Properties

Label 1920.2.b.e.191.6
Level 19201920
Weight 22
Character 1920.191
Analytic conductor 15.33115.331
Analytic rank 00
Dimension 88
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] = [1920,2,Mod(191,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 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("1920.191"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1920=2735 1920 = 2^{7} \cdot 3 \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1920.b (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,0,0,8,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 15.331277188115.3312771881
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.10070523904.11
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x810x4+81 x^{8} - 10x^{4} + 81 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 253 2^{5}\cdot 3
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 191.6
Root 0.4208611.68014i-0.420861 - 1.68014i of defining polynomial
Character χ\chi == 1920.191
Dual form 1920.2.b.e.191.5

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+(0.420861+1.68014i)q3+1.00000q52.16991iq7+(2.64575+1.41421i)q95.15587iq13+(0.420861+1.68014i)q15+2.32744iq17+3.06871q19+(3.645750.913230i)q21+5.59388q23+1.00000q25+(3.489573.85005i)q271.29150q29+7.91094iq312.16991iq355.15587iq37+(8.662592.16991i)q397.48331iq41+8.66259q43+(2.64575+1.41421i)q45+11.7313q47+2.29150q49+(3.91044+0.979531i)q51+8.58301q53+(1.29150+5.15587i)q57+4.33981iq598.48528iq61+(3.06871+5.74103i)q635.15587iq658.66259q67+(2.35425+9.39851i)q69+11.1878q712.00000q73+(0.420861+1.68014i)q75+3.57113iq79+(5.000007.48331i)q81+5.74103iq83+2.32744iq85+(0.5435442.16991i)q871.00197iq8911.1878q91+(13.2915+3.32941i)q93+3.06871q9516.5830q97+O(q100)q+(0.420861 + 1.68014i) q^{3} +1.00000 q^{5} -2.16991i q^{7} +(-2.64575 + 1.41421i) q^{9} -5.15587i q^{13} +(0.420861 + 1.68014i) q^{15} +2.32744i q^{17} +3.06871 q^{19} +(3.64575 - 0.913230i) q^{21} +5.59388 q^{23} +1.00000 q^{25} +(-3.48957 - 3.85005i) q^{27} -1.29150 q^{29} +7.91094i q^{31} -2.16991i q^{35} -5.15587i q^{37} +(8.66259 - 2.16991i) q^{39} -7.48331i q^{41} +8.66259 q^{43} +(-2.64575 + 1.41421i) q^{45} +11.7313 q^{47} +2.29150 q^{49} +(-3.91044 + 0.979531i) q^{51} +8.58301 q^{53} +(1.29150 + 5.15587i) q^{57} +4.33981i q^{59} -8.48528i q^{61} +(3.06871 + 5.74103i) q^{63} -5.15587i q^{65} -8.66259 q^{67} +(2.35425 + 9.39851i) q^{69} +11.1878 q^{71} -2.00000 q^{73} +(0.420861 + 1.68014i) q^{75} +3.57113i q^{79} +(5.00000 - 7.48331i) q^{81} +5.74103i q^{83} +2.32744i q^{85} +(-0.543544 - 2.16991i) q^{87} -1.00197i q^{89} -11.1878 q^{91} +(-13.2915 + 3.32941i) q^{93} +3.06871 q^{95} -16.5830 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+8q5+8q21+8q25+32q2924q4916q5332q57+40q6916q73+40q8164q9348q97+O(q100) 8 q + 8 q^{5} + 8 q^{21} + 8 q^{25} + 32 q^{29} - 24 q^{49} - 16 q^{53} - 32 q^{57} + 40 q^{69} - 16 q^{73} + 40 q^{81} - 64 q^{93} - 48 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1920Z)×\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times.

nn 511511 641641 901901 15371537
χ(n)\chi(n) 1-1 1-1 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 0.420861 + 1.68014i 0.242984 + 0.970030i
44 0 0
55 1.00000 0.447214
66 0 0
77 2.16991i 0.820148i −0.912052 0.410074i 0.865503π-0.865503\pi
0.912052 0.410074i 0.134497π-0.134497\pi
88 0 0
99 −2.64575 + 1.41421i −0.881917 + 0.471405i
1010 0 0
1111 0 0 1.00000 00
−1.00000 π\pi
1212 0 0
1313 5.15587i 1.42998i −0.699134 0.714991i 0.746431π-0.746431\pi
0.699134 0.714991i 0.253569π-0.253569\pi
1414 0 0
1515 0.420861 + 1.68014i 0.108666 + 0.433811i
1616 0 0
1717 2.32744i 0.564488i 0.959343 + 0.282244i 0.0910788π0.0910788\pi
−0.959343 + 0.282244i 0.908921π0.908921\pi
1818 0 0
1919 3.06871 0.704011 0.352005 0.935998i 0.385500π-0.385500\pi
0.352005 + 0.935998i 0.385500π0.385500\pi
2020 0 0
2121 3.64575 0.913230i 0.795568 0.199283i
2222 0 0
2323 5.59388 1.16640 0.583202 0.812327i 0.301799π-0.301799\pi
0.583202 + 0.812327i 0.301799π0.301799\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 −3.48957 3.85005i −0.671569 0.740942i
2828 0 0
2929 −1.29150 −0.239826 −0.119913 0.992784i 0.538262π-0.538262\pi
−0.119913 + 0.992784i 0.538262π0.538262\pi
3030 0 0
3131 7.91094i 1.42085i 0.703774 + 0.710424i 0.251497π0.251497\pi
−0.703774 + 0.710424i 0.748503π0.748503\pi
3232 0 0
3333 0 0
3434 0 0
3535 2.16991i 0.366781i
3636 0 0
3737 5.15587i 0.847620i −0.905751 0.423810i 0.860692π-0.860692\pi
0.905751 0.423810i 0.139308π-0.139308\pi
3838 0 0
3939 8.66259 2.16991i 1.38713 0.347463i
4040 0 0
4141 7.48331i 1.16870i −0.811503 0.584349i 0.801350π-0.801350\pi
0.811503 0.584349i 0.198650π-0.198650\pi
4242 0 0
4343 8.66259 1.32103 0.660517 0.750812i 0.270337π-0.270337\pi
0.660517 + 0.750812i 0.270337π0.270337\pi
4444 0 0
4545 −2.64575 + 1.41421i −0.394405 + 0.210819i
4646 0 0
4747 11.7313 1.71119 0.855593 0.517649i 0.173193π-0.173193\pi
0.855593 + 0.517649i 0.173193π0.173193\pi
4848 0 0
4949 2.29150 0.327358
5050 0 0
5151 −3.91044 + 0.979531i −0.547570 + 0.137162i
5252 0 0
5353 8.58301 1.17897 0.589483 0.807781i 0.299331π-0.299331\pi
0.589483 + 0.807781i 0.299331π0.299331\pi
5454 0 0
5555 0 0
5656 0 0
5757 1.29150 + 5.15587i 0.171064 + 0.682912i
5858 0 0
5959 4.33981i 0.564996i 0.959268 + 0.282498i 0.0911630π0.0911630\pi
−0.959268 + 0.282498i 0.908837π0.908837\pi
6060 0 0
6161 8.48528i 1.08643i −0.839594 0.543214i 0.817207π-0.817207\pi
0.839594 0.543214i 0.182793π-0.182793\pi
6262 0 0
6363 3.06871 + 5.74103i 0.386621 + 0.723302i
6464 0 0
6565 5.15587i 0.639507i
6666 0 0
6767 −8.66259 −1.05830 −0.529152 0.848527i 0.677490π-0.677490\pi
−0.529152 + 0.848527i 0.677490π0.677490\pi
6868 0 0
6969 2.35425 + 9.39851i 0.283418 + 1.13145i
7070 0 0
7171 11.1878 1.32774 0.663872 0.747847i 0.268912π-0.268912\pi
0.663872 + 0.747847i 0.268912π0.268912\pi
7272 0 0
7373 −2.00000 −0.234082 −0.117041 0.993127i 0.537341π-0.537341\pi
−0.117041 + 0.993127i 0.537341π0.537341\pi
7474 0 0
7575 0.420861 + 1.68014i 0.0485969 + 0.194006i
7676 0 0
7777 0 0
7878 0 0
7979 3.57113i 0.401783i 0.979613 + 0.200892i 0.0643839π0.0643839\pi
−0.979613 + 0.200892i 0.935616π0.935616\pi
8080 0 0
8181 5.00000 7.48331i 0.555556 0.831479i
8282 0 0
8383 5.74103i 0.630160i 0.949065 + 0.315080i 0.102031π0.102031\pi
−0.949065 + 0.315080i 0.897969π0.897969\pi
8484 0 0
8585 2.32744i 0.252447i
8686 0 0
8787 −0.543544 2.16991i −0.0582740 0.232638i
8888 0 0
8989 1.00197i 0.106208i −0.998589 0.0531041i 0.983088π-0.983088\pi
0.998589 0.0531041i 0.0169115π-0.0169115\pi
9090 0 0
9191 −11.1878 −1.17280
9292 0 0
9393 −13.2915 + 3.32941i −1.37826 + 0.345244i
9494 0 0
9595 3.06871 0.314843
9696 0 0
9797 −16.5830 −1.68375 −0.841875 0.539673i 0.818548π-0.818548\pi
−0.841875 + 0.539673i 0.818548π0.818548\pi
9898 0 0
9999 0 0
100100 0 0
101101 −13.2915 −1.32255 −0.661277 0.750142i 0.729985π-0.729985\pi
−0.661277 + 0.750142i 0.729985π0.729985\pi
102102 0 0
103103 6.50972i 0.641422i −0.947177 0.320711i 0.896078π-0.896078\pi
0.947177 0.320711i 0.103922π-0.103922\pi
104104 0 0
105105 3.64575 0.913230i 0.355789 0.0891221i
106106 0 0
107107 5.74103i 0.555007i −0.960725 0.277503i 0.910493π-0.910493\pi
0.960725 0.277503i 0.0895070π-0.0895070\pi
108108 0 0
109109 1.82646i 0.174943i 0.996167 + 0.0874716i 0.0278787π0.0278787\pi
−0.996167 + 0.0874716i 0.972121π0.972121\pi
110110 0 0
111111 8.66259 2.16991i 0.822217 0.205958i
112112 0 0
113113 7.98430i 0.751100i 0.926802 + 0.375550i 0.122546π0.122546\pi
−0.926802 + 0.375550i 0.877454π0.877454\pi
114114 0 0
115115 5.59388 0.521632
116116 0 0
117117 7.29150 + 13.6412i 0.674100 + 1.26112i
118118 0 0
119119 5.05034 0.462964
120120 0 0
121121 11.0000 1.00000
122122 0 0
123123 12.5730 3.14944i 1.13367 0.283975i
124124 0 0
125125 1.00000 0.0894427
126126 0 0
127127 17.9918i 1.59651i 0.602317 + 0.798257i 0.294244π0.294244\pi
−0.602317 + 0.798257i 0.705756π0.705756\pi
128128 0 0
129129 3.64575 + 14.5544i 0.320991 + 1.28144i
130130 0 0
131131 15.8219i 1.38236i −0.722681 0.691182i 0.757090π-0.757090\pi
0.722681 0.691182i 0.242910π-0.242910\pi
132132 0 0
133133 6.65882i 0.577393i
134134 0 0
135135 −3.48957 3.85005i −0.300335 0.331359i
136136 0 0
137137 18.2960i 1.56314i 0.623820 + 0.781568i 0.285580π0.285580\pi
−0.623820 + 0.781568i 0.714420π0.714420\pi
138138 0 0
139139 −9.20614 −0.780854 −0.390427 0.920634i 0.627673π-0.627673\pi
−0.390427 + 0.920634i 0.627673π0.627673\pi
140140 0 0
141141 4.93725 + 19.7103i 0.415792 + 1.65990i
142142 0 0
143143 0 0
144144 0 0
145145 −1.29150 −0.107253
146146 0 0
147147 0.964405 + 3.85005i 0.0795428 + 0.317547i
148148 0 0
149149 −6.00000 −0.491539 −0.245770 0.969328i 0.579041π-0.579041\pi
−0.245770 + 0.969328i 0.579041π0.579041\pi
150150 0 0
151151 16.5906i 1.35012i −0.737762 0.675061i 0.764117π-0.764117\pi
0.737762 0.675061i 0.235883π-0.235883\pi
152152 0 0
153153 −3.29150 6.15784i −0.266102 0.497832i
154154 0 0
155155 7.91094i 0.635422i
156156 0 0
157157 1.50295i 0.119948i −0.998200 0.0599742i 0.980898π-0.980898\pi
0.998200 0.0599742i 0.0191019π-0.0191019\pi
158158 0 0
159159 3.61226 + 14.4207i 0.286471 + 1.14363i
160160 0 0
161161 12.1382i 0.956624i
162162 0 0
163163 19.8504 1.55480 0.777400 0.629007i 0.216538π-0.216538\pi
0.777400 + 0.629007i 0.216538π0.216538\pi
164164 0 0
165165 0 0
166166 0 0
167167 11.7313 0.907796 0.453898 0.891054i 0.350033π-0.350033\pi
0.453898 + 0.891054i 0.350033π0.350033\pi
168168 0 0
169169 −13.5830 −1.04485
170170 0 0
171171 −8.11905 + 4.33981i −0.620879 + 0.331874i
172172 0 0
173173 6.00000 0.456172 0.228086 0.973641i 0.426753π-0.426753\pi
0.228086 + 0.973641i 0.426753π0.426753\pi
174174 0 0
175175 2.16991i 0.164030i
176176 0 0
177177 −7.29150 + 1.82646i −0.548063 + 0.137285i
178178 0 0
179179 4.33981i 0.324373i −0.986760 0.162186i 0.948145π-0.948145\pi
0.986760 0.162186i 0.0518546π-0.0518546\pi
180180 0 0
181181 0 0 1.00000 00
−1.00000 π\pi
182182 0 0
183183 14.2565 3.57113i 1.05387 0.263985i
184184 0 0
185185 5.15587i 0.379067i
186186 0 0
187187 0 0
188188 0 0
189189 −8.35425 + 7.57205i −0.607682 + 0.550786i
190190 0 0
191191 −5.05034 −0.365430 −0.182715 0.983166i 0.558488π-0.558488\pi
−0.182715 + 0.983166i 0.558488π0.558488\pi
192192 0 0
193193 12.5830 0.905745 0.452872 0.891575i 0.350399π-0.350399\pi
0.452872 + 0.891575i 0.350399π0.350399\pi
194194 0 0
195195 8.66259 2.16991i 0.620341 0.155390i
196196 0 0
197197 −20.5830 −1.46648 −0.733239 0.679971i 0.761992π-0.761992\pi
−0.733239 + 0.679971i 0.761992π0.761992\pi
198198 0 0
199199 3.57113i 0.253151i −0.991957 0.126575i 0.959601π-0.959601\pi
0.991957 0.126575i 0.0403985π-0.0403985\pi
200200 0 0
201201 −3.64575 14.5544i −0.257151 1.02659i
202202 0 0
203203 2.80244i 0.196693i
204204 0 0
205205 7.48331i 0.522657i
206206 0 0
207207 −14.8000 + 7.91094i −1.02867 + 0.549848i
208208 0 0
209209 0 0
210210 0 0
211211 −26.5313 −1.82649 −0.913246 0.407409i 0.866432π-0.866432\pi
−0.913246 + 0.407409i 0.866432π0.866432\pi
212212 0 0
213213 4.70850 + 18.7970i 0.322621 + 1.28795i
214214 0 0
215215 8.66259 0.590784
216216 0 0
217217 17.1660 1.16530
218218 0 0
219219 −0.841723 3.36028i −0.0568784 0.227067i
220220 0 0
221221 12.0000 0.807207
222222 0 0
223223 26.6714i 1.78605i 0.450007 + 0.893025i 0.351422π0.351422\pi
−0.450007 + 0.893025i 0.648578π0.648578\pi
224224 0 0
225225 −2.64575 + 1.41421i −0.176383 + 0.0942809i
226226 0 0
227227 18.7605i 1.24518i 0.782550 + 0.622588i 0.213919π0.213919\pi
−0.782550 + 0.622588i 0.786081π0.786081\pi
228228 0 0
229229 27.2823i 1.80287i −0.432919 0.901433i 0.642516π-0.642516\pi
0.432919 0.901433i 0.357484π-0.357484\pi
230230 0 0
231231 0 0
232232 0 0
233233 8.98626i 0.588710i 0.955696 + 0.294355i 0.0951048π0.0951048\pi
−0.955696 + 0.294355i 0.904895π0.904895\pi
234234 0 0
235235 11.7313 0.765266
236236 0 0
237237 −6.00000 + 1.50295i −0.389742 + 0.0976271i
238238 0 0
239239 −6.13742 −0.396997 −0.198498 0.980101i 0.563606π-0.563606\pi
−0.198498 + 0.980101i 0.563606π0.563606\pi
240240 0 0
241241 5.29150 0.340856 0.170428 0.985370i 0.445485π-0.445485\pi
0.170428 + 0.985370i 0.445485π0.445485\pi
242242 0 0
243243 14.6773 + 5.25127i 0.941551 + 0.336869i
244244 0 0
245245 2.29150 0.146399
246246 0 0
247247 15.8219i 1.00672i
248248 0 0
249249 −9.64575 + 2.41618i −0.611275 + 0.153119i
250250 0 0
251251 17.3593i 1.09571i 0.836574 + 0.547853i 0.184555π0.184555\pi
−0.836574 + 0.547853i 0.815445π0.815445\pi
252252 0 0
253253 0 0
254254 0 0
255255 −3.91044 + 0.979531i −0.244881 + 0.0613406i
256256 0 0
257257 1.32548i 0.0826810i 0.999145 + 0.0413405i 0.0131628π0.0131628\pi
−0.999145 + 0.0413405i 0.986837π0.986837\pi
258258 0 0
259259 −11.1878 −0.695174
260260 0 0
261261 3.41699 1.82646i 0.211507 0.113055i
262262 0 0
263263 −17.8687 −1.10183 −0.550917 0.834560i 0.685722π-0.685722\pi
−0.550917 + 0.834560i 0.685722π0.685722\pi
264264 0 0
265265 8.58301 0.527250
266266 0 0
267267 1.68345 0.421689i 0.103025 0.0258070i
268268 0 0
269269 23.1660 1.41246 0.706228 0.707984i 0.250395π-0.250395\pi
0.706228 + 0.707984i 0.250395π0.250395\pi
270270 0 0
271271 0.768687i 0.0466944i 0.999727 + 0.0233472i 0.00743232π0.00743232\pi
−0.999727 + 0.0233472i 0.992568π0.992568\pi
272272 0 0
273273 −4.70850 18.7970i −0.284971 1.13765i
274274 0 0
275275 0 0
276276 0 0
277277 22.1264i 1.32945i −0.747089 0.664724i 0.768549π-0.768549\pi
0.747089 0.664724i 0.231451π-0.231451\pi
278278 0 0
279279 −11.1878 20.9304i −0.669794 1.25307i
280280 0 0
281281 3.83039i 0.228502i 0.993452 + 0.114251i 0.0364468π0.0364468\pi
−0.993452 + 0.114251i 0.963553π0.963553\pi
282282 0 0
283283 24.9007 1.48019 0.740096 0.672501i 0.234780π-0.234780\pi
0.740096 + 0.672501i 0.234780π0.234780\pi
284284 0 0
285285 1.29150 + 5.15587i 0.0765020 + 0.305407i
286286 0 0
287287 −16.2381 −0.958505
288288 0 0
289289 11.5830 0.681353
290290 0 0
291291 −6.97915 27.8618i −0.409125 1.63329i
292292 0 0
293293 −23.1660 −1.35337 −0.676686 0.736271i 0.736585π-0.736585\pi
−0.676686 + 0.736271i 0.736585π0.736585\pi
294294 0 0
295295 4.33981i 0.252674i
296296 0 0
297297 0 0
298298 0 0
299299 28.8413i 1.66794i
300300 0 0
301301 18.7970i 1.08344i
302302 0 0
303303 −5.59388 22.3316i −0.321360 1.28292i
304304 0 0
305305 8.48528i 0.485866i
306306 0 0
307307 −7.57551 −0.432357 −0.216178 0.976354i 0.569359π-0.569359\pi
−0.216178 + 0.976354i 0.569359π0.569359\pi
308308 0 0
309309 10.9373 2.73969i 0.622199 0.155856i
310310 0 0
311311 −23.4626 −1.33044 −0.665221 0.746646i 0.731663π-0.731663\pi
−0.665221 + 0.746646i 0.731663π0.731663\pi
312312 0 0
313313 −27.1660 −1.53551 −0.767757 0.640741i 0.778627π-0.778627\pi
−0.767757 + 0.640741i 0.778627π0.778627\pi
314314 0 0
315315 3.06871 + 5.74103i 0.172902 + 0.323471i
316316 0 0
317317 32.5830 1.83004 0.915022 0.403404i 0.132173π-0.132173\pi
0.915022 + 0.403404i 0.132173π0.132173\pi
318318 0 0
319319 0 0
320320 0 0
321321 9.64575 2.41618i 0.538373 0.134858i
322322 0 0
323323 7.14226i 0.397406i
324324 0 0
325325 5.15587i 0.285996i
326326 0 0
327327 −3.06871 + 0.768687i −0.169700 + 0.0425085i
328328 0 0
329329 25.4558i 1.40343i
330330 0 0
331331 −30.4946 −1.67613 −0.838067 0.545568i 0.816314π-0.816314\pi
−0.838067 + 0.545568i 0.816314π0.816314\pi
332332 0 0
333333 7.29150 + 13.6412i 0.399572 + 0.747531i
334334 0 0
335335 −8.66259 −0.473288
336336 0 0
337337 −12.5830 −0.685440 −0.342720 0.939438i 0.611348π-0.611348\pi
−0.342720 + 0.939438i 0.611348π0.611348\pi
338338 0 0
339339 −13.4148 + 3.36028i −0.728589 + 0.182506i
340340 0 0
341341 0 0
342342 0 0
343343 20.1617i 1.08863i
344344 0 0
345345 2.35425 + 9.39851i 0.126748 + 0.505999i
346346 0 0
347347 30.2425i 1.62351i −0.584002 0.811753i 0.698514π-0.698514\pi
0.584002 0.811753i 0.301486π-0.301486\pi
348348 0 0
349349 30.9352i 1.65592i −0.560784 0.827962i 0.689500π-0.689500\pi
0.560784 0.827962i 0.310500π-0.310500\pi
350350 0 0
351351 −19.8504 + 17.9918i −1.05953 + 0.960331i
352352 0 0
353353 24.9549i 1.32821i 0.747638 + 0.664107i 0.231188π0.231188\pi
−0.747638 + 0.664107i 0.768812π0.768812\pi
354354 0 0
355355 11.1878 0.593785
356356 0 0
357357 2.12549 + 8.48528i 0.112493 + 0.449089i
358358 0 0
359359 −28.5129 −1.50486 −0.752428 0.658675i 0.771117π-0.771117\pi
−0.752428 + 0.658675i 0.771117π0.771117\pi
360360 0 0
361361 −9.58301 −0.504369
362362 0 0
363363 4.62948 + 18.4816i 0.242984 + 0.970030i
364364 0 0
365365 −2.00000 −0.104685
366366 0 0
367367 33.8137i 1.76506i −0.470257 0.882530i 0.655839π-0.655839\pi
0.470257 0.882530i 0.344161π-0.344161\pi
368368 0 0
369369 10.5830 + 19.7990i 0.550929 + 1.03069i
370370 0 0
371371 18.6243i 0.966927i
372372 0 0
373373 15.4676i 0.800883i −0.916322 0.400441i 0.868857π-0.868857\pi
0.916322 0.400441i 0.131143π-0.131143\pi
374374 0 0
375375 0.420861 + 1.68014i 0.0217332 + 0.0867621i
376376 0 0
377377 6.65882i 0.342947i
378378 0 0
379379 9.20614 0.472887 0.236444 0.971645i 0.424018π-0.424018\pi
0.236444 + 0.971645i 0.424018π0.424018\pi
380380 0 0
381381 −30.2288 + 7.57205i −1.54867 + 0.387928i
382382 0 0
383383 −10.6442 −0.543894 −0.271947 0.962312i 0.587668π-0.587668\pi
−0.271947 + 0.962312i 0.587668π0.587668\pi
384384 0 0
385385 0 0
386386 0 0
387387 −22.9191 + 12.2508i −1.16504 + 0.622741i
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 13.0194i 0.658422i
392392 0 0
393393 26.5830 6.65882i 1.34094 0.335893i
394394 0 0
395395 3.57113i 0.179683i
396396 0 0
397397 1.50295i 0.0754309i 0.999289 + 0.0377154i 0.0120080π0.0120080\pi
−0.999289 + 0.0377154i 0.987992π0.987992\pi
398398 0 0
399399 11.1878 2.80244i 0.560089 0.140298i
400400 0 0
401401 26.2803i 1.31238i 0.754597 + 0.656189i 0.227832π0.227832\pi
−0.754597 + 0.656189i 0.772168π0.772168\pi
402402 0 0
403403 40.7878 2.03178
404404 0 0
405405 5.00000 7.48331i 0.248452 0.371849i
406406 0 0
407407 0 0
408408 0 0
409409 −7.87451 −0.389369 −0.194685 0.980866i 0.562368π-0.562368\pi
−0.194685 + 0.980866i 0.562368π0.562368\pi
410410 0 0
411411 −30.7399 + 7.70010i −1.51629 + 0.379818i
412412 0 0
413413 9.41699 0.463380
414414 0 0
415415 5.74103i 0.281816i
416416 0 0
417417 −3.87451 15.4676i −0.189735 0.757452i
418418 0 0
419419 37.5210i 1.83302i 0.400013 + 0.916509i 0.369006π0.369006\pi
−0.400013 + 0.916509i 0.630994π0.630994\pi
420420 0 0
421421 4.83236i 0.235515i −0.993042 0.117757i 0.962429π-0.962429\pi
0.993042 0.117757i 0.0375705π-0.0375705\pi
422422 0 0
423423 −31.0381 + 16.5906i −1.50912 + 0.806661i
424424 0 0
425425 2.32744i 0.112898i
426426 0 0
427427 −18.4123 −0.891032
428428 0 0
429429 0 0
430430 0 0
431431 −1.08709 −0.0523632 −0.0261816 0.999657i 0.508335π-0.508335\pi
−0.0261816 + 0.999657i 0.508335π0.508335\pi
432432 0 0
433433 7.41699 0.356438 0.178219 0.983991i 0.442966π-0.442966\pi
0.178219 + 0.983991i 0.442966π0.442966\pi
434434 0 0
435435 −0.543544 2.16991i −0.0260609 0.104039i
436436 0 0
437437 17.1660 0.821162
438438 0 0
439439 5.10850i 0.243815i 0.992541 + 0.121908i 0.0389012π0.0389012\pi
−0.992541 + 0.121908i 0.961099π0.961099\pi
440440 0 0
441441 −6.06275 + 3.24067i −0.288702 + 0.154318i
442442 0 0
443443 1.40122i 0.0665740i 0.999446 + 0.0332870i 0.0105975π0.0105975\pi
−0.999446 + 0.0332870i 0.989402π0.989402\pi
444444 0 0
445445 1.00197i 0.0474978i
446446 0 0
447447 −2.52517 10.0808i −0.119436 0.476808i
448448 0 0
449449 19.7990i 0.934372i −0.884159 0.467186i 0.845268π-0.845268\pi
0.884159 0.467186i 0.154732π-0.154732\pi
450450 0 0
451451 0 0
452452 0 0
453453 27.8745 6.98233i 1.30966 0.328059i
454454 0 0
455455 −11.1878 −0.524490
456456 0 0
457457 16.5830 0.775720 0.387860 0.921718i 0.373214π-0.373214\pi
0.387860 + 0.921718i 0.373214π0.373214\pi
458458 0 0
459459 8.96077 8.12179i 0.418253 0.379093i
460460 0 0
461461 13.2915 0.619047 0.309523 0.950892i 0.399830π-0.399830\pi
0.309523 + 0.950892i 0.399830π0.399830\pi
462462 0 0
463463 9.31216i 0.432773i −0.976308 0.216386i 0.930573π-0.930573\pi
0.976308 0.216386i 0.0694271π-0.0694271\pi
464464 0 0
465465 −13.2915 + 3.32941i −0.616379 + 0.154398i
466466 0 0
467467 5.74103i 0.265663i 0.991139 + 0.132832i 0.0424070π0.0424070\pi
−0.991139 + 0.132832i 0.957593π0.957593\pi
468468 0 0
469469 18.7970i 0.867966i
470470 0 0
471471 2.52517 0.632534i 0.116354 0.0291456i
472472 0 0
473473 0 0
474474 0 0
475475 3.06871 0.140802
476476 0 0
477477 −22.7085 + 12.1382i −1.03975 + 0.555770i
478478 0 0
479479 −16.2381 −0.741938 −0.370969 0.928645i 0.620974π-0.620974\pi
−0.370969 + 0.928645i 0.620974π0.620974\pi
480480 0 0
481481 −26.5830 −1.21208
482482 0 0
483483 20.3939 5.10850i 0.927955 0.232445i
484484 0 0
485485 −16.5830 −0.752995
486486 0 0
487487 17.9918i 0.815286i 0.913141 + 0.407643i 0.133649π0.133649\pi
−0.913141 + 0.407643i 0.866351π0.866351\pi
488488 0 0
489489 8.35425 + 33.3514i 0.377792 + 1.50820i
490490 0 0
491491 24.5015i 1.10574i 0.833268 + 0.552869i 0.186467π0.186467\pi
−0.833268 + 0.552869i 0.813533π0.813533\pi
492492 0 0
493493 3.00590i 0.135379i
494494 0 0
495495 0 0
496496 0 0
497497 24.2764i 1.08895i
498498 0 0
499499 −3.06871 −0.137374 −0.0686872 0.997638i 0.521881π-0.521881\pi
−0.0686872 + 0.997638i 0.521881π0.521881\pi
500500 0 0
501501 4.93725 + 19.7103i 0.220580 + 0.880589i
502502 0 0
503503 0.543544 0.0242354 0.0121177 0.999927i 0.496143π-0.496143\pi
0.0121177 + 0.999927i 0.496143π0.496143\pi
504504 0 0
505505 −13.2915 −0.591464
506506 0 0
507507 −5.71656 22.8214i −0.253881 1.01353i
508508 0 0
509509 −3.87451 −0.171735 −0.0858673 0.996307i 0.527366π-0.527366\pi
−0.0858673 + 0.996307i 0.527366π0.527366\pi
510510 0 0
511511 4.33981i 0.191982i
512512 0 0
513513 −10.7085 11.8147i −0.472792 0.521631i
514514 0 0
515515 6.50972i 0.286853i
516516 0 0
517517 0 0
518518 0 0
519519 2.52517 + 10.0808i 0.110843 + 0.442500i
520520 0 0
521521 18.6196i 0.815737i 0.913041 + 0.407869i 0.133728π0.133728\pi
−0.913041 + 0.407869i 0.866272π0.866272\pi
522522 0 0
523523 38.2626 1.67311 0.836554 0.547885i 0.184567π-0.184567\pi
0.836554 + 0.547885i 0.184567π0.184567\pi
524524 0 0
525525 3.64575 0.913230i 0.159114 0.0398566i
526526 0 0
527527 −18.4123 −0.802051
528528 0 0
529529 8.29150 0.360500
530530 0 0
531531 −6.13742 11.4821i −0.266342 0.498279i
532532 0 0
533533 −38.5830 −1.67122
534534 0 0
535535 5.74103i 0.248207i
536536 0 0
537537 7.29150 1.82646i 0.314652 0.0788176i
538538 0 0
539539 0 0
540540 0 0
541541 16.9706i 0.729621i 0.931082 + 0.364811i 0.118866π0.118866\pi
−0.931082 + 0.364811i 0.881134π0.881134\pi
542542 0 0
543543 0 0
544544 0 0
545545 1.82646i 0.0782370i
546546 0 0
547547 −24.9007 −1.06468 −0.532338 0.846532i 0.678687π-0.678687\pi
−0.532338 + 0.846532i 0.678687π0.678687\pi
548548 0 0
549549 12.0000 + 22.4499i 0.512148 + 0.958140i
550550 0 0
551551 −3.96325 −0.168840
552552 0 0
553553 7.74902 0.329522
554554 0 0
555555 8.66259 2.16991i 0.367707 0.0921074i
556556 0 0
557557 −37.7490 −1.59948 −0.799739 0.600348i 0.795029π-0.795029\pi
−0.799739 + 0.600348i 0.795029π0.795029\pi
558558 0 0
559559 44.6632i 1.88905i
560560 0 0
561561 0 0
562562 0 0
563563 8.54348i 0.360065i 0.983661 + 0.180032i 0.0576202π0.0576202\pi
−0.983661 + 0.180032i 0.942380π0.942380\pi
564564 0 0
565565 7.98430i 0.335902i
566566 0 0
567567 −16.2381 10.8495i −0.681936 0.455638i
568568 0 0
569569 34.7656i 1.45745i −0.684806 0.728725i 0.740113π-0.740113\pi
0.684806 0.728725i 0.259887π-0.259887\pi
570570 0 0
571571 −30.4946 −1.27616 −0.638079 0.769971i 0.720271π-0.720271\pi
−0.638079 + 0.769971i 0.720271π0.720271\pi
572572 0 0
573573 −2.12549 8.48528i −0.0887937 0.354478i
574574 0 0
575575 5.59388 0.233281
576576 0 0
577577 2.00000 0.0832611 0.0416305 0.999133i 0.486745π-0.486745\pi
0.0416305 + 0.999133i 0.486745π0.486745\pi
578578 0 0
579579 5.29570 + 21.1412i 0.220082 + 0.878600i
580580 0 0
581581 12.4575 0.516825
582582 0 0
583583 0 0
584584 0 0
585585 7.29150 + 13.6412i 0.301467 + 0.563992i
586586 0 0
587587 30.2425i 1.24824i −0.781327 0.624122i 0.785457π-0.785457\pi
0.781327 0.624122i 0.214543π-0.214543\pi
588588 0 0
589589 24.2764i 1.00029i
590590 0 0
591591 −8.66259 34.5824i −0.356331 1.42253i
592592 0 0
593593 4.33138i 0.177868i 0.996038 + 0.0889342i 0.0283461π0.0283461\pi
−0.996038 + 0.0889342i 0.971654π0.971654\pi
594594 0 0
595595 5.05034 0.207044
596596 0 0
597597 6.00000 1.50295i 0.245564 0.0615116i
598598 0 0
599599 6.13742 0.250768 0.125384 0.992108i 0.459984π-0.459984\pi
0.125384 + 0.992108i 0.459984π0.459984\pi
600600 0 0
601601 22.4575 0.916061 0.458031 0.888936i 0.348555π-0.348555\pi
0.458031 + 0.888936i 0.348555π0.348555\pi
602602 0 0
603603 22.9191 12.2508i 0.933337 0.498889i
604604 0 0
605605 11.0000 0.447214
606606 0 0
607607 31.0112i 1.25871i 0.777119 + 0.629354i 0.216680π0.216680\pi
−0.777119 + 0.629354i 0.783320π0.783320\pi
608608 0 0
609609 −4.70850 + 1.17944i −0.190798 + 0.0477933i
610610 0 0
611611 60.4851i 2.44697i
612612 0 0
613613 28.7853i 1.16263i 0.813680 + 0.581313i 0.197461π0.197461\pi
−0.813680 + 0.581313i 0.802539π0.802539\pi
614614 0 0
615615 12.5730 3.14944i 0.506993 0.126998i
616616 0 0
617617 38.9195i 1.56684i −0.621492 0.783421i 0.713473π-0.713473\pi
0.621492 0.783421i 0.286527π-0.286527\pi
618618 0 0
619619 25.4442 1.02269 0.511345 0.859375i 0.329147π-0.329147\pi
0.511345 + 0.859375i 0.329147π0.329147\pi
620620 0 0
621621 −19.5203 21.5367i −0.783321 0.864239i
622622 0 0
623623 −2.17417 −0.0871065
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 0 0
628628 0 0
629629 12.0000 0.478471
630630 0 0
631631 9.44832i 0.376132i −0.982156 0.188066i 0.939778π-0.939778\pi
0.982156 0.188066i 0.0602218π-0.0602218\pi
632632 0 0
633633 −11.1660 44.5764i −0.443809 1.77175i
634634 0 0
635635 17.9918i 0.713982i
636636 0 0
637637 11.8147i 0.468115i
638638 0 0
639639 −29.6000 + 15.8219i −1.17096 + 0.625904i
640640 0 0
641641 28.1068i 1.11015i 0.831800 + 0.555076i 0.187311π0.187311\pi
−0.831800 + 0.555076i 0.812689π0.812689\pi
642642 0 0
643643 13.7129 0.540785 0.270393 0.962750i 0.412847π-0.412847\pi
0.270393 + 0.962750i 0.412847π0.412847\pi
644644 0 0
645645 3.64575 + 14.5544i 0.143551 + 0.573078i
646646 0 0
647647 −29.0565 −1.14233 −0.571164 0.820836i 0.693508π-0.693508\pi
−0.571164 + 0.820836i 0.693508π0.693508\pi
648648 0 0
649649 0 0
650650 0 0
651651 7.22451 + 28.8413i 0.283151 + 1.13038i
652652 0 0
653653 −0.833990 −0.0326365 −0.0163183 0.999867i 0.505194π-0.505194\pi
−0.0163183 + 0.999867i 0.505194π0.505194\pi
654654 0 0
655655 15.8219i 0.618212i
656656 0 0
657657 5.29150 2.82843i 0.206441 0.110347i
658658 0 0
659659 4.33981i 0.169055i 0.996421 + 0.0845276i 0.0269381π0.0269381\pi
−0.996421 + 0.0845276i 0.973062π0.973062\pi
660660 0 0
661661 8.48528i 0.330039i −0.986290 0.165020i 0.947231π-0.947231\pi
0.986290 0.165020i 0.0527687π-0.0527687\pi
662662 0 0
663663 5.05034 + 20.1617i 0.196139 + 0.783015i
664664 0 0
665665 6.65882i 0.258218i
666666 0 0
667667 −7.22451 −0.279734
668668 0 0
669669 −44.8118 + 11.2250i −1.73252 + 0.433982i
670670 0 0
671671 0 0
672672 0 0
673673 36.5830 1.41017 0.705086 0.709122i 0.250909π-0.250909\pi
0.705086 + 0.709122i 0.250909π0.250909\pi
674674 0 0
675675 −3.48957 3.85005i −0.134314 0.148188i
676676 0 0
677677 −0.833990 −0.0320528 −0.0160264 0.999872i 0.505102π-0.505102\pi
−0.0160264 + 0.999872i 0.505102π0.505102\pi
678678 0 0
679679 35.9836i 1.38092i
680680 0 0
681681 −31.5203 + 7.89556i −1.20786 + 0.302559i
682682 0 0
683683 38.9222i 1.48932i 0.667446 + 0.744658i 0.267387π0.267387\pi
−0.667446 + 0.744658i 0.732613π0.732613\pi
684684 0 0
685685 18.2960i 0.699056i
686686 0 0
687687 45.8381 11.4821i 1.74883 0.438068i
688688 0 0
689689 44.2529i 1.68590i
690690 0 0
691691 −10.2932 −0.391573 −0.195786 0.980647i 0.562726π-0.562726\pi
−0.195786 + 0.980647i 0.562726π0.562726\pi
692692 0 0
693693 0 0
694694 0 0
695695 −9.20614 −0.349209
696696 0 0
697697 17.4170 0.659716
698698 0 0
699699 −15.0982 + 3.78197i −0.571066 + 0.143047i
700700 0 0
701701 6.00000 0.226617 0.113308 0.993560i 0.463855π-0.463855\pi
0.113308 + 0.993560i 0.463855π0.463855\pi
702702 0 0
703703 15.8219i 0.596734i
704704 0 0
705705 4.93725 + 19.7103i 0.185948 + 0.742331i
706706 0 0
707707 28.8413i 1.08469i
708708 0 0
709709 10.3117i 0.387266i 0.981074 + 0.193633i 0.0620270π0.0620270\pi
−0.981074 + 0.193633i 0.937973π0.937973\pi
710710 0 0
711711 −5.05034 9.44832i −0.189402 0.354340i
712712 0 0
713713 44.2529i 1.65728i
714714 0 0
715715 0 0
716716 0 0
717717 −2.58301 10.3117i −0.0964641 0.385099i
718718 0 0
719719 22.3755 0.834466 0.417233 0.908800i 0.363000π-0.363000\pi
0.417233 + 0.908800i 0.363000π0.363000\pi
720720 0 0
721721 −14.1255 −0.526061
722722 0 0
723723 2.22699 + 8.89047i 0.0828226 + 0.330640i
724724 0 0
725725 −1.29150 −0.0479652
726726 0 0
727727 26.6714i 0.989188i 0.869124 + 0.494594i 0.164683π0.164683\pi
−0.869124 + 0.494594i 0.835317π0.835317\pi
728728 0 0
729729 −2.64575 + 26.8701i −0.0979908 + 0.995187i
730730 0 0
731731 20.1617i 0.745707i
732732 0 0
733733 15.4676i 0.571309i −0.958333 0.285655i 0.907789π-0.907789\pi
0.958333 0.285655i 0.0922110π-0.0922110\pi
734734 0 0
735735 0.964405 + 3.85005i 0.0355726 + 0.142011i
736736 0 0
737737 0 0
738738 0 0
739739 −25.4442 −0.935981 −0.467991 0.883733i 0.655022π-0.655022\pi
−0.467991 + 0.883733i 0.655022π0.655022\pi
740740 0 0
741741 26.5830 6.65882i 0.976551 0.244618i
742742 0 0
743743 36.2810 1.33102 0.665510 0.746389i 0.268214π-0.268214\pi
0.665510 + 0.746389i 0.268214π0.268214\pi
744744 0 0
745745 −6.00000 −0.219823
746746 0 0
747747 −8.11905 15.1894i −0.297060 0.555749i
748748 0 0
749749 −12.4575 −0.455188
750750 0 0
751751 41.0921i 1.49947i −0.661737 0.749736i 0.730181π-0.730181\pi
0.661737 0.749736i 0.269819π-0.269819\pi
752752 0 0
753753 −29.1660 + 7.30584i −1.06287 + 0.266240i
754754 0 0
755755 16.5906i 0.603793i
756756 0 0
757757 53.0617i 1.92856i 0.264887 + 0.964279i 0.414665π0.414665\pi
−0.264887 + 0.964279i 0.585335π0.585335\pi
758758 0 0
759759 0 0
760760 0 0
761761 48.9078i 1.77290i 0.462820 + 0.886452i 0.346838π0.346838\pi
−0.462820 + 0.886452i 0.653162π0.653162\pi
762762 0 0
763763 3.96325 0.143479
764764 0 0
765765 −3.29150 6.15784i −0.119005 0.222637i
766766 0 0
767767 22.3755 0.807933
768768 0 0
769769 −4.58301 −0.165267 −0.0826337 0.996580i 0.526333π-0.526333\pi
−0.0826337 + 0.996580i 0.526333π0.526333\pi
770770 0 0
771771 −2.22699 + 0.557842i −0.0802031 + 0.0200902i
772772 0 0
773773 13.7490 0.494518 0.247259 0.968949i 0.420470π-0.420470\pi
0.247259 + 0.968949i 0.420470π0.420470\pi
774774 0 0
775775 7.91094i 0.284169i
776776 0 0
777777 −4.70850 18.7970i −0.168916 0.674339i
778778 0 0
779779 22.9641i 0.822776i
780780 0 0
781781 0 0
782782 0 0
783783 4.50679 + 4.97235i 0.161060 + 0.177697i
784784 0 0
785785 1.50295i 0.0536426i
786786 0 0
787787 −7.57551 −0.270038 −0.135019 0.990843i 0.543109π-0.543109\pi
−0.135019 + 0.990843i 0.543109π0.543109\pi
788788 0 0
789789 −7.52026 30.0220i −0.267728 1.06881i
790790 0 0
791791 17.3252 0.616013
792792 0 0
793793 −43.7490 −1.55357
794794 0 0
795795 3.61226 + 14.4207i 0.128114 + 0.511448i
796796 0 0
797797 32.5830 1.15415 0.577075 0.816691i 0.304194π-0.304194\pi
0.577075 + 0.816691i 0.304194π0.304194\pi
798798 0 0
799799 27.3040i 0.965944i
800800 0 0
801801 1.41699 + 2.65095i 0.0500670 + 0.0936669i
802802 0 0
803803 0 0
804804 0 0
805805 12.1382i 0.427815i
806806 0 0
807807 9.74968 + 38.9222i 0.343205 + 1.37013i
808808 0 0
809809 36.5921i 1.28651i −0.765652 0.643255i 0.777584π-0.777584\pi
0.765652 0.643255i 0.222416π-0.222416\pi
810810 0 0
811811 −36.6320 −1.28632 −0.643162 0.765730i 0.722378π-0.722378\pi
−0.643162 + 0.765730i 0.722378π0.722378\pi
812812 0 0
813813 −1.29150 + 0.323511i −0.0452950 + 0.0113460i
814814 0 0
815815 19.8504 0.695328
816816 0 0
817817 26.5830 0.930022
818818 0 0
819819 29.6000 15.8219i 1.03431 0.552861i
820820 0 0
821821 −6.00000 −0.209401 −0.104701 0.994504i 0.533388π-0.533388\pi
−0.104701 + 0.994504i 0.533388π0.533388\pi
822822 0 0
823823 33.8137i 1.17867i 0.807889 + 0.589335i 0.200610π0.200610\pi
−0.807889 + 0.589335i 0.799390π0.799390\pi
824824 0 0
825825 0 0
826826 0 0
827827 8.54348i 0.297086i −0.988906 0.148543i 0.952542π-0.952542\pi
0.988906 0.148543i 0.0474583π-0.0474583\pi
828828 0 0
829829 32.1147i 1.11539i 0.830046 + 0.557694i 0.188314π0.188314\pi
−0.830046 + 0.557694i 0.811686π0.811686\pi
830830 0 0
831831 37.1755 9.31216i 1.28961 0.323035i
832832 0 0
833833 5.33334i 0.184789i
834834 0 0
835835 11.7313 0.405979
836836 0 0
837837 30.4575 27.6058i 1.05277 0.954197i
838838 0 0
839839 53.0626 1.83193 0.915963 0.401263i 0.131429π-0.131429\pi
0.915963 + 0.401263i 0.131429π0.131429\pi
840840 0 0
841841 −27.3320 −0.942483
842842 0 0
843843 −6.43560 + 1.61206i −0.221654 + 0.0555225i
844844 0 0
845845 −13.5830 −0.467270
846846 0 0
847847 23.8690i 0.820148i
848848 0 0
849849 10.4797 + 41.8367i 0.359664 + 1.43583i
850850 0 0
851851 28.8413i 0.988668i
852852 0 0
853853 46.4028i 1.58880i −0.607393 0.794401i 0.707785π-0.707785\pi
0.607393 0.794401i 0.292215π-0.292215\pi
854854 0 0
855855 −8.11905 + 4.33981i −0.277666 + 0.148419i
856856 0 0
857857 18.2960i 0.624981i 0.949921 + 0.312490i 0.101163π0.101163\pi
−0.949921 + 0.312490i 0.898837π0.898837\pi
858858 0 0
859859 −25.4442 −0.868146 −0.434073 0.900878i 0.642924π-0.642924\pi
−0.434073 + 0.900878i 0.642924π0.642924\pi
860860 0 0
861861 −6.83399 27.2823i −0.232902 0.929778i
862862 0 0
863863 12.8184 0.436343 0.218172 0.975910i 0.429991π-0.429991\pi
0.218172 + 0.975910i 0.429991π0.429991\pi
864864 0 0
865865 6.00000 0.204006
866866 0 0
867867 4.87484 + 19.4611i 0.165558 + 0.660933i
868868 0 0
869869 0 0
870870 0 0
871871 44.6632i 1.51336i
872872 0 0
873873 43.8745 23.4519i 1.48493 0.793727i
874874 0 0
875875 2.16991i 0.0733563i
876876 0 0
877877 29.4323i 0.993857i −0.867791 0.496929i 0.834461π-0.834461\pi
0.867791 0.496929i 0.165539π-0.165539\pi
878878 0 0
879879 −9.74968 38.9222i −0.328849 1.31281i
880880 0 0
881881 13.1402i 0.442704i 0.975194 + 0.221352i 0.0710469π0.0710469\pi
−0.975194 + 0.221352i 0.928953π0.928953\pi
882882 0 0
883883 −14.8000 −0.498060 −0.249030 0.968496i 0.580112π-0.580112\pi
−0.249030 + 0.968496i 0.580112π0.580112\pi
884884 0 0
885885 −7.29150 + 1.82646i −0.245101 + 0.0613958i
886886 0 0
887887 −6.68097 −0.224325 −0.112162 0.993690i 0.535778π-0.535778\pi
−0.112162 + 0.993690i 0.535778π0.535778\pi
888888 0 0
889889 39.0405 1.30938
890890 0 0
891891 0 0
892892 0 0
893893 36.0000 1.20469
894894 0 0
895895 4.33981i 0.145064i
896896 0 0
897897 48.4575 12.1382i 1.61795 0.405283i
898898 0 0
899899 10.2170i 0.340756i
900900 0 0
901901 19.9765i 0.665512i
902902 0 0
903903 31.5817 7.91094i 1.05097 0.263260i
904904 0 0
905905 0 0
906906 0 0
907907 13.7129 0.455330 0.227665 0.973739i 0.426891π-0.426891\pi
0.227665 + 0.973739i 0.426891π0.426891\pi
908908 0 0
909909 35.1660 18.7970i 1.16638 0.623458i
910910 0 0
911911 45.8381 1.51869 0.759343 0.650691i 0.225521π-0.225521\pi
0.759343 + 0.650691i 0.225521π0.225521\pi
912912 0 0
913913 0 0
914914 0 0
915915 14.2565 3.57113i 0.471304 0.118058i
916916 0 0
917917 −34.3320 −1.13374
918918 0 0
919919 12.2508i 0.404115i 0.979374 + 0.202058i 0.0647628π0.0647628\pi
−0.979374 + 0.202058i 0.935237π0.935237\pi
920920 0 0
921921 −3.18824 12.7279i −0.105056 0.419399i
922922 0 0
923923 57.6827i 1.89865i
924924 0 0
925925 5.15587i 0.169524i
926926 0 0
927927 9.20614 + 17.2231i 0.302369 + 0.565681i
928928 0 0
929929 16.1461i 0.529735i −0.964285 0.264868i 0.914672π-0.914672\pi
0.964285 0.264868i 0.0853283π-0.0853283\pi
930930 0 0
931931 7.03196 0.230463
932932 0 0
933933 −9.87451 39.4205i −0.323277 1.29057i
934934 0 0
935935 0 0
936936 0 0
937937 −36.3320 −1.18692 −0.593458 0.804865i 0.702238π-0.702238\pi
−0.593458 + 0.804865i 0.702238π0.702238\pi
938938 0 0
939939 −11.4331 45.6427i −0.373106 1.48949i
940940 0 0
941941 −42.4575 −1.38408 −0.692038 0.721861i 0.743287π-0.743287\pi
−0.692038 + 0.721861i 0.743287π0.743287\pi
942942 0 0
943943 41.8608i 1.36317i
944944 0 0
945945 −8.35425 + 7.57205i −0.271764 + 0.246319i
946946 0 0
947947 38.9222i 1.26480i 0.774642 + 0.632400i 0.217930π0.217930\pi
−0.774642 + 0.632400i 0.782070π0.782070\pi
948948 0 0
949949 10.3117i 0.334733i
950950 0 0
951951 13.7129 + 54.7441i 0.444672 + 1.77520i
952952 0 0
953953 28.6078i 0.926697i 0.886176 + 0.463348i 0.153352π0.153352\pi
−0.886176 + 0.463348i 0.846648π0.846648\pi
954954 0 0
955955 −5.05034 −0.163425
956956 0 0
957957 0 0
958958 0 0
959959 39.7007 1.28200
960960 0 0
961961 −31.5830 −1.01881
962962 0 0
963963 8.11905 + 15.1894i 0.261633 + 0.489470i
964964 0 0
965965 12.5830 0.405061
966966 0 0
967967 32.5486i 1.04669i −0.852120 0.523346i 0.824683π-0.824683\pi
0.852120 0.523346i 0.175317π-0.175317\pi
968968 0 0
969969 −12.0000 + 3.00590i −0.385496 + 0.0965634i
970970 0 0
971971 49.0030i 1.57258i 0.617856 + 0.786291i 0.288001π0.288001\pi
−0.617856 + 0.786291i 0.711999π0.711999\pi
972972 0 0
973973 19.9765i 0.640416i
974974 0 0
975975 8.66259 2.16991i 0.277425 0.0694926i
976976 0 0
977977 1.32548i 0.0424058i −0.999775 0.0212029i 0.993250π-0.993250\pi
0.999775 0.0212029i 0.00674959π-0.00674959\pi
978978 0 0
979979 0 0
980980 0 0
981981 −2.58301 4.83236i −0.0824690 0.154285i
982982 0 0
983983 −35.1939 −1.12251 −0.561256 0.827642i 0.689682π-0.689682\pi
−0.561256 + 0.827642i 0.689682π0.689682\pi
984984 0 0
985985 −20.5830 −0.655829
986986 0 0
987987 42.7694 10.7134i 1.36137 0.341011i
988988 0 0
989989 48.4575 1.54086
990990 0 0
991991 23.7328i 0.753898i 0.926234 + 0.376949i 0.123027π0.123027\pi
−0.926234 + 0.376949i 0.876973π0.876973\pi
992992 0 0
993993 −12.8340 51.2352i −0.407274 1.62590i
994994 0 0
995995 3.57113i 0.113212i
996996 0 0
997997 5.15587i 0.163288i 0.996662 + 0.0816440i 0.0260171π0.0260171\pi
−0.996662 + 0.0816440i 0.973983π0.973983\pi
998998 0 0
999999 −19.8504 + 17.9918i −0.628037 + 0.569235i
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 1920.2.b.e.191.6 yes 8
3.2 odd 2 1920.2.b.c.191.5 yes 8
4.3 odd 2 inner 1920.2.b.e.191.3 yes 8
8.3 odd 2 1920.2.b.c.191.6 yes 8
8.5 even 2 1920.2.b.c.191.3 8
12.11 even 2 1920.2.b.c.191.4 yes 8
24.5 odd 2 inner 1920.2.b.e.191.4 yes 8
24.11 even 2 inner 1920.2.b.e.191.5 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1920.2.b.c.191.3 8 8.5 even 2
1920.2.b.c.191.4 yes 8 12.11 even 2
1920.2.b.c.191.5 yes 8 3.2 odd 2
1920.2.b.c.191.6 yes 8 8.3 odd 2
1920.2.b.e.191.3 yes 8 4.3 odd 2 inner
1920.2.b.e.191.4 yes 8 24.5 odd 2 inner
1920.2.b.e.191.5 yes 8 24.11 even 2 inner
1920.2.b.e.191.6 yes 8 1.1 even 1 trivial