LMFDB - Embedded newform 592.2.bc.g.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(33,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("592.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bc (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 296)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	592.49
Dual form			592.2.bc.g.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.714590 + 0.599612i) q^{3} +(-2.46699 + 0.897912i) q^{5} +(-3.18160 + 1.15801i) q^{7} +(-0.369841 - 2.09747i) q^{9} +(0.622664 + 1.07848i) q^{11} +(0.564386 - 3.20079i) q^{13} +(-2.30129 - 0.837600i) q^{15} +(-1.30849 - 7.42080i) q^{17} +(-0.803967 - 0.674609i) q^{19} +(-2.96789 - 1.08022i) q^{21} +(0.113710 - 0.196952i) q^{23} +(1.44959 - 1.21635i) q^{25} +(2.39263 - 4.14416i) q^{27} +(-2.96136 - 5.12922i) q^{29} -7.32779 q^{31} +(-0.201724 + 1.14403i) q^{33} +(6.80919 - 5.71359i) q^{35} +(-1.52734 + 5.88789i) q^{37} +(2.32254 - 1.94884i) q^{39} +(-1.30197 + 7.38387i) q^{41} -3.93777 q^{43} +(2.79574 + 4.84236i) q^{45} +(-3.87141 + 6.70548i) q^{47} +(3.41928 - 2.86912i) q^{49} +(3.51457 - 6.08742i) q^{51} +(7.65285 + 2.78541i) q^{53} +(-2.50449 - 2.10152i) q^{55} +(-0.170003 - 0.964137i) q^{57} +(8.89397 + 3.23714i) q^{59} +(0.453786 - 2.57355i) q^{61} +(3.60557 + 6.24503i) q^{63} +(1.48169 + 8.40310i) q^{65} +(-6.57694 + 2.39381i) q^{67} +(0.199351 - 0.0725578i) q^{69} +(-10.6575 - 8.94266i) q^{71} -12.7621 q^{73} +1.76520 q^{75} +(-3.22996 - 2.71026i) q^{77} +(6.77570 - 2.46615i) q^{79} +(-1.80951 + 0.658608i) q^{81} +(-2.24007 - 12.7041i) q^{83} +(9.89126 + 17.1322i) q^{85} +(0.959387 - 5.44095i) q^{87} +(-2.47099 - 0.899365i) q^{89} +(1.91089 + 10.8372i) q^{91} +(-5.23636 - 4.39383i) q^{93} +(2.58912 + 0.942363i) q^{95} +(-1.63655 + 2.83459i) q^{97} +(2.03180 - 1.70489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{5} + 3 q^{7} + 3 q^{11} + 9 q^{13} - 3 q^{15} - 27 q^{17} - 9 q^{19} + 15 q^{21} + 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{29} + 6 q^{31} - 6 q^{33} - 9 q^{35} + 9 q^{37} + 12 q^{39} + 48 q^{43}+ \cdots + 6 q^{99}+O(q^{100}) $ 30 * q - 6 * q^5 + 3 * q^7 + 3 * q^11 + 9 * q^13 - 3 * q^15 - 27 * q^17 - 9 * q^19 + 15 * q^21 + 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^29 + 6 * q^31 - 6 * q^33 - 9 * q^35 + 9 * q^37 + 12 * q^39 + 48 * q^43 + 51 * q^45 - 6 * q^47 - 21 * q^49 - 12 * q^51 - 15 * q^53 - 21 * q^55 + 51 * q^57 + 36 * q^61 + 36 * q^63 - 6 * q^65 + 27 * q^67 - 15 * q^69 - 27 * q^71 - 114 * q^73 - 84 * q^75 - 105 * q^77 + 18 * q^79 - 12 * q^81 + 30 * q^83 + 21 * q^85 + 99 * q^87 + 39 * q^89 + 72 * q^91 - 3 * q^93 - 66 * q^95 - 12 * q^97 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

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
$3$	0.714590	+	0.599612i	0.412569	+	0.346186i	0.825328	−	0.564654i	$-0.190990\pi$
$3$	0.714590	+	0.599612i	0.412569	+	0.346186i	−0.412759	+	0.910840i	$0.635435\pi$
$4$		0			0
$5$	−2.46699	+	0.897912i	−1.10327	+	0.401558i	−0.828522	−	0.559957i	$-0.810818\pi$
$5$	−2.46699	+	0.897912i	−1.10327	+	0.401558i	−0.274751	+	0.961515i	$0.588595\pi$
$6$		0			0
$7$	−3.18160	+	1.15801i	−1.20253	+	0.437686i	−0.864107	−	0.503308i	$-0.832116\pi$
$7$	−3.18160	+	1.15801i	−1.20253	+	0.437686i	−0.338424	+	0.940994i	$0.609894\pi$
$8$		0			0
$9$	−0.369841	−	2.09747i	−0.123280	−	0.699157i
$10$		0			0
$11$	0.622664	+	1.07848i	0.187740	+	0.325175i	0.944496	−	0.328522i	$-0.106550\pi$
$11$	0.622664	+	1.07848i	0.187740	+	0.325175i	−0.756756	+	0.653697i	$0.773217\pi$
$12$		0			0
$13$	0.564386	−	3.20079i	0.156532	−	0.887740i	−0.800839	−	0.598880i	$-0.795613\pi$
$13$	0.564386	−	3.20079i	0.156532	−	0.887740i	0.957371	−	0.288860i	$-0.0932762\pi$
$14$		0			0
$15$	−2.30129	−	0.837600i	−0.594190	−	0.216267i
$16$		0			0
$17$	−1.30849	−	7.42080i	−0.317355	−	1.79981i	−0.558700	−	0.829370i	$-0.688700\pi$
$17$	−1.30849	−	7.42080i	−0.317355	−	1.79981i	0.241345	−	0.970439i	$-0.422411\pi$
$18$		0			0
$19$	−0.803967	−	0.674609i	−0.184443	−	0.154766i	0.545891	−	0.837856i	$-0.316191\pi$
$19$	−0.803967	−	0.674609i	−0.184443	−	0.154766i	−0.730334	+	0.683090i	$0.760636\pi$
$20$		0			0
$21$	−2.96789	−	1.08022i	−0.647647	−	0.235724i
$22$		0			0
$23$	0.113710	−	0.196952i	0.0237102	−	0.0410673i	−0.853927	−	0.520393i	$-0.825785\pi$
$23$	0.113710	−	0.196952i	0.0237102	−	0.0410673i	0.877637	+	0.479326i	$0.159119\pi$
$24$		0			0
$25$	1.44959	−	1.21635i	0.289917	−	0.243269i
$26$		0			0
$27$	2.39263	−	4.14416i	0.460462	−	0.797543i
$28$		0			0
$29$	−2.96136	−	5.12922i	−0.549910	−	0.952472i	−0.998280	−	0.0586242i	$-0.981329\pi$
$29$	−2.96136	−	5.12922i	−0.549910	−	0.952472i	0.448370	−	0.893848i	$-0.352005\pi$
$30$		0			0
$31$	−7.32779			−1.31611			−0.658055	−	0.752970i	$-0.728620\pi$
$31$	−7.32779			−1.31611			−0.658055	+	0.752970i	$0.728620\pi$
$32$		0			0
$33$	−0.201724	+	1.14403i	−0.0351156	+	0.199150i
$34$		0			0
$35$	6.80919	−	5.71359i	1.15096	−	0.965773i
$36$		0			0
$37$	−1.52734	+	5.88789i	−0.251093	+	0.967963i
$37$	−1.52734	+	5.88789i	−0.251093	+	0.967963i
$38$		0			0
$39$	2.32254	−	1.94884i	0.371904	−	0.312064i
$40$		0			0
$41$	−1.30197	+	7.38387i	−0.203334	+	1.15317i	0.696705	+	0.717358i	$0.254649\pi$
$41$	−1.30197	+	7.38387i	−0.203334	+	1.15317i	−0.900039	+	0.435809i	$0.856462\pi$
$42$		0			0
$43$	−3.93777			−0.600505			−0.300253	−	0.953860i	$-0.597071\pi$
$43$	−3.93777			−0.600505			−0.300253	+	0.953860i	$0.597071\pi$
$44$		0			0
$45$	2.79574	+	4.84236i	0.416764	+	0.721856i
$46$		0			0
$47$	−3.87141	+	6.70548i	−0.564703	+	0.978095i	0.432374	+	0.901694i	$0.357676\pi$
$47$	−3.87141	+	6.70548i	−0.564703	+	0.978095i	−0.997077	+	0.0764005i	$0.975657\pi$
$48$		0			0
$49$	3.41928	−	2.86912i	0.488468	−	0.409874i
$50$		0			0
$51$	3.51457	−	6.08742i	0.492138	−	0.852409i
$52$		0			0
$53$	7.65285	+	2.78541i	1.05120	+	0.382606i	0.809116	−	0.587650i	$-0.199947\pi$
$53$	7.65285	+	2.78541i	1.05120	+	0.382606i	0.242085	+	0.970255i	$0.422169\pi$
$54$		0			0
$55$	−2.50449	−	2.10152i	−0.337706	−	0.283369i
$56$		0			0
$57$	−0.170003	−	0.964137i	−0.0225175	−	0.127703i
$58$		0			0
$59$	8.89397	+	3.23714i	1.15790	+	0.421440i	0.848345	−	0.529443i	$-0.177599\pi$
$59$	8.89397	+	3.23714i	1.15790	+	0.421440i	0.309551	+	0.950883i	$0.399821\pi$
$60$		0			0
$61$	0.453786	−	2.57355i	0.0581014	−	0.329509i	−0.941878	−	0.335955i	$-0.890941\pi$
$61$	0.453786	−	2.57355i	0.0581014	−	0.329509i	0.999979	+	0.00644632i	$0.00205194\pi$
$62$		0			0
$63$	3.60557	+	6.24503i	0.454259	+	0.786800i
$64$		0			0
$65$	1.48169	+	8.40310i	0.183781	+	1.04228i
$66$		0			0
$67$	−6.57694	+	2.39381i	−0.803501	+	0.292450i	−0.710936	−	0.703256i	$-0.751729\pi$
$67$	−6.57694	+	2.39381i	−0.803501	+	0.292450i	−0.0925645	+	0.995707i	$0.529506\pi$
$68$		0			0
$69$	0.199351	−	0.0725578i	0.0239990	−	0.00873493i
$70$		0			0
$71$	−10.6575	−	8.94266i	−1.26481	−	1.06130i	−0.995153	−	0.0983415i	$-0.968646\pi$
$71$	−10.6575	−	8.94266i	−1.26481	−	1.06130i	−0.269654	−	0.962957i	$-0.586909\pi$
$72$		0			0
$73$	−12.7621			−1.49369			−0.746843	−	0.665000i	$-0.768431\pi$
$73$	−12.7621			−1.49369			−0.746843	+	0.665000i	$0.768431\pi$
$74$		0			0
$75$	1.76520			0.203827
$76$		0			0
$77$	−3.22996	−	2.71026i	−0.368088	−	0.308863i
$78$		0			0
$79$	6.77570	−	2.46615i	0.762326	−	0.277464i	0.0685433	−	0.997648i	$-0.478165\pi$
$79$	6.77570	−	2.46615i	0.762326	−	0.277464i	0.693783	+	0.720184i	$0.255943\pi$
$80$		0			0
$81$	−1.80951	+	0.658608i	−0.201057	+	0.0731787i
$82$		0			0
$83$	−2.24007	−	12.7041i	−0.245880	−	1.39445i	−0.818441	−	0.574591i	$-0.805161\pi$
$83$	−2.24007	−	12.7041i	−0.245880	−	1.39445i	0.572561	−	0.819862i	$-0.305950\pi$
$84$		0			0
$85$	9.89126	+	17.1322i	1.07286	+	1.85824i
$86$		0			0
$87$	0.959387	−	5.44095i	0.102857	−	0.583332i
$88$		0			0
$89$	−2.47099	−	0.899365i	−0.261924	−	0.0953325i	0.207720	−	0.978188i	$-0.433396\pi$
$89$	−2.47099	−	0.899365i	−0.261924	−	0.0953325i	−0.469644	+	0.882856i	$0.655618\pi$
$90$		0			0
$91$	1.91089	+	10.8372i	0.200316	+	1.13605i
$92$		0			0
$93$	−5.23636	−	4.39383i	−0.542985	−	0.455619i
$94$		0			0
$95$	2.58912	+	0.942363i	0.265638	+	0.0966844i
$96$		0			0
$97$	−1.63655	+	2.83459i	−0.166167	+	0.287809i	−0.937069	−	0.349144i	$-0.886472\pi$
$97$	−1.63655	+	2.83459i	−0.166167	+	0.287809i	0.770902	+	0.636953i	$0.219806\pi$
$98$		0			0
$99$	2.03180	−	1.70489i	0.204204	−	0.171347i
$100$		0			0
$101$	2.31341	−	4.00694i	0.230193	−	0.398706i	−0.727672	−	0.685925i	$-0.759398\pi$
$101$	2.31341	−	4.00694i	0.230193	−	0.398706i	0.957865	+	0.287220i	$0.0927310\pi$
$102$		0			0
$103$	5.85346	+	10.1385i	0.576759	+	0.998976i	0.995848	+	0.0910308i	$0.0290162\pi$
$103$	5.85346	+	10.1385i	0.576759	+	0.998976i	−0.419089	+	0.907945i	$0.637651\pi$
$104$		0			0
$105$	8.29172			0.809189
$106$		0			0
$107$	2.25971	−	12.8155i	0.218455	−	1.23892i	−0.656355	−	0.754452i	$-0.727903\pi$
$107$	2.25971	−	12.8155i	0.218455	−	1.23892i	0.874810	−	0.484467i	$-0.160986\pi$
$108$		0			0
$109$	−0.104826	+	0.0879597i	−0.0100405	+	0.00842501i	−0.647794	−	0.761815i	$-0.724308\pi$
$109$	−0.104826	+	0.0879597i	−0.0100405	+	0.00842501i	0.637754	+	0.770240i	$0.279864\pi$
$110$		0			0
$111$	−4.62187	+	3.29162i	−0.438688	+	0.312426i
$112$		0			0
$113$	5.70275	−	4.78518i	0.536470	−	0.450152i	−0.333859	−	0.942623i	$-0.608351\pi$
$113$	5.70275	−	4.78518i	0.536470	−	0.450152i	0.870329	+	0.492471i	$0.163906\pi$
$114$		0			0
$115$	−0.103677	+	0.587981i	−0.00966792	+	0.0548295i
$116$		0			0
$117$	−6.92230			−0.639966
$118$		0			0
$119$	12.7564	+	22.0948i	1.16938	+	2.02543i
$120$		0			0
$121$	4.72458	−	8.18321i	0.429507	−	0.743928i
$122$		0			0
$123$	−5.35783	+	4.49576i	−0.483100	+	0.405369i
$124$		0			0
$125$	4.07935	−	7.06564i	0.364868	−	0.631970i
$126$		0			0
$127$	−19.1828	−	6.98197i	−1.70220	−	0.619550i	−0.706127	−	0.708085i	$-0.749559\pi$
$127$	−19.1828	−	6.98197i	−1.70220	−	0.619550i	−0.996073	+	0.0885354i	$0.971781\pi$
$128$		0			0
$129$	−2.81389	−	2.36114i	−0.247750	−	0.207887i
$130$		0			0
$131$	1.65466	+	9.38404i	0.144568	+	0.819887i	0.967713	+	0.252055i	$0.0811065\pi$
$131$	1.65466	+	9.38404i	0.144568	+	0.819887i	−0.823145	+	0.567832i	$0.807782\pi$
$132$		0			0
$133$	3.33910	+	1.21533i	0.289537	+	0.105383i
$134$		0			0
$135$	−2.18151	+	12.3720i	−0.187755	+	1.06481i
$136$		0			0
$137$	4.74114	+	8.21190i	0.405063	+	0.701590i	0.994329	−	0.106349i	$-0.0339162\pi$
$137$	4.74114	+	8.21190i	0.405063	+	0.701590i	−0.589266	+	0.807939i	$0.700583\pi$
$138$		0			0
$139$	3.23003	+	18.3184i	0.273968	+	1.55375i	0.742222	+	0.670154i	$0.233772\pi$
$139$	3.23003	+	18.3184i	0.273968	+	1.55375i	−0.468255	+	0.883593i	$0.655117\pi$
$140$		0			0
$141$	−6.78716	+	2.47032i	−0.571582	+	0.208039i
$142$		0			0
$143$	3.80343	−	1.38433i	0.318059	−	0.115764i
$144$		0			0
$145$	11.9112	+	9.99471i	0.989174	+	0.830016i
$146$		0			0
$147$	4.16374			0.343419
$148$		0			0
$149$	8.02290			0.657261			0.328631	−	0.944458i	$-0.393413\pi$
$149$	8.02290			0.657261			0.328631	+	0.944458i	$0.393413\pi$
$150$		0			0
$151$	2.04800	+	1.71848i	0.166664	+	0.139848i	0.722305	−	0.691575i	$-0.243083\pi$
$151$	2.04800	+	1.71848i	0.166664	+	0.139848i	−0.555641	+	0.831422i	$0.687527\pi$
$152$		0			0
$153$	−15.0810	+	5.48903i	−1.21922	+	0.443762i
$154$		0			0
$155$	18.0776	−	6.57971i	1.45203	−	0.528495i
$156$		0			0
$157$	−1.40926	−	7.99229i	−0.112471	−	0.637854i	−0.987971	−	0.154637i	$-0.950579\pi$
$157$	−1.40926	−	7.99229i	−0.112471	−	0.637854i	0.875501	−	0.483217i	$-0.160532\pi$
$158$		0			0
$159$	3.79848	+	6.57917i	0.301239	+	0.521762i
$160$		0			0
$161$	−0.133709	+	0.758299i	−0.0105377	+	0.0597623i
$162$		0			0
$163$	−8.54919	−	3.11165i	−0.669624	−	0.243723i	−0.0152382	−	0.999884i	$-0.504851\pi$
$163$	−8.54919	−	3.11165i	−0.669624	−	0.243723i	−0.654386	+	0.756161i	$0.727073\pi$
$164$		0			0
$165$	−0.529589	−	3.00345i	−0.0412284	−	0.233818i
$166$		0			0
$167$	−15.5178	−	13.0210i	−1.20081	−	1.00760i	−0.999607	−	0.0280460i	$-0.991071\pi$
$167$	−15.5178	−	13.0210i	−1.20081	−	1.00760i	−0.201200	−	0.979550i	$-0.564484\pi$
$168$		0			0
$169$	2.28947	+	0.833299i	0.176113	+	0.0640999i
$170$		0			0
$171$	−1.11763	+	1.93579i	−0.0854674	+	0.148034i
$172$		0			0
$173$	14.4874	−	12.1563i	1.10145	−	0.924229i	0.103931	−	0.994584i	$-0.466858\pi$
$173$	14.4874	−	12.1563i	1.10145	−	0.924229i	0.997522	+	0.0703555i	$0.0224134\pi$
$174$		0			0
$175$	−3.20346	+	5.54856i	−0.242159	+	0.419432i
$176$		0			0
$177$	4.41451	+	7.64616i	0.331815	+	0.574721i
$178$		0			0
$179$	13.4598			1.00604			0.503018	−	0.864276i	$-0.332223\pi$
$179$	13.4598			1.00604			0.503018	+	0.864276i	$0.332223\pi$
$180$		0			0
$181$	−2.34928	+	13.3234i	−0.174621	+	0.990323i	0.763960	+	0.645263i	$0.223252\pi$
$181$	−2.34928	+	13.3234i	−0.174621	+	0.990323i	−0.938581	+	0.345060i	$0.887859\pi$
$182$		0			0
$183$	1.86740	−	1.56694i	0.138042	−	0.115831i
$184$		0			0
$185$	−1.51888	−	15.8968i	−0.111670	−	1.16876i
$186$		0			0
$187$	7.18848	−	6.03185i	0.525673	−	0.441092i
$188$		0			0
$189$	−2.81343	+	15.9557i	−0.204647	+	1.16061i
$190$		0			0
$191$	2.36093			0.170831			0.0854155	−	0.996345i	$-0.472778\pi$
$191$	2.36093			0.170831			0.0854155	+	0.996345i	$0.472778\pi$
$192$		0			0
$193$	4.63768	+	8.03270i	0.333827	+	0.578206i	0.983259	−	0.182214i	$-0.0583264\pi$
$193$	4.63768	+	8.03270i	0.333827	+	0.578206i	−0.649431	+	0.760420i	$0.724993\pi$
$194$		0			0
$195$	−3.97980	+	6.89321i	−0.284999	+	0.493633i
$196$		0			0
$197$	−1.05645	+	0.886469i	−0.0752691	+	0.0631583i	−0.679646	−	0.733540i	$-0.737867\pi$
$197$	−1.05645	+	0.886469i	−0.0752691	+	0.0631583i	0.604377	+	0.796699i	$0.293422\pi$
$198$		0			0
$199$	−1.97499	+	3.42079i	−0.140003	+	0.242493i	−0.927498	−	0.373829i	$-0.878045\pi$
$199$	−1.97499	+	3.42079i	−0.140003	+	0.242493i	0.787494	+	0.616322i	$0.211378\pi$
$200$		0			0
$201$	−6.13517	−	2.23302i	−0.432742	−	0.157505i
$202$		0			0
$203$	15.3615	+	12.8898i	1.07817	+	0.904690i
$204$		0			0
$205$	−3.41810	−	19.3850i	−0.238730	−	1.35391i
$206$		0			0
$207$	−0.455155	−	0.165663i	−0.0316355	−	0.0115144i
$208$		0			0
$209$	0.226954	−	1.28712i	0.0156987	−	0.0890320i
$210$		0			0
$211$	10.4164	+	18.0417i	0.717095	+	1.24204i	0.962146	+	0.272534i	$0.0878619\pi$
$211$	10.4164	+	18.0417i	0.717095	+	1.24204i	−0.245051	+	0.969510i	$0.578805\pi$
$212$		0			0
$213$	−2.25358	−	12.7807i	−0.154413	−	0.875717i
$214$		0			0
$215$	9.71446	−	3.53578i	0.662521	−	0.241138i
$216$		0			0
$217$	23.3141	−	8.48563i	1.58266	−	0.576042i
$218$		0			0
$219$	−9.11964	−	7.65229i	−0.616248	−	0.517094i
$220$		0			0
$221$	−24.4909			−1.64744
$222$		0			0
$223$	−24.9633			−1.67166			−0.835832	−	0.548985i	$-0.815014\pi$
$223$	−24.9633			−1.67166			−0.835832	+	0.548985i	$0.815014\pi$
$224$		0			0
$225$	−3.08737	−	2.59061i	−0.205824	−	0.172707i
$226$		0			0
$227$	−0.996856	+	0.362826i	−0.0661637	+	0.0240816i	−0.374890	−	0.927069i	$-0.622320\pi$
$227$	−0.996856	+	0.362826i	−0.0661637	+	0.0240816i	0.308726	+	0.951151i	$0.400097\pi$
$228$		0			0
$229$	5.99574	−	2.18227i	0.396210	−	0.144209i	−0.136228	−	0.990677i	$-0.543498\pi$
$229$	5.99574	−	2.18227i	0.396210	−	0.144209i	0.532438	+	0.846469i	$0.321276\pi$
$230$		0			0
$231$	−0.682993	−	3.87345i	−0.0449376	−	0.254854i
$232$		0			0
$233$	4.79443	+	8.30419i	0.314093	+	0.544026i	0.979244	−	0.202683i	$-0.0649662\pi$
$233$	4.79443	+	8.30419i	0.314093	+	0.544026i	−0.665151	+	0.746709i	$0.731633\pi$
$234$		0			0
$235$	3.52981	−	20.0186i	0.230260	−	1.30587i
$236$		0			0
$237$	6.32059	+	2.30051i	0.410566	+	0.149434i
$238$		0			0
$239$	−2.28199	−	12.9418i	−0.147610	−	0.837138i	−0.965234	−	0.261386i	$-0.915821\pi$
$239$	−2.28199	−	12.9418i	−0.147610	−	0.837138i	0.817624	−	0.575752i	$-0.195291\pi$
$240$		0			0
$241$	−3.56189	−	2.98878i	−0.229441	−	0.192524i	0.520818	−	0.853668i	$-0.325627\pi$
$241$	−3.56189	−	2.98878i	−0.229441	−	0.192524i	−0.750259	+	0.661143i	$0.770071\pi$
$242$		0			0
$243$	−15.1780	−	5.52434i	−0.973668	−	0.354386i
$244$		0			0
$245$	−5.85912	+	10.1483i	−0.374326	+	0.648351i
$246$		0			0
$247$	−2.61303	+	2.19259i	−0.166263	+	0.139511i
$248$		0			0
$249$	6.01678	−	10.4214i	0.381298	−	0.660427i
$250$		0			0
$251$	−8.89316	−	15.4034i	−0.561331	−	0.972254i	−0.997381	−	0.0723317i	$-0.976956\pi$
$251$	−8.89316	−	15.4034i	−0.561331	−	0.972254i	0.436049	−	0.899923i	$-0.356377\pi$
$252$		0			0
$253$	0.283213			0.0178054
$254$		0			0
$255$	−3.20446	+	18.1734i	−0.200671	+	1.13806i
$256$		0			0
$257$	−13.3966	+	11.2411i	−0.835660	+	0.701202i	−0.956583	−	0.291460i	$-0.905859\pi$
$257$	−13.3966	+	11.2411i	−0.835660	+	0.701202i	0.120923	+	0.992662i	$0.461414\pi$
$258$		0			0
$259$	−1.95885	−	20.5016i	−0.121717	−	1.27391i
$260$		0			0
$261$	−9.66316	+	8.10835i	−0.598134	+	0.501894i
$262$		0			0
$263$	1.37219	−	7.78206i	0.0846127	−	0.479862i	−0.912827	−	0.408347i	$-0.866105\pi$
$263$	1.37219	−	7.78206i	0.0846127	−	0.479862i	0.997439	−	0.0715154i	$-0.0227835\pi$
$264$		0			0
$265$	−21.3806			−1.31340
$266$		0			0
$267$	−1.22647	−	2.12431i	−0.0750588	−	0.130006i
$268$		0			0
$269$	3.22251	−	5.58155i	0.196480	−	0.340313i	−0.750905	−	0.660410i	$-0.770382\pi$
$269$	3.22251	−	5.58155i	0.196480	−	0.340313i	0.947385	+	0.320097i	$0.103716\pi$
$270$		0			0
$271$	13.8349	−	11.6089i	0.840410	−	0.705187i	−0.117246	−	0.993103i	$-0.537407\pi$
$271$	13.8349	−	11.6089i	0.840410	−	0.705187i	0.957656	+	0.287915i	$0.0929622\pi$
$272$		0			0
$273$	−5.13261	+	8.88994i	−0.310640	+	0.538044i
$274$		0			0
$275$	2.21442	+	0.805982i	0.133534	+	0.0486025i
$276$		0			0
$277$	20.4091	+	17.1252i	1.22626	+	1.02896i	0.998473	+	0.0552461i	$0.0175943\pi$
$277$	20.4091	+	17.1252i	1.22626	+	1.02896i	0.227790	+	0.973710i	$0.426850\pi$
$278$		0			0
$279$	2.71011	+	15.3698i	0.162250	+	0.920166i
$280$		0			0
$281$	3.47714	+	1.26558i	0.207429	+	0.0754979i	0.443645	−	0.896203i	$-0.353685\pi$
$281$	3.47714	+	1.26558i	0.207429	+	0.0754979i	−0.236216	+	0.971701i	$0.575907\pi$
$282$		0			0
$283$	3.63239	−	20.6003i	0.215923	−	1.22456i	−0.663375	−	0.748287i	$-0.730876\pi$
$283$	3.63239	−	20.6003i	0.215923	−	1.22456i	0.879298	−	0.476272i	$-0.158012\pi$
$284$		0			0
$285$	1.28511	+	2.22587i	0.0761232	+	0.131849i
$286$		0			0
$287$	−4.40821	−	25.0002i	−0.260208	−	1.47572i
$288$		0			0
$289$	−37.3814	+	13.6057i	−2.19891	+	0.800336i
$290$		0			0
$291$	−2.86912	+	1.04427i	−0.168191	+	0.0612164i
$292$		0			0
$293$	−19.2124	−	16.1211i	−1.12240	−	0.941805i	−0.123676	−	0.992323i	$-0.539468\pi$
$293$	−19.2124	−	16.1211i	−1.12240	−	0.941805i	−0.998723	+	0.0505175i	$0.983913\pi$
$294$		0			0
$295$	−24.8480			−1.44671
$296$		0			0
$297$	5.95921			0.345789
$298$		0			0
$299$	−0.566225	−	0.475120i	−0.0327457	−	0.0274769i
$300$		0			0
$301$	12.5284	−	4.55997i	0.722126	−	0.262832i
$302$		0			0
$303$	4.05575	−	1.47617i	0.232997	−	0.0848039i
$304$		0			0
$305$	1.19133	+	6.75639i	0.0682155	+	0.386870i
$306$		0			0
$307$	−10.9498	−	18.9656i	−0.624939	−	1.08243i	−0.988553	−	0.150876i	$-0.951791\pi$
$307$	−10.9498	−	18.9656i	−0.624939	−	1.08243i	0.363614	−	0.931550i	$-0.381543\pi$
$308$		0			0
$309$	−1.89634	+	10.7547i	−0.107879	+	0.611812i
$310$		0			0
$311$	−0.490564	−	0.178551i	−0.0278173	−	0.0101247i	0.328074	−	0.944652i	$-0.393600\pi$
$311$	−0.490564	−	0.178551i	−0.0278173	−	0.0101247i	−0.355891	+	0.934527i	$0.615823\pi$
$312$		0			0
$313$	−4.67797	−	26.5301i	−0.264415	−	1.49957i	−0.770696	−	0.637202i	$-0.780092\pi$
$313$	−4.67797	−	26.5301i	−0.264415	−	1.49957i	0.506282	−	0.862368i	$-0.331020\pi$
$314$		0			0
$315$	−14.5024	−	12.1690i	−0.817118	−	0.685643i
$316$		0			0
$317$	12.9323	+	4.70698i	0.726352	+	0.264370i	0.678620	−	0.734490i	$-0.262578\pi$
$317$	12.9323	+	4.70698i	0.726352	+	0.264370i	0.0477320	+	0.998860i	$0.484801\pi$
$318$		0			0
$319$	3.68786	−	6.38756i	0.206480	−	0.357635i
$320$		0			0
$321$	9.29909	−	7.80286i	0.519024	−	0.435513i
$322$		0			0
$323$	−3.95416	+	6.84880i	−0.220015	+	0.381077i
$324$		0			0
$325$	−3.07515	−	5.32631i	−0.170578	−	0.295451i
$326$		0			0
$327$	−0.127649			−0.00705903
$328$		0			0
$329$	4.55228	−	25.8173i	0.250975	−	1.42335i
$330$		0			0
$331$	−15.5503	+	13.0482i	−0.854719	+	0.717194i	−0.960824	−	0.277161i	$-0.910607\pi$
$331$	−15.5503	+	13.0482i	−0.854719	+	0.717194i	0.106105	+	0.994355i	$0.466162\pi$
$332$		0			0
$333$	12.9145	+	1.02596i	0.707713	+	0.0562224i
$334$		0			0
$335$	14.0758	−	11.8110i	0.769045	−	0.645305i
$336$		0			0
$337$	−5.77178	+	32.7334i	−0.314409	+	1.78310i	0.261107	+	0.965310i	$0.415913\pi$
$337$	−5.77178	+	32.7334i	−0.314409	+	1.78310i	−0.575516	+	0.817791i	$0.695199\pi$
$338$		0			0
$339$	6.94438			0.377167
$340$		0			0
$341$	−4.56275	−	7.90291i	−0.247087	−	0.427966i
$342$		0			0
$343$	4.29394	−	7.43732i	0.231851	−	0.401577i
$344$		0			0
$345$	−0.426647	+	0.357999i	−0.0229699	+	0.0192740i
$346$		0			0
$347$	−11.2032	+	19.4045i	−0.601418	+	1.04169i	0.391188	+	0.920311i	$0.372064\pi$
$347$	−11.2032	+	19.4045i	−0.601418	+	1.04169i	−0.992607	+	0.121377i	$0.961269\pi$
$348$		0			0
$349$	−28.6222	−	10.4176i	−1.53211	−	0.557644i	−0.567975	−	0.823046i	$-0.692273\pi$
$349$	−28.6222	−	10.4176i	−1.53211	−	0.557644i	−0.964138	+	0.265402i	$0.914495\pi$
$350$		0			0
$351$	−11.9142	−	9.99721i	−0.635934	−	0.533612i
$352$		0			0
$353$	−3.47525	−	19.7091i	−0.184969	−	1.04901i	−0.925995	−	0.377536i	$-0.876772\pi$
$353$	−3.47525	−	19.7091i	−0.184969	−	1.04901i	0.741026	−	0.671476i	$-0.234340\pi$
$354$		0			0
$355$	34.3216	+	12.4920i	1.82160	+	0.663008i
$356$		0			0
$357$	−4.13268	+	23.4376i	−0.218725	+	1.24045i
$358$		0			0
$359$	12.6779	+	21.9587i	0.669113	+	1.15894i	0.978152	+	0.207889i	$0.0666592\pi$
$359$	12.6779	+	21.9587i	0.669113	+	1.15894i	−0.309039	+	0.951049i	$0.600007\pi$
$360$		0			0
$361$	−3.10805	−	17.6266i	−0.163582	−	0.927717i
$362$		0			0
$363$	8.28289	−	3.01473i	0.434739	−	0.158232i
$364$		0			0
$365$	31.4839	−	11.4592i	1.64794	−	0.599802i
$366$		0			0
$367$	3.13156	+	2.62769i	0.163466	+	0.137164i	0.720852	−	0.693090i	$-0.243751\pi$
$367$	3.13156	+	2.62769i	0.163466	+	0.137164i	−0.557385	+	0.830254i	$0.688195\pi$
$368$		0			0
$369$	15.9690			0.831311
$370$		0			0
$371$	−27.5738			−1.43156
$372$		0			0
$373$	−7.03559	−	5.90356i	−0.364289	−	0.305675i	0.442208	−	0.896912i	$-0.354195\pi$
$373$	−7.03559	−	5.90356i	−0.364289	−	0.305675i	−0.806498	+	0.591237i	$0.798640\pi$
$374$		0			0
$375$	7.15171	−	2.60301i	0.369313	−	0.134419i
$376$		0			0
$377$	−18.0889	+	6.58383i	−0.931626	+	0.339084i
$378$		0			0
$379$	0.949204	+	5.38320i	0.0487573	+	0.276516i	0.999433	−	0.0336702i	$-0.0107196\pi$
$379$	0.949204	+	5.38320i	0.0487573	+	0.276516i	−0.950676	+	0.310187i	$0.899608\pi$
$380$		0			0
$381$	−9.52137	−	16.4915i	−0.487795	−	0.844885i
$382$		0			0
$383$	5.04396	−	28.6057i	0.257734	−	1.46168i	−0.531222	−	0.847233i	$-0.678267\pi$
$383$	5.04396	−	28.6057i	0.257734	−	1.46168i	0.788956	−	0.614450i	$-0.210622\pi$
$384$		0			0
$385$	10.4019	+	3.78597i	0.530128	+	0.192951i
$386$		0			0
$387$	1.45635	+	8.25936i	0.0740304	+	0.419847i
$388$		0			0
$389$	15.6096	+	13.0980i	0.791438	+	0.664095i	0.946101	−	0.323872i	$-0.104985\pi$
$389$	15.6096	+	13.0980i	0.791438	+	0.664095i	−0.154663	+	0.987967i	$0.549429\pi$
$390$		0			0
$391$	−1.61033	−	0.586112i	−0.0814379	−	0.0296410i
$392$		0			0
$393$	−4.44438	+	7.69789i	−0.224189	+	0.388307i
$394$		0			0
$395$	−14.5012	+	12.1680i	−0.729636	+	0.612237i
$396$		0			0
$397$	−3.84463	+	6.65910i	−0.192957	+	0.334211i	−0.946229	−	0.323498i	$-0.895141\pi$
$397$	−3.84463	+	6.65910i	−0.192957	+	0.334211i	0.753272	+	0.657709i	$0.228474\pi$
$398$		0			0
$399$	1.65736	+	2.87063i	0.0829718	+	0.143711i
$400$		0			0
$401$	14.7251			0.735338			0.367669	−	0.929957i	$-0.380156\pi$
$401$	14.7251			0.735338			0.367669	+	0.929957i	$0.380156\pi$
$402$		0			0
$403$	−4.13570	+	23.4547i	−0.206014	+	1.16836i
$404$		0			0
$405$	3.87268	−	3.24956i	0.192435	−	0.161472i
$406$		0			0
$407$	−7.30102	+	2.01896i	−0.361898	+	0.100076i
$408$		0			0
$409$	2.63421	−	2.21037i	0.130253	−	0.109296i	−0.575334	−	0.817919i	$-0.695128\pi$
$409$	2.63421	−	2.21037i	0.130253	−	0.109296i	0.705587	+	0.708623i	$0.250683\pi$
$410$		0			0
$411$	−1.53598	+	8.71099i	−0.0757644	+	0.429681i
$412$		0			0
$413$	−32.0457			−1.57686
$414$		0			0
$415$	16.9334	+	29.3295i	0.831226	+	1.43973i
$416$		0			0
$417$	−8.67579	+	15.0269i	−0.424855	+	0.735871i
$418$		0			0
$419$	−23.9931	+	20.1326i	−1.17214	+	0.983541i	−0.999999	−	0.00153152i	$-0.999513\pi$
$419$	−23.9931	+	20.1326i	−1.17214	+	0.983541i	−0.172140	+	0.985073i	$0.555068\pi$
$420$		0			0
$421$	−0.199850	+	0.346151i	−0.00974011	+	0.0168704i	−0.870854	−	0.491541i	$-0.836434\pi$
$421$	−0.199850	+	0.346151i	−0.00974011	+	0.0168704i	0.861114	+	0.508411i	$0.169767\pi$
$422$		0			0
$423$	15.4963	+	5.64021i	0.753458	+	0.274236i
$424$		0			0
$425$	−10.9230	−	9.16552i	−0.529845	−	0.444593i
$426$		0			0
$427$	1.53642	+	8.71349i	0.0743527	+	0.421675i
$428$		0			0
$429$	3.54795	+	1.29135i	0.171297	+	0.0623470i
$430$		0			0
$431$	0.839936	−	4.76352i	0.0404583	−	0.229450i	−0.957873	−	0.287191i	$-0.907279\pi$
$431$	0.839936	−	4.76352i	0.0404583	−	0.229450i	0.998332	+	0.0577406i	$0.0183896\pi$
$432$		0			0
$433$	−4.89095	−	8.47137i	−0.235044	−	0.407108i	0.724241	−	0.689546i	$-0.242190\pi$
$433$	−4.89095	−	8.47137i	−0.235044	−	0.407108i	−0.959285	+	0.282438i	$0.908857\pi$
$434$		0			0
$435$	2.51870	+	14.2842i	0.120762	+	0.684877i
$436$		0			0
$437$	−0.224285	+	0.0816330i	−0.0107290	+	0.00390504i
$438$		0			0
$439$	37.0174	−	13.4732i	1.76674	−	0.643042i	0.766744	−	0.641952i	$-0.221875\pi$
$439$	37.0174	−	13.4732i	1.76674	−	0.643042i	0.999999	−	0.00108969i	$-0.000346859\pi$
$440$		0			0
$441$	−7.28247	−	6.11072i	−0.346784	−	0.290987i
$442$		0			0
$443$	15.2550			0.724788			0.362394	−	0.932025i	$-0.381960\pi$
$443$	15.2550			0.724788			0.362394	+	0.932025i	$0.381960\pi$
$444$		0			0
$445$	6.90345			0.327255
$446$		0			0
$447$	5.73308	+	4.81063i	0.271165	+	0.227535i
$448$		0			0
$449$	30.8222	−	11.2184i	1.45459	−	0.529428i	0.510721	−	0.859746i	$-0.329378\pi$
$449$	30.8222	−	11.2184i	1.45459	−	0.529428i	0.943869	+	0.330319i	$0.107156\pi$
$450$		0			0
$451$	−8.77408	+	3.19350i	−0.413155	+	0.150376i
$452$		0			0
$453$	0.433062	+	2.45601i	0.0203470	+	0.115394i
$454$		0			0
$455$	−14.4450	−	25.0195i	−0.677192	−	1.17293i
$456$		0			0
$457$	6.46679	−	36.6750i	0.302504	−	1.71558i	−0.332525	−	0.943095i	$-0.607900\pi$
$457$	6.46679	−	36.6750i	0.302504	−	1.71558i	0.635028	−	0.772489i	$-0.280988\pi$
$458$		0			0
$459$	−33.8837	−	12.3327i	−1.58156	−	0.575639i
$460$		0			0
$461$	4.75723	+	26.9796i	0.221566	+	1.25657i	0.869141	+	0.494564i	$0.164672\pi$
$461$	4.75723	+	26.9796i	0.221566	+	1.25657i	−0.647575	+	0.762002i	$0.724217\pi$
$462$		0			0
$463$	−0.676688	−	0.567808i	−0.0314483	−	0.0263883i	0.626928	−	0.779077i	$-0.284312\pi$
$463$	−0.676688	−	0.567808i	−0.0314483	−	0.0263883i	−0.658376	+	0.752689i	$0.728756\pi$
$464$		0			0
$465$	16.8633	+	6.13775i	0.782019	+	0.284632i
$466$		0			0
$467$	1.83634	−	3.18064i	0.0849758	−	0.147182i	−0.820405	−	0.571783i	$-0.806252\pi$
$467$	1.83634	−	3.18064i	0.0849758	−	0.147182i	0.905381	+	0.424600i	$0.139585\pi$
$468$		0			0
$469$	18.1531	−	15.2323i	0.838234	−	0.703362i
$470$		0			0
$471$	3.78523	−	6.55621i	0.174414	−	0.302094i
$472$		0			0
$473$	−2.45191	−	4.24683i	−0.112739	−	0.195269i
$474$		0			0
$475$	−1.98598			−0.0911229
$476$		0			0
$477$	3.01198	−	17.0818i	0.137909	−	0.782121i
$478$		0			0
$479$	18.2228	−	15.2908i	0.832623	−	0.698654i	−0.123268	−	0.992373i	$-0.539338\pi$
$479$	18.2228	−	15.2908i	0.832623	−	0.698654i	0.955892	+	0.293720i	$0.0948932\pi$
$480$		0			0
$481$	17.9839	+	8.21173i	0.819995	+	0.374423i
$482$		0			0
$483$	−0.550232	+	0.461700i	−0.0250364	+	0.0210081i
$484$		0			0
$485$	1.49215	−	8.46240i	0.0677550	−	0.384258i
$486$		0			0
$487$	15.7470			0.713565			0.356782	−	0.934188i	$-0.383874\pi$
$487$	15.7470			0.713565			0.356782	+	0.934188i	$0.383874\pi$
$488$		0			0
$489$	−4.24338	−	7.34975i	−0.191892	−	0.332367i
$490$		0			0
$491$	−0.943381	+	1.63398i	−0.0425742	+	0.0737406i	−0.886527	−	0.462676i	$-0.846889\pi$
$491$	−0.943381	+	1.63398i	−0.0425742	+	0.0737406i	0.843953	+	0.536417i	$0.180223\pi$
$492$		0			0
$493$	−34.1880	+	28.6872i	−1.53975	+	1.29200i
$494$		0			0
$495$	−3.48161	+	6.03032i	−0.156487	+	0.271043i
$496$		0			0
$497$	44.2634	+	16.1106i	1.98548	+	0.722657i
$498$		0			0
$499$	27.1748	+	22.8023i	1.21651	+	1.02077i	0.999000	+	0.0447151i	$0.0142380\pi$
$499$	27.1748	+	22.8023i	1.21651	+	1.02077i	0.217510	+	0.976058i	$0.430206\pi$
$500$		0			0
$501$	−3.28133	−	18.6094i	−0.146599	−	0.831405i
$502$		0			0
$503$	−30.7970	−	11.2092i	−1.37317	−	0.499793i	−0.453070	−	0.891475i	$-0.649671\pi$
$503$	−30.7970	−	11.2092i	−1.37317	−	0.499793i	−0.920101	+	0.391682i	$0.871893\pi$
$504$		0			0
$505$	−2.10928	+	11.9623i	−0.0938618	+	0.532317i
$506$		0			0
$507$	1.13638	+	1.96826i	0.0504682	+	0.0874136i
$508$		0			0
$509$	−4.56507	−	25.8898i	−0.202343	−	1.14755i	−0.901566	−	0.432642i	$-0.857581\pi$
$509$	−4.56507	−	25.8898i	−0.202343	−	1.14755i	0.699222	−	0.714904i	$-0.253530\pi$
$510$		0			0
$511$	40.6038	−	14.7786i	1.79620	−	0.653765i
$512$		0			0
$513$	−4.71928	+	1.71768i	−0.208361	+	0.0758373i
$514$		0			0
$515$	−23.5439	−	19.7557i	−1.03747	−	0.870540i
$516$		0			0
$517$	−9.64235			−0.424070
$518$		0			0
$519$	17.6416			0.774380
$520$		0			0
$521$	−20.9631	−	17.5902i	−0.918412	−	0.770639i	0.0552886	−	0.998470i	$-0.482392\pi$
$521$	−20.9631	−	17.5902i	−0.918412	−	0.770639i	−0.973701	+	0.227831i	$0.926837\pi$
$522$		0			0
$523$	−37.7012	+	13.7221i	−1.64856	+	0.600026i	−0.988505	−	0.151191i	$-0.951689\pi$
$523$	−37.7012	+	13.7221i	−1.64856	+	0.600026i	−0.660054	+	0.751218i	$0.729467\pi$
$524$		0			0
$525$	−5.61615	+	2.04411i	−0.245109	+	0.0892123i
$526$		0			0
$527$	9.58832	+	54.3781i	0.417674	+	2.36875i
$528$		0			0
$529$	11.4741	+	19.8738i	0.498876	+	0.864078i
$530$		0			0
$531$	3.50045	−	19.8521i	0.151907	−	0.861506i
$532$		0			0
$533$	22.8994	+	8.33470i	0.991883	+	0.361016i
$534$		0			0
$535$	5.93247	+	33.6447i	0.256483	+	1.45459i
$536$		0			0
$537$	9.61827	+	8.07069i	0.415059	+	0.348276i
$538$		0			0
$539$	5.22336	+	1.90115i	0.224986	+	0.0818882i
$540$		0			0
$541$	−13.2494	+	22.9486i	−0.569635	+	0.986636i	0.426967	+	0.904267i	$0.359582\pi$
$541$	−13.2494	+	22.9486i	−0.569635	+	0.986636i	−0.996602	+	0.0823693i	$0.973751\pi$
$542$		0			0
$543$	−9.66766	+	8.11213i	−0.414879	+	0.348125i
$544$		0			0
$545$	0.179626	−	0.311121i	0.00769431	−	0.0133269i
$546$		0			0
$547$	−14.8012	−	25.6364i	−0.632853	−	1.09613i	−0.986966	−	0.160931i	$-0.948550\pi$
$547$	−14.8012	−	25.6364i	−0.632853	−	1.09613i	0.354113	−	0.935203i	$-0.384783\pi$
$548$		0			0
$549$	−5.56577			−0.237541
$550$		0			0
$551$	−1.07938	+	6.12148i	−0.0459832	+	0.260784i
$552$		0			0
$553$	−18.7017	+	15.6926i	−0.795279	+	0.667319i
$554$		0			0
$555$	8.44654	−	12.2704i	0.358535	−	0.520851i
$556$		0			0
$557$	1.56151	−	1.31026i	0.0661633	−	0.0555176i	−0.609106	−	0.793089i	$-0.708472\pi$
$557$	1.56151	−	1.31026i	0.0661633	−	0.0555176i	0.675270	+	0.737571i	$0.264027\pi$
$558$		0			0
$559$	−2.22242	+	12.6040i	−0.0939985	+	0.533092i
$560$		0			0
$561$	8.75358			0.369576
$562$		0			0
$563$	21.5625	+	37.3473i	0.908751	+	1.57400i	0.815802	+	0.578332i	$0.196296\pi$
$563$	21.5625	+	37.3473i	0.908751	+	1.57400i	0.0929493	+	0.995671i	$0.470371\pi$
$564$		0			0
$565$	−9.77198	+	16.9256i	−0.411110	+	0.712064i
$566$		0			0
$567$	4.99446	−	4.19085i	0.209748	−	0.175999i
$568$		0			0
$569$	2.16570	−	3.75110i	0.0907908	−	0.157254i	−0.817053	−	0.576562i	$-0.804394\pi$
$569$	2.16570	−	3.75110i	0.0907908	−	0.157254i	0.907844	+	0.419308i	$0.137727\pi$
$570$		0			0
$571$	−25.9464	−	9.44371i	−1.08582	−	0.395207i	−0.263751	−	0.964591i	$-0.584960\pi$
$571$	−25.9464	−	9.44371i	−1.08582	−	0.395207i	−0.822072	+	0.569384i	$0.807182\pi$
$572$		0			0
$573$	1.68710	+	1.41564i	0.0704795	+	0.0591393i
$574$		0			0
$575$	−0.0747291	−	0.423810i	−0.00311642	−	0.0176741i
$576$		0			0
$577$	−28.6487	−	10.4273i	−1.19266	−	0.434093i	−0.332004	−	0.943278i	$-0.607725\pi$
$577$	−28.6487	−	10.4273i	−1.19266	−	0.434093i	−0.860657	+	0.509185i	$0.829947\pi$
$578$		0			0
$579$	−1.50246	+	8.52089i	−0.0624402	+	0.354116i
$580$		0			0
$581$	21.8384	+	37.8252i	0.906010	+	1.56925i
$582$		0			0
$583$	1.76113	+	9.98786i	0.0729385	+	0.413655i
$584$		0			0
$585$	17.0773	−	6.21561i	0.706058	−	0.256984i
$586$		0			0
$587$	−3.46775	+	1.26216i	−0.143129	+	0.0520948i	−0.412591	−	0.910916i	$-0.635376\pi$
$587$	−3.46775	+	1.26216i	−0.143129	+	0.0520948i	0.269462	+	0.963011i	$0.413154\pi$
$588$		0			0
$589$	5.89130	+	4.94339i	0.242747	+	0.203689i
$590$		0			0
$591$	−1.28647			−0.0529182
$592$		0			0
$593$	−0.261315			−0.0107309			−0.00536546	−	0.999986i	$-0.501708\pi$
$593$	−0.261315			−0.0107309			−0.00536546	+	0.999986i	$0.501708\pi$
$594$		0			0
$595$	−51.3092	−	43.0535i	−2.10347	−	1.76502i
$596$		0			0
$597$	−3.46245	+	1.26023i	−0.141709	+	0.0515778i
$598$		0			0
$599$	8.61184	−	3.13445i	0.351870	−	0.128070i	−0.160037	−	0.987111i	$-0.551161\pi$
$599$	8.61184	−	3.13445i	0.351870	−	0.128070i	0.511907	+	0.859041i	$0.328939\pi$
$600$		0			0
$601$	1.02400	+	5.80742i	0.0417700	+	0.236890i	0.998544	−	0.0539429i	$-0.0171789\pi$
$601$	1.02400	+	5.80742i	0.0417700	+	0.236890i	−0.956774	+	0.290832i	$0.906068\pi$
$602$		0			0
$603$	7.45336	+	12.9096i	0.303524	+	0.525720i
$604$		0			0
$605$	−4.30770	+	24.4302i	−0.175133	+	0.993228i
$606$		0			0
$607$	28.7256	+	10.4552i	1.16593	+	0.424365i	0.851214	−	0.524819i	$-0.175867\pi$
$607$	28.7256	+	10.4552i	1.16593	+	0.424365i	0.314721	+	0.949184i	$0.398089\pi$
$608$		0			0
$609$	3.24828	+	18.4219i	0.131627	+	0.746494i
$610$		0			0
$611$	19.2779	+	16.1761i	0.779899	+	0.654413i
$612$		0			0
$613$	−1.91751	−	0.697915i	−0.0774473	−	0.0281885i	0.303006	−	0.952989i	$-0.402010\pi$
$613$	−1.91751	−	0.697915i	−0.0774473	−	0.0281885i	−0.380453	+	0.924800i	$0.624232\pi$
$614$		0			0
$615$	9.18095	−	15.9019i	0.370211	−	0.641225i
$616$		0			0
$617$	6.14266	−	5.15431i	0.247294	−	0.207505i	−0.510712	−	0.859752i	$-0.670618\pi$
$617$	6.14266	−	5.15431i	0.247294	−	0.207505i	0.758006	+	0.652247i	$0.226174\pi$
$618$		0			0
$619$	−5.81923	+	10.0792i	−0.233895	+	0.405118i	−0.958951	−	0.283572i	$-0.908480\pi$
$619$	−5.81923	+	10.0792i	−0.233895	+	0.405118i	0.725056	+	0.688690i	$0.241814\pi$
$620$		0			0
$621$	−0.544133	−	0.942466i	−0.0218353	−	0.0378199i
$622$		0			0
$623$	8.90316			0.356697
$624$		0			0
$625$	−5.36238	+	30.4116i	−0.214495	+	1.21646i
$626$		0			0
$627$	0.933953	−	0.783679i	0.0372985	−	0.0312971i
$628$		0			0
$629$	45.6914	+	3.62983i	1.82183	+	0.144731i
$630$		0			0
$631$	23.8402	−	20.0043i	0.949063	−	0.796358i	−0.0300766	−	0.999548i	$-0.509575\pi$
$631$	23.8402	−	20.0043i	0.949063	−	0.796358i	0.979139	+	0.203189i	$0.0651307\pi$
$632$		0			0
$633$	−3.37459	+	19.1382i	−0.134128	+	0.760677i
$634$		0			0
$635$	53.5931			2.12678
$636$		0			0
$637$	−7.25365	−	12.5637i	−0.287400	−	0.497791i
$638$		0			0
$639$	−14.8154	+	25.6610i	−0.586088	+	1.01514i
$640$		0			0
$641$	−25.2141	+	21.1571i	−0.995897	+	0.835657i	−0.986411	−	0.164298i	$-0.947464\pi$
$641$	−25.2141	+	21.1571i	−0.995897	+	0.835657i	−0.00948626	+	0.999955i	$0.503020\pi$
$642$		0			0
$643$	5.30025	−	9.18031i	0.209022	−	0.362036i	−0.742385	−	0.669974i	$-0.766305\pi$
$643$	5.30025	−	9.18031i	0.209022	−	0.362036i	0.951407	+	0.307937i	$0.0996388\pi$
$644$		0			0
$645$	9.06195	+	3.29828i	0.356814	+	0.129870i
$646$		0			0
$647$	−31.5917	−	26.5086i	−1.24200	−	1.04216i	−0.997365	−	0.0725450i	$-0.976888\pi$
$647$	−31.5917	−	26.5086i	−1.24200	−	1.04216i	−0.244634	−	0.969616i	$-0.578668\pi$
$648$		0			0
$649$	2.04674	+	11.6077i	0.0803417	+	0.455641i
$650$		0			0
$651$	21.7481	+	7.91566i	0.852375	+	0.310239i
$652$		0			0
$653$	7.29955	−	41.3978i	0.285653	−	1.62002i	−0.417289	−	0.908774i	$-0.637020\pi$
$653$	7.29955	−	41.3978i	0.285653	−	1.62002i	0.702943	−	0.711247i	$-0.251869\pi$
$654$		0			0
$655$	−12.5081	−	21.6646i	−0.488731	−	0.846506i
$656$		0			0
$657$	4.71993	+	26.7680i	0.184142	+	1.04432i
$658$		0			0
$659$	19.7147	−	7.17557i	0.767977	−	0.279521i	0.0718269	−	0.997417i	$-0.477117\pi$
$659$	19.7147	−	7.17557i	0.767977	−	0.279521i	0.696150	+	0.717896i	$0.254895\pi$
$660$		0			0
$661$	11.7123	−	4.26293i	0.455556	−	0.165809i	−0.104042	−	0.994573i	$-0.533178\pi$
$661$	11.7123	−	4.26293i	0.455556	−	0.165809i	0.559598	+	0.828764i	$0.310955\pi$
$662$		0			0
$663$	−17.5010	−	14.6851i	−0.679681	−	0.570320i
$664$		0			0
$665$	−9.32881			−0.361756
$666$		0			0
$667$	−1.34695			−0.0521540
$668$		0			0
$669$	−17.8385	−	14.9683i	−0.689676	−	0.578707i
$670$		0			0
$671$	3.05809	−	1.11305i	0.118056	−	0.0429690i
$672$		0			0
$673$	−44.2357	+	16.1005i	−1.70516	+	0.620628i	−0.996397	−	0.0848166i	$-0.972970\pi$
$673$	−44.2357	+	16.1005i	−1.70516	+	0.620628i	−0.708765	+	0.705445i	$0.750747\pi$
$674$		0			0
$675$	−1.57241	−	8.91758i	−0.0605221	−	0.343238i
$676$		0			0
$677$	16.6746	+	28.8812i	0.640856	+	1.10999i	0.985242	+	0.171166i	$0.0547536\pi$
$677$	16.6746	+	28.8812i	0.640856	+	1.10999i	−0.344387	+	0.938828i	$0.611913\pi$
$678$		0			0
$679$	1.92437	−	10.9137i	0.0738507	−	0.418828i
$680$		0			0
$681$	−0.929898	−	0.338455i	−0.0356338	−	0.0129696i
$682$		0			0
$683$	1.03627	+	5.87697i	0.0396517	+	0.224876i	0.998194	−	0.0600747i	$-0.0191339\pi$
$683$	1.03627	+	5.87697i	0.0396517	+	0.224876i	−0.958542	+	0.284951i	$0.908023\pi$
$684$		0			0
$685$	−19.0699	−	16.0016i	−0.728625	−	0.611389i
$686$		0			0
$687$	5.59301	+	2.03569i	0.213387	+	0.0776664i
$688$		0			0
$689$	13.2347	−	22.9231i	0.504201	−	0.873302i
$690$		0			0
$691$	−7.73164	+	6.48761i	−0.294125	+	0.246800i	−0.777894	−	0.628395i	$-0.783712\pi$
$691$	−7.73164	+	6.48761i	−0.294125	+	0.246800i	0.483769	+	0.875196i	$0.339268\pi$
$692$		0			0
$693$	−4.49011	+	7.77710i	−0.170565	+	0.295428i
$694$		0			0
$695$	−24.4168	−	42.2911i	−0.926181	−	1.60419i
$696$		0			0
$697$	56.4978			2.14001
$698$		0			0
$699$	−1.55324	+	8.80889i	−0.0587491	+	0.333183i
$700$		0			0
$701$	−18.3592	+	15.4052i	−0.693416	+	0.581845i	−0.919892	−	0.392172i	$-0.871724\pi$
$701$	−18.3592	+	15.4052i	−0.693416	+	0.581845i	0.226476	+	0.974017i	$0.427279\pi$
$702$		0			0
$703$	5.19995	−	3.70332i	0.196120	−	0.139673i
$704$		0			0
$705$	14.5257	−	12.1885i	0.547071	−	0.459047i
$706$		0			0
$707$	−2.72027	+	15.4274i	−0.102306	+	0.580208i
$708$		0			0
$709$	3.33993			0.125434			0.0627168	−	0.998031i	$-0.480024\pi$
$709$	3.33993			0.125434			0.0627168	+	0.998031i	$0.480024\pi$
$710$		0			0
$711$	−7.67862	−	13.2998i	−0.287971	−	0.498780i
$712$		0			0
$713$	−0.833244	+	1.44322i	−0.0312052	+	0.0540491i
$714$		0			0
$715$	−8.14002	+	6.83029i	−0.304419	+	0.255438i
$716$		0			0
$717$	6.12939	−	10.6164i	0.228906	−	0.396477i
$718$		0			0
$719$	−29.0244	−	10.5640i	−1.08243	−	0.393972i	−0.261617	−	0.965172i	$-0.584256\pi$
$719$	−29.0244	−	10.5640i	−1.08243	−	0.393972i	−0.820811	+	0.571200i	$0.806478\pi$
$720$		0			0
$721$	−30.3638	−	25.4783i	−1.13081	−	0.948861i
$722$		0			0
$723$	−0.753181	−	4.27150i	−0.0280111	−	0.158859i
$724$		0			0
$725$	−10.5317	−	3.83321i	−0.391136	−	0.142362i
$726$		0			0
$727$	−0.0553353	+	0.313822i	−0.00205227	+	0.0116390i	−0.985817	−	0.167826i	$-0.946325\pi$
$727$	−0.0553353	+	0.313822i	−0.00205227	+	0.0116390i	0.983764	+	0.179465i	$0.0574365\pi$
$728$		0			0
$729$	−4.64512	−	8.04558i	−0.172041	−	0.297984i
$730$		0			0
$731$	5.15253	+	29.2214i	0.190573	+	1.08079i
$732$		0			0
$733$	30.2544	−	11.0117i	1.11747	−	0.406726i	0.283742	−	0.958901i	$-0.408424\pi$
$733$	30.2544	−	11.0117i	1.11747	−	0.406726i	0.833728	+	0.552175i	$0.186202\pi$
$734$		0			0
$735$	−10.2719	+	3.73867i	−0.378885	+	0.137903i
$736$		0			0
$737$	−6.67691	−	5.60259i	−0.245947	−	0.206374i
$738$		0			0
$739$	31.0155			1.14092			0.570461	−	0.821325i	$-0.306765\pi$
$739$	31.0155			1.14092			0.570461	+	0.821325i	$0.306765\pi$
$740$		0			0
$741$	−3.18195			−0.116892
$742$		0			0
$743$	−2.11789	−	1.77712i	−0.0776980	−	0.0651964i	0.603111	−	0.797657i	$-0.293927\pi$
$743$	−2.11789	−	1.77712i	−0.0776980	−	0.0651964i	−0.680809	+	0.732461i	$0.738372\pi$
$744$		0			0
$745$	−19.7924	+	7.20386i	−0.725139	+	0.263929i
$746$		0			0
$747$	−25.8179	+	9.39696i	−0.944629	+	0.343817i
$748$		0			0
$749$	7.65091	+	43.3905i	0.279558	+	1.58545i
$750$		0			0
$751$	−14.0482	−	24.3323i	−0.512628	−	0.887897i	−0.999893	−	0.0146429i	$-0.995339\pi$
$751$	−14.0482	−	24.3323i	−0.512628	−	0.887897i	0.487265	−	0.873254i	$-0.337994\pi$
$752$		0			0
$753$	2.88111	−	16.3396i	0.104993	−	0.595447i
$754$		0			0
$755$	−6.59545	−	2.40055i	−0.240033	−	0.0873649i
$756$		0			0
$757$	−5.72565	−	32.4718i	−0.208102	−	1.18021i	−0.892483	−	0.451082i	$-0.851038\pi$
$757$	−5.72565	−	32.4718i	−0.208102	−	1.18021i	0.684380	−	0.729125i	$-0.260073\pi$
$758$		0			0
$759$	0.202381	+	0.169818i	0.00734597	+	0.00616400i
$760$		0			0
$761$	5.00448	+	1.82148i	0.181412	+	0.0660286i	0.431129	−	0.902290i	$-0.358115\pi$
$761$	5.00448	+	1.82148i	0.181412	+	0.0660286i	−0.249717	+	0.968319i	$0.580338\pi$
$762$		0			0
$763$	0.231657	−	0.401242i	0.00838655	−	0.0145259i
$764$		0			0
$765$	32.2760	−	27.0828i	1.16694	−	0.979180i
$766$		0			0
$767$	15.3810	−	26.6407i	0.555377	−	0.961942i
$768$		0			0
$769$	−17.9353	−	31.0648i	−0.646762	−	1.12022i	−0.983892	−	0.178766i	$-0.942789\pi$
$769$	−17.9353	−	31.0648i	−0.646762	−	1.12022i	0.337130	−	0.941458i	$-0.390544\pi$
$770$		0			0
$771$	−16.3134			−0.587513
$772$		0			0
$773$	0.584521	−	3.31498i	0.0210238	−	0.119232i	−0.972490	−	0.232946i	$-0.925164\pi$
$773$	0.584521	−	3.31498i	0.0210238	−	0.119232i	0.993514	+	0.113714i	$0.0362747\pi$
$774$		0			0
$775$	−10.6223	+	8.91313i	−0.381563	+	0.320169i
$776$		0			0
$777$	10.8932	−	15.8248i	0.390792	−	0.567710i
$778$		0			0
$779$	6.02797	−	5.05806i	0.215974	−	0.181224i
$780$		0			0
$781$	3.00852	−	17.0622i	0.107653	−	0.610532i
$782$		0			0
$783$	−28.3417			−1.01285
$784$		0			0
$785$	10.6530	+	18.4515i	0.380222	+	0.658563i
$786$		0			0
$787$	20.2776	−	35.1219i	0.722820	−	1.25196i	−0.237045	−	0.971499i	$-0.576179\pi$
$787$	20.2776	−	35.1219i	0.722820	−	1.25196i	0.959865	−	0.280462i	$-0.0904878\pi$
$788$		0			0
$789$	5.64677	−	4.73820i	0.201030	−	0.168684i
$790$		0			0
$791$	−12.6026	+	21.8283i	−0.448097	+	0.776127i
$792$		0			0
$793$	−7.98128	−	2.90495i	−0.283424	−	0.103158i
$794$		0			0
$795$	−15.2783	−	12.8201i	−0.541867	−	0.454681i
$796$		0			0
$797$	−7.10571	−	40.2985i	−0.251697	−	1.42745i	−0.804410	−	0.594075i	$-0.797518\pi$
$797$	−7.10571	−	40.2985i	−0.251697	−	1.42745i	0.552713	−	0.833372i	$-0.313593\pi$
$798$		0			0
$799$	54.8257	+	19.9549i	1.93960	+	0.705955i
$800$		0			0
$801$	−0.972521	+	5.51544i	−0.0343623	+	0.194878i
$802$		0			0
$803$	−7.94647	−	13.7637i	−0.280425	−	0.485710i
$804$		0			0
$805$	−0.351028	−	1.99078i	−0.0123721	−	0.0701657i
$806$		0			0
$807$	5.64954	−	2.05626i	0.198873	−	0.0723839i
$808$		0			0
$809$	−43.8247	+	15.9509i	−1.54079	+	0.560803i	−0.966235	−	0.257661i	$-0.917048\pi$
$809$	−43.8247	+	15.9509i	−1.54079	+	0.560803i	−0.574558	+	0.818464i	$0.694826\pi$
$810$		0			0
$811$	−19.0963	−	16.0237i	−0.670562	−	0.562668i	0.242670	−	0.970109i	$-0.421977\pi$
$811$	−19.0963	−	16.0237i	−0.670562	−	0.562668i	−0.913232	+	0.407441i	$0.866421\pi$
$812$		0			0
$813$	16.8471			0.590853
$814$		0			0
$815$	23.8848			0.836647
$816$		0			0
$817$	3.16584	+	2.65646i	0.110759	+	0.0929377i
$818$		0			0
$819$	22.0240	−	8.01607i	0.769580	−	0.280104i
$820$		0			0
$821$	−32.2949	+	11.7544i	−1.12710	+	0.410231i	−0.837238	−	0.546838i	$-0.815831\pi$
$821$	−32.2949	+	11.7544i	−1.12710	+	0.410231i	−0.289861	+	0.957069i	$0.593609\pi$
$822$		0			0
$823$	3.74718	+	21.2513i	0.130619	+	0.740774i	0.977811	+	0.209488i	$0.0671799\pi$
$823$	3.74718	+	21.2513i	0.130619	+	0.740774i	−0.847193	+	0.531286i	$0.821709\pi$
$824$		0			0
$825$	1.09912	+	1.90374i	0.0382666	+	0.0662796i
$826$		0			0
$827$	4.05290	−	22.9852i	0.140933	−	0.799272i	−0.829610	−	0.558344i	$-0.811437\pi$
$827$	4.05290	−	22.9852i	0.140933	−	0.799272i	0.970543	−	0.240928i	$-0.0774519\pi$
$828$		0			0
$829$	17.5307	+	6.38067i	0.608868	+	0.221610i	0.628008	−	0.778207i	$-0.283871\pi$
$829$	17.5307	+	6.38067i	0.608868	+	0.221610i	−0.0191401	+	0.999817i	$0.506093\pi$
$830$		0			0
$831$	4.31561	+	24.4751i	0.149707	+	0.849030i
$832$		0			0
$833$	−25.7652	−	21.6196i	−0.892712	−	0.749074i
$834$		0			0
$835$	49.9741	+	18.1891i	1.72943	+	0.629460i
$836$		0			0
$837$	−17.5327	+	30.3675i	−0.606018	+	1.04965i
$838$		0			0
$839$	−19.0280	+	15.9664i	−0.656919	+	0.551220i	−0.909161	−	0.416444i	$-0.863276\pi$
$839$	−19.0280	+	15.9664i	−0.656919	+	0.551220i	0.252243	+	0.967664i	$0.418832\pi$
$840$		0			0
$841$	−3.03927	+	5.26417i	−0.104802	+	0.181523i
$842$		0			0
$843$	1.72587	+	2.98930i	0.0594423	+	0.102957i
$844$		0			0
$845$	−6.39634			−0.220041
$846$		0			0
$847$	−5.55550	+	31.5068i	−0.190889	+	1.08259i
$848$		0			0
$849$	14.9478	−	12.5427i	0.513009	−	0.430465i
$850$		0			0
$851$	0.985957	+	0.970325i	0.0337982	+	0.0332623i
$852$		0			0
$853$	−27.6465	+	23.1982i	−0.946599	+	0.794291i	−0.978722	−	0.205193i	$-0.934218\pi$
$853$	−27.6465	+	23.1982i	−0.946599	+	0.794291i	0.0321226	+	0.999484i	$0.489773\pi$
$854$		0			0
$855$	1.01902	−	5.77913i	0.0348496	−	0.197642i
$856$		0			0
$857$	−23.1215			−0.789814			−0.394907	−	0.918721i	$-0.629223\pi$
$857$	−23.1215			−0.789814			−0.394907	+	0.918721i	$0.629223\pi$
$858$		0			0
$859$	−17.2312	−	29.8454i	−0.587922	−	1.01831i	−0.994504	−	0.104697i	$-0.966613\pi$
$859$	−17.2312	−	29.8454i	−0.587922	−	1.01831i	0.406582	−	0.913614i	$-0.366721\pi$
$860$		0			0
$861$	11.8404	−	20.5081i	0.403518	−	0.698914i
$862$		0			0
$863$	−28.1125	+	23.5892i	−0.956960	+	0.802985i	−0.980456	−	0.196739i	$-0.936965\pi$
$863$	−28.1125	+	23.5892i	−0.956960	+	0.802985i	0.0234960	+	0.999724i	$0.492520\pi$
$864$		0			0
$865$	−24.8249	+	42.9980i	−0.844071	+	1.46197i
$866$		0			0
$867$	−34.8705	−	12.6918i	−1.18426	−	0.431037i
$868$		0			0
$869$	6.87870	+	5.77191i	0.233344	+	0.195799i
$870$		0			0
$871$	3.95015	+	22.4024i	0.133846	+	0.759078i
$872$		0			0
$873$	6.55073	+	2.38427i	0.221709	+	0.0806954i
$874$		0			0
$875$	−4.79679	+	27.2040i	−0.162161	+	0.919662i
$876$		0			0
$877$	−7.04975	−	12.2105i	−0.238053	−	0.412320i	0.722102	−	0.691786i	$-0.243176\pi$
$877$	−7.04975	−	12.2105i	−0.238053	−	0.412320i	−0.960156	+	0.279466i	$0.909843\pi$
$878$		0			0
$879$	−4.06257	−	23.0400i	−0.137027	−	0.777119i
$880$		0			0
$881$	34.2171	−	12.4540i	1.15280	−	0.419587i	0.306283	−	0.951940i	$-0.400915\pi$
$881$	34.2171	−	12.4540i	1.15280	−	0.419587i	0.846522	+	0.532354i	$0.178692\pi$
$882$		0			0
$883$	−3.95749	+	1.44041i	−0.133180	+	0.0484736i	−0.407750	−	0.913093i	$-0.633687\pi$
$883$	−3.95749	+	1.44041i	−0.133180	+	0.0484736i	0.274570	+	0.961567i	$0.411464\pi$
$884$		0			0
$885$	−17.7562	−	14.8992i	−0.596867	−	0.500830i
$886$		0			0
$887$	10.5188			0.353188			0.176594	−	0.984284i	$-0.443492\pi$
$887$	10.5188			0.353188			0.176594	+	0.984284i	$0.443492\pi$
$888$		0			0
$889$	69.1172			2.31812
$890$		0			0
$891$	−1.83702	−	1.54144i	−0.0615423	−	0.0516402i
$892$		0			0
$893$	7.63606	−	2.77930i	0.255531	−	0.0930057i
$894$		0			0
$895$	−33.2054	+	12.0858i	−1.10993	+	0.403982i
$896$		0			0
$897$	−0.119732	−	0.679031i	−0.00399772	−	0.0226722i
$898$		0			0
$899$	21.7002	+	37.5858i	0.723742	+	1.25356i
$900$		0			0
$901$	10.6563	−	60.4350i	0.355013	−	2.01338i
$902$		0			0
$903$	11.6869	+	4.25368i	0.388916	+	0.141554i
$904$		0			0
$905$	−6.16761	−	34.9783i	−0.205018	−	1.16272i
$906$		0			0
$907$	23.4994	+	19.7184i	0.780286	+	0.654738i	0.943321	−	0.331883i	$-0.107684\pi$
$907$	23.4994	+	19.7184i	0.780286	+	0.654738i	−0.163035	+	0.986620i	$0.552128\pi$
$908$		0			0
$909$	−9.26003	−	3.37038i	−0.307136	−	0.111788i
$910$		0			0
$911$	−6.03455	+	10.4521i	−0.199934	+	0.346295i	−0.948507	−	0.316757i	$-0.897406\pi$
$911$	−6.03455	+	10.4521i	−0.199934	+	0.346295i	0.748573	+	0.663052i	$0.230739\pi$
$912$		0			0
$913$	12.3063	−	10.3262i	0.407280	−	0.341749i
$914$		0			0
$915$	−3.19990	+	5.54238i	−0.105785	+	0.183226i
$916$		0			0
$917$	−16.1312	−	27.9401i	−0.532701	−	0.922664i
$918$		0			0
$919$	3.94293			0.130065			0.0650327	−	0.997883i	$-0.479285\pi$
$919$	3.94293			0.130065			0.0650327	+	0.997883i	$0.479285\pi$
$920$		0			0
$921$	3.54740	−	20.1183i	0.116891	−	0.662920i
$922$		0			0
$923$	−34.6385	+	29.0652i	−1.14014	+	0.956691i
$924$		0			0
$925$	4.94771	+	10.3928i	0.162680	+	0.341712i
$926$		0			0
$927$	19.1003	−	16.0271i	0.627338	−	0.526399i
$928$		0			0
$929$	−7.19718	+	40.8172i	−0.236132	+	1.33917i	0.604085	+	0.796920i	$0.293539\pi$
$929$	−7.19718	+	40.8172i	−0.236132	+	1.33917i	−0.840217	+	0.542250i	$0.817573\pi$
$930$		0			0
$931$	−4.68452			−0.153529
$932$		0			0
$933$	−0.243491	−	0.421738i	−0.00797153	−	0.0138071i
$934$		0			0
$935$	−12.3179	+	21.3351i	−0.402837	+	0.697734i
$936$		0			0
$937$	−2.45023	+	2.05599i	−0.0800455	+	0.0671662i	−0.681932	−	0.731415i	$-0.738860\pi$
$937$	−2.45023	+	2.05599i	−0.0800455	+	0.0671662i	0.601887	+	0.798581i	$0.294416\pi$
$938$		0			0
$939$	12.5649	−	21.7631i	0.410041	−	0.710213i
$940$		0			0
$941$	−4.69883	−	1.71023i	−0.153177	−	0.0557520i	0.264294	−	0.964442i	$-0.414861\pi$
$941$	−4.69883	−	1.71023i	−0.153177	−	0.0557520i	−0.417471	+	0.908690i	$0.637083\pi$
$942$		0			0
$943$	1.30622	+	1.09605i	0.0425363	+	0.0356922i
$944$		0			0
$945$	−7.38614	−	41.8889i	−0.240271	−	1.36265i
$946$		0			0
$947$	−19.3880	−	7.05667i	−0.630026	−	0.229311i	0.00721636	−	0.999974i	$-0.497703\pi$
$947$	−19.3880	−	7.05667i	−0.630026	−	0.229311i	−0.637243	+	0.770663i	$0.719925\pi$
$948$		0			0
$949$	−7.20273	+	40.8487i	−0.233810	+	1.32600i
$950$		0			0
$951$	6.41895	+	11.1179i	0.208149	+	0.360524i
$952$		0			0
$953$	0.215365	+	1.22139i	0.00697635	+	0.0395648i	0.988097	−	0.153831i	$-0.0491610\pi$
$953$	0.215365	+	1.22139i	0.00697635	+	0.0395648i	−0.981121	+	0.193396i	$0.938050\pi$
$954$		0			0
$955$	−5.82440	+	2.11991i	−0.188473	+	0.0685986i
$956$		0			0
$957$	6.46536	−	2.35320i	0.208996	−	0.0760681i
$958$		0			0
$959$	−24.5939	−	20.6367i	−0.794177	−	0.666394i
$960$		0			0
$961$	22.6964			0.732143
$962$		0			0
$963$	−27.7158			−0.893130
$964$		0			0
$965$	−18.6538	−	15.6524i	−0.600486	−	0.503868i
$966$		0			0
$967$	30.3246	−	11.0373i	0.975173	−	0.354934i	0.195212	−	0.980761i	$-0.437461\pi$
$967$	30.3246	−	11.0373i	0.975173	−	0.354934i	0.779962	+	0.625827i	$0.215238\pi$
$968$		0			0
$969$	−6.93222	+	2.52312i	−0.222695	+	0.0810544i
$970$		0			0
$971$	3.97330	+	22.5337i	0.127509	+	0.723141i	0.979786	+	0.200050i	$0.0641103\pi$
$971$	3.97330	+	22.5337i	0.127509	+	0.723141i	−0.852276	+	0.523092i	$0.824779\pi$
$972$		0			0
$973$	−31.4895	−	54.5414i	−1.00951	−	1.74852i
$974$		0			0
$975$	0.996252	−	5.65002i	0.0319056	−	0.180946i
$976$		0			0
$977$	−45.0795	−	16.4076i	−1.44222	−	0.524926i	−0.501815	−	0.864975i	$-0.667334\pi$
$977$	−45.0795	−	16.4076i	−1.44222	−	0.524926i	−0.940408	+	0.340049i	$0.889556\pi$
$978$		0			0
$979$	−0.568641	−	3.22492i	−0.0181738	−	0.103069i
$980$		0			0
$981$	0.223262	+	0.187339i	0.00712820	+	0.00598127i
$982$		0			0
$983$	−23.6561	−	8.61011i	−0.754512	−	0.274620i	−0.0640089	−	0.997949i	$-0.520389\pi$
$983$	−23.6561	−	8.61011i	−0.754512	−	0.274620i	−0.690503	+	0.723329i	$0.742611\pi$
$984$		0			0
$985$	1.81029	−	3.13551i	0.0576806	−	0.0999058i
$986$		0			0
$987$	18.7334	−	15.7192i	0.596290	−	0.500346i
$988$		0			0
$989$	−0.447765	+	0.775552i	−0.0142381	+	0.0246611i
$990$		0			0
$991$	−5.92932	−	10.2699i	−0.188351	−	0.326234i	0.756350	−	0.654168i	$-0.226981\pi$
$991$	−5.92932	−	10.2699i	−0.188351	−	0.326234i	−0.944701	+	0.327934i	$0.893648\pi$
$992$		0			0
$993$	−18.9359			−0.600913
$994$		0			0
$995$	1.80073	−	10.2124i	0.0570868	−	0.323756i
$996$		0			0
$997$	−9.84239	+	8.25875i	−0.311712	+	0.261557i	−0.785199	−	0.619243i	$-0.787439\pi$
$997$	−9.84239	+	8.25875i	−0.311712	+	0.261557i	0.473487	+	0.880801i	$0.342995\pi$
$998$		0			0
$999$	20.7460	+	20.4171i	0.656374	+	0.645967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bc.g.49.4		30
4.3	odd	2		296.2.u.b.49.2	✓	30
37.34	even	9	inner	592.2.bc.g.145.4		30
148.71	odd	18		296.2.u.b.145.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.u.b.49.2	✓	30	4.3	odd	2
296.2.u.b.145.2	yes	30	148.71	odd	18
592.2.bc.g.49.4		30	1.1	even	1	trivial
592.2.bc.g.145.4		30	37.34	even	9	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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bc (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.714590 + 0.599612i) q^{3} +(-2.46699 + 0.897912i) q^{5} +(-3.18160 + 1.15801i) q^{7} +(-0.369841 - 2.09747i) q^{9} +(0.622664 + 1.07848i) q^{11} +(0.564386 - 3.20079i) q^{13} +(-2.30129 - 0.837600i) q^{15} +(-1.30849 - 7.42080i) q^{17} +(-0.803967 - 0.674609i) q^{19} +(-2.96789 - 1.08022i) q^{21} +(0.113710 - 0.196952i) q^{23} +(1.44959 - 1.21635i) q^{25} +(2.39263 - 4.14416i) q^{27} +(-2.96136 - 5.12922i) q^{29} -7.32779 q^{31} +(-0.201724 + 1.14403i) q^{33} +(6.80919 - 5.71359i) q^{35} +(-1.52734 + 5.88789i) q^{37} +(2.32254 - 1.94884i) q^{39} +(-1.30197 + 7.38387i) q^{41} -3.93777 q^{43} +(2.79574 + 4.84236i) q^{45} +(-3.87141 + 6.70548i) q^{47} +(3.41928 - 2.86912i) q^{49} +(3.51457 - 6.08742i) q^{51} +(7.65285 + 2.78541i) q^{53} +(-2.50449 - 2.10152i) q^{55} +(-0.170003 - 0.964137i) q^{57} +(8.89397 + 3.23714i) q^{59} +(0.453786 - 2.57355i) q^{61} +(3.60557 + 6.24503i) q^{63} +(1.48169 + 8.40310i) q^{65} +(-6.57694 + 2.39381i) q^{67} +(0.199351 - 0.0725578i) q^{69} +(-10.6575 - 8.94266i) q^{71} -12.7621 q^{73} +1.76520 q^{75} +(-3.22996 - 2.71026i) q^{77} +(6.77570 - 2.46615i) q^{79} +(-1.80951 + 0.658608i) q^{81} +(-2.24007 - 12.7041i) q^{83} +(9.89126 + 17.1322i) q^{85} +(0.959387 - 5.44095i) q^{87} +(-2.47099 - 0.899365i) q^{89} +(1.91089 + 10.8372i) q^{91} +(-5.23636 - 4.39383i) q^{93} +(2.58912 + 0.942363i) q^{95} +(-1.63655 + 2.83459i) q^{97} +(2.03180 - 1.70489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{5} + 3 q^{7} + 3 q^{11} + 9 q^{13} - 3 q^{15} - 27 q^{17} - 9 q^{19} + 15 q^{21} + 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{29} + 6 q^{31} - 6 q^{33} - 9 q^{35} + 9 q^{37} + 12 q^{39} + 48 q^{43}+ \cdots + 6 q^{99}+O(q^{100}) \) 30 * q - 6 * q^5 + 3 * q^7 + 3 * q^11 + 9 * q^13 - 3 * q^15 - 27 * q^17 - 9 * q^19 + 15 * q^21 + 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^29 + 6 * q^31 - 6 * q^33 - 9 * q^35 + 9 * q^37 + 12 * q^39 + 48 * q^43 + 51 * q^45 - 6 * q^47 - 21 * q^49 - 12 * q^51 - 15 * q^53 - 21 * q^55 + 51 * q^57 + 36 * q^61 + 36 * q^63 - 6 * q^65 + 27 * q^67 - 15 * q^69 - 27 * q^71 - 114 * q^73 - 84 * q^75 - 105 * q^77 + 18 * q^79 - 12 * q^81 + 30 * q^83 + 21 * q^85 + 99 * q^87 + 39 * q^89 + 72 * q^91 - 3 * q^93 - 66 * q^95 - 12 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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