LMFDB - Embedded newform 572.2.x.a.181.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(25,572)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("572.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.x (of order $10$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			181.5
Character	$\chi$	$=$	572.181
Dual form			572.2.x.a.493.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.480503 - 0.349106i) q^{3} +(-1.45044 - 0.471277i) q^{5} +(-0.743441 - 1.02326i) q^{7} +(-0.818043 - 2.51768i) q^{9} +O(q^{10})$	\(q+(-0.480503 - 0.349106i) q^{3} +(-1.45044 - 0.471277i) q^{5} +(-0.743441 - 1.02326i) q^{7} +(-0.818043 - 2.51768i) q^{9} +(-1.57515 + 2.91871i) q^{11} +(0.260637 + 3.59612i) q^{13} +(0.532415 + 0.732807i) q^{15} +(-1.14257 + 3.51647i) q^{17} +(-2.92672 + 4.02829i) q^{19} +0.751218i q^{21} +5.05102 q^{23} +(-2.16341 - 1.57181i) q^{25} +(-1.03647 + 3.18993i) q^{27} +(-0.976091 + 0.709172i) q^{29} +(-9.08737 + 2.95267i) q^{31} +(1.77581 - 0.852554i) q^{33} +(0.596080 + 1.83454i) q^{35} +(-4.14494 - 5.70503i) q^{37} +(1.13019 - 1.81893i) q^{39} +(-1.39987 + 1.92675i) q^{41} -3.12533 q^{43} +4.03727i q^{45} +(-1.79076 + 2.46477i) q^{47} +(1.66876 - 5.13593i) q^{49} +(1.77663 - 1.29080i) q^{51} +(0.231163 + 0.711448i) q^{53} +(3.66019 - 3.49109i) q^{55} +(2.81260 - 0.913868i) q^{57} +(5.06515 + 6.97158i) q^{59} +(-1.00338 + 3.08809i) q^{61} +(-1.96807 + 2.70882i) q^{63} +(1.31673 - 5.33879i) q^{65} +1.48660i q^{67} +(-2.42703 - 1.76334i) q^{69} +(7.23642 + 2.35126i) q^{71} +(-4.94331 - 6.80389i) q^{73} +(0.490796 + 1.51051i) q^{75} +(4.15764 - 0.558101i) q^{77} +(0.704732 + 2.16894i) q^{79} +(-4.81334 + 3.49710i) q^{81} +(-2.92315 - 0.949790i) q^{83} +(3.31446 - 4.56197i) q^{85} +0.716590 q^{87} -16.0687i q^{89} +(3.48599 - 2.94020i) q^{91} +(5.39730 + 1.75369i) q^{93} +(6.14348 - 4.46350i) q^{95} +(15.0175 - 4.87947i) q^{97} +(8.63692 + 1.57810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^9	$ 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) $ 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.480503	−	0.349106i	−0.277418	−	0.201556i	0.440372	−	0.897815i	$-0.354846\pi$
$3$	−0.480503	−	0.349106i	−0.277418	−	0.201556i	−0.717791	+	0.696259i	$0.754846\pi$
$4$		0			0
$5$	−1.45044	−	0.471277i	−0.648657	−	0.210761i	−0.0338351	−	0.999427i	$-0.510772\pi$
$5$	−1.45044	−	0.471277i	−0.648657	−	0.210761i	−0.614822	+	0.788666i	$0.710772\pi$
$6$		0			0
$7$	−0.743441	−	1.02326i	−0.280994	−	0.386756i	0.645068	−	0.764125i	$-0.276829\pi$
$7$	−0.743441	−	1.02326i	−0.280994	−	0.386756i	−0.926063	+	0.377369i	$0.876829\pi$
$8$		0			0
$9$	−0.818043	−	2.51768i	−0.272681	−	0.839226i
$10$		0			0
$11$	−1.57515	+	2.91871i	−0.474927	+	0.880025i
$11$	−1.57515	+	2.91871i	−0.474927	+	0.880025i
$12$		0			0
$13$	0.260637	+	3.59612i	0.0722877	+	0.997384i
$13$	0.260637	+	3.59612i	0.0722877	+	0.997384i
$14$		0			0
$15$	0.532415	+	0.732807i	0.137469	+	0.189210i
$16$		0			0
$17$	−1.14257	+	3.51647i	−0.277114	+	0.852869i	0.711538	+	0.702647i	$0.247999\pi$
$17$	−1.14257	+	3.51647i	−0.277114	+	0.852869i	−0.988652	+	0.150222i	$0.952001\pi$
$18$		0			0
$19$	−2.92672	+	4.02829i	−0.671436	+	0.924153i	−0.999792	−	0.0204016i	$-0.993506\pi$
$19$	−2.92672	+	4.02829i	−0.671436	+	0.924153i	0.328356	+	0.944554i	$0.393506\pi$
$20$		0			0
$21$			0.751218i			0.163929i
$22$		0			0
$23$	5.05102			1.05321			0.526605	−	0.850110i	$-0.323465\pi$
$23$	5.05102			1.05321			0.526605	+	0.850110i	$0.323465\pi$
$24$		0			0
$25$	−2.16341	−	1.57181i	−0.432681	−	0.314361i
$26$		0			0
$27$	−1.03647	+	3.18993i	−0.199469	+	0.613902i
$28$		0			0
$29$	−0.976091	+	0.709172i	−0.181256	+	0.131690i	−0.674713	−	0.738080i	$-0.735733\pi$
$29$	−0.976091	+	0.709172i	−0.181256	+	0.131690i	0.493458	+	0.869770i	$0.335733\pi$
$30$		0			0
$31$	−9.08737	+	2.95267i	−1.63214	+	0.530315i	−0.974762	−	0.223246i	$-0.928335\pi$
$31$	−9.08737	+	2.95267i	−1.63214	+	0.530315i	−0.657378	+	0.753561i	$0.728335\pi$
$32$		0			0
$33$	1.77581	−	0.852554i	0.309128	−	0.148411i
$34$		0			0
$35$	0.596080	+	1.83454i	0.100756	+	0.310095i
$36$		0			0
$37$	−4.14494	−	5.70503i	−0.681425	−	0.937901i	0.318525	−	0.947914i	$-0.396812\pi$
$37$	−4.14494	−	5.70503i	−0.681425	−	0.937901i	−0.999950	+	0.0100138i	$0.996812\pi$
$38$		0			0
$39$	1.13019	−	1.81893i	0.180975	−	0.291263i
$40$		0			0
$41$	−1.39987	+	1.92675i	−0.218622	+	0.300908i	−0.904215	−	0.427078i	$-0.859543\pi$
$41$	−1.39987	+	1.92675i	−0.218622	+	0.300908i	0.685593	+	0.727985i	$0.259543\pi$
$42$		0			0
$43$	−3.12533			−0.476608			−0.238304	−	0.971191i	$-0.576591\pi$
$43$	−3.12533			−0.476608			−0.238304	+	0.971191i	$0.576591\pi$
$44$		0			0
$45$			4.03727i			0.601840i
$46$		0			0
$47$	−1.79076	+	2.46477i	−0.261209	+	0.359524i	−0.919397	−	0.393330i	$-0.871323\pi$
$47$	−1.79076	+	2.46477i	−0.261209	+	0.359524i	0.658188	+	0.752853i	$0.271323\pi$
$48$		0			0
$49$	1.66876	−	5.13593i	0.238395	−	0.733704i
$50$		0			0
$51$	1.77663	−	1.29080i	0.248778	−	0.180747i
$52$		0			0
$53$	0.231163	+	0.711448i	0.0317527	+	0.0977249i	0.965677	−	0.259746i	$-0.0836390\pi$
$53$	0.231163	+	0.711448i	0.0317527	+	0.0977249i	−0.933924	+	0.357471i	$0.883639\pi$
$54$		0			0
$55$	3.66019	−	3.49109i	0.493540	−	0.470738i
$56$		0			0
$57$	2.81260	−	0.913868i	0.372537	−	0.121045i
$58$		0			0
$59$	5.06515	+	6.97158i	0.659427	+	0.907623i	0.999462	−	0.0327896i	$-0.0104391\pi$
$59$	5.06515	+	6.97158i	0.659427	+	0.907623i	−0.340036	+	0.940413i	$0.610439\pi$
$60$		0			0
$61$	−1.00338	+	3.08809i	−0.128470	+	0.395389i	−0.994517	−	0.104573i	$-0.966653\pi$
$61$	−1.00338	+	3.08809i	−0.128470	+	0.395389i	0.866048	+	0.499961i	$0.166653\pi$
$62$		0			0
$63$	−1.96807	+	2.70882i	−0.247954	+	0.341279i
$64$		0			0
$65$	1.31673	−	5.33879i	0.163320	−	0.662195i
$66$		0			0
$67$			1.48660i			0.181617i	0.995868	+	0.0908085i	$0.0289451\pi$
$67$			1.48660i			0.181617i	−0.995868	+	0.0908085i	$0.971055\pi$
$68$		0			0
$69$	−2.42703	−	1.76334i	−0.292180	−	0.212281i
$70$		0			0
$71$	7.23642	+	2.35126i	0.858805	+	0.279043i	0.705129	−	0.709079i	$-0.250889\pi$
$71$	7.23642	+	2.35126i	0.858805	+	0.279043i	0.153676	+	0.988121i	$0.450889\pi$
$72$		0			0
$73$	−4.94331	−	6.80389i	−0.578571	−	0.796335i	0.414967	−	0.909837i	$-0.363793\pi$
$73$	−4.94331	−	6.80389i	−0.578571	−	0.796335i	−0.993538	+	0.113502i	$0.963793\pi$
$74$		0			0
$75$	0.490796	+	1.51051i	0.0566722	+	0.174419i
$76$		0			0
$77$	4.15764	−	0.558101i	0.473807	−	0.0636015i
$78$		0			0
$79$	0.704732	+	2.16894i	0.0792885	+	0.244025i	0.982842	−	0.184451i	$-0.0590507\pi$
$79$	0.704732	+	2.16894i	0.0792885	+	0.244025i	−0.903553	+	0.428476i	$0.859051\pi$
$80$		0			0
$81$	−4.81334	+	3.49710i	−0.534816	+	0.388567i
$82$		0			0
$83$	−2.92315	−	0.949790i	−0.320858	−	0.104253i	0.144160	−	0.989554i	$-0.453952\pi$
$83$	−2.92315	−	0.949790i	−0.320858	−	0.104253i	−0.465018	+	0.885301i	$0.653952\pi$
$84$		0			0
$85$	3.31446	−	4.56197i	0.359504	−	0.494815i
$86$		0			0
$87$	0.716590			0.0768265
$88$		0			0
$89$		−	16.0687i		−	1.70327i	−0.524132	−	0.851637i	$-0.675610\pi$
$89$		−	16.0687i		−	1.70327i	0.524132	−	0.851637i	$-0.324390\pi$
$90$		0			0
$91$	3.48599	−	2.94020i	0.365431	−	0.308217i
$92$		0			0
$93$	5.39730	+	1.75369i	0.559674	+	0.181849i
$94$		0			0
$95$	6.14348	−	4.46350i	0.630307	−	0.457945i
$96$		0			0
$97$	15.0175	−	4.87947i	1.52479	−	0.495435i	0.577659	−	0.816278i	$-0.303966\pi$
$97$	15.0175	−	4.87947i	1.52479	−	0.495435i	0.947132	+	0.320843i	$0.103966\pi$
$98$		0			0
$99$	8.63692	+	1.57810i	0.868043	+	0.158605i
$100$		0			0
$101$	1.00321	+	3.08756i	0.0998229	+	0.307223i	0.988481	−	0.151348i	$-0.0483614\pi$
$101$	1.00321	+	3.08756i	0.0998229	+	0.307223i	−0.888658	+	0.458571i	$0.848361\pi$
$102$		0			0
$103$	−14.1930	+	10.3118i	−1.39847	+	1.01605i	−0.403600	+	0.914936i	$0.632241\pi$
$103$	−14.1930	+	10.3118i	−1.39847	+	1.01605i	−0.994875	+	0.101115i	$0.967759\pi$
$104$		0			0
$105$	0.354032	−	1.08960i	0.0345500	−	0.106334i
$106$		0			0
$107$	−12.7857	−	9.28932i	−1.23604	−	0.898033i	−0.238708	−	0.971091i	$-0.576724\pi$
$107$	−12.7857	−	9.28932i	−1.23604	−	0.898033i	−0.997328	+	0.0730586i	$0.976724\pi$
$108$		0			0
$109$		−	8.67163i		−	0.830592i	−0.909686	−	0.415296i	$-0.863678\pi$
$109$		−	8.67163i		−	0.830592i	0.909686	−	0.415296i	$-0.136322\pi$
$110$		0			0
$111$			4.18830i			0.397536i
$112$		0			0
$113$	−11.9767	−	8.70157i	−1.12667	−	0.818574i	−0.141464	−	0.989943i	$-0.545181\pi$
$113$	−11.9767	−	8.70157i	−1.12667	−	0.818574i	−0.985207	+	0.171369i	$0.945181\pi$
$114$		0			0
$115$	−7.32620	−	2.38043i	−0.683172	−	0.221976i
$116$		0			0
$117$	8.84065	−	3.59798i	0.817319	−	0.332633i
$118$		0			0
$119$	4.44769	−	1.44514i	0.407719	−	0.132476i
$120$		0			0
$121$	−6.03777	−	9.19485i	−0.548889	−	0.835896i
$122$		0			0
$123$	1.34528	−	0.437107i	0.121300	−	0.0394126i
$124$		0			0
$125$	6.87925	+	9.46847i	0.615299	+	0.846886i
$126$		0			0
$127$	−5.38695	+	16.5793i	−0.478015	+	1.47118i	0.363833	+	0.931464i	$0.381468\pi$
$127$	−5.38695	+	16.5793i	−0.478015	+	1.47118i	−0.841848	+	0.539714i	$0.818532\pi$
$128$		0			0
$129$	1.50173	+	1.09107i	0.132220	+	0.0960633i
$130$		0			0
$131$	12.3465			1.07872			0.539359	−	0.842076i	$-0.318667\pi$
$131$	12.3465			1.07872			0.539359	+	0.842076i	$0.318667\pi$
$132$		0			0
$133$	6.29783			0.546091
$134$		0			0
$135$	3.00668	−	4.13834i	0.258774	−	0.356171i
$136$		0			0
$137$	3.65016	+	1.18601i	0.311854	+	0.101328i	0.460763	−	0.887523i	$-0.347576\pi$
$137$	3.65016	+	1.18601i	0.311854	+	0.101328i	−0.148908	+	0.988851i	$0.547576\pi$
$138$		0			0
$139$	7.69736	−	5.59246i	0.652882	−	0.474346i	−0.211370	−	0.977406i	$-0.567792\pi$
$139$	7.69736	−	5.59246i	0.652882	−	0.474346i	0.864252	+	0.503060i	$0.167792\pi$
$140$		0			0
$141$	1.72093	−	0.559164i	0.144928	−	0.0470901i
$142$		0			0
$143$	−10.9066	−	4.90372i	−0.912054	−	0.410070i
$144$		0			0
$145$	1.74998	−	0.568603i	0.145328	−	0.0472199i
$146$		0			0
$147$	−2.59483	+	1.88525i	−0.214018	+	0.155493i
$148$		0			0
$149$	22.1028	+	7.18164i	1.81073	+	0.588343i	0.999996	+	0.00293353i	$0.000933774\pi$
$149$	22.1028	+	7.18164i	1.81073	+	0.588343i	0.810738	+	0.585409i	$0.199066\pi$
$150$		0			0
$151$	7.05159	−	9.70568i	0.573850	−	0.789837i	−0.419154	−	0.907915i	$-0.637673\pi$
$151$	7.05159	−	9.70568i	0.573850	−	0.789837i	0.993004	+	0.118078i	$0.0376734\pi$
$152$		0			0
$153$	9.78801			0.791313
$154$		0			0
$155$	14.5722			1.17047
$156$		0			0
$157$	−11.4842	−	8.34378i	−0.916542	−	0.665906i	0.0261192	−	0.999659i	$-0.491685\pi$
$157$	−11.4842	−	8.34378i	−0.916542	−	0.665906i	−0.942661	+	0.333752i	$0.891685\pi$
$158$		0			0
$159$	0.137296	−	0.422553i	0.0108883	−	0.0335106i
$160$		0			0
$161$	−3.75513	−	5.16850i	−0.295946	−	0.407335i
$162$		0			0
$163$	−10.5145	+	3.41637i	−0.823559	+	0.267591i	−0.690330	−	0.723495i	$-0.742535\pi$
$163$	−10.5145	+	3.41637i	−0.823559	+	0.267591i	−0.133229	+	0.991085i	$0.542535\pi$
$164$		0			0
$165$	−2.97749	+	0.399683i	−0.231797	+	0.0311153i
$166$		0			0
$167$	2.14611	−	0.697314i	0.166071	−	0.0539598i	−0.224801	−	0.974405i	$-0.572173\pi$
$167$	2.14611	−	0.697314i	0.166071	−	0.0539598i	0.390873	+	0.920445i	$0.372173\pi$
$168$		0			0
$169$	−12.8641	+	1.87456i	−0.989549	+	0.144197i
$170$		0			0
$171$	12.5361	+	4.07323i	0.958660	+	0.311488i
$172$		0			0
$173$	6.84223	+	4.97117i	0.520205	+	0.377951i	0.816681	−	0.577089i	$-0.195811\pi$
$173$	6.84223	+	4.97117i	0.520205	+	0.377951i	−0.296476	+	0.955040i	$0.595811\pi$
$174$		0			0
$175$			3.38227i			0.255676i
$176$		0			0
$177$		−	5.11814i		−	0.384703i
$178$		0			0
$179$	−13.0071	−	9.45023i	−0.972198	−	0.706343i	−0.0162463	−	0.999868i	$-0.505172\pi$
$179$	−13.0071	−	9.45023i	−0.972198	−	0.706343i	−0.955951	+	0.293525i	$0.905172\pi$
$180$		0			0
$181$	1.68713	−	5.19245i	0.125403	−	0.385952i	−0.868571	−	0.495565i	$-0.834961\pi$
$181$	1.68713	−	5.19245i	0.125403	−	0.385952i	0.993974	+	0.109613i	$0.0349612\pi$
$182$		0			0
$183$	1.56019	−	1.13355i	0.115333	−	0.0837942i
$184$		0			0
$185$	3.32335	+	10.2282i	0.244338	+	0.751994i
$186$		0			0
$187$	−8.46384	−	8.87382i	−0.618937	−	0.648918i
$188$		0			0
$189$	4.03468	−	1.31095i	0.293480	−	0.0953573i
$190$		0			0
$191$	−7.92828	+	5.76023i	−0.573670	+	0.416796i	−0.836437	−	0.548064i	$-0.815365\pi$
$191$	−7.92828	+	5.76023i	−0.573670	+	0.416796i	0.262766	+	0.964860i	$0.415365\pi$
$192$		0			0
$193$	−24.2610	−	7.88289i	−1.74635	−	0.567423i	−0.750703	−	0.660640i	$-0.770285\pi$
$193$	−24.2610	−	7.88289i	−1.74635	−	0.567423i	−0.995646	+	0.0932171i	$0.970285\pi$
$194$		0			0
$195$	−2.49649	+	2.10563i	−0.178778	+	0.150787i
$196$		0			0
$197$			17.6231i			1.25559i	0.778377	+	0.627797i	$0.216043\pi$
$197$			17.6231i			1.25559i	−0.778377	+	0.627797i	$0.783957\pi$
$198$		0			0
$199$	9.80583			0.695117			0.347559	−	0.937658i	$-0.387011\pi$
$199$	9.80583			0.695117			0.347559	+	0.937658i	$0.387011\pi$
$200$		0			0
$201$	0.518980	−	0.714315i	0.0366060	−	0.0503839i
$202$		0			0
$203$	1.45133	+	0.471567i	0.101864	+	0.0330975i
$204$		0			0
$205$	2.93846	−	2.13491i	0.205231	−	0.149109i
$206$		0			0
$207$	−4.13195	−	12.7168i	−0.287190	−	0.883881i
$208$		0			0
$209$	−7.14738	−	14.8874i	−0.494394	−	1.02979i
$210$		0			0
$211$	4.74803	+	14.6129i	0.326868	+	1.00599i	0.970591	+	0.240736i	$0.0773889\pi$
$211$	4.74803	+	14.6129i	0.326868	+	1.00599i	−0.643723	+	0.765259i	$0.722611\pi$
$212$		0			0
$213$	−2.65628	−	3.65606i	−0.182005	−	0.250509i
$214$		0			0
$215$	4.53311	+	1.47290i	0.309155	+	0.100451i
$216$		0			0
$217$	9.77727	+	7.10361i	0.663725	+	0.482224i
$218$		0			0
$219$			4.99502i			0.337532i
$220$		0			0
$221$	−12.9434	−	3.19230i	−0.870670	−	0.214737i
$222$		0			0
$223$	−9.81298	+	13.5064i	−0.657126	+	0.904456i	−0.999382	−	0.0351508i	$-0.988809\pi$
$223$	−9.81298	+	13.5064i	−0.657126	+	0.904456i	0.342256	+	0.939607i	$0.388809\pi$
$224$		0			0
$225$	−2.18754	+	6.73257i	−0.145836	+	0.448838i
$226$		0			0
$227$	11.8514	+	16.3121i	0.786606	+	1.08267i	0.994522	+	0.104523i	$0.0333317\pi$
$227$	11.8514	+	16.3121i	0.786606	+	1.08267i	−0.207917	+	0.978147i	$0.566668\pi$
$228$		0			0
$229$	0.750800	−	0.243950i	0.0496142	−	0.0161206i	−0.284105	−	0.958793i	$-0.591696\pi$
$229$	0.750800	−	0.243950i	0.0496142	−	0.0161206i	0.333719	+	0.942673i	$0.391696\pi$
$230$		0			0
$231$	−2.19259	−	1.18329i	−0.144262	−	0.0778545i
$232$		0			0
$233$	2.95626	+	9.09843i	0.193671	+	0.596058i	0.999990	+	0.00457646i	$0.00145674\pi$
$233$	2.95626	+	9.09843i	0.193671	+	0.596058i	−0.806319	+	0.591482i	$0.798543\pi$
$234$		0			0
$235$	3.75898	−	2.73106i	0.245209	−	0.178155i
$236$		0			0
$237$	0.418564	−	1.28821i	0.0271886	−	0.0836781i
$238$		0			0
$239$	1.75006	−	2.40875i	0.113202	−	0.155809i	−0.748656	−	0.662958i	$-0.769301\pi$
$239$	1.75006	−	2.40875i	0.113202	−	0.155809i	0.861858	+	0.507149i	$0.169301\pi$
$240$		0			0
$241$		−	2.03117i		−	0.130839i	−0.997858	−	0.0654196i	$-0.979161\pi$
$241$		−	2.03117i		−	0.130839i	0.997858	−	0.0654196i	$-0.0208386\pi$
$242$		0			0
$243$	13.5959			0.872180
$244$		0			0
$245$	−4.84089	+	6.66291i	−0.309273	+	0.425678i
$246$		0			0
$247$	−15.2490	−	9.47492i	−0.970271	−	0.602875i
$248$		0			0
$249$	1.07301	+	1.47687i	0.0679990	+	0.0935926i
$250$		0			0
$251$	−0.902459	−	2.77748i	−0.0569627	−	0.175313i	0.918527	−	0.395358i	$-0.129380\pi$
$251$	−0.902459	−	2.77748i	−0.0569627	−	0.175313i	−0.975490	+	0.220045i	$0.929380\pi$
$252$		0			0
$253$	−7.95613	+	14.7425i	−0.500198	+	0.926851i
$254$		0			0
$255$	−3.18522	+	1.03494i	−0.199466	+	0.0648104i
$256$		0			0
$257$	−7.15575	+	5.19896i	−0.446364	+	0.324302i	−0.788158	−	0.615472i	$-0.788965\pi$
$257$	−7.15575	+	5.19896i	−0.446364	+	0.324302i	0.341795	+	0.939775i	$0.388965\pi$
$258$		0			0
$259$	−2.75620	+	8.48271i	−0.171262	+	0.527090i
$260$		0			0
$261$	2.58395	+	1.87735i	0.159943	+	0.116205i
$262$		0			0
$263$	5.16466			0.318467			0.159233	−	0.987241i	$-0.449098\pi$
$263$	5.16466			0.318467			0.159233	+	0.987241i	$0.449098\pi$
$264$		0			0
$265$		−	1.14086i		−	0.0700822i
$266$		0			0
$267$	−5.60966	+	7.72103i	−0.343305	+	0.472519i
$268$		0			0
$269$	−2.40143	+	7.39085i	−0.146418	+	0.450628i	−0.997191	−	0.0749059i	$-0.976134\pi$
$269$	−2.40143	+	7.39085i	−0.146418	+	0.450628i	0.850773	+	0.525534i	$0.176134\pi$
$270$		0			0
$271$	−15.3800	−	21.1687i	−0.934268	−	1.28591i	−0.958171	−	0.286196i	$-0.907609\pi$
$271$	−15.3800	−	21.1687i	−0.934268	−	1.28591i	0.0239030	−	0.999714i	$-0.492391\pi$
$272$		0			0
$273$	−2.70147	+	0.195795i	−0.163500	+	0.0118501i
$274$		0			0
$275$	7.99536	−	3.83853i	0.482138	−	0.231472i
$276$		0			0
$277$	4.25861	+	13.1067i	0.255875	+	0.787503i	0.993656	+	0.112462i	$0.0358738\pi$
$277$	4.25861	+	13.1067i	0.255875	+	0.787503i	−0.737781	+	0.675040i	$0.764126\pi$
$278$		0			0
$279$	14.8677	+	20.4637i	0.890107	+	1.22513i
$280$		0			0
$281$	−27.4771	−	8.92785i	−1.63915	−	0.532591i	−0.662799	−	0.748798i	$-0.730632\pi$
$281$	−27.4771	−	8.92785i	−1.63915	−	0.532591i	−0.976348	+	0.216207i	$0.930632\pi$
$282$		0			0
$283$	−19.2571	−	13.9911i	−1.14472	−	0.831686i	−0.156948	−	0.987607i	$-0.550165\pi$
$283$	−19.2571	−	13.9911i	−1.14472	−	0.831686i	−0.987770	+	0.155921i	$0.950165\pi$
$284$		0			0
$285$	−4.51019			−0.267161
$286$		0			0
$287$	3.01228			0.177809
$288$		0			0
$289$	2.69320	+	1.95672i	0.158423	+	0.115101i
$290$		0			0
$291$	−8.91937	−	2.89808i	−0.522863	−	0.169888i
$292$		0			0
$293$	11.9315	+	16.4222i	0.697043	+	0.959397i	0.999980	+	0.00638660i	$0.00203293\pi$
$293$	11.9315	+	16.4222i	0.697043	+	0.959397i	−0.302937	+	0.953011i	$0.597967\pi$
$294$		0			0
$295$	−4.06116	−	12.4990i	−0.236450	−	0.727718i
$296$		0			0
$297$	−7.67788	−	8.04979i	−0.445516	−	0.467096i
$298$		0			0
$299$	1.31648	+	18.1641i	0.0761341	+	1.05045i
$300$		0			0
$301$	2.32350	+	3.19802i	0.133924	+	0.184331i
$302$		0			0
$303$	0.595839	−	1.83380i	0.0342301	−	0.105349i
$304$		0			0
$305$	2.91069	−	4.00622i	0.166665	−	0.229395i
$306$		0			0
$307$		−	12.4227i		−	0.708998i	−0.935056	−	0.354499i	$-0.884651\pi$
$307$		−	12.4227i		−	0.708998i	0.935056	−	0.354499i	$-0.115349\pi$
$308$		0			0
$309$	10.4197			0.592754
$310$		0			0
$311$	−8.25942	−	6.00082i	−0.468349	−	0.340275i	0.328449	−	0.944522i	$-0.393474\pi$
$311$	−8.25942	−	6.00082i	−0.468349	−	0.340275i	−0.796797	+	0.604247i	$0.793474\pi$
$312$		0			0
$313$	−7.15521	+	22.0215i	−0.404436	+	1.24473i	0.516929	+	0.856028i	$0.327075\pi$
$313$	−7.15521	+	22.0215i	−0.404436	+	1.24473i	−0.921365	+	0.388698i	$0.872925\pi$
$314$		0			0
$315$	4.13117	−	3.00147i	0.232765	−	0.169114i
$316$		0			0
$317$	−12.5730	+	4.08522i	−0.706171	+	0.229449i	−0.640017	−	0.768361i	$-0.721073\pi$
$317$	−12.5730	+	4.08522i	−0.706171	+	0.229449i	−0.0661536	+	0.997809i	$0.521073\pi$
$318$		0			0
$319$	−0.532374	−	3.96599i	−0.0298072	−	0.222053i
$320$		0			0
$321$	2.90059	+	8.92709i	0.161895	+	0.498261i
$322$		0			0
$323$	−10.8214	−	14.8943i	−0.602117	−	0.828743i
$324$		0			0
$325$	5.08854	−	8.18954i	0.282261	−	0.454274i
$326$		0			0
$327$	−3.02731	+	4.16674i	−0.167411	+	0.230421i
$328$		0			0
$329$	3.85342			0.212446
$330$		0			0
$331$			6.66784i			0.366497i	0.983067	+	0.183249i	$0.0586614\pi$
$331$			6.66784i			0.366497i	−0.983067	+	0.183249i	$0.941339\pi$
$332$		0			0
$333$	−10.9727	+	15.1026i	−0.601299	+	0.827617i
$334$		0			0
$335$	0.700600	−	2.15623i	0.0382779	−	0.117807i
$336$		0			0
$337$	26.2125	−	19.0445i	1.42789	−	1.03742i	0.437482	−	0.899227i	$-0.355871\pi$
$337$	26.2125	−	19.0445i	1.42789	−	1.03742i	0.990405	−	0.138193i	$-0.0441295\pi$
$338$		0			0
$339$	2.71706	+	8.36225i	0.147570	+	0.454175i
$340$		0			0
$341$	5.69603	−	31.1743i	0.308457	−	1.68819i
$342$		0			0
$343$	−14.9164	+	4.84664i	−0.805410	+	0.261694i
$344$		0			0
$345$	2.68924	+	3.70142i	0.144784	+	0.199278i
$346$		0			0
$347$	−4.73143	+	14.5619i	−0.253997	+	0.781721i	0.740029	+	0.672575i	$0.234812\pi$
$347$	−4.73143	+	14.5619i	−0.253997	+	0.781721i	−0.994026	+	0.109146i	$0.965188\pi$
$348$		0			0
$349$	−3.60609	+	4.96335i	−0.193029	+	0.265682i	−0.894551	−	0.446966i	$-0.852504\pi$
$349$	−3.60609	+	4.96335i	−0.193029	+	0.265682i	0.701521	+	0.712648i	$0.252504\pi$
$350$		0			0
$351$	−11.7415	−	2.89586i	−0.626715	−	0.154569i
$352$		0			0
$353$			13.2641i			0.705976i	0.935628	+	0.352988i	$0.114834\pi$
$353$			13.2641i			0.705976i	−0.935628	+	0.352988i	$0.885166\pi$
$354$		0			0
$355$	−9.38791	−	6.82072i	−0.498259	−	0.362006i
$356$		0			0
$357$	−2.64164	−	0.858320i	−0.139810	−	0.0454271i
$358$		0			0
$359$	10.4778	+	14.4215i	0.552998	+	0.761137i	0.990415	−	0.138122i	$-0.0441066\pi$
$359$	10.4778	+	14.4215i	0.552998	+	0.761137i	−0.437417	+	0.899259i	$0.644107\pi$
$360$		0			0
$361$	−1.79007	−	5.50928i	−0.0942144	−	0.289962i
$362$		0			0
$363$	−0.308807	+	6.52597i	−0.0162082	+	0.342525i
$364$		0			0
$365$	3.96347	+	12.1983i	0.207458	+	0.638489i
$366$		0			0
$367$	−4.20522	+	3.05527i	−0.219511	+	0.159484i	−0.692106	−	0.721795i	$-0.743317\pi$
$367$	−4.20522	+	3.05527i	−0.219511	+	0.159484i	0.472596	+	0.881279i	$0.343317\pi$
$368$		0			0
$369$	5.99608	+	1.94825i	0.312144	+	0.101422i
$370$		0			0
$371$	0.556139	−	0.765460i	0.0288733	−	0.0397407i
$372$		0			0
$373$	7.28188			0.377042			0.188521	−	0.982069i	$-0.439631\pi$
$373$	7.28188			0.377042			0.188521	+	0.982069i	$0.439631\pi$
$374$		0			0
$375$		−	6.95121i		−	0.358959i
$376$		0			0
$377$	−2.80467	−	3.32530i	−0.144448	−	0.171262i
$378$		0			0
$379$	22.0129	+	7.15241i	1.13072	+	0.367395i	0.813851	−	0.581073i	$-0.197367\pi$
$379$	22.0129	+	7.15241i	1.13072	+	0.367395i	0.316873	+	0.948468i	$0.397367\pi$
$380$		0			0
$381$	8.37638	−	6.08580i	0.429135	−	0.311785i
$382$		0			0
$383$	−8.69836	+	2.82627i	−0.444465	+	0.144416i	−0.522695	−	0.852520i	$-0.675073\pi$
$383$	−8.69836	+	2.82627i	−0.444465	+	0.144416i	0.0782296	+	0.996935i	$0.475073\pi$
$384$		0			0
$385$	−6.29343	−	1.14991i	−0.320743	−	0.0586046i
$386$		0			0
$387$	2.55665	+	7.86857i	0.129962	+	0.399982i
$388$		0			0
$389$	−6.09601	+	4.42901i	−0.309080	+	0.224560i	−0.731502	−	0.681840i	$-0.761180\pi$
$389$	−6.09601	+	4.42901i	−0.309080	+	0.224560i	0.422422	+	0.906399i	$0.361180\pi$
$390$		0			0
$391$	−5.77114	+	17.7617i	−0.291859	+	0.898250i
$392$		0			0
$393$	−5.93252	−	4.31023i	−0.299256	−	0.217422i
$394$		0			0
$395$		−	3.47804i		−	0.174999i
$396$		0			0
$397$			5.77061i			0.289619i	0.989460	+	0.144809i	$0.0462569\pi$
$397$			5.77061i			0.289619i	−0.989460	+	0.144809i	$0.953743\pi$
$398$		0			0
$399$	−3.02612	−	2.19861i	−0.151496	−	0.110068i
$400$		0			0
$401$	−19.5986	−	6.36797i	−0.978708	−	0.318001i	−0.224382	−	0.974501i	$-0.572036\pi$
$401$	−19.5986	−	6.36797i	−0.978708	−	0.318001i	−0.754326	+	0.656500i	$0.772036\pi$
$402$		0			0
$403$	−12.9866	−	31.9097i	−0.646911	−	1.58954i
$404$		0			0
$405$	8.62958	−	2.80392i	0.428807	−	0.139328i
$406$		0			0
$407$	23.1803	−	3.11160i	1.14900	−	0.154236i
$408$		0			0
$409$	24.0684	−	7.82028i	1.19010	−	0.386688i	0.353992	−	0.935248i	$-0.384824\pi$
$409$	24.0684	−	7.82028i	1.19010	−	0.386688i	0.836111	+	0.548560i	$0.184824\pi$
$410$		0			0
$411$	−1.33987	−	1.84417i	−0.0660909	−	0.0909664i
$412$		0			0
$413$	3.36809	−	10.3659i	0.165733	−	0.510074i
$414$		0			0
$415$	3.79225	+	2.75523i	0.186154	+	0.135249i
$416$		0			0
$417$	−5.65096			−0.276729
$418$		0			0
$419$	15.3661			0.750685			0.375343	−	0.926886i	$-0.377525\pi$
$419$	15.3661			0.750685			0.375343	+	0.926886i	$0.377525\pi$
$420$		0			0
$421$	−12.9531	+	17.8284i	−0.631294	+	0.868902i	−0.998114	−	0.0613904i	$-0.980447\pi$
$421$	−12.9531	+	17.8284i	−0.631294	+	0.868902i	0.366820	+	0.930292i	$0.380447\pi$
$422$		0			0
$423$	7.67041	+	2.49227i	0.372948	+	0.121178i
$424$		0			0
$425$	7.99906	−	5.81166i	0.388011	−	0.281907i
$426$		0			0
$427$	3.90587	−	1.26909i	0.189018	−	0.0614157i
$428$		0			0
$429$	3.52873	+	6.16380i	0.170368	+	0.297591i
$430$		0			0
$431$	34.0791	−	11.0730i	1.64153	−	0.533367i	0.664653	−	0.747152i	$-0.268579\pi$
$431$	34.0791	−	11.0730i	1.64153	−	0.533367i	0.976881	+	0.213785i	$0.0685793\pi$
$432$		0			0
$433$	−17.5266	+	12.7338i	−0.842276	+	0.611949i	−0.923005	−	0.384787i	$-0.874275\pi$
$433$	−17.5266	+	12.7338i	−0.842276	+	0.611949i	0.0807298	+	0.996736i	$0.474275\pi$
$434$		0			0
$435$	−1.03937	−	0.337712i	−0.0498341	−	0.0161921i
$436$		0			0
$437$	−14.7829	+	20.3469i	−0.707163	+	0.973326i
$438$		0			0
$439$	8.05525			0.384456			0.192228	−	0.981350i	$-0.438429\pi$
$439$	8.05525			0.384456			0.192228	+	0.981350i	$0.438429\pi$
$440$		0			0
$441$	−14.2957			−0.680749
$442$		0			0
$443$	−25.8304	−	18.7668i	−1.22724	−	0.891640i	−0.230557	−	0.973059i	$-0.574055\pi$
$443$	−25.8304	−	18.7668i	−1.22724	−	0.891640i	−0.996680	+	0.0814190i	$0.974055\pi$
$444$		0			0
$445$	−7.57279	+	23.3066i	−0.358984	+	1.10484i
$446$		0			0
$447$	−8.11331	−	11.1670i	−0.383746	−	0.528182i
$448$		0			0
$449$	8.81942	−	2.86560i	0.416214	−	0.135236i	−0.0934213	−	0.995627i	$-0.529780\pi$
$449$	8.81942	−	2.86560i	0.416214	−	0.135236i	0.509635	+	0.860391i	$0.329780\pi$
$450$		0			0
$451$	−3.41862	−	7.12073i	−0.160977	−	0.335302i
$452$		0			0
$453$	−6.77661	+	2.20185i	−0.318393	+	0.103452i
$454$		0			0
$455$	−6.44188	+	2.62172i	−0.302000	+	0.122908i
$456$		0			0
$457$	9.11534	+	2.96175i	0.426398	+	0.138545i	0.514351	−	0.857580i	$-0.328033\pi$
$457$	9.11534	+	2.96175i	0.426398	+	0.138545i	−0.0879537	+	0.996125i	$0.528033\pi$
$458$		0			0
$459$	−10.0330	−	7.28943i	−0.468302	−	0.340242i
$460$		0			0
$461$			37.3526i			1.73969i	0.493329	+	0.869843i	$0.335780\pi$
$461$			37.3526i			1.73969i	−0.493329	+	0.869843i	$0.664220\pi$
$462$		0			0
$463$		−	11.5620i		−	0.537331i	−0.963234	−	0.268666i	$-0.913417\pi$
$463$		−	11.5620i		−	0.537331i	0.963234	−	0.268666i	$-0.0865826\pi$
$464$		0			0
$465$	−7.00199	−	5.08724i	−0.324710	−	0.235915i
$466$		0			0
$467$	1.53968	−	4.73866i	0.0712480	−	0.219279i	−0.909092	−	0.416596i	$-0.863223\pi$
$467$	1.53968	−	4.73866i	0.0712480	−	0.219279i	0.980340	+	0.197317i	$0.0632229\pi$
$468$		0			0
$469$	1.52118	−	1.10520i	0.0702414	−	0.0510334i
$470$		0			0
$471$	2.60534	+	8.01842i	0.120048	+	0.369469i
$472$		0			0
$473$	4.92288	−	9.12194i	0.226354	−	0.419427i
$474$		0			0
$475$	12.6634	−	4.11458i	0.581036	−	0.188790i
$476$		0			0
$477$	1.60209	−	1.16399i	0.0733549	−	0.0532954i
$478$		0			0
$479$	29.9180	+	9.72094i	1.36699	+	0.444161i	0.898370	−	0.439240i	$-0.144752\pi$
$479$	29.9180	+	9.72094i	1.36699	+	0.444161i	0.468618	+	0.883401i	$0.344752\pi$
$480$		0			0
$481$	19.4356	−	16.3927i	0.886188	−	0.747441i
$482$		0			0
$483$			3.79442i			0.172652i
$484$		0			0
$485$	−24.0815			−1.09349
$486$		0			0
$487$	12.9897	−	17.8787i	0.588617	−	0.810162i	−0.405990	−	0.913878i	$-0.633073\pi$
$487$	12.9897	−	17.8787i	0.588617	−	0.810162i	0.994607	+	0.103715i	$0.0330731\pi$
$488$		0			0
$489$	6.24492	+	2.02910i	0.282405	+	0.0917589i
$490$		0			0
$491$	1.28060	−	0.930413i	0.0577928	−	0.0419890i	−0.558514	−	0.829495i	$-0.688628\pi$
$491$	1.28060	−	0.930413i	0.0577928	−	0.0419890i	0.616307	+	0.787506i	$0.288628\pi$
$492$		0			0
$493$	−1.37853	−	4.24267i	−0.0620858	−	0.191080i
$494$		0			0
$495$	−11.7836	−	6.35932i	−0.529635	−	0.285830i
$496$		0			0
$497$	−2.97391	−	9.15276i	−0.133398	−	0.410557i
$498$		0			0
$499$	−17.8457	−	24.5626i	−0.798885	−	1.09957i	−0.992944	−	0.118582i	$-0.962165\pi$
$499$	−17.8457	−	24.5626i	−0.798885	−	1.09957i	0.194059	−	0.980990i	$-0.437835\pi$
$500$		0			0
$501$	−1.27465	−	0.414159i	−0.0569471	−	0.0185032i
$502$		0			0
$503$	27.8994	+	20.2701i	1.24397	+	0.903798i	0.997856	−	0.0654421i	$-0.0208458\pi$
$503$	27.8994	+	20.2701i	1.24397	+	0.903798i	0.246115	+	0.969241i	$0.420846\pi$
$504$		0			0
$505$		−	4.95111i		−	0.220321i
$506$		0			0
$507$	6.83567	+	3.59021i	0.303583	+	0.159447i
$508$		0			0
$509$	13.9904	−	19.2562i	0.620115	−	0.853514i	−0.377247	−	0.926113i	$-0.623129\pi$
$509$	13.9904	−	19.2562i	0.620115	−	0.853514i	0.997361	+	0.0725983i	$0.0231291\pi$
$510$		0			0
$511$	−3.28708	+	10.1166i	−0.145412	+	0.447531i
$512$		0			0
$513$	−9.81649	−	13.5112i	−0.433408	−	0.596535i
$514$		0			0
$515$	25.4458	−	8.26783i	1.12127	−	0.364324i
$516$		0			0
$517$	−4.37323	−	9.10911i	−0.192335	−	0.400618i
$518$		0			0
$519$	−1.55225	−	4.77732i	−0.0681360	−	0.209701i
$520$		0			0
$521$	27.7702	−	20.1762i	1.21663	−	0.883935i	0.220816	−	0.975315i	$-0.429128\pi$
$521$	27.7702	−	20.1762i	1.21663	−	0.883935i	0.995816	+	0.0913801i	$0.0291278\pi$
$522$		0			0
$523$	−2.89708	+	8.91631i	−0.126681	+	0.389883i	−0.994204	−	0.107514i	$-0.965711\pi$
$523$	−2.89708	+	8.91631i	−0.126681	+	0.389883i	0.867523	+	0.497397i	$0.165711\pi$
$524$		0			0
$525$	1.18077	−	1.62519i	0.0515330	−	0.0709292i
$526$		0			0
$527$		−	35.3291i		−	1.53896i
$528$		0			0
$529$	2.51276			0.109250
$530$		0			0
$531$	13.4087	−	18.4555i	0.581887	−	0.800899i
$532$		0			0
$533$	−7.29368	−	4.53190i	−0.315924	−	0.196298i
$534$		0			0
$535$	14.1670	+	19.4992i	0.612493	+	0.843024i
$536$		0			0
$537$	2.95083	+	9.08172i	0.127338	+	0.391905i
$538$		0			0
$539$	12.3617	+	12.9605i	0.532458	+	0.558249i
$540$		0			0
$541$	−16.6800	+	5.41967i	−0.717130	+	0.233010i	−0.644778	−	0.764370i	$-0.723050\pi$
$541$	−16.6800	+	5.41967i	−0.717130	+	0.233010i	−0.0723515	+	0.997379i	$0.523050\pi$
$542$		0			0
$543$	−2.62338	+	1.90600i	−0.112580	+	0.0817942i
$544$		0			0
$545$	−4.08674	+	12.5777i	−0.175057	+	0.538769i
$546$		0			0
$547$	−3.99414	−	2.90191i	−0.170777	−	0.124077i	0.499114	−	0.866537i	$-0.333659\pi$
$547$	−3.99414	−	2.90191i	−0.170777	−	0.124077i	−0.669891	+	0.742460i	$0.733659\pi$
$548$		0			0
$549$	8.59561			0.366852
$550$		0			0
$551$		−	6.00753i		−	0.255929i
$552$		0			0
$553$	1.69546	−	2.33360i	0.0720984	−	0.0992349i
$554$		0			0
$555$	1.97385	−	6.07489i	0.0837853	−	0.257865i
$556$		0			0
$557$	−16.1256	−	22.1949i	−0.683262	−	0.940429i	0.316705	−	0.948524i	$-0.397423\pi$
$557$	−16.1256	−	22.1949i	−0.683262	−	0.940429i	−0.999967	+	0.00809461i	$0.997423\pi$
$558$		0			0
$559$	−0.814576	−	11.2391i	−0.0344529	−	0.475361i
$560$		0			0
$561$	0.968998	+	7.21867i	0.0409111	+	0.304772i
$562$		0			0
$563$	4.30377	+	13.2456i	0.181382	+	0.558237i	0.999867	−	0.0162905i	$-0.00518565\pi$
$563$	4.30377	+	13.2456i	0.181382	+	0.558237i	−0.818485	+	0.574528i	$0.805186\pi$
$564$		0			0
$565$	13.2706	+	18.2654i	0.558299	+	0.768433i
$566$		0			0
$567$	7.15688	+	2.32541i	0.300561	+	0.0976581i
$568$		0			0
$569$	8.51977	+	6.18997i	0.357167	+	0.259497i	0.751870	−	0.659312i	$-0.229152\pi$
$569$	8.51977	+	6.18997i	0.357167	+	0.259497i	−0.394702	+	0.918809i	$0.629152\pi$
$570$		0			0
$571$	−0.509279			−0.0213126			−0.0106563	−	0.999943i	$-0.503392\pi$
$571$	−0.509279			−0.0213126			−0.0106563	+	0.999943i	$0.503392\pi$
$572$		0			0
$573$	5.82049			0.243154
$574$		0			0
$575$	−10.9274	−	7.93922i	−0.455704	−	0.331088i
$576$		0			0
$577$	37.4704	+	12.1749i	1.55991	+	0.506847i	0.956785	−	0.290796i	$-0.0939201\pi$
$577$	37.4704	+	12.1749i	1.55991	+	0.506847i	0.603130	+	0.797643i	$0.293920\pi$
$578$		0			0
$579$	8.90554	+	12.2574i	0.370101	+	0.509401i
$580$		0			0
$581$	1.20131	+	3.69726i	0.0498388	+	0.153388i
$582$		0			0
$583$	−2.44063	−	0.445941i	−0.101081	−	0.0184690i
$584$		0			0
$585$	−14.5185	+	1.05226i	−0.600266	+	0.0435056i
$586$		0			0
$587$	11.6322	+	16.0104i	0.480113	+	0.660819i	0.978527	−	0.206121i	$-0.0660839\pi$
$587$	11.6322	+	16.0104i	0.480113	+	0.660819i	−0.498414	+	0.866939i	$0.666084\pi$
$588$		0			0
$589$	14.7020	−	45.2482i	0.605786	−	1.86442i
$590$		0			0
$591$	6.15232	−	8.46794i	0.253073	−	0.348325i
$592$		0			0
$593$		−	44.8868i		−	1.84328i	−0.388046	−	0.921640i	$-0.626850\pi$
$593$		−	44.8868i		−	1.84328i	0.388046	−	0.921640i	$-0.373150\pi$
$594$		0			0
$595$	−7.13218			−0.292391
$596$		0			0
$597$	−4.71173	−	3.42327i	−0.192838	−	0.140105i
$598$		0			0
$599$	12.6159	−	38.8278i	0.515472	−	1.58646i	−0.266950	−	0.963710i	$-0.586016\pi$
$599$	12.6159	−	38.8278i	0.515472	−	1.58646i	0.782422	−	0.622749i	$-0.213984\pi$
$600$		0			0
$601$	−6.89457	+	5.00920i	−0.281236	+	0.204330i	−0.719456	−	0.694538i	$-0.755609\pi$
$601$	−6.89457	+	5.00920i	−0.281236	+	0.204330i	0.438221	+	0.898867i	$0.355609\pi$
$602$		0			0
$603$	3.74278	−	1.21610i	0.152418	−	0.0495235i
$604$		0			0
$605$	4.42412	+	16.1821i	0.179866	+	0.657894i
$606$		0			0
$607$	−12.7687	−	39.2979i	−0.518264	−	1.59505i	−0.777263	−	0.629176i	$-0.783393\pi$
$607$	−12.7687	−	39.2979i	−0.518264	−	1.59505i	0.258999	−	0.965878i	$-0.416607\pi$
$608$		0			0
$609$	−0.532743	−	0.733258i	−0.0215878	−	0.0297131i
$610$		0			0
$611$	−9.33034	−	5.79738i	−0.377465	−	0.234537i
$612$		0			0
$613$	−1.67219	+	2.30157i	−0.0675390	+	0.0929595i	−0.841450	−	0.540335i	$-0.818298\pi$
$613$	−1.67219	+	2.30157i	−0.0675390	+	0.0929595i	0.773911	+	0.633294i	$0.218298\pi$
$614$		0			0
$615$	−2.15725			−0.0869885
$616$		0			0
$617$			8.27961i			0.333325i	0.986014	+	0.166662i	$0.0532990\pi$
$617$			8.27961i			0.333325i	−0.986014	+	0.166662i	$0.946701\pi$
$618$		0			0
$619$	0.419151	−	0.576912i	0.0168471	−	0.0231880i	−0.800510	−	0.599319i	$-0.795438\pi$
$619$	0.419151	−	0.576912i	0.0168471	−	0.0231880i	0.817357	+	0.576131i	$0.195438\pi$
$620$		0			0
$621$	−5.23523	+	16.1124i	−0.210082	+	0.646567i
$622$		0			0
$623$	−16.4424	+	11.9461i	−0.658751	+	0.478611i
$624$		0			0
$625$	−1.38393	−	4.25931i	−0.0553573	−	0.170372i
$626$		0			0
$627$	−1.76296	+	9.64864i	−0.0704057	+	0.385330i
$628$		0			0
$629$	24.7974	−	8.05718i	0.988739	−	0.321261i
$630$		0			0
$631$	2.34005	+	3.22080i	0.0931557	+	0.128218i	0.853051	−	0.521828i	$-0.174750\pi$
$631$	2.34005	+	3.22080i	0.0931557	+	0.128218i	−0.759895	+	0.650046i	$0.774750\pi$
$632$		0			0
$633$	2.82001	−	8.67911i	0.112085	−	0.344964i
$634$		0			0
$635$	15.6269	−	21.5086i	0.620135	−	0.853543i
$636$		0			0
$637$	18.9043	+	4.66246i	0.749018	+	0.184733i
$638$		0			0
$639$		−	20.1424i		−	0.796821i
$640$		0			0
$641$	21.6645	+	15.7402i	0.855696	+	0.621700i	0.926711	−	0.375776i	$-0.122624\pi$
$641$	21.6645	+	15.7402i	0.855696	+	0.621700i	−0.0710145	+	0.997475i	$0.522624\pi$
$642$		0			0
$643$	−14.1211	−	4.58823i	−0.556882	−	0.180942i	0.0170357	−	0.999855i	$-0.494577\pi$
$643$	−14.1211	−	4.58823i	−0.556882	−	0.180942i	−0.573918	+	0.818913i	$0.694577\pi$
$644$		0			0
$645$	−1.66397	−	2.29026i	−0.0655189	−	0.0901790i
$646$		0			0
$647$	5.34156	+	16.4396i	0.209998	+	0.646309i	0.999471	+	0.0325228i	$0.0103542\pi$
$647$	5.34156	+	16.4396i	0.209998	+	0.646309i	−0.789473	+	0.613786i	$0.789646\pi$
$648$		0			0
$649$	−28.3265	+	3.80240i	−1.11191	+	0.149257i
$650$		0			0
$651$	−2.21810	−	6.82660i	−0.0869341	−	0.267556i
$652$		0			0
$653$	−3.11923	+	2.26626i	−0.122065	+	0.0886854i	−0.647143	−	0.762369i	$-0.724036\pi$
$653$	−3.11923	+	2.26626i	−0.122065	+	0.0886854i	0.525078	+	0.851054i	$0.324036\pi$
$654$		0			0
$655$	−17.9079	−	5.81862i	−0.699718	−	0.227352i
$656$		0			0
$657$	−13.0862	+	18.0115i	−0.510539	+	0.702697i
$658$		0			0
$659$	−43.3693			−1.68943			−0.844714	−	0.535218i	$-0.820229\pi$
$659$	−43.3693			−1.68943			−0.844714	+	0.535218i	$0.820229\pi$
$660$		0			0
$661$			28.7188i			1.11703i	0.829493	+	0.558517i	$0.188629\pi$
$661$			28.7188i			1.11703i	−0.829493	+	0.558517i	$0.811371\pi$
$662$		0			0
$663$	5.10491	+	6.05253i	0.198258	+	0.235061i
$664$		0			0
$665$	−9.13463	−	2.96802i	−0.354226	−	0.115095i
$666$		0			0
$667$	−4.93025	+	3.58204i	−0.190900	+	0.138697i
$668$		0			0
$669$	9.43032	−	3.06410i	0.364597	−	0.118465i
$670$		0			0
$671$	−7.43276	−	7.79279i	−0.286938	−	0.300837i
$672$		0			0
$673$	8.51666	+	26.2116i	0.328293	+	1.01038i	0.969932	+	0.243375i	$0.0782546\pi$
$673$	8.51666	+	26.2116i	0.328293	+	1.01038i	−0.641639	+	0.767007i	$0.721745\pi$
$674$		0			0
$675$	7.25626	−	5.27198i	0.279294	−	0.202919i
$676$		0			0
$677$	−10.8322	+	33.3381i	−0.416315	+	1.28129i	0.494754	+	0.869033i	$0.335258\pi$
$677$	−10.8322	+	33.3381i	−0.416315	+	1.28129i	−0.911069	+	0.412253i	$0.864742\pi$
$678$		0			0
$679$	−16.1576	−	11.7392i	−0.620070	−	0.450507i
$680$		0			0
$681$		−	11.9754i		−	0.458898i
$682$		0			0
$683$		−	28.6569i		−	1.09653i	−0.836306	−	0.548263i	$-0.815289\pi$
$683$		−	28.6569i		−	1.09653i	0.836306	−	0.548263i	$-0.184711\pi$
$684$		0			0
$685$	−4.73541	−	3.44048i	−0.180931	−	0.131454i
$686$		0			0
$687$	−0.445925	−	0.144890i	−0.0170131	−	0.00552790i
$688$		0			0
$689$	−2.49820	+	1.01672i	−0.0951739	+	0.0387340i
$690$		0			0
$691$	−28.7986	+	9.35724i	−1.09555	+	0.355966i	−0.800389	−	0.599481i	$-0.795374\pi$
$691$	−28.7986	+	9.35724i	−1.09555	+	0.355966i	−0.295162	+	0.955447i	$0.595374\pi$
$692$		0			0
$693$	−4.80624	−	10.0110i	−0.182574	−	0.380288i
$694$		0			0
$695$	−13.8002	+	4.48395i	−0.523470	+	0.170086i
$696$		0			0
$697$	−5.17591	−	7.12403i	−0.196052	−	0.269842i
$698$		0			0
$699$	1.75582	−	5.40387i	0.0664113	−	0.204393i
$700$		0			0
$701$	36.1833	+	26.2887i	1.36662	+	0.992911i	0.997992	+	0.0633353i	$0.0201737\pi$
$701$	36.1833	+	26.2887i	1.36662	+	0.992911i	0.368632	+	0.929575i	$0.379826\pi$
$702$		0			0
$703$	35.1126			1.32430
$704$		0			0
$705$	−2.75963			−0.103934
$706$		0			0
$707$	2.41355	−	3.32196i	0.0907707	−	0.124935i
$708$		0			0
$709$	34.2059	+	11.1142i	1.28463	+	0.417402i	0.870209	−	0.492683i	$-0.163984\pi$
$709$	34.2059	+	11.1142i	1.28463	+	0.417402i	0.414422	+	0.910085i	$0.363984\pi$
$710$		0			0
$711$	4.88419	−	3.54857i	0.183172	−	0.133082i
$712$		0			0
$713$	−45.9005	+	14.9140i	−1.71899	+	0.558532i
$714$		0			0
$715$	13.5083	+	12.2526i	0.505184	+	0.458220i
$716$		0			0
$717$	−1.68181	+	0.546454i	−0.0628085	+	0.0204077i
$718$		0			0
$719$	−31.5649	+	22.9333i	−1.17717	+	0.855267i	−0.991850	−	0.127411i	$-0.959333\pi$
$719$	−31.5649	+	22.9333i	−1.17717	+	0.855267i	−0.185323	+	0.982678i	$0.559333\pi$
$720$		0			0
$721$	21.1033	+	6.85687i	0.785927	+	0.255363i
$722$		0			0
$723$	−0.709093	+	0.975983i	−0.0263714	+	0.0362972i
$724$		0			0
$725$	3.22636			0.119824
$726$		0			0
$727$	8.96457			0.332477			0.166239	−	0.986086i	$-0.446838\pi$
$727$	8.96457			0.332477			0.166239	+	0.986086i	$0.446838\pi$
$728$		0			0
$729$	7.90715	+	5.74488i	0.292857	+	0.212773i
$730$		0			0
$731$	3.57091	−	10.9901i	0.132075	−	0.406484i
$732$		0			0
$733$	13.6267	+	18.7556i	0.503314	+	0.692753i	0.982774	−	0.184811i	$-0.0591673\pi$
$733$	13.6267	+	18.7556i	0.503314	+	0.692753i	−0.479460	+	0.877564i	$0.659167\pi$
$734$		0			0
$735$	4.65212	−	1.51157i	0.171596	−	0.0557549i
$736$		0			0
$737$	−4.33896	−	2.34162i	−0.159828	−	0.0862548i
$738$		0			0
$739$	1.67488	−	0.544200i	0.0616113	−	0.0200187i	−0.278049	−	0.960567i	$-0.589688\pi$
$739$	1.67488	−	0.544200i	0.0616113	−	0.0200187i	0.339660	+	0.940548i	$0.389688\pi$
$740$		0			0
$741$	4.01944	+	9.87624i	0.147658	+	0.362813i
$742$		0			0
$743$	0.0357199	+	0.0116061i	0.00131044	+	0.000425787i	0.309672	−	0.950843i	$-0.399781\pi$
$743$	0.0357199	+	0.0116061i	0.00131044	+	0.000425787i	−0.308362	+	0.951269i	$0.599781\pi$
$744$		0			0
$745$	−28.6743	−	20.8331i	−1.05055	−	0.763266i
$746$		0			0
$747$			8.13653i			0.297700i
$748$		0			0
$749$			19.9891i			0.730386i
$750$		0			0
$751$	33.3558	+	24.2344i	1.21717	+	0.884327i	0.995862	−	0.0908764i	$-0.0289668\pi$
$751$	33.3558	+	24.2344i	1.21717	+	0.884327i	0.221310	+	0.975204i	$0.428967\pi$
$752$		0			0
$753$	−0.536001	+	1.64964i	−0.0195330	+	0.0601163i
$754$		0			0
$755$	−14.8020	+	10.7543i	−0.538699	+	0.391388i
$756$		0			0
$757$	3.36973	+	10.3710i	0.122475	+	0.376939i	0.993433	−	0.114419i	$-0.0365007\pi$
$757$	3.36973	+	10.3710i	0.122475	+	0.376939i	−0.870958	+	0.491358i	$0.836501\pi$
$758$		0			0
$759$	8.96962	−	4.30626i	0.325577	−	0.156307i
$760$		0			0
$761$	−34.8368	+	11.3192i	−1.26283	+	0.410319i	−0.862503	−	0.506052i	$-0.831104\pi$
$761$	−34.8368	+	11.3192i	−1.26283	+	0.410319i	−0.400329	+	0.916371i	$0.631104\pi$
$762$		0			0
$763$	−8.87333	+	6.44685i	−0.321236	+	0.233392i
$764$		0			0
$765$	−14.1969	−	4.61286i	−0.513291	−	0.166778i
$766$		0			0
$767$	−23.7505	+	20.0319i	−0.857580	+	0.723311i
$768$		0			0
$769$			22.9678i			0.828240i	0.910222	+	0.414120i	$0.135911\pi$
$769$			22.9678i			0.828240i	−0.910222	+	0.414120i	$0.864089\pi$
$770$		0			0
$771$	5.25334			0.189195
$772$		0			0
$773$	−2.57157	+	3.53946i	−0.0924930	+	0.127306i	−0.852756	−	0.522310i	$-0.825070\pi$
$773$	−2.57157	+	3.53946i	−0.0924930	+	0.127306i	0.760263	+	0.649616i	$0.225070\pi$
$774$		0			0
$775$	24.3007	+	7.89578i	0.872907	+	0.283625i
$776$		0			0
$777$	4.28572	−	3.11376i	0.153749	−	0.111705i
$778$		0			0
$779$	−3.66448	−	11.2781i	−0.131294	−	0.404081i
$780$		0			0
$781$	−18.2611	+	17.4174i	−0.653434	+	0.623245i
$782$		0			0
$783$	−1.25052	−	3.84870i	−0.0446898	−	0.137541i
$784$		0			0
$785$	12.7250	+	17.5144i	0.454174	+	0.625117i
$786$		0			0
$787$	−35.2880	−	11.4658i	−1.25788	−	0.408710i	−0.397141	−	0.917757i	$-0.629998\pi$
$787$	−35.2880	−	11.4658i	−1.25788	−	0.408710i	−0.860738	+	0.509048i	$0.829998\pi$
$788$		0			0
$789$	−2.48163	−	1.80301i	−0.0883485	−	0.0641889i
$790$		0			0
$791$			18.7244i			0.665761i
$792$		0			0
$793$	−11.3666	−	2.80340i	−0.403641	−	0.0995518i
$794$		0			0
$795$	−0.398279	+	0.548184i	−0.0141255	+	0.0194421i
$796$		0			0
$797$	11.3021	−	34.7844i	0.400342	−	1.23213i	−0.524380	−	0.851484i	$-0.675703\pi$
$797$	11.3021	−	34.7844i	0.400342	−	1.23213i	0.924722	−	0.380642i	$-0.124297\pi$
$798$		0			0
$799$	−6.62122	−	9.11333i	−0.234242	−	0.322406i
$800$		0			0
$801$	−40.4557	+	13.1448i	−1.42943	+	0.464450i
$802$		0			0
$803$	27.6451	−	3.71094i	0.975574	−	0.130956i
$804$		0			0
$805$	3.01081	+	9.26631i	0.106117	+	0.326595i
$806$		0			0
$807$	3.73408	−	2.71297i	0.131446	−	0.0955010i
$808$		0			0
$809$	11.4520	−	35.2455i	0.402629	−	1.23917i	−0.520229	−	0.854027i	$-0.674154\pi$
$809$	11.4520	−	35.2455i	0.402629	−	1.23917i	0.922859	−	0.385139i	$-0.125846\pi$
$810$		0			0
$811$	−25.0215	+	34.4391i	−0.878624	+	1.20932i	0.0981766	+	0.995169i	$0.468699\pi$
$811$	−25.0215	+	34.4391i	−0.878624	+	1.20932i	−0.976800	+	0.214153i	$0.931301\pi$
$812$		0			0
$813$			15.5409i			0.545042i
$814$		0			0
$815$	16.8607			0.590605
$816$		0			0
$817$	9.14697	−	12.5897i	0.320012	−	0.440459i
$818$		0			0
$819$	−10.2542	−	6.37140i	−0.358310	−	0.222635i
$820$		0			0
$821$	−10.5835	−	14.5669i	−0.369366	−	0.508389i	0.583362	−	0.812212i	$-0.301737\pi$
$821$	−10.5835	−	14.5669i	−0.369366	−	0.508389i	−0.952728	+	0.303823i	$0.901737\pi$
$822$		0			0
$823$	−0.533343	−	1.64146i	−0.0185912	−	0.0572177i	0.941331	−	0.337486i	$-0.109577\pi$
$823$	−0.533343	−	1.64146i	−0.0185912	−	0.0572177i	−0.959922	+	0.280268i	$0.909577\pi$
$824$		0			0
$825$	−5.18184	−	0.946802i	−0.180409	−	0.0329634i
$826$		0			0
$827$	−8.24969	+	2.68049i	−0.286870	+	0.0932096i	−0.448917	−	0.893573i	$-0.648190\pi$
$827$	−8.24969	+	2.68049i	−0.286870	+	0.0932096i	0.162048	+	0.986783i	$0.448190\pi$
$828$		0			0
$829$	13.4442	−	9.76782i	0.466938	−	0.339250i	−0.329309	−	0.944222i	$-0.606816\pi$
$829$	13.4442	−	9.76782i	0.466938	−	0.339250i	0.796247	+	0.604972i	$0.206816\pi$
$830$		0			0
$831$	2.52933	−	7.78449i	0.0877416	−	0.270041i
$832$		0			0
$833$	16.1537	+	11.7363i	0.559691	+	0.406639i
$834$		0			0
$835$	−3.44144			−0.119096
$836$		0			0
$837$		−	32.0484i		−	1.10776i
$838$		0			0
$839$	−27.0489	+	37.2297i	−0.933833	+	1.28531i	0.0245122	+	0.999700i	$0.492197\pi$
$839$	−27.0489	+	37.2297i	−0.933833	+	1.28531i	−0.958345	+	0.285612i	$0.907803\pi$
$840$		0			0
$841$	−8.51166	+	26.1962i	−0.293506	+	0.903317i
$842$		0			0
$843$	10.0861	+	13.8823i	0.347382	+	0.478131i
$844$		0			0
$845$	19.5421	+	3.34363i	0.672269	+	0.115024i
$846$		0			0
$847$	−4.91999	+	13.0140i	−0.169053	+	0.447168i
$848$		0			0
$849$	4.36872	+	13.4455i	0.149934	+	0.461450i
$850$		0			0
$851$	−20.9362	−	28.8162i	−0.717683	−	0.987806i
$852$		0			0
$853$	−0.227265	−	0.0738428i	−0.00778139	−	0.00252833i	0.305124	−	0.952313i	$-0.401302\pi$
$853$	−0.227265	−	0.0738428i	−0.00778139	−	0.00252833i	−0.312905	+	0.949784i	$0.601302\pi$
$854$		0			0
$855$	−16.2633	−	11.8160i	−0.556192	−	0.404097i
$856$		0			0
$857$	−4.37437			−0.149426			−0.0747128	−	0.997205i	$-0.523804\pi$
$857$	−4.37437			−0.149426			−0.0747128	+	0.997205i	$0.523804\pi$
$858$		0			0
$859$	27.9519			0.953708			0.476854	−	0.878983i	$-0.341777\pi$
$859$	27.9519			0.953708			0.476854	+	0.878983i	$0.341777\pi$
$860$		0			0
$861$	−1.44741	−	1.05160i	−0.0493276	−	0.0358386i
$862$		0			0
$863$	−26.2465	−	8.52800i	−0.893441	−	0.290297i	−0.173914	−	0.984761i	$-0.555641\pi$
$863$	−26.2465	−	8.52800i	−0.893441	−	0.290297i	−0.719527	+	0.694464i	$0.755641\pi$
$864$		0			0
$865$	−7.58145	−	10.4350i	−0.257777	−	0.354800i
$866$		0			0
$867$	−0.610986	−	1.88042i	−0.0207502	−	0.0638624i
$868$		0			0
$869$	−7.44058	−	1.35951i	−0.252404	−	0.0461182i
$870$		0			0
$871$	−5.34599	+	0.387463i	−0.181142	+	0.0131287i
$872$		0			0
$873$	−24.5698	−	33.8175i	−0.831563	−	1.14455i
$874$		0			0
$875$	4.57439	−	14.0785i	0.154642	−	0.475941i
$876$		0			0
$877$	7.79628	−	10.7307i	0.263262	−	0.362348i	−0.656839	−	0.754031i	$-0.728107\pi$
$877$	7.79628	−	10.7307i	0.263262	−	0.362348i	0.920100	+	0.391683i	$0.128107\pi$
$878$		0			0
$879$		−	12.0563i		−	0.406648i
$880$		0			0
$881$	−47.1067			−1.58707			−0.793533	−	0.608527i	$-0.791761\pi$
$881$	−47.1067			−1.58707			−0.793533	+	0.608527i	$0.791761\pi$
$882$		0			0
$883$	−7.73794	−	5.62194i	−0.260402	−	0.189193i	0.449922	−	0.893068i	$-0.351452\pi$
$883$	−7.73794	−	5.62194i	−0.260402	−	0.189193i	−0.710324	+	0.703874i	$0.751452\pi$
$884$		0			0
$885$	−2.41206	+	7.42356i	−0.0810805	+	0.249540i
$886$		0			0
$887$	−28.2835	+	20.5492i	−0.949668	+	0.689974i	−0.950728	−	0.310025i	$-0.899663\pi$
$887$	−28.2835	+	20.5492i	−0.949668	+	0.689974i	0.00106000	+	0.999999i	$0.499663\pi$
$888$		0			0
$889$	20.9698	−	6.81352i	0.703306	−	0.228518i
$890$		0			0
$891$	−2.62527	−	19.5572i	−0.0879498	−	0.655192i
$892$		0			0
$893$	−4.68774	−	14.4274i	−0.156869	−	0.482794i
$894$		0			0
$895$	14.4124	+	19.8370i	0.481753	+	0.663076i
$896$		0			0
$897$	5.70860	−	9.18746i	0.190605	−	0.306761i
$898$		0			0
$899$	6.77616	−	9.32658i	0.225998	−	0.311059i
$900$		0			0
$901$	−2.76591			−0.0921457
$902$		0			0
$903$		−	2.34780i		−	0.0781300i
$904$		0			0
$905$	−4.89416	+	6.73624i	−0.162687	+	0.223920i
$906$		0			0
$907$	7.70157	−	23.7030i	0.255726	−	0.787045i	−0.737959	−	0.674845i	$-0.764210\pi$
$907$	7.70157	−	23.7030i	0.255726	−	0.787045i	0.993686	−	0.112200i	$-0.0357896\pi$
$908$		0			0
$909$	6.95281	−	5.05151i	0.230610	−	0.167548i
$910$		0			0
$911$	−0.950646	−	2.92579i	−0.0314963	−	0.0969356i	0.934073	−	0.357083i	$-0.116229\pi$
$911$	−0.950646	−	2.92579i	−0.0314963	−	0.0969356i	−0.965569	+	0.260148i	$0.916229\pi$
$912$		0			0
$913$	7.37658	−	7.03578i	0.244129	−	0.232850i
$914$		0			0
$915$	−2.79718	+	0.908860i	−0.0924721	+	0.0300460i
$916$		0			0
$917$	−9.17890	−	12.6337i	−0.303114	−	0.417200i
$918$		0			0
$919$	−14.5643	+	44.8244i	−0.480433	+	1.47862i	0.358054	+	0.933701i	$0.383440\pi$
$919$	−14.5643	+	44.8244i	−0.480433	+	1.47862i	−0.838487	+	0.544921i	$0.816560\pi$
$920$		0			0
$921$	−4.33682	+	5.96912i	−0.142903	+	0.196689i
$922$		0			0
$923$	−6.56932	+	26.6359i	−0.216232	+	0.876730i
$924$		0			0
$925$			18.8573i			0.620026i
$926$		0			0
$927$	37.5722	+	27.2978i	1.23403	+	0.896578i
$928$		0			0
$929$	−18.4563	−	5.99681i	−0.605531	−	0.196749i	−0.00982547	−	0.999952i	$-0.503128\pi$
$929$	−18.4563	−	5.99681i	−0.605531	−	0.196749i	−0.595706	+	0.803203i	$0.703128\pi$
$930$		0			0
$931$	15.8050	+	21.7537i	0.517988	+	0.712949i
$932$		0			0
$933$	1.87375	+	5.76682i	0.0613439	+	0.188797i
$934$		0			0
$935$	8.09428	+	16.8598i	0.264711	+	0.551373i
$936$		0			0
$937$	−10.2840	−	31.6510i	−0.335965	−	1.03399i	−0.966245	−	0.257626i	$-0.917060\pi$
$937$	−10.2840	−	31.6510i	−0.335965	−	1.03399i	0.630279	−	0.776368i	$-0.282940\pi$
$938$		0			0
$939$	11.1259	−	8.08345i	0.363080	−	0.263793i
$940$		0			0
$941$	−20.4559	−	6.64651i	−0.666842	−	0.216670i	−0.0440165	−	0.999031i	$-0.514015\pi$
$941$	−20.4559	−	6.64651i	−0.666842	−	0.216670i	−0.622826	+	0.782361i	$0.714015\pi$
$942$		0			0
$943$	−7.07074	+	9.73204i	−0.230255	+	0.316919i
$944$		0			0
$945$	−6.46988			−0.210465
$946$		0			0
$947$			1.76659i			0.0574066i	0.999588	+	0.0287033i	$0.00913780\pi$
$947$			1.76659i			0.0574066i	−0.999588	+	0.0287033i	$0.990862\pi$
$948$		0			0
$949$	23.1792	−	19.5501i	0.752428	−	0.634623i
$950$		0			0
$951$	7.46754	+	2.42635i	0.242151	+	0.0786798i
$952$		0			0
$953$	−10.5158	+	7.64021i	−0.340642	+	0.247491i	−0.744933	−	0.667140i	$-0.767518\pi$
$953$	−10.5158	+	7.64021i	−0.340642	+	0.247491i	0.404291	+	0.914630i	$0.367518\pi$
$954$		0			0
$955$	14.2142	−	4.61847i	0.459960	−	0.149450i
$956$		0			0
$957$	−1.12874	+	2.09152i	−0.0364870	+	0.0676093i
$958$		0			0
$959$	−1.50009	−	4.61679i	−0.0484403	−	0.149084i
$960$		0			0
$961$	48.7826	−	35.4426i	1.57363	−	1.14331i
$962$		0			0
$963$	−12.9283	+	39.7892i	−0.416609	+	1.28219i
$964$		0			0
$965$	31.4742	+	22.8673i	1.01319	+	0.736126i
$966$		0			0
$967$			42.1823i			1.35649i	0.734836	+	0.678245i	$0.237259\pi$
$967$			42.1823i			1.35649i	−0.734836	+	0.678245i	$0.762741\pi$
$968$		0			0
$969$			10.9346i			0.351269i
$970$		0			0
$971$	8.36117	+	6.07475i	0.268323	+	0.194948i	0.713808	−	0.700341i	$-0.246969\pi$
$971$	8.36117	+	6.07475i	0.268323	+	0.194948i	−0.445485	+	0.895289i	$0.646969\pi$
$972$		0			0
$973$	−11.4451	−	3.71873i	−0.366912	−	0.119217i
$974$		0			0
$975$	−5.30407	+	2.15866i	−0.169866	+	0.0691323i
$976$		0			0
$977$	−11.8933	+	3.86438i	−0.380501	+	0.123632i	−0.493022	−	0.870017i	$-0.664108\pi$
$977$	−11.8933	+	3.86438i	−0.380501	+	0.123632i	0.112520	+	0.993649i	$0.464108\pi$
$978$		0			0
$979$	46.8998	+	25.3106i	1.49892	+	0.808931i
$980$		0			0
$981$	−21.8324	+	7.09377i	−0.697054	+	0.226487i
$982$		0			0
$983$	25.5090	+	35.1102i	0.813612	+	1.11984i	0.990756	+	0.135656i	$0.0433142\pi$
$983$	25.5090	+	35.1102i	0.813612	+	1.11984i	−0.177144	+	0.984185i	$0.556686\pi$
$984$		0			0
$985$	8.30536	−	25.5613i	0.264631	−	0.814449i
$986$		0			0
$987$	−1.85158	−	1.34525i	−0.0589365	−	0.0428198i
$988$		0			0
$989$	−15.7861			−0.501968
$990$		0			0
$991$	−13.6615			−0.433971			−0.216985	−	0.976175i	$-0.569622\pi$
$991$	−13.6615			−0.433971			−0.216985	+	0.976175i	$0.569622\pi$
$992$		0			0
$993$	2.32778	−	3.20391i	0.0738698	−	0.101673i
$994$		0			0
$995$	−14.2228	−	4.62126i	−0.450893	−	0.146504i
$996$		0			0
$997$	−27.3421	+	19.8652i	−0.865933	+	0.629137i	−0.929492	−	0.368841i	$-0.879755\pi$
$997$	−27.3421	+	19.8652i	−0.865933	+	0.629137i	0.0635597	+	0.997978i	$0.479755\pi$
$998$		0			0
$999$	22.4947	−	7.30898i	0.711702	−	0.231246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.x.a.181.5	✓	56
11.9	even	5	inner	572.2.x.a.493.6	yes	56
13.12	even	2	inner	572.2.x.a.181.6	yes	56
143.64	even	10	inner	572.2.x.a.493.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.x.a.181.5	✓	56	1.1	even	1	trivial
572.2.x.a.181.6	yes	56	13.12	even	2	inner
572.2.x.a.493.5	yes	56	143.64	even	10	inner
572.2.x.a.493.6	yes	56	11.9	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.480503 - 0.349106i) q^{3} +(-1.45044 - 0.471277i) q^{5} +(-0.743441 - 1.02326i) q^{7} +(-0.818043 - 2.51768i) q^{9} +O(q^{10})\)	\(q+(-0.480503 - 0.349106i) q^{3} +(-1.45044 - 0.471277i) q^{5} +(-0.743441 - 1.02326i) q^{7} +(-0.818043 - 2.51768i) q^{9} +(-1.57515 + 2.91871i) q^{11} +(0.260637 + 3.59612i) q^{13} +(0.532415 + 0.732807i) q^{15} +(-1.14257 + 3.51647i) q^{17} +(-2.92672 + 4.02829i) q^{19} +0.751218i q^{21} +5.05102 q^{23} +(-2.16341 - 1.57181i) q^{25} +(-1.03647 + 3.18993i) q^{27} +(-0.976091 + 0.709172i) q^{29} +(-9.08737 + 2.95267i) q^{31} +(1.77581 - 0.852554i) q^{33} +(0.596080 + 1.83454i) q^{35} +(-4.14494 - 5.70503i) q^{37} +(1.13019 - 1.81893i) q^{39} +(-1.39987 + 1.92675i) q^{41} -3.12533 q^{43} +4.03727i q^{45} +(-1.79076 + 2.46477i) q^{47} +(1.66876 - 5.13593i) q^{49} +(1.77663 - 1.29080i) q^{51} +(0.231163 + 0.711448i) q^{53} +(3.66019 - 3.49109i) q^{55} +(2.81260 - 0.913868i) q^{57} +(5.06515 + 6.97158i) q^{59} +(-1.00338 + 3.08809i) q^{61} +(-1.96807 + 2.70882i) q^{63} +(1.31673 - 5.33879i) q^{65} +1.48660i q^{67} +(-2.42703 - 1.76334i) q^{69} +(7.23642 + 2.35126i) q^{71} +(-4.94331 - 6.80389i) q^{73} +(0.490796 + 1.51051i) q^{75} +(4.15764 - 0.558101i) q^{77} +(0.704732 + 2.16894i) q^{79} +(-4.81334 + 3.49710i) q^{81} +(-2.92315 - 0.949790i) q^{83} +(3.31446 - 4.56197i) q^{85} +0.716590 q^{87} -16.0687i q^{89} +(3.48599 - 2.94020i) q^{91} +(5.39730 + 1.75369i) q^{93} +(6.14348 - 4.46350i) q^{95} +(15.0175 - 4.87947i) q^{97} +(8.63692 + 1.57810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^9	\( 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) \) 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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