LMFDB - Embedded newform 798.2.bu.a.53.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 12, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,-81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.7
Character	$\chi$	$=$	798.53
Dual form			798.2.bu.a.527.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 + 0.984808i) q^{2} +(-1.15251 - 1.29295i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.20215 + 3.30288i) q^{5} +(1.07318 - 1.35952i) q^{6} +(0.891053 + 2.49119i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.343437 + 2.98028i) q^{9} +(-3.46145 - 0.610347i) q^{10} +0.804204i q^{11} +(1.52522 + 0.820793i) q^{12} +(0.0233648 + 0.00411984i) q^{13} +(-2.29861 + 1.31011i) q^{14} +(5.65594 - 2.25228i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.35107 - 1.61014i) q^{17} +(-2.99464 + 0.179300i) q^{18} +(0.187916 - 4.35485i) q^{19} -3.51485i q^{20} +(2.19403 - 4.02321i) q^{21} +(-0.791987 + 0.139649i) q^{22} +(-0.615888 - 0.108598i) q^{23} +(-0.543472 + 1.64458i) q^{24} +(-5.63361 - 4.72716i) q^{25} +0.0237252i q^{26} +(4.24916 - 2.99075i) q^{27} +(-1.68935 - 2.03619i) q^{28} +(-5.76527 + 2.09839i) q^{29} +(3.20021 + 5.17891i) q^{30} +(-2.10756 + 1.21680i) q^{31} +(0.766044 + 0.642788i) q^{32} +(1.03980 - 0.926854i) q^{33} +(1.35107 - 1.61014i) q^{34} +(-9.29927 - 0.0517406i) q^{35} +(-0.696589 - 2.91801i) q^{36} +(-8.59558 + 4.96266i) q^{37} +(4.32132 - 0.571150i) q^{38} +(-0.0216014 - 0.0349577i) q^{39} +(3.46145 - 0.610347i) q^{40} +(-0.0216849 - 0.122981i) q^{41} +(4.34308 + 1.46208i) q^{42} +(-5.10632 + 4.28471i) q^{43} +(-0.275054 - 0.755705i) q^{44} +(-9.43063 - 4.71707i) q^{45} -0.625389i q^{46} +(0.429351 - 0.511681i) q^{47} +(-1.71397 - 0.249637i) q^{48} +(-5.41205 + 4.43957i) q^{49} +(3.67708 - 6.36889i) q^{50} +(-0.524710 + 3.60257i) q^{51} +(-0.0233648 + 0.00411984i) q^{52} +(7.53475 - 2.74243i) q^{53} +(3.68318 + 3.66527i) q^{54} +(-2.65619 - 0.966774i) q^{55} +(1.71191 - 2.01727i) q^{56} +(-5.84717 + 4.77604i) q^{57} +(-3.06763 - 5.31330i) q^{58} +(1.11835 - 0.938406i) q^{59} +(-4.54452 + 4.05090i) q^{60} +(2.45219 - 13.9071i) q^{61} +(-1.56429 - 1.86425i) q^{62} +(-7.73045 + 1.80002i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0416953 + 0.0722184i) q^{65} +(1.09333 + 0.863052i) q^{66} +(8.75434 + 1.54363i) q^{67} +(1.82029 + 1.05095i) q^{68} +(0.569407 + 0.921472i) q^{69} +(-1.56385 - 9.16698i) q^{70} +(-1.64670 + 1.38174i) q^{71} +(2.75271 - 1.19271i) q^{72} +(-12.1358 - 4.41708i) q^{73} +(-6.37987 - 7.60324i) q^{74} +(0.380818 + 12.7321i) q^{75} +(1.31286 + 4.15649i) q^{76} +(-2.00343 + 0.716589i) q^{77} +(0.0306755 - 0.0273436i) q^{78} +(10.3629 + 12.3500i) q^{79} +(1.20215 + 3.30288i) q^{80} +(-8.76410 - 2.04708i) q^{81} +(0.117347 - 0.0427110i) q^{82} +(-11.0662 - 6.38908i) q^{83} +(-0.685698 + 4.53098i) q^{84} +(6.94229 - 2.52679i) q^{85} +(-5.10632 - 4.28471i) q^{86} +(9.35764 + 5.03579i) q^{87} +(0.696461 - 0.402102i) q^{88} +(-4.33594 + 1.57815i) q^{89} +(3.00779 - 10.1065i) q^{90} +(0.0105560 + 0.0618771i) q^{91} +(0.615888 - 0.108598i) q^{92} +(4.00225 + 1.32259i) q^{93} +(0.578463 + 0.333976i) q^{94} +(14.1576 + 5.85584i) q^{95} +(-0.0517826 - 1.73128i) q^{96} +(-1.23185 + 3.38447i) q^{97} +(-5.31191 - 4.55890i) q^{98} +(-2.39675 - 0.276194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−1.15251	−	1.29295i	−0.665402	−	0.746485i
$3$	−1.15251	−	1.29295i	−0.665402	−	0.746485i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.20215	+	3.30288i	−0.537617	+	1.47709i	0.312201	+	0.950016i	$0.398934\pi$
$5$	−1.20215	+	3.30288i	−0.537617	+	1.47709i	−0.849818	+	0.527076i	$0.823288\pi$
$6$	1.07318	−	1.35952i	0.438122	−	0.555022i
$7$	0.891053	+	2.49119i	0.336787	+	0.941581i
$7$	0.891053	+	2.49119i	0.336787	+	0.941581i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.343437	+	2.98028i	−0.114479	+	0.993426i
$10$	−3.46145	−	0.610347i	−1.09461	−	0.193009i
$11$			0.804204i			0.242477i	0.992623	+	0.121238i	$0.0386865\pi$
$11$			0.804204i			0.242477i	−0.992623	+	0.121238i	$0.961313\pi$
$12$	1.52522	+	0.820793i	0.440293	+	0.236943i
$13$	0.0233648	+	0.00411984i	0.00648023	+	0.00114264i	0.176887	−	0.984231i	$-0.443397\pi$
$13$	0.0233648	+	0.00411984i	0.00648023	+	0.00114264i	−0.170407	+	0.985374i	$0.554508\pi$
$14$	−2.29861	+	1.31011i	−0.614330	+	0.350141i
$15$	5.65594	−	2.25228i	1.46036	−	0.581537i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.35107	−	1.61014i	−0.327682	−	0.390517i	0.576901	−	0.816814i	$-0.304262\pi$
$17$	−1.35107	−	1.61014i	−0.327682	−	0.390517i	−0.904583	+	0.426298i	$0.859818\pi$
$18$	−2.99464	+	0.179300i	−0.705843	+	0.0422614i
$19$	0.187916	−	4.35485i	0.0431109	−	0.999070i
$19$	0.187916	−	4.35485i	0.0431109	−	0.999070i
$20$		−	3.51485i		−	0.785944i
$21$	2.19403	−	4.02321i	0.478777	−	0.877936i
$22$	−0.791987	+	0.139649i	−0.168852	+	0.0297732i
$23$	−0.615888	−	0.108598i	−0.128422	−	0.0226442i	0.109068	−	0.994034i	$-0.465213\pi$
$23$	−0.615888	−	0.108598i	−0.128422	−	0.0226442i	−0.237489	+	0.971390i	$0.576325\pi$
$24$	−0.543472	+	1.64458i	−0.110936	+	0.335698i
$25$	−5.63361	−	4.72716i	−1.12672	−	0.945433i
$26$			0.0237252i			0.00465290i
$27$	4.24916	−	2.99075i	0.817752	−	0.575571i
$28$	−1.68935	−	2.03619i	−0.319258	−	0.384804i
$29$	−5.76527	+	2.09839i	−1.07058	+	0.389660i	−0.816395	−	0.577494i	$-0.804031\pi$
$29$	−5.76527	+	2.09839i	−1.07058	+	0.389660i	−0.254188	+	0.967155i	$0.581808\pi$
$30$	3.20021	+	5.17891i	0.584276	+	0.945536i
$31$	−2.10756	+	1.21680i	−0.378529	+	0.218544i	−0.677178	−	0.735819i	$-0.736797\pi$
$31$	−2.10756	+	1.21680i	−0.378529	+	0.218544i	0.298649	+	0.954363i	$0.403464\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	1.03980	−	0.926854i	0.181005	−	0.161345i
$34$	1.35107	−	1.61014i	0.231706	−	0.276137i
$35$	−9.29927	−	0.0517406i	−1.57186	−	0.00874576i
$36$	−0.696589	−	2.91801i	−0.116098	−	0.486334i
$37$	−8.59558	+	4.96266i	−1.41310	+	0.815856i	−0.995680	−	0.0928552i	$-0.970401\pi$
$37$	−8.59558	+	4.96266i	−1.41310	+	0.815856i	−0.417425	+	0.908711i	$0.637067\pi$
$38$	4.32132	−	0.571150i	0.701010	−	0.0926528i
$39$	−0.0216014	−	0.0349577i	−0.00345900	−	0.00559771i
$40$	3.46145	−	0.610347i	0.547303	−	0.0965043i
$41$	−0.0216849	−	0.122981i	−0.00338662	−	0.0192065i	0.983068	−	0.183243i	$-0.0586596\pi$
$41$	−0.0216849	−	0.122981i	−0.00338662	−	0.0192065i	−0.986454	+	0.164037i	$0.947548\pi$
$42$	4.34308	+	1.46208i	0.670152	+	0.225604i
$43$	−5.10632	+	4.28471i	−0.778707	+	0.653412i	−0.942923	−	0.333012i	$-0.891935\pi$
$43$	−5.10632	+	4.28471i	−0.778707	+	0.653412i	0.164216	+	0.986424i	$0.447491\pi$
$44$	−0.275054	−	0.755705i	−0.0414660	−	0.113927i
$45$	−9.43063	−	4.71707i	−1.40583	−	0.703179i
$46$		−	0.625389i		−	0.0922086i
$47$	0.429351	−	0.511681i	0.0626273	−	0.0746363i	−0.733821	−	0.679343i	$-0.762265\pi$
$47$	0.429351	−	0.511681i	0.0626273	−	0.0746363i	0.796449	+	0.604706i	$0.206709\pi$
$48$	−1.71397	−	0.249637i	−0.247390	−	0.0360320i
$49$	−5.41205	+	4.43957i	−0.773150	+	0.634224i
$50$	3.67708	−	6.36889i	0.520018	−	0.900697i
$51$	−0.524710	+	3.60257i	−0.0734741	+	0.504461i
$52$	−0.0233648	+	0.00411984i	−0.00324011	+	0.000571319i
$53$	7.53475	−	2.74243i	1.03498	−	0.376701i	0.232004	−	0.972715i	$-0.425472\pi$
$53$	7.53475	−	2.74243i	1.03498	−	0.376701i	0.802974	+	0.596014i	$0.203250\pi$
$54$	3.68318	+	3.66527i	0.501217	+	0.498780i
$55$	−2.65619	−	0.966774i	−0.358160	−	0.130360i
$56$	1.71191	−	2.01727i	0.228763	−	0.269569i
$57$	−5.84717	+	4.77604i	−0.774477	+	0.632602i
$58$	−3.06763	−	5.31330i	−0.402800	−	0.697670i
$59$	1.11835	−	0.938406i	0.145597	−	0.122170i	−0.567080	−	0.823663i	$-0.691927\pi$
$59$	1.11835	−	0.938406i	0.145597	−	0.122170i	0.712677	+	0.701493i	$0.247483\pi$
$60$	−4.54452	+	4.05090i	−0.586695	+	0.522969i
$61$	2.45219	−	13.9071i	0.313971	−	1.78062i	−0.263961	−	0.964533i	$-0.585029\pi$
$61$	2.45219	−	13.9071i	0.313971	−	1.78062i	0.577932	−	0.816085i	$-0.303860\pi$
$62$	−1.56429	−	1.86425i	−0.198665	−	0.236760i
$63$	−7.73045	+	1.80002i	−0.973946	+	0.226781i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.0416953	+	0.0722184i	−0.00517167	+	0.00895759i
$66$	1.09333	+	0.863052i	0.134580	+	0.106234i
$67$	8.75434	+	1.54363i	1.06951	+	0.188584i	0.680574	−	0.732679i	$-0.261730\pi$
$67$	8.75434	+	1.54363i	1.06951	+	0.188584i	0.388939	+	0.921263i	$0.372842\pi$
$68$	1.82029	+	1.05095i	0.220743	+	0.127446i
$69$	0.569407	+	0.921472i	0.0685485	+	0.110932i
$70$	−1.56385	−	9.16698i	−0.186915	−	1.09566i
$71$	−1.64670	+	1.38174i	−0.195427	+	0.163983i	−0.735251	−	0.677795i	$-0.762936\pi$
$71$	−1.64670	+	1.38174i	−0.195427	+	0.163983i	0.539823	+	0.841778i	$0.318491\pi$
$72$	2.75271	−	1.19271i	0.324410	−	0.140563i
$73$	−12.1358	−	4.41708i	−1.42039	−	0.516980i	−0.486230	−	0.873831i	$-0.661628\pi$
$73$	−12.1358	−	4.41708i	−1.42039	−	0.516980i	−0.934161	+	0.356851i	$0.883851\pi$
$74$	−6.37987	−	7.60324i	−0.741645	−	0.883858i
$75$	0.380818	+	12.7321i	0.0439731	+	1.47017i
$76$	1.31286	+	4.15649i	0.150596	+	0.476782i
$77$	−2.00343	+	0.716589i	−0.228312	+	0.0816629i
$78$	0.0306755	−	0.0273436i	0.00347332	−	0.00309605i
$79$	10.3629	+	12.3500i	1.16592	+	1.38949i	0.905689	+	0.423943i	$0.139354\pi$
$79$	10.3629	+	12.3500i	1.16592	+	1.38949i	0.260231	+	0.965546i	$0.416201\pi$
$80$	1.20215	+	3.30288i	0.134404	+	0.369273i
$81$	−8.76410	−	2.04708i	−0.973789	−	0.227453i
$82$	0.117347	−	0.0427110i	0.0129589	−	0.00471664i
$83$	−11.0662	−	6.38908i	−1.21468	−	0.701293i	−0.250901	−	0.968013i	$-0.580727\pi$
$83$	−11.0662	−	6.38908i	−1.21468	−	0.701293i	−0.963774	+	0.266720i	$0.914060\pi$
$84$	−0.685698	+	4.53098i	−0.0748158	+	0.494371i
$85$	6.94229	−	2.52679i	0.752997	−	0.274068i
$86$	−5.10632	−	4.28471i	−0.550629	−	0.462032i
$87$	9.35764	+	5.03579i	1.00324	+	0.539893i
$88$	0.696461	−	0.402102i	0.0742430	−	0.0428642i
$89$	−4.33594	+	1.57815i	−0.459609	+	0.167284i	−0.561439	−	0.827518i	$-0.689752\pi$
$89$	−4.33594	+	1.57815i	−0.459609	+	0.167284i	0.101831	+	0.994802i	$0.467530\pi$
$90$	3.00779	−	10.1065i	0.317049	−	1.06531i
$91$	0.0105560	+	0.0618771i	0.00110657	+	0.00648648i
$92$	0.615888	−	0.108598i	0.0642108	−	0.0113221i
$93$	4.00225	+	1.32259i	0.415014	+	0.137147i
$94$	0.578463	+	0.333976i	0.0596639	+	0.0344470i
$95$	14.1576	+	5.85584i	1.45254	+	0.600796i
$96$	−0.0517826	−	1.73128i	−0.00528504	−	0.176698i
$97$	−1.23185	+	3.38447i	−0.125075	+	0.343641i	−0.986388	−	0.164433i	$-0.947420\pi$
$97$	−1.23185	+	3.38447i	−0.125075	+	0.343641i	0.861313	+	0.508075i	$0.169643\pi$
$98$	−5.31191	−	4.55890i	−0.536584	−	0.460519i
$99$	−2.39675	−	0.276194i	−0.240883	−	0.0277585i
$100$	6.91065	+	2.51527i	0.691065	+	0.251527i
$101$	5.50647	−	6.56236i	0.547915	−	0.652979i	−0.419028	−	0.907973i	$-0.637629\pi$
$101$	5.50647	−	6.56236i	0.547915	−	0.652979i	0.966943	+	0.254994i	$0.0820735\pi$
$102$	−3.63895	+	0.108841i	−0.360310	+	0.0107769i
$103$	0.808282	+	0.466662i	0.0796424	+	0.0459816i	0.539292	−	0.842119i	$-0.318692\pi$
$103$	0.808282	+	0.466662i	0.0796424	+	0.0459816i	−0.459650	+	0.888100i	$0.652025\pi$
$104$	−0.00811451	−	0.0222944i	−0.000795693	−	0.00218615i
$105$	10.6506	+	12.0831i	1.03939	+	1.17919i
$106$	4.00916	+	6.94407i	0.389404	+	0.674467i
$107$	4.36632			0.422108			0.211054	−	0.977474i	$-0.432310\pi$
$107$	4.36632			0.422108			0.211054	+	0.977474i	$0.432310\pi$
$108$	−2.97001	+	4.26369i	−0.285789	+	0.410274i
$109$	−14.0686	+	2.48067i	−1.34753	+	0.237605i	−0.800411	−	0.599451i	$-0.795385\pi$
$109$	−14.0686	+	2.48067i	−1.34753	+	0.237605i	−0.547116	+	0.837057i	$0.684274\pi$
$110$	0.490844	−	2.78371i	0.0468001	−	0.265417i
$111$	16.3230	+	5.39413i	1.54931	+	0.511988i
$112$	2.28389	+	1.33560i	0.215808	+	0.126203i
$113$	11.7056			1.10117			0.550585	−	0.834779i	$-0.314405\pi$
$113$	11.7056			1.10117			0.550585	+	0.834779i	$0.314405\pi$
$114$	−5.71883	−	4.92899i	−0.535618	−	0.461642i
$115$	1.09907	−	1.90365i	0.102489	−	0.177517i
$116$	4.69989	−	3.94367i	0.436374	−	0.366161i
$117$	−0.0203026	+	0.0682186i	−0.00187698	+	0.00630682i
$118$	1.11835	+	0.938406i	0.102952	+	0.0863873i
$119$	2.80729	−	4.80049i	0.257344	−	0.440060i
$120$	−4.77851	−	3.77205i	−0.436216	−	0.344339i
$121$	10.3533			0.941205
$122$	14.1216			1.27851
$123$	−0.134017	+	0.169775i	−0.0120839	+	0.0153081i
$124$	1.56429	−	1.86425i	0.140477	−	0.167414i
$125$	7.16594	−	4.13726i	0.640941	−	0.370048i
$126$	−3.11505	−	7.30044i	−0.277511	−	0.650375i
$127$	1.91237	+	0.337203i	0.169696	+	0.0299219i	0.257850	−	0.966185i	$-0.416986\pi$
$127$	1.91237	+	0.337203i	0.169696	+	0.0299219i	−0.0881546	+	0.996107i	$0.528097\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	11.4250	+	1.66404i	1.00592	+	0.146510i
$130$	−0.0783615	−	0.0285213i	−0.00687276	−	0.00250148i
$131$	−14.1443	+	2.49402i	−1.23579	+	0.217904i	−0.753112	−	0.657892i	$-0.771448\pi$
$131$	−14.1443	+	2.49402i	−1.23579	+	0.217904i	−0.482681	+	0.875796i	$0.660337\pi$
$132$	−0.660086	+	1.22659i	−0.0574531	+	0.106761i
$133$	11.0162	−	3.41227i	0.955225	−	0.295881i
$134$			8.88939i			0.767927i
$135$	4.76997	+	17.6298i	0.410534	+	1.51733i
$136$	−0.718889	+	1.97513i	−0.0616442	+	0.169366i
$137$	4.40292	+	12.0969i	0.376167	+	1.03351i	0.972932	+	0.231093i	$0.0742302\pi$
$137$	4.40292	+	12.0969i	0.376167	+	1.03351i	−0.596765	+	0.802416i	$0.703548\pi$
$138$	−0.808597	+	0.720768i	−0.0688323	+	0.0613558i
$139$	−0.718192	+	4.07307i	−0.0609163	+	0.345473i	0.939082	+	0.343693i	$0.111678\pi$
$139$	−0.718192	+	4.07307i	−0.0609163	+	0.345473i	−0.999998	+	0.00178056i	$0.999433\pi$
$140$	8.75615	−	3.13192i	0.740030	−	0.264695i
$141$	−1.15641	+	0.0345883i	−0.0973872	+	0.00291286i
$142$	−1.64670	−	1.38174i	−0.138188	−	0.115953i
$143$	−0.00331320	+	0.0187901i	−0.000277063	+	0.00157130i
$144$	1.65260	+	2.50378i	0.137716	+	0.208648i
$145$		−	21.5645i		−	1.79084i
$146$	2.24261	−	12.7185i	0.185600	−	1.05259i
$147$	11.9776	+	1.88086i	0.987894	+	0.155130i
$148$	6.37987	−	7.60324i	0.524422	−	0.624982i
$149$	−11.2437	−	13.3997i	−0.921119	−	1.09775i	−0.994940	−	0.100475i	$-0.967964\pi$
$149$	−11.2437	−	13.3997i	−0.921119	−	1.09775i	0.0738209	−	0.997272i	$-0.476481\pi$
$150$	−12.4725	+	2.58594i	−1.01838	+	0.211141i
$151$	9.48948	+	5.47875i	0.772243	+	0.445854i	0.833674	−	0.552257i	$-0.186233\pi$
$151$	9.48948	+	5.47875i	0.772243	+	0.445854i	−0.0614314	+	0.998111i	$0.519567\pi$
$152$	−3.86537	+	2.01468i	−0.313523	+	0.163412i
$153$	5.26268	−	3.47358i	0.425462	−	0.280822i
$154$	−1.05359	−	1.84855i	−0.0849010	−	0.148961i
$155$	−1.48534	−	8.42380i	−0.119306	−	0.676616i
$156$	0.0322549	+	0.0254613i	0.00258246	+	0.00203854i
$157$	2.58983	+	14.6877i	0.206691	+	1.17220i	0.894756	+	0.446555i	$0.147349\pi$
$157$	2.58983	+	14.6877i	0.206691	+	1.17220i	−0.688065	+	0.725649i	$0.741540\pi$
$158$	−10.3629	+	12.3500i	−0.824430	+	0.982517i
$159$	−12.2297	−	6.58138i	−0.969879	−	0.521937i
$160$	−3.04395	+	1.75742i	−0.240645	+	0.138937i
$161$	−0.278252	−	1.63106i	−0.0219293	−	0.128546i
$162$	0.494105	−	8.98643i	0.0388206	−	0.706040i
$163$	−7.36519	+	12.7569i	−0.576886	+	0.999196i	0.418948	+	0.908010i	$0.362399\pi$
$163$	−7.36519	+	12.7569i	−0.576886	+	0.999196i	−0.995834	+	0.0911855i	$0.970934\pi$
$164$	0.0624393	+	0.108148i	0.00487569	+	0.00844494i
$165$	1.81130	+	4.54854i	0.141009	+	0.354103i
$166$	4.37039	−	12.0076i	0.339208	−	0.931967i
$167$	16.9030	+	14.1833i	1.30799	+	1.09754i	0.988704	+	0.149879i	$0.0478885\pi$
$167$	16.9030	+	14.1833i	1.30799	+	1.09754i	0.319289	+	0.947657i	$0.396556\pi$
$168$	−4.58122	+	0.111516i	−0.353449	+	0.00860368i
$169$	−12.2155	−	4.44607i	−0.939652	−	0.342005i
$170$	3.69391	+	6.39805i	0.283310	+	0.490708i
$171$	12.9141	+	2.05566i	0.987567	+	0.157200i
$172$	3.33291	−	5.77278i	0.254132	−	0.440170i
$173$	−2.81921	−	15.9885i	−0.214340	−	1.21558i	−0.882048	−	0.471160i	$-0.843835\pi$
$173$	−2.81921	−	15.9885i	−0.214340	−	1.21558i	0.667708	−	0.744424i	$-0.267276\pi$
$174$	−3.33434	+	10.0899i	−0.252776	+	0.764916i
$175$	6.75641	−	18.2466i	0.510736	−	1.37931i
$176$	0.516933	+	0.616056i	0.0389653	+	0.0464370i
$177$	−2.50222	−	0.364445i	−0.188078	−	0.0273934i
$178$	−2.30711	−	3.99602i	−0.172925	−	0.299515i
$179$	−3.58769			−0.268156			−0.134078	−	0.990971i	$-0.542807\pi$
$179$	−3.58769			−0.268156			−0.134078	+	0.990971i	$0.542807\pi$
$180$	10.4752	+	1.20713i	0.780777	+	0.0899741i
$181$	5.94904	+	16.3449i	0.442189	+	1.21490i	0.938049	+	0.346501i	$0.112630\pi$
$181$	5.94904	+	16.3449i	0.442189	+	1.21490i	−0.495861	+	0.868402i	$0.665147\pi$
$182$	−0.0591040	+	0.0211404i	−0.00438108	+	0.00156703i
$183$	−20.8073	+	12.8575i	−1.53812	+	0.950453i
$184$	0.213896	+	0.587674i	0.0157686	+	0.0433239i
$185$	−6.05789	−	34.3560i	−0.445385	−	2.52590i
$186$	−0.607518	+	4.17112i	−0.0445454	+	0.305841i
$187$	1.29488	−	1.08654i	0.0946912	−	0.0794554i
$188$	−0.228453	+	0.627669i	−0.0166616	+	0.0457775i
$189$	11.2368	+	7.92055i	0.817355	+	0.576135i
$190$	−3.30843	+	14.9594i	−0.240019	+	1.08527i
$191$	−3.80477	+	2.19668i	−0.275303	+	0.158947i	−0.631295	−	0.775543i	$-0.717476\pi$
$191$	−3.80477	+	2.19668i	−0.275303	+	0.158947i	0.355992	+	0.934489i	$0.384143\pi$
$192$	1.69598	−	0.351629i	0.122397	−	0.0253766i
$193$	−8.33736	+	22.9067i	−0.600136	+	1.64886i	0.150861	+	0.988555i	$0.451795\pi$
$193$	−8.33736	+	22.9067i	−0.600136	+	1.64886i	−0.750997	+	0.660306i	$0.770427\pi$
$194$	−3.54696	−	0.625425i	−0.254657	−	0.0449029i
$195$	0.141429	−	0.0293226i	0.0101279	−	0.00209983i
$196$	3.56724	−	6.02286i	0.254803	−	0.430204i
$197$	−0.579935	−	0.334826i	−0.0413187	−	0.0238553i	0.479198	−	0.877707i	$-0.340927\pi$
$197$	−0.579935	−	0.334826i	−0.0413187	−	0.0238553i	−0.520517	+	0.853851i	$0.674261\pi$
$198$	−0.144194	−	2.40830i	−0.0102474	−	0.171150i
$199$	−1.02115	+	5.79123i	−0.0723874	+	0.410529i	0.926985	+	0.375099i	$0.122391\pi$
$199$	−1.02115	+	5.79123i	−0.0723874	+	0.410529i	−0.999372	+	0.0354304i	$0.988720\pi$
$200$	−1.27704	+	7.24243i	−0.0903001	+	0.512117i
$201$	−8.09365	−	13.0980i	−0.570882	−	0.923860i
$202$	7.41885	+	4.28328i	0.521989	+	0.301370i
$203$	−10.3646	−	12.4926i	−0.727455	−	0.876808i
$204$	−0.739086	−	3.56477i	−0.0517463	−	0.249584i
$205$	0.432261	+	0.0762193i	0.0301904	+	0.00532339i
$206$	−0.319216	+	0.877038i	−0.0222408	+	0.0611061i
$207$	0.535170	−	1.79822i	0.0371969	−	0.124985i
$208$	0.0205467	−	0.0118626i	0.00142465	−	0.000822524i
$209$	3.50219	+	0.151123i	0.242251	+	0.0104534i
$210$	−10.0501	+	12.5870i	−0.693522	+	0.868587i
$211$	1.63730	−	4.49843i	0.112716	−	0.309685i	−0.870489	−	0.492187i	$-0.836197\pi$
$211$	1.63730	−	4.49843i	0.112716	−	0.309685i	0.983205	+	0.182502i	$0.0584197\pi$
$212$	−6.14239	+	5.15407i	−0.421861	+	0.353983i
$213$	3.68437	+	0.536623i	0.252449	+	0.0367688i
$214$	0.758203	+	4.29999i	0.0518297	+	0.293941i
$215$	−8.01332	−	22.0164i	−0.546504	−	1.50151i
$216$	−4.71465	−	2.18451i	−0.320791	−	0.148637i
$217$	−4.90923	−	4.16610i	−0.333261	−	0.282813i
$218$	−4.88597	−	13.4241i	−0.330920	−	0.909195i
$219$	8.27561	+	20.7818i	0.559214	+	1.40430i
$220$	2.82666			0.190573
$221$	−0.0249339	−	0.0431868i	−0.00167724	−	0.00290506i
$222$	−2.47773	+	17.0117i	−0.166294	+	1.14175i
$223$	12.7379	+	15.1804i	0.852992	+	1.01656i	0.999626	+	0.0273653i	$0.00871172\pi$
$223$	12.7379	+	15.1804i	0.852992	+	1.01656i	−0.146634	+	0.989191i	$0.546844\pi$
$224$	−0.918719	+	2.48112i	−0.0613845	+	0.165777i
$225$	16.0230	−	15.1662i	1.06820	−	1.01108i
$226$	2.03265	+	11.5278i	0.135210	+	0.766815i
$227$	−9.17719	+	15.8954i	−0.609111	+	1.05501i	0.382276	+	0.924048i	$0.375140\pi$
$227$	−9.17719	+	15.8954i	−0.609111	+	1.05501i	−0.991387	+	0.130964i	$0.958193\pi$
$228$	3.86104	−	6.48786i	0.255704	−	0.429669i
$229$	12.3061	+	21.3149i	0.813213	+	1.40853i	0.910604	+	0.413280i	$0.135617\pi$
$229$	12.3061	+	21.3149i	0.813213	+	1.40853i	−0.0973912	+	0.995246i	$0.531050\pi$
$230$	2.06558	+	0.751811i	0.136201	+	0.0495730i
$231$	3.23548	+	1.76445i	0.212879	+	0.116092i
$232$	4.69989	+	3.94367i	0.308563	+	0.258915i
$233$	−8.18816	+	22.4968i	−0.536424	+	1.47381i	0.314875	+	0.949133i	$0.398037\pi$
$233$	−8.18816	+	22.4968i	−0.536424	+	1.47381i	−0.851299	+	0.524680i	$0.824185\pi$
$234$	−0.0707078	−	0.00814813i	−0.00462231	−	0.000532660i
$235$	1.17387	+	2.03321i	0.0765751	+	0.132632i
$236$	−0.729950	+	1.26431i	−0.0475157	+	0.0822996i
$237$	4.02461	−	27.6323i	0.261427	−	1.79491i
$238$	5.21504	+	1.93105i	0.338041	+	0.125171i
$239$	7.77171	−	4.48700i	0.502710	−	0.290240i	−0.227122	−	0.973866i	$-0.572932\pi$
$239$	7.77171	−	4.48700i	0.502710	−	0.290240i	0.729832	+	0.683626i	$0.239598\pi$
$240$	2.88496	−	5.36092i	0.186224	−	0.346046i
$241$	5.07993	−	6.05402i	0.327227	−	0.389974i	−0.577200	−	0.816603i	$-0.695855\pi$
$241$	5.07993	−	6.05402i	0.327227	−	0.389974i	0.904427	+	0.426629i	$0.140299\pi$
$242$	1.79782	+	10.1960i	0.115568	+	0.655422i
$243$	7.45396	+	13.6908i	0.478172	+	0.878266i
$244$	2.45219	+	13.9071i	0.156986	+	0.890309i
$245$	−8.15725	−	23.2123i	−0.521148	−	1.48298i
$246$	−0.190467	−	0.102499i	−0.0121438	−	0.00653513i
$247$	0.0223319	−	0.100976i	0.00142095	−	0.00642494i
$248$	2.10756	+	1.21680i	0.133830	+	0.0772670i
$249$	4.49317	+	21.6716i	0.284743	+	1.37338i
$250$	5.31876	+	6.33865i	0.336388	+	0.400891i
$251$	−9.64775	+	11.4977i	−0.608961	+	0.725731i	−0.979130	−	0.203233i	$-0.934855\pi$
$251$	−9.64775	+	11.4977i	−0.608961	+	0.725731i	0.370170	+	0.928964i	$0.379300\pi$
$252$	6.64861	−	4.33544i	0.418823	−	0.273107i
$253$	0.0873348	−	0.495300i	0.00549069	−	0.0311392i
$254$			1.94188i			0.121844i
$255$	−11.2681	−	6.06388i	−0.705634	−	0.379735i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−0.658326	−	0.552401i	−0.0410652	−	0.0344578i	0.622024	−	0.782998i	$-0.286311\pi$
$257$	−0.658326	−	0.552401i	−0.0410652	−	0.0344578i	−0.663089	+	0.748540i	$0.730755\pi$
$258$	0.345174	+	11.5404i	0.0214896	+	0.718473i
$259$	−20.0220	−	16.9912i	−1.24411	−	1.05578i
$260$	0.0144806	−	0.0821237i	0.000898050	−	0.00509310i
$261$	−4.27376	−	17.9028i	−0.264539	−	1.10815i
$262$	−4.91226	−	13.4963i	−0.303481	−	0.833806i
$263$	−8.38029	+	23.0247i	−0.516751	+	1.41976i	0.357329	+	0.933978i	$0.383687\pi$
$263$	−8.38029	+	23.0247i	−0.516751	+	1.41976i	−0.874080	+	0.485782i	$0.838535\pi$
$264$	−1.32258	−	0.437062i	−0.0813990	−	0.0268993i
$265$			28.1832i			1.73128i
$266$	5.27337	+	10.2563i	0.323331	+	0.628854i
$267$	7.03769	+	3.78731i	0.430700	+	0.231780i
$268$	−8.75434	+	1.54363i	−0.534757	+	0.0942920i
$269$	−8.93095	−	3.25060i	−0.544529	−	0.198192i	0.0550848	−	0.998482i	$-0.482457\pi$
$269$	−8.93095	−	3.25060i	−0.544529	−	0.198192i	−0.599614	+	0.800289i	$0.704679\pi$
$270$	−16.5337	+	7.75889i	−1.00621	+	0.472191i
$271$	−13.9589	−	5.08064i	−0.847945	−	0.308627i	−0.118743	−	0.992925i	$-0.537886\pi$
$271$	−13.9589	−	5.08064i	−0.847945	−	0.308627i	−0.729202	+	0.684298i	$0.760109\pi$
$272$	−2.06996	−	0.364989i	−0.125510	−	0.0221307i
$273$	0.0678381	−	0.0849624i	0.00410575	−	0.00514216i
$274$	−11.1486	+	6.43663i	−0.673510	+	0.388851i
$275$	3.80161	−	4.53058i	0.229245	−	0.273204i
$276$	−0.850229	−	0.671152i	−0.0511778	−	0.0403986i
$277$	−25.6283			−1.53985			−0.769927	−	0.638132i	$-0.779707\pi$
$277$	−25.6283			−1.53985			−0.769927	+	0.638132i	$0.779707\pi$
$278$	−4.13590			−0.248055
$279$	−2.90259	−	6.69902i	−0.173774	−	0.401060i
$280$	4.60483	+	8.07928i	0.275191	+	0.482829i
$281$	7.23866	+	6.07396i	0.431822	+	0.362342i	0.832639	−	0.553816i	$-0.186829\pi$
$281$	7.23866	+	6.07396i	0.431822	+	0.362342i	−0.400816	+	0.916158i	$0.631274\pi$
$282$	−0.234871	−	1.13283i	−0.0139864	−	0.0674593i
$283$	−9.12453	+	7.65639i	−0.542397	+	0.455125i	−0.872357	−	0.488870i	$-0.837409\pi$
$283$	−9.12453	+	7.65639i	−0.542397	+	0.455125i	0.329960	+	0.943995i	$0.392965\pi$
$284$	1.07481	−	1.86162i	0.0637780	−	0.110467i
$285$	−8.74551	−	25.0540i	−0.518039	−	1.48407i
$286$	−0.0190799			−0.00112822
$287$	0.287047	−	0.163604i	0.0169439	−	0.00965725i
$288$	−2.17877	+	2.06227i	−0.128385	+	0.121520i
$289$	2.18485	−	12.3909i	0.128521	−	0.728877i
$290$	21.2369	−	3.74464i	1.24708	−	0.219893i
$291$	5.79567	−	2.30793i	0.339748	−	0.135293i
$292$	12.9147			0.755775
$293$	−4.15025	−	7.18844i	−0.242460	−	0.419953i	0.718954	−	0.695057i	$-0.244621\pi$
$293$	−4.15025	−	7.18844i	−0.242460	−	0.419953i	−0.961414	+	0.275104i	$0.911288\pi$
$294$	0.227602	+	12.1222i	0.0132740	+	0.706982i
$295$	1.75502	+	4.82187i	0.102181	+	0.280740i
$296$	8.59558	+	4.96266i	0.499608	+	0.288449i
$297$	2.40518	+	3.41720i	0.139563	+	0.198286i
$298$	11.2437	−	13.3997i	0.651329	−	0.776224i
$299$	−0.0139427	−	0.00507473i	−0.000806327	−	0.000293479i
$300$	−4.71248	−	11.8340i	−0.272075	−	0.683236i
$301$	−15.2240	−	8.90290i	−0.877499	−	0.513155i
$302$	−3.74769	+	10.2967i	−0.215655	+	0.592508i
$303$	−14.8311	+	0.443599i	−0.852023	+	0.0254841i
$304$	−2.65529	−	3.45680i	−0.152291	−	0.198261i
$305$	42.9855	+	24.8177i	2.46134	+	1.42106i
$306$	4.33466	+	4.57954i	0.247796	+	0.261795i
$307$	18.2554	−	3.21891i	1.04189	−	0.183713i	0.373580	−	0.927598i	$-0.378130\pi$
$307$	18.2554	−	3.21891i	1.04189	−	0.183713i	0.668308	+	0.743885i	$0.267019\pi$
$308$	1.63752	−	1.35859i	0.0933061	−	0.0774126i
$309$	−0.328184	−	1.58290i	−0.0186697	−	0.0900481i
$310$	8.03789	−	2.92555i	0.456522	−	0.166160i
$311$	15.6993	−	9.06397i	0.890223	−	0.513970i	0.0162075	−	0.999869i	$-0.494841\pi$
$311$	15.6993	−	9.06397i	0.890223	−	0.513970i	0.874015	+	0.485898i	$0.161507\pi$
$312$	−0.0194735	+	0.0361862i	−0.00110247	+	0.00204864i
$313$	−4.03598	−	3.38659i	−0.228127	−	0.191421i	0.521558	−	0.853216i	$-0.325351\pi$
$313$	−4.03598	−	3.38659i	−0.228127	−	0.191421i	−0.749686	+	0.661794i	$0.769795\pi$
$314$	−14.0148	+	5.10097i	−0.790901	+	0.287865i
$315$	3.34792	−	27.6966i	0.188634	−	1.56053i
$316$	−13.9619	−	8.06092i	−0.785420	−	0.453462i
$317$	18.5265	−	6.74310i	1.04055	−	0.378730i	0.235463	−	0.971883i	$-0.424339\pi$
$317$	18.5265	−	6.74310i	1.04055	−	0.378730i	0.805090	+	0.593153i	$0.202117\pi$
$318$	4.35773	−	13.1868i	0.244369	−	0.739476i
$319$	−1.68753	−	4.63645i	−0.0944836	−	0.259592i
$320$	−2.25930	−	2.69253i	−0.126299	−	0.150517i
$321$	−5.03223	−	5.64543i	−0.280872	−	0.315097i
$322$	1.55796	−	0.557255i	0.0868219	−	0.0310546i
$323$	−7.26581	+	5.58113i	−0.404280	+	0.310542i
$324$	8.93570	−	1.07388i	0.496428	−	0.0596599i
$325$	−0.112153	−	0.133659i	−0.00622113	−	0.00741406i
$326$	−13.8420	−	5.03808i	−0.766639	−	0.279034i
$327$	19.4216	+	15.3310i	1.07402	+	0.847805i
$328$	−0.0956625	+	0.0802704i	−0.00528208	+	0.00443219i
$329$	1.65727	+	0.613660i	0.0913681	+	0.0338322i
$330$	−4.16490	+	2.57362i	−0.229270	+	0.141673i
$331$	−9.94459	−	5.74151i	−0.546604	−	0.315582i	0.201147	−	0.979561i	$-0.435533\pi$
$331$	−9.94459	−	5.74151i	−0.546604	−	0.315582i	−0.747751	+	0.663979i	$0.768866\pi$
$332$	12.5840	+	2.21891i	0.690639	+	0.121778i
$333$	−11.8381	−	27.3216i	−0.648722	−	1.49721i
$334$	−11.0326	+	19.1091i	−0.603680	+	1.04560i
$335$	−15.6224	+	27.0589i	−0.853545	+	1.47838i
$336$	−0.905343	−	4.49225i	−0.0493905	−	0.245073i
$337$	−6.91743	−	8.24387i	−0.376817	−	0.449072i	0.543990	−	0.839092i	$-0.316913\pi$
$337$	−6.91743	−	8.24387i	−0.376817	−	0.449072i	−0.920807	+	0.390019i	$0.872468\pi$
$338$	2.25733	−	12.8019i	0.122782	−	0.696334i
$339$	−13.4908	−	15.1347i	−0.732721	−	0.822006i
$340$	−5.65940	+	4.74880i	−0.306924	+	0.257540i
$341$	−0.978558	−	1.69491i	−0.0529919	−	0.0917846i
$342$	0.218084	+	13.0749i	0.0117926	+	0.707008i
$343$	−15.8822	−	9.52654i	−0.857559	−	0.514385i
$344$	6.26383	+	2.27985i	0.337723	+	0.122921i
$345$	−3.72802	+	0.772933i	−0.200710	+	0.0416133i
$346$	15.2561	−	5.55275i	0.820171	−	0.298518i
$347$	−20.8433	+	3.67524i	−1.11893	+	0.197297i	−0.702370	−	0.711812i	$-0.747875\pi$
$347$	−20.8433	+	3.67524i	−1.11893	+	0.197297i	−0.416558	+	0.909109i	$0.636764\pi$
$348$	−10.5156	−	1.53159i	−0.563698	−	0.0821019i
$349$	13.6773	−	23.6898i	0.732129	−	1.26808i	−0.223843	−	0.974625i	$-0.571860\pi$
$349$	13.6773	−	23.6898i	0.732129	−	1.26808i	0.955972	−	0.293459i	$-0.0948064\pi$
$350$	19.1426	+	3.48528i	1.02321	+	0.186296i
$351$	0.111602	−	0.0523725i	0.00595689	−	0.00279544i
$352$	−0.516933	+	0.616056i	−0.0275526	+	0.0328359i
$353$			2.15905i			0.114915i	0.998348	+	0.0574573i	$0.0182993\pi$
$353$			2.15905i			0.114915i	−0.998348	+	0.0574573i	$0.981701\pi$
$354$	−0.0755975	−	2.52749i	−0.00401796	−	0.134335i
$355$	−2.58416	−	7.09991i	−0.137153	−	0.376824i
$356$	3.53469	−	2.96596i	0.187338	−	0.157195i
$357$	−9.44223	+	1.90293i	−0.499736	+	0.100714i
$358$	−0.622995	−	3.53318i	−0.0329263	−	0.186734i
$359$	24.9467	−	4.39878i	1.31664	−	0.232159i	0.529170	−	0.848516i	$-0.322503\pi$
$359$	24.9467	−	4.39878i	1.31664	−	0.232159i	0.787467	+	0.616357i	$0.211392\pi$
$360$	0.630213	+	10.5257i	0.0332151	+	0.554753i
$361$	−18.9294	−	1.63669i	−0.996283	−	0.0861416i
$362$	−15.0635	+	8.69691i	−0.791720	+	0.457100i
$363$	−11.9322	−	13.3862i	−0.626280	−	0.702595i
$364$	−0.0310826	−	0.0545351i	−0.00162917	−	0.00285842i
$365$	29.1782	−	34.7732i	1.52725	−	1.82011i
$366$	−16.2753	−	18.2585i	−0.850724	−	0.954389i
$367$	9.83941	+	8.25625i	0.513613	+	0.430973i	0.862398	−	0.506230i	$-0.168961\pi$
$367$	9.83941	+	8.25625i	0.513613	+	0.430973i	−0.348785	+	0.937203i	$0.613406\pi$
$368$	−0.541603	+	0.312695i	−0.0282330	+	0.0163003i
$369$	0.373966	−	0.0223907i	0.0194679	−	0.00116562i
$370$	32.7821	−	11.9317i	1.70426	−	0.620300i
$371$	13.5458	+	16.3268i	0.703261	+	0.847648i
$372$	−4.21324	+	0.126018i	−0.218446	+	0.00653375i
$373$		−	4.67756i		−	0.242195i	−0.992641	−	0.121097i	$-0.961359\pi$
$373$		−	4.67756i		−	0.242195i	0.992641	−	0.121097i	$-0.0386414\pi$
$374$	1.29488	+	1.08654i	0.0669568	+	0.0561834i
$375$	−13.6081	−	4.49697i	−0.702719	−	0.232222i
$376$	−0.657804	−	0.115989i	−0.0339237	−	0.00598165i
$377$	−0.143349	+	0.0252763i	−0.00738286	+	0.00130180i
$378$	−5.84897	+	12.4414i	−0.300839	+	0.639919i
$379$		−	12.8121i		−	0.658114i	−0.944310	−	0.329057i	$-0.893269\pi$
$379$		−	12.8121i		−	0.658114i	0.944310	−	0.329057i	$-0.106731\pi$
$380$	−15.3066	−	0.660496i	−0.785213	−	0.0338828i
$381$	−1.76805	−	2.86123i	−0.0905797	−	0.146585i
$382$	−2.82400	−	3.36552i	−0.144489	−	0.172195i
$383$	20.6073	−	17.2916i	1.05298	−	0.883558i	0.0595792	−	0.998224i	$-0.481024\pi$
$383$	20.6073	−	17.2916i	1.05298	−	0.883558i	0.993404	+	0.114666i	$0.0365797\pi$
$384$	0.640791	+	1.60916i	0.0327002	+	0.0821170i
$385$	0.0416100	−	7.47852i	0.00212064	−	0.381140i
$386$	−24.0065	−	4.23299i	−1.22190	−	0.215453i
$387$	−11.0159	−	16.6898i	−0.559971	−	0.848389i
$388$		−	3.60168i		−	0.182848i
$389$	29.2630	+	5.15986i	1.48369	+	0.261615i	0.856053	−	0.516888i	$-0.172910\pi$
$389$	29.2630	+	5.15986i	1.48369	+	0.261615i	0.627641	+	0.778503i	$0.284021\pi$
$390$	0.0534360	+	0.134189i	0.00270584	+	0.00679490i
$391$	0.657250	+	1.13839i	0.0332386	+	0.0575709i
$392$	6.55080	+	2.46719i	0.330865	+	0.124612i
$393$	19.5261	+	15.4135i	0.984962	+	0.777507i
$394$	0.229034	−	0.629266i	0.0115386	−	0.0317020i
$395$	−53.2485	+	19.3809i	−2.67922	+	0.975157i
$396$	2.34667	−	0.560200i	0.117925	−	0.0281511i
$397$	−1.81113	−	10.2714i	−0.0908980	−	0.515508i	−0.995927	−	0.0901591i	$-0.971262\pi$
$397$	−1.81113	−	10.2714i	−0.0908980	−	0.515508i	0.905029	−	0.425349i	$-0.139849\pi$
$398$	−5.88057			−0.294766
$399$	−17.1082	−	10.3107i	−0.856480	−	0.516181i
$400$	−7.35416			−0.367708
$401$	5.88840	+	33.3947i	0.294052	+	1.66765i	0.671029	+	0.741431i	$0.265853\pi$
$401$	5.88840	+	33.3947i	0.294052	+	1.66765i	−0.376976	+	0.926223i	$0.623036\pi$
$402$	11.4935	−	10.2451i	0.573246	−	0.510980i
$403$	−0.0542558	+	0.0197475i	−0.00270267	+	0.000983693i
$404$	−2.92993	+	8.04993i	−0.145770	+	0.400499i
$405$	17.2970	−	26.4859i	0.859495	−	1.31609i
$406$	10.5030	−	12.3765i	0.521255	−	0.614235i
$407$	−3.99099	−	6.91260i	−0.197826	−	0.342645i
$408$	3.38227	−	1.34687i	0.167447	−	0.0666801i
$409$	−34.3120	−	6.05013i	−1.69662	−	0.299160i	−0.760108	−	0.649797i	$-0.774854\pi$
$409$	−34.3120	−	6.05013i	−1.69662	−	0.299160i	−0.936511	+	0.350637i	$0.885965\pi$
$410$			0.438929i			0.0216772i
$411$	10.5663	−	19.6346i	0.521197	−	0.968502i
$412$	−0.919145	−	0.162070i	−0.0452830	−	0.00798462i
$413$	3.33426	+	1.94985i	0.164068	+	0.0959458i
$414$	1.86383	+	0.214782i	0.0916024	+	0.0105560i
$415$	34.4056	−	28.8697i	1.68890	−	1.41716i
$416$	0.0152503	+	0.0181746i	0.000747707	+	0.000891082i
$417$	6.09400	−	3.76567i	0.298424	−	0.184406i
$418$	0.459321	+	3.47522i	0.0224661	+	0.169979i
$419$		−	28.3468i		−	1.38483i	−0.721499	−	0.692415i	$-0.756547\pi$
$419$		−	28.3468i		−	1.38483i	0.721499	−	0.692415i	$-0.243453\pi$
$420$	−14.1410	−	7.71169i	−0.690009	−	0.376292i
$421$	24.8043	−	4.37367i	1.20889	−	0.213160i	0.467351	−	0.884072i	$-0.345208\pi$
$421$	24.8043	−	4.37367i	1.20889	−	0.213160i	0.741537	+	0.670912i	$0.234097\pi$
$422$	4.71441	+	0.831277i	0.229494	+	0.0404659i
$423$	1.37750	+	1.45532i	0.0669761	+	0.0707598i
$424$	−6.14239	−	5.15407i	−0.298301	−	0.250304i
$425$			15.4576i			0.749806i
$426$	0.111313	+	3.72158i	0.00539312	+	0.180311i
$427$	36.8302	−	6.28307i	1.78234	−	0.304059i
$428$	−4.10300	+	1.49337i	−0.198326	+	0.0721847i
$429$	0.0281131	−	0.0173720i	0.00135731	−	0.000838726i
$430$	20.2904	−	11.7147i	0.978492	−	0.564932i
$431$	−8.34327	−	7.00084i	−0.401881	−	0.337219i	0.419339	−	0.907830i	$-0.362262\pi$
$431$	−8.34327	−	7.00084i	−0.401881	−	0.337219i	−0.821220	+	0.570611i	$0.806706\pi$
$432$	1.33263	−	5.02236i	0.0641161	−	0.241638i
$433$	−2.97475	+	3.54517i	−0.142957	+	0.170370i	−0.832772	−	0.553616i	$-0.813248\pi$
$433$	−2.97475	+	3.54517i	−0.142957	+	0.170370i	0.689815	+	0.723986i	$0.257692\pi$
$434$	3.25033	−	5.55809i	0.156021	−	0.266797i
$435$	−27.8819	+	24.8534i	−1.33683	+	1.19163i
$436$	12.3717	−	7.14281i	0.592498	−	0.342079i
$437$	−0.588662	+	2.66169i	−0.0281595	+	0.127326i
$438$	−19.0290	+	11.7586i	−0.909240	+	0.561848i
$439$	−8.45355	+	1.49059i	−0.403466	+	0.0711419i	−0.371699	−	0.928353i	$-0.621225\pi$
$439$	−8.45355	+	1.49059i	−0.403466	+	0.0711419i	−0.0317671	+	0.999495i	$0.510113\pi$
$440$	0.490844	+	2.78371i	0.0234001	+	0.132708i
$441$	−11.3724	−	17.6541i	−0.541545	−	0.840672i
$442$	0.0382010	−	0.0320544i	0.00181704	−	0.00152467i
$443$	6.59700	+	18.1251i	0.313433	+	0.861150i	0.991957	+	0.126572i	$0.0403975\pi$
$443$	6.59700	+	18.1251i	0.313433	+	0.861150i	−0.678524	+	0.734578i	$0.737380\pi$
$444$	−17.1835	+	0.513959i	−0.815492	+	0.0243914i
$445$		−	16.2182i		−	0.768819i
$446$	−12.7379	+	15.1804i	−0.603156	+	0.718814i
$447$	−4.36667	+	29.9808i	−0.206536	+	1.41804i
$448$	−2.60296	−	0.473920i	−0.122978	−	0.0223906i
$449$	2.47949	−	4.29461i	0.117015	−	0.202675i	−0.801569	−	0.597903i	$-0.796001\pi$
$449$	2.47949	−	4.29461i	0.117015	−	0.202675i	0.918583	+	0.395228i	$0.129334\pi$
$450$	17.7182	+	13.1460i	0.835244	+	0.619710i
$451$	0.0989022	−	0.0174391i	0.00465712	−	0.000821176i
$452$	−10.9997	+	4.00355i	−0.517380	+	0.188311i
$453$	−3.85298	−	18.5837i	−0.181029	−	0.873140i
$454$	−17.2475	−	6.27757i	−0.809464	−	0.294621i
$455$	−0.217062	−	0.0395205i	−0.0101760	−	0.00185275i
$456$	7.05976	+	2.67578i	0.330604	+	0.125305i
$457$	4.94049	+	8.55719i	0.231107	+	0.400288i	0.958134	−	0.286320i	$-0.0924321\pi$
$457$	4.94049	+	8.55719i	0.231107	+	0.400288i	−0.727027	+	0.686608i	$0.759099\pi$
$458$	−18.8541	+	15.8205i	−0.880994	+	0.739242i
$459$	−10.5565	−	2.80104i	−0.492733	−	0.130741i
$460$	−0.381705	+	2.16475i	−0.0177971	+	0.100932i
$461$	24.0943	+	28.7145i	1.12218	+	1.33737i	0.934839	+	0.355072i	$0.115544\pi$
$461$	24.0943	+	28.7145i	1.12218	+	1.33737i	0.187345	+	0.982294i	$0.440012\pi$
$462$	−1.17581	+	3.49272i	−0.0547036	+	0.162496i
$463$	13.3721	−	23.1612i	0.621456	−	1.07639i	−0.367758	−	0.929921i	$-0.619875\pi$
$463$	13.3721	−	23.1612i	0.621456	−	1.07639i	0.989215	−	0.146473i	$-0.0467921\pi$
$464$	−3.06763	+	5.31330i	−0.142411	+	0.246664i
$465$	−9.17967	+	11.6290i	−0.425697	+	0.539282i
$466$	−23.5769	−	4.15724i	−1.09218	−	0.192580i
$467$	2.67881	+	1.54661i	0.123960	+	0.0715686i	0.560698	−	0.828020i	$-0.310533\pi$
$467$	2.67881	+	1.54661i	0.123960	+	0.0715686i	−0.436738	+	0.899589i	$0.643866\pi$
$468$	−0.00425394	−	0.0710485i	−0.000196638	−	0.00328422i
$469$	3.95512	+	23.1842i	0.182631	+	1.07055i
$470$	−1.79848	+	1.50910i	−0.0829577	+	0.0696098i
$471$	16.0056	−	20.2762i	0.737499	−	0.934279i
$472$	−1.37186	−	0.499315i	−0.0631449	−	0.0229829i
$473$	−3.44578	−	4.10653i	−0.158437	−	0.188818i
$474$	27.9114	−	0.834832i	1.28201	−	0.0383451i
$475$	−21.6447	+	23.6452i	−0.993128	+	1.08492i
$476$	−0.996127	+	5.47114i	−0.0456574	+	0.250769i
$477$	5.58547	+	23.3975i	0.255741	+	1.07130i
$478$	5.76838	+	6.87449i	0.263839	+	0.314432i
$479$	5.89071	+	16.1846i	0.269153	+	0.739493i	0.998469	+	0.0553155i	$0.0176165\pi$
$479$	5.89071	+	16.1846i	0.269153	+	0.739493i	−0.729315	+	0.684178i	$0.760161\pi$
$480$	5.78044	+	1.91022i	0.263840	+	0.0871892i
$481$	−0.221279	+	0.0805391i	−0.0100895	+	0.00367227i
$482$	6.84417	+	3.95148i	0.311743	+	0.179985i
$483$	−1.78819	+	2.23958i	−0.0813655	+	0.101904i
$484$	−9.72888	+	3.54102i	−0.442222	+	0.160956i
$485$	−9.69764	−	8.13728i	−0.440347	−	0.369495i
$486$	−12.1885	+	9.71810i	−0.552880	+	0.440822i
$487$	−34.3755	+	19.8467i	−1.55770	+	0.899339i	−0.560225	+	0.828340i	$0.689285\pi$
$487$	−34.3755	+	19.8467i	−1.55770	+	0.899339i	−0.997476	+	0.0709992i	$0.977381\pi$
$488$	−13.2700	+	4.82988i	−0.600704	+	0.218638i
$489$	24.9825	−	5.17963i	1.12975	−	0.234231i
$490$	21.4432	−	12.0641i	0.968705	−	0.545001i
$491$	−24.2532	+	4.27649i	−1.09453	+	0.192996i	−0.691633	−	0.722249i	$-0.743108\pi$
$491$	−24.2532	+	4.27649i	−1.09453	+	0.192996i	−0.402899	+	0.915245i	$0.631997\pi$
$492$	0.0678680	−	0.205373i	0.00305972	−	0.00925891i
$493$	11.1680	+	6.44783i	0.502980	+	0.290396i
$494$	0.103320	+	0.00445835i	0.00464858	+	0.000200591i
$495$	3.79349	−	7.58415i	0.170505	−	0.340882i
$496$	−0.832342	+	2.28684i	−0.0373732	+	0.102682i
$497$	−4.90948	−	2.87103i	−0.220220	−	0.128783i
$498$	−20.5621	+	8.18814i	−0.921409	+	0.366919i
$499$	13.6733	+	4.97666i	0.612100	+	0.222786i	0.629422	−	0.777064i	$-0.283292\pi$
$499$	13.6733	+	4.97666i	0.612100	+	0.222786i	−0.0173221	+	0.999850i	$0.505514\pi$
$500$	−5.31876	+	6.33865i	−0.237862	+	0.283473i
$501$	−1.14260	−	38.2011i	−0.0510476	−	1.70670i
$502$	−12.9984	−	7.50462i	−0.580146	−	0.334947i
$503$	12.2565	+	33.6746i	0.546492	+	1.50147i	0.838415	+	0.545033i	$0.183483\pi$
$503$	12.2565	+	33.6746i	0.546492	+	1.50147i	−0.291923	+	0.956442i	$0.594295\pi$
$504$	5.42409	+	5.79476i	0.241608	+	0.258119i
$505$	15.0551	+	26.0761i	0.669942	+	1.16037i
$506$	0.502941			0.0223584
$507$	8.32993	+	20.9181i	0.369945	+	0.929007i
$508$	−1.91237	+	0.337203i	−0.0848479	+	0.0149610i
$509$	2.36138	−	13.3920i	0.104666	−	0.593591i	−0.886687	−	0.462370i	$-0.846999\pi$
$509$	2.36138	−	13.3920i	0.104666	−	0.593591i	0.991353	−	0.131221i	$-0.0418898\pi$
$510$	4.01507	−	12.1499i	0.177790	−	0.538005i
$511$	0.190112	−	34.1685i	0.00841004	−	1.51153i
$512$	1.00000			0.0441942
$513$	−12.2258	−	19.0665i	−0.539782	−	0.841805i
$514$	0.429692	−	0.744248i	0.0189529	−	0.0328274i
$515$	−2.51300	+	2.10866i	−0.110736	+	0.0929187i
$516$	−11.3051	+	2.34390i	−0.497681	+	0.103184i
$517$	0.411496	+	0.345286i	0.0180976	+	0.0151857i
$518$	13.2563	−	22.6684i	0.582448	−	0.995991i
$519$	−17.4232	+	22.0720i	−0.764792	+	0.968854i
$520$	0.0833906			0.00365692
$521$	−41.6197			−1.82339			−0.911695	−	0.410867i	$-0.865226\pi$
$521$	−41.6197			−1.82339			−0.911695	+	0.410867i	$0.865226\pi$
$522$	16.8886	−	7.31762i	0.739196	−	0.320283i
$523$	8.02905	−	9.56865i	0.351086	−	0.418408i	−0.561382	−	0.827557i	$-0.689730\pi$
$523$	8.02905	−	9.56865i	0.351086	−	0.418408i	0.912468	+	0.409149i	$0.134174\pi$
$524$	12.4383	−	7.18125i	0.543369	−	0.313714i
$525$	−31.3787	+	12.2937i	−1.36948	+	0.536539i
$526$	−24.1301	−	4.25478i	−1.05212	−	0.185517i
$527$	4.80669	+	1.74949i	0.209383	+	0.0762090i
$528$	0.200759	−	1.37838i	0.00873692	−	0.0599863i
$529$	−21.2454	−	7.73270i	−0.923713	−	0.336204i
$530$	−27.7550	+	4.89396i	−1.20560	+	0.212580i
$531$	2.41263	+	3.65527i	0.104699	+	0.158625i
$532$	−9.18477	+	6.97424i	−0.398210	+	0.302372i
$533$		−	0.00296277i		−	0.000128332i
$534$	−2.50769	+	7.58843i	−0.108518	+	0.328384i
$535$	−5.24897	+	14.4214i	−0.226933	+	0.623492i
$536$	−3.04035	−	8.35330i	−0.131323	−	0.360808i
$537$	4.13485	+	4.63870i	0.178432	+	0.200175i
$538$	1.65037	−	9.35973i	0.0711526	−	0.403526i
$539$	−3.57032	−	4.35239i	−0.153784	−	0.187471i
$540$	−10.5121	−	14.9352i	−0.452367	−	0.642707i
$541$	−24.4495	−	20.5155i	−1.05116	−	0.882032i	−0.0579490	−	0.998320i	$-0.518456\pi$
$541$	−24.4495	−	20.5155i	−1.05116	−	0.882032i	−0.993216	+	0.116288i	$0.962901\pi$
$542$	2.57951	−	14.6291i	0.110799	−	0.628374i
$543$	14.2767	−	26.5294i	0.612673	−	1.13849i
$544$		−	2.10189i		−	0.0901178i
$545$	8.71919	−	49.4490i	0.373489	−	2.11816i
$546$	0.0954516	+	0.0520539i	0.00408495	+	0.00222770i
$547$	1.52023	−	1.81174i	0.0650002	−	0.0774642i	−0.732565	−	0.680698i	$-0.761677\pi$
$547$	1.52023	−	1.81174i	0.0650002	−	0.0774642i	0.797565	+	0.603233i	$0.206121\pi$
$548$	−8.27478	−	9.86149i	−0.353481	−	0.421262i
$549$	40.6048	+	12.0844i	1.73297	+	0.515750i
$550$	5.12189	+	2.95712i	0.218398	+	0.126092i
$551$	8.05476	+	25.5012i	0.343144	+	1.08639i
$552$	0.513315	−	0.953857i	0.0218481	−	0.0405988i
$553$	−21.5324	+	36.8206i	−0.915651	+	1.56577i
$554$	−4.45030	−	25.2389i	−0.189075	−	1.07230i
$555$	−37.4388	+	47.4282i	−1.58919	+	2.01322i
$556$	−0.718192	−	4.07307i	−0.0304581	−	0.172737i
$557$	−25.8133	+	30.7630i	−1.09374	+	1.30347i	−0.144299	+	0.989534i	$0.546093\pi$
$557$	−25.8133	+	30.7630i	−1.09374	+	1.30347i	−0.949444	+	0.313938i	$0.898352\pi$
$558$	6.09321	−	4.02177i	0.257946	−	0.170255i
$559$	−0.136960	+	0.0790742i	−0.00579281	+	0.00334448i
$560$	−7.15691	+	5.93782i	−0.302435	+	0.250919i
$561$	−2.89720	−	0.421974i	−0.122320	−	0.0178158i
$562$	−4.72470	+	8.18342i	−0.199299	+	0.345197i
$563$	7.45594	+	12.9141i	0.314230	+	0.544263i	0.979274	−	0.202542i	$-0.0649203\pi$
$563$	7.45594	+	12.9141i	0.314230	+	0.544263i	−0.665043	+	0.746805i	$0.731587\pi$
$564$	1.07484	−	0.428018i	0.0452589	−	0.0180228i
$565$	−14.0719	+	38.6621i	−0.592008	+	1.62653i
$566$	−9.12453	−	7.65639i	−0.383532	−	0.321822i
$567$	−2.70963	−	23.6571i	−0.113794	−	0.993504i
$568$	2.01998	+	0.735211i	0.0847563	+	0.0308488i
$569$	−2.57602	−	4.46180i	−0.107993	−	0.187049i	0.806964	−	0.590600i	$-0.201109\pi$
$569$	−2.57602	−	4.46180i	−0.107993	−	0.187049i	−0.914957	+	0.403552i	$0.867776\pi$
$570$	23.1547	−	12.9632i	0.969845	−	0.542970i
$571$	16.6543	−	28.8460i	0.696959	−	1.20717i	−0.272557	−	0.962140i	$-0.587869\pi$
$571$	16.6543	−	28.8460i	0.696959	−	1.20717i	0.969516	−	0.245029i	$-0.0787975\pi$
$572$	−0.00331320	−	0.0187901i	−0.000138532	−	0.000785652i
$573$	7.22524	+	2.38767i	0.301839	+	0.0997464i
$574$	0.210964	+	0.254277i	0.00880547	+	0.0106133i
$575$	2.95632	+	3.52320i	0.123287	+	0.146928i
$576$	−2.40928	−	1.78756i	−0.100387	−	0.0744818i
$577$	16.7700	+	29.0465i	0.698144	+	1.20922i	0.969109	+	0.246632i	$0.0793239\pi$
$577$	16.7700	+	29.0465i	0.698144	+	1.20922i	−0.270965	+	0.962589i	$0.587343\pi$
$578$	12.5821			0.523345
$579$	39.2261	−	15.6204i	1.63018	−	0.649163i
$580$	7.37551	+	20.2640i	0.306251	+	0.841418i
$581$	6.05583	−	33.2611i	0.251238	−	1.37990i
$582$	3.27927	+	5.30686i	0.135930	+	0.219976i
$583$	2.20547	+	6.05948i	0.0913413	+	0.250958i
$584$	2.24261	+	12.7185i	0.0927999	+	0.526294i
$585$	−0.200911	−	0.149066i	−0.00830665	−	0.00616312i
$586$	6.35855	−	5.33545i	0.262669	−	0.220406i
$587$	−3.63617	+	9.99031i	−0.150081	+	0.412344i	−0.991837	−	0.127515i	$-0.959300\pi$
$587$	−3.63617	+	9.99031i	−0.150081	+	0.412344i	0.841756	+	0.539859i	$0.181522\pi$
$588$	−11.8985	+	2.32915i	−0.490687	+	0.0960523i
$589$	4.90294	+	9.40677i	0.202022	+	0.387599i
$590$	−4.44386	+	2.56567i	−0.182951	+	0.105627i
$591$	0.235469	+	1.13572i	0.00968589	+	0.0467172i
$592$	−3.39466	+	9.32675i	−0.139520	+	0.383327i
$593$	14.3925	+	2.53778i	0.591027	+	0.104214i	0.461160	−	0.887317i	$-0.347434\pi$
$593$	14.3925	+	2.53778i	0.591027	+	0.104214i	0.129868	+	0.991531i	$0.458545\pi$
$594$	−2.94763	+	2.96203i	−0.120943	+	0.121533i
$595$	12.4806	+	15.0430i	0.511657	+	0.616705i
$596$	15.1486	+	8.74604i	0.620510	+	0.358252i
$597$	8.66466	−	5.35416i	0.354621	−	0.219131i
$598$	0.00257651	−	0.0146121i	0.000105361	−	0.000597533i
$599$	7.23214	−	41.0155i	0.295497	−	1.67585i	−0.369678	−	0.929160i	$-0.620532\pi$
$599$	7.23214	−	41.0155i	0.295497	−	1.67585i	0.665175	−	0.746687i	$-0.268357\pi$
$600$	10.8359	−	6.69584i	0.442374	−	0.273357i
$601$	−14.9221	−	8.61526i	−0.608684	−	0.351424i	0.163766	−	0.986499i	$-0.447636\pi$
$601$	−14.9221	−	8.61526i	−0.608684	−	0.351424i	−0.772450	+	0.635075i	$0.780969\pi$
$602$	6.12402	−	16.5387i	0.249597	−	0.674068i
$603$	−7.60700	+	25.5602i	−0.309781	+	1.04089i
$604$	−10.7910	−	1.90275i	−0.439081	−	0.0774218i
$605$	−12.4462	+	34.1955i	−0.506008	+	1.39025i
$606$	−3.01225	−	14.5287i	−0.122364	−	0.590189i
$607$	−14.1226	+	8.15370i	−0.573220	+	0.330949i	−0.758434	−	0.651750i	$-0.774035\pi$
$607$	−14.1226	+	8.15370i	−0.573220	+	0.330949i	0.185214	+	0.982698i	$0.440702\pi$
$608$	2.94319	−	3.21522i	0.119362	−	0.130394i
$609$	−4.20694	+	27.7988i	−0.170474	+	1.12646i
$610$	−16.9763	+	46.6420i	−0.687350	+	1.88848i
$611$	0.0121397	−	0.0101865i	0.000491121	−	0.000412100i
$612$	−3.75726	+	5.06404i	−0.151878	+	0.204702i
$613$	2.18608	+	12.3979i	0.0882950	+	0.500746i	0.996597	+	0.0824305i	$0.0262683\pi$
$613$	2.18608	+	12.3979i	0.0882950	+	0.500746i	−0.908302	+	0.418316i	$0.862621\pi$
$614$	6.34002	+	17.4191i	0.255862	+	0.702976i
$615$	−0.399638	−	0.646735i	−0.0161150	−	0.0260789i
$616$	1.62230	+	1.37672i	0.0653642	+	0.0554697i
$617$	6.00601	+	16.5014i	0.241793	+	0.664321i	0.999925	+	0.0122199i	$0.00388982\pi$
$617$	6.00601	+	16.5014i	0.241793	+	0.664321i	−0.758132	+	0.652101i	$0.773888\pi$
$618$	1.50186	−	0.598066i	0.0604139	−	0.0240577i
$619$	10.1137			0.406503			0.203251	−	0.979127i	$-0.434849\pi$
$619$	10.1137			0.406503			0.203251	+	0.979127i	$0.434849\pi$
$620$	4.27687	+	7.40776i	0.171763	+	0.297503i
$621$	−2.94180	+	1.38052i	−0.118050	+	0.0553984i
$622$	11.6524	+	13.8868i	0.467219	+	0.556810i
$623$	−7.79503	−	9.39543i	−0.312301	−	0.376420i
$624$	−0.0390180	−	0.0128940i	−0.00156197	−	0.000516173i
$625$	−1.33485	−	7.57034i	−0.0533942	−	0.302814i
$626$	2.63430	−	4.56274i	0.105288	−	0.182364i
$627$	−3.84091	−	4.70232i	−0.153391	−	0.187793i
$628$	−7.45712	−	12.9161i	−0.297572	−	0.515409i
$629$	19.6038	+	7.13520i	0.781655	+	0.284499i
$630$	27.8572	−	1.51242i	1.10986	−	0.0602561i
$631$	−23.2203	−	19.4841i	−0.924385	−	0.775651i	0.0504161	−	0.998728i	$-0.483945\pi$
$631$	−23.2203	−	19.4841i	−0.924385	−	0.775651i	−0.974801	+	0.223078i	$0.928390\pi$
$632$	5.51400	−	15.1496i	0.219335	−	0.602618i
$633$	−7.70325	+	3.06755i	−0.306177	+	0.121924i
$634$	9.85775	+	17.0741i	0.391501	+	0.678100i
$635$	−3.41270	+	5.91097i	−0.135429	+	0.234570i
$636$	13.7431	+	2.00167i	0.544950	+	0.0793713i
$637$	−0.144742	+	0.0814327i	−0.00573487	+	0.00322648i
$638$	4.27298	−	2.46700i	0.169169	−	0.0976697i
$639$	−3.55244	−	5.38216i	−0.140533	−	0.212915i
$640$	2.25930	−	2.69253i	0.0893067	−	0.106432i
$641$	3.37159	+	19.1212i	0.133170	+	0.755243i	0.976117	+	0.217246i	$0.0697075\pi$
$641$	3.37159	+	19.1212i	0.133170	+	0.755243i	−0.842947	+	0.537997i	$0.819181\pi$
$642$	4.68583	−	5.93610i	0.184935	−	0.234279i
$643$	−0.840524	−	4.76685i	−0.0331470	−	0.187986i	0.963738	−	0.266849i	$-0.0859823\pi$
$643$	−0.840524	−	4.76685i	−0.0331470	−	0.187986i	−0.996886	+	0.0788624i	$0.974871\pi$
$644$	0.819327	+	1.43753i	0.0322860	+	0.0566465i
$645$	−19.2307	+	35.7350i	−0.757207	+	1.40706i
$646$	−6.75803	−	6.18627i	−0.265891	−	0.243396i
$647$	8.48666	+	4.89978i	0.333645	+	0.192630i	0.657458	−	0.753491i	$-0.271632\pi$
$647$	8.48666	+	4.89978i	0.333645	+	0.192630i	−0.323813	+	0.946121i	$0.604965\pi$
$648$	2.60923	+	8.61347i	0.102500	+	0.338369i
$649$	0.754670	+	0.899381i	0.0296234	+	0.0353038i
$650$	0.112153	−	0.133659i	0.00439900	−	0.00524253i
$651$	0.271387	+	11.1489i	0.0106365	+	0.436959i
$652$	2.55790	−	14.5066i	0.100175	−	0.568122i
$653$		−	31.7215i		−	1.24136i	−0.784064	−	0.620679i	$-0.786857\pi$
$653$		−	31.7215i		−	1.24136i	0.784064	−	0.620679i	$-0.213143\pi$
$654$	−11.7255	+	21.7887i	−0.458505	+	0.852007i
$655$	8.76611	−	49.7151i	0.342520	−	1.94253i
$656$	−0.0956625	−	0.0802704i	−0.00373499	−	0.00313403i
$657$	17.3320	−	34.6511i	0.676186	−	1.35187i
$658$	−0.316555	+	1.73865i	−0.0123406	+	0.0677797i
$659$	1.57010	−	8.90446i	0.0611623	−	0.346868i	−0.938835	−	0.344368i	$-0.888093\pi$
$659$	1.57010	−	8.90446i	0.0611623	−	0.346868i	0.999997	−	0.00250004i	$-0.000795787\pi$
$660$	−3.25775	−	3.65472i	−0.126808	−	0.142260i
$661$	5.33142	+	14.6480i	0.207368	+	0.569740i	0.999157	−	0.0410557i	$-0.0130721\pi$
$661$	5.33142	+	14.6480i	0.207368	+	0.569740i	−0.791789	+	0.610795i	$0.790850\pi$
$662$	3.92743	−	10.7905i	0.152644	−	0.419385i
$663$	−0.0271018	+	0.0820116i	−0.00105255	+	0.00318507i
$664$			12.7782i			0.495889i
$665$	−1.97280	+	40.4872i	−0.0765021	+	1.57003i
$666$	24.8508	−	16.4026i	0.962950	−	0.635586i
$667$	3.77864	−	0.666276i	0.146310	−	0.0257983i
$668$	−20.7346	−	7.54678i	−0.802246	−	0.291994i
$669$	4.94697	−	33.9650i	0.191261	−	1.31316i
$670$	−29.3606	−	10.6864i	−1.13430	−	0.412851i
$671$	11.1841	+	1.97206i	0.431759	+	0.0761307i
$672$	4.26680	−	1.67166i	0.164595	−	0.0644857i
$673$	−1.12232	+	0.647971i	−0.0432622	+	0.0249774i	−0.521475	−	0.853266i	$-0.674618\pi$
$673$	−1.12232	+	0.647971i	−0.0432622	+	0.0249774i	0.478213	+	0.878244i	$0.341285\pi$
$674$	6.91743	−	8.24387i	0.266450	−	0.317542i
$675$	−38.0759	−	3.23773i	−1.46554	−	0.124620i
$676$	12.9994			0.499978
$677$	−37.7626			−1.45134			−0.725668	−	0.688045i	$-0.758469\pi$
$677$	−37.7626			−1.45134			−0.725668	+	0.688045i	$0.758469\pi$
$678$	12.5621	−	15.9140i	0.482446	−	0.611173i
$679$	−9.52901	−	0.0530188i	−0.365690	−	0.00203468i
$680$	−5.65940	−	4.74880i	−0.217028	−	0.182108i
$681$	31.1287	−	6.45393i	1.19285	−	0.247315i
$682$	1.49924	−	1.25801i	0.0574088	−	0.0481717i
$683$	15.2742	−	26.4557i	0.584452	−	1.01230i	−0.410492	−	0.911864i	$-0.634643\pi$
$683$	15.2742	−	26.4557i	0.584452	−	1.01230i	0.994944	−	0.100436i	$-0.0320238\pi$
$684$	−12.8384	+	2.48520i	−0.490887	+	0.0950240i
$685$	−45.2476			−1.72882
$686$	6.62390	−	17.2952i	0.252902	−	0.660334i
$687$	13.3761	−	40.4768i	0.510329	−	1.54429i
$688$	−1.15751	+	6.56456i	−0.0441296	+	0.250271i
$689$	0.187346	−	0.0330342i	0.00713733	−	0.00125850i
$690$	−1.40855	−	3.53717i	−0.0536228	−	0.134658i
$691$	0.742811			0.0282579			0.0141289	−	0.999900i	$-0.495502\pi$
$691$	0.742811			0.0282579			0.0141289	+	0.999900i	$0.495502\pi$
$692$	8.11758	+	14.0601i	0.308584	+	0.534483i
$693$	−1.44758	−	6.21687i	−0.0549891	−	0.236159i
$694$	−7.23881	−	19.8885i	−0.274782	−	0.754956i
$695$	−12.5895	−	7.26854i	−0.477546	−	0.275711i
$696$	−0.317700	−	10.6218i	−0.0120424	−	0.402620i
$697$	−0.168720	+	0.201072i	−0.00639071	+	0.00761615i
$698$	25.7049	+	9.35582i	0.972945	+	0.354123i
$699$	38.5242	−	15.3409i	1.45712	−	0.580247i
$700$	−0.108258	+	19.4570i	−0.00409175	+	0.735405i
$701$	−11.6854	+	32.1053i	−0.441350	+	1.21260i	0.497254	+	0.867605i	$0.334342\pi$
$701$	−11.6854	+	32.1053i	−0.441350	+	1.21260i	−0.938604	+	0.344995i	$0.887881\pi$
$702$	0.0709564	+	0.100812i	0.00267808	+	0.00380492i
$703$	19.9964	+	38.3650i	0.754178	+	1.44696i
$704$	−0.696461	−	0.402102i	−0.0262489	−	0.0151548i
$705$	1.27594	−	3.86106i	0.0480545	−	0.145416i
$706$	−2.12625	+	0.374915i	−0.0800224	+	0.0141101i
$707$	21.2546	+	7.87026i	0.799363	+	0.295991i
$708$	2.47597	−	0.513343i	0.0930525	−	0.0192926i
$709$	−19.6837	+	7.16428i	−0.739237	+	0.269060i	−0.684069	−	0.729417i	$-0.739792\pi$
$709$	−19.6837	+	7.16428i	−0.739237	+	0.269060i	−0.0551675	+	0.998477i	$0.517569\pi$
$710$	6.54331	−	3.77778i	0.245566	−	0.141778i
$711$	−40.3656	+	26.6429i	−1.51383	+	0.999187i
$712$	3.53469	+	2.96596i	0.132468	+	0.111154i
$713$	1.43017	−	0.520537i	0.0535601	−	0.0194943i
$714$	−3.51365	−	8.96834i	−0.131495	−	0.335632i
$715$	−0.0580783	−	0.0335315i	−0.00217201	−	0.00125401i
$716$	3.37132	−	1.22706i	0.125992	−	0.0458574i
$717$	−14.7585	−	4.87712i	−0.551165	−	0.182139i
$718$	8.66390	+	23.8039i	0.323334	+	0.888353i
$719$	−14.2992	−	17.0411i	−0.533271	−	0.635527i	0.430394	−	0.902641i	$-0.358375\pi$
$719$	−14.2992	−	17.0411i	−0.533271	−	0.635527i	−0.963665	+	0.267114i	$0.913930\pi$
$720$	−10.2564	+	2.44841i	−0.382232	+	0.0912467i
$721$	−0.442321	+	2.42940i	−0.0164729	+	0.0904758i
$722$	−1.67523	−	18.9260i	−0.0623454	−	0.704353i
$723$	−13.6822	+	0.409236i	−0.508847	+	0.0152197i
$724$	−11.1805	−	13.3244i	−0.415521	−	0.495199i
$725$	42.3987	+	15.4319i	1.57465	+	0.573125i
$726$	11.1109	−	14.0755i	0.412363	−	0.522389i
$727$	5.68836	−	4.77310i	0.210970	−	0.177024i	−0.531180	−	0.847259i	$-0.678251\pi$
$727$	5.68836	−	4.77310i	0.210970	−	0.177024i	0.742149	+	0.670235i	$0.233807\pi$
$728$	0.0483092	−	0.0400803i	0.00179046	−	0.00148547i
$729$	9.11077	−	25.4164i	0.337436	−	0.941349i
$730$	39.3116	+	22.6966i	1.45499	+	0.840038i
$731$	13.7980	+	2.43296i	0.510337	+	0.0899862i
$732$	15.1550	−	19.1986i	0.560144	−	0.709601i
$733$	−19.6368	+	34.0119i	−0.725300	+	1.25626i	0.233550	+	0.972345i	$0.424966\pi$
$733$	−19.6368	+	34.0119i	−0.725300	+	1.25626i	−0.958850	+	0.283912i	$0.908368\pi$
$734$	−6.42222	+	11.1236i	−0.237048	+	0.410580i
$735$	−20.6111	+	37.2994i	−0.760251	+	1.37581i
$736$	−0.401992	−	0.479076i	−0.0148176	−	0.0176590i
$737$	−1.24139	+	7.04028i	−0.0457273	+	0.259332i
$738$	0.0869891	+	0.364397i	0.00320211	+	0.0134136i
$739$	10.2557	−	8.60557i	0.377263	−	0.316561i	−0.434364	−	0.900737i	$-0.643027\pi$
$739$	10.2557	−	8.60557i	0.377263	−	0.316561i	0.811627	+	0.584177i	$0.198582\pi$
$740$	17.4430	+	30.2122i	0.641217	+	1.11062i
$741$	−0.156295	+	0.0875018i	−0.00574162	+	0.00321446i
$742$	−13.7266	+	16.1751i	−0.503920	+	0.593807i
$743$	40.8646	+	14.8735i	1.49918	+	0.545655i	0.955847	−	0.293865i	$-0.0949417\pi$
$743$	40.8646	+	14.8735i	1.49918	+	0.545655i	0.543328	+	0.839520i	$0.317164\pi$
$744$	−0.855726	−	4.12735i	−0.0313724	−	0.151316i
$745$	57.7742	−	21.0281i	2.11668	−	0.770409i
$746$	4.60650	−	0.812250i	0.168656	−	0.0297386i
$747$	22.8418	−	30.7861i	0.835737	−	1.12641i
$748$	−0.845175	+	1.46389i	−0.0309027	+	0.0535250i
$749$	3.89062	+	10.8773i	0.142160	+	0.397449i
$750$	2.06563	−	14.1822i	0.0754260	−	0.517862i
$751$	19.7998	−	23.5965i	0.722505	−	0.861048i	−0.272366	−	0.962194i	$-0.587806\pi$
$751$	19.7998	−	23.5965i	0.722505	−	0.861048i	0.994872	+	0.101145i	$0.0322507\pi$
$752$		−	0.667952i		−	0.0243577i
$753$	25.9851	−	0.777218i	0.946951	−	0.0283234i
$754$	−0.0497847	−	0.136782i	−0.00181305	−	0.00498132i
$755$	−29.5034	+	24.7563i	−1.07374	+	0.900974i
$756$	−13.2681	−	3.59968i	−0.482556	−	0.130919i
$757$	−0.457547	−	2.59488i	−0.0166298	−	0.0943124i	0.975363	−	0.220605i	$-0.0708032\pi$
$757$	−0.457547	−	2.59488i	−0.0166298	−	0.0943124i	−0.991993	+	0.126293i	$0.959692\pi$
$758$	12.6175	−	2.22480i	0.458287	−	0.0808084i
$759$	−0.741052	+	0.457919i	−0.0268985	+	0.0166214i
$760$	−2.00751	−	15.1888i	−0.0728199	−	0.550955i
$761$	−21.4452	+	12.3814i	−0.777388	+	0.448825i	−0.835504	−	0.549485i	$-0.814824\pi$
$761$	−21.4452	+	12.3814i	−0.777388	+	0.448825i	0.0581161	+	0.998310i	$0.481491\pi$
$762$	2.51075	−	2.23803i	0.0909548	−	0.0810754i
$763$	−18.7157	−	32.8371i	−0.677554	−	1.18878i
$764$	2.82400	−	3.36552i	0.102169	−	0.121760i
$765$	5.14628	+	21.5577i	0.186064	+	0.779421i
$766$	20.6073	+	17.2916i	0.744572	+	0.624770i
$767$	0.0299961	−	0.0173182i	0.00108310	−	0.000625325i
$768$	−1.47344	+	0.910483i	−0.0531681	+	0.0328542i
$769$	17.2415	−	6.27540i	0.621745	−	0.226297i	−0.0118893	−	0.999929i	$-0.503785\pi$
$769$	17.2415	−	6.27540i	0.621745	−	0.226297i	0.633634	+	0.773633i	$0.281562\pi$
$770$	7.37213	−	1.25765i	0.265673	−	0.0453227i
$771$	0.0445011	+	1.48783i	0.00160267	+	0.0535829i
$772$		−	24.3768i		−	0.877340i
$773$	−12.7129	−	10.6674i	−0.457251	−	0.383679i	0.384868	−	0.922972i	$-0.374247\pi$
$773$	−12.7129	−	10.6674i	−0.457251	−	0.383679i	−0.842118	+	0.539293i	$0.818692\pi$
$774$	14.5233	−	13.7467i	0.522030	−	0.494116i
$775$	17.6252	+	3.10780i	0.633116	+	0.111636i
$776$	3.54696	−	0.625425i	0.127329	−	0.0224515i
$777$	1.10684	+	45.4701i	0.0397075	+	1.63123i
$778$			29.7144i			1.06531i
$779$	−0.539640	+	0.0713244i	−0.0193346	+	0.00255546i
$780$	−0.122871	+	0.0759258i	−0.00439948	+	0.00271858i
$781$	−1.11121	−	1.32428i	−0.0397621	−	0.0473866i
$782$	−1.00697	+	0.844944i	−0.0360090	+	0.0302151i
$783$	−18.2218	+	26.1589i	−0.651194	+	0.934842i
$784$	−1.29217	+	6.87970i	−0.0461490	+	0.245704i
$785$	−51.6249	−	9.10287i	−1.84257	−	0.324895i
$786$	−11.7886	+	21.9060i	−0.420487	+	0.781361i
$787$			30.6945i			1.09414i	0.837086	+	0.547071i	$0.184257\pi$
$787$			30.6945i			1.09414i	−0.837086	+	0.547071i	$0.815743\pi$
$788$	0.659478	+	0.116284i	0.0234929	+	0.00414244i
$789$	39.4281	−	15.7009i	1.40368	−	0.558966i
$790$	−28.3329	−	49.0741i	−1.00804	−	1.74598i
$791$	10.4303	+	29.1608i	0.370859	+	1.03684i
$792$	0.959185	+	2.21374i	0.0340832	+	0.0786620i
$793$	0.114590	−	0.314833i	0.00406921	−	0.0111801i
$794$	9.80088	−	3.56723i	0.347820	−	0.126596i
$795$	36.4394	−	32.4814i	1.29237	−	1.15200i
$796$	−1.02115	−	5.79123i	−0.0361937	−	0.205265i
$797$	−0.484417			−0.0171589			−0.00857947	−	0.999963i	$-0.502731\pi$
$797$	−0.484417			−0.0171589			−0.00857947	+	0.999963i	$0.502731\pi$
$798$	7.18326	−	18.6387i	0.254285	−	0.659803i
$799$	−1.40396			−0.0496686
$800$	−1.27704	−	7.24243i	−0.0451501	−	0.256059i
$801$	−3.21421	−	13.4643i	−0.113569	−	0.475738i
$802$	−31.8649	+	11.5979i	−1.12519	+	0.409535i
$803$	3.55224	−	9.75969i	0.125356	−	0.344412i
$804$	12.0853	+	9.53988i	0.426216	+	0.336446i
$805$	5.72169	+	1.04175i	0.201663	+	0.0367167i
$806$	−0.0288689	−	0.0500024i	−0.00101686	−	0.00176126i
$807$	6.09015	+	15.2936i	0.214384	+	0.538361i
$808$	−8.43641	−	1.48757i	−0.296792	−	0.0523324i
$809$			24.1768i			0.850010i	0.905191	+	0.425005i	$0.139728\pi$
$809$			24.1768i			0.850010i	−0.905191	+	0.425005i	$0.860272\pi$
$810$	29.0871	+	12.4350i	1.02202	+	0.436921i
$811$	14.7751	+	2.60524i	0.518822	+	0.0914824i	0.426927	−	0.904286i	$-0.359596\pi$
$811$	14.7751	+	2.60524i	0.518822	+	0.0914824i	0.0918957	+	0.995769i	$0.470707\pi$
$812$	14.0123	+	8.19429i	0.491735	+	0.287563i
$813$	9.51882	+	23.9037i	0.333840	+	0.838339i
$814$	6.11456	−	5.13072i	0.214315	−	0.179832i
$815$	−33.2803	−	39.6620i	−1.16576	−	1.38930i
$816$	1.91374	+	3.09701i	0.0669942	+	0.108417i
$817$	17.6997	+	23.0424i	0.619234	+	0.806152i
$818$		−	34.8413i		−	1.21820i
$819$	−0.188036	+	0.0102088i	−0.00657052	+	0.000356725i
$820$	−0.432261	+	0.0762193i	−0.0150952	+	0.00266169i
$821$	−41.3411	−	7.28956i	−1.44282	−	0.254407i	−0.603200	−	0.797590i	$-0.706108\pi$
$821$	−41.3411	−	7.28956i	−1.44282	−	0.254407i	−0.839615	+	0.543182i	$0.817219\pi$
$822$	21.1711	+	6.99626i	0.738427	+	0.244022i
$823$	33.7650	+	28.3322i	1.17697	+	0.987597i	0.999994	+	0.00338258i	$0.00107671\pi$
$823$	33.7650	+	28.3322i	1.17697	+	0.987597i	0.176978	+	0.984215i	$0.443368\pi$
$824$		−	0.933324i		−	0.0325139i
$825$	−10.2392	+	0.306255i	−0.356483	+	0.0106624i
$826$	−1.34124	+	3.62219i	−0.0466677	+	0.126032i
$827$	49.9035	−	18.1634i	1.73532	−	0.631603i	0.736330	−	0.676622i	$-0.236557\pi$
$827$	49.9035	−	18.1634i	1.73532	−	0.631603i	0.998986	+	0.0450189i	$0.0143348\pi$
$828$	0.112132	+	1.87281i	0.00389687	+	0.0650848i
$829$	−2.26090	+	1.30533i	−0.0785241	+	0.0453359i	−0.538748	−	0.842467i	$-0.681102\pi$
$829$	−2.26090	+	1.30533i	−0.0785241	+	0.0453359i	0.460224	+	0.887803i	$0.347769\pi$
$830$	34.4056	+	28.8697i	1.19424	+	1.00208i
$831$	29.5369	+	33.1361i	1.02462	+	1.14948i
$832$	−0.0152503	+	0.0181746i	−0.000528709	+	0.000630090i
$833$	14.4604	+	2.71600i	0.501022	+	0.0941039i
$834$	4.76668	+	5.34752i	0.165056	+	0.185169i
$835$	−67.1656	+	38.7781i	−2.32436	+	1.34197i
$836$	−3.34267	+	1.05581i	−0.115609	+	0.0365159i
$837$	−5.31622	+	11.4736i	−0.183755	+	0.396585i
$838$	27.9161	−	4.92236i	0.964346	−	0.170040i
$839$	5.04811	+	28.6292i	0.174280	+	0.988391i	0.938972	+	0.343995i	$0.111780\pi$
$839$	5.04811	+	28.6292i	0.174280	+	0.988391i	−0.764692	+	0.644396i	$0.777109\pi$
$840$	5.13898	−	15.2653i	0.177312	−	0.526702i
$841$	6.61978	−	5.55466i	0.228268	−	0.191540i
$842$	8.61445	+	23.6680i	0.296873	+	0.815653i
$843$	−0.489315	−	16.3595i	−0.0168529	−	0.563452i
$844$			4.78713i			0.164780i
$845$	29.3696	−	35.0014i	1.01035	−	1.20408i
$846$	−1.19401	+	1.60928i	−0.0410508	+	0.0553282i
$847$	9.22530	+	25.7919i	0.316985	+	0.886221i
$848$	4.00916	−	6.94407i	0.137675	−	0.238460i
$849$	20.4154	+	2.97348i	0.700656	+	0.102050i
$850$	−15.2228	+	2.68419i	−0.522138	+	0.0920670i
$851$	5.83285	−	2.12298i	0.199948	−	0.0727749i
$852$	−3.64571	+	0.755866i	−0.124900	+	0.0258956i
$853$	−33.3330	−	12.1322i	−1.14130	−	0.415399i	−0.298916	−	0.954279i	$-0.596625\pi$
$853$	−33.3330	−	12.1322i	−1.14130	−	0.415399i	−0.842382	+	0.538881i	$0.818847\pi$
$854$	12.5831	+	35.1796i	0.430585	+	1.20382i
$855$	−22.3143	+	40.1825i	−0.763132	+	1.37421i
$856$	−2.18316	−	3.78134i	−0.0746189	−	0.129244i
$857$	25.0910	−	21.0538i	0.857092	−	0.719185i	−0.104248	−	0.994551i	$-0.533243\pi$
$857$	25.0910	−	21.0538i	0.857092	−	0.719185i	0.961339	+	0.275366i	$0.0887990\pi$
$858$	0.0219898	+	0.0246694i	0.000750721	+	0.000842199i
$859$	2.63662	−	14.9530i	0.0899602	−	0.510190i	−0.906215	−	0.422816i	$-0.861042\pi$
$859$	2.63662	−	14.9530i	0.0899602	−	0.510190i	0.996176	−	0.0873735i	$-0.0278474\pi$
$860$	15.0601	+	17.9479i	0.513546	+	0.612020i
$861$	−0.542357	−	0.182582i	−0.0184835	−	0.00622238i
$862$	5.44569	−	9.43220i	0.185481	−	0.321262i
$863$	8.64878	−	14.9801i	0.294408	−	0.509929i	−0.680439	−	0.732805i	$-0.738211\pi$
$863$	8.64878	−	14.9801i	0.294408	−	0.509929i	0.974847	+	0.222875i	$0.0715442\pi$
$864$	5.17747	+	0.440258i	0.176141	+	0.0149779i
$865$	56.1972	+	9.90908i	1.91076	+	0.336919i
$866$	−4.00787	−	2.31394i	−0.136193	−	0.0786310i
$867$	−18.5389	+	11.4558i	−0.629613	+	0.389058i
$868$	6.03806	+	2.23580i	0.204945	+	0.0758879i
$869$	−9.93196	+	8.33391i	−0.336919	+	0.282708i
$870$	−29.3174	−	23.1425i	−0.993954	−	0.784605i
$871$	0.198184	+	0.0721331i	0.00671521	+	0.00244414i
$872$	9.18262	+	10.9434i	0.310963	+	0.370591i
$873$	−9.66361	−	4.83360i	−0.327064	−	0.163593i
$874$	−2.72347	−	0.117521i	−0.0921229	−	0.00397520i
$875$	16.6919	+	14.1652i	0.564290	+	0.478871i
$876$	−14.8843	−	16.6980i	−0.502894	−	0.564174i
$877$	−20.2437	−	24.1255i	−0.683581	−	0.814661i	0.306982	−	0.951715i	$-0.400681\pi$
$877$	−20.2437	−	24.1255i	−0.683581	−	0.814661i	−0.990563	+	0.137055i	$0.956236\pi$
$878$	−2.93589	−	8.06629i	−0.0990814	−	0.272224i
$879$	−4.51108	+	13.6508i	−0.152155	+	0.460431i
$880$	−2.65619	+	0.966774i	−0.0895401	+	0.0325899i
$881$	−40.5870	−	23.4329i	−1.36741	−	0.789474i	−0.376813	−	0.926290i	$-0.622980\pi$
$881$	−40.5870	−	23.4329i	−1.36741	−	0.789474i	−0.990597	+	0.136815i	$0.956313\pi$
$882$	15.4111	−	14.2653i	0.518919	−	0.480337i
$883$	8.99543	−	3.27407i	0.302720	−	0.110181i	−0.186194	−	0.982513i	$-0.559615\pi$
$883$	8.99543	−	3.27407i	0.302720	−	0.110181i	0.488914	+	0.872332i	$0.337393\pi$
$884$	0.0382010	+	0.0320544i	0.00128484	+	0.00107811i
$885$	4.21176	−	7.82641i	0.141577	−	0.263082i
$886$	−16.7042	+	9.64417i	−0.561188	+	0.324002i
$887$	−52.3377	+	19.0493i	−1.75733	+	0.639614i	−0.999911	−	0.0133192i	$-0.995760\pi$
$887$	−52.3377	+	19.0493i	−1.75733	+	0.639614i	−0.757415	+	0.652934i	$0.773538\pi$
$888$	−3.49003	−	16.8332i	−0.117118	−	0.564884i
$889$	0.863990	+	5.06455i	0.0289773	+	0.169860i
$890$	15.9719	−	2.81627i	0.535378	−	0.0944016i
$891$	1.64627	−	7.04813i	0.0551520	−	0.236121i
$892$	−17.1617	−	9.90832i	−0.574616	−	0.331755i
$893$	−2.14761	−	1.96591i	−0.0718670	−	0.0657867i
$894$	−30.2836	+	0.905786i	−1.01284	+	0.0302940i
$895$	4.31294	−	11.8497i	0.144166	−	0.396092i
$896$	0.0147206	−	2.64571i	0.000491780	−	0.0883870i
$897$	0.00950774	+	0.0238759i	0.000317454	+	0.000797192i
$898$	4.65992	+	1.69607i	0.155504	+	0.0565987i
$899$	9.59734	−	11.4377i	0.320089	−	0.381468i
$900$	−9.86958	+	19.7318i	−0.328986	+	0.657727i
$901$	−14.5957	−	8.42681i	−0.486252	−	0.280738i
$902$	0.0343484	+	0.0943714i	0.00114368	+	0.00314222i
$903$	6.03486	+	29.9446i	0.200828	+	0.996494i
$904$	−5.85279	−	10.1373i	−0.194661	−	0.337163i
$905$	−61.1367			−2.03225
$906$	17.6323	−	7.02147i	0.585795	−	0.233273i
$907$	18.0067	−	3.17506i	0.597901	−	0.105426i	0.133497	−	0.991049i	$-0.457379\pi$
$907$	18.0067	−	3.17506i	0.597901	−	0.105426i	0.464405	+	0.885623i	$0.346268\pi$
$908$	3.18720	−	18.0755i	0.105771	−	0.599858i
$909$	17.6665	+	18.6646i	0.585962	+	0.619065i
$910$	0.00122756	−	0.220627i	4.06932e−5	−	0.00731373i
$911$	55.8059			1.84893			0.924465	−	0.381266i	$-0.124512\pi$
$911$	55.8059			1.84893			0.924465	+	0.381266i	$0.124512\pi$
$912$	−1.40921	+	7.41715i	−0.0466637	+	0.245606i
$913$	5.13813	−	8.89950i	0.170047	−	0.294531i
$914$	−7.56927	+	6.35138i	−0.250369	+	0.210085i
$915$	−17.4532	−	84.1807i	−0.576986	−	2.78293i
$916$	−18.8541	−	15.8205i	−0.622957	−	0.522723i
$917$	−18.8164	−	33.0138i	−0.621373	−	1.09021i
$918$	0.925374	−	10.8825i	0.0305419	−	0.359175i
$919$	39.8154			1.31339			0.656695	−	0.754156i	$-0.271954\pi$
$919$	39.8154			1.31339			0.656695	+	0.754156i	$0.271954\pi$
$920$	−2.19815			−0.0724708
$921$	−25.2014	−	19.8934i	−0.830414	−	0.655511i
$922$	−24.0943	+	28.7145i	−0.793504	+	0.945661i
$923$	−0.0441674	+	0.0255000i	−0.00145379	+	0.000839344i
$924$	−3.64384	−	0.551441i	−0.119873	−	0.0181411i
$925$	71.8835	+	12.6750i	2.36351	+	0.416751i
$926$	25.1314	+	9.14709i	0.825870	+	0.300592i
$927$	−1.66838	+	2.24864i	−0.0547967	+	0.0738549i
$928$	−5.76527	−	2.09839i	−0.189254	−	0.0688829i
$929$	28.9942	−	5.11245i	0.951268	−	0.167734i	0.323581	−	0.946200i	$-0.395113\pi$
$929$	28.9942	−	5.11245i	0.951268	−	0.167734i	0.627686	+	0.778466i	$0.284002\pi$
$930$	−13.0464	−	7.02086i	−0.427807	−	0.230223i
$931$	18.3166	+	24.4029i	0.600303	+	0.799773i
$932$		−	23.9406i		−	0.784200i
$933$	−29.8128	−	9.85202i	−0.976028	−	0.322541i
$934$	−1.05794	+	2.90668i	−0.0346170	+	0.0951093i
$935$	2.03205	+	5.58302i	0.0664552	+	0.182584i
$936$	0.0692304	−	0.0165267i	0.00226287	−	0.000540194i
$937$	8.67086	−	49.1749i	0.283265	−	1.60647i	−0.428154	−	0.903706i	$-0.640836\pi$
$937$	8.67086	−	49.1749i	0.283265	−	1.60647i	0.711419	−	0.702768i	$-0.248053\pi$
$938$	−22.1452	+	7.92093i	−0.723065	+	0.258627i
$939$	0.272822	+	9.12140i	0.00890321	+	0.297666i
$940$	−1.79848	−	1.50910i	−0.0586600	−	0.0492215i
$941$	10.2410	−	58.0798i	0.333848	−	1.89335i	−0.104468	−	0.994528i	$-0.533314\pi$
$941$	10.2410	−	58.0798i	0.333848	−	1.89335i	0.438317	−	0.898821i	$-0.355575\pi$
$942$	22.7475	+	12.2415i	0.741154	+	0.398850i
$943$			0.0780977i			0.00254321i
$944$	0.253509	−	1.43772i	0.00825102	−	0.0467939i
$945$	−39.6689	+	27.5920i	−1.29043	+	0.897567i
$946$	3.44578	−	4.10653i	0.112032	−	0.133515i
$947$	20.0484	+	23.8928i	0.651487	+	0.776412i	0.986137	−	0.165931i	$-0.0530628\pi$
$947$	20.0484	+	23.8928i	0.651487	+	0.776412i	−0.334651	+	0.942342i	$0.608618\pi$
$948$	5.66891	+	27.3424i	0.184118	+	0.888039i
$949$	−0.265353	−	0.153202i	−0.00861374	−	0.00497314i
$950$	−27.0446	−	17.2099i	−0.877441	−	0.558364i
$951$	−30.0705	−	16.1823i	−0.975102	−	0.524749i
$952$	−5.56099	−	0.0309410i	−0.180233	−	0.00100281i
$953$	3.64620	+	20.6786i	0.118112	+	0.669847i	0.985162	+	0.171626i	$0.0549020\pi$
$953$	3.64620	+	20.6786i	0.118112	+	0.669847i	−0.867050	+	0.498221i	$0.833987\pi$
$954$	−22.0721	+	9.56355i	−0.714612	+	0.309631i
$955$	−2.68148	−	15.2074i	−0.0867706	−	0.492101i
$956$	−5.76838	+	6.87449i	−0.186563	+	0.222337i
$957$	−4.04980	+	7.52545i	−0.130911	+	0.243263i
$958$	−14.9158	+	8.61164i	−0.481908	+	0.278230i
$959$	−26.2125	+	21.7475i	−0.846445	+	0.702263i
$960$	−0.877437	+	6.02433i	−0.0283191	+	0.194435i
$961$	−12.5388	+	21.7178i	−0.404477	+	0.700575i
$962$	−0.117740	−	0.203932i	−0.00379610	−	0.00657504i
$963$	−1.49956	+	13.0128i	−0.0483225	+	0.419333i
$964$	−2.70297	+	7.42636i	−0.0870569	+	0.239187i
$965$	−65.6353	−	55.0745i	−2.11287	−	1.77291i
$966$	−2.51607	−	1.37212i	−0.0809533	−	0.0441474i
$967$	5.23852	+	1.90666i	0.168459	+	0.0613142i	0.424873	−	0.905253i	$-0.360319\pi$
$967$	5.23852	+	1.90666i	0.168459	+	0.0613142i	−0.256414	+	0.966567i	$0.582541\pi$
$968$	−5.17663	−	8.96618i	−0.166383	−	0.288184i
$969$	15.5900	+	2.96201i	0.500824	+	0.0951535i
$970$	6.32968	−	10.9633i	0.203234	−	0.352011i
$971$	−7.51500	−	42.6197i	−0.241168	−	1.36773i	−0.829227	−	0.558913i	$-0.811219\pi$
$971$	−7.51500	−	42.6197i	−0.241168	−	1.36773i	0.588059	−	0.808818i	$-0.299892\pi$
$972$	−11.6870	−	10.3158i	−0.374860	−	0.330878i
$973$	−10.7867	+	1.84017i	−0.345807	+	0.0589932i
$974$	−25.5144	−	30.4069i	−0.817535	−	0.974300i
$975$	−0.0435565	+	0.299051i	−0.00139492	+	0.00957731i
$976$	−7.06081	−	12.2297i	−0.226011	−	0.391462i
$977$	35.4858			1.13529			0.567645	−	0.823273i	$-0.307855\pi$
$977$	35.4858			1.13529			0.567645	+	0.823273i	$0.307855\pi$
$978$	9.43909	+	23.7035i	0.301829	+	0.757954i
$979$	−1.26916	−	3.48698i	−0.0405624	−	0.111444i
$980$	15.6044	+	19.0225i	0.498464	+	0.607652i
$981$	−2.56142	−	42.7803i	−0.0817797	−	1.36587i
$982$	−8.42305	−	23.1421i	−0.268790	−	0.738495i
$983$	−0.317241	−	1.79917i	−0.0101184	−	0.0573845i	0.979330	−	0.202267i	$-0.0648308\pi$
$983$	−0.317241	−	1.79917i	−0.0101184	−	0.0573845i	−0.989449	+	0.144882i	$0.953720\pi$
$984$	0.214038	+	0.0311743i	0.00682327	+	0.000993801i
$985$	1.80306	−	1.51294i	0.0574502	−	0.0482064i
$986$	−4.41058	+	12.1180i	−0.140461	+	0.385914i
$987$	−1.11659	−	2.85001i	−0.0355414	−	0.0907169i
$988$	0.0135507	+	0.102524i	0.000431104	+	0.00326173i
$989$	3.61023	−	2.08437i	0.114799	−	0.0662791i
$990$	8.12766	+	2.41888i	0.258314	+	0.0768771i
$991$	10.8868	−	29.9111i	0.345829	−	0.950158i	−0.637839	−	0.770169i	$-0.720172\pi$
$991$	10.8868	−	29.9111i	0.345829	−	0.950158i	0.983669	−	0.179989i	$-0.0576061\pi$
$992$	−2.39663	−	0.422591i	−0.0760931	−	0.0134173i
$993$	4.03776	+	19.4750i	0.128135	+	0.618021i
$994$	1.97489	−	5.33345i	0.0626397	−	0.169167i
$995$	−17.9001	−	10.3347i	−0.567473	−	0.327631i
$996$	−11.6343	−	18.8278i	−0.368647	−	0.596583i
$997$	−3.59787	+	20.4045i	−0.113946	+	0.646218i	0.873321	+	0.487145i	$0.161962\pi$
$997$	−3.59787	+	20.4045i	−0.113946	+	0.646218i	−0.987267	+	0.159073i	$0.949149\pi$
$998$	−2.52672	+	14.3297i	−0.0799819	+	0.453600i
$999$	−21.6819	+	46.7944i	−0.685985	+	1.48051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.a.53.7	✓	162
3.2	odd	2		798.2.bu.b.53.27	yes	162
7.2	even	3		798.2.cc.a.737.25	yes	162
19.14	odd	18		798.2.cc.b.641.11	yes	162
21.2	odd	6		798.2.cc.b.737.11	yes	162
57.14	even	18		798.2.cc.a.641.25	yes	162
133.128	odd	18		798.2.bu.b.527.27	yes	162
399.128	even	18	inner	798.2.bu.a.527.7	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.53.7	✓	162	1.1	even	1	trivial
798.2.bu.a.527.7	yes	162	399.128	even	18	inner
798.2.bu.b.53.27	yes	162	3.2	odd	2
798.2.bu.b.527.27	yes	162	133.128	odd	18
798.2.cc.a.641.25	yes	162	57.14	even	18
798.2.cc.a.737.25	yes	162	7.2	even	3
798.2.cc.b.641.11	yes	162	19.14	odd	18
798.2.cc.b.737.11	yes	162	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-1.15251 - 1.29295i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.20215 + 3.30288i) q^{5} +(1.07318 - 1.35952i) q^{6} +(0.891053 + 2.49119i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.343437 + 2.98028i) q^{9} +(-3.46145 - 0.610347i) q^{10} +0.804204i q^{11} +(1.52522 + 0.820793i) q^{12} +(0.0233648 + 0.00411984i) q^{13} +(-2.29861 + 1.31011i) q^{14} +(5.65594 - 2.25228i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.35107 - 1.61014i) q^{17} +(-2.99464 + 0.179300i) q^{18} +(0.187916 - 4.35485i) q^{19} -3.51485i q^{20} +(2.19403 - 4.02321i) q^{21} +(-0.791987 + 0.139649i) q^{22} +(-0.615888 - 0.108598i) q^{23} +(-0.543472 + 1.64458i) q^{24} +(-5.63361 - 4.72716i) q^{25} +0.0237252i q^{26} +(4.24916 - 2.99075i) q^{27} +(-1.68935 - 2.03619i) q^{28} +(-5.76527 + 2.09839i) q^{29} +(3.20021 + 5.17891i) q^{30} +(-2.10756 + 1.21680i) q^{31} +(0.766044 + 0.642788i) q^{32} +(1.03980 - 0.926854i) q^{33} +(1.35107 - 1.61014i) q^{34} +(-9.29927 - 0.0517406i) q^{35} +(-0.696589 - 2.91801i) q^{36} +(-8.59558 + 4.96266i) q^{37} +(4.32132 - 0.571150i) q^{38} +(-0.0216014 - 0.0349577i) q^{39} +(3.46145 - 0.610347i) q^{40} +(-0.0216849 - 0.122981i) q^{41} +(4.34308 + 1.46208i) q^{42} +(-5.10632 + 4.28471i) q^{43} +(-0.275054 - 0.755705i) q^{44} +(-9.43063 - 4.71707i) q^{45} -0.625389i q^{46} +(0.429351 - 0.511681i) q^{47} +(-1.71397 - 0.249637i) q^{48} +(-5.41205 + 4.43957i) q^{49} +(3.67708 - 6.36889i) q^{50} +(-0.524710 + 3.60257i) q^{51} +(-0.0233648 + 0.00411984i) q^{52} +(7.53475 - 2.74243i) q^{53} +(3.68318 + 3.66527i) q^{54} +(-2.65619 - 0.966774i) q^{55} +(1.71191 - 2.01727i) q^{56} +(-5.84717 + 4.77604i) q^{57} +(-3.06763 - 5.31330i) q^{58} +(1.11835 - 0.938406i) q^{59} +(-4.54452 + 4.05090i) q^{60} +(2.45219 - 13.9071i) q^{61} +(-1.56429 - 1.86425i) q^{62} +(-7.73045 + 1.80002i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0416953 + 0.0722184i) q^{65} +(1.09333 + 0.863052i) q^{66} +(8.75434 + 1.54363i) q^{67} +(1.82029 + 1.05095i) q^{68} +(0.569407 + 0.921472i) q^{69} +(-1.56385 - 9.16698i) q^{70} +(-1.64670 + 1.38174i) q^{71} +(2.75271 - 1.19271i) q^{72} +(-12.1358 - 4.41708i) q^{73} +(-6.37987 - 7.60324i) q^{74} +(0.380818 + 12.7321i) q^{75} +(1.31286 + 4.15649i) q^{76} +(-2.00343 + 0.716589i) q^{77} +(0.0306755 - 0.0273436i) q^{78} +(10.3629 + 12.3500i) q^{79} +(1.20215 + 3.30288i) q^{80} +(-8.76410 - 2.04708i) q^{81} +(0.117347 - 0.0427110i) q^{82} +(-11.0662 - 6.38908i) q^{83} +(-0.685698 + 4.53098i) q^{84} +(6.94229 - 2.52679i) q^{85} +(-5.10632 - 4.28471i) q^{86} +(9.35764 + 5.03579i) q^{87} +(0.696461 - 0.402102i) q^{88} +(-4.33594 + 1.57815i) q^{89} +(3.00779 - 10.1065i) q^{90} +(0.0105560 + 0.0618771i) q^{91} +(0.615888 - 0.108598i) q^{92} +(4.00225 + 1.32259i) q^{93} +(0.578463 + 0.333976i) q^{94} +(14.1576 + 5.85584i) q^{95} +(-0.0517826 - 1.73128i) q^{96} +(-1.23185 + 3.38447i) q^{97} +(-5.31191 - 4.55890i) q^{98} +(-2.39675 - 0.276194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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