Properties

Label 1920.2.y.j.1567.4
Level 19201920
Weight 22
Character 1920.1567
Analytic conductor 15.33115.331
Analytic rank 00
Dimension 1616
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(223,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 3])) 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("1920.223"); 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.y (of order 44, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,0,16,0,4,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == 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: 1616
Relative dimension: 88 over Q(i)\Q(i)
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x166x15+14x1410x1326x12+78x1166x1074x9+233x8++256 x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 212 2^{12}
Twist minimal: no (minimal twist has level 240)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 1567.4
Root 1.38194+0.300388i1.38194 + 0.300388i of defining polynomial
Character χ\chi == 1920.1567
Dual form 1920.2.y.j.223.4

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+1.00000q3+(0.311968+2.21420i)q5+(1.96597+1.96597i)q7+1.00000q9+(0.8703960.870396i)q11+5.88276iq13+(0.311968+2.21420i)q15+(2.69398+2.69398i)q17+(2.40037+2.40037i)q19+(1.96597+1.96597i)q21+(2.63907+2.63907i)q23+(4.805351.38152i)q25+1.00000q27+(7.436467.43646i)q297.72239iq31+(0.8703960.870396i)q33+(4.96636+3.73972i)q35+4.49007iq37+5.88276iq394.84873iq41+0.461098iq43+(0.311968+2.21420i)q45+(4.666934.66693i)q47+0.730041iq49+(2.69398+2.69398i)q51+2.41272q53+(1.65569+2.19876i)q55+(2.40037+2.40037i)q57+(6.47458+6.47458i)q59+(8.50808+8.50808i)q61+(1.96597+1.96597i)q63+(13.02561.83523i)q65+6.40870iq67+(2.63907+2.63907i)q69+13.3214q71+(1.629331.62933i)q73+(4.805351.38152i)q75+3.42234q77+4.14482q79+1.00000q810.241277q83+(6.80545+5.12458i)q85+(7.436467.43646i)q87+2.86287q89+(11.5653+11.5653i)q917.72239iq93+(4.566056.06373i)q95+(3.18909+3.18909i)q97+(0.8703960.870396i)q99+O(q100)q+1.00000 q^{3} +(-0.311968 + 2.21420i) q^{5} +(1.96597 + 1.96597i) q^{7} +1.00000 q^{9} +(0.870396 - 0.870396i) q^{11} +5.88276i q^{13} +(-0.311968 + 2.21420i) q^{15} +(2.69398 + 2.69398i) q^{17} +(-2.40037 + 2.40037i) q^{19} +(1.96597 + 1.96597i) q^{21} +(-2.63907 + 2.63907i) q^{23} +(-4.80535 - 1.38152i) q^{25} +1.00000 q^{27} +(-7.43646 - 7.43646i) q^{29} -7.72239i q^{31} +(0.870396 - 0.870396i) q^{33} +(-4.96636 + 3.73972i) q^{35} +4.49007i q^{37} +5.88276i q^{39} -4.84873i q^{41} +0.461098i q^{43} +(-0.311968 + 2.21420i) q^{45} +(4.66693 - 4.66693i) q^{47} +0.730041i q^{49} +(2.69398 + 2.69398i) q^{51} +2.41272 q^{53} +(1.65569 + 2.19876i) q^{55} +(-2.40037 + 2.40037i) q^{57} +(6.47458 + 6.47458i) q^{59} +(-8.50808 + 8.50808i) q^{61} +(1.96597 + 1.96597i) q^{63} +(-13.0256 - 1.83523i) q^{65} +6.40870i q^{67} +(-2.63907 + 2.63907i) q^{69} +13.3214 q^{71} +(-1.62933 - 1.62933i) q^{73} +(-4.80535 - 1.38152i) q^{75} +3.42234 q^{77} +4.14482 q^{79} +1.00000 q^{81} -0.241277 q^{83} +(-6.80545 + 5.12458i) q^{85} +(-7.43646 - 7.43646i) q^{87} +2.86287 q^{89} +(-11.5653 + 11.5653i) q^{91} -7.72239i q^{93} +(-4.56605 - 6.06373i) q^{95} +(3.18909 + 3.18909i) q^{97} +(0.870396 - 0.870396i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+16q3+4q5+4q7+16q9+4q158q17+8q19+4q21+32q25+16q2712q2920q35+4q45+32q478q5116q53+4q55+8q57++48q97+O(q100) 16 q + 16 q^{3} + 4 q^{5} + 4 q^{7} + 16 q^{9} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} + 32 q^{25} + 16 q^{27} - 12 q^{29} - 20 q^{35} + 4 q^{45} + 32 q^{47} - 8 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

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

nn 511511 641641 901901 15371537
χ(n)\chi(n) 1-1 11 e(14)e\left(\frac{1}{4}\right) e(14)e\left(\frac{1}{4}\right)

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 1.00000 0.577350
44 0 0
55 −0.311968 + 2.21420i −0.139516 + 0.990220i
66 0 0
77 1.96597 + 1.96597i 0.743065 + 0.743065i 0.973167 0.230101i 0.0739058π-0.0739058\pi
−0.230101 + 0.973167i 0.573906π0.573906\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 0.870396 0.870396i 0.262434 0.262434i −0.563608 0.826042i 0.690587π-0.690587\pi
0.826042 + 0.563608i 0.190587π0.190587\pi
1212 0 0
1313 5.88276i 1.63158i 0.578345 + 0.815792i 0.303699π0.303699\pi
−0.578345 + 0.815792i 0.696301π0.696301\pi
1414 0 0
1515 −0.311968 + 2.21420i −0.0805497 + 0.571704i
1616 0 0
1717 2.69398 + 2.69398i 0.653387 + 0.653387i 0.953807 0.300420i 0.0971268π-0.0971268\pi
−0.300420 + 0.953807i 0.597127π0.597127\pi
1818 0 0
1919 −2.40037 + 2.40037i −0.550682 + 0.550682i −0.926638 0.375956i 0.877314π-0.877314\pi
0.375956 + 0.926638i 0.377314π0.377314\pi
2020 0 0
2121 1.96597 + 1.96597i 0.429009 + 0.429009i
2222 0 0
2323 −2.63907 + 2.63907i −0.550284 + 0.550284i −0.926523 0.376239i 0.877217π-0.877217\pi
0.376239 + 0.926523i 0.377217π0.377217\pi
2424 0 0
2525 −4.80535 1.38152i −0.961070 0.276303i
2626 0 0
2727 1.00000 0.192450
2828 0 0
2929 −7.43646 7.43646i −1.38092 1.38092i −0.842996 0.537919i 0.819210π-0.819210\pi
−0.537919 0.842996i 0.680790π-0.680790\pi
3030 0 0
3131 7.72239i 1.38698i −0.720465 0.693491i 0.756072π-0.756072\pi
0.720465 0.693491i 0.243928π-0.243928\pi
3232 0 0
3333 0.870396 0.870396i 0.151516 0.151516i
3434 0 0
3535 −4.96636 + 3.73972i −0.839467 + 0.632128i
3636 0 0
3737 4.49007i 0.738163i 0.929397 + 0.369081i 0.120328π0.120328\pi
−0.929397 + 0.369081i 0.879672π0.879672\pi
3838 0 0
3939 5.88276i 0.941996i
4040 0 0
4141 4.84873i 0.757244i −0.925551 0.378622i 0.876398π-0.876398\pi
0.925551 0.378622i 0.123602π-0.123602\pi
4242 0 0
4343 0.461098i 0.0703168i 0.999382 + 0.0351584i 0.0111936π0.0111936\pi
−0.999382 + 0.0351584i 0.988806π0.988806\pi
4444 0 0
4545 −0.311968 + 2.21420i −0.0465054 + 0.330073i
4646 0 0
4747 4.66693 4.66693i 0.680742 0.680742i −0.279425 0.960167i 0.590144π-0.590144\pi
0.960167 + 0.279425i 0.0901439π0.0901439\pi
4848 0 0
4949 0.730041i 0.104292i
5050 0 0
5151 2.69398 + 2.69398i 0.377233 + 0.377233i
5252 0 0
5353 2.41272 0.331413 0.165706 0.986175i 0.447010π-0.447010\pi
0.165706 + 0.986175i 0.447010π0.447010\pi
5454 0 0
5555 1.65569 + 2.19876i 0.223254 + 0.296481i
5656 0 0
5757 −2.40037 + 2.40037i −0.317936 + 0.317936i
5858 0 0
5959 6.47458 + 6.47458i 0.842919 + 0.842919i 0.989238 0.146318i 0.0467424π-0.0467424\pi
−0.146318 + 0.989238i 0.546742π0.546742\pi
6060 0 0
6161 −8.50808 + 8.50808i −1.08935 + 1.08935i −0.0937523 + 0.995596i 0.529886π0.529886\pi
−0.995596 + 0.0937523i 0.970114π0.970114\pi
6262 0 0
6363 1.96597 + 1.96597i 0.247688 + 0.247688i
6464 0 0
6565 −13.0256 1.83523i −1.61563 0.227632i
6666 0 0
6767 6.40870i 0.782948i 0.920189 + 0.391474i 0.128035π0.128035\pi
−0.920189 + 0.391474i 0.871965π0.871965\pi
6868 0 0
6969 −2.63907 + 2.63907i −0.317706 + 0.317706i
7070 0 0
7171 13.3214 1.58096 0.790482 0.612486i 0.209830π-0.209830\pi
0.790482 + 0.612486i 0.209830π0.209830\pi
7272 0 0
7373 −1.62933 1.62933i −0.190699 0.190699i 0.605299 0.795998i 0.293053π-0.293053\pi
−0.795998 + 0.605299i 0.793053π0.793053\pi
7474 0 0
7575 −4.80535 1.38152i −0.554874 0.159524i
7676 0 0
7777 3.42234 0.390011
7878 0 0
7979 4.14482 0.466328 0.233164 0.972437i 0.425092π-0.425092\pi
0.233164 + 0.972437i 0.425092π0.425092\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 −0.241277 −0.0264836 −0.0132418 0.999912i 0.504215π-0.504215\pi
−0.0132418 + 0.999912i 0.504215π0.504215\pi
8484 0 0
8585 −6.80545 + 5.12458i −0.738155 + 0.555839i
8686 0 0
8787 −7.43646 7.43646i −0.797272 0.797272i
8888 0 0
8989 2.86287 0.303464 0.151732 0.988422i 0.451515π-0.451515\pi
0.151732 + 0.988422i 0.451515π0.451515\pi
9090 0 0
9191 −11.5653 + 11.5653i −1.21237 + 1.21237i
9292 0 0
9393 7.72239i 0.800775i
9494 0 0
9595 −4.56605 6.06373i −0.468467 0.622125i
9696 0 0
9797 3.18909 + 3.18909i 0.323803 + 0.323803i 0.850224 0.526421i 0.176466π-0.176466\pi
−0.526421 + 0.850224i 0.676466π0.676466\pi
9898 0 0
9999 0.870396 0.870396i 0.0874781 0.0874781i
100100 0 0
101101 −6.90372 6.90372i −0.686946 0.686946i 0.274610 0.961556i 0.411451π-0.411451\pi
−0.961556 + 0.274610i 0.911451π0.911451\pi
102102 0 0
103103 −4.09832 + 4.09832i −0.403819 + 0.403819i −0.879577 0.475757i 0.842174π-0.842174\pi
0.475757 + 0.879577i 0.342174π0.342174\pi
104104 0 0
105105 −4.96636 + 3.73972i −0.484667 + 0.364959i
106106 0 0
107107 10.0579 0.972333 0.486166 0.873866i 0.338395π-0.338395\pi
0.486166 + 0.873866i 0.338395π0.338395\pi
108108 0 0
109109 −11.2123 11.2123i −1.07394 1.07394i −0.997039 0.0769025i 0.975497π-0.975497\pi
−0.0769025 0.997039i 0.524503π-0.524503\pi
110110 0 0
111111 4.49007i 0.426178i
112112 0 0
113113 −0.420404 + 0.420404i −0.0395483 + 0.0395483i −0.726604 0.687056i 0.758903π-0.758903\pi
0.687056 + 0.726604i 0.258903π0.258903\pi
114114 0 0
115115 −5.02012 6.66672i −0.468128 0.621675i
116116 0 0
117117 5.88276i 0.543861i
118118 0 0
119119 10.5926i 0.971018i
120120 0 0
121121 9.48482i 0.862257i
122122 0 0
123123 4.84873i 0.437195i
124124 0 0
125125 4.55807 10.2090i 0.407686 0.913122i
126126 0 0
127127 −12.1223 + 12.1223i −1.07568 + 1.07568i −0.0787895 + 0.996891i 0.525106π0.525106\pi
−0.996891 + 0.0787895i 0.974894π0.974894\pi
128128 0 0
129129 0.461098i 0.0405974i
130130 0 0
131131 9.02309 + 9.02309i 0.788351 + 0.788351i 0.981224 0.192873i 0.0617804π-0.0617804\pi
−0.192873 + 0.981224i 0.561780π0.561780\pi
132132 0 0
133133 −9.43808 −0.818385
134134 0 0
135135 −0.311968 + 2.21420i −0.0268499 + 0.190568i
136136 0 0
137137 −8.12950 + 8.12950i −0.694550 + 0.694550i −0.963230 0.268679i 0.913413π-0.913413\pi
0.268679 + 0.963230i 0.413413π0.413413\pi
138138 0 0
139139 2.98593 + 2.98593i 0.253263 + 0.253263i 0.822307 0.569044i 0.192687π-0.192687\pi
−0.569044 + 0.822307i 0.692687π0.692687\pi
140140 0 0
141141 4.66693 4.66693i 0.393027 0.393027i
142142 0 0
143143 5.12033 + 5.12033i 0.428184 + 0.428184i
144144 0 0
145145 18.7857 14.1459i 1.56007 1.17475i
146146 0 0
147147 0.730041i 0.0602128i
148148 0 0
149149 0.994977 0.994977i 0.0815117 0.0815117i −0.665175 0.746687i 0.731643π-0.731643\pi
0.746687 + 0.665175i 0.231643π0.231643\pi
150150 0 0
151151 18.1365 1.47592 0.737962 0.674842i 0.235788π-0.235788\pi
0.737962 + 0.674842i 0.235788π0.235788\pi
152152 0 0
153153 2.69398 + 2.69398i 0.217796 + 0.217796i
154154 0 0
155155 17.0989 + 2.40914i 1.37342 + 0.193506i
156156 0 0
157157 10.3489 0.825932 0.412966 0.910746i 0.364493π-0.364493\pi
0.412966 + 0.910746i 0.364493π0.364493\pi
158158 0 0
159159 2.41272 0.191341
160160 0 0
161161 −10.3766 −0.817793
162162 0 0
163163 13.2079 1.03453 0.517263 0.855827i 0.326951π-0.326951\pi
0.517263 + 0.855827i 0.326951π0.326951\pi
164164 0 0
165165 1.65569 + 2.19876i 0.128896 + 0.171174i
166166 0 0
167167 −0.0169530 0.0169530i −0.00131186 0.00131186i 0.706451 0.707762i 0.250295π-0.250295\pi
−0.707762 + 0.706451i 0.750295π0.750295\pi
168168 0 0
169169 −21.6069 −1.66207
170170 0 0
171171 −2.40037 + 2.40037i −0.183561 + 0.183561i
172172 0 0
173173 3.43931i 0.261486i 0.991416 + 0.130743i 0.0417363π0.0417363\pi
−0.991416 + 0.130743i 0.958264π0.958264\pi
174174 0 0
175175 −6.73114 12.1632i −0.508827 0.919449i
176176 0 0
177177 6.47458 + 6.47458i 0.486660 + 0.486660i
178178 0 0
179179 0.816756 0.816756i 0.0610472 0.0610472i −0.675924 0.736971i 0.736255π-0.736255\pi
0.736971 + 0.675924i 0.236255π0.236255\pi
180180 0 0
181181 15.2070 + 15.2070i 1.13032 + 1.13032i 0.990123 + 0.140201i 0.0447748π0.0447748\pi
0.140201 + 0.990123i 0.455225π0.455225\pi
182182 0 0
183183 −8.50808 + 8.50808i −0.628935 + 0.628935i
184184 0 0
185185 −9.94190 1.40076i −0.730943 0.102986i
186186 0 0
187187 4.68966 0.342942
188188 0 0
189189 1.96597 + 1.96597i 0.143003 + 0.143003i
190190 0 0
191191 0.536269i 0.0388031i 0.999812 + 0.0194015i 0.00617609π0.00617609\pi
−0.999812 + 0.0194015i 0.993824π0.993824\pi
192192 0 0
193193 −7.70962 + 7.70962i −0.554951 + 0.554951i −0.927866 0.372915i 0.878358π-0.878358\pi
0.372915 + 0.927866i 0.378358π0.378358\pi
194194 0 0
195195 −13.0256 1.83523i −0.932783 0.131424i
196196 0 0
197197 19.6564i 1.40046i −0.713916 0.700231i 0.753080π-0.753080\pi
0.713916 0.700231i 0.246920π-0.246920\pi
198198 0 0
199199 9.32963i 0.661360i −0.943743 0.330680i 0.892722π-0.892722\pi
0.943743 0.330680i 0.107278π-0.107278\pi
200200 0 0
201201 6.40870i 0.452035i
202202 0 0
203203 29.2396i 2.05222i
204204 0 0
205205 10.7361 + 1.51265i 0.749838 + 0.105648i
206206 0 0
207207 −2.63907 + 2.63907i −0.183428 + 0.183428i
208208 0 0
209209 4.17854i 0.289036i
210210 0 0
211211 −7.58277 7.58277i −0.522019 0.522019i 0.396162 0.918181i 0.370342π-0.370342\pi
−0.918181 + 0.396162i 0.870342π0.870342\pi
212212 0 0
213213 13.3214 0.912769
214214 0 0
215215 −1.02096 0.143848i −0.0696291 0.00981033i
216216 0 0
217217 15.1820 15.1820i 1.03062 1.03062i
218218 0 0
219219 −1.62933 1.62933i −0.110100 0.110100i
220220 0 0
221221 −15.8481 + 15.8481i −1.06606 + 1.06606i
222222 0 0
223223 8.76331 + 8.76331i 0.586835 + 0.586835i 0.936773 0.349938i 0.113797π-0.113797\pi
−0.349938 + 0.936773i 0.613797π0.613797\pi
224224 0 0
225225 −4.80535 1.38152i −0.320357 0.0921011i
226226 0 0
227227 25.0028i 1.65949i −0.558141 0.829746i 0.688485π-0.688485\pi
0.558141 0.829746i 0.311515π-0.311515\pi
228228 0 0
229229 7.89911 7.89911i 0.521988 0.521988i −0.396183 0.918171i 0.629666π-0.629666\pi
0.918171 + 0.396183i 0.129666π0.129666\pi
230230 0 0
231231 3.42234 0.225173
232232 0 0
233233 7.91066 + 7.91066i 0.518245 + 0.518245i 0.917040 0.398795i 0.130572π-0.130572\pi
−0.398795 + 0.917040i 0.630572π0.630572\pi
234234 0 0
235235 8.87759 + 11.7895i 0.579110 + 0.769059i
236236 0 0
237237 4.14482 0.269235
238238 0 0
239239 11.4515 0.740735 0.370368 0.928885i 0.379232π-0.379232\pi
0.370368 + 0.928885i 0.379232π0.379232\pi
240240 0 0
241241 20.9793 1.35139 0.675697 0.737180i 0.263843π-0.263843\pi
0.675697 + 0.737180i 0.263843π0.263843\pi
242242 0 0
243243 1.00000 0.0641500
244244 0 0
245245 −1.61646 0.227749i −0.103272 0.0145504i
246246 0 0
247247 −14.1208 14.1208i −0.898484 0.898484i
248248 0 0
249249 −0.241277 −0.0152903
250250 0 0
251251 15.6566 15.6566i 0.988233 0.988233i −0.0116985 0.999932i 0.503724π-0.503724\pi
0.999932 + 0.0116985i 0.00372383π0.00372383\pi
252252 0 0
253253 4.59407i 0.288826i
254254 0 0
255255 −6.80545 + 5.12458i −0.426174 + 0.320914i
256256 0 0
257257 −8.44246 8.44246i −0.526626 0.526626i 0.392939 0.919565i 0.371459π-0.371459\pi
−0.919565 + 0.392939i 0.871459π0.871459\pi
258258 0 0
259259 −8.82732 + 8.82732i −0.548503 + 0.548503i
260260 0 0
261261 −7.43646 7.43646i −0.460305 0.460305i
262262 0 0
263263 10.4796 10.4796i 0.646200 0.646200i −0.305872 0.952073i 0.598948π-0.598948\pi
0.952073 + 0.305872i 0.0989480π0.0989480\pi
264264 0 0
265265 −0.752691 + 5.34225i −0.0462375 + 0.328172i
266266 0 0
267267 2.86287 0.175205
268268 0 0
269269 5.49337 + 5.49337i 0.334937 + 0.334937i 0.854458 0.519521i 0.173890π-0.173890\pi
−0.519521 + 0.854458i 0.673890π0.673890\pi
270270 0 0
271271 29.9569i 1.81975i 0.414883 + 0.909875i 0.363822π0.363822\pi
−0.414883 + 0.909875i 0.636178π0.636178\pi
272272 0 0
273273 −11.5653 + 11.5653i −0.699964 + 0.699964i
274274 0 0
275275 −5.38502 + 2.98009i −0.324729 + 0.179706i
276276 0 0
277277 7.29980i 0.438602i 0.975657 + 0.219301i 0.0703777π0.0703777\pi
−0.975657 + 0.219301i 0.929622π0.929622\pi
278278 0 0
279279 7.72239i 0.462328i
280280 0 0
281281 9.84488i 0.587296i −0.955914 0.293648i 0.905131π-0.905131\pi
0.955914 0.293648i 0.0948694π-0.0948694\pi
282282 0 0
283283 2.84482i 0.169107i −0.996419 0.0845535i 0.973054π-0.973054\pi
0.996419 0.0845535i 0.0269464π-0.0269464\pi
284284 0 0
285285 −4.56605 6.06373i −0.270470 0.359184i
286286 0 0
287287 9.53244 9.53244i 0.562682 0.562682i
288288 0 0
289289 2.48490i 0.146171i
290290 0 0
291291 3.18909 + 3.18909i 0.186948 + 0.186948i
292292 0 0
293293 −27.6123 −1.61313 −0.806563 0.591149i 0.798675π-0.798675\pi
−0.806563 + 0.591149i 0.798675π0.798675\pi
294294 0 0
295295 −16.3559 + 12.3162i −0.952276 + 0.717074i
296296 0 0
297297 0.870396 0.870396i 0.0505055 0.0505055i
298298 0 0
299299 −15.5250 15.5250i −0.897834 0.897834i
300300 0 0
301301 −0.906503 + 0.906503i −0.0522500 + 0.0522500i
302302 0 0
303303 −6.90372 6.90372i −0.396608 0.396608i
304304 0 0
305305 −16.1843 21.4928i −0.926712 1.23068i
306306 0 0
307307 23.7612i 1.35612i −0.735006 0.678061i 0.762820π-0.762820\pi
0.735006 0.678061i 0.237180π-0.237180\pi
308308 0 0
309309 −4.09832 + 4.09832i −0.233145 + 0.233145i
310310 0 0
311311 −12.2337 −0.693707 −0.346854 0.937919i 0.612750π-0.612750\pi
−0.346854 + 0.937919i 0.612750π0.612750\pi
312312 0 0
313313 10.9229 + 10.9229i 0.617400 + 0.617400i 0.944864 0.327464i 0.106194π-0.106194\pi
−0.327464 + 0.944864i 0.606194π0.606194\pi
314314 0 0
315315 −4.96636 + 3.73972i −0.279822 + 0.210709i
316316 0 0
317317 21.5403 1.20982 0.604911 0.796293i 0.293209π-0.293209\pi
0.604911 + 0.796293i 0.293209π0.293209\pi
318318 0 0
319319 −12.9453 −0.724799
320320 0 0
321321 10.0579 0.561377
322322 0 0
323323 −12.9331 −0.719617
324324 0 0
325325 8.12713 28.2687i 0.450812 1.56807i
326326 0 0
327327 −11.2123 11.2123i −0.620040 0.620040i
328328 0 0
329329 18.3501 1.01167
330330 0 0
331331 −21.2143 + 21.2143i −1.16604 + 1.16604i −0.182914 + 0.983129i 0.558553π0.558553\pi
−0.983129 + 0.182914i 0.941447π0.941447\pi
332332 0 0
333333 4.49007i 0.246054i
334334 0 0
335335 −14.1901 1.99931i −0.775290 0.109234i
336336 0 0
337337 1.41673 + 1.41673i 0.0771744 + 0.0771744i 0.744640 0.667466i 0.232621π-0.232621\pi
−0.667466 + 0.744640i 0.732621π0.732621\pi
338338 0 0
339339 −0.420404 + 0.420404i −0.0228332 + 0.0228332i
340340 0 0
341341 −6.72154 6.72154i −0.363992 0.363992i
342342 0 0
343343 12.3265 12.3265i 0.665570 0.665570i
344344 0 0
345345 −5.02012 6.66672i −0.270274 0.358924i
346346 0 0
347347 −6.70115 −0.359736 −0.179868 0.983691i 0.557567π-0.557567\pi
−0.179868 + 0.983691i 0.557567π0.557567\pi
348348 0 0
349349 −7.28479 7.28479i −0.389946 0.389946i 0.484722 0.874668i 0.338921π-0.338921\pi
−0.874668 + 0.484722i 0.838921π0.838921\pi
350350 0 0
351351 5.88276i 0.313999i
352352 0 0
353353 1.08305 1.08305i 0.0576448 0.0576448i −0.677697 0.735342i 0.737022π-0.737022\pi
0.735342 + 0.677697i 0.237022π0.237022\pi
354354 0 0
355355 −4.15585 + 29.4963i −0.220570 + 1.56550i
356356 0 0
357357 10.5926i 0.560618i
358358 0 0
359359 35.6985i 1.88409i 0.335483 + 0.942046i 0.391101π0.391101\pi
−0.335483 + 0.942046i 0.608899π0.608899\pi
360360 0 0
361361 7.47647i 0.393499i
362362 0 0
363363 9.48482i 0.497824i
364364 0 0
365365 4.11596 3.09936i 0.215439 0.162228i
366366 0 0
367367 15.5759 15.5759i 0.813056 0.813056i −0.172035 0.985091i 0.555034π-0.555034\pi
0.985091 + 0.172035i 0.0550341π0.0550341\pi
368368 0 0
369369 4.84873i 0.252415i
370370 0 0
371371 4.74333 + 4.74333i 0.246261 + 0.246261i
372372 0 0
373373 6.11186 0.316460 0.158230 0.987402i 0.449421π-0.449421\pi
0.158230 + 0.987402i 0.449421π0.449421\pi
374374 0 0
375375 4.55807 10.2090i 0.235378 0.527191i
376376 0 0
377377 43.7469 43.7469i 2.25308 2.25308i
378378 0 0
379379 −25.5981 25.5981i −1.31488 1.31488i −0.917768 0.397116i 0.870011π-0.870011\pi
−0.397116 0.917768i 0.629989π-0.629989\pi
380380 0 0
381381 −12.1223 + 12.1223i −0.621045 + 0.621045i
382382 0 0
383383 −2.46156 2.46156i −0.125780 0.125780i 0.641415 0.767194i 0.278348π-0.278348\pi
−0.767194 + 0.641415i 0.778348π0.778348\pi
384384 0 0
385385 −1.06766 + 7.57773i −0.0544129 + 0.386197i
386386 0 0
387387 0.461098i 0.0234389i
388388 0 0
389389 23.1160 23.1160i 1.17203 1.17203i 0.190302 0.981726i 0.439053π-0.439053\pi
0.981726 0.190302i 0.0609468π-0.0609468\pi
390390 0 0
391391 −14.2192 −0.719096
392392 0 0
393393 9.02309 + 9.02309i 0.455155 + 0.455155i
394394 0 0
395395 −1.29305 + 9.17745i −0.0650603 + 0.461768i
396396 0 0
397397 29.1851 1.46476 0.732379 0.680897i 0.238410π-0.238410\pi
0.732379 + 0.680897i 0.238410π0.238410\pi
398398 0 0
399399 −9.43808 −0.472495
400400 0 0
401401 1.70478 0.0851329 0.0425664 0.999094i 0.486447π-0.486447\pi
0.0425664 + 0.999094i 0.486447π0.486447\pi
402402 0 0
403403 45.4290 2.26298
404404 0 0
405405 −0.311968 + 2.21420i −0.0155018 + 0.110024i
406406 0 0
407407 3.90814 + 3.90814i 0.193719 + 0.193719i
408408 0 0
409409 7.11999 0.352061 0.176030 0.984385i 0.443674π-0.443674\pi
0.176030 + 0.984385i 0.443674π0.443674\pi
410410 0 0
411411 −8.12950 + 8.12950i −0.400999 + 0.400999i
412412 0 0
413413 25.4576i 1.25269i
414414 0 0
415415 0.0752705 0.534235i 0.00369488 0.0262245i
416416 0 0
417417 2.98593 + 2.98593i 0.146222 + 0.146222i
418418 0 0
419419 15.1825 15.1825i 0.741713 0.741713i −0.231194 0.972908i 0.574263π-0.574263\pi
0.972908 + 0.231194i 0.0742633π0.0742633\pi
420420 0 0
421421 8.92932 + 8.92932i 0.435188 + 0.435188i 0.890389 0.455201i 0.150432π-0.150432\pi
−0.455201 + 0.890389i 0.650432π0.650432\pi
422422 0 0
423423 4.66693 4.66693i 0.226914 0.226914i
424424 0 0
425425 −9.22376 16.6673i −0.447418 0.808484i
426426 0 0
427427 −33.4532 −1.61891
428428 0 0
429429 5.12033 + 5.12033i 0.247212 + 0.247212i
430430 0 0
431431 23.7988i 1.14635i −0.819434 0.573173i 0.805712π-0.805712\pi
0.819434 0.573173i 0.194288π-0.194288\pi
432432 0 0
433433 −18.7878 + 18.7878i −0.902886 + 0.902886i −0.995685 0.0927987i 0.970419π-0.970419\pi
0.0927987 + 0.995685i 0.470419π0.470419\pi
434434 0 0
435435 18.7857 14.1459i 0.900707 0.678242i
436436 0 0
437437 12.6695i 0.606062i
438438 0 0
439439 29.1333i 1.39046i −0.718789 0.695229i 0.755303π-0.755303\pi
0.718789 0.695229i 0.244697π-0.244697\pi
440440 0 0
441441 0.730041i 0.0347639i
442442 0 0
443443 38.7016i 1.83877i 0.393360 + 0.919384i 0.371313π0.371313\pi
−0.393360 + 0.919384i 0.628687π0.628687\pi
444444 0 0
445445 −0.893124 + 6.33897i −0.0423381 + 0.300496i
446446 0 0
447447 0.994977 0.994977i 0.0470608 0.0470608i
448448 0 0
449449 9.96141i 0.470108i −0.971982 0.235054i 0.924473π-0.924473\pi
0.971982 0.235054i 0.0755267π-0.0755267\pi
450450 0 0
451451 −4.22031 4.22031i −0.198727 0.198727i
452452 0 0
453453 18.1365 0.852126
454454 0 0
455455 −21.9999 29.2159i −1.03137 1.36966i
456456 0 0
457457 −1.77907 + 1.77907i −0.0832213 + 0.0832213i −0.747492 0.664271i 0.768742π-0.768742\pi
0.664271 + 0.747492i 0.268742π0.268742\pi
458458 0 0
459459 2.69398 + 2.69398i 0.125744 + 0.125744i
460460 0 0
461461 8.51698 8.51698i 0.396675 0.396675i −0.480383 0.877059i 0.659502π-0.659502\pi
0.877059 + 0.480383i 0.159502π0.159502\pi
462462 0 0
463463 0.964355 + 0.964355i 0.0448174 + 0.0448174i 0.729160 0.684343i 0.239911π-0.239911\pi
−0.684343 + 0.729160i 0.739911π0.739911\pi
464464 0 0
465465 17.0989 + 2.40914i 0.792943 + 0.111721i
466466 0 0
467467 4.65741i 0.215519i 0.994177 + 0.107760i 0.0343677π0.0343677\pi
−0.994177 + 0.107760i 0.965632π0.965632\pi
468468 0 0
469469 −12.5993 + 12.5993i −0.581781 + 0.581781i
470470 0 0
471471 10.3489 0.476852
472472 0 0
473473 0.401338 + 0.401338i 0.0184535 + 0.0184535i
474474 0 0
475475 14.8508 8.21846i 0.681399 0.377089i
476476 0 0
477477 2.41272 0.110471
478478 0 0
479479 −22.6790 −1.03623 −0.518114 0.855311i 0.673366π-0.673366\pi
−0.518114 + 0.855311i 0.673366π0.673366\pi
480480 0 0
481481 −26.4140 −1.20437
482482 0 0
483483 −10.3766 −0.472153
484484 0 0
485485 −8.05618 + 6.06639i −0.365812 + 0.275461i
486486 0 0
487487 −4.16034 4.16034i −0.188523 0.188523i 0.606534 0.795057i 0.292559π-0.292559\pi
−0.795057 + 0.606534i 0.792559π0.792559\pi
488488 0 0
489489 13.2079 0.597283
490490 0 0
491491 0.218295 0.218295i 0.00985151 0.00985151i −0.702164 0.712015i 0.747783π-0.747783\pi
0.712015 + 0.702164i 0.247783π0.247783\pi
492492 0 0
493493 40.0674i 1.80455i
494494 0 0
495495 1.65569 + 2.19876i 0.0744179 + 0.0988271i
496496 0 0
497497 26.1895 + 26.1895i 1.17476 + 1.17476i
498498 0 0
499499 −14.9638 + 14.9638i −0.669871 + 0.669871i −0.957686 0.287815i 0.907071π-0.907071\pi
0.287815 + 0.957686i 0.407071π0.407071\pi
500500 0 0
501501 −0.0169530 0.0169530i −0.000757405 0.000757405i
502502 0 0
503503 20.3166 20.3166i 0.905872 0.905872i −0.0900637 0.995936i 0.528707π-0.528707\pi
0.995936 + 0.0900637i 0.0287071π0.0287071\pi
504504 0 0
505505 17.4399 13.1325i 0.776067 0.584387i
506506 0 0
507507 −21.6069 −0.959595
508508 0 0
509509 −18.0574 18.0574i −0.800381 0.800381i 0.182774 0.983155i 0.441492π-0.441492\pi
−0.983155 + 0.182774i 0.941492π0.941492\pi
510510 0 0
511511 6.40641i 0.283403i
512512 0 0
513513 −2.40037 + 2.40037i −0.105979 + 0.105979i
514514 0 0
515515 −7.79595 10.3530i −0.343531 0.456209i
516516 0 0
517517 8.12416i 0.357300i
518518 0 0
519519 3.43931i 0.150969i
520520 0 0
521521 3.75389i 0.164461i 0.996613 + 0.0822305i 0.0262044π0.0262044\pi
−0.996613 + 0.0822305i 0.973796π0.973796\pi
522522 0 0
523523 30.3429i 1.32680i −0.748263 0.663402i 0.769112π-0.769112\pi
0.748263 0.663402i 0.230888π-0.230888\pi
524524 0 0
525525 −6.73114 12.1632i −0.293771 0.530844i
526526 0 0
527527 20.8040 20.8040i 0.906237 0.906237i
528528 0 0
529529 9.07065i 0.394376i
530530 0 0
531531 6.47458 + 6.47458i 0.280973 + 0.280973i
532532 0 0
533533 28.5239 1.23551
534534 0 0
535535 −3.13773 + 22.2702i −0.135656 + 0.962823i
536536 0 0
537537 0.816756 0.816756i 0.0352456 0.0352456i
538538 0 0
539539 0.635425 + 0.635425i 0.0273697 + 0.0273697i
540540 0 0
541541 −25.0252 + 25.0252i −1.07592 + 1.07592i −0.0790451 + 0.996871i 0.525187π0.525187\pi
−0.996871 + 0.0790451i 0.974813π0.974813\pi
542542 0 0
543543 15.2070 + 15.2070i 0.652593 + 0.652593i
544544 0 0
545545 28.3241 21.3283i 1.21327 0.913606i
546546 0 0
547547 31.6172i 1.35185i −0.736969 0.675927i 0.763744π-0.763744\pi
0.736969 0.675927i 0.236256π-0.236256\pi
548548 0 0
549549 −8.50808 + 8.50808i −0.363116 + 0.363116i
550550 0 0
551551 35.7005 1.52089
552552 0 0
553553 8.14857 + 8.14857i 0.346512 + 0.346512i
554554 0 0
555555 −9.94190 1.40076i −0.422010 0.0594588i
556556 0 0
557557 5.06043 0.214418 0.107209 0.994237i 0.465809π-0.465809\pi
0.107209 + 0.994237i 0.465809π0.465809\pi
558558 0 0
559559 −2.71253 −0.114728
560560 0 0
561561 4.68966 0.197998
562562 0 0
563563 −10.2694 −0.432804 −0.216402 0.976304i 0.569432π-0.569432\pi
−0.216402 + 0.976304i 0.569432π0.569432\pi
564564 0 0
565565 −0.799706 1.06201i −0.0336439 0.0446791i
566566 0 0
567567 1.96597 + 1.96597i 0.0825628 + 0.0825628i
568568 0 0
569569 −30.5352 −1.28010 −0.640052 0.768332i 0.721087π-0.721087\pi
−0.640052 + 0.768332i 0.721087π0.721087\pi
570570 0 0
571571 15.6507 15.6507i 0.654962 0.654962i −0.299222 0.954184i 0.596727π-0.596727\pi
0.954184 + 0.299222i 0.0967271π0.0967271\pi
572572 0 0
573573 0.536269i 0.0224030i
574574 0 0
575575 16.3276 9.03573i 0.680906 0.376816i
576576 0 0
577577 −24.2221 24.2221i −1.00838 1.00838i −0.999965 0.00841548i 0.997321π-0.997321\pi
−0.00841548 0.999965i 0.502679π-0.502679\pi
578578 0 0
579579 −7.70962 + 7.70962i −0.320401 + 0.320401i
580580 0 0
581581 −0.474342 0.474342i −0.0196790 0.0196790i
582582 0 0
583583 2.10002 2.10002i 0.0869741 0.0869741i
584584 0 0
585585 −13.0256 1.83523i −0.538542 0.0758775i
586586 0 0
587587 −4.75989 −0.196461 −0.0982307 0.995164i 0.531318π-0.531318\pi
−0.0982307 + 0.995164i 0.531318π0.531318\pi
588588 0 0
589589 18.5366 + 18.5366i 0.763786 + 0.763786i
590590 0 0
591591 19.6564i 0.808557i
592592 0 0
593593 4.52357 4.52357i 0.185761 0.185761i −0.608100 0.793861i 0.708068π-0.708068\pi
0.793861 + 0.608100i 0.208068π0.208068\pi
594594 0 0
595595 −23.4540 3.30454i −0.961522 0.135473i
596596 0 0
597597 9.32963i 0.381836i
598598 0 0
599599 4.69105i 0.191671i 0.995397 + 0.0958356i 0.0305523π0.0305523\pi
−0.995397 + 0.0958356i 0.969448π0.969448\pi
600600 0 0
601601 2.24346i 0.0915126i 0.998953 + 0.0457563i 0.0145698π0.0145698\pi
−0.998953 + 0.0457563i 0.985430π0.985430\pi
602602 0 0
603603 6.40870i 0.260983i
604604 0 0
605605 −21.0013 2.95896i −0.853824 0.120299i
606606 0 0
607607 20.2716 20.2716i 0.822800 0.822800i −0.163709 0.986509i 0.552346π-0.552346\pi
0.986509 + 0.163709i 0.0523457π0.0523457\pi
608608 0 0
609609 29.2396i 1.18485i
610610 0 0
611611 27.4545 + 27.4545i 1.11069 + 1.11069i
612612 0 0
613613 10.2599 0.414392 0.207196 0.978299i 0.433566π-0.433566\pi
0.207196 + 0.978299i 0.433566π0.433566\pi
614614 0 0
615615 10.7361 + 1.51265i 0.432919 + 0.0609958i
616616 0 0
617617 −16.5590 + 16.5590i −0.666640 + 0.666640i −0.956937 0.290297i 0.906246π-0.906246\pi
0.290297 + 0.956937i 0.406246π0.406246\pi
618618 0 0
619619 14.3984 + 14.3984i 0.578720 + 0.578720i 0.934550 0.355831i 0.115802π-0.115802\pi
−0.355831 + 0.934550i 0.615802π0.615802\pi
620620 0 0
621621 −2.63907 + 2.63907i −0.105902 + 0.105902i
622622 0 0
623623 5.62831 + 5.62831i 0.225493 + 0.225493i
624624 0 0
625625 21.1828 + 13.2773i 0.847313 + 0.531094i
626626 0 0
627627 4.17854i 0.166875i
628628 0 0
629629 −12.0962 + 12.0962i −0.482306 + 0.482306i
630630 0 0
631631 −14.9606 −0.595571 −0.297785 0.954633i 0.596248π-0.596248\pi
−0.297785 + 0.954633i 0.596248π0.596248\pi
632632 0 0
633633 −7.58277 7.58277i −0.301388 0.301388i
634634 0 0
635635 −23.0594 30.6230i −0.915086 1.21524i
636636 0 0
637637 −4.29466 −0.170161
638638 0 0
639639 13.3214 0.526988
640640 0 0
641641 −36.0219 −1.42278 −0.711390 0.702797i 0.751934π-0.751934\pi
−0.711390 + 0.702797i 0.751934π0.751934\pi
642642 0 0
643643 5.24582 0.206875 0.103437 0.994636i 0.467016π-0.467016\pi
0.103437 + 0.994636i 0.467016π0.467016\pi
644644 0 0
645645 −1.02096 0.143848i −0.0402004 0.00566400i
646646 0 0
647647 −28.2923 28.2923i −1.11229 1.11229i −0.992841 0.119445i 0.961888π-0.961888\pi
−0.119445 0.992841i 0.538112π-0.538112\pi
648648 0 0
649649 11.2709 0.442422
650650 0 0
651651 15.1820 15.1820i 0.595028 0.595028i
652652 0 0
653653 9.14647i 0.357929i 0.983856 + 0.178965i 0.0572747π0.0572747\pi
−0.983856 + 0.178965i 0.942725π0.942725\pi
654654 0 0
655655 −22.7938 + 17.1640i −0.890629 + 0.670653i
656656 0 0
657657 −1.62933 1.62933i −0.0635662 0.0635662i
658658 0 0
659659 13.0731 13.0731i 0.509256 0.509256i −0.405042 0.914298i 0.632743π-0.632743\pi
0.914298 + 0.405042i 0.132743π0.132743\pi
660660 0 0
661661 −10.8969 10.8969i −0.423839 0.423839i 0.462684 0.886523i 0.346886π-0.346886\pi
−0.886523 + 0.462684i 0.846886π0.846886\pi
662662 0 0
663663 −15.8481 + 15.8481i −0.615488 + 0.615488i
664664 0 0
665665 2.94437 20.8978i 0.114178 0.810381i
666666 0 0
667667 39.2506 1.51979
668668 0 0
669669 8.76331 + 8.76331i 0.338809 + 0.338809i
670670 0 0
671671 14.8108i 0.571764i
672672 0 0
673673 13.7432 13.7432i 0.529762 0.529762i −0.390740 0.920501i 0.627781π-0.627781\pi
0.920501 + 0.390740i 0.127781π0.127781\pi
674674 0 0
675675 −4.80535 1.38152i −0.184958 0.0531746i
676676 0 0
677677 10.5396i 0.405070i −0.979275 0.202535i 0.935082π-0.935082\pi
0.979275 0.202535i 0.0649181π-0.0649181\pi
678678 0 0
679679 12.5393i 0.481214i
680680 0 0
681681 25.0028i 0.958108i
682682 0 0
683683 36.3666i 1.39153i 0.718270 + 0.695765i 0.244934π0.244934\pi
−0.718270 + 0.695765i 0.755066π0.755066\pi
684684 0 0
685685 −15.4642 20.5365i −0.590856 0.784658i
686686 0 0
687687 7.89911 7.89911i 0.301370 0.301370i
688688 0 0
689689 14.1935i 0.540728i
690690 0 0
691691 7.71130 + 7.71130i 0.293352 + 0.293352i 0.838403 0.545051i 0.183490π-0.183490\pi
−0.545051 + 0.838403i 0.683490π0.683490\pi
692692 0 0
693693 3.42234 0.130004
694694 0 0
695695 −7.54295 + 5.67992i −0.286120 + 0.215452i
696696 0 0
697697 13.0624 13.0624i 0.494774 0.494774i
698698 0 0
699699 7.91066 + 7.91066i 0.299209 + 0.299209i
700700 0 0
701701 −8.27188 + 8.27188i −0.312425 + 0.312425i −0.845848 0.533424i 0.820905π-0.820905\pi
0.533424 + 0.845848i 0.320905π0.320905\pi
702702 0 0
703703 −10.7778 10.7778i −0.406493 0.406493i
704704 0 0
705705 8.87759 + 11.7895i 0.334349 + 0.444016i
706706 0 0
707707 27.1450i 1.02089i
708708 0 0
709709 −24.1462 + 24.1462i −0.906828 + 0.906828i −0.996015 0.0891868i 0.971573π-0.971573\pi
0.0891868 + 0.996015i 0.471573π0.471573\pi
710710 0 0
711711 4.14482 0.155443
712712 0 0
713713 20.3799 + 20.3799i 0.763234 + 0.763234i
714714 0 0
715715 −12.9348 + 9.74005i −0.483734 + 0.364257i
716716 0 0
717717 11.4515 0.427664
718718 0 0
719719 5.46091 0.203658 0.101829 0.994802i 0.467531π-0.467531\pi
0.101829 + 0.994802i 0.467531π0.467531\pi
720720 0 0
721721 −16.1143 −0.600128
722722 0 0
723723 20.9793 0.780227
724724 0 0
725725 25.4612 + 46.0084i 0.945606 + 1.70871i
726726 0 0
727727 0.818679 + 0.818679i 0.0303631 + 0.0303631i 0.722125 0.691762i 0.243165π-0.243165\pi
−0.691762 + 0.722125i 0.743165π0.743165\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −1.24219 + 1.24219i −0.0459441 + 0.0459441i
732732 0 0
733733 3.99744i 0.147649i −0.997271 0.0738245i 0.976480π-0.976480\pi
0.997271 0.0738245i 0.0235205π-0.0235205\pi
734734 0 0
735735 −1.61646 0.227749i −0.0596239 0.00840066i
736736 0 0
737737 5.57811 + 5.57811i 0.205472 + 0.205472i
738738 0 0
739739 22.1967 22.1967i 0.816517 0.816517i −0.169084 0.985602i 0.554081π-0.554081\pi
0.985602 + 0.169084i 0.0540811π0.0540811\pi
740740 0 0
741741 −14.1208 14.1208i −0.518740 0.518740i
742742 0 0
743743 29.4601 29.4601i 1.08078 1.08078i 0.0843481 0.996436i 0.473119π-0.473119\pi
0.996436 0.0843481i 0.0268808π-0.0268808\pi
744744 0 0
745745 1.89268 + 2.51348i 0.0693423 + 0.0920867i
746746 0 0
747747 −0.241277 −0.00882785
748748 0 0
749749 19.7735 + 19.7735i 0.722506 + 0.722506i
750750 0 0
751751 33.6280i 1.22710i 0.789654 + 0.613552i 0.210260π0.210260\pi
−0.789654 + 0.613552i 0.789740π0.789740\pi
752752 0 0
753753 15.6566 15.6566i 0.570557 0.570557i
754754 0 0
755755 −5.65799 + 40.1577i −0.205915 + 1.46149i
756756 0 0
757757 22.0813i 0.802560i 0.915955 + 0.401280i 0.131435π0.131435\pi
−0.915955 + 0.401280i 0.868565π0.868565\pi
758758 0 0
759759 4.59407i 0.166754i
760760 0 0
761761 0.186655i 0.00676626i 0.999994 + 0.00338313i 0.00107689π0.00107689\pi
−0.999994 + 0.00338313i 0.998923π0.998923\pi
762762 0 0
763763 44.0859i 1.59602i
764764 0 0
765765 −6.80545 + 5.12458i −0.246052 + 0.185280i
766766 0 0
767767 −38.0884 + 38.0884i −1.37529 + 1.37529i
768768 0 0
769769 2.52000i 0.0908734i −0.998967 0.0454367i 0.985532π-0.985532\pi
0.998967 0.0454367i 0.0144679π-0.0144679\pi
770770 0 0
771771 −8.44246 8.44246i −0.304048 0.304048i
772772 0 0
773773 −3.95359 −0.142201 −0.0711003 0.997469i 0.522651π-0.522651\pi
−0.0711003 + 0.997469i 0.522651π0.522651\pi
774774 0 0
775775 −10.6686 + 37.1088i −0.383228 + 1.33299i
776776 0 0
777777 −8.82732 + 8.82732i −0.316678 + 0.316678i
778778 0 0
779779 11.6387 + 11.6387i 0.417001 + 0.417001i
780780 0 0
781781 11.5949 11.5949i 0.414899 0.414899i
782782 0 0
783783 −7.43646 7.43646i −0.265757 0.265757i
784784 0 0
785785 −3.22852 + 22.9145i −0.115231 + 0.817855i
786786 0 0
787787 25.3395i 0.903255i 0.892207 + 0.451628i 0.149156π0.149156\pi
−0.892207 + 0.451628i 0.850844π0.850844\pi
788788 0 0
789789 10.4796 10.4796i 0.373084 0.373084i
790790 0 0
791791 −1.65300 −0.0587739
792792 0 0
793793 −50.0510 50.0510i −1.77736 1.77736i
794794 0 0
795795 −0.752691 + 5.34225i −0.0266952 + 0.189470i
796796 0 0
797797 −40.2492 −1.42570 −0.712849 0.701317i 0.752596π-0.752596\pi
−0.712849 + 0.701317i 0.752596π0.752596\pi
798798 0 0
799799 25.1453 0.889576
800800 0 0
801801 2.86287 0.101155
802802 0 0
803803 −2.83632 −0.100092
804804 0 0
805805 3.23717 22.9759i 0.114095 0.809795i
806806 0 0
807807 5.49337 + 5.49337i 0.193376 + 0.193376i
808808 0 0
809809 10.5847 0.372137 0.186069 0.982537i 0.440425π-0.440425\pi
0.186069 + 0.982537i 0.440425π0.440425\pi
810810 0 0
811811 14.0997 14.0997i 0.495109 0.495109i −0.414803 0.909911i 0.636149π-0.636149\pi
0.909911 + 0.414803i 0.136149π0.136149\pi
812812 0 0
813813 29.9569i 1.05063i
814814 0 0
815815 −4.12045 + 29.2450i −0.144333 + 1.02441i
816816 0 0
817817 −1.10681 1.10681i −0.0387222 0.0387222i
818818 0 0
819819 −11.5653 + 11.5653i −0.404125 + 0.404125i
820820 0 0
821821 −11.4283 11.4283i −0.398851 0.398851i 0.478977 0.877828i 0.341008π-0.341008\pi
−0.877828 + 0.478977i 0.841008π0.841008\pi
822822 0 0
823823 −10.9724 + 10.9724i −0.382475 + 0.382475i −0.871993 0.489518i 0.837173π-0.837173\pi
0.489518 + 0.871993i 0.337173π0.337173\pi
824824 0 0
825825 −5.38502 + 2.98009i −0.187482 + 0.103753i
826826 0 0
827827 −24.8187 −0.863032 −0.431516 0.902105i 0.642021π-0.642021\pi
−0.431516 + 0.902105i 0.642021π0.642021\pi
828828 0 0
829829 −7.79087 7.79087i −0.270588 0.270588i 0.558749 0.829337i 0.311282π-0.311282\pi
−0.829337 + 0.558749i 0.811282π0.811282\pi
830830 0 0
831831 7.29980i 0.253227i
832832 0 0
833833 −1.96672 + 1.96672i −0.0681428 + 0.0681428i
834834 0 0
835835 0.0428261 0.0322485i 0.00148206 0.00111601i
836836 0 0
837837 7.72239i 0.266925i
838838 0 0
839839 12.7895i 0.441542i 0.975326 + 0.220771i 0.0708573π0.0708573\pi
−0.975326 + 0.220771i 0.929143π0.929143\pi
840840 0 0
841841 81.6018i 2.81386i
842842 0 0
843843 9.84488i 0.339076i
844844 0 0
845845 6.74065 47.8419i 0.231885 1.64581i
846846 0 0
847847 −18.6468 + 18.6468i −0.640713 + 0.640713i
848848 0 0
849849 2.84482i 0.0976340i
850850 0 0
851851 −11.8496 11.8496i −0.406199 0.406199i
852852 0 0
853853 −5.84193 −0.200024 −0.100012 0.994986i 0.531888π-0.531888\pi
−0.100012 + 0.994986i 0.531888π0.531888\pi
854854 0 0
855855 −4.56605 6.06373i −0.156156 0.207375i
856856 0 0
857857 −26.9251 + 26.9251i −0.919745 + 0.919745i −0.997011 0.0772652i 0.975381π-0.975381\pi
0.0772652 + 0.997011i 0.475381π0.475381\pi
858858 0 0
859859 2.05019 + 2.05019i 0.0699516 + 0.0699516i 0.741217 0.671265i 0.234249π-0.234249\pi
−0.671265 + 0.741217i 0.734249π0.734249\pi
860860 0 0
861861 9.53244 9.53244i 0.324865 0.324865i
862862 0 0
863863 18.1091 + 18.1091i 0.616443 + 0.616443i 0.944617 0.328175i 0.106433π-0.106433\pi
−0.328175 + 0.944617i 0.606433π0.606433\pi
864864 0 0
865865 −7.61532 1.07295i −0.258929 0.0364815i
866866 0 0
867867 2.48490i 0.0843916i
868868 0 0
869869 3.60763 3.60763i 0.122381 0.122381i
870870 0 0
871871 −37.7009 −1.27745
872872 0 0
873873 3.18909 + 3.18909i 0.107934 + 0.107934i
874874 0 0
875875 29.0316 11.1096i 0.981446 0.375572i
876876 0 0
877877 47.2518 1.59558 0.797791 0.602934i 0.206002π-0.206002\pi
0.797791 + 0.602934i 0.206002π0.206002\pi
878878 0 0
879879 −27.6123 −0.931338
880880 0 0
881881 11.4431 0.385527 0.192763 0.981245i 0.438255π-0.438255\pi
0.192763 + 0.981245i 0.438255π0.438255\pi
882882 0 0
883883 −46.1246 −1.55222 −0.776109 0.630599i 0.782809π-0.782809\pi
−0.776109 + 0.630599i 0.782809π0.782809\pi
884884 0 0
885885 −16.3559 + 12.3162i −0.549797 + 0.414003i
886886 0 0
887887 25.0305 + 25.0305i 0.840441 + 0.840441i 0.988916 0.148475i 0.0474365π-0.0474365\pi
−0.148475 + 0.988916i 0.547436π0.547436\pi
888888 0 0
889889 −47.6641 −1.59860
890890 0 0
891891 0.870396 0.870396i 0.0291594 0.0291594i
892892 0 0
893893 22.4047i 0.749745i
894894 0 0
895895 1.55366 + 2.06326i 0.0519331 + 0.0689672i
896896 0 0
897897 −15.5250 15.5250i −0.518365 0.518365i
898898 0 0
899899 −57.4272 + 57.4272i −1.91531 + 1.91531i
900900 0 0
901901 6.49984 + 6.49984i 0.216541 + 0.216541i
902902 0 0
903903 −0.906503 + 0.906503i −0.0301665 + 0.0301665i
904904 0 0
905905 −38.4153 + 28.9271i −1.27697 + 0.961571i
906906 0 0
907907 25.0169 0.830671 0.415336 0.909668i 0.363664π-0.363664\pi
0.415336 + 0.909668i 0.363664π0.363664\pi
908908 0 0
909909 −6.90372 6.90372i −0.228982 0.228982i
910910 0 0
911911 5.76809i 0.191105i −0.995424 0.0955527i 0.969538π-0.969538\pi
0.995424 0.0955527i 0.0304618π-0.0304618\pi
912912 0 0
913913 −0.210006 + 0.210006i −0.00695019 + 0.00695019i
914914 0 0
915915 −16.1843 21.4928i −0.535038 0.710531i
916916 0 0
917917 35.4782i 1.17159i
918918 0 0
919919 0.398221i 0.0131361i 0.999978 + 0.00656804i 0.00209069π0.00209069\pi
−0.999978 + 0.00656804i 0.997909π0.997909\pi
920920 0 0
921921 23.7612i 0.782958i
922922 0 0
923923 78.3668i 2.57947i
924924 0 0
925925 6.20310 21.5764i 0.203957 0.709426i
926926 0 0
927927 −4.09832 + 4.09832i −0.134606 + 0.134606i
928928 0 0
929929 4.71373i 0.154653i 0.997006 + 0.0773263i 0.0246383π0.0246383\pi
−0.997006 + 0.0773263i 0.975362π0.975362\pi
930930 0 0
931931 −1.75237 1.75237i −0.0574315 0.0574315i
932932 0 0
933933 −12.2337 −0.400512
934934 0 0
935935 −1.46302 + 10.3839i −0.0478460 + 0.339588i
936936 0 0
937937 −7.20557 + 7.20557i −0.235396 + 0.235396i −0.814940 0.579545i 0.803230π-0.803230\pi
0.579545 + 0.814940i 0.303230π0.303230\pi
938938 0 0
939939 10.9229 + 10.9229i 0.356456 + 0.356456i
940940 0 0
941941 36.0800 36.0800i 1.17617 1.17617i 0.195464 0.980711i 0.437379π-0.437379\pi
0.980711 0.195464i 0.0626212π-0.0626212\pi
942942 0 0
943943 12.7961 + 12.7961i 0.416699 + 0.416699i
944944 0 0
945945 −4.96636 + 3.73972i −0.161556 + 0.121653i
946946 0 0
947947 27.2599i 0.885828i −0.896564 0.442914i 0.853945π-0.853945\pi
0.896564 0.442914i 0.146055π-0.146055\pi
948948 0 0
949949 9.58495 9.58495i 0.311141 0.311141i
950950 0 0
951951 21.5403 0.698491
952952 0 0
953953 17.4014 + 17.4014i 0.563687 + 0.563687i 0.930353 0.366666i 0.119501π-0.119501\pi
−0.366666 + 0.930353i 0.619501π0.619501\pi
954954 0 0
955955 −1.18741 0.167299i −0.0384236 0.00541365i
956956 0 0
957957 −12.9453 −0.418463
958958 0 0
959959 −31.9646 −1.03219
960960 0 0
961961 −28.6353 −0.923721
962962 0 0
963963 10.0579 0.324111
964964 0 0
965965 −14.6655 19.4758i −0.472099 0.626948i
966966 0 0
967967 28.3082 + 28.3082i 0.910331 + 0.910331i 0.996298 0.0859674i 0.0273981π-0.0273981\pi
−0.0859674 + 0.996298i 0.527398π0.527398\pi
968968 0 0
969969 −12.9331 −0.415471
970970 0 0
971971 25.2474 25.2474i 0.810229 0.810229i −0.174439 0.984668i 0.555811π-0.555811\pi
0.984668 + 0.174439i 0.0558112π0.0558112\pi
972972 0 0
973973 11.7405i 0.376382i
974974 0 0
975975 8.12713 28.2687i 0.260277 0.905324i
976976 0 0
977977 15.1184 + 15.1184i 0.483680 + 0.483680i 0.906305 0.422625i 0.138891π-0.138891\pi
−0.422625 + 0.906305i 0.638891π0.638891\pi
978978 0 0
979979 2.49183 2.49183i 0.0796393 0.0796393i
980980 0 0
981981 −11.2123 11.2123i −0.357980 0.357980i
982982 0 0
983983 −29.6618 + 29.6618i −0.946063 + 0.946063i −0.998618 0.0525548i 0.983264π-0.983264\pi
0.0525548 + 0.998618i 0.483264π0.483264\pi
984984 0 0
985985 43.5232 + 6.13217i 1.38677 + 0.195387i
986986 0 0
987987 18.3501 0.584089
988988 0 0
989989 −1.21687 1.21687i −0.0386942 0.0386942i
990990 0 0
991991 35.7662i 1.13615i −0.822977 0.568075i 0.807688π-0.807688\pi
0.822977 0.568075i 0.192312π-0.192312\pi
992992 0 0
993993 −21.2143 + 21.2143i −0.673215 + 0.673215i
994994 0 0
995995 20.6577 + 2.91054i 0.654892 + 0.0922704i
996996 0 0
997997 53.1029i 1.68178i −0.541203 0.840892i 0.682031π-0.682031\pi
0.541203 0.840892i 0.317969π-0.317969\pi
998998 0 0
999999 4.49007i 0.142059i
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.y.j.1567.4 16
4.3 odd 2 1920.2.y.i.1567.4 16
5.3 odd 4 1920.2.bc.j.1183.8 16
8.3 odd 2 240.2.y.e.187.2 yes 16
8.5 even 2 960.2.y.e.847.5 16
16.3 odd 4 1920.2.bc.j.607.8 16
16.5 even 4 240.2.bc.e.67.6 yes 16
16.11 odd 4 960.2.bc.e.367.1 16
16.13 even 4 1920.2.bc.i.607.8 16
20.3 even 4 1920.2.bc.i.1183.8 16
24.11 even 2 720.2.z.f.667.7 16
40.3 even 4 240.2.bc.e.43.6 yes 16
40.13 odd 4 960.2.bc.e.463.1 16
48.5 odd 4 720.2.bd.f.307.3 16
80.3 even 4 inner 1920.2.y.j.223.4 16
80.13 odd 4 1920.2.y.i.223.4 16
80.43 even 4 960.2.y.e.943.5 16
80.53 odd 4 240.2.y.e.163.2 16
120.83 odd 4 720.2.bd.f.523.3 16
240.53 even 4 720.2.z.f.163.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.y.e.163.2 16 80.53 odd 4
240.2.y.e.187.2 yes 16 8.3 odd 2
240.2.bc.e.43.6 yes 16 40.3 even 4
240.2.bc.e.67.6 yes 16 16.5 even 4
720.2.z.f.163.7 16 240.53 even 4
720.2.z.f.667.7 16 24.11 even 2
720.2.bd.f.307.3 16 48.5 odd 4
720.2.bd.f.523.3 16 120.83 odd 4
960.2.y.e.847.5 16 8.5 even 2
960.2.y.e.943.5 16 80.43 even 4
960.2.bc.e.367.1 16 16.11 odd 4
960.2.bc.e.463.1 16 40.13 odd 4
1920.2.y.i.223.4 16 80.13 odd 4
1920.2.y.i.1567.4 16 4.3 odd 2
1920.2.y.j.223.4 16 80.3 even 4 inner
1920.2.y.j.1567.4 16 1.1 even 1 trivial
1920.2.bc.i.607.8 16 16.13 even 4
1920.2.bc.i.1183.8 16 20.3 even 4
1920.2.bc.j.607.8 16 16.3 odd 4
1920.2.bc.j.1183.8 16 5.3 odd 4