LMFDB - Embedded newform 345.2.t.a.4.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [345,2,Mod(4,345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(345, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("345.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.t (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			4.10
Character	$\chi$	$=$	345.4
Dual form			345.2.t.a.259.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.853361 + 0.389717i) q^{2} +(0.281733 + 0.959493i) q^{3} +(-0.733376 + 0.846361i) q^{4} +(1.71593 - 1.43374i) q^{5} +(-0.614350 - 0.708998i) q^{6} +(-3.82750 + 0.550312i) q^{7} +(0.824602 - 2.80834i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-0.905553 + 1.89222i) q^{10} +(-2.40180 + 5.25922i) q^{11} +(-1.01869 - 0.465221i) q^{12} +(-0.921789 - 0.132533i) q^{13} +(3.05178 - 1.96126i) q^{14} +(1.85909 + 1.24249i) q^{15} +(0.0720174 + 0.500892i) q^{16} +(-4.01108 + 3.47562i) q^{17} +(0.507196 - 0.789213i) q^{18} +(1.07509 - 1.24073i) q^{19} +(-0.0449608 + 2.50376i) q^{20} +(-1.60635 - 3.51742i) q^{21} -5.42404i q^{22} +(-4.21393 - 2.28972i) q^{23} +2.92690 q^{24} +(0.888804 - 4.92037i) q^{25} +(0.838270 - 0.246138i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(2.34124 - 3.64303i) q^{28} +(4.14344 + 4.78179i) q^{29} +(-2.07070 - 0.335772i) q^{30} +(-7.44322 - 2.18553i) q^{31} +(2.90814 + 4.52515i) q^{32} +(-5.72285 - 0.822822i) q^{33} +(2.06839 - 4.52914i) q^{34} +(-5.77871 + 6.43192i) q^{35} +(0.159378 - 1.10850i) q^{36} +(-2.37022 - 3.68813i) q^{37} +(-0.433912 + 1.47777i) q^{38} +(-0.132533 - 0.921789i) q^{39} +(-2.61146 - 6.00116i) q^{40} +(-1.83297 - 1.17798i) q^{41} +(2.74160 + 2.37561i) q^{42} +(2.28567 + 7.78427i) q^{43} +(-2.68977 - 5.88978i) q^{44} +(-0.668393 + 2.13383i) q^{45} +(4.48834 + 0.311715i) q^{46} +6.42334i q^{47} +(-0.460313 + 0.210218i) q^{48} +(7.63049 - 2.24051i) q^{49} +(1.15908 + 4.54523i) q^{50} +(-4.46488 - 2.86941i) q^{51} +(0.788189 - 0.682969i) q^{52} +(7.37727 - 1.06069i) q^{53} +(0.900138 + 0.264304i) q^{54} +(3.41901 + 12.4680i) q^{55} +(-1.61071 + 11.2027i) q^{56} +(1.49336 + 0.681993i) q^{57} +(-5.39940 - 2.46582i) q^{58} +(0.201629 - 1.40236i) q^{59} +(-2.41501 + 0.662251i) q^{60} +(5.12770 + 1.50563i) q^{61} +(7.20350 - 1.03571i) q^{62} +(2.92238 - 2.53226i) q^{63} +(-5.09664 - 3.27541i) q^{64} +(-1.77174 + 1.09418i) q^{65} +(5.20432 - 1.52813i) q^{66} +(-2.93815 + 1.34181i) q^{67} -5.94375i q^{68} +(1.00977 - 4.68832i) q^{69} +(2.42470 - 7.74081i) q^{70} +(3.79033 + 8.29967i) q^{71} +(0.824602 + 2.80834i) q^{72} +(-0.193447 - 0.167623i) q^{73} +(3.45998 + 2.22360i) q^{74} +(4.97146 - 0.533427i) q^{75} +(0.261653 + 1.81984i) q^{76} +(6.29870 - 21.4514i) q^{77} +(0.472336 + 0.734969i) q^{78} +(1.06527 - 7.40910i) q^{79} +(0.841723 + 0.756240i) q^{80} +(0.415415 - 0.909632i) q^{81} +(2.02327 + 0.290902i) q^{82} +(7.36517 + 11.4604i) q^{83} +(4.15507 + 1.22004i) q^{84} +(-1.89959 + 11.7147i) q^{85} +(-4.98416 - 5.75203i) q^{86} +(-3.42075 + 5.32279i) q^{87} +(12.7891 + 11.0818i) q^{88} +(-1.51999 + 0.446311i) q^{89} +(-0.261211 - 2.08142i) q^{90} +3.60109 q^{91} +(5.02832 - 1.88728i) q^{92} -7.75746i q^{93} +(-2.50329 - 5.48143i) q^{94} +(0.0659105 - 3.67039i) q^{95} +(-3.52253 + 4.06522i) q^{96} +(-7.10064 + 11.0488i) q^{97} +(-5.63839 + 4.88570i) q^{98} +(-0.822822 - 5.72285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) $ 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$-1$

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 $

$2$	−0.853361	+	0.389717i	−0.603417	+	0.275571i	−0.693608	−	0.720353i	$-0.743980\pi$
$2$	−0.853361	+	0.389717i	−0.603417	+	0.275571i	0.0901902	+	0.995925i	$0.471253\pi$
$3$	0.281733	+	0.959493i	0.162658	+	0.553964i
$3$	0.281733	+	0.959493i	0.162658	+	0.553964i
$4$	−0.733376	+	0.846361i	−0.366688	+	0.423180i
$5$	1.71593	−	1.43374i	0.767385	−	0.641186i
$5$	1.71593	−	1.43374i	0.767385	−	0.641186i
$6$	−0.614350	−	0.708998i	−0.250807	−	0.289447i
$7$	−3.82750	+	0.550312i	−1.44666	+	0.207998i	−0.820478	−	0.571678i	$-0.806293\pi$
$7$	−3.82750	+	0.550312i	−1.44666	+	0.207998i	−0.626182	+	0.779677i	$0.715383\pi$
$8$	0.824602	−	2.80834i	0.291541	−	0.992896i
$9$	−0.841254	+	0.540641i	−0.280418	+	0.180214i
$10$	−0.905553	+	1.89222i	−0.286361	+	0.598372i
$11$	−2.40180	+	5.25922i	−0.724171	+	1.58571i	0.0837934	+	0.996483i	$0.473296\pi$
$11$	−2.40180	+	5.25922i	−0.724171	+	1.58571i	−0.807965	+	0.589231i	$0.799431\pi$
$12$	−1.01869	−	0.465221i	−0.294071	−	0.134298i
$13$	−0.921789	−	0.132533i	−0.255658	−	0.0367581i	0.0132939	−	0.999912i	$-0.495768\pi$
$13$	−0.921789	−	0.132533i	−0.255658	−	0.0367581i	−0.268952	+	0.963154i	$0.586677\pi$
$14$	3.05178	−	1.96126i	0.815622	−	0.524168i
$15$	1.85909	+	1.24249i	0.480015	+	0.320809i
$16$	0.0720174	+	0.500892i	0.0180043	+	0.125223i
$17$	−4.01108	+	3.47562i	−0.972830	+	0.842962i	−0.987610	−	0.156929i	$-0.949841\pi$
$17$	−4.01108	+	3.47562i	−0.972830	+	0.842962i	0.0147803	+	0.999891i	$0.495295\pi$
$18$	0.507196	−	0.789213i	0.119547	−	0.186019i
$19$	1.07509	−	1.24073i	0.246644	−	0.284642i	−0.618906	−	0.785465i	$-0.712424\pi$
$19$	1.07509	−	1.24073i	0.246644	−	0.284642i	0.865550	+	0.500823i	$0.166969\pi$
$20$	−0.0449608	+	2.50376i	−0.0100535	+	0.559858i
$21$	−1.60635	−	3.51742i	−0.350535	−	0.767564i
$22$		−	5.42404i		−	1.15641i
$23$	−4.21393	−	2.28972i	−0.878665	−	0.477439i
$23$	−4.21393	−	2.28972i	−0.878665	−	0.477439i
$24$	2.92690			0.597450
$25$	0.888804	−	4.92037i	0.177761	−	0.984074i
$26$	0.838270	−	0.246138i	0.164398	−	0.0482717i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	2.34124	−	3.64303i	0.442452	−	0.688469i
$29$	4.14344	+	4.78179i	0.769418	+	0.887956i	0.996298	−	0.0859667i	$-0.0273979\pi$
$29$	4.14344	+	4.78179i	0.769418	+	0.887956i	−0.226880	+	0.973923i	$0.572852\pi$
$30$	−2.07070	−	0.335772i	−0.378056	−	0.0613033i
$31$	−7.44322	−	2.18553i	−1.33684	−	0.392532i	−0.466301	−	0.884626i	$-0.654413\pi$
$31$	−7.44322	−	2.18553i	−1.33684	−	0.392532i	−0.870542	+	0.492094i	$0.836232\pi$
$32$	2.90814	+	4.52515i	0.514090	+	0.799940i
$33$	−5.72285	−	0.822822i	−0.996220	−	0.143235i
$34$	2.06839	−	4.52914i	0.354726	−	0.776742i
$35$	−5.77871	+	6.43192i	−0.976780	+	1.08719i
$36$	0.159378	−	1.10850i	0.0265630	−	0.184749i
$37$	−2.37022	−	3.68813i	−0.389662	−	0.606326i	0.589898	−	0.807478i	$-0.299168\pi$
$37$	−2.37022	−	3.68813i	−0.389662	−	0.606326i	−0.979560	+	0.201152i	$0.935531\pi$
$38$	−0.433912	+	1.47777i	−0.0703899	+	0.239726i
$39$	−0.132533	−	0.921789i	−0.0212223	−	0.147604i
$40$	−2.61146	−	6.00116i	−0.412907	−	0.948866i
$41$	−1.83297	−	1.17798i	−0.286262	−	0.183970i	0.389627	−	0.920973i	$-0.372604\pi$
$41$	−1.83297	−	1.17798i	−0.286262	−	0.183970i	−0.675889	+	0.737003i	$0.736240\pi$
$42$	2.74160	+	2.37561i	0.423038	+	0.366564i
$43$	2.28567	+	7.78427i	0.348561	+	1.18709i	0.928158	+	0.372186i	$0.121392\pi$
$43$	2.28567	+	7.78427i	0.348561	+	1.18709i	−0.579597	+	0.814903i	$0.696790\pi$
$44$	−2.68977	−	5.88978i	−0.405498	−	0.887917i
$45$	−0.668393	+	2.13383i	−0.0996381	+	0.318093i
$46$	4.48834	+	0.311715i	0.661770	+	0.0459599i
$47$			6.42334i			0.936941i	0.883479	+	0.468470i	$0.155195\pi$
$47$			6.42334i			0.936941i	−0.883479	+	0.468470i	$0.844805\pi$
$48$	−0.460313	+	0.210218i	−0.0664404	+	0.0303423i
$49$	7.63049	−	2.24051i	1.09007	−	0.320073i
$50$	1.15908	+	4.54523i	0.163919	+	0.642793i
$51$	−4.46488	−	2.86941i	−0.625209	−	0.401797i
$52$	0.788189	−	0.682969i	0.109302	−	0.0947108i
$53$	7.37727	−	1.06069i	1.01335	−	0.145697i	0.384417	−	0.923160i	$-0.374403\pi$
$53$	7.37727	−	1.06069i	1.01335	−	0.145697i	0.628929	+	0.777462i	$0.283493\pi$
$54$	0.900138	+	0.264304i	0.122493	+	0.0359673i
$55$	3.41901	+	12.4680i	0.461019	+	1.68118i
$56$	−1.61071	+	11.2027i	−0.215240	+	1.49702i
$57$	1.49336	+	0.681993i	0.197800	+	0.0903322i
$58$	−5.39940	−	2.46582i	−0.708976	−	0.323778i
$59$	0.201629	−	1.40236i	0.0262499	−	0.182572i	−0.972478	−	0.232994i	$-0.925148\pi$
$59$	0.201629	−	1.40236i	0.0262499	−	0.182572i	0.998728	+	0.0504223i	$0.0160567\pi$
$60$	−2.41501	+	0.662251i	−0.311776	+	0.0854962i
$61$	5.12770	+	1.50563i	0.656535	+	0.192776i	0.592998	−	0.805204i	$-0.297944\pi$
$61$	5.12770	+	1.50563i	0.656535	+	0.192776i	0.0635361	+	0.997980i	$0.479762\pi$
$62$	7.20350	−	1.03571i	0.914845	−	0.131535i
$63$	2.92238	−	2.53226i	0.368185	−	0.319034i
$64$	−5.09664	−	3.27541i	−0.637079	−	0.409426i
$65$	−1.77174	+	1.09418i	−0.219757	+	0.135717i
$66$	5.20432	−	1.52813i	0.640608	−	0.188100i
$67$	−2.93815	+	1.34181i	−0.358952	+	0.163928i	−0.586725	−	0.809786i	$-0.699583\pi$
$67$	−2.93815	+	1.34181i	−0.358952	+	0.163928i	0.227773	+	0.973714i	$0.426856\pi$
$68$		−	5.94375i		−	0.720786i
$69$	1.00977	−	4.68832i	0.121562	−	0.564408i
$70$	2.42470	−	7.74081i	0.289807	−	0.925204i
$71$	3.79033	+	8.29967i	0.449830	+	0.984990i	0.989689	+	0.143234i	$0.0457502\pi$
$71$	3.79033	+	8.29967i	0.449830	+	0.984990i	−0.539859	+	0.841755i	$0.681522\pi$
$72$	0.824602	+	2.80834i	0.0971802	+	0.330965i
$73$	−0.193447	−	0.167623i	−0.0226413	−	0.0196188i	0.643467	−	0.765474i	$-0.277496\pi$
$73$	−0.193447	−	0.167623i	−0.0226413	−	0.0196188i	−0.666108	+	0.745855i	$0.732041\pi$
$74$	3.45998	+	2.22360i	0.402215	+	0.258488i
$75$	4.97146	−	0.533427i	0.574055	−	0.0615949i
$76$	0.261653	+	1.81984i	0.0300136	+	0.208749i
$77$	6.29870	−	21.4514i	0.717804	−	2.44462i
$78$	0.472336	+	0.734969i	0.0534815	+	0.0832188i
$79$	1.06527	−	7.40910i	0.119852	−	0.833589i	−0.837865	−	0.545877i	$-0.816197\pi$
$79$	1.06527	−	7.40910i	0.119852	−	0.833589i	0.957717	−	0.287711i	$-0.0928944\pi$
$80$	0.841723	+	0.756240i	0.0941075	+	0.0845502i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	2.02327	+	0.290902i	0.223432	+	0.0321247i
$83$	7.36517	+	11.4604i	0.808432	+	1.25794i	0.962876	+	0.269943i	$0.0870050\pi$
$83$	7.36517	+	11.4604i	0.808432	+	1.25794i	−0.154444	+	0.988002i	$0.549359\pi$
$84$	4.15507	+	1.22004i	0.453355	+	0.133117i
$85$	−1.89959	+	11.7147i	−0.206040	+	1.27064i
$86$	−4.98416	−	5.75203i	−0.537456	−	0.620257i
$87$	−3.42075	+	5.32279i	−0.366743	+	0.570663i
$88$	12.7891	+	11.0818i	1.36332	+	1.18133i
$89$	−1.51999	+	0.446311i	−0.161119	+	0.0473088i	−0.361297	−	0.932451i	$-0.617666\pi$
$89$	−1.51999	+	0.446311i	−0.161119	+	0.0473088i	0.200178	+	0.979759i	$0.435848\pi$
$90$	−0.261211	−	2.08142i	−0.0275341	−	0.219400i
$91$	3.60109			0.377496
$92$	5.02832	−	1.88728i	0.524238	−	0.196763i
$93$		−	7.75746i		−	0.804411i
$94$	−2.50329	−	5.48143i	−0.258194	−	0.565366i
$95$	0.0659105	−	3.67039i	0.00676227	−	0.376575i
$96$	−3.52253	+	4.06522i	−0.359517	+	0.414904i
$97$	−7.10064	+	11.0488i	−0.720961	+	1.12184i	0.266479	+	0.963841i	$0.414140\pi$
$97$	−7.10064	+	11.0488i	−0.720961	+	1.12184i	−0.987440	+	0.157996i	$0.949497\pi$
$98$	−5.63839	+	4.88570i	−0.569564	+	0.493530i
$99$	−0.822822	−	5.72285i	−0.0826967	−	0.575168i
$100$	3.51258	+	4.36073i	0.351258	+	0.436073i
$101$	12.1204	−	7.78933i	1.20603	−	0.775067i	0.226039	−	0.974118i	$-0.427422\pi$
$101$	12.1204	−	7.78933i	1.20603	−	0.775067i	0.979989	+	0.199051i	$0.0637859\pi$
$102$	4.92842	+	0.708599i	0.487986	+	0.0701618i
$103$	1.82424	+	0.833101i	0.179747	+	0.0820879i	0.503256	−	0.864137i	$-0.332135\pi$
$103$	1.82424	+	0.833101i	0.179747	+	0.0820879i	−0.323509	+	0.946225i	$0.604863\pi$
$104$	−1.13231	+	2.47941i	−0.111032	+	0.243126i
$105$	−7.79943	−	3.73255i	−0.761147	−	0.364260i
$106$	−5.88211	+	3.78020i	−0.571321	+	0.367166i
$107$	−1.93670	+	6.59579i	−0.187228	+	0.637639i	0.811362	+	0.584544i	$0.198727\pi$
$107$	−1.93670	+	6.59579i	−0.187228	+	0.637639i	−0.998589	+	0.0530947i	$0.983091\pi$
$108$	1.10850	−	0.159378i	0.106665	−	0.0153361i
$109$	8.20550	+	9.46965i	0.785945	+	0.907028i	0.997524	−	0.0703325i	$-0.0224060\pi$
$109$	8.20550	+	9.46965i	0.785945	+	0.907028i	−0.211579	+	0.977361i	$0.567861\pi$
$110$	−7.77663	−	9.30724i	−0.741473	−	0.887411i
$111$	2.87097	−	3.31328i	0.272501	−	0.314482i
$112$	−0.551294	−	1.87753i	−0.0520923	−	0.177410i
$113$	1.27536	−	0.582439i	0.119976	−	0.0547913i	−0.354523	−	0.935047i	$-0.615357\pi$
$113$	1.27536	−	0.582439i	0.119976	−	0.0547913i	0.474499	+	0.880256i	$0.342629\pi$
$114$	−1.54016			−0.144249
$115$	−10.5136	+	2.11268i	−0.980402	+	0.197008i
$116$	−7.08582			−0.657902
$117$	0.847111	−	0.386863i	0.0783155	−	0.0357655i
$118$	0.374462	+	1.27530i	0.0344720	+	0.117401i
$119$	13.4397	−	15.5103i	1.23202	−	1.42183i
$120$	5.02234	−	4.19639i	0.458474	−	0.383077i
$121$	−14.6872	−	16.9500i	−1.33520	−	1.54091i
$122$	−4.96255	+	0.713507i	−0.449288	+	0.0645979i
$123$	0.613856	−	2.09060i	0.0553495	−	0.188503i
$124$	7.30842	−	4.69684i	0.656316	−	0.421789i
$125$	−5.52939	−	9.71730i	−0.494563	−	0.869142i
$126$	−1.50698	+	3.29983i	−0.134253	+	0.293972i
$127$	−13.3739	−	6.10764i	−1.18674	−	0.541965i	−0.278507	−	0.960434i	$-0.589840\pi$
$127$	−13.3739	−	6.10764i	−1.18674	−	0.541965i	−0.908231	+	0.418469i	$0.862567\pi$
$128$	−5.02285	−	0.722177i	−0.443961	−	0.0638320i
$129$	−6.82500	+	4.38616i	−0.600908	+	0.386180i
$130$	1.08551	−	1.62421i	0.0952056	−	0.142453i
$131$	2.60989	+	18.1522i	0.228027	+	1.58597i	0.706403	+	0.707810i	$0.250317\pi$
$131$	2.60989	+	18.1522i	0.228027	+	1.58597i	−0.478375	+	0.878156i	$0.658774\pi$
$132$	4.89340	−	4.24016i	0.425916	−	0.369058i
$133$	−3.43214	+	5.34052i	−0.297604	+	0.463082i
$134$	1.98438	−	2.29009i	0.171424	−	0.197834i
$135$	−2.23571	−	0.0401473i	−0.192419	−	0.00345533i
$136$	6.45316	+	14.1305i	0.553354	+	1.21168i
$137$			6.33785i			0.541479i	0.962653	+	0.270740i	$0.0872682\pi$
$137$			6.33785i			0.541479i	−0.962653	+	0.270740i	$0.912732\pi$
$138$	0.965424	+	4.39436i	0.0821824	+	0.374072i
$139$	12.9650			1.09968			0.549838	−	0.835271i	$-0.314689\pi$
$139$	12.9650			1.09968			0.549838	+	0.835271i	$0.314689\pi$
$140$	−1.20576	−	9.60789i	−0.101905	−	0.812015i
$141$	−6.16315	+	1.80966i	−0.519031	+	0.152401i
$142$	−6.46904	−	5.60546i	−0.542870	−	0.470400i
$143$	2.91098	−	4.52957i	0.243428	−	0.378782i
$144$	−0.331388	−	0.382442i	−0.0276156	−	0.0318701i
$145$	13.9657	+	2.26459i	1.15979	+	0.188064i
$146$	0.230406	+	0.0676532i	0.0190685	+	0.00559902i
$147$	4.29951	+	6.69017i	0.354618	+	0.551796i
$148$	4.85975	+	0.698727i	0.399469	+	0.0574350i
$149$	−6.77707	+	14.8397i	−0.555199	+	1.21572i	0.399112	+	0.916902i	$0.369318\pi$
$149$	−6.77707	+	14.8397i	−0.555199	+	1.21572i	−0.954311	+	0.298814i	$0.903409\pi$
$150$	−4.03457	+	2.39267i	−0.329421	+	0.195361i
$151$	2.76403	−	19.2243i	0.224934	−	1.56445i	−0.494057	−	0.869429i	$-0.664487\pi$
$151$	2.76403	−	19.2243i	0.224934	−	1.56445i	0.718991	−	0.695019i	$-0.244604\pi$
$152$	−2.59785	−	4.04233i	−0.210713	−	0.327876i
$153$	1.49527	−	5.09243i	0.120886	−	0.411699i
$154$	2.98491	+	20.7605i	0.240531	+	1.67293i
$155$	−15.9055	+	6.92141i	−1.27756	+	0.555941i
$156$	0.877363	+	0.563847i	0.0702452	+	0.0451439i
$157$	−0.684113	−	0.592788i	−0.0545982	−	0.0473096i	0.627134	−	0.778911i	$-0.284228\pi$
$157$	−0.684113	−	0.592788i	−0.0545982	−	0.0473096i	−0.681732	+	0.731602i	$0.738773\pi$
$158$	1.97839	+	6.73779i	0.157392	+	0.536030i
$159$	3.09614	+	6.77961i	0.245540	+	0.537658i
$160$	11.4780	+	3.59532i	0.907416	+	0.284235i
$161$	17.3889	+	6.44492i	1.37044	+	0.507931i
$162$			0.938139i			0.0737071i
$163$	−3.24591	+	1.48236i	−0.254239	+	0.116107i	−0.538458	−	0.842652i	$-0.680993\pi$
$163$	−3.24591	+	1.48236i	−0.254239	+	0.116107i	0.284219	+	0.958759i	$0.408266\pi$
$164$	2.34125	−	0.687454i	0.182821	−	0.0536812i
$165$	−10.9997	+	6.79315i	−0.856325	+	0.528846i
$166$	−10.7515	−	6.90955i	−0.834476	−	0.536285i
$167$	0.404875	−	0.350827i	0.0313302	−	0.0271478i	−0.639055	−	0.769161i	$-0.720674\pi$
$167$	0.404875	−	0.350827i	0.0313302	−	0.0271478i	0.670385	+	0.742013i	$0.266129\pi$
$168$	−11.2027	+	1.61071i	−0.864307	+	0.124269i
$169$	−11.6413	−	3.41819i	−0.895483	−	0.262938i
$170$	−2.94439	−	10.7372i	−0.225824	−	0.823506i
$171$	−0.233640	+	1.62500i	−0.0178669	+	0.124267i
$172$	−8.26455	−	3.77429i	−0.630166	−	0.287787i
$173$	−7.20982	−	3.29262i	−0.548153	−	0.250333i	0.122034	−	0.992526i	$-0.461058\pi$
$173$	−7.20982	−	3.29262i	−0.548153	−	0.250333i	−0.670186	+	0.742193i	$0.733786\pi$
$174$	0.844753	−	5.87539i	0.0640406	−	0.445412i
$175$	−0.694161	+	19.3218i	−0.0524736	+	1.46059i
$176$	−2.80727	−	0.824289i	−0.211606	−	0.0621331i
$177$	1.40236	−	0.201629i	0.105408	−	0.0151554i
$178$	1.12317	−	0.973231i	0.0841851	−	0.0729468i
$179$	−16.8903	−	10.8547i	−1.26244	−	0.811319i	−0.273822	−	0.961780i	$-0.588288\pi$
$179$	−16.8903	−	10.8547i	−1.26244	−	0.811319i	−0.988616	+	0.150461i	$0.951924\pi$
$180$	−1.31581	−	2.13060i	−0.0980748	−	0.158806i
$181$	−18.0113	+	5.28860i	−1.33877	+	0.393099i	−0.871231	−	0.490873i	$-0.836678\pi$
$181$	−18.0113	+	5.28860i	−1.33877	+	0.393099i	−0.467540	+	0.883972i	$0.654860\pi$
$182$	−3.07303	+	1.40340i	−0.227788	+	0.104027i
$183$			5.34418i			0.395053i
$184$	−9.90510	+	9.94602i	−0.730214	+	0.733230i
$185$	−9.35493	−	2.93030i	−0.687788	−	0.215440i
$186$	3.02321	+	6.61991i	0.221673	+	0.485395i
$187$	−8.64522	−	29.4429i	−0.632201	−	2.15308i
$188$	−5.43646	−	4.71072i	−0.396495	−	0.343565i
$189$	3.25301	+	2.09058i	0.236622	+	0.152068i
$190$	1.37417	+	3.15786i	0.0996927	+	0.229095i
$191$	−2.53445	−	17.6275i	−0.183386	−	1.27548i	−0.848683	−	0.528901i	$-0.822604\pi$
$191$	−2.53445	−	17.6275i	−0.183386	−	1.27548i	0.665297	−	0.746579i	$-0.268305\pi$
$192$	1.70684	−	5.81298i	0.123181	−	0.419515i
$193$	−8.35621	−	13.0025i	−0.601493	−	0.935942i	−0.999825	−	0.0187003i	$-0.994047\pi$
$193$	−8.35621	−	13.0025i	−0.601493	−	0.935942i	0.398332	−	0.917241i	$-0.369589\pi$
$194$	1.75350	−	12.1959i	0.125894	−	0.875612i
$195$	−1.54902	−	1.39170i	−0.110928	−	0.0996620i
$196$	−3.69973	+	8.10128i	−0.264266	+	0.578663i
$197$	20.2419	+	2.91034i	1.44217	+	0.207353i	0.818579	−	0.574394i	$-0.194762\pi$
$197$	20.2419	+	2.91034i	1.44217	+	0.207353i	0.623595	+	0.781747i	$0.285671\pi$
$198$	2.93246	+	4.56299i	0.208401	+	0.324278i
$199$	−4.36803	−	1.28257i	−0.309641	−	0.0909189i	0.123220	−	0.992379i	$-0.460678\pi$
$199$	−4.36803	−	1.28257i	−0.309641	−	0.0909189i	−0.432861	+	0.901460i	$0.642496\pi$
$200$	−13.0851	−	6.55340i	−0.925259	−	0.463396i
$201$	−2.11523	−	2.44110i	−0.149197	−	0.172182i
$202$	−7.30747	+	11.3707i	−0.514152	+	0.800036i
$203$	−18.4905	−	16.0221i	−1.29778	−	1.12453i
$204$	5.70299	−	1.67455i	0.399289	−	0.117242i
$205$	−4.83416	+	0.606672i	−0.337632	+	0.0423718i
$206$	−1.88141			−0.131084
$207$	4.78290	−	0.351990i	0.332434	−	0.0244650i
$208$		−	0.471262i		−	0.0326761i
$209$	3.94308	+	8.63414i	0.272748	+	0.597236i
$210$	8.11037	+	0.145641i	0.559669	+	0.0100502i
$211$	8.22933	−	9.49715i	0.566530	−	0.653811i	−0.398123	−	0.917332i	$-0.630338\pi$
$211$	8.22933	−	9.49715i	0.566530	−	0.653811i	0.964654	+	0.263521i	$0.0848839\pi$
$212$	−4.51258	+	7.02172i	−0.309926	+	0.482254i
$213$	−6.89562	+	5.97509i	−0.472480	+	0.409406i
$214$	−0.917788	−	6.38335i	−0.0627387	−	0.436357i
$215$	15.0826	+	10.0802i	1.02863	+	0.687463i
$216$	−2.46226	+	1.58240i	−0.167536	+	0.107669i
$217$	29.6917	+	4.26902i	2.01560	+	0.289800i
$218$	−10.6927	−	4.88321i	−0.724204	−	0.330733i
$219$	0.106333	−	0.232836i	0.00718529	−	0.0157336i
$220$	−13.0598	−	6.25000i	−0.880493	−	0.421375i
$221$	4.15801	−	2.67219i	0.279698	−	0.179751i
$222$	−1.15873	+	3.94629i	−0.0777692	+	0.264858i
$223$	−11.6761	+	1.67877i	−0.781891	+	0.112419i	−0.521689	−	0.853135i	$-0.674698\pi$
$223$	−11.6761	+	1.67877i	−0.781891	+	0.112419i	−0.260201	+	0.965554i	$0.583789\pi$
$224$	−13.6211	−	15.7196i	−0.910101	−	1.05031i
$225$	1.91244	+	4.61980i	0.127496	+	0.307987i
$226$	−0.861360	+	0.994062i	−0.0572968	+	0.0661240i
$227$	2.06008	+	7.01597i	0.136732	+	0.465667i	0.999180	−	0.0404785i	$-0.0128882\pi$
$227$	2.06008	+	7.01597i	0.136732	+	0.465667i	−0.862448	+	0.506145i	$0.831070\pi$
$228$	−1.67240	+	0.763761i	−0.110758	+	0.0505813i
$229$	9.24517			0.610938			0.305469	−	0.952202i	$-0.401187\pi$
$229$	9.24517			0.610938			0.305469	+	0.952202i	$0.401187\pi$
$230$	8.14858	−	5.90022i	0.537302	−	0.389049i
$231$	22.3570			1.47098
$232$	16.8456	−	7.69311i	1.10597	−	0.505077i
$233$	−3.16160	−	10.7674i	−0.207123	−	0.705397i	−0.995879	−	0.0906902i	$-0.971093\pi$
$233$	−3.16160	−	10.7674i	−0.207123	−	0.705397i	0.788756	−	0.614706i	$-0.210725\pi$
$234$	−0.572125	+	0.660267i	−0.0374010	+	0.0431630i
$235$	9.20938	+	11.0220i	0.600753	+	0.718995i
$236$	1.03903	+	1.19911i	0.0676353	+	0.0780554i
$237$	7.40910	−	1.06527i	0.481273	−	0.0691965i
$238$	−5.42433	+	18.4736i	−0.351607	+	1.19746i
$239$	−11.3745	+	7.30997i	−0.735757	+	0.472843i	−0.854086	−	0.520132i	$-0.825883\pi$
$239$	−11.3745	+	7.30997i	−0.735757	+	0.472843i	0.118329	+	0.992974i	$0.462246\pi$
$240$	−0.488466	+	1.02068i	−0.0315303	+	0.0658849i
$241$	−9.83129	+	21.5275i	−0.633289	+	1.38671i	0.272159	+	0.962252i	$0.412262\pi$
$241$	−9.83129	+	21.5275i	−0.633289	+	1.38671i	−0.905448	+	0.424457i	$0.860465\pi$
$242$	19.1392	+	8.74059i	1.23032	+	0.561866i
$243$	0.989821	+	0.142315i	0.0634971	+	0.00912950i
$244$	−5.03483	+	3.23569i	−0.322322	+	0.207144i
$245$	9.88104	−	14.7847i	0.631277	−	0.944557i
$246$	0.290902	+	2.02327i	0.0185472	+	0.128999i
$247$	−1.15545	+	1.00120i	−0.0735194	+	0.0637049i
$248$	−12.2754	+	19.1009i	−0.779488	+	1.21291i
$249$	−8.92119	+	10.2956i	−0.565357	+	0.652457i
$250$	8.50556	+	6.13747i	0.537939	+	0.388168i
$251$	−1.77811	−	3.89352i	−0.112233	−	0.245757i	0.845178	−	0.534486i	$-0.179495\pi$
$251$	−1.77811	−	3.89352i	−0.112233	−	0.245757i	−0.957411	+	0.288729i	$0.906767\pi$
$252$			4.33048i			0.272795i
$253$	22.1632	−	16.6625i	1.39339	−	1.04756i
$254$	13.7930			0.865449
$255$	−11.7754	+	1.47777i	−0.737403	+	0.0925418i
$256$	16.1937	−	4.75490i	1.01211	−	0.297181i
$257$	−8.09491	−	7.01428i	−0.504946	−	0.437539i	0.364765	−	0.931100i	$-0.381149\pi$
$257$	−8.09491	−	7.01428i	−0.504946	−	0.437539i	−0.869711	+	0.493561i	$0.835695\pi$
$258$	4.11483	−	6.40280i	0.256178	−	0.398621i
$259$	11.1016	+	12.8120i	0.689823	+	0.796098i
$260$	0.373276	−	2.30198i	0.0231496	−	0.142763i
$261$	−6.07092	−	1.78258i	−0.375780	−	0.110339i
$262$	−9.30141	−	14.4733i	−0.574643	−	0.894162i
$263$	17.8859	+	2.57161i	1.10289	+	0.158572i	0.669630	−	0.742695i	$-0.266453\pi$
$263$	17.8859	+	2.57161i	1.10289	+	0.158572i	0.433264	+	0.901267i	$0.357362\pi$
$264$	−7.02983	+	15.3932i	−0.432656	+	0.947385i
$265$	11.1381	−	12.3971i	0.684208	−	0.761550i
$266$	0.847566	−	5.89495i	0.0519676	−	0.361443i
$267$	−0.856464	−	1.33268i	−0.0524147	−	0.0815589i
$268$	1.01911	−	3.47078i	0.0622522	−	0.212012i
$269$	1.25246	+	8.71106i	0.0763640	+	0.531123i	0.991714	+	0.128464i	$0.0410048\pi$
$269$	1.25246	+	8.71106i	0.0763640	+	0.531123i	−0.915350	+	0.402659i	$0.868086\pi$
$270$	1.92351	−	0.837033i	0.117061	−	0.0509402i
$271$	19.4848	+	12.5221i	1.18362	+	0.760665i	0.976048	−	0.217555i	$-0.0698082\pi$
$271$	19.4848	+	12.5221i	1.18362	+	0.760665i	0.207570	+	0.978220i	$0.433445\pi$
$272$	−2.02978	−	1.75881i	−0.123073	−	0.106644i
$273$	1.01454	+	3.45522i	0.0614029	+	0.209119i
$274$	−2.46997	−	5.40847i	−0.149216	−	0.326738i
$275$	23.7426	+	16.4922i	1.43173	+	0.994516i
$276$	3.22747	+	4.29293i	0.194271	+	0.258404i
$277$		−	14.6044i		−	0.877492i	−0.898611	−	0.438746i	$-0.855423\pi$
$277$		−	14.6044i		−	0.877492i	0.898611	−	0.438746i	$-0.144577\pi$
$278$	−11.0638	+	5.05267i	−0.663564	+	0.303039i
$279$	7.44322	−	2.18553i	0.445614	−	0.130844i
$280$	13.2979	+	21.5323i	0.794699	+	1.28680i
$281$	−12.8213	−	8.23977i	−0.764856	−	0.491543i	0.0991203	−	0.995075i	$-0.468397\pi$
$281$	−12.8213	−	8.23977i	−0.764856	−	0.491543i	−0.863976	+	0.503532i	$0.832033\pi$
$282$	4.55414	−	3.94618i	0.271195	−	0.234992i
$283$	28.7386	−	4.13198i	1.70833	−	0.245621i	0.782255	−	0.622959i	$-0.214069\pi$
$283$	28.7386	−	4.13198i	1.70833	−	0.245621i	0.926076	+	0.377338i	$0.123160\pi$
$284$	−9.80425	−	2.87879i	−0.581775	−	0.170825i
$285$	3.54029	−	0.970829i	0.209709	−	0.0575069i
$286$	−0.718865	+	4.99982i	−0.0425074	+	0.295645i
$287$	7.66397	+	3.50002i	0.452390	+	0.206599i
$288$	−4.89296	−	2.23454i	−0.288320	−	0.131671i
$289$	1.58947	−	11.0550i	0.0934982	−	0.650295i
$290$	−12.8003	+	3.51014i	−0.751660	+	0.206123i
$291$	−12.6017	−	3.70020i	−0.738727	−	0.216910i
$292$	0.283739	−	0.0407955i	0.0166046	−	0.00238737i
$293$	18.6288	−	16.1420i	1.08831	−	0.943025i	0.0897110	−	0.995968i	$-0.471406\pi$
$293$	18.6288	−	16.1420i	1.08831	−	0.943025i	0.998598	+	0.0529431i	$0.0168602\pi$
$294$	−6.27631	−	4.03354i	−0.366042	−	0.235241i
$295$	−1.66464	−	2.69543i	−0.0969188	−	0.156934i
$296$	−12.3120	+	3.61513i	−0.715621	+	0.210125i
$297$	5.25922	−	2.40180i	0.305171	−	0.139367i
$298$		−	15.3048i		−	0.886581i
$299$	3.58089	+	2.66912i	0.207088	+	0.154359i
$300$	−3.19448	+	4.59885i	−0.184433	+	0.265515i
$301$	−13.0322	−	28.5365i	−0.751162	−	1.64482i
$302$	5.13330	+	17.4824i	0.295388	+	1.00600i
$303$	10.8885	+	9.43497i	0.625530	+	0.542025i
$304$	0.698895	+	0.449152i	0.0400844	+	0.0257607i
$305$	10.9574	−	4.76822i	0.627420	−	0.273027i
$306$	0.708599	+	4.92842i	0.0405079	+	0.281739i
$307$	0.878247	−	2.99103i	0.0501242	−	0.170707i	−0.930627	−	0.365969i	$-0.880738\pi$
$307$	0.878247	−	2.99103i	0.0501242	−	0.170707i	0.980751	+	0.195262i	$0.0625557\pi$
$308$	13.5363	+	21.0629i	0.771303	+	1.20017i
$309$	−0.285408	+	1.98505i	−0.0162363	+	0.112926i
$310$	10.8757	−	12.1051i	0.617700	−	0.687524i
$311$	2.78024	−	6.08787i	0.157653	−	0.345212i	−0.814279	−	0.580474i	$-0.802867\pi$
$311$	2.78024	−	6.08787i	0.157653	−	0.345212i	0.971932	+	0.235262i	$0.0755948\pi$
$312$	−2.69798	−	0.387911i	−0.152743	−	0.0219611i
$313$	−1.46470	−	2.27912i	−0.0827898	−	0.128823i	0.797389	−	0.603465i	$-0.206214\pi$
$313$	−1.46470	−	2.27912i	−0.0827898	−	0.128823i	−0.880179	+	0.474642i	$0.842578\pi$
$314$	0.814815	+	0.239251i	0.0459827	+	0.0135017i
$315$	1.38400	−	8.53508i	0.0779796	−	0.480897i
$316$	5.48953	+	6.33525i	0.308810	+	0.356386i
$317$	−12.7368	+	19.8189i	−0.715372	+	1.11314i	0.273136	+	0.961975i	$0.411939\pi$
$317$	−12.7368	+	19.8189i	−0.715372	+	1.11314i	−0.988508	+	0.151165i	$0.951697\pi$
$318$	−5.28426	−	4.57884i	−0.296326	−	0.256768i
$319$	−35.1002	+	10.3064i	−1.96524	+	0.577045i
$320$	−13.4415	+	1.68687i	−0.751404	+	0.0942989i
$321$	−6.87424			−0.383683
$322$	−17.3507	+	1.27690i	−0.966916	+	0.0711587i
$323$			8.71327i			0.484819i
$324$	0.465221	+	1.01869i	0.0258456	+	0.0565940i
$325$	−1.47140	+	4.41775i	−0.0816187	+	0.245053i
$326$	2.19223	−	2.52997i	0.121417	−	0.140122i
$327$	−6.77431	+	10.5410i	−0.374620	+	0.582920i
$328$	−4.81964	+	4.17624i	−0.266120	+	0.230594i
$329$	−3.53484	−	24.5854i	−0.194882	−	1.35544i
$330$	6.73930	−	10.0838i	0.370986	−	0.555094i
$331$	−4.06686	+	2.61361i	−0.223535	+	0.143657i	−0.647616	−	0.761967i	$-0.724234\pi$
$331$	−4.06686	+	2.61361i	−0.223535	+	0.143657i	0.424081	+	0.905624i	$0.360597\pi$
$332$	−15.1011	−	2.17121i	−0.828780	−	0.119161i
$333$	3.98791	+	1.82122i	0.218536	+	0.0998022i
$334$	−0.208782	+	0.457169i	−0.0114240	+	0.0250152i
$335$	−3.11785	+	6.51497i	−0.170346	+	0.355951i
$336$	1.64616	−	1.05792i	0.0898055	−	0.0577145i
$337$	−1.09698	+	3.73597i	−0.0597562	+	0.203511i	−0.983960	−	0.178388i	$-0.942912\pi$
$337$	−1.09698	+	3.73597i	−0.0597562	+	0.203511i	0.924204	+	0.381899i	$0.124730\pi$
$338$	11.2663	−	1.61986i	0.612808	−	0.0881085i
$339$	0.918158	+	1.05961i	0.0498675	+	0.0575502i
$340$	−8.52177	−	10.1990i	−0.462158	−	0.553121i
$341$	29.3713	−	33.8963i	1.59055	−	1.83559i
$342$	−0.433912	−	1.47777i	−0.0234633	−	0.0799086i
$343$	−3.35077	+	1.53025i	−0.180925	+	0.0826256i
$344$	23.7456			1.28028
$345$	−4.98913	−	9.49255i	−0.268606	−	0.511062i
$346$	7.43577			0.399749
$347$	0.686902	−	0.313698i	0.0368749	−	0.0168402i	−0.396892	−	0.917865i	$-0.629911\pi$
$347$	0.686902	−	0.313698i	0.0368749	−	0.0168402i	0.433767	+	0.901025i	$0.357184\pi$
$348$	−1.99631	−	6.79879i	−0.107013	−	0.364454i
$349$	−10.6118	+	12.2467i	−0.568038	+	0.655551i	−0.964989	−	0.262289i	$-0.915523\pi$
$349$	−10.6118	+	12.2467i	−0.568038	+	0.655551i	0.396952	+	0.917840i	$0.370068\pi$
$350$	−6.93768	−	16.7590i	−0.370835	−	0.895808i
$351$	0.609851	+	0.703806i	0.0325514	+	0.0375664i
$352$	−30.7835	+	4.42600i	−1.64077	+	0.235907i
$353$	1.60234	−	5.45708i	0.0852841	−	0.290451i	−0.905797	−	0.423712i	$-0.860727\pi$
$353$	1.60234	−	5.45708i	0.0852841	−	0.290451i	0.991081	+	0.133261i	$0.0425450\pi$
$354$	−1.11814	+	0.718587i	−0.0594286	+	0.0381925i
$355$	18.4035	+	8.80728i	0.976754	+	0.467442i
$356$	0.736987	−	1.61378i	0.0390602	−	0.0855300i
$357$	18.6684	+	8.52559i	0.988038	+	0.451222i
$358$	18.6438	+	2.68057i	0.985353	+	0.141672i
$359$	−8.58815	+	5.51927i	−0.453265	+	0.291296i	−0.747285	−	0.664503i	$-0.768643\pi$
$359$	−8.58815	+	5.51927i	−0.453265	+	0.291296i	0.294020	+	0.955799i	$0.405007\pi$
$360$	5.44137	+	3.63663i	0.286785	+	0.191667i
$361$	2.32041	+	16.1388i	0.122127	+	0.849411i
$362$	13.3091	−	11.5324i	0.699511	−	0.606130i
$363$	12.1255	−	18.8677i	0.636425	−	0.990296i
$364$	−2.64095	+	3.04782i	−0.138423	+	0.159749i
$365$	−0.572268	−	0.0102764i	−0.0299539	−	0.000537891i
$366$	−2.08272	−	4.56051i	−0.108865	−	0.238382i
$367$			13.6771i			0.713939i	0.934116	+	0.356970i	$0.116190\pi$
$367$			13.6771i			0.713939i	−0.934116	+	0.356970i	$0.883810\pi$
$368$	0.843424	−	2.27562i	0.0439665	−	0.118625i
$369$	2.17886			0.113427
$370$	9.12512	−	1.14517i	0.474392	−	0.0595348i
$371$	−27.6528	+	8.11960i	−1.43566	+	0.421549i
$372$	6.56561	+	5.68913i	0.340411	+	0.294968i
$373$	−13.5336	+	21.0587i	−0.700745	+	1.09038i	0.290311	+	0.956932i	$0.406241\pi$
$373$	−13.5336	+	21.0587i	−0.700745	+	1.09038i	−0.991056	+	0.133447i	$0.957395\pi$
$374$	18.8519	+	21.7562i	0.974808	+	1.12499i
$375$	7.76587	−	8.04309i	0.401028	−	0.415343i
$376$	18.0389	+	5.29670i	0.930285	+	0.273156i
$377$	−3.18564	−	4.95695i	−0.164069	−	0.255296i
$378$	−3.59073	−	0.516269i	−0.184687	−	0.0265540i
$379$	−12.2482	+	26.8199i	−0.629150	+	1.37765i	0.279523	+	0.960139i	$0.409824\pi$
$379$	−12.2482	+	26.8199i	−0.629150	+	1.37765i	−0.908673	+	0.417508i	$0.862904\pi$
$380$	3.05814	+	2.74756i	0.156879	+	0.140947i
$381$	2.09238	−	14.5529i	0.107196	−	0.745565i
$382$	9.03253	+	14.0549i	0.462145	+	0.719111i
$383$	−4.05694	+	13.8167i	−0.207300	+	0.705999i	0.788548	+	0.614973i	$0.210833\pi$
$383$	−4.05694	+	13.8167i	−0.207300	+	0.705999i	−0.995848	+	0.0910265i	$0.970985\pi$
$384$	−0.722177	−	5.02285i	−0.0368534	−	0.256321i
$385$	−19.9476	−	45.8397i	−1.01662	−	2.33621i
$386$	12.1982	+	7.83928i	0.620870	+	0.399009i
$387$	−6.13132	−	5.31282i	−0.311672	−	0.270066i
$388$	−4.14384	−	14.1126i	−0.210372	−	0.716460i
$389$	−0.455668	−	0.997773i	−0.0231033	−	0.0505891i	0.897729	−	0.440549i	$-0.145216\pi$
$389$	−0.455668	−	0.997773i	−0.0231033	−	0.0505891i	−0.920832	+	0.389960i	$0.872489\pi$
$390$	1.86424	+	0.583947i	0.0943997	+	0.0295693i
$391$	24.8606	−	5.46178i	1.25725	−	0.276214i
$392$		−	23.2765i		−	1.17564i
$393$	−16.6816	+	7.61824i	−0.841477	+	0.384290i
$394$	−18.4078	+	5.40503i	−0.927374	+	0.272302i
$395$	−8.79477	−	14.2408i	−0.442513	−	0.716531i
$396$	5.44703	+	3.50059i	0.273724	+	0.175912i
$397$	−8.77854	+	7.60665i	−0.440582	+	0.381767i	−0.846714	−	0.532048i	$-0.821423\pi$
$397$	−8.77854	+	7.60665i	−0.440582	+	0.381767i	0.406132	+	0.913814i	$0.366877\pi$
$398$	4.22734	−	0.607800i	0.211898	−	0.0304663i
$399$	−6.09114	−	1.78852i	−0.304938	−	0.0895379i
$400$	2.52858	+	0.0908424i	0.126429	+	0.00454212i
$401$	−2.42676	+	16.8785i	−0.121187	+	0.842872i	0.835028	+	0.550207i	$0.185451\pi$
$401$	−2.42676	+	16.8785i	−0.121187	+	0.842872i	−0.956215	+	0.292665i	$0.905458\pi$
$402$	2.75639	+	1.25880i	0.137476	+	0.0627833i
$403$	6.57143	+	3.00107i	0.327346	+	0.149494i
$404$	−2.29625	+	15.9708i	−0.114243	+	0.794575i
$405$	−0.591351	−	2.15646i	−0.0293844	−	0.107155i
$406$	22.0232	+	6.46659i	1.09299	+	0.320932i
$407$	25.0895	−	3.60733i	1.24364	−	0.178809i
$408$	−11.7400	+	10.1728i	−0.581217	+	0.503627i
$409$	−15.5012	−	9.96205i	−0.766487	−	0.492592i	0.0980368	−	0.995183i	$-0.468744\pi$
$409$	−15.5012	−	9.96205i	−0.766487	−	0.492592i	−0.864524	+	0.502591i	$0.832380\pi$
$410$	3.88885	−	2.40166i	0.192057	−	0.118610i
$411$	−6.08112	+	1.78558i	−0.299960	+	0.0880761i
$412$	−2.04295	+	0.932986i	−0.100649	+	0.0459649i
$413$			5.47850i			0.269580i
$414$	−3.94436	+	2.16435i	−0.193855	+	0.106372i
$415$	29.0693	+	9.10553i	1.42696	+	0.446973i
$416$	−2.08096	−	4.55666i	−0.102027	−	0.223408i
$417$	3.65266	+	12.4398i	0.178871	+	0.609180i
$418$	−6.72974	−	5.83135i	−0.329162	−	0.285221i
$419$	−23.8211	−	15.3089i	−1.16374	−	0.747890i	−0.191411	−	0.981510i	$-0.561306\pi$
$419$	−23.8211	−	15.3089i	−1.16374	−	0.747890i	−0.972328	+	0.233620i	$0.924943\pi$
$420$	8.87900	−	3.86377i	0.433251	−	0.188533i
$421$	−3.98258	−	27.6995i	−0.194099	−	1.34999i	−0.821017	−	0.570904i	$-0.806593\pi$
$421$	−3.98258	−	27.6995i	−0.194099	−	1.34999i	0.626918	−	0.779085i	$-0.284316\pi$
$422$	−3.32139	+	11.3116i	−0.161683	+	0.550640i
$423$	−3.47272	−	5.40366i	−0.168849	−	0.262735i
$424$	3.10453	−	21.5925i	0.150769	−	1.04862i
$425$	13.5363	+	22.8251i	0.656606	+	1.10718i
$426$	3.55586	−	7.78624i	0.172282	−	0.377245i
$427$	−20.4548	−	2.94096i	−0.989879	−	0.142323i
$428$	−4.16209	−	6.47634i	−0.201182	−	0.313046i
$429$	5.16621	+	1.51694i	0.249427	+	0.0732384i
$430$	−16.7993	−	2.72408i	−0.810136	−	0.131367i
$431$	−14.5433	−	16.7839i	−0.700528	−	0.808452i	0.288296	−	0.957541i	$-0.406911\pi$
$431$	−14.5433	−	16.7839i	−0.700528	−	0.808452i	−0.988824	+	0.149089i	$0.952366\pi$
$432$	0.273587	−	0.425710i	0.0131630	−	0.0204820i
$433$	−1.17980	−	1.02230i	−0.0566976	−	0.0491287i	0.626051	−	0.779782i	$-0.284670\pi$
$433$	−1.17980	−	1.02230i	−0.0566976	−	0.0491287i	−0.682749	+	0.730653i	$0.739216\pi$
$434$	−27.0014	+	7.92834i	−1.29611	+	0.380572i
$435$	1.76172	+	14.0380i	0.0844681	+	0.673069i
$436$	−14.0325			−0.672033
$437$	−7.37128	+	2.76667i	−0.352616	+	0.132348i
$438$			0.240133i			0.0114740i
$439$	3.94245	+	8.63276i	0.188163	+	0.412019i	0.980078	−	0.198612i	$-0.0636432\pi$
$439$	3.94245	+	8.63276i	0.188163	+	0.412019i	−0.791915	+	0.610631i	$0.790916\pi$
$440$	37.8336	+	0.679390i	1.80365	+	0.0323887i
$441$	−5.20786	+	6.01019i	−0.247993	+	0.286200i
$442$	−2.50688	+	3.90079i	−0.119240	+	0.185541i
$443$	26.0371	−	22.5613i	1.23706	−	1.07192i	0.242244	−	0.970215i	$-0.422117\pi$
$443$	26.0371	−	22.5613i	1.23706	−	1.07192i	0.994815	−	0.101702i	$-0.0324288\pi$
$444$	0.698727	+	4.85975i	0.0331601	+	0.230634i
$445$	−1.96831	+	2.94511i	−0.0933066	+	0.139611i
$446$	9.30970	−	5.98298i	0.440827	−	0.283302i
$447$	−16.1479	−	2.32172i	−0.763770	−	0.109814i
$448$	21.3099	+	9.73190i	1.00680	+	0.459789i
$449$	−10.1531	+	22.2322i	−0.479155	+	1.04920i	0.503540	+	0.863972i	$0.332031\pi$
$449$	−10.1531	+	22.2322i	−0.479155	+	1.04920i	−0.982695	+	0.185231i	$0.940697\pi$
$450$	−3.43242	−	3.19705i	−0.161806	−	0.150710i
$451$	10.5977	−	6.81073i	0.499026	−	0.320705i
$452$	−0.442367	+	1.50656i	−0.0208072	+	0.0708628i
$453$	19.2243	−	2.76403i	0.903235	−	0.129866i
$454$	−4.49223	−	5.18431i	−0.210831	−	0.243312i
$455$	6.17920	−	5.16301i	0.289685	−	0.242045i
$456$	3.14669	−	3.63147i	0.147357	−	0.170059i
$457$	−3.42949	−	11.6798i	−0.160425	−	0.546357i	−0.999995	−	0.00310569i	$-0.999011\pi$
$457$	−3.42949	−	11.6798i	−0.160425	−	0.546357i	0.839570	−	0.543251i	$-0.182807\pi$
$458$	−7.88947	+	3.60300i	−0.368651	+	0.168357i
$459$	5.30742			0.247729
$460$	5.92236	−	10.4477i	0.276131	−	0.487127i
$461$	2.54869			0.118704			0.0593521	−	0.998237i	$-0.481097\pi$
$461$	2.54869			0.118704			0.0593521	+	0.998237i	$0.481097\pi$
$462$	−19.0786	+	8.71291i	−0.887618	+	0.405361i
$463$	−4.07739	−	13.8863i	−0.189493	−	0.645353i	−0.998354	−	0.0573531i	$-0.981734\pi$
$463$	−4.07739	−	13.8863i	−0.189493	−	0.645353i	0.808861	−	0.587999i	$-0.200084\pi$
$464$	−2.09676	+	2.41979i	−0.0973396	+	0.112336i
$465$	−11.1221	−	13.3112i	−0.515777	−	0.617293i
$466$	6.89423	+	7.95636i	0.319369	+	0.368571i
$467$	−24.1159	+	3.46735i	−1.11595	+	0.160450i	−0.675524	−	0.737338i	$-0.736082\pi$
$467$	−24.1159	+	3.46735i	−1.11595	+	0.160450i	−0.440428	+	0.897788i	$0.645173\pi$
$468$	−0.293825	+	1.00068i	−0.0135821	+	0.0462563i
$469$	10.5074	−	6.75267i	0.485185	−	0.311809i
$470$	−12.1544	−	5.81668i	−0.560640	−	0.268303i
$471$	0.376039	−	0.823410i	0.0173269	−	0.0379407i
$472$	−3.77204	−	1.72263i	−0.173622	−	0.0792906i
$473$	−46.4289	−	6.67547i	−2.13480	−	0.306938i
$474$	−5.90748	+	3.79651i	−0.271340	+	0.174379i
$475$	−5.14928	−	6.39262i	−0.236265	−	0.293314i
$476$	3.27092	+	22.7497i	0.149922	+	1.04273i
$477$	−5.63270	+	4.88077i	−0.257904	+	0.223475i
$478$	6.85777	−	10.6709i	0.313667	−	0.488075i
$479$	−20.3992	+	23.5419i	−0.932062	+	1.07566i	0.0649092	+	0.997891i	$0.479324\pi$
$479$	−20.3992	+	23.5419i	−0.932062	+	1.07566i	−0.996972	+	0.0777662i	$0.975221\pi$
$480$	−0.215955	+	12.0260i	−0.00985693	+	0.548909i
$481$	1.69604	+	3.71382i	0.0773329	+	0.169335i
$482$		−	22.2022i		−	1.01128i
$483$	−1.28484	+	18.5003i	−0.0584623	+	0.841791i
$484$	25.1171			1.14168
$485$	3.65690	+	29.1394i	0.166051	+	1.32315i
$486$	−0.900138	+	0.264304i	−0.0408311	+	0.0119891i
$487$	23.8634	+	20.6778i	1.08136	+	0.937000i	0.998226	−	0.0595385i	$-0.0189629\pi$
$487$	23.8634	+	20.6778i	1.08136	+	0.937000i	0.0831299	+	0.996539i	$0.473508\pi$
$488$	8.45662	−	13.1588i	0.382813	−	0.595669i
$489$	−2.33679	−	2.69680i	−0.105673	−	0.121954i
$490$	−2.67027	+	16.4675i	−0.120630	+	0.743924i
$491$	16.8969	+	4.96137i	0.762545	+	0.223903i	0.639807	−	0.768536i	$-0.279014\pi$
$491$	16.8969	+	4.96137i	0.762545	+	0.223903i	0.122738	+	0.992439i	$0.460833\pi$
$492$	1.31921	+	2.05274i	0.0594748	+	0.0925446i
$493$	−33.2394	−	4.77910i	−1.49703	−	0.215240i
$494$	0.595829	−	1.30468i	0.0268076	−	0.0587005i
$495$	−9.61696	−	8.64028i	−0.432250	−	0.388352i
$496$	0.558672	−	3.88565i	0.0250851	−	0.174471i
$497$	−19.0749	−	29.6812i	−0.855627	−	1.33138i
$498$	3.60062	−	12.2626i	0.161348	−	0.549500i
$499$	−4.92719	−	34.2693i	−0.220571	−	1.53411i	−0.735886	−	0.677105i	$-0.763234\pi$
$499$	−4.92719	−	34.2693i	−0.220571	−	1.53411i	0.515315	−	0.857001i	$-0.327675\pi$
$500$	12.2795	+	2.44657i	0.549154	+	0.109414i
$501$	0.450682	+	0.289636i	0.0201350	+	0.0129400i
$502$	3.03474	+	2.62962i	0.135447	+	0.117366i
$503$	9.96180	+	33.9268i	0.444175	+	1.51272i	0.812466	+	0.583009i	$0.198125\pi$
$503$	9.96180	+	33.9268i	0.444175	+	1.51272i	−0.368291	+	0.929711i	$0.620057\pi$
$504$	−4.70163	−	10.2951i	−0.209427	−	0.458581i
$505$	9.62993	−	30.7434i	0.428526	−	1.36806i
$506$	−12.4195	+	22.8565i	−0.552114	+	1.01610i
$507$		−	12.1327i		−	0.538834i
$508$	14.9773	−	6.83992i	0.664512	−	0.303472i
$509$	27.8958	−	8.19094i	1.23646	−	0.363057i	0.402774	−	0.915299i	$-0.368046\pi$
$509$	27.8958	−	8.19094i	1.23646	−	0.363057i	0.833684	+	0.552242i	$0.186228\pi$
$510$	9.47274	−	5.85014i	0.419460	−	0.259049i
$511$	0.832664	+	0.535121i	0.0368349	+	0.0236724i
$512$	−4.29591	+	3.72242i	−0.189854	+	0.164509i
$513$	−1.62500	+	0.233640i	−0.0717457	+	0.0103155i
$514$	9.64146	+	2.83099i	0.425267	+	0.124870i
$515$	4.32470	−	1.18593i	0.190569	−	0.0522585i
$516$	1.29302	−	8.99312i	0.0569218	−	0.395900i
$517$	−33.7818	−	15.4276i	−1.48572	−	0.678506i
$518$	−14.4668	−	6.60675i	−0.635633	−	0.290284i
$519$	1.12800	−	7.84541i	0.0495137	−	0.344375i
$520$	1.61186	+	5.87791i	0.0706847	+	0.257763i
$521$	7.83099	+	2.29939i	0.343082	+	0.100738i	0.448734	−	0.893665i	$-0.351875\pi$
$521$	7.83099	+	2.29939i	0.343082	+	0.100738i	−0.105652	+	0.994403i	$0.533693\pi$
$522$	5.87539	−	0.844753i	0.257159	−	0.0369738i
$523$	−33.6384	+	29.1478i	−1.47090	+	1.27455i	−0.584701	+	0.811249i	$0.698788\pi$
$523$	−33.6384	+	29.1478i	−1.47090	+	1.27455i	−0.886203	+	0.463297i	$0.846666\pi$
$524$	−17.2773	−	11.1035i	−0.754764	−	0.485058i
$525$	−18.7347	+	4.77755i	−0.817651	+	0.208509i
$526$	−16.2654	+	4.77594i	−0.709204	+	0.208241i
$527$	37.4514	−	17.1035i	1.63141	−	0.745040i
$528$		−	2.92579i		−	0.127329i
$529$	12.5144	+	19.2974i	0.544104	+	0.839018i
$530$	−4.67345	+	14.9199i	−0.203002	+	0.648081i
$531$	0.588553	+	1.28875i	0.0255410	+	0.0559270i
$532$	−2.00295	−	6.82144i	−0.0868391	−	0.295747i
$533$	1.53349	+	1.32878i	0.0664230	+	0.0575558i
$534$	1.25024	+	0.803482i	0.0541033	+	0.0347701i
$535$	6.13339	+	14.0946i	0.265169	+	0.609363i
$536$	1.34544	+	9.35776i	0.0581143	+	0.404194i
$537$	5.65648	−	19.2642i	0.244095	−	0.831312i
$538$	−4.46365	−	6.94558i	−0.192442	−	0.299445i
$539$	−6.54359	+	45.5117i	−0.281852	+	1.96033i
$540$	1.67359	−	1.86277i	0.0720200	−	0.0801609i
$541$	−14.1618	+	31.0100i	−0.608864	+	1.33323i	0.314485	+	0.949262i	$0.398168\pi$
$541$	−14.1618	+	31.0100i	−0.608864	+	1.33323i	−0.923349	+	0.383963i	$0.874559\pi$
$542$	−21.5077	−	3.09234i	−0.923833	−	0.132827i
$543$	−10.1488	−	15.7918i	−0.435525	−	0.677690i
$544$	−27.3924	−	8.04315i	−1.17444	−	0.344847i
$545$	27.6570	+	4.48470i	1.18470	+	0.192104i
$546$	−2.21233	−	2.55316i	−0.0946789	−	0.109265i
$547$	0.0883744	−	0.137513i	0.00377861	−	0.00587964i	−0.839359	−	0.543577i	$-0.817069\pi$
$547$	0.0883744	−	0.137513i	0.00377861	−	0.00587964i	0.843138	+	0.537698i	$0.180706\pi$
$548$	−5.36411	−	4.64802i	−0.229143	−	0.198554i
$549$	−5.12770	+	1.50563i	−0.218845	+	0.0642586i
$550$	−26.6883	−	4.82090i	−1.13799	−	0.205564i
$551$	10.3875			0.442522
$552$	−12.3337	−	6.70176i	−0.524958	−	0.285246i
$553$			28.9446i			1.23085i
$554$	5.69157	+	12.4628i	0.241812	+	0.529494i
$555$	0.176010	−	9.80155i	0.00747119	−	0.416053i
$556$	−9.50821	+	10.9731i	−0.403238	+	0.465361i
$557$	−2.99698	+	4.66339i	−0.126986	+	0.197594i	−0.898925	−	0.438102i	$-0.855651\pi$
$557$	−2.99698	+	4.66339i	−0.126986	+	0.197594i	0.771939	+	0.635697i	$0.219287\pi$
$558$	−5.50002	+	4.76580i	−0.232834	+	0.201752i
$559$	−1.07523	−	7.47838i	−0.0454773	−	0.316302i
$560$	−3.63787	−	2.43130i	−0.153728	−	0.102741i
$561$	25.8146	−	16.5900i	1.08989	−	0.700432i
$562$	14.1524	+	2.03481i	0.596983	+	0.0858332i
$563$	−9.65235	−	4.40808i	−0.406798	−	0.185779i	0.201497	−	0.979489i	$-0.435419\pi$
$563$	−9.65235	−	4.40808i	−0.406798	−	0.185779i	−0.608296	+	0.793711i	$0.708146\pi$
$564$	2.98828	−	6.54341i	0.125829	−	0.275527i
$565$	1.35337	−	2.82796i	0.0569365	−	0.118973i
$566$	−22.9141	+	14.7260i	−0.963150	+	0.618979i
$567$	−1.08942	+	3.71023i	−0.0457514	+	0.155815i
$568$	26.4338	−	3.80060i	1.10914	−	0.159470i
$569$	20.6953	+	23.8837i	0.867593	+	1.00126i	0.999949	+	0.0100534i	$0.00320015\pi$
$569$	20.6953	+	23.8837i	0.867593	+	1.00126i	−0.132357	+	0.991202i	$0.542254\pi$
$570$	−2.64279	+	2.20818i	−0.110694	+	0.0924904i
$571$	12.7883	−	14.7585i	0.535173	−	0.617623i	−0.422191	−	0.906507i	$-0.638739\pi$
$571$	12.7883	−	14.7585i	0.535173	−	0.617623i	0.957364	+	0.288884i	$0.0932843\pi$
$572$	1.69881	+	5.78562i	0.0710308	+	0.241909i
$573$	16.1994	−	7.39803i	0.676740	−	0.309057i
$574$	−7.90415			−0.329913
$575$	−15.0116	+	18.6990i	−0.626027	+	0.779801i
$576$	6.05838			0.252433
$577$	16.9020	−	7.71886i	0.703637	−	0.321340i	−0.0312671	−	0.999511i	$-0.509954\pi$
$577$	16.9020	−	7.71886i	0.703637	−	0.321340i	0.734904	+	0.678171i	$0.237227\pi$
$578$	2.95193	+	10.0534i	0.122784	+	0.418165i
$579$	10.1216	−	11.6810i	0.420640	−	0.485444i
$580$	−12.1587	+	10.1592i	−0.504864	+	0.421838i
$581$	−34.4970	−	39.8117i	−1.43118	−	1.65167i
$582$	12.1959	−	1.75350i	0.505535	−	0.0726849i
$583$	−12.1404	+	41.3463i	−0.502802	+	1.71239i
$584$	−0.630258	+	0.405042i	−0.0260803	+	0.0167608i
$585$	0.898921	−	1.87836i	0.0371658	−	0.0776607i
$586$	−9.60632	+	21.0349i	−0.396834	+	0.868944i
$587$	16.8378	+	7.68956i	0.694970	+	0.317382i	0.731395	−	0.681954i	$-0.238870\pi$
$587$	16.8378	+	7.68956i	0.694970	+	0.317382i	−0.0364251	+	0.999336i	$0.511597\pi$
$588$	−8.81546	−	1.26747i	−0.363543	−	0.0522696i
$589$	−10.7138	+	6.88535i	−0.441455	+	0.283706i
$590$	2.47099	+	1.65144i	0.101729	+	0.0679887i
$591$	2.91034	+	20.2419i	0.119716	+	0.832640i
$592$	1.67666	−	1.45283i	0.0689103	−	0.0597111i
$593$	6.59202	−	10.2574i	0.270702	−	0.421220i	−0.679113	−	0.734034i	$-0.737635\pi$
$593$	6.59202	−	10.2574i	0.270702	−	0.421220i	0.949814	+	0.312814i	$0.101272\pi$
$594$	−3.55199	+	4.09921i	−0.145740	+	0.168193i
$595$	0.823946	−	45.8835i	0.0337785	−	1.88104i
$596$	−7.58961	−	16.6189i	−0.310882	−	0.680738i
$597$		−	4.55243i		−	0.186319i
$598$	−4.09600	−	0.882191i	−0.167498	−	0.0360755i
$599$	4.75408			0.194247			0.0971233	−	0.995272i	$-0.469036\pi$
$599$	4.75408			0.194247			0.0971233	+	0.995272i	$0.469036\pi$
$600$	2.60143	−	14.4014i	0.106203	−	0.587935i
$601$	14.8665	−	4.36521i	0.606419	−	0.178061i	0.0359141	−	0.999355i	$-0.488566\pi$
$601$	14.8665	−	4.36521i	0.606419	−	0.178061i	0.570505	+	0.821294i	$0.306748\pi$
$602$	22.2423	+	19.2731i	0.906528	+	0.785511i
$603$	1.74629	−	2.71728i	0.0711145	−	0.110656i
$604$	14.2436	+	16.4380i	0.579563	+	0.668852i
$605$	−49.5040	−	8.02729i	−2.01262	−	0.326356i
$606$	−12.9688	−	3.80799i	−0.526822	−	0.154689i
$607$	−17.6768	−	27.5057i	−0.717480	−	1.11642i	−0.988112	−	0.153737i	$-0.950869\pi$
$607$	−17.6768	−	27.5057i	−0.717480	−	1.11642i	0.270632	−	0.962683i	$-0.412767\pi$
$608$	8.74098	+	1.25676i	0.354494	+	0.0509685i
$609$	10.1637	−	22.2555i	0.411855	−	0.901838i
$610$	−7.49238	+	8.33931i	−0.303358	+	0.337649i
$611$	0.851307	−	5.92097i	0.0344402	−	0.239537i
$612$	3.21344	+	5.00020i	0.129895	+	0.202121i
$613$	−4.77179	+	16.2512i	−0.192731	+	0.656381i	0.805254	+	0.592930i	$0.202029\pi$
$613$	−4.77179	+	16.2512i	−0.192731	+	0.656381i	−0.997985	+	0.0634511i	$0.979789\pi$
$614$	0.416195	+	2.89470i	0.0167963	+	0.116821i
$615$	−1.94404	−	4.46742i	−0.0783912	−	0.180144i
$616$	−55.0488	−	35.3777i	−2.21798	−	1.42541i
$617$	28.2103	+	24.4443i	1.13570	+	0.984091i	0.999978	−	0.00665515i	$-0.00211842\pi$
$617$	28.2103	+	24.4443i	1.13570	+	0.984091i	0.135724	+	0.990747i	$0.456664\pi$
$618$	−0.530053	−	1.80520i	−0.0213219	−	0.0726156i
$619$	10.2297	+	22.3999i	0.411166	+	0.900328i	0.996015	+	0.0891857i	$0.0284265\pi$
$619$	10.2297	+	22.3999i	0.411166	+	0.900328i	−0.584849	+	0.811142i	$0.698846\pi$
$620$	5.80669	−	18.5378i	0.233202	−	0.744495i
$621$	1.68523	+	4.48999i	0.0676259	+	0.180177i
$622$			6.27866i			0.251751i
$623$	5.57217	−	2.54473i	0.223244	−	0.101952i
$624$	0.452172	−	0.132770i	0.0181014	−	0.00531504i
$625$	−23.4201	−	8.74648i	−0.936802	−	0.349859i
$626$	2.13813	+	1.37409i	0.0854569	+	0.0549198i
$627$	−7.17350	+	6.21587i	−0.286482	+	0.248238i
$628$	1.00342	−	0.144271i	0.0400410	−	0.00575702i
$629$	22.3257	+	6.55542i	0.890184	+	0.261382i
$630$	2.14521	+	7.82288i	0.0854674	+	0.311671i
$631$	4.97461	−	34.5992i	0.198036	−	1.37737i	−0.611938	−	0.790905i	$-0.709610\pi$
$631$	4.97461	−	34.5992i	0.198036	−	1.37737i	0.809974	−	0.586465i	$-0.199481\pi$
$632$	−19.9288	−	9.10118i	−0.792725	−	0.362026i
$633$	11.4309	+	5.22033i	0.454338	+	0.207489i
$634$	3.14536	−	21.8764i	0.124918	−	0.868825i
$635$	−31.7053	+	8.69433i	−1.25819	+	0.345024i
$636$	−8.00863	−	2.35155i	−0.317563	−	0.0932449i
$637$	−7.33064	+	1.05399i	−0.290451	+	0.0417605i
$638$	25.9366	−	22.4742i	1.02684	−	0.889762i
$639$	−7.67577	−	4.93292i	−0.303649	−	0.195143i
$640$	−9.65425	+	5.96224i	−0.381618	+	0.235678i
$641$	16.2541	−	4.77262i	0.641997	−	0.188507i	0.0554999	−	0.998459i	$-0.482325\pi$
$641$	16.2541	−	4.77262i	0.641997	−	0.188507i	0.586497	+	0.809951i	$0.300507\pi$
$642$	5.86621	−	2.67901i	0.231521	−	0.105732i
$643$		−	15.3484i		−	0.605282i	−0.953105	−	0.302641i	$-0.902132\pi$
$643$		−	15.3484i		−	0.605282i	0.953105	−	0.302641i	$-0.0978683\pi$
$644$	−18.2073	+	9.99072i	−0.717469	+	0.393689i
$645$	−5.42260	+	17.3116i	−0.213515	+	0.681643i
$646$	−3.39571	−	7.43556i	−0.133602	−	0.292548i
$647$	9.07783	+	30.9162i	0.356886	+	1.21544i	0.920940	+	0.389705i	$0.127423\pi$
$647$	9.07783	+	30.9162i	0.356886	+	1.21544i	−0.564054	+	0.825738i	$0.690759\pi$
$648$	−2.21200	−	1.91671i	−0.0868956	−	0.0752954i
$649$	6.89105	+	4.42861i	0.270498	+	0.173838i
$650$	−0.466033	−	4.34336i	−0.0182793	−	0.170361i
$651$	4.26902	+	29.6917i	0.167316	+	1.16371i
$652$	1.12586	−	3.83434i	0.0440922	−	0.150164i
$653$	12.2309	+	19.0316i	0.478632	+	0.744765i	0.993662	−	0.112406i	$-0.0358558\pi$
$653$	12.2309	+	19.0316i	0.478632	+	0.744765i	−0.515031	+	0.857172i	$0.672219\pi$
$654$	1.67291	−	11.6354i	0.0654161	−	0.454979i
$655$	30.5039	+	27.4059i	1.19188	+	1.07084i
$656$	0.458035	−	1.00296i	0.0178833	−	0.0391589i
$657$	0.253362	+	0.0364279i	0.00988459	+	0.00142119i
$658$	12.5978	+	19.6026i	0.491115	+	0.764189i
$659$	10.9755	+	3.22269i	0.427544	+	0.125538i	0.488423	−	0.872607i	$-0.337572\pi$
$659$	10.9755	+	3.22269i	0.427544	+	0.125538i	−0.0608791	+	0.998145i	$0.519390\pi$
$660$	2.31745	−	14.2916i	0.0902067	−	0.556301i
$661$	28.8836	+	33.3335i	1.12344	+	1.29652i	0.950199	+	0.311643i	$0.100879\pi$
$661$	28.8836	+	33.3335i	1.12344	+	1.29652i	0.173243	+	0.984879i	$0.444575\pi$
$662$	2.45193	−	3.81528i	0.0952971	−	0.148285i
$663$	3.73539	+	3.23673i	0.145071	+	0.125704i
$664$	38.2580	−	11.2336i	1.48470	−	0.435947i
$665$	1.76759	+	14.0847i	0.0685442	+	0.546182i
$666$	−4.11289			−0.159371
$667$	−6.51124	−	29.6374i	−0.252116	−	1.14757i
$668$			0.599958i			0.0232131i
$669$	−4.90031	−	10.7302i	−0.189457	−	0.414853i
$670$	0.121655	−	6.77470i	0.00469996	−	0.261729i
$671$	−20.2342	+	23.3515i	−0.781131	+	0.901473i
$672$	11.2454	−	17.4981i	0.433799	−	0.675005i
$673$	10.8272	−	9.38182i	0.417358	−	0.361642i	−0.420723	−	0.907189i	$-0.638223\pi$
$673$	10.8272	−	9.38182i	0.417358	−	0.361642i	0.838080	+	0.545547i	$0.183678\pi$
$674$	−0.519851	−	3.61564i	−0.0200239	−	0.139269i
$675$	−3.89387	+	3.13652i	−0.149875	+	0.120725i
$676$	11.4304	−	7.34590i	0.439633	−	0.282535i
$677$	−23.6993	−	3.40744i	−0.910838	−	0.130959i	−0.329062	−	0.944308i	$-0.606733\pi$
$677$	−23.6993	−	3.40744i	−0.910838	−	0.130959i	−0.581775	+	0.813349i	$0.697642\pi$
$678$	−1.19647	−	0.546409i	−0.0459501	−	0.0209847i
$679$	21.0974	−	46.1969i	0.809645	−	1.77287i
$680$	31.3325	+	14.9947i	1.20155	+	0.575020i
$681$	−6.15139	+	3.95326i	−0.235722	+	0.151489i
$682$	−11.8544	+	40.3723i	−0.453928	+	1.54594i
$683$	−6.77181	+	0.973639i	−0.259116	+	0.0372553i	−0.270649	−	0.962678i	$-0.587238\pi$
$683$	−6.77181	+	0.973639i	−0.259116	+	0.0372553i	0.0115324	+	0.999933i	$0.496329\pi$
$684$	−1.20399	−	1.38948i	−0.0460359	−	0.0531282i
$685$	9.08680	+	10.8753i	0.347189	+	0.415523i
$686$	2.26306	−	2.61171i	0.0864039	−	0.0997155i
$687$	2.60467	+	8.87067i	0.0993742	+	0.338437i
$688$	−3.73447	+	1.70547i	−0.142375	+	0.0650206i
$689$	−6.94087			−0.264426
$690$	7.95694	+	6.15623i	0.302916	+	0.234363i
$691$	−22.9069			−0.871420			−0.435710	−	0.900087i	$-0.643503\pi$
$691$	−22.9069			−0.871420			−0.435710	+	0.900087i	$0.643503\pi$
$692$	8.07425	−	3.68739i	0.306937	−	0.140173i
$693$	6.29870	+	21.4514i	0.239268	+	0.814872i
$694$	−0.463922	+	0.535395i	−0.0176103	+	0.0203233i
$695$	22.2470	−	18.5884i	0.843875	−	0.705097i
$696$	12.1274	+	13.9958i	0.459689	+	0.530509i
$697$	11.4464	−	1.64575i	0.433564	−	0.0623371i
$698$	4.28297	−	14.5865i	0.162113	−	0.552106i
$699$	9.44053	−	6.06706i	0.357074	−	0.229477i
$700$	−15.8442	−	14.7577i	−0.598853	−	0.557788i
$701$	4.93046	−	10.7962i	0.186221	−	0.407767i	−0.793378	−	0.608729i	$-0.791680\pi$
$701$	4.93046	−	10.7962i	0.186221	−	0.407767i	0.979599	+	0.200962i	$0.0644069\pi$
$702$	−0.794708	−	0.362931i	−0.0299943	−	0.0136979i
$703$	−7.12417	−	1.02430i	−0.268693	−	0.0386323i
$704$	29.4672	−	18.9374i	1.11059	−	0.713731i
$705$	−7.98093	+	11.9416i	−0.300579	+	0.449746i
$706$	0.759339	+	5.28132i	0.0285781	+	0.198765i
$707$	−42.1044	+	36.4837i	−1.58350	+	1.37211i
$708$	−0.857807	+	1.33477i	−0.0322384	+	0.0501639i
$709$	13.5244	−	15.6080i	0.507921	−	0.586172i	−0.442644	−	0.896698i	$-0.645959\pi$
$709$	13.5244	−	15.6080i	0.507921	−	0.586172i	0.950565	+	0.310525i	$0.100505\pi$
$710$	−19.1371	−	0.343652i	−0.718204	−	0.0128970i
$711$	3.10950	+	6.80886i	0.116615	+	0.255352i
$712$			4.63668i			0.173767i
$713$	26.3610	+	26.2525i	0.987227	+	0.983165i
$714$	−19.2535			−0.720543
$715$	−1.49918	−	11.9460i	−0.0560663	−	0.446755i
$716$	21.5739	−	6.33467i	0.806255	−	0.236738i
$717$	−10.2184	−	8.85433i	−0.381615	−	0.330671i
$718$	5.17784	−	8.05688i	0.193235	−	0.300680i
$719$	−28.6375	−	33.0494i	−1.06800	−	1.23253i	−0.971460	−	0.237205i	$-0.923769\pi$
$719$	−28.6375	−	33.0494i	−1.06800	−	1.23253i	−0.0965377	−	0.995329i	$-0.530777\pi$
$720$	−1.11696	−	0.181119i	−0.0416265	−	0.00674992i
$721$	−7.44074	−	2.18480i	−0.277107	−	0.0813661i
$722$	−8.26972	−	12.8679i	−0.307767	−	0.478895i
$723$	−23.4253	−	3.36805i	−0.871196	−	0.125259i
$724$	8.73300	−	19.1226i	0.324559	−	0.710686i
$725$	27.2109	−	16.1372i	1.01059	−	0.599321i
$726$	−2.99439	+	20.8265i	−0.111132	+	0.772942i
$727$	28.3933	+	44.1809i	1.05305	+	1.63858i	0.717502	+	0.696557i	$0.245285\pi$
$727$	28.3933	+	44.1809i	1.05305	+	1.63858i	0.335549	+	0.942023i	$0.391078\pi$
$728$	2.96946	−	10.1131i	0.110056	−	0.374815i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	0.492356	−	0.214253i	0.0182229	−	0.00792986i
$731$	−36.2231	−	23.2792i	−1.33976	−	0.861012i
$732$	−4.52310	−	3.91929i	−0.167179	−	0.144861i
$733$	0.196843	+	0.670386i	0.00727056	+	0.0247613i	0.963048	−	0.269328i	$-0.0868017\pi$
$733$	0.196843	+	0.670386i	0.00727056	+	0.0247613i	−0.955778	+	0.294090i	$0.904984\pi$
$734$	−5.33020	−	11.6715i	−0.196741	−	0.430803i
$735$	16.9696	+	5.31547i	0.625933	+	0.196064i
$736$	−1.89337	−	25.7275i	−0.0697906	−	0.948326i
$737$		−	18.6751i		−	0.687907i
$738$	−1.85935	+	0.849138i	−0.0684438	+	0.0312572i
$739$	−44.5305	+	13.0753i	−1.63808	+	0.480984i	−0.965795	−	0.259308i	$-0.916506\pi$
$739$	−44.5305	+	13.0753i	−1.63808	+	0.480984i	−0.672286	+	0.740292i	$0.734687\pi$
$740$	9.34077	−	5.76864i	0.343373	−	0.212059i
$741$	−1.28617	−	0.826573i	−0.0472488	−	0.0303649i
$742$	20.4335	−	17.7057i	0.750137	−	0.649998i
$743$	−6.21911	+	0.894173i	−0.228157	+	0.0328040i	−0.255445	−	0.966824i	$-0.582222\pi$
$743$	−6.21911	+	0.894173i	−0.228157	+	0.0328040i	0.0272880	+	0.999628i	$0.491313\pi$
$744$	−21.7855	−	6.39681i	−0.798697	−	0.234518i
$745$	9.64727	+	35.1804i	0.353449	+	1.28891i
$746$	3.34212	−	23.2450i	0.122364	−	0.851059i
$747$	−12.3919	−	5.65921i	−0.453398	−	0.207060i
$748$	31.2595	+	14.2757i	1.14296	+	0.521973i
$749$	3.78298	−	26.3112i	0.138227	−	0.961390i
$750$	−3.49256	+	9.89015i	−0.127530	+	0.361137i
$751$	12.0555	+	3.53982i	0.439912	+	0.129170i	0.494186	−	0.869356i	$-0.335466\pi$
$751$	12.0555	+	3.53982i	0.439912	+	0.129170i	−0.0542737	+	0.998526i	$0.517284\pi$
$752$	−3.21740	+	0.462592i	−0.117327	+	0.0168690i
$753$	3.23485	−	2.80302i	0.117885	−	0.102148i
$754$	4.65030	+	2.98857i	0.169354	+	0.108837i
$755$	−22.8196	−	36.9503i	−0.830492	−	1.34476i
$756$	−4.15507	+	1.22004i	−0.151118	+	0.0443723i
$757$	45.7807	−	20.9073i	1.66393	−	0.759890i	0.664000	−	0.747732i	$-0.268857\pi$
$757$	45.7807	−	20.9073i	1.66393	−	0.759890i	0.999926	−	0.0121571i	$-0.00386984\pi$
$758$		−	27.6604i		−	1.00467i
$759$	22.2317	+	16.5710i	0.806958	+	0.601490i
$760$	−10.2533	−	3.21171i	−0.371928	−	0.116501i
$761$	1.66424	+	3.64418i	0.0603287	+	0.132101i	0.937395	−	0.348268i	$-0.113230\pi$
$761$	1.66424	+	3.64418i	0.0603287	+	0.132101i	−0.877066	+	0.480369i	$0.840503\pi$
$762$	3.88593	+	13.2343i	0.140773	+	0.479427i
$763$	−36.6178	−	31.7295i	−1.32566	−	1.14869i
$764$	16.7779	+	10.7825i	0.607004	+	0.390098i
$765$	−4.73542	−	10.8821i	−0.171210	−	0.393442i
$766$	−1.92256	−	13.3717i	−0.0694648	−	0.483138i
$767$	−0.371719	+	1.26596i	−0.0134220	+	0.0457112i
$768$	9.12458	+	14.1981i	0.329255	+	0.512331i
$769$	−3.28990	+	22.8817i	−0.118637	+	0.825136i	0.840423	+	0.541931i	$0.182307\pi$
$769$	−3.28990	+	22.8817i	−0.118637	+	0.825136i	−0.959059	+	0.283205i	$0.908602\pi$
$770$	34.8870	+	31.3439i	1.25724	+	1.12956i
$771$	4.44955	−	9.74316i	0.160247	−	0.350891i
$772$	17.1331	+	2.46336i	0.616632	+	0.0886583i
$773$	−5.58965	−	8.69766i	−0.201046	−	0.312833i	0.726061	−	0.687630i	$-0.241349\pi$
$773$	−5.58965	−	8.69766i	−0.201046	−	0.312833i	−0.927107	+	0.374797i	$0.877712\pi$
$774$	7.30272	+	2.14427i	0.262491	+	0.0770743i
$775$	−17.3692	+	34.6809i	−0.623919	+	1.24577i
$776$	25.1736	+	29.0518i	0.903678	+	1.04290i
$777$	−9.16531	+	14.2615i	−0.328804	+	0.511629i
$778$	0.777698	+	0.673879i	0.0278818	+	0.0241597i
$779$	−3.43217	+	1.00778i	−0.122970	+	0.0361073i
$780$	2.31390	−	0.290387i	0.0828508	−	0.0103975i
$781$	−52.7534			−1.88767
$782$	−19.0865	+	14.3495i	−0.682532	+	0.513136i
$783$		−	6.32721i		−	0.226116i
$784$	1.67178	+	3.66069i	0.0597065	+	0.130739i
$785$	−2.02379	−	0.0363418i	−0.0722321	−	0.00129710i
$786$	11.2665	−	13.0022i	0.401862	−	0.463774i
$787$	5.30530	−	8.25521i	0.189113	−	0.294266i	−0.733730	−	0.679441i	$-0.762222\pi$
$787$	5.30530	−	8.25521i	0.189113	−	0.294266i	0.922844	+	0.385175i	$0.125859\pi$
$788$	−17.3081	+	14.9976i	−0.616576	+	0.534266i
$789$	2.57161	+	17.8859i	0.0915518	+	0.636756i
$790$	13.0550	+	8.72505i	0.464475	+	0.310423i
$791$	−4.56094	+	2.93114i	−0.162168	+	0.104219i
$792$	−16.7502	−	2.40831i	−0.595192	−	0.0855757i
$793$	−4.52711	−	2.06746i	−0.160762	−	0.0734178i
$794$	4.52683	−	9.91237i	0.160651	−	0.351777i
$795$	15.0329	+	7.19426i	0.533163	+	0.255154i
$796$	4.28892	−	2.75632i	0.152017	−	0.0976952i
$797$	5.10114	−	17.3729i	0.180692	−	0.615379i	−0.818474	−	0.574543i	$-0.805180\pi$
$797$	5.10114	−	17.3729i	0.180692	−	0.615379i	0.999166	−	0.0408359i	$-0.0130021\pi$
$798$	5.89495	−	0.847566i	0.208679	−	0.0300035i
$799$	−22.3251	−	25.7645i	−0.789805	−	0.911484i
$800$	24.8501	−	10.2871i	0.878585	−	0.363705i
$801$	1.03741	−	1.19723i	0.0366550	−	0.0423021i
$802$	−4.50693	−	15.3492i	−0.159145	−	0.541999i
$803$	1.34619	−	0.614783i	0.0475059	−	0.0216952i
$804$	3.61731			0.127573
$805$	39.0784	−	13.8721i	1.37733	−	0.488926i
$806$	−6.77737			−0.238723
$807$	−8.00535	+	3.65592i	−0.281802	+	0.128694i
$808$	−11.8805	−	40.4613i	−0.417955	−	1.42343i
$809$	26.4330	−	30.5053i	0.929333	−	1.07251i	−0.0678644	−	0.997695i	$-0.521619\pi$
$809$	26.4330	−	30.5053i	0.929333	−	1.07251i	0.997198	−	0.0748131i	$-0.0238360\pi$
$810$	1.34504	+	1.60978i	0.0472600	+	0.0565618i
$811$	4.46310	+	5.15069i	0.156721	+	0.180865i	0.828680	−	0.559723i	$-0.189092\pi$
$811$	4.46310	+	5.15069i	0.156721	+	0.180865i	−0.671959	+	0.740588i	$0.734547\pi$
$812$	27.1210	−	3.89941i	0.951760	−	0.136842i
$813$	−6.52539	+	22.2234i	−0.228855	+	0.779410i
$814$	−20.0046	+	12.8562i	−0.701160	+	0.450608i
$815$	−3.44443	+	7.19740i	−0.120653	+	0.252114i
$816$	1.11571	−	2.44307i	0.0390578	−	0.0855246i
$817$	12.1154	+	5.53294i	0.423866	+	0.193573i
$818$	17.1105	+	2.46012i	0.598256	+	0.0860162i
$819$	−3.02943	+	1.94689i	−0.105857	+	0.0680300i
$820$	3.03179	−	4.53636i	0.105875	−	0.158417i
$821$	3.26063	+	22.6782i	0.113797	+	0.791473i	0.964168	+	0.265291i	$0.0854679\pi$
$821$	3.26063	+	22.6782i	0.113797	+	0.791473i	−0.850372	+	0.526182i	$0.823623\pi$
$822$	4.49352	−	3.89366i	0.156730	−	0.135807i
$823$	17.8604	−	27.7913i	0.622575	−	0.968745i	−0.376528	−	0.926405i	$-0.622882\pi$
$823$	17.8604	−	27.7913i	0.622575	−	0.968745i	0.999103	−	0.0423403i	$-0.0134814\pi$
$824$	3.84389	−	4.43609i	0.133908	−	0.154539i
$825$	−9.13507	+	27.4272i	−0.318042	+	0.954893i
$826$	−2.13507	−	4.67514i	−0.0742884	−	0.162669i
$827$			3.35526i			0.116674i	0.998297	+	0.0583368i	$0.0185797\pi$
$827$			3.35526i			0.116674i	−0.998297	+	0.0583368i	$0.981420\pi$
$828$	−3.20975	+	4.30620i	−0.111547	+	0.149651i
$829$	−16.7850			−0.582966			−0.291483	−	0.956576i	$-0.594149\pi$
$829$	−16.7850			−0.582966			−0.291483	+	0.956576i	$0.594149\pi$
$830$	−28.3552	+	3.55849i	−0.984223	+	0.123517i
$831$	14.0128	−	4.11453i	0.486098	−	0.142731i
$832$	4.26392	+	3.69471i	0.147825	+	0.128091i
$833$	−22.8193	+	35.5075i	−0.790642	+	1.23026i
$834$	−7.96504	−	9.19215i	−0.275807	−	0.318298i
$835$	0.191744	−	1.18248i	0.00663556	−	0.0409213i
$836$	−10.1994	−	2.99480i	−0.352752	−	0.103577i
$837$	4.19400	+	6.52599i	0.144966	+	0.225571i
$838$	26.2942	+	3.78053i	0.908318	+	0.130596i
$839$	4.10775	−	8.99471i	0.141815	−	0.310532i	−0.825375	−	0.564585i	$-0.809036\pi$
$839$	4.10775	−	8.99471i	0.141815	−	0.310532i	0.967190	+	0.254053i	$0.0817636\pi$
$840$	−16.9137	+	18.8256i	−0.583577	+	0.649544i
$841$	−1.57025	+	10.9213i	−0.0541466	+	0.376598i
$842$	14.1935	+	22.0856i	0.489141	+	0.761119i
$843$	4.29381	−	14.6234i	0.147887	−	0.503656i
$844$	2.00283	+	13.9300i	0.0689401	+	0.479489i
$845$	−24.8763	+	10.8252i	−0.855772	+	0.372397i
$846$	5.06938	+	3.25789i	0.174289	+	0.112009i
$847$	65.5433	+	56.7936i	2.25209	+	1.95145i
$848$	1.06258	+	3.61883i	0.0364893	+	0.124271i
$849$	12.0612	+	26.4103i	0.413939	+	0.906401i
$850$	−20.4467	−	14.2028i	−0.701315	−	0.487151i
$851$	1.54316	+	20.9687i	0.0528987	+	0.718797i
$852$		−	10.2182i		−	0.350068i
$853$	47.7773	−	21.8192i	1.63586	−	0.747074i	0.636164	−	0.771554i	$-0.280520\pi$
$853$	47.7773	−	21.8192i	1.63586	−	0.747074i	0.999700	+	0.0244793i	$0.00779279\pi$
$854$	18.6015	−	5.46190i	0.636531	−	0.186902i
$855$	1.92892	+	3.12337i	0.0659676	+	0.106817i
$856$	16.9262	+	10.8778i	0.578525	+	0.371795i
$857$	−11.9199	+	10.3287i	−0.407177	+	0.352821i	−0.834241	−	0.551401i	$-0.814094\pi$
$857$	−11.9199	+	10.3287i	−0.407177	+	0.352821i	0.427063	+	0.904222i	$0.359548\pi$
$858$	−4.99982	+	0.718865i	−0.170691	+	0.0245417i
$859$	28.8045	+	8.45776i	0.982797	+	0.288575i	0.733378	−	0.679821i	$-0.237942\pi$
$859$	28.8045	+	8.45776i	0.982797	+	0.288575i	0.249418	+	0.968396i	$0.419761\pi$
$860$	−19.5927	+	5.37277i	−0.668105	+	0.183210i
$861$	−1.19905	+	8.33959i	−0.0408636	+	0.284212i
$862$	18.9517	+	8.65495i	0.645497	+	0.294789i
$863$	−26.5195	−	12.1110i	−0.902733	−	0.412264i	−0.0907018	−	0.995878i	$-0.528911\pi$
$863$	−26.5195	−	12.1110i	−0.902733	−	0.412264i	−0.812032	+	0.583614i	$0.801638\pi$
$864$	0.765519	−	5.32430i	0.0260435	−	0.181136i
$865$	−17.0923	+	4.68710i	−0.581154	+	0.159366i
$866$	1.40520	+	0.412605i	0.0477508	+	0.0140209i
$867$	11.0550	−	1.58947i	0.375448	−	0.0539812i
$868$	−25.3883	+	21.9991i	−0.861735	+	0.746697i
$869$	36.4075	+	23.3977i	1.23504	+	0.793712i
$870$	−6.97422	−	11.2929i	−0.236448	−	0.382865i
$871$	2.88619	−	0.847461i	0.0977947	−	0.0287151i
$872$	33.3602	−	15.2351i	1.12972	−	0.515926i
$873$		−	13.1337i		−	0.444510i
$874$	5.21215	−	5.23368i	0.176304	−	0.177032i
$875$	26.5113	+	34.1501i	0.896245	+	1.15448i
$876$	0.119081	+	0.260752i	0.00402339	+	0.00880999i
$877$	2.74376	+	9.34439i	0.0926502	+	0.315538i	0.992758	−	0.120129i	$-0.0383308\pi$
$877$	2.74376	+	9.34439i	0.0926502	+	0.315538i	−0.900108	+	0.435667i	$0.856513\pi$
$878$	−6.72867	−	5.83042i	−0.227082	−	0.196767i
$879$	20.7365	+	13.3265i	0.699424	+	0.449492i
$880$	−5.99888	+	2.61047i	−0.202222	+	0.0879988i
$881$	4.74445	+	32.9984i	0.159845	+	1.11174i	0.898917	+	0.438118i	$0.144355\pi$
$881$	4.74445	+	32.9984i	0.159845	+	1.11174i	−0.739073	+	0.673626i	$0.764736\pi$
$882$	2.10191	−	7.15845i	0.0707751	−	0.241038i
$883$	−11.9813	−	18.6432i	−0.403201	−	0.627394i	0.578977	−	0.815344i	$-0.303452\pi$
$883$	−11.9813	−	18.6432i	−0.403201	−	0.627394i	−0.982179	+	0.187950i	$0.939816\pi$
$884$	−0.787745	+	5.47889i	−0.0264947	+	0.184275i
$885$	2.11727	−	2.35660i	0.0711711	−	0.0792161i
$886$	−13.4265	+	29.4000i	−0.451073	+	0.987712i
$887$	−0.861789	−	0.123907i	−0.0289360	−	0.00416037i	0.127832	−	0.991796i	$-0.459198\pi$
$887$	−0.861789	−	0.123907i	−0.0289360	−	0.00416037i	−0.156768	+	0.987636i	$0.550107\pi$
$888$	−6.93739	−	10.7948i	−0.232803	−	0.362249i
$889$	54.5496	+	16.0172i	1.82954	+	0.537200i
$890$	0.531918	−	3.28032i	0.0178299	−	0.109957i
$891$	3.78621	+	4.36952i	0.126843	+	0.146384i
$892$	7.14213	−	11.1134i	0.239136	−	0.372103i
$893$	7.96960	+	6.90570i	0.266693	+	0.231091i
$894$	14.6848	−	4.31185i	0.491134	−	0.144210i
$895$	−44.5452	+	5.59029i	−1.48898	+	0.186863i
$896$	19.6224			0.655538
$897$	−1.55215	+	4.18782i	−0.0518248	+	0.139827i
$898$		−	22.9289i		−	0.765149i
$899$	−20.3899	−	44.6476i	−0.680040	−	1.48908i
$900$	−5.31256	−	1.76943i	−0.177085	−	0.0589811i
$901$	−25.9043	+	29.8951i	−0.862996	+	0.995951i
$902$	−6.38941	+	9.94211i	−0.212744	+	0.331036i
$903$	23.7090	−	20.5439i	0.788985	−	0.683659i
$904$	−0.584017	−	4.06193i	−0.0194241	−	0.135098i
$905$	−23.3236	+	34.8983i	−0.775304	+	1.16006i
$906$	−15.3280	+	9.85074i	−0.509240	+	0.327269i
$907$	30.9969	+	4.45668i	1.02923	+	0.147982i	0.636186	−	0.771536i	$-0.280511\pi$
$907$	30.9969	+	4.45668i	1.02923	+	0.147982i	0.393049	+	0.919518i	$0.371420\pi$
$908$	−7.44885	−	3.40178i	−0.247199	−	0.112892i
$909$	−5.98513	+	13.1056i	−0.198514	+	0.434685i
$910$	−3.26098	+	6.81405i	−0.108100	+	0.225883i
$911$	42.7775	−	27.4914i	1.41728	−	0.910831i	0.417283	−	0.908776i	$-0.362982\pi$
$911$	42.7775	−	27.4914i	1.41728	−	0.910831i	0.999998	−	0.00205491i	$-0.000654099\pi$
$912$	−0.234057	+	0.797126i	−0.00775041	+	0.0263955i
$913$	−77.9626	+	11.2093i	−2.58018	+	0.370974i
$914$	7.47840	+	8.63053i	0.247363	+	0.285473i
$915$	7.66214	+	9.17021i	0.253302	+	0.303158i
$916$	−6.78018	+	7.82475i	−0.224024	+	0.258537i
$917$	−19.9788	−	68.0414i	−0.659757	−	2.24692i
$918$	−4.52914	+	2.06839i	−0.149484	+	0.0682671i
$919$	13.8102			0.455556			0.227778	−	0.973713i	$-0.426854\pi$
$919$	13.8102			0.455556			0.227778	+	0.973713i	$0.426854\pi$
$920$	−2.73646	+	31.2679i	−0.0902184	+	1.03087i
$921$	3.11731			0.102719
$922$	−2.17495	+	0.993267i	−0.0716282	+	0.0327115i
$923$	−2.39391	−	8.15289i	−0.0787964	−	0.268356i
$924$	−16.3961	+	18.9221i	−0.539392	+	0.622492i
$925$	−20.2536	+	8.38433i	−0.665936	+	0.275675i
$926$	8.89123	+	10.2610i	0.292184	+	0.337198i
$927$	−1.98505	+	0.285408i	−0.0651977	+	0.00937402i
$928$	−9.58860	+	32.6558i	−0.314761	+	1.07198i
$929$	−10.7307	+	6.89619i	−0.352062	+	0.226257i	−0.704703	−	0.709502i	$-0.748920\pi$
$929$	−10.7307	+	6.89619i	−0.352062	+	0.226257i	0.352641	+	0.935759i	$0.385284\pi$
$930$	14.6788	+	7.02479i	0.481337	+	0.230352i
$931$	5.42363	−	11.8761i	0.177752	−	0.389223i
$932$	11.4318	+	5.22071i	0.374459	+	0.171010i
$933$	6.62456	+	0.952468i	0.216878	+	0.0311824i
$934$	19.2283	−	12.3573i	0.629169	−	0.404342i
$935$	−57.0479	−	38.1269i	−1.86567	−	1.24688i
$936$	−0.387911	−	2.69798i	−0.0126793	−	0.0881863i
$937$	−10.8895	+	9.43583i	−0.355746	+	0.308255i	−0.814337	−	0.580392i	$-0.802899\pi$
$937$	−10.8895	+	9.43583i	−0.355746	+	0.308255i	0.458592	+	0.888647i	$0.348354\pi$
$938$	−6.33494	+	9.85736i	−0.206843	+	0.321854i
$939$	1.77414	−	2.04747i	0.0578970	−	0.0668167i
$940$	−16.0825	−	0.288799i	−0.524553	−	0.00941958i
$941$	−22.7591	−	49.8354i	−0.741925	−	1.62459i	−0.780363	−	0.625327i	$-0.784965\pi$
$941$	−22.7591	−	49.8354i	−0.741925	−	1.62459i	0.0384381	−	0.999261i	$-0.487762\pi$
$942$			0.849214i			0.0276689i
$943$	5.02678	+	9.16091i	0.163694	+	0.298320i
$944$	0.716953			0.0233348
$945$	8.57927	−	1.07667i	0.279084	−	0.0350242i
$946$	42.2221	−	12.3975i	1.37276	−	0.403079i
$947$	−2.59070	−	2.24486i	−0.0841865	−	0.0729480i	0.611751	−	0.791050i	$-0.290465\pi$
$947$	−2.59070	−	2.24486i	−0.0841865	−	0.0729480i	−0.695937	+	0.718102i	$0.745011\pi$
$948$	−4.53205	+	7.05201i	−0.147194	+	0.229039i
$949$	0.156102	+	0.180151i	0.00506728	+	0.00584795i
$950$	6.88551	+	3.44845i	0.223395	+	0.111883i
$951$	−22.6045	−	6.63728i	−0.733001	−	0.215228i
$952$	−32.4757	−	50.5331i	−1.05254	−	1.63779i
$953$	7.65592	+	1.10076i	0.248000	+	0.0356570i	0.265194	−	0.964195i	$-0.414564\pi$
$953$	7.65592	+	1.10076i	0.248000	+	0.0356570i	−0.0171939	+	0.999852i	$0.505473\pi$
$954$	2.90461	−	6.36022i	0.0940403	−	0.205920i
$955$	−29.6221	−	26.6137i	−0.958548	−	0.861200i
$956$	2.15494	−	14.9879i	0.0696956	−	0.484744i
$957$	−19.7778	−	30.7748i	−0.639324	−	0.994807i
$958$	8.23319	−	28.0397i	0.266002	−	0.905920i
$959$	−3.48779	−	24.2581i	−0.112627	−	0.783336i
$960$	−5.40545	−	12.4218i	−0.174460	−	0.400912i
$961$	24.5462	+	15.7749i	0.791813	+	0.508867i
$962$	−2.89467	−	2.50825i	−0.0933280	−	0.0808692i
$963$	−1.93670	−	6.59579i	−0.0624092	−	0.212546i
$964$	−11.0100	−	24.1086i	−0.354609	−	0.776485i
$965$	−32.9808	−	10.3308i	−1.06169	−	0.332559i
$966$	−6.11343	−	16.2881i	−0.196696	−	0.524062i
$967$		−	50.0599i		−	1.60982i	−0.593398	−	0.804909i	$-0.702214\pi$
$967$		−	50.0599i		−	1.60982i	0.593398	−	0.804909i	$-0.297786\pi$
$968$	−59.7124	+	27.2697i	−1.91923	+	0.876482i
$969$	−8.36032	+	2.45481i	−0.268572	+	0.0788599i
$970$	−14.4768	−	23.4413i	−0.464821	−	0.752653i
$971$	−50.7109	−	32.5899i	−1.62739	−	1.04586i	−0.950943	−	0.309367i	$-0.899883\pi$
$971$	−50.7109	−	32.5899i	−1.62739	−	1.04586i	−0.676446	−	0.736492i	$-0.736481\pi$
$972$	−0.846361	+	0.733376i	−0.0271470	+	0.0235230i
$973$	−49.6235	+	7.13479i	−1.59086	+	0.228731i
$974$	−28.4226	−	8.34563i	−0.910720	−	0.267411i
$975$	−4.65334	−	0.167177i	−0.149026	−	0.00535395i
$976$	−0.384874	+	2.67685i	−0.0123195	+	0.0856840i
$977$	8.40359	+	3.83779i	0.268855	+	0.122782i	0.545281	−	0.838253i	$-0.316423\pi$
$977$	8.40359	+	3.83779i	0.268855	+	0.122782i	−0.276426	+	0.961035i	$0.589150\pi$
$978$	3.04512	+	1.39066i	0.0973720	+	0.0444683i
$979$	1.30348	−	9.06593i	0.0416595	−	0.289748i
$980$	5.26663	+	19.2056i	0.168236	+	0.613501i
$981$	−12.0226	−	3.53015i	−0.383852	−	0.112709i
$982$	−16.3527	+	2.35116i	−0.521834	+	0.0750284i
$983$	−3.00150	+	2.60082i	−0.0957331	+	0.0829532i	−0.701412	−	0.712756i	$-0.747447\pi$
$983$	−3.00150	+	2.60082i	−0.0957331	+	0.0829532i	0.605679	+	0.795709i	$0.292901\pi$
$984$	−5.36492	−	3.44782i	−0.171027	−	0.109913i
$985$	38.9062	−	24.0276i	1.23966	−	0.765582i
$986$	30.2277	−	8.87565i	0.962645	−	0.282658i
$987$	22.5936	−	10.3182i	0.719162	−	0.328430i
$988$		−	1.71218i		−	0.0544718i
$989$	8.19213	−	38.0359i	0.260494	−	1.20947i
$990$	11.5740	+	3.62539i	0.367846	+	0.115222i
$991$	19.2332	+	42.1149i	0.610964	+	1.33783i	0.921912	+	0.387398i	$0.126626\pi$
$991$	19.2332	+	42.1149i	0.610964	+	1.33783i	−0.310948	+	0.950427i	$0.600647\pi$
$992$	−11.7561	−	40.0375i	−0.373256	−	1.27119i
$993$	−3.65351	−	3.16579i	−0.115941	−	0.100463i
$994$	27.8450	+	17.8949i	0.883191	+	0.567592i
$995$	−9.33407	+	4.06180i	−0.295910	+	0.128768i
$996$	−2.17121	−	15.1011i	−0.0687974	−	0.478496i
$997$	−16.1976	+	55.1641i	−0.512984	+	1.74706i	0.140457	+	0.990087i	$0.455143\pi$
$997$	−16.1976	+	55.1641i	−0.512984	+	1.74706i	−0.653441	+	0.756977i	$0.726675\pi$
$998$	17.5600	+	27.3239i	0.555852	+	0.864923i
$999$	−0.623922	+	4.33947i	−0.0197400	+	0.137295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.t.a.4.10	✓	240
5.4	even	2	inner	345.2.t.a.4.15	yes	240
23.6	even	11	inner	345.2.t.a.259.15	yes	240
115.29	even	22	inner	345.2.t.a.259.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.10	✓	240	1.1	even	1	trivial
345.2.t.a.4.15	yes	240	5.4	even	2	inner
345.2.t.a.259.10	yes	240	115.29	even	22	inner
345.2.t.a.259.15	yes	240	23.6	even	11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.853361 + 0.389717i) q^{2} +(0.281733 + 0.959493i) q^{3} +(-0.733376 + 0.846361i) q^{4} +(1.71593 - 1.43374i) q^{5} +(-0.614350 - 0.708998i) q^{6} +(-3.82750 + 0.550312i) q^{7} +(0.824602 - 2.80834i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-0.905553 + 1.89222i) q^{10} +(-2.40180 + 5.25922i) q^{11} +(-1.01869 - 0.465221i) q^{12} +(-0.921789 - 0.132533i) q^{13} +(3.05178 - 1.96126i) q^{14} +(1.85909 + 1.24249i) q^{15} +(0.0720174 + 0.500892i) q^{16} +(-4.01108 + 3.47562i) q^{17} +(0.507196 - 0.789213i) q^{18} +(1.07509 - 1.24073i) q^{19} +(-0.0449608 + 2.50376i) q^{20} +(-1.60635 - 3.51742i) q^{21} -5.42404i q^{22} +(-4.21393 - 2.28972i) q^{23} +2.92690 q^{24} +(0.888804 - 4.92037i) q^{25} +(0.838270 - 0.246138i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(2.34124 - 3.64303i) q^{28} +(4.14344 + 4.78179i) q^{29} +(-2.07070 - 0.335772i) q^{30} +(-7.44322 - 2.18553i) q^{31} +(2.90814 + 4.52515i) q^{32} +(-5.72285 - 0.822822i) q^{33} +(2.06839 - 4.52914i) q^{34} +(-5.77871 + 6.43192i) q^{35} +(0.159378 - 1.10850i) q^{36} +(-2.37022 - 3.68813i) q^{37} +(-0.433912 + 1.47777i) q^{38} +(-0.132533 - 0.921789i) q^{39} +(-2.61146 - 6.00116i) q^{40} +(-1.83297 - 1.17798i) q^{41} +(2.74160 + 2.37561i) q^{42} +(2.28567 + 7.78427i) q^{43} +(-2.68977 - 5.88978i) q^{44} +(-0.668393 + 2.13383i) q^{45} +(4.48834 + 0.311715i) q^{46} +6.42334i q^{47} +(-0.460313 + 0.210218i) q^{48} +(7.63049 - 2.24051i) q^{49} +(1.15908 + 4.54523i) q^{50} +(-4.46488 - 2.86941i) q^{51} +(0.788189 - 0.682969i) q^{52} +(7.37727 - 1.06069i) q^{53} +(0.900138 + 0.264304i) q^{54} +(3.41901 + 12.4680i) q^{55} +(-1.61071 + 11.2027i) q^{56} +(1.49336 + 0.681993i) q^{57} +(-5.39940 - 2.46582i) q^{58} +(0.201629 - 1.40236i) q^{59} +(-2.41501 + 0.662251i) q^{60} +(5.12770 + 1.50563i) q^{61} +(7.20350 - 1.03571i) q^{62} +(2.92238 - 2.53226i) q^{63} +(-5.09664 - 3.27541i) q^{64} +(-1.77174 + 1.09418i) q^{65} +(5.20432 - 1.52813i) q^{66} +(-2.93815 + 1.34181i) q^{67} -5.94375i q^{68} +(1.00977 - 4.68832i) q^{69} +(2.42470 - 7.74081i) q^{70} +(3.79033 + 8.29967i) q^{71} +(0.824602 + 2.80834i) q^{72} +(-0.193447 - 0.167623i) q^{73} +(3.45998 + 2.22360i) q^{74} +(4.97146 - 0.533427i) q^{75} +(0.261653 + 1.81984i) q^{76} +(6.29870 - 21.4514i) q^{77} +(0.472336 + 0.734969i) q^{78} +(1.06527 - 7.40910i) q^{79} +(0.841723 + 0.756240i) q^{80} +(0.415415 - 0.909632i) q^{81} +(2.02327 + 0.290902i) q^{82} +(7.36517 + 11.4604i) q^{83} +(4.15507 + 1.22004i) q^{84} +(-1.89959 + 11.7147i) q^{85} +(-4.98416 - 5.75203i) q^{86} +(-3.42075 + 5.32279i) q^{87} +(12.7891 + 11.0818i) q^{88} +(-1.51999 + 0.446311i) q^{89} +(-0.261211 - 2.08142i) q^{90} +3.60109 q^{91} +(5.02832 - 1.88728i) q^{92} -7.75746i q^{93} +(-2.50329 - 5.48143i) q^{94} +(0.0659105 - 3.67039i) q^{95} +(-3.52253 + 4.06522i) q^{96} +(-7.10064 + 11.0488i) q^{97} +(-5.63839 + 4.88570i) q^{98} +(-0.822822 - 5.72285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) \) 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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