LMFDB - Embedded newform 676.2.f.h.239.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(99,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("676.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.f (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:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.3
Root			$-0.00757716 - 1.41419i$ of defining polynomial
Character	$\chi$	$=$	676.239
Dual form			676.2.f.h.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.700535 - 1.22852i) q^{2} +1.61663i q^{3} +(-1.01850 + 1.72124i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(1.98605 - 1.13250i) q^{6} +(1.44528 - 1.44528i) q^{7} +(2.82806 + 0.0454612i) q^{8} +0.386509 q^{9} +O(q^{10})$	\(q+(-0.700535 - 1.22852i) q^{2} +1.61663i q^{3} +(-1.01850 + 1.72124i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(1.98605 - 1.13250i) q^{6} +(1.44528 - 1.44528i) q^{7} +(2.82806 + 0.0454612i) q^{8} +0.386509 q^{9} +(2.94755 + 0.806745i) q^{10} +(3.06191 - 3.06191i) q^{11} +(-2.78260 - 1.64654i) q^{12} +(-2.78801 - 0.763079i) q^{14} +(-2.47018 - 2.47018i) q^{15} +(-1.92531 - 3.50617i) q^{16} +4.78801i q^{17} +(-0.270763 - 0.474833i) q^{18} +(1.64974 + 1.64974i) q^{19} +(-1.07376 - 4.18627i) q^{20} +(2.33648 + 2.33648i) q^{21} +(-5.90657 - 1.61663i) q^{22} -4.91612 q^{23} +(-0.0734939 + 4.57193i) q^{24} +0.330547i q^{25} +5.47473i q^{27} +(1.01564 + 3.95968i) q^{28} +5.88494 q^{29} +(-1.30421 + 4.76510i) q^{30} +(0.420375 + 0.420375i) q^{31} +(-2.95864 + 4.82146i) q^{32} +(4.94997 + 4.94997i) q^{33} +(5.88215 - 3.35417i) q^{34} +4.41671i q^{35} +(-0.393660 + 0.665273i) q^{36} +(1.36603 + 1.36603i) q^{37} +(0.871034 - 3.18244i) q^{38} +(-4.39069 + 4.25176i) q^{40} +(1.09808 - 1.09808i) q^{41} +(1.23362 - 4.50718i) q^{42} +11.1896 q^{43} +(2.15170 + 8.38882i) q^{44} +(-0.590579 + 0.590579i) q^{45} +(3.44391 + 6.03953i) q^{46} +(-8.07035 + 8.07035i) q^{47} +(5.66817 - 3.11251i) q^{48} +2.82235i q^{49} +(0.406082 - 0.231559i) q^{50} -7.74044 q^{51} -1.33055 q^{53} +(6.72579 - 3.83524i) q^{54} +9.35707i q^{55} +(4.15304 - 4.02163i) q^{56} +(-2.66702 + 2.66702i) q^{57} +(-4.12261 - 7.22975i) q^{58} +(-4.74477 + 4.74477i) q^{59} +(6.76765 - 1.73588i) q^{60} -0.717056 q^{61} +(0.221950 - 0.810926i) q^{62} +(0.558613 - 0.558613i) q^{63} +(7.99587 + 0.257134i) q^{64} +(2.61349 - 9.54874i) q^{66} +(-5.00844 - 5.00844i) q^{67} +(-8.24130 - 4.87660i) q^{68} -7.94754i q^{69} +(5.42600 - 3.09406i) q^{70} +(-1.24081 - 1.24081i) q^{71} +(1.09307 + 0.0175712i) q^{72} +(5.35696 + 5.35696i) q^{73} +(0.721236 - 2.63513i) q^{74} -0.534371 q^{75} +(-4.51987 + 1.15933i) q^{76} -8.85061i q^{77} -1.11723i q^{79} +(8.29919 + 2.41553i) q^{80} -7.69108 q^{81} +(-2.11824 - 0.579764i) q^{82} +(-2.45738 - 2.45738i) q^{83} +(-6.40134 + 1.64192i) q^{84} +(-7.31599 - 7.31599i) q^{85} +(-7.83871 - 13.7466i) q^{86} +9.51377i q^{87} +(8.79846 - 8.52006i) q^{88} +(-1.37745 - 1.37745i) q^{89} +(1.13926 + 0.311814i) q^{90} +(5.00708 - 8.46180i) q^{92} +(-0.679591 + 0.679591i) q^{93} +(15.5681 + 4.26099i) q^{94} -5.04156 q^{95} +(-7.79451 - 4.78302i) q^{96} +(0.971599 - 0.971599i) q^{97} +(3.46730 - 1.97715i) q^{98} +(1.18345 - 1.18345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 12 q^{5} + 4 q^{6} + 10 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 12 * q^5 + 4 * q^6 + 10 * q^8 - 8 * q^9	$ 16 q - 2 q^{2} - 12 q^{5} + 4 q^{6} + 10 q^{8} - 8 q^{9} + 8 q^{14} + 4 q^{16} - 6 q^{18} - 22 q^{20} - 28 q^{21} + 4 q^{24} - 36 q^{28} + 16 q^{29} - 2 q^{32} + 28 q^{33} + 14 q^{34} + 8 q^{37} - 40 q^{40} - 24 q^{41} + 56 q^{42} - 8 q^{44} + 20 q^{45} + 56 q^{46} + 20 q^{48} - 32 q^{50} - 32 q^{53} + 44 q^{54} + 12 q^{57} + 30 q^{58} - 24 q^{60} - 8 q^{61} + 56 q^{66} - 32 q^{68} + 28 q^{70} - 46 q^{72} + 20 q^{73} - 8 q^{74} - 8 q^{76} - 22 q^{80} - 96 q^{81} - 48 q^{84} - 52 q^{85} + 16 q^{86} + 44 q^{89} - 12 q^{92} + 112 q^{93} + 76 q^{94} - 72 q^{96} - 52 q^{97} + 70 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 12 * q^5 + 4 * q^6 + 10 * q^8 - 8 * q^9 + 8 * q^14 + 4 * q^16 - 6 * q^18 - 22 * q^20 - 28 * q^21 + 4 * q^24 - 36 * q^28 + 16 * q^29 - 2 * q^32 + 28 * q^33 + 14 * q^34 + 8 * q^37 - 40 * q^40 - 24 * q^41 + 56 * q^42 - 8 * q^44 + 20 * q^45 + 56 * q^46 + 20 * q^48 - 32 * q^50 - 32 * q^53 + 44 * q^54 + 12 * q^57 + 30 * q^58 - 24 * q^60 - 8 * q^61 + 56 * q^66 - 32 * q^68 + 28 * q^70 - 46 * q^72 + 20 * q^73 - 8 * q^74 - 8 * q^76 - 22 * q^80 - 96 * q^81 - 48 * q^84 - 52 * q^85 + 16 * q^86 + 44 * q^89 - 12 * q^92 + 112 * q^93 + 76 * q^94 - 72 * q^96 - 52 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.700535	−	1.22852i	−0.495353	−	0.868692i
$2$	−0.700535	−	1.22852i	−0.495353	−	0.868692i
$3$			1.61663i			0.933361i	0.884426	+	0.466681i	$0.154550\pi$
$3$			1.61663i			0.933361i	−0.884426	+	0.466681i	$0.845450\pi$
$4$	−1.01850	+	1.72124i	−0.509251	+	0.860618i
$5$	−1.52798	+	1.52798i	−0.683334	+	0.683334i	−0.960750	−	0.277416i	$-0.910522\pi$
$5$	−1.52798	+	1.52798i	−0.683334	+	0.683334i	0.277416	+	0.960750i	$0.410522\pi$
$6$	1.98605	−	1.13250i	0.810804	−	0.462343i
$7$	1.44528	−	1.44528i	0.546264	−	0.546264i	−0.379094	−	0.925358i	$-0.623764\pi$
$7$	1.44528	−	1.44528i	0.546264	−	0.546264i	0.925358	+	0.379094i	$0.123764\pi$
$8$	2.82806	+	0.0454612i	0.999871	+	0.0160730i
$9$	0.386509			0.128836
$10$	2.94755	+	0.806745i	0.932098	+	0.255115i
$11$	3.06191	−	3.06191i	0.923200	−	0.923200i	−0.0740545	−	0.997254i	$-0.523594\pi$
$11$	3.06191	−	3.06191i	0.923200	−	0.923200i	0.997254	+	0.0740545i	$0.0235939\pi$
$12$	−2.78260	−	1.64654i	−0.803268	−	0.475315i
$13$		0			0
$13$		0			0
$14$	−2.78801	−	0.763079i	−0.745128	−	0.203942i
$15$	−2.47018	−	2.47018i	−0.637798	−	0.637798i
$16$	−1.92531	−	3.50617i	−0.481326	−	0.876541i
$17$			4.78801i			1.16126i	0.814166	+	0.580632i	$0.197194\pi$
$17$			4.78801i			1.16126i	−0.814166	+	0.580632i	$0.802806\pi$
$18$	−0.270763	−	0.474833i	−0.0638195	−	0.111919i
$19$	1.64974	+	1.64974i	0.378477	+	0.378477i	0.870553	−	0.492075i	$-0.163762\pi$
$19$	1.64974	+	1.64974i	0.378477	+	0.378477i	−0.492075	+	0.870553i	$0.663762\pi$
$20$	−1.07376	−	4.18627i	−0.240101	−	0.936078i
$21$	2.33648	+	2.33648i	0.509861	+	0.509861i
$22$	−5.90657	−	1.61663i	−1.25929	−	0.344667i
$23$	−4.91612			−1.02508			−0.512541	−	0.858663i	$-0.671296\pi$
$23$	−4.91612			−1.02508			−0.512541	+	0.858663i	$0.671296\pi$
$24$	−0.0734939	+	4.57193i	−0.0150019	+	0.933241i
$25$			0.330547i			0.0661093i
$26$		0			0
$27$			5.47473i			1.05361i
$28$	1.01564	+	3.95968i	0.191939	+	0.748310i
$29$	5.88494			1.09281			0.546403	−	0.837522i	$-0.315997\pi$
$29$	5.88494			1.09281			0.546403	+	0.837522i	$0.315997\pi$
$30$	−1.30421	+	4.76510i	−0.238115	+	0.869984i
$31$	0.420375	+	0.420375i	0.0755017	+	0.0755017i	0.743849	−	0.668348i	$-0.232998\pi$
$31$	0.420375	+	0.420375i	0.0755017	+	0.0755017i	−0.668348	+	0.743849i	$0.732998\pi$
$32$	−2.95864	+	4.82146i	−0.523018	+	0.852322i
$33$	4.94997	+	4.94997i	0.861679	+	0.861679i
$34$	5.88215	−	3.35417i	1.00878	−	0.575235i
$35$			4.41671i			0.746561i
$36$	−0.393660	+	0.665273i	−0.0656101	+	0.110879i
$37$	1.36603	+	1.36603i	0.224573	+	0.224573i	0.810421	−	0.585848i	$-0.199238\pi$
$37$	1.36603	+	1.36603i	0.224573	+	0.224573i	−0.585848	+	0.810421i	$0.699238\pi$
$38$	0.871034	−	3.18244i	0.141300	−	0.516260i
$39$		0			0
$40$	−4.39069	+	4.25176i	−0.694229	+	0.672263i
$41$	1.09808	−	1.09808i	0.171491	−	0.171491i	−0.616143	−	0.787634i	$-0.711306\pi$
$41$	1.09808	−	1.09808i	0.171491	−	0.171491i	0.787634	+	0.616143i	$0.211306\pi$
$42$	1.23362	−	4.50718i	0.190351	−	0.695474i
$43$	11.1896			1.70640			0.853200	−	0.521584i	$-0.174659\pi$
$43$	11.1896			1.70640			0.853200	+	0.521584i	$0.174659\pi$
$44$	2.15170	+	8.38882i	0.324382	+	1.26466i
$45$	−0.590579	+	0.590579i	−0.0880383	+	0.0880383i
$46$	3.44391	+	6.03953i	0.507777	+	0.890480i
$47$	−8.07035	+	8.07035i	−1.17718	+	1.17718i	−0.196722	+	0.980459i	$0.563030\pi$
$47$	−8.07035	+	8.07035i	−1.17718	+	1.17718i	−0.980459	+	0.196722i	$0.936970\pi$
$48$	5.66817	−	3.11251i	0.818130	−	0.449251i
$49$			2.82235i			0.403192i
$50$	0.406082	−	0.231559i	0.0574286	−	0.0327474i
$51$	−7.74044			−1.08388
$52$		0			0
$53$	−1.33055			−0.182765			−0.0913823	−	0.995816i	$-0.529129\pi$
$53$	−1.33055			−0.182765			−0.0913823	+	0.995816i	$0.529129\pi$
$54$	6.72579	−	3.83524i	0.915265	−	0.521910i
$55$			9.35707i			1.26171i
$56$	4.15304	−	4.02163i	0.554973	−	0.537413i
$57$	−2.66702	+	2.66702i	−0.353256	+	0.353256i
$58$	−4.12261	−	7.22975i	−0.541325	−	0.949312i
$59$	−4.74477	+	4.74477i	−0.617716	+	0.617716i	−0.944945	−	0.327229i	$-0.893885\pi$
$59$	−4.74477	+	4.74477i	−0.617716	+	0.617716i	0.327229	+	0.944945i	$0.393885\pi$
$60$	6.76765	−	1.73588i	0.873699	−	0.224101i
$61$	−0.717056			−0.0918096			−0.0459048	−	0.998946i	$-0.514617\pi$
$61$	−0.717056			−0.0918096			−0.0459048	+	0.998946i	$0.514617\pi$
$62$	0.221950	−	0.810926i	0.0281877	−	0.102988i
$63$	0.558613	−	0.558613i	0.0703786	−	0.0703786i
$64$	7.99587	+	0.257134i	0.999483	+	0.0321418i
$65$		0			0
$66$	2.61349	−	9.54874i	0.321698	−	1.17537i
$67$	−5.00844	−	5.00844i	−0.611878	−	0.611878i	0.331557	−	0.943435i	$-0.392426\pi$
$67$	−5.00844	−	5.00844i	−0.611878	−	0.611878i	−0.943435	+	0.331557i	$0.892426\pi$
$68$	−8.24130	−	4.87660i	−0.999404	−	0.591375i
$69$		−	7.94754i		−	0.956771i
$70$	5.42600	−	3.09406i	0.648531	−	0.369811i
$71$	−1.24081	−	1.24081i	−0.147257	−	0.147257i	0.629634	−	0.776892i	$-0.283205\pi$
$71$	−1.24081	−	1.24081i	−0.147257	−	0.147257i	−0.776892	+	0.629634i	$0.783205\pi$
$72$	1.09307	+	0.0175712i	0.128820	+	0.00207078i
$73$	5.35696	+	5.35696i	0.626985	+	0.626985i	0.947308	−	0.320323i	$-0.103792\pi$
$73$	5.35696	+	5.35696i	0.626985	+	0.626985i	−0.320323	+	0.947308i	$0.603792\pi$
$74$	0.721236	−	2.63513i	0.0838420	−	0.306328i
$75$	−0.534371			−0.0617039
$76$	−4.51987	+	1.15933i	−0.518464	+	0.132984i
$77$		−	8.85061i		−	1.00862i
$78$		0			0
$79$		−	1.11723i		−	0.125698i	−0.998023	−	0.0628489i	$-0.979981\pi$
$79$		−	1.11723i		−	0.125698i	0.998023	−	0.0628489i	$-0.0200186\pi$
$80$	8.29919	+	2.41553i	0.927877	+	0.270064i
$81$	−7.69108			−0.854565
$82$	−2.11824	−	0.579764i	−0.233921	−	0.0640242i
$83$	−2.45738	−	2.45738i	−0.269733	−	0.269733i	0.559260	−	0.828992i	$-0.311085\pi$
$83$	−2.45738	−	2.45738i	−0.269733	−	0.269733i	−0.828992	+	0.559260i	$0.811085\pi$
$84$	−6.40134	+	1.64192i	−0.698443	+	0.179148i
$85$	−7.31599	−	7.31599i	−0.793531	−	0.793531i
$86$	−7.83871	−	13.7466i	−0.845270	−	1.48234i
$87$			9.51377i			1.01998i
$88$	8.79846	−	8.52006i	0.937919	−	0.908242i
$89$	−1.37745	−	1.37745i	−0.146009	−	0.146009i	0.630324	−	0.776333i	$-0.282922\pi$
$89$	−1.37745	−	1.37745i	−0.146009	−	0.146009i	−0.776333	+	0.630324i	$0.782922\pi$
$90$	1.13926	+	0.311814i	0.120088	+	0.0328681i
$91$		0			0
$92$	5.00708	−	8.46180i	0.522024	−	0.882203i
$93$	−0.679591	+	0.679591i	−0.0704703	+	0.0704703i
$94$	15.5681	+	4.26099i	1.60573	+	0.439488i
$95$	−5.04156			−0.517253
$96$	−7.79451	−	4.78302i	−0.795524	−	0.488165i
$97$	0.971599	−	0.971599i	0.0986509	−	0.0986509i	−0.656059	−	0.754710i	$-0.727778\pi$
$97$	0.971599	−	0.971599i	0.0986509	−	0.0986509i	0.754710	+	0.656059i	$0.227778\pi$
$98$	3.46730	−	1.97715i	0.350250	−	0.199722i
$99$	1.18345	−	1.18345i	0.118942	−	0.118942i
$100$	−0.568949	−	0.336663i	−0.0568949	−	0.0336663i
$101$		−	0.869948i		−	0.0865631i	−0.999063	−	0.0432815i	$-0.986219\pi$
$101$		−	0.869948i		−	0.0865631i	0.999063	−	0.0432815i	$-0.0137812\pi$
$102$	5.42245	+	9.50926i	0.536902	+	0.941557i
$103$	11.5743			1.14045			0.570225	−	0.821489i	$-0.306856\pi$
$103$	11.5743			1.14045			0.570225	+	0.821489i	$0.306856\pi$
$104$		0			0
$105$	−7.14019			−0.696811
$106$	0.932094	+	1.63460i	0.0905330	+	0.158766i
$107$			8.05755i			0.778953i	0.921036	+	0.389476i	$0.127344\pi$
$107$			8.05755i			0.778953i	−0.921036	+	0.389476i	$0.872656\pi$
$108$	−9.42330	−	5.57603i	−0.906758	−	0.536553i
$109$	12.0811	−	12.0811i	1.15716	−	1.15716i	0.172075	−	0.985084i	$-0.444953\pi$
$109$	12.0811	−	12.0811i	1.15716	−	1.15716i	0.985084	−	0.172075i	$-0.0550472\pi$
$110$	11.4953	−	6.55495i	1.09604	−	0.624990i
$111$	−2.20836	+	2.20836i	−0.209608	+	0.209608i
$112$	−7.84998	−	2.28478i	−0.741754	−	0.215892i
$113$	8.94091			0.841090			0.420545	−	0.907272i	$-0.361839\pi$
$113$	8.94091			0.841090			0.420545	+	0.907272i	$0.361839\pi$
$114$	5.14483	+	1.40814i	0.481857	+	0.131884i
$115$	7.51174	−	7.51174i	0.700473	−	0.700473i
$116$	−5.99383	+	10.1294i	−0.556513	+	0.940489i
$117$		0			0
$118$	9.15289	+	2.50515i	0.842592	+	0.230617i
$119$	6.92001	+	6.92001i	0.634356	+	0.634356i
$120$	−6.87352	−	7.09812i	−0.627464	−	0.647967i
$121$		−	7.75055i		−	0.704595i
$122$	0.502322	+	0.880914i	0.0454781	+	0.0797542i
$123$	1.77518	+	1.77518i	0.160063	+	0.160063i
$124$	−1.15172	+	0.295412i	−0.103427	+	0.0265288i
$125$	−8.14498	−	8.14498i	−0.728509	−	0.728509i
$126$	−1.07759	−	0.294937i	−0.0959996	−	0.0262751i
$127$	−1.55040			−0.137576			−0.0687879	−	0.997631i	$-0.521913\pi$
$127$	−1.55040			−0.137576			−0.0687879	+	0.997631i	$0.521913\pi$
$128$	−5.28549	−	10.0032i	−0.467176	−	0.884165i
$129$			18.0895i			1.59269i
$130$		0			0
$131$			4.10898i			0.359003i	0.983758	+	0.179502i	$0.0574485\pi$
$131$			4.10898i			0.359003i	−0.983758	+	0.179502i	$0.942552\pi$
$132$	−13.5616	+	3.47851i	−1.18039	+	0.302765i
$133$	4.76868			0.413497
$134$	−2.64436	+	9.66154i	−0.228438	+	0.834630i
$135$	−8.36529	−	8.36529i	−0.719969	−	0.719969i
$136$	−0.217669	+	13.5408i	−0.0186649	+	1.16111i
$137$	−8.36953	−	8.36953i	−0.715057	−	0.715057i	0.252532	−	0.967589i	$-0.418737\pi$
$137$	−8.36953	−	8.36953i	−0.715057	−	0.715057i	−0.967589	+	0.252532i	$0.918737\pi$
$138$	−9.76368	+	5.56753i	−0.831140	+	0.473939i
$139$		−	8.43151i		−	0.715152i	−0.933884	−	0.357576i	$-0.883603\pi$
$139$		−	8.43151i		−	0.715152i	0.933884	−	0.357576i	$-0.116397\pi$
$140$	−7.60221	−	4.49843i	−0.642504	−	0.380187i
$141$	−13.0468	−	13.0468i	−1.09874	−	1.09874i
$142$	−0.655125	+	2.39359i	−0.0549769	+	0.200865i
$143$		0			0
$144$	−0.744148	−	1.35517i	−0.0620123	−	0.112930i
$145$	−8.99208	+	8.99208i	−0.746752	+	0.746752i
$146$	2.82838	−	10.3339i	0.234078	−	0.855236i
$147$	−4.56269			−0.376324
$148$	−3.74255	+	0.959952i	−0.307636	+	0.0789075i
$149$	0.998854	−	0.998854i	0.0818293	−	0.0818293i	−0.665007	−	0.746837i	$-0.731572\pi$
$149$	0.998854	−	0.998854i	0.0818293	−	0.0818293i	0.746837	+	0.665007i	$0.231572\pi$
$150$	0.374346	+	0.656484i	0.0305652	+	0.0536017i
$151$	−6.88689	+	6.88689i	−0.560447	+	0.560447i	−0.929435	−	0.368987i	$-0.879705\pi$
$151$	−6.88689	+	6.88689i	−0.560447	+	0.560447i	0.368987	+	0.929435i	$0.379705\pi$
$152$	4.59058	+	4.74058i	0.372345	+	0.384512i
$153$			1.85061i			0.149613i
$154$	−10.8731	+	6.20016i	−0.876181	+	0.499623i
$155$	−1.28465			−0.103186
$156$		0			0
$157$	14.0877			1.12432			0.562162	−	0.827027i	$-0.309970\pi$
$157$	14.0877			1.12432			0.562162	+	0.827027i	$0.309970\pi$
$158$	−1.37253	+	0.782655i	−0.109193	+	0.0622647i
$159$		−	2.15100i		−	0.170585i
$160$	−2.84636	−	11.8878i	−0.225024	−	0.939816i
$161$	−7.10515	+	7.10515i	−0.559965	+	0.559965i
$162$	5.38787	+	9.44862i	0.423311	+	0.742354i
$163$	14.4445	−	14.4445i	1.13138	−	1.13138i	0.141437	−	0.989947i	$-0.454828\pi$
$163$	14.4445	−	14.4445i	1.13138	−	1.13138i	0.989947	−	0.141437i	$-0.0451721\pi$
$164$	0.771655	+	3.00844i	0.0602561	+	0.234920i
$165$	−15.1269			−1.17763
$166$	−1.29745	+	4.74041i	−0.100702	+	0.367927i
$167$	−8.66208	+	8.66208i	−0.670292	+	0.670292i	−0.957783	−	0.287492i	$-0.907179\pi$
$167$	−8.66208	+	8.66208i	−0.670292	+	0.670292i	0.287492	+	0.957783i	$0.407179\pi$
$168$	6.50149	+	6.71392i	0.501601	+	0.517990i
$169$		0			0
$170$	−3.86271	+	14.1129i	−0.296256	+	1.08241i
$171$	0.637641	+	0.637641i	0.0487616	+	0.0487616i
$172$	−11.3966	+	19.2600i	−0.868986	+	1.46856i
$173$			6.76382i			0.514244i	0.966379	+	0.257122i	$0.0827742\pi$
$173$			6.76382i			0.514244i	−0.966379	+	0.257122i	$0.917226\pi$
$174$	11.6878	−	6.66473i	0.886051	−	0.505252i
$175$	0.477732	+	0.477732i	0.0361131	+	0.0361131i
$176$	−16.6307	−	4.84045i	−1.25358	−	0.364862i
$177$	−7.67053	−	7.67053i	−0.576552	−	0.576552i
$178$	−0.727265	+	2.65716i	−0.0545109	+	0.199163i
$179$	−7.67988			−0.574021			−0.287011	−	0.957927i	$-0.592661\pi$
$179$	−7.67988			−0.574021			−0.287011	+	0.957927i	$0.592661\pi$
$180$	−0.415019	−	1.61803i	−0.0309337	−	0.120601i
$181$		−	10.6994i		−	0.795283i	−0.917541	−	0.397642i	$-0.869829\pi$
$181$		−	10.6994i		−	0.795283i	0.917541	−	0.397642i	$-0.130171\pi$
$182$		0			0
$183$		−	1.15921i		−	0.0856915i
$184$	−13.9031	−	0.223493i	−1.02495	−	0.0164761i
$185$	−4.17452			−0.306917
$186$	1.31097	+	0.358812i	0.0961247	+	0.0263093i
$187$	14.6605	+	14.6605i	1.07208	+	1.07208i
$188$	−5.67130	−	22.1106i	−0.413622	−	1.61258i
$189$	7.91250	+	7.91250i	0.575550	+	0.575550i
$190$	3.53178	+	6.19363i	0.256223	+	0.449333i
$191$		−	14.4541i		−	1.04586i	−0.852374	−	0.522932i	$-0.824838\pi$
$191$		−	14.4541i		−	1.04586i	0.852374	−	0.522932i	$-0.175162\pi$
$192$	−0.415691	+	12.9264i	−0.0299999	+	0.932879i
$193$	13.8403	+	13.8403i	0.996244	+	0.996244i	0.999993	−	0.00374890i	$-0.00119331\pi$
$193$	13.8403	+	13.8403i	0.996244	+	0.996244i	−0.00374890	+	0.999993i	$0.501193\pi$
$194$	−1.87426	−	0.512986i	−0.134564	−	0.0368303i
$195$		0			0
$196$	−4.85792	−	2.87457i	−0.346994	−	0.205326i
$197$	1.87901	−	1.87901i	0.133874	−	0.133874i	−0.636994	−	0.770868i	$-0.719823\pi$
$197$	1.87901	−	1.87901i	0.133874	−	0.133874i	0.770868	+	0.636994i	$0.219823\pi$
$198$	−2.28294	−	0.624842i	−0.162242	−	0.0444056i
$199$	−16.5739			−1.17489			−0.587445	−	0.809264i	$-0.699866\pi$
$199$	−16.5739			−1.17489			−0.587445	+	0.809264i	$0.699866\pi$
$200$	−0.0150270	+	0.934806i	−0.00106257	+	0.0661008i
$201$	8.09679	−	8.09679i	0.571104	−	0.571104i
$202$	−1.06875	+	0.609429i	−0.0751966	+	0.0428793i
$203$	8.50538	−	8.50538i	0.596960	−	0.596960i
$204$	7.88366	−	13.3231i	0.551967	−	0.932806i
$205$			3.35568i			0.234371i
$206$	−8.10820	−	14.2192i	−0.564925	−	0.990700i
$207$	−1.90012			−0.132068
$208$		0			0
$209$	10.1027			0.698820
$210$	5.00195	+	8.77184i	0.345167	+	0.605314i
$211$		−	27.6380i		−	1.90268i	−0.308141	−	0.951341i	$-0.599707\pi$
$211$		−	27.6380i		−	1.90268i	0.308141	−	0.951341i	$-0.400293\pi$
$212$	1.35517	−	2.29018i	0.0930731	−	0.157291i
$213$	2.00593	−	2.00593i	0.137444	−	0.137444i
$214$	9.89883	−	5.64459i	0.676670	−	0.385856i
$215$	−17.0975	+	17.0975i	−1.16604	+	1.16604i
$216$	−0.248888	+	15.4829i	−0.0169347	+	1.05348i
$217$	1.21512			0.0824876
$218$	−23.3050	−	6.37859i	−1.57842	−	0.432013i
$219$	−8.66022	+	8.66022i	−0.585204	+	0.585204i
$220$	−16.1057	−	9.53020i	−1.08585	−	0.642526i
$221$		0			0
$222$	4.26003	+	1.16597i	0.285915	+	0.0782549i
$223$	−2.14915	−	2.14915i	−0.143918	−	0.143918i	0.631477	−	0.775395i	$-0.282449\pi$
$223$	−2.14915	−	2.14915i	−0.143918	−	0.143918i	−0.775395	+	0.631477i	$0.782449\pi$
$224$	2.69229	+	11.2444i	0.179886	+	0.751298i
$225$			0.127759i			0.00851728i
$226$	−6.26341	−	10.9840i	−0.416636	−	0.730648i
$227$	−6.69130	−	6.69130i	−0.444117	−	0.444117i	0.449276	−	0.893393i	$-0.351682\pi$
$227$	−6.69130	−	6.69130i	−0.444117	−	0.444117i	−0.893393	+	0.449276i	$0.851682\pi$
$228$	−1.87421	−	7.30695i	−0.124122	−	0.483915i
$229$	−3.49493	−	3.49493i	−0.230952	−	0.230952i	0.582138	−	0.813090i	$-0.302216\pi$
$229$	−3.49493	−	3.49493i	−0.230952	−	0.230952i	−0.813090	+	0.582138i	$0.802216\pi$
$230$	−14.4905	−	3.96606i	−0.955476	−	0.261514i
$231$	14.3082			0.941408
$232$	16.6430	+	0.267537i	1.09267	+	0.0175646i
$233$			21.3205i			1.39675i	0.715731	+	0.698376i	$0.246094\pi$
$233$			21.3205i			1.39675i	−0.715731	+	0.698376i	$0.753906\pi$
$234$		0			0
$235$		−	24.6627i		−	1.60882i
$236$	−3.33430	−	12.9994i	−0.217045	−	0.846190i
$237$	1.80614			0.117321
$238$	3.65363	−	13.3490i	0.236830	−	0.865290i
$239$	−5.96711	−	5.96711i	−0.385981	−	0.385981i	0.487271	−	0.873251i	$-0.337993\pi$
$239$	−5.96711	−	5.96711i	−0.385981	−	0.385981i	−0.873251	+	0.487271i	$0.837993\pi$
$240$	−3.90501	+	13.4167i	−0.252067	+	0.866045i
$241$	14.6657	+	14.6657i	0.944704	+	0.944704i	0.998549	−	0.0538457i	$-0.0171479\pi$
$241$	14.6657	+	14.6657i	0.944704	+	0.944704i	−0.0538457	+	0.998549i	$0.517148\pi$
$242$	−9.52167	+	5.42953i	−0.612076	+	0.349023i
$243$			3.99056i			0.255994i
$244$	0.730323	−	1.23422i	0.0467541	−	0.0790130i
$245$	−4.31249	−	4.31249i	−0.275515	−	0.275515i
$246$	0.937263	−	3.42442i	0.0597577	−	0.218333i
$247$		0			0
$248$	1.16974	+	1.20796i	0.0742784	+	0.0767054i
$249$	3.97267	−	3.97267i	0.251758	−	0.251758i
$250$	−4.30039	+	15.7121i	−0.271981	+	0.993718i
$251$	5.91492			0.373347			0.186673	−	0.982422i	$-0.440229\pi$
$251$	5.91492			0.373347			0.186673	+	0.982422i	$0.440229\pi$
$252$	0.392556	+	1.53045i	0.0247287	+	0.0964095i
$253$	−15.0527	+	15.0527i	−0.946355	+	0.946355i
$254$	1.08611	+	1.90469i	0.0681485	+	0.119511i
$255$	11.8273	−	11.8273i	0.740651	−	0.740651i
$256$	−8.58640	+	13.5009i	−0.536650	+	0.843805i
$257$		−	28.2733i		−	1.76364i	−0.471587	−	0.881819i	$-0.656319\pi$
$257$		−	28.2733i		−	1.76364i	0.471587	−	0.881819i	$-0.343681\pi$
$258$	22.2232	−	12.6723i	1.38355	−	0.788942i
$259$	3.94857			0.245352
$260$		0			0
$261$	2.27458			0.140793
$262$	5.04794	−	2.87848i	0.311863	−	0.177833i
$263$		−	13.3948i		−	0.825956i	−0.910741	−	0.412978i	$-0.864489\pi$
$263$		−	13.3948i		−	0.825956i	0.910741	−	0.412978i	$-0.135511\pi$
$264$	13.7738	+	14.2238i	0.847718	+	0.875417i
$265$	2.03305	−	2.03305i	0.124889	−	0.124889i
$266$	−3.34062	−	5.85839i	−0.204827	−	0.359201i
$267$	2.22682	−	2.22682i	0.136279	−	0.136279i
$268$	13.7218	−	3.51960i	0.838193	−	0.214994i
$269$	22.9309			1.39812			0.699060	−	0.715063i	$-0.253602\pi$
$269$	22.9309			1.39812			0.699060	+	0.715063i	$0.253602\pi$
$270$	−4.41671	+	16.1371i	−0.268793	+	0.982070i
$271$	−6.78755	+	6.78755i	−0.412314	+	0.412314i	−0.882544	−	0.470230i	$-0.844171\pi$
$271$	−6.78755	+	6.78755i	−0.412314	+	0.412314i	0.470230	+	0.882544i	$0.344171\pi$
$272$	16.7876	−	9.21839i	1.01790	−	0.558947i
$273$		0			0
$274$	−4.41895	+	16.1452i	−0.266959	+	0.975370i
$275$	1.01210	+	1.01210i	0.0610321	+	0.0610321i
$276$	13.6796	+	8.09459i	0.823415	+	0.487237i
$277$		−	1.10006i		−	0.0660963i	−0.999454	−	0.0330482i	$-0.989479\pi$
$277$		−	1.10006i		−	0.0660963i	0.999454	−	0.0330482i	$-0.0105215\pi$
$278$	−10.3582	+	5.90657i	−0.621247	+	0.354252i
$279$	0.162479	+	0.162479i	0.00972736	+	0.00972736i
$280$	−0.200789	+	12.4907i	−0.0119994	+	0.746464i
$281$	6.74660	+	6.74660i	0.402469	+	0.402469i	0.879102	−	0.476634i	$-0.158143\pi$
$281$	6.74660	+	6.74660i	0.402469	+	0.402469i	−0.476634	+	0.879102i	$0.658143\pi$
$282$	−6.88845	+	25.1679i	−0.410201	+	1.49872i
$283$	21.1543			1.25749			0.628746	−	0.777610i	$-0.283568\pi$
$283$	21.1543			1.25749			0.628746	+	0.777610i	$0.283568\pi$
$284$	3.39950	−	0.871959i	0.201723	−	0.0517413i
$285$		−	8.15033i		−	0.482784i
$286$		0			0
$287$		−	3.17405i		−	0.187358i
$288$	−1.14354	+	1.86354i	−0.0673838	+	0.109810i
$289$	−5.92507			−0.348534
$290$	17.3462	+	4.74765i	1.01860	+	0.278792i
$291$	1.57072	+	1.57072i	0.0920770	+	0.0920770i
$292$	−14.6767	+	3.76452i	−0.858887	+	0.220302i
$293$	−12.8077	−	12.8077i	−0.748231	−	0.748231i	0.225916	−	0.974147i	$-0.427463\pi$
$293$	−12.8077	−	12.8077i	−0.748231	−	0.748231i	−0.974147	+	0.225916i	$0.927463\pi$
$294$	3.19632	+	5.60533i	0.186413	+	0.326910i
$295$		−	14.4998i		−	0.844212i
$296$	3.80110	+	3.92531i	0.220935	+	0.228154i
$297$	16.7631	+	16.7631i	0.972695	+	0.972695i
$298$	−1.92684	−	0.527376i	−0.111619	−	0.0305501i
$299$		0			0
$300$	0.544259	−	0.919779i	0.0314228	−	0.0531035i
$301$	16.1721	−	16.1721i	0.932144	−	0.932144i
$302$	13.2852	+	3.63615i	0.764475	+	0.209237i
$303$	1.40638			0.0807946
$304$	2.60802	−	8.96054i	0.149580	−	0.513922i
$305$	1.09565	−	1.09565i	0.0627366	−	0.0627366i
$306$	2.27350	−	1.29642i	0.129968	−	0.0741112i
$307$	7.26086	−	7.26086i	0.414399	−	0.414399i	−0.468869	−	0.883268i	$-0.655338\pi$
$307$	7.26086	−	7.26086i	0.414399	−	0.414399i	0.883268	+	0.468869i	$0.155338\pi$
$308$	15.2340	+	9.01437i	0.868037	+	0.513641i
$309$			18.7114i			1.06445i
$310$	0.899943	+	1.57822i	0.0511133	+	0.0896366i
$311$	−9.77167			−0.554101			−0.277050	−	0.960855i	$-0.589357\pi$
$311$	−9.77167			−0.554101			−0.277050	+	0.960855i	$0.589357\pi$
$312$		0			0
$313$	−31.6333			−1.78802			−0.894010	−	0.448047i	$-0.852120\pi$
$313$	−31.6333			−1.78802			−0.894010	+	0.448047i	$0.852120\pi$
$314$	−9.86894	−	17.3070i	−0.556937	−	0.976691i
$315$			1.70710i			0.0961842i
$316$	1.92301	+	1.13790i	0.108178	+	0.0640117i
$317$	−14.7813	+	14.7813i	−0.830201	+	0.830201i	−0.987544	−	0.157343i	$-0.949707\pi$
$317$	−14.7813	+	14.7813i	−0.830201	+	0.830201i	0.157343	+	0.987544i	$0.449707\pi$
$318$	−2.64254	+	1.50685i	−0.148186	+	0.0845000i
$319$	18.0191	−	18.0191i	1.00888	−	1.00888i
$320$	−12.6104	+	11.8246i	−0.704944	+	0.661017i
$321$	−13.0261			−0.727044
$322$	13.7062	+	3.75139i	0.763817	+	0.209057i
$323$	−7.89900	+	7.89900i	−0.439512	+	0.439512i
$324$	7.83339	−	13.2382i	0.435188	−	0.735454i
$325$		0			0
$326$	−27.8643	−	7.62645i	−1.54326	−	0.422390i
$327$	19.5307	+	19.5307i	1.08005	+	1.08005i
$328$	3.15535	−	3.05551i	0.174225	−	0.168712i
$329$			23.3278i			1.28610i
$330$	10.5969	+	18.5837i	0.583342	+	1.02300i
$331$	8.59585	+	8.59585i	0.472470	+	0.472470i	0.902713	−	0.430243i	$-0.141572\pi$
$331$	8.59585	+	8.59585i	0.472470	+	0.472470i	−0.430243	+	0.902713i	$0.641572\pi$
$332$	6.73258	−	1.72688i	0.369498	−	0.0947750i
$333$	0.527981	+	0.527981i	0.0289332	+	0.0289332i
$334$	16.7096	+	4.57341i	0.914308	+	0.250246i
$335$	15.3056			0.836235
$336$	3.69365	−	12.6905i	0.201505	−	0.692324i
$337$		−	18.7726i		−	1.02261i	−0.859401	−	0.511303i	$-0.829163\pi$
$337$		−	18.7726i		−	1.02261i	0.859401	−	0.511303i	$-0.170837\pi$
$338$		0			0
$339$			14.4541i			0.785041i
$340$	20.0439	−	5.14119i	1.08703	−	0.278820i
$341$	2.57430			0.139406
$342$	0.336663	−	1.23004i	0.0182046	−	0.0665130i
$343$	14.1960	+	14.1960i	0.766513	+	0.766513i
$344$	31.6449	+	0.508693i	1.70618	+	0.0274269i
$345$	12.1437	+	12.1437i	0.653794	+	0.653794i
$346$	8.30946	−	4.73829i	0.446719	−	0.254732i
$347$			7.98761i			0.428798i	0.976746	+	0.214399i	$0.0687792\pi$
$347$			7.98761i			0.428798i	−0.976746	+	0.214399i	$0.931221\pi$
$348$	−16.3754	−	9.68980i	−0.877816	−	0.519428i
$349$	−7.25198	−	7.25198i	−0.388190	−	0.388190i	0.485852	−	0.874041i	$-0.338510\pi$
$349$	−7.25198	−	7.25198i	−0.388190	−	0.388190i	−0.874041	+	0.485852i	$0.838510\pi$
$350$	0.252233	−	0.921568i	0.0134824	−	0.0492599i
$351$		0			0
$352$	5.70379	+	23.8219i	0.304013	+	1.26971i
$353$	−3.34267	+	3.34267i	−0.177912	+	0.177912i	−0.790445	−	0.612533i	$-0.790151\pi$
$353$	−3.34267	+	3.34267i	−0.177912	+	0.177912i	0.612533	+	0.790445i	$0.290151\pi$
$354$	−4.04989	+	14.7968i	−0.215249	+	0.786443i
$355$	3.79187			0.201252
$356$	3.77384	−	0.967977i	0.200013	−	0.0513027i
$357$	−11.1871	+	11.1871i	−0.592084	+	0.592084i
$358$	5.38002	+	9.43485i	0.284343	+	0.498647i
$359$	25.8704	−	25.8704i	1.36539	−	1.36539i	0.498492	−	0.866894i	$-0.333887\pi$
$359$	25.8704	−	25.8704i	1.36539	−	1.36539i	0.866894	−	0.498492i	$-0.166113\pi$
$360$	−1.69704	+	1.64334i	−0.0894419	+	0.0866119i
$361$		−	13.5567i		−	0.713510i
$362$	−13.1444	+	7.49533i	−0.690856	+	0.393946i
$363$	12.5298			0.657642
$364$		0			0
$365$	−16.3707			−0.856880
$366$	−1.42411	+	0.812069i	−0.0744395	+	0.0424475i
$367$		−	20.4007i		−	1.06491i	−0.846459	−	0.532454i	$-0.821270\pi$
$367$		−	20.4007i		−	1.06491i	0.846459	−	0.532454i	$-0.178730\pi$
$368$	9.46503	+	17.2367i	0.493399	+	0.898526i
$369$	0.424416	−	0.424416i	0.0220942	−	0.0220942i
$370$	2.92440	+	5.12847i	0.152032	+	0.266616i
$371$	−1.92301	+	1.92301i	−0.0998377	+	0.0998377i
$372$	−0.477572	−	1.86190i	−0.0247609	−	0.0965352i
$373$	−20.6447			−1.06894			−0.534471	−	0.845187i	$-0.679489\pi$
$373$	−20.6447			−1.06894			−0.534471	+	0.845187i	$0.679489\pi$
$374$	7.74044	−	28.2808i	0.400249	−	1.46236i
$375$	13.1674	−	13.1674i	0.679962	−	0.679962i
$376$	−23.1903	+	22.4566i	−1.19595	+	1.15811i
$377$		0			0
$378$	4.17765	−	15.2636i	0.214875	−	0.785076i
$379$	10.0323	+	10.0323i	0.515322	+	0.515322i	0.916152	−	0.400830i	$-0.131278\pi$
$379$	10.0323	+	10.0323i	0.515322	+	0.515322i	−0.400830	+	0.916152i	$0.631278\pi$
$380$	5.13484	−	8.67771i	0.263412	−	0.445157i
$381$		−	2.50642i		−	0.128408i
$382$	−17.7571	+	10.1256i	−0.908534	+	0.518072i
$383$	−10.9628	−	10.9628i	−0.560171	−	0.560171i	0.369185	−	0.929356i	$-0.379637\pi$
$383$	−10.9628	−	10.9628i	−0.560171	−	0.560171i	−0.929356	+	0.369185i	$0.879637\pi$
$384$	16.1714	−	8.54468i	0.825245	−	0.436044i
$385$	13.5236	+	13.5236i	0.689225	+	0.689225i
$386$	7.30740	−	26.6986i	0.371937	−	1.35892i
$387$	4.32489			0.219846
$388$	0.682775	+	2.66193i	0.0346627	+	0.135139i
$389$		−	33.5493i		−	1.70102i	−0.525963	−	0.850508i	$-0.676295\pi$
$389$		−	33.5493i		−	1.70102i	0.525963	−	0.850508i	$-0.323705\pi$
$390$		0			0
$391$		−	23.5384i		−	1.19039i
$392$	−0.128307	+	7.98177i	−0.00648049	+	0.403140i
$393$	−6.64269			−0.335080
$394$	−3.62471	−	0.992083i	−0.182610	−	0.0499804i
$395$	1.70710	+	1.70710i	0.0858935	+	0.0858935i
$396$	0.831653	+	3.24236i	0.0417921	+	0.162935i
$397$	−8.80721	−	8.80721i	−0.442021	−	0.442021i	0.450669	−	0.892691i	$-0.351185\pi$
$397$	−8.80721	−	8.80721i	−0.442021	−	0.442021i	−0.892691	+	0.450669i	$0.851185\pi$
$398$	11.6106	+	20.3613i	0.581985	+	1.02062i
$399$			7.70918i			0.385942i
$400$	1.15895	−	0.636403i	0.0579476	−	0.0318202i
$401$	10.3026	+	10.3026i	0.514487	+	0.514487i	0.915898	−	0.401411i	$-0.131480\pi$
$401$	10.3026	+	10.3026i	0.514487	+	0.514487i	−0.401411	+	0.915898i	$0.631480\pi$
$402$	−15.6191	−	4.27496i	−0.779011	−	0.213215i
$403$		0			0
$404$	1.49739	+	0.886044i	0.0744977	+	0.0440824i
$405$	11.7518	−	11.7518i	0.583953	−	0.583953i
$406$	−16.4073	−	4.49068i	−0.814281	−	0.222869i
$407$	8.36529			0.414652
$408$	−21.8905	−	0.351890i	−1.08374	−	0.0174211i
$409$	13.7151	−	13.7151i	0.678167	−	0.678167i	−0.281419	−	0.959585i	$-0.590805\pi$
$409$	13.7151	−	13.7151i	0.678167	−	0.678167i	0.959585	+	0.281419i	$0.0908049\pi$
$410$	4.12251	−	2.35077i	0.203596	−	0.116096i
$411$	13.5304	−	13.5304i	0.667407	−	0.667407i
$412$	−11.7885	+	19.9221i	−0.580776	+	0.981492i
$413$			13.7150i			0.674871i
$414$	1.33110	+	2.33433i	0.0654201	+	0.114726i
$415$	7.50966			0.368635
$416$		0			0
$417$	13.6306			0.667495
$418$	−7.07731	−	12.4114i	−0.346163	−	0.607059i
$419$		−	2.93625i		−	0.143445i	−0.997425	−	0.0717226i	$-0.977150\pi$
$419$		−	2.93625i		−	0.143445i	0.997425	−	0.0717226i	$-0.0228496\pi$
$420$	7.27230	−	12.2900i	0.354852	−	0.599688i
$421$	−4.53947	+	4.53947i	−0.221240	+	0.221240i	−0.809021	−	0.587780i	$-0.800002\pi$
$421$	−4.53947	+	4.53947i	−0.221240	+	0.221240i	0.587780	+	0.809021i	$0.300002\pi$
$422$	−33.9538	+	19.3614i	−1.65284	+	0.942499i
$423$	−3.11926	+	3.11926i	−0.151664	+	0.151664i
$424$	−3.76287	−	0.0604883i	−0.182741	−	0.00293757i
$425$	−1.58266			−0.0767704
$426$	−3.86954	−	1.05909i	−0.187480	−	0.0513133i
$427$	−1.03634	+	1.03634i	−0.0501522	+	0.0501522i
$428$	−13.8689	−	8.20663i	−0.670381	−	0.396683i
$429$		0			0
$430$	32.9820	+	9.02717i	1.59053	+	0.435329i
$431$	−13.4108	−	13.4108i	−0.645974	−	0.645974i	0.306044	−	0.952018i	$-0.400995\pi$
$431$	−13.4108	−	13.4108i	−0.645974	−	0.645974i	−0.952018	+	0.306044i	$0.900995\pi$
$432$	19.1953	−	10.5405i	0.923535	−	0.507131i
$433$			4.97230i			0.238954i	0.992837	+	0.119477i	$0.0381217\pi$
$433$			4.97230i			0.238954i	−0.992837	+	0.119477i	$0.961878\pi$
$434$	−0.851233	−	1.49279i	−0.0408605	−	0.0716563i
$435$	−14.5369	−	14.5369i	−0.696989	−	0.696989i
$436$	8.48979	+	33.0990i	0.406587	+	1.58516i
$437$	−8.11034	−	8.11034i	−0.387970	−	0.387970i
$438$	16.7060	+	4.57244i	0.798244	+	0.218479i
$439$	−39.1690			−1.86943			−0.934717	−	0.355392i	$-0.884347\pi$
$439$	−39.1690			−1.86943			−0.934717	+	0.355392i	$0.884347\pi$
$440$	−0.425384	+	26.4624i	−0.0202794	+	1.26154i
$441$			1.09086i			0.0519458i
$442$		0			0
$443$			38.1735i			1.81368i	0.421477	+	0.906839i	$0.361512\pi$
$443$			38.1735i			1.81368i	−0.421477	+	0.906839i	$0.638488\pi$
$444$	−1.55189	−	6.05032i	−0.0736492	−	0.287135i
$445$	4.20942			0.199546
$446$	−1.13471	+	4.14581i	−0.0537301	+	0.196310i
$447$	1.61478	+	1.61478i	0.0763763	+	0.0763763i
$448$	11.9279	−	11.1846i	0.563539	−	0.528423i
$449$	−2.22105	−	2.22105i	−0.104818	−	0.104818i	0.652753	−	0.757571i	$-0.273614\pi$
$449$	−2.22105	−	2.22105i	−0.104818	−	0.104818i	−0.757571	+	0.652753i	$0.773614\pi$
$450$	0.156954	−	0.0894998i	0.00739890	−	0.00421906i
$451$		−	6.72441i		−	0.316640i
$452$	−9.10633	+	15.3894i	−0.428326	+	0.723857i
$453$	−11.1336	−	11.1336i	−0.523100	−	0.523100i
$454$	−3.53288	+	12.9079i	−0.165806	+	0.605796i
$455$		0			0
$456$	−7.66376	+	7.42126i	−0.358888	+	0.347533i
$457$	−24.0359	+	24.0359i	−1.12435	+	1.12435i	−0.133270	+	0.991080i	$0.542548\pi$
$457$	−24.0359	+	24.0359i	−1.12435	+	1.12435i	−0.991080	+	0.133270i	$0.957452\pi$
$458$	−1.84526	+	6.74190i	−0.0862232	+	0.315028i
$459$	−26.2131			−1.22352
$460$	5.27875	+	20.5802i	0.246123	+	0.959556i
$461$	16.7869	−	16.7869i	0.781842	−	0.781842i	−0.198299	−	0.980142i	$-0.563542\pi$
$461$	16.7869	−	16.7869i	0.781842	−	0.781842i	0.980142	+	0.198299i	$0.0635418\pi$
$462$	−10.0234	−	17.5778i	−0.466329	−	0.817793i
$463$	−24.4048	+	24.4048i	−1.13419	+	1.13419i	−0.144713	+	0.989474i	$0.546226\pi$
$463$	−24.4048	+	24.4048i	−1.13419	+	1.13419i	−0.989474	+	0.144713i	$0.953774\pi$
$464$	−11.3303	−	20.6336i	−0.525997	−	0.957890i
$465$		−	2.07681i		−	0.0963096i
$466$	26.1926	−	14.9358i	1.21335	−	0.691885i
$467$	−17.7779			−0.822661			−0.411331	−	0.911486i	$-0.634936\pi$
$467$	−17.7779			−0.822661			−0.411331	+	0.911486i	$0.634936\pi$
$468$		0			0
$469$	−14.4772			−0.668494
$470$	−30.2985	+	17.2771i	−1.39757	+	0.796931i
$471$			22.7746i			1.04940i
$472$	−13.6342	+	13.2028i	−0.627565	+	0.607708i
$473$	34.2615	−	34.2615i	1.57535	−	1.57535i
$474$	−1.26526	−	2.21887i	−0.0581155	−	0.101916i
$475$	−0.545317	+	0.545317i	−0.0250209	+	0.0250209i
$476$	−18.9590	+	4.86292i	−0.868985	+	0.222892i
$477$	−0.514268			−0.0235467
$478$	−3.15052	+	11.5109i	−0.144102	+	0.526495i
$479$	5.62626	−	5.62626i	0.257071	−	0.257071i	−0.566791	−	0.823862i	$-0.691815\pi$
$479$	5.62626	−	5.62626i	0.257071	−	0.257071i	0.823862	+	0.566791i	$0.191815\pi$
$480$	19.2182	−	4.60150i	0.877188	−	0.210029i
$481$		0			0
$482$	7.74324	−	28.2910i	0.352695	−	1.28862i
$483$	−11.4864	−	11.4864i	−0.522649	−	0.522649i
$484$	13.3405	+	7.89395i	0.606387	+	0.358816i
$485$			2.96917i			0.134823i
$486$	4.90247	−	2.79552i	0.222380	−	0.126808i
$487$	16.0705	+	16.0705i	0.728226	+	0.728226i	0.970266	−	0.242040i	$-0.0778167\pi$
$487$	16.0705	+	16.0705i	0.728226	+	0.728226i	−0.242040	+	0.970266i	$0.577817\pi$
$488$	−2.02788	−	0.0325982i	−0.0917977	−	0.00147565i
$489$	23.3515	+	23.3515i	1.05599	+	1.05599i
$490$	−2.27691	+	8.31901i	−0.102861	+	0.375815i
$491$	0.0592093			0.00267208			0.00133604	−	0.999999i	$-0.499575\pi$
$491$	0.0592093			0.00267208			0.00133604	+	0.999999i	$0.499575\pi$
$492$	−4.86354	+	1.24748i	−0.219265	+	0.0562407i
$493$			28.1772i			1.26904i
$494$		0			0
$495$			3.61659i			0.162554i
$496$	0.664555	−	2.28326i	0.0298394	−	0.102521i
$497$	−3.58663			−0.160882
$498$	−7.66349	−	2.09750i	−0.343409	−	0.0939911i
$499$	−25.7335	−	25.7335i	−1.15199	−	1.15199i	−0.986153	−	0.165836i	$-0.946968\pi$
$499$	−25.7335	−	25.7335i	−1.15199	−	1.15199i	−0.165836	−	0.986153i	$-0.553032\pi$
$500$	22.3151	−	5.72375i	0.997962	−	0.255974i
$501$	−14.0034	−	14.0034i	−0.625624	−	0.625624i
$502$	−4.14361	−	7.26658i	−0.184938	−	0.324323i
$503$		−	16.9045i		−	0.753734i	−0.926267	−	0.376867i	$-0.877001\pi$
$503$		−	16.9045i		−	0.753734i	0.926267	−	0.376867i	$-0.122999\pi$
$504$	1.60519	−	1.55440i	0.0715007	−	0.0692383i
$505$	1.32926	+	1.32926i	0.0591515	+	0.0591515i
$506$	29.0374	+	7.94754i	1.29087	+	0.353311i
$507$		0			0
$508$	1.57909	−	2.66860i	0.0700606	−	0.118400i
$509$	14.2443	−	14.2443i	0.631369	−	0.631369i	−0.317042	−	0.948411i	$-0.602690\pi$
$509$	14.2443	−	14.2443i	0.631369	−	0.631369i	0.948411	+	0.317042i	$0.102690\pi$
$510$	−22.8154	−	6.24457i	−1.01028	−	0.276514i
$511$	15.4846			0.684998
$512$	22.6011	+	1.09069i	0.998838	+	0.0482023i
$513$	−9.03190	+	9.03190i	−0.398768	+	0.398768i
$514$	−34.7342	+	19.8064i	−1.53206	+	0.873623i
$515$	−17.6853	+	17.6853i	−0.779308	+	0.779308i
$516$	−31.1362	−	18.4242i	−1.37070	−	0.811078i
$517$			49.4213i			2.17355i
$518$	−2.76611	−	4.85088i	−0.121536	−	0.213136i
$519$	−10.9346			−0.479975
$520$		0			0
$521$	4.77166			0.209050			0.104525	−	0.994522i	$-0.466668\pi$
$521$	4.77166			0.209050			0.104525	+	0.994522i	$0.466668\pi$
$522$	−1.59342	−	2.79436i	−0.0697423	−	0.122306i
$523$			16.9515i			0.741239i	0.928785	+	0.370620i	$0.120855\pi$
$523$			16.9515i			0.741239i	−0.928785	+	0.370620i	$0.879145\pi$
$524$	−7.07252	−	4.18500i	−0.308964	−	0.182823i
$525$	−0.772315	+	0.772315i	−0.0337066	+	0.0337066i
$526$	−16.4557	+	9.38349i	−0.717501	+	0.409140i
$527$	−2.01276	+	2.01276i	−0.0876774	+	0.0876774i
$528$	7.82521	−	26.8856i	0.340549	−	1.17005i
$529$	1.16821			0.0507918
$530$	−3.92186	−	1.07341i	−0.170355	−	0.0466261i
$531$	−1.83390	+	1.83390i	−0.0795843	+	0.0795843i
$532$	−4.85691	+	8.20802i	−0.210574	+	0.355863i
$533$		0			0
$534$	−4.29565	−	1.17572i	−0.185891	−	0.0508783i
$535$	−12.3118	−	12.3118i	−0.532285	−	0.532285i
$536$	−13.9365	−	14.3919i	−0.601965	−	0.621634i
$537$		−	12.4155i		−	0.535769i
$538$	−16.0639	−	28.1709i	−0.692562	−	1.21454i
$539$	8.64176	+	8.64176i	0.372227	+	0.372227i
$540$	22.9187	−	5.87856i	0.986264	−	0.252973i
$541$	−5.07631	−	5.07631i	−0.218248	−	0.218248i	0.589512	−	0.807760i	$-0.299320\pi$
$541$	−5.07631	−	5.07631i	−0.218248	−	0.218248i	−0.807760	+	0.589512i	$0.799320\pi$
$542$	13.0935	+	3.58370i	0.562415	+	0.153933i
$543$	17.2970			0.742287
$544$	−23.0852	−	14.1660i	−0.989770	−	0.607362i
$545$			36.9194i			1.58145i
$546$		0			0
$547$		−	32.0440i		−	1.37010i	−0.728494	−	0.685052i	$-0.759779\pi$
$547$		−	32.0440i		−	1.37010i	0.728494	−	0.685052i	$-0.240221\pi$
$548$	22.9303	−	5.88155i	0.979535	−	0.251247i
$549$	−0.277149			−0.0118284
$550$	0.534371	−	1.95240i	0.0227857	−	0.0832505i
$551$	9.70865	+	9.70865i	0.413602	+	0.413602i
$552$	0.361305	−	22.4761i	0.0153782	−	0.956648i
$553$	−1.61470	−	1.61470i	−0.0686641	−	0.0686641i
$554$	−1.35144	+	0.770631i	−0.0574173	+	0.0327410i
$555$		−	6.74866i		−	0.286464i
$556$	14.5126	+	8.58752i	0.615472	+	0.364192i
$557$	−11.2827	−	11.2827i	−0.478065	−	0.478065i	0.426447	−	0.904512i	$-0.359765\pi$
$557$	−11.2827	−	11.2827i	−0.478065	−	0.478065i	−0.904512	+	0.426447i	$0.859765\pi$
$558$	0.0857858	−	0.313430i	0.00363160	−	0.0132686i
$559$		0			0
$560$	15.4857	−	8.50352i	0.654392	−	0.359339i
$561$	−23.7005	+	23.7005i	−1.00064	+	1.00064i
$562$	3.56208	−	13.0145i	0.150257	−	0.548985i
$563$	5.58944			0.235567			0.117783	−	0.993039i	$-0.462421\pi$
$563$	5.58944			0.235567			0.117783	+	0.993039i	$0.462421\pi$
$564$	35.7447	−	9.16840i	1.50512	−	0.386059i
$565$	−13.6615	+	13.6615i	−0.574745	+	0.574745i
$566$	−14.8193	−	25.9884i	−0.622903	−	1.09237i
$567$	−11.1157	+	11.1157i	−0.466818	+	0.466818i
$568$	−3.45268	−	3.56550i	−0.144871	−	0.149605i
$569$		−	31.0626i		−	1.30221i	−0.758987	−	0.651106i	$-0.774305\pi$
$569$		−	31.0626i		−	1.30221i	0.758987	−	0.651106i	$-0.225695\pi$
$570$	−10.0128	+	5.70959i	−0.419390	+	0.239148i
$571$	9.21948			0.385823			0.192912	−	0.981216i	$-0.438207\pi$
$571$	9.21948			0.385823			0.192912	+	0.981216i	$0.438207\pi$
$572$		0			0
$573$	23.3670			0.976169
$574$	−3.89937	+	2.22353i	−0.162757	+	0.0928084i
$575$		−	1.62501i		−	0.0677674i
$576$	3.09048	+	0.0993847i	0.128770	+	0.00414103i
$577$	−28.6991	+	28.6991i	−1.19476	+	1.19476i	−0.219044	+	0.975715i	$0.570294\pi$
$577$	−28.6991	+	28.6991i	−1.19476	+	1.19476i	−0.975715	+	0.219044i	$0.929706\pi$
$578$	4.15072	+	7.27904i	0.172647	+	0.302768i
$579$	−22.3746	+	22.3746i	−0.929856	+	0.929856i
$580$	−6.31904	−	24.6360i	−0.262384	−	1.02295i
$581$	−7.10319			−0.294690
$582$	0.829309	−	3.02999i	0.0343759	−	0.125597i
$583$	−4.07401	+	4.07401i	−0.168728	+	0.168728i
$584$	14.9063	+	15.3934i	0.616826	+	0.636981i
$585$		0			0
$586$	−6.76220	+	24.7066i	−0.279344	+	1.02062i
$587$	−4.45054	−	4.45054i	−0.183694	−	0.183694i	0.609270	−	0.792963i	$-0.291463\pi$
$587$	−4.45054	−	4.45054i	−0.183694	−	0.183694i	−0.792963	+	0.609270i	$0.791463\pi$
$588$	4.64711	−	7.85346i	0.191644	−	0.323871i
$589$			1.38702i			0.0571513i
$590$	−17.8133	+	10.1576i	−0.733361	+	0.418183i
$591$	3.03767	+	3.03767i	0.124953	+	0.124953i
$592$	2.15950	−	7.41953i	0.0887547	−	0.304941i
$593$	−23.4963	−	23.4963i	−0.964878	−	0.964878i	0.0345259	−	0.999404i	$-0.489008\pi$
$593$	−23.4963	−	23.4963i	−0.964878	−	0.964878i	−0.999404	+	0.0345259i	$0.989008\pi$
$594$	8.85061	−	32.3369i	0.363145	−	1.32680i
$595$	−21.1473			−0.866954
$596$	0.701928	+	2.73660i	0.0287521	+	0.112095i
$597$		−	26.7938i		−	1.09660i
$598$		0			0
$599$			23.9175i			0.977241i	0.872496	+	0.488621i	$0.162500\pi$
$599$			23.9175i			0.977241i	−0.872496	+	0.488621i	$0.837500\pi$
$600$	−1.51124	−	0.0242932i	−0.0616959	−	0.000991764i
$601$	−28.4166			−1.15914			−0.579569	−	0.814923i	$-0.696779\pi$
$601$	−28.4166			−1.15914			−0.579569	+	0.814923i	$0.696779\pi$
$602$	−31.1968	−	8.53856i	−1.27149	−	0.348006i
$603$	−1.93581	−	1.93581i	−0.0788322	−	0.0788322i
$604$	−4.83965	−	18.8683i	−0.196923	−	0.767740i
$605$	11.8427	+	11.8427i	0.481474	+	0.481474i
$606$	−0.985221	−	1.72776i	−0.0400218	−	0.0701856i
$607$			35.0522i			1.42272i	0.702826	+	0.711362i	$0.251921\pi$
$607$			35.0522i			1.42272i	−0.702826	+	0.711362i	$0.748079\pi$
$608$	−12.8352	+	3.07318i	−0.520535	+	0.124634i
$609$	13.7500	+	13.7500i	0.557180	+	0.557180i
$610$	−2.11356	−	0.578481i	−0.0855755	−	0.0234220i
$611$		0			0
$612$	−3.18534	−	1.88485i	−0.128760	−	0.0761906i
$613$	−6.44885	+	6.44885i	−0.260466	+	0.260466i	−0.825244	−	0.564777i	$-0.808962\pi$
$613$	−6.44885	+	6.44885i	−0.260466	+	0.260466i	0.564777	+	0.825244i	$0.308962\pi$
$614$	−14.0066	−	3.83360i	−0.565259	−	0.154711i
$615$	−5.42489			−0.218753
$616$	0.402359	−	25.0301i	0.0162115	−	1.00849i
$617$	5.37668	−	5.37668i	0.216457	−	0.216457i	−0.590547	−	0.807004i	$-0.701088\pi$
$617$	5.37668	−	5.37668i	0.216457	−	0.216457i	0.807004	+	0.590547i	$0.201088\pi$
$618$	22.9872	−	13.1080i	0.924681	−	0.527279i
$619$	−25.6801	+	25.6801i	−1.03217	+	1.03217i	−0.0327040	+	0.999465i	$0.510412\pi$
$619$	−25.6801	+	25.6801i	−1.03217	+	1.03217i	−0.999465	+	0.0327040i	$0.989588\pi$
$620$	1.30842	−	2.21119i	0.0525475	−	0.0888035i
$621$		−	26.9144i		−	1.08004i
$622$	6.84539	+	12.0047i	0.274475	+	0.481343i
$623$	−3.98158			−0.159519
$624$		0			0
$625$	23.2380			0.929520
$626$	22.1602	+	38.8620i	0.885701	+	1.55324i
$627$			16.3324i			0.652252i
$628$	−14.3484	+	24.2483i	−0.572563	+	0.967613i
$629$	−6.54055	+	6.54055i	−0.260789	+	0.260789i
$630$	2.09720	−	1.19588i	0.0835544	−	0.0476451i
$631$	15.2503	−	15.2503i	0.607106	−	0.607106i	−0.335083	−	0.942189i	$-0.608764\pi$
$631$	15.2503	−	15.2503i	0.607106	−	0.607106i	0.942189	+	0.335083i	$0.108764\pi$
$632$	0.0507904	−	3.15958i	0.00202033	−	0.125681i
$633$	44.6805			1.77589
$634$	28.5139	+	7.80425i	1.13243	+	0.309946i
$635$	2.36898	−	2.36898i	0.0940102	−	0.0940102i
$636$	3.70238	+	2.19080i	0.146809	+	0.0868709i
$637$		0			0
$638$	−34.7598	−	9.51377i	−1.37616	−	0.376654i
$639$	−0.479585	−	0.479585i	−0.0189721	−	0.0189721i
$640$	23.3608	+	7.20855i	0.923417	+	0.284943i
$641$		−	48.3526i		−	1.90981i	−0.296904	−	0.954907i	$-0.595954\pi$
$641$		−	48.3526i		−	1.90981i	0.296904	−	0.954907i	$-0.404046\pi$
$642$	9.12521	+	16.0027i	0.360143	+	0.631578i
$643$	0.0529335	+	0.0529335i	0.00208749	+	0.00208749i	0.708150	−	0.706062i	$-0.249530\pi$
$643$	0.0529335	+	0.0529335i	0.00208749	+	0.00208749i	−0.706062	+	0.708150i	$0.749530\pi$
$644$	−4.99303	−	19.4663i	−0.196753	−	0.767078i
$645$	−27.6403	−	27.6403i	−1.08834	−	1.08834i
$646$	15.2376	+	4.17052i	0.599514	+	0.164087i
$647$	3.73780			0.146948			0.0734741	−	0.997297i	$-0.476591\pi$
$647$	3.73780			0.146948			0.0734741	+	0.997297i	$0.476591\pi$
$648$	−21.7509	−	0.349646i	−0.854454	−	0.0137354i
$649$			29.0561i			1.14055i
$650$		0			0
$651$			1.96440i			0.0769908i
$652$	10.1507	+	39.5743i	0.397531	+	1.54985i
$653$	40.4504			1.58295			0.791473	−	0.611205i	$-0.209315\pi$
$653$	40.4504			1.58295			0.791473	+	0.611205i	$0.209315\pi$
$654$	10.3118	−	37.6756i	0.403224	−	1.47323i
$655$	−6.27844	−	6.27844i	−0.245319	−	0.245319i
$656$	−5.96417	−	1.73591i	−0.232862	−	0.0677757i
$657$	2.07051	+	2.07051i	0.0807785	+	0.0807785i
$658$	28.6586	−	16.3419i	1.11723	−	0.637074i
$659$			38.8733i			1.51429i	0.653246	+	0.757145i	$0.273407\pi$
$659$			38.8733i			1.51429i	−0.653246	+	0.757145i	$0.726593\pi$
$660$	15.4068	−	26.0370i	0.599709	−	1.01349i
$661$	−28.6251	−	28.6251i	−1.11339	−	1.11339i	−0.992689	−	0.120700i	$-0.961486\pi$
$661$	−28.6251	−	28.6251i	−1.11339	−	1.11339i	−0.120700	−	0.992689i	$-0.538514\pi$
$662$	4.53845	−	16.5818i	0.176392	−	0.644471i
$663$		0			0
$664$	−6.83791	−	7.06134i	−0.265362	−	0.274033i
$665$	−7.28645	+	7.28645i	−0.282556	+	0.282556i
$666$	0.278764	−	1.01850i	0.0108019	−	0.0394662i
$667$	−28.9311			−1.12022
$668$	−6.08713	−	23.7318i	−0.235518	−	0.918212i
$669$	3.47438	−	3.47438i	0.134327	−	0.134327i
$670$	−10.7221	−	18.8032i	−0.414231	−	0.726430i
$671$	−2.19556	+	2.19556i	−0.0847586	+	0.0847586i
$672$	−18.1780	+	4.35244i	−0.701233	+	0.167899i
$673$		−	13.5161i		−	0.521007i	−0.965473	−	0.260504i	$-0.916111\pi$
$673$		−	13.5161i		−	0.521007i	0.965473	−	0.260504i	$-0.0838886\pi$
$674$	−23.0624	+	13.1508i	−0.888330	+	0.506551i
$675$	−1.80965			−0.0696536
$676$		0			0
$677$	40.3341			1.55017			0.775083	−	0.631860i	$-0.217708\pi$
$677$	40.3341			1.55017			0.775083	+	0.631860i	$0.217708\pi$
$678$	17.7571	−	10.1256i	0.681958	−	0.388872i
$679$		−	2.80846i		−	0.107779i
$680$	−20.3575	−	21.0227i	−0.780674	−	0.806183i
$681$	10.8174	−	10.8174i	0.414522	−	0.414522i
$682$	−1.80339	−	3.16257i	−0.0690553	−	0.121101i
$683$	−5.18372	+	5.18372i	−0.198350	+	0.198350i	−0.799292	−	0.600943i	$-0.794792\pi$
$683$	−5.18372	+	5.18372i	−0.198350	+	0.198350i	0.600943	+	0.799292i	$0.294792\pi$
$684$	−1.74697	+	0.448092i	−0.0667971	+	0.0171332i
$685$	25.5770			0.977246
$686$	7.49523	−	27.3848i	0.286169	−	1.04556i
$687$	5.65001	−	5.65001i	0.215561	−	0.215561i
$688$	−21.5434	−	39.2326i	−0.821335	−	1.49573i
$689$		0			0
$690$	6.41164	−	23.4258i	0.244087	−	0.891805i
$691$	16.4082	+	16.4082i	0.624197	+	0.624197i	0.946602	−	0.322405i	$-0.104491\pi$
$691$	16.4082	+	16.4082i	0.624197	+	0.624197i	−0.322405	+	0.946602i	$0.604491\pi$
$692$	−11.6421	−	6.88897i	−0.442567	−	0.261879i
$693$		−	3.42084i		−	0.129947i
$694$	9.81291	−	5.59560i	0.372493	−	0.212406i
$695$	12.8832	+	12.8832i	0.488687	+	0.488687i
$696$	−0.432508	+	26.9055i	−0.0163942	+	1.01985i
$697$	5.25760	+	5.25760i	0.199146	+	0.199146i
$698$	−3.82891	+	13.9894i	−0.144926	+	0.529508i
$699$	−34.4674			−1.30368
$700$	−1.30886	+	0.335718i	−0.0494702	+	0.0126889i
$701$		−	1.83613i		−	0.0693497i	−0.999399	−	0.0346748i	$-0.988960\pi$
$701$		−	1.83613i		−	0.0693497i	0.999399	−	0.0346748i	$-0.0110396\pi$
$702$		0			0
$703$			4.50718i			0.169992i
$704$	25.2699	−	23.6953i	0.952396	−	0.893049i
$705$	39.8704			1.50161
$706$	6.44818	+	1.76487i	0.242680	+	0.0664217i
$707$	−1.25732	−	1.25732i	−0.0472863	−	0.0472863i
$708$	21.0152	−	5.39034i	0.789801	−	0.202581i
$709$	3.75305	+	3.75305i	0.140949	+	0.140949i	0.774060	−	0.633112i	$-0.218223\pi$
$709$	3.75305	+	3.75305i	0.140949	+	0.140949i	−0.633112	+	0.774060i	$0.718223\pi$
$710$	−2.65634	−	4.65837i	−0.0996906	−	0.174826i
$711$		−	0.431818i		−	0.0161944i
$712$	−3.83288	−	3.95812i	−0.143643	−	0.148337i
$713$	−2.06662	−	2.06662i	−0.0773954	−	0.0773954i
$714$	21.5805	+	5.90657i	0.807628	+	0.221048i
$715$		0			0
$716$	7.82197	−	13.2189i	0.292321	−	0.494013i
$717$	9.64661	−	9.64661i	0.360259	−	0.360259i
$718$	−49.9053	−	13.6591i	−1.86245	−	0.509752i
$719$	33.4093			1.24596			0.622979	−	0.782238i	$-0.285922\pi$
$719$	33.4093			1.24596			0.622979	+	0.782238i	$0.285922\pi$
$720$	3.20771	+	0.933622i	0.119544	+	0.0347941i
$721$	16.7281	−	16.7281i	0.622986	−	0.622986i
$722$	−16.6546	+	9.49693i	−0.619820	+	0.353439i
$723$	−23.7091	+	23.7091i	−0.881750	+	0.881750i
$724$	18.4163	+	10.8974i	0.684435	+	0.404999i
$725$			1.94525i			0.0722447i
$726$	−8.77753	−	15.3930i	−0.325765	−	0.571288i
$727$	23.0787			0.855941			0.427970	−	0.903793i	$-0.359229\pi$
$727$	23.0787			0.855941			0.427970	+	0.903793i	$0.359229\pi$
$728$		0			0
$729$	−29.5245			−1.09350
$730$	11.4682	+	20.1116i	0.424458	+	0.744365i
$731$			53.5760i			1.98158i
$732$	1.99528	+	1.18066i	0.0737477	+	0.0436385i
$733$	31.3372	−	31.3372i	1.15746	−	1.15746i	0.172445	−	0.985019i	$-0.444833\pi$
$733$	31.3372	−	31.3372i	1.15746	−	1.15746i	0.985019	−	0.172445i	$-0.0551668\pi$
$734$	−25.0626	+	14.2914i	−0.925077	+	0.527505i
$735$	6.97170	−	6.97170i	0.257155	−	0.257155i
$736$	14.5450	−	23.7029i	0.536136	−	0.873699i
$737$	−30.6708			−1.12977
$738$	−0.818721	−	0.224084i	−0.0301375	−	0.00824864i
$739$	26.1672	−	26.1672i	0.962575	−	0.962575i	−0.0367496	−	0.999325i	$-0.511700\pi$
$739$	26.1672	−	26.1672i	0.962575	−	0.962575i	0.999325	+	0.0367496i	$0.0117004\pi$
$740$	4.25176	−	7.18534i	0.156298	−	0.264138i
$741$		0			0
$742$	3.70958	+	1.01531i	0.136183	+	0.0372733i
$743$	−8.93719	−	8.93719i	−0.327874	−	0.327874i	0.523904	−	0.851778i	$-0.324475\pi$
$743$	−8.93719	−	8.93719i	−0.327874	−	0.327874i	−0.851778	+	0.523904i	$0.824475\pi$
$744$	−1.95282	+	1.89103i	−0.0715939	+	0.0693286i
$745$			3.05246i			0.111833i
$746$	14.4623	+	25.3623i	0.529503	+	0.928581i
$747$	−0.949800	−	0.949800i	−0.0347514	−	0.0347514i
$748$	−40.1658	+	10.3024i	−1.46861	+	0.376693i
$749$	11.6454	+	11.6454i	0.425513	+	0.425513i
$750$	−25.4006	−	6.95214i	−0.927499	−	0.253856i
$751$	−21.5861			−0.787689			−0.393844	−	0.919177i	$-0.628855\pi$
$751$	−21.5861			−0.787689			−0.393844	+	0.919177i	$0.628855\pi$
$752$	43.8339	+	12.7581i	1.59846	+	0.465240i
$753$			9.56224i			0.348467i
$754$		0			0
$755$		−	21.0461i		−	0.765946i
$756$	−21.6782	+	5.56038i	−0.788428	+	0.202229i
$757$	−7.44817			−0.270708			−0.135354	−	0.990797i	$-0.543217\pi$
$757$	−7.44817			−0.270708			−0.135354	+	0.990797i	$0.543217\pi$
$758$	5.29684	−	19.3527i	0.192390	−	0.702922i
$759$	−24.3346	−	24.3346i	−0.883291	−	0.883291i
$760$	−14.2578	−	0.229195i	−0.517186	−	0.00831378i
$761$	21.0562	+	21.0562i	0.763287	+	0.763287i	0.976915	−	0.213628i	$-0.0685282\pi$
$761$	21.0562	+	21.0562i	0.763287	+	0.763287i	−0.213628	+	0.976915i	$0.568528\pi$
$762$	−3.07918	+	1.75584i	−0.111547	+	0.0636072i
$763$		−	34.9211i		−	1.26423i
$764$	24.8790	+	14.7216i	0.900090	+	0.532608i
$765$	−2.82770	−	2.82770i	−0.102236	−	0.102236i
$766$	−5.78813	+	21.1477i	−0.209134	+	0.764098i
$767$		0			0
$768$	−21.8259	−	13.8810i	−0.787575	−	0.500888i
$769$	33.5991	−	33.5991i	1.21161	−	1.21161i	0.241119	−	0.970496i	$-0.422486\pi$
$769$	33.5991	−	33.5991i	1.21161	−	1.21161i	0.970496	−	0.241119i	$-0.0775144\pi$
$770$	7.14019	−	26.0876i	0.257315	−	0.940133i
$771$	45.7074			1.64611
$772$	−37.9187	+	9.72602i	−1.36472	+	0.350047i
$773$	−18.1660	+	18.1660i	−0.653387	+	0.653387i	−0.953807	−	0.300420i	$-0.902873\pi$
$773$	−18.1660	+	18.1660i	−0.653387	+	0.653387i	0.300420	+	0.953807i	$0.402873\pi$
$774$	−3.02973	−	5.31319i	−0.108901	−	0.190979i
$775$	−0.138954	+	0.138954i	−0.00499136	+	0.00499136i
$776$	2.79191	−	2.70357i	0.100224	−	0.0970526i
$777$			6.38338i			0.229002i
$778$	−41.2158	+	23.5024i	−1.47766	+	0.842603i
$779$	3.62309			0.129811
$780$		0			0
$781$	−7.59850			−0.271896
$782$	−28.9173	+	16.4895i	−1.03408	+	0.589663i
$783$			32.2185i			1.15139i
$784$	9.89561	−	5.43388i	0.353415	−	0.194067i
$785$	−21.5258	+	21.5258i	−0.768288	+	0.768288i
$786$	4.65344	+	8.16066i	0.165983	+	0.291081i
$787$	8.42635	−	8.42635i	0.300367	−	0.300367i	−0.540790	−	0.841157i	$-0.681875\pi$
$787$	8.42635	−	8.42635i	0.300367	−	0.300367i	0.841157	+	0.540790i	$0.181875\pi$
$788$	1.32044	+	5.14800i	0.0470389	+	0.183390i
$789$	21.6544			0.770916
$790$	0.901317	−	3.29308i	0.0320674	−	0.117163i
$791$	12.9221	−	12.9221i	0.459457	−	0.459457i
$792$	3.40068	−	3.29308i	0.120838	−	0.117015i
$793$		0			0
$794$	−4.65004	+	16.9896i	−0.165024	+	0.602937i
$795$	3.28669	+	3.28669i	0.116567	+	0.116567i
$796$	16.8805	−	28.5275i	0.598314	−	1.01113i
$797$		−	14.2233i		−	0.503816i	−0.967751	−	0.251908i	$-0.918942\pi$
$797$		−	14.2233i		−	0.503816i	0.967751	−	0.251908i	$-0.0810581\pi$
$798$	9.47085	−	5.40055i	0.335265	−	0.191177i
$799$	−38.6409	−	38.6409i	−1.36702	−	1.36702i
$800$	−1.59372	−	0.977968i	−0.0563464	−	0.0345764i
$801$	−0.532395	−	0.532395i	−0.0188113	−	0.0188113i
$802$	5.43957	−	19.8742i	0.192078	−	0.701783i
$803$	32.8050			1.15766
$804$	5.68989	+	22.1831i	0.200667	+	0.782337i
$805$		−	21.7131i		−	0.765286i
$806$		0			0
$807$			37.0707i			1.30495i
$808$	0.0395489	−	2.46027i	0.00139133	−	0.0865519i
$809$	−6.22787			−0.218960			−0.109480	−	0.993989i	$-0.534919\pi$
$809$	−6.22787			−0.218960			−0.109480	+	0.993989i	$0.534919\pi$
$810$	−22.6699	−	6.20475i	−0.796538	−	0.218013i
$811$	8.66022	+	8.66022i	0.304102	+	0.304102i	0.842616	−	0.538515i	$-0.181014\pi$
$811$	8.66022	+	8.66022i	0.304102	+	0.304102i	−0.538515	+	0.842616i	$0.681014\pi$
$812$	5.97701	+	23.3025i	0.209752	+	0.817758i
$813$	−10.9730	−	10.9730i	−0.384838	−	0.384838i
$814$	−5.86017	−	10.2769i	−0.205399	−	0.360205i
$815$			44.1420i			1.54623i
$816$	14.9027	+	27.1393i	0.521699	+	0.950065i
$817$	18.4600	+	18.4600i	0.645833	+	0.645833i
$818$	−26.4571	−	7.24130i	−0.925050	−	0.253186i
$819$		0			0
$820$	−5.77592	−	3.41777i	−0.201704	−	0.119354i
$821$	−12.2099	+	12.2099i	−0.426129	+	0.426129i	−0.887308	−	0.461178i	$-0.847427\pi$
$821$	−12.2099	+	12.2099i	−0.426129	+	0.426129i	0.461178	+	0.887308i	$0.347427\pi$
$822$	−26.1009	−	7.14381i	−0.910373	−	0.249169i
$823$	17.2243			0.600402			0.300201	−	0.953876i	$-0.402946\pi$
$823$	17.2243			0.600402			0.300201	+	0.953876i	$0.402946\pi$
$824$	32.7328	+	0.526182i	1.14030	+	0.0183304i
$825$	−1.63620	+	1.63620i	−0.0569650	+	0.0569650i
$826$	16.8491	−	9.60784i	0.586255	−	0.334299i
$827$	−7.89012	+	7.89012i	−0.274366	+	0.274366i	−0.830855	−	0.556489i	$-0.812148\pi$
$827$	−7.89012	+	7.89012i	−0.274366	+	0.274366i	0.556489	+	0.830855i	$0.312148\pi$
$828$	1.93528	−	3.27056i	0.0672557	−	0.113660i
$829$			20.6382i			0.716793i	0.933570	+	0.358396i	$0.116676\pi$
$829$			20.6382i			0.716793i	−0.933570	+	0.358396i	$0.883324\pi$
$830$	−5.26078	−	9.22574i	−0.182604	−	0.320230i
$831$	1.77839			0.0616917
$832$		0			0
$833$	−13.5134			−0.468213
$834$	−9.54873	−	16.7455i	−0.330646	−	0.579848i
$835$		−	26.4710i		−	0.916066i
$836$	−10.2897	+	17.3892i	−0.355875	+	0.601417i
$837$	−2.30144	+	2.30144i	−0.0795495	+	0.0795495i
$838$	−3.60723	+	2.05694i	−0.124610	+	0.0710560i
$839$	−11.2106	+	11.2106i	−0.387032	+	0.387032i	−0.873627	−	0.486596i	$-0.838239\pi$
$839$	−11.2106	+	11.2106i	−0.387032	+	0.387032i	0.486596	+	0.873627i	$0.338239\pi$
$840$	−20.1929	−	0.324602i	−0.696721	−	0.0111998i
$841$	5.63256			0.194226
$842$	8.75687	+	2.39676i	0.301782	+	0.0825977i
$843$	−10.9068	+	10.9068i	−0.375649	+	0.375649i
$844$	47.5716	+	28.1494i	1.63748	+	0.968943i
$845$		0			0
$846$	6.01722	+	1.64691i	0.206876	+	0.0566220i
$847$	−11.2017	−	11.2017i	−0.384895	−	0.384895i
$848$	2.56171	+	4.66512i	0.0879694	+	0.160201i
$849$			34.1987i			1.17370i
$850$	1.10871	+	1.94432i	0.0380284	+	0.0666898i
$851$	−6.71554	−	6.71554i	−0.230206	−	0.230206i
$852$	1.40963	+	5.49573i	0.0482933	+	0.188281i
$853$	−1.25966	−	1.25966i	−0.0431300	−	0.0431300i	0.685213	−	0.728343i	$-0.259709\pi$
$853$	−1.25966	−	1.25966i	−0.0431300	−	0.0431300i	−0.728343	+	0.685213i	$0.759709\pi$
$854$	1.99916	+	0.547170i	0.0684099	+	0.0187238i
$855$	−1.94861			−0.0666410
$856$	−0.366306	+	22.7872i	−0.0125201	+	0.778852i
$857$			2.39366i			0.0817658i	0.999164	+	0.0408829i	$0.0130171\pi$
$857$			2.39366i			0.0817658i	−0.999164	+	0.0408829i	$0.986983\pi$
$858$		0			0
$859$		−	17.8687i		−	0.609673i	−0.952405	−	0.304837i	$-0.901398\pi$
$859$		−	17.8687i		−	0.609673i	0.952405	−	0.304837i	$-0.0986018\pi$
$860$	−12.0150	−	46.8427i	−0.409708	−	1.59732i
$861$	5.13126			0.174873
$862$	−7.08063	+	25.8700i	−0.241167	+	0.881137i
$863$	16.3496	+	16.3496i	0.556546	+	0.556546i	0.928322	−	0.371776i	$-0.121251\pi$
$863$	16.3496	+	16.3496i	0.556546	+	0.556546i	−0.371776	+	0.928322i	$0.621251\pi$
$864$	−26.3962	−	16.1977i	−0.898017	−	0.551058i
$865$	−10.3350	−	10.3350i	−0.351400	−	0.351400i
$866$	6.10855	−	3.48327i	0.207577	−	0.118366i
$867$		−	9.57865i		−	0.325308i
$868$	−1.23760	+	2.09151i	−0.0420069	+	0.0709903i
$869$	−3.42084	−	3.42084i	−0.116044	−	0.116044i
$870$	−7.67519	+	28.0423i	−0.260213	+	0.950725i
$871$		0			0
$872$	34.7153	−	33.6169i	1.17561	−	1.13841i
$873$	0.375532	−	0.375532i	0.0127098	−	0.0127098i
$874$	−4.28211	+	15.6452i	−0.144844	+	0.529208i
$875$	−23.5435			−0.795916
$876$	−6.08583	−	23.7267i	−0.205621	−	0.801652i
$877$	−4.19767	+	4.19767i	−0.141745	+	0.141745i	−0.774419	−	0.632673i	$-0.781958\pi$
$877$	−4.19767	+	4.19767i	−0.141745	+	0.141745i	0.632673	+	0.774419i	$0.281958\pi$
$878$	27.4392	+	48.1197i	0.926030	+	1.62396i
$879$	20.7052	−	20.7052i	0.698370	−	0.698370i
$880$	32.8075	−	18.0152i	1.10594	−	0.607293i
$881$			37.1080i			1.25020i	0.780545	+	0.625099i	$0.214942\pi$
$881$			37.1080i			1.25020i	−0.780545	+	0.625099i	$0.785058\pi$
$882$	1.34014	−	0.764187i	0.0451249	−	0.0257315i
$883$	31.7405			1.06815			0.534077	−	0.845436i	$-0.320659\pi$
$883$	31.7405			1.06815			0.534077	+	0.845436i	$0.320659\pi$
$884$		0			0
$885$	23.4408			0.787955
$886$	46.8968	−	26.7419i	1.57553	−	0.898411i
$887$			37.0707i			1.24471i	0.782734	+	0.622356i	$0.213825\pi$
$887$			37.0707i			1.24471i	−0.782734	+	0.622356i	$0.786175\pi$
$888$	−6.34576	+	6.14498i	−0.212950	+	0.206212i
$889$	−2.24076	+	2.24076i	−0.0751526	+	0.0751526i
$890$	−2.94885	−	5.17134i	−0.0988455	−	0.173344i
$891$	−23.5494	+	23.5494i	−0.788934	+	0.788934i
$892$	5.88810	−	1.51028i	0.197148	−	0.0505678i
$893$	−26.6280			−0.891073
$894$	0.852572	−	3.11499i	0.0285143	−	0.104181i
$895$	11.7347	−	11.7347i	0.392248	−	0.392248i
$896$	−22.0964	−	6.81837i	−0.738188	−	0.227786i
$897$		0			0
$898$	−1.17267	+	4.28452i	−0.0391326	+	0.142976i
$899$	2.47389	+	2.47389i	0.0825087	+	0.0825087i
$900$	−0.219904	−	0.130123i	−0.00733013	−	0.00433744i
$901$		−	6.37067i		−	0.212238i
$902$	−8.26105	+	4.71069i	−0.275063	+	0.156849i
$903$	26.1443	+	26.1443i	0.870027	+	0.870027i
$904$	25.2854	+	0.406464i	0.840981	+	0.0135188i
$905$	16.3485	+	16.3485i	0.543444	+	0.543444i
$906$	−5.87831	+	21.4772i	−0.195294	+	0.713532i
$907$	−32.9487			−1.09404			−0.547021	−	0.837119i	$-0.684238\pi$
$907$	−32.9487			−1.09404			−0.547021	+	0.837119i	$0.684238\pi$
$908$	18.3324	−	4.70220i	0.608382	−	0.156048i
$909$		−	0.336243i		−	0.0111525i
$910$		0			0
$911$			22.6697i			0.751082i	0.926806	+	0.375541i	$0.122543\pi$
$911$			22.6697i			0.751082i	−0.926806	+	0.375541i	$0.877457\pi$
$912$	14.4859	+	4.21619i	0.479675	+	0.139612i
$913$	−15.0485			−0.498034
$914$	46.3664	+	12.6905i	1.53366	+	0.419764i
$915$	1.77126	+	1.77126i	0.0585559	+	0.0585559i
$916$	9.57520	−	2.45600i	0.316373	−	0.0811487i
$917$	5.93861	+	5.93861i	0.196110	+	0.196110i
$918$	18.3632	+	32.2032i	0.606075	+	1.06286i
$919$		−	8.67159i		−	0.286049i	−0.989719	−	0.143025i	$-0.954317\pi$
$919$		−	8.67159i		−	0.286049i	0.989719	−	0.143025i	$-0.0456828\pi$
$920$	21.5851	−	20.9022i	0.711641	−	0.689124i
$921$	11.7381	+	11.7381i	0.386784	+	0.386784i
$922$	−32.3827	−	8.86315i	−1.06647	−	0.291892i
$923$		0			0
$924$	−14.5729	+	24.6277i	−0.479413	+	0.810192i
$925$	−0.451535	+	0.451535i	−0.0148464	+	0.0148464i
$926$	47.0781	+	12.8853i	1.54708	+	0.423436i
$927$	4.47357			0.146931
$928$	−17.4114	+	28.3740i	−0.571558	+	0.931423i
$929$	−9.98245	+	9.98245i	−0.327514	+	0.327514i	−0.851640	−	0.524127i	$-0.824392\pi$
$929$	−9.98245	+	9.98245i	−0.327514	+	0.327514i	0.524127	+	0.851640i	$0.324392\pi$
$930$	−2.55139	+	1.45487i	−0.0836633	+	0.0477072i
$931$	−4.65615	+	4.65615i	−0.152599	+	0.152599i
$932$	−36.6976	−	21.7150i	−1.20207	−	0.711298i
$933$		−	15.7972i		−	0.517176i
$934$	12.4540	+	21.8404i	0.407508	+	0.714639i
$935$	−44.8018			−1.46518
$936$		0			0
$937$	−8.23591			−0.269055			−0.134528	−	0.990910i	$-0.542952\pi$
$937$	−8.23591			−0.269055			−0.134528	+	0.990910i	$0.542952\pi$
$938$	10.1418	+	17.7854i	0.331140	+	0.580715i
$939$		−	51.1393i		−	1.66887i
$940$	42.4503	+	25.1190i	1.38458	+	0.819292i
$941$	4.15205	−	4.15205i	0.135353	−	0.135353i	−0.636184	−	0.771537i	$-0.719488\pi$
$941$	4.15205	−	4.15205i	0.135353	−	0.135353i	0.771537	+	0.636184i	$0.219488\pi$
$942$	27.9790	−	15.9544i	0.911605	−	0.519823i
$943$	−5.39827	+	5.39827i	−0.175792	+	0.175792i
$944$	25.7711	+	7.50081i	0.838776	+	0.244131i
$945$	−24.1803			−0.786586
$946$	−66.0923	−	18.0895i	−2.14884	−	0.588139i
$947$	2.02371	−	2.02371i	0.0657617	−	0.0657617i	−0.673461	−	0.739223i	$-0.735193\pi$
$947$	2.02371	−	2.02371i	0.0657617	−	0.0657617i	0.739223	+	0.673461i	$0.235193\pi$
$948$	−1.83956	+	3.10879i	−0.0597461	+	0.100969i
$949$		0			0
$950$	1.05194	+	0.287917i	0.0341296	+	0.00934127i
$951$	−23.8959	−	23.8959i	−0.774878	−	0.774878i
$952$	19.2556	+	19.8848i	0.624078	+	0.644470i
$953$			8.82548i			0.285885i	0.989731	+	0.142943i	$0.0456564\pi$
$953$			8.82548i			0.285885i	−0.989731	+	0.142943i	$0.954344\pi$
$954$	0.360263	+	0.631787i	0.0116639	+	0.0204549i
$955$	22.0856	+	22.0856i	0.714675	+	0.714675i
$956$	16.3483	−	4.19329i	0.528743	−	0.135621i
$957$	29.1303	+	29.1303i	0.941648	+	0.941648i
$958$	−10.8533	−	2.97056i	−0.350656	−	0.0959745i
$959$	−24.1926			−0.781219
$960$	−19.1161	−	20.3864i	−0.616968	−	0.657968i
$961$		−	30.6466i		−	0.988599i
$962$		0			0
$963$			3.11432i			0.100357i
$964$	−40.1803	+	10.3061i	−1.29412	+	0.331937i
$965$	−42.2953			−1.36153
$966$	−6.06460	+	22.1578i	−0.195125	+	0.712917i
$967$	31.1406	+	31.1406i	1.00142	+	1.00142i	0.999999	+	0.00141655i	$0.000450902\pi$
$967$	31.1406	+	31.1406i	1.00142	+	1.00142i	0.00141655	+	0.999999i	$0.499549\pi$
$968$	0.352349	−	21.9190i	0.0113249	−	0.704504i
$969$	−12.7698	−	12.7698i	−0.410223	−	0.410223i
$970$	3.64767	−	2.08001i	0.117120	−	0.0667850i
$971$		−	15.5573i		−	0.499258i	−0.968342	−	0.249629i	$-0.919691\pi$
$971$		−	15.5573i		−	0.499258i	0.968342	−	0.249629i	$-0.0803087\pi$
$972$	−6.86869	−	4.06439i	−0.220313	−	0.130366i
$973$	−12.1859	−	12.1859i	−0.390661	−	0.390661i
$974$	8.48494	−	31.0009i	0.271875	−	0.993332i
$975$		0			0
$976$	1.38055	+	2.51412i	0.0441904	+	0.0804749i
$977$	−31.6023	+	31.6023i	−1.01105	+	1.01105i	−0.0111091	+	0.999938i	$0.503536\pi$
$977$	−31.6023	+	31.6023i	−1.01105	+	1.01105i	−0.999938	+	0.0111091i	$0.996464\pi$
$978$	12.3291	−	45.0462i	0.394242	−	1.44042i
$979$	−8.43522			−0.269591
$980$	11.8151	−	3.03053i	0.377419	−	0.0968068i
$981$	4.66945	−	4.66945i	0.149084	−	0.149084i
$982$	−0.0414781	−	0.0727395i	−0.00132362	−	0.00232121i
$983$	21.2250	−	21.2250i	0.676971	−	0.676971i	−0.282343	−	0.959314i	$-0.591112\pi$
$983$	21.2250	−	21.2250i	0.676971	−	0.676971i	0.959314	+	0.282343i	$0.0911115\pi$
$984$	4.93962	+	5.10103i	0.157469	+	0.162615i
$985$			5.74219i			0.182961i
$986$	34.6161	−	19.7391i	1.10240	−	0.628621i
$987$	−37.7124			−1.20040
$988$		0			0
$989$	−55.0094			−1.74920
$990$	4.44304	−	2.53355i	0.141209	−	0.0805215i
$991$		−	18.5141i		−	0.588120i	−0.955787	−	0.294060i	$-0.904993\pi$
$991$		−	18.5141i		−	0.588120i	0.955787	−	0.294060i	$-0.0950065\pi$
$992$	−3.27056	+	0.783084i	−0.103840	+	0.0248630i
$993$	−13.8963	+	13.8963i	−0.440986	+	0.440986i
$994$	2.51256	+	4.40623i	0.0796936	+	0.139757i
$995$	25.3246	−	25.3246i	0.802843	−	0.802843i
$996$	2.79173	+	10.8841i	0.0884594	+	0.344875i
$997$	−54.5558			−1.72780			−0.863900	−	0.503664i	$-0.831985\pi$
$997$	−54.5558			−1.72780			−0.863900	+	0.503664i	$0.831985\pi$
$998$	−13.5868	+	49.6412i	−0.430083	+	1.57137i
$999$	−7.47862	+	7.47862i	−0.236613	+	0.236613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.f.h.239.3		16
4.3	odd	2	inner	676.2.f.h.239.7		16
13.2	odd	12		676.2.l.i.319.3		16
13.3	even	3		52.2.l.b.19.4	yes	16
13.4	even	6		676.2.l.i.587.4		16
13.5	odd	4		676.2.f.i.99.2		16
13.6	odd	12		676.2.l.k.427.4		16
13.7	odd	12		52.2.l.b.11.1	✓	16
13.8	odd	4	inner	676.2.f.h.99.7		16
13.9	even	3		676.2.l.m.587.1		16
13.10	even	6		676.2.l.k.19.1		16
13.11	odd	12		676.2.l.m.319.2		16
13.12	even	2		676.2.f.i.239.6		16
39.20	even	12		468.2.cb.f.271.4		16
39.29	odd	6		468.2.cb.f.19.1		16
52.3	odd	6		52.2.l.b.19.1	yes	16
52.7	even	12		52.2.l.b.11.4	yes	16
52.11	even	12		676.2.l.m.319.1		16
52.15	even	12		676.2.l.i.319.4		16
52.19	even	12		676.2.l.k.427.1		16
52.23	odd	6		676.2.l.k.19.4		16
52.31	even	4		676.2.f.i.99.6		16
52.35	odd	6		676.2.l.m.587.2		16
52.43	odd	6		676.2.l.i.587.3		16
52.47	even	4	inner	676.2.f.h.99.3		16
52.51	odd	2		676.2.f.i.239.2		16
104.3	odd	6		832.2.bu.n.383.2		16
104.29	even	6		832.2.bu.n.383.3		16
104.59	even	12		832.2.bu.n.63.3		16
104.85	odd	12		832.2.bu.n.63.2		16
156.59	odd	12		468.2.cb.f.271.1		16
156.107	even	6		468.2.cb.f.19.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.11.1	✓	16	13.7	odd	12
52.2.l.b.11.4	yes	16	52.7	even	12
52.2.l.b.19.1	yes	16	52.3	odd	6
52.2.l.b.19.4	yes	16	13.3	even	3
468.2.cb.f.19.1		16	39.29	odd	6
468.2.cb.f.19.4		16	156.107	even	6
468.2.cb.f.271.1		16	156.59	odd	12
468.2.cb.f.271.4		16	39.20	even	12
676.2.f.h.99.3		16	52.47	even	4	inner
676.2.f.h.99.7		16	13.8	odd	4	inner
676.2.f.h.239.3		16	1.1	even	1	trivial
676.2.f.h.239.7		16	4.3	odd	2	inner
676.2.f.i.99.2		16	13.5	odd	4
676.2.f.i.99.6		16	52.31	even	4
676.2.f.i.239.2		16	52.51	odd	2
676.2.f.i.239.6		16	13.12	even	2
676.2.l.i.319.3		16	13.2	odd	12
676.2.l.i.319.4		16	52.15	even	12
676.2.l.i.587.3		16	52.43	odd	6
676.2.l.i.587.4		16	13.4	even	6
676.2.l.k.19.1		16	13.10	even	6
676.2.l.k.19.4		16	52.23	odd	6
676.2.l.k.427.1		16	52.19	even	12
676.2.l.k.427.4		16	13.6	odd	12
676.2.l.m.319.1		16	52.11	even	12
676.2.l.m.319.2		16	13.11	odd	12
676.2.l.m.587.1		16	13.9	even	3
676.2.l.m.587.2		16	52.35	odd	6
832.2.bu.n.63.2		16	104.85	odd	12
832.2.bu.n.63.3		16	104.59	even	12
832.2.bu.n.383.2		16	104.3	odd	6
832.2.bu.n.383.3		16	104.29	even	6

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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.700535 - 1.22852i) q^{2} +1.61663i q^{3} +(-1.01850 + 1.72124i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(1.98605 - 1.13250i) q^{6} +(1.44528 - 1.44528i) q^{7} +(2.82806 + 0.0454612i) q^{8} +0.386509 q^{9} +O(q^{10})\)	\(q+(-0.700535 - 1.22852i) q^{2} +1.61663i q^{3} +(-1.01850 + 1.72124i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(1.98605 - 1.13250i) q^{6} +(1.44528 - 1.44528i) q^{7} +(2.82806 + 0.0454612i) q^{8} +0.386509 q^{9} +(2.94755 + 0.806745i) q^{10} +(3.06191 - 3.06191i) q^{11} +(-2.78260 - 1.64654i) q^{12} +(-2.78801 - 0.763079i) q^{14} +(-2.47018 - 2.47018i) q^{15} +(-1.92531 - 3.50617i) q^{16} +4.78801i q^{17} +(-0.270763 - 0.474833i) q^{18} +(1.64974 + 1.64974i) q^{19} +(-1.07376 - 4.18627i) q^{20} +(2.33648 + 2.33648i) q^{21} +(-5.90657 - 1.61663i) q^{22} -4.91612 q^{23} +(-0.0734939 + 4.57193i) q^{24} +0.330547i q^{25} +5.47473i q^{27} +(1.01564 + 3.95968i) q^{28} +5.88494 q^{29} +(-1.30421 + 4.76510i) q^{30} +(0.420375 + 0.420375i) q^{31} +(-2.95864 + 4.82146i) q^{32} +(4.94997 + 4.94997i) q^{33} +(5.88215 - 3.35417i) q^{34} +4.41671i q^{35} +(-0.393660 + 0.665273i) q^{36} +(1.36603 + 1.36603i) q^{37} +(0.871034 - 3.18244i) q^{38} +(-4.39069 + 4.25176i) q^{40} +(1.09808 - 1.09808i) q^{41} +(1.23362 - 4.50718i) q^{42} +11.1896 q^{43} +(2.15170 + 8.38882i) q^{44} +(-0.590579 + 0.590579i) q^{45} +(3.44391 + 6.03953i) q^{46} +(-8.07035 + 8.07035i) q^{47} +(5.66817 - 3.11251i) q^{48} +2.82235i q^{49} +(0.406082 - 0.231559i) q^{50} -7.74044 q^{51} -1.33055 q^{53} +(6.72579 - 3.83524i) q^{54} +9.35707i q^{55} +(4.15304 - 4.02163i) q^{56} +(-2.66702 + 2.66702i) q^{57} +(-4.12261 - 7.22975i) q^{58} +(-4.74477 + 4.74477i) q^{59} +(6.76765 - 1.73588i) q^{60} -0.717056 q^{61} +(0.221950 - 0.810926i) q^{62} +(0.558613 - 0.558613i) q^{63} +(7.99587 + 0.257134i) q^{64} +(2.61349 - 9.54874i) q^{66} +(-5.00844 - 5.00844i) q^{67} +(-8.24130 - 4.87660i) q^{68} -7.94754i q^{69} +(5.42600 - 3.09406i) q^{70} +(-1.24081 - 1.24081i) q^{71} +(1.09307 + 0.0175712i) q^{72} +(5.35696 + 5.35696i) q^{73} +(0.721236 - 2.63513i) q^{74} -0.534371 q^{75} +(-4.51987 + 1.15933i) q^{76} -8.85061i q^{77} -1.11723i q^{79} +(8.29919 + 2.41553i) q^{80} -7.69108 q^{81} +(-2.11824 - 0.579764i) q^{82} +(-2.45738 - 2.45738i) q^{83} +(-6.40134 + 1.64192i) q^{84} +(-7.31599 - 7.31599i) q^{85} +(-7.83871 - 13.7466i) q^{86} +9.51377i q^{87} +(8.79846 - 8.52006i) q^{88} +(-1.37745 - 1.37745i) q^{89} +(1.13926 + 0.311814i) q^{90} +(5.00708 - 8.46180i) q^{92} +(-0.679591 + 0.679591i) q^{93} +(15.5681 + 4.26099i) q^{94} -5.04156 q^{95} +(-7.79451 - 4.78302i) q^{96} +(0.971599 - 0.971599i) q^{97} +(3.46730 - 1.97715i) q^{98} +(1.18345 - 1.18345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 12 q^{5} + 4 q^{6} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 12 * q^5 + 4 * q^6 + 10 * q^8 - 8 * q^9	\( 16 q - 2 q^{2} - 12 q^{5} + 4 q^{6} + 10 q^{8} - 8 q^{9} + 8 q^{14} + 4 q^{16} - 6 q^{18} - 22 q^{20} - 28 q^{21} + 4 q^{24} - 36 q^{28} + 16 q^{29} - 2 q^{32} + 28 q^{33} + 14 q^{34} + 8 q^{37} - 40 q^{40} - 24 q^{41} + 56 q^{42} - 8 q^{44} + 20 q^{45} + 56 q^{46} + 20 q^{48} - 32 q^{50} - 32 q^{53} + 44 q^{54} + 12 q^{57} + 30 q^{58} - 24 q^{60} - 8 q^{61} + 56 q^{66} - 32 q^{68} + 28 q^{70} - 46 q^{72} + 20 q^{73} - 8 q^{74} - 8 q^{76} - 22 q^{80} - 96 q^{81} - 48 q^{84} - 52 q^{85} + 16 q^{86} + 44 q^{89} - 12 q^{92} + 112 q^{93} + 76 q^{94} - 72 q^{96} - 52 q^{97} + 70 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 12 * q^5 + 4 * q^6 + 10 * q^8 - 8 * q^9 + 8 * q^14 + 4 * q^16 - 6 * q^18 - 22 * q^20 - 28 * q^21 + 4 * q^24 - 36 * q^28 + 16 * q^29 - 2 * q^32 + 28 * q^33 + 14 * q^34 + 8 * q^37 - 40 * q^40 - 24 * q^41 + 56 * q^42 - 8 * q^44 + 20 * q^45 + 56 * q^46 + 20 * q^48 - 32 * q^50 - 32 * q^53 + 44 * q^54 + 12 * q^57 + 30 * q^58 - 24 * q^60 - 8 * q^61 + 56 * q^66 - 32 * q^68 + 28 * q^70 - 46 * q^72 + 20 * q^73 - 8 * q^74 - 8 * q^76 - 22 * q^80 - 96 * q^81 - 48 * q^84 - 52 * q^85 + 16 * q^86 + 44 * q^89 - 12 * q^92 + 112 * q^93 + 76 * q^94 - 72 * q^96 - 52 * q^97 + 70 * q^98

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