Properties

Label 1920.2.b.f.191.3
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 / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1920,2,Mod(191,1920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
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")
 
//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

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 15.331277188115.3312771881
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.3288334336.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+8x68x5+14x4+8x316x2+7 x^{8} + 8x^{6} - 8x^{5} + 14x^{4} + 8x^{3} - 16x^{2} + 7 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 25 2^{5}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 191.3
Root 0.7071070.179070i-0.707107 - 0.179070i of defining polynomial
Character χ\chi == 1920.191
Dual form 1920.2.b.f.191.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.137051.30656i)q3+1.00000q51.08239iq7+(0.414214+2.97127i)q92.16478iq11+1.74053iq13+(1.137051.30656i)q15+4.20201iq17+3.21608q19+(1.41421+1.23074i)q21+5.49019q23+1.00000q25+(4.353132.83730i)q27+0.828427q29+3.69552iq31+(2.82843+2.46148i)q331.08239iq3510.1445iq37+(2.274111.97908i)q39+2.46148iq41+8.70626q43+(0.414214+2.97127i)q4510.0384q47+5.82843q49+(5.490194.77791i)q51+2.00000q532.16478iq55+(3.656854.20201i)q5710.4525iq59+10.8655iq61+(3.21608+0.448342i)q63+1.74053iq65+4.15804q67+(6.242647.17327i)q691.88393q71+3.65685q73+(1.137051.30656i)q752.34315q77+11.9832iq79+(8.656852.46148i)q8110.0042iq83+4.20201iq85+(0.9419671.08239i)q87+3.48106iq89+1.88393q91+(4.828434.20201i)q93+3.21608q95+9.31371q97+(6.43215+0.896683i)q99+O(q100)q+(-1.13705 - 1.30656i) q^{3} +1.00000 q^{5} -1.08239i q^{7} +(-0.414214 + 2.97127i) q^{9} -2.16478i q^{11} +1.74053i q^{13} +(-1.13705 - 1.30656i) q^{15} +4.20201i q^{17} +3.21608 q^{19} +(-1.41421 + 1.23074i) q^{21} +5.49019 q^{23} +1.00000 q^{25} +(4.35313 - 2.83730i) q^{27} +0.828427 q^{29} +3.69552i q^{31} +(-2.82843 + 2.46148i) q^{33} -1.08239i q^{35} -10.1445i q^{37} +(2.27411 - 1.97908i) q^{39} +2.46148i q^{41} +8.70626 q^{43} +(-0.414214 + 2.97127i) q^{45} -10.0384 q^{47} +5.82843 q^{49} +(5.49019 - 4.77791i) q^{51} +2.00000 q^{53} -2.16478i q^{55} +(-3.65685 - 4.20201i) q^{57} -10.4525i q^{59} +10.8655i q^{61} +(3.21608 + 0.448342i) q^{63} +1.74053i q^{65} +4.15804 q^{67} +(-6.24264 - 7.17327i) q^{69} -1.88393 q^{71} +3.65685 q^{73} +(-1.13705 - 1.30656i) q^{75} -2.34315 q^{77} +11.9832i q^{79} +(-8.65685 - 2.46148i) q^{81} -10.0042i q^{83} +4.20201i q^{85} +(-0.941967 - 1.08239i) q^{87} +3.48106i q^{89} +1.88393 q^{91} +(4.82843 - 4.20201i) q^{93} +3.21608 q^{95} +9.31371 q^{97} +(6.43215 + 0.896683i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+8q5+8q9+8q2516q29+8q45+24q49+16q53+16q5716q6916q7364q7724q81+16q9316q97+O(q100) 8 q + 8 q^{5} + 8 q^{9} + 8 q^{25} - 16 q^{29} + 8 q^{45} + 24 q^{49} + 16 q^{53} + 16 q^{57} - 16 q^{69} - 16 q^{73} - 64 q^{77} - 24 q^{81} + 16 q^{93} - 16 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 −1.13705 1.30656i −0.656479 0.754344i
44 0 0
55 1.00000 0.447214
66 0 0
77 1.08239i 0.409106i −0.978856 0.204553i 0.934426π-0.934426\pi
0.978856 0.204553i 0.0655740π-0.0655740\pi
88 0 0
99 −0.414214 + 2.97127i −0.138071 + 0.990422i
1010 0 0
1111 2.16478i 0.652707i −0.945248 0.326354i 0.894180π-0.894180\pi
0.945248 0.326354i 0.105820π-0.105820\pi
1212 0 0
1313 1.74053i 0.482736i 0.970434 + 0.241368i 0.0775960π0.0775960\pi
−0.970434 + 0.241368i 0.922404π0.922404\pi
1414 0 0
1515 −1.13705 1.30656i −0.293586 0.337353i
1616 0 0
1717 4.20201i 1.01914i 0.860430 + 0.509568i 0.170195π0.170195\pi
−0.860430 + 0.509568i 0.829805π0.829805\pi
1818 0 0
1919 3.21608 0.737818 0.368909 0.929465i 0.379731π-0.379731\pi
0.368909 + 0.929465i 0.379731π0.379731\pi
2020 0 0
2121 −1.41421 + 1.23074i −0.308607 + 0.268569i
2222 0 0
2323 5.49019 1.14478 0.572391 0.819981i 0.306016π-0.306016\pi
0.572391 + 0.819981i 0.306016π0.306016\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 4.35313 2.83730i 0.837760 0.546038i
2828 0 0
2929 0.828427 0.153835 0.0769175 0.997037i 0.475492π-0.475492\pi
0.0769175 + 0.997037i 0.475492π0.475492\pi
3030 0 0
3131 3.69552i 0.663735i 0.943326 + 0.331867i 0.107679π0.107679\pi
−0.943326 + 0.331867i 0.892321π0.892321\pi
3232 0 0
3333 −2.82843 + 2.46148i −0.492366 + 0.428488i
3434 0 0
3535 1.08239i 0.182958i
3636 0 0
3737 10.1445i 1.66775i −0.551952 0.833876i 0.686117π-0.686117\pi
0.551952 0.833876i 0.313883π-0.313883\pi
3838 0 0
3939 2.27411 1.97908i 0.364149 0.316906i
4040 0 0
4141 2.46148i 0.384418i 0.981354 + 0.192209i 0.0615652π0.0615652\pi
−0.981354 + 0.192209i 0.938435π0.938435\pi
4242 0 0
4343 8.70626 1.32769 0.663846 0.747869i 0.268923π-0.268923\pi
0.663846 + 0.747869i 0.268923π0.268923\pi
4444 0 0
4545 −0.414214 + 2.97127i −0.0617473 + 0.442930i
4646 0 0
4747 −10.0384 −1.46425 −0.732126 0.681169i 0.761472π-0.761472\pi
−0.732126 + 0.681169i 0.761472π0.761472\pi
4848 0 0
4949 5.82843 0.832632
5050 0 0
5151 5.49019 4.77791i 0.768780 0.669041i
5252 0 0
5353 2.00000 0.274721 0.137361 0.990521i 0.456138π-0.456138\pi
0.137361 + 0.990521i 0.456138π0.456138\pi
5454 0 0
5555 2.16478i 0.291899i
5656 0 0
5757 −3.65685 4.20201i −0.484362 0.556569i
5858 0 0
5959 10.4525i 1.36080i −0.732841 0.680400i 0.761806π-0.761806\pi
0.732841 0.680400i 0.238194π-0.238194\pi
6060 0 0
6161 10.8655i 1.39118i 0.718437 + 0.695592i 0.244858π0.244858\pi
−0.718437 + 0.695592i 0.755142π0.755142\pi
6262 0 0
6363 3.21608 + 0.448342i 0.405188 + 0.0564857i
6464 0 0
6565 1.74053i 0.215886i
6666 0 0
6767 4.15804 0.507986 0.253993 0.967206i 0.418256π-0.418256\pi
0.253993 + 0.967206i 0.418256π0.418256\pi
6868 0 0
6969 −6.24264 7.17327i −0.751526 0.863561i
7070 0 0
7171 −1.88393 −0.223582 −0.111791 0.993732i 0.535659π-0.535659\pi
−0.111791 + 0.993732i 0.535659π0.535659\pi
7272 0 0
7373 3.65685 0.428002 0.214001 0.976833i 0.431350π-0.431350\pi
0.214001 + 0.976833i 0.431350π0.431350\pi
7474 0 0
7575 −1.13705 1.30656i −0.131296 0.150869i
7676 0 0
7777 −2.34315 −0.267026
7878 0 0
7979 11.9832i 1.34822i 0.738631 + 0.674110i 0.235473π0.235473\pi
−0.738631 + 0.674110i 0.764527π0.764527\pi
8080 0 0
8181 −8.65685 2.46148i −0.961873 0.273498i
8282 0 0
8383 10.0042i 1.09810i −0.835790 0.549050i 0.814990π-0.814990\pi
0.835790 0.549050i 0.185010π-0.185010\pi
8484 0 0
8585 4.20201i 0.455772i
8686 0 0
8787 −0.941967 1.08239i −0.100989 0.116045i
8888 0 0
8989 3.48106i 0.368991i 0.982833 + 0.184496i 0.0590651π0.0590651\pi
−0.982833 + 0.184496i 0.940935π0.940935\pi
9090 0 0
9191 1.88393 0.197490
9292 0 0
9393 4.82843 4.20201i 0.500685 0.435728i
9494 0 0
9595 3.21608 0.329962
9696 0 0
9797 9.31371 0.945664 0.472832 0.881153i 0.343232π-0.343232\pi
0.472832 + 0.881153i 0.343232π0.343232\pi
9898 0 0
9999 6.43215 + 0.896683i 0.646456 + 0.0901200i
100100 0 0
101101 1.51472 0.150720 0.0753601 0.997156i 0.475989π-0.475989\pi
0.0753601 + 0.997156i 0.475989π0.475989\pi
102102 0 0
103103 19.8226i 1.95318i −0.215108 0.976590i 0.569011π-0.569011\pi
0.215108 0.976590i 0.430989π-0.430989\pi
104104 0 0
105105 −1.41421 + 1.23074i −0.138013 + 0.120108i
106106 0 0
107107 9.10748i 0.880453i −0.897887 0.440227i 0.854898π-0.854898\pi
0.897887 0.440227i 0.145102π-0.145102\pi
108108 0 0
109109 2.46148i 0.235767i −0.993027 0.117883i 0.962389π-0.962389\pi
0.993027 0.117883i 0.0376109π-0.0376109\pi
110110 0 0
111111 −13.2545 + 11.5349i −1.25806 + 1.09484i
112112 0 0
113113 12.6060i 1.18587i −0.805249 0.592937i 0.797968π-0.797968\pi
0.805249 0.592937i 0.202032π-0.202032\pi
114114 0 0
115115 5.49019 0.511962
116116 0 0
117117 −5.17157 0.720950i −0.478112 0.0666519i
118118 0 0
119119 4.54822 0.416935
120120 0 0
121121 6.31371 0.573973
122122 0 0
123123 3.21608 2.79884i 0.289984 0.252362i
124124 0 0
125125 1.00000 0.0894427
126126 0 0
127127 8.47343i 0.751895i 0.926641 + 0.375948i 0.122683π0.122683\pi
−0.926641 + 0.375948i 0.877317π0.877317\pi
128128 0 0
129129 −9.89949 11.3753i −0.871602 1.00154i
130130 0 0
131131 11.3492i 0.991583i −0.868442 0.495792i 0.834878π-0.834878\pi
0.868442 0.495792i 0.165122π-0.165122\pi
132132 0 0
133133 3.48106i 0.301846i
134134 0 0
135135 4.35313 2.83730i 0.374658 0.244196i
136136 0 0
137137 16.0871i 1.37441i −0.726463 0.687206i 0.758837π-0.758837\pi
0.726463 0.687206i 0.241163π-0.241163\pi
138138 0 0
139139 3.21608 0.272784 0.136392 0.990655i 0.456449π-0.456449\pi
0.136392 + 0.990655i 0.456449π0.456449\pi
140140 0 0
141141 11.4142 + 13.1158i 0.961250 + 1.10455i
142142 0 0
143143 3.76787 0.315085
144144 0 0
145145 0.828427 0.0687971
146146 0 0
147147 −6.62724 7.61521i −0.546606 0.628092i
148148 0 0
149149 13.3137 1.09070 0.545351 0.838208i 0.316396π-0.316396\pi
0.545351 + 0.838208i 0.316396π0.316396\pi
150150 0 0
151151 4.96362i 0.403934i 0.979392 + 0.201967i 0.0647333π0.0647333\pi
−0.979392 + 0.201967i 0.935267π0.935267\pi
152152 0 0
153153 −12.4853 1.74053i −1.00938 0.140713i
154154 0 0
155155 3.69552i 0.296831i
156156 0 0
157157 15.0675i 1.20252i −0.799055 0.601259i 0.794666π-0.794666\pi
0.799055 0.601259i 0.205334π-0.205334\pi
158158 0 0
159159 −2.27411 2.61313i −0.180349 0.207234i
160160 0 0
161161 5.94253i 0.468337i
162162 0 0
163163 −2.27411 −0.178122 −0.0890610 0.996026i 0.528387π-0.528387\pi
−0.0890610 + 0.996026i 0.528387π0.528387\pi
164164 0 0
165165 −2.82843 + 2.46148i −0.220193 + 0.191626i
166166 0 0
167167 8.15447 0.631012 0.315506 0.948924i 0.397826π-0.397826\pi
0.315506 + 0.948924i 0.397826π0.397826\pi
168168 0 0
169169 9.97056 0.766966
170170 0 0
171171 −1.33214 + 9.55582i −0.101871 + 0.730752i
172172 0 0
173173 −21.3137 −1.62045 −0.810226 0.586118i 0.800655π-0.800655\pi
−0.810226 + 0.586118i 0.800655π0.800655\pi
174174 0 0
175175 1.08239i 0.0818212i
176176 0 0
177177 −13.6569 + 11.8851i −1.02651 + 0.893336i
178178 0 0
179179 0 0 1.00000 00
−1.00000 π\pi
180180 0 0
181181 23.7701i 1.76682i 0.468601 + 0.883410i 0.344758π0.344758\pi
−0.468601 + 0.883410i 0.655242π0.655242\pi
182182 0 0
183183 14.1964 12.3547i 1.04943 0.913282i
184184 0 0
185185 10.1445i 0.745841i
186186 0 0
187187 9.09644 0.665197
188188 0 0
189189 −3.07107 4.71179i −0.223387 0.342733i
190190 0 0
191191 −17.4125 −1.25993 −0.629963 0.776625i 0.716930π-0.716930\pi
−0.629963 + 0.776625i 0.716930π0.716930\pi
192192 0 0
193193 9.31371 0.670415 0.335208 0.942144i 0.391194π-0.391194\pi
0.335208 + 0.942144i 0.391194π0.391194\pi
194194 0 0
195195 2.27411 1.97908i 0.162852 0.141725i
196196 0 0
197197 2.00000 0.142494 0.0712470 0.997459i 0.477302π-0.477302\pi
0.0712470 + 0.997459i 0.477302π0.477302\pi
198198 0 0
199199 10.1899i 0.722341i −0.932500 0.361170i 0.882377π-0.882377\pi
0.932500 0.361170i 0.117623π-0.117623\pi
200200 0 0
201201 −4.72792 5.43275i −0.333482 0.383196i
202202 0 0
203203 0.896683i 0.0629348i
204204 0 0
205205 2.46148i 0.171917i
206206 0 0
207207 −2.27411 + 16.3128i −0.158062 + 1.13382i
208208 0 0
209209 6.96211i 0.481579i
210210 0 0
211211 16.8607 1.16074 0.580370 0.814353i 0.302908π-0.302908\pi
0.580370 + 0.814353i 0.302908π0.302908\pi
212212 0 0
213213 2.14214 + 2.46148i 0.146777 + 0.168658i
214214 0 0
215215 8.70626 0.593762
216216 0 0
217217 4.00000 0.271538
218218 0 0
219219 −4.15804 4.77791i −0.280975 0.322861i
220220 0 0
221221 −7.31371 −0.491973
222222 0 0
223223 25.4203i 1.70227i −0.524948 0.851134i 0.675915π-0.675915\pi
0.524948 0.851134i 0.324085π-0.324085\pi
224224 0 0
225225 −0.414214 + 2.97127i −0.0276142 + 0.198084i
226226 0 0
227227 19.1886i 1.27359i 0.771033 + 0.636795i 0.219740π0.219740\pi
−0.771033 + 0.636795i 0.780260π0.780260\pi
228228 0 0
229229 8.40401i 0.555353i −0.960675 0.277676i 0.910436π-0.910436\pi
0.960675 0.277676i 0.0895643π-0.0895643\pi
230230 0 0
231231 2.66428 + 3.06147i 0.175297 + 0.201430i
232232 0 0
233233 19.5681i 1.28195i 0.767561 + 0.640975i 0.221470π0.221470\pi
−0.767561 + 0.640975i 0.778530π0.778530\pi
234234 0 0
235235 −10.0384 −0.654833
236236 0 0
237237 15.6569 13.6256i 1.01702 0.885078i
238238 0 0
239239 −24.6250 −1.59286 −0.796430 0.604730i 0.793281π-0.793281\pi
−0.796430 + 0.604730i 0.793281π0.793281\pi
240240 0 0
241241 20.1421 1.29747 0.648735 0.761015i 0.275299π-0.275299\pi
0.648735 + 0.761015i 0.275299π0.275299\pi
242242 0 0
243243 6.62724 + 14.1096i 0.425138 + 0.905129i
244244 0 0
245245 5.82843 0.372365
246246 0 0
247247 5.59767i 0.356171i
248248 0 0
249249 −13.0711 + 11.3753i −0.828345 + 0.720879i
250250 0 0
251251 18.7402i 1.18287i 0.806352 + 0.591436i 0.201439π0.201439\pi
−0.806352 + 0.591436i 0.798561π0.798561\pi
252252 0 0
253253 11.8851i 0.747208i
254254 0 0
255255 5.49019 4.77791i 0.343809 0.299204i
256256 0 0
257257 19.5681i 1.22063i 0.792160 + 0.610313i 0.208956π0.208956\pi
−0.792160 + 0.610313i 0.791044π0.791044\pi
258258 0 0
259259 −10.9804 −0.682287
260260 0 0
261261 −0.343146 + 2.46148i −0.0212402 + 0.152362i
262262 0 0
263263 29.3349 1.80887 0.904433 0.426617i 0.140295π-0.140295\pi
0.904433 + 0.426617i 0.140295π0.140295\pi
264264 0 0
265265 2.00000 0.122859
266266 0 0
267267 4.54822 3.95815i 0.278346 0.242235i
268268 0 0
269269 −2.68629 −0.163786 −0.0818930 0.996641i 0.526097π-0.526097\pi
−0.0818930 + 0.996641i 0.526097π0.526097\pi
270270 0 0
271271 31.9916i 1.94335i 0.236323 + 0.971674i 0.424058π0.424058\pi
−0.236323 + 0.971674i 0.575942π0.575942\pi
272272 0 0
273273 −2.14214 2.46148i −0.129648 0.148975i
274274 0 0
275275 2.16478i 0.130541i
276276 0 0
277277 1.74053i 0.104578i 0.998632 + 0.0522891i 0.0166517π0.0166517\pi
−0.998632 + 0.0522891i 0.983348π0.983348\pi
278278 0 0
279279 −10.9804 1.53073i −0.657378 0.0916426i
280280 0 0
281281 9.42359i 0.562164i 0.959684 + 0.281082i 0.0906933π0.0906933\pi
−0.959684 + 0.281082i 0.909307π0.909307\pi
282282 0 0
283283 −19.6866 −1.17025 −0.585124 0.810944i 0.698954π-0.698954\pi
−0.585124 + 0.810944i 0.698954π0.698954\pi
284284 0 0
285285 −3.65685 4.20201i −0.216613 0.248905i
286286 0 0
287287 2.66428 0.157268
288288 0 0
289289 −0.656854 −0.0386385
290290 0 0
291291 −10.5902 12.1689i −0.620808 0.713356i
292292 0 0
293293 −5.31371 −0.310430 −0.155215 0.987881i 0.549607π-0.549607\pi
−0.155215 + 0.987881i 0.549607π0.549607\pi
294294 0 0
295295 10.4525i 0.608568i
296296 0 0
297297 −6.14214 9.42359i −0.356403 0.546812i
298298 0 0
299299 9.55582i 0.552627i
300300 0 0
301301 9.42359i 0.543167i
302302 0 0
303303 −1.72232 1.97908i −0.0989446 0.113695i
304304 0 0
305305 10.8655i 0.622156i
306306 0 0
307307 −28.7831 −1.64274 −0.821368 0.570398i 0.806789π-0.806789\pi
−0.821368 + 0.570398i 0.806789π0.806789\pi
308308 0 0
309309 −25.8995 + 22.5394i −1.47337 + 1.28222i
310310 0 0
311311 −23.8447 −1.35211 −0.676054 0.736852i 0.736311π-0.736311\pi
−0.676054 + 0.736852i 0.736311π0.736311\pi
312312 0 0
313313 29.3137 1.65691 0.828454 0.560057i 0.189221π-0.189221\pi
0.828454 + 0.560057i 0.189221π0.189221\pi
314314 0 0
315315 3.21608 + 0.448342i 0.181205 + 0.0252612i
316316 0 0
317317 −17.3137 −0.972435 −0.486217 0.873838i 0.661624π-0.661624\pi
−0.486217 + 0.873838i 0.661624π0.661624\pi
318318 0 0
319319 1.79337i 0.100409i
320320 0 0
321321 −11.8995 + 10.3557i −0.664165 + 0.577999i
322322 0 0
323323 13.5140i 0.751937i
324324 0 0
325325 1.74053i 0.0965471i
326326 0 0
327327 −3.21608 + 2.79884i −0.177849 + 0.154776i
328328 0 0
329329 10.8655i 0.599034i
330330 0 0
331331 −29.7250 −1.63384 −0.816918 0.576754i 0.804319π-0.804319\pi
−0.816918 + 0.576754i 0.804319π0.804319\pi
332332 0 0
333333 30.1421 + 4.20201i 1.65178 + 0.230269i
334334 0 0
335335 4.15804 0.227178
336336 0 0
337337 18.9706 1.03339 0.516696 0.856169i 0.327162π-0.327162\pi
0.516696 + 0.856169i 0.327162π0.327162\pi
338338 0 0
339339 −16.4706 + 14.3337i −0.894558 + 0.778501i
340340 0 0
341341 8.00000 0.433224
342342 0 0
343343 13.8854i 0.749741i
344344 0 0
345345 −6.24264 7.17327i −0.336092 0.386196i
346346 0 0
347347 0.819760i 0.0440070i 0.999758 + 0.0220035i 0.00700450π0.00700450\pi
−0.999758 + 0.0220035i 0.992996π0.992996\pi
348348 0 0
349349 3.48106i 0.186337i −0.995650 0.0931683i 0.970301π-0.970301\pi
0.995650 0.0931683i 0.0296995π-0.0296995\pi
350350 0 0
351351 4.93839 + 7.57675i 0.263592 + 0.404417i
352352 0 0
353353 9.12496i 0.485673i 0.970067 + 0.242836i 0.0780778π0.0780778\pi
−0.970067 + 0.242836i 0.921922π0.921922\pi
354354 0 0
355355 −1.88393 −0.0999888
356356 0 0
357357 −5.17157 5.94253i −0.273709 0.314512i
358358 0 0
359359 2.66428 0.140616 0.0703078 0.997525i 0.477602π-0.477602\pi
0.0703078 + 0.997525i 0.477602π0.477602\pi
360360 0 0
361361 −8.65685 −0.455624
362362 0 0
363363 −7.17903 8.24926i −0.376801 0.432974i
364364 0 0
365365 3.65685 0.191408
366366 0 0
367367 25.9456i 1.35435i 0.735824 + 0.677173i 0.236795π0.236795\pi
−0.735824 + 0.677173i 0.763205π0.763205\pi
368368 0 0
369369 −7.31371 1.01958i −0.380736 0.0530771i
370370 0 0
371371 2.16478i 0.112390i
372372 0 0
373373 17.1067i 0.885749i 0.896584 + 0.442874i 0.146041π0.146041\pi
−0.896584 + 0.442874i 0.853959π0.853959\pi
374374 0 0
375375 −1.13705 1.30656i −0.0587172 0.0674706i
376376 0 0
377377 1.44190i 0.0742617i
378378 0 0
379379 14.9768 0.769306 0.384653 0.923061i 0.374321π-0.374321\pi
0.384653 + 0.923061i 0.374321π0.374321\pi
380380 0 0
381381 11.0711 9.63475i 0.567188 0.493603i
382382 0 0
383383 33.8831 1.73134 0.865672 0.500611i 0.166891π-0.166891\pi
0.865672 + 0.500611i 0.166891π0.166891\pi
384384 0 0
385385 −2.34315 −0.119418
386386 0 0
387387 −3.60625 + 25.8686i −0.183316 + 1.31498i
388388 0 0
389389 25.3137 1.28346 0.641728 0.766932i 0.278218π-0.278218\pi
0.641728 + 0.766932i 0.278218π0.278218\pi
390390 0 0
391391 23.0698i 1.16669i
392392 0 0
393393 −14.8284 + 12.9046i −0.747995 + 0.650953i
394394 0 0
395395 11.9832i 0.602942i
396396 0 0
397397 26.9526i 1.35271i 0.736576 + 0.676355i 0.236442π0.236442\pi
−0.736576 + 0.676355i 0.763558π0.763558\pi
398398 0 0
399399 −4.54822 + 3.95815i −0.227696 + 0.198155i
400400 0 0
401401 11.8851i 0.593512i 0.954953 + 0.296756i 0.0959048π0.0959048\pi
−0.954953 + 0.296756i 0.904095π0.904095\pi
402402 0 0
403403 −6.43215 −0.320408
404404 0 0
405405 −8.65685 2.46148i −0.430163 0.122312i
406406 0 0
407407 −21.9607 −1.08855
408408 0 0
409409 12.1421 0.600390 0.300195 0.953878i 0.402948π-0.402948\pi
0.300195 + 0.953878i 0.402948π0.402948\pi
410410 0 0
411411 −21.0188 + 18.2919i −1.03678 + 0.902272i
412412 0 0
413413 −11.3137 −0.556711
414414 0 0
415415 10.0042i 0.491085i
416416 0 0
417417 −3.65685 4.20201i −0.179077 0.205773i
418418 0 0
419419 16.0502i 0.784102i 0.919943 + 0.392051i 0.128234π0.128234\pi
−0.919943 + 0.392051i 0.871766π0.871766\pi
420420 0 0
421421 17.8276i 0.868864i −0.900705 0.434432i 0.856949π-0.856949\pi
0.900705 0.434432i 0.143051π-0.143051\pi
422422 0 0
423423 4.15804 29.8268i 0.202171 1.45023i
424424 0 0
425425 4.20201i 0.203827i
426426 0 0
427427 11.7607 0.569141
428428 0 0
429429 −4.28427 4.92296i −0.206847 0.237683i
430430 0 0
431431 −32.9411 −1.58672 −0.793359 0.608754i 0.791670π-0.791670\pi
−0.793359 + 0.608754i 0.791670π0.791670\pi
432432 0 0
433433 −21.3137 −1.02427 −0.512136 0.858905i 0.671146π-0.671146\pi
−0.512136 + 0.858905i 0.671146π0.671146\pi
434434 0 0
435435 −0.941967 1.08239i −0.0451639 0.0518967i
436436 0 0
437437 17.6569 0.844642
438438 0 0
439439 8.92177i 0.425813i 0.977073 + 0.212906i 0.0682929π0.0682929\pi
−0.977073 + 0.212906i 0.931707π0.931707\pi
440440 0 0
441441 −2.41421 + 17.3178i −0.114963 + 0.824658i
442442 0 0
443443 15.6018i 0.741265i 0.928780 + 0.370633i 0.120859π0.120859\pi
−0.928780 + 0.370633i 0.879141π0.879141\pi
444444 0 0
445445 3.48106i 0.165018i
446446 0 0
447447 −15.1384 17.3952i −0.716022 0.822765i
448448 0 0
449449 27.6735i 1.30599i −0.757361 0.652997i 0.773511π-0.773511\pi
0.757361 0.652997i 0.226489π-0.226489\pi
450450 0 0
451451 5.32857 0.250913
452452 0 0
453453 6.48528 5.64391i 0.304705 0.265174i
454454 0 0
455455 1.88393 0.0883202
456456 0 0
457457 7.65685 0.358173 0.179086 0.983833i 0.442686π-0.442686\pi
0.179086 + 0.983833i 0.442686π0.442686\pi
458458 0 0
459459 11.9223 + 18.2919i 0.556487 + 0.853792i
460460 0 0
461461 −36.8284 −1.71527 −0.857635 0.514258i 0.828067π-0.828067\pi
−0.857635 + 0.514258i 0.828067π0.828067\pi
462462 0 0
463463 17.1326i 0.796218i −0.917338 0.398109i 0.869667π-0.869667\pi
0.917338 0.398109i 0.130333π-0.130333\pi
464464 0 0
465465 4.82843 4.20201i 0.223913 0.194863i
466466 0 0
467467 28.2191i 1.30583i 0.757433 + 0.652913i 0.226453π0.226453\pi
−0.757433 + 0.652913i 0.773547π0.773547\pi
468468 0 0
469469 4.50063i 0.207820i
470470 0 0
471471 −19.6866 + 17.1326i −0.907112 + 0.789427i
472472 0 0
473473 18.8472i 0.866594i
474474 0 0
475475 3.21608 0.147564
476476 0 0
477477 −0.828427 + 5.94253i −0.0379311 + 0.272090i
478478 0 0
479479 33.7215 1.54077 0.770386 0.637577i 0.220063π-0.220063\pi
0.770386 + 0.637577i 0.220063π0.220063\pi
480480 0 0
481481 17.6569 0.805083
482482 0 0
483483 −7.76429 + 6.75699i −0.353288 + 0.307453i
484484 0 0
485485 9.31371 0.422914
486486 0 0
487487 0.185709i 0.00841528i −0.999991 0.00420764i 0.998661π-0.998661\pi
0.999991 0.00420764i 0.00133934π-0.00133934\pi
488488 0 0
489489 2.58579 + 2.97127i 0.116933 + 0.134365i
490490 0 0
491491 20.0083i 0.902963i 0.892280 + 0.451482i 0.149104π0.149104\pi
−0.892280 + 0.451482i 0.850896π0.850896\pi
492492 0 0
493493 3.48106i 0.156779i
494494 0 0
495495 6.43215 + 0.896683i 0.289104 + 0.0403029i
496496 0 0
497497 2.03916i 0.0914686i
498498 0 0
499499 −34.2733 −1.53428 −0.767141 0.641479i 0.778321π-0.778321\pi
−0.767141 + 0.641479i 0.778321π0.778321\pi
500500 0 0
501501 −9.27208 10.6543i −0.414246 0.476000i
502502 0 0
503503 4.70983 0.210001 0.105001 0.994472i 0.466516π-0.466516\pi
0.105001 + 0.994472i 0.466516π0.466516\pi
504504 0 0
505505 1.51472 0.0674041
506506 0 0
507507 −11.3371 13.0272i −0.503497 0.578557i
508508 0 0
509509 33.1127 1.46769 0.733847 0.679314i 0.237723π-0.237723\pi
0.733847 + 0.679314i 0.237723π0.237723\pi
510510 0 0
511511 3.95815i 0.175098i
512512 0 0
513513 14.0000 9.12496i 0.618115 0.402877i
514514 0 0
515515 19.8226i 0.873489i
516516 0 0
517517 21.7310i 0.955727i
518518 0 0
519519 24.2349 + 27.8477i 1.06379 + 1.22238i
520520 0 0
521521 33.6160i 1.47275i −0.676576 0.736373i 0.736537π-0.736537\pi
0.676576 0.736373i 0.263463π-0.263463\pi
522522 0 0
523523 9.48661 0.414821 0.207410 0.978254i 0.433496π-0.433496\pi
0.207410 + 0.978254i 0.433496π0.433496\pi
524524 0 0
525525 −1.41421 + 1.23074i −0.0617213 + 0.0537139i
526526 0 0
527527 −15.5286 −0.676436
528528 0 0
529529 7.14214 0.310528
530530 0 0
531531 31.0572 + 4.32957i 1.34777 + 0.187887i
532532 0 0
533533 −4.28427 −0.185572
534534 0 0
535535 9.10748i 0.393751i
536536 0 0
537537 0 0
538538 0 0
539539 12.6173i 0.543465i
540540 0 0
541541 21.7310i 0.934288i −0.884181 0.467144i 0.845283π-0.845283\pi
0.884181 0.467144i 0.154717π-0.154717\pi
542542 0 0
543543 31.0572 27.0279i 1.33279 1.15988i
544544 0 0
545545 2.46148i 0.105438i
546546 0 0
547547 −11.3705 −0.486169 −0.243085 0.970005i 0.578159π-0.578159\pi
−0.243085 + 0.970005i 0.578159π0.578159\pi
548548 0 0
549549 −32.2843 4.50063i −1.37786 0.192082i
550550 0 0
551551 2.66428 0.113502
552552 0 0
553553 12.9706 0.551564
554554 0 0
555555 −13.2545 + 11.5349i −0.562621 + 0.489629i
556556 0 0
557557 −15.6569 −0.663402 −0.331701 0.943385i 0.607623π-0.607623\pi
−0.331701 + 0.943385i 0.607623π0.607623\pi
558558 0 0
559559 15.1535i 0.640924i
560560 0 0
561561 −10.3431 11.8851i −0.436688 0.501788i
562562 0 0
563563 11.7975i 0.497207i 0.968605 + 0.248603i 0.0799715π0.0799715\pi
−0.968605 + 0.248603i 0.920028π0.920028\pi
564564 0 0
565565 12.6060i 0.530339i
566566 0 0
567567 −2.66428 + 9.37011i −0.111889 + 0.393508i
568568 0 0
569569 17.8276i 0.747372i 0.927555 + 0.373686i 0.121906π0.121906\pi
−0.927555 + 0.373686i 0.878094π0.878094\pi
570570 0 0
571571 −35.0536 −1.46695 −0.733474 0.679718i 0.762102π-0.762102\pi
−0.733474 + 0.679718i 0.762102π0.762102\pi
572572 0 0
573573 19.7990 + 22.7506i 0.827115 + 0.950418i
574574 0 0
575575 5.49019 0.228957
576576 0 0
577577 −25.3137 −1.05382 −0.526912 0.849920i 0.676650π-0.676650\pi
−0.526912 + 0.849920i 0.676650π0.676650\pi
578578 0 0
579579 −10.5902 12.1689i −0.440113 0.505724i
580580 0 0
581581 −10.8284 −0.449239
582582 0 0
583583 4.32957i 0.179312i
584584 0 0
585585 −5.17157 0.720950i −0.213818 0.0298076i
586586 0 0
587587 22.6215i 0.933687i −0.884340 0.466844i 0.845391π-0.845391\pi
0.884340 0.466844i 0.154609π-0.154609\pi
588588 0 0
589589 11.8851i 0.489716i
590590 0 0
591591 −2.27411 2.61313i −0.0935444 0.107490i
592592 0 0
593593 7.68306i 0.315506i −0.987479 0.157753i 0.949575π-0.949575\pi
0.987479 0.157753i 0.0504249π-0.0504249\pi
594594 0 0
595595 4.54822 0.186459
596596 0 0
597597 −13.3137 + 11.5864i −0.544894 + 0.474201i
598598 0 0
599599 −11.7607 −0.480530 −0.240265 0.970707i 0.577234π-0.577234\pi
−0.240265 + 0.970707i 0.577234π0.577234\pi
600600 0 0
601601 0.142136 0.00579783 0.00289892 0.999996i 0.499077π-0.499077\pi
0.00289892 + 0.999996i 0.499077π0.499077\pi
602602 0 0
603603 −1.72232 + 12.3547i −0.0701382 + 0.503120i
604604 0 0
605605 6.31371 0.256689
606606 0 0
607607 31.1718i 1.26522i −0.774469 0.632612i 0.781983π-0.781983\pi
0.774469 0.632612i 0.218017π-0.218017\pi
608608 0 0
609609 −1.17157 + 1.01958i −0.0474745 + 0.0413154i
610610 0 0
611611 17.4721i 0.706846i
612612 0 0
613613 22.0296i 0.889767i −0.895588 0.444884i 0.853245π-0.853245\pi
0.895588 0.444884i 0.146755π-0.146755\pi
614614 0 0
615615 3.21608 2.79884i 0.129685 0.112860i
616616 0 0
617617 29.4140i 1.18416i −0.805877 0.592082i 0.798306π-0.798306\pi
0.805877 0.592082i 0.201694π-0.201694\pi
618618 0 0
619619 −18.7447 −0.753412 −0.376706 0.926333i 0.622943π-0.622943\pi
−0.376706 + 0.926333i 0.622943π0.622943\pi
620620 0 0
621621 23.8995 15.5773i 0.959054 0.625095i
622622 0 0
623623 3.76787 0.150956
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 −9.09644 + 7.91630i −0.363277 + 0.316147i
628628 0 0
629629 42.6274 1.69967
630630 0 0
631631 30.7235i 1.22308i 0.791213 + 0.611541i 0.209450π0.209450\pi
−0.791213 + 0.611541i 0.790550π0.790550\pi
632632 0 0
633633 −19.1716 22.0296i −0.762002 0.875598i
634634 0 0
635635 8.47343i 0.336258i
636636 0 0
637637 10.1445i 0.401941i
638638 0 0
639639 0.780351 5.59767i 0.0308702 0.221440i
640640 0 0
641641 26.2316i 1.03609i −0.855354 0.518043i 0.826661π-0.826661\pi
0.855354 0.518043i 0.173339π-0.173339\pi
642642 0 0
643643 4.15804 0.163977 0.0819886 0.996633i 0.473873π-0.473873\pi
0.0819886 + 0.996633i 0.473873π0.473873\pi
644644 0 0
645645 −9.89949 11.3753i −0.389792 0.447901i
646646 0 0
647647 −25.5670 −1.00514 −0.502571 0.864536i 0.667612π-0.667612\pi
−0.502571 + 0.864536i 0.667612π0.667612\pi
648648 0 0
649649 −22.6274 −0.888204
650650 0 0
651651 −4.54822 5.22625i −0.178259 0.204833i
652652 0 0
653653 −27.6569 −1.08230 −0.541148 0.840927i 0.682010π-0.682010\pi
−0.541148 + 0.840927i 0.682010π0.682010\pi
654654 0 0
655655 11.3492i 0.443449i
656656 0 0
657657 −1.51472 + 10.8655i −0.0590948 + 0.423903i
658658 0 0
659659 7.91630i 0.308375i 0.988042 + 0.154188i 0.0492760π0.0492760\pi
−0.988042 + 0.154188i 0.950724π0.950724\pi
660660 0 0
661661 46.5207i 1.80945i −0.426001 0.904723i 0.640078π-0.640078\pi
0.426001 0.904723i 0.359922π-0.359922\pi
662662 0 0
663663 8.31609 + 9.55582i 0.322970 + 0.371117i
664664 0 0
665665 3.48106i 0.134990i
666666 0 0
667667 4.54822 0.176108
668668 0 0
669669 −33.2132 + 28.9043i −1.28410 + 1.11750i
670670 0 0
671671 23.5214 0.908035
672672 0 0
673673 −14.6863 −0.566115 −0.283057 0.959103i 0.591349π-0.591349\pi
−0.283057 + 0.959103i 0.591349π0.591349\pi
674674 0 0
675675 4.35313 2.83730i 0.167552 0.109208i
676676 0 0
677677 9.02944 0.347029 0.173515 0.984831i 0.444488π-0.444488\pi
0.173515 + 0.984831i 0.444488π0.444488\pi
678678 0 0
679679 10.0811i 0.386877i
680680 0 0
681681 25.0711 21.8184i 0.960725 0.836085i
682682 0 0
683683 21.7248i 0.831275i −0.909530 0.415638i 0.863558π-0.863558\pi
0.909530 0.415638i 0.136442π-0.136442\pi
684684 0 0
685685 16.0871i 0.614655i
686686 0 0
687687 −10.9804 + 9.55582i −0.418927 + 0.364577i
688688 0 0
689689 3.48106i 0.132618i
690690 0 0
691691 32.3893 1.23215 0.616074 0.787688i 0.288722π-0.288722\pi
0.616074 + 0.787688i 0.288722π0.288722\pi
692692 0 0
693693 0.970563 6.96211i 0.0368686 0.264469i
694694 0 0
695695 3.21608 0.121993
696696 0 0
697697 −10.3431 −0.391775
698698 0 0
699699 25.5670 22.2500i 0.967032 0.841574i
700700 0 0
701701 1.31371 0.0496181 0.0248090 0.999692i 0.492102π-0.492102\pi
0.0248090 + 0.999692i 0.492102π0.492102\pi
702702 0 0
703703 32.6256i 1.23050i
704704 0 0
705705 11.4142 + 13.1158i 0.429884 + 0.493970i
706706 0 0
707707 1.63952i 0.0616605i
708708 0 0
709709 34.2133i 1.28491i 0.766324 + 0.642454i 0.222084π0.222084\pi
−0.766324 + 0.642454i 0.777916π0.777916\pi
710710 0 0
711711 −35.6054 4.96362i −1.33531 0.186150i
712712 0 0
713713 20.2891i 0.759832i
714714 0 0
715715 3.76787 0.140910
716716 0 0
717717 28.0000 + 32.1741i 1.04568 + 1.20157i
718718 0 0
719719 9.09644 0.339240 0.169620 0.985510i 0.445746π-0.445746\pi
0.169620 + 0.985510i 0.445746π0.445746\pi
720720 0 0
721721 −21.4558 −0.799057
722722 0 0
723723 −22.9027 26.3170i −0.851761 0.978739i
724724 0 0
725725 0.828427 0.0307670
726726 0 0
727727 37.2947i 1.38319i 0.722288 + 0.691593i 0.243091π0.243091\pi
−0.722288 + 0.691593i 0.756909π0.756909\pi
728728 0 0
729729 10.8995 24.7022i 0.403685 0.914898i
730730 0 0
731731 36.5838i 1.35310i
732732 0 0
733733 36.7985i 1.35918i 0.733591 + 0.679591i 0.237843π0.237843\pi
−0.733591 + 0.679591i 0.762157π0.762157\pi
734734 0 0
735735 −6.62724 7.61521i −0.244449 0.280891i
736736 0 0
737737 9.00127i 0.331566i
738738 0 0
739739 31.6090 1.16275 0.581377 0.813634i 0.302514π-0.302514\pi
0.581377 + 0.813634i 0.302514π0.302514\pi
740740 0 0
741741 7.31371 6.36486i 0.268676 0.233819i
742742 0 0
743743 11.9223 0.437388 0.218694 0.975793i 0.429820π-0.429820\pi
0.218694 + 0.975793i 0.429820π0.429820\pi
744744 0 0
745745 13.3137 0.487777
746746 0 0
747747 29.7250 + 4.14386i 1.08758 + 0.151616i
748748 0 0
749749 −9.85786 −0.360199
750750 0 0
751751 24.6005i 0.897686i 0.893611 + 0.448843i 0.148164π0.148164\pi
−0.893611 + 0.448843i 0.851836π0.851836\pi
752752 0 0
753753 24.4853 21.3087i 0.892293 0.776531i
754754 0 0
755755 4.96362i 0.180645i
756756 0 0
757757 1.74053i 0.0632606i 0.999500 + 0.0316303i 0.0100699π0.0100699\pi
−0.999500 + 0.0316303i 0.989930π0.989930\pi
758758 0 0
759759 −15.5286 + 13.5140i −0.563652 + 0.490526i
760760 0 0
761761 28.6931i 1.04012i 0.854129 + 0.520062i 0.174091π0.174091\pi
−0.854129 + 0.520062i 0.825909π0.825909\pi
762762 0 0
763763 −2.66428 −0.0964536
764764 0 0
765765 −12.4853 1.74053i −0.451406 0.0629289i
766766 0 0
767767 18.1929 0.656907
768768 0 0
769769 12.3431 0.445105 0.222553 0.974921i 0.428561π-0.428561\pi
0.222553 + 0.974921i 0.428561π0.428561\pi
770770 0 0
771771 25.5670 22.2500i 0.920773 0.801315i
772772 0 0
773773 −28.6274 −1.02966 −0.514828 0.857293i 0.672144π-0.672144\pi
−0.514828 + 0.857293i 0.672144π0.672144\pi
774774 0 0
775775 3.69552i 0.132747i
776776 0 0
777777 12.4853 + 14.3465i 0.447907 + 0.514679i
778778 0 0
779779 7.91630i 0.283631i
780780 0 0
781781 4.07831i 0.145933i
782782 0 0
783783 3.60625 2.35049i 0.128877 0.0839998i
784784 0 0
785785 15.0675i 0.537782i
786786 0 0
787787 −15.9188 −0.567443 −0.283721 0.958907i 0.591569π-0.591569\pi
−0.283721 + 0.958907i 0.591569π0.591569\pi
788788 0 0
789789 −33.3553 38.3278i −1.18748 1.36451i
790790 0 0
791791 −13.6447 −0.485148
792792 0 0
793793 −18.9117 −0.671574
794794 0 0
795795 −2.27411 2.61313i −0.0806543 0.0926780i
796796 0 0
797797 26.0000 0.920967 0.460484 0.887668i 0.347676π-0.347676\pi
0.460484 + 0.887668i 0.347676π0.347676\pi
798798 0 0
799799 42.1814i 1.49227i
800800 0 0
801801 −10.3431 1.44190i −0.365457 0.0509470i
802802 0 0
803803 7.91630i 0.279360i
804804 0 0
805805 5.94253i 0.209447i
806806 0 0
807807 3.05446 + 3.50981i 0.107522 + 0.123551i
808808 0 0
809809 1.44190i 0.0506945i −0.999679 0.0253473i 0.991931π-0.991931\pi
0.999679 0.0253473i 0.00806915π-0.00806915\pi
810810 0 0
811811 2.43573 0.0855299 0.0427649 0.999085i 0.486383π-0.486383\pi
0.0427649 + 0.999085i 0.486383π0.486383\pi
812812 0 0
813813 41.7990 36.3762i 1.46595 1.27577i
814814 0 0
815815 −2.27411 −0.0796586
816816 0 0
817817 28.0000 0.979596
818818 0 0
819819 −0.780351 + 5.59767i −0.0272677 + 0.195598i
820820 0 0
821821 18.0000 0.628204 0.314102 0.949389i 0.398297π-0.398297\pi
0.314102 + 0.949389i 0.398297π0.398297\pi
822822 0 0
823823 11.5349i 0.402081i 0.979583 + 0.201041i 0.0644323π0.0644323\pi
−0.979583 + 0.201041i 0.935568π0.935568\pi
824824 0 0
825825 −2.82843 + 2.46148i −0.0984732 + 0.0856977i
826826 0 0
827827 51.8142i 1.80176i −0.434073 0.900878i 0.642924π-0.642924\pi
0.434073 0.900878i 0.357076π-0.357076\pi
828828 0 0
829829 26.2316i 0.911062i 0.890220 + 0.455531i 0.150551π0.150551\pi
−0.890220 + 0.455531i 0.849449π0.849449\pi
830830 0 0
831831 2.27411 1.97908i 0.0788880 0.0686534i
832832 0 0
833833 24.4911i 0.848566i
834834 0 0
835835 8.15447 0.282197
836836 0 0
837837 10.4853 + 16.0871i 0.362424 + 0.556051i
838838 0 0
839839 −46.5858 −1.60832 −0.804160 0.594413i 0.797384π-0.797384\pi
−0.804160 + 0.594413i 0.797384π0.797384\pi
840840 0 0
841841 −28.3137 −0.976335
842842 0 0
843843 12.3125 10.7151i 0.424065 0.369049i
844844 0 0
845845 9.97056 0.342998
846846 0 0
847847 6.83391i 0.234816i
848848 0 0
849849 22.3848 + 25.7218i 0.768244 + 0.882771i
850850 0 0
851851 55.6954i 1.90921i
852852 0 0
853853 22.0296i 0.754279i −0.926156 0.377140i 0.876908π-0.876908\pi
0.926156 0.377140i 0.123092π-0.123092\pi
854854 0 0
855855 −1.33214 + 9.55582i −0.0455583 + 0.326802i
856856 0 0
857857 21.6073i 0.738091i 0.929411 + 0.369045i 0.120315π0.120315\pi
−0.929411 + 0.369045i 0.879685π0.879685\pi
858858 0 0
859859 36.9375 1.26029 0.630146 0.776476i 0.282995π-0.282995\pi
0.630146 + 0.776476i 0.282995π0.282995\pi
860860 0 0
861861 −3.02944 3.48106i −0.103243 0.118634i
862862 0 0
863863 28.2313 0.961004 0.480502 0.876994i 0.340455π-0.340455\pi
0.480502 + 0.876994i 0.340455π0.340455\pi
864864 0 0
865865 −21.3137 −0.724688
866866 0 0
867867 0.746879 + 0.858221i 0.0253653 + 0.0291467i
868868 0 0
869869 25.9411 0.879992
870870 0 0
871871 7.23719i 0.245223i
872872 0 0
873873 −3.85786 + 27.6735i −0.130569 + 0.936607i
874874 0 0
875875 1.08239i 0.0365915i
876876 0 0
877877 12.1837i 0.411414i −0.978614 0.205707i 0.934051π-0.934051\pi
0.978614 0.205707i 0.0659494π-0.0659494\pi
878878 0 0
879879 6.04198 + 6.94269i 0.203791 + 0.234171i
880880 0 0
881881 43.0396i 1.45004i 0.688727 + 0.725021i 0.258170π0.258170\pi
−0.688727 + 0.725021i 0.741830π0.741830\pi
882882 0 0
883883 32.5509 1.09543 0.547713 0.836666i 0.315499π-0.315499\pi
0.547713 + 0.836666i 0.315499π0.315499\pi
884884 0 0
885885 −13.6569 + 11.8851i −0.459070 + 0.399512i
886886 0 0
887887 −3.60625 −0.121086 −0.0605430 0.998166i 0.519283π-0.519283\pi
−0.0605430 + 0.998166i 0.519283π0.519283\pi
888888 0 0
889889 9.17157 0.307605
890890 0 0
891891 −5.32857 + 18.7402i −0.178514 + 0.627821i
892892 0 0
893893 −32.2843 −1.08035
894894 0 0
895895 0 0
896896 0 0
897897 12.4853 10.8655i 0.416871 0.362788i
898898 0 0
899899 3.06147i 0.102106i
900900 0 0
901901 8.40401i 0.279978i
902902 0 0
903903 −12.3125 + 10.7151i −0.409735 + 0.356577i
904904 0 0
905905 23.7701i 0.790146i
906906 0 0
907907 44.3117 1.47134 0.735672 0.677338i 0.236866π-0.236866\pi
0.735672 + 0.677338i 0.236866π0.236866\pi
908908 0 0
909909 −0.627417 + 4.50063i −0.0208101 + 0.149277i
910910 0 0
911911 −10.9804 −0.363796 −0.181898 0.983317i 0.558224π-0.558224\pi
−0.181898 + 0.983317i 0.558224π0.558224\pi
912912 0 0
913913 −21.6569 −0.716737
914914 0 0
915915 14.1964 12.3547i 0.469320 0.408432i
916916 0 0
917917 −12.2843 −0.405662
918918 0 0
919919 16.3128i 0.538110i 0.963125 + 0.269055i 0.0867113π0.0867113\pi
−0.963125 + 0.269055i 0.913289π0.913289\pi
920920 0 0
921921 32.7279 + 37.6069i 1.07842 + 1.23919i
922922 0 0
923923 3.27904i 0.107931i
924924 0 0
925925 10.1445i 0.333550i
926926 0 0
927927 58.8983 + 8.21080i 1.93447 + 0.269678i
928928 0 0
929929 44.4815i 1.45939i 0.683772 + 0.729696i 0.260338π0.260338\pi
−0.683772 + 0.729696i 0.739662π0.739662\pi
930930 0 0
931931 18.7447 0.614332
932932 0 0
933933 27.1127 + 31.1546i 0.887630 + 1.01995i
934934 0 0
935935 9.09644 0.297485
936936 0 0
937937 −44.9117 −1.46720 −0.733600 0.679581i 0.762162π-0.762162\pi
−0.733600 + 0.679581i 0.762162π0.762162\pi
938938 0 0
939939 −33.3313 38.3002i −1.08773 1.24988i
940940 0 0
941941 −37.1127 −1.20984 −0.604920 0.796286i 0.706795π-0.706795\pi
−0.604920 + 0.796286i 0.706795π0.706795\pi
942942 0 0
943943 13.5140i 0.440075i
944944 0 0
945945 −3.07107 4.71179i −0.0999018 0.153275i
946946 0 0
947947 10.3756i 0.337161i 0.985688 + 0.168581i 0.0539183π0.0539183\pi
−0.985688 + 0.168581i 0.946082π0.946082\pi
948948 0 0
949949 6.36486i 0.206612i
950950 0 0
951951 19.6866 + 22.6215i 0.638383 + 0.733551i
952952 0 0
953953 53.1842i 1.72280i −0.507923 0.861402i 0.669587π-0.669587\pi
0.507923 0.861402i 0.330413π-0.330413\pi
954954 0 0
955955 −17.4125 −0.563456
956956 0 0
957957 −2.34315 + 2.03916i −0.0757431 + 0.0659165i
958958 0 0
959959 −17.4125 −0.562280
960960 0 0
961961 17.3431 0.559456
962962 0 0
963963 27.0608 + 3.77244i 0.872021 + 0.121565i
964964 0 0
965965 9.31371 0.299819
966966 0 0
967967 14.0711i 0.452496i 0.974070 + 0.226248i 0.0726460π0.0726460\pi
−0.974070 + 0.226248i 0.927354π0.927354\pi
968968 0 0
969969 17.6569 15.3661i 0.567220 0.493631i
970970 0 0
971971 2.16478i 0.0694712i −0.999397 0.0347356i 0.988941π-0.988941\pi
0.999397 0.0347356i 0.0110589π-0.0110589\pi
972972 0 0
973973 3.48106i 0.111598i
974974 0 0
975975 2.27411 1.97908i 0.0728298 0.0633811i
976976 0 0
977977 14.6452i 0.468541i −0.972172 0.234270i 0.924730π-0.924730\pi
0.972172 0.234270i 0.0752701π-0.0752701\pi
978978 0 0
979979 7.53574 0.240843
980980 0 0
981981 7.31371 + 1.01958i 0.233509 + 0.0325526i
982982 0 0
983983 −28.2313 −0.900438 −0.450219 0.892918i 0.648654π-0.648654\pi
−0.450219 + 0.892918i 0.648654π0.648654\pi
984984 0 0
985985 2.00000 0.0637253
986986 0 0
987987 14.1964 12.3547i 0.451878 0.393253i
988988 0 0
989989 47.7990 1.51992
990990 0 0
991991 52.3713i 1.66363i −0.555053 0.831815i 0.687302π-0.687302\pi
0.555053 0.831815i 0.312698π-0.312698\pi
992992 0 0
993993 33.7990 + 38.8376i 1.07258 + 1.23247i
994994 0 0
995995 10.1899i 0.323041i
996996 0 0
997997 22.0296i 0.697685i 0.937181 + 0.348842i 0.113425π0.113425\pi
−0.937181 + 0.348842i 0.886575π0.886575\pi
998998 0 0
999999 −28.7831 44.1605i −0.910656 1.39718i
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.f.191.3 yes 8
3.2 odd 2 1920.2.b.d.191.4 yes 8
4.3 odd 2 inner 1920.2.b.f.191.6 yes 8
8.3 odd 2 1920.2.b.d.191.3 8
8.5 even 2 1920.2.b.d.191.6 yes 8
12.11 even 2 1920.2.b.d.191.5 yes 8
24.5 odd 2 inner 1920.2.b.f.191.5 yes 8
24.11 even 2 inner 1920.2.b.f.191.4 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1920.2.b.d.191.3 8 8.3 odd 2
1920.2.b.d.191.4 yes 8 3.2 odd 2
1920.2.b.d.191.5 yes 8 12.11 even 2
1920.2.b.d.191.6 yes 8 8.5 even 2
1920.2.b.f.191.3 yes 8 1.1 even 1 trivial
1920.2.b.f.191.4 yes 8 24.11 even 2 inner
1920.2.b.f.191.5 yes 8 24.5 odd 2 inner
1920.2.b.f.191.6 yes 8 4.3 odd 2 inner