Properties

Label 2548.2.u.c.1765.6
Level 25482548
Weight 22
Character 2548.1765
Analytic conductor 20.34620.346
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] = [2548,2,Mod(589,2548)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) 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("2548.589"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2548=227213 2548 = 2^{2} \cdot 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2548.u (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,0,0,0,0,0,0,0,-14,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 20.345882435020.3458824350
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ6)\Q(\zeta_{6})
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: x16+38x14+587x12+4762x10+21849x8+56552x6+76456x4+42624x2+2704 x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 364)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 1765.6
Root 1.75101i1.75101i of defining polynomial
Character χ\chi == 2548.1765
Dual form 2548.2.u.c.589.6

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+(0.875503+1.51642i)q3+1.38536iq5+(0.0330100+0.0571750i)q9+(0.9984420.576451i)q11+(1.65348+3.20406i)q13+(2.10079+1.21289i)q15+(0.7812461.35316i)q17+(7.26523+4.19458i)q19+(1.110671.92374i)q23+3.08077q25+5.13741q27+(1.434912.48533i)q296.65024iq31+(1.74828+1.00937i)q33+(3.014361.74034i)q37+(3.41106+5.31253i)q39+(10.8758+6.27917i)q41+(3.07841+5.33196i)q43+(0.07920810.0457308i)q45+7.40432iq47+2.73593q51+11.2301q53+(0.798593+1.38320i)q55+14.6895iq57+(6.976344.02779i)q59+(0.8292071.43623i)q61+(4.43879+2.29067i)q65+(3.21406+1.85564i)q67+(1.944793.36848i)q69+(8.60538+4.96832i)q71+3.30200iq73+(2.69722+4.67173i)q75+4.64811q79+(4.59685+7.96198i)q811.82551iq83+(1.87462+1.08231i)q85+(2.512534.35183i)q87+(2.05837+1.18840i)q89+(10.08455.82230i)q93+(5.81102+10.0650i)q95+(6.53519+3.77309i)q97+0.0761145iq99+O(q100)q+(0.875503 + 1.51642i) q^{3} +1.38536i q^{5} +(-0.0330100 + 0.0571750i) q^{9} +(0.998442 - 0.576451i) q^{11} +(1.65348 + 3.20406i) q^{13} +(-2.10079 + 1.21289i) q^{15} +(0.781246 - 1.35316i) q^{17} +(7.26523 + 4.19458i) q^{19} +(-1.11067 - 1.92374i) q^{23} +3.08077 q^{25} +5.13741 q^{27} +(-1.43491 - 2.48533i) q^{29} -6.65024i q^{31} +(1.74828 + 1.00937i) q^{33} +(3.01436 - 1.74034i) q^{37} +(-3.41106 + 5.31253i) q^{39} +(-10.8758 + 6.27917i) q^{41} +(-3.07841 + 5.33196i) q^{43} +(-0.0792081 - 0.0457308i) q^{45} +7.40432i q^{47} +2.73593 q^{51} +11.2301 q^{53} +(0.798593 + 1.38320i) q^{55} +14.6895i q^{57} +(-6.97634 - 4.02779i) q^{59} +(0.829207 - 1.43623i) q^{61} +(-4.43879 + 2.29067i) q^{65} +(-3.21406 + 1.85564i) q^{67} +(1.94479 - 3.36848i) q^{69} +(8.60538 + 4.96832i) q^{71} +3.30200i q^{73} +(2.69722 + 4.67173i) q^{75} +4.64811 q^{79} +(4.59685 + 7.96198i) q^{81} -1.82551i q^{83} +(1.87462 + 1.08231i) q^{85} +(2.51253 - 4.35183i) q^{87} +(-2.05837 + 1.18840i) q^{89} +(10.0845 - 5.82230i) q^{93} +(-5.81102 + 10.0650i) q^{95} +(6.53519 + 3.77309i) q^{97} +0.0761145i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q14q9+6q1110q13+6q152q1744q25+12q2722q2942q33+12q37+24q3936q41+6q43+30q454q51+8q532q55+18q59++42q97+O(q100) 16 q - 14 q^{9} + 6 q^{11} - 10 q^{13} + 6 q^{15} - 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} - 42 q^{33} + 12 q^{37} + 24 q^{39} - 36 q^{41} + 6 q^{43} + 30 q^{45} - 4 q^{51} + 8 q^{53} - 2 q^{55} + 18 q^{59}+ \cdots + 42 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2548Z)×\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times.

nn 197197 885885 12751275
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 11 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.875503 + 1.51642i 0.505472 + 0.875503i 0.999980 + 0.00632977i 0.00201484π0.00201484\pi
−0.494508 + 0.869173i 0.664652π0.664652\pi
44 0 0
55 1.38536i 0.619553i 0.950809 + 0.309777i 0.100254π0.100254\pi
−0.950809 + 0.309777i 0.899746π0.899746\pi
66 0 0
77 0 0
88 0 0
99 −0.0330100 + 0.0571750i −0.0110033 + 0.0190583i
1010 0 0
1111 0.998442 0.576451i 0.301042 0.173806i −0.341869 0.939748i 0.611060π-0.611060\pi
0.642911 + 0.765941i 0.277727π0.277727\pi
1212 0 0
1313 1.65348 + 3.20406i 0.458593 + 0.888647i
1414 0 0
1515 −2.10079 + 1.21289i −0.542420 + 0.313167i
1616 0 0
1717 0.781246 1.35316i 0.189480 0.328189i −0.755597 0.655037i 0.772653π-0.772653\pi
0.945077 + 0.326848i 0.105986π0.105986\pi
1818 0 0
1919 7.26523 + 4.19458i 1.66676 + 0.962303i 0.969368 + 0.245612i 0.0789888π0.0789888\pi
0.697390 + 0.716692i 0.254345π0.254345\pi
2020 0 0
2121 0 0
2222 0 0
2323 −1.11067 1.92374i −0.231591 0.401127i 0.726685 0.686970i 0.241060π-0.241060\pi
−0.958276 + 0.285843i 0.907726π0.907726\pi
2424 0 0
2525 3.08077 0.616154
2626 0 0
2727 5.13741 0.988696
2828 0 0
2929 −1.43491 2.48533i −0.266455 0.461514i 0.701489 0.712681i 0.252519π-0.252519\pi
−0.967944 + 0.251167i 0.919186π0.919186\pi
3030 0 0
3131 6.65024i 1.19442i −0.802086 0.597209i 0.796276π-0.796276\pi
0.802086 0.597209i 0.203724π-0.203724\pi
3232 0 0
3333 1.74828 + 1.00937i 0.304336 + 0.175708i
3434 0 0
3535 0 0
3636 0 0
3737 3.01436 1.74034i 0.495557 0.286110i −0.231320 0.972878i 0.574304π-0.574304\pi
0.726877 + 0.686768i 0.240971π0.240971\pi
3838 0 0
3939 −3.41106 + 5.31253i −0.546207 + 0.850685i
4040 0 0
4141 −10.8758 + 6.27917i −1.69852 + 0.980641i −0.751353 + 0.659901i 0.770598π0.770598\pi
−0.947167 + 0.320740i 0.896068π0.896068\pi
4242 0 0
4343 −3.07841 + 5.33196i −0.469453 + 0.813116i −0.999390 0.0349208i 0.988882π-0.988882\pi
0.529937 + 0.848037i 0.322215π0.322215\pi
4444 0 0
4545 −0.0792081 0.0457308i −0.0118076 0.00681715i
4646 0 0
4747 7.40432i 1.08003i 0.841655 + 0.540015i 0.181582π0.181582\pi
−0.841655 + 0.540015i 0.818418π0.818418\pi
4848 0 0
4949 0 0
5050 0 0
5151 2.73593 0.383107
5252 0 0
5353 11.2301 1.54257 0.771285 0.636490i 0.219614π-0.219614\pi
0.771285 + 0.636490i 0.219614π0.219614\pi
5454 0 0
5555 0.798593 + 1.38320i 0.107682 + 0.186511i
5656 0 0
5757 14.6895i 1.94567i
5858 0 0
5959 −6.97634 4.02779i −0.908243 0.524374i −0.0283773 0.999597i 0.509034π-0.509034\pi
−0.879865 + 0.475223i 0.842367π0.842367\pi
6060 0 0
6161 0.829207 1.43623i 0.106169 0.183890i −0.808046 0.589119i 0.799475π-0.799475\pi
0.914215 + 0.405229i 0.132808π0.132808\pi
6262 0 0
6363 0 0
6464 0 0
6565 −4.43879 + 2.29067i −0.550564 + 0.284123i
6666 0 0
6767 −3.21406 + 1.85564i −0.392660 + 0.226702i −0.683312 0.730126i 0.739461π-0.739461\pi
0.290652 + 0.956829i 0.406128π0.406128\pi
6868 0 0
6969 1.94479 3.36848i 0.234125 0.405517i
7070 0 0
7171 8.60538 + 4.96832i 1.02127 + 0.589631i 0.914472 0.404650i 0.132607π-0.132607\pi
0.106799 + 0.994281i 0.465940π0.465940\pi
7272 0 0
7373 3.30200i 0.386470i 0.981153 + 0.193235i 0.0618979π0.0618979\pi
−0.981153 + 0.193235i 0.938102π0.938102\pi
7474 0 0
7575 2.69722 + 4.67173i 0.311448 + 0.539444i
7676 0 0
7777 0 0
7878 0 0
7979 4.64811 0.522953 0.261477 0.965210i 0.415791π-0.415791\pi
0.261477 + 0.965210i 0.415791π0.415791\pi
8080 0 0
8181 4.59685 + 7.96198i 0.510761 + 0.884664i
8282 0 0
8383 1.82551i 0.200376i −0.994969 0.100188i 0.968056π-0.968056\pi
0.994969 0.100188i 0.0319445π-0.0319445\pi
8484 0 0
8585 1.87462 + 1.08231i 0.203331 + 0.117393i
8686 0 0
8787 2.51253 4.35183i 0.269371 0.466565i
8888 0 0
8989 −2.05837 + 1.18840i −0.218187 + 0.125970i −0.605111 0.796141i 0.706871π-0.706871\pi
0.386923 + 0.922112i 0.373538π0.373538\pi
9090 0 0
9191 0 0
9292 0 0
9393 10.0845 5.82230i 1.04572 0.603744i
9494 0 0
9595 −5.81102 + 10.0650i −0.596198 + 1.03265i
9696 0 0
9797 6.53519 + 3.77309i 0.663548 + 0.383099i 0.793627 0.608404i 0.208190π-0.208190\pi
−0.130080 + 0.991504i 0.541523π0.541523\pi
9898 0 0
9999 0.0761145i 0.00764980i
100100 0 0
101101 −6.60026 11.4320i −0.656751 1.13753i −0.981452 0.191709i 0.938597π-0.938597\pi
0.324701 0.945817i 0.394736π-0.394736\pi
102102 0 0
103103 −5.90120 −0.581463 −0.290731 0.956805i 0.593899π-0.593899\pi
−0.290731 + 0.956805i 0.593899π0.593899\pi
104104 0 0
105105 0 0
106106 0 0
107107 −5.09634 8.82712i −0.492682 0.853350i 0.507283 0.861780i 0.330650π-0.330650\pi
−0.999964 + 0.00842995i 0.997317π0.997317\pi
108108 0 0
109109 6.14856i 0.588925i −0.955663 0.294463i 0.904859π-0.904859\pi
0.955663 0.294463i 0.0951407π-0.0951407\pi
110110 0 0
111111 5.27816 + 3.04734i 0.500980 + 0.289241i
112112 0 0
113113 −7.29876 + 12.6418i −0.686609 + 1.18924i 0.286319 + 0.958134i 0.407568π0.407568\pi
−0.972928 + 0.231108i 0.925765π0.925765\pi
114114 0 0
115115 2.66508 1.53868i 0.248520 0.143483i
116116 0 0
117117 −0.237773 0.0112283i −0.0219822 0.00103806i
118118 0 0
119119 0 0
120120 0 0
121121 −4.83541 + 8.37517i −0.439583 + 0.761380i
122122 0 0
123123 −19.0436 10.9949i −1.71711 0.991373i
124124 0 0
125125 11.1948i 1.00129i
126126 0 0
127127 4.36114 + 7.55372i 0.386989 + 0.670284i 0.992043 0.125900i 0.0401818π-0.0401818\pi
−0.605054 + 0.796184i 0.706849π0.706849\pi
128128 0 0
129129 −10.7806 −0.949180
130130 0 0
131131 −19.4433 −1.69877 −0.849385 0.527773i 0.823027π-0.823027\pi
−0.849385 + 0.527773i 0.823027π0.823027\pi
132132 0 0
133133 0 0
134134 0 0
135135 7.11718i 0.612550i
136136 0 0
137137 2.90516 + 1.67730i 0.248205 + 0.143301i 0.618942 0.785437i 0.287562π-0.287562\pi
−0.370737 + 0.928738i 0.620895π0.620895\pi
138138 0 0
139139 −3.95629 + 6.85250i −0.335568 + 0.581222i −0.983594 0.180397i 0.942262π-0.942262\pi
0.648025 + 0.761619i 0.275595π0.275595\pi
140140 0 0
141141 −11.2280 + 6.48250i −0.945570 + 0.545925i
142142 0 0
143143 3.49789 + 2.24592i 0.292508 + 0.187813i
144144 0 0
145145 3.44308 1.98787i 0.285933 0.165083i
146146 0 0
147147 0 0
148148 0 0
149149 2.04756 + 1.18216i 0.167743 + 0.0968464i 0.581521 0.813531i 0.302458π-0.302458\pi
−0.413778 + 0.910378i 0.635791π0.635791\pi
150150 0 0
151151 11.5883i 0.943041i −0.881855 0.471520i 0.843705π-0.843705\pi
0.881855 0.471520i 0.156295π-0.156295\pi
152152 0 0
153153 0.0515779 + 0.0893355i 0.00416982 + 0.00722235i
154154 0 0
155155 9.21299 0.740005
156156 0 0
157157 9.03642 0.721184 0.360592 0.932724i 0.382575π-0.382575\pi
0.360592 + 0.932724i 0.382575π0.382575\pi
158158 0 0
159159 9.83196 + 17.0295i 0.779725 + 1.35052i
160160 0 0
161161 0 0
162162 0 0
163163 −18.4945 10.6778i −1.44860 0.836351i −0.450203 0.892926i 0.648648π-0.648648\pi
−0.998398 + 0.0565755i 0.981982π0.981982\pi
164164 0 0
165165 −1.39834 + 2.42200i −0.108861 + 0.188552i
166166 0 0
167167 2.75508 1.59065i 0.213194 0.123088i −0.389601 0.920984i 0.627387π-0.627387\pi
0.602795 + 0.797896i 0.294054π0.294054\pi
168168 0 0
169169 −7.53201 + 10.5957i −0.579385 + 0.815054i
170170 0 0
171171 −0.479650 + 0.276926i −0.0366798 + 0.0211771i
172172 0 0
173173 −2.66952 + 4.62374i −0.202960 + 0.351537i −0.949481 0.313825i 0.898389π-0.898389\pi
0.746521 + 0.665362i 0.231723π0.231723\pi
174174 0 0
175175 0 0
176176 0 0
177177 14.1054i 1.06023i
178178 0 0
179179 4.92279 + 8.52652i 0.367947 + 0.637302i 0.989244 0.146272i 0.0467276π-0.0467276\pi
−0.621298 + 0.783575i 0.713394π0.713394\pi
180180 0 0
181181 −15.1253 −1.12425 −0.562127 0.827051i 0.690017π-0.690017\pi
−0.562127 + 0.827051i 0.690017π0.690017\pi
182182 0 0
183183 2.90389 0.214662
184184 0 0
185185 2.41100 + 4.17598i 0.177260 + 0.307024i
186186 0 0
187187 1.80140i 0.131731i
188188 0 0
189189 0 0
190190 0 0
191191 11.0900 19.2084i 0.802443 1.38987i −0.115561 0.993300i 0.536867π-0.536867\pi
0.918004 0.396571i 0.129800π-0.129800\pi
192192 0 0
193193 −6.03781 + 3.48593i −0.434611 + 0.250923i −0.701309 0.712857i 0.747401π-0.747401\pi
0.266698 + 0.963780i 0.414067π0.414067\pi
194194 0 0
195195 −7.35978 4.72556i −0.527045 0.338404i
196196 0 0
197197 17.0895 9.86660i 1.21757 0.702966i 0.253175 0.967421i 0.418525π-0.418525\pi
0.964398 + 0.264455i 0.0851919π0.0851919\pi
198198 0 0
199199 6.90193 11.9545i 0.489265 0.847431i −0.510659 0.859783i 0.670599π-0.670599\pi
0.999924 + 0.0123521i 0.00393191π0.00393191\pi
200200 0 0
201201 −5.62784 3.24923i −0.396957 0.229183i
202202 0 0
203203 0 0
204204 0 0
205205 −8.69892 15.0670i −0.607559 1.05232i
206206 0 0
207207 0.146653 0.0101931
208208 0 0
209209 9.67188 0.669018
210210 0 0
211211 4.73718 + 8.20504i 0.326121 + 0.564859i 0.981739 0.190235i 0.0609249π-0.0609249\pi
−0.655617 + 0.755093i 0.727592π0.727592\pi
212212 0 0
213213 17.3991i 1.19217i
214214 0 0
215215 −7.38670 4.26471i −0.503769 0.290851i
216216 0 0
217217 0 0
218218 0 0
219219 −5.00720 + 2.89091i −0.338355 + 0.195350i
220220 0 0
221221 5.62738 + 0.265740i 0.378538 + 0.0178756i
222222 0 0
223223 −12.6335 + 7.29395i −0.846001 + 0.488439i −0.859300 0.511473i 0.829100π-0.829100\pi
0.0132984 + 0.999912i 0.495767π0.495767\pi
224224 0 0
225225 −0.101696 + 0.176143i −0.00677974 + 0.0117429i
226226 0 0
227227 6.20380 + 3.58176i 0.411760 + 0.237730i 0.691546 0.722333i 0.256930π-0.256930\pi
−0.279785 + 0.960063i 0.590263π0.590263\pi
228228 0 0
229229 12.3005i 0.812839i 0.913687 + 0.406420i 0.133223π0.133223\pi
−0.913687 + 0.406420i 0.866777π0.866777\pi
230230 0 0
231231 0 0
232232 0 0
233233 −18.8037 −1.23187 −0.615936 0.787796i 0.711222π-0.711222\pi
−0.615936 + 0.787796i 0.711222π0.711222\pi
234234 0 0
235235 −10.2577 −0.669136
236236 0 0
237237 4.06943 + 7.04846i 0.264338 + 0.457847i
238238 0 0
239239 1.60295i 0.103686i −0.998655 0.0518432i 0.983490π-0.983490\pi
0.998655 0.0518432i 0.0165096π-0.0165096\pi
240240 0 0
241241 15.9051 + 9.18284i 1.02454 + 0.591519i 0.915416 0.402509i 0.131862π-0.131862\pi
0.109125 + 0.994028i 0.465195π0.465195\pi
242242 0 0
243243 −0.342988 + 0.594073i −0.0220027 + 0.0381098i
244244 0 0
245245 0 0
246246 0 0
247247 −1.42679 + 30.2139i −0.0907842 + 1.92246i
248248 0 0
249249 2.76824 1.59824i 0.175430 0.101285i
250250 0 0
251251 7.18228 12.4401i 0.453341 0.785210i −0.545250 0.838274i 0.683565π-0.683565\pi
0.998591 + 0.0530634i 0.0168986π0.0168986\pi
252252 0 0
253253 −2.21788 1.28049i −0.139437 0.0805040i
254254 0 0
255255 3.79026i 0.237355i
256256 0 0
257257 −8.68283 15.0391i −0.541620 0.938113i −0.998811 0.0487448i 0.984478π-0.984478\pi
0.457191 0.889368i 0.348855π-0.348855\pi
258258 0 0
259259 0 0
260260 0 0
261261 0.189465 0.0117276
262262 0 0
263263 −8.37095 14.4989i −0.516175 0.894042i −0.999824 0.0187793i 0.994022π-0.994022\pi
0.483648 0.875262i 0.339311π-0.339311\pi
264264 0 0
265265 15.5577i 0.955704i
266266 0 0
267267 −3.60422 2.08090i −0.220575 0.127349i
268268 0 0
269269 12.3957 21.4700i 0.755781 1.30905i −0.189204 0.981938i 0.560591π-0.560591\pi
0.944985 0.327114i 0.106076π-0.106076\pi
270270 0 0
271271 17.5211 10.1158i 1.06433 0.614493i 0.137706 0.990473i 0.456027π-0.456027\pi
0.926628 + 0.375980i 0.122694π0.122694\pi
272272 0 0
273273 0 0
274274 0 0
275275 3.07597 1.77591i 0.185488 0.107091i
276276 0 0
277277 5.52664 9.57242i 0.332064 0.575151i −0.650853 0.759204i 0.725588π-0.725588\pi
0.982916 + 0.184053i 0.0589218π0.0589218\pi
278278 0 0
279279 0.380227 + 0.219524i 0.0227636 + 0.0131426i
280280 0 0
281281 3.18955i 0.190273i 0.995464 + 0.0951363i 0.0303287π0.0303287\pi
−0.995464 + 0.0951363i 0.969671π0.969671\pi
282282 0 0
283283 −8.96481 15.5275i −0.532903 0.923015i −0.999262 0.0384190i 0.987768π-0.987768\pi
0.466359 0.884596i 0.345565π-0.345565\pi
284284 0 0
285285 −20.3503 −1.20545
286286 0 0
287287 0 0
288288 0 0
289289 7.27931 + 12.6081i 0.428195 + 0.741655i
290290 0 0
291291 13.2134i 0.774584i
292292 0 0
293293 14.6945 + 8.48385i 0.858460 + 0.495632i 0.863496 0.504355i 0.168270π-0.168270\pi
−0.00503646 + 0.999987i 0.501603π0.501603\pi
294294 0 0
295295 5.57996 9.66477i 0.324878 0.562705i
296296 0 0
297297 5.12941 2.96147i 0.297639 0.171842i
298298 0 0
299299 4.32730 6.73952i 0.250255 0.389757i
300300 0 0
301301 0 0
302302 0 0
303303 11.5571 20.0175i 0.663938 1.14997i
304304 0 0
305305 1.98970 + 1.14875i 0.113930 + 0.0657774i
306306 0 0
307307 26.9884i 1.54031i −0.637857 0.770155i 0.720179π-0.720179\pi
0.637857 0.770155i 0.279821π-0.279821\pi
308308 0 0
309309 −5.16652 8.94868i −0.293913 0.509072i
310310 0 0
311311 −28.3781 −1.60918 −0.804588 0.593834i 0.797614π-0.797614\pi
−0.804588 + 0.593834i 0.797614π0.797614\pi
312312 0 0
313313 16.6674 0.942095 0.471047 0.882108i 0.343876π-0.343876\pi
0.471047 + 0.882108i 0.343876π0.343876\pi
314314 0 0
315315 0 0
316316 0 0
317317 28.7427i 1.61435i 0.590312 + 0.807175i 0.299005π0.299005\pi
−0.590312 + 0.807175i 0.700995π0.700995\pi
318318 0 0
319319 −2.86534 1.65430i −0.160428 0.0926233i
320320 0 0
321321 8.92372 15.4563i 0.498073 0.862688i
322322 0 0
323323 11.3519 6.55401i 0.631635 0.364675i
324324 0 0
325325 5.09399 + 9.87097i 0.282564 + 0.547543i
326326 0 0
327327 9.32377 5.38308i 0.515606 0.297685i
328328 0 0
329329 0 0
330330 0 0
331331 22.6827 + 13.0959i 1.24675 + 0.719814i 0.970461 0.241260i 0.0775606π-0.0775606\pi
0.276293 + 0.961073i 0.410894π0.410894\pi
332332 0 0
333333 0.229794i 0.0125927i
334334 0 0
335335 −2.57073 4.45264i −0.140454 0.243274i
336336 0 0
337337 4.47831 0.243949 0.121975 0.992533i 0.461077π-0.461077\pi
0.121975 + 0.992533i 0.461077π0.461077\pi
338338 0 0
339339 −25.5603 −1.38825
340340 0 0
341341 −3.83353 6.63988i −0.207597 0.359569i
342342 0 0
343343 0 0
344344 0 0
345345 4.66657 + 2.69424i 0.251239 + 0.145053i
346346 0 0
347347 13.4606 23.3144i 0.722602 1.25158i −0.237351 0.971424i 0.576279π-0.576279\pi
0.959953 0.280160i 0.0903874π-0.0903874\pi
348348 0 0
349349 −17.9560 + 10.3669i −0.961164 + 0.554928i −0.896531 0.442981i 0.853921π-0.853921\pi
−0.0646328 + 0.997909i 0.520588π0.520588\pi
350350 0 0
351351 8.49461 + 16.4606i 0.453409 + 0.878601i
352352 0 0
353353 9.78961 5.65204i 0.521049 0.300828i −0.216315 0.976324i 0.569404π-0.569404\pi
0.737364 + 0.675496i 0.236070π0.236070\pi
354354 0 0
355355 −6.88292 + 11.9216i −0.365308 + 0.632731i
356356 0 0
357357 0 0
358358 0 0
359359 17.7453i 0.936559i −0.883580 0.468279i 0.844874π-0.844874\pi
0.883580 0.468279i 0.155126π-0.155126\pi
360360 0 0
361361 25.6891 + 44.4948i 1.35206 + 2.34183i
362362 0 0
363363 −16.9337 −0.888786
364364 0 0
365365 −4.57447 −0.239439
366366 0 0
367367 4.78155 + 8.28189i 0.249595 + 0.432311i 0.963413 0.268020i 0.0863692π-0.0863692\pi
−0.713819 + 0.700331i 0.753036π0.753036\pi
368368 0 0
369369 0.829101i 0.0431613i
370370 0 0
371371 0 0
372372 0 0
373373 −5.94176 + 10.2914i −0.307653 + 0.532870i −0.977848 0.209314i 0.932877π-0.932877\pi
0.670196 + 0.742184i 0.266210π0.266210\pi
374374 0 0
375375 −16.9760 + 9.80108i −0.876635 + 0.506125i
376376 0 0
377377 5.59056 8.70697i 0.287928 0.448432i
378378 0 0
379379 −14.9391 + 8.62512i −0.767372 + 0.443042i −0.831936 0.554871i 0.812768π-0.812768\pi
0.0645643 + 0.997914i 0.479434π0.479434\pi
380380 0 0
381381 −7.63639 + 13.2266i −0.391224 + 0.677620i
382382 0 0
383383 11.2843 + 6.51499i 0.576600 + 0.332900i 0.759781 0.650179i 0.225306π-0.225306\pi
−0.183181 + 0.983079i 0.558639π0.558639\pi
384384 0 0
385385 0 0
386386 0 0
387387 −0.203236 0.352016i −0.0103311 0.0178940i
388388 0 0
389389 24.1585 1.22488 0.612442 0.790516i 0.290187π-0.290187\pi
0.612442 + 0.790516i 0.290187π0.290187\pi
390390 0 0
391391 −3.47083 −0.175528
392392 0 0
393393 −17.0227 29.4841i −0.858680 1.48728i
394394 0 0
395395 6.43932i 0.323997i
396396 0 0
397397 −4.17021 2.40767i −0.209297 0.120838i 0.391688 0.920098i 0.371891π-0.371891\pi
−0.600985 + 0.799261i 0.705225π0.705225\pi
398398 0 0
399399 0 0
400400 0 0
401401 −6.94702 + 4.01086i −0.346918 + 0.200293i −0.663327 0.748330i 0.730856π-0.730856\pi
0.316409 + 0.948623i 0.397523π0.397523\pi
402402 0 0
403403 21.3078 10.9960i 1.06142 0.547751i
404404 0 0
405405 −11.0302 + 6.36831i −0.548097 + 0.316444i
406406 0 0
407407 2.00644 3.47526i 0.0994555 0.172262i
408408 0 0
409409 8.63206 + 4.98372i 0.426828 + 0.246429i 0.697994 0.716103i 0.254076π-0.254076\pi
−0.271166 + 0.962532i 0.587409π0.587409\pi
410410 0 0
411411 5.87391i 0.289739i
412412 0 0
413413 0 0
414414 0 0
415415 2.52900 0.124144
416416 0 0
417417 −13.8550 −0.678481
418418 0 0
419419 −14.8442 25.7109i −0.725187 1.25606i −0.958897 0.283754i 0.908420π-0.908420\pi
0.233710 0.972306i 0.424913π-0.424913\pi
420420 0 0
421421 13.1380i 0.640305i −0.947366 0.320152i 0.896266π-0.896266\pi
0.947366 0.320152i 0.103734π-0.103734\pi
422422 0 0
423423 −0.423342 0.244416i −0.0205836 0.0118839i
424424 0 0
425425 2.40684 4.16877i 0.116749 0.202215i
426426 0 0
427427 0 0
428428 0 0
429429 −0.343336 + 7.27056i −0.0165764 + 0.351026i
430430 0 0
431431 −12.4729 + 7.20126i −0.600800 + 0.346872i −0.769356 0.638820i 0.779423π-0.779423\pi
0.168556 + 0.985692i 0.446090π0.446090\pi
432432 0 0
433433 18.1596 31.4534i 0.872695 1.51155i 0.0134964 0.999909i 0.495704π-0.495704\pi
0.859198 0.511643i 0.170963π-0.170963\pi
434434 0 0
435435 6.02886 + 3.48076i 0.289062 + 0.166890i
436436 0 0
437437 18.6352i 0.891443i
438438 0 0
439439 −10.2722 17.7920i −0.490266 0.849166i 0.509671 0.860369i 0.329767π-0.329767\pi
−0.999937 + 0.0112036i 0.996434π0.996434\pi
440440 0 0
441441 0 0
442442 0 0
443443 −25.3211 −1.20304 −0.601521 0.798857i 0.705439π-0.705439\pi
−0.601521 + 0.798857i 0.705439π0.705439\pi
444444 0 0
445445 −1.64637 2.85160i −0.0780454 0.135179i
446446 0 0
447447 4.13994i 0.195812i
448448 0 0
449449 −29.0997 16.8007i −1.37330 0.792876i −0.381959 0.924179i 0.624751π-0.624751\pi
−0.991342 + 0.131303i 0.958084π0.958084\pi
450450 0 0
451451 −7.23926 + 12.5388i −0.340883 + 0.590427i
452452 0 0
453453 17.5726 10.1456i 0.825635 0.476680i
454454 0 0
455455 0 0
456456 0 0
457457 32.9050 18.9977i 1.53923 0.888677i 0.540350 0.841441i 0.318292π-0.318292\pi
0.998884 0.0472361i 0.0150413π-0.0150413\pi
458458 0 0
459459 4.01359 6.95174i 0.187338 0.324479i
460460 0 0
461461 31.4812 + 18.1757i 1.46623 + 0.846525i 0.999287 0.0377645i 0.0120237π-0.0120237\pi
0.466938 + 0.884290i 0.345357π0.345357\pi
462462 0 0
463463 35.3400i 1.64239i −0.570649 0.821194i 0.693308π-0.693308\pi
0.570649 0.821194i 0.306692π-0.306692\pi
464464 0 0
465465 8.06600 + 13.9707i 0.374052 + 0.647877i
466466 0 0
467467 29.5717 1.36842 0.684208 0.729287i 0.260148π-0.260148\pi
0.684208 + 0.729287i 0.260148π0.260148\pi
468468 0 0
469469 0 0
470470 0 0
471471 7.91141 + 13.7030i 0.364538 + 0.631399i
472472 0 0
473473 7.09820i 0.326376i
474474 0 0
475475 22.3825 + 12.9225i 1.02698 + 0.592927i
476476 0 0
477477 −0.370705 + 0.642079i −0.0169734 + 0.0293988i
478478 0 0
479479 −18.8339 + 10.8738i −0.860545 + 0.496836i −0.864195 0.503157i 0.832172π-0.832172\pi
0.00364974 + 0.999993i 0.498838π0.498838\pi
480480 0 0
481481 10.5603 + 6.78057i 0.481510 + 0.309167i
482482 0 0
483483 0 0
484484 0 0
485485 −5.22710 + 9.05361i −0.237350 + 0.411103i
486486 0 0
487487 −26.0217 15.0236i −1.17916 0.680786i −0.223337 0.974741i 0.571695π-0.571695\pi
−0.955819 + 0.293955i 0.905028π0.905028\pi
488488 0 0
489489 37.3938i 1.69101i
490490 0 0
491491 −20.0899 34.7967i −0.906643 1.57035i −0.818696 0.574227i 0.805303π-0.805303\pi
−0.0879471 0.996125i 0.528031π-0.528031\pi
492492 0 0
493493 −4.48406 −0.201952
494494 0 0
495495 −0.105446 −0.00473946
496496 0 0
497497 0 0
498498 0 0
499499 11.7400i 0.525554i 0.964857 + 0.262777i 0.0846383π0.0846383\pi
−0.964857 + 0.262777i 0.915362π0.915362\pi
500500 0 0
501501 4.82416 + 2.78523i 0.215528 + 0.124435i
502502 0 0
503503 −16.6965 + 28.9191i −0.744459 + 1.28944i 0.205989 + 0.978554i 0.433959π0.433959\pi
−0.950447 + 0.310886i 0.899374π0.899374\pi
504504 0 0
505505 15.8375 9.14376i 0.704758 0.406892i
506506 0 0
507507 −22.6618 2.14509i −1.00644 0.0952667i
508508 0 0
509509 17.9983 10.3913i 0.797759 0.460586i −0.0449282 0.998990i 0.514306π-0.514306\pi
0.842687 + 0.538404i 0.180973π0.180973\pi
510510 0 0
511511 0 0
512512 0 0
513513 37.3245 + 21.5493i 1.64792 + 0.951425i
514514 0 0
515515 8.17531i 0.360247i
516516 0 0
517517 4.26822 + 7.39278i 0.187716 + 0.325134i
518518 0 0
519519 −9.34869 −0.410362
520520 0 0
521521 −7.50239 −0.328686 −0.164343 0.986403i 0.552550π-0.552550\pi
−0.164343 + 0.986403i 0.552550π0.552550\pi
522522 0 0
523523 3.66289 + 6.34431i 0.160167 + 0.277417i 0.934928 0.354836i 0.115463π-0.115463\pi
−0.774762 + 0.632254i 0.782130π0.782130\pi
524524 0 0
525525 0 0
526526 0 0
527527 −8.99882 5.19547i −0.391995 0.226318i
528528 0 0
529529 9.03282 15.6453i 0.392731 0.680230i
530530 0 0
531531 0.460578 0.265915i 0.0199874 0.0115397i
532532 0 0
533533 −38.1018 24.4644i −1.65037 1.05967i
534534 0 0
535535 12.2288 7.06028i 0.528696 0.305243i
536536 0 0
537537 −8.61983 + 14.9300i −0.371973 + 0.644277i
538538 0 0
539539 0 0
540540 0 0
541541 11.6924i 0.502698i 0.967897 + 0.251349i 0.0808741π0.0808741\pi
−0.967897 + 0.251349i 0.919126π0.919126\pi
542542 0 0
543543 −13.2422 22.9362i −0.568278 0.984287i
544544 0 0
545545 8.51799 0.364871
546546 0 0
547547 5.10513 0.218280 0.109140 0.994026i 0.465190π-0.465190\pi
0.109140 + 0.994026i 0.465190π0.465190\pi
548548 0 0
549549 0.0547442 + 0.0948197i 0.00233643 + 0.00404681i
550550 0 0
551551 24.0753i 1.02564i
552552 0 0
553553 0 0
554554 0 0
555555 −4.22168 + 7.31216i −0.179200 + 0.310384i
556556 0 0
557557 10.8544 6.26679i 0.459916 0.265532i −0.252093 0.967703i 0.581119π-0.581119\pi
0.712009 + 0.702171i 0.247786π0.247786\pi
558558 0 0
559559 −22.1740 1.04712i −0.937860 0.0442884i
560560 0 0
561561 2.73167 1.57713i 0.115331 0.0665865i
562562 0 0
563563 −1.95315 + 3.38296i −0.0823155 + 0.142575i −0.904244 0.427016i 0.859565π-0.859565\pi
0.821929 + 0.569590i 0.192898π0.192898\pi
564564 0 0
565565 −17.5135 10.1114i −0.736799 0.425391i
566566 0 0
567567 0 0
568568 0 0
569569 −23.0664 39.9523i −0.966996 1.67489i −0.704155 0.710046i 0.748674π-0.748674\pi
−0.262841 0.964839i 0.584659π-0.584659\pi
570570 0 0
571571 −30.1160 −1.26031 −0.630157 0.776467i 0.717010π-0.717010\pi
−0.630157 + 0.776467i 0.717010π0.717010\pi
572572 0 0
573573 38.8372 1.62245
574574 0 0
575575 −3.42172 5.92660i −0.142696 0.247156i
576576 0 0
577577 25.6300i 1.06699i 0.845803 + 0.533496i 0.179122π0.179122\pi
−0.845803 + 0.533496i 0.820878π0.820878\pi
578578 0 0
579579 −10.5722 6.10388i −0.439367 0.253669i
580580 0 0
581581 0 0
582582 0 0
583583 11.2126 6.47358i 0.464377 0.268108i
584584 0 0
585585 0.0155553 0.329403i 0.000643133 0.0136191i
586586 0 0
587587 −11.4147 + 6.59025i −0.471133 + 0.272009i −0.716714 0.697367i 0.754355π-0.754355\pi
0.245581 + 0.969376i 0.421021π0.421021\pi
588588 0 0
589589 27.8950 48.3155i 1.14939 1.99081i
590590 0 0
591591 29.9237 + 17.2765i 1.23090 + 0.710659i
592592 0 0
593593 6.53704i 0.268444i 0.990951 + 0.134222i 0.0428536π0.0428536\pi
−0.990951 + 0.134222i 0.957146π0.957146\pi
594594 0 0
595595 0 0
596596 0 0
597597 24.1706 0.989238
598598 0 0
599599 12.4244 0.507649 0.253824 0.967250i 0.418311π-0.418311\pi
0.253824 + 0.967250i 0.418311π0.418311\pi
600600 0 0
601601 −9.27019 16.0564i −0.378139 0.654956i 0.612653 0.790352i 0.290102π-0.290102\pi
−0.990791 + 0.135397i 0.956769π0.956769\pi
602602 0 0
603603 0.245018i 0.00997792i
604604 0 0
605605 −11.6027 6.69880i −0.471715 0.272345i
606606 0 0
607607 7.87226 13.6351i 0.319525 0.553434i −0.660864 0.750506i 0.729810π-0.729810\pi
0.980389 + 0.197072i 0.0631433π0.0631433\pi
608608 0 0
609609 0 0
610610 0 0
611611 −23.7239 + 12.2429i −0.959766 + 0.495294i
612612 0 0
613613 16.6796 9.62996i 0.673682 0.388950i −0.123788 0.992309i 0.539504π-0.539504\pi
0.797470 + 0.603358i 0.206171π0.206171\pi
614614 0 0
615615 15.2319 26.3824i 0.614208 1.06384i
616616 0 0
617617 37.5872 + 21.7010i 1.51320 + 0.873649i 0.999881 + 0.0154532i 0.00491911π0.00491911\pi
0.513323 + 0.858195i 0.328414π0.328414\pi
618618 0 0
619619 13.3880i 0.538109i 0.963125 + 0.269054i 0.0867111π0.0867111\pi
−0.963125 + 0.269054i 0.913289π0.913289\pi
620620 0 0
621621 −5.70598 9.88305i −0.228973 0.396593i
622622 0 0
623623 0 0
624624 0 0
625625 −0.105015 −0.00420059
626626 0 0
627627 8.46776 + 14.6666i 0.338170 + 0.585727i
628628 0 0
629629 5.43854i 0.216849i
630630 0 0
631631 13.1568 + 7.59606i 0.523762 + 0.302394i 0.738473 0.674283i 0.235547π-0.235547\pi
−0.214710 + 0.976678i 0.568881π0.568881\pi
632632 0 0
633633 −8.29484 + 14.3671i −0.329690 + 0.571040i
634634 0 0
635635 −10.4646 + 6.04177i −0.415277 + 0.239760i
636636 0 0
637637 0 0
638638 0 0
639639 −0.568127 + 0.328008i −0.0224747 + 0.0129758i
640640 0 0
641641 −17.9671 + 31.1199i −0.709658 + 1.22916i 0.255326 + 0.966855i 0.417817π0.417817\pi
−0.964984 + 0.262309i 0.915516π0.915516\pi
642642 0 0
643643 −7.72476 4.45989i −0.304635 0.175881i 0.339888 0.940466i 0.389611π-0.389611\pi
−0.644523 + 0.764585i 0.722944π0.722944\pi
644644 0 0
645645 14.9351i 0.588068i
646646 0 0
647647 −4.88360 8.45865i −0.191994 0.332544i 0.753917 0.656970i 0.228162π-0.228162\pi
−0.945911 + 0.324426i 0.894829π0.894829\pi
648648 0 0
649649 −9.28730 −0.364558
650650 0 0
651651 0 0
652652 0 0
653653 −8.26858 14.3216i −0.323575 0.560448i 0.657648 0.753325i 0.271551π-0.271551\pi
−0.981223 + 0.192877i 0.938218π0.938218\pi
654654 0 0
655655 26.9361i 1.05248i
656656 0 0
657657 −0.188792 0.108999i −0.00736547 0.00425245i
658658 0 0
659659 −7.82010 + 13.5448i −0.304628 + 0.527631i −0.977178 0.212420i 0.931865π-0.931865\pi
0.672550 + 0.740051i 0.265199π0.265199\pi
660660 0 0
661661 21.9320 12.6624i 0.853056 0.492512i −0.00862494 0.999963i 0.502745π-0.502745\pi
0.861681 + 0.507451i 0.169412π0.169412\pi
662662 0 0
663663 4.52381 + 8.76610i 0.175690 + 0.340447i
664664 0 0
665665 0 0
666666 0 0
667667 −3.18742 + 5.52077i −0.123417 + 0.213765i
668668 0 0
669669 −22.1213 12.7717i −0.855259 0.493784i
670670 0 0
671671 1.91199i 0.0738114i
672672 0 0
673673 −4.08919 7.08268i −0.157627 0.273017i 0.776386 0.630258i 0.217051π-0.217051\pi
−0.934012 + 0.357241i 0.883718π0.883718\pi
674674 0 0
675675 15.8272 0.609189
676676 0 0
677677 −44.9616 −1.72801 −0.864007 0.503480i 0.832053π-0.832053\pi
−0.864007 + 0.503480i 0.832053π0.832053\pi
678678 0 0
679679 0 0
680680 0 0
681681 12.5434i 0.480663i
682682 0 0
683683 17.7090 + 10.2243i 0.677616 + 0.391222i 0.798956 0.601389i 0.205386π-0.205386\pi
−0.121340 + 0.992611i 0.538719π0.538719\pi
684684 0 0
685685 −2.32367 + 4.02471i −0.0887827 + 0.153776i
686686 0 0
687687 −18.6526 + 10.7691i −0.711643 + 0.410867i
688688 0 0
689689 18.5687 + 35.9818i 0.707411 + 1.37080i
690690 0 0
691691 29.1943 16.8554i 1.11061 0.641208i 0.171619 0.985163i 0.445100π-0.445100\pi
0.938986 + 0.343955i 0.111767π0.111767\pi
692692 0 0
693693 0 0
694694 0 0
695695 −9.49320 5.48090i −0.360098 0.207902i
696696 0 0
697697 19.6223i 0.743248i
698698 0 0
699699 −16.4627 28.5142i −0.622676 1.07851i
700700 0 0
701701 −29.6172 −1.11862 −0.559312 0.828957i 0.688935π-0.688935\pi
−0.559312 + 0.828957i 0.688935π0.688935\pi
702702 0 0
703703 29.2000 1.10130
704704 0 0
705705 −8.98062 15.5549i −0.338230 0.585831i
706706 0 0
707707 0 0
708708 0 0
709709 8.59653 + 4.96321i 0.322849 + 0.186397i 0.652662 0.757649i 0.273652π-0.273652\pi
−0.329813 + 0.944046i 0.606986π0.606986\pi
710710 0 0
711711 −0.153434 + 0.265756i −0.00575423 + 0.00996661i
712712 0 0
713713 −12.7933 + 7.38623i −0.479114 + 0.276616i
714714 0 0
715715 −3.11141 + 4.84584i −0.116360 + 0.181224i
716716 0 0
717717 2.43074 1.40339i 0.0907778 0.0524106i
718718 0 0
719719 10.3425 17.9138i 0.385711 0.668071i −0.606157 0.795345i 0.707290π-0.707290\pi
0.991868 + 0.127274i 0.0406229π0.0406229\pi
720720 0 0
721721 0 0
722722 0 0
723723 32.1584i 1.19598i
724724 0 0
725725 −4.42061 7.65673i −0.164177 0.284364i
726726 0 0
727727 −4.83449 −0.179301 −0.0896506 0.995973i 0.528575π-0.528575\pi
−0.0896506 + 0.995973i 0.528575π0.528575\pi
728728 0 0
729729 26.3800 0.977035
730730 0 0
731731 4.80999 + 8.33115i 0.177904 + 0.308139i
732732 0 0
733733 12.7037i 0.469223i 0.972089 + 0.234612i 0.0753819π0.0753819\pi
−0.972089 + 0.234612i 0.924618π0.924618\pi
734734 0 0
735735 0 0
736736 0 0
737737 −2.13937 + 3.70549i −0.0788046 + 0.136494i
738738 0 0
739739 −2.23852 + 1.29241i −0.0823451 + 0.0475420i −0.540607 0.841275i 0.681805π-0.681805\pi
0.458262 + 0.888817i 0.348472π0.348472\pi
740740 0 0
741741 −47.0660 + 24.2888i −1.72901 + 0.892270i
742742 0 0
743743 9.98318 5.76379i 0.366247 0.211453i −0.305570 0.952169i 0.598847π-0.598847\pi
0.671818 + 0.740717i 0.265514π0.265514\pi
744744 0 0
745745 −1.63772 + 2.83662i −0.0600015 + 0.103926i
746746 0 0
747747 0.104374 + 0.0602602i 0.00381884 + 0.00220481i
748748 0 0
749749 0 0
750750 0 0
751751 −3.50269 6.06684i −0.127815 0.221382i 0.795015 0.606590i 0.207463π-0.207463\pi
−0.922830 + 0.385208i 0.874130π0.874130\pi
752752 0 0
753753 25.1524 0.916605
754754 0 0
755755 16.0540 0.584264
756756 0 0
757757 8.60091 + 14.8972i 0.312605 + 0.541449i 0.978926 0.204217i 0.0654649π-0.0654649\pi
−0.666320 + 0.745666i 0.732132π0.732132\pi
758758 0 0
759759 4.48431i 0.162770i
760760 0 0
761761 −29.9238 17.2765i −1.08474 0.626274i −0.152567 0.988293i 0.548754π-0.548754\pi
−0.932170 + 0.362020i 0.882087π0.882087\pi
762762 0 0
763763 0 0
764764 0 0
765765 −0.123762 + 0.0714541i −0.00447463 + 0.00258343i
766766 0 0
767767 1.37005 29.0125i 0.0494697 1.04758i
768768 0 0
769769 −9.48253 + 5.47474i −0.341949 + 0.197424i −0.661133 0.750268i 0.729924π-0.729924\pi
0.319185 + 0.947693i 0.396591π0.396591\pi
770770 0 0
771771 15.2037 26.3335i 0.547547 0.948379i
772772 0 0
773773 −19.0556 11.0018i −0.685384 0.395707i 0.116496 0.993191i 0.462834π-0.462834\pi
−0.801880 + 0.597484i 0.796167π0.796167\pi
774774 0 0
775775 20.4878i 0.735945i
776776 0 0
777777 0 0
778778 0 0
779779 −105.354 −3.77470
780780 0 0
781781 11.4560 0.409926
782782 0 0
783783 −7.37171 12.7682i −0.263443 0.456297i
784784 0 0
785785 12.5187i 0.446812i
786786 0 0
787787 −34.0548 19.6616i −1.21392 0.700859i −0.250312 0.968165i 0.580533π-0.580533\pi
−0.963612 + 0.267306i 0.913866π0.913866\pi
788788 0 0
789789 14.6576 25.3877i 0.521824 0.903826i
790790 0 0
791791 0 0
792792 0 0
793793 5.97284 + 0.282054i 0.212102 + 0.0100160i
794794 0 0
795795 −23.5920 + 13.6208i −0.836721 + 0.483081i
796796 0 0
797797 27.2620 47.2192i 0.965669 1.67259i 0.257863 0.966181i 0.416982π-0.416982\pi
0.707806 0.706407i 0.249685π-0.249685\pi
798798 0 0
799799 10.0192 + 5.78460i 0.354454 + 0.204644i
800800 0 0
801801 0.156917i 0.00554438i
802802 0 0
803803 1.90344 + 3.29685i 0.0671709 + 0.116343i
804804 0 0
805805 0 0
806806 0 0
807807 43.4100 1.52810
808808 0 0
809809 −1.56318 2.70751i −0.0549586 0.0951911i 0.837237 0.546840i 0.184169π-0.184169\pi
−0.892196 + 0.451649i 0.850836π0.850836\pi
810810 0 0
811811 4.48741i 0.157574i −0.996891 0.0787872i 0.974895π-0.974895\pi
0.996891 0.0787872i 0.0251048π-0.0251048\pi
812812 0 0
813813 30.6796 + 17.7129i 1.07598 + 0.621218i
814814 0 0
815815 14.7926 25.6216i 0.518164 0.897486i
816816 0 0
817817 −44.7307 + 25.8253i −1.56493 + 0.903512i
818818 0 0
819819 0 0
820820 0 0
821821 −21.3797 + 12.3436i −0.746158 + 0.430795i −0.824304 0.566147i 0.808433π-0.808433\pi
0.0781459 + 0.996942i 0.475100π0.475100\pi
822822 0 0
823823 −5.50672 + 9.53791i −0.191952 + 0.332471i −0.945897 0.324467i 0.894815π-0.894815\pi
0.753945 + 0.656938i 0.228148π0.228148\pi
824824 0 0
825825 5.38604 + 3.10963i 0.187518 + 0.108263i
826826 0 0
827827 23.8575i 0.829605i −0.909911 0.414803i 0.863851π-0.863851\pi
0.909911 0.414803i 0.136149π-0.136149\pi
828828 0 0
829829 −10.2157 17.6941i −0.354806 0.614541i 0.632279 0.774741i 0.282120π-0.282120\pi
−0.987085 + 0.160199i 0.948786π0.948786\pi
830830 0 0
831831 19.3544 0.671395
832832 0 0
833833 0 0
834834 0 0
835835 2.20362 + 3.81679i 0.0762595 + 0.132085i
836836 0 0
837837 34.1650i 1.18092i
838838 0 0
839839 −21.0080 12.1290i −0.725276 0.418738i 0.0914153 0.995813i 0.470861π-0.470861\pi
−0.816692 + 0.577074i 0.804194π0.804194\pi
840840 0 0
841841 10.3821 17.9823i 0.358003 0.620080i
842842 0 0
843843 −4.83668 + 2.79246i −0.166584 + 0.0961775i
844844 0 0
845845 −14.6789 10.4346i −0.504969 0.358960i
846846 0 0
847847 0 0
848848 0 0
849849 15.6974 27.1888i 0.538734 0.933115i
850850 0 0
851851 −6.69592 3.86589i −0.229533 0.132521i
852852 0 0
853853 51.8470i 1.77521i −0.460608 0.887604i 0.652369π-0.652369\pi
0.460608 0.887604i 0.347631π-0.347631\pi
854854 0 0
855855 −0.383643 0.664490i −0.0131203 0.0227251i
856856 0 0
857857 26.9054 0.919071 0.459536 0.888159i 0.348016π-0.348016\pi
0.459536 + 0.888159i 0.348016π0.348016\pi
858858 0 0
859859 −33.4509 −1.14133 −0.570665 0.821183i 0.693315π-0.693315\pi
−0.570665 + 0.821183i 0.693315π0.693315\pi
860860 0 0
861861 0 0
862862 0 0
863863 5.94352i 0.202320i 0.994870 + 0.101160i 0.0322554π0.0322554\pi
−0.994870 + 0.101160i 0.967745π0.967745\pi
864864 0 0
865865 −6.40557 3.69825i −0.217796 0.125744i
866866 0 0
867867 −12.7461 + 22.0769i −0.432881 + 0.749771i
868868 0 0
869869 4.64087 2.67941i 0.157431 0.0908926i
870870 0 0
871871 −11.2600 7.22978i −0.381529 0.244972i
872872 0 0
873873 −0.431453 + 0.249099i −0.0146025 + 0.00843074i
874874 0 0
875875 0 0
876876 0 0
877877 43.0073 + 24.8303i 1.45225 + 0.838458i 0.998609 0.0527255i 0.0167908π-0.0167908\pi
0.453643 + 0.891184i 0.350124π0.350124\pi
878878 0 0
879879 29.7105i 1.00211i
880880 0 0
881881 10.6452 + 18.4381i 0.358647 + 0.621195i 0.987735 0.156139i 0.0499049π-0.0499049\pi
−0.629088 + 0.777334i 0.716572π0.716572\pi
882882 0 0
883883 −32.8053 −1.10399 −0.551993 0.833848i 0.686133π-0.686133\pi
−0.551993 + 0.833848i 0.686133π0.686133\pi
884884 0 0
885885 19.5411 0.656866
886886 0 0
887887 −8.61790 14.9266i −0.289361 0.501187i 0.684297 0.729204i 0.260109π-0.260109\pi
−0.973657 + 0.228016i 0.926776π0.926776\pi
888888 0 0
889889 0 0
890890 0 0
891891 9.17938 + 5.29972i 0.307521 + 0.177547i
892892 0 0
893893 −31.0580 + 53.7941i −1.03932 + 1.80015i
894894 0 0
895895 −11.8123 + 6.81985i −0.394843 + 0.227963i
896896 0 0
897897 14.0085 + 0.661520i 0.467730 + 0.0220875i
898898 0 0
899899 −16.5280 + 9.54247i −0.551241 + 0.318259i
900900 0 0
901901 8.77345 15.1961i 0.292286 0.506254i
902902 0 0
903903 0 0
904904 0 0
905905 20.9540i 0.696535i
906906 0 0
907907 −17.3178 29.9953i −0.575028 0.995978i −0.996039 0.0889223i 0.971658π-0.971658\pi
0.421010 0.907056i 0.361676π-0.361676\pi
908908 0 0
909909 0.871499 0.0289058
910910 0 0
911911 −7.85153 −0.260133 −0.130066 0.991505i 0.541519π-0.541519\pi
−0.130066 + 0.991505i 0.541519π0.541519\pi
912912 0 0
913913 −1.05232 1.82267i −0.0348267 0.0603216i
914914 0 0
915915 4.02294i 0.132994i
916916 0 0
917917 0 0
918918 0 0
919919 18.3659 31.8106i 0.605834 1.04934i −0.386085 0.922463i 0.626173π-0.626173\pi
0.991919 0.126872i 0.0404937π-0.0404937\pi
920920 0 0
921921 40.9256 23.6284i 1.34854 0.778583i
922922 0 0
923923 −1.68997 + 35.7872i −0.0556260 + 1.17795i
924924 0 0
925925 9.28654 5.36159i 0.305339 0.176288i
926926 0 0
927927 0.194799 0.337401i 0.00639803 0.0110817i
928928 0 0
929929 −28.6355 16.5327i −0.939501 0.542421i −0.0496975 0.998764i 0.515826π-0.515826\pi
−0.889804 + 0.456343i 0.849159π0.849159\pi
930930 0 0
931931 0 0
932932 0 0
933933 −24.8451 43.0330i −0.813393 1.40884i
934934 0 0
935935 2.49559 0.0816146
936936 0 0
937937 45.8626 1.49826 0.749132 0.662421i 0.230471π-0.230471\pi
0.749132 + 0.662421i 0.230471π0.230471\pi
938938 0 0
939939 14.5923 + 25.2746i 0.476202 + 0.824806i
940940 0 0
941941 5.77729i 0.188334i −0.995556 0.0941671i 0.969981π-0.969981\pi
0.995556 0.0941671i 0.0300188π-0.0300188\pi
942942 0 0
943943 24.1590 + 13.9482i 0.786724 + 0.454215i
944944 0 0
945945 0 0
946946 0 0
947947 −0.0487521 + 0.0281471i −0.00158423 + 0.000914656i −0.500792 0.865568i 0.666958π-0.666958\pi
0.499208 + 0.866482i 0.333624π0.333624\pi
948948 0 0
949949 −10.5798 + 5.45979i −0.343435 + 0.177232i
950950 0 0
951951 −43.5858 + 25.1643i −1.41337 + 0.816008i
952952 0 0
953953 −20.0778 + 34.7758i −0.650385 + 1.12650i 0.332645 + 0.943052i 0.392059π0.392059\pi
−0.983030 + 0.183447i 0.941274π0.941274\pi
954954 0 0
955955 26.6106 + 15.3636i 0.861099 + 0.497156i
956956 0 0
957957 5.79339i 0.187274i
958958 0 0
959959 0 0
960960 0 0
961961 −13.2257 −0.426634
962962 0 0
963963 0.672920 0.0216846
964964 0 0
965965 −4.82928 8.36456i −0.155460 0.269265i
966966 0 0
967967 32.3647i 1.04078i 0.853929 + 0.520390i 0.174213π0.174213\pi
−0.853929 + 0.520390i 0.825787π0.825787\pi
968968 0 0
969969 19.8772 + 11.4761i 0.638547 + 0.368665i
970970 0 0
971971 −15.3459 + 26.5799i −0.492473 + 0.852989i −0.999962 0.00866935i 0.997240π-0.997240\pi
0.507489 + 0.861658i 0.330574π0.330574\pi
972972 0 0
973973 0 0
974974 0 0
975975 −10.5087 + 16.3667i −0.336547 + 0.524153i
976976 0 0
977977 4.87565 2.81496i 0.155986 0.0900585i −0.419975 0.907536i 0.637961π-0.637961\pi
0.575961 + 0.817477i 0.304628π0.304628\pi
978978 0 0
979979 −1.37011 + 2.37310i −0.0437890 + 0.0758447i
980980 0 0
981981 0.351544 + 0.202964i 0.0112239 + 0.00648014i
982982 0 0
983983 6.66363i 0.212537i −0.994337 0.106268i 0.966110π-0.966110\pi
0.994337 0.106268i 0.0338903π-0.0338903\pi
984984 0 0
985985 13.6688 + 23.6751i 0.435525 + 0.754351i
986986 0 0
987987 0 0
988988 0 0
989989 13.6764 0.434884
990990 0 0
991991 26.4156 + 45.7532i 0.839120 + 1.45340i 0.890631 + 0.454726i 0.150263π0.150263\pi
−0.0515115 + 0.998672i 0.516404π0.516404\pi
992992 0 0
993993 45.8618i 1.45538i
994994 0 0
995995 16.5613 + 9.56167i 0.525029 + 0.303125i
996996 0 0
997997 −7.31833 + 12.6757i −0.231774 + 0.401444i −0.958330 0.285663i 0.907786π-0.907786\pi
0.726556 + 0.687107i 0.241120π0.241120\pi
998998 0 0
999999 15.4860 8.94085i 0.489955 0.282876i
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 2548.2.u.c.1765.6 16
7.2 even 3 2548.2.bq.c.361.3 16
7.3 odd 6 2548.2.bb.d.569.3 16
7.4 even 3 2548.2.bb.c.569.6 16
7.5 odd 6 2548.2.bq.e.361.6 16
7.6 odd 2 364.2.u.a.309.3 yes 16
13.4 even 6 inner 2548.2.u.c.589.6 16
21.20 even 2 3276.2.cf.c.1765.6 16
28.27 even 2 1456.2.cc.f.673.6 16
91.4 even 6 2548.2.bq.c.1941.3 16
91.17 odd 6 2548.2.bq.e.1941.6 16
91.30 even 6 2548.2.bb.c.1733.6 16
91.41 even 12 4732.2.a.t.1.6 8
91.55 odd 6 4732.2.g.k.337.11 16
91.62 odd 6 4732.2.g.k.337.12 16
91.69 odd 6 364.2.u.a.225.3 16
91.76 even 12 4732.2.a.s.1.6 8
91.82 odd 6 2548.2.bb.d.1733.3 16
273.251 even 6 3276.2.cf.c.2773.3 16
364.251 even 6 1456.2.cc.f.225.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
364.2.u.a.225.3 16 91.69 odd 6
364.2.u.a.309.3 yes 16 7.6 odd 2
1456.2.cc.f.225.6 16 364.251 even 6
1456.2.cc.f.673.6 16 28.27 even 2
2548.2.u.c.589.6 16 13.4 even 6 inner
2548.2.u.c.1765.6 16 1.1 even 1 trivial
2548.2.bb.c.569.6 16 7.4 even 3
2548.2.bb.c.1733.6 16 91.30 even 6
2548.2.bb.d.569.3 16 7.3 odd 6
2548.2.bb.d.1733.3 16 91.82 odd 6
2548.2.bq.c.361.3 16 7.2 even 3
2548.2.bq.c.1941.3 16 91.4 even 6
2548.2.bq.e.361.6 16 7.5 odd 6
2548.2.bq.e.1941.6 16 91.17 odd 6
3276.2.cf.c.1765.6 16 21.20 even 2
3276.2.cf.c.2773.3 16 273.251 even 6
4732.2.a.s.1.6 8 91.76 even 12
4732.2.a.t.1.6 8 91.41 even 12
4732.2.g.k.337.11 16 91.55 odd 6
4732.2.g.k.337.12 16 91.62 odd 6