Properties

Label 1920.2.h.g.1151.2
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,6)\Q(i, \sqrt{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+9 x^{4} + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1151.2
Root 1.22474+1.22474i1.22474 + 1.22474i of defining polynomial
Character χ\chi == 1920.1151
Dual form 1920.2.h.g.1151.1

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+(1.22474+1.22474i)q3+1.00000iq50.449490iq73.00000iq92.00000q11+2.89898q13+(1.224741.22474i)q152.00000iq17+2.00000iq19+(0.550510+0.550510i)q214.44949q231.00000q25+(3.67423+3.67423i)q270.898979iq298.00000iq31+(2.449492.44949i)q33+0.449490q356.00000q37+(3.55051+3.55051i)q397.79796iq416.44949iq43+3.00000q458.44949q47+6.79796q49+(2.44949+2.44949i)q516.89898iq532.00000iq55+(2.449492.44949i)q571.10102q59+8.89898q611.34847q63+2.89898iq65+11.3485iq67+(5.449495.44949i)q690.898979q71+10.8990q73+(1.224741.22474i)q75+0.898979iq774.89898iq799.00000q81+12.2474q83+2.00000q85+(1.10102+1.10102i)q879.79796iq891.30306iq91+(9.79796+9.79796i)q932.00000q95+18.8990q97+6.00000iq99+O(q100)q+(-1.22474 + 1.22474i) q^{3} +1.00000i q^{5} -0.449490i q^{7} -3.00000i q^{9} -2.00000 q^{11} +2.89898 q^{13} +(-1.22474 - 1.22474i) q^{15} -2.00000i q^{17} +2.00000i q^{19} +(0.550510 + 0.550510i) q^{21} -4.44949 q^{23} -1.00000 q^{25} +(3.67423 + 3.67423i) q^{27} -0.898979i q^{29} -8.00000i q^{31} +(2.44949 - 2.44949i) q^{33} +0.449490 q^{35} -6.00000 q^{37} +(-3.55051 + 3.55051i) q^{39} -7.79796i q^{41} -6.44949i q^{43} +3.00000 q^{45} -8.44949 q^{47} +6.79796 q^{49} +(2.44949 + 2.44949i) q^{51} -6.89898i q^{53} -2.00000i q^{55} +(-2.44949 - 2.44949i) q^{57} -1.10102 q^{59} +8.89898 q^{61} -1.34847 q^{63} +2.89898i q^{65} +11.3485i q^{67} +(5.44949 - 5.44949i) q^{69} -0.898979 q^{71} +10.8990 q^{73} +(1.22474 - 1.22474i) q^{75} +0.898979i q^{77} -4.89898i q^{79} -9.00000 q^{81} +12.2474 q^{83} +2.00000 q^{85} +(1.10102 + 1.10102i) q^{87} -9.79796i q^{89} -1.30306i q^{91} +(9.79796 + 9.79796i) q^{93} -2.00000 q^{95} +18.8990 q^{97} +6.00000i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q8q118q13+12q218q234q258q3524q3724q39+12q4524q4712q4924q59+16q61+24q63+12q69+16q71+24q73++56q97+O(q100) 4 q - 8 q^{11} - 8 q^{13} + 12 q^{21} - 8 q^{23} - 4 q^{25} - 8 q^{35} - 24 q^{37} - 24 q^{39} + 12 q^{45} - 24 q^{47} - 12 q^{49} - 24 q^{59} + 16 q^{61} + 24 q^{63} + 12 q^{69} + 16 q^{71} + 24 q^{73}+ \cdots + 56 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 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 −1.22474 + 1.22474i −0.707107 + 0.707107i
44 0 0
55 1.00000i 0.447214i
66 0 0
77 0.449490i 0.169891i −0.996386 0.0849456i 0.972928π-0.972928\pi
0.996386 0.0849456i 0.0270716π-0.0270716\pi
88 0 0
99 3.00000i 1.00000i
1010 0 0
1111 −2.00000 −0.603023 −0.301511 0.953463i 0.597491π-0.597491\pi
−0.301511 + 0.953463i 0.597491π0.597491\pi
1212 0 0
1313 2.89898 0.804032 0.402016 0.915633i 0.368310π-0.368310\pi
0.402016 + 0.915633i 0.368310π0.368310\pi
1414 0 0
1515 −1.22474 1.22474i −0.316228 0.316228i
1616 0 0
1717 2.00000i 0.485071i −0.970143 0.242536i 0.922021π-0.922021\pi
0.970143 0.242536i 0.0779791π-0.0779791\pi
1818 0 0
1919 2.00000i 0.458831i 0.973329 + 0.229416i 0.0736815π0.0736815\pi
−0.973329 + 0.229416i 0.926318π0.926318\pi
2020 0 0
2121 0.550510 + 0.550510i 0.120131 + 0.120131i
2222 0 0
2323 −4.44949 −0.927783 −0.463891 0.885892i 0.653547π-0.653547\pi
−0.463891 + 0.885892i 0.653547π0.653547\pi
2424 0 0
2525 −1.00000 −0.200000
2626 0 0
2727 3.67423 + 3.67423i 0.707107 + 0.707107i
2828 0 0
2929 0.898979i 0.166936i −0.996510 0.0834681i 0.973400π-0.973400\pi
0.996510 0.0834681i 0.0265997π-0.0265997\pi
3030 0 0
3131 8.00000i 1.43684i −0.695608 0.718421i 0.744865π-0.744865\pi
0.695608 0.718421i 0.255135π-0.255135\pi
3232 0 0
3333 2.44949 2.44949i 0.426401 0.426401i
3434 0 0
3535 0.449490 0.0759776
3636 0 0
3737 −6.00000 −0.986394 −0.493197 0.869918i 0.664172π-0.664172\pi
−0.493197 + 0.869918i 0.664172π0.664172\pi
3838 0 0
3939 −3.55051 + 3.55051i −0.568537 + 0.568537i
4040 0 0
4141 7.79796i 1.21784i −0.793233 0.608918i 0.791604π-0.791604\pi
0.793233 0.608918i 0.208396π-0.208396\pi
4242 0 0
4343 6.44949i 0.983538i −0.870726 0.491769i 0.836350π-0.836350\pi
0.870726 0.491769i 0.163650π-0.163650\pi
4444 0 0
4545 3.00000 0.447214
4646 0 0
4747 −8.44949 −1.23248 −0.616242 0.787557i 0.711346π-0.711346\pi
−0.616242 + 0.787557i 0.711346π0.711346\pi
4848 0 0
4949 6.79796 0.971137
5050 0 0
5151 2.44949 + 2.44949i 0.342997 + 0.342997i
5252 0 0
5353 6.89898i 0.947648i −0.880620 0.473824i 0.842873π-0.842873\pi
0.880620 0.473824i 0.157127π-0.157127\pi
5454 0 0
5555 2.00000i 0.269680i
5656 0 0
5757 −2.44949 2.44949i −0.324443 0.324443i
5858 0 0
5959 −1.10102 −0.143341 −0.0716703 0.997428i 0.522833π-0.522833\pi
−0.0716703 + 0.997428i 0.522833π0.522833\pi
6060 0 0
6161 8.89898 1.13940 0.569699 0.821854i 0.307060π-0.307060\pi
0.569699 + 0.821854i 0.307060π0.307060\pi
6262 0 0
6363 −1.34847 −0.169891
6464 0 0
6565 2.89898i 0.359574i
6666 0 0
6767 11.3485i 1.38644i 0.720728 + 0.693218i 0.243808π0.243808\pi
−0.720728 + 0.693218i 0.756192π0.756192\pi
6868 0 0
6969 5.44949 5.44949i 0.656041 0.656041i
7070 0 0
7171 −0.898979 −0.106689 −0.0533446 0.998576i 0.516988π-0.516988\pi
−0.0533446 + 0.998576i 0.516988π0.516988\pi
7272 0 0
7373 10.8990 1.27563 0.637815 0.770190i 0.279839π-0.279839\pi
0.637815 + 0.770190i 0.279839π0.279839\pi
7474 0 0
7575 1.22474 1.22474i 0.141421 0.141421i
7676 0 0
7777 0.898979i 0.102448i
7878 0 0
7979 4.89898i 0.551178i −0.961276 0.275589i 0.911127π-0.911127\pi
0.961276 0.275589i 0.0888729π-0.0888729\pi
8080 0 0
8181 −9.00000 −1.00000
8282 0 0
8383 12.2474 1.34433 0.672166 0.740400i 0.265364π-0.265364\pi
0.672166 + 0.740400i 0.265364π0.265364\pi
8484 0 0
8585 2.00000 0.216930
8686 0 0
8787 1.10102 + 1.10102i 0.118042 + 0.118042i
8888 0 0
8989 9.79796i 1.03858i −0.854598 0.519291i 0.826196π-0.826196\pi
0.854598 0.519291i 0.173804π-0.173804\pi
9090 0 0
9191 1.30306i 0.136598i
9292 0 0
9393 9.79796 + 9.79796i 1.01600 + 1.01600i
9494 0 0
9595 −2.00000 −0.205196
9696 0 0
9797 18.8990 1.91890 0.959450 0.281878i 0.0909573π-0.0909573\pi
0.959450 + 0.281878i 0.0909573π0.0909573\pi
9898 0 0
9999 6.00000i 0.603023i
100100 0 0
101101 12.8990i 1.28350i −0.766915 0.641748i 0.778209π-0.778209\pi
0.766915 0.641748i 0.221791π-0.221791\pi
102102 0 0
103103 1.34847i 0.132869i 0.997791 + 0.0664343i 0.0211623π0.0211623\pi
−0.997791 + 0.0664343i 0.978838π0.978838\pi
104104 0 0
105105 −0.550510 + 0.550510i −0.0537243 + 0.0537243i
106106 0 0
107107 5.55051 0.536588 0.268294 0.963337i 0.413540π-0.413540\pi
0.268294 + 0.963337i 0.413540π0.413540\pi
108108 0 0
109109 −3.10102 −0.297024 −0.148512 0.988911i 0.547448π-0.547448\pi
−0.148512 + 0.988911i 0.547448π0.547448\pi
110110 0 0
111111 7.34847 7.34847i 0.697486 0.697486i
112112 0 0
113113 10.8990i 1.02529i 0.858601 + 0.512645i 0.171334π0.171334\pi
−0.858601 + 0.512645i 0.828666π0.828666\pi
114114 0 0
115115 4.44949i 0.414917i
116116 0 0
117117 8.69694i 0.804032i
118118 0 0
119119 −0.898979 −0.0824093
120120 0 0
121121 −7.00000 −0.636364
122122 0 0
123123 9.55051 + 9.55051i 0.861141 + 0.861141i
124124 0 0
125125 1.00000i 0.0894427i
126126 0 0
127127 5.34847i 0.474600i −0.971436 0.237300i 0.923738π-0.923738\pi
0.971436 0.237300i 0.0762624π-0.0762624\pi
128128 0 0
129129 7.89898 + 7.89898i 0.695466 + 0.695466i
130130 0 0
131131 0.202041 0.0176524 0.00882620 0.999961i 0.497190π-0.497190\pi
0.00882620 + 0.999961i 0.497190π0.497190\pi
132132 0 0
133133 0.898979 0.0779514
134134 0 0
135135 −3.67423 + 3.67423i −0.316228 + 0.316228i
136136 0 0
137137 1.10102i 0.0940665i 0.998893 + 0.0470333i 0.0149767π0.0149767\pi
−0.998893 + 0.0470333i 0.985023π0.985023\pi
138138 0 0
139139 2.00000i 0.169638i 0.996396 + 0.0848189i 0.0270312π0.0270312\pi
−0.996396 + 0.0848189i 0.972969π0.972969\pi
140140 0 0
141141 10.3485 10.3485i 0.871498 0.871498i
142142 0 0
143143 −5.79796 −0.484850
144144 0 0
145145 0.898979 0.0746562
146146 0 0
147147 −8.32577 + 8.32577i −0.686698 + 0.686698i
148148 0 0
149149 3.79796i 0.311141i −0.987825 0.155570i 0.950278π-0.950278\pi
0.987825 0.155570i 0.0497216π-0.0497216\pi
150150 0 0
151151 23.5959i 1.92021i −0.279642 0.960104i 0.590216π-0.590216\pi
0.279642 0.960104i 0.409784π-0.409784\pi
152152 0 0
153153 −6.00000 −0.485071
154154 0 0
155155 8.00000 0.642575
156156 0 0
157157 −10.0000 −0.798087 −0.399043 0.916932i 0.630658π-0.630658\pi
−0.399043 + 0.916932i 0.630658π0.630658\pi
158158 0 0
159159 8.44949 + 8.44949i 0.670088 + 0.670088i
160160 0 0
161161 2.00000i 0.157622i
162162 0 0
163163 5.55051i 0.434750i −0.976088 0.217375i 0.930251π-0.930251\pi
0.976088 0.217375i 0.0697494π-0.0697494\pi
164164 0 0
165165 2.44949 + 2.44949i 0.190693 + 0.190693i
166166 0 0
167167 21.3485 1.65199 0.825997 0.563674i 0.190613π-0.190613\pi
0.825997 + 0.563674i 0.190613π0.190613\pi
168168 0 0
169169 −4.59592 −0.353532
170170 0 0
171171 6.00000 0.458831
172172 0 0
173173 7.79796i 0.592868i 0.955053 + 0.296434i 0.0957975π0.0957975\pi
−0.955053 + 0.296434i 0.904203π0.904203\pi
174174 0 0
175175 0.449490i 0.0339782i
176176 0 0
177177 1.34847 1.34847i 0.101357 0.101357i
178178 0 0
179179 22.8990 1.71155 0.855775 0.517348i 0.173081π-0.173081\pi
0.855775 + 0.517348i 0.173081π0.173081\pi
180180 0 0
181181 −17.5959 −1.30789 −0.653947 0.756540i 0.726888π-0.726888\pi
−0.653947 + 0.756540i 0.726888π0.726888\pi
182182 0 0
183183 −10.8990 + 10.8990i −0.805676 + 0.805676i
184184 0 0
185185 6.00000i 0.441129i
186186 0 0
187187 4.00000i 0.292509i
188188 0 0
189189 1.65153 1.65153i 0.120131 0.120131i
190190 0 0
191191 −3.10102 −0.224382 −0.112191 0.993687i 0.535787π-0.535787\pi
−0.112191 + 0.993687i 0.535787π0.535787\pi
192192 0 0
193193 24.6969 1.77772 0.888862 0.458175i 0.151497π-0.151497\pi
0.888862 + 0.458175i 0.151497π0.151497\pi
194194 0 0
195195 −3.55051 3.55051i −0.254257 0.254257i
196196 0 0
197197 20.6969i 1.47460i −0.675568 0.737298i 0.736101π-0.736101\pi
0.675568 0.737298i 0.263899π-0.263899\pi
198198 0 0
199199 12.8990i 0.914384i −0.889368 0.457192i 0.848855π-0.848855\pi
0.889368 0.457192i 0.151145π-0.151145\pi
200200 0 0
201201 −13.8990 13.8990i −0.980358 0.980358i
202202 0 0
203203 −0.404082 −0.0283610
204204 0 0
205205 7.79796 0.544633
206206 0 0
207207 13.3485i 0.927783i
208208 0 0
209209 4.00000i 0.276686i
210210 0 0
211211 18.8990i 1.30106i −0.759481 0.650530i 0.774547π-0.774547\pi
0.759481 0.650530i 0.225453π-0.225453\pi
212212 0 0
213213 1.10102 1.10102i 0.0754407 0.0754407i
214214 0 0
215215 6.44949 0.439852
216216 0 0
217217 −3.59592 −0.244107
218218 0 0
219219 −13.3485 + 13.3485i −0.902006 + 0.902006i
220220 0 0
221221 5.79796i 0.390013i
222222 0 0
223223 12.4495i 0.833679i 0.908980 + 0.416840i 0.136862π0.136862\pi
−0.908980 + 0.416840i 0.863138π0.863138\pi
224224 0 0
225225 3.00000i 0.200000i
226226 0 0
227227 −21.1464 −1.40354 −0.701769 0.712405i 0.747606π-0.747606\pi
−0.701769 + 0.712405i 0.747606π0.747606\pi
228228 0 0
229229 −19.7980 −1.30829 −0.654143 0.756371i 0.726971π-0.726971\pi
−0.654143 + 0.756371i 0.726971π0.726971\pi
230230 0 0
231231 −1.10102 1.10102i −0.0724418 0.0724418i
232232 0 0
233233 11.7980i 0.772910i 0.922308 + 0.386455i 0.126301π0.126301\pi
−0.922308 + 0.386455i 0.873699π0.873699\pi
234234 0 0
235235 8.44949i 0.551184i
236236 0 0
237237 6.00000 + 6.00000i 0.389742 + 0.389742i
238238 0 0
239239 6.20204 0.401177 0.200588 0.979676i 0.435715π-0.435715\pi
0.200588 + 0.979676i 0.435715π0.435715\pi
240240 0 0
241241 −23.5959 −1.51995 −0.759973 0.649954i 0.774788π-0.774788\pi
−0.759973 + 0.649954i 0.774788π0.774788\pi
242242 0 0
243243 11.0227 11.0227i 0.707107 0.707107i
244244 0 0
245245 6.79796i 0.434306i
246246 0 0
247247 5.79796i 0.368915i
248248 0 0
249249 −15.0000 + 15.0000i −0.950586 + 0.950586i
250250 0 0
251251 −27.7980 −1.75459 −0.877296 0.479950i 0.840655π-0.840655\pi
−0.877296 + 0.479950i 0.840655π0.840655\pi
252252 0 0
253253 8.89898 0.559474
254254 0 0
255255 −2.44949 + 2.44949i −0.153393 + 0.153393i
256256 0 0
257257 10.8990i 0.679860i −0.940451 0.339930i 0.889597π-0.889597\pi
0.940451 0.339930i 0.110403π-0.110403\pi
258258 0 0
259259 2.69694i 0.167580i
260260 0 0
261261 −2.69694 −0.166936
262262 0 0
263263 −12.4495 −0.767668 −0.383834 0.923402i 0.625397π-0.625397\pi
−0.383834 + 0.923402i 0.625397π0.625397\pi
264264 0 0
265265 6.89898 0.423801
266266 0 0
267267 12.0000 + 12.0000i 0.734388 + 0.734388i
268268 0 0
269269 21.5959i 1.31673i 0.752700 + 0.658363i 0.228751π0.228751\pi
−0.752700 + 0.658363i 0.771249π0.771249\pi
270270 0 0
271271 12.0000i 0.728948i −0.931214 0.364474i 0.881249π-0.881249\pi
0.931214 0.364474i 0.118751π-0.118751\pi
272272 0 0
273273 1.59592 + 1.59592i 0.0965893 + 0.0965893i
274274 0 0
275275 2.00000 0.120605
276276 0 0
277277 −2.00000 −0.120168 −0.0600842 0.998193i 0.519137π-0.519137\pi
−0.0600842 + 0.998193i 0.519137π0.519137\pi
278278 0 0
279279 −24.0000 −1.43684
280280 0 0
281281 17.5959i 1.04968i −0.851200 0.524842i 0.824124π-0.824124\pi
0.851200 0.524842i 0.175876π-0.175876\pi
282282 0 0
283283 13.1464i 0.781474i −0.920502 0.390737i 0.872220π-0.872220\pi
0.920502 0.390737i 0.127780π-0.127780\pi
284284 0 0
285285 2.44949 2.44949i 0.145095 0.145095i
286286 0 0
287287 −3.50510 −0.206900
288288 0 0
289289 13.0000 0.764706
290290 0 0
291291 −23.1464 + 23.1464i −1.35687 + 1.35687i
292292 0 0
293293 27.7980i 1.62397i 0.583675 + 0.811987i 0.301614π0.301614\pi
−0.583675 + 0.811987i 0.698386π0.698386\pi
294294 0 0
295295 1.10102i 0.0641039i
296296 0 0
297297 −7.34847 7.34847i −0.426401 0.426401i
298298 0 0
299299 −12.8990 −0.745967
300300 0 0
301301 −2.89898 −0.167094
302302 0 0
303303 15.7980 + 15.7980i 0.907569 + 0.907569i
304304 0 0
305305 8.89898i 0.509554i
306306 0 0
307307 27.3485i 1.56086i −0.625243 0.780430i 0.715000π-0.715000\pi
0.625243 0.780430i 0.285000π-0.285000\pi
308308 0 0
309309 −1.65153 1.65153i −0.0939523 0.0939523i
310310 0 0
311311 24.4949 1.38898 0.694489 0.719503i 0.255630π-0.255630\pi
0.694489 + 0.719503i 0.255630π0.255630\pi
312312 0 0
313313 −0.202041 −0.0114200 −0.00571002 0.999984i 0.501818π-0.501818\pi
−0.00571002 + 0.999984i 0.501818π0.501818\pi
314314 0 0
315315 1.34847i 0.0759776i
316316 0 0
317317 20.6969i 1.16246i 0.813741 + 0.581228i 0.197428π0.197428\pi
−0.813741 + 0.581228i 0.802572π0.802572\pi
318318 0 0
319319 1.79796i 0.100666i
320320 0 0
321321 −6.79796 + 6.79796i −0.379425 + 0.379425i
322322 0 0
323323 4.00000 0.222566
324324 0 0
325325 −2.89898 −0.160806
326326 0 0
327327 3.79796 3.79796i 0.210028 0.210028i
328328 0 0
329329 3.79796i 0.209388i
330330 0 0
331331 13.1010i 0.720097i 0.932934 + 0.360049i 0.117240π0.117240\pi
−0.932934 + 0.360049i 0.882760π0.882760\pi
332332 0 0
333333 18.0000i 0.986394i
334334 0 0
335335 −11.3485 −0.620033
336336 0 0
337337 −4.20204 −0.228900 −0.114450 0.993429i 0.536511π-0.536511\pi
−0.114450 + 0.993429i 0.536511π0.536511\pi
338338 0 0
339339 −13.3485 13.3485i −0.724989 0.724989i
340340 0 0
341341 16.0000i 0.866449i
342342 0 0
343343 6.20204i 0.334879i
344344 0 0
345345 5.44949 + 5.44949i 0.293391 + 0.293391i
346346 0 0
347347 −17.1464 −0.920468 −0.460234 0.887798i 0.652235π-0.652235\pi
−0.460234 + 0.887798i 0.652235π0.652235\pi
348348 0 0
349349 −14.0000 −0.749403 −0.374701 0.927146i 0.622255π-0.622255\pi
−0.374701 + 0.927146i 0.622255π0.622255\pi
350350 0 0
351351 10.6515 + 10.6515i 0.568537 + 0.568537i
352352 0 0
353353 26.4949i 1.41018i 0.709117 + 0.705091i 0.249094π0.249094\pi
−0.709117 + 0.705091i 0.750906π0.750906\pi
354354 0 0
355355 0.898979i 0.0477129i
356356 0 0
357357 1.10102 1.10102i 0.0582722 0.0582722i
358358 0 0
359359 8.00000 0.422224 0.211112 0.977462i 0.432292π-0.432292\pi
0.211112 + 0.977462i 0.432292π0.432292\pi
360360 0 0
361361 15.0000 0.789474
362362 0 0
363363 8.57321 8.57321i 0.449977 0.449977i
364364 0 0
365365 10.8990i 0.570479i
366366 0 0
367367 4.44949i 0.232261i −0.993234 0.116131i 0.962951π-0.962951\pi
0.993234 0.116131i 0.0370492π-0.0370492\pi
368368 0 0
369369 −23.3939 −1.21784
370370 0 0
371371 −3.10102 −0.160997
372372 0 0
373373 5.59592 0.289746 0.144873 0.989450i 0.453723π-0.453723\pi
0.144873 + 0.989450i 0.453723π0.453723\pi
374374 0 0
375375 1.22474 + 1.22474i 0.0632456 + 0.0632456i
376376 0 0
377377 2.60612i 0.134222i
378378 0 0
379379 10.0000i 0.513665i −0.966456 0.256833i 0.917321π-0.917321\pi
0.966456 0.256833i 0.0826790π-0.0826790\pi
380380 0 0
381381 6.55051 + 6.55051i 0.335593 + 0.335593i
382382 0 0
383383 −35.1464 −1.79590 −0.897949 0.440099i 0.854943π-0.854943\pi
−0.897949 + 0.440099i 0.854943π0.854943\pi
384384 0 0
385385 −0.898979 −0.0458162
386386 0 0
387387 −19.3485 −0.983538
388388 0 0
389389 0.202041i 0.0102439i 0.999987 + 0.00512194i 0.00163037π0.00163037\pi
−0.999987 + 0.00512194i 0.998370π0.998370\pi
390390 0 0
391391 8.89898i 0.450041i
392392 0 0
393393 −0.247449 + 0.247449i −0.0124821 + 0.0124821i
394394 0 0
395395 4.89898 0.246494
396396 0 0
397397 −38.4949 −1.93200 −0.966002 0.258535i 0.916760π-0.916760\pi
−0.966002 + 0.258535i 0.916760π0.916760\pi
398398 0 0
399399 −1.10102 + 1.10102i −0.0551200 + 0.0551200i
400400 0 0
401401 15.5959i 0.778823i 0.921064 + 0.389411i 0.127322π0.127322\pi
−0.921064 + 0.389411i 0.872678π0.872678\pi
402402 0 0
403403 23.1918i 1.15527i
404404 0 0
405405 9.00000i 0.447214i
406406 0 0
407407 12.0000 0.594818
408408 0 0
409409 −4.00000 −0.197787 −0.0988936 0.995098i 0.531530π-0.531530\pi
−0.0988936 + 0.995098i 0.531530π0.531530\pi
410410 0 0
411411 −1.34847 1.34847i −0.0665151 0.0665151i
412412 0 0
413413 0.494897i 0.0243523i
414414 0 0
415415 12.2474i 0.601204i
416416 0 0
417417 −2.44949 2.44949i −0.119952 0.119952i
418418 0 0
419419 7.30306 0.356778 0.178389 0.983960i 0.442911π-0.442911\pi
0.178389 + 0.983960i 0.442911π0.442911\pi
420420 0 0
421421 −36.4949 −1.77865 −0.889326 0.457273i 0.848826π-0.848826\pi
−0.889326 + 0.457273i 0.848826π0.848826\pi
422422 0 0
423423 25.3485i 1.23248i
424424 0 0
425425 2.00000i 0.0970143i
426426 0 0
427427 4.00000i 0.193574i
428428 0 0
429429 7.10102 7.10102i 0.342841 0.342841i
430430 0 0
431431 16.4949 0.794531 0.397266 0.917704i 0.369959π-0.369959\pi
0.397266 + 0.917704i 0.369959π0.369959\pi
432432 0 0
433433 9.10102 0.437367 0.218684 0.975796i 0.429824π-0.429824\pi
0.218684 + 0.975796i 0.429824π0.429824\pi
434434 0 0
435435 −1.10102 + 1.10102i −0.0527899 + 0.0527899i
436436 0 0
437437 8.89898i 0.425696i
438438 0 0
439439 28.4949i 1.35999i 0.733218 + 0.679994i 0.238017π0.238017\pi
−0.733218 + 0.679994i 0.761983π0.761983\pi
440440 0 0
441441 20.3939i 0.971137i
442442 0 0
443443 −24.2474 −1.15203 −0.576016 0.817439i 0.695393π-0.695393\pi
−0.576016 + 0.817439i 0.695393π0.695393\pi
444444 0 0
445445 9.79796 0.464468
446446 0 0
447447 4.65153 + 4.65153i 0.220010 + 0.220010i
448448 0 0
449449 25.5959i 1.20795i −0.797005 0.603973i 0.793583π-0.793583\pi
0.797005 0.603973i 0.206417π-0.206417\pi
450450 0 0
451451 15.5959i 0.734383i
452452 0 0
453453 28.8990 + 28.8990i 1.35779 + 1.35779i
454454 0 0
455455 1.30306 0.0610885
456456 0 0
457457 −27.7980 −1.30033 −0.650167 0.759791i 0.725301π-0.725301\pi
−0.650167 + 0.759791i 0.725301π0.725301\pi
458458 0 0
459459 7.34847 7.34847i 0.342997 0.342997i
460460 0 0
461461 42.2929i 1.96977i −0.173196 0.984887i 0.555409π-0.555409\pi
0.173196 0.984887i 0.444591π-0.444591\pi
462462 0 0
463463 25.8434i 1.20104i 0.799609 + 0.600522i 0.205040π0.205040\pi
−0.799609 + 0.600522i 0.794960π0.794960\pi
464464 0 0
465465 −9.79796 + 9.79796i −0.454369 + 0.454369i
466466 0 0
467467 13.1464 0.608344 0.304172 0.952617i 0.401620π-0.401620\pi
0.304172 + 0.952617i 0.401620π0.401620\pi
468468 0 0
469469 5.10102 0.235543
470470 0 0
471471 12.2474 12.2474i 0.564333 0.564333i
472472 0 0
473473 12.8990i 0.593096i
474474 0 0
475475 2.00000i 0.0917663i
476476 0 0
477477 −20.6969 −0.947648
478478 0 0
479479 41.3939 1.89133 0.945667 0.325136i 0.105410π-0.105410\pi
0.945667 + 0.325136i 0.105410π0.105410\pi
480480 0 0
481481 −17.3939 −0.793093
482482 0 0
483483 −2.44949 2.44949i −0.111456 0.111456i
484484 0 0
485485 18.8990i 0.858158i
486486 0 0
487487 17.3485i 0.786134i −0.919510 0.393067i 0.871414π-0.871414\pi
0.919510 0.393067i 0.128586π-0.128586\pi
488488 0 0
489489 6.79796 + 6.79796i 0.307414 + 0.307414i
490490 0 0
491491 −3.79796 −0.171399 −0.0856997 0.996321i 0.527313π-0.527313\pi
−0.0856997 + 0.996321i 0.527313π0.527313\pi
492492 0 0
493493 −1.79796 −0.0809760
494494 0 0
495495 −6.00000 −0.269680
496496 0 0
497497 0.404082i 0.0181256i
498498 0 0
499499 27.3939i 1.22632i −0.789959 0.613159i 0.789898π-0.789898\pi
0.789959 0.613159i 0.210102π-0.210102\pi
500500 0 0
501501 −26.1464 + 26.1464i −1.16814 + 1.16814i
502502 0 0
503503 −16.9444 −0.755513 −0.377756 0.925905i 0.623304π-0.623304\pi
−0.377756 + 0.925905i 0.623304π0.623304\pi
504504 0 0
505505 12.8990 0.573997
506506 0 0
507507 5.62883 5.62883i 0.249985 0.249985i
508508 0 0
509509 16.8990i 0.749034i 0.927220 + 0.374517i 0.122191π0.122191\pi
−0.927220 + 0.374517i 0.877809π0.877809\pi
510510 0 0
511511 4.89898i 0.216718i
512512 0 0
513513 −7.34847 + 7.34847i −0.324443 + 0.324443i
514514 0 0
515515 −1.34847 −0.0594207
516516 0 0
517517 16.8990 0.743216
518518 0 0
519519 −9.55051 9.55051i −0.419221 0.419221i
520520 0 0
521521 6.20204i 0.271716i 0.990728 + 0.135858i 0.0433791π0.0433791\pi
−0.990728 + 0.135858i 0.956621π0.956621\pi
522522 0 0
523523 40.2474i 1.75990i −0.475068 0.879949i 0.657577π-0.657577\pi
0.475068 0.879949i 0.342423π-0.342423\pi
524524 0 0
525525 −0.550510 0.550510i −0.0240262 0.0240262i
526526 0 0
527527 −16.0000 −0.696971
528528 0 0
529529 −3.20204 −0.139219
530530 0 0
531531 3.30306i 0.143341i
532532 0 0
533533 22.6061i 0.979180i
534534 0 0
535535 5.55051i 0.239969i
536536 0 0
537537 −28.0454 + 28.0454i −1.21025 + 1.21025i
538538 0 0
539539 −13.5959 −0.585618
540540 0 0
541541 −26.0000 −1.11783 −0.558914 0.829226i 0.688782π-0.688782\pi
−0.558914 + 0.829226i 0.688782π0.688782\pi
542542 0 0
543543 21.5505 21.5505i 0.924821 0.924821i
544544 0 0
545545 3.10102i 0.132833i
546546 0 0
547547 18.0454i 0.771566i 0.922590 + 0.385783i 0.126069π0.126069\pi
−0.922590 + 0.385783i 0.873931π0.873931\pi
548548 0 0
549549 26.6969i 1.13940i
550550 0 0
551551 1.79796 0.0765956
552552 0 0
553553 −2.20204 −0.0936403
554554 0 0
555555 7.34847 + 7.34847i 0.311925 + 0.311925i
556556 0 0
557557 6.00000i 0.254228i −0.991888 0.127114i 0.959429π-0.959429\pi
0.991888 0.127114i 0.0405714π-0.0405714\pi
558558 0 0
559559 18.6969i 0.790796i
560560 0 0
561561 −4.89898 4.89898i −0.206835 0.206835i
562562 0 0
563563 18.4495 0.777553 0.388777 0.921332i 0.372898π-0.372898\pi
0.388777 + 0.921332i 0.372898π0.372898\pi
564564 0 0
565565 −10.8990 −0.458524
566566 0 0
567567 4.04541i 0.169891i
568568 0 0
569569 9.59592i 0.402282i 0.979562 + 0.201141i 0.0644649π0.0644649\pi
−0.979562 + 0.201141i 0.935535π0.935535\pi
570570 0 0
571571 28.6969i 1.20093i 0.799651 + 0.600465i 0.205018π0.205018\pi
−0.799651 + 0.600465i 0.794982π0.794982\pi
572572 0 0
573573 3.79796 3.79796i 0.158662 0.158662i
574574 0 0
575575 4.44949 0.185557
576576 0 0
577577 −11.7980 −0.491155 −0.245578 0.969377i 0.578978π-0.578978\pi
−0.245578 + 0.969377i 0.578978π0.578978\pi
578578 0 0
579579 −30.2474 + 30.2474i −1.25704 + 1.25704i
580580 0 0
581581 5.50510i 0.228390i
582582 0 0
583583 13.7980i 0.571453i
584584 0 0
585585 8.69694 0.359574
586586 0 0
587587 4.24745 0.175311 0.0876555 0.996151i 0.472063π-0.472063\pi
0.0876555 + 0.996151i 0.472063π0.472063\pi
588588 0 0
589589 16.0000 0.659269
590590 0 0
591591 25.3485 + 25.3485i 1.04270 + 1.04270i
592592 0 0
593593 11.3031i 0.464161i 0.972697 + 0.232081i 0.0745533π0.0745533\pi
−0.972697 + 0.232081i 0.925447π0.925447\pi
594594 0 0
595595 0.898979i 0.0368546i
596596 0 0
597597 15.7980 + 15.7980i 0.646567 + 0.646567i
598598 0 0
599599 41.3939 1.69131 0.845654 0.533732i 0.179211π-0.179211\pi
0.845654 + 0.533732i 0.179211π0.179211\pi
600600 0 0
601601 13.7980 0.562830 0.281415 0.959586i 0.409196π-0.409196\pi
0.281415 + 0.959586i 0.409196π0.409196\pi
602602 0 0
603603 34.0454 1.38644
604604 0 0
605605 7.00000i 0.284590i
606606 0 0
607607 37.3485i 1.51593i −0.652297 0.757964i 0.726194π-0.726194\pi
0.652297 0.757964i 0.273806π-0.273806\pi
608608 0 0
609609 0.494897 0.494897i 0.0200543 0.0200543i
610610 0 0
611611 −24.4949 −0.990957
612612 0 0
613613 6.49490 0.262326 0.131163 0.991361i 0.458129π-0.458129\pi
0.131163 + 0.991361i 0.458129π0.458129\pi
614614 0 0
615615 −9.55051 + 9.55051i −0.385114 + 0.385114i
616616 0 0
617617 46.0000i 1.85189i 0.377658 + 0.925945i 0.376729π0.376729\pi
−0.377658 + 0.925945i 0.623271π0.623271\pi
618618 0 0
619619 11.7980i 0.474200i −0.971485 0.237100i 0.923803π-0.923803\pi
0.971485 0.237100i 0.0761969π-0.0761969\pi
620620 0 0
621621 −16.3485 16.3485i −0.656041 0.656041i
622622 0 0
623623 −4.40408 −0.176446
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 4.89898 + 4.89898i 0.195646 + 0.195646i
628628 0 0
629629 12.0000i 0.478471i
630630 0 0
631631 16.0000i 0.636950i 0.947931 + 0.318475i 0.103171π0.103171\pi
−0.947931 + 0.318475i 0.896829π0.896829\pi
632632 0 0
633633 23.1464 + 23.1464i 0.919988 + 0.919988i
634634 0 0
635635 5.34847 0.212248
636636 0 0
637637 19.7071 0.780825
638638 0 0
639639 2.69694i 0.106689i
640640 0 0
641641 6.00000i 0.236986i 0.992955 + 0.118493i 0.0378063π0.0378063\pi
−0.992955 + 0.118493i 0.962194π0.962194\pi
642642 0 0
643643 23.3485i 0.920774i 0.887718 + 0.460387i 0.152289π0.152289\pi
−0.887718 + 0.460387i 0.847711π0.847711\pi
644644 0 0
645645 −7.89898 + 7.89898i −0.311022 + 0.311022i
646646 0 0
647647 30.2474 1.18915 0.594575 0.804040i 0.297320π-0.297320\pi
0.594575 + 0.804040i 0.297320π0.297320\pi
648648 0 0
649649 2.20204 0.0864377
650650 0 0
651651 4.40408 4.40408i 0.172610 0.172610i
652652 0 0
653653 1.10102i 0.0430863i 0.999768 + 0.0215431i 0.00685792π0.00685792\pi
−0.999768 + 0.0215431i 0.993142π0.993142\pi
654654 0 0
655655 0.202041i 0.00789440i
656656 0 0
657657 32.6969i 1.27563i
658658 0 0
659659 34.4949 1.34373 0.671865 0.740673i 0.265493π-0.265493\pi
0.671865 + 0.740673i 0.265493π0.265493\pi
660660 0 0
661661 −7.10102 −0.276198 −0.138099 0.990418i 0.544099π-0.544099\pi
−0.138099 + 0.990418i 0.544099π0.544099\pi
662662 0 0
663663 7.10102 + 7.10102i 0.275781 + 0.275781i
664664 0 0
665665 0.898979i 0.0348609i
666666 0 0
667667 4.00000i 0.154881i
668668 0 0
669669 −15.2474 15.2474i −0.589500 0.589500i
670670 0 0
671671 −17.7980 −0.687083
672672 0 0
673673 −3.30306 −0.127324 −0.0636618 0.997972i 0.520278π-0.520278\pi
−0.0636618 + 0.997972i 0.520278π0.520278\pi
674674 0 0
675675 −3.67423 3.67423i −0.141421 0.141421i
676676 0 0
677677 12.6969i 0.487983i −0.969777 0.243991i 0.921543π-0.921543\pi
0.969777 0.243991i 0.0784569π-0.0784569\pi
678678 0 0
679679 8.49490i 0.326004i
680680 0 0
681681 25.8990 25.8990i 0.992451 0.992451i
682682 0 0
683683 −4.65153 −0.177986 −0.0889929 0.996032i 0.528365π-0.528365\pi
−0.0889929 + 0.996032i 0.528365π0.528365\pi
684684 0 0
685685 −1.10102 −0.0420678
686686 0 0
687687 24.2474 24.2474i 0.925098 0.925098i
688688 0 0
689689 20.0000i 0.761939i
690690 0 0
691691 20.6969i 0.787349i 0.919250 + 0.393674i 0.128796π0.128796\pi
−0.919250 + 0.393674i 0.871204π0.871204\pi
692692 0 0
693693 2.69694 0.102448
694694 0 0
695695 −2.00000 −0.0758643
696696 0 0
697697 −15.5959 −0.590738
698698 0 0
699699 −14.4495 14.4495i −0.546530 0.546530i
700700 0 0
701701 43.3939i 1.63896i −0.573105 0.819482i 0.694261π-0.694261\pi
0.573105 0.819482i 0.305739π-0.305739\pi
702702 0 0
703703 12.0000i 0.452589i
704704 0 0
705705 10.3485 + 10.3485i 0.389746 + 0.389746i
706706 0 0
707707 −5.79796 −0.218055
708708 0 0
709709 43.7980 1.64487 0.822433 0.568861i 0.192616π-0.192616\pi
0.822433 + 0.568861i 0.192616π0.192616\pi
710710 0 0
711711 −14.6969 −0.551178
712712 0 0
713713 35.5959i 1.33308i
714714 0 0
715715 5.79796i 0.216831i
716716 0 0
717717 −7.59592 + 7.59592i −0.283675 + 0.283675i
718718 0 0
719719 −33.3939 −1.24538 −0.622691 0.782468i 0.713961π-0.713961\pi
−0.622691 + 0.782468i 0.713961π0.713961\pi
720720 0 0
721721 0.606123 0.0225732
722722 0 0
723723 28.8990 28.8990i 1.07476 1.07476i
724724 0 0
725725 0.898979i 0.0333873i
726726 0 0
727727 3.14643i 0.116695i −0.998296 0.0583473i 0.981417π-0.981417\pi
0.998296 0.0583473i 0.0185831π-0.0185831\pi
728728 0 0
729729 27.0000i 1.00000i
730730 0 0
731731 −12.8990 −0.477086
732732 0 0
733733 −14.0000 −0.517102 −0.258551 0.965998i 0.583245π-0.583245\pi
−0.258551 + 0.965998i 0.583245π0.583245\pi
734734 0 0
735735 −8.32577 8.32577i −0.307100 0.307100i
736736 0 0
737737 22.6969i 0.836052i
738738 0 0
739739 3.79796i 0.139710i 0.997557 + 0.0698551i 0.0222537π0.0222537\pi
−0.997557 + 0.0698551i 0.977746π0.977746\pi
740740 0 0
741741 −7.10102 7.10102i −0.260863 0.260863i
742742 0 0
743743 0.853572 0.0313145 0.0156573 0.999877i 0.495016π-0.495016\pi
0.0156573 + 0.999877i 0.495016π0.495016\pi
744744 0 0
745745 3.79796 0.139146
746746 0 0
747747 36.7423i 1.34433i
748748 0 0
749749 2.49490i 0.0911616i
750750 0 0
751751 9.39388i 0.342787i −0.985203 0.171394i 0.945173π-0.945173\pi
0.985203 0.171394i 0.0548270π-0.0548270\pi
752752 0 0
753753 34.0454 34.0454i 1.24068 1.24068i
754754 0 0
755755 23.5959 0.858743
756756 0 0
757757 19.3939 0.704882 0.352441 0.935834i 0.385352π-0.385352\pi
0.352441 + 0.935834i 0.385352π0.385352\pi
758758 0 0
759759 −10.8990 + 10.8990i −0.395608 + 0.395608i
760760 0 0
761761 33.7980i 1.22518i −0.790403 0.612588i 0.790129π-0.790129\pi
0.790403 0.612588i 0.209871π-0.209871\pi
762762 0 0
763763 1.39388i 0.0504617i
764764 0 0
765765 6.00000i 0.216930i
766766 0 0
767767 −3.19184 −0.115251
768768 0 0
769769 −31.7980 −1.14666 −0.573332 0.819323i 0.694349π-0.694349\pi
−0.573332 + 0.819323i 0.694349π0.694349\pi
770770 0 0
771771 13.3485 + 13.3485i 0.480733 + 0.480733i
772772 0 0
773773 24.6969i 0.888287i 0.895956 + 0.444144i 0.146492π0.146492\pi
−0.895956 + 0.444144i 0.853508π0.853508\pi
774774 0 0
775775 8.00000i 0.287368i
776776 0 0
777777 −3.30306 3.30306i −0.118497 0.118497i
778778 0 0
779779 15.5959 0.558782
780780 0 0
781781 1.79796 0.0643360
782782 0 0
783783 3.30306 3.30306i 0.118042 0.118042i
784784 0 0
785785 10.0000i 0.356915i
786786 0 0
787787 13.1464i 0.468620i −0.972162 0.234310i 0.924717π-0.924717\pi
0.972162 0.234310i 0.0752830π-0.0752830\pi
788788 0 0
789789 15.2474 15.2474i 0.542824 0.542824i
790790 0 0
791791 4.89898 0.174188
792792 0 0
793793 25.7980 0.916112
794794 0 0
795795 −8.44949 + 8.44949i −0.299673 + 0.299673i
796796 0 0
797797 1.10102i 0.0390001i 0.999810 + 0.0195001i 0.00620746π0.00620746\pi
−0.999810 + 0.0195001i 0.993793π0.993793\pi
798798 0 0
799799 16.8990i 0.597843i
800800 0 0
801801 −29.3939 −1.03858
802802 0 0
803803 −21.7980 −0.769233
804804 0 0
805805 −2.00000 −0.0704907
806806 0 0
807807 −26.4495 26.4495i −0.931066 0.931066i
808808 0 0
809809 8.40408i 0.295472i −0.989027 0.147736i 0.952801π-0.952801\pi
0.989027 0.147736i 0.0471986π-0.0471986\pi
810810 0 0
811811 1.50510i 0.0528513i 0.999651 + 0.0264256i 0.00841252π0.00841252\pi
−0.999651 + 0.0264256i 0.991587π0.991587\pi
812812 0 0
813813 14.6969 + 14.6969i 0.515444 + 0.515444i
814814 0 0
815815 5.55051 0.194426
816816 0 0
817817 12.8990 0.451278
818818 0 0
819819 −3.90918 −0.136598
820820 0 0
821821 37.5959i 1.31211i 0.754715 + 0.656053i 0.227775π0.227775\pi
−0.754715 + 0.656053i 0.772225π0.772225\pi
822822 0 0
823823 7.55051i 0.263194i 0.991303 + 0.131597i 0.0420105π0.0420105\pi
−0.991303 + 0.131597i 0.957989π0.957989\pi
824824 0 0
825825 −2.44949 + 2.44949i −0.0852803 + 0.0852803i
826826 0 0
827827 1.14643 0.0398652 0.0199326 0.999801i 0.493655π-0.493655\pi
0.0199326 + 0.999801i 0.493655π0.493655\pi
828828 0 0
829829 −24.4949 −0.850743 −0.425371 0.905019i 0.639857π-0.639857\pi
−0.425371 + 0.905019i 0.639857π0.639857\pi
830830 0 0
831831 2.44949 2.44949i 0.0849719 0.0849719i
832832 0 0
833833 13.5959i 0.471071i
834834 0 0
835835 21.3485i 0.738794i
836836 0 0
837837 29.3939 29.3939i 1.01600 1.01600i
838838 0 0
839839 −17.7980 −0.614454 −0.307227 0.951636i 0.599401π-0.599401\pi
−0.307227 + 0.951636i 0.599401π0.599401\pi
840840 0 0
841841 28.1918 0.972132
842842 0 0
843843 21.5505 + 21.5505i 0.742239 + 0.742239i
844844 0 0
845845 4.59592i 0.158104i
846846 0 0
847847 3.14643i 0.108113i
848848 0 0
849849 16.1010 + 16.1010i 0.552586 + 0.552586i
850850 0 0
851851 26.6969 0.915159
852852 0 0
853853 50.8990 1.74275 0.871374 0.490619i 0.163229π-0.163229\pi
0.871374 + 0.490619i 0.163229π0.163229\pi
854854 0 0
855855 6.00000i 0.205196i
856856 0 0
857857 8.69694i 0.297082i −0.988906 0.148541i 0.952542π-0.952542\pi
0.988906 0.148541i 0.0474577π-0.0474577\pi
858858 0 0
859859 37.5959i 1.28276i 0.767225 + 0.641378i 0.221637π0.221637\pi
−0.767225 + 0.641378i 0.778363π0.778363\pi
860860 0 0
861861 4.29286 4.29286i 0.146300 0.146300i
862862 0 0
863863 −44.9444 −1.52992 −0.764962 0.644075i 0.777242π-0.777242\pi
−0.764962 + 0.644075i 0.777242π0.777242\pi
864864 0 0
865865 −7.79796 −0.265139
866866 0 0
867867 −15.9217 + 15.9217i −0.540729 + 0.540729i
868868 0 0
869869 9.79796i 0.332373i
870870 0 0
871871 32.8990i 1.11474i
872872 0 0
873873 56.6969i 1.91890i
874874 0 0
875875 −0.449490 −0.0151955
876876 0 0
877877 −2.00000 −0.0675352 −0.0337676 0.999430i 0.510751π-0.510751\pi
−0.0337676 + 0.999430i 0.510751π0.510751\pi
878878 0 0
879879 −34.0454 34.0454i −1.14832 1.14832i
880880 0 0
881881 8.20204i 0.276334i 0.990409 + 0.138167i 0.0441210π0.0441210\pi
−0.990409 + 0.138167i 0.955879π0.955879\pi
882882 0 0
883883 18.4495i 0.620875i 0.950594 + 0.310437i 0.100476π0.100476\pi
−0.950594 + 0.310437i 0.899524π0.899524\pi
884884 0 0
885885 1.34847 + 1.34847i 0.0453283 + 0.0453283i
886886 0 0
887887 −47.1464 −1.58302 −0.791511 0.611155i 0.790705π-0.790705\pi
−0.791511 + 0.611155i 0.790705π0.790705\pi
888888 0 0
889889 −2.40408 −0.0806303
890890 0 0
891891 18.0000 0.603023
892892 0 0
893893 16.8990i 0.565503i
894894 0 0
895895 22.8990i 0.765428i
896896 0 0
897897 15.7980 15.7980i 0.527478 0.527478i
898898 0 0
899899 −7.19184 −0.239861
900900 0 0
901901 −13.7980 −0.459677
902902 0 0
903903 3.55051 3.55051i 0.118154 0.118154i
904904 0 0
905905 17.5959i 0.584908i
906906 0 0
907907 2.94439i 0.0977668i 0.998804 + 0.0488834i 0.0155663π0.0155663\pi
−0.998804 + 0.0488834i 0.984434π0.984434\pi
908908 0 0
909909 −38.6969 −1.28350
910910 0 0
911911 −14.6969 −0.486931 −0.243466 0.969910i 0.578284π-0.578284\pi
−0.243466 + 0.969910i 0.578284π0.578284\pi
912912 0 0
913913 −24.4949 −0.810663
914914 0 0
915915 −10.8990 10.8990i −0.360309 0.360309i
916916 0 0
917917 0.0908154i 0.00299899i
918918 0 0
919919 44.4949i 1.46775i −0.679284 0.733876i 0.737709π-0.737709\pi
0.679284 0.733876i 0.262291π-0.262291\pi
920920 0 0
921921 33.4949 + 33.4949i 1.10369 + 1.10369i
922922 0 0
923923 −2.60612 −0.0857816
924924 0 0
925925 6.00000 0.197279
926926 0 0
927927 4.04541 0.132869
928928 0 0
929929 34.0000i 1.11550i −0.830008 0.557752i 0.811664π-0.811664\pi
0.830008 0.557752i 0.188336π-0.188336\pi
930930 0 0
931931 13.5959i 0.445588i
932932 0 0
933933 −30.0000 + 30.0000i −0.982156 + 0.982156i
934934 0 0
935935 −4.00000 −0.130814
936936 0 0
937937 2.49490 0.0815047 0.0407524 0.999169i 0.487025π-0.487025\pi
0.0407524 + 0.999169i 0.487025π0.487025\pi
938938 0 0
939939 0.247449 0.247449i 0.00807518 0.00807518i
940940 0 0
941941 24.4949i 0.798511i −0.916840 0.399255i 0.869269π-0.869269\pi
0.916840 0.399255i 0.130731π-0.130731\pi
942942 0 0
943943 34.6969i 1.12989i
944944 0 0
945945 1.65153 + 1.65153i 0.0537243 + 0.0537243i
946946 0 0
947947 6.44949 0.209580 0.104790 0.994494i 0.466583π-0.466583\pi
0.104790 + 0.994494i 0.466583π0.466583\pi
948948 0 0
949949 31.5959 1.02565
950950 0 0
951951 −25.3485 25.3485i −0.821980 0.821980i
952952 0 0
953953 10.8990i 0.353053i 0.984296 + 0.176526i 0.0564861π0.0564861\pi
−0.984296 + 0.176526i 0.943514π0.943514\pi
954954 0 0
955955 3.10102i 0.100347i
956956 0 0
957957 −2.20204 2.20204i −0.0711819 0.0711819i
958958 0 0
959959 0.494897 0.0159811
960960 0 0
961961 −33.0000 −1.06452
962962 0 0
963963 16.6515i 0.536588i
964964 0 0
965965 24.6969i 0.795023i
966966 0 0
967967 5.75255i 0.184990i 0.995713 + 0.0924948i 0.0294841π0.0294841\pi
−0.995713 + 0.0924948i 0.970516π0.970516\pi
968968 0 0
969969 −4.89898 + 4.89898i −0.157378 + 0.157378i
970970 0 0
971971 −20.2020 −0.648314 −0.324157 0.946003i 0.605081π-0.605081\pi
−0.324157 + 0.946003i 0.605081π0.605081\pi
972972 0 0
973973 0.898979 0.0288200
974974 0 0
975975 3.55051 3.55051i 0.113707 0.113707i
976976 0 0
977977 45.1918i 1.44581i −0.690945 0.722907i 0.742805π-0.742805\pi
0.690945 0.722907i 0.257195π-0.257195\pi
978978 0 0
979979 19.5959i 0.626288i
980980 0 0
981981 9.30306i 0.297024i
982982 0 0
983983 −7.95459 −0.253712 −0.126856 0.991921i 0.540489π-0.540489\pi
−0.126856 + 0.991921i 0.540489π0.540489\pi
984984 0 0
985985 20.6969 0.659459
986986 0 0
987987 −4.65153 4.65153i −0.148060 0.148060i
988988 0 0
989989 28.6969i 0.912510i
990990 0 0
991991 47.1918i 1.49910i −0.661949 0.749549i 0.730270π-0.730270\pi
0.661949 0.749549i 0.269730π-0.269730\pi
992992 0 0
993993 −16.0454 16.0454i −0.509186 0.509186i
994994 0 0
995995 12.8990 0.408925
996996 0 0
997997 42.0908 1.33303 0.666515 0.745492i 0.267785π-0.267785\pi
0.666515 + 0.745492i 0.267785π0.267785\pi
998998 0 0
999999 −22.0454 22.0454i −0.697486 0.697486i
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.g.1151.2 yes 4
3.2 odd 2 1920.2.h.i.1151.4 yes 4
4.3 odd 2 1920.2.h.i.1151.3 yes 4
8.3 odd 2 1920.2.h.h.1151.2 yes 4
8.5 even 2 1920.2.h.j.1151.3 yes 4
12.11 even 2 inner 1920.2.h.g.1151.1 4
24.5 odd 2 1920.2.h.h.1151.1 yes 4
24.11 even 2 1920.2.h.j.1151.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1920.2.h.g.1151.1 4 12.11 even 2 inner
1920.2.h.g.1151.2 yes 4 1.1 even 1 trivial
1920.2.h.h.1151.1 yes 4 24.5 odd 2
1920.2.h.h.1151.2 yes 4 8.3 odd 2
1920.2.h.i.1151.3 yes 4 4.3 odd 2
1920.2.h.i.1151.4 yes 4 3.2 odd 2
1920.2.h.j.1151.3 yes 4 8.5 even 2
1920.2.h.j.1151.4 yes 4 24.11 even 2