LMFDB - Embedded newform 572.2.x.a.181.6

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			181.6
Character	$\chi$	$=$	572.181
Dual form			572.2.x.a.493.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.480503 - 0.349106i) q^{3} +(1.45044 + 0.471277i) q^{5} +(0.743441 + 1.02326i) q^{7} +(-0.818043 - 2.51768i) q^{9} +O(q^{10})$	\(q+(-0.480503 - 0.349106i) q^{3} +(1.45044 + 0.471277i) q^{5} +(0.743441 + 1.02326i) q^{7} +(-0.818043 - 2.51768i) q^{9} +(1.57515 - 2.91871i) q^{11} +(1.90289 + 3.06252i) q^{13} +(-0.532415 - 0.732807i) q^{15} +(-1.14257 + 3.51647i) q^{17} +(2.92672 - 4.02829i) q^{19} -0.751218i q^{21} +5.05102 q^{23} +(-2.16341 - 1.57181i) q^{25} +(-1.03647 + 3.18993i) q^{27} +(-0.976091 + 0.709172i) q^{29} +(9.08737 - 2.95267i) q^{31} +(-1.77581 + 0.852554i) q^{33} +(0.596080 + 1.83454i) q^{35} +(4.14494 + 5.70503i) q^{37} +(0.154801 - 2.13586i) q^{39} +(1.39987 - 1.92675i) q^{41} -3.12533 q^{43} -4.03727i q^{45} +(1.79076 - 2.46477i) q^{47} +(1.66876 - 5.13593i) q^{49} +(1.77663 - 1.29080i) q^{51} +(0.231163 + 0.711448i) q^{53} +(3.66019 - 3.49109i) q^{55} +(-2.81260 + 0.913868i) q^{57} +(-5.06515 - 6.97158i) q^{59} +(-1.00338 + 3.08809i) q^{61} +(1.96807 - 2.70882i) q^{63} +(1.31673 + 5.33879i) q^{65} -1.48660i q^{67} +(-2.42703 - 1.76334i) q^{69} +(-7.23642 - 2.35126i) q^{71} +(4.94331 + 6.80389i) q^{73} +(0.490796 + 1.51051i) q^{75} +(4.15764 - 0.558101i) q^{77} +(0.704732 + 2.16894i) q^{79} +(-4.81334 + 3.49710i) q^{81} +(2.92315 + 0.949790i) q^{83} +(-3.31446 + 4.56197i) q^{85} +0.716590 q^{87} +16.0687i q^{89} +(-1.71907 + 4.22395i) q^{91} +(-5.39730 - 1.75369i) q^{93} +(6.14348 - 4.46350i) q^{95} +(-15.0175 + 4.87947i) q^{97} +(-8.63692 - 1.57810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.614822	−	0.788666i	$-0.289228\pi$
$5$	1.45044	+	0.471277i	0.648657	+	0.210761i	0.0338351	+	0.999427i	$0.489228\pi$
$6$		0			0
$7$	0.743441	+	1.02326i	0.280994	+	0.386756i	0.926063	−	0.377369i	$-0.123171\pi$
$7$	0.743441	+	1.02326i	0.280994	+	0.386756i	−0.645068	+	0.764125i	$0.723171\pi$
$8$		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
$13$	1.90289	+	3.06252i	0.527766	+	0.849390i
$13$	1.90289	+	3.06252i	0.527766	+	0.849390i
$14$		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	−0.328356	−	0.944554i	$-0.606494\pi$
$19$	2.92672	−	4.02829i	0.671436	−	0.924153i	0.999792	+	0.0204016i	$0.00649449\pi$
$20$		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	0.657378	−	0.753561i	$-0.271665\pi$
$31$	9.08737	−	2.95267i	1.63214	−	0.530315i	0.974762	+	0.223246i	$0.0716654\pi$
$32$		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	0.999950	−	0.0100138i	$-0.00318755\pi$
$37$	4.14494	+	5.70503i	0.681425	+	0.937901i	−0.318525	+	0.947914i	$0.603188\pi$
$38$		0			0
$39$	0.154801	−	2.13586i	0.0247880	−	0.342011i
$40$		0			0
$41$	1.39987	−	1.92675i	0.218622	−	0.300908i	−0.685593	−	0.727985i	$-0.740457\pi$
$41$	1.39987	−	1.92675i	0.218622	−	0.300908i	0.904215	+	0.427078i	$0.140457\pi$
$42$		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	−0.658188	−	0.752853i	$-0.728677\pi$
$47$	1.79076	−	2.46477i	0.261209	−	0.359524i	0.919397	+	0.393330i	$0.128677\pi$
$48$		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	0.340036	−	0.940413i	$-0.389561\pi$
$59$	−5.06515	−	6.97158i	−0.659427	−	0.907623i	−0.999462	+	0.0327896i	$0.989561\pi$
$60$		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	$-0.971055\pi$
$67$		−	1.48660i		−	0.181617i	0.995868	−	0.0908085i	$-0.0289451\pi$
$68$		0			0
$69$	−2.42703	−	1.76334i	−0.292180	−	0.212281i
$70$		0			0
$71$	−7.23642	−	2.35126i	−0.858805	−	0.279043i	−0.153676	−	0.988121i	$-0.549111\pi$
$71$	−7.23642	−	2.35126i	−0.858805	−	0.279043i	−0.705129	+	0.709079i	$0.749111\pi$
$72$		0			0
$73$	4.94331	+	6.80389i	0.578571	+	0.796335i	0.993538	−	0.113502i	$-0.0362068\pi$
$73$	4.94331	+	6.80389i	0.578571	+	0.796335i	−0.414967	+	0.909837i	$0.636207\pi$
$74$		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	0.465018	−	0.885301i	$-0.346048\pi$
$83$	2.92315	+	0.949790i	0.320858	+	0.104253i	−0.144160	+	0.989554i	$0.546048\pi$
$84$		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	$0.324390\pi$
$89$			16.0687i			1.70327i	−0.524132	+	0.851637i	$0.675610\pi$
$90$		0			0
$91$	−1.71907	+	4.22395i	−0.180207	+	0.442790i
$92$		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	−0.947132	−	0.320843i	$-0.896034\pi$
$97$	−15.0175	+	4.87947i	−1.52479	+	0.495435i	−0.577659	+	0.816278i	$0.696034\pi$
$98$		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	$0.136322\pi$
$109$			8.67163i			0.830592i	−0.909686	+	0.415296i	$0.863678\pi$
$110$		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
$117$	6.15379	−	7.29612i	0.568918	−	0.674527i
$118$		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	0.148908	−	0.988851i	$-0.452424\pi$
$137$	−3.65016	−	1.18601i	−0.311854	−	0.101328i	−0.460763	+	0.887523i	$0.652424\pi$
$138$		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
$143$	11.9360	−	0.730035i	0.998135	−	0.0610486i
$144$		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	$-0.999066\pi$
$149$	−22.1028	−	7.18164i	−1.81073	−	0.588343i	−0.810738	−	0.585409i	$-0.800934\pi$
$150$		0			0
$151$	−7.05159	+	9.70568i	−0.573850	+	0.789837i	−0.993004	−	0.118078i	$-0.962327\pi$
$151$	−7.05159	+	9.70568i	−0.573850	+	0.789837i	0.419154	+	0.907915i	$0.362327\pi$
$152$		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	0.133229	−	0.991085i	$-0.457465\pi$
$163$	10.5145	−	3.41637i	0.823559	−	0.267591i	0.690330	+	0.723495i	$0.257465\pi$
$164$		0			0
$165$	−2.97749	+	0.399683i	−0.231797	+	0.0311153i
$166$		0			0
$167$	−2.14611	+	0.697314i	−0.166071	+	0.0539598i	−0.390873	−	0.920445i	$-0.627827\pi$
$167$	−2.14611	+	0.697314i	−0.166071	+	0.0539598i	0.224801	+	0.974405i	$0.427827\pi$
$168$		0			0
$169$	−5.75805	+	11.6552i	−0.442927	+	0.896558i
$170$		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	0.995646	−	0.0932171i	$-0.0297151\pi$
$193$	24.2610	+	7.88289i	1.74635	+	0.567423i	0.750703	+	0.660640i	$0.229715\pi$
$194$		0			0
$195$	1.23111	−	3.02498i	0.0881616	−	0.216623i
$196$		0			0
$197$		−	17.6231i		−	1.25559i	−0.778377	−	0.627797i	$-0.783957\pi$
$197$		−	17.6231i		−	1.25559i	0.778377	−	0.627797i	$-0.216043\pi$
$198$		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	−0.342256	−	0.939607i	$-0.611191\pi$
$223$	9.81298	−	13.5064i	0.657126	−	0.904456i	0.999382	+	0.0351508i	$0.0111911\pi$
$224$		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	$-0.966668\pi$
$227$	−11.8514	−	16.3121i	−0.786606	−	1.08267i	0.207917	−	0.978147i	$-0.433332\pi$
$228$		0			0
$229$	−0.750800	+	0.243950i	−0.0496142	+	0.0161206i	−0.333719	−	0.942673i	$-0.608304\pi$
$229$	−0.750800	+	0.243950i	−0.0496142	+	0.0161206i	0.284105	+	0.958793i	$0.408304\pi$
$230$		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	−0.861858	−	0.507149i	$-0.830699\pi$
$239$	−1.75006	+	2.40875i	−0.113202	+	0.155809i	0.748656	+	0.662958i	$0.230699\pi$
$240$		0			0
$241$			2.03117i			0.130839i	0.997858	+	0.0654196i	$0.0208386\pi$
$241$			2.03117i			0.130839i	−0.997858	+	0.0654196i	$0.979161\pi$
$242$		0			0
$243$	13.5959			0.872180
$244$		0			0
$245$	4.84089	−	6.66291i	0.309273	−	0.425678i
$246$		0			0
$247$	17.9059	+	1.29777i	1.13933	+	0.0825753i
$248$		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	$0.0923907\pi$
$271$	15.3800	+	21.1687i	0.934268	+	1.28591i	−0.0239030	+	0.999714i	$0.507609\pi$
$272$		0			0
$273$	2.30062	−	1.42948i	0.139240	−	0.0865162i
$274$		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	0.976348	−	0.216207i	$-0.0693685\pi$
$281$	27.4771	+	8.92785i	1.63915	+	0.532591i	0.662799	+	0.748798i	$0.269368\pi$
$282$		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	$-0.997967\pi$
$293$	−11.9315	−	16.4222i	−0.697043	−	0.959397i	0.302937	−	0.953011i	$-0.402033\pi$
$294$		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
$299$	9.61151	+	15.4688i	0.555848	+	0.894586i
$300$		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	$0.115349\pi$
$307$			12.4227i			0.708998i	−0.935056	+	0.354499i	$0.884651\pi$
$308$		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	0.0661536	−	0.997809i	$-0.478927\pi$
$317$	12.5730	−	4.08522i	0.706171	−	0.229449i	0.640017	+	0.768361i	$0.278927\pi$
$318$		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
$325$	0.696974	−	9.61645i	0.0386612	−	0.533424i
$326$		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	$-0.941339\pi$
$331$		−	6.66784i		−	0.366497i	0.983067	−	0.183249i	$-0.0586614\pi$
$332$		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	−0.701521	−	0.712648i	$-0.747496\pi$
$349$	3.60609	−	4.96335i	0.193029	−	0.265682i	0.894551	+	0.446966i	$0.147496\pi$
$350$		0			0
$351$	−11.7415	+	2.89586i	−0.626715	+	0.154569i
$352$		0			0
$353$		−	13.2641i		−	0.705976i	−0.935628	−	0.352988i	$-0.885166\pi$
$353$		−	13.2641i		−	0.705976i	0.935628	−	0.352988i	$-0.114834\pi$
$354$		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	0.437417	−	0.899259i	$-0.355893\pi$
$359$	−10.4778	−	14.4215i	−0.552998	−	0.761137i	−0.990415	+	0.138122i	$0.955893\pi$
$360$		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
$377$	−4.02924	−	1.63983i	−0.207517	−	0.0844553i
$378$		0			0
$379$	−22.0129	−	7.15241i	−1.13072	−	0.367395i	−0.316873	−	0.948468i	$-0.602633\pi$
$379$	−22.0129	−	7.15241i	−1.13072	−	0.367395i	−0.813851	+	0.581073i	$0.802633\pi$
$380$		0			0
$381$	8.37638	−	6.08580i	0.429135	−	0.311785i
$382$		0			0
$383$	8.69836	−	2.82627i	0.444465	−	0.144416i	−0.0782296	−	0.996935i	$-0.524927\pi$
$383$	8.69836	−	2.82627i	0.444465	−	0.144416i	0.522695	+	0.852520i	$0.324927\pi$
$384$		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	$-0.953743\pi$
$397$		−	5.77061i		−	0.289619i	0.989460	−	0.144809i	$-0.0462569\pi$
$398$		0			0
$399$	−3.02612	−	2.19861i	−0.151496	−	0.110068i
$400$		0			0
$401$	19.5986	+	6.36797i	0.978708	+	0.318001i	0.754326	−	0.656500i	$-0.227964\pi$
$401$	19.5986	+	6.36797i	0.978708	+	0.318001i	0.224382	+	0.974501i	$0.427964\pi$
$402$		0			0
$403$	26.3348	+	22.2117i	1.31183	+	1.10644i
$404$		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	−0.836111	−	0.548560i	$-0.815176\pi$
$409$	−24.0684	+	7.82028i	−1.19010	+	0.386688i	−0.353992	+	0.935248i	$0.615176\pi$
$410$		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	−0.366820	−	0.930292i	$-0.619553\pi$
$421$	12.9531	−	17.8284i	0.631294	−	0.868902i	0.998114	+	0.0613904i	$0.0195535\pi$
$422$		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
$429$	−5.99012	−	3.81612i	−0.289206	−	0.184244i
$430$		0			0
$431$	−34.0791	+	11.0730i	−1.64153	+	0.533367i	−0.976881	−	0.213785i	$-0.931421\pi$
$431$	−34.0791	+	11.0730i	−1.64153	+	0.533367i	−0.664653	+	0.747152i	$0.731421\pi$
$432$		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	−0.509635	−	0.860391i	$-0.670220\pi$
$449$	−8.81942	+	2.86560i	−0.416214	+	0.135236i	0.0934213	+	0.995627i	$0.470220\pi$
$450$		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
$455$	−4.48406	+	5.31643i	−0.210216	+	0.249238i
$456$		0			0
$457$	−9.11534	−	2.96175i	−0.426398	−	0.138545i	0.0879537	−	0.996125i	$-0.471967\pi$
$457$	−9.11534	−	2.96175i	−0.426398	−	0.138545i	−0.514351	+	0.857580i	$0.671967\pi$
$458$		0			0
$459$	−10.0330	−	7.28943i	−0.468302	−	0.340242i
$460$		0			0
$461$		−	37.3526i		−	1.73969i	−0.493329	−	0.869843i	$-0.664220\pi$
$461$		−	37.3526i		−	1.73969i	0.493329	−	0.869843i	$-0.335780\pi$
$462$		0			0
$463$			11.5620i			0.537331i	0.963234	+	0.268666i	$0.0865826\pi$
$463$			11.5620i			0.537331i	−0.963234	+	0.268666i	$0.913417\pi$
$464$		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	−0.468618	−	0.883401i	$-0.655248\pi$
$479$	−29.9180	−	9.72094i	−1.36699	−	0.444161i	−0.898370	+	0.439240i	$0.855248\pi$
$480$		0			0
$481$	−9.58440	+	23.5500i	−0.437011	+	1.07379i
$482$		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	−0.994607	−	0.103715i	$-0.966927\pi$
$487$	−12.9897	+	17.8787i	−0.588617	+	0.810162i	0.405990	+	0.913878i	$0.366927\pi$
$488$		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	$0.0378347\pi$
$499$	17.8457	+	24.5626i	0.798885	+	1.09957i	−0.194059	+	0.980990i	$0.562165\pi$
$500$		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	−0.997361	−	0.0725983i	$-0.976871\pi$
$509$	−13.9904	+	19.2562i	−0.620115	+	0.853514i	0.377247	+	0.926113i	$0.376871\pi$
$510$		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
$533$	8.56449	+	0.620731i	0.370969	+	0.0268869i
$534$		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	0.0723515	−	0.997379i	$-0.476950\pi$
$541$	16.6800	−	5.41967i	0.717130	−	0.233010i	0.644778	+	0.764370i	$0.276950\pi$
$542$		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	0.999967	−	0.00809461i	$-0.00257662\pi$
$557$	16.1256	+	22.1949i	0.683262	+	0.940429i	−0.316705	+	0.948524i	$0.602577\pi$
$558$		0			0
$559$	−5.94714	−	9.57138i	−0.251537	−	0.404826i
$560$		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	−0.603130	−	0.797643i	$-0.706080\pi$
$577$	−37.4704	−	12.1749i	−1.55991	−	0.506847i	−0.956785	+	0.290796i	$0.906080\pi$
$578$		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
$585$	12.3642	−	7.68246i	0.511197	−	0.317631i
$586$		0			0
$587$	−11.6322	−	16.0104i	−0.480113	−	0.660819i	0.498414	−	0.866939i	$-0.333916\pi$
$587$	−11.6322	−	16.0104i	−0.480113	−	0.660819i	−0.978527	+	0.206121i	$0.933916\pi$
$588$		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	$0.373150\pi$
$593$			44.8868i			1.84328i	−0.388046	+	0.921640i	$0.626850\pi$
$594$		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
$611$	10.9560	+	0.794063i	0.443233	+	0.0321243i
$612$		0			0
$613$	1.67219	−	2.30157i	0.0675390	−	0.0929595i	−0.773911	−	0.633294i	$-0.781702\pi$
$613$	1.67219	−	2.30157i	0.0675390	−	0.0929595i	0.841450	+	0.540335i	$0.181702\pi$
$614$		0			0
$615$	−2.15725			−0.0869885
$616$		0			0
$617$		−	8.27961i		−	0.333325i	−0.986014	−	0.166662i	$-0.946701\pi$
$617$		−	8.27961i		−	0.333325i	0.986014	−	0.166662i	$-0.0532990\pi$
$618$		0			0
$619$	−0.419151	+	0.576912i	−0.0168471	+	0.0231880i	−0.817357	−	0.576131i	$-0.804562\pi$
$619$	−0.419151	+	0.576912i	−0.0168471	+	0.0231880i	0.800510	+	0.599319i	$0.204562\pi$
$620$		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	0.759895	−	0.650046i	$-0.225250\pi$
$631$	−2.34005	−	3.22080i	−0.0931557	−	0.128218i	−0.853051	+	0.521828i	$0.825250\pi$
$632$		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	0.573918	−	0.818913i	$-0.305423\pi$
$643$	14.1211	+	4.58823i	0.556882	+	0.180942i	−0.0170357	+	0.999855i	$0.505423\pi$
$644$		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	$-0.811371\pi$
$661$		−	28.7188i		−	1.11703i	0.829493	−	0.558517i	$-0.188629\pi$
$662$		0			0
$663$	7.33380	+	2.98472i	0.284821	+	0.115917i
$664$		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	$0.184711\pi$
$683$			28.6569i			1.09653i	−0.836306	+	0.548263i	$0.815289\pi$
$684$		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
$689$	−1.73895	+	2.06175i	−0.0662486	+	0.0785463i
$690$		0			0
$691$	28.7986	−	9.35724i	1.09555	−	0.355966i	0.295162	−	0.955447i	$-0.404626\pi$
$691$	28.7986	−	9.35724i	1.09555	−	0.355966i	0.800389	+	0.599481i	$0.204626\pi$
$692$		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	−0.414422	−	0.910085i	$-0.636016\pi$
$709$	−34.2059	−	11.1142i	−1.28463	−	0.417402i	−0.870209	+	0.492683i	$0.836016\pi$
$710$		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
$715$	17.6565	+	4.56627i	0.660314	+	0.170769i
$716$		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	0.479460	−	0.877564i	$-0.340833\pi$
$733$	−13.6267	−	18.7556i	−0.503314	−	0.692753i	−0.982774	+	0.184811i	$0.940833\pi$
$734$		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	−0.339660	−	0.940548i	$-0.610312\pi$
$739$	−1.67488	+	0.544200i	−0.0616113	+	0.0200187i	0.278049	+	0.960567i	$0.410312\pi$
$740$		0			0
$741$	−8.15078	−	6.87464i	−0.299427	−	0.252546i
$742$		0			0
$743$	−0.0357199	−	0.0116061i	−0.00131044	−	0.000425787i	0.308362	−	0.951269i	$-0.400219\pi$
$743$	−0.0357199	−	0.0116061i	−0.00131044	−	0.000425787i	−0.309672	+	0.950843i	$0.600219\pi$
$744$		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	0.400329	−	0.916371i	$-0.368896\pi$
$761$	34.8368	−	11.3192i	1.26283	−	0.410319i	0.862503	+	0.506052i	$0.168896\pi$
$762$		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
$767$	11.7122	−	28.7783i	0.422903	−	1.03912i
$768$		0			0
$769$		−	22.9678i		−	0.828240i	−0.910222	−	0.414120i	$-0.864089\pi$
$769$		−	22.9678i		−	0.828240i	0.910222	−	0.414120i	$-0.135911\pi$
$770$		0			0
$771$	5.25334			0.189195
$772$		0			0
$773$	2.57157	−	3.53946i	0.0924930	−	0.127306i	−0.760263	−	0.649616i	$-0.774930\pi$
$773$	2.57157	−	3.53946i	0.0924930	−	0.127306i	0.852756	+	0.522310i	$0.174930\pi$
$774$		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	0.860738	−	0.509048i	$-0.170002\pi$
$787$	35.2880	+	11.4658i	1.25788	+	0.408710i	0.397141	+	0.917757i	$0.370002\pi$
$788$		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	$-0.531301\pi$
$811$	25.0215	−	34.4391i	0.878624	−	1.20932i	0.976800	−	0.214153i	$-0.0686990\pi$
$812$		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
$819$	12.0408	+	0.872686i	0.420740	+	0.0304941i
$820$		0			0
$821$	10.5835	+	14.5669i	0.369366	+	0.508389i	0.952728	−	0.303823i	$-0.0982633\pi$
$821$	10.5835	+	14.5669i	0.369366	+	0.508389i	−0.583362	+	0.812212i	$0.698263\pi$
$822$		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	−0.162048	−	0.986783i	$-0.551810\pi$
$827$	8.24969	−	2.68049i	0.286870	−	0.0932096i	0.448917	+	0.893573i	$0.351810\pi$
$828$		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	$-0.507803\pi$
$839$	27.0489	−	37.2297i	0.933833	−	1.28531i	0.958345	−	0.285612i	$-0.0921968\pi$
$840$		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
$845$	−13.8446	+	14.1916i	−0.476268	+	0.488206i
$846$		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	0.312905	−	0.949784i	$-0.398698\pi$
$853$	0.227265	+	0.0738428i	0.00778139	+	0.00252833i	−0.305124	+	0.952313i	$0.598698\pi$
$854$		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	0.719527	−	0.694464i	$-0.244359\pi$
$863$	26.2465	+	8.52800i	0.893441	+	0.290297i	0.173914	+	0.984761i	$0.444359\pi$
$864$		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
$871$	4.55274	−	2.82883i	0.154264	−	0.0958512i
$872$		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	−0.920100	−	0.391683i	$-0.871893\pi$
$877$	−7.79628	+	10.7307i	−0.263262	+	0.362348i	0.656839	+	0.754031i	$0.271893\pi$
$878$		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
$897$	0.781903	−	10.7882i	0.0261070	−	0.360209i
$898$		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	0.595706	−	0.803203i	$-0.296872\pi$
$929$	18.4563	+	5.99681i	0.605531	+	0.196749i	0.00982547	+	0.999952i	$0.496872\pi$
$930$		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	0.622826	−	0.782361i	$-0.285985\pi$
$941$	20.4559	+	6.64651i	0.666842	+	0.216670i	0.0440165	+	0.999031i	$0.485985\pi$
$942$		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	$-0.990862\pi$
$947$		−	1.76659i		−	0.0574066i	0.999588	−	0.0287033i	$-0.00913780\pi$
$948$		0			0
$949$	−11.4305	+	28.0860i	−0.371049	+	0.911711i
$950$		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	$-0.762741\pi$
$967$		−	42.1823i		−	1.35649i	0.734836	−	0.678245i	$-0.237259\pi$
$968$		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
$975$	−3.69205	+	4.37741i	−0.118240	+	0.140189i
$976$		0			0
$977$	11.8933	−	3.86438i	0.380501	−	0.123632i	−0.112520	−	0.993649i	$-0.535892\pi$
$977$	11.8933	−	3.86438i	0.380501	−	0.123632i	0.493022	+	0.870017i	$0.335892\pi$
$978$		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	$-0.956686\pi$
$983$	−25.5090	−	35.1102i	−0.813612	−	1.11984i	0.177144	−	0.984185i	$-0.443314\pi$
$984$		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.181.6	yes	56
11.9	even	5	inner	572.2.x.a.493.5	yes	56
13.12	even	2	inner	572.2.x.a.181.5	✓	56
143.64	even	10	inner	572.2.x.a.493.6	yes	56

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

\(f(q)\)	\(=\)	\(q+(-0.480503 - 0.349106i) q^{3} +(1.45044 + 0.471277i) q^{5} +(0.743441 + 1.02326i) q^{7} +(-0.818043 - 2.51768i) q^{9} +O(q^{10})\)	\(q+(-0.480503 - 0.349106i) q^{3} +(1.45044 + 0.471277i) q^{5} +(0.743441 + 1.02326i) q^{7} +(-0.818043 - 2.51768i) q^{9} +(1.57515 - 2.91871i) q^{11} +(1.90289 + 3.06252i) q^{13} +(-0.532415 - 0.732807i) q^{15} +(-1.14257 + 3.51647i) q^{17} +(2.92672 - 4.02829i) q^{19} -0.751218i q^{21} +5.05102 q^{23} +(-2.16341 - 1.57181i) q^{25} +(-1.03647 + 3.18993i) q^{27} +(-0.976091 + 0.709172i) q^{29} +(9.08737 - 2.95267i) q^{31} +(-1.77581 + 0.852554i) q^{33} +(0.596080 + 1.83454i) q^{35} +(4.14494 + 5.70503i) q^{37} +(0.154801 - 2.13586i) q^{39} +(1.39987 - 1.92675i) q^{41} -3.12533 q^{43} -4.03727i q^{45} +(1.79076 - 2.46477i) q^{47} +(1.66876 - 5.13593i) q^{49} +(1.77663 - 1.29080i) q^{51} +(0.231163 + 0.711448i) q^{53} +(3.66019 - 3.49109i) q^{55} +(-2.81260 + 0.913868i) q^{57} +(-5.06515 - 6.97158i) q^{59} +(-1.00338 + 3.08809i) q^{61} +(1.96807 - 2.70882i) q^{63} +(1.31673 + 5.33879i) q^{65} -1.48660i q^{67} +(-2.42703 - 1.76334i) q^{69} +(-7.23642 - 2.35126i) q^{71} +(4.94331 + 6.80389i) q^{73} +(0.490796 + 1.51051i) q^{75} +(4.15764 - 0.558101i) q^{77} +(0.704732 + 2.16894i) q^{79} +(-4.81334 + 3.49710i) q^{81} +(2.92315 + 0.949790i) q^{83} +(-3.31446 + 4.56197i) q^{85} +0.716590 q^{87} +16.0687i q^{89} +(-1.71907 + 4.22395i) q^{91} +(-5.39730 - 1.75369i) q^{93} +(6.14348 - 4.46350i) q^{95} +(-15.0175 + 4.87947i) q^{97} +(-8.63692 - 1.57810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more