LMFDB - Embedded newform 462.2.u.a.139.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, degree $4$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.4
Character	$\chi$	$=$	462.139
Dual form			462.2.u.a.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.12216 + 1.54452i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.488107 - 2.60034i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.12216 + 1.54452i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.488107 - 2.60034i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} -1.90913 q^{10} +(-0.215110 - 3.30964i) q^{11} +1.00000i q^{12} +(-2.19973 - 1.59820i) q^{13} +(1.81681 + 1.92333i) q^{14} +(-0.589954 - 1.81569i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.34007 + 2.42671i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(1.23236 - 3.79280i) q^{19} +(1.12216 - 1.54452i) q^{20} +(-1.26777 + 2.32223i) q^{21} +(2.80399 + 1.77133i) q^{22} +6.88157 q^{23} +(-0.809017 - 0.587785i) q^{24} +(0.418787 - 1.28889i) q^{25} +(2.58594 - 0.840221i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-2.62390 + 0.339331i) q^{28} +(6.78796 - 2.20554i) q^{29} +(1.81569 + 0.589954i) q^{30} +(1.61579 - 2.22395i) q^{31} -1.00000i q^{32} +(-0.818154 + 3.21413i) q^{33} -4.12856i q^{34} +(4.56400 - 2.16410i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.321233 + 0.988653i) q^{37} +(2.34408 + 3.22635i) q^{38} +(1.59820 + 2.19973i) q^{39} +(0.589954 + 1.81569i) q^{40} +(2.51353 - 7.73587i) q^{41} +(-1.13355 - 2.39062i) q^{42} -1.21706i q^{43} +(-3.08118 + 1.22732i) q^{44} +1.90913i q^{45} +(-4.04489 + 5.56731i) q^{46} +(7.21926 + 2.34568i) q^{47} +(0.951057 - 0.309017i) q^{48} +(-6.52350 - 2.53848i) q^{49} +(0.796579 + 1.09640i) q^{50} +(3.92649 - 1.27579i) q^{51} +(-0.840221 + 2.58594i) q^{52} +(-3.96828 - 2.88312i) q^{53} +1.00000 q^{54} +(4.87042 - 4.04618i) q^{55} +(1.26777 - 2.32223i) q^{56} +(-2.34408 + 3.22635i) q^{57} +(-2.20554 + 6.78796i) q^{58} +(3.13164 - 1.01753i) q^{59} +(-1.54452 + 1.12216i) q^{60} +(-6.21098 + 4.51254i) q^{61} +(0.849472 + 2.61440i) q^{62} +(1.92333 - 1.81681i) q^{63} +(0.809017 + 0.587785i) q^{64} -5.19095i q^{65} +(-2.11939 - 2.55112i) q^{66} +1.75788 q^{67} +(3.34007 + 2.42671i) q^{68} +(-6.54476 - 2.12652i) q^{69} +(-0.931859 + 4.96438i) q^{70} +(-10.1359 + 7.36420i) q^{71} +(0.587785 + 0.809017i) q^{72} +(2.13629 + 6.57482i) q^{73} +(-0.988653 - 0.321233i) q^{74} +(-0.796579 + 1.09640i) q^{75} -3.98799 q^{76} +(-8.71118 - 1.05610i) q^{77} -2.71901 q^{78} +(-1.00449 + 1.38256i) q^{79} +(-1.81569 - 0.589954i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.78103 + 6.58052i) q^{82} +(1.15480 - 0.839010i) q^{83} +(2.60034 + 0.488107i) q^{84} +(-7.49618 - 2.43566i) q^{85} +(0.984619 + 0.715368i) q^{86} -7.13729 q^{87} +(0.818154 - 3.21413i) q^{88} +7.07430i q^{89} +(-1.54452 - 1.12216i) q^{90} +(-5.22955 + 4.93994i) q^{91} +(-2.12652 - 6.54476i) q^{92} +(-2.22395 + 1.61579i) q^{93} +(-6.14107 + 4.46175i) q^{94} +(7.24095 - 2.35273i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(3.78817 - 5.21398i) q^{97} +(5.88810 - 3.78554i) q^{98} +(1.77133 - 2.80399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.12216	+	1.54452i	0.501845	+	0.690730i	0.982518	−	0.186170i	$-0.0596076\pi$
$5$	1.12216	+	1.54452i	0.501845	+	0.690730i	−0.480673	+	0.876900i	$0.659608\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	0.488107	−	2.60034i	0.184487	−	0.982835i
$7$	0.488107	−	2.60034i	0.184487	−	0.982835i
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−1.90913			−0.603720
$11$	−0.215110	−	3.30964i	−0.0648581	−	0.997894i
$11$	−0.215110	−	3.30964i	−0.0648581	−	0.997894i
$12$			1.00000i			0.288675i
$13$	−2.19973	−	1.59820i	−0.610095	−	0.443260i	0.239353	−	0.970933i	$-0.423065\pi$
$13$	−2.19973	−	1.59820i	−0.610095	−	0.443260i	−0.849448	+	0.527673i	$0.823065\pi$
$14$	1.81681	+	1.92333i	0.485564	+	0.514031i
$15$	−0.589954	−	1.81569i	−0.152325	−	0.468809i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.34007	+	2.42671i	−0.810087	+	0.588563i	−0.913856	−	0.406039i	$-0.866910\pi$
$17$	−3.34007	+	2.42671i	−0.810087	+	0.588563i	0.103769	+	0.994601i	$0.466910\pi$
$18$	−0.951057	+	0.309017i	−0.224166	+	0.0728360i
$19$	1.23236	−	3.79280i	0.282722	−	0.870128i	−0.704350	−	0.709852i	$-0.748762\pi$
$19$	1.23236	−	3.79280i	0.282722	−	0.870128i	0.987072	−	0.160276i	$-0.0512384\pi$
$20$	1.12216	−	1.54452i	0.250922	−	0.345365i
$21$	−1.26777	+	2.32223i	−0.276649	+	0.506753i
$22$	2.80399	+	1.77133i	0.597814	+	0.377649i
$23$	6.88157			1.43491			0.717453	−	0.696607i	$-0.245308\pi$
$23$	6.88157			1.43491			0.717453	+	0.696607i	$0.245308\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	0.418787	−	1.28889i	0.0837573	−	0.257778i
$26$	2.58594	−	0.840221i	0.507144	−	0.164781i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−2.62390	+	0.339331i	−0.495871	+	0.0641276i
$29$	6.78796	−	2.20554i	1.26049	−	0.409559i	0.398823	−	0.917028i	$-0.369419\pi$
$29$	6.78796	−	2.20554i	1.26049	−	0.409559i	0.861670	+	0.507469i	$0.169419\pi$
$30$	1.81569	+	0.589954i	0.331498	+	0.107710i
$31$	1.61579	−	2.22395i	0.290205	−	0.399432i	−0.638876	−	0.769310i	$-0.720600\pi$
$31$	1.61579	−	2.22395i	0.290205	−	0.399432i	0.929081	+	0.369877i	$0.120600\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.818154	+	3.21413i	−0.142422	+	0.559508i
$34$		−	4.12856i		−	0.708042i
$35$	4.56400	−	2.16410i	0.771457	−	0.365800i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	0.321233	+	0.988653i	0.0528104	+	0.162534i	0.973983	−	0.226620i	$-0.0727675\pi$
$37$	0.321233	+	0.988653i	0.0528104	+	0.162534i	−0.921173	+	0.389154i	$0.872768\pi$
$38$	2.34408	+	3.22635i	0.380260	+	0.523383i
$39$	1.59820	+	2.19973i	0.255916	+	0.352238i
$40$	0.589954	+	1.81569i	0.0932799	+	0.287086i
$41$	2.51353	−	7.73587i	0.392548	−	1.20814i	−0.538306	−	0.842749i	$-0.680936\pi$
$41$	2.51353	−	7.73587i	0.392548	−	1.20814i	0.930855	−	0.365390i	$-0.119064\pi$
$42$	−1.13355	−	2.39062i	−0.174911	−	0.368880i
$43$		−	1.21706i		−	0.185599i	−0.995685	−	0.0927997i	$-0.970418\pi$
$43$		−	1.21706i		−	0.185599i	0.995685	−	0.0927997i	$-0.0295816\pi$
$44$	−3.08118	+	1.22732i	−0.464506	+	0.185025i
$45$			1.90913i			0.284596i
$46$	−4.04489	+	5.56731i	−0.596386	+	0.820855i
$47$	7.21926	+	2.34568i	1.05304	+	0.342152i	0.783859	−	0.620938i	$-0.213248\pi$
$47$	7.21926	+	2.34568i	1.05304	+	0.342152i	0.269177	+	0.963091i	$0.413248\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	−6.52350	−	2.53848i	−0.931929	−	0.362641i
$50$	0.796579	+	1.09640i	0.112653	+	0.155054i
$51$	3.92649	−	1.27579i	0.549819	−	0.178647i
$52$	−0.840221	+	2.58594i	−0.116518	+	0.358605i
$53$	−3.96828	−	2.88312i	−0.545085	−	0.396027i	0.280885	−	0.959741i	$-0.409372\pi$
$53$	−3.96828	−	2.88312i	−0.545085	−	0.396027i	−0.825970	+	0.563714i	$0.809372\pi$
$54$	1.00000			0.136083
$55$	4.87042	−	4.04618i	0.656727	−	0.545587i
$56$	1.26777	−	2.32223i	0.169412	−	0.310322i
$57$	−2.34408	+	3.22635i	−0.310481	+	0.427340i
$58$	−2.20554	+	6.78796i	−0.289602	+	0.891303i
$59$	3.13164	−	1.01753i	0.407705	−	0.132471i	−0.0979824	−	0.995188i	$-0.531239\pi$
$59$	3.13164	−	1.01753i	0.407705	−	0.132471i	0.505687	+	0.862717i	$0.331239\pi$
$60$	−1.54452	+	1.12216i	−0.199397	+	0.144870i
$61$	−6.21098	+	4.51254i	−0.795234	+	0.577771i	−0.909512	−	0.415677i	$-0.863545\pi$
$61$	−6.21098	+	4.51254i	−0.795234	+	0.577771i	0.114278	+	0.993449i	$0.463545\pi$
$62$	0.849472	+	2.61440i	0.107883	+	0.332030i
$63$	1.92333	−	1.81681i	0.242316	−	0.228897i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$		−	5.19095i		−	0.643858i
$66$	−2.11939	−	2.55112i	−0.260878	−	0.314021i
$67$	1.75788			0.214759			0.107379	−	0.994218i	$-0.465754\pi$
$67$	1.75788			0.214759			0.107379	+	0.994218i	$0.465754\pi$
$68$	3.34007	+	2.42671i	0.405043	+	0.294281i
$69$	−6.54476	−	2.12652i	−0.787897	−	0.256003i
$70$	−0.931859	+	4.96438i	−0.111378	+	0.593357i
$71$	−10.1359	+	7.36420i	−1.20292	+	0.873969i	−0.994568	−	0.104086i	$-0.966808\pi$
$71$	−10.1359	+	7.36420i	−1.20292	+	0.873969i	−0.208347	+	0.978055i	$0.566808\pi$
$72$	0.587785	+	0.809017i	0.0692712	+	0.0953436i
$73$	2.13629	+	6.57482i	0.250033	+	0.769524i	0.994768	+	0.102163i	$0.0325763\pi$
$73$	2.13629	+	6.57482i	0.250033	+	0.769524i	−0.744734	+	0.667361i	$0.767424\pi$
$74$	−0.988653	−	0.321233i	−0.114929	−	0.0373426i
$75$	−0.796579	+	1.09640i	−0.0919811	+	0.126601i
$76$	−3.98799			−0.457454
$77$	−8.71118	−	1.05610i	−0.992731	−	0.120354i
$78$	−2.71901			−0.307868
$79$	−1.00449	+	1.38256i	−0.113014	+	0.155551i	−0.861777	−	0.507287i	$-0.830648\pi$
$79$	−1.00449	+	1.38256i	−0.113014	+	0.155551i	0.748763	+	0.662838i	$0.230648\pi$
$80$	−1.81569	−	0.589954i	−0.203000	−	0.0659588i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	4.78103	+	6.58052i	0.527976	+	0.726697i
$83$	1.15480	−	0.839010i	0.126756	−	0.0920933i	−0.522601	−	0.852577i	$-0.675038\pi$
$83$	1.15480	−	0.839010i	0.126756	−	0.0920933i	0.649357	+	0.760484i	$0.275038\pi$
$84$	2.60034	+	0.488107i	0.283720	+	0.0532568i
$85$	−7.49618	−	2.43566i	−0.813075	−	0.264184i
$86$	0.984619	+	0.715368i	0.106174	+	0.0771401i
$87$	−7.13729			−0.765197
$88$	0.818154	−	3.21413i	0.0872155	−	0.342627i
$89$			7.07430i			0.749874i	0.927050	+	0.374937i	$0.122336\pi$
$89$			7.07430i			0.749874i	−0.927050	+	0.374937i	$0.877664\pi$
$90$	−1.54452	−	1.12216i	−0.162807	−	0.118286i
$91$	−5.22955	+	4.93994i	−0.548206	+	0.517847i
$92$	−2.12652	−	6.54476i	−0.221705	−	0.682339i
$93$	−2.22395	+	1.61579i	−0.230612	+	0.167550i
$94$	−6.14107	+	4.46175i	−0.633403	+	0.460194i
$95$	7.24095	−	2.35273i	0.742906	−	0.241385i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	3.78817	−	5.21398i	0.384631	−	0.529399i	−0.572173	−	0.820133i	$-0.693899\pi$
$97$	3.78817	−	5.21398i	0.384631	−	0.529399i	0.956804	+	0.290734i	$0.0938994\pi$
$98$	5.88810	−	3.78554i	0.594787	−	0.382397i
$99$	1.77133	−	2.80399i	0.178025	−	0.281812i
$100$	−1.35522			−0.135522
$101$	8.75254	+	6.35909i	0.870910	+	0.632753i	0.930831	−	0.365450i	$-0.119085\pi$
$101$	8.75254	+	6.35909i	0.870910	+	0.632753i	−0.0599210	+	0.998203i	$0.519085\pi$
$102$	−1.27579	+	3.92649i	−0.126322	+	0.388781i
$103$	−10.3277	+	3.35566i	−1.01761	+	0.330643i	−0.769883	−	0.638186i	$-0.779685\pi$
$103$	−10.3277	+	3.35566i	−1.01761	+	0.330643i	−0.247732	+	0.968829i	$0.579685\pi$
$104$	−1.59820	−	2.19973i	−0.156716	−	0.215701i
$105$	−5.00937	+	0.647827i	−0.488864	+	0.0632215i
$106$	4.66499	−	1.51575i	0.453104	−	0.147222i
$107$	−9.02140	−	2.93123i	−0.872132	−	0.283373i	−0.161445	−	0.986882i	$-0.551616\pi$
$107$	−9.02140	−	2.93123i	−0.872132	−	0.283373i	−0.710686	+	0.703509i	$0.751616\pi$
$108$	−0.587785	+	0.809017i	−0.0565597	+	0.0778477i
$109$		−	18.9852i		−	1.81846i	−0.416298	−	0.909228i	$-0.636673\pi$
$109$		−	18.9852i		−	1.81846i	0.416298	−	0.909228i	$-0.363327\pi$
$110$	0.410673	+	6.31854i	0.0391562	+	0.602449i
$111$		−	1.03953i		−	0.0986680i
$112$	1.13355	+	2.39062i	0.107111	+	0.225892i
$113$	−3.93992	+	12.1258i	−0.370636	+	1.14070i	0.575740	+	0.817633i	$0.304714\pi$
$113$	−3.93992	+	12.1258i	−0.370636	+	1.14070i	−0.946376	+	0.323068i	$0.895286\pi$
$114$	−1.23236	−	3.79280i	−0.115421	−	0.355228i
$115$	7.72221	+	10.6287i	0.720100	+	0.991133i
$116$	−4.19519	−	5.77419i	−0.389514	−	0.536120i
$117$	−0.840221	−	2.58594i	−0.0776785	−	0.239070i
$118$	−1.01753	+	3.13164i	−0.0936714	+	0.288291i
$119$	4.67994	+	9.86981i	0.429009	+	0.904764i
$120$		−	1.90913i		−	0.174279i
$121$	−10.9075	+	1.42387i	−0.991587	+	0.129443i
$122$		−	7.67719i		−	0.695060i
$123$	−4.78103	+	6.58052i	−0.431091	+	0.593345i
$124$	−2.61440	−	0.849472i	−0.234780	−	0.0762848i
$125$	11.5391	−	3.74929i	1.03209	−	0.335346i
$126$	0.339331	+	2.62390i	0.0302300	+	0.233756i
$127$	−7.38628	−	10.1663i	−0.655426	−	0.902117i	0.343893	−	0.939009i	$-0.388254\pi$
$127$	−7.38628	−	10.1663i	−0.655426	−	0.902117i	−0.999319	+	0.0368922i	$0.988254\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−0.376091	+	1.15749i	−0.0331130	+	0.101911i
$130$	4.19957	+	3.05116i	0.368326	+	0.267605i
$131$	0.710341			0.0620628			0.0310314	−	0.999518i	$-0.490121\pi$
$131$	0.710341			0.0620628			0.0310314	+	0.999518i	$0.490121\pi$
$132$	3.30964	−	0.215110i	0.288067	−	0.0187229i
$133$	−9.26104	−	5.05583i	−0.803034	−	0.438396i
$134$	−1.03325	+	1.42215i	−0.0892596	+	0.122855i
$135$	0.589954	−	1.81569i	0.0507751	−	0.156270i
$136$	−3.92649	+	1.27579i	−0.336694	+	0.109398i
$137$	−14.7546	+	10.7198i	−1.26057	+	0.915858i	−0.998786	−	0.0492679i	$-0.984311\pi$
$137$	−14.7546	+	10.7198i	−1.26057	+	0.915858i	−0.261785	+	0.965126i	$0.584311\pi$
$138$	5.56731	−	4.04489i	0.473921	−	0.344324i
$139$	−6.36306	−	19.5835i	−0.539708	−	1.66105i	−0.733251	−	0.679958i	$-0.761998\pi$
$139$	−6.36306	−	19.5835i	−0.539708	−	1.66105i	0.193544	−	0.981092i	$-0.438002\pi$
$140$	−3.46854	−	3.67188i	−0.293145	−	0.310331i
$141$	−6.14107	−	4.46175i	−0.517171	−	0.375747i
$142$		−	12.5287i		−	1.05139i
$143$	−4.81627	+	7.62410i	−0.402757	+	0.637559i
$144$	−1.00000			−0.0833333
$145$	11.0237	+	8.00917i	0.915466	+	0.665125i
$146$	−6.57482	−	2.13629i	−0.544136	−	0.176800i
$147$	5.41979	+	4.43012i	0.447016	+	0.365390i
$148$	0.840999	−	0.611021i	0.0691297	−	0.0502257i
$149$	−11.0994	−	15.2771i	−0.909301	−	1.25155i	−0.967405	−	0.253236i	$-0.918505\pi$
$149$	−11.0994	−	15.2771i	−0.909301	−	1.25155i	0.0581031	−	0.998311i	$-0.481495\pi$
$150$	−0.418787	−	1.28889i	−0.0341938	−	0.105238i
$151$	15.5959	+	5.06741i	1.26918	+	0.412380i	0.864755	−	0.502193i	$-0.167473\pi$
$151$	15.5959	+	5.06741i	1.26918	+	0.412380i	0.404420	+	0.914573i	$0.367473\pi$
$152$	2.34408	−	3.22635i	0.190130	−	0.261692i
$153$	−4.12856			−0.333774
$154$	5.97471	−	6.42673i	0.481455	−	0.517881i
$155$	5.24810			0.421537
$156$	1.59820	−	2.19973i	0.127958	−	0.176119i
$157$	12.6177	+	4.09974i	1.00700	+	0.327195i	0.765661	−	0.643245i	$-0.222412\pi$
$157$	12.6177	+	4.09974i	1.00700	+	0.327195i	0.241343	+	0.970440i	$0.422412\pi$
$158$	−0.528092	−	1.62530i	−0.0420128	−	0.129302i
$159$	2.88312	+	3.96828i	0.228646	+	0.314705i
$160$	1.54452	−	1.12216i	0.122105	−	0.0887144i
$161$	3.35894	−	17.8944i	0.264722	−	1.41028i
$162$	−0.951057	−	0.309017i	−0.0747221	−	0.0242787i
$163$	11.8632	+	8.61911i	0.929196	+	0.675101i	0.945796	−	0.324762i	$-0.105284\pi$
$163$	11.8632	+	8.61911i	0.929196	+	0.675101i	−0.0165995	+	0.999862i	$0.505284\pi$
$164$	−8.13397			−0.635156
$165$	−5.88238	+	2.34311i	−0.457943	+	0.182411i
$166$			1.42741i			0.110788i
$167$	−0.813770	−	0.591239i	−0.0629714	−	0.0457514i	0.555854	−	0.831280i	$-0.312391\pi$
$167$	−0.813770	−	0.591239i	−0.0629714	−	0.0457514i	−0.618826	+	0.785528i	$0.712391\pi$
$168$	−1.92333	+	1.81681i	−0.148388	+	0.140170i
$169$	−1.73265	−	5.33254i	−0.133281	−	0.410195i
$170$	6.37664	−	4.63290i	0.489066	−	0.355327i
$171$	3.22635	−	2.34408i	0.246725	−	0.179256i
$172$	−1.15749	+	0.376091i	−0.0882577	+	0.0286767i
$173$	−5.63370	+	17.3388i	−0.428322	+	1.31824i	0.471454	+	0.881890i	$0.343729\pi$
$173$	−5.63370	+	17.3388i	−0.428322	+	1.31824i	−0.899777	+	0.436350i	$0.856271\pi$
$174$	4.19519	−	5.77419i	0.318037	−	0.437740i
$175$	−3.14714	−	1.71810i	−0.237902	−	0.129876i
$176$	2.11939	+	2.55112i	0.159755	+	0.192298i
$177$	−3.29280			−0.247502
$178$	−5.72323	−	4.15817i	−0.428974	−	0.311668i
$179$	1.25932	−	3.87579i	0.0941259	−	0.289690i	−0.892899	−	0.450257i	$-0.851332\pi$
$179$	1.25932	−	3.87579i	0.0941259	−	0.289690i	0.987025	+	0.160567i	$0.0513323\pi$
$180$	1.81569	−	0.589954i	0.135334	−	0.0439726i
$181$	9.68475	+	13.3299i	0.719862	+	0.990805i	0.999528	+	0.0307077i	$0.00977610\pi$
$181$	9.68475	+	13.3299i	0.719862	+	0.990805i	−0.279667	+	0.960097i	$0.590224\pi$
$182$	−0.922646	−	7.13442i	−0.0683911	−	0.528839i
$183$	7.30144	−	2.37238i	0.539738	−	0.175372i
$184$	6.54476	+	2.12652i	0.482486	+	0.156769i
$185$	−1.16652	+	1.60558i	−0.0857642	+	0.118044i
$186$		−	2.74895i		−	0.201563i
$187$	8.75001	+	10.5324i	0.639864	+	0.770208i
$188$		−	7.59077i		−	0.553614i
$189$	−2.39062	+	1.13355i	−0.173892	+	0.0824539i
$190$	−2.35273	+	7.24095i	−0.170685	+	0.525314i
$191$	8.03783	+	24.7379i	0.581597	+	1.78997i	0.612528	+	0.790449i	$0.290153\pi$
$191$	8.03783	+	24.7379i	0.581597	+	1.78997i	−0.0309311	+	0.999522i	$0.509847\pi$
$192$	−0.587785	−	0.809017i	−0.0424197	−	0.0583858i
$193$	13.2069	+	18.1777i	0.950654	+	1.30846i	0.951236	+	0.308463i	$0.0998145\pi$
$193$	13.2069	+	18.1777i	0.950654	+	1.30846i	−0.000582623		1.00000i	$0.500185\pi$
$194$	1.99156	+	6.12940i	0.142986	+	0.440065i
$195$	−1.60409	+	4.93689i	−0.114871	+	0.353538i
$196$	−0.398368	+	6.98866i	−0.0284549	+	0.499190i
$197$			18.1214i			1.29109i	0.763720	+	0.645547i	$0.223371\pi$
$197$			18.1214i			1.29109i	−0.763720	+	0.645547i	$0.776629\pi$
$198$	1.22732	+	3.08118i	0.0872216	+	0.218970i
$199$		−	0.713487i		−	0.0505778i	−0.999680	−	0.0252889i	$-0.991949\pi$
$199$		−	0.713487i		−	0.0505778i	0.999680	−	0.0252889i	$-0.00805056\pi$
$200$	0.796579	−	1.09640i	0.0563267	−	0.0775270i
$201$	−1.67184	−	0.543214i	−0.117923	−	0.0383154i
$202$	−10.2892	+	3.34317i	−0.723947	+	0.235225i
$203$	−2.42190	−	18.7275i	−0.169984	−	1.31441i
$204$	−2.42671	−	3.34007i	−0.169903	−	0.233852i
$205$	14.7688	−	4.79867i	1.03150	−	0.335153i
$206$	3.35566	−	10.3277i	0.233800	−	0.719562i
$207$	5.56731	+	4.04489i	0.386955	+	0.281139i
$208$	2.71901			0.188530
$209$	−12.8179	−	3.26279i	−0.886633	−	0.225692i
$210$	2.42033	−	4.43345i	0.167019	−	0.305937i
$211$	−1.62246	+	2.23313i	−0.111695	+	0.153735i	−0.861204	−	0.508259i	$-0.830289\pi$
$211$	−1.62246	+	2.23313i	−0.111695	+	0.153735i	0.749510	+	0.661994i	$0.230289\pi$
$212$	−1.51575	+	4.66499i	−0.104102	+	0.320393i
$213$	11.9155	−	3.87159i	0.816438	−	0.265277i
$214$	7.67406	−	5.57553i	0.524588	−	0.381136i
$215$	1.87977	−	1.36573i	0.128199	−	0.0931420i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	−4.99433	−	5.28712i	−0.339037	−	0.358913i
$218$	15.3594	+	11.1592i	1.04027	+	0.755800i
$219$		−	6.91317i		−	0.467149i
$220$	−5.35319	−	3.38170i	−0.360912	−	0.227994i
$221$	11.2256			0.755116
$222$	0.840999	+	0.611021i	0.0564441	+	0.0410091i
$223$	3.49261	+	1.13482i	0.233883	+	0.0759931i	0.423613	−	0.905843i	$-0.360762\pi$
$223$	3.49261	+	1.13482i	0.233883	+	0.0759931i	−0.189731	+	0.981836i	$0.560762\pi$
$224$	−2.60034	−	0.488107i	−0.173742	−	0.0326130i
$225$	1.09640	−	0.796579i	0.0730932	−	0.0531053i
$226$	−7.49417	−	10.3148i	−0.498505	−	0.686133i
$227$	0.199367	+	0.613587i	0.0132324	+	0.0407252i	0.957455	−	0.288584i	$-0.0931843\pi$
$227$	0.199367	+	0.613587i	0.0132324	+	0.0407252i	−0.944222	+	0.329309i	$0.893184\pi$
$228$	3.79280	+	1.23236i	0.251184	+	0.0816148i
$229$	1.63099	−	2.24486i	0.107779	−	0.148345i	−0.751720	−	0.659482i	$-0.770776\pi$
$229$	1.63099	−	2.24486i	0.107779	−	0.148345i	0.859499	+	0.511137i	$0.170776\pi$
$230$	−13.1378			−0.866282
$231$	7.95847	+	3.69631i	0.523629	+	0.243200i
$232$	7.13729			0.468586
$233$	−8.21976	+	11.3135i	−0.538495	+	0.741174i	−0.988395	−	0.151904i	$-0.951459\pi$
$233$	−8.21976	+	11.3135i	−0.538495	+	0.741174i	0.449901	+	0.893079i	$0.351459\pi$
$234$	2.58594	+	0.840221i	0.169048	+	0.0549270i
$235$	4.47821	+	13.7825i	0.292126	+	0.899071i
$236$	−1.93546	−	2.66393i	−0.125988	−	0.173407i
$237$	1.38256	−	1.00449i	0.0898072	−	0.0652487i
$238$	−10.7356	−	2.01518i	−0.695888	−	0.130625i
$239$	3.05379	+	0.992237i	0.197533	+	0.0641824i	0.406113	−	0.913823i	$-0.366884\pi$
$239$	3.05379	+	0.992237i	0.197533	+	0.0641824i	−0.208580	+	0.978005i	$0.566884\pi$
$240$	1.54452	+	1.12216i	0.0996983	+	0.0724350i
$241$	24.4115			1.57248			0.786242	−	0.617919i	$-0.212024\pi$
$241$	24.4115			1.57248			0.786242	+	0.617919i	$0.212024\pi$
$242$	5.25930	−	9.66125i	0.338081	−	0.621049i
$243$		−	1.00000i		−	0.0641500i
$244$	6.21098	+	4.51254i	0.397617	+	0.288886i
$245$	−3.39967	−	12.9243i	−0.217197	−	0.825700i
$246$	−2.51353	−	7.73587i	−0.160257	−	0.493221i
$247$	−8.77249	+	6.37359i	−0.558180	+	0.405542i
$248$	2.22395	−	1.61579i	0.141221	−	0.102603i
$249$	−1.35755	+	0.441094i	−0.0860310	+	0.0279532i
$250$	−3.74929	+	11.5391i	−0.237126	+	0.729798i
$251$	3.43611	−	4.72940i	0.216885	−	0.298517i	−0.686686	−	0.726954i	$-0.740935\pi$
$251$	3.43611	−	4.72940i	0.216885	−	0.298517i	0.903572	+	0.428437i	$0.140935\pi$
$252$	−2.32223	−	1.26777i	−0.146287	−	0.0798617i
$253$	−1.48030	−	22.7755i	−0.0930654	−	1.43189i
$254$	12.5663			0.788479
$255$	6.37664	+	4.63290i	0.399320	+	0.290123i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−17.5661	+	5.70759i	−1.09575	+	0.356030i	−0.800464	−	0.599381i	$-0.795414\pi$
$257$	−17.5661	+	5.70759i	−1.09575	+	0.356030i	−0.295282	+	0.955410i	$0.595414\pi$
$258$	−0.715368	−	0.984619i	−0.0445368	−	0.0612997i
$259$	2.72763	−	0.352746i	0.169487	−	0.0219185i
$260$	−4.93689	+	1.60409i	−0.306173	+	0.0994816i
$261$	6.78796	+	2.20554i	0.420164	+	0.136520i
$262$	−0.417528	+	0.574678i	−0.0257950	+	0.0355037i
$263$		−	9.05216i		−	0.558180i	−0.960265	−	0.279090i	$-0.909967\pi$
$263$		−	9.05216i		−	0.558180i	0.960265	−	0.279090i	$-0.0900328\pi$
$264$	−1.77133	+	2.80399i	−0.109018	+	0.172574i
$265$		−	9.36439i		−	0.575250i
$266$	9.53376	−	4.52060i	0.584552	−	0.277176i
$267$	2.18608	−	6.72806i	0.133786	−	0.411750i
$268$	−0.543214	−	1.67184i	−0.0331821	−	0.102124i
$269$	−13.8793	−	19.1032i	−0.846236	−	1.16474i	−0.984680	−	0.174374i	$-0.944210\pi$
$269$	−13.8793	−	19.1032i	−0.846236	−	1.16474i	0.138444	−	0.990370i	$-0.455790\pi$
$270$	1.12216	+	1.54452i	0.0682924	+	0.0939964i
$271$	−9.94012	−	30.5925i	−0.603819	−	1.85836i	−0.504711	−	0.863288i	$-0.668401\pi$
$271$	−9.94012	−	30.5925i	−0.603819	−	1.85836i	−0.0991078	−	0.995077i	$-0.531599\pi$
$272$	1.27579	−	3.92649i	0.0773564	−	0.238079i
$273$	6.50012	−	3.08215i	0.393405	−	0.186540i
$274$		−	18.2377i		−	1.10178i
$275$	−4.35586	−	1.10878i	−0.262668	−	0.0668619i
$276$			6.88157i			0.414222i
$277$	−8.40015	+	11.5618i	−0.504716	+	0.694682i	−0.983017	−	0.183514i	$-0.941253\pi$
$277$	−8.40015	+	11.5618i	−0.504716	+	0.694682i	0.478301	+	0.878196i	$0.341253\pi$
$278$	19.5835	+	6.36306i	1.17454	+	0.381631i
$279$	2.61440	−	0.849472i	0.156520	−	0.0508565i
$280$	5.00937	−	0.647827i	0.299367	−	0.0387151i
$281$	13.0935	+	18.0216i	0.781090	+	1.07508i	0.995161	+	0.0982601i	$0.0313277\pi$
$281$	13.0935	+	18.0216i	0.781090	+	1.07508i	−0.214071	+	0.976818i	$0.568672\pi$
$282$	7.21926	−	2.34568i	0.429900	−	0.139683i
$283$	7.19759	−	22.1519i	0.427852	−	1.31679i	−0.472384	−	0.881393i	$-0.656607\pi$
$283$	7.19759	−	22.1519i	0.427852	−	1.31679i	0.900236	−	0.435401i	$-0.143393\pi$
$284$	10.1359	+	7.36420i	0.601458	+	0.436985i
$285$	−7.61359			−0.450990
$286$	−3.33709	−	8.37778i	−0.197326	−	0.495389i
$287$	−18.8890	−	10.3120i	−1.11498	−	0.608696i
$288$	0.587785	−	0.809017i	0.0346356	−	0.0476718i
$289$	0.0139034	−	0.0427904i	0.000817849	−	0.00251708i
$290$	−12.9591	+	4.21067i	−0.760985	+	0.247259i
$291$	−5.21398	+	3.78817i	−0.305649	+	0.222067i
$292$	5.59287	−	4.06346i	0.327298	−	0.237796i
$293$	0.0227379	+	0.0699800i	0.00132836	+	0.00408828i	0.951719	−	0.306972i	$-0.0993158\pi$
$293$	0.0227379	+	0.0699800i	0.00132836	+	0.00408828i	−0.950390	+	0.311060i	$0.899316\pi$
$294$	−6.76971	+	1.78074i	−0.394817	+	0.103855i
$295$	5.08580	+	3.69505i	0.296107	+	0.215134i
$296$			1.03953i			0.0604216i
$297$	−2.55112	+	2.11939i	−0.148031	+	0.122979i
$298$	18.8835			1.09389
$299$	−15.1376	−	10.9981i	−0.875429	−	0.636037i
$300$	1.28889	+	0.418787i	0.0744142	+	0.0241787i
$301$	−3.16476	−	0.594053i	−0.182414	−	0.0342407i
$302$	−13.2667	+	9.63879i	−0.763410	+	0.554650i
$303$	−6.35909	−	8.75254i	−0.365320	−	0.502820i
$304$	1.23236	+	3.79280i	0.0706805	+	0.217532i
$305$	−13.9394	−	4.52919i	−0.798168	−	0.259340i
$306$	2.42671	−	3.34007i	0.138726	−	0.190939i
$307$	−13.2297			−0.755059			−0.377530	−	0.925998i	$-0.623226\pi$
$307$	−13.2297			−0.755059			−0.377530	+	0.925998i	$0.623226\pi$
$308$	1.68749	+	8.61118i	0.0961538	+	0.490667i
$309$	10.8591			0.617755
$310$	−3.08476	+	4.24580i	−0.175202	+	0.241145i
$311$	30.0805	+	9.77374i	1.70571	+	0.554218i	0.989609	−	0.143782i	$-0.0459263\pi$
$311$	30.0805	+	9.77374i	1.70571	+	0.554218i	0.716098	+	0.698000i	$0.245926\pi$
$312$	0.840221	+	2.58594i	0.0475682	+	0.146400i
$313$	19.2646	+	26.5154i	1.08890	+	1.49874i	0.849332	+	0.527859i	$0.177005\pi$
$313$	19.2646	+	26.5154i	1.08890	+	1.49874i	0.239565	+	0.970880i	$0.422995\pi$
$314$	−10.7333	+	7.79818i	−0.605713	+	0.440076i
$315$	4.96438	+	0.931859i	0.279711	+	0.0525043i
$316$	1.62530	+	0.528092i	0.0914303	+	0.0297075i
$317$	−2.61599	−	1.90063i	−0.146928	−	0.106750i	0.511893	−	0.859049i	$-0.328945\pi$
$317$	−2.61599	−	1.90063i	−0.146928	−	0.106750i	−0.658821	+	0.752300i	$0.728945\pi$
$318$	−4.90506			−0.275062
$319$	−8.75972	−	21.9913i	−0.490450	−	1.23128i
$320$			1.90913i			0.106724i
$321$	7.67406	+	5.57553i	0.428324	+	0.311196i
$322$	12.5025	+	13.2355i	0.696739	+	0.737586i
$323$	5.08785	+	15.6588i	0.283096	+	0.871279i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	−2.98112	+	2.16591i	−0.165363	+	0.120143i
$326$	−13.9460	+	4.53133i	−0.772398	+	0.250967i
$327$	−5.86676	+	18.0560i	−0.324433	+	0.998501i
$328$	4.78103	−	6.58052i	0.263988	−	0.363348i
$329$	9.62332	−	17.6276i	0.530551	−	0.971839i
$330$	1.56196	−	6.13619i	0.0859832	−	0.337786i
$331$	−15.9912			−0.878954			−0.439477	−	0.898254i	$-0.644836\pi$
$331$	−15.9912			−0.878954			−0.439477	+	0.898254i	$0.644836\pi$
$332$	−1.15480	−	0.839010i	−0.0633778	−	0.0460466i
$333$	−0.321233	+	0.988653i	−0.0176035	+	0.0541779i
$334$	0.956645	−	0.310833i	0.0523453	−	0.0170080i
$335$	1.97262	+	2.71507i	0.107776	+	0.148340i
$336$	−0.339331	−	2.62390i	−0.0185120	−	0.143146i
$337$	8.65290	−	2.81150i	0.471354	−	0.153152i	−0.0637019	−	0.997969i	$-0.520291\pi$
$337$	8.65290	−	2.81150i	0.471354	−	0.153152i	0.535055	+	0.844817i	$0.320291\pi$
$338$	5.33254	+	1.73265i	0.290052	+	0.0942436i
$339$	7.49417	−	10.3148i	0.407027	−	0.560225i
$340$			7.88196i			0.427459i
$341$	−7.70804	−	4.86930i	−0.417414	−	0.263687i
$342$			3.98799i			0.215646i
$343$	−9.78508	+	15.7243i	−0.528345	+	0.849030i
$344$	0.376091	−	1.15749i	0.0202775	−	0.0624076i
$345$	−4.05981	−	12.4948i	−0.218573	−	0.672698i
$346$	−10.7159	−	14.7492i	−0.576092	−	0.792923i
$347$	−1.31526	−	1.81030i	−0.0706068	−	0.0971819i	0.772253	−	0.635315i	$-0.219130\pi$
$347$	−1.31526	−	1.81030i	−0.0706068	−	0.0971819i	−0.842860	+	0.538133i	$0.819130\pi$
$348$	2.20554	+	6.78796i	0.118229	+	0.363873i
$349$	−10.8651	+	33.4393i	−0.581595	+	1.78997i	0.0309397	+	0.999521i	$0.490150\pi$
$349$	−10.8651	+	33.4393i	−0.581595	+	1.78997i	−0.612535	+	0.790444i	$0.709850\pi$
$350$	3.23982	−	1.53622i	0.173176	−	0.0821142i
$351$			2.71901i			0.145130i
$352$	−3.30964	+	0.215110i	−0.176404	+	0.0114654i
$353$			25.2151i			1.34206i	0.741429	+	0.671031i	$0.234148\pi$
$353$			25.2151i			1.34206i	−0.741429	+	0.671031i	$0.765852\pi$
$354$	1.93546	−	2.66393i	0.102869	−	0.141586i
$355$	−22.7483	−	7.39136i	−1.20735	−	0.392293i
$356$	6.72806	−	2.18608i	0.356586	−	0.115862i
$357$	−1.40095	−	10.8329i	−0.0741461	−	0.573339i
$358$	2.39537	+	3.29694i	0.126599	+	0.174249i
$359$	24.0137	−	7.80253i	1.26740	−	0.411802i	0.403271	−	0.915080i	$-0.367873\pi$
$359$	24.0137	−	7.80253i	1.26740	−	0.411802i	0.864124	+	0.503279i	$0.167873\pi$
$360$	−0.589954	+	1.81569i	−0.0310933	+	0.0956953i
$361$	2.50468	+	1.81976i	0.131825	+	0.0957766i
$362$	−16.4767			−0.865995
$363$	10.8136	+	2.01640i	0.567567	+	0.105834i
$364$	6.31419	+	3.44707i	0.330953	+	0.180676i
$365$	−7.75767	+	10.6775i	−0.406055	+	0.558887i
$366$	−2.37238	+	7.30144i	−0.124006	+	0.381652i
$367$	5.12799	−	1.66619i	0.267679	−	0.0869742i	−0.172102	−	0.985079i	$-0.555056\pi$
$367$	5.12799	−	1.66619i	0.267679	−	0.0869742i	0.439781	+	0.898105i	$0.355056\pi$
$368$	−5.56731	+	4.04489i	−0.290216	+	0.210854i
$369$	6.58052	−	4.78103i	0.342568	−	0.248890i
$370$	−0.613276	−	1.88747i	−0.0318827	−	0.0981248i
$371$	−9.43403	+	8.91158i	−0.489790	+	0.462666i
$372$	2.22395	+	1.61579i	0.115306	+	0.0837749i
$373$		−	6.68899i		−	0.346343i	−0.984892	−	0.173171i	$-0.944599\pi$
$373$		−	6.68899i		−	0.346343i	0.984892	−	0.173171i	$-0.0554014\pi$
$374$	−13.6640	+	0.888095i	−0.706551	+	0.0459223i
$375$	−12.1329			−0.626543
$376$	6.14107	+	4.46175i	0.316701	+	0.230097i
$377$	−18.4566	−	5.99690i	−0.950561	−	0.308856i
$378$	0.488107	−	2.60034i	0.0251055	−	0.133747i
$379$	18.8923	−	13.7260i	0.970431	−	0.705060i	0.0148815	−	0.999889i	$-0.495263\pi$
$379$	18.8923	−	13.7260i	0.970431	−	0.705060i	0.955550	+	0.294830i	$0.0952629\pi$
$380$	−4.47515	−	6.15952i	−0.229571	−	0.315977i
$381$	3.88320	+	11.9512i	0.198942	+	0.612281i
$382$	−24.7379	−	8.03783i	−1.26570	−	0.411251i
$383$	8.32573	−	11.4594i	0.425425	−	0.585547i	−0.541471	−	0.840720i	$-0.682132\pi$
$383$	8.32573	−	11.4594i	0.425425	−	0.585547i	0.966896	+	0.255173i	$0.0821323\pi$
$384$	1.00000			0.0510310
$385$	−8.14416	−	14.6397i	−0.415065	−	0.746108i
$386$	−22.4689			−1.14364
$387$	0.715368	−	0.984619i	0.0363642	−	0.0500510i
$388$	−6.12940	−	1.99156i	−0.311173	−	0.101106i
$389$	−8.15943	−	25.1121i	−0.413699	−	1.27324i	−0.913409	−	0.407043i	$-0.866560\pi$
$389$	−8.15943	−	25.1121i	−0.413699	−	1.27324i	0.499709	−	0.866193i	$-0.333440\pi$
$390$	−3.05116	−	4.19957i	−0.154502	−	0.212653i
$391$	−22.9850	+	16.6995i	−1.16240	+	0.844532i
$392$	−5.41979	−	4.43012i	−0.273741	−	0.223755i
$393$	−0.675575	−	0.219507i	−0.0340782	−	0.0110727i
$394$	−14.6605	−	10.6515i	−0.738585	−	0.536614i
$395$	−3.26259			−0.164159
$396$	−3.21413	−	0.818154i	−0.161516	−	0.0411138i
$397$			8.98173i			0.450780i	0.974269	+	0.225390i	$0.0723656\pi$
$397$			8.98173i			0.450780i	−0.974269	+	0.225390i	$0.927634\pi$
$398$	0.577223	+	0.419377i	0.0289336	+	0.0210215i
$399$	7.24544	+	7.67020i	0.362725	+	0.383990i
$400$	0.418787	+	1.28889i	0.0209393	+	0.0644446i
$401$	−18.3662	+	13.3438i	−0.917164	+	0.666358i	−0.942816	−	0.333312i	$-0.891834\pi$
$401$	−18.3662	+	13.3438i	−0.917164	+	0.666358i	0.0256527	+	0.999671i	$0.491834\pi$
$402$	1.42215	−	1.03325i	0.0709305	−	0.0515340i
$403$	−7.10860	+	2.30972i	−0.354105	+	0.115056i
$404$	3.34317	−	10.2892i	0.166329	−	0.511908i
$405$	−1.12216	+	1.54452i	−0.0557605	+	0.0767478i
$406$	16.5744	+	9.04840i	0.822576	+	0.449065i
$407$	3.20299	−	1.27584i	0.158766	−	0.0632408i
$408$	4.12856			0.204394
$409$	−20.7446	−	15.0718i	−1.02575	−	0.745254i	−0.0582999	−	0.998299i	$-0.518568\pi$
$409$	−20.7446	−	15.0718i	−1.02575	−	0.745254i	−0.967455	+	0.253045i	$0.918568\pi$
$410$	−4.79867	+	14.7688i	−0.236989	+	0.729378i
$411$	17.3451	−	5.63576i	0.855569	−	0.277991i
$412$	6.38285	+	8.78523i	0.314460	+	0.432817i
$413$	−1.11735	−	8.63999i	−0.0549812	−	0.425146i
$414$	−6.54476	+	2.12652i	−0.321658	+	0.104513i
$415$	2.59173	+	0.842105i	0.127223	+	0.0413373i
$416$	−1.59820	+	2.19973i	−0.0783580	+	0.107851i
$417$			20.5913i			1.00836i
$418$	10.1738	−	8.45209i	0.497618	−	0.413405i
$419$			31.0233i			1.51559i	0.652494	+	0.757794i	$0.273723\pi$
$419$			31.0233i			1.51559i	−0.652494	+	0.757794i	$0.726277\pi$
$420$	2.16410	+	4.56400i	0.105597	+	0.222701i
$421$	8.37167	−	25.7654i	0.408010	−	1.25573i	−0.510345	−	0.859970i	$-0.670482\pi$
$421$	8.37167	−	25.7654i	0.408010	−	1.25573i	0.918355	−	0.395757i	$-0.129518\pi$
$422$	−0.852979	−	2.62520i	−0.0415224	−	0.127793i
$423$	4.46175	+	6.14107i	0.216937	+	0.298589i
$424$	−2.88312	−	3.96828i	−0.140017	−	0.192716i
$425$	1.72898	+	5.32127i	0.0838681	+	0.258119i
$426$	−3.87159	+	11.9155i	−0.187579	+	0.577309i
$427$	8.70250	+	18.3532i	0.421144	+	0.888175i
$428$			9.48566i			0.458507i
$429$	6.93652	−	5.76264i	0.334899	−	0.278223i
$430$			2.32352i			0.112050i
$431$	5.33158	−	7.33829i	0.256813	−	0.353473i	−0.661070	−	0.750325i	$-0.729897\pi$
$431$	5.33158	−	7.33829i	0.256813	−	0.353473i	0.917883	+	0.396852i	$0.129897\pi$
$432$	0.951057	+	0.309017i	0.0457577	+	0.0148676i
$433$	22.3025	−	7.24653i	1.07179	−	0.348246i	0.280606	−	0.959823i	$-0.409464\pi$
$433$	22.3025	−	7.24653i	1.07179	−	0.348246i	0.791185	+	0.611577i	$0.209464\pi$
$434$	7.21297	−	0.932804i	0.346233	−	0.0447760i
$435$	−8.00917	−	11.0237i	−0.384010	−	0.528545i
$436$	−18.0560	+	5.86676i	−0.864727	+	0.280967i
$437$	8.48055	−	26.1004i	0.405679	−	1.24855i
$438$	5.59287	+	4.06346i	0.267238	+	0.194160i
$439$	22.9690			1.09625			0.548125	−	0.836396i	$-0.315342\pi$
$439$	22.9690			1.09625			0.548125	+	0.836396i	$0.315342\pi$
$440$	5.88238	−	2.34311i	0.280431	−	0.111703i
$441$	−3.78554	−	5.88810i	−0.180264	−	0.280386i
$442$	−6.59825	+	9.08171i	−0.313847	+	0.431973i
$443$	−0.592518	+	1.82358i	−0.0281514	+	0.0866411i	−0.964145	−	0.265376i	$-0.914504\pi$
$443$	−0.592518	+	1.82358i	−0.0281514	+	0.0866411i	0.935994	+	0.352017i	$0.114504\pi$
$444$	−0.988653	+	0.321233i	−0.0469194	+	0.0152450i
$445$	−10.9264	+	7.93848i	−0.517960	+	0.376320i
$446$	−2.97099	+	2.15855i	−0.140681	+	0.102210i
$447$	5.83532	+	17.9593i	0.276001	+	0.849444i
$448$	1.92333	−	1.81681i	0.0908686	−	0.0858364i
$449$	14.3703	+	10.4406i	0.678176	+	0.492724i	0.872752	−	0.488164i	$-0.162333\pi$
$449$	14.3703	+	10.4406i	0.678176	+	0.492724i	−0.194576	+	0.980887i	$0.562333\pi$
$450$			1.35522i			0.0638858i
$451$	−26.1436	−	6.65484i	−1.23106	−	0.313364i
$452$	12.7498			0.599702
$453$	−13.2667	−	9.63879i	−0.623322	−	0.452870i
$454$	−0.613587	−	0.199367i	−0.0287971	−	0.00935673i
$455$	−13.4982	−	2.53374i	−0.632806	−	0.118783i
$456$	−3.22635	+	2.34408i	−0.151088	+	0.109772i
$457$	11.7566	+	16.1816i	0.549952	+	0.756944i	0.990006	−	0.141027i	$-0.0450406\pi$
$457$	11.7566	+	16.1816i	0.549952	+	0.756944i	−0.440054	+	0.897971i	$0.645041\pi$
$458$	0.857462	+	2.63900i	0.0400666	+	0.123312i
$459$	3.92649	+	1.27579i	0.183273	+	0.0595490i
$460$	7.72221	−	10.6287i	0.360050	−	0.495566i
$461$	−16.3460			−0.761308			−0.380654	−	0.924717i	$-0.624301\pi$
$461$	−16.3460			−0.761308			−0.380654	+	0.924717i	$0.624301\pi$
$462$	−7.66825	+	4.26590i	−0.356759	+	0.198468i
$463$	−26.7178			−1.24168			−0.620841	−	0.783937i	$-0.713209\pi$
$463$	−26.7178			−1.24168			−0.620841	+	0.783937i	$0.713209\pi$
$464$	−4.19519	+	5.77419i	−0.194757	+	0.268060i
$465$	−4.99124	−	1.62175i	−0.231463	−	0.0752069i
$466$	−4.32139	−	13.2999i	−0.200184	−	0.616104i
$467$	−11.6965	−	16.0988i	−0.541247	−	0.744963i	0.447545	−	0.894261i	$-0.352298\pi$
$467$	−11.6965	−	16.0988i	−0.541247	−	0.744963i	−0.988792	+	0.149299i	$0.952298\pi$
$468$	−2.19973	+	1.59820i	−0.101682	+	0.0738766i
$469$	0.858032	−	4.57107i	0.0396202	−	0.211073i
$470$	−13.7825	−	4.47821i	−0.635739	−	0.206564i
$471$	−10.7333	−	7.79818i	−0.494563	−	0.359321i
$472$	3.29280			0.151564
$473$	−4.02802	+	0.261801i	−0.185209	+	0.0120376i
$474$			1.70894i			0.0784944i
$475$	−4.37242	−	3.17675i	−0.200620	−	0.145759i
$476$	7.94056	−	7.50083i	0.363955	−	0.343800i
$477$	−1.51575	−	4.66499i	−0.0694013	−	0.213595i
$478$	−2.59771	+	1.88735i	−0.118816	+	0.0863252i
$479$	2.22341	−	1.61540i	0.101590	−	0.0738095i	−0.535831	−	0.844326i	$-0.680001\pi$
$479$	2.22341	−	1.61540i	0.101590	−	0.0738095i	0.637421	+	0.770516i	$0.280001\pi$
$480$	−1.81569	+	0.589954i	−0.0828746	+	0.0269276i
$481$	0.873437	−	2.68816i	0.0398253	−	0.122570i
$482$	−14.3487	+	19.7493i	−0.653566	+	0.899557i
$483$	−8.72422	+	15.9806i	−0.396966	+	0.727143i
$484$	4.72477	+	9.93360i	0.214762	+	0.451527i
$485$	12.3040			0.558697
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	7.61161	−	23.4261i	0.344915	−	1.06154i	−0.616714	−	0.787187i	$-0.711537\pi$
$487$	7.61161	−	23.4261i	0.344915	−	1.06154i	0.961629	−	0.274352i	$-0.0884635\pi$
$488$	−7.30144	+	2.37238i	−0.330521	+	0.107393i
$489$	−8.61911	−	11.8632i	−0.389770	−	0.536472i
$490$	12.4542	+	4.84630i	0.562624	+	0.218933i
$491$	−7.19483	+	2.33774i	−0.324698	+	0.105501i	−0.466830	−	0.884347i	$-0.654604\pi$
$491$	−7.19483	+	2.33774i	−0.324698	+	0.105501i	0.142132	+	0.989848i	$0.454604\pi$
$492$	7.73587	+	2.51353i	0.348760	+	0.113319i
$493$	−17.3201	+	23.8391i	−0.780058	+	1.07366i
$494$		−	10.8434i		−	0.487867i
$495$	6.31854	−	0.410673i	0.283997	−	0.0184584i
$496$			2.74895i			0.123431i
$497$	14.2020	+	29.9514i	0.637045	+	1.34350i
$498$	0.441094	−	1.35755i	0.0197659	−	0.0608331i
$499$	1.75709	+	5.40777i	0.0786581	+	0.242085i	0.982652	−	0.185462i	$-0.0593780\pi$
$499$	1.75709	+	5.40777i	0.0786581	+	0.242085i	−0.903993	+	0.427546i	$0.859378\pi$
$500$	−7.13157	−	9.81576i	−0.318933	−	0.438974i
$501$	0.591239	+	0.813770i	0.0264146	+	0.0363566i
$502$	1.80647	+	5.55975i	0.0806267	+	0.248144i
$503$	−11.3574	+	34.9546i	−0.506404	+	1.55855i	0.291994	+	0.956420i	$0.405681\pi$
$503$	−11.3574	+	34.9546i	−0.506404	+	1.55855i	−0.798398	+	0.602130i	$0.794319\pi$
$504$	2.39062	−	1.13355i	0.106487	−	0.0504925i
$505$			20.6544i			0.919107i
$506$	19.2959	+	12.1895i	0.857807	+	0.541891i
$507$			5.60696i			0.249014i
$508$	−7.38628	+	10.1663i	−0.327713	+	0.451058i
$509$	−7.52368	−	2.44459i	−0.333481	−	0.108355i	0.137490	−	0.990503i	$-0.456096\pi$
$509$	−7.52368	−	2.44459i	−0.333481	−	0.108355i	−0.470971	+	0.882148i	$0.656096\pi$
$510$	−7.49618	+	2.43566i	−0.331937	+	0.107853i
$511$	18.1395	−	2.34585i	0.802443	−	0.103774i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−3.79280	+	1.23236i	−0.167456	+	0.0544098i
$514$	5.70759	−	17.5661i	0.251751	−	0.774810i
$515$	−16.7722	−	12.1857i	−0.739069	−	0.536965i
$516$	1.21706			0.0535779
$517$	6.21042	−	24.3977i	0.273134	−	1.07301i
$518$	−1.31788	+	2.41404i	−0.0579044	+	0.106067i
$519$	10.7159	−	14.7492i	0.470377	−	0.647419i
$520$	1.60409	−	4.93689i	0.0703441	−	0.216497i
$521$	9.78679	−	3.17992i	0.428767	−	0.139315i	−0.0866802	−	0.996236i	$-0.527626\pi$
$521$	9.78679	−	3.17992i	0.428767	−	0.139315i	0.515447	+	0.856921i	$0.327626\pi$
$522$	−5.77419	+	4.19519i	−0.252729	+	0.183619i
$523$	−3.62725	+	2.63535i	−0.158609	+	0.115236i	−0.664259	−	0.747503i	$-0.731253\pi$
$523$	−3.62725	+	2.63535i	−0.158609	+	0.115236i	0.505650	+	0.862739i	$0.331253\pi$
$524$	−0.219507	−	0.675575i	−0.00958923	−	0.0295126i
$525$	2.46219	+	2.60653i	0.107459	+	0.113758i
$526$	7.32335	+	5.32073i	0.319313	+	0.231995i
$527$			11.3492i			0.494379i
$528$	−1.22732	−	3.08118i	−0.0534121	−	0.134091i
$529$	24.3560			1.05896
$530$	7.57595	+	5.50425i	0.329078	+	0.239089i
$531$	3.13164	+	1.01753i	0.135902	+	0.0441571i
$532$	−1.94656	+	10.3701i	−0.0843942	+	0.449601i
$533$	−17.8925	+	12.9997i	−0.775011	+	0.563079i
$534$	4.15817	+	5.72323i	0.179942	+	0.247668i
$535$	−5.59610	−	17.2230i	−0.241941	−	0.744617i
$536$	1.67184	+	0.543214i	0.0722125	+	0.0234633i
$537$	−2.39537	+	3.29694i	−0.103368	+	0.142273i
$538$	23.6129			1.01802
$539$	−6.99820	+	22.1365i	−0.301434	+	0.953487i
$540$	−1.90913			−0.0821559
$541$	8.63926	−	11.8909i	0.371431	−	0.511231i	−0.581858	−	0.813290i	$-0.697674\pi$
$541$	8.63926	−	11.8909i	0.371431	−	0.511231i	0.953289	+	0.302059i	$0.0976741\pi$
$542$	30.5925	+	9.94012i	1.31406	+	0.426965i
$543$	−5.09158	−	15.6703i	−0.218500	−	0.672475i
$544$	2.42671	+	3.34007i	0.104044	+	0.143204i
$545$	29.3231	−	21.3045i	1.25606	−	0.912583i
$546$	−1.32717	+	7.07035i	−0.0567976	+	0.302583i
$547$	−17.9817	−	5.84260i	−0.768840	−	0.249811i	−0.101772	−	0.994808i	$-0.532451\pi$
$547$	−17.9817	−	5.84260i	−0.768840	−	0.249811i	−0.667069	+	0.744996i	$0.732451\pi$
$548$	14.7546	+	10.7198i	0.630285	+	0.457929i
$549$	−7.67719			−0.327654
$550$	3.45733	−	2.87224i	0.147421	−	0.122473i
$551$		−	28.4634i		−	1.21258i
$552$	−5.56731	−	4.04489i	−0.236960	−	0.172162i
$553$	3.10483	+	3.28686i	0.132031	+	0.139771i
$554$	−4.41622	−	13.5917i	−0.187627	−	0.577457i
$555$	1.60558	−	1.16652i	0.0681529	−	0.0495160i
$556$	−16.6587	+	12.1033i	−0.706486	+	0.513292i
$557$	19.3654	−	6.29221i	0.820539	−	0.266609i	0.131484	−	0.991318i	$-0.458026\pi$
$557$	19.3654	−	6.29221i	0.820539	−	0.266609i	0.689055	+	0.724709i	$0.258026\pi$
$558$	−0.849472	+	2.61440i	−0.0359610	+	0.110677i
$559$	−1.94509	+	2.67719i	−0.0822687	+	0.113233i
$560$	−2.42033	+	4.43345i	−0.102278	+	0.187347i
$561$	−5.06705	−	12.7208i	−0.213931	−	0.537075i
$562$	−22.2759			−0.939653
$563$	14.5310	+	10.5574i	0.612411	+	0.444942i	0.850262	−	0.526359i	$-0.176443\pi$
$563$	14.5310	+	10.5574i	0.612411	+	0.444942i	−0.237852	+	0.971301i	$0.576443\pi$
$564$	−2.34568	+	7.21926i	−0.0987709	+	0.303985i
$565$	−23.1498	+	7.52181i	−0.973918	+	0.316445i
$566$	13.6906	+	18.8435i	0.575460	+	0.792053i
$567$	2.62390	−	0.339331i	0.110193	−	0.0142506i
$568$	−11.9155	+	3.87159i	−0.499964	+	0.162448i
$569$	21.5381	+	6.99814i	0.902922	+	0.293377i	0.723443	−	0.690384i	$-0.242559\pi$
$569$	21.5381	+	6.99814i	0.902922	+	0.293377i	0.179480	+	0.983762i	$0.442559\pi$
$570$	4.47515	−	6.15952i	0.187444	−	0.257994i
$571$			27.7551i			1.16151i	0.814077	+	0.580757i	$0.197243\pi$
$571$			27.7551i			1.16151i	−0.814077	+	0.580757i	$0.802757\pi$
$572$	8.73926	+	2.22457i	0.365407	+	0.0930140i
$573$		−	26.0110i		−	1.08662i
$574$	19.4452	−	9.22029i	0.811628	−	0.384847i
$575$	2.88191	−	8.86960i	0.120184	−	0.369888i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	21.3210	+	29.3458i	0.887605	+	1.22168i	0.974256	+	0.225445i	$0.0723835\pi$
$577$	21.3210	+	29.3458i	0.887605	+	1.22168i	−0.0866511	+	0.996239i	$0.527617\pi$
$578$	0.0264459	+	0.0363997i	0.00110000	+	0.00151403i
$579$	−6.94328	−	21.3692i	−0.288553	−	0.888074i
$580$	4.21067	−	12.9591i	0.174838	−	0.538098i
$581$	−1.61804	−	3.41239i	−0.0671278	−	0.141570i
$582$		−	6.44483i		−	0.267147i
$583$	−8.68848	+	13.7538i	−0.359840	+	0.569622i
$584$			6.91317i			0.286069i
$585$	3.05116	−	4.19957i	0.126150	−	0.173631i
$586$	−0.0699800	−	0.0227379i	−0.00289085	−	0.000939294i
$587$	41.9338	−	13.6251i	1.73079	−	0.562368i	0.737229	−	0.675643i	$-0.236134\pi$
$587$	41.9338	−	13.6251i	1.73079	−	0.562368i	0.993564	+	0.113275i	$0.0361341\pi$
$588$	2.53848	−	6.52350i	0.104685	−	0.269025i
$589$	−6.44375	−	8.86907i	−0.265510	−	0.365444i
$590$	−5.97871	+	1.94260i	−0.246140	+	0.0799756i
$591$	5.59981	−	17.2345i	0.230346	−	0.708931i
$592$	−0.840999	−	0.611021i	−0.0345648	−	0.0251128i
$593$	10.1642			0.417396			0.208698	−	0.977980i	$-0.433077\pi$
$593$	10.1642			0.417396			0.208698	+	0.977980i	$0.433077\pi$
$594$	−0.215110	−	3.30964i	−0.00882608	−	0.135796i
$595$	−9.99247	+	18.3037i	−0.409651	+	0.750380i
$596$	−11.0994	+	15.2771i	−0.454651	+	0.625773i
$597$	−0.220480	+	0.678566i	−0.00902363	+	0.0277719i
$598$	17.7953	−	5.78204i	0.727704	−	0.236445i
$599$	23.5283	−	17.0943i	0.961341	−	0.698455i	0.00787939	−	0.999969i	$-0.497492\pi$
$599$	23.5283	−	17.0943i	0.961341	−	0.698455i	0.953462	+	0.301514i	$0.0974919\pi$
$600$	−1.09640	+	0.796579i	−0.0447602	+	0.0325202i
$601$	5.99331	+	18.4455i	0.244472	+	0.752408i	0.995723	+	0.0923912i	$0.0294510\pi$
$601$	5.99331	+	18.4455i	0.244472	+	0.752408i	−0.751250	+	0.660017i	$0.770549\pi$
$602$	2.34080	−	2.21117i	0.0954037	−	0.0901204i
$603$	1.42215	+	1.03325i	0.0579145	+	0.0420774i
$604$		−	16.3985i		−	0.667245i
$605$	−14.4391	−	15.2490i	−0.587033	−	0.619958i
$606$	10.8187			0.439481
$607$	−38.3875	−	27.8902i	−1.55810	−	1.13203i	−0.937544	−	0.347868i	$-0.886906\pi$
$607$	−38.3875	−	27.8902i	−1.55810	−	1.13203i	−0.620559	−	0.784160i	$-0.713094\pi$
$608$	−3.79280	−	1.23236i	−0.153818	−	0.0499786i
$609$	−3.48376	+	18.5593i	−0.141169	+	0.752063i
$610$	11.8576	−	8.61502i	0.480099	−	0.348812i
$611$	−12.1315	−	16.6976i	−0.490790	−	0.675514i
$612$	1.27579	+	3.92649i	0.0515709	+	0.158719i
$613$	−8.33984	−	2.70978i	−0.336843	−	0.109447i	0.135712	−	0.990748i	$-0.456668\pi$
$613$	−8.33984	−	2.70978i	−0.336843	−	0.109447i	−0.472554	+	0.881302i	$0.656668\pi$
$614$	7.77622	−	10.7031i	0.313823	−	0.431940i
$615$	−15.5288			−0.626182
$616$	−7.95847	−	3.69631i	−0.320656	−	0.148929i
$617$	−13.0687			−0.526124			−0.263062	−	0.964779i	$-0.584732\pi$
$617$	−13.0687			−0.526124			−0.263062	+	0.964779i	$0.584732\pi$
$618$	−6.38285	+	8.78523i	−0.256756	+	0.353394i
$619$	−4.54010	−	1.47517i	−0.182482	−	0.0592920i	0.216351	−	0.976316i	$-0.430585\pi$
$619$	−4.54010	−	1.47517i	−0.182482	−	0.0592920i	−0.398833	+	0.917024i	$0.630585\pi$
$620$	−1.62175	−	4.99124i	−0.0651311	−	0.200453i
$621$	−4.04489	−	5.56731i	−0.162316	−	0.223408i
$622$	−25.5880	+	18.5908i	−1.02598	+	0.745422i
$623$	18.3956	+	3.45301i	0.737002	+	0.138342i
$624$	−2.58594	−	0.840221i	−0.103520	−	0.0336358i
$625$	13.2576	+	9.63219i	0.530303	+	0.385288i
$626$	−32.7748			−1.30995
$627$	11.1823	+	7.06405i	0.446578	+	0.282111i
$628$		−	13.2670i		−	0.529413i
$629$	−3.47211	−	2.52264i	−0.138442	−	0.100584i
$630$	−3.67188	+	3.46854i	−0.146291	+	0.138190i
$631$	6.04031	+	18.5902i	0.240461	+	0.740062i	0.996350	+	0.0853628i	$0.0272049\pi$
$631$	6.04031	+	18.5902i	0.240461	+	0.740062i	−0.755889	+	0.654700i	$0.772795\pi$
$632$	−1.38256	+	1.00449i	−0.0549954	+	0.0399565i
$633$	2.23313	−	1.62246i	0.0887589	−	0.0644871i
$634$	3.07528	−	0.999218i	0.122135	−	0.0396840i
$635$	7.41353	−	22.8165i	0.294197	−	0.905445i
$636$	2.88312	−	3.96828i	0.114323	−	0.157352i
$637$	10.2929	+	16.0098i	0.407821	+	0.634332i
$638$	22.9402	+	5.83940i	0.908210	+	0.231184i
$639$	−12.5287			−0.495629
$640$	−1.54452	−	1.12216i	−0.0610525	−	0.0443572i
$641$	8.97699	−	27.6283i	0.354570	−	1.09125i	−0.601689	−	0.798731i	$-0.705505\pi$
$641$	8.97699	−	27.6283i	0.354570	−	1.09125i	0.956259	−	0.292523i	$-0.0944947\pi$
$642$	−9.02140	+	2.93123i	−0.356046	+	0.115686i
$643$	28.1940	+	38.8057i	1.11186	+	1.53035i	0.818642	+	0.574304i	$0.194727\pi$
$643$	28.1940	+	38.8057i	1.11186	+	1.53035i	0.293221	+	0.956045i	$0.405273\pi$
$644$	−18.0566	+	2.33513i	−0.711528	+	0.0920171i
$645$	−2.20980	+	0.718007i	−0.0870107	+	0.0282715i
$646$	−15.6588	−	5.08785i	−0.616087	−	0.200179i
$647$	18.6901	−	25.7248i	0.734785	−	1.01134i	−0.264117	−	0.964491i	$-0.585081\pi$
$647$	18.6901	−	25.7248i	0.734785	−	1.01134i	0.998902	−	0.0468537i	$-0.0149195\pi$
$648$			1.00000i			0.0392837i
$649$	−4.04131	−	10.1457i	−0.158635	−	0.398255i
$650$		−	3.68487i		−	0.144532i
$651$	3.11608	+	6.57169i	0.122129	+	0.257565i
$652$	4.53133	−	13.9460i	0.177461	−	0.546168i
$653$	−2.68238	−	8.25550i	−0.104969	−	0.323063i	0.884754	−	0.466059i	$-0.154326\pi$
$653$	−2.68238	−	8.25550i	−0.104969	−	0.323063i	−0.989723	+	0.142996i	$0.954326\pi$
$654$	−11.1592	−	15.3594i	−0.436361	−	0.600599i
$655$	0.797115	+	1.09714i	0.0311459	+	0.0428686i
$656$	2.51353	+	7.73587i	0.0981371	+	0.302035i
$657$	−2.13629	+	6.57482i	−0.0833445	+	0.256508i
$658$	8.60455	+	18.1466i	0.335440	+	0.707430i
$659$			8.85864i			0.345084i	0.985002	+	0.172542i	$0.0551980\pi$
$659$			8.85864i			0.345084i	−0.985002	+	0.172542i	$0.944802\pi$
$660$	4.04618	+	4.87042i	0.157498	+	0.189581i
$661$			13.7111i			0.533299i	0.963794	+	0.266649i	$0.0859165\pi$
$661$			13.7111i			0.533299i	−0.963794	+	0.266649i	$0.914083\pi$
$662$	9.39937	−	12.9371i	0.365317	−	0.502816i
$663$	−10.6762	−	3.46890i	−0.414629	−	0.134721i
$664$	1.35755	−	0.441094i	0.0526830	−	0.0171177i
$665$	−2.58353	−	19.9773i	−0.100185	−	0.774686i
$666$	−0.611021	−	0.840999i	−0.0236766	−	0.0325880i
$667$	46.7118	−	15.1776i	1.80869	−	0.587679i
$668$	−0.310833	+	0.956645i	−0.0120265	+	0.0370137i
$669$	−2.97099	−	2.15855i	−0.114865	−	0.0834545i
$670$	−3.35602			−0.129654
$671$	16.2709	+	19.5854i	0.628132	+	0.756087i
$672$	2.32223	+	1.26777i	0.0895821	+	0.0489051i
$673$	24.7380	−	34.0490i	0.953580	−	1.31249i	0.00366159	−	0.999993i	$-0.498834\pi$
$673$	24.7380	−	34.0490i	0.953580	−	1.31249i	0.949919	−	0.312497i	$-0.101166\pi$
$674$	−2.81150	+	8.65290i	−0.108295	+	0.333297i
$675$	−1.28889	+	0.418787i	−0.0496095	+	0.0161191i
$676$	−4.53613	+	3.29569i	−0.174467	+	0.126757i
$677$	18.5546	−	13.4807i	0.713113	−	0.518107i	−0.171064	−	0.985260i	$-0.554720\pi$
$677$	18.5546	−	13.4807i	0.713113	−	0.518107i	0.884176	+	0.467153i	$0.154720\pi$
$678$	3.93992	+	12.1258i	0.151312	+	0.465689i
$679$	−11.7091	−	12.3955i	−0.449352	−	0.475696i
$680$	−6.37664	−	4.63290i	−0.244533	−	0.177663i
$681$		−	0.645164i		−	0.0247227i
$682$	8.47001	−	3.37383i	0.324334	−	0.129191i
$683$	−32.6961			−1.25108			−0.625541	−	0.780191i	$-0.715122\pi$
$683$	−32.6961			−1.25108			−0.625541	+	0.780191i	$0.715122\pi$
$684$	−3.22635	−	2.34408i	−0.123363	−	0.0896282i
$685$	−33.1140	−	10.7594i	−1.26522	−	0.411095i
$686$	−6.96967	−	17.1588i	−0.266103	−	0.655125i
$687$	−2.24486	+	1.63099i	−0.0856469	+	0.0622261i
$688$	0.715368	+	0.984619i	0.0272731	+	0.0375383i
$689$	4.12133	+	12.6842i	0.157010	+	0.483228i
$690$	12.4948	+	4.05981i	0.475669	+	0.154554i
$691$	−6.99712	+	9.63071i	−0.266183	+	0.366369i	−0.921096	−	0.389334i	$-0.872705\pi$
$691$	−6.99712	+	9.63071i	−0.266183	+	0.366369i	0.654914	+	0.755704i	$0.272705\pi$
$692$	18.2310			0.693040
$693$	−6.42673	−	5.97471i	−0.244131	−	0.226960i
$694$	2.23765			0.0849401
$695$	23.1067	−	31.8036i	0.876487	−	1.20638i
$696$	−6.78796	−	2.20554i	−0.257297	−	0.0836009i
$697$	10.3773	+	31.9380i	0.393067	+	1.20974i
$698$	−20.6666	−	28.4452i	−0.782243	−	1.07667i
$699$	11.3135	−	8.21976i	0.427917	−	0.310900i
$700$	−0.661493	+	3.52403i	−0.0250021	+	0.133196i
$701$	18.3841	+	5.97334i	0.694356	+	0.225610i	0.634870	−	0.772619i	$-0.281054\pi$
$701$	18.3841	+	5.97334i	0.694356	+	0.225610i	0.0594865	+	0.998229i	$0.481054\pi$
$702$	−2.19973	−	1.59820i	−0.0830234	−	0.0603200i
$703$	4.14564			0.156356
$704$	1.77133	−	2.80399i	0.0667595	−	0.105680i
$705$		−	14.4918i		−	0.545792i
$706$	−20.3994	−	14.8210i	−0.767742	−	0.557797i
$707$	20.8080	−	19.6556i	0.782564	−	0.739226i
$708$	1.01753	+	3.13164i	0.0382412	+	0.117694i
$709$	28.6813	−	20.8382i	1.07715	−	0.782595i	0.0999656	−	0.994991i	$-0.468127\pi$
$709$	28.6813	−	20.8382i	1.07715	−	0.782595i	0.977184	+	0.212396i	$0.0681267\pi$
$710$	19.3508	−	14.0592i	0.726224	−	0.527633i
$711$	−1.62530	+	0.528092i	−0.0609536	+	0.0198050i
$712$	−2.18608	+	6.72806i	−0.0819267	+	0.252145i
$713$	11.1192	−	15.3042i	0.416417	−	0.573148i
$714$	9.58748	+	5.23404i	0.358802	+	0.195879i
$715$	−17.1802	+	1.11663i	−0.642503	+	0.0417595i
$716$	−4.07524			−0.152299
$717$	−2.59771	−	1.88735i	−0.0970132	−	0.0704842i
$718$	−7.80253	+	24.0137i	−0.291188	+	0.896184i
$719$	−34.1264	+	11.0883i	−1.27270	+	0.413525i	−0.866003	−	0.500039i	$-0.833319\pi$
$719$	−34.1264	+	11.0883i	−1.27270	+	0.413525i	−0.406696	+	0.913564i	$0.633319\pi$
$720$	−1.12216	−	1.54452i	−0.0418204	−	0.0575608i
$721$	3.68485	+	28.4933i	0.137231	+	1.06115i
$722$	−2.94443	+	0.956702i	−0.109580	+	0.0356048i
$723$	−23.2167	−	7.54357i	−0.863439	−	0.280548i
$724$	9.68475	−	13.3299i	0.359931	−	0.495402i
$725$		−	9.67260i		−	0.359232i
$726$	−7.98738	+	7.56318i	−0.296440	+	0.280696i
$727$		−	5.33422i		−	0.197835i	−0.995096	−	0.0989176i	$-0.968462\pi$
$727$		−	5.33422i		−	0.197835i	0.995096	−	0.0989176i	$-0.0315380\pi$
$728$	−6.50012	+	3.08215i	−0.240911	+	0.114232i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−4.07845	−	12.5522i	−0.150950	−	0.464577i
$731$	2.95344	+	4.06506i	0.109237	+	0.150352i
$732$	−4.51254	−	6.21098i	−0.166788	−	0.229564i
$733$	−11.6517	−	35.8604i	−0.430367	−	1.32453i	−0.897761	−	0.440484i	$-0.854807\pi$
$733$	−11.6517	−	35.8604i	−0.430367	−	1.32453i	0.467394	−	0.884049i	$-0.345193\pi$
$734$	−1.66619	+	5.12799i	−0.0615001	+	0.189278i
$735$	−0.760537	+	13.3423i	−0.0280528	+	0.492136i
$736$		−	6.88157i		−	0.253658i
$737$	−0.378137	−	5.81794i	−0.0139289	−	0.214307i
$738$			8.13397i			0.299416i
$739$	−13.3796	+	18.4155i	−0.492178	+	0.677425i	−0.980788	−	0.195078i	$-0.937504\pi$
$739$	−13.3796	+	18.4155i	−0.492178	+	0.677425i	0.488610	+	0.872502i	$0.337504\pi$
$740$	1.88747	+	0.613276i	0.0693847	+	0.0225445i
$741$	10.3127	−	3.35079i	0.378846	−	0.123094i
$742$	−1.66444	−	12.8704i	−0.0611035	−	0.472487i
$743$	−1.73681	−	2.39052i	−0.0637174	−	0.0876995i	0.775969	−	0.630771i	$-0.217261\pi$
$743$	−1.73681	−	2.39052i	−0.0637174	−	0.0876995i	−0.839686	+	0.543071i	$0.817261\pi$
$744$	−2.61440	+	0.849472i	−0.0958487	+	0.0311431i
$745$	11.1404	−	34.2866i	0.408152	−	1.25616i
$746$	5.41150	+	3.93169i	0.198129	+	0.143949i
$747$	1.42741			0.0522262
$748$	7.31304	−	11.5765i	0.267391	−	0.423277i
$749$	−12.0256	+	22.0279i	−0.439406	+	0.804883i
$750$	7.13157	−	9.81576i	0.260408	−	0.358421i
$751$	−12.3752	+	38.0871i	−0.451579	+	1.38982i	0.423527	+	0.905884i	$0.360792\pi$
$751$	−12.3752	+	38.0871i	−0.451579	+	1.38982i	−0.875105	+	0.483933i	$0.839208\pi$
$752$	−7.21926	+	2.34568i	−0.263259	+	0.0855381i
$753$	−4.72940	+	3.43611i	−0.172349	+	0.125219i
$754$	15.7001	−	11.4068i	0.571764	−	0.415411i
$755$	9.67435	+	29.7746i	0.352085	+	1.08361i
$756$	1.81681	+	1.92333i	0.0660769	+	0.0699507i
$757$	−5.01663	−	3.64480i	−0.182333	−	0.132472i	0.492875	−	0.870100i	$-0.335946\pi$
$757$	−5.01663	−	3.64480i	−0.182333	−	0.132472i	−0.675208	+	0.737628i	$0.735946\pi$
$758$			23.3521i			0.848188i
$759$	−5.63018	+	22.1183i	−0.204363	+	0.802842i
$760$	7.61359			0.276174
$761$	25.4521	+	18.4921i	0.922639	+	0.670336i	0.944179	−	0.329432i	$-0.106857\pi$
$761$	25.4521	+	18.4921i	0.922639	+	0.670336i	−0.0215405	+	0.999768i	$0.506857\pi$
$762$	−11.9512	−	3.88320i	−0.432948	−	0.140673i
$763$	−49.3680	−	9.26683i	−1.78724	−	0.335482i
$764$	21.0433	−	15.2889i	0.761320	−	0.553131i
$765$	−4.63290	−	6.37664i	−0.167503	−	0.230548i
$766$	4.37710	+	13.4713i	0.158151	+	0.486738i
$767$	−8.51498	−	2.76668i	−0.307458	−	0.0998992i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	9.26308			0.334035			0.167018	−	0.985954i	$-0.446586\pi$
$769$	9.26308			0.334035			0.167018	+	0.985954i	$0.446586\pi$
$770$	16.6308	+	2.01623i	0.599332	+	0.0726599i
$771$	18.4701			0.665186
$772$	13.2069	−	18.1777i	0.475327	−	0.654231i
$773$	−36.0597	−	11.7165i	−1.29698	−	0.421413i	−0.422448	−	0.906387i	$-0.638829\pi$
$773$	−36.0597	−	11.7165i	−1.29698	−	0.421413i	−0.874529	+	0.484974i	$0.838829\pi$
$774$	0.376091	+	1.15749i	0.0135183	+	0.0416051i
$775$	−2.18975	−	3.01394i	−0.0786583	−	0.108264i
$776$	5.21398	−	3.78817i	0.187171	−	0.135988i
$777$	−2.70313	−	0.507402i	−0.0969744	−	0.0182030i
$778$	25.1121	+	8.15943i	0.900314	+	0.292530i
$779$	−26.2430	−	19.0667i	−0.940254	−	0.683135i
$780$	5.19095			0.185866
$781$	26.5532	+	31.9622i	0.950148	+	1.14370i
$782$		−	28.4110i		−	1.01597i
$783$	−5.77419	−	4.19519i	−0.206353	−	0.149924i
$784$	6.76971	−	1.78074i	0.241775	−	0.0635980i
$785$	7.82694	+	24.0889i	0.279356	+	0.859768i
$786$	0.574678	−	0.417528i	0.0204981	−	0.0148927i
$787$	−20.9772	+	15.2408i	−0.747757	+	0.543277i	−0.895131	−	0.445804i	$-0.852918\pi$
$787$	−20.9772	+	15.2408i	−0.747757	+	0.543277i	0.147374	+	0.989081i	$0.452918\pi$
$788$	17.2345	−	5.59981i	0.613952	−	0.199485i
$789$	−2.79727	+	8.60912i	−0.0995855	+	0.306493i
$790$	1.91771	−	2.63949i	0.0682289	−	0.0939090i
$791$	29.6081	+	16.1638i	1.05274	+	0.574719i
$792$	2.55112	−	2.11939i	0.0906500	−	0.0753091i
$793$	20.8744			0.741271
$794$	−7.26637	−	5.27933i	−0.257874	−	0.187356i
$795$	−2.89376	+	8.90607i	−0.102631	+	0.315866i
$796$	−0.678566	+	0.220480i	−0.0240512	+	0.00781469i
$797$	−4.17131	−	5.74131i	−0.147755	−	0.203368i	0.728724	−	0.684808i	$-0.240114\pi$
$797$	−4.17131	−	5.74131i	−0.147755	−	0.203368i	−0.876479	+	0.481440i	$0.840114\pi$
$798$	−10.4641	+	1.35325i	−0.370425	+	0.0479045i
$799$	−29.8051	+	9.68427i	−1.05443	+	0.342605i
$800$	−1.28889	−	0.418787i	−0.0455692	−	0.0148063i
$801$	−4.15817	+	5.72323i	−0.146922	+	0.202220i
$802$		−	22.7019i		−	0.801631i
$803$	21.3007	−	8.48465i	0.751687	−	0.299417i
$804$			1.75788i			0.0619956i
$805$	31.4075	−	14.8924i	1.10697	−	0.524888i
$806$	2.30972	−	7.10860i	0.0813566	−	0.250390i
$807$	7.29678	+	22.4572i	0.256859	+	0.790530i
$808$	6.35909	+	8.75254i	0.223712	+	0.307913i
$809$	23.8566	+	32.8358i	0.838753	+	1.15444i	0.986230	+	0.165379i	$0.0528847\pi$
$809$	23.8566	+	32.8358i	0.838753	+	1.15444i	−0.147477	+	0.989065i	$0.547115\pi$
$810$	−0.589954	−	1.81569i	−0.0207289	−	0.0637969i
$811$	−7.43785	+	22.8914i	−0.261178	+	0.803824i	0.731371	+	0.681980i	$0.238881\pi$
$811$	−7.43785	+	22.8914i	−0.261178	+	0.803824i	−0.992549	+	0.121844i	$0.961119\pi$
$812$	−17.0625	+	8.09049i	−0.598777	+	0.283921i
$813$			32.1669i			1.12814i
$814$	−0.850497	+	3.34119i	−0.0298099	+	0.117109i
$815$			27.9949i			0.980619i
$816$	−2.42671	+	3.34007i	−0.0849517	+	0.116926i
$817$	−4.61605	−	1.49985i	−0.161495	−	0.0524730i
$818$	24.3867	−	7.92373i	0.852662	−	0.277047i
$819$	−7.13442	+	0.922646i	−0.249297	+	0.0322399i
$820$	−9.12760	−	12.5631i	−0.318750	−	0.438721i
$821$	−31.5692	+	10.2574i	−1.10177	+	0.357987i	−0.802784	−	0.596270i	$-0.796649\pi$
$821$	−31.5692	+	10.2574i	−1.10177	+	0.357987i	−0.298987	+	0.954257i	$0.596649\pi$
$822$	−5.63576	+	17.3451i	−0.196570	+	0.604979i
$823$	−35.2052	−	25.5781i	−1.22718	−	0.891596i	−0.230502	−	0.973072i	$-0.574037\pi$
$823$	−35.2052	−	25.5781i	−1.22718	−	0.891596i	−0.996675	+	0.0814755i	$0.974037\pi$
$824$	−10.8591			−0.378296
$825$	3.80003	+	2.40055i	0.132300	+	0.0835763i
$826$	7.64666	+	4.17450i	0.266061	+	0.145249i
$827$	3.67801	−	5.06235i	0.127897	−	0.176035i	−0.740266	−	0.672314i	$-0.765301\pi$
$827$	3.67801	−	5.06235i	0.127897	−	0.176035i	0.868163	+	0.496279i	$0.165301\pi$
$828$	2.12652	−	6.54476i	0.0739018	−	0.227446i
$829$	2.02371	−	0.657543i	0.0702863	−	0.0228374i	−0.273663	−	0.961826i	$-0.588235\pi$
$829$	2.02371	−	0.657543i	0.0702863	−	0.0228374i	0.343949	+	0.938988i	$0.388235\pi$
$830$	−2.20466	+	1.60178i	−0.0765249	+	0.0555986i
$831$	11.5618	−	8.40015i	0.401075	−	0.291398i
$832$	−0.840221	−	2.58594i	−0.0291294	−	0.0896512i
$833$	27.9491	−	7.35190i	0.968380	−	0.254728i
$834$	−16.6587	−	12.1033i	−0.576844	−	0.419102i
$835$		−	1.92035i		−	0.0664564i
$836$	0.857857	+	13.1988i	0.0296696	+	0.456490i
$837$	−2.74895			−0.0950175
$838$	−25.0984	−	18.2350i	−0.867009	−	0.629919i
$839$	−42.1193	−	13.6854i	−1.45412	−	0.472472i	−0.527852	−	0.849337i	$-0.677002\pi$
$839$	−42.1193	−	13.6854i	−1.45412	−	0.472472i	−0.926269	+	0.376864i	$0.877002\pi$
$840$	−4.96438	−	0.931859i	−0.171287	−	0.0321522i
$841$	17.7505	−	12.8965i	0.612087	−	0.444707i
$842$	15.9239	+	21.9173i	0.548773	+	0.755321i
$843$	−6.88364	−	21.1857i	−0.237085	−	0.729673i
$844$	2.62520	+	0.852979i	0.0903631	+	0.0293607i
$845$	6.29190	−	8.66006i	0.216448	−	0.297915i
$846$	−7.59077			−0.260976
$847$	−1.62145	+	29.0581i	−0.0557136	+	0.998447i
$848$	4.90506			0.168440
$849$	−13.6906	+	18.8435i	−0.469861	+	0.646708i
$850$	−5.32127	−	1.72898i	−0.182518	−	0.0593037i
$851$	2.21059	+	6.80349i	0.0757780	+	0.233221i
$852$	−7.36420	−	10.1359i	−0.252293	−	0.347252i
$853$	15.3618	−	11.1610i	0.525977	−	0.382145i	−0.292874	−	0.956151i	$-0.594612\pi$
$853$	15.3618	−	11.1610i	0.525977	−	0.382145i	0.818851	+	0.574007i	$0.194612\pi$
$854$	−19.9633	−	3.74729i	−0.683129	−	0.128230i
$855$	7.24095	+	2.35273i	0.247635	+	0.0804616i
$856$	−7.67406	−	5.57553i	−0.262294	−	0.190568i
$857$	34.1118			1.16524			0.582619	−	0.812746i	$-0.302028\pi$
$857$	34.1118			1.16524			0.582619	+	0.812746i	$0.302028\pi$
$858$	0.584887	+	8.99896i	0.0199677	+	0.307219i
$859$		−	16.6970i		−	0.569694i	−0.958573	−	0.284847i	$-0.908057\pi$
$859$		−	16.6970i		−	0.569694i	0.958573	−	0.284847i	$-0.0919429\pi$
$860$	−1.87977	−	1.36573i	−0.0640995	−	0.0465710i
$861$	14.7779	+	15.6443i	0.503630	+	0.533156i
$862$	2.80298	+	8.62668i	0.0954698	+	0.293826i
$863$	−16.4968	+	11.9856i	−0.561556	+	0.407994i	−0.832028	−	0.554733i	$-0.812820\pi$
$863$	−16.4968	+	11.9856i	−0.561556	+	0.407994i	0.270472	+	0.962728i	$0.412820\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−33.1019	+	10.7555i	−1.12550	+	0.365697i
$866$	−7.24653	+	22.3025i	−0.246247	+	0.757871i
$867$	−0.0264459	+	0.0363997i	−0.000898150	+	0.00123620i
$868$	−3.48502	+	6.38370i	−0.118289	+	0.216677i
$869$	4.79187	+	3.02710i	0.162553	+	0.102687i
$870$	13.6260			0.461965
$871$	−3.86685	−	2.80943i	−0.131023	−	0.0951940i
$872$	5.86676	−	18.0560i	0.198674	−	0.611455i
$873$	6.12940	−	1.99156i	0.207449	−	0.0674041i
$874$	16.1310	+	22.2024i	0.545638	+	0.751006i
$875$	−4.11709	−	31.8356i	−0.139183	−	1.07624i
$876$	−6.57482	+	2.13629i	−0.222142	+	0.0721785i
$877$	10.3046	+	3.34816i	0.347961	+	0.113059i	0.477783	−	0.878478i	$-0.341441\pi$
$877$	10.3046	+	3.34816i	0.347961	+	0.113059i	−0.129822	+	0.991537i	$0.541441\pi$
$878$	−13.5008	+	18.5823i	−0.455631	+	0.627123i
$879$		−	0.0735814i		−	0.00248184i
$880$	−1.56196	+	6.13619i	−0.0526537	+	0.206851i
$881$		−	5.09128i		−	0.171530i	−0.996315	−	0.0857648i	$-0.972667\pi$
$881$		−	5.09128i		−	0.171530i	0.996315	−	0.0857648i	$-0.0273334\pi$
$882$	6.98866	+	0.398368i	0.235320	+	0.0134138i
$883$	−13.9190	+	42.8382i	−0.468410	+	1.44162i	0.386232	+	0.922402i	$0.373776\pi$
$883$	−13.9190	+	42.8382i	−0.468410	+	1.44162i	−0.854642	+	0.519217i	$0.826224\pi$
$884$	−3.46890	−	10.6762i	−0.116672	−	0.359079i
$885$	−3.69505	−	5.08580i	−0.124208	−	0.170957i
$886$	−1.12704	−	1.55123i	−0.0378635	−	0.0521147i
$887$	2.99211	+	9.20876i	0.100465	+	0.309200i	0.988639	−	0.150307i	$-0.0480262\pi$
$887$	2.99211	+	9.20876i	0.100465	+	0.309200i	−0.888174	+	0.459507i	$0.848026\pi$
$888$	0.321233	−	0.988653i	0.0107799	−	0.0331770i
$889$	−30.0412	+	14.2446i	−1.00755	+	0.477747i
$890$		−	13.5058i		−	0.452714i
$891$	3.08118	−	1.22732i	0.103224	−	0.0411167i
$892$		−	3.67235i		−	0.122959i
$893$	17.7934	−	24.4905i	0.595433	−	0.819543i
$894$	−17.9593	−	5.83532i	−0.600648	−	0.195162i
$895$	7.39938	−	2.40420i	0.247334	−	0.0803637i
$896$	0.339331	+	2.62390i	0.0113363	+	0.0876584i
$897$	10.9981	+	15.1376i	0.367216	+	0.505429i
$898$	−16.8933	+	5.48896i	−0.563736	+	0.183169i
$899$	6.06292	−	18.6598i	0.202210	−	0.622338i
$900$	−1.09640	−	0.796579i	−0.0365466	−	0.0265526i
$901$	20.2508			0.674653
$902$	20.7507	−	17.2390i	0.690923	−	0.573997i
$903$	2.82629	+	1.54294i	0.0940530	+	0.0513459i
$904$	−7.49417	+	10.3148i	−0.249252	+	0.343066i
$905$	−9.72048	+	29.9166i	−0.323120	+	0.994460i
$906$	15.5959	−	5.06741i	0.518139	−	0.168353i
$907$	31.1086	−	22.6017i	1.03294	−	0.750478i	0.0640482	−	0.997947i	$-0.479599\pi$
$907$	31.1086	−	22.6017i	1.03294	−	0.750478i	0.968896	+	0.247469i	$0.0795988\pi$
$908$	0.521948	−	0.379218i	0.0173215	−	0.0125848i
$909$	3.34317	+	10.2892i	0.110886	+	0.341272i
$910$	9.98389	−	9.43100i	0.330963	−	0.312635i
$911$	−1.74791	−	1.26993i	−0.0579108	−	0.0420746i	0.558453	−	0.829536i	$-0.311395\pi$
$911$	−1.74791	−	1.26993i	−0.0579108	−	0.0420746i	−0.616364	+	0.787461i	$0.711395\pi$
$912$		−	3.98799i		−	0.132055i
$913$	−3.02523	−	3.64149i	−0.100121	−	0.120516i
$914$	−20.0016			−0.661593
$915$	11.8576	+	8.61502i	0.391999	+	0.284804i
$916$	−2.63900	−	0.857462i	−0.0871949	−	0.0283313i
$917$	0.346722	−	1.84713i	0.0114498	−	0.0609975i
$918$	−3.34007	+	2.42671i	−0.110239	+	0.0800932i
$919$	17.8319	+	24.5435i	0.588220	+	0.809616i	0.994566	−	0.104103i	$-0.0331972\pi$
$919$	17.8319	+	24.5435i	0.588220	+	0.809616i	−0.406346	+	0.913719i	$0.633197\pi$
$920$	4.05981	+	12.4948i	0.133848	+	0.411942i
$921$	12.5822	+	4.08820i	0.414597	+	0.134711i
$922$	9.60793	−	13.2242i	0.316420	−	0.435515i
$923$	34.0658			1.12129
$924$	1.05610	−	8.71118i	0.0347431	−	0.286577i
$925$	1.40880			0.0463209
$926$	15.7043	−	21.6152i	0.516076	−	0.710318i
$927$	−10.3277	−	3.35566i	−0.339205	−	0.110214i
$928$	−2.20554	−	6.78796i	−0.0724005	−	0.222826i
$929$	6.02613	+	8.29426i	0.197711	+	0.272126i	0.896349	−	0.443350i	$-0.146210\pi$
$929$	6.02613	+	8.29426i	0.197711	+	0.272126i	−0.698638	+	0.715476i	$0.746210\pi$
$930$	4.24580	−	3.08476i	0.139225	−	0.101153i
$931$	−17.6672	+	21.6140i	−0.579021	+	0.708372i
$932$	13.2999	+	4.32139i	0.435651	+	0.141552i
$933$	−25.5880	−	18.5908i	−0.837713	−	0.608634i
$934$	19.8992			0.651121
$935$	−6.44865	+	25.3336i	−0.210893	+	0.828498i
$936$		−	2.71901i		−	0.0888737i
$937$	−6.04418	−	4.39135i	−0.197455	−	0.143459i	0.484665	−	0.874700i	$-0.338942\pi$
$937$	−6.04418	−	4.39135i	−0.197455	−	0.143459i	−0.682119	+	0.731241i	$0.738942\pi$
$938$	3.19374	+	3.38097i	0.104279	+	0.110393i
$939$	−10.1280	−	31.1707i	−0.330514	−	1.01722i
$940$	11.7241	−	8.51805i	0.382398	−	0.277828i
$941$	−6.90963	+	5.02014i	−0.225247	+	0.163652i	−0.694686	−	0.719314i	$-0.744456\pi$
$941$	−6.90963	+	5.02014i	−0.225247	+	0.163652i	0.469438	+	0.882965i	$0.344456\pi$
$942$	12.6177	−	4.09974i	0.411107	−	0.133577i
$943$	17.2971	−	53.2349i	0.563270	−	1.73357i
$944$	−1.93546	+	2.66393i	−0.0629939	+	0.0867037i
$945$	−4.43345	−	2.42033i	−0.144220	−	0.0787333i
$946$	2.15581	−	3.41262i	0.0700914	−	0.110954i
$947$	14.3206			0.465358			0.232679	−	0.972554i	$-0.425251\pi$
$947$	14.3206			0.465358			0.232679	+	0.972554i	$0.425251\pi$
$948$	−1.38256	−	1.00449i	−0.0449036	−	0.0326244i
$949$	5.80859	−	17.8770i	0.188555	−	0.580312i
$950$	5.14009	−	1.67012i	0.166766	−	0.0541857i
$951$	1.90063	+	2.61599i	0.0616320	+	0.0848292i
$952$	1.40095	+	10.8329i	0.0454050	+	0.351097i
$953$	−24.9335	+	8.10139i	−0.807676	+	0.262430i	−0.683613	−	0.729844i	$-0.739592\pi$
$953$	−24.9335	+	8.10139i	−0.807676	+	0.262430i	−0.124063	+	0.992274i	$0.539592\pi$
$954$	4.66499	+	1.51575i	0.151035	+	0.0490741i
$955$	−29.1884	+	40.1744i	−0.944515	+	1.30001i
$956$		−	3.21094i		−	0.103849i
$957$	1.53530	+	23.6219i	0.0496293	+	0.763586i
$958$			2.74828i			0.0887929i
$959$	20.6734	+	43.5994i	0.667579	+	1.40790i
$960$	0.589954	−	1.81569i	0.0190407	−	0.0586012i
$961$	7.24437	+	22.2959i	0.233689	+	0.719222i
$962$	1.66138	+	2.28669i	0.0535649	+	0.0737258i
$963$	−5.57553	−	7.67406i	−0.179669	−	0.247293i
$964$	−7.54357	−	23.2167i	−0.242962	−	0.747760i
$965$	−13.2556	+	40.7966i	−0.426714	+	1.31329i
$966$	−7.80063	−	16.4512i	−0.250981	−	0.529309i
$967$			7.95189i			0.255715i	0.991793	+	0.127858i	$0.0408101\pi$
$967$			7.95189i			0.255715i	−0.991793	+	0.127858i	$0.959190\pi$
$968$	−10.8136	−	2.01640i	−0.347563	−	0.0648097i
$969$		−	16.4646i		−	0.528920i
$970$	−7.23212	+	9.95416i	−0.232209	+	0.319609i
$971$	−3.14087	−	1.02053i	−0.100795	−	0.0327504i	0.258185	−	0.966095i	$-0.416876\pi$
$971$	−3.14087	−	1.02053i	−0.100795	−	0.0327504i	−0.358980	+	0.933345i	$0.616876\pi$
$972$	−0.951057	+	0.309017i	−0.0305052	+	0.00991172i
$973$	−54.0295	+	6.98727i	−1.73211	+	0.224002i
$974$	14.4781	+	19.9275i	0.463910	+	0.638517i
$975$	3.50452	−	1.13869i	0.112234	−	0.0364671i
$976$	2.37238	−	7.30144i	0.0759381	−	0.233713i
$977$	−12.0874	−	8.78203i	−0.386711	−	0.280962i	0.377395	−	0.926052i	$-0.376820\pi$
$977$	−12.0874	−	8.78203i	−0.386711	−	0.280962i	−0.764106	+	0.645090i	$0.776820\pi$
$978$	14.6637			0.468894
$979$	23.4134	−	1.52175i	0.748295	−	0.0486354i
$980$	−11.2411	+	7.22709i	−0.359085	+	0.230861i
$981$	11.1592	−	15.3594i	0.356287	−	0.490387i
$982$	2.33774	−	7.19483i	0.0746003	−	0.229596i
$983$	−4.67661	+	1.51952i	−0.149161	+	0.0484652i	−0.382646	−	0.923895i	$-0.624987\pi$
$983$	−4.67661	+	1.51952i	−0.149161	+	0.0484652i	0.233485	+	0.972360i	$0.424987\pi$
$984$	−6.58052	+	4.78103i	−0.209779	+	0.152414i
$985$	−27.9888	+	20.3351i	−0.891797	+	0.647929i
$986$	−9.10571	−	28.0245i	−0.289985	−	0.892482i
$987$	−14.5995	+	13.7910i	−0.464708	+	0.438973i
$988$	8.77249	+	6.37359i	0.279090	+	0.202771i
$989$		−	8.37526i		−	0.266318i
$990$	−3.38170	+	5.35319i	−0.107478	+	0.170136i
$991$	−45.0334			−1.43053			−0.715266	−	0.698852i	$-0.753695\pi$
$991$	−45.0334			−1.43053			−0.715266	+	0.698852i	$0.753695\pi$
$992$	−2.22395	−	1.61579i	−0.0706103	−	0.0513014i
$993$	15.2085	+	4.94154i	0.482627	+	0.156815i
$994$	−32.5789	−	6.11535i	−1.03334	−	0.193967i
$995$	1.10199	−	0.800646i	0.0349356	−	0.0253822i
$996$	0.839010	+	1.15480i	0.0265850	+	0.0365912i
$997$	6.69325	+	20.5997i	0.211977	+	0.652399i	0.999354	+	0.0359275i	$0.0114385\pi$
$997$	6.69325	+	20.5997i	0.211977	+	0.652399i	−0.787377	+	0.616472i	$0.788561\pi$
$998$	−5.40777	−	1.75709i	−0.171180	−	0.0556197i
$999$	0.611021	−	0.840999i	0.0193319	−	0.0266080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.a.139.4	✓	32
7.6	odd	2		462.2.u.b.139.1	yes	32
11.8	odd	10		462.2.u.b.349.1	yes	32
77.41	even	10	inner	462.2.u.a.349.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.139.4	✓	32	1.1	even	1	trivial
462.2.u.a.349.4	yes	32	77.41	even	10	inner
462.2.u.b.139.1	yes	32	7.6	odd	2
462.2.u.b.349.1	yes	32	11.8	odd	10

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.12216 + 1.54452i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.488107 - 2.60034i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.12216 + 1.54452i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.488107 - 2.60034i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} -1.90913 q^{10} +(-0.215110 - 3.30964i) q^{11} +1.00000i q^{12} +(-2.19973 - 1.59820i) q^{13} +(1.81681 + 1.92333i) q^{14} +(-0.589954 - 1.81569i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.34007 + 2.42671i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(1.23236 - 3.79280i) q^{19} +(1.12216 - 1.54452i) q^{20} +(-1.26777 + 2.32223i) q^{21} +(2.80399 + 1.77133i) q^{22} +6.88157 q^{23} +(-0.809017 - 0.587785i) q^{24} +(0.418787 - 1.28889i) q^{25} +(2.58594 - 0.840221i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-2.62390 + 0.339331i) q^{28} +(6.78796 - 2.20554i) q^{29} +(1.81569 + 0.589954i) q^{30} +(1.61579 - 2.22395i) q^{31} -1.00000i q^{32} +(-0.818154 + 3.21413i) q^{33} -4.12856i q^{34} +(4.56400 - 2.16410i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.321233 + 0.988653i) q^{37} +(2.34408 + 3.22635i) q^{38} +(1.59820 + 2.19973i) q^{39} +(0.589954 + 1.81569i) q^{40} +(2.51353 - 7.73587i) q^{41} +(-1.13355 - 2.39062i) q^{42} -1.21706i q^{43} +(-3.08118 + 1.22732i) q^{44} +1.90913i q^{45} +(-4.04489 + 5.56731i) q^{46} +(7.21926 + 2.34568i) q^{47} +(0.951057 - 0.309017i) q^{48} +(-6.52350 - 2.53848i) q^{49} +(0.796579 + 1.09640i) q^{50} +(3.92649 - 1.27579i) q^{51} +(-0.840221 + 2.58594i) q^{52} +(-3.96828 - 2.88312i) q^{53} +1.00000 q^{54} +(4.87042 - 4.04618i) q^{55} +(1.26777 - 2.32223i) q^{56} +(-2.34408 + 3.22635i) q^{57} +(-2.20554 + 6.78796i) q^{58} +(3.13164 - 1.01753i) q^{59} +(-1.54452 + 1.12216i) q^{60} +(-6.21098 + 4.51254i) q^{61} +(0.849472 + 2.61440i) q^{62} +(1.92333 - 1.81681i) q^{63} +(0.809017 + 0.587785i) q^{64} -5.19095i q^{65} +(-2.11939 - 2.55112i) q^{66} +1.75788 q^{67} +(3.34007 + 2.42671i) q^{68} +(-6.54476 - 2.12652i) q^{69} +(-0.931859 + 4.96438i) q^{70} +(-10.1359 + 7.36420i) q^{71} +(0.587785 + 0.809017i) q^{72} +(2.13629 + 6.57482i) q^{73} +(-0.988653 - 0.321233i) q^{74} +(-0.796579 + 1.09640i) q^{75} -3.98799 q^{76} +(-8.71118 - 1.05610i) q^{77} -2.71901 q^{78} +(-1.00449 + 1.38256i) q^{79} +(-1.81569 - 0.589954i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.78103 + 6.58052i) q^{82} +(1.15480 - 0.839010i) q^{83} +(2.60034 + 0.488107i) q^{84} +(-7.49618 - 2.43566i) q^{85} +(0.984619 + 0.715368i) q^{86} -7.13729 q^{87} +(0.818154 - 3.21413i) q^{88} +7.07430i q^{89} +(-1.54452 - 1.12216i) q^{90} +(-5.22955 + 4.93994i) q^{91} +(-2.12652 - 6.54476i) q^{92} +(-2.22395 + 1.61579i) q^{93} +(-6.14107 + 4.46175i) q^{94} +(7.24095 - 2.35273i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(3.78817 - 5.21398i) q^{97} +(5.88810 - 3.78554i) q^{98} +(1.77133 - 2.80399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

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