LMFDB - Embedded newform 82.2.d.b.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,2,Mod(37,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	82.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.654773296574$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			51.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	82.51
Dual form			82.2.d.b.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{2} -0.618034 q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 1.53884i) q^{5} +(-0.500000 - 0.363271i) q^{6} +(2.11803 - 1.53884i) q^{7} +(-0.309017 + 0.951057i) q^{8} -2.61803 q^{9} +(-0.500000 + 1.53884i) q^{10} +(0.927051 - 2.85317i) q^{11} +(-0.190983 - 0.587785i) q^{12} +(-5.04508 - 3.66547i) q^{13} +2.61803 q^{14} +(-0.309017 - 0.951057i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.30902 + 4.02874i) q^{17} +(-2.11803 - 1.53884i) q^{18} +(1.42705 - 1.03681i) q^{19} +(-1.30902 + 0.951057i) q^{20} +(-1.30902 + 0.951057i) q^{21} +(2.42705 - 1.76336i) q^{22} +(1.30902 + 0.951057i) q^{23} +(0.190983 - 0.587785i) q^{24} +(1.92705 - 1.40008i) q^{25} +(-1.92705 - 5.93085i) q^{26} +3.47214 q^{27} +(2.11803 + 1.53884i) q^{28} +(-0.163119 - 0.502029i) q^{29} +(0.309017 - 0.951057i) q^{30} +(-1.88197 + 5.79210i) q^{31} -1.00000 q^{32} +(-0.572949 + 1.76336i) q^{33} +(-3.42705 + 2.48990i) q^{34} +(3.42705 + 2.48990i) q^{35} +(-0.809017 - 2.48990i) q^{36} +(0.454915 + 1.40008i) q^{37} +1.76393 q^{38} +(3.11803 + 2.26538i) q^{39} -1.61803 q^{40} +(2.19098 + 6.01661i) q^{41} -1.61803 q^{42} +(-7.85410 - 5.70634i) q^{43} +3.00000 q^{44} +(-1.30902 - 4.02874i) q^{45} +(0.500000 + 1.53884i) q^{46} +(1.23607 + 0.898056i) q^{47} +(0.500000 - 0.363271i) q^{48} +(-0.0450850 + 0.138757i) q^{49} +2.38197 q^{50} +(0.809017 - 2.48990i) q^{51} +(1.92705 - 5.93085i) q^{52} +(3.66312 + 11.2739i) q^{53} +(2.80902 + 2.04087i) q^{54} +4.85410 q^{55} +(0.809017 + 2.48990i) q^{56} +(-0.881966 + 0.640786i) q^{57} +(0.163119 - 0.502029i) q^{58} +(4.11803 + 2.99193i) q^{59} +(0.809017 - 0.587785i) q^{60} +(2.80902 - 2.04087i) q^{61} +(-4.92705 + 3.57971i) q^{62} +(-5.54508 + 4.02874i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.11803 - 9.59632i) q^{65} +(-1.50000 + 1.08981i) q^{66} +(-4.76393 - 14.6619i) q^{67} -4.23607 q^{68} +(-0.809017 - 0.587785i) q^{69} +(1.30902 + 4.02874i) q^{70} +(1.19098 - 3.66547i) q^{71} +(0.809017 - 2.48990i) q^{72} -16.1803 q^{73} +(-0.454915 + 1.40008i) q^{74} +(-1.19098 + 0.865300i) q^{75} +(1.42705 + 1.03681i) q^{76} +(-2.42705 - 7.46969i) q^{77} +(1.19098 + 3.66547i) q^{78} +14.0000 q^{79} +(-1.30902 - 0.951057i) q^{80} +5.70820 q^{81} +(-1.76393 + 6.15537i) q^{82} -16.0902 q^{83} +(-1.30902 - 0.951057i) q^{84} -6.85410 q^{85} +(-3.00000 - 9.23305i) q^{86} +(0.100813 + 0.310271i) q^{87} +(2.42705 + 1.76336i) q^{88} +(5.04508 - 3.66547i) q^{89} +(1.30902 - 4.02874i) q^{90} -16.3262 q^{91} +(-0.500000 + 1.53884i) q^{92} +(1.16312 - 3.57971i) q^{93} +(0.472136 + 1.45309i) q^{94} +(2.30902 + 1.67760i) q^{95} +0.618034 q^{96} +(1.69098 + 5.20431i) q^{97} +(-0.118034 + 0.0857567i) q^{98} +(-2.42705 + 7.46969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + q^{8} - 6 q^{9} - 2 q^{10} - 3 q^{11} - 3 q^{12} - 9 q^{13} + 6 q^{14} + q^{15} - q^{16} - 3 q^{17} - 4 q^{18} - q^{19} - 3 q^{20} - 3 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) $ 4 * q + q^2 + 2 * q^3 - q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + q^8 - 6 * q^9 - 2 * q^10 - 3 * q^11 - 3 * q^12 - 9 * q^13 + 6 * q^14 + q^15 - q^16 - 3 * q^17 - 4 * q^18 - q^19 - 3 * q^20 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^24 + q^25 - q^26 - 4 * q^27 + 4 * q^28 + 15 * q^29 - q^30 - 12 * q^31 - 4 * q^32 - 9 * q^33 - 7 * q^34 + 7 * q^35 - q^36 + 13 * q^37 + 16 * q^38 + 8 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 - 18 * q^43 + 12 * q^44 - 3 * q^45 + 2 * q^46 - 4 * q^47 + 2 * q^48 + 11 * q^49 + 14 * q^50 + q^51 + q^52 - q^53 + 9 * q^54 + 6 * q^55 + q^56 - 8 * q^57 - 15 * q^58 + 12 * q^59 + q^60 + 9 * q^61 - 13 * q^62 - 11 * q^63 - q^64 + 8 * q^65 - 6 * q^66 - 28 * q^67 - 8 * q^68 - q^69 + 3 * q^70 + 7 * q^71 + q^72 - 20 * q^73 - 13 * q^74 - 7 * q^75 - q^76 - 3 * q^77 + 7 * q^78 + 56 * q^79 - 3 * q^80 - 4 * q^81 - 16 * q^82 - 42 * q^83 - 3 * q^84 - 14 * q^85 - 12 * q^86 + 25 * q^87 + 3 * q^88 + 9 * q^89 + 3 * q^90 - 34 * q^91 - 2 * q^92 - 11 * q^93 - 16 * q^94 + 7 * q^95 - 2 * q^96 + 9 * q^97 + 4 * q^98 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.618034			−0.356822			−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034			−0.356822			−0.178411	+	0.983956i	$0.557096\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.500000	+	1.53884i	0.223607	+	0.688191i	0.998430	+	0.0560130i	$0.0178388\pi$
$5$	0.500000	+	1.53884i	0.223607	+	0.688191i	−0.774823	+	0.632178i	$0.782161\pi$
$6$	−0.500000	−	0.363271i	−0.204124	−	0.148305i
$7$	2.11803	−	1.53884i	0.800542	−	0.581628i	−0.110531	−	0.993873i	$-0.535255\pi$
$7$	2.11803	−	1.53884i	0.800542	−	0.581628i	0.911073	+	0.412245i	$0.135255\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.61803			−0.872678
$10$	−0.500000	+	1.53884i	−0.158114	+	0.486624i
$11$	0.927051	−	2.85317i	0.279516	−	0.860263i	−0.708473	−	0.705738i	$-0.750615\pi$
$11$	0.927051	−	2.85317i	0.279516	−	0.860263i	0.987989	−	0.154525i	$-0.0493846\pi$
$12$	−0.190983	−	0.587785i	−0.0551320	−	0.169679i
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.994777	−	0.102070i	$-0.967453\pi$
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.404478	−	0.914548i	$-0.632547\pi$
$14$	2.61803			0.699699
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.30902	+	4.02874i	−0.317483	+	0.977113i	0.657237	+	0.753684i	$0.271725\pi$
$17$	−1.30902	+	4.02874i	−0.317483	+	0.977113i	−0.974720	+	0.223429i	$0.928275\pi$
$18$	−2.11803	−	1.53884i	−0.499225	−	0.362708i
$19$	1.42705	−	1.03681i	0.327388	−	0.237861i	−0.411934	−	0.911214i	$-0.635146\pi$
$19$	1.42705	−	1.03681i	0.327388	−	0.237861i	0.739321	+	0.673353i	$0.235146\pi$
$20$	−1.30902	+	0.951057i	−0.292705	+	0.212663i
$21$	−1.30902	+	0.951057i	−0.285651	+	0.207538i
$22$	2.42705	−	1.76336i	0.517449	−	0.375949i
$23$	1.30902	+	0.951057i	0.272949	+	0.198309i	0.715836	−	0.698268i	$-0.246046\pi$
$23$	1.30902	+	0.951057i	0.272949	+	0.198309i	−0.442887	+	0.896577i	$0.646046\pi$
$24$	0.190983	−	0.587785i	0.0389842	−	0.119981i
$25$	1.92705	−	1.40008i	0.385410	−	0.280017i
$26$	−1.92705	−	5.93085i	−0.377926	−	1.16314i
$27$	3.47214			0.668213
$28$	2.11803	+	1.53884i	0.400271	+	0.290814i
$29$	−0.163119	−	0.502029i	−0.0302904	−	0.0932244i	0.934768	−	0.355258i	$-0.115607\pi$
$29$	−0.163119	−	0.502029i	−0.0302904	−	0.0932244i	−0.965059	+	0.262033i	$0.915607\pi$
$30$	0.309017	−	0.951057i	0.0564185	−	0.173638i
$31$	−1.88197	+	5.79210i	−0.338011	+	1.04029i	0.627209	+	0.778851i	$0.284197\pi$
$31$	−1.88197	+	5.79210i	−0.338011	+	1.04029i	−0.965220	+	0.261440i	$0.915803\pi$
$32$	−1.00000			−0.176777
$33$	−0.572949	+	1.76336i	−0.0997376	+	0.306961i
$34$	−3.42705	+	2.48990i	−0.587734	+	0.427014i
$35$	3.42705	+	2.48990i	0.579277	+	0.420870i
$36$	−0.809017	−	2.48990i	−0.134836	−	0.414983i
$37$	0.454915	+	1.40008i	0.0747876	+	0.230172i	0.981461	−	0.191660i	$-0.0613871\pi$
$37$	0.454915	+	1.40008i	0.0747876	+	0.230172i	−0.906674	+	0.421832i	$0.861387\pi$
$38$	1.76393			0.286148
$39$	3.11803	+	2.26538i	0.499285	+	0.362752i
$40$	−1.61803			−0.255834
$41$	2.19098	+	6.01661i	0.342174	+	0.939637i
$41$	2.19098	+	6.01661i	0.342174	+	0.939637i
$42$	−1.61803			−0.249668
$43$	−7.85410	−	5.70634i	−1.19774	−	0.870209i	−0.203679	−	0.979038i	$-0.565290\pi$
$43$	−7.85410	−	5.70634i	−1.19774	−	0.870209i	−0.994060	+	0.108829i	$0.965290\pi$
$44$	3.00000			0.452267
$45$	−1.30902	−	4.02874i	−0.195137	−	0.600569i
$46$	0.500000	+	1.53884i	0.0737210	+	0.226890i
$47$	1.23607	+	0.898056i	0.180299	+	0.130995i	0.674274	−	0.738481i	$-0.264457\pi$
$47$	1.23607	+	0.898056i	0.180299	+	0.130995i	−0.493975	+	0.869476i	$0.664457\pi$
$48$	0.500000	−	0.363271i	0.0721688	−	0.0524337i
$49$	−0.0450850	+	0.138757i	−0.00644071	+	0.0198225i
$50$	2.38197			0.336861
$51$	0.809017	−	2.48990i	0.113285	−	0.348655i
$52$	1.92705	−	5.93085i	0.267234	−	0.822461i
$53$	3.66312	+	11.2739i	0.503168	+	1.54859i	0.803829	+	0.594861i	$0.202793\pi$
$53$	3.66312	+	11.2739i	0.503168	+	1.54859i	−0.300661	+	0.953731i	$0.597207\pi$
$54$	2.80902	+	2.04087i	0.382259	+	0.277727i
$55$	4.85410			0.654527
$56$	0.809017	+	2.48990i	0.108109	+	0.332727i
$57$	−0.881966	+	0.640786i	−0.116819	+	0.0848742i
$58$	0.163119	−	0.502029i	0.0214186	−	0.0659196i
$59$	4.11803	+	2.99193i	0.536122	+	0.389516i	0.822643	−	0.568558i	$-0.192499\pi$
$59$	4.11803	+	2.99193i	0.536122	+	0.389516i	−0.286521	+	0.958074i	$0.592499\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	2.80902	−	2.04087i	0.359658	−	0.261307i	−0.393252	−	0.919431i	$-0.628650\pi$
$61$	2.80902	−	2.04087i	0.359658	−	0.261307i	0.752909	+	0.658124i	$0.228650\pi$
$62$	−4.92705	+	3.57971i	−0.625736	+	0.454624i
$63$	−5.54508	+	4.02874i	−0.698615	+	0.507574i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	3.11803	−	9.59632i	0.386745	−	1.19028i
$66$	−1.50000	+	1.08981i	−0.184637	+	0.134147i
$67$	−4.76393	−	14.6619i	−0.582007	−	1.79123i	−0.610971	−	0.791653i	$-0.709221\pi$
$67$	−4.76393	−	14.6619i	−0.582007	−	1.79123i	0.0289644	−	0.999580i	$-0.490779\pi$
$68$	−4.23607			−0.513699
$69$	−0.809017	−	0.587785i	−0.0973942	−	0.0707610i
$70$	1.30902	+	4.02874i	0.156457	+	0.481527i
$71$	1.19098	−	3.66547i	0.141344	−	0.435011i	−0.855179	−	0.518333i	$-0.826553\pi$
$71$	1.19098	−	3.66547i	0.141344	−	0.435011i	0.996523	+	0.0833216i	$0.0265529\pi$
$72$	0.809017	−	2.48990i	0.0953436	−	0.293437i
$73$	−16.1803			−1.89377			−0.946883	−	0.321579i	$-0.895786\pi$
$73$	−16.1803			−1.89377			−0.946883	+	0.321579i	$0.895786\pi$
$74$	−0.454915	+	1.40008i	−0.0528828	+	0.162757i
$75$	−1.19098	+	0.865300i	−0.137523	+	0.0999162i
$76$	1.42705	+	1.03681i	0.163694	+	0.118931i
$77$	−2.42705	−	7.46969i	−0.276588	−	0.851251i
$78$	1.19098	+	3.66547i	0.134852	+	0.415033i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	−1.30902	−	0.951057i	−0.146353	−	0.106331i
$81$	5.70820			0.634245
$82$	−1.76393	+	6.15537i	−0.194794	+	0.679747i
$83$	−16.0902			−1.76613			−0.883063	−	0.469255i	$-0.844523\pi$
$83$	−16.0902			−1.76613			−0.883063	+	0.469255i	$0.844523\pi$
$84$	−1.30902	−	0.951057i	−0.142825	−	0.103769i
$85$	−6.85410			−0.743432
$86$	−3.00000	−	9.23305i	−0.323498	−	0.995625i
$87$	0.100813	+	0.310271i	0.0108083	+	0.0332645i
$88$	2.42705	+	1.76336i	0.258725	+	0.187974i
$89$	5.04508	−	3.66547i	0.534778	−	0.388539i	−0.287364	−	0.957821i	$-0.592779\pi$
$89$	5.04508	−	3.66547i	0.534778	−	0.388539i	0.822142	+	0.569283i	$0.192779\pi$
$90$	1.30902	−	4.02874i	0.137983	−	0.424666i
$91$	−16.3262			−1.71145
$92$	−0.500000	+	1.53884i	−0.0521286	+	0.160435i
$93$	1.16312	−	3.57971i	0.120610	−	0.371199i
$94$	0.472136	+	1.45309i	0.0486971	+	0.149874i
$95$	2.30902	+	1.67760i	0.236900	+	0.172118i
$96$	0.618034			0.0630778
$97$	1.69098	+	5.20431i	0.171693	+	0.528418i	0.999467	−	0.0326444i	$-0.0103929\pi$
$97$	1.69098	+	5.20431i	0.171693	+	0.528418i	−0.827774	+	0.561062i	$0.810393\pi$
$98$	−0.118034	+	0.0857567i	−0.0119232	+	0.00866274i
$99$	−2.42705	+	7.46969i	−0.243928	+	0.750733i
$100$	1.92705	+	1.40008i	0.192705	+	0.140008i
$101$	−6.30902	+	4.58377i	−0.627771	+	0.456102i	−0.855627	−	0.517593i	$-0.826828\pi$
$101$	−6.30902	+	4.58377i	−0.627771	+	0.456102i	0.227857	+	0.973695i	$0.426828\pi$
$102$	2.11803	−	1.53884i	0.209717	−	0.152368i
$103$	9.89919	−	7.19218i	0.975396	−	0.708667i	0.0187209	−	0.999825i	$-0.494041\pi$
$103$	9.89919	−	7.19218i	0.975396	−	0.708667i	0.956675	+	0.291158i	$0.0940406\pi$
$104$	5.04508	−	3.66547i	0.494711	−	0.359429i
$105$	−2.11803	−	1.53884i	−0.206699	−	0.150176i
$106$	−3.66312	+	11.2739i	−0.355794	+	1.09502i
$107$	4.61803	−	3.35520i	0.446442	−	0.324359i	−0.341747	−	0.939792i	$-0.611019\pi$
$107$	4.61803	−	3.35520i	0.446442	−	0.324359i	0.788189	+	0.615433i	$0.211019\pi$
$108$	1.07295	+	3.30220i	0.103245	+	0.317754i
$109$	7.47214			0.715701			0.357850	−	0.933779i	$-0.383510\pi$
$109$	7.47214			0.715701			0.357850	+	0.933779i	$0.383510\pi$
$110$	3.92705	+	2.85317i	0.374430	+	0.272039i
$111$	−0.281153	−	0.865300i	−0.0266859	−	0.0821306i
$112$	−0.809017	+	2.48990i	−0.0764449	+	0.235273i
$113$	5.51722	−	16.9803i	0.519016	−	1.59737i	−0.256837	−	0.966455i	$-0.582680\pi$
$113$	5.51722	−	16.9803i	0.519016	−	1.59737i	0.775853	−	0.630914i	$-0.217320\pi$
$114$	−1.09017			−0.102104
$115$	−0.809017	+	2.48990i	−0.0754412	+	0.232184i
$116$	0.427051	−	0.310271i	0.0396507	−	0.0288079i
$117$	13.2082	+	9.59632i	1.22110	+	0.887180i
$118$	1.57295	+	4.84104i	0.144802	+	0.445654i
$119$	3.42705	+	10.5474i	0.314157	+	0.966877i
$120$	1.00000			0.0912871
$121$	1.61803	+	1.17557i	0.147094	+	0.106870i
$122$	3.47214			0.314352
$123$	−1.35410	−	3.71847i	−0.122095	−	0.335283i
$124$	−6.09017			−0.546913
$125$	9.66312	+	7.02067i	0.864296	+	0.627948i
$126$	−6.85410			−0.610612
$127$	2.10081	+	6.46564i	0.186417	+	0.573733i	0.999970	−	0.00775835i	$-0.00246958\pi$
$127$	2.10081	+	6.46564i	0.186417	+	0.573733i	−0.813553	+	0.581491i	$0.802470\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	4.85410	+	3.52671i	0.427380	+	0.310510i
$130$	8.16312	−	5.93085i	0.715953	−	0.520170i
$131$	−2.82624	+	8.69827i	−0.246930	+	0.759971i	0.748384	+	0.663266i	$0.230830\pi$
$131$	−2.82624	+	8.69827i	−0.246930	+	0.759971i	−0.995313	+	0.0967048i	$0.969170\pi$
$132$	−1.85410			−0.161379
$133$	1.42705	−	4.39201i	0.123741	−	0.380836i
$134$	4.76393	−	14.6619i	0.411541	−	1.26659i
$135$	1.73607	+	5.34307i	0.149417	+	0.459858i
$136$	−3.42705	−	2.48990i	−0.293867	−	0.213507i
$137$	−6.76393			−0.577882			−0.288941	−	0.957347i	$-0.593303\pi$
$137$	−6.76393			−0.577882			−0.288941	+	0.957347i	$0.593303\pi$
$138$	−0.309017	−	0.951057i	−0.0263053	−	0.0809593i
$139$	−0.190983	+	0.138757i	−0.0161990	+	0.0117692i	−0.595855	−	0.803092i	$-0.703187\pi$
$139$	−0.190983	+	0.138757i	−0.0161990	+	0.0117692i	0.579656	+	0.814861i	$0.303187\pi$
$140$	−1.30902	+	4.02874i	−0.110632	+	0.340491i
$141$	−0.763932	−	0.555029i	−0.0643347	−	0.0467419i
$142$	3.11803	−	2.26538i	0.261660	−	0.190107i
$143$	−15.1353	+	10.9964i	−1.26567	+	0.919566i
$144$	2.11803	−	1.53884i	0.176503	−	0.128237i
$145$	0.690983	−	0.502029i	0.0573830	−	0.0416912i
$146$	−13.0902	−	9.51057i	−1.08335	−	0.787100i
$147$	0.0278640	−	0.0857567i	0.00229819	−	0.00707309i
$148$	−1.19098	+	0.865300i	−0.0978982	+	0.0711272i
$149$	−3.52786	−	10.8576i	−0.289014	−	0.889493i	−0.985167	−	0.171600i	$-0.945106\pi$
$149$	−3.52786	−	10.8576i	−0.289014	−	0.889493i	0.696153	−	0.717894i	$-0.254894\pi$
$150$	−1.47214			−0.120199
$151$	12.3262	+	8.95554i	1.00310	+	0.728791i	0.962750	−	0.270395i	$-0.0871542\pi$
$151$	12.3262	+	8.95554i	1.00310	+	0.728791i	0.0403454	+	0.999186i	$0.487154\pi$
$152$	0.545085	+	1.67760i	0.0442122	+	0.136071i
$153$	3.42705	−	10.5474i	0.277061	−	0.852705i
$154$	2.42705	−	7.46969i	0.195577	−	0.601925i
$155$	−9.85410			−0.791501
$156$	−1.19098	+	3.66547i	−0.0953550	+	0.293472i
$157$	−2.38197	+	1.73060i	−0.190102	+	0.138117i	−0.678765	−	0.734355i	$-0.737485\pi$
$157$	−2.38197	+	1.73060i	−0.190102	+	0.138117i	0.488664	+	0.872472i	$0.337485\pi$
$158$	11.3262	+	8.22899i	0.901067	+	0.654664i
$159$	−2.26393	−	6.96767i	−0.179541	−	0.552572i
$160$	−0.500000	−	1.53884i	−0.0395285	−	0.121656i
$161$	4.23607			0.333849
$162$	4.61803	+	3.35520i	0.362827	+	0.263609i
$163$	4.03444			0.316002			0.158001	−	0.987439i	$-0.449495\pi$
$163$	4.03444			0.316002			0.158001	+	0.987439i	$0.449495\pi$
$164$	−5.04508	+	3.94298i	−0.393955	+	0.307895i
$165$	−3.00000			−0.233550
$166$	−13.0172	−	9.45756i	−1.01033	−	0.734049i
$167$	−24.0344			−1.85984			−0.929920	−	0.367761i	$-0.880125\pi$
$167$	−24.0344			−1.85984			−0.929920	+	0.367761i	$0.880125\pi$
$168$	−0.500000	−	1.53884i	−0.0385758	−	0.118724i
$169$	8.00000	+	24.6215i	0.615385	+	1.89396i
$170$	−5.54508	−	4.02874i	−0.425289	−	0.308990i
$171$	−3.73607	+	2.71441i	−0.285704	+	0.207576i
$172$	3.00000	−	9.23305i	0.228748	−	0.704014i
$173$	−3.76393			−0.286166			−0.143083	−	0.989711i	$-0.545702\pi$
$173$	−3.76393			−0.286166			−0.143083	+	0.989711i	$0.545702\pi$
$174$	−0.100813	+	0.310271i	−0.00764262	+	0.0235216i
$175$	1.92705	−	5.93085i	0.145671	−	0.448330i
$176$	0.927051	+	2.85317i	0.0698791	+	0.215066i
$177$	−2.54508	−	1.84911i	−0.191300	−	0.138988i
$178$	6.23607			0.467413
$179$	−7.52786	−	23.1684i	−0.562659	−	1.73169i	−0.674807	−	0.737995i	$-0.735773\pi$
$179$	−7.52786	−	23.1684i	−0.562659	−	1.73169i	0.112148	−	0.993692i	$-0.464227\pi$
$180$	3.42705	−	2.48990i	0.255437	−	0.185586i
$181$	1.86475	−	5.73910i	0.138605	−	0.426584i	−0.857528	−	0.514437i	$-0.828001\pi$
$181$	1.86475	−	5.73910i	0.138605	−	0.426584i	0.996133	+	0.0878537i	$0.0280008\pi$
$182$	−13.2082	−	9.59632i	−0.979057	−	0.711327i
$183$	−1.73607	+	1.26133i	−0.128334	+	0.0932400i
$184$	−1.30902	+	0.951057i	−0.0965020	+	0.0701128i
$185$	−1.92705	+	1.40008i	−0.141680	+	0.102936i
$186$	3.04508	−	2.21238i	0.223276	−	0.162220i
$187$	10.2812	+	7.46969i	0.751832	+	0.546238i
$188$	−0.472136	+	1.45309i	−0.0344341	+	0.105977i
$189$	7.35410	−	5.34307i	0.534932	−	0.388651i
$190$	0.881966	+	2.71441i	0.0639845	+	0.196924i
$191$	5.00000			0.361787			0.180894	−	0.983503i	$-0.442101\pi$
$191$	5.00000			0.361787			0.180894	+	0.983503i	$0.442101\pi$
$192$	0.500000	+	0.363271i	0.0360844	+	0.0262168i
$193$	−3.73607	−	11.4984i	−0.268928	−	0.827675i	−0.990762	−	0.135610i	$-0.956701\pi$
$193$	−3.73607	−	11.4984i	−0.268928	−	0.827675i	0.721834	−	0.692066i	$-0.243299\pi$
$194$	−1.69098	+	5.20431i	−0.121406	+	0.373648i
$195$	−1.92705	+	5.93085i	−0.137999	+	0.424717i
$196$	−0.145898			−0.0104213
$197$	−0.982779	+	3.02468i	−0.0700201	+	0.215500i	−0.979943	−	0.199277i	$-0.936140\pi$
$197$	−0.982779	+	3.02468i	−0.0700201	+	0.215500i	0.909923	+	0.414777i	$0.136140\pi$
$198$	−6.35410	+	4.61653i	−0.451566	+	0.328082i
$199$	−5.28115	−	3.83698i	−0.374371	−	0.271996i	0.384650	−	0.923062i	$-0.374322\pi$
$199$	−5.28115	−	3.83698i	−0.374371	−	0.271996i	−0.759021	+	0.651066i	$0.774322\pi$
$200$	0.736068	+	2.26538i	0.0520479	+	0.160187i
$201$	2.94427	+	9.06154i	0.207673	+	0.639152i
$202$	−7.79837			−0.548692
$203$	−1.11803	−	0.812299i	−0.0784706	−	0.0570122i
$204$	2.61803			0.183299
$205$	−8.16312	+	6.37988i	−0.570137	+	0.445590i
$206$	12.2361			0.852527
$207$	−3.42705	−	2.48990i	−0.238197	−	0.173060i
$208$	6.23607			0.432394
$209$	−1.63525	−	5.03280i	−0.113113	−	0.348126i
$210$	−0.809017	−	2.48990i	−0.0558275	−	0.171819i
$211$	−5.04508	−	3.66547i	−0.347318	−	0.252341i	0.400425	−	0.916330i	$-0.368862\pi$
$211$	−5.04508	−	3.66547i	−0.347318	−	0.252341i	−0.747743	+	0.663988i	$0.768862\pi$
$212$	−9.59017	+	6.96767i	−0.658656	+	0.478541i
$213$	−0.736068	+	2.26538i	−0.0504345	+	0.155222i
$214$	5.70820			0.390205
$215$	4.85410	−	14.9394i	0.331047	−	1.01886i
$216$	−1.07295	+	3.30220i	−0.0730049	+	0.224686i
$217$	4.92705	+	15.1639i	0.334470	+	1.02939i
$218$	6.04508	+	4.39201i	0.409425	+	0.297465i
$219$	10.0000			0.675737
$220$	1.50000	+	4.61653i	0.101130	+	0.311246i
$221$	21.3713	−	15.5272i	1.43759	−	1.04447i
$222$	0.281153	−	0.865300i	0.0188698	−	0.0580751i
$223$	20.7984	+	15.1109i	1.39276	+	1.01190i	0.995556	+	0.0941715i	$0.0300202\pi$
$223$	20.7984	+	15.1109i	1.39276	+	1.01190i	0.397206	+	0.917729i	$0.369980\pi$
$224$	−2.11803	+	1.53884i	−0.141517	+	0.102818i
$225$	−5.04508	+	3.66547i	−0.336339	+	0.244365i
$226$	14.4443	−	10.4944i	0.960819	−	0.698076i
$227$	15.0902	−	10.9637i	1.00157	−	0.727683i	0.0391456	−	0.999234i	$-0.487536\pi$
$227$	15.0902	−	10.9637i	1.00157	−	0.727683i	0.962424	+	0.271550i	$0.0875364\pi$
$228$	−0.881966	−	0.640786i	−0.0584096	−	0.0424371i
$229$	3.28115	−	10.0984i	0.216825	−	0.667318i	−0.782194	−	0.623035i	$-0.785900\pi$
$229$	3.28115	−	10.0984i	0.216825	−	0.667318i	0.999019	−	0.0442832i	$-0.0141004\pi$
$230$	−2.11803	+	1.53884i	−0.139659	+	0.101468i
$231$	1.50000	+	4.61653i	0.0986928	+	0.303745i
$232$	0.527864			0.0346560
$233$	−10.7533	−	7.81272i	−0.704471	−	0.511828i	0.176914	−	0.984226i	$-0.443389\pi$
$233$	−10.7533	−	7.81272i	−0.704471	−	0.511828i	−0.881385	+	0.472398i	$0.843389\pi$
$234$	5.04508	+	15.5272i	0.329808	+	1.01504i
$235$	−0.763932	+	2.35114i	−0.0498334	+	0.153372i
$236$	−1.57295	+	4.84104i	−0.102390	+	0.315125i
$237$	−8.65248			−0.562039
$238$	−3.42705	+	10.5474i	−0.222143	+	0.683685i
$239$	−20.4443	+	14.8536i	−1.32243	+	0.960802i	−0.322531	+	0.946559i	$0.604534\pi$
$239$	−20.4443	+	14.8536i	−1.32243	+	0.960802i	−0.999899	+	0.0142429i	$0.995466\pi$
$240$	0.809017	+	0.587785i	0.0522218	+	0.0379414i
$241$	−4.72542	−	14.5434i	−0.304391	−	0.936820i	−0.979904	−	0.199472i	$-0.936077\pi$
$241$	−4.72542	−	14.5434i	−0.304391	−	0.936820i	0.675512	−	0.737349i	$-0.263923\pi$
$242$	0.618034	+	1.90211i	0.0397287	+	0.122272i
$243$	−13.9443			−0.894525
$244$	2.80902	+	2.04087i	0.179829	+	0.130653i
$245$	−0.236068			−0.0150818
$246$	1.09017	−	3.80423i	0.0695067	−	0.242549i
$247$	−11.0000			−0.699913
$248$	−4.92705	−	3.57971i	−0.312868	−	0.227312i
$249$	9.94427			0.630193
$250$	3.69098	+	11.3597i	0.233438	+	0.718449i
$251$	5.42705	+	16.7027i	0.342552	+	1.05427i	0.962881	+	0.269926i	$0.0869992\pi$
$251$	5.42705	+	16.7027i	0.342552	+	1.05427i	−0.620329	+	0.784342i	$0.713001\pi$
$252$	−5.54508	−	4.02874i	−0.349308	−	0.253787i
$253$	3.92705	−	2.85317i	0.246892	−	0.179377i
$254$	−2.10081	+	6.46564i	−0.131817	+	0.405690i
$255$	4.23607			0.265273
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.47214	+	4.53077i	−0.0918293	+	0.282622i	−0.986414	−	0.164276i	$-0.947471\pi$
$257$	−1.47214	+	4.53077i	−0.0918293	+	0.282622i	0.894585	+	0.446898i	$0.147471\pi$
$258$	1.85410	+	5.70634i	0.115431	+	0.355261i
$259$	3.11803	+	2.26538i	0.193745	+	0.140764i
$260$	10.0902			0.625766
$261$	0.427051	+	1.31433i	0.0264338	+	0.0813548i
$262$	−7.39919	+	5.37582i	−0.457123	+	0.332120i
$263$	0.0278640	−	0.0857567i	0.00171817	−	0.00528799i	−0.950194	−	0.311660i	$-0.899115\pi$
$263$	0.0278640	−	0.0857567i	0.00171817	−	0.00528799i	0.951912	+	0.306372i	$0.0991151\pi$
$264$	−1.50000	−	1.08981i	−0.0923186	−	0.0670734i
$265$	−15.5172	+	11.2739i	−0.953215	+	0.692551i
$266$	3.73607	−	2.71441i	0.229073	−	0.166431i
$267$	−3.11803	+	2.26538i	−0.190821	+	0.138639i
$268$	12.4721	−	9.06154i	0.761857	−	0.553521i
$269$	4.89919	+	3.55947i	0.298709	+	0.217025i	0.727036	−	0.686599i	$-0.240897\pi$
$269$	4.89919	+	3.55947i	0.298709	+	0.217025i	−0.428328	+	0.903623i	$0.640897\pi$
$270$	−1.73607	+	5.34307i	−0.105654	+	0.325169i
$271$	21.1353	−	15.3557i	1.28388	−	0.932790i	0.284213	−	0.958761i	$-0.408268\pi$
$271$	21.1353	−	15.3557i	1.28388	−	0.932790i	0.999663	+	0.0259713i	$0.00826784\pi$
$272$	−1.30902	−	4.02874i	−0.0793708	−	0.244278i
$273$	10.0902			0.610685
$274$	−5.47214	−	3.97574i	−0.330584	−	0.240183i
$275$	−2.20820	−	6.79615i	−0.133160	−	0.409823i
$276$	0.309017	−	0.951057i	0.0186006	−	0.0572469i
$277$	−4.82624	+	14.8536i	−0.289981	+	0.892468i	0.694881	+	0.719125i	$0.255457\pi$
$277$	−4.82624	+	14.8536i	−0.289981	+	0.892468i	−0.984861	+	0.173343i	$0.944543\pi$
$278$	−0.236068			−0.0141584
$279$	4.92705	−	15.1639i	0.294975	−	0.907839i
$280$	−3.42705	+	2.48990i	−0.204805	+	0.148800i
$281$	−8.04508	−	5.84510i	−0.479930	−	0.348689i	0.321369	−	0.946954i	$-0.395857\pi$
$281$	−8.04508	−	5.84510i	−0.479930	−	0.348689i	−0.801298	+	0.598265i	$0.795857\pi$
$282$	−0.291796	−	0.898056i	−0.0173762	−	0.0534785i
$283$	−5.40983	−	16.6497i	−0.321581	−	0.989725i	−0.972960	−	0.230972i	$-0.925809\pi$
$283$	−5.40983	−	16.6497i	−0.321581	−	0.989725i	0.651379	−	0.758752i	$-0.274191\pi$
$284$	3.85410			0.228699
$285$	−1.42705	−	1.03681i	−0.0845312	−	0.0614155i
$286$	−18.7082			−1.10624
$287$	13.8992	+	9.37181i	0.820443	+	0.553200i
$288$	2.61803			0.154269
$289$	−0.763932	−	0.555029i	−0.0449372	−	0.0326488i
$290$	0.854102			0.0501546
$291$	−1.04508	−	3.21644i	−0.0612640	−	0.188551i
$292$	−5.00000	−	15.3884i	−0.292603	−	0.900539i
$293$	5.50000	+	3.99598i	0.321313	+	0.233448i	0.736736	−	0.676181i	$-0.236366\pi$
$293$	5.50000	+	3.99598i	0.321313	+	0.233448i	−0.415422	+	0.909629i	$0.636366\pi$
$294$	0.0729490	−	0.0530006i	0.00425447	−	0.00309106i
$295$	−2.54508	+	7.83297i	−0.148181	+	0.456053i
$296$	−1.47214			−0.0855662
$297$	3.21885	−	9.90659i	0.186776	−	0.574839i
$298$	3.52786	−	10.8576i	0.204364	−	0.628967i
$299$	−3.11803	−	9.59632i	−0.180321	−	0.554970i
$300$	−1.19098	−	0.865300i	−0.0687614	−	0.0499581i
$301$	−25.4164			−1.46498
$302$	4.70820	+	14.4904i	0.270927	+	0.833827i
$303$	3.89919	−	2.83293i	0.224002	−	0.162747i
$304$	−0.545085	+	1.67760i	−0.0312628	+	0.0962169i
$305$	4.54508	+	3.30220i	0.260251	+	0.189083i
$306$	8.97214	−	6.51864i	0.512903	−	0.372646i
$307$	18.1803	−	13.2088i	1.03761	−	0.753865i	0.0677899	−	0.997700i	$-0.478405\pi$
$307$	18.1803	−	13.2088i	1.03761	−	0.753865i	0.969817	+	0.243834i	$0.0784053\pi$
$308$	6.35410	−	4.61653i	0.362059	−	0.263051i
$309$	−6.11803	+	4.44501i	−0.348043	+	0.252868i
$310$	−7.97214	−	5.79210i	−0.452787	−	0.328969i
$311$	−1.40983	+	4.33901i	−0.0799441	+	0.246043i	−0.983038	−	0.183399i	$-0.941290\pi$
$311$	−1.40983	+	4.33901i	−0.0799441	+	0.246043i	0.903094	+	0.429442i	$0.141290\pi$
$312$	−3.11803	+	2.26538i	−0.176524	+	0.128252i
$313$	0.708204	+	2.17963i	0.0400301	+	0.123200i	0.969075	−	0.246768i	$-0.0793686\pi$
$313$	0.708204	+	2.17963i	0.0400301	+	0.123200i	−0.929044	+	0.369968i	$0.879369\pi$
$314$	−2.94427			−0.166155
$315$	−8.97214	−	6.51864i	−0.505523	−	0.367284i
$316$	4.32624	+	13.3148i	0.243370	+	0.749016i
$317$	−4.19098	+	12.8985i	−0.235389	+	0.724453i	0.761681	+	0.647953i	$0.224375\pi$
$317$	−4.19098	+	12.8985i	−0.235389	+	0.724453i	−0.997070	+	0.0765002i	$0.975625\pi$
$318$	2.26393	−	6.96767i	0.126955	−	0.390727i
$319$	−1.58359			−0.0886641
$320$	0.500000	−	1.53884i	0.0279508	−	0.0860239i
$321$	−2.85410	+	2.07363i	−0.159300	+	0.115739i
$322$	3.42705	+	2.48990i	0.190982	+	0.138757i
$323$	2.30902	+	7.10642i	0.128477	+	0.395412i
$324$	1.76393	+	5.42882i	0.0979962	+	0.301601i
$325$	−14.8541			−0.823957
$326$	3.26393	+	2.37139i	0.180772	+	0.131339i
$327$	−4.61803			−0.255378
$328$	−6.39919	+	0.224514i	−0.353336	+	0.0123967i
$329$	4.00000			0.220527
$330$	−2.42705	−	1.76336i	−0.133605	−	0.0970695i
$331$	−10.0902			−0.554606			−0.277303	−	0.960783i	$-0.589441\pi$
$331$	−10.0902			−0.554606			−0.277303	+	0.960783i	$0.589441\pi$
$332$	−4.97214	−	15.3027i	−0.272881	−	0.839843i
$333$	−1.19098	−	3.66547i	−0.0652655	−	0.200866i
$334$	−19.4443	−	14.1271i	−1.06394	−	0.773000i
$335$	20.1803	−	14.6619i	1.10257	−	0.801064i
$336$	0.500000	−	1.53884i	0.0272772	−	0.0839507i
$337$	−26.7639			−1.45792			−0.728962	−	0.684554i	$-0.759997\pi$
$337$	−26.7639			−1.45792			−0.728962	+	0.684554i	$0.759997\pi$
$338$	−8.00000	+	24.6215i	−0.435143	+	1.33923i
$339$	−3.40983	+	10.4944i	−0.185197	+	0.569976i
$340$	−2.11803	−	6.51864i	−0.114867	−	0.353523i
$341$	14.7812	+	10.7391i	0.800444	+	0.581557i
$342$	−4.61803			−0.249715
$343$	5.78115	+	17.7926i	0.312153	+	0.960708i
$344$	7.85410	−	5.70634i	0.423465	−	0.307665i
$345$	0.500000	−	1.53884i	0.0269191	−	0.0828485i
$346$	−3.04508	−	2.21238i	−0.163705	−	0.118938i
$347$	23.2533	−	16.8945i	1.24830	−	0.906944i	0.250180	−	0.968199i	$-0.419510\pi$
$347$	23.2533	−	16.8945i	1.24830	−	0.906944i	0.998122	+	0.0612549i	$0.0195103\pi$
$348$	−0.263932	+	0.191758i	−0.0141482	+	0.0102793i
$349$	−5.16312	+	3.75123i	−0.276375	+	0.200798i	−0.717335	−	0.696729i	$-0.754638\pi$
$349$	−5.16312	+	3.75123i	−0.276375	+	0.200798i	0.440960	+	0.897527i	$0.354638\pi$
$350$	5.04508	−	3.66547i	0.269671	−	0.195928i
$351$	−17.5172	−	12.7270i	−0.935000	−	0.679317i
$352$	−0.927051	+	2.85317i	−0.0494120	+	0.152074i
$353$	−6.16312	+	4.47777i	−0.328030	+	0.238328i	−0.739594	−	0.673053i	$-0.764983\pi$
$353$	−6.16312	+	4.47777i	−0.328030	+	0.238328i	0.411564	+	0.911381i	$0.364983\pi$
$354$	−0.972136	−	2.99193i	−0.0516684	−	0.159019i
$355$	6.23607			0.330976
$356$	5.04508	+	3.66547i	0.267389	+	0.194269i
$357$	−2.11803	−	6.51864i	−0.112098	−	0.345003i
$358$	7.52786	−	23.1684i	0.397860	−	1.22449i
$359$	−3.47214	+	10.6861i	−0.183252	+	0.563993i	−0.999914	−	0.0131242i	$-0.995822\pi$
$359$	−3.47214	+	10.6861i	−0.183252	+	0.563993i	0.816662	+	0.577117i	$0.195822\pi$
$360$	4.23607			0.223260
$361$	−4.90983	+	15.1109i	−0.258412	+	0.795311i
$362$	4.88197	−	3.54696i	0.256590	−	0.186424i
$363$	−1.00000	−	0.726543i	−0.0524864	−	0.0381336i
$364$	−5.04508	−	15.5272i	−0.264434	−	0.813845i
$365$	−8.09017	−	24.8990i	−0.423459	−	1.30327i
$366$	−2.14590			−0.112168
$367$	−7.42705	−	5.39607i	−0.387689	−	0.281672i	0.376819	−	0.926287i	$-0.377018\pi$
$367$	−7.42705	−	5.39607i	−0.387689	−	0.281672i	−0.764508	+	0.644614i	$0.777018\pi$
$368$	−1.61803			−0.0843459
$369$	−5.73607	−	15.7517i	−0.298608	−	0.820000i
$370$	−2.38197			−0.123833
$371$	25.1074	+	18.2416i	1.30351	+	0.947056i
$372$	3.76393			0.195151
$373$	7.78115	+	23.9479i	0.402893	+	1.23998i	0.922642	+	0.385658i	$0.126025\pi$
$373$	7.78115	+	23.9479i	0.402893	+	1.23998i	−0.519749	+	0.854319i	$0.673975\pi$
$374$	3.92705	+	12.0862i	0.203063	+	0.624964i
$375$	−5.97214	−	4.33901i	−0.308400	−	0.224066i
$376$	−1.23607	+	0.898056i	−0.0637453	+	0.0463137i
$377$	−1.01722	+	3.13068i	−0.0523895	+	0.161238i
$378$	9.09017			0.467548
$379$	−4.64590	+	14.2986i	−0.238644	+	0.734470i	0.757973	+	0.652285i	$0.226190\pi$
$379$	−4.64590	+	14.2986i	−0.238644	+	0.734470i	−0.996617	+	0.0821845i	$0.973810\pi$
$380$	−0.881966	+	2.71441i	−0.0452439	+	0.139246i
$381$	−1.29837	−	3.99598i	−0.0665177	−	0.204720i
$382$	4.04508	+	2.93893i	0.206965	+	0.150369i
$383$	−3.18034			−0.162508			−0.0812539	−	0.996693i	$-0.525892\pi$
$383$	−3.18034			−0.162508			−0.0812539	+	0.996693i	$0.525892\pi$
$384$	0.190983	+	0.587785i	0.00974606	+	0.0299953i
$385$	10.2812	−	7.46969i	0.523976	−	0.380691i
$386$	3.73607	−	11.4984i	0.190161	−	0.585255i
$387$	20.5623	+	14.9394i	1.04524	+	0.759412i
$388$	−4.42705	+	3.21644i	−0.224749	+	0.163290i
$389$	−30.3156	+	22.0256i	−1.53706	+	1.11674i	−0.584917	+	0.811093i	$0.698873\pi$
$389$	−30.3156	+	22.0256i	−1.53706	+	1.11674i	−0.952145	+	0.305647i	$0.901127\pi$
$390$	−5.04508	+	3.66547i	−0.255468	+	0.185608i
$391$	−5.54508	+	4.02874i	−0.280427	+	0.203742i
$392$	−0.118034	−	0.0857567i	−0.00596162	−	0.00433137i
$393$	1.74671	−	5.37582i	0.0881099	−	0.271174i
$394$	−2.57295	+	1.86936i	−0.129623	+	0.0941768i
$395$	7.00000	+	21.5438i	0.352208	+	1.08399i
$396$	−7.85410			−0.394683
$397$	21.4164	+	15.5599i	1.07486	+	0.780931i	0.976779	−	0.214248i	$-0.0687301\pi$
$397$	21.4164	+	15.5599i	1.07486	+	0.780931i	0.0980794	+	0.995179i	$0.468730\pi$
$398$	−2.01722	−	6.20837i	−0.101114	−	0.311197i
$399$	−0.881966	+	2.71441i	−0.0441535	+	0.135891i
$400$	−0.736068	+	2.26538i	−0.0368034	+	0.113269i
$401$	24.8885			1.24287			0.621437	−	0.783464i	$-0.286549\pi$
$401$	24.8885			1.24287			0.621437	+	0.783464i	$0.286549\pi$
$402$	−2.94427	+	9.06154i	−0.146847	+	0.451948i
$403$	30.7254	−	22.3233i	1.53054	−	1.11200i
$404$	−6.30902	−	4.58377i	−0.313885	−	0.228051i
$405$	2.85410	+	8.78402i	0.141821	+	0.436482i
$406$	−0.427051	−	1.31433i	−0.0211942	−	0.0652290i
$407$	4.41641			0.218913
$408$	2.11803	+	1.53884i	0.104858	+	0.0761840i
$409$	−0.270510			−0.0133759			−0.00668793	−	0.999978i	$-0.502129\pi$
$409$	−0.270510			−0.0133759			−0.00668793	+	0.999978i	$0.502129\pi$
$410$	−10.3541	+	0.363271i	−0.511353	+	0.0179407i
$411$	4.18034			0.206201
$412$	9.89919	+	7.19218i	0.487698	+	0.354333i
$413$	13.3262			0.655741
$414$	−1.30902	−	4.02874i	−0.0643347	−	0.198002i
$415$	−8.04508	−	24.7602i	−0.394918	−	1.21543i
$416$	5.04508	+	3.66547i	0.247356	+	0.179714i
$417$	0.118034	−	0.0857567i	0.00578015	−	0.00419952i
$418$	1.63525	−	5.03280i	0.0799829	−	0.246162i
$419$	−17.9787			−0.878318			−0.439159	−	0.898409i	$-0.644723\pi$
$419$	−17.9787			−0.878318			−0.439159	+	0.898409i	$0.644723\pi$
$420$	0.809017	−	2.48990i	0.0394760	−	0.121495i
$421$	−8.41641	+	25.9030i	−0.410191	+	1.26244i	0.506292	+	0.862362i	$0.331016\pi$
$421$	−8.41641	+	25.9030i	−0.410191	+	1.26244i	−0.916483	+	0.400075i	$0.868984\pi$
$422$	−1.92705	−	5.93085i	−0.0938074	−	0.288709i
$423$	−3.23607	−	2.35114i	−0.157343	−	0.114316i
$424$	−11.8541			−0.575686
$425$	3.11803	+	9.59632i	0.151247	+	0.465490i
$426$	−1.92705	+	1.40008i	−0.0933659	+	0.0678343i
$427$	2.80902	−	8.64527i	0.135938	−	0.418374i
$428$	4.61803	+	3.35520i	0.223221	+	0.162180i
$429$	9.35410	−	6.79615i	0.451620	−	0.328121i
$430$	12.7082	−	9.23305i	0.612844	−	0.445257i
$431$	9.51722	−	6.91467i	0.458428	−	0.333068i	−0.334486	−	0.942401i	$-0.608563\pi$
$431$	9.51722	−	6.91467i	0.458428	−	0.333068i	0.792914	+	0.609333i	$0.208563\pi$
$432$	−2.80902	+	2.04087i	−0.135149	+	0.0981914i
$433$	6.76393	+	4.91428i	0.325054	+	0.236165i	0.738329	−	0.674441i	$-0.235615\pi$
$433$	6.76393	+	4.91428i	0.325054	+	0.236165i	−0.413275	+	0.910606i	$0.635615\pi$
$434$	−4.92705	+	15.1639i	−0.236506	+	0.727891i
$435$	−0.427051	+	0.310271i	−0.0204755	+	0.0148763i
$436$	2.30902	+	7.10642i	0.110582	+	0.340336i
$437$	2.85410			0.136530
$438$	8.09017	+	5.87785i	0.386563	+	0.280855i
$439$	−7.16312	−	22.0458i	−0.341877	−	1.05219i	−0.963234	−	0.268662i	$-0.913419\pi$
$439$	−7.16312	−	22.0458i	−0.341877	−	1.05219i	0.621357	−	0.783527i	$-0.286581\pi$
$440$	−1.50000	+	4.61653i	−0.0715097	+	0.220084i
$441$	0.118034	−	0.363271i	0.00562067	−	0.0172986i
$442$	26.4164			1.25650
$443$	−7.19756	+	22.1518i	−0.341966	+	1.05246i	0.621221	+	0.783635i	$0.286637\pi$
$443$	−7.19756	+	22.1518i	−0.341966	+	1.05246i	−0.963188	+	0.268829i	$0.913363\pi$
$444$	0.736068	−	0.534785i	0.0349322	−	0.0253798i
$445$	8.16312	+	5.93085i	0.386969	+	0.281149i
$446$	7.94427	+	24.4500i	0.376172	+	1.15774i
$447$	2.18034	+	6.71040i	0.103127	+	0.317391i
$448$	−2.61803			−0.123690
$449$	−5.57295	−	4.04898i	−0.263004	−	0.191083i	0.448466	−	0.893800i	$-0.351970\pi$
$449$	−5.57295	−	4.04898i	−0.263004	−	0.191083i	−0.711470	+	0.702716i	$0.751970\pi$
$450$	−6.23607			−0.293971
$451$	19.1976	−	0.673542i	0.903978	−	0.0317159i
$452$	17.8541			0.839786
$453$	−7.61803	−	5.53483i	−0.357926	−	0.260049i
$454$	18.6525			0.875404
$455$	−8.16312	−	25.1235i	−0.382693	−	1.17781i
$456$	−0.336881	−	1.03681i	−0.0157759	−	0.0485532i
$457$	8.66312	+	6.29412i	0.405244	+	0.294427i	0.771673	−	0.636019i	$-0.219420\pi$
$457$	8.66312	+	6.29412i	0.405244	+	0.294427i	−0.366430	+	0.930446i	$0.619420\pi$
$458$	8.59017	−	6.24112i	0.401392	−	0.291629i
$459$	−4.54508	+	13.9883i	−0.212146	+	0.652919i
$460$	−2.61803			−0.122066
$461$	9.60081	−	29.5483i	0.447154	−	1.37620i	−0.432949	−	0.901418i	$-0.642527\pi$
$461$	9.60081	−	29.5483i	0.447154	−	1.37620i	0.880104	−	0.474782i	$-0.157473\pi$
$462$	−1.50000	+	4.61653i	−0.0697863	+	0.214780i
$463$	−5.30902	−	16.3395i	−0.246731	−	0.759360i	−0.995347	−	0.0963559i	$-0.969281\pi$
$463$	−5.30902	−	16.3395i	−0.246731	−	0.759360i	0.748616	−	0.663004i	$-0.230719\pi$
$464$	0.427051	+	0.310271i	0.0198253	+	0.0144040i
$465$	6.09017			0.282425
$466$	−4.10739	−	12.6412i	−0.190271	−	0.585595i
$467$	−22.6525	+	16.4580i	−1.04823	+	0.761585i	−0.971875	−	0.235496i	$-0.924329\pi$
$467$	−22.6525	+	16.4580i	−1.04823	+	0.761585i	−0.0763562	+	0.997081i	$0.524329\pi$
$468$	−5.04508	+	15.5272i	−0.233209	+	0.717744i
$469$	−32.6525	−	23.7234i	−1.50775	−	1.09545i
$470$	−2.00000	+	1.45309i	−0.0922531	+	0.0670258i
$471$	1.47214	−	1.06957i	0.0678324	−	0.0492832i
$472$	−4.11803	+	2.99193i	−0.189548	+	0.137715i
$473$	−23.5623	+	17.1190i	−1.08340	+	0.787133i
$474$	−7.00000	−	5.08580i	−0.321521	−	0.233598i
$475$	1.29837	−	3.99598i	0.0595735	−	0.183348i
$476$	−8.97214	+	6.51864i	−0.411237	+	0.298781i
$477$	−9.59017	−	29.5155i	−0.439104	−	1.35142i
$478$	−25.2705			−1.15585
$479$	−21.5623	−	15.6659i	−0.985207	−	0.715795i	−0.0263407	−	0.999653i	$-0.508385\pi$
$479$	−21.5623	−	15.6659i	−0.985207	−	0.715795i	−0.958866	+	0.283858i	$0.908385\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	2.83688	−	8.73102i	0.129351	−	0.398100i
$482$	4.72542	−	14.5434i	0.215237	−	0.662432i
$483$	−2.61803			−0.119125
$484$	−0.618034	+	1.90211i	−0.0280925	+	0.0864597i
$485$	−7.16312	+	5.20431i	−0.325260	+	0.236316i
$486$	−11.2812	−	8.19624i	−0.511723	−	0.371789i
$487$	−3.87132	−	11.9147i	−0.175426	−	0.539907i	0.824226	−	0.566261i	$-0.191610\pi$
$487$	−3.87132	−	11.9147i	−0.175426	−	0.539907i	−0.999653	+	0.0263537i	$0.991610\pi$
$488$	1.07295	+	3.30220i	0.0485701	+	0.149483i
$489$	−2.49342			−0.112756
$490$	−0.190983	−	0.138757i	−0.00862773	−	0.00626841i
$491$	26.4721			1.19467			0.597335	−	0.801992i	$-0.296226\pi$
$491$	26.4721			1.19467			0.597335	+	0.801992i	$0.296226\pi$
$492$	3.11803	−	2.43690i	0.140572	−	0.109864i
$493$	2.23607			0.100707
$494$	−8.89919	−	6.46564i	−0.400393	−	0.290903i
$495$	−12.7082			−0.571191
$496$	−1.88197	−	5.79210i	−0.0845028	−	0.260073i
$497$	−3.11803	−	9.59632i	−0.139863	−	0.430454i
$498$	8.04508	+	5.84510i	0.360509	+	0.261925i
$499$	−27.2533	+	19.8007i	−1.22002	+	0.886400i	−0.996102	−	0.0882071i	$-0.971886\pi$
$499$	−27.2533	+	19.8007i	−1.22002	+	0.886400i	−0.223923	+	0.974607i	$0.571886\pi$
$500$	−3.69098	+	11.3597i	−0.165066	+	0.508020i
$501$	14.8541			0.663632
$502$	−5.42705	+	16.7027i	−0.242221	+	0.745480i
$503$	−1.27458	+	3.92274i	−0.0568305	+	0.174906i	−0.975442	−	0.220255i	$-0.929311\pi$
$503$	−1.27458	+	3.92274i	−0.0568305	+	0.174906i	0.918612	+	0.395161i	$0.129311\pi$
$504$	−2.11803	−	6.51864i	−0.0943447	−	0.290363i
$505$	−10.2082	−	7.41669i	−0.454259	−	0.330039i
$506$	4.85410			0.215791
$507$	−4.94427	−	15.2169i	−0.219583	−	0.675806i
$508$	−5.50000	+	3.99598i	−0.244023	+	0.177293i
$509$	9.92705	−	30.5523i	0.440009	−	1.35421i	−0.447857	−	0.894105i	$-0.647813\pi$
$509$	9.92705	−	30.5523i	0.440009	−	1.35421i	0.887866	−	0.460103i	$-0.152187\pi$
$510$	3.42705	+	2.48990i	0.151752	+	0.110255i
$511$	−34.2705	+	24.8990i	−1.51604	+	1.10147i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	4.95492	−	3.59996i	0.218765	−	0.158942i
$514$	−3.85410	+	2.80017i	−0.169997	+	0.123510i
$515$	16.0172	+	11.6372i	0.705803	+	0.512796i
$516$	−1.85410	+	5.70634i	−0.0816223	+	0.251208i
$517$	3.70820	−	2.69417i	0.163087	−	0.118489i
$518$	1.19098	+	3.66547i	0.0523288	+	0.161051i
$519$	2.32624			0.102111
$520$	8.16312	+	5.93085i	0.357976	+	0.260085i
$521$	2.29837	+	7.07367i	0.100694	+	0.309903i	0.988696	−	0.149937i	$-0.0479069\pi$
$521$	2.29837	+	7.07367i	0.100694	+	0.309903i	−0.888002	+	0.459840i	$0.847907\pi$
$522$	−0.427051	+	1.31433i	−0.0186915	+	0.0575266i
$523$	−4.91641	+	15.1311i	−0.214980	+	0.661639i	0.784176	+	0.620539i	$0.213086\pi$
$523$	−4.91641	+	15.1311i	−0.214980	+	0.661639i	−0.999155	+	0.0410998i	$0.986914\pi$
$524$	−9.14590			−0.399540
$525$	−1.19098	+	3.66547i	−0.0519788	+	0.159974i
$526$	0.0729490	−	0.0530006i	0.00318073	−	0.00231093i
$527$	−20.8713	−	15.1639i	−0.909169	−	0.660550i
$528$	−0.572949	−	1.76336i	−0.0249344	−	0.0767402i
$529$	−6.29837	−	19.3844i	−0.273842	−	0.842800i
$530$	−19.1803			−0.833141
$531$	−10.7812	−	7.83297i	−0.467862	−	0.339922i
$532$	4.61803			0.200217
$533$	11.0000	−	38.3853i	0.476463	−	1.66265i
$534$	−3.85410			−0.166783
$535$	7.47214	+	5.42882i	0.323049	+	0.234709i
$536$	15.4164			0.665887
$537$	4.65248	+	14.3188i	0.200769	+	0.617904i
$538$	1.87132	+	5.75934i	0.0806785	+	0.248303i
$539$	0.354102	+	0.257270i	0.0152523	+	0.0110814i
$540$	−4.54508	+	3.30220i	−0.195589	+	0.142104i
$541$	7.13525	−	21.9601i	0.306769	−	0.944137i	−0.672243	−	0.740331i	$-0.734669\pi$
$541$	7.13525	−	21.9601i	0.306769	−	0.944137i	0.979011	−	0.203806i	$-0.0653311\pi$
$542$	26.1246			1.12215
$543$	−1.15248	+	3.54696i	−0.0494575	+	0.152214i
$544$	1.30902	−	4.02874i	0.0561236	−	0.172731i
$545$	3.73607	+	11.4984i	0.160036	+	0.492539i
$546$	8.16312	+	5.93085i	0.349349	+	0.253817i
$547$	9.00000			0.384812			0.192406	−	0.981315i	$-0.438371\pi$
$547$	9.00000			0.384812			0.192406	+	0.981315i	$0.438371\pi$
$548$	−2.09017	−	6.43288i	−0.0892876	−	0.274799i
$549$	−7.35410	+	5.34307i	−0.313865	+	0.228037i
$550$	2.20820	−	6.79615i	0.0941581	−	0.289789i
$551$	−0.753289	−	0.547296i	−0.0320912	−	0.0233156i
$552$	0.809017	−	0.587785i	0.0344340	−	0.0250178i
$553$	29.6525	−	21.5438i	1.26095	−	0.916135i
$554$	−12.6353	+	9.18005i	−0.536821	+	0.390023i
$555$	1.19098	−	0.865300i	0.0505544	−	0.0367299i
$556$	−0.190983	−	0.138757i	−0.00809948	−	0.00588462i
$557$	0.343459	−	1.05706i	0.0145528	−	0.0447890i	−0.943516	−	0.331326i	$-0.892504\pi$
$557$	0.343459	−	1.05706i	0.0145528	−	0.0447890i	0.958069	+	0.286537i	$0.0925041\pi$
$558$	12.8992	−	9.37181i	0.546066	−	0.396740i
$559$	18.7082	+	57.5779i	0.791273	+	2.43529i
$560$	−4.23607			−0.179007
$561$	−6.35410	−	4.61653i	−0.268270	−	0.194910i
$562$	−3.07295	−	9.45756i	−0.129625	−	0.398943i
$563$	2.85410	−	8.78402i	0.120286	−	0.370202i	−0.872727	−	0.488209i	$-0.837650\pi$
$563$	2.85410	−	8.78402i	0.120286	−	0.370202i	0.993013	+	0.118007i	$0.0376504\pi$
$564$	0.291796	−	0.898056i	0.0122868	−	0.0378150i
$565$	28.8885			1.21535
$566$	5.40983	−	16.6497i	0.227392	−	0.699841i
$567$	12.0902	−	8.78402i	0.507739	−	0.368894i
$568$	3.11803	+	2.26538i	0.130830	+	0.0950534i
$569$	12.0517	+	37.0912i	0.505232	+	1.55494i	0.800380	+	0.599493i	$0.204631\pi$
$569$	12.0517	+	37.0912i	0.505232	+	1.55494i	−0.295148	+	0.955451i	$0.595369\pi$
$570$	−0.545085	−	1.67760i	−0.0228311	−	0.0702669i
$571$	−6.12461			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$571$	−6.12461			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$572$	−15.1353	−	10.9964i	−0.632837	−	0.459783i
$573$	−3.09017			−0.129094
$574$	5.73607	+	15.7517i	0.239419	+	0.657463i
$575$	3.85410			0.160727
$576$	2.11803	+	1.53884i	0.0882514	+	0.0641184i
$577$	13.4721			0.560852			0.280426	−	0.959876i	$-0.409524\pi$
$577$	13.4721			0.560852			0.280426	+	0.959876i	$0.409524\pi$
$578$	−0.291796	−	0.898056i	−0.0121371	−	0.0373542i
$579$	2.30902	+	7.10642i	0.0959595	+	0.295333i
$580$	0.690983	+	0.502029i	0.0286915	+	0.0208456i
$581$	−34.0795	+	24.7602i	−1.41386	+	1.02723i
$582$	1.04508	−	3.21644i	0.0433202	−	0.133326i
$583$	35.5623			1.47284
$584$	5.00000	−	15.3884i	0.206901	−	0.636777i
$585$	−8.16312	+	25.1235i	−0.337503	+	1.03873i
$586$	2.10081	+	6.46564i	0.0867838	+	0.267093i
$587$	−9.73607	−	7.07367i	−0.401851	−	0.291962i	0.368444	−	0.929650i	$-0.379891\pi$
$587$	−9.73607	−	7.07367i	−0.401851	−	0.291962i	−0.770294	+	0.637689i	$0.779891\pi$
$588$	0.0901699			0.00371855
$589$	3.31966	+	10.2169i	0.136784	+	0.420979i
$590$	−6.66312	+	4.84104i	−0.274316	+	0.199302i
$591$	0.607391	−	1.86936i	0.0249847	−	0.0768951i
$592$	−1.19098	−	0.865300i	−0.0489491	−	0.0355636i
$593$	6.76393	−	4.91428i	0.277761	−	0.201805i	−0.440179	−	0.897910i	$-0.645085\pi$
$593$	6.76393	−	4.91428i	0.277761	−	0.201805i	0.717940	+	0.696105i	$0.245085\pi$
$594$	8.42705	−	6.12261i	0.345766	−	0.251214i
$595$	−14.5172	+	10.5474i	−0.595148	+	0.432400i
$596$	9.23607	−	6.71040i	0.378324	−	0.274869i
$597$	3.26393	+	2.37139i	0.133584	+	0.0970543i
$598$	3.11803	−	9.59632i	0.127506	−	0.392423i
$599$	−19.7984	+	14.3844i	−0.808940	+	0.587729i	−0.913523	−	0.406787i	$-0.866649\pi$
$599$	−19.7984	+	14.3844i	−0.808940	+	0.587729i	0.104583	+	0.994516i	$0.466649\pi$
$600$	−0.454915	−	1.40008i	−0.0185718	−	0.0571582i
$601$	−27.1803			−1.10871			−0.554355	−	0.832281i	$-0.687035\pi$
$601$	−27.1803			−1.10871			−0.554355	+	0.832281i	$0.687035\pi$
$602$	−20.5623	−	14.9394i	−0.838057	−	0.608884i
$603$	12.4721	+	38.3853i	0.507905	+	1.56317i
$604$	−4.70820	+	14.4904i	−0.191574	+	0.589604i
$605$	−1.00000	+	3.07768i	−0.0406558	+	0.125126i
$606$	4.81966			0.195785
$607$	12.2188	−	37.6057i	0.495948	−	1.52637i	−0.319527	−	0.947577i	$-0.603524\pi$
$607$	12.2188	−	37.6057i	0.495948	−	1.52637i	0.815475	−	0.578793i	$-0.196476\pi$
$608$	−1.42705	+	1.03681i	−0.0578746	+	0.0420483i
$609$	0.690983	+	0.502029i	0.0280000	+	0.0203432i
$610$	1.73607	+	5.34307i	0.0702913	+	0.216334i
$611$	−2.94427	−	9.06154i	−0.119112	−	0.366591i
$612$	11.0902			0.448294
$613$	19.4615	+	14.1396i	0.786042	+	0.571093i	0.906786	−	0.421591i	$-0.138528\pi$
$613$	19.4615	+	14.1396i	0.786042	+	0.571093i	−0.120744	+	0.992684i	$0.538528\pi$
$614$	22.4721			0.906902
$615$	5.04508	−	3.94298i	0.203437	−	0.158996i
$616$	7.85410			0.316451
$617$	12.8541	+	9.33905i	0.517487	+	0.375976i	0.815656	−	0.578537i	$-0.196376\pi$
$617$	12.8541	+	9.33905i	0.517487	+	0.375976i	−0.298170	+	0.954513i	$0.596376\pi$
$618$	−7.56231			−0.304201
$619$	0.0729490	+	0.224514i	0.00293207	+	0.00902398i	0.952512	−	0.304502i	$-0.0984899\pi$
$619$	0.0729490	+	0.224514i	0.00293207	+	0.00902398i	−0.949580	+	0.313526i	$0.898490\pi$
$620$	−3.04508	−	9.37181i	−0.122294	−	0.376381i
$621$	4.54508	+	3.30220i	0.182388	+	0.132513i
$622$	−3.69098	+	2.68166i	−0.147995	+	0.107525i
$623$	5.04508	−	15.5272i	0.202127	−	0.622083i
$624$	−3.85410			−0.154288
$625$	−2.29180	+	7.05342i	−0.0916718	+	0.282137i
$626$	−0.708204	+	2.17963i	−0.0283055	+	0.0871154i
$627$	1.01064	+	3.11044i	0.0403612	+	0.124219i
$628$	−2.38197	−	1.73060i	−0.0950508	−	0.0690584i
$629$	−6.23607			−0.248648
$630$	−3.42705	−	10.5474i	−0.136537	−	0.420218i
$631$	−6.47214	+	4.70228i	−0.257652	+	0.187195i	−0.709111	−	0.705097i	$-0.750904\pi$
$631$	−6.47214	+	4.70228i	−0.257652	+	0.187195i	0.451459	+	0.892292i	$0.350904\pi$
$632$	−4.32624	+	13.3148i	−0.172089	+	0.529634i
$633$	3.11803	+	2.26538i	0.123931	+	0.0900409i
$634$	−10.9721	+	7.97172i	−0.435759	+	0.316598i
$635$	−8.89919	+	6.46564i	−0.353153	+	0.256581i
$636$	5.92705	−	4.30625i	0.235023	−	0.170754i
$637$	0.736068	−	0.534785i	0.0291641	−	0.0211889i
$638$	−1.28115	−	0.930812i	−0.0507213	−	0.0368512i
$639$	−3.11803	+	9.59632i	−0.123348	+	0.379625i
$640$	1.30902	−	0.951057i	0.0517434	−	0.0375938i
$641$	−1.48278	−	4.56352i	−0.0585663	−	0.180248i	0.917494	−	0.397751i	$-0.130209\pi$
$641$	−1.48278	−	4.56352i	−0.0585663	−	0.180248i	−0.976060	+	0.217502i	$0.930209\pi$
$642$	−3.52786			−0.139234
$643$	−5.76393	−	4.18774i	−0.227307	−	0.165148i	0.468303	−	0.883568i	$-0.344866\pi$
$643$	−5.76393	−	4.18774i	−0.227307	−	0.165148i	−0.695610	+	0.718420i	$0.744866\pi$
$644$	1.30902	+	4.02874i	0.0515825	+	0.158755i
$645$	−3.00000	+	9.23305i	−0.118125	+	0.363551i
$646$	−2.30902	+	7.10642i	−0.0908471	+	0.279598i
$647$	−18.3820			−0.722670			−0.361335	−	0.932436i	$-0.617679\pi$
$647$	−18.3820			−0.722670			−0.361335	+	0.932436i	$0.617679\pi$
$648$	−1.76393	+	5.42882i	−0.0692938	+	0.213264i
$649$	12.3541	−	8.97578i	0.484941	−	0.352330i
$650$	−12.0172	−	8.73102i	−0.471354	−	0.342459i
$651$	−3.04508	−	9.37181i	−0.119346	−	0.367310i
$652$	1.24671	+	3.83698i	0.0488250	+	0.150268i
$653$	27.8328			1.08918			0.544591	−	0.838702i	$-0.316685\pi$
$653$	27.8328			1.08918			0.544591	+	0.838702i	$0.316685\pi$
$654$	−3.73607	−	2.71441i	−0.146092	−	0.106142i
$655$	−14.7984			−0.578220
$656$	−5.30902	−	3.57971i	−0.207282	−	0.139764i
$657$	42.3607			1.65265
$658$	3.23607	+	2.35114i	0.126155	+	0.0916570i
$659$	20.6525			0.804506			0.402253	−	0.915528i	$-0.368227\pi$
$659$	20.6525			0.804506			0.402253	+	0.915528i	$0.368227\pi$
$660$	−0.927051	−	2.85317i	−0.0360854	−	0.111059i
$661$	−0.611456	−	1.88187i	−0.0237829	−	0.0731962i	0.938461	−	0.345386i	$-0.112252\pi$
$661$	−0.611456	−	1.88187i	−0.0237829	−	0.0731962i	−0.962244	+	0.272190i	$0.912252\pi$
$662$	−8.16312	−	5.93085i	−0.317269	−	0.230509i
$663$	−13.2082	+	9.59632i	−0.512964	+	0.372690i
$664$	4.97214	−	15.3027i	0.192956	−	0.593858i
$665$	7.47214			0.289757
$666$	1.19098	−	3.66547i	0.0461497	−	0.142034i
$667$	0.263932	−	0.812299i	0.0102195	−	0.0314524i
$668$	−7.42705	−	22.8581i	−0.287361	−	0.884407i
$669$	−12.8541	−	9.33905i	−0.496968	−	0.361069i
$670$	24.9443			0.963681
$671$	−3.21885	−	9.90659i	−0.124262	−	0.382440i
$672$	1.30902	−	0.951057i	0.0504964	−	0.0366878i
$673$	−4.40983	+	13.5721i	−0.169986	+	0.523165i	−0.999369	−	0.0355165i	$-0.988692\pi$
$673$	−4.40983	+	13.5721i	−0.169986	+	0.523165i	0.829383	+	0.558681i	$0.188692\pi$
$674$	−21.6525	−	15.7314i	−0.834022	−	0.605953i
$675$	6.69098	−	4.86128i	0.257536	−	0.187111i
$676$	−20.9443	+	15.2169i	−0.805549	+	0.585266i
$677$	−25.9894	+	18.8824i	−0.998852	+	0.725709i	−0.961842	−	0.273606i	$-0.911783\pi$
$677$	−25.9894	+	18.8824i	−0.998852	+	0.725709i	−0.0370104	+	0.999315i	$0.511783\pi$
$678$	−8.92705	+	6.48588i	−0.342841	+	0.249089i
$679$	11.5902	+	8.42075i	0.444790	+	0.323159i
$680$	2.11803	−	6.51864i	0.0812229	−	0.249978i
$681$	−9.32624	+	6.77591i	−0.357382	+	0.259653i
$682$	5.64590	+	17.3763i	0.216193	+	0.665372i
$683$	−13.2016			−0.505146			−0.252573	−	0.967578i	$-0.581277\pi$
$683$	−13.2016			−0.505146			−0.252573	+	0.967578i	$0.581277\pi$
$684$	−3.73607	−	2.71441i	−0.142852	−	0.103788i
$685$	−3.38197	−	10.4086i	−0.129218	−	0.397693i
$686$	−5.78115	+	17.7926i	−0.220725	+	0.679323i
$687$	−2.02786	+	6.24112i	−0.0773678	+	0.238114i
$688$	9.70820			0.370122
$689$	22.8435	−	70.3049i	0.870266	−	2.67840i
$690$	1.30902	−	0.951057i	0.0498334	−	0.0362061i
$691$	2.90983	+	2.11412i	0.110695	+	0.0804247i	0.641756	−	0.766909i	$-0.278206\pi$
$691$	2.90983	+	2.11412i	0.110695	+	0.0804247i	−0.531061	+	0.847334i	$0.678206\pi$
$692$	−1.16312	−	3.57971i	−0.0442151	−	0.136080i
$693$	6.35410	+	19.5559i	0.241372	+	0.742868i
$694$	28.7426			1.09106
$695$	−0.309017	−	0.224514i	−0.0117217	−	0.00851630i
$696$	−0.326238			−0.0123660
$697$	−27.1074	+	0.951057i	−1.02677	+	0.0360238i
$698$	−6.38197			−0.241561
$699$	6.64590	+	4.82853i	0.251371	+	0.182632i
$700$	6.23607			0.235701
$701$	11.1697	+	34.3768i	0.421874	+	1.29839i	0.905956	+	0.423371i	$0.139153\pi$
$701$	11.1697	+	34.3768i	0.421874	+	1.29839i	−0.484083	+	0.875022i	$0.660847\pi$
$702$	−6.69098	−	20.5927i	−0.252535	−	0.777222i
$703$	2.10081	+	1.52633i	0.0792337	+	0.0575666i
$704$	−2.42705	+	1.76336i	−0.0914729	+	0.0664590i
$705$	0.472136	−	1.45309i	0.0177817	−	0.0547263i
$706$	−7.61803			−0.286708
$707$	−6.30902	+	19.4172i	−0.237275	+	0.730257i
$708$	0.972136	−	2.99193i	0.0365351	−	0.112443i
$709$	−8.73607	−	26.8869i	−0.328090	−	1.00976i	−0.970026	−	0.242999i	$-0.921869\pi$
$709$	−8.73607	−	26.8869i	−0.328090	−	1.00976i	0.641937	−	0.766758i	$-0.278131\pi$
$710$	5.04508	+	3.66547i	0.189339	+	0.137563i
$711$	−36.6525			−1.37458
$712$	1.92705	+	5.93085i	0.0722193	+	0.222268i
$713$	−7.97214	+	5.79210i	−0.298559	+	0.216916i
$714$	2.11803	−	6.51864i	0.0792654	−	0.243954i
$715$	−24.4894	−	17.7926i	−0.915850	−	0.665404i
$716$	19.7082	−	14.3188i	0.736530	−	0.535120i
$717$	12.6353	−	9.18005i	0.471872	−	0.342835i
$718$	−9.09017	+	6.60440i	−0.339242	+	0.246474i
$719$	−30.1074	+	21.8743i	−1.12282	+	0.815774i	−0.984634	−	0.174633i	$-0.944126\pi$
$719$	−30.1074	+	21.8743i	−1.12282	+	0.815774i	−0.138183	+	0.990407i	$0.544126\pi$
$720$	3.42705	+	2.48990i	0.127719	+	0.0927930i
$721$	9.89919	−	30.4666i	0.368665	−	1.13463i
$722$	−12.8541	+	9.33905i	−0.478380	+	0.347564i
$723$	2.92047	+	8.98829i	0.108614	+	0.334278i
$724$	6.03444			0.224268
$725$	−1.01722	−	0.739054i	−0.0377786	−	0.0274478i
$726$	−0.381966	−	1.17557i	−0.0141761	−	0.0436295i
$727$	−3.00000	+	9.23305i	−0.111264	+	0.342435i	−0.991149	−	0.132751i	$-0.957619\pi$
$727$	−3.00000	+	9.23305i	−0.111264	+	0.342435i	0.879886	+	0.475186i	$0.157619\pi$
$728$	5.04508	−	15.5272i	0.186983	−	0.575475i
$729$	−8.50658			−0.315058
$730$	8.09017	−	24.8990i	0.299431	−	0.921553i
$731$	33.2705	−	24.1724i	1.23055	−	0.894050i
$732$	−1.73607	−	1.26133i	−0.0641669	−	0.0466200i
$733$	5.33688	+	16.4252i	0.197122	+	0.606680i	0.999945	+	0.0104624i	$0.00333035\pi$
$733$	5.33688	+	16.4252i	0.197122	+	0.606680i	−0.802823	+	0.596217i	$0.796670\pi$
$734$	−2.83688	−	8.73102i	−0.104711	−	0.322268i
$735$	0.145898			0.00538153
$736$	−1.30902	−	0.951057i	−0.0482510	−	0.0350564i
$737$	−46.2492			−1.70361
$738$	4.61803	−	16.1150i	0.169992	−	0.593200i
$739$	−19.8328			−0.729562			−0.364781	−	0.931093i	$-0.618856\pi$
$739$	−19.8328			−0.729562			−0.364781	+	0.931093i	$0.618856\pi$
$740$	−1.92705	−	1.40008i	−0.0708398	−	0.0514681i
$741$	6.79837			0.249745
$742$	9.59017	+	29.5155i	0.352066	+	1.08355i
$743$	−9.23607	−	28.4257i	−0.338838	−	1.04284i	−0.964800	−	0.262984i	$-0.915293\pi$
$743$	−9.23607	−	28.4257i	−0.338838	−	1.04284i	0.625962	−	0.779854i	$-0.284707\pi$
$744$	3.04508	+	2.21238i	0.111638	+	0.0811099i
$745$	14.9443	−	10.8576i	0.547516	−	0.397793i
$746$	−7.78115	+	23.9479i	−0.284888	+	0.876796i
$747$	42.1246			1.54126
$748$	−3.92705	+	12.0862i	−0.143587	+	0.441916i
$749$	4.61803	−	14.2128i	0.168739	−	0.519326i
$750$	−2.28115	−	7.02067i	−0.0832959	−	0.256359i
$751$	−6.02786	−	4.37950i	−0.219960	−	0.159810i	0.472349	−	0.881412i	$-0.343406\pi$
$751$	−6.02786	−	4.37950i	−0.219960	−	0.159810i	−0.692309	+	0.721602i	$0.743406\pi$
$752$	−1.52786			−0.0557155
$753$	−3.35410	−	10.3229i	−0.122230	−	0.376186i
$754$	−2.66312	+	1.93487i	−0.0969851	+	0.0704638i
$755$	−7.61803	+	23.4459i	−0.277249	+	0.853284i
$756$	7.35410	+	5.34307i	0.267466	+	0.194325i
$757$	11.0623	−	8.03724i	0.402066	−	0.292118i	−0.368316	−	0.929701i	$-0.620065\pi$
$757$	11.0623	−	8.03724i	0.402066	−	0.292118i	0.770382	+	0.637582i	$0.220065\pi$
$758$	−12.1631	+	8.83702i	−0.441784	+	0.320975i
$759$	−2.42705	+	1.76336i	−0.0880964	+	0.0640058i
$760$	−2.30902	+	1.67760i	−0.0837568	+	0.0608529i
$761$	−0.427051	−	0.310271i	−0.0154806	−	0.0112473i	0.580018	−	0.814604i	$-0.303045\pi$
$761$	−0.427051	−	0.310271i	−0.0154806	−	0.0112473i	−0.595499	+	0.803356i	$0.703045\pi$
$762$	1.29837	−	3.99598i	0.0470351	−	0.144759i
$763$	15.8262	−	11.4984i	0.572948	−	0.416271i
$764$	1.54508	+	4.75528i	0.0558992	+	0.172040i
$765$	17.9443			0.648777
$766$	−2.57295	−	1.86936i	−0.0929644	−	0.0675426i
$767$	−9.80902	−	30.1891i	−0.354183	−	1.09006i
$768$	−0.190983	+	0.587785i	−0.00689151	+	0.0212099i
$769$	8.92705	−	27.4746i	0.321918	−	0.990761i	−0.650895	−	0.759168i	$-0.725606\pi$
$769$	8.92705	−	27.4746i	0.321918	−	0.990761i	0.972813	−	0.231593i	$-0.0743938\pi$
$770$	12.7082			0.457972
$771$	0.909830	−	2.80017i	0.0327667	−	0.100846i
$772$	9.78115	−	7.10642i	0.352031	−	0.255766i
$773$	−12.2812	−	8.92278i	−0.441722	−	0.320930i	0.344597	−	0.938751i	$-0.388016\pi$
$773$	−12.2812	−	8.92278i	−0.441722	−	0.320930i	−0.786319	+	0.617821i	$0.788016\pi$
$774$	7.85410	+	24.1724i	0.282310	+	0.868860i
$775$	4.48278	+	13.7966i	0.161026	+	0.495588i
$776$	−5.47214			−0.196438
$777$	−1.92705	−	1.40008i	−0.0691326	−	0.0502278i
$778$	−37.4721			−1.34344
$779$	9.36475	+	6.31437i	0.335527	+	0.226236i
$780$	−6.23607			−0.223287
$781$	−9.35410	−	6.79615i	−0.334716	−	0.243185i
$782$	−6.85410			−0.245102
$783$	−0.566371	−	1.74311i	−0.0202405	−	0.0622937i
$784$	−0.0450850	−	0.138757i	−0.00161018	−	0.00495562i
$785$	−3.85410	−	2.80017i	−0.137559	−	0.0999423i
$786$	4.57295	−	3.32244i	0.163112	−	0.118508i
$787$	−3.95492	+	12.1720i	−0.140977	+	0.433884i	−0.996472	−	0.0839281i	$-0.973253\pi$
$787$	−3.95492	+	12.1720i	−0.140977	+	0.433884i	0.855494	+	0.517812i	$0.173253\pi$
$788$	−3.18034			−0.113295
$789$	−0.0172209	+	0.0530006i	−0.000613081	+	0.00188687i
$790$	−7.00000	+	21.5438i	−0.249049	+	0.766493i
$791$	−14.4443	−	44.4549i	−0.513579	−	1.58063i
$792$	−6.35410	−	4.61653i	−0.225783	−	0.164041i
$793$	−21.6525			−0.768902
$794$	8.18034	+	25.1765i	0.290309	+	0.893480i
$795$	9.59017	−	6.96767i	0.340128	−	0.247118i
$796$	2.01722	−	6.20837i	0.0714985	−	0.220050i
$797$	18.4164	+	13.3803i	0.652343	+	0.473955i	0.864068	−	0.503374i	$-0.167908\pi$
$797$	18.4164	+	13.3803i	0.652343	+	0.473955i	−0.211726	+	0.977329i	$0.567908\pi$
$798$	−2.30902	+	1.67760i	−0.0817383	+	0.0593864i
$799$	−5.23607	+	3.80423i	−0.185239	+	0.134584i
$800$	−1.92705	+	1.40008i	−0.0681315	+	0.0495005i
$801$	−13.2082	+	9.59632i	−0.466689	+	0.339069i
$802$	20.1353	+	14.6291i	0.711001	+	0.516572i
$803$	−15.0000	+	46.1653i	−0.529339	+	1.62914i
$804$	−7.70820	+	5.60034i	−0.271847	+	0.197509i
$805$	2.11803	+	6.51864i	0.0746509	+	0.229752i
$806$	37.9787			1.33774
$807$	−3.02786	−	2.19987i	−0.106586	−	0.0774392i
$808$	−2.40983	−	7.41669i	−0.0847775	−	0.260918i
$809$	−9.45492	+	29.0992i	−0.332417	+	1.02307i	0.635563	+	0.772049i	$0.280768\pi$
$809$	−9.45492	+	29.0992i	−0.332417	+	1.02307i	−0.967980	+	0.251026i	$0.919232\pi$
$810$	−2.85410	+	8.78402i	−0.100283	+	0.308639i
$811$	19.0689			0.669599			0.334800	−	0.942289i	$-0.391331\pi$
$811$	19.0689			0.669599			0.334800	+	0.942289i	$0.391331\pi$
$812$	0.427051	−	1.31433i	0.0149866	−	0.0461239i
$813$	−13.0623	+	9.49032i	−0.458115	+	0.332840i
$814$	3.57295	+	2.59590i	0.125232	+	0.0909862i
$815$	2.01722	+	6.20837i	0.0706602	+	0.217470i
$816$	0.809017	+	2.48990i	0.0283213	+	0.0871639i
$817$	−17.1246			−0.599114
$818$	−0.218847	−	0.159002i	−0.00765181	−	0.00555936i
$819$	42.7426			1.49355
$820$	−8.59017	−	5.79210i	−0.299982	−	0.202269i
$821$	10.4377			0.364278			0.182139	−	0.983273i	$-0.441698\pi$
$821$	10.4377			0.364278			0.182139	+	0.983273i	$0.441698\pi$
$822$	3.38197	+	2.45714i	0.117960	+	0.0857027i
$823$	1.43769			0.0501149			0.0250574	−	0.999686i	$-0.492023\pi$
$823$	1.43769			0.0501149			0.0250574	+	0.999686i	$0.492023\pi$
$824$	3.78115	+	11.6372i	0.131723	+	0.405401i
$825$	1.36475	+	4.20025i	0.0475143	+	0.146234i
$826$	10.7812	+	7.83297i	0.375124	+	0.272544i
$827$	9.51722	−	6.91467i	0.330946	−	0.240446i	−0.409886	−	0.912137i	$-0.634431\pi$
$827$	9.51722	−	6.91467i	0.330946	−	0.240446i	0.740832	+	0.671690i	$0.234431\pi$
$828$	1.30902	−	4.02874i	0.0454915	−	0.140008i
$829$	10.2918			0.357449			0.178724	−	0.983899i	$-0.442803\pi$
$829$	10.2918			0.357449			0.178724	+	0.983899i	$0.442803\pi$
$830$	8.04508	−	24.7602i	0.279249	−	0.859440i
$831$	2.98278	−	9.18005i	0.103471	−	0.318452i
$832$	1.92705	+	5.93085i	0.0668085	+	0.205615i
$833$	−0.500000	−	0.363271i	−0.0173240	−	0.0125866i
$834$	0.145898			0.00505204
$835$	−12.0172	−	36.9852i	−0.415873	−	1.27993i
$836$	4.28115	−	3.11044i	0.148067	−	0.107577i
$837$	−6.53444	+	20.1109i	−0.225863	+	0.695136i
$838$	−14.5451	−	10.5676i	−0.502452	−	0.365052i
$839$	18.6074	−	13.5191i	0.642398	−	0.466730i	−0.218275	−	0.975887i	$-0.570043\pi$
$839$	18.6074	−	13.5191i	0.642398	−	0.466730i	0.860673	+	0.509158i	$0.170043\pi$
$840$	2.11803	−	1.53884i	0.0730791	−	0.0530951i
$841$	23.2361	−	16.8820i	0.801244	−	0.582138i
$842$	−22.0344	+	16.0090i	−0.759357	+	0.551705i
$843$	4.97214	+	3.61247i	0.171249	+	0.124420i
$844$	1.92705	−	5.93085i	0.0663318	−	0.204148i
$845$	−33.8885	+	24.6215i	−1.16580	+	0.847004i
$846$	−1.23607	−	3.80423i	−0.0424969	−	0.130792i
$847$	5.23607			0.179913
$848$	−9.59017	−	6.96767i	−0.329328	−	0.239271i
$849$	3.34346	+	10.2901i	0.114747	+	0.353156i
$850$	−3.11803	+	9.59632i	−0.106948	+	0.329151i
$851$	−0.736068	+	2.26538i	−0.0252321	+	0.0776564i
$852$	−2.38197			−0.0816048
$853$	4.19098	−	12.8985i	0.143497	−	0.441637i	−0.853318	−	0.521391i	$-0.825413\pi$
$853$	4.19098	−	12.8985i	0.143497	−	0.441637i	0.996815	+	0.0797538i	$0.0254134\pi$
$854$	7.35410	−	5.34307i	0.251652	−	0.182836i
$855$	−6.04508	−	4.39201i	−0.206738	−	0.150204i
$856$	1.76393	+	5.42882i	0.0602900	+	0.185553i
$857$	5.60081	+	17.2375i	0.191320	+	0.588823i	1.00000		0.000573603i	$0.000182584\pi$
$857$	5.60081	+	17.2375i	0.191320	+	0.588823i	−0.808680	+	0.588249i	$0.799817\pi$
$858$	11.5623			0.394731
$859$	3.61803	+	2.62866i	0.123446	+	0.0896886i	0.647795	−	0.761815i	$-0.275691\pi$
$859$	3.61803	+	2.62866i	0.123446	+	0.0896886i	−0.524349	+	0.851503i	$0.675691\pi$
$860$	15.7082			0.535645
$861$	−8.59017	−	5.79210i	−0.292752	−	0.197394i
$862$	11.7639			0.400681
$863$	2.38197	+	1.73060i	0.0810831	+	0.0589103i	0.627588	−	0.778545i	$-0.284042\pi$
$863$	2.38197	+	1.73060i	0.0810831	+	0.0589103i	−0.546505	+	0.837456i	$0.684042\pi$
$864$	−3.47214			−0.118124
$865$	−1.88197	−	5.79210i	−0.0639888	−	0.196937i
$866$	2.58359	+	7.95148i	0.0877940	+	0.270202i
$867$	0.472136	+	0.343027i	0.0160346	+	0.0116498i
$868$	−12.8992	+	9.37181i	−0.437827	+	0.318100i
$869$	12.9787	−	39.9444i	0.440273	−	1.35502i
$870$	−0.527864			−0.0178963
$871$	−29.7082	+	91.4325i	−1.00662	+	3.09807i
$872$	−2.30902	+	7.10642i	−0.0781932	+	0.240654i
$873$	−4.42705	−	13.6251i	−0.149833	−	0.461138i
$874$	2.30902	+	1.67760i	0.0781037	+	0.0567456i
$875$	31.2705			1.05714
$876$	3.09017	+	9.51057i	0.104407	+	0.321332i
$877$	−29.3435	+	21.3193i	−0.990858	+	0.719901i	−0.960109	−	0.279627i	$-0.909789\pi$
$877$	−29.3435	+	21.3193i	−0.990858	+	0.719901i	−0.0307493	+	0.999527i	$0.509789\pi$
$878$	7.16312	−	22.0458i	0.241744	−	0.744010i
$879$	−3.39919	−	2.46965i	−0.114652	−	0.0832994i
$880$	−3.92705	+	2.85317i	−0.132381	+	0.0961803i
$881$	37.0344	−	26.9071i	1.24772	−	0.906523i	0.249635	−	0.968340i	$-0.419690\pi$
$881$	37.0344	−	26.9071i	1.24772	−	0.906523i	0.998088	+	0.0618170i	$0.0196895\pi$
$882$	0.309017	−	0.224514i	0.0104051	−	0.00755978i
$883$	0.600813	−	0.436516i	0.0202190	−	0.0146899i	−0.577630	−	0.816299i	$-0.696022\pi$
$883$	0.600813	−	0.436516i	0.0202190	−	0.0146899i	0.597849	+	0.801609i	$0.296022\pi$
$884$	21.3713	+	15.5272i	0.718795	+	0.522235i
$885$	1.57295	−	4.84104i	0.0528741	−	0.162730i
$886$	−18.8435	+	13.6906i	−0.633058	+	0.459944i
$887$	−3.97871	−	12.2452i	−0.133592	−	0.411154i	0.861776	−	0.507289i	$-0.169352\pi$
$887$	−3.97871	−	12.2452i	−0.133592	−	0.411154i	−0.995368	+	0.0961343i	$0.969352\pi$
$888$	0.909830			0.0305319
$889$	14.3992	+	10.4616i	0.482933	+	0.350872i
$890$	3.11803	+	9.59632i	0.104517	+	0.321669i
$891$	5.29180	−	16.2865i	0.177282	−	0.545617i
$892$	−7.94427	+	24.4500i	−0.265994	+	0.818645i
$893$	2.69505			0.0901864
$894$	−2.18034	+	6.71040i	−0.0729215	+	0.224429i
$895$	31.8885	−	23.1684i	1.06592	−	0.774434i
$896$	−2.11803	−	1.53884i	−0.0707585	−	0.0514091i
$897$	1.92705	+	5.93085i	0.0643424	+	0.198025i
$898$	−2.12868	−	6.55139i	−0.0710349	−	0.218623i
$899$	3.21478			0.107219
$900$	−5.04508	−	3.66547i	−0.168169	−	0.122182i
$901$	−50.2148			−1.67290
$902$	15.9271	+	10.7391i	0.530313	+	0.357574i
$903$	15.7082			0.522736
$904$	14.4443	+	10.4944i	0.480409	+	0.349038i
$905$	9.76393			0.324564
$906$	−2.90983	−	8.95554i	−0.0966726	−	0.297528i
$907$	−12.2639	−	37.7445i	−0.407217	−	1.25329i	−0.919030	−	0.394188i	$-0.871026\pi$
$907$	−12.2639	−	37.7445i	−0.407217	−	1.25329i	0.511812	−	0.859097i	$-0.328974\pi$
$908$	15.0902	+	10.9637i	0.500785	+	0.363842i
$909$	16.5172	−	12.0005i	0.547842	−	0.398030i
$910$	8.16312	−	25.1235i	0.270605	−	0.832836i
$911$	42.4853			1.40760			0.703800	−	0.710398i	$-0.251485\pi$
$911$	42.4853			1.40760			0.703800	+	0.710398i	$0.251485\pi$
$912$	0.336881	−	1.03681i	0.0111552	−	0.0343323i
$913$	−14.9164	+	45.9080i	−0.493661	+	1.51933i
$914$	3.30902	+	10.1841i	0.109453	+	0.336860i
$915$	−2.80902	−	2.04087i	−0.0928632	−	0.0674691i
$916$	10.6180			0.350830
$917$	7.39919	+	22.7724i	0.244343	+	0.752009i
$918$	−11.8992	+	8.64527i	−0.392732	+	0.285336i
$919$	10.6525	−	32.7849i	0.351393	−	1.08148i	−0.606679	−	0.794947i	$-0.707499\pi$
$919$	10.6525	−	32.7849i	0.351393	−	1.08148i	0.958072	−	0.286529i	$-0.0925014\pi$
$920$	−2.11803	−	1.53884i	−0.0698295	−	0.0507341i
$921$	−11.2361	+	8.16348i	−0.370241	+	0.268996i
$922$	25.1353	−	18.2618i	0.827786	−	0.601421i
$923$	−19.4443	+	14.1271i	−0.640016	+	0.464999i
$924$	−3.92705	+	2.85317i	−0.129190	+	0.0938624i
$925$	2.83688	+	2.06111i	0.0932761	+	0.0677690i
$926$	5.30902	−	16.3395i	0.174465	−	0.536948i
$927$	−25.9164	+	18.8294i	−0.851207	+	0.618438i
$928$	0.163119	+	0.502029i	0.00535464	+	0.0164799i
$929$	−27.8328			−0.913165			−0.456583	−	0.889681i	$-0.650927\pi$
$929$	−27.8328			−0.913165			−0.456583	+	0.889681i	$0.650927\pi$
$930$	4.92705	+	3.57971i	0.161564	+	0.117383i
$931$	0.0795268	+	0.244758i	0.00260639	+	0.00802163i
$932$	4.10739	−	12.6412i	0.134542	−	0.414078i
$933$	0.871323	−	2.68166i	0.0285258	−	0.0877935i
$934$	−28.0000			−0.916188
$935$	−6.35410	+	19.5559i	−0.207801	+	0.639547i
$936$	−13.2082	+	9.59632i	−0.431724	+	0.313666i
$937$	−36.0238	−	26.1728i	−1.17685	−	0.855029i	−0.185034	−	0.982732i	$-0.559239\pi$
$937$	−36.0238	−	26.1728i	−1.17685	−	0.855029i	−0.991812	+	0.127703i	$0.959239\pi$
$938$	−12.4721	−	38.3853i	−0.407230	−	1.25332i
$939$	−0.437694	−	1.34708i	−0.0142836	−	0.0439604i
$940$	−2.47214			−0.0806322
$941$	−24.4164	−	17.7396i	−0.795952	−	0.578293i	0.113772	−	0.993507i	$-0.463707\pi$
$941$	−24.4164	−	17.7396i	−0.795952	−	0.578293i	−0.909724	+	0.415214i	$0.863707\pi$
$942$	1.81966			0.0592877
$943$	−2.85410	+	9.95959i	−0.0929423	+	0.324329i
$944$	−5.09017			−0.165671
$945$	11.8992	+	8.64527i	0.387081	+	0.281231i
$946$	−29.1246			−0.946923
$947$	−0.0172209	−	0.0530006i	−0.000559605	−	0.00172229i	0.950776	−	0.309878i	$-0.100288\pi$
$947$	−0.0172209	−	0.0530006i	−0.000559605	−	0.00172229i	−0.951336	+	0.308156i	$0.900288\pi$
$948$	−2.67376	−	8.22899i	−0.0868398	−	0.267265i
$949$	81.6312	+	59.3085i	2.64986	+	1.92524i
$950$	3.39919	−	2.46965i	0.110284	−	0.0801262i
$951$	2.59017	−	7.97172i	0.0839920	−	0.258501i
$952$	−11.0902			−0.359434
$953$	12.2254	−	37.6260i	0.396020	−	1.21883i	−0.532144	−	0.846654i	$-0.678613\pi$
$953$	12.2254	−	37.6260i	0.396020	−	1.21883i	0.928164	−	0.372171i	$-0.121387\pi$
$954$	9.59017	−	29.5155i	0.310493	−	0.955600i
$955$	2.50000	+	7.69421i	0.0808981	+	0.248979i
$956$	−20.4443	−	14.8536i	−0.661215	−	0.480401i
$957$	0.978714			0.0316373
$958$	−8.23607	−	25.3480i	−0.266095	−	0.818957i
$959$	−14.3262	+	10.4086i	−0.462618	+	0.336112i
$960$	−0.309017	+	0.951057i	−0.00997348	+	0.0306952i
$961$	−4.92705	−	3.57971i	−0.158937	−	0.115475i
$962$	7.42705	−	5.39607i	0.239458	−	0.173976i
$963$	−12.0902	+	8.78402i	−0.389600	+	0.283061i
$964$	12.3713	−	8.98829i	0.398453	−	0.289493i
$965$	15.8262	−	11.4984i	0.509465	−	0.370148i
$966$	−2.11803	−	1.53884i	−0.0681466	−	0.0495114i
$967$	9.26393	−	28.5115i	0.297908	−	0.916866i	−0.684321	−	0.729181i	$-0.739901\pi$
$967$	9.26393	−	28.5115i	0.297908	−	0.916866i	0.982229	−	0.187686i	$-0.0600986\pi$
$968$	−1.61803	+	1.17557i	−0.0520056	+	0.0377843i
$969$	−1.42705	−	4.39201i	−0.0458435	−	0.141092i
$970$	−8.85410			−0.284288
$971$	9.92705	+	7.21242i	0.318574	+	0.231458i	0.735567	−	0.677452i	$-0.236916\pi$
$971$	9.92705	+	7.21242i	0.318574	+	0.231458i	−0.416993	+	0.908910i	$0.636916\pi$
$972$	−4.30902	−	13.2618i	−0.138212	−	0.425372i
$973$	−0.190983	+	0.587785i	−0.00612263	+	0.0188435i
$974$	3.87132	−	11.9147i	0.124045	−	0.381772i
$975$	9.18034			0.294006
$976$	−1.07295	+	3.30220i	−0.0343443	+	0.105701i
$977$	−46.4058	+	33.7158i	−1.48465	+	1.07866i	−0.508631	+	0.860984i	$0.669848\pi$
$977$	−46.4058	+	33.7158i	−1.48465	+	1.07866i	−0.976021	+	0.217678i	$0.930152\pi$
$978$	−2.01722	−	1.46560i	−0.0645036	−	0.0468646i
$979$	−5.78115	−	17.7926i	−0.184766	−	0.568653i
$980$	−0.0729490	−	0.224514i	−0.00233027	−	0.00717184i
$981$	−19.5623			−0.624576
$982$	21.4164	+	15.5599i	0.683425	+	0.496537i
$983$	47.8115			1.52495			0.762475	−	0.647017i	$-0.223984\pi$
$983$	47.8115			1.52495			0.762475	+	0.647017i	$0.223984\pi$
$984$	3.95492	−	0.138757i	0.126078	−	0.00442342i
$985$	−5.14590			−0.163962
$986$	1.80902	+	1.31433i	0.0576108	+	0.0418567i
$987$	−2.47214			−0.0786890
$988$	−3.39919	−	10.4616i	−0.108143	−	0.332829i
$989$	−4.85410	−	14.9394i	−0.154351	−	0.475045i
$990$	−10.2812	−	7.46969i	−0.326756	−	0.237402i
$991$	−5.82624	+	4.23301i	−0.185077	+	0.134466i	−0.676466	−	0.736474i	$-0.736489\pi$
$991$	−5.82624	+	4.23301i	−0.185077	+	0.134466i	0.491389	+	0.870940i	$0.336489\pi$
$992$	1.88197	−	5.79210i	0.0597525	−	0.183899i
$993$	6.23607			0.197896
$994$	3.11803	−	9.59632i	0.0988980	−	0.304377i
$995$	3.26393	−	10.0453i	0.103474	−	0.318459i
$996$	3.07295	+	9.45756i	0.0973701	+	0.299674i
$997$	−10.4549	−	7.59594i	−0.331110	−	0.240566i	0.409791	−	0.912179i	$-0.365602\pi$
$997$	−10.4549	−	7.59594i	−0.331110	−	0.240566i	−0.740902	+	0.671614i	$0.765602\pi$
$998$	−33.6869			−1.06634
$999$	1.57953	+	4.86128i	0.0499740	+	0.153804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.2.d.b.51.1	yes	4
3.2	odd	2		738.2.h.b.379.1		4
4.3	odd	2		656.2.u.b.625.1		4
41.18	even	5		3362.2.a.h.1.1		2
41.23	even	10		3362.2.a.e.1.2		2
41.37	even	5	inner	82.2.d.b.37.1	✓	4
123.119	odd	10		738.2.h.b.37.1		4
164.119	odd	10		656.2.u.b.529.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.2.d.b.37.1	✓	4	41.37	even	5	inner
82.2.d.b.51.1	yes	4	1.1	even	1	trivial
656.2.u.b.529.1		4	164.119	odd	10
656.2.u.b.625.1		4	4.3	odd	2
738.2.h.b.37.1		4	123.119	odd	10
738.2.h.b.379.1		4	3.2	odd	2
3362.2.a.e.1.2		2	41.23	even	10
3362.2.a.h.1.1		2	41.18	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	82.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} -0.618034 q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 1.53884i) q^{5} +(-0.500000 - 0.363271i) q^{6} +(2.11803 - 1.53884i) q^{7} +(-0.309017 + 0.951057i) q^{8} -2.61803 q^{9} +(-0.500000 + 1.53884i) q^{10} +(0.927051 - 2.85317i) q^{11} +(-0.190983 - 0.587785i) q^{12} +(-5.04508 - 3.66547i) q^{13} +2.61803 q^{14} +(-0.309017 - 0.951057i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.30902 + 4.02874i) q^{17} +(-2.11803 - 1.53884i) q^{18} +(1.42705 - 1.03681i) q^{19} +(-1.30902 + 0.951057i) q^{20} +(-1.30902 + 0.951057i) q^{21} +(2.42705 - 1.76336i) q^{22} +(1.30902 + 0.951057i) q^{23} +(0.190983 - 0.587785i) q^{24} +(1.92705 - 1.40008i) q^{25} +(-1.92705 - 5.93085i) q^{26} +3.47214 q^{27} +(2.11803 + 1.53884i) q^{28} +(-0.163119 - 0.502029i) q^{29} +(0.309017 - 0.951057i) q^{30} +(-1.88197 + 5.79210i) q^{31} -1.00000 q^{32} +(-0.572949 + 1.76336i) q^{33} +(-3.42705 + 2.48990i) q^{34} +(3.42705 + 2.48990i) q^{35} +(-0.809017 - 2.48990i) q^{36} +(0.454915 + 1.40008i) q^{37} +1.76393 q^{38} +(3.11803 + 2.26538i) q^{39} -1.61803 q^{40} +(2.19098 + 6.01661i) q^{41} -1.61803 q^{42} +(-7.85410 - 5.70634i) q^{43} +3.00000 q^{44} +(-1.30902 - 4.02874i) q^{45} +(0.500000 + 1.53884i) q^{46} +(1.23607 + 0.898056i) q^{47} +(0.500000 - 0.363271i) q^{48} +(-0.0450850 + 0.138757i) q^{49} +2.38197 q^{50} +(0.809017 - 2.48990i) q^{51} +(1.92705 - 5.93085i) q^{52} +(3.66312 + 11.2739i) q^{53} +(2.80902 + 2.04087i) q^{54} +4.85410 q^{55} +(0.809017 + 2.48990i) q^{56} +(-0.881966 + 0.640786i) q^{57} +(0.163119 - 0.502029i) q^{58} +(4.11803 + 2.99193i) q^{59} +(0.809017 - 0.587785i) q^{60} +(2.80902 - 2.04087i) q^{61} +(-4.92705 + 3.57971i) q^{62} +(-5.54508 + 4.02874i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.11803 - 9.59632i) q^{65} +(-1.50000 + 1.08981i) q^{66} +(-4.76393 - 14.6619i) q^{67} -4.23607 q^{68} +(-0.809017 - 0.587785i) q^{69} +(1.30902 + 4.02874i) q^{70} +(1.19098 - 3.66547i) q^{71} +(0.809017 - 2.48990i) q^{72} -16.1803 q^{73} +(-0.454915 + 1.40008i) q^{74} +(-1.19098 + 0.865300i) q^{75} +(1.42705 + 1.03681i) q^{76} +(-2.42705 - 7.46969i) q^{77} +(1.19098 + 3.66547i) q^{78} +14.0000 q^{79} +(-1.30902 - 0.951057i) q^{80} +5.70820 q^{81} +(-1.76393 + 6.15537i) q^{82} -16.0902 q^{83} +(-1.30902 - 0.951057i) q^{84} -6.85410 q^{85} +(-3.00000 - 9.23305i) q^{86} +(0.100813 + 0.310271i) q^{87} +(2.42705 + 1.76336i) q^{88} +(5.04508 - 3.66547i) q^{89} +(1.30902 - 4.02874i) q^{90} -16.3262 q^{91} +(-0.500000 + 1.53884i) q^{92} +(1.16312 - 3.57971i) q^{93} +(0.472136 + 1.45309i) q^{94} +(2.30902 + 1.67760i) q^{95} +0.618034 q^{96} +(1.69098 + 5.20431i) q^{97} +(-0.118034 + 0.0857567i) q^{98} +(-2.42705 + 7.46969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + q^{8} - 6 q^{9} - 2 q^{10} - 3 q^{11} - 3 q^{12} - 9 q^{13} + 6 q^{14} + q^{15} - q^{16} - 3 q^{17} - 4 q^{18} - q^{19} - 3 q^{20} - 3 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 - q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + q^8 - 6 * q^9 - 2 * q^10 - 3 * q^11 - 3 * q^12 - 9 * q^13 + 6 * q^14 + q^15 - q^16 - 3 * q^17 - 4 * q^18 - q^19 - 3 * q^20 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^24 + q^25 - q^26 - 4 * q^27 + 4 * q^28 + 15 * q^29 - q^30 - 12 * q^31 - 4 * q^32 - 9 * q^33 - 7 * q^34 + 7 * q^35 - q^36 + 13 * q^37 + 16 * q^38 + 8 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 - 18 * q^43 + 12 * q^44 - 3 * q^45 + 2 * q^46 - 4 * q^47 + 2 * q^48 + 11 * q^49 + 14 * q^50 + q^51 + q^52 - q^53 + 9 * q^54 + 6 * q^55 + q^56 - 8 * q^57 - 15 * q^58 + 12 * q^59 + q^60 + 9 * q^61 - 13 * q^62 - 11 * q^63 - q^64 + 8 * q^65 - 6 * q^66 - 28 * q^67 - 8 * q^68 - q^69 + 3 * q^70 + 7 * q^71 + q^72 - 20 * q^73 - 13 * q^74 - 7 * q^75 - q^76 - 3 * q^77 + 7 * q^78 + 56 * q^79 - 3 * q^80 - 4 * q^81 - 16 * q^82 - 42 * q^83 - 3 * q^84 - 14 * q^85 - 12 * q^86 + 25 * q^87 + 3 * q^88 + 9 * q^89 + 3 * q^90 - 34 * q^91 - 2 * q^92 - 11 * q^93 - 16 * q^94 + 7 * q^95 - 2 * q^96 + 9 * q^97 + 4 * q^98 - 3 * q^99

Introduction

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