LMFDB - Embedded newform 273.2.p.f.265.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(34,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("273.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 60x^{8} - 8x^{7} + 80x^{5} + 320x^{4} + 160x^{3} + 32x^{2} - 32x + 16 $ x^12 + 60x^8 - 8x^7 + 80x^5 + 320x^4 + 160x^3 + 32x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			265.1
Root			$-0.863233 - 0.863233i$ of defining polynomial
Character	$\chi$	$=$	273.265
Dual form			273.2.p.f.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94644 + 1.94644i) q^{2} -1.00000i q^{3} -5.57728i q^{4} +(0.136767 + 0.136767i) q^{5} +(1.94644 + 1.94644i) q^{6} +(-2.24723 + 1.39641i) q^{7} +(6.96297 + 6.96297i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.94644 + 1.94644i) q^{2} -1.00000i q^{3} -5.57728i q^{4} +(0.136767 + 0.136767i) q^{5} +(1.94644 + 1.94644i) q^{6} +(-2.24723 + 1.39641i) q^{7} +(6.96297 + 6.96297i) q^{8} -1.00000 q^{9} -0.532416 q^{10} +(0.555612 + 0.555612i) q^{11} -5.57728 q^{12} +(-1.81044 - 3.11806i) q^{13} +(1.65606 - 7.09214i) q^{14} +(0.136767 - 0.136767i) q^{15} -15.9515 q^{16} -4.49445 q^{17} +(1.94644 - 1.94644i) q^{18} +(-4.15330 - 4.15330i) q^{19} +(0.762785 - 0.762785i) q^{20} +(1.39641 + 2.24723i) q^{21} -2.16293 q^{22} +0.423984i q^{23} +(6.96297 - 6.96297i) q^{24} -4.96259i q^{25} +(9.59305 + 2.54521i) q^{26} +1.00000i q^{27} +(7.78819 + 12.5334i) q^{28} -7.01375 q^{29} +0.532416i q^{30} +(0.273533 + 0.273533i) q^{31} +(17.1227 - 17.1227i) q^{32} +(0.555612 - 0.555612i) q^{33} +(8.74820 - 8.74820i) q^{34} +(-0.498328 - 0.116363i) q^{35} +5.57728i q^{36} +(5.75334 + 5.75334i) q^{37} +16.1683 q^{38} +(-3.11806 + 1.81044i) q^{39} +1.90460i q^{40} +(-7.29133 - 7.29133i) q^{41} +(-7.09214 - 1.65606i) q^{42} +1.86728i q^{43} +(3.09880 - 3.09880i) q^{44} +(-0.136767 - 0.136767i) q^{45} +(-0.825261 - 0.825261i) q^{46} +(-4.75098 + 4.75098i) q^{47} +15.9515i q^{48} +(3.10006 - 6.27612i) q^{49} +(9.65940 + 9.65940i) q^{50} +4.49445i q^{51} +(-17.3903 + 10.0973i) q^{52} -4.31687 q^{53} +(-1.94644 - 1.94644i) q^{54} +0.151978i q^{55} +(-25.3706 - 5.92419i) q^{56} +(-4.15330 + 4.15330i) q^{57} +(13.6519 - 13.6519i) q^{58} +(-0.691676 + 0.691676i) q^{59} +(-0.762785 - 0.762785i) q^{60} -8.11937i q^{61} -1.06483 q^{62} +(2.24723 - 1.39641i) q^{63} +34.7539i q^{64} +(0.178839 - 0.674054i) q^{65} +2.16293i q^{66} +(0.837691 - 0.837691i) q^{67} +25.0668i q^{68} +0.423984 q^{69} +(1.19646 - 0.743473i) q^{70} +(1.00520 - 1.00520i) q^{71} +(-6.96297 - 6.96297i) q^{72} +(-6.81854 + 6.81854i) q^{73} -22.3971 q^{74} -4.96259 q^{75} +(-23.1641 + 23.1641i) q^{76} +(-2.02445 - 0.472722i) q^{77} +(2.54521 - 9.59305i) q^{78} +10.9777 q^{79} +(-2.18163 - 2.18163i) q^{80} +1.00000 q^{81} +28.3843 q^{82} +(6.91260 + 6.91260i) q^{83} +(12.5334 - 7.78819i) q^{84} +(-0.614691 - 0.614691i) q^{85} +(-3.63455 - 3.63455i) q^{86} +7.01375i q^{87} +7.73742i q^{88} +(6.46820 - 6.46820i) q^{89} +0.532416 q^{90} +(8.42257 + 4.47887i) q^{91} +2.36468 q^{92} +(0.273533 - 0.273533i) q^{93} -18.4950i q^{94} -1.13606i q^{95} +(-17.1227 - 17.1227i) q^{96} +(3.19087 + 3.19087i) q^{97} +(6.18201 + 18.2502i) q^{98} +(-0.555612 - 0.555612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9	$ 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9} - 4 q^{11} - 28 q^{12} + 12 q^{15} - 36 q^{16} - 8 q^{17} + 8 q^{20} + 12 q^{21} + 32 q^{22} + 4 q^{26} + 12 q^{28} - 8 q^{29} + 24 q^{31} + 20 q^{32} - 4 q^{33} - 20 q^{35} - 4 q^{37} + 40 q^{38} - 16 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 20 q^{46} + 32 q^{47} + 20 q^{50} - 56 q^{52} - 16 q^{53} - 20 q^{56} + 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} - 32 q^{67} + 16 q^{69} - 20 q^{70} - 12 q^{71} - 32 q^{73} - 64 q^{74} + 4 q^{75} - 12 q^{77} + 16 q^{78} + 24 q^{79} - 4 q^{80} + 12 q^{81} + 28 q^{84} - 32 q^{85} + 4 q^{89} + 32 q^{91} + 112 q^{92} + 24 q^{93} - 20 q^{96} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9 - 4 * q^11 - 28 * q^12 + 12 * q^15 - 36 * q^16 - 8 * q^17 + 8 * q^20 + 12 * q^21 + 32 * q^22 + 4 * q^26 + 12 * q^28 - 8 * q^29 + 24 * q^31 + 20 * q^32 - 4 * q^33 - 20 * q^35 - 4 * q^37 + 40 * q^38 - 16 * q^39 - 20 * q^41 + 8 * q^44 - 12 * q^45 + 20 * q^46 + 32 * q^47 + 20 * q^50 - 56 * q^52 - 16 * q^53 - 20 * q^56 + 8 * q^59 - 8 * q^60 + 4 * q^63 - 16 * q^65 - 32 * q^67 + 16 * q^69 - 20 * q^70 - 12 * q^71 - 32 * q^73 - 64 * q^74 + 4 * q^75 - 12 * q^77 + 16 * q^78 + 24 * q^79 - 4 * q^80 + 12 * q^81 + 28 * q^84 - 32 * q^85 + 4 * q^89 + 32 * q^91 + 112 * q^92 + 24 * q^93 - 20 * q^96 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.94644	+	1.94644i	−1.37634	+	1.37634i	−0.525629	+	0.850714i	$0.676170\pi$
$2$	−1.94644	+	1.94644i	−1.37634	+	1.37634i	−0.850714	+	0.525629i	$0.823830\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		−	5.57728i		−	2.78864i
$5$	0.136767	+	0.136767i	0.0611638	+	0.0611638i	0.737027	−	0.675863i	$-0.236229\pi$
$5$	0.136767	+	0.136767i	0.0611638	+	0.0611638i	−0.675863	+	0.737027i	$0.736229\pi$
$6$	1.94644	+	1.94644i	0.794632	+	0.794632i
$7$	−2.24723	+	1.39641i	−0.849372	+	0.527795i
$7$	−2.24723	+	1.39641i	−0.849372	+	0.527795i
$8$	6.96297	+	6.96297i	2.46178	+	2.46178i
$9$	−1.00000			−0.333333
$10$	−0.532416			−0.168365
$11$	0.555612	+	0.555612i	0.167523	+	0.167523i	0.785890	−	0.618367i	$-0.212205\pi$
$11$	0.555612	+	0.555612i	0.167523	+	0.167523i	−0.618367	+	0.785890i	$0.712205\pi$
$12$	−5.57728			−1.61002
$13$	−1.81044	−	3.11806i	−0.502126	−	0.864795i
$13$	−1.81044	−	3.11806i	−0.502126	−	0.864795i
$14$	1.65606	−	7.09214i	0.442601	−	1.89545i
$15$	0.136767	−	0.136767i	0.0353130	−	0.0353130i
$16$	−15.9515			−3.98787
$17$	−4.49445			−1.09007			−0.545033	−	0.838415i	$-0.683483\pi$
$17$	−4.49445			−1.09007			−0.545033	+	0.838415i	$0.683483\pi$
$18$	1.94644	−	1.94644i	0.458781	−	0.458781i
$19$	−4.15330	−	4.15330i	−0.952832	−	0.952832i	0.0461051	−	0.998937i	$-0.485319\pi$
$19$	−4.15330	−	4.15330i	−0.952832	−	0.952832i	−0.998937	+	0.0461051i	$0.985319\pi$
$20$	0.762785	−	0.762785i	0.170564	−	0.170564i
$21$	1.39641	+	2.24723i	0.304722	+	0.490385i
$22$	−2.16293			−0.461139
$23$			0.423984i			0.0884068i	0.999023	+	0.0442034i	$0.0140750\pi$
$23$			0.423984i			0.0884068i	−0.999023	+	0.0442034i	$0.985925\pi$
$24$	6.96297	−	6.96297i	1.42131	−	1.42131i
$25$		−	4.96259i		−	0.992518i
$26$	9.59305	+	2.54521i	1.88135	+	0.499157i
$27$			1.00000i			0.192450i
$28$	7.78819	+	12.5334i	1.47183	+	2.36859i
$29$	−7.01375			−1.30242			−0.651210	−	0.758897i	$-0.725738\pi$
$29$	−7.01375			−1.30242			−0.651210	+	0.758897i	$0.725738\pi$
$30$			0.532416i			0.0972055i
$31$	0.273533	+	0.273533i	0.0491280	+	0.0491280i	0.731244	−	0.682116i	$-0.238940\pi$
$31$	0.273533	+	0.273533i	0.0491280	+	0.0491280i	−0.682116	+	0.731244i	$0.738940\pi$
$32$	17.1227	−	17.1227i	3.02690	−	3.02690i
$33$	0.555612	−	0.555612i	0.0967196	−	0.0967196i
$34$	8.74820	−	8.74820i	1.50030	−	1.50030i
$35$	−0.498328	−	0.116363i	−0.0842328	−	0.0196689i
$36$			5.57728i			0.929547i
$37$	5.75334	+	5.75334i	0.945843	+	0.945843i	0.998607	−	0.0527641i	$-0.0168031\pi$
$37$	5.75334	+	5.75334i	0.945843	+	0.945843i	−0.0527641	+	0.998607i	$0.516803\pi$
$38$	16.1683			2.62285
$39$	−3.11806	+	1.81044i	−0.499289	+	0.289902i
$40$			1.90460i			0.301144i
$41$	−7.29133	−	7.29133i	−1.13871	−	1.13871i	−0.988681	−	0.150033i	$-0.952062\pi$
$41$	−7.29133	−	7.29133i	−1.13871	−	1.13871i	−0.150033	−	0.988681i	$-0.547938\pi$
$42$	−7.09214	−	1.65606i	−1.09434	−	0.255536i
$43$			1.86728i			0.284758i	0.989812	+	0.142379i	$0.0454751\pi$
$43$			1.86728i			0.284758i	−0.989812	+	0.142379i	$0.954525\pi$
$44$	3.09880	−	3.09880i	0.467162	−	0.467162i
$45$	−0.136767	−	0.136767i	−0.0203879	−	0.0203879i
$46$	−0.825261	−	0.825261i	−0.121678	−	0.121678i
$47$	−4.75098	+	4.75098i	−0.693002	+	0.693002i	−0.962891	−	0.269890i	$-0.913013\pi$
$47$	−4.75098	+	4.75098i	−0.693002	+	0.693002i	0.269890	+	0.962891i	$0.413013\pi$
$48$			15.9515i			2.30240i
$49$	3.10006	−	6.27612i	0.442866	−	0.896588i
$50$	9.65940	+	9.65940i	1.36605	+	1.36605i
$51$			4.49445i			0.629349i
$52$	−17.3903	+	10.0973i	−2.41160	+	1.40025i
$53$	−4.31687			−0.592968			−0.296484	−	0.955038i	$-0.595814\pi$
$53$	−4.31687			−0.592968			−0.296484	+	0.955038i	$0.595814\pi$
$54$	−1.94644	−	1.94644i	−0.264877	−	0.264877i
$55$			0.151978i			0.0204927i
$56$	−25.3706	−	5.92419i	−3.39029	−	0.791654i
$57$	−4.15330	+	4.15330i	−0.550118	+	0.550118i
$58$	13.6519	−	13.6519i	1.79258	−	1.79258i
$59$	−0.691676	+	0.691676i	−0.0900485	+	0.0900485i	−0.750696	−	0.660648i	$-0.770282\pi$
$59$	−0.691676	+	0.691676i	−0.0900485	+	0.0900485i	0.660648	+	0.750696i	$0.270282\pi$
$60$	−0.762785	−	0.762785i	−0.0984751	−	0.0984751i
$61$		−	8.11937i		−	1.03958i	−0.854294	−	0.519789i	$-0.826010\pi$
$61$		−	8.11937i		−	1.03958i	0.854294	−	0.519789i	$-0.173990\pi$
$62$	−1.06483			−0.135234
$63$	2.24723	−	1.39641i	0.283124	−	0.175932i
$64$			34.7539i			4.34423i
$65$	0.178839	−	0.674054i	0.0221822	−	0.0836061i
$66$			2.16293i			0.266239i
$67$	0.837691	−	0.837691i	0.102340	−	0.102340i	−0.654083	−	0.756423i	$-0.726945\pi$
$67$	0.837691	−	0.837691i	0.102340	−	0.102340i	0.756423	+	0.654083i	$0.226945\pi$
$68$			25.0668i			3.03980i
$69$	0.423984			0.0510417
$70$	1.19646	−	0.743473i	0.143004	−	0.0888621i
$71$	1.00520	−	1.00520i	0.119296	−	0.119296i	−0.644939	−	0.764234i	$-0.723117\pi$
$71$	1.00520	−	1.00520i	0.119296	−	0.119296i	0.764234	+	0.644939i	$0.223117\pi$
$72$	−6.96297	−	6.96297i	−0.820594	−	0.820594i
$73$	−6.81854	+	6.81854i	−0.798050	+	0.798050i	−0.982788	−	0.184738i	$-0.940856\pi$
$73$	−6.81854	+	6.81854i	−0.798050	+	0.798050i	0.184738	+	0.982788i	$0.440856\pi$
$74$	−22.3971			−2.60361
$75$	−4.96259			−0.573031
$76$	−23.1641	+	23.1641i	−2.65710	+	2.65710i
$77$	−2.02445	−	0.472722i	−0.230708	−	0.0538717i
$78$	2.54521	−	9.59305i	0.288188	−	1.08620i
$79$	10.9777			1.23509			0.617546	−	0.786535i	$-0.288127\pi$
$79$	10.9777			1.23509			0.617546	+	0.786535i	$0.288127\pi$
$80$	−2.18163	−	2.18163i	−0.243914	−	0.243914i
$81$	1.00000			0.111111
$82$	28.3843			3.13452
$83$	6.91260	+	6.91260i	0.758756	+	0.758756i	0.976096	−	0.217340i	$-0.0697380\pi$
$83$	6.91260	+	6.91260i	0.758756	+	0.758756i	−0.217340	+	0.976096i	$0.569738\pi$
$84$	12.5334	−	7.78819i	1.36751	−	0.849761i
$85$	−0.614691	−	0.614691i	−0.0666726	−	0.0666726i
$86$	−3.63455	−	3.63455i	−0.391924	−	0.391924i
$87$			7.01375i			0.751953i
$88$			7.73742i			0.824812i
$89$	6.46820	−	6.46820i	0.685628	−	0.685628i	−0.275635	−	0.961262i	$-0.588888\pi$
$89$	6.46820	−	6.46820i	0.685628	−	0.685628i	0.961262	+	0.275635i	$0.0888880\pi$
$90$	0.532416			0.0561216
$91$	8.42257	+	4.47887i	0.882926	+	0.469513i
$92$	2.36468			0.246535
$93$	0.273533	−	0.273533i	0.0283641	−	0.0283641i
$94$		−	18.4950i		−	1.90762i
$95$		−	1.13606i		−	0.116558i
$96$	−17.1227	−	17.1227i	−1.74758	−	1.74758i
$97$	3.19087	+	3.19087i	0.323984	+	0.323984i	0.850293	−	0.526309i	$-0.176425\pi$
$97$	3.19087	+	3.19087i	0.323984	+	0.323984i	−0.526309	+	0.850293i	$0.676425\pi$
$98$	6.18201	+	18.2502i	0.624478	+	1.84355i
$99$	−0.555612	−	0.555612i	−0.0558411	−	0.0558411i
$100$	−27.6778			−2.76778
$101$	9.40173			0.935507			0.467753	−	0.883859i	$-0.345064\pi$
$101$	9.40173			0.935507			0.467753	+	0.883859i	$0.345064\pi$
$102$	−8.74820	−	8.74820i	−0.866201	−	0.866201i
$103$	1.84027			0.181328			0.0906638	−	0.995882i	$-0.471101\pi$
$103$	1.84027			0.181328			0.0906638	+	0.995882i	$0.471101\pi$
$104$	9.10493	−	34.3170i	0.892812	−	3.36506i
$105$	−0.116363	+	0.498328i	−0.0113558	+	0.0486318i
$106$	8.40254	−	8.40254i	0.816127	−	0.816127i
$107$	9.88514			0.955632			0.477816	−	0.878460i	$-0.341428\pi$
$107$	9.88514			0.955632			0.477816	+	0.878460i	$0.341428\pi$
$108$	5.57728			0.536674
$109$	−9.76428	+	9.76428i	−0.935248	+	0.935248i	−0.998027	−	0.0627794i	$-0.980004\pi$
$109$	−9.76428	+	9.76428i	−0.935248	+	0.935248i	0.0627794	+	0.998027i	$0.480004\pi$
$110$	−0.295817	−	0.295817i	−0.0282050	−	0.0282050i
$111$	5.75334	−	5.75334i	0.546083	−	0.546083i
$112$	35.8466	−	22.2749i	3.38719	−	2.10478i
$113$	−9.96741			−0.937655			−0.468828	−	0.883290i	$-0.655323\pi$
$113$	−9.96741			−0.937655			−0.468828	+	0.883290i	$0.655323\pi$
$114$		−	16.1683i		−	1.51430i
$115$	−0.0579868	+	0.0579868i	−0.00540730	+	0.00540730i
$116$			39.1176i			3.63198i
$117$	1.81044	+	3.11806i	0.167375	+	0.288265i
$118$		−	2.69261i		−	0.247875i
$119$	10.1001	−	6.27612i	0.925871	−	0.575331i
$120$	1.90460			0.173866
$121$		−	10.3826i		−	0.943872i
$122$	15.8039	+	15.8039i	1.43082	+	1.43082i
$123$	−7.29133	+	7.29133i	−0.657437	+	0.657437i
$124$	1.52557	−	1.52557i	0.137000	−	0.137000i
$125$	1.36255	−	1.36255i	0.121870	−	0.121870i
$126$	−1.65606	+	7.09214i	−0.147534	+	0.631818i
$127$		−	2.97774i		−	0.264232i	−0.991234	−	0.132116i	$-0.957823\pi$
$127$		−	2.97774i		−	0.264232i	0.991234	−	0.132116i	$-0.0421771\pi$
$128$	−33.4009	−	33.4009i	−2.95225	−	2.95225i
$129$	1.86728			0.164405
$130$	0.963908	+	1.66011i	0.0845403	+	0.145601i
$131$			17.4307i			1.52293i	0.648206	+	0.761465i	$0.275520\pi$
$131$			17.4307i			1.52293i	−0.648206	+	0.761465i	$0.724480\pi$
$132$	−3.09880	−	3.09880i	−0.269716	−	0.269716i
$133$	15.1331	+	3.53368i	1.31221	+	0.306409i
$134$			3.26104i			0.281711i
$135$	−0.136767	+	0.136767i	−0.0117710	+	0.0117710i
$136$	−31.2948	−	31.2948i	−2.68350	−	2.68350i
$137$	−7.44628	−	7.44628i	−0.636178	−	0.636178i	0.313432	−	0.949611i	$-0.398521\pi$
$137$	−7.44628	−	7.44628i	−0.636178	−	0.636178i	−0.949611	+	0.313432i	$0.898521\pi$
$138$	−0.825261	+	0.825261i	−0.0702509	+	0.0702509i
$139$			18.7436i			1.58981i	0.606732	+	0.794906i	$0.292480\pi$
$139$			18.7436i			1.58981i	−0.606732	+	0.794906i	$0.707520\pi$
$140$	−0.648988	+	2.77932i	−0.0548495	+	0.234895i
$141$	4.75098	+	4.75098i	0.400105	+	0.400105i
$142$			3.91314i			0.328383i
$143$	0.726530	−	2.73833i	0.0607555	−	0.228991i
$144$	15.9515			1.32929
$145$	−0.959246	−	0.959246i	−0.0796610	−	0.0796610i
$146$		−	26.5438i		−	2.19678i
$147$	−6.27612	−	3.10006i	−0.517645	−	0.255689i
$148$	32.0880	−	32.0880i	2.63762	−	2.63762i
$149$	−7.56936	+	7.56936i	−0.620106	+	0.620106i	−0.945558	−	0.325452i	$-0.894483\pi$
$149$	−7.56936	+	7.56936i	−0.620106	+	0.620106i	0.325452	+	0.945558i	$0.394483\pi$
$150$	9.65940	−	9.65940i	0.788687	−	0.788687i
$151$	−9.52340	−	9.52340i	−0.775004	−	0.775004i	0.203973	−	0.978977i	$-0.434615\pi$
$151$	−9.52340	−	9.52340i	−0.775004	−	0.775004i	−0.978977	+	0.203973i	$0.934615\pi$
$152$		−	57.8386i		−	4.69133i
$153$	4.49445			0.363355
$154$	4.86060	−	3.02035i	0.391679	−	0.243387i
$155$			0.0748203i			0.00600971i
$156$	10.0973	+	17.3903i	0.808434	+	1.39234i
$157$		−	18.1301i		−	1.44694i	−0.690354	−	0.723471i	$-0.742545\pi$
$157$		−	18.1301i		−	1.44694i	0.690354	−	0.723471i	$-0.257455\pi$
$158$	−21.3676	+	21.3676i	−1.69991	+	1.69991i
$159$			4.31687i			0.342350i
$160$	4.68363			0.370274
$161$	−0.592057	−	0.952789i	−0.0466607	−	0.0750903i
$162$	−1.94644	+	1.94644i	−0.152927	+	0.152927i
$163$	−0.674757	−	0.674757i	−0.0528510	−	0.0528510i	0.680187	−	0.733038i	$-0.261898\pi$
$163$	−0.674757	−	0.674757i	−0.0528510	−	0.0528510i	−0.733038	+	0.680187i	$0.761898\pi$
$164$	−40.6658	+	40.6658i	−3.17546	+	3.17546i
$165$	0.151978			0.0118315
$166$	−26.9100			−2.08862
$167$	−5.13896	+	5.13896i	−0.397665	+	0.397665i	−0.877409	−	0.479744i	$-0.840730\pi$
$167$	−5.13896	+	5.13896i	−0.397665	+	0.397665i	0.479744	+	0.877409i	$0.340730\pi$
$168$	−5.92419	+	25.3706i	−0.457061	+	1.95738i
$169$	−6.44461	+	11.2901i	−0.495740	+	0.868471i
$170$	2.39292			0.183529
$171$	4.15330	+	4.15330i	0.317611	+	0.317611i
$172$	10.4143			0.794086
$173$	0.655393			0.0498286			0.0249143	−	0.999690i	$-0.492069\pi$
$173$	0.655393			0.0498286			0.0249143	+	0.999690i	$0.492069\pi$
$174$	−13.6519	−	13.6519i	−1.03494	−	1.03494i
$175$	6.92983	+	11.1521i	0.523846	+	0.843017i
$176$	−8.86284	−	8.86284i	−0.668062	−	0.668062i
$177$	0.691676	+	0.691676i	0.0519895	+	0.0519895i
$178$			25.1800i			1.88732i
$179$		−	23.7340i		−	1.77397i	−0.461802	−	0.886983i	$-0.652797\pi$
$179$		−	23.7340i		−	1.77397i	0.461802	−	0.886983i	$-0.347203\pi$
$180$	−0.762785	+	0.762785i	−0.0568547	+	0.0568547i
$181$	7.42950			0.552230			0.276115	−	0.961125i	$-0.410953\pi$
$181$	7.42950			0.552230			0.276115	+	0.961125i	$0.410953\pi$
$182$	−25.1119	+	7.67619i	−1.86142	+	0.568997i
$183$	−8.11937			−0.600201
$184$	−2.95219	+	2.95219i	−0.217638	+	0.217638i
$185$			1.57373i			0.115703i
$186$			1.06483i			0.0780773i
$187$	−2.49717	−	2.49717i	−0.182611	−	0.182611i
$188$	26.4976	+	26.4976i	1.93253	+	1.93253i
$189$	−1.39641	−	2.24723i	−0.101574	−	0.163462i
$190$	2.21128	+	2.21128i	0.160423	+	0.160423i
$191$	19.3050			1.39686			0.698431	−	0.715678i	$-0.253882\pi$
$191$	19.3050			1.39686			0.698431	+	0.715678i	$0.253882\pi$
$192$	34.7539			2.50814
$193$	5.06291	+	5.06291i	0.364436	+	0.364436i	0.865443	−	0.501007i	$-0.167037\pi$
$193$	5.06291	+	5.06291i	0.364436	+	0.364436i	−0.501007	+	0.865443i	$0.667037\pi$
$194$	−12.4217			−0.891825
$195$	−0.674054	−	0.178839i	−0.0482700	−	0.0128069i
$196$	−35.0037	−	17.2899i	−2.50026	−	1.23499i
$197$	11.0333	−	11.0333i	0.786093	−	0.786093i	−0.194758	−	0.980851i	$-0.562392\pi$
$197$	11.0333	−	11.0333i	0.786093	−	0.786093i	0.980851	+	0.194758i	$0.0623923\pi$
$198$	2.16293			0.153713
$199$	12.6458			0.896436			0.448218	−	0.893924i	$-0.352059\pi$
$199$	12.6458			0.896436			0.448218	+	0.893924i	$0.352059\pi$
$200$	34.5544	−	34.5544i	2.44336	−	2.44336i
$201$	−0.837691	−	0.837691i	−0.0590862	−	0.0590862i
$202$	−18.2999	+	18.2999i	−1.28758	+	1.28758i
$203$	15.7615	−	9.79409i	1.10624	−	0.687410i
$204$	25.0668			1.75503
$205$		−	1.99442i		−	0.139296i
$206$	−3.58199	+	3.58199i	−0.249569	+	0.249569i
$207$		−	0.423984i		−	0.0294689i
$208$	28.8792	+	49.7378i	2.00241	+	3.44869i
$209$		−	4.61524i		−	0.319243i
$210$	−0.743473	−	1.19646i	−0.0513045	−	0.0825636i
$211$	−19.1491			−1.31828			−0.659139	−	0.752021i	$-0.729079\pi$
$211$	−19.1491			−1.31828			−0.659139	+	0.752021i	$0.729079\pi$
$212$			24.0764i			1.65357i
$213$	−1.00520	−	1.00520i	−0.0688753	−	0.0688753i
$214$	−19.2409	+	19.2409i	−1.31528	+	1.31528i
$215$	−0.255381	+	0.255381i	−0.0174169	+	0.0174169i
$216$	−6.96297	+	6.96297i	−0.473770	+	0.473770i
$217$	−0.996656	−	0.232726i	−0.0676574	−	0.0157984i
$218$		−	38.0112i		−	2.57444i
$219$	6.81854	+	6.81854i	0.460754	+	0.460754i
$220$	0.847625			0.0571469
$221$	8.13694	+	14.0140i	0.547350	+	0.942683i
$222$			22.3971i			1.50319i
$223$	3.78445	+	3.78445i	0.253426	+	0.253426i	0.822374	−	0.568948i	$-0.192649\pi$
$223$	3.78445	+	3.78445i	0.253426	+	0.253426i	−0.568948	+	0.822374i	$0.692649\pi$
$224$	−14.5683	+	62.3891i	−0.973383	+	4.16855i
$225$			4.96259i			0.330839i
$226$	19.4010	−	19.4010i	1.29054	−	1.29054i
$227$	−12.8654	−	12.8654i	−0.853908	−	0.853908i	0.136704	−	0.990612i	$-0.456349\pi$
$227$	−12.8654	−	12.8654i	−0.853908	−	0.853908i	−0.990612	+	0.136704i	$0.956349\pi$
$228$	23.1641	+	23.1641i	1.53408	+	1.53408i
$229$	6.95379	−	6.95379i	0.459519	−	0.459519i	−0.438978	−	0.898498i	$-0.644659\pi$
$229$	6.95379	−	6.95379i	0.459519	−	0.459519i	0.898498	+	0.438978i	$0.144659\pi$
$230$		−	0.225736i		−	0.0148846i
$231$	−0.472722	+	2.02445i	−0.0311028	+	0.133199i
$232$	−48.8365	−	48.8365i	−3.20628	−	3.20628i
$233$		−	19.3196i		−	1.26567i	−0.774288	−	0.632833i	$-0.781892\pi$
$233$		−	19.3196i		−	1.26567i	0.774288	−	0.632833i	$-0.218108\pi$
$234$	−9.59305	−	2.54521i	−0.627117	−	0.166386i
$235$	−1.29955			−0.0847733
$236$	3.85767	+	3.85767i	0.251113	+	0.251113i
$237$		−	10.9777i		−	0.713081i
$238$	−7.44309	+	31.8753i	−0.482464	+	2.06617i
$239$	−14.4989	+	14.4989i	−0.937859	+	0.937859i	−0.998179	−	0.0603204i	$-0.980788\pi$
$239$	−14.4989	+	14.4989i	−0.937859	+	0.937859i	0.0603204	+	0.998179i	$0.480788\pi$
$240$	−2.18163	+	2.18163i	−0.140824	+	0.140824i
$241$	5.11691	−	5.11691i	0.329609	−	0.329609i	−0.522828	−	0.852438i	$-0.675123\pi$
$241$	5.11691	−	5.11691i	0.329609	−	0.329609i	0.852438	+	0.522828i	$0.175123\pi$
$242$	20.2091	+	20.2091i	1.29909	+	1.29909i
$243$		−	1.00000i		−	0.0641500i
$244$	−45.2840			−2.89901
$245$	1.28235	−	0.434378i	0.0819261	−	0.0277514i
$246$		−	28.3843i		−	1.80972i
$247$	−5.43094	+	20.4695i	−0.345562	+	1.30244i
$248$			3.80921i			0.241885i
$249$	6.91260	−	6.91260i	0.438068	−	0.438068i
$250$			5.30425i			0.335470i
$251$	−15.9764			−1.00842			−0.504211	−	0.863580i	$-0.668217\pi$
$251$	−15.9764			−1.00842			−0.504211	+	0.863580i	$0.668217\pi$
$252$	−7.78819	−	12.5334i	−0.490610	−	0.789531i
$253$	−0.235571	+	0.235571i	−0.0148102	+	0.0148102i
$254$	5.79601	+	5.79601i	0.363674	+	0.363674i
$255$	−0.614691	+	0.614691i	−0.0384934	+	0.0384934i
$256$	60.5183			3.78240
$257$	−10.3506			−0.645652			−0.322826	−	0.946458i	$-0.604633\pi$
$257$	−10.3506			−0.645652			−0.322826	+	0.946458i	$0.604633\pi$
$258$	−3.63455	+	3.63455i	−0.226277	+	0.226277i
$259$	−20.9631	−	4.89502i	−1.30258	−	0.304162i
$260$	−3.75939	−	0.997434i	−0.233147	−	0.0618582i
$261$	7.01375			0.434140
$262$	−33.9279	−	33.9279i	−2.09607	−	2.09607i
$263$	−10.9315			−0.674064			−0.337032	−	0.941493i	$-0.609423\pi$
$263$	−10.9315			−0.674064			−0.337032	+	0.941493i	$0.609423\pi$
$264$	7.73742			0.476205
$265$	−0.590403	−	0.590403i	−0.0362682	−	0.0362682i
$266$	−36.3339	+	22.5776i	−2.22777	+	1.38432i
$267$	−6.46820	−	6.46820i	−0.395847	−	0.395847i
$268$	−4.67204	−	4.67204i	−0.285390	−	0.285390i
$269$		−	0.890429i		−	0.0542904i	−0.999632	−	0.0271452i	$-0.991358\pi$
$269$		−	0.890429i		−	0.0542904i	0.999632	−	0.0271452i	$-0.00864165\pi$
$270$		−	0.532416i		−	0.0324018i
$271$	15.2932	−	15.2932i	0.928996	−	0.928996i	−0.0686449	−	0.997641i	$-0.521868\pi$
$271$	15.2932	−	15.2932i	0.928996	−	0.928996i	0.997641	+	0.0686449i	$0.0218676\pi$
$272$	71.6933			4.34704
$273$	4.47887	−	8.42257i	0.271074	−	0.509757i
$274$	28.9875			1.75120
$275$	2.75727	−	2.75727i	0.166270	−	0.166270i
$276$		−	2.36468i		−	0.142337i
$277$		−	9.83129i		−	0.590705i	−0.955388	−	0.295353i	$-0.904563\pi$
$277$		−	9.83129i		−	0.590705i	0.955388	−	0.295353i	$-0.0954371\pi$
$278$	−36.4834	−	36.4834i	−2.18813	−	2.18813i
$279$	−0.273533	−	0.273533i	−0.0163760	−	0.0163760i
$280$	−2.65961	−	4.28008i	−0.158942	−	0.255783i
$281$	−12.8526	−	12.8526i	−0.766720	−	0.766720i	0.210808	−	0.977528i	$-0.432391\pi$
$281$	−12.8526	−	12.8526i	−0.766720	−	0.766720i	−0.977528	+	0.210808i	$0.932391\pi$
$282$	−18.4950			−1.10136
$283$	−2.25769			−0.134206			−0.0671029	−	0.997746i	$-0.521376\pi$
$283$	−2.25769			−0.134206			−0.0671029	+	0.997746i	$0.521376\pi$
$284$	−5.60629	−	5.60629i	−0.332672	−	0.332672i
$285$	−1.13606			−0.0672946
$286$	3.91586	+	6.74416i	0.231550	+	0.398791i
$287$	26.5670	+	6.20356i	1.56820	+	0.366185i
$288$	−17.1227	+	17.1227i	−1.00897	+	1.00897i
$289$	3.20012			0.188242
$290$	3.73423			0.219282
$291$	3.19087	−	3.19087i	0.187052	−	0.187052i
$292$	38.0289	+	38.0289i	2.22547	+	2.22547i
$293$	3.42417	−	3.42417i	0.200042	−	0.200042i	−0.599976	−	0.800018i	$-0.704823\pi$
$293$	3.42417	−	3.42417i	0.200042	−	0.200042i	0.800018	+	0.599976i	$0.204823\pi$
$294$	18.2502	−	6.18201i	1.06437	−	0.360542i
$295$	−0.189196			−0.0110154
$296$			80.1207i			4.65692i
$297$	−0.555612	+	0.555612i	−0.0322399	+	0.0322399i
$298$		−	29.4667i		−	1.70696i
$299$	1.32201	−	0.767598i	0.0764538	−	0.0443913i
$300$			27.6778i			1.59798i
$301$	−2.60750	−	4.19620i	−0.150294	−	0.241865i
$302$	37.0735			2.13334
$303$		−	9.40173i		−	0.540115i
$304$	66.2513	+	66.2513i	3.79977	+	3.79977i
$305$	1.11046	−	1.11046i	0.0635846	−	0.0635846i
$306$	−8.74820	+	8.74820i	−0.500101	+	0.500101i
$307$	−11.2000	+	11.2000i	−0.639216	+	0.639216i	−0.950362	−	0.311146i	$-0.899287\pi$
$307$	−11.2000	+	11.2000i	−0.639216	+	0.639216i	0.311146	+	0.950362i	$0.399287\pi$
$308$	−2.63651	+	11.2909i	−0.150229	+	0.643360i
$309$		−	1.84027i		−	0.104690i
$310$	−0.145633	−	0.145633i	−0.00827143	−	0.00827143i
$311$	18.6012			1.05477			0.527387	−	0.849625i	$-0.323172\pi$
$311$	18.6012			1.05477			0.527387	+	0.849625i	$0.323172\pi$
$312$	−34.3170	−	9.10493i	−1.94282	−	0.515465i
$313$		−	31.7181i		−	1.79281i	−0.443234	−	0.896406i	$-0.646169\pi$
$313$		−	31.7181i		−	1.79281i	0.443234	−	0.896406i	$-0.353831\pi$
$314$	35.2893	+	35.2893i	1.99149	+	1.99149i
$315$	0.498328	+	0.116363i	0.0280776	+	0.00655630i
$316$		−	61.2260i		−	3.44423i
$317$	−9.54944	+	9.54944i	−0.536350	+	0.536350i	−0.922455	−	0.386105i	$-0.873820\pi$
$317$	−9.54944	+	9.54944i	−0.536350	+	0.536350i	0.386105	+	0.922455i	$0.373820\pi$
$318$	−8.40254	−	8.40254i	−0.471191	−	0.471191i
$319$	−3.89692	−	3.89692i	−0.218186	−	0.218186i
$320$	−4.75316	+	4.75316i	−0.265710	+	0.265710i
$321$		−	9.88514i		−	0.551735i
$322$	3.00696	+	0.702144i	0.167571	+	0.0391289i
$323$	18.6668	+	18.6668i	1.03865	+	1.03865i
$324$		−	5.57728i		−	0.309849i
$325$	−15.4737	+	8.98447i	−0.858324	+	0.498369i
$326$	2.62675			0.145482
$327$	9.76428	+	9.76428i	0.539966	+	0.539966i
$328$		−	101.539i		−	5.60653i
$329$	4.04220	−	17.3109i	0.222854	−	0.954379i
$330$	−0.295817	+	0.295817i	−0.0162842	+	0.0162842i
$331$	−12.3494	+	12.3494i	−0.678783	+	0.678783i	−0.959725	−	0.280942i	$-0.909353\pi$
$331$	−12.3494	+	12.3494i	−0.678783	+	0.678783i	0.280942	+	0.959725i	$0.409353\pi$
$332$	38.5535	−	38.5535i	2.11590	−	2.11590i
$333$	−5.75334	−	5.75334i	−0.315281	−	0.315281i
$334$		−	20.0054i		−	1.09465i
$335$	0.229136			0.0125190
$336$	−22.2749	−	35.8466i	−1.21519	−	1.95559i
$337$			24.8518i			1.35376i	0.736091	+	0.676882i	$0.236669\pi$
$337$			24.8518i			1.35376i	−0.736091	+	0.676882i	$0.763331\pi$
$338$	−9.43151	−	34.5197i	−0.513007	−	1.87762i
$339$			9.96741i			0.541356i
$340$	−3.42830	+	3.42830i	−0.185926	+	0.185926i
$341$			0.303956i			0.0164602i
$342$	−16.1683			−0.874282
$343$	1.79752	+	18.4328i	0.0970567	+	0.995279i
$344$	−13.0018	+	13.0018i	−0.701011	+	0.701011i
$345$	0.0579868	+	0.0579868i	0.00312191	+	0.00312191i
$346$	−1.27569	+	1.27569i	−0.0685813	+	0.0685813i
$347$	−15.5180			−0.833052			−0.416526	−	0.909124i	$-0.636753\pi$
$347$	−15.5180			−0.833052			−0.416526	+	0.909124i	$0.636753\pi$
$348$	39.1176			2.09693
$349$	8.67730	−	8.67730i	0.464485	−	0.464485i	−0.435637	−	0.900122i	$-0.643477\pi$
$349$	8.67730	−	8.67730i	0.464485	−	0.464485i	0.900122	+	0.435637i	$0.143477\pi$
$350$	−35.1954	−	8.21835i	−1.88127	−	0.439289i
$351$	3.11806	−	1.81044i	0.166430	−	0.0966341i
$352$	19.0272			1.01415
$353$	−24.8207	−	24.8207i	−1.32107	−	1.32107i	−0.912910	−	0.408160i	$-0.866171\pi$
$353$	−24.8207	−	24.8207i	−1.32107	−	1.32107i	−0.408160	−	0.912910i	$-0.633829\pi$
$354$	−2.69261			−0.143111
$355$	0.274956			0.0145931
$356$	−36.0750	−	36.0750i	−1.91197	−	1.91197i
$357$	−6.27612	−	10.1001i	−0.332167	−	0.534552i
$358$	46.1970	+	46.1970i	2.44159	+	2.44159i
$359$	−8.95183	−	8.95183i	−0.472459	−	0.472459i	0.430250	−	0.902710i	$-0.358425\pi$
$359$	−8.95183	−	8.95183i	−0.472459	−	0.472459i	−0.902710	+	0.430250i	$0.858425\pi$
$360$		−	1.90460i		−	0.100381i
$361$			15.4997i			0.815776i
$362$	−14.4611	+	14.4611i	−0.760058	+	0.760058i
$363$	−10.3826			−0.544945
$364$	24.9799	−	46.9751i	1.30930	−	2.46216i
$365$	−1.86510			−0.0976236
$366$	15.8039	−	15.8039i	0.826083	−	0.826083i
$367$			21.0453i			1.09855i	0.835640	+	0.549277i	$0.185097\pi$
$367$			21.0453i			1.09855i	−0.835640	+	0.549277i	$0.814903\pi$
$368$		−	6.76318i		−	0.352555i
$369$	7.29133	+	7.29133i	0.379571	+	0.379571i
$370$	−3.06317	−	3.06317i	−0.159247	−	0.159247i
$371$	9.70099	−	6.02814i	0.503650	−	0.312965i
$372$	−1.52557	−	1.52557i	−0.0790971	−	0.0790971i
$373$	−17.6419			−0.913462			−0.456731	−	0.889605i	$-0.650980\pi$
$373$	−17.6419			−0.913462			−0.456731	+	0.889605i	$0.650980\pi$
$374$	9.72121			0.502672
$375$	−1.36255	−	1.36255i	−0.0703617	−	0.0703617i
$376$	−66.1619			−3.41204
$377$	12.6980	+	21.8693i	0.653979	+	1.12633i
$378$	7.09214	+	1.65606i	0.364780	+	0.0851786i
$379$	−4.45288	+	4.45288i	−0.228729	+	0.228729i	−0.812162	−	0.583433i	$-0.801709\pi$
$379$	−4.45288	+	4.45288i	−0.228729	+	0.228729i	0.583433	+	0.812162i	$0.301709\pi$
$380$	−6.33615			−0.325037
$381$	−2.97774			−0.152554
$382$	−37.5761	+	37.5761i	−1.92256	+	1.92256i
$383$	9.10197	+	9.10197i	0.465089	+	0.465089i	0.900319	−	0.435230i	$-0.143333\pi$
$383$	9.10197	+	9.10197i	0.465089	+	0.465089i	−0.435230	+	0.900319i	$0.643333\pi$
$384$	−33.4009	+	33.4009i	−1.70448	+	1.70448i
$385$	−0.212224	−	0.341530i	−0.0108160	−	0.0174060i
$386$	−19.7093			−1.00318
$387$		−	1.86728i		−	0.0949192i
$388$	17.7964	−	17.7964i	0.903474	−	0.903474i
$389$			5.48639i			0.278171i	0.990280	+	0.139086i	$0.0444163\pi$
$389$			5.48639i			0.278171i	−0.990280	+	0.139086i	$0.955584\pi$
$390$	1.66011	−	0.963908i	0.0840628	−	0.0488094i
$391$		−	1.90558i		−	0.0963692i
$392$	65.2861	−	22.1148i	3.29744	−	1.11697i
$393$	17.4307			0.879264
$394$			42.9515i			2.16387i
$395$	1.50139	+	1.50139i	0.0755430	+	0.0755430i
$396$	−3.09880	+	3.09880i	−0.155721	+	0.155721i
$397$	−21.4027	+	21.4027i	−1.07417	+	1.07417i	−0.0771530	+	0.997019i	$0.524583\pi$
$397$	−21.4027	+	21.4027i	−1.07417	+	1.07417i	−0.997019	+	0.0771530i	$0.975417\pi$
$398$	−24.6143	+	24.6143i	−1.23380	+	1.23380i
$399$	3.53368	−	15.1331i	0.176905	−	0.757604i
$400$			79.1607i			3.95804i
$401$	−1.09699	−	1.09699i	−0.0547810	−	0.0547810i	0.679186	−	0.733967i	$-0.262333\pi$
$401$	−1.09699	−	1.09699i	−0.0547810	−	0.0547810i	−0.733967	+	0.679186i	$0.762333\pi$
$402$	3.26104			0.162646
$403$	0.357678	−	1.34811i	0.0178172	−	0.0671540i
$404$		−	52.4361i		−	2.60879i
$405$	0.136767	+	0.136767i	0.00679598	+	0.00679598i
$406$	−11.6152	+	49.7425i	−0.576452	+	2.46868i
$407$			6.39325i			0.316901i
$408$	−31.2948	+	31.2948i	−1.54932	+	1.54932i
$409$	9.83744	+	9.83744i	0.486430	+	0.486430i	0.907178	−	0.420748i	$-0.138232\pi$
$409$	9.83744	+	9.83744i	0.486430	+	0.486430i	−0.420748	+	0.907178i	$0.638232\pi$
$410$	3.88202	+	3.88202i	0.191719	+	0.191719i
$411$	−7.44628	+	7.44628i	−0.367298	+	0.367298i
$412$		−	10.2637i		−	0.505657i
$413$	0.588487	−	2.52022i	0.0289576	−	0.124012i
$414$	0.825261	+	0.825261i	0.0405594	+	0.0405594i
$415$			1.89082i			0.0928169i
$416$	−84.3894	−	22.3901i	−4.13753	−	1.09776i
$417$	18.7436			0.917879
$418$	8.98331	+	8.98331i	0.439388	+	0.439388i
$419$		−	15.2437i		−	0.744706i	−0.928091	−	0.372353i	$-0.878551\pi$
$419$		−	15.2437i		−	0.744706i	0.928091	−	0.372353i	$-0.121449\pi$
$420$	2.77932	+	0.648988i	0.135617	+	0.0316674i
$421$	−6.81477	+	6.81477i	−0.332132	+	0.332132i	−0.853396	−	0.521264i	$-0.825461\pi$
$421$	−6.81477	+	6.81477i	−0.332132	+	0.332132i	0.521264	+	0.853396i	$0.325461\pi$
$422$	37.2726	−	37.2726i	1.81440	−	1.81440i
$423$	4.75098	−	4.75098i	0.231001	−	0.231001i
$424$	−30.0583	−	30.0583i	−1.45976	−	1.45976i
$425$			22.3041i			1.08191i
$426$	3.91314			0.189592
$427$	11.3380	+	18.2461i	0.548684	+	0.882989i
$428$		−	55.1322i		−	2.66492i
$429$	−2.73833	−	0.726530i	−0.132208	−	0.0350772i
$430$		−	0.994171i		−	0.0479432i
$431$	15.8122	−	15.8122i	0.761646	−	0.761646i	−0.214974	−	0.976620i	$-0.568967\pi$
$431$	15.8122	−	15.8122i	0.761646	−	0.761646i	0.976620	+	0.214974i	$0.0689667\pi$
$432$		−	15.9515i		−	0.767467i
$433$	13.2868			0.638525			0.319263	−	0.947666i	$-0.396565\pi$
$433$	13.2868			0.638525			0.319263	+	0.947666i	$0.396565\pi$
$434$	2.39292	−	1.48695i	0.114864	−	0.0713757i
$435$	−0.959246	+	0.959246i	−0.0459923	+	0.0459923i
$436$	54.4581	+	54.4581i	2.60807	+	2.60807i
$437$	1.76093	−	1.76093i	0.0842368	−	0.0842368i
$438$	−26.5438			−1.26831
$439$	−1.47611			−0.0704508			−0.0352254	−	0.999379i	$-0.511215\pi$
$439$	−1.47611			−0.0704508			−0.0352254	+	0.999379i	$0.511215\pi$
$440$	−1.05822	+	1.05822i	−0.0504487	+	0.0504487i
$441$	−3.10006	+	6.27612i	−0.147622	+	0.298863i
$442$	−43.1155	−	11.4393i	−2.05080	−	0.544114i
$443$	0.500905			0.0237987			0.0118994	−	0.999929i	$-0.496212\pi$
$443$	0.500905			0.0237987			0.0118994	+	0.999929i	$0.496212\pi$
$444$	−32.0880	−	32.0880i	−1.52283	−	1.52283i
$445$	1.76927			0.0838713
$446$	−14.7324			−0.697602
$447$	7.56936	+	7.56936i	0.358018	+	0.358018i
$448$	−48.5308	−	78.0998i	−2.29286	−	3.68987i
$449$	−1.55163	−	1.55163i	−0.0732259	−	0.0732259i	0.669545	−	0.742771i	$-0.266489\pi$
$449$	−1.55163	−	1.55163i	−0.0732259	−	0.0732259i	−0.742771	+	0.669545i	$0.766489\pi$
$450$	−9.65940	−	9.65940i	−0.455348	−	0.455348i
$451$		−	8.10230i		−	0.381522i
$452$			55.5911i			2.61478i
$453$	−9.52340	+	9.52340i	−0.447449	+	0.447449i
$454$	50.0836			2.35054
$455$	0.539367	+	1.76449i	0.0252859	+	0.0827203i
$456$	−57.8386			−2.70854
$457$	21.1001	−	21.1001i	0.987023	−	0.987023i	−0.0128943	−	0.999917i	$-0.504104\pi$
$457$	21.1001	−	21.1001i	0.987023	−	0.987023i	0.999917	+	0.0128943i	$0.00410450\pi$
$458$			27.0703i			1.26491i
$459$		−	4.49445i		−	0.209783i
$460$	0.323409	+	0.323409i	0.0150790	+	0.0150790i
$461$	0.542495	+	0.542495i	0.0252665	+	0.0252665i	0.719627	−	0.694361i	$-0.244313\pi$
$461$	0.542495	+	0.542495i	0.0252665	+	0.0252665i	−0.694361	+	0.719627i	$0.744313\pi$
$462$	−3.02035	−	4.86060i	−0.140519	−	0.226136i
$463$	−10.7562	−	10.7562i	−0.499882	−	0.499882i	0.411519	−	0.911401i	$-0.364998\pi$
$463$	−10.7562	−	10.7562i	−0.499882	−	0.499882i	−0.911401	+	0.411519i	$0.864998\pi$
$464$	111.880			5.19389
$465$	0.0748203			0.00346971
$466$	37.6044	+	37.6044i	1.74199	+	1.74199i
$467$	−31.8438			−1.47356			−0.736778	−	0.676135i	$-0.763654\pi$
$467$	−31.8438			−1.47356			−0.736778	+	0.676135i	$0.763654\pi$
$468$	17.3903	−	10.0973i	0.803867	−	0.466749i
$469$	−0.712719	+	3.05225i	−0.0329103	+	0.140940i
$470$	2.52950	−	2.52950i	0.116677	−	0.116677i
$471$	−18.1301			−0.835393
$472$	−9.63224			−0.443360
$473$	−1.03748	+	1.03748i	−0.0477035	+	0.0477035i
$474$	21.3676	+	21.3676i	0.981444	+	0.981444i
$475$	−20.6111	+	20.6111i	−0.945702	+	0.945702i
$476$	−35.0037	−	56.3309i	−1.60439	−	2.58192i
$477$	4.31687			0.197656
$478$		−	56.4427i		−	2.58163i
$479$	−3.51478	+	3.51478i	−0.160595	+	0.160595i	−0.782830	−	0.622236i	$-0.786225\pi$
$479$	−3.51478	+	3.51478i	−0.160595	+	0.160595i	0.622236	+	0.782830i	$0.286225\pi$
$480$		−	4.68363i		−	0.213778i
$481$	7.52319	−	28.3553i	0.343028	−	1.29289i
$482$			19.9196i			0.907311i
$483$	−0.952789	+	0.592057i	−0.0433534	+	0.0269395i
$484$	−57.9066			−2.63212
$485$			0.872808i			0.0396322i
$486$	1.94644	+	1.94644i	0.0882924	+	0.0882924i
$487$	−3.57589	+	3.57589i	−0.162039	+	0.162039i	−0.783469	−	0.621430i	$-0.786552\pi$
$487$	−3.57589	+	3.57589i	−0.162039	+	0.162039i	0.621430	+	0.783469i	$0.286552\pi$
$488$	56.5350	−	56.5350i	2.55922	−	2.55922i
$489$	−0.674757	+	0.674757i	−0.0305136	+	0.0305136i
$490$	−1.65052	+	3.34151i	−0.0745630	+	0.150954i
$491$		−	4.24758i		−	0.191691i	−0.995396	−	0.0958453i	$-0.969445\pi$
$491$		−	4.24758i		−	0.191691i	0.995396	−	0.0958453i	$-0.0305554\pi$
$492$	40.6658	+	40.6658i	1.83336	+	1.83336i
$493$	31.5230			1.41972
$494$	−29.2718	−	50.4138i	−1.31700	−	2.26822i
$495$		−	0.151978i		−	0.00683091i
$496$	−4.36326	−	4.36326i	−0.195916	−	0.195916i
$497$	−0.855240	+	3.66259i	−0.0383627	+	0.164290i
$498$			26.9100i			1.20586i
$499$	−3.69487	+	3.69487i	−0.165405	+	0.165405i	−0.784956	−	0.619551i	$-0.787315\pi$
$499$	−3.69487	+	3.69487i	−0.165405	+	0.165405i	0.619551	+	0.784956i	$0.287315\pi$
$500$	−7.59932	−	7.59932i	−0.339852	−	0.339852i
$501$	5.13896	+	5.13896i	0.229592	+	0.229592i
$502$	31.0972	−	31.0972i	1.38793	−	1.38793i
$503$		−	16.9237i		−	0.754591i	−0.926093	−	0.377296i	$-0.876854\pi$
$503$		−	16.9237i		−	0.754591i	0.926093	−	0.377296i	$-0.123146\pi$
$504$	25.3706	+	5.92419i	1.13010	+	0.263885i
$505$	1.28584	+	1.28584i	0.0572192	+	0.0572192i
$506$		−	0.917050i		−	0.0407679i
$507$	11.2901	+	6.44461i	0.501412	+	0.286215i
$508$	−16.6077			−0.736848
$509$	25.1102	+	25.1102i	1.11299	+	1.11299i	0.992744	+	0.120244i	$0.0383677\pi$
$509$	25.1102	+	25.1102i	1.11299	+	1.11299i	0.120244	+	0.992744i	$0.461632\pi$
$510$		−	2.39292i		−	0.105960i
$511$	5.80131	−	24.8443i	0.256635	−	1.09905i
$512$	−50.9936	+	50.9936i	−2.25362	+	2.25362i
$513$	4.15330	−	4.15330i	0.183373	−	0.183373i
$514$	20.1468	−	20.1468i	0.888638	−	0.888638i
$515$	0.251688	+	0.251688i	0.0110907	+	0.0110907i
$516$		−	10.4143i		−	0.458466i
$517$	−5.27940			−0.232188
$518$	50.3313	−	31.2756i	2.21143	−	1.37417i
$519$		−	0.655393i		−	0.0287686i
$520$	5.93867	−	3.44817i	0.260428	−	0.151212i
$521$			6.34020i			0.277769i	0.990309	+	0.138885i	$0.0443517\pi$
$521$			6.34020i			0.277769i	−0.990309	+	0.138885i	$0.955648\pi$
$522$	−13.6519	+	13.6519i	−0.597526	+	0.597526i
$523$		−	2.80026i		−	0.122447i	−0.998124	−	0.0612234i	$-0.980500\pi$
$523$		−	2.80026i		−	0.122447i	0.998124	−	0.0612234i	$-0.0195002\pi$
$524$	97.2161			4.24690
$525$	11.1521	−	6.92983i	0.486716	−	0.302442i
$526$	21.2775	−	21.2775i	0.927743	−	0.927743i
$527$	−1.22938	−	1.22938i	−0.0535527	−	0.0535527i
$528$	−8.86284	+	8.86284i	−0.385706	+	0.385706i
$529$	22.8202			0.992184
$530$	2.29837			0.0998349
$531$	0.691676	−	0.691676i	0.0300162	−	0.0300162i
$532$	19.7083	−	84.4017i	0.854465	−	3.65928i
$533$	−9.53430	+	35.9353i	−0.412976	+	1.55653i
$534$	25.1800			1.08964
$535$	1.35196	+	1.35196i	0.0584501	+	0.0584501i
$536$	11.6656			0.503879
$537$	−23.7340			−1.02420
$538$	1.73317	+	1.73317i	0.0747223	+	0.0747223i
$539$	5.20952	−	1.76466i	0.224390	−	0.0760091i
$540$	0.762785	+	0.762785i	0.0328250	+	0.0328250i
$541$	1.50569	+	1.50569i	0.0647345	+	0.0647345i	0.738733	−	0.673998i	$-0.235425\pi$
$541$	1.50569	+	1.50569i	0.0647345	+	0.0647345i	−0.673998	+	0.738733i	$0.735425\pi$
$542$			59.5347i			2.55723i
$543$		−	7.42950i		−	0.318830i
$544$	−76.9574	+	76.9574i	−3.29952	+	3.29952i
$545$	−2.67085			−0.114407
$546$	7.67619	+	25.1119i	0.328511	+	1.07469i
$547$	−2.65090			−0.113344			−0.0566722	−	0.998393i	$-0.518049\pi$
$547$	−2.65090			−0.113344			−0.0566722	+	0.998393i	$0.518049\pi$
$548$	−41.5300	+	41.5300i	−1.77407	+	1.77407i
$549$			8.11937i			0.346526i
$550$			10.7338i			0.457689i
$551$	29.1302	+	29.1302i	1.24099	+	1.24099i
$552$	2.95219	+	2.95219i	0.125654	+	0.125654i
$553$	−24.6695	+	15.3295i	−1.04905	+	0.651875i
$554$	19.1361	+	19.1361i	0.813013	+	0.813013i
$555$	1.57373			0.0668010
$556$	104.538			4.43342
$557$	−1.67493	−	1.67493i	−0.0709691	−	0.0709691i	0.670731	−	0.741700i	$-0.265980\pi$
$557$	−1.67493	−	1.67493i	−0.0709691	−	0.0709691i	−0.741700	+	0.670731i	$0.765980\pi$
$558$	1.06483			0.0450780
$559$	5.82229	−	3.38060i	0.246257	−	0.142984i
$560$	7.94908	+	1.85616i	0.335910	+	0.0784371i
$561$	−2.49717	+	2.49717i	−0.105431	+	0.105431i
$562$	50.0336			2.11054
$563$	−27.1654			−1.14489			−0.572443	−	0.819945i	$-0.694004\pi$
$563$	−27.1654			−1.14489			−0.572443	+	0.819945i	$0.694004\pi$
$564$	26.4976	−	26.4976i	1.11575	−	1.11575i
$565$	−1.36321	−	1.36321i	−0.0573506	−	0.0573506i
$566$	4.39447	−	4.39447i	0.184713	−	0.184713i
$567$	−2.24723	+	1.39641i	−0.0943747	+	0.0586439i
$568$	13.9984			0.587359
$569$			12.5703i			0.526973i	0.964663	+	0.263487i	$0.0848725\pi$
$569$			12.5703i			0.526973i	−0.964663	+	0.263487i	$0.915127\pi$
$570$	2.21128	−	2.21128i	0.0926205	−	0.0926205i
$571$		−	19.6741i		−	0.823334i	−0.911334	−	0.411667i	$-0.864947\pi$
$571$		−	19.6741i		−	0.823334i	0.911334	−	0.411667i	$-0.135053\pi$
$572$	−15.2725	−	4.05206i	−0.638574	−	0.169425i
$573$		−	19.3050i		−	0.806478i
$574$	−63.7860	+	39.6362i	−2.66238	+	1.65438i
$575$	2.10406			0.0877454
$576$		−	34.7539i		−	1.44808i
$577$	−11.0080	−	11.0080i	−0.458271	−	0.458271i	0.439817	−	0.898087i	$-0.355043\pi$
$577$	−11.0080	−	11.0080i	−0.458271	−	0.458271i	−0.898087	+	0.439817i	$0.855043\pi$
$578$	−6.22885	+	6.22885i	−0.259086	+	0.259086i
$579$	5.06291	−	5.06291i	0.210407	−	0.210407i
$580$	−5.34998	+	5.34998i	−0.222146	+	0.222146i
$581$	−25.1870	−	5.88133i	−1.04493	−	0.243999i
$582$			12.4217i			0.514896i
$583$	−2.39851	−	2.39851i	−0.0993359	−	0.0993359i
$584$	−94.9546			−3.92925
$585$	−0.178839	+	0.674054i	−0.00739408	+	0.0278687i
$586$			13.3299i			0.550653i
$587$	−21.5168	−	21.5168i	−0.888093	−	0.888093i	0.106247	−	0.994340i	$-0.466117\pi$
$587$	−21.5168	−	21.5168i	−0.888093	−	0.888093i	−0.994340	+	0.106247i	$0.966117\pi$
$588$	−17.2899	+	35.0037i	−0.713023	+	1.44353i
$589$		−	2.27213i		−	0.0936214i
$590$	0.368260	−	0.368260i	0.0151610	−	0.0151610i
$591$	−11.0333	−	11.0333i	−0.453851	−	0.453851i
$592$	−91.7744	−	91.7744i	−3.77190	−	3.77190i
$593$	27.5375	−	27.5375i	1.13083	−	1.13083i	0.140792	−	0.990039i	$-0.455035\pi$
$593$	27.5375	−	27.5375i	1.13083	−	1.13083i	0.990039	−	0.140792i	$-0.0449649\pi$
$594$		−	2.16293i		−	0.0887463i
$595$	2.23971	+	0.522987i	0.0918193	+	0.0214404i
$596$	42.2164	+	42.2164i	1.72925	+	1.72925i
$597$		−	12.6458i		−	0.517558i
$598$	−1.07913	+	4.06730i	−0.0441289	+	0.166324i
$599$	40.3864			1.65014			0.825072	−	0.565028i	$-0.191134\pi$
$599$	40.3864			1.65014			0.825072	+	0.565028i	$0.191134\pi$
$600$	−34.5544	−	34.5544i	−1.41068	−	1.41068i
$601$			44.9596i			1.83394i	0.398957	+	0.916969i	$0.369372\pi$
$601$			44.9596i			1.83394i	−0.398957	+	0.916969i	$0.630628\pi$
$602$	13.2430	+	3.09233i	0.539745	+	0.126034i
$603$	−0.837691	+	0.837691i	−0.0341134	+	0.0341134i
$604$	−53.1147	+	53.1147i	−2.16121	+	2.16121i
$605$	1.41999	−	1.41999i	0.0577308	−	0.0577308i
$606$	18.2999	+	18.2999i	0.743384	+	0.743384i
$607$		−	18.1530i		−	0.736807i	−0.929666	−	0.368403i	$-0.879904\pi$
$607$		−	18.1530i		−	0.736807i	0.929666	−	0.368403i	$-0.120096\pi$
$608$	−142.232			−5.76825
$609$	−9.79409	−	15.7615i	−0.396877	−	0.638688i
$610$			4.32289i			0.175029i
$611$	23.4152	+	6.21248i	0.947278	+	0.251330i
$612$		−	25.0668i		−	1.01327i
$613$	23.5436	−	23.5436i	0.950917	−	0.950917i	−0.0479336	−	0.998851i	$-0.515264\pi$
$613$	23.5436	−	23.5436i	0.950917	−	0.950917i	0.998851	+	0.0479336i	$0.0152636\pi$
$614$		−	43.6002i		−	1.75956i
$615$	−1.99442			−0.0804227
$616$	−10.8046	−	17.3877i	−0.435331	−	0.700572i
$617$	−18.3137	+	18.3137i	−0.737283	+	0.737283i	−0.972051	−	0.234768i	$-0.924567\pi$
$617$	−18.3137	+	18.3137i	−0.737283	+	0.737283i	0.234768	+	0.972051i	$0.424567\pi$
$618$	3.58199	+	3.58199i	0.144089	+	0.144089i
$619$	7.94244	−	7.94244i	0.319234	−	0.319234i	−0.529239	−	0.848473i	$-0.677523\pi$
$619$	7.94244	−	7.94244i	0.319234	−	0.319234i	0.848473	+	0.529239i	$0.177523\pi$
$620$	0.417294			0.0167589
$621$	−0.423984			−0.0170139
$622$	−36.2061	+	36.2061i	−1.45173	+	1.45173i
$623$	−5.50323	+	23.5678i	−0.220482	+	0.944224i
$624$	49.7378	−	28.8792i	1.99110	−	1.15609i
$625$	−24.4402			−0.977610
$626$	61.7374	+	61.7374i	2.46752	+	2.46752i
$627$	−4.61524			−0.184315
$628$	−101.117			−4.03500
$629$	−25.8581	−	25.8581i	−1.03103	−	1.03103i
$630$	−1.19646	+	0.743473i	−0.0476681	+	0.0296207i
$631$	4.98693	+	4.98693i	0.198527	+	0.198527i	0.799368	−	0.600842i	$-0.205168\pi$
$631$	4.98693	+	4.98693i	0.198527	+	0.198527i	−0.600842	+	0.799368i	$0.705168\pi$
$632$	76.4377	+	76.4377i	3.04053	+	3.04053i
$633$			19.1491i			0.761108i
$634$		−	37.1749i		−	1.47640i
$635$	0.407256	−	0.407256i	0.0161614	−	0.0161614i
$636$	24.0764			0.954691
$637$	−25.1818	+	1.69636i	−0.997739	+	0.0672121i
$638$	15.1703			0.600597
$639$	−1.00520	+	1.00520i	−0.0397652	+	0.0397652i
$640$		−	9.13626i		−	0.361142i
$641$		−	15.8095i		−	0.624437i	−0.950010	−	0.312219i	$-0.898928\pi$
$641$		−	15.8095i		−	0.624437i	0.950010	−	0.312219i	$-0.101072\pi$
$642$	19.2409	+	19.2409i	0.759376	+	0.759376i
$643$	16.3789	+	16.3789i	0.645922	+	0.645922i	0.952005	−	0.306083i	$-0.0990186\pi$
$643$	16.3789	+	16.3789i	0.645922	+	0.645922i	−0.306083	+	0.952005i	$0.599019\pi$
$644$	−5.31397	+	3.30207i	−0.209400	+	0.130120i
$645$	0.255381	+	0.255381i	0.0100556	+	0.0100556i
$646$	−72.6677			−2.85907
$647$	−15.4382			−0.606939			−0.303469	−	0.952841i	$-0.598145\pi$
$647$	−15.4382			−0.606939			−0.303469	+	0.952841i	$0.598145\pi$
$648$	6.96297	+	6.96297i	0.273531	+	0.273531i
$649$	−0.768607			−0.0301705
$650$	12.6308	−	47.6064i	0.495422	−	1.86727i
$651$	−0.232726	+	0.996656i	−0.00912124	+	0.0390620i
$652$	−3.76331	+	3.76331i	−0.147383	+	0.147383i
$653$	−46.5139			−1.82023			−0.910114	−	0.414358i	$-0.864006\pi$
$653$	−46.5139			−1.82023			−0.910114	+	0.414358i	$0.864006\pi$
$654$	−38.0112			−1.48636
$655$	−2.38394	+	2.38394i	−0.0931483	+	0.0931483i
$656$	116.308	+	116.308i	4.54105	+	4.54105i
$657$	6.81854	−	6.81854i	0.266017	−	0.266017i
$658$	25.8267	+	41.5625i	1.00683	+	1.62028i
$659$	22.5967			0.880243			0.440121	−	0.897938i	$-0.354935\pi$
$659$	22.5967			0.880243			0.440121	+	0.897938i	$0.354935\pi$
$660$		−	0.847625i		−	0.0329938i
$661$	−23.1578	+	23.1578i	−0.900733	+	0.900733i	−0.995499	−	0.0947669i	$-0.969789\pi$
$661$	−23.1578	+	23.1578i	−0.900733	+	0.900733i	0.0947669	+	0.995499i	$0.469789\pi$
$662$		−	48.0747i		−	1.86848i
$663$	14.0140	−	8.13694i	0.544258	−	0.316013i
$664$			96.2644i			3.73579i
$665$	1.58641	+	2.55299i	0.0615185	+	0.0990008i
$666$	22.3971			0.867870
$667$		−	2.97372i		−	0.115143i
$668$	28.6614	+	28.6614i	1.10894	+	1.10894i
$669$	3.78445	−	3.78445i	0.146315	−	0.146315i
$670$	−0.446000	+	0.446000i	−0.0172305	+	0.0172305i
$671$	4.51122	−	4.51122i	0.174154	−	0.174154i
$672$	62.3891	+	14.5683i	2.40671	+	0.561983i
$673$		−	16.3686i		−	0.630961i	−0.948932	−	0.315481i	$-0.897834\pi$
$673$		−	16.3686i		−	0.630961i	0.948932	−	0.315481i	$-0.102166\pi$
$674$	−48.3726	−	48.3726i	−1.86324	−	1.86324i
$675$	4.96259			0.191010
$676$	62.9682	+	35.9434i	2.42185	+	1.38244i
$677$			42.4344i			1.63089i	0.578836	+	0.815444i	$0.303507\pi$
$677$			42.4344i			1.63089i	−0.578836	+	0.815444i	$0.696493\pi$
$678$	−19.4010	−	19.4010i	−0.745091	−	0.745091i
$679$	−11.6264	−	2.71484i	−0.446180	−	0.104186i
$680$		−	8.56015i		−	0.328267i
$681$	−12.8654	+	12.8654i	−0.493004	+	0.493004i
$682$	−0.591634	−	0.591634i	−0.0226548	−	0.0226548i
$683$	17.5222	+	17.5222i	0.670468	+	0.670468i	0.957824	−	0.287356i	$-0.0927762\pi$
$683$	17.5222	+	17.5222i	0.670468	+	0.670468i	−0.287356	+	0.957824i	$0.592776\pi$
$684$	23.1641	−	23.1641i	0.885701	−	0.885701i
$685$		−	2.03680i		−	0.0778222i
$686$	−39.3772	−	32.3797i	−1.50343	−	1.23626i
$687$	−6.95379	−	6.95379i	−0.265304	−	0.265304i
$688$		−	29.7859i		−	1.13558i
$689$	7.81543	+	13.4603i	0.297744	+	0.512795i
$690$	−0.225736			−0.00859363
$691$	−23.9437	−	23.9437i	−0.910860	−	0.910860i	0.0854795	−	0.996340i	$-0.472758\pi$
$691$	−23.9437	−	23.9437i	−0.910860	−	0.910860i	−0.996340	+	0.0854795i	$0.972758\pi$
$692$		−	3.65531i		−	0.138954i
$693$	2.02445	+	0.472722i	0.0769025	+	0.0179572i
$694$	30.2050	−	30.2050i	1.14657	−	1.14657i
$695$	−2.56350	+	2.56350i	−0.0972390	+	0.0972390i
$696$	−48.8365	+	48.8365i	−1.85114	+	1.85114i
$697$	32.7705	+	32.7705i	1.24127	+	1.24127i
$698$			33.7797i			1.27858i
$699$	−19.3196			−0.730733
$700$	62.1982	−	38.6496i	2.35087	−	1.46082i
$701$		−	11.2063i		−	0.423255i	−0.977350	−	0.211628i	$-0.932124\pi$
$701$		−	11.2063i		−	0.423255i	0.977350	−	0.211628i	$-0.0678764\pi$
$702$	−2.54521	+	9.59305i	−0.0960628	+	0.362066i
$703$		−	47.7906i		−	1.80246i
$704$	−19.3097	+	19.3097i	−0.727760	+	0.727760i
$705$			1.29955i			0.0489439i
$706$	96.6240			3.63649
$707$	−21.1278	+	13.1287i	−0.794593	+	0.493756i
$708$	3.85767	−	3.85767i	0.144980	−	0.144980i
$709$	−9.73998	−	9.73998i	−0.365793	−	0.365793i	0.500148	−	0.865940i	$-0.333279\pi$
$709$	−9.73998	−	9.73998i	−0.365793	−	0.365793i	−0.865940	+	0.500148i	$0.833279\pi$
$710$	−0.535186	+	0.535186i	−0.0200852	+	0.0200852i
$711$	−10.9777			−0.411698
$712$	90.0758			3.37573
$713$	−0.115974	+	0.115974i	−0.00434325	+	0.00434325i
$714$	31.8753	+	7.44309i	1.19290	+	0.278551i
$715$	0.473877	−	0.275147i	0.0177220	−	0.0102899i
$716$	−132.371			−4.94695
$717$	14.4989	+	14.4989i	0.541473	+	0.541473i
$718$	34.8485			1.30053
$719$	8.87534			0.330994			0.165497	−	0.986210i	$-0.447077\pi$
$719$	8.87534			0.330994			0.165497	+	0.986210i	$0.447077\pi$
$720$	2.18163	+	2.18163i	0.0813046	+	0.0813046i
$721$	−4.13551	+	2.56978i	−0.154015	+	0.0957037i
$722$	−30.1694	−	30.1694i	−1.12279	−	1.12279i
$723$	−5.11691	−	5.11691i	−0.190300	−	0.190300i
$724$		−	41.4364i		−	1.53997i
$725$			34.8064i			1.29268i
$726$	20.2091	−	20.2091i	0.750031	−	0.750031i
$727$	0.610509			0.0226425			0.0113213	−	0.999936i	$-0.496396\pi$
$727$	0.610509			0.0226425			0.0113213	+	0.999936i	$0.496396\pi$
$728$	27.4599	+	89.8324i	1.01773	+	3.32941i
$729$	−1.00000			−0.0370370
$730$	3.63030	−	3.63030i	0.134364	−	0.134364i
$731$		−	8.39241i		−	0.310404i
$732$			45.2840i			1.67375i
$733$	−20.8483	−	20.8483i	−0.770051	−	0.770051i	0.208064	−	0.978115i	$-0.433284\pi$
$733$	−20.8483	−	20.8483i	−0.770051	−	0.770051i	−0.978115	+	0.208064i	$0.933284\pi$
$734$	−40.9634	−	40.9634i	−1.51199	−	1.51199i
$735$	−0.434378	−	1.28235i	−0.0160223	−	0.0473001i
$736$	7.25977	+	7.25977i	0.267599	+	0.267599i
$737$	0.930862			0.0342888
$738$	−28.3843			−1.04484
$739$	−4.86809	−	4.86809i	−0.179076	−	0.179076i	0.611877	−	0.790953i	$-0.290415\pi$
$739$	−4.86809	−	4.86809i	−0.179076	−	0.179076i	−0.790953	+	0.611877i	$0.790415\pi$
$740$	8.77712			0.322653
$741$	20.4695	+	5.43094i	0.751967	+	0.199511i
$742$	−7.14900	+	30.6158i	−0.262448	+	1.12394i
$743$	−1.97638	+	1.97638i	−0.0725063	+	0.0725063i	−0.742430	−	0.669924i	$-0.766327\pi$
$743$	−1.97638	+	1.97638i	−0.0725063	+	0.0725063i	0.669924	+	0.742430i	$0.266327\pi$
$744$	3.80921			0.139652
$745$	−2.07047			−0.0758561
$746$	34.3389	−	34.3389i	1.25724	−	1.25724i
$747$	−6.91260	−	6.91260i	−0.252919	−	0.252919i
$748$	−13.9274	+	13.9274i	−0.509237	+	0.509237i
$749$	−22.2142	+	13.8037i	−0.811687	+	0.504378i
$750$	5.30425			0.193684
$751$		−	12.9526i		−	0.472649i	−0.971674	−	0.236324i	$-0.924057\pi$
$751$		−	12.9526i		−	0.472649i	0.971674	−	0.236324i	$-0.0759428\pi$
$752$	75.7853	−	75.7853i	2.76360	−	2.76360i
$753$			15.9764i			0.582213i
$754$	−67.2832	−	17.8515i	−2.45031	−	0.650112i
$755$		−	2.60497i		−	0.0948044i
$756$	−12.5334	+	7.78819i	−0.455836	+	0.283254i
$757$	29.8979			1.08666			0.543328	−	0.839520i	$-0.317164\pi$
$757$	29.8979			1.08666			0.543328	+	0.839520i	$0.317164\pi$
$758$		−	17.3346i		−	0.629619i
$759$	0.235571	+	0.235571i	0.00855068	+	0.00855068i
$760$	7.91038	−	7.91038i	0.286940	−	0.286940i
$761$	−9.08532	+	9.08532i	−0.329343	+	0.329343i	−0.852336	−	0.522994i	$-0.824815\pi$
$761$	−9.08532	+	9.08532i	−0.329343	+	0.329343i	0.522994	+	0.852336i	$0.324815\pi$
$762$	5.79601	−	5.79601i	0.209967	−	0.209967i
$763$	8.30758	−	35.5775i	0.300755	−	1.28799i
$764$		−	107.669i		−	3.89534i
$765$	0.614691	+	0.614691i	0.0222242	+	0.0222242i
$766$	−35.4329			−1.28024
$767$	3.40892	+	0.904450i	0.123089	+	0.0326578i
$768$		−	60.5183i		−	2.18377i
$769$	−15.5692	−	15.5692i	−0.561441	−	0.561441i	0.368275	−	0.929717i	$-0.379948\pi$
$769$	−15.5692	−	15.5692i	−0.561441	−	0.561441i	−0.929717	+	0.368275i	$0.879948\pi$
$770$	1.07785	+	0.251685i	0.0388430	+	0.00907010i
$771$			10.3506i			0.372767i
$772$	28.2373	−	28.2373i	1.01628	−	1.01628i
$773$	−4.63232	−	4.63232i	−0.166613	−	0.166613i	0.618876	−	0.785489i	$-0.287588\pi$
$773$	−4.63232	−	4.63232i	−0.166613	−	0.166613i	−0.785489	+	0.618876i	$0.787588\pi$
$774$	3.63455	+	3.63455i	0.130641	+	0.130641i
$775$	1.35743	−	1.35743i	0.0487604	−	0.0487604i
$776$			44.4359i			1.59515i
$777$	−4.89502	+	20.9631i	−0.175608	+	0.752047i
$778$	−10.6789	−	10.6789i	−0.382859	−	0.382859i
$779$			60.5661i			2.17001i
$780$	−0.997434	+	3.75939i	−0.0357139	+	0.134608i
$781$	1.11700			0.0399696
$782$	3.70910	+	3.70910i	0.132637	+	0.132637i
$783$		−	7.01375i		−	0.250651i
$784$	−49.4506	+	100.113i	−1.76609	+	3.57548i
$785$	2.47960	−	2.47960i	0.0885006	−	0.0885006i
$786$	−33.9279	+	33.9279i	−1.21017	+	1.21017i
$787$	−13.9297	+	13.9297i	−0.496539	+	0.496539i	−0.910359	−	0.413820i	$-0.864194\pi$
$787$	−13.9297	+	13.9297i	−0.496539	+	0.496539i	0.413820	+	0.910359i	$0.364194\pi$
$788$	−61.5360	−	61.5360i	−2.19213	−	2.19213i
$789$			10.9315i			0.389171i
$790$	−5.84473			−0.207946
$791$	22.3990	−	13.9186i	0.796418	−	0.494889i
$792$		−	7.73742i		−	0.274937i
$793$	−25.3167	+	14.6996i	−0.899022	+	0.521999i
$794$		−	83.3184i		−	2.95686i
$795$	−0.590403	+	0.590403i	−0.0209394	+	0.0209394i
$796$		−	70.5291i		−	2.49984i
$797$	5.31507			0.188270			0.0941348	−	0.995559i	$-0.469992\pi$
$797$	5.31507			0.188270			0.0941348	+	0.995559i	$0.469992\pi$
$798$	22.5776	+	36.3339i	0.799240	+	1.28620i
$799$	21.3531	−	21.3531i	0.755417	−	0.755417i
$800$	−84.9731	−	84.9731i	−3.00425	−	3.00425i
$801$	−6.46820	+	6.46820i	−0.228543	+	0.228543i
$802$	4.27045			0.150795
$803$	−7.57693			−0.267384
$804$	−4.67204	+	4.67204i	−0.164770	+	0.164770i
$805$	0.0493360	−	0.211283i	0.00173887	−	0.00744676i
$806$	1.92782	+	3.32021i	0.0679044	+	0.116950i
$807$	−0.890429			−0.0313446
$808$	65.4640	+	65.4640i	2.30301	+	2.30301i
$809$	19.9739			0.702243			0.351122	−	0.936330i	$-0.385800\pi$
$809$	19.9739			0.702243			0.351122	+	0.936330i	$0.385800\pi$
$810$	−0.532416			−0.0187072
$811$	−16.2355	−	16.2355i	−0.570105	−	0.570105i	0.362053	−	0.932158i	$-0.382076\pi$
$811$	−16.2355	−	16.2355i	−0.570105	−	0.570105i	−0.932158	+	0.362053i	$0.882076\pi$
$812$	−54.6244	−	87.9062i	−1.91694	−	3.08490i
$813$	−15.2932	−	15.2932i	−0.536356	−	0.536356i
$814$	−12.4441	−	12.4441i	−0.436165	−	0.436165i
$815$		−	0.184568i		−	0.00646514i
$816$		−	71.6933i		−	2.50977i
$817$	7.75537	−	7.75537i	0.271326	−	0.271326i
$818$	−38.2960			−1.33899
$819$	−8.42257	−	4.47887i	−0.294309	−	0.156504i
$820$	−11.1234			−0.388447
$821$	−13.7431	+	13.7431i	−0.479638	+	0.479638i	−0.905016	−	0.425378i	$-0.860141\pi$
$821$	−13.7431	+	13.7431i	−0.479638	+	0.479638i	0.425378	+	0.905016i	$0.360141\pi$
$822$		−	28.9875i		−	1.01106i
$823$		−	37.8629i		−	1.31982i	−0.751345	−	0.659909i	$-0.770595\pi$
$823$		−	37.8629i		−	1.31982i	0.751345	−	0.659909i	$-0.229405\pi$
$824$	12.8138	+	12.8138i	0.446389	+	0.446389i
$825$	−2.75727	−	2.75727i	−0.0959960	−	0.0959960i
$826$	3.76000	+	6.05092i	0.130827	+	0.210538i
$827$	−22.6682	−	22.6682i	−0.788252	−	0.788252i	0.192956	−	0.981207i	$-0.438193\pi$
$827$	−22.6682	−	22.6682i	−0.788252	−	0.788252i	−0.981207	+	0.192956i	$0.938193\pi$
$828$	−2.36468			−0.0821783
$829$	33.7537			1.17231			0.586156	−	0.810198i	$-0.300640\pi$
$829$	33.7537			1.17231			0.586156	+	0.810198i	$0.300640\pi$
$830$	−3.68038	−	3.68038i	−0.127748	−	0.127748i
$831$	−9.83129			−0.341044
$832$	108.365	−	62.9198i	3.75687	−	2.18135i
$833$	−13.9331	+	28.2077i	−0.482752	+	0.977339i
$834$	−36.4834	+	36.4834i	−1.26332	+	1.26332i
$835$	−1.40568			−0.0486454
$836$	−25.7405			−0.890254
$837$	−0.273533	+	0.273533i	−0.00945468	+	0.00945468i
$838$	29.6711	+	29.6711i	1.02497	+	1.02497i
$839$	29.1042	−	29.1042i	1.00479	−	1.00479i	0.00479972	−	0.999988i	$-0.498472\pi$
$839$	29.1042	−	29.1042i	1.00479	−	1.00479i	0.999988	−	0.00479972i	$-0.00152780\pi$
$840$	−4.28008	+	2.65961i	−0.147677	+	0.0917654i
$841$	20.1927			0.696299
$842$		−	26.5291i		−	0.914254i
$843$	−12.8526	+	12.8526i	−0.442666	+	0.442666i
$844$			106.800i			3.67620i
$845$	−2.42552	+	0.662704i	−0.0834404	+	0.0227977i
$846$			18.4950i			0.635872i
$847$	14.4984	+	23.3320i	0.498171	+	0.801698i
$848$	68.8605			2.36468
$849$			2.25769i			0.0774838i
$850$	−43.4137	−	43.4137i	−1.48908	−	1.48908i
$851$	−2.43932	+	2.43932i	−0.0836190	+	0.0836190i
$852$	−5.60629	+	5.60629i	−0.192068	+	0.192068i
$853$	−9.97247	+	9.97247i	−0.341451	+	0.341451i	−0.856913	−	0.515462i	$-0.827620\pi$
$853$	−9.97247	+	9.97247i	−0.341451	+	0.341451i	0.515462	+	0.856913i	$0.327620\pi$
$854$	−57.5837	−	13.4462i	−1.97047	−	0.460118i
$855$			1.13606i			0.0388526i
$856$	68.8300	+	68.8300i	2.35256	+	2.35256i
$857$	20.2894			0.693071			0.346536	−	0.938037i	$-0.387358\pi$
$857$	20.2894			0.693071			0.346536	+	0.938037i	$0.387358\pi$
$858$	6.74416	−	3.91586i	0.230242	−	0.133685i
$859$			1.65917i			0.0566102i	0.999599	+	0.0283051i	$0.00901100\pi$
$859$			1.65917i			0.0566102i	−0.999599	+	0.0283051i	$0.990989\pi$
$860$	1.42433	+	1.42433i	0.0485694	+	0.0485694i
$861$	6.20356	−	26.5670i	0.211417	−	0.905400i
$862$			61.5550i			2.09657i
$863$	17.5175	−	17.5175i	0.596303	−	0.596303i	−0.343024	−	0.939327i	$-0.611451\pi$
$863$	17.5175	−	17.5175i	0.596303	−	0.596303i	0.939327	+	0.343024i	$0.111451\pi$
$864$	17.1227	+	17.1227i	0.582527	+	0.582527i
$865$	0.0896359	+	0.0896359i	0.00304771	+	0.00304771i
$866$	−25.8621	+	25.8621i	−0.878830	+	0.878830i
$867$		−	3.20012i		−	0.108682i
$868$	−1.29798	+	5.55863i	−0.0440562	+	0.188672i
$869$	6.09937	+	6.09937i	0.206907	+	0.206907i
$870$		−	3.73423i		−	0.126602i
$871$	−4.12856	−	1.09538i	−0.139891	−	0.0371156i
$872$	−135.977			−4.60475
$873$	−3.19087	−	3.19087i	−0.107995	−	0.107995i
$874$			6.85511i			0.231878i
$875$	−1.15928	+	4.96464i	−0.0391906	+	0.167835i
$876$	38.0289	−	38.0289i	1.28488	−	1.28488i
$877$	18.6974	−	18.6974i	0.631366	−	0.631366i	−0.317044	−	0.948411i	$-0.602690\pi$
$877$	18.6974	−	18.6974i	0.631366	−	0.631366i	0.948411	+	0.317044i	$0.102690\pi$
$878$	2.87316	−	2.87316i	0.0969645	−	0.0969645i
$879$	−3.42417	−	3.42417i	−0.115494	−	0.115494i
$880$		−	2.42428i		−	0.0817225i
$881$	−21.0446			−0.709009			−0.354505	−	0.935054i	$-0.615350\pi$
$881$	−21.0446			−0.709009			−0.354505	+	0.935054i	$0.615350\pi$
$882$	−6.18201	−	18.2502i	−0.208159	−	0.614516i
$883$			54.5106i			1.83443i	0.398395	+	0.917214i	$0.369567\pi$
$883$			54.5106i			1.83443i	−0.398395	+	0.917214i	$0.630433\pi$
$884$	78.1599	−	45.3820i	2.62880	−	1.52636i
$885$			0.189196i			0.00635976i
$886$	−0.974984	+	0.974984i	−0.0327552	+	0.0327552i
$887$		−	19.8555i		−	0.666682i	−0.942806	−	0.333341i	$-0.891824\pi$
$887$		−	19.8555i		−	0.666682i	0.942806	−	0.333341i	$-0.108176\pi$
$888$	80.1207			2.68867
$889$	4.15816	+	6.69167i	0.139460	+	0.224431i
$890$	−3.44378	+	3.44378i	−0.115436	+	0.115436i
$891$	0.555612	+	0.555612i	0.0186137	+	0.0186137i
$892$	21.1070	−	21.1070i	0.706713	−	0.706713i
$893$	39.4645			1.32063
$894$	−29.4667			−0.985512
$895$	3.24602	−	3.24602i	0.108503	−	0.108503i
$896$	121.701	+	28.4180i	4.06575	+	0.949378i
$897$	−0.767598	−	1.32201i	−0.0256294	−	0.0441406i
$898$	6.04031			0.201568
$899$	−1.91849	−	1.91849i	−0.0639853	−	0.0639853i
$900$	27.6778			0.922592
$901$	19.4020			0.646374
$902$	15.7707	+	15.7707i	0.525106	+	0.525106i
$903$	−4.19620	+	2.60750i	−0.139641	+	0.0867720i
$904$	−69.4028	−	69.4028i	−2.30830	−	2.30830i
$905$	1.01611	+	1.01611i	0.0337765	+	0.0337765i
$906$		−	37.0735i		−	1.23169i
$907$		−	18.8416i		−	0.625626i	−0.949815	−	0.312813i	$-0.898729\pi$
$907$		−	18.8416i		−	0.625626i	0.949815	−	0.312813i	$-0.101271\pi$
$908$	−71.7541	+	71.7541i	−2.38124	+	2.38124i
$909$	−9.40173			−0.311836
$910$	−4.48432	−	2.38462i	−0.148654	−	0.0790495i
$911$	0.701569			0.0232440			0.0116220	−	0.999932i	$-0.496301\pi$
$911$	0.701569			0.0232440			0.0116220	+	0.999932i	$0.496301\pi$
$912$	66.2513	−	66.2513i	2.19380	−	2.19380i
$913$			7.68144i			0.254219i
$914$			82.1404i			2.71696i
$915$	−1.11046	−	1.11046i	−0.0367106	−	0.0367106i
$916$	−38.7832	−	38.7832i	−1.28143	−	1.28143i
$917$	−24.3405	−	39.1708i	−0.803794	−	1.29353i
$918$	8.74820	+	8.74820i	0.288734	+	0.288734i
$919$	10.6633			0.351750			0.175875	−	0.984412i	$-0.443724\pi$
$919$	10.6633			0.351750			0.175875	+	0.984412i	$0.443724\pi$
$920$	−0.807522			−0.0266232
$921$	11.2000	+	11.2000i	0.369052	+	0.369052i
$922$	−2.11187			−0.0695508
$923$	−4.95414	−	1.31442i	−0.163067	−	0.0432648i
$924$	11.2909	+	2.63651i	0.371444	+	0.0867346i
$925$	28.5515	−	28.5515i	0.938766	−	0.938766i
$926$	41.8726			1.37602
$927$	−1.84027			−0.0604425
$928$	−120.095	+	120.095i	−3.94230	+	3.94230i
$929$	−1.31466	−	1.31466i	−0.0431326	−	0.0431326i	0.685212	−	0.728344i	$-0.259710\pi$
$929$	−1.31466	−	1.31466i	−0.0431326	−	0.0431326i	−0.728344	+	0.685212i	$0.759710\pi$
$930$	−0.145633	+	0.145633i	−0.00477551	+	0.00477551i
$931$	−38.9420	+	13.1911i	−1.27627	+	0.432321i
$932$	−107.751			−3.52949
$933$		−	18.6012i		−	0.608974i
$934$	61.9821	−	61.9821i	2.02812	−	2.02812i
$935$		−	0.683059i		−	0.0223384i
$936$	−9.10493	+	34.3170i	−0.297604	+	1.12169i
$937$		−	15.3362i		−	0.501012i	−0.968115	−	0.250506i	$-0.919403\pi$
$937$		−	15.3362i		−	0.501012i	0.968115	−	0.250506i	$-0.0805969\pi$
$938$	−4.55375	−	7.32829i	−0.148685	−	0.239277i
$939$	−31.7181			−1.03508
$940$			7.24796i			0.236402i
$941$	−28.8840	−	28.8840i	−0.941590	−	0.941590i	0.0567959	−	0.998386i	$-0.481912\pi$
$941$	−28.8840	−	28.8840i	−0.941590	−	0.941590i	−0.998386	+	0.0567959i	$0.981912\pi$
$942$	35.2893	−	35.2893i	1.14979	−	1.14979i
$943$	3.09141	−	3.09141i	0.100670	−	0.100670i
$944$	11.0333	−	11.0333i	0.359102	−	0.359102i
$945$	0.116363	−	0.498328i	0.00378528	−	0.0162106i
$946$		−	4.03880i		−	0.131313i
$947$	−25.5186	−	25.5186i	−0.829243	−	0.829243i	0.158169	−	0.987412i	$-0.449441\pi$
$947$	−25.5186	−	25.5186i	−0.829243	−	0.829243i	−0.987412	+	0.158169i	$0.949441\pi$
$948$	−61.2260			−1.98853
$949$	33.6052	+	8.91607i	1.09087	+	0.289428i
$950$		−	80.2367i		−	2.60322i
$951$	9.54944	+	9.54944i	0.309662	+	0.309662i
$952$	114.027	+	26.6260i	3.69563	+	0.862954i
$953$			6.16200i			0.199607i	0.995007	+	0.0998034i	$0.0318214\pi$
$953$			6.16200i			0.199607i	−0.995007	+	0.0998034i	$0.968179\pi$
$954$	−8.40254	+	8.40254i	−0.272042	+	0.272042i
$955$	2.64028	+	2.64028i	0.0854374	+	0.0854374i
$956$	80.8647	+	80.8647i	2.61535	+	2.61535i
$957$	−3.89692	+	3.89692i	−0.125970	+	0.125970i
$958$		−	13.6827i		−	0.442067i
$959$	27.1316	+	6.33540i	0.876124	+	0.204581i
$960$	4.75316	+	4.75316i	0.153408	+	0.153408i
$961$		−	30.8504i		−	0.995173i
$962$	40.5486	+	69.8355i	1.30734	+	2.25159i
$963$	−9.88514			−0.318544
$964$	−28.5385	−	28.5385i	−0.919162	−	0.919162i
$965$			1.38487i			0.0445807i
$966$	0.702144	−	3.00696i	0.0225911	−	0.0967472i
$967$	4.83625	−	4.83625i	0.155523	−	0.155523i	−0.625056	−	0.780580i	$-0.714924\pi$
$967$	4.83625	−	4.83625i	0.155523	−	0.155523i	0.780580	+	0.625056i	$0.214924\pi$
$968$	72.2937	−	72.2937i	2.32361	−	2.32361i
$969$	18.6668	−	18.6668i	0.599664	−	0.599664i
$970$	−1.69887	−	1.69887i	−0.0545475	−	0.0545475i
$971$			3.33201i			0.106929i	0.998570	+	0.0534647i	$0.0170265\pi$
$971$			3.33201i			0.106929i	−0.998570	+	0.0534647i	$0.982974\pi$
$972$	−5.57728			−0.178891
$973$	−26.1738	−	42.1212i	−0.839095	−	1.35034i
$974$		−	13.9205i		−	0.446043i
$975$	8.98447	+	15.4737i	0.287733	+	0.495554i
$976$			129.516i			4.14571i
$977$	−27.4570	+	27.4570i	−0.878427	+	0.878427i	−0.993372	−	0.114945i	$-0.963331\pi$
$977$	−27.4570	+	27.4570i	−0.878427	+	0.878427i	0.114945	+	0.993372i	$0.463331\pi$
$978$		−	2.62675i		−	0.0839942i
$979$	7.18762			0.229717
$980$	−2.42265	−	7.15201i	−0.0773887	−	0.228463i
$981$	9.76428	−	9.76428i	0.311749	−	0.311749i
$982$	8.26767	+	8.26767i	0.263832	+	0.263832i
$983$	26.1066	−	26.1066i	0.832670	−	0.832670i	−0.155211	−	0.987881i	$-0.549606\pi$
$983$	26.1066	−	26.1066i	0.832670	−	0.832670i	0.987881	+	0.155211i	$0.0496059\pi$
$984$	−101.539			−3.23693
$985$	3.01798			0.0961609
$986$	−61.3577	+	61.3577i	−1.95403	+	1.95403i
$987$	−17.3109	−	4.04220i	−0.551011	−	0.128665i
$988$	114.164	+	30.2899i	3.63205	+	0.963649i
$989$	−0.791697			−0.0251745
$990$	0.295817	+	0.295817i	0.00940168	+	0.00940168i
$991$	−4.19648			−0.133306			−0.0666529	−	0.997776i	$-0.521232\pi$
$991$	−4.19648			−0.133306			−0.0666529	+	0.997776i	$0.521232\pi$
$992$	9.36727			0.297411
$993$	12.3494	+	12.3494i	0.391896	+	0.391896i
$994$	−5.46436	−	8.79371i	−0.173319	−	0.278919i
$995$	1.72952	+	1.72952i	0.0548295	+	0.0548295i
$996$	−38.5535	−	38.5535i	−1.22161	−	1.22161i
$997$			47.2495i			1.49641i	0.663470	+	0.748203i	$0.269083\pi$
$997$			47.2495i			1.49641i	−0.663470	+	0.748203i	$0.730917\pi$
$998$		−	14.3837i		−	0.455308i
$999$	−5.75334	+	5.75334i	−0.182028	+	0.182028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.p.f.265.1	yes	12
3.2	odd	2		819.2.y.f.811.6		12
7.6	odd	2		273.2.p.e.265.1	yes	12
13.8	odd	4		273.2.p.e.34.1	✓	12
21.20	even	2		819.2.y.g.811.6		12
39.8	even	4		819.2.y.g.307.6		12
91.34	even	4	inner	273.2.p.f.34.1	yes	12
273.125	odd	4		819.2.y.f.307.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.e.34.1	✓	12	13.8	odd	4
273.2.p.e.265.1	yes	12	7.6	odd	2
273.2.p.f.34.1	yes	12	91.34	even	4	inner
273.2.p.f.265.1	yes	12	1.1	even	1	trivial
819.2.y.f.307.6		12	273.125	odd	4
819.2.y.f.811.6		12	3.2	odd	2
819.2.y.g.307.6		12	39.8	even	4
819.2.y.g.811.6		12	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94644 + 1.94644i) q^{2} -1.00000i q^{3} -5.57728i q^{4} +(0.136767 + 0.136767i) q^{5} +(1.94644 + 1.94644i) q^{6} +(-2.24723 + 1.39641i) q^{7} +(6.96297 + 6.96297i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.94644 + 1.94644i) q^{2} -1.00000i q^{3} -5.57728i q^{4} +(0.136767 + 0.136767i) q^{5} +(1.94644 + 1.94644i) q^{6} +(-2.24723 + 1.39641i) q^{7} +(6.96297 + 6.96297i) q^{8} -1.00000 q^{9} -0.532416 q^{10} +(0.555612 + 0.555612i) q^{11} -5.57728 q^{12} +(-1.81044 - 3.11806i) q^{13} +(1.65606 - 7.09214i) q^{14} +(0.136767 - 0.136767i) q^{15} -15.9515 q^{16} -4.49445 q^{17} +(1.94644 - 1.94644i) q^{18} +(-4.15330 - 4.15330i) q^{19} +(0.762785 - 0.762785i) q^{20} +(1.39641 + 2.24723i) q^{21} -2.16293 q^{22} +0.423984i q^{23} +(6.96297 - 6.96297i) q^{24} -4.96259i q^{25} +(9.59305 + 2.54521i) q^{26} +1.00000i q^{27} +(7.78819 + 12.5334i) q^{28} -7.01375 q^{29} +0.532416i q^{30} +(0.273533 + 0.273533i) q^{31} +(17.1227 - 17.1227i) q^{32} +(0.555612 - 0.555612i) q^{33} +(8.74820 - 8.74820i) q^{34} +(-0.498328 - 0.116363i) q^{35} +5.57728i q^{36} +(5.75334 + 5.75334i) q^{37} +16.1683 q^{38} +(-3.11806 + 1.81044i) q^{39} +1.90460i q^{40} +(-7.29133 - 7.29133i) q^{41} +(-7.09214 - 1.65606i) q^{42} +1.86728i q^{43} +(3.09880 - 3.09880i) q^{44} +(-0.136767 - 0.136767i) q^{45} +(-0.825261 - 0.825261i) q^{46} +(-4.75098 + 4.75098i) q^{47} +15.9515i q^{48} +(3.10006 - 6.27612i) q^{49} +(9.65940 + 9.65940i) q^{50} +4.49445i q^{51} +(-17.3903 + 10.0973i) q^{52} -4.31687 q^{53} +(-1.94644 - 1.94644i) q^{54} +0.151978i q^{55} +(-25.3706 - 5.92419i) q^{56} +(-4.15330 + 4.15330i) q^{57} +(13.6519 - 13.6519i) q^{58} +(-0.691676 + 0.691676i) q^{59} +(-0.762785 - 0.762785i) q^{60} -8.11937i q^{61} -1.06483 q^{62} +(2.24723 - 1.39641i) q^{63} +34.7539i q^{64} +(0.178839 - 0.674054i) q^{65} +2.16293i q^{66} +(0.837691 - 0.837691i) q^{67} +25.0668i q^{68} +0.423984 q^{69} +(1.19646 - 0.743473i) q^{70} +(1.00520 - 1.00520i) q^{71} +(-6.96297 - 6.96297i) q^{72} +(-6.81854 + 6.81854i) q^{73} -22.3971 q^{74} -4.96259 q^{75} +(-23.1641 + 23.1641i) q^{76} +(-2.02445 - 0.472722i) q^{77} +(2.54521 - 9.59305i) q^{78} +10.9777 q^{79} +(-2.18163 - 2.18163i) q^{80} +1.00000 q^{81} +28.3843 q^{82} +(6.91260 + 6.91260i) q^{83} +(12.5334 - 7.78819i) q^{84} +(-0.614691 - 0.614691i) q^{85} +(-3.63455 - 3.63455i) q^{86} +7.01375i q^{87} +7.73742i q^{88} +(6.46820 - 6.46820i) q^{89} +0.532416 q^{90} +(8.42257 + 4.47887i) q^{91} +2.36468 q^{92} +(0.273533 - 0.273533i) q^{93} -18.4950i q^{94} -1.13606i q^{95} +(-17.1227 - 17.1227i) q^{96} +(3.19087 + 3.19087i) q^{97} +(6.18201 + 18.2502i) q^{98} +(-0.555612 - 0.555612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9	\( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9} - 4 q^{11} - 28 q^{12} + 12 q^{15} - 36 q^{16} - 8 q^{17} + 8 q^{20} + 12 q^{21} + 32 q^{22} + 4 q^{26} + 12 q^{28} - 8 q^{29} + 24 q^{31} + 20 q^{32} - 4 q^{33} - 20 q^{35} - 4 q^{37} + 40 q^{38} - 16 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 20 q^{46} + 32 q^{47} + 20 q^{50} - 56 q^{52} - 16 q^{53} - 20 q^{56} + 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} - 32 q^{67} + 16 q^{69} - 20 q^{70} - 12 q^{71} - 32 q^{73} - 64 q^{74} + 4 q^{75} - 12 q^{77} + 16 q^{78} + 24 q^{79} - 4 q^{80} + 12 q^{81} + 28 q^{84} - 32 q^{85} + 4 q^{89} + 32 q^{91} + 112 q^{92} + 24 q^{93} - 20 q^{96} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9 - 4 * q^11 - 28 * q^12 + 12 * q^15 - 36 * q^16 - 8 * q^17 + 8 * q^20 + 12 * q^21 + 32 * q^22 + 4 * q^26 + 12 * q^28 - 8 * q^29 + 24 * q^31 + 20 * q^32 - 4 * q^33 - 20 * q^35 - 4 * q^37 + 40 * q^38 - 16 * q^39 - 20 * q^41 + 8 * q^44 - 12 * q^45 + 20 * q^46 + 32 * q^47 + 20 * q^50 - 56 * q^52 - 16 * q^53 - 20 * q^56 + 8 * q^59 - 8 * q^60 + 4 * q^63 - 16 * q^65 - 32 * q^67 + 16 * q^69 - 20 * q^70 - 12 * q^71 - 32 * q^73 - 64 * q^74 + 4 * q^75 - 12 * q^77 + 16 * q^78 + 24 * q^79 - 4 * q^80 + 12 * q^81 + 28 * q^84 - 32 * q^85 + 4 * q^89 + 32 * q^91 + 112 * q^92 + 24 * q^93 - 20 * q^96 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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