LMFDB - Embedded newform 234.2.z.a.227.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.10
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.22215 - 1.22733i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.02684 - 3.83221i) q^{5} +(-1.50183 + 0.862849i) q^{6} +(1.13597 + 1.13597i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.0126964 + 2.99997i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.22215 - 1.22733i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.02684 - 3.83221i) q^{5} +(-1.50183 + 0.862849i) q^{6} +(1.13597 + 1.13597i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.0126964 + 2.99997i) q^{9} +(-3.43586 - 1.98370i) q^{10} +(-4.79442 - 1.28466i) q^{11} +(0.444746 + 1.67398i) q^{12} +(3.50956 + 0.826424i) q^{13} +(1.39127 - 0.803251i) q^{14} +(-5.95834 + 3.42326i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.584080 - 1.01166i) q^{17} +(2.89447 + 0.788714i) q^{18} +(-4.16646 - 1.11640i) q^{19} +(-2.80537 + 2.80537i) q^{20} +(0.00588804 - 2.78254i) q^{21} +(-2.48178 + 4.29856i) q^{22} +3.27000 q^{23} +(1.73205 + 0.00366513i) q^{24} +(-9.30128 - 5.37010i) q^{25} +(1.70661 - 3.17608i) q^{26} +(3.69749 - 3.65084i) q^{27} +(-0.415793 - 1.55176i) q^{28} +(6.50012 - 3.75285i) q^{29} +(1.76448 + 6.64132i) q^{30} +(7.25468 + 1.94388i) q^{31} +(0.965926 - 0.258819i) q^{32} +(4.28280 + 7.45441i) q^{33} +(-1.12836 + 0.302342i) q^{34} +(5.51972 - 3.18681i) q^{35} +(1.51098 - 2.59170i) q^{36} +(-4.28775 + 1.14890i) q^{37} +(-2.15672 + 3.73555i) q^{38} +(-3.27491 - 5.31742i) q^{39} +(1.98370 + 3.43586i) q^{40} +(3.96124 + 3.96124i) q^{41} +(-2.68620 - 0.725861i) q^{42} +0.889621i q^{43} +(3.50976 + 3.50976i) q^{44} +(11.4835 + 3.12914i) q^{45} +(0.846338 - 3.15858i) q^{46} +(0.653187 + 2.43773i) q^{47} +(0.451827 - 1.67208i) q^{48} -4.41915i q^{49} +(-7.59446 + 7.59446i) q^{50} +(-0.527807 + 1.95326i) q^{51} +(-2.62616 - 2.47048i) q^{52} -6.60181i q^{53} +(-2.56946 - 4.51640i) q^{54} +(-9.84618 + 17.0541i) q^{55} -1.60650 q^{56} +(3.72185 + 6.47805i) q^{57} +(-1.94262 - 7.24995i) q^{58} +(-2.12761 - 7.94034i) q^{59} +(6.87171 + 0.0145410i) q^{60} +14.1185 q^{61} +(3.75530 - 6.50436i) q^{62} +(-3.42230 + 3.39345i) q^{63} -1.00000i q^{64} +(6.77077 - 12.6008i) q^{65} +(8.30888 - 2.20752i) q^{66} +(2.33692 - 2.33692i) q^{67} +1.16816i q^{68} +(-3.99643 - 4.01338i) q^{69} +(-1.64961 - 6.15644i) q^{70} +(-0.942701 + 3.51821i) q^{71} +(-2.11232 - 2.13028i) q^{72} +(-3.33343 - 3.33343i) q^{73} +4.43901i q^{74} +(4.77666 + 17.9788i) q^{75} +(3.05006 + 3.05006i) q^{76} +(-3.98698 - 6.90565i) q^{77} +(-5.98384 + 1.78708i) q^{78} +(-1.16902 + 2.02480i) q^{79} +(3.83221 - 1.02684i) q^{80} +(-8.99968 - 0.0761775i) q^{81} +(4.85151 - 2.80102i) q^{82} +(-10.5532 + 2.82772i) q^{83} +(-1.39637 + 2.40680i) q^{84} +(-4.47663 + 1.19951i) q^{85} +(0.859308 + 0.230251i) q^{86} +(-12.5501 - 3.39128i) q^{87} +(4.29856 - 2.48178i) q^{88} +(1.78297 + 6.65415i) q^{89} +(5.99466 - 10.2823i) q^{90} +(3.04796 + 4.92554i) q^{91} +(-2.83190 - 1.63500i) q^{92} +(-6.48051 - 11.2796i) q^{93} +2.52372 q^{94} +(-8.55656 + 14.8204i) q^{95} +(-1.49816 - 0.869198i) q^{96} +(-4.52385 + 4.52385i) q^{97} +(-4.26857 - 1.14376i) q^{98} +(3.91482 - 14.3668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−1.22215	−	1.22733i	−0.705609	−	0.708601i
$3$	−1.22215	−	1.22733i	−0.705609	−	0.708601i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	1.02684	−	3.83221i	0.459215	−	1.71381i	−0.216176	−	0.976354i	$-0.569358\pi$
$5$	1.02684	−	3.83221i	0.459215	−	1.71381i	0.675391	−	0.737460i	$-0.263975\pi$
$6$	−1.50183	+	0.862849i	−0.613119	+	0.352257i
$7$	1.13597	+	1.13597i	0.429356	+	0.429356i	0.888409	−	0.459053i	$-0.151811\pi$
$7$	1.13597	+	1.13597i	0.429356	+	0.429356i	−0.459053	+	0.888409i	$0.651811\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.0126964	+	2.99997i	−0.00423212	+	0.999991i
$10$	−3.43586	−	1.98370i	−1.08651	−	0.627300i
$11$	−4.79442	−	1.28466i	−1.44557	−	0.387340i	−0.551092	−	0.834445i	$-0.685788\pi$
$11$	−4.79442	−	1.28466i	−1.44557	−	0.387340i	−0.894482	+	0.447105i	$0.852455\pi$
$12$	0.444746	+	1.67398i	0.128387	+	0.483236i
$13$	3.50956	+	0.826424i	0.973377	+	0.229209i
$13$	3.50956	+	0.826424i	0.973377	+	0.229209i
$14$	1.39127	−	0.803251i	0.371833	−	0.214678i
$15$	−5.95834	+	3.42326i	−1.53844	+	0.883882i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.584080	−	1.01166i	−0.141660	−	0.245363i	0.786462	−	0.617639i	$-0.211911\pi$
$17$	−0.584080	−	1.01166i	−0.141660	−	0.245363i	−0.928122	+	0.372276i	$0.878577\pi$
$18$	2.89447	+	0.788714i	0.682232	+	0.185902i
$19$	−4.16646	−	1.11640i	−0.955853	−	0.256120i	−0.253009	−	0.967464i	$-0.581420\pi$
$19$	−4.16646	−	1.11640i	−0.955853	−	0.256120i	−0.702844	+	0.711344i	$0.748087\pi$
$20$	−2.80537	+	2.80537i	−0.627300	+	0.627300i
$21$	0.00588804	−	2.78254i	0.00128488	−	0.607199i
$22$	−2.48178	+	4.29856i	−0.529116	+	0.916457i
$23$	3.27000			0.681842			0.340921	−	0.940092i	$-0.389261\pi$
$23$	3.27000			0.681842			0.340921	+	0.940092i	$0.389261\pi$
$24$	1.73205	+	0.00366513i	0.353553	+	0.000748142i
$25$	−9.30128	−	5.37010i	−1.86026	−	1.07402i
$26$	1.70661	−	3.17608i	0.334693	−	0.622881i
$27$	3.69749	−	3.65084i	0.711581	−	0.702604i
$28$	−0.415793	−	1.55176i	−0.0785775	−	0.293255i
$29$	6.50012	−	3.75285i	1.20704	−	0.696886i	0.244930	−	0.969541i	$-0.421235\pi$
$29$	6.50012	−	3.75285i	1.20704	−	0.696886i	0.962112	+	0.272654i	$0.0879015\pi$
$30$	1.76448	+	6.64132i	0.322149	+	1.21253i
$31$	7.25468	+	1.94388i	1.30298	+	0.349132i	0.842576	−	0.538578i	$-0.181038\pi$
$31$	7.25468	+	1.94388i	1.30298	+	0.349132i	0.460403	+	0.887710i	$0.347705\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	4.28280	+	7.45441i	0.745539	+	1.29765i
$34$	−1.12836	+	0.302342i	−0.193512	+	0.0518513i
$35$	5.51972	−	3.18681i	0.933002	−	0.538669i
$36$	1.51098	−	2.59170i	0.251830	−	0.431951i
$37$	−4.28775	+	1.14890i	−0.704902	+	0.188878i	−0.593425	−	0.804889i	$-0.702225\pi$
$37$	−4.28775	+	1.14890i	−0.704902	+	0.188878i	−0.111477	+	0.993767i	$0.535558\pi$
$38$	−2.15672	+	3.73555i	−0.349866	+	0.605986i
$39$	−3.27491	−	5.31742i	−0.524406	−	0.851468i
$40$	1.98370	+	3.43586i	0.313650	+	0.543257i
$41$	3.96124	+	3.96124i	0.618642	+	0.618642i	0.945183	−	0.326541i	$-0.105883\pi$
$41$	3.96124	+	3.96124i	0.618642	+	0.618642i	−0.326541	+	0.945183i	$0.605883\pi$
$42$	−2.68620	−	0.725861i	−0.414490	−	0.112003i
$43$			0.889621i			0.135666i	0.997697	+	0.0678330i	$0.0216085\pi$
$43$			0.889621i			0.135666i	−0.997697	+	0.0678330i	$0.978392\pi$
$44$	3.50976	+	3.50976i	0.529116	+	0.529116i
$45$	11.4835	+	3.12914i	1.71186	+	0.466464i
$46$	0.846338	−	3.15858i	0.124786	−	0.465707i
$47$	0.653187	+	2.43773i	0.0952772	+	0.355579i	0.997061	−	0.0766074i	$-0.0244088\pi$
$47$	0.653187	+	2.43773i	0.0952772	+	0.355579i	−0.901784	+	0.432187i	$0.857742\pi$
$48$	0.451827	−	1.67208i	0.0652156	−	0.241344i
$49$		−	4.41915i		−	0.631308i
$50$	−7.59446	+	7.59446i	−1.07402	+	1.07402i
$51$	−0.527807	+	1.95326i	−0.0739077	+	0.273511i
$52$	−2.62616	−	2.47048i	−0.364183	−	0.342595i
$53$		−	6.60181i		−	0.906828i	−0.891300	−	0.453414i	$-0.850206\pi$
$53$		−	6.60181i		−	0.906828i	0.891300	−	0.453414i	$-0.149794\pi$
$54$	−2.56946	−	4.51640i	−0.349659	−	0.614605i
$55$	−9.84618	+	17.0541i	−1.32766	+	2.29957i
$56$	−1.60650			−0.214678
$57$	3.72185	+	6.47805i	0.492971	+	0.858039i
$58$	−1.94262	−	7.24995i	−0.255078	−	0.951964i
$59$	−2.12761	−	7.94034i	−0.276991	−	1.03374i	−0.954495	−	0.298225i	$-0.903605\pi$
$59$	−2.12761	−	7.94034i	−0.276991	−	1.03374i	0.677505	−	0.735519i	$-0.263061\pi$
$60$	6.87171	+	0.0145410i	0.887134	+	0.00187724i
$61$	14.1185			1.80769			0.903847	−	0.427856i	$-0.140731\pi$
$61$	14.1185			1.80769			0.903847	+	0.427856i	$0.140731\pi$
$62$	3.75530	−	6.50436i	0.476923	−	0.826055i
$63$	−3.42230	+	3.39345i	−0.431169	+	0.427535i
$64$		−	1.00000i		−	0.125000i
$65$	6.77077	−	12.6008i	0.839811	−	1.56293i
$66$	8.30888	−	2.20752i	1.02275	−	0.271727i
$67$	2.33692	−	2.33692i	0.285500	−	0.285500i	−0.549798	−	0.835298i	$-0.685295\pi$
$67$	2.33692	−	2.33692i	0.285500	−	0.285500i	0.835298	+	0.549798i	$0.185295\pi$
$68$			1.16816i			0.141660i
$69$	−3.99643	−	4.01338i	−0.481114	−	0.483154i
$70$	−1.64961	−	6.15644i	−0.197167	−	0.735836i
$71$	−0.942701	+	3.51821i	−0.111878	+	0.417534i	−0.999034	−	0.0439344i	$-0.986011\pi$
$71$	−0.942701	+	3.51821i	−0.111878	+	0.417534i	0.887156	+	0.461469i	$0.152677\pi$
$72$	−2.11232	−	2.13028i	−0.248940	−	0.251056i
$73$	−3.33343	−	3.33343i	−0.390149	−	0.390149i	0.484592	−	0.874741i	$-0.338968\pi$
$73$	−3.33343	−	3.33343i	−0.390149	−	0.390149i	−0.874741	+	0.484592i	$0.838968\pi$
$74$			4.43901i			0.516024i
$75$	4.77666	+	17.9788i	0.551561	+	2.07602i
$76$	3.05006	+	3.05006i	0.349866	+	0.349866i
$77$	−3.98698	−	6.90565i	−0.454358	−	0.786971i
$78$	−5.98384	+	1.78708i	−0.677537	+	0.202346i
$79$	−1.16902	+	2.02480i	−0.131525	+	0.227808i	−0.924265	−	0.381753i	$-0.875321\pi$
$79$	−1.16902	+	2.02480i	−0.131525	+	0.227808i	0.792740	+	0.609560i	$0.208654\pi$
$80$	3.83221	−	1.02684i	0.428454	−	0.114804i
$81$	−8.99968	−	0.0761775i	−0.999964	−	0.00846416i
$82$	4.85151	−	2.80102i	0.535760	−	0.309321i
$83$	−10.5532	+	2.82772i	−1.15837	+	0.310383i	−0.786313	−	0.617829i	$-0.788012\pi$
$83$	−10.5532	+	2.82772i	−1.15837	+	0.310383i	−0.372052	+	0.928212i	$0.621346\pi$
$84$	−1.39637	+	2.40680i	−0.152356	+	0.262604i
$85$	−4.47663	+	1.19951i	−0.485559	+	0.130105i
$86$	0.859308	+	0.230251i	0.0926616	+	0.0248286i
$87$	−12.5501	−	3.39128i	−1.34551	−	0.363583i
$88$	4.29856	−	2.48178i	0.458228	−	0.264558i
$89$	1.78297	+	6.65415i	0.188995	+	0.705338i	0.993740	+	0.111718i	$0.0356352\pi$
$89$	1.78297	+	6.65415i	0.188995	+	0.705338i	−0.804745	+	0.593620i	$0.797698\pi$
$90$	5.99466	−	10.2823i	0.631892	−	1.08385i
$91$	3.04796	+	4.92554i	0.319513	+	0.516337i
$92$	−2.83190	−	1.63500i	−0.295246	−	0.170460i
$93$	−6.48051	−	11.2796i	−0.671998	−	1.16964i
$94$	2.52372			0.260302
$95$	−8.55656	+	14.8204i	−0.877884	+	1.52054i
$96$	−1.49816	−	0.869198i	−0.152906	−	0.0887121i
$97$	−4.52385	+	4.52385i	−0.459328	+	0.459328i	−0.898435	−	0.439107i	$-0.855295\pi$
$97$	−4.52385	+	4.52385i	−0.459328	+	0.459328i	0.439107	+	0.898435i	$0.355295\pi$
$98$	−4.26857	−	1.14376i	−0.431191	−	0.115537i
$99$	3.91482	−	14.3668i	0.393455	−	1.44392i
$100$	5.37010	+	9.30128i	0.537010	+	0.930128i
$101$	8.14806	+	14.1129i	0.810762	+	1.40428i	0.912331	+	0.409453i	$0.134281\pi$
$101$	8.14806	+	14.1129i	0.810762	+	1.40428i	−0.101569	+	0.994829i	$0.532386\pi$
$102$	1.75010	+	1.01536i	0.173285	+	0.100536i
$103$	−2.00231	+	1.15604i	−0.197294	+	0.113908i	−0.595393	−	0.803435i	$-0.703003\pi$
$103$	−2.00231	+	1.15604i	−0.197294	+	0.113908i	0.398099	+	0.917343i	$0.369670\pi$
$104$	−3.06600	+	1.89726i	−0.300647	+	0.186042i
$105$	−10.6572	−	2.87977i	−1.04004	−	0.281037i
$106$	−6.37686	−	1.70867i	−0.619375	−	0.165961i
$107$	8.90852	+	5.14333i	0.861219	+	0.497225i	0.864420	−	0.502770i	$-0.167686\pi$
$107$	8.90852	+	5.14333i	0.861219	+	0.497225i	−0.00320143	+	0.999995i	$0.501019\pi$
$108$	−5.02753	+	1.31297i	−0.483775	+	0.126341i
$109$	5.93227	−	5.93227i	0.568208	−	0.568208i	−0.363418	−	0.931626i	$-0.618390\pi$
$109$	5.93227	−	5.93227i	0.568208	−	0.568208i	0.931626	+	0.363418i	$0.118390\pi$
$110$	13.9246	+	13.9246i	1.32766	+	1.32766i
$111$	6.65036	+	3.85838i	0.631225	+	0.366221i
$112$	−0.415793	+	1.55176i	−0.0392888	+	0.146628i
$113$	−3.05689	−	1.76490i	−0.287568	−	0.166028i	0.349276	−	0.937020i	$-0.386427\pi$
$113$	−3.05689	−	1.76490i	−0.287568	−	0.166028i	−0.636845	+	0.770992i	$0.719761\pi$
$114$	7.22060	−	1.91839i	0.676272	−	0.179674i
$115$	3.35775	−	12.5313i	0.313112	−	1.16855i
$116$	−7.50570			−0.696886
$117$	−2.52381	+	10.5181i	−0.233326	+	0.972399i
$118$	−8.22044			−0.756753
$119$	0.485713	−	1.81271i	0.0445253	−	0.166171i
$120$	1.79257	−	6.63380i	0.163639	−	0.605580i
$121$	11.8099	+	6.81843i	1.07362	+	0.619857i
$122$	3.65415	−	13.6375i	0.330831	−	1.23468i
$123$	0.0205322	−	9.70300i	0.00185133	−	0.874890i
$124$	−5.31079	−	5.31079i	−0.476923	−	0.476923i
$125$	−16.1034	+	16.1034i	−1.44033	+	1.44033i
$126$	2.39207	+	4.18397i	0.213102	+	0.372738i
$127$	11.2191	+	6.47732i	0.995530	+	0.574769i	0.906923	−	0.421297i	$-0.138425\pi$
$127$	11.2191	+	6.47732i	0.995530	+	0.574769i	0.0886073	+	0.996067i	$0.471758\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	1.09186	−	1.08725i	0.0961331	−	0.0957271i
$130$	−10.4190	−	9.80138i	−0.913806	−	0.859638i
$131$	1.69814	−	0.980422i	0.148367	−	0.0856599i	−0.423979	−	0.905672i	$-0.639367\pi$
$131$	1.69814	−	0.980422i	0.148367	−	0.0856599i	0.572346	+	0.820012i	$0.306033\pi$
$132$	0.0181921	−	8.59711i	0.00158342	−	0.748282i
$133$	−3.46477	−	6.00117i	−0.300434	−	0.520367i
$134$	−1.65245	−	2.86212i	−0.142750	−	0.247250i
$135$	−10.1940	−	17.9183i	−0.877363	−	1.54216i
$136$	1.12836	+	0.302342i	0.0967558	+	0.0259256i
$137$	−11.8942	+	11.8942i	−1.01619	+	1.01619i	−0.0163266	+	0.999867i	$0.505197\pi$
$137$	−11.8942	+	11.8942i	−1.01619	+	1.01619i	−0.999867	+	0.0163266i	$0.994803\pi$
$138$	−4.91098	+	2.82152i	−0.418050	+	0.240183i
$139$	−8.03591	+	13.9186i	−0.681597	+	1.18056i	0.292896	+	0.956144i	$0.405381\pi$
$139$	−8.03591	+	13.9186i	−0.681597	+	1.18056i	−0.974493	+	0.224417i	$0.927952\pi$
$140$	−6.37362			−0.538669
$141$	2.19361	−	3.78095i	0.184736	−	0.318413i
$142$	3.15434	+	1.82116i	0.264706	+	0.152828i
$143$	−15.7647	−	8.47083i	−1.31831	−	0.708366i
$144$	−2.60440	+	1.48899i	−0.217033	+	0.124083i
$145$	−7.70712	−	28.7634i	−0.640042	−	2.38867i
$146$	−4.08261	+	2.35709i	−0.337879	+	0.195074i
$147$	−5.42378	+	5.40087i	−0.447346	+	0.445456i
$148$	4.28775	+	1.14890i	0.352451	+	0.0944390i
$149$	−2.75173	+	0.737323i	−0.225430	+	0.0604039i	−0.369766	−	0.929125i	$-0.620562\pi$
$149$	−2.75173	+	0.737323i	−0.225430	+	0.0604039i	0.144336	+	0.989529i	$0.453895\pi$
$150$	18.6025	+	0.0393642i	1.51889	+	0.00321407i
$151$	4.59840	−	1.23214i	0.374213	−	0.100270i	−0.0668104	−	0.997766i	$-0.521282\pi$
$151$	4.59840	−	1.23214i	0.374213	−	0.100270i	0.441023	+	0.897496i	$0.354616\pi$
$152$	3.73555	−	2.15672i	0.302993	−	0.174933i
$153$	3.04236	−	1.73938i	0.245960	−	0.140621i
$154$	−7.70225	+	2.06381i	−0.620665	+	0.166307i
$155$	14.8987	−	25.8054i	1.19669	−	2.07274i
$156$	0.177450	+	6.24248i	0.0142074	+	0.499798i
$157$	3.96212	+	6.86259i	0.316211	+	0.547694i	0.979694	−	0.200497i	$-0.0642558\pi$
$157$	3.96212	+	6.86259i	0.316211	+	0.547694i	−0.663483	+	0.748192i	$0.730922\pi$
$158$	1.65324	+	1.65324i	0.131525	+	0.131525i
$159$	−8.10262	+	8.06840i	−0.642580	+	0.639866i
$160$		−	3.96739i		−	0.313650i
$161$	3.71461	+	3.71461i	0.292753	+	0.292753i
$162$	−2.40287	+	8.67330i	−0.188787	+	0.681439i
$163$	−4.59427	+	17.1461i	−0.359851	+	1.34298i	0.514417	+	0.857540i	$0.328008\pi$
$163$	−4.59427	+	17.1461i	−0.359851	+	1.34298i	−0.874268	+	0.485443i	$0.838658\pi$
$164$	−1.44991	−	5.41115i	−0.113219	−	0.422540i
$165$	32.9646	−	8.75811i	2.56629	−	0.681818i
$166$			10.9255i			0.847982i
$167$	8.02165	−	8.02165i	0.620734	−	0.620734i	−0.324985	−	0.945719i	$-0.605359\pi$
$167$	8.02165	−	8.02165i	0.620734	−	0.620734i	0.945719	+	0.324985i	$0.105359\pi$
$168$	1.96339	+	1.97171i	0.151479	+	0.152121i
$169$	11.6340	+	5.80077i	0.894927	+	0.446213i
$170$			4.63455i			0.355454i
$171$	3.40207	−	12.4851i	0.260163	−	0.954760i
$172$	0.444811	−	0.770434i	0.0339165	−	0.0587451i
$173$	−16.7460			−1.27317			−0.636586	−	0.771206i	$-0.719654\pi$
$173$	−16.7460			−1.27317			−0.636586	+	0.771206i	$0.719654\pi$
$174$	−6.52393	+	11.2448i	−0.494578	+	0.852463i
$175$	−4.46570	−	16.6662i	−0.337575	−	1.25985i
$176$	−1.28466	−	4.79442i	−0.0968350	−	0.361393i
$177$	−7.14519	+	12.3156i	−0.537065	+	0.925695i
$178$	6.88888			0.516343
$179$	−2.08607	+	3.61317i	−0.155920	+	0.270061i	−0.933394	−	0.358854i	$-0.883168\pi$
$179$	−2.08607	+	3.61317i	−0.155920	+	0.270061i	0.777474	+	0.628916i	$0.216501\pi$
$180$	−8.38041	−	8.45165i	−0.624639	−	0.629949i
$181$			7.52589i			0.559395i	0.960088	+	0.279698i	$0.0902342\pi$
$181$			7.52589i			0.559395i	−0.960088	+	0.279698i	$0.909766\pi$
$182$	5.54658	−	1.66928i	0.411140	−	0.123735i
$183$	−17.2550	−	17.3282i	−1.27553	−	1.28093i
$184$	−2.31224	+	2.31224i	−0.170460	+	0.170460i
$185$			17.6113i			1.29481i
$186$	−12.5726	+	3.34031i	−0.921865	+	0.244923i
$187$	1.50069	+	5.60066i	0.109741	+	0.409561i
$188$	0.653187	−	2.43773i	0.0476386	−	0.177790i
$189$	8.34746	+	0.0529920i	0.607188	+	0.00385460i
$190$	12.1008	+	12.1008i	0.877884	+	0.877884i
$191$		−	12.1030i		−	0.875741i	−0.899038	−	0.437871i	$-0.855733\pi$
$191$		−	12.1030i		−	0.875741i	0.899038	−	0.437871i	$-0.144267\pi$
$192$	−1.22733	+	1.22215i	−0.0885752	+	0.0882011i
$193$	11.2728	+	11.2728i	0.811435	+	0.811435i	0.984849	−	0.173414i	$-0.0554798\pi$
$193$	11.2728	+	11.2728i	0.811435	+	0.811435i	−0.173414	+	0.984849i	$0.555480\pi$
$194$	3.19885	+	5.54057i	0.229664	+	0.397789i
$195$	−23.7402	+	7.09003i	−1.70007	+	0.507727i
$196$	−2.20958	+	3.82710i	−0.157827	+	0.273364i
$197$	−12.3667	+	3.31364i	−0.881090	+	0.236087i	−0.670877	−	0.741568i	$-0.734082\pi$
$197$	−12.3667	+	3.31364i	−0.881090	+	0.236087i	−0.210212	+	0.977656i	$0.567416\pi$
$198$	−12.8641	−	7.49984i	−0.914209	−	0.532990i
$199$	11.0194	−	6.36204i	0.781143	−	0.450993i	−0.0556924	−	0.998448i	$-0.517737\pi$
$199$	11.0194	−	6.36204i	0.781143	−	0.450993i	0.836835	+	0.547455i	$0.184403\pi$
$200$	10.3742	−	2.77977i	0.733569	−	0.196559i
$201$	−5.72424	−	0.0121129i	−0.403757	−	0.000854377i
$202$	15.7408	−	4.21775i	1.10752	−	0.296760i
$203$	11.6470	+	3.12082i	0.817462	+	0.219038i
$204$	1.43372	−	1.42767i	0.100381	−	0.0999568i
$205$	19.2478	−	11.1127i	1.34433	−	0.776148i
$206$	0.598408	+	2.23329i	0.0416931	+	0.155601i
$207$	−0.0415171	+	9.80991i	−0.00288564	+	0.681836i
$208$	1.03908	+	3.45258i	0.0720470	+	0.239393i
$209$	18.5416	+	10.7050i	1.28255	+	0.740480i
$210$	−5.53993	+	9.54873i	−0.382292	+	0.658925i
$211$	15.7297			1.08288			0.541439	−	0.840740i	$-0.317880\pi$
$211$	15.7297			1.08288			0.541439	+	0.840740i	$0.317880\pi$
$212$	−3.30090	+	5.71733i	−0.226707	+	0.392668i
$213$	5.47014	−	3.14277i	0.374808	−	0.215339i
$214$	7.27377	−	7.27377i	0.497225	−	0.497225i
$215$	3.40921	+	0.913495i	0.232506	+	0.0622999i
$216$	−0.0329860	+	5.19605i	−0.00224441	+	0.353546i
$217$	6.03289	+	10.4493i	0.409539	+	0.709343i
$218$	−4.19475	−	7.26551i	−0.284104	−	0.492083i
$219$	−0.0172781	+	8.16519i	−0.00116755	+	0.551753i
$220$	17.0541	−	9.84618i	1.14979	−	0.663829i
$221$	−1.21381	−	4.03317i	−0.0816496	−	0.271300i
$222$	5.44815	−	5.42514i	0.365656	−	0.364111i
$223$	−0.176545	−	0.0473050i	−0.0118223	−	0.00316778i	0.252903	−	0.967492i	$-0.418615\pi$
$223$	−0.176545	−	0.0473050i	−0.0118223	−	0.00316778i	−0.264725	+	0.964324i	$0.585281\pi$
$224$	1.39127	+	0.803251i	0.0929582	+	0.0536694i
$225$	16.2282	−	27.8354i	1.08188	−	1.85569i
$226$	−2.49594	+	2.49594i	−0.166028	+	0.166028i
$227$	−9.38287	−	9.38287i	−0.622763	−	0.622763i	0.323474	−	0.946237i	$-0.395149\pi$
$227$	−9.38287	−	9.38287i	−0.622763	−	0.622763i	−0.946237	+	0.323474i	$0.895149\pi$
$228$	0.0158093	−	7.47108i	0.00104700	−	0.494785i
$229$	2.33894	−	8.72905i	0.154562	−	0.576832i	−0.844581	−	0.535428i	$-0.820150\pi$
$229$	2.33894	−	8.72905i	0.154562	−	0.576832i	0.999142	−	0.0414037i	$-0.0131830\pi$
$230$	−11.2353	−	6.48668i	−0.740831	−	0.427719i
$231$	−3.60285	+	13.3331i	−0.237050	+	0.877253i
$232$	−1.94262	+	7.24995i	−0.127539	+	0.475982i
$233$	−5.07704			−0.332608			−0.166304	−	0.986075i	$-0.553183\pi$
$233$	−5.07704			−0.332608			−0.166304	+	0.986075i	$0.553183\pi$
$234$	9.50649	+	5.16010i	0.621459	+	0.337326i
$235$	10.0126			0.653150
$236$	−2.12761	+	7.94034i	−0.138495	+	0.516872i
$237$	3.91382	−	1.03983i	0.254230	−	0.0675445i
$238$	−1.62523	−	0.938326i	−0.105348	−	0.0608226i
$239$	7.78032	−	29.0366i	0.503267	−	1.87822i	0.0256107	−	0.999672i	$-0.491847\pi$
$239$	7.78032	−	29.0366i	0.503267	−	1.87822i	0.477657	−	0.878547i	$-0.341486\pi$
$240$	−5.94380	−	3.44845i	−0.383671	−	0.222596i
$241$	−12.3855	−	12.3855i	−0.797818	−	0.797818i	0.184933	−	0.982751i	$-0.440793\pi$
$241$	−12.3855	−	12.3855i	−0.797818	−	0.797818i	−0.982751	+	0.184933i	$0.940793\pi$
$242$	9.64271	−	9.64271i	0.619857	−	0.619857i
$243$	10.9055	+	11.1387i	0.699586	+	0.714548i
$244$	−12.2270	−	7.05927i	−0.782755	−	0.451924i
$245$	−16.9351	−	4.53775i	−1.08194	−	0.289906i
$246$	−9.36706	−	2.53115i	−0.597222	−	0.161380i
$247$	−13.6998	−	7.36134i	−0.871700	−	0.468391i
$248$	−6.50436	+	3.75530i	−0.413028	+	0.238462i
$249$	16.3682	+	9.49640i	1.03729	+	0.601810i
$250$	11.3868	+	19.7225i	0.720164	+	1.24736i
$251$	12.2713	+	21.2544i	0.774555	+	1.34157i	0.935044	+	0.354531i	$0.115360\pi$
$251$	12.2713	+	21.2544i	0.774555	+	1.34157i	−0.160489	+	0.987038i	$0.551307\pi$
$252$	4.66052	−	1.22767i	0.293585	−	0.0773357i
$253$	−15.6778	−	4.20084i	−0.985652	−	0.264105i
$254$	9.16032	−	9.16032i	0.574769	−	0.574769i
$255$	6.94332	+	4.02834i	0.434807	+	0.252264i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	21.1342			1.31831			0.659156	−	0.752006i	$-0.270914\pi$
$257$	21.1342			1.31831			0.659156	+	0.752006i	$0.270914\pi$
$258$	−0.767609	−	1.33606i	−0.0477892	−	0.0831794i
$259$	−6.17586	−	3.56564i	−0.383750	−	0.221558i
$260$	−12.1640	+	7.52719i	−0.754382	+	0.466817i
$261$	11.1759	+	19.5478i	0.691772	+	1.20998i
$262$	−0.507504	−	1.89403i	−0.0313537	−	0.117014i
$263$	1.13283	−	0.654042i	0.0698535	−	0.0403299i	−0.464666	−	0.885486i	$-0.653826\pi$
$263$	1.13283	−	0.654042i	0.0698535	−	0.0403299i	0.534520	+	0.845156i	$0.320492\pi$
$264$	−8.29946	−	2.24267i	−0.510796	−	0.138027i
$265$	−25.2995	−	6.77898i	−1.55413	−	0.416429i
$266$	−6.69343	+	1.79350i	−0.410401	+	0.109967i
$267$	5.98780	−	10.3207i	0.366447	−	0.631615i
$268$	−3.19229	+	0.855370i	−0.195000	+	0.0522501i
$269$	−24.6923	+	14.2561i	−1.50552	+	0.869210i	−0.505536	+	0.862805i	$0.668705\pi$
$269$	−24.6923	+	14.2561i	−1.50552	+	0.869210i	−0.999979	+	0.00640436i	$0.997961\pi$
$270$	−19.9462	+	5.20908i	−1.21389	+	0.317015i
$271$	1.05690	−	0.283196i	0.0642021	−	0.0172029i	−0.226575	−	0.973994i	$-0.572753\pi$
$271$	1.05690	−	0.283196i	0.0642021	−	0.0172029i	0.290777	+	0.956791i	$0.406086\pi$
$272$	0.584080	−	1.01166i	0.0354151	−	0.0613407i
$273$	2.32022	−	9.76061i	0.140426	−	0.590739i
$274$	8.41050	+	14.5674i	0.508097	+	0.880049i
$275$	37.6955	+	37.6955i	2.27312	+	2.27312i
$276$	1.45432	+	5.47390i	0.0875398	+	0.329490i
$277$			13.7751i			0.827665i	0.910353	+	0.413832i	$0.135810\pi$
$277$			13.7751i			0.827665i	−0.910353	+	0.413832i	$0.864190\pi$
$278$	11.3645	+	11.3645i	0.681597	+	0.681597i
$279$	−5.92371	+	21.7392i	−0.354643	+	1.30149i
$280$	−1.64961	+	6.15644i	−0.0985833	+	0.367918i
$281$	−1.17120	−	4.37098i	−0.0698680	−	0.260751i	0.922153	−	0.386826i	$-0.126429\pi$
$281$	−1.17120	−	4.37098i	−0.0698680	−	0.260751i	−0.992021	+	0.126075i	$0.959762\pi$
$282$	−3.08437	−	3.09745i	−0.183671	−	0.184450i
$283$		−	3.88372i		−	0.230863i	−0.993315	−	0.115432i	$-0.963175\pi$
$283$		−	3.88372i		−	0.230863i	0.993315	−	0.115432i	$-0.0368251\pi$
$284$	2.57551	−	2.57551i	0.152828	−	0.152828i
$285$	28.6470	−	7.61100i	1.69690	−	0.450836i
$286$	−12.2624	+	13.0351i	−0.725090	+	0.770780i
$287$			8.99968i			0.531235i
$288$	0.764186	+	2.90104i	0.0450301	+	0.170945i
$289$	7.81770	−	13.5407i	0.459865	−	0.796509i
$290$	−29.7780			−1.74863
$291$	11.0811	+	0.0234484i	0.649586	+	0.00137457i
$292$	1.22012	+	4.55356i	0.0714022	+	0.266477i
$293$	1.41790	+	5.29169i	0.0828348	+	0.309144i	0.994895	−	0.100912i	$-0.0321760\pi$
$293$	1.41790	+	5.29169i	0.0828348	+	0.309144i	−0.912061	+	0.410056i	$0.865509\pi$
$294$	3.81306	+	6.63681i	0.222382	+	0.387067i
$295$	−32.6137			−1.89884
$296$	2.21950	−	3.84429i	0.129006	−	0.223445i
$297$	−22.4174	+	12.7536i	−1.30079	+	0.740041i
$298$			2.84880i			0.165026i
$299$	11.4763	+	2.70241i	0.663689	+	0.156284i
$300$	4.85271	−	17.9585i	0.280171	−	1.03683i
$301$	−1.01058	+	1.01058i	−0.0582489	+	0.0582489i
$302$		−	4.76062i		−	0.273943i
$303$	7.36303	−	27.2484i	0.422995	−	1.56538i
$304$	−1.11640	−	4.16646i	−0.0640300	−	0.238963i
$305$	14.4974	−	54.1052i	0.830121	−	3.09805i
$306$	−0.892693	−	3.38888i	−0.0510318	−	0.193729i
$307$	0.236798	+	0.236798i	0.0135148	+	0.0135148i	0.713832	−	0.700317i	$-0.246958\pi$
$307$	0.236798	+	0.236798i	0.0135148	+	0.0135148i	−0.700317	+	0.713832i	$0.746958\pi$
$308$			7.97395i			0.454358i
$309$	3.86597	+	1.04466i	0.219927	+	0.0594284i
$310$	−21.0700	−	21.0700i	−1.19669	−	1.19669i
$311$	7.57359	+	13.1178i	0.429459	+	0.743844i	0.996825	−	0.0796211i	$-0.0253710\pi$
$311$	7.57359	+	13.1178i	0.429459	+	0.743844i	−0.567366	+	0.823465i	$0.692038\pi$
$312$	6.07570	+	1.44427i	0.343969	+	0.0817656i
$313$	−6.19713	+	10.7337i	−0.350282	+	0.606707i	−0.986299	−	0.164969i	$-0.947248\pi$
$313$	−6.19713	+	10.7337i	−0.350282	+	0.606707i	0.636016	+	0.771675i	$0.280581\pi$
$314$	7.65422	−	2.05094i	0.431953	−	0.115741i
$315$	9.49026	+	16.5995i	0.534716	+	0.935274i
$316$	2.02480	−	1.16902i	0.113904	−	0.0657624i
$317$	−12.2024	+	3.26964i	−0.685358	+	0.183641i	−0.584663	−	0.811276i	$-0.698773\pi$
$317$	−12.2024	+	3.26964i	−0.685358	+	0.183641i	−0.100695	+	0.994917i	$0.532107\pi$
$318$	5.69637	+	9.91479i	0.319436	+	0.555994i
$319$	−35.9855	+	9.64228i	−2.01480	+	0.539864i
$320$	−3.83221	−	1.02684i	−0.214227	−	0.0574019i
$321$	−4.57496	−	17.2197i	−0.255349	−	0.961107i
$322$	4.54945	−	2.62663i	0.253531	−	0.146376i
$323$	1.30414	+	4.86710i	0.0725640	+	0.270813i
$324$	7.75586	+	4.56581i	0.430881	+	0.253656i
$325$	−28.2054	−	26.5335i	−1.56456	−	1.47181i
$326$	15.3727	+	8.87545i	0.851417	+	0.491566i
$327$	−14.5310	−	0.0307486i	−0.803566	−	0.00170040i
$328$	−5.60204			−0.309321
$329$	−2.02718	+	3.51118i	−0.111762	+	0.193578i
$330$	0.0721751	−	34.1081i	0.00397311	−	1.87759i
$331$	−1.01667	+	1.01667i	−0.0558814	+	0.0558814i	−0.734495	−	0.678614i	$-0.762581\pi$
$331$	−1.01667	+	1.01667i	−0.0558814	+	0.0558814i	0.678614	+	0.734495i	$0.262581\pi$
$332$	10.5532	+	2.82772i	0.579183	+	0.155191i
$333$	−3.39223	−	12.8777i	−0.185893	−	0.705695i
$334$	−5.67216	−	9.82447i	−0.310367	−	0.537571i
$335$	−6.55591	−	11.3552i	−0.358188	−	0.620399i
$336$	2.41269	−	1.38617i	0.131623	−	0.0756217i
$337$	−16.5630	+	9.56266i	−0.902245	+	0.520911i	−0.877928	−	0.478793i	$-0.841074\pi$
$337$	−16.5630	+	9.56266i	−0.902245	+	0.520911i	−0.0243169	+	0.999704i	$0.507741\pi$
$338$	8.61423	−	9.73628i	0.468552	−	0.529584i
$339$	1.56986	+	5.90880i	0.0852633	+	0.320922i
$340$	4.47663	+	1.19951i	0.242779	+	0.0650526i
$341$	−32.2848	−	18.6396i	−1.74832	−	1.00939i
$342$	−11.1792	−	6.51753i	−0.604500	−	0.352428i
$343$	12.9718	−	12.9718i	0.700411	−	0.700411i
$344$	−0.629057	−	0.629057i	−0.0339165	−	0.0339165i
$345$	−19.4838	+	11.1941i	−1.04897	+	0.602668i
$346$	−4.33418	+	16.1754i	−0.233007	+	0.869593i
$347$	−26.1877	−	15.1195i	−1.40583	−	0.811655i	−0.410845	−	0.911705i	$-0.634766\pi$
$347$	−26.1877	−	15.1195i	−1.40583	−	0.811655i	−0.994982	+	0.100050i	$0.968100\pi$
$348$	9.17309	+	9.21199i	0.491729	+	0.493815i
$349$	4.76513	−	17.7837i	0.255072	−	0.951940i	−0.712979	−	0.701185i	$-0.752655\pi$
$349$	4.76513	−	17.7837i	0.255072	−	0.951940i	0.968051	−	0.250755i	$-0.0806788\pi$
$350$	−17.2541			−0.922272
$351$	15.9937	−	9.75714i	0.853680	−	0.520798i
$352$	−4.96355			−0.264558
$353$	−4.98551	+	18.6062i	−0.265352	+	0.990307i	0.696683	+	0.717380i	$0.254659\pi$
$353$	−4.98551	+	18.6062i	−0.265352	+	0.990307i	−0.962035	+	0.272928i	$0.912008\pi$
$354$	10.0466	+	10.0892i	0.533972	+	0.536236i
$355$	12.5145	+	7.22525i	0.664200	+	0.383476i
$356$	1.78297	−	6.65415i	0.0944974	−	0.352669i
$357$	−2.81841	+	1.61927i	−0.149166	+	0.0857007i
$358$	2.95014	+	2.95014i	0.155920	+	0.155920i
$359$	14.9056	−	14.9056i	0.786685	−	0.786685i	−0.194264	−	0.980949i	$-0.562232\pi$
$359$	14.9056	−	14.9056i	0.786685	−	0.786685i	0.980949	+	0.194264i	$0.0622319\pi$
$360$	−10.3327	+	5.90741i	−0.544580	+	0.311348i
$361$	−0.341404	−	0.197110i	−0.0179686	−	0.0103742i
$362$	7.26945	+	1.94784i	0.382074	+	0.102376i
$363$	−6.06494	−	22.8278i	−0.318327	−	1.19815i
$364$	−0.176839	−	5.78962i	−0.00926890	−	0.303459i
$365$	−16.1973	+	9.35151i	−0.847805	+	0.489480i
$366$	−21.2036	+	12.1822i	−1.10833	+	0.636773i
$367$	−10.6338	−	18.4183i	−0.555079	−	0.961425i	−0.997897	−	0.0648137i	$-0.979355\pi$
$367$	−10.6338	−	18.4183i	−0.555079	−	0.961425i	0.442818	−	0.896611i	$-0.353979\pi$
$368$	1.63500	+	2.83190i	0.0852302	+	0.147623i
$369$	−11.9339	+	11.8333i	−0.621254	+	0.616018i
$370$	17.0112	+	4.55814i	0.884370	+	0.236966i
$371$	7.49944	−	7.49944i	0.389352	−	0.389352i
$372$	−0.0275273	+	13.0087i	−0.00142722	+	0.674470i
$373$	9.97036	−	17.2692i	0.516246	−	0.894164i	−0.483576	−	0.875302i	$-0.660662\pi$
$373$	9.97036	−	17.2692i	0.516246	−	0.894164i	0.999822	−	0.0188617i	$-0.00600423\pi$
$374$	5.79823			0.299819
$375$	39.4449	+	0.0834682i	2.03693	+	0.00431028i
$376$	−2.18561	−	1.26186i	−0.112714	−	0.0650755i
$377$	25.9140	−	7.79899i	1.33464	−	0.401669i
$378$	2.21167	−	8.04931i	0.113756	−	0.414012i
$379$	−7.46317	−	27.8529i	−0.383357	−	1.43071i	−0.840740	−	0.541439i	$-0.817880\pi$
$379$	−7.46317	−	27.8529i	−0.383357	−	1.43071i	0.457383	−	0.889270i	$-0.348787\pi$
$380$	14.8204	−	8.55656i	0.760270	−	0.438942i
$381$	−5.76153	−	21.6858i	−0.295172	−	1.11100i
$382$	−11.6906	−	3.13248i	−0.598142	−	0.160272i
$383$	−19.0277	+	5.09845i	−0.972268	+	0.260519i	−0.709785	−	0.704418i	$-0.751208\pi$
$383$	−19.0277	+	5.09845i	−0.972268	+	0.260519i	−0.262483	+	0.964937i	$0.584541\pi$
$384$	0.862849	+	1.50183i	0.0440321	+	0.0766399i
$385$	−30.5578	+	8.18795i	−1.55737	+	0.417296i
$386$	13.8063	−	7.97109i	0.702724	−	0.405718i
$387$	−2.66884	−	0.0112949i	−0.135665	−	0.000574155i
$388$	6.17970	−	1.65585i	0.313727	−	0.0840628i
$389$	−1.75344	+	3.03705i	−0.0889030	+	0.153984i	−0.907048	−	0.421028i	$-0.861669\pi$
$389$	−1.75344	+	3.03705i	−0.0889030	+	0.153984i	0.818145	+	0.575012i	$0.195003\pi$
$390$	0.704015	+	24.7663i	0.0356492	+	1.25409i
$391$	−1.90994	−	3.30812i	−0.0965899	−	0.167299i
$392$	3.12481	+	3.12481i	0.157827	+	0.157827i
$393$	−3.27869	−	0.885962i	−0.165388	−	0.0446909i
$394$			12.8029i			0.645002i
$395$	6.55906	+	6.55906i	0.330022	+	0.330022i
$396$	−10.5738	+	10.4846i	−0.531351	+	0.526872i
$397$	−3.67258	+	13.7062i	−0.184321	+	0.687896i	0.810454	+	0.585803i	$0.199221\pi$
$397$	−3.67258	+	13.7062i	−0.184321	+	0.687896i	−0.994775	+	0.102093i	$0.967446\pi$
$398$	−3.29323	−	12.2905i	−0.165075	−	0.616068i
$399$	−3.13096	+	11.5868i	−0.156744	+	0.580064i
$400$		−	10.7402i		−	0.537010i
$401$	−21.6185	+	21.6185i	−1.07957	+	1.07957i	−0.0830271	+	0.996547i	$0.526459\pi$
$401$	−21.6185	+	21.6185i	−1.07957	+	1.07957i	−0.996547	+	0.0830271i	$0.973541\pi$
$402$	−1.49324	+	5.52605i	−0.0744761	+	0.275614i
$403$	23.8543	+	12.8176i	1.18827	+	0.638491i
$404$		−	16.2961i		−	0.810762i
$405$	−9.53312	+	34.4104i	−0.473705	+	1.70987i
$406$	6.02895	−	10.4425i	0.299212	−	0.518250i
$407$	22.0333			1.09215
$408$	−1.00795	−	1.75438i	−0.0499008	−	0.0868546i
$409$	−4.86654	−	18.1622i	−0.240635	−	0.898061i	−0.975527	−	0.219878i	$-0.929434\pi$
$409$	−4.86654	−	18.1622i	−0.240635	−	0.898061i	0.734893	−	0.678183i	$-0.237233\pi$
$410$	−5.75238	−	21.4682i	−0.284090	−	1.06024i
$411$	29.1347	+	0.0616511i	1.43711	+	0.00304103i
$412$	2.31207			0.113908
$413$	6.60308	−	11.4369i	0.324916	−	0.562771i
$414$	9.46490	+	2.57909i	0.465174	+	0.126756i
$415$			43.3457i			2.12776i
$416$	3.60387	−	0.110077i	0.176694	−	0.00539698i
$417$	26.9039	−	7.14789i	1.31749	−	0.350033i
$418$	15.1392	−	15.1392i	0.740480	−	0.740480i
$419$		−	4.51803i		−	0.220720i	−0.993892	−	0.110360i	$-0.964800\pi$
$419$		−	4.51803i		−	0.220720i	0.993892	−	0.110360i	$-0.0352004\pi$
$420$	7.78952	+	7.82256i	0.380090	+	0.381702i
$421$	8.52459	+	31.8142i	0.415463	+	1.55053i	0.783907	+	0.620879i	$0.213224\pi$
$421$	8.52459	+	31.8142i	0.415463	+	1.55053i	−0.368444	+	0.929650i	$0.620109\pi$
$422$	4.07115	−	15.1937i	0.198180	−	0.739620i
$423$	−7.32141	+	1.92859i	−0.355979	+	0.0937715i
$424$	4.66818	+	4.66818i	0.226707	+	0.226707i
$425$			12.5463i			0.608583i
$426$	−1.61991	−	6.09716i	−0.0784848	−	0.295408i
$427$	16.0382	+	16.0382i	0.776144	+	0.776144i
$428$	−5.14333	−	8.90852i	−0.248612	−	0.430609i
$429$	8.87024	+	29.7011i	0.428259	+	1.43398i
$430$	1.76474	−	3.05661i	0.0851032	−	0.147403i
$431$	−10.5837	+	2.83588i	−0.509797	+	0.136600i	−0.504543	−	0.863386i	$-0.668339\pi$
$431$	−10.5837	+	2.83588i	−0.509797	+	0.136600i	−0.00525390	+	0.999986i	$0.501672\pi$
$432$	5.01046	+	1.37670i	0.241066	+	0.0662364i
$433$	−7.59434	+	4.38459i	−0.364960	+	0.210710i	−0.671255	−	0.741227i	$-0.734244\pi$
$433$	−7.59434	+	4.38459i	−0.364960	+	0.210710i	0.306294	+	0.951937i	$0.400911\pi$
$434$	11.6546	−	3.12285i	0.559441	−	0.149902i
$435$	−25.8830	+	44.6124i	−1.24099	+	2.13900i
$436$	−8.10363	+	2.17136i	−0.388093	+	0.103989i
$437$	−13.6243	−	3.65063i	−0.651740	−	0.174633i
$438$	7.88250	+	2.13000i	0.376640	+	0.101775i
$439$	−28.3760	+	16.3829i	−1.35431	+	0.781913i	−0.988850	−	0.148913i	$-0.952423\pi$
$439$	−28.3760	+	16.3829i	−1.35431	+	0.781913i	−0.365463	+	0.930826i	$0.619089\pi$
$440$	−5.09676	−	19.0214i	−0.242978	−	0.906807i
$441$	13.2573	+	0.0561072i	0.631302	+	0.00267177i
$442$	−4.20990	+	0.128588i	−0.200245	+	0.00611630i
$443$	−25.8748	−	14.9388i	−1.22935	−	0.709766i	−0.262457	−	0.964944i	$-0.584533\pi$
$443$	−25.8748	−	14.9388i	−1.22935	−	0.709766i	−0.966894	+	0.255178i	$0.917866\pi$
$444$	−3.83020	−	6.66663i	−0.181773	−	0.316384i
$445$	27.3309			1.29561
$446$	−0.0913862	+	0.158286i	−0.00432726	+	0.00749504i
$447$	4.26797	+	2.47617i	0.201868	+	0.117119i
$448$	1.13597	−	1.13597i	0.0536694	−	0.0536694i
$449$	14.4946	+	3.88382i	0.684043	+	0.183289i	0.584072	−	0.811702i	$-0.301458\pi$
$449$	14.4946	+	3.88382i	0.684043	+	0.183289i	0.0999708	+	0.994990i	$0.468125\pi$
$450$	−22.6868	−	22.8796i	−1.06946	−	1.07855i
$451$	−13.9030	−	24.0807i	−0.654667	−	1.13392i
$452$	1.76490	+	3.05689i	0.0830138	+	0.143784i
$453$	−7.13219	−	4.13792i	−0.335099	−	0.194416i
$454$	−11.4916	+	6.63469i	−0.539329	+	0.311382i
$455$	22.0054	−	6.62268i	1.03163	−	0.310476i
$456$	−7.21242	−	1.94893i	−0.337753	−	0.0912670i
$457$	−3.48437	−	0.933634i	−0.162992	−	0.0436736i	0.176400	−	0.984319i	$-0.443555\pi$
$457$	−3.48437	−	0.933634i	−0.162992	−	0.0436736i	−0.339392	+	0.940645i	$0.610221\pi$
$458$	−7.82625	−	4.51849i	−0.365697	−	0.211135i
$459$	−5.85302	−	1.60820i	−0.273196	−	0.0750646i
$460$	−9.17355	+	9.17355i	−0.427719	+	0.427719i
$461$	23.4663	+	23.4663i	1.09293	+	1.09293i	0.995214	+	0.0977199i	$0.0311549\pi$
$461$	23.4663	+	23.4663i	1.09293	+	1.09293i	0.0977199	+	0.995214i	$0.468845\pi$
$462$	11.9463	+	6.93094i	0.555792	+	0.322457i
$463$	−0.949249	+	3.54265i	−0.0441154	+	0.164641i	−0.984469	−	0.175557i	$-0.943827\pi$
$463$	−0.949249	+	3.54265i	−0.0441154	+	0.164641i	0.940354	+	0.340198i	$0.110494\pi$
$464$	6.50012	+	3.75285i	0.301761	+	0.174222i
$465$	−49.8803	+	13.2523i	−2.31314	+	0.614561i
$466$	−1.31403	+	4.90405i	−0.0608715	+	0.227176i
$467$	5.90589			0.273292			0.136646	−	0.990620i	$-0.456368\pi$
$467$	5.90589			0.273292			0.136646	+	0.990620i	$0.456368\pi$
$468$	7.44473	−	7.84704i	0.344133	−	0.362729i
$469$	5.30932			0.245162
$470$	2.59145	−	9.67142i	0.119535	−	0.446109i
$471$	3.58038	−	13.2500i	0.164975	−	0.610526i
$472$	7.11911	+	4.11022i	0.327684	+	0.189188i
$473$	1.14286	−	4.26522i	0.0525489	−	0.196115i
$474$	0.00856921	−	4.04959i	0.000393597	−	0.186004i
$475$	32.7583	+	32.7583i	1.50305	+	1.50305i
$476$	−1.32699	+	1.32699i	−0.0608226	+	0.0608226i
$477$	19.8052	+	0.0838189i	0.906820	+	0.00383780i
$478$	−26.0335	−	15.0304i	−1.19074	−	0.687476i
$479$	−20.7549	−	5.56127i	−0.948318	−	0.254101i	−0.248669	−	0.968588i	$-0.579993\pi$
$479$	−20.7549	−	5.56127i	−0.948318	−	0.254101i	−0.699648	+	0.714487i	$0.746660\pi$
$480$	−4.86931	+	4.84875i	−0.222253	+	0.221314i
$481$	−15.9976	+	0.488634i	−0.729428	+	0.0222798i
$482$	−15.1690	+	8.75785i	−0.690931	+	0.398909i
$483$	0.0192539	−	9.09889i	0.000876082	−	0.414014i
$484$	−6.81843	−	11.8099i	−0.309929	−	0.536812i
$485$	12.6911	+	21.9816i	0.576272	+	0.998133i
$486$	13.5817	−	7.65096i	0.616079	−	0.347055i
$487$	41.0392	+	10.9964i	1.85966	+	0.498295i	0.999923	−	0.0124347i	$-0.00395819\pi$
$487$	41.0392	+	10.9964i	1.85966	+	0.498295i	0.859741	+	0.510730i	$0.170625\pi$
$488$	−9.98332	+	9.98332i	−0.451924	+	0.451924i
$489$	26.6588	−	15.3164i	1.20555	−	0.692630i
$490$	−8.76625	+	15.1836i	−0.396019	+	0.685925i
$491$	20.5848			0.928981			0.464490	−	0.885578i	$-0.346238\pi$
$491$	20.5848			0.928981			0.464490	+	0.885578i	$0.346238\pi$
$492$	−4.86928	+	8.39277i	−0.219524	+	0.378376i
$493$	−7.59319	−	4.38393i	−0.341980	−	0.197442i
$494$	−10.6563	+	11.3278i	−0.479449	+	0.509661i
$495$	−51.0368	−	29.7548i	−2.29393	−	1.33738i
$496$	1.94388	+	7.25468i	0.0872830	+	0.325745i
$497$	−5.06745	+	2.92569i	−0.227306	+	0.131235i
$498$	13.4092	−	13.3526i	0.600881	−	0.598344i
$499$	−19.3716	−	5.19060i	−0.867190	−	0.232363i	−0.202318	−	0.979320i	$-0.564847\pi$
$499$	−19.3716	−	5.19060i	−0.867190	−	0.232363i	−0.664872	+	0.746957i	$0.731514\pi$
$500$	21.9976	−	5.89424i	0.983762	−	0.263598i
$501$	−19.6489	−	0.0415784i	−0.877848	−	0.00185759i
$502$	23.7063	−	6.35207i	1.05806	−	0.283507i
$503$	12.7223	−	7.34523i	0.567260	−	0.327508i	−0.188794	−	0.982017i	$-0.560458\pi$
$503$	12.7223	−	7.34523i	0.567260	−	0.327508i	0.756054	+	0.654509i	$0.227125\pi$
$504$	0.0203967	−	4.81946i	0.000908542	−	0.214676i
$505$	62.4501	−	16.7335i	2.77899	−	0.744629i
$506$	−8.11541	+	14.0563i	−0.360774	+	0.624879i
$507$	−7.09907	−	21.3683i	−0.315281	−	0.948998i
$508$	−6.47732	−	11.2191i	−0.287385	−	0.497765i
$509$	5.51076	+	5.51076i	0.244260	+	0.244260i	0.818610	−	0.574350i	$-0.194745\pi$
$509$	5.51076	+	5.51076i	0.244260	+	0.244260i	−0.574350	+	0.818610i	$0.694745\pi$
$510$	5.68814	−	5.66412i	0.251875	−	0.250811i
$511$		−	7.57335i		−	0.335025i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−19.4812	+	11.0832i	−0.860118	+	0.489335i
$514$	5.46992	−	20.4140i	0.241268	−	0.900424i
$515$	2.37412	+	8.86034i	0.104616	+	0.390433i
$516$	−1.48921	+	0.395656i	−0.0655586	+	0.0174178i
$517$		−	12.5266i		−	0.550920i
$518$	−5.04257	+	5.04257i	−0.221558	+	0.221558i
$519$	20.4661	+	20.5529i	0.898362	+	0.902172i
$520$	4.12242	+	13.6977i	0.180780	+	0.600686i
$521$		−	2.05915i		−	0.0902131i	−0.998982	−	0.0451065i	$-0.985637\pi$
$521$		−	2.05915i		−	0.0902131i	0.998982	−	0.0451065i	$-0.0143627\pi$
$522$	21.7743	−	5.73575i	0.953035	−	0.251047i
$523$	−10.5734	+	18.3136i	−0.462342	+	0.800800i	−0.999077	−	0.0429511i	$-0.986324\pi$
$523$	−10.5734	+	18.3136i	−0.462342	+	0.800800i	0.536735	+	0.843751i	$0.319657\pi$
$524$	−1.96084			−0.0856599
$525$	−14.9972	+	25.8495i	−0.654534	+	1.12817i
$526$	−0.338557	−	1.26351i	−0.0147618	−	0.0550917i
$527$	−2.27077	−	8.47463i	−0.0989163	−	0.369161i
$528$	−4.31431	+	7.43622i	−0.187756	+	0.323620i
$529$	−12.3071			−0.535092
$530$	−13.0960	+	22.6829i	−0.568853	+	0.985282i
$531$	23.8478	−	6.28195i	1.03491	−	0.272613i
$532$			6.92955i			0.300434i
$533$	10.6286	+	17.1759i	0.460374	+	0.743970i
$534$	−8.41925	−	8.45495i	−0.364336	−	0.365882i
$535$	28.8579	−	28.8579i	1.24764	−	1.24764i
$536$			3.30490i			0.142750i
$537$	6.98406	−	1.85554i	0.301384	−	0.0800726i
$538$	7.37950	+	27.5407i	0.318153	+	1.18736i
$539$	−5.67712	+	21.1873i	−0.244531	+	0.912601i
$540$	−0.130868	+	20.6148i	−0.00563168	+	0.887118i
$541$	−5.41302	−	5.41302i	−0.232724	−	0.232724i	0.581105	−	0.813829i	$-0.302621\pi$
$541$	−5.41302	−	5.41302i	−0.232724	−	0.232724i	−0.813829	+	0.581105i	$0.802621\pi$
$542$		−	1.09418i		−	0.0469992i
$543$	9.23678	−	9.19777i	0.396388	−	0.394714i
$544$	−0.826014	−	0.826014i	−0.0354151	−	0.0354151i
$545$	−16.6422	−	28.8251i	−0.712873	−	1.23473i
$546$	−8.82751	−	4.76739i	−0.377783	−	0.204026i
$547$	10.3483	−	17.9238i	0.442461	−	0.766365i	−0.555411	−	0.831576i	$-0.687439\pi$
$547$	10.3483	−	17.9238i	0.442461	−	0.766365i	0.997871	+	0.0652117i	$0.0207723\pi$
$548$	16.2478	−	4.35359i	0.694073	−	0.185976i
$549$	−0.179254	+	42.3553i	−0.00765038	+	1.80768i
$550$	46.1674	−	26.6548i	1.96858	−	1.13656i
$551$	−31.2722	+	8.37937i	−1.33224	+	0.356973i
$552$	5.66379	+	0.0119850i	0.241067	+	0.000510114i
$553$	−3.62807	+	0.972140i	−0.154281	+	0.0413396i
$554$	13.3057	+	3.56526i	0.565306	+	0.151473i
$555$	21.6149	−	21.5236i	0.917502	−	0.913628i
$556$	13.9186	−	8.03591i	0.590280	−	0.340799i
$557$	2.69183	+	10.0460i	0.114056	+	0.425664i	0.999215	−	0.0396260i	$-0.0126167\pi$
$557$	2.69183	+	10.0460i	0.114056	+	0.425664i	−0.885158	+	0.465290i	$0.845950\pi$
$558$	19.4652	+	11.3484i	0.824029	+	0.480415i
$559$	−0.735204	+	3.12218i	−0.0310958	+	0.132054i
$560$	5.51972	+	3.18681i	0.233251	+	0.134667i
$561$	5.03980	−	8.68670i	0.212781	−	0.366753i
$562$	−4.52518			−0.190883
$563$	6.03582	−	10.4543i	0.254379	−	0.440598i	−0.710347	−	0.703851i	$-0.751462\pi$
$563$	6.03582	−	10.4543i	0.254379	−	0.440598i	0.964727	+	0.263253i	$0.0847955\pi$
$564$	−3.79020	+	2.17759i	−0.159596	+	0.0916932i
$565$	−9.90238	+	9.90238i	−0.416596	+	0.416596i
$566$	−3.75139	−	1.00518i	−0.157683	−	0.0422509i
$567$	−10.1368	−	10.3099i	−0.425706	−	0.432974i
$568$	−1.82116	−	3.15434i	−0.0764141	−	0.132353i
$569$	1.54996	+	2.68461i	0.0649777	+	0.112545i	0.896684	−	0.442671i	$-0.145969\pi$
$569$	1.54996	+	2.68461i	0.0649777	+	0.112545i	−0.831706	+	0.555216i	$0.812636\pi$
$570$	0.0627218	−	29.6407i	0.00262713	−	1.24151i
$571$	16.8061	−	9.70302i	0.703314	−	0.406059i	−0.105266	−	0.994444i	$-0.533569\pi$
$571$	16.8061	−	9.70302i	0.703314	−	0.406059i	0.808581	+	0.588385i	$0.200236\pi$
$572$	9.41717	+	15.2183i	0.393752	+	0.636308i
$573$	−14.8544	+	14.7917i	−0.620551	+	0.617931i
$574$	8.69303	+	2.32929i	0.362840	+	0.0972227i
$575$	−30.4152	−	17.5602i	−1.26840	−	0.732311i
$576$	2.99997	+	0.0126964i	0.124999	+	0.000529015i
$577$	−13.0940	+	13.0940i	−0.545109	+	0.545109i	−0.925022	−	0.379913i	$-0.875954\pi$
$577$	−13.0940	+	13.0940i	−0.545109	+	0.545109i	0.379913	+	0.925022i	$0.375954\pi$
$578$	−11.0559	−	11.0559i	−0.459865	−	0.459865i
$579$	0.0584302	−	27.6126i	0.00242827	−	1.14754i
$580$	−7.70712	+	28.7634i	−0.320021	+	1.19433i
$581$	−15.2003	−	8.77590i	−0.630615	−	0.364086i
$582$	2.89065	−	10.6975i	0.119821	−	0.443424i
$583$	−8.48109	+	31.6519i	−0.351251	+	1.31089i
$584$	4.71419			0.195074
$585$	37.7160	+	20.4721i	1.55936	+	0.846418i
$586$	5.47836			0.226309
$587$	−1.29304	+	4.82567i	−0.0533693	+	0.199177i	−0.987463	−	0.157851i	$-0.949543\pi$
$587$	−1.29304	+	4.82567i	−0.0533693	+	0.199177i	0.934094	+	0.357028i	$0.116210\pi$
$588$	7.39756	−	1.96540i	0.305070	−	0.0810519i
$589$	−28.0562	−	16.1983i	−1.15604	−	0.667437i
$590$	−8.44105	+	31.5024i	−0.347513	+	1.29693i
$591$	19.1809	+	11.1283i	0.788997	+	0.457756i
$592$	−3.13885	−	3.13885i	−0.129006	−	0.129006i
$593$	6.13688	−	6.13688i	0.252012	−	0.252012i	−0.569783	−	0.821795i	$-0.692973\pi$
$593$	6.13688	−	6.13688i	0.252012	−	0.252012i	0.821795	+	0.569783i	$0.192973\pi$
$594$	6.51702	+	24.9544i	0.267396	+	1.02389i
$595$	−6.44792	−	3.72271i	−0.264339	−	0.152616i
$596$	2.75173	+	0.737323i	0.112715	+	0.0302019i
$597$	−21.2757	−	5.74908i	−0.870756	−	0.235294i
$598$	5.58060	−	10.3858i	0.228208	−	0.424706i
$599$	−14.0676	+	8.12194i	−0.574787	+	0.331853i	−0.759059	−	0.651022i	$-0.774341\pi$
$599$	−14.0676	+	8.12194i	−0.574787	+	0.331853i	0.184272	+	0.982875i	$0.441007\pi$
$600$	−16.0906	−	9.33535i	−0.656895	−	0.381114i
$601$	6.33982	+	10.9809i	0.258607	+	0.447920i	0.965869	−	0.259032i	$-0.0834034\pi$
$601$	6.33982	+	10.9809i	0.258607	+	0.447920i	−0.707262	+	0.706951i	$0.750070\pi$
$602$	0.714589	+	1.23770i	0.0291245	+	0.0504450i
$603$	6.98101	+	7.04035i	0.284289	+	0.286705i
$604$	−4.59840	−	1.23214i	−0.187106	−	0.0501350i
$605$	38.2564	−	38.2564i	1.55534	−	1.55534i
$606$	−24.4143	−	14.1646i	−0.991762	−	0.575396i
$607$	−5.02483	+	8.70325i	−0.203951	+	0.353254i	−0.949798	−	0.312863i	$-0.898712\pi$
$607$	−5.02483	+	8.70325i	−0.203951	+	0.353254i	0.745847	+	0.666118i	$0.232045\pi$
$608$	−4.31344			−0.174933
$609$	−10.4042	−	18.1089i	−0.421598	−	0.733811i
$610$	−48.5094	−	28.0069i	−1.96409	−	1.13397i
$611$	0.277804	+	9.09517i	0.0112388	+	0.367951i
$612$	−3.50445	−	0.0148314i	−0.141659	−	0.000599523i
$613$	−1.97714	−	7.37880i	−0.0798561	−	0.298027i	0.914434	−	0.404734i	$-0.132636\pi$
$613$	−1.97714	−	7.37880i	−0.0798561	−	0.298027i	−0.994290	+	0.106707i	$0.965969\pi$
$614$	0.290017	−	0.167441i	0.0117041	−	0.00675738i
$615$	−37.1628	−	10.0421i	−1.49855	−	0.404935i
$616$	7.70225	+	2.06381i	0.310332	+	0.0831533i
$617$	35.3332	−	9.46750i	1.42246	−	0.381147i	0.536104	−	0.844152i	$-0.319895\pi$
$617$	35.3332	−	9.46750i	1.42246	−	0.381147i	0.886356	+	0.463005i	$0.153229\pi$
$618$	2.00965	−	3.46386i	0.0808399	−	0.139337i
$619$	42.7139	−	11.4452i	1.71682	−	0.460020i	0.739737	−	0.672896i	$-0.234950\pi$
$619$	42.7139	−	11.4452i	1.71682	−	0.460020i	0.977079	+	0.212877i	$0.0682832\pi$
$620$	−25.8054	+	14.8987i	−1.03637	+	0.598347i
$621$	12.0908	−	11.9382i	0.485186	−	0.479065i
$622$	14.6310	−	3.92038i	0.586652	−	0.157193i
$623$	−5.53350	+	9.58430i	−0.221695	+	0.383987i
$624$	2.96756	−	5.49487i	0.118798	−	0.219971i
$625$	18.3254	+	31.7405i	0.733015	+	1.26962i
$626$	8.76406	+	8.76406i	0.350282	+	0.350282i
$627$	−9.52202	−	35.8399i	−0.380273	−	1.43131i
$628$		−	7.92424i		−	0.316211i
$629$	3.66669	+	3.66669i	0.146200	+	0.146200i
$630$	18.4901	−	4.87063i	0.736664	−	0.194051i
$631$	5.78419	−	21.5869i	0.230265	−	0.859360i	−0.749962	−	0.661481i	$-0.769928\pi$
$631$	5.78419	−	21.5869i	0.230265	−	0.859360i	0.980226	−	0.197879i	$-0.0634053\pi$
$632$	−0.605128	−	2.25837i	−0.0240707	−	0.0898331i
$633$	−19.2241	−	19.3056i	−0.764089	−	0.767329i
$634$			12.6329i			0.501717i
$635$	36.3426	−	36.3426i	1.44221	−	1.44221i
$636$	11.0513	−	2.93613i	0.438212	−	0.116425i
$637$	3.65209	−	15.5093i	0.144701	−	0.614501i
$638$			37.2549i			1.47494i
$639$	−10.5426	−	2.87275i	−0.417057	−	0.113644i
$640$	−1.98370	+	3.43586i	−0.0784124	+	0.135814i
$641$	2.13469			0.0843153			0.0421577	−	0.999111i	$-0.486577\pi$
$641$	2.13469			0.0843153			0.0421577	+	0.999111i	$0.486577\pi$
$642$	−17.8170	−	0.0377020i	−0.703181	−	0.00148798i
$643$	−3.13025	−	11.6822i	−0.123445	−	0.460702i	0.876335	−	0.481703i	$-0.159982\pi$
$643$	−3.13025	−	11.6822i	−0.123445	−	0.460702i	−0.999779	+	0.0210004i	$0.993315\pi$
$644$	−1.35964	−	5.07426i	−0.0535774	−	0.199954i
$645$	−3.04540	−	5.30067i	−0.119913	−	0.208714i
$646$	5.03879			0.198249
$647$	0.758934	−	1.31451i	0.0298368	−	0.0516788i	−0.850721	−	0.525617i	$-0.823835\pi$
$647$	0.758934	−	1.31451i	0.0298368	−	0.0516788i	0.880558	+	0.473938i	$0.157168\pi$
$648$	6.41760	−	6.30987i	0.252107	−	0.247875i
$649$			40.8026i			1.60164i
$650$	−32.9295	+	20.3770i	−1.29160	+	0.799251i
$651$	5.45164	−	20.1749i	0.213667	−	0.790719i
$652$	12.5518	−	12.5518i	0.491566	−	0.491566i
$653$		−	5.53990i		−	0.216793i	−0.994108	−	0.108397i	$-0.965428\pi$
$653$		−	5.53990i		−	0.216793i	0.994108	−	0.108397i	$-0.0345716\pi$
$654$	−3.79060	+	14.0279i	−0.148224	+	0.548534i
$655$	−2.01347	−	7.51436i	−0.0786726	−	0.293610i
$656$	−1.44991	+	5.41115i	−0.0566097	+	0.211270i
$657$	10.0425	−	9.95789i	0.391797	−	0.388494i
$658$	2.86687	+	2.86687i	0.111762	+	0.111762i
$659$		−	30.0667i		−	1.17123i	−0.810588	−	0.585616i	$-0.800852\pi$
$659$		−	30.0667i		−	1.17123i	0.810588	−	0.585616i	$-0.199148\pi$
$660$	−32.9272	−	8.89754i	−1.28169	−	0.346336i
$661$	−21.3974	−	21.3974i	−0.832261	−	0.832261i	0.155565	−	0.987826i	$-0.450280\pi$
$661$	−21.3974	−	21.3974i	−0.832261	−	0.832261i	−0.987826	+	0.155565i	$0.950280\pi$
$662$	0.718896	+	1.24516i	0.0279407	+	0.0483947i
$663$	−3.46659	+	6.41889i	−0.134631	+	0.249289i
$664$	5.46274	−	9.46175i	0.211996	−	0.367187i
$665$	−26.5555	+	7.11551i	−1.02978	+	0.275928i
$666$	−13.3169	−	0.0563593i	−0.516020	−	0.00218388i
$667$	21.2554	−	12.2718i	0.823012	−	0.475166i
$668$	−10.9578	+	2.93613i	−0.423969	+	0.113602i
$669$	0.157705	+	0.274493i	0.00609723	+	0.0106125i
$670$	−12.6650	+	3.39359i	−0.489293	+	0.131106i
$671$	−67.6903	−	18.1376i	−2.61315	−	0.700193i
$672$	−0.714486	−	2.68925i	−0.0275619	−	0.103740i
$673$	24.1458	−	13.9406i	0.930753	−	0.537371i	0.0437034	−	0.999045i	$-0.486084\pi$
$673$	24.1458	−	13.9406i	0.930753	−	0.537371i	0.887050	+	0.461674i	$0.152751\pi$
$674$	4.95000	+	18.4736i	0.190667	+	0.711578i
$675$	−53.9967	+	14.1016i	−2.07833	+	0.542771i
$676$	−7.17499	−	10.8406i	−0.275961	−	0.416948i
$677$	−33.3037	−	19.2279i	−1.27997	−	0.738989i	−0.303124	−	0.952951i	$-0.598030\pi$
$677$	−33.3037	−	19.2279i	−1.27997	−	0.738989i	−0.976842	+	0.213962i	$0.931363\pi$
$678$	6.11377	+	0.0129372i	0.234798	+	0.000496849i
$679$	−10.2779			−0.394430
$680$	2.31728	−	4.01364i	0.0888634	−	0.153916i
$681$	−0.0486340	+	22.9832i	−0.00186366	+	0.880718i
$682$	−26.3604	+	26.3604i	−1.00939	+	1.00939i
$683$	−27.1625	−	7.27817i	−1.03934	−	0.278491i	−0.301502	−	0.953465i	$-0.597488\pi$
$683$	−27.1625	−	7.27817i	−1.03934	−	0.278491i	−0.737841	+	0.674974i	$0.764155\pi$
$684$	−9.18883	+	9.11139i	−0.351344	+	0.348383i
$685$	33.3677	+	57.7946i	1.27492	+	2.20822i
$686$	−9.17244	−	15.8871i	−0.350205	−	0.606574i
$687$	−13.5720	+	7.79755i	−0.517804	+	0.297495i
$688$	−0.770434	+	0.444811i	−0.0293725	+	0.0169582i
$689$	5.45589	−	23.1695i	0.207853	−	0.882686i
$690$	5.76986	+	21.7171i	0.219655	+	0.826757i
$691$	28.0645	+	7.51985i	1.06762	+	0.286069i	0.749516	−	0.661986i	$-0.230286\pi$
$691$	28.0645	+	7.51985i	1.06762	+	0.286069i	0.318107	+	0.948055i	$0.396953\pi$
$692$	14.5024	+	8.37298i	0.551300	+	0.318293i
$693$	20.7674	−	11.8731i	0.788887	−	0.451024i
$694$	−21.3821	+	21.3821i	−0.811655	+	0.811655i
$695$	45.0874	+	45.0874i	1.71026	+	1.71026i
$696$	11.2723	−	6.47628i	0.427274	−	0.245483i
$697$	1.69373	−	6.32110i	0.0641547	−	0.239429i
$698$	−15.9444	−	9.20552i	−0.603506	−	0.348434i
$699$	6.20491	+	6.23122i	0.234691	+	0.235687i
$700$	−4.46570	+	16.6662i	−0.168788	+	0.629924i
$701$	24.1668			0.912769			0.456384	−	0.889783i	$-0.349144\pi$
$701$	24.1668			0.912769			0.456384	+	0.889783i	$0.349144\pi$
$702$	−5.28521	−	17.9741i	−0.199477	−	0.678387i
$703$	19.1474			0.722158
$704$	−1.28466	+	4.79442i	−0.0484175	+	0.180697i
$705$	−12.2369	−	12.2888i	−0.460868	−	0.462823i
$706$	16.6818	+	9.63127i	0.627830	+	0.362478i
$707$	−6.77582	+	25.2877i	−0.254831	+	0.951041i
$708$	12.3457	−	7.09300i	0.463980	−	0.266571i
$709$	−33.7351	−	33.7351i	−1.26695	−	1.26695i	−0.947657	−	0.319290i	$-0.896556\pi$
$709$	−33.7351	−	33.7351i	−1.26695	−	1.26695i	−0.319290	−	0.947657i	$-0.603444\pi$
$710$	10.2180	−	10.2180i	0.383476	−	0.383476i
$711$	−6.05950	−	3.53273i	−0.227249	−	0.132488i
$712$	−5.96594	−	3.44444i	−0.223583	−	0.129086i
$713$	23.7228	+	6.35650i	0.888425	+	0.238053i
$714$	0.834634	+	3.14147i	0.0312354	+	0.117567i
$715$	−48.6497	+	51.7152i	−1.81939	+	1.93404i
$716$	3.61317	−	2.08607i	0.135031	−	0.0779600i
$717$	−45.1463	+	25.9380i	−1.68602	+	0.968672i
$718$	−10.5398	−	18.2555i	−0.393342	−	0.681289i
$719$	22.5283	+	39.0202i	0.840165	+	1.45521i	0.889755	+	0.456438i	$0.150875\pi$
$719$	22.5283	+	39.0202i	0.840165	+	1.45521i	−0.0495902	+	0.998770i	$0.515792\pi$
$720$	3.03183	+	11.5096i	0.112989	+	0.428936i
$721$	−3.58778	−	0.961344i	−0.133616	−	0.0358023i
$722$	−0.278755	+	0.278755i	−0.0103742	+	0.0103742i
$723$	−0.0641973	+	30.3380i	−0.00238752	+	1.12828i
$724$	3.76295	−	6.51761i	0.139849	−	0.242225i
$725$	−80.6126			−2.99388
$726$	−23.6197	−	0.0499809i	−0.876608	−	0.00185496i
$727$	41.1027	+	23.7307i	1.52442	+	0.880122i	0.999582	+	0.0289169i	$0.00920581\pi$
$727$	41.1027	+	23.7307i	1.52442	+	0.880122i	0.524834	+	0.851205i	$0.324128\pi$
$728$	−5.63812	−	1.32765i	−0.208962	−	0.0492060i
$729$	0.342794	−	26.9978i	0.0126961	−	0.999919i
$730$	4.84070	+	18.0657i	0.179162	+	0.668643i
$731$	0.899991	−	0.519610i	0.0332874	−	0.0192185i
$732$	6.27917	+	23.6341i	0.232085	+	0.873542i
$733$	14.7901	+	3.96299i	0.546285	+	0.146377i	0.521398	−	0.853314i	$-0.325411\pi$
$733$	14.7901	+	3.96299i	0.546285	+	0.146377i	0.0248869	+	0.999690i	$0.492077\pi$
$734$	−20.5429	+	5.50445i	−0.758252	+	0.203173i
$735$	15.1279	+	26.3308i	0.558002	+	0.971227i
$736$	3.15858	−	0.846338i	0.116427	−	0.0311964i
$737$	−14.2063	+	8.20202i	−0.523296	+	0.302125i
$738$	8.34139	+	14.5900i	0.307051	+	0.537064i
$739$	−39.2148	+	10.5076i	−1.44254	+	0.386527i	−0.893422	−	0.449218i	$-0.851702\pi$
$739$	−39.2148	+	10.5076i	−1.44254	+	0.386527i	−0.549117	+	0.835746i	$0.685036\pi$
$740$	8.80564	−	15.2518i	0.323702	−	0.560668i
$741$	7.70845	+	25.8110i	0.283177	+	0.948189i
$742$	−5.30291	−	9.18490i	−0.194676	−	0.337188i
$743$	14.5312	+	14.5312i	0.533096	+	0.533096i	0.921492	−	0.388396i	$-0.126971\pi$
$743$	14.5312	+	14.5312i	0.533096	+	0.533096i	−0.388396	+	0.921492i	$0.626971\pi$
$744$	12.5583	+	3.39349i	0.460410	+	0.124411i
$745$			11.3023i			0.414084i
$746$	−14.1002	−	14.1002i	−0.516246	−	0.516246i
$747$	−8.34911	−	31.6952i	−0.305478	−	1.15967i
$748$	1.50069	−	5.60066i	0.0548707	−	0.204780i
$749$	4.27713	+	15.9625i	0.156283	+	0.583255i
$750$	10.2897	−	38.0793i	0.375727	−	1.39046i
$751$			3.12033i			0.113862i	0.998378	+	0.0569312i	$0.0181316\pi$
$751$			3.12033i			0.113862i	−0.998378	+	0.0569312i	$0.981868\pi$
$752$	−1.78454	+	1.78454i	−0.0650755	+	0.0650755i
$753$	11.0890	−	41.0371i	0.404105	−	1.49547i
$754$	−0.826206	−	27.0496i	−0.0300887	−	0.985087i
$755$		−	18.8872i		−	0.687377i
$756$	−7.20261	−	4.21962i	−0.261957	−	0.153466i
$757$	16.5089	−	28.5942i	0.600026	−	1.03928i	−0.392791	−	0.919628i	$-0.628490\pi$
$757$	16.5089	−	28.5942i	0.600026	−	1.03928i	0.992816	−	0.119647i	$-0.0381764\pi$
$758$	−28.8355			−1.04735
$759$	14.0047	+	24.3759i	0.508340	+	0.884789i
$760$	−4.42920	−	16.5300i	−0.160664	−	0.599606i
$761$	0.400658	+	1.49527i	0.0145238	+	0.0542036i	0.972807	−	0.231615i	$-0.0744011\pi$
$761$	0.400658	+	1.49527i	0.0145238	+	0.0542036i	−0.958284	+	0.285819i	$0.907734\pi$
$762$	−22.4381	−	0.0474805i	−0.812845	−	0.00172004i
$763$	13.4777			0.487926
$764$	−6.05149	+	10.4815i	−0.218935	+	0.379207i
$765$	−3.54166	−	13.4450i	−0.128049	−	0.486105i
$766$			19.6989i			0.711750i
$767$	−0.904884	−	29.6254i	−0.0326735	−	1.06971i
$768$	1.67398	−	0.444746i	0.0604045	−	0.0160484i
$769$	−30.4959	+	30.4959i	−1.09971	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.22215 - 1.22733i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.02684 - 3.83221i) q^{5} +(-1.50183 + 0.862849i) q^{6} +(1.13597 + 1.13597i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.0126964 + 2.99997i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.22215 - 1.22733i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.02684 - 3.83221i) q^{5} +(-1.50183 + 0.862849i) q^{6} +(1.13597 + 1.13597i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.0126964 + 2.99997i) q^{9} +(-3.43586 - 1.98370i) q^{10} +(-4.79442 - 1.28466i) q^{11} +(0.444746 + 1.67398i) q^{12} +(3.50956 + 0.826424i) q^{13} +(1.39127 - 0.803251i) q^{14} +(-5.95834 + 3.42326i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.584080 - 1.01166i) q^{17} +(2.89447 + 0.788714i) q^{18} +(-4.16646 - 1.11640i) q^{19} +(-2.80537 + 2.80537i) q^{20} +(0.00588804 - 2.78254i) q^{21} +(-2.48178 + 4.29856i) q^{22} +3.27000 q^{23} +(1.73205 + 0.00366513i) q^{24} +(-9.30128 - 5.37010i) q^{25} +(1.70661 - 3.17608i) q^{26} +(3.69749 - 3.65084i) q^{27} +(-0.415793 - 1.55176i) q^{28} +(6.50012 - 3.75285i) q^{29} +(1.76448 + 6.64132i) q^{30} +(7.25468 + 1.94388i) q^{31} +(0.965926 - 0.258819i) q^{32} +(4.28280 + 7.45441i) q^{33} +(-1.12836 + 0.302342i) q^{34} +(5.51972 - 3.18681i) q^{35} +(1.51098 - 2.59170i) q^{36} +(-4.28775 + 1.14890i) q^{37} +(-2.15672 + 3.73555i) q^{38} +(-3.27491 - 5.31742i) q^{39} +(1.98370 + 3.43586i) q^{40} +(3.96124 + 3.96124i) q^{41} +(-2.68620 - 0.725861i) q^{42} +0.889621i q^{43} +(3.50976 + 3.50976i) q^{44} +(11.4835 + 3.12914i) q^{45} +(0.846338 - 3.15858i) q^{46} +(0.653187 + 2.43773i) q^{47} +(0.451827 - 1.67208i) q^{48} -4.41915i q^{49} +(-7.59446 + 7.59446i) q^{50} +(-0.527807 + 1.95326i) q^{51} +(-2.62616 - 2.47048i) q^{52} -6.60181i q^{53} +(-2.56946 - 4.51640i) q^{54} +(-9.84618 + 17.0541i) q^{55} -1.60650 q^{56} +(3.72185 + 6.47805i) q^{57} +(-1.94262 - 7.24995i) q^{58} +(-2.12761 - 7.94034i) q^{59} +(6.87171 + 0.0145410i) q^{60} +14.1185 q^{61} +(3.75530 - 6.50436i) q^{62} +(-3.42230 + 3.39345i) q^{63} -1.00000i q^{64} +(6.77077 - 12.6008i) q^{65} +(8.30888 - 2.20752i) q^{66} +(2.33692 - 2.33692i) q^{67} +1.16816i q^{68} +(-3.99643 - 4.01338i) q^{69} +(-1.64961 - 6.15644i) q^{70} +(-0.942701 + 3.51821i) q^{71} +(-2.11232 - 2.13028i) q^{72} +(-3.33343 - 3.33343i) q^{73} +4.43901i q^{74} +(4.77666 + 17.9788i) q^{75} +(3.05006 + 3.05006i) q^{76} +(-3.98698 - 6.90565i) q^{77} +(-5.98384 + 1.78708i) q^{78} +(-1.16902 + 2.02480i) q^{79} +(3.83221 - 1.02684i) q^{80} +(-8.99968 - 0.0761775i) q^{81} +(4.85151 - 2.80102i) q^{82} +(-10.5532 + 2.82772i) q^{83} +(-1.39637 + 2.40680i) q^{84} +(-4.47663 + 1.19951i) q^{85} +(0.859308 + 0.230251i) q^{86} +(-12.5501 - 3.39128i) q^{87} +(4.29856 - 2.48178i) q^{88} +(1.78297 + 6.65415i) q^{89} +(5.99466 - 10.2823i) q^{90} +(3.04796 + 4.92554i) q^{91} +(-2.83190 - 1.63500i) q^{92} +(-6.48051 - 11.2796i) q^{93} +2.52372 q^{94} +(-8.55656 + 14.8204i) q^{95} +(-1.49816 - 0.869198i) q^{96} +(-4.52385 + 4.52385i) q^{97} +(-4.26857 - 1.14376i) q^{98} +(3.91482 - 14.3668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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