LMFDB - Embedded newform 273.2.bd.a.127.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [273,2,Mod(43,273)] 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("273.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(273, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-8] 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.7
Root			$-1.98765i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.a.43.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72135 - 0.993824i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.975372 - 1.68939i) q^{4} -2.85284i q^{5} +(-1.72135 - 0.993824i) q^{6} +(-0.866025 - 0.500000i) q^{7} +0.0979034i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.83522 - 4.91075i) q^{10} +(-1.99765 + 1.15335i) q^{11} -1.95074 q^{12} +(3.55173 - 0.620648i) q^{13} -1.98765 q^{14} +(-2.47063 + 1.42642i) q^{15} +(2.04804 + 3.54731i) q^{16} +(1.26358 - 2.18858i) q^{17} +1.98765i q^{18} +(3.98796 + 2.30245i) q^{19} +(-4.81957 - 2.78258i) q^{20} +1.00000i q^{21} +(-2.29245 + 3.97063i) q^{22} +(-2.05173 - 3.55370i) q^{23} +(0.0847868 - 0.0489517i) q^{24} -3.13870 q^{25} +(5.49697 - 4.59815i) q^{26} +1.00000 q^{27} +(-1.68939 + 0.975372i) q^{28} +(1.34038 + 2.32161i) q^{29} +(-2.83522 + 4.91075i) q^{30} +0.917134i q^{31} +(6.88124 + 3.97288i) q^{32} +(1.99765 + 1.15335i) q^{33} -5.02309i q^{34} +(-1.42642 + 2.47063i) q^{35} +(0.975372 + 1.68939i) q^{36} +(5.14175 - 2.96859i) q^{37} +9.15293 q^{38} +(-2.31336 - 2.76557i) q^{39} +0.279303 q^{40} +(-3.59587 + 2.07608i) q^{41} +(0.993824 + 1.72135i) q^{42} +(-5.33109 + 9.23371i) q^{43} +4.49977i q^{44} +(2.47063 + 1.42642i) q^{45} +(-7.06351 - 4.07812i) q^{46} +0.601438i q^{47} +(2.04804 - 3.54731i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-5.40281 + 3.11932i) q^{50} -2.52716 q^{51} +(2.41574 - 6.60564i) q^{52} +1.41822 q^{53} +(1.72135 - 0.993824i) q^{54} +(3.29031 + 5.69899i) q^{55} +(0.0489517 - 0.0847868i) q^{56} -4.60490i q^{57} +(4.61455 + 2.66421i) q^{58} +(-4.22370 - 2.43855i) q^{59} +5.56516i q^{60} +(-6.72454 + 11.6472i) q^{61} +(0.911469 + 1.57871i) q^{62} +(0.866025 - 0.500000i) q^{63} +7.60122 q^{64} +(-1.77061 - 10.1325i) q^{65} +4.58489 q^{66} +(-12.3776 + 7.14624i) q^{67} +(-2.46492 - 4.26936i) q^{68} +(-2.05173 + 3.55370i) q^{69} +5.67044i q^{70} +(10.6572 + 6.15292i) q^{71} +(-0.0847868 - 0.0489517i) q^{72} -10.8999i q^{73} +(5.90052 - 10.2200i) q^{74} +(1.56935 + 2.71819i) q^{75} +(7.77950 - 4.49149i) q^{76} +2.30669 q^{77} +(-6.73060 - 2.46144i) q^{78} +6.67402 q^{79} +(10.1199 - 5.84274i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.12651 + 7.14733i) q^{82} -17.4987i q^{83} +(1.68939 + 0.975372i) q^{84} +(-6.24367 - 3.60479i) q^{85} +21.1926i q^{86} +(1.34038 - 2.32161i) q^{87} +(-0.112916 - 0.195577i) q^{88} +(-9.36923 + 5.40933i) q^{89} +5.67044 q^{90} +(-3.38621 - 1.23837i) q^{91} -8.00480 q^{92} +(0.794261 - 0.458567i) q^{93} +(0.597723 + 1.03529i) q^{94} +(6.56853 - 11.3770i) q^{95} -7.94577i q^{96} +(4.46293 + 2.57667i) q^{97} +(1.72135 + 0.993824i) q^{98} -2.30669i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30}+ \cdots - 54 q^{97}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	1.72135	−	0.993824i	1.21718	−	0.702740i	0.252867	−	0.967501i	$-0.418627\pi$
$2$	1.72135	−	0.993824i	1.21718	−	0.702740i	0.964314	+	0.264761i	$0.0852932\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.975372	−	1.68939i	0.487686	−	0.844697i
$5$		−	2.85284i		−	1.27583i	−0.770107	−	0.637915i	$-0.779797\pi$
$5$		−	2.85284i		−	1.27583i	0.770107	−	0.637915i	$-0.220203\pi$
$6$	−1.72135	−	0.993824i	−0.702740	−	0.405727i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			0.0979034i			0.0346141i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.83522	−	4.91075i	−0.896576	−	1.55291i
$11$	−1.99765	+	1.15335i	−0.602315	+	0.347747i	−0.769952	−	0.638102i	$-0.779720\pi$
$11$	−1.99765	+	1.15335i	−0.602315	+	0.347747i	0.167637	+	0.985849i	$0.446386\pi$
$12$	−1.95074			−0.563131
$13$	3.55173	−	0.620648i	0.985073	−	0.172137i
$13$	3.55173	−	0.620648i	0.985073	−	0.172137i
$14$	−1.98765			−0.531221
$15$	−2.47063	+	1.42642i	−0.637915	+	0.368300i
$16$	2.04804	+	3.54731i	0.512011	+	0.886829i
$17$	1.26358	−	2.18858i	0.306463	−	0.530809i	−0.671123	−	0.741346i	$-0.734188\pi$
$17$	1.26358	−	2.18858i	0.306463	−	0.530809i	0.977586	+	0.210537i	$0.0675212\pi$
$18$			1.98765i			0.468493i
$19$	3.98796	+	2.30245i	0.914902	+	0.528219i	0.882005	−	0.471240i	$-0.156193\pi$
$19$	3.98796	+	2.30245i	0.914902	+	0.528219i	0.0328966	+	0.999459i	$0.489527\pi$
$20$	−4.81957	−	2.78258i	−1.07769	−	0.622204i
$21$			1.00000i			0.218218i
$22$	−2.29245	+	3.97063i	−0.488751	+	0.846542i
$23$	−2.05173	−	3.55370i	−0.427815	−	0.740998i	0.568863	−	0.822432i	$-0.307383\pi$
$23$	−2.05173	−	3.55370i	−0.427815	−	0.740998i	−0.996679	+	0.0814340i	$0.974050\pi$
$24$	0.0847868	−	0.0489517i	0.0173070	−	0.00999222i
$25$	−3.13870			−0.627740
$26$	5.49697	−	4.59815i	1.07804	−	0.901771i
$27$	1.00000			0.192450
$28$	−1.68939	+	0.975372i	−0.319265	+	0.184328i
$29$	1.34038	+	2.32161i	0.248903	+	0.431113i	0.963222	−	0.268708i	$-0.0865966\pi$
$29$	1.34038	+	2.32161i	0.248903	+	0.431113i	−0.714319	+	0.699821i	$0.753263\pi$
$30$	−2.83522	+	4.91075i	−0.517638	+	0.896576i
$31$			0.917134i			0.164722i	0.996603	+	0.0823610i	$0.0262461\pi$
$31$			0.917134i			0.164722i	−0.996603	+	0.0823610i	$0.973754\pi$
$32$	6.88124	+	3.97288i	1.21644	+	0.702313i
$33$	1.99765	+	1.15335i	0.347747	+	0.200772i
$34$		−	5.02309i		−	0.861454i
$35$	−1.42642	+	2.47063i	−0.241109	+	0.417613i
$36$	0.975372	+	1.68939i	0.162562	+	0.281566i
$37$	5.14175	−	2.96859i	0.845299	−	0.488034i	−0.0137630	−	0.999905i	$-0.504381\pi$
$37$	5.14175	−	2.96859i	0.845299	−	0.488034i	0.859062	+	0.511872i	$0.171048\pi$
$38$	9.15293			1.48480
$39$	−2.31336	−	2.76557i	−0.370434	−	0.442845i
$40$	0.279303			0.0441616
$41$	−3.59587	+	2.07608i	−0.561581	+	0.324229i	−0.753780	−	0.657127i	$-0.771771\pi$
$41$	−3.59587	+	2.07608i	−0.561581	+	0.324229i	0.192199	+	0.981356i	$0.438438\pi$
$42$	0.993824	+	1.72135i	0.153350	+	0.265611i
$43$	−5.33109	+	9.23371i	−0.812983	+	1.40813i	0.0977843	+	0.995208i	$0.468824\pi$
$43$	−5.33109	+	9.23371i	−0.812983	+	1.40813i	−0.910767	+	0.412920i	$0.864509\pi$
$44$			4.49977i			0.678365i
$45$	2.47063	+	1.42642i	0.368300	+	0.212638i
$46$	−7.06351	−	4.07812i	−1.04146	−	0.601286i
$47$			0.601438i			0.0877287i	0.999037	+	0.0438643i	$0.0139669\pi$
$47$			0.601438i			0.0877287i	−0.999037	+	0.0438643i	$0.986033\pi$
$48$	2.04804	−	3.54731i	0.295610	−	0.512011i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−5.40281	+	3.11932i	−0.764073	+	0.441138i
$51$	−2.52716			−0.353872
$52$	2.41574	−	6.60564i	0.335003	−	0.916037i
$53$	1.41822			0.194808			0.0974038	−	0.995245i	$-0.468946\pi$
$53$	1.41822			0.194808			0.0974038	+	0.995245i	$0.468946\pi$
$54$	1.72135	−	0.993824i	0.234247	−	0.135242i
$55$	3.29031	+	5.69899i	0.443666	+	0.768451i
$56$	0.0489517	−	0.0847868i	0.00654145	−	0.0113301i
$57$		−	4.60490i		−	0.609934i
$58$	4.61455	+	2.66421i	0.605920	+	0.349828i
$59$	−4.22370	−	2.43855i	−0.549879	−	0.317473i	0.199194	−	0.979960i	$-0.436168\pi$
$59$	−4.22370	−	2.43855i	−0.549879	−	0.317473i	−0.749073	+	0.662487i	$0.769501\pi$
$60$			5.56516i			0.718459i
$61$	−6.72454	+	11.6472i	−0.860989	+	1.49128i	0.00998547	+	0.999950i	$0.496821\pi$
$61$	−6.72454	+	11.6472i	−0.860989	+	1.49128i	−0.870975	+	0.491327i	$0.836512\pi$
$62$	0.911469	+	1.57871i	0.115757	+	0.200497i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	7.60122			0.950152
$65$	−1.77061	−	10.1325i	−0.219617	−	1.25678i
$66$	4.58489			0.564361
$67$	−12.3776	+	7.14624i	−1.51217	+	0.873052i	−0.512271	+	0.858824i	$0.671196\pi$
$67$	−12.3776	+	7.14624i	−1.51217	+	0.873052i	−0.999899	+	0.0142283i	$0.995471\pi$
$68$	−2.46492	−	4.26936i	−0.298915	−	0.517736i
$69$	−2.05173	+	3.55370i	−0.246999	+	0.427815i
$70$			5.67044i			0.677748i
$71$	10.6572	+	6.15292i	1.26477	+	0.730217i	0.973994	−	0.226573i	$-0.0727521\pi$
$71$	10.6572	+	6.15292i	1.26477	+	0.730217i	0.290779	+	0.956790i	$0.406085\pi$
$72$	−0.0847868	−	0.0489517i	−0.00999222	−	0.00576901i
$73$		−	10.8999i		−	1.27573i	−0.770146	−	0.637867i	$-0.779817\pi$
$73$		−	10.8999i		−	1.27573i	0.770146	−	0.637867i	$-0.220183\pi$
$74$	5.90052	−	10.2200i	0.685921	−	1.18805i
$75$	1.56935	+	2.71819i	0.181213	+	0.313870i
$76$	7.77950	−	4.49149i	0.892369	−	0.515210i
$77$	2.30669			0.262872
$78$	−6.73060	−	2.46144i	−0.762090	−	0.278703i
$79$	6.67402			0.750886			0.375443	−	0.926846i	$-0.377491\pi$
$79$	6.67402			0.750886			0.375443	+	0.926846i	$0.377491\pi$
$80$	10.1199	−	5.84274i	1.13144	−	0.653238i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.12651	+	7.14733i	−0.455697	+	0.789290i
$83$		−	17.4987i		−	1.92073i	−0.278742	−	0.960366i	$-0.589917\pi$
$83$		−	17.4987i		−	1.92073i	0.278742	−	0.960366i	$-0.410083\pi$
$84$	1.68939	+	0.975372i	0.184328	+	0.106422i
$85$	−6.24367	−	3.60479i	−0.677221	−	0.390994i
$86$			21.1926i			2.28526i
$87$	1.34038	−	2.32161i	0.143704	−	0.248903i
$88$	−0.112916	−	0.195577i	−0.0120369	−	0.0208486i
$89$	−9.36923	+	5.40933i	−0.993137	+	0.573388i	−0.906210	−	0.422827i	$-0.861038\pi$
$89$	−9.36923	+	5.40933i	−0.993137	+	0.573388i	−0.0869262	+	0.996215i	$0.527704\pi$
$90$	5.67044			0.597717
$91$	−3.38621	−	1.23837i	−0.354972	−	0.129816i
$92$	−8.00480			−0.834558
$93$	0.794261	−	0.458567i	0.0823610	−	0.0475512i
$94$	0.597723	+	1.03529i	0.0616504	+	0.106782i
$95$	6.56853	−	11.3770i	0.673917	−	1.16726i
$96$		−	7.94577i		−	0.810962i
$97$	4.46293	+	2.57667i	0.453142	+	0.261621i	0.709156	−	0.705052i	$-0.249076\pi$
$97$	4.46293	+	2.57667i	0.453142	+	0.261621i	−0.256015	+	0.966673i	$0.582409\pi$
$98$	1.72135	+	0.993824i	0.173883	+	0.100391i
$99$		−	2.30669i		−	0.231831i
$100$	−3.06140	+	5.30250i	−0.306140	+	0.530250i
$101$	−5.91293	−	10.2415i	−0.588358	−	1.01907i	−0.994448	−	0.105233i	$-0.966441\pi$
$101$	−5.91293	−	10.2415i	−0.588358	−	1.01907i	0.406089	−	0.913833i	$-0.366892\pi$
$102$	−4.35013	+	2.51155i	−0.430727	+	0.248680i
$103$	−18.1000			−1.78345			−0.891725	−	0.452578i	$-0.850504\pi$
$103$	−18.1000			−1.78345			−0.891725	+	0.452578i	$0.850504\pi$
$104$	0.0607635	+	0.347727i	0.00595835	+	0.0340974i
$105$	2.85284			0.278409
$106$	2.44126	−	1.40946i	0.237116	−	0.136899i
$107$	1.78333	+	3.08881i	0.172401	+	0.298607i	0.939259	−	0.343210i	$-0.111514\pi$
$107$	1.78333	+	3.08881i	0.172401	+	0.298607i	−0.766858	+	0.641817i	$0.778181\pi$
$108$	0.975372	−	1.68939i	0.0938552	−	0.162562i
$109$		−	11.5102i		−	1.10248i	−0.834348	−	0.551238i	$-0.814155\pi$
$109$		−	11.5102i		−	1.10248i	0.834348	−	0.551238i	$-0.185845\pi$
$110$	11.3276	+	6.53998i	1.08004	+	0.623563i
$111$	−5.14175	−	2.96859i	−0.488034	−	0.281766i
$112$		−	4.09609i		−	0.387044i
$113$	1.02600	−	1.77708i	0.0965176	−	0.167173i	−0.813723	−	0.581252i	$-0.802563\pi$
$113$	1.02600	−	1.77708i	0.0965176	−	0.167173i	0.910241	+	0.414079i	$0.135896\pi$
$114$	−4.57646	−	7.92667i	−0.428625	−	0.742400i
$115$	−10.1381	+	5.85326i	−0.945387	+	0.545819i
$116$	5.22949			0.485546
$117$	−1.23837	+	3.38621i	−0.114487	+	0.313056i
$118$	−9.69397			−0.892403
$119$	−2.18858	+	1.26358i	−0.200627	+	0.115832i
$120$	−0.139651	−	0.241883i	−0.0127484	−	0.0220808i
$121$	−2.83959	+	4.91831i	−0.258144	+	0.447119i
$122$			26.7320i			2.42021i
$123$	3.59587	+	2.07608i	0.324229	+	0.187194i
$124$	1.54940	+	0.894547i	0.139140	+	0.0803327i
$125$		−	5.30999i		−	0.474940i
$126$	0.993824	−	1.72135i	0.0885369	−	0.153350i
$127$	9.07892	+	15.7251i	0.805623	+	1.39538i	0.915869	+	0.401476i	$0.131503\pi$
$127$	9.07892	+	15.7251i	0.805623	+	1.39538i	−0.110246	+	0.993904i	$0.535164\pi$
$128$	−0.678089	+	0.391495i	−0.0599352	+	0.0346036i
$129$	10.6622			0.938752
$130$	−13.1178	−	15.6820i	−1.15051	−	1.37540i
$131$	1.96602			0.171772			0.0858860	−	0.996305i	$-0.472628\pi$
$131$	1.96602			0.171772			0.0858860	+	0.996305i	$0.472628\pi$
$132$	3.89691	−	2.24988i	0.339183	−	0.195827i
$133$	−2.30245	−	3.98796i	−0.199648	−	0.345800i
$134$	−14.2042	+	24.6024i	−1.22706	+	2.12532i
$135$		−	2.85284i		−	0.245533i
$136$	0.214269	+	0.123709i	0.0183735	+	0.0106079i
$137$	10.9997	+	6.35067i	0.939766	+	0.542574i	0.889887	−	0.456181i	$-0.150783\pi$
$137$	10.9997	+	6.35067i	0.939766	+	0.542574i	0.0498793	+	0.998755i	$0.484116\pi$
$138$			8.15624i			0.694305i
$139$	0.989648	−	1.71412i	0.0839409	−	0.145390i	−0.820999	−	0.570930i	$-0.806583\pi$
$139$	0.989648	−	1.71412i	0.0839409	−	0.145390i	0.904939	+	0.425540i	$0.139916\pi$
$140$	2.78258	+	4.81957i	0.235171	+	0.407328i
$141$	0.520860	−	0.300719i	0.0438643	−	0.0253251i
$142$	24.4597			2.05261
$143$	−6.37931	+	5.33621i	−0.533465	+	0.446237i
$144$	−4.09609			−0.341340
$145$	6.62319	−	3.82390i	0.550026	−	0.317558i
$146$	−10.8326	−	18.7625i	−0.896509	−	1.55280i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$		−	11.5819i		−	0.952029i
$149$	−20.3745	−	11.7632i	−1.66914	−	0.963678i	−0.968103	−	0.250554i	$-0.919387\pi$
$149$	−20.3745	−	11.7632i	−1.66914	−	0.963678i	−0.701038	−	0.713124i	$-0.747279\pi$
$150$	5.40281	+	3.11932i	0.441138	+	0.254691i
$151$			11.7828i			0.958872i	0.877577	+	0.479436i	$0.159159\pi$
$151$			11.7828i			0.958872i	−0.877577	+	0.479436i	$0.840841\pi$
$152$	−0.225418	+	0.390435i	−0.0182838	+	0.0316685i
$153$	1.26358	+	2.18858i	0.102154	+	0.176936i
$154$	3.97063	−	2.29245i	0.319963	−	0.184731i
$155$	2.61644			0.210157
$156$	−6.92852	+	1.21073i	−0.554725	+	0.0969356i
$157$	−2.26601			−0.180848			−0.0904238	−	0.995903i	$-0.528822\pi$
$157$	−2.26601			−0.180848			−0.0904238	+	0.995903i	$0.528822\pi$
$158$	11.4883	−	6.63280i	0.913964	−	0.527677i
$159$	−0.709110	−	1.22821i	−0.0562361	−	0.0974038i
$160$	11.3340	−	19.6311i	0.896032	−	1.55197i
$161$			4.10346i			0.323398i
$162$	−1.72135	−	0.993824i	−0.135242	−	0.0780822i
$163$	−14.9883	−	8.65350i	−1.17397	−	0.677794i	−0.219361	−	0.975644i	$-0.570397\pi$
$163$	−14.9883	−	8.65350i	−1.17397	−	0.677794i	−0.954613	+	0.297850i	$0.903731\pi$
$164$			8.09979i			0.632488i
$165$	3.29031	−	5.69899i	0.256150	−	0.443666i
$166$	−17.3906	−	30.1215i	−1.34977	−	2.33788i
$167$	−12.8234	+	7.40357i	−0.992301	+	0.572906i	−0.905961	−	0.423360i	$-0.860850\pi$
$167$	−12.8234	+	7.40357i	−0.992301	+	0.572906i	−0.0863400	+	0.996266i	$0.527517\pi$
$168$	−0.0979034			−0.00755341
$169$	12.2296	−	4.40875i	0.940738	−	0.339135i
$170$	−14.3301			−1.09907
$171$	−3.98796	+	2.30245i	−0.304967	+	0.176073i
$172$	10.3996	+	18.0126i	0.792961	+	1.37345i
$173$	0.675104	−	1.16931i	0.0513272	−	0.0889013i	−0.839220	−	0.543792i	$-0.816988\pi$
$173$	0.675104	−	1.16931i	0.0513272	−	0.0889013i	0.890547	+	0.454890i	$0.150322\pi$
$174$		−	5.32842i		−	0.403947i
$175$	2.71819	+	1.56935i	0.205476	+	0.118632i
$176$	−8.18256	−	4.72420i	−0.616784	−	0.356100i
$177$			4.87711i			0.366586i
$178$	−10.7518	+	18.6227i	−0.805884	+	1.39583i
$179$	−2.41602	−	4.18467i	−0.180582	−	0.312777i	0.761497	−	0.648168i	$-0.224465\pi$
$179$	−2.41602	−	4.18467i	−0.180582	−	0.312777i	−0.942079	+	0.335392i	$0.891131\pi$
$180$	4.81957	−	2.78258i	0.359230	−	0.207401i
$181$	17.8164			1.32429			0.662143	−	0.749378i	$-0.269647\pi$
$181$	17.8164			1.32429			0.662143	+	0.749378i	$0.269647\pi$
$182$	−7.05959	+	1.23363i	−0.523292	+	0.0914427i
$183$	13.4491			0.994185
$184$	0.347919	−	0.200871i	0.0256490	−	0.0148084i
$185$	−8.46892	−	14.6686i	−0.622647	−	1.07846i
$186$	0.911469	−	1.57871i	0.0668322	−	0.115757i
$187$			5.82937i			0.426286i
$188$	1.01607	+	0.586625i	0.0741042	+	0.0427841i
$189$	−0.866025	−	0.500000i	−0.0629941	−	0.0363696i
$190$		−	26.1118i		−	1.89435i
$191$	−0.116212	+	0.201285i	−0.00840879	+	0.0145645i	−0.870199	−	0.492700i	$-0.836010\pi$
$191$	−0.116212	+	0.201285i	−0.00840879	+	0.0145645i	0.861790	+	0.507265i	$0.169343\pi$
$192$	−3.80061	−	6.58285i	−0.274285	−	0.475076i
$193$	22.3393	−	12.8976i	1.60802	−	0.928392i	0.618209	−	0.786014i	$-0.287859\pi$
$193$	22.3393	−	12.8976i	1.60802	−	0.928392i	0.989812	−	0.142378i	$-0.0454748\pi$
$194$	10.2430			0.735407
$195$	−7.88972	+	6.59965i	−0.564994	+	0.472611i
$196$	1.95074			0.139339
$197$	10.9075	−	6.29745i	0.777127	−	0.448674i	−0.0582842	−	0.998300i	$-0.518563\pi$
$197$	10.9075	−	6.29745i	0.777127	−	0.448674i	0.835411	+	0.549626i	$0.185230\pi$
$198$	−2.29245	−	3.97063i	−0.162917	−	0.282181i
$199$	−0.608439	+	1.05385i	−0.0431311	+	0.0747052i	−0.886785	−	0.462182i	$-0.847067\pi$
$199$	−0.608439	+	1.05385i	−0.0431311	+	0.0747052i	0.843654	+	0.536887i	$0.180400\pi$
$200$		−	0.307289i		−	0.0217286i
$201$	12.3776	+	7.14624i	0.873052	+	0.504057i
$202$	−20.3565	−	11.7528i	−1.43228	−	0.826925i
$203$		−	2.68077i		−	0.188153i
$204$	−2.46492	+	4.26936i	−0.172579	+	0.298915i
$205$	5.92272	+	10.2585i	0.413661	+	0.716481i
$206$	−31.1566	+	17.9882i	−2.17078	+	1.25330i
$207$	4.10346			0.285210
$208$	9.47573	+	11.3280i	0.657024	+	0.785455i
$209$	−10.6221			−0.734746
$210$	4.91075	−	2.83522i	0.338874	−	0.195649i
$211$	−0.997461	−	1.72765i	−0.0686681	−	0.118937i	0.829647	−	0.558288i	$-0.188542\pi$
$211$	−0.997461	−	1.72765i	−0.0686681	−	0.118937i	−0.898315	+	0.439352i	$0.855208\pi$
$212$	1.38329	−	2.39593i	0.0950049	−	0.164553i
$213$		−	12.3058i		−	0.843182i
$214$	6.13948	+	3.54463i	0.419686	+	0.242306i
$215$	26.3423	+	15.2087i	1.79653	+	1.03723i
$216$			0.0979034i			0.00666148i
$217$	0.458567	−	0.794261i	0.0311295	−	0.0539180i
$218$	−11.4391	−	19.8131i	−0.774754	−	1.34191i
$219$	−9.43957	+	5.44994i	−0.637867	+	0.368273i
$220$	12.8371			0.865478
$221$	3.12955	−	8.55749i	0.210516	−	0.575639i
$222$	−11.8010			−0.792033
$223$	24.8533	−	14.3491i	1.66430	−	0.960884i	0.693675	−	0.720288i	$-0.255990\pi$
$223$	24.8533	−	14.3491i	1.66430	−	0.960884i	0.970625	−	0.240597i	$-0.0773431\pi$
$224$	−3.97288	−	6.88124i	−0.265450	−	0.459772i
$225$	1.56935	−	2.71819i	0.104623	−	0.181213i
$226$		−	4.07864i		−	0.271307i
$227$	7.20768	+	4.16136i	0.478390	+	0.276199i	0.719745	−	0.694238i	$-0.244258\pi$
$227$	7.20768	+	4.16136i	0.478390	+	0.276199i	−0.241355	+	0.970437i	$0.577592\pi$
$228$	−7.77950	−	4.49149i	−0.515210	−	0.297456i
$229$		−	1.24569i		−	0.0823173i	−0.999153	−	0.0411587i	$-0.986895\pi$
$229$		−	1.24569i		−	0.0823173i	0.999153	−	0.0411587i	$-0.0131049\pi$
$230$	−11.6342	+	20.1511i	−0.767138	+	1.32872i
$231$	−1.15335	−	1.99765i	−0.0758846	−	0.131436i
$232$	−0.227294	+	0.131228i	−0.0149226	+	0.00861555i
$233$	−9.67623			−0.633911			−0.316955	−	0.948440i	$-0.602661\pi$
$233$	−9.67623			−0.633911			−0.316955	+	0.948440i	$0.602661\pi$
$234$	1.23363	+	7.05959i	0.0806449	+	0.461500i
$235$	1.71581			0.111927
$236$	−8.23936	+	4.75700i	−0.536336	+	0.309654i
$237$	−3.33701	−	5.77987i	−0.216762	−	0.375443i
$238$	−2.51155	+	4.35013i	−0.162799	+	0.281977i
$239$			7.45095i			0.481962i	0.970530	+	0.240981i	$0.0774691\pi$
$239$			7.45095i			0.481962i	−0.970530	+	0.240981i	$0.922531\pi$
$240$	−10.1199	−	5.84274i	−0.653238	−	0.377147i
$241$	−10.2532	−	5.91970i	−0.660468	−	0.381321i	0.131987	−	0.991251i	$-0.457864\pi$
$241$	−10.2532	−	5.91970i	−0.660468	−	0.381321i	−0.792455	+	0.609930i	$0.791198\pi$
$242$			11.2882i			0.725633i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	13.1179	+	22.7208i	0.839785	+	1.45455i
$245$	2.47063	−	1.42642i	0.157843	−	0.0911307i
$246$	8.25302			0.526194
$247$	15.5932	+	5.70257i	0.992171	+	0.362846i
$248$	−0.0897905			−0.00570170
$249$	−15.1543	+	8.74935i	−0.960366	+	0.554468i
$250$	−5.27720	−	9.14037i	−0.333759	−	0.578088i
$251$	−13.4680	+	23.3272i	−0.850091	+	1.47240i	0.0310350	+	0.999518i	$0.490120\pi$
$251$	−13.4680	+	23.3272i	−0.850091	+	1.47240i	−0.881126	+	0.472882i	$0.843214\pi$
$252$		−	1.95074i		−	0.122885i
$253$	8.19730	+	4.73271i	0.515360	+	0.297543i
$254$	31.2560	+	18.0457i	1.96118	+	1.13229i
$255$			7.20957i			0.451481i
$256$	−8.37937	+	14.5135i	−0.523711	+	0.907094i
$257$	11.1196	+	19.2597i	0.693621	+	1.20139i	0.970643	+	0.240523i	$0.0773189\pi$
$257$	11.1196	+	19.2597i	0.693621	+	1.20139i	−0.277023	+	0.960863i	$0.589348\pi$
$258$	18.3534	−	10.5963i	1.14263	−	0.659698i
$259$	−5.93718			−0.368919
$260$	−18.8448	−	6.89172i	−1.16871	−	0.427407i
$261$	−2.68077			−0.165935
$262$	3.38422	−	1.95388i	0.209078	−	0.120711i
$263$	−2.45030	−	4.24404i	−0.151092	−	0.261699i	0.780537	−	0.625109i	$-0.214946\pi$
$263$	−2.45030	−	4.24404i	−0.151092	−	0.261699i	−0.931629	+	0.363410i	$0.881612\pi$
$264$	−0.112916	+	0.195577i	−0.00694953	+	0.0120369i
$265$		−	4.04596i		−	0.248541i
$266$	−7.92667	−	4.57646i	−0.486015	−	0.280601i
$267$	9.36923	+	5.40933i	0.573388	+	0.331046i
$268$			27.8810i			1.70310i
$269$	−13.7048	+	23.7374i	−0.835597	+	1.44730i	0.0579466	+	0.998320i	$0.481545\pi$
$269$	−13.7048	+	23.7374i	−0.835597	+	1.44730i	−0.893544	+	0.448977i	$0.851789\pi$
$270$	−2.83522	−	4.91075i	−0.172546	−	0.298859i
$271$	17.7004	−	10.2193i	1.07522	−	0.620781i	0.145620	−	0.989341i	$-0.453482\pi$
$271$	17.7004	−	10.2193i	1.07522	−	0.620781i	0.929604	+	0.368559i	$0.120149\pi$
$272$	10.3514			0.627648
$273$	0.620648	+	3.55173i	0.0375633	+	0.214961i
$274$	25.2458			1.52515
$275$	6.27004	−	3.62001i	0.378097	−	0.218295i
$276$	4.00240	+	6.93236i	0.240916	+	0.417279i
$277$	−1.64527	+	2.84969i	−0.0988548	+	0.171221i	−0.911211	−	0.411940i	$-0.864851\pi$
$277$	−1.64527	+	2.84969i	−0.0988548	+	0.171221i	0.812356	+	0.583162i	$0.198185\pi$
$278$		−	3.93414i		−	0.235954i
$279$	−0.794261	−	0.458567i	−0.0475512	−	0.0274537i
$280$	−0.241883	−	0.139651i	−0.0144553	−	0.00834577i
$281$		−	23.7022i		−	1.41395i	−0.707236	−	0.706977i	$-0.750058\pi$
$281$		−	23.7022i		−	1.41395i	0.707236	−	0.706977i	$-0.249942\pi$
$282$	0.597723	−	1.03529i	0.0355939	−	0.0616504i
$283$	3.19561	+	5.53496i	0.189959	+	0.329019i	0.945236	−	0.326386i	$-0.105831\pi$
$283$	3.19561	+	5.53496i	0.189959	+	0.329019i	−0.755277	+	0.655406i	$0.772498\pi$
$284$	20.7894	−	12.0028i	1.23362	−	0.712234i
$285$	−13.1371			−0.778172
$286$	−5.67779	+	15.5254i	−0.335735	+	0.918037i
$287$	4.15216			0.245094
$288$	−6.88124	+	3.97288i	−0.405481	+	0.234104i
$289$	5.30674	+	9.19155i	0.312161	+	0.540679i
$290$	7.60057	−	13.1646i	0.446321	−	0.773050i
$291$		−	5.15334i		−	0.302094i
$292$	−18.4142	−	10.6314i	−1.07761	−	0.622158i
$293$	19.0735	+	11.0121i	1.11429	+	0.643333i	0.939936	−	0.341350i	$-0.110884\pi$
$293$	19.0735	+	11.0121i	1.11429	+	0.643333i	0.174350	+	0.984684i	$0.444218\pi$
$294$		−	1.98765i		−	0.115922i
$295$	−6.95681	+	12.0495i	−0.405041	+	0.701551i
$296$	0.290635	+	0.503395i	0.0168928	+	0.0292592i
$297$	−1.99765	+	1.15335i	−0.115916	+	0.0669239i
$298$	−46.7622			−2.70886
$299$	−9.49279	−	11.3484i	−0.548982	−	0.656294i
$300$	6.12280			0.353500
$301$	9.23371	−	5.33109i	0.532222	−	0.307279i
$302$	11.7100	+	20.2824i	0.673838	+	1.16712i
$303$	−5.91293	+	10.2415i	−0.339689	+	0.588358i
$304$			18.8621i			1.08181i
$305$	33.2277	+	19.1840i	1.90262	+	1.09848i
$306$	4.35013	+	2.51155i	0.248680	+	0.143576i
$307$			10.7195i			0.611797i	0.952064	+	0.305898i	$0.0989568\pi$
$307$			10.7195i			0.611797i	−0.952064	+	0.305898i	$0.901043\pi$
$308$	2.24988	−	3.89691i	0.128199	−	0.222047i
$309$	9.05002	+	15.6751i	0.514838	+	0.891725i
$310$	4.50381	−	2.60028i	0.255799	−	0.147686i
$311$	−8.16438			−0.462960			−0.231480	−	0.972840i	$-0.574357\pi$
$311$	−8.16438			−0.462960			−0.231480	+	0.972840i	$0.574357\pi$
$312$	0.270758	−	0.226486i	0.0153287	−	0.0128222i
$313$	−12.6727			−0.716304			−0.358152	−	0.933663i	$-0.616593\pi$
$313$	−12.6727			−0.716304			−0.358152	+	0.933663i	$0.616593\pi$
$314$	−3.90061	+	2.25202i	−0.220124	+	0.127089i
$315$	−1.42642	−	2.47063i	−0.0803697	−	0.139204i
$316$	6.50965	−	11.2750i	0.366197	−	0.634271i
$317$			1.58156i			0.0888291i	0.999013	+	0.0444146i	$0.0141423\pi$
$317$			1.58156i			0.0888291i	−0.999013	+	0.0444146i	$0.985858\pi$
$318$	−2.44126	−	1.40946i	−0.136899	−	0.0790387i
$319$	−5.35525	−	3.09185i	−0.299836	−	0.173111i
$320$		−	21.6851i		−	1.21223i
$321$	1.78333	−	3.08881i	0.0995357	−	0.172401i
$322$	4.07812	+	7.06351i	0.227265	+	0.393634i
$323$	10.0782	−	5.81865i	0.560766	−	0.323758i
$324$	−1.95074			−0.108375
$325$	−11.1478	+	1.94803i	−0.618370	+	0.108057i
$326$	−34.4002			−1.90525
$327$	−9.96812	+	5.75510i	−0.551238	+	0.318258i
$328$	−0.203255	−	0.352048i	−0.0112229	−	0.0194386i
$329$	0.300719	−	0.520860i	0.0165792	−	0.0287160i
$330$		−	13.0800i		−	0.720028i
$331$	−21.1631	−	12.2185i	−1.16323	−	0.671592i	−0.211155	−	0.977453i	$-0.567722\pi$
$331$	−21.1631	−	12.2185i	−1.16323	−	0.671592i	−0.952076	+	0.305861i	$0.901056\pi$
$332$	−29.5622	−	17.0677i	−1.62244	−	0.936714i
$333$			5.93718i			0.325356i
$334$	−14.7157	+	25.4883i	−0.805207	+	1.39466i
$335$	20.3871	+	35.3115i	1.11387	+	1.92927i
$336$	−3.54731	+	2.04804i	−0.193522	+	0.111730i
$337$	−14.8194			−0.807266			−0.403633	−	0.914921i	$-0.632253\pi$
$337$	−14.8194			−0.807266			−0.403633	+	0.914921i	$0.632253\pi$
$338$	16.6699	−	19.7431i	0.906725	−	1.07388i
$339$	−2.05199			−0.111449
$340$	−12.1798	+	7.03201i	−0.660543	+	0.381365i
$341$	−1.05777	−	1.83212i	−0.0572816	−	0.0992146i
$342$	−4.57646	+	7.92667i	−0.247467	+	0.428625i
$343$		−	1.00000i		−	0.0539949i
$344$	−0.904012	−	0.521931i	−0.0487410	−	0.0281407i
$345$	10.1381	+	5.85326i	0.545819	+	0.315129i
$346$		−	2.68374i		−	0.144279i
$347$	9.18756	−	15.9133i	0.493214	−	0.854272i	−0.506755	−	0.862090i	$-0.669155\pi$
$347$	9.18756	−	15.9133i	0.493214	−	0.854272i	0.999969	+	0.00781789i	$0.00248854\pi$
$348$	−2.61475	−	4.52887i	−0.140165	−	0.242773i
$349$	9.69361	−	5.59661i	0.518887	−	0.299579i	−0.217592	−	0.976040i	$-0.569820\pi$
$349$	9.69361	−	5.59661i	0.518887	−	0.299579i	0.736479	+	0.676460i	$0.236487\pi$
$350$	6.23863			0.333469
$351$	3.55173	−	0.620648i	0.189577	−	0.0331277i
$352$	−18.3284			−0.976909
$353$	17.6126	−	10.1686i	0.937424	−	0.541222i	0.0482721	−	0.998834i	$-0.484629\pi$
$353$	17.6126	−	10.1686i	0.937424	−	0.541222i	0.889152	+	0.457612i	$0.151295\pi$
$354$	4.84699	+	8.39523i	0.257614	+	0.446201i
$355$	17.5533	−	30.4032i	0.931633	−	1.61364i
$356$			21.1044i			1.11853i
$357$	2.18858	+	1.26358i	0.115832	+	0.0668756i
$358$	−8.31765	−	4.80220i	−0.439601	−	0.253804i
$359$		−	5.14966i		−	0.271789i	−0.990723	−	0.135894i	$-0.956609\pi$
$359$		−	5.14966i		−	0.271789i	0.990723	−	0.135894i	$-0.0433908\pi$
$360$	−0.139651	+	0.241883i	−0.00736027	+	0.0127484i
$361$	1.10257	+	1.90970i	0.0580299	+	0.100511i
$362$	30.6684	−	17.7064i	1.61190	−	0.930628i
$363$	5.67917			0.298079
$364$	−5.39491	+	4.51278i	−0.282770	+	0.236534i
$365$	−31.0956			−1.62762
$366$	23.1506	−	13.3660i	1.21010	−	0.698653i
$367$	−7.64529	−	13.2420i	−0.399081	−	0.691228i	0.594532	−	0.804072i	$-0.297337\pi$
$367$	−7.64529	−	13.2420i	−0.399081	−	0.691228i	−0.993613	+	0.112844i	$0.964004\pi$
$368$	8.40406	−	14.5563i	0.438092	−	0.758798i
$369$		−	4.15216i		−	0.216153i
$370$	−29.1560	−	16.8332i	−1.51575	−	0.875118i
$371$	−1.22821	−	0.709110i	−0.0637657	−	0.0368152i
$372$		−	1.78909i		−	0.0927602i
$373$	8.54274	−	14.7965i	0.442326	−	0.766131i	−0.555536	−	0.831493i	$-0.687487\pi$
$373$	8.54274	−	14.7965i	0.442326	−	0.766131i	0.997862	+	0.0653615i	$0.0208200\pi$
$374$	5.79337	+	10.0344i	0.299568	+	0.518867i
$375$	−4.59859	+	2.65500i	−0.237470	+	0.137103i
$376$	−0.0588828			−0.00303665
$377$	6.20159	+	7.41384i	0.319398	+	0.381832i
$378$	−1.98765			−0.102234
$379$	−3.83043	+	2.21150i	−0.196756	+	0.113597i	−0.595142	−	0.803621i	$-0.702904\pi$
$379$	−3.83043	+	2.21150i	−0.196756	+	0.113597i	0.398385	+	0.917218i	$0.369571\pi$
$380$	−12.8135	−	22.1937i	−0.657320	−	1.13851i
$381$	9.07892	−	15.7251i	0.465127	−	0.805623i
$382$			0.461976i			0.0236368i
$383$	3.59163	+	2.07363i	0.183524	+	0.105957i	0.588947	−	0.808172i	$-0.299543\pi$
$383$	3.59163	+	2.07363i	0.183524	+	0.105957i	−0.405424	+	0.914129i	$0.632876\pi$
$384$	0.678089	+	0.391495i	0.0346036	+	0.0199784i
$385$		−	6.58062i		−	0.335380i
$386$	25.6359	−	44.4028i	1.30484	−	2.26004i
$387$	−5.33109	−	9.23371i	−0.270994	−	0.469376i
$388$	8.70603	−	5.02643i	0.441982	−	0.255178i
$389$	−34.7497			−1.76188			−0.880940	−	0.473228i	$-0.843089\pi$
$389$	−34.7497			−1.76188			−0.880940	+	0.473228i	$0.843089\pi$
$390$	−7.02210	+	19.2013i	−0.355578	+	0.972297i
$391$	−10.3701			−0.524438
$392$	−0.0847868	+	0.0489517i	−0.00428238	+	0.00247243i
$393$	−0.983010	−	1.70262i	−0.0495863	−	0.0858860i
$394$	12.5171	−	21.6803i	0.630603	−	1.09224i
$395$		−	19.0399i		−	0.958002i
$396$	−3.89691	−	2.24988i	−0.195827	−	0.113061i
$397$	7.19190	+	4.15224i	0.360951	+	0.208395i	0.669498	−	0.742814i	$-0.266509\pi$
$397$	7.19190	+	4.15224i	0.360951	+	0.208395i	−0.308547	+	0.951209i	$0.599843\pi$
$398$			2.41872i			0.121240i
$399$	−2.30245	+	3.98796i	−0.115267	+	0.199648i
$400$	−6.42819	−	11.1340i	−0.321410	−	0.556698i
$401$	30.7625	−	17.7607i	1.53620	−	0.886928i	0.537148	−	0.843488i	$-0.319502\pi$
$401$	30.7625	−	17.7607i	1.53620	−	0.886928i	0.999056	−	0.0434398i	$-0.0138317\pi$
$402$	28.4084			1.41688
$403$	0.569217	+	3.25741i	0.0283547	+	0.162263i
$404$	−23.0692			−1.14774
$405$	−2.47063	+	1.42642i	−0.122767	+	0.0708794i
$406$	−2.66421	−	4.61455i	−0.132223	−	0.229016i
$407$	−6.84763	+	11.8604i	−0.339424	+	0.587900i
$408$		−	0.247417i		−	0.0122490i
$409$	−0.987309	−	0.570023i	−0.0488193	−	0.0281858i	0.475392	−	0.879774i	$-0.342306\pi$
$409$	−0.987309	−	0.570023i	−0.0488193	−	0.0281858i	−0.524211	+	0.851588i	$0.675640\pi$
$410$	20.3902	+	11.7723i	1.00700	+	0.581391i
$411$		−	12.7013i		−	0.626511i
$412$	−17.6543	+	30.5781i	−0.869763	+	1.50647i
$413$	2.43855	+	4.22370i	0.119993	+	0.207835i
$414$	7.06351	−	4.07812i	0.347152	−	0.200429i
$415$	−49.9210			−2.45053
$416$	26.9061	+	9.83979i	1.31918	+	0.482436i
$417$	−1.97930			−0.0969265
$418$	−18.2844	+	10.5565i	−0.894318	+	0.516335i
$419$	−15.2618	−	26.4342i	−0.745587	−	1.29139i	−0.949920	−	0.312493i	$-0.898836\pi$
$419$	−15.2618	−	26.4342i	−0.745587	−	1.29139i	0.204333	−	0.978901i	$-0.434497\pi$
$420$	2.78258	−	4.81957i	0.135776	−	0.235171i
$421$			15.4138i			0.751223i	0.926777	+	0.375611i	$0.122567\pi$
$421$			15.4138i			0.751223i	−0.926777	+	0.375611i	$0.877433\pi$
$422$	−3.43397	−	1.98260i	−0.167163	−	0.0965115i
$423$	−0.520860	−	0.300719i	−0.0253251	−	0.0146214i
$424$			0.138849i			0.00674308i
$425$	−3.96599	+	6.86930i	−0.192379	+	0.333210i
$426$	−12.2298	−	21.1827i	−0.592538	−	1.02631i
$427$	11.6472	−	6.72454i	0.563650	−	0.325423i
$428$	6.95763			0.336310
$429$	7.81095	+	2.85654i	0.377116	+	0.137915i
$430$	60.4592			2.91560
$431$	−11.7884	+	6.80604i	−0.567828	+	0.327835i	−0.756281	−	0.654247i	$-0.772986\pi$
$431$	−11.7884	+	6.80604i	−0.567828	+	0.327835i	0.188454	+	0.982082i	$0.439652\pi$
$432$	2.04804	+	3.54731i	0.0985365	+	0.170670i
$433$	−11.8187	+	20.4706i	−0.567969	+	0.983752i	0.428797	+	0.903401i	$0.358938\pi$
$433$	−11.8187	+	20.4706i	−0.567969	+	0.983752i	−0.996767	+	0.0803512i	$0.974396\pi$
$434$		−	1.82294i		−	0.0875039i
$435$	−6.62319	−	3.82390i	−0.317558	−	0.183342i
$436$	−19.4453	−	11.2267i	−0.931259	−	0.537663i
$437$		−	18.8960i		−	0.903920i
$438$	−10.8326	+	18.7625i	−0.517600	+	0.896509i
$439$	−15.8359	−	27.4286i	−0.755807	−	1.30910i	−0.944972	−	0.327151i	$-0.893912\pi$
$439$	−15.8359	−	27.4286i	−0.755807	−	1.30910i	0.189165	−	0.981945i	$-0.439422\pi$
$440$	−0.557950	+	0.322133i	−0.0265992	+	0.0153571i
$441$	−1.00000			−0.0476190
$442$	−3.11757	−	17.8407i	−0.148288	−	0.848595i
$443$	10.5318			0.500379			0.250190	−	0.968197i	$-0.419507\pi$
$443$	10.5318			0.500379			0.250190	+	0.968197i	$0.419507\pi$
$444$	−10.0302	+	5.79096i	−0.476014	+	0.274827i
$445$	15.4320	+	26.7289i	0.731545	+	1.26707i
$446$	28.5209	−	49.3996i	1.35050	−	2.33914i
$447$			23.5264i			1.11276i
$448$	−6.58285	−	3.80061i	−0.311010	−	0.179562i
$449$	−12.9526	−	7.47819i	−0.611271	−	0.352917i	0.162192	−	0.986759i	$-0.448144\pi$
$449$	−12.9526	−	7.47819i	−0.611271	−	0.352917i	−0.773463	+	0.633842i	$0.781477\pi$
$450$		−	6.23863i		−	0.294092i
$451$	4.78887	−	8.29457i	0.225499	−	0.390576i
$452$	−2.00146	−	3.46662i	−0.0941406	−	0.163056i
$453$	10.2042	−	5.89141i	0.479436	−	0.276803i
$454$	16.5426			0.776384
$455$	−3.53287	+	9.66033i	−0.165623	+	0.452883i
$456$	0.450836			0.0211123
$457$	11.4196	−	6.59314i	0.534189	−	0.308414i	−0.208532	−	0.978016i	$-0.566868\pi$
$457$	11.4196	−	6.59314i	0.534189	−	0.308414i	0.742720	+	0.669602i	$0.233535\pi$
$458$	−1.23799	−	2.14427i	−0.0578476	−	0.100195i
$459$	1.26358	−	2.18858i	0.0589787	−	0.102154i
$460$			22.8364i			1.06475i
$461$	−4.14734	−	2.39447i	−0.193161	−	0.111522i	0.400301	−	0.916384i	$-0.368906\pi$
$461$	−4.14734	−	2.39447i	−0.193161	−	0.111522i	−0.593462	+	0.804862i	$0.702239\pi$
$462$	−3.97063	−	2.29245i	−0.184731	−	0.106654i
$463$			19.4696i			0.904827i	0.891808	+	0.452414i	$0.149437\pi$
$463$			19.4696i			0.904827i	−0.891808	+	0.452414i	$0.850563\pi$
$464$	−5.49033	+	9.50953i	−0.254882	+	0.441469i
$465$	−1.30822	−	2.26590i	−0.0606672	−	0.105079i
$466$	−16.6562	+	9.61647i	−0.771584	+	0.445474i
$467$	−7.28924			−0.337306			−0.168653	−	0.985675i	$-0.553942\pi$
$467$	−7.28924			−0.337306			−0.168653	+	0.985675i	$0.553942\pi$
$468$	4.51278	+	5.39491i	0.208603	+	0.249380i
$469$	14.2925			0.659965
$470$	2.95351	−	1.70521i	0.136235	−	0.0786554i
$471$	1.13301	+	1.96243i	0.0522062	+	0.0904238i
$472$	0.238743	−	0.413515i	0.0109890	−	0.0190335i
$473$		−	24.5943i		−	1.13085i
$474$	−11.4883	−	6.63280i	−0.527677	−	0.304655i
$475$	−12.5170	−	7.22671i	−0.574320	−	0.331584i
$476$			4.92983i			0.225959i
$477$	−0.709110	+	1.22821i	−0.0324679	+	0.0562361i
$478$	7.40493	+	12.8257i	0.338694	+	0.586635i
$479$	−10.6770	+	6.16437i	−0.487844	+	0.281657i	−0.723680	−	0.690136i	$-0.757551\pi$
$479$	−10.6770	+	6.16437i	−0.487844	+	0.281657i	0.235835	+	0.971793i	$0.424217\pi$
$480$	−22.6680			−1.03465
$481$	16.4197	−	13.7349i	0.748673	−	0.626256i
$482$	−23.5326			−1.07188
$483$	3.55370	−	2.05173i	0.161699	−	0.0933570i
$484$	5.53931	+	9.59436i	0.251787	+	0.436107i
$485$	7.35083	−	12.7320i	0.333784	−	0.578131i
$486$			1.98765i			0.0901615i
$487$	12.2957	+	7.09893i	0.557172	+	0.321683i	0.752010	−	0.659152i	$-0.229085\pi$
$487$	12.2957	+	7.09893i	0.557172	+	0.321683i	−0.194838	+	0.980835i	$0.562418\pi$
$488$	−1.14031	−	0.658356i	−0.0516192	−	0.0298024i
$489$			17.3070i			0.782649i
$490$	2.83522	−	4.91075i	0.128082	−	0.221845i
$491$	0.285751	+	0.494935i	0.0128957	+	0.0223361i	0.872401	−	0.488790i	$-0.162562\pi$
$491$	0.285751	+	0.494935i	0.0128957	+	0.0223361i	−0.859506	+	0.511126i	$0.829228\pi$
$492$	7.01463	−	4.04990i	0.316244	−	0.182583i
$493$	6.77472			0.305118
$494$	32.5087	−	5.68074i	1.46264	−	0.255589i
$495$	−6.58062			−0.295777
$496$	−3.25336	+	1.87833i	−0.146080	+	0.0843395i
$497$	−6.15292	−	10.6572i	−0.275996	−	0.478040i
$498$	−17.3906	+	30.1215i	−0.779293	+	1.34977i
$499$		−	39.7298i		−	1.77855i	−0.457375	−	0.889274i	$-0.651210\pi$
$499$		−	39.7298i		−	1.77855i	0.457375	−	0.889274i	$-0.348790\pi$
$500$	−8.97067	−	5.17922i	−0.401180	−	0.231622i
$501$	12.8234	+	7.40357i	0.572906	+	0.330767i
$502$			53.5392i			2.38957i
$503$	16.4237	−	28.4468i	0.732299	−	1.26838i	−0.223600	−	0.974681i	$-0.571781\pi$
$503$	16.4237	−	28.4468i	0.732299	−	1.26838i	0.955899	−	0.293697i	$-0.0948857\pi$
$504$	0.0489517	+	0.0847868i	0.00218048	+	0.00377671i
$505$	−29.2173	+	16.8686i	−1.30015	+	0.750644i
$506$	18.8139			0.836381
$507$	−9.93288	−	8.38676i	−0.441135	−	0.372469i
$508$	35.4213			1.57157
$509$	−33.2726	+	19.2100i	−1.47478	+	0.851467i	−0.999596	−	0.0284178i	$-0.990953\pi$
$509$	−33.2726	+	19.2100i	−1.47478	+	0.851467i	−0.475188	+	0.879885i	$0.657620\pi$
$510$	7.16504	+	12.4102i	0.317273	+	0.549534i
$511$	−5.44994	+	9.43957i	−0.241091	+	0.417582i
$512$			31.7445i			1.40292i
$513$	3.98796	+	2.30245i	0.176073	+	0.101656i
$514$	38.2815	+	22.1018i	1.68852	+	0.974870i
$515$			51.6365i			2.27538i
$516$	10.3996	−	18.0126i	0.457816	−	0.792961i
$517$	−0.693666	−	1.20146i	−0.0305074	−	0.0528403i
$518$	−10.2200	+	5.90052i	−0.449041	+	0.259254i
$519$	−1.35021			−0.0592675
$520$	0.992008	−	0.173349i	0.0435024	−	0.00760184i
$521$	−9.38277			−0.411067			−0.205533	−	0.978650i	$-0.565893\pi$
$521$	−9.38277			−0.411067			−0.205533	+	0.978650i	$0.565893\pi$
$522$	−4.61455	+	2.66421i	−0.201973	+	0.116609i
$523$	1.15233	+	1.99589i	0.0503878	+	0.0872741i	0.890119	−	0.455728i	$-0.150621\pi$
$523$	1.15233	+	1.99589i	0.0503878	+	0.0872741i	−0.839731	+	0.543002i	$0.817288\pi$
$524$	1.91760	−	3.32138i	0.0837708	−	0.145095i
$525$		−	3.13870i		−	0.136984i
$526$	−8.43566	−	4.87033i	−0.367812	−	0.212356i
$527$	2.00722	+	1.15887i	0.0874359	+	0.0504812i
$528$			9.44841i			0.411189i
$529$	3.08080	−	5.33611i	0.133948	−	0.232005i
$530$	−4.02097	−	6.96452i	−0.174660	−	0.302520i
$531$	4.22370	−	2.43855i	0.183293	−	0.105824i
$532$	−8.98299			−0.389462
$533$	−11.4831	+	9.60544i	−0.497386	+	0.416058i
$534$	21.5037			0.930555
$535$	8.81190	−	5.08755i	0.380971	−	0.219954i
$536$	−0.699641	−	1.21181i	−0.0302199	−	0.0523424i
$537$	−2.41602	+	4.18467i	−0.104259	+	0.180582i
$538$			54.4807i			2.34883i
$539$	−1.99765	−	1.15335i	−0.0860450	−	0.0496781i
$540$	−4.81957	−	2.78258i	−0.207401	−	0.119743i
$541$			6.63606i			0.285307i	0.989773	+	0.142653i	$0.0455634\pi$
$541$			6.63606i			0.285307i	−0.989773	+	0.142653i	$0.954437\pi$
$542$	20.3125	−	35.1822i	0.872495	−	1.51121i
$543$	−8.90822	−	15.4295i	−0.382288	−	0.662143i
$544$	17.3900	−	10.0401i	0.745588	−	0.430466i
$545$	−32.8368			−1.40657
$546$	4.59815	+	5.49697i	0.196783	+	0.235249i
$547$	4.37197			0.186932			0.0934660	−	0.995622i	$-0.470205\pi$
$547$	4.37197			0.186932			0.0934660	+	0.995622i	$0.470205\pi$
$548$	21.4576	−	12.3885i	0.916622	−	0.529212i
$549$	−6.72454	−	11.6472i	−0.286996	−	0.497093i
$550$	7.19530	−	12.4626i	0.306809	−	0.531408i
$551$			12.3447i			0.525901i
$552$	−0.347919	−	0.200871i	−0.0148084	−	0.00854965i
$553$	−5.77987	−	3.33701i	−0.245785	−	0.141904i
$554$			6.54044i			0.277877i
$555$	−8.46892	+	14.6686i	−0.359486	+	0.622647i
$556$	−1.93055	−	3.34381i	−0.0818736	−	0.141809i
$557$	−22.4732	+	12.9749i	−0.952218	+	0.549763i	−0.893769	−	0.448527i	$-0.851949\pi$
$557$	−22.4732	+	12.9749i	−0.952218	+	0.549763i	−0.0584488	+	0.998290i	$0.518615\pi$
$558$	−1.82294			−0.0771712
$559$	−13.2037	+	36.1044i	−0.558457	+	1.52705i
$560$	−11.6855			−0.493802
$561$	5.04838	−	2.91468i	0.213143	−	0.123058i
$562$	−23.5558	−	40.7999i	−0.993642	−	1.72104i
$563$	−12.5063	+	21.6615i	−0.527078	+	0.912925i	0.472424	+	0.881371i	$0.343379\pi$
$563$	−12.5063	+	21.6615i	−0.527078	+	0.912925i	−0.999502	+	0.0315540i	$0.989954\pi$
$564$		−	1.17325i		−	0.0494028i
$565$	−5.06972	−	2.92700i	−0.213285	−	0.123140i
$566$	11.0015	+	6.35174i	0.462429	+	0.266984i
$567$			1.00000i			0.0419961i
$568$	−0.602392	+	1.04337i	−0.0252758	+	0.0437790i
$569$	8.74030	+	15.1386i	0.366413	+	0.634645i	0.989002	−	0.147904i	$-0.0472525\pi$
$569$	8.74030	+	15.1386i	0.366413	+	0.634645i	−0.622589	+	0.782549i	$0.713919\pi$
$570$	−22.6135	+	13.0559i	−0.947176	+	0.546852i
$571$	−36.0126			−1.50708			−0.753539	−	0.657403i	$-0.771655\pi$
$571$	−36.0126			−1.50708			−0.753539	+	0.657403i	$0.771655\pi$
$572$	2.79277	+	15.9820i	0.116772	+	0.668239i
$573$	0.232424			0.00970964
$574$	7.14733	−	4.12651i	0.298324	−	0.172237i
$575$	6.43977	+	11.1540i	0.268557	+	0.465154i
$576$	−3.80061	+	6.58285i	−0.158359	+	0.274285i
$577$		−	25.7297i		−	1.07114i	−0.844491	−	0.535571i	$-0.820097\pi$
$577$		−	25.7297i		−	1.07114i	0.844491	−	0.535571i	$-0.179903\pi$
$578$	18.2696	+	10.5479i	0.759914	+	0.438736i
$579$	−22.3393	−	12.8976i	−0.928392	−	0.536007i
$580$		−	14.9189i		−	0.619474i
$581$	−8.74935	+	15.1543i	−0.362984	+	0.628707i
$582$	−5.12152	−	8.87073i	−0.212294	−	0.367703i
$583$	−2.83311	+	1.63570i	−0.117336	+	0.0677437i
$584$	1.06714			0.0441584
$585$	9.66033	+	3.53287i	0.399405	+	0.146066i
$586$	43.7763			1.80838
$587$	7.40084	−	4.27288i	0.305465	−	0.176361i	−0.339430	−	0.940631i	$-0.610234\pi$
$587$	7.40084	−	4.27288i	0.305465	−	0.176361i	0.644896	+	0.764271i	$0.276901\pi$
$588$	−0.975372	−	1.68939i	−0.0402237	−	0.0696694i
$589$	−2.11166	+	3.65750i	−0.0870093	+	0.150704i
$590$			27.6554i			1.13855i
$591$	−10.9075	−	6.29745i	−0.448674	−	0.259042i
$592$	21.0611	+	12.1596i	0.865604	+	0.499757i
$593$		−	3.34043i		−	0.137175i	−0.997645	−	0.0685875i	$-0.978151\pi$
$593$		−	3.34043i		−	0.137175i	0.997645	−	0.0685875i	$-0.0218492\pi$
$594$	−2.29245	+	3.97063i	−0.0940602	+	0.162917i
$595$	3.60479	+	6.24367i	0.147782	+	0.255966i
$596$	−39.7453	+	22.9470i	−1.62803	+	0.939945i
$597$	1.21688			0.0498035
$598$	−27.6188	−	10.1004i	−1.12942	−	0.413037i
$599$	41.7075			1.70412			0.852062	−	0.523442i	$-0.175352\pi$
$599$	41.7075			1.70412			0.852062	+	0.523442i	$0.175352\pi$
$600$	−0.266120	+	0.153645i	−0.0108643	+	0.00627252i
$601$	0.301244	+	0.521769i	0.0122880	+	0.0212834i	0.872104	−	0.489321i	$-0.162755\pi$
$601$	0.301244	+	0.521769i	0.0122880	+	0.0212834i	−0.859816	+	0.510604i	$0.829422\pi$
$602$	10.5963	−	18.3534i	0.431874	−	0.748027i
$603$		−	14.2925i		−	0.582035i
$604$	19.9058	+	11.4926i	0.809956	+	0.467629i
$605$	14.0311	+	8.10089i	0.570447	+	0.329348i
$606$			23.5056i			0.954851i
$607$	8.28101	−	14.3431i	0.336116	−	0.582170i	−0.647583	−	0.761995i	$-0.724220\pi$
$607$	8.28101	−	14.3431i	0.336116	−	0.582170i	0.983699	+	0.179826i	$0.0575533\pi$
$608$	18.2948	+	31.6874i	0.741950	+	1.28510i
$609$	−2.32161	+	1.34038i	−0.0940765	+	0.0543151i
$610$	76.2623			3.08777
$611$	0.373281	+	2.13614i	0.0151013	+	0.0864192i
$612$	4.92983			0.199277
$613$	−1.64698	+	0.950882i	−0.0665207	+	0.0384058i	−0.532891	−	0.846184i	$-0.678895\pi$
$613$	−1.64698	+	0.950882i	−0.0665207	+	0.0384058i	0.466371	+	0.884589i	$0.345561\pi$
$614$	10.6533	+	18.4521i	0.429934	+	0.744667i
$615$	5.92272	−	10.2585i	0.238827	−	0.413661i
$616$			0.225833i			0.00909907i
$617$	15.7184	+	9.07500i	0.632797	+	0.365346i	0.781835	−	0.623486i	$-0.214284\pi$
$617$	15.7184	+	9.07500i	0.632797	+	0.365346i	−0.149037	+	0.988832i	$0.547617\pi$
$618$	31.1566	+	17.9882i	1.25330	+	0.723594i
$619$		−	10.0824i		−	0.405247i	−0.979257	−	0.202624i	$-0.935053\pi$
$619$		−	10.0824i		−	0.405247i	0.979257	−	0.202624i	$-0.0649468\pi$
$620$	2.55200	−	4.42019i	0.102491	−	0.177519i
$621$	−2.05173	−	3.55370i	−0.0823331	−	0.142605i
$622$	−14.0538	+	8.11396i	−0.563506	+	0.325340i
$623$	10.8187			0.433440
$624$	5.07247	−	13.8702i	0.203061	−	0.555253i
$625$	−30.8421			−1.23368
$626$	−21.8142	+	12.5945i	−0.871872	+	0.503375i
$627$	5.31105	+	9.19900i	0.212103	+	0.367373i
$628$	−2.21021	+	3.82819i	−0.0881969	+	0.152761i
$629$		−	15.0042i		−	0.598256i
$630$	−4.91075	−	2.83522i	−0.195649	−	0.112958i
$631$	−27.3443	−	15.7872i	−1.08856	−	0.628480i	−0.155366	−	0.987857i	$-0.549656\pi$
$631$	−27.3443	−	15.7872i	−1.08856	−	0.628480i	−0.933192	+	0.359377i	$0.882989\pi$
$632$			0.653409i			0.0259912i
$633$	−0.997461	+	1.72765i	−0.0396455	+	0.0686681i
$634$	1.57179	+	2.72242i	0.0624238	+	0.108121i
$635$	44.8613	−	25.9007i	1.78027	−	1.02784i
$636$	−2.76659			−0.109702
$637$	2.31336	+	2.76557i	0.0916588	+	0.109576i
$638$	−12.2910			−0.486607
$639$	−10.6572	+	6.15292i	−0.421591	+	0.243406i
$640$	1.11687	+	1.93448i	0.0441483	+	0.0764670i
$641$	−10.8705	+	18.8282i	−0.429358	+	0.743669i	−0.996816	−	0.0797326i	$-0.974593\pi$
$641$	−10.8705	+	18.8282i	−0.429358	+	0.743669i	0.567459	+	0.823402i	$0.307927\pi$
$642$		−	7.08926i		−	0.279791i
$643$	−29.7903	−	17.1995i	−1.17482	−	0.678280i	−0.220006	−	0.975498i	$-0.570608\pi$
$643$	−29.7903	−	17.1995i	−1.17482	−	0.678280i	−0.954810	+	0.297218i	$0.903941\pi$
$644$	6.93236	+	4.00240i	0.273173	+	0.157717i
$645$		−	30.4175i		−	1.19769i
$646$	11.5654	−	20.0319i	0.455036	−	0.788145i
$647$	9.89812	+	17.1441i	0.389135	+	0.674002i	0.992333	−	0.123589i	$-0.0394405\pi$
$647$	9.89812	+	17.1441i	0.389135	+	0.674002i	−0.603198	+	0.797591i	$0.706107\pi$
$648$	0.0847868	−	0.0489517i	0.00333074	−	0.00192300i
$649$	11.2500			0.441601
$650$	−17.2533	+	14.4322i	−0.676732	+	0.566078i
$651$	−0.917134			−0.0359453
$652$	−29.2383	+	16.8808i	−1.14506	+	0.661101i
$653$	1.83747	+	3.18260i	0.0719059	+	0.124545i	0.899737	−	0.436433i	$-0.143759\pi$
$653$	1.83747	+	3.18260i	0.0719059	+	0.124545i	−0.827831	+	0.560978i	$0.810425\pi$
$654$	−11.4391	+	19.8131i	−0.447305	+	0.774754i
$655$		−	5.60874i		−	0.219152i
$656$	−14.7290	−	8.50379i	−0.575071	−	0.332017i
$657$	9.43957	+	5.44994i	0.368273	+	0.212622i
$658$		−	1.19545i		−	0.0466033i
$659$	21.3407	−	36.9633i	0.831317	−	1.43988i	−0.0656764	−	0.997841i	$-0.520921\pi$
$659$	21.3407	−	36.9633i	0.831317	−	1.43988i	0.896994	−	0.442043i	$-0.145746\pi$
$660$	−6.41856	−	11.1173i	−0.249842	−	0.432739i
$661$	−0.714640	+	0.412597i	−0.0277963	+	0.0160482i	−0.513834	−	0.857890i	$-0.671775\pi$
$661$	−0.714640	+	0.412597i	−0.0277963	+	0.0160482i	0.486037	+	0.873938i	$0.338442\pi$
$662$	−48.5723			−1.88782
$663$	−8.97578	+	1.56847i	−0.348590	+	0.0609145i
$664$	1.71318			0.0664844
$665$	−11.3770	+	6.56853i	−0.441182	+	0.254717i
$666$	5.90052	+	10.2200i	0.228640	+	0.396017i
$667$	5.50021	−	9.52665i	0.212969	−	0.368873i
$668$			28.8849i			1.11759i
$669$	−24.8533	−	14.3491i	−0.960884	−	0.554767i
$670$	70.1867	+	40.5223i	2.71155	+	1.56551i
$671$		−	31.0229i		−	1.19763i
$672$	−3.97288	+	6.88124i	−0.153257	+	0.265450i
$673$	−13.0183	−	22.5484i	−0.501820	−	0.869177i	−0.999998	−	0.00210260i	$-0.999331\pi$
$673$	−13.0183	−	22.5484i	−0.501820	−	0.869177i	0.498178	−	0.867075i	$-0.334003\pi$
$674$	−25.5095	+	14.7279i	−0.982589	+	0.567298i
$675$	−3.13870			−0.120809
$676$	4.48029	−	24.9608i	0.172319	−	0.960030i
$677$	−50.7000			−1.94856			−0.974280	−	0.225342i	$-0.927650\pi$
$677$	−50.7000			−1.94856			−0.974280	+	0.225342i	$0.927650\pi$
$678$	−3.53220	+	2.03932i	−0.135654	+	0.0783196i
$679$	−2.57667	−	4.46293i	−0.0988836	−	0.171271i
$680$	0.352921	−	0.611277i	0.0135339	−	0.0234414i
$681$		−	8.32271i		−	0.318927i
$682$	−3.64160	−	2.10248i	−0.139444	−	0.0805081i
$683$	−9.14978	−	5.28263i	−0.350107	−	0.202134i	0.314626	−	0.949216i	$-0.398121\pi$
$683$	−9.14978	−	5.28263i	−0.350107	−	0.202134i	−0.664732	+	0.747082i	$0.731454\pi$
$684$			8.98299i			0.343473i
$685$	18.1175	−	31.3803i	0.692232	−	1.19898i
$686$	−0.993824	−	1.72135i	−0.0379444	−	0.0657216i
$687$	−1.07880	+	0.622843i	−0.0411587	+	0.0237630i
$688$	−43.6732			−1.66502
$689$	5.03714	−	0.880216i	0.191900	−	0.0335335i
$690$	23.2684			0.885815
$691$	44.7827	−	25.8553i	1.70361	−	0.983582i	0.761578	−	0.648074i	$-0.224425\pi$
$691$	44.7827	−	25.8553i	1.70361	−	0.983582i	0.942037	−	0.335509i	$-0.108908\pi$
$692$	−1.31695	−	2.28103i	−0.0500631	−	0.0867118i
$693$	−1.15335	+	1.99765i	−0.0438120	+	0.0758846i
$694$		−	36.5233i		−	1.38640i
$695$	−4.89011	−	2.82331i	−0.185493	−	0.107094i
$696$	0.227294	+	0.131228i	0.00861555	+	0.00497419i
$697$			10.4931i			0.397456i
$698$	11.1241	−	19.2675i	0.421053	−	0.729285i
$699$	4.83811	+	8.37986i	0.182994	+	0.316955i
$700$	5.30250	−	3.06140i	0.200416	−	0.115710i
$701$	47.4231			1.79115			0.895573	−	0.444915i	$-0.146766\pi$
$701$	47.4231			1.79115			0.895573	+	0.444915i	$0.146766\pi$
$702$	5.49697	−	4.59815i	0.207470	−	0.173546i
$703$	27.3402			1.03115
$704$	−15.1846	+	8.76684i	−0.572291	+	0.330413i
$705$	−0.857903	−	1.48593i	−0.0323105	−	0.0559634i
$706$	20.2117	−	35.0076i	0.760676	−	1.31753i
$707$			11.8259i			0.444757i
$708$	8.23936	+	4.75700i	0.309654	+	0.178779i
$709$	−16.7276	−	9.65771i	−0.628220	−	0.362703i	0.151843	−	0.988405i	$-0.451479\pi$
$709$	−16.7276	−	9.65771i	−0.628220	−	0.362703i	−0.780062	+	0.625702i	$0.784813\pi$
$710$		−	69.7796i		−	2.61878i
$711$	−3.33701	+	5.77987i	−0.125148	+	0.216762i
$712$	−0.529592	−	0.917280i	−0.0198473	−	0.0343765i
$713$	3.25922	−	1.88171i	0.122059	−	0.0704706i
$714$	5.02309			0.187985
$715$	15.2234	+	18.1992i	0.569322	+	0.680610i
$716$	−9.42607			−0.352269
$717$	6.45271	−	3.72547i	0.240981	−	0.139130i
$718$	−5.11785	−	8.86438i	−0.190997	−	0.330816i
$719$	−7.29982	+	12.6437i	−0.272237	+	0.471529i	−0.969434	−	0.245350i	$-0.921097\pi$
$719$	−7.29982	+	12.6437i	−0.272237	+	0.471529i	0.697197	+	0.716880i	$0.254430\pi$
$720$			11.6855i			0.435492i
$721$	15.6751	+	9.05002i	0.583771	+	0.337040i
$722$	3.79582	+	2.19152i	0.141266	+	0.0815598i
$723$			11.8394i			0.440312i
$724$	17.3777	−	30.0990i	0.645836	−	1.11862i
$725$	−4.20706	−	7.28685i	−0.156246	−	0.270627i
$726$	9.77586	−	5.64410i	0.362816	−	0.209472i
$727$	32.4357			1.20297			0.601487	−	0.798883i	$-0.294575\pi$
$727$	32.4357			1.20297			0.601487	+	0.798883i	$0.294575\pi$
$728$	0.121241	−	0.331522i	0.00449347	−	0.0122870i
$729$	1.00000			0.0370370
$730$	−53.5266	+	30.9036i	−1.98111	+	1.14379i
$731$	13.4725	+	23.3350i	0.498298	+	0.863077i
$732$	13.1179	−	22.7208i	0.484850	−	0.839785i
$733$			33.4061i			1.23388i	0.787009	+	0.616941i	$0.211628\pi$
$733$			33.4061i			1.23388i	−0.787009	+	0.616941i	$0.788372\pi$
$734$	−26.3205	−	15.1961i	−0.971507	−	0.560900i
$735$	−2.47063	−	1.42642i	−0.0911307	−	0.0526143i
$736$		−	32.6052i		−	1.20184i
$737$	16.4842	−	28.5514i	0.607202	−	1.05171i
$738$	−4.12651	−	7.14733i	−0.151899	−	0.263097i
$739$	36.0797	−	20.8306i	1.32721	−	0.766266i	0.342344	−	0.939575i	$-0.388779\pi$
$739$	36.0797	−	20.8306i	1.32721	−	0.766266i	0.984868	+	0.173308i	$0.0554457\pi$
$740$	−33.0414			−1.21463
$741$	−2.85802	−	16.3554i	−0.104992	−	0.600830i
$742$	−2.81892			−0.103486
$743$	2.27160	−	1.31151i	0.0833370	−	0.0481146i	−0.457752	−	0.889080i	$-0.651345\pi$
$743$	2.27160	−	1.31151i	0.0833370	−	0.0481146i	0.541089	+	0.840965i	$0.318012\pi$
$744$	0.0448953	+	0.0777609i	0.00164594	+	0.00285085i
$745$	−33.5585	+	58.1251i	−1.22949	+	2.12954i
$746$		−	33.9599i		−	1.24336i
$747$	15.1543	+	8.74935i	0.554468	+	0.320122i
$748$	9.84810	+	5.68580i	0.360082	+	0.207894i
$749$		−	3.56666i		−	0.130323i
$750$	−5.27720	+	9.14037i	−0.192696	+	0.333759i
$751$	11.5544	+	20.0128i	0.421625	+	0.730276i	0.996099	−	0.0882471i	$-0.0281265\pi$
$751$	11.5544	+	20.0128i	0.421625	+	0.730276i	−0.574474	+	0.818523i	$0.694793\pi$
$752$	−2.13349	+	1.23177i	−0.0778003	+	0.0449180i
$753$	26.9359			0.981600
$754$	18.0432	+	6.59855i	0.657094	+	0.240305i
$755$	33.6145			1.22336
$756$	−1.68939	+	0.975372i	−0.0614427	+	0.0354739i
$757$	2.42554	+	4.20116i	0.0881578	+	0.152694i	0.906732	−	0.421706i	$-0.138569\pi$
$757$	2.42554	+	4.20116i	0.0881578	+	0.152694i	−0.818575	+	0.574400i	$0.805235\pi$
$758$	−4.39569	+	7.61355i	−0.159659	+	0.276537i
$759$		−	9.46542i		−	0.343573i
$760$	1.11385	+	0.643081i	0.0404036	+	0.0233270i
$761$	−27.2947	−	15.7586i	−0.989431	−	0.571248i	−0.0843267	−	0.996438i	$-0.526874\pi$
$761$	−27.2947	−	15.7586i	−0.989431	−	0.571248i	−0.905104	+	0.425190i	$0.860207\pi$
$762$		−	36.0914i		−	1.30745i
$763$	−5.75510	+	9.96812i	−0.208349	+	0.360870i
$764$	0.226700	+	0.392655i	0.00820170	+	0.0142058i
$765$	6.24367	−	3.60479i	0.225740	−	0.130331i
$766$	8.24328			0.297842
$767$	−16.5149	−	6.03966i	−0.596320	−	0.218079i
$768$	16.7587			0.604729
$769$	−14.6361	+	8.45018i	−0.527793	+	0.304721i	−0.740117	−	0.672478i	$-0.765230\pi$
$769$	−14.6361	+	8.45018i	−0.527793	+	0.304721i	0.212324	+	0.977199i	$0.431897\pi$
$770$	−6.53998	−	11.3276i	−0.235685	−	0.408218i
$771$	11.1196	−	19.2597i	0.400462	−	0.693621i
$772$		−	50.3199i		−	1.81105i
$773$	23.0049	+	13.2819i	0.827429	+	0.477717i	0.852972	−	0.521957i	$-0.174798\pi$
$773$	23.0049	+	13.2819i	0.827429	+	0.477717i	−0.0255424	+	0.999674i	$0.508131\pi$
$774$	−18.3534	−	10.5963i	−0.659698	−	0.380877i
$775$		−	2.87861i		−	0.103403i
$776$	−0.252265	+	0.436936i	−0.00905578	+	0.0156851i
$777$	2.96859	+	5.14175i	0.106498	+	0.184459i
$778$	−59.8165	+	34.5351i	−2.14453	+	1.23814i
$779$	−19.1203			−0.685055
$780$	3.45401	+	19.7660i	0.123673	+	0.707735i
$781$	−28.3858			−1.01572
$782$	−17.8506	+	10.3060i	−0.638335	+	0.368543i
$783$	1.34038	+	2.32161i	0.0479014	+	0.0829677i
$784$	−2.04804	+	3.54731i	−0.0731444	+	0.126690i
$785$			6.46458i			0.230731i
$786$	−3.38422	−	1.95388i	−0.120711	−	0.0696925i
$787$	−17.7808	−	10.2657i	−0.633816	−	0.365934i	0.148412	−	0.988926i	$-0.452584\pi$
$787$	−17.7808	−	10.2657i	−0.633816	−	0.365934i	−0.782228	+	0.622992i	$0.785917\pi$
$788$		−	24.5694i		−	0.875249i
$789$	−2.45030	+	4.24404i	−0.0872329	+	0.151092i
$790$	−18.9223	−	32.7744i	−0.673226	−	1.16606i
$791$	−1.77708	+	1.02600i	−0.0631856	+	0.0364802i
$792$	0.225833			0.00802463
$793$	−16.6549	+	45.5415i	−0.591434	+	1.61723i
$794$	16.5064			0.585790
$795$	−3.50390	+	2.02298i	−0.124271	+	0.0717477i
$796$	1.18691	+	2.05579i	0.0420688	+	0.0728654i
$797$	−23.4311	+	40.5838i	−0.829971	+	1.43755i	0.0680885	+	0.997679i	$0.478310\pi$
$797$	−23.4311	+	40.5838i	−0.829971	+	1.43755i	−0.898060	+	0.439873i	$0.855023\pi$
$798$			9.15293i			0.324010i
$799$	1.31629	+	0.759963i	0.0465672	+	0.0268856i
$800$	−21.5981	−	12.4697i	−0.763610	−	0.440870i
$801$		−	10.8187i		−	0.382258i
$802$	35.3020	−	61.1449i	1.24656	−	2.15910i
$803$	12.5713	+	21.7742i	0.443633	+	0.768394i
$804$	24.1456	−	13.9405i	0.851550	−	0.491643i
$805$	11.7065			0.412601
$806$	4.21712	+	5.04146i	0.148542	+	0.177578i
$807$	27.4096			0.964864
$808$	1.00268	−	0.578895i	0.0352740	−	0.0203655i
$809$	20.2776	+	35.1218i	0.712922	+	1.23482i	0.963756	+	0.266787i	$0.0859620\pi$
$809$	20.2776	+	35.1218i	0.712922	+	1.23482i	−0.250833	+	0.968030i	$0.580705\pi$
$810$	−2.83522	+	4.91075i	−0.0996195	+	0.172546i
$811$		−	15.8829i		−	0.557724i	−0.960331	−	0.278862i	$-0.910043\pi$
$811$		−	15.8829i		−	0.557724i	0.960331	−	0.278862i	$-0.0899573\pi$
$812$	−4.52887	−	2.61475i	−0.158932	−	0.0917596i
$813$	−17.7004	−	10.2193i	−0.620781	−	0.358408i
$814$			27.2213i			0.954108i
$815$	−24.6870	+	42.7592i	−0.864749	+	1.49779i
$816$	−5.17572	−	8.96461i	−0.181187	−	0.313824i
$817$	−42.5204	+	24.5491i	−1.48760	+	0.858866i
$818$	−2.26601			−0.0792292
$819$	2.76557	−	2.31336i	0.0966367	−	0.0808354i
$820$	23.1074			0.806946
$821$	−38.5951	+	22.2829i	−1.34698	+	0.777678i	−0.987820	−	0.155599i	$-0.950269\pi$
$821$	−38.5951	+	22.2829i	−1.34698	+	0.777678i	−0.359157	+	0.933277i	$0.616936\pi$
$822$	−12.6229	−	21.8635i	−0.440274	−	0.762577i
$823$	−14.0512	+	24.3374i	−0.489795	+	0.848350i	−0.999931	−	0.0117441i	$-0.996262\pi$
$823$	−14.0512	+	24.3374i	−0.489795	+	0.848350i	0.510136	+	0.860094i	$0.329595\pi$
$824$		−	1.77205i		−	0.0617325i
$825$	−6.27004	−	3.62001i	−0.218295	−	0.126032i
$826$	8.39523	+	4.84699i	0.292107	+	0.168648i
$827$		−	41.0346i		−	1.42691i	−0.700699	−	0.713457i	$-0.747128\pi$
$827$		−	41.0346i		−	1.42691i	0.700699	−	0.713457i	$-0.252872\pi$
$828$	4.00240	−	6.93236i	0.139093	−	0.240916i
$829$	5.11381	+	8.85738i	0.177610	+	0.307629i	0.941061	−	0.338236i	$-0.109830\pi$
$829$	5.11381	+	8.85738i	0.177610	+	0.307629i	−0.763451	+	0.645865i	$0.776497\pi$
$830$	−85.9317	+	49.6127i	−2.98273	+	1.72208i
$831$	3.29054			0.114148
$832$	26.9975	−	4.71768i	0.935970	−	0.163556i
$833$	2.52716			0.0875607
$834$	−3.40707	+	1.96707i	−0.117977	+	0.0681141i
$835$	21.1212	+	36.5830i	0.730930	+	1.26601i
$836$	−10.3605	+	17.9449i	−0.358325	+	0.620637i
$837$			0.917134i			0.0317008i
$838$	−52.5419	−	30.3351i	−1.81503	−	1.04791i
$839$	29.8124	+	17.2122i	1.02924	+	0.594230i	0.916766	−	0.399425i	$-0.130790\pi$
$839$	29.8124	+	17.2122i	1.02924	+	0.594230i	0.112471	+	0.993655i	$0.464123\pi$
$840$			0.279303i			0.00963686i
$841$	10.9067	−	18.8910i	0.376095	−	0.651415i
$842$	15.3186	+	26.5326i	0.527914	+	0.914374i
$843$	−20.5267	+	11.8511i	−0.706977	+	0.408173i
$844$	−3.89158			−0.133954
$845$	−12.5775	−	34.8891i	−0.432678	−	1.20022i
$846$	−1.19545			−0.0411003
$847$	4.91831	−	2.83959i	0.168995	−	0.0975693i
$848$	2.90458	+	5.03087i	0.0997436	+	0.172761i
$849$	3.19561	−	5.53496i	0.109673	−	0.189959i
$850$			15.7660i			0.540769i
$851$	−21.0990	−	12.1815i	−0.723264	−	0.417577i
$852$	−20.7894	−	12.0028i	−0.712234	−	0.411208i
$853$		−	19.9376i		−	0.682650i	−0.939945	−	0.341325i	$-0.889124\pi$
$853$		−	19.9376i		−	0.682650i	0.939945	−	0.341325i	$-0.110876\pi$
$854$	13.3660	−	23.1506i	0.457376	−	0.792198i
$855$	6.56853	+	11.3770i	0.224639	+	0.389086i
$856$	−0.302405	+	0.174594i	−0.0103360	+	0.00596749i
$857$	−5.68966			−0.194355			−0.0971776	−	0.995267i	$-0.530981\pi$
$857$	−5.68966			−0.194355			−0.0971776	+	0.995267i	$0.530981\pi$
$858$	16.2843	−	2.84560i	0.555937	−	0.0971473i
$859$	−17.3268			−0.591182			−0.295591	−	0.955315i	$-0.595517\pi$
$859$	−17.3268			−0.591182			−0.295591	+	0.955315i	$0.595517\pi$
$860$	51.3871	−	29.6684i	1.75229	−	1.01168i
$861$	−2.07608	−	3.59587i	−0.0707525	−	0.122547i
$862$	−13.5280	+	23.4312i	−0.460766	+	0.798070i
$863$			53.7906i			1.83105i	0.402257	+	0.915527i	$0.368226\pi$
$863$			53.7906i			1.83105i	−0.402257	+	0.915527i	$0.631774\pi$
$864$	6.88124	+	3.97288i	0.234104	+	0.135160i
$865$	−3.33587	−	1.92596i	−0.113423	−	0.0654847i
$866$			46.9827i			1.59654i
$867$	5.30674	−	9.19155i	0.180226	−	0.312161i
$868$	−0.894547	−	1.54940i	−0.0303629	−	0.0525901i
$869$	−13.3324	+	7.69745i	−0.452270	+	0.261118i
$870$	−15.2011			−0.515367
$871$	−39.5268	+	33.0637i	−1.33931	+	1.12032i
$872$	1.12689			0.0381612
$873$	−4.46293	+	2.57667i	−0.151047	+	0.0872071i
$874$	−18.7793	−	32.5268i	−0.635221	−	1.10023i
$875$	−2.65500	+	4.59859i	−0.0897552	+	0.155461i
$876$			21.2629i			0.718406i
$877$	41.4687	+	23.9420i	1.40030	+	0.808462i	0.994423	−	0.105466i	$-0.0336334\pi$
$877$	41.4687	+	23.9420i	1.40030	+	0.808462i	0.405875	+	0.913929i	$0.366967\pi$
$878$	−54.5184	−	31.4762i	−1.83991	−	1.06227i
$879$		−	22.0242i		−	0.742857i
$880$	−13.4774	+	23.3435i	−0.454323	+	0.786911i
$881$	−6.64002	−	11.5009i	−0.223708	−	0.387474i	0.732223	−	0.681065i	$-0.238483\pi$
$881$	−6.64002	−	11.5009i	−0.223708	−	0.387474i	−0.955931	+	0.293591i	$0.905150\pi$
$882$	−1.72135	+	0.993824i	−0.0579610	+	0.0334638i
$883$	15.0727			0.507236			0.253618	−	0.967304i	$-0.418379\pi$
$883$	15.0727			0.507236			0.253618	+	0.967304i	$0.418379\pi$
$884$	−11.4045	−	13.6338i	−0.383575	−	0.458554i
$885$	13.9136			0.467701
$886$	18.1289	−	10.4667i	0.609052	−	0.351636i
$887$	−0.413898	−	0.716892i	−0.0138973	−	0.0240709i	0.858993	−	0.511987i	$-0.171090\pi$
$887$	−0.413898	−	0.716892i	−0.0138973	−	0.0240709i	−0.872890	+	0.487916i	$0.837757\pi$
$888$	0.290635	−	0.503395i	0.00975308	−	0.0168928i
$889$		−	18.1578i		−	0.608994i
$890$	53.1277	+	30.6733i	1.78084	+	1.02817i
$891$	1.99765	+	1.15335i	0.0669239	+	0.0386385i
$892$		−	55.9827i		−	1.87444i
$893$	−1.38478	+	2.39851i	−0.0463399	+	0.0802631i
$894$	23.3811	+	40.4972i	0.781981	+	1.35443i
$895$	−11.9382	+	6.89252i	−0.399050	+	0.230391i
$896$	0.782990			0.0261578
$897$	−5.08160	+	13.8952i	−0.169670	+	0.463947i
$898$	−29.7280			−0.992036
$899$	−2.12923	+	1.22931i	−0.0710138	+	0.0409998i
$900$	−3.06140	−	5.30250i	−0.102047	−	0.176750i
$901$	1.79203	−	3.10389i	0.0597012	−	0.103406i
$902$		−	19.0372i		−	0.633869i
$903$	−9.23371	−	5.33109i	−0.307279	−	0.177407i
$904$	0.173982	+	0.100449i	0.00578655	+	0.00334087i
$905$		−	50.8275i		−	1.68956i
$906$	11.7100	−	20.2824i	0.389040	−	0.673838i
$907$	−4.43003	−	7.67304i	−0.147097	−	0.254779i	0.783057	−	0.621951i	$-0.213660\pi$
$907$	−4.43003	−	7.67304i	−0.147097	−	0.254779i	−0.930153	+	0.367172i	$0.880326\pi$
$908$	14.0603	−	8.11774i	0.466609	−	0.269397i
$909$	11.8259			0.392239
$910$	3.51935	+	20.1399i	0.116665	+	0.667631i
$911$	56.3640			1.86742			0.933711	−	0.358027i	$-0.116550\pi$
$911$	56.3640			1.86742			0.933711	+	0.358027i	$0.116550\pi$
$912$	16.3350	−	9.43104i	0.540907	−	0.312293i
$913$	20.1821	+	34.9564i	0.667929	+	1.15689i
$914$	13.1048	−	22.6982i	0.433469	−	0.750791i
$915$		−	38.3681i		−	1.26841i
$916$	−2.10446	−	1.21501i	−0.0695332	−	0.0401450i
$917$	−1.70262	−	0.983010i	−0.0562256	−	0.0324619i
$918$		−	5.02309i		−	0.165787i
$919$	7.72345	−	13.3774i	0.254773	−	0.441280i	−0.710061	−	0.704140i	$-0.751333\pi$
$919$	7.72345	−	13.3774i	0.254773	−	0.441280i	0.964834	+	0.262861i	$0.0846659\pi$
$920$	−0.573054	−	0.992559i	−0.0188930	−	0.0327237i
$921$	9.28340	−	5.35977i	0.305898	−	0.176610i
$922$	−9.51872			−0.313482
$923$	41.6702	+	15.2392i	1.37159	+	0.501604i
$924$	−4.49977			−0.148031
$925$	−16.1384	+	9.31752i	−0.530628	+	0.306358i
$926$	19.3493	+	33.5140i	0.635858	+	1.10134i
$927$	9.05002	−	15.6751i	0.297242	−	0.514838i
$928$			21.3008i			0.699232i
$929$	−6.27538	−	3.62310i	−0.205889	−	0.118870i	0.393511	−	0.919320i	$-0.371260\pi$
$929$	−6.27538	−	3.62310i	−0.205889	−	0.118870i	−0.599399	+	0.800450i	$0.704594\pi$
$930$	−4.50381	−	2.60028i	−0.147686	−	0.0852664i
$931$			4.60490i			0.150920i
$932$	−9.43792	+	16.3470i	−0.309149	+	0.535463i
$933$	4.08219	+	7.07056i	0.133645	+	0.231480i
$934$	−12.5474	+	7.24423i	−0.410562	+	0.237038i
$935$	16.6303			0.543868
$936$	−0.331522	−	0.121241i	−0.0108361	−	0.00396287i
$937$	10.6692			0.348548			0.174274	−	0.984697i	$-0.444242\pi$
$937$	10.6692			0.348548			0.174274	+	0.984697i	$0.444242\pi$
$938$	24.6024	−	14.2042i	0.803297	−	0.463784i
$939$	6.33636	+	10.9749i	0.206779	+	0.358152i
$940$	1.67355	−	2.89867i	0.0545851	−	0.0945443i
$941$			34.4575i			1.12328i	0.827381	+	0.561642i	$0.189830\pi$
$941$			34.4575i			1.12328i	−0.827381	+	0.561642i	$0.810170\pi$
$942$	3.90061	+	2.25202i	0.127089	+	0.0733748i
$943$	14.7555	+	8.51911i	0.480506	+	0.277420i
$944$		−	19.9771i		−	0.650198i
$945$	−1.42642	+	2.47063i	−0.0464015	+	0.0803697i
$946$	−24.4425	−	42.3356i	−0.794693	−	1.37645i
$947$	7.25075	−	4.18622i	0.235618	−	0.136034i	−0.377543	−	0.925992i	$-0.623231\pi$
$947$	7.25075	−	4.18622i	0.235618	−	0.136034i	0.613161	+	0.789958i	$0.289898\pi$
$948$	−13.0193			−0.422847
$949$	−6.76499	−	38.7134i	−0.219601	−	1.25669i
$950$	−28.7283			−0.932069
$951$	1.36967	−	0.790779i	0.0444146	−	0.0256428i
$952$	−0.123709	−	0.214269i	−0.00400942	−	0.00694451i
$953$	−9.20790	+	15.9486i	−0.298273	+	0.516624i	−0.975741	−	0.218928i	$-0.929744\pi$
$953$	−9.20790	+	15.9486i	−0.298273	+	0.516624i	0.677468	+	0.735552i	$0.263077\pi$
$954$			2.81892i			0.0912660i
$955$	0.574233	+	0.331534i	0.0185818	+	0.0107282i
$956$	12.5876	+	7.26745i	0.407112	+	0.235046i
$957$			6.18371i			0.199891i
$958$	−12.2526	+	21.2221i	−0.395863	+	0.685655i
$959$	−6.35067	−	10.9997i	−0.205074	−	0.355198i
$960$	−18.7798	+	10.8425i	−0.606116	+	0.349941i
$961$	30.1589			0.972867
$962$	14.6140	−	39.9608i	0.471175	−	1.28839i
$963$	−3.56666			−0.114934
$964$	−20.0014	+	11.5478i	−0.644202	+	0.371930i
$965$	−36.7949	−	63.7306i	−1.18447	−	2.05156i
$966$	4.07812	−	7.06351i	0.131211	−	0.227265i
$967$			24.6033i			0.791189i	0.918425	+	0.395595i	$0.129461\pi$
$967$			24.6033i			0.791189i	−0.918425	+	0.395595i	$0.870539\pi$
$968$	−0.481519	−	0.278005i	−0.0154766	−	0.00893542i
$969$	−10.0782	−	5.81865i	−0.323758	−	0.186922i
$970$		−	29.2217i		−	0.938254i
$971$	18.3663	−	31.8114i	0.589403	−	1.02088i	−0.404908	−	0.914358i	$-0.632696\pi$
$971$	18.3663	−	31.8114i	0.589403	−	1.02088i	0.994311	−	0.106518i	$-0.0339703\pi$
$972$	0.975372	+	1.68939i	0.0312851	+	0.0541873i
$973$	−1.71412	+	0.989648i	−0.0549522	+	0.0317267i
$974$	28.2204			0.904238
$975$	7.26095	+	8.68028i	0.232537	+	0.277991i
$976$	−55.0886			−1.76334
$977$	34.6185	−	19.9870i	1.10755	−	0.639442i	0.169353	−	0.985556i	$-0.445832\pi$
$977$	34.6185	−	19.9870i	1.10755	−	0.639442i	0.938192	+	0.346114i	$0.112499\pi$
$978$	17.2001	+	29.7914i	0.549999	+	0.952626i
$979$	12.4777	−	21.6119i	0.398788	−	0.690720i
$980$		−	5.56516i		−	0.177773i
$981$	9.96812	+	5.75510i	0.318258	+	0.183746i
$982$	0.983756	+	0.567972i	0.0313929	+	0.0181247i
$983$		−	16.6132i		−	0.529878i	−0.964265	−	0.264939i	$-0.914648\pi$
$983$		−	16.6132i		−	0.529878i	0.964265	−	0.264939i	$-0.0853518\pi$
$984$	−0.203255	+	0.352048i	−0.00647953	+	0.0112229i
$985$	−17.9656	−	31.1173i	−0.572432	−	0.991481i
$986$	11.6617	−	6.73287i	0.371384	−	0.214418i
$987$	−0.601438			−0.0191440
$988$	24.8430	−	20.7809i	0.790363	−	0.661129i
$989$	43.7518			1.39123
$990$	−11.3276	+	6.53998i	−0.360014	+	0.207854i
$991$	13.1679	+	22.8075i	0.418292	+	0.724503i	0.995768	−	0.0919047i	$-0.0292955\pi$
$991$	13.1679	+	22.8075i	0.418292	+	0.724503i	−0.577476	+	0.816408i	$0.695962\pi$
$992$	−3.64367	+	6.31102i	−0.115687	+	0.200375i
$993$			24.4371i			0.775487i
$994$	−21.1827	−	12.2298i	−0.671875	−	0.387907i
$995$	3.00646	+	1.73578i	0.0953111	+	0.0550279i
$996$			34.1355i			1.08162i
$997$	12.8068	−	22.1820i	0.405595	−	0.702510i	−0.588796	−	0.808282i	$-0.700398\pi$
$997$	12.8068	−	22.1820i	0.405595	−	0.702510i	0.994390	+	0.105771i	$0.0337312\pi$
$998$	−39.4844	−	68.3890i	−1.24986	−	2.16481i
$999$	5.14175	−	2.96859i	0.162678	−	0.0939221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.a.127.7	yes	16
3.2	odd	2		819.2.ct.b.127.2		16
13.2	odd	12		3549.2.a.bb.1.8		8
13.4	even	6	inner	273.2.bd.a.43.7	✓	16
13.11	odd	12		3549.2.a.bd.1.1		8
39.17	odd	6		819.2.ct.b.316.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.7	✓	16	13.4	even	6	inner
273.2.bd.a.127.7	yes	16	1.1	even	1	trivial
819.2.ct.b.127.2		16	3.2	odd	2
819.2.ct.b.316.2		16	39.17	odd	6
3549.2.a.bb.1.8		8	13.2	odd	12
3549.2.a.bd.1.1		8	13.11	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72135 - 0.993824i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.975372 - 1.68939i) q^{4} -2.85284i q^{5} +(-1.72135 - 0.993824i) q^{6} +(-0.866025 - 0.500000i) q^{7} +0.0979034i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.83522 - 4.91075i) q^{10} +(-1.99765 + 1.15335i) q^{11} -1.95074 q^{12} +(3.55173 - 0.620648i) q^{13} -1.98765 q^{14} +(-2.47063 + 1.42642i) q^{15} +(2.04804 + 3.54731i) q^{16} +(1.26358 - 2.18858i) q^{17} +1.98765i q^{18} +(3.98796 + 2.30245i) q^{19} +(-4.81957 - 2.78258i) q^{20} +1.00000i q^{21} +(-2.29245 + 3.97063i) q^{22} +(-2.05173 - 3.55370i) q^{23} +(0.0847868 - 0.0489517i) q^{24} -3.13870 q^{25} +(5.49697 - 4.59815i) q^{26} +1.00000 q^{27} +(-1.68939 + 0.975372i) q^{28} +(1.34038 + 2.32161i) q^{29} +(-2.83522 + 4.91075i) q^{30} +0.917134i q^{31} +(6.88124 + 3.97288i) q^{32} +(1.99765 + 1.15335i) q^{33} -5.02309i q^{34} +(-1.42642 + 2.47063i) q^{35} +(0.975372 + 1.68939i) q^{36} +(5.14175 - 2.96859i) q^{37} +9.15293 q^{38} +(-2.31336 - 2.76557i) q^{39} +0.279303 q^{40} +(-3.59587 + 2.07608i) q^{41} +(0.993824 + 1.72135i) q^{42} +(-5.33109 + 9.23371i) q^{43} +4.49977i q^{44} +(2.47063 + 1.42642i) q^{45} +(-7.06351 - 4.07812i) q^{46} +0.601438i q^{47} +(2.04804 - 3.54731i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-5.40281 + 3.11932i) q^{50} -2.52716 q^{51} +(2.41574 - 6.60564i) q^{52} +1.41822 q^{53} +(1.72135 - 0.993824i) q^{54} +(3.29031 + 5.69899i) q^{55} +(0.0489517 - 0.0847868i) q^{56} -4.60490i q^{57} +(4.61455 + 2.66421i) q^{58} +(-4.22370 - 2.43855i) q^{59} +5.56516i q^{60} +(-6.72454 + 11.6472i) q^{61} +(0.911469 + 1.57871i) q^{62} +(0.866025 - 0.500000i) q^{63} +7.60122 q^{64} +(-1.77061 - 10.1325i) q^{65} +4.58489 q^{66} +(-12.3776 + 7.14624i) q^{67} +(-2.46492 - 4.26936i) q^{68} +(-2.05173 + 3.55370i) q^{69} +5.67044i q^{70} +(10.6572 + 6.15292i) q^{71} +(-0.0847868 - 0.0489517i) q^{72} -10.8999i q^{73} +(5.90052 - 10.2200i) q^{74} +(1.56935 + 2.71819i) q^{75} +(7.77950 - 4.49149i) q^{76} +2.30669 q^{77} +(-6.73060 - 2.46144i) q^{78} +6.67402 q^{79} +(10.1199 - 5.84274i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.12651 + 7.14733i) q^{82} -17.4987i q^{83} +(1.68939 + 0.975372i) q^{84} +(-6.24367 - 3.60479i) q^{85} +21.1926i q^{86} +(1.34038 - 2.32161i) q^{87} +(-0.112916 - 0.195577i) q^{88} +(-9.36923 + 5.40933i) q^{89} +5.67044 q^{90} +(-3.38621 - 1.23837i) q^{91} -8.00480 q^{92} +(0.794261 - 0.458567i) q^{93} +(0.597723 + 1.03529i) q^{94} +(6.56853 - 11.3770i) q^{95} -7.94577i q^{96} +(4.46293 + 2.57667i) q^{97} +(1.72135 + 0.993824i) q^{98} -2.30669i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30}+ \cdots - 54 q^{97}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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