LMFDB - Embedded newform 273.2.p.f.265.4

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			265.4
Root			$0.236276 + 0.236276i$ of defining polynomial
Character	$\chi$	$=$	273.265
Dual form			273.2.p.f.34.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.695639 - 0.695639i) q^{2} -1.00000i q^{3} +1.03217i q^{4} +(1.23628 + 1.23628i) q^{5} +(-0.695639 - 0.695639i) q^{6} +(1.20338 + 2.35624i) q^{7} +(2.10930 + 2.10930i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.695639 - 0.695639i) q^{2} -1.00000i q^{3} +1.03217i q^{4} +(1.23628 + 1.23628i) q^{5} +(-0.695639 - 0.695639i) q^{6} +(1.20338 + 2.35624i) q^{7} +(2.10930 + 2.10930i) q^{8} -1.00000 q^{9} +1.72000 q^{10} +(0.436434 + 0.436434i) q^{11} +1.03217 q^{12} +(-2.38061 - 2.70790i) q^{13} +(2.47621 + 0.801978i) q^{14} +(1.23628 - 1.23628i) q^{15} +0.870270 q^{16} +2.40676 q^{17} +(-0.695639 + 0.695639i) q^{18} +(-3.04121 - 3.04121i) q^{19} +(-1.27605 + 1.27605i) q^{20} +(2.35624 - 1.20338i) q^{21} +0.607201 q^{22} -5.07339i q^{23} +(2.10930 - 2.10930i) q^{24} -1.94324i q^{25} +(-3.53976 - 0.227675i) q^{26} +1.00000i q^{27} +(-2.43205 + 1.24209i) q^{28} +0.166822 q^{29} -1.72000i q^{30} +(2.47255 + 2.47255i) q^{31} +(-3.61320 + 3.61320i) q^{32} +(0.436434 - 0.436434i) q^{33} +(1.67423 - 1.67423i) q^{34} +(-1.42526 + 4.40068i) q^{35} -1.03217i q^{36} +(-5.59931 - 5.59931i) q^{37} -4.23117 q^{38} +(-2.70790 + 2.38061i) q^{39} +5.21535i q^{40} +(4.82807 + 4.82807i) q^{41} +(0.801978 - 2.47621i) q^{42} -6.37008i q^{43} +(-0.450476 + 0.450476i) q^{44} +(-1.23628 - 1.23628i) q^{45} +(-3.52924 - 3.52924i) q^{46} +(-2.64599 + 2.64599i) q^{47} -0.870270i q^{48} +(-4.10376 + 5.67090i) q^{49} +(-1.35179 - 1.35179i) q^{50} -2.40676i q^{51} +(2.79502 - 2.45720i) q^{52} +6.46466 q^{53} +(0.695639 + 0.695639i) q^{54} +1.07911i q^{55} +(-2.43174 + 7.50830i) q^{56} +(-3.04121 + 3.04121i) q^{57} +(0.116048 - 0.116048i) q^{58} +(-6.95599 + 6.95599i) q^{59} +(1.27605 + 1.27605i) q^{60} -3.67293i q^{61} +3.44001 q^{62} +(-1.20338 - 2.35624i) q^{63} +6.76750i q^{64} +(0.404620 - 6.29080i) q^{65} -0.607201i q^{66} +(-1.59968 + 1.59968i) q^{67} +2.48419i q^{68} -5.07339 q^{69} +(2.06981 + 4.05275i) q^{70} +(-1.65815 + 1.65815i) q^{71} +(-2.10930 - 2.10930i) q^{72} +(4.88992 - 4.88992i) q^{73} -7.79020 q^{74} -1.94324 q^{75} +(3.13906 - 3.13906i) q^{76} +(-0.503150 + 1.55354i) q^{77} +(-0.227675 + 3.53976i) q^{78} -9.79014 q^{79} +(1.07589 + 1.07589i) q^{80} +1.00000 q^{81} +6.71719 q^{82} +(4.07668 + 4.07668i) q^{83} +(1.24209 + 2.43205i) q^{84} +(2.97542 + 2.97542i) q^{85} +(-4.43127 - 4.43127i) q^{86} -0.166822i q^{87} +1.84114i q^{88} +(11.9654 - 11.9654i) q^{89} -1.72000 q^{90} +(3.51569 - 8.86791i) q^{91} +5.23662 q^{92} +(2.47255 - 2.47255i) q^{93} +3.68131i q^{94} -7.51956i q^{95} +(3.61320 + 3.61320i) q^{96} +(-1.41557 - 1.41557i) q^{97} +(1.09016 + 6.79963i) q^{98} +(-0.436434 - 0.436434i) 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 $

$2$	0.695639	−	0.695639i	0.491891	−	0.491891i	−0.417011	−	0.908902i	$-0.636922\pi$
$2$	0.695639	−	0.695639i	0.491891	−	0.491891i	0.908902	+	0.417011i	$0.136922\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$			1.03217i			0.516087i
$5$	1.23628	+	1.23628i	0.552880	+	0.552880i	0.927271	−	0.374391i	$-0.122148\pi$
$5$	1.23628	+	1.23628i	0.552880	+	0.552880i	−0.374391	+	0.927271i	$0.622148\pi$
$6$	−0.695639	−	0.695639i	−0.283993	−	0.283993i
$7$	1.20338	+	2.35624i	0.454834	+	0.890576i
$7$	1.20338	+	2.35624i	0.454834	+	0.890576i
$8$	2.10930	+	2.10930i	0.745749	+	0.745749i
$9$	−1.00000			−0.333333
$10$	1.72000			0.543913
$11$	0.436434	+	0.436434i	0.131590	+	0.131590i	0.769834	−	0.638244i	$-0.220339\pi$
$11$	0.436434	+	0.436434i	0.131590	+	0.131590i	−0.638244	+	0.769834i	$0.720339\pi$
$12$	1.03217			0.297963
$13$	−2.38061	−	2.70790i	−0.660262	−	0.751036i
$13$	−2.38061	−	2.70790i	−0.660262	−	0.751036i
$14$	2.47621	+	0.801978i	0.661795	+	0.214338i
$15$	1.23628	−	1.23628i	0.319205	−	0.319205i
$16$	0.870270			0.217567
$17$	2.40676			0.583724			0.291862	−	0.956460i	$-0.405725\pi$
$17$	2.40676			0.583724			0.291862	+	0.956460i	$0.405725\pi$
$18$	−0.695639	+	0.695639i	−0.163964	+	0.163964i
$19$	−3.04121	−	3.04121i	−0.697702	−	0.697702i	0.266212	−	0.963914i	$-0.414228\pi$
$19$	−3.04121	−	3.04121i	−0.697702	−	0.697702i	−0.963914	+	0.266212i	$0.914228\pi$
$20$	−1.27605	+	1.27605i	−0.285334	+	0.285334i
$21$	2.35624	−	1.20338i	0.514174	−	0.262599i
$22$	0.607201			0.129456
$23$		−	5.07339i		−	1.05787i	−0.848661	−	0.528937i	$-0.822591\pi$
$23$		−	5.07339i		−	1.05787i	0.848661	−	0.528937i	$-0.177409\pi$
$24$	2.10930	−	2.10930i	0.430558	−	0.430558i
$25$		−	1.94324i		−	0.388648i
$26$	−3.53976	−	0.227675i	−0.694204	−	0.0446508i
$27$			1.00000i			0.192450i
$28$	−2.43205	+	1.24209i	−0.459615	+	0.234734i
$29$	0.166822			0.0309781			0.0154890	−	0.999880i	$-0.495069\pi$
$29$	0.166822			0.0309781			0.0154890	+	0.999880i	$0.495069\pi$
$30$		−	1.72000i		−	0.314028i
$31$	2.47255	+	2.47255i	0.444084	+	0.444084i	0.893382	−	0.449298i	$-0.148326\pi$
$31$	2.47255	+	2.47255i	0.444084	+	0.444084i	−0.449298	+	0.893382i	$0.648326\pi$
$32$	−3.61320	+	3.61320i	−0.638730	+	0.638730i
$33$	0.436434	−	0.436434i	0.0759735	−	0.0759735i
$34$	1.67423	−	1.67423i	0.287128	−	0.287128i
$35$	−1.42526	+	4.40068i	−0.240913	+	0.743850i
$36$		−	1.03217i		−	0.172029i
$37$	−5.59931	−	5.59931i	−0.920521	−	0.920521i	0.0765450	−	0.997066i	$-0.475611\pi$
$37$	−5.59931	−	5.59931i	−0.920521	−	0.920521i	−0.997066	+	0.0765450i	$0.975611\pi$
$38$	−4.23117			−0.686386
$39$	−2.70790	+	2.38061i	−0.433611	+	0.381202i
$40$			5.21535i			0.824619i
$41$	4.82807	+	4.82807i	0.754018	+	0.754018i	0.975227	−	0.221209i	$-0.0710001\pi$
$41$	4.82807	+	4.82807i	0.754018	+	0.754018i	−0.221209	+	0.975227i	$0.571000\pi$
$42$	0.801978	−	2.47621i	0.123748	−	0.382087i
$43$		−	6.37008i		−	0.971428i	−0.874118	−	0.485714i	$-0.838560\pi$
$43$		−	6.37008i		−	0.971428i	0.874118	−	0.485714i	$-0.161440\pi$
$44$	−0.450476	+	0.450476i	−0.0679118	+	0.0679118i
$45$	−1.23628	−	1.23628i	−0.184293	−	0.184293i
$46$	−3.52924	−	3.52924i	−0.520359	−	0.520359i
$47$	−2.64599	+	2.64599i	−0.385957	+	0.385957i	−0.873243	−	0.487285i	$-0.837987\pi$
$47$	−2.64599	+	2.64599i	−0.385957	+	0.385957i	0.487285	+	0.873243i	$0.337987\pi$
$48$		−	0.870270i		−	0.125613i
$49$	−4.10376	+	5.67090i	−0.586252	+	0.810129i
$50$	−1.35179	−	1.35179i	−0.191173	−	0.191173i
$51$		−	2.40676i		−	0.337013i
$52$	2.79502	−	2.45720i	0.387600	−	0.340752i
$53$	6.46466			0.887990			0.443995	−	0.896029i	$-0.353561\pi$
$53$	6.46466			0.887990			0.443995	+	0.896029i	$0.353561\pi$
$54$	0.695639	+	0.695639i	0.0946644	+	0.0946644i
$55$			1.07911i			0.145507i
$56$	−2.43174	+	7.50830i	−0.324954	+	1.00334i
$57$	−3.04121	+	3.04121i	−0.402818	+	0.402818i
$58$	0.116048	−	0.116048i	0.0152378	−	0.0152378i
$59$	−6.95599	+	6.95599i	−0.905593	+	0.905593i	−0.995913	−	0.0903198i	$-0.971211\pi$
$59$	−6.95599	+	6.95599i	−0.905593	+	0.905593i	0.0903198	+	0.995913i	$0.471211\pi$
$60$	1.27605	+	1.27605i	0.164738	+	0.164738i
$61$		−	3.67293i		−	0.470271i	−0.971963	−	0.235135i	$-0.924447\pi$
$61$		−	3.67293i		−	0.470271i	0.971963	−	0.235135i	$-0.0755533\pi$
$62$	3.44001			0.436881
$63$	−1.20338	−	2.35624i	−0.151611	−	0.296859i
$64$			6.76750i			0.845938i
$65$	0.404620	−	6.29080i	0.0501869	−	0.780278i
$66$		−	0.607201i		−	0.0747413i
$67$	−1.59968	+	1.59968i	−0.195433	+	0.195433i	−0.798039	−	0.602606i	$-0.794129\pi$
$67$	−1.59968	+	1.59968i	−0.195433	+	0.195433i	0.602606	+	0.798039i	$0.294129\pi$
$68$			2.48419i			0.301252i
$69$	−5.07339			−0.610764
$70$	2.06981	+	4.05275i	0.247390	+	0.484396i
$71$	−1.65815	+	1.65815i	−0.196786	+	0.196786i	−0.798621	−	0.601835i	$-0.794437\pi$
$71$	−1.65815	+	1.65815i	−0.196786	+	0.196786i	0.601835	+	0.798621i	$0.294437\pi$
$72$	−2.10930	−	2.10930i	−0.248583	−	0.248583i
$73$	4.88992	−	4.88992i	0.572322	−	0.572322i	−0.360455	−	0.932777i	$-0.617378\pi$
$73$	4.88992	−	4.88992i	0.572322	−	0.572322i	0.932777	+	0.360455i	$0.117378\pi$
$74$	−7.79020			−0.905592
$75$	−1.94324			−0.224386
$76$	3.13906	−	3.13906i	0.360075	−	0.360075i
$77$	−0.503150	+	1.55354i	−0.0573393	+	0.177042i
$78$	−0.227675	+	3.53976i	−0.0257791	+	0.400799i
$79$	−9.79014			−1.10148			−0.550739	−	0.834678i	$-0.685654\pi$
$79$	−9.79014			−1.10148			−0.550739	+	0.834678i	$0.685654\pi$
$80$	1.07589	+	1.07589i	0.120289	+	0.120289i
$81$	1.00000			0.111111
$82$	6.71719			0.741789
$83$	4.07668	+	4.07668i	0.447474	+	0.447474i	0.894514	−	0.447040i	$-0.147522\pi$
$83$	4.07668	+	4.07668i	0.447474	+	0.447474i	−0.447040	+	0.894514i	$0.647522\pi$
$84$	1.24209	+	2.43205i	0.135524	+	0.265359i
$85$	2.97542	+	2.97542i	0.322729	+	0.322729i
$86$	−4.43127	−	4.43127i	−0.477836	−	0.477836i
$87$		−	0.166822i		−	0.0178852i
$88$			1.84114i			0.196266i
$89$	11.9654	−	11.9654i	1.26833	−	1.26833i	0.321378	−	0.946951i	$-0.395854\pi$
$89$	11.9654	−	11.9654i	1.26833	−	1.26833i	0.946951	−	0.321378i	$-0.104146\pi$
$90$	−1.72000			−0.181304
$91$	3.51569	−	8.86791i	0.368545	−	0.929610i
$92$	5.23662			0.545955
$93$	2.47255	−	2.47255i	0.256392	−	0.256392i
$94$			3.68131i			0.379698i
$95$		−	7.51956i		−	0.771490i
$96$	3.61320	+	3.61320i	0.368771	+	0.368771i
$97$	−1.41557	−	1.41557i	−0.143730	−	0.143730i	0.631580	−	0.775310i	$-0.282407\pi$
$97$	−1.41557	−	1.41557i	−0.143730	−	0.143730i	−0.775310	+	0.631580i	$0.782407\pi$
$98$	1.09016	+	6.79963i	0.110123	+	0.686867i
$99$	−0.436434	−	0.436434i	−0.0438633	−	0.0438633i
$100$	2.00576			0.200576
$101$	−16.8635			−1.67798			−0.838992	−	0.544144i	$-0.816855\pi$
$101$	−16.8635			−1.67798			−0.838992	+	0.544144i	$0.816855\pi$
$102$	−1.67423	−	1.67423i	−0.165774	−	0.165774i
$103$	−14.7431			−1.45268			−0.726342	−	0.687333i	$-0.758781\pi$
$103$	−14.7431			−1.45268			−0.726342	+	0.687333i	$0.758781\pi$
$104$	0.690350	−	10.7332i	0.0676944	−	1.05247i
$105$	4.40068	+	1.42526i	0.429462	+	0.139091i
$106$	4.49707	−	4.49707i	0.436794	−	0.436794i
$107$	−11.0553			−1.06876			−0.534379	−	0.845245i	$-0.679454\pi$
$107$	−11.0553			−1.06876			−0.534379	+	0.845245i	$0.679454\pi$
$108$	−1.03217			−0.0993210
$109$	9.27976	−	9.27976i	0.888840	−	0.888840i	−0.105572	−	0.994412i	$-0.533667\pi$
$109$	9.27976	−	9.27976i	0.888840	−	0.888840i	0.994412	+	0.105572i	$0.0336672\pi$
$110$	0.750668	+	0.750668i	0.0715734	+	0.0715734i
$111$	−5.59931	+	5.59931i	−0.531463	+	0.531463i
$112$	1.04726	+	2.05057i	0.0989571	+	0.193760i
$113$	12.3107			1.15810			0.579048	−	0.815294i	$-0.303425\pi$
$113$	12.3107			1.15810			0.579048	+	0.815294i	$0.303425\pi$
$114$			4.23117i			0.396285i
$115$	6.27211	−	6.27211i	0.584877	−	0.584877i
$116$			0.172189i			0.0159874i
$117$	2.38061	+	2.70790i	0.220087	+	0.250345i
$118$			9.67771i			0.890906i
$119$	2.89624	+	5.67090i	0.265498	+	0.519851i
$120$	5.21535			0.476094
$121$		−	10.6191i		−	0.965368i
$122$	−2.55503	−	2.55503i	−0.231322	−	0.231322i
$123$	4.82807	−	4.82807i	0.435333	−	0.435333i
$124$	−2.55210	+	2.55210i	−0.229186	+	0.229186i
$125$	8.58377	−	8.58377i	0.767755	−	0.767755i
$126$	−2.47621	−	0.801978i	−0.220598	−	0.0714459i
$127$			17.7901i			1.57862i	0.613995	+	0.789310i	$0.289562\pi$
$127$			17.7901i			1.57862i	−0.613995	+	0.789310i	$0.710438\pi$
$128$	−2.51866	−	2.51866i	−0.222621	−	0.222621i
$129$	−6.37008			−0.560854
$130$	−4.09465	−	4.65759i	−0.359125	−	0.408498i
$131$			2.33242i			0.203784i	0.994795	+	0.101892i	$0.0324896\pi$
$131$			2.33242i			0.203784i	−0.994795	+	0.101892i	$0.967510\pi$
$132$	0.450476	+	0.450476i	0.0392089	+	0.0392089i
$133$	3.50611	−	10.8256i	0.304018	−	0.938695i
$134$			2.22560i			0.192263i
$135$	−1.23628	+	1.23628i	−0.106402	+	0.106402i
$136$	5.07656	+	5.07656i	0.435312	+	0.435312i
$137$	9.74888	+	9.74888i	0.832903	+	0.832903i	0.987913	−	0.155010i	$-0.0495410\pi$
$137$	9.74888	+	9.74888i	0.832903	+	0.832903i	−0.155010	+	0.987913i	$0.549541\pi$
$138$	−3.52924	+	3.52924i	−0.300429	+	0.300429i
$139$			17.5778i			1.49093i	0.666546	+	0.745463i	$0.267772\pi$
$139$			17.5778i			1.49093i	−0.666546	+	0.745463i	$0.732228\pi$
$140$	−4.54226	−	1.47112i	−0.383891	−	0.124332i
$141$	2.64599	+	2.64599i	0.222833	+	0.222833i
$142$			2.30695i			0.193595i
$143$	0.142840	−	2.22080i	0.0119449	−	0.185712i
$144$	−0.870270			−0.0725225
$145$	0.206238	+	0.206238i	0.0171272	+	0.0171272i
$146$		−	6.80324i		−	0.563040i
$147$	5.67090	+	4.10376i	0.467728	+	0.338473i
$148$	5.77946	−	5.77946i	0.475069	−	0.475069i
$149$	−0.269612	+	0.269612i	−0.0220875	+	0.0220875i	−0.718064	−	0.695977i	$-0.754972\pi$
$149$	−0.269612	+	0.269612i	−0.0220875	+	0.0220875i	0.695977	+	0.718064i	$0.254972\pi$
$150$	−1.35179	+	1.35179i	−0.110374	+	0.110374i
$151$	−3.72152	−	3.72152i	−0.302853	−	0.302853i	0.539276	−	0.842129i	$-0.318698\pi$
$151$	−3.72152	−	3.72152i	−0.302853	−	0.302853i	−0.842129	+	0.539276i	$0.818698\pi$
$152$		−	12.8296i		−	1.04062i
$153$	−2.40676			−0.194575
$154$	0.730692	+	1.43071i	0.0588809	+	0.115290i
$155$			6.11352i			0.491050i
$156$	−2.45720	−	2.79502i	−0.196734	−	0.223781i
$157$			17.5809i			1.40311i	0.712618	+	0.701553i	$0.247510\pi$
$157$			17.5809i			1.40311i	−0.712618	+	0.701553i	$0.752490\pi$
$158$	−6.81040	+	6.81040i	−0.541807	+	0.541807i
$159$		−	6.46466i		−	0.512681i
$160$	−8.93383			−0.706281
$161$	11.9541	−	6.10520i	0.942118	−	0.481157i
$162$	0.695639	−	0.695639i	0.0546545	−	0.0546545i
$163$	−1.00752	−	1.00752i	−0.0789148	−	0.0789148i	0.666548	−	0.745462i	$-0.267771\pi$
$163$	−1.00752	−	1.00752i	−0.0789148	−	0.0789148i	−0.745462	+	0.666548i	$0.767771\pi$
$164$	−4.98341	+	4.98341i	−0.389139	+	0.389139i
$165$	1.07911			0.0840084
$166$	5.67180			0.440217
$167$	16.0507	−	16.0507i	1.24204	−	1.24204i	0.282889	−	0.959153i	$-0.408707\pi$
$167$	16.0507	−	16.0507i	1.24204	−	1.24204i	0.959153	−	0.282889i	$-0.0912929\pi$
$168$	7.50830	+	2.43174i	0.579278	+	0.187612i
$169$	−1.66541	+	12.8929i	−0.128109	+	0.991760i
$170$	4.13963			0.317495
$171$	3.04121	+	3.04121i	0.232567	+	0.232567i
$172$	6.57503			0.501341
$173$	12.8330			0.975676			0.487838	−	0.872934i	$-0.337786\pi$
$173$	12.8330			0.975676			0.487838	+	0.872934i	$0.337786\pi$
$174$	−0.116048	−	0.116048i	−0.00879757	−	0.00879757i
$175$	4.57875	−	2.33845i	0.346121	−	0.176770i
$176$	0.379816	+	0.379816i	0.0286297	+	0.0286297i
$177$	6.95599	+	6.95599i	0.522844	+	0.522844i
$178$		−	16.6472i		−	1.24776i
$179$		−	17.3893i		−	1.29974i	−0.760046	−	0.649869i	$-0.774824\pi$
$179$		−	17.3893i		−	1.29974i	0.760046	−	0.649869i	$-0.225176\pi$
$180$	1.27605	−	1.27605i	0.0951113	−	0.0951113i
$181$	−14.1584			−1.05238			−0.526191	−	0.850366i	$-0.676380\pi$
$181$	−14.1584			−1.05238			−0.526191	+	0.850366i	$0.676380\pi$
$182$	−3.72321	−	8.61452i	−0.275983	−	0.638550i
$183$	−3.67293			−0.271511
$184$	10.7013	−	10.7013i	0.788909	−	0.788909i
$185$		−	13.8446i		−	1.01787i
$186$		−	3.44001i		−	0.252234i
$187$	1.05039	+	1.05039i	0.0768122	+	0.0768122i
$188$	−2.73112	−	2.73112i	−0.199188	−	0.199188i
$189$	−2.35624	+	1.20338i	−0.171391	+	0.0875329i
$190$	−5.23090	−	5.23090i	−0.379489	−	0.379489i
$191$	−1.61029			−0.116516			−0.0582581	−	0.998302i	$-0.518555\pi$
$191$	−1.61029			−0.116516			−0.0582581	+	0.998302i	$0.518555\pi$
$192$	6.76750			0.488403
$193$	15.5701	+	15.5701i	1.12076	+	1.12076i	0.991627	+	0.129132i	$0.0412190\pi$
$193$	15.5701	+	15.5701i	1.12076	+	1.12076i	0.129132	+	0.991627i	$0.458781\pi$
$194$	−1.96946			−0.141399
$195$	−6.29080	−	0.404620i	−0.450493	−	0.0289754i
$196$	−5.85336	−	4.23580i	−0.418097	−	0.302557i
$197$	−12.8905	+	12.8905i	−0.918408	+	0.918408i	−0.996914	−	0.0785057i	$-0.974985\pi$
$197$	−12.8905	+	12.8905i	−0.918408	+	0.918408i	0.0785057	+	0.996914i	$0.474985\pi$
$198$	−0.607201			−0.0431519
$199$	13.5710			0.962024			0.481012	−	0.876714i	$-0.340269\pi$
$199$	13.5710			0.962024			0.481012	+	0.876714i	$0.340269\pi$
$200$	4.09887	−	4.09887i	0.289834	−	0.289834i
$201$	1.59968	+	1.59968i	0.112833	+	0.112833i
$202$	−11.7309	+	11.7309i	−0.825385	+	0.825385i
$203$	0.200750	+	0.393073i	0.0140899	+	0.0275883i
$204$	2.48419			0.173928
$205$			11.9377i			0.833762i
$206$	−10.2559	+	10.2559i	−0.714562	+	0.714562i
$207$			5.07339i			0.352625i
$208$	−2.07177	−	2.35660i	−0.143651	−	0.163401i
$209$		−	2.65458i		−	0.183621i
$210$	4.05275	−	2.06981i	0.279666	−	0.142831i
$211$	−12.1333			−0.835292			−0.417646	−	0.908610i	$-0.637145\pi$
$211$	−12.1333			−0.835292			−0.417646	+	0.908610i	$0.637145\pi$
$212$			6.67266i			0.458280i
$213$	1.65815	+	1.65815i	0.113615	+	0.113615i
$214$	−7.69050	+	7.69050i	−0.525712	+	0.525712i
$215$	7.87518	−	7.87518i	0.537083	−	0.537083i
$216$	−2.10930	+	2.10930i	−0.143519	+	0.143519i
$217$	−2.85052	+	8.80135i	−0.193506	+	0.597475i
$218$		−	12.9107i		−	0.874425i
$219$	−4.88992	−	4.88992i	−0.330430	−	0.330430i
$220$	−1.11383			−0.0750941
$221$	−5.72954	−	6.51725i	−0.385411	−	0.438397i
$222$			7.79020i			0.522844i
$223$	−4.74466	−	4.74466i	−0.317726	−	0.317726i	0.530167	−	0.847893i	$-0.322129\pi$
$223$	−4.74466	−	4.74466i	−0.317726	−	0.317726i	−0.847893	+	0.530167i	$0.822129\pi$
$224$	−12.8616	−	4.16553i	−0.859354	−	0.278321i
$225$			1.94324i			0.129549i
$226$	8.56381	−	8.56381i	0.569656	−	0.569656i
$227$	10.5233	+	10.5233i	0.698454	+	0.698454i	0.964077	−	0.265623i	$-0.0855776\pi$
$227$	10.5233	+	10.5233i	0.698454	+	0.698454i	−0.265623	+	0.964077i	$0.585578\pi$
$228$	−3.13906	−	3.13906i	−0.207889	−	0.207889i
$229$	−20.7310	+	20.7310i	−1.36994	+	1.36994i	−0.509427	+	0.860514i	$0.670142\pi$
$229$	−20.7310	+	20.7310i	−1.36994	+	1.36994i	−0.860514	+	0.509427i	$0.829858\pi$
$230$		−	8.72624i		−	0.575391i
$231$	1.55354	+	0.503150i	0.102215	+	0.0331048i
$232$	0.351877	+	0.351877i	0.0231019	+	0.0231019i
$233$			6.37148i			0.417409i	0.977979	+	0.208705i	$0.0669247\pi$
$233$			6.37148i			0.417409i	−0.977979	+	0.208705i	$0.933075\pi$
$234$	3.53976	+	0.227675i	0.231401	+	0.0148836i
$235$	−6.54235			−0.426776
$236$	−7.17979	−	7.17979i	−0.467365	−	0.467365i
$237$			9.79014i			0.635938i
$238$	5.95963	+	1.93016i	0.386306	+	0.125114i
$239$	−18.6706	+	18.6706i	−1.20770	+	1.20770i	−0.235935	+	0.971769i	$0.575815\pi$
$239$	−18.6706	+	18.6706i	−1.20770	+	1.20770i	−0.971769	+	0.235935i	$0.924185\pi$
$240$	1.07589	−	1.07589i	0.0694487	−	0.0694487i
$241$	2.22932	−	2.22932i	0.143603	−	0.143603i	−0.631650	−	0.775253i	$-0.717622\pi$
$241$	2.22932	−	2.22932i	0.143603	−	0.143603i	0.775253	+	0.631650i	$0.217622\pi$
$242$	−7.38702	−	7.38702i	−0.474856	−	0.474856i
$243$		−	1.00000i		−	0.0641500i
$244$	3.79110			0.242700
$245$	−12.0842	+	1.93742i	−0.772030	+	0.123777i
$246$		−	6.71719i		−	0.428272i
$247$	−0.995356	+	15.4752i	−0.0633330	+	0.984665i
$248$			10.4307i			0.662350i
$249$	4.07668	−	4.07668i	0.258349	−	0.258349i
$250$		−	11.9424i		−	0.755304i
$251$	1.06046			0.0669356			0.0334678	−	0.999440i	$-0.489345\pi$
$251$	1.06046			0.0669356			0.0334678	+	0.999440i	$0.489345\pi$
$252$	2.43205	−	1.24209i	0.153205	−	0.0782446i
$253$	2.21420	−	2.21420i	0.139206	−	0.139206i
$254$	12.3755	+	12.3755i	0.776509	+	0.776509i
$255$	2.97542	−	2.97542i	0.186328	−	0.186328i
$256$	−17.0392			−1.06495
$257$	7.75932			0.484013			0.242007	−	0.970275i	$-0.422194\pi$
$257$	7.75932			0.484013			0.242007	+	0.970275i	$0.422194\pi$
$258$	−4.43127	+	4.43127i	−0.275879	+	0.275879i
$259$	6.45525	−	19.9314i	0.401110	−	1.23848i
$260$	6.49320	+	0.417638i	0.402691	+	0.0259008i
$261$	−0.166822			−0.0103260
$262$	1.62252	+	1.62252i	0.100240	+	0.100240i
$263$	−5.08859			−0.313776			−0.156888	−	0.987616i	$-0.550146\pi$
$263$	−5.08859			−0.313776			−0.156888	+	0.987616i	$0.550146\pi$
$264$	1.84114			0.113314
$265$	7.99211	+	7.99211i	0.490951	+	0.490951i
$266$	−5.09170	−	9.96966i	−0.312192	−	0.611279i
$267$	−11.9654	−	11.9654i	−0.732270	−	0.732270i
$268$	−1.65115	−	1.65115i	−0.100860	−	0.100860i
$269$		−	12.9830i		−	0.791585i	−0.918340	−	0.395793i	$-0.870470\pi$
$269$		−	12.9830i		−	0.791585i	0.918340	−	0.395793i	$-0.129530\pi$
$270$			1.72000i			0.104676i
$271$	−5.68824	+	5.68824i	−0.345536	+	0.345536i	−0.858444	−	0.512908i	$-0.828568\pi$
$271$	−5.68824	+	5.68824i	−0.345536	+	0.345536i	0.512908	+	0.858444i	$0.328568\pi$
$272$	2.09453			0.126999
$273$	−8.86791	−	3.51569i	−0.536711	−	0.212779i
$274$	13.5634			0.819395
$275$	0.848097	−	0.848097i	0.0511422	−	0.0511422i
$276$		−	5.23662i		−	0.315207i
$277$			7.99926i			0.480629i	0.970695	+	0.240314i	$0.0772505\pi$
$277$			7.99926i			0.480629i	−0.970695	+	0.240314i	$0.922749\pi$
$278$	12.2278	+	12.2278i	0.733373	+	0.733373i
$279$	−2.47255	−	2.47255i	−0.148028	−	0.148028i
$280$	−12.2886	+	6.27604i	−0.734386	+	0.375065i
$281$	−12.1673	−	12.1673i	−0.725839	−	0.725839i	0.243949	−	0.969788i	$-0.421557\pi$
$281$	−12.1673	−	12.1673i	−0.725839	−	0.725839i	−0.969788	+	0.243949i	$0.921557\pi$
$282$	3.68131			0.219219
$283$	−3.07612			−0.182857			−0.0914283	−	0.995812i	$-0.529143\pi$
$283$	−3.07612			−0.182857			−0.0914283	+	0.995812i	$0.529143\pi$
$284$	−1.71150	−	1.71150i	−0.101559	−	0.101559i
$285$	−7.51956			−0.445420
$286$	−1.44551	−	1.64424i	−0.0854747	−	0.0972258i
$287$	−5.56612	+	17.1861i	−0.328557	+	1.01446i
$288$	3.61320	−	3.61320i	0.212910	−	0.212910i
$289$	−11.2075			−0.659266
$290$	0.286935			0.0168494
$291$	−1.41557	+	1.41557i	−0.0829825	+	0.0829825i
$292$	5.04725	+	5.04725i	0.295368	+	0.295368i
$293$	18.7336	−	18.7336i	1.09443	−	1.09443i	0.0993799	−	0.995050i	$-0.468314\pi$
$293$	18.7336	−	18.7336i	1.09443	−	1.09443i	0.995050	−	0.0993799i	$-0.0316859\pi$
$294$	6.79963	−	1.09016i	0.396563	−	0.0635795i
$295$	−17.1991			−1.00137
$296$		−	23.6212i		−	1.37296i
$297$	−0.436434	+	0.436434i	−0.0253245	+	0.0253245i
$298$			0.375105i			0.0217293i
$299$	−13.7382	+	12.0777i	−0.794501	+	0.698474i
$300$		−	2.00576i		−	0.115803i
$301$	15.0095	−	7.66561i	0.865130	−	0.441838i
$302$	−5.17767			−0.297942
$303$			16.8635i			0.968784i
$304$	−2.64668	−	2.64668i	−0.151797	−	0.151797i
$305$	4.54076	−	4.54076i	0.260003	−	0.260003i
$306$	−1.67423	+	1.67423i	−0.0957095	+	0.0957095i
$307$	4.74652	−	4.74652i	0.270898	−	0.270898i	−0.558563	−	0.829462i	$-0.688647\pi$
$307$	4.74652	−	4.74652i	0.270898	−	0.270898i	0.829462	+	0.558563i	$0.188647\pi$
$308$	−1.60352	−	0.519338i	−0.0913693	−	0.0295920i
$309$			14.7431i			0.838708i
$310$	4.25280	+	4.25280i	0.241543	+	0.241543i
$311$	−25.2400			−1.43123			−0.715616	−	0.698494i	$-0.753854\pi$
$311$	−25.2400			−1.43123			−0.715616	+	0.698494i	$0.753854\pi$
$312$	−10.7332	−	0.690350i	−0.607646	−	0.0390834i
$313$		−	4.80127i		−	0.271384i	−0.990751	−	0.135692i	$-0.956674\pi$
$313$		−	4.80127i		−	0.271384i	0.990751	−	0.135692i	$-0.0433257\pi$
$314$	12.2299	+	12.2299i	0.690175	+	0.690175i
$315$	1.42526	−	4.40068i	0.0803043	−	0.247950i
$316$		−	10.1051i		−	0.568458i
$317$	−12.4651	+	12.4651i	−0.700111	+	0.700111i	−0.964434	−	0.264324i	$-0.914851\pi$
$317$	−12.4651	+	12.4651i	−0.700111	+	0.700111i	0.264324	+	0.964434i	$0.414851\pi$
$318$	−4.49707	−	4.49707i	−0.252183	−	0.252183i
$319$	0.0728069	+	0.0728069i	0.00407640	+	0.00407640i
$320$	−8.36651	+	8.36651i	−0.467702	+	0.467702i
$321$			11.0553i			0.617047i
$322$	4.06874	−	12.5628i	0.226742	−	0.700096i
$323$	−7.31945	−	7.31945i	−0.407265	−	0.407265i
$324$			1.03217i			0.0573430i
$325$	−5.26210	+	4.62610i	−0.291889	+	0.256610i
$326$	−1.40174			−0.0776349
$327$	−9.27976	−	9.27976i	−0.513172	−	0.513172i
$328$			20.3677i			1.12462i
$329$	−9.41872	−	3.05047i	−0.519271	−	0.168178i
$330$	0.750668	−	0.750668i	0.0413229	−	0.0413229i
$331$	4.48479	−	4.48479i	0.246506	−	0.246506i	−0.573029	−	0.819535i	$-0.694232\pi$
$331$	4.48479	−	4.48479i	0.246506	−	0.246506i	0.819535	+	0.573029i	$0.194232\pi$
$332$	−4.20785	+	4.20785i	−0.230936	+	0.230936i
$333$	5.59931	+	5.59931i	0.306840	+	0.306840i
$334$		−	22.3310i		−	1.22190i
$335$	−3.95530			−0.216101
$336$	2.05057	−	1.04726i	0.111868	−	0.0571329i
$337$			12.2741i			0.668611i	0.942465	+	0.334306i	$0.108502\pi$
$337$			12.2741i			0.668611i	−0.942465	+	0.334306i	$0.891498\pi$
$338$	7.81026	+	10.1273i	0.424822	+	0.550853i
$339$		−	12.3107i		−	0.668627i
$340$	−3.07115	+	3.07115i	−0.166556	+	0.166556i
$341$			2.15821i			0.116874i
$342$	4.23117			0.228795
$343$	−18.3004	−	2.84523i	−0.988129	−	0.153628i
$344$	13.4364	−	13.4364i	0.724442	−	0.724442i
$345$	−6.27211	−	6.27211i	−0.337679	−	0.337679i
$346$	8.92714	−	8.92714i	0.479926	−	0.479926i
$347$	32.4407			1.74151			0.870754	−	0.491719i	$-0.163631\pi$
$347$	32.4407			1.74151			0.870754	+	0.491719i	$0.163631\pi$
$348$	0.172189			0.00923032
$349$	20.5692	−	20.5692i	1.10104	−	1.10104i	0.106760	−	0.994285i	$-0.465952\pi$
$349$	20.5692	−	20.5692i	1.10104	−	1.10104i	0.994285	−	0.106760i	$-0.0340477\pi$
$350$	1.55844	−	4.81187i	0.0833019	−	0.257205i
$351$	2.70790	−	2.38061i	0.144537	−	0.127067i
$352$	−3.15385			−0.168101
$353$	9.10052	+	9.10052i	0.484372	+	0.484372i	0.906525	−	0.422153i	$-0.138725\pi$
$353$	9.10052	+	9.10052i	0.484372	+	0.484372i	−0.422153	+	0.906525i	$0.638725\pi$
$354$	9.67771			0.514365
$355$	−4.09987			−0.217598
$356$	12.3504	+	12.3504i	0.654568	+	0.654568i
$357$	5.67090	−	2.89624i	0.300136	−	0.153285i
$358$	−12.0967	−	12.0967i	−0.639329	−	0.639329i
$359$	17.3029	+	17.3029i	0.913215	+	0.913215i	0.996524	−	0.0833092i	$-0.0265489\pi$
$359$	17.3029	+	17.3029i	0.913215	+	0.913215i	−0.0833092	+	0.996524i	$0.526549\pi$
$360$		−	5.21535i		−	0.274873i
$361$		−	0.502056i		−	0.0264240i
$362$	−9.84910	+	9.84910i	−0.517657	+	0.517657i
$363$	−10.6191			−0.557356
$364$	9.15323	+	3.62881i	0.479760	+	0.190201i
$365$	12.0906			0.632851
$366$	−2.55503	+	2.55503i	−0.133554	+	0.133554i
$367$		−	19.1370i		−	0.998941i	−0.866331	−	0.499471i	$-0.833528\pi$
$367$		−	19.1370i		−	0.998941i	0.866331	−	0.499471i	$-0.166472\pi$
$368$		−	4.41522i		−	0.230159i
$369$	−4.82807	−	4.82807i	−0.251339	−	0.251339i
$370$	−9.63083	−	9.63083i	−0.500683	−	0.500683i
$371$	7.77943	+	15.2323i	0.403888	+	0.790823i
$372$	2.55210	+	2.55210i	0.132320	+	0.132320i
$373$	8.12926			0.420917			0.210459	−	0.977603i	$-0.432504\pi$
$373$	8.12926			0.420917			0.210459	+	0.977603i	$0.432504\pi$
$374$	1.46138			0.0755664
$375$	−8.58377	−	8.58377i	−0.443264	−	0.443264i
$376$	−11.1624			−0.575655
$377$	−0.397138	−	0.451737i	−0.0204536	−	0.0232656i
$378$	−0.801978	+	2.47621i	−0.0412493	+	0.127362i
$379$	10.0128	−	10.0128i	0.514321	−	0.514321i	−0.401526	−	0.915848i	$-0.631520\pi$
$379$	10.0128	−	10.0128i	0.514321	−	0.514321i	0.915848	+	0.401526i	$0.131520\pi$
$380$	7.76149			0.398156
$381$	17.7901			0.911417
$382$	−1.12018	+	1.12018i	−0.0573133	+	0.0573133i
$383$	27.1171	+	27.1171i	1.38562	+	1.38562i	0.834284	+	0.551334i	$0.185881\pi$
$383$	27.1171	+	27.1171i	1.38562	+	1.38562i	0.551334	+	0.834284i	$0.314119\pi$
$384$	−2.51866	+	2.51866i	−0.128530	+	0.128530i
$385$	−2.54264	+	1.29857i	−0.129585	+	0.0661814i
$386$	21.6623			1.10258
$387$			6.37008i			0.323809i
$388$	1.46112	−	1.46112i	0.0741771	−	0.0741771i
$389$			34.8952i			1.76926i	0.466297	+	0.884628i	$0.345588\pi$
$389$			34.8952i			1.76926i	−0.466297	+	0.884628i	$0.654412\pi$
$390$	−4.65759	+	4.09465i	−0.235846	+	0.207341i
$391$		−	12.2104i		−	0.617506i
$392$	−20.6177	+	3.30556i	−1.04135	+	0.166956i
$393$	2.33242			0.117655
$394$			17.9342i			0.903513i
$395$	−12.1033	−	12.1033i	−0.608984	−	0.608984i
$396$	0.450476	−	0.450476i	0.0226373	−	0.0226373i
$397$	21.8818	−	21.8818i	1.09822	−	1.09822i	0.103599	−	0.994619i	$-0.466964\pi$
$397$	21.8818	−	21.8818i	1.09822	−	1.09822i	0.994619	−	0.103599i	$-0.0330359\pi$
$398$	9.44053	−	9.44053i	0.473211	−	0.473211i
$399$	−10.8256	−	3.50611i	−0.541956	−	0.175525i
$400$		−	1.69114i		−	0.0845572i
$401$	7.79276	+	7.79276i	0.389152	+	0.389152i	0.874385	−	0.485233i	$-0.161265\pi$
$401$	7.79276	+	7.79276i	0.389152	+	0.389152i	−0.485233	+	0.874385i	$0.661265\pi$
$402$	2.22560			0.111003
$403$	0.809240	−	12.5816i	0.0403111	−	0.626734i
$404$		−	17.4061i		−	0.865985i
$405$	1.23628	+	1.23628i	0.0614311	+	0.0614311i
$406$	0.413087	+	0.133788i	0.0205011	+	0.00663977i
$407$		−	4.88746i		−	0.242263i
$408$	5.07656	−	5.07656i	0.251327	−	0.251327i
$409$	22.4425	+	22.4425i	1.10971	+	1.10971i	0.993188	+	0.116524i	$0.0371751\pi$
$409$	22.4425	+	22.4425i	1.10971	+	1.10971i	0.116524	+	0.993188i	$0.462825\pi$
$410$	8.30430	+	8.30430i	0.410120	+	0.410120i
$411$	9.74888	−	9.74888i	0.480877	−	0.480877i
$412$		−	15.2175i		−	0.749711i
$413$	−24.7607	−	8.01932i	−1.21839	−	0.394605i
$414$	3.52924	+	3.52924i	0.173453	+	0.173453i
$415$			10.0798i			0.494799i
$416$	18.3858	+	1.18256i	0.901438	+	0.0579799i
$417$	17.5778			0.860787
$418$	−1.84663	−	1.84663i	−0.0903215	−	0.0903215i
$419$			31.2454i			1.52644i	0.646141	+	0.763218i	$0.276382\pi$
$419$			31.2454i			1.52644i	−0.646141	+	0.763218i	$0.723618\pi$
$420$	−1.47112	+	4.54226i	−0.0717831	+	0.221640i
$421$	17.2565	−	17.2565i	0.841029	−	0.841029i	−0.147964	−	0.988993i	$-0.547272\pi$
$421$	17.2565	−	17.2565i	0.841029	−	0.841029i	0.988993	+	0.147964i	$0.0472720\pi$
$422$	−8.44041	+	8.44041i	−0.410873	+	0.410873i
$423$	2.64599	−	2.64599i	0.128652	−	0.128652i
$424$	13.6359	+	13.6359i	0.662218	+	0.662218i
$425$		−	4.67691i		−	0.226863i
$426$	2.30695			0.111772
$427$	8.65432	−	4.41992i	0.418812	−	0.213895i
$428$		−	11.4110i		−	0.551571i
$429$	−2.22080	−	0.142840i	−0.107221	−	0.00689639i
$430$		−	10.9566i		−	0.528372i
$431$	−11.9765	+	11.9765i	−0.576886	+	0.576886i	−0.934044	−	0.357158i	$-0.883746\pi$
$431$	−11.9765	+	11.9765i	−0.576886	+	0.576886i	0.357158	+	0.934044i	$0.383746\pi$
$432$			0.870270i			0.0418709i
$433$	−17.0143			−0.817655			−0.408827	−	0.912612i	$-0.634062\pi$
$433$	−17.0143			−0.817655			−0.408827	+	0.912612i	$0.634062\pi$
$434$	4.13963	+	8.10549i	0.198708	+	0.389076i
$435$	0.206238	−	0.206238i	0.00988837	−	0.00988837i
$436$	9.57833	+	9.57833i	0.458719	+	0.458719i
$437$	−15.4292	+	15.4292i	−0.738081	+	0.738081i
$438$	−6.80324			−0.325071
$439$	28.1092			1.34158			0.670790	−	0.741648i	$-0.265955\pi$
$439$	28.1092			1.34158			0.670790	+	0.741648i	$0.265955\pi$
$440$	−2.27616	+	2.27616i	−0.108512	+	0.108512i
$441$	4.10376	−	5.67090i	0.195417	−	0.270043i
$442$	−8.51934	−	0.547958i	−0.405224	−	0.0260637i
$443$	19.0605			0.905591			0.452795	−	0.891614i	$-0.350427\pi$
$443$	19.0605			0.905591			0.452795	+	0.891614i	$0.350427\pi$
$444$	−5.77946	−	5.77946i	−0.274281	−	0.274281i
$445$	29.5851			1.40247
$446$	−6.60114			−0.312573
$447$	0.269612	+	0.269612i	0.0127522	+	0.0127522i
$448$	−15.9459	+	8.14386i	−0.753372	+	0.384761i
$449$	−10.1856	−	10.1856i	−0.480690	−	0.480690i	0.424662	−	0.905352i	$-0.360393\pi$
$449$	−10.1856	−	10.1856i	−0.480690	−	0.480690i	−0.905352	+	0.424662i	$0.860393\pi$
$450$	1.35179	+	1.35179i	0.0637242	+	0.0637242i
$451$			4.21427i			0.198442i
$452$			12.7068i			0.597678i
$453$	−3.72152	+	3.72152i	−0.174852	+	0.174852i
$454$	14.6408			0.687126
$455$	15.3096	−	6.61682i	0.717723	−	0.310201i
$456$	−12.8296			−0.600803
$457$	7.05936	−	7.05936i	0.330223	−	0.330223i	−0.522448	−	0.852671i	$-0.674981\pi$
$457$	7.05936	−	7.05936i	0.330223	−	0.330223i	0.852671	+	0.522448i	$0.174981\pi$
$458$			28.8425i			1.34772i
$459$			2.40676i			0.112338i
$460$	6.47390	+	6.47390i	0.301847	+	0.301847i
$461$	−29.3823	−	29.3823i	−1.36847	−	1.36847i	−0.862623	−	0.505847i	$-0.831180\pi$
$461$	−29.3823	−	29.3823i	−1.36847	−	1.36847i	−0.505847	−	0.862623i	$-0.668820\pi$
$462$	1.43071	−	0.730692i	0.0665628	−	0.0339949i
$463$	−5.98784	−	5.98784i	−0.278278	−	0.278278i	0.554143	−	0.832421i	$-0.313046\pi$
$463$	−5.98784	−	5.98784i	−0.278278	−	0.278278i	−0.832421	+	0.554143i	$0.813046\pi$
$464$	0.145180			0.00673982
$465$	6.11352			0.283508
$466$	4.43224	+	4.43224i	0.205320	+	0.205320i
$467$	−26.7048			−1.23575			−0.617875	−	0.786276i	$-0.712006\pi$
$467$	−26.7048			−1.23575			−0.617875	+	0.786276i	$0.712006\pi$
$468$	−2.79502	+	2.45720i	−0.129200	+	0.113584i
$469$	−5.69427	−	1.84422i	−0.262937	−	0.0851582i
$470$	−4.55111	+	4.55111i	−0.209927	+	0.209927i
$471$	17.5809			0.810083
$472$	−29.3445			−1.35069
$473$	2.78012	−	2.78012i	0.127830	−	0.127830i
$474$	6.81040	+	6.81040i	0.312812	+	0.312812i
$475$	−5.90981	+	5.90981i	−0.271161	+	0.271161i
$476$	−5.85336	+	2.98942i	−0.268288	+	0.137020i
$477$	−6.46466			−0.295997
$478$			25.9760i			1.18812i
$479$	−9.06708	+	9.06708i	−0.414285	+	0.414285i	−0.883228	−	0.468943i	$-0.844635\pi$
$479$	−9.06708	+	9.06708i	−0.414285	+	0.414285i	0.468943	+	0.883228i	$0.344635\pi$
$480$			8.93383i			0.407772i
$481$	−1.83259	+	28.4921i	−0.0835591	+	1.29913i
$482$		−	3.10160i		−	0.141274i
$483$	−6.10520	−	11.9541i	−0.277796	−	0.543932i
$484$	10.9607			0.498214
$485$		−	3.50008i		−	0.158931i
$486$	−0.695639	−	0.695639i	−0.0315548	−	0.0315548i
$487$	10.1182	−	10.1182i	0.458500	−	0.458500i	−0.439663	−	0.898163i	$-0.644902\pi$
$487$	10.1182	−	10.1182i	0.458500	−	0.458500i	0.898163	+	0.439663i	$0.144902\pi$
$488$	7.74730	−	7.74730i	0.350704	−	0.350704i
$489$	−1.00752	+	1.00752i	−0.0455615	+	0.0455615i
$490$	−7.05849	+	9.75397i	−0.318870	+	0.440639i
$491$		−	33.4254i		−	1.50847i	−0.656607	−	0.754233i	$-0.728009\pi$
$491$		−	33.4254i		−	1.50847i	0.656607	−	0.754233i	$-0.271991\pi$
$492$	4.98341	+	4.98341i	0.224669	+	0.224669i
$493$	0.401500			0.0180827
$494$	10.0728	+	11.4576i	0.453195	+	0.515501i
$495$		−	1.07911i		−	0.0485022i
$496$	2.15179	+	2.15179i	0.0966181	+	0.0966181i
$497$	−5.90239	−	1.91162i	−0.264758	−	0.0857481i
$498$		−	5.67180i		−	0.254159i
$499$	−6.16674	+	6.16674i	−0.276061	+	0.276061i	−0.831535	−	0.555473i	$-0.812537\pi$
$499$	−6.16674	+	6.16674i	−0.276061	+	0.276061i	0.555473	+	0.831535i	$0.312537\pi$
$500$	8.85994	+	8.85994i	0.396228	+	0.396228i
$501$	−16.0507	−	16.0507i	−0.717093	−	0.717093i
$502$	0.737697	−	0.737697i	0.0329250	−	0.0329250i
$503$			24.5304i			1.09376i	0.837212	+	0.546878i	$0.184184\pi$
$503$			24.5304i			1.09376i	−0.837212	+	0.546878i	$0.815816\pi$
$504$	2.43174	−	7.50830i	0.108318	−	0.334446i
$505$	−20.8480	−	20.8480i	−0.927723	−	0.927723i
$506$		−	3.08057i		−	0.136948i
$507$	12.8929	+	1.66541i	0.572593	+	0.0739636i
$508$	−18.3625			−0.814705
$509$	−2.00075	−	2.00075i	−0.0886819	−	0.0886819i	0.661374	−	0.750056i	$-0.269974\pi$
$509$	−2.00075	−	2.00075i	−0.0886819	−	0.0886819i	−0.750056	+	0.661374i	$0.769974\pi$
$510$		−	4.13963i		−	0.183306i
$511$	17.4063	+	5.63742i	0.770008	+	0.249385i
$512$	−6.81578	+	6.81578i	−0.301218	+	0.301218i
$513$	3.04121	−	3.04121i	0.134273	−	0.134273i
$514$	5.39768	−	5.39768i	0.238082	−	0.238082i
$515$	−18.2266	−	18.2266i	−0.803160	−	0.803160i
$516$		−	6.57503i		−	0.289449i
$517$	−2.30960			−0.101576
$518$	−9.37455	−	18.3556i	−0.411894	−	0.806499i
$519$		−	12.8330i		−	0.563307i
$520$	14.1226	−	12.4157i	0.619318	−	0.544464i
$521$		−	23.3476i		−	1.02288i	−0.859320	−	0.511438i	$-0.829113\pi$
$521$		−	23.3476i		−	1.02288i	0.859320	−	0.511438i	$-0.170887\pi$
$522$	−0.116048	+	0.116048i	−0.00507928	+	0.00507928i
$523$		−	14.2481i		−	0.623026i	−0.950242	−	0.311513i	$-0.899164\pi$
$523$		−	14.2481i		−	0.623026i	0.950242	−	0.311513i	$-0.100836\pi$
$524$	−2.40746			−0.105170
$525$	−2.33845	−	4.57875i	−0.102058	−	0.199833i
$526$	−3.53982	+	3.53982i	−0.154343	+	0.154343i
$527$	5.95083	+	5.95083i	0.259222	+	0.259222i
$528$	0.379816	−	0.379816i	0.0165294	−	0.0165294i
$529$	−2.73925			−0.119098
$530$	11.1192			0.482989
$531$	6.95599	−	6.95599i	0.301864	−	0.301864i
$532$	11.1739	+	3.61891i	0.484448	+	0.156900i
$533$	1.58018	−	24.5677i	0.0684450	−	1.06414i
$534$	−16.6472			−0.720394
$535$	−13.6674	−	13.6674i	−0.590894	−	0.590894i
$536$	−6.74842			−0.291487
$537$	−17.3893			−0.750404
$538$	−9.03145	−	9.03145i	−0.389373	−	0.389373i
$539$	−4.26600	+	0.683953i	−0.183750	+	0.0294599i
$540$	−1.27605	−	1.27605i	−0.0549125	−	0.0549125i
$541$	9.94575	+	9.94575i	0.427601	+	0.427601i	0.887811	−	0.460209i	$-0.152226\pi$
$541$	9.94575	+	9.94575i	0.427601	+	0.427601i	−0.460209	+	0.887811i	$0.652226\pi$
$542$			7.91392i			0.339932i
$543$			14.1584i			0.607593i
$544$	−8.69609	+	8.69609i	−0.372842	+	0.372842i
$545$	22.9447			0.982843
$546$	−8.61452	+	3.72321i	−0.368667	+	0.159339i
$547$	−23.3108			−0.996700			−0.498350	−	0.866976i	$-0.666061\pi$
$547$	−23.3108			−0.996700			−0.498350	+	0.866976i	$0.666061\pi$
$548$	−10.0625	+	10.0625i	−0.429850	+	0.429850i
$549$			3.67293i			0.156757i
$550$		−	1.17994i		−	0.0503127i
$551$	−0.507341	−	0.507341i	−0.0216135	−	0.0216135i
$552$	−10.7013	−	10.7013i	−0.455477	−	0.455477i
$553$	−11.7812	−	23.0680i	−0.500989	−	0.980949i
$554$	5.56459	+	5.56459i	0.236417	+	0.236417i
$555$	−13.8446			−0.587670
$556$	−18.1433			−0.769448
$557$	12.9583	+	12.9583i	0.549061	+	0.549061i	0.926169	−	0.377108i	$-0.123082\pi$
$557$	12.9583	+	12.9583i	0.549061	+	0.549061i	−0.377108	+	0.926169i	$0.623082\pi$
$558$	−3.44001			−0.145627
$559$	−17.2495	+	15.1647i	−0.729577	+	0.641397i
$560$	−1.24036	+	3.82978i	−0.0524148	+	0.161838i
$561$	1.05039	−	1.05039i	0.0443475	−	0.0443475i
$562$	−16.9280			−0.714067
$563$	1.17695			0.0496027			0.0248013	−	0.999692i	$-0.492105\pi$
$563$	1.17695			0.0496027			0.0248013	+	0.999692i	$0.492105\pi$
$564$	−2.73112	+	2.73112i	−0.115001	+	0.115001i
$565$	15.2195	+	15.2195i	0.640287	+	0.640287i
$566$	−2.13987	+	2.13987i	−0.0899455	+	0.0899455i
$567$	1.20338	+	2.35624i	0.0505371	+	0.0989529i
$568$	−6.99507			−0.293506
$569$		−	21.1294i		−	0.885791i	−0.896573	−	0.442895i	$-0.853951\pi$
$569$		−	21.1294i		−	0.885791i	0.896573	−	0.442895i	$-0.146049\pi$
$570$	−5.23090	+	5.23090i	−0.219098	+	0.219098i
$571$		−	41.5084i		−	1.73707i	−0.495626	−	0.868536i	$-0.665061\pi$
$571$		−	41.5084i		−	1.73707i	0.495626	−	0.868536i	$-0.334939\pi$
$572$	2.29225	+	0.147436i	0.0958438	+	0.00616461i
$573$			1.61029i			0.0672707i
$574$	8.08331	+	15.8273i	0.337391	+	0.660620i
$575$	−9.85881			−0.411141
$576$		−	6.76750i		−	0.281979i
$577$	−23.3813	−	23.3813i	−0.973375	−	0.973375i	0.0262795	−	0.999655i	$-0.491634\pi$
$577$	−23.3813	−	23.3813i	−0.973375	−	0.973375i	−0.999655	+	0.0262795i	$0.991634\pi$
$578$	−7.79639	+	7.79639i	−0.324287	+	0.324287i
$579$	15.5701	−	15.5701i	0.647071	−	0.647071i
$580$	−0.212874	+	0.212874i	−0.00883910	+	0.00883910i
$581$	−4.69987	+	14.5114i	−0.194983	+	0.602036i
$582$			1.96946i			0.0816366i
$583$	2.82140	+	2.82140i	0.116850	+	0.116850i
$584$	20.6286			0.853618
$585$	−0.404620	+	6.29080i	−0.0167290	+	0.260093i
$586$		−	26.0637i		−	1.07668i
$587$	−8.99127	−	8.99127i	−0.371109	−	0.371109i	0.496772	−	0.867881i	$-0.334519\pi$
$587$	−8.99127	−	8.99127i	−0.371109	−	0.371109i	−0.867881	+	0.496772i	$0.834519\pi$
$588$	−4.23580	+	5.85336i	−0.174681	+	0.241388i
$589$		−	15.0391i		−	0.619676i
$590$	−11.9643	+	11.9643i	−0.492564	+	0.492564i
$591$	12.8905	+	12.8905i	0.530243	+	0.530243i
$592$	−4.87291	−	4.87291i	−0.200275	−	0.200275i
$593$	3.14300	−	3.14300i	0.129068	−	0.129068i	−0.639622	−	0.768690i	$-0.720909\pi$
$593$	3.14300	−	3.14300i	0.129068	−	0.129068i	0.768690	+	0.639622i	$0.220909\pi$
$594$			0.607201i			0.0249138i
$595$	−3.43025	+	10.5914i	−0.140627	+	0.434203i
$596$	−0.278287	−	0.278287i	−0.0113991	−	0.0113991i
$597$		−	13.5710i		−	0.555425i
$598$	−1.15508	+	17.9586i	−0.0472349	+	0.734381i
$599$	−3.89314			−0.159069			−0.0795347	−	0.996832i	$-0.525343\pi$
$599$	−3.89314			−0.159069			−0.0795347	+	0.996832i	$0.525343\pi$
$600$	−4.09887	−	4.09887i	−0.167336	−	0.167336i
$601$			17.2457i			0.703467i	0.936100	+	0.351733i	$0.114408\pi$
$601$			17.2457i			0.703467i	−0.936100	+	0.351733i	$0.885592\pi$
$602$	5.10866	−	15.7737i	0.208213	−	0.642886i
$603$	1.59968	−	1.59968i	0.0651442	−	0.0651442i
$604$	3.84126	−	3.84126i	0.156299	−	0.156299i
$605$	13.1281	−	13.1281i	0.533732	−	0.533732i
$606$	11.7309	+	11.7309i	0.476536	+	0.476536i
$607$			29.7179i			1.20621i	0.797661	+	0.603106i	$0.206070\pi$
$607$			29.7179i			1.20621i	−0.797661	+	0.603106i	$0.793930\pi$
$608$	21.9770			0.891286
$609$	0.393073	−	0.200750i	0.0159281	−	0.00813480i
$610$		−	6.31745i		−	0.255786i
$611$	13.4641	+	0.866004i	0.544701	+	0.0350348i
$612$		−	2.48419i		−	0.100417i
$613$	−31.5296	+	31.5296i	−1.27347	+	1.27347i	−0.329210	+	0.944257i	$0.606782\pi$
$613$	−31.5296	+	31.5296i	−1.27347	+	1.27347i	−0.944257	+	0.329210i	$0.893218\pi$
$614$		−	6.60373i		−	0.266505i
$615$	11.9377			0.481373
$616$	−4.33817	+	2.21559i	−0.174790	+	0.0892685i
$617$	−22.1403	+	22.1403i	−0.891336	+	0.891336i	−0.994649	−	0.103313i	$-0.967056\pi$
$617$	−22.1403	+	22.1403i	−0.891336	+	0.891336i	0.103313	+	0.994649i	$0.467056\pi$
$618$	10.2559	+	10.2559i	0.412553	+	0.412553i
$619$	−3.28951	+	3.28951i	−0.132216	+	0.132216i	−0.770118	−	0.637902i	$-0.779803\pi$
$619$	−3.28951	+	3.28951i	−0.132216	+	0.132216i	0.637902	+	0.770118i	$0.279803\pi$
$620$	−6.31021			−0.253424
$621$	5.07339			0.203588
$622$	−17.5580	+	17.5580i	−0.704010	+	0.704010i
$623$	42.5923	+	13.7945i	1.70642	+	0.552664i
$624$	−2.35660	+	2.07177i	−0.0943396	+	0.0829372i
$625$	11.5076			0.460304
$626$	−3.33995	−	3.33995i	−0.133491	−	0.133491i
$627$	−2.65458			−0.106014
$628$	−18.1465			−0.724124
$629$	−13.4762	−	13.4762i	−0.537330	−	0.537330i
$630$	−2.06981	−	4.05275i	−0.0824634	−	0.161465i
$631$	17.0276	+	17.0276i	0.677858	+	0.677858i	0.959515	−	0.281657i	$-0.0908840\pi$
$631$	17.0276	+	17.0276i	0.677858	+	0.677858i	−0.281657	+	0.959515i	$0.590884\pi$
$632$	−20.6503	−	20.6503i	−0.821426	−	0.821426i
$633$			12.1333i			0.482256i
$634$			17.3424i			0.688756i
$635$	−21.9935	+	21.9935i	−0.872787	+	0.872787i
$636$	6.67266			0.264588
$637$	25.1257	−	2.38762i	0.995515	−	0.0946011i
$638$	0.101295			0.00401029
$639$	1.65815	−	1.65815i	0.0655954	−	0.0655954i
$640$		−	6.22753i		−	0.246165i
$641$		−	25.5087i		−	1.00753i	−0.863840	−	0.503766i	$-0.831947\pi$
$641$		−	25.5087i		−	1.00753i	0.863840	−	0.503766i	$-0.168053\pi$
$642$	7.69050	+	7.69050i	0.303520	+	0.303520i
$643$	−32.2837	−	32.2837i	−1.27314	−	1.27314i	−0.944430	−	0.328714i	$-0.893385\pi$
$643$	−32.2837	−	32.2837i	−1.27314	−	1.27314i	−0.328714	−	0.944430i	$-0.606615\pi$
$644$	6.30163	+	12.3387i	0.248319	+	0.486214i
$645$	−7.87518	−	7.87518i	−0.310085	−	0.310085i
$646$	−10.1834			−0.400660
$647$	3.98609			0.156709			0.0783547	−	0.996926i	$-0.475033\pi$
$647$	3.98609			0.156709			0.0783547	+	0.996926i	$0.475033\pi$
$648$	2.10930	+	2.10930i	0.0828610	+	0.0828610i
$649$	−6.07167			−0.238334
$650$	−0.442428	+	6.87861i	−0.0173534	+	0.269801i
$651$	8.80135	+	2.85052i	0.344952	+	0.111721i
$652$	1.03993	−	1.03993i	0.0407269	−	0.0407269i
$653$	−16.3776			−0.640903			−0.320452	−	0.947265i	$-0.603835\pi$
$653$	−16.3776			−0.640903			−0.320452	+	0.947265i	$0.603835\pi$
$654$	−12.9107			−0.504849
$655$	−2.88351	+	2.88351i	−0.112668	+	0.112668i
$656$	4.20172	+	4.20172i	0.164050	+	0.164050i
$657$	−4.88992	+	4.88992i	−0.190774	+	0.190774i
$658$	−8.67405	+	4.43000i	−0.338150	+	0.172699i
$659$	23.6671			0.921939			0.460970	−	0.887416i	$-0.347502\pi$
$659$	23.6671			0.921939			0.460970	+	0.887416i	$0.347502\pi$
$660$			1.11383i			0.0433556i
$661$	−22.3640	+	22.3640i	−0.869858	+	0.869858i	−0.992456	−	0.122598i	$-0.960877\pi$
$661$	−22.3640	+	22.3640i	−0.869858	+	0.869858i	0.122598	+	0.992456i	$0.460877\pi$
$662$		−	6.23958i		−	0.242508i
$663$	−6.51725	+	5.72954i	−0.253109	+	0.222517i
$664$			17.1979i			0.667407i
$665$	17.7179	−	9.04887i	0.687071	−	0.350900i
$666$	7.79020			0.301864
$667$		−	0.846353i		−	0.0327709i
$668$	16.5671	+	16.5671i	0.641001	+	0.641001i
$669$	−4.74466	+	4.74466i	−0.183439	+	0.183439i
$670$	−2.75146	+	2.75146i	−0.106298	+	0.106298i
$671$	1.60299	−	1.60299i	0.0618828	−	0.0618828i
$672$	−4.16553	+	12.8616i	−0.160689	+	0.496148i
$673$			15.2079i			0.586222i	0.956078	+	0.293111i	$0.0946905\pi$
$673$			15.2079i			0.586222i	−0.956078	+	0.293111i	$0.905309\pi$
$674$	8.53832	+	8.53832i	0.328884	+	0.328884i
$675$	1.94324			0.0747954
$676$	−13.3077	−	1.71900i	−0.511834	−	0.0661152i
$677$		−	37.3151i		−	1.43414i	−0.697003	−	0.717068i	$-0.745484\pi$
$677$		−	37.3151i		−	1.43414i	0.697003	−	0.717068i	$-0.254516\pi$
$678$	−8.56381	−	8.56381i	−0.328891	−	0.328891i
$679$	1.63197	−	5.03891i	0.0626291	−	0.193376i
$680$			12.5521i			0.481350i
$681$	10.5233	−	10.5233i	0.403253	−	0.403253i
$682$	1.50134	+	1.50134i	0.0574892	+	0.0574892i
$683$	−10.3303	−	10.3303i	−0.395280	−	0.395280i	0.481285	−	0.876564i	$-0.340170\pi$
$683$	−10.3303	−	10.3303i	−0.395280	−	0.395280i	−0.876564	+	0.481285i	$0.840170\pi$
$684$	−3.13906	+	3.13906i	−0.120025	+	0.120025i
$685$			24.1046i			0.920990i
$686$	−14.7097	+	10.7512i	−0.561620	+	0.410483i
$687$	20.7310	+	20.7310i	0.790936	+	0.790936i
$688$		−	5.54369i		−	0.211351i
$689$	−15.3898	−	17.5056i	−0.586306	−	0.666912i
$690$	−8.72624			−0.332202
$691$	1.69742	+	1.69742i	0.0645730	+	0.0645730i	0.738656	−	0.674083i	$-0.235461\pi$
$691$	1.69742	+	1.69742i	0.0645730	+	0.0645730i	−0.674083	+	0.738656i	$0.735461\pi$
$692$			13.2459i			0.503533i
$693$	0.503150	−	1.55354i	0.0191131	−	0.0590141i
$694$	22.5670	−	22.5670i	0.856632	−	0.856632i
$695$	−21.7310	+	21.7310i	−0.824303	+	0.824303i
$696$	0.351877	−	0.351877i	0.0133379	−	0.0133379i
$697$	11.6200	+	11.6200i	0.440138	+	0.440138i
$698$		−	28.6175i		−	1.08319i
$699$	6.37148			0.240991
$700$	2.41369	+	4.72606i	0.0912289	+	0.178628i
$701$			26.1912i			0.989227i	0.869113	+	0.494613i	$0.164690\pi$
$701$			26.1912i			0.989227i	−0.869113	+	0.494613i	$0.835310\pi$
$702$	0.227675	−	3.53976i	0.00859304	−	0.133600i
$703$			34.0574i			1.28450i
$704$	−2.95357	+	2.95357i	−0.111317	+	0.111317i
$705$			6.54235i			0.246399i
$706$	12.6613			0.476516
$707$	−20.2932	−	39.7346i	−0.763204	−	1.49437i
$708$	−7.17979	+	7.17979i	−0.269833	+	0.269833i
$709$	−29.5289	−	29.5289i	−1.10898	−	1.10898i	−0.993285	−	0.115697i	$-0.963090\pi$
$709$	−29.5289	−	29.5289i	−1.10898	−	1.10898i	−0.115697	−	0.993285i	$-0.536910\pi$
$710$	−2.85202	+	2.85202i	−0.107035	+	0.107035i
$711$	9.79014			0.367159
$712$	50.4771			1.89171
$713$	12.5442	−	12.5442i	0.469785	−	0.469785i
$714$	1.93016	−	5.95963i	0.0722346	−	0.223034i
$715$	2.92211	−	2.56893i	0.109281	−	0.0960725i
$716$	17.9488			0.670778
$717$	18.6706	+	18.6706i	0.697268	+	0.697268i
$718$	24.0732			0.898404
$719$	−19.7112			−0.735104			−0.367552	−	0.930003i	$-0.619804\pi$
$719$	−19.7112			−0.735104			−0.367552	+	0.930003i	$0.619804\pi$
$720$	−1.07589	−	1.07589i	−0.0400962	−	0.0400962i
$721$	−17.7416	−	34.7384i	−0.660730	−	1.29373i
$722$	−0.349249	−	0.349249i	−0.0129977	−	0.0129977i
$723$	−2.22932	−	2.22932i	−0.0829092	−	0.0829092i
$724$		−	14.6139i		−	0.543121i
$725$		−	0.324176i		−	0.0120396i
$726$	−7.38702	+	7.38702i	−0.274158	+	0.274158i
$727$	34.0497			1.26283			0.631417	−	0.775443i	$-0.282474\pi$
$727$	34.0497			1.26283			0.631417	+	0.775443i	$0.282474\pi$
$728$	26.1207	−	11.2894i	0.968098	−	0.418414i
$729$	−1.00000			−0.0370370
$730$	8.41068	−	8.41068i	0.311293	−	0.311293i
$731$		−	15.3312i		−	0.567046i
$732$		−	3.79110i		−	0.140123i
$733$	0.266410	+	0.266410i	0.00984010	+	0.00984010i	0.712010	−	0.702170i	$-0.247785\pi$
$733$	0.266410	+	0.266410i	0.00984010	+	0.00984010i	−0.702170	+	0.712010i	$0.747785\pi$
$734$	−13.3124	−	13.3124i	−0.491370	−	0.491370i
$735$	1.93742	+	12.0842i	0.0714627	+	0.445732i
$736$	18.3312	+	18.3312i	0.675696	+	0.675696i
$737$	−1.39631			−0.0514339
$738$	−6.71719			−0.247263
$739$	−18.9905	−	18.9905i	−0.698578	−	0.698578i	0.265526	−	0.964104i	$-0.414454\pi$
$739$	−18.9905	−	18.9905i	−0.698578	−	0.698578i	−0.964104	+	0.265526i	$0.914454\pi$
$740$	14.2900			0.525312
$741$	15.4752	+	0.995356i	0.568497	+	0.0365653i
$742$	16.0079	+	5.18452i	0.587667	+	0.190330i
$743$	−1.44435	+	1.44435i	−0.0529882	+	0.0529882i	−0.733104	−	0.680116i	$-0.761929\pi$
$743$	−1.44435	+	1.44435i	−0.0529882	+	0.0529882i	0.680116	+	0.733104i	$0.261929\pi$
$744$	10.4307			0.382408
$745$	−0.666630			−0.0244234
$746$	5.65503	−	5.65503i	0.207045	−	0.207045i
$747$	−4.07668	−	4.07668i	−0.149158	−	0.149158i
$748$	−1.08419	+	1.08419i	−0.0396418	+	0.0396418i
$749$	−13.3037	−	26.0490i	−0.486107	−	0.951810i
$750$	−11.9424			−0.436075
$751$			13.5207i			0.493377i	0.969095	+	0.246688i	$0.0793424\pi$
$751$			13.5207i			0.493377i	−0.969095	+	0.246688i	$0.920658\pi$
$752$	−2.30273	+	2.30273i	−0.0839718	+	0.0839718i
$753$		−	1.06046i		−	0.0386453i
$754$	−0.590510	−	0.0379812i	−0.0215051	−	0.00138320i
$755$		−	9.20167i		−	0.334883i
$756$	−1.24209	−	2.43205i	−0.0451746	−	0.0884529i
$757$	11.6360			0.422916			0.211458	−	0.977387i	$-0.432179\pi$
$757$	11.6360			0.422916			0.211458	+	0.977387i	$0.432179\pi$
$758$		−	13.9305i		−	0.505980i
$759$	−2.21420	−	2.21420i	−0.0803704	−	0.0803704i
$760$	15.8610	−	15.8610i	0.575338	−	0.575338i
$761$	24.6474	−	24.6474i	0.893469	−	0.893469i	−0.101379	−	0.994848i	$-0.532325\pi$
$761$	24.6474	−	24.6474i	0.893469	−	0.893469i	0.994848	+	0.101379i	$0.0323254\pi$
$762$	12.3755	−	12.3755i	0.448317	−	0.448317i
$763$	33.0324	+	10.6983i	1.19585	+	0.387305i
$764$		−	1.66210i		−	0.0601325i
$765$	−2.97542	−	2.97542i	−0.107576	−	0.107576i
$766$	37.7274			1.36315
$767$	35.3956	+	2.27662i	1.27806	+	0.0822041i
$768$			17.0392i			0.614848i
$769$	19.3743	+	19.3743i	0.698654	+	0.698654i	0.964120	−	0.265466i	$-0.0855259\pi$
$769$	19.3743	+	19.3743i	0.698654	+	0.698654i	−0.265466	+	0.964120i	$0.585526\pi$
$770$	−0.865420	+	2.67210i	−0.0311876	+	0.0962956i
$771$		−	7.75932i		−	0.279445i
$772$	−16.0710	+	16.0710i	−0.578409	+	0.578409i
$773$	−2.08951	−	2.08951i	−0.0751544	−	0.0751544i	0.668530	−	0.743685i	$-0.266924\pi$
$773$	−2.08951	−	2.08951i	−0.0751544	−	0.0751544i	−0.743685	+	0.668530i	$0.766924\pi$
$774$	4.43127	+	4.43127i	0.159279	+	0.159279i
$775$	4.80477	−	4.80477i	0.172592	−	0.172592i
$776$		−	5.97174i		−	0.214373i
$777$	−19.9314	−	6.45525i	−0.715036	−	0.231581i
$778$	24.2744	+	24.2744i	0.870281	+	0.870281i
$779$		−	29.3664i		−	1.05216i
$780$	0.417638	−	6.49320i	0.0149538	−	0.232494i
$781$	−1.44735			−0.0517902
$782$	−8.49403	−	8.49403i	−0.303746	−	0.303746i
$783$			0.166822i			0.00596174i
$784$	−3.57138	+	4.93521i	−0.127549	+	0.176258i
$785$	−21.7348	+	21.7348i	−0.775748	+	0.775748i
$786$	1.62252	−	1.62252i	0.0578733	−	0.0578733i
$787$	−1.65961	+	1.65961i	−0.0591588	+	0.0591588i	−0.736067	−	0.676908i	$-0.763319\pi$
$787$	−1.65961	+	1.65961i	−0.0591588	+	0.0591588i	0.676908	+	0.736067i	$0.263319\pi$
$788$	−13.3052	−	13.3052i	−0.473978	−	0.473978i
$789$			5.08859i			0.181159i
$790$	−16.8391			−0.599108
$791$	14.8144	+	29.0071i	0.526741	+	1.03137i
$792$		−	1.84114i		−	0.0654220i
$793$	−9.94592	+	8.74381i	−0.353190	+	0.310502i
$794$		−	30.4437i		−	1.08041i
$795$	7.99211	−	7.99211i	0.283451	−	0.283451i
$796$			14.0077i			0.496488i
$797$	−11.8936			−0.421294			−0.210647	−	0.977562i	$-0.567557\pi$
$797$	−11.8936			−0.421294			−0.210647	+	0.977562i	$0.567557\pi$
$798$	−9.96966	+	5.09170i	−0.352922	+	0.180244i
$799$	−6.36825	+	6.36825i	−0.225293	+	0.225293i
$800$	7.02132	+	7.02132i	0.248241	+	0.248241i
$801$	−11.9654	+	11.9654i	−0.422776	+	0.422776i
$802$	10.8419			0.382841
$803$	4.26826			0.150624
$804$	−1.65115	+	1.65115i	−0.0582316	+	0.0582316i
$805$	22.3263	+	7.23090i	0.786900	+	0.254856i
$806$	−8.18931	−	9.31518i	−0.288456	−	0.328113i
$807$	−12.9830			−0.457022
$808$	−35.5702	−	35.5702i	−1.25136	−	1.25136i
$809$	−44.3950			−1.56084			−0.780422	−	0.625253i	$-0.784996\pi$
$809$	−44.3950			−1.56084			−0.780422	+	0.625253i	$0.784996\pi$
$810$	1.72000			0.0604348
$811$	−6.35365	−	6.35365i	−0.223107	−	0.223107i	0.586699	−	0.809805i	$-0.300427\pi$
$811$	−6.35365	−	6.35365i	−0.223107	−	0.223107i	−0.809805	+	0.586699i	$0.800427\pi$
$812$	−0.405720	+	0.207209i	−0.0142380	+	0.00727161i
$813$	5.68824	+	5.68824i	0.199495	+	0.199495i
$814$	−3.39991	−	3.39991i	−0.119167	−	0.119167i
$815$		−	2.49114i		−	0.0872608i
$816$		−	2.09453i		−	0.0733231i
$817$	−19.3728	+	19.3728i	−0.677767	+	0.677767i
$818$	31.2238			1.09171
$819$	−3.51569	+	8.86791i	−0.122848	+	0.309870i
$820$	−12.3217			−0.430294
$821$	7.24883	−	7.24883i	0.252986	−	0.252986i	−0.569208	−	0.822194i	$-0.692750\pi$
$821$	7.24883	−	7.24883i	0.252986	−	0.252986i	0.822194	+	0.569208i	$0.192750\pi$
$822$		−	13.5634i		−	0.473078i
$823$			13.7328i			0.478694i	0.970934	+	0.239347i	$0.0769333\pi$
$823$			13.7328i			0.478694i	−0.970934	+	0.239347i	$0.923067\pi$
$824$	−31.0977	−	31.0977i	−1.08334	−	1.08334i
$825$	−0.848097	−	0.848097i	−0.0295270	−	0.0295270i
$826$	−22.8030	+	11.6459i	−0.793419	+	0.405214i
$827$	30.3908	+	30.3908i	1.05679	+	1.05679i	0.998287	+	0.0585057i	$0.0186336\pi$
$827$	30.3908	+	30.3908i	1.05679	+	1.05679i	0.0585057	+	0.998287i	$0.481366\pi$
$828$	−5.23662			−0.181985
$829$	−4.89544			−0.170026			−0.0850128	−	0.996380i	$-0.527093\pi$
$829$	−4.89544			−0.170026			−0.0850128	+	0.996380i	$0.527093\pi$
$830$	7.01191	+	7.01191i	0.243387	+	0.243387i
$831$	7.99926			0.277491
$832$	18.3257	−	16.1108i	0.635330	−	0.558541i
$833$	−9.87676	+	13.6485i	−0.342209	+	0.472892i
$834$	12.2278	−	12.2278i	0.423413	−	0.423413i
$835$	39.6862			1.37340
$836$	2.73999			0.0947644
$837$	−2.47255	+	2.47255i	−0.0854639	+	0.0854639i
$838$	21.7355	+	21.7355i	0.750840	+	0.750840i
$839$	−20.0820	+	20.0820i	−0.693306	+	0.693306i	−0.962958	−	0.269652i	$-0.913091\pi$
$839$	−20.0820	+	20.0820i	−0.693306	+	0.693306i	0.269652	+	0.962958i	$0.413091\pi$
$840$	6.27604	+	12.2886i	0.216544	+	0.423998i
$841$	−28.9722			−0.999040
$842$		−	24.0085i		−	0.827388i
$843$	−12.1673	+	12.1673i	−0.419063	+	0.419063i
$844$		−	12.5237i		−	0.431083i
$845$	−17.9981	+	13.8803i	−0.619153	+	0.477495i
$846$		−	3.68131i		−	0.126566i
$847$	25.0211	−	12.7787i	0.859734	−	0.439082i
$848$	5.62600			0.193198
$849$			3.07612i			0.105572i
$850$	−3.25344	−	3.25344i	−0.111592	−	0.111592i
$851$	−28.4075	+	28.4075i	−0.973796	+	0.973796i
$852$	−1.71150	+	1.71150i	−0.0586350	+	0.0586350i
$853$	24.0164	−	24.0164i	0.822307	−	0.822307i	−0.164132	−	0.986438i	$-0.552482\pi$
$853$	24.0164	−	24.0164i	0.822307	−	0.822307i	0.986438	+	0.164132i	$0.0524823\pi$
$854$	2.94561	−	9.09495i	0.100797	−	0.311223i
$855$			7.51956i			0.257163i
$856$	−23.3189	−	23.3189i	−0.797025	−	0.797025i
$857$	11.2917			0.385718			0.192859	−	0.981226i	$-0.438224\pi$
$857$	11.2917			0.385718			0.192859	+	0.981226i	$0.438224\pi$
$858$	−1.64424	+	1.44551i	−0.0561334	+	0.0493488i
$859$		−	46.2098i		−	1.57666i	−0.615254	−	0.788329i	$-0.710947\pi$
$859$		−	46.2098i		−	1.57666i	0.615254	−	0.788329i	$-0.289053\pi$
$860$	8.12855	+	8.12855i	0.277181	+	0.277181i
$861$	17.1861	+	5.56612i	0.585701	+	0.189693i
$862$			16.6626i			0.567529i
$863$	11.2107	−	11.2107i	0.381616	−	0.381616i	−0.490068	−	0.871684i	$-0.663028\pi$
$863$	11.2107	−	11.2107i	0.381616	−	0.381616i	0.871684	+	0.490068i	$0.163028\pi$
$864$	−3.61320	−	3.61320i	−0.122924	−	0.122924i
$865$	15.8651	+	15.8651i	0.539431	+	0.539431i
$866$	−11.8358	+	11.8358i	−0.402197	+	0.402197i
$867$			11.2075i			0.380628i
$868$	−9.08452	−	2.94223i	−0.308349	−	0.0998659i
$869$	−4.27275	−	4.27275i	−0.144943	−	0.144943i
$870$		−	0.286935i		−	0.00972799i
$871$	8.14000	+	0.523560i	0.275813	+	0.0177401i
$872$	39.1476			1.32570
$873$	1.41557	+	1.41557i	0.0479099	+	0.0479099i
$874$			21.4664i			0.726110i
$875$	30.5550	+	9.89593i	1.03295	+	0.334543i
$876$	5.04725	−	5.04725i	0.170531	−	0.170531i
$877$	5.66466	−	5.66466i	0.191282	−	0.191282i	−0.604968	−	0.796250i	$-0.706814\pi$
$877$	5.66466	−	5.66466i	0.191282	−	0.191282i	0.796250	+	0.604968i	$0.206814\pi$
$878$	19.5539	−	19.5539i	0.659911	−	0.659911i
$879$	−18.7336	−	18.7336i	−0.631869	−	0.631869i
$880$			0.939114i			0.0316575i
$881$	−52.6930			−1.77527			−0.887636	−	0.460546i	$-0.847654\pi$
$881$	−52.6930			−1.77527			−0.887636	+	0.460546i	$0.847654\pi$
$882$	−1.09016	−	6.79963i	−0.0367077	−	0.228956i
$883$			2.48665i			0.0836824i	0.999124	+	0.0418412i	$0.0133224\pi$
$883$			2.48665i			0.0836824i	−0.999124	+	0.0418412i	$0.986678\pi$
$884$	6.72693	−	5.91388i	0.226251	−	0.198905i
$885$			17.1991i			0.578140i
$886$	13.2592	−	13.2592i	0.445452	−	0.445452i
$887$			4.40886i			0.148035i	0.997257	+	0.0740175i	$0.0235821\pi$
$887$			4.40886i			0.148035i	−0.997257	+	0.0740175i	$0.976418\pi$
$888$	−23.6212			−0.792676
$889$	−41.9179	+	21.4083i	−1.40588	+	0.718010i
$890$	20.5805	−	20.5805i	0.689860	−	0.689860i
$891$	0.436434	+	0.436434i	0.0146211	+	0.0146211i
$892$	4.89731	−	4.89731i	0.163974	−	0.163974i
$893$	16.0940			0.538566
$894$	0.375105			0.0125454
$895$	21.4980	−	21.4980i	0.718598	−	0.718598i
$896$	2.90368	−	8.96549i	0.0970052	−	0.299516i
$897$	12.0777	+	13.7382i	0.403264	+	0.458705i
$898$	−14.1710			−0.472894
$899$	0.412476	+	0.412476i	0.0137569	+	0.0137569i
$900$	−2.00576			−0.0668588
$901$	15.5589			0.518341
$902$	2.93161	+	2.93161i	0.0976119	+	0.0976119i
$903$	−7.66561	−	15.0095i	−0.255096	−	0.499483i
$904$	25.9670	+	25.9670i	0.863649	+	0.863649i
$905$	−17.5036	−	17.5036i	−0.581841	−	0.581841i
$906$			5.17767i			0.172017i
$907$		−	49.1741i		−	1.63280i	−0.577487	−	0.816400i	$-0.695966\pi$
$907$		−	49.1741i		−	1.63280i	0.577487	−	0.816400i	$-0.304034\pi$
$908$	−10.8618	+	10.8618i	−0.360463	+	0.360463i
$909$	16.8635			0.559328
$910$	6.04700	−	15.2528i	0.200456	−	0.505627i
$911$	−2.22608			−0.0737535			−0.0368767	−	0.999320i	$-0.511741\pi$
$911$	−2.22608			−0.0737535			−0.0368767	+	0.999320i	$0.511741\pi$
$912$	−2.64668	+	2.64668i	−0.0876402	+	0.0876402i
$913$			3.55841i			0.117766i
$914$		−	9.82152i		−	0.324867i
$915$	−4.54076	−	4.54076i	−0.150113	−	0.150113i
$916$	−21.3980	−	21.3980i	−0.707008	−	0.707008i
$917$	−5.49574	+	2.80678i	−0.181485	+	0.0926880i
$918$	1.67423	+	1.67423i	0.0552579	+	0.0552579i
$919$	27.8737			0.919469			0.459734	−	0.888056i	$-0.347945\pi$
$919$	27.8737			0.919469			0.459734	+	0.888056i	$0.347945\pi$
$920$	26.4595			0.872343
$921$	−4.74652	−	4.74652i	−0.156403	−	0.156403i
$922$	−40.8789			−1.34628
$923$	8.43751	+	0.542695i	0.277724	+	0.0178630i
$924$	−0.519338	+	1.60352i	−0.0170850	+	0.0527521i
$925$	−10.8808	+	10.8808i	−0.357759	+	0.357759i
$926$	−8.33074			−0.273765
$927$	14.7431			0.484228
$928$	−0.602762	+	0.602762i	−0.0197866	+	0.0197866i
$929$	29.7110	+	29.7110i	0.974785	+	0.974785i	0.999690	−	0.0249045i	$-0.00792816\pi$
$929$	29.7110	+	29.7110i	0.974785	+	0.974785i	−0.0249045	+	0.999690i	$0.507928\pi$
$930$	4.25280	−	4.25280i	0.139455	−	0.139455i
$931$	29.7268	−	4.76600i	0.974258	−	0.156199i
$932$	−6.57647			−0.215419
$933$			25.2400i			0.826322i
$934$	−18.5769	+	18.5769i	−0.607854	+	0.607854i
$935$			2.59715i			0.0849358i
$936$	−0.690350	+	10.7332i	−0.0225648	+	0.350825i
$937$		−	11.3062i		−	0.369357i	−0.982799	−	0.184678i	$-0.940876\pi$
$937$		−	11.3062i		−	0.369357i	0.982799	−	0.184678i	$-0.0591243\pi$
$938$	−5.24406	+	2.67824i	−0.171225	+	0.0874477i
$939$	−4.80127			−0.156683
$940$		−	6.75284i		−	0.220253i
$941$	−19.9739	−	19.9739i	−0.651129	−	0.651129i	0.302136	−	0.953265i	$-0.402300\pi$
$941$	−19.9739	−	19.9739i	−0.651129	−	0.651129i	−0.953265	+	0.302136i	$0.902300\pi$
$942$	12.2299	−	12.2299i	0.398473	−	0.398473i
$943$	24.4947	−	24.4947i	0.797656	−	0.797656i
$944$	−6.05359	+	6.05359i	−0.197028	+	0.197028i
$945$	−4.40068	−	1.42526i	−0.143154	−	0.0463637i
$946$		−	3.86792i		−	0.125757i
$947$	−2.51571	−	2.51571i	−0.0817495	−	0.0817495i	0.665050	−	0.746799i	$-0.268410\pi$
$947$	−2.51571	−	2.51571i	−0.0817495	−	0.0817495i	−0.746799	+	0.665050i	$0.768410\pi$
$948$	−10.1051			−0.328199
$949$	−24.8824	−	1.60042i	−0.807717	−	0.0519518i
$950$			8.22218i			0.266763i
$951$	12.4651	+	12.4651i	0.404209	+	0.404209i
$952$	−5.85259	+	18.0706i	−0.189684	+	0.585673i
$953$			44.6048i			1.44489i	0.691427	+	0.722446i	$0.256982\pi$
$953$			44.6048i			1.44489i	−0.691427	+	0.722446i	$0.743018\pi$
$954$	−4.49707	+	4.49707i	−0.145598	+	0.145598i
$955$	−1.99076	−	1.99076i	−0.0644194	−	0.0644194i
$956$	−19.2714	−	19.2714i	−0.623280	−	0.623280i
$957$	0.0728069	−	0.0728069i	0.00235351	−	0.00235351i
$958$			12.6148i			0.407566i
$959$	−11.2391	+	34.7023i	−0.362931	+	1.12060i
$960$	8.36651	+	8.36651i	0.270028	+	0.270028i
$961$		−	18.7730i		−	0.605580i
$962$	18.5454	+	21.0950i	0.597928	+	0.680132i
$963$	11.0553			0.356252
$964$	2.30104	+	2.30104i	0.0741116	+	0.0741116i
$965$			38.4979i			1.23929i
$966$	−12.5628	−	4.06874i	−0.404200	−	0.130910i
$967$	−14.7534	+	14.7534i	−0.474437	+	0.474437i	−0.903347	−	0.428910i	$-0.858898\pi$
$967$	−14.7534	+	14.7534i	−0.474437	+	0.474437i	0.428910	+	0.903347i	$0.358898\pi$
$968$	22.3987	−	22.3987i	0.719923	−	0.719923i
$969$	−7.31945	+	7.31945i	−0.235135	+	0.235135i
$970$	−2.43479	−	2.43479i	−0.0781765	−	0.0781765i
$971$			6.72360i			0.215770i	0.994163	+	0.107885i	$0.0344079\pi$
$971$			6.72360i			0.215770i	−0.994163	+	0.107885i	$0.965592\pi$
$972$	1.03217			0.0331070
$973$	−41.4175	+	21.1527i	−1.32778	+	0.678124i
$974$		−	14.0773i		−	0.451064i
$975$	4.62610	+	5.26210i	0.148154	+	0.168522i
$976$		−	3.19644i		−	0.102316i
$977$	28.0472	−	28.0472i	0.897311	−	0.897311i	−0.0978869	−	0.995198i	$-0.531208\pi$
$977$	28.0472	−	28.0472i	0.897311	−	0.897311i	0.995198	+	0.0978869i	$0.0312083\pi$
$978$			1.40174i			0.0448226i
$979$	10.4442			0.333799
$980$	−1.99975	−	12.4730i	−0.0638797	−	0.398435i
$981$	−9.27976	+	9.27976i	−0.296280	+	0.296280i
$982$	−23.2520	−	23.2520i	−0.742001	−	0.742001i
$983$	31.8528	−	31.8528i	1.01595	−	1.01595i	0.0160758	−	0.999871i	$-0.494883\pi$
$983$	31.8528	−	31.8528i	1.01595	−	1.01595i	0.999871	−	0.0160758i	$-0.00511732\pi$
$984$	20.3677			0.649298
$985$	−31.8724			−1.01554
$986$	0.279299	−	0.279299i	0.00889469	−	0.00889469i
$987$	−3.05047	+	9.41872i	−0.0970975	+	0.299801i
$988$	−15.9731	−	1.02738i	−0.508173	−	0.0326853i
$989$	−32.3179			−1.02765
$990$	−0.750668	−	0.750668i	−0.0238578	−	0.0238578i
$991$	−10.7436			−0.341282			−0.170641	−	0.985333i	$-0.554584\pi$
$991$	−10.7436			−0.341282			−0.170641	+	0.985333i	$0.554584\pi$
$992$	−17.8677			−0.567299
$993$	−4.48479	−	4.48479i	−0.142320	−	0.142320i
$994$	−5.43573	+	2.77613i	−0.172411	+	0.0880535i
$995$	16.7775	+	16.7775i	0.531884	+	0.531884i
$996$	4.20785	+	4.20785i	0.133331	+	0.133331i
$997$			12.5550i			0.397622i	0.980038	+	0.198811i	$0.0637079\pi$
$997$			12.5550i			0.397622i	−0.980038	+	0.198811i	$0.936292\pi$
$998$			8.57965i			0.271584i
$999$	5.59931	−	5.59931i	0.177154	−	0.177154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.p.f.265.4	yes	12
3.2	odd	2		819.2.y.f.811.3		12
7.6	odd	2		273.2.p.e.265.4	yes	12
13.8	odd	4		273.2.p.e.34.4	✓	12
21.20	even	2		819.2.y.g.811.3		12
39.8	even	4		819.2.y.g.307.3		12
91.34	even	4	inner	273.2.p.f.34.4	yes	12
273.125	odd	4		819.2.y.f.307.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.e.34.4	✓	12	13.8	odd	4
273.2.p.e.265.4	yes	12	7.6	odd	2
273.2.p.f.34.4	yes	12	91.34	even	4	inner
273.2.p.f.265.4	yes	12	1.1	even	1	trivial
819.2.y.f.307.3		12	273.125	odd	4
819.2.y.f.811.3		12	3.2	odd	2
819.2.y.g.307.3		12	39.8	even	4
819.2.y.g.811.3		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)

\(f(q)\)	\(=\)	\(q+(0.695639 - 0.695639i) q^{2} -1.00000i q^{3} +1.03217i q^{4} +(1.23628 + 1.23628i) q^{5} +(-0.695639 - 0.695639i) q^{6} +(1.20338 + 2.35624i) q^{7} +(2.10930 + 2.10930i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.695639 - 0.695639i) q^{2} -1.00000i q^{3} +1.03217i q^{4} +(1.23628 + 1.23628i) q^{5} +(-0.695639 - 0.695639i) q^{6} +(1.20338 + 2.35624i) q^{7} +(2.10930 + 2.10930i) q^{8} -1.00000 q^{9} +1.72000 q^{10} +(0.436434 + 0.436434i) q^{11} +1.03217 q^{12} +(-2.38061 - 2.70790i) q^{13} +(2.47621 + 0.801978i) q^{14} +(1.23628 - 1.23628i) q^{15} +0.870270 q^{16} +2.40676 q^{17} +(-0.695639 + 0.695639i) q^{18} +(-3.04121 - 3.04121i) q^{19} +(-1.27605 + 1.27605i) q^{20} +(2.35624 - 1.20338i) q^{21} +0.607201 q^{22} -5.07339i q^{23} +(2.10930 - 2.10930i) q^{24} -1.94324i q^{25} +(-3.53976 - 0.227675i) q^{26} +1.00000i q^{27} +(-2.43205 + 1.24209i) q^{28} +0.166822 q^{29} -1.72000i q^{30} +(2.47255 + 2.47255i) q^{31} +(-3.61320 + 3.61320i) q^{32} +(0.436434 - 0.436434i) q^{33} +(1.67423 - 1.67423i) q^{34} +(-1.42526 + 4.40068i) q^{35} -1.03217i q^{36} +(-5.59931 - 5.59931i) q^{37} -4.23117 q^{38} +(-2.70790 + 2.38061i) q^{39} +5.21535i q^{40} +(4.82807 + 4.82807i) q^{41} +(0.801978 - 2.47621i) q^{42} -6.37008i q^{43} +(-0.450476 + 0.450476i) q^{44} +(-1.23628 - 1.23628i) q^{45} +(-3.52924 - 3.52924i) q^{46} +(-2.64599 + 2.64599i) q^{47} -0.870270i q^{48} +(-4.10376 + 5.67090i) q^{49} +(-1.35179 - 1.35179i) q^{50} -2.40676i q^{51} +(2.79502 - 2.45720i) q^{52} +6.46466 q^{53} +(0.695639 + 0.695639i) q^{54} +1.07911i q^{55} +(-2.43174 + 7.50830i) q^{56} +(-3.04121 + 3.04121i) q^{57} +(0.116048 - 0.116048i) q^{58} +(-6.95599 + 6.95599i) q^{59} +(1.27605 + 1.27605i) q^{60} -3.67293i q^{61} +3.44001 q^{62} +(-1.20338 - 2.35624i) q^{63} +6.76750i q^{64} +(0.404620 - 6.29080i) q^{65} -0.607201i q^{66} +(-1.59968 + 1.59968i) q^{67} +2.48419i q^{68} -5.07339 q^{69} +(2.06981 + 4.05275i) q^{70} +(-1.65815 + 1.65815i) q^{71} +(-2.10930 - 2.10930i) q^{72} +(4.88992 - 4.88992i) q^{73} -7.79020 q^{74} -1.94324 q^{75} +(3.13906 - 3.13906i) q^{76} +(-0.503150 + 1.55354i) q^{77} +(-0.227675 + 3.53976i) q^{78} -9.79014 q^{79} +(1.07589 + 1.07589i) q^{80} +1.00000 q^{81} +6.71719 q^{82} +(4.07668 + 4.07668i) q^{83} +(1.24209 + 2.43205i) q^{84} +(2.97542 + 2.97542i) q^{85} +(-4.43127 - 4.43127i) q^{86} -0.166822i q^{87} +1.84114i q^{88} +(11.9654 - 11.9654i) q^{89} -1.72000 q^{90} +(3.51569 - 8.86791i) q^{91} +5.23662 q^{92} +(2.47255 - 2.47255i) q^{93} +3.68131i q^{94} -7.51956i q^{95} +(3.61320 + 3.61320i) q^{96} +(-1.41557 - 1.41557i) q^{97} +(1.09016 + 6.79963i) q^{98} +(-0.436434 - 0.436434i) 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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