e.587.1 4 52.7 even 12
832.2.bu.d.63.1 4 104.35 odd 6
832.2.bu.d.63.1 4 104.61 even 6
832.2.bu.d.383.1 4 104.67 even 12
832.2.bu.d.383.1 4 104.93 odd 12