LMFDB - Embedded newform 48.2.k.a.11.4

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			11.4
Root			$1.35164 + 0.416001i$ of defining polynomial
Character	$\chi$	$=$	48.11
Dual form			48.2.k.a.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.416001 + 1.35164i) q^{2} +(-1.43726 + 0.966579i) q^{3} +(-1.65389 + 1.12457i) q^{4} +(1.57184 - 1.57184i) q^{5} +(-1.90437 - 1.54057i) q^{6} +2.24914 q^{7} +(-2.20804 - 1.76765i) q^{8} +(1.13145 - 2.77846i) q^{9} +O(q^{10})$	\(q+(0.416001 + 1.35164i) q^{2} +(-1.43726 + 0.966579i) q^{3} +(-1.65389 + 1.12457i) q^{4} +(1.57184 - 1.57184i) q^{5} +(-1.90437 - 1.54057i) 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} +(1.29008 - 3.21492i) 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} +(4.22617 + 0.373476i) q^{18} +(-3.77846 - 3.77846i) q^{19} +(-0.832001 + 4.36729i) q^{20} +(-3.23261 + 2.17397i) q^{21} +(1.05863 - 2.00000i) q^{22} +2.26290i q^{23} +(4.88210 + 0.406327i) q^{24} +0.0586332i q^{25} +(-5.74333 - 3.04004i) q^{26} +(1.05941 + 5.08701i) q^{27} +(-3.71982 + 2.52932i) q^{28} +(3.23584 + 3.23584i) q^{29} +(-5.41491 + 0.571841i) 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} +(1.25328 + 5.86765i) 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} +(-4.28321 - 3.46496i) q^{42} +(3.77846 - 3.77846i) q^{43} +(3.14368 + 0.598895i) q^{44} +(-2.58884 - 6.14575i) q^{45} +(-3.05863 + 0.941367i) q^{46} +3.74258 q^{47} +(1.48175 + 6.76790i) q^{48} -1.94137 q^{49} +(-0.0792512 + 0.0243914i) q^{50} +(1.60839 + 2.39161i) q^{51} +(1.71982 - 9.02760i) q^{52} +(-0.972946 + 0.972946i) q^{53} +(-6.43511 + 3.54815i) 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} +(-3.02553 - 7.08114i) 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} +(0.411625 + 3.89778i) q^{66} +(8.02760 + 8.02760i) q^{67} +(1.87129 + 2.75207i) q^{68} +(-2.18727 - 3.25238i) q^{69} +(6.24914 + 3.30777i) q^{70} +11.0950i q^{71} +(-7.40961 + 4.13494i) q^{72} +6.38101i q^{73} +(-2.15925 + 4.07933i) q^{74} +(-0.0566736 - 0.0842713i) q^{75} +(10.4983 + 2.00000i) q^{76} +(-2.54479 - 2.54479i) q^{77} +(11.1931 - 1.18205i) 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} +(2.90158 - 7.23080i) 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} +(7.22991 - 6.05582i) q^{90} +(-7.30777 + 7.30777i) q^{91} +(-2.54479 - 3.74258i) q^{92} +(1.26407 + 1.87961i) q^{93} +(1.55691 + 5.05863i) q^{94} -11.8783 q^{95} +(-8.53138 + 4.81824i) q^{96} -5.67418 q^{97} +(-0.807610 - 2.62404i) q^{98} +(-4.42386 + 1.86351i) 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
$3$	−1.43726	+	0.966579i	−0.829804	+	0.558055i
$3$	−1.43726	+	0.966579i	−0.829804	+	0.558055i
$4$	−1.65389	+	1.12457i	−0.826943	+	0.562285i
$5$	1.57184	−	1.57184i	0.702949	−	0.702949i	−0.262094	−	0.965042i	$-0.584413\pi$
$5$	1.57184	−	1.57184i	0.702949	−	0.702949i	0.965042	+	0.262094i	$0.0844130\pi$
$6$	−1.90437	−	1.54057i	−0.777458	−	0.628935i
$7$	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	0.515653	−	0.856798i	$-0.327549\pi$
$11$	−1.13145	−	1.13145i	−0.341145	−	0.341145i	−0.856798	+	0.515653i	$0.827549\pi$
$12$	1.29008	−	3.21492i	0.372415	−	0.928066i
$13$	−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	$-0.935324\pi$
$17$		−	1.66400i		−	0.403580i	0.979429	−	0.201790i	$-0.0646758\pi$
$18$	4.22617	+	0.373476i	0.996118	+	0.0880293i
$19$	−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
$21$	−3.23261	+	2.17397i	−0.705412	+	0.474400i
$22$	1.05863	−	2.00000i	0.225701	−	0.426401i
$23$			2.26290i			0.471847i	0.971772	+	0.235923i	$0.0758114\pi$
$23$			2.26290i			0.471847i	−0.971772	+	0.235923i	$0.924189\pi$
$24$	4.88210	+	0.406327i	0.996554	+	0.0829412i
$25$			0.0586332i			0.0117266i
$26$	−5.74333	−	3.04004i	−1.12636	−	0.596201i
$27$	1.05941	+	5.08701i	0.203884	+	0.978995i
$28$	−3.71982	+	2.52932i	−0.702981	+	0.477996i
$29$	3.23584	+	3.23584i	0.600881	+	0.600881i	0.940546	−	0.339665i	$-0.110314\pi$
$29$	3.23584	+	3.23584i	0.600881	+	0.600881i	−0.339665	+	0.940546i	$0.610314\pi$
$30$	−5.41491	+	0.571841i	−0.988622	+	0.104403i
$31$		−	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
$36$	1.25328	+	5.86765i	0.208880	+	0.977941i
$37$	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	$-0.793897\pi$
$41$	−10.2143			−1.59520			−0.797600	+	0.603187i	$0.793897\pi$
$42$	−4.28321	−	3.46496i	−0.660913	−	0.534655i
$43$	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
$45$	−2.58884	−	6.14575i	−0.385921	−	0.916154i
$46$	−3.05863	+	0.941367i	−0.450971	+	0.138797i
$47$	3.74258			0.545911			0.272955	−	0.962027i	$-0.411999\pi$
$47$	3.74258			0.545911			0.272955	+	0.962027i	$0.411999\pi$
$48$	1.48175	+	6.76790i	0.213872	+	0.976862i
$49$	−1.94137			−0.277338
$50$	−0.0792512	+	0.0243914i	−0.0112078	+	0.00344947i
$51$	1.60839	+	2.39161i	0.225220	+	0.334892i
$52$	1.71982	−	9.02760i	0.238497	−	1.25190i
$53$	−0.972946	+	0.972946i	−0.133644	+	0.133644i	−0.770765	−	0.637120i	$-0.780126\pi$
$53$	−0.972946	+	0.972946i	−0.133644	+	0.133644i	0.637120	+	0.770765i	$0.280126\pi$
$54$	−6.43511	+	3.54815i	−0.875708	+	0.482841i
$55$	−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	0.407579	−	0.913170i	$-0.366373\pi$
$59$	−3.88352	−	3.88352i	−0.505591	−	0.505591i	−0.913170	+	0.407579i	$0.866373\pi$
$60$	−3.02553	−	7.08114i	−0.390594	−	0.914171i
$61$	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
$66$	0.411625	+	3.89778i	0.0506675	+	0.479783i
$67$	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
$69$	−2.18727	−	3.25238i	−0.263316	−	0.391540i
$70$	6.24914	+	3.30777i	0.746915	+	0.395355i
$71$			11.0950i			1.31674i	0.752695	+	0.658370i	$0.228754\pi$
$71$			11.0950i			1.31674i	−0.752695	+	0.658370i	$0.771246\pi$
$72$	−7.40961	+	4.13494i	−0.873231	+	0.487307i
$73$			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
$75$	−0.0566736	−	0.0842713i	−0.00654410	−	0.00973081i
$76$	10.4983	+	2.00000i	1.20424	+	0.229416i
$77$	−2.54479	−	2.54479i	−0.290005	−	0.290005i
$78$	11.1931	−	1.18205i	1.26737	−	0.133841i
$79$		−	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	−0.835738	−	0.549129i	$-0.814960\pi$
$83$	−2.61113	+	2.61113i	−0.286608	+	0.286608i	0.549129	+	0.835738i	$0.314960\pi$
$84$	2.90158	−	7.23080i	0.316588	−	0.788945i
$85$	−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	$-0.372586\pi$
$89$	7.35247			0.779360			0.389680	+	0.920950i	$0.372586\pi$
$90$	7.22991	−	6.05582i	0.762100	−	0.638340i
$91$	−7.30777	+	7.30777i	−0.766063	+	0.766063i
$92$	−2.54479	−	3.74258i	−0.265312	−	0.390191i
$93$	1.26407	+	1.87961i	0.131078	+	0.194907i
$94$	1.55691	+	5.05863i	0.160583	+	0.521758i
$95$	−11.8783			−1.21868
$96$	−8.53138	+	4.81824i	−0.870731	+	0.491760i
$97$	−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
$99$	−4.42386	+	1.86351i	−0.444614	+	0.187289i
$100$	−0.0659371	−	0.0969726i	−0.00659371	−	0.00969726i
$101$	10.3064	−	10.3064i	1.02553	−	1.02553i	0.0258621	−	0.999666i	$-0.491767\pi$
$101$	10.3064	−	10.3064i	1.02553	−	1.02553i	0.999666	−	0.0258621i	$-0.00823308\pi$
$102$	−2.56351	+	3.16888i	−0.253826	+	0.313766i
$103$	−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	0.813689	−	0.581301i	$-0.197456\pi$
$107$	2.40384	+	2.40384i	0.232388	+	0.232388i	−0.581301	+	0.813689i	$0.697456\pi$
$108$	−7.47284	−	7.22195i	−0.719075	−	0.694933i
$109$	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	$-0.731014\pi$
$113$		−	15.9027i		−	1.49600i	0.663697	−	0.748002i	$-0.268986\pi$
$114$	1.37461	+	13.0166i	0.128744	+	1.21911i
$115$	3.55691	+	3.55691i	0.331684	+	0.331684i
$116$	−8.99065	−	1.71279i	−0.834761	−	0.159028i
$117$	5.35136	+	12.7038i	0.494734	+	1.17447i
$118$	3.63359	−	6.86469i	0.334499	−	0.631946i
$119$		−	3.74258i		−	0.343081i
$120$	8.31257	−	7.03520i	0.758830	−	0.642223i
$121$		−	8.43965i		−	0.767241i
$122$	7.40733	+	3.92082i	0.670628	+	0.354975i
$123$	14.6806	−	9.87290i	1.32370	−	0.890209i
$124$	1.47068	+	2.16291i	0.132071	+	0.194235i
$125$	7.95137	+	7.95137i	0.711192	+	0.711192i
$126$	9.50525	+	0.840001i	0.846795	+	0.0748332i
$127$			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	−0.516801	−	0.856106i	$-0.672877\pi$
$131$	3.88352	−	3.88352i	0.339305	−	0.339305i	0.856106	+	0.516801i	$0.172877\pi$
$132$	−5.09718	+	2.17785i	−0.443652	+	0.189557i
$133$	−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	$-0.537194\pi$
$137$	−2.72911			−0.233164			−0.116582	+	0.993181i	$0.537194\pi$
$138$	3.48615	−	4.30940i	0.296761	−	0.366841i
$139$	−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
$141$	−5.37907	+	3.61750i	−0.452999	+	0.304648i
$142$	−14.9966	+	4.61555i	−1.25848	+	0.387328i
$143$	7.35247			0.614845
$144$	−8.67137	−	8.29502i	−0.722614	−	0.691252i
$145$	10.1725			0.844777
$146$	−8.62486	+	2.65451i	−0.713799	+	0.219689i
$147$	2.79025	−	1.87649i	0.230136	−	0.154770i
$148$	−6.41205	−	1.22154i	−0.527067	−	0.100410i
$149$	−12.5693	+	12.5693i	−1.02972	+	1.02972i	−0.0301744	+	0.999545i	$0.509606\pi$
$149$	−12.5693	+	12.5693i	−1.02972	+	1.02972i	−0.999545	+	0.0301744i	$0.990394\pi$
$150$	0.0903285	−	0.111659i	0.00737529	−	0.00911696i
$151$	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
$156$	6.25405	+	14.6374i	0.500725	+	1.17193i
$157$	−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
$162$	5.81938	−	11.3197i	0.457214	−	0.889357i
$163$	−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
$165$	5.11222	−	3.43804i	0.397986	−	0.267651i
$166$	−4.61555	−	2.44309i	−0.358236	−	0.189620i
$167$		−	16.9678i		−	1.31301i	−0.754321	−	0.656505i	$-0.772034\pi$
$167$		−	16.9678i		−	1.31301i	0.754321	−	0.656505i	$-0.227966\pi$
$168$	10.9805	+	0.913888i	0.847166	+	0.0705080i
$169$		−	8.11383i		−	0.624141i
$170$	2.44722	−	4.62336i	0.187693	−	0.354596i
$171$	−14.7734	+	6.22315i	−1.12975	+	0.475896i
$172$	−2.00000	+	10.4983i	−0.152499	+	0.800486i
$173$	−16.3119	−	16.3119i	−1.24017	−	1.24017i	−0.959930	−	0.280241i	$-0.909586\pi$
$173$	−16.3119	−	16.3119i	−1.24017	−	1.24017i	−0.280241	−	0.959930i	$-0.590414\pi$
$174$	−1.17721	−	11.1473i	−0.0892441	−	0.845075i
$175$			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	−0.655304	−	0.755365i	$-0.727459\pi$
$179$	1.33873	−	1.33873i	0.100062	−	0.100062i	0.755365	+	0.655304i	$0.227459\pi$
$180$	11.1930	+	7.25305i	0.834275	+	0.540610i
$181$	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
$186$	−2.01472	+	2.49049i	−0.147726	+	0.182612i
$187$	−1.88273	+	1.88273i	−0.137679	+	0.137679i
$188$	−6.18980	+	4.20879i	−0.451437	+	0.306958i
$189$	2.38276	+	11.4414i	0.173320	+	0.832239i
$190$	−4.94137	−	16.0552i	−0.358484	−	1.16477i
$191$	24.5398			1.77563			0.887817	−	0.460197i	$-0.152221\pi$
$191$	24.5398			1.77563			0.887817	+	0.460197i	$0.152221\pi$
$192$	−10.0616	−	9.52701i	−0.726135	−	0.687553i
$193$	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
$195$	−9.87290	−	14.6806i	−0.707013	−	1.05130i
$196$	3.21080	−	2.18320i	0.229343	−	0.155943i
$197$	−1.28995	+	1.28995i	−0.0919052	+	0.0919052i	−0.751565	−	0.659659i	$-0.770701\pi$
$197$	−1.28995	+	1.28995i	−0.0919052	+	0.0919052i	0.659659	+	0.751565i	$0.270701\pi$
$198$	−4.35913	−	5.20426i	−0.309790	−	0.369851i
$199$	−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
$204$	−5.34963	−	2.14670i	−0.374549	−	0.150299i
$205$	−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
$210$	−12.1789	+	1.28615i	−0.840423	+	0.0887528i
$211$	−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
$213$	−10.7242	−	15.9465i	−0.734813	−	1.09264i
$214$	−2.24914	+	4.24914i	−0.153748	+	0.290465i
$215$		−	11.8783i		−	0.810091i
$216$	6.65281	−	13.1050i	0.452666	−	0.891680i
$217$		−	2.94137i		−	0.199673i
$218$	15.7733	+	8.34905i	1.06830	+	0.565469i
$219$	−6.16776	−	9.17120i	−0.416778	−	0.619732i
$220$	5.88273	−	4.00000i	0.396614	−	0.269680i
$221$	5.40658	+	5.40658i	0.363686	+	0.363686i
$222$	−0.839576	−	7.95015i	−0.0563486	−	0.533579i
$223$			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	$0.537967\pi$
$227$	−16.7523	+	16.7523i	−1.11189	+	1.11189i	−0.992895	+	0.118994i	$0.962033\pi$
$228$	−17.0219	+	7.27290i	−1.12731	+	0.481659i
$229$	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	$-0.494773\pi$
$233$	0.501329			0.0328431			0.0164216	+	0.999865i	$0.494773\pi$
$234$	−14.9449	+	12.5179i	−0.976979	+	0.818324i
$235$	5.88273	−	5.88273i	0.383747	−	0.383747i
$236$	10.7902	+	2.05561i	0.702382	+	0.133809i
$237$	2.60225	+	3.86944i	0.169034	+	0.251347i
$238$	5.05863	−	1.55691i	0.327902	−	0.100920i
$239$	−30.4585			−1.97019			−0.985097	−	0.171999i	$-0.944978\pi$
$239$	−30.4585			−1.97019			−0.985097	+	0.171999i	$0.944978\pi$
$240$	12.9671	+	8.30899i	0.837024	+	0.536343i
$241$	−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
$243$	15.3327	+	2.81216i	0.983593	+	0.180400i
$244$	−2.21811	+	11.6431i	−0.142000	+	0.745376i
$245$	−3.05152	+	3.05152i	−0.194954	+	0.194954i
$246$	19.4518	+	15.7358i	1.24020	+	1.00328i
$247$	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	0.978409	−	0.206679i	$-0.0662656\pi$
$251$	12.2265	+	12.2265i	0.771730	+	0.771730i	−0.206679	+	0.978409i	$0.566266\pi$
$252$	2.81881	+	13.1972i	0.177568	+	0.831343i
$253$	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	$-0.924997\pi$
$257$		−	7.48515i		−	0.466911i	0.972367	−	0.233455i	$-0.0750033\pi$
$258$	−13.0166	+	1.37461i	−0.810377	+	0.0855798i
$259$	5.19051	+	5.19051i	0.322522	+	0.322522i
$260$	−11.4867	−	16.8932i	−0.712372	−	1.04767i
$261$	12.6518	−	5.32946i	0.783129	−	0.329885i
$262$	6.86469	+	3.63359i	0.424102	+	0.224484i
$263$			10.2659i			0.633023i	0.948589	+	0.316511i	$0.102512\pi$
$263$			10.2659i			0.633023i	−0.948589	+	0.316511i	$0.897488\pi$
$264$	−5.06411	−	5.98358i	−0.311674	−	0.368264i
$265$			3.05863i			0.187890i
$266$	7.95137	−	15.0219i	0.487530	−	0.921055i
$267$	−10.5674	+	7.10675i	−0.646716	+	0.434926i
$268$	−22.3043	−	4.24914i	−1.36245	−	0.259558i
$269$	2.76963	+	2.76963i	0.168867	+	0.168867i	0.786481	−	0.617614i	$-0.211901\pi$
$269$	2.76963	+	2.76963i	0.168867	+	0.168867i	−0.617614	+	0.786481i	$0.711901\pi$
$270$	−4.53785	+	15.6921i	−0.276165	+	0.954990i
$271$		−	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
$276$	7.27502	+	2.91933i	0.437905	+	0.175723i
$277$	−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	$-0.268076\pi$
$281$	22.3228			1.33167			0.665833	+	0.746101i	$0.268076\pi$
$282$	−7.12727	−	5.76570i	−0.424422	−	0.343343i
$283$	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
$285$	17.0722	−	11.4813i	1.01127	−	0.680093i
$286$	3.05863	+	9.93793i	0.180861	+	0.587642i
$287$	−22.9733			−1.35607
$288$	7.60463	−	15.1713i	0.448107	−	0.893980i
$289$	14.2311			0.837123
$290$	4.23175	+	13.7496i	0.248497	+	0.807402i
$291$	8.15529	−	5.48455i	0.478071	−	0.321510i
$292$	−7.17590	−	10.5535i	−0.419938	−	0.617595i
$293$	−6.37953	+	6.37953i	−0.372696	+	0.372696i	−0.868458	−	0.495762i	$-0.834889\pi$
$293$	−6.37953	+	6.37953i	−0.372696	+	0.372696i	0.495762	+	0.868458i	$0.334889\pi$
$294$	3.69709	+	2.99081i	0.215619	+	0.174428i
$295$	−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
$300$	0.188501	+	0.0756417i	0.0108831	+	0.00436717i
$301$	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
$306$	0.621466	−	7.03236i	0.0355268	−	0.402013i
$307$	−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
$309$	11.6876	−	7.86010i	0.664887	−	0.447146i
$310$	1.92332	−	3.63359i	0.109237	−	0.206374i
$311$			9.52861i			0.540318i	0.962816	+	0.270159i	$0.0870763\pi$
$311$			9.52861i			0.540318i	−0.962816	+	0.270159i	$0.912924\pi$
$312$	−17.1828	+	14.5424i	−0.972787	+	0.823302i
$313$			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
$315$	−5.82265	−	13.8227i	−0.328069	−	0.778818i
$316$	3.02760	+	4.45264i	0.170316	+	0.250480i
$317$	−15.5287	−	15.5287i	−0.872178	−	0.872178i	0.120532	−	0.992709i	$-0.461540\pi$
$317$	−15.5287	−	15.5287i	−0.872178	−	0.872178i	−0.992709	+	0.120532i	$0.961540\pi$
$318$	3.35175	−	0.353961i	0.187957	−	0.0198491i
$319$		−	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
$324$	17.7210	+	3.15675i	0.984502	+	0.175375i
$325$	−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
$330$	6.77370	+	5.47968i	0.372880	+	0.301646i
$331$	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
$333$	9.02318	−	3.80092i	0.494467	−	0.208289i
$334$	22.9345	−	7.05863i	1.25492	−	0.386231i
$335$	25.2362			1.37880
$336$	3.33266	+	15.2220i	0.181811	+	0.830426i
$337$	−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
$339$	15.3713	+	22.8564i	0.834852	+	1.24139i
$340$	7.26719	+	1.38445i	0.394119	+	0.0750825i
$341$	−1.47968	+	1.47968i	−0.0801291	+	0.0801291i
$342$	−14.5572	−	17.3796i	−0.787165	−	0.939779i
$343$	−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	0.864135	−	0.503260i	$-0.167866\pi$
$347$	6.72235	+	6.72235i	0.360875	+	0.360875i	−0.503260	+	0.864135i	$0.667866\pi$
$348$	14.5775	−	6.22846i	0.781435	−	0.333880i
$349$	−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	$0.211738\pi$
$353$			23.1928i			1.23443i	−0.786796	+	0.617213i	$0.788262\pi$
$354$	1.41284	+	13.3785i	0.0750915	+	0.711060i
$355$	17.4396	+	17.4396i	0.925600	+	0.925600i
$356$	−12.1602	+	8.26837i	−0.644487	+	0.438223i
$357$	3.61750	+	5.37907i	0.191458	+	0.284690i
$358$	2.36641	+	1.25258i	0.125068	+	0.0662008i
$359$		−	27.3664i		−	1.44434i	−0.691713	−	0.722172i	$-0.743144\pi$
$359$		−	27.3664i		−	1.44434i	0.691713	−	0.722172i	$-0.256856\pi$
$360$	−5.14726	+	18.1462i	−0.271284	+	0.956388i
$361$			9.55348i			0.502815i
$362$	−9.58633	+	18.1108i	−0.503846	+	0.951881i
$363$	8.15759	+	12.1300i	0.428162	+	0.636659i
$364$	3.86813	−	20.3043i	0.202745	−	1.06424i
$365$	10.0299	+	10.0299i	0.524991	+	0.524991i
$366$	−14.4361	+	1.52452i	−0.754585	+	0.0796879i
$367$		−	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
$372$	−4.20438	−	1.68714i	−0.217987	−	0.0874740i
$373$	−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
$378$	−14.4735	+	7.98028i	−0.744435	+	0.410461i
$379$	−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
$381$	−7.17689	−	10.6717i	−0.367683	−	0.546729i
$382$	10.2086	+	33.1690i	0.522315	+	1.69707i
$383$	26.4965			1.35391			0.676953	−	0.736027i	$-0.263300\pi$
$383$	26.4965			1.35391			0.676953	+	0.736027i	$0.263300\pi$
$384$	8.69149	−	17.5630i	0.443536	−	0.896257i
$385$	−8.00000			−0.407718
$386$	3.48651	+	11.3282i	0.177459	+	0.576588i
$387$	−6.22315	−	14.7734i	−0.316341	−	0.750975i
$388$	9.38445	−	6.38101i	0.476423	−	0.323947i
$389$	2.35506	−	2.35506i	0.119406	−	0.119406i	−0.644879	−	0.764285i	$-0.723092\pi$
$389$	2.35506	−	2.35506i	0.119406	−	0.119406i	0.764285	+	0.644879i	$0.223092\pi$
$390$	15.7358	−	19.4518i	0.796813	−	0.984979i
$391$	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
$396$	5.22092	−	8.05697i	0.262361	−	0.404878i
$397$	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	$0.0413426\pi$
$401$			5.18714i			0.259033i	−0.991577	+	0.129517i	$0.958657\pi$
$402$	−2.92047	−	27.6546i	−0.145660	−	1.37929i
$403$	4.24914	+	4.24914i	0.211665	+	0.211665i
$404$	−5.45536	+	28.6360i	−0.271414	+	1.42469i
$405$	−20.0048	+	0.239367i	−0.994048	+	0.0118943i
$406$	−6.80949	+	12.8647i	−0.337949	+	0.638464i
$407$		−	5.22225i		−	0.258858i
$408$	0.676130	−	8.12383i	0.0334734	−	0.402189i
$409$			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
$411$	3.92245	−	2.63790i	0.193480	−	0.130118i
$412$	13.4492	−	9.14486i	0.662595	−	0.450535i
$413$	−8.73458	−	8.73458i	−0.429801	−	0.429801i
$414$	−0.845139	+	9.56339i	−0.0415363	+	0.470015i
$415$			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	$-0.411477\pi$
$419$	25.3026	−	25.3026i	1.23611	−	1.23611i	0.961578	−	0.274533i	$-0.0885232\pi$
$420$	−6.80484	−	15.9265i	−0.332042	−	0.777133i
$421$	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
$426$	17.0927	−	21.1291i	0.828144	−	1.02371i
$427$	9.42504	−	9.42504i	0.456110	−	0.456110i
$428$	−6.67897	−	1.27239i	−0.322840	−	0.0615035i
$429$	−10.5674	+	7.10675i	−0.510200	+	0.343117i
$430$	16.0552	−	4.94137i	0.774250	−	0.238294i
$431$	−15.4882			−0.746038			−0.373019	−	0.927824i	$-0.621677\pi$
$431$	−15.4882			−0.746038			−0.373019	+	0.927824i	$0.621677\pi$
$432$	20.4808	+	3.54056i	0.985384	+	0.170345i
$433$	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
$435$	−14.6205	+	9.83249i	−0.700999	+	0.471432i
$436$	−4.72326	+	24.7931i	−0.226203	+	1.18737i
$437$	8.55026	−	8.55026i	0.409014	−	0.409014i
$438$	9.83041	−	12.1518i	0.469715	−	0.580637i
$439$	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	0.259749	−	0.965676i	$-0.416360\pi$
$443$	−14.8580	−	14.8580i	−0.705927	−	0.705927i	−0.965676	+	0.259749i	$0.916360\pi$
$444$	10.3965	−	4.44208i	0.493397	−	0.210812i
$445$	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	$-0.730921\pi$
$449$		−	31.7079i		−	1.49639i	0.663480	−	0.748194i	$-0.269079\pi$
$450$	−0.0218981	+	0.247794i	−0.00103229	+	0.0116811i
$451$	11.5569	+	11.5569i	0.544194	+	0.544194i
$452$	17.8837	+	26.3013i	0.841180	+	1.23711i
$453$	−24.2390	+	16.3011i	−1.13885	+	0.765891i
$454$	−29.6121	−	15.6742i	−1.38977	−	0.735626i
$455$			22.9733i			1.07701i
$456$	−16.9115	−	19.9821i	−0.791954	−	0.935747i
$457$		−	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
$459$	8.46480	−	1.76286i	0.395103	−	0.0822833i
$460$	−9.88273	−	1.88273i	−0.460785	−	0.0877829i
$461$	−0.921303	−	0.921303i	−0.0429094	−	0.0429094i	0.685327	−	0.728236i	$-0.259659\pi$
$461$	−0.921303	−	0.921303i	−0.0429094	−	0.0429094i	−0.728236	+	0.685327i	$0.759659\pi$
$462$	0.925802	+	8.76665i	0.0430722	+	0.407862i
$463$			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	−0.222848	−	0.974853i	$-0.571535\pi$
$467$	16.2510	−	16.2510i	0.752005	−	0.752005i	0.974853	+	0.222848i	$0.0715355\pi$
$468$	−23.1369	−	14.9927i	−1.06950	−	0.693039i
$469$	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
$474$	−4.14757	+	5.12701i	−0.190504	+	0.235491i
$475$	0.221543	−	0.221543i	0.0101651	−	0.0101651i
$476$	4.20879	+	6.18980i	0.192910	+	0.283709i
$477$	1.60245	+	3.80413i	0.0733712	+	0.174179i
$478$	−12.6707	−	41.1690i	−0.579546	−	1.88303i
$479$	−11.7456			−0.536669			−0.268335	−	0.963326i	$-0.586473\pi$
$479$	−11.7456			−0.536669			−0.268335	+	0.963326i	$0.586473\pi$
$480$	−5.83646	+	20.9835i	−0.266397	+	0.957761i
$481$	−14.9966			−0.683784
$482$	−6.44587	−	20.9435i	−0.293601	−	0.953951i
$483$	−4.91948	−	7.31506i	−0.223844	−	0.332847i
$484$	9.49098	+	13.9582i	0.431408	+	0.634465i
$485$	−8.91891	+	8.91891i	−0.404987	+	0.404987i
$486$	2.57737	+	21.8942i	0.116912	+	0.993142i
$487$	−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	0.896355	−	0.443337i	$-0.146206\pi$
$491$	10.0382	+	10.0382i	0.453018	+	0.453018i	−0.443337	+	0.896355i	$0.646206\pi$
$492$	−13.1773	+	32.8380i	−0.594076	+	1.48045i
$493$	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
$498$	8.99519	−	0.949937i	0.403084	−	0.0425677i
$499$	−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
$501$	16.4008	+	24.3872i	0.732732	+	1.08954i
$502$	−11.4396	+	21.6121i	−0.510576	+	0.964596i
$503$			21.7131i			0.968138i	0.875030	+	0.484069i	$0.160842\pi$
$503$			21.7131i			0.968138i	−0.875030	+	0.484069i	$0.839158\pi$
$504$	−16.6652	+	9.30006i	−0.742329	+	0.414257i
$505$		−	32.4001i		−	1.44179i
$506$	4.52579	+	2.39558i	0.201196	+	0.106496i
$507$	7.84266	+	11.6617i	0.348305	+	0.517914i
$508$	−8.34998	−	12.2802i	−0.370470	−	0.544845i
$509$	16.1276	+	16.1276i	0.714842	+	0.714842i	0.967544	−	0.252702i	$-0.0813192\pi$
$509$	16.1276	+	16.1276i	0.714842	+	0.714842i	−0.252702	+	0.967544i	$0.581319\pi$
$510$	0.951545	+	9.01042i	0.0421351	+	0.398988i
$511$			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
$516$	−7.27290	−	17.0219i	−0.320171	−	0.749349i
$517$	−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	$-0.460233\pi$
$521$	5.68847			0.249216			0.124608	+	0.992206i	$0.460233\pi$
$522$	12.4667	+	14.8837i	0.545653	+	0.651443i
$523$	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
$525$	−0.127467	−	0.189538i	−0.00556311	−	0.00827211i
$526$	−13.8759	+	4.27062i	−0.605016	+	0.186208i
$527$	−2.17614			−0.0947941
$528$	5.98101	−	9.33405i	0.260290	−	0.406212i
$529$	17.8793			0.777361
$530$	−4.13419	+	1.27239i	−0.179578	+	0.0552692i
$531$	−15.1842	+	6.39619i	−0.658938	+	0.277571i
$532$	23.6121	+	4.49828i	1.02371	+	0.195025i
$533$	33.1876	−	33.1876i	1.43751	−	1.43751i
$534$	−14.0019	−	11.3270i	−0.605920	−	0.490167i
$535$	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
$540$	−23.0979	+	0.394357i	−0.993975	+	0.0169704i
$541$	−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
$546$	25.1749	−	2.65859i	1.07739	−	0.113777i
$547$	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
$549$	−6.90180	−	16.3845i	−0.294562	−	0.699273i
$550$	0.117266	+	0.0620710i	0.00500025	+	0.00264672i
$551$		−	24.4530i		−	1.04173i
$552$	−0.919477	+	11.0477i	−0.0391356	+	0.470221i
$553$		−	6.05520i		−	0.257493i
$554$	0.754180	−	1.42482i	0.0320421	−	0.0605348i
$555$	−10.4272	+	7.01244i	−0.442610	+	0.297662i
$556$	0.0146079	−	0.0766789i	0.000619513	−	0.00325191i
$557$	18.1602	+	18.1602i	0.769473	+	0.769473i	0.978014	−	0.208540i	$-0.0668713\pi$
$557$	18.1602	+	18.1602i	0.769473	+	0.769473i	−0.208540	+	0.978014i	$0.566871\pi$
$558$	0.488423	−	5.52687i	0.0206766	−	0.233971i
$559$			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	−0.837687	−	0.546150i	$-0.816093\pi$
$563$	−6.91748	+	6.91748i	−0.291537	+	0.291537i	0.546150	+	0.837687i	$0.316093\pi$
$564$	4.82824	−	12.0321i	0.203305	−	0.506641i
$565$	−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	$-0.775196\pi$
$569$	−36.2961			−1.52161			−0.760807	+	0.648979i	$0.775196\pi$
$570$	22.6207	+	18.2993i	0.947475	+	0.766474i
$571$	−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
$573$	−35.2701	+	23.7196i	−1.47343	+	0.990901i
$574$	−9.55691	−	31.0518i	−0.398898	−	1.29608i
$575$	−0.132681			−0.00553317
$576$	23.6698	+	3.96746i	0.986242	+	0.165311i
$577$	−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
$579$	−12.0457	+	8.10092i	−0.500603	+	0.336663i
$580$	−16.8241	+	11.4396i	−0.698583	+	0.475006i
$581$	−5.87279	+	5.87279i	−0.243644	+	0.243644i
$582$	10.8058	+	8.74148i	0.447913	+	0.362346i
$583$	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	$-0.917633\pi$
$587$	−29.6211	−	29.6211i	−1.22259	−	1.22259i	−0.255885	−	0.966707i	$-0.582367\pi$
$588$	−2.50453	+	6.24133i	−0.103285	+	0.257388i
$589$	−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	$0.146456\pi$
$593$			21.6263i			0.888086i	−0.896005	+	0.444043i	$0.853544\pi$
$594$	11.2955	+	3.26645i	0.463462	+	0.134024i
$595$	−5.88273	−	5.88273i	−0.241169	−	0.241169i
$596$	6.65315	−	34.9233i	0.272524	−	1.43052i
$597$	18.8270	−	12.6614i	0.770539	−	0.518198i
$598$	6.87930	−	12.9966i	0.281315	−	0.531469i
$599$			29.8079i			1.21792i	0.793201	+	0.608959i	$0.208413\pi$
$599$			29.8079i			1.21792i	−0.793201	+	0.608959i	$0.791587\pi$
$600$	−0.0238243	+	0.286253i	−0.000972621	+	0.0116862i
$601$		−	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
$603$	31.3872	−	13.2215i	1.27818	−	0.538422i
$604$	−27.8923	+	18.9655i	−1.13492	+	0.771696i
$605$	−13.2658	−	13.2658i	−0.539331	−	0.539331i
$606$	−35.5051	+	3.74951i	−1.44229	+	0.152313i
$607$			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
$612$	9.76378	−	2.08547i	0.394677	−	0.0842999i
$613$	−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	$-0.442542\pi$
$617$	8.91891			0.359062			0.179531	+	0.983752i	$0.442542\pi$
$618$	15.4861	+	12.5277i	0.622944	+	0.503939i
$619$	−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
$621$	−11.5114	+	2.39734i	−0.461936	+	0.0962018i
$622$	−12.8793	+	3.96391i	−0.516413	+	0.158938i
$623$	16.5367			0.662531
$624$	−26.8043	−	17.1754i	−1.07303	−	0.687568i
$625$	24.7034			0.988136
$626$	−34.0196	+	10.4703i	−1.35970	+	0.418479i
$627$	−8.26451	−	12.2890i	−0.330053	−	0.490774i
$628$	2.84053	−	14.9103i	0.113349	−	0.594987i
$629$	3.84014	−	3.84014i	0.153116	−	0.153116i
$630$	16.2611	−	13.6204i	0.647857	−	0.542649i
$631$	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
$636$	1.87276	+	4.38312i	0.0742597	+	0.173802i
$637$	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	$0.106546\pi$
$641$			16.6343i			0.657016i	−0.944501	+	0.328508i	$0.893454\pi$
$642$	−0.874526	−	8.28110i	−0.0345148	−	0.326829i
$643$	−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
$645$	11.4813	+	17.0722i	0.452075	+	0.672217i
$646$	−11.1138	−	5.88273i	−0.437268	−	0.231453i
$647$			48.2095i			1.89531i	0.319293	+	0.947656i	$0.396555\pi$
$647$			48.2095i			1.89531i	−0.319293	+	0.947656i	$0.603445\pi$
$648$	3.10516	+	25.2657i	0.121982	+	0.992532i
$649$			8.78801i			0.344960i
$650$	0.178247	−	0.336749i	0.00699143	−	0.0132084i
$651$	2.84306	+	4.22752i	0.111428	+	0.165689i
$652$	24.3810	+	4.64476i	0.954834	+	0.181903i
$653$	24.2281	+	24.2281i	0.948121	+	0.948121i	0.998719	−	0.0505983i	$-0.0161128\pi$
$653$	24.2281	+	24.2281i	0.948121	+	0.948121i	−0.0505983	+	0.998719i	$0.516113\pi$
$654$	−30.7404	+	3.24633i	−1.20204	+	0.126942i
$655$		−	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	−0.867138	−	0.498067i	$-0.834043\pi$
$659$	−9.47442	+	9.47442i	−0.369071	+	0.369071i	0.498067	+	0.867138i	$0.334043\pi$
$660$	−4.58872	+	11.4352i	−0.178616	+	0.445114i
$661$	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
$666$	8.89115	+	10.6149i	0.344525	+	0.411321i
$667$	−7.32238	+	7.32238i	−0.283524	+	0.283524i
$668$	19.0815	+	28.0629i	0.738286	+	1.08579i
$669$	−20.8506	−	31.0039i	−0.806130	−	1.19868i
$670$	10.4983	+	34.1104i	0.405584	+	1.31780i
$671$	−9.48269			−0.366075
$672$	−19.1883	+	10.8369i	−0.740204	+	0.418043i
$673$	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
$675$	−0.298267	+	0.0621166i	−0.0114803	+	0.00239087i
$676$	9.12457	+	13.4194i	0.350945	+	0.516129i
$677$	−5.59631	+	5.59631i	−0.215084	+	0.215084i	−0.806423	−	0.591339i	$-0.798599\pi$
$677$	−5.59631	+	5.59631i	−0.215084	+	0.215084i	0.591339	+	0.806423i	$0.298599\pi$
$678$	−24.4993	+	30.2848i	−0.940889	+	1.16308i
$679$	−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	0.225155	−	0.974323i	$-0.427711\pi$
$683$	−19.5790	−	19.5790i	−0.749168	−	0.749168i	−0.974323	+	0.225155i	$0.927711\pi$
$684$	17.4352	−	26.9061i	0.666651	−	1.02878i
$685$	−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
$690$	−1.29402	−	12.2534i	−0.0492624	−	0.466478i
$691$	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
$693$	−9.94988	+	4.19129i	−0.377965	+	0.159214i
$694$	−6.28973	+	11.8827i	−0.238755	+	0.451062i
$695$			0.0867582i			0.00329093i
$696$	14.4829	+	17.1125i	0.548973	+	0.648649i
$697$			16.9966i			0.643791i
$698$	−4.86254	−	2.57383i	−0.184050	−	0.0974207i
$699$	−0.720541	+	0.484574i	−0.0272534	+	0.0183283i
$700$	−0.148302	−	0.218105i	−0.00560528	−	0.00824360i
$701$	−15.2117	−	15.2117i	−0.574537	−	0.574537i	0.358856	−	0.933393i	$-0.383167\pi$
$701$	−15.2117	−	15.2117i	−0.574537	−	0.574537i	−0.933393	+	0.358856i	$0.883167\pi$
$702$	9.38016	−	32.4370i	0.354031	−	1.22426i
$703$		−	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
$708$	−17.4953	+	7.47513i	−0.657512	+	0.280932i
$709$	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
$714$	−5.76570	+	7.12727i	−0.215776	+	0.266731i
$715$	11.5569	−	11.5569i	0.432204	−	0.432204i
$716$	−0.708614	+	3.71961i	−0.0264822	+	0.139009i
$717$	43.7768	−	29.4405i	1.63488	−	1.09948i
$718$	36.9897	−	11.3845i	1.38044	−	0.424864i
$719$	3.52314			0.131391			0.0656954	−	0.997840i	$-0.479073\pi$
$719$	3.52314			0.131391			0.0656954	+	0.997840i	$0.479073\pi$
$720$	−26.6685	+	0.591559i	−0.993875	+	0.0220461i
$721$	−18.2897			−0.681145
$722$	−12.9129	+	3.97425i	−0.480569	+	0.147906i
$723$	22.2702	−	14.9770i	0.828236	−	0.557000i
$724$	−28.4672	−	5.42322i	−1.05798	−	0.201552i
$725$	−0.189728	+	0.189728i	−0.00704631	+	0.00704631i
$726$	−13.0019	+	16.0722i	−0.482545	+	0.596497i
$727$	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
$732$	−8.06602	−	18.8782i	−0.298129	−	0.697760i
$733$	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
$738$	−43.1672	−	3.81479i	−1.58901	−	0.140424i
$739$	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
$741$	−35.2898	+	23.7329i	−1.29640	+	0.871849i
$742$	−3.86813	−	2.04746i	−0.142003	−	0.0751647i
$743$		−	38.5942i		−	1.41588i	−0.706271	−	0.707941i	$-0.749624\pi$
$743$		−	38.5942i		−	1.41588i	0.706271	−	0.707941i	$-0.250376\pi$
$744$	0.531384	−	6.38468i	0.0194815	−	0.234074i
$745$			39.5139i			1.44768i
$746$	12.2868	−	23.2125i	0.449850	−	0.849870i
$747$	4.30055	+	10.2093i	0.157349	+	0.373537i
$748$	0.996562	−	5.23109i	0.0364379	−	0.191268i
$749$	5.40658	+	5.40658i	0.197552	+	0.197552i
$750$	−2.89273	−	27.3920i	−0.105628	−	1.00022i
$751$		−	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
$756$	−16.8075	−	16.2432i	−0.611282	−	0.590759i
$757$	−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	$-0.538699\pi$
$761$	−6.69113			−0.242553			−0.121277	+	0.992619i	$0.538699\pi$
$762$	11.4388	−	14.1401i	0.414384	−	0.512240i
$763$	20.0698	−	20.0698i	0.726576	−	0.726576i
$764$	−40.5860	+	27.5967i	−1.46835	+	0.998413i
$765$	−10.2265	+	4.30783i	−0.369741	+	0.155750i
$766$	11.0225	+	35.8138i	0.398261	+	1.29400i
$767$	25.2362			0.911227
$768$	27.3546	+	4.44160i	0.987073	+	0.160272i
$769$	−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
$771$	7.23499	+	10.7581i	0.260562	+	0.387445i
$772$	−13.8613	+	9.42504i	−0.498877	+	0.339215i
$773$	−10.6859	+	10.6859i	−0.384344	+	0.384344i	−0.872665	−	0.488320i	$-0.837610\pi$
$773$	−10.6859	+	10.6859i	−0.384344	+	0.384344i	0.488320	+	0.872665i	$0.337610\pi$
$774$	17.3796	−	14.5572i	0.624696	−	0.523249i
$775$	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
$780$	32.8380	+	13.1773i	1.17579	+	0.471821i
$781$	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
$786$	−13.3785	+	1.41284i	−0.477196	+	0.0503942i
$787$	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
$789$	−9.92281	−	14.7548i	−0.353262	−	0.525285i
$790$	3.95941	−	7.48024i	0.140870	−	0.266135i
$791$		−	35.7675i		−	1.27175i
$792$	13.0621	+	3.70512i	0.464140	+	0.131656i
$793$			27.2311i			0.967005i
$794$	8.28812	+	4.38704i	0.294134	+	0.155690i
$795$	−2.95641	−	4.39606i	−0.104853	−	0.155912i
$796$	21.6646	−	14.7310i	0.767882	−	0.522126i
$797$	−2.63695	−	2.63695i	−0.0934055	−	0.0934055i	0.658860	−	0.752266i	$-0.271039\pi$
$797$	−2.63695	−	2.63695i	−0.0934055	−	0.0934055i	−0.752266	+	0.658860i	$0.771039\pi$
$798$	3.09170	+	29.2761i	0.109445	+	1.03636i
$799$		−	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
$804$	36.1643	−	15.4518i	1.27542	−	0.544942i
$805$	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	$-0.462868\pi$
$809$	6.62090			0.232778			0.116389	+	0.993204i	$0.462868\pi$
$810$	−8.64556	−	26.9399i	−0.303774	−	0.946570i
$811$	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
$813$	27.7267	+	41.2284i	0.972417	+	1.44594i
$814$	7.05863	−	2.17246i	0.247405	−	0.0761447i
$815$	−27.5859			−0.966291
$816$	11.2618	−	2.46563i	0.394242	−	0.0863143i
$817$	−28.5535			−0.998960
$818$	−20.1115	+	6.18980i	−0.703183	+	0.216421i
$819$	12.0360	+	28.5727i	0.420571	+	0.998411i
$820$	8.49828	−	44.6087i	0.296773	−	1.55780i
$821$	7.91085	−	7.91085i	0.276090	−	0.276090i	−0.555456	−	0.831546i	$-0.687456\pi$
$821$	7.91085	−	7.91085i	0.276090	−	0.276090i	0.831546	+	0.555456i	$0.187456\pi$
$822$	5.19725	+	4.20439i	0.181275	+	0.146645i
$823$	−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	0.516829	−	0.856089i	$-0.327112\pi$
$827$	−9.75631	−	9.75631i	−0.339260	−	0.339260i	−0.856089	+	0.516829i	$0.827112\pi$
$828$	−13.2779	+	2.83605i	−0.461438	+	0.0985595i
$829$	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
$834$	0.0950724	−	0.0100401i	0.00329209	−	0.000347661i
$835$	−26.6707	−	26.6707i	−0.922979	−	0.922979i
$836$	−9.61537	−	14.1412i	−0.332554	−	0.489082i
$837$	6.65266	−	1.38547i	0.229949	−	0.0478888i
$838$	44.7259	+	23.6742i	1.54503	+	0.817811i
$839$			37.8109i			1.30538i	0.757626	+	0.652689i	$0.226359\pi$
$839$			37.8109i			1.30538i	−0.757626	+	0.652689i	$0.773641\pi$
$840$	18.6961	−	15.8232i	0.645078	−	0.545951i
$841$		−	8.05863i		−	0.277884i
$842$	−6.67290	+	12.6066i	−0.229963	+	0.434453i
$843$	−32.0837	+	21.5767i	−1.10502	+	0.743142i
$844$	23.5354	+	4.48367i	0.810123	+	0.154334i
$845$	−12.7536	−	12.7536i	−0.438739	−	0.438739i
$846$	15.8168	+	1.39776i	0.543792	+	0.0480561i
$847$		−	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
$852$	35.6696	+	14.3135i	1.22202	+	0.490374i
$853$	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	$-0.495683\pi$
$857$	0.794026			0.0271234			0.0135617	+	0.999908i	$0.495683\pi$
$858$	−14.0019	−	11.3270i	−0.478016	−	0.386698i
$859$	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
$861$	33.0187	−	22.2055i	1.12527	−	0.756762i
$862$	−6.44309	−	20.9345i	−0.219452	−	0.713032i
$863$	−21.4069			−0.728699			−0.364349	−	0.931262i	$-0.618709\pi$
$863$	−21.4069			−0.728699			−0.364349	+	0.931262i	$0.618709\pi$
$864$	3.73446	+	29.1557i	0.127049	+	0.991896i
$865$	−51.2794			−1.74355
$866$	10.6288	+	34.5346i	0.361182	+	1.17353i
$867$	−20.4538	+	13.7555i	−0.694648	+	0.467161i
$868$	3.30777	+	4.86469i	0.112273	+	0.165118i
$869$	−3.04612	+	3.04612i	−0.103332	+	0.103332i
$870$	−19.3722	−	15.6714i	−0.656778	−	0.531310i
$871$	−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
$876$	20.5144	+	8.23204i	0.693118	+	0.278135i
$877$	−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	$0.0583064\pi$
$881$			10.8132i			0.364305i	−0.983270	+	0.182152i	$0.941694\pi$
$882$	−8.20455	−	0.725055i	−0.276261	−	0.0244139i
$883$	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
$885$	17.5469	−	11.8005i	0.589833	−	0.396671i
$886$	13.9018	−	26.2637i	0.467041	−	0.882348i
$887$		−	12.0977i		−	0.406201i	−0.979158	−	0.203101i	$-0.934898\pi$
$887$		−	12.0977i		−	0.406201i	0.979158	−	0.203101i	$-0.0651018\pi$
$888$	10.3291	+	12.2045i	0.346621	+	0.409556i
$889$			16.7000i			0.560099i
$890$	20.4285	+	10.8132i	0.684766	+	0.362458i
$891$	0.172302	+	14.4000i	0.00577235	+	0.482417i
$892$	−24.2587	−	35.6769i	−0.812241	−	1.19455i
$893$	−14.1412	−	14.1412i	−0.473216	−	0.473216i
$894$	43.3006	−	4.57276i	1.44819	−	0.152936i
$895$		−	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
$900$	−0.344039	+	0.0734839i	−0.0114680	+	0.00244946i
$901$	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
$906$	−32.1167	−	25.9812i	−1.06701	−	0.863169i
$907$	−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
$909$	−16.9748	−	40.2972i	−0.563018	−	1.33657i
$910$	−31.0518	+	9.55691i	−1.02936	+	0.316809i
$911$	28.0629			0.929765			0.464882	−	0.885372i	$-0.346097\pi$
$911$	28.0629			0.929765			0.464882	+	0.885372i	$0.346097\pi$
$912$	19.9735	−	31.1709i	0.661388	−	1.03217i
$913$	5.90871			0.195550
$914$	32.2717	−	9.93237i	1.06745	−	0.328534i
$915$	12.7334	+	18.9340i	0.420952	+	0.625937i
$916$	−9.35342	−	1.78189i	−0.309046	−	0.0588755i
$917$	8.73458	−	8.73458i	0.288441	−	0.288441i
$918$	5.90412	+	10.7080i	0.194865	+	0.353418i
$919$	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
$924$	−11.4643	+	4.89829i	−0.377147	+	0.161142i
$925$	−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	$-0.748181\pi$
$929$		−	43.3502i		−	1.42227i	0.703054	−	0.711137i	$-0.251819\pi$
$930$	0.747838	+	7.08147i	0.0245226	+	0.232211i
$931$	7.33537	+	7.33537i	0.240407	+	0.240407i
$932$	−0.829141	+	0.563779i	−0.0271594	+	0.0184672i
$933$	−9.21016	−	13.6951i	−0.301527	−	0.448358i
$934$	28.7259	+	15.2051i	0.939941	+	0.497527i
$935$			5.91872i			0.193563i
$936$	10.6399	−	37.5099i	0.347775	−	1.22605i
$937$		−	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
$939$	−24.3279	−	36.1745i	−0.793910	−	1.18051i
$940$	−3.11383	+	16.3449i	−0.101562	+	0.533113i
$941$	−1.85373	−	1.85373i	−0.0604299	−	0.0604299i	0.676246	−	0.736676i	$-0.263606\pi$
$941$	−1.85373	−	1.85373i	−0.0604299	−	0.0604299i	−0.736676	+	0.676246i	$0.763606\pi$
$942$	18.4870	−	1.95232i	0.602338	−	0.0636099i
$943$		−	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	$0.504969\pi$
$947$	−31.2499	+	31.2499i	−1.01549	+	1.01549i	−0.999878	+	0.0156087i	$0.995031\pi$
$948$	−8.65528	−	3.47320i	−0.281110	−	0.112804i
$949$	−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	$-0.208686\pi$
$953$	48.9411			1.58536			0.792679	+	0.609639i	$0.208686\pi$
$954$	−4.47521	+	3.74846i	−0.144890	+	0.121361i
$955$	38.5726	−	38.5726i	1.24818	−	1.24818i
$956$	50.3749	−	34.2527i	1.62924	−	1.10781i
$957$	7.07766	+	10.5242i	0.228788	+	0.340199i
$958$	−4.88617	−	15.8759i	−0.157865	−	0.512926i
$959$	−6.13815			−0.198211
$960$	−30.7902	+	0.840321i	−0.993749	+	0.0271212i
$961$	29.2897			0.944830
$962$	−6.23858	−	20.2700i	−0.201140	−	0.653532i
$963$	9.39880	−	3.95915i	0.302872	−	0.127582i
$964$	25.6267	−	17.4250i	0.825381	−	0.561223i
$965$	13.1736	−	13.1736i	0.424074	−	0.424074i
$966$	7.84085	−	9.69245i	0.252275	−	0.311850i
$967$	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	0.708170	−	0.706041i	$-0.249521\pi$
$971$	0.0663404	+	0.0663404i	0.00212897	+	0.00212897i	−0.706041	+	0.708170i	$0.749521\pi$
$972$	−28.5210	+	12.5917i	−0.914812	+	0.403879i
$973$	−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	$-0.982549\pi$
$977$		−	3.42557i		−	0.109594i	0.998498	−	0.0547969i	$-0.0174511\pi$
$978$	3.19238	+	30.2295i	0.102081	+	0.966632i
$979$	−8.31894	−	8.31894i	−0.265875	−	0.265875i
$980$	1.61522	−	8.47852i	0.0515963	−	0.270836i
$981$	−14.6968	−	34.8893i	−0.469232	−	1.11393i
$982$	−9.39218	+	17.7440i	−0.299717	+	0.566233i
$983$		−	30.5911i		−	0.975706i	−0.872926	−	0.487853i	$-0.837780\pi$
$983$		−	30.5911i		−	0.975706i	0.872926	−	0.487853i	$-0.162220\pi$
$984$	−49.8671	−	4.15034i	−1.58970	−	0.132308i
$985$			4.05520i			0.129209i
$986$	9.51780	+	5.03793i	0.303109	+	0.160440i
$987$	−12.0983	+	8.13626i	−0.385092	+	0.258980i
$988$	−40.6087	+	27.6121i	−1.29193	+	0.878458i
$989$	8.55026	+	8.55026i	0.271882	+	0.271882i
$990$	−15.0321	−	1.32842i	−0.477752	−	0.0422201i
$991$			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
$996$	5.02598	+	11.7631i	0.159254	+	0.372729i
$997$	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.11.4	yes	12
3.2	odd	2	inner	48.2.k.a.11.3	✓	12
4.3	odd	2		192.2.k.a.143.5		12
8.3	odd	2		384.2.k.a.287.2		12
8.5	even	2		384.2.k.b.287.5		12
12.11	even	2		192.2.k.a.143.2		12
16.3	odd	4	inner	48.2.k.a.35.3	yes	12
16.5	even	4		384.2.k.a.95.5		12
16.11	odd	4		384.2.k.b.95.2		12
16.13	even	4		192.2.k.a.47.2		12
24.5	odd	2		384.2.k.b.287.2		12
24.11	even	2		384.2.k.a.287.5		12
48.5	odd	4		384.2.k.a.95.2		12
48.11	even	4		384.2.k.b.95.5		12
48.29	odd	4		192.2.k.a.47.5		12
48.35	even	4	inner	48.2.k.a.35.4	yes	12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.416001 + 1.35164i) q^{2} +(-1.43726 + 0.966579i) q^{3} +(-1.65389 + 1.12457i) q^{4} +(1.57184 - 1.57184i) q^{5} +(-1.90437 - 1.54057i) q^{6} +2.24914 q^{7} +(-2.20804 - 1.76765i) q^{8} +(1.13145 - 2.77846i) q^{9} +O(q^{10})\)	\(q+(0.416001 + 1.35164i) q^{2} +(-1.43726 + 0.966579i) q^{3} +(-1.65389 + 1.12457i) q^{4} +(1.57184 - 1.57184i) q^{5} +(-1.90437 - 1.54057i) 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} +(1.29008 - 3.21492i) 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} +(4.22617 + 0.373476i) q^{18} +(-3.77846 - 3.77846i) q^{19} +(-0.832001 + 4.36729i) q^{20} +(-3.23261 + 2.17397i) q^{21} +(1.05863 - 2.00000i) q^{22} +2.26290i q^{23} +(4.88210 + 0.406327i) q^{24} +0.0586332i q^{25} +(-5.74333 - 3.04004i) q^{26} +(1.05941 + 5.08701i) q^{27} +(-3.71982 + 2.52932i) q^{28} +(3.23584 + 3.23584i) q^{29} +(-5.41491 + 0.571841i) 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} +(1.25328 + 5.86765i) 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} +(-4.28321 - 3.46496i) q^{42} +(3.77846 - 3.77846i) q^{43} +(3.14368 + 0.598895i) q^{44} +(-2.58884 - 6.14575i) q^{45} +(-3.05863 + 0.941367i) q^{46} +3.74258 q^{47} +(1.48175 + 6.76790i) q^{48} -1.94137 q^{49} +(-0.0792512 + 0.0243914i) q^{50} +(1.60839 + 2.39161i) q^{51} +(1.71982 - 9.02760i) q^{52} +(-0.972946 + 0.972946i) q^{53} +(-6.43511 + 3.54815i) 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} +(-3.02553 - 7.08114i) 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} +(0.411625 + 3.89778i) q^{66} +(8.02760 + 8.02760i) q^{67} +(1.87129 + 2.75207i) q^{68} +(-2.18727 - 3.25238i) q^{69} +(6.24914 + 3.30777i) q^{70} +11.0950i q^{71} +(-7.40961 + 4.13494i) q^{72} +6.38101i q^{73} +(-2.15925 + 4.07933i) q^{74} +(-0.0566736 - 0.0842713i) q^{75} +(10.4983 + 2.00000i) q^{76} +(-2.54479 - 2.54479i) q^{77} +(11.1931 - 1.18205i) 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} +(2.90158 - 7.23080i) 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} +(7.22991 - 6.05582i) q^{90} +(-7.30777 + 7.30777i) q^{91} +(-2.54479 - 3.74258i) q^{92} +(1.26407 + 1.87961i) q^{93} +(1.55691 + 5.05863i) q^{94} -11.8783 q^{95} +(-8.53138 + 4.81824i) q^{96} -5.67418 q^{97} +(-0.807610 - 2.62404i) q^{98} +(-4.42386 + 1.86351i) 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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