LMFDB - Embedded newform 368.2.m.e.81.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [368,2,Mod(49,368)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("368.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(368, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, not minimal)

Newform invariants

comment:select newform

sage:traces = [30,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	368.81
Dual form			368.2.m.e.209.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.152362 - 1.05970i) q^{3} +(3.40226 - 0.998994i) q^{5} +(2.50777 + 2.89412i) q^{7} +(1.77873 + 0.522282i) q^{9} +(-3.68793 - 2.37009i) q^{11} +(-3.41282 + 3.93861i) q^{13} +(-0.540259 - 3.75758i) q^{15} +(-0.214855 - 0.470467i) q^{17} +(-1.65968 + 3.63420i) q^{19} +(3.44899 - 2.21653i) q^{21} +(4.65821 - 1.14066i) q^{23} +(6.37112 - 4.09447i) q^{25} +(2.15870 - 4.72689i) q^{27} +(-3.83811 - 8.40428i) q^{29} +(-0.500611 - 3.48182i) q^{31} +(-3.07349 + 3.54699i) q^{33} +(11.4233 + 7.34130i) q^{35} +(-3.30106 - 0.969277i) q^{37} +(3.65376 + 4.21666i) q^{39} +(-10.3725 + 3.04564i) q^{41} +(0.0556469 - 0.387033i) q^{43} +6.57346 q^{45} -1.50879 q^{47} +(-1.09082 + 7.58681i) q^{49} +(-0.531290 + 0.156001i) q^{51} +(-0.488784 - 0.564087i) q^{53} +(-14.9150 - 4.37944i) q^{55} +(3.59829 + 2.31248i) q^{57} +(-3.73262 + 4.30768i) q^{59} +(-0.845488 - 5.88050i) q^{61} +(2.94909 + 6.45762i) q^{63} +(-7.67667 + 16.8096i) q^{65} +(-2.28890 + 1.47099i) q^{67} +(-0.499028 - 5.11009i) q^{69} +(3.24103 - 2.08288i) q^{71} +(-2.40161 + 5.25880i) q^{73} +(-3.36819 - 7.37531i) q^{75} +(-2.38916 - 16.6170i) q^{77} +(1.80406 - 2.08200i) q^{79} +(-0.00158009 - 0.00101546i) q^{81} +(2.62166 + 0.769789i) q^{83} +(-1.20099 - 1.38601i) q^{85} +(-9.49080 + 2.78675i) q^{87} +(-1.11383 + 7.74687i) q^{89} -19.9574 q^{91} -3.76596 q^{93} +(-2.01613 + 14.0225i) q^{95} +(1.85193 - 0.543776i) q^{97} +(-5.32198 - 6.14189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41}+ \cdots + 17 q^{99}+O(q^{100}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$	$1$

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
$3$	0.152362	−	1.05970i	0.0879662	−	0.611818i	−0.897381	−	0.441257i	$-0.854533\pi$
$3$	0.152362	−	1.05970i	0.0879662	−	0.611818i	0.985347	−	0.170561i	$-0.0545581\pi$
$4$		0			0
$5$	3.40226	−	0.998994i	1.52154	−	0.446764i	0.589089	−	0.808068i	$-0.299487\pi$
$5$	3.40226	−	0.998994i	1.52154	−	0.446764i	0.932448	+	0.361305i	$0.117669\pi$
$6$		0			0
$7$	2.50777	+	2.89412i	0.947847	+	1.09387i	0.995476	+	0.0950089i	$0.0302880\pi$
$7$	2.50777	+	2.89412i	0.947847	+	1.09387i	−0.0476292	+	0.998865i	$0.515167\pi$
$8$		0			0
$9$	1.77873	+	0.522282i	0.592910	+	0.174094i
$10$		0			0
$11$	−3.68793	−	2.37009i	−1.11195	−	0.714609i	−0.150236	−	0.988650i	$-0.548003\pi$
$11$	−3.68793	−	2.37009i	−1.11195	−	0.714609i	−0.961718	+	0.274041i	$0.911640\pi$
$12$		0			0
$13$	−3.41282	+	3.93861i	−0.946547	+	1.09237i	0.0490653	+	0.998796i	$0.484376\pi$
$13$	−3.41282	+	3.93861i	−0.946547	+	1.09237i	−0.995612	+	0.0935776i	$0.970170\pi$
$14$		0			0
$15$	−0.540259	−	3.75758i	−0.139494	−	0.970204i
$16$		0			0
$17$	−0.214855	−	0.470467i	−0.0521101	−	0.114105i	0.881786	−	0.471650i	$-0.156341\pi$
$17$	−0.214855	−	0.470467i	−0.0521101	−	0.114105i	−0.933896	+	0.357545i	$0.883614\pi$
$18$		0			0
$19$	−1.65968	+	3.63420i	−0.380758	+	0.833743i	0.618106	+	0.786095i	$0.287900\pi$
$19$	−1.65968	+	3.63420i	−0.380758	+	0.833743i	−0.998864	+	0.0476488i	$0.984827\pi$
$20$		0			0
$21$	3.44899	−	2.21653i	0.752630	−	0.483686i
$22$		0			0
$23$	4.65821	−	1.14066i	0.971303	−	0.237845i
$23$	4.65821	−	1.14066i	0.971303	−	0.237845i
$24$		0			0
$25$	6.37112	−	4.09447i	1.27422	−	0.818894i
$26$		0			0
$27$	2.15870	−	4.72689i	0.415442	−	0.909691i
$28$		0			0
$29$	−3.83811	−	8.40428i	−0.712719	−	1.56064i	−0.823836	−	0.566829i	$-0.808170\pi$
$29$	−3.83811	−	8.40428i	−0.712719	−	1.56064i	0.111117	−	0.993807i	$-0.464557\pi$
$30$		0			0
$31$	−0.500611	−	3.48182i	−0.0899123	−	0.625354i	−0.984094	−	0.177649i	$-0.943151\pi$
$31$	−0.500611	−	3.48182i	−0.0899123	−	0.625354i	0.894182	−	0.447705i	$-0.147758\pi$
$32$		0			0
$33$	−3.07349	+	3.54699i	−0.535025	+	0.617452i
$34$		0			0
$35$	11.4233	+	7.34130i	1.93089	+	1.24091i
$36$		0			0
$37$	−3.30106	−	0.969277i	−0.542690	−	0.159348i	−0.00111322	−	0.999999i	$-0.500354\pi$
$37$	−3.30106	−	0.969277i	−0.542690	−	0.159348i	−0.541577	+	0.840651i	$0.682173\pi$
$38$		0			0
$39$	3.65376	+	4.21666i	0.585070	+	0.675206i
$40$		0			0
$41$	−10.3725	+	3.04564i	−1.61991	+	0.475649i	−0.960994	−	0.276568i	$-0.910803\pi$
$41$	−10.3725	+	3.04564i	−1.61991	+	0.475649i	−0.658916	+	0.752216i	$0.728985\pi$
$42$		0			0
$43$	0.0556469	−	0.387033i	0.00848608	−	0.0590220i	−0.985138	−	0.171763i	$-0.945054\pi$
$43$	0.0556469	−	0.387033i	0.00848608	−	0.0590220i	0.993624	+	0.112741i	$0.0359629\pi$
$44$		0			0
$45$	6.57346			0.979913
$46$		0			0
$47$	−1.50879			−0.220080			−0.110040	−	0.993927i	$-0.535098\pi$
$47$	−1.50879			−0.220080			−0.110040	+	0.993927i	$0.535098\pi$
$48$		0			0
$49$	−1.09082	+	7.58681i	−0.155831	+	1.08383i
$50$		0			0
$51$	−0.531290	+	0.156001i	−0.0743955	+	0.0218445i
$52$		0			0
$53$	−0.488784	−	0.564087i	−0.0671397	−	0.0774834i	0.721186	−	0.692741i	$-0.243597\pi$
$53$	−0.488784	−	0.564087i	−0.0671397	−	0.0774834i	−0.788326	+	0.615258i	$0.789052\pi$
$54$		0			0
$55$	−14.9150	−	4.37944i	−2.01114	−	0.590524i
$56$		0			0
$57$	3.59829	+	2.31248i	0.476605	+	0.306296i
$58$		0			0
$59$	−3.73262	+	4.30768i	−0.485946	+	0.560812i	−0.944778	−	0.327712i	$-0.893723\pi$
$59$	−3.73262	+	4.30768i	−0.485946	+	0.560812i	0.458832	+	0.888523i	$0.348268\pi$
$60$		0			0
$61$	−0.845488	−	5.88050i	−0.108254	−	0.752921i	−0.969563	−	0.244841i	$-0.921264\pi$
$61$	−0.845488	−	5.88050i	−0.108254	−	0.752921i	0.861310	−	0.508080i	$-0.169645\pi$
$62$		0			0
$63$	2.94909	+	6.45762i	0.371551	+	0.813583i
$64$		0			0
$65$	−7.67667	+	16.8096i	−0.952173	+	2.08497i
$66$		0			0
$67$	−2.28890	+	1.47099i	−0.279634	+	0.179710i	−0.672938	−	0.739698i	$-0.734968\pi$
$67$	−2.28890	+	1.47099i	−0.279634	+	0.179710i	0.393305	+	0.919408i	$0.371332\pi$
$68$		0			0
$69$	−0.499028	−	5.11009i	−0.0600759	−	0.615183i
$70$		0			0
$71$	3.24103	−	2.08288i	0.384639	−	0.247193i	−0.334004	−	0.942572i	$-0.608400\pi$
$71$	3.24103	−	2.08288i	0.384639	−	0.247193i	0.718643	+	0.695379i	$0.244764\pi$
$72$		0			0
$73$	−2.40161	+	5.25880i	−0.281087	+	0.615496i	−0.996535	−	0.0831705i	$-0.973495\pi$
$73$	−2.40161	+	5.25880i	−0.281087	+	0.615496i	0.715448	+	0.698666i	$0.246223\pi$
$74$		0			0
$75$	−3.36819	−	7.37531i	−0.388925	−	0.851628i
$76$		0			0
$77$	−2.38916	−	16.6170i	−0.272270	−	1.89368i
$78$		0			0
$79$	1.80406	−	2.08200i	0.202973	−	0.234243i	−0.645132	−	0.764071i	$-0.723198\pi$
$79$	1.80406	−	2.08200i	0.202973	−	0.234243i	0.848106	+	0.529827i	$0.177743\pi$
$80$		0			0
$81$	−0.00158009	−	0.00101546i	−0.000175565	−	0.000112829i
$82$		0			0
$83$	2.62166	+	0.769789i	0.287765	+	0.0844954i	0.422429	−	0.906396i	$-0.361177\pi$
$83$	2.62166	+	0.769789i	0.287765	+	0.0844954i	−0.134665	+	0.990891i	$0.542996\pi$
$84$		0			0
$85$	−1.20099	−	1.38601i	−0.130265	−	0.150334i
$86$		0			0
$87$	−9.49080	+	2.78675i	−1.01752	+	0.298771i
$88$		0			0
$89$	−1.11383	+	7.74687i	−0.118066	+	0.821167i	0.841616	+	0.540077i	$0.181605\pi$
$89$	−1.11383	+	7.74687i	−0.118066	+	0.821167i	−0.959681	+	0.281090i	$0.909304\pi$
$90$		0			0
$91$	−19.9574			−2.09210
$92$		0			0
$93$	−3.76596			−0.390512
$94$		0			0
$95$	−2.01613	+	14.0225i	−0.206851	+	1.43868i
$96$		0			0
$97$	1.85193	−	0.543776i	0.188035	−	0.0552121i	−0.186359	−	0.982482i	$-0.559669\pi$
$97$	1.85193	−	0.543776i	0.188035	−	0.0552121i	0.374394	+	0.927270i	$0.377851\pi$
$98$		0			0
$99$	−5.32198	−	6.14189i	−0.534879	−	0.617283i
$100$		0			0
$101$	8.90549	+	2.61489i	0.886129	+	0.260191i	0.692961	−	0.720975i	$-0.256306\pi$
$101$	8.90549	+	2.61489i	0.886129	+	0.260191i	0.193168	+	0.981166i	$0.438124\pi$
$102$		0			0
$103$	0.429977	+	0.276329i	0.0423669	+	0.0272275i	0.561653	−	0.827373i	$-0.310166\pi$
$103$	0.429977	+	0.276329i	0.0423669	+	0.0272275i	−0.519286	+	0.854601i	$0.673802\pi$
$104$		0			0
$105$	9.52005	−	10.9867i	0.929061	−	1.07219i
$106$		0			0
$107$	−0.269784	−	1.87639i	−0.0260810	−	0.181398i	0.972617	−	0.232415i	$-0.0746627\pi$
$107$	−0.269784	−	1.87639i	−0.0260810	−	0.181398i	−0.998698	+	0.0510174i	$0.983754\pi$
$108$		0			0
$109$	7.51112	+	16.4470i	0.719434	+	1.57534i	0.814695	+	0.579889i	$0.196904\pi$
$109$	7.51112	+	16.4470i	0.719434	+	1.57534i	−0.0952610	+	0.995452i	$0.530369\pi$
$110$		0			0
$111$	−1.53010	+	3.35045i	−0.145230	+	0.318010i
$112$		0			0
$113$	8.73507	−	5.61369i	0.821726	−	0.528091i	−0.0609129	−	0.998143i	$-0.519401\pi$
$113$	8.73507	−	5.61369i	0.821726	−	0.528091i	0.882639	+	0.470052i	$0.155765\pi$
$114$		0			0
$115$	14.7089	−	8.53435i	1.37161	−	0.795832i
$116$		0			0
$117$	−8.12755	+	5.22326i	−0.751392	+	0.482891i
$118$		0			0
$119$	0.822781	−	1.80164i	0.0754242	−	0.165156i
$120$		0			0
$121$	3.41396	+	7.47553i	0.310360	+	0.679594i
$122$		0			0
$123$	1.64709	+	11.4558i	0.148513	+	1.03293i
$124$		0			0
$125$	5.97551	−	6.89611i	0.534466	−	0.616807i
$126$		0			0
$127$	−16.3325	−	10.4962i	−1.44927	−	0.931391i	−0.999264	−	0.0383661i	$-0.987785\pi$
$127$	−16.3325	−	10.4962i	−1.44927	−	0.931391i	−0.450008	−	0.893024i	$-0.648579\pi$
$128$		0			0
$129$	−0.401660	−	0.117938i	−0.0353642	−	0.0103839i
$130$		0			0
$131$	4.47245	+	5.16148i	0.390759	+	0.450960i	0.916709	−	0.399555i	$-0.130835\pi$
$131$	4.47245	+	5.16148i	0.390759	+	0.450960i	−0.525950	+	0.850516i	$0.676290\pi$
$132$		0			0
$133$	−14.6799	+	4.31041i	−1.27291	+	0.373760i
$134$		0			0
$135$	2.62232	−	18.2386i	0.225693	−	1.56973i
$136$		0			0
$137$	−2.24390			−0.191709			−0.0958546	−	0.995395i	$-0.530558\pi$
$137$	−2.24390			−0.191709			−0.0958546	+	0.995395i	$0.530558\pi$
$138$		0			0
$139$	11.5961			0.983566			0.491783	−	0.870718i	$-0.336345\pi$
$139$	11.5961			0.983566			0.491783	+	0.870718i	$0.336345\pi$
$140$		0			0
$141$	−0.229883	+	1.59887i	−0.0193596	+	0.134649i
$142$		0			0
$143$	21.9211	−	6.43662i	1.83314	−	0.538257i
$144$		0			0
$145$	−21.4541	−	24.7593i	−1.78166	−	2.05615i
$146$		0			0
$147$	7.87354	+	2.31188i	0.649398	+	0.190681i
$148$		0			0
$149$	−8.22485	−	5.28579i	−0.673806	−	0.433029i	0.158490	−	0.987361i	$-0.449338\pi$
$149$	−8.22485	−	5.28579i	−0.673806	−	0.433029i	−0.832296	+	0.554332i	$0.812974\pi$
$150$		0			0
$151$	−13.3049	+	15.3547i	−1.08274	+	1.24955i	−0.116144	+	0.993232i	$0.537053\pi$
$151$	−13.3049	+	15.3547i	−1.08274	+	1.24955i	−0.966594	+	0.256314i	$0.917492\pi$
$152$		0			0
$153$	−0.136453	−	0.949049i	−0.0110315	−	0.0767261i
$154$		0			0
$155$	−5.18153	−	11.3460i	−0.416190	−	0.911330i
$156$		0			0
$157$	5.24526	−	11.4855i	0.418618	−	0.916645i	−0.576421	−	0.817153i	$-0.695551\pi$
$157$	5.24526	−	11.4855i	0.418618	−	0.916645i	0.995038	−	0.0994918i	$-0.0317217\pi$
$158$		0			0
$159$	−0.672235	+	0.432019i	−0.0533117	+	0.0342614i
$160$		0			0
$161$	14.9829	+	10.6209i	1.18082	+	0.837043i
$162$		0			0
$163$	−9.20744	+	5.91726i	−0.721182	+	0.463476i	−0.849048	−	0.528316i	$-0.822824\pi$
$163$	−9.20744	+	5.91726i	−0.721182	+	0.463476i	0.127866	+	0.991791i	$0.459187\pi$
$164$		0			0
$165$	−6.91338	+	15.1382i	−0.538206	+	1.17851i
$166$		0			0
$167$	1.94375	+	4.25622i	0.150412	+	0.329356i	0.969807	−	0.243873i	$-0.0784180\pi$
$167$	1.94375	+	4.25622i	0.150412	+	0.329356i	−0.819395	+	0.573229i	$0.805691\pi$
$168$		0			0
$169$	−2.01518	−	14.0159i	−0.155014	−	1.07814i
$170$		0			0
$171$	−4.85021	+	5.59744i	−0.370905	+	0.428047i
$172$		0			0
$173$	14.2401	+	9.15158i	1.08266	+	0.695781i	0.955170	−	0.296059i	$-0.0956724\pi$
$173$	14.2401	+	9.15158i	1.08266	+	0.695781i	0.127487	+	0.991840i	$0.459309\pi$
$174$		0			0
$175$	27.8272	+	8.17079i	2.10354	+	0.617654i
$176$		0			0
$177$	3.99613	+	4.61178i	0.300368	+	0.346643i
$178$		0			0
$179$	11.6236	−	3.41298i	0.868785	−	0.255098i	0.183187	−	0.983078i	$-0.441359\pi$
$179$	11.6236	−	3.41298i	0.868785	−	0.255098i	0.685599	+	0.727980i	$0.259541\pi$
$180$		0			0
$181$	−0.979074	+	6.80961i	−0.0727740	+	0.506154i	0.920534	+	0.390662i	$0.127754\pi$
$181$	−0.979074	+	6.80961i	−0.0727740	+	0.506154i	−0.993308	+	0.115493i	$0.963155\pi$
$182$		0			0
$183$	−6.36039			−0.470173
$184$		0			0
$185$	−12.1994			−0.896914
$186$		0			0
$187$	−0.322679	+	2.24428i	−0.0235966	+	0.164118i
$188$		0			0
$189$	19.0937	−	5.60642i	1.38886	−	0.407807i
$190$		0			0
$191$	8.23926	+	9.50861i	0.596172	+	0.688019i	0.971001	−	0.239075i	$-0.0768441\pi$
$191$	8.23926	+	9.50861i	0.596172	+	0.688019i	−0.374829	+	0.927094i	$0.622299\pi$
$192$		0			0
$193$	−8.06502	−	2.36810i	−0.580533	−	0.170460i	−0.0217349	−	0.999764i	$-0.506919\pi$
$193$	−8.06502	−	2.36810i	−0.580533	−	0.170460i	−0.558798	+	0.829304i	$0.688737\pi$
$194$		0			0
$195$	16.6435	+	10.6961i	1.19186	+	0.765963i
$196$		0			0
$197$	13.1882	−	15.2200i	0.939621	−	1.08438i	−0.0566754	−	0.998393i	$-0.518050\pi$
$197$	13.1882	−	15.2200i	0.939621	−	1.08438i	0.996296	−	0.0859876i	$-0.0274045\pi$
$198$		0			0
$199$	−3.72047	−	25.8764i	−0.263737	−	1.83433i	−0.504096	−	0.863647i	$-0.668174\pi$
$199$	−3.72047	−	25.8764i	−0.263737	−	1.83433i	0.240359	−	0.970684i	$-0.422735\pi$
$200$		0			0
$201$	1.21006	+	2.64967i	0.0853513	+	0.186893i
$202$		0			0
$203$	14.6979	−	32.1839i	1.03159	−	2.25887i
$204$		0			0
$205$	−32.2473	+	20.7241i	−2.25225	+	1.44743i
$206$		0			0
$207$	8.88144	+	0.403966i	0.617302	+	0.0280776i
$208$		0			0
$209$	14.7342	−	9.46910i	1.01919	−	0.654991i
$210$		0			0
$211$	−11.2163	+	24.5603i	−0.772161	+	1.69080i	−0.0503259	+	0.998733i	$0.516026\pi$
$211$	−11.2163	+	24.5603i	−0.772161	+	1.69080i	−0.721835	+	0.692065i	$0.756701\pi$
$212$		0			0
$213$	−1.71342	−	3.75187i	−0.117402	−	0.257074i
$214$		0			0
$215$	−0.197318	−	1.37238i	−0.0134570	−	0.0935954i
$216$		0			0
$217$	8.82139	−	10.1804i	0.598835	−	0.691093i
$218$		0			0
$219$	5.20683	+	3.34623i	0.351845	+	0.226117i
$220$		0			0
$221$	2.58625	+	0.759391i	0.173970	+	0.0510822i
$222$		0			0
$223$	9.62075	+	11.1029i	0.644253	+	0.743508i	0.980121	−	0.198401i	$-0.0635749\pi$
$223$	9.62075	+	11.1029i	0.644253	+	0.743508i	−0.335868	+	0.941909i	$0.609029\pi$
$224$		0			0
$225$	13.4710	−	3.95543i	0.898064	−	0.263695i
$226$		0			0
$227$	1.14162	−	7.94017i	0.0757723	−	0.527008i	−0.916217	−	0.400683i	$-0.868773\pi$
$227$	1.14162	−	7.94017i	0.0757723	−	0.527008i	0.991989	−	0.126325i	$-0.0403181\pi$
$228$		0			0
$229$	14.7699			0.976022			0.488011	−	0.872837i	$-0.337723\pi$
$229$	14.7699			0.976022			0.488011	+	0.872837i	$0.337723\pi$
$230$		0			0
$231$	−17.9730			−1.18254
$232$		0			0
$233$	0.219073	−	1.52369i	0.0143520	−	0.0998201i	−0.981386	−	0.192044i	$-0.938488\pi$
$233$	0.219073	−	1.52369i	0.0143520	−	0.0998201i	0.995738	+	0.0922238i	$0.0293975\pi$
$234$		0			0
$235$	−5.13331	+	1.50728i	−0.334860	+	0.0983238i
$236$		0			0
$237$	−1.93143	−	2.22898i	−0.125460	−	0.144788i
$238$		0			0
$239$	14.2674	+	4.18930i	0.922884	+	0.270983i	0.708455	−	0.705756i	$-0.249393\pi$
$239$	14.2674	+	4.18930i	0.922884	+	0.270983i	0.214429	+	0.976739i	$0.431211\pi$
$240$		0			0
$241$	8.88105	+	5.70750i	0.572079	+	0.367653i	0.794469	−	0.607305i	$-0.207749\pi$
$241$	8.88105	+	5.70750i	0.572079	+	0.367653i	−0.222390	+	0.974958i	$0.571386\pi$
$242$		0			0
$243$	10.2076	−	11.7802i	0.654818	−	0.755701i
$244$		0			0
$245$	3.86792	+	26.9020i	0.247113	+	1.71871i
$246$		0			0
$247$	−8.64949	−	18.9397i	−0.550354	−	1.20511i
$248$		0			0
$249$	1.21519	−	2.66089i	0.0770093	−	0.168627i
$250$		0			0
$251$	−25.2318	+	16.2155i	−1.59262	+	1.02351i	−0.621963	+	0.783047i	$0.713665\pi$
$251$	−25.2318	+	16.2155i	−1.59262	+	1.02351i	−0.970657	+	0.240468i	$0.922699\pi$
$252$		0			0
$253$	−19.8826	−	6.83368i	−1.25001	−	0.429630i
$254$		0			0
$255$	−1.65174	+	1.06151i	−0.103436	+	0.0664744i
$256$		0			0
$257$	0.775774	−	1.69871i	0.0483915	−	0.105963i	−0.883892	−	0.467691i	$-0.845086\pi$
$257$	0.775774	−	1.69871i	0.0483915	−	0.105963i	0.932283	+	0.361728i	$0.117813\pi$
$258$		0			0
$259$	−5.47308	−	11.9844i	−0.340081	−	0.744672i
$260$		0			0
$261$	−2.43755	−	16.9535i	−0.150880	−	1.04940i
$262$		0			0
$263$	−2.23230	+	2.57622i	−0.137650	+	0.158856i	−0.820389	−	0.571806i	$-0.806243\pi$
$263$	−2.23230	+	2.57622i	−0.137650	+	0.158856i	0.682739	+	0.730662i	$0.260789\pi$
$264$		0			0
$265$	−2.22649	−	1.43088i	−0.136772	−	0.0878982i
$266$		0			0
$267$	8.03965	+	2.36066i	0.492019	+	0.144470i
$268$		0			0
$269$	4.77778	+	5.51385i	0.291306	+	0.336185i	0.882472	−	0.470365i	$-0.155878\pi$
$269$	4.77778	+	5.51385i	0.291306	+	0.336185i	−0.591166	+	0.806550i	$0.701332\pi$
$270$		0			0
$271$	9.34474	−	2.74386i	0.567653	−	0.166678i	0.0147021	−	0.999892i	$-0.495320\pi$
$271$	9.34474	−	2.74386i	0.567653	−	0.166678i	0.552951	+	0.833214i	$0.313502\pi$
$272$		0			0
$273$	−3.04074	+	21.1488i	−0.184034	+	1.27998i
$274$		0			0
$275$	−33.2005			−2.00207
$276$		0			0
$277$	20.9394			1.25813			0.629064	−	0.777354i	$-0.283439\pi$
$277$	20.9394			1.25813			0.629064	+	0.777354i	$0.283439\pi$
$278$		0			0
$279$	0.928043	−	6.45468i	0.0555605	−	0.386432i
$280$		0			0
$281$	−17.4908	+	5.13577i	−1.04342	+	0.306374i	−0.758154	−	0.652076i	$-0.773898\pi$
$281$	−17.4908	+	5.13577i	−1.04342	+	0.306374i	−0.285261	+	0.958450i	$0.592080\pi$
$282$		0			0
$283$	−21.0978	−	24.3482i	−1.25414	−	1.44735i	−0.844904	−	0.534919i	$-0.820342\pi$
$283$	−21.0978	−	24.3482i	−1.25414	−	1.44735i	−0.409232	−	0.912430i	$-0.634203\pi$
$284$		0			0
$285$	14.5525	+	4.27299i	0.862014	+	0.253110i
$286$		0			0
$287$	−34.8262	−	22.3815i	−2.05573	−	1.32114i
$288$		0			0
$289$	10.9575	−	12.6456i	0.644556	−	0.743858i
$290$		0			0
$291$	−0.294076	−	2.04534i	−0.0172390	−	0.119900i
$292$		0			0
$293$	−12.0679	−	26.4249i	−0.705012	−	1.54376i	−0.833786	−	0.552088i	$-0.813831\pi$
$293$	−12.0679	−	26.4249i	−0.705012	−	1.54376i	0.128773	−	0.991674i	$-0.458896\pi$
$294$		0			0
$295$	−8.39601	+	18.3847i	−0.488835	+	1.07040i
$296$		0			0
$297$	−19.1643	+	12.3162i	−1.11203	+	0.714656i
$298$		0			0
$299$	−11.4050	+	22.2397i	−0.659569	+	1.28616i
$300$		0			0
$301$	1.25967	−	0.809540i	0.0726061	−	0.0466611i
$302$		0			0
$303$	4.12785	−	9.03874i	0.237139	−	0.519262i
$304$		0			0
$305$	−8.75115	−	19.1624i	−0.501090	−	1.09723i
$306$		0			0
$307$	0.845802	+	5.88268i	0.0482725	+	0.335742i	0.999619	+	0.0276180i	$0.00879221\pi$
$307$	0.845802	+	5.88268i	0.0482725	+	0.335742i	−0.951346	+	0.308124i	$0.900299\pi$
$308$		0			0
$309$	0.358338	−	0.413545i	0.0203852	−	0.0235257i
$310$		0			0
$311$	3.54060	+	2.27540i	0.200769	+	0.129026i	0.637162	−	0.770730i	$-0.280108\pi$
$311$	3.54060	+	2.27540i	0.200769	+	0.129026i	−0.436393	+	0.899756i	$0.643744\pi$
$312$		0			0
$313$	−0.942074	−	0.276618i	−0.0532492	−	0.0156354i	0.254999	−	0.966941i	$-0.417925\pi$
$313$	−0.942074	−	0.276618i	−0.0532492	−	0.0156354i	−0.308249	+	0.951306i	$0.599743\pi$
$314$		0			0
$315$	16.4847	+	19.0244i	0.928808	+	1.07190i
$316$		0			0
$317$	1.83926	−	0.540057i	0.103303	−	0.0303326i	−0.229672	−	0.973268i	$-0.573765\pi$
$317$	1.83926	−	0.540057i	0.103303	−	0.0303326i	0.332976	+	0.942935i	$0.391947\pi$
$318$		0			0
$319$	−5.76423	+	40.0911i	−0.322735	+	2.24467i
$320$		0			0
$321$	−2.02952			−0.113277
$322$		0			0
$323$	2.06637			0.114976
$324$		0			0
$325$	−5.61699	+	39.0670i	−0.311575	+	2.16705i
$326$		0			0
$327$	18.5733	−	5.45363i	1.02711	−	0.301586i
$328$		0			0
$329$	−3.78371	−	4.36663i	−0.208602	−	0.240740i
$330$		0			0
$331$	1.79967	+	0.528432i	0.0989191	+	0.0290453i	0.330818	−	0.943695i	$-0.392676\pi$
$331$	1.79967	+	0.528432i	0.0989191	+	0.0290453i	−0.231898	+	0.972740i	$0.574494\pi$
$332$		0			0
$333$	−5.36545	−	3.44816i	−0.294025	−	0.188958i
$334$		0			0
$335$	−6.31793	+	7.29128i	−0.345185	+	0.398365i
$336$		0			0
$337$	0.904120	+	6.28829i	0.0492505	+	0.342545i	0.999516	+	0.0311043i	$0.00990242\pi$
$337$	0.904120	+	6.28829i	0.0492505	+	0.342545i	−0.950266	+	0.311441i	$0.899188\pi$
$338$		0			0
$339$	−4.61793	−	10.1119i	−0.250812	−	0.549201i
$340$		0			0
$341$	−6.40602	+	14.0272i	−0.346905	+	0.759617i
$342$		0			0
$343$	−2.14176	+	1.37643i	−0.115644	+	0.0743200i
$344$		0			0
$345$	−6.80277	−	16.8873i	−0.366249	−	0.909184i
$346$		0			0
$347$	−5.17071	+	3.32302i	−0.277578	+	0.178389i	−0.672022	−	0.740531i	$-0.734574\pi$
$347$	−5.17071	+	3.32302i	−0.277578	+	0.178389i	0.394443	+	0.918920i	$0.370937\pi$
$348$		0			0
$349$	−9.79875	+	21.4563i	−0.524515	+	1.14853i	0.443187	+	0.896429i	$0.353848\pi$
$349$	−9.79875	+	21.4563i	−0.524515	+	1.14853i	−0.967702	+	0.252098i	$0.918879\pi$
$350$		0			0
$351$	11.2501	+	24.6343i	0.600487	+	1.31488i
$352$		0			0
$353$	0.442169	+	3.07535i	0.0235343	+	0.163684i	0.998199	−	0.0599854i	$-0.0191054\pi$
$353$	0.442169	+	3.07535i	0.0235343	+	0.163684i	−0.974665	+	0.223670i	$0.928196\pi$
$354$		0			0
$355$	8.94603	−	10.3243i	0.474806	−	0.547955i
$356$		0			0
$357$	−1.78384	−	1.14640i	−0.0944107	−	0.0606741i
$358$		0			0
$359$	−16.6971	−	4.90272i	−0.881241	−	0.258756i	−0.190351	−	0.981716i	$-0.560963\pi$
$359$	−16.6971	−	4.90272i	−0.881241	−	0.258756i	−0.690889	+	0.722961i	$0.742781\pi$
$360$		0			0
$361$	1.98948	+	2.29598i	0.104709	+	0.120841i
$362$		0			0
$363$	8.44198	−	2.47879i	0.443089	−	0.130103i
$364$		0			0
$365$	−2.91740	+	20.2910i	−0.152704	+	1.06208i
$366$		0			0
$367$	33.2650			1.73642			0.868210	−	0.496197i	$-0.165270\pi$
$367$	33.2650			1.73642			0.868210	+	0.496197i	$0.165270\pi$
$368$		0			0
$369$	−20.0405			−1.04327
$370$		0			0
$371$	0.406778	−	2.82920i	0.0211188	−	0.146885i
$372$		0			0
$373$	11.0769	−	3.25246i	0.573539	−	0.168406i	0.0179143	−	0.999840i	$-0.494297\pi$
$373$	11.0769	−	3.25246i	0.573539	−	0.168406i	0.555625	+	0.831433i	$0.312479\pi$
$374$		0			0
$375$	−6.39737	−	7.38296i	−0.330359	−	0.381254i
$376$		0			0
$377$	46.2000	+	13.5655i	2.37942	+	0.698660i
$378$		0			0
$379$	−16.3980	−	10.5384i	−0.842309	−	0.541319i	0.0468579	−	0.998902i	$-0.485079\pi$
$379$	−16.3980	−	10.5384i	−0.842309	−	0.541319i	−0.889167	+	0.457582i	$0.848716\pi$
$380$		0			0
$381$	−13.6113	+	15.7083i	−0.697328	+	0.804760i
$382$		0			0
$383$	−3.50132	−	24.3522i	−0.178909	−	1.24434i	−0.859293	−	0.511484i	$-0.829096\pi$
$383$	−3.50132	−	24.3522i	−0.178909	−	1.24434i	0.680383	−	0.732856i	$-0.261813\pi$
$384$		0			0
$385$	−24.7288	−	54.1485i	−1.26029	−	2.75966i
$386$		0			0
$387$	0.301121	−	0.659363i	0.0153069	−	0.0335173i
$388$		0			0
$389$	0.457844	−	0.294239i	0.0232136	−	0.0149185i	−0.528983	−	0.848633i	$-0.677426\pi$
$389$	0.457844	−	0.294239i	0.0232136	−	0.0149185i	0.552196	+	0.833714i	$0.313790\pi$
$390$		0			0
$391$	−1.53749	−	1.94646i	−0.0777540	−	0.0984366i
$392$		0			0
$393$	6.15105	−	3.95304i	0.310279	−	0.199404i
$394$		0			0
$395$	4.05799	−	8.88576i	0.204180	−	0.447091i
$396$		0			0
$397$	0.909326	+	1.99115i	0.0456378	+	0.0999327i	0.931078	−	0.364821i	$-0.118870\pi$
$397$	0.909326	+	1.99115i	0.0456378	+	0.0999327i	−0.885440	+	0.464754i	$0.846143\pi$
$398$		0			0
$399$	2.33108	+	16.2131i	0.116700	+	0.811668i
$400$		0			0
$401$	2.59606	−	2.99601i	0.129641	−	0.149614i	−0.687218	−	0.726452i	$-0.741168\pi$
$401$	2.59606	−	2.99601i	0.129641	−	0.149614i	0.816859	+	0.576838i	$0.195714\pi$
$402$		0			0
$403$	15.4220	+	9.91114i	0.768226	+	0.493709i
$404$		0			0
$405$	−0.00639031	−	0.00187636i	−0.000317537	−	9.32373e-5i
$406$		0			0
$407$	9.87680	+	11.3984i	0.489575	+	0.564999i
$408$		0			0
$409$	−2.69246	+	0.790577i	−0.133133	+	0.0390915i	−0.347620	−	0.937635i	$-0.613010\pi$
$409$	−2.69246	+	0.790577i	−0.133133	+	0.0390915i	0.214487	+	0.976727i	$0.431192\pi$
$410$		0			0
$411$	−0.341884	+	2.37786i	−0.0168639	+	0.117291i
$412$		0			0
$413$	−21.8275			−1.07406
$414$		0			0
$415$	9.68859			0.475594
$416$		0			0
$417$	1.76680	−	12.2884i	0.0865205	−	0.601764i
$418$		0			0
$419$	−1.24429	+	0.365357i	−0.0607877	+	0.0178489i	−0.311985	−	0.950087i	$-0.600994\pi$
$419$	−1.24429	+	0.365357i	−0.0607877	+	0.0178489i	0.251197	+	0.967936i	$0.419176\pi$
$420$		0			0
$421$	−15.1401	−	17.4727i	−0.737886	−	0.851565i	0.255450	−	0.966822i	$-0.417776\pi$
$421$	−15.1401	−	17.4727i	−0.737886	−	0.851565i	−0.993336	+	0.115257i	$0.963231\pi$
$422$		0			0
$423$	−2.68374	−	0.788016i	−0.130488	−	0.0383147i
$424$		0			0
$425$	−3.29518	−	2.11768i	−0.159840	−	0.102723i
$426$		0			0
$427$	14.8986	−	17.1939i	0.720993	−	0.832070i
$428$		0			0
$429$	−3.48095	−	24.2105i	−0.168062	−	1.16889i
$430$		0			0
$431$	−9.71241	−	21.2672i	−0.467830	−	1.02441i	−0.985632	−	0.168905i	$-0.945977\pi$
$431$	−9.71241	−	21.2672i	−0.467830	−	1.02441i	0.517802	−	0.855500i	$-0.326750\pi$
$432$		0			0
$433$	−5.19415	+	11.3736i	−0.249615	+	0.546581i	−0.992415	−	0.122933i	$-0.960770\pi$
$433$	−5.19415	+	11.3736i	−0.249615	+	0.546581i	0.742800	+	0.669513i	$0.233497\pi$
$434$		0			0
$435$	−29.5062	+	18.9625i	−1.41472	+	0.909182i
$436$		0			0
$437$	−3.58575	+	18.8220i	−0.171530	+	0.900379i
$438$		0			0
$439$	17.8160	−	11.4497i	0.850314	−	0.546463i	−0.0413589	−	0.999144i	$-0.513169\pi$
$439$	17.8160	−	11.4497i	0.850314	−	0.546463i	0.891673	+	0.452681i	$0.149532\pi$
$440$		0			0
$441$	−5.90272	+	12.9252i	−0.281082	+	0.615484i
$442$		0			0
$443$	7.13793	+	15.6299i	0.339133	+	0.742599i	0.999969	−	0.00793242i	$-0.00252499\pi$
$443$	7.13793	+	15.6299i	0.339133	+	0.742599i	−0.660835	+	0.750531i	$0.729798\pi$
$444$		0			0
$445$	3.94953	+	27.4696i	0.187226	+	1.30218i
$446$		0			0
$447$	−6.85451	+	7.91052i	−0.324207	+	0.374155i
$448$		0			0
$449$	−19.5999	−	12.5961i	−0.924975	−	0.594446i	−0.0108783	−	0.999941i	$-0.503463\pi$
$449$	−19.5999	−	12.5961i	−0.924975	−	0.594446i	−0.914097	+	0.405495i	$0.867099\pi$
$450$		0			0
$451$	45.4715	+	13.3516i	2.14117	+	0.628704i
$452$		0			0
$453$	14.2442	+	16.4387i	0.669251	+	0.772356i
$454$		0			0
$455$	−67.9001	+	19.9373i	−3.18321	+	0.934674i
$456$		0			0
$457$	5.47543	−	38.0824i	0.256130	−	1.78142i	−0.303655	−	0.952782i	$-0.598207\pi$
$457$	5.47543	−	38.0824i	0.256130	−	1.78142i	0.559784	−	0.828638i	$-0.310884\pi$
$458$		0			0
$459$	−2.68766			−0.125449
$460$		0			0
$461$	−10.0360			−0.467424			−0.233712	−	0.972306i	$-0.575087\pi$
$461$	−10.0360			−0.467424			−0.233712	+	0.972306i	$0.575087\pi$
$462$		0			0
$463$	−3.28697	+	22.8614i	−0.152759	+	1.06246i	0.758810	+	0.651312i	$0.225781\pi$
$463$	−3.28697	+	22.8614i	−0.152759	+	1.06246i	−0.911569	+	0.411147i	$0.865128\pi$
$464$		0			0
$465$	−12.8128	+	3.76217i	−0.594178	+	0.174467i
$466$		0			0
$467$	19.4471	+	22.4432i	0.899907	+	1.03855i	0.999055	+	0.0434749i	$0.0138428\pi$
$467$	19.4471	+	22.4432i	0.899907	+	1.03855i	−0.0991479	+	0.995073i	$0.531612\pi$
$468$		0			0
$469$	−9.99725	−	2.93546i	−0.461630	−	0.135547i
$470$		0			0
$471$	−11.3720	−	7.30836i	−0.523996	−	0.336752i
$472$		0			0
$473$	−1.12253	+	1.29546i	−0.0516138	+	0.0595655i
$474$		0			0
$475$	4.30608	+	29.9495i	0.197577	+	1.37418i
$476$		0			0
$477$	−0.574802	−	1.25864i	−0.0263184	−	0.0576293i
$478$		0			0
$479$	11.0209	−	24.1324i	0.503558	−	1.10264i	−0.471738	−	0.881739i	$-0.656373\pi$
$479$	11.0209	−	24.1324i	0.503558	−	1.10264i	0.975296	−	0.220900i	$-0.0708994\pi$
$480$		0			0
$481$	15.0835	−	9.69359i	0.687749	−	0.441990i
$482$		0			0
$483$	13.5378	−	14.2592i	0.615990	−	0.648815i
$484$		0			0
$485$	5.75752	−	3.70014i	0.261436	−	0.168015i
$486$		0			0
$487$	14.5857	−	31.9382i	0.660941	−	1.44726i	−0.220702	−	0.975341i	$-0.570835\pi$
$487$	14.5857	−	31.9382i	0.660941	−	1.44726i	0.881643	−	0.471917i	$-0.156438\pi$
$488$		0			0
$489$	4.86766	+	10.6587i	0.220123	+	0.482002i
$490$		0			0
$491$	−4.73319	−	32.9201i	−0.213606	−	1.48566i	−0.760981	−	0.648774i	$-0.775282\pi$
$491$	−4.73319	−	32.9201i	−0.213606	−	1.48566i	0.547375	−	0.836888i	$-0.315627\pi$
$492$		0			0
$493$	−3.12930	+	3.61141i	−0.140937	+	0.162650i
$494$		0			0
$495$	−24.2425	−	15.5797i	−1.08962	−	0.700255i
$496$		0			0
$497$	14.1558	+	4.15653i	0.634977	+	0.186446i
$498$		0			0
$499$	−8.32485	−	9.60738i	−0.372671	−	0.430086i	0.538174	−	0.842834i	$-0.319114\pi$
$499$	−8.32485	−	9.60738i	−0.372671	−	0.430086i	−0.910845	+	0.412748i	$0.864569\pi$
$500$		0			0
$501$	4.80646	−	1.41131i	0.214737	−	0.0630525i
$502$		0			0
$503$	−2.01872	+	14.0405i	−0.0900101	+	0.626034i	0.894019	+	0.448028i	$0.147874\pi$
$503$	−2.01872	+	14.0405i	−0.0900101	+	0.626034i	−0.984029	+	0.178006i	$0.943036\pi$
$504$		0			0
$505$	32.9110			1.46452
$506$		0			0
$507$	−15.1596			−0.673263
$508$		0			0
$509$	−4.43595	+	30.8527i	−0.196620	+	1.36752i	0.617383	+	0.786662i	$0.288193\pi$
$509$	−4.43595	+	30.8527i	−0.196620	+	1.36752i	−0.814003	+	0.580860i	$0.802716\pi$
$510$		0			0
$511$	−21.2423	+	6.23729i	−0.939702	+	0.275922i
$512$		0			0
$513$	13.5957	+	15.6903i	0.600266	+	0.692744i
$514$		0			0
$515$	1.73894	+	0.510600i	0.0766271	+	0.0224997i
$516$		0			0
$517$	5.56433	+	3.57598i	0.244719	+	0.157271i
$518$		0			0
$519$	11.8676	−	13.6959i	0.520929	−	0.601184i
$520$		0			0
$521$	−2.93426	−	20.4082i	−0.128552	−	0.894101i	−0.947391	−	0.320078i	$-0.896291\pi$
$521$	−2.93426	−	20.4082i	−0.128552	−	0.894101i	0.818839	−	0.574023i	$-0.194618\pi$
$522$		0			0
$523$	−13.4428	−	29.4356i	−0.587811	−	1.28713i	−0.936756	−	0.349984i	$-0.886187\pi$
$523$	−13.4428	−	29.4356i	−0.587811	−	1.28713i	0.348945	−	0.937143i	$-0.386540\pi$
$524$		0			0
$525$	12.8984	−	28.2435i	0.562932	−	1.23265i
$526$		0			0
$527$	−1.53053	+	0.983609i	−0.0666707	+	0.0428467i
$528$		0			0
$529$	20.3978	−	10.6269i	0.886860	−	0.462039i
$530$		0			0
$531$	−8.88915	+	5.71271i	−0.385756	+	0.247910i
$532$		0			0
$533$	23.4039	−	51.2474i	1.01374	−	2.21977i
$534$		0			0
$535$	−2.79238	−	6.11445i	−0.120725	−	0.264351i
$536$		0			0
$537$	−1.84575	−	12.8375i	−0.0796501	−	0.553979i
$538$		0			0
$539$	22.0043	−	25.3943i	0.947792	−	1.09381i
$540$		0			0
$541$	12.5267	+	8.05042i	0.538565	+	0.346115i	0.781477	−	0.623934i	$-0.214466\pi$
$541$	12.5267	+	8.05042i	0.538565	+	0.346115i	−0.242913	+	0.970048i	$0.578103\pi$
$542$		0			0
$543$	7.06697	+	2.07505i	0.303273	+	0.0890489i
$544$		0			0
$545$	41.9853	+	48.4536i	1.79845	+	2.07552i
$546$		0			0
$547$	20.6863	−	6.07406i	0.884484	−	0.259708i	0.192220	−	0.981352i	$-0.438431\pi$
$547$	20.6863	−	6.07406i	0.884484	−	0.259708i	0.692264	+	0.721644i	$0.256613\pi$
$548$		0			0
$549$	1.56739	−	10.9014i	0.0668944	−	0.465261i
$550$		0			0
$551$	36.9129			1.57254
$552$		0			0
$553$	10.5497			0.448620
$554$		0			0
$555$	−1.85872	+	12.9277i	−0.0788981	+	0.548748i
$556$		0			0
$557$	32.3712	−	9.50503i	1.37161	−	0.402741i	0.488769	−	0.872413i	$-0.337446\pi$
$557$	32.3712	−	9.50503i	1.37161	−	0.402741i	0.882841	+	0.469672i	$0.155628\pi$
$558$		0			0
$559$	1.33446	+	1.54005i	0.0564416	+	0.0651370i
$560$		0			0
$561$	2.32910	+	0.683885i	0.0983346	+	0.0288737i
$562$		0			0
$563$	22.0338	+	14.1602i	0.928612	+	0.596783i	0.915144	−	0.403126i	$-0.132077\pi$
$563$	22.0338	+	14.1602i	0.928612	+	0.596783i	0.0134680	+	0.999909i	$0.495713\pi$
$564$		0			0
$565$	24.1109	−	27.8255i	1.01435	−	1.17063i
$566$		0			0
$567$	−0.00102363	−	0.00711950i	−4.29884e−5	−	0.000298991i
$568$		0			0
$569$	7.19516	+	15.7552i	0.301637	+	0.660493i	0.998384	−	0.0568239i	$-0.0180974\pi$
$569$	7.19516	+	15.7552i	0.301637	+	0.660493i	−0.696747	+	0.717317i	$0.745370\pi$
$570$		0			0
$571$	−10.7111	+	23.4541i	−0.448247	+	0.981523i	0.541764	+	0.840531i	$0.317757\pi$
$571$	−10.7111	+	23.4541i	−0.448247	+	0.981523i	−0.990011	+	0.140993i	$0.954971\pi$
$572$		0			0
$573$	11.3316	−	7.28239i	0.473385	−	0.304226i
$574$		0			0
$575$	25.0076	−	26.3402i	1.04289	−	1.09846i
$576$		0			0
$577$	−27.2326	+	17.5013i	−1.13371	+	0.728589i	−0.966330	−	0.257304i	$-0.917166\pi$
$577$	−27.2326	+	17.5013i	−1.13371	+	0.728589i	−0.167376	+	0.985893i	$0.553529\pi$
$578$		0			0
$579$	−3.73828	+	8.18569i	−0.155358	+	0.340186i
$580$		0			0
$581$	4.34666	+	9.51785i	0.180330	+	0.394867i
$582$		0			0
$583$	0.465666	+	3.23878i	0.0192859	+	0.134137i
$584$		0			0
$585$	−22.4340	+	25.8903i	−0.927533	+	1.07043i
$586$		0			0
$587$	0.923193	+	0.593300i	0.0381043	+	0.0244881i	0.559554	−	0.828794i	$-0.310972\pi$
$587$	0.923193	+	0.593300i	0.0381043	+	0.0244881i	−0.521450	+	0.853282i	$0.674609\pi$
$588$		0			0
$589$	13.4845	+	3.95941i	0.555619	+	0.163145i
$590$		0			0
$591$	−14.1193	−	16.2945i	−0.580789	−	0.670266i
$592$		0			0
$593$	−34.9467	+	10.2613i	−1.43509	+	0.421380i	−0.904581	−	0.426301i	$-0.859816\pi$
$593$	−34.9467	+	10.2613i	−1.43509	+	0.421380i	−0.530506	+	0.847681i	$0.677998\pi$
$594$		0			0
$595$	0.999489	−	6.95160i	0.0409751	−	0.284988i
$596$		0			0
$597$	−27.9881			−1.14548
$598$		0			0
$599$	30.3382			1.23959			0.619793	−	0.784765i	$-0.287217\pi$
$599$	30.3382			1.23959			0.619793	+	0.784765i	$0.287217\pi$
$600$		0			0
$601$	−4.86175	+	33.8142i	−0.198315	+	1.37931i	0.610858	+	0.791740i	$0.290825\pi$
$601$	−4.86175	+	33.8142i	−0.198315	+	1.37931i	−0.809173	+	0.587570i	$0.800084\pi$
$602$		0			0
$603$	−4.83961	+	1.42104i	−0.197084	+	0.0578691i
$604$		0			0
$605$	19.0832	+	22.0232i	0.775842	+	0.895370i
$606$		0			0
$607$	7.46270	+	2.19125i	0.302902	+	0.0889400i	0.429652	−	0.902995i	$-0.358636\pi$
$607$	7.46270	+	2.19125i	0.302902	+	0.0889400i	−0.126750	+	0.991935i	$0.540455\pi$
$608$		0			0
$609$	−31.8659	−	20.4790i	−1.29127	−	0.829850i
$610$		0			0
$611$	5.14925	−	5.94255i	0.208316	−	0.240410i
$612$		0			0
$613$	−3.31554	−	23.0601i	−0.133913	−	0.931387i	−0.940384	−	0.340114i	$-0.889534\pi$
$613$	−3.31554	−	23.0601i	−0.133913	−	0.931387i	0.806471	−	0.591274i	$-0.201375\pi$
$614$		0			0
$615$	17.0481	+	37.3301i	0.687444	+	1.50529i
$616$		0			0
$617$	5.83273	−	12.7719i	0.234817	−	0.514177i	−0.755137	−	0.655567i	$-0.772430\pi$
$617$	5.83273	−	12.7719i	0.234817	−	0.514177i	0.989954	+	0.141390i	$0.0451570\pi$
$618$		0			0
$619$	−5.00010	+	3.21337i	−0.200971	+	0.129156i	−0.637256	−	0.770653i	$-0.719930\pi$
$619$	−5.00010	+	3.21337i	−0.200971	+	0.129156i	0.436285	+	0.899809i	$0.356294\pi$
$620$		0			0
$621$	4.66387	−	24.4812i	0.187155	−	0.982396i
$622$		0			0
$623$	−25.2136	+	16.2038i	−1.01016	+	0.649191i
$624$		0			0
$625$	−2.28936	+	5.01299i	−0.0915743	+	0.200520i
$626$		0			0
$627$	−7.78947	−	17.0566i	−0.311082	−	0.681173i
$628$		0			0
$629$	0.253236	+	1.76129i	0.0100972	+	0.0702274i
$630$		0			0
$631$	−19.3896	+	22.3768i	−0.771888	+	0.890806i	−0.996496	−	0.0836428i	$-0.973345\pi$
$631$	−19.3896	+	22.3768i	−0.771888	+	0.890806i	0.224608	+	0.974449i	$0.427890\pi$
$632$		0			0
$633$	24.3176	+	15.6279i	0.966536	+	0.621155i
$634$		0			0
$635$	−66.0530	−	19.3949i	−2.62123	−	0.769663i
$636$		0			0
$637$	−26.1587	−	30.1887i	−1.03644	−	1.19612i
$638$		0			0
$639$	6.85276	−	2.01215i	0.271091	−	0.0795995i
$640$		0			0
$641$	2.95382	−	20.5443i	0.116669	−	0.811450i	−0.844513	−	0.535535i	$-0.820110\pi$
$641$	2.95382	−	20.5443i	0.116669	−	0.811450i	0.961182	−	0.275915i	$-0.0889808\pi$
$642$		0			0
$643$	−10.9240			−0.430801			−0.215400	−	0.976526i	$-0.569106\pi$
$643$	−10.9240			−0.430801			−0.215400	+	0.976526i	$0.569106\pi$
$644$		0			0
$645$	−1.48437			−0.0584471
$646$		0			0
$647$	−6.32753	+	44.0089i	−0.248761	+	1.73017i	0.356633	+	0.934244i	$0.383925\pi$
$647$	−6.32753	+	44.0089i	−0.248761	+	1.73017i	−0.605394	+	0.795926i	$0.706985\pi$
$648$		0			0
$649$	23.9753	−	7.03977i	0.941111	−	0.276335i
$650$		0			0
$651$	−9.44416	−	10.8991i	−0.370146	−	0.427171i
$652$		0			0
$653$	−17.1761	−	5.04335i	−0.672151	−	0.197361i	−0.0721905	−	0.997391i	$-0.522999\pi$
$653$	−17.1761	−	5.04335i	−0.672151	−	0.197361i	−0.599961	+	0.800029i	$0.704817\pi$
$654$		0			0
$655$	20.3727	+	13.0927i	0.796028	+	0.511576i
$656$		0			0
$657$	−7.01839	+	8.09966i	−0.273814	+	0.315998i
$658$		0			0
$659$	4.26612	+	29.6715i	0.166184	+	1.15584i	0.886682	+	0.462380i	$0.153004\pi$
$659$	4.26612	+	29.6715i	0.166184	+	1.15584i	−0.720498	+	0.693457i	$0.756087\pi$
$660$		0			0
$661$	9.90995	+	21.6998i	0.385452	+	0.844023i	0.998540	+	0.0540083i	$0.0171997\pi$
$661$	9.90995	+	21.6998i	0.385452	+	0.844023i	−0.613088	+	0.790014i	$0.710073\pi$
$662$		0			0
$663$	1.19877	−	2.62495i	0.0465565	−	0.101944i
$664$		0			0
$665$	−45.6388	+	29.3303i	−1.76980	+	1.13738i
$666$		0			0
$667$	−27.4652	−	34.7709i	−1.06346	−	1.34633i
$668$		0			0
$669$	13.2316	−	8.50345i	0.511564	−	0.328762i
$670$		0			0
$671$	−10.8192	+	23.6908i	−0.417671	+	0.914573i
$672$		0			0
$673$	17.7599	+	38.8887i	0.684594	+	1.49905i	0.857701	+	0.514148i	$0.171892\pi$
$673$	17.7599	+	38.8887i	0.684594	+	1.49905i	−0.173108	+	0.984903i	$0.555381\pi$
$674$		0			0
$675$	−5.60078	−	38.9543i	−0.215574	−	1.49935i
$676$		0			0
$677$	−0.828600	+	0.956256i	−0.0318457	+	0.0367519i	−0.771449	−	0.636291i	$-0.780468\pi$
$677$	−0.828600	+	0.956256i	−0.0318457	+	0.0367519i	0.739603	+	0.673043i	$0.235013\pi$
$678$		0			0
$679$	6.21797	+	3.99605i	0.238624	+	0.153354i
$680$		0			0
$681$	−8.24026	−	2.41956i	−0.315768	−	0.0927177i
$682$		0			0
$683$	25.5344	+	29.4682i	0.977046	+	1.12757i	0.991815	+	0.127680i	$0.0407531\pi$
$683$	25.5344	+	29.4682i	0.977046	+	1.12757i	−0.0147694	+	0.999891i	$0.504701\pi$
$684$		0			0
$685$	−7.63432	+	2.24164i	−0.291693	+	0.0856487i
$686$		0			0
$687$	2.25037	−	15.6517i	0.0858569	−	0.597148i
$688$		0			0
$689$	3.88985			0.148192
$690$		0			0
$691$	−8.04344			−0.305987			−0.152993	−	0.988227i	$-0.548891\pi$
$691$	−8.04344			−0.305987			−0.152993	+	0.988227i	$0.548891\pi$
$692$		0			0
$693$	4.42907	−	30.8049i	0.168247	−	1.17018i
$694$		0			0
$695$	39.4529	−	11.5844i	1.49653	−	0.439421i
$696$		0			0
$697$	3.66146	+	4.22555i	0.138688	+	0.160054i
$698$		0			0
$699$	−1.58127	−	0.464304i	−0.0598092	−	0.0175616i
$700$		0			0
$701$	−32.0057	−	20.5688i	−1.20884	−	0.776873i	−0.228375	−	0.973573i	$-0.573341\pi$
$701$	−32.0057	−	20.5688i	−1.20884	−	0.776873i	−0.980464	+	0.196700i	$0.936977\pi$
$702$		0			0
$703$	9.00126	−	10.3880i	0.339489	−	0.391791i
$704$		0			0
$705$	0.815140	+	5.66942i	0.0306999	+	0.213523i
$706$		0			0
$707$	14.7651	+	32.3311i	0.555299	+	1.21594i
$708$		0			0
$709$	−19.9593	+	43.7047i	−0.749586	+	1.64136i	0.0175230	+	0.999846i	$0.494422\pi$
$709$	−19.9593	+	43.7047i	−0.749586	+	1.64136i	−0.767109	+	0.641517i	$0.778305\pi$
$710$		0			0
$711$	4.29633	−	2.76109i	0.161125	−	0.103549i
$712$		0			0
$713$	−6.30354	−	15.6480i	−0.236069	−	0.586023i
$714$		0			0
$715$	68.1512	−	43.7981i	2.54871	−	1.63796i
$716$		0			0
$717$	6.61321	−	14.4809i	0.246975	−	0.540800i
$718$		0			0
$719$	−11.6453	−	25.4996i	−0.434296	−	0.950975i	−0.992610	−	0.121346i	$-0.961279\pi$
$719$	−11.6453	−	25.4996i	−0.434296	−	0.950975i	0.558314	−	0.829629i	$-0.311448\pi$
$720$		0			0
$721$	0.278552	+	1.93737i	0.0103738	+	0.0721516i
$722$		0			0
$723$	7.40137	−	8.54164i	0.275260	−	0.317667i
$724$		0			0
$725$	−58.8641	−	37.8297i	−2.18616	−	1.40496i
$726$		0			0
$727$	15.4496	+	4.53641i	0.572994	+	0.168246i	0.555377	−	0.831599i	$-0.312574\pi$
$727$	15.4496	+	4.53641i	0.572994	+	0.168246i	0.0176167	+	0.999845i	$0.494392\pi$
$728$		0			0
$729$	−10.9319	−	12.6161i	−0.404886	−	0.467264i
$730$		0			0
$731$	−0.194042	+	0.0569760i	−0.00717692	+	0.00210733i
$732$		0			0
$733$	2.35565	−	16.3839i	0.0870079	−	0.605154i	−0.898936	−	0.438079i	$-0.855659\pi$
$733$	2.35565	−	16.3839i	0.0870079	−	0.605154i	0.985944	−	0.167074i	$-0.0534320\pi$
$734$		0			0
$735$	29.0974			1.07327
$736$		0			0
$737$	11.9277			0.439362
$738$		0			0
$739$	−0.962976	+	6.69764i	−0.0354236	+	0.246377i	−0.999838	−	0.0180200i	$-0.994264\pi$
$739$	−0.962976	+	6.69764i	−0.0354236	+	0.246377i	0.964414	+	0.264397i	$0.0851728\pi$
$740$		0			0
$741$	−21.3883	+	6.28017i	−0.785718	+	0.230708i
$742$		0			0
$743$	−19.9896	−	23.0693i	−0.733349	−	0.846330i	0.259496	−	0.965744i	$-0.416444\pi$
$743$	−19.9896	−	23.0693i	−0.733349	−	0.846330i	−0.992844	+	0.119415i	$0.961898\pi$
$744$		0			0
$745$	−33.2636	−	9.76706i	−1.21868	−	0.357838i
$746$		0			0
$747$	4.26118	+	2.73849i	0.155908	+	0.100196i
$748$		0			0
$749$	4.75394	−	5.48634i	0.173705	−	0.200466i
$750$		0			0
$751$	−4.37947	−	30.4599i	−0.159809	−	1.11150i	−0.898983	−	0.437983i	$-0.855693\pi$
$751$	−4.37947	−	30.4599i	−0.159809	−	1.11150i	0.739174	−	0.673515i	$-0.235216\pi$
$752$		0			0
$753$	13.3392	+	29.2088i	0.486108	+	1.06443i
$754$		0			0
$755$	−29.9275	+	65.5321i	−1.08917	+	2.38496i
$756$		0			0
$757$	−0.599505	+	0.385278i	−0.0217894	+	0.0140032i	−0.551490	−	0.834181i	$-0.685941\pi$
$757$	−0.599505	+	0.385278i	−0.0217894	+	0.0140032i	0.529701	+	0.848185i	$0.322304\pi$
$758$		0			0
$759$	−10.2710	+	20.0284i	−0.372814	+	0.726986i
$760$		0			0
$761$	−31.0091	+	19.9283i	−1.12408	+	0.722402i	−0.964316	−	0.264753i	$-0.914709\pi$
$761$	−31.0091	+	19.9283i	−1.12408	+	0.722402i	−0.159763	+	0.987155i	$0.551073\pi$
$762$		0			0
$763$	−28.7636	+	62.9834i	−1.04131	+	2.28015i
$764$		0			0
$765$	−1.41234	−	3.09260i	−0.0510633	−	0.111813i
$766$		0			0
$767$	−4.22747	−	29.4027i	−0.152645	−	1.06167i
$768$		0			0
$769$	12.1617	−	14.0353i	0.438561	−	0.506126i	−0.492841	−	0.870120i	$-0.664041\pi$
$769$	12.1617	−	14.0353i	0.438561	−	0.506126i	0.931402	+	0.363993i	$0.118587\pi$
$770$		0			0
$771$	−1.68192	−	1.08091i	−0.0605730	−	0.0389279i
$772$		0			0
$773$	20.5853	+	6.04438i	0.740400	+	0.217401i	0.630118	−	0.776499i	$-0.283006\pi$
$773$	20.5853	+	6.04438i	0.740400	+	0.217401i	0.110282	+	0.993900i	$0.464825\pi$
$774$		0			0
$775$	−17.4457	−	20.1334i	−0.626667	−	0.723212i
$776$		0			0
$777$	−13.5337	+	3.97386i	−0.485520	+	0.142561i
$778$		0			0
$779$	6.14660	−	42.7505i	0.220225	−	1.53170i
$780$		0			0
$781$	−16.8893			−0.604347
$782$		0			0
$783$	−48.0115			−1.71579
$784$		0			0
$785$	6.37179	−	44.3167i	0.227419	−	1.58173i
$786$		0			0
$787$	11.6449	−	3.41924i	0.415095	−	0.121883i	−0.0675150	−	0.997718i	$-0.521507\pi$
$787$	11.6449	−	3.41924i	0.415095	−	0.121883i	0.482610	+	0.875835i	$0.339689\pi$
$788$		0			0
$789$	2.38990	+	2.75809i	0.0850826	+	0.0981906i
$790$		0			0
$791$	38.1522	+	11.2025i	1.35654	+	0.398315i
$792$		0			0
$793$	26.0465	+	16.7391i	0.924938	+	0.594421i
$794$		0			0
$795$	−1.85553	+	2.14140i	−0.0658090	+	0.0759477i
$796$		0			0
$797$	0.825462	+	5.74122i	0.0292394	+	0.203364i	0.999204	−	0.0398798i	$-0.0126975\pi$
$797$	0.825462	+	5.74122i	0.0292394	+	0.203364i	−0.969965	+	0.243244i	$0.921788\pi$
$798$		0			0
$799$	0.324172	+	0.709839i	0.0114684	+	0.0251123i
$800$		0			0
$801$	−6.02726	+	13.1979i	−0.212963	+	0.466323i
$802$		0			0
$803$	21.3208	−	13.7021i	0.752395	−	0.483535i
$804$		0			0
$805$	61.5860	+	21.1672i	2.17062	+	0.746045i
$806$		0			0
$807$	6.57097	−	4.22291i	0.231309	−	0.148653i
$808$		0			0
$809$	−7.83044	+	17.1463i	−0.275304	+	0.602831i	−0.995894	−	0.0905303i	$-0.971144\pi$
$809$	−7.83044	+	17.1463i	−0.275304	+	0.602831i	0.720590	+	0.693361i	$0.243871\pi$
$810$		0			0
$811$	12.0857	+	26.4639i	0.424385	+	0.929273i	0.994205	+	0.107503i	$0.0342857\pi$
$811$	12.0857	+	26.4639i	0.424385	+	0.929273i	−0.569820	+	0.821770i	$0.692987\pi$
$812$		0			0
$813$	−1.48389	−	10.3207i	−0.0520423	−	0.361962i
$814$		0			0
$815$	−25.4148	+	29.3302i	−0.890241	+	1.02739i
$816$		0			0
$817$	1.31420	+	0.844585i	0.0459780	+	0.0295483i
$818$		0			0
$819$	−35.4987	−	10.4234i	−1.24043	−	0.364222i
$820$		0			0
$821$	−6.49968	−	7.50102i	−0.226840	−	0.261788i	0.630908	−	0.775858i	$-0.282683\pi$
$821$	−6.49968	−	7.50102i	−0.226840	−	0.261788i	−0.857748	+	0.514070i	$0.828137\pi$
$822$		0			0
$823$	−50.4992	+	14.8279i	−1.76029	+	0.516868i	−0.992329	−	0.123629i	$-0.960547\pi$
$823$	−50.4992	+	14.8279i	−1.76029	+	0.516868i	−0.767961	+	0.640496i	$0.778729\pi$
$824$		0			0
$825$	−5.05849	+	35.1826i	−0.176114	+	1.22490i
$826$		0			0
$827$	−10.9941			−0.382302			−0.191151	−	0.981561i	$-0.561222\pi$
$827$	−10.9941			−0.382302			−0.191151	+	0.981561i	$0.561222\pi$
$828$		0			0
$829$	47.8423			1.66163			0.830815	−	0.556548i	$-0.187875\pi$
$829$	47.8423			1.66163			0.830815	+	0.556548i	$0.187875\pi$
$830$		0			0
$831$	3.19037	−	22.1895i	0.110673	−	0.769745i
$832$		0			0
$833$	3.80371	−	1.11687i	0.131791	−	0.0386973i
$834$		0			0
$835$	10.8651	+	12.5390i	0.376001	+	0.433929i
$836$		0			0
$837$	−17.5389	−	5.14988i	−0.606232	−	0.178006i
$838$		0			0
$839$	6.06387	+	3.89701i	0.209348	+	0.134540i	0.641113	−	0.767446i	$-0.278473\pi$
$839$	6.06387	+	3.89701i	0.209348	+	0.134540i	−0.431765	+	0.901986i	$0.642109\pi$
$840$		0			0
$841$	−36.9100	+	42.5964i	−1.27276	+	1.46884i
$842$		0			0
$843$	2.77744	+	19.3175i	0.0956601	+	0.665331i
$844$		0			0
$845$	−20.8579	−	45.6724i	−0.717534	−	1.57118i
$846$		0			0
$847$	−13.0737	+	28.6273i	−0.449216	+	0.983646i
$848$		0			0
$849$	−29.0163	+	18.6476i	−0.995836	+	0.639985i
$850$		0			0
$851$	−16.4826	−	0.749701i	−0.565017	−	0.0256994i
$852$		0			0
$853$	−13.9853	+	8.98780i	−0.478847	+	0.307736i	−0.757706	−	0.652596i	$-0.773680\pi$
$853$	−13.9853	+	8.98780i	−0.478847	+	0.307736i	0.278859	+	0.960332i	$0.410044\pi$
$854$		0			0
$855$	−10.9099	+	23.8893i	−0.373109	+	0.816996i
$856$		0			0
$857$	−14.4798	−	31.7063i	−0.494619	−	1.08307i	−0.978181	−	0.207755i	$-0.933384\pi$
$857$	−14.4798	−	31.7063i	−0.494619	−	1.08307i	0.483561	−	0.875310i	$-0.339343\pi$
$858$		0			0
$859$	0.868624	+	6.04141i	0.0296371	+	0.206130i	0.999260	−	0.0384761i	$-0.0122503\pi$
$859$	0.868624	+	6.04141i	0.0296371	+	0.206130i	−0.969622	+	0.244606i	$0.921341\pi$
$860$		0			0
$861$	−29.0238	+	33.4953i	−0.989129	+	1.14152i
$862$		0			0
$863$	−23.2158	−	14.9199i	−0.790275	−	0.507879i	0.0821538	−	0.996620i	$-0.473820\pi$
$863$	−23.2158	−	14.9199i	−0.790275	−	0.507879i	−0.872429	+	0.488740i	$0.837457\pi$
$864$		0			0
$865$	57.5910	+	16.9102i	1.95815	+	0.574965i
$866$		0			0
$867$	−11.7310	−	13.5383i	−0.398406	−	0.459785i
$868$		0			0
$869$	−11.5878	+	3.40249i	−0.393089	+	0.115421i
$870$		0			0
$871$	2.01797	−	14.0353i	0.0683764	−	0.475568i
$872$		0			0
$873$	3.57809			0.121100
$874$		0			0
$875$	34.9434			1.18130
$876$		0			0
$877$	3.43819	−	23.9131i	0.116099	−	0.807490i	−0.845685	−	0.533682i	$-0.820808\pi$
$877$	3.43819	−	23.9131i	0.116099	−	0.807490i	0.961785	−	0.273807i	$-0.0882831\pi$
$878$		0			0
$879$	−29.8412	+	8.76217i	−1.00652	+	0.295541i
$880$		0			0
$881$	8.67217	+	10.0082i	0.292173	+	0.337186i	0.882791	−	0.469766i	$-0.155662\pi$
$881$	8.67217	+	10.0082i	0.292173	+	0.337186i	−0.590618	+	0.806951i	$0.701116\pi$
$882$		0			0
$883$	−29.8656	−	8.76934i	−1.00506	−	0.295112i	−0.262528	−	0.964924i	$-0.584556\pi$
$883$	−29.8656	−	8.76934i	−1.00506	−	0.295112i	−0.742530	+	0.669813i	$0.766374\pi$
$884$		0			0
$885$	18.2030	+	11.6984i	0.611888	+	0.393237i
$886$		0			0
$887$	16.5842	−	19.1392i	0.556845	−	0.642633i	−0.405620	−	0.914042i	$-0.632944\pi$
$887$	16.5842	−	19.1392i	0.556845	−	0.642633i	0.962464	+	0.271409i	$0.0874897\pi$
$888$		0			0
$889$	−10.5807	−	73.5902i	−0.354865	−	2.46814i
$890$		0			0
$891$	0.00342053	+	0.00748991i	0.000114592	+	0.000250921i
$892$		0			0
$893$	2.50412	−	5.48327i	0.0837973	−	0.183490i
$894$		0			0
$895$	36.1368	−	23.2237i	1.20792	−	0.776283i
$896$		0			0
$897$	21.8297	+	15.4744i	0.728874	+	0.516674i
$898$		0			0
$899$	−27.3408	+	17.5709i	−0.911868	+	0.586022i
$900$		0			0
$901$	−0.160367	+	0.351154i	−0.00534259	+	0.0116986i
$902$		0			0
$903$	−0.665944	−	1.45821i	−0.0221612	−	0.0485263i
$904$		0			0
$905$	3.47169	+	24.1461i	0.115403	+	0.802645i
$906$		0			0
$907$	1.80362	−	2.08149i	0.0598884	−	0.0691148i	−0.725015	−	0.688733i	$-0.758167\pi$
$907$	1.80362	−	2.08149i	0.0598884	−	0.0691148i	0.784903	+	0.619618i	$0.212713\pi$
$908$		0			0
$909$	14.4747	+	9.30235i	0.480097	+	0.308540i
$910$		0			0
$911$	13.9831	+	4.10581i	0.463281	+	0.136031i	0.505039	−	0.863096i	$-0.331478\pi$
$911$	13.9831	+	4.10581i	0.463281	+	0.136031i	−0.0417588	+	0.999128i	$0.513296\pi$
$912$		0			0
$913$	−7.84404	−	9.05251i	−0.259600	−	0.299594i
$914$		0			0
$915$	−21.6397	+	6.35399i	−0.715386	+	0.210056i
$916$		0			0
$917$	−3.72207	+	25.8876i	−0.122914	+	0.854883i
$918$		0			0
$919$	−22.2003			−0.732320			−0.366160	−	0.930552i	$-0.619328\pi$
$919$	−22.2003			−0.732320			−0.366160	+	0.930552i	$0.619328\pi$
$920$		0			0
$921$	6.36275			0.209660
$922$		0			0
$923$	−2.85740	+	19.8736i	−0.0940524	+	0.654149i
$924$		0			0
$925$	−25.0001	+	7.34069i	−0.821998	+	0.241360i
$926$		0			0
$927$	0.620491	+	0.716085i	0.0203796	+	0.0235193i
$928$		0			0
$929$	−42.5637	−	12.4978i	−1.39647	−	0.410041i	−0.505000	−	0.863119i	$-0.668508\pi$
$929$	−42.5637	−	12.4978i	−1.39647	−	0.410041i	−0.891471	+	0.453078i	$0.850326\pi$
$930$		0			0
$931$	−25.7616	−	16.5560i	−0.844302	−	0.542600i
$932$		0			0
$933$	2.95070	−	3.40529i	0.0966015	−	0.111484i
$934$		0			0
$935$	1.14418	+	7.95798i	0.0374188	+	0.260254i
$936$		0			0
$937$	8.99032	+	19.6861i	0.293701	+	0.643115i	0.997751	−	0.0670354i	$-0.0213540\pi$
$937$	8.99032	+	19.6861i	0.293701	+	0.643115i	−0.704050	+	0.710151i	$0.748627\pi$
$938$		0			0
$939$	−0.436668	+	0.956169i	−0.0142501	+	0.0312034i
$940$		0			0
$941$	−0.100106	+	0.0643339i	−0.00326335	+	0.00209723i	−0.542271	−	0.840203i	$-0.682436\pi$
$941$	−0.100106	+	0.0643339i	−0.00326335	+	0.00209723i	0.539008	+	0.842301i	$0.318799\pi$
$942$		0			0
$943$	−44.8431	+	26.0187i	−1.46029	+	0.847286i
$944$		0			0
$945$	59.3610	−	38.1490i	1.93101	−	1.24099i
$946$		0			0
$947$	20.6069	−	45.1229i	0.669636	−	1.46630i	−0.203627	−	0.979049i	$-0.565273\pi$
$947$	20.6069	−	45.1229i	0.669636	−	1.46630i	0.873263	−	0.487249i	$-0.162000\pi$
$948$		0			0
$949$	−12.5161	−	27.4063i	−0.406288	−	0.889648i
$950$		0			0
$951$	−0.292064	−	2.03135i	−0.00947084	−	0.0658711i
$952$		0			0
$953$	1.95809	−	2.25975i	0.0634287	−	0.0732006i	−0.723148	−	0.690693i	$-0.757306\pi$
$953$	1.95809	−	2.25975i	0.0634287	−	0.0732006i	0.786577	+	0.617492i	$0.211851\pi$
$954$		0			0
$955$	37.5311	+	24.1198i	1.21448	+	0.780499i
$956$		0			0
$957$	41.6063	+	12.2167i	1.34494	+	0.394910i
$958$		0			0
$959$	−5.62718	−	6.49411i	−0.181711	−	0.209706i
$960$		0			0
$961$	17.8718	−	5.24763i	0.576510	−	0.169279i
$962$		0			0
$963$	0.500132	−	3.47849i	0.0161165	−	0.112093i
$964$		0			0
$965$	−29.8050			−0.959457
$966$		0			0
$967$	22.6066			0.726980			0.363490	−	0.931598i	$-0.381585\pi$
$967$	22.6066			0.726980			0.363490	+	0.931598i	$0.381585\pi$
$968$		0			0
$969$	0.314835	−	2.18973i	0.0101140	−	0.0703442i
$970$		0			0
$971$	−14.6935	+	4.31439i	−0.471536	+	0.138455i	−0.508863	−	0.860848i	$-0.669934\pi$
$971$	−14.6935	+	4.31439i	−0.471536	+	0.138455i	0.0373270	+	0.999303i	$0.488116\pi$
$972$		0			0
$973$	29.0803	+	33.5604i	0.932270	+	1.07590i
$974$		0			0
$975$	40.5435	+	11.9046i	1.29843	+	0.381254i
$976$		0			0
$977$	−2.91804	−	1.87531i	−0.0933563	−	0.0599964i	0.493130	−	0.869956i	$-0.335853\pi$
$977$	−2.91804	−	1.87531i	−0.0933563	−	0.0599964i	−0.586486	+	0.809959i	$0.699489\pi$
$978$		0			0
$979$	22.4685	−	25.9301i	0.718098	−	0.828729i
$980$		0			0
$981$	4.77024	+	33.1778i	0.152302	+	1.05928i
$982$		0			0
$983$	11.4071	+	24.9780i	0.363829	+	0.796675i	0.999691	+	0.0248716i	$0.00791769\pi$
$983$	11.4071	+	24.9780i	0.363829	+	0.796675i	−0.635861	+	0.771803i	$0.719355\pi$
$984$		0			0
$985$	29.6650	−	64.9573i	0.945206	−	2.06971i
$986$		0			0
$987$	−5.20381	+	3.34429i	−0.165639	+	0.106450i
$988$		0			0
$989$	−0.182259	−	1.86635i	−0.00579551	−	0.0593466i
$990$		0			0
$991$	20.2771	−	13.0313i	0.644123	−	0.413952i	−0.177392	−	0.984140i	$-0.556766\pi$
$991$	20.2771	−	13.0313i	0.644123	−	0.413952i	0.821514	+	0.570188i	$0.193130\pi$
$992$		0			0
$993$	0.834181	−	1.82660i	0.0264719	−	0.0579655i
$994$		0			0
$995$	−38.5084	−	84.3216i	−1.22080	−	2.67317i
$996$		0			0
$997$	3.80364	+	26.4549i	0.120462	+	0.837834i	0.957034	+	0.289976i	$0.0936474\pi$
$997$	3.80364	+	26.4549i	0.120462	+	0.837834i	−0.836571	+	0.547858i	$0.815443\pi$
$998$		0			0
$999$	−11.7077	+	13.5114i	−0.370414	+	0.427480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.e.81.3		30
4.3	odd	2		184.2.i.b.81.1	yes	30
23.2	even	11	inner	368.2.m.e.209.3		30
23.5	odd	22		8464.2.a.ch.1.7		15
23.18	even	11		8464.2.a.cg.1.7		15
92.51	even	22		4232.2.a.ba.1.9		15
92.71	odd	22		184.2.i.b.25.1	✓	30
92.87	odd	22		4232.2.a.bb.1.9		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.25.1	✓	30	92.71	odd	22
184.2.i.b.81.1	yes	30	4.3	odd	2
368.2.m.e.81.3		30	1.1	even	1	trivial
368.2.m.e.209.3		30	23.2	even	11	inner
4232.2.a.ba.1.9		15	92.51	even	22
4232.2.a.bb.1.9		15	92.87	odd	22
8464.2.a.cg.1.7		15	23.18	even	11
8464.2.a.ch.1.7		15	23.5	odd	22

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.152362 - 1.05970i) q^{3} +(3.40226 - 0.998994i) q^{5} +(2.50777 + 2.89412i) q^{7} +(1.77873 + 0.522282i) q^{9} +(-3.68793 - 2.37009i) q^{11} +(-3.41282 + 3.93861i) q^{13} +(-0.540259 - 3.75758i) q^{15} +(-0.214855 - 0.470467i) q^{17} +(-1.65968 + 3.63420i) q^{19} +(3.44899 - 2.21653i) q^{21} +(4.65821 - 1.14066i) q^{23} +(6.37112 - 4.09447i) q^{25} +(2.15870 - 4.72689i) q^{27} +(-3.83811 - 8.40428i) q^{29} +(-0.500611 - 3.48182i) q^{31} +(-3.07349 + 3.54699i) q^{33} +(11.4233 + 7.34130i) q^{35} +(-3.30106 - 0.969277i) q^{37} +(3.65376 + 4.21666i) q^{39} +(-10.3725 + 3.04564i) q^{41} +(0.0556469 - 0.387033i) q^{43} +6.57346 q^{45} -1.50879 q^{47} +(-1.09082 + 7.58681i) q^{49} +(-0.531290 + 0.156001i) q^{51} +(-0.488784 - 0.564087i) q^{53} +(-14.9150 - 4.37944i) q^{55} +(3.59829 + 2.31248i) q^{57} +(-3.73262 + 4.30768i) q^{59} +(-0.845488 - 5.88050i) q^{61} +(2.94909 + 6.45762i) q^{63} +(-7.67667 + 16.8096i) q^{65} +(-2.28890 + 1.47099i) q^{67} +(-0.499028 - 5.11009i) q^{69} +(3.24103 - 2.08288i) q^{71} +(-2.40161 + 5.25880i) q^{73} +(-3.36819 - 7.37531i) q^{75} +(-2.38916 - 16.6170i) q^{77} +(1.80406 - 2.08200i) q^{79} +(-0.00158009 - 0.00101546i) q^{81} +(2.62166 + 0.769789i) q^{83} +(-1.20099 - 1.38601i) q^{85} +(-9.49080 + 2.78675i) q^{87} +(-1.11383 + 7.74687i) q^{89} -19.9574 q^{91} -3.76596 q^{93} +(-2.01613 + 14.0225i) q^{95} +(1.85193 - 0.543776i) q^{97} +(-5.32198 - 6.14189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41}+ \cdots + 17 q^{99}+O(q^{100}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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