LMFDB - Embedded newform 546.2.k.c.373.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (of order $3$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.4
Root			$-1.38232 - 0.298668i$ of defining polynomial
Character	$\chi$	$=$	546.373
Dual form			546.2.k.c.445.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.75410 - 3.03819i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.12588 - 2.39424i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.75410 - 3.03819i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.12588 - 2.39424i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.50820 q^{10} -6.40782 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.213022 - 3.59925i) q^{13} +(-2.63641 + 0.222079i) q^{14} +(1.75410 - 3.03819i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.33890 + 4.05110i) q^{17} +(-0.500000 - 0.866025i) q^{18} +5.23821 q^{19} +(1.75410 + 3.03819i) q^{20} +(1.12588 - 2.39424i) q^{21} +(3.20391 + 5.54934i) q^{22} +(1.08480 + 1.87894i) q^{23} +1.00000 q^{24} +(-3.65372 - 6.32843i) q^{25} +(-3.01053 + 1.98411i) q^{26} +1.00000 q^{27} +(1.51053 + 2.17216i) q^{28} +(-1.23033 + 2.13099i) q^{29} -3.50820 q^{30} +(4.46035 + 7.72555i) q^{31} +(-0.500000 + 0.866025i) q^{32} -6.40782 q^{33} +4.67781 q^{34} +(-5.29925 - 7.62037i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.94981 - 3.37717i) q^{37} +(-2.61911 - 4.53642i) q^{38} +(-0.213022 - 3.59925i) q^{39} +(1.75410 - 3.03819i) q^{40} +(5.09300 - 8.82134i) q^{41} +(-2.63641 + 0.222079i) q^{42} +(-1.19338 - 2.06699i) q^{43} +(3.20391 - 5.54934i) q^{44} +(1.75410 - 3.03819i) q^{45} +(1.08480 - 1.87894i) q^{46} +(-2.44070 + 4.22742i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-4.46478 - 5.39126i) q^{49} +(-3.65372 + 6.32843i) q^{50} +(-2.33890 + 4.05110i) q^{51} +(3.22356 + 1.61514i) q^{52} +(-1.05395 - 1.82549i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-11.2399 + 19.4682i) q^{55} +(1.12588 - 2.39424i) q^{56} +5.23821 q^{57} +2.46066 q^{58} +(5.89729 - 10.2144i) q^{59} +(1.75410 + 3.03819i) q^{60} +9.35561 q^{61} +(4.46035 - 7.72555i) q^{62} +(1.12588 - 2.39424i) q^{63} +1.00000 q^{64} +(-11.3089 - 5.66624i) q^{65} +(3.20391 + 5.54934i) q^{66} +7.28922 q^{67} +(-2.33890 - 4.05110i) q^{68} +(1.08480 + 1.87894i) q^{69} +(-3.94981 + 8.39947i) q^{70} +(2.79339 + 4.83829i) q^{71} +1.00000 q^{72} +(4.23175 + 7.32961i) q^{73} +(-1.94981 + 3.37717i) q^{74} +(-3.65372 - 6.32843i) q^{75} +(-2.61911 + 4.53642i) q^{76} +(-7.21444 + 15.3419i) q^{77} +(-3.01053 + 1.98411i) q^{78} +(0.893764 - 1.54804i) q^{79} -3.50820 q^{80} +1.00000 q^{81} -10.1860 q^{82} -2.59218 q^{83} +(1.51053 + 2.17216i) q^{84} +(8.20533 + 14.2121i) q^{85} +(-1.19338 + 2.06699i) q^{86} +(-1.23033 + 2.13099i) q^{87} -6.40782 q^{88} +(-3.50376 - 6.06869i) q^{89} -3.50820 q^{90} +(-8.85732 - 3.54230i) q^{91} -2.16961 q^{92} +(4.46035 + 7.72555i) q^{93} +4.88140 q^{94} +(9.18834 - 15.9147i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-4.92513 - 8.53057i) q^{97} +(-2.43658 + 6.56225i) q^{98} -6.40782 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 2 * q^5 - 4 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} + 4 q^{23} + 8 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 4 q^{32} - 8 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 6 q^{37} - 4 q^{38} + 3 q^{39} + 2 q^{40} + 12 q^{41} + 3 q^{42} + 4 q^{44} + 2 q^{45} + 4 q^{46} + 7 q^{47} - 4 q^{48} - 7 q^{49} + 2 q^{50} - 2 q^{51} + 9 q^{52} - q^{53} - 4 q^{54} - 25 q^{55} - 3 q^{56} + 8 q^{57} - 4 q^{58} + 16 q^{59} + 2 q^{60} + 8 q^{61} + 14 q^{62} - 3 q^{63} + 8 q^{64} + q^{65} + 4 q^{66} - 38 q^{67} - 2 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} + 8 q^{72} - 7 q^{73} - 6 q^{74} + 2 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 24 q^{82} - 64 q^{83} + 15 q^{85} + 2 q^{87} - 8 q^{88} - 11 q^{89} - 4 q^{90} - 20 q^{91} - 8 q^{92} + 14 q^{93} - 14 q^{94} + 28 q^{95} - 4 q^{96} + 11 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 2 * q^5 - 4 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 + 4 * q^23 + 8 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 4 * q^32 - 8 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 6 * q^37 - 4 * q^38 + 3 * q^39 + 2 * q^40 + 12 * q^41 + 3 * q^42 + 4 * q^44 + 2 * q^45 + 4 * q^46 + 7 * q^47 - 4 * q^48 - 7 * q^49 + 2 * q^50 - 2 * q^51 + 9 * q^52 - q^53 - 4 * q^54 - 25 * q^55 - 3 * q^56 + 8 * q^57 - 4 * q^58 + 16 * q^59 + 2 * q^60 + 8 * q^61 + 14 * q^62 - 3 * q^63 + 8 * q^64 + q^65 + 4 * q^66 - 38 * q^67 - 2 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 + 8 * q^72 - 7 * q^73 - 6 * q^74 + 2 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 24 * q^82 - 64 * q^83 + 15 * q^85 + 2 * q^87 - 8 * q^88 - 11 * q^89 - 4 * q^90 - 20 * q^91 - 8 * q^92 + 14 * q^93 - 14 * q^94 + 28 * q^95 - 4 * q^96 + 11 * q^97 + 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.75410	−	3.03819i	0.784457	−	1.35872i	−0.144866	−	0.989451i	$-0.546275\pi$
$5$	1.75410	−	3.03819i	0.784457	−	1.35872i	0.929323	−	0.369268i	$-0.120391\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.12588	−	2.39424i	0.425543	−	0.904938i
$7$	1.12588	−	2.39424i	0.425543	−	0.904938i
$8$	1.00000			0.353553
$9$	1.00000			0.333333
$10$	−3.50820			−1.10939
$11$	−6.40782			−1.93203			−0.966015	−	0.258485i	$-0.916777\pi$
$11$	−6.40782			−1.93203			−0.966015	+	0.258485i	$0.916777\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.213022	−	3.59925i	−0.0590817	−	0.998253i
$13$	−0.213022	−	3.59925i	−0.0590817	−	0.998253i
$14$	−2.63641	+	0.222079i	−0.704611	+	0.0593532i
$15$	1.75410	−	3.03819i	0.452906	−	0.784457i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.33890	+	4.05110i	−0.567267	+	0.982536i	0.429567	+	0.903035i	$0.358666\pi$
$17$	−2.33890	+	4.05110i	−0.567267	+	0.982536i	−0.996835	+	0.0795010i	$0.974667\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	5.23821			1.20173			0.600864	−	0.799351i	$-0.294823\pi$
$19$	5.23821			1.20173			0.600864	+	0.799351i	$0.294823\pi$
$20$	1.75410	+	3.03819i	0.392228	+	0.679359i
$21$	1.12588	−	2.39424i	0.245687	−	0.522466i
$22$	3.20391	+	5.54934i	0.683076	+	1.18312i
$23$	1.08480	+	1.87894i	0.226197	+	0.391785i	0.956678	−	0.291148i	$-0.0940372\pi$
$23$	1.08480	+	1.87894i	0.226197	+	0.391785i	−0.730481	+	0.682933i	$0.760704\pi$
$24$	1.00000			0.204124
$25$	−3.65372	−	6.32843i	−0.730745	−	1.26569i
$26$	−3.01053	+	1.98411i	−0.590414	+	0.389116i
$27$	1.00000			0.192450
$28$	1.51053	+	2.17216i	0.285464	+	0.410500i
$29$	−1.23033	+	2.13099i	−0.228467	+	0.395716i	−0.957354	−	0.288918i	$-0.906705\pi$
$29$	−1.23033	+	2.13099i	−0.228467	+	0.395716i	0.728887	+	0.684634i	$0.240038\pi$
$30$	−3.50820			−0.640506
$31$	4.46035	+	7.72555i	0.801102	+	1.38755i	0.918892	+	0.394510i	$0.129086\pi$
$31$	4.46035	+	7.72555i	0.801102	+	1.38755i	−0.117790	+	0.993039i	$0.537581\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−6.40782			−1.11546
$34$	4.67781			0.802237
$35$	−5.29925	−	7.62037i	−0.895737	−	1.28808i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.94981	−	3.37717i	−0.320547	−	0.555204i	0.660054	−	0.751218i	$-0.270533\pi$
$37$	−1.94981	−	3.37717i	−0.320547	−	0.555204i	−0.980601	+	0.196014i	$0.937200\pi$
$38$	−2.61911	−	4.53642i	−0.424875	−	0.735905i
$39$	−0.213022	−	3.59925i	−0.0341108	−	0.576342i
$40$	1.75410	−	3.03819i	0.277347	−	0.480380i
$41$	5.09300	−	8.82134i	0.795393	−	1.37766i	−0.127196	−	0.991878i	$-0.540598\pi$
$41$	5.09300	−	8.82134i	0.795393	−	1.37766i	0.922589	−	0.385784i	$-0.126069\pi$
$42$	−2.63641	+	0.222079i	−0.406808	+	0.0342676i
$43$	−1.19338	−	2.06699i	−0.181988	−	0.315213i	0.760569	−	0.649257i	$-0.224920\pi$
$43$	−1.19338	−	2.06699i	−0.181988	−	0.315213i	−0.942558	+	0.334044i	$0.891587\pi$
$44$	3.20391	−	5.54934i	0.483008	−	0.836594i
$45$	1.75410	−	3.03819i	0.261486	−	0.452906i
$46$	1.08480	−	1.87894i	0.159946	−	0.277034i
$47$	−2.44070	+	4.22742i	−0.356013	+	0.616632i	−0.987291	−	0.158924i	$-0.949197\pi$
$47$	−2.44070	+	4.22742i	−0.356013	+	0.616632i	0.631278	+	0.775557i	$0.282531\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−4.46478	−	5.39126i	−0.637826	−	0.770180i
$50$	−3.65372	+	6.32843i	−0.516714	+	0.894976i
$51$	−2.33890	+	4.05110i	−0.327512	+	0.567267i
$52$	3.22356	+	1.61514i	0.447027	+	0.223980i
$53$	−1.05395	−	1.82549i	−0.144771	−	0.250750i	0.784517	−	0.620108i	$-0.212911\pi$
$53$	−1.05395	−	1.82549i	−0.144771	−	0.250750i	−0.929287	+	0.369358i	$0.879578\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−11.2399	+	19.4682i	−1.51559	+	2.62509i
$56$	1.12588	−	2.39424i	0.150452	−	0.319944i
$57$	5.23821			0.693818
$58$	2.46066			0.323101
$59$	5.89729	−	10.2144i	0.767761	−	1.32980i	−0.171013	−	0.985269i	$-0.554704\pi$
$59$	5.89729	−	10.2144i	0.767761	−	1.32980i	0.938774	−	0.344533i	$-0.111963\pi$
$60$	1.75410	+	3.03819i	0.226453	+	0.392228i
$61$	9.35561			1.19786			0.598932	−	0.800800i	$-0.295592\pi$
$61$	9.35561			1.19786			0.598932	+	0.800800i	$0.295592\pi$
$62$	4.46035	−	7.72555i	0.566464	−	0.981145i
$63$	1.12588	−	2.39424i	0.141848	−	0.301646i
$64$	1.00000			0.125000
$65$	−11.3089	−	5.66624i	−1.40269	−	0.702811i
$66$	3.20391	+	5.54934i	0.394374	+	0.683076i
$67$	7.28922			0.890520			0.445260	−	0.895401i	$-0.353111\pi$
$67$	7.28922			0.890520			0.445260	+	0.895401i	$0.353111\pi$
$68$	−2.33890	−	4.05110i	−0.283634	−	0.491268i
$69$	1.08480	+	1.87894i	0.130595	+	0.226197i
$70$	−3.94981	+	8.39947i	−0.472093	+	1.00393i
$71$	2.79339	+	4.83829i	0.331514	+	0.574199i	0.982809	−	0.184625i	$-0.0591072\pi$
$71$	2.79339	+	4.83829i	0.331514	+	0.574199i	−0.651295	+	0.758825i	$0.725774\pi$
$72$	1.00000			0.117851
$73$	4.23175	+	7.32961i	0.495289	+	0.857866i	0.999985	−	0.00543110i	$-0.00172878\pi$
$73$	4.23175	+	7.32961i	0.495289	+	0.857866i	−0.504696	+	0.863297i	$0.668395\pi$
$74$	−1.94981	+	3.37717i	−0.226661	+	0.392588i
$75$	−3.65372	−	6.32843i	−0.421896	−	0.730745i
$76$	−2.61911	+	4.53642i	−0.300432	+	0.520364i
$77$	−7.21444	+	15.3419i	−0.822162	+	1.74837i
$78$	−3.01053	+	1.98411i	−0.340876	+	0.224656i
$79$	0.893764	−	1.54804i	0.100556	−	0.174169i	−0.811358	−	0.584550i	$-0.801271\pi$
$79$	0.893764	−	1.54804i	0.100556	−	0.174169i	0.911914	+	0.410381i	$0.134604\pi$
$80$	−3.50820			−0.392228
$81$	1.00000			0.111111
$82$	−10.1860			−1.12486
$83$	−2.59218			−0.284529			−0.142264	−	0.989829i	$-0.545438\pi$
$83$	−2.59218			−0.284529			−0.142264	+	0.989829i	$0.545438\pi$
$84$	1.51053	+	2.17216i	0.164813	+	0.237002i
$85$	8.20533	+	14.2121i	0.889993	+	1.54151i
$86$	−1.19338	+	2.06699i	−0.128685	+	0.222889i
$87$	−1.23033	+	2.13099i	−0.131905	+	0.228467i
$88$	−6.40782			−0.683076
$89$	−3.50376	−	6.06869i	−0.371398	−	0.643280i	0.618383	−	0.785877i	$-0.287788\pi$
$89$	−3.50376	−	6.06869i	−0.371398	−	0.643280i	−0.989781	+	0.142597i	$0.954455\pi$
$90$	−3.50820			−0.369796
$91$	−8.85732	−	3.54230i	−0.928499	−	0.371334i
$92$	−2.16961			−0.226197
$93$	4.46035	+	7.72555i	0.462516	+	0.801102i
$94$	4.88140			0.503478
$95$	9.18834	−	15.9147i	0.942704	−	1.63281i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−4.92513	−	8.53057i	−0.500071	−	0.866149i	−1.00000		8.21569e-5i	$-0.999974\pi$
$97$	−4.92513	−	8.53057i	−0.500071	−	0.866149i	0.499929	−	0.866066i	$-0.333359\pi$
$98$	−2.43658	+	6.56225i	−0.246132	+	0.662887i
$99$	−6.40782			−0.644010
$100$	7.30745			0.730745
$101$	13.8203			1.37517			0.687586	−	0.726103i	$-0.258670\pi$
$101$	13.8203			1.37517			0.687586	+	0.726103i	$0.258670\pi$
$102$	4.67781			0.463172
$103$	−6.56658	+	11.3737i	−0.647025	+	1.12068i	0.336805	+	0.941574i	$0.390654\pi$
$103$	−6.56658	+	11.3737i	−0.647025	+	1.12068i	−0.983830	+	0.179105i	$0.942680\pi$
$104$	−0.213022	−	3.59925i	−0.0208885	−	0.352936i
$105$	−5.29925	−	7.62037i	−0.517154	−	0.743672i
$106$	−1.05395	+	1.82549i	−0.102368	+	0.177307i
$107$	4.88232	+	8.45642i	0.471991	+	0.817513i	0.999486	−	0.0320452i	$-0.0102020\pi$
$107$	4.88232	+	8.45642i	0.471991	+	0.817513i	−0.527495	+	0.849558i	$0.676869\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	1.14786	+	1.98816i	0.109945	+	0.190431i	0.915748	−	0.401753i	$-0.131599\pi$
$109$	1.14786	+	1.98816i	0.109945	+	0.190431i	−0.805803	+	0.592184i	$0.798266\pi$
$110$	22.4799			2.14337
$111$	−1.94981	−	3.37717i	−0.185068	−	0.320547i
$112$	−2.63641	+	0.222079i	−0.249118	+	0.0209845i
$113$	1.96268	+	3.39947i	0.184634	+	0.319795i	0.943453	−	0.331506i	$-0.107557\pi$
$113$	1.96268	+	3.39947i	0.184634	+	0.319795i	−0.758819	+	0.651301i	$0.774223\pi$
$114$	−2.61911	−	4.53642i	−0.245302	−	0.424875i
$115$	7.61142			0.709768
$116$	−1.23033	−	2.13099i	−0.114233	−	0.197858i
$117$	−0.213022	−	3.59925i	−0.0196939	−	0.332751i
$118$	−11.7946			−1.08578
$119$	7.06598	+	10.1610i	0.647738	+	0.931453i
$120$	1.75410	−	3.03819i	0.160127	−	0.277347i
$121$	30.0602			2.73274
$122$	−4.67781	−	8.10220i	−0.423509	−	0.733539i
$123$	5.09300	−	8.82134i	0.459220	−	0.795393i
$124$	−8.92069			−0.801102
$125$	−8.09497			−0.724036
$126$	−2.63641	+	0.222079i	−0.234870	+	0.0197844i
$127$	3.51196	−	6.08289i	0.311636	−	0.539769i	−0.667081	−	0.744985i	$-0.732457\pi$
$127$	3.51196	−	6.08289i	0.311636	−	0.539769i	0.978717	+	0.205216i	$0.0657898\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.19338	−	2.06699i	−0.105071	−	0.181988i
$130$	0.747323	+	12.6269i	0.0655446	+	1.10745i
$131$	−4.56251	+	7.90250i	−0.398628	+	0.690444i	−0.993557	−	0.113334i	$-0.963847\pi$
$131$	−4.56251	+	7.90250i	−0.398628	+	0.690444i	0.594929	+	0.803778i	$0.297180\pi$
$132$	3.20391	−	5.54934i	0.278865	−	0.483008i
$133$	5.89760	−	12.5415i	0.511387	−	1.08749i
$134$	−3.64461	−	6.31265i	−0.314846	−	0.545330i
$135$	1.75410	−	3.03819i	0.150969	−	0.261486i
$136$	−2.33890	+	4.05110i	−0.200559	+	0.347379i
$137$	−7.53370	+	13.0488i	−0.643648	+	1.11483i	0.340964	+	0.940076i	$0.389246\pi$
$137$	−7.53370	+	13.0488i	−0.643648	+	1.11483i	−0.984612	+	0.174754i	$0.944087\pi$
$138$	1.08480	−	1.87894i	0.0923447	−	0.159946i
$139$	7.02519	+	12.1680i	0.595869	+	1.03208i	0.993424	+	0.114497i	$0.0365255\pi$
$139$	7.02519	+	12.1680i	0.595869	+	1.03208i	−0.397555	+	0.917578i	$0.630141\pi$
$140$	9.24906	−	0.779098i	0.781688	−	0.0658458i
$141$	−2.44070	+	4.22742i	−0.205544	+	0.356013i
$142$	2.79339	−	4.83829i	0.234416	−	0.406020i
$143$	1.36501	+	23.0634i	0.114148	+	1.92866i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.31624	+	7.47595i	0.358444	+	0.620844i
$146$	4.23175	−	7.32961i	0.350222	−	0.606603i
$147$	−4.46478	−	5.39126i	−0.368249	−	0.444664i
$148$	3.89962			0.320547
$149$	1.22934			0.100711			0.0503555	−	0.998731i	$-0.483965\pi$
$149$	1.22934			0.100711			0.0503555	+	0.998731i	$0.483965\pi$
$150$	−3.65372	+	6.32843i	−0.298325	+	0.516714i
$151$	8.17245	+	14.1551i	0.665065	+	1.15193i	0.979268	+	0.202570i	$0.0649294\pi$
$151$	8.17245	+	14.1551i	0.665065	+	1.15193i	−0.314203	+	0.949356i	$0.601737\pi$
$152$	5.23821			0.424875
$153$	−2.33890	+	4.05110i	−0.189089	+	0.327512i
$154$	16.8937	−	1.42304i	1.36133	−	0.114672i
$155$	31.2955			2.51372
$156$	3.22356	+	1.61514i	0.258091	+	0.129315i
$157$	−7.98494	−	13.8303i	−0.637267	−	1.10378i	−0.986030	−	0.166568i	$-0.946731\pi$
$157$	−7.98494	−	13.8303i	−0.637267	−	1.10378i	0.348763	−	0.937211i	$-0.386602\pi$
$158$	−1.78753			−0.142208
$159$	−1.05395	−	1.82549i	−0.0835834	−	0.144771i
$160$	1.75410	+	3.03819i	0.138674	+	0.240190i
$161$	5.71999	−	0.481825i	0.450798	−	0.0379731i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	7.78633			0.609872			0.304936	−	0.952373i	$-0.401365\pi$
$163$	7.78633			0.609872			0.304936	+	0.952373i	$0.401365\pi$
$164$	5.09300	+	8.82134i	0.397697	+	0.688831i
$165$	−11.2399	+	19.4682i	−0.875029	+	1.51559i
$166$	1.29609	+	2.24489i	0.100596	+	0.174237i
$167$	3.32333	−	5.75618i	0.257167	−	0.445427i	−0.708315	−	0.705897i	$-0.750544\pi$
$167$	3.32333	−	5.75618i	0.257167	−	0.445427i	0.965482	+	0.260470i	$0.0838776\pi$
$168$	1.12588	−	2.39424i	0.0868636	−	0.184720i
$169$	−12.9092	+	1.53344i	−0.993019	+	0.117957i
$170$	8.20533	−	14.2121i	0.629320	−	1.09001i
$171$	5.23821			0.400576
$172$	2.38675			0.181988
$173$	−14.6067			−1.11053			−0.555265	−	0.831673i	$-0.687383\pi$
$173$	−14.6067			−1.11053			−0.555265	+	0.831673i	$0.687383\pi$
$174$	2.46066			0.186542
$175$	−19.2655	+	1.62283i	−1.45633	+	0.122675i
$176$	3.20391	+	5.54934i	0.241504	+	0.418297i
$177$	5.89729	−	10.2144i	0.443267	−	0.767761i
$178$	−3.50376	+	6.06869i	−0.262618	+	0.454867i
$179$	−14.1285			−1.05601			−0.528006	−	0.849240i	$-0.677060\pi$
$179$	−14.1285			−1.05601			−0.528006	+	0.849240i	$0.677060\pi$
$180$	1.75410	+	3.03819i	0.130743	+	0.226453i
$181$	−13.6453			−1.01425			−0.507124	−	0.861873i	$-0.669291\pi$
$181$	−13.6453			−1.01425			−0.507124	+	0.861873i	$0.669291\pi$
$182$	1.36093	+	9.44181i	0.100879	+	0.699874i
$183$	9.35561			0.691587
$184$	1.08480	+	1.87894i	0.0799729	+	0.138517i
$185$	−13.6807			−1.00582
$186$	4.46035	−	7.72555i	0.327048	−	0.566464i
$187$	14.9873	−	25.9587i	1.09598	−	1.89829i
$188$	−2.44070	−	4.22742i	−0.178006	−	0.308316i
$189$	1.12588	−	2.39424i	0.0818958	−	0.174155i
$190$	−18.3767			−1.33318
$191$	−2.43145			−0.175933			−0.0879666	−	0.996123i	$-0.528037\pi$
$191$	−2.43145			−0.175933			−0.0879666	+	0.996123i	$0.528037\pi$
$192$	1.00000			0.0721688
$193$	3.51754			0.253198			0.126599	−	0.991954i	$-0.459594\pi$
$193$	3.51754			0.253198			0.126599	+	0.991954i	$0.459594\pi$
$194$	−4.92513	+	8.53057i	−0.353604	+	0.612460i
$195$	−11.3089	−	5.66624i	−0.809845	−	0.405768i
$196$	6.90136	−	1.17099i	0.492954	−	0.0836418i
$197$	1.15702	−	2.00402i	0.0824345	−	0.142781i	−0.821861	−	0.569689i	$-0.807064\pi$
$197$	1.15702	−	2.00402i	0.0824345	−	0.142781i	0.904295	+	0.426908i	$0.140397\pi$
$198$	3.20391	+	5.54934i	0.227692	+	0.394374i
$199$	−2.84733	+	4.93173i	−0.201842	+	0.349601i	−0.949122	−	0.314909i	$-0.898026\pi$
$199$	−2.84733	+	4.93173i	−0.201842	+	0.349601i	0.747280	+	0.664509i	$0.231359\pi$
$200$	−3.65372	−	6.32843i	−0.258357	−	0.447488i
$201$	7.28922			0.514142
$202$	−6.91016	−	11.9687i	−0.486197	−	0.842118i
$203$	3.71691	+	5.34495i	0.260876	+	0.375142i
$204$	−2.33890	−	4.05110i	−0.163756	−	0.283634i
$205$	−17.8673	−	30.9470i	−1.24790	−	2.16143i
$206$	13.1332			0.915031
$207$	1.08480	+	1.87894i	0.0753991	+	0.130595i
$208$	−3.01053	+	1.98411i	−0.208743	+	0.137573i
$209$	−33.5655			−2.32178
$210$	−3.94981	+	8.39947i	−0.272563	+	0.579619i
$211$	0.291966	−	0.505700i	0.0200998	−	0.0348139i	−0.855801	−	0.517306i	$-0.826935\pi$
$211$	0.291966	−	0.505700i	0.0200998	−	0.0348139i	0.875900	+	0.482492i	$0.160268\pi$
$212$	2.10789			0.144771
$213$	2.79339	+	4.83829i	0.191400	+	0.331514i
$214$	4.88232	−	8.45642i	0.333748	−	0.578069i
$215$	−8.37320			−0.571048
$216$	1.00000			0.0680414
$217$	23.5186	−	1.98110i	1.59655	−	0.134486i
$218$	1.14786	−	1.98816i	0.0777430	−	0.134655i
$219$	4.23175	+	7.32961i	0.285955	+	0.495289i
$220$	−11.2399	−	19.4682i	−0.757797	−	1.31254i
$221$	15.0792	+	7.55533i	1.01433	+	0.508227i
$222$	−1.94981	+	3.37717i	−0.130863	+	0.226661i
$223$	−7.25749	+	12.5703i	−0.485998	+	0.841773i	−0.999870	−	0.0160938i	$-0.994877\pi$
$223$	−7.25749	+	12.5703i	−0.485998	+	0.841773i	0.513873	+	0.857866i	$0.328210\pi$
$224$	1.51053	+	2.17216i	0.100927	+	0.145134i
$225$	−3.65372	−	6.32843i	−0.243582	−	0.421896i
$226$	1.96268	−	3.39947i	0.130556	−	0.226129i
$227$	−10.1232	+	17.5339i	−0.671899	+	1.16376i	0.305466	+	0.952203i	$0.401188\pi$
$227$	−10.1232	+	17.5339i	−0.671899	+	1.16376i	−0.977365	+	0.211560i	$0.932146\pi$
$228$	−2.61911	+	4.53642i	−0.173455	+	0.300432i
$229$	−0.668929	+	1.15862i	−0.0442041	+	0.0765637i	−0.887281	−	0.461229i	$-0.847409\pi$
$229$	−0.668929	+	1.15862i	−0.0442041	+	0.0765637i	0.843077	+	0.537793i	$0.180742\pi$
$230$	−3.80571	−	6.59168i	−0.250941	−	0.434643i
$231$	−7.21444	+	15.3419i	−0.474676	+	1.00942i
$232$	−1.23033	+	2.13099i	−0.0807752	+	0.139907i
$233$	6.97568	−	12.0822i	0.456992	−	0.791534i	−0.541808	−	0.840502i	$-0.682260\pi$
$233$	6.97568	−	12.0822i	0.456992	−	0.791534i	0.998800	+	0.0489686i	$0.0155934\pi$
$234$	−3.01053	+	1.98411i	−0.196805	+	0.129705i
$235$	8.56246	+	14.8306i	0.558553	+	0.967443i
$236$	5.89729	+	10.2144i	0.383881	+	0.664901i
$237$	0.893764	−	1.54804i	0.0580562	−	0.100556i
$238$	5.26665	−	11.1998i	0.341386	−	0.725975i
$239$	9.05495			0.585716			0.292858	−	0.956156i	$-0.405394\pi$
$239$	9.05495			0.585716			0.292858	+	0.956156i	$0.405394\pi$
$240$	−3.50820			−0.226453
$241$	−10.0551	+	17.4159i	−0.647705	+	1.12186i	0.335965	+	0.941875i	$0.390938\pi$
$241$	−10.0551	+	17.4159i	−0.647705	+	1.12186i	−0.983670	+	0.179983i	$0.942396\pi$
$242$	−15.0301	−	26.0329i	−0.966171	−	1.67346i
$243$	1.00000			0.0641500
$244$	−4.67781	+	8.10220i	−0.299466	+	0.518690i
$245$	−24.2113	+	4.10805i	−1.54681	+	0.262454i
$246$	−10.1860			−0.649436
$247$	−1.11585	−	18.8536i	−0.0710001	−	1.19963i
$248$	4.46035	+	7.72555i	0.283232	+	0.490573i
$249$	−2.59218			−0.164273
$250$	4.04749	+	7.01045i	0.255986	+	0.443380i
$251$	4.09035	+	7.08469i	0.258181	+	0.447182i	0.965755	−	0.259457i	$-0.0835437\pi$
$251$	4.09035	+	7.08469i	0.258181	+	0.447182i	−0.707574	+	0.706639i	$0.750210\pi$
$252$	1.51053	+	2.17216i	0.0951547	+	0.136833i
$253$	−6.95123	−	12.0399i	−0.437020	−	0.756941i
$254$	−7.02391			−0.440719
$255$	8.20533	+	14.2121i	0.513838	+	0.889993i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.87696	−	8.44715i	−0.304217	−	0.526919i	0.672870	−	0.739761i	$-0.265061\pi$
$257$	−4.87696	−	8.44715i	−0.304217	−	0.526919i	−0.977087	+	0.212842i	$0.931728\pi$
$258$	−1.19338	+	2.06699i	−0.0742964	+	0.128685i
$259$	−10.2810	+	0.866025i	−0.638832	+	0.0538122i
$260$	10.5615	−	6.96065i	0.654999	−	0.431681i
$261$	−1.23033	+	2.13099i	−0.0761555	+	0.131905i
$262$	9.12502			0.563745
$263$	−2.94716			−0.181730			−0.0908648	−	0.995863i	$-0.528963\pi$
$263$	−2.94716			−0.181730			−0.0908648	+	0.995863i	$0.528963\pi$
$264$	−6.40782			−0.394374
$265$	−7.39490			−0.454265
$266$	−13.8101	+	1.16330i	−0.846751	+	0.0713264i
$267$	−3.50376	−	6.06869i	−0.214427	−	0.371398i
$268$	−3.64461	+	6.31265i	−0.222630	+	0.385607i
$269$	11.9676	−	20.7285i	0.729679	−	1.26384i	−0.227340	−	0.973816i	$-0.573003\pi$
$269$	11.9676	−	20.7285i	0.729679	−	1.26384i	0.957019	−	0.290026i	$-0.0936639\pi$
$270$	−3.50820			−0.213502
$271$	−9.68335	−	16.7721i	−0.588222	−	1.01883i	−0.994465	−	0.105065i	$-0.966495\pi$
$271$	−9.68335	−	16.7721i	−0.588222	−	1.01883i	0.406244	−	0.913765i	$-0.366838\pi$
$272$	4.67781			0.283634
$273$	−8.85732	−	3.54230i	−0.536069	−	0.214390i
$274$	15.0674			0.910255
$275$	23.4124	+	40.5515i	1.41182	+	2.44535i
$276$	−2.16961			−0.130595
$277$	−1.21710	+	2.10807i	−0.0731282	+	0.126662i	−0.900271	−	0.435330i	$-0.856632\pi$
$277$	−1.21710	+	2.10807i	−0.0731282	+	0.126662i	0.827143	+	0.561992i	$0.189965\pi$
$278$	7.02519	−	12.1680i	0.421343	−	0.729787i
$279$	4.46035	+	7.72555i	0.267034	+	0.462516i
$280$	−5.29925	−	7.62037i	−0.316691	−	0.455404i
$281$	−2.80329			−0.167230			−0.0836152	−	0.996498i	$-0.526647\pi$
$281$	−2.80329			−0.167230			−0.0836152	+	0.996498i	$0.526647\pi$
$282$	4.88140			0.290683
$283$	−16.9541			−1.00782			−0.503909	−	0.863757i	$-0.668105\pi$
$283$	−16.9541			−1.00782			−0.503909	+	0.863757i	$0.668105\pi$
$284$	−5.58678			−0.331514
$285$	9.18834	−	15.9147i	0.544270	−	0.942704i
$286$	19.2910	−	12.7138i	1.14070	−	0.751784i
$287$	−15.3863	−	22.1257i	−0.908224	−	1.30604i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−2.44094	−	4.22782i	−0.143584	−	0.248696i
$290$	4.31624	−	7.47595i	0.253458	−	0.439003i
$291$	−4.92513	−	8.53057i	−0.288716	−	0.500071i
$292$	−8.46350			−0.495289
$293$	2.84568	+	4.92886i	0.166246	+	0.287947i	0.937097	−	0.349069i	$-0.113502\pi$
$293$	2.84568	+	4.92886i	0.166246	+	0.287947i	−0.770851	+	0.637016i	$0.780169\pi$
$294$	−2.43658	+	6.56225i	−0.142104	+	0.382718i
$295$	−20.6888	−	35.8341i	−1.20455	−	2.08634i
$296$	−1.94981	−	3.37717i	−0.113331	−	0.196294i
$297$	−6.40782			−0.371820
$298$	−0.614668	−	1.06464i	−0.0356067	−	0.0616727i
$299$	6.53168	−	4.30474i	0.377737	−	0.248950i
$300$	7.30745			0.421896
$301$	−6.29247	+	0.530048i	−0.362692	+	0.0305515i
$302$	8.17245	−	14.1551i	0.470272	−	0.814535i
$303$	13.8203			0.793956
$304$	−2.61911	−	4.53642i	−0.150216	−	0.260182i
$305$	16.4107	−	28.4241i	0.939672	−	1.62756i
$306$	4.67781			0.267412
$307$	3.48603			0.198958			0.0994791	−	0.995040i	$-0.468282\pi$
$307$	3.48603			0.198958			0.0994791	+	0.995040i	$0.468282\pi$
$308$	−9.67923	−	13.9188i	−0.551525	−	0.793099i
$309$	−6.56658	+	11.3737i	−0.373560	+	0.647025i
$310$	−15.6478	−	27.1027i	−0.888734	−	1.53933i
$311$	12.0016	+	20.7873i	0.680546	+	1.17874i	0.974814	+	0.223018i	$0.0715908\pi$
$311$	12.0016	+	20.7873i	0.680546	+	1.17874i	−0.294268	+	0.955723i	$0.595076\pi$
$312$	−0.213022	−	3.59925i	−0.0120600	−	0.203768i
$313$	−8.77758	+	15.2032i	−0.496138	+	0.859337i	−0.999990	−	0.00445337i	$-0.998582\pi$
$313$	−8.77758	+	15.2032i	−0.496138	+	0.859337i	0.503852	+	0.863790i	$0.331916\pi$
$314$	−7.98494	+	13.8303i	−0.450616	+	0.780490i
$315$	−5.29925	−	7.62037i	−0.298579	−	0.429359i
$316$	0.893764	+	1.54804i	0.0502781	+	0.0870843i
$317$	−1.42018	+	2.45983i	−0.0797655	+	0.138158i	−0.903149	−	0.429328i	$-0.858750\pi$
$317$	−1.42018	+	2.45983i	−0.0797655	+	0.138158i	0.823383	+	0.567486i	$0.192084\pi$
$318$	−1.05395	+	1.82549i	−0.0591024	+	0.102368i
$319$	7.88374	−	13.6550i	0.441405	−	0.764535i
$320$	1.75410	−	3.03819i	0.0980571	−	0.169840i
$321$	4.88232	+	8.45642i	0.272504	+	0.471991i
$322$	−3.27727	−	4.71274i	−0.182635	−	0.262631i
$323$	−12.2517	+	21.2205i	−0.681701	+	1.18074i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−21.9993	+	14.4988i	−1.22030	+	0.804247i
$326$	−3.89316	−	6.74316i	−0.215622	−	0.373469i
$327$	1.14786	+	1.98816i	0.0634769	+	0.109945i
$328$	5.09300	−	8.82134i	0.281214	−	0.487077i
$329$	7.37352	+	10.6032i	0.406515	+	0.584573i
$330$	22.4799			1.23748
$331$	−18.8749			−1.03746			−0.518729	−	0.854939i	$-0.673595\pi$
$331$	−18.8749			−1.03746			−0.518729	+	0.854939i	$0.673595\pi$
$332$	1.29609	−	2.24489i	0.0711321	−	0.123204i
$333$	−1.94981	−	3.37717i	−0.106849	−	0.185068i
$334$	−6.64666			−0.363689
$335$	12.7860	−	22.1460i	0.698575	−	1.20997i
$336$	−2.63641	+	0.222079i	−0.143828	+	0.0121154i
$337$	10.9560			0.596813			0.298407	−	0.954439i	$-0.403545\pi$
$337$	10.9560			0.596813			0.298407	+	0.954439i	$0.403545\pi$
$338$	7.78262	+	10.4130i	0.423319	+	0.566393i
$339$	1.96268	+	3.39947i	0.106598	+	0.184634i
$340$	−16.4107			−0.889993
$341$	−28.5811	−	49.5039i	−1.54775	−	2.68079i
$342$	−2.61911	−	4.53642i	−0.141625	−	0.245302i
$343$	−17.9348	+	4.61985i	−0.968388	+	0.249449i
$344$	−1.19338	−	2.06699i	−0.0643426	−	0.111445i
$345$	7.61142			0.409785
$346$	7.30337	+	12.6498i	0.392632	+	0.680058i
$347$	16.0515	−	27.8020i	0.861688	−	1.49249i	−0.00861062	−	0.999963i	$-0.502741\pi$
$347$	16.0515	−	27.8020i	0.861688	−	1.49249i	0.870299	−	0.492524i	$-0.163926\pi$
$348$	−1.23033	−	2.13099i	−0.0659526	−	0.114233i
$349$	−9.04373	+	15.6642i	−0.484100	+	0.838485i	−0.999833	−	0.0182638i	$-0.994186\pi$
$349$	−9.04373	+	15.6642i	−0.484100	+	0.838485i	0.515734	+	0.856749i	$0.327519\pi$
$350$	11.0381	+	15.8730i	0.590013	+	0.848445i
$351$	−0.213022	−	3.59925i	−0.0113703	−	0.192114i
$352$	3.20391	−	5.54934i	0.170769	−	0.295781i
$353$	−27.4645			−1.46179			−0.730894	−	0.682491i	$-0.760897\pi$
$353$	−27.4645			−1.46179			−0.730894	+	0.682491i	$0.760897\pi$
$354$	−11.7946			−0.626875
$355$	19.5995			1.04023
$356$	7.00752			0.371398
$357$	7.06598	+	10.1610i	0.373971	+	0.537775i
$358$	7.06425	+	12.2356i	0.373357	+	0.646673i
$359$	−10.8390	+	18.7738i	−0.572063	+	0.990842i	0.424291	+	0.905526i	$0.360523\pi$
$359$	−10.8390	+	18.7738i	−0.572063	+	0.990842i	−0.996354	+	0.0853162i	$0.972810\pi$
$360$	1.75410	−	3.03819i	0.0924491	−	0.160127i
$361$	8.43886			0.444151
$362$	6.82265	+	11.8172i	0.358591	+	0.621097i
$363$	30.0602			1.57775
$364$	7.49638	−	5.89951i	0.392917	−	0.309218i
$365$	29.6916			1.55413
$366$	−4.67781	−	8.10220i	−0.244513	−	0.423509i
$367$	15.3217			0.799788			0.399894	−	0.916561i	$-0.369047\pi$
$367$	15.3217			0.799788			0.399894	+	0.916561i	$0.369047\pi$
$368$	1.08480	−	1.87894i	0.0565494	−	0.0979463i
$369$	5.09300	−	8.82134i	0.265131	−	0.459220i
$370$	6.84033	+	11.8478i	0.355612	+	0.615937i
$371$	−5.55728	+	0.468119i	−0.288520	+	0.0243035i
$372$	−8.92069			−0.462516
$373$	−33.3585			−1.72724			−0.863618	−	0.504147i	$-0.831807\pi$
$373$	−33.3585			−1.72724			−0.863618	+	0.504147i	$0.831807\pi$
$374$	−29.9745			−1.54995
$375$	−8.09497			−0.418023
$376$	−2.44070	+	4.22742i	−0.125870	+	0.218012i
$377$	7.93208	+	3.97432i	0.408523	+	0.204688i
$378$	−2.63641	+	0.222079i	−0.135603	+	0.0114225i
$379$	8.43868	−	14.6162i	0.433466	−	0.750785i	−0.563703	−	0.825977i	$-0.690624\pi$
$379$	8.43868	−	14.6162i	0.433466	−	0.750785i	0.997169	+	0.0751926i	$0.0239571\pi$
$380$	9.18834	+	15.9147i	0.471352	+	0.816405i
$381$	3.51196	−	6.08289i	0.179923	−	0.311636i
$382$	1.21572	+	2.10569i	0.0622018	+	0.107737i
$383$	21.5866			1.10302			0.551512	−	0.834167i	$-0.314051\pi$
$383$	21.5866			1.10302			0.551512	+	0.834167i	$0.314051\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	33.9566	+	48.8300i	1.73059	+	2.48861i
$386$	−1.75877	−	3.04628i	−0.0895191	−	0.155052i
$387$	−1.19338	−	2.06699i	−0.0606628	−	0.105071i
$388$	9.85026			0.500071
$389$	8.68908	+	15.0499i	0.440554	+	0.763062i	0.997731	−	0.0673322i	$-0.0214487\pi$
$389$	8.68908	+	15.0499i	0.440554	+	0.763062i	−0.557177	+	0.830394i	$0.688115\pi$
$390$	0.747323	+	12.6269i	0.0378422	+	0.639387i
$391$	−10.1490			−0.513258
$392$	−4.46478	−	5.39126i	−0.225506	−	0.272300i
$393$	−4.56251	+	7.90250i	−0.230148	+	0.398628i
$394$	−2.31405			−0.116580
$395$	−3.13550	−	5.43084i	−0.157764	−	0.273255i
$396$	3.20391	−	5.54934i	0.161003	−	0.278865i
$397$	5.87435			0.294825			0.147413	−	0.989075i	$-0.452905\pi$
$397$	5.87435			0.294825			0.147413	+	0.989075i	$0.452905\pi$
$398$	5.69467			0.285448
$399$	5.89760	−	12.5415i	0.295249	−	0.627863i
$400$	−3.65372	+	6.32843i	−0.182686	+	0.316422i
$401$	6.98855	+	12.1045i	0.348992	+	0.604471i	0.986071	−	0.166327i	$-0.0531908\pi$
$401$	6.98855	+	12.1045i	0.348992	+	0.604471i	−0.637079	+	0.770799i	$0.719857\pi$
$402$	−3.64461	−	6.31265i	−0.181777	−	0.314846i
$403$	26.8560	−	17.6996i	1.33779	−	0.881681i
$404$	−6.91016	+	11.9687i	−0.343793	+	0.595467i
$405$	1.75410	−	3.03819i	0.0871619	−	0.150969i
$406$	2.77041	−	5.89142i	0.137493	−	0.292386i
$407$	12.4940	+	21.6403i	0.619307	+	1.07267i
$408$	−2.33890	+	4.05110i	−0.115793	+	0.200559i
$409$	18.7448	−	32.4670i	0.926873	−	1.60539i	0.138352	−	0.990383i	$-0.455819\pi$
$409$	18.7448	−	32.4670i	0.926873	−	1.60539i	0.788521	−	0.615008i	$-0.210847\pi$
$410$	−17.8673	+	30.9470i	−0.882401	+	1.52836i
$411$	−7.53370	+	13.0488i	−0.371610	+	0.643648i
$412$	−6.56658	−	11.3737i	−0.323512	−	0.560340i
$413$	−17.8161	−	25.6197i	−0.876673	−	1.26066i
$414$	1.08480	−	1.87894i	0.0533152	−	0.0923447i
$415$	−4.54694	+	7.87553i	−0.223200	+	0.386594i
$416$	3.22356	+	1.61514i	0.158048	+	0.0791889i
$417$	7.02519	+	12.1680i	0.344025	+	0.595869i
$418$	16.7828	+	29.0686i	0.820872	+	1.42179i
$419$	−16.9548	+	29.3665i	−0.828294	+	1.43465i	0.0710814	+	0.997471i	$0.477355\pi$
$419$	−16.9548	+	29.3665i	−0.828294	+	1.43465i	−0.899375	+	0.437177i	$0.855978\pi$
$420$	9.24906	−	0.779098i	0.451308	−	0.0380161i
$421$	−10.5503			−0.514192			−0.257096	−	0.966386i	$-0.582766\pi$
$421$	−10.5503			−0.514192			−0.257096	+	0.966386i	$0.582766\pi$
$422$	−0.583933			−0.0284254
$423$	−2.44070	+	4.22742i	−0.118671	+	0.205544i
$424$	−1.05395	−	1.82549i	−0.0511842	−	0.0886536i
$425$	34.1828			1.65811
$426$	2.79339	−	4.83829i	0.135340	−	0.234416i
$427$	10.5333	−	22.3996i	0.509742	−	1.08399i
$428$	−9.76463			−0.471991
$429$	1.36501	+	23.0634i	0.0659032	+	1.11351i
$430$	4.18660	+	7.25141i	0.201896	+	0.349694i
$431$	−25.6086			−1.23352			−0.616761	−	0.787151i	$-0.711555\pi$
$431$	−25.6086			−1.23352			−0.616761	+	0.787151i	$0.711555\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	3.68968	+	6.39071i	0.177315	+	0.307118i	0.940960	−	0.338518i	$-0.109926\pi$
$433$	3.68968	+	6.39071i	0.177315	+	0.307118i	−0.763645	+	0.645636i	$0.776592\pi$
$434$	−13.4750	−	19.3772i	−0.646821	−	0.930135i
$435$	4.31624	+	7.47595i	0.206948	+	0.358444i
$436$	−2.29572			−0.109945
$437$	5.68244	+	9.84227i	0.271828	+	0.470820i
$438$	4.23175	−	7.32961i	0.202201	−	0.350222i
$439$	11.5255	+	19.9628i	0.550082	+	0.952771i	0.998268	+	0.0588301i	$0.0187370\pi$
$439$	11.5255	+	19.9628i	0.550082	+	0.952771i	−0.448186	+	0.893941i	$0.647930\pi$
$440$	−11.2399	+	19.4682i	−0.535844	+	0.928108i
$441$	−4.46478	−	5.39126i	−0.212609	−	0.256727i
$442$	−0.996476	−	16.8366i	−0.0473975	−	0.800836i
$443$	9.05605	−	15.6855i	0.430266	−	0.745242i	−0.566630	−	0.823972i	$-0.691753\pi$
$443$	9.05605	−	15.6855i	0.430266	−	0.745242i	0.996896	+	0.0787300i	$0.0250865\pi$
$444$	3.89962			0.185068
$445$	−24.5837			−1.16538
$446$	14.5150			0.687304
$447$	1.22934			0.0581456
$448$	1.12588	−	2.39424i	0.0531929	−	0.113117i
$449$	−9.23084	−	15.9883i	−0.435630	−	0.754534i	0.561717	−	0.827330i	$-0.310141\pi$
$449$	−9.23084	−	15.9883i	−0.435630	−	0.754534i	−0.997347	+	0.0727961i	$0.976808\pi$
$450$	−3.65372	+	6.32843i	−0.172238	+	0.298325i
$451$	−32.6350	+	56.5256i	−1.53672	+	2.66168i
$452$	−3.92536			−0.184634
$453$	8.17245	+	14.1551i	0.383975	+	0.665065i
$454$	20.2464			0.950209
$455$	−26.2988	+	20.6966i	−1.23291	+	0.970274i
$456$	5.23821			0.245302
$457$	8.90233	+	15.4193i	0.416433	+	0.721283i	0.995578	−	0.0939414i	$-0.0299466\pi$
$457$	8.90233	+	15.4193i	0.416433	+	0.721283i	−0.579145	+	0.815225i	$0.696613\pi$
$458$	1.33786			0.0625140
$459$	−2.33890	+	4.05110i	−0.109171	+	0.189089i
$460$	−3.80571	+	6.59168i	−0.177442	+	0.307339i
$461$	−2.51030	−	4.34797i	−0.116916	−	0.202505i	0.801628	−	0.597823i	$-0.203968\pi$
$461$	−2.51030	−	4.34797i	−0.116916	−	0.202505i	−0.918544	+	0.395318i	$0.870634\pi$
$462$	16.8937	−	1.42304i	0.785965	−	0.0662060i
$463$	−25.0075			−1.16220			−0.581099	−	0.813833i	$-0.697377\pi$
$463$	−25.0075			−1.16220			−0.581099	+	0.813833i	$0.697377\pi$
$464$	2.46066			0.114233
$465$	31.2955			1.45130
$466$	−13.9514			−0.646284
$467$	12.9128	−	22.3656i	0.597532	−	1.03496i	−0.395653	−	0.918400i	$-0.629482\pi$
$467$	12.9128	−	22.3656i	0.597532	−	1.03496i	0.993184	−	0.116555i	$-0.0371851\pi$
$468$	3.22356	+	1.61514i	0.149009	+	0.0746601i
$469$	8.20680	−	17.4522i	0.378955	−	0.805866i
$470$	8.56246	−	14.8306i	0.394957	−	0.684085i
$471$	−7.98494	−	13.8303i	−0.367926	−	0.637267i
$472$	5.89729	−	10.2144i	0.271445	−	0.470156i
$473$	7.64695	+	13.2449i	0.351607	+	0.609001i
$474$	−1.78753			−0.0821039
$475$	−19.1390	−	33.1497i	−0.878156	−	1.52101i
$476$	−12.3326	+	1.03884i	−0.565265	+	0.0476153i
$477$	−1.05395	−	1.82549i	−0.0482569	−	0.0835834i
$478$	−4.52748	−	7.84182i	−0.207082	−	0.358677i
$479$	23.1137			1.05609			0.528047	−	0.849215i	$-0.322925\pi$
$479$	23.1137			1.05609			0.528047	+	0.849215i	$0.322925\pi$
$480$	1.75410	+	3.03819i	0.0800633	+	0.138674i
$481$	−11.7399	+	7.73728i	−0.535296	+	0.352790i
$482$	20.1102			0.915993
$483$	5.71999	−	0.481825i	0.260269	−	0.0219238i
$484$	−15.0301	+	26.0329i	−0.683186	+	1.18331i
$485$	−34.5566			−1.56914
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	8.13701	−	14.0937i	0.368723	−	0.638647i	−0.620643	−	0.784093i	$-0.713128\pi$
$487$	8.13701	−	14.0937i	0.368723	−	0.638647i	0.989366	+	0.145446i	$0.0464617\pi$
$488$	9.35561			0.423509
$489$	7.78633			0.352110
$490$	15.6633	+	18.9136i	0.707598	+	0.854430i
$491$	−19.0299	+	32.9608i	−0.858809	+	1.48750i	0.0142561	+	0.999898i	$0.495462\pi$
$491$	−19.0299	+	32.9608i	−0.858809	+	1.48750i	−0.873065	+	0.487603i	$0.837871\pi$
$492$	5.09300	+	8.82134i	0.229610	+	0.397697i
$493$	−5.75525	−	9.96838i	−0.259203	−	0.448953i
$494$	−15.7698	+	10.3932i	−0.709517	+	0.467611i
$495$	−11.2399	+	19.4682i	−0.505198	+	0.875029i
$496$	4.46035	−	7.72555i	0.200275	−	0.346887i
$497$	14.7291	−	1.24071i	0.660689	−	0.0556533i
$498$	1.29609	+	2.24489i	0.0580792	+	0.100596i
$499$	17.1178	−	29.6489i	0.766297	−	1.32727i	−0.173261	−	0.984876i	$-0.555430\pi$
$499$	17.1178	−	29.6489i	0.766297	−	1.32727i	0.939558	−	0.342389i	$-0.111236\pi$
$500$	4.04749	−	7.01045i	0.181009	−	0.313517i
$501$	3.32333	−	5.75618i	0.148476	−	0.257167i
$502$	4.09035	−	7.08469i	0.182561	−	0.316205i
$503$	−1.12053	−	1.94081i	−0.0499619	−	0.0865365i	0.839963	−	0.542644i	$-0.182577\pi$
$503$	−1.12053	−	1.94081i	−0.0499619	−	0.0865365i	−0.889925	+	0.456107i	$0.849243\pi$
$504$	1.12588	−	2.39424i	0.0501507	−	0.106648i
$505$	24.2422	−	41.9887i	1.07876	−	1.86847i
$506$	−6.95123	+	12.0399i	−0.309020	+	0.535238i
$507$	−12.9092	+	1.53344i	−0.573320	+	0.0681025i
$508$	3.51196	+	6.08289i	0.155818	+	0.269884i
$509$	12.9164	+	22.3718i	0.572509	+	0.991614i	0.996307	+	0.0858576i	$0.0273630\pi$
$509$	12.9164	+	22.3718i	0.572509	+	0.991614i	−0.423799	+	0.905756i	$0.639304\pi$
$510$	8.20533	−	14.2121i	0.363338	−	0.629320i
$511$	22.3133	−	1.87957i	0.987083	−	0.0831472i
$512$	1.00000			0.0441942
$513$	5.23821			0.231273
$514$	−4.87696	+	8.44715i	−0.215114	+	0.372588i
$515$	23.0369	+	39.9010i	1.01513	+	1.75825i
$516$	2.38675			0.105071
$517$	15.6396	−	27.0885i	0.687828	−	1.19135i
$518$	5.89051	+	8.47062i	0.258814	+	0.372178i
$519$	−14.6067			−0.641165
$520$	−11.3089	−	5.66624i	−0.495927	−	0.248481i
$521$	−12.1715	−	21.0817i	−0.533245	−	0.923607i	−0.999246	−	0.0388230i	$-0.987639\pi$
$521$	−12.1715	−	21.0817i	−0.533245	−	0.923607i	0.466001	−	0.884784i	$-0.345694\pi$
$522$	2.46066			0.107700
$523$	−4.44354	−	7.69644i	−0.194303	−	0.336542i	0.752369	−	0.658742i	$-0.228911\pi$
$523$	−4.44354	−	7.69644i	−0.194303	−	0.336542i	−0.946672	+	0.322200i	$0.895578\pi$
$524$	−4.56251	−	7.90250i	−0.199314	−	0.345222i
$525$	−19.2655	+	1.62283i	−0.840813	+	0.0708262i
$526$	1.47358	+	2.55232i	0.0642511	+	0.111286i
$527$	−41.7293			−1.81776
$528$	3.20391	+	5.54934i	0.139432	+	0.241504i
$529$	9.14640	−	15.8420i	0.397669	−	0.688784i
$530$	3.69745	+	6.40417i	0.160607	+	0.278180i
$531$	5.89729	−	10.2144i	0.255920	−	0.443267i
$532$	7.91249	+	11.3782i	0.343050	+	0.493310i
$533$	−32.8351	−	16.4519i	−1.42225	−	0.712609i
$534$	−3.50376	+	6.06869i	−0.151622	+	0.262618i
$535$	34.2563			1.48103
$536$	7.28922			0.314846
$537$	−14.1285			−0.609689
$538$	−23.9353			−1.03192
$539$	28.6095	+	34.5462i	1.23230	+	1.48801i
$540$	1.75410	+	3.03819i	0.0754844	+	0.130743i
$541$	8.01702	−	13.8859i	0.344679	−	0.597001i	−0.640617	−	0.767861i	$-0.721321\pi$
$541$	8.01702	−	13.8859i	0.344679	−	0.597001i	0.985295	+	0.170860i	$0.0546545\pi$
$542$	−9.68335	+	16.7721i	−0.415936	+	0.720422i
$543$	−13.6453			−0.585576
$544$	−2.33890	−	4.05110i	−0.100280	−	0.173689i
$545$	8.05385			0.344989
$546$	1.36093	+	9.44181i	0.0582426	+	0.404072i
$547$	−10.3955			−0.444481			−0.222240	−	0.974992i	$-0.571337\pi$
$547$	−10.3955			−0.444481			−0.222240	+	0.974992i	$0.571337\pi$
$548$	−7.53370	−	13.0488i	−0.321824	−	0.557415i
$549$	9.35561			0.399288
$550$	23.4124	−	40.5515i	0.998308	−	1.72912i
$551$	−6.44473	+	11.1626i	−0.274555	+	0.475543i
$552$	1.08480	+	1.87894i	0.0461724	+	0.0799729i
$553$	−2.70012	−	3.88280i	−0.114821	−	0.165113i
$554$	2.43419			0.103419
$555$	−13.6807			−0.580711
$556$	−14.0504			−0.595869
$557$	32.3902			1.37242			0.686209	−	0.727404i	$-0.259274\pi$
$557$	32.3902			1.37242			0.686209	+	0.727404i	$0.259274\pi$
$558$	4.46035	−	7.72555i	0.188821	−	0.327048i
$559$	−7.18540	+	4.73558i	−0.303910	+	0.200294i
$560$	−3.94981	+	8.39947i	−0.166910	+	0.354942i
$561$	14.9873	−	25.9587i	0.632763	−	1.09598i
$562$	1.40165	+	2.42772i	0.0591248	+	0.102407i
$563$	1.21655	−	2.10712i	0.0512713	−	0.0888045i	−0.839251	−	0.543745i	$-0.817006\pi$
$563$	1.21655	−	2.10712i	0.0512713	−	0.0888045i	0.890522	+	0.454940i	$0.150339\pi$
$564$	−2.44070	−	4.22742i	−0.102772	−	0.178006i
$565$	13.7710			0.579348
$566$	8.47705	+	14.6827i	0.356317	+	0.617159i
$567$	1.12588	−	2.39424i	0.0472826	−	0.100549i
$568$	2.79339	+	4.83829i	0.117208	+	0.203010i
$569$	3.97033	+	6.87681i	0.166445	+	0.288291i	0.937167	−	0.348880i	$-0.113438\pi$
$569$	3.97033	+	6.87681i	0.166445	+	0.288291i	−0.770723	+	0.637171i	$0.780105\pi$
$570$	−18.3767			−0.769714
$571$	18.0463	+	31.2571i	0.755214	+	1.30807i	0.945268	+	0.326295i	$0.105800\pi$
$571$	18.0463	+	31.2571i	0.755214	+	1.30807i	−0.190054	+	0.981774i	$0.560866\pi$
$572$	−20.6560	−	10.3496i	−0.863669	−	0.432737i
$573$	−2.43145			−0.101575
$574$	−11.4682	+	24.3878i	−0.478675	+	1.01793i
$575$	7.92715	−	13.7302i	0.330585	−	0.572590i
$576$	1.00000			0.0416667
$577$	−16.3980	−	28.4021i	−0.682657	−	1.18240i	−0.974167	−	0.225829i	$-0.927491\pi$
$577$	−16.3980	−	28.4021i	−0.682657	−	1.18240i	0.291510	−	0.956568i	$-0.405842\pi$
$578$	−2.44094	+	4.22782i	−0.101530	+	0.175854i
$579$	3.51754			0.146184
$580$	−8.63248			−0.358444
$581$	−2.91848	+	6.20630i	−0.121079	+	0.257481i
$582$	−4.92513	+	8.53057i	−0.204153	+	0.353604i
$583$	6.75350	+	11.6974i	0.279701	+	0.484457i
$584$	4.23175	+	7.32961i	0.175111	+	0.303301i
$585$	−11.3089	−	5.66624i	−0.467564	−	0.234270i
$586$	2.84568	−	4.92886i	0.117554	−	0.203609i
$587$	10.9482	−	18.9629i	0.451881	−	0.782681i	−0.546622	−	0.837380i	$-0.684086\pi$
$587$	10.9482	−	18.9629i	0.451881	−	0.782681i	0.998503	+	0.0546984i	$0.0174197\pi$
$588$	6.90136	−	1.17099i	0.284607	−	0.0482906i
$589$	23.3642	+	40.4680i	0.962707	+	1.66746i
$590$	−20.6888	+	35.8341i	−0.851746	+	1.47527i
$591$	1.15702	−	2.00402i	0.0475936	−	0.0824345i
$592$	−1.94981	+	3.37717i	−0.0801368	+	0.138801i
$593$	3.25002	−	5.62921i	0.133463	−	0.231164i	−0.791547	−	0.611109i	$-0.790724\pi$
$593$	3.25002	−	5.62921i	0.133463	−	0.231164i	0.925009	+	0.379945i	$0.124057\pi$
$594$	3.20391	+	5.54934i	0.131458	+	0.227692i
$595$	43.2653	−	3.64447i	1.77370	−	0.149409i
$596$	−0.614668	+	1.06464i	−0.0251778	+	0.0436092i
$597$	−2.84733	+	4.93173i	−0.116534	+	0.201842i
$598$	−6.99386	−	3.50423i	−0.286000	−	0.143299i
$599$	1.40105	+	2.42668i	0.0572452	+	0.0991516i	0.893228	−	0.449604i	$-0.148435\pi$
$599$	1.40105	+	2.42668i	0.0572452	+	0.0991516i	−0.835983	+	0.548756i	$0.815102\pi$
$600$	−3.65372	−	6.32843i	−0.149163	−	0.258357i
$601$	−11.8591	+	20.5405i	−0.483741	+	0.837864i	−0.999826	−	0.0186737i	$-0.994056\pi$
$601$	−11.8591	+	20.5405i	−0.483741	+	0.837864i	0.516085	+	0.856538i	$0.327389\pi$
$602$	3.60527	+	5.18442i	0.146940	+	0.211301i
$603$	7.28922			0.296840
$604$	−16.3449			−0.665065
$605$	52.7285	−	91.3284i	2.14372	−	3.71303i
$606$	−6.91016	−	11.9687i	−0.280706	−	0.486197i
$607$	−11.8430			−0.480694			−0.240347	−	0.970687i	$-0.577261\pi$
$607$	−11.8430			−0.480694			−0.240347	+	0.970687i	$0.577261\pi$
$608$	−2.61911	+	4.53642i	−0.106219	+	0.183976i
$609$	3.71691	+	5.34495i	0.150617	+	0.216589i
$610$	−32.8213			−1.32890
$611$	15.7355	+	7.88417i	0.636589	+	0.318959i
$612$	−2.33890	−	4.05110i	−0.0945446	−	0.163756i
$613$	−16.1979			−0.654227			−0.327114	−	0.944985i	$-0.606076\pi$
$613$	−16.1979			−0.654227			−0.327114	+	0.944985i	$0.606076\pi$
$614$	−1.74302	−	3.01899i	−0.0703424	−	0.121837i
$615$	−17.8673	−	30.9470i	−0.720477	−	1.24790i
$616$	−7.21444	+	15.3419i	−0.290678	+	0.618142i
$617$	−22.0973	−	38.2737i	−0.889606	−	1.54084i	−0.840342	−	0.542057i	$-0.817646\pi$
$617$	−22.0973	−	38.2737i	−0.889606	−	1.54084i	−0.0492637	−	0.998786i	$-0.515687\pi$
$618$	13.1332			0.528293
$619$	−17.0272	−	29.4920i	−0.684383	−	1.18539i	−0.973630	−	0.228131i	$-0.926738\pi$
$619$	−17.0272	−	29.4920i	−0.684383	−	1.18539i	0.289248	−	0.957254i	$-0.406595\pi$
$620$	−15.6478	+	27.1027i	−0.628430	+	1.08847i
$621$	1.08480	+	1.87894i	0.0435317	+	0.0753991i
$622$	12.0016	−	20.7873i	0.481219	−	0.833496i
$623$	−18.4747	+	1.55622i	−0.740174	+	0.0623488i
$624$	−3.01053	+	1.98411i	−0.120518	+	0.0794279i
$625$	4.06923	−	7.04812i	0.162769	−	0.281925i
$626$	17.5552			0.701646
$627$	−33.5655			−1.34048
$628$	15.9699			0.637267
$629$	18.2417			0.727344
$630$	−3.94981	+	8.39947i	−0.157364	+	0.334643i
$631$	−0.712707	−	1.23444i	−0.0283724	−	0.0491424i	0.851491	−	0.524370i	$-0.175699\pi$
$631$	−0.712707	−	1.23444i	−0.0283724	−	0.0491424i	−0.879863	+	0.475227i	$0.842366\pi$
$632$	0.893764	−	1.54804i	0.0355520	−	0.0615779i
$633$	0.291966	−	0.505700i	0.0116046	−	0.0200998i
$634$	2.84037			0.112805
$635$	−12.3206	−	21.3400i	−0.488929	−	0.846850i
$636$	2.10789			0.0835834
$637$	−18.4534	+	17.2183i	−0.731151	+	0.682216i
$638$	−15.7675			−0.624240
$639$	2.79339	+	4.83829i	0.110505	+	0.191400i
$640$	−3.50820			−0.138674
$641$	11.6001	−	20.0919i	0.458175	−	0.793582i	−0.540690	−	0.841222i	$-0.681837\pi$
$641$	11.6001	−	20.0919i	0.458175	−	0.793582i	0.998865	+	0.0476400i	$0.0151700\pi$
$642$	4.88232	−	8.45642i	0.192690	−	0.333748i
$643$	3.41821	+	5.92052i	0.134801	+	0.233482i	0.925521	−	0.378695i	$-0.123627\pi$
$643$	3.41821	+	5.92052i	0.134801	+	0.233482i	−0.790720	+	0.612178i	$0.790294\pi$
$644$	−2.44272	+	5.19457i	−0.0962567	+	0.204695i
$645$	−8.37320			−0.329695
$646$	24.5033			0.964071
$647$	−42.5965			−1.67464			−0.837320	−	0.546713i	$-0.815879\pi$
$647$	−42.5965			−1.67464			−0.837320	+	0.546713i	$0.815879\pi$
$648$	1.00000			0.0392837
$649$	−37.7888	+	65.4521i	−1.48334	+	2.56922i
$650$	23.5560	+	11.8026i	0.923941	+	0.462935i
$651$	23.5186	−	1.98110i	0.921768	−	0.0776454i
$652$	−3.89316	+	6.74316i	−0.152468	+	0.264082i
$653$	19.7223	+	34.1601i	0.771794	+	1.33679i	0.936579	+	0.350457i	$0.113974\pi$
$653$	19.7223	+	34.1601i	0.771794	+	1.33679i	−0.164784	+	0.986330i	$0.552693\pi$
$654$	1.14786	−	1.98816i	0.0448850	−	0.0777430i
$655$	16.0062	+	27.7235i	0.625413	+	1.08325i
$656$	−10.1860			−0.397697
$657$	4.23175	+	7.32961i	0.165096	+	0.285955i
$658$	5.49588	−	11.6873i	0.214252	−	0.455617i
$659$	0.667872	+	1.15679i	0.0260166	+	0.0450621i	0.878741	−	0.477300i	$-0.158384\pi$
$659$	0.667872	+	1.15679i	0.0260166	+	0.0450621i	−0.852724	+	0.522362i	$0.825051\pi$
$660$	−11.2399	−	19.4682i	−0.437514	−	0.757797i
$661$	−12.8932			−0.501488			−0.250744	−	0.968053i	$-0.580675\pi$
$661$	−12.8932			−0.501488			−0.250744	+	0.968053i	$0.580675\pi$
$662$	9.43745	+	16.3461i	0.366797	+	0.635311i
$663$	15.0792	+	7.55533i	0.585626	+	0.293425i
$664$	−2.59218			−0.100596
$665$	−27.7586	−	39.9171i	−1.07643	−	1.54792i
$666$	−1.94981	+	3.37717i	−0.0755537	+	0.130863i
$667$	−5.33867			−0.206714
$668$	3.32333	+	5.75618i	0.128584	+	0.222713i
$669$	−7.25749	+	12.5703i	−0.280591	+	0.485998i
$670$	−25.5720			−0.987934
$671$	−59.9491			−2.31431
$672$	1.51053	+	2.17216i	0.0582701	+	0.0837930i
$673$	−13.8759	+	24.0338i	−0.534877	+	0.926434i	0.464292	+	0.885682i	$0.346309\pi$
$673$	−13.8759	+	24.0338i	−0.534877	+	0.926434i	−0.999169	+	0.0407519i	$0.987025\pi$
$674$	−5.47802	−	9.48821i	−0.211005	−	0.365472i
$675$	−3.65372	−	6.32843i	−0.140632	−	0.243582i
$676$	5.12662	−	11.9465i	0.197178	−	0.459479i
$677$	−1.50219	+	2.60188i	−0.0577340	+	0.0999982i	−0.893448	−	0.449167i	$-0.851721\pi$
$677$	−1.50219	+	2.60188i	−0.0577340	+	0.0999982i	0.835714	+	0.549165i	$0.185054\pi$
$678$	1.96268	−	3.39947i	0.0753764	−	0.130556i
$679$	−25.9694	+	2.18754i	−0.996613	+	0.0839500i
$680$	8.20533	+	14.2121i	0.314660	+	0.545007i
$681$	−10.1232	+	17.5339i	−0.387921	+	0.671899i
$682$	−28.5811	+	49.5039i	−1.09443	+	1.89560i
$683$	7.43467	−	12.8772i	0.284480	−	0.492733i	−0.688003	−	0.725708i	$-0.741513\pi$
$683$	7.43467	−	12.8772i	0.284480	−	0.492733i	0.972483	+	0.232974i	$0.0748458\pi$
$684$	−2.61911	+	4.53642i	−0.100144	+	0.173455i
$685$	26.4297	+	45.7776i	1.00983	+	1.74907i
$686$	12.9683	+	13.2221i	0.495132	+	0.504821i
$687$	−0.668929	+	1.15862i	−0.0255212	+	0.0442041i
$688$	−1.19338	+	2.06699i	−0.0454971	+	0.0788033i
$689$	−6.34588	+	4.18229i	−0.241759	+	0.159333i
$690$	−3.80571	−	6.59168i	−0.144881	−	0.250941i
$691$	−4.19053	−	7.25822i	−0.159415	−	0.276116i	0.775243	−	0.631664i	$-0.217628\pi$
$691$	−4.19053	−	7.25822i	−0.159415	−	0.276116i	−0.934658	+	0.355548i	$0.884294\pi$
$692$	7.30337	−	12.6498i	0.277633	−	0.480874i
$693$	−7.21444	+	15.3419i	−0.274054	+	0.582789i
$694$	−32.1029			−1.21861
$695$	49.2915			1.86973
$696$	−1.23033	+	2.13099i	−0.0466356	+	0.0807752i
$697$	23.8241	+	41.2645i	0.902401	+	1.56300i
$698$	18.0875			0.684620
$699$	6.97568	−	12.0822i	0.263845	−	0.456992i
$700$	8.22731	−	17.4958i	0.310963	−	0.661279i
$701$	39.2809			1.48362			0.741809	−	0.670611i	$-0.233968\pi$
$701$	39.2809			1.48362			0.741809	+	0.670611i	$0.233968\pi$
$702$	−3.01053	+	1.98411i	−0.113625	+	0.0748854i
$703$	−10.2135	−	17.6904i	−0.385211	−	0.667204i
$704$	−6.40782			−0.241504
$705$	8.56246	+	14.8306i	0.322481	+	0.558553i
$706$	13.7323	+	23.7850i	0.516820	+	0.895159i
$707$	15.5600	−	33.0892i	0.585195	−	1.24445i
$708$	5.89729	+	10.2144i	0.221634	+	0.383881i
$709$	19.3204			0.725592			0.362796	−	0.931869i	$-0.381822\pi$
$709$	19.3204			0.725592			0.362796	+	0.931869i	$0.381822\pi$
$710$	−9.79976	−	16.9737i	−0.367778	−	0.637011i
$711$	0.893764	−	1.54804i	0.0335188	−	0.0580562i
$712$	−3.50376	−	6.06869i	−0.131309	−	0.227434i
$713$	−9.67721	+	16.7614i	−0.362414	+	0.627720i
$714$	5.26665	−	11.1998i	0.197100	−	0.419142i
$715$	72.4652	+	36.3083i	2.71004	+	1.35785i
$716$	7.06425	−	12.2356i	0.264003	−	0.457267i
$717$	9.05495			0.338163
$718$	21.6781			0.809019
$719$	−28.4410			−1.06067			−0.530335	−	0.847788i	$-0.677934\pi$
$719$	−28.4410			−1.06067			−0.530335	+	0.847788i	$0.677934\pi$
$720$	−3.50820			−0.130743
$721$	19.8381	+	28.5274i	0.738809	+	1.06241i
$722$	−4.21943	−	7.30827i	−0.157031	−	0.271986i
$723$	−10.0551	+	17.4159i	−0.373953	+	0.647705i
$724$	6.82265	−	11.8172i	0.253562	−	0.439182i
$725$	17.9811			0.667803
$726$	−15.0301	−	26.0329i	−0.557819	−	0.966171i
$727$	−48.4057			−1.79527			−0.897634	−	0.440741i	$-0.854716\pi$
$727$	−48.4057			−1.79527			−0.897634	+	0.440741i	$0.854716\pi$
$728$	−8.85732	−	3.54230i	−0.328274	−	0.131287i
$729$	1.00000			0.0370370
$730$	−14.8458	−	25.7137i	−0.549468	−	0.951707i
$731$	11.1648			0.412944
$732$	−4.67781	+	8.10220i	−0.172897	+	0.299466i
$733$	−3.69118	+	6.39332i	−0.136337	+	0.236143i	−0.926107	−	0.377260i	$-0.876866\pi$
$733$	−3.69118	+	6.39332i	−0.136337	+	0.236143i	0.789770	+	0.613403i	$0.210200\pi$
$734$	−7.66086	−	13.2690i	−0.282768	−	0.489768i
$735$	−24.2113	+	4.10805i	−0.893049	+	0.151528i
$736$	−2.16961			−0.0799729
$737$	−46.7080			−1.72051
$738$	−10.1860			−0.374952
$739$	4.82426			0.177463			0.0887316	−	0.996056i	$-0.471719\pi$
$739$	4.82426			0.177463			0.0887316	+	0.996056i	$0.471719\pi$
$740$	6.84033	−	11.8478i	0.251455	−	0.435533i
$741$	−1.11585	−	18.8536i	−0.0409920	−	0.692606i
$742$	3.18404	+	4.57868i	0.116890	+	0.168089i
$743$	17.8556	−	30.9268i	0.655059	−	1.13460i	−0.326820	−	0.945087i	$-0.605977\pi$
$743$	17.8556	−	30.9268i	0.655059	−	1.13460i	0.981879	−	0.189509i	$-0.0606895\pi$
$744$	4.46035	+	7.72555i	0.163524	+	0.283232i
$745$	2.15637	−	3.73495i	0.0790035	−	0.136838i
$746$	16.6792	+	28.8893i	0.610670	+	1.05771i
$747$	−2.59218			−0.0948429
$748$	14.9873	+	25.9587i	0.547989	+	0.949145i
$749$	25.7436	−	2.16852i	0.940651	−	0.0792361i
$750$	4.04749	+	7.01045i	0.147793	+	0.255986i
$751$	−6.54845	−	11.3422i	−0.238956	−	0.413885i	0.721459	−	0.692457i	$-0.243472\pi$
$751$	−6.54845	−	11.3422i	−0.238956	−	0.413885i	−0.960415	+	0.278573i	$0.910139\pi$
$752$	4.88140			0.178006
$753$	4.09035	+	7.08469i	0.149061	+	0.258181i
$754$	−0.524175	−	8.85654i	−0.0190893	−	0.322536i
$755$	57.3411			2.08686
$756$	1.51053	+	2.17216i	0.0549376	+	0.0790008i
$757$	−22.0344	+	38.1646i	−0.800852	+	1.38712i	0.118204	+	0.992989i	$0.462286\pi$
$757$	−22.0344	+	38.1646i	−0.800852	+	1.38712i	−0.919056	+	0.394127i	$0.871047\pi$
$758$	−16.8774			−0.613013
$759$	−6.95123	−	12.0399i	−0.252314	−	0.437020i
$760$	9.18834	−	15.9147i	0.333296	−	0.577286i
$761$	−8.61142			−0.312164			−0.156082	−	0.987744i	$-0.549886\pi$
$761$	−8.61142			−0.312164			−0.156082	+	0.987744i	$0.549886\pi$
$762$	−7.02391			−0.254449
$763$	6.05248	−	0.509833i	0.219115	−	0.0184572i
$764$	1.21572	−	2.10569i	0.0439833	−	0.0761814i
$765$	8.20533	+	14.2121i	0.296664	+	0.513838i
$766$	−10.7933	−	18.6945i	−0.389978	−	0.675461i
$767$	−38.0205	−	19.0499i	−1.37284	−	0.687853i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−3.20391	+	5.54934i	−0.115536	+	0.200114i	−0.917994	−	0.396595i	$-0.870192\pi$
$769$	−3.20391	+	5.54934i	−0.115536	+	0.200114i	0.802458	+	0.596709i	$0.203525\pi$
$770$	25.3097	−	53.8223i	0.912098	−	1.93962i
$771$	−4.87696	−	8.44715i	−0.175640	−	0.304217i
$772$	−1.75877	+	3.04628i	−0.0632996	+	0.109638i
$773$	−6.29082	+	10.8960i	−0.226265	+	0.391902i	−0.956698	−	0.291082i	$-0.905985\pi$
$773$	−6.29082	+	10.8960i	−0.226265	+	0.391902i	0.730433	+	0.682984i	$0.239318\pi$
$774$	−1.19338	+	2.06699i	−0.0428951	+	0.0742964i
$775$	32.5937	−	56.4540i	1.17080	−	2.02789i
$776$	−4.92513	−	8.53057i	−0.176802	−	0.306230i
$777$	−10.2810	+	0.866025i	−0.368830	+	0.0310685i
$778$	8.68908	−	15.0499i	0.311519	−	0.539566i
$779$	26.6782	−	46.2080i	0.955846	−	1.65557i
$780$	10.5615	−	6.96065i	0.378164	−	0.249231i
$781$	−17.8995	−	31.0029i	−0.640496	−	1.10937i
$782$	5.07451	+	8.78930i	0.181464	+	0.314305i
$783$	−1.23033	+	2.13099i	−0.0439684	+	0.0761555i
$784$	−2.43658	+	6.56225i	−0.0870206	+	0.234366i
$785$	−56.0255			−1.99963
$786$	9.12502			0.325479
$787$	9.60693	−	16.6397i	0.342450	−	0.593141i	−0.642437	−	0.766338i	$-0.722077\pi$
$787$	9.60693	−	16.6397i	0.342450	−	0.593141i	0.984887	+	0.173198i	$0.0554099\pi$
$788$	1.15702	+	2.00402i	0.0412172	+	0.0713904i
$789$	−2.94716			−0.104922
$790$	−3.13550	+	5.43084i	−0.111556	+	0.193221i
$791$	10.3489	−	0.871742i	0.367964	−	0.0309956i
$792$	−6.40782			−0.227692
$793$	−1.99295	−	33.6732i	−0.0707718	−	1.19577i
$794$	−2.93718	−	5.08734i	−0.104237	−	0.180543i
$795$	−7.39490			−0.262270
$796$	−2.84733	−	4.93173i	−0.100921	−	0.174800i
$797$	−8.43333	−	14.6070i	−0.298724	−	0.517405i	0.677120	−	0.735872i	$-0.263228\pi$
$797$	−8.43333	−	14.6070i	−0.298724	−	0.517405i	−0.975844	+	0.218467i	$0.929894\pi$
$798$	−13.8101	+	1.16330i	−0.488872	+	0.0411803i
$799$	−11.4171	−	19.7750i	−0.403909	−	0.699591i
$800$	7.30745			0.258357
$801$	−3.50376	−	6.06869i	−0.123799	−	0.214427i
$802$	6.98855	−	12.1045i	0.246774	−	0.427426i
$803$	−27.1163	−	46.9668i	−0.956914	−	1.65742i
$804$	−3.64461	+	6.31265i	−0.128536	+	0.222630i
$805$	8.56955	−	18.2236i	0.302037	−	0.642296i
$806$	−28.7563	−	14.4082i	−1.01290	−	0.507507i
$807$	11.9676	−	20.7285i	0.421280	−	0.729679i
$808$	13.8203			0.486197
$809$	8.76049			0.308002			0.154001	−	0.988071i	$-0.450784\pi$
$809$	8.76049			0.308002			0.154001	+	0.988071i	$0.450784\pi$
$810$	−3.50820			−0.123265
$811$	−32.7259			−1.14916			−0.574581	−	0.818448i	$-0.694835\pi$
$811$	−32.7259			−1.14916			−0.574581	+	0.818448i	$0.694835\pi$
$812$	−6.48732	+	0.546462i	−0.227660	+	0.0191770i
$813$	−9.68335	−	16.7721i	−0.339610	−	0.588222i
$814$	12.4940	−	21.6403i	0.437916	−	0.758493i
$815$	13.6580	−	23.6563i	0.478418	−	0.828645i
$816$	4.67781			0.163756
$817$	−6.25116	−	10.8273i	−0.218701	−	0.378800i
$818$	−37.4897			−1.31080
$819$	−8.85732	−	3.54230i	−0.309500	−	0.123778i
$820$	35.7345			1.24790
$821$	−7.34756	−	12.7263i	−0.256432	−	0.444152i	0.708852	−	0.705357i	$-0.249213\pi$
$821$	−7.34756	−	12.7263i	−0.256432	−	0.444152i	−0.965283	+	0.261205i	$0.915880\pi$
$822$	15.0674			0.525536
$823$	−20.6994	+	35.8525i	−0.721537	+	1.24974i	0.238846	+	0.971057i	$0.423231\pi$
$823$	−20.6994	+	35.8525i	−0.721537	+	1.24974i	−0.960384	+	0.278682i	$0.910103\pi$
$824$	−6.56658	+	11.3737i	−0.228758	+	0.396220i
$825$	23.4124	+	40.5515i	0.815115	+	1.41182i
$826$	−13.2793	+	28.2391i	−0.462046	+	0.982563i
$827$	37.8157			1.31498			0.657491	−	0.753462i	$-0.271618\pi$
$827$	37.8157			1.31498			0.657491	+	0.753462i	$0.271618\pi$
$828$	−2.16961			−0.0753991
$829$	34.4239			1.19559			0.597796	−	0.801648i	$-0.296043\pi$
$829$	34.4239			1.19559			0.597796	+	0.801648i	$0.296043\pi$
$830$	9.09387			0.315653
$831$	−1.21710	+	2.10807i	−0.0422206	+	0.0731282i
$832$	−0.213022	−	3.59925i	−0.00738521	−	0.124782i
$833$	32.2832	−	5.47764i	1.11855	−	0.189789i
$834$	7.02519	−	12.1680i	0.243262	−	0.421343i
$835$	−11.6589	−	20.1938i	−0.403473	−	0.698836i
$836$	16.7828	−	29.0686i	0.580444	−	1.00536i
$837$	4.46035	+	7.72555i	0.154172	+	0.267034i
$838$	33.9095			1.17138
$839$	−0.709771	−	1.22936i	−0.0245040	−	0.0424422i	0.853513	−	0.521071i	$-0.174467\pi$
$839$	−0.709771	−	1.22936i	−0.0245040	−	0.0424422i	−0.878017	+	0.478629i	$0.841134\pi$
$840$	−5.29925	−	7.62037i	−0.182841	−	0.262928i
$841$	11.4726	+	19.8711i	0.395606	+	0.685210i
$842$	5.27517	+	9.13685i	0.181794	+	0.314877i
$843$	−2.80329			−0.0965505
$844$	0.291966	+	0.505700i	0.0100499	+	0.0174069i
$845$	−17.9852	+	41.9105i	−0.618710	+	1.44177i
$846$	4.88140			0.167826
$847$	33.8442	−	71.9713i	1.16290	−	2.47296i
$848$	−1.05395	+	1.82549i	−0.0361927	+	0.0626875i
$849$	−16.9541			−0.581864
$850$	−17.0914	−	29.6032i	−0.586230	−	1.01538i
$851$	4.23033	−	7.32715i	0.145014	−	0.251171i
$852$	−5.58678			−0.191400
$853$	36.8892			1.26306			0.631531	−	0.775351i	$-0.282427\pi$
$853$	36.8892			1.26306			0.631531	+	0.775351i	$0.282427\pi$
$854$	−24.6653	+	2.07769i	−0.844028	+	0.0710970i
$855$	9.18834	−	15.9147i	0.314235	−	0.544270i
$856$	4.88232	+	8.45642i	0.166874	+	0.289034i
$857$	13.9245	+	24.1180i	0.475653	+	0.823855i	0.999611	−	0.0278890i	$-0.00887851\pi$
$857$	13.9245	+	24.1180i	0.475653	+	0.823855i	−0.523958	+	0.851744i	$0.675545\pi$
$858$	19.2910	−	12.7138i	0.658583	−	0.434043i
$859$	−25.2862	+	43.7970i	−0.862754	+	1.49433i	0.00650572	+	0.999979i	$0.497929\pi$
$859$	−25.2862	+	43.7970i	−0.862754	+	1.49433i	−0.869260	+	0.494355i	$0.835404\pi$
$860$	4.18660	−	7.25141i	0.142762	−	0.247271i
$861$	−15.3863	−	22.1257i	−0.524364	−	0.754040i
$862$	12.8043	+	22.1777i	0.436116	+	0.755375i
$863$	14.5501	−	25.2016i	0.495293	−	0.857872i	−0.504693	−	0.863299i	$-0.668394\pi$
$863$	14.5501	−	25.2016i	0.495293	−	0.857872i	0.999985	+	0.00542701i	$0.00172748\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−25.6217	+	44.3780i	−0.871163	+	1.50890i
$866$	3.68968	−	6.39071i	0.125380	−	0.217165i
$867$	−2.44094	−	4.22782i	−0.0828985	−	0.143584i
$868$	−10.0436	+	21.3583i	−0.340903	+	0.724948i
$869$	−5.72708	+	9.91959i	−0.194278	+	0.336499i
$870$	4.31624	−	7.47595i	0.146334	−	0.253458i
$871$	−1.55277	−	26.2358i	−0.0526135	−	0.888965i
$872$	1.14786	+	1.98816i	0.0388715	+	0.0673275i
$873$	−4.92513	−	8.53057i	−0.166690	−	0.288716i
$874$	5.68244	−	9.84227i	0.192211	−	0.332920i
$875$	−9.11398	+	19.3813i	−0.308109	+	0.655208i
$876$	−8.46350			−0.285955
$877$	1.11266			0.0375720			0.0187860	−	0.999824i	$-0.494020\pi$
$877$	1.11266			0.0375720			0.0187860	+	0.999824i	$0.494020\pi$
$878$	11.5255	−	19.9628i	0.388967	−	0.673711i
$879$	2.84568	+	4.92886i	0.0959823	+	0.166246i
$880$	22.4799			0.757797
$881$	−8.14254	+	14.1033i	−0.274329	+	0.475152i	−0.969966	−	0.243242i	$-0.921789\pi$
$881$	−8.14254	+	14.1033i	−0.274329	+	0.475152i	0.695636	+	0.718394i	$0.255122\pi$
$882$	−2.43658	+	6.56225i	−0.0820438	+	0.220962i
$883$	−37.0876			−1.24810			−0.624048	−	0.781386i	$-0.714513\pi$
$883$	−37.0876			−1.24810			−0.624048	+	0.781386i	$0.714513\pi$
$884$	−14.0827	+	9.28128i	−0.473652	+	0.312163i
$885$	−20.6888	−	35.8341i	−0.695448	−	1.20455i
$886$	−18.1121			−0.608488
$887$	10.8028	+	18.7110i	0.362722	+	0.628252i	0.988408	−	0.151823i	$-0.0485143\pi$
$887$	10.8028	+	18.7110i	0.362722	+	0.628252i	−0.625686	+	0.780075i	$0.715181\pi$
$888$	−1.94981	−	3.37717i	−0.0654314	−	0.113331i
$889$	−10.6099	−	15.2571i	−0.355843	−	0.511706i
$890$	12.2919	+	21.2902i	0.412025	+	0.713647i
$891$	−6.40782			−0.214670
$892$	−7.25749	−	12.5703i	−0.242999	−	0.420886i
$893$	−12.7849	+	22.1441i	−0.427831	+	0.741024i
$894$	−0.614668	−	1.06464i	−0.0205576	−	0.0356067i
$895$	−24.7828	+	42.9250i	−0.828396	+	1.43482i
$896$	−2.63641	+	0.222079i	−0.0880764	+	0.00741914i
$897$	6.53168	−	4.30474i	0.218086	−	0.143731i
$898$	−9.23084	+	15.9883i	−0.308037	+	0.533536i
$899$	−21.9508			−0.732100
$900$	7.30745			0.243582
$901$	9.86031			0.328495
$902$	65.2701			2.17326
$903$	−6.29247	+	0.530048i	−0.209400	+	0.0176389i
$904$	1.96268	+	3.39947i	0.0652778	+	0.113065i
$905$	−23.9352	+	41.4570i	−0.795633	+	1.37808i
$906$	8.17245	−	14.1551i	0.271512	−	0.470272i
$907$	−29.0539			−0.964720			−0.482360	−	0.875973i	$-0.660220\pi$
$907$	−29.0539			−0.964720			−0.482360	+	0.875973i	$0.660220\pi$
$908$	−10.1232	−	17.5339i	−0.335950	−	0.581882i
$909$	13.8203			0.458391
$910$	31.0732	+	12.4271i	1.03007	+	0.411954i
$911$	−22.2791			−0.738141			−0.369071	−	0.929401i	$-0.620324\pi$
$911$	−22.2791			−0.738141			−0.369071	+	0.929401i	$0.620324\pi$
$912$	−2.61911	−	4.53642i	−0.0867273	−	0.150216i
$913$	16.6102			0.549718
$914$	8.90233	−	15.4193i	0.294463	−	0.510024i
$915$	16.4107	−	28.4241i	0.542520	−	0.939672i
$916$	−0.668929	−	1.15862i	−0.0221020	−	0.0382819i
$917$	13.7836	+	19.8210i	0.455176	+	0.654548i
$918$	4.67781			0.154391
$919$	−35.1435			−1.15928			−0.579639	−	0.814873i	$-0.696806\pi$
$919$	−35.1435			−1.15928			−0.579639	+	0.814873i	$0.696806\pi$
$920$	7.61142			0.250941
$921$	3.48603			0.114869
$922$	−2.51030	+	4.34797i	−0.0826723	+	0.143193i
$923$	16.8192	−	11.0848i	0.553610	−	0.364860i
$924$	−9.67923	−	13.9188i	−0.318423	−	0.457896i
$925$	−14.2481	+	24.6785i	−0.468476	+	0.811425i
$926$	12.5038	+	21.6571i	0.410899	+	0.711698i
$927$	−6.56658	+	11.3737i	−0.215675	+	0.373560i
$928$	−1.23033	−	2.13099i	−0.0403876	−	0.0699533i
$929$	−36.7445			−1.20555			−0.602774	−	0.797912i	$-0.705938\pi$
$929$	−36.7445			−1.20555			−0.602774	+	0.797912i	$0.705938\pi$
$930$	−15.6478	−	27.1027i	−0.513111	−	0.888734i
$931$	−23.3875	−	28.2406i	−0.766494	−	0.925547i
$932$	6.97568	+	12.0822i	0.228496	+	0.395767i
$933$	12.0016	+	20.7873i	0.392914	+	0.680546i
$934$	−25.8255			−0.845037
$935$	−52.5783	−	91.0683i	−1.71949	−	2.97825i
$936$	−0.213022	−	3.59925i	−0.00696285	−	0.117645i
$937$	18.5284			0.605295			0.302647	−	0.953103i	$-0.402130\pi$
$937$	18.5284			0.605295			0.302647	+	0.953103i	$0.402130\pi$
$938$	−19.2174	+	1.61878i	−0.627471	+	0.0528552i
$939$	−8.77758	+	15.2032i	−0.286446	+	0.496138i
$940$	−17.1249			−0.558553
$941$	22.5985	+	39.1417i	0.736689	+	1.27598i	0.953979	+	0.299875i	$0.0969450\pi$
$941$	22.5985	+	39.1417i	0.736689	+	1.27598i	−0.217290	+	0.976107i	$0.569722\pi$
$942$	−7.98494	+	13.8303i	−0.260163	+	0.450616i
$943$	22.0996			0.719664
$944$	−11.7946			−0.383881
$945$	−5.29925	−	7.62037i	−0.172385	−	0.247891i
$946$	7.64695	−	13.2449i	0.248624	−	0.430629i
$947$	−14.4333	−	24.9993i	−0.469020	−	0.812367i	0.530353	−	0.847777i	$-0.322059\pi$
$947$	−14.4333	−	24.9993i	−0.469020	−	0.812367i	−0.999373	+	0.0354104i	$0.988726\pi$
$948$	0.893764	+	1.54804i	0.0290281	+	0.0502781i
$949$	25.4797	−	16.7925i	0.827105	−	0.545108i
$950$	−19.1390	+	33.1497i	−0.620950	+	1.07552i
$951$	−1.42018	+	2.45983i	−0.0460526	+	0.0797655i
$952$	7.06598	+	10.1610i	0.229010	+	0.329318i
$953$	8.36687	+	14.4919i	0.271030	+	0.469437i	0.969126	−	0.246567i	$-0.0793025\pi$
$953$	8.36687	+	14.4919i	0.271030	+	0.469437i	−0.698096	+	0.716004i	$0.745969\pi$
$954$	−1.05395	+	1.82549i	−0.0341228	+	0.0591024i
$955$	−4.26500	+	7.38719i	−0.138012	+	0.239044i
$956$	−4.52748	+	7.84182i	−0.146429	+	0.253623i
$957$	7.88374	−	13.6550i	0.254845	−	0.441405i
$958$	−11.5569	−	20.0171i	−0.373386	−	0.646723i
$959$	22.7598	+	32.7288i	0.734953	+	1.05687i
$960$	1.75410	−	3.03819i	0.0566133	−	0.0980571i
$961$	−24.2894	+	42.0704i	−0.783528	+	1.35711i
$962$	12.5707	+	6.29845i	0.405294	+	0.203070i
$963$	4.88232	+	8.45642i	0.157330	+	0.272504i
$964$	−10.0551	−	17.4159i	−0.323852	−	0.560929i
$965$	6.17012	−	10.6870i	0.198623	−	0.344025i
$966$	−3.27727	−	4.71274i	−0.105444	−	0.151630i
$967$	−3.01759			−0.0970392			−0.0485196	−	0.998822i	$-0.515450\pi$
$967$	−3.01759			−0.0970392			−0.0485196	+	0.998822i	$0.515450\pi$
$968$	30.0602			0.966171
$969$	−12.2517	+	21.2205i	−0.393580	+	0.681701i
$970$	17.2783	+	29.9269i	0.554774	+	0.960896i
$971$	25.6802			0.824116			0.412058	−	0.911158i	$-0.364810\pi$
$971$	25.6802			0.824116			0.412058	+	0.911158i	$0.364810\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	37.0426	−	3.12030i	1.18753	−	0.100032i
$974$	−16.2740			−0.521453
$975$	−21.9993	+	14.4988i	−0.704542	+	0.464332i
$976$	−4.67781	−	8.10220i	−0.149733	−	0.259345i
$977$	−40.6502			−1.30052			−0.650258	−	0.759713i	$-0.725339\pi$
$977$	−40.6502			−1.30052			−0.650258	+	0.759713i	$0.725339\pi$
$978$	−3.89316	−	6.74316i	−0.124490	−	0.215622i
$979$	22.4515	+	38.8871i	0.717552	+	1.24284i
$980$	8.54799	−	23.0217i	0.273056	−	0.735400i
$981$	1.14786	+	1.98816i	0.0366484	+	0.0634769i
$982$	38.0599			1.21454
$983$	−2.39794	−	4.15335i	−0.0764823	−	0.132471i	0.825248	−	0.564771i	$-0.191036\pi$
$983$	−2.39794	−	4.15335i	−0.0764823	−	0.132471i	−0.901730	+	0.432300i	$0.857702\pi$
$984$	5.09300	−	8.82134i	0.162359	−	0.281214i
$985$	−4.05906	−	7.03051i	−0.129333	−	0.224011i
$986$	−5.75525	+	9.96838i	−0.183284	+	0.317458i
$987$	7.37352	+	10.6032i	0.234702	+	0.337503i
$988$	16.8857	+	8.46047i	0.537205	+	0.269163i
$989$	2.58916	−	4.48456i	0.0823306	−	0.142601i
$990$	22.4799			0.714458
$991$	−39.1431			−1.24342			−0.621710	−	0.783247i	$-0.713562\pi$
$991$	−39.1431			−1.24342			−0.621710	+	0.783247i	$0.713562\pi$
$992$	−8.92069			−0.283232
$993$	−18.8749			−0.598977
$994$	−8.43901	−	12.1354i	−0.267669	−	0.384911i
$995$	9.98901	+	17.3015i	0.316673	+	0.548494i
$996$	1.29609	−	2.24489i	0.0410682	−	0.0711321i
$997$	28.7246	−	49.7524i	0.909716	−	1.57567i	0.0952567	−	0.995453i	$-0.469633\pi$
$997$	28.7246	−	49.7524i	0.909716	−	1.57567i	0.814459	−	0.580221i	$-0.197034\pi$
$998$	−34.2356			−1.08371
$999$	−1.94981	−	3.37717i	−0.0616893	−	0.106849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.c.373.4	yes	8
3.2	odd	2		1638.2.p.h.919.1		8
7.4	even	3		546.2.j.c.529.4	yes	8
13.3	even	3		546.2.j.c.289.4	✓	8
21.11	odd	6		1638.2.m.h.1621.1		8
39.29	odd	6		1638.2.m.h.289.1		8
91.81	even	3	inner	546.2.k.c.445.4	yes	8
273.263	odd	6		1638.2.p.h.991.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.4	✓	8	13.3	even	3
546.2.j.c.529.4	yes	8	7.4	even	3
546.2.k.c.373.4	yes	8	1.1	even	1	trivial
546.2.k.c.445.4	yes	8	91.81	even	3	inner
1638.2.m.h.289.1		8	39.29	odd	6
1638.2.m.h.1621.1		8	21.11	odd	6
1638.2.p.h.919.1		8	3.2	odd	2
1638.2.p.h.991.1		8	273.263	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.75410 - 3.03819i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.12588 - 2.39424i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.75410 - 3.03819i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.12588 - 2.39424i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.50820 q^{10} -6.40782 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.213022 - 3.59925i) q^{13} +(-2.63641 + 0.222079i) q^{14} +(1.75410 - 3.03819i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.33890 + 4.05110i) q^{17} +(-0.500000 - 0.866025i) q^{18} +5.23821 q^{19} +(1.75410 + 3.03819i) q^{20} +(1.12588 - 2.39424i) q^{21} +(3.20391 + 5.54934i) q^{22} +(1.08480 + 1.87894i) q^{23} +1.00000 q^{24} +(-3.65372 - 6.32843i) q^{25} +(-3.01053 + 1.98411i) q^{26} +1.00000 q^{27} +(1.51053 + 2.17216i) q^{28} +(-1.23033 + 2.13099i) q^{29} -3.50820 q^{30} +(4.46035 + 7.72555i) q^{31} +(-0.500000 + 0.866025i) q^{32} -6.40782 q^{33} +4.67781 q^{34} +(-5.29925 - 7.62037i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.94981 - 3.37717i) q^{37} +(-2.61911 - 4.53642i) q^{38} +(-0.213022 - 3.59925i) q^{39} +(1.75410 - 3.03819i) q^{40} +(5.09300 - 8.82134i) q^{41} +(-2.63641 + 0.222079i) q^{42} +(-1.19338 - 2.06699i) q^{43} +(3.20391 - 5.54934i) q^{44} +(1.75410 - 3.03819i) q^{45} +(1.08480 - 1.87894i) q^{46} +(-2.44070 + 4.22742i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-4.46478 - 5.39126i) q^{49} +(-3.65372 + 6.32843i) q^{50} +(-2.33890 + 4.05110i) q^{51} +(3.22356 + 1.61514i) q^{52} +(-1.05395 - 1.82549i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-11.2399 + 19.4682i) q^{55} +(1.12588 - 2.39424i) q^{56} +5.23821 q^{57} +2.46066 q^{58} +(5.89729 - 10.2144i) q^{59} +(1.75410 + 3.03819i) q^{60} +9.35561 q^{61} +(4.46035 - 7.72555i) q^{62} +(1.12588 - 2.39424i) q^{63} +1.00000 q^{64} +(-11.3089 - 5.66624i) q^{65} +(3.20391 + 5.54934i) q^{66} +7.28922 q^{67} +(-2.33890 - 4.05110i) q^{68} +(1.08480 + 1.87894i) q^{69} +(-3.94981 + 8.39947i) q^{70} +(2.79339 + 4.83829i) q^{71} +1.00000 q^{72} +(4.23175 + 7.32961i) q^{73} +(-1.94981 + 3.37717i) q^{74} +(-3.65372 - 6.32843i) q^{75} +(-2.61911 + 4.53642i) q^{76} +(-7.21444 + 15.3419i) q^{77} +(-3.01053 + 1.98411i) q^{78} +(0.893764 - 1.54804i) q^{79} -3.50820 q^{80} +1.00000 q^{81} -10.1860 q^{82} -2.59218 q^{83} +(1.51053 + 2.17216i) q^{84} +(8.20533 + 14.2121i) q^{85} +(-1.19338 + 2.06699i) q^{86} +(-1.23033 + 2.13099i) q^{87} -6.40782 q^{88} +(-3.50376 - 6.06869i) q^{89} -3.50820 q^{90} +(-8.85732 - 3.54230i) q^{91} -2.16961 q^{92} +(4.46035 + 7.72555i) q^{93} +4.88140 q^{94} +(9.18834 - 15.9147i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-4.92513 - 8.53057i) q^{97} +(-2.43658 + 6.56225i) q^{98} -6.40782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 2 * q^5 - 4 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} + 4 q^{23} + 8 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 4 q^{32} - 8 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 6 q^{37} - 4 q^{38} + 3 q^{39} + 2 q^{40} + 12 q^{41} + 3 q^{42} + 4 q^{44} + 2 q^{45} + 4 q^{46} + 7 q^{47} - 4 q^{48} - 7 q^{49} + 2 q^{50} - 2 q^{51} + 9 q^{52} - q^{53} - 4 q^{54} - 25 q^{55} - 3 q^{56} + 8 q^{57} - 4 q^{58} + 16 q^{59} + 2 q^{60} + 8 q^{61} + 14 q^{62} - 3 q^{63} + 8 q^{64} + q^{65} + 4 q^{66} - 38 q^{67} - 2 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} + 8 q^{72} - 7 q^{73} - 6 q^{74} + 2 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 24 q^{82} - 64 q^{83} + 15 q^{85} + 2 q^{87} - 8 q^{88} - 11 q^{89} - 4 q^{90} - 20 q^{91} - 8 q^{92} + 14 q^{93} - 14 q^{94} + 28 q^{95} - 4 q^{96} + 11 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 2 * q^5 - 4 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 + 4 * q^23 + 8 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 4 * q^32 - 8 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 6 * q^37 - 4 * q^38 + 3 * q^39 + 2 * q^40 + 12 * q^41 + 3 * q^42 + 4 * q^44 + 2 * q^45 + 4 * q^46 + 7 * q^47 - 4 * q^48 - 7 * q^49 + 2 * q^50 - 2 * q^51 + 9 * q^52 - q^53 - 4 * q^54 - 25 * q^55 - 3 * q^56 + 8 * q^57 - 4 * q^58 + 16 * q^59 + 2 * q^60 + 8 * q^61 + 14 * q^62 - 3 * q^63 + 8 * q^64 + q^65 + 4 * q^66 - 38 * q^67 - 2 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 + 8 * q^72 - 7 * q^73 - 6 * q^74 + 2 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 24 * q^82 - 64 * q^83 + 15 * q^85 + 2 * q^87 - 8 * q^88 - 11 * q^89 - 4 * q^90 - 20 * q^91 - 8 * q^92 + 14 * q^93 - 14 * q^94 + 28 * q^95 - 4 * q^96 + 11 * q^97 + 2 * q^98 - 8 * q^99

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