Properties

Label 1764.2.i.d.373.2
Level 17641764
Weight 22
Character 1764.373
Analytic conductor 14.08614.086
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1764,2,Mod(373,1764)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1764.373");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1764=223272 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1764.i (of order 33, 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: 14.085610916614.0856109166
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x63x5+10x415x3+19x212x+3 x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 373.2
Root 0.500000+1.41036i0.500000 + 1.41036i of defining polynomial
Character χ\chi == 1764.373
Dual form 1764.2.i.d.1537.2

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+(0.6195621.61745i)q3+(0.119562+0.207087i)q5+(2.23229+2.00422i)q9+(2.562384.43818i)q11+(2.44282+4.23109i)q13+(0.2608770.321688i)q15+(1.85185+3.20750i)q17+(1.830093.16982i)q19+(3.710536.42683i)q23+(2.471414.28061i)q25+(4.62476+2.36887i)q27+(1.732293.00041i)q29+0.717370q31+(8.766081.39480i)q33+(2.30150+3.98632i)q37+(8.35705+1.32972i)q39+(2.801504.85235i)q41+(6.2443310.8155i)q43+(0.6819430.222649i)q454.33981q47+(4.040634.98251i)q51+(0.471410+0.816506i)q53+1.22545q55+(6.260880.996189i)q577.57893q595.50808q611.16827q650.660190q67+(8.09617+9.98342i)q69+13.7414q71+(1.830093.16982i)q73+(8.454861.34528i)q756.22545q79+(0.9662088.94799i)q81+(4.85185+8.40365i)q83+(0.442820+0.766987i)q85+(3.77975+4.66082i)q87+(3.74433+6.48536i)q89+(0.4444551.16031i)q93+0.875237q95+(8.5744214.8513i)q97+(3.17511+15.0429i)q99+O(q100)q+(-0.619562 - 1.61745i) q^{3} +(0.119562 + 0.207087i) q^{5} +(-2.23229 + 2.00422i) q^{9} +(2.56238 - 4.43818i) q^{11} +(-2.44282 + 4.23109i) q^{13} +(0.260877 - 0.321688i) q^{15} +(1.85185 + 3.20750i) q^{17} +(1.83009 - 3.16982i) q^{19} +(-3.71053 - 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(4.62476 + 2.36887i) q^{27} +(-1.73229 - 3.00041i) q^{29} +0.717370 q^{31} +(-8.76608 - 1.39480i) q^{33} +(-2.30150 + 3.98632i) q^{37} +(8.35705 + 1.32972i) q^{39} +(2.80150 - 4.85235i) q^{41} +(-6.24433 - 10.8155i) q^{43} +(-0.681943 - 0.222649i) q^{45} -4.33981 q^{47} +(4.04063 - 4.98251i) q^{51} +(0.471410 + 0.816506i) q^{53} +1.22545 q^{55} +(-6.26088 - 0.996189i) q^{57} -7.57893 q^{59} -5.50808 q^{61} -1.16827 q^{65} -0.660190 q^{67} +(-8.09617 + 9.98342i) q^{69} +13.7414 q^{71} +(-1.83009 - 3.16982i) q^{73} +(-8.45486 - 1.34528i) q^{75} -6.22545 q^{79} +(0.966208 - 8.94799i) q^{81} +(4.85185 + 8.40365i) q^{83} +(-0.442820 + 0.766987i) q^{85} +(-3.77975 + 4.66082i) q^{87} +(-3.74433 + 6.48536i) q^{89} +(-0.444455 - 1.16031i) q^{93} +0.875237 q^{95} +(-8.57442 - 14.8513i) q^{97} +(3.17511 + 15.0429i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q4q3+q54q92q11+3q13+q15+2q17+3q1914q23+6q257q27q29+6q3117q33+3q37+6q393q43+13q4542q47+8q99+O(q100) 6 q - 4 q^{3} + q^{5} - 4 q^{9} - 2 q^{11} + 3 q^{13} + q^{15} + 2 q^{17} + 3 q^{19} - 14 q^{23} + 6 q^{25} - 7 q^{27} - q^{29} + 6 q^{31} - 17 q^{33} + 3 q^{37} + 6 q^{39} - 3 q^{43} + 13 q^{45} - 42 q^{47}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1764Z)×\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times.

nn 785785 883883 10811081
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11 e(13)e\left(\frac{1}{3}\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 −0.619562 1.61745i −0.357704 0.933835i
44 0 0
55 0.119562 + 0.207087i 0.0534696 + 0.0926120i 0.891521 0.452979i 0.149639π-0.149639\pi
−0.838052 + 0.545591i 0.816305π0.816305\pi
66 0 0
77 0 0
88 0 0
99 −2.23229 + 2.00422i −0.744096 + 0.668073i
1010 0 0
1111 2.56238 4.43818i 0.772587 1.33816i −0.163554 0.986534i 0.552296π-0.552296\pi
0.936141 0.351626i 0.114371π-0.114371\pi
1212 0 0
1313 −2.44282 + 4.23109i −0.677516 + 1.17349i 0.298210 + 0.954500i 0.403610π0.403610\pi
−0.975727 + 0.218993i 0.929723π0.929723\pi
1414 0 0
1515 0.260877 0.321688i 0.0673581 0.0830595i
1616 0 0
1717 1.85185 + 3.20750i 0.449139 + 0.777932i 0.998330 0.0577649i 0.0183974π-0.0183974\pi
−0.549191 + 0.835697i 0.685064π0.685064\pi
1818 0 0
1919 1.83009 3.16982i 0.419853 0.727206i −0.576072 0.817399i 0.695415π-0.695415\pi
0.995924 + 0.0901932i 0.0287484π0.0287484\pi
2020 0 0
2121 0 0
2222 0 0
2323 −3.71053 6.42683i −0.773700 1.34009i −0.935522 0.353267i 0.885071π-0.885071\pi
0.161823 0.986820i 0.448263π-0.448263\pi
2424 0 0
2525 2.47141 4.28061i 0.494282 0.856122i
2626 0 0
2727 4.62476 + 2.36887i 0.890036 + 0.455890i
2828 0 0
2929 −1.73229 3.00041i −0.321678 0.557162i 0.659157 0.752006i 0.270913π-0.270913\pi
−0.980834 + 0.194844i 0.937580π0.937580\pi
3030 0 0
3131 0.717370 0.128843 0.0644217 0.997923i 0.479480π-0.479480\pi
0.0644217 + 0.997923i 0.479480π0.479480\pi
3232 0 0
3333 −8.76608 1.39480i −1.52598 0.242804i
3434 0 0
3535 0 0
3636 0 0
3737 −2.30150 + 3.98632i −0.378365 + 0.655348i −0.990825 0.135154i 0.956847π-0.956847\pi
0.612459 + 0.790502i 0.290180π0.290180\pi
3838 0 0
3939 8.35705 + 1.32972i 1.33820 + 0.212925i
4040 0 0
4141 2.80150 4.85235i 0.437522 0.757810i −0.559976 0.828509i 0.689190π-0.689190\pi
0.997498 + 0.0706992i 0.0225230π0.0225230\pi
4242 0 0
4343 −6.24433 10.8155i −0.952251 1.64935i −0.740538 0.672015i 0.765429π-0.765429\pi
−0.211713 0.977332i 0.567904π-0.567904\pi
4444 0 0
4545 −0.681943 0.222649i −0.101658 0.0331906i
4646 0 0
4747 −4.33981 −0.633026 −0.316513 0.948588i 0.602512π-0.602512\pi
−0.316513 + 0.948588i 0.602512π0.602512\pi
4848 0 0
4949 0 0
5050 0 0
5151 4.04063 4.98251i 0.565801 0.697691i
5252 0 0
5353 0.471410 + 0.816506i 0.0647531 + 0.112156i 0.896584 0.442873i 0.146041π-0.146041\pi
−0.831831 + 0.555029i 0.812707π0.812707\pi
5454 0 0
5555 1.22545 0.165240
5656 0 0
5757 −6.26088 0.996189i −0.829273 0.131948i
5858 0 0
5959 −7.57893 −0.986693 −0.493347 0.869833i 0.664227π-0.664227\pi
−0.493347 + 0.869833i 0.664227π0.664227\pi
6060 0 0
6161 −5.50808 −0.705237 −0.352619 0.935767i 0.614709π-0.614709\pi
−0.352619 + 0.935767i 0.614709π0.614709\pi
6262 0 0
6363 0 0
6464 0 0
6565 −1.16827 −0.144906
6666 0 0
6767 −0.660190 −0.0806550 −0.0403275 0.999187i 0.512840π-0.512840\pi
−0.0403275 + 0.999187i 0.512840π0.512840\pi
6868 0 0
6969 −8.09617 + 9.98342i −0.974665 + 1.20186i
7070 0 0
7171 13.7414 1.63081 0.815405 0.578891i 0.196514π-0.196514\pi
0.815405 + 0.578891i 0.196514π0.196514\pi
7272 0 0
7373 −1.83009 3.16982i −0.214196 0.370999i 0.738827 0.673895i 0.235380π-0.235380\pi
−0.953024 + 0.302896i 0.902047π0.902047\pi
7474 0 0
7575 −8.45486 1.34528i −0.976283 0.155340i
7676 0 0
7777 0 0
7878 0 0
7979 −6.22545 −0.700418 −0.350209 0.936672i 0.613889π-0.613889\pi
−0.350209 + 0.936672i 0.613889π0.613889\pi
8080 0 0
8181 0.966208 8.94799i 0.107356 0.994221i
8282 0 0
8383 4.85185 + 8.40365i 0.532560 + 0.922420i 0.999277 + 0.0380138i 0.0121031π0.0121031\pi
−0.466718 + 0.884406i 0.654564π0.654564\pi
8484 0 0
8585 −0.442820 + 0.766987i −0.0480306 + 0.0831914i
8686 0 0
8787 −3.77975 + 4.66082i −0.405232 + 0.499693i
8888 0 0
8989 −3.74433 + 6.48536i −0.396898 + 0.687447i −0.993341 0.115208i 0.963247π-0.963247\pi
0.596444 + 0.802655i 0.296580π0.296580\pi
9090 0 0
9191 0 0
9292 0 0
9393 −0.444455 1.16031i −0.0460878 0.120318i
9494 0 0
9595 0.875237 0.0897974
9696 0 0
9797 −8.57442 14.8513i −0.870600 1.50792i −0.861377 0.507967i 0.830397π-0.830397\pi
−0.00922376 0.999957i 0.502936π-0.502936\pi
9898 0 0
9999 3.17511 + 15.0429i 0.319110 + 1.51186i
100100 0 0
101101 3.59097 6.21975i 0.357315 0.618888i −0.630196 0.776436i 0.717026π-0.717026\pi
0.987511 + 0.157548i 0.0503589π0.0503589\pi
102102 0 0
103103 −6.41423 11.1098i −0.632013 1.09468i −0.987140 0.159860i 0.948896π-0.948896\pi
0.355127 0.934818i 0.384438π-0.384438\pi
104104 0 0
105105 0 0
106106 0 0
107107 −3.78263 + 6.55171i −0.365681 + 0.633377i −0.988885 0.148681i 0.952497π-0.952497\pi
0.623204 + 0.782059i 0.285830π0.285830\pi
108108 0 0
109109 3.49028 + 6.04535i 0.334309 + 0.579040i 0.983352 0.181712i 0.0581639π-0.0581639\pi
−0.649043 + 0.760752i 0.724831π0.724831\pi
110110 0 0
111111 7.87360 + 1.25280i 0.747329 + 0.118910i
112112 0 0
113113 9.78495 16.9480i 0.920491 1.59434i 0.121834 0.992550i 0.461122π-0.461122\pi
0.798657 0.601787i 0.205544π-0.205544\pi
114114 0 0
115115 0.887275 1.53681i 0.0827388 0.143308i
116116 0 0
117117 −3.02696 14.3410i −0.279842 1.32582i
118118 0 0
119119 0 0
120120 0 0
121121 −7.63160 13.2183i −0.693782 1.20167i
122122 0 0
123123 −9.58414 1.52496i −0.864172 0.137501i
124124 0 0
125125 2.37756 0.212655
126126 0 0
127127 −16.8090 −1.49156 −0.745780 0.666192i 0.767923π-0.767923\pi
−0.745780 + 0.666192i 0.767923π0.767923\pi
128128 0 0
129129 −13.6248 + 16.8007i −1.19959 + 1.47922i
130130 0 0
131131 2.44966 + 4.24293i 0.214027 + 0.370706i 0.952971 0.303061i 0.0980085π-0.0980085\pi
−0.738944 + 0.673767i 0.764675π0.764675\pi
132132 0 0
133133 0 0
134134 0 0
135135 0.0623817 + 1.24095i 0.00536896 + 0.106804i
136136 0 0
137137 −2.72257 + 4.71563i −0.232605 + 0.402884i −0.958574 0.284844i 0.908058π-0.908058\pi
0.725969 + 0.687727i 0.241392π0.241392\pi
138138 0 0
139139 2.83009 4.90187i 0.240046 0.415771i −0.720681 0.693266i 0.756171π-0.756171\pi
0.960727 + 0.277495i 0.0895043π0.0895043\pi
140140 0 0
141141 2.68878 + 7.01942i 0.226436 + 0.591142i
142142 0 0
143143 12.5189 + 21.6833i 1.04688 + 1.81325i
144144 0 0
145145 0.414230 0.717468i 0.0343999 0.0595824i
146146 0 0
147147 0 0
148148 0 0
149149 −1.14132 1.97682i −0.0935002 0.161947i 0.815481 0.578783i 0.196472π-0.196472\pi
−0.908982 + 0.416836i 0.863139π0.863139\pi
150150 0 0
151151 −5.63160 + 9.75422i −0.458293 + 0.793787i −0.998871 0.0475071i 0.984872π-0.984872\pi
0.540578 + 0.841294i 0.318206π0.318206\pi
152152 0 0
153153 −10.5624 3.44854i −0.853918 0.278798i
154154 0 0
155155 0.0857699 + 0.148558i 0.00688921 + 0.0119325i
156156 0 0
157157 −5.54583 −0.442605 −0.221303 0.975205i 0.571031π-0.571031\pi
−0.221303 + 0.975205i 0.571031π0.571031\pi
158158 0 0
159159 1.02859 1.26836i 0.0815725 0.100587i
160160 0 0
161161 0 0
162162 0 0
163163 −3.33009 + 5.76789i −0.260833 + 0.451776i −0.966464 0.256804i 0.917331π-0.917331\pi
0.705630 + 0.708580i 0.250664π0.250664\pi
164164 0 0
165165 −0.759242 1.98210i −0.0591069 0.154307i
166166 0 0
167167 2.20370 3.81691i 0.170527 0.295362i −0.768077 0.640357i 0.778786π-0.778786\pi
0.938604 + 0.344996i 0.112120π0.112120\pi
168168 0 0
169169 −5.43474 9.41325i −0.418057 0.724096i
170170 0 0
171171 2.26771 + 10.7439i 0.173416 + 0.821603i
172172 0 0
173173 −25.3308 −1.92586 −0.962932 0.269745i 0.913061π-0.913061\pi
−0.962932 + 0.269745i 0.913061π0.913061\pi
174174 0 0
175175 0 0
176176 0 0
177177 4.69562 + 12.2585i 0.352944 + 0.921409i
178178 0 0
179179 −4.77292 8.26693i −0.356744 0.617899i 0.630670 0.776051i 0.282780π-0.282780\pi
−0.987415 + 0.158151i 0.949447π0.949447\pi
180180 0 0
181181 −12.3743 −0.919774 −0.459887 0.887978i 0.652110π-0.652110\pi
−0.459887 + 0.887978i 0.652110π0.652110\pi
182182 0 0
183183 3.41260 + 8.90904i 0.252266 + 0.658575i
184184 0 0
185185 −1.10069 −0.0809241
186186 0 0
187187 18.9806 1.38800
188188 0 0
189189 0 0
190190 0 0
191191 13.1683 0.952823 0.476411 0.879223i 0.341937π-0.341937\pi
0.476411 + 0.879223i 0.341937π0.341937\pi
192192 0 0
193193 11.1488 0.802511 0.401256 0.915966i 0.368574π-0.368574\pi
0.401256 + 0.915966i 0.368574π0.368574\pi
194194 0 0
195195 0.723815 + 1.88962i 0.0518335 + 0.135318i
196196 0 0
197197 −0.144194 −0.0102734 −0.00513669 0.999987i 0.501635π-0.501635\pi
−0.00513669 + 0.999987i 0.501635π0.501635\pi
198198 0 0
199199 −9.73461 16.8608i −0.690068 1.19523i −0.971815 0.235744i 0.924247π-0.924247\pi
0.281747 0.959489i 0.409086π-0.409086\pi
200200 0 0
201201 0.409028 + 1.06782i 0.0288506 + 0.0753185i
202202 0 0
203203 0 0
204204 0 0
205205 1.33981 0.0935764
206206 0 0
207207 21.1638 + 6.90981i 1.47098 + 0.480265i
208208 0 0
209209 −9.37880 16.2446i −0.648745 1.12366i
210210 0 0
211211 1.61436 2.79615i 0.111137 0.192495i −0.805092 0.593150i 0.797884π-0.797884\pi
0.916229 + 0.400655i 0.131217π0.131217\pi
212212 0 0
213213 −8.51367 22.2261i −0.583347 1.52291i
214214 0 0
215215 1.49316 2.58623i 0.101833 0.176380i
216216 0 0
217217 0 0
218218 0 0
219219 −3.99316 + 4.92398i −0.269833 + 0.332732i
220220 0 0
221221 −18.0949 −1.21720
222222 0 0
223223 10.3856 + 17.9885i 0.695474 + 1.20460i 0.970021 + 0.243022i 0.0781389π0.0781389\pi
−0.274547 + 0.961574i 0.588528π0.588528\pi
224224 0 0
225225 3.06238 + 14.5088i 0.204159 + 0.967253i
226226 0 0
227227 10.9714 19.0030i 0.728198 1.26128i −0.229446 0.973321i 0.573691π-0.573691\pi
0.957644 0.287955i 0.0929752π-0.0929752\pi
228228 0 0
229229 11.3856 + 19.7205i 0.752384 + 1.30317i 0.946664 + 0.322222i 0.104430π0.104430\pi
−0.194280 + 0.980946i 0.562237π0.562237\pi
230230 0 0
231231 0 0
232232 0 0
233233 12.8908 22.3276i 0.844507 1.46273i −0.0415414 0.999137i 0.513227π-0.513227\pi
0.886049 0.463592i 0.153440π-0.153440\pi
234234 0 0
235235 −0.518875 0.898718i −0.0338477 0.0586259i
236236 0 0
237237 3.85705 + 10.0694i 0.250542 + 0.654075i
238238 0 0
239239 13.6488 23.6405i 0.882870 1.52918i 0.0347345 0.999397i 0.488941π-0.488941\pi
0.848136 0.529779i 0.177725π-0.177725\pi
240240 0 0
241241 5.01724 8.69011i 0.323189 0.559779i −0.657955 0.753057i 0.728578π-0.728578\pi
0.981144 + 0.193277i 0.0619118π0.0619118\pi
242242 0 0
243243 −15.0715 + 3.98104i −0.966840 + 0.255384i
244244 0 0
245245 0 0
246246 0 0
247247 8.94119 + 15.4866i 0.568914 + 0.985388i
248248 0 0
249249 10.5865 13.0542i 0.670890 0.827276i
250250 0 0
251251 28.3171 1.78736 0.893680 0.448705i 0.148115π-0.148115\pi
0.893680 + 0.448705i 0.148115π0.148115\pi
252252 0 0
253253 −38.0312 −2.39100
254254 0 0
255255 1.51492 + 0.241044i 0.0948678 + 0.0150947i
256256 0 0
257257 14.4315 + 24.9960i 0.900210 + 1.55921i 0.827221 + 0.561877i 0.189921π0.189921\pi
0.0729899 + 0.997333i 0.476746π0.476746\pi
258258 0 0
259259 0 0
260260 0 0
261261 9.88044 + 3.22589i 0.611584 + 0.199678i
262262 0 0
263263 0.604645 1.04728i 0.0372840 0.0645778i −0.846781 0.531941i 0.821463π-0.821463\pi
0.884065 + 0.467363i 0.154796π0.154796\pi
264264 0 0
265265 −0.112725 + 0.195246i −0.00692465 + 0.0119938i
266266 0 0
267267 12.8096 + 2.03818i 0.783934 + 0.124734i
268268 0 0
269269 4.50684 + 7.80607i 0.274787 + 0.475944i 0.970081 0.242780i 0.0780594π-0.0780594\pi
−0.695295 + 0.718725i 0.744726π0.744726\pi
270270 0 0
271271 8.80150 15.2447i 0.534653 0.926047i −0.464527 0.885559i 0.653776π-0.653776\pi
0.999180 0.0404876i 0.0128911π-0.0128911\pi
272272 0 0
273273 0 0
274274 0 0
275275 −12.6654 21.9371i −0.763752 1.32286i
276276 0 0
277277 −0.727085 + 1.25935i −0.0436863 + 0.0756669i −0.887042 0.461689i 0.847244π-0.847244\pi
0.843355 + 0.537356i 0.180577π0.180577\pi
278278 0 0
279279 −1.60138 + 1.43777i −0.0958718 + 0.0860768i
280280 0 0
281281 10.1482 + 17.5771i 0.605388 + 1.04856i 0.991990 + 0.126316i 0.0403154π0.0403154\pi
−0.386602 + 0.922247i 0.626351π0.626351\pi
282282 0 0
283283 4.60301 0.273621 0.136810 0.990597i 0.456315π-0.456315\pi
0.136810 + 0.990597i 0.456315π0.456315\pi
284284 0 0
285285 −0.542263 1.41565i −0.0321209 0.0838559i
286286 0 0
287287 0 0
288288 0 0
289289 1.64132 2.84284i 0.0965479 0.167226i
290290 0 0
291291 −18.7089 + 23.0700i −1.09674 + 1.35239i
292292 0 0
293293 −3.53667 + 6.12569i −0.206614 + 0.357867i −0.950646 0.310278i 0.899578π-0.899578\pi
0.744031 + 0.668145i 0.232911π0.232911\pi
294294 0 0
295295 −0.906150 1.56950i −0.0527581 0.0913797i
296296 0 0
297297 22.3639 14.4556i 1.29768 0.838796i
298298 0 0
299299 36.2567 2.09678
300300 0 0
301301 0 0
302302 0 0
303303 −12.2850 1.95470i −0.705752 0.112295i
304304 0 0
305305 −0.658555 1.14065i −0.0377088 0.0653135i
306306 0 0
307307 −15.7518 −0.899006 −0.449503 0.893279i 0.648399π-0.648399\pi
−0.449503 + 0.893279i 0.648399π0.648399\pi
308308 0 0
309309 −13.9955 + 17.2579i −0.796175 + 0.981767i
310310 0 0
311311 19.6238 1.11276 0.556382 0.830926i 0.312189π-0.312189\pi
0.556382 + 0.830926i 0.312189π0.312189\pi
312312 0 0
313313 25.4854 1.44052 0.720259 0.693705i 0.244023π-0.244023\pi
0.720259 + 0.693705i 0.244023π0.244023\pi
314314 0 0
315315 0 0
316316 0 0
317317 8.28263 0.465199 0.232599 0.972573i 0.425277π-0.425277\pi
0.232599 + 0.972573i 0.425277π0.425277\pi
318318 0 0
319319 −17.7551 −0.994096
320320 0 0
321321 12.9406 + 2.05903i 0.722276 + 0.114924i
322322 0 0
323323 13.5562 0.754289
324324 0 0
325325 12.0744 + 20.9135i 0.669768 + 1.16007i
326326 0 0
327327 7.61560 9.39083i 0.421144 0.519314i
328328 0 0
329329 0 0
330330 0 0
331331 −11.9806 −0.658512 −0.329256 0.944241i 0.606798π-0.606798\pi
−0.329256 + 0.944241i 0.606798π0.606798\pi
332332 0 0
333333 −2.85185 13.5113i −0.156280 0.740417i
334334 0 0
335335 −0.0789334 0.136717i −0.00431259 0.00746963i
336336 0 0
337337 6.46006 11.1892i 0.351902 0.609512i −0.634681 0.772774i 0.718868π-0.718868\pi
0.986583 + 0.163262i 0.0522017π0.0522017\pi
338338 0 0
339339 −33.4750 5.32632i −1.81811 0.289286i
340340 0 0
341341 1.83818 3.18381i 0.0995428 0.172413i
342342 0 0
343343 0 0
344344 0 0
345345 −3.03543 0.482977i −0.163422 0.0260026i
346346 0 0
347347 16.1866 0.868942 0.434471 0.900686i 0.356935π-0.356935\pi
0.434471 + 0.900686i 0.356935π0.356935\pi
348348 0 0
349349 −9.05718 15.6875i −0.484820 0.839732i 0.515028 0.857173i 0.327781π-0.327781\pi
−0.999848 + 0.0174409i 0.994448π0.994448\pi
350350 0 0
351351 −21.3204 + 13.7811i −1.13800 + 0.735578i
352352 0 0
353353 −5.84897 + 10.1307i −0.311309 + 0.539203i −0.978646 0.205553i 0.934101π-0.934101\pi
0.667337 + 0.744756i 0.267434π0.267434\pi
354354 0 0
355355 1.64295 + 2.84567i 0.0871987 + 0.151033i
356356 0 0
357357 0 0
358358 0 0
359359 −17.8623 + 30.9383i −0.942734 + 1.63286i −0.182507 + 0.983205i 0.558421π0.558421\pi
−0.760227 + 0.649658i 0.774912π0.774912\pi
360360 0 0
361361 2.80150 + 4.85235i 0.147448 + 0.255387i
362362 0 0
363363 −16.6517 + 20.5333i −0.873989 + 1.07772i
364364 0 0
365365 0.437618 0.757977i 0.0229060 0.0396743i
366366 0 0
367367 8.52696 14.7691i 0.445103 0.770942i −0.552956 0.833210i 0.686500π-0.686500\pi
0.998059 + 0.0622687i 0.0198336π0.0198336\pi
368368 0 0
369369 3.47141 + 16.4467i 0.180714 + 0.856179i
370370 0 0
371371 0 0
372372 0 0
373373 12.9617 + 22.4503i 0.671131 + 1.16243i 0.977584 + 0.210547i 0.0675246π0.0675246\pi
−0.306453 + 0.951886i 0.599142π0.599142\pi
374374 0 0
375375 −1.47304 3.84558i −0.0760677 0.198585i
376376 0 0
377377 16.9267 0.871767
378378 0 0
379379 26.8446 1.37892 0.689458 0.724326i 0.257849π-0.257849\pi
0.689458 + 0.724326i 0.257849π0.257849\pi
380380 0 0
381381 10.4142 + 27.1878i 0.533537 + 1.39287i
382382 0 0
383383 12.4263 + 21.5229i 0.634953 + 1.09977i 0.986525 + 0.163610i 0.0523137π0.0523137\pi
−0.351573 + 0.936161i 0.614353π0.614353\pi
384384 0 0
385385 0 0
386386 0 0
387387 35.6157 + 11.6283i 1.81045 + 0.591098i
388388 0 0
389389 9.12640 15.8074i 0.462727 0.801466i −0.536369 0.843984i 0.680204π-0.680204\pi
0.999096 + 0.0425174i 0.0135378π0.0135378\pi
390390 0 0
391391 13.7427 23.8030i 0.694998 1.20377i
392392 0 0
393393 5.34501 6.59095i 0.269620 0.332470i
394394 0 0
395395 −0.744325 1.28921i −0.0374511 0.0648671i
396396 0 0
397397 6.18715 10.7164i 0.310524 0.537843i −0.667952 0.744204i 0.732829π-0.732829\pi
0.978476 + 0.206361i 0.0661622π0.0661622\pi
398398 0 0
399399 0 0
400400 0 0
401401 5.48113 + 9.49359i 0.273714 + 0.474087i 0.969810 0.243862i 0.0784144π-0.0784144\pi
−0.696096 + 0.717949i 0.745081π0.745081\pi
402402 0 0
403403 −1.75241 + 3.03526i −0.0872935 + 0.151197i
404404 0 0
405405 1.96853 0.869747i 0.0978171 0.0432181i
406406 0 0
407407 11.7947 + 20.4290i 0.584640 + 1.01263i
408408 0 0
409409 13.3204 0.658650 0.329325 0.944217i 0.393179π-0.393179\pi
0.329325 + 0.944217i 0.393179π0.393179\pi
410410 0 0
411411 9.31410 + 1.48200i 0.459431 + 0.0731015i
412412 0 0
413413 0 0
414414 0 0
415415 −1.16019 + 2.00951i −0.0569515 + 0.0986429i
416416 0 0
417417 −9.68194 1.54053i −0.474127 0.0754399i
418418 0 0
419419 2.35705 4.08253i 0.115149 0.199445i −0.802690 0.596396i 0.796599π-0.796599\pi
0.917839 + 0.396952i 0.129932π0.129932\pi
420420 0 0
421421 −9.65856 16.7291i −0.470729 0.815327i 0.528710 0.848802i 0.322676π-0.322676\pi
−0.999440 + 0.0334755i 0.989342π0.989342\pi
422422 0 0
423423 9.68770 8.69793i 0.471032 0.422908i
424424 0 0
425425 18.3067 0.888006
426426 0 0
427427 0 0
428428 0 0
429429 27.3155 33.6828i 1.31880 1.62622i
430430 0 0
431431 15.1397 + 26.2227i 0.729253 + 1.26310i 0.957199 + 0.289429i 0.0934655π0.0934655\pi
−0.227947 + 0.973674i 0.573201π0.573201\pi
432432 0 0
433433 −34.2060 −1.64384 −0.821918 0.569606i 0.807096π-0.807096\pi
−0.821918 + 0.569606i 0.807096π0.807096\pi
434434 0 0
435435 −1.41711 0.225481i −0.0679452 0.0108110i
436436 0 0
437437 −27.1625 −1.29936
438438 0 0
439439 0.622440 0.0297075 0.0148537 0.999890i 0.495272π-0.495272\pi
0.0148537 + 0.999890i 0.495272π0.495272\pi
440440 0 0
441441 0 0
442442 0 0
443443 −5.17867 −0.246046 −0.123023 0.992404i 0.539259π-0.539259\pi
−0.123023 + 0.992404i 0.539259π0.539259\pi
444444 0 0
445445 −1.79071 −0.0848878
446446 0 0
447447 −2.49028 + 3.07078i −0.117786 + 0.145243i
448448 0 0
449449 −10.4977 −0.495416 −0.247708 0.968835i 0.579677π-0.579677\pi
−0.247708 + 0.968835i 0.579677π0.579677\pi
450450 0 0
451451 −14.3571 24.8671i −0.676047 1.17095i
452452 0 0
453453 19.2661 + 3.06549i 0.905199 + 0.144029i
454454 0 0
455455 0 0
456456 0 0
457457 −3.20929 −0.150124 −0.0750621 0.997179i 0.523916π-0.523916\pi
−0.0750621 + 0.997179i 0.523916π0.523916\pi
458458 0 0
459459 0.966208 + 19.2207i 0.0450987 + 0.897146i
460460 0 0
461461 −18.1150 31.3762i −0.843702 1.46133i −0.886744 0.462261i 0.847038π-0.847038\pi
0.0430418 0.999073i 0.486295π-0.486295\pi
462462 0 0
463463 −14.5253 + 25.1586i −0.675049 + 1.16922i 0.301406 + 0.953496i 0.402544π0.402544\pi
−0.976455 + 0.215723i 0.930789π0.930789\pi
464464 0 0
465465 0.187145 0.230769i 0.00867865 0.0107017i
466466 0 0
467467 −18.7466 + 32.4701i −0.867491 + 1.50254i −0.00293952 + 0.999996i 0.500936π0.500936\pi
−0.864552 + 0.502544i 0.832398π0.832398\pi
468468 0 0
469469 0 0
470470 0 0
471471 3.43598 + 8.97010i 0.158322 + 0.413320i
472472 0 0
473473 −64.0014 −2.94279
474474 0 0
475475 −9.04583 15.6678i −0.415051 0.718890i
476476 0 0
477477 −2.68878 0.877867i −0.123111 0.0401948i
478478 0 0
479479 14.9549 25.9026i 0.683305 1.18352i −0.290661 0.956826i 0.593875π-0.593875\pi
0.973966 0.226693i 0.0727914π-0.0727914\pi
480480 0 0
481481 −11.2443 19.4757i −0.512697 0.888017i
482482 0 0
483483 0 0
484484 0 0
485485 2.05034 3.55130i 0.0931013 0.161256i
486486 0 0
487487 −10.6316 18.4145i −0.481764 0.834439i 0.518017 0.855370i 0.326670π-0.326670\pi
−0.999781 + 0.0209309i 0.993337π0.993337\pi
488488 0 0
489489 11.3925 + 1.81270i 0.515186 + 0.0819729i
490490 0 0
491491 10.6985 18.5303i 0.482816 0.836262i −0.516989 0.855992i 0.672947π-0.672947\pi
0.999805 + 0.0197296i 0.00628054π0.00628054\pi
492492 0 0
493493 6.41586 11.1126i 0.288956 0.500487i
494494 0 0
495495 −2.73556 + 2.45607i −0.122954 + 0.110392i
496496 0 0
497497 0 0
498498 0 0
499499 −7.28263 12.6139i −0.326015 0.564675i 0.655702 0.755020i 0.272373π-0.272373\pi
−0.981717 + 0.190345i 0.939039π0.939039\pi
500500 0 0
501501 −7.53899 1.19955i −0.336817 0.0535921i
502502 0 0
503503 −2.92339 −0.130348 −0.0651738 0.997874i 0.520760π-0.520760\pi
−0.0651738 + 0.997874i 0.520760π0.520760\pi
504504 0 0
505505 1.71737 0.0764220
506506 0 0
507507 −11.8583 + 14.6225i −0.526645 + 0.649408i
508508 0 0
509509 −9.62025 16.6628i −0.426410 0.738564i 0.570141 0.821547i 0.306889π-0.306889\pi
−0.996551 + 0.0829830i 0.973555π0.973555\pi
510510 0 0
511511 0 0
512512 0 0
513513 15.9727 10.3244i 0.705210 0.455833i
514514 0 0
515515 1.53379 2.65661i 0.0675869 0.117064i
516516 0 0
517517 −11.1202 + 19.2608i −0.489068 + 0.847091i
518518 0 0
519519 15.6940 + 40.9713i 0.688889 + 1.79844i
520520 0 0
521521 13.8743 + 24.0310i 0.607844 + 1.05282i 0.991595 + 0.129380i 0.0412986π0.0412986\pi
−0.383751 + 0.923436i 0.625368π0.625368\pi
522522 0 0
523523 −1.36840 + 2.37014i −0.0598360 + 0.103639i −0.894392 0.447285i 0.852391π-0.852391\pi
0.834556 + 0.550924i 0.185724π0.185724\pi
524524 0 0
525525 0 0
526526 0 0
527527 1.32846 + 2.30096i 0.0578686 + 0.100231i
528528 0 0
529529 −16.0361 + 27.7754i −0.697222 + 1.20762i
530530 0 0
531531 16.9184 15.1898i 0.734194 0.659183i
532532 0 0
533533 13.6871 + 23.7068i 0.592856 + 1.02686i
534534 0 0
535535 −1.80903 −0.0782112
536536 0 0
537537 −10.4142 + 12.8418i −0.449407 + 0.554166i
538538 0 0
539539 0 0
540540 0 0
541541 5.98865 10.3726i 0.257472 0.445955i −0.708092 0.706120i 0.750444π-0.750444\pi
0.965564 + 0.260165i 0.0837771π0.0837771\pi
542542 0 0
543543 7.66664 + 20.0148i 0.329007 + 0.858917i
544544 0 0
545545 −0.834608 + 1.44558i −0.0357507 + 0.0619220i
546546 0 0
547547 10.7346 + 18.5929i 0.458979 + 0.794975i 0.998907 0.0467363i 0.0148821π-0.0148821\pi
−0.539928 + 0.841711i 0.681549π0.681549\pi
548548 0 0
549549 12.2956 11.0394i 0.524764 0.471150i
550550 0 0
551551 −12.6810 −0.540229
552552 0 0
553553 0 0
554554 0 0
555555 0.681943 + 1.78031i 0.0289469 + 0.0755698i
556556 0 0
557557 15.9246 + 27.5823i 0.674748 + 1.16870i 0.976542 + 0.215325i 0.0690812π0.0690812\pi
−0.301794 + 0.953373i 0.597585π0.597585\pi
558558 0 0
559559 61.0150 2.58066
560560 0 0
561561 −11.7596 30.7001i −0.496492 1.29616i
562562 0 0
563563 −35.5483 −1.49818 −0.749091 0.662467i 0.769510π-0.769510\pi
−0.749091 + 0.662467i 0.769510π0.769510\pi
564564 0 0
565565 4.67962 0.196873
566566 0 0
567567 0 0
568568 0 0
569569 21.7486 0.911748 0.455874 0.890044i 0.349327π-0.349327\pi
0.455874 + 0.890044i 0.349327π0.349327\pi
570570 0 0
571571 −9.59974 −0.401737 −0.200868 0.979618i 0.564376π-0.564376\pi
−0.200868 + 0.979618i 0.564376π0.564376\pi
572572 0 0
573573 −8.15856 21.2990i −0.340829 0.889779i
574574 0 0
575575 −36.6810 −1.52970
576576 0 0
577577 6.50916 + 11.2742i 0.270980 + 0.469351i 0.969113 0.246617i 0.0793190π-0.0793190\pi
−0.698133 + 0.715968i 0.745986π0.745986\pi
578578 0 0
579579 −6.90739 18.0327i −0.287061 0.749413i
580580 0 0
581581 0 0
582582 0 0
583583 4.83173 0.200110
584584 0 0
585585 2.60791 2.34147i 0.107824 0.0968079i
586586 0 0
587587 8.64364 + 14.9712i 0.356761 + 0.617928i 0.987418 0.158134i 0.0505477π-0.0505477\pi
−0.630657 + 0.776062i 0.717214π0.717214\pi
588588 0 0
589589 1.31285 2.27393i 0.0540952 0.0936957i
590590 0 0
591591 0.0893369 + 0.233226i 0.00367483 + 0.00959364i
592592 0 0
593593 6.20765 10.7520i 0.254918 0.441531i −0.709955 0.704247i 0.751285π-0.751285\pi
0.964873 + 0.262716i 0.0846182π0.0846182\pi
594594 0 0
595595 0 0
596596 0 0
597597 −21.2404 + 26.1916i −0.869310 + 1.07195i
598598 0 0
599599 −7.88564 −0.322199 −0.161099 0.986938i 0.551504π-0.551504\pi
−0.161099 + 0.986938i 0.551504π0.551504\pi
600600 0 0
601601 11.1413 + 19.2973i 0.454464 + 0.787154i 0.998657 0.0518055i 0.0164976π-0.0164976\pi
−0.544193 + 0.838960i 0.683164π0.683164\pi
602602 0 0
603603 1.47373 1.32317i 0.0600151 0.0538835i
604604 0 0
605605 1.82489 3.16081i 0.0741925 0.128505i
606606 0 0
607607 11.0458 + 19.1319i 0.448336 + 0.776541i 0.998278 0.0586617i 0.0186833π-0.0186833\pi
−0.549942 + 0.835203i 0.685350π0.685350\pi
608608 0 0
609609 0 0
610610 0 0
611611 10.6014 18.3621i 0.428886 0.742852i
612612 0 0
613613 14.7632 + 25.5706i 0.596280 + 1.03279i 0.993365 + 0.115005i 0.0366885π0.0366885\pi
−0.397085 + 0.917782i 0.629978π0.629978\pi
614614 0 0
615615 −0.830095 2.16708i −0.0334727 0.0873849i
616616 0 0
617617 5.01655 8.68892i 0.201959 0.349803i −0.747201 0.664598i 0.768603π-0.768603\pi
0.949159 + 0.314796i 0.101936π0.101936\pi
618618 0 0
619619 −19.1283 + 33.1312i −0.768833 + 1.33166i 0.169364 + 0.985554i 0.445829π0.445829\pi
−0.938196 + 0.346103i 0.887505π0.887505\pi
620620 0 0
621621 −1.93598 38.5124i −0.0776883 1.54545i
622622 0 0
623623 0 0
624624 0 0
625625 −12.0728 20.9107i −0.482911 0.836427i
626626 0 0
627627 −20.4640 + 25.2343i −0.817254 + 1.00776i
628628 0 0
629629 −17.0482 −0.679754
630630 0 0
631631 −23.0377 −0.917118 −0.458559 0.888664i 0.651634π-0.651634\pi
−0.458559 + 0.888664i 0.651634π0.651634\pi
632632 0 0
633633 −5.52283 0.878756i −0.219513 0.0349274i
634634 0 0
635635 −2.00972 3.48093i −0.0797531 0.138136i
636636 0 0
637637 0 0
638638 0 0
639639 −30.6748 + 27.5409i −1.21348 + 1.08950i
640640 0 0
641641 8.68646 15.0454i 0.343094 0.594257i −0.641911 0.766779i 0.721858π-0.721858\pi
0.985006 + 0.172522i 0.0551916π0.0551916\pi
642642 0 0
643643 −9.47949 + 16.4190i −0.373835 + 0.647501i −0.990152 0.139997i 0.955291π-0.955291\pi
0.616317 + 0.787498i 0.288624π0.288624\pi
644644 0 0
645645 −5.10821 0.812785i −0.201136 0.0320034i
646646 0 0
647647 9.50972 + 16.4713i 0.373865 + 0.647554i 0.990157 0.139964i 0.0446988π-0.0446988\pi
−0.616291 + 0.787518i 0.711366π0.711366\pi
648648 0 0
649649 −19.4201 + 33.6366i −0.762306 + 1.32035i
650650 0 0
651651 0 0
652652 0 0
653653 3.59329 + 6.22377i 0.140616 + 0.243555i 0.927729 0.373255i 0.121758π-0.121758\pi
−0.787112 + 0.616810i 0.788425π0.788425\pi
654654 0 0
655655 −0.585770 + 1.01458i −0.0228879 + 0.0396430i
656656 0 0
657657 10.4383 + 3.40803i 0.407237 + 0.132960i
658658 0 0
659659 −12.7261 22.0423i −0.495740 0.858647i 0.504248 0.863559i 0.331770π-0.331770\pi
−0.999988 + 0.00491209i 0.998436π0.998436\pi
660660 0 0
661661 −8.28590 −0.322284 −0.161142 0.986931i 0.551518π-0.551518\pi
−0.161142 + 0.986931i 0.551518π0.551518\pi
662662 0 0
663663 11.2109 + 29.2676i 0.435396 + 1.13666i
664664 0 0
665665 0 0
666666 0 0
667667 −12.8554 + 22.2662i −0.497764 + 0.862152i
668668 0 0
669669 22.6609 27.9432i 0.876120 1.08035i
670670 0 0
671671 −14.1138 + 24.4458i −0.544857 + 0.943721i
672672 0 0
673673 5.91586 + 10.2466i 0.228040 + 0.394977i 0.957227 0.289338i 0.0934350π-0.0934350\pi
−0.729187 + 0.684314i 0.760102π0.760102\pi
674674 0 0
675675 21.5699 13.9423i 0.830226 0.536641i
676676 0 0
677677 −13.6063 −0.522932 −0.261466 0.965213i 0.584206π-0.584206\pi
−0.261466 + 0.965213i 0.584206π0.584206\pi
678678 0 0
679679 0 0
680680 0 0
681681 −37.5339 5.97215i −1.43830 0.228853i
682682 0 0
683683 −1.79071 3.10160i −0.0685196 0.118679i 0.829730 0.558165i 0.188494π-0.188494\pi
−0.898250 + 0.439485i 0.855161π0.855161\pi
684684 0 0
685685 −1.30206 −0.0497492
686686 0 0
687687 24.8428 30.6338i 0.947813 1.16875i
688688 0 0
689689 −4.60628 −0.175485
690690 0 0
691691 −11.7174 −0.445750 −0.222875 0.974847i 0.571544π-0.571544\pi
−0.222875 + 0.974847i 0.571544π0.571544\pi
692692 0 0
693693 0 0
694694 0 0
695695 1.35348 0.0513405
696696 0 0
697697 20.7518 0.786032
698698 0 0
699699 −44.1004 7.01697i −1.66803 0.265406i
700700 0 0
701701 −10.5926 −0.400077 −0.200039 0.979788i 0.564107π-0.564107\pi
−0.200039 + 0.979788i 0.564107π0.564107\pi
702702 0 0
703703 8.42395 + 14.5907i 0.317715 + 0.550299i
704704 0 0
705705 −1.13216 + 1.39606i −0.0426394 + 0.0525788i
706706 0 0
707707 0 0
708708 0 0
709709 38.2977 1.43830 0.719150 0.694855i 0.244532π-0.244532\pi
0.719150 + 0.694855i 0.244532π0.244532\pi
710710 0 0
711711 13.8970 12.4772i 0.521178 0.467930i
712712 0 0
713713 −2.66182 4.61042i −0.0996861 0.172661i
714714 0 0
715715 −2.99355 + 5.18499i −0.111953 + 0.193908i
716716 0 0
717717 −46.6936 7.42957i −1.74380 0.277463i
718718 0 0
719719 20.8376 36.0918i 0.777112 1.34600i −0.156488 0.987680i 0.550017π-0.550017\pi
0.933600 0.358318i 0.116650π-0.116650\pi
720720 0 0
721721 0 0
722722 0 0
723723 −17.1643 2.73107i −0.638348 0.101570i
724724 0 0
725725 −17.1248 −0.635998
726726 0 0
727727 −16.4126 28.4274i −0.608709 1.05432i −0.991453 0.130461i 0.958354π-0.958354\pi
0.382744 0.923854i 0.374979π-0.374979\pi
728728 0 0
729729 15.7769 + 21.9110i 0.584329 + 0.811517i
730730 0 0
731731 23.1271 40.0573i 0.855386 1.48157i
732732 0 0
733733 4.64884 + 8.05203i 0.171709 + 0.297408i 0.939017 0.343870i 0.111738π-0.111738\pi
−0.767309 + 0.641278i 0.778405π0.778405\pi
734734 0 0
735735 0 0
736736 0 0
737737 −1.69166 + 2.93004i −0.0623130 + 0.107929i
738738 0 0
739739 −5.68878 9.85326i −0.209265 0.362458i 0.742218 0.670158i 0.233774π-0.233774\pi
−0.951483 + 0.307701i 0.900441π0.900441\pi
740740 0 0
741741 19.5092 24.0568i 0.716687 0.883749i
742742 0 0
743743 1.16182 2.01234i 0.0426232 0.0738256i −0.843927 0.536458i 0.819762π-0.819762\pi
0.886550 + 0.462633i 0.153095π0.153095\pi
744744 0 0
745745 0.272915 0.472703i 0.00999883 0.0173185i
746746 0 0
747747 −27.6735 9.03518i −1.01252 0.330580i
748748 0 0
749749 0 0
750750 0 0
751751 5.56690 + 9.64215i 0.203139 + 0.351847i 0.949538 0.313652i 0.101552π-0.101552\pi
−0.746399 + 0.665498i 0.768219π0.768219\pi
752752 0 0
753753 −17.5442 45.8015i −0.639346 1.66910i
754754 0 0
755755 −2.69329 −0.0980190
756756 0 0
757757 52.1639 1.89593 0.947964 0.318376i 0.103138π-0.103138\pi
0.947964 + 0.318376i 0.103138π0.103138\pi
758758 0 0
759759 23.5627 + 61.5136i 0.855271 + 2.23280i
760760 0 0
761761 −23.5127 40.7252i −0.852336 1.47629i −0.879095 0.476647i 0.841852π-0.841852\pi
0.0267592 0.999642i 0.491481π-0.491481\pi
762762 0 0
763763 0 0
764764 0 0
765765 −0.548709 2.59964i −0.0198386 0.0939903i
766766 0 0
767767 18.5140 32.0671i 0.668501 1.15788i
768768 0 0
769769 −3.30314 + 5.72121i −0.119114 + 0.206312i −0.919417 0.393284i 0.871339π-0.871339\pi
0.800303 + 0.599596i 0.204672π0.204672\pi
770770 0 0
771771 31.4887 38.8288i 1.13404 1.39838i
772772 0 0
773773 9.54351 + 16.5298i 0.343256 + 0.594537i 0.985035 0.172352i 0.0551368π-0.0551368\pi
−0.641779 + 0.766889i 0.721803π0.721803\pi
774774 0 0
775775 1.77292 3.07078i 0.0636850 0.110306i
776776 0 0
777777 0 0
778778 0 0
779779 −10.2540 17.7605i −0.367389 0.636337i
780780 0 0
781781 35.2108 60.9869i 1.25994 2.18228i
782782 0 0
783783 −0.903827 17.9797i −0.0323001 0.642544i
784784 0 0
785785 −0.663069 1.14847i −0.0236659 0.0409906i
786786 0 0
787787 −50.9007 −1.81441 −0.907207 0.420685i 0.861790π-0.861790\pi
−0.907207 + 0.420685i 0.861790π0.861790\pi
788788 0 0
789789 −2.06853 0.329131i −0.0736416 0.0117174i
790790 0 0
791791 0 0
792792 0 0
793793 13.4552 23.3052i 0.477810 0.827591i
794794 0 0
795795 0.385640 + 0.0613605i 0.0136772 + 0.00217623i
796796 0 0
797797 4.38727 7.59898i 0.155405 0.269170i −0.777801 0.628510i 0.783665π-0.783665\pi
0.933207 + 0.359341i 0.116998π0.116998\pi
798798 0 0
799799 −8.03667 13.9199i −0.284317 0.492451i
800800 0 0
801801 −4.63968 21.9816i −0.163935 0.776683i
802802 0 0
803803 −18.7576 −0.661942
804804 0 0
805805 0 0
806806 0 0
807807 9.83366 12.1259i 0.346161 0.426853i
808808 0 0
809809 4.75692 + 8.23923i 0.167244 + 0.289676i 0.937450 0.348120i 0.113180π-0.113180\pi
−0.770206 + 0.637796i 0.779846π0.779846\pi
810810 0 0
811811 25.0118 0.878282 0.439141 0.898418i 0.355283π-0.355283\pi
0.439141 + 0.898418i 0.355283π0.355283\pi
812812 0 0
813813 −30.1105 4.79099i −1.05602 0.168027i
814814 0 0
815815 −1.59261 −0.0557866
816816 0 0
817817 −45.7108 −1.59922
818818 0 0
819819 0 0
820820 0 0
821821 −35.5940 −1.24224 −0.621119 0.783716i 0.713322π-0.713322\pi
−0.621119 + 0.783716i 0.713322π0.713322\pi
822822 0 0
823823 16.0000 0.557725 0.278862 0.960331i 0.410043π-0.410043\pi
0.278862 + 0.960331i 0.410043π0.410043\pi
824824 0 0
825825 −27.6352 + 34.0770i −0.962133 + 1.18641i
826826 0 0
827827 −25.4531 −0.885090 −0.442545 0.896746i 0.645924π-0.645924\pi
−0.442545 + 0.896746i 0.645924π0.645924\pi
828828 0 0
829829 −8.77292 15.1951i −0.304696 0.527749i 0.672498 0.740099i 0.265222π-0.265222\pi
−0.977194 + 0.212350i 0.931888π0.931888\pi
830830 0 0
831831 2.48741 + 0.395780i 0.0862872 + 0.0137294i
832832 0 0
833833 0 0
834834 0 0
835835 1.05391 0.0364721
836836 0 0
837837 3.31767 + 1.69936i 0.114675 + 0.0587384i
838838 0 0
839839 12.0562 + 20.8820i 0.416227 + 0.720927i 0.995556 0.0941668i 0.0300187π-0.0300187\pi
−0.579329 + 0.815094i 0.696685π0.696685\pi
840840 0 0
841841 8.49837 14.7196i 0.293047 0.507572i
842842 0 0
843843 22.1427 27.3042i 0.762635 0.940408i
844844 0 0
845845 1.29957 2.25093i 0.0447067 0.0774342i
846846 0 0
847847 0 0
848848 0 0
849849 −2.85185 7.44514i −0.0978752 0.255516i
850850 0 0
851851 34.1592 1.17096
852852 0 0
853853 16.2616 + 28.1659i 0.556785 + 0.964381i 0.997762 + 0.0668621i 0.0212988π0.0212988\pi
−0.440977 + 0.897518i 0.645368π0.645368\pi
854854 0 0
855855 −1.95378 + 1.75417i −0.0668178 + 0.0599912i
856856 0 0
857857 −0.299870 + 0.519390i −0.0102434 + 0.0177420i −0.871102 0.491103i 0.836594π-0.836594\pi
0.860858 + 0.508845i 0.169927π0.169927\pi
858858 0 0
859859 −13.2174 22.8932i −0.450971 0.781104i 0.547476 0.836822i 0.315589π-0.315589\pi
−0.998447 + 0.0557171i 0.982255π0.982255\pi
860860 0 0
861861 0 0
862862 0 0
863863 −9.92270 + 17.1866i −0.337773 + 0.585039i −0.984013 0.178094i 0.943007π-0.943007\pi
0.646241 + 0.763134i 0.276340π0.276340\pi
864864 0 0
865865 −3.02859 5.24567i −0.102975 0.178358i
866866 0 0
867867 −5.61505 0.893429i −0.190697 0.0303424i
868868 0 0
869869 −15.9520 + 27.6296i −0.541134 + 0.937271i
870870 0 0
871871 1.61273 2.79332i 0.0546451 0.0946481i
872872 0 0
873873 48.9059 + 15.9674i 1.65521 + 0.540415i
874874 0 0
875875 0 0
876876 0 0
877877 −10.2352 17.7278i −0.345617 0.598626i 0.639849 0.768501i 0.278997π-0.278997\pi
−0.985466 + 0.169875i 0.945664π0.945664\pi
878878 0 0
879879 12.0992 + 1.92514i 0.408095 + 0.0649334i
880880 0 0
881881 31.1683 1.05009 0.525043 0.851076i 0.324049π-0.324049\pi
0.525043 + 0.851076i 0.324049π0.324049\pi
882882 0 0
883883 −2.64187 −0.0889060 −0.0444530 0.999011i 0.514154π-0.514154\pi
−0.0444530 + 0.999011i 0.514154π0.514154\pi
884884 0 0
885885 −1.97717 + 2.43805i −0.0664618 + 0.0819542i
886886 0 0
887887 −11.5825 20.0615i −0.388902 0.673599i 0.603400 0.797439i 0.293812π-0.293812\pi
−0.992302 + 0.123840i 0.960479π0.960479\pi
888888 0 0
889889 0 0
890890 0 0
891891 −37.2369 27.2164i −1.24748 0.911782i
892892 0 0
893893 −7.94226 + 13.7564i −0.265778 + 0.460341i
894894 0 0
895895 1.14132 1.97682i 0.0381500 0.0660777i
896896 0 0
897897 −22.4632 58.6433i −0.750026 1.95804i
898898 0 0
899899 −1.24269 2.15240i −0.0414460 0.0717866i
900900 0 0
901901 −1.74596 + 3.02409i −0.0581664 + 0.100747i
902902 0 0
903903 0 0
904904 0 0
905905 −1.47949 2.56255i −0.0491799 0.0851821i
906906 0 0
907907 25.0264 43.3470i 0.830988 1.43931i −0.0662676 0.997802i 0.521109π-0.521109\pi
0.897256 0.441511i 0.145558π-0.145558\pi
908908 0 0
909909 4.44966 + 21.0814i 0.147586 + 0.699224i
910910 0 0
911911 5.42231 + 9.39172i 0.179649 + 0.311161i 0.941760 0.336285i 0.109170π-0.109170\pi
−0.762111 + 0.647446i 0.775837π0.775837\pi
912912 0 0
913913 49.7292 1.64579
914914 0 0
915915 −1.43693 + 1.77188i −0.0475034 + 0.0585767i
916916 0 0
917917 0 0
918918 0 0
919919 −5.59549 + 9.69166i −0.184578 + 0.319699i −0.943434 0.331560i 0.892425π-0.892425\pi
0.758856 + 0.651258i 0.225759π0.225759\pi
920920 0 0
921921 9.75924 + 25.4778i 0.321578 + 0.839523i
922922 0 0
923923 −33.5679 + 58.1413i −1.10490 + 1.91374i
924924 0 0
925925 11.3759 + 19.7037i 0.374038 + 0.647853i
926926 0 0
927927 36.5848 + 11.9447i 1.20160 + 0.392315i
928928 0 0
929929 −41.2955 −1.35486 −0.677431 0.735586i 0.736907π-0.736907\pi
−0.677431 + 0.735586i 0.736907π0.736907\pi
930930 0 0
931931 0 0
932932 0 0
933933 −12.1582 31.7405i −0.398040 1.03914i
934934 0 0
935935 2.26935 + 3.93063i 0.0742156 + 0.128545i
936936 0 0
937937 33.5620 1.09642 0.548211 0.836340i 0.315309π-0.315309\pi
0.548211 + 0.836340i 0.315309π0.315309\pi
938938 0 0
939939 −15.7898 41.2213i −0.515279 1.34521i
940940 0 0
941941 −50.4224 −1.64372 −0.821862 0.569686i 0.807065π-0.807065\pi
−0.821862 + 0.569686i 0.807065π0.807065\pi
942942 0 0
943943 −41.5803 −1.35404
944944 0 0
945945 0 0
946946 0 0
947947 20.2424 0.657789 0.328895 0.944367i 0.393324π-0.393324\pi
0.328895 + 0.944367i 0.393324π0.393324\pi
948948 0 0
949949 17.8824 0.580486
950950 0 0
951951 −5.13160 13.3967i −0.166404 0.434419i
952952 0 0
953953 −29.3685 −0.951340 −0.475670 0.879624i 0.657794π-0.657794\pi
−0.475670 + 0.879624i 0.657794π0.657794\pi
954954 0 0
955955 1.57442 + 2.72698i 0.0509470 + 0.0882429i
956956 0 0
957957 11.0004 + 28.7180i 0.355592 + 0.928321i
958958 0 0
959959 0 0
960960 0 0
961961 −30.4854 −0.983399
962962 0 0
963963 −4.68715 22.2065i −0.151041 0.715595i
964964 0 0
965965 1.33297 + 2.30878i 0.0429099 + 0.0743222i
966966 0 0
967967 15.2157 26.3544i 0.489305 0.847501i −0.510619 0.859807i 0.670584π-0.670584\pi
0.999924 + 0.0123057i 0.00391714π0.00391714\pi
968968 0 0
969969 −8.39892 21.9265i −0.269812 0.704381i
970970 0 0
971971 3.59329 6.22377i 0.115314 0.199730i −0.802591 0.596530i 0.796546π-0.796546\pi
0.917905 + 0.396799i 0.129879π0.129879\pi
972972 0 0
973973 0 0
974974 0 0
975975 26.3457 32.4870i 0.843738 1.04042i
976976 0 0
977977 28.5426 0.913157 0.456579 0.889683i 0.349075π-0.349075\pi
0.456579 + 0.889683i 0.349075π0.349075\pi
978978 0 0
979979 19.1888 + 33.2359i 0.613276 + 1.06223i
980980 0 0
981981 −19.9075 6.49966i −0.635598 0.207518i
982982 0 0
983983 2.20821 3.82473i 0.0704310 0.121990i −0.828659 0.559753i 0.810896π-0.810896\pi
0.899090 + 0.437763i 0.144229π0.144229\pi
984984 0 0
985985 −0.0172400 0.0298606i −0.000549313 0.000951438i
986986 0 0
987987 0 0
988988 0 0
989989 −46.3396 + 80.2625i −1.47351 + 2.55220i
990990 0 0
991991 2.90671 + 5.03456i 0.0923345 + 0.159928i 0.908493 0.417900i 0.137234π-0.137234\pi
−0.816159 + 0.577828i 0.803900π0.803900\pi
992992 0 0
993993 7.42270 + 19.3780i 0.235552 + 0.614941i
994994 0 0
995995 2.32777 4.03182i 0.0737953 0.127817i
996996 0 0
997997 −26.3204 + 45.5882i −0.833575 + 1.44379i 0.0616108 + 0.998100i 0.480376π0.480376\pi
−0.895186 + 0.445694i 0.852957π0.852957\pi
998998 0 0
999999 −20.0870 + 12.9838i −0.635525 + 0.410790i
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 1764.2.i.d.373.2 6
3.2 odd 2 5292.2.i.e.1549.2 6
7.2 even 3 1764.2.j.e.589.3 6
7.3 odd 6 1764.2.l.e.949.3 6
7.4 even 3 1764.2.l.f.949.1 6
7.5 odd 6 252.2.j.a.85.1 6
7.6 odd 2 1764.2.i.g.373.2 6
9.2 odd 6 5292.2.l.f.3313.2 6
9.7 even 3 1764.2.l.f.961.1 6
21.2 odd 6 5292.2.j.d.1765.2 6
21.5 even 6 756.2.j.b.253.2 6
21.11 odd 6 5292.2.l.f.361.2 6
21.17 even 6 5292.2.l.e.361.2 6
21.20 even 2 5292.2.i.f.1549.2 6
28.19 even 6 1008.2.r.j.337.3 6
63.2 odd 6 5292.2.j.d.3529.2 6
63.5 even 6 2268.2.a.h.1.2 3
63.11 odd 6 5292.2.i.e.2125.2 6
63.16 even 3 1764.2.j.e.1177.3 6
63.20 even 6 5292.2.l.e.3313.2 6
63.25 even 3 inner 1764.2.i.d.1537.2 6
63.34 odd 6 1764.2.l.e.961.3 6
63.38 even 6 5292.2.i.f.2125.2 6
63.40 odd 6 2268.2.a.i.1.2 3
63.47 even 6 756.2.j.b.505.2 6
63.52 odd 6 1764.2.i.g.1537.2 6
63.61 odd 6 252.2.j.a.169.1 yes 6
84.47 odd 6 3024.2.r.j.1009.2 6
252.47 odd 6 3024.2.r.j.2017.2 6
252.103 even 6 9072.2.a.by.1.2 3
252.131 odd 6 9072.2.a.bv.1.2 3
252.187 even 6 1008.2.r.j.673.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.j.a.85.1 6 7.5 odd 6
252.2.j.a.169.1 yes 6 63.61 odd 6
756.2.j.b.253.2 6 21.5 even 6
756.2.j.b.505.2 6 63.47 even 6
1008.2.r.j.337.3 6 28.19 even 6
1008.2.r.j.673.3 6 252.187 even 6
1764.2.i.d.373.2 6 1.1 even 1 trivial
1764.2.i.d.1537.2 6 63.25 even 3 inner
1764.2.i.g.373.2 6 7.6 odd 2
1764.2.i.g.1537.2 6 63.52 odd 6
1764.2.j.e.589.3 6 7.2 even 3
1764.2.j.e.1177.3 6 63.16 even 3
1764.2.l.e.949.3 6 7.3 odd 6
1764.2.l.e.961.3 6 63.34 odd 6
1764.2.l.f.949.1 6 7.4 even 3
1764.2.l.f.961.1 6 9.7 even 3
2268.2.a.h.1.2 3 63.5 even 6
2268.2.a.i.1.2 3 63.40 odd 6
3024.2.r.j.1009.2 6 84.47 odd 6
3024.2.r.j.2017.2 6 252.47 odd 6
5292.2.i.e.1549.2 6 3.2 odd 2
5292.2.i.e.2125.2 6 63.11 odd 6
5292.2.i.f.1549.2 6 21.20 even 2
5292.2.i.f.2125.2 6 63.38 even 6
5292.2.j.d.1765.2 6 21.2 odd 6
5292.2.j.d.3529.2 6 63.2 odd 6
5292.2.l.e.361.2 6 21.17 even 6
5292.2.l.e.3313.2 6 63.20 even 6
5292.2.l.f.361.2 6 21.11 odd 6
5292.2.l.f.3313.2 6 9.2 odd 6
9072.2.a.bv.1.2 3 252.131 odd 6
9072.2.a.by.1.2 3 252.103 even 6