LMFDB - Embedded newform 676.2.f.h.239.7

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			239.7
Root			$-0.713659 + 1.22094i$ of defining polynomial
Character	$\chi$	$=$	676.239
Dual form			676.2.f.h.99.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22852 + 0.700535i) q^{2} -1.61663i q^{3} +(1.01850 + 1.72124i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(1.13250 - 1.98605i) q^{6} +(-1.44528 + 1.44528i) q^{7} +(0.0454612 + 2.82806i) q^{8} +0.386509 q^{9} +O(q^{10})$	\(q+(1.22852 + 0.700535i) q^{2} -1.61663i q^{3} +(1.01850 + 1.72124i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(1.13250 - 1.98605i) q^{6} +(-1.44528 + 1.44528i) q^{7} +(0.0454612 + 2.82806i) 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} +(0.474833 + 0.270763i) q^{18} +(-1.64974 - 1.64974i) q^{19} +(-4.18627 - 1.07376i) q^{20} +(2.33648 + 2.33648i) q^{21} +(-5.90657 + 1.61663i) q^{22} +4.91612 q^{23} +(4.57193 - 0.0734939i) q^{24} +0.330547i q^{25} -5.47473i q^{27} +(-3.95968 - 1.01564i) q^{28} +5.88494 q^{29} +(1.30421 + 4.76510i) q^{30} +(-0.420375 - 0.420375i) q^{31} +(-4.82146 + 2.95864i) q^{32} +(4.94997 + 4.94997i) q^{33} +(-3.35417 + 5.88215i) 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} +(-8.38882 - 2.15170i) q^{44} +(-0.590579 + 0.590579i) q^{45} +(6.03953 + 3.44391i) q^{46} +(8.07035 - 8.07035i) q^{47} +(5.66817 + 3.11251i) q^{48} +2.82235i q^{49} +(-0.231559 + 0.406082i) q^{50} +7.74044 q^{51} -1.33055 q^{53} +(3.83524 - 6.72579i) q^{54} -9.35707i q^{55} +(-4.15304 - 4.02163i) q^{56} +(-2.66702 + 2.66702i) q^{57} +(7.22975 + 4.12261i) q^{58} +(4.74477 - 4.74477i) q^{59} +(-1.73588 + 6.76765i) 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} +(3.09406 - 5.42600i) q^{70} +(1.24081 + 1.24081i) q^{71} +(0.0175712 + 1.09307i) q^{72} +(5.35696 + 5.35696i) q^{73} +(0.721236 + 2.63513i) q^{74} +0.534371 q^{75} +(1.15933 - 4.51987i) q^{76} -8.85061i q^{77} +1.11723i q^{79} +(-2.41553 - 8.29919i) q^{80} -7.69108 q^{81} +(2.11824 - 0.579764i) q^{82} +(2.45738 + 2.45738i) q^{83} +(-1.64192 + 6.40134i) q^{84} +(-7.31599 - 7.31599i) q^{85} +(-13.7466 - 7.83871i) 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} +(4.78302 + 7.79451i) q^{96} +(0.971599 - 0.971599i) q^{97} +(-1.97715 + 3.46730i) 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 $

$2$	1.22852	+	0.700535i	0.868692	+	0.495353i
$2$	1.22852	+	0.700535i	0.868692	+	0.495353i
$3$		−	1.61663i		−	0.933361i	−0.884426	−	0.466681i	$-0.845450\pi$
$3$		−	1.61663i		−	0.933361i	0.884426	−	0.466681i	$-0.154550\pi$
$4$	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	$0.410522\pi$
$6$	1.13250	−	1.98605i	0.462343	−	0.810804i
$7$	−1.44528	+	1.44528i	−0.546264	+	0.546264i	−0.925358	−	0.379094i	$-0.876236\pi$
$7$	−1.44528	+	1.44528i	−0.546264	+	0.546264i	0.379094	+	0.925358i	$0.376236\pi$
$8$	0.0454612	+	2.82806i	0.0160730	+	0.999871i
$9$	0.386509			0.128836
$10$	−2.94755	+	0.806745i	−0.932098	+	0.255115i
$11$	−3.06191	+	3.06191i	−0.923200	+	0.923200i	−0.997254	−	0.0740545i	$-0.976406\pi$
$11$	−3.06191	+	3.06191i	−0.923200	+	0.923200i	0.0740545	+	0.997254i	$0.476406\pi$
$12$	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	$0.802806\pi$
$18$	0.474833	+	0.270763i	0.111919	+	0.0638195i
$19$	−1.64974	−	1.64974i	−0.378477	−	0.378477i	0.492075	−	0.870553i	$-0.336238\pi$
$19$	−1.64974	−	1.64974i	−0.378477	−	0.378477i	−0.870553	+	0.492075i	$0.836238\pi$
$20$	−4.18627	−	1.07376i	−0.936078	−	0.240101i
$21$	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	$-0.328704\pi$
$23$	4.91612			1.02508			0.512541	+	0.858663i	$0.328704\pi$
$24$	4.57193	−	0.0734939i	0.933241	−	0.0150019i
$25$			0.330547i			0.0661093i
$26$		0			0
$27$		−	5.47473i		−	1.05361i
$28$	−3.95968	−	1.01564i	−0.748310	−	0.191939i
$29$	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	0.668348	−	0.743849i	$-0.267002\pi$
$31$	−0.420375	−	0.420375i	−0.0755017	−	0.0755017i	−0.743849	+	0.668348i	$0.767002\pi$
$32$	−4.82146	+	2.95864i	−0.852322	+	0.523018i
$33$	4.94997	+	4.94997i	0.861679	+	0.861679i
$34$	−3.35417	+	5.88215i	−0.575235	+	1.00878i
$35$		−	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	$-0.825341\pi$
$43$	−11.1896			−1.70640			−0.853200	+	0.521584i	$0.825341\pi$
$44$	−8.38882	−	2.15170i	−1.26466	−	0.324382i
$45$	−0.590579	+	0.590579i	−0.0880383	+	0.0880383i
$46$	6.03953	+	3.44391i	0.890480	+	0.507777i
$47$	8.07035	−	8.07035i	1.17718	−	1.17718i	0.196722	−	0.980459i	$-0.436970\pi$
$47$	8.07035	−	8.07035i	1.17718	−	1.17718i	0.980459	−	0.196722i	$-0.0630296\pi$
$48$	5.66817	+	3.11251i	0.818130	+	0.449251i
$49$			2.82235i			0.403192i
$50$	−0.231559	+	0.406082i	−0.0327474	+	0.0574286i
$51$	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	$0.529129\pi$
$54$	3.83524	−	6.72579i	0.521910	−	0.915265i
$55$		−	9.35707i		−	1.26171i
$56$	−4.15304	−	4.02163i	−0.554973	−	0.537413i
$57$	−2.66702	+	2.66702i	−0.353256	+	0.353256i
$58$	7.22975	+	4.12261i	0.949312	+	0.541325i
$59$	4.74477	−	4.74477i	0.617716	−	0.617716i	−0.327229	−	0.944945i	$-0.606115\pi$
$59$	4.74477	−	4.74477i	0.617716	−	0.617716i	0.944945	+	0.327229i	$0.106115\pi$
$60$	−1.73588	+	6.76765i	−0.224101	+	0.873699i
$61$	−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	0.943435	−	0.331557i	$-0.107574\pi$
$67$	5.00844	+	5.00844i	0.611878	+	0.611878i	−0.331557	+	0.943435i	$0.607574\pi$
$68$	−8.24130	+	4.87660i	−0.999404	+	0.591375i
$69$		−	7.94754i		−	0.956771i
$70$	3.09406	−	5.42600i	0.369811	−	0.648531i
$71$	1.24081	+	1.24081i	0.147257	+	0.147257i	0.776892	−	0.629634i	$-0.216795\pi$
$71$	1.24081	+	1.24081i	0.147257	+	0.147257i	−0.629634	+	0.776892i	$0.716795\pi$
$72$	0.0175712	+	1.09307i	0.00207078	+	0.128820i
$73$	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
$76$	1.15933	−	4.51987i	0.132984	−	0.518464i
$77$		−	8.85061i		−	1.00862i
$78$		0			0
$79$			1.11723i			0.125698i	0.998023	+	0.0628489i	$0.0200186\pi$
$79$			1.11723i			0.125698i	−0.998023	+	0.0628489i	$0.979981\pi$
$80$	−2.41553	−	8.29919i	−0.270064	−	0.927877i
$81$	−7.69108			−0.854565
$82$	2.11824	−	0.579764i	0.233921	−	0.0640242i
$83$	2.45738	+	2.45738i	0.269733	+	0.269733i	0.828992	−	0.559260i	$-0.188915\pi$
$83$	2.45738	+	2.45738i	0.269733	+	0.269733i	−0.559260	+	0.828992i	$0.688915\pi$
$84$	−1.64192	+	6.40134i	−0.179148	+	0.698443i
$85$	−7.31599	−	7.31599i	−0.793531	−	0.793531i
$86$	−13.7466	−	7.83871i	−1.48234	−	0.845270i
$87$		−	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
$96$	4.78302	+	7.79451i	0.488165	+	0.795524i
$97$	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	$0.227778\pi$
$98$	−1.97715	+	3.46730i	−0.199722	+	0.350250i
$99$	−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	$-0.0137812\pi$
$102$	9.50926	+	5.42245i	0.941557	+	0.536902i
$103$	−11.5743			−1.14045			−0.570225	−	0.821489i	$-0.693144\pi$
$103$	−11.5743			−1.14045			−0.570225	+	0.821489i	$0.693144\pi$
$104$		0			0
$105$	−7.14019			−0.696811
$106$	−1.63460	−	0.932094i	−0.158766	−	0.0905330i
$107$		−	8.05755i		−	0.778953i	−0.921036	−	0.389476i	$-0.872656\pi$
$107$		−	8.05755i		−	0.778953i	0.921036	−	0.389476i	$-0.127344\pi$
$108$	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	$-0.0550472\pi$
$110$	6.55495	−	11.4953i	0.624990	−	1.09604i
$111$	2.20836	−	2.20836i	0.209608	−	0.209608i
$112$	−2.28478	−	7.84998i	−0.215892	−	0.741754i
$113$	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
$122$	−0.880914	−	0.502322i	−0.0797542	−	0.0454781i
$123$	−1.77518	−	1.77518i	−0.160063	−	0.160063i
$124$	0.295412	−	1.15172i	0.0265288	−	0.103427i
$125$	−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	$-0.478087\pi$
$127$	1.55040			0.137576			0.0687879	+	0.997631i	$0.478087\pi$
$128$	−10.0032	−	5.28549i	−0.884165	−	0.467176i
$129$			18.0895i			1.59269i
$130$		0			0
$131$		−	4.10898i		−	0.359003i	−0.983758	−	0.179502i	$-0.942552\pi$
$131$		−	4.10898i		−	0.359003i	0.983758	−	0.179502i	$-0.0574485\pi$
$132$	−3.47851	+	13.5616i	−0.302765	+	1.18039i
$133$	4.76868			0.413497
$134$	2.64436	+	9.66154i	0.228438	+	0.834630i
$135$	8.36529	+	8.36529i	0.719969	+	0.719969i
$136$	−13.5408	+	0.217669i	−1.16111	+	0.0186649i
$137$	−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	$0.918737\pi$
$138$	5.56753	−	9.76368i	0.473939	−	0.831140i
$139$			8.43151i			0.715152i	0.933884	+	0.357576i	$0.116397\pi$
$139$			8.43151i			0.715152i	−0.933884	+	0.357576i	$0.883603\pi$
$140$	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
$148$	−0.959952	+	3.74255i	−0.0789075	+	0.307636i
$149$	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	$0.231572\pi$
$150$	0.656484	+	0.374346i	0.0536017	+	0.0305652i
$151$	6.88689	−	6.88689i	0.560447	−	0.560447i	−0.368987	−	0.929435i	$-0.620295\pi$
$151$	6.88689	−	6.88689i	0.560447	−	0.560447i	0.929435	+	0.368987i	$0.120295\pi$
$152$	4.59058	−	4.74058i	0.372345	−	0.384512i
$153$			1.85061i			0.149613i
$154$	6.20016	−	10.8731i	0.499623	−	0.876181i
$155$	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	$0.309970\pi$
$158$	−0.782655	+	1.37253i	−0.0622647	+	0.109193i
$159$			2.15100i			0.170585i
$160$	2.84636	−	11.8878i	0.225024	−	0.939816i
$161$	−7.10515	+	7.10515i	−0.559965	+	0.559965i
$162$	−9.44862	−	5.38787i	−0.742354	−	0.423311i
$163$	−14.4445	+	14.4445i	−1.13138	+	1.13138i	−0.141437	+	0.989947i	$0.545172\pi$
$163$	−14.4445	+	14.4445i	−1.13138	+	1.13138i	−0.989947	+	0.141437i	$0.954828\pi$
$164$	3.00844	+	0.771655i	0.234920	+	0.0602561i
$165$	−15.1269			−1.17763
$166$	1.29745	+	4.74041i	0.100702	+	0.367927i
$167$	8.66208	−	8.66208i	0.670292	−	0.670292i	−0.287492	−	0.957783i	$-0.592821\pi$
$167$	8.66208	−	8.66208i	0.670292	−	0.670292i	0.957783	+	0.287492i	$0.0928213\pi$
$168$	−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	$0.917226\pi$
$174$	6.66473	−	11.6878i	0.505252	−	0.886051i
$175$	−0.477732	−	0.477732i	−0.0361131	−	0.0361131i
$176$	−4.84045	−	16.6307i	−0.364862	−	1.25358i
$177$	−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	$-0.407339\pi$
$179$	7.67988			0.574021			0.287011	+	0.957927i	$0.407339\pi$
$180$	−1.61803	−	0.415019i	−0.120601	−	0.0309337i
$181$		−	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
$184$	0.223493	+	13.9031i	0.0164761	+	1.02495i
$185$	−4.17452			−0.306917
$186$	−1.31097	+	0.358812i	−0.0961247	+	0.0263093i
$187$	−14.6605	−	14.6605i	−1.07208	−	1.07208i
$188$	22.1106	+	5.67130i	1.61258	+	0.413622i
$189$	7.91250	+	7.91250i	0.575550	+	0.575550i
$190$	6.19363	+	3.53178i	0.449333	+	0.256223i
$191$			14.4541i			1.04586i	0.852374	+	0.522932i	$0.175162\pi$
$191$			14.4541i			1.04586i	−0.852374	+	0.522932i	$0.824838\pi$
$192$	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	$-0.300134\pi$
$199$	16.5739			1.17489			0.587445	+	0.809264i	$0.300134\pi$
$200$	−0.934806	+	0.0150270i	−0.0661008	+	0.00106257i
$201$	8.09679	−	8.09679i	0.571104	−	0.571104i
$202$	0.609429	−	1.06875i	0.0428793	−	0.0751966i
$203$	−8.50538	+	8.50538i	−0.596960	+	0.596960i
$204$	7.88366	+	13.3231i	0.551967	+	0.932806i
$205$			3.35568i			0.234371i
$206$	−14.2192	−	8.10820i	−0.990700	−	0.564925i
$207$	1.90012			0.132068
$208$		0			0
$209$	10.1027			0.698820
$210$	−8.77184	−	5.00195i	−0.605314	−	0.345167i
$211$			27.6380i			1.90268i	0.308141	+	0.951341i	$0.400293\pi$
$211$			27.6380i			1.90268i	−0.308141	+	0.951341i	$0.599707\pi$
$212$	−1.35517	−	2.29018i	−0.0930731	−	0.157291i
$213$	2.00593	−	2.00593i	0.137444	−	0.137444i
$214$	5.64459	−	9.89883i	0.385856	−	0.676670i
$215$	17.0975	−	17.0975i	1.16604	−	1.16604i
$216$	15.4829	−	0.248888i	1.05348	−	0.0169347i
$217$	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	0.775395	−	0.631477i	$-0.217551\pi$
$223$	2.14915	+	2.14915i	0.143918	+	0.143918i	−0.631477	+	0.775395i	$0.717551\pi$
$224$	2.69229	−	11.2444i	0.179886	−	0.751298i
$225$			0.127759i			0.00851728i
$226$	10.9840	+	6.26341i	0.730648	+	0.416636i
$227$	6.69130	+	6.69130i	0.444117	+	0.444117i	0.893393	−	0.449276i	$-0.148318\pi$
$227$	6.69130	+	6.69130i	0.444117	+	0.444117i	−0.449276	+	0.893393i	$0.648318\pi$
$228$	−7.30695	−	1.87421i	−0.483915	−	0.124122i
$229$	−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
$232$	0.267537	+	16.6430i	0.0175646	+	1.09267i
$233$			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
$236$	12.9994	+	3.33430i	0.846190	+	0.217045i
$237$	1.80614			0.117321
$238$	−3.65363	−	13.3490i	−0.236830	−	0.865290i
$239$	5.96711	+	5.96711i	0.385981	+	0.385981i	0.873251	−	0.487271i	$-0.162007\pi$
$239$	5.96711	+	5.96711i	0.385981	+	0.385981i	−0.487271	+	0.873251i	$0.662007\pi$
$240$	−13.4167	+	3.90501i	−0.866045	+	0.252067i
$241$	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	$0.517148\pi$
$242$	5.42953	−	9.52167i	0.349023	−	0.612076i
$243$		−	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	$-0.559771\pi$
$251$	−5.91492			−0.373347			−0.186673	+	0.982422i	$0.559771\pi$
$252$	−1.53045	−	0.392556i	−0.0964095	−	0.0247287i
$253$	−15.0527	+	15.0527i	−0.946355	+	0.946355i
$254$	1.90469	+	1.08611i	0.119511	+	0.0681485i
$255$	−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	$-0.343681\pi$
$258$	−12.6723	+	22.2232i	−0.788942	+	1.38355i
$259$	−3.94857			−0.245352
$260$		0			0
$261$	2.27458			0.140793
$262$	2.87848	−	5.04794i	0.177833	−	0.311863i
$263$			13.3948i			0.825956i	0.910741	+	0.412978i	$0.135511\pi$
$263$			13.3948i			0.825956i	−0.910741	+	0.412978i	$0.864489\pi$
$264$	−13.7738	+	14.2238i	−0.847718	+	0.875417i
$265$	2.03305	−	2.03305i	0.124889	−	0.124889i
$266$	5.85839	+	3.34062i	0.359201	+	0.204827i
$267$	−2.22682	+	2.22682i	−0.136279	+	0.136279i
$268$	−3.51960	+	13.7218i	−0.214994	+	0.838193i
$269$	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	−0.470230	−	0.882544i	$-0.655829\pi$
$271$	6.78755	−	6.78755i	0.412314	−	0.412314i	0.882544	+	0.470230i	$0.155829\pi$
$272$	−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	$-0.0105215\pi$
$278$	−5.90657	+	10.3582i	−0.354252	+	0.621247i
$279$	−0.162479	−	0.162479i	−0.00972736	−	0.00972736i
$280$	12.4907	−	0.200789i	0.746464	−	0.0119994i
$281$	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	$-0.716432\pi$
$283$	−21.1543			−1.25749			−0.628746	+	0.777610i	$0.716432\pi$
$284$	−0.871959	+	3.39950i	−0.0517413	+	0.201723i
$285$		−	8.15033i		−	0.482784i
$286$		0			0
$287$			3.17405i			0.187358i
$288$	−1.86354	+	1.14354i	−0.109810	+	0.0673838i
$289$	−5.92507			−0.348534
$290$	−17.3462	+	4.74765i	−1.01860	+	0.278792i
$291$	−1.57072	−	1.57072i	−0.0920770	−	0.0920770i
$292$	−3.76452	+	14.6767i	−0.220302	+	0.858887i
$293$	−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	$0.927463\pi$
$294$	5.60533	+	3.19632i	0.326910	+	0.186413i
$295$			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
$304$	8.96054	−	2.60802i	0.513922	−	0.149580i
$305$	1.09565	−	1.09565i	0.0627366	−	0.0627366i
$306$	−1.29642	+	2.27350i	−0.0741112	+	0.129968i
$307$	−7.26086	+	7.26086i	−0.414399	+	0.414399i	−0.883268	−	0.468869i	$-0.844662\pi$
$307$	−7.26086	+	7.26086i	−0.414399	+	0.414399i	0.468869	+	0.883268i	$0.344662\pi$
$308$	15.2340	−	9.01437i	0.868037	−	0.513641i
$309$			18.7114i			1.06445i
$310$	1.57822	+	0.899943i	0.0896366	+	0.0511133i
$311$	9.77167			0.554101			0.277050	−	0.960855i	$-0.410643\pi$
$311$	9.77167			0.554101			0.277050	+	0.960855i	$0.410643\pi$
$312$		0			0
$313$	−31.6333			−1.78802			−0.894010	−	0.448047i	$-0.852120\pi$
$313$	−31.6333			−1.78802			−0.894010	+	0.448047i	$0.852120\pi$
$314$	17.3070	+	9.86894i	0.976691	+	0.556937i
$315$		−	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	$0.449707\pi$
$318$	−1.50685	+	2.64254i	−0.0845000	+	0.148186i
$319$	−18.0191	+	18.0191i	−1.00888	+	1.00888i
$320$	11.8246	−	12.6104i	0.661017	−	0.704944i
$321$	−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
$330$	−18.5837	−	10.5969i	−1.02300	−	0.583342i
$331$	−8.59585	−	8.59585i	−0.472470	−	0.472470i	0.430243	−	0.902713i	$-0.358428\pi$
$331$	−8.59585	−	8.59585i	−0.472470	−	0.472470i	−0.902713	+	0.430243i	$0.858428\pi$
$332$	−1.72688	+	6.73258i	−0.0947750	+	0.369498i
$333$	0.527981	+	0.527981i	0.0289332	+	0.0289332i
$334$	16.7096	−	4.57341i	0.914308	−	0.250246i
$335$	−15.3056			−0.836235
$336$	−12.6905	+	3.69365i	−0.692324	+	0.201505i
$337$		−	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
$340$	5.14119	−	20.0439i	0.278820	−	1.08703i
$341$	2.57430			0.139406
$342$	−0.336663	−	1.23004i	−0.0182046	−	0.0665130i
$343$	−14.1960	−	14.1960i	−0.766513	−	0.766513i
$344$	−0.508693	−	31.6449i	−0.0274269	−	1.70618i
$345$	12.1437	+	12.1437i	0.653794	+	0.653794i
$346$	−4.73829	+	8.30946i	−0.254732	+	0.446719i
$347$		−	7.98761i		−	0.428798i	−0.976746	−	0.214399i	$-0.931221\pi$
$347$		−	7.98761i		−	0.428798i	0.976746	−	0.214399i	$-0.0687792\pi$
$348$	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
$356$	0.967977	−	3.77384i	0.0513027	−	0.200013i
$357$	−11.1871	+	11.1871i	−0.592084	+	0.592084i
$358$	9.43485	+	5.38002i	0.498647	+	0.284343i
$359$	−25.8704	+	25.8704i	−1.36539	+	1.36539i	−0.498492	+	0.866894i	$0.666113\pi$
$359$	−25.8704	+	25.8704i	−1.36539	+	1.36539i	−0.866894	+	0.498492i	$0.833887\pi$
$360$	−1.69704	−	1.64334i	−0.0894419	−	0.0866119i
$361$		−	13.5567i		−	0.713510i
$362$	7.49533	−	13.1444i	0.393946	−	0.690856i
$363$	−12.5298			−0.657642
$364$		0			0
$365$	−16.3707			−0.856880
$366$	−0.812069	+	1.42411i	−0.0424475	+	0.0744395i
$367$			20.4007i			1.06491i	0.846459	+	0.532454i	$0.178730\pi$
$367$			20.4007i			1.06491i	−0.846459	+	0.532454i	$0.821270\pi$
$368$	−9.46503	+	17.2367i	−0.493399	+	0.898526i
$369$	0.424416	−	0.424416i	0.0220942	−	0.0220942i
$370$	−5.12847	−	2.92440i	−0.266616	−	0.152032i
$371$	1.92301	−	1.92301i	0.0998377	−	0.0998377i
$372$	−1.86190	−	0.477572i	−0.0965352	−	0.0247609i
$373$	−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	0.400830	−	0.916152i	$-0.368722\pi$
$379$	−10.0323	−	10.0323i	−0.515322	−	0.515322i	−0.916152	+	0.400830i	$0.868722\pi$
$380$	5.13484	+	8.67771i	0.263412	+	0.445157i
$381$		−	2.50642i		−	0.128408i
$382$	−10.1256	+	17.7571i	−0.518072	+	0.908534i
$383$	10.9628	+	10.9628i	0.560171	+	0.560171i	0.929356	−	0.369185i	$-0.120363\pi$
$383$	10.9628	+	10.9628i	0.560171	+	0.560171i	−0.369185	+	0.929356i	$0.620363\pi$
$384$	−8.54468	+	16.1714i	−0.436044	+	0.825245i
$385$	13.5236	+	13.5236i	0.689225	+	0.689225i
$386$	7.30740	+	26.6986i	0.371937	+	1.35892i
$387$	−4.32489			−0.219846
$388$	2.66193	+	0.682775i	0.135139	+	0.0346627i
$389$		−	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
$392$	−7.98177	+	0.128307i	−0.403140	+	0.00648049i
$393$	−6.64269			−0.335080
$394$	3.62471	−	0.992083i	0.182610	−	0.0499804i
$395$	−1.70710	−	1.70710i	−0.0858935	−	0.0858935i
$396$	−3.24236	−	0.831653i	−0.162935	−	0.0417921i
$397$	−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	$0.851185\pi$
$398$	20.3613	+	11.6106i	1.02062	+	0.581985i
$399$		−	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
$408$	0.351890	+	21.8905i	0.0174211	+	1.08374i
$409$	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	$0.0908049\pi$
$410$	−2.35077	+	4.12251i	−0.116096	+	0.203596i
$411$	−13.5304	+	13.5304i	−0.667407	+	0.667407i
$412$	−11.7885	−	19.9221i	−0.580776	−	0.981492i
$413$			13.7150i			0.674871i
$414$	2.33433	+	1.33110i	0.114726	+	0.0654201i
$415$	−7.50966			−0.368635
$416$		0			0
$417$	13.6306			0.667495
$418$	12.4114	+	7.07731i	0.607059	+	0.346163i
$419$			2.93625i			0.143445i	0.997425	+	0.0717226i	$0.0228496\pi$
$419$			2.93625i			0.143445i	−0.997425	+	0.0717226i	$0.977150\pi$
$420$	−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	$0.300002\pi$
$422$	−19.3614	+	33.9538i	−0.942499	+	1.65284i
$423$	3.11926	−	3.11926i	0.151664	−	0.151664i
$424$	−0.0604883	−	3.76287i	−0.00293757	−	0.182741i
$425$	−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	0.952018	−	0.306044i	$-0.0990053\pi$
$431$	13.4108	+	13.4108i	0.645974	+	0.645974i	−0.306044	+	0.952018i	$0.599005\pi$
$432$	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	$0.961878\pi$
$434$	1.49279	+	0.851233i	0.0716563	+	0.0408605i
$435$	14.5369	+	14.5369i	0.696989	+	0.696989i
$436$	33.0990	+	8.48979i	1.58516	+	0.406587i
$437$	−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	$-0.115653\pi$
$439$	39.1690			1.86943			0.934717	+	0.355392i	$0.115653\pi$
$440$	26.4624	−	0.425384i	1.26154	−	0.0202794i
$441$			1.09086i			0.0519458i
$442$		0			0
$443$		−	38.1735i		−	1.81368i	−0.421477	−	0.906839i	$-0.638488\pi$
$443$		−	38.1735i		−	1.81368i	0.421477	−	0.906839i	$-0.361512\pi$
$444$	6.05032	+	1.55189i	0.287135	+	0.0736492i
$445$	4.20942			0.199546
$446$	1.13471	+	4.14581i	0.0537301	+	0.196310i
$447$	−1.61478	−	1.61478i	−0.0763763	−	0.0763763i
$448$	11.1846	−	11.9279i	0.528423	−	0.563539i
$449$	−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	$0.773614\pi$
$450$	−0.0894998	+	0.156954i	−0.00421906	+	0.00739890i
$451$			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
$460$	−20.5802	−	5.27875i	−0.959556	−	0.246123i
$461$	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	$0.0635418\pi$
$462$	−17.5778	−	10.0234i	−0.817793	−	0.466329i
$463$	24.4048	−	24.4048i	1.13419	−	1.13419i	0.144713	−	0.989474i	$-0.453774\pi$
$463$	24.4048	−	24.4048i	1.13419	−	1.13419i	0.989474	−	0.144713i	$-0.0462258\pi$
$464$	−11.3303	+	20.6336i	−0.525997	+	0.957890i
$465$		−	2.07681i		−	0.0963096i
$466$	−14.9358	+	26.1926i	−0.691885	+	1.21335i
$467$	17.7779			0.822661			0.411331	−	0.911486i	$-0.365064\pi$
$467$	17.7779			0.822661			0.411331	+	0.911486i	$0.365064\pi$
$468$		0			0
$469$	−14.4772			−0.668494
$470$	−17.2771	+	30.2985i	−0.796931	+	1.39757i
$471$		−	22.7746i		−	1.04940i
$472$	13.6342	+	13.2028i	0.627565	+	0.607708i
$473$	34.2615	−	34.2615i	1.57535	−	1.57535i
$474$	2.21887	+	1.26526i	0.101916	+	0.0581155i
$475$	0.545317	−	0.545317i	0.0250209	−	0.0250209i
$476$	4.86292	−	18.9590i	0.222892	−	0.868985i
$477$	−0.514268			−0.0235467
$478$	3.15052	+	11.5109i	0.144102	+	0.526495i
$479$	−5.62626	+	5.62626i	−0.257071	+	0.257071i	−0.823862	−	0.566791i	$-0.808185\pi$
$479$	−5.62626	+	5.62626i	−0.257071	+	0.257071i	0.566791	+	0.823862i	$0.308185\pi$
$480$	−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
$486$	2.79552	−	4.90247i	0.126808	−	0.222380i
$487$	−16.0705	−	16.0705i	−0.728226	−	0.728226i	0.242040	−	0.970266i	$-0.422183\pi$
$487$	−16.0705	−	16.0705i	−0.728226	−	0.728226i	−0.970266	+	0.242040i	$0.922183\pi$
$488$	−0.0325982	−	2.02788i	−0.00147565	−	0.0917977i
$489$	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	$-0.500425\pi$
$491$	−0.0592093			−0.00267208			−0.00133604	+	0.999999i	$0.500425\pi$
$492$	1.24748	−	4.86354i	0.0562407	−	0.219265i
$493$			28.1772i			1.26904i
$494$		0			0
$495$		−	3.61659i		−	0.162554i
$496$	2.28326	−	0.664555i	0.102521	−	0.0298394i
$497$	−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	$0.0530323\pi$
$499$	25.7335	+	25.7335i	1.15199	+	1.15199i	0.165836	+	0.986153i	$0.446968\pi$
$500$	5.72375	−	22.3151i	0.255974	−	0.997962i
$501$	−14.0034	−	14.0034i	−0.625624	−	0.625624i
$502$	−7.26658	−	4.14361i	−0.324323	−	0.184938i
$503$			16.9045i			0.753734i	0.926267	+	0.376867i	$0.122999\pi$
$503$			16.9045i			0.753734i	−0.926267	+	0.376867i	$0.877001\pi$
$504$	−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
$512$	−1.09069	−	22.6011i	−0.0482023	−	0.998838i
$513$	−9.03190	+	9.03190i	−0.398768	+	0.398768i
$514$	19.8064	−	34.7342i	0.873623	−	1.53206i
$515$	17.6853	−	17.6853i	0.779308	−	0.779308i
$516$	−31.1362	+	18.4242i	−1.37070	+	0.811078i
$517$			49.4213i			2.17355i
$518$	−4.85088	−	2.76611i	−0.213136	−	0.121536i
$519$	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	$0.466668\pi$
$522$	2.79436	+	1.59342i	0.122306	+	0.0697423i
$523$		−	16.9515i		−	0.741239i	−0.928785	−	0.370620i	$-0.879145\pi$
$523$		−	16.9515i		−	0.741239i	0.928785	−	0.370620i	$-0.120855\pi$
$524$	7.07252	−	4.18500i	0.308964	−	0.182823i
$525$	−0.772315	+	0.772315i	−0.0337066	+	0.0337066i
$526$	−9.38349	+	16.4557i	−0.409140	+	0.717501i
$527$	2.01276	−	2.01276i	0.0876774	−	0.0876774i
$528$	−26.8856	+	7.82521i	−1.17005	+	0.340549i
$529$	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
$538$	28.1709	+	16.0639i	1.21454	+	0.692562i
$539$	−8.64176	−	8.64176i	−0.372227	−	0.372227i
$540$	−5.87856	+	22.9187i	−0.252973	+	0.986264i
$541$	−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
$544$	−14.1660	−	23.0852i	−0.607362	−	0.989770i
$545$			36.9194i			1.58145i
$546$		0			0
$547$			32.0440i			1.37010i	0.728494	+	0.685052i	$0.240221\pi$
$547$			32.0440i			1.37010i	−0.728494	+	0.685052i	$0.759779\pi$
$548$	5.88155	−	22.9303i	0.251247	−	0.979535i
$549$	−0.277149			−0.0118284
$550$	−0.534371	−	1.95240i	−0.0227857	−	0.0832505i
$551$	−9.70865	−	9.70865i	−0.413602	−	0.413602i
$552$	22.4761	−	0.361305i	0.956648	−	0.0153782i
$553$	−1.61470	−	1.61470i	−0.0686641	−	0.0686641i
$554$	0.770631	−	1.35144i	0.0327410	−	0.0574173i
$555$			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	$-0.537579\pi$
$563$	−5.58944			−0.235567			−0.117783	+	0.993039i	$0.537579\pi$
$564$	9.16840	−	35.7447i	0.386059	−	1.50512i
$565$	−13.6615	+	13.6615i	−0.574745	+	0.574745i
$566$	−25.9884	−	14.8193i	−1.09237	−	0.622903i
$567$	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	$-0.225695\pi$
$570$	5.70959	−	10.0128i	0.239148	−	0.419390i
$571$	−9.21948			−0.385823			−0.192912	−	0.981216i	$-0.561793\pi$
$571$	−9.21948			−0.385823			−0.192912	+	0.981216i	$0.561793\pi$
$572$		0			0
$573$	23.3670			0.976169
$574$	−2.22353	+	3.89937i	−0.0928084	+	0.162757i
$575$			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	$0.929706\pi$
$578$	−7.27904	−	4.15072i	−0.302768	−	0.172647i
$579$	22.3746	−	22.3746i	0.929856	−	0.929856i
$580$	−24.6360	−	6.31904i	−1.02295	−	0.262384i
$581$	−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	0.792963	−	0.609270i	$-0.208537\pi$
$587$	4.45054	+	4.45054i	0.183694	+	0.183694i	−0.609270	+	0.792963i	$0.708537\pi$
$588$	4.64711	+	7.85346i	0.191644	+	0.323871i
$589$			1.38702i			0.0571513i
$590$	−10.1576	+	17.8133i	−0.418183	+	0.733361i
$591$	−3.03767	−	3.03767i	−0.124953	−	0.124953i
$592$	−7.41953	+	2.15950i	−0.304941	+	0.0887547i
$593$	−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
$596$	2.73660	+	0.701928i	0.112095	+	0.0287521i
$597$		−	26.7938i		−	1.09660i
$598$		0			0
$599$		−	23.9175i		−	0.977241i	−0.872496	−	0.488621i	$-0.837500\pi$
$599$		−	23.9175i		−	0.977241i	0.872496	−	0.488621i	$-0.162500\pi$
$600$	0.0242932	+	1.51124i	0.000991764	+	0.0616959i
$601$	−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
$604$	18.8683	+	4.83965i	0.767740	+	0.196923i
$605$	11.8427	+	11.8427i	0.481474	+	0.481474i
$606$	−1.72776	−	0.985221i	−0.0701856	−	0.0400218i
$607$		−	35.0522i		−	1.42272i	−0.702826	−	0.711362i	$-0.748079\pi$
$607$		−	35.0522i		−	1.42272i	0.702826	−	0.711362i	$-0.251921\pi$
$608$	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
$616$	25.0301	−	0.402359i	1.00849	−	0.0162115i
$617$	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	$0.201088\pi$
$618$	−13.1080	+	22.9872i	−0.527279	+	0.924681i
$619$	25.6801	−	25.6801i	1.03217	−	1.03217i	0.0327040	−	0.999465i	$-0.489588\pi$
$619$	25.6801	−	25.6801i	1.03217	−	1.03217i	0.999465	−	0.0327040i	$-0.0104119\pi$
$620$	1.30842	+	2.21119i	0.0525475	+	0.0888035i
$621$		−	26.9144i		−	1.08004i
$622$	12.0047	+	6.84539i	0.481343	+	0.274475i
$623$	3.98158			0.159519
$624$		0			0
$625$	23.2380			0.929520
$626$	−38.8620	−	22.1602i	−1.55324	−	0.885701i
$627$		−	16.3324i		−	0.652252i
$628$	14.3484	+	24.2483i	0.572563	+	0.967613i
$629$	−6.54055	+	6.54055i	−0.260789	+	0.260789i
$630$	1.19588	−	2.09720i	0.0476451	−	0.0835544i
$631$	−15.2503	+	15.2503i	−0.607106	+	0.607106i	−0.942189	−	0.335083i	$-0.891236\pi$
$631$	−15.2503	+	15.2503i	−0.607106	+	0.607106i	0.335083	+	0.942189i	$0.391236\pi$
$632$	−3.15958	+	0.0507904i	−0.125681	+	0.00202033i
$633$	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	$-0.404046\pi$
$642$	−16.0027	−	9.12521i	−0.631578	−	0.360143i
$643$	−0.0529335	−	0.0529335i	−0.00208749	−	0.00208749i	0.706062	−	0.708150i	$-0.250470\pi$
$643$	−0.0529335	−	0.0529335i	−0.00208749	−	0.00208749i	−0.708150	+	0.706062i	$0.750470\pi$
$644$	−19.4663	−	4.99303i	−0.767078	−	0.196753i
$645$	−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	$-0.523409\pi$
$647$	−3.73780			−0.146948			−0.0734741	+	0.997297i	$0.523409\pi$
$648$	−0.349646	−	21.7509i	−0.0137354	−	0.854454i
$649$			29.0561i			1.14055i
$650$		0			0
$651$		−	1.96440i		−	0.0769908i
$652$	−39.5743	−	10.1507i	−1.54985	−	0.397531i
$653$	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
$656$	1.73591	+	5.96417i	0.0677757	+	0.232862i
$657$	2.07051	+	2.07051i	0.0807785	+	0.0807785i
$658$	−16.3419	+	28.6586i	−0.637074	+	1.11723i
$659$		−	38.8733i		−	1.51429i	−0.653246	−	0.757145i	$-0.726593\pi$
$659$		−	38.8733i		−	1.51429i	0.653246	−	0.757145i	$-0.273407\pi$
$660$	−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
$668$	23.7318	+	6.08713i	0.918212	+	0.235518i
$669$	3.47438	−	3.47438i	0.134327	−	0.134327i
$670$	−18.8032	−	10.7221i	−0.726430	−	0.414231i
$671$	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	$-0.0838886\pi$
$674$	13.1508	−	23.0624i	0.506551	−	0.888330i
$675$	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	$0.217708\pi$
$678$	10.1256	−	17.7571i	0.388872	−	0.681958i
$679$			2.80846i			0.107779i
$680$	20.3575	−	21.0227i	0.780674	−	0.806183i
$681$	10.8174	−	10.8174i	0.414522	−	0.414522i
$682$	3.16257	+	1.80339i	0.121101	+	0.0690553i
$683$	5.18372	−	5.18372i	0.198350	−	0.198350i	−0.600943	−	0.799292i	$-0.705208\pi$
$683$	5.18372	−	5.18372i	0.198350	−	0.198350i	0.799292	+	0.600943i	$0.205208\pi$
$684$	0.448092	−	1.74697i	0.0171332	−	0.0667971i
$685$	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	0.322405	−	0.946602i	$-0.395509\pi$
$691$	−16.4082	−	16.4082i	−0.624197	−	0.624197i	−0.946602	+	0.322405i	$0.895509\pi$
$692$	−11.6421	+	6.88897i	−0.442567	+	0.261879i
$693$		−	3.42084i		−	0.129947i
$694$	5.59560	−	9.81291i	0.212406	−	0.372493i
$695$	−12.8832	−	12.8832i	−0.488687	−	0.488687i
$696$	26.9055	−	0.432508i	1.01985	−	0.0163942i
$697$	5.25760	+	5.25760i	0.199146	+	0.199146i
$698$	−3.82891	−	13.9894i	−0.144926	−	0.529508i
$699$	34.4674			1.30368
$700$	0.335718	−	1.30886i	0.0126889	−	0.0494702i
$701$		−	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
$704$	23.6953	−	25.2699i	0.893049	−	0.952396i
$705$	39.8704			1.50161
$706$	−6.44818	+	1.76487i	−0.242680	+	0.0664217i
$707$	1.25732	+	1.25732i	0.0472863	+	0.0472863i
$708$	5.39034	−	21.0152i	0.202581	−	0.789801i
$709$	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	$0.718223\pi$
$710$	−4.65837	−	2.65634i	−0.174826	−	0.0996906i
$711$			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	$-0.714078\pi$
$719$	−33.4093			−1.24596			−0.622979	+	0.782238i	$0.714078\pi$
$720$	−0.933622	−	3.20771i	−0.0347941	−	0.119544i
$721$	16.7281	−	16.7281i	0.622986	−	0.622986i
$722$	9.49693	−	16.6546i	0.353439	−	0.619820i
$723$	23.7091	−	23.7091i	0.881750	−	0.881750i
$724$	18.4163	−	10.8974i	0.684435	−	0.404999i
$725$			1.94525i			0.0722447i
$726$	−15.3930	−	8.77753i	−0.571288	−	0.325765i
$727$	−23.0787			−0.855941			−0.427970	−	0.903793i	$-0.640771\pi$
$727$	−23.0787			−0.855941			−0.427970	+	0.903793i	$0.640771\pi$
$728$		0			0
$729$	−29.5245			−1.09350
$730$	−20.1116	−	11.4682i	−0.744365	−	0.424458i
$731$		−	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	$-0.0551668\pi$
$734$	−14.2914	+	25.0626i	−0.527505	+	0.925077i
$735$	−6.97170	+	6.97170i	−0.257155	+	0.257155i
$736$	−23.7029	+	14.5450i	−0.873699	+	0.536136i
$737$	−30.6708			−1.12977
$738$	0.818721	−	0.224084i	0.0301375	−	0.00824864i
$739$	−26.1672	+	26.1672i	−0.962575	+	0.962575i	−0.999325	−	0.0367496i	$-0.988300\pi$
$739$	−26.1672	+	26.1672i	−0.962575	+	0.962575i	0.0367496	+	0.999325i	$0.488300\pi$
$740$	−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	0.851778	−	0.523904i	$-0.175525\pi$
$743$	8.93719	+	8.93719i	0.327874	+	0.327874i	−0.523904	+	0.851778i	$0.675525\pi$
$744$	−1.95282	−	1.89103i	−0.0715939	−	0.0693286i
$745$			3.05246i			0.111833i
$746$	−25.3623	−	14.4623i	−0.928581	−	0.529503i
$747$	0.949800	+	0.949800i	0.0347514	+	0.0347514i
$748$	10.3024	−	40.1658i	0.376693	−	1.46861i
$749$	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	$-0.371145\pi$
$751$	21.5861			0.787689			0.393844	+	0.919177i	$0.371145\pi$
$752$	12.7581	+	43.8339i	0.465240	+	1.59846i
$753$			9.56224i			0.348467i
$754$		0			0
$755$			21.0461i			0.765946i
$756$	−5.56038	+	21.6782i	−0.202229	+	0.788428i
$757$	−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
$760$	0.229195	+	14.2578i	0.00831378	+	0.517186i
$761$	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	$0.568528\pi$
$762$	1.75584	−	3.07918i	0.0636072	−	0.111547i
$763$			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
$772$	−9.72602	+	37.9187i	−0.350047	+	1.36472i
$773$	−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	$0.402873\pi$
$774$	−5.31319	−	3.02973i	−0.190979	−	0.108901i
$775$	0.138954	−	0.138954i	0.00499136	−	0.00499136i
$776$	2.79191	+	2.70357i	0.100224	+	0.0970526i
$777$			6.38338i			0.229002i
$778$	23.5024	−	41.2158i	0.842603	−	1.47766i
$779$	−3.62309			−0.129811
$780$		0			0
$781$	−7.59850			−0.271896
$782$	−16.4895	+	28.9173i	−0.589663	+	1.03408i
$783$		−	32.2185i		−	1.15139i
$784$	−9.89561	−	5.43388i	−0.353415	−	0.194067i
$785$	−21.5258	+	21.5258i	−0.768288	+	0.768288i
$786$	−8.16066	−	4.65344i	−0.291081	−	0.165983i
$787$	−8.42635	+	8.42635i	−0.300367	+	0.300367i	−0.841157	−	0.540790i	$-0.818125\pi$
$787$	−8.42635	+	8.42635i	−0.300367	+	0.300367i	0.540790	+	0.841157i	$0.318125\pi$
$788$	5.14800	+	1.32044i	0.183390	+	0.0470389i
$789$	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	$-0.0810581\pi$
$798$	5.40055	−	9.47085i	0.191177	−	0.335265i
$799$	38.6409	+	38.6409i	1.36702	+	1.36702i
$800$	−0.977968	−	1.59372i	−0.0345764	−	0.0563464i
$801$	−0.532395	−	0.532395i	−0.0188113	−	0.0188113i
$802$	5.43957	+	19.8742i	0.192078	+	0.701783i
$803$	−32.8050			−1.15766
$804$	22.1831	+	5.68989i	0.782337	+	0.200667i
$805$		−	21.7131i		−	0.765286i
$806$		0			0
$807$		−	37.0707i		−	1.30495i
$808$	2.46027	−	0.0395489i	0.0865519	−	0.00139133i
$809$	−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	0.538515	−	0.842616i	$-0.318986\pi$
$811$	−8.66022	−	8.66022i	−0.304102	−	0.304102i	−0.842616	+	0.538515i	$0.818986\pi$
$812$	−23.3025	−	5.97701i	−0.817758	−	0.209752i
$813$	−10.9730	−	10.9730i	−0.384838	−	0.384838i
$814$	−10.2769	−	5.86017i	−0.360205	−	0.205399i
$815$		−	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	$-0.597054\pi$
$823$	−17.2243			−0.600402			−0.300201	+	0.953876i	$0.597054\pi$
$824$	−0.526182	−	32.7328i	−0.0183304	−	1.14030i
$825$	−1.63620	+	1.63620i	−0.0569650	+	0.0569650i
$826$	−9.60784	+	16.8491i	−0.334299	+	0.586255i
$827$	7.89012	−	7.89012i	0.274366	−	0.274366i	−0.556489	−	0.830855i	$-0.687852\pi$
$827$	7.89012	−	7.89012i	0.274366	−	0.274366i	0.830855	+	0.556489i	$0.187852\pi$
$828$	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	$0.883324\pi$
$830$	−9.22574	−	5.26078i	−0.320230	−	0.182604i
$831$	−1.77839			−0.0616917
$832$		0			0
$833$	−13.5134			−0.468213
$834$	16.7455	+	9.54873i	0.579848	+	0.330646i
$835$			26.4710i			0.916066i
$836$	10.2897	+	17.3892i	0.355875	+	0.601417i
$837$	−2.30144	+	2.30144i	−0.0795495	+	0.0795495i
$838$	−2.05694	+	3.60723i	−0.0710560	+	0.124610i
$839$	11.2106	−	11.2106i	0.387032	−	0.387032i	−0.486596	−	0.873627i	$-0.661761\pi$
$839$	11.2106	−	11.2106i	0.387032	−	0.387032i	0.873627	+	0.486596i	$0.161761\pi$
$840$	−0.324602	−	20.1929i	−0.0111998	−	0.696721i
$841$	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
$850$	−1.94432	−	1.10871i	−0.0666898	−	0.0380284i
$851$	6.71554	+	6.71554i	0.230206	+	0.230206i
$852$	5.49573	+	1.40963i	0.188281	+	0.0482933i
$853$	−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
$856$	22.7872	−	0.366306i	0.778852	−	0.0125201i
$857$			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	$0.0986018\pi$
$859$			17.8687i			0.609673i	−0.952405	+	0.304837i	$0.901398\pi$
$860$	46.8427	+	12.0150i	1.59732	+	0.409708i
$861$	5.13126			0.174873
$862$	7.08063	+	25.8700i	0.241167	+	0.881137i
$863$	−16.3496	−	16.3496i	−0.556546	−	0.556546i	0.371776	−	0.928322i	$-0.378749\pi$
$863$	−16.3496	−	16.3496i	−0.556546	−	0.556546i	−0.928322	+	0.371776i	$0.878749\pi$
$864$	16.1977	+	26.3962i	0.551058	+	0.898017i
$865$	−10.3350	−	10.3350i	−0.351400	−	0.351400i
$866$	−3.48327	+	6.10855i	−0.118366	+	0.207577i
$867$			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
$876$	23.7267	+	6.08583i	0.801652	+	0.205621i
$877$	−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	$0.281958\pi$
$878$	48.1197	+	27.4392i	1.62396	+	0.926030i
$879$	−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	$0.785058\pi$
$882$	−0.764187	+	1.34014i	−0.0257315	+	0.0451249i
$883$	−31.7405			−1.06815			−0.534077	−	0.845436i	$-0.679341\pi$
$883$	−31.7405			−1.06815			−0.534077	+	0.845436i	$0.679341\pi$
$884$		0			0
$885$	23.4408			0.787955
$886$	26.7419	−	46.8968i	0.898411	−	1.57553i
$887$		−	37.0707i		−	1.24471i	−0.782734	−	0.622356i	$-0.786175\pi$
$887$		−	37.0707i		−	1.24471i	0.782734	−	0.622356i	$-0.213825\pi$
$888$	6.34576	+	6.14498i	0.212950	+	0.206212i
$889$	−2.24076	+	2.24076i	−0.0751526	+	0.0751526i
$890$	5.17134	+	2.94885i	0.173344	+	0.0988455i
$891$	23.5494	−	23.5494i	0.788934	−	0.788934i
$892$	−1.51028	+	5.88810i	−0.0505678	+	0.197148i
$893$	−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
$902$	−4.71069	+	8.26105i	−0.156849	+	0.275063i
$903$	−26.1443	−	26.1443i	−0.870027	−	0.870027i
$904$	0.406464	+	25.2854i	0.0135188	+	0.840981i
$905$	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	$-0.315762\pi$
$907$	32.9487			1.09404			0.547021	+	0.837119i	$0.315762\pi$
$908$	−4.70220	+	18.3324i	−0.156048	+	0.608382i
$909$		−	0.336243i		−	0.0111525i
$910$		0			0
$911$		−	22.6697i		−	0.751082i	−0.926806	−	0.375541i	$-0.877457\pi$
$911$		−	22.6697i		−	0.751082i	0.926806	−	0.375541i	$-0.122543\pi$
$912$	−4.21619	−	14.4859i	−0.139612	−	0.479675i
$913$	−15.0485			−0.498034
$914$	−46.3664	+	12.6905i	−1.53366	+	0.419764i
$915$	−1.77126	−	1.77126i	−0.0585559	−	0.0585559i
$916$	2.45600	−	9.57520i	0.0811487	−	0.316373i
$917$	5.93861	+	5.93861i	0.196110	+	0.196110i
$918$	32.2032	+	18.3632i	1.06286	+	0.606075i
$919$			8.67159i			0.286049i	0.989719	+	0.143025i	$0.0456828\pi$
$919$			8.67159i			0.286049i	−0.989719	+	0.143025i	$0.954317\pi$
$920$	−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
$928$	−28.3740	+	17.4114i	−0.931423	+	0.571558i
$929$	−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	$0.324392\pi$
$930$	1.45487	−	2.55139i	0.0477072	−	0.0836633i
$931$	4.65615	−	4.65615i	0.152599	−	0.152599i
$932$	−36.6976	+	21.7150i	−1.20207	+	0.711298i
$933$		−	15.7972i		−	0.517176i
$934$	21.8404	+	12.4540i	0.714639	+	0.407508i
$935$	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	$0.542952\pi$
$938$	−17.7854	−	10.1418i	−0.580715	−	0.331140i
$939$			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	$0.219488\pi$
$942$	15.9544	−	27.9790i	0.519823	−	0.911605i
$943$	5.39827	−	5.39827i	0.175792	−	0.175792i
$944$	7.50081	+	25.7711i	0.244131	+	0.838776i
$945$	−24.1803			−0.786586
$946$	66.0923	−	18.0895i	2.14884	−	0.588139i
$947$	−2.02371	+	2.02371i	−0.0657617	+	0.0657617i	−0.739223	−	0.673461i	$-0.764807\pi$
$947$	−2.02371	+	2.02371i	−0.0657617	+	0.0657617i	0.673461	+	0.739223i	$0.264807\pi$
$948$	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	$0.954344\pi$
$954$	−0.631787	−	0.360263i	−0.0204549	−	0.0116639i
$955$	−22.0856	−	22.0856i	−0.714675	−	0.714675i
$956$	−4.19329	+	16.3483i	−0.135621	+	0.528743i
$957$	29.1303	+	29.1303i	0.941648	+	0.941648i
$958$	−10.8533	+	2.97056i	−0.350656	+	0.0959745i
$959$	24.1926			0.781219
$960$	−20.3864	−	19.1161i	−0.657968	−	0.616968i
$961$		−	30.6466i		−	0.988599i
$962$		0			0
$963$		−	3.11432i		−	0.100357i
$964$	−10.3061	+	40.1803i	−0.331937	+	1.29412i
$965$	−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	$-0.999549\pi$
$967$	−31.1406	−	31.1406i	−1.00142	−	1.00142i	−0.00141655	−	0.999999i	$-0.500451\pi$
$968$	21.9190	−	0.352349i	0.704504	−	0.0113249i
$969$	−12.7698	−	12.7698i	−0.410223	−	0.410223i
$970$	−2.08001	+	3.64767i	−0.0667850	+	0.117120i
$971$			15.5573i			0.499258i	0.968342	+	0.249629i	$0.0803087\pi$
$971$			15.5573i			0.499258i	−0.968342	+	0.249629i	$0.919691\pi$
$972$	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
$980$	3.03053	−	11.8151i	0.0968068	−	0.377419i
$981$	4.66945	−	4.66945i	0.149084	−	0.149084i
$982$	−0.0727395	−	0.0414781i	−0.00232121	−	0.00132362i
$983$	−21.2250	+	21.2250i	−0.676971	+	0.676971i	−0.959314	−	0.282343i	$-0.908888\pi$
$983$	−21.2250	+	21.2250i	−0.676971	+	0.676971i	0.282343	+	0.959314i	$0.408888\pi$
$984$	4.93962	−	5.10103i	0.157469	−	0.162615i
$985$			5.74219i			0.182961i
$986$	−19.7391	+	34.6161i	−0.628621	+	1.10240i
$987$	37.7124			1.20040
$988$		0			0
$989$	−55.0094			−1.74920
$990$	2.53355	−	4.44304i	0.0805215	−	0.141209i
$991$			18.5141i			0.588120i	0.955787	+	0.294060i	$0.0950065\pi$
$991$			18.5141i			0.588120i	−0.955787	+	0.294060i	$0.904993\pi$
$992$	3.27056	+	0.783084i	0.103840	+	0.0248630i
$993$	−13.8963	+	13.8963i	−0.440986	+	0.440986i
$994$	−4.40623	−	2.51256i	−0.139757	−	0.0796936i
$995$	−25.3246	+	25.3246i	−0.802843	+	0.802843i
$996$	10.8841	+	2.79173i	0.344875	+	0.0884594i
$997$	−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.239.7		16
4.3	odd	2	inner	676.2.f.h.239.3		16
13.2	odd	12		676.2.l.i.319.4		16
13.3	even	3		52.2.l.b.19.1	yes	16
13.4	even	6		676.2.l.i.587.3		16
13.5	odd	4		676.2.f.i.99.6		16
13.6	odd	12		676.2.l.k.427.1		16
13.7	odd	12		52.2.l.b.11.4	yes	16
13.8	odd	4	inner	676.2.f.h.99.3		16
13.9	even	3		676.2.l.m.587.2		16
13.10	even	6		676.2.l.k.19.4		16
13.11	odd	12		676.2.l.m.319.1		16
13.12	even	2		676.2.f.i.239.2		16
39.20	even	12		468.2.cb.f.271.1		16
39.29	odd	6		468.2.cb.f.19.4		16
52.3	odd	6		52.2.l.b.19.4	yes	16
52.7	even	12		52.2.l.b.11.1	✓	16
52.11	even	12		676.2.l.m.319.2		16
52.15	even	12		676.2.l.i.319.3		16
52.19	even	12		676.2.l.k.427.4		16
52.23	odd	6		676.2.l.k.19.1		16
52.31	even	4		676.2.f.i.99.2		16
52.35	odd	6		676.2.l.m.587.1		16
52.43	odd	6		676.2.l.i.587.4		16
52.47	even	4	inner	676.2.f.h.99.7		16
52.51	odd	2		676.2.f.i.239.6		16
104.3	odd	6		832.2.bu.n.383.3		16
104.29	even	6		832.2.bu.n.383.2		16
104.59	even	12		832.2.bu.n.63.2		16
104.85	odd	12		832.2.bu.n.63.3		16
156.59	odd	12		468.2.cb.f.271.4		16
156.107	even	6		468.2.cb.f.19.1		16

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

\(f(q)\)	\(=\)	\(q+(1.22852 + 0.700535i) q^{2} -1.61663i q^{3} +(1.01850 + 1.72124i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(1.13250 - 1.98605i) q^{6} +(-1.44528 + 1.44528i) q^{7} +(0.0454612 + 2.82806i) q^{8} +0.386509 q^{9} +O(q^{10})\)	\(q+(1.22852 + 0.700535i) q^{2} -1.61663i q^{3} +(1.01850 + 1.72124i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(1.13250 - 1.98605i) q^{6} +(-1.44528 + 1.44528i) q^{7} +(0.0454612 + 2.82806i) 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} +(0.474833 + 0.270763i) q^{18} +(-1.64974 - 1.64974i) q^{19} +(-4.18627 - 1.07376i) q^{20} +(2.33648 + 2.33648i) q^{21} +(-5.90657 + 1.61663i) q^{22} +4.91612 q^{23} +(4.57193 - 0.0734939i) q^{24} +0.330547i q^{25} -5.47473i q^{27} +(-3.95968 - 1.01564i) q^{28} +5.88494 q^{29} +(1.30421 + 4.76510i) q^{30} +(-0.420375 - 0.420375i) q^{31} +(-4.82146 + 2.95864i) q^{32} +(4.94997 + 4.94997i) q^{33} +(-3.35417 + 5.88215i) 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} +(-8.38882 - 2.15170i) q^{44} +(-0.590579 + 0.590579i) q^{45} +(6.03953 + 3.44391i) q^{46} +(8.07035 - 8.07035i) q^{47} +(5.66817 + 3.11251i) q^{48} +2.82235i q^{49} +(-0.231559 + 0.406082i) q^{50} +7.74044 q^{51} -1.33055 q^{53} +(3.83524 - 6.72579i) q^{54} -9.35707i q^{55} +(-4.15304 - 4.02163i) q^{56} +(-2.66702 + 2.66702i) q^{57} +(7.22975 + 4.12261i) q^{58} +(4.74477 - 4.74477i) q^{59} +(-1.73588 + 6.76765i) 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} +(3.09406 - 5.42600i) q^{70} +(1.24081 + 1.24081i) q^{71} +(0.0175712 + 1.09307i) q^{72} +(5.35696 + 5.35696i) q^{73} +(0.721236 + 2.63513i) q^{74} +0.534371 q^{75} +(1.15933 - 4.51987i) q^{76} -8.85061i q^{77} +1.11723i q^{79} +(-2.41553 - 8.29919i) q^{80} -7.69108 q^{81} +(2.11824 - 0.579764i) q^{82} +(2.45738 + 2.45738i) q^{83} +(-1.64192 + 6.40134i) q^{84} +(-7.31599 - 7.31599i) q^{85} +(-13.7466 - 7.83871i) 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} +(4.78302 + 7.79451i) q^{96} +(0.971599 - 0.971599i) q^{97} +(-1.97715 + 3.46730i) 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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