Properties

Label 1920.2.h.i.1151.1
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 / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1920,2,Mod(1151,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1920.1151"); 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

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,0,0,0,0,0,0,8,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 15.331277188115.3312771881
Analytic rank: 00
Dimension: 44
Coefficient field: Q(i,6)\Q(i, \sqrt{6})
Copy content comment:defining polynomial
 
Copy content 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 1151.1
Root 1.224741.22474i-1.22474 - 1.22474i of defining polynomial
Character χ\chi == 1920.1151
Dual form 1920.2.h.i.1151.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.224741.22474i)q31.00000iq5+4.44949iq7+3.00000iq9+2.00000q116.89898q13+(1.22474+1.22474i)q15+2.00000iq17+2.00000iq19+(5.449495.44949i)q210.449490q231.00000q25+(3.674233.67423i)q278.89898iq298.00000iq31+(2.449492.44949i)q33+4.44949q356.00000q37+(8.44949+8.44949i)q3911.7980iq411.55051iq43+3.00000q45+3.55051q4712.7980q49+(2.449492.44949i)q512.89898iq532.00000iq55+(2.449492.44949i)q57+10.8990q590.898979q6113.3485q63+6.89898iq653.34847iq67+(0.550510+0.550510i)q698.89898q71+1.10102q73+(1.22474+1.22474i)q75+8.89898iq77+4.89898iq799.00000q81+12.2474q83+2.00000q85+(10.8990+10.8990i)q879.79796iq8930.6969iq91+(9.79796+9.79796i)q93+2.00000q95+9.10102q97+6.00000iq99+O(q100)q+(-1.22474 - 1.22474i) q^{3} -1.00000i q^{5} +4.44949i q^{7} +3.00000i q^{9} +2.00000 q^{11} -6.89898 q^{13} +(-1.22474 + 1.22474i) q^{15} +2.00000i q^{17} +2.00000i q^{19} +(5.44949 - 5.44949i) q^{21} -0.449490 q^{23} -1.00000 q^{25} +(3.67423 - 3.67423i) q^{27} -8.89898i q^{29} -8.00000i q^{31} +(-2.44949 - 2.44949i) q^{33} +4.44949 q^{35} -6.00000 q^{37} +(8.44949 + 8.44949i) q^{39} -11.7980i q^{41} -1.55051i q^{43} +3.00000 q^{45} +3.55051 q^{47} -12.7980 q^{49} +(2.44949 - 2.44949i) q^{51} -2.89898i q^{53} -2.00000i q^{55} +(2.44949 - 2.44949i) q^{57} +10.8990 q^{59} -0.898979 q^{61} -13.3485 q^{63} +6.89898i q^{65} -3.34847i q^{67} +(0.550510 + 0.550510i) q^{69} -8.89898 q^{71} +1.10102 q^{73} +(1.22474 + 1.22474i) q^{75} +8.89898i q^{77} +4.89898i q^{79} -9.00000 q^{81} +12.2474 q^{83} +2.00000 q^{85} +(-10.8990 + 10.8990i) q^{87} -9.79796i q^{89} -30.6969i q^{91} +(-9.79796 + 9.79796i) q^{93} +2.00000 q^{95} +9.10102 q^{97} +6.00000i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+8q118q13+12q21+8q234q25+8q3524q37+24q39+12q45+24q4712q49+24q59+16q6124q63+12q6916q71+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 4.44949i 1.68175i 0.541230 + 0.840875i 0.317959π0.317959\pi
−0.541230 + 0.840875i 0.682041π0.682041\pi
88 0 0
99 3.00000i 1.00000i
1010 0 0
1111 2.00000 0.603023 0.301511 0.953463i 0.402509π-0.402509\pi
0.301511 + 0.953463i 0.402509π0.402509\pi
1212 0 0
1313 −6.89898 −1.91343 −0.956716 0.291022i 0.906005π-0.906005\pi
−0.956716 + 0.291022i 0.906005π0.906005\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 0.0779791π0.0779791\pi
−0.970143 + 0.242536i 0.922021π0.922021\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 5.44949 5.44949i 1.18918 1.18918i
2222 0 0
2323 −0.449490 −0.0937251 −0.0468625 0.998901i 0.514922π-0.514922\pi
−0.0468625 + 0.998901i 0.514922π0.514922\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 8.89898i 1.65250i −0.563304 0.826250i 0.690470π-0.690470\pi
0.563304 0.826250i 0.309530π-0.309530\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 4.44949 0.752101
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 8.44949 + 8.44949i 1.35300 + 1.35300i
4040 0 0
4141 11.7980i 1.84253i −0.388934 0.921266i 0.627156π-0.627156\pi
0.388934 0.921266i 0.372844π-0.372844\pi
4242 0 0
4343 1.55051i 0.236451i −0.992987 0.118225i 0.962279π-0.962279\pi
0.992987 0.118225i 0.0377205π-0.0377205\pi
4444 0 0
4545 3.00000 0.447214
4646 0 0
4747 3.55051 0.517895 0.258948 0.965891i 0.416624π-0.416624\pi
0.258948 + 0.965891i 0.416624π0.416624\pi
4848 0 0
4949 −12.7980 −1.82828
5050 0 0
5151 2.44949 2.44949i 0.342997 0.342997i
5252 0 0
5353 2.89898i 0.398205i −0.979979 0.199103i 0.936197π-0.936197\pi
0.979979 0.199103i 0.0638027π-0.0638027\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 10.8990 1.41893 0.709463 0.704743i 0.248937π-0.248937\pi
0.709463 + 0.704743i 0.248937π0.248937\pi
6060 0 0
6161 −0.898979 −0.115103 −0.0575513 0.998343i 0.518329π-0.518329\pi
−0.0575513 + 0.998343i 0.518329π0.518329\pi
6262 0 0
6363 −13.3485 −1.68175
6464 0 0
6565 6.89898i 0.855713i
6666 0 0
6767 3.34847i 0.409081i −0.978858 0.204540i 0.934430π-0.934430\pi
0.978858 0.204540i 0.0655699π-0.0655699\pi
6868 0 0
6969 0.550510 + 0.550510i 0.0662736 + 0.0662736i
7070 0 0
7171 −8.89898 −1.05611 −0.528057 0.849209i 0.677079π-0.677079\pi
−0.528057 + 0.849209i 0.677079π0.677079\pi
7272 0 0
7373 1.10102 0.128865 0.0644324 0.997922i 0.479476π-0.479476\pi
0.0644324 + 0.997922i 0.479476π0.479476\pi
7474 0 0
7575 1.22474 + 1.22474i 0.141421 + 0.141421i
7676 0 0
7777 8.89898i 1.01413i
7878 0 0
7979 4.89898i 0.551178i 0.961276 + 0.275589i 0.0888729π0.0888729\pi
−0.961276 + 0.275589i 0.911127π0.911127\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 −10.8990 + 10.8990i −1.16849 + 1.16849i
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 30.6969i 3.21791i
9292 0 0
9393 −9.79796 + 9.79796i −1.01600 + 1.01600i
9494 0 0
9595 2.00000 0.205196
9696 0 0
9797 9.10102 0.924069 0.462034 0.886862i 0.347120π-0.347120\pi
0.462034 + 0.886862i 0.347120π0.347120\pi
9898 0 0
9999 6.00000i 0.603023i
100100 0 0
101101 3.10102i 0.308563i 0.988027 + 0.154282i 0.0493063π0.0493063\pi
−0.988027 + 0.154282i 0.950694π0.950694\pi
102102 0 0
103103 13.3485i 1.31526i −0.753339 0.657632i 0.771558π-0.771558\pi
0.753339 0.657632i 0.228442π-0.228442\pi
104104 0 0
105105 −5.44949 5.44949i −0.531816 0.531816i
106106 0 0
107107 −10.4495 −1.01019 −0.505095 0.863064i 0.668543π-0.668543\pi
−0.505095 + 0.863064i 0.668543π0.668543\pi
108108 0 0
109109 −12.8990 −1.23550 −0.617749 0.786375i 0.711955π-0.711955\pi
−0.617749 + 0.786375i 0.711955π0.711955\pi
110110 0 0
111111 7.34847 + 7.34847i 0.697486 + 0.697486i
112112 0 0
113113 1.10102i 0.103575i −0.998658 0.0517876i 0.983508π-0.983508\pi
0.998658 0.0517876i 0.0164919π-0.0164919\pi
114114 0 0
115115 0.449490i 0.0419151i
116116 0 0
117117 20.6969i 1.91343i
118118 0 0
119119 −8.89898 −0.815768
120120 0 0
121121 −7.00000 −0.636364
122122 0 0
123123 −14.4495 + 14.4495i −1.30287 + 1.30287i
124124 0 0
125125 1.00000i 0.0894427i
126126 0 0
127127 9.34847i 0.829543i 0.909926 + 0.414771i 0.136138π0.136138\pi
−0.909926 + 0.414771i 0.863862π0.863862\pi
128128 0 0
129129 −1.89898 + 1.89898i −0.167196 + 0.167196i
130130 0 0
131131 −19.7980 −1.72976 −0.864878 0.501982i 0.832604π-0.832604\pi
−0.864878 + 0.501982i 0.832604π0.832604\pi
132132 0 0
133133 −8.89898 −0.771639
134134 0 0
135135 −3.67423 3.67423i −0.316228 0.316228i
136136 0 0
137137 10.8990i 0.931163i −0.885005 0.465581i 0.845845π-0.845845\pi
0.885005 0.465581i 0.154155π-0.154155\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 −4.34847 4.34847i −0.366207 0.366207i
142142 0 0
143143 −13.7980 −1.15384
144144 0 0
145145 −8.89898 −0.739020
146146 0 0
147147 15.6742 + 15.6742i 1.29279 + 1.29279i
148148 0 0
149149 15.7980i 1.29422i −0.762397 0.647110i 0.775978π-0.775978\pi
0.762397 0.647110i 0.224022π-0.224022\pi
150150 0 0
151151 15.5959i 1.26918i 0.772850 + 0.634589i 0.218831π0.218831\pi
−0.772850 + 0.634589i 0.781169π0.781169\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 −3.55051 + 3.55051i −0.281574 + 0.281574i
160160 0 0
161161 2.00000i 0.157622i
162162 0 0
163163 10.4495i 0.818467i −0.912430 0.409234i 0.865796π-0.865796\pi
0.912430 0.409234i 0.134204π-0.134204\pi
164164 0 0
165165 −2.44949 + 2.44949i −0.190693 + 0.190693i
166166 0 0
167167 −6.65153 −0.514711 −0.257355 0.966317i 0.582851π-0.582851\pi
−0.257355 + 0.966317i 0.582851π0.582851\pi
168168 0 0
169169 34.5959 2.66122
170170 0 0
171171 −6.00000 −0.458831
172172 0 0
173173 11.7980i 0.896982i 0.893787 + 0.448491i 0.148038π0.148038\pi
−0.893787 + 0.448491i 0.851962π0.851962\pi
174174 0 0
175175 4.44949i 0.336350i
176176 0 0
177177 −13.3485 13.3485i −1.00333 1.00333i
178178 0 0
179179 −13.1010 −0.979216 −0.489608 0.871943i 0.662860π-0.662860\pi
−0.489608 + 0.871943i 0.662860π0.662860\pi
180180 0 0
181181 21.5959 1.60521 0.802606 0.596510i 0.203446π-0.203446\pi
0.802606 + 0.596510i 0.203446π0.203446\pi
182182 0 0
183183 1.10102 + 1.10102i 0.0813898 + 0.0813898i
184184 0 0
185185 6.00000i 0.441129i
186186 0 0
187187 4.00000i 0.292509i
188188 0 0
189189 16.3485 + 16.3485i 1.18918 + 1.18918i
190190 0 0
191191 12.8990 0.933337 0.466669 0.884432i 0.345454π-0.345454\pi
0.466669 + 0.884432i 0.345454π0.345454\pi
192192 0 0
193193 −4.69694 −0.338093 −0.169047 0.985608i 0.554069π-0.554069\pi
−0.169047 + 0.985608i 0.554069π0.554069\pi
194194 0 0
195195 8.44949 8.44949i 0.605081 0.605081i
196196 0 0
197197 8.69694i 0.619631i −0.950797 0.309816i 0.899733π-0.899733\pi
0.950797 0.309816i 0.100267π-0.100267\pi
198198 0 0
199199 3.10102i 0.219826i −0.993941 0.109913i 0.964943π-0.964943\pi
0.993941 0.109913i 0.0350571π-0.0350571\pi
200200 0 0
201201 −4.10102 + 4.10102i −0.289264 + 0.289264i
202202 0 0
203203 39.5959 2.77909
204204 0 0
205205 −11.7980 −0.824005
206206 0 0
207207 1.34847i 0.0937251i
208208 0 0
209209 4.00000i 0.276686i
210210 0 0
211211 9.10102i 0.626540i −0.949664 0.313270i 0.898576π-0.898576\pi
0.949664 0.313270i 0.101424π-0.101424\pi
212212 0 0
213213 10.8990 + 10.8990i 0.746786 + 0.746786i
214214 0 0
215215 −1.55051 −0.105744
216216 0 0
217217 35.5959 2.41641
218218 0 0
219219 −1.34847 1.34847i −0.0911211 0.0911211i
220220 0 0
221221 13.7980i 0.928151i
222222 0 0
223223 7.55051i 0.505620i 0.967516 + 0.252810i 0.0813547π0.0813547\pi
−0.967516 + 0.252810i 0.918645π0.918645\pi
224224 0 0
225225 3.00000i 0.200000i
226226 0 0
227227 −13.1464 −0.872559 −0.436280 0.899811i 0.643704π-0.643704\pi
−0.436280 + 0.899811i 0.643704π0.643704\pi
228228 0 0
229229 −0.202041 −0.0133512 −0.00667562 0.999978i 0.502125π-0.502125\pi
−0.00667562 + 0.999978i 0.502125π0.502125\pi
230230 0 0
231231 10.8990 10.8990i 0.717100 0.717100i
232232 0 0
233233 7.79796i 0.510861i 0.966827 + 0.255431i 0.0822172π0.0822172\pi
−0.966827 + 0.255431i 0.917783π0.917783\pi
234234 0 0
235235 3.55051i 0.231610i
236236 0 0
237237 6.00000 6.00000i 0.389742 0.389742i
238238 0 0
239239 −25.7980 −1.66873 −0.834366 0.551211i 0.814166π-0.814166\pi
−0.834366 + 0.551211i 0.814166π0.814166\pi
240240 0 0
241241 15.5959 1.00462 0.502311 0.864687i 0.332483π-0.332483\pi
0.502311 + 0.864687i 0.332483π0.332483\pi
242242 0 0
243243 11.0227 + 11.0227i 0.707107 + 0.707107i
244244 0 0
245245 12.7980i 0.817632i
246246 0 0
247247 13.7980i 0.877943i
248248 0 0
249249 −15.0000 15.0000i −0.950586 0.950586i
250250 0 0
251251 8.20204 0.517708 0.258854 0.965916i 0.416655π-0.416655\pi
0.258854 + 0.965916i 0.416655π0.416655\pi
252252 0 0
253253 −0.898979 −0.0565184
254254 0 0
255255 −2.44949 2.44949i −0.153393 0.153393i
256256 0 0
257257 1.10102i 0.0686798i 0.999410 + 0.0343399i 0.0109329π0.0109329\pi
−0.999410 + 0.0343399i 0.989067π0.989067\pi
258258 0 0
259259 26.6969i 1.65887i
260260 0 0
261261 26.6969 1.65250
262262 0 0
263263 7.55051 0.465584 0.232792 0.972526i 0.425214π-0.425214\pi
0.232792 + 0.972526i 0.425214π0.425214\pi
264264 0 0
265265 −2.89898 −0.178083
266266 0 0
267267 −12.0000 + 12.0000i −0.734388 + 0.734388i
268268 0 0
269269 17.5959i 1.07284i 0.843951 + 0.536421i 0.180224π0.180224\pi
−0.843951 + 0.536421i 0.819776π0.819776\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 −37.5959 + 37.5959i −2.27541 + 2.27541i
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 21.5959i 1.28830i −0.764897 0.644152i 0.777210π-0.777210\pi
0.764897 0.644152i 0.222790π-0.222790\pi
282282 0 0
283283 21.1464i 1.25702i 0.777800 + 0.628512i 0.216336π0.216336\pi
−0.777800 + 0.628512i 0.783664π0.783664\pi
284284 0 0
285285 −2.44949 2.44949i −0.145095 0.145095i
286286 0 0
287287 52.4949 3.09868
288288 0 0
289289 13.0000 0.764706
290290 0 0
291291 −11.1464 11.1464i −0.653415 0.653415i
292292 0 0
293293 8.20204i 0.479168i −0.970876 0.239584i 0.922989π-0.922989\pi
0.970876 0.239584i 0.0770111π-0.0770111\pi
294294 0 0
295295 10.8990i 0.634563i
296296 0 0
297297 7.34847 7.34847i 0.426401 0.426401i
298298 0 0
299299 3.10102 0.179337
300300 0 0
301301 6.89898 0.397651
302302 0 0
303303 3.79796 3.79796i 0.218187 0.218187i
304304 0 0
305305 0.898979i 0.0514754i
306306 0 0
307307 12.6515i 0.722061i −0.932554 0.361030i 0.882425π-0.882425\pi
0.932554 0.361030i 0.117575π-0.117575\pi
308308 0 0
309309 −16.3485 + 16.3485i −0.930032 + 0.930032i
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 −19.7980 −1.11905 −0.559523 0.828815i 0.689016π-0.689016\pi
−0.559523 + 0.828815i 0.689016π0.689016\pi
314314 0 0
315315 13.3485i 0.752101i
316316 0 0
317317 8.69694i 0.488469i 0.969716 + 0.244234i 0.0785366π0.0785366\pi
−0.969716 + 0.244234i 0.921463π0.921463\pi
318318 0 0
319319 17.7980i 0.996494i
320320 0 0
321321 12.7980 + 12.7980i 0.714312 + 0.714312i
322322 0 0
323323 −4.00000 −0.222566
324324 0 0
325325 6.89898 0.382687
326326 0 0
327327 15.7980 + 15.7980i 0.873629 + 0.873629i
328328 0 0
329329 15.7980i 0.870970i
330330 0 0
331331 22.8990i 1.25864i 0.777146 + 0.629321i 0.216667π0.216667\pi
−0.777146 + 0.629321i 0.783333π0.783333\pi
332332 0 0
333333 18.0000i 0.986394i
334334 0 0
335335 −3.34847 −0.182946
336336 0 0
337337 −23.7980 −1.29636 −0.648179 0.761488i 0.724469π-0.724469\pi
−0.648179 + 0.761488i 0.724469π0.724469\pi
338338 0 0
339339 −1.34847 + 1.34847i −0.0732388 + 0.0732388i
340340 0 0
341341 16.0000i 0.866449i
342342 0 0
343343 25.7980i 1.39296i
344344 0 0
345345 0.550510 0.550510i 0.0296385 0.0296385i
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 −25.3485 + 25.3485i −1.35300 + 1.35300i
352352 0 0
353353 22.4949i 1.19728i 0.801017 + 0.598641i 0.204292π0.204292\pi
−0.801017 + 0.598641i 0.795708π0.795708\pi
354354 0 0
355355 8.89898i 0.472309i
356356 0 0
357357 10.8990 + 10.8990i 0.576835 + 0.576835i
358358 0 0
359359 −8.00000 −0.422224 −0.211112 0.977462i 0.567708π-0.567708\pi
−0.211112 + 0.977462i 0.567708π0.567708\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 1.10102i 0.0576300i
366366 0 0
367367 0.449490i 0.0234632i 0.999931 + 0.0117316i 0.00373437π0.00373437\pi
−0.999931 + 0.0117316i 0.996266π0.996266\pi
368368 0 0
369369 35.3939 1.84253
370370 0 0
371371 12.8990 0.669682
372372 0 0
373373 −33.5959 −1.73953 −0.869765 0.493466i 0.835730π-0.835730\pi
−0.869765 + 0.493466i 0.835730π0.835730\pi
374374 0 0
375375 1.22474 1.22474i 0.0632456 0.0632456i
376376 0 0
377377 61.3939i 3.16195i
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 11.4495 11.4495i 0.586575 0.586575i
382382 0 0
383383 0.853572 0.0436155 0.0218077 0.999762i 0.493058π-0.493058\pi
0.0218077 + 0.999762i 0.493058π0.493058\pi
384384 0 0
385385 8.89898 0.453534
386386 0 0
387387 4.65153 0.236451
388388 0 0
389389 19.7980i 1.00380i −0.864927 0.501898i 0.832635π-0.832635\pi
0.864927 0.501898i 0.167365π-0.167365\pi
390390 0 0
391391 0.898979i 0.0454633i
392392 0 0
393393 24.2474 + 24.2474i 1.22312 + 1.22312i
394394 0 0
395395 4.89898 0.246494
396396 0 0
397397 10.4949 0.526724 0.263362 0.964697i 0.415169π-0.415169\pi
0.263362 + 0.964697i 0.415169π0.415169\pi
398398 0 0
399399 10.8990 + 10.8990i 0.545631 + 0.545631i
400400 0 0
401401 23.5959i 1.17832i 0.808015 + 0.589162i 0.200542π0.200542\pi
−0.808015 + 0.589162i 0.799458π0.799458\pi
402402 0 0
403403 55.1918i 2.74930i
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 −13.3485 + 13.3485i −0.658431 + 0.658431i
412412 0 0
413413 48.4949i 2.38628i
414414 0 0
415415 12.2474i 0.601204i
416416 0 0
417417 2.44949 2.44949i 0.119952 0.119952i
418418 0 0
419419 −36.6969 −1.79276 −0.896381 0.443284i 0.853813π-0.853813\pi
−0.896381 + 0.443284i 0.853813π0.853813\pi
420420 0 0
421421 12.4949 0.608964 0.304482 0.952518i 0.401517π-0.401517\pi
0.304482 + 0.952518i 0.401517π0.401517\pi
422422 0 0
423423 10.6515i 0.517895i
424424 0 0
425425 2.00000i 0.0970143i
426426 0 0
427427 4.00000i 0.193574i
428428 0 0
429429 16.8990 + 16.8990i 0.815890 + 0.815890i
430430 0 0
431431 32.4949 1.56522 0.782612 0.622510i 0.213887π-0.213887\pi
0.782612 + 0.622510i 0.213887π0.213887\pi
432432 0 0
433433 18.8990 0.908227 0.454113 0.890944i 0.349956π-0.349956\pi
0.454113 + 0.890944i 0.349956π0.349956\pi
434434 0 0
435435 10.8990 + 10.8990i 0.522566 + 0.522566i
436436 0 0
437437 0.898979i 0.0430040i
438438 0 0
439439 20.4949i 0.978168i −0.872237 0.489084i 0.837331π-0.837331\pi
0.872237 0.489084i 0.162669π-0.162669\pi
440440 0 0
441441 38.3939i 1.82828i
442442 0 0
443443 −0.247449 −0.0117566 −0.00587832 0.999983i 0.501871π-0.501871\pi
−0.00587832 + 0.999983i 0.501871π0.501871\pi
444444 0 0
445445 −9.79796 −0.464468
446446 0 0
447447 −19.3485 + 19.3485i −0.915151 + 0.915151i
448448 0 0
449449 13.5959i 0.641631i −0.947142 0.320816i 0.896043π-0.896043\pi
0.947142 0.320816i 0.103957π-0.103957\pi
450450 0 0
451451 23.5959i 1.11109i
452452 0 0
453453 19.1010 19.1010i 0.897444 0.897444i
454454 0 0
455455 −30.6969 −1.43909
456456 0 0
457457 −8.20204 −0.383675 −0.191838 0.981427i 0.561445π-0.561445\pi
−0.191838 + 0.981427i 0.561445π0.561445\pi
458458 0 0
459459 7.34847 + 7.34847i 0.342997 + 0.342997i
460460 0 0
461461 26.2929i 1.22458i −0.790633 0.612290i 0.790248π-0.790248\pi
0.790633 0.612290i 0.209752π-0.209752\pi
462462 0 0
463463 37.8434i 1.75873i −0.476148 0.879365i 0.657967π-0.657967\pi
0.476148 0.879365i 0.342033π-0.342033\pi
464464 0 0
465465 9.79796 + 9.79796i 0.454369 + 0.454369i
466466 0 0
467467 21.1464 0.978540 0.489270 0.872132i 0.337263π-0.337263\pi
0.489270 + 0.872132i 0.337263π0.337263\pi
468468 0 0
469469 14.8990 0.687971
470470 0 0
471471 12.2474 + 12.2474i 0.564333 + 0.564333i
472472 0 0
473473 3.10102i 0.142585i
474474 0 0
475475 2.00000i 0.0917663i
476476 0 0
477477 8.69694 0.398205
478478 0 0
479479 17.3939 0.794747 0.397373 0.917657i 0.369922π-0.369922\pi
0.397373 + 0.917657i 0.369922π0.369922\pi
480480 0 0
481481 41.3939 1.88740
482482 0 0
483483 −2.44949 + 2.44949i −0.111456 + 0.111456i
484484 0 0
485485 9.10102i 0.413256i
486486 0 0
487487 2.65153i 0.120152i −0.998194 0.0600762i 0.980866π-0.980866\pi
0.998194 0.0600762i 0.0191344π-0.0191344\pi
488488 0 0
489489 −12.7980 + 12.7980i −0.578744 + 0.578744i
490490 0 0
491491 −15.7980 −0.712952 −0.356476 0.934304i 0.616022π-0.616022\pi
−0.356476 + 0.934304i 0.616022π0.616022\pi
492492 0 0
493493 17.7980 0.801580
494494 0 0
495495 6.00000 0.269680
496496 0 0
497497 39.5959i 1.77612i
498498 0 0
499499 31.3939i 1.40538i 0.711495 + 0.702691i 0.248019π0.248019\pi
−0.711495 + 0.702691i 0.751981π0.751981\pi
500500 0 0
501501 8.14643 + 8.14643i 0.363956 + 0.363956i
502502 0 0
503503 −36.9444 −1.64727 −0.823634 0.567121i 0.808057π-0.808057\pi
−0.823634 + 0.567121i 0.808057π0.808057\pi
504504 0 0
505505 3.10102 0.137994
506506 0 0
507507 −42.3712 42.3712i −1.88177 1.88177i
508508 0 0
509509 7.10102i 0.314747i −0.987539 0.157374i 0.949697π-0.949697\pi
0.987539 0.157374i 0.0503027π-0.0503027\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 −13.3485 −0.588204
516516 0 0
517517 7.10102 0.312303
518518 0 0
519519 14.4495 14.4495i 0.634262 0.634262i
520520 0 0
521521 25.7980i 1.13023i −0.825012 0.565115i 0.808832π-0.808832\pi
0.825012 0.565115i 0.191168π-0.191168\pi
522522 0 0
523523 15.7526i 0.688811i −0.938821 0.344405i 0.888081π-0.888081\pi
0.938821 0.344405i 0.111919π-0.111919\pi
524524 0 0
525525 −5.44949 + 5.44949i −0.237835 + 0.237835i
526526 0 0
527527 16.0000 0.696971
528528 0 0
529529 −22.7980 −0.991216
530530 0 0
531531 32.6969i 1.41893i
532532 0 0
533533 81.3939i 3.52556i
534534 0 0
535535 10.4495i 0.451771i
536536 0 0
537537 16.0454 + 16.0454i 0.692410 + 0.692410i
538538 0 0
539539 −25.5959 −1.10249
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 −26.4495 26.4495i −1.13506 1.13506i
544544 0 0
545545 12.8990i 0.552532i
546546 0 0
547547 26.0454i 1.11362i −0.830639 0.556811i 0.812025π-0.812025\pi
0.830639 0.556811i 0.187975π-0.187975\pi
548548 0 0
549549 2.69694i 0.115103i
550550 0 0
551551 17.7980 0.758219
552552 0 0
553553 −21.7980 −0.926944
554554 0 0
555555 7.34847 7.34847i 0.311925 0.311925i
556556 0 0
557557 6.00000i 0.254228i 0.991888 + 0.127114i 0.0405714π0.0405714\pi
−0.991888 + 0.127114i 0.959429π0.959429\pi
558558 0 0
559559 10.6969i 0.452432i
560560 0 0
561561 4.89898 4.89898i 0.206835 0.206835i
562562 0 0
563563 −13.5505 −0.571086 −0.285543 0.958366i 0.592174π-0.592174\pi
−0.285543 + 0.958366i 0.592174π0.592174\pi
564564 0 0
565565 −1.10102 −0.0463203
566566 0 0
567567 40.0454i 1.68175i
568568 0 0
569569 29.5959i 1.24073i 0.784315 + 0.620363i 0.213015π0.213015\pi
−0.784315 + 0.620363i 0.786985π0.786985\pi
570570 0 0
571571 0.696938i 0.0291660i −0.999894 0.0145830i 0.995358π-0.995358\pi
0.999894 0.0145830i 0.00464207π-0.00464207\pi
572572 0 0
573573 −15.7980 15.7980i −0.659969 0.659969i
574574 0 0
575575 0.449490 0.0187450
576576 0 0
577577 7.79796 0.324633 0.162317 0.986739i 0.448103π-0.448103\pi
0.162317 + 0.986739i 0.448103π0.448103\pi
578578 0 0
579579 5.75255 + 5.75255i 0.239068 + 0.239068i
580580 0 0
581581 54.4949i 2.26083i
582582 0 0
583583 5.79796i 0.240127i
584584 0 0
585585 −20.6969 −0.855713
586586 0 0
587587 20.2474 0.835702 0.417851 0.908516i 0.362783π-0.362783\pi
0.417851 + 0.908516i 0.362783π0.362783\pi
588588 0 0
589589 16.0000 0.659269
590590 0 0
591591 −10.6515 + 10.6515i −0.438145 + 0.438145i
592592 0 0
593593 40.6969i 1.67122i −0.549321 0.835611i 0.685114π-0.685114\pi
0.549321 0.835611i 0.314886π-0.314886\pi
594594 0 0
595595 8.89898i 0.364823i
596596 0 0
597597 −3.79796 + 3.79796i −0.155440 + 0.155440i
598598 0 0
599599 17.3939 0.710695 0.355347 0.934734i 0.384363π-0.384363\pi
0.355347 + 0.934734i 0.384363π0.384363\pi
600600 0 0
601601 −5.79796 −0.236504 −0.118252 0.992984i 0.537729π-0.537729\pi
−0.118252 + 0.992984i 0.537729π0.537729\pi
602602 0 0
603603 10.0454 0.409081
604604 0 0
605605 7.00000i 0.284590i
606606 0 0
607607 22.6515i 0.919397i −0.888075 0.459699i 0.847957π-0.847957\pi
0.888075 0.459699i 0.152043π-0.152043\pi
608608 0 0
609609 −48.4949 48.4949i −1.96511 1.96511i
610610 0 0
611611 −24.4949 −0.990957
612612 0 0
613613 −42.4949 −1.71635 −0.858176 0.513355i 0.828402π-0.828402\pi
−0.858176 + 0.513355i 0.828402π0.828402\pi
614614 0 0
615615 14.4495 + 14.4495i 0.582660 + 0.582660i
616616 0 0
617617 46.0000i 1.85189i −0.377658 0.925945i 0.623271π-0.623271\pi
0.377658 0.925945i 0.376729π-0.376729\pi
618618 0 0
619619 7.79796i 0.313426i 0.987644 + 0.156713i 0.0500898π0.0500898\pi
−0.987644 + 0.156713i 0.949910π0.949910\pi
620620 0 0
621621 −1.65153 + 1.65153i −0.0662736 + 0.0662736i
622622 0 0
623623 43.5959 1.74663
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 −11.1464 + 11.1464i −0.443031 + 0.443031i
634634 0 0
635635 9.34847 0.370983
636636 0 0
637637 88.2929 3.49829
638638 0 0
639639 26.6969i 1.05611i
640640 0 0
641641 6.00000i 0.236986i −0.992955 0.118493i 0.962194π-0.962194\pi
0.992955 0.118493i 0.0378063π-0.0378063\pi
642642 0 0
643643 8.65153i 0.341183i 0.985342 + 0.170592i 0.0545679π0.0545679\pi
−0.985342 + 0.170592i 0.945432π0.945432\pi
644644 0 0
645645 1.89898 + 1.89898i 0.0747722 + 0.0747722i
646646 0 0
647647 −5.75255 −0.226156 −0.113078 0.993586i 0.536071π-0.536071\pi
−0.113078 + 0.993586i 0.536071π0.536071\pi
648648 0 0
649649 21.7980 0.855645
650650 0 0
651651 −43.5959 43.5959i −1.70866 1.70866i
652652 0 0
653653 10.8990i 0.426510i −0.976997 0.213255i 0.931593π-0.931593\pi
0.976997 0.213255i 0.0684065π-0.0684065\pi
654654 0 0
655655 19.7980i 0.773570i
656656 0 0
657657 3.30306i 0.128865i
658658 0 0
659659 14.4949 0.564641 0.282321 0.959320i 0.408896π-0.408896\pi
0.282321 + 0.959320i 0.408896π0.408896\pi
660660 0 0
661661 −16.8990 −0.657294 −0.328647 0.944453i 0.606593π-0.606593\pi
−0.328647 + 0.944453i 0.606593π0.606593\pi
662662 0 0
663663 −16.8990 + 16.8990i −0.656302 + 0.656302i
664664 0 0
665665 8.89898i 0.345088i
666666 0 0
667667 4.00000i 0.154881i
668668 0 0
669669 9.24745 9.24745i 0.357527 0.357527i
670670 0 0
671671 −1.79796 −0.0694094
672672 0 0
673673 −32.6969 −1.26037 −0.630187 0.776443i 0.717022π-0.717022\pi
−0.630187 + 0.776443i 0.717022π0.717022\pi
674674 0 0
675675 −3.67423 + 3.67423i −0.141421 + 0.141421i
676676 0 0
677677 16.6969i 0.641715i −0.947127 0.320858i 0.896029π-0.896029\pi
0.947127 0.320858i 0.103971π-0.103971\pi
678678 0 0
679679 40.4949i 1.55405i
680680 0 0
681681 16.1010 + 16.1010i 0.616992 + 0.616992i
682682 0 0
683683 19.3485 0.740349 0.370174 0.928962i 0.379298π-0.379298\pi
0.370174 + 0.928962i 0.379298π0.379298\pi
684684 0 0
685685 −10.8990 −0.416429
686686 0 0
687687 0.247449 + 0.247449i 0.00944076 + 0.00944076i
688688 0 0
689689 20.0000i 0.761939i
690690 0 0
691691 8.69694i 0.330847i −0.986223 0.165424i 0.947101π-0.947101\pi
0.986223 0.165424i 0.0528991π-0.0528991\pi
692692 0 0
693693 −26.6969 −1.01413
694694 0 0
695695 2.00000 0.0758643
696696 0 0
697697 23.5959 0.893759
698698 0 0
699699 9.55051 9.55051i 0.361233 0.361233i
700700 0 0
701701 15.3939i 0.581419i −0.956811 0.290709i 0.906109π-0.906109\pi
0.956811 0.290709i 0.0938913π-0.0938913\pi
702702 0 0
703703 12.0000i 0.452589i
704704 0 0
705705 −4.34847 + 4.34847i −0.163773 + 0.163773i
706706 0 0
707707 −13.7980 −0.518926
708708 0 0
709709 24.2020 0.908927 0.454463 0.890765i 0.349831π-0.349831\pi
0.454463 + 0.890765i 0.349831π0.349831\pi
710710 0 0
711711 −14.6969 −0.551178
712712 0 0
713713 3.59592i 0.134668i
714714 0 0
715715 13.7980i 0.516014i
716716 0 0
717717 31.5959 + 31.5959i 1.17997 + 1.17997i
718718 0 0
719719 −25.3939 −0.947032 −0.473516 0.880785i 0.657015π-0.657015\pi
−0.473516 + 0.880785i 0.657015π0.657015\pi
720720 0 0
721721 59.3939 2.21194
722722 0 0
723723 −19.1010 19.1010i −0.710375 0.710375i
724724 0 0
725725 8.89898i 0.330500i
726726 0 0
727727 31.1464i 1.15516i 0.816335 + 0.577579i 0.196002π0.196002\pi
−0.816335 + 0.577579i 0.803998π0.803998\pi
728728 0 0
729729 27.0000i 1.00000i
730730 0 0
731731 3.10102 0.114695
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 15.6742 15.6742i 0.578153 0.578153i
736736 0 0
737737 6.69694i 0.246685i
738738 0 0
739739 15.7980i 0.581137i −0.956854 0.290569i 0.906156π-0.906156\pi
0.956854 0.290569i 0.0938445π-0.0938445\pi
740740 0 0
741741 −16.8990 + 16.8990i −0.620800 + 0.620800i
742742 0 0
743743 −35.1464 −1.28940 −0.644699 0.764437i 0.723017π-0.723017\pi
−0.644699 + 0.764437i 0.723017π0.723017\pi
744744 0 0
745745 −15.7980 −0.578792
746746 0 0
747747 36.7423i 1.34433i
748748 0 0
749749 46.4949i 1.69889i
750750 0 0
751751 49.3939i 1.80241i 0.433395 + 0.901204i 0.357316π0.357316\pi
−0.433395 + 0.901204i 0.642684π0.642684\pi
752752 0 0
753753 −10.0454 10.0454i −0.366075 0.366075i
754754 0 0
755755 15.5959 0.567594
756756 0 0
757757 −39.3939 −1.43179 −0.715897 0.698205i 0.753982π-0.753982\pi
−0.715897 + 0.698205i 0.753982π0.753982\pi
758758 0 0
759759 1.10102 + 1.10102i 0.0399645 + 0.0399645i
760760 0 0
761761 14.2020i 0.514824i 0.966302 + 0.257412i 0.0828697π0.0828697\pi
−0.966302 + 0.257412i 0.917130π0.917130\pi
762762 0 0
763763 57.3939i 2.07780i
764764 0 0
765765 6.00000i 0.216930i
766766 0 0
767767 −75.1918 −2.71502
768768 0 0
769769 −12.2020 −0.440017 −0.220008 0.975498i 0.570608π-0.570608\pi
−0.220008 + 0.975498i 0.570608π0.570608\pi
770770 0 0
771771 1.34847 1.34847i 0.0485639 0.0485639i
772772 0 0
773773 4.69694i 0.168937i 0.996426 + 0.0844686i 0.0269193π0.0269193\pi
−0.996426 + 0.0844686i 0.973081π0.973081\pi
774774 0 0
775775 8.00000i 0.287368i
776776 0 0
777777 −32.6969 + 32.6969i −1.17300 + 1.17300i
778778 0 0
779779 23.5959 0.845411
780780 0 0
781781 −17.7980 −0.636861
782782 0 0
783783 −32.6969 32.6969i −1.16849 1.16849i
784784 0 0
785785 10.0000i 0.356915i
786786 0 0
787787 21.1464i 0.753789i 0.926256 + 0.376894i 0.123008π0.123008\pi
−0.926256 + 0.376894i 0.876992π0.876992\pi
788788 0 0
789789 −9.24745 9.24745i −0.329218 0.329218i
790790 0 0
791791 4.89898 0.174188
792792 0 0
793793 6.20204 0.220241
794794 0 0
795795 3.55051 + 3.55051i 0.125924 + 0.125924i
796796 0 0
797797 10.8990i 0.386062i −0.981193 0.193031i 0.938168π-0.938168\pi
0.981193 0.193031i 0.0618317π-0.0618317\pi
798798 0 0
799799 7.10102i 0.251216i
800800 0 0
801801 29.3939 1.03858
802802 0 0
803803 2.20204 0.0777083
804804 0 0
805805 −2.00000 −0.0704907
806806 0 0
807807 21.5505 21.5505i 0.758614 0.758614i
808808 0 0
809809 47.5959i 1.67338i 0.547674 + 0.836692i 0.315513π0.315513\pi
−0.547674 + 0.836692i 0.684487π0.684487\pi
810810 0 0
811811 50.4949i 1.77312i 0.462618 + 0.886558i 0.346910π0.346910\pi
−0.462618 + 0.886558i 0.653090π0.653090\pi
812812 0 0
813813 −14.6969 + 14.6969i −0.515444 + 0.515444i
814814 0 0
815815 −10.4495 −0.366030
816816 0 0
817817 3.10102 0.108491
818818 0 0
819819 92.0908 3.21791
820820 0 0
821821 1.59592i 0.0556979i 0.999612 + 0.0278490i 0.00886575π0.00886575\pi
−0.999612 + 0.0278490i 0.991134π0.991134\pi
822822 0 0
823823 12.4495i 0.433962i 0.976176 + 0.216981i 0.0696210π0.0696210\pi
−0.976176 + 0.216981i 0.930379π0.930379\pi
824824 0 0
825825 2.44949 + 2.44949i 0.0852803 + 0.0852803i
826826 0 0
827827 33.1464 1.15261 0.576307 0.817233i 0.304493π-0.304493\pi
0.576307 + 0.817233i 0.304493π0.304493\pi
828828 0 0
829829 24.4949 0.850743 0.425371 0.905019i 0.360143π-0.360143\pi
0.425371 + 0.905019i 0.360143π0.360143\pi
830830 0 0
831831 2.44949 + 2.44949i 0.0849719 + 0.0849719i
832832 0 0
833833 25.5959i 0.886846i
834834 0 0
835835 6.65153i 0.230186i
836836 0 0
837837 −29.3939 29.3939i −1.01600 1.01600i
838838 0 0
839839 −1.79796 −0.0620724 −0.0310362 0.999518i 0.509881π-0.509881\pi
−0.0310362 + 0.999518i 0.509881π0.509881\pi
840840 0 0
841841 −50.1918 −1.73075
842842 0 0
843843 −26.4495 + 26.4495i −0.910969 + 0.910969i
844844 0 0
845845 34.5959i 1.19014i
846846 0 0
847847 31.1464i 1.07020i
848848 0 0
849849 25.8990 25.8990i 0.888851 0.888851i
850850 0 0
851851 2.69694 0.0924499
852852 0 0
853853 41.1010 1.40727 0.703636 0.710561i 0.251559π-0.251559\pi
0.703636 + 0.710561i 0.251559π0.251559\pi
854854 0 0
855855 6.00000i 0.205196i
856856 0 0
857857 20.6969i 0.706994i −0.935436 0.353497i 0.884992π-0.884992\pi
0.935436 0.353497i 0.115008π-0.115008\pi
858858 0 0
859859 1.59592i 0.0544520i −0.999629 0.0272260i 0.991333π-0.991333\pi
0.999629 0.0272260i 0.00866738π-0.00866738\pi
860860 0 0
861861 −64.2929 64.2929i −2.19109 2.19109i
862862 0 0
863863 −8.94439 −0.304470 −0.152235 0.988344i 0.548647π-0.548647\pi
−0.152235 + 0.988344i 0.548647π0.548647\pi
864864 0 0
865865 11.7980 0.401143
866866 0 0
867867 −15.9217 15.9217i −0.540729 0.540729i
868868 0 0
869869 9.79796i 0.332373i
870870 0 0
871871 23.1010i 0.782748i
872872 0 0
873873 27.3031i 0.924069i
874874 0 0
875875 −4.44949 −0.150420
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 −10.0454 + 10.0454i −0.338823 + 0.338823i
880880 0 0
881881 27.7980i 0.936537i −0.883586 0.468269i 0.844878π-0.844878\pi
0.883586 0.468269i 0.155122π-0.155122\pi
882882 0 0
883883 13.5505i 0.456011i 0.973660 + 0.228005i 0.0732204π0.0732204\pi
−0.973660 + 0.228005i 0.926780π0.926780\pi
884884 0 0
885885 −13.3485 + 13.3485i −0.448704 + 0.448704i
886886 0 0
887887 12.8536 0.431581 0.215790 0.976440i 0.430767π-0.430767\pi
0.215790 + 0.976440i 0.430767π0.430767\pi
888888 0 0
889889 −41.5959 −1.39508
890890 0 0
891891 −18.0000 −0.603023
892892 0 0
893893 7.10102i 0.237627i
894894 0 0
895895 13.1010i 0.437919i
896896 0 0
897897 −3.79796 3.79796i −0.126810 0.126810i
898898 0 0
899899 −71.1918 −2.37438
900900 0 0
901901 5.79796 0.193158
902902 0 0
903903 −8.44949 8.44949i −0.281181 0.281181i
904904 0 0
905905 21.5959i 0.717873i
906906 0 0
907907 50.9444i 1.69158i −0.533515 0.845790i 0.679129π-0.679129\pi
0.533515 0.845790i 0.320871π-0.320871\pi
908908 0 0
909909 −9.30306 −0.308563
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 1.10102 1.10102i 0.0363986 0.0363986i
916916 0 0
917917 88.0908i 2.90902i
918918 0 0
919919 4.49490i 0.148273i 0.997248 + 0.0741365i 0.0236200π0.0236200\pi
−0.997248 + 0.0741365i 0.976380π0.976380\pi
920920 0 0
921921 −15.4949 + 15.4949i −0.510574 + 0.510574i
922922 0 0
923923 61.3939 2.02080
924924 0 0
925925 6.00000 0.197279
926926 0 0
927927 40.0454 1.31526
928928 0 0
929929 34.0000i 1.11550i 0.830008 + 0.557752i 0.188336π0.188336\pi
−0.830008 + 0.557752i 0.811664π0.811664\pi
930930 0 0
931931 25.5959i 0.838872i
932932 0 0
933933 −30.0000 30.0000i −0.982156 0.982156i
934934 0 0
935935 4.00000 0.130814
936936 0 0
937937 −46.4949 −1.51892 −0.759461 0.650553i 0.774537π-0.774537\pi
−0.759461 + 0.650553i 0.774537π0.774537\pi
938938 0 0
939939 24.2474 + 24.2474i 0.791286 + 0.791286i
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 5.30306i 0.172691i
944944 0 0
945945 16.3485 16.3485i 0.531816 0.531816i
946946 0 0
947947 −1.55051 −0.0503848 −0.0251924 0.999683i 0.508020π-0.508020\pi
−0.0251924 + 0.999683i 0.508020π0.508020\pi
948948 0 0
949949 −7.59592 −0.246574
950950 0 0
951951 10.6515 10.6515i 0.345400 0.345400i
952952 0 0
953953 1.10102i 0.0356656i −0.999841 0.0178328i 0.994323π-0.994323\pi
0.999841 0.0178328i 0.00567665π-0.00567665\pi
954954 0 0
955955 12.8990i 0.417401i
956956 0 0
957957 −21.7980 + 21.7980i −0.704628 + 0.704628i
958958 0 0
959959 48.4949 1.56598
960960 0 0
961961 −33.0000 −1.06452
962962 0 0
963963 31.3485i 1.01019i
964964 0 0
965965 4.69694i 0.151200i
966966 0 0
967967 30.2474i 0.972692i 0.873766 + 0.486346i 0.161671π0.161671\pi
−0.873766 + 0.486346i 0.838329π0.838329\pi
968968 0 0
969969 4.89898 + 4.89898i 0.157378 + 0.157378i
970970 0 0
971971 39.7980 1.27718 0.638589 0.769548i 0.279519π-0.279519\pi
0.638589 + 0.769548i 0.279519π0.279519\pi
972972 0 0
973973 −8.89898 −0.285288
974974 0 0
975975 −8.44949 8.44949i −0.270600 0.270600i
976976 0 0
977977 33.1918i 1.06190i −0.847403 0.530950i 0.821835π-0.821835\pi
0.847403 0.530950i 0.178165π-0.178165\pi
978978 0 0
979979 19.5959i 0.626288i
980980 0 0
981981 38.6969i 1.23550i
982982 0 0
983983 52.0454 1.65999 0.829995 0.557770i 0.188343π-0.188343\pi
0.829995 + 0.557770i 0.188343π0.188343\pi
984984 0 0
985985 −8.69694 −0.277108
986986 0 0
987987 19.3485 19.3485i 0.615869 0.615869i
988988 0 0
989989 0.696938i 0.0221614i
990990 0 0
991991 31.1918i 0.990841i 0.868653 + 0.495421i 0.164986π0.164986\pi
−0.868653 + 0.495421i 0.835014π0.835014\pi
992992 0 0
993993 28.0454 28.0454i 0.889994 0.889994i
994994 0 0
995995 −3.10102 −0.0983090
996996 0 0
997997 −46.0908 −1.45971 −0.729855 0.683602i 0.760413π-0.760413\pi
−0.729855 + 0.683602i 0.760413π0.760413\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.i.1151.1 yes 4
3.2 odd 2 1920.2.h.g.1151.3 4
4.3 odd 2 1920.2.h.g.1151.4 yes 4
8.3 odd 2 1920.2.h.j.1151.1 yes 4
8.5 even 2 1920.2.h.h.1151.4 yes 4
12.11 even 2 inner 1920.2.h.i.1151.2 yes 4
24.5 odd 2 1920.2.h.j.1151.2 yes 4
24.11 even 2 1920.2.h.h.1151.3 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1920.2.h.g.1151.3 4 3.2 odd 2
1920.2.h.g.1151.4 yes 4 4.3 odd 2
1920.2.h.h.1151.3 yes 4 24.11 even 2
1920.2.h.h.1151.4 yes 4 8.5 even 2
1920.2.h.i.1151.1 yes 4 1.1 even 1 trivial
1920.2.h.i.1151.2 yes 4 12.11 even 2 inner
1920.2.h.j.1151.1 yes 4 8.3 odd 2
1920.2.h.j.1151.2 yes 4 24.5 odd 2