LMFDB - Embedded newform 48.2.k.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,2,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	48.k (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:	$0.383281929702$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.3
Root			$-1.35164 - 0.416001i$ of defining polynomial
Character	$\chi$	$=$	48.11
Dual form			48.2.k.a.35.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.416001 - 1.35164i) q^{2} +(0.966579 - 1.43726i) q^{3} +(-1.65389 + 1.12457i) q^{4} +(-1.57184 + 1.57184i) q^{5} +(-2.34477 - 0.708570i) q^{6} +2.24914 q^{7} +(2.20804 + 1.76765i) q^{8} +(-1.13145 - 2.77846i) q^{9} +O(q^{10})$	\(q+(-0.416001 - 1.35164i) q^{2} +(0.966579 - 1.43726i) q^{3} +(-1.65389 + 1.12457i) q^{4} +(-1.57184 + 1.57184i) q^{5} +(-2.34477 - 0.708570i) q^{6} +2.24914 q^{7} +(2.20804 + 1.76765i) q^{8} +(-1.13145 - 2.77846i) q^{9} +(2.77846 + 1.47068i) q^{10} +(1.13145 + 1.13145i) q^{11} +(0.0176901 + 3.46406i) q^{12} +(-3.24914 + 3.24914i) q^{13} +(-0.935644 - 3.04004i) q^{14} +(0.739839 + 3.77846i) q^{15} +(1.47068 - 3.71982i) q^{16} +1.66400i q^{17} +(-3.28480 + 2.68516i) q^{18} +(-3.77846 - 3.77846i) q^{19} +(0.832001 - 4.36729i) q^{20} +(2.17397 - 3.23261i) q^{21} +(1.05863 - 2.00000i) q^{22} -2.26290i q^{23} +(4.67481 - 1.46496i) q^{24} +0.0586332i q^{25} +(5.74333 + 3.04004i) q^{26} +(-5.08701 - 1.05941i) q^{27} +(-3.71982 + 2.52932i) q^{28} +(-3.23584 - 3.23584i) q^{29} +(4.79936 - 2.57184i) q^{30} -1.30777i q^{31} +(-5.63969 - 0.440392i) q^{32} +(2.71982 - 0.532554i) q^{33} +(2.24914 - 0.692226i) q^{34} +(-3.53529 + 3.53529i) q^{35} +(4.99586 + 3.32286i) q^{36} +(2.30777 + 2.30777i) q^{37} +(-3.53529 + 6.67897i) q^{38} +(1.52932 + 7.81042i) q^{39} +(-6.24914 + 0.692226i) q^{40} +10.2143 q^{41} +(-5.27371 - 1.59367i) q^{42} +(3.77846 - 3.77846i) q^{43} +(-3.14368 - 0.598895i) q^{44} +(6.14575 + 2.58884i) q^{45} +(-3.05863 + 0.941367i) q^{46} -3.74258 q^{47} +(-3.92483 - 5.70926i) q^{48} -1.94137 q^{49} +(0.0792512 - 0.0243914i) q^{50} +(2.39161 + 1.60839i) q^{51} +(1.71982 - 9.02760i) q^{52} +(0.972946 - 0.972946i) q^{53} +(0.684253 + 7.31654i) q^{54} -3.55691 q^{55} +(4.96619 + 3.97568i) q^{56} +(-9.08281 + 1.77846i) q^{57} +(-3.02760 + 5.71982i) q^{58} +(3.88352 + 3.88352i) q^{59} +(-5.47275 - 5.41714i) q^{60} +(4.19051 - 4.19051i) q^{61} +(-1.76765 + 0.544035i) q^{62} +(-2.54479 - 6.24914i) q^{63} +(1.75086 + 7.80605i) q^{64} -10.2143i q^{65} +(-1.85127 - 3.45469i) q^{66} +(8.02760 + 8.02760i) q^{67} +(-1.87129 - 2.75207i) q^{68} +(-3.25238 - 2.18727i) q^{69} +(6.24914 + 3.30777i) q^{70} -11.0950i q^{71} +(2.41305 - 8.13494i) q^{72} +6.38101i q^{73} +(2.15925 - 4.07933i) q^{74} +(0.0842713 + 0.0566736i) q^{75} +(10.4983 + 2.00000i) q^{76} +(2.54479 + 2.54479i) q^{77} +(9.92072 - 5.31623i) q^{78} -2.69223i q^{79} +(3.53529 + 8.15865i) q^{80} +(-6.43965 + 6.28736i) q^{81} +(-4.24914 - 13.8061i) q^{82} +(2.61113 - 2.61113i) q^{83} +(0.0397875 + 7.79115i) q^{84} +(-2.61555 - 2.61555i) q^{85} +(-6.67897 - 3.53529i) q^{86} +(-7.77846 + 1.52306i) q^{87} +(0.498281 + 4.49828i) q^{88} -7.35247 q^{89} +(0.942549 - 9.38383i) q^{90} +(-7.30777 + 7.30777i) q^{91} +(2.54479 + 3.74258i) q^{92} +(-1.87961 - 1.26407i) q^{93} +(1.55691 + 5.05863i) q^{94} +11.8783 q^{95} +(-6.08416 + 7.68004i) q^{96} -5.67418 q^{97} +(0.807610 + 2.62404i) q^{98} +(1.86351 - 4.42386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7}+O(q^{10}) $ 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7	$ 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 8 q^{12} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 12 q^{19} - 8 q^{21} + 16 q^{22} + 24 q^{24} + 10 q^{27} - 8 q^{28} + 28 q^{30} - 4 q^{33} - 8 q^{34} + 20 q^{36} - 4 q^{37} + 20 q^{39} - 40 q^{40} - 24 q^{42} + 12 q^{43} - 12 q^{45} - 40 q^{46} - 48 q^{48} - 20 q^{49} + 24 q^{51} - 16 q^{52} - 52 q^{54} + 24 q^{55} + 32 q^{58} - 16 q^{60} + 12 q^{61} + 56 q^{64} + 28 q^{66} + 28 q^{67} + 4 q^{69} + 40 q^{70} + 40 q^{72} - 34 q^{75} + 56 q^{76} + 60 q^{78} - 4 q^{81} - 16 q^{82} + 16 q^{84} + 32 q^{85} - 60 q^{87} - 64 q^{88} - 16 q^{90} - 56 q^{91} + 28 q^{93} - 48 q^{94} - 56 q^{96} - 8 q^{97} - 52 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 - 8 * q^12 - 4 * q^13 + 16 * q^16 + 4 * q^18 - 12 * q^19 - 8 * q^21 + 16 * q^22 + 24 * q^24 + 10 * q^27 - 8 * q^28 + 28 * q^30 - 4 * q^33 - 8 * q^34 + 20 * q^36 - 4 * q^37 + 20 * q^39 - 40 * q^40 - 24 * q^42 + 12 * q^43 - 12 * q^45 - 40 * q^46 - 48 * q^48 - 20 * q^49 + 24 * q^51 - 16 * q^52 - 52 * q^54 + 24 * q^55 + 32 * q^58 - 16 * q^60 + 12 * q^61 + 56 * q^64 + 28 * q^66 + 28 * q^67 + 4 * q^69 + 40 * q^70 + 40 * q^72 - 34 * q^75 + 56 * q^76 + 60 * q^78 - 4 * q^81 - 16 * q^82 + 16 * q^84 + 32 * q^85 - 60 * q^87 - 64 * q^88 - 16 * q^90 - 56 * q^91 + 28 * q^93 - 48 * q^94 - 56 * q^96 - 8 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.416001	−	1.35164i	−0.294157	−	0.955757i
$2$	−0.416001	−	1.35164i	−0.294157	−	0.955757i
$3$	0.966579	−	1.43726i	0.558055	−	0.829804i
$3$	0.966579	−	1.43726i	0.558055	−	0.829804i
$4$	−1.65389	+	1.12457i	−0.826943	+	0.562285i
$5$	−1.57184	+	1.57184i	−0.702949	+	0.702949i	−0.965042	−	0.262094i	$-0.915587\pi$
$5$	−1.57184	+	1.57184i	−0.702949	+	0.702949i	0.262094	+	0.965042i	$0.415587\pi$
$6$	−2.34477	−	0.708570i	−0.957247	−	0.289272i
$7$	2.24914			0.850095			0.425048	−	0.905171i	$-0.360257\pi$
$7$	2.24914			0.850095			0.425048	+	0.905171i	$0.360257\pi$
$8$	2.20804	+	1.76765i	0.780659	+	0.624957i
$9$	−1.13145	−	2.77846i	−0.377150	−	0.926152i
$10$	2.77846	+	1.47068i	0.878625	+	0.465071i
$11$	1.13145	+	1.13145i	0.341145	+	0.341145i	0.856798	−	0.515653i	$-0.172451\pi$
$11$	1.13145	+	1.13145i	0.341145	+	0.341145i	−0.515653	+	0.856798i	$0.672451\pi$
$12$	0.0176901	+	3.46406i	0.00510669	+	0.999987i
$13$	−3.24914	+	3.24914i	−0.901149	+	0.901149i	−0.995536	−	0.0943862i	$-0.969911\pi$
$13$	−3.24914	+	3.24914i	−0.901149	+	0.901149i	0.0943862	+	0.995536i	$0.469911\pi$
$14$	−0.935644	−	3.04004i	−0.250061	−	0.812485i
$15$	0.739839	+	3.77846i	0.191026	+	0.975593i
$16$	1.47068	−	3.71982i	0.367671	−	0.929956i
$17$			1.66400i			0.403580i	0.979429	+	0.201790i	$0.0646758\pi$
$17$			1.66400i			0.403580i	−0.979429	+	0.201790i	$0.935324\pi$
$18$	−3.28480	+	2.68516i	−0.774236	+	0.632897i
$19$	−3.77846	−	3.77846i	−0.866838	−	0.866838i	0.125283	−	0.992121i	$-0.460016\pi$
$19$	−3.77846	−	3.77846i	−0.866838	−	0.866838i	−0.992121	+	0.125283i	$0.960016\pi$
$20$	0.832001	−	4.36729i	0.186041	−	0.976556i
$21$	2.17397	−	3.23261i	0.474400	−	0.705412i
$22$	1.05863	−	2.00000i	0.225701	−	0.426401i
$23$		−	2.26290i		−	0.471847i	−0.971772	−	0.235923i	$-0.924189\pi$
$23$		−	2.26290i		−	0.471847i	0.971772	−	0.235923i	$-0.0758114\pi$
$24$	4.67481	−	1.46496i	0.954243	−	0.299034i
$25$			0.0586332i			0.0117266i
$26$	5.74333	+	3.04004i	1.12636	+	0.596201i
$27$	−5.08701	−	1.05941i	−0.978995	−	0.203884i
$28$	−3.71982	+	2.52932i	−0.702981	+	0.477996i
$29$	−3.23584	−	3.23584i	−0.600881	−	0.600881i	0.339665	−	0.940546i	$-0.389686\pi$
$29$	−3.23584	−	3.23584i	−0.600881	−	0.600881i	−0.940546	+	0.339665i	$0.889686\pi$
$30$	4.79936	−	2.57184i	0.876239	−	0.469552i
$31$		−	1.30777i		−	0.234883i	−0.993080	−	0.117442i	$-0.962531\pi$
$31$		−	1.30777i		−	0.234883i	0.993080	−	0.117442i	$-0.0374693\pi$
$32$	−5.63969	−	0.440392i	−0.996965	−	0.0778511i
$33$	2.71982	−	0.532554i	0.473461	−	0.0927058i
$34$	2.24914	−	0.692226i	0.385724	−	0.118716i
$35$	−3.53529	+	3.53529i	−0.597573	+	0.597573i
$36$	4.99586	+	3.32286i	0.832643	+	0.553810i
$37$	2.30777	+	2.30777i	0.379396	+	0.379396i	0.870884	−	0.491488i	$-0.163547\pi$
$37$	2.30777	+	2.30777i	0.379396	+	0.379396i	−0.491488	+	0.870884i	$0.663547\pi$
$38$	−3.53529	+	6.67897i	−0.573500	+	1.08347i
$39$	1.52932	+	7.81042i	0.244887	+	1.25067i
$40$	−6.24914	+	0.692226i	−0.988076	+	0.109451i
$41$	10.2143			1.59520			0.797600	−	0.603187i	$-0.206103\pi$
$41$	10.2143			1.59520			0.797600	+	0.603187i	$0.206103\pi$
$42$	−5.27371	−	1.59367i	−0.813751	−	0.245909i
$43$	3.77846	−	3.77846i	0.576209	−	0.576209i	−0.357647	−	0.933857i	$-0.616421\pi$
$43$	3.77846	−	3.77846i	0.576209	−	0.576209i	0.933857	+	0.357647i	$0.116421\pi$
$44$	−3.14368	−	0.598895i	−0.473928	−	0.0902867i
$45$	6.14575	+	2.58884i	0.916154	+	0.385921i
$46$	−3.05863	+	0.941367i	−0.450971	+	0.138797i
$47$	−3.74258			−0.545911			−0.272955	−	0.962027i	$-0.588001\pi$
$47$	−3.74258			−0.545911			−0.272955	+	0.962027i	$0.588001\pi$
$48$	−3.92483	−	5.70926i	−0.566501	−	0.824061i
$49$	−1.94137			−0.277338
$50$	0.0792512	−	0.0243914i	0.0112078	−	0.00344947i
$51$	2.39161	+	1.60839i	0.334892	+	0.225220i
$52$	1.71982	−	9.02760i	0.238497	−	1.25190i
$53$	0.972946	−	0.972946i	0.133644	−	0.133644i	−0.637120	−	0.770765i	$-0.719874\pi$
$53$	0.972946	−	0.972946i	0.133644	−	0.133644i	0.770765	+	0.637120i	$0.219874\pi$
$54$	0.684253	+	7.31654i	0.0931150	+	0.995655i
$55$	−3.55691			−0.479614
$56$	4.96619	+	3.97568i	0.663635	+	0.531273i
$57$	−9.08281	+	1.77846i	−1.20305	+	0.235562i
$58$	−3.02760	+	5.71982i	−0.397543	+	0.751050i
$59$	3.88352	+	3.88352i	0.505591	+	0.505591i	0.913170	−	0.407579i	$-0.133627\pi$
$59$	3.88352	+	3.88352i	0.505591	+	0.505591i	−0.407579	+	0.913170i	$0.633627\pi$
$60$	−5.47275	−	5.41714i	−0.706529	−	0.699350i
$61$	4.19051	−	4.19051i	0.536539	−	0.536539i	−0.385971	−	0.922511i	$-0.626134\pi$
$61$	4.19051	−	4.19051i	0.536539	−	0.536539i	0.922511	+	0.385971i	$0.126134\pi$
$62$	−1.76765	+	0.544035i	−0.224491	+	0.0690925i
$63$	−2.54479	−	6.24914i	−0.320613	−	0.787318i
$64$	1.75086	+	7.80605i	0.218857	+	0.975757i
$65$		−	10.2143i		−	1.26692i
$66$	−1.85127	−	3.45469i	−0.227876	−	0.425243i
$67$	8.02760	+	8.02760i	0.980727	+	0.980727i	0.999818	−	0.0190906i	$-0.00607710\pi$
$67$	8.02760	+	8.02760i	0.980727	+	0.980727i	−0.0190906	+	0.999818i	$0.506077\pi$
$68$	−1.87129	−	2.75207i	−0.226927	−	0.333738i
$69$	−3.25238	−	2.18727i	−0.391540	−	0.263316i
$70$	6.24914	+	3.30777i	0.746915	+	0.395355i
$71$		−	11.0950i		−	1.31674i	−0.752695	−	0.658370i	$-0.771246\pi$
$71$		−	11.0950i		−	1.31674i	0.752695	−	0.658370i	$-0.228754\pi$
$72$	2.41305	−	8.13494i	0.284380	−	0.958712i
$73$			6.38101i			0.746841i	0.927662	+	0.373421i	$0.121815\pi$
$73$			6.38101i			0.746841i	−0.927662	+	0.373421i	$0.878185\pi$
$74$	2.15925	−	4.07933i	0.251008	−	0.474212i
$75$	0.0842713	+	0.0566736i	0.00973081	+	0.00654410i
$76$	10.4983	+	2.00000i	1.20424	+	0.229416i
$77$	2.54479	+	2.54479i	0.290005	+	0.290005i
$78$	9.92072	−	5.31623i	1.12330	−	0.601945i
$79$		−	2.69223i		−	0.302899i	−0.988465	−	0.151450i	$-0.951606\pi$
$79$		−	2.69223i		−	0.302899i	0.988465	−	0.151450i	$-0.0483941\pi$
$80$	3.53529	+	8.15865i	0.395258	+	0.912165i
$81$	−6.43965	+	6.28736i	−0.715516	+	0.698596i
$82$	−4.24914	−	13.8061i	−0.469239	−	1.52462i
$83$	2.61113	−	2.61113i	0.286608	−	0.286608i	−0.549129	−	0.835738i	$-0.685040\pi$
$83$	2.61113	−	2.61113i	0.286608	−	0.286608i	0.835738	+	0.549129i	$0.185040\pi$
$84$	0.0397875	+	7.79115i	0.00434117	+	0.850084i
$85$	−2.61555	−	2.61555i	−0.283696	−	0.283696i
$86$	−6.67897	−	3.53529i	−0.720212	−	0.381220i
$87$	−7.77846	+	1.52306i	−0.833938	+	0.163289i
$88$	0.498281	+	4.49828i	0.0531169	+	0.479518i
$89$	−7.35247			−0.779360			−0.389680	−	0.920950i	$-0.627414\pi$
$89$	−7.35247			−0.779360			−0.389680	+	0.920950i	$0.627414\pi$
$90$	0.942549	−	9.38383i	0.0993534	−	0.989142i
$91$	−7.30777	+	7.30777i	−0.766063	+	0.766063i
$92$	2.54479	+	3.74258i	0.265312	+	0.390191i
$93$	−1.87961	−	1.26407i	−0.194907	−	0.131078i
$94$	1.55691	+	5.05863i	0.160583	+	0.521758i
$95$	11.8783			1.21868
$96$	−6.08416	+	7.68004i	−0.620962	+	0.783840i
$97$	−5.67418			−0.576126			−0.288063	−	0.957611i	$-0.593011\pi$
$97$	−5.67418			−0.576126			−0.288063	+	0.957611i	$0.593011\pi$
$98$	0.807610	+	2.62404i	0.0815809	+	0.265068i
$99$	1.86351	−	4.42386i	0.187289	−	0.444614i
$100$	−0.0659371	−	0.0969726i	−0.00659371	−	0.00969726i
$101$	−10.3064	+	10.3064i	−1.02553	+	1.02553i	−0.0258621	+	0.999666i	$0.508233\pi$
$101$	−10.3064	+	10.3064i	−1.02553	+	1.02553i	−0.999666	+	0.0258621i	$0.991767\pi$
$102$	1.17906	−	3.90170i	0.116745	−	0.386326i
$103$	−8.13187			−0.801257			−0.400629	−	0.916241i	$-0.631208\pi$
$103$	−8.13187			−0.801257			−0.400629	+	0.916241i	$0.631208\pi$
$104$	−12.9176	+	1.43090i	−1.26667	+	0.140311i
$105$	1.66400	+	8.49828i	0.162390	+	0.829347i
$106$	−1.71982	−	0.910331i	−0.167044	−	0.0884192i
$107$	−2.40384	−	2.40384i	−0.232388	−	0.232388i	0.581301	−	0.813689i	$-0.302544\pi$
$107$	−2.40384	−	2.40384i	−0.232388	−	0.232388i	−0.813689	+	0.581301i	$0.802544\pi$
$108$	9.60472	−	3.96855i	0.924214	−	0.381874i
$109$	8.92332	−	8.92332i	0.854699	−	0.854699i	−0.136009	−	0.990708i	$-0.543427\pi$
$109$	8.92332	−	8.92332i	0.854699	−	0.854699i	0.990708	+	0.136009i	$0.0434275\pi$
$110$	1.47968	+	4.80768i	0.141082	+	0.458395i
$111$	5.54752	−	1.08623i	0.526548	−	0.103100i
$112$	3.30777	−	8.36641i	0.312555	−	0.790551i
$113$			15.9027i			1.49600i	0.663697	+	0.748002i	$0.268986\pi$
$113$			15.9027i			1.49600i	−0.663697	+	0.748002i	$0.731014\pi$
$114$	6.18230	+	11.5369i	0.579025	+	1.08053i
$115$	3.55691	+	3.55691i	0.331684	+	0.331684i
$116$	8.99065	+	1.71279i	0.834761	+	0.159028i
$117$	12.7038	+	5.35136i	1.17447	+	0.494734i
$118$	3.63359	−	6.86469i	0.334499	−	0.631946i
$119$			3.74258i			0.343081i
$120$	−5.04538	+	9.65075i	−0.460578	+	0.880989i
$121$		−	8.43965i		−	0.767241i
$122$	−7.40733	−	3.92082i	−0.670628	−	0.354975i
$123$	9.87290	−	14.6806i	0.890209	−	1.32370i
$124$	1.47068	+	2.16291i	0.132071	+	0.194235i
$125$	−7.95137	−	7.95137i	−0.711192	−	0.711192i
$126$	−7.38798	+	6.03929i	−0.658174	+	0.538023i
$127$			7.42504i			0.658866i	0.944179	+	0.329433i	$0.106858\pi$
$127$			7.42504i			0.658866i	−0.944179	+	0.329433i	$0.893142\pi$
$128$	9.82265	−	5.61386i	0.868208	−	0.496200i
$129$	−1.77846	−	9.08281i	−0.156584	−	0.799697i
$130$	−13.8061	+	4.24914i	−1.21087	+	0.372674i
$131$	−3.88352	+	3.88352i	−0.339305	+	0.339305i	−0.856106	−	0.516801i	$-0.827123\pi$
$131$	−3.88352	+	3.88352i	−0.339305	+	0.339305i	0.516801	+	0.856106i	$0.327123\pi$
$132$	−3.89939	+	3.93942i	−0.339398	+	0.342882i
$133$	−8.49828	−	8.49828i	−0.736894	−	0.736894i
$134$	7.51097	−	14.1899i	0.648849	−	1.22582i
$135$	9.66119	−	6.33074i	0.831503	−	0.544864i
$136$	−2.94137	+	3.67418i	−0.252220	+	0.315058i
$137$	2.72911			0.233164			0.116582	−	0.993181i	$-0.462806\pi$
$137$	2.72911			0.233164			0.116582	+	0.993181i	$0.462806\pi$
$138$	−1.60342	+	5.30597i	−0.136492	+	0.451674i
$139$	−0.0275977	+	0.0275977i	−0.00234080	+	0.00234080i	−0.708276	−	0.705935i	$-0.750527\pi$
$139$	−0.0275977	+	0.0275977i	−0.00234080	+	0.00234080i	0.705935	+	0.708276i	$0.250527\pi$
$140$	1.87129	−	9.82265i	0.158153	−	0.830166i
$141$	−3.61750	+	5.37907i	−0.304648	+	0.452999i
$142$	−14.9966	+	4.61555i	−1.25848	+	0.387328i
$143$	−7.35247			−0.614845
$144$	−11.9994	+	0.122559i	−0.999948	+	0.0102132i
$145$	10.1725			0.844777
$146$	8.62486	−	2.65451i	0.713799	−	0.219689i
$147$	−1.87649	+	2.79025i	−0.154770	+	0.230136i
$148$	−6.41205	−	1.22154i	−0.527067	−	0.100410i
$149$	12.5693	−	12.5693i	1.02972	−	1.02972i	0.0301744	−	0.999545i	$-0.490394\pi$
$149$	12.5693	−	12.5693i	1.02972	−	1.02972i	0.999545	−	0.0301744i	$-0.00960626\pi$
$150$	0.0415457	−	0.137481i	0.00339219	−	0.0112253i
$151$	16.8647			1.37243			0.686214	−	0.727399i	$-0.259271\pi$
$151$	16.8647			1.37243			0.686214	+	0.727399i	$0.259271\pi$
$152$	−1.66400	−	15.0219i	−0.134968	−	1.21844i
$153$	4.62336	−	1.88273i	0.373777	−	0.152210i
$154$	2.38101	−	4.49828i	0.191868	−	0.362482i
$155$	2.05561	+	2.05561i	0.165111	+	0.165111i
$156$	−11.3127	−	11.1977i	−0.905740	−	0.896536i
$157$	−5.36641	+	5.36641i	−0.428286	+	0.428286i	−0.888044	−	0.459758i	$-0.847936\pi$
$157$	−5.36641	+	5.36641i	−0.428286	+	0.428286i	0.459758	+	0.888044i	$0.347936\pi$
$158$	−3.63893	+	1.11997i	−0.289498	+	0.0890999i
$159$	−0.457950	−	2.33881i	−0.0363178	−	0.185480i
$160$	9.55691	−	8.17246i	0.755540	−	0.646090i
$161$		−	5.08957i		−	0.401115i
$162$	11.1772	+	6.08857i	0.878162	+	0.478363i
$163$	−8.77502	−	8.77502i	−0.687313	−	0.687313i	0.274325	−	0.961637i	$-0.411546\pi$
$163$	−8.77502	−	8.77502i	−0.687313	−	0.687313i	−0.961637	+	0.274325i	$0.911546\pi$
$164$	−16.8932	+	11.4867i	−1.31914	+	0.896957i
$165$	−3.43804	+	5.11222i	−0.267651	+	0.397986i
$166$	−4.61555	−	2.44309i	−0.358236	−	0.189620i
$167$			16.9678i			1.31301i	0.754321	+	0.656505i	$0.227966\pi$
$167$			16.9678i			1.31301i	−0.754321	+	0.656505i	$0.772034\pi$
$168$	10.5143	−	3.29490i	0.811197	−	0.254207i
$169$		−	8.11383i		−	0.624141i
$170$	−2.44722	+	4.62336i	−0.187693	+	0.354596i
$171$	−6.22315	+	14.7734i	−0.475896	+	1.12975i
$172$	−2.00000	+	10.4983i	−0.152499	+	0.800486i
$173$	16.3119	+	16.3119i	1.24017	+	1.24017i	0.959930	+	0.280241i	$0.0904144\pi$
$173$	16.3119	+	16.3119i	1.24017	+	1.24017i	0.280241	+	0.959930i	$0.409586\pi$
$174$	5.29448	+	9.88012i	0.401373	+	0.749010i
$175$			0.131874i			0.00996875i
$176$	5.87279	−	2.54479i	0.442678	−	0.191821i
$177$	9.33537	−	1.82791i	0.701689	−	0.137394i
$178$	3.05863	+	9.93793i	0.229254	+	0.744879i
$179$	−1.33873	+	1.33873i	−0.100062	+	0.100062i	−0.755365	−	0.655304i	$-0.772541\pi$
$179$	−1.33873	+	1.33873i	−0.100062	+	0.100062i	0.655304	+	0.755365i	$0.272541\pi$
$180$	−13.0757	+	2.62969i	−0.974605	+	0.196005i
$181$	10.2457	+	10.2457i	0.761557	+	0.761557i	0.976604	−	0.215047i	$-0.0689904\pi$
$181$	10.2457	+	10.2457i	0.761557	+	0.761557i	−0.215047	+	0.976604i	$0.568990\pi$
$182$	12.9176	+	6.83747i	0.957513	+	0.506827i
$183$	−1.97240	−	10.0733i	−0.145804	−	0.744641i
$184$	4.00000	−	4.99656i	0.294884	−	0.368351i
$185$	−7.25491			−0.533391
$186$	−0.926649	+	3.06642i	−0.0679452	+	0.224841i
$187$	−1.88273	+	1.88273i	−0.137679	+	0.137679i
$188$	6.18980	−	4.20879i	0.451437	−	0.306958i
$189$	−11.4414	−	2.38276i	−0.832239	−	0.173320i
$190$	−4.94137	−	16.0552i	−0.358484	−	1.16477i
$191$	−24.5398			−1.77563			−0.887817	−	0.460197i	$-0.847779\pi$
$191$	−24.5398			−1.77563			−0.887817	+	0.460197i	$0.847779\pi$
$192$	12.9117	+	5.02873i	0.931821	+	0.362917i
$193$	8.38101			0.603279			0.301639	−	0.953422i	$-0.402466\pi$
$193$	8.38101			0.603279			0.301639	+	0.953422i	$0.402466\pi$
$194$	2.36046	+	7.66948i	0.169471	+	0.550636i
$195$	−14.6806	−	9.87290i	−1.05130	−	0.707013i
$196$	3.21080	−	2.18320i	0.229343	−	0.155943i
$197$	1.28995	−	1.28995i	0.0919052	−	0.0919052i	−0.659659	−	0.751565i	$-0.729299\pi$
$197$	1.28995	−	1.28995i	0.0919052	−	0.0919052i	0.751565	+	0.659659i	$0.229299\pi$
$198$	−6.75470	−	0.678470i	−0.480036	−	0.0482167i
$199$	−13.0992			−0.928579			−0.464290	−	0.885683i	$-0.653690\pi$
$199$	−13.0992			−0.928579			−0.464290	+	0.885683i	$0.653690\pi$
$200$	−0.103643	+	0.129464i	−0.00732864	+	0.00915450i
$201$	19.2971	−	3.77846i	1.36111	−	0.266512i
$202$	18.2181	+	9.64315i	1.28182	+	0.678489i
$203$	−7.27787	−	7.27787i	−0.510806	−	0.510806i
$204$	−5.76420	+	0.0294364i	−0.403575	+	0.00206096i
$205$	−16.0552	+	16.0552i	−1.12134	+	1.12134i
$206$	3.38287	+	10.9914i	0.235695	+	0.765807i
$207$	−6.28736	+	2.56035i	−0.437002	+	0.177957i
$208$	7.30777	+	16.8647i	0.506703	+	1.16936i
$209$		−	8.55026i		−	0.591434i
$210$	10.7944	−	5.78443i	0.744886	−	0.399164i
$211$	−8.47068	−	8.47068i	−0.583146	−	0.583146i	0.352621	−	0.935766i	$-0.385291\pi$
$211$	−8.47068	−	8.47068i	−0.583146	−	0.583146i	−0.935766	+	0.352621i	$0.885291\pi$
$212$	−0.514997	+	2.70329i	−0.0353701	+	0.185663i
$213$	−15.9465	−	10.7242i	−1.09264	−	0.734813i
$214$	−2.24914	+	4.24914i	−0.153748	+	0.290465i
$215$			11.8783i			0.810091i
$216$	−9.35964	−	11.3312i	−0.636843	−	0.770993i
$217$		−	2.94137i		−	0.199673i
$218$	−15.7733	−	8.34905i	−1.06830	−	0.565469i
$219$	9.17120	+	6.16776i	0.619732	+	0.416778i
$220$	5.88273	−	4.00000i	0.396614	−	0.269680i
$221$	−5.40658	−	5.40658i	−0.363686	−	0.363686i
$222$	−3.77597	−	7.04641i	−0.253427	−	0.472924i
$223$			21.5715i			1.44454i	0.691613	+	0.722268i	$0.256900\pi$
$223$			21.5715i			1.44454i	−0.691613	+	0.722268i	$0.743100\pi$
$224$	−12.6844	−	0.990504i	−0.847515	−	0.0661808i
$225$	0.162910	−	0.0663404i	0.0108606	−	0.00442269i
$226$	21.4948	−	6.61555i	1.42982	−	0.440060i
$227$	16.7523	−	16.7523i	1.11189	−	1.11189i	0.118994	−	0.992895i	$-0.462033\pi$
$227$	16.7523	−	16.7523i	1.11189	−	1.11189i	0.992895	−	0.118994i	$-0.0379668\pi$
$228$	13.0219	−	13.1556i	0.862400	−	0.871253i
$229$	3.36641	+	3.36641i	0.222458	+	0.222458i	0.809533	−	0.587074i	$-0.199720\pi$
$229$	3.36641	+	3.36641i	0.222458	+	0.222458i	−0.587074	+	0.809533i	$0.699720\pi$
$230$	3.32801	−	6.28736i	0.219442	−	0.414576i
$231$	6.11727	−	1.19779i	0.402487	−	0.0788087i
$232$	−1.42504	−	12.8647i	−0.0935585	−	0.844608i
$233$	−0.501329			−0.0328431			−0.0164216	−	0.999865i	$-0.505227\pi$
$233$	−0.501329			−0.0328431			−0.0164216	+	0.999865i	$0.505227\pi$
$234$	1.94834	−	19.3972i	0.127367	−	1.26804i
$235$	5.88273	−	5.88273i	0.383747	−	0.383747i
$236$	−10.7902	−	2.05561i	−0.702382	−	0.133809i
$237$	−3.86944	−	2.60225i	−0.251347	−	0.169034i
$238$	5.05863	−	1.55691i	0.327902	−	0.100920i
$239$	30.4585			1.97019			0.985097	−	0.171999i	$-0.0550225\pi$
$239$	30.4585			1.97019			0.985097	+	0.171999i	$0.0550225\pi$
$240$	15.1433	+	2.80484i	0.977494	+	0.181052i
$241$	−15.4948			−0.998111			−0.499055	−	0.866570i	$-0.666320\pi$
$241$	−15.4948			−0.998111			−0.499055	+	0.866570i	$0.666320\pi$
$242$	−11.4074	+	3.51090i	−0.733296	+	0.225689i
$243$	2.81216	+	15.3327i	0.180400	+	0.983593i
$244$	−2.21811	+	11.6431i	−0.142000	+	0.745376i
$245$	3.05152	−	3.05152i	0.194954	−	0.194954i
$246$	−23.9501	−	7.23752i	−1.52700	−	0.461447i
$247$	24.5535			1.56230
$248$	2.31168	−	2.88761i	0.146792	−	0.183364i
$249$	−1.22901	−	6.27674i	−0.0778856	−	0.397772i
$250$	−7.43965	+	14.0552i	−0.470525	+	0.888929i
$251$	−12.2265	−	12.2265i	−0.771730	−	0.771730i	0.206679	−	0.978409i	$-0.433734\pi$
$251$	−12.2265	−	12.2265i	−0.771730	−	0.771730i	−0.978409	+	0.206679i	$0.933734\pi$
$252$	11.2364	+	7.47358i	0.707826	+	0.470791i
$253$	2.56035	−	2.56035i	0.160968	−	0.160968i
$254$	10.0360	−	3.08882i	0.629716	−	0.193810i
$255$	−6.28736	+	1.23109i	−0.393730	+	0.0770941i
$256$	−11.6742	−	10.9414i	−0.729636	−	0.683835i
$257$			7.48515i			0.466911i	0.972367	+	0.233455i	$0.0750033\pi$
$257$			7.48515i			0.466911i	−0.972367	+	0.233455i	$0.924997\pi$
$258$	−11.5369	+	6.18230i	−0.718256	+	0.384893i
$259$	5.19051	+	5.19051i	0.322522	+	0.322522i
$260$	11.4867	+	16.8932i	0.712372	+	1.04767i
$261$	−5.32946	+	12.6518i	−0.329885	+	0.783129i
$262$	6.86469	+	3.63359i	0.424102	+	0.224484i
$263$		−	10.2659i		−	0.633023i	−0.948589	−	0.316511i	$-0.897488\pi$
$263$		−	10.2659i		−	0.633023i	0.948589	−	0.316511i	$-0.102512\pi$
$264$	6.94684	+	3.63178i	0.427548	+	0.223521i
$265$			3.05863i			0.187890i
$266$	−7.95137	+	15.0219i	−0.487530	+	0.921055i
$267$	−7.10675	+	10.5674i	−0.434926	+	0.646716i
$268$	−22.3043	−	4.24914i	−1.36245	−	0.259558i
$269$	−2.76963	−	2.76963i	−0.168867	−	0.168867i	0.617614	−	0.786481i	$-0.288099\pi$
$269$	−2.76963	−	2.76963i	−0.168867	−	0.168867i	−0.786481	+	0.617614i	$0.788099\pi$
$270$	−12.5760	−	10.4249i	−0.765350	−	0.634439i
$271$		−	28.6854i		−	1.74251i	−0.490830	−	0.871255i	$-0.663306\pi$
$271$		−	28.6854i		−	1.74251i	0.490830	−	0.871255i	$-0.336694\pi$
$272$	6.18980	+	2.44722i	0.375312	+	0.148385i
$273$	3.43965	+	17.5667i	0.208177	+	1.06319i
$274$	−1.13531	−	3.68879i	−0.0685867	−	0.222848i
$275$	−0.0663404	+	0.0663404i	−0.00400048	+	0.00400048i
$276$	7.83880	−	0.0400309i	0.471841	−	0.00240957i
$277$	−0.806055	−	0.806055i	−0.0484311	−	0.0484311i	0.682476	−	0.730908i	$-0.260903\pi$
$277$	−0.806055	−	0.806055i	−0.0484311	−	0.0484311i	−0.730908	+	0.682476i	$0.760903\pi$
$278$	0.0487829	+	0.0258216i	0.00292580	+	0.00154868i
$279$	−3.63359	+	1.47968i	−0.217538	+	0.0885861i
$280$	−14.0552	+	1.55691i	−0.839959	+	0.0930434i
$281$	−22.3228			−1.33167			−0.665833	−	0.746101i	$-0.731924\pi$
$281$	−22.3228			−1.33167			−0.665833	+	0.746101i	$0.731924\pi$
$282$	8.77547	+	2.65188i	0.522571	+	0.157917i
$283$	8.08279	−	8.08279i	0.480472	−	0.480472i	−0.424810	−	0.905282i	$-0.639659\pi$
$283$	8.08279	−	8.08279i	0.480472	−	0.480472i	0.905282	+	0.424810i	$0.139659\pi$
$284$	12.4772	+	18.3500i	0.740383	+	1.08887i
$285$	11.4813	−	17.0722i	0.680093	−	1.01127i
$286$	3.05863	+	9.93793i	0.180861	+	0.587642i
$287$	22.9733			1.35607
$288$	5.15740	+	16.1679i	0.303903	+	0.952703i
$289$	14.2311			0.837123
$290$	−4.23175	−	13.7496i	−0.248497	−	0.807402i
$291$	−5.48455	+	8.15529i	−0.321510	+	0.478071i
$292$	−7.17590	−	10.5535i	−0.419938	−	0.617595i
$293$	6.37953	−	6.37953i	0.372696	−	0.372696i	−0.495762	−	0.868458i	$-0.665111\pi$
$293$	6.37953	−	6.37953i	0.372696	−	0.372696i	0.868458	+	0.495762i	$0.165111\pi$
$294$	4.55205	+	1.37559i	0.265481	+	0.0802262i
$295$	−12.2086			−0.710809
$296$	1.01633	+	9.17498i	0.0590727	+	0.533285i
$297$	−4.55702	−	6.95436i	−0.264425	−	0.403533i
$298$	−22.2181	−	11.7604i	−1.28706	−	0.681262i
$299$	7.35247	+	7.35247i	0.425204	+	0.425204i
$300$	−0.203109	+	0.00103723i	−0.0117265	+	5.98843e-5i
$301$	8.49828	−	8.49828i	0.489833	−	0.489833i
$302$	−7.01572	−	22.7951i	−0.403709	−	1.31171i
$303$	4.85106	+	24.7750i	0.278686	+	1.42329i
$304$	−19.6121	+	8.49828i	−1.12483	+	0.487410i
$305$			13.1736i			0.754319i
$306$	−4.46811	−	5.46592i	−0.255425	−	0.312466i
$307$	−6.58795	−	6.58795i	−0.375994	−	0.375994i	0.493661	−	0.869655i	$-0.335659\pi$
$307$	−6.58795	−	6.58795i	−0.375994	−	0.375994i	−0.869655	+	0.493661i	$0.835659\pi$
$308$	−7.07058	−	1.34700i	−0.402884	−	0.0767523i
$309$	−7.86010	+	11.6876i	−0.447146	+	0.664887i
$310$	1.92332	−	3.63359i	0.109237	−	0.206374i
$311$		−	9.52861i		−	0.540318i	−0.962816	−	0.270159i	$-0.912924\pi$
$311$		−	9.52861i		−	0.540318i	0.962816	−	0.270159i	$-0.0870763\pi$
$312$	−10.4293	+	19.9490i	−0.590441	+	1.12939i
$313$			25.1690i			1.42264i	0.702870	+	0.711319i	$0.251902\pi$
$313$			25.1690i			1.42264i	−0.702870	+	0.711319i	$0.748098\pi$
$314$	9.48590	+	5.02105i	0.535321	+	0.283354i
$315$	13.8227	+	5.82265i	0.778818	+	0.328069i
$316$	3.02760	+	4.45264i	0.170316	+	0.250480i
$317$	15.5287	+	15.5287i	0.872178	+	0.872178i	0.992709	−	0.120532i	$-0.0384600\pi$
$317$	15.5287	+	15.5287i	0.872178	+	0.872178i	−0.120532	+	0.992709i	$0.538460\pi$
$318$	−2.97073	+	1.59193i	−0.166590	+	0.0892711i
$319$		−	7.32238i		−	0.409975i
$320$	−15.0219	−	9.51780i	−0.839752	−	0.532061i
$321$	−5.77846	+	1.13145i	−0.322522	+	0.0631513i
$322$	−6.87930	+	2.11727i	−0.383368	+	0.117991i
$323$	6.28736	−	6.28736i	0.349838	−	0.349838i
$324$	3.57987	−	17.6404i	0.198882	−	0.980024i
$325$	−0.190507	−	0.190507i	−0.0105674	−	0.0105674i
$326$	−8.21029	+	15.5111i	−0.454726	+	0.859082i
$327$	−4.20006	−	21.4503i	−0.232264	−	1.18620i
$328$	22.5535	+	18.0552i	1.24531	+	0.996931i
$329$	−8.41758			−0.464076
$330$	8.34013	+	2.52032i	0.459109	+	0.138739i
$331$	2.58795	−	2.58795i	0.142247	−	0.142247i	−0.632397	−	0.774644i	$-0.717929\pi$
$331$	2.58795	−	2.58795i	0.142247	−	0.142247i	0.774644	+	0.632397i	$0.217929\pi$
$332$	−1.38211	+	7.25491i	−0.0758533	+	0.398165i
$333$	3.80092	−	9.02318i	0.208289	−	0.494467i
$334$	22.9345	−	7.05863i	1.25492	−	0.386231i
$335$	−25.2362			−1.37880
$336$	−8.82750	−	12.8409i	−0.481580	−	0.700531i
$337$	−23.1690			−1.26210			−0.631049	−	0.775743i	$-0.717375\pi$
$337$	−23.1690			−1.26210			−0.631049	+	0.775743i	$0.717375\pi$
$338$	−10.9670	+	3.37536i	−0.596527	+	0.183595i
$339$	22.8564	+	15.3713i	1.24139	+	0.834852i
$340$	7.26719	+	1.38445i	0.394119	+	0.0750825i
$341$	1.47968	−	1.47968i	0.0801291	−	0.0801291i
$342$	22.5572	+	2.26574i	1.21976	+	0.122517i
$343$	−20.1104			−1.08586
$344$	15.0219	−	1.66400i	0.809929	−	0.0897170i
$345$	8.55026	−	1.67418i	0.460331	−	0.0901349i
$346$	15.2621	−	28.8337i	0.820497	−	1.55011i
$347$	−6.72235	−	6.72235i	−0.360875	−	0.360875i	0.503260	−	0.864135i	$-0.332134\pi$
$347$	−6.72235	−	6.72235i	−0.360875	−	0.360875i	−0.864135	+	0.503260i	$0.832134\pi$
$348$	11.1519	−	11.2664i	0.597805	−	0.603942i
$349$	−2.75086	+	2.75086i	−0.147250	+	0.147250i	−0.776888	−	0.629638i	$-0.783203\pi$
$349$	−2.75086	+	2.75086i	−0.147250	+	0.147250i	0.629638	+	0.776888i	$0.283203\pi$
$350$	0.178247	−	0.0548598i	0.00952771	−	0.00293238i
$351$	19.9706	−	13.0862i	1.06595	−	0.698491i
$352$	−5.88273	−	6.87930i	−0.313551	−	0.366668i
$353$		−	23.1928i		−	1.23443i	−0.786796	−	0.617213i	$-0.788262\pi$
$353$		−	23.1928i		−	1.23443i	0.786796	−	0.617213i	$-0.211738\pi$
$354$	−6.35420	−	11.8577i	−0.337722	−	0.630229i
$355$	17.4396	+	17.4396i	0.925600	+	0.925600i
$356$	12.1602	−	8.26837i	0.644487	−	0.438223i
$357$	5.37907	+	3.61750i	0.284690	+	0.191458i
$358$	2.36641	+	1.25258i	0.125068	+	0.0662008i
$359$			27.3664i			1.44434i	0.691713	+	0.722172i	$0.256856\pi$
$359$			27.3664i			1.44434i	−0.691713	+	0.722172i	$0.743144\pi$
$360$	8.99390	+	16.5798i	0.474020	+	0.873830i
$361$			9.55348i			0.502815i
$362$	9.58633	−	18.1108i	0.503846	−	0.951881i
$363$	−12.1300	−	8.15759i	−0.636659	−	0.428162i
$364$	3.86813	−	20.3043i	0.202745	−	1.06424i
$365$	−10.0299	−	10.0299i	−0.524991	−	0.524991i
$366$	−12.7950	+	6.85649i	−0.668807	+	0.358395i
$367$		−	26.0406i		−	1.35931i	−0.733533	−	0.679654i	$-0.762130\pi$
$367$		−	26.0406i		−	1.35931i	0.733533	−	0.679654i	$-0.237870\pi$
$368$	−8.41758	−	3.32801i	−0.438797	−	0.173484i
$369$	−11.5569	−	28.3799i	−0.601629	−	1.47740i
$370$	3.01805	+	9.80605i	0.156901	+	0.509793i
$371$	2.18829	−	2.18829i	0.113611	−	0.113611i
$372$	4.53020	−	0.0231346i	0.234880	−	0.00119948i
$373$	−13.1319	−	13.1319i	−0.679943	−	0.679943i	0.280044	−	0.959987i	$-0.409651\pi$
$373$	−13.1319	−	13.1319i	−0.679943	−	0.679943i	−0.959987	+	0.280044i	$0.909651\pi$
$374$	3.32801	+	1.76157i	0.172087	+	0.0910885i
$375$	−19.1138	+	3.74258i	−0.987034	+	0.193266i
$376$	−8.26375	−	6.61555i	−0.426170	−	0.341171i
$377$	21.0274			1.08297
$378$	1.53898	+	16.4559i	0.0791566	+	0.846402i
$379$	−17.4526	+	17.4526i	−0.896482	+	0.896482i	−0.995123	−	0.0986413i	$-0.968550\pi$
$379$	−17.4526	+	17.4526i	−0.896482	+	0.896482i	0.0986413	+	0.995123i	$0.468550\pi$
$380$	−19.6453	+	13.3579i	−1.00778	+	0.685248i
$381$	10.6717	+	7.17689i	0.546729	+	0.367683i
$382$	10.2086	+	33.1690i	0.522315	+	1.69707i
$383$	−26.4965			−1.35391			−0.676953	−	0.736027i	$-0.736700\pi$
$383$	−26.4965			−1.35391			−0.676953	+	0.736027i	$0.736700\pi$
$384$	1.42578	−	19.5440i	0.0727589	−	0.997350i
$385$	−8.00000			−0.407718
$386$	−3.48651	−	11.3282i	−0.177459	−	0.576588i
$387$	−14.7734	−	6.22315i	−0.750975	−	0.316341i
$388$	9.38445	−	6.38101i	0.476423	−	0.323947i
$389$	−2.35506	+	2.35506i	−0.119406	+	0.119406i	−0.764285	−	0.644879i	$-0.776908\pi$
$389$	−2.35506	+	2.35506i	−0.119406	+	0.119406i	0.644879	+	0.764285i	$0.276908\pi$
$390$	−7.23752	+	23.9501i	−0.366486	+	1.21276i
$391$	3.76547			0.190428
$392$	−4.28661	−	3.43165i	−0.216507	−	0.173324i
$393$	1.82791	+	9.33537i	0.0922058	+	0.470907i
$394$	−2.28018	−	1.20693i	−0.114874	−	0.0608045i
$395$	4.23175	+	4.23175i	0.212923	+	0.212923i
$396$	1.89291	+	9.41220i	0.0951224	+	0.472981i
$397$	4.68879	−	4.68879i	0.235324	−	0.235324i	−0.579587	−	0.814910i	$-0.696786\pi$
$397$	4.68879	−	4.68879i	0.235324	−	0.235324i	0.814910	+	0.579587i	$0.196786\pi$
$398$	5.44928	+	17.7055i	0.273148	+	0.887496i
$399$	−20.4285	+	4.00000i	−1.02271	+	0.200250i
$400$	0.218105	+	0.0862308i	0.0109053	+	0.00431154i
$401$		−	5.18714i		−	0.259033i	−0.991577	−	0.129517i	$-0.958657\pi$
$401$		−	5.18714i		−	0.259033i	0.991577	−	0.129517i	$-0.0413426\pi$
$402$	−13.1347	−	24.5110i	−0.655101	−	1.22250i
$403$	4.24914	+	4.24914i	0.211665	+	0.211665i
$404$	5.45536	−	28.6360i	0.271414	−	1.42469i
$405$	0.239367	−	20.0048i	0.0118943	−	0.994048i
$406$	−6.80949	+	12.8647i	−0.337949	+	0.638464i
$407$			5.22225i			0.258858i
$408$	2.43770	+	7.77890i	0.120684	+	0.385113i
$409$			14.8793i			0.735734i	0.929878	+	0.367867i	$0.119912\pi$
$409$			14.8793i			0.735734i	−0.929878	+	0.367867i	$0.880088\pi$
$410$	28.3799	+	15.0219i	1.40158	+	0.741881i
$411$	2.63790	−	3.92245i	0.130118	−	0.193480i
$412$	13.4492	−	9.14486i	0.662595	−	0.450535i
$413$	8.73458	+	8.73458i	0.429801	+	0.429801i
$414$	6.07623	+	7.43317i	0.298631	+	0.365321i
$415$			8.20855i			0.402942i
$416$	19.7550	−	16.8932i	0.968570	−	0.828259i
$417$	0.0129898	+	0.0663404i	0.000636111	+	0.00324870i
$418$	−11.5569	+	3.55691i	−0.565267	+	0.173974i
$419$	−25.3026	+	25.3026i	−1.23611	+	1.23611i	−0.274533	+	0.961578i	$0.588523\pi$
$419$	−25.3026	+	25.3026i	−1.23611	+	1.23611i	−0.961578	+	0.274533i	$0.911477\pi$
$420$	−12.3090	−	12.1839i	−0.600617	−	0.594514i
$421$	7.13187	+	7.13187i	0.347586	+	0.347586i	0.859210	−	0.511623i	$-0.170956\pi$
$421$	7.13187	+	7.13187i	0.347586	+	0.347586i	−0.511623	+	0.859210i	$0.670956\pi$
$422$	−7.92554	+	14.9732i	−0.385809	+	0.728882i
$423$	4.23453	+	10.3986i	0.205890	+	0.505597i
$424$	3.86813	−	0.428478i	0.187853	−	0.0208087i
$425$	−0.0975657			−0.00473263
$426$	−7.86161	+	26.0153i	−0.380896	+	1.26045i
$427$	9.42504	−	9.42504i	0.456110	−	0.456110i
$428$	6.67897	+	1.27239i	0.322840	+	0.0615035i
$429$	−7.10675	+	10.5674i	−0.343117	+	0.510200i
$430$	16.0552	−	4.94137i	0.774250	−	0.238294i
$431$	15.4882			0.746038			0.373019	−	0.927824i	$-0.378323\pi$
$431$	15.4882			0.746038			0.373019	+	0.927824i	$0.378323\pi$
$432$	−11.4222	+	17.3647i	−0.549551	+	0.835460i
$433$	25.5500			1.22786			0.613928	−	0.789362i	$-0.289588\pi$
$433$	25.5500			1.22786			0.613928	+	0.789362i	$0.289588\pi$
$434$	−3.97568	+	1.22361i	−0.190839	+	0.0587352i
$435$	9.83249	−	14.6205i	0.471432	−	0.700999i
$436$	−4.72326	+	24.7931i	−0.226203	+	1.18737i
$437$	−8.55026	+	8.55026i	−0.409014	+	0.409014i
$438$	4.52139	−	14.9620i	0.216041	−	0.714911i
$439$	2.63703			0.125859			0.0629293	−	0.998018i	$-0.479956\pi$
$439$	2.63703			0.125859			0.0629293	+	0.998018i	$0.479956\pi$
$440$	−7.85380	−	6.28736i	−0.374415	−	0.299738i
$441$	2.19656	+	5.39400i	0.104598	+	0.256857i
$442$	−5.05863	+	9.55691i	−0.240615	+	0.454576i
$443$	14.8580	+	14.8580i	0.705927	+	0.705927i	0.965676	−	0.259749i	$-0.0836399\pi$
$443$	14.8580	+	14.8580i	0.705927	+	0.705927i	−0.259749	+	0.965676i	$0.583640\pi$
$444$	−7.95343	+	8.03508i	−0.377453	+	0.381328i
$445$	11.5569	−	11.5569i	0.547850	−	0.547850i
$446$	29.1570	−	8.97377i	1.38063	−	0.424920i
$447$	−5.91617	−	30.2147i	−0.279825	−	1.42910i
$448$	3.93793	+	17.5569i	0.186050	+	0.829486i
$449$			31.7079i			1.49639i	0.663480	+	0.748194i	$0.269079\pi$
$449$			31.7079i			1.49639i	−0.663480	+	0.748194i	$0.730921\pi$
$450$	−0.157439	−	0.192598i	−0.00742176	−	0.00907918i
$451$	11.5569	+	11.5569i	0.544194	+	0.544194i
$452$	−17.8837	−	26.3013i	−0.841180	−	1.23711i
$453$	16.3011	−	24.2390i	0.765891	−	1.13885i
$454$	−29.6121	−	15.6742i	−1.38977	−	0.735626i
$455$		−	22.9733i		−	1.07701i
$456$	−23.1989	−	12.1283i	−1.08639	−	0.567959i
$457$		−	23.8759i		−	1.11687i	−0.829550	−	0.558433i	$-0.811403\pi$
$457$		−	23.8759i		−	1.11687i	0.829550	−	0.558433i	$-0.188597\pi$
$458$	3.14976	−	5.95061i	0.147179	−	0.278054i
$459$	1.76286	−	8.46480i	0.0822833	−	0.395103i
$460$	−9.88273	−	1.88273i	−0.460785	−	0.0877829i
$461$	0.921303	+	0.921303i	0.0429094	+	0.0429094i	0.728236	−	0.685327i	$-0.240341\pi$
$461$	0.921303	+	0.921303i	0.0429094	+	0.0429094i	−0.685327	+	0.728236i	$0.740341\pi$
$462$	−4.16377	−	7.77009i	−0.193716	−	0.361497i
$463$			26.1510i			1.21534i	0.794190	+	0.607670i	$0.207895\pi$
$463$			26.1510i			1.21534i	−0.794190	+	0.607670i	$0.792105\pi$
$464$	−16.7957	+	7.27787i	−0.779719	+	0.337866i
$465$	4.94137	−	0.967542i	0.229150	−	0.0448687i
$466$	0.208553	+	0.677618i	0.00966104	+	0.0313901i
$467$	−16.2510	+	16.2510i	−0.752005	+	0.752005i	−0.974853	−	0.222848i	$-0.928465\pi$
$467$	−16.2510	+	16.2510i	−0.752005	+	0.752005i	0.222848	+	0.974853i	$0.428465\pi$
$468$	−27.0287	+	5.43581i	−1.24940	+	0.251270i
$469$	18.0552	+	18.0552i	0.833711	+	0.833711i
$470$	−10.3986	−	5.50414i	−0.479651	−	0.253887i
$471$	2.52588	+	12.9000i	0.116386	+	0.594400i
$472$	1.71027	+	15.4396i	0.0787217	+	0.710667i
$473$	8.55026			0.393141
$474$	−1.90763	+	6.31264i	−0.0876203	+	0.289949i
$475$	0.221543	−	0.221543i	0.0101651	−	0.0101651i
$476$	−4.20879	−	6.18980i	−0.192910	−	0.283709i
$477$	−3.80413	−	1.60245i	−0.174179	−	0.0733712i
$478$	−12.6707	−	41.1690i	−0.579546	−	1.88303i
$479$	11.7456			0.536669			0.268335	−	0.963326i	$-0.413527\pi$
$479$	11.7456			0.536669			0.268335	+	0.963326i	$0.413527\pi$
$480$	−2.50846	−	21.6351i	−0.114495	−	0.987504i
$481$	−14.9966			−0.683784
$482$	6.44587	+	20.9435i	0.293601	+	0.953951i
$483$	−7.31506	−	4.91948i	−0.332847	−	0.223844i
$484$	9.49098	+	13.9582i	0.431408	+	0.634465i
$485$	8.91891	−	8.91891i	0.404987	−	0.404987i
$486$	19.5545	−	10.1795i	0.887010	−	0.461750i
$487$	−0.783513			−0.0355044			−0.0177522	−	0.999842i	$-0.505651\pi$
$487$	−0.783513			−0.0355044			−0.0177522	+	0.999842i	$0.505651\pi$
$488$	16.6601	−	1.84547i	0.754169	−	0.0835403i
$489$	−21.0938	+	4.13026i	−0.953893	+	0.186777i
$490$	−5.39400	−	2.85514i	−0.243676	−	0.128982i
$491$	−10.0382	−	10.0382i	−0.453018	−	0.453018i	0.443337	−	0.896355i	$-0.353794\pi$
$491$	−10.0382	−	10.0382i	−0.453018	−	0.453018i	−0.896355	+	0.443337i	$0.853794\pi$
$492$	0.180691	+	35.3828i	0.00814619	+	1.59518i
$493$	5.38445	−	5.38445i	0.242504	−	0.242504i
$494$	−10.2143	−	33.1876i	−0.459561	−	1.49318i
$495$	4.02447	+	9.88273i	0.180886	+	0.444196i
$496$	−4.86469	−	1.92332i	−0.218431	−	0.0863597i
$497$		−	24.9543i		−	1.11935i
$498$	−7.97265	+	4.27232i	−0.357263	+	0.191447i
$499$	−29.9655	−	29.9655i	−1.34144	−	1.34144i	−0.894627	−	0.446815i	$-0.852558\pi$
$499$	−29.9655	−	29.9655i	−1.34144	−	1.34144i	−0.446815	−	0.894627i	$-0.647442\pi$
$500$	22.0925	+	4.20879i	0.988008	+	0.188223i
$501$	24.3872	+	16.4008i	1.08954	+	0.732732i
$502$	−11.4396	+	21.6121i	−0.510576	+	0.964596i
$503$		−	21.7131i		−	0.968138i	−0.875030	−	0.484069i	$-0.839158\pi$
$503$		−	21.7131i		−	0.968138i	0.875030	−	0.484069i	$-0.160842\pi$
$504$	5.42728	−	18.2966i	0.241750	−	0.814996i
$505$		−	32.4001i		−	1.44179i
$506$	−4.52579	−	2.39558i	−0.201196	−	0.106496i
$507$	−11.6617	−	7.84266i	−0.517914	−	0.348305i
$508$	−8.34998	−	12.2802i	−0.370470	−	0.544845i
$509$	−16.1276	−	16.1276i	−0.714842	−	0.714842i	0.252702	−	0.967544i	$-0.418681\pi$
$509$	−16.1276	−	16.1276i	−0.714842	−	0.714842i	−0.967544	+	0.252702i	$0.918681\pi$
$510$	4.27955	+	7.98614i	0.189502	+	0.353632i
$511$			14.3518i			0.634886i
$512$	−9.93237	+	20.3310i	−0.438953	+	0.898510i
$513$	15.2181	+	23.2240i	0.671896	+	1.02536i
$514$	10.1173	−	3.11383i	0.446253	−	0.137345i
$515$	12.7820	−	12.7820i	0.563243	−	0.563243i
$516$	13.1556	+	13.0219i	0.579144	+	0.573259i
$517$	−4.23453	−	4.23453i	−0.186235	−	0.186235i
$518$	4.85647	−	9.17498i	0.213381	−	0.403125i
$519$	39.2112	−	7.67774i	1.72118	−	0.337015i
$520$	18.0552	−	22.5535i	0.791773	−	0.989035i
$521$	−5.68847			−0.249216			−0.124608	−	0.992206i	$-0.539767\pi$
$521$	−5.68847			−0.249216			−0.124608	+	0.992206i	$0.539767\pi$
$522$	19.3179	+	1.94036i	0.845520	+	0.0849274i
$523$	13.6612	−	13.6612i	0.597362	−	0.597362i	−0.342248	−	0.939610i	$-0.611188\pi$
$523$	13.6612	−	13.6612i	0.597362	−	0.597362i	0.939610	+	0.342248i	$0.111188\pi$
$524$	2.05561	−	10.7902i	0.0897998	−	0.471372i
$525$	0.189538	+	0.127467i	0.00827211	+	0.00556311i
$526$	−13.8759	+	4.27062i	−0.605016	+	0.186208i
$527$	2.17614			0.0947941
$528$	2.01899	−	10.9005i	0.0878654	−	0.474383i
$529$	17.8793			0.777361
$530$	4.13419	−	1.27239i	0.179578	−	0.0552692i
$531$	6.39619	−	15.1842i	0.277571	−	0.658938i
$532$	23.6121	+	4.49828i	1.02371	+	0.195025i
$533$	−33.1876	+	33.1876i	−1.43751	+	1.43751i
$534$	17.2398	+	5.20974i	0.746040	+	0.225447i
$535$	7.55691			0.326714
$536$	3.53529	+	31.9152i	0.152701	+	1.37853i
$537$	0.630120	+	3.21811i	0.0271917	+	0.138871i
$538$	−2.59139	+	4.89572i	−0.111723	+	0.211070i
$539$	−2.19656	−	2.19656i	−0.0946124	−	0.0946124i
$540$	−8.85915	+	21.3350i	−0.381237	+	0.918113i
$541$	−24.5715	+	24.5715i	−1.05641	+	1.05641i	−0.0581016	+	0.998311i	$0.518505\pi$
$541$	−24.5715	+	24.5715i	−1.05641	+	1.05641i	−0.998311	+	0.0581016i	$0.981495\pi$
$542$	−38.7724	+	11.9331i	−1.66542	+	0.512572i
$543$	24.6291	−	4.82248i	1.05693	−	0.206953i
$544$	0.732814	−	9.38445i	0.0314191	−	0.402355i
$545$			28.0521i			1.20162i
$546$	22.3131	−	11.9570i	0.954912	−	0.511710i
$547$	3.56990	+	3.56990i	0.152638	+	0.152638i	0.779295	−	0.626657i	$-0.215577\pi$
$547$	3.56990	+	3.56990i	0.152638	+	0.152638i	−0.626657	+	0.779295i	$0.715577\pi$
$548$	−4.51364	+	3.06908i	−0.192813	+	0.131104i
$549$	−16.3845	−	6.90180i	−0.699273	−	0.294562i
$550$	0.117266	+	0.0620710i	0.00500025	+	0.00264672i
$551$			24.4530i			1.04173i
$552$	−3.31506	−	10.5786i	−0.141098	−	0.450256i
$553$		−	6.05520i		−	0.257493i
$554$	−0.754180	+	1.42482i	−0.0320421	+	0.0605348i
$555$	−7.01244	+	10.4272i	−0.297662	+	0.442610i
$556$	0.0146079	−	0.0766789i	0.000619513	−	0.00325191i
$557$	−18.1602	−	18.1602i	−0.769473	−	0.769473i	0.208540	−	0.978014i	$-0.433129\pi$
$557$	−18.1602	−	18.1602i	−0.769473	−	0.769473i	−0.978014	+	0.208540i	$0.933129\pi$
$558$	3.51158	+	4.29578i	0.148657	+	0.181855i
$559$			24.5535i			1.03850i
$560$	7.95137	+	18.3500i	0.336007	+	0.775427i
$561$	0.886172	+	4.52579i	0.0374142	+	0.191079i
$562$	9.28629	+	30.1725i	0.391719	+	1.27275i
$563$	6.91748	−	6.91748i	0.291537	−	0.291537i	−0.546150	−	0.837687i	$-0.683907\pi$
$563$	6.91748	−	6.91748i	0.291537	−	0.291537i	0.837687	+	0.546150i	$0.183907\pi$
$564$	−0.0662065	−	12.9645i	−0.00278780	−	0.545904i
$565$	−24.9966	−	24.9966i	−1.05161	−	1.05161i
$566$	−14.2875	−	7.56262i	−0.600549	−	0.317880i
$567$	−14.4837	+	14.1412i	−0.608257	+	0.593873i
$568$	19.6121	−	24.4983i	0.822906	−	1.02793i
$569$	36.2961			1.52161			0.760807	−	0.648979i	$-0.224804\pi$
$569$	36.2961			1.52161			0.760807	+	0.648979i	$0.224804\pi$
$570$	−27.8518	−	8.41658i	−1.16658	−	0.352532i
$571$	−33.5224	+	33.5224i	−1.40287	+	1.40287i	−0.612056	+	0.790814i	$0.709657\pi$
$571$	−33.5224	+	33.5224i	−1.40287	+	1.40287i	−0.790814	+	0.612056i	$0.790343\pi$
$572$	12.1602	−	8.26837i	0.508442	−	0.345718i
$573$	−23.7196	+	35.2701i	−0.990901	+	1.47343i
$574$	−9.55691	−	31.0518i	−0.398898	−	1.29608i
$575$	0.132681			0.00553317
$576$	19.7078	−	13.6968i	0.821158	−	0.570702i
$577$	−18.9345			−0.788253			−0.394127	−	0.919056i	$-0.628953\pi$
$577$	−18.9345			−0.788253			−0.394127	+	0.919056i	$0.628953\pi$
$578$	−5.92015	−	19.2354i	−0.246246	−	0.800086i
$579$	8.10092	−	12.0457i	0.336663	−	0.500603i
$580$	−16.8241	+	11.4396i	−0.698583	+	0.475006i
$581$	5.87279	−	5.87279i	0.243644	−	0.243644i
$582$	13.3046	+	4.02055i	0.551495	+	0.166657i
$583$	2.20168			0.0911842
$584$	−11.2794	+	14.0895i	−0.466744	+	0.583028i
$585$	−28.3799	+	11.5569i	−1.17336	+	0.477820i
$586$	−11.2767	−	5.96896i	−0.465838	−	0.246576i
$587$	29.6211	+	29.6211i	1.22259	+	1.22259i	0.966707	+	0.255885i	$0.0823667\pi$
$587$	29.6211	+	29.6211i	1.22259	+	1.22259i	0.255885	+	0.966707i	$0.417633\pi$
$588$	−0.0343430	−	6.72500i	−0.00141628	−	0.277335i
$589$	−4.94137	+	4.94137i	−0.203605	+	0.203605i
$590$	5.07877	+	16.5016i	0.209090	+	0.679361i
$591$	−0.607159	−	3.10084i	−0.0249752	−	0.127551i
$592$	11.9785	−	5.19051i	0.492314	−	0.213329i
$593$		−	21.6263i		−	0.888086i	−0.896005	−	0.444043i	$-0.853544\pi$
$593$		−	21.6263i		−	0.888086i	0.896005	−	0.444043i	$-0.146456\pi$
$594$	−7.50410	+	9.05249i	−0.307897	+	0.371428i
$595$	−5.88273	−	5.88273i	−0.241169	−	0.241169i
$596$	−6.65315	+	34.9233i	−0.272524	+	1.43052i
$597$	−12.6614	+	18.8270i	−0.518198	+	0.770539i
$598$	6.87930	−	12.9966i	0.281315	−	0.531469i
$599$		−	29.8079i		−	1.21792i	−0.793201	−	0.608959i	$-0.791587\pi$
$599$		−	29.8079i		−	1.21792i	0.793201	−	0.608959i	$-0.208413\pi$
$600$	0.0858953	+	0.274099i	0.00350666	+	0.0111901i
$601$		−	32.8432i		−	1.33970i	−0.742495	−	0.669851i	$-0.766358\pi$
$601$		−	32.8432i		−	1.33970i	0.742495	−	0.669851i	$-0.233642\pi$
$602$	−15.0219	−	7.95137i	−0.612249	−	0.324073i
$603$	13.2215	−	31.3872i	0.538422	−	1.27818i
$604$	−27.8923	+	18.9655i	−1.13492	+	0.771696i
$605$	13.2658	+	13.2658i	0.539331	+	0.539331i
$606$	31.4690	−	16.8633i	1.27834	−	0.685026i
$607$			6.95597i			0.282334i	0.989986	+	0.141167i	$0.0450855\pi$
$607$			6.95597i			0.282334i	−0.989986	+	0.141167i	$0.954915\pi$
$608$	19.6453	+	22.9733i	0.796722	+	0.931691i
$609$	−17.4948	+	3.42557i	−0.708927	+	0.138811i
$610$	17.8061	−	5.48024i	0.720946	−	0.221888i
$611$	12.1602	−	12.1602i	0.491947	−	0.491947i
$612$	−5.52925	+	8.31312i	−0.223507	+	0.336038i
$613$	−13.5389	−	13.5389i	−0.546830	−	0.546830i	0.378693	−	0.925522i	$-0.376374\pi$
$613$	−13.5389	−	13.5389i	−0.546830	−	0.546830i	−0.925522	+	0.378693i	$0.876374\pi$
$614$	−6.16398	+	11.6452i	−0.248758	+	0.469960i
$615$	7.55691	+	38.5942i	0.304724	+	1.55627i
$616$	1.12070	+	10.1173i	0.0451545	+	0.407636i
$617$	−8.91891			−0.359062			−0.179531	−	0.983752i	$-0.557458\pi$
$617$	−8.91891			−0.359062			−0.179531	+	0.983752i	$0.557458\pi$
$618$	19.0673	+	5.76200i	0.767001	+	0.231782i
$619$	−1.64658	+	1.64658i	−0.0661818	+	0.0661818i	−0.739423	−	0.673241i	$-0.764902\pi$
$619$	−1.64658	+	1.64658i	−0.0661818	+	0.0661818i	0.673241	+	0.739423i	$0.264902\pi$
$620$	−5.71143	−	1.08807i	−0.229377	−	0.0436979i
$621$	−2.39734	+	11.5114i	−0.0962018	+	0.461936i
$622$	−12.8793	+	3.96391i	−0.516413	+	0.158938i
$623$	−16.5367			−0.662531
$624$	31.3025	+	5.79787i	1.25310	+	0.232100i
$625$	24.7034			0.988136
$626$	34.0196	−	10.4703i	1.35970	−	0.418479i
$627$	−12.2890	−	8.26451i	−0.490774	−	0.330053i
$628$	2.84053	−	14.9103i	0.113349	−	0.594987i
$629$	−3.84014	+	3.84014i	−0.153116	+	0.153116i
$630$	2.11993	−	21.1055i	0.0844599	−	0.840865i
$631$	19.2457			0.766159			0.383080	−	0.923715i	$-0.374863\pi$
$631$	19.2457			0.766159			0.383080	+	0.923715i	$0.374863\pi$
$632$	4.75890	−	5.94454i	0.189299	−	0.236461i
$633$	−20.3622	+	3.98701i	−0.809324	+	0.158469i
$634$	14.5293	−	27.4492i	0.577033	−	1.09015i
$635$	−11.6710	−	11.6710i	−0.463149	−	0.463149i
$636$	3.38755	+	3.35313i	0.134325	+	0.132960i
$637$	6.30777	−	6.30777i	0.249923	−	0.249923i
$638$	−9.89726	+	3.04612i	−0.391836	+	0.120597i
$639$	−30.8271	+	12.5535i	−1.21950	+	0.496608i
$640$	−6.61555	+	24.2637i	−0.261502	+	0.959109i
$641$		−	16.6343i		−	0.657016i	−0.944501	−	0.328508i	$-0.893454\pi$
$641$		−	16.6343i		−	0.657016i	0.944501	−	0.328508i	$-0.106546\pi$
$642$	3.93316	+	7.33974i	0.155229	+	0.289676i
$643$	−4.77502	−	4.77502i	−0.188308	−	0.188308i	0.606656	−	0.794964i	$-0.292511\pi$
$643$	−4.77502	−	4.77502i	−0.188308	−	0.188308i	−0.794964	+	0.606656i	$0.792511\pi$
$644$	5.72358	+	8.41758i	0.225541	+	0.331699i
$645$	17.0722	+	11.4813i	0.672217	+	0.452075i
$646$	−11.1138	−	5.88273i	−0.437268	−	0.231453i
$647$		−	48.2095i		−	1.89531i	−0.319293	−	0.947656i	$-0.603445\pi$
$647$		−	48.2095i		−	1.89531i	0.319293	−	0.947656i	$-0.396555\pi$
$648$	−25.3328	+	2.49972i	−0.995167	+	0.0981983i
$649$			8.78801i			0.344960i
$650$	−0.178247	+	0.336749i	−0.00699143	+	0.0132084i
$651$	−4.22752	−	2.84306i	−0.165689	−	0.111428i
$652$	24.3810	+	4.64476i	0.954834	+	0.181903i
$653$	−24.2281	−	24.2281i	−0.948121	−	0.948121i	0.0505983	−	0.998719i	$-0.483887\pi$
$653$	−24.2281	−	24.2281i	−0.948121	−	0.948121i	−0.998719	+	0.0505983i	$0.983887\pi$
$654$	−27.2459	+	14.6003i	−1.06540	+	0.570917i
$655$		−	12.2086i		−	0.477028i
$656$	15.0219	−	37.9953i	0.586509	−	1.48347i
$657$	17.7294	−	7.21979i	0.691689	−	0.281671i
$658$	3.50172	+	11.3776i	0.136511	+	0.443544i
$659$	9.47442	−	9.47442i	0.369071	−	0.369071i	−0.498067	−	0.867138i	$-0.665957\pi$
$659$	9.47442	−	9.47442i	0.369071	−	0.369071i	0.867138	+	0.498067i	$0.165957\pi$
$660$	−0.0629221	−	12.3214i	−0.00244924	−	0.479608i
$661$	23.0406	+	23.0406i	0.896175	+	0.896175i	0.995095	−	0.0989204i	$-0.0315389\pi$
$661$	23.0406	+	23.0406i	0.896175	+	0.896175i	−0.0989204	+	0.995095i	$0.531539\pi$
$662$	−4.57458	−	2.42140i	−0.177796	−	0.0941104i
$663$	−12.9966	+	2.54479i	−0.504745	+	0.0988313i
$664$	10.3810	−	1.14992i	0.402862	−	0.0446255i
$665$	26.7159			1.03600
$666$	−13.7773	−	1.38385i	−0.533860	−	0.0536231i
$667$	−7.32238	+	7.32238i	−0.283524	+	0.283524i
$668$	−19.0815	−	28.0629i	−0.738286	−	1.08579i
$669$	31.0039	+	20.8506i	1.19868	+	0.806130i
$670$	10.4983	+	34.1104i	0.405584	+	1.31780i
$671$	9.48269			0.366075
$672$	−13.6841	+	17.2735i	−0.527877	+	0.666339i
$673$	29.7846			1.14811			0.574055	−	0.818816i	$-0.305369\pi$
$673$	29.7846			1.14811			0.574055	+	0.818816i	$0.305369\pi$
$674$	9.63833	+	31.3163i	0.371255	+	1.20626i
$675$	0.0621166	−	0.298267i	0.00239087	−	0.0114803i
$676$	9.12457	+	13.4194i	0.350945	+	0.516129i
$677$	5.59631	−	5.59631i	0.215084	−	0.215084i	−0.591339	−	0.806423i	$-0.701401\pi$
$677$	5.59631	−	5.59631i	0.215084	−	0.215084i	0.806423	+	0.591339i	$0.201401\pi$
$678$	11.2682	−	37.2882i	0.432752	−	1.43204i
$679$	−12.7620			−0.489762
$680$	−1.15187	−	10.3986i	−0.0441721	−	0.398768i
$681$	−7.88503	−	40.2699i	−0.302155	−	1.54314i
$682$	−2.61555	−	1.38445i	−0.100154	−	0.0530134i
$683$	19.5790	+	19.5790i	0.749168	+	0.749168i	0.974323	−	0.225155i	$-0.0722887\pi$
$683$	19.5790	+	19.5790i	0.749168	+	0.749168i	−0.225155	+	0.974323i	$0.572289\pi$
$684$	−6.32135	−	31.4319i	−0.241703	−	1.20183i
$685$	−4.28973	+	4.28973i	−0.163902	+	0.163902i
$686$	8.36594	+	27.1821i	0.319413	+	1.03782i
$687$	8.09231	−	1.58451i	0.308741	−	0.0604529i
$688$	−8.49828	−	19.6121i	−0.323994	−	0.747705i
$689$			6.32248i			0.240867i
$690$	−5.81981	−	10.8605i	−0.221556	−	0.413450i
$691$	3.98701	+	3.98701i	0.151673	+	0.151673i	0.778865	−	0.627192i	$-0.215796\pi$
$691$	3.98701	+	3.98701i	0.151673	+	0.151673i	−0.627192	+	0.778865i	$0.715796\pi$
$692$	−45.3219	−	8.63416i	−1.72288	−	0.328221i
$693$	4.19129	−	9.94988i	0.159214	−	0.377965i
$694$	−6.28973	+	11.8827i	−0.238755	+	0.451062i
$695$		−	0.0867582i		−	0.00329093i
$696$	−19.8674	−	10.3866i	−0.753070	−	0.393702i
$697$			16.9966i			0.643791i
$698$	4.86254	+	2.57383i	0.184050	+	0.0974207i
$699$	−0.484574	+	0.720541i	−0.0183283	+	0.0272534i
$700$	−0.148302	−	0.218105i	−0.00560528	−	0.00824360i
$701$	15.2117	+	15.2117i	0.574537	+	0.574537i	0.933393	−	0.358856i	$-0.116833\pi$
$701$	15.2117	+	15.2117i	0.574537	+	0.574537i	−0.358856	+	0.933393i	$0.616833\pi$
$702$	−25.9957	−	21.5492i	−0.981145	−	0.813324i
$703$		−	17.4396i		−	0.657749i
$704$	−6.85114	+	10.8132i	−0.258212	+	0.407536i
$705$	−2.76891	−	14.1412i	−0.104283	−	0.532587i
$706$	−31.3484	+	9.64820i	−1.17981	+	0.363115i
$707$	−23.1806	+	23.1806i	−0.871796	+	0.871796i
$708$	−13.3840	+	13.5214i	−0.503003	+	0.508167i
$709$	20.3009	+	20.3009i	0.762416	+	0.762416i	0.976759	−	0.214342i	$-0.0687608\pi$
$709$	20.3009	+	20.3009i	0.762416	+	0.762416i	−0.214342	+	0.976759i	$0.568761\pi$
$710$	16.3173	−	30.8271i	0.612377	−	1.15692i
$711$	−7.48024	+	3.04612i	−0.280531	+	0.114238i
$712$	−16.2345	−	12.9966i	−0.608415	−	0.487067i
$713$	−2.95936			−0.110829
$714$	2.65188	−	8.77547i	0.0992439	−	0.328414i
$715$	11.5569	−	11.5569i	0.432204	−	0.432204i
$716$	0.708614	−	3.71961i	0.0264822	−	0.139009i
$717$	29.4405	−	43.7768i	1.09948	−	1.63488i
$718$	36.9897	−	11.3845i	1.38044	−	0.424864i
$719$	−3.52314			−0.131391			−0.0656954	−	0.997840i	$-0.520927\pi$
$719$	−3.52314			−0.131391			−0.0656954	+	0.997840i	$0.520927\pi$
$720$	18.6685	−	19.0537i	0.695733	−	0.710091i
$721$	−18.2897			−0.681145
$722$	12.9129	−	3.97425i	0.480569	−	0.147906i
$723$	−14.9770	+	22.2702i	−0.557000	+	0.828236i
$724$	−28.4672	−	5.42322i	−1.05798	−	0.201552i
$725$	0.189728	−	0.189728i	0.00704631	−	0.00704631i
$726$	−5.98008	+	19.7890i	−0.221942	+	0.734439i
$727$	20.3664			0.755348			0.377674	−	0.925939i	$-0.376724\pi$
$727$	20.3664			0.755348			0.377674	+	0.925939i	$0.376724\pi$
$728$	−29.0534	+	3.21829i	−1.07679	+	0.119278i
$729$	24.7553	+	10.7785i	0.916863	+	0.399202i
$730$	−9.38445	+	17.7294i	−0.347334	+	0.656194i
$731$	6.28736	+	6.28736i	0.232547	+	0.232547i
$732$	14.5903	+	14.4420i	0.539272	+	0.533793i
$733$	2.48024	−	2.48024i	0.0916096	−	0.0916096i	−0.659817	−	0.751426i	$-0.729366\pi$
$733$	2.48024	−	2.48024i	0.0916096	−	0.0916096i	0.751426	+	0.659817i	$0.229366\pi$
$734$	−35.1976	+	10.8329i	−1.29917	+	0.399850i
$735$	−1.43630	−	7.33537i	−0.0529787	−	0.270569i
$736$	−0.996562	+	12.7620i	−0.0367338	+	0.470415i
$737$			18.1656i			0.669140i
$738$	−33.5518	+	27.4269i	−1.23506	+	1.00960i
$739$	15.7931	+	15.7931i	0.580957	+	0.580957i	0.935166	−	0.354209i	$-0.115250\pi$
$739$	15.7931	+	15.7931i	0.580957	+	0.580957i	−0.354209	+	0.935166i	$0.615250\pi$
$740$	11.9988	−	8.15865i	0.441084	−	0.299918i
$741$	23.7329	−	35.2898i	0.871849	−	1.29640i
$742$	−3.86813	−	2.04746i	−0.142003	−	0.0751647i
$743$			38.5942i			1.41588i	0.706271	+	0.707941i	$0.250376\pi$
$743$			38.5942i			1.41588i	−0.706271	+	0.707941i	$0.749624\pi$
$744$	−1.91584	−	6.11360i	−0.0702380	−	0.224135i
$745$			39.5139i			1.44768i
$746$	−12.2868	+	23.2125i	−0.449850	+	0.849870i
$747$	−10.2093	−	4.30055i	−0.373537	−	0.157349i
$748$	0.996562	−	5.23109i	0.0364379	−	0.191268i
$749$	−5.40658	−	5.40658i	−0.197552	−	0.197552i
$750$	13.0100	+	24.2782i	0.475058	+	0.886514i
$751$		−	17.6527i		−	0.644156i	−0.946713	−	0.322078i	$-0.895619\pi$
$751$		−	17.6527i		−	0.644156i	0.946713	−	0.322078i	$-0.104381\pi$
$752$	−5.50414	+	13.9217i	−0.200716	+	0.507673i
$753$	−29.3906	+	5.75481i	−1.07105	+	0.209717i
$754$	−8.74742	−	28.4216i	−0.318562	−	1.03505i
$755$	−26.5086	+	26.5086i	−0.964747	+	0.964747i
$756$	21.6024	−	8.92583i	0.785670	−	0.324629i
$757$	−32.7440	−	32.7440i	−1.19010	−	1.19010i	−0.977039	−	0.213062i	$-0.931657\pi$
$757$	−32.7440	−	32.7440i	−1.19010	−	1.19010i	−0.213062	−	0.977039i	$-0.568343\pi$
$758$	30.8501	+	16.3295i	1.12053	+	0.593113i
$759$	−1.20512	−	6.15468i	−0.0437429	−	0.223401i
$760$	26.2277	+	20.9966i	0.951377	+	0.761625i
$761$	6.69113			0.242553			0.121277	−	0.992619i	$-0.461301\pi$
$761$	6.69113			0.242553			0.121277	+	0.992619i	$0.461301\pi$
$762$	5.26116	−	17.4100i	0.190592	−	0.630697i
$763$	20.0698	−	20.0698i	0.726576	−	0.726576i
$764$	40.5860	−	27.5967i	1.46835	−	0.998413i
$765$	−4.30783	+	10.2265i	−0.155750	+	0.369741i
$766$	11.0225	+	35.8138i	0.398261	+	1.29400i
$767$	−25.2362			−0.911227
$768$	−27.0096	+	6.20317i	−0.974626	+	0.223837i
$769$	−5.03265			−0.181482			−0.0907411	−	0.995875i	$-0.528924\pi$
$769$	−5.03265			−0.181482			−0.0907411	+	0.995875i	$0.528924\pi$
$770$	3.32801	+	10.8132i	0.119933	+	0.389679i
$771$	10.7581	+	7.23499i	0.387445	+	0.260562i
$772$	−13.8613	+	9.42504i	−0.498877	+	0.339215i
$773$	10.6859	−	10.6859i	0.384344	−	0.384344i	−0.488320	−	0.872665i	$-0.662390\pi$
$773$	10.6859	−	10.6859i	0.384344	−	0.384344i	0.872665	+	0.488320i	$0.162390\pi$
$774$	−2.26574	+	22.5572i	−0.0814403	+	0.810803i
$775$	0.0766789			0.00275439
$776$	−12.5288	−	10.0299i	−0.449758	−	0.360054i
$777$	12.4772	−	2.44309i	0.447616	−	0.0876452i
$778$	4.16291	+	2.20350i	0.149248	+	0.0789992i
$779$	−38.5942	−	38.5942i	−1.38278	−	1.38278i
$780$	35.3828	−	0.180691i	1.26691	−	0.00646979i
$781$	12.5535	−	12.5535i	0.449199	−	0.449199i
$782$	−1.56644	−	5.08957i	−0.0560157	−	0.182003i
$783$	13.0327	+	19.8888i	0.465750	+	0.710769i
$784$	−2.85514	+	7.22154i	−0.101969	+	0.257912i
$785$		−	16.8703i		−	0.602126i
$786$	11.8577	−	6.35420i	0.422950	−	0.226647i
$787$	16.0974	+	16.0974i	0.573810	+	0.573810i	0.933191	−	0.359381i	$-0.117012\pi$
$787$	16.0974	+	16.0974i	0.573810	+	0.573810i	−0.359381	+	0.933191i	$0.617012\pi$
$788$	−0.682792	+	3.58407i	−0.0243235	+	0.127677i
$789$	−14.7548	−	9.92281i	−0.525285	−	0.353262i
$790$	3.95941	−	7.48024i	0.140870	−	0.266135i
$791$			35.7675i			1.27175i
$792$	11.9345	−	6.47403i	0.424074	−	0.230045i
$793$			27.2311i			0.967005i
$794$	−8.28812	−	4.38704i	−0.294134	−	0.155690i
$795$	4.39606	+	2.95641i	0.155912	+	0.104853i
$796$	21.6646	−	14.7310i	0.767882	−	0.522126i
$797$	2.63695	+	2.63695i	0.0934055	+	0.0934055i	0.752266	−	0.658860i	$-0.228961\pi$
$797$	2.63695	+	2.63695i	0.0934055	+	0.0934055i	−0.658860	+	0.752266i	$0.728961\pi$
$798$	13.9049	+	25.9481i	0.492227	+	0.918553i
$799$		−	6.22766i		−	0.220319i
$800$	0.0258216	−	0.330673i	0.000912931	−	0.0116910i
$801$	8.31894	+	20.4285i	0.293935	+	0.721806i
$802$	−7.01117	+	2.15785i	−0.247573	+	0.0761965i
$803$	−7.21979	+	7.21979i	−0.254781	+	0.254781i
$804$	−27.6660	+	27.9501i	−0.975706	+	0.985723i
$805$	8.00000	+	8.00000i	0.281963	+	0.281963i
$806$	3.97568	−	7.51097i	0.140037	−	0.264563i
$807$	−6.65775	+	1.30362i	−0.234364	+	0.0458896i
$808$	−40.9751	+	4.53887i	−1.44150	+	0.159677i
$809$	−6.62090			−0.232778			−0.116389	−	0.993204i	$-0.537132\pi$
$809$	−6.62090			−0.232778			−0.116389	+	0.993204i	$0.537132\pi$
$810$	−27.1390	+	7.99849i	−0.953567	+	0.281038i
$811$	4.01299	−	4.01299i	0.140915	−	0.140915i	−0.633130	−	0.774045i	$-0.718230\pi$
$811$	4.01299	−	4.01299i	0.140915	−	0.140915i	0.774045	+	0.633130i	$0.218230\pi$
$812$	20.2212	+	3.85230i	0.709626	+	0.135189i
$813$	−41.2284	−	27.7267i	−1.44594	−	0.972417i
$814$	7.05863	−	2.17246i	0.247405	−	0.0761447i
$815$	27.5859			0.966291
$816$	9.50023	−	6.53093i	0.332575	−	0.228628i
$817$	−28.5535			−0.998960
$818$	20.1115	−	6.18980i	0.703183	−	0.216421i
$819$	28.5727	+	12.0360i	0.998411	+	0.420571i
$820$	8.49828	−	44.6087i	0.296773	−	1.55780i
$821$	−7.91085	+	7.91085i	−0.276090	+	0.276090i	−0.831546	−	0.555456i	$-0.812544\pi$
$821$	−7.91085	+	7.91085i	−0.276090	+	0.276090i	0.555456	+	0.831546i	$0.312544\pi$
$822$	−6.39913	−	1.93377i	−0.223195	−	0.0674478i
$823$	−44.9751			−1.56773			−0.783866	−	0.620930i	$-0.786755\pi$
$823$	−44.9751			−1.56773			−0.783866	+	0.620930i	$0.786755\pi$
$824$	−17.9555	−	14.3743i	−0.625509	−	0.500751i
$825$	0.0312253	+	0.159472i	0.00108713	+	0.00555210i
$826$	8.17246	−	15.4396i	0.284356	−	0.537214i
$827$	9.75631	+	9.75631i	0.339260	+	0.339260i	0.856089	−	0.516829i	$-0.172888\pi$
$827$	9.75631	+	9.75631i	0.339260	+	0.339260i	−0.516829	+	0.856089i	$0.672888\pi$
$828$	7.51929	−	11.3051i	0.261313	−	0.392880i
$829$	18.6336	−	18.6336i	0.647171	−	0.647171i	−0.305137	−	0.952308i	$-0.598702\pi$
$829$	18.6336	−	18.6336i	0.647171	−	0.647171i	0.952308	+	0.305137i	$0.0987023\pi$
$830$	11.0950	−	3.41476i	0.385115	−	0.118528i
$831$	−1.93763	+	0.379397i	−0.0672156	+	0.0131611i
$832$	−31.0518	−	19.6742i	−1.07653	−	0.682079i
$833$		−	3.23044i		−	0.111928i
$834$	0.0842649	−	0.0451552i	0.00291786	−	0.00156360i
$835$	−26.6707	−	26.6707i	−0.922979	−	0.922979i
$836$	9.61537	+	14.1412i	0.332554	+	0.489082i
$837$	−1.38547	+	6.65266i	−0.0478888	+	0.229949i
$838$	44.7259	+	23.6742i	1.54503	+	0.817811i
$839$		−	37.8109i		−	1.30538i	−0.757626	−	0.652689i	$-0.773641\pi$
$839$		−	37.8109i		−	1.30538i	0.757626	−	0.652689i	$-0.226359\pi$
$840$	−11.3478	+	21.7059i	−0.391535	+	0.748924i
$841$		−	8.05863i		−	0.277884i
$842$	6.67290	−	12.6066i	0.229963	−	0.434453i
$843$	−21.5767	+	32.0837i	−0.743142	+	1.10502i
$844$	23.5354	+	4.48367i	0.810123	+	0.154334i
$845$	12.7536	+	12.7536i	0.438739	+	0.438739i
$846$	12.2936	−	10.0494i	0.422664	−	0.345506i
$847$		−	18.9820i		−	0.652228i
$848$	−2.18829	−	5.05008i	−0.0751463	−	0.173421i
$849$	−3.80444	−	19.4298i	−0.130568	−	0.666828i
$850$	0.0405874	+	0.131874i	0.00139214	+	0.00452325i
$851$	5.22225	−	5.22225i	0.179017	−	0.179017i
$852$	38.4339	−	0.196272i	1.31672	−	0.00672418i
$853$	24.0992	+	24.0992i	0.825142	+	0.825142i	0.986840	−	0.161699i	$-0.0516972\pi$
$853$	24.0992	+	24.0992i	0.825142	+	0.825142i	−0.161699	+	0.986840i	$0.551697\pi$
$854$	−16.6601	−	8.81848i	−0.570098	−	0.301762i
$855$	−13.4396	−	33.0033i	−0.459626	−	1.12869i
$856$	−1.05863	−	9.55691i	−0.0361833	−	0.326649i
$857$	−0.794026			−0.0271234			−0.0135617	−	0.999908i	$-0.504317\pi$
$857$	−0.794026			−0.0271234			−0.0135617	+	0.999908i	$0.504317\pi$
$858$	17.2398	+	5.20974i	0.588558	+	0.177858i
$859$	2.65775	−	2.65775i	0.0906814	−	0.0906814i	−0.660311	−	0.750992i	$-0.729576\pi$
$859$	2.65775	−	2.65775i	0.0906814	−	0.0906814i	0.750992	+	0.660311i	$0.229576\pi$
$860$	−13.3579	−	19.6453i	−0.455502	−	0.669899i
$861$	22.2055	−	33.0187i	0.756762	−	1.12527i
$862$	−6.44309	−	20.9345i	−0.219452	−	0.713032i
$863$	21.4069			0.728699			0.364349	−	0.931262i	$-0.381291\pi$
$863$	21.4069			0.728699			0.364349	+	0.931262i	$0.381291\pi$
$864$	28.2226	+	8.21502i	0.960151	+	0.279481i
$865$	−51.2794			−1.74355
$866$	−10.6288	−	34.5346i	−0.361182	−	1.17353i
$867$	13.7555	−	20.4538i	0.467161	−	0.694648i
$868$	3.30777	+	4.86469i	0.112273	+	0.165118i
$869$	3.04612	−	3.04612i	0.103332	−	0.103332i
$870$	−23.8520	−	7.20790i	−0.808660	−	0.244371i
$871$	−52.1656			−1.76756
$872$	35.4763	−	3.92976i	1.20138	−	0.133078i
$873$	6.42004	+	15.7655i	0.217286	+	0.533580i
$874$	15.1138	+	8.00000i	0.511233	+	0.270604i
$875$	−17.8837	−	17.8837i	−0.604581	−	0.604581i
$876$	−22.1042	+	0.112881i	−0.746832	+	0.00381389i
$877$	−20.0923	+	20.0923i	−0.678470	+	0.678470i	−0.959654	−	0.281184i	$-0.909273\pi$
$877$	−20.0923	+	20.0923i	−0.678470	+	0.678470i	0.281184	+	0.959654i	$0.409273\pi$
$878$	−1.09701	−	3.56433i	−0.0370222	−	0.120290i
$879$	−3.00274	−	15.3354i	−0.101280	−	0.517249i
$880$	−5.23109	+	13.2311i	−0.176340	+	0.446020i
$881$		−	10.8132i		−	0.364305i	−0.983270	−	0.182152i	$-0.941694\pi$
$881$		−	10.8132i		−	0.364305i	0.983270	−	0.182152i	$-0.0583064\pi$
$882$	6.37701	−	5.21287i	0.214725	−	0.175527i
$883$	12.5665	+	12.5665i	0.422895	+	0.422895i	0.886199	−	0.463304i	$-0.153336\pi$
$883$	12.5665	+	12.5665i	0.422895	+	0.422895i	−0.463304	+	0.886199i	$0.653336\pi$
$884$	15.0219	+	2.86179i	0.505243	+	0.0962525i
$885$	−11.8005	+	17.5469i	−0.396671	+	0.589833i
$886$	13.9018	−	26.2637i	0.467041	−	0.882348i
$887$			12.0977i			0.406201i	0.979158	+	0.203101i	$0.0651018\pi$
$887$			12.0977i			0.406201i	−0.979158	+	0.203101i	$0.934898\pi$
$888$	14.1692	+	7.40762i	0.475488	+	0.248583i
$889$			16.7000i			0.560099i
$890$	−20.4285	−	10.8132i	−0.684766	−	0.362458i
$891$	−14.4000	−	0.172302i	−0.482417	−	0.00577235i
$892$	−24.2587	−	35.6769i	−0.812241	−	1.19455i
$893$	14.1412	+	14.1412i	0.473216	+	0.473216i
$894$	−38.3784	+	20.5659i	−1.28356	+	0.687826i
$895$		−	4.20855i		−	0.140676i
$896$	22.0925	−	12.6264i	0.738060	−	0.421817i
$897$	17.6742	−	3.46069i	0.590124	−	0.115549i
$898$	42.8578	−	13.1905i	1.43018	−	0.440173i
$899$	−4.23175	+	4.23175i	−0.141137	+	0.141137i
$900$	−0.194830	+	0.292923i	−0.00649433	+	0.00976410i
$901$	1.61899	+	1.61899i	0.0539362	+	0.0539362i
$902$	10.8132	−	20.4285i	0.360039	−	0.680196i
$903$	−4.00000	−	20.4285i	−0.133112	−	0.679819i
$904$	−28.1104	+	35.1138i	−0.934938	+	1.16787i
$905$	−32.2092			−1.07067
$906$	−39.5438	−	11.9498i	−1.31375	−	0.397006i
$907$	−14.3388	+	14.3388i	−0.476112	+	0.476112i	−0.903886	−	0.427774i	$-0.859298\pi$
$907$	−14.3388	+	14.3388i	−0.476112	+	0.476112i	0.427774	+	0.903886i	$0.359298\pi$
$908$	−8.86727	+	46.5455i	−0.294271	+	1.54467i
$909$	40.2972	+	16.9748i	1.33657	+	0.563018i
$910$	−31.0518	+	9.55691i	−1.02936	+	0.316809i
$911$	−28.0629			−0.929765			−0.464882	−	0.885372i	$-0.653903\pi$
$911$	−28.0629			−0.929765			−0.464882	+	0.885372i	$0.653903\pi$
$912$	−6.74240	+	36.4020i	−0.223263	+	1.20539i
$913$	5.90871			0.195550
$914$	−32.2717	+	9.93237i	−1.06745	+	0.328534i
$915$	18.9340	+	12.7334i	0.625937	+	0.420952i
$916$	−9.35342	−	1.78189i	−0.309046	−	0.0588755i
$917$	−8.73458	+	8.73458i	−0.288441	+	0.288441i
$918$	−12.1747	+	1.13860i	−0.401827	+	0.0375793i
$919$	25.4734			0.840289			0.420144	−	0.907457i	$-0.361979\pi$
$919$	25.4734			0.840289			0.420144	+	0.907457i	$0.361979\pi$
$920$	1.56644	+	14.1412i	0.0516439	+	0.466220i
$921$	−15.8364	+	3.10084i	−0.521827	+	0.102176i
$922$	0.862012	−	1.62854i	0.0283888	−	0.0536330i
$923$	36.0494	+	36.0494i	1.18658	+	1.18658i
$924$	−8.77027	+	8.86030i	−0.288521	+	0.291483i
$925$	−0.135312	+	0.135312i	−0.00444903	+	0.00444903i
$926$	35.3468	−	10.8788i	1.16157	−	0.357500i
$927$	9.20080	+	22.5941i	0.302194	+	0.742086i
$928$	16.8241	+	19.6742i	0.552278	+	0.645837i
$929$			43.3502i			1.42227i	0.703054	+	0.711137i	$0.251819\pi$
$929$			43.3502i			1.42227i	−0.703054	+	0.711137i	$0.748181\pi$
$930$	−3.36339	−	6.27647i	−0.110290	−	0.205814i
$931$	7.33537	+	7.33537i	0.240407	+	0.240407i
$932$	0.829141	−	0.563779i	0.0271594	−	0.0184672i
$933$	−13.6951	−	9.21016i	−0.448358	−	0.301527i
$934$	28.7259	+	15.2051i	0.939941	+	0.497527i
$935$		−	5.91872i		−	0.193563i
$936$	18.5912	+	34.2719i	0.607673	+	1.12021i
$937$		−	15.5500i		−	0.507998i	−0.967205	−	0.253999i	$-0.918254\pi$
$937$		−	15.5500i		−	0.507998i	0.967205	−	0.253999i	$-0.0817459\pi$
$938$	16.8932	−	31.9152i	0.551584	−	1.04207i
$939$	36.1745	+	24.3279i	1.18051	+	0.793910i
$940$	−3.11383	+	16.3449i	−0.101562	+	0.533113i
$941$	1.85373	+	1.85373i	0.0604299	+	0.0604299i	0.736676	−	0.676246i	$-0.236394\pi$
$941$	1.85373	+	1.85373i	0.0604299	+	0.0604299i	−0.676246	+	0.736676i	$0.736394\pi$
$942$	16.3854	−	8.78050i	0.533867	−	0.286084i
$943$		−	23.1138i		−	0.752690i
$944$	20.1574	−	8.73458i	0.656069	−	0.284287i
$945$	21.7294	−	14.2387i	0.706857	−	0.463186i
$946$	−3.55691	−	11.5569i	−0.115645	−	0.375748i
$947$	31.2499	−	31.2499i	1.01549	−	1.01549i	0.0156087	−	0.999878i	$-0.495031\pi$
$947$	31.2499	−	31.2499i	1.01549	−	1.01549i	0.999878	−	0.0156087i	$-0.00496860\pi$
$948$	9.32602	−	0.0476257i	0.302895	−	0.00154681i
$949$	−20.7328	−	20.7328i	−0.673016	−	0.673016i
$950$	−0.391609	−	0.207285i	−0.0127055	−	0.00672522i
$951$	37.3285	−	7.30909i	1.21046	−	0.237014i
$952$	−6.61555	+	8.26375i	−0.214411	+	0.267830i
$953$	−48.9411			−1.58536			−0.792679	−	0.609639i	$-0.791314\pi$
$953$	−48.9411			−1.58536			−0.792679	+	0.609639i	$0.791314\pi$
$954$	−0.583424	+	5.80845i	−0.0188891	+	0.188056i
$955$	38.5726	−	38.5726i	1.24818	−	1.24818i
$956$	−50.3749	+	34.2527i	−1.62924	+	1.10781i
$957$	−10.5242	−	7.07766i	−0.340199	−	0.228788i
$958$	−4.88617	−	15.8759i	−0.157865	−	0.512926i
$959$	6.13815			0.198211
$960$	−28.1995	+	12.3908i	−0.910135	+	0.399911i
$961$	29.2897			0.944830
$962$	6.23858	+	20.2700i	0.201140	+	0.653532i
$963$	−3.95915	+	9.39880i	−0.127582	+	0.302872i
$964$	25.6267	−	17.4250i	0.825381	−	0.561223i
$965$	−13.1736	+	13.1736i	−0.424074	+	0.424074i
$966$	−3.60632	+	11.9339i	−0.116031	+	0.383966i
$967$	18.5129			0.595334			0.297667	−	0.954670i	$-0.403791\pi$
$967$	18.5129			0.595334			0.297667	+	0.954670i	$0.403791\pi$
$968$	14.9183	−	18.6351i	0.479492	−	0.598953i
$969$	−2.95936	−	15.1138i	−0.0950683	−	0.485526i
$970$	−15.7655	−	8.34492i	−0.506199	−	0.267939i
$971$	−0.0663404	−	0.0663404i	−0.00212897	−	0.00212897i	0.706041	−	0.708170i	$-0.250479\pi$
$971$	−0.0663404	−	0.0663404i	−0.00212897	−	0.00212897i	−0.708170	+	0.706041i	$0.750479\pi$
$972$	−21.8937	−	22.1961i	−0.702241	−	0.711940i
$973$	−0.0620710	+	0.0620710i	−0.00198991	+	0.00198991i
$974$	0.325942	+	1.05903i	0.0104439	+	0.0339336i
$975$	−0.457950	+	0.0896687i	−0.0146661	+	0.00287170i
$976$	−9.42504	−	21.7509i	−0.301688	−	0.696228i
$977$			3.42557i			0.109594i	0.998498	+	0.0547969i	$0.0174511\pi$
$977$			3.42557i			0.109594i	−0.998498	+	0.0547969i	$0.982549\pi$
$978$	14.3577	+	26.7931i	0.459107	+	0.856748i
$979$	−8.31894	−	8.31894i	−0.265875	−	0.265875i
$980$	−1.61522	+	8.47852i	−0.0515963	+	0.270836i
$981$	−34.8893	−	14.6968i	−1.11393	−	0.469232i
$982$	−9.39218	+	17.7440i	−0.299717	+	0.566233i
$983$			30.5911i			0.975706i	0.872926	+	0.487853i	$0.162220\pi$
$983$			30.5911i			0.975706i	−0.872926	+	0.487853i	$0.837780\pi$
$984$	47.7498	−	14.9635i	1.52221	−	0.477019i
$985$			4.05520i			0.129209i
$986$	−9.51780	−	5.03793i	−0.303109	−	0.160440i
$987$	−8.13626	+	12.0983i	−0.258980	+	0.385092i
$988$	−40.6087	+	27.6121i	−1.29193	+	0.878458i
$989$	−8.55026	−	8.55026i	−0.271882	−	0.271882i
$990$	11.6838	−	9.55087i	0.371334	−	0.303547i
$991$			24.2975i			0.771834i	0.922533	+	0.385917i	$0.126115\pi$
$991$			24.2975i			0.771834i	−0.922533	+	0.385917i	$0.873885\pi$
$992$	−0.575933	+	7.37543i	−0.0182859	+	0.234170i
$993$	−1.21811	−	6.22102i	−0.0386554	−	0.197418i
$994$	−33.7294	+	10.3810i	−1.06983	+	0.329266i
$995$	20.5899	−	20.5899i	0.652743	−	0.652743i
$996$	9.09128	+	8.99890i	0.288068	+	0.285141i
$997$	10.3078	+	10.3078i	0.326450	+	0.326450i	0.851235	−	0.524785i	$-0.175854\pi$
$997$	10.3078	+	10.3078i	0.326450	+	0.326450i	−0.524785	+	0.851235i	$0.675854\pi$
$998$	−28.0371	+	52.9684i	−0.887498	+	1.67669i
$999$	−9.29478	−	14.1845i	−0.294074	−	0.448779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.2.k.a.11.3	✓	12
3.2	odd	2	inner	48.2.k.a.11.4	yes	12
4.3	odd	2		192.2.k.a.143.2		12
8.3	odd	2		384.2.k.a.287.5		12
8.5	even	2		384.2.k.b.287.2		12
12.11	even	2		192.2.k.a.143.5		12
16.3	odd	4	inner	48.2.k.a.35.4	yes	12
16.5	even	4		384.2.k.a.95.2		12
16.11	odd	4		384.2.k.b.95.5		12
16.13	even	4		192.2.k.a.47.5		12
24.5	odd	2		384.2.k.b.287.5		12
24.11	even	2		384.2.k.a.287.2		12
48.5	odd	4		384.2.k.a.95.5		12
48.11	even	4		384.2.k.b.95.2		12
48.29	odd	4		192.2.k.a.47.2		12
48.35	even	4	inner	48.2.k.a.35.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.k.a.11.3	✓	12	1.1	even	1	trivial
48.2.k.a.11.4	yes	12	3.2	odd	2	inner
48.2.k.a.35.3	yes	12	48.35	even	4	inner
48.2.k.a.35.4	yes	12	16.3	odd	4	inner
192.2.k.a.47.2		12	48.29	odd	4
192.2.k.a.47.5		12	16.13	even	4
192.2.k.a.143.2		12	4.3	odd	2
192.2.k.a.143.5		12	12.11	even	2
384.2.k.a.95.2		12	16.5	even	4
384.2.k.a.95.5		12	48.5	odd	4
384.2.k.a.287.2		12	24.11	even	2
384.2.k.a.287.5		12	8.3	odd	2
384.2.k.b.95.2		12	48.11	even	4
384.2.k.b.95.5		12	16.11	odd	4
384.2.k.b.287.2		12	8.5	even	2
384.2.k.b.287.5		12	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.416001 - 1.35164i) q^{2} +(0.966579 - 1.43726i) q^{3} +(-1.65389 + 1.12457i) q^{4} +(-1.57184 + 1.57184i) q^{5} +(-2.34477 - 0.708570i) q^{6} +2.24914 q^{7} +(2.20804 + 1.76765i) q^{8} +(-1.13145 - 2.77846i) q^{9} +O(q^{10})\)	\(q+(-0.416001 - 1.35164i) q^{2} +(0.966579 - 1.43726i) q^{3} +(-1.65389 + 1.12457i) q^{4} +(-1.57184 + 1.57184i) q^{5} +(-2.34477 - 0.708570i) q^{6} +2.24914 q^{7} +(2.20804 + 1.76765i) q^{8} +(-1.13145 - 2.77846i) q^{9} +(2.77846 + 1.47068i) q^{10} +(1.13145 + 1.13145i) q^{11} +(0.0176901 + 3.46406i) q^{12} +(-3.24914 + 3.24914i) q^{13} +(-0.935644 - 3.04004i) q^{14} +(0.739839 + 3.77846i) q^{15} +(1.47068 - 3.71982i) q^{16} +1.66400i q^{17} +(-3.28480 + 2.68516i) q^{18} +(-3.77846 - 3.77846i) q^{19} +(0.832001 - 4.36729i) q^{20} +(2.17397 - 3.23261i) q^{21} +(1.05863 - 2.00000i) q^{22} -2.26290i q^{23} +(4.67481 - 1.46496i) q^{24} +0.0586332i q^{25} +(5.74333 + 3.04004i) q^{26} +(-5.08701 - 1.05941i) q^{27} +(-3.71982 + 2.52932i) q^{28} +(-3.23584 - 3.23584i) q^{29} +(4.79936 - 2.57184i) q^{30} -1.30777i q^{31} +(-5.63969 - 0.440392i) q^{32} +(2.71982 - 0.532554i) q^{33} +(2.24914 - 0.692226i) q^{34} +(-3.53529 + 3.53529i) q^{35} +(4.99586 + 3.32286i) q^{36} +(2.30777 + 2.30777i) q^{37} +(-3.53529 + 6.67897i) q^{38} +(1.52932 + 7.81042i) q^{39} +(-6.24914 + 0.692226i) q^{40} +10.2143 q^{41} +(-5.27371 - 1.59367i) q^{42} +(3.77846 - 3.77846i) q^{43} +(-3.14368 - 0.598895i) q^{44} +(6.14575 + 2.58884i) q^{45} +(-3.05863 + 0.941367i) q^{46} -3.74258 q^{47} +(-3.92483 - 5.70926i) q^{48} -1.94137 q^{49} +(0.0792512 - 0.0243914i) q^{50} +(2.39161 + 1.60839i) q^{51} +(1.71982 - 9.02760i) q^{52} +(0.972946 - 0.972946i) q^{53} +(0.684253 + 7.31654i) q^{54} -3.55691 q^{55} +(4.96619 + 3.97568i) q^{56} +(-9.08281 + 1.77846i) q^{57} +(-3.02760 + 5.71982i) q^{58} +(3.88352 + 3.88352i) q^{59} +(-5.47275 - 5.41714i) q^{60} +(4.19051 - 4.19051i) q^{61} +(-1.76765 + 0.544035i) q^{62} +(-2.54479 - 6.24914i) q^{63} +(1.75086 + 7.80605i) q^{64} -10.2143i q^{65} +(-1.85127 - 3.45469i) q^{66} +(8.02760 + 8.02760i) q^{67} +(-1.87129 - 2.75207i) q^{68} +(-3.25238 - 2.18727i) q^{69} +(6.24914 + 3.30777i) q^{70} -11.0950i q^{71} +(2.41305 - 8.13494i) q^{72} +6.38101i q^{73} +(2.15925 - 4.07933i) q^{74} +(0.0842713 + 0.0566736i) q^{75} +(10.4983 + 2.00000i) q^{76} +(2.54479 + 2.54479i) q^{77} +(9.92072 - 5.31623i) q^{78} -2.69223i q^{79} +(3.53529 + 8.15865i) q^{80} +(-6.43965 + 6.28736i) q^{81} +(-4.24914 - 13.8061i) q^{82} +(2.61113 - 2.61113i) q^{83} +(0.0397875 + 7.79115i) q^{84} +(-2.61555 - 2.61555i) q^{85} +(-6.67897 - 3.53529i) q^{86} +(-7.77846 + 1.52306i) q^{87} +(0.498281 + 4.49828i) q^{88} -7.35247 q^{89} +(0.942549 - 9.38383i) q^{90} +(-7.30777 + 7.30777i) q^{91} +(2.54479 + 3.74258i) q^{92} +(-1.87961 - 1.26407i) q^{93} +(1.55691 + 5.05863i) q^{94} +11.8783 q^{95} +(-6.08416 + 7.68004i) q^{96} -5.67418 q^{97} +(0.807610 + 2.62404i) q^{98} +(1.86351 - 4.42386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7}+O(q^{10}) \) 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7	\( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 8 q^{12} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 12 q^{19} - 8 q^{21} + 16 q^{22} + 24 q^{24} + 10 q^{27} - 8 q^{28} + 28 q^{30} - 4 q^{33} - 8 q^{34} + 20 q^{36} - 4 q^{37} + 20 q^{39} - 40 q^{40} - 24 q^{42} + 12 q^{43} - 12 q^{45} - 40 q^{46} - 48 q^{48} - 20 q^{49} + 24 q^{51} - 16 q^{52} - 52 q^{54} + 24 q^{55} + 32 q^{58} - 16 q^{60} + 12 q^{61} + 56 q^{64} + 28 q^{66} + 28 q^{67} + 4 q^{69} + 40 q^{70} + 40 q^{72} - 34 q^{75} + 56 q^{76} + 60 q^{78} - 4 q^{81} - 16 q^{82} + 16 q^{84} + 32 q^{85} - 60 q^{87} - 64 q^{88} - 16 q^{90} - 56 q^{91} + 28 q^{93} - 48 q^{94} - 56 q^{96} - 8 q^{97} - 52 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 - 8 * q^12 - 4 * q^13 + 16 * q^16 + 4 * q^18 - 12 * q^19 - 8 * q^21 + 16 * q^22 + 24 * q^24 + 10 * q^27 - 8 * q^28 + 28 * q^30 - 4 * q^33 - 8 * q^34 + 20 * q^36 - 4 * q^37 + 20 * q^39 - 40 * q^40 - 24 * q^42 + 12 * q^43 - 12 * q^45 - 40 * q^46 - 48 * q^48 - 20 * q^49 + 24 * q^51 - 16 * q^52 - 52 * q^54 + 24 * q^55 + 32 * q^58 - 16 * q^60 + 12 * q^61 + 56 * q^64 + 28 * q^66 + 28 * q^67 + 4 * q^69 + 40 * q^70 + 40 * q^72 - 34 * q^75 + 56 * q^76 + 60 * q^78 - 4 * q^81 - 16 * q^82 + 16 * q^84 + 32 * q^85 - 60 * q^87 - 64 * q^88 - 16 * q^90 - 56 * q^91 + 28 * q^93 - 48 * q^94 - 56 * q^96 - 8 * q^97 - 52 * q^99

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