LMFDB - Embedded newform 546.2.bz.b.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	546.31
Dual form			546.2.bz.b.229.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.272675 + 1.01764i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.64349 + 0.109436i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.272675 + 1.01764i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.64349 + 0.109436i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.526768 + 0.912388i) q^{10} +(-1.13497 + 0.304114i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.201804 + 3.59990i) q^{13} +(2.52509 + 0.789892i) q^{14} +(0.744962 - 0.744962i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.53464 - 4.39013i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-1.54908 + 5.78125i) q^{19} +(-0.744962 + 0.744962i) q^{20} +(-2.23461 - 1.41652i) q^{21} -1.17501 q^{22} +(5.58669 - 3.22548i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(3.36889 + 1.94503i) q^{25} +(-0.736795 + 3.52947i) q^{26} -1.00000i q^{27} +(2.23461 + 1.41652i) q^{28} +3.12716 q^{29} +(0.912388 - 0.526768i) q^{30} +(-3.79127 + 1.01587i) q^{31} +(0.258819 + 0.965926i) q^{32} +(1.13497 + 0.304114i) q^{33} +(3.58452 - 3.58452i) q^{34} +(-0.832179 + 2.66027i) q^{35} +1.00000i q^{36} +(-0.363278 + 1.35577i) q^{37} +(-2.99260 + 5.18333i) q^{38} +(1.62518 - 3.21851i) q^{39} +(-0.912388 + 0.526768i) q^{40} +(2.05936 + 2.05936i) q^{41} +(-1.79184 - 1.94661i) q^{42} -1.78833i q^{43} +(-1.13497 - 0.304114i) q^{44} +(-1.01764 + 0.272675i) q^{45} +(6.23115 - 1.66963i) q^{46} +(-6.63638 - 1.77821i) q^{47} -1.00000i q^{48} +(6.97605 + 0.578587i) q^{49} +(2.75069 + 2.75069i) q^{50} +(-4.39013 + 2.53464i) q^{51} +(-1.62518 + 3.21851i) q^{52} +(-0.443410 + 0.768008i) q^{53} +(0.258819 - 0.965926i) q^{54} -1.23791i q^{55} +(1.79184 + 1.94661i) q^{56} +(4.23217 - 4.23217i) q^{57} +(3.02060 + 0.809368i) q^{58} +(-1.77116 - 6.61005i) q^{59} +(1.01764 - 0.272675i) q^{60} +(-9.72877 + 5.61691i) q^{61} -3.92502 q^{62} +(1.22697 + 2.34405i) q^{63} +1.00000i q^{64} +(-3.71842 - 0.776239i) q^{65} +(1.01758 + 0.587503i) q^{66} +(-3.07560 - 11.4783i) q^{67} +(4.39013 - 2.53464i) q^{68} -6.45096 q^{69} +(-1.49235 + 2.35424i) q^{70} +(4.62139 - 4.62139i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-2.31854 - 8.65290i) q^{73} +(-0.701798 + 1.21555i) q^{74} +(-1.94503 - 3.36889i) q^{75} +(-4.23217 + 4.23217i) q^{76} +(-3.03356 + 0.679714i) q^{77} +(2.40282 - 2.68821i) q^{78} +(-3.14704 - 5.45082i) q^{79} +(-1.01764 + 0.272675i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.45619 + 2.52219i) q^{82} +(-9.80685 - 9.80685i) q^{83} +(-1.22697 - 2.34405i) q^{84} +(3.77642 + 3.77642i) q^{85} +(0.462854 - 1.72740i) q^{86} +(-2.70820 - 1.56358i) q^{87} +(-1.01758 - 0.587503i) q^{88} +(-7.08351 - 1.89802i) q^{89} -1.05354 q^{90} +(0.139506 + 9.53837i) q^{91} +6.45096 q^{92} +(3.79127 + 1.01587i) q^{93} +(-5.95001 - 3.43524i) q^{94} +(-5.46082 - 3.15280i) q^{95} +(0.258819 - 0.965926i) q^{96} +(-1.59617 - 1.59617i) q^{97} +(6.58860 + 2.36441i) q^{98} +(-0.830855 - 0.830855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.272675	+	1.01764i	−0.121944	+	0.455101i	−0.999712	−	0.0239842i	$-0.992365\pi$
$5$	−0.272675	+	1.01764i	−0.121944	+	0.455101i	0.877768	+	0.479085i	$0.159032\pi$
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	2.64349	+	0.109436i	0.999144	+	0.0413630i
$7$	2.64349	+	0.109436i	0.999144	+	0.0413630i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.526768	+	0.912388i	−0.166579	+	0.288522i
$11$	−1.13497	+	0.304114i	−0.342206	+	0.0916938i	−0.425829	−	0.904804i	$-0.640017\pi$
$11$	−1.13497	+	0.304114i	−0.342206	+	0.0916938i	0.0836231	+	0.996497i	$0.473351\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.201804	+	3.59990i	0.0559703	+	0.998432i
$13$	0.201804	+	3.59990i	0.0559703	+	0.998432i
$14$	2.52509	+	0.789892i	0.674858	+	0.211108i
$15$	0.744962	−	0.744962i	0.192348	−	0.192348i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.53464	−	4.39013i	0.614741	−	1.06476i	−0.375689	−	0.926746i	$-0.622594\pi$
$17$	2.53464	−	4.39013i	0.614741	−	1.06476i	0.990430	−	0.138017i	$-0.0440727\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	−1.54908	+	5.78125i	−0.355384	+	1.32631i	0.524617	+	0.851338i	$0.324208\pi$
$19$	−1.54908	+	5.78125i	−0.355384	+	1.32631i	−0.880001	+	0.474972i	$0.842458\pi$
$20$	−0.744962	+	0.744962i	−0.166579	+	0.166579i
$21$	−2.23461	−	1.41652i	−0.487632	−	0.309110i
$22$	−1.17501			−0.250512
$23$	5.58669	−	3.22548i	1.16491	−	0.672559i	0.212431	−	0.977176i	$-0.431862\pi$
$23$	5.58669	−	3.22548i	1.16491	−	0.672559i	0.952475	+	0.304617i	$0.0985286\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$	3.36889	+	1.94503i	0.673779	+	0.389006i
$26$	−0.736795	+	3.52947i	−0.144497	+	0.692185i
$27$		−	1.00000i		−	0.192450i
$28$	2.23461	+	1.41652i	0.422301	+	0.267697i
$29$	3.12716			0.580699			0.290349	−	0.956921i	$-0.406229\pi$
$29$	3.12716			0.580699			0.290349	+	0.956921i	$0.406229\pi$
$30$	0.912388	−	0.526768i	0.166579	−	0.0961741i
$31$	−3.79127	+	1.01587i	−0.680933	+	0.182455i	−0.582675	−	0.812706i	$-0.697994\pi$
$31$	−3.79127	+	1.01587i	−0.680933	+	0.182455i	−0.0982582	+	0.995161i	$0.531327\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	1.13497	+	0.304114i	0.197573	+	0.0529394i
$34$	3.58452	−	3.58452i	0.614741	−	0.614741i
$35$	−0.832179	+	2.66027i	−0.140664	+	0.449668i
$36$			1.00000i			0.166667i
$37$	−0.363278	+	1.35577i	−0.0597225	+	0.222887i	−0.989337	−	0.145647i	$-0.953474\pi$
$37$	−0.363278	+	1.35577i	−0.0597225	+	0.222887i	0.929614	+	0.368534i	$0.120140\pi$
$38$	−2.99260	+	5.18333i	−0.485463	+	0.840847i
$39$	1.62518	−	3.21851i	0.260237	−	0.515373i
$40$	−0.912388	+	0.526768i	−0.144261	+	0.0832893i
$41$	2.05936	+	2.05936i	0.321618	+	0.321618i	0.849387	−	0.527770i	$-0.176972\pi$
$41$	2.05936	+	2.05936i	0.321618	+	0.321618i	−0.527770	+	0.849387i	$0.676972\pi$
$42$	−1.79184	−	1.94661i	−0.276488	−	0.300369i
$43$		−	1.78833i		−	0.272718i	−0.990659	−	0.136359i	$-0.956460\pi$
$43$		−	1.78833i		−	0.272718i	0.990659	−	0.136359i	$-0.0435401\pi$
$44$	−1.13497	−	0.304114i	−0.171103	−	0.0458469i
$45$	−1.01764	+	0.272675i	−0.151700	+	0.0406480i
$46$	6.23115	−	1.66963i	0.918732	−	0.246174i
$47$	−6.63638	−	1.77821i	−0.968015	−	0.259379i	−0.260026	−	0.965602i	$-0.583731\pi$
$47$	−6.63638	−	1.77821i	−0.968015	−	0.259379i	−0.707990	+	0.706223i	$0.750398\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.97605	+	0.578587i	0.996578	+	0.0826553i
$50$	2.75069	+	2.75069i	0.389006	+	0.389006i
$51$	−4.39013	+	2.53464i	−0.614741	+	0.354921i
$52$	−1.62518	+	3.21851i	−0.225372	+	0.446327i
$53$	−0.443410	+	0.768008i	−0.0609070	+	0.105494i	−0.894871	−	0.446325i	$-0.852733\pi$
$53$	−0.443410	+	0.768008i	−0.0609070	+	0.105494i	0.833964	+	0.551819i	$0.186066\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$		−	1.23791i		−	0.166920i
$56$	1.79184	+	1.94661i	0.239445	+	0.260127i
$57$	4.23217	−	4.23217i	0.560565	−	0.560565i
$58$	3.02060	+	0.809368i	0.396625	+	0.106275i
$59$	−1.77116	−	6.61005i	−0.230585	−	0.860555i	−0.980090	−	0.198556i	$-0.936375\pi$
$59$	−1.77116	−	6.61005i	−0.230585	−	0.860555i	0.749505	−	0.661999i	$-0.230292\pi$
$60$	1.01764	−	0.272675i	0.131376	−	0.0352022i
$61$	−9.72877	+	5.61691i	−1.24564	+	0.719171i	−0.970237	−	0.242157i	$-0.922145\pi$
$61$	−9.72877	+	5.61691i	−1.24564	+	0.719171i	−0.275404	+	0.961329i	$0.588812\pi$
$62$	−3.92502			−0.498477
$63$	1.22697	+	2.34405i	0.154584	+	0.295322i
$64$			1.00000i			0.125000i
$65$	−3.71842	−	0.776239i	−0.461213	−	0.0962806i
$66$	1.01758	+	0.587503i	0.125256	+	0.0723166i
$67$	−3.07560	−	11.4783i	−0.375744	−	1.40230i	−0.852255	−	0.523127i	$-0.824765\pi$
$67$	−3.07560	−	11.4783i	−0.375744	−	1.40230i	0.476510	−	0.879169i	$-0.341901\pi$
$68$	4.39013	−	2.53464i	0.532381	−	0.307370i
$69$	−6.45096			−0.776604
$70$	−1.49235	+	2.35424i	−0.178370	+	0.281385i
$71$	4.62139	−	4.62139i	0.548458	−	0.548458i	−0.377537	−	0.925995i	$-0.623229\pi$
$71$	4.62139	−	4.62139i	0.548458	−	0.548458i	0.925995	+	0.377537i	$0.123229\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−2.31854	−	8.65290i	−0.271364	−	1.01275i	−0.958239	−	0.285969i	$-0.907684\pi$
$73$	−2.31854	−	8.65290i	−0.271364	−	1.01275i	0.686874	−	0.726776i	$-0.258982\pi$
$74$	−0.701798	+	1.21555i	−0.0815824	+	0.141305i
$75$	−1.94503	−	3.36889i	−0.224593	−	0.389006i
$76$	−4.23217	+	4.23217i	−0.485463	+	0.485463i
$77$	−3.03356	+	0.679714i	−0.345706	+	0.0774606i
$78$	2.40282	−	2.68821i	0.272065	−	0.304380i
$79$	−3.14704	−	5.45082i	−0.354069	−	0.613266i	0.632889	−	0.774242i	$-0.281869\pi$
$79$	−3.14704	−	5.45082i	−0.354069	−	0.613266i	−0.986958	+	0.160977i	$0.948536\pi$
$80$	−1.01764	+	0.272675i	−0.113775	+	0.0304860i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.45619	+	2.52219i	0.160809	+	0.278529i
$83$	−9.80685	−	9.80685i	−1.07644	−	1.07644i	−0.996826	−	0.0796163i	$-0.974631\pi$
$83$	−9.80685	−	9.80685i	−1.07644	−	1.07644i	−0.0796163	−	0.996826i	$-0.525369\pi$
$84$	−1.22697	−	2.34405i	−0.133873	−	0.255756i
$85$	3.77642	+	3.77642i	0.409610	+	0.409610i
$86$	0.462854	−	1.72740i	0.0499108	−	0.186270i
$87$	−2.70820	−	1.56358i	−0.290349	−	0.167633i
$88$	−1.01758	−	0.587503i	−0.108475	−	0.0626280i
$89$	−7.08351	−	1.89802i	−0.750851	−	0.201190i	−0.136955	−	0.990577i	$-0.543732\pi$
$89$	−7.08351	−	1.89802i	−0.750851	−	0.201190i	−0.613895	+	0.789387i	$0.710398\pi$
$90$	−1.05354			−0.111052
$91$	0.139506	+	9.53837i	0.0146242	+	0.999893i
$92$	6.45096			0.672559
$93$	3.79127	+	1.01587i	0.393137	+	0.105341i
$94$	−5.95001	−	3.43524i	−0.613697	−	0.354318i
$95$	−5.46082	−	3.15280i	−0.560268	−	0.323471i
$96$	0.258819	−	0.965926i	0.0264156	−	0.0985844i
$97$	−1.59617	−	1.59617i	−0.162067	−	0.162067i	0.621415	−	0.783482i	$-0.286558\pi$
$97$	−1.59617	−	1.59617i	−0.162067	−	0.162067i	−0.783482	+	0.621415i	$0.786558\pi$
$98$	6.58860	+	2.36441i	0.665549	+	0.238841i
$99$	−0.830855	−	0.830855i	−0.0835040	−	0.0835040i
$100$	1.94503	+	3.36889i	0.194503	+	0.336889i
$101$	1.74185	−	3.01697i	0.173321	−	0.300200i	−0.766258	−	0.642533i	$-0.777884\pi$
$101$	1.74185	−	3.01697i	0.173321	−	0.300200i	0.939579	+	0.342333i	$0.111217\pi$
$102$	−4.89655	+	1.31203i	−0.484831	+	0.129910i
$103$	6.15063	+	10.6532i	0.606039	+	1.04969i	0.991886	+	0.127128i	$0.0405759\pi$
$103$	6.15063	+	10.6532i	0.606039	+	1.04969i	−0.385847	+	0.922563i	$0.626091\pi$
$104$	−2.40282	+	2.68821i	−0.235616	+	0.263601i
$105$	2.05082	−	1.88777i	0.200140	−	0.184228i
$106$	−0.627076	+	0.627076i	−0.0609070	+	0.0609070i
$107$	0.481464	+	0.833919i	0.0465448	+	0.0806180i	0.888359	−	0.459149i	$-0.151846\pi$
$107$	0.481464	+	0.833919i	0.0465448	+	0.0806180i	−0.841814	+	0.539767i	$0.818512\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	1.37003	+	5.11304i	0.131225	+	0.489740i	0.999985	−	0.00549422i	$-0.00174887\pi$
$109$	1.37003	+	5.11304i	0.131225	+	0.489740i	−0.868759	+	0.495234i	$0.835082\pi$
$110$	0.320395	−	1.19573i	0.0305484	−	0.114008i
$111$	0.992493	−	0.992493i	0.0942033	−	0.0942033i
$112$	1.22697	+	2.34405i	0.115938	+	0.221491i
$113$	−5.78395			−0.544108			−0.272054	−	0.962282i	$-0.587703\pi$
$113$	−5.78395			−0.544108			−0.272054	+	0.962282i	$0.587703\pi$
$114$	5.18333	−	2.99260i	0.485463	−	0.280282i
$115$	1.75901	+	6.56473i	0.164029	+	0.612164i
$116$	2.70820	+	1.56358i	0.251450	+	0.145175i
$117$	−3.01670	+	1.97472i	−0.278894	+	0.182563i
$118$		−	6.84323i		−	0.629970i
$119$	7.18073	−	11.3279i	0.658257	−	1.03842i
$120$	1.05354			0.0961741
$121$	−8.33061	+	4.80968i	−0.757328	+	0.437244i
$122$	−10.8510	+	2.90753i	−0.982406	+	0.263235i
$123$	−0.753777	−	2.81313i	−0.0679658	−	0.253652i
$124$	−3.79127	−	1.01587i	−0.340466	−	0.0912277i
$125$	−6.62276	+	6.62276i	−0.592357	+	0.592357i
$126$	0.578477	+	2.58174i	0.0515349	+	0.229999i
$127$		−	9.34710i		−	0.829421i	−0.909954	−	0.414710i	$-0.863883\pi$
$127$		−	9.34710i		−	0.829421i	0.909954	−	0.414710i	$-0.136117\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−0.894166	+	1.54874i	−0.0787269	+	0.136359i
$130$	−3.39081	−	1.71219i	−0.297394	−	0.150169i
$131$	3.83308	−	2.21303i	0.334898	−	0.193353i	−0.323116	−	0.946359i	$-0.604730\pi$
$131$	3.83308	−	2.21303i	0.334898	−	0.193353i	0.658013	+	0.753006i	$0.271397\pi$
$132$	0.830855	+	0.830855i	0.0723166	+	0.0723166i
$133$	−4.72766	+	15.1131i	−0.409940	+	1.31048i
$134$		−	11.8832i		−	1.02655i
$135$	1.01764	+	0.272675i	0.0875842	+	0.0234681i
$136$	4.89655	−	1.31203i	0.419876	−	0.112505i
$137$	−2.24414	+	0.601316i	−0.191730	+	0.0513739i	−0.353406	−	0.935470i	$-0.614977\pi$
$137$	−2.24414	+	0.601316i	−0.191730	+	0.0513739i	0.161676	+	0.986844i	$0.448310\pi$
$138$	−6.23115	−	1.66963i	−0.530430	−	0.142128i
$139$		−	22.4574i		−	1.90481i	−0.304833	−	0.952406i	$-0.598601\pi$
$139$		−	22.4574i		−	1.90481i	0.304833	−	0.952406i	$-0.401399\pi$
$140$	−2.05082	+	1.88777i	−0.173326	+	0.159546i
$141$	4.85817	+	4.85817i	0.409131	+	0.409131i
$142$	5.66002	−	3.26782i	0.474979	−	0.274229i
$143$	−1.32382	−	4.02440i	−0.110703	−	0.336537i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.852698	+	3.18231i	−0.0708127	+	0.264276i
$146$		−	8.95814i		−	0.741381i
$147$	−5.75214	−	3.98909i	−0.474429	−	0.329015i
$148$	−0.992493	+	0.992493i	−0.0815824	+	0.0815824i
$149$	−11.4423	−	3.06595i	−0.937387	−	0.251172i	−0.242385	−	0.970180i	$-0.577930\pi$
$149$	−11.4423	−	3.06595i	−0.937387	−	0.251172i	−0.695002	+	0.719008i	$0.744596\pi$
$150$	−1.00682	−	3.75751i	−0.0822067	−	0.306800i
$151$	5.89624	−	1.57989i	0.479829	−	0.128570i	−0.0107940	−	0.999942i	$-0.503436\pi$
$151$	5.89624	−	1.57989i	0.479829	−	0.128570i	0.490623	+	0.871372i	$0.336769\pi$
$152$	−5.18333	+	2.99260i	−0.420423	+	0.242732i
$153$	5.06928			0.409827
$154$	−3.10611	−	0.128588i	−0.250298	−	0.0103619i
$155$		−	4.13514i		−	0.332143i
$156$	3.01670	−	1.97472i	0.241529	−	0.158104i
$157$	18.9073	+	10.9161i	1.50897	+	0.871202i	0.999945	+	0.0104469i	$0.00332543\pi$
$157$	18.9073	+	10.9161i	1.50897	+	0.871202i	0.509020	+	0.860755i	$0.330008\pi$
$158$	−1.62903	−	6.07960i	−0.129598	−	0.483667i
$159$	0.768008	−	0.443410i	0.0609070	−	0.0351647i
$160$	−1.05354			−0.0832893
$161$	15.1213	−	7.91512i	1.19173	−	0.623799i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−5.77223	+	21.5422i	−0.452116	+	1.68732i	0.244316	+	0.969696i	$0.421437\pi$
$163$	−5.77223	+	21.5422i	−0.452116	+	1.68732i	−0.696432	+	0.717623i	$0.745230\pi$
$164$	0.753777	+	2.81313i	0.0588601	+	0.219669i
$165$	−0.618955	+	1.07206i	−0.0481856	+	0.0834599i
$166$	−6.93449	−	12.0109i	−0.538221	−	0.932226i
$167$	−1.81395	+	1.81395i	−0.140368	+	0.140368i	−0.773799	−	0.633431i	$-0.781646\pi$
$167$	−1.81395	+	1.81395i	−0.140368	+	0.140368i	0.633431	+	0.773799i	$0.281646\pi$
$168$	−0.578477	−	2.58174i	−0.0446305	−	0.199185i
$169$	−12.9186	+	1.45295i	−0.993735	+	0.111765i
$170$	2.67033	+	4.62515i	0.204805	+	0.354733i
$171$	−5.78125	+	1.54908i	−0.442103	+	0.118461i
$172$	0.894166	−	1.54874i	0.0681795	−	0.118090i
$173$	9.79357	+	16.9630i	0.744591	+	1.28967i	0.950386	+	0.311075i	$0.100689\pi$
$173$	9.79357	+	16.9630i	0.744591	+	1.28967i	−0.205794	+	0.978595i	$0.565978\pi$
$174$	−2.21123	−	2.21123i	−0.167633	−	0.167633i
$175$	8.69277	+	5.51035i	0.657112	+	0.416543i
$176$	−0.830855	−	0.830855i	−0.0626280	−	0.0626280i
$177$	−1.77116	+	6.61005i	−0.133128	+	0.496842i
$178$	−6.35090	−	3.66670i	−0.476020	−	0.274830i
$179$	4.48926	+	2.59187i	0.335543	+	0.193726i	0.658299	−	0.752756i	$-0.271276\pi$
$179$	4.48926	+	2.59187i	0.335543	+	0.193726i	−0.322756	+	0.946482i	$0.604609\pi$
$180$	−1.01764	−	0.272675i	−0.0758502	−	0.0203240i
$181$	15.2703			1.13503			0.567516	−	0.823362i	$-0.307904\pi$
$181$	15.2703			1.13503			0.567516	+	0.823362i	$0.307904\pi$
$182$	−2.33396	+	9.24947i	−0.173005	+	0.685616i
$183$	11.2338			0.830427
$184$	6.23115	+	1.66963i	0.459366	+	0.123087i
$185$	−1.28063	−	0.739369i	−0.0941534	−	0.0543595i
$186$	3.39916	+	1.96251i	0.249239	+	0.143898i
$187$	−1.54164	+	5.75348i	−0.112736	+	0.420736i
$188$	−4.85817	−	4.85817i	−0.354318	−	0.354318i
$189$	0.109436	−	2.64349i	0.00796032	−	0.192285i
$190$	−4.45874	−	4.45874i	−0.323471	−	0.323471i
$191$	−13.3268	−	23.0827i	−0.964292	−	1.67020i	−0.711506	−	0.702680i	$-0.751987\pi$
$191$	−13.3268	−	23.0827i	−0.964292	−	1.67020i	−0.252786	−	0.967522i	$-0.581347\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	5.74146	−	1.53842i	0.413279	−	0.110738i	−0.0461874	−	0.998933i	$-0.514707\pi$
$193$	5.74146	−	1.53842i	0.413279	−	0.110738i	0.459467	+	0.888195i	$0.348040\pi$
$194$	−1.12866	−	1.95490i	−0.0810333	−	0.140354i
$195$	2.83212	+	2.53145i	0.202813	+	0.181281i
$196$	5.75214	+	3.98909i	0.410867	+	0.284935i
$197$	18.6732	−	18.6732i	1.33041	−	1.33041i	0.425413	−	0.904999i	$-0.360129\pi$
$197$	18.6732	−	18.6732i	1.33041	−	1.33041i	0.904999	−	0.425413i	$-0.139871\pi$
$198$	−0.587503	−	1.01758i	−0.0417520	−	0.0723166i
$199$	9.81669	−	17.0030i	0.695887	−	1.20531i	−0.273994	−	0.961731i	$-0.588345\pi$
$199$	9.81669	−	17.0030i	0.695887	−	1.20531i	0.969881	−	0.243580i	$-0.0783218\pi$
$200$	1.00682	+	3.75751i	0.0711931	+	0.265696i
$201$	−3.07560	+	11.4783i	−0.216936	+	0.809616i
$202$	2.46335	−	2.46335i	0.173321	−	0.173321i
$203$	8.26660	+	0.342225i	0.580202	+	0.0240195i
$204$	−5.06928			−0.354921
$205$	−2.65721	+	1.53414i	−0.185588	+	0.107149i
$206$	3.18380	+	11.8821i	0.221826	+	0.827865i
$207$	5.58669	+	3.22548i	0.388302	+	0.224186i
$208$	−3.01670	+	1.97472i	−0.209171	+	0.136922i
$209$		−	7.03264i		−	0.486458i
$210$	2.46953	−	1.29265i	0.170414	−	0.0892016i
$211$	20.5051			1.41163			0.705814	−	0.708397i	$-0.250582\pi$
$211$	20.5051			1.41163			0.705814	+	0.708397i	$0.250582\pi$
$212$	−0.768008	+	0.443410i	−0.0527470	+	0.0304535i
$213$	−6.31294	+	1.69155i	−0.432555	+	0.115903i
$214$	0.249224	+	0.930116i	0.0170366	+	0.0635814i
$215$	1.81987	+	0.487633i	0.124114	+	0.0332563i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−10.1334	+	2.27053i	−0.687897	+	0.154134i
$218$			5.29341i			0.358515i
$219$	−2.31854	+	8.65290i	−0.156672	+	0.584709i
$220$	0.618955	−	1.07206i	0.0417299	−	0.0722784i
$221$	16.3155	+	8.23851i	1.09750	+	0.554182i
$222$	1.21555	−	0.701798i	0.0815824	−	0.0471016i
$223$	−6.85790	−	6.85790i	−0.459239	−	0.459239i	0.439167	−	0.898406i	$-0.355274\pi$
$223$	−6.85790	−	6.85790i	−0.459239	−	0.459239i	−0.898406	+	0.439167i	$0.855274\pi$
$224$	0.578477	+	2.58174i	0.0386511	+	0.172500i
$225$			3.89006i			0.259338i
$226$	−5.58687	−	1.49700i	−0.371633	−	0.0995787i
$227$	−14.7315	+	3.94730i	−0.977766	+	0.261992i	−0.712104	−	0.702074i	$-0.752257\pi$
$227$	−14.7315	+	3.94730i	−0.977766	+	0.261992i	−0.265663	+	0.964066i	$0.585591\pi$
$228$	5.78125	−	1.54908i	0.382873	−	0.102590i
$229$	−4.56809	−	1.22402i	−0.301868	−	0.0808853i	0.104706	−	0.994503i	$-0.466610\pi$
$229$	−4.56809	−	1.22402i	−0.301868	−	0.0808853i	−0.406574	+	0.913618i	$0.633277\pi$
$230$			6.79631i			0.448135i
$231$	2.96699	+	0.928128i	0.195214	+	0.0610663i
$232$	2.21123	+	2.21123i	0.145175	+	0.145175i
$233$	8.40629	−	4.85338i	0.550715	−	0.317955i	−0.198696	−	0.980061i	$-0.563670\pi$
$233$	8.40629	−	4.85338i	0.550715	−	0.317955i	0.749410	+	0.662106i	$0.230337\pi$
$234$	−3.42501	+	1.12665i	−0.223900	+	0.0736514i
$235$	3.61915	−	6.26855i	0.236087	−	0.408915i
$236$	1.77116	−	6.61005i	0.115293	−	0.430278i
$237$			6.29407i			0.408844i
$238$	9.86792	−	9.08337i	0.639642	−	0.588787i
$239$	−12.8314	+	12.8314i	−0.829995	+	0.829995i	−0.987516	−	0.157521i	$-0.949650\pi$
$239$	−12.8314	+	12.8314i	−0.829995	+	0.829995i	0.157521	+	0.987516i	$0.449650\pi$
$240$	1.01764	+	0.272675i	0.0656882	+	0.0176011i
$241$	5.68140	+	21.2033i	0.365971	+	1.36582i	0.866099	+	0.499872i	$0.166620\pi$
$241$	5.68140	+	21.2033i	0.365971	+	1.36582i	−0.500128	+	0.865952i	$0.666714\pi$
$242$	−9.29159	+	2.48967i	−0.597286	+	0.160042i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−11.2338			−0.719171
$245$	−2.49098	+	6.94132i	−0.159143	+	0.443464i
$246$		−	2.91237i		−	0.185686i
$247$	−21.1245	−	4.40986i	−1.34412	−	0.280593i
$248$	−3.39916	−	1.96251i	−0.215847	−	0.124619i
$249$	3.58956	+	13.3964i	0.227479	+	0.848963i
$250$	−8.11119	+	4.68300i	−0.512997	+	0.296179i
$251$	4.15095			0.262005			0.131003	−	0.991382i	$-0.458180\pi$
$251$	4.15095			0.262005			0.131003	+	0.991382i	$0.458180\pi$
$252$	−0.109436	+	2.64349i	−0.00689384	+	0.166524i
$253$	−5.35981	+	5.35981i	−0.336968	+	0.336968i
$254$	2.41921	−	9.02860i	0.151795	−	0.566505i
$255$	−1.38227	−	5.15869i	−0.0865609	−	0.323050i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.55319	+	14.8146i	0.533533	+	0.924107i	0.999233	+	0.0391638i	$0.0124694\pi$
$257$	8.55319	+	14.8146i	0.533533	+	0.924107i	−0.465700	+	0.884943i	$0.654197\pi$
$258$	−1.26454	+	1.26454i	−0.0787269	+	0.0787269i
$259$	−1.10869	+	3.54421i	−0.0688907	+	0.220226i
$260$	−2.83212	−	2.53145i	−0.175641	−	0.156994i
$261$	1.56358	+	2.70820i	0.0967831	+	0.167633i
$262$	4.27524	−	1.14555i	0.264125	−	0.0707722i
$263$	−15.7300	+	27.2451i	−0.969953	+	1.68001i	−0.274278	+	0.961650i	$0.588439\pi$
$263$	−15.7300	+	27.2451i	−0.969953	+	1.68001i	−0.695675	+	0.718357i	$0.744894\pi$
$264$	0.587503	+	1.01758i	0.0361583	+	0.0626280i
$265$	−0.660647	−	0.660647i	−0.0405832	−	0.0405832i
$266$	−8.47813	+	13.3746i	−0.519828	+	0.820047i
$267$	5.18549	+	5.18549i	0.317347	+	0.317347i
$268$	3.07560	−	11.4783i	0.187872	−	0.701148i
$269$	−28.0341	−	16.1855i	−1.70927	−	0.986848i	−0.935461	−	0.353430i	$-0.885015\pi$
$269$	−28.0341	−	16.1855i	−1.70927	−	0.986848i	−0.773810	−	0.633418i	$-0.781651\pi$
$270$	0.912388	+	0.526768i	0.0555262	+	0.0320580i
$271$	7.57420	+	2.02950i	0.460100	+	0.123283i	0.481421	−	0.876489i	$-0.340121\pi$
$271$	7.57420	+	2.02950i	0.460100	+	0.123283i	−0.0213215	+	0.999773i	$0.506787\pi$
$272$	5.06928			0.307370
$273$	4.64837	−	8.33023i	0.281332	−	0.504168i
$274$	−2.32331			−0.140356
$275$	−4.41510	−	1.18302i	−0.266241	−	0.0713389i
$276$	−5.58669	−	3.22548i	−0.336279	−	0.194151i
$277$	−4.20420	−	2.42730i	−0.252606	−	0.145842i	0.368351	−	0.929687i	$-0.379922\pi$
$277$	−4.20420	−	2.42730i	−0.252606	−	0.145842i	−0.620957	+	0.783845i	$0.713256\pi$
$278$	5.81240	−	21.6922i	0.348605	−	1.30101i
$279$	−2.77540	−	2.77540i	−0.166159	−	0.166159i
$280$	−2.46953	+	1.29265i	−0.147583	+	0.0772509i
$281$	−4.18018	−	4.18018i	−0.249368	−	0.249368i	0.571343	−	0.820711i	$-0.306423\pi$
$281$	−4.18018	−	4.18018i	−0.249368	−	0.249368i	−0.820711	+	0.571343i	$0.806423\pi$
$282$	3.43524	+	5.95001i	0.204566	+	0.354318i
$283$	14.2259	−	24.6400i	0.845643	−	1.46470i	−0.0394189	−	0.999223i	$-0.512551\pi$
$283$	14.2259	−	24.6400i	0.845643	−	1.46470i	0.885062	−	0.465474i	$-0.154116\pi$
$284$	6.31294	−	1.69155i	0.374604	−	0.100375i
$285$	3.15280	+	5.46082i	0.186756	+	0.323471i
$286$	−0.237121	−	4.22990i	−0.0140212	−	0.250119i
$287$	5.21852	+	5.66925i	0.308039	+	0.334645i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	−4.34881	−	7.53237i	−0.255813	−	0.443080i
$290$	−1.64729	+	2.85318i	−0.0967319	+	0.167545i
$291$	0.584239	+	2.18041i	0.0342487	+	0.127818i
$292$	2.31854	−	8.65290i	0.135682	−	0.506373i
$293$	4.61778	−	4.61778i	0.269774	−	0.269774i	−0.559235	−	0.829009i	$-0.688905\pi$
$293$	4.61778	−	4.61778i	0.269774	−	0.269774i	0.829009	+	0.559235i	$0.188905\pi$
$294$	−4.52369	−	5.34193i	−0.263827	−	0.311548i
$295$	7.20958			0.419758
$296$	−1.21555	+	0.701798i	−0.0706524	+	0.0407912i
$297$	0.304114	+	1.13497i	0.0176465	+	0.0658576i
$298$	−10.2589	−	5.92295i	−0.594279	−	0.343107i
$299$	12.7388	+	19.4606i	0.736705	+	1.12544i
$300$		−	3.89006i		−	0.224593i
$301$	0.195708	−	4.72743i	0.0112804	−	0.272485i
$302$	6.10423			0.351259
$303$	−3.01697	+	1.74185i	−0.173321	+	0.100067i
$304$	−5.78125	+	1.54908i	−0.331578	+	0.0888459i
$305$	−3.06318	−	11.4319i	−0.175397	−	0.654591i
$306$	4.89655	+	1.31203i	0.279917	+	0.0750036i
$307$	−3.54555	+	3.54555i	−0.202355	+	0.202355i	−0.801008	−	0.598653i	$-0.795703\pi$
$307$	−3.54555	+	3.54555i	−0.202355	+	0.202355i	0.598653	+	0.801008i	$0.295703\pi$
$308$	−2.96699	−	0.928128i	−0.169060	−	0.0528850i
$309$		−	12.3013i		−	0.699794i
$310$	1.07025	−	3.99424i	0.0607863	−	0.226858i
$311$	0.174431	−	0.302124i	0.00989109	−	0.0171319i	−0.861037	−	0.508541i	$-0.830185\pi$
$311$	0.174431	−	0.302124i	0.00989109	−	0.0171319i	0.870929	+	0.491410i	$0.163518\pi$
$312$	3.42501	−	1.12665i	0.193903	−	0.0637840i
$313$	−8.48554	+	4.89913i	−0.479631	+	0.276915i	−0.720263	−	0.693701i	$-0.755979\pi$
$313$	−8.48554	+	4.89913i	−0.479631	+	0.276915i	0.240632	+	0.970616i	$0.422645\pi$
$314$	15.4377	+	15.4377i	0.871202	+	0.871202i
$315$	−2.71995	+	0.609446i	−0.153252	+	0.0343384i
$316$		−	6.29407i		−	0.354069i
$317$	27.7092	+	7.42465i	1.55630	+	0.417010i	0.931490	−	0.363766i	$-0.118509\pi$
$317$	27.7092	+	7.42465i	1.55630	+	0.417010i	0.624811	+	0.780776i	$0.285176\pi$
$318$	0.856602	−	0.229526i	0.0480358	−	0.0128712i
$319$	−3.54923	+	0.951012i	−0.198718	+	0.0532465i
$320$	−1.01764	−	0.272675i	−0.0568876	−	0.0152430i
$321$		−	0.962927i		−	0.0537453i
$322$	16.6547	−	3.73173i	0.928128	−	0.207961i
$323$	21.4541	+	21.4541i	1.19374	+	1.19374i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−6.32206	+	12.5202i	−0.350685	+	0.694495i
$326$	−11.1511	+	19.3142i	−0.617601	+	1.06972i
$327$	1.37003	−	5.11304i	0.0757631	−	0.282752i
$328$			2.91237i			0.160809i
$329$	−17.3486	−	5.42694i	−0.956458	−	0.299197i
$330$	−0.875334	+	0.875334i	−0.0481856	+	0.0481856i
$331$	−11.9538	−	3.20301i	−0.657040	−	0.176053i	−0.0851303	−	0.996370i	$-0.527131\pi$
$331$	−11.9538	−	3.20301i	−0.657040	−	0.176053i	−0.571910	+	0.820316i	$0.693797\pi$
$332$	−3.58956	−	13.3964i	−0.197003	−	0.735223i
$333$	−1.35577	+	0.363278i	−0.0742958	+	0.0199075i
$334$	−2.22163	+	1.28266i	−0.121562	+	0.0701838i
$335$	12.5194			0.684006
$336$	0.109436	−	2.64349i	0.00597024	−	0.144214i
$337$		−	14.0948i		−	0.767791i	−0.923377	−	0.383896i	$-0.874582\pi$
$337$		−	14.0948i		−	0.767791i	0.923377	−	0.383896i	$-0.125418\pi$
$338$	−12.8544	−	1.94013i	−0.699188	−	0.105529i
$339$	5.00905	+	2.89197i	0.272054	+	0.157070i
$340$	1.38227	+	5.15869i	0.0749639	+	0.279769i
$341$	3.99404	−	2.30596i	0.216289	−	0.124875i
$342$	−5.98519			−0.323642
$343$	18.3778	+	2.29292i	0.992306	+	0.123806i
$344$	1.26454	−	1.26454i	0.0681795	−	0.0681795i
$345$	1.75901	−	6.56473i	0.0947021	−	0.353433i
$346$	5.06952	+	18.9197i	0.272539	+	1.01713i
$347$	−16.2593	+	28.1619i	−0.872844	+	1.51181i	−0.0138027	+	0.999905i	$0.504394\pi$
$347$	−16.2593	+	28.1619i	−0.872844	+	1.51181i	−0.859042	+	0.511906i	$0.828940\pi$
$348$	−1.56358	−	2.70820i	−0.0838166	−	0.145175i
$349$	−3.70116	+	3.70116i	−0.198119	+	0.198119i	−0.799193	−	0.601074i	$-0.794739\pi$
$349$	−3.70116	+	3.70116i	−0.198119	+	0.198119i	0.601074	+	0.799193i	$0.294739\pi$
$350$	6.97039	+	7.57244i	0.372583	+	0.404764i
$351$	3.59990	−	0.201804i	0.192148	−	0.0107715i
$352$	−0.587503	−	1.01758i	−0.0313140	−	0.0542375i
$353$	16.9523	−	4.54237i	0.902282	−	0.241766i	0.222286	−	0.974981i	$-0.428648\pi$
$353$	16.9523	−	4.54237i	0.902282	−	0.241766i	0.679996	+	0.733216i	$0.261981\pi$
$354$	−3.42161	+	5.92641i	−0.181857	+	0.314985i
$355$	3.44276	+	5.96303i	0.182723	+	0.316485i
$356$	−5.18549	−	5.18549i	−0.274830	−	0.274830i
$357$	−11.8826	+	6.21985i	−0.628895	+	0.329190i
$358$	3.66546	+	3.66546i	0.193726	+	0.193726i
$359$	4.74656	−	17.7144i	0.250514	−	0.934930i	−0.720018	−	0.693956i	$-0.755866\pi$
$359$	4.74656	−	17.7144i	0.250514	−	0.934930i	0.970531	−	0.240974i	$-0.0774670\pi$
$360$	−0.912388	−	0.526768i	−0.0480871	−	0.0277631i
$361$	−14.5687	−	8.41126i	−0.766776	−	0.442698i
$362$	14.7500	+	3.95225i	0.775242	+	0.207725i
$363$	9.61936			0.504886
$364$	−4.64837	+	8.33023i	−0.243641	+	0.436622i
$365$	9.43772			0.493993
$366$	10.8510	+	2.90753i	0.567192	+	0.151979i
$367$	16.2895	+	9.40474i	0.850304	+	0.490923i	0.860753	−	0.509022i	$-0.169993\pi$
$367$	16.2895	+	9.40474i	0.850304	+	0.490923i	−0.0104493	+	0.999945i	$0.503326\pi$
$368$	5.58669	+	3.22548i	0.291226	+	0.168140i
$369$	−0.753777	+	2.81313i	−0.0392401	+	0.146446i
$370$	−1.04563	−	1.04563i	−0.0543595	−	0.0543595i
$371$	−1.25620	+	1.98169i	−0.0652184	+	0.102884i
$372$	2.77540	+	2.77540i	0.143898	+	0.143898i
$373$	−4.68278	−	8.11081i	−0.242465	−	0.419962i	0.718951	−	0.695061i	$-0.244623\pi$
$373$	−4.68278	−	8.11081i	−0.242465	−	0.419962i	−0.961416	+	0.275099i	$0.911289\pi$
$374$	−2.97822	+	5.15843i	−0.154000	+	0.266736i
$375$	9.04686	−	2.42410i	0.467178	−	0.125180i
$376$	−3.43524	−	5.95001i	−0.177159	−	0.306849i
$377$	0.631073	+	11.2575i	0.0325019	+	0.579788i
$378$	0.789892	−	2.52509i	0.0406277	−	0.129877i
$379$	−3.15926	+	3.15926i	−0.162280	+	0.162280i	−0.783576	−	0.621296i	$-0.786607\pi$
$379$	−3.15926	+	3.15926i	−0.162280	+	0.162280i	0.621296	+	0.783576i	$0.286607\pi$
$380$	−3.15280	−	5.46082i	−0.161735	−	0.280134i
$381$	−4.67355	+	8.09482i	−0.239433	+	0.414710i
$382$	−6.89845	−	25.7454i	−0.352955	−	1.31725i
$383$	−3.73533	+	13.9404i	−0.190866	+	0.712323i	0.802432	+	0.596744i	$0.203539\pi$
$383$	−3.73533	+	13.9404i	−0.190866	+	0.712323i	−0.993298	+	0.115579i	$0.963128\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	0.135472	−	3.27240i	0.00690431	−	0.166777i
$386$	5.94400			0.302542
$387$	1.54874	−	0.894166i	0.0787269	−	0.0454530i
$388$	−0.584239	−	2.18041i	−0.0296603	−	0.110694i
$389$	12.7223	+	7.34523i	0.645047	+	0.372418i	0.786556	−	0.617519i	$-0.211862\pi$
$389$	12.7223	+	7.34523i	0.645047	+	0.372418i	−0.141509	+	0.989937i	$0.545196\pi$
$390$	2.08043	+	3.17820i	0.105347	+	0.160934i
$391$		−	32.7017i		−	1.65380i
$392$	4.52369	+	5.34193i	0.228481	+	0.269808i
$393$	−4.42606			−0.223265
$394$	22.8699	−	13.2040i	1.15217	−	0.665206i
$395$	6.40508	−	1.71624i	0.322274	−	0.0863532i
$396$	−0.304114	−	1.13497i	−0.0152823	−	0.0570343i
$397$	1.74045	+	0.466352i	0.0873507	+	0.0234055i	0.302230	−	0.953235i	$-0.402269\pi$
$397$	1.74045	+	0.466352i	0.0873507	+	0.0234055i	−0.214879	+	0.976641i	$0.568936\pi$
$398$	13.8829	−	13.8829i	0.695887	−	0.695887i
$399$	11.6508	−	10.7245i	0.583272	−	0.536898i
$400$			3.89006i			0.194503i
$401$	−6.50768	+	24.2870i	−0.324978	+	1.21283i	0.589356	+	0.807873i	$0.299381\pi$
$401$	−6.50768	+	24.2870i	−0.324978	+	1.21283i	−0.914334	+	0.404961i	$0.867285\pi$
$402$	−5.94160	+	10.2912i	−0.296340	+	0.513276i
$403$	−4.42212	−	13.4432i	−0.220281	−	0.669653i
$404$	3.01697	−	1.74185i	0.150100	−	0.0866603i
$405$	−0.744962	−	0.744962i	−0.0370174	−	0.0370174i
$406$	7.89635	+	2.47012i	0.391889	+	0.122590i
$407$		−	1.64923i		−	0.0817495i
$408$	−4.89655	−	1.31203i	−0.242415	−	0.0649550i
$409$	24.4012	−	6.53829i	1.20656	−	0.323298i	0.401150	−	0.916012i	$-0.368610\pi$
$409$	24.4012	−	6.53829i	1.20656	−	0.323298i	0.805413	+	0.592715i	$0.201944\pi$
$410$	−2.96374	+	0.794131i	−0.146368	+	0.0392193i
$411$	2.24414	+	0.601316i	0.110695	+	0.0296607i
$412$			12.3013i			0.606039i
$413$	−3.95865	−	17.6674i	−0.194793	−	0.869356i
$414$	4.56151	+	4.56151i	0.224186	+	0.224186i
$415$	12.6539	−	7.30573i	0.621155	−	0.358624i
$416$	−3.42501	+	1.12665i	−0.167925	+	0.0552386i
$417$	−11.2287	+	19.4487i	−0.549872	+	0.952406i
$418$	1.82018	−	6.79300i	0.0890279	−	0.332257i
$419$		−	1.19341i		−	0.0583019i	−0.999575	−	0.0291510i	$-0.990720\pi$
$419$		−	1.19341i		−	0.0583019i	0.999575	−	0.0291510i	$-0.00928035\pi$
$420$	2.71995	−	0.609446i	0.132720	−	0.0297379i
$421$	−16.9207	+	16.9207i	−0.824667	+	0.824667i	−0.986773	−	0.162107i	$-0.948171\pi$
$421$	−16.9207	+	16.9207i	−0.824667	+	0.824667i	0.162107	+	0.986773i	$0.448171\pi$
$422$	19.8064	+	5.30710i	0.964160	+	0.258346i
$423$	−1.77821	−	6.63638i	−0.0864596	−	0.322672i
$424$	−0.856602	+	0.229526i	−0.0416003	+	0.0111468i
$425$	17.0779	−	9.85992i	0.828399	−	0.478276i
$426$	−6.53563			−0.316652
$427$	−26.3326	+	13.7835i	−1.27432	+	0.667032i
$428$			0.962927i			0.0465448i
$429$	−0.865738	+	4.14714i	−0.0417982	+	0.200226i
$430$	1.63165	+	0.942035i	0.0786852	+	0.0454289i
$431$	7.87709	+	29.3977i	0.379426	+	1.41604i	0.846768	+	0.531962i	$0.178545\pi$
$431$	7.87709	+	29.3977i	0.379426	+	1.41604i	−0.467342	+	0.884076i	$0.654788\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	3.38394			0.162622			0.0813108	−	0.996689i	$-0.474089\pi$
$433$	3.38394			0.162622			0.0813108	+	0.996689i	$0.474089\pi$
$434$	−10.3757	−	0.429539i	−0.498051	−	0.0206185i
$435$	2.32961	−	2.32961i	0.111696	−	0.111696i
$436$	−1.37003	+	5.11304i	−0.0656127	+	0.244870i
$437$	9.99306	+	37.2946i	0.478033	+	1.78404i
$438$	−4.47907	+	7.75798i	−0.214018	+	0.370691i
$439$	−17.7101	−	30.6749i	−0.845259	−	1.46403i	−0.885396	−	0.464837i	$-0.846113\pi$
$439$	−17.7101	−	30.6749i	−0.845259	−	1.46403i	0.0401377	−	0.999194i	$-0.487220\pi$
$440$	0.875334	−	0.875334i	0.0417299	−	0.0417299i
$441$	2.98695	+	6.33073i	0.142236	+	0.301463i
$442$	13.6273	+	12.1806i	0.648184	+	0.579370i
$443$	9.02498	+	15.6317i	0.428790	+	0.742685i	0.996766	−	0.0803595i	$-0.0256068\pi$
$443$	9.02498	+	15.6317i	0.428790	+	0.742685i	−0.567976	+	0.823045i	$0.692274\pi$
$444$	1.35577	−	0.363278i	0.0643420	−	0.0172404i
$445$	3.86299	−	6.69090i	0.183123	−	0.317179i
$446$	−4.84927	−	8.39918i	−0.229619	−	0.397713i
$447$	8.37632	+	8.37632i	0.396186	+	0.396186i
$448$	−0.109436	+	2.64349i	−0.00517038	+	0.124893i
$449$	−25.5364	−	25.5364i	−1.20514	−	1.20514i	−0.972584	−	0.232554i	$-0.925292\pi$
$449$	−25.5364	−	25.5364i	−1.20514	−	1.20514i	−0.232554	−	0.972584i	$-0.574708\pi$
$450$	−1.00682	+	3.75751i	−0.0474621	+	0.177131i
$451$	−2.96358	−	1.71103i	−0.139550	−	0.0805691i
$452$	−5.00905	−	2.89197i	−0.235606	−	0.136027i
$453$	−5.89624	−	1.57989i	−0.277029	−	0.0742298i
$454$	−15.2512			−0.715775
$455$	−9.74464	−	2.45891i	−0.456836	−	0.115275i
$456$	5.98519			0.280282
$457$	4.75695	+	1.27462i	0.222521	+	0.0596242i	0.368357	−	0.929685i	$-0.379921\pi$
$457$	4.75695	+	1.27462i	0.222521	+	0.0596242i	−0.145836	+	0.989309i	$0.546587\pi$
$458$	−4.09564	−	2.36462i	−0.191377	−	0.110491i
$459$	−4.39013	−	2.53464i	−0.204914	−	0.118307i
$460$	−1.75901	+	6.56473i	−0.0820145	+	0.306082i
$461$	−26.3259	−	26.3259i	−1.22612	−	1.22612i	−0.965419	−	0.260702i	$-0.916046\pi$
$461$	−26.3259	−	26.3259i	−1.22612	−	1.22612i	−0.260702	−	0.965419i	$-0.583954\pi$
$462$	2.62568	+	1.66442i	0.122158	+	0.0774357i
$463$	−11.5245	−	11.5245i	−0.535588	−	0.535588i	0.386642	−	0.922230i	$-0.373635\pi$
$463$	−11.5245	−	11.5245i	−0.535588	−	0.535588i	−0.922230	+	0.386642i	$0.873635\pi$
$464$	1.56358	+	2.70820i	0.0725873	+	0.125725i
$465$	−2.06757	+	3.58114i	−0.0958813	+	0.166071i
$466$	9.37600	−	2.51229i	0.434335	−	0.116380i
$467$	−17.0885	−	29.5981i	−0.790760	−	1.36964i	−0.925497	−	0.378756i	$-0.876352\pi$
$467$	−17.0885	−	29.5981i	−0.790760	−	1.36964i	0.134736	−	0.990882i	$-0.456981\pi$
$468$	−3.59990	+	0.201804i	−0.166405	+	0.00932839i
$469$	−6.87416	−	30.6793i	−0.317419	−	1.41664i
$470$	5.11825	−	5.11825i	0.236087	−	0.236087i
$471$	−10.9161	−	18.9073i	−0.502988	−	0.871202i
$472$	3.42161	−	5.92641i	0.157493	−	0.272785i
$473$	0.543856	+	2.02970i	0.0250065	+	0.0933257i
$474$	−1.62903	+	6.07960i	−0.0748236	+	0.279246i
$475$	−16.4634	+	16.4634i	−0.755393	+	0.755393i
$476$	11.8826	−	6.21985i	0.544639	−	0.285086i
$477$	−0.886819			−0.0406047
$478$	−15.7152	+	9.07318i	−0.718797	+	0.414997i
$479$	−5.01443	−	18.7141i	−0.229115	−	0.855069i	−0.980714	−	0.195449i	$-0.937384\pi$
$479$	−5.01443	−	18.7141i	−0.229115	−	0.855069i	0.751599	−	0.659620i	$-0.229283\pi$
$480$	0.912388	+	0.526768i	0.0416446	+	0.0240435i
$481$	−4.95395	−	1.03416i	−0.225881	−	0.0471538i
$482$			21.9513i			0.999852i
$483$	−17.0530	−	0.705969i	−0.775939	−	0.0321227i
$484$	−9.61936			−0.437244
$485$	2.05956	−	1.18909i	0.0935197	−	0.0539936i
$486$	0.965926	−	0.258819i	0.0438153	−	0.0117403i
$487$	−4.40916	−	16.4552i	−0.199798	−	0.745657i	−0.990972	−	0.134066i	$-0.957197\pi$
$487$	−4.40916	−	16.4552i	−0.199798	−	0.745657i	0.791174	−	0.611591i	$-0.209470\pi$
$488$	−10.8510	−	2.90753i	−0.491203	−	0.131617i
$489$	15.7700	−	15.7700i	0.713145	−	0.713145i
$490$	−4.20265	+	6.06008i	−0.189856	+	0.273767i
$491$			14.1517i			0.638657i	0.947644	+	0.319329i	$0.103457\pi$
$491$			14.1517i			0.638657i	−0.947644	+	0.319329i	$0.896543\pi$
$492$	0.753777	−	2.81313i	0.0339829	−	0.126826i
$493$	7.92622	−	13.7286i	0.356979	−	0.618306i
$494$	−19.2634	−	9.72703i	−0.866700	−	0.437640i
$495$	1.07206	−	0.618955i	0.0481856	−	0.0278200i
$496$	−2.77540	−	2.77540i	−0.124619	−	0.124619i
$497$	12.7223	−	11.7108i	0.570675	−	0.525303i
$498$			13.8690i			0.621484i
$499$	−30.4531	−	8.15988i	−1.36327	−	0.365286i	−0.498252	−	0.867032i	$-0.666024\pi$
$499$	−30.4531	−	8.15988i	−1.36327	−	0.365286i	−0.865015	+	0.501746i	$0.832691\pi$
$500$	−9.04686	+	2.42410i	−0.404588	+	0.108409i
$501$	2.47790	−	0.663952i	0.110704	−	0.0296632i
$502$	4.00951	+	1.07434i	0.178953	+	0.0479503i
$503$			15.7099i			0.700471i	0.936662	+	0.350236i	$0.113898\pi$
$503$			15.7099i			0.700471i	−0.936662	+	0.350236i	$0.886102\pi$
$504$	−0.789892	+	2.52509i	−0.0351846	+	0.112476i
$505$	2.59522	+	2.59522i	0.115486	+	0.115486i
$506$	−6.56440	+	3.78996i	−0.291823	+	0.168484i
$507$	11.9143	+	5.20099i	0.529131	+	0.230984i
$508$	4.67355	−	8.09482i	0.207355	−	0.359150i
$509$	7.54493	−	28.1581i	0.334423	−	1.24808i	−0.570070	−	0.821596i	$-0.693084\pi$
$509$	7.54493	−	28.1581i	0.334423	−	1.24808i	0.904493	−	0.426488i	$-0.140249\pi$
$510$		−	5.34067i		−	0.236489i
$511$	−5.18208	−	23.1276i	−0.229242	−	1.02310i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	5.78125	+	1.54908i	0.255249	+	0.0683936i
$514$	4.42746	+	16.5235i	0.195287	+	0.728820i
$515$	−12.5182	+	3.35424i	−0.551618	+	0.147806i
$516$	−1.54874	+	0.894166i	−0.0681795	+	0.0393634i
$517$	8.07286			0.355044
$518$	−1.98822	+	3.13649i	−0.0873574	+	0.137809i
$519$		−	19.5871i		−	0.859780i
$520$	−2.08043	−	3.17820i	−0.0912330	−	0.139373i
$521$	14.3013	+	8.25685i	0.626551	+	0.361739i	0.779415	−	0.626508i	$-0.215516\pi$
$521$	14.3013	+	8.25685i	0.626551	+	0.361739i	−0.152864	+	0.988247i	$0.548850\pi$
$522$	0.809368	+	3.02060i	0.0354251	+	0.132208i
$523$	−4.40758	+	2.54472i	−0.192730	+	0.111273i	−0.593260	−	0.805011i	$-0.702159\pi$
$523$	−4.40758	+	2.54472i	−0.192730	+	0.111273i	0.400530	+	0.916284i	$0.368826\pi$
$524$	4.42606			0.193353
$525$	−4.77299	−	9.11849i	−0.208310	−	0.397963i
$526$	−22.2456	+	22.2456i	−0.969953	+	0.969953i
$527$	−5.14973	+	19.2190i	−0.224326	+	0.837194i
$528$	0.304114	+	1.13497i	0.0132349	+	0.0493932i
$529$	9.30742	−	16.1209i	0.404670	−	0.700910i
$530$	−0.467148	−	0.809124i	−0.0202916	−	0.0351461i
$531$	4.83889	−	4.83889i	0.209990	−	0.209990i
$532$	−11.6508	+	10.7245i	−0.505128	+	0.464968i
$533$	−6.99789	+	7.82907i	−0.303112	+	0.339114i
$534$	3.66670	+	6.35090i	0.158673	+	0.274830i
$535$	−0.979910	+	0.262566i	−0.0423652	+	0.0113517i
$536$	5.94160	−	10.2912i	0.256638	−	0.444510i
$537$	−2.59187	−	4.48926i	−0.111848	−	0.193726i
$538$	−22.8898	−	22.8898i	−0.986848	−	0.986848i
$539$	−8.09355	+	1.46483i	−0.348614	+	0.0630949i
$540$	0.744962	+	0.744962i	0.0320580	+	0.0320580i
$541$	−0.519341	+	1.93821i	−0.0223282	+	0.0833300i	−0.976191	−	0.216913i	$-0.930401\pi$
$541$	−0.519341	+	1.93821i	−0.0223282	+	0.0833300i	0.953863	+	0.300243i	$0.0970678\pi$
$542$	6.79084	+	3.92069i	0.291692	+	0.168408i
$543$	−13.2245	−	7.63515i	−0.567516	−	0.327656i
$544$	4.89655	+	1.31203i	0.209938	+	0.0562527i
$545$	−5.57679			−0.238883
$546$	6.64600	−	6.84329i	0.284423	−	0.292866i
$547$	−22.4682			−0.960673			−0.480336	−	0.877084i	$-0.659485\pi$
$547$	−22.4682			−0.960673			−0.480336	+	0.877084i	$0.659485\pi$
$548$	−2.24414	−	0.601316i	−0.0958650	−	0.0256869i
$549$	−9.72877	−	5.61691i	−0.415214	−	0.239724i
$550$	−3.95847	−	2.28542i	−0.168790	−	0.0974508i
$551$	−4.84422	+	18.0789i	−0.206371	+	0.770186i
$552$	−4.56151	−	4.56151i	−0.194151	−	0.194151i
$553$	−7.72263	−	14.7536i	−0.328400	−	0.627386i
$554$	−3.43271	−	3.43271i	−0.145842	−	0.145842i
$555$	0.739369	+	1.28063i	0.0313845	+	0.0543595i
$556$	11.2287	−	19.4487i	0.476203	−	0.824808i
$557$	26.4949	−	7.09929i	1.12263	−	0.300807i	0.350680	−	0.936495i	$-0.385950\pi$
$557$	26.4949	−	7.09929i	1.12263	−	0.300807i	0.771946	+	0.635689i	$0.219284\pi$
$558$	−1.96251	−	3.39916i	−0.0830796	−	0.143898i
$559$	6.43781	−	0.360892i	0.272290	−	0.0152641i
$560$	−2.71995	+	0.609446i	−0.114939	+	0.0257538i
$561$	4.21184	−	4.21184i	0.177824	−	0.177824i
$562$	−2.95583	−	5.11965i	−0.124684	−	0.215959i
$563$	−17.2993	+	29.9633i	−0.729079	+	1.26280i	0.228193	+	0.973616i	$0.426718\pi$
$563$	−17.2993	+	29.9633i	−0.729079	+	1.26280i	−0.957273	+	0.289187i	$0.906615\pi$
$564$	1.77821	+	6.63638i	0.0748762	+	0.279442i
$565$	1.57714	−	5.88596i	0.0663507	−	0.247624i
$566$	20.1185	−	20.1185i	0.845643	−	0.845643i
$567$	−1.41652	+	2.23461i	−0.0594882	+	0.0938447i
$568$	6.53563			0.274229
$569$	−16.5652	+	9.56394i	−0.694450	+	0.400941i	−0.805277	−	0.592899i	$-0.797983\pi$
$569$	−16.5652	+	9.56394i	−0.694450	+	0.400941i	0.110827	+	0.993840i	$0.464650\pi$
$570$	1.63201	+	6.09075i	0.0683575	+	0.255114i
$571$	−25.1326	−	14.5103i	−1.05177	−	0.607239i	−0.128625	−	0.991693i	$-0.541056\pi$
$571$	−25.1326	−	14.5103i	−1.05177	−	0.607239i	−0.923144	+	0.384455i	$0.874390\pi$
$572$	0.865738	−	4.14714i	0.0361983	−	0.173401i
$573$			26.6536i			1.11347i
$574$	3.57339	+	6.82673i	0.149150	+	0.284942i
$575$	25.0946			1.04652
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	3.42870	−	0.918717i	0.142739	−	0.0382467i	−0.186742	−	0.982409i	$-0.559793\pi$
$577$	3.42870	−	0.918717i	0.142739	−	0.0382467i	0.329481	+	0.944162i	$0.393126\pi$
$578$	−2.25111	−	8.40127i	−0.0936339	−	0.349447i
$579$	−5.74146	−	1.53842i	−0.238607	−	0.0639346i
$580$	−2.32961	+	2.32961i	−0.0967319	+	0.0967319i
$581$	−24.8511	−	26.9975i	−1.03100	−	1.12005i
$582$			2.25733i			0.0935692i
$583$	0.269694	−	1.00651i	0.0111696	−	0.0416855i
$584$	4.47907	−	7.75798i	0.185345	−	0.321027i
$585$	−1.18697	−	3.60836i	−0.0490750	−	0.149187i
$586$	5.65560	−	3.26526i	0.233631	−	0.134887i
$587$	−8.10224	−	8.10224i	−0.334415	−	0.334415i	0.519845	−	0.854260i	$-0.325990\pi$
$587$	−8.10224	−	8.10224i	−0.334415	−	0.334415i	−0.854260	+	0.519845i	$0.825990\pi$
$588$	−2.98695	−	6.33073i	−0.123180	−	0.261075i
$589$		−	23.4920i		−	0.967970i
$590$	6.96392	+	1.86598i	0.286700	+	0.0768210i
$591$	−25.5081	+	6.83488i	−1.04926	+	0.281149i
$592$	−1.35577	+	0.363278i	−0.0557218	+	0.0149306i
$593$	12.7120	+	3.40618i	0.522020	+	0.139875i	0.510201	−	0.860055i	$-0.329571\pi$
$593$	12.7120	+	3.40618i	0.522020	+	0.139875i	0.0118192	+	0.999930i	$0.496238\pi$
$594$			1.17501i			0.0482111i
$595$	9.56964	+	10.3962i	0.392317	+	0.426203i
$596$	−8.37632	−	8.37632i	−0.343107	−	0.343107i
$597$	−17.0030	+	9.81669i	−0.695887	+	0.401770i
$598$	7.26797	+	22.0946i	0.297209	+	0.903514i
$599$	2.52057	−	4.36575i	0.102988	−	0.178380i	−0.809927	−	0.586531i	$-0.800493\pi$
$599$	2.52057	−	4.36575i	0.102988	−	0.178380i	0.912914	+	0.408151i	$0.133826\pi$
$600$	1.00682	−	3.75751i	0.0411034	−	0.153400i
$601$			41.2165i			1.68126i	0.541613	+	0.840628i	$0.317814\pi$
$601$			41.2165i			1.68126i	−0.541613	+	0.840628i	$0.682186\pi$
$602$	1.41259	−	4.51569i	0.0575728	−	0.184046i
$603$	8.40269	−	8.40269i	0.342184	−	0.342184i
$604$	5.89624	+	1.57989i	0.239914	+	0.0642849i
$605$	−2.62296	−	9.78901i	−0.106638	−	0.397980i
$606$	−3.36500	+	0.901648i	−0.136694	+	0.0366269i
$607$	12.3109	−	7.10770i	0.499684	−	0.288493i	−0.228899	−	0.973450i	$-0.573513\pi$
$607$	12.3109	−	7.10770i	0.499684	−	0.288493i	0.728583	+	0.684957i	$0.240179\pi$
$608$	−5.98519			−0.242732
$609$	−6.98797	−	4.42968i	−0.283167	−	0.179500i
$610$		−	11.8352i		−	0.479194i
$611$	5.06214	−	24.2491i	0.204792	−	0.981015i
$612$	4.39013	+	2.53464i	0.177460	+	0.102457i
$613$	−2.60937	−	9.73830i	−0.105391	−	0.393326i	0.892998	−	0.450061i	$-0.148598\pi$
$613$	−2.60937	−	9.73830i	−0.105391	−	0.393326i	−0.998389	+	0.0567348i	$0.981931\pi$
$614$	−4.34240	+	2.50709i	−0.175245	+	0.101178i
$615$	3.06828			0.123725
$616$	−2.62568	−	1.66442i	−0.105792	−	0.0670613i
$617$	−27.0273	+	27.0273i	−1.08808	+	1.08808i	−0.0923529	+	0.995726i	$0.529439\pi$
$617$	−27.0273	+	27.0273i	−1.08808	+	1.08808i	−0.995726	+	0.0923529i	$0.970561\pi$
$618$	3.18380	−	11.8821i	0.128071	−	0.477968i
$619$	1.76110	+	6.57252i	0.0707847	+	0.264172i	0.992244	−	0.124302i	$-0.0396691\pi$
$619$	1.76110	+	6.57252i	0.0707847	+	0.264172i	−0.921460	+	0.388474i	$0.873002\pi$
$620$	2.06757	−	3.58114i	0.0830356	−	0.143822i
$621$	−3.22548	−	5.58669i	−0.129434	−	0.224186i
$622$	0.246683	−	0.246683i	0.00989109	−	0.00989109i
$623$	−18.5175	−	5.79259i	−0.741886	−	0.232075i
$624$	3.59990	−	0.201804i	0.144111	−	0.00807862i
$625$	4.79146	+	8.29905i	0.191658	+	0.331962i
$626$	−9.46438	+	2.53597i	−0.378273	+	0.101358i
$627$	−3.51632	+	6.09044i	−0.140428	+	0.243229i
$628$	10.9161	+	18.9073i	0.435601	+	0.754483i
$629$	5.03123	+	5.03123i	0.200608	+	0.200608i
$630$	−2.78501	−	0.115295i	−0.110957	−	0.00459346i
$631$	11.0014	+	11.0014i	0.437958	+	0.437958i	0.891324	−	0.453366i	$-0.149777\pi$
$631$	11.0014	+	11.0014i	0.437958	+	0.437958i	−0.453366	+	0.891324i	$0.649777\pi$
$632$	1.62903	−	6.07960i	0.0647991	−	0.241834i
$633$	−17.7579	−	10.2525i	−0.705814	−	0.407502i
$634$	24.8434	+	14.3433i	0.986656	+	0.569646i
$635$	9.51195	+	2.54872i	0.377470	+	0.101143i
$636$	0.886819			0.0351647
$637$	−0.675062	+	25.2298i	−0.0267469	+	0.999642i
$638$	−3.67443			−0.145472
$639$	6.31294	+	1.69155i	0.249736	+	0.0669165i
$640$	−0.912388	−	0.526768i	−0.0360653	−	0.0208223i
$641$	−19.3404	−	11.1662i	−0.763901	−	0.441039i	0.0667935	−	0.997767i	$-0.478723\pi$
$641$	−19.3404	−	11.1662i	−0.763901	−	0.441039i	−0.830695	+	0.556728i	$0.812056\pi$
$642$	0.249224	−	0.930116i	0.00983608	−	0.0367088i
$643$	11.0313	+	11.0313i	0.435031	+	0.435031i	0.890336	−	0.455305i	$-0.150470\pi$
$643$	11.0313	+	11.0313i	0.435031	+	0.435031i	−0.455305	+	0.890336i	$0.650470\pi$
$644$	17.0530	+	0.705969i	0.671983	+	0.0278191i
$645$	−1.33224	−	1.33224i	−0.0524568	−	0.0524568i
$646$	15.1703	+	26.2758i	0.596868	+	1.03381i
$647$	13.5282	−	23.4316i	0.531850	−	0.921192i	−0.467459	−	0.884015i	$-0.654830\pi$
$647$	13.5282	−	23.4316i	0.531850	−	0.921192i	0.999309	−	0.0371765i	$-0.0118364\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	4.02042	+	6.96356i	0.157815	+	0.273344i
$650$	−9.34711	+	10.4573i	−0.366624	+	0.410169i
$651$	9.91101	+	3.10034i	0.388443	+	0.121512i
$652$	−15.7700	+	15.7700i	−0.617601	+	0.617601i
$653$	−14.4344	−	25.0010i	−0.564860	−	0.978366i	−0.997063	−	0.0765895i	$-0.975597\pi$
$653$	−14.4344	−	25.0010i	−0.564860	−	0.978366i	0.432203	−	0.901776i	$-0.357736\pi$
$654$	2.64670	−	4.58422i	0.103494	−	0.179257i
$655$	1.20688	+	4.50412i	0.0471565	+	0.175991i
$656$	−0.753777	+	2.81313i	−0.0294301	+	0.109834i
$657$	6.33436	−	6.33436i	0.247127	−	0.247127i
$658$	−15.3528	−	9.73217i	−0.598516	−	0.379399i
$659$	15.3968			0.599774			0.299887	−	0.953975i	$-0.403051\pi$
$659$	15.3968			0.599774			0.299887	+	0.953975i	$0.403051\pi$
$660$	−1.07206	+	0.618955i	−0.0417299	+	0.0240928i
$661$	3.34507	+	12.4840i	0.130108	+	0.485570i	0.999970	−	0.00772513i	$-0.00245901\pi$
$661$	3.34507	+	12.4840i	0.130108	+	0.485570i	−0.869862	+	0.493295i	$0.835792\pi$
$662$	−10.7175	−	6.18774i	−0.416547	−	0.240493i
$663$	−10.0104	−	15.2925i	−0.388772	−	0.593912i
$664$		−	13.8690i		−	0.538221i
$665$	−14.0906	−	8.93201i	−0.546409	−	0.346369i
$666$	−1.40360			−0.0543883
$667$	17.4705	−	10.0866i	0.676459	−	0.390554i
$668$	−2.47790	+	0.663952i	−0.0958729	+	0.0256891i
$669$	2.51017	+	9.36807i	0.0970486	+	0.362190i
$670$	12.0928	+	3.24025i	0.467185	+	0.125182i
$671$	9.33367	−	9.33367i	0.360322	−	0.360322i
$672$	0.789892	−	2.52509i	0.0304708	−	0.0974074i
$673$			3.01477i			0.116211i	0.998310	+	0.0581055i	$0.0185060\pi$
$673$			3.01477i			0.116211i	−0.998310	+	0.0581055i	$0.981494\pi$
$674$	3.64800	−	13.6145i	0.140516	−	0.524411i
$675$	1.94503	−	3.36889i	0.0748643	−	0.129669i
$676$	−11.9143	−	5.20099i	−0.458241	−	0.200038i
$677$	−7.18095	+	4.14592i	−0.275986	+	0.159341i	−0.631605	−	0.775290i	$-0.717604\pi$
$677$	−7.18095	+	4.14592i	−0.275986	+	0.159341i	0.355619	+	0.934631i	$0.384270\pi$
$678$	4.08987	+	4.08987i	0.157070	+	0.157070i
$679$	−4.04478	−	4.39414i	−0.155224	−	0.168632i
$680$			5.34067i			0.204805i
$681$	14.7315	+	3.94730i	0.564514	+	0.151261i
$682$	4.45477	−	1.19365i	0.170582	−	0.0457073i
$683$	−35.6858	+	9.56199i	−1.36548	+	0.365880i	−0.865826	−	0.500345i	$-0.833206\pi$
$683$	−35.6858	+	9.56199i	−1.36548	+	0.365880i	−0.499655	+	0.866225i	$0.666540\pi$
$684$	−5.78125	−	1.54908i	−0.221052	−	0.0592306i
$685$		−	2.44768i		−	0.0935212i
$686$	17.1581	+	6.97131i	0.655100	+	0.266166i
$687$	3.34408	+	3.34408i	0.127584	+	0.127584i
$688$	1.54874	−	0.894166i	0.0590452	−	0.0340897i
$689$	−2.85423	−	1.44124i	−0.108738	−	0.0549070i
$690$	3.39815	−	5.88578i	0.129366	−	0.224068i
$691$	−7.48390	+	27.9303i	−0.284701	+	1.06252i	0.664357	+	0.747416i	$0.268706\pi$
$691$	−7.48390	+	27.9303i	−0.284701	+	1.06252i	−0.949058	+	0.315103i	$0.897961\pi$
$692$			19.5871i			0.744591i
$693$	−2.10543	−	2.28728i	−0.0799786	−	0.0868865i
$694$	−22.9941	+	22.9941i	−0.872844	+	0.872844i
$695$	22.8535	+	6.12357i	0.866882	+	0.232280i
$696$	−0.809368	−	3.02060i	−0.0306790	−	0.114496i
$697$	14.2606	−	3.82111i	0.540158	−	0.144735i
$698$	−4.53298	+	2.61711i	−0.171576	+	0.0990593i
$699$	−9.70675			−0.367143
$700$	4.77299	+	9.11849i	0.180402	+	0.344646i
$701$		−	40.8735i		−	1.54377i	−0.635762	−	0.771885i	$-0.719314\pi$
$701$		−	40.8735i		−	1.54377i	0.635762	−	0.771885i	$-0.280686\pi$
$702$	3.52947	+	0.736795i	0.133211	+	0.0278085i
$703$	−7.27530	−	4.20040i	−0.274393	−	0.158421i
$704$	−0.304114	−	1.13497i	−0.0114617	−	0.0427757i
$705$	−6.26855	+	3.61915i	−0.236087	+	0.136305i
$706$	17.5504			0.660516
$707$	4.93472	−	7.78471i	0.185589	−	0.292774i
$708$	−4.83889	+	4.83889i	−0.181857	+	0.181857i
$709$	−8.16850	+	30.4853i	−0.306775	+	1.14490i	0.624633	+	0.780919i	$0.285249\pi$
$709$	−8.16850	+	30.4853i	−0.306775	+	1.14490i	−0.931407	+	0.363979i	$0.881418\pi$
$710$	1.78210	+	6.65090i	0.0668812	+	0.249604i
$711$	3.14704	−	5.45082i	0.118023	−	0.204422i
$712$	−3.66670	−	6.35090i	−0.137415	−	0.238010i
$713$	−17.9040	+	17.9040i	−0.670511	+	0.670511i
$714$	−13.0876	+	2.93247i	−0.489789	+	0.109745i
$715$	4.45635	−	0.249815i	0.166658	−	0.00934255i
$716$	2.59187	+	4.48926i	0.0968629	+	0.167771i
$717$	17.5280	−	4.69662i	0.654596	−	0.175399i
$718$	9.16965	−	15.8823i	0.342208	−	0.592722i
$719$	8.82429	+	15.2841i	0.329091	+	0.570002i	0.982332	−	0.187148i	$-0.0599245\pi$
$719$	8.82429	+	15.2841i	0.329091	+	0.570002i	−0.653241	+	0.757150i	$0.726591\pi$
$720$	−0.744962	−	0.744962i	−0.0277631	−	0.0277631i
$721$	15.0933	+	28.8347i	0.562102	+	1.07386i
$722$	−11.8953	−	11.8953i	−0.442698	−	0.442698i
$723$	5.68140	−	21.2033i	0.211294	−	0.788559i
$724$	13.2245	+	7.63515i	0.491484	+	0.283758i
$725$	10.5351	+	6.08242i	0.391262	+	0.225895i
$726$	9.29159	+	2.48967i	0.344843	+	0.0924005i
$727$	45.8265			1.69961			0.849805	−	0.527098i	$-0.176720\pi$
$727$	45.8265			1.69961			0.849805	+	0.527098i	$0.176720\pi$
$728$	−6.64600	+	6.84329i	−0.246317	+	0.253629i
$729$	−1.00000			−0.0370370
$730$	9.11613	+	2.44266i	0.337403	+	0.0904069i
$731$	−7.85100	−	4.53278i	−0.290380	−	0.167651i
$732$	9.72877	+	5.61691i	0.359586	+	0.207607i
$733$	−2.85321	+	10.6483i	−0.105386	+	0.393305i	−0.998389	−	0.0567460i	$-0.981927\pi$
$733$	−2.85321	+	10.6483i	−0.105386	+	0.393305i	0.893003	+	0.450051i	$0.148594\pi$
$734$	13.3003	+	13.3003i	0.490923	+	0.490923i
$735$	5.62791	−	4.76586i	0.207589	−	0.175792i
$736$	4.56151	+	4.56151i	0.168140	+	0.168140i
$737$	6.98141	+	12.0922i	0.257164	+	0.445421i
$738$	−1.45619	+	2.52219i	−0.0536029	+	0.0928430i
$739$	40.9848	−	10.9818i	1.50765	−	0.403974i	0.591996	−	0.805941i	$-0.298340\pi$
$739$	40.9848	−	10.9818i	1.50765	−	0.403974i	0.915654	+	0.401967i	$0.131673\pi$
$740$	−0.739369	−	1.28063i	−0.0271798	−	0.0470767i
$741$	16.0895	+	14.3813i	0.591061	+	0.528311i
$742$	−1.72629	+	1.58904i	−0.0633742	+	0.0583356i
$743$	−22.8439	+	22.8439i	−0.838063	+	0.838063i	−0.988604	−	0.150541i	$-0.951898\pi$
$743$	−22.8439	+	22.8439i	−0.838063	+	0.838063i	0.150541	+	0.988604i	$0.451898\pi$
$744$	1.96251	+	3.39916i	0.0719490	+	0.124619i
$745$	6.24004	−	10.8081i	0.228617	−	0.395977i
$746$	−2.42398	−	9.04643i	−0.0887483	−	0.331213i
$747$	3.58956	−	13.3964i	0.131335	−	0.490149i
$748$	−4.21184	+	4.21184i	−0.154000	+	0.154000i
$749$	1.18148	+	2.25714i	0.0431704	+	0.0824743i
$750$	9.36599			0.341998
$751$	26.0921	−	15.0643i	0.952115	−	0.549704i	0.0583777	−	0.998295i	$-0.481407\pi$
$751$	26.0921	−	15.0643i	0.952115	−	0.549704i	0.893737	+	0.448591i	$0.148074\pi$
$752$	−1.77821	−	6.63638i	−0.0648447	−	0.242004i
$753$	−3.59483	−	2.07547i	−0.131003	−	0.0756344i
$754$	−2.30407	+	11.0372i	−0.0839094	+	0.401951i
$755$			6.43102i			0.234049i
$756$	1.41652	−	2.23461i	0.0515183	−	0.0812719i
$757$	−19.7253			−0.716930			−0.358465	−	0.933543i	$-0.616700\pi$
$757$	−19.7253			−0.716930			−0.358465	+	0.933543i	$0.616700\pi$
$758$	−3.86929	+	2.23393i	−0.140539	+	0.0811401i
$759$	7.32163	−	1.96183i	0.265758	−	0.0712098i
$760$	−1.63201	−	6.09075i	−0.0591993	−	0.220935i
$761$	3.89815	+	1.04451i	0.141308	+	0.0378633i	0.328780	−	0.944407i	$-0.393363\pi$
$761$	3.89815	+	1.04451i	0.141308	+	0.0378633i	−0.187472	+	0.982270i	$0.560029\pi$
$762$	−6.60939	+	6.60939i	−0.239433	+	0.239433i
$763$	3.06212	+	13.6662i	0.110856	+	0.494749i
$764$		−	26.6536i		−	0.964292i
$765$	−1.38227	+	5.15869i	−0.0499759	+	0.186513i
$766$	−7.21610	+	12.4987i	−0.260728	+	0.451595i
$767$	23.4381	−	7.70992i	0.846300	−	0.278389i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	6.16074	+	6.16074i	0.222162	+	0.222162i	0.809408	−	0.587246i	$-0.199788\pi$
$769$	6.16074	+	6.16074i	0.222162	+	0.222162i	−0.587246	+	0.809408i	$0.699788\pi$
$770$	0.977815	−	3.12583i	0.0352380	−	0.112647i
$771$		−	17.1064i		−	0.616071i
$772$	5.74146	+	1.53842i	0.206640	+	0.0553689i
$773$	44.3180	−	11.8750i	1.59401	−	0.427113i	0.650783	−	0.759264i	$-0.274441\pi$
$773$	44.3180	−	11.8750i	1.59401	−	0.427113i	0.943226	+	0.332150i	$0.107774\pi$
$774$	1.72740	−	0.462854i	0.0620899	−	0.0166369i
$775$	−14.7483	−	3.95179i	−0.529774	−	0.141953i
$776$		−	2.25733i		−	0.0810333i
$777$	2.73226	−	2.51503i	0.0980192	−	0.0902261i
$778$	10.3877	+	10.3877i	0.372418	+	0.372418i
$779$	−15.0958	+	8.71555i	−0.540862	+	0.312267i
$780$	1.18697	+	3.60836i	0.0425002	+	0.129200i
$781$	−3.83970	+	6.65056i	−0.137395	+	0.237976i
$782$	8.46383	−	31.5874i	0.302666	−	1.12956i
$783$		−	3.12716i		−	0.111756i
$784$	2.98695	+	6.33073i	0.106677	+	0.226097i
$785$	−16.2642	+	16.2642i	−0.580494	+	0.580494i
$786$	−4.27524	−	1.14555i	−0.152493	−	0.0408604i
$787$	8.90961	+	33.2511i	0.317593	+	1.18527i	0.921551	+	0.388258i	$0.126923\pi$
$787$	8.90961	+	33.2511i	0.317593	+	1.18527i	−0.603957	+	0.797017i	$0.706410\pi$
$788$	25.5081	−	6.83488i	0.908688	−	0.243482i
$789$	27.2451	−	15.7300i	0.969953	−	0.560002i
$790$	6.63102			0.235921
$791$	−15.2898	−	0.632974i	−0.543642	−	0.0225060i
$792$		−	1.17501i		−	0.0417520i
$793$	−22.1836	−	33.8891i	−0.787763	−	1.20344i
$794$	1.56044	+	0.900923i	0.0553781	+	0.0319726i
$795$	0.241813	+	0.902460i	0.00857624	+	0.0320070i
$796$	17.0030	−	9.81669i	0.602656	−	0.347943i
$797$	−22.0319			−0.780409			−0.390204	−	0.920728i	$-0.627596\pi$
$797$	−22.0319			−0.780409			−0.390204	+	0.920728i	$0.627596\pi$
$798$	14.0296	−	7.34364i	0.496641	−	0.259962i
$799$	−24.6274	+	24.6274i	−0.871255	+	0.871255i
$800$	−1.00682	+	3.75751i	−0.0355966	+	0.132848i
$801$	−1.89802	−	7.08351i	−0.0670633	−	0.250284i
$802$	−12.5719	+	21.7751i	−0.443928	+	0.768906i
$803$	5.26293	+	9.11567i	0.185725	+	0.321685i
$804$	−8.40269	+	8.40269i	−0.296340	+	0.296340i
$805$	3.93151	+	17.5463i	0.138568	+	0.618425i
$806$	−0.792083	−	14.1297i	−0.0278999	−	0.497696i
$807$	16.1855	+	28.0341i	0.569757	+	0.986848i
$808$	3.36500	−	0.901648i	0.118380	−	0.0317199i
$809$	18.3643	−	31.8079i	0.645654	−	1.11831i	−0.338496	−	0.940968i	$-0.609918\pi$
$809$	18.3643	−	31.8079i	0.645654	−	1.11831i	0.984150	−	0.177338i	$-0.0567485\pi$
$810$	−0.526768	−	0.912388i	−0.0185087	−	0.0320580i
$811$	24.0681	+	24.0681i	0.845144	+	0.845144i	0.989523	−	0.144379i	$-0.0461183\pi$
$811$	24.0681	+	24.0681i	0.845144	+	0.845144i	−0.144379	+	0.989523i	$0.546118\pi$
$812$	6.98797	+	4.42968i	0.245230	+	0.155451i
$813$	−5.54470	−	5.54470i	−0.194461	−	0.194461i
$814$	0.426853	−	1.59304i	0.0149612	−	0.0558360i
$815$	−20.3482	−	11.7481i	−0.712768	−	0.411517i
$816$	−4.39013	−	2.53464i	−0.153685	−	0.0887302i
$817$	10.3388	+	2.77027i	0.361709	+	0.0969195i
$818$	25.2620			0.883265
$819$	−8.19072	+	4.89000i	−0.286207	+	0.170870i
$820$	−3.06828			−0.107149
$821$	36.3779	+	9.74742i	1.26960	+	0.340187i	0.829876	−	0.557948i	$-0.188411\pi$
$821$	36.3779	+	9.74742i	1.26960	+	0.340187i	0.439720	+	0.898135i	$0.355078\pi$
$822$	2.01204	+	1.16165i	0.0701780	+	0.0405173i
$823$	25.5124	+	14.7296i	0.889305	+	0.513441i	0.873715	−	0.486438i	$-0.161704\pi$
$823$	25.5124	+	14.7296i	0.889305	+	0.513441i	0.0155900	+	0.999878i	$0.495037\pi$
$824$	−3.18380	+	11.8821i	−0.110913	+	0.413932i
$825$	3.23208	+	3.23208i	0.112526	+	0.112526i
$826$	0.748897	−	18.0900i	0.0260575	−	0.629431i
$827$	7.78910	+	7.78910i	0.270854	+	0.270854i	0.829444	−	0.558590i	$-0.188658\pi$
$827$	7.78910	+	7.78910i	0.270854	+	0.270854i	−0.558590	+	0.829444i	$0.688658\pi$
$828$	3.22548	+	5.58669i	0.112093	+	0.194151i
$829$	9.99718	−	17.3156i	0.347216	−	0.601396i	−0.638537	−	0.769591i	$-0.720460\pi$
$829$	9.99718	−	17.3156i	0.347216	−	0.601396i	0.985754	+	0.168194i	$0.0537936\pi$
$830$	14.1136	−	3.78172i	0.489890	−	0.131266i
$831$	2.42730	+	4.20420i	0.0842020	+	0.145842i
$832$	−3.59990	+	0.201804i	−0.124804	+	0.00699629i
$833$	20.2218	−	29.1592i	0.700646	−	1.01031i
$834$	−15.8798	+	15.8798i	−0.549872	+	0.549872i
$835$	−1.35132	−	2.34056i	−0.0467645	−	0.0809984i
$836$	3.51632	−	6.09044i	0.121614	−	0.210642i
$837$	1.01587	+	3.79127i	0.0351136	+	0.131046i
$838$	0.308877	−	1.15275i	0.0106700	−	0.0398210i
$839$	−6.26481	+	6.26481i	−0.216285	+	0.216285i	−0.806931	−	0.590646i	$-0.798873\pi$
$839$	−6.26481	+	6.26481i	−0.216285	+	0.216285i	0.590646	+	0.806931i	$0.298873\pi$
$840$	2.78501	+	0.115295i	0.0960918	+	0.00397806i
$841$	−19.2209			−0.662789
$842$	−20.7236	+	11.9648i	−0.714182	+	0.412333i
$843$	1.53005	+	5.71023i	0.0526977	+	0.196671i
$844$	17.7579	+	10.2525i	0.611253	+	0.352907i
$845$	2.04399	−	13.5426i	0.0703155	−	0.465879i
$846$		−	6.87048i		−	0.236212i
$847$	−22.5482	+	11.8027i	−0.774766	+	0.405544i
$848$	−0.886819			−0.0304535
$849$	−24.6400	+	14.2259i	−0.845643	+	0.488232i
$850$	19.0479	−	5.10387i	0.653338	−	0.175061i
$851$	2.34349	+	8.74602i	0.0803337	+	0.299810i
$852$	−6.31294	−	1.69155i	−0.216278	−	0.0579514i
$853$	−19.1027	+	19.1027i	−0.654063	+	0.654063i	−0.953969	−	0.299906i	$-0.903045\pi$
$853$	−19.1027	+	19.1027i	−0.654063	+	0.654063i	0.299906	+	0.953969i	$0.403045\pi$
$854$	−29.0027	+	6.49851i	−0.992454	+	0.222374i
$855$		−	6.30561i		−	0.215647i
$856$	−0.249224	+	0.930116i	−0.00851830	+	0.0317907i
$857$	−20.3680	+	35.2784i	−0.695757	+	1.20509i	0.274167	+	0.961682i	$0.411598\pi$
$857$	−20.3680	+	35.2784i	−0.695757	+	1.20509i	−0.969925	+	0.243405i	$0.921736\pi$
$858$	−1.90960	+	3.78176i	−0.0651926	+	0.129107i
$859$	−27.1474	+	15.6736i	−0.926258	+	0.534775i	−0.885626	−	0.464399i	$-0.846270\pi$
$859$	−27.1474	+	15.6736i	−0.926258	+	0.534775i	−0.0406321	+	0.999174i	$0.512937\pi$
$860$	1.33224	+	1.33224i	0.0454289	+	0.0454289i
$861$	−1.68474	−	7.51897i	−0.0574158	−	0.256246i
$862$			30.4348i			1.03661i
$863$	33.5109	+	8.97921i	1.14072	+	0.305656i	0.779242	−	0.626723i	$-0.215604\pi$
$863$	33.5109	+	8.97921i	1.14072	+	0.305656i	0.361481	+	0.932379i	$0.382271\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−19.9326	+	5.34092i	−0.677728	+	0.181597i
$866$	3.26863	+	0.875828i	0.111073	+	0.0297618i
$867$			8.69763i			0.295387i
$868$	−9.91101	−	3.10034i	−0.336402	−	0.105232i
$869$	5.22946	+	5.22946i	0.177397	+	0.177397i
$870$	2.85318	−	1.64729i	0.0967319	−	0.0558482i
$871$	40.7000	−	13.3882i	1.37907	−	0.453642i
$872$	−2.64670	+	4.58422i	−0.0896287	+	0.155241i
$873$	0.584239	−	2.18041i	0.0197735	−	0.0737957i
$874$			38.6102i			1.30601i
$875$	−18.2319	+	16.7824i	−0.616352	+	0.567349i
$876$	−6.33436	+	6.33436i	−0.214018	+	0.214018i
$877$	38.3833	+	10.2848i	1.29611	+	0.347292i	0.839979	−	0.542619i	$-0.182567\pi$
$877$	38.3833	+	10.2848i	1.29611	+	0.347292i	0.456134	+	0.889911i	$0.349234\pi$
$878$	−9.16744	−	34.2134i	−0.309386	−	1.15464i
$879$	−6.30801	+	1.69023i	−0.212764	+	0.0570099i
$880$	1.07206	−	0.618955i	0.0361392	−	0.0208650i
$881$	19.0788			0.642781			0.321391	−	0.946947i	$-0.395850\pi$
$881$	19.0788			0.642781			0.321391	+	0.946947i	$0.395850\pi$
$882$	1.24666	+	6.88809i	0.0419773	+	0.231934i
$883$		−	20.8870i		−	0.702902i	−0.936206	−	0.351451i	$-0.885688\pi$
$883$		−	20.8870i		−	0.702902i	0.936206	−	0.351451i	$-0.114312\pi$
$884$	10.0104	+	15.2925i	0.336686	+	0.514343i
$885$	−6.24368	−	3.60479i	−0.209879	−	0.121174i
$886$	4.67167	+	17.4349i	0.156948	+	0.585737i
$887$	−3.56778	+	2.05986i	−0.119794	+	0.0691633i	−0.558700	−	0.829370i	$-0.688700\pi$
$887$	−3.56778	+	2.05986i	−0.119794	+	0.0691633i	0.438906	+	0.898533i	$0.355366\pi$
$888$	1.40360			0.0471016
$889$	1.02291	−	24.7089i	0.0343074	−	0.828711i
$890$	5.46310	−	5.46310i	0.183123	−	0.183123i
$891$	0.304114	−	1.13497i	0.0101882	−	0.0380229i
$892$	−2.51017	−	9.36807i	−0.0840466	−	0.313666i
$893$	20.5606	−	35.6120i	0.688034	−	1.19171i
$894$	5.92295	+	10.2589i	0.198093	+	0.343107i
$895$	−3.86169	+	3.86169i	−0.129082	+	0.129082i
$896$	−0.789892	+	2.52509i	−0.0263884	+	0.0843573i
$897$	−1.30183	−	23.2228i	−0.0434668	−	0.775386i
$898$	−18.0570	−	31.2756i	−0.602569	−	1.04368i
$899$	−11.8559	+	3.17678i	−0.395417	+	0.105952i
$900$	−1.94503	+	3.36889i	−0.0648344	+	0.112296i
$901$	2.24777	+	3.89325i	0.0748841	+	0.129703i
$902$	−2.41976	−	2.41976i	−0.0805691	−	0.0805691i
$903$	−2.53320	+	3.99622i	−0.0842997	+	0.132986i
$904$	−4.08987	−	4.08987i	−0.136027	−	0.136027i
$905$	−4.16383	+	15.5396i	−0.138410	+	0.516554i
$906$	−5.28642	−	3.05212i	−0.175630	−	0.101400i
$907$	20.0127	+	11.5543i	0.664509	+	0.383655i	0.793993	−	0.607927i	$-0.207999\pi$
$907$	20.0127	+	11.5543i	0.664509	+	0.383655i	−0.129484	+	0.991582i	$0.541332\pi$
$908$	−14.7315	−	3.94730i	−0.488883	−	0.130996i
$909$	3.48370			0.115547
$910$	−8.77618	−	4.89722i	−0.290928	−	0.162341i
$911$	−35.1881			−1.16583			−0.582917	−	0.812532i	$-0.698089\pi$
$911$	−35.1881			−1.16583			−0.582917	+	0.812532i	$0.698089\pi$
$912$	5.78125	+	1.54908i	0.191436	+	0.0512952i
$913$	14.1129	+	8.14807i	0.467068	+	0.269662i
$914$	4.26496	+	2.46238i	0.141072	+	0.0814482i
$915$	−3.06318	+	11.4319i	−0.101266	+	0.377928i
$916$	−3.34408	−	3.34408i	−0.110491	−	0.110491i
$917$	10.3749	−	5.43064i	0.342609	−	0.179335i
$918$	−3.58452	−	3.58452i	−0.118307	−	0.118307i
$919$	−14.6577	−	25.3878i	−0.483512	−	0.837467i	0.516309	−	0.856403i	$-0.327306\pi$
$919$	−14.6577	−	25.3878i	−0.483512	−	0.837467i	−0.999821	+	0.0189352i	$0.993972\pi$
$920$	−3.39815	+	5.88578i	−0.112034	+	0.194048i
$921$	4.84332	−	1.29776i	0.159593	−	0.0427627i
$922$	−18.6153	−	32.2426i	−0.613061	−	1.06185i
$923$	17.5692	+	15.7039i	0.578296	+	0.516901i
$924$	2.10543	+	2.28728i	0.0692635	+	0.0752460i
$925$	−3.86086	+	3.86086i	−0.126944	+	0.126944i
$926$	−8.14903	−	14.1145i	−0.267794	−	0.463832i
$927$	−6.15063	+	10.6532i	−0.202013	+	0.349897i
$928$	0.809368	+	3.02060i	0.0265688	+	0.0991561i
$929$	10.9554	−	40.8860i	0.359434	−	1.34143i	−0.515377	−	0.856964i	$-0.672348\pi$
$929$	10.9554	−	40.8860i	0.359434	−	1.34143i	0.874811	−	0.484464i	$-0.160985\pi$
$930$	−2.92399	+	2.92399i	−0.0958813	+	0.0958813i
$931$	−14.1514	+	39.4340i	−0.463794	+	1.29240i
$932$	9.70675			0.317955
$933$	−0.302124	+	0.174431i	−0.00989109	+	0.00571063i
$934$	−8.84565	−	33.0124i	−0.289438	−	1.08020i
$935$	−5.43458	−	3.13766i	−0.177730	−	0.102612i
$936$	−3.52947	−	0.736795i	−0.115364	−	0.0240829i
$937$		−	16.6317i		−	0.543332i	−0.962392	−	0.271666i	$-0.912425\pi$
$937$		−	16.6317i		−	0.543332i	0.962392	−	0.271666i	$-0.0875747\pi$
$938$	1.30045	−	31.4131i	0.0424613	−	1.02567i
$939$	9.79825			0.319754
$940$	6.26855	−	3.61915i	0.204457	−	0.118044i
$941$	8.27880	−	2.21830i	0.269881	−	0.0723145i	−0.121340	−	0.992611i	$-0.538719\pi$
$941$	8.27880	−	2.21830i	0.269881	−	0.0723145i	0.391222	+	0.920296i	$0.372053\pi$
$942$	−5.65060	−	21.0883i	−0.184107	−	0.687095i
$943$	18.1474	+	4.86258i	0.590961	+	0.158347i
$944$	4.83889	−	4.83889i	0.157493	−	0.157493i
$945$	2.66027	+	0.832179i	0.0865386	+	0.0270708i
$946$			2.10130i			0.0683191i
$947$	−14.5721	+	54.3838i	−0.473530	+	1.76724i	0.153403	+	0.988164i	$0.450977\pi$
$947$	−14.5721	+	54.3838i	−0.473530	+	1.76724i	−0.626932	+	0.779074i	$0.715690\pi$
$948$	−3.14704	+	5.45082i	−0.102211	+	0.177035i
$949$	30.6817	−	10.0927i	0.995969	−	0.327623i
$950$	−20.1635	+	11.6414i	−0.654190	+	0.377697i
$951$	−20.2845	−	20.2845i	−0.657771	−	0.657771i
$952$	13.0876	−	2.93247i	0.424170	−	0.0950418i
$953$			41.8221i			1.35475i	0.735638	+	0.677375i	$0.236883\pi$
$953$			41.8221i			1.35475i	−0.735638	+	0.677375i	$0.763117\pi$
$954$	−0.856602	−	0.229526i	−0.0277335	−	0.00743117i
$955$	27.1236	−	7.26776i	0.877700	−	0.235179i
$956$	−17.5280	+	4.69662i	−0.566897	+	0.151900i
$957$	3.54923	+	0.951012i	0.114730	+	0.0307419i
$958$		−	19.3743i		−	0.625954i
$959$	−5.99816	+	1.34398i	−0.193691	+	0.0433994i
$960$	0.744962	+	0.744962i	0.0240435	+	0.0240435i
$961$	−13.5050	+	7.79713i	−0.435646	+	0.251520i
$962$	−4.51749	−	2.28110i	−0.145650	−	0.0735456i
$963$	−0.481464	+	0.833919i	−0.0155149	+	0.0268727i
$964$	−5.68140	+	21.2033i	−0.182986	+	0.682912i
$965$			6.26221i			0.201588i
$966$	−16.2892	−	5.09556i	−0.524097	−	0.163947i
$967$	−36.8456	+	36.8456i	−1.18487	+	1.18487i	−0.206408	+	0.978466i	$0.566177\pi$
$967$	−36.8456	+	36.8456i	−1.18487	+	1.18487i	−0.978466	+	0.206408i	$0.933823\pi$
$968$	−9.29159	−	2.48967i	−0.298643	−	0.0800212i
$969$	−7.85273	−	29.3068i	−0.252266	−	0.941470i
$970$	2.29714	−	0.615516i	0.0737567	−	0.0197630i
$971$	19.1476	−	11.0549i	0.614477	−	0.354769i	−0.160239	−	0.987078i	$-0.551226\pi$
$971$	19.1476	−	11.0549i	0.614477	−	0.354769i	0.774716	+	0.632310i	$0.217893\pi$
$972$	1.00000			0.0320750
$973$	2.45765	−	59.3658i	0.0787888	−	1.90318i
$974$		−	17.0357i		−	0.545859i
$975$	11.7352	−	7.68178i	0.375826	−	0.246014i
$976$	−9.72877	−	5.61691i	−0.311410	−	0.179793i
$977$	−3.32031	−	12.3916i	−0.106226	−	0.396441i	0.892255	−	0.451531i	$-0.149122\pi$
$977$	−3.32031	−	12.3916i	−0.106226	−	0.396441i	−0.998481	+	0.0550902i	$0.982455\pi$
$978$	19.3142	−	11.1511i	0.617601	−	0.356572i
$979$	8.61678			0.275393
$980$	−5.62791	+	4.76586i	−0.179777	+	0.152240i
$981$	−3.74300	+	3.74300i	−0.119505	+	0.119505i
$982$	−3.66273	+	13.6695i	−0.116882	+	0.436211i
$983$	−1.69080	−	6.31014i	−0.0539281	−	0.201262i	0.933706	−	0.358042i	$-0.116555\pi$
$983$	−1.69080	−	6.31014i	−0.0539281	−	0.201262i	−0.987634	+	0.156779i	$0.949889\pi$
$984$	1.45619	−	2.52219i	0.0464215	−	0.0804044i
$985$	13.9108	+	24.0943i	0.443236	+	0.767708i
$986$	11.2094	−	11.2094i	0.356979	−	0.356979i
$987$	12.3108	+	13.3742i	0.391858	+	0.425704i
$988$	−16.0895	−	14.3813i	−0.511874	−	0.457531i
$989$	−5.76822	−	9.99085i	−0.183419	−	0.317691i
$990$	1.19573	−	0.320395i	0.0380028	−	0.0101828i
$991$	−13.2663	+	22.9779i	−0.421417	+	0.729916i	−0.996078	−	0.0884757i	$-0.971800\pi$
$991$	−13.2663	+	22.9779i	−0.421417	+	0.729916i	0.574661	+	0.818391i	$0.305134\pi$
$992$	−1.96251	−	3.39916i	−0.0623097	−	0.107924i
$993$	8.75079	+	8.75079i	0.277698	+	0.277698i
$994$	15.3198	−	8.01902i	0.485915	−	0.254348i
$995$	14.6261	+	14.6261i	0.463679	+	0.463679i
$996$	−3.58956	+	13.3964i	−0.113739	+	0.424481i
$997$	−29.5376	−	17.0536i	−0.935466	−	0.540092i	−0.0469299	−	0.998898i	$-0.514944\pi$
$997$	−29.5376	−	17.0536i	−0.935466	−	0.540092i	−0.888536	+	0.458807i	$0.848277\pi$
$998$	−27.3035	−	15.7637i	−0.864276	−	0.498990i
$999$	1.35577	+	0.363278i	0.0428947	+	0.0114936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.b.31.7	yes	40
7.5	odd	6		546.2.bz.a.187.2	yes	40
13.8	odd	4		546.2.bz.a.73.2	✓	40
91.47	even	12	inner	546.2.bz.b.229.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.73.2	✓	40	13.8	odd	4
546.2.bz.a.187.2	yes	40	7.5	odd	6
546.2.bz.b.31.7	yes	40	1.1	even	1	trivial
546.2.bz.b.229.7	yes	40	91.47	even	12	inner

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.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.272675 + 1.01764i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.64349 + 0.109436i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.272675 + 1.01764i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.64349 + 0.109436i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.526768 + 0.912388i) q^{10} +(-1.13497 + 0.304114i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.201804 + 3.59990i) q^{13} +(2.52509 + 0.789892i) q^{14} +(0.744962 - 0.744962i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.53464 - 4.39013i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-1.54908 + 5.78125i) q^{19} +(-0.744962 + 0.744962i) q^{20} +(-2.23461 - 1.41652i) q^{21} -1.17501 q^{22} +(5.58669 - 3.22548i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(3.36889 + 1.94503i) q^{25} +(-0.736795 + 3.52947i) q^{26} -1.00000i q^{27} +(2.23461 + 1.41652i) q^{28} +3.12716 q^{29} +(0.912388 - 0.526768i) q^{30} +(-3.79127 + 1.01587i) q^{31} +(0.258819 + 0.965926i) q^{32} +(1.13497 + 0.304114i) q^{33} +(3.58452 - 3.58452i) q^{34} +(-0.832179 + 2.66027i) q^{35} +1.00000i q^{36} +(-0.363278 + 1.35577i) q^{37} +(-2.99260 + 5.18333i) q^{38} +(1.62518 - 3.21851i) q^{39} +(-0.912388 + 0.526768i) q^{40} +(2.05936 + 2.05936i) q^{41} +(-1.79184 - 1.94661i) q^{42} -1.78833i q^{43} +(-1.13497 - 0.304114i) q^{44} +(-1.01764 + 0.272675i) q^{45} +(6.23115 - 1.66963i) q^{46} +(-6.63638 - 1.77821i) q^{47} -1.00000i q^{48} +(6.97605 + 0.578587i) q^{49} +(2.75069 + 2.75069i) q^{50} +(-4.39013 + 2.53464i) q^{51} +(-1.62518 + 3.21851i) q^{52} +(-0.443410 + 0.768008i) q^{53} +(0.258819 - 0.965926i) q^{54} -1.23791i q^{55} +(1.79184 + 1.94661i) q^{56} +(4.23217 - 4.23217i) q^{57} +(3.02060 + 0.809368i) q^{58} +(-1.77116 - 6.61005i) q^{59} +(1.01764 - 0.272675i) q^{60} +(-9.72877 + 5.61691i) q^{61} -3.92502 q^{62} +(1.22697 + 2.34405i) q^{63} +1.00000i q^{64} +(-3.71842 - 0.776239i) q^{65} +(1.01758 + 0.587503i) q^{66} +(-3.07560 - 11.4783i) q^{67} +(4.39013 - 2.53464i) q^{68} -6.45096 q^{69} +(-1.49235 + 2.35424i) q^{70} +(4.62139 - 4.62139i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-2.31854 - 8.65290i) q^{73} +(-0.701798 + 1.21555i) q^{74} +(-1.94503 - 3.36889i) q^{75} +(-4.23217 + 4.23217i) q^{76} +(-3.03356 + 0.679714i) q^{77} +(2.40282 - 2.68821i) q^{78} +(-3.14704 - 5.45082i) q^{79} +(-1.01764 + 0.272675i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.45619 + 2.52219i) q^{82} +(-9.80685 - 9.80685i) q^{83} +(-1.22697 - 2.34405i) q^{84} +(3.77642 + 3.77642i) q^{85} +(0.462854 - 1.72740i) q^{86} +(-2.70820 - 1.56358i) q^{87} +(-1.01758 - 0.587503i) q^{88} +(-7.08351 - 1.89802i) q^{89} -1.05354 q^{90} +(0.139506 + 9.53837i) q^{91} +6.45096 q^{92} +(3.79127 + 1.01587i) q^{93} +(-5.95001 - 3.43524i) q^{94} +(-5.46082 - 3.15280i) q^{95} +(0.258819 - 0.965926i) q^{96} +(-1.59617 - 1.59617i) q^{97} +(6.58860 + 2.36441i) q^{98} +(-0.830855 - 0.830855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

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