LMFDB - Embedded newform 234.2.f.d.133.1

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			133.1
Root			$1.34059 + 0.450356i$ of defining polynomial
Character	$\chi$	$=$	234.133
Dual form			234.2.f.d.139.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(-1.66659 - 0.471659i) q^{3} +1.00000 q^{4} +(1.09436 + 1.89549i) q^{5} +(-1.66659 - 0.471659i) q^{6} +(0.790433 + 1.36907i) q^{7} +1.00000 q^{8} +(2.55508 + 1.57213i) q^{9} +(1.09436 + 1.89549i) q^{10} -0.502937 q^{11} +(-1.66659 - 0.471659i) q^{12} +(3.40297 - 1.19155i) q^{13} +(0.790433 + 1.36907i) q^{14} +(-0.929831 - 3.67517i) q^{15} +1.00000 q^{16} +(1.89590 - 3.28380i) q^{17} +(2.55508 + 1.57213i) q^{18} +(-0.516111 + 0.893931i) q^{19} +(1.09436 + 1.89549i) q^{20} +(-0.671597 - 2.65450i) q^{21} -0.502937 q^{22} +(-4.21490 + 7.30043i) q^{23} +(-1.66659 - 0.471659i) q^{24} +(0.104754 - 0.181438i) q^{25} +(3.40297 - 1.19155i) q^{26} +(-3.51677 - 3.82523i) q^{27} +(0.790433 + 1.36907i) q^{28} -5.21474 q^{29} +(-0.929831 - 3.67517i) q^{30} +(-2.50207 - 4.33370i) q^{31} +1.00000 q^{32} +(0.838191 + 0.237215i) q^{33} +(1.89590 - 3.28380i) q^{34} +(-1.73004 + 2.99651i) q^{35} +(2.55508 + 1.57213i) q^{36} +(0.0315070 + 0.0545717i) q^{37} +(-0.516111 + 0.893931i) q^{38} +(-6.23338 + 0.380797i) q^{39} +(1.09436 + 1.89549i) q^{40} +(-2.71729 + 4.70648i) q^{41} +(-0.671597 - 2.65450i) q^{42} +(-4.98693 - 8.63762i) q^{43} -0.502937 q^{44} +(-0.183778 + 6.56359i) q^{45} +(-4.21490 + 7.30043i) q^{46} +(4.15412 - 7.19514i) q^{47} +(-1.66659 - 0.471659i) q^{48} +(2.25043 - 3.89786i) q^{49} +(0.104754 - 0.181438i) q^{50} +(-4.70853 + 4.57854i) q^{51} +(3.40297 - 1.19155i) q^{52} -9.99466 q^{53} +(-3.51677 - 3.82523i) q^{54} +(-0.550393 - 0.953309i) q^{55} +(0.790433 + 1.36907i) q^{56} +(1.28178 - 1.24639i) q^{57} -5.21474 q^{58} +0.601981 q^{59} +(-0.929831 - 3.67517i) q^{60} +(1.43215 + 2.48055i) q^{61} +(-2.50207 - 4.33370i) q^{62} +(-0.132739 + 4.74074i) q^{63} +1.00000 q^{64} +(5.98265 + 5.14629i) q^{65} +(0.838191 + 0.237215i) q^{66} +(2.98971 - 5.17833i) q^{67} +(1.89590 - 3.28380i) q^{68} +(10.4679 - 10.1789i) q^{69} +(-1.73004 + 2.99651i) q^{70} +(-4.15444 + 7.19570i) q^{71} +(2.55508 + 1.57213i) q^{72} +13.8427 q^{73} +(0.0315070 + 0.0545717i) q^{74} +(-0.260159 + 0.252976i) q^{75} +(-0.516111 + 0.893931i) q^{76} +(-0.397537 - 0.688555i) q^{77} +(-6.23338 + 0.380797i) q^{78} +(2.13387 - 3.69598i) q^{79} +(1.09436 + 1.89549i) q^{80} +(4.05682 + 8.03382i) q^{81} +(-2.71729 + 4.70648i) q^{82} +(4.74173 - 8.21292i) q^{83} +(-0.671597 - 2.65450i) q^{84} +8.29919 q^{85} +(-4.98693 - 8.63762i) q^{86} +(8.69086 + 2.45958i) q^{87} -0.502937 q^{88} +(3.21174 + 5.56289i) q^{89} +(-0.183778 + 6.56359i) q^{90} +(4.32114 + 3.71706i) q^{91} +(-4.21490 + 7.30043i) q^{92} +(2.12590 + 8.40265i) q^{93} +(4.15412 - 7.19514i) q^{94} -2.25925 q^{95} +(-1.66659 - 0.471659i) q^{96} +(-3.79321 - 6.57004i) q^{97} +(2.25043 - 3.89786i) q^{98} +(-1.28504 - 0.790681i) 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
$3$	−1.66659	−	0.471659i	−0.962209	−	0.272312i
$3$	−1.66659	−	0.471659i	−0.962209	−	0.272312i
$4$	1.00000			0.500000
$5$	1.09436	+	1.89549i	0.489413	+	0.847687i	0.999926	−	0.0121825i	$-0.00387790\pi$
$5$	1.09436	+	1.89549i	0.489413	+	0.847687i	−0.510513	+	0.859870i	$0.670545\pi$
$6$	−1.66659	−	0.471659i	−0.680384	−	0.192554i
$7$	0.790433	+	1.36907i	0.298755	+	0.517460i	0.975851	−	0.218435i	$-0.0700952\pi$
$7$	0.790433	+	1.36907i	0.298755	+	0.517460i	−0.677096	+	0.735895i	$0.736762\pi$
$8$	1.00000			0.353553
$9$	2.55508	+	1.57213i	0.851692	+	0.524043i
$10$	1.09436	+	1.89549i	0.346067	+	0.599406i
$11$	−0.502937			−0.151641			−0.0758205	−	0.997121i	$-0.524158\pi$
$11$	−0.502937			−0.151641			−0.0758205	+	0.997121i	$0.524158\pi$
$12$	−1.66659	−	0.471659i	−0.481104	−	0.136156i
$13$	3.40297	−	1.19155i	0.943814	−	0.330478i
$13$	3.40297	−	1.19155i	0.943814	−	0.330478i
$14$	0.790433	+	1.36907i	0.211252	+	0.365899i
$15$	−0.929831	−	3.67517i	−0.240081	−	0.948925i
$16$	1.00000			0.250000
$17$	1.89590	−	3.28380i	0.459824	−	0.796438i	−0.539128	−	0.842224i	$-0.681246\pi$
$17$	1.89590	−	3.28380i	0.459824	−	0.796438i	0.998951	+	0.0457862i	$0.0145793\pi$
$18$	2.55508	+	1.57213i	0.602237	+	0.370554i
$19$	−0.516111	+	0.893931i	−0.118404	+	0.205082i	−0.919135	−	0.393942i	$-0.871111\pi$
$19$	−0.516111	+	0.893931i	−0.118404	+	0.205082i	0.800731	+	0.599024i	$0.204444\pi$
$20$	1.09436	+	1.89549i	0.244706	+	0.423844i
$21$	−0.671597	−	2.65450i	−0.146554	−	0.579259i
$22$	−0.502937			−0.107226
$23$	−4.21490	+	7.30043i	−0.878868	+	1.52224i	−0.0262842	+	0.999655i	$0.508367\pi$
$23$	−4.21490	+	7.30043i	−0.878868	+	1.52224i	−0.852584	+	0.522590i	$0.824966\pi$
$24$	−1.66659	−	0.471659i	−0.340192	−	0.0962770i
$25$	0.104754	−	0.181438i	0.0209507	−	0.0362877i
$26$	3.40297	−	1.19155i	0.667377	−	0.233683i
$27$	−3.51677	−	3.82523i	−0.676802	−	0.736165i
$28$	0.790433	+	1.36907i	0.149378	+	0.258730i
$29$	−5.21474			−0.968353			−0.484176	−	0.874970i	$-0.660881\pi$
$29$	−5.21474			−0.968353			−0.484176	+	0.874970i	$0.660881\pi$
$30$	−0.929831	−	3.67517i	−0.169763	−	0.670992i
$31$	−2.50207	−	4.33370i	−0.449384	−	0.778356i	0.548962	−	0.835847i	$-0.315023\pi$
$31$	−2.50207	−	4.33370i	−0.449384	−	0.778356i	−0.998346	+	0.0574911i	$0.981690\pi$
$32$	1.00000			0.176777
$33$	0.838191	+	0.237215i	0.145910	+	0.0412938i
$34$	1.89590	−	3.28380i	0.325144	−	0.563167i
$35$	−1.73004	+	2.99651i	−0.292429	+	0.506502i
$36$	2.55508	+	1.57213i	0.425846	+	0.262021i
$37$	0.0315070	+	0.0545717i	0.00517971	+	0.00897153i	0.868604	−	0.495508i	$-0.165018\pi$
$37$	0.0315070	+	0.0545717i	0.00517971	+	0.00897153i	−0.863424	+	0.504479i	$0.831685\pi$
$38$	−0.516111	+	0.893931i	−0.0837243	+	0.145015i
$39$	−6.23338	+	0.380797i	−0.998139	+	0.0609764i
$40$	1.09436	+	1.89549i	0.173033	+	0.299703i
$41$	−2.71729	+	4.70648i	−0.424369	+	0.735029i	−0.996361	−	0.0852299i	$-0.972838\pi$
$41$	−2.71729	+	4.70648i	−0.424369	+	0.735029i	0.571992	+	0.820259i	$0.306171\pi$
$42$	−0.671597	−	2.65450i	−0.103630	−	0.409598i
$43$	−4.98693	−	8.63762i	−0.760500	−	1.31723i	−0.942593	−	0.333944i	$-0.891620\pi$
$43$	−4.98693	−	8.63762i	−0.760500	−	1.31723i	0.182092	−	0.983281i	$-0.441713\pi$
$44$	−0.502937			−0.0758205
$45$	−0.183778	+	6.56359i	−0.0273960	+	0.978442i
$46$	−4.21490	+	7.30043i	−0.621454	+	1.07639i
$47$	4.15412	−	7.19514i	0.605940	−	1.04952i	−0.385962	−	0.922515i	$-0.626130\pi$
$47$	4.15412	−	7.19514i	0.605940	−	1.04952i	0.991902	−	0.127005i	$-0.0405363\pi$
$48$	−1.66659	−	0.471659i	−0.240552	−	0.0680781i
$49$	2.25043	−	3.89786i	0.321490	−	0.556838i
$50$	0.104754	−	0.181438i	0.0148144	−	0.0256593i
$51$	−4.70853	+	4.57854i	−0.659326	+	0.641124i
$52$	3.40297	−	1.19155i	0.471907	−	0.165239i
$53$	−9.99466			−1.37287			−0.686436	−	0.727190i	$-0.740826\pi$
$53$	−9.99466			−1.37287			−0.686436	+	0.727190i	$0.740826\pi$
$54$	−3.51677	−	3.82523i	−0.478571	−	0.520547i
$55$	−0.550393	−	0.953309i	−0.0742150	−	0.128544i
$56$	0.790433	+	1.36907i	0.105626	+	0.182950i
$57$	1.28178	−	1.24639i	0.169776	−	0.165089i
$58$	−5.21474			−0.684729
$59$	0.601981			0.0783713			0.0391857	−	0.999232i	$-0.487524\pi$
$59$	0.601981			0.0783713			0.0391857	+	0.999232i	$0.487524\pi$
$60$	−0.929831	−	3.67517i	−0.120041	−	0.474463i
$61$	1.43215	+	2.48055i	0.183367	+	0.317602i	0.943025	−	0.332721i	$-0.107967\pi$
$61$	1.43215	+	2.48055i	0.183367	+	0.317602i	−0.759658	+	0.650323i	$0.774634\pi$
$62$	−2.50207	−	4.33370i	−0.317763	−	0.550381i
$63$	−0.132739	+	4.74074i	−0.0167235	+	0.597277i
$64$	1.00000			0.125000
$65$	5.98265	+	5.14629i	0.742056	+	0.638319i
$66$	0.838191	+	0.237215i	0.103174	+	0.0291991i
$67$	2.98971	−	5.17833i	0.365251	−	0.632634i	−0.623565	−	0.781771i	$-0.714316\pi$
$67$	2.98971	−	5.17833i	0.365251	−	0.632634i	0.988816	+	0.149138i	$0.0476498\pi$
$68$	1.89590	−	3.28380i	0.229912	−	0.398219i
$69$	10.4679	−	10.1789i	1.26018	−	1.22539i
$70$	−1.73004	+	2.99651i	−0.206779	+	0.358151i
$71$	−4.15444	+	7.19570i	−0.493041	+	0.853972i	−0.999968	−	0.00801703i	$-0.997448\pi$
$71$	−4.15444	+	7.19570i	−0.493041	+	0.853972i	0.506927	+	0.861989i	$0.330781\pi$
$72$	2.55508	+	1.57213i	0.301119	+	0.185277i
$73$	13.8427			1.62017			0.810085	−	0.586312i	$-0.199421\pi$
$73$	13.8427			1.62017			0.810085	+	0.586312i	$0.199421\pi$
$74$	0.0315070	+	0.0545717i	0.00366261	+	0.00634383i
$75$	−0.260159	+	0.252976i	−0.0300405	+	0.0292112i
$76$	−0.516111	+	0.893931i	−0.0592020	+	0.102541i
$77$	−0.397537	−	0.688555i	−0.0453036	−	0.0784681i
$78$	−6.23338	+	0.380797i	−0.705791	+	0.0431168i
$79$	2.13387	−	3.69598i	0.240080	−	0.415830i	−0.720657	−	0.693292i	$-0.756160\pi$
$79$	2.13387	−	3.69598i	0.240080	−	0.415830i	0.960737	+	0.277461i	$0.0894931\pi$
$80$	1.09436	+	1.89549i	0.122353	+	0.211922i
$81$	4.05682	+	8.03382i	0.450758	+	0.892646i
$82$	−2.71729	+	4.70648i	−0.300074	+	0.519744i
$83$	4.74173	−	8.21292i	0.520472	−	0.901485i	−0.479244	−	0.877682i	$-0.659089\pi$
$83$	4.74173	−	8.21292i	0.520472	−	0.901485i	0.999717	−	0.0238031i	$-0.00757748\pi$
$84$	−0.671597	−	2.65450i	−0.0732772	−	0.289630i
$85$	8.29919			0.900174
$86$	−4.98693	−	8.63762i	−0.537755	−	0.931419i
$87$	8.69086	+	2.45958i	0.931758	+	0.263695i
$88$	−0.502937			−0.0536132
$89$	3.21174	+	5.56289i	0.340443	+	0.589665i	0.984515	−	0.175300i	$-0.0560895\pi$
$89$	3.21174	+	5.56289i	0.340443	+	0.589665i	−0.644072	+	0.764965i	$0.722756\pi$
$90$	−0.183778	+	6.56359i	−0.0193719	+	0.691863i
$91$	4.32114	+	3.71706i	0.452978	+	0.389653i
$92$	−4.21490	+	7.30043i	−0.439434	+	0.761122i
$93$	2.12590	+	8.40265i	0.220445	+	0.871314i
$94$	4.15412	−	7.19514i	0.428464	−	0.742122i
$95$	−2.25925			−0.231794
$96$	−1.66659	−	0.471659i	−0.170096	−	0.0481385i
$97$	−3.79321	−	6.57004i	−0.385142	−	0.667086i	0.606646	−	0.794972i	$-0.292514\pi$
$97$	−3.79321	−	6.57004i	−0.385142	−	0.667086i	−0.991789	+	0.127885i	$0.959181\pi$
$98$	2.25043	−	3.89786i	0.227328	−	0.393744i
$99$	−1.28504	−	0.790681i	−0.129151	−	0.0794664i
$100$	0.104754	−	0.181438i	0.0104754	−	0.0181438i
$101$	−17.5638			−1.74766			−0.873831	−	0.486231i	$-0.838372\pi$
$101$	−17.5638			−1.74766			−0.873831	+	0.486231i	$0.838372\pi$
$102$	−4.70853	+	4.57854i	−0.466214	+	0.453343i
$103$	4.75462	+	8.23524i	0.468486	+	0.811442i	0.999351	−	0.0360142i	$-0.0114661\pi$
$103$	4.75462	+	8.23524i	0.468486	+	0.811442i	−0.530865	+	0.847457i	$0.678133\pi$
$104$	3.40297	−	1.19155i	0.333689	−	0.116842i
$105$	4.29660	−	4.17798i	0.419305	−	0.407729i
$106$	−9.99466			−0.970767
$107$	−0.805993	−	1.39602i	−0.0779183	−	0.134958i	0.824433	−	0.565959i	$-0.191494\pi$
$107$	−0.805993	−	1.39602i	−0.0779183	−	0.134958i	−0.902352	+	0.431001i	$0.858161\pi$
$108$	−3.51677	−	3.82523i	−0.338401	−	0.368083i
$109$	−17.8183			−1.70668			−0.853339	−	0.521356i	$-0.825426\pi$
$109$	−17.8183			−1.70668			−0.853339	+	0.521356i	$0.825426\pi$
$110$	−0.550393	−	0.953309i	−0.0524780	−	0.0908945i
$111$	−0.0267701	−	0.105809i	−0.00254091	−	0.0100430i
$112$	0.790433	+	1.36907i	0.0746889	+	0.129365i
$113$	11.5614			1.08760			0.543802	−	0.839213i	$-0.316984\pi$
$113$	11.5614			1.08760			0.543802	+	0.839213i	$0.316984\pi$
$114$	1.28178	−	1.24639i	0.120050	−	0.116735i
$115$	−18.4505			−1.72052
$116$	−5.21474			−0.484176
$117$	10.5681	+	2.30539i	0.977023	+	0.213134i
$118$	0.601981			0.0554169
$119$	5.99433			0.549499
$120$	−0.929831	−	3.67517i	−0.0848815	−	0.335496i
$121$	−10.7471			−0.977005
$122$	1.43215	+	2.48055i	0.129660	+	0.224578i
$123$	6.74848	−	6.56217i	0.608490	−	0.591691i
$124$	−2.50207	−	4.33370i	−0.224692	−	0.389178i
$125$	11.4021			1.01984
$126$	−0.132739	+	4.74074i	−0.0118253	+	0.422338i
$127$	2.02802	+	3.51263i	0.179958	+	0.311696i	0.941866	−	0.335989i	$-0.109071\pi$
$127$	2.02802	+	3.51263i	0.179958	+	0.311696i	−0.761908	+	0.647685i	$0.775737\pi$
$128$	1.00000			0.0883883
$129$	4.23718	+	16.7476i	0.373063	+	1.47454i
$130$	5.98265	+	5.14629i	0.524713	+	0.451360i
$131$	−1.85535	−	3.21356i	−0.162103	−	0.280770i	0.773520	−	0.633772i	$-0.218494\pi$
$131$	−1.85535	−	3.21356i	−0.162103	−	0.280770i	−0.935623	+	0.353002i	$0.885161\pi$
$132$	0.838191	+	0.237215i	0.0729552	+	0.0206469i
$133$	−1.63180			−0.141495
$134$	2.98971	−	5.17833i	0.258272	−	0.447340i
$135$	3.40206	−	10.8522i	0.292803	−	0.934005i
$136$	1.89590	−	3.28380i	0.162572	−	0.281583i
$137$	−2.38751	−	4.13529i	−0.203979	−	0.353302i	0.745828	−	0.666139i	$-0.232054\pi$
$137$	−2.38751	−	4.13529i	−0.203979	−	0.353302i	−0.949807	+	0.312837i	$0.898721\pi$
$138$	10.4679	−	10.1789i	0.891083	−	0.866482i
$139$	14.9600			1.26889			0.634443	−	0.772969i	$-0.281229\pi$
$139$	14.9600			1.26889			0.634443	+	0.772969i	$0.281229\pi$
$140$	−1.73004	+	2.99651i	−0.146215	+	0.253251i
$141$	−10.3169	+	10.0321i	−0.868838	+	0.844852i
$142$	−4.15444	+	7.19570i	−0.348633	+	0.603849i
$143$	−1.71148	+	0.599276i	−0.143121	+	0.0501140i
$144$	2.55508	+	1.57213i	0.212923	+	0.131011i
$145$	−5.70680	−	9.88447i	−0.473924	−	0.820861i
$146$	13.8427			1.14563
$147$	−5.58902	+	5.43472i	−0.460975	+	0.448248i
$148$	0.0315070	+	0.0545717i	0.00258986	+	0.00448576i
$149$	4.24030			0.347379			0.173689	−	0.984800i	$-0.444431\pi$
$149$	4.24030			0.347379			0.173689	+	0.984800i	$0.444431\pi$
$150$	−0.260159	+	0.252976i	−0.0212419	+	0.0206554i
$151$	−5.98383	+	10.3643i	−0.486957	+	0.843434i	−0.999888	−	0.0149958i	$-0.995227\pi$
$151$	−5.98383	+	10.3643i	−0.486957	+	0.843434i	0.512931	+	0.858430i	$0.328560\pi$
$152$	−0.516111	+	0.893931i	−0.0418621	+	0.0725074i
$153$	10.0067	−	5.40975i	0.808996	−	0.437352i
$154$	−0.397537	−	0.688555i	−0.0320345	−	0.0554853i
$155$	5.47632	−	9.48526i	0.439869	−	0.761875i
$156$	−6.23338	+	0.380797i	−0.499070	+	0.0304882i
$157$	8.87870	+	15.3784i	0.708598	+	1.22733i	0.965377	+	0.260857i	$0.0840052\pi$
$157$	8.87870	+	15.3784i	0.708598	+	1.22733i	−0.256780	+	0.966470i	$0.582661\pi$
$158$	2.13387	−	3.69598i	0.169762	−	0.294036i
$159$	16.6570	+	4.71407i	1.32099	+	0.373850i
$160$	1.09436	+	1.89549i	0.0865167	+	0.149851i
$161$	−13.3264			−1.05027
$162$	4.05682	+	8.03382i	0.318734	+	0.631196i
$163$	−10.4495	+	18.0991i	−0.818468	+	1.41763i	0.0883435	+	0.996090i	$0.471843\pi$
$163$	−10.4495	+	18.0991i	−0.818468	+	1.41763i	−0.906811	+	0.421537i	$0.861491\pi$
$164$	−2.71729	+	4.70648i	−0.212185	+	0.367515i
$165$	0.467646	+	1.84838i	0.0364062	+	0.143896i
$166$	4.74173	−	8.21292i	0.368030	−	0.637446i
$167$	10.5288	−	18.2365i	0.814746	−	1.41118i	−0.0947633	−	0.995500i	$-0.530209\pi$
$167$	10.5288	−	18.2365i	0.814746	−	1.41118i	0.909510	−	0.415682i	$-0.136457\pi$
$168$	−0.671597	−	2.65450i	−0.0518148	−	0.204799i
$169$	10.1604	−	8.10965i	0.781569	−	0.623819i
$170$	8.29919			0.636519
$171$	−2.72408	+	1.47267i	−0.208315	+	0.112618i
$172$	−4.98693	−	8.63762i	−0.380250	−	0.658613i
$173$	−5.99936	−	10.3912i	−0.456123	−	0.790028i	0.542629	−	0.839972i	$-0.317429\pi$
$173$	−5.99936	−	10.3912i	−0.456123	−	0.790028i	−0.998752	+	0.0499444i	$0.984096\pi$
$174$	8.69086	+	2.45958i	0.658852	+	0.186460i
$175$	0.331202			0.0250365
$176$	−0.502937			−0.0379103
$177$	−1.00326	−	0.283930i	−0.0754096	−	0.0213415i
$178$	3.21174	+	5.56289i	0.240730	+	0.416956i
$179$	−1.33168	−	2.30654i	−0.0995346	−	0.172399i	0.811958	−	0.583717i	$-0.198402\pi$
$179$	−1.33168	−	2.30654i	−0.0995346	−	0.172399i	−0.911492	+	0.411318i	$0.865069\pi$
$180$	−0.183778	+	6.56359i	−0.0136980	+	0.489221i
$181$	−8.09512			−0.601705			−0.300853	−	0.953671i	$-0.597271\pi$
$181$	−8.09512			−0.601705			−0.300853	+	0.953671i	$0.597271\pi$
$182$	4.32114	+	3.71706i	0.320304	+	0.275527i
$183$	−1.21683	−	4.80955i	−0.0899508	−	0.355532i
$184$	−4.21490	+	7.30043i	−0.310727	+	0.538195i
$185$	−0.0689599	+	0.119442i	−0.00507003	+	0.00878156i
$186$	2.12590	+	8.40265i	0.155878	+	0.616112i
$187$	−0.953518	+	1.65154i	−0.0697281	+	0.120773i
$188$	4.15412	−	7.19514i	0.302970	−	0.524760i
$189$	2.45723	−	7.83828i	0.178737	−	0.570151i
$190$	−2.25925			−0.163903
$191$	11.9953	+	20.7764i	0.867948	+	1.50333i	0.864090	+	0.503337i	$0.167895\pi$
$191$	11.9953	+	20.7764i	0.867948	+	1.50333i	0.00385779	+	0.999993i	$0.498772\pi$
$192$	−1.66659	−	0.471659i	−0.120276	−	0.0340391i
$193$	2.79996	−	4.84966i	0.201545	−	0.349087i	−0.747481	−	0.664283i	$-0.768737\pi$
$193$	2.79996	−	4.84966i	0.201545	−	0.349087i	0.949026	+	0.315196i	$0.102070\pi$
$194$	−3.79321	−	6.57004i	−0.272337	−	0.471701i
$195$	−7.54335	−	11.3986i	−0.540191	−	0.816267i
$196$	2.25043	−	3.89786i	0.160745	−	0.278419i
$197$	0.0520349	+	0.0901272i	0.00370734	+	0.00642129i	0.867873	−	0.496786i	$-0.165487\pi$
$197$	0.0520349	+	0.0901272i	0.00370734	+	0.00642129i	−0.864166	+	0.503207i	$0.832153\pi$
$198$	−1.28504	−	0.790681i	−0.0913239	−	0.0561913i
$199$	−9.85896	+	17.0762i	−0.698883	+	1.21050i	0.269971	+	0.962868i	$0.412986\pi$
$199$	−9.85896	+	17.0762i	−0.698883	+	1.21050i	−0.968854	+	0.247632i	$0.920347\pi$
$200$	0.104754	−	0.181438i	0.00740719	−	0.0128296i
$201$	−7.42504	+	7.22005i	−0.523722	+	0.509263i
$202$	−17.5638			−1.23578
$203$	−4.12190	−	7.13934i	−0.289301	−	0.501083i
$204$	−4.70853	+	4.57854i	−0.329663	+	0.320562i
$205$	−11.8948			−0.830767
$206$	4.75462	+	8.23524i	0.331270	+	0.573776i
$207$	−22.2466	+	12.0268i	−1.54625	+	0.835918i
$208$	3.40297	−	1.19155i	0.235953	−	0.0826195i
$209$	0.259571	−	0.449590i	0.0179549	−	0.0310988i
$210$	4.29660	−	4.17798i	0.296493	−	0.288308i
$211$	−8.01373	+	13.8802i	−0.551688	+	0.955551i	0.446465	+	0.894801i	$0.352683\pi$
$211$	−8.01373	+	13.8802i	−0.551688	+	0.955551i	−0.998153	+	0.0607501i	$0.980651\pi$
$212$	−9.99466			−0.686436
$213$	10.3177	−	10.0328i	0.706956	−	0.687438i
$214$	−0.805993	−	1.39602i	−0.0550965	−	0.0954300i
$215$	10.9150	−	18.9053i	0.744397	−	1.28933i
$216$	−3.51677	−	3.82523i	−0.239286	−	0.260274i
$217$	3.95543	−	6.85100i	0.268512	−	0.465076i
$218$	−17.8183			−1.20680
$219$	−23.0702	−	6.52905i	−1.55894	−	0.441193i
$220$	−0.550393	−	0.953309i	−0.0371075	−	0.0642721i
$221$	2.53887	−	13.4337i	0.170783	−	0.903651i
$222$	−0.0267701	−	0.105809i	−0.00179669	−	0.00710146i
$223$	−5.51471			−0.369292			−0.184646	−	0.982805i	$-0.559114\pi$
$223$	−5.51471			−0.369292			−0.184646	+	0.982805i	$0.559114\pi$
$224$	0.790433	+	1.36907i	0.0528130	+	0.0914748i
$225$	0.552898	−	0.298903i	0.0368599	−	0.0199269i
$226$	11.5614			0.769053
$227$	−10.7089	−	18.5484i	−0.710775	−	1.23110i	−0.964567	−	0.263839i	$-0.915011\pi$
$227$	−10.7089	−	18.5484i	−0.710775	−	1.23110i	0.253792	−	0.967259i	$-0.418322\pi$
$228$	1.28178	−	1.24639i	0.0848879	−	0.0825443i
$229$	−11.8440	−	20.5144i	−0.782672	−	1.35563i	−0.930380	−	0.366596i	$-0.880523\pi$
$229$	−11.8440	−	20.5144i	−0.782672	−	1.35563i	0.147708	−	0.989031i	$-0.452810\pi$
$230$	−18.4505			−1.21659
$231$	0.337770	+	1.33504i	0.0222237	+	0.0878395i
$232$	−5.21474			−0.342364
$233$	−5.93580			−0.388867			−0.194434	−	0.980916i	$-0.562287\pi$
$233$	−5.93580			−0.388867			−0.194434	+	0.980916i	$0.562287\pi$
$234$	10.5681	+	2.30539i	0.690860	+	0.150708i
$235$	18.1844			1.18622
$236$	0.601981			0.0391857
$237$	−5.29955	+	5.15324i	−0.344243	+	0.334739i
$238$	5.99433			0.388555
$239$	2.91836	+	5.05475i	0.188773	+	0.326964i	0.944841	−	0.327528i	$-0.106216\pi$
$239$	2.91836	+	5.05475i	0.188773	+	0.326964i	−0.756068	+	0.654493i	$0.772882\pi$
$240$	−0.929831	−	3.67517i	−0.0600203	−	0.237231i
$241$	5.79116	+	10.0306i	0.373042	+	0.646127i	0.990032	−	0.140844i	$-0.0449815\pi$
$241$	5.79116	+	10.0306i	0.373042	+	0.646127i	−0.616990	+	0.786971i	$0.711648\pi$
$242$	−10.7471			−0.690847
$243$	−2.97185	−	15.3026i	−0.190644	−	0.981659i
$244$	1.43215	+	2.48055i	0.0916837	+	0.158801i
$245$	9.85113			0.629366
$246$	6.74848	−	6.56217i	0.430267	−	0.418388i
$247$	−0.691143	+	3.65699i	−0.0439764	+	0.232689i
$248$	−2.50207	−	4.33370i	−0.158881	−	0.275191i
$249$	−11.7762	+	11.4511i	−0.746289	+	0.725685i
$250$	11.4021			0.721135
$251$	−1.29273	+	2.23908i	−0.0815967	+	0.141330i	−0.903936	−	0.427668i	$-0.859335\pi$
$251$	−1.29273	+	2.23908i	−0.0815967	+	0.141330i	0.822339	+	0.568997i	$0.192669\pi$
$252$	−0.132739	+	4.74074i	−0.00836176	+	0.298638i
$253$	2.11983	−	3.67165i	0.133273	−	0.230835i
$254$	2.02802	+	3.51263i	0.127249	+	0.220402i
$255$	−13.8314	−	3.91439i	−0.866155	−	0.245129i
$256$	1.00000			0.0625000
$257$	−10.8198	+	18.7404i	−0.674919	+	1.16899i	0.301574	+	0.953443i	$0.402488\pi$
$257$	−10.8198	+	18.7404i	−0.674919	+	1.16899i	−0.976493	+	0.215550i	$0.930845\pi$
$258$	4.23718	+	16.7476i	0.263796	+	1.04266i
$259$	−0.0498083	+	0.0862705i	−0.00309494	+	0.00536058i
$260$	5.98265	+	5.14629i	0.371028	+	0.319160i
$261$	−13.3241	−	8.19824i	−0.824738	−	0.507459i
$262$	−1.85535	−	3.21356i	−0.114624	−	0.198535i
$263$	13.7198			0.846002			0.423001	−	0.906129i	$-0.360977\pi$
$263$	13.7198			0.846002			0.423001	+	0.906129i	$0.360977\pi$
$264$	0.838191	+	0.237215i	0.0515871	+	0.0145995i
$265$	−10.9378	−	18.9447i	−0.671901	−	1.16377i
$266$	−1.63180			−0.100052
$267$	−2.72888	−	10.7859i	−0.167004	−	0.660088i
$268$	2.98971	−	5.17833i	0.182626	−	0.316317i
$269$	−5.25005	+	9.09335i	−0.320101	+	0.554431i	−0.980509	−	0.196476i	$-0.937050\pi$
$269$	−5.25005	+	9.09335i	−0.320101	+	0.554431i	0.660408	+	0.750907i	$0.270384\pi$
$270$	3.40206	−	10.8522i	0.207043	−	0.660441i
$271$	−13.4122	−	23.2307i	−0.814735	−	1.41116i	−0.909518	−	0.415664i	$-0.863549\pi$
$271$	−13.4122	−	23.2307i	−0.814735	−	1.41116i	0.0947835	−	0.995498i	$-0.469784\pi$
$272$	1.89590	−	3.28380i	0.114956	−	0.199109i
$273$	−5.44840	−	8.23293i	−0.329752	−	0.498280i
$274$	−2.38751	−	4.13529i	−0.144235	−	0.249822i
$275$	−0.0526844	+	0.0912520i	−0.00317699	+	0.00550270i
$276$	10.4679	−	10.1789i	0.630091	−	0.612695i
$277$	12.1261	+	21.0031i	0.728590	+	1.26195i	0.957479	+	0.288502i	$0.0931571\pi$
$277$	12.1261	+	21.0031i	0.728590	+	1.26195i	−0.228890	+	0.973452i	$0.573510\pi$
$278$	14.9600			0.897238
$279$	0.420177	−	15.0065i	0.0251553	−	0.898416i
$280$	−1.73004	+	2.99651i	−0.103389	+	0.179076i
$281$	−11.9542	+	20.7053i	−0.713129	+	1.23518i	0.250547	+	0.968104i	$0.419390\pi$
$281$	−11.9542	+	20.7053i	−0.713129	+	1.23518i	−0.963677	+	0.267072i	$0.913944\pi$
$282$	−10.3169	+	10.0321i	−0.614361	+	0.597400i
$283$	−12.3190	+	21.3371i	−0.732288	+	1.26836i	0.223615	+	0.974678i	$0.428214\pi$
$283$	−12.3190	+	21.3371i	−0.732288	+	1.26836i	−0.955903	+	0.293683i	$0.905119\pi$
$284$	−4.15444	+	7.19570i	−0.246520	+	0.426986i
$285$	3.76525	+	1.06559i	0.223034	+	0.0631203i
$286$	−1.71148	+	0.599276i	−0.101202	+	0.0354360i
$287$	−8.59134			−0.507131
$288$	2.55508	+	1.57213i	0.150559	+	0.0926386i
$289$	1.31112	+	2.27092i	0.0771245	+	0.133583i
$290$	−5.70680	−	9.88447i	−0.335115	−	0.580436i
$291$	3.22293	+	12.7387i	0.188932	+	0.746755i
$292$	13.8427			0.810085
$293$	9.05213			0.528831			0.264415	−	0.964409i	$-0.414821\pi$
$293$	9.05213			0.528831			0.264415	+	0.964409i	$0.414821\pi$
$294$	−5.58902	+	5.43472i	−0.325958	+	0.316959i
$295$	0.658784	+	1.14105i	0.0383559	+	0.0664344i
$296$	0.0315070	+	0.0545717i	0.00183131	+	0.00317191i
$297$	1.76871	+	1.92385i	0.102631	+	0.111633i
$298$	4.24030			0.245634
$299$	−5.64433	+	29.8654i	−0.326420	+	1.72716i
$300$	−0.260159	+	0.252976i	−0.0150203	+	0.0146056i
$301$	7.88367	−	13.6549i	0.454407	−	0.787056i
$302$	−5.98383	+	10.3643i	−0.344331	+	0.596398i
$303$	29.2717	+	8.28411i	1.68161	+	0.475910i
$304$	−0.516111	+	0.893931i	−0.0296010	+	0.0512704i
$305$	−3.13456	+	5.42922i	−0.179485	+	0.310876i
$306$	10.0067	−	5.40975i	0.572046	−	0.309255i
$307$	18.3002			1.04445			0.522225	−	0.852808i	$-0.325102\pi$
$307$	18.3002			1.04445			0.522225	+	0.852808i	$0.325102\pi$
$308$	−0.397537	−	0.688555i	−0.0226518	−	0.0392341i
$309$	−4.03980	−	15.9674i	−0.229816	−	0.908352i
$310$	5.47632	−	9.48526i	0.311034	−	0.538727i
$311$	5.21196	+	9.02738i	0.295543	+	0.511896i	0.975111	−	0.221717i	$-0.0711661\pi$
$311$	5.21196	+	9.02738i	0.295543	+	0.511896i	−0.679568	+	0.733613i	$0.737833\pi$
$312$	−6.23338	+	0.380797i	−0.352896	+	0.0215584i
$313$	15.1740	−	26.2821i	0.857685	−	1.48555i	−0.0164472	−	0.999865i	$-0.505236\pi$
$313$	15.1740	−	26.2821i	0.857685	−	1.48555i	0.874132	−	0.485689i	$-0.161431\pi$
$314$	8.87870	+	15.3784i	0.501054	+	0.867851i
$315$	−9.13127	+	4.93647i	−0.514489	+	0.278138i
$316$	2.13387	−	3.69598i	0.120040	−	0.207915i
$317$	3.71925	−	6.44193i	0.208894	−	0.361815i	−0.742472	−	0.669877i	$-0.766347\pi$
$317$	3.71925	−	6.44193i	0.208894	−	0.361815i	0.951366	+	0.308062i	$0.0996803\pi$
$318$	16.6570	+	4.71407i	0.934081	+	0.264352i
$319$	2.62268			0.146842
$320$	1.09436	+	1.89549i	0.0611766	+	0.105961i
$321$	0.684817	+	2.70675i	0.0382228	+	0.151076i
$322$	−13.3264			−0.742651
$323$	1.95699	+	3.38961i	0.108890	+	0.188603i
$324$	4.05682	+	8.03382i	0.225379	+	0.446323i
$325$	0.140279	−	0.742249i	0.00778129	−	0.0411726i
$326$	−10.4495	+	18.0991i	−0.578744	+	1.00241i
$327$	29.6958	+	8.40414i	1.64218	+	0.464750i
$328$	−2.71729	+	4.70648i	−0.150037	+	0.259872i
$329$	13.1342			0.724112
$330$	0.467646	+	1.84838i	0.0257431	+	0.101750i
$331$	1.70727	+	2.95708i	0.0938401	+	0.162536i	0.909124	−	0.416526i	$-0.136752\pi$
$331$	1.70727	+	2.95708i	0.0938401	+	0.162536i	−0.815284	+	0.579062i	$0.803419\pi$
$332$	4.74173	−	8.21292i	0.260236	−	0.450742i
$333$	−0.00529102	+	0.188968i	−0.000289946	+	0.0103554i
$334$	10.5288	−	18.2365i	0.576113	−	0.997857i
$335$	13.0873			0.715034
$336$	−0.671597	−	2.65450i	−0.0366386	−	0.144815i
$337$	−6.02371	−	10.4334i	−0.328133	−	0.568342i	0.654009	−	0.756487i	$-0.273086\pi$
$337$	−6.02371	−	10.4334i	−0.328133	−	0.568342i	−0.982141	+	0.188145i	$0.939753\pi$
$338$	10.1604	−	8.10965i	0.552653	−	0.441107i
$339$	−19.2682	−	5.45304i	−1.04650	−	0.296168i
$340$	8.29919			0.450087
$341$	1.25838	+	2.17958i	0.0681451	+	0.118031i
$342$	−2.72408	+	1.47267i	−0.147301	+	0.0796327i
$343$	18.1813			0.981699
$344$	−4.98693	−	8.63762i	−0.268878	−	0.465710i
$345$	30.7495	+	8.70234i	1.65550	+	0.468518i
$346$	−5.99936	−	10.3912i	−0.322528	−	0.558634i
$347$	7.72226			0.414553			0.207276	−	0.978282i	$-0.433540\pi$
$347$	7.72226			0.414553			0.207276	+	0.978282i	$0.433540\pi$
$348$	8.69086	+	2.45958i	0.465879	+	0.131847i
$349$	26.4081			1.41359			0.706797	−	0.707416i	$-0.250139\pi$
$349$	26.4081			1.41359			0.706797	+	0.707416i	$0.250139\pi$
$350$	0.331202			0.0177035
$351$	−16.5254	−	8.82671i	−0.882061	−	0.471135i
$352$	−0.502937			−0.0268066
$353$	−34.2383			−1.82232			−0.911161	−	0.412050i	$-0.864813\pi$
$353$	−34.2383			−1.82232			−0.911161	+	0.412050i	$0.864813\pi$
$354$	−1.00326	−	0.283930i	−0.0533226	−	0.0150907i
$355$	−18.1858			−0.965202
$356$	3.21174	+	5.56289i	0.170222	+	0.294833i
$357$	−9.99012	−	2.82728i	−0.528733	−	0.149635i
$358$	−1.33168	−	2.30654i	−0.0703816	−	0.121904i
$359$	20.0071			1.05593			0.527967	−	0.849265i	$-0.322955\pi$
$359$	20.0071			1.05593			0.527967	+	0.849265i	$0.322955\pi$
$360$	−0.183778	+	6.56359i	−0.00968594	+	0.345931i
$361$	8.96726	+	15.5317i	0.471961	+	0.817460i
$362$	−8.09512			−0.425470
$363$	17.9110	+	5.06895i	0.940083	+	0.266051i
$364$	4.32114	+	3.71706i	0.226489	+	0.194827i
$365$	15.1489	+	26.2387i	0.792932	+	1.37340i
$366$	−1.21683	−	4.80955i	−0.0636049	−	0.251399i
$367$	27.7949			1.45088			0.725440	−	0.688285i	$-0.241636\pi$
$367$	27.7949			1.45088			0.725440	+	0.688285i	$0.241636\pi$
$368$	−4.21490	+	7.30043i	−0.219717	+	0.380561i
$369$	−14.3421	+	7.75349i	−0.746619	+	0.403631i
$370$	−0.0689599	+	0.119442i	−0.00358506	+	0.00620950i
$371$	−7.90010	−	13.6834i	−0.410153	−	0.710406i
$372$	2.12590	+	8.40265i	0.110223	+	0.435657i
$373$	−12.3059			−0.637174			−0.318587	−	0.947894i	$-0.603208\pi$
$373$	−12.3059			−0.637174			−0.318587	+	0.947894i	$0.603208\pi$
$374$	−0.953518	+	1.65154i	−0.0493052	+	0.0853992i
$375$	−19.0028	−	5.37793i	−0.981298	−	0.277715i
$376$	4.15412	−	7.19514i	0.214232	−	0.371061i
$377$	−17.7456	+	6.21365i	−0.913945	+	0.320019i
$378$	2.45723	−	7.83828i	0.126386	−	0.403158i
$379$	−4.55621	−	7.89159i	−0.234037	−	0.405364i	0.724956	−	0.688796i	$-0.241860\pi$
$379$	−4.55621	−	7.89159i	−0.234037	−	0.405364i	−0.958992	+	0.283432i	$0.908527\pi$
$380$	−2.25925			−0.115897
$381$	−1.72312	−	6.81067i	−0.0882782	−	0.348921i
$382$	11.9953	+	20.7764i	0.613732	+	1.06301i
$383$	−5.01951			−0.256485			−0.128242	−	0.991743i	$-0.540934\pi$
$383$	−5.01951			−0.256485			−0.128242	+	0.991743i	$0.540934\pi$
$384$	−1.66659	−	0.471659i	−0.0850481	−	0.0240693i
$385$	0.870098	−	1.50705i	0.0443443	−	0.0768066i
$386$	2.79996	−	4.84966i	0.142514	−	0.246841i
$387$	0.837465	−	29.9099i	0.0425708	−	1.52041i
$388$	−3.79321	−	6.57004i	−0.192571	−	0.333543i
$389$	11.1313	−	19.2800i	0.564380	−	0.977535i	−0.432727	−	0.901525i	$-0.642449\pi$
$389$	11.1313	−	19.2800i	0.564380	−	0.977535i	0.997107	−	0.0760100i	$-0.0242181\pi$
$390$	−7.54335	−	11.3986i	−0.381973	−	0.577188i
$391$	15.9821	+	27.6818i	0.808249	+	1.39993i
$392$	2.25043	−	3.89786i	0.113664	−	0.196872i
$393$	1.57641	+	6.23080i	0.0795195	+	0.314302i
$394$	0.0520349	+	0.0901272i	0.00262148	+	0.00454054i
$395$	9.34091			0.469992
$396$	−1.28504	−	0.790681i	−0.0645757	−	0.0397332i
$397$	−13.0759	+	22.6481i	−0.656259	+	1.13667i	0.325317	+	0.945605i	$0.394529\pi$
$397$	−13.0759	+	22.6481i	−0.656259	+	1.13667i	−0.981577	+	0.191069i	$0.938804\pi$
$398$	−9.85896	+	17.0762i	−0.494185	+	0.855953i
$399$	2.71956	+	0.769655i	0.136148	+	0.0385310i
$400$	0.104754	−	0.181438i	0.00523768	−	0.00907192i
$401$	13.0125	−	22.5384i	0.649815	−	1.12551i	−0.333352	−	0.942802i	$-0.608180\pi$
$401$	13.0125	−	22.5384i	0.649815	−	1.12551i	0.983167	−	0.182709i	$-0.0584868\pi$
$402$	−7.42504	+	7.22005i	−0.370327	+	0.360104i
$403$	−13.6783	−	11.7661i	−0.681365	−	0.586112i
$404$	−17.5638			−0.873831
$405$	−10.7884	+	16.4815i	−0.536078	+	0.818974i
$406$	−4.12190	−	7.13934i	−0.204566	−	0.354320i
$407$	−0.0158460	−	0.0274461i	−0.000785457	−	0.00136045i
$408$	−4.70853	+	4.57854i	−0.233107	+	0.226672i
$409$	−11.7798			−0.582475			−0.291238	−	0.956651i	$-0.594067\pi$
$409$	−11.7798			−0.582475			−0.291238	+	0.956651i	$0.594067\pi$
$410$	−11.8948			−0.587441
$411$	2.02857	+	8.01795i	0.100062	+	0.395496i
$412$	4.75462	+	8.23524i	0.234243	+	0.405721i
$413$	0.475826	+	0.824154i	0.0234139	+	0.0405540i
$414$	−22.2466	+	12.0268i	−1.09336	+	0.591084i
$415$	20.7566			1.01890
$416$	3.40297	−	1.19155i	0.166844	−	0.0584208i
$417$	−24.9322	−	7.05600i	−1.22093	−	0.345534i
$418$	0.259571	−	0.449590i	0.0126960	−	0.0219902i
$419$	−14.9908	+	25.9648i	−0.732348	+	1.26846i	0.223529	+	0.974697i	$0.428242\pi$
$419$	−14.9908	+	25.9648i	−0.732348	+	1.26846i	−0.955877	+	0.293767i	$0.905091\pi$
$420$	4.29660	−	4.17798i	0.209652	−	0.203864i
$421$	−9.62578	+	16.6723i	−0.469132	+	0.812560i	−0.999377	−	0.0352841i	$-0.988766\pi$
$421$	−9.62578	+	16.6723i	−0.469132	+	0.812560i	0.530246	+	0.847844i	$0.322100\pi$
$422$	−8.01373	+	13.8802i	−0.390102	+	0.675677i
$423$	21.9258	−	11.8533i	1.06607	−	0.576328i
$424$	−9.99466			−0.485383
$425$	−0.397205	−	0.687979i	−0.0192673	−	0.0333719i
$426$	10.3177	−	10.0328i	0.499893	−	0.486092i
$427$	−2.26403	+	3.92141i	−0.109564	+	0.189770i
$428$	−0.805993	−	1.39602i	−0.0389591	−	0.0674792i
$429$	3.13499	−	0.191517i	0.151359	−	0.00924653i
$430$	10.9150	−	18.9053i	0.526368	−	0.911696i
$431$	−4.11765	−	7.13198i	−0.198340	−	0.343535i	0.749650	−	0.661834i	$-0.230222\pi$
$431$	−4.11765	−	7.13198i	−0.198340	−	0.343535i	−0.947990	+	0.318299i	$0.896888\pi$
$432$	−3.51677	−	3.82523i	−0.169200	−	0.184041i
$433$	1.34932	−	2.33708i	0.0648440	−	0.112313i	−0.831781	−	0.555104i	$-0.812678\pi$
$433$	1.34932	−	2.33708i	0.0648440	−	0.112313i	0.896625	+	0.442791i	$0.146012\pi$
$434$	3.95543	−	6.85100i	0.189867	−	0.328859i
$435$	4.84882	+	19.1651i	0.232483	+	0.918895i
$436$	−17.8183			−0.853339
$437$	−4.35072	−	7.53567i	−0.208123	−	0.360480i
$438$	−23.0702	−	6.52905i	−1.10234	−	0.311970i
$439$	29.8318			1.42379			0.711896	−	0.702285i	$-0.247837\pi$
$439$	29.8318			1.42379			0.711896	+	0.702285i	$0.247837\pi$
$440$	−0.550393	−	0.953309i	−0.0262390	−	0.0454472i
$441$	11.8780	−	6.42137i	0.565618	−	0.305779i
$442$	2.53887	−	13.4337i	0.120762	−	0.638977i
$443$	1.33729	−	2.31625i	0.0635364	−	0.110048i	−0.832507	−	0.554014i	$-0.813095\pi$
$443$	1.33729	−	2.31625i	0.0635364	−	0.110048i	0.896044	+	0.443966i	$0.146429\pi$
$444$	−0.0267701	−	0.105809i	−0.00127045	−	0.00502149i
$445$	−7.02959	+	12.1756i	−0.333235	+	0.577179i
$446$	−5.51471			−0.261129
$447$	−7.06686	−	1.99998i	−0.334251	−	0.0945956i
$448$	0.790433	+	1.36907i	0.0373444	+	0.0646824i
$449$	−1.88447	+	3.26401i	−0.0889338	+	0.154038i	−0.907061	−	0.421000i	$-0.861679\pi$
$449$	−1.88447	+	3.26401i	−0.0889338	+	0.154038i	0.818127	+	0.575038i	$0.195013\pi$
$450$	0.552898	−	0.298903i	0.0260639	−	0.0140904i
$451$	1.36662	−	2.36706i	0.0643518	−	0.111461i
$452$	11.5614			0.543802
$453$	14.8610	−	14.4508i	0.698232	−	0.678956i
$454$	−10.7089	−	18.5484i	−0.502594	−	0.870518i
$455$	−2.31675	+	12.2585i	−0.108611	+	0.574685i
$456$	1.28178	−	1.24639i	0.0600248	−	0.0583676i
$457$	22.8754			1.07006			0.535032	−	0.844832i	$-0.320300\pi$
$457$	22.8754			1.07006			0.535032	+	0.844832i	$0.320300\pi$
$458$	−11.8440	−	20.5144i	−0.553433	−	0.958573i
$459$	−19.2287	+	4.29610i	−0.897519	+	0.200525i
$460$	−18.4505			−0.860258
$461$	−9.21067	−	15.9533i	−0.428984	−	0.743021i	0.567800	−	0.823167i	$-0.307795\pi$
$461$	−9.21067	−	15.9533i	−0.428984	−	0.743021i	−0.996783	+	0.0801455i	$0.974461\pi$
$462$	0.337770	+	1.33504i	0.0157145	+	0.0621119i
$463$	9.45153	+	16.3705i	0.439250	+	0.760803i	0.997632	−	0.0687812i	$-0.0219110\pi$
$463$	9.45153	+	16.3705i	0.439250	+	0.760803i	−0.558382	+	0.829584i	$0.688578\pi$
$464$	−5.21474			−0.242088
$465$	−13.6006	+	13.2251i	−0.630713	+	0.613301i
$466$	−5.93580			−0.274970
$467$	24.6818			1.14214			0.571068	−	0.820903i	$-0.306529\pi$
$467$	24.6818			1.14214			0.571068	+	0.820903i	$0.306529\pi$
$468$	10.5681	+	2.30539i	0.488512	+	0.106567i
$469$	9.45266			0.436483
$470$	18.1844			0.838784
$471$	−7.54385	−	29.8172i	−0.347602	−	1.37391i
$472$	0.601981			0.0277084
$473$	2.50811	+	4.34418i	0.115323	+	0.199745i
$474$	−5.29955	+	5.15324i	−0.243416	+	0.236696i
$475$	0.108129	+	0.187285i	0.00496130	+	0.00859322i
$476$	5.99433			0.274750
$477$	−25.5371	−	15.7129i	−1.16926	−	0.719444i
$478$	2.91836	+	5.05475i	0.133483	+	0.231199i
$479$	36.6440			1.67431			0.837154	−	0.546967i	$-0.184218\pi$
$479$	36.6440			1.67431			0.837154	+	0.546967i	$0.184218\pi$
$480$	−0.929831	−	3.67517i	−0.0424408	−	0.167748i
$481$	0.172242	+	0.148163i	0.00785358	+	0.00675567i
$482$	5.79116	+	10.0306i	0.263780	+	0.456881i
$483$	22.2097	+	6.28551i	1.01058	+	0.286001i
$484$	−10.7471			−0.488502
$485$	8.30228	−	14.3800i	0.376987	−	0.652961i
$486$	−2.97185	−	15.3026i	−0.134806	−	0.694138i
$487$	−4.39414	+	7.61087i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$487$	−4.39414	+	7.61087i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$488$	1.43215	+	2.48055i	0.0648302	+	0.112289i
$489$	25.9517	−	25.2352i	1.17357	−	1.14117i
$490$	9.85113			0.445029
$491$	8.82292	−	15.2817i	0.398173	−	0.689655i	−0.595328	−	0.803483i	$-0.702978\pi$
$491$	8.82292	−	15.2817i	0.398173	−	0.689655i	0.993501	+	0.113828i	$0.0363111\pi$
$492$	6.74848	−	6.56217i	0.304245	−	0.295845i
$493$	−9.88663	+	17.1242i	−0.445272	+	0.771233i
$494$	−0.691143	+	3.65699i	−0.0310960	+	0.164536i
$495$	0.0924286	−	3.30107i	0.00415436	−	0.148372i
$496$	−2.50207	−	4.33370i	−0.112346	−	0.194589i
$497$	−13.1352			−0.589195
$498$	−11.7762	+	11.4511i	−0.527706	+	0.513137i
$499$	−19.3003	−	33.4291i	−0.864000	−	1.49649i	−0.868037	−	0.496499i	$-0.834618\pi$
$499$	−19.3003	−	33.4291i	−0.864000	−	1.49649i	0.00403743	−	0.999992i	$-0.498715\pi$
$500$	11.4021			0.509920
$501$	−26.1487	+	25.4268i	−1.16824	+	1.13599i
$502$	−1.29273	+	2.23908i	−0.0576976	+	0.0999351i
$503$	−1.82085	+	3.15380i	−0.0811876	+	0.140621i	−0.903760	−	0.428039i	$-0.859205\pi$
$503$	−1.82085	+	3.15380i	−0.0811876	+	0.140621i	0.822573	+	0.568660i	$0.192538\pi$
$504$	−0.132739	+	4.74074i	−0.00591266	+	0.211169i
$505$	−19.2211	−	33.2919i	−0.855327	−	1.48147i
$506$	2.11983	−	3.67165i	0.0942379	−	0.163225i
$507$	−20.7582	+	8.72325i	−0.921906	+	0.387413i
$508$	2.02802	+	3.51263i	0.0899788	+	0.155848i
$509$	−8.80595	+	15.2524i	−0.390317	+	0.676049i	−0.992491	−	0.122316i	$-0.960968\pi$
$509$	−8.80595	+	15.2524i	−0.390317	+	0.676049i	0.602174	+	0.798365i	$0.294301\pi$
$510$	−13.8314	−	3.91439i	−0.612464	−	0.173332i
$511$	10.9418	+	18.9517i	0.484035	+	0.838373i
$512$	1.00000			0.0441942
$513$	5.23453	−	1.16950i	0.231110	−	0.0516348i
$514$	−10.8198	+	18.7404i	−0.477239	+	0.826603i
$515$	−10.4065	+	18.0246i	−0.458566	+	0.794260i
$516$	4.23718	+	16.7476i	0.186532	+	0.737270i
$517$	−2.08926	+	3.61870i	−0.0918854	+	0.159150i
$518$	−0.0498083	+	0.0862705i	−0.00218845	+	0.00379051i
$519$	5.09740	+	20.1476i	0.223751	+	0.884380i
$520$	5.98265	+	5.14629i	0.262356	+	0.225680i
$521$	−17.1950			−0.753327			−0.376663	−	0.926350i	$-0.622929\pi$
$521$	−17.1950			−0.753327			−0.376663	+	0.926350i	$0.622929\pi$
$522$	−13.3241	−	8.19824i	−0.583178	−	0.358827i
$523$	−12.1008	−	20.9592i	−0.529131	−	0.916482i	−0.999423	−	0.0339708i	$-0.989185\pi$
$523$	−12.1008	−	20.9592i	−0.529131	−	0.916482i	0.470292	−	0.882511i	$-0.344149\pi$
$524$	−1.85535	−	3.21356i	−0.0810514	−	0.140385i
$525$	−0.551980	−	0.156215i	−0.0240904	−	0.00681777i
$526$	13.7198			0.598214
$527$	−18.9747			−0.826550
$528$	0.838191	+	0.237215i	0.0364776	+	0.0103234i
$529$	−24.0308	−	41.6226i	−1.04482	−	1.80968i
$530$	−10.9378	−	18.9447i	−0.475106	−	0.822907i
$531$	1.53811	+	0.946392i	0.0667482	+	0.0410699i
$532$	−1.63180			−0.0707477
$533$	−3.63882	+	19.2538i	−0.157615	+	0.833975i
$534$	−2.72888	−	10.7859i	−0.118090	−	0.466753i
$535$	1.76409	−	3.05550i	0.0762683	−	0.132101i
$536$	2.98971	−	5.17833i	0.129136	−	0.223670i
$537$	1.13147	+	4.47217i	0.0488267	+	0.192988i
$538$	−5.25005	+	9.09335i	−0.226346	+	0.392042i
$539$	−1.13182	+	1.96038i	−0.0487511	+	0.0844395i
$540$	3.40206	−	10.8522i	0.146401	−	0.467002i
$541$	15.1390			0.650876			0.325438	−	0.945563i	$-0.394488\pi$
$541$	15.1390			0.650876			0.325438	+	0.945563i	$0.394488\pi$
$542$	−13.4122	−	23.2307i	−0.576104	−	0.997842i
$543$	13.4913	+	3.81813i	0.578966	+	0.163852i
$544$	1.89590	−	3.28380i	0.0812861	−	0.140792i
$545$	−19.4996	−	33.7743i	−0.835270	−	1.44673i
$546$	−5.44840	−	8.23293i	−0.233170	−	0.352337i
$547$	−15.6144	+	27.0449i	−0.667623	+	1.15636i	0.310944	+	0.950428i	$0.399355\pi$
$547$	−15.6144	+	27.0449i	−0.667623	+	1.15636i	−0.978567	+	0.205929i	$0.933979\pi$
$548$	−2.38751	−	4.13529i	−0.101989	−	0.176651i
$549$	−0.240503	+	8.58951i	−0.0102644	+	0.366591i
$550$	−0.0526844	+	0.0912520i	−0.00224647	+	0.00389100i
$551$	2.69139	−	4.66162i	0.114657	−	0.198592i
$552$	10.4679	−	10.1789i	0.445541	−	0.433241i
$553$	6.74674			0.286900
$554$	12.1261	+	21.0031i	0.515191	+	0.892336i
$555$	0.171264	−	0.166536i	0.00726976	−	0.00706906i
$556$	14.9600			0.634443
$557$	14.7933	+	25.6228i	0.626814	+	1.08567i	0.988187	+	0.153252i	$0.0489746\pi$
$557$	14.7933	+	25.6228i	0.626814	+	1.08567i	−0.361374	+	0.932421i	$0.617692\pi$
$558$	0.420177	−	15.0065i	0.0177875	−	0.635276i
$559$	−27.2626	−	23.4514i	−1.15308	−	0.991887i
$560$	−1.73004	+	2.99651i	−0.0731073	+	0.126626i
$561$	2.36809	−	2.30272i	0.0999810	−	0.0972207i
$562$	−11.9542	+	20.7053i	−0.504259	+	0.873402i
$563$	−18.3886			−0.774989			−0.387495	−	0.921872i	$-0.626659\pi$
$563$	−18.3886			−0.774989			−0.387495	+	0.921872i	$0.626659\pi$
$564$	−10.3169	+	10.0321i	−0.434419	+	0.422426i
$565$	12.6523	+	21.9145i	0.532287	+	0.921949i
$566$	−12.3190	+	21.3371i	−0.517806	+	0.896866i
$567$	−7.79221	+	11.9043i	−0.327242	+	0.499932i
$568$	−4.15444	+	7.19570i	−0.174316	+	0.301925i
$569$	11.9512			0.501022			0.250511	−	0.968114i	$-0.419401\pi$
$569$	11.9512			0.501022			0.250511	+	0.968114i	$0.419401\pi$
$570$	3.76525	+	1.06559i	0.157709	+	0.0446328i
$571$	−7.09377	−	12.2868i	−0.296865	−	0.514186i	0.678552	−	0.734553i	$-0.262608\pi$
$571$	−7.09377	−	12.2868i	−0.296865	−	0.514186i	−0.975417	+	0.220367i	$0.929275\pi$
$572$	−1.71148	+	0.599276i	−0.0715605	+	0.0250570i
$573$	−10.1919	−	40.2836i	−0.425772	−	1.68287i
$574$	−8.59134			−0.358595
$575$	0.883052	+	1.52949i	0.0368258	+	0.0637842i
$576$	2.55508	+	1.57213i	0.106461	+	0.0655054i
$577$	−12.1846			−0.507251			−0.253626	−	0.967302i	$-0.581623\pi$
$577$	−12.1846			−0.507251			−0.253626	+	0.967302i	$0.581623\pi$
$578$	1.31112	+	2.27092i	0.0545352	+	0.0944578i
$579$	−6.95378	+	6.76180i	−0.288989	+	0.281011i
$580$	−5.70680	−	9.88447i	−0.236962	−	0.410430i
$581$	14.9921			0.621976
$582$	3.22293	+	12.7387i	0.133595	+	0.528036i
$583$	5.02668			0.208184
$584$	13.8427			0.572817
$585$	7.19548	+	22.5547i	0.297497	+	0.932520i
$586$	9.05213			0.373940
$587$	44.4050			1.83279			0.916394	−	0.400277i	$-0.131086\pi$
$587$	44.4050			1.83279			0.916394	+	0.400277i	$0.131086\pi$
$588$	−5.58902	+	5.43472i	−0.230487	+	0.224124i
$589$	5.16538			0.212836
$590$	0.658784	+	1.14105i	0.0271217	+	0.0469762i
$591$	−0.0442119	−	0.174748i	−0.00181863	−	0.00718818i
$592$	0.0315070	+	0.0545717i	0.00129493	+	0.00224288i
$593$	−23.5622			−0.967585			−0.483793	−	0.875183i	$-0.660741\pi$
$593$	−23.5622			−0.967585			−0.483793	+	0.875183i	$0.660741\pi$
$594$	1.76871	+	1.92385i	0.0725711	+	0.0789364i
$595$	6.55995	+	11.3622i	0.268932	+	0.465804i
$596$	4.24030			0.173689
$597$	24.4850	−	23.8091i	1.00211	−	0.974440i
$598$	−5.64433	+	29.8654i	−0.230814	+	1.22129i
$599$	8.29582	+	14.3688i	0.338958	+	0.587093i	0.984237	−	0.176854i	$-0.0565921\pi$
$599$	8.29582	+	14.3688i	0.338958	+	0.587093i	−0.645279	+	0.763947i	$0.723259\pi$
$600$	−0.260159	+	0.252976i	−0.0106209	+	0.0103277i
$601$	−18.4642			−0.753172			−0.376586	−	0.926382i	$-0.622902\pi$
$601$	−18.4642			−0.753172			−0.376586	+	0.926382i	$0.622902\pi$
$602$	7.88367	−	13.6549i	0.321314	−	0.556533i
$603$	15.7799	−	8.53081i	0.642609	−	0.347402i
$604$	−5.98383	+	10.3643i	−0.243479	+	0.421717i
$605$	−11.7611	−	20.3709i	−0.478159	−	0.828195i
$606$	29.2717	+	8.28411i	1.18908	+	0.336519i
$607$	−24.4901			−0.994022			−0.497011	−	0.867744i	$-0.665569\pi$
$607$	−24.4901			−0.994022			−0.497011	+	0.867744i	$0.665569\pi$
$608$	−0.516111	+	0.893931i	−0.0209311	+	0.0362537i
$609$	3.50220	+	13.8425i	0.141916	+	0.560927i
$610$	−3.13456	+	5.42922i	−0.126915	+	0.219823i
$611$	5.56293	−	29.4347i	0.225052	−	1.19080i
$612$	10.0067	−	5.40975i	0.404498	−	0.218676i
$613$	−7.45946	−	12.9202i	−0.301285	−	0.521841i	0.675142	−	0.737687i	$-0.264082\pi$
$613$	−7.45946	−	12.9202i	−0.301285	−	0.521841i	−0.976427	+	0.215847i	$0.930749\pi$
$614$	18.3002			0.738538
$615$	19.8238	+	5.61028i	0.799371	+	0.226228i
$616$	−0.397537	−	0.688555i	−0.0160172	−	0.0277427i
$617$	−6.78895			−0.273313			−0.136656	−	0.990618i	$-0.543636\pi$
$617$	−6.78895			−0.273313			−0.136656	+	0.990618i	$0.543636\pi$
$618$	−4.03980	−	15.9674i	−0.162504	−	0.642302i
$619$	−14.8515	+	25.7236i	−0.596934	+	1.03392i	0.396337	+	0.918105i	$0.370281\pi$
$619$	−14.8515	+	25.7236i	−0.596934	+	1.03392i	−0.993271	+	0.115815i	$0.963052\pi$
$620$	5.47632	−	9.48526i	0.219934	−	0.380937i
$621$	42.7486	−	9.55094i	1.71544	−	0.383266i
$622$	5.21196	+	9.02738i	0.208980	+	0.361965i
$623$	−5.07732	+	8.79418i	−0.203419	+	0.352331i
$624$	−6.23338	+	0.380797i	−0.249535	+	0.0152441i
$625$	11.9543	+	20.7054i	0.478171	+	0.828217i
$626$	15.1740	−	26.2821i	0.606475	−	1.05044i
$627$	−0.644653	+	0.626856i	−0.0257450	+	0.0250342i
$628$	8.87870	+	15.3784i	0.354299	+	0.613664i
$629$	0.238936			0.00952702
$630$	−9.13127	+	4.93647i	−0.363798	+	0.196674i
$631$	−2.92669	+	5.06917i	−0.116510	+	0.201800i	−0.918382	−	0.395695i	$-0.870504\pi$
$631$	−2.92669	+	5.06917i	−0.116510	+	0.201800i	0.801873	+	0.597495i	$0.203837\pi$
$632$	2.13387	−	3.69598i	0.0848810	−	0.147018i
$633$	19.9023	−	19.3529i	0.791047	−	0.769208i
$634$	3.71925	−	6.44193i	0.147710	−	0.255842i
$635$	−4.43877	+	7.68817i	−0.176147	+	0.305096i
$636$	16.6570	+	4.71407i	0.660495	+	0.186925i
$637$	3.01363	−	15.9458i	0.119405	−	0.631797i
$638$	2.62268			0.103833
$639$	−21.9275	+	11.8542i	−0.867437	+	0.468946i
$640$	1.09436	+	1.89549i	0.0432584	+	0.0749257i
$641$	−10.4953	−	18.1784i	−0.414539	−	0.718003i	0.580841	−	0.814017i	$-0.302724\pi$
$641$	−10.4953	−	18.1784i	−0.414539	−	0.718003i	−0.995380	+	0.0960144i	$0.969391\pi$
$642$	0.684817	+	2.70675i	0.0270276	+	0.106827i
$643$	21.4715			0.846753			0.423376	−	0.905954i	$-0.360845\pi$
$643$	21.4715			0.846753			0.423376	+	0.905954i	$0.360845\pi$
$644$	−13.3264			−0.525133
$645$	−27.1078	+	26.3594i	−1.06737	+	1.03790i
$646$	1.95699	+	3.38961i	0.0769968	+	0.133362i
$647$	−22.9293	−	39.7147i	−0.901443	−	1.56135i	−0.825622	−	0.564224i	$-0.809175\pi$
$647$	−22.9293	−	39.7147i	−0.901443	−	1.56135i	−0.0758216	−	0.997121i	$-0.524158\pi$
$648$	4.05682	+	8.03382i	0.159367	+	0.315598i
$649$	−0.302758			−0.0118843
$650$	0.140279	−	0.742249i	0.00550220	−	0.0291134i
$651$	−9.82343	+	9.55223i	−0.385011	+	0.374381i
$652$	−10.4495	+	18.0991i	−0.409234	+	0.708814i
$653$	18.3421	−	31.7694i	0.717781	−	1.24323i	−0.244096	−	0.969751i	$-0.578491\pi$
$653$	18.3421	−	31.7694i	0.717781	−	1.24323i	0.961877	−	0.273483i	$-0.0881756\pi$
$654$	29.6958	+	8.40414i	1.16120	+	0.328628i
$655$	4.06084	−	7.03359i	0.158670	−	0.274825i
$656$	−2.71729	+	4.70648i	−0.106092	+	0.183757i
$657$	35.3692	+	21.7626i	1.37989	+	0.849039i
$658$	13.1342			0.512024
$659$	6.30720	+	10.9244i	0.245693	+	0.425554i	0.962326	−	0.271897i	$-0.0876510\pi$
$659$	6.30720	+	10.9244i	0.245693	+	0.425554i	−0.716633	+	0.697451i	$0.754318\pi$
$660$	0.467646	+	1.84838i	0.0182031	+	0.0719480i
$661$	−9.45509	+	16.3767i	−0.367761	+	0.636980i	−0.989215	−	0.146470i	$-0.953209\pi$
$661$	−9.45509	+	16.3767i	−0.367761	+	0.636980i	0.621455	+	0.783450i	$0.286542\pi$
$662$	1.70727	+	2.95708i	0.0663550	+	0.114930i
$663$	−10.5674	+	21.1911i	−0.410404	+	0.822994i
$664$	4.74173	−	8.21292i	0.184015	−	0.318723i
$665$	−1.78578	−	3.09306i	−0.0692496	−	0.119944i
$666$	−0.00529102	+	0.188968i	−0.000205023	+	0.00732235i
$667$	21.9796	−	38.0698i	0.851055	−	1.47407i
$668$	10.5288	−	18.2365i	0.407373	−	0.705591i
$669$	9.19079	+	2.60106i	0.355336	+	0.100563i
$670$	13.0873			0.505605
$671$	−0.720278	−	1.24756i	−0.0278060	−	0.0481615i
$672$	−0.671597	−	2.65450i	−0.0259074	−	0.102399i
$673$	−42.6161			−1.64273			−0.821365	−	0.570402i	$-0.806787\pi$
$673$	−42.6161			−1.64273			−0.821365	+	0.570402i	$0.806787\pi$
$674$	−6.02371	−	10.4334i	−0.232025	−	0.401879i
$675$	−1.06244	+	0.237371i	−0.0408932	+	0.00913640i
$676$	10.1604	−	8.10965i	0.390784	−	0.311910i
$677$	−0.843701	+	1.46133i	−0.0324261	+	0.0561636i	−0.881783	−	0.471655i	$-0.843657\pi$
$677$	−0.843701	+	1.46133i	−0.0324261	+	0.0561636i	0.849357	+	0.527819i	$0.176990\pi$
$678$	−19.2682	−	5.45304i	−0.739989	−	0.209423i
$679$	5.99656	−	10.3863i	0.230127	−	0.398591i
$680$	8.29919			0.318260
$681$	9.09889	+	35.9635i	0.348670	+	1.37813i
$682$	1.25838	+	2.17958i	0.0481859	+	0.0834604i
$683$	8.86025	−	15.3464i	0.339028	−	0.587214i	−0.645222	−	0.763995i	$-0.723235\pi$
$683$	8.86025	−	15.3464i	0.339028	−	0.587214i	0.984250	+	0.176781i	$0.0565686\pi$
$684$	−2.72408	+	1.47267i	−0.104158	+	0.0563088i
$685$	5.22560	−	9.05100i	0.199660	−	0.345821i
$686$	18.1813			0.694166
$687$	10.0633	+	39.7754i	0.383939	+	1.51753i
$688$	−4.98693	−	8.63762i	−0.190125	−	0.329306i
$689$	−34.0115	+	11.9092i	−1.29574	+	0.453704i
$690$	30.7495	+	8.70234i	1.17061	+	0.331292i
$691$	−9.61795			−0.365884			−0.182942	−	0.983124i	$-0.558562\pi$
$691$	−9.61795			−0.365884			−0.182942	+	0.983124i	$0.558562\pi$
$692$	−5.99936	−	10.3912i	−0.228061	−	0.395014i
$693$	0.0667592	−	2.38429i	0.00253597	−	0.0905717i
$694$	7.72226			0.293133
$695$	16.3716	+	28.3564i	0.621009	+	1.07562i
$696$	8.69086	+	2.45958i	0.329426	+	0.0932301i
$697$	10.3034	+	17.8461i	0.390270	+	0.675968i
$698$	26.4081			0.999562
$699$	9.89257	+	2.79967i	0.374171	+	0.105893i
$700$	0.331202			0.0125183
$701$	−0.852825			−0.0322108			−0.0161054	−	0.999870i	$-0.505127\pi$
$701$	−0.852825			−0.0322108			−0.0161054	+	0.999870i	$0.505127\pi$
$702$	−16.5254	−	8.82671i	−0.623711	−	0.333143i
$703$	−0.0650444			−0.00245320
$704$	−0.502937			−0.0189551
$705$	−30.3060	−	8.57683i	−1.14139	−	0.323022i
$706$	−34.2383			−1.28858
$707$	−13.8830	−	24.0460i	−0.522123	−	0.904344i
$708$	−1.00326	−	0.283930i	−0.0377048	−	0.0106707i
$709$	−12.9136	−	22.3670i	−0.484980	−	0.840011i	0.514871	−	0.857268i	$-0.327840\pi$
$709$	−12.9136	−	22.3670i	−0.484980	−	0.840011i	−0.999851	+	0.0172572i	$0.994507\pi$
$710$	−18.1858			−0.682501
$711$	11.2628	−	6.08878i	0.422387	−	0.228347i
$712$	3.21174	+	5.56289i	0.120365	+	0.208478i
$713$	42.1839			1.57980
$714$	−9.99012	−	2.82728i	−0.373871	−	0.105808i
$715$	−3.00889	−	2.58826i	−0.112526	−	0.0967954i
$716$	−1.33168	−	2.30654i	−0.0497673	−	0.0861995i
$717$	−2.47960	−	9.80068i	−0.0926025	−	0.366013i
$718$	20.0071			0.746658
$719$	−5.75979	+	9.97624i	−0.214804	+	0.372051i	−0.953212	−	0.302303i	$-0.902245\pi$
$719$	−5.75979	+	9.97624i	−0.214804	+	0.372051i	0.738408	+	0.674354i	$0.235578\pi$
$720$	−0.183778	+	6.56359i	−0.00684900	+	0.244610i
$721$	−7.51641	+	13.0188i	−0.279926	+	0.484846i
$722$	8.96726	+	15.5317i	0.333727	+	0.578032i
$723$	−4.92050	−	19.4484i	−0.182995	−	0.723293i
$724$	−8.09512			−0.300853
$725$	−0.546262	+	0.946154i	−0.0202877	+	0.0351393i
$726$	17.9110	+	5.06895i	0.664739	+	0.188126i
$727$	−9.39286	+	16.2689i	−0.348362	+	0.603381i	−0.985959	−	0.166990i	$-0.946595\pi$
$727$	−9.39286	+	16.2689i	−0.348362	+	0.603381i	0.637597	+	0.770370i	$0.279929\pi$
$728$	4.32114	+	3.71706i	0.160152	+	0.137763i
$729$	−2.26471	+	26.9049i	−0.0838782	+	0.996476i
$730$	15.1489	+	26.2387i	0.560687	+	0.971139i
$731$	−37.8189			−1.39878
$732$	−1.21683	−	4.80955i	−0.0449754	−	0.177766i
$733$	18.9323	+	32.7917i	0.699279	+	1.21119i	0.968717	+	0.248169i	$0.0798290\pi$
$733$	18.9323	+	32.7917i	0.699279	+	1.21119i	−0.269437	+	0.963018i	$0.586838\pi$
$734$	27.7949			1.02593
$735$	−16.4178	−	4.64638i	−0.605581	−	0.171384i
$736$	−4.21490	+	7.30043i	−0.155363	+	0.269097i
$737$	−1.50363	+	2.60437i	−0.0553871	+	0.0959332i
$738$	−14.3421	+	7.75349i	−0.527939	+	0.285410i
$739$	−3.39393	−	5.87846i	−0.124848	−	0.216243i	0.796826	−	0.604209i	$-0.206511\pi$
$739$	−3.39393	−	5.87846i	−0.124848	−	0.216243i	−0.921673	+	0.387967i	$0.873178\pi$
$740$	−0.0689599	+	0.119442i	−0.00253502	+	0.00439078i
$741$	2.87671	−	5.76874i	0.105679	−	0.211920i
$742$	−7.90010	−	13.6834i	−0.290022	−	0.502333i
$743$	5.55678	−	9.62462i	0.203858	−	0.353093i	−0.745910	−	0.666047i	$-0.767985\pi$
$743$	5.55678	−	9.62462i	0.203858	−	0.353093i	0.949768	+	0.312954i	$0.101318\pi$
$744$	2.12590	+	8.40265i	0.0779392	+	0.308056i
$745$	4.64041	+	8.03743i	0.170012	+	0.294469i
$746$	−12.3059			−0.450550
$747$	25.0272	−	13.5300i	0.915699	−	0.495037i
$748$	−0.953518	+	1.65154i	−0.0348641	+	0.0603863i
$749$	1.27417	−	2.20692i	0.0465570	−	0.0806391i
$750$	−19.0028	−	5.37793i	−0.693883	−	0.196374i
$751$	3.58697	−	6.21282i	0.130891	−	0.226709i	−0.793130	−	0.609053i	$-0.791550\pi$
$751$	3.58697	−	6.21282i	0.130891	−	0.226709i	0.924020	+	0.382344i	$0.124883\pi$
$752$	4.15412	−	7.19514i	0.151485	−	0.262380i
$753$	3.21055	−	3.12191i	0.116999	−	0.113769i
$754$	−17.7456	+	6.21365i	−0.646257	+	0.226288i
$755$	−26.1938			−0.953292
$756$	2.45723	−	7.83828i	0.0893687	−	0.285075i
$757$	−18.5543	−	32.1370i	−0.674368	−	1.16804i	−0.976653	−	0.214822i	$-0.931083\pi$
$757$	−18.5543	−	32.1370i	−0.674368	−	1.16804i	0.302286	−	0.953217i	$-0.402250\pi$
$758$	−4.55621	−	7.89159i	−0.165489	−	0.286635i
$759$	−5.26466	+	5.11932i	−0.191095	+	0.185820i
$760$	−2.25925			−0.0819514
$761$	−17.1003			−0.619887			−0.309943	−	0.950755i	$-0.600310\pi$
$761$	−17.1003			−0.619887			−0.309943	+	0.950755i	$0.600310\pi$
$762$	−1.72312	−	6.81067i	−0.0624221	−	0.246724i
$763$	−14.0841	−	24.3944i	−0.509880	−	0.883137i
$764$	11.9953	+	20.7764i	0.433974	+	0.751665i
$765$	21.2051	+	13.0474i	0.766671	+	0.471730i
$766$	−5.01951			−0.181362
$767$	2.04852	−	0.717294i	0.0739679	−	0.0259000i
$768$	−1.66659	−	0.471659i	−0.0601381	−	0.0170195i
$769$	12.2695	−	21.2513i	0.442448	−	0.766343i	−0.555422	−	0.831568i	$-0.687443\pi$
$769$	12.2695	−	21.2513i	0.442448	−	0.766343i	0.997871	+	0.0652257i	$0.0207767\pi$
$770$	0.870098	−	1.50705i	0.0313561	−	0.0543104i
$771$	26.8712	−	26.1294i	0.967744	−	0.941027i
$772$	2.79996	−	4.84966i	0.100773	−	0.174543i
$773$	11.3259	−	19.6170i	0.407363	−	0.705573i	−0.587231	−	0.809420i	$-0.699782\pi$
$773$	11.3259	−	19.6170i	0.407363	−	0.705573i	0.994593	+	0.103847i	$0.0331152\pi$
$774$	0.837465	−	29.9099i	0.0301021	−	1.07509i
$775$	−1.04840			−0.0376597
$776$	−3.79321	−	6.57004i	−0.136168	−	0.235851i
$777$	0.123700	−	0.120285i	0.00443773	−	0.00431521i
$778$	11.1313	−	19.2800i	0.399077	−	0.691222i
$779$	−2.80485	−	4.85814i	−0.100494	−	0.174061i
$780$	−7.54335	−	11.3986i	−0.270095	−	0.408134i
$781$	2.08942	−	3.61898i	0.0747653	−	0.129497i
$782$	15.9821	+	27.6818i	0.571518	+	0.989899i
$783$	18.3390	+	19.9476i	0.655383	+	0.712868i
$784$	2.25043	−	3.89786i	0.0803726	−	0.139209i
$785$	−19.4330	+	33.6589i	−0.693593	+	1.20134i
$786$	1.57641	+	6.23080i	0.0562288	+	0.222245i
$787$	31.6876			1.12954			0.564771	−	0.825248i	$-0.308964\pi$
$787$	31.6876			1.12954			0.564771	+	0.825248i	$0.308964\pi$
$788$	0.0520349	+	0.0901272i	0.00185367	+	0.00321065i
$789$	−22.8654	−	6.47109i	−0.814031	−	0.230377i
$790$	9.34091			0.332335
$791$	9.13851	+	15.8284i	0.324928	+	0.562792i
$792$	−1.28504	−	0.790681i	−0.0456619	−	0.0280956i
$793$	7.82925	+	6.73475i	0.278025	+	0.239158i
$794$	−13.0759	+	22.6481i	−0.464045	+	0.803750i
$795$	9.29334	+	36.7321i	0.329601	+	1.30275i
$796$	−9.85896	+	17.0762i	−0.349441	+	0.605250i
$797$	29.3558			1.03983			0.519917	−	0.854217i	$-0.325963\pi$
$797$	29.3558			1.03983			0.519917	+	0.854217i	$0.325963\pi$
$798$	2.71956	+	0.769655i	0.0962712	+	0.0272455i
$799$	−15.7516	−	27.2826i	−0.557251	−	0.965188i
$800$	0.104754	−	0.181438i	0.00370360	−	0.00641482i
$801$	−0.539353	+	19.2629i	−0.0190571	+	0.680620i
$802$	13.0125	−	22.5384i	0.459488	−	0.795857i
$803$	−6.96202			−0.245684
$804$	−7.42504	+	7.22005i	−0.261861	+	0.254632i
$805$	−14.5839	−	25.2600i	−0.514014	−	0.890298i
$806$	−13.6783	−	11.7661i	−0.481797	−	0.414444i
$807$	13.0387	−	12.6787i	0.458983	−	0.446311i
$808$	−17.5638			−0.617891
$809$	12.6075	+	21.8369i	0.443257	+	0.767743i	0.997929	−	0.0643259i	$-0.0204897\pi$
$809$	12.6075	+	21.8369i	0.443257	+	0.767743i	−0.554672	+	0.832069i	$0.687156\pi$
$810$	−10.7884	+	16.4815i	−0.379065	+	0.579102i
$811$	19.9539			0.700677			0.350338	−	0.936623i	$-0.386067\pi$
$811$	19.9539			0.700677			0.350338	+	0.936623i	$0.386067\pi$
$812$	−4.12190	−	7.13934i	−0.144650	−	0.250542i
$813$	11.3958	+	45.0421i	0.399668	+	1.57969i
$814$	−0.0158460	−	0.0274461i	−0.000555402	−	0.000961985i
$815$	−45.7420			−1.60227
$816$	−4.70853	+	4.57854i	−0.164832	+	0.160281i
$817$	10.2953			0.360185
$818$	−11.7798			−0.411872
$819$	5.19714	+	16.2907i	0.181603	+	0.569245i
$820$	−11.8948			−0.415383
$821$	−42.8230			−1.49453			−0.747266	−	0.664525i	$-0.768634\pi$
$821$	−42.8230			−1.49453			−0.747266	+	0.664525i	$0.768634\pi$
$822$	2.02857	+	8.01795i	0.0707544	+	0.279658i
$823$	−28.2340			−0.984177			−0.492088	−	0.870545i	$-0.663766\pi$
$823$	−28.2340			−0.984177			−0.492088	+	0.870545i	$0.663766\pi$
$824$	4.75462	+	8.23524i	0.165635	+	0.286888i
$825$	0.130843	−	0.127231i	0.00455538	−	0.00442962i
$826$	0.475826	+	0.824154i	0.0165561	+	0.0286760i
$827$	19.0288			0.661696			0.330848	−	0.943684i	$-0.392665\pi$
$827$	19.0288			0.661696			0.330848	+	0.943684i	$0.392665\pi$
$828$	−22.2466	+	12.0268i	−0.773123	+	0.417959i
$829$	17.7356	+	30.7190i	0.615983	+	1.06691i	0.990211	+	0.139577i	$0.0445742\pi$
$829$	17.7356	+	30.7190i	0.615983	+	1.06691i	−0.374229	+	0.927337i	$0.622092\pi$
$830$	20.7566			0.720473
$831$	−10.3031	−	40.7231i	−0.357409	−	1.41267i
$832$	3.40297	−	1.19155i	0.117977	−	0.0413097i
$833$	−8.53320	−	14.7799i	−0.295658	−	0.512094i
$834$	−24.9322	−	7.05600i	−0.863331	−	0.244329i
$835$	46.0894			1.59499
$836$	0.259571	−	0.449590i	0.00897746	−	0.0155494i
$837$	−7.77822	+	24.8116i	−0.268855	+	0.857614i
$838$	−14.9908	+	25.9648i	−0.517848	+	0.896940i
$839$	−28.8184	−	49.9149i	−0.994921	−	1.72325i	−0.584632	−	0.811299i	$-0.698761\pi$
$839$	−28.8184	−	49.9149i	−0.994921	−	1.72325i	−0.410289	−	0.911955i	$-0.634572\pi$
$840$	4.29660	−	4.17798i	0.148247	−	0.144154i
$841$	−1.80649			−0.0622926
$842$	−9.62578	+	16.6723i	−0.331726	+	0.574567i
$843$	29.6887	−	28.8691i	1.02253	−	0.994304i
$844$	−8.01373	+	13.8802i	−0.275844	+	0.477775i
$845$	26.4909	+	10.3840i	0.911313	+	0.357221i
$846$	21.9258	−	11.8533i	0.753824	−	0.407526i
$847$	−8.49482	−	14.7135i	−0.291886	−	0.505561i
$848$	−9.99466			−0.343218
$849$	30.5946	−	29.7500i	1.05000	−	1.02102i
$850$	−0.397205	−	0.687979i	−0.0136240	−	0.0235975i
$851$	−0.531195			−0.0182091
$852$	10.3177	−	10.0328i	0.353478	−	0.343719i
$853$	−20.3319	+	35.2159i	−0.696152	+	1.20577i	0.273639	+	0.961832i	$0.411773\pi$
$853$	−20.3319	+	35.2159i	−0.696152	+	1.20577i	−0.969791	+	0.243938i	$0.921561\pi$
$854$	−2.26403	+	3.92141i	−0.0774735	+	0.134188i
$855$	−5.77254	−	3.55182i	−0.197417	−	0.121470i
$856$	−0.805993	−	1.39602i	−0.0275483	−	0.0477150i
$857$	7.25844	−	12.5720i	0.247944	−	0.429451i	−0.715011	−	0.699113i	$-0.753579\pi$
$857$	7.25844	−	12.5720i	0.247944	−	0.429451i	0.962955	+	0.269662i	$0.0869119\pi$
$858$	3.13499	−	0.191517i	0.107027	−	0.00653828i
$859$	−10.3569	−	17.9386i	−0.353372	−	0.612058i	0.633466	−	0.773770i	$-0.281632\pi$
$859$	−10.3569	−	17.9386i	−0.353372	−	0.612058i	−0.986838	+	0.161713i	$0.948298\pi$
$860$	10.9150	−	18.9053i	0.372198	−	0.644667i
$861$	14.3183	+	4.05218i	0.487966	+	0.138098i
$862$	−4.11765	−	7.13198i	−0.140248	−	0.242916i
$863$	−42.2200			−1.43719			−0.718594	−	0.695430i	$-0.755214\pi$
$863$	−42.2200			−1.43719			−0.718594	+	0.695430i	$0.755214\pi$
$864$	−3.51677	−	3.82523i	−0.119643	−	0.130137i
$865$	13.1309	−	22.7434i	0.446465	−	0.773299i
$866$	1.34932	−	2.33708i	0.0458516	−	0.0794173i
$867$	−1.11400	−	4.40310i	−0.0378334	−	0.149537i
$868$	3.95543	−	6.85100i	0.134256	−	0.232538i
$869$	−1.07320	+	1.85884i	−0.0364059	+	0.0630569i
$870$	4.84882	+	19.1651i	0.164391	+	0.649757i
$871$	4.00363	−	21.1841i	0.135658	−	0.717796i
$872$	−17.8183			−0.603402
$873$	0.637001	−	22.7504i	0.0215592	−	0.769983i
$874$	−4.35072	−	7.53567i	−0.147165	−	0.254898i
$875$	9.01263	+	15.6103i	0.304682	+	0.527726i
$876$	−23.0702	−	6.52905i	−0.779471	−	0.220596i
$877$	0.304202			0.0102722			0.00513609	−	0.999987i	$-0.498365\pi$
$877$	0.304202			0.0102722			0.00513609	+	0.999987i	$0.498365\pi$
$878$	29.8318			1.00677
$879$	−15.0862	−	4.26952i	−0.508846	−	0.144007i
$880$	−0.550393	−	0.953309i	−0.0185538	−	0.0321361i
$881$	8.50208	+	14.7260i	0.286442	+	0.496133i	0.972958	−	0.230982i	$-0.0741939\pi$
$881$	8.50208	+	14.7260i	0.286442	+	0.496133i	−0.686516	+	0.727115i	$0.740861\pi$
$882$	11.8780	−	6.42137i	0.399952	−	0.216219i
$883$	−31.1680			−1.04889			−0.524443	−	0.851446i	$-0.675726\pi$
$883$	−31.1680			−1.04889			−0.524443	+	0.851446i	$0.675726\pi$
$884$	2.53887	−	13.4337i	0.0853914	−	0.451825i
$885$	−0.559741	−	2.21239i	−0.0188155	−	0.0743685i
$886$	1.33729	−	2.31625i	0.0449270	−	0.0778159i
$887$	−6.41145	+	11.1050i	−0.215276	+	0.372868i	−0.953358	−	0.301843i	$-0.902398\pi$
$887$	−6.41145	+	11.1050i	−0.215276	+	0.372868i	0.738082	+	0.674711i	$0.235732\pi$
$888$	−0.0267701	−	0.105809i	−0.000898347	−	0.00355073i
$889$	−3.20603	+	5.55300i	−0.107527	+	0.186242i
$890$	−7.02959	+	12.1756i	−0.235632	+	0.408127i
$891$	−2.04032	−	4.04050i	−0.0683534	−	0.135362i
$892$	−5.51471			−0.184646
$893$	4.28797	+	7.42699i	0.143492	+	0.248535i
$894$	−7.06686	−	1.99998i	−0.236351	−	0.0668892i
$895$	2.91468	−	5.04837i	0.0974269	−	0.168748i
$896$	0.790433	+	1.36907i	0.0264065	+	0.0457374i
$897$	23.4931	−	47.1114i	0.784412	−	1.57300i
$898$	−1.88447	+	3.26401i	−0.0628857	+	0.108921i
$899$	13.0476	+	22.5991i	0.435163	+	0.753724i
$900$	0.552898	−	0.298903i	0.0184299	−	0.00996343i
$901$	−18.9489	+	32.8204i	−0.631279	+	1.09341i
$902$	1.36662	−	2.36706i	0.0455036	−	0.0788146i
$903$	−19.5794	+	19.0388i	−0.651560	+	0.633572i
$904$	11.5614			0.384526
$905$	−8.85897	−	15.3442i	−0.294482	−	0.510058i
$906$	14.8610	−	14.4508i	0.493725	−	0.480094i
$907$	41.7253			1.38546			0.692732	−	0.721195i	$-0.256407\pi$
$907$	41.7253			1.38546			0.692732	+	0.721195i	$0.256407\pi$
$908$	−10.7089	−	18.5484i	−0.355387	−	0.615549i
$909$	−44.8768	−	27.6125i	−1.48847	−	0.915850i
$910$	−2.31675	+	12.2585i	−0.0767996	+	0.406364i
$911$	2.74971	−	4.76264i	0.0911020	−	0.157793i	−0.816873	−	0.576817i	$-0.804294\pi$
$911$	2.74971	−	4.76264i	0.0911020	−	0.157793i	0.907975	+	0.419024i	$0.137628\pi$
$912$	1.28178	−	1.24639i	0.0424439	−	0.0412722i
$913$	−2.38479	+	4.13058i	−0.0789250	+	0.136702i
$914$	22.8754			0.756649
$915$	7.78479	−	7.56987i	0.257357	−	0.250252i
$916$	−11.8440	−	20.5144i	−0.391336	−	0.677814i
$917$	2.93306	−	5.08021i	0.0968581	−	0.167763i
$918$	−19.2287	+	4.29610i	−0.634642	+	0.141792i
$919$	−20.2614	+	35.0938i	−0.668362	+	1.15764i	0.310000	+	0.950736i	$0.399671\pi$
$919$	−20.2614	+	35.0938i	−0.668362	+	1.15764i	−0.978362	+	0.206900i	$0.933662\pi$
$920$	−18.4505			−0.608295
$921$	−30.4991	−	8.63148i	−1.00498	−	0.284417i
$922$	−9.21067	−	15.9533i	−0.303337	−	0.525395i
$923$	−5.56335	+	29.4370i	−0.183120	+	0.968930i
$924$	0.337770	+	1.33504i	0.0111118	+	0.0439197i
$925$	0.0132019			0.000434075
$926$	9.45153	+	16.3705i	0.310596	+	0.537969i
$927$	−0.798452	+	28.5165i	−0.0262246	+	0.936606i
$928$	−5.21474			−0.171182
$929$	15.0423	+	26.0541i	0.493523	+	0.854807i	0.999972	−	0.00746317i	$-0.00237562\pi$
$929$	15.0423	+	26.0541i	0.493523	+	0.854807i	−0.506449	+	0.862270i	$0.669042\pi$
$930$	−13.6006	+	13.2251i	−0.445982	+	0.433669i
$931$	2.32295	+	4.02346i	0.0761315	+	0.131864i
$932$	−5.93580			−0.194434
$933$	−4.42838	−	17.5032i	−0.144979	−	0.573031i
$934$	24.6818			0.807613
$935$	−4.17397			−0.136503
$936$	10.5681	+	2.30539i	0.345430	+	0.0753542i
$937$	5.81770			0.190056			0.0950279	−	0.995475i	$-0.469706\pi$
$937$	5.81770			0.190056			0.0950279	+	0.995475i	$0.469706\pi$
$938$	9.45266			0.308640
$939$	−37.6851	+	36.6447i	−1.22981	+	1.19585i
$940$	18.1844			0.593110
$941$	16.7402	+	28.9948i	0.545714	+	0.945204i	0.998562	+	0.0536160i	$0.0170747\pi$
$941$	16.7402	+	28.9948i	0.545714	+	0.945204i	−0.452848	+	0.891588i	$0.649592\pi$
$942$	−7.54385	−	29.8172i	−0.245792	−	0.971498i
$943$	−22.9062	−	39.6748i	−0.745930	−	1.29199i
$944$	0.601981			0.0195928
$945$	17.5465	−	3.92024i	0.570786	−	0.127526i
$946$	2.50811	+	4.34418i	0.0815457	+	0.141241i
$947$	−43.5979			−1.41674			−0.708371	−	0.705841i	$-0.750569\pi$
$947$	−43.5979			−1.41674			−0.708371	+	0.705841i	$0.750569\pi$
$948$	−5.29955	+	5.15324i	−0.172121	+	0.167369i
$949$	47.1064	−	16.4944i	1.52914	−	0.535430i
$950$	0.108129	+	0.187285i	0.00350817	+	0.00607632i
$951$	−9.23688	+	8.98187i	−0.299526	+	0.291257i
$952$	5.99433			0.194277
$953$	−29.1665	+	50.5179i	−0.944795	+	1.63643i	−0.188635	+	0.982047i	$0.560406\pi$
$953$	−29.1665	+	50.5179i	−0.944795	+	1.63643i	−0.756160	+	0.654386i	$0.772927\pi$
$954$	−25.5371	−	15.7129i	−0.826794	−	0.508724i
$955$	−26.2543	+	45.4738i	−0.849569	+	1.47150i
$956$	2.91836	+	5.05475i	0.0943865	+	0.163482i
$957$	−4.37095	−	1.23701i	−0.141293	−	0.0399869i
$958$	36.6440			1.18391
$959$	3.77434	−	6.53734i	0.121880	−	0.211102i
$960$	−0.929831	−	3.67517i	−0.0300102	−	0.118616i
$961$	2.97934	−	5.16036i	0.0961076	−	0.166463i
$962$	0.172242	+	0.148163i	0.00555332	+	0.00477698i
$963$	0.135352	−	4.83406i	0.00436165	−	0.155775i
$964$	5.79116	+	10.0306i	0.186521	+	0.323063i
$965$	12.2566			0.394555
$966$	22.2097	+	6.28551i	0.714585	+	0.202233i
$967$	−7.60966	−	13.1803i	−0.244710	−	0.423850i	0.717340	−	0.696723i	$-0.245359\pi$
$967$	−7.60966	−	13.1803i	−0.244710	−	0.423850i	−0.962050	+	0.272873i	$0.912026\pi$
$968$	−10.7471			−0.345423
$969$	−1.66277	−	6.57214i	−0.0534159	−	0.211127i
$970$	8.30228	−	14.3800i	0.266570	−	0.461713i
$971$	9.56971	−	16.5752i	0.307107	−	0.531924i	−0.670621	−	0.741800i	$-0.733972\pi$
$971$	9.56971	−	16.5752i	0.307107	−	0.531924i	0.977728	+	0.209875i	$0.0673058\pi$
$972$	−2.97185	−	15.3026i	−0.0953222	−	0.490830i
$973$	11.8248	+	20.4812i	0.379087	+	0.656598i
$974$	−4.39414	+	7.61087i	−0.140797	+	0.243868i
$975$	−0.583877	+	1.17086i	−0.0186990	+	0.0374977i
$976$	1.43215	+	2.48055i	0.0458419	+	0.0794004i
$977$	23.3594	−	40.4597i	0.747335	−	1.29442i	−0.201761	−	0.979435i	$-0.564666\pi$
$977$	23.3594	−	40.4597i	0.747335	−	1.29442i	0.949096	−	0.314987i	$-0.102000\pi$
$978$	25.9517	−	25.2352i	0.829842	−	0.806932i
$979$	−1.61530	−	2.79778i	−0.0516252	−	0.0894175i
$980$	9.85113			0.314683
$981$	−45.5270	−	28.0126i	−1.45356	−	0.894373i
$982$	8.82292	−	15.2817i	0.281551	−	0.487660i
$983$	−4.32744	+	7.49535i	−0.138024	+	0.239064i	−0.926749	−	0.375682i	$-0.877408\pi$
$983$	−4.32744	+	7.49535i	−0.138024	+	0.239064i	0.788725	+	0.614747i	$0.210742\pi$
$984$	6.74848	−	6.56217i	0.215134	−	0.209194i
$985$	−0.113890	+	0.197263i	−0.00362883	+	0.00628532i
$986$	−9.88663	+	17.1242i	−0.314855	+	0.545344i
$987$	−21.8894	−	6.19486i	−0.696747	−	0.197185i
$988$	−0.691143	+	3.65699i	−0.0219882	+	0.116344i
$989$	84.0778			2.67352
$990$	0.0924286	−	3.30107i	0.00293757	−	0.104915i
$991$	−2.67182	−	4.62773i	−0.0848733	−	0.147005i	0.820464	−	0.571698i	$-0.193715\pi$
$991$	−2.67182	−	4.62773i	−0.0848733	−	0.147005i	−0.905337	+	0.424693i	$0.860382\pi$
$992$	−2.50207	−	4.33370i	−0.0794407	−	0.137595i
$993$	−1.45060	−	5.73350i	−0.0460332	−	0.181947i
$994$	−13.1352			−0.416624
$995$	−43.1570			−1.36817
$996$	−11.7762	+	11.4511i	−0.373144	+	0.362843i
$997$	−2.19341	−	3.79910i	−0.0694661	−	0.120319i	0.829200	−	0.558952i	$-0.188796\pi$
$997$	−2.19341	−	3.79910i	−0.0694661	−	0.120319i	−0.898666	+	0.438633i	$0.855463\pi$
$998$	−19.3003	−	33.4291i	−0.610940	−	1.05818i
$999$	0.0979464	−	0.312437i	0.00309889	−	0.00988507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.f.d.133.1	✓	12
3.2	odd	2		702.2.f.c.289.2		12
9.4	even	3		234.2.g.c.211.4	yes	12
9.5	odd	6		702.2.g.d.523.2		12
13.9	even	3		234.2.g.c.61.4	yes	12
39.35	odd	6		702.2.g.d.451.2		12
117.22	even	3	inner	234.2.f.d.139.1	yes	12
117.113	odd	6		702.2.f.c.685.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.f.d.133.1	✓	12	1.1	even	1	trivial
234.2.f.d.139.1	yes	12	117.22	even	3	inner
234.2.g.c.61.4	yes	12	13.9	even	3
234.2.g.c.211.4	yes	12	9.4	even	3
702.2.f.c.289.2		12	3.2	odd	2
702.2.f.c.685.2		12	117.113	odd	6
702.2.g.d.451.2		12	39.35	odd	6
702.2.g.d.523.2		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} +(-1.66659 - 0.471659i) q^{3} +1.00000 q^{4} +(1.09436 + 1.89549i) q^{5} +(-1.66659 - 0.471659i) q^{6} +(0.790433 + 1.36907i) q^{7} +1.00000 q^{8} +(2.55508 + 1.57213i) q^{9} +(1.09436 + 1.89549i) q^{10} -0.502937 q^{11} +(-1.66659 - 0.471659i) q^{12} +(3.40297 - 1.19155i) q^{13} +(0.790433 + 1.36907i) q^{14} +(-0.929831 - 3.67517i) q^{15} +1.00000 q^{16} +(1.89590 - 3.28380i) q^{17} +(2.55508 + 1.57213i) q^{18} +(-0.516111 + 0.893931i) q^{19} +(1.09436 + 1.89549i) q^{20} +(-0.671597 - 2.65450i) q^{21} -0.502937 q^{22} +(-4.21490 + 7.30043i) q^{23} +(-1.66659 - 0.471659i) q^{24} +(0.104754 - 0.181438i) q^{25} +(3.40297 - 1.19155i) q^{26} +(-3.51677 - 3.82523i) q^{27} +(0.790433 + 1.36907i) q^{28} -5.21474 q^{29} +(-0.929831 - 3.67517i) q^{30} +(-2.50207 - 4.33370i) q^{31} +1.00000 q^{32} +(0.838191 + 0.237215i) q^{33} +(1.89590 - 3.28380i) q^{34} +(-1.73004 + 2.99651i) q^{35} +(2.55508 + 1.57213i) q^{36} +(0.0315070 + 0.0545717i) q^{37} +(-0.516111 + 0.893931i) q^{38} +(-6.23338 + 0.380797i) q^{39} +(1.09436 + 1.89549i) q^{40} +(-2.71729 + 4.70648i) q^{41} +(-0.671597 - 2.65450i) q^{42} +(-4.98693 - 8.63762i) q^{43} -0.502937 q^{44} +(-0.183778 + 6.56359i) q^{45} +(-4.21490 + 7.30043i) q^{46} +(4.15412 - 7.19514i) q^{47} +(-1.66659 - 0.471659i) q^{48} +(2.25043 - 3.89786i) q^{49} +(0.104754 - 0.181438i) q^{50} +(-4.70853 + 4.57854i) q^{51} +(3.40297 - 1.19155i) q^{52} -9.99466 q^{53} +(-3.51677 - 3.82523i) q^{54} +(-0.550393 - 0.953309i) q^{55} +(0.790433 + 1.36907i) q^{56} +(1.28178 - 1.24639i) q^{57} -5.21474 q^{58} +0.601981 q^{59} +(-0.929831 - 3.67517i) q^{60} +(1.43215 + 2.48055i) q^{61} +(-2.50207 - 4.33370i) q^{62} +(-0.132739 + 4.74074i) q^{63} +1.00000 q^{64} +(5.98265 + 5.14629i) q^{65} +(0.838191 + 0.237215i) q^{66} +(2.98971 - 5.17833i) q^{67} +(1.89590 - 3.28380i) q^{68} +(10.4679 - 10.1789i) q^{69} +(-1.73004 + 2.99651i) q^{70} +(-4.15444 + 7.19570i) q^{71} +(2.55508 + 1.57213i) q^{72} +13.8427 q^{73} +(0.0315070 + 0.0545717i) q^{74} +(-0.260159 + 0.252976i) q^{75} +(-0.516111 + 0.893931i) q^{76} +(-0.397537 - 0.688555i) q^{77} +(-6.23338 + 0.380797i) q^{78} +(2.13387 - 3.69598i) q^{79} +(1.09436 + 1.89549i) q^{80} +(4.05682 + 8.03382i) q^{81} +(-2.71729 + 4.70648i) q^{82} +(4.74173 - 8.21292i) q^{83} +(-0.671597 - 2.65450i) q^{84} +8.29919 q^{85} +(-4.98693 - 8.63762i) q^{86} +(8.69086 + 2.45958i) q^{87} -0.502937 q^{88} +(3.21174 + 5.56289i) q^{89} +(-0.183778 + 6.56359i) q^{90} +(4.32114 + 3.71706i) q^{91} +(-4.21490 + 7.30043i) q^{92} +(2.12590 + 8.40265i) q^{93} +(4.15412 - 7.19514i) q^{94} -2.25925 q^{95} +(-1.66659 - 0.471659i) q^{96} +(-3.79321 - 6.57004i) q^{97} +(2.25043 - 3.89786i) q^{98} +(-1.28504 - 0.790681i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more