LMFDB - Embedded newform 234.2.f.d.133.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(133,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.133"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,12] 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.157365759791601.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{10} + 11x^{8} - 6x^{7} - 17x^{6} - 12x^{5} + 44x^{4} + 16x^{2} - 96x + 64 $ x^12 - 3x^11 + x^10 + 11x^8 - 6x^7 - 17x^6 - 12x^5 + 44x^4 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.5
Root			$1.40369 - 0.172227i$ of defining polynomial
Character	$\chi$	$=$	234.133
Dual form			234.2.f.d.139.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(1.25033 + 1.19862i) q^{3} +1.00000 q^{4} +(1.44068 + 2.49532i) q^{5} +(1.25033 + 1.19862i) q^{6} +(-2.39007 - 4.13973i) q^{7} +1.00000 q^{8} +(0.126635 + 2.99733i) q^{9} +(1.44068 + 2.49532i) q^{10} -3.77813 q^{11} +(1.25033 + 1.19862i) q^{12} +(-0.0450041 - 3.60527i) q^{13} +(-2.39007 - 4.13973i) q^{14} +(-1.18962 + 4.84679i) q^{15} +1.00000 q^{16} +(1.17963 - 2.04317i) q^{17} +(0.126635 + 2.99733i) q^{18} +(-2.90578 + 5.03295i) q^{19} +(1.44068 + 2.49532i) q^{20} +(1.97358 - 8.04080i) q^{21} -3.77813 q^{22} +(2.39782 - 4.15315i) q^{23} +(1.25033 + 1.19862i) q^{24} +(-1.65109 + 2.85977i) q^{25} +(-0.0450041 - 3.60527i) q^{26} +(-3.43431 + 3.89943i) q^{27} +(-2.39007 - 4.13973i) q^{28} +6.93228 q^{29} +(-1.18962 + 4.84679i) q^{30} +(0.501382 + 0.868419i) q^{31} +1.00000 q^{32} +(-4.72390 - 4.52853i) q^{33} +(1.17963 - 2.04317i) q^{34} +(6.88664 - 11.9280i) q^{35} +(0.126635 + 2.99733i) q^{36} +(0.590760 + 1.02323i) q^{37} +(-2.90578 + 5.03295i) q^{38} +(4.26507 - 4.56171i) q^{39} +(1.44068 + 2.49532i) q^{40} +(-0.693978 + 1.20200i) q^{41} +(1.97358 - 8.04080i) q^{42} +(-3.98744 - 6.90645i) q^{43} -3.77813 q^{44} +(-7.29686 + 4.63417i) q^{45} +(2.39782 - 4.15315i) q^{46} +(-5.24912 + 9.09174i) q^{47} +(1.25033 + 1.19862i) q^{48} +(-7.92491 + 13.7263i) q^{49} +(-1.65109 + 2.85977i) q^{50} +(3.92390 - 1.14071i) q^{51} +(-0.0450041 - 3.60527i) q^{52} -3.79134 q^{53} +(-3.43431 + 3.89943i) q^{54} +(-5.44306 - 9.42766i) q^{55} +(-2.39007 - 4.13973i) q^{56} +(-9.66575 + 2.80992i) q^{57} +6.93228 q^{58} +1.10523 q^{59} +(-1.18962 + 4.84679i) q^{60} +(1.37333 + 2.37868i) q^{61} +(0.501382 + 0.868419i) q^{62} +(12.1055 - 7.68807i) q^{63} +1.00000 q^{64} +(8.93148 - 5.30632i) q^{65} +(-4.72390 - 4.52853i) q^{66} +(3.93397 - 6.81383i) q^{67} +(1.17963 - 2.04317i) q^{68} +(7.97609 - 2.31872i) q^{69} +(6.88664 - 11.9280i) q^{70} +(-2.34406 + 4.06004i) q^{71} +(0.126635 + 2.99733i) q^{72} -10.6407 q^{73} +(0.590760 + 1.02323i) q^{74} +(-5.49218 + 1.59663i) q^{75} +(-2.90578 + 5.03295i) q^{76} +(9.03002 + 15.6404i) q^{77} +(4.26507 - 4.56171i) q^{78} +(-3.65213 + 6.32568i) q^{79} +(1.44068 + 2.49532i) q^{80} +(-8.96793 + 0.759135i) q^{81} +(-0.693978 + 1.20200i) q^{82} +(6.00937 - 10.4085i) q^{83} +(1.97358 - 8.04080i) q^{84} +6.79783 q^{85} +(-3.98744 - 6.90645i) q^{86} +(8.66761 + 8.30915i) q^{87} -3.77813 q^{88} +(2.23089 + 3.86402i) q^{89} +(-7.29686 + 4.63417i) q^{90} +(-14.8173 + 8.80317i) q^{91} +(2.39782 - 4.15315i) q^{92} +(-0.414010 + 1.68677i) q^{93} +(-5.24912 + 9.09174i) q^{94} -16.7451 q^{95} +(1.25033 + 1.19862i) q^{96} +(-1.82934 - 3.16850i) q^{97} +(-7.92491 + 13.7263i) q^{98} +(-0.478445 - 11.3243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} + q^{5} - 5 q^{7} + 12 q^{8} + 12 q^{9} + q^{10} - 16 q^{11} - q^{13} - 5 q^{14} - 3 q^{15} + 12 q^{16} + 3 q^{17} + 12 q^{18} - 7 q^{19} + q^{20} + 18 q^{21} - 16 q^{22}+ \cdots + 3 q^{99}+O(q^{100}) $ 12 * q + 12 * q^2 + 12 * q^4 + q^5 - 5 * q^7 + 12 * q^8 + 12 * q^9 + q^10 - 16 * q^11 - q^13 - 5 * q^14 - 3 * q^15 + 12 * q^16 + 3 * q^17 + 12 * q^18 - 7 * q^19 + q^20 + 18 * q^21 - 16 * q^22 + q^23 - 13 * q^25 - q^26 - 9 * q^27 - 5 * q^28 - 2 * q^29 - 3 * q^30 - 14 * q^31 + 12 * q^32 - 36 * q^33 + 3 * q^34 - 5 * q^35 + 12 * q^36 - 7 * q^37 - 7 * q^38 + q^40 + 9 * q^41 + 18 * q^42 - 8 * q^43 - 16 * q^44 - 27 * q^45 + q^46 - 13 * q^47 - 3 * q^49 - 13 * q^50 - 36 * q^51 - q^52 - 12 * q^53 - 9 * q^54 - 20 * q^55 - 5 * q^56 - 12 * q^57 - 2 * q^58 - 8 * q^59 - 3 * q^60 + 28 * q^61 - 14 * q^62 + 12 * q^63 + 12 * q^64 + 35 * q^65 - 36 * q^66 + 4 * q^67 + 3 * q^68 + 54 * q^69 - 5 * q^70 - 13 * q^71 + 12 * q^72 + 54 * q^73 - 7 * q^74 - 30 * q^75 - 7 * q^76 - 4 * q^77 - 6 * q^79 + q^80 - 12 * q^81 + 9 * q^82 + 30 * q^83 + 18 * q^84 + 18 * q^85 - 8 * q^86 - 6 * q^87 - 16 * q^88 + 3 * q^89 - 27 * q^90 - 12 * q^91 + q^92 + 42 * q^93 - 13 * q^94 + 42 * q^95 - 24 * q^97 - 3 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.25033	+	1.19862i	0.721877	+	0.692022i
$3$	1.25033	+	1.19862i	0.721877	+	0.692022i
$4$	1.00000			0.500000
$5$	1.44068	+	2.49532i	0.644290	+	1.11594i	0.984465	+	0.175580i	$0.0561802\pi$
$5$	1.44068	+	2.49532i	0.644290	+	1.11594i	−0.340175	+	0.940362i	$0.610486\pi$
$6$	1.25033	+	1.19862i	0.510444	+	0.489333i
$7$	−2.39007	−	4.13973i	−0.903363	−	1.56467i	−0.823100	−	0.567897i	$-0.807757\pi$
$7$	−2.39007	−	4.13973i	−0.903363	−	1.56467i	−0.0802633	−	0.996774i	$-0.525576\pi$
$8$	1.00000			0.353553
$9$	0.126635	+	2.99733i	0.0422118	+	0.999109i
$10$	1.44068	+	2.49532i	0.455582	+	0.789090i
$11$	−3.77813			−1.13915			−0.569575	−	0.821939i	$-0.692892\pi$
$11$	−3.77813			−1.13915			−0.569575	+	0.821939i	$0.692892\pi$
$12$	1.25033	+	1.19862i	0.360938	+	0.346011i
$13$	−0.0450041	−	3.60527i	−0.0124819	−	0.999922i
$13$	−0.0450041	−	3.60527i	−0.0124819	−	0.999922i
$14$	−2.39007	−	4.13973i	−0.638774	−	1.10639i
$15$	−1.18962	+	4.84679i	−0.307159	+	1.25144i
$16$	1.00000			0.250000
$17$	1.17963	−	2.04317i	0.286101	−	0.495542i	−0.686774	−	0.726871i	$-0.740974\pi$
$17$	1.17963	−	2.04317i	0.286101	−	0.495542i	0.972876	+	0.231329i	$0.0743073\pi$
$18$	0.126635	+	2.99733i	0.0298482	+	0.706477i
$19$	−2.90578	+	5.03295i	−0.666631	+	1.15464i	0.312210	+	0.950013i	$0.398931\pi$
$19$	−2.90578	+	5.03295i	−0.666631	+	1.15464i	−0.978840	+	0.204625i	$0.934402\pi$
$20$	1.44068	+	2.49532i	0.322145	+	0.557971i
$21$	1.97358	−	8.04080i	0.430669	−	1.75465i
$22$	−3.77813			−0.805501
$23$	2.39782	−	4.15315i	0.499980	−	0.865991i	−0.500020	−	0.866014i	$-0.666674\pi$
$23$	2.39782	−	4.15315i	0.499980	−	0.865991i	1.00000		2.27897e-5i	$7.25419e-6\pi$
$24$	1.25033	+	1.19862i	0.255222	+	0.244667i
$25$	−1.65109	+	2.85977i	−0.330218	+	0.571955i
$26$	−0.0450041	−	3.60527i	−0.00882603	−	0.707052i
$27$	−3.43431	+	3.89943i	−0.660933	+	0.750445i
$28$	−2.39007	−	4.13973i	−0.451681	−	0.782335i
$29$	6.93228			1.28729			0.643646	−	0.765323i	$-0.277421\pi$
$29$	6.93228			1.28729			0.643646	+	0.765323i	$0.277421\pi$
$30$	−1.18962	+	4.84679i	−0.217194	+	0.884898i
$31$	0.501382	+	0.868419i	0.0900508	+	0.155973i	0.907532	−	0.419982i	$-0.137964\pi$
$31$	0.501382	+	0.868419i	0.0900508	+	0.155973i	−0.817481	+	0.575955i	$0.804630\pi$
$32$	1.00000			0.176777
$33$	−4.72390	−	4.52853i	−0.822326	−	0.788317i
$34$	1.17963	−	2.04317i	0.202304	−	0.350401i
$35$	6.88664	−	11.9280i	1.16405	−	2.01620i
$36$	0.126635	+	2.99733i	0.0211059	+	0.499554i
$37$	0.590760	+	1.02323i	0.0971204	+	0.168217i	0.910492	−	0.413528i	$-0.135703\pi$
$37$	0.590760	+	1.02323i	0.0971204	+	0.168217i	−0.813371	+	0.581745i	$0.802370\pi$
$38$	−2.90578	+	5.03295i	−0.471379	+	0.816453i
$39$	4.26507	−	4.56171i	0.682957	−	0.730458i
$40$	1.44068	+	2.49532i	0.227791	+	0.394545i
$41$	−0.693978	+	1.20200i	−0.108381	+	0.187722i	−0.915115	−	0.403194i	$-0.867900\pi$
$41$	−0.693978	+	1.20200i	−0.108381	+	0.187722i	0.806733	+	0.590916i	$0.201233\pi$
$42$	1.97358	−	8.04080i	0.304529	−	1.24072i
$43$	−3.98744	−	6.90645i	−0.608079	−	1.05322i	−0.991557	−	0.129673i	$-0.958607\pi$
$43$	−3.98744	−	6.90645i	−0.608079	−	1.05322i	0.383478	−	0.923550i	$-0.374726\pi$
$44$	−3.77813			−0.569575
$45$	−7.29686	+	4.63417i	−1.08775	+	0.690821i
$46$	2.39782	−	4.15315i	0.353539	−	0.612348i
$47$	−5.24912	+	9.09174i	−0.765663	+	1.32617i	0.174233	+	0.984704i	$0.444255\pi$
$47$	−5.24912	+	9.09174i	−0.765663	+	1.32617i	−0.939896	+	0.341462i	$0.889078\pi$
$48$	1.25033	+	1.19862i	0.180469	+	0.173005i
$49$	−7.92491	+	13.7263i	−1.13213	+	1.96091i
$50$	−1.65109	+	2.85977i	−0.233500	+	0.404433i
$51$	3.92390	−	1.14071i	0.549456	−	0.159732i
$52$	−0.0450041	−	3.60527i	−0.00624095	−	0.499961i
$53$	−3.79134			−0.520781			−0.260390	−	0.965503i	$-0.583851\pi$
$53$	−3.79134			−0.520781			−0.260390	+	0.965503i	$0.583851\pi$
$54$	−3.43431	+	3.89943i	−0.467350	+	0.530645i
$55$	−5.44306	−	9.42766i	−0.733943	−	1.27123i
$56$	−2.39007	−	4.13973i	−0.319387	−	0.553195i
$57$	−9.66575	+	2.80992i	−1.28026	+	0.372183i
$58$	6.93228			0.910253
$59$	1.10523			0.143889			0.0719445	−	0.997409i	$-0.477080\pi$
$59$	1.10523			0.143889			0.0719445	+	0.997409i	$0.477080\pi$
$60$	−1.18962	+	4.84679i	−0.153579	+	0.625718i
$61$	1.37333	+	2.37868i	0.175837	+	0.304559i	0.940451	−	0.339930i	$-0.110403\pi$
$61$	1.37333	+	2.37868i	0.175837	+	0.304559i	−0.764613	+	0.644489i	$0.777070\pi$
$62$	0.501382	+	0.868419i	0.0636755	+	0.110289i
$63$	12.1055	−	7.68807i	1.52514	−	0.968605i
$64$	1.00000			0.125000
$65$	8.93148	−	5.30632i	1.10781	−	0.658169i
$66$	−4.72390	−	4.52853i	−0.581472	−	0.557424i
$67$	3.93397	−	6.81383i	0.480611	−	0.832442i	−0.519142	−	0.854688i	$-0.673748\pi$
$67$	3.93397	−	6.81383i	0.480611	−	0.832442i	0.999753	+	0.0222461i	$0.00708175\pi$
$68$	1.17963	−	2.04317i	0.143051	−	0.247771i
$69$	7.97609	−	2.31872i	0.960209	−	0.279142i
$70$	6.88664	−	11.9280i	0.823111	−	1.42567i
$71$	−2.34406	+	4.06004i	−0.278189	+	0.481838i	−0.970935	−	0.239344i	$-0.923068\pi$
$71$	−2.34406	+	4.06004i	−0.278189	+	0.481838i	0.692746	+	0.721182i	$0.256401\pi$
$72$	0.126635	+	2.99733i	0.0149241	+	0.353238i
$73$	−10.6407			−1.24540			−0.622698	−	0.782462i	$-0.713964\pi$
$73$	−10.6407			−1.24540			−0.622698	+	0.782462i	$0.713964\pi$
$74$	0.590760	+	1.02323i	0.0686745	+	0.118948i
$75$	−5.49218	+	1.59663i	−0.634182	+	0.184363i
$76$	−2.90578	+	5.03295i	−0.333315	+	0.577319i
$77$	9.03002	+	15.6404i	1.02907	+	1.78239i
$78$	4.26507	−	4.56171i	0.482924	−	0.516512i
$79$	−3.65213	+	6.32568i	−0.410897	+	0.711694i	−0.994988	−	0.0999939i	$-0.968118\pi$
$79$	−3.65213	+	6.32568i	−0.410897	+	0.711694i	0.584091	+	0.811688i	$0.301451\pi$
$80$	1.44068	+	2.49532i	0.161072	+	0.278986i
$81$	−8.96793	+	0.759135i	−0.996436	+	0.0843483i
$82$	−0.693978	+	1.20200i	−0.0766370	+	0.132739i
$83$	6.00937	−	10.4085i	0.659614	−	1.14248i	−0.321102	−	0.947045i	$-0.604053\pi$
$83$	6.00937	−	10.4085i	0.659614	−	1.14248i	0.980716	−	0.195440i	$-0.0626135\pi$
$84$	1.97358	−	8.04080i	0.215335	−	0.877323i
$85$	6.79783			0.737328
$86$	−3.98744	−	6.90645i	−0.429977	−	0.744741i
$87$	8.66761	+	8.30915i	0.929266	+	0.890834i
$88$	−3.77813			−0.402750
$89$	2.23089	+	3.86402i	0.236474	+	0.409585i	0.959700	−	0.281026i	$-0.0906748\pi$
$89$	2.23089	+	3.86402i	0.236474	+	0.409585i	−0.723226	+	0.690611i	$0.757342\pi$
$90$	−7.29686	+	4.63417i	−0.769156	+	0.488484i
$91$	−14.8173	+	8.80317i	−1.55327	+	0.922823i
$92$	2.39782	−	4.15315i	0.249990	−	0.432996i
$93$	−0.414010	+	1.68677i	−0.0429308	+	0.174910i
$94$	−5.24912	+	9.09174i	−0.541405	+	0.937741i
$95$	−16.7451			−1.71801
$96$	1.25033	+	1.19862i	0.127611	+	0.122333i
$97$	−1.82934	−	3.16850i	−0.185741	−	0.321713i	0.758085	−	0.652156i	$-0.226135\pi$
$97$	−1.82934	−	3.16850i	−0.185741	−	0.321713i	−0.943826	+	0.330443i	$0.892802\pi$
$98$	−7.92491	+	13.7263i	−0.800536	+	1.38657i
$99$	−0.478445	−	11.3243i	−0.0480856	−	1.13813i
$100$	−1.65109	+	2.85977i	−0.165109	+	0.285977i
$101$	8.10134			0.806113			0.403057	−	0.915175i	$-0.367948\pi$
$101$	8.10134			0.806113			0.403057	+	0.915175i	$0.367948\pi$
$102$	3.92390	−	1.14071i	0.388524	−	0.112947i
$103$	6.62448	+	11.4739i	0.652729	+	1.13056i	0.982458	+	0.186485i	$0.0597095\pi$
$103$	6.62448	+	11.4739i	0.652729	+	1.13056i	−0.329728	+	0.944076i	$0.606957\pi$
$104$	−0.0450041	−	3.60527i	−0.00441302	−	0.353526i
$105$	22.9077	−	6.65947i	2.23556	−	0.649898i
$106$	−3.79134			−0.368248
$107$	−1.32937	−	2.30253i	−0.128515	−	0.222594i	0.794587	−	0.607151i	$-0.207688\pi$
$107$	−1.32937	−	2.30253i	−0.128515	−	0.222594i	−0.923101	+	0.384557i	$0.874354\pi$
$108$	−3.43431	+	3.89943i	−0.330467	+	0.375222i
$109$	2.53982			0.243270			0.121635	−	0.992575i	$-0.461186\pi$
$109$	2.53982			0.243270			0.121635	+	0.992575i	$0.461186\pi$
$110$	−5.44306	−	9.42766i	−0.518976	−	0.898892i
$111$	−0.487813	+	1.98746i	−0.0463012	+	0.188642i
$112$	−2.39007	−	4.13973i	−0.225841	−	0.391168i
$113$	3.00622			0.282801			0.141401	−	0.989952i	$-0.454839\pi$
$113$	3.00622			0.282801			0.141401	+	0.989952i	$0.454839\pi$
$114$	−9.66575	+	2.80992i	−0.905280	+	0.263173i
$115$	13.8179			1.28853
$116$	6.93228			0.643646
$117$	10.8005	−	0.591447i	0.998504	−	0.0546793i
$118$	1.10523			0.101745
$119$	−11.2776			−1.03381
$120$	−1.18962	+	4.84679i	−0.108597	+	0.442449i
$121$	3.27429			0.297663
$122$	1.37333	+	2.37868i	0.124336	+	0.215356i
$123$	−2.30844	+	0.671086i	−0.208145	+	0.0605098i
$124$	0.501382	+	0.868419i	0.0450254	+	0.0779863i
$125$	4.89200			0.437554
$126$	12.1055	−	7.68807i	1.07844	−	0.684907i
$127$	0.626292	+	1.08477i	0.0555745	+	0.0962578i	0.892474	−	0.451098i	$-0.148968\pi$
$127$	0.626292	+	1.08477i	0.0555745	+	0.0962578i	−0.836900	+	0.547356i	$0.815634\pi$
$128$	1.00000			0.0883883
$129$	3.29258	−	13.4147i	0.289896	−	1.18110i
$130$	8.93148	−	5.30632i	0.783342	−	0.465395i
$131$	4.54154	+	7.86618i	0.396796	+	0.687271i	0.993329	−	0.115318i	$-0.0367886\pi$
$131$	4.54154	+	7.86618i	0.396796	+	0.687271i	−0.596532	+	0.802589i	$0.703455\pi$
$132$	−4.72390	−	4.52853i	−0.411163	−	0.394158i
$133$	27.7801			2.40884
$134$	3.93397	−	6.81383i	0.339843	−	0.588625i
$135$	−14.6781	−	2.95191i	−1.26329	−	0.254060i
$136$	1.17963	−	2.04317i	0.101152	−	0.175201i
$137$	5.92225	+	10.2576i	0.505972	+	0.876369i	0.999976	+	0.00690921i	$0.00219929\pi$
$137$	5.92225	+	10.2576i	0.505972	+	0.876369i	−0.494005	+	0.869459i	$0.664467\pi$
$138$	7.97609	−	2.31872i	0.678970	−	0.197383i
$139$	14.6543			1.24296			0.621481	−	0.783429i	$-0.286531\pi$
$139$	14.6543			1.24296			0.621481	+	0.783429i	$0.286531\pi$
$140$	6.88664	−	11.9280i	0.582027	−	1.00810i
$141$	−17.4606	+	5.07597i	−1.47045	+	0.427473i
$142$	−2.34406	+	4.06004i	−0.196709	+	0.340711i
$143$	0.170032	+	13.6212i	0.0142188	+	1.13906i
$144$	0.126635	+	2.99733i	0.0105529	+	0.249777i
$145$	9.98716	+	17.2983i	0.829389	+	1.43654i
$146$	−10.6407			−0.880629
$147$	−26.3613	+	7.66349i	−2.17425	+	0.632074i
$148$	0.590760	+	1.02323i	0.0485602	+	0.0841087i
$149$	−2.93221			−0.240216			−0.120108	−	0.992761i	$-0.538324\pi$
$149$	−2.93221			−0.240216			−0.120108	+	0.992761i	$0.538324\pi$
$150$	−5.49218	+	1.59663i	−0.448435	+	0.130364i
$151$	3.09803	−	5.36595i	0.252114	−	0.436675i	−0.711993	−	0.702186i	$-0.752207\pi$
$151$	3.09803	−	5.36595i	0.252114	−	0.436675i	0.964108	+	0.265511i	$0.0855407\pi$
$152$	−2.90578	+	5.03295i	−0.235690	+	0.408226i
$153$	6.27343	+	3.27699i	0.507177	+	0.264929i
$154$	9.03002	+	15.6404i	0.727660	+	1.26034i
$155$	−1.44466	+	2.50222i	−0.116038	+	0.200983i
$156$	4.26507	−	4.56171i	0.341479	−	0.365229i
$157$	−9.25665	−	16.0330i	−0.738761	−	1.27957i	−0.953054	−	0.302802i	$-0.902078\pi$
$157$	−9.25665	−	16.0330i	−0.738761	−	1.27957i	0.214293	−	0.976769i	$-0.431255\pi$
$158$	−3.65213	+	6.32568i	−0.290548	+	0.503244i
$159$	−4.74042	−	4.54437i	−0.375940	−	0.360392i
$160$	1.44068	+	2.49532i	0.113895	+	0.197273i
$161$	−22.9239			−1.80665
$162$	−8.96793	+	0.759135i	−0.704587	+	0.0596433i
$163$	4.35185	−	7.53762i	0.340863	−	0.590392i	−0.643730	−	0.765252i	$-0.722614\pi$
$163$	4.35185	−	7.53762i	0.340863	−	0.590392i	0.984593	+	0.174861i	$0.0559475\pi$
$164$	−0.693978	+	1.20200i	−0.0541906	+	0.0938608i
$165$	4.49455	−	18.3118i	0.349900	−	1.42557i
$166$	6.00937	−	10.4085i	0.466417	−	0.807859i
$167$	−8.94428	+	15.4919i	−0.692129	+	1.19880i	0.279010	+	0.960288i	$0.409994\pi$
$167$	−8.94428	+	15.4919i	−0.692129	+	1.19880i	−0.971139	+	0.238514i	$0.923340\pi$
$168$	1.97358	−	8.04080i	0.152265	−	0.620361i
$169$	−12.9959	+	0.324504i	−0.999688	+	0.0249618i
$170$	6.79783			0.521370
$171$	−15.4534	−	8.07221i	−1.18175	−	0.617297i
$172$	−3.98744	−	6.90645i	−0.304039	−	0.526612i
$173$	9.18636	+	15.9112i	0.698426	+	1.20971i	0.969012	+	0.247014i	$0.0794493\pi$
$173$	9.18636	+	15.9112i	0.698426	+	1.20971i	−0.270586	+	0.962696i	$0.587217\pi$
$174$	8.66761	+	8.30915i	0.657090	+	0.629915i
$175$	15.7849			1.19323
$176$	−3.77813			−0.284788
$177$	1.38190	+	1.32475i	0.103870	+	0.0995743i
$178$	2.23089	+	3.86402i	0.167212	+	0.289620i
$179$	−3.28324	−	5.68673i	−0.245401	−	0.425046i	0.716844	−	0.697234i	$-0.245586\pi$
$179$	−3.28324	−	5.68673i	−0.245401	−	0.425046i	−0.962244	+	0.272188i	$0.912253\pi$
$180$	−7.29686	+	4.63417i	−0.543876	+	0.345411i
$181$	−0.608557			−0.0452337			−0.0226169	−	0.999744i	$-0.507200\pi$
$181$	−0.608557			−0.0452337			−0.0226169	+	0.999744i	$0.507200\pi$
$182$	−14.8173	+	8.80317i	−1.09833	+	0.652534i
$183$	−1.13401	+	4.62023i	−0.0838287	+	0.341537i
$184$	2.39782	−	4.15315i	0.176770	−	0.306174i
$185$	−1.70219	+	2.94828i	−0.125147	+	0.216762i
$186$	−0.414010	+	1.68677i	−0.0303567	+	0.123680i
$187$	−4.45678	+	7.71938i	−0.325912	+	0.564497i
$188$	−5.24912	+	9.09174i	−0.382831	+	0.663083i
$189$	24.3508	+	4.89720i	1.77126	+	0.356219i
$190$	−16.7451			−1.21482
$191$	−5.76077	−	9.97795i	−0.416835	−	0.721979i	0.578784	−	0.815481i	$-0.303527\pi$
$191$	−5.76077	−	9.97795i	−0.416835	−	0.721979i	−0.995619	+	0.0935014i	$0.970194\pi$
$192$	1.25033	+	1.19862i	0.0902346	+	0.0865027i
$193$	−8.76136	+	15.1751i	−0.630656	+	1.09233i	0.356762	+	0.934195i	$0.383881\pi$
$193$	−8.76136	+	15.1751i	−0.630656	+	1.09233i	−0.987418	+	0.158133i	$0.949452\pi$
$194$	−1.82934	−	3.16850i	−0.131339	−	0.227485i
$195$	17.5275	+	4.07078i	1.25517	+	0.291515i
$196$	−7.92491	+	13.7263i	−0.566065	+	0.980453i
$197$	−4.49370	−	7.78331i	−0.320163	−	0.554538i	0.660359	−	0.750950i	$-0.270404\pi$
$197$	−4.49370	−	7.78331i	−0.320163	−	0.554538i	−0.980521	+	0.196412i	$0.937071\pi$
$198$	−0.478445	−	11.3243i	−0.0340016	−	0.804783i
$199$	13.3927	−	23.1968i	0.949383	−	1.64438i	0.202656	−	0.979250i	$-0.435043\pi$
$199$	13.3927	−	23.1968i	0.949383	−	1.64438i	0.746727	−	0.665130i	$-0.231624\pi$
$200$	−1.65109	+	2.85977i	−0.116750	+	0.202217i
$201$	13.0859	−	3.80420i	0.923009	−	0.268327i
$202$	8.10134			0.570008
$203$	−16.5687	−	28.6978i	−1.16289	−	2.01419i
$204$	3.92390	−	1.14071i	0.274728	−	0.0798659i
$205$	−3.99919			−0.279315
$206$	6.62448	+	11.4739i	0.461549	+	0.799427i
$207$	12.7520	+	6.66112i	0.886324	+	0.462980i
$208$	−0.0450041	−	3.60527i	−0.00312047	−	0.249981i
$209$	10.9784	−	19.0152i	0.759392	−	1.31531i
$210$	22.9077	−	6.65947i	1.58078	−	0.459547i
$211$	−5.81398	+	10.0701i	−0.400251	+	0.693255i	−0.993756	−	0.111576i	$-0.964410\pi$
$211$	−5.81398	+	10.0701i	−0.400251	+	0.693255i	0.593505	+	0.804830i	$0.297744\pi$
$212$	−3.79134			−0.260390
$213$	−7.79727	+	2.26674i	−0.534260	+	0.155314i
$214$	−1.32937	−	2.30253i	−0.0908737	−	0.157398i
$215$	11.4892	−	19.8999i	0.783558	−	1.35716i
$216$	−3.43431	+	3.89943i	−0.233675	+	0.265322i
$217$	2.39668	−	4.15117i	0.162697	−	0.281800i
$218$	2.53982			0.172018
$219$	−13.3043	−	12.7541i	−0.899023	−	0.861842i
$220$	−5.44306	−	9.42766i	−0.366971	−	0.635613i
$221$	−7.41928	−	4.16092i	−0.499074	−	0.279894i
$222$	−0.487813	+	1.98746i	−0.0327399	+	0.133390i
$223$	13.4250			0.899004			0.449502	−	0.893279i	$-0.351602\pi$
$223$	13.4250			0.899004			0.449502	+	0.893279i	$0.351602\pi$
$224$	−2.39007	−	4.13973i	−0.159694	−	0.276597i
$225$	−8.78076	−	4.58671i	−0.585384	−	0.305781i
$226$	3.00622			0.199971
$227$	−1.09211	−	1.89158i	−0.0724856	−	0.125549i	0.827504	−	0.561459i	$-0.189760\pi$
$227$	−1.09211	−	1.89158i	−0.0724856	−	0.125549i	−0.899990	+	0.435910i	$0.856426\pi$
$228$	−9.66575	+	2.80992i	−0.640130	+	0.186092i
$229$	−9.58555	−	16.6027i	−0.633431	−	1.09713i	−0.986845	−	0.161668i	$-0.948313\pi$
$229$	−9.58555	−	16.6027i	−0.633431	−	1.09713i	0.353414	−	0.935467i	$-0.385021\pi$
$230$	13.8179			0.911127
$231$	−7.45643	+	30.3792i	−0.490597	+	1.99881i
$232$	6.93228			0.455126
$233$	−3.59859			−0.235751			−0.117876	−	0.993028i	$-0.537608\pi$
$233$	−3.59859			−0.235751			−0.117876	+	0.993028i	$0.537608\pi$
$234$	10.8005	−	0.591447i	0.706049	−	0.0386641i
$235$	−30.2491			−1.97323
$236$	1.10523			0.0719445
$237$	−12.1484	+	3.53166i	−0.789125	+	0.229406i
$238$	−11.2776			−0.731016
$239$	−1.63290	−	2.82827i	−0.105624	−	0.182945i	0.808369	−	0.588676i	$-0.200351\pi$
$239$	−1.63290	−	2.82827i	−0.105624	−	0.182945i	−0.913993	+	0.405730i	$0.867017\pi$
$240$	−1.18962	+	4.84679i	−0.0767897	+	0.312859i
$241$	−10.8271	−	18.7531i	−0.697435	−	1.20799i	−0.969353	−	0.245673i	$-0.920991\pi$
$241$	−10.8271	−	18.7531i	−0.697435	−	1.20799i	0.271917	−	0.962321i	$-0.412342\pi$
$242$	3.27429			0.210479
$243$	−12.1228	−	9.79994i	−0.777675	−	0.628667i
$244$	1.37333	+	2.37868i	0.0879186	+	0.152280i
$245$	−45.6689			−2.91768
$246$	−2.30844	+	0.671086i	−0.147181	+	0.0427869i
$247$	18.2759	+	10.2496i	1.16287	+	0.652167i
$248$	0.501382	+	0.868419i	0.0318378	+	0.0551446i
$249$	19.9895	−	5.81114i	1.26678	−	0.368266i
$250$	4.89200			0.309398
$251$	−12.8310	+	22.2240i	−0.809887	+	1.40277i	0.103055	+	0.994676i	$0.467138\pi$
$251$	−12.8310	+	22.2240i	−0.809887	+	1.40277i	−0.912942	+	0.408090i	$0.866195\pi$
$252$	12.1055	−	7.68807i	0.762572	−	0.484303i
$253$	−9.05929	+	15.6911i	−0.569553	+	0.986494i
$254$	0.626292	+	1.08477i	0.0392971	+	0.0680645i
$255$	8.49951	+	8.14800i	0.532260	+	0.510247i
$256$	1.00000			0.0625000
$257$	−0.566168	+	0.980632i	−0.0353166	+	0.0611702i	−0.883143	−	0.469103i	$-0.844577\pi$
$257$	−0.566168	+	0.980632i	−0.0353166	+	0.0611702i	0.847827	+	0.530273i	$0.177911\pi$
$258$	3.29258	−	13.4147i	0.204987	−	0.835164i
$259$	2.82392	−	4.89117i	0.175470	−	0.303923i
$260$	8.93148	−	5.30632i	0.553907	−	0.329084i
$261$	0.877872	+	20.7783i	0.0543389	+	1.28614i
$262$	4.54154	+	7.86618i	0.280577	+	0.485974i
$263$	11.3194			0.697987			0.348993	−	0.937125i	$-0.386524\pi$
$263$	11.3194			0.697987			0.348993	+	0.937125i	$0.386524\pi$
$264$	−4.72390	−	4.52853i	−0.290736	−	0.278712i
$265$	−5.46209	−	9.46063i	−0.335534	−	0.581162i
$266$	27.7801			1.70331
$267$	−1.84213	+	7.50527i	−0.112737	+	0.459315i
$268$	3.93397	−	6.81383i	0.240305	−	0.416221i
$269$	−1.92322	+	3.33111i	−0.117261	+	0.203101i	−0.918681	−	0.395000i	$-0.870745\pi$
$269$	−1.92322	+	3.33111i	−0.117261	+	0.203101i	0.801421	+	0.598101i	$0.204078\pi$
$270$	−14.6781	−	2.95191i	−0.893278	−	0.179647i
$271$	−12.0427	−	20.8585i	−0.731541	−	1.26707i	−0.956224	−	0.292634i	$-0.905468\pi$
$271$	−12.0427	−	20.8585i	−0.731541	−	1.26707i	0.224684	−	0.974432i	$-0.427865\pi$
$272$	1.17963	−	2.04317i	0.0715253	−	0.123885i
$273$	−29.0781	−	6.75340i	−1.75988	−	0.408735i
$274$	5.92225	+	10.2576i	0.357776	+	0.619686i
$275$	6.23805	−	10.8046i	0.376168	−	0.651543i
$276$	7.97609	−	2.31872i	0.480104	−	0.139571i
$277$	−4.45259	−	7.71211i	−0.267530	−	0.463376i	0.700693	−	0.713463i	$-0.252874\pi$
$277$	−4.45259	−	7.71211i	−0.267530	−	0.463376i	−0.968223	+	0.250087i	$0.919541\pi$
$278$	14.6543			0.878906
$279$	−2.53944	+	1.61278i	−0.152032	+	0.0965544i
$280$	6.88664	−	11.9280i	0.411556	−	0.712835i
$281$	6.95175	−	12.0408i	0.414707	−	0.718293i	−0.580691	−	0.814124i	$-0.697218\pi$
$281$	6.95175	−	12.0408i	0.414707	−	0.718293i	0.995398	+	0.0958311i	$0.0305509\pi$
$282$	−17.4606	+	5.07597i	−1.03977	+	0.302269i
$283$	8.84688	−	15.3232i	0.525892	−	0.910872i	−0.473653	−	0.880712i	$-0.657065\pi$
$283$	8.84688	−	15.3232i	0.525892	−	0.910872i	0.999545	−	0.0301607i	$-0.00960191\pi$
$284$	−2.34406	+	4.06004i	−0.139095	+	0.240919i
$285$	−20.9369	−	20.0710i	−1.24019	−	1.18890i
$286$	0.170032	+	13.6212i	0.0100542	+	0.805438i
$287$	6.63463			0.391630
$288$	0.126635	+	2.99733i	0.00746206	+	0.176619i
$289$	5.71697	+	9.90208i	0.336292	+	0.582475i
$290$	9.98716	+	17.2983i	0.586466	+	1.01579i
$291$	1.51055	−	6.15434i	0.0885502	−	0.360774i
$292$	−10.6407			−0.622698
$293$	8.48551			0.495729			0.247864	−	0.968795i	$-0.420271\pi$
$293$	8.48551			0.495729			0.247864	+	0.968795i	$0.420271\pi$
$294$	−26.3613	+	7.66349i	−1.53742	+	0.446944i
$295$	1.59228	+	2.75791i	0.0927061	+	0.160572i
$296$	0.590760	+	1.02323i	0.0343372	+	0.0594738i
$297$	12.9753	−	14.7325i	0.752902	−	0.854869i
$298$	−2.93221			−0.169859
$299$	−15.0811	−	8.45788i	−0.872164	−	0.489132i
$300$	−5.49218	+	1.59663i	−0.317091	+	0.0921813i
$301$	−19.0605	+	33.0138i	−1.09863	+	1.90289i
$302$	3.09803	−	5.36595i	0.178272	−	0.308776i
$303$	10.1293	+	9.71040i	0.581914	+	0.557848i
$304$	−2.90578	+	5.03295i	−0.166658	+	0.288660i
$305$	−3.95705	+	6.85382i	−0.226580	+	0.392449i
$306$	6.27343	+	3.27699i	0.358628	+	0.187333i
$307$	27.3530			1.56112			0.780559	−	0.625082i	$-0.214935\pi$
$307$	27.3530			1.56112			0.780559	+	0.625082i	$0.214935\pi$
$308$	9.03002	+	15.6404i	0.514533	+	0.891197i
$309$	−5.47009	+	22.2864i	−0.311182	+	1.26783i
$310$	−1.44466	+	2.50222i	−0.0820510	+	0.142116i
$311$	12.2548	+	21.2259i	0.694903	+	1.20361i	0.970213	+	0.242252i	$0.0778862\pi$
$311$	12.2548	+	21.2259i	0.694903	+	1.20361i	−0.275310	+	0.961356i	$0.588780\pi$
$312$	4.26507	−	4.56171i	0.241462	−	0.258256i
$313$	−6.63578	+	11.4935i	−0.375076	+	0.649651i	−0.990338	−	0.138671i	$-0.955717\pi$
$313$	−6.63578	+	11.4935i	−0.375076	+	0.649651i	0.615262	+	0.788323i	$0.289050\pi$
$314$	−9.25665	−	16.0330i	−0.522383	−	0.904793i
$315$	36.6242	+	19.1310i	2.06354	+	1.07791i
$316$	−3.65213	+	6.32568i	−0.205448	+	0.355847i
$317$	−0.149603	+	0.259121i	−0.00840256	+	0.0145537i	−0.870196	−	0.492706i	$-0.836008\pi$
$317$	−0.149603	+	0.259121i	−0.00840256	+	0.0145537i	0.861794	+	0.507259i	$0.169341\pi$
$318$	−4.74042	−	4.54437i	−0.265829	−	0.254835i
$319$	−26.1911			−1.46642
$320$	1.44068	+	2.49532i	0.0805362	+	0.139493i
$321$	1.09771	−	4.47232i	0.0612682	−	0.249621i
$322$	−22.9239			−1.27750
$323$	6.85546	+	11.8740i	0.381448	+	0.660687i
$324$	−8.96793	+	0.759135i	−0.498218	+	0.0421742i
$325$	10.3846	+	5.82393i	0.576032	+	0.323054i
$326$	4.35185	−	7.53762i	0.241026	−	0.417470i
$327$	3.17560	+	3.04427i	0.175611	+	0.168348i
$328$	−0.693978	+	1.20200i	−0.0383185	+	0.0663696i
$329$	50.1831			2.76668
$330$	4.49455	−	18.3118i	0.247417	−	1.00803i
$331$	−10.5581	−	18.2872i	−0.580328	−	1.00516i	−0.995440	−	0.0953874i	$-0.969591\pi$
$331$	−10.5581	−	18.2872i	−0.580328	−	1.00516i	0.415112	−	0.909770i	$-0.363742\pi$
$332$	6.00937	−	10.4085i	0.329807	−	0.571242i
$333$	−2.99213	+	1.90028i	−0.163968	+	0.104135i
$334$	−8.94428	+	15.4919i	−0.489409	+	0.847681i
$335$	22.6703			1.23861
$336$	1.97358	−	8.04080i	0.107667	−	0.438661i
$337$	−10.2316	−	17.7217i	−0.557351	−	0.965361i	−0.997716	−	0.0675418i	$-0.978484\pi$
$337$	−10.2316	−	17.7217i	−0.557351	−	0.965361i	0.440365	−	0.897819i	$-0.354849\pi$
$338$	−12.9959	+	0.324504i	−0.706886	+	0.0176507i
$339$	3.75876	+	3.60330i	0.204148	+	0.195705i
$340$	6.79783			0.368664
$341$	−1.89429	−	3.28100i	−0.102581	−	0.177676i
$342$	−15.4534	−	8.07221i	−0.835623	−	0.436495i
$343$	42.3034			2.28417
$344$	−3.98744	−	6.90645i	−0.214988	−	0.372371i
$345$	17.2769	+	16.5624i	0.930159	+	0.891690i
$346$	9.18636	+	15.9112i	0.493862	+	0.855394i
$347$	−23.5164			−1.26242			−0.631212	−	0.775610i	$-0.717442\pi$
$347$	−23.5164			−1.26242			−0.631212	+	0.775610i	$0.717442\pi$
$348$	8.66761	+	8.30915i	0.464633	+	0.445417i
$349$	9.29392			0.497492			0.248746	−	0.968569i	$-0.419982\pi$
$349$	9.29392			0.497492			0.248746	+	0.968569i	$0.419982\pi$
$350$	15.7849			0.843740
$351$	14.2130	+	12.2061i	0.758636	+	0.651515i
$352$	−3.77813			−0.201375
$353$	15.1687			0.807351			0.403676	−	0.914902i	$-0.367732\pi$
$353$	15.1687			0.807351			0.403676	+	0.914902i	$0.367732\pi$
$354$	1.38190	+	1.32475i	0.0734472	+	0.0704096i
$355$	−13.5081			−0.716937
$356$	2.23089	+	3.86402i	0.118237	+	0.204793i
$357$	−14.1007	−	13.5175i	−0.746286	−	0.715421i
$358$	−3.28324	−	5.68673i	−0.173524	−	0.300553i
$359$	15.1803			0.801185			0.400592	−	0.916256i	$-0.368804\pi$
$359$	15.1803			0.801185			0.400592	+	0.916256i	$0.368804\pi$
$360$	−7.29686	+	4.63417i	−0.384578	+	0.244242i
$361$	−7.38707	−	12.7948i	−0.388793	−	0.673409i
$362$	−0.608557			−0.0319851
$363$	4.09394	+	3.92462i	0.214876	+	0.205989i
$364$	−14.8173	+	8.80317i	−0.776637	+	0.461411i
$365$	−15.3298	−	26.5519i	−0.802396	−	1.38979i
$366$	−1.13401	+	4.62023i	−0.0592758	+	0.241503i
$367$	−12.3318			−0.643717			−0.321858	−	0.946788i	$-0.604307\pi$
$367$	−12.3318			−0.643717			−0.321858	+	0.946788i	$0.604307\pi$
$368$	2.39782	−	4.15315i	0.124995	−	0.216498i
$369$	−3.69068	−	1.92786i	−0.192129	−	0.100360i
$370$	−1.70219	+	2.94828i	−0.0884925	+	0.153274i
$371$	9.06159	+	15.6951i	0.470454	+	0.814851i
$372$	−0.414010	+	1.68677i	−0.0214654	+	0.0874550i
$373$	23.2521			1.20395			0.601974	−	0.798516i	$-0.294381\pi$
$373$	23.2521			1.20395			0.601974	+	0.798516i	$0.294381\pi$
$374$	−4.45678	+	7.71938i	−0.230455	+	0.399159i
$375$	6.11661	+	5.86364i	0.315860	+	0.302797i
$376$	−5.24912	+	9.09174i	−0.270703	+	0.468871i
$377$	−0.311981	−	24.9927i	−0.0160678	−	1.28719i
$378$	24.3508	+	4.89720i	1.25247	+	0.251885i
$379$	13.8465	+	23.9829i	0.711248	+	1.23192i	0.964389	+	0.264488i	$0.0852030\pi$
$379$	13.8465	+	23.9829i	0.711248	+	1.23192i	−0.253141	+	0.967429i	$0.581464\pi$
$380$	−16.7451			−0.859007
$381$	−0.517154	+	2.10700i	−0.0264946	+	0.107945i
$382$	−5.76077	−	9.97795i	−0.294747	−	0.510517i
$383$	29.5563			1.51025			0.755127	−	0.655578i	$-0.227575\pi$
$383$	29.5563			1.51025			0.755127	+	0.655578i	$0.227575\pi$
$384$	1.25033	+	1.19862i	0.0638055	+	0.0611667i
$385$	−26.0187	+	45.0656i	−1.32603	+	2.29676i
$386$	−8.76136	+	15.1751i	−0.445941	+	0.772393i
$387$	20.1959	−	12.8263i	1.02662	−	0.651995i
$388$	−1.82934	−	3.16850i	−0.0928705	−	0.160856i
$389$	4.56147	−	7.90070i	0.231276	−	0.400582i	−0.726908	−	0.686735i	$-0.759043\pi$
$389$	4.56147	−	7.90070i	0.231276	−	0.400582i	0.958184	+	0.286153i	$0.0923767\pi$
$390$	17.5275	+	4.07078i	0.887540	+	0.206132i
$391$	−5.65706	−	9.79832i	−0.286090	−	0.495522i
$392$	−7.92491	+	13.7263i	−0.400268	+	0.693285i
$393$	−3.75012	+	15.2789i	−0.189169	+	0.770717i
$394$	−4.49370	−	7.78331i	−0.226389	−	0.392118i
$395$	−21.0461			−1.05895
$396$	−0.478445	−	11.3243i	−0.0240428	−	0.569067i
$397$	10.4876	−	18.1651i	0.526358	−	0.911679i	−0.473170	−	0.880971i	$-0.656891\pi$
$397$	10.4876	−	18.1651i	0.526358	−	0.911679i	0.999528	−	0.0307078i	$-0.00977614\pi$
$398$	13.3927	−	23.1968i	0.671315	−	1.16275i
$399$	34.7342	+	33.2977i	1.73888	+	1.66697i
$400$	−1.65109	+	2.85977i	−0.0825546	+	0.142989i
$401$	4.09832	−	7.09850i	0.204660	−	0.354482i	−0.745364	−	0.666658i	$-0.767724\pi$
$401$	4.09832	−	7.09850i	0.204660	−	0.354482i	0.950024	+	0.312175i	$0.101058\pi$
$402$	13.0859	−	3.80420i	0.652666	−	0.189736i
$403$	3.10832	−	1.84670i	0.154836	−	0.0919906i
$404$	8.10134			0.403057
$405$	−14.8142	−	21.2842i	−0.736122	−	1.05762i
$406$	−16.5687	−	28.6978i	−0.822289	−	1.42425i
$407$	−2.23197	−	3.86589i	−0.110635	−	0.191625i
$408$	3.92390	−	1.14071i	0.194262	−	0.0564737i
$409$	−22.2821			−1.10178			−0.550890	−	0.834578i	$-0.685711\pi$
$409$	−22.2821			−1.10178			−0.550890	+	0.834578i	$0.685711\pi$
$410$	−3.99919			−0.197506
$411$	−4.89022	+	19.9239i	−0.241217	+	0.982773i
$412$	6.62448	+	11.4739i	0.326365	+	0.565280i
$413$	−2.64159	−	4.57536i	−0.129984	−	0.225139i
$414$	12.7520	+	6.66112i	0.626726	+	0.327376i
$415$	34.6302			1.69993
$416$	−0.0450041	−	3.60527i	−0.00220651	−	0.176763i
$417$	18.3227	+	17.5649i	0.897265	+	0.860156i
$418$	10.9784	−	19.0152i	0.536972	−	0.930062i
$419$	−14.2408	+	24.6658i	−0.695708	+	1.20500i	0.274233	+	0.961663i	$0.411576\pi$
$419$	−14.2408	+	24.6658i	−0.695708	+	1.20500i	−0.969941	+	0.243339i	$0.921757\pi$
$420$	22.9077	−	6.65947i	1.11778	−	0.324949i
$421$	5.96859	−	10.3379i	0.290891	−	0.503839i	−0.683129	−	0.730297i	$-0.739382\pi$
$421$	5.96859	−	10.3379i	0.290891	−	0.503839i	0.974021	+	0.226459i	$0.0727149\pi$
$422$	−5.81398	+	10.0701i	−0.283020	+	0.490205i
$423$	−27.9156	−	14.5820i	−1.35730	−	0.709000i
$424$	−3.79134			−0.184124
$425$	3.89534	+	6.74693i	0.188952	+	0.327274i
$426$	−7.79727	+	2.26674i	−0.377779	+	0.109824i
$427$	6.56473	−	11.3705i	0.317690	−	0.550255i
$428$	−1.32937	−	2.30253i	−0.0642574	−	0.111297i
$429$	−16.1140	+	17.2347i	−0.777991	+	0.832101i
$430$	11.4892	−	19.8999i	0.554059	−	0.959658i
$431$	−2.23690	−	3.87443i	−0.107748	−	0.186625i	0.807110	−	0.590401i	$-0.201031\pi$
$431$	−2.23690	−	3.87443i	−0.107748	−	0.186625i	−0.914858	+	0.403777i	$0.867697\pi$
$432$	−3.43431	+	3.89943i	−0.165233	+	0.187611i
$433$	5.29421	−	9.16984i	0.254424	−	0.440674i	−0.710315	−	0.703884i	$-0.751448\pi$
$433$	5.29421	−	9.16984i	0.254424	−	0.440674i	0.964739	+	0.263209i	$0.0847810\pi$
$434$	2.39668	−	4.15117i	0.115044	−	0.199262i
$435$	−8.24678	+	33.5993i	−0.395403	+	1.61096i
$436$	2.53982			0.121635
$437$	13.9351	+	24.1362i	0.666604	+	1.15459i
$438$	−13.3043	−	12.7541i	−0.635705	−	0.609414i
$439$	−0.183907			−0.00877739			−0.00438869	−	0.999990i	$-0.501397\pi$
$439$	−0.183907			−0.00877739			−0.00438869	+	0.999990i	$0.501397\pi$
$440$	−5.44306	−	9.42766i	−0.259488	−	0.449446i
$441$	−42.1459	−	22.0153i	−2.00695	−	1.04835i
$442$	−7.41928	−	4.16092i	−0.352899	−	0.197915i
$443$	5.46285	−	9.46193i	0.259548	−	0.449550i	−0.706573	−	0.707640i	$-0.749760\pi$
$443$	5.46285	−	9.46193i	0.259548	−	0.449550i	0.966121	+	0.258090i	$0.0830932\pi$
$444$	−0.487813	+	1.98746i	−0.0231506	+	0.0943208i
$445$	−6.42798	+	11.1336i	−0.304716	+	0.527783i
$446$	13.4250			0.635692
$447$	−3.66623	−	3.51460i	−0.173407	−	0.166235i
$448$	−2.39007	−	4.13973i	−0.112920	−	0.195584i
$449$	−13.8839	+	24.0476i	−0.655222	+	1.13488i	0.326617	+	0.945157i	$0.394091\pi$
$449$	−13.8839	+	24.0476i	−0.655222	+	1.13488i	−0.981838	+	0.189720i	$0.939242\pi$
$450$	−8.78076	−	4.58671i	−0.413929	−	0.216220i
$451$	2.62194	−	4.54133i	0.123462	−	0.213843i
$452$	3.00622			0.141401
$453$	10.3053	−	2.99584i	0.484184	−	0.140757i
$454$	−1.09211	−	1.89158i	−0.0512551	−	0.0887764i
$455$	−43.3136	−	24.2914i	−2.03057	−	1.13880i
$456$	−9.66575	+	2.80992i	−0.452640	+	0.131587i
$457$	−20.8576			−0.975675			−0.487838	−	0.872934i	$-0.662214\pi$
$457$	−20.8576			−0.975675			−0.487838	+	0.872934i	$0.662214\pi$
$458$	−9.58555	−	16.6027i	−0.447903	−	0.775792i
$459$	3.91599	+	11.6167i	0.182783	+	0.542223i
$460$	13.8179			0.644264
$461$	2.03096	+	3.51772i	0.0945911	+	0.163837i	0.909438	−	0.415840i	$-0.136512\pi$
$461$	2.03096	+	3.51772i	0.0945911	+	0.163837i	−0.814847	+	0.579676i	$0.803179\pi$
$462$	−7.45643	+	30.3792i	−0.346905	+	1.41337i
$463$	−6.80110	−	11.7799i	−0.316074	−	0.547456i	0.663591	−	0.748095i	$-0.269032\pi$
$463$	−6.80110	−	11.7799i	−0.316074	−	0.547456i	−0.979665	+	0.200639i	$0.935698\pi$
$464$	6.93228			0.321823
$465$	−4.80549	+	1.39700i	−0.222849	+	0.0647844i
$466$	−3.59859			−0.166701
$467$	−24.3640			−1.12743			−0.563716	−	0.825968i	$-0.690629\pi$
$467$	−24.3640			−1.12743			−0.563716	+	0.825968i	$0.690629\pi$
$468$	10.8005	−	0.591447i	0.499252	−	0.0273396i
$469$	−37.6099			−1.73666
$470$	−30.2491			−1.39529
$471$	7.64357	−	31.1416i	0.352197	−	1.43493i
$472$	1.10523			0.0508724
$473$	15.0651	+	26.0935i	0.692693	+	1.19978i
$474$	−12.1484	+	3.53166i	−0.557995	+	0.162214i
$475$	−9.59541	−	16.6197i	−0.440267	−	0.762566i
$476$	−11.2776			−0.516907
$477$	−0.480118	−	11.3639i	−0.0219831	−	0.520317i
$478$	−1.63290	−	2.82827i	−0.0746872	−	0.129362i
$479$	−14.1172			−0.645030			−0.322515	−	0.946564i	$-0.604528\pi$
$479$	−14.1172			−0.645030			−0.322515	+	0.946564i	$0.604528\pi$
$480$	−1.18962	+	4.84679i	−0.0542985	+	0.221225i
$481$	3.66242	−	2.17590i	0.166992	−	0.0992125i
$482$	−10.8271	−	18.7531i	−0.493161	−	0.854180i
$483$	−28.6623	−	27.4769i	−1.30418	−	1.25024i
$484$	3.27429			0.148831
$485$	5.27096	−	9.12957i	0.239342	−	0.414552i
$486$	−12.1228	−	9.79994i	−0.549899	−	0.444534i
$487$	−5.30269	+	9.18453i	−0.240288	+	0.416191i	−0.960796	−	0.277256i	$-0.910575\pi$
$487$	−5.30269	+	9.18453i	−0.240288	+	0.416191i	0.720508	+	0.693446i	$0.243908\pi$
$488$	1.37333	+	2.37868i	0.0621679	+	0.107678i
$489$	14.4759	−	4.20829i	0.654625	−	0.190306i
$490$	−45.6689			−2.06311
$491$	−1.19842	+	2.07572i	−0.0540838	+	0.0936759i	−0.891800	−	0.452430i	$-0.850557\pi$
$491$	−1.19842	+	2.07572i	−0.0540838	+	0.0936759i	0.837716	+	0.546106i	$0.183890\pi$
$492$	−2.30844	+	0.671086i	−0.104073	+	0.0302549i
$493$	8.17749	−	14.1638i	0.368296	−	0.637907i
$494$	18.2759	+	10.2496i	0.822273	+	0.461151i
$495$	27.5685	−	17.5085i	1.23911	−	0.786949i
$496$	0.501382	+	0.868419i	0.0225127	+	0.0389931i
$497$	22.4099			1.00522
$498$	19.9895	−	5.81114i	0.895752	−	0.260403i
$499$	−8.30677	−	14.3877i	−0.371862	−	0.644084i	0.617990	−	0.786186i	$-0.287947\pi$
$499$	−8.30677	−	14.3877i	−0.371862	−	0.644084i	−0.989852	+	0.142102i	$0.954614\pi$
$500$	4.89200			0.218777
$501$	−29.7522	+	8.64923i	−1.32923	+	0.386419i
$502$	−12.8310	+	22.2240i	−0.572677	+	0.991905i
$503$	15.1027	−	26.1586i	0.673396	−	1.16636i	−0.303539	−	0.952819i	$-0.598168\pi$
$503$	15.1027	−	26.1586i	0.673396	−	1.16636i	0.976935	−	0.213537i	$-0.0684983\pi$
$504$	12.1055	−	7.68807i	0.539220	−	0.342454i
$505$	11.6714	+	20.2155i	0.519370	+	0.899576i
$506$	−9.05929	+	15.6911i	−0.402734	+	0.697557i
$507$	−16.6381	−	15.1714i	−0.738926	−	0.673787i
$508$	0.626292	+	1.08477i	0.0277872	+	0.0481289i
$509$	19.9507	−	34.5556i	0.884299	−	1.53165i	0.0377833	−	0.999286i	$-0.487970\pi$
$509$	19.9507	−	34.5556i	0.884299	−	1.53165i	0.846515	−	0.532364i	$-0.178696\pi$
$510$	8.49951	+	8.14800i	0.376365	+	0.360799i
$511$	25.4320	+	44.0495i	1.12505	+	1.94864i
$512$	1.00000			0.0441942
$513$	−9.64628	−	28.6156i	−0.425894	−	1.26341i
$514$	−0.566168	+	0.980632i	−0.0249726	+	0.0432538i
$515$	−19.0875	+	33.0604i	−0.841094	+	1.45682i
$516$	3.29258	−	13.4147i	0.144948	−	0.590550i
$517$	19.8319	−	34.3498i	0.872205	−	1.51070i
$518$	2.82392	−	4.89117i	0.124076	−	0.214906i
$519$	−7.58553	+	30.9052i	−0.332968	+	1.35659i
$520$	8.93148	−	5.30632i	0.391671	−	0.232698i
$521$	−19.8064			−0.867735			−0.433867	−	0.900977i	$-0.642851\pi$
$521$	−19.8064			−0.867735			−0.433867	+	0.900977i	$0.642851\pi$
$522$	0.877872	+	20.7783i	0.0384234	+	0.909441i
$523$	−0.0254495	−	0.0440799i	−0.00111283	−	0.00192748i	0.865468	−	0.500963i	$-0.167021\pi$
$523$	−0.0254495	−	0.0440799i	−0.00111283	−	0.00192748i	−0.866581	+	0.499036i	$0.833688\pi$
$524$	4.54154	+	7.86618i	0.198398	+	0.343636i
$525$	19.7363	+	18.9201i	0.861364	+	0.825740i
$526$	11.3194			0.493551
$527$	2.36577			0.103055
$528$	−4.72390	−	4.52853i	−0.205581	−	0.197079i
$529$	0.000907866		0.00157247i	3.94724e−5		6.83682e-5i
$530$	−5.46209	−	9.46063i	−0.237258	−	0.410943i
$531$	0.139961	+	3.31274i	0.00607381	+	0.143761i
$532$	27.7801			1.20442
$533$	4.36478	+	2.44788i	0.189060	+	0.106030i
$534$	−1.84213	+	7.50527i	−0.0797169	+	0.324785i
$535$	3.83037	−	6.63440i	0.165602	−	0.286830i
$536$	3.93397	−	6.81383i	0.169921	−	0.294313i
$537$	2.71109	−	11.0456i	0.116992	−	0.476654i
$538$	−1.92322	+	3.33111i	−0.0829158	+	0.143614i
$539$	29.9413	−	51.8599i	1.28967	−	2.23377i
$540$	−14.6781	−	2.95191i	−0.631643	−	0.127030i
$541$	27.5053			1.18255			0.591273	−	0.806472i	$-0.298626\pi$
$541$	27.5053			1.18255			0.591273	+	0.806472i	$0.298626\pi$
$542$	−12.0427	−	20.8585i	−0.517278	−	0.895951i
$543$	−0.760896	−	0.729427i	−0.0326532	−	0.0313027i
$544$	1.17963	−	2.04317i	0.0505760	−	0.0876003i
$545$	3.65905	+	6.33766i	0.156737	+	0.271476i
$546$	−29.0781	−	6.75340i	−1.24443	−	0.289019i
$547$	−14.2255	+	24.6393i	−0.608238	+	1.05350i	0.383293	+	0.923627i	$0.374790\pi$
$547$	−14.2255	+	24.6393i	−0.608238	+	1.05350i	−0.991531	+	0.129872i	$0.958543\pi$
$548$	5.92225	+	10.2576i	0.252986	+	0.438184i
$549$	−6.95577	+	4.41755i	−0.296865	+	0.188537i
$550$	6.23805	−	10.8046i	0.265991	−	0.460710i
$551$	−20.1436	+	34.8898i	−0.858148	+	1.48636i
$552$	7.97609	−	2.31872i	0.339485	−	0.0986915i
$553$	34.9154			1.48476
$554$	−4.45259	−	7.71211i	−0.189172	−	0.327656i
$555$	−5.66214	+	1.64604i	−0.240345	+	0.0698704i
$556$	14.6543			0.621481
$557$	−5.98629	−	10.3686i	−0.253647	−	0.439330i	0.710880	−	0.703313i	$-0.248297\pi$
$557$	−5.98629	−	10.3686i	−0.253647	−	0.439330i	−0.964527	+	0.263983i	$0.914964\pi$
$558$	−2.53944	+	1.61278i	−0.107503	+	0.0682743i
$559$	−24.7202	+	14.6866i	−1.04555	+	0.621178i
$560$	6.88664	−	11.9280i	0.291014	−	0.504051i
$561$	−14.8250	+	4.30977i	−0.625912	+	0.181959i
$562$	6.95175	−	12.0408i	0.293242	−	0.507910i
$563$	−8.94023			−0.376786			−0.188393	−	0.982094i	$-0.560328\pi$
$563$	−8.94023			−0.376786			−0.188393	+	0.982094i	$0.560328\pi$
$564$	−17.4606	+	5.07597i	−0.735225	+	0.213737i
$565$	4.33099	+	7.50149i	0.182206	+	0.315590i
$566$	8.84688	−	15.3232i	0.371862	−	0.644084i
$567$	24.5766	+	35.3104i	1.03212	+	1.48290i
$568$	−2.34406	+	4.06004i	−0.0983547	+	0.170355i
$569$	−22.0591			−0.924768			−0.462384	−	0.886680i	$-0.653006\pi$
$569$	−22.0591			−0.924768			−0.462384	+	0.886680i	$0.653006\pi$
$570$	−20.9369	−	20.0710i	−0.876949	−	0.840681i
$571$	0.326310	+	0.565185i	0.0136556	+	0.0236523i	0.872772	−	0.488127i	$-0.162320\pi$
$571$	0.326310	+	0.565185i	0.0136556	+	0.0236523i	−0.859117	+	0.511780i	$0.828986\pi$
$572$	0.170032	+	13.6212i	0.00710938	+	0.569531i
$573$	4.75689	−	19.3807i	0.198722	−	0.809639i
$574$	6.63463			0.276924
$575$	7.91805	+	13.7145i	0.330205	+	0.571932i
$576$	0.126635	+	2.99733i	0.00527647	+	0.124889i
$577$	−18.8841			−0.786156			−0.393078	−	0.919505i	$-0.628590\pi$
$577$	−18.8841			−0.786156			−0.393078	+	0.919505i	$0.628590\pi$
$578$	5.71697	+	9.90208i	0.237794	+	0.411872i
$579$	−29.1437	+	8.47235i	−1.21117	+	0.352099i
$580$	9.98716	+	17.2983i	0.414694	+	0.718272i
$581$	−57.4513			−2.38348
$582$	1.51055	−	6.15434i	0.0626144	−	0.255106i
$583$	14.3242			0.593248
$584$	−10.6407			−0.440314
$585$	17.0358	+	26.0986i	0.704345	+	1.07904i
$586$	8.48551			0.350533
$587$	26.1046			1.07745			0.538726	−	0.842481i	$-0.318906\pi$
$587$	26.1046			1.07745			0.538726	+	0.842481i	$0.318906\pi$
$588$	−26.3613	+	7.66349i	−1.08712	+	0.316037i
$589$	−5.82761			−0.240123
$590$	1.59228	+	2.75791i	0.0655531	+	0.113541i
$591$	3.71062	−	15.1179i	0.152634	−	0.621868i
$592$	0.590760	+	1.02323i	0.0242801	+	0.0420544i
$593$	25.3817			1.04230			0.521150	−	0.853465i	$-0.325503\pi$
$593$	25.3817			1.04230			0.521150	+	0.853465i	$0.325503\pi$
$594$	12.9753	−	14.7325i	0.532382	−	0.604484i
$595$	−16.2473	−	28.1412i	−0.666075	−	1.15368i
$596$	−2.93221			−0.120108
$597$	44.5494	−	12.9509i	1.82328	−	0.530046i
$598$	−15.0811	−	8.45788i	−0.616713	−	0.345869i
$599$	2.74141	+	4.74826i	0.112011	+	0.194009i	0.916581	−	0.399849i	$-0.130938\pi$
$599$	2.74141	+	4.74826i	0.112011	+	0.194009i	−0.804570	+	0.593858i	$0.797604\pi$
$600$	−5.49218	+	1.59663i	−0.224217	+	0.0651820i
$601$	18.8262			0.767935			0.383967	−	0.923347i	$-0.374557\pi$
$601$	18.8262			0.767935			0.383967	+	0.923347i	$0.374557\pi$
$602$	−19.0605	+	33.0138i	−0.776850	+	1.34554i
$603$	20.9215	+	10.9285i	0.851987	+	0.445043i
$604$	3.09803	−	5.36595i	0.126057	−	0.218337i
$605$	4.71719	+	8.17042i	0.191781	+	0.332175i
$606$	10.1293	+	9.71040i	0.411476	+	0.394458i
$607$	−37.1042			−1.50601			−0.753007	−	0.658012i	$-0.771398\pi$
$607$	−37.1042			−1.50601			−0.753007	+	0.658012i	$0.771398\pi$
$608$	−2.90578	+	5.03295i	−0.117845	+	0.204113i
$609$	13.6814	−	55.7410i	0.554397	−	2.25874i
$610$	−3.95705	+	6.85382i	−0.160216	+	0.277503i
$611$	33.0144	+	18.5153i	1.33562	+	0.749050i
$612$	6.27343	+	3.27699i	0.253589	+	0.132464i
$613$	−17.9074	−	31.0165i	−0.723272	−	1.25274i	−0.959681	−	0.281090i	$-0.909304\pi$
$613$	−17.9074	−	31.0165i	−0.723272	−	1.25274i	0.236409	−	0.971654i	$-0.424029\pi$
$614$	27.3530			1.10388
$615$	−5.00029	−	4.79349i	−0.201631	−	0.193292i
$616$	9.03002	+	15.6404i	0.363830	+	0.630172i
$617$	−41.7347			−1.68018			−0.840089	−	0.542449i	$-0.817497\pi$
$617$	−41.7347			−1.68018			−0.840089	+	0.542449i	$0.817497\pi$
$618$	−5.47009	+	22.2864i	−0.220039	+	0.896490i
$619$	1.82631	−	3.16326i	0.0734055	−	0.127142i	−0.826986	−	0.562222i	$-0.809947\pi$
$619$	1.82631	−	3.16326i	0.0734055	−	0.127142i	0.900392	+	0.435080i	$0.143280\pi$
$620$	−1.44466	+	2.50222i	−0.0580188	+	0.100492i
$621$	7.96003	+	23.6133i	0.319425	+	0.947570i
$622$	12.2548	+	21.2259i	0.491371	+	0.851079i
$623$	10.6640	−	18.4706i	0.427244	−	0.740008i
$624$	4.26507	−	4.56171i	0.170739	−	0.182615i
$625$	15.3033	+	26.5060i	0.612130	+	1.06024i
$626$	−6.63578	+	11.4935i	−0.265219	+	0.459373i
$627$	36.5185	−	10.6163i	1.45841	−	0.423973i
$628$	−9.25665	−	16.0330i	−0.369380	−	0.639786i
$629$	2.78750			0.111145
$630$	36.6242	+	19.1310i	1.45914	+	0.762197i
$631$	−19.6832	+	34.0922i	−0.783574	+	1.35719i	0.146273	+	0.989244i	$0.453272\pi$
$631$	−19.6832	+	34.0922i	−0.783574	+	1.35719i	−0.929847	+	0.367946i	$0.880061\pi$
$632$	−3.65213	+	6.32568i	−0.145274	+	0.251622i
$633$	−19.3396	+	5.62219i	−0.768679	+	0.223462i
$634$	−0.149603	+	0.259121i	−0.00594151	+	0.0102910i
$635$	−1.80457	+	3.12560i	−0.0716121	+	0.124036i
$636$	−4.74042	−	4.54437i	−0.187970	−	0.180196i
$637$	49.8438	+	27.9537i	1.97488	+	1.10757i
$638$	−26.1911			−1.03691
$639$	−12.4661	−	6.51178i	−0.493151	−	0.257602i
$640$	1.44068	+	2.49532i	0.0569477	+	0.0986363i
$641$	−20.2048	−	34.9958i	−0.798043	−	1.38225i	−0.920889	−	0.389825i	$-0.872536\pi$
$641$	−20.2048	−	34.9958i	−0.798043	−	1.38225i	0.122847	−	0.992426i	$-0.460798\pi$
$642$	1.09771	−	4.47232i	0.0433231	−	0.176508i
$643$	27.5359			1.08591			0.542955	−	0.839762i	$-0.317306\pi$
$643$	27.5359			1.08591			0.542955	+	0.839762i	$0.317306\pi$
$644$	−22.9239			−0.903327
$645$	38.2176	−	11.1102i	1.50482	−	0.437464i
$646$	6.85546	+	11.8740i	0.269724	+	0.467176i
$647$	−4.10212	−	7.10508i	−0.161271	−	0.279330i	0.774054	−	0.633120i	$-0.218226\pi$
$647$	−4.10212	−	7.10508i	−0.161271	−	0.279330i	−0.935325	+	0.353790i	$0.884893\pi$
$648$	−8.96793	+	0.759135i	−0.352293	+	0.0298216i
$649$	−4.17571			−0.163911
$650$	10.3846	+	5.82393i	0.407316	+	0.228433i
$651$	7.97229	−	2.31762i	0.312459	−	0.0908347i
$652$	4.35185	−	7.53762i	0.170431	−	0.295196i
$653$	6.96356	−	12.0612i	0.272505	−	0.471993i	−0.696997	−	0.717074i	$-0.745481\pi$
$653$	6.96356	−	12.0612i	0.272505	−	0.471993i	0.969503	+	0.245081i	$0.0788144\pi$
$654$	3.17560	+	3.04427i	0.124176	+	0.119040i
$655$	−13.0858	+	22.6652i	−0.511303	+	0.885603i
$656$	−0.693978	+	1.20200i	−0.0270953	+	0.0469304i
$657$	−1.34749	−	31.8936i	−0.0525704	−	1.24429i
$658$	50.1831			1.95634
$659$	−19.3822	−	33.5710i	−0.755025	−	1.30774i	−0.945362	−	0.326023i	$-0.894291\pi$
$659$	−19.3822	−	33.5710i	−0.755025	−	1.30774i	0.190337	−	0.981719i	$-0.439042\pi$
$660$	4.49455	−	18.3118i	0.174950	−	0.712786i
$661$	2.44512	−	4.23507i	0.0951040	−	0.164725i	−0.814548	−	0.580096i	$-0.803015\pi$
$661$	2.44512	−	4.23507i	0.0951040	−	0.164725i	0.909652	+	0.415371i	$0.136348\pi$
$662$	−10.5581	−	18.2872i	−0.410354	−	0.710754i
$663$	−4.28917	−	14.0954i	−0.166578	−	0.547419i
$664$	6.00937	−	10.4085i	0.233209	−	0.403929i
$665$	40.0221	+	69.3203i	1.55199	+	2.68812i
$666$	−2.99213	+	1.90028i	−0.115943	+	0.0736343i
$667$	16.6224	−	28.7908i	0.643620	−	1.11478i
$668$	−8.94428	+	15.4919i	−0.346064	+	0.599401i
$669$	16.7856	+	16.0914i	0.648970	+	0.622130i
$670$	22.6703			0.875829
$671$	−5.18864	−	8.98698i	−0.200305	−	0.346939i
$672$	1.97358	−	8.04080i	0.0761323	−	0.310181i
$673$	−26.5143			−1.02205			−0.511026	−	0.859565i	$-0.670735\pi$
$673$	−26.5143			−1.02205			−0.511026	+	0.859565i	$0.670735\pi$
$674$	−10.2316	−	17.7217i	−0.394107	−	0.682613i
$675$	−5.48112	−	16.2597i	−0.210968	−	0.625835i
$676$	−12.9959	+	0.324504i	−0.499844	+	0.0124809i
$677$	−19.5453	+	33.8535i	−0.751187	+	1.30109i	0.196060	+	0.980592i	$0.437185\pi$
$677$	−19.5453	+	33.8535i	−0.751187	+	1.30109i	−0.947248	+	0.320503i	$0.896148\pi$
$678$	3.75876	+	3.60330i	0.144354	+	0.138384i
$679$	−8.74450	+	15.1459i	−0.335583	+	0.581247i
$680$	6.79783			0.260685
$681$	0.901794	−	3.67411i	0.0345568	−	0.140792i
$682$	−1.89429	−	3.28100i	−0.0725360	−	0.125636i
$683$	−18.5335	+	32.1009i	−0.709163	+	1.22831i	0.256005	+	0.966676i	$0.417594\pi$
$683$	−18.5335	+	32.1009i	−0.709163	+	1.22831i	−0.965168	+	0.261631i	$0.915740\pi$
$684$	−15.4534	−	8.07221i	−0.590874	−	0.308649i
$685$	−17.0641	+	29.5558i	−0.651985	+	1.12927i
$686$	42.3034			1.61515
$687$	7.91516	−	32.2482i	0.301982	−	1.23034i
$688$	−3.98744	−	6.90645i	−0.152020	−	0.263306i
$689$	0.170626	+	13.6688i	0.00650033	+	0.520740i
$690$	17.2769	+	16.5624i	0.657721	+	0.630520i
$691$	29.6106			1.12644			0.563220	−	0.826307i	$-0.309562\pi$
$691$	29.6106			1.12644			0.563220	+	0.826307i	$0.309562\pi$
$692$	9.18636	+	15.9112i	0.349213	+	0.604855i
$693$	−45.7360	+	29.0465i	−1.73737	+	1.10339i
$694$	−23.5164			−0.892669
$695$	21.1121	+	36.5672i	0.800827	+	1.38707i
$696$	8.66761	+	8.30915i	0.328545	+	0.314957i
$697$	1.63727	+	2.83583i	0.0620160	+	0.107415i
$698$	9.29392			0.351780
$699$	−4.49941	−	4.31333i	−0.170183	−	0.163145i
$700$	15.7849			0.596614
$701$	6.38011			0.240973			0.120487	−	0.992715i	$-0.461555\pi$
$701$	6.38011			0.240973			0.120487	+	0.992715i	$0.461555\pi$
$702$	14.2130	+	12.2061i	0.536437	+	0.460691i
$703$	−6.86647			−0.258974
$704$	−3.77813			−0.142394
$705$	−37.8213	−	36.2571i	−1.42443	−	1.36552i
$706$	15.1687			0.570883
$707$	−19.3628	−	33.5373i	−0.728213	−	1.26130i
$708$	1.38190	+	1.32475i	0.0519350	+	0.0497871i
$709$	−25.0857	−	43.4497i	−0.942114	−	1.63179i	−0.761430	−	0.648247i	$-0.775502\pi$
$709$	−25.0857	−	43.4497i	−0.942114	−	1.63179i	−0.180684	−	0.983541i	$-0.557831\pi$
$710$	−13.5081			−0.506951
$711$	−19.4226	−	10.1456i	−0.728404	−	0.380489i
$712$	2.23089	+	3.86402i	0.0836062	+	0.144810i
$713$	4.80889			0.180095
$714$	−14.1007	−	13.5175i	−0.527704	−	0.505879i
$715$	−33.7443	+	20.0480i	−1.26197	+	0.749753i
$716$	−3.28324	−	5.68673i	−0.122700	−	0.212523i
$717$	1.34835	−	5.49348i	0.0503550	−	0.205158i
$718$	15.1803			0.566523
$719$	17.6035	−	30.4902i	0.656501	−	1.13709i	−0.325015	−	0.945709i	$-0.605369\pi$
$719$	17.6035	−	30.4902i	0.656501	−	1.13709i	0.981515	−	0.191384i	$-0.0612975\pi$
$720$	−7.29686	+	4.63417i	−0.271938	+	0.172705i
$721$	31.6660	−	54.8471i	1.17930	−	2.04261i
$722$	−7.38707	−	12.7948i	−0.274918	−	0.476172i
$723$	8.94036	−	36.4251i	0.332496	−	1.35466i
$724$	−0.608557			−0.0226169
$725$	−11.4458	+	19.8248i	−0.425087	+	0.736273i
$726$	4.09394	+	3.92462i	0.151940	+	0.145656i
$727$	−17.1921	+	29.7775i	−0.637618	+	1.10439i	0.348335	+	0.937370i	$0.386747\pi$
$727$	−17.1921	+	29.7775i	−0.637618	+	1.10439i	−0.985954	+	0.167018i	$0.946586\pi$
$728$	−14.8173	+	8.80317i	−0.549165	+	0.326267i
$729$	−3.41103	−	26.7837i	−0.126334	−	0.991988i
$730$	−15.3298	−	26.5519i	−0.567380	−	0.982731i
$731$	−18.8147			−0.695888
$732$	−1.13401	+	4.62023i	−0.0419143	+	0.170769i
$733$	9.96336	+	17.2570i	0.368005	+	0.637404i	0.989254	−	0.146210i	$-0.0467076\pi$
$733$	9.96336	+	17.2570i	0.368005	+	0.637404i	−0.621248	+	0.783614i	$0.713374\pi$
$734$	−12.3318			−0.455176
$735$	−57.1010	−	54.7395i	−2.10620	−	2.01910i
$736$	2.39782	−	4.15315i	0.0883849	−	0.153087i
$737$	−14.8631	+	25.7436i	−0.547488	+	0.948276i
$738$	−3.69068	−	1.92786i	−0.135856	−	0.0709656i
$739$	21.3790	+	37.0295i	0.786439	+	1.36215i	0.928135	+	0.372243i	$0.121411\pi$
$739$	21.3790	+	37.0295i	0.786439	+	1.36215i	−0.141696	+	0.989910i	$0.545256\pi$
$740$	−1.70219	+	2.94828i	−0.0625737	+	0.108381i
$741$	10.5655	+	34.7212i	0.388135	+	1.27551i
$742$	9.06159	+	15.6951i	0.332661	+	0.576186i
$743$	−20.0243	+	34.6831i	−0.734621	+	1.27240i	0.220269	+	0.975439i	$0.429307\pi$
$743$	−20.0243	+	34.6831i	−0.734621	+	1.27240i	−0.954890	+	0.296961i	$0.904027\pi$
$744$	−0.414010	+	1.68677i	−0.0151783	+	0.0618401i
$745$	−4.22437	−	7.31682i	−0.154769	−	0.268068i
$746$	23.2521			0.851320
$747$	31.9588	+	16.6939i	1.16931	+	0.610800i
$748$	−4.45678	+	7.71938i	−0.162956	+	0.282248i
$749$	−6.35457	+	11.0064i	−0.232191	+	0.402167i
$750$	6.11661	+	5.86364i	0.223347	+	0.214110i
$751$	−5.85785	+	10.1461i	−0.213756	+	0.370236i	−0.952887	−	0.303326i	$-0.901903\pi$
$751$	−5.85785	+	10.1461i	−0.213756	+	0.370236i	0.739131	+	0.673562i	$0.235236\pi$
$752$	−5.24912	+	9.09174i	−0.191416	+	0.331542i
$753$	−42.6810	+	12.4078i	−1.55538	+	0.452164i
$754$	−0.311981	−	24.9927i	−0.0113617	−	0.910182i
$755$	17.8530			0.649739
$756$	24.3508	+	4.89720i	0.885631	+	0.178109i
$757$	−0.283616	−	0.491238i	−0.0103082	−	0.0178543i	0.860825	−	0.508901i	$-0.169948\pi$
$757$	−0.283616	−	0.491238i	−0.0103082	−	0.0178543i	−0.871133	+	0.491046i	$0.836615\pi$
$758$	13.8465	+	23.9829i	0.502928	+	0.871097i
$759$	−30.1347	+	8.76045i	−1.09382	+	0.317984i
$760$	−16.7451			−0.607409
$761$	42.4202			1.53773			0.768866	−	0.639409i	$-0.220821\pi$
$761$	42.4202			1.53773			0.768866	+	0.639409i	$0.220821\pi$
$762$	−0.517154	+	2.10700i	−0.0187345	+	0.0763286i
$763$	−6.07035	−	10.5142i	−0.219761	−	0.380638i
$764$	−5.76077	−	9.97795i	−0.208417	−	0.360990i
$765$	0.860846	+	20.3753i	0.0311239	+	0.736671i
$766$	29.5563			1.06791
$767$	−0.0497400	−	3.98466i	−0.00179601	−	0.143878i
$768$	1.25033	+	1.19862i	0.0451173	+	0.0432514i
$769$	−6.78331	+	11.7490i	−0.244612	+	0.423681i	−0.962023	−	0.272970i	$-0.911994\pi$
$769$	−6.78331	+	11.7490i	−0.244612	+	0.423681i	0.717410	+	0.696651i	$0.245327\pi$
$770$	−26.0187	+	45.0656i	−0.937647	+	1.62405i
$771$	−1.88330	+	0.547492i	−0.0678253	+	0.0197174i
$772$	−8.76136	+	15.1751i	−0.315328	+	0.546164i
$773$	−26.4595	+	45.8292i	−0.951682	+	1.64836i	−0.209898	+	0.977723i	$0.567313\pi$
$773$	−26.4595	+	45.8292i	−0.951682	+	1.64836i	−0.741784	+	0.670638i	$0.766020\pi$
$774$	20.1959	−	12.8263i	0.725927	−	0.461030i
$775$	−3.31131			−0.118946
$776$	−1.82934	−	3.16850i	−0.0656693	−	0.113743i
$777$	9.39347	−	2.73077i	0.336989	−	0.0979658i
$778$	4.56147	−	7.90070i	0.163537	−	0.283254i
$779$	−4.03309	−	6.98551i	−0.144500	−	0.250282i
$780$	17.5275	+	4.07078i	0.627586	+	0.145757i
$781$	8.85618	−	15.3394i	0.316899	−	0.548885i
$782$	−5.65706	−	9.79832i	−0.202296	−	0.350387i
$783$	−23.8076	+	27.0319i	−0.850814	+	0.966041i
$784$	−7.92491	+	13.7263i	−0.283032	+	0.490226i
$785$	26.6716	−	46.1966i	0.951952	−	1.64883i
$786$	−3.75012	+	15.2789i	−0.133762	+	0.544979i
$787$	32.9136			1.17324			0.586622	−	0.809861i	$-0.300458\pi$
$787$	32.9136			1.17324			0.586622	+	0.809861i	$0.300458\pi$
$788$	−4.49370	−	7.78331i	−0.160081	−	0.277269i
$789$	14.1530	+	13.5677i	0.503861	+	0.483022i
$790$	−21.0461			−0.748788
$791$	−7.18508	−	12.4449i	−0.255472	−	0.442491i
$792$	−0.478445	−	11.3243i	−0.0170008	−	0.402391i
$793$	8.51399	−	5.05829i	0.302341	−	0.179625i
$794$	10.4876	−	18.1651i	0.372191	−	0.644654i
$795$	4.51026	−	18.3758i	0.159962	−	0.651724i
$796$	13.3927	−	23.1968i	0.474692	−	0.822190i
$797$	35.2580			1.24890			0.624451	−	0.781064i	$-0.285323\pi$
$797$	35.2580			1.24890			0.624451	+	0.781064i	$0.285323\pi$
$798$	34.7342	+	33.2977i	1.22958	+	1.17872i
$799$	12.3840	+	21.4497i	0.438114	+	0.758836i
$800$	−1.65109	+	2.85977i	−0.0583749	+	0.101108i
$801$	−11.2992	+	7.17603i	−0.399238	+	0.253553i
$802$	4.09832	−	7.09850i	0.144717	−	0.250657i
$803$	40.2019			1.41869
$804$	13.0859	−	3.80420i	0.461505	−	0.134164i
$805$	−33.0259	−	57.2025i	−1.16401	−	2.01612i
$806$	3.10832	−	1.84670i	0.109486	−	0.0650472i
$807$	−6.39737	+	1.85978i	−0.225198	+	0.0654672i
$808$	8.10134			0.285004
$809$	−6.67685	−	11.5646i	−0.234746	−	0.406591i	0.724453	−	0.689324i	$-0.242092\pi$
$809$	−6.67685	−	11.5646i	−0.234746	−	0.406591i	−0.959199	+	0.282733i	$0.908759\pi$
$810$	−14.8142	−	21.2842i	−0.520517	−	0.747851i
$811$	−18.2295			−0.640124			−0.320062	−	0.947397i	$-0.603704\pi$
$811$	−18.2295			−0.640124			−0.320062	+	0.947397i	$0.603704\pi$
$812$	−16.5687	−	28.6978i	−0.581446	−	1.00709i
$813$	9.94410	−	40.5146i	0.348755	−	1.42091i
$814$	−2.23197	−	3.86589i	−0.0782305	−	0.135499i
$815$	25.0784			0.878458
$816$	3.92390	−	1.14071i	0.137364	−	0.0399330i
$817$	46.3464			1.62146
$818$	−22.2821			−0.779075
$819$	−28.2624	−	43.2974i	−0.987567	−	1.51293i
$820$	−3.99919			−0.139658
$821$	−34.7480			−1.21271			−0.606357	−	0.795192i	$-0.707370\pi$
$821$	−34.7480			−1.21271			−0.606357	+	0.795192i	$0.707370\pi$
$822$	−4.89022	+	19.9239i	−0.170566	+	0.694926i
$823$	16.1729			0.563753			0.281877	−	0.959451i	$-0.409043\pi$
$823$	16.1729			0.563753			0.281877	+	0.959451i	$0.409043\pi$
$824$	6.62448	+	11.4739i	0.230775	+	0.399714i
$825$	20.7502	−	6.03227i	0.722429	−	0.210017i
$826$	−2.64159	−	4.57536i	−0.0919125	−	0.159197i
$827$	16.8548			0.586099			0.293049	−	0.956097i	$-0.405330\pi$
$827$	16.8548			0.586099			0.293049	+	0.956097i	$0.405330\pi$
$828$	12.7520	+	6.66112i	0.443162	+	0.231490i
$829$	19.5455	+	33.8538i	0.678843	+	1.17579i	0.975330	+	0.220753i	$0.0708516\pi$
$829$	19.5455	+	33.8538i	0.678843	+	1.17579i	−0.296487	+	0.955037i	$0.595815\pi$
$830$	34.6302			1.20203
$831$	3.67667	−	14.9796i	0.127542	−	0.519637i
$832$	−0.0450041	−	3.60527i	−0.00156024	−	0.124990i
$833$	18.6968	+	32.3839i	0.647807	+	1.12204i
$834$	18.3227	+	17.5649i	0.634462	+	0.608222i
$835$	−51.5432			−1.78373
$836$	10.9784	−	19.0152i	0.379696	−	0.657653i
$837$	−5.10823	−	1.02732i	−0.176566	−	0.0355093i
$838$	−14.2408	+	24.6658i	−0.491940	+	0.852065i
$839$	16.2196	+	28.0931i	0.559962	+	0.969882i	0.997499	+	0.0706819i	$0.0225175\pi$
$839$	16.2196	+	28.0931i	0.559962	+	0.969882i	−0.437537	+	0.899200i	$0.644149\pi$
$840$	22.9077	−	6.65947i	0.790390	−	0.229774i
$841$	19.0565			0.657120
$842$	5.96859	−	10.3379i	0.205691	−	0.356268i
$843$	23.1242	−	6.72243i	0.796441	−	0.231533i
$844$	−5.81398	+	10.0701i	−0.200125	+	0.346627i
$845$	−19.5327	−	31.9616i	−0.671945	−	1.09951i
$846$	−27.9156	−	14.5820i	−0.959759	−	0.501339i
$847$	−7.82580	−	13.5547i	−0.268898	−	0.465744i
$848$	−3.79134			−0.130195
$849$	29.4282	−	8.55505i	1.00997	−	0.293609i
$850$	3.89534	+	6.74693i	0.133609	+	0.231418i
$851$	5.66615			0.194233
$852$	−7.79727	+	2.26674i	−0.267130	+	0.0776572i
$853$	−20.6426	+	35.7540i	−0.706789	+	1.22419i	0.259254	+	0.965809i	$0.416523\pi$
$853$	−20.6426	+	35.7540i	−0.706789	+	1.22419i	−0.966042	+	0.258384i	$0.916810\pi$
$854$	6.56473	−	11.3705i	0.224641	−	0.389089i
$855$	−2.12052	−	50.1906i	−0.0725204	−	1.71648i
$856$	−1.32937	−	2.30253i	−0.0454368	−	0.0786989i
$857$	−14.5384	+	25.1813i	−0.496624	+	0.860178i	−0.999992	−	0.00389422i	$-0.998760\pi$
$857$	−14.5384	+	25.1813i	−0.496624	+	0.860178i	0.503369	+	0.864072i	$0.332094\pi$
$858$	−16.1140	+	17.2347i	−0.550123	+	0.588385i
$859$	22.3386	+	38.6915i	0.762181	+	1.32014i	0.941724	+	0.336387i	$0.109205\pi$
$859$	22.3386	+	38.6915i	0.762181	+	1.32014i	−0.179542	+	0.983750i	$0.557462\pi$
$860$	11.4892	−	19.8999i	0.391779	−	0.678581i
$861$	8.29546	+	7.95238i	0.282709	+	0.271016i
$862$	−2.23690	−	3.87443i	−0.0761892	−	0.131964i
$863$	47.5211			1.61764			0.808819	−	0.588057i	$-0.200107\pi$
$863$	47.5211			1.61764			0.808819	+	0.588057i	$0.200107\pi$
$864$	−3.43431	+	3.89943i	−0.116838	+	0.132661i
$865$	−26.4691	+	45.8459i	−0.899977	+	1.55881i
$866$	5.29421	−	9.16984i	0.179905	−	0.311604i
$867$	−4.72072	+	19.2333i	−0.160324	+	0.653197i
$868$	2.39668	−	4.15117i	0.0813486	−	0.140900i
$869$	13.7982	−	23.8992i	0.468073	−	0.810726i
$870$	−8.24678	+	33.5993i	−0.279592	+	1.13912i
$871$	−24.7427	−	13.8764i	−0.838376	−	0.470183i
$872$	2.53982			0.0860090
$873$	9.26538	−	5.88436i	0.313586	−	0.199155i
$874$	13.9351	+	24.1362i	0.471360	+	0.816420i
$875$	−11.6923	−	20.2516i	−0.395270	−	0.684628i
$876$	−13.3043	−	12.7541i	−0.449511	−	0.430921i
$877$	3.79752			0.128233			0.0641165	−	0.997942i	$-0.479577\pi$
$877$	3.79752			0.128233			0.0641165	+	0.997942i	$0.479577\pi$
$878$	−0.183907			−0.00620655
$879$	10.6097	+	10.1709i	0.357855	+	0.343055i
$880$	−5.44306	−	9.42766i	−0.183486	−	0.317806i
$881$	2.67642	+	4.63569i	0.0901708	+	0.156180i	0.907583	−	0.419873i	$-0.137925\pi$
$881$	2.67642	+	4.63569i	0.0901708	+	0.156180i	−0.817412	+	0.576053i	$0.804592\pi$
$882$	−42.1459	−	22.0153i	−1.41913	−	0.741293i
$883$	−31.8747			−1.07267			−0.536335	−	0.844005i	$-0.680192\pi$
$883$	−31.8747			−1.07267			−0.536335	+	0.844005i	$0.680192\pi$
$884$	−7.41928	−	4.16092i	−0.249537	−	0.139947i
$885$	−1.31481	+	5.35682i	−0.0441967	+	0.180068i
$886$	5.46285	−	9.46193i	0.183528	−	0.317880i
$887$	21.4331	−	37.1232i	0.719653	−	1.24648i	−0.241484	−	0.970405i	$-0.577634\pi$
$887$	21.4331	−	37.1232i	0.719653	−	1.24648i	0.961137	−	0.276071i	$-0.0890326\pi$
$888$	−0.487813	+	1.98746i	−0.0163699	+	0.0666949i
$889$	2.99377	−	5.18536i	0.100408	−	0.173911i
$890$	−6.42798	+	11.1336i	−0.215466	+	0.373199i
$891$	33.8820	−	2.86811i	1.13509	−	0.0960854i
$892$	13.4250			0.449502
$893$	−30.5055	−	52.8371i	−1.02083	−	1.76813i
$894$	−3.66623	−	3.51460i	−0.122617	−	0.117546i
$895$	9.46016	−	16.3855i	0.316218	−	0.547706i
$896$	−2.39007	−	4.13973i	−0.0798468	−	0.138299i
$897$	−8.71859	−	28.6516i	−0.291105	−	0.956650i
$898$	−13.8839	+	24.0476i	−0.463312	+	0.802479i
$899$	3.47572	+	6.02012i	0.115922	+	0.200782i
$900$	−8.78076	−	4.58671i	−0.292692	−	0.152890i
$901$	−4.47237	+	7.74636i	−0.148996	+	0.258069i
$902$	2.62194	−	4.54133i	0.0873011	−	0.151210i
$903$	−63.4029	+	18.4318i	−2.10991	+	0.613372i
$904$	3.00622			0.0999853
$905$	−0.876734	−	1.51855i	−0.0291436	−	0.0504782i
$906$	10.3053	−	2.99584i	0.342370	−	0.0995301i
$907$	−2.16512			−0.0718915			−0.0359457	−	0.999354i	$-0.511444\pi$
$907$	−2.16512			−0.0718915			−0.0359457	+	0.999354i	$0.511444\pi$
$908$	−1.09211	−	1.89158i	−0.0362428	−	0.0627744i
$909$	1.02592	+	24.2824i	0.0340275	+	0.805395i
$910$	−43.3136	−	24.2914i	−1.43583	−	0.805252i
$911$	9.48786	−	16.4335i	0.314347	−	0.544465i	−0.664952	−	0.746887i	$-0.731548\pi$
$911$	9.48786	−	16.4335i	0.314347	−	0.544465i	0.979298	+	0.202422i	$0.0648811\pi$
$912$	−9.66575	+	2.80992i	−0.320065	+	0.0930459i
$913$	−22.7042	+	39.3248i	−0.751399	+	1.30146i
$914$	−20.8576			−0.689907
$915$	−13.1627	+	3.82652i	−0.435146	+	0.126501i
$916$	−9.58555	−	16.6027i	−0.316716	−	0.548567i
$917$	21.7092	−	37.6015i	0.716902	−	1.24171i
$918$	3.91599	+	11.6167i	0.129247	+	0.383410i
$919$	1.08251	−	1.87496i	0.0357087	−	0.0618493i	−0.847619	−	0.530606i	$-0.821964\pi$
$919$	1.08251	−	1.87496i	0.0357087	−	0.0618493i	0.883327	+	0.468756i	$0.155298\pi$
$920$	13.8179			0.455564
$921$	34.2002	+	32.7858i	1.12693	+	1.08033i
$922$	2.03096	+	3.51772i	0.0668860	+	0.115850i
$923$	14.7430	+	8.26826i	0.485272	+	0.272153i
$924$	−7.45643	+	30.3792i	−0.245299	+	0.999403i
$925$	−3.90160			−0.128284
$926$	−6.80110	−	11.7799i	−0.223498	−	0.387110i
$927$	−33.5522	+	21.3087i	−1.10200	+	0.699871i
$928$	6.93228			0.227563
$929$	−3.21922	−	5.57585i	−0.105619	−	0.182938i	0.808372	−	0.588672i	$-0.200349\pi$
$929$	−3.21922	−	5.57585i	−0.105619	−	0.182938i	−0.913991	+	0.405734i	$0.867016\pi$
$930$	−4.80549	+	1.39700i	−0.157578	+	0.0458095i
$931$	−46.0560	−	79.7713i	−1.50942	−	2.61440i
$932$	−3.59859			−0.117876
$933$	−10.1192	+	41.2280i	−0.331288	+	1.34974i
$934$	−24.3640			−0.797215
$935$	−25.6831			−0.839928
$936$	10.8005	−	0.591447i	0.353024	−	0.0193320i
$937$	−30.2446			−0.988048			−0.494024	−	0.869448i	$-0.664474\pi$
$937$	−30.2446			−0.988048			−0.494024	+	0.869448i	$0.664474\pi$
$938$	−37.6099			−1.22801
$939$	−22.0732	+	6.41688i	−0.720332	+	0.209407i
$940$	−30.2491			−0.986617
$941$	22.9105	+	39.6821i	0.746860	+	1.29360i	0.949321	+	0.314310i	$0.101773\pi$
$941$	22.9105	+	39.6821i	0.746860	+	1.29360i	−0.202460	+	0.979291i	$0.564894\pi$
$942$	7.64357	−	31.1416i	0.249041	−	1.01465i
$943$	3.32807	+	5.76439i	0.108377	+	0.187714i
$944$	1.10523			0.0359722
$945$	22.8615	+	67.8184i	0.743686	+	2.20613i
$946$	15.0651	+	26.0935i	0.489808	+	0.848372i
$947$	−34.6037			−1.12447			−0.562234	−	0.826978i	$-0.690058\pi$
$947$	−34.6037			−1.12447			−0.562234	+	0.826978i	$0.690058\pi$
$948$	−12.1484	+	3.53166i	−0.394562	+	0.114703i
$949$	0.478874	+	38.3625i	0.0155449	+	1.24530i
$950$	−9.59541	−	16.6197i	−0.311316	−	0.539215i
$951$	−0.497640	+	0.144668i	−0.0161371	+	0.00469120i
$952$	−11.2776			−0.365508
$953$	−20.2595	+	35.0905i	−0.656270	+	1.13669i	0.325303	+	0.945610i	$0.394534\pi$
$953$	−20.2595	+	35.0905i	−0.656270	+	1.13669i	−0.981574	+	0.191084i	$0.938800\pi$
$954$	−0.480118	−	11.3639i	−0.0155444	−	0.367920i
$955$	16.5988	−	28.7500i	0.537125	−	0.930328i
$956$	−1.63290	−	2.82827i	−0.0528118	−	0.0914727i
$957$	−32.7474	−	31.3931i	−1.05857	−	1.01479i
$958$	−14.1172			−0.456105
$959$	28.3092	−	49.0330i	0.914152	−	1.58336i
$960$	−1.18962	+	4.84679i	−0.0383948	+	0.156429i
$961$	14.9972	−	25.9760i	0.483782	−	0.837934i
$962$	3.66242	−	2.17590i	0.118081	−	0.0701538i
$963$	6.73309	−	4.27613i	0.216971	−	0.137796i
$964$	−10.8271	−	18.7531i	−0.348718	−	0.603997i
$965$	−50.4891			−1.62530
$966$	−28.6623	−	27.4769i	−0.922196	−	0.884056i
$967$	−0.985525	−	1.70698i	−0.0316924	−	0.0548928i	0.849744	−	0.527195i	$-0.176756\pi$
$967$	−0.985525	−	1.70698i	−0.0316924	−	0.0548928i	−0.881437	+	0.472302i	$0.843423\pi$
$968$	3.27429			0.105240
$969$	−5.66081	+	23.0634i	−0.181851	+	0.740905i
$970$	5.27096	−	9.12957i	0.169240	−	0.293133i
$971$	−28.1892	+	48.8252i	−0.904635	+	1.56687i	−0.0832293	+	0.996530i	$0.526523\pi$
$971$	−28.1892	+	48.8252i	−0.904635	+	1.56687i	−0.821406	+	0.570344i	$0.806810\pi$
$972$	−12.1228	−	9.79994i	−0.388837	−	0.314333i
$973$	−35.0249	−	60.6648i	−1.12285	−	1.94483i
$974$	−5.30269	+	9.18453i	−0.169909	+	0.294291i
$975$	6.00344	+	19.7289i	0.192264	+	0.631832i
$976$	1.37333	+	2.37868i	0.0439593	+	0.0761398i
$977$	0.714119	−	1.23689i	0.0228467	−	0.0395716i	−0.854376	−	0.519655i	$-0.826060\pi$
$977$	0.714119	−	1.23689i	0.0228467	−	0.0395716i	0.877223	+	0.480084i	$0.159394\pi$
$978$	14.4759	−	4.20829i	0.462890	−	0.134566i
$979$	−8.42861	−	14.5988i	−0.269379	−	0.466579i
$980$	−45.6689			−1.45884
$981$	0.321631	+	7.61266i	0.0102689	+	0.243053i
$982$	−1.19842	+	2.07572i	−0.0382430	+	0.0662389i
$983$	−24.8037	+	42.9613i	−0.791115	+	1.37025i	0.134162	+	0.990959i	$0.457166\pi$
$983$	−24.8037	+	42.9613i	−0.791115	+	1.37025i	−0.925277	+	0.379292i	$0.876168\pi$
$984$	−2.30844	+	0.671086i	−0.0735905	+	0.0213934i
$985$	12.9479	−	22.4265i	0.412555	−	0.714566i
$986$	8.17749	−	14.1638i	0.260424	−	0.451068i
$987$	62.7453	+	60.1503i	1.99721	+	1.91461i
$988$	18.2759	+	10.2496i	0.581435	+	0.326083i
$989$	−38.2447			−1.21611
$990$	27.5685	−	17.5085i	0.876184	−	0.556457i
$991$	1.00008	+	1.73218i	0.0317685	+	0.0550246i	0.881473	−	0.472235i	$-0.156553\pi$
$991$	1.00008	+	1.73218i	0.0317685	+	0.0550246i	−0.849704	+	0.527260i	$0.823219\pi$
$992$	0.501382	+	0.868419i	0.0159189	+	0.0275723i
$993$	8.71826	−	35.5202i	0.276666	−	1.12720i
$994$	22.4099			0.710800
$995$	77.1781			2.44671
$996$	19.9895	−	5.81114i	0.633392	−	0.184133i
$997$	−10.8344	−	18.7657i	−0.343127	−	0.594314i	0.641884	−	0.766802i	$-0.278153\pi$
$997$	−10.8344	−	18.7657i	−0.343127	−	0.594314i	−0.985012	+	0.172487i	$0.944820\pi$
$998$	−8.30677	−	14.3877i	−0.262946	−	0.455436i
$999$	−6.01885	−	1.21045i	−0.190428	−	0.0382970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.f.d.133.5	✓	12
3.2	odd	2		702.2.f.c.289.1		12
9.4	even	3		234.2.g.c.211.3	yes	12
9.5	odd	6		702.2.g.d.523.1		12
13.9	even	3		234.2.g.c.61.3	yes	12
39.35	odd	6		702.2.g.d.451.1		12
117.22	even	3	inner	234.2.f.d.139.5	yes	12
117.113	odd	6		702.2.f.c.685.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.f.d.133.5	✓	12	1.1	even	1	trivial
234.2.f.d.139.5	yes	12	117.22	even	3	inner
234.2.g.c.61.3	yes	12	13.9	even	3
234.2.g.c.211.3	yes	12	9.4	even	3
702.2.f.c.289.1		12	3.2	odd	2
702.2.f.c.685.1		12	117.113	odd	6
702.2.g.d.451.1		12	39.35	odd	6
702.2.g.d.523.1		12	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.25033 + 1.19862i) q^{3} +1.00000 q^{4} +(1.44068 + 2.49532i) q^{5} +(1.25033 + 1.19862i) q^{6} +(-2.39007 - 4.13973i) q^{7} +1.00000 q^{8} +(0.126635 + 2.99733i) q^{9} +(1.44068 + 2.49532i) q^{10} -3.77813 q^{11} +(1.25033 + 1.19862i) q^{12} +(-0.0450041 - 3.60527i) q^{13} +(-2.39007 - 4.13973i) q^{14} +(-1.18962 + 4.84679i) q^{15} +1.00000 q^{16} +(1.17963 - 2.04317i) q^{17} +(0.126635 + 2.99733i) q^{18} +(-2.90578 + 5.03295i) q^{19} +(1.44068 + 2.49532i) q^{20} +(1.97358 - 8.04080i) q^{21} -3.77813 q^{22} +(2.39782 - 4.15315i) q^{23} +(1.25033 + 1.19862i) q^{24} +(-1.65109 + 2.85977i) q^{25} +(-0.0450041 - 3.60527i) q^{26} +(-3.43431 + 3.89943i) q^{27} +(-2.39007 - 4.13973i) q^{28} +6.93228 q^{29} +(-1.18962 + 4.84679i) q^{30} +(0.501382 + 0.868419i) q^{31} +1.00000 q^{32} +(-4.72390 - 4.52853i) q^{33} +(1.17963 - 2.04317i) q^{34} +(6.88664 - 11.9280i) q^{35} +(0.126635 + 2.99733i) q^{36} +(0.590760 + 1.02323i) q^{37} +(-2.90578 + 5.03295i) q^{38} +(4.26507 - 4.56171i) q^{39} +(1.44068 + 2.49532i) q^{40} +(-0.693978 + 1.20200i) q^{41} +(1.97358 - 8.04080i) q^{42} +(-3.98744 - 6.90645i) q^{43} -3.77813 q^{44} +(-7.29686 + 4.63417i) q^{45} +(2.39782 - 4.15315i) q^{46} +(-5.24912 + 9.09174i) q^{47} +(1.25033 + 1.19862i) q^{48} +(-7.92491 + 13.7263i) q^{49} +(-1.65109 + 2.85977i) q^{50} +(3.92390 - 1.14071i) q^{51} +(-0.0450041 - 3.60527i) q^{52} -3.79134 q^{53} +(-3.43431 + 3.89943i) q^{54} +(-5.44306 - 9.42766i) q^{55} +(-2.39007 - 4.13973i) q^{56} +(-9.66575 + 2.80992i) q^{57} +6.93228 q^{58} +1.10523 q^{59} +(-1.18962 + 4.84679i) q^{60} +(1.37333 + 2.37868i) q^{61} +(0.501382 + 0.868419i) q^{62} +(12.1055 - 7.68807i) q^{63} +1.00000 q^{64} +(8.93148 - 5.30632i) q^{65} +(-4.72390 - 4.52853i) q^{66} +(3.93397 - 6.81383i) q^{67} +(1.17963 - 2.04317i) q^{68} +(7.97609 - 2.31872i) q^{69} +(6.88664 - 11.9280i) q^{70} +(-2.34406 + 4.06004i) q^{71} +(0.126635 + 2.99733i) q^{72} -10.6407 q^{73} +(0.590760 + 1.02323i) q^{74} +(-5.49218 + 1.59663i) q^{75} +(-2.90578 + 5.03295i) q^{76} +(9.03002 + 15.6404i) q^{77} +(4.26507 - 4.56171i) q^{78} +(-3.65213 + 6.32568i) q^{79} +(1.44068 + 2.49532i) q^{80} +(-8.96793 + 0.759135i) q^{81} +(-0.693978 + 1.20200i) q^{82} +(6.00937 - 10.4085i) q^{83} +(1.97358 - 8.04080i) q^{84} +6.79783 q^{85} +(-3.98744 - 6.90645i) q^{86} +(8.66761 + 8.30915i) q^{87} -3.77813 q^{88} +(2.23089 + 3.86402i) q^{89} +(-7.29686 + 4.63417i) q^{90} +(-14.8173 + 8.80317i) q^{91} +(2.39782 - 4.15315i) q^{92} +(-0.414010 + 1.68677i) q^{93} +(-5.24912 + 9.09174i) q^{94} -16.7451 q^{95} +(1.25033 + 1.19862i) q^{96} +(-1.82934 - 3.16850i) q^{97} +(-7.92491 + 13.7263i) q^{98} +(-0.478445 - 11.3243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} + q^{5} - 5 q^{7} + 12 q^{8} + 12 q^{9} + q^{10} - 16 q^{11} - q^{13} - 5 q^{14} - 3 q^{15} + 12 q^{16} + 3 q^{17} + 12 q^{18} - 7 q^{19} + q^{20} + 18 q^{21} - 16 q^{22}+ \cdots + 3 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 + q^5 - 5 * q^7 + 12 * q^8 + 12 * q^9 + q^10 - 16 * q^11 - q^13 - 5 * q^14 - 3 * q^15 + 12 * q^16 + 3 * q^17 + 12 * q^18 - 7 * q^19 + q^20 + 18 * q^21 - 16 * q^22 + q^23 - 13 * q^25 - q^26 - 9 * q^27 - 5 * q^28 - 2 * q^29 - 3 * q^30 - 14 * q^31 + 12 * q^32 - 36 * q^33 + 3 * q^34 - 5 * q^35 + 12 * q^36 - 7 * q^37 - 7 * q^38 + q^40 + 9 * q^41 + 18 * q^42 - 8 * q^43 - 16 * q^44 - 27 * q^45 + q^46 - 13 * q^47 - 3 * q^49 - 13 * q^50 - 36 * q^51 - q^52 - 12 * q^53 - 9 * q^54 - 20 * q^55 - 5 * q^56 - 12 * q^57 - 2 * q^58 - 8 * q^59 - 3 * q^60 + 28 * q^61 - 14 * q^62 + 12 * q^63 + 12 * q^64 + 35 * q^65 - 36 * q^66 + 4 * q^67 + 3 * q^68 + 54 * q^69 - 5 * q^70 - 13 * q^71 + 12 * q^72 + 54 * q^73 - 7 * q^74 - 30 * q^75 - 7 * q^76 - 4 * q^77 - 6 * q^79 + q^80 - 12 * q^81 + 9 * q^82 + 30 * q^83 + 18 * q^84 + 18 * q^85 - 8 * q^86 - 6 * q^87 - 16 * q^88 + 3 * q^89 - 27 * q^90 - 12 * q^91 + q^92 + 42 * q^93 - 13 * q^94 + 42 * q^95 - 24 * q^97 - 3 * q^98 + 3 * q^99

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