Properties

Label 1400.2.bh.a.249.1
Level 14001400
Weight 22
Character 1400.249
Analytic conductor 11.17911.179
Analytic rank 00
Dimension 44
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1400,2,Mod(249,1400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1400.249");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1400=23527 1400 = 2^{3} \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1400.bh (of order 66, degree 22, not 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: 11.179056283011.1790562830
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 249.1
Root 0.8660250.500000i-0.866025 - 0.500000i of defining polynomial
Character χ\chi == 1400.249
Dual form 1400.2.bh.a.849.1

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+(0.8660250.500000i)q3+(1.732052.00000i)q7+(1.000001.73205i)q9+(1.50000+2.59808i)q11+6.00000iq13+(4.33013+2.50000i)q17+(0.500000+0.866025i)q19+(2.50000+0.866025i)q21+(6.062183.50000i)q23+5.00000iq272.00000q29+(2.500004.33013i)q31+(2.598081.50000i)q33+(2.598081.50000i)q37+(3.000005.19615i)q392.00000q41+4.00000iq43+(4.330132.50000i)q47+(1.000006.92820i)q49+(2.500004.33013i)q51+(0.8660250.500000i)q531.00000iq57+(7.5000012.9904i)q59+(2.50000+4.33013i)q61+(5.196151.00000i)q63+(7.79423+4.50000i)q677.00000q69+(6.06218+3.50000i)q73+(2.59808+7.50000i)q77+(0.500000+0.866025i)q79+(0.500000+0.866025i)q8112.0000iq83+(1.73205+1.00000i)q87+(3.50000+6.06218i)q89+(12.0000+10.3923i)q91+(4.33013+2.50000i)q932.00000iq97+6.00000q99+O(q100)q+(-0.866025 - 0.500000i) q^{3} +(1.73205 - 2.00000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +6.00000i q^{13} +(4.33013 + 2.50000i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.50000 + 0.866025i) q^{21} +(6.06218 - 3.50000i) q^{23} +5.00000i q^{27} -2.00000 q^{29} +(2.50000 - 4.33013i) q^{31} +(2.59808 - 1.50000i) q^{33} +(2.59808 - 1.50000i) q^{37} +(3.00000 - 5.19615i) q^{39} -2.00000 q^{41} +4.00000i q^{43} +(4.33013 - 2.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-2.50000 - 4.33013i) q^{51} +(-0.866025 - 0.500000i) q^{53} -1.00000i q^{57} +(7.50000 - 12.9904i) q^{59} +(2.50000 + 4.33013i) q^{61} +(-5.19615 - 1.00000i) q^{63} +(7.79423 + 4.50000i) q^{67} -7.00000 q^{69} +(6.06218 + 3.50000i) q^{73} +(2.59808 + 7.50000i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000i q^{83} +(1.73205 + 1.00000i) q^{87} +(3.50000 + 6.06218i) q^{89} +(12.0000 + 10.3923i) q^{91} +(-4.33013 + 2.50000i) q^{93} -2.00000i q^{97} +6.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q96q11+2q1910q218q29+10q31+12q398q414q4910q51+30q59+10q6128q69+2q792q81+14q89+48q91+24q99+O(q100) 4 q - 4 q^{9} - 6 q^{11} + 2 q^{19} - 10 q^{21} - 8 q^{29} + 10 q^{31} + 12 q^{39} - 8 q^{41} - 4 q^{49} - 10 q^{51} + 30 q^{59} + 10 q^{61} - 28 q^{69} + 2 q^{79} - 2 q^{81} + 14 q^{89} + 48 q^{91} + 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1400Z)×\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times.

nn 351351 701701 801801 11771177
χ(n)\chi(n) 11 11 e(23)e\left(\frac{2}{3}\right) 1-1

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 −0.866025 0.500000i −0.500000 0.288675i 0.228714 0.973494i 0.426548π-0.426548\pi
−0.728714 + 0.684819i 0.759881π0.759881\pi
44 0 0
55 0 0
66 0 0
77 1.73205 2.00000i 0.654654 0.755929i
88 0 0
99 −1.00000 1.73205i −0.333333 0.577350i
1010 0 0
1111 −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i 0.982718π-0.982718\pi
0.546259 + 0.837616i 0.316051π0.316051\pi
1212 0 0
1313 6.00000i 1.66410i 0.554700 + 0.832050i 0.312833π0.312833\pi
−0.554700 + 0.832050i 0.687167π0.687167\pi
1414 0 0
1515 0 0
1616 0 0
1717 4.33013 + 2.50000i 1.05021 + 0.606339i 0.922708 0.385499i 0.125971π-0.125971\pi
0.127502 + 0.991838i 0.459304π0.459304\pi
1818 0 0
1919 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i 0.130073π-0.130073\pi
−0.802955 + 0.596040i 0.796740π0.796740\pi
2020 0 0
2121 −2.50000 + 0.866025i −0.545545 + 0.188982i
2222 0 0
2323 6.06218 3.50000i 1.26405 0.729800i 0.290196 0.956967i 0.406280π-0.406280\pi
0.973856 + 0.227167i 0.0729463π0.0729463\pi
2424 0 0
2525 0 0
2626 0 0
2727 5.00000i 0.962250i
2828 0 0
2929 −2.00000 −0.371391 −0.185695 0.982607i 0.559454π-0.559454\pi
−0.185695 + 0.982607i 0.559454π0.559454\pi
3030 0 0
3131 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i 0.685109π-0.685109\pi
0.998322 + 0.0579057i 0.0184423π0.0184423\pi
3232 0 0
3333 2.59808 1.50000i 0.452267 0.261116i
3434 0 0
3535 0 0
3636 0 0
3737 2.59808 1.50000i 0.427121 0.246598i −0.270998 0.962580i 0.587354π-0.587354\pi
0.698119 + 0.715981i 0.254020π0.254020\pi
3838 0 0
3939 3.00000 5.19615i 0.480384 0.832050i
4040 0 0
4141 −2.00000 −0.312348 −0.156174 0.987730i 0.549916π-0.549916\pi
−0.156174 + 0.987730i 0.549916π0.549916\pi
4242 0 0
4343 4.00000i 0.609994i 0.952353 + 0.304997i 0.0986555π0.0986555\pi
−0.952353 + 0.304997i 0.901344π0.901344\pi
4444 0 0
4545 0 0
4646 0 0
4747 4.33013 2.50000i 0.631614 0.364662i −0.149763 0.988722i 0.547851π-0.547851\pi
0.781377 + 0.624059i 0.214518π0.214518\pi
4848 0 0
4949 −1.00000 6.92820i −0.142857 0.989743i
5050 0 0
5151 −2.50000 4.33013i −0.350070 0.606339i
5252 0 0
5353 −0.866025 0.500000i −0.118958 0.0686803i 0.439340 0.898321i 0.355212π-0.355212\pi
−0.558298 + 0.829640i 0.688546π0.688546\pi
5454 0 0
5555 0 0
5656 0 0
5757 1.00000i 0.132453i
5858 0 0
5959 7.50000 12.9904i 0.976417 1.69120i 0.301239 0.953549i 0.402600π-0.402600\pi
0.675178 0.737655i 0.264067π-0.264067\pi
6060 0 0
6161 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i 0.0629528π-0.0629528\pi
−0.660415 + 0.750901i 0.729619π0.729619\pi
6262 0 0
6363 −5.19615 1.00000i −0.654654 0.125988i
6464 0 0
6565 0 0
6666 0 0
6767 7.79423 + 4.50000i 0.952217 + 0.549762i 0.893769 0.448528i 0.148052π-0.148052\pi
0.0584478 + 0.998290i 0.481385π0.481385\pi
6868 0 0
6969 −7.00000 −0.842701
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 6.06218 + 3.50000i 0.709524 + 0.409644i 0.810885 0.585206i 0.198986π-0.198986\pi
−0.101361 + 0.994850i 0.532320π0.532320\pi
7474 0 0
7575 0 0
7676 0 0
7777 2.59808 + 7.50000i 0.296078 + 0.854704i
7878 0 0
7979 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i 0.148751π-0.148751\pi
−0.836527 + 0.547926i 0.815418π0.815418\pi
8080 0 0
8181 −0.500000 + 0.866025i −0.0555556 + 0.0962250i
8282 0 0
8383 12.0000i 1.31717i −0.752506 0.658586i 0.771155π-0.771155\pi
0.752506 0.658586i 0.228845π-0.228845\pi
8484 0 0
8585 0 0
8686 0 0
8787 1.73205 + 1.00000i 0.185695 + 0.107211i
8888 0 0
8989 3.50000 + 6.06218i 0.370999 + 0.642590i 0.989720 0.143022i 0.0456819π-0.0456819\pi
−0.618720 + 0.785611i 0.712349π0.712349\pi
9090 0 0
9191 12.0000 + 10.3923i 1.25794 + 1.08941i
9292 0 0
9393 −4.33013 + 2.50000i −0.449013 + 0.259238i
9494 0 0
9595 0 0
9696 0 0
9797 2.00000i 0.203069i −0.994832 0.101535i 0.967625π-0.967625\pi
0.994832 0.101535i 0.0323753π-0.0323753\pi
9898 0 0
9999 6.00000 0.603023
100100 0 0
101101 −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i 0.881021π-0.881021\pi
0.781697 + 0.623658i 0.214354π0.214354\pi
102102 0 0
103103 12.9904 7.50000i 1.27998 0.738997i 0.303136 0.952947i 0.401966π-0.401966\pi
0.976845 + 0.213950i 0.0686331π0.0686331\pi
104104 0 0
105105 0 0
106106 0 0
107107 7.79423 4.50000i 0.753497 0.435031i −0.0734594 0.997298i 0.523404π-0.523404\pi
0.826956 + 0.562267i 0.190071π0.190071\pi
108108 0 0
109109 −2.50000 + 4.33013i −0.239457 + 0.414751i −0.960558 0.278078i 0.910303π-0.910303\pi
0.721102 + 0.692829i 0.243636π0.243636\pi
110110 0 0
111111 −3.00000 −0.284747
112112 0 0
113113 18.0000i 1.69330i 0.532152 + 0.846649i 0.321383π0.321383\pi
−0.532152 + 0.846649i 0.678617π0.678617\pi
114114 0 0
115115 0 0
116116 0 0
117117 10.3923 6.00000i 0.960769 0.554700i
118118 0 0
119119 12.5000 4.33013i 1.14587 0.396942i
120120 0 0
121121 1.00000 + 1.73205i 0.0909091 + 0.157459i
122122 0 0
123123 1.73205 + 1.00000i 0.156174 + 0.0901670i
124124 0 0
125125 0 0
126126 0 0
127127 8.00000i 0.709885i 0.934888 + 0.354943i 0.115500π0.115500\pi
−0.934888 + 0.354943i 0.884500π0.884500\pi
128128 0 0
129129 2.00000 3.46410i 0.176090 0.304997i
130130 0 0
131131 −2.50000 4.33013i −0.218426 0.378325i 0.735901 0.677089i 0.236759π-0.236759\pi
−0.954327 + 0.298764i 0.903426π0.903426\pi
132132 0 0
133133 2.59808 + 0.500000i 0.225282 + 0.0433555i
134134 0 0
135135 0 0
136136 0 0
137137 −9.52628 5.50000i −0.813885 0.469897i 0.0344182 0.999408i 0.489042π-0.489042\pi
−0.848303 + 0.529511i 0.822376π0.822376\pi
138138 0 0
139139 12.0000 1.01783 0.508913 0.860818i 0.330047π-0.330047\pi
0.508913 + 0.860818i 0.330047π0.330047\pi
140140 0 0
141141 −5.00000 −0.421076
142142 0 0
143143 −15.5885 9.00000i −1.30357 0.752618i
144144 0 0
145145 0 0
146146 0 0
147147 −2.59808 + 6.50000i −0.214286 + 0.536111i
148148 0 0
149149 −8.50000 14.7224i −0.696347 1.20611i −0.969724 0.244202i 0.921474π-0.921474\pi
0.273377 0.961907i 0.411859π-0.411859\pi
150150 0 0
151151 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i 0.768119π-0.768119\pi
0.949637 + 0.313353i 0.101452π0.101452\pi
152152 0 0
153153 10.0000i 0.808452i
154154 0 0
155155 0 0
156156 0 0
157157 7.79423 + 4.50000i 0.622047 + 0.359139i 0.777666 0.628678i 0.216404π-0.216404\pi
−0.155618 + 0.987817i 0.549737π0.549737\pi
158158 0 0
159159 0.500000 + 0.866025i 0.0396526 + 0.0686803i
160160 0 0
161161 3.50000 18.1865i 0.275839 1.43330i
162162 0 0
163163 −11.2583 + 6.50000i −0.881820 + 0.509119i −0.871258 0.490825i 0.836695π-0.836695\pi
−0.0105623 + 0.999944i 0.503362π0.503362\pi
164164 0 0
165165 0 0
166166 0 0
167167 12.0000i 0.928588i −0.885681 0.464294i 0.846308π-0.846308\pi
0.885681 0.464294i 0.153692π-0.153692\pi
168168 0 0
169169 −23.0000 −1.76923
170170 0 0
171171 1.00000 1.73205i 0.0764719 0.132453i
172172 0 0
173173 11.2583 6.50000i 0.855955 0.494186i −0.00670064 0.999978i 0.502133π-0.502133\pi
0.862656 + 0.505792i 0.168800π0.168800\pi
174174 0 0
175175 0 0
176176 0 0
177177 −12.9904 + 7.50000i −0.976417 + 0.563735i
178178 0 0
179179 −6.50000 + 11.2583i −0.485833 + 0.841487i −0.999867 0.0162823i 0.994817π-0.994817\pi
0.514035 + 0.857769i 0.328150π0.328150\pi
180180 0 0
181181 −10.0000 −0.743294 −0.371647 0.928374i 0.621207π-0.621207\pi
−0.371647 + 0.928374i 0.621207π0.621207\pi
182182 0 0
183183 5.00000i 0.369611i
184184 0 0
185185 0 0
186186 0 0
187187 −12.9904 + 7.50000i −0.949951 + 0.548454i
188188 0 0
189189 10.0000 + 8.66025i 0.727393 + 0.629941i
190190 0 0
191191 5.50000 + 9.52628i 0.397966 + 0.689297i 0.993475 0.114051i 0.0363829π-0.0363829\pi
−0.595509 + 0.803349i 0.703050π0.703050\pi
192192 0 0
193193 2.59808 + 1.50000i 0.187014 + 0.107972i 0.590584 0.806976i 0.298898π-0.298898\pi
−0.403570 + 0.914949i 0.632231π0.632231\pi
194194 0 0
195195 0 0
196196 0 0
197197 6.00000i 0.427482i −0.976890 0.213741i 0.931435π-0.931435\pi
0.976890 0.213741i 0.0685649π-0.0685649\pi
198198 0 0
199199 −6.50000 + 11.2583i −0.460773 + 0.798082i −0.999000 0.0447181i 0.985761π-0.985761\pi
0.538227 + 0.842800i 0.319094π0.319094\pi
200200 0 0
201201 −4.50000 7.79423i −0.317406 0.549762i
202202 0 0
203203 −3.46410 + 4.00000i −0.243132 + 0.280745i
204204 0 0
205205 0 0
206206 0 0
207207 −12.1244 7.00000i −0.842701 0.486534i
208208 0 0
209209 −3.00000 −0.207514
210210 0 0
211211 −4.00000 −0.275371 −0.137686 0.990476i 0.543966π-0.543966\pi
−0.137686 + 0.990476i 0.543966π0.543966\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 −4.33013 12.5000i −0.293948 0.848555i
218218 0 0
219219 −3.50000 6.06218i −0.236508 0.409644i
220220 0 0
221221 −15.0000 + 25.9808i −1.00901 + 1.74766i
222222 0 0
223223 24.0000i 1.60716i 0.595198 + 0.803579i 0.297074π0.297074\pi
−0.595198 + 0.803579i 0.702926π0.702926\pi
224224 0 0
225225 0 0
226226 0 0
227227 −9.52628 5.50000i −0.632281 0.365048i 0.149354 0.988784i 0.452281π-0.452281\pi
−0.781635 + 0.623736i 0.785614π0.785614\pi
228228 0 0
229229 11.5000 + 19.9186i 0.759941 + 1.31626i 0.942880 + 0.333133i 0.108106π0.108106\pi
−0.182939 + 0.983124i 0.558561π0.558561\pi
230230 0 0
231231 1.50000 7.79423i 0.0986928 0.512823i
232232 0 0
233233 −9.52628 + 5.50000i −0.624087 + 0.360317i −0.778459 0.627696i 0.783998π-0.783998\pi
0.154371 + 0.988013i 0.450665π0.450665\pi
234234 0 0
235235 0 0
236236 0 0
237237 1.00000i 0.0649570i
238238 0 0
239239 −20.0000 −1.29369 −0.646846 0.762620i 0.723912π-0.723912\pi
−0.646846 + 0.762620i 0.723912π0.723912\pi
240240 0 0
241241 8.50000 14.7224i 0.547533 0.948355i −0.450910 0.892570i 0.648900π-0.648900\pi
0.998443 0.0557856i 0.0177663π-0.0177663\pi
242242 0 0
243243 13.8564 8.00000i 0.888889 0.513200i
244244 0 0
245245 0 0
246246 0 0
247247 −5.19615 + 3.00000i −0.330623 + 0.190885i
248248 0 0
249249 −6.00000 + 10.3923i −0.380235 + 0.658586i
250250 0 0
251251 16.0000 1.00991 0.504956 0.863145i 0.331509π-0.331509\pi
0.504956 + 0.863145i 0.331509π0.331509\pi
252252 0 0
253253 21.0000i 1.32026i
254254 0 0
255255 0 0
256256 0 0
257257 −18.1865 + 10.5000i −1.13444 + 0.654972i −0.945049 0.326929i 0.893986π-0.893986\pi
−0.189396 + 0.981901i 0.560653π0.560653\pi
258258 0 0
259259 1.50000 7.79423i 0.0932055 0.484310i
260260 0 0
261261 2.00000 + 3.46410i 0.123797 + 0.214423i
262262 0 0
263263 −7.79423 4.50000i −0.480613 0.277482i 0.240059 0.970758i 0.422833π-0.422833\pi
−0.720672 + 0.693276i 0.756167π0.756167\pi
264264 0 0
265265 0 0
266266 0 0
267267 7.00000i 0.428393i
268268 0 0
269269 −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i 0.921803π-0.921803\pi
0.695606 + 0.718423i 0.255136π0.255136\pi
270270 0 0
271271 3.50000 + 6.06218i 0.212610 + 0.368251i 0.952531 0.304443i 0.0984703π-0.0984703\pi
−0.739921 + 0.672694i 0.765137π0.765137\pi
272272 0 0
273273 −5.19615 15.0000i −0.314485 0.907841i
274274 0 0
275275 0 0
276276 0 0
277277 14.7224 + 8.50000i 0.884585 + 0.510716i 0.872167 0.489207i 0.162714π-0.162714\pi
0.0124177 + 0.999923i 0.496047π0.496047\pi
278278 0 0
279279 −10.0000 −0.598684
280280 0 0
281281 6.00000 0.357930 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
282282 0 0
283283 −11.2583 6.50000i −0.669238 0.386385i 0.126550 0.991960i 0.459610π-0.459610\pi
−0.795788 + 0.605575i 0.792943π0.792943\pi
284284 0 0
285285 0 0
286286 0 0
287287 −3.46410 + 4.00000i −0.204479 + 0.236113i
288288 0 0
289289 4.00000 + 6.92820i 0.235294 + 0.407541i
290290 0 0
291291 −1.00000 + 1.73205i −0.0586210 + 0.101535i
292292 0 0
293293 6.00000i 0.350524i −0.984522 0.175262i 0.943923π-0.943923\pi
0.984522 0.175262i 0.0560772π-0.0560772\pi
294294 0 0
295295 0 0
296296 0 0
297297 −12.9904 7.50000i −0.753778 0.435194i
298298 0 0
299299 21.0000 + 36.3731i 1.21446 + 2.10351i
300300 0 0
301301 8.00000 + 6.92820i 0.461112 + 0.399335i
302302 0 0
303303 2.59808 1.50000i 0.149256 0.0861727i
304304 0 0
305305 0 0
306306 0 0
307307 4.00000i 0.228292i 0.993464 + 0.114146i 0.0364132π0.0364132\pi
−0.993464 + 0.114146i 0.963587π0.963587\pi
308308 0 0
309309 −15.0000 −0.853320
310310 0 0
311311 −7.50000 + 12.9904i −0.425286 + 0.736617i −0.996447 0.0842210i 0.973160π-0.973160\pi
0.571161 + 0.820838i 0.306493π0.306493\pi
312312 0 0
313313 0.866025 0.500000i 0.0489506 0.0282617i −0.475325 0.879810i 0.657669π-0.657669\pi
0.524276 + 0.851549i 0.324336π0.324336\pi
314314 0 0
315315 0 0
316316 0 0
317317 2.59808 1.50000i 0.145922 0.0842484i −0.425261 0.905071i 0.639818π-0.639818\pi
0.571184 + 0.820822i 0.306484π0.306484\pi
318318 0 0
319319 3.00000 5.19615i 0.167968 0.290929i
320320 0 0
321321 −9.00000 −0.502331
322322 0 0
323323 5.00000i 0.278207i
324324 0 0
325325 0 0
326326 0 0
327327 4.33013 2.50000i 0.239457 0.138250i
328328 0 0
329329 2.50000 12.9904i 0.137829 0.716183i
330330 0 0
331331 −14.5000 25.1147i −0.796992 1.38043i −0.921567 0.388221i 0.873090π-0.873090\pi
0.124574 0.992210i 0.460243π-0.460243\pi
332332 0 0
333333 −5.19615 3.00000i −0.284747 0.164399i
334334 0 0
335335 0 0
336336 0 0
337337 10.0000i 0.544735i −0.962193 0.272367i 0.912193π-0.912193\pi
0.962193 0.272367i 0.0878066π-0.0878066\pi
338338 0 0
339339 9.00000 15.5885i 0.488813 0.846649i
340340 0 0
341341 7.50000 + 12.9904i 0.406148 + 0.703469i
342342 0 0
343343 −15.5885 10.0000i −0.841698 0.539949i
344344 0 0
345345 0 0
346346 0 0
347347 −12.9904 7.50000i −0.697360 0.402621i 0.109003 0.994041i 0.465234π-0.465234\pi
−0.806363 + 0.591420i 0.798567π0.798567\pi
348348 0 0
349349 −2.00000 −0.107058 −0.0535288 0.998566i 0.517047π-0.517047\pi
−0.0535288 + 0.998566i 0.517047π0.517047\pi
350350 0 0
351351 −30.0000 −1.60128
352352 0 0
353353 2.59808 + 1.50000i 0.138282 + 0.0798369i 0.567545 0.823343i 0.307893π-0.307893\pi
−0.429263 + 0.903179i 0.641227π0.641227\pi
354354 0 0
355355 0 0
356356 0 0
357357 −12.9904 2.50000i −0.687524 0.132314i
358358 0 0
359359 10.5000 + 18.1865i 0.554169 + 0.959849i 0.997968 + 0.0637221i 0.0202971π0.0202971\pi
−0.443799 + 0.896126i 0.646370π0.646370\pi
360360 0 0
361361 9.00000 15.5885i 0.473684 0.820445i
362362 0 0
363363 2.00000i 0.104973i
364364 0 0
365365 0 0
366366 0 0
367367 −19.9186 11.5000i −1.03974 0.600295i −0.119982 0.992776i 0.538284π-0.538284\pi
−0.919760 + 0.392481i 0.871617π0.871617\pi
368368 0 0
369369 2.00000 + 3.46410i 0.104116 + 0.180334i
370370 0 0
371371 −2.50000 + 0.866025i −0.129794 + 0.0449618i
372372 0 0
373373 −9.52628 + 5.50000i −0.493252 + 0.284779i −0.725923 0.687776i 0.758587π-0.758587\pi
0.232671 + 0.972556i 0.425254π0.425254\pi
374374 0 0
375375 0 0
376376 0 0
377377 12.0000i 0.618031i
378378 0 0
379379 −24.0000 −1.23280 −0.616399 0.787434i 0.711409π-0.711409\pi
−0.616399 + 0.787434i 0.711409π0.711409\pi
380380 0 0
381381 4.00000 6.92820i 0.204926 0.354943i
382382 0 0
383383 2.59808 1.50000i 0.132755 0.0766464i −0.432151 0.901801i 0.642245π-0.642245\pi
0.564907 + 0.825155i 0.308912π0.308912\pi
384384 0 0
385385 0 0
386386 0 0
387387 6.92820 4.00000i 0.352180 0.203331i
388388 0 0
389389 −14.5000 + 25.1147i −0.735179 + 1.27337i 0.219465 + 0.975620i 0.429569π0.429569\pi
−0.954645 + 0.297747i 0.903765π0.903765\pi
390390 0 0
391391 35.0000 1.77003
392392 0 0
393393 5.00000i 0.252217i
394394 0 0
395395 0 0
396396 0 0
397397 −14.7224 + 8.50000i −0.738898 + 0.426603i −0.821668 0.569966i 0.806956π-0.806956\pi
0.0827707 + 0.996569i 0.473623π0.473623\pi
398398 0 0
399399 −2.00000 1.73205i −0.100125 0.0867110i
400400 0 0
401401 −13.5000 23.3827i −0.674158 1.16768i −0.976714 0.214544i 0.931173π-0.931173\pi
0.302556 0.953131i 0.402160π-0.402160\pi
402402 0 0
403403 25.9808 + 15.0000i 1.29419 + 0.747203i
404404 0 0
405405 0 0
406406 0 0
407407 9.00000i 0.446113i
408408 0 0
409409 13.5000 23.3827i 0.667532 1.15620i −0.311060 0.950390i 0.600684π-0.600684\pi
0.978592 0.205809i 0.0659826π-0.0659826\pi
410410 0 0
411411 5.50000 + 9.52628i 0.271295 + 0.469897i
412412 0 0
413413 −12.9904 37.5000i −0.639215 1.84525i
414414 0 0
415415 0 0
416416 0 0
417417 −10.3923 6.00000i −0.508913 0.293821i
418418 0 0
419419 −20.0000 −0.977064 −0.488532 0.872546i 0.662467π-0.662467\pi
−0.488532 + 0.872546i 0.662467π0.662467\pi
420420 0 0
421421 34.0000 1.65706 0.828529 0.559946i 0.189178π-0.189178\pi
0.828529 + 0.559946i 0.189178π0.189178\pi
422422 0 0
423423 −8.66025 5.00000i −0.421076 0.243108i
424424 0 0
425425 0 0
426426 0 0
427427 12.9904 + 2.50000i 0.628649 + 0.120983i
428428 0 0
429429 9.00000 + 15.5885i 0.434524 + 0.752618i
430430 0 0
431431 −1.50000 + 2.59808i −0.0722525 + 0.125145i −0.899888 0.436121i 0.856352π-0.856352\pi
0.827636 + 0.561266i 0.189685π0.189685\pi
432432 0 0
433433 2.00000i 0.0961139i 0.998845 + 0.0480569i 0.0153029π0.0153029\pi
−0.998845 + 0.0480569i 0.984697π0.984697\pi
434434 0 0
435435 0 0
436436 0 0
437437 6.06218 + 3.50000i 0.289993 + 0.167428i
438438 0 0
439439 10.5000 + 18.1865i 0.501138 + 0.867996i 0.999999 + 0.00131415i 0.000418308π0.000418308\pi
−0.498861 + 0.866682i 0.666248π0.666248\pi
440440 0 0
441441 −11.0000 + 8.66025i −0.523810 + 0.412393i
442442 0 0
443443 26.8468 15.5000i 1.27553 0.736427i 0.299506 0.954094i 0.403178π-0.403178\pi
0.976023 + 0.217667i 0.0698447π0.0698447\pi
444444 0 0
445445 0 0
446446 0 0
447447 17.0000i 0.804072i
448448 0 0
449449 26.0000 1.22702 0.613508 0.789689i 0.289758π-0.289758\pi
0.613508 + 0.789689i 0.289758π0.289758\pi
450450 0 0
451451 3.00000 5.19615i 0.141264 0.244677i
452452 0 0
453453 −4.33013 + 2.50000i −0.203447 + 0.117460i
454454 0 0
455455 0 0
456456 0 0
457457 −14.7224 + 8.50000i −0.688686 + 0.397613i −0.803120 0.595818i 0.796828π-0.796828\pi
0.114433 + 0.993431i 0.463495π0.463495\pi
458458 0 0
459459 −12.5000 + 21.6506i −0.583450 + 1.01057i
460460 0 0
461461 −30.0000 −1.39724 −0.698620 0.715493i 0.746202π-0.746202\pi
−0.698620 + 0.715493i 0.746202π0.746202\pi
462462 0 0
463463 16.0000i 0.743583i 0.928316 + 0.371792i 0.121256π0.121256\pi
−0.928316 + 0.371792i 0.878744π0.878744\pi
464464 0 0
465465 0 0
466466 0 0
467467 −2.59808 + 1.50000i −0.120225 + 0.0694117i −0.558906 0.829231i 0.688779π-0.688779\pi
0.438682 + 0.898642i 0.355446π0.355446\pi
468468 0 0
469469 22.5000 7.79423i 1.03895 0.359904i
470470 0 0
471471 −4.50000 7.79423i −0.207349 0.359139i
472472 0 0
473473 −10.3923 6.00000i −0.477839 0.275880i
474474 0 0
475475 0 0
476476 0 0
477477 2.00000i 0.0915737i
478478 0 0
479479 15.5000 26.8468i 0.708213 1.22666i −0.257306 0.966330i 0.582835π-0.582835\pi
0.965519 0.260331i 0.0838317π-0.0838317\pi
480480 0 0
481481 9.00000 + 15.5885i 0.410365 + 0.710772i
482482 0 0
483483 −12.1244 + 14.0000i −0.551677 + 0.637022i
484484 0 0
485485 0 0
486486 0 0
487487 −6.06218 3.50000i −0.274703 0.158600i 0.356320 0.934364i 0.384031π-0.384031\pi
−0.631023 + 0.775764i 0.717365π0.717365\pi
488488 0 0
489489 13.0000 0.587880
490490 0 0
491491 −24.0000 −1.08310 −0.541552 0.840667i 0.682163π-0.682163\pi
−0.541552 + 0.840667i 0.682163π0.682163\pi
492492 0 0
493493 −8.66025 5.00000i −0.390038 0.225189i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 −17.5000 30.3109i −0.783408 1.35690i −0.929946 0.367697i 0.880146π-0.880146\pi
0.146538 0.989205i 0.453187π-0.453187\pi
500500 0 0
501501 −6.00000 + 10.3923i −0.268060 + 0.464294i
502502 0 0
503503 32.0000i 1.42681i 0.700752 + 0.713405i 0.252848π0.252848\pi
−0.700752 + 0.713405i 0.747152π0.747152\pi
504504 0 0
505505 0 0
506506 0 0
507507 19.9186 + 11.5000i 0.884615 + 0.510733i
508508 0 0
509509 −4.50000 7.79423i −0.199459 0.345473i 0.748894 0.662690i 0.230585π-0.230585\pi
−0.948353 + 0.317217i 0.897252π0.897252\pi
510510 0 0
511511 17.5000 6.06218i 0.774154 0.268175i
512512 0 0
513513 −4.33013 + 2.50000i −0.191180 + 0.110378i
514514 0 0
515515 0 0
516516 0 0
517517 15.0000i 0.659699i
518518 0 0
519519 −13.0000 −0.570637
520520 0 0
521521 16.5000 28.5788i 0.722878 1.25206i −0.236963 0.971519i 0.576152π-0.576152\pi
0.959841 0.280543i 0.0905145π-0.0905145\pi
522522 0 0
523523 6.06218 3.50000i 0.265081 0.153044i −0.361569 0.932345i 0.617759π-0.617759\pi
0.626650 + 0.779301i 0.284426π0.284426\pi
524524 0 0
525525 0 0
526526 0 0
527527 21.6506 12.5000i 0.943116 0.544509i
528528 0 0
529529 13.0000 22.5167i 0.565217 0.978985i
530530 0 0
531531 −30.0000 −1.30189
532532 0 0
533533 12.0000i 0.519778i
534534 0 0
535535 0 0
536536 0 0
537537 11.2583 6.50000i 0.485833 0.280496i
538538 0 0
539539 19.5000 + 7.79423i 0.839924 + 0.335721i
540540 0 0
541541 20.5000 + 35.5070i 0.881364 + 1.52657i 0.849825 + 0.527064i 0.176707π0.176707\pi
0.0315385 + 0.999503i 0.489959π0.489959\pi
542542 0 0
543543 8.66025 + 5.00000i 0.371647 + 0.214571i
544544 0 0
545545 0 0
546546 0 0
547547 8.00000i 0.342055i −0.985266 0.171028i 0.945291π-0.945291\pi
0.985266 0.171028i 0.0547087π-0.0547087\pi
548548 0 0
549549 5.00000 8.66025i 0.213395 0.369611i
550550 0 0
551551 −1.00000 1.73205i −0.0426014 0.0737878i
552552 0 0
553553 2.59808 + 0.500000i 0.110481 + 0.0212622i
554554 0 0
555555 0 0
556556 0 0
557557 4.33013 + 2.50000i 0.183473 + 0.105928i 0.588924 0.808189i 0.299552π-0.299552\pi
−0.405450 + 0.914117i 0.632885π0.632885\pi
558558 0 0
559559 −24.0000 −1.01509
560560 0 0
561561 15.0000 0.633300
562562 0 0
563563 −35.5070 20.5000i −1.49644 0.863972i −0.496452 0.868064i 0.665364π-0.665364\pi
−0.999992 + 0.00409232i 0.998697π0.998697\pi
564564 0 0
565565 0 0
566566 0 0
567567 0.866025 + 2.50000i 0.0363696 + 0.104990i
568568 0 0
569569 −16.5000 28.5788i −0.691716 1.19809i −0.971275 0.237959i 0.923522π-0.923522\pi
0.279559 0.960128i 0.409812π-0.409812\pi
570570 0 0
571571 6.50000 11.2583i 0.272017 0.471146i −0.697362 0.716720i 0.745643π-0.745643\pi
0.969378 + 0.245573i 0.0789761π0.0789761\pi
572572 0 0
573573 11.0000i 0.459532i
574574 0 0
575575 0 0
576576 0 0
577577 28.5788 + 16.5000i 1.18975 + 0.686904i 0.958250 0.285930i 0.0923026π-0.0923026\pi
0.231502 + 0.972834i 0.425636π0.425636\pi
578578 0 0
579579 −1.50000 2.59808i −0.0623379 0.107972i
580580 0 0
581581 −24.0000 20.7846i −0.995688 0.862291i
582582 0 0
583583 2.59808 1.50000i 0.107601 0.0621237i
584584 0 0
585585 0 0
586586 0 0
587587 20.0000i 0.825488i −0.910847 0.412744i 0.864570π-0.864570\pi
0.910847 0.412744i 0.135430π-0.135430\pi
588588 0 0
589589 5.00000 0.206021
590590 0 0
591591 −3.00000 + 5.19615i −0.123404 + 0.213741i
592592 0 0
593593 38.9711 22.5000i 1.60035 0.923964i 0.608937 0.793219i 0.291596π-0.291596\pi
0.991416 0.130746i 0.0417372π-0.0417372\pi
594594 0 0
595595 0 0
596596 0 0
597597 11.2583 6.50000i 0.460773 0.266027i
598598 0 0
599599 −8.50000 + 14.7224i −0.347301 + 0.601542i −0.985769 0.168106i 0.946235π-0.946235\pi
0.638468 + 0.769648i 0.279568π0.279568\pi
600600 0 0
601601 22.0000 0.897399 0.448699 0.893683i 0.351887π-0.351887\pi
0.448699 + 0.893683i 0.351887π0.351887\pi
602602 0 0
603603 18.0000i 0.733017i
604604 0 0
605605 0 0
606606 0 0
607607 11.2583 6.50000i 0.456962 0.263827i −0.253804 0.967256i 0.581682π-0.581682\pi
0.710766 + 0.703429i 0.248349π0.248349\pi
608608 0 0
609609 5.00000 1.73205i 0.202610 0.0701862i
610610 0 0
611611 15.0000 + 25.9808i 0.606835 + 1.05107i
612612 0 0
613613 37.2391 + 21.5000i 1.50407 + 0.868377i 0.999989 + 0.00472215i 0.00150311π0.00150311\pi
0.504084 + 0.863655i 0.331830π0.331830\pi
614614 0 0
615615 0 0
616616 0 0
617617 30.0000i 1.20775i 0.797077 + 0.603877i 0.206378π0.206378\pi
−0.797077 + 0.603877i 0.793622π0.793622\pi
618618 0 0
619619 −4.50000 + 7.79423i −0.180870 + 0.313276i −0.942177 0.335115i 0.891225π-0.891225\pi
0.761307 + 0.648392i 0.224558π0.224558\pi
620620 0 0
621621 17.5000 + 30.3109i 0.702251 + 1.21633i
622622 0 0
623623 18.1865 + 3.50000i 0.728628 + 0.140225i
624624 0 0
625625 0 0
626626 0 0
627627 2.59808 + 1.50000i 0.103757 + 0.0599042i
628628 0 0
629629 15.0000 0.598089
630630 0 0
631631 −16.0000 −0.636950 −0.318475 0.947931i 0.603171π-0.603171\pi
−0.318475 + 0.947931i 0.603171π0.603171\pi
632632 0 0
633633 3.46410 + 2.00000i 0.137686 + 0.0794929i
634634 0 0
635635 0 0
636636 0 0
637637 41.5692 6.00000i 1.64703 0.237729i
638638 0 0
639639 0 0
640640 0 0
641641 8.50000 14.7224i 0.335730 0.581501i −0.647895 0.761730i 0.724350π-0.724350\pi
0.983625 + 0.180229i 0.0576838π0.0576838\pi
642642 0 0
643643 44.0000i 1.73519i 0.497271 + 0.867595i 0.334335π0.334335\pi
−0.497271 + 0.867595i 0.665665π0.665665\pi
644644 0 0
645645 0 0
646646 0 0
647647 −12.9904 7.50000i −0.510705 0.294855i 0.222419 0.974951i 0.428605π-0.428605\pi
−0.733123 + 0.680096i 0.761938π0.761938\pi
648648 0 0
649649 22.5000 + 38.9711i 0.883202 + 1.52975i
650650 0 0
651651 −2.50000 + 12.9904i −0.0979827 + 0.509133i
652652 0 0
653653 −30.3109 + 17.5000i −1.18616 + 0.684828i −0.957431 0.288663i 0.906789π-0.906789\pi
−0.228726 + 0.973491i 0.573456π0.573456\pi
654654 0 0
655655 0 0
656656 0 0
657657 14.0000i 0.546192i
658658 0 0
659659 −44.0000 −1.71400 −0.856998 0.515319i 0.827673π-0.827673\pi
−0.856998 + 0.515319i 0.827673π0.827673\pi
660660 0 0
661661 −11.5000 + 19.9186i −0.447298 + 0.774743i −0.998209 0.0598209i 0.980947π-0.980947\pi
0.550911 + 0.834564i 0.314280π0.314280\pi
662662 0 0
663663 25.9808 15.0000i 1.00901 0.582552i
664664 0 0
665665 0 0
666666 0 0
667667 −12.1244 + 7.00000i −0.469457 + 0.271041i
668668 0 0
669669 12.0000 20.7846i 0.463947 0.803579i
670670 0 0
671671 −15.0000 −0.579069
672672 0 0
673673 26.0000i 1.00223i 0.865382 + 0.501113i 0.167076π0.167076\pi
−0.865382 + 0.501113i 0.832924π0.832924\pi
674674 0 0
675675 0 0
676676 0 0
677677 33.7750 19.5000i 1.29808 0.749446i 0.318006 0.948089i 0.396987π-0.396987\pi
0.980072 + 0.198643i 0.0636533π0.0636533\pi
678678 0 0
679679 −4.00000 3.46410i −0.153506 0.132940i
680680 0 0
681681 5.50000 + 9.52628i 0.210760 + 0.365048i
682682 0 0
683683 23.3827 + 13.5000i 0.894714 + 0.516563i 0.875481 0.483252i 0.160544π-0.160544\pi
0.0192323 + 0.999815i 0.493878π0.493878\pi
684684 0 0
685685 0 0
686686 0 0
687687 23.0000i 0.877505i
688688 0 0
689689 3.00000 5.19615i 0.114291 0.197958i
690690 0 0
691691 −2.50000 4.33013i −0.0951045 0.164726i 0.814548 0.580097i 0.196985π-0.196985\pi
−0.909652 + 0.415371i 0.863652π0.863652\pi
692692 0 0
693693 10.3923 12.0000i 0.394771 0.455842i
694694 0 0
695695 0 0
696696 0 0
697697 −8.66025 5.00000i −0.328031 0.189389i
698698 0 0
699699 11.0000 0.416058
700700 0 0
701701 −50.0000 −1.88847 −0.944237 0.329267i 0.893198π-0.893198\pi
−0.944237 + 0.329267i 0.893198π0.893198\pi
702702 0 0
703703 2.59808 + 1.50000i 0.0979883 + 0.0565736i
704704 0 0
705705 0 0
706706 0 0
707707 2.59808 + 7.50000i 0.0977107 + 0.282067i
708708 0 0
709709 −14.5000 25.1147i −0.544559 0.943204i −0.998635 0.0522406i 0.983364π-0.983364\pi
0.454076 0.890963i 0.349970π-0.349970\pi
710710 0 0
711711 1.00000 1.73205i 0.0375029 0.0649570i
712712 0 0
713713 35.0000i 1.31076i
714714 0 0
715715 0 0
716716 0 0
717717 17.3205 + 10.0000i 0.646846 + 0.373457i
718718 0 0
719719 −19.5000 33.7750i −0.727227 1.25959i −0.958051 0.286599i 0.907475π-0.907475\pi
0.230823 0.972996i 0.425858π-0.425858\pi
720720 0 0
721721 7.50000 38.9711i 0.279315 1.45136i
722722 0 0
723723 −14.7224 + 8.50000i −0.547533 + 0.316118i
724724 0 0
725725 0 0
726726 0 0
727727 32.0000i 1.18681i 0.804902 + 0.593407i 0.202218π0.202218\pi
−0.804902 + 0.593407i 0.797782π0.797782\pi
728728 0 0
729729 −13.0000 −0.481481
730730 0 0
731731 −10.0000 + 17.3205i −0.369863 + 0.640622i
732732 0 0
733733 −16.4545 + 9.50000i −0.607760 + 0.350891i −0.772088 0.635515i 0.780788π-0.780788\pi
0.164328 + 0.986406i 0.447454π0.447454\pi
734734 0 0
735735 0 0
736736 0 0
737737 −23.3827 + 13.5000i −0.861312 + 0.497279i
738738 0 0
739739 −2.50000 + 4.33013i −0.0919640 + 0.159286i −0.908337 0.418238i 0.862648π-0.862648\pi
0.816373 + 0.577524i 0.195981π0.195981\pi
740740 0 0
741741 6.00000 0.220416
742742 0 0
743743 16.0000i 0.586983i 0.955962 + 0.293492i 0.0948173π0.0948173\pi
−0.955962 + 0.293492i 0.905183π0.905183\pi
744744 0 0
745745 0 0
746746 0 0
747747 −20.7846 + 12.0000i −0.760469 + 0.439057i
748748 0 0
749749 4.50000 23.3827i 0.164426 0.854385i
750750 0 0
751751 −26.5000 45.8993i −0.966999 1.67489i −0.704146 0.710055i 0.748670π-0.748670\pi
−0.262852 0.964836i 0.584663π-0.584663\pi
752752 0 0
753753 −13.8564 8.00000i −0.504956 0.291536i
754754 0 0
755755 0 0
756756 0 0
757757 10.0000i 0.363456i 0.983349 + 0.181728i 0.0581691π0.0581691\pi
−0.983349 + 0.181728i 0.941831π0.941831\pi
758758 0 0
759759 10.5000 18.1865i 0.381126 0.660129i
760760 0 0
761761 −1.50000 2.59808i −0.0543750 0.0941802i 0.837557 0.546350i 0.183983π-0.183983\pi
−0.891932 + 0.452170i 0.850650π0.850650\pi
762762 0 0
763763 4.33013 + 12.5000i 0.156761 + 0.452530i
764764 0 0
765765 0 0
766766 0 0
767767 77.9423 + 45.0000i 2.81433 + 1.62486i
768768 0 0
769769 −22.0000 −0.793340 −0.396670 0.917961i 0.629834π-0.629834\pi
−0.396670 + 0.917961i 0.629834π0.629834\pi
770770 0 0
771771 21.0000 0.756297
772772 0 0
773773 16.4545 + 9.50000i 0.591827 + 0.341691i 0.765819 0.643056i 0.222334π-0.222334\pi
−0.173993 + 0.984747i 0.555667π0.555667\pi
774774 0 0
775775 0 0
776776 0 0
777777 −5.19615 + 6.00000i −0.186411 + 0.215249i
778778 0 0
779779 −1.00000 1.73205i −0.0358287 0.0620572i
780780 0 0
781781 0 0
782782 0 0
783783 10.0000i 0.357371i
784784 0 0
785785 0 0
786786 0 0
787787 14.7224 + 8.50000i 0.524798 + 0.302992i 0.738896 0.673820i 0.235348π-0.235348\pi
−0.214097 + 0.976812i 0.568681π0.568681\pi
788788 0 0
789789 4.50000 + 7.79423i 0.160204 + 0.277482i
790790 0 0
791791 36.0000 + 31.1769i 1.28001 + 1.10852i
792792 0 0
793793 −25.9808 + 15.0000i −0.922604 + 0.532666i
794794 0 0
795795 0 0
796796 0 0
797797 18.0000i 0.637593i 0.947823 + 0.318796i 0.103279π0.103279\pi
−0.947823 + 0.318796i 0.896721π0.896721\pi
798798 0 0
799799 25.0000 0.884436
800800 0 0
801801 7.00000 12.1244i 0.247333 0.428393i
802802 0 0
803803 −18.1865 + 10.5000i −0.641789 + 0.370537i
804804 0 0
805805 0 0
806806 0 0
807807 7.79423 4.50000i 0.274370 0.158408i
808808 0 0
809809 19.5000 33.7750i 0.685583 1.18747i −0.287670 0.957730i 0.592880π-0.592880\pi
0.973253 0.229736i 0.0737862π-0.0737862\pi
810810 0 0
811811 12.0000 0.421377 0.210688 0.977553i 0.432429π-0.432429\pi
0.210688 + 0.977553i 0.432429π0.432429\pi
812812 0 0
813813 7.00000i 0.245501i
814814 0 0
815815 0 0
816816 0 0
817817 −3.46410 + 2.00000i −0.121194 + 0.0699711i
818818 0 0
819819 6.00000 31.1769i 0.209657 1.08941i
820820 0 0
821821 4.50000 + 7.79423i 0.157051 + 0.272020i 0.933804 0.357785i 0.116468π-0.116468\pi
−0.776753 + 0.629805i 0.783135π0.783135\pi
822822 0 0
823823 40.7032 + 23.5000i 1.41882 + 0.819159i 0.996196 0.0871445i 0.0277742π-0.0277742\pi
0.422628 + 0.906303i 0.361108π0.361108\pi
824824 0 0
825825 0 0
826826 0 0
827827 36.0000i 1.25184i −0.779886 0.625921i 0.784723π-0.784723\pi
0.779886 0.625921i 0.215277π-0.215277\pi
828828 0 0
829829 5.50000 9.52628i 0.191023 0.330861i −0.754567 0.656223i 0.772153π-0.772153\pi
0.945589 + 0.325362i 0.105486π0.105486\pi
830830 0 0
831831 −8.50000 14.7224i −0.294862 0.510716i
832832 0 0
833833 12.9904 32.5000i 0.450090 1.12606i
834834 0 0
835835 0 0
836836 0 0
837837 21.6506 + 12.5000i 0.748355 + 0.432063i
838838 0 0
839839 24.0000 0.828572 0.414286 0.910147i 0.364031π-0.364031\pi
0.414286 + 0.910147i 0.364031π0.364031\pi
840840 0 0
841841 −25.0000 −0.862069
842842 0 0
843843 −5.19615 3.00000i −0.178965 0.103325i
844844 0 0
845845 0 0
846846 0 0
847847 5.19615 + 1.00000i 0.178542 + 0.0343604i
848848 0 0
849849 6.50000 + 11.2583i 0.223079 + 0.386385i
850850 0 0
851851 10.5000 18.1865i 0.359935 0.623426i
852852 0 0
853853 34.0000i 1.16414i −0.813139 0.582069i 0.802243π-0.802243\pi
0.813139 0.582069i 0.197757π-0.197757\pi
854854 0 0
855855 0 0
856856 0 0
857857 −33.7750 19.5000i −1.15373 0.666107i −0.203938 0.978984i 0.565374π-0.565374\pi
−0.949794 + 0.312877i 0.898707π0.898707\pi
858858 0 0
859859 0.500000 + 0.866025i 0.0170598 + 0.0295484i 0.874429 0.485153i 0.161236π-0.161236\pi
−0.857369 + 0.514701i 0.827903π0.827903\pi
860860 0 0
861861 5.00000 1.73205i 0.170400 0.0590281i
862862 0 0
863863 −14.7224 + 8.50000i −0.501157 + 0.289343i −0.729191 0.684310i 0.760104π-0.760104\pi
0.228034 + 0.973653i 0.426770π0.426770\pi
864864 0 0
865865 0 0
866866 0 0
867867 8.00000i 0.271694i
868868 0 0
869869 −3.00000 −0.101768
870870 0 0
871871 −27.0000 + 46.7654i −0.914860 + 1.58458i
872872 0 0
873873 −3.46410 + 2.00000i −0.117242 + 0.0676897i
874874 0 0
875875 0 0
876876 0 0
877877 19.9186 11.5000i 0.672603 0.388327i −0.124459 0.992225i 0.539720π-0.539720\pi
0.797062 + 0.603897i 0.206386π0.206386\pi
878878 0 0
879879 −3.00000 + 5.19615i −0.101187 + 0.175262i
880880 0 0
881881 −14.0000 −0.471672 −0.235836 0.971793i 0.575783π-0.575783\pi
−0.235836 + 0.971793i 0.575783π0.575783\pi
882882 0 0
883883 20.0000i 0.673054i 0.941674 + 0.336527i 0.109252π0.109252\pi
−0.941674 + 0.336527i 0.890748π0.890748\pi
884884 0 0
885885 0 0
886886 0 0
887887 −2.59808 + 1.50000i −0.0872349 + 0.0503651i −0.542983 0.839744i 0.682705π-0.682705\pi
0.455748 + 0.890109i 0.349372π0.349372\pi
888888 0 0
889889 16.0000 + 13.8564i 0.536623 + 0.464729i
890890 0 0
891891 −1.50000 2.59808i −0.0502519 0.0870388i
892892 0 0
893893 4.33013 + 2.50000i 0.144902 + 0.0836593i
894894 0 0
895895 0 0
896896 0 0
897897 42.0000i 1.40234i
898898 0 0
899899 −5.00000 + 8.66025i −0.166759 + 0.288836i
900900 0 0
901901 −2.50000 4.33013i −0.0832871 0.144257i
902902 0 0
903903 −3.46410 10.0000i −0.115278 0.332779i
904904 0 0
905905 0 0
906906 0 0
907907 0.866025 + 0.500000i 0.0287559 + 0.0166022i 0.514309 0.857605i 0.328048π-0.328048\pi
−0.485553 + 0.874207i 0.661382π0.661382\pi
908908 0 0
909909 6.00000 0.199007
910910 0 0
911911 16.0000 0.530104 0.265052 0.964234i 0.414611π-0.414611\pi
0.265052 + 0.964234i 0.414611π0.414611\pi
912912 0 0
913913 31.1769 + 18.0000i 1.03181 + 0.595713i
914914 0 0
915915 0 0
916916 0 0
917917 −12.9904 2.50000i −0.428980 0.0825573i
918918 0 0
919919 −5.50000 9.52628i −0.181428 0.314243i 0.760939 0.648824i 0.224739π-0.224739\pi
−0.942367 + 0.334581i 0.891405π0.891405\pi
920920 0 0
921921 2.00000 3.46410i 0.0659022 0.114146i
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 −25.9808 15.0000i −0.853320 0.492665i
928928 0 0
929929 3.50000 + 6.06218i 0.114831 + 0.198894i 0.917712 0.397246i 0.130034π-0.130034\pi
−0.802881 + 0.596139i 0.796701π0.796701\pi
930930 0 0
931931 5.50000 4.33013i 0.180255 0.141914i
932932 0 0
933933 12.9904 7.50000i 0.425286 0.245539i
934934 0 0
935935 0 0
936936 0 0
937937 6.00000i 0.196011i −0.995186 0.0980057i 0.968754π-0.968754\pi
0.995186 0.0980057i 0.0312463π-0.0312463\pi
938938 0 0
939939 −1.00000 −0.0326338
940940 0 0
941941 16.5000 28.5788i 0.537885 0.931644i −0.461133 0.887331i 0.652557π-0.652557\pi
0.999018 0.0443125i 0.0141097π-0.0141097\pi
942942 0 0
943943 −12.1244 + 7.00000i −0.394823 + 0.227951i
944944 0 0
945945 0 0
946946 0 0
947947 32.0429 18.5000i 1.04126 0.601169i 0.121067 0.992644i 0.461368π-0.461368\pi
0.920189 + 0.391475i 0.128035π0.128035\pi
948948 0 0
949949 −21.0000 + 36.3731i −0.681689 + 1.18072i
950950 0 0
951951 −3.00000 −0.0972817
952952 0 0
953953 22.0000i 0.712650i −0.934362 0.356325i 0.884030π-0.884030\pi
0.934362 0.356325i 0.115970π-0.115970\pi
954954 0 0
955955 0 0
956956 0 0
957957 −5.19615 + 3.00000i −0.167968 + 0.0969762i
958958 0 0
959959 −27.5000 + 9.52628i −0.888021 + 0.307620i
960960 0 0
961961 3.00000 + 5.19615i 0.0967742 + 0.167618i
962962 0 0
963963 −15.5885 9.00000i −0.502331 0.290021i
964964 0 0
965965 0 0
966966 0 0
967967 48.0000i 1.54358i 0.635880 + 0.771788i 0.280637π0.280637\pi
−0.635880 + 0.771788i 0.719363π0.719363\pi
968968 0 0
969969 2.50000 4.33013i 0.0803116 0.139104i
970970 0 0
971971 17.5000 + 30.3109i 0.561602 + 0.972723i 0.997357 + 0.0726575i 0.0231480π0.0231480\pi
−0.435755 + 0.900065i 0.643519π0.643519\pi
972972 0 0
973973 20.7846 24.0000i 0.666324 0.769405i
974974 0 0
975975 0 0
976976 0 0
977977 −2.59808 1.50000i −0.0831198 0.0479893i 0.457864 0.889022i 0.348615π-0.348615\pi
−0.540984 + 0.841033i 0.681948π0.681948\pi
978978 0 0
979979 −21.0000 −0.671163
980980 0 0
981981 10.0000 0.319275
982982 0 0
983983 −18.1865 10.5000i −0.580060 0.334898i 0.181097 0.983465i 0.442035π-0.442035\pi
−0.761157 + 0.648567i 0.775369π0.775369\pi
984984 0 0
985985 0 0
986986 0 0
987987 −8.66025 + 10.0000i −0.275659 + 0.318304i
988988 0 0
989989 14.0000 + 24.2487i 0.445174 + 0.771064i
990990 0 0
991991 −7.50000 + 12.9904i −0.238245 + 0.412653i −0.960211 0.279276i 0.909906π-0.909906\pi
0.721966 + 0.691929i 0.243239π0.243239\pi
992992 0 0
993993 29.0000i 0.920287i
994994 0 0
995995 0 0
996996 0 0
997997 35.5070 + 20.5000i 1.12452 + 0.649242i 0.942551 0.334063i 0.108420π-0.108420\pi
0.181968 + 0.983304i 0.441753π0.441753\pi
998998 0 0
999999 7.50000 + 12.9904i 0.237289 + 0.410997i
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 1400.2.bh.a.249.1 4
5.2 odd 4 1400.2.q.d.1201.1 2
5.3 odd 4 56.2.i.b.25.1 yes 2
5.4 even 2 inner 1400.2.bh.a.249.2 4
7.2 even 3 inner 1400.2.bh.a.849.2 4
15.8 even 4 504.2.s.c.361.1 2
20.3 even 4 112.2.i.a.81.1 2
35.2 odd 12 1400.2.q.d.401.1 2
35.3 even 12 392.2.a.e.1.1 1
35.9 even 6 inner 1400.2.bh.a.849.1 4
35.13 even 4 392.2.i.b.361.1 2
35.17 even 12 9800.2.a.s.1.1 1
35.18 odd 12 392.2.a.c.1.1 1
35.23 odd 12 56.2.i.b.9.1 2
35.32 odd 12 9800.2.a.be.1.1 1
35.33 even 12 392.2.i.b.177.1 2
40.3 even 4 448.2.i.d.193.1 2
40.13 odd 4 448.2.i.b.193.1 2
60.23 odd 4 1008.2.s.g.865.1 2
105.23 even 12 504.2.s.c.289.1 2
105.38 odd 12 3528.2.a.j.1.1 1
105.53 even 12 3528.2.a.p.1.1 1
105.68 odd 12 3528.2.s.q.3313.1 2
105.83 odd 4 3528.2.s.q.361.1 2
140.3 odd 12 784.2.a.c.1.1 1
140.23 even 12 112.2.i.a.65.1 2
140.83 odd 4 784.2.i.h.753.1 2
140.103 odd 12 784.2.i.h.177.1 2
140.123 even 12 784.2.a.h.1.1 1
280.3 odd 12 3136.2.a.t.1.1 1
280.53 odd 12 3136.2.a.u.1.1 1
280.93 odd 12 448.2.i.b.65.1 2
280.123 even 12 3136.2.a.j.1.1 1
280.163 even 12 448.2.i.d.65.1 2
280.213 even 12 3136.2.a.i.1.1 1
420.23 odd 12 1008.2.s.g.289.1 2
420.143 even 12 7056.2.a.u.1.1 1
420.263 odd 12 7056.2.a.bj.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.i.b.9.1 2 35.23 odd 12
56.2.i.b.25.1 yes 2 5.3 odd 4
112.2.i.a.65.1 2 140.23 even 12
112.2.i.a.81.1 2 20.3 even 4
392.2.a.c.1.1 1 35.18 odd 12
392.2.a.e.1.1 1 35.3 even 12
392.2.i.b.177.1 2 35.33 even 12
392.2.i.b.361.1 2 35.13 even 4
448.2.i.b.65.1 2 280.93 odd 12
448.2.i.b.193.1 2 40.13 odd 4
448.2.i.d.65.1 2 280.163 even 12
448.2.i.d.193.1 2 40.3 even 4
504.2.s.c.289.1 2 105.23 even 12
504.2.s.c.361.1 2 15.8 even 4
784.2.a.c.1.1 1 140.3 odd 12
784.2.a.h.1.1 1 140.123 even 12
784.2.i.h.177.1 2 140.103 odd 12
784.2.i.h.753.1 2 140.83 odd 4
1008.2.s.g.289.1 2 420.23 odd 12
1008.2.s.g.865.1 2 60.23 odd 4
1400.2.q.d.401.1 2 35.2 odd 12
1400.2.q.d.1201.1 2 5.2 odd 4
1400.2.bh.a.249.1 4 1.1 even 1 trivial
1400.2.bh.a.249.2 4 5.4 even 2 inner
1400.2.bh.a.849.1 4 35.9 even 6 inner
1400.2.bh.a.849.2 4 7.2 even 3 inner
3136.2.a.i.1.1 1 280.213 even 12
3136.2.a.j.1.1 1 280.123 even 12
3136.2.a.t.1.1 1 280.3 odd 12
3136.2.a.u.1.1 1 280.53 odd 12
3528.2.a.j.1.1 1 105.38 odd 12
3528.2.a.p.1.1 1 105.53 even 12
3528.2.s.q.361.1 2 105.83 odd 4
3528.2.s.q.3313.1 2 105.68 odd 12
7056.2.a.u.1.1 1 420.143 even 12
7056.2.a.bj.1.1 1 420.263 odd 12
9800.2.a.s.1.1 1 35.17 even 12
9800.2.a.be.1.1 1 35.32 odd 12