LMFDB - Embedded newform 273.2.p.e.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.e.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94644 + 1.94644i) q^{2} +1.00000i q^{3} -5.57728i q^{4} +(-0.136767 - 0.136767i) q^{5} +(-1.94644 - 1.94644i) q^{6} +(1.39641 - 2.24723i) q^{7} +(6.96297 + 6.96297i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(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} +(1.39641 - 2.24723i) 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} +(2.24723 + 1.39641i) 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} +(-12.5334 - 7.78819i) 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} +(-1.39641 + 2.24723i) 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} +(0.743473 - 1.19646i) 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} +(7.78819 - 12.5334i) 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} +(9.53511 + 0.285633i) 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} +(18.2502 + 6.18201i) q^{98} +(-0.555612 - 0.555612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9	$ 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9} - 4 q^{11} + 28 q^{12} + 12 q^{15} - 36 q^{16} + 8 q^{17} - 8 q^{20} + 4 q^{21} + 32 q^{22} - 4 q^{26} - 28 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} - 12 q^{63} - 16 q^{65} - 32 q^{67} - 16 q^{69} + 52 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} + 12 q^{84} - 32 q^{85} - 4 q^{89} - 40 q^{91} + 112 q^{92} + 24 q^{93} + 20 q^{96} + 136 q^{98} + 4 q^{99}+O(q^{100}) $ 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9 - 4 * q^11 + 28 * q^12 + 12 * q^15 - 36 * q^16 + 8 * q^17 - 8 * q^20 + 4 * q^21 + 32 * q^22 - 4 * q^26 - 28 * 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 - 12 * q^63 - 16 * q^65 - 32 * q^67 - 16 * q^69 + 52 * 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 + 12 * q^84 - 32 * q^85 - 4 * q^89 - 40 * q^91 + 112 * q^92 + 24 * q^93 + 20 * q^96 + 136 * 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	0.675863	−	0.737027i	$-0.263771\pi$
$5$	−0.136767	−	0.136767i	−0.0611638	−	0.0611638i	−0.737027	+	0.675863i	$0.763771\pi$
$6$	−1.94644	−	1.94644i	−0.794632	−	0.794632i
$7$	1.39641	−	2.24723i	0.527795	−	0.849372i
$7$	1.39641	−	2.24723i	0.527795	−	0.849372i
$8$	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	$-0.316517\pi$
$17$	4.49445			1.09007			0.545033	+	0.838415i	$0.316517\pi$
$18$	1.94644	−	1.94644i	0.458781	−	0.458781i
$19$	4.15330	+	4.15330i	0.952832	+	0.952832i	0.998937	−	0.0461051i	$-0.0146809\pi$
$19$	4.15330	+	4.15330i	0.952832	+	0.952832i	−0.0461051	+	0.998937i	$0.514681\pi$
$20$	−0.762785	+	0.762785i	−0.170564	+	0.170564i
$21$	2.24723	+	1.39641i	0.490385	+	0.304722i
$22$	−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
$28$	−12.5334	−	7.78819i	−2.36859	−	1.47183i
$29$	−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	0.682116	−	0.731244i	$-0.261060\pi$
$31$	−0.273533	−	0.273533i	−0.0491280	−	0.0491280i	−0.731244	+	0.682116i	$0.761060\pi$
$32$	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	$0.0479380\pi$
$41$	7.29133	+	7.29133i	1.13871	+	1.13871i	0.150033	+	0.988681i	$0.452062\pi$
$42$	−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	−0.269890	−	0.962891i	$-0.586987\pi$
$47$	4.75098	−	4.75098i	0.693002	−	0.693002i	0.962891	+	0.269890i	$0.0869872\pi$
$48$		−	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	−0.660648	−	0.750696i	$-0.729718\pi$
$59$	0.691676	−	0.691676i	0.0900485	−	0.0900485i	0.750696	+	0.660648i	$0.229718\pi$
$60$	−0.762785	−	0.762785i	−0.0984751	−	0.0984751i
$61$			8.11937i			1.03958i	0.854294	+	0.519789i	$0.173990\pi$
$61$			8.11937i			1.03958i	−0.854294	+	0.519789i	$0.826010\pi$
$62$	1.06483			0.135234
$63$	−1.39641	+	2.24723i	−0.175932	+	0.283124i
$64$			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
$70$	0.743473	−	1.19646i	0.0888621	−	0.143004i
$71$	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	−0.184738	−	0.982788i	$-0.559144\pi$
$73$	6.81854	−	6.81854i	0.798050	−	0.798050i	0.982788	+	0.184738i	$0.0591436\pi$
$74$	−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	0.217340	−	0.976096i	$-0.430262\pi$
$83$	−6.91260	−	6.91260i	−0.758756	−	0.758756i	−0.976096	+	0.217340i	$0.930262\pi$
$84$	7.78819	−	12.5334i	0.849761	−	1.36751i
$85$	−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	−0.961262	−	0.275635i	$-0.911112\pi$
$89$	−6.46820	+	6.46820i	−0.685628	+	0.685628i	0.275635	+	0.961262i	$0.411112\pi$
$90$	−0.532416			−0.0561216
$91$	9.53511	+	0.285633i	0.999552	+	0.0299425i
$92$	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	0.526309	−	0.850293i	$-0.323575\pi$
$97$	−3.19087	−	3.19087i	−0.323984	−	0.323984i	−0.850293	+	0.526309i	$0.823575\pi$
$98$	18.2502	+	6.18201i	1.84355	+	0.624478i
$99$	−0.555612	−	0.555612i	−0.0558411	−	0.0558411i
$100$	−27.6778			−2.76778
$101$	−9.40173			−0.935507			−0.467753	−	0.883859i	$-0.654936\pi$
$101$	−9.40173			−0.935507			−0.467753	+	0.883859i	$0.654936\pi$
$102$	−8.74820	−	8.74820i	−0.866201	−	0.866201i
$103$	−1.84027			−0.181328			−0.0906638	−	0.995882i	$-0.528899\pi$
$103$	−1.84027			−0.181328			−0.0906638	+	0.995882i	$0.528899\pi$
$104$	−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
$112$	−22.2749	+	35.8466i	−2.10478	+	3.38719i
$113$	−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
$119$	6.27612	−	10.1001i	0.575331	−	0.925871i
$120$	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	$-0.724480\pi$
$131$		−	17.4307i		−	1.52293i	0.648206	−	0.761465i	$-0.275520\pi$
$132$	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	$-0.707520\pi$
$139$		−	18.7436i		−	1.58981i	0.606732	−	0.794906i	$-0.292480\pi$
$140$	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
$154$	−3.02035	+	4.86060i	−0.243387	+	0.391679i
$155$			0.0748203i			0.00600971i
$156$	10.0973	+	17.3903i	0.808434	+	1.39234i
$157$			18.1301i			1.44694i	0.690354	+	0.723471i	$0.257455\pi$
$157$			18.1301i			1.44694i	−0.690354	+	0.723471i	$0.742545\pi$
$158$	−21.3676	+	21.3676i	−1.69991	+	1.69991i
$159$		−	4.31687i		−	0.342350i
$160$	−4.68363			−0.370274
$161$	0.952789	+	0.592057i	0.0750903	+	0.0466607i
$162$	−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	−0.479744	−	0.877409i	$-0.659270\pi$
$167$	5.13896	−	5.13896i	0.397665	−	0.397665i	0.877409	+	0.479744i	$0.159270\pi$
$168$	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	$-0.507931\pi$
$173$	−0.655393			−0.0498286			−0.0249143	+	0.999690i	$0.507931\pi$
$174$	13.6519	+	13.6519i	1.03494	+	1.03494i
$175$	−11.1521	−	6.92983i	−0.843017	−	0.523846i
$176$	−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	$-0.589047\pi$
$181$	−7.42950			−0.552230			−0.276115	+	0.961125i	$0.589047\pi$
$182$	−19.1155	+	18.0036i	−1.41694	+	1.33451i
$183$	−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
$189$	−2.24723	−	1.39641i	−0.163462	−	0.101574i
$190$	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	$-0.647941\pi$
$199$	−12.6458			−0.896436			−0.448218	+	0.893924i	$0.647941\pi$
$200$	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
$203$	−9.79409	+	15.7615i	−0.687410	+	1.10624i
$204$	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
$210$	1.19646	+	0.743473i	0.0825636	+	0.0513045i
$211$	−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	0.568948	−	0.822374i	$-0.307351\pi$
$223$	−3.78445	−	3.78445i	−0.253426	−	0.253426i	−0.822374	+	0.568948i	$0.807351\pi$
$224$	−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	0.990612	−	0.136704i	$-0.0436508\pi$
$227$	12.8654	+	12.8654i	0.853908	+	0.853908i	−0.136704	+	0.990612i	$0.543651\pi$
$228$	23.1641	+	23.1641i	1.53408	+	1.53408i
$229$	−6.95379	+	6.95379i	−0.459519	+	0.459519i	−0.898498	−	0.438978i	$-0.855341\pi$
$229$	−6.95379	+	6.95379i	−0.459519	+	0.459519i	0.438978	+	0.898498i	$0.355341\pi$
$230$			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	−0.852438	−	0.522828i	$-0.824877\pi$
$241$	−5.11691	+	5.11691i	−0.329609	+	0.329609i	0.522828	+	0.852438i	$0.324877\pi$
$242$	20.2091	+	20.2091i	1.29909	+	1.29909i
$243$			1.00000i			0.0641500i
$244$	45.2840			2.89901
$245$	−0.434378	+	1.28235i	−0.0277514	+	0.0819261i
$246$		−	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	$-0.331783\pi$
$251$	15.9764			1.00842			0.504211	+	0.863580i	$0.331783\pi$
$252$	12.5334	+	7.78819i	0.789531	+	0.490610i
$253$	−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	$-0.395367\pi$
$257$	10.3506			0.645652			0.322826	+	0.946458i	$0.395367\pi$
$258$	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
$266$	−22.5776	+	36.3339i	−1.38432	+	2.22777i
$267$	−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	$0.00864165\pi$
$269$			0.890429i			0.0542904i	−0.999632	+	0.0271452i	$0.991358\pi$
$270$		−	0.532416i		−	0.0324018i
$271$	−15.2932	+	15.2932i	−0.928996	+	0.928996i	−0.997641	−	0.0686449i	$-0.978132\pi$
$271$	−15.2932	+	15.2932i	−0.928996	+	0.928996i	0.0686449	+	0.997641i	$0.478132\pi$
$272$	−71.6933			−4.34704
$273$	−0.285633	+	9.53511i	−0.0172873	+	0.577091i
$274$	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
$280$	−4.28008	−	2.65961i	−0.255783	−	0.158942i
$281$	−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	$-0.478624\pi$
$283$	2.25769			0.134206			0.0671029	+	0.997746i	$0.478624\pi$
$284$	−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	−0.800018	−	0.599976i	$-0.795177\pi$
$293$	−3.42417	+	3.42417i	−0.200042	+	0.200042i	0.599976	+	0.800018i	$0.295177\pi$
$294$	−6.18201	+	18.2502i	−0.360542	+	1.06437i
$295$	−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
$301$	4.19620	+	2.60750i	0.241865	+	0.150294i
$302$	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	−0.311146	−	0.950362i	$-0.600713\pi$
$307$	11.2000	−	11.2000i	0.639216	−	0.639216i	0.950362	+	0.311146i	$0.100713\pi$
$308$	−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	$-0.676828\pi$
$311$	−18.6012			−1.05477			−0.527387	+	0.849625i	$0.676828\pi$
$312$	−34.3170	−	9.10493i	−1.94282	−	0.515465i
$313$			31.7181i			1.79281i	0.443234	+	0.896406i	$0.353831\pi$
$313$			31.7181i			1.79281i	−0.443234	+	0.896406i	$0.646169\pi$
$314$	−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
$336$	−35.8466	−	22.2749i	−1.95559	−	1.21519i
$337$			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
$343$	−18.4328	−	1.79752i	−0.995279	−	0.0970567i
$344$	−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	−0.900122	−	0.435637i	$-0.856523\pi$
$349$	−8.67730	+	8.67730i	−0.464485	+	0.464485i	0.435637	+	0.900122i	$0.356523\pi$
$350$	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	$0.133829\pi$
$353$	24.8207	+	24.8207i	1.32107	+	1.32107i	0.408160	+	0.912910i	$0.366171\pi$
$354$	−2.69261			−0.143111
$355$	−0.274956			−0.0145931
$356$	36.0750	+	36.0750i	1.91197	+	1.91197i
$357$	10.1001	+	6.27612i	0.534552	+	0.332167i
$358$	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
$364$	1.59306	−	53.1800i	0.0834988	−	2.78739i
$365$	−1.86510			−0.0976236
$366$	15.8039	−	15.8039i	0.826083	−	0.826083i
$367$		−	21.0453i		−	1.09855i	−0.835640	−	0.549277i	$-0.814903\pi$
$367$		−	21.0453i		−	1.09855i	0.835640	−	0.549277i	$-0.185097\pi$
$368$		−	6.76318i		−	0.352555i
$369$	−7.29133	−	7.29133i	−0.379571	−	0.379571i
$370$	3.06317	+	3.06317i	0.159247	+	0.159247i
$371$	−6.02814	+	9.70099i	−0.312965	+	0.503650i
$372$	−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	0.435230	−	0.900319i	$-0.356667\pi$
$383$	−9.10197	−	9.10197i	−0.465089	−	0.465089i	−0.900319	+	0.435230i	$0.856667\pi$
$384$	33.4009	−	33.4009i	1.70448	−	1.70448i
$385$	−0.341530	−	0.212224i	−0.0174060	−	0.0108160i
$386$	−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
$392$	22.1148	−	65.2861i	1.11697	−	3.29744i
$393$	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	$-0.475417\pi$
$397$	21.4027	−	21.4027i	1.07417	−	1.07417i	0.997019	−	0.0771530i	$-0.0245830\pi$
$398$	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	0.420748	−	0.907178i	$-0.361768\pi$
$409$	−9.83744	−	9.83744i	−0.486430	−	0.486430i	−0.907178	+	0.420748i	$0.861768\pi$
$410$	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	$0.121449\pi$
$419$			15.2437i			0.744706i	−0.928091	+	0.372353i	$0.878551\pi$
$420$	−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
$427$	18.2461	+	11.3380i	0.882989	+	0.548684i
$428$		−	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	$-0.603435\pi$
$433$	−13.2868			−0.638525			−0.319263	+	0.947666i	$0.603435\pi$
$434$	1.48695	−	2.39292i	0.0713757	−	0.114864i
$435$	−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	$-0.488785\pi$
$439$	1.47611			0.0704508			0.0352254	+	0.999379i	$0.488785\pi$
$440$	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
$448$	78.0998	+	48.5308i	3.68987	+	2.29286i
$449$	−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
$455$	−1.26502	−	1.34315i	−0.0593050	−	0.0629678i
$456$	−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	0.694361	−	0.719627i	$-0.255687\pi$
$461$	−0.542495	−	0.542495i	−0.0252665	−	0.0252665i	−0.719627	+	0.694361i	$0.755687\pi$
$462$	−4.86060	−	3.02035i	−0.226136	−	0.140519i
$463$	−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	$-0.236346\pi$
$467$	31.8438			1.47356			0.736778	+	0.676135i	$0.236346\pi$
$468$	−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
$476$	−56.3309	−	35.0037i	−2.58192	−	1.60439i
$477$	4.31687			0.197656
$478$		−	56.4427i		−	2.58163i
$479$	3.51478	−	3.51478i	0.160595	−	0.160595i	−0.622236	−	0.782830i	$-0.713775\pi$
$479$	3.51478	−	3.51478i	0.160595	−	0.160595i	0.782830	+	0.622236i	$0.213775\pi$
$480$		−	4.68363i		−	0.213778i
$481$	−7.52319	+	28.3553i	−0.343028	+	1.29289i
$482$		−	19.9196i		−	0.907311i
$483$	−0.592057	+	0.952789i	−0.0269395	+	0.0433534i
$484$	−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	$0.123146\pi$
$503$			16.9237i			0.754591i	−0.926093	+	0.377296i	$0.876854\pi$
$504$	−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	$-0.961632\pi$
$509$	−25.1102	−	25.1102i	−1.11299	−	1.11299i	−0.120244	−	0.992744i	$-0.538368\pi$
$510$			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
$518$	−31.2756	+	50.3313i	−1.37417	+	2.21143i
$519$		−	0.655393i		−	0.0287686i
$520$	5.93867	−	3.44817i	0.260428	−	0.151212i
$521$		−	6.34020i		−	0.277769i	−0.990309	−	0.138885i	$-0.955648\pi$
$521$		−	6.34020i		−	0.277769i	0.990309	−	0.138885i	$-0.0443517\pi$
$522$	−13.6519	+	13.6519i	−0.597526	+	0.597526i
$523$			2.80026i			0.122447i	0.998124	+	0.0612234i	$0.0195002\pi$
$523$			2.80026i			0.122447i	−0.998124	+	0.0612234i	$0.980500\pi$
$524$	−97.2161			−4.24690
$525$	6.92983	−	11.1521i	0.302442	−	0.486716i
$526$	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
$539$	1.76466	−	5.20952i	0.0760091	−	0.224390i
$540$	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
$546$	−18.0036	−	19.1155i	−0.770482	−	0.818069i
$547$	−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
$553$	15.3295	−	24.6695i	0.651875	−	1.04905i
$554$	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	$-0.305996\pi$
$563$	27.1654			1.14489			0.572443	+	0.819945i	$0.305996\pi$
$564$	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
$567$	1.39641	−	2.24723i	0.0586439	−	0.0943747i
$568$	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
$574$	−39.6362	+	63.7860i	−1.65438	+	2.66238i
$575$	2.10406			0.0877454
$576$		−	34.7539i		−	1.44808i
$577$	11.0080	+	11.0080i	0.458271	+	0.458271i	0.898087	−	0.439817i	$-0.144957\pi$
$577$	11.0080	+	11.0080i	0.458271	+	0.458271i	−0.439817	+	0.898087i	$0.644957\pi$
$578$	−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	0.994340	−	0.106247i	$-0.0338834\pi$
$587$	21.5168	+	21.5168i	0.888093	+	0.888093i	−0.106247	+	0.994340i	$0.533883\pi$
$588$	−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	$0.544965\pi$
$593$	−27.5375	+	27.5375i	−1.13083	+	1.13083i	−0.990039	+	0.140792i	$0.955035\pi$
$594$			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	$-0.630628\pi$
$601$		−	44.9596i		−	1.83394i	0.398957	−	0.916969i	$-0.369372\pi$
$602$	−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	$0.120096\pi$
$607$			18.1530i			0.736807i	−0.929666	+	0.368403i	$0.879904\pi$
$608$	142.232			5.76825
$609$	−15.7615	−	9.79409i	−0.638688	−	0.396877i
$610$			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
$616$	17.3877	+	10.8046i	0.700572	+	0.435331i
$617$	−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	−0.848473	−	0.529239i	$-0.822477\pi$
$619$	−7.94244	+	7.94244i	−0.319234	+	0.319234i	0.529239	+	0.848473i	$0.322477\pi$
$620$	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
$630$	−0.743473	+	1.19646i	−0.0296207	+	0.0476681i
$631$	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
$637$	13.9568	−	21.0287i	0.552990	−	0.833188i
$638$	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	0.306083	−	0.952005i	$-0.400981\pi$
$643$	−16.3789	−	16.3789i	−0.645922	−	0.645922i	−0.952005	+	0.306083i	$0.900981\pi$
$644$	3.30207	−	5.31397i	0.130120	−	0.209400i
$645$	0.255381	+	0.255381i	0.0100556	+	0.0100556i
$646$	−72.6677			−2.85907
$647$	15.4382			0.606939			0.303469	−	0.952841i	$-0.401855\pi$
$647$	15.4382			0.606939			0.303469	+	0.952841i	$0.401855\pi$
$648$	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
$658$	41.5625	+	25.8267i	1.62028	+	1.00683i
$659$	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	−0.0947669	−	0.995499i	$-0.530211\pi$
$661$	23.1578	−	23.1578i	0.900733	−	0.900733i	0.995499	+	0.0947669i	$0.0302106\pi$
$662$		−	48.0747i		−	1.86848i
$663$	−14.0140	+	8.13694i	−0.544258	+	0.316013i
$664$		−	96.2644i		−	3.73579i
$665$	−2.55299	−	1.58641i	−0.0990008	−	0.0615185i
$666$	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	$-0.696493\pi$
$677$		−	42.4344i		−	1.63089i	0.578836	−	0.815444i	$-0.303507\pi$
$678$	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	0.996340	−	0.0854795i	$-0.0272422\pi$
$691$	23.9437	+	23.9437i	0.910860	+	0.910860i	−0.0854795	+	0.996340i	$0.527242\pi$
$692$			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
$700$	−38.6496	+	62.1982i	−1.46082	+	2.35087i
$701$		−	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
$707$	−13.1287	+	21.1278i	−0.493756	+	0.794593i
$708$	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	$-0.552923\pi$
$719$	−8.87534			−0.330994			−0.165497	+	0.986210i	$0.552923\pi$
$720$	−2.18163	−	2.18163i	−0.0813046	−	0.0813046i
$721$	−2.56978	+	4.13551i	−0.0957037	+	0.154015i
$722$	−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	$-0.503604\pi$
$727$	−0.610509			−0.0226425			−0.0113213	+	0.999936i	$0.503604\pi$
$728$	64.4039	+	68.3816i	2.38697	+	2.53439i
$729$	−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	0.978115	−	0.208064i	$-0.0667164\pi$
$733$	20.8483	+	20.8483i	0.770051	+	0.770051i	−0.208064	+	0.978115i	$0.566716\pi$
$734$	40.9634	+	40.9634i	1.51199	+	1.51199i
$735$	−1.28235	−	0.434378i	−0.0473001	−	0.0160223i
$736$	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
$749$	13.8037	−	22.2142i	0.504378	−	0.811687i
$750$	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
$756$	−7.78819	+	12.5334i	−0.283254	+	0.455836i
$757$	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	−0.522994	−	0.852336i	$-0.675185\pi$
$761$	9.08532	−	9.08532i	0.329343	−	0.329343i	0.852336	+	0.522994i	$0.175185\pi$
$762$	−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	0.929717	−	0.368275i	$-0.120052\pi$
$769$	15.5692	+	15.5692i	0.561441	+	0.561441i	−0.368275	+	0.929717i	$0.620052\pi$
$770$	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	0.785489	−	0.618876i	$-0.212412\pi$
$773$	4.63232	+	4.63232i	0.166613	+	0.166613i	−0.618876	+	0.785489i	$0.712412\pi$
$774$	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	−0.413820	−	0.910359i	$-0.635806\pi$
$787$	13.9297	−	13.9297i	0.496539	−	0.496539i	0.910359	+	0.413820i	$0.135806\pi$
$788$	−61.5360	−	61.5360i	−2.19213	−	2.19213i
$789$		−	10.9315i		−	0.389171i
$790$	5.84473			0.207946
$791$	−13.9186	+	22.3990i	−0.494889	+	0.796418i
$792$		−	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	$-0.530008\pi$
$797$	−5.31507			−0.188270			−0.0941348	+	0.995559i	$0.530008\pi$
$798$	−36.3339	−	22.5776i	−1.28620	−	0.799240i
$799$	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	0.932158	−	0.362053i	$-0.117924\pi$
$811$	16.2355	+	16.2355i	0.570105	+	0.570105i	−0.362053	+	0.932158i	$0.617924\pi$
$812$	87.9062	+	54.6244i	3.08490	+	1.91694i
$813$	−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
$819$	−9.53511	−	0.285633i	−0.333184	−	0.00998083i
$820$	−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
$826$	6.05092	+	3.76000i	0.210538	+	0.130827i
$827$	−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	$-0.699360\pi$
$829$	−33.7537			−1.17231			−0.586156	+	0.810198i	$0.699360\pi$
$830$	−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	$0.501528\pi$
$839$	−29.1042	+	29.1042i	−1.00479	+	1.00479i	−0.999988	+	0.00479972i	$0.998472\pi$
$840$	2.65961	−	4.28008i	0.0917654	−	0.147677i
$841$	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
$847$	−23.3320	−	14.4984i	−0.801698	−	0.498171i
$848$	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	−0.515462	−	0.856913i	$-0.672380\pi$
$853$	9.97247	−	9.97247i	0.341451	−	0.341451i	0.856913	+	0.515462i	$0.172380\pi$
$854$	−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	$-0.612642\pi$
$857$	−20.2894			−0.693071			−0.346536	+	0.938037i	$0.612642\pi$
$858$	6.74416	−	3.91586i	0.230242	−	0.133685i
$859$		−	1.65917i		−	0.0566102i	−0.999599	−	0.0283051i	$-0.990989\pi$
$859$		−	1.65917i		−	0.0566102i	0.999599	−	0.0283051i	$-0.00901100\pi$
$860$	−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	$-0.384650\pi$
$881$	21.0446			0.709009			0.354505	+	0.935054i	$0.384650\pi$
$882$	−18.2502	−	6.18201i	−0.614516	−	0.208159i
$883$			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	$0.108176\pi$
$887$			19.8555i			0.666682i	−0.942806	+	0.333341i	$0.891824\pi$
$888$	−80.1207			−2.68867
$889$	−6.69167	−	4.15816i	−0.224431	−	0.139460i
$890$	−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
$903$	−2.60750	+	4.19620i	−0.0867720	+	0.139641i
$904$	−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
$910$	5.07665	+	0.152076i	0.168289	+	0.00504126i
$911$	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
$917$	−39.1708	−	24.3405i	−1.29353	−	0.803794i
$918$	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	0.728344	−	0.685212i	$-0.240290\pi$
$929$	1.31466	+	1.31466i	0.0431326	+	0.0431326i	−0.685212	+	0.728344i	$0.740290\pi$
$930$	0.145633	−	0.145633i	0.00477551	−	0.00477551i
$931$	13.1911	−	38.9420i	0.432321	−	1.27627i
$932$	−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	$0.0805969\pi$
$937$			15.3362i			0.501012i	−0.968115	+	0.250506i	$0.919403\pi$
$938$	7.32829	+	4.55375i	0.239277	+	0.148685i
$939$	−31.7181			−1.03508
$940$			7.24796i			0.236402i
$941$	28.8840	+	28.8840i	0.941590	+	0.941590i	0.998386	−	0.0567959i	$-0.0180884\pi$
$941$	28.8840	+	28.8840i	0.941590	+	0.941590i	−0.0567959	+	0.998386i	$0.518088\pi$
$942$	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	$-0.982974\pi$
$971$		−	3.33201i		−	0.106929i	0.998570	−	0.0534647i	$-0.0170265\pi$
$972$	5.57728			0.178891
$973$	−42.1212	−	26.1738i	−1.35034	−	0.839095i
$974$		−	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
$980$	7.15201	+	2.42265i	0.228463	+	0.0773887i
$981$	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	−0.987881	−	0.155211i	$-0.950394\pi$
$983$	−26.1066	+	26.1066i	−0.832670	+	0.832670i	0.155211	+	0.987881i	$0.450394\pi$
$984$	−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
$994$	8.79371	+	5.46436i	0.278919	+	0.173319i
$995$	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	$-0.730917\pi$
$997$		−	47.2495i		−	1.49641i	0.663470	−	0.748203i	$-0.269083\pi$
$998$		−	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.e.265.1	yes	12
3.2	odd	2		819.2.y.g.811.6		12
7.6	odd	2		273.2.p.f.265.1	yes	12
13.8	odd	4		273.2.p.f.34.1	yes	12
21.20	even	2		819.2.y.f.811.6		12
39.8	even	4		819.2.y.f.307.6		12
91.34	even	4	inner	273.2.p.e.34.1	✓	12
273.125	odd	4		819.2.y.g.307.6		12

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

\(f(q)\)	\(=\)	\(q+(-1.94644 + 1.94644i) q^{2} +1.00000i q^{3} -5.57728i q^{4} +(-0.136767 - 0.136767i) q^{5} +(-1.94644 - 1.94644i) q^{6} +(1.39641 - 2.24723i) q^{7} +(6.96297 + 6.96297i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(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} +(1.39641 - 2.24723i) 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} +(2.24723 + 1.39641i) 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} +(-12.5334 - 7.78819i) 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} +(-1.39641 + 2.24723i) 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} +(0.743473 - 1.19646i) 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} +(7.78819 - 12.5334i) 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} +(9.53511 + 0.285633i) 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} +(18.2502 + 6.18201i) q^{98} +(-0.555612 - 0.555612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9	\( 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9} - 4 q^{11} + 28 q^{12} + 12 q^{15} - 36 q^{16} + 8 q^{17} - 8 q^{20} + 4 q^{21} + 32 q^{22} - 4 q^{26} - 28 q^{28} - 8 q^{29} - 24 q^{31} + 20 q^{32} + 4 q^{33} - 20 q^{35} - 4 q^{37} - 40 q^{38} - 16 q^{39} + 20 q^{41} + 8 q^{44} + 12 q^{45} + 20 q^{46} - 32 q^{47} + 20 q^{50} + 56 q^{52} - 16 q^{53} + 20 q^{56} - 8 q^{59} - 8 q^{60} - 12 q^{63} - 16 q^{65} - 32 q^{67} - 16 q^{69} + 52 q^{70} - 12 q^{71} + 32 q^{73} - 64 q^{74} - 4 q^{75} + 12 q^{77} + 16 q^{78} + 24 q^{79} + 4 q^{80} + 12 q^{81} + 12 q^{84} - 32 q^{85} - 4 q^{89} - 40 q^{91} + 112 q^{92} + 24 q^{93} + 20 q^{96} + 136 q^{98} + 4 q^{99}+O(q^{100}) \) 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9 - 4 * q^11 + 28 * q^12 + 12 * q^15 - 36 * q^16 + 8 * q^17 - 8 * q^20 + 4 * q^21 + 32 * q^22 - 4 * q^26 - 28 * 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 - 12 * q^63 - 16 * q^65 - 32 * q^67 - 16 * q^69 + 52 * 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 + 12 * q^84 - 32 * q^85 - 4 * q^89 - 40 * q^91 + 112 * q^92 + 24 * q^93 + 20 * q^96 + 136 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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