Properties

Label 6760.2.a.o.1.2
Level 67606760
Weight 22
Character 6760.1
Self dual yes
Analytic conductor 53.97953.979
Analytic rank 11
Dimension 22
CM no
Inner twists 11

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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] = [6760,2,Mod(1,6760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6760.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 6760=235132 6760 = 2^{3} \cdot 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 6760.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,-2,0,2,0,0,0,2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 53.978871766453.9788717664
Analytic rank: 11
Dimension: 22
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: x23 x^{2} - 3 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 520)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.732051.73205 of defining polynomial
Character χ\chi == 6760.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+0.732051q3+1.00000q53.46410q72.46410q92.73205q11+0.732051q15+7.46410q17+2.73205q192.53590q210.732051q23+1.00000q254.00000q27+9.46410q29+0.196152q312.00000q333.46410q350.535898q417.26795q432.46410q454.53590q47+5.00000q49+5.46410q510.535898q532.73205q55+2.00000q575.66025q5912.3923q61+8.53590q63+12.9282q670.535898q699.26795q71+2.92820q73+0.732051q75+9.46410q776.53590q79+4.46410q81+10.3923q83+7.46410q85+6.92820q87+12.9282q89+0.143594q93+2.73205q9515.8564q97+6.73205q99+O(q100)q+0.732051 q^{3} +1.00000 q^{5} -3.46410 q^{7} -2.46410 q^{9} -2.73205 q^{11} +0.732051 q^{15} +7.46410 q^{17} +2.73205 q^{19} -2.53590 q^{21} -0.732051 q^{23} +1.00000 q^{25} -4.00000 q^{27} +9.46410 q^{29} +0.196152 q^{31} -2.00000 q^{33} -3.46410 q^{35} -0.535898 q^{41} -7.26795 q^{43} -2.46410 q^{45} -4.53590 q^{47} +5.00000 q^{49} +5.46410 q^{51} -0.535898 q^{53} -2.73205 q^{55} +2.00000 q^{57} -5.66025 q^{59} -12.3923 q^{61} +8.53590 q^{63} +12.9282 q^{67} -0.535898 q^{69} -9.26795 q^{71} +2.92820 q^{73} +0.732051 q^{75} +9.46410 q^{77} -6.53590 q^{79} +4.46410 q^{81} +10.3923 q^{83} +7.46410 q^{85} +6.92820 q^{87} +12.9282 q^{89} +0.143594 q^{93} +2.73205 q^{95} -15.8564 q^{97} +6.73205 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q3+2q5+2q92q112q15+8q17+2q1912q21+2q23+2q258q27+12q2910q314q338q4118q43+2q4516q47++10q99+O(q100) 2 q - 2 q^{3} + 2 q^{5} + 2 q^{9} - 2 q^{11} - 2 q^{15} + 8 q^{17} + 2 q^{19} - 12 q^{21} + 2 q^{23} + 2 q^{25} - 8 q^{27} + 12 q^{29} - 10 q^{31} - 4 q^{33} - 8 q^{41} - 18 q^{43} + 2 q^{45} - 16 q^{47}+ \cdots + 10 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.732051 0.422650 0.211325 0.977416i 0.432222π-0.432222\pi
0.211325 + 0.977416i 0.432222π0.432222\pi
44 0 0
55 1.00000 0.447214
66 0 0
77 −3.46410 −1.30931 −0.654654 0.755929i 0.727186π-0.727186\pi
−0.654654 + 0.755929i 0.727186π0.727186\pi
88 0 0
99 −2.46410 −0.821367
1010 0 0
1111 −2.73205 −0.823744 −0.411872 0.911242i 0.635125π-0.635125\pi
−0.411872 + 0.911242i 0.635125π0.635125\pi
1212 0 0
1313 0 0
1414 0 0
1515 0.732051 0.189015
1616 0 0
1717 7.46410 1.81031 0.905155 0.425081i 0.139754π-0.139754\pi
0.905155 + 0.425081i 0.139754π0.139754\pi
1818 0 0
1919 2.73205 0.626775 0.313388 0.949625i 0.398536π-0.398536\pi
0.313388 + 0.949625i 0.398536π0.398536\pi
2020 0 0
2121 −2.53590 −0.553378
2222 0 0
2323 −0.732051 −0.152643 −0.0763216 0.997083i 0.524318π-0.524318\pi
−0.0763216 + 0.997083i 0.524318π0.524318\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 −4.00000 −0.769800
2828 0 0
2929 9.46410 1.75744 0.878720 0.477338i 0.158398π-0.158398\pi
0.878720 + 0.477338i 0.158398π0.158398\pi
3030 0 0
3131 0.196152 0.0352300 0.0176150 0.999845i 0.494393π-0.494393\pi
0.0176150 + 0.999845i 0.494393π0.494393\pi
3232 0 0
3333 −2.00000 −0.348155
3434 0 0
3535 −3.46410 −0.585540
3636 0 0
3737 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3838 0 0
3939 0 0
4040 0 0
4141 −0.535898 −0.0836933 −0.0418466 0.999124i 0.513324π-0.513324\pi
−0.0418466 + 0.999124i 0.513324π0.513324\pi
4242 0 0
4343 −7.26795 −1.10835 −0.554176 0.832400i 0.686967π-0.686967\pi
−0.554176 + 0.832400i 0.686967π0.686967\pi
4444 0 0
4545 −2.46410 −0.367327
4646 0 0
4747 −4.53590 −0.661629 −0.330814 0.943696i 0.607323π-0.607323\pi
−0.330814 + 0.943696i 0.607323π0.607323\pi
4848 0 0
4949 5.00000 0.714286
5050 0 0
5151 5.46410 0.765127
5252 0 0
5353 −0.535898 −0.0736113 −0.0368057 0.999322i 0.511718π-0.511718\pi
−0.0368057 + 0.999322i 0.511718π0.511718\pi
5454 0 0
5555 −2.73205 −0.368390
5656 0 0
5757 2.00000 0.264906
5858 0 0
5959 −5.66025 −0.736902 −0.368451 0.929647i 0.620112π-0.620112\pi
−0.368451 + 0.929647i 0.620112π0.620112\pi
6060 0 0
6161 −12.3923 −1.58667 −0.793336 0.608784i 0.791658π-0.791658\pi
−0.793336 + 0.608784i 0.791658π0.791658\pi
6262 0 0
6363 8.53590 1.07542
6464 0 0
6565 0 0
6666 0 0
6767 12.9282 1.57943 0.789716 0.613473i 0.210228π-0.210228\pi
0.789716 + 0.613473i 0.210228π0.210228\pi
6868 0 0
6969 −0.535898 −0.0645146
7070 0 0
7171 −9.26795 −1.09990 −0.549952 0.835197i 0.685354π-0.685354\pi
−0.549952 + 0.835197i 0.685354π0.685354\pi
7272 0 0
7373 2.92820 0.342720 0.171360 0.985208i 0.445184π-0.445184\pi
0.171360 + 0.985208i 0.445184π0.445184\pi
7474 0 0
7575 0.732051 0.0845299
7676 0 0
7777 9.46410 1.07853
7878 0 0
7979 −6.53590 −0.735346 −0.367673 0.929955i 0.619845π-0.619845\pi
−0.367673 + 0.929955i 0.619845π0.619845\pi
8080 0 0
8181 4.46410 0.496011
8282 0 0
8383 10.3923 1.14070 0.570352 0.821401i 0.306807π-0.306807\pi
0.570352 + 0.821401i 0.306807π0.306807\pi
8484 0 0
8585 7.46410 0.809595
8686 0 0
8787 6.92820 0.742781
8888 0 0
8989 12.9282 1.37039 0.685193 0.728361i 0.259718π-0.259718\pi
0.685193 + 0.728361i 0.259718π0.259718\pi
9090 0 0
9191 0 0
9292 0 0
9393 0.143594 0.0148900
9494 0 0
9595 2.73205 0.280302
9696 0 0
9797 −15.8564 −1.60997 −0.804987 0.593292i 0.797828π-0.797828\pi
−0.804987 + 0.593292i 0.797828π0.797828\pi
9898 0 0
9999 6.73205 0.676597
100100 0 0
101101 4.92820 0.490375 0.245187 0.969476i 0.421151π-0.421151\pi
0.245187 + 0.969476i 0.421151π0.421151\pi
102102 0 0
103103 −6.19615 −0.610525 −0.305263 0.952268i 0.598744π-0.598744\pi
−0.305263 + 0.952268i 0.598744π0.598744\pi
104104 0 0
105105 −2.53590 −0.247478
106106 0 0
107107 −20.0526 −1.93855 −0.969277 0.245972i 0.920893π-0.920893\pi
−0.969277 + 0.245972i 0.920893π0.920893\pi
108108 0 0
109109 −15.8564 −1.51877 −0.759384 0.650643i 0.774500π-0.774500\pi
−0.759384 + 0.650643i 0.774500π0.774500\pi
110110 0 0
111111 0 0
112112 0 0
113113 −18.3923 −1.73020 −0.865101 0.501597i 0.832746π-0.832746\pi
−0.865101 + 0.501597i 0.832746π0.832746\pi
114114 0 0
115115 −0.732051 −0.0682641
116116 0 0
117117 0 0
118118 0 0
119119 −25.8564 −2.37025
120120 0 0
121121 −3.53590 −0.321445
122122 0 0
123123 −0.392305 −0.0353729
124124 0 0
125125 1.00000 0.0894427
126126 0 0
127127 −1.80385 −0.160066 −0.0800328 0.996792i 0.525503π-0.525503\pi
−0.0800328 + 0.996792i 0.525503π0.525503\pi
128128 0 0
129129 −5.32051 −0.468445
130130 0 0
131131 −2.92820 −0.255838 −0.127919 0.991785i 0.540830π-0.540830\pi
−0.127919 + 0.991785i 0.540830π0.540830\pi
132132 0 0
133133 −9.46410 −0.820642
134134 0 0
135135 −4.00000 −0.344265
136136 0 0
137137 −8.92820 −0.762788 −0.381394 0.924413i 0.624556π-0.624556\pi
−0.381394 + 0.924413i 0.624556π0.624556\pi
138138 0 0
139139 −13.4641 −1.14201 −0.571005 0.820947i 0.693446π-0.693446\pi
−0.571005 + 0.820947i 0.693446π0.693446\pi
140140 0 0
141141 −3.32051 −0.279637
142142 0 0
143143 0 0
144144 0 0
145145 9.46410 0.785951
146146 0 0
147147 3.66025 0.301893
148148 0 0
149149 7.85641 0.643622 0.321811 0.946804i 0.395708π-0.395708\pi
0.321811 + 0.946804i 0.395708π0.395708\pi
150150 0 0
151151 −11.8038 −0.960583 −0.480292 0.877109i 0.659469π-0.659469\pi
−0.480292 + 0.877109i 0.659469π0.659469\pi
152152 0 0
153153 −18.3923 −1.48693
154154 0 0
155155 0.196152 0.0157553
156156 0 0
157157 −7.85641 −0.627009 −0.313505 0.949587i 0.601503π-0.601503\pi
−0.313505 + 0.949587i 0.601503π0.601503\pi
158158 0 0
159159 −0.392305 −0.0311118
160160 0 0
161161 2.53590 0.199857
162162 0 0
163163 8.92820 0.699311 0.349655 0.936878i 0.386299π-0.386299\pi
0.349655 + 0.936878i 0.386299π0.386299\pi
164164 0 0
165165 −2.00000 −0.155700
166166 0 0
167167 21.3205 1.64983 0.824915 0.565256i 0.191223π-0.191223\pi
0.824915 + 0.565256i 0.191223π0.191223\pi
168168 0 0
169169 0 0
170170 0 0
171171 −6.73205 −0.514813
172172 0 0
173173 −2.39230 −0.181884 −0.0909418 0.995856i 0.528988π-0.528988\pi
−0.0909418 + 0.995856i 0.528988π0.528988\pi
174174 0 0
175175 −3.46410 −0.261861
176176 0 0
177177 −4.14359 −0.311452
178178 0 0
179179 −21.8564 −1.63362 −0.816812 0.576904i 0.804261π-0.804261\pi
−0.816812 + 0.576904i 0.804261π0.804261\pi
180180 0 0
181181 6.53590 0.485810 0.242905 0.970050i 0.421900π-0.421900\pi
0.242905 + 0.970050i 0.421900π0.421900\pi
182182 0 0
183183 −9.07180 −0.670607
184184 0 0
185185 0 0
186186 0 0
187187 −20.3923 −1.49123
188188 0 0
189189 13.8564 1.00791
190190 0 0
191191 18.9282 1.36960 0.684798 0.728733i 0.259890π-0.259890\pi
0.684798 + 0.728733i 0.259890π0.259890\pi
192192 0 0
193193 2.00000 0.143963 0.0719816 0.997406i 0.477068π-0.477068\pi
0.0719816 + 0.997406i 0.477068π0.477068\pi
194194 0 0
195195 0 0
196196 0 0
197197 −8.92820 −0.636108 −0.318054 0.948073i 0.603029π-0.603029\pi
−0.318054 + 0.948073i 0.603029π0.603029\pi
198198 0 0
199199 −6.92820 −0.491127 −0.245564 0.969380i 0.578973π-0.578973\pi
−0.245564 + 0.969380i 0.578973π0.578973\pi
200200 0 0
201201 9.46410 0.667546
202202 0 0
203203 −32.7846 −2.30103
204204 0 0
205205 −0.535898 −0.0374288
206206 0 0
207207 1.80385 0.125376
208208 0 0
209209 −7.46410 −0.516303
210210 0 0
211211 2.92820 0.201586 0.100793 0.994907i 0.467862π-0.467862\pi
0.100793 + 0.994907i 0.467862π0.467862\pi
212212 0 0
213213 −6.78461 −0.464874
214214 0 0
215215 −7.26795 −0.495670
216216 0 0
217217 −0.679492 −0.0461269
218218 0 0
219219 2.14359 0.144851
220220 0 0
221221 0 0
222222 0 0
223223 −25.3205 −1.69559 −0.847793 0.530327i 0.822069π-0.822069\pi
−0.847793 + 0.530327i 0.822069π0.822069\pi
224224 0 0
225225 −2.46410 −0.164273
226226 0 0
227227 −18.0000 −1.19470 −0.597351 0.801980i 0.703780π-0.703780\pi
−0.597351 + 0.801980i 0.703780π0.703780\pi
228228 0 0
229229 −19.4641 −1.28622 −0.643112 0.765772i 0.722357π-0.722357\pi
−0.643112 + 0.765772i 0.722357π0.722357\pi
230230 0 0
231231 6.92820 0.455842
232232 0 0
233233 18.0000 1.17922 0.589610 0.807688i 0.299282π-0.299282\pi
0.589610 + 0.807688i 0.299282π0.299282\pi
234234 0 0
235235 −4.53590 −0.295889
236236 0 0
237237 −4.78461 −0.310794
238238 0 0
239239 −25.2679 −1.63445 −0.817224 0.576320i 0.804488π-0.804488\pi
−0.817224 + 0.576320i 0.804488π0.804488\pi
240240 0 0
241241 −20.2487 −1.30433 −0.652167 0.758075i 0.726140π-0.726140\pi
−0.652167 + 0.758075i 0.726140π0.726140\pi
242242 0 0
243243 15.2679 0.979439
244244 0 0
245245 5.00000 0.319438
246246 0 0
247247 0 0
248248 0 0
249249 7.60770 0.482118
250250 0 0
251251 23.3205 1.47198 0.735989 0.676994i 0.236718π-0.236718\pi
0.735989 + 0.676994i 0.236718π0.236718\pi
252252 0 0
253253 2.00000 0.125739
254254 0 0
255255 5.46410 0.342175
256256 0 0
257257 6.00000 0.374270 0.187135 0.982334i 0.440080π-0.440080\pi
0.187135 + 0.982334i 0.440080π0.440080\pi
258258 0 0
259259 0 0
260260 0 0
261261 −23.3205 −1.44350
262262 0 0
263263 −11.6603 −0.719002 −0.359501 0.933145i 0.617053π-0.617053\pi
−0.359501 + 0.933145i 0.617053π0.617053\pi
264264 0 0
265265 −0.535898 −0.0329200
266266 0 0
267267 9.46410 0.579194
268268 0 0
269269 −0.143594 −0.00875505 −0.00437753 0.999990i 0.501393π-0.501393\pi
−0.00437753 + 0.999990i 0.501393π0.501393\pi
270270 0 0
271271 23.1244 1.40470 0.702352 0.711830i 0.252133π-0.252133\pi
0.702352 + 0.711830i 0.252133π0.252133\pi
272272 0 0
273273 0 0
274274 0 0
275275 −2.73205 −0.164749
276276 0 0
277277 −21.3205 −1.28103 −0.640513 0.767948i 0.721278π-0.721278\pi
−0.640513 + 0.767948i 0.721278π0.721278\pi
278278 0 0
279279 −0.483340 −0.0289368
280280 0 0
281281 4.53590 0.270589 0.135295 0.990805i 0.456802π-0.456802\pi
0.135295 + 0.990805i 0.456802π0.456802\pi
282282 0 0
283283 −24.0526 −1.42978 −0.714888 0.699239i 0.753522π-0.753522\pi
−0.714888 + 0.699239i 0.753522π0.753522\pi
284284 0 0
285285 2.00000 0.118470
286286 0 0
287287 1.85641 0.109580
288288 0 0
289289 38.7128 2.27722
290290 0 0
291291 −11.6077 −0.680455
292292 0 0
293293 −6.92820 −0.404750 −0.202375 0.979308i 0.564866π-0.564866\pi
−0.202375 + 0.979308i 0.564866π0.564866\pi
294294 0 0
295295 −5.66025 −0.329553
296296 0 0
297297 10.9282 0.634119
298298 0 0
299299 0 0
300300 0 0
301301 25.1769 1.45117
302302 0 0
303303 3.60770 0.207257
304304 0 0
305305 −12.3923 −0.709581
306306 0 0
307307 16.5359 0.943754 0.471877 0.881665i 0.343577π-0.343577\pi
0.471877 + 0.881665i 0.343577π0.343577\pi
308308 0 0
309309 −4.53590 −0.258038
310310 0 0
311311 31.3205 1.77602 0.888012 0.459821i 0.152086π-0.152086\pi
0.888012 + 0.459821i 0.152086π0.152086\pi
312312 0 0
313313 10.3923 0.587408 0.293704 0.955896i 0.405112π-0.405112\pi
0.293704 + 0.955896i 0.405112π0.405112\pi
314314 0 0
315315 8.53590 0.480943
316316 0 0
317317 1.85641 0.104266 0.0521331 0.998640i 0.483398π-0.483398\pi
0.0521331 + 0.998640i 0.483398π0.483398\pi
318318 0 0
319319 −25.8564 −1.44768
320320 0 0
321321 −14.6795 −0.819329
322322 0 0
323323 20.3923 1.13466
324324 0 0
325325 0 0
326326 0 0
327327 −11.6077 −0.641907
328328 0 0
329329 15.7128 0.866275
330330 0 0
331331 8.58846 0.472064 0.236032 0.971745i 0.424153π-0.424153\pi
0.236032 + 0.971745i 0.424153π0.424153\pi
332332 0 0
333333 0 0
334334 0 0
335335 12.9282 0.706343
336336 0 0
337337 22.3923 1.21979 0.609893 0.792484i 0.291212π-0.291212\pi
0.609893 + 0.792484i 0.291212π0.291212\pi
338338 0 0
339339 −13.4641 −0.731270
340340 0 0
341341 −0.535898 −0.0290205
342342 0 0
343343 6.92820 0.374088
344344 0 0
345345 −0.535898 −0.0288518
346346 0 0
347347 2.19615 0.117896 0.0589478 0.998261i 0.481225π-0.481225\pi
0.0589478 + 0.998261i 0.481225π0.481225\pi
348348 0 0
349349 −12.5359 −0.671031 −0.335516 0.942035i 0.608911π-0.608911\pi
−0.335516 + 0.942035i 0.608911π0.608911\pi
350350 0 0
351351 0 0
352352 0 0
353353 6.92820 0.368751 0.184376 0.982856i 0.440974π-0.440974\pi
0.184376 + 0.982856i 0.440974π0.440974\pi
354354 0 0
355355 −9.26795 −0.491892
356356 0 0
357357 −18.9282 −1.00179
358358 0 0
359359 −11.1244 −0.587121 −0.293561 0.955940i 0.594840π-0.594840\pi
−0.293561 + 0.955940i 0.594840π0.594840\pi
360360 0 0
361361 −11.5359 −0.607153
362362 0 0
363363 −2.58846 −0.135859
364364 0 0
365365 2.92820 0.153269
366366 0 0
367367 −1.41154 −0.0736819 −0.0368410 0.999321i 0.511729π-0.511729\pi
−0.0368410 + 0.999321i 0.511729π0.511729\pi
368368 0 0
369369 1.32051 0.0687429
370370 0 0
371371 1.85641 0.0963798
372372 0 0
373373 −7.85641 −0.406789 −0.203395 0.979097i 0.565197π-0.565197\pi
−0.203395 + 0.979097i 0.565197π0.565197\pi
374374 0 0
375375 0.732051 0.0378029
376376 0 0
377377 0 0
378378 0 0
379379 20.1962 1.03741 0.518703 0.854954i 0.326415π-0.326415\pi
0.518703 + 0.854954i 0.326415π0.326415\pi
380380 0 0
381381 −1.32051 −0.0676517
382382 0 0
383383 1.60770 0.0821494 0.0410747 0.999156i 0.486922π-0.486922\pi
0.0410747 + 0.999156i 0.486922π0.486922\pi
384384 0 0
385385 9.46410 0.482335
386386 0 0
387387 17.9090 0.910364
388388 0 0
389389 −18.0000 −0.912636 −0.456318 0.889817i 0.650832π-0.650832\pi
−0.456318 + 0.889817i 0.650832π0.650832\pi
390390 0 0
391391 −5.46410 −0.276331
392392 0 0
393393 −2.14359 −0.108130
394394 0 0
395395 −6.53590 −0.328857
396396 0 0
397397 5.07180 0.254546 0.127273 0.991868i 0.459378π-0.459378\pi
0.127273 + 0.991868i 0.459378π0.459378\pi
398398 0 0
399399 −6.92820 −0.346844
400400 0 0
401401 10.7846 0.538558 0.269279 0.963062i 0.413215π-0.413215\pi
0.269279 + 0.963062i 0.413215π0.413215\pi
402402 0 0
403403 0 0
404404 0 0
405405 4.46410 0.221823
406406 0 0
407407 0 0
408408 0 0
409409 −33.3205 −1.64759 −0.823797 0.566886i 0.808148π-0.808148\pi
−0.823797 + 0.566886i 0.808148π0.808148\pi
410410 0 0
411411 −6.53590 −0.322392
412412 0 0
413413 19.6077 0.964832
414414 0 0
415415 10.3923 0.510138
416416 0 0
417417 −9.85641 −0.482670
418418 0 0
419419 −25.4641 −1.24400 −0.622001 0.783016i 0.713680π-0.713680\pi
−0.622001 + 0.783016i 0.713680π0.713680\pi
420420 0 0
421421 19.0718 0.929503 0.464751 0.885441i 0.346144π-0.346144\pi
0.464751 + 0.885441i 0.346144π0.346144\pi
422422 0 0
423423 11.1769 0.543440
424424 0 0
425425 7.46410 0.362062
426426 0 0
427427 42.9282 2.07744
428428 0 0
429429 0 0
430430 0 0
431431 22.0526 1.06223 0.531117 0.847298i 0.321772π-0.321772\pi
0.531117 + 0.847298i 0.321772π0.321772\pi
432432 0 0
433433 15.0718 0.724304 0.362152 0.932119i 0.382042π-0.382042\pi
0.362152 + 0.932119i 0.382042π0.382042\pi
434434 0 0
435435 6.92820 0.332182
436436 0 0
437437 −2.00000 −0.0956730
438438 0 0
439439 −13.8564 −0.661330 −0.330665 0.943748i 0.607273π-0.607273\pi
−0.330665 + 0.943748i 0.607273π0.607273\pi
440440 0 0
441441 −12.3205 −0.586691
442442 0 0
443443 28.4449 1.35146 0.675728 0.737151i 0.263829π-0.263829\pi
0.675728 + 0.737151i 0.263829π0.263829\pi
444444 0 0
445445 12.9282 0.612856
446446 0 0
447447 5.75129 0.272027
448448 0 0
449449 14.3923 0.679215 0.339607 0.940567i 0.389706π-0.389706\pi
0.339607 + 0.940567i 0.389706π0.389706\pi
450450 0 0
451451 1.46410 0.0689419
452452 0 0
453453 −8.64102 −0.405990
454454 0 0
455455 0 0
456456 0 0
457457 30.7846 1.44004 0.720022 0.693952i 0.244132π-0.244132\pi
0.720022 + 0.693952i 0.244132π0.244132\pi
458458 0 0
459459 −29.8564 −1.39358
460460 0 0
461461 12.2487 0.570479 0.285240 0.958456i 0.407927π-0.407927\pi
0.285240 + 0.958456i 0.407927π0.407927\pi
462462 0 0
463463 −27.8564 −1.29460 −0.647298 0.762237i 0.724101π-0.724101\pi
−0.647298 + 0.762237i 0.724101π0.724101\pi
464464 0 0
465465 0.143594 0.00665899
466466 0 0
467467 18.5885 0.860171 0.430086 0.902788i 0.358483π-0.358483\pi
0.430086 + 0.902788i 0.358483π0.358483\pi
468468 0 0
469469 −44.7846 −2.06796
470470 0 0
471471 −5.75129 −0.265005
472472 0 0
473473 19.8564 0.912999
474474 0 0
475475 2.73205 0.125355
476476 0 0
477477 1.32051 0.0604619
478478 0 0
479479 −11.1244 −0.508285 −0.254142 0.967167i 0.581793π-0.581793\pi
−0.254142 + 0.967167i 0.581793π0.581793\pi
480480 0 0
481481 0 0
482482 0 0
483483 1.85641 0.0844694
484484 0 0
485485 −15.8564 −0.720002
486486 0 0
487487 39.8564 1.80607 0.903033 0.429571i 0.141335π-0.141335\pi
0.903033 + 0.429571i 0.141335π0.141335\pi
488488 0 0
489489 6.53590 0.295564
490490 0 0
491491 −33.4641 −1.51021 −0.755107 0.655602i 0.772415π-0.772415\pi
−0.755107 + 0.655602i 0.772415π0.772415\pi
492492 0 0
493493 70.6410 3.18151
494494 0 0
495495 6.73205 0.302583
496496 0 0
497497 32.1051 1.44011
498498 0 0
499499 −24.1962 −1.08317 −0.541584 0.840646i 0.682175π-0.682175\pi
−0.541584 + 0.840646i 0.682175π0.682175\pi
500500 0 0
501501 15.6077 0.697300
502502 0 0
503503 −41.1244 −1.83364 −0.916822 0.399296i 0.869255π-0.869255\pi
−0.916822 + 0.399296i 0.869255π0.869255\pi
504504 0 0
505505 4.92820 0.219302
506506 0 0
507507 0 0
508508 0 0
509509 3.46410 0.153544 0.0767718 0.997049i 0.475539π-0.475539\pi
0.0767718 + 0.997049i 0.475539π0.475539\pi
510510 0 0
511511 −10.1436 −0.448726
512512 0 0
513513 −10.9282 −0.482492
514514 0 0
515515 −6.19615 −0.273035
516516 0 0
517517 12.3923 0.545013
518518 0 0
519519 −1.75129 −0.0768730
520520 0 0
521521 8.39230 0.367674 0.183837 0.982957i 0.441148π-0.441148\pi
0.183837 + 0.982957i 0.441148π0.441148\pi
522522 0 0
523523 17.5167 0.765950 0.382975 0.923759i 0.374900π-0.374900\pi
0.382975 + 0.923759i 0.374900π0.374900\pi
524524 0 0
525525 −2.53590 −0.110676
526526 0 0
527527 1.46410 0.0637773
528528 0 0
529529 −22.4641 −0.976700
530530 0 0
531531 13.9474 0.605267
532532 0 0
533533 0 0
534534 0 0
535535 −20.0526 −0.866948
536536 0 0
537537 −16.0000 −0.690451
538538 0 0
539539 −13.6603 −0.588389
540540 0 0
541541 −38.3923 −1.65061 −0.825307 0.564684i 0.808998π-0.808998\pi
−0.825307 + 0.564684i 0.808998π0.808998\pi
542542 0 0
543543 4.78461 0.205327
544544 0 0
545545 −15.8564 −0.679214
546546 0 0
547547 −8.33975 −0.356582 −0.178291 0.983978i 0.557057π-0.557057\pi
−0.178291 + 0.983978i 0.557057π0.557057\pi
548548 0 0
549549 30.5359 1.30324
550550 0 0
551551 25.8564 1.10152
552552 0 0
553553 22.6410 0.962794
554554 0 0
555555 0 0
556556 0 0
557557 −21.8564 −0.926086 −0.463043 0.886336i 0.653242π-0.653242\pi
−0.463043 + 0.886336i 0.653242π0.653242\pi
558558 0 0
559559 0 0
560560 0 0
561561 −14.9282 −0.630269
562562 0 0
563563 40.7321 1.71665 0.858326 0.513105i 0.171505π-0.171505\pi
0.858326 + 0.513105i 0.171505π0.171505\pi
564564 0 0
565565 −18.3923 −0.773770
566566 0 0
567567 −15.4641 −0.649431
568568 0 0
569569 −17.4641 −0.732133 −0.366067 0.930589i 0.619296π-0.619296\pi
−0.366067 + 0.930589i 0.619296π0.619296\pi
570570 0 0
571571 −27.3205 −1.14333 −0.571664 0.820488i 0.693702π-0.693702\pi
−0.571664 + 0.820488i 0.693702π0.693702\pi
572572 0 0
573573 13.8564 0.578860
574574 0 0
575575 −0.732051 −0.0305286
576576 0 0
577577 30.6410 1.27560 0.637801 0.770201i 0.279844π-0.279844\pi
0.637801 + 0.770201i 0.279844π0.279844\pi
578578 0 0
579579 1.46410 0.0608460
580580 0 0
581581 −36.0000 −1.49353
582582 0 0
583583 1.46410 0.0606369
584584 0 0
585585 0 0
586586 0 0
587587 −1.21539 −0.0501645 −0.0250823 0.999685i 0.507985π-0.507985\pi
−0.0250823 + 0.999685i 0.507985π0.507985\pi
588588 0 0
589589 0.535898 0.0220813
590590 0 0
591591 −6.53590 −0.268851
592592 0 0
593593 −40.6410 −1.66893 −0.834463 0.551064i 0.814222π-0.814222\pi
−0.834463 + 0.551064i 0.814222π0.814222\pi
594594 0 0
595595 −25.8564 −1.06001
596596 0 0
597597 −5.07180 −0.207575
598598 0 0
599599 −33.4641 −1.36731 −0.683653 0.729807i 0.739610π-0.739610\pi
−0.683653 + 0.729807i 0.739610π0.739610\pi
600600 0 0
601601 −3.85641 −0.157306 −0.0786531 0.996902i 0.525062π-0.525062\pi
−0.0786531 + 0.996902i 0.525062π0.525062\pi
602602 0 0
603603 −31.8564 −1.29729
604604 0 0
605605 −3.53590 −0.143755
606606 0 0
607607 −13.5167 −0.548624 −0.274312 0.961641i 0.588450π-0.588450\pi
−0.274312 + 0.961641i 0.588450π0.588450\pi
608608 0 0
609609 −24.0000 −0.972529
610610 0 0
611611 0 0
612612 0 0
613613 0.143594 0.00579969 0.00289984 0.999996i 0.499077π-0.499077\pi
0.00289984 + 0.999996i 0.499077π0.499077\pi
614614 0 0
615615 −0.392305 −0.0158193
616616 0 0
617617 45.7128 1.84033 0.920164 0.391533i 0.128055π-0.128055\pi
0.920164 + 0.391533i 0.128055π0.128055\pi
618618 0 0
619619 18.3397 0.737137 0.368568 0.929601i 0.379848π-0.379848\pi
0.368568 + 0.929601i 0.379848π0.379848\pi
620620 0 0
621621 2.92820 0.117505
622622 0 0
623623 −44.7846 −1.79426
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 −5.46410 −0.218215
628628 0 0
629629 0 0
630630 0 0
631631 7.80385 0.310666 0.155333 0.987862i 0.450355π-0.450355\pi
0.155333 + 0.987862i 0.450355π0.450355\pi
632632 0 0
633633 2.14359 0.0852002
634634 0 0
635635 −1.80385 −0.0715835
636636 0 0
637637 0 0
638638 0 0
639639 22.8372 0.903424
640640 0 0
641641 −0.928203 −0.0366618 −0.0183309 0.999832i 0.505835π-0.505835\pi
−0.0183309 + 0.999832i 0.505835π0.505835\pi
642642 0 0
643643 9.60770 0.378891 0.189445 0.981891i 0.439331π-0.439331\pi
0.189445 + 0.981891i 0.439331π0.439331\pi
644644 0 0
645645 −5.32051 −0.209495
646646 0 0
647647 0.339746 0.0133568 0.00667840 0.999978i 0.497874π-0.497874\pi
0.00667840 + 0.999978i 0.497874π0.497874\pi
648648 0 0
649649 15.4641 0.607019
650650 0 0
651651 −0.497423 −0.0194955
652652 0 0
653653 −33.7128 −1.31928 −0.659642 0.751580i 0.729292π-0.729292\pi
−0.659642 + 0.751580i 0.729292π0.729292\pi
654654 0 0
655655 −2.92820 −0.114414
656656 0 0
657657 −7.21539 −0.281499
658658 0 0
659659 39.3205 1.53171 0.765855 0.643014i 0.222316π-0.222316\pi
0.765855 + 0.643014i 0.222316π0.222316\pi
660660 0 0
661661 −20.9282 −0.814013 −0.407006 0.913425i 0.633427π-0.633427\pi
−0.407006 + 0.913425i 0.633427π0.633427\pi
662662 0 0
663663 0 0
664664 0 0
665665 −9.46410 −0.367002
666666 0 0
667667 −6.92820 −0.268261
668668 0 0
669669 −18.5359 −0.716639
670670 0 0
671671 33.8564 1.30701
672672 0 0
673673 28.5359 1.09998 0.549989 0.835172i 0.314632π-0.314632\pi
0.549989 + 0.835172i 0.314632π0.314632\pi
674674 0 0
675675 −4.00000 −0.153960
676676 0 0
677677 9.60770 0.369254 0.184627 0.982809i 0.440892π-0.440892\pi
0.184627 + 0.982809i 0.440892π0.440892\pi
678678 0 0
679679 54.9282 2.10795
680680 0 0
681681 −13.1769 −0.504940
682682 0 0
683683 −24.9282 −0.953851 −0.476926 0.878944i 0.658249π-0.658249\pi
−0.476926 + 0.878944i 0.658249π0.658249\pi
684684 0 0
685685 −8.92820 −0.341129
686686 0 0
687687 −14.2487 −0.543622
688688 0 0
689689 0 0
690690 0 0
691691 −43.9090 −1.67038 −0.835188 0.549965i 0.814641π-0.814641\pi
−0.835188 + 0.549965i 0.814641π0.814641\pi
692692 0 0
693693 −23.3205 −0.885873
694694 0 0
695695 −13.4641 −0.510722
696696 0 0
697697 −4.00000 −0.151511
698698 0 0
699699 13.1769 0.498397
700700 0 0
701701 29.7128 1.12224 0.561119 0.827735i 0.310371π-0.310371\pi
0.561119 + 0.827735i 0.310371π0.310371\pi
702702 0 0
703703 0 0
704704 0 0
705705 −3.32051 −0.125058
706706 0 0
707707 −17.0718 −0.642051
708708 0 0
709709 −5.60770 −0.210601 −0.105301 0.994440i 0.533581π-0.533581\pi
−0.105301 + 0.994440i 0.533581π0.533581\pi
710710 0 0
711711 16.1051 0.603989
712712 0 0
713713 −0.143594 −0.00537762
714714 0 0
715715 0 0
716716 0 0
717717 −18.4974 −0.690799
718718 0 0
719719 −34.6410 −1.29189 −0.645946 0.763383i 0.723537π-0.723537\pi
−0.645946 + 0.763383i 0.723537π0.723537\pi
720720 0 0
721721 21.4641 0.799365
722722 0 0
723723 −14.8231 −0.551276
724724 0 0
725725 9.46410 0.351488
726726 0 0
727727 −34.9808 −1.29736 −0.648682 0.761059i 0.724680π-0.724680\pi
−0.648682 + 0.761059i 0.724680π0.724680\pi
728728 0 0
729729 −2.21539 −0.0820515
730730 0 0
731731 −54.2487 −2.00646
732732 0 0
733733 15.8564 0.585670 0.292835 0.956163i 0.405401π-0.405401\pi
0.292835 + 0.956163i 0.405401π0.405401\pi
734734 0 0
735735 3.66025 0.135011
736736 0 0
737737 −35.3205 −1.30105
738738 0 0
739739 −1.26795 −0.0466423 −0.0233211 0.999728i 0.507424π-0.507424\pi
−0.0233211 + 0.999728i 0.507424π0.507424\pi
740740 0 0
741741 0 0
742742 0 0
743743 −25.3205 −0.928919 −0.464460 0.885594i 0.653751π-0.653751\pi
−0.464460 + 0.885594i 0.653751π0.653751\pi
744744 0 0
745745 7.85641 0.287836
746746 0 0
747747 −25.6077 −0.936937
748748 0 0
749749 69.4641 2.53816
750750 0 0
751751 45.4641 1.65901 0.829504 0.558500i 0.188623π-0.188623\pi
0.829504 + 0.558500i 0.188623π0.188623\pi
752752 0 0
753753 17.0718 0.622131
754754 0 0
755755 −11.8038 −0.429586
756756 0 0
757757 −23.4641 −0.852817 −0.426409 0.904531i 0.640221π-0.640221\pi
−0.426409 + 0.904531i 0.640221π0.640221\pi
758758 0 0
759759 1.46410 0.0531435
760760 0 0
761761 14.0000 0.507500 0.253750 0.967270i 0.418336π-0.418336\pi
0.253750 + 0.967270i 0.418336π0.418336\pi
762762 0 0
763763 54.9282 1.98853
764764 0 0
765765 −18.3923 −0.664975
766766 0 0
767767 0 0
768768 0 0
769769 −15.0718 −0.543503 −0.271751 0.962367i 0.587603π-0.587603\pi
−0.271751 + 0.962367i 0.587603π0.587603\pi
770770 0 0
771771 4.39230 0.158185
772772 0 0
773773 −5.07180 −0.182420 −0.0912099 0.995832i 0.529073π-0.529073\pi
−0.0912099 + 0.995832i 0.529073π0.529073\pi
774774 0 0
775775 0.196152 0.00704600
776776 0 0
777777 0 0
778778 0 0
779779 −1.46410 −0.0524569
780780 0 0
781781 25.3205 0.906039
782782 0 0
783783 −37.8564 −1.35288
784784 0 0
785785 −7.85641 −0.280407
786786 0 0
787787 −18.3923 −0.655615 −0.327807 0.944745i 0.606310π-0.606310\pi
−0.327807 + 0.944745i 0.606310π0.606310\pi
788788 0 0
789789 −8.53590 −0.303886
790790 0 0
791791 63.7128 2.26537
792792 0 0
793793 0 0
794794 0 0
795795 −0.392305 −0.0139136
796796 0 0
797797 46.7846 1.65720 0.828598 0.559844i 0.189139π-0.189139\pi
0.828598 + 0.559844i 0.189139π0.189139\pi
798798 0 0
799799 −33.8564 −1.19775
800800 0 0
801801 −31.8564 −1.12559
802802 0 0
803803 −8.00000 −0.282314
804804 0 0
805805 2.53590 0.0893787
806806 0 0
807807 −0.105118 −0.00370032
808808 0 0
809809 8.67949 0.305155 0.152577 0.988292i 0.451243π-0.451243\pi
0.152577 + 0.988292i 0.451243π0.451243\pi
810810 0 0
811811 −35.9090 −1.26093 −0.630467 0.776216i 0.717137π-0.717137\pi
−0.630467 + 0.776216i 0.717137π0.717137\pi
812812 0 0
813813 16.9282 0.593698
814814 0 0
815815 8.92820 0.312741
816816 0 0
817817 −19.8564 −0.694688
818818 0 0
819819 0 0
820820 0 0
821821 12.9282 0.451197 0.225599 0.974220i 0.427566π-0.427566\pi
0.225599 + 0.974220i 0.427566π0.427566\pi
822822 0 0
823823 26.5885 0.926815 0.463408 0.886145i 0.346627π-0.346627\pi
0.463408 + 0.886145i 0.346627π0.346627\pi
824824 0 0
825825 −2.00000 −0.0696311
826826 0 0
827827 −3.46410 −0.120459 −0.0602293 0.998185i 0.519183π-0.519183\pi
−0.0602293 + 0.998185i 0.519183π0.519183\pi
828828 0 0
829829 44.3923 1.54181 0.770904 0.636951i 0.219805π-0.219805\pi
0.770904 + 0.636951i 0.219805π0.219805\pi
830830 0 0
831831 −15.6077 −0.541425
832832 0 0
833833 37.3205 1.29308
834834 0 0
835835 21.3205 0.737827
836836 0 0
837837 −0.784610 −0.0271201
838838 0 0
839839 −34.4449 −1.18917 −0.594584 0.804033i 0.702683π-0.702683\pi
−0.594584 + 0.804033i 0.702683π0.702683\pi
840840 0 0
841841 60.5692 2.08859
842842 0 0
843843 3.32051 0.114364
844844 0 0
845845 0 0
846846 0 0
847847 12.2487 0.420871
848848 0 0
849849 −17.6077 −0.604295
850850 0 0
851851 0 0
852852 0 0
853853 7.71281 0.264082 0.132041 0.991244i 0.457847π-0.457847\pi
0.132041 + 0.991244i 0.457847π0.457847\pi
854854 0 0
855855 −6.73205 −0.230231
856856 0 0
857857 −4.14359 −0.141542 −0.0707712 0.997493i 0.522546π-0.522546\pi
−0.0707712 + 0.997493i 0.522546π0.522546\pi
858858 0 0
859859 −12.3923 −0.422820 −0.211410 0.977397i 0.567806π-0.567806\pi
−0.211410 + 0.977397i 0.567806π0.567806\pi
860860 0 0
861861 1.35898 0.0463140
862862 0 0
863863 33.6077 1.14402 0.572010 0.820247i 0.306164π-0.306164\pi
0.572010 + 0.820247i 0.306164π0.306164\pi
864864 0 0
865865 −2.39230 −0.0813408
866866 0 0
867867 28.3397 0.962468
868868 0 0
869869 17.8564 0.605737
870870 0 0
871871 0 0
872872 0 0
873873 39.0718 1.32238
874874 0 0
875875 −3.46410 −0.117108
876876 0 0
877877 41.7128 1.40854 0.704271 0.709931i 0.251274π-0.251274\pi
0.704271 + 0.709931i 0.251274π0.251274\pi
878878 0 0
879879 −5.07180 −0.171067
880880 0 0
881881 5.46410 0.184090 0.0920451 0.995755i 0.470660π-0.470660\pi
0.0920451 + 0.995755i 0.470660π0.470660\pi
882882 0 0
883883 22.5885 0.760162 0.380081 0.924953i 0.375896π-0.375896\pi
0.380081 + 0.924953i 0.375896π0.375896\pi
884884 0 0
885885 −4.14359 −0.139285
886886 0 0
887887 12.4449 0.417858 0.208929 0.977931i 0.433002π-0.433002\pi
0.208929 + 0.977931i 0.433002π0.433002\pi
888888 0 0
889889 6.24871 0.209575
890890 0 0
891891 −12.1962 −0.408586
892892 0 0
893893 −12.3923 −0.414693
894894 0 0
895895 −21.8564 −0.730579
896896 0 0
897897 0 0
898898 0 0
899899 1.85641 0.0619146
900900 0 0
901901 −4.00000 −0.133259
902902 0 0
903903 18.4308 0.613338
904904 0 0
905905 6.53590 0.217261
906906 0 0
907907 −36.8372 −1.22316 −0.611579 0.791183i 0.709465π-0.709465\pi
−0.611579 + 0.791183i 0.709465π0.709465\pi
908908 0 0
909909 −12.1436 −0.402778
910910 0 0
911911 −20.7846 −0.688625 −0.344312 0.938855i 0.611888π-0.611888\pi
−0.344312 + 0.938855i 0.611888π0.611888\pi
912912 0 0
913913 −28.3923 −0.939648
914914 0 0
915915 −9.07180 −0.299904
916916 0 0
917917 10.1436 0.334971
918918 0 0
919919 39.3205 1.29706 0.648532 0.761187i 0.275383π-0.275383\pi
0.648532 + 0.761187i 0.275383π0.275383\pi
920920 0 0
921921 12.1051 0.398877
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 15.2679 0.501465
928928 0 0
929929 −43.1769 −1.41659 −0.708294 0.705917i 0.750535π-0.750535\pi
−0.708294 + 0.705917i 0.750535π0.750535\pi
930930 0 0
931931 13.6603 0.447697
932932 0 0
933933 22.9282 0.750636
934934 0 0
935935 −20.3923 −0.666900
936936 0 0
937937 −27.0718 −0.884397 −0.442199 0.896917i 0.645801π-0.645801\pi
−0.442199 + 0.896917i 0.645801π0.645801\pi
938938 0 0
939939 7.60770 0.248268
940940 0 0
941941 −22.3923 −0.729968 −0.364984 0.931014i 0.618926π-0.618926\pi
−0.364984 + 0.931014i 0.618926π0.618926\pi
942942 0 0
943943 0.392305 0.0127752
944944 0 0
945945 13.8564 0.450749
946946 0 0
947947 −22.3923 −0.727652 −0.363826 0.931467i 0.618530π-0.618530\pi
−0.363826 + 0.931467i 0.618530π0.618530\pi
948948 0 0
949949 0 0
950950 0 0
951951 1.35898 0.0440681
952952 0 0
953953 −1.21539 −0.0393704 −0.0196852 0.999806i 0.506266π-0.506266\pi
−0.0196852 + 0.999806i 0.506266π0.506266\pi
954954 0 0
955955 18.9282 0.612502
956956 0 0
957957 −18.9282 −0.611862
958958 0 0
959959 30.9282 0.998724
960960 0 0
961961 −30.9615 −0.998759
962962 0 0
963963 49.4115 1.59226
964964 0 0
965965 2.00000 0.0643823
966966 0 0
967967 18.0000 0.578841 0.289420 0.957202i 0.406537π-0.406537\pi
0.289420 + 0.957202i 0.406537π0.406537\pi
968968 0 0
969969 14.9282 0.479563
970970 0 0
971971 43.7128 1.40281 0.701405 0.712762i 0.252556π-0.252556\pi
0.701405 + 0.712762i 0.252556π0.252556\pi
972972 0 0
973973 46.6410 1.49524
974974 0 0
975975 0 0
976976 0 0
977977 2.92820 0.0936815 0.0468408 0.998902i 0.485085π-0.485085\pi
0.0468408 + 0.998902i 0.485085π0.485085\pi
978978 0 0
979979 −35.3205 −1.12885
980980 0 0
981981 39.0718 1.24747
982982 0 0
983983 15.8564 0.505741 0.252870 0.967500i 0.418625π-0.418625\pi
0.252870 + 0.967500i 0.418625π0.418625\pi
984984 0 0
985985 −8.92820 −0.284476
986986 0 0
987987 11.5026 0.366131
988988 0 0
989989 5.32051 0.169182
990990 0 0
991991 −53.8564 −1.71081 −0.855403 0.517964i 0.826690π-0.826690\pi
−0.855403 + 0.517964i 0.826690π0.826690\pi
992992 0 0
993993 6.28719 0.199518
994994 0 0
995995 −6.92820 −0.219639
996996 0 0
997997 −9.32051 −0.295183 −0.147592 0.989048i 0.547152π-0.547152\pi
−0.147592 + 0.989048i 0.547152π0.547152\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 6760.2.a.o.1.2 2
13.12 even 2 520.2.a.e.1.2 2
39.38 odd 2 4680.2.a.bd.1.2 2
52.51 odd 2 1040.2.a.l.1.1 2
65.12 odd 4 2600.2.d.m.1249.2 4
65.38 odd 4 2600.2.d.m.1249.3 4
65.64 even 2 2600.2.a.v.1.1 2
104.51 odd 2 4160.2.a.w.1.2 2
104.77 even 2 4160.2.a.bk.1.1 2
156.155 even 2 9360.2.a.cr.1.1 2
260.259 odd 2 5200.2.a.bn.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
520.2.a.e.1.2 2 13.12 even 2
1040.2.a.l.1.1 2 52.51 odd 2
2600.2.a.v.1.1 2 65.64 even 2
2600.2.d.m.1249.2 4 65.12 odd 4
2600.2.d.m.1249.3 4 65.38 odd 4
4160.2.a.w.1.2 2 104.51 odd 2
4160.2.a.bk.1.1 2 104.77 even 2
4680.2.a.bd.1.2 2 39.38 odd 2
5200.2.a.bn.1.2 2 260.259 odd 2
6760.2.a.o.1.2 2 1.1 even 1 trivial
9360.2.a.cr.1.1 2 156.155 even 2