Properties

Label 1920.2.h.l.1151.4
Level 19201920
Weight 22
Character 1920.1151
Analytic conductor 15.33115.331
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1920,2,Mod(1151,1920)]
 
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, 0, 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("1920.1151");
 
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.h (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: 44
Coefficient field: Q(i,5)\Q(i, \sqrt{5})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+3x2+1 x^{4} + 3x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1151.4
Root 1.61803i1.61803i of defining polynomial
Character χ\chi == 1920.1151
Dual form 1920.2.h.l.1151.3

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+(1.61803+0.618034i)q3+1.00000iq52.00000iq7+(2.23607+2.00000i)q96.47214q11+3.23607q13+(0.618034+1.61803i)q15+5.23607iq170.763932iq19+(1.236073.23607i)q21+8.47214q231.00000q25+(2.38197+4.61803i)q27+0.472136iq29+9.23607iq31+(10.47214.00000i)q33+2.00000q35+5.70820q37+(5.23607+2.00000i)q39+10.4721iq41+3.70820iq43+(2.00000+2.23607i)q45+4.47214q47+3.00000q49+(3.23607+8.47214i)q51+4.47214iq536.47214iq55+(0.4721361.23607i)q572.47214q593.52786q61+(4.000004.47214i)q63+3.23607iq656.76393iq67+(13.7082+5.23607i)q694.00000q71+8.47214q73+(1.618030.618034i)q75+12.9443iq7714.1803iq79+(1.00000+8.94427i)q81+1.70820q835.23607q85+(0.291796+0.763932i)q8710.4721iq896.47214iq91+(5.70820+14.9443i)q93+0.763932q953.52786q97+(14.472112.9443i)q99+O(q100)q+(1.61803 + 0.618034i) q^{3} +1.00000i q^{5} -2.00000i q^{7} +(2.23607 + 2.00000i) q^{9} -6.47214 q^{11} +3.23607 q^{13} +(-0.618034 + 1.61803i) q^{15} +5.23607i q^{17} -0.763932i q^{19} +(1.23607 - 3.23607i) q^{21} +8.47214 q^{23} -1.00000 q^{25} +(2.38197 + 4.61803i) q^{27} +0.472136i q^{29} +9.23607i q^{31} +(-10.4721 - 4.00000i) q^{33} +2.00000 q^{35} +5.70820 q^{37} +(5.23607 + 2.00000i) q^{39} +10.4721i q^{41} +3.70820i q^{43} +(-2.00000 + 2.23607i) q^{45} +4.47214 q^{47} +3.00000 q^{49} +(-3.23607 + 8.47214i) q^{51} +4.47214i q^{53} -6.47214i q^{55} +(0.472136 - 1.23607i) q^{57} -2.47214 q^{59} -3.52786 q^{61} +(4.00000 - 4.47214i) q^{63} +3.23607i q^{65} -6.76393i q^{67} +(13.7082 + 5.23607i) q^{69} -4.00000 q^{71} +8.47214 q^{73} +(-1.61803 - 0.618034i) q^{75} +12.9443i q^{77} -14.1803i q^{79} +(1.00000 + 8.94427i) q^{81} +1.70820 q^{83} -5.23607 q^{85} +(-0.291796 + 0.763932i) q^{87} -10.4721i q^{89} -6.47214i q^{91} +(-5.70820 + 14.9443i) q^{93} +0.763932 q^{95} -3.52786 q^{97} +(-14.4721 - 12.9443i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q38q11+4q13+2q154q21+16q234q25+14q2724q33+8q354q37+12q398q45+12q494q5116q57+8q5932q61+40q99+O(q100) 4 q + 2 q^{3} - 8 q^{11} + 4 q^{13} + 2 q^{15} - 4 q^{21} + 16 q^{23} - 4 q^{25} + 14 q^{27} - 24 q^{33} + 8 q^{35} - 4 q^{37} + 12 q^{39} - 8 q^{45} + 12 q^{49} - 4 q^{51} - 16 q^{57} + 8 q^{59} - 32 q^{61}+ \cdots - 40 q^{99}+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 11 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 1.61803 + 0.618034i 0.934172 + 0.356822i
44 0 0
55 1.00000i 0.447214i
66 0 0
77 2.00000i 0.755929i −0.925820 0.377964i 0.876624π-0.876624\pi
0.925820 0.377964i 0.123376π-0.123376\pi
88 0 0
99 2.23607 + 2.00000i 0.745356 + 0.666667i
1010 0 0
1111 −6.47214 −1.95142 −0.975711 0.219061i 0.929701π-0.929701\pi
−0.975711 + 0.219061i 0.929701π0.929701\pi
1212 0 0
1313 3.23607 0.897524 0.448762 0.893651i 0.351865π-0.351865\pi
0.448762 + 0.893651i 0.351865π0.351865\pi
1414 0 0
1515 −0.618034 + 1.61803i −0.159576 + 0.417775i
1616 0 0
1717 5.23607i 1.26993i 0.772540 + 0.634967i 0.218986π0.218986\pi
−0.772540 + 0.634967i 0.781014π0.781014\pi
1818 0 0
1919 0.763932i 0.175258i −0.996153 0.0876290i 0.972071π-0.972071\pi
0.996153 0.0876290i 0.0279290π-0.0279290\pi
2020 0 0
2121 1.23607 3.23607i 0.269732 0.706168i
2222 0 0
2323 8.47214 1.76656 0.883281 0.468844i 0.155329π-0.155329\pi
0.883281 + 0.468844i 0.155329π0.155329\pi
2424 0 0
2525 −1.00000 −0.200000
2626 0 0
2727 2.38197 + 4.61803i 0.458410 + 0.888741i
2828 0 0
2929 0.472136i 0.0876734i 0.999039 + 0.0438367i 0.0139581π0.0139581\pi
−0.999039 + 0.0438367i 0.986042π0.986042\pi
3030 0 0
3131 9.23607i 1.65885i 0.558620 + 0.829423i 0.311331π0.311331\pi
−0.558620 + 0.829423i 0.688669π0.688669\pi
3232 0 0
3333 −10.4721 4.00000i −1.82296 0.696311i
3434 0 0
3535 2.00000 0.338062
3636 0 0
3737 5.70820 0.938423 0.469211 0.883086i 0.344538π-0.344538\pi
0.469211 + 0.883086i 0.344538π0.344538\pi
3838 0 0
3939 5.23607 + 2.00000i 0.838442 + 0.320256i
4040 0 0
4141 10.4721i 1.63547i 0.575593 + 0.817736i 0.304771π0.304771\pi
−0.575593 + 0.817736i 0.695229π0.695229\pi
4242 0 0
4343 3.70820i 0.565496i 0.959194 + 0.282748i 0.0912460π0.0912460\pi
−0.959194 + 0.282748i 0.908754π0.908754\pi
4444 0 0
4545 −2.00000 + 2.23607i −0.298142 + 0.333333i
4646 0 0
4747 4.47214 0.652328 0.326164 0.945313i 0.394244π-0.394244\pi
0.326164 + 0.945313i 0.394244π0.394244\pi
4848 0 0
4949 3.00000 0.428571
5050 0 0
5151 −3.23607 + 8.47214i −0.453140 + 1.18634i
5252 0 0
5353 4.47214i 0.614295i 0.951662 + 0.307148i 0.0993745π0.0993745\pi
−0.951662 + 0.307148i 0.900625π0.900625\pi
5454 0 0
5555 6.47214i 0.872703i
5656 0 0
5757 0.472136 1.23607i 0.0625359 0.163721i
5858 0 0
5959 −2.47214 −0.321845 −0.160922 0.986967i 0.551447π-0.551447\pi
−0.160922 + 0.986967i 0.551447π0.551447\pi
6060 0 0
6161 −3.52786 −0.451697 −0.225848 0.974162i 0.572515π-0.572515\pi
−0.225848 + 0.974162i 0.572515π0.572515\pi
6262 0 0
6363 4.00000 4.47214i 0.503953 0.563436i
6464 0 0
6565 3.23607i 0.401385i
6666 0 0
6767 6.76393i 0.826346i −0.910653 0.413173i 0.864421π-0.864421\pi
0.910653 0.413173i 0.135579π-0.135579\pi
6868 0 0
6969 13.7082 + 5.23607i 1.65027 + 0.630349i
7070 0 0
7171 −4.00000 −0.474713 −0.237356 0.971423i 0.576281π-0.576281\pi
−0.237356 + 0.971423i 0.576281π0.576281\pi
7272 0 0
7373 8.47214 0.991589 0.495794 0.868440i 0.334877π-0.334877\pi
0.495794 + 0.868440i 0.334877π0.334877\pi
7474 0 0
7575 −1.61803 0.618034i −0.186834 0.0713644i
7676 0 0
7777 12.9443i 1.47514i
7878 0 0
7979 14.1803i 1.59541i −0.603046 0.797706i 0.706046π-0.706046\pi
0.603046 0.797706i 0.293954π-0.293954\pi
8080 0 0
8181 1.00000 + 8.94427i 0.111111 + 0.993808i
8282 0 0
8383 1.70820 0.187500 0.0937499 0.995596i 0.470115π-0.470115\pi
0.0937499 + 0.995596i 0.470115π0.470115\pi
8484 0 0
8585 −5.23607 −0.567931
8686 0 0
8787 −0.291796 + 0.763932i −0.0312838 + 0.0819021i
8888 0 0
8989 10.4721i 1.11004i −0.831836 0.555022i 0.812710π-0.812710\pi
0.831836 0.555022i 0.187290π-0.187290\pi
9090 0 0
9191 6.47214i 0.678464i
9292 0 0
9393 −5.70820 + 14.9443i −0.591913 + 1.54965i
9494 0 0
9595 0.763932 0.0783778
9696 0 0
9797 −3.52786 −0.358200 −0.179100 0.983831i 0.557319π-0.557319\pi
−0.179100 + 0.983831i 0.557319π0.557319\pi
9898 0 0
9999 −14.4721 12.9443i −1.45450 1.30095i
100100 0 0
101101 9.41641i 0.936968i −0.883472 0.468484i 0.844800π-0.844800\pi
0.883472 0.468484i 0.155200π-0.155200\pi
102102 0 0
103103 8.47214i 0.834784i −0.908726 0.417392i 0.862944π-0.862944\pi
0.908726 0.417392i 0.137056π-0.137056\pi
104104 0 0
105105 3.23607 + 1.23607i 0.315808 + 0.120628i
106106 0 0
107107 −8.76393 −0.847241 −0.423621 0.905840i 0.639241π-0.639241\pi
−0.423621 + 0.905840i 0.639241π0.639241\pi
108108 0 0
109109 −18.9443 −1.81453 −0.907266 0.420557i 0.861835π-0.861835\pi
−0.907266 + 0.420557i 0.861835π0.861835\pi
110110 0 0
111111 9.23607 + 3.52786i 0.876649 + 0.334850i
112112 0 0
113113 19.1246i 1.79909i 0.436826 + 0.899546i 0.356103π0.356103\pi
−0.436826 + 0.899546i 0.643897π0.643897\pi
114114 0 0
115115 8.47214i 0.790031i
116116 0 0
117117 7.23607 + 6.47214i 0.668975 + 0.598349i
118118 0 0
119119 10.4721 0.959979
120120 0 0
121121 30.8885 2.80805
122122 0 0
123123 −6.47214 + 16.9443i −0.583573 + 1.52781i
124124 0 0
125125 1.00000i 0.0894427i
126126 0 0
127127 10.0000i 0.887357i −0.896186 0.443678i 0.853673π-0.853673\pi
0.896186 0.443678i 0.146327π-0.146327\pi
128128 0 0
129129 −2.29180 + 6.00000i −0.201781 + 0.528271i
130130 0 0
131131 −13.8885 −1.21345 −0.606724 0.794913i 0.707517π-0.707517\pi
−0.606724 + 0.794913i 0.707517π0.707517\pi
132132 0 0
133133 −1.52786 −0.132483
134134 0 0
135135 −4.61803 + 2.38197i −0.397457 + 0.205007i
136136 0 0
137137 12.6525i 1.08097i −0.841352 0.540487i 0.818240π-0.818240\pi
0.841352 0.540487i 0.181760π-0.181760\pi
138138 0 0
139139 8.18034i 0.693847i 0.937893 + 0.346924i 0.112774π0.112774\pi
−0.937893 + 0.346924i 0.887226π0.887226\pi
140140 0 0
141141 7.23607 + 2.76393i 0.609387 + 0.232765i
142142 0 0
143143 −20.9443 −1.75145
144144 0 0
145145 −0.472136 −0.0392088
146146 0 0
147147 4.85410 + 1.85410i 0.400360 + 0.152924i
148148 0 0
149149 10.0000i 0.819232i 0.912258 + 0.409616i 0.134337π0.134337\pi
−0.912258 + 0.409616i 0.865663π0.865663\pi
150150 0 0
151151 1.23607i 0.100590i 0.998734 + 0.0502949i 0.0160161π0.0160161\pi
−0.998734 + 0.0502949i 0.983984π0.983984\pi
152152 0 0
153153 −10.4721 + 11.7082i −0.846622 + 0.946552i
154154 0 0
155155 −9.23607 −0.741859
156156 0 0
157157 −1.70820 −0.136330 −0.0681648 0.997674i 0.521714π-0.521714\pi
−0.0681648 + 0.997674i 0.521714π0.521714\pi
158158 0 0
159159 −2.76393 + 7.23607i −0.219194 + 0.573858i
160160 0 0
161161 16.9443i 1.33540i
162162 0 0
163163 1.23607i 0.0968163i −0.998828 0.0484082i 0.984585π-0.984585\pi
0.998828 0.0484082i 0.0154148π-0.0154148\pi
164164 0 0
165165 4.00000 10.4721i 0.311400 0.815255i
166166 0 0
167167 14.9443 1.15642 0.578211 0.815887i 0.303751π-0.303751\pi
0.578211 + 0.815887i 0.303751π0.303751\pi
168168 0 0
169169 −2.52786 −0.194451
170170 0 0
171171 1.52786 1.70820i 0.116839 0.130630i
172172 0 0
173173 11.5279i 0.876447i −0.898866 0.438224i 0.855608π-0.855608\pi
0.898866 0.438224i 0.144392π-0.144392\pi
174174 0 0
175175 2.00000i 0.151186i
176176 0 0
177177 −4.00000 1.52786i −0.300658 0.114841i
178178 0 0
179179 10.4721 0.782724 0.391362 0.920237i 0.372004π-0.372004\pi
0.391362 + 0.920237i 0.372004π0.372004\pi
180180 0 0
181181 13.4164 0.997234 0.498617 0.866822i 0.333841π-0.333841\pi
0.498617 + 0.866822i 0.333841π0.333841\pi
182182 0 0
183183 −5.70820 2.18034i −0.421963 0.161175i
184184 0 0
185185 5.70820i 0.419675i
186186 0 0
187187 33.8885i 2.47818i
188188 0 0
189189 9.23607 4.76393i 0.671825 0.346525i
190190 0 0
191191 −5.52786 −0.399982 −0.199991 0.979798i 0.564091π-0.564091\pi
−0.199991 + 0.979798i 0.564091π0.564091\pi
192192 0 0
193193 −14.9443 −1.07571 −0.537856 0.843037i 0.680766π-0.680766\pi
−0.537856 + 0.843037i 0.680766π0.680766\pi
194194 0 0
195195 −2.00000 + 5.23607i −0.143223 + 0.374963i
196196 0 0
197197 10.0000i 0.712470i 0.934396 + 0.356235i 0.115940π0.115940\pi
−0.934396 + 0.356235i 0.884060π0.884060\pi
198198 0 0
199199 4.29180i 0.304237i −0.988362 0.152119i 0.951390π-0.951390\pi
0.988362 0.152119i 0.0486096π-0.0486096\pi
200200 0 0
201201 4.18034 10.9443i 0.294858 0.771949i
202202 0 0
203203 0.944272 0.0662749
204204 0 0
205205 −10.4721 −0.731406
206206 0 0
207207 18.9443 + 16.9443i 1.31672 + 1.17771i
208208 0 0
209209 4.94427i 0.342002i
210210 0 0
211211 13.7082i 0.943712i −0.881676 0.471856i 0.843584π-0.843584\pi
0.881676 0.471856i 0.156416π-0.156416\pi
212212 0 0
213213 −6.47214 2.47214i −0.443463 0.169388i
214214 0 0
215215 −3.70820 −0.252897
216216 0 0
217217 18.4721 1.25397
218218 0 0
219219 13.7082 + 5.23607i 0.926315 + 0.353821i
220220 0 0
221221 16.9443i 1.13980i
222222 0 0
223223 14.9443i 1.00074i −0.865811 0.500371i 0.833197π-0.833197\pi
0.865811 0.500371i 0.166803π-0.166803\pi
224224 0 0
225225 −2.23607 2.00000i −0.149071 0.133333i
226226 0 0
227227 6.29180 0.417601 0.208801 0.977958i 0.433044π-0.433044\pi
0.208801 + 0.977958i 0.433044π0.433044\pi
228228 0 0
229229 2.94427 0.194563 0.0972815 0.995257i 0.468985π-0.468985\pi
0.0972815 + 0.995257i 0.468985π0.468985\pi
230230 0 0
231231 −8.00000 + 20.9443i −0.526361 + 1.37803i
232232 0 0
233233 3.70820i 0.242933i −0.992596 0.121466i 0.961240π-0.961240\pi
0.992596 0.121466i 0.0387596π-0.0387596\pi
234234 0 0
235235 4.47214i 0.291730i
236236 0 0
237237 8.76393 22.9443i 0.569279 1.49039i
238238 0 0
239239 3.41641 0.220989 0.110495 0.993877i 0.464757π-0.464757\pi
0.110495 + 0.993877i 0.464757π0.464757\pi
240240 0 0
241241 5.05573 0.325668 0.162834 0.986653i 0.447936π-0.447936\pi
0.162834 + 0.986653i 0.447936π0.447936\pi
242242 0 0
243243 −3.90983 + 15.0902i −0.250816 + 0.968035i
244244 0 0
245245 3.00000i 0.191663i
246246 0 0
247247 2.47214i 0.157298i
248248 0 0
249249 2.76393 + 1.05573i 0.175157 + 0.0669040i
250250 0 0
251251 1.52786 0.0964379 0.0482190 0.998837i 0.484645π-0.484645\pi
0.0482190 + 0.998837i 0.484645π0.484645\pi
252252 0 0
253253 −54.8328 −3.44731
254254 0 0
255255 −8.47214 3.23607i −0.530546 0.202650i
256256 0 0
257257 1.23607i 0.0771038i −0.999257 0.0385519i 0.987726π-0.987726\pi
0.999257 0.0385519i 0.0122745π-0.0122745\pi
258258 0 0
259259 11.4164i 0.709381i
260260 0 0
261261 −0.944272 + 1.05573i −0.0584490 + 0.0653479i
262262 0 0
263263 −11.8885 −0.733079 −0.366540 0.930402i 0.619458π-0.619458\pi
−0.366540 + 0.930402i 0.619458π0.619458\pi
264264 0 0
265265 −4.47214 −0.274721
266266 0 0
267267 6.47214 16.9443i 0.396088 1.03697i
268268 0 0
269269 14.0000i 0.853595i 0.904347 + 0.426798i 0.140358π0.140358\pi
−0.904347 + 0.426798i 0.859642π0.859642\pi
270270 0 0
271271 5.81966i 0.353519i −0.984254 0.176760i 0.943438π-0.943438\pi
0.984254 0.176760i 0.0565615π-0.0565615\pi
272272 0 0
273273 4.00000 10.4721i 0.242091 0.633803i
274274 0 0
275275 6.47214 0.390284
276276 0 0
277277 18.6525 1.12072 0.560359 0.828250i 0.310663π-0.310663\pi
0.560359 + 0.828250i 0.310663π0.310663\pi
278278 0 0
279279 −18.4721 + 20.6525i −1.10590 + 1.23643i
280280 0 0
281281 14.4721i 0.863335i 0.902033 + 0.431668i 0.142075π0.142075\pi
−0.902033 + 0.431668i 0.857925π0.857925\pi
282282 0 0
283283 6.76393i 0.402074i −0.979584 0.201037i 0.935569π-0.935569\pi
0.979584 0.201037i 0.0644312π-0.0644312\pi
284284 0 0
285285 1.23607 + 0.472136i 0.0732183 + 0.0279669i
286286 0 0
287287 20.9443 1.23630
288288 0 0
289289 −10.4164 −0.612730
290290 0 0
291291 −5.70820 2.18034i −0.334621 0.127814i
292292 0 0
293293 2.58359i 0.150935i −0.997148 0.0754675i 0.975955π-0.975955\pi
0.997148 0.0754675i 0.0240449π-0.0240449\pi
294294 0 0
295295 2.47214i 0.143933i
296296 0 0
297297 −15.4164 29.8885i −0.894551 1.73431i
298298 0 0
299299 27.4164 1.58553
300300 0 0
301301 7.41641 0.427475
302302 0 0
303303 5.81966 15.2361i 0.334331 0.875289i
304304 0 0
305305 3.52786i 0.202005i
306306 0 0
307307 23.1246i 1.31979i 0.751357 + 0.659896i 0.229400π0.229400\pi
−0.751357 + 0.659896i 0.770600π0.770600\pi
308308 0 0
309309 5.23607 13.7082i 0.297870 0.779832i
310310 0 0
311311 20.0000 1.13410 0.567048 0.823685i 0.308085π-0.308085\pi
0.567048 + 0.823685i 0.308085π0.308085\pi
312312 0 0
313313 −11.8885 −0.671980 −0.335990 0.941866i 0.609071π-0.609071\pi
−0.335990 + 0.941866i 0.609071π0.609071\pi
314314 0 0
315315 4.47214 + 4.00000i 0.251976 + 0.225374i
316316 0 0
317317 27.8885i 1.56638i −0.621785 0.783188i 0.713592π-0.713592\pi
0.621785 0.783188i 0.286408π-0.286408\pi
318318 0 0
319319 3.05573i 0.171088i
320320 0 0
321321 −14.1803 5.41641i −0.791469 0.302314i
322322 0 0
323323 4.00000 0.222566
324324 0 0
325325 −3.23607 −0.179505
326326 0 0
327327 −30.6525 11.7082i −1.69509 0.647465i
328328 0 0
329329 8.94427i 0.493114i
330330 0 0
331331 7.23607i 0.397730i 0.980027 + 0.198865i 0.0637256π0.0637256\pi
−0.980027 + 0.198865i 0.936274π0.936274\pi
332332 0 0
333333 12.7639 + 11.4164i 0.699459 + 0.625615i
334334 0 0
335335 6.76393 0.369553
336336 0 0
337337 16.4721 0.897294 0.448647 0.893709i 0.351906π-0.351906\pi
0.448647 + 0.893709i 0.351906π0.351906\pi
338338 0 0
339339 −11.8197 + 30.9443i −0.641956 + 1.68066i
340340 0 0
341341 59.7771i 3.23711i
342342 0 0
343343 20.0000i 1.07990i
344344 0 0
345345 −5.23607 + 13.7082i −0.281900 + 0.738025i
346346 0 0
347347 −15.2361 −0.817915 −0.408957 0.912553i 0.634108π-0.634108\pi
−0.408957 + 0.912553i 0.634108π0.634108\pi
348348 0 0
349349 34.9443 1.87052 0.935262 0.353956i 0.115164π-0.115164\pi
0.935262 + 0.353956i 0.115164π0.115164\pi
350350 0 0
351351 7.70820 + 14.9443i 0.411433 + 0.797666i
352352 0 0
353353 9.23607i 0.491586i 0.969322 + 0.245793i 0.0790484π0.0790484\pi
−0.969322 + 0.245793i 0.920952π0.920952\pi
354354 0 0
355355 4.00000i 0.212298i
356356 0 0
357357 16.9443 + 6.47214i 0.896786 + 0.342542i
358358 0 0
359359 4.58359 0.241913 0.120956 0.992658i 0.461404π-0.461404\pi
0.120956 + 0.992658i 0.461404π0.461404\pi
360360 0 0
361361 18.4164 0.969285
362362 0 0
363363 49.9787 + 19.0902i 2.62320 + 1.00197i
364364 0 0
365365 8.47214i 0.443452i
366366 0 0
367367 35.3050i 1.84290i 0.388493 + 0.921452i 0.372996π0.372996\pi
−0.388493 + 0.921452i 0.627004π0.627004\pi
368368 0 0
369369 −20.9443 + 23.4164i −1.09032 + 1.21901i
370370 0 0
371371 8.94427 0.464363
372372 0 0
373373 −11.5967 −0.600457 −0.300228 0.953867i 0.597063π-0.597063\pi
−0.300228 + 0.953867i 0.597063π0.597063\pi
374374 0 0
375375 0.618034 1.61803i 0.0319151 0.0835549i
376376 0 0
377377 1.52786i 0.0786890i
378378 0 0
379379 21.7082i 1.11508i −0.830152 0.557538i 0.811746π-0.811746\pi
0.830152 0.557538i 0.188254π-0.188254\pi
380380 0 0
381381 6.18034 16.1803i 0.316628 0.828944i
382382 0 0
383383 −14.9443 −0.763617 −0.381808 0.924242i 0.624699π-0.624699\pi
−0.381808 + 0.924242i 0.624699π0.624699\pi
384384 0 0
385385 −12.9443 −0.659701
386386 0 0
387387 −7.41641 + 8.29180i −0.376997 + 0.421496i
388388 0 0
389389 14.9443i 0.757705i −0.925457 0.378852i 0.876319π-0.876319\pi
0.925457 0.378852i 0.123681π-0.123681\pi
390390 0 0
391391 44.3607i 2.24342i
392392 0 0
393393 −22.4721 8.58359i −1.13357 0.432985i
394394 0 0
395395 14.1803 0.713490
396396 0 0
397397 −20.1803 −1.01282 −0.506411 0.862292i 0.669028π-0.669028\pi
−0.506411 + 0.862292i 0.669028π0.669028\pi
398398 0 0
399399 −2.47214 0.944272i −0.123762 0.0472727i
400400 0 0
401401 18.8328i 0.940466i −0.882542 0.470233i 0.844170π-0.844170\pi
0.882542 0.470233i 0.155830π-0.155830\pi
402402 0 0
403403 29.8885i 1.48885i
404404 0 0
405405 −8.94427 + 1.00000i −0.444444 + 0.0496904i
406406 0 0
407407 −36.9443 −1.83126
408408 0 0
409409 2.58359 0.127750 0.0638752 0.997958i 0.479654π-0.479654\pi
0.0638752 + 0.997958i 0.479654π0.479654\pi
410410 0 0
411411 7.81966 20.4721i 0.385715 1.00982i
412412 0 0
413413 4.94427i 0.243292i
414414 0 0
415415 1.70820i 0.0838524i
416416 0 0
417417 −5.05573 + 13.2361i −0.247580 + 0.648173i
418418 0 0
419419 19.0557 0.930933 0.465467 0.885065i 0.345887π-0.345887\pi
0.465467 + 0.885065i 0.345887π0.345887\pi
420420 0 0
421421 −23.3050 −1.13581 −0.567907 0.823093i 0.692247π-0.692247\pi
−0.567907 + 0.823093i 0.692247π0.692247\pi
422422 0 0
423423 10.0000 + 8.94427i 0.486217 + 0.434885i
424424 0 0
425425 5.23607i 0.253987i
426426 0 0
427427 7.05573i 0.341451i
428428 0 0
429429 −33.8885 12.9443i −1.63615 0.624955i
430430 0 0
431431 −28.0000 −1.34871 −0.674356 0.738406i 0.735579π-0.735579\pi
−0.674356 + 0.738406i 0.735579π0.735579\pi
432432 0 0
433433 −26.3607 −1.26681 −0.633407 0.773819i 0.718344π-0.718344\pi
−0.633407 + 0.773819i 0.718344π0.718344\pi
434434 0 0
435435 −0.763932 0.291796i −0.0366277 0.0139906i
436436 0 0
437437 6.47214i 0.309604i
438438 0 0
439439 24.6525i 1.17660i 0.808643 + 0.588299i 0.200202π0.200202\pi
−0.808643 + 0.588299i 0.799798π0.799798\pi
440440 0 0
441441 6.70820 + 6.00000i 0.319438 + 0.285714i
442442 0 0
443443 −1.34752 −0.0640228 −0.0320114 0.999488i 0.510191π-0.510191\pi
−0.0320114 + 0.999488i 0.510191π0.510191\pi
444444 0 0
445445 10.4721 0.496427
446446 0 0
447447 −6.18034 + 16.1803i −0.292320 + 0.765304i
448448 0 0
449449 36.9443i 1.74351i −0.489944 0.871754i 0.662983π-0.662983\pi
0.489944 0.871754i 0.337017π-0.337017\pi
450450 0 0
451451 67.7771i 3.19150i
452452 0 0
453453 −0.763932 + 2.00000i −0.0358927 + 0.0939682i
454454 0 0
455455 6.47214 0.303418
456456 0 0
457457 2.58359 0.120855 0.0604277 0.998173i 0.480754π-0.480754\pi
0.0604277 + 0.998173i 0.480754π0.480754\pi
458458 0 0
459459 −24.1803 + 12.4721i −1.12864 + 0.582149i
460460 0 0
461461 0.472136i 0.0219896i 0.999940 + 0.0109948i 0.00349982π0.00349982\pi
−0.999940 + 0.0109948i 0.996500π0.996500\pi
462462 0 0
463463 26.3607i 1.22508i −0.790438 0.612542i 0.790147π-0.790147\pi
0.790438 0.612542i 0.209853π-0.209853\pi
464464 0 0
465465 −14.9443 5.70820i −0.693024 0.264712i
466466 0 0
467467 34.6525 1.60353 0.801763 0.597643i 0.203896π-0.203896\pi
0.801763 + 0.597643i 0.203896π0.203896\pi
468468 0 0
469469 −13.5279 −0.624659
470470 0 0
471471 −2.76393 1.05573i −0.127355 0.0486454i
472472 0 0
473473 24.0000i 1.10352i
474474 0 0
475475 0.763932i 0.0350516i
476476 0 0
477477 −8.94427 + 10.0000i −0.409530 + 0.457869i
478478 0 0
479479 −32.3607 −1.47860 −0.739299 0.673378i 0.764843π-0.764843\pi
−0.739299 + 0.673378i 0.764843π0.764843\pi
480480 0 0
481481 18.4721 0.842257
482482 0 0
483483 10.4721 27.4164i 0.476499 1.24749i
484484 0 0
485485 3.52786i 0.160192i
486486 0 0
487487 16.4721i 0.746424i −0.927746 0.373212i 0.878256π-0.878256\pi
0.927746 0.373212i 0.121744π-0.121744\pi
488488 0 0
489489 0.763932 2.00000i 0.0345462 0.0904431i
490490 0 0
491491 −20.0000 −0.902587 −0.451294 0.892375i 0.649037π-0.649037\pi
−0.451294 + 0.892375i 0.649037π0.649037\pi
492492 0 0
493493 −2.47214 −0.111339
494494 0 0
495495 12.9443 14.4721i 0.581802 0.650474i
496496 0 0
497497 8.00000i 0.358849i
498498 0 0
499499 17.7082i 0.792728i −0.918093 0.396364i 0.870272π-0.870272\pi
0.918093 0.396364i 0.129728π-0.129728\pi
500500 0 0
501501 24.1803 + 9.23607i 1.08030 + 0.412637i
502502 0 0
503503 −11.8885 −0.530084 −0.265042 0.964237i 0.585386π-0.585386\pi
−0.265042 + 0.964237i 0.585386π0.585386\pi
504504 0 0
505505 9.41641 0.419025
506506 0 0
507507 −4.09017 1.56231i −0.181651 0.0693844i
508508 0 0
509509 31.3050i 1.38757i −0.720183 0.693784i 0.755942π-0.755942\pi
0.720183 0.693784i 0.244058π-0.244058\pi
510510 0 0
511511 16.9443i 0.749570i
512512 0 0
513513 3.52786 1.81966i 0.155759 0.0803400i
514514 0 0
515515 8.47214 0.373327
516516 0 0
517517 −28.9443 −1.27297
518518 0 0
519519 7.12461 18.6525i 0.312736 0.818753i
520520 0 0
521521 20.0000i 0.876216i 0.898922 + 0.438108i 0.144351π0.144351\pi
−0.898922 + 0.438108i 0.855649π0.855649\pi
522522 0 0
523523 12.6525i 0.553254i 0.960977 + 0.276627i 0.0892167π0.0892167\pi
−0.960977 + 0.276627i 0.910783π0.910783\pi
524524 0 0
525525 −1.23607 + 3.23607i −0.0539464 + 0.141234i
526526 0 0
527527 −48.3607 −2.10662
528528 0 0
529529 48.7771 2.12074
530530 0 0
531531 −5.52786 4.94427i −0.239889 0.214563i
532532 0 0
533533 33.8885i 1.46788i
534534 0 0
535535 8.76393i 0.378898i
536536 0 0
537537 16.9443 + 6.47214i 0.731199 + 0.279293i
538538 0 0
539539 −19.4164 −0.836324
540540 0 0
541541 26.3607 1.13333 0.566667 0.823947i 0.308233π-0.308233\pi
0.566667 + 0.823947i 0.308233π0.308233\pi
542542 0 0
543543 21.7082 + 8.29180i 0.931588 + 0.355835i
544544 0 0
545545 18.9443i 0.811483i
546546 0 0
547547 32.0689i 1.37117i −0.727994 0.685583i 0.759547π-0.759547\pi
0.727994 0.685583i 0.240453π-0.240453\pi
548548 0 0
549549 −7.88854 7.05573i −0.336675 0.301131i
550550 0 0
551551 0.360680 0.0153655
552552 0 0
553553 −28.3607 −1.20602
554554 0 0
555555 −3.52786 + 9.23607i −0.149749 + 0.392049i
556556 0 0
557557 36.2492i 1.53593i −0.640492 0.767964i 0.721270π-0.721270\pi
0.640492 0.767964i 0.278730π-0.278730\pi
558558 0 0
559559 12.0000i 0.507546i
560560 0 0
561561 20.9443 54.8328i 0.884268 2.31504i
562562 0 0
563563 14.0689 0.592933 0.296466 0.955043i 0.404192π-0.404192\pi
0.296466 + 0.955043i 0.404192π0.404192\pi
564564 0 0
565565 −19.1246 −0.804578
566566 0 0
567567 17.8885 2.00000i 0.751248 0.0839921i
568568 0 0
569569 36.9443i 1.54878i −0.632706 0.774392i 0.718056π-0.718056\pi
0.632706 0.774392i 0.281944π-0.281944\pi
570570 0 0
571571 2.65248i 0.111003i −0.998459 0.0555013i 0.982324π-0.982324\pi
0.998459 0.0555013i 0.0176757π-0.0176757\pi
572572 0 0
573573 −8.94427 3.41641i −0.373652 0.142722i
574574 0 0
575575 −8.47214 −0.353312
576576 0 0
577577 34.3607 1.43045 0.715227 0.698892i 0.246323π-0.246323\pi
0.715227 + 0.698892i 0.246323π0.246323\pi
578578 0 0
579579 −24.1803 9.23607i −1.00490 0.383838i
580580 0 0
581581 3.41641i 0.141736i
582582 0 0
583583 28.9443i 1.19875i
584584 0 0
585585 −6.47214 + 7.23607i −0.267590 + 0.299175i
586586 0 0
587587 −18.6525 −0.769870 −0.384935 0.922944i 0.625776π-0.625776\pi
−0.384935 + 0.922944i 0.625776π0.625776\pi
588588 0 0
589589 7.05573 0.290726
590590 0 0
591591 −6.18034 + 16.1803i −0.254225 + 0.665570i
592592 0 0
593593 9.23607i 0.379280i 0.981854 + 0.189640i 0.0607321π0.0607321\pi
−0.981854 + 0.189640i 0.939268π0.939268\pi
594594 0 0
595595 10.4721i 0.429316i
596596 0 0
597597 2.65248 6.94427i 0.108559 0.284210i
598598 0 0
599599 43.4164 1.77395 0.886973 0.461821i 0.152804π-0.152804\pi
0.886973 + 0.461821i 0.152804π0.152804\pi
600600 0 0
601601 −44.4721 −1.81406 −0.907028 0.421070i 0.861655π-0.861655\pi
−0.907028 + 0.421070i 0.861655π0.861655\pi
602602 0 0
603603 13.5279 15.1246i 0.550897 0.615922i
604604 0 0
605605 30.8885i 1.25580i
606606 0 0
607607 12.4721i 0.506228i 0.967436 + 0.253114i 0.0814548π0.0814548\pi
−0.967436 + 0.253114i 0.918545π0.918545\pi
608608 0 0
609609 1.52786 + 0.583592i 0.0619122 + 0.0236483i
610610 0 0
611611 14.4721 0.585480
612612 0 0
613613 −15.2361 −0.615379 −0.307689 0.951487i 0.599556π-0.599556\pi
−0.307689 + 0.951487i 0.599556π0.599556\pi
614614 0 0
615615 −16.9443 6.47214i −0.683259 0.260982i
616616 0 0
617617 1.23607i 0.0497622i −0.999690 0.0248811i 0.992079π-0.992079\pi
0.999690 0.0248811i 0.00792072π-0.00792072\pi
618618 0 0
619619 1.34752i 0.0541616i 0.999633 + 0.0270808i 0.00862114π0.00862114\pi
−0.999633 + 0.0270808i 0.991379π0.991379\pi
620620 0 0
621621 20.1803 + 39.1246i 0.809809 + 1.57002i
622622 0 0
623623 −20.9443 −0.839115
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 −3.05573 + 8.00000i −0.122034 + 0.319489i
628628 0 0
629629 29.8885i 1.19173i
630630 0 0
631631 15.7082i 0.625334i −0.949863 0.312667i 0.898778π-0.898778\pi
0.949863 0.312667i 0.101222π-0.101222\pi
632632 0 0
633633 8.47214 22.1803i 0.336737 0.881589i
634634 0 0
635635 10.0000 0.396838
636636 0 0
637637 9.70820 0.384653
638638 0 0
639639 −8.94427 8.00000i −0.353830 0.316475i
640640 0 0
641641 25.3050i 0.999485i −0.866174 0.499743i 0.833428π-0.833428\pi
0.866174 0.499743i 0.166572π-0.166572\pi
642642 0 0
643643 19.7082i 0.777216i 0.921403 + 0.388608i 0.127044π0.127044\pi
−0.921403 + 0.388608i 0.872956π0.872956\pi
644644 0 0
645645 −6.00000 2.29180i −0.236250 0.0902394i
646646 0 0
647647 35.8885 1.41092 0.705462 0.708748i 0.250739π-0.250739\pi
0.705462 + 0.708748i 0.250739π0.250739\pi
648648 0 0
649649 16.0000 0.628055
650650 0 0
651651 29.8885 + 11.4164i 1.17142 + 0.447444i
652652 0 0
653653 36.4721i 1.42726i −0.700520 0.713632i 0.747049π-0.747049\pi
0.700520 0.713632i 0.252951π-0.252951\pi
654654 0 0
655655 13.8885i 0.542670i
656656 0 0
657657 18.9443 + 16.9443i 0.739086 + 0.661059i
658658 0 0
659659 −5.52786 −0.215335 −0.107668 0.994187i 0.534338π-0.534338\pi
−0.107668 + 0.994187i 0.534338π0.534338\pi
660660 0 0
661661 31.5279 1.22629 0.613146 0.789970i 0.289904π-0.289904\pi
0.613146 + 0.789970i 0.289904π0.289904\pi
662662 0 0
663663 −10.4721 + 27.4164i −0.406704 + 1.06477i
664664 0 0
665665 1.52786i 0.0592480i
666666 0 0
667667 4.00000i 0.154881i
668668 0 0
669669 9.23607 24.1803i 0.357087 0.934866i
670670 0 0
671671 22.8328 0.881451
672672 0 0
673673 9.41641 0.362976 0.181488 0.983393i 0.441909π-0.441909\pi
0.181488 + 0.983393i 0.441909π0.441909\pi
674674 0 0
675675 −2.38197 4.61803i −0.0916819 0.177748i
676676 0 0
677677 30.3607i 1.16686i 0.812165 + 0.583428i 0.198289π0.198289\pi
−0.812165 + 0.583428i 0.801711π0.801711\pi
678678 0 0
679679 7.05573i 0.270774i
680680 0 0
681681 10.1803 + 3.88854i 0.390111 + 0.149009i
682682 0 0
683683 −32.7639 −1.25368 −0.626839 0.779149i 0.715651π-0.715651\pi
−0.626839 + 0.779149i 0.715651π0.715651\pi
684684 0 0
685685 12.6525 0.483426
686686 0 0
687687 4.76393 + 1.81966i 0.181755 + 0.0694244i
688688 0 0
689689 14.4721i 0.551344i
690690 0 0
691691 34.0689i 1.29604i 0.761623 + 0.648021i 0.224403π0.224403\pi
−0.761623 + 0.648021i 0.775597π0.775597\pi
692692 0 0
693693 −25.8885 + 28.9443i −0.983424 + 1.09950i
694694 0 0
695695 −8.18034 −0.310298
696696 0 0
697697 −54.8328 −2.07694
698698 0 0
699699 2.29180 6.00000i 0.0866837 0.226941i
700700 0 0
701701 35.8885i 1.35549i 0.735296 + 0.677746i 0.237043π0.237043\pi
−0.735296 + 0.677746i 0.762957π0.762957\pi
702702 0 0
703703 4.36068i 0.164466i
704704 0 0
705705 −2.76393 + 7.23607i −0.104096 + 0.272526i
706706 0 0
707707 −18.8328 −0.708281
708708 0 0
709709 −10.0000 −0.375558 −0.187779 0.982211i 0.560129π-0.560129\pi
−0.187779 + 0.982211i 0.560129π0.560129\pi
710710 0 0
711711 28.3607 31.7082i 1.06361 1.18915i
712712 0 0
713713 78.2492i 2.93046i
714714 0 0
715715 20.9443i 0.783271i
716716 0 0
717717 5.52786 + 2.11146i 0.206442 + 0.0788538i
718718 0 0
719719 36.9443 1.37779 0.688894 0.724862i 0.258096π-0.258096\pi
0.688894 + 0.724862i 0.258096π0.258096\pi
720720 0 0
721721 −16.9443 −0.631038
722722 0 0
723723 8.18034 + 3.12461i 0.304230 + 0.116206i
724724 0 0
725725 0.472136i 0.0175347i
726726 0 0
727727 49.4164i 1.83275i 0.400317 + 0.916377i 0.368900π0.368900\pi
−0.400317 + 0.916377i 0.631100π0.631100\pi
728728 0 0
729729 −15.6525 + 22.0000i −0.579721 + 0.814815i
730730 0 0
731731 −19.4164 −0.718142
732732 0 0
733733 8.76393 0.323703 0.161852 0.986815i 0.448253π-0.448253\pi
0.161852 + 0.986815i 0.448253π0.448253\pi
734734 0 0
735735 −1.85410 + 4.85410i −0.0683896 + 0.179046i
736736 0 0
737737 43.7771i 1.61255i
738738 0 0
739739 30.6525i 1.12757i −0.825922 0.563785i 0.809345π-0.809345\pi
0.825922 0.563785i 0.190655π-0.190655\pi
740740 0 0
741741 1.52786 4.00000i 0.0561275 0.146944i
742742 0 0
743743 −33.4164 −1.22593 −0.612965 0.790110i 0.710023π-0.710023\pi
−0.612965 + 0.790110i 0.710023π0.710023\pi
744744 0 0
745745 −10.0000 −0.366372
746746 0 0
747747 3.81966 + 3.41641i 0.139754 + 0.125000i
748748 0 0
749749 17.5279i 0.640454i
750750 0 0
751751 16.0689i 0.586362i 0.956057 + 0.293181i 0.0947138π0.0947138\pi
−0.956057 + 0.293181i 0.905286π0.905286\pi
752752 0 0
753753 2.47214 + 0.944272i 0.0900896 + 0.0344112i
754754 0 0
755755 −1.23607 −0.0449851
756756 0 0
757757 7.59675 0.276108 0.138054 0.990425i 0.455915π-0.455915\pi
0.138054 + 0.990425i 0.455915π0.455915\pi
758758 0 0
759759 −88.7214 33.8885i −3.22038 1.23008i
760760 0 0
761761 20.0000i 0.724999i −0.931984 0.362500i 0.881923π-0.881923\pi
0.931984 0.362500i 0.118077π-0.118077\pi
762762 0 0
763763 37.8885i 1.37166i
764764 0 0
765765 −11.7082 10.4721i −0.423311 0.378621i
766766 0 0
767767 −8.00000 −0.288863
768768 0 0
769769 14.3607 0.517859 0.258930 0.965896i 0.416630π-0.416630\pi
0.258930 + 0.965896i 0.416630π0.416630\pi
770770 0 0
771771 0.763932 2.00000i 0.0275123 0.0720282i
772772 0 0
773773 46.0000i 1.65451i −0.561830 0.827253i 0.689903π-0.689903\pi
0.561830 0.827253i 0.310097π-0.310097\pi
774774 0 0
775775 9.23607i 0.331769i
776776 0 0
777777 7.05573 18.4721i 0.253123 0.662684i
778778 0 0
779779 8.00000 0.286630
780780 0 0
781781 25.8885 0.926365
782782 0 0
783783 −2.18034 + 1.12461i −0.0779190 + 0.0401903i
784784 0 0
785785 1.70820i 0.0609684i
786786 0 0
787787 7.70820i 0.274768i 0.990518 + 0.137384i 0.0438694π0.0438694\pi
−0.990518 + 0.137384i 0.956131π0.956131\pi
788788 0 0
789789 −19.2361 7.34752i −0.684822 0.261579i
790790 0 0
791791 38.2492 1.35999
792792 0 0
793793 −11.4164 −0.405409
794794 0 0
795795 −7.23607 2.76393i −0.256637 0.0980266i
796796 0 0
797797 30.9443i 1.09610i −0.836445 0.548051i 0.815370π-0.815370\pi
0.836445 0.548051i 0.184630π-0.184630\pi
798798 0 0
799799 23.4164i 0.828413i
800800 0 0
801801 20.9443 23.4164i 0.740029 0.827378i
802802 0 0
803803 −54.8328 −1.93501
804804 0 0
805805 16.9443 0.597207
806806 0 0
807807 −8.65248 + 22.6525i −0.304582 + 0.797405i
808808 0 0
809809 45.3050i 1.59284i 0.604746 + 0.796419i 0.293275π0.293275\pi
−0.604746 + 0.796419i 0.706725π0.706725\pi
810810 0 0
811811 36.7639i 1.29096i −0.763779 0.645478i 0.776658π-0.776658\pi
0.763779 0.645478i 0.223342π-0.223342\pi
812812 0 0
813813 3.59675 9.41641i 0.126143 0.330248i
814814 0 0
815815 1.23607 0.0432976
816816 0 0
817817 2.83282 0.0991077
818818 0 0
819819 12.9443 14.4721i 0.452309 0.505697i
820820 0 0
821821 12.1115i 0.422693i −0.977411 0.211346i 0.932215π-0.932215\pi
0.977411 0.211346i 0.0677848π-0.0677848\pi
822822 0 0
823823 26.3607i 0.918876i −0.888210 0.459438i 0.848051π-0.848051\pi
0.888210 0.459438i 0.151949π-0.151949\pi
824824 0 0
825825 10.4721 + 4.00000i 0.364593 + 0.139262i
826826 0 0
827827 −13.1246 −0.456387 −0.228194 0.973616i 0.573282π-0.573282\pi
−0.228194 + 0.973616i 0.573282π0.573282\pi
828828 0 0
829829 −30.0000 −1.04194 −0.520972 0.853574i 0.674430π-0.674430\pi
−0.520972 + 0.853574i 0.674430π0.674430\pi
830830 0 0
831831 30.1803 + 11.5279i 1.04694 + 0.399897i
832832 0 0
833833 15.7082i 0.544257i
834834 0 0
835835 14.9443i 0.517168i
836836 0 0
837837 −42.6525 + 22.0000i −1.47429 + 0.760431i
838838 0 0
839839 30.4721 1.05201 0.526007 0.850480i 0.323688π-0.323688\pi
0.526007 + 0.850480i 0.323688π0.323688\pi
840840 0 0
841841 28.7771 0.992313
842842 0 0
843843 −8.94427 + 23.4164i −0.308057 + 0.806504i
844844 0 0
845845 2.52786i 0.0869612i
846846 0 0
847847 61.7771i 2.12269i
848848 0 0
849849 4.18034 10.9443i 0.143469 0.375606i
850850 0 0
851851 48.3607 1.65778
852852 0 0
853853 −41.1246 −1.40808 −0.704040 0.710160i 0.748622π-0.748622\pi
−0.704040 + 0.710160i 0.748622π0.748622\pi
854854 0 0
855855 1.70820 + 1.52786i 0.0584193 + 0.0522518i
856856 0 0
857857 50.7639i 1.73406i −0.498253 0.867031i 0.666025π-0.666025\pi
0.498253 0.867031i 0.333975π-0.333975\pi
858858 0 0
859859 36.1803i 1.23446i 0.786784 + 0.617229i 0.211745π0.211745\pi
−0.786784 + 0.617229i 0.788255π0.788255\pi
860860 0 0
861861 33.8885 + 12.9443i 1.15492 + 0.441140i
862862 0 0
863863 10.3607 0.352682 0.176341 0.984329i 0.443574π-0.443574\pi
0.176341 + 0.984329i 0.443574π0.443574\pi
864864 0 0
865865 11.5279 0.391959
866866 0 0
867867 −16.8541 6.43769i −0.572395 0.218636i
868868 0 0
869869 91.7771i 3.11332i
870870 0 0
871871 21.8885i 0.741665i
872872 0 0
873873 −7.88854 7.05573i −0.266987 0.238800i
874874 0 0
875875 −2.00000 −0.0676123
876876 0 0
877877 6.29180 0.212459 0.106229 0.994342i 0.466122π-0.466122\pi
0.106229 + 0.994342i 0.466122π0.466122\pi
878878 0 0
879879 1.59675 4.18034i 0.0538570 0.140999i
880880 0 0
881881 0.360680i 0.0121516i −0.999982 0.00607581i 0.998066π-0.998066\pi
0.999982 0.00607581i 0.00193400π-0.00193400\pi
882882 0 0
883883 58.5410i 1.97006i 0.172377 + 0.985031i 0.444855π0.444855\pi
−0.172377 + 0.985031i 0.555145π0.555145\pi
884884 0 0
885885 1.52786 4.00000i 0.0513586 0.134459i
886886 0 0
887887 −4.83282 −0.162270 −0.0811350 0.996703i 0.525855π-0.525855\pi
−0.0811350 + 0.996703i 0.525855π0.525855\pi
888888 0 0
889889 −20.0000 −0.670778
890890 0 0
891891 −6.47214 57.8885i −0.216825 1.93934i
892892 0 0
893893 3.41641i 0.114326i
894894 0 0
895895 10.4721i 0.350045i
896896 0 0
897897 44.3607 + 16.9443i 1.48116 + 0.565753i
898898 0 0
899899 −4.36068 −0.145437
900900 0 0
901901 −23.4164 −0.780114
902902 0 0
903903 12.0000 + 4.58359i 0.399335 + 0.152532i
904904 0 0
905905 13.4164i 0.445976i
906906 0 0
907907 49.5967i 1.64683i 0.567437 + 0.823416i 0.307935π0.307935\pi
−0.567437 + 0.823416i 0.692065π0.692065\pi
908908 0 0
909909 18.8328 21.0557i 0.624645 0.698374i
910910 0 0
911911 24.9443 0.826441 0.413220 0.910631i 0.364404π-0.364404\pi
0.413220 + 0.910631i 0.364404π0.364404\pi
912912 0 0
913913 −11.0557 −0.365891
914914 0 0
915915 2.18034 5.70820i 0.0720798 0.188707i
916916 0 0
917917 27.7771i 0.917280i
918918 0 0
919919 8.29180i 0.273521i −0.990604 0.136761i 0.956331π-0.956331\pi
0.990604 0.136761i 0.0436691π-0.0436691\pi
920920 0 0
921921 −14.2918 + 37.4164i −0.470931 + 1.23291i
922922 0 0
923923 −12.9443 −0.426066
924924 0 0
925925 −5.70820 −0.187685
926926 0 0
927927 16.9443 18.9443i 0.556523 0.622212i
928928 0 0
929929 33.8885i 1.11185i 0.831233 + 0.555924i 0.187635π0.187635\pi
−0.831233 + 0.555924i 0.812365π0.812365\pi
930930 0 0
931931 2.29180i 0.0751106i
932932 0 0
933933 32.3607 + 12.3607i 1.05944 + 0.404670i
934934 0 0
935935 33.8885 1.10827
936936 0 0
937937 0.111456 0.00364111 0.00182056 0.999998i 0.499420π-0.499420\pi
0.00182056 + 0.999998i 0.499420π0.499420\pi
938938 0 0
939939 −19.2361 7.34752i −0.627745 0.239777i
940940 0 0
941941 15.5279i 0.506194i 0.967441 + 0.253097i 0.0814492π0.0814492\pi
−0.967441 + 0.253097i 0.918551π0.918551\pi
942942 0 0
943943 88.7214i 2.88916i
944944 0 0
945945 4.76393 + 9.23607i 0.154971 + 0.300449i
946946 0 0
947947 −24.7639 −0.804720 −0.402360 0.915482i 0.631810π-0.631810\pi
−0.402360 + 0.915482i 0.631810π0.631810\pi
948948 0 0
949949 27.4164 0.889974
950950 0 0
951951 17.2361 45.1246i 0.558918 1.46327i
952952 0 0
953953 33.5967i 1.08831i 0.838986 + 0.544153i 0.183149π0.183149\pi
−0.838986 + 0.544153i 0.816851π0.816851\pi
954954 0 0
955955 5.52786i 0.178877i
956956 0 0
957957 1.88854 4.94427i 0.0610480 0.159826i
958958 0 0
959959 −25.3050 −0.817140
960960 0 0
961961 −54.3050 −1.75177
962962 0 0
963963 −19.5967 17.5279i −0.631496 0.564828i
964964 0 0
965965 14.9443i 0.481073i
966966 0 0
967967 23.5279i 0.756605i 0.925682 + 0.378303i 0.123492π0.123492\pi
−0.925682 + 0.378303i 0.876508π0.876508\pi
968968 0 0
969969 6.47214 + 2.47214i 0.207915 + 0.0794164i
970970 0 0
971971 −9.52786 −0.305764 −0.152882 0.988244i 0.548855π-0.548855\pi
−0.152882 + 0.988244i 0.548855π0.548855\pi
972972 0 0
973973 16.3607 0.524499
974974 0 0
975975 −5.23607 2.00000i −0.167688 0.0640513i
976976 0 0
977977 8.29180i 0.265278i 0.991164 + 0.132639i 0.0423451π0.0423451\pi
−0.991164 + 0.132639i 0.957655π0.957655\pi
978978 0 0
979979 67.7771i 2.16617i
980980 0 0
981981 −42.3607 37.8885i −1.35247 1.20969i
982982 0 0
983983 36.2492 1.15617 0.578085 0.815976i 0.303800π-0.303800\pi
0.578085 + 0.815976i 0.303800π0.303800\pi
984984 0 0
985985 −10.0000 −0.318626
986986 0 0
987987 5.52786 14.4721i 0.175954 0.460653i
988988 0 0
989989 31.4164i 0.998984i
990990 0 0
991991 5.23607i 0.166329i 0.996536 + 0.0831646i 0.0265027π0.0265027\pi
−0.996536 + 0.0831646i 0.973497π0.973497\pi
992992 0 0
993993 −4.47214 + 11.7082i −0.141919 + 0.371549i
994994 0 0
995995 4.29180 0.136059
996996 0 0
997997 56.1803 1.77925 0.889625 0.456693i 0.150966π-0.150966\pi
0.889625 + 0.456693i 0.150966π0.150966\pi
998998 0 0
999999 13.5967 + 26.3607i 0.430182 + 0.834015i
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.h.l.1151.4 yes 4
3.2 odd 2 1920.2.h.f.1151.2 yes 4
4.3 odd 2 1920.2.h.f.1151.1 yes 4
8.3 odd 2 1920.2.h.k.1151.4 yes 4
8.5 even 2 1920.2.h.e.1151.1 4
12.11 even 2 inner 1920.2.h.l.1151.3 yes 4
24.5 odd 2 1920.2.h.k.1151.3 yes 4
24.11 even 2 1920.2.h.e.1151.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1920.2.h.e.1151.1 4 8.5 even 2
1920.2.h.e.1151.2 yes 4 24.11 even 2
1920.2.h.f.1151.1 yes 4 4.3 odd 2
1920.2.h.f.1151.2 yes 4 3.2 odd 2
1920.2.h.k.1151.3 yes 4 24.5 odd 2
1920.2.h.k.1151.4 yes 4 8.3 odd 2
1920.2.h.l.1151.3 yes 4 12.11 even 2 inner
1920.2.h.l.1151.4 yes 4 1.1 even 1 trivial