LMFDB - Embedded newform 546.2.bz.a.73.2

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			73.2
Character	$\chi$	$=$	546.73
Dual form			546.2.bz.a.187.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.01764 - 0.272675i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.109436 - 2.64349i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.01764 - 0.272675i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.109436 - 2.64349i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.526768 - 0.912388i) q^{10} +(0.304114 + 1.13497i) 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} +(-0.965926 + 0.258819i) q^{18} +(-5.78125 - 1.54908i) q^{19} +(0.744962 + 0.744962i) q^{20} +(-1.41652 + 2.23461i) q^{21} -1.17501 q^{22} +(-5.58669 + 3.22548i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(-3.36889 - 1.94503i) q^{25} +(-3.42501 - 1.12665i) q^{26} -1.00000i q^{27} +(-1.41652 + 2.23461i) q^{28} +3.12716 q^{29} +(-0.912388 + 0.526768i) q^{30} +(-1.01587 - 3.79127i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.304114 - 1.13497i) q^{33} +(-3.58452 - 3.58452i) q^{34} +(-0.832179 + 2.66027i) q^{35} -1.00000i q^{36} +(1.35577 + 0.363278i) q^{37} +(2.99260 - 5.18333i) q^{38} +(1.97472 - 3.01670i) q^{39} +(-0.912388 + 0.526768i) q^{40} +(-2.05936 + 2.05936i) q^{41} +(-1.79184 - 1.94661i) q^{42} +1.78833i q^{43} +(0.304114 - 1.13497i) q^{44} +(-0.272675 - 1.01764i) q^{45} +(-1.66963 - 6.23115i) q^{46} +(-1.77821 + 6.63638i) q^{47} -1.00000i q^{48} +(-6.97605 - 0.578587i) q^{49} +(2.75069 - 2.75069i) q^{50} +(4.39013 - 2.53464i) q^{51} +(1.97472 - 3.01670i) q^{52} +(-0.443410 + 0.768008i) q^{53} +(0.965926 + 0.258819i) q^{54} -1.23791i q^{55} +(-1.79184 - 1.94661i) q^{56} +(4.23217 + 4.23217i) q^{57} +(-0.809368 + 3.02060i) q^{58} +(-6.61005 + 1.77116i) q^{59} +(-0.272675 - 1.01764i) q^{60} +(-9.72877 + 5.61691i) q^{61} +3.92502 q^{62} +(2.34405 - 1.22697i) q^{63} -1.00000i q^{64} +(1.18697 - 3.60836i) q^{65} +(1.01758 + 0.587503i) q^{66} +(11.4783 - 3.07560i) q^{67} +(4.39013 - 2.53464i) q^{68} +6.45096 q^{69} +(-2.35424 - 1.49235i) q^{70} +(4.62139 + 4.62139i) q^{71} +(0.965926 + 0.258819i) q^{72} +(-8.65290 + 2.31854i) 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} +(-0.272675 - 1.01764i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.45619 - 2.52219i) q^{82} +(9.80685 - 9.80685i) q^{83} +(2.34405 - 1.22697i) q^{84} +(3.77642 - 3.77642i) q^{85} +(-1.72740 - 0.462854i) q^{86} +(-2.70820 - 1.56358i) q^{87} +(1.01758 + 0.587503i) q^{88} +(-1.89802 + 7.08351i) q^{89} +1.05354 q^{90} +(9.49420 + 0.927426i) q^{91} +6.45096 q^{92} +(-1.01587 + 3.79127i) q^{93} +(-5.95001 - 3.43524i) q^{94} +(5.46082 + 3.15280i) q^{95} +(0.965926 + 0.258819i) q^{96} +(1.59617 - 1.59617i) q^{97} +(2.36441 - 6.58860i) 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} + 32 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} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 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} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 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} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 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 + 32 * 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 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * 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 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * 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 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−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
$5$	−1.01764	−	0.272675i	−0.455101	−	0.121944i	0.0239842	−	0.999712i	$-0.492365\pi$
$5$	−1.01764	−	0.272675i	−0.455101	−	0.121944i	−0.479085	+	0.877768i	$0.659032\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	0.109436	−	2.64349i	0.0413630	−	0.999144i
$7$	0.109436	−	2.64349i	0.0413630	−	0.999144i
$8$	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
$11$	0.304114	+	1.13497i	0.0916938	+	0.342206i	0.996497	−	0.0836231i	$-0.0266492\pi$
$11$	0.304114	+	1.13497i	0.0916938	+	0.342206i	−0.904804	+	0.425829i	$0.859983\pi$
$12$	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	$0.377406\pi$
$17$	−2.53464	+	4.39013i	−0.614741	+	1.06476i	−0.990430	+	0.138017i	$0.955927\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	−5.78125	−	1.54908i	−1.32631	−	0.355384i	−0.474972	−	0.880001i	$-0.657542\pi$
$19$	−5.78125	−	1.54908i	−1.32631	−	0.355384i	−0.851338	+	0.524617i	$0.824208\pi$
$20$	0.744962	+	0.744962i	0.166579	+	0.166579i
$21$	−1.41652	+	2.23461i	−0.309110	+	0.487632i
$22$	−1.17501			−0.250512
$23$	−5.58669	+	3.22548i	−1.16491	+	0.672559i	−0.952475	−	0.304617i	$-0.901471\pi$
$23$	−5.58669	+	3.22548i	−1.16491	+	0.672559i	−0.212431	+	0.977176i	$0.568138\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	−3.36889	−	1.94503i	−0.673779	−	0.389006i
$26$	−3.42501	−	1.12665i	−0.671699	−	0.220954i
$27$		−	1.00000i		−	0.192450i
$28$	−1.41652	+	2.23461i	−0.267697	+	0.422301i
$29$	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
$31$	−1.01587	−	3.79127i	−0.182455	−	0.680933i	−0.995161	−	0.0982582i	$-0.968673\pi$
$31$	−1.01587	−	3.79127i	−0.182455	−	0.680933i	0.812706	−	0.582675i	$-0.197994\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.304114	−	1.13497i	0.0529394	−	0.197573i
$34$	−3.58452	−	3.58452i	−0.614741	−	0.614741i
$35$	−0.832179	+	2.66027i	−0.140664	+	0.449668i
$36$		−	1.00000i		−	0.166667i
$37$	1.35577	+	0.363278i	0.222887	+	0.0597225i	0.368534	−	0.929614i	$-0.379860\pi$
$37$	1.35577	+	0.363278i	0.222887	+	0.0597225i	−0.145647	+	0.989337i	$0.546526\pi$
$38$	2.99260	−	5.18333i	0.485463	−	0.840847i
$39$	1.97472	−	3.01670i	0.316208	−	0.483059i
$40$	−0.912388	+	0.526768i	−0.144261	+	0.0832893i
$41$	−2.05936	+	2.05936i	−0.321618	+	0.321618i	−0.849387	−	0.527770i	$-0.823028\pi$
$41$	−2.05936	+	2.05936i	−0.321618	+	0.321618i	0.527770	+	0.849387i	$0.323028\pi$
$42$	−1.79184	−	1.94661i	−0.276488	−	0.300369i
$43$			1.78833i			0.272718i	0.990659	+	0.136359i	$0.0435401\pi$
$43$			1.78833i			0.272718i	−0.990659	+	0.136359i	$0.956460\pi$
$44$	0.304114	−	1.13497i	0.0458469	−	0.171103i
$45$	−0.272675	−	1.01764i	−0.0406480	−	0.151700i
$46$	−1.66963	−	6.23115i	−0.246174	−	0.918732i
$47$	−1.77821	+	6.63638i	−0.259379	+	0.968015i	0.706223	+	0.707990i	$0.250398\pi$
$47$	−1.77821	+	6.63638i	−0.259379	+	0.968015i	−0.965602	+	0.260026i	$0.916269\pi$
$48$		−	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
$52$	1.97472	−	3.01670i	0.273844	−	0.418341i
$53$	−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	$0.186066\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$		−	1.23791i		−	0.166920i
$56$	−1.79184	−	1.94661i	−0.239445	−	0.260127i
$57$	4.23217	+	4.23217i	0.560565	+	0.560565i
$58$	−0.809368	+	3.02060i	−0.106275	+	0.396625i
$59$	−6.61005	+	1.77116i	−0.860555	+	0.230585i	−0.661999	−	0.749505i	$-0.730292\pi$
$59$	−6.61005	+	1.77116i	−0.860555	+	0.230585i	−0.198556	+	0.980090i	$0.563625\pi$
$60$	−0.272675	−	1.01764i	−0.0352022	−	0.131376i
$61$	−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
$63$	2.34405	−	1.22697i	0.295322	−	0.154584i
$64$		−	1.00000i		−	0.125000i
$65$	1.18697	−	3.60836i	0.147225	−	0.447562i
$66$	1.01758	+	0.587503i	0.125256	+	0.0723166i
$67$	11.4783	−	3.07560i	1.40230	−	0.375744i	0.523127	−	0.852255i	$-0.324765\pi$
$67$	11.4783	−	3.07560i	1.40230	−	0.375744i	0.879169	+	0.476510i	$0.158099\pi$
$68$	4.39013	−	2.53464i	0.532381	−	0.307370i
$69$	6.45096			0.776604
$70$	−2.35424	−	1.49235i	−0.281385	−	0.178370i
$71$	4.62139	+	4.62139i	0.548458	+	0.548458i	0.925995	−	0.377537i	$-0.123229\pi$
$71$	4.62139	+	4.62139i	0.548458	+	0.548458i	−0.377537	+	0.925995i	$0.623229\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	−8.65290	+	2.31854i	−1.01275	+	0.271364i	−0.726776	−	0.686874i	$-0.758982\pi$
$73$	−8.65290	+	2.31854i	−1.01275	+	0.271364i	−0.285969	+	0.958239i	$0.592316\pi$
$74$	−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	$0.948536\pi$
$80$	−0.272675	−	1.01764i	−0.0304860	−	0.113775i
$81$	−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	0.0796163	−	0.996826i	$-0.474631\pi$
$83$	9.80685	−	9.80685i	1.07644	−	1.07644i	0.996826	−	0.0796163i	$-0.0253695\pi$
$84$	2.34405	−	1.22697i	0.255756	−	0.133873i
$85$	3.77642	−	3.77642i	0.409610	−	0.409610i
$86$	−1.72740	−	0.462854i	−0.186270	−	0.0499108i
$87$	−2.70820	−	1.56358i	−0.290349	−	0.167633i
$88$	1.01758	+	0.587503i	0.108475	+	0.0626280i
$89$	−1.89802	+	7.08351i	−0.201190	+	0.750851i	0.789387	+	0.613895i	$0.210398\pi$
$89$	−1.89802	+	7.08351i	−0.201190	+	0.750851i	−0.990577	+	0.136955i	$0.956268\pi$
$90$	1.05354			0.111052
$91$	9.49420	+	0.927426i	0.995263	+	0.0972206i
$92$	6.45096			0.672559
$93$	−1.01587	+	3.79127i	−0.105341	+	0.393137i
$94$	−5.95001	−	3.43524i	−0.613697	−	0.354318i
$95$	5.46082	+	3.15280i	0.560268	+	0.323471i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	1.59617	−	1.59617i	0.162067	−	0.162067i	−0.621415	−	0.783482i	$-0.713442\pi$
$97$	1.59617	−	1.59617i	0.162067	−	0.162067i	0.783482	+	0.621415i	$0.213442\pi$
$98$	2.36441	−	6.58860i	0.238841	−	0.665549i
$99$	−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	−0.939579	−	0.342333i	$-0.888783\pi$
$101$	−1.74185	+	3.01697i	−0.173321	+	0.300200i	0.766258	+	0.642533i	$0.222116\pi$
$102$	1.31203	+	4.89655i	0.129910	+	0.484831i
$103$	−6.15063	−	10.6532i	−0.606039	−	1.04969i	−0.991886	−	0.127128i	$-0.959424\pi$
$103$	−6.15063	−	10.6532i	−0.606039	−	1.04969i	0.385847	−	0.922563i	$-0.373909\pi$
$104$	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
$109$	−5.11304	+	1.37003i	−0.489740	+	0.131225i	−0.495234	−	0.868759i	$-0.664918\pi$
$109$	−5.11304	+	1.37003i	−0.489740	+	0.131225i	0.00549422	+	0.999985i	$0.498251\pi$
$110$	1.19573	+	0.320395i	0.114008	+	0.0305484i
$111$	−0.992493	−	0.992493i	−0.0942033	−	0.0942033i
$112$	2.34405	−	1.22697i	0.221491	−	0.115938i
$113$	−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
$115$	6.56473	−	1.75901i	0.612164	−	0.164029i
$116$	−2.70820	−	1.56358i	−0.251450	−	0.145175i
$117$	−3.21851	+	1.62518i	−0.297551	+	0.150248i
$118$		−	6.84323i		−	0.629970i
$119$	11.3279	+	7.18073i	1.03842	+	0.658257i
$120$	1.05354			0.0961741
$121$	8.33061	−	4.80968i	0.757328	−	0.437244i
$122$	−2.90753	−	10.8510i	−0.263235	−	0.982406i
$123$	2.81313	−	0.753777i	0.253652	−	0.0679658i
$124$	−1.01587	+	3.79127i	−0.0912277	+	0.340466i
$125$	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	$0.136117\pi$
$127$			9.34710i			0.829421i	−0.909954	+	0.414710i	$0.863883\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	0.894166	−	1.54874i	0.0787269	−	0.136359i
$130$	3.17820	+	2.08043i	0.278747	+	0.182466i
$131$	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
$135$	−0.272675	+	1.01764i	−0.0234681	+	0.0875842i
$136$	1.31203	+	4.89655i	0.112505	+	0.419876i
$137$	0.601316	+	2.24414i	0.0513739	+	0.191730i	0.986844	−	0.161676i	$-0.0516900\pi$
$137$	0.601316	+	2.24414i	0.0513739	+	0.191730i	−0.935470	+	0.353406i	$0.885023\pi$
$138$	−1.66963	+	6.23115i	−0.142128	+	0.530430i
$139$		−	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
$143$	−4.14714	+	0.865738i	−0.346802	+	0.0723967i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.18231	−	0.852698i	−0.264276	−	0.0708127i
$146$		−	8.95814i		−	0.741381i
$147$	5.75214	+	3.98909i	0.474429	+	0.329015i
$148$	−0.992493	−	0.992493i	−0.0815824	−	0.0815824i
$149$	3.06595	−	11.4423i	0.251172	−	0.937387i	−0.719008	−	0.695002i	$-0.755404\pi$
$149$	3.06595	−	11.4423i	0.251172	−	0.937387i	0.970180	−	0.242385i	$-0.0779298\pi$
$150$	−3.75751	+	1.00682i	−0.306800	+	0.0822067i
$151$	−1.57989	−	5.89624i	−0.128570	−	0.479829i	0.871372	−	0.490623i	$-0.163231\pi$
$151$	−1.57989	−	5.89624i	−0.128570	−	0.479829i	−0.999942	+	0.0107940i	$0.996564\pi$
$152$	−5.18333	+	2.99260i	−0.420423	+	0.242732i
$153$	−5.06928			−0.409827
$154$	−0.128588	+	3.10611i	−0.0103619	+	0.250298i
$155$			4.13514i			0.332143i
$156$	−3.21851	+	1.62518i	−0.257687	+	0.130119i
$157$	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	$0.330008\pi$
$158$	6.07960	−	1.62903i	0.483667	−	0.129598i
$159$	0.768008	−	0.443410i	0.0609070	−	0.0351647i
$160$	1.05354			0.0832893
$161$	7.91512	+	15.1213i	0.623799	+	1.19173i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	21.5422	+	5.77223i	1.68732	+	0.452116i	0.969696	−	0.244316i	$-0.0785635\pi$
$163$	21.5422	+	5.77223i	1.68732	+	0.452116i	0.717623	+	0.696432i	$0.245230\pi$
$164$	2.81313	−	0.753777i	0.219669	−	0.0588601i
$165$	−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	$-0.218354\pi$
$167$	1.81395	+	1.81395i	0.140368	+	0.140368i	−0.633431	+	0.773799i	$0.718354\pi$
$168$	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
$171$	−1.54908	−	5.78125i	−0.118461	−	0.442103i
$172$	0.894166	−	1.54874i	0.0681795	−	0.118090i
$173$	−9.79357	−	16.9630i	−0.744591	−	1.28967i	−0.950386	−	0.311075i	$-0.899311\pi$
$173$	−9.79357	−	16.9630i	−0.744591	−	1.28967i	0.205794	−	0.978595i	$-0.434022\pi$
$174$	2.21123	−	2.21123i	0.167633	−	0.167633i
$175$	−5.51035	+	8.69277i	−0.416543	+	0.657112i
$176$	−0.830855	+	0.830855i	−0.0626280	+	0.0626280i
$177$	6.61005	+	1.77116i	0.496842	+	0.133128i
$178$	−6.35090	−	3.66670i	−0.476020	−	0.274830i
$179$	−4.48926	−	2.59187i	−0.335543	−	0.193726i	0.322756	−	0.946482i	$-0.395391\pi$
$179$	−4.48926	−	2.59187i	−0.335543	−	0.193726i	−0.658299	+	0.752756i	$0.728724\pi$
$180$	−0.272675	+	1.01764i	−0.0203240	+	0.0758502i
$181$	−15.2703			−1.13503			−0.567516	−	0.823362i	$-0.692096\pi$
$181$	−15.2703			−1.13503			−0.567516	+	0.823362i	$0.692096\pi$
$182$	−3.35310	+	8.93066i	−0.248549	+	0.661985i
$183$	11.2338			0.830427
$184$	−1.66963	+	6.23115i	−0.123087	+	0.459366i
$185$	−1.28063	−	0.739369i	−0.0941534	−	0.0543595i
$186$	−3.39916	−	1.96251i	−0.249239	−	0.143898i
$187$	−5.75348	−	1.54164i	−0.420736	−	0.112736i
$188$	4.85817	−	4.85817i	0.354318	−	0.354318i
$189$	−2.64349	−	0.109436i	−0.192285	−	0.00796032i
$190$	−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
$193$	−1.53842	−	5.74146i	−0.110738	−	0.413279i	0.888195	−	0.459467i	$-0.151960\pi$
$193$	−1.53842	−	5.74146i	−0.110738	−	0.413279i	−0.998933	+	0.0461874i	$0.985293\pi$
$194$	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	0.904999	+	0.425413i	$0.139871\pi$
$197$	18.6732	+	18.6732i	1.33041	+	1.33041i	0.425413	+	0.904999i	$0.360129\pi$
$198$	−0.587503	−	1.01758i	−0.0417520	−	0.0723166i
$199$	−9.81669	+	17.0030i	−0.695887	+	1.20531i	0.273994	+	0.961731i	$0.411655\pi$
$199$	−9.81669	+	17.0030i	−0.695887	+	1.20531i	−0.969881	+	0.243580i	$0.921678\pi$
$200$	−3.75751	+	1.00682i	−0.265696	+	0.0711931i
$201$	−11.4783	−	3.07560i	−0.809616	−	0.216936i
$202$	−2.46335	−	2.46335i	−0.173321	−	0.173321i
$203$	0.342225	−	8.26660i	0.0240195	−	0.580202i
$204$	−5.06928			−0.354921
$205$	2.65721	−	1.53414i	0.185588	−	0.107149i
$206$	11.8821	−	3.18380i	0.827865	−	0.221826i
$207$	−5.58669	−	3.22548i	−0.388302	−	0.224186i
$208$	−3.21851	+	1.62518i	−0.223163	+	0.112686i
$209$		−	7.03264i		−	0.486458i
$210$	1.29265	+	2.46953i	0.0892016	+	0.170414i
$211$	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
$213$	−1.69155	−	6.31294i	−0.115903	−	0.432555i
$214$	−0.930116	+	0.249224i	−0.0635814	+	0.0170366i
$215$	0.487633	−	1.81987i	0.0332563	−	0.124114i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−10.1334	+	2.27053i	−0.687897	+	0.154134i
$218$		−	5.29341i		−	0.358515i
$219$	8.65290	+	2.31854i	0.584709	+	0.156672i
$220$	−0.618955	+	1.07206i	−0.0417299	+	0.0722784i
$221$	−15.2925	−	10.0104i	−1.02869	−	0.673372i
$222$	1.21555	−	0.701798i	0.0815824	−	0.0471016i
$223$	6.85790	−	6.85790i	0.459239	−	0.459239i	−0.439167	−	0.898406i	$-0.644726\pi$
$223$	6.85790	−	6.85790i	0.459239	−	0.459239i	0.898406	+	0.439167i	$0.144726\pi$
$224$	0.578477	+	2.58174i	0.0386511	+	0.172500i
$225$		−	3.89006i		−	0.259338i
$226$	1.49700	−	5.58687i	0.0995787	−	0.371633i
$227$	−3.94730	−	14.7315i	−0.261992	−	0.977766i	−0.964066	−	0.265663i	$-0.914409\pi$
$227$	−3.94730	−	14.7315i	−0.261992	−	0.977766i	0.702074	−	0.712104i	$-0.252257\pi$
$228$	−1.54908	−	5.78125i	−0.102590	−	0.382873i
$229$	−1.22402	+	4.56809i	−0.0808853	+	0.301868i	−0.994503	−	0.104706i	$-0.966610\pi$
$229$	−1.22402	+	4.56809i	−0.0808853	+	0.301868i	0.913618	+	0.406574i	$0.133277\pi$
$230$			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	−0.749410	−	0.662106i	$-0.769663\pi$
$233$	−8.40629	+	4.85338i	−0.550715	+	0.317955i	0.198696	+	0.980061i	$0.436330\pi$
$234$	−0.736795	−	3.52947i	−0.0481658	−	0.230728i
$235$	3.61915	−	6.26855i	0.236087	−	0.408915i
$236$	6.61005	+	1.77116i	0.430278	+	0.115293i
$237$			6.29407i			0.408844i
$238$	−9.86792	+	9.08337i	−0.639642	+	0.588787i
$239$	−12.8314	−	12.8314i	−0.829995	−	0.829995i	0.157521	−	0.987516i	$-0.449650\pi$
$239$	−12.8314	−	12.8314i	−0.829995	−	0.829995i	−0.987516	+	0.157521i	$0.949650\pi$
$240$	−0.272675	+	1.01764i	−0.0176011	+	0.0656882i
$241$	21.2033	−	5.68140i	1.36582	−	0.365971i	0.499872	−	0.866099i	$-0.333380\pi$
$241$	21.2033	−	5.68140i	1.36582	−	0.365971i	0.865952	+	0.500128i	$0.166714\pi$
$242$	2.48967	+	9.29159i	0.160042	+	0.597286i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	11.2338			0.719171
$245$	6.94132	+	2.49098i	0.443464	+	0.159143i
$246$			2.91237i			0.185686i
$247$	6.74322	−	20.4993i	0.429061	−	1.30434i
$248$	−3.39916	−	1.96251i	−0.215847	−	0.124619i
$249$	−13.3964	+	3.58956i	−0.848963	+	0.227479i
$250$	−8.11119	+	4.68300i	−0.512997	+	0.296179i
$251$	−4.15095			−0.262005			−0.131003	−	0.991382i	$-0.541820\pi$
$251$	−4.15095			−0.262005			−0.131003	+	0.991382i	$0.541820\pi$
$252$	−2.64349	−	0.109436i	−0.166524	−	0.00689384i
$253$	−5.35981	−	5.35981i	−0.336968	−	0.336968i
$254$	−9.02860	−	2.41921i	−0.566505	−	0.151795i
$255$	−5.15869	+	1.38227i	−0.323050	+	0.0865609i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.55319	−	14.8146i	−0.533533	−	0.924107i	−0.999233	−	0.0391638i	$-0.987531\pi$
$257$	−8.55319	−	14.8146i	−0.533533	−	0.924107i	0.465700	−	0.884943i	$-0.345803\pi$
$258$	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
$262$	1.14555	+	4.27524i	0.0707722	+	0.264125i
$263$	−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
$266$	−13.3746	−	8.47813i	−0.820047	−	0.519828i
$267$	5.18549	−	5.18549i	0.317347	−	0.317347i
$268$	−11.4783	−	3.07560i	−0.701148	−	0.187872i
$269$	−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
$271$	2.02950	−	7.57420i	0.123283	−	0.460100i	−0.876489	−	0.481421i	$-0.840121\pi$
$271$	2.02950	−	7.57420i	0.123283	−	0.460100i	0.999773	+	0.0213215i	$0.00678735\pi$
$272$	−5.06928			−0.307370
$273$	−7.75851	−	5.55028i	−0.469566	−	0.335918i
$274$	−2.32331			−0.140356
$275$	1.18302	−	4.41510i	0.0713389	−	0.266241i
$276$	−5.58669	−	3.22548i	−0.336279	−	0.194151i
$277$	4.20420	+	2.42730i	0.252606	+	0.145842i	0.620957	−	0.783845i	$-0.286744\pi$
$277$	4.20420	+	2.42730i	0.252606	+	0.145842i	−0.368351	+	0.929687i	$0.620078\pi$
$278$	21.6922	+	5.81240i	1.30101	+	0.348605i
$279$	2.77540	−	2.77540i	0.166159	−	0.166159i
$280$	1.29265	+	2.46953i	0.0772509	+	0.147583i
$281$	−4.18018	+	4.18018i	−0.249368	+	0.249368i	−0.820711	−	0.571343i	$-0.806423\pi$
$281$	−4.18018	+	4.18018i	−0.249368	+	0.249368i	0.571343	+	0.820711i	$0.306423\pi$
$282$	3.43524	+	5.95001i	0.204566	+	0.354318i
$283$	−14.2259	+	24.6400i	−0.845643	+	1.46470i	0.0394189	+	0.999223i	$0.487449\pi$
$283$	−14.2259	+	24.6400i	−0.845643	+	1.46470i	−0.885062	+	0.465474i	$0.845884\pi$
$284$	−1.69155	−	6.31294i	−0.100375	−	0.374604i
$285$	−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
$291$	−2.18041	+	0.584239i	−0.127818	+	0.0342487i
$292$	8.65290	+	2.31854i	0.506373	+	0.135682i
$293$	−4.61778	−	4.61778i	−0.269774	−	0.269774i	0.559235	−	0.829009i	$-0.311095\pi$
$293$	−4.61778	−	4.61778i	−0.269774	−	0.269774i	−0.829009	+	0.559235i	$0.811095\pi$
$294$	−5.34193	+	4.52369i	−0.311548	+	0.263827i
$295$	7.20958			0.419758
$296$	1.21555	−	0.701798i	0.0706524	−	0.0407912i
$297$	1.13497	−	0.304114i	0.0658576	−	0.0176465i
$298$	10.2589	+	5.92295i	0.594279	+	0.343107i
$299$	−10.4840	−	20.7624i	−0.606304	−	1.20072i
$300$		−	3.89006i		−	0.224593i
$301$	4.72743	+	0.195708i	0.272485	+	0.0112804i
$302$	6.10423			0.351259
$303$	3.01697	−	1.74185i	0.173321	−	0.100067i
$304$	−1.54908	−	5.78125i	−0.0888459	−	0.331578i
$305$	11.4319	−	3.06318i	0.654591	−	0.175397i
$306$	1.31203	−	4.89655i	0.0750036	−	0.279917i
$307$	3.54555	+	3.54555i	0.202355	+	0.202355i	0.801008	−	0.598653i	$-0.204297\pi$
$307$	3.54555	+	3.54555i	0.202355	+	0.202355i	−0.598653	+	0.801008i	$0.704297\pi$
$308$	−2.96699	−	0.928128i	−0.169060	−	0.0528850i
$309$			12.3013i			0.699794i
$310$	−3.99424	−	1.07025i	−0.226858	−	0.0607863i
$311$	−0.174431	+	0.302124i	−0.00989109	+	0.0171319i	−0.870929	−	0.491410i	$-0.836482\pi$
$311$	−0.174431	+	0.302124i	−0.00989109	+	0.0171319i	0.861037	+	0.508541i	$0.169815\pi$
$312$	−0.736795	−	3.52947i	−0.0417128	−	0.199817i
$313$	−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
$317$	−7.42465	+	27.7092i	−0.417010	+	1.55630i	0.363766	+	0.931490i	$0.381491\pi$
$317$	−7.42465	+	27.7092i	−0.417010	+	1.55630i	−0.780776	+	0.624811i	$0.785176\pi$
$318$	0.229526	+	0.856602i	0.0128712	+	0.0480358i
$319$	0.951012	+	3.54923i	0.0532465	+	0.198718i
$320$	−0.272675	+	1.01764i	−0.0152430	+	0.0568876i
$321$		−	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
$325$	7.68178	−	11.7352i	0.426108	−	0.650950i
$326$	−11.1511	+	19.3142i	−0.617601	+	1.06972i
$327$	5.11304	+	1.37003i	0.282752	+	0.0757631i
$328$			2.91237i			0.160809i
$329$	17.3486	+	5.42694i	0.956458	+	0.299197i
$330$	−0.875334	−	0.875334i	−0.0481856	−	0.0481856i
$331$	3.20301	−	11.9538i	0.176053	−	0.657040i	−0.820316	−	0.571910i	$-0.806203\pi$
$331$	3.20301	−	11.9538i	0.176053	−	0.657040i	0.996370	−	0.0851303i	$-0.0271307\pi$
$332$	−13.3964	+	3.58956i	−0.735223	+	0.197003i
$333$	0.363278	+	1.35577i	0.0199075	+	0.0742958i
$334$	−2.22163	+	1.28266i	−0.121562	+	0.0701838i
$335$	−12.5194			−0.684006
$336$	−2.64349	−	0.109436i	−0.144214	−	0.00597024i
$337$			14.0948i			0.767791i	0.923377	+	0.383896i	$0.125418\pi$
$337$			14.0948i			0.767791i	−0.923377	+	0.383896i	$0.874582\pi$
$338$	4.74701	−	12.1023i	0.258203	−	0.658279i
$339$	5.00905	+	2.89197i	0.272054	+	0.157070i
$340$	−5.15869	+	1.38227i	−0.279769	+	0.0749639i
$341$	3.99404	−	2.30596i	0.216289	−	0.124875i
$342$	5.98519			0.323642
$343$	−2.29292	+	18.3778i	−0.123806	+	0.992306i
$344$	1.26454	+	1.26454i	0.0681795	+	0.0681795i
$345$	−6.56473	−	1.75901i	−0.353433	−	0.0947021i
$346$	18.9197	−	5.06952i	1.01713	−	0.272539i
$347$	−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	$-0.205261\pi$
$349$	3.70116	+	3.70116i	0.198119	+	0.198119i	−0.601074	+	0.799193i	$0.705261\pi$
$350$	−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
$353$	4.54237	+	16.9523i	0.241766	+	0.902282i	0.974981	+	0.222286i	$0.0713519\pi$
$353$	4.54237	+	16.9523i	0.241766	+	0.902282i	−0.733216	+	0.679996i	$0.761981\pi$
$354$	−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
$357$	−6.21985	−	11.8826i	−0.329190	−	0.628895i
$358$	3.66546	−	3.66546i	0.193726	−	0.193726i
$359$	−17.7144	−	4.74656i	−0.934930	−	0.250514i	−0.240974	−	0.970531i	$-0.577467\pi$
$359$	−17.7144	−	4.74656i	−0.934930	−	0.250514i	−0.693956	+	0.720018i	$0.744134\pi$
$360$	−0.912388	−	0.526768i	−0.0480871	−	0.0277631i
$361$	14.5687	+	8.41126i	0.766776	+	0.442698i
$362$	3.95225	−	14.7500i	0.207725	−	0.775242i
$363$	−9.61936			−0.504886
$364$	−7.75851	−	5.55028i	−0.406656	−	0.290913i
$365$	9.43772			0.493993
$366$	−2.90753	+	10.8510i	−0.151979	+	0.567192i
$367$	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
$369$	−2.81313	−	0.753777i	−0.146446	−	0.0392401i
$370$	1.04563	−	1.04563i	0.0543595	−	0.0543595i
$371$	1.98169	+	1.25620i	0.102884	+	0.0652184i
$372$	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
$375$	−2.42410	−	9.04686i	−0.125180	−	0.467178i
$376$	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	0.621296	−	0.783576i	$-0.286607\pi$
$379$	−3.15926	−	3.15926i	−0.162280	−	0.162280i	−0.783576	+	0.621296i	$0.786607\pi$
$380$	−3.15280	−	5.46082i	−0.161735	−	0.280134i
$381$	4.67355	−	8.09482i	0.239433	−	0.414710i
$382$	25.7454	−	6.89845i	1.31725	−	0.352955i
$383$	−13.9404	−	3.73533i	−0.712323	−	0.190866i	−0.115579	−	0.993298i	$-0.536872\pi$
$383$	−13.9404	−	3.73533i	−0.712323	−	0.190866i	−0.596744	+	0.802432i	$0.703539\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−3.27240	−	0.135472i	−0.166777	−	0.00690431i
$386$	5.94400			0.302542
$387$	−1.54874	+	0.894166i	−0.0787269	+	0.0454530i
$388$	−2.18041	+	0.584239i	−0.110694	+	0.0296603i
$389$	−12.7223	−	7.34523i	−0.645047	−	0.372418i	0.141509	−	0.989937i	$-0.454804\pi$
$389$	−12.7223	−	7.34523i	−0.645047	−	0.372418i	−0.786556	+	0.617519i	$0.788138\pi$
$390$	−1.71219	−	3.39081i	−0.0866999	−	0.171700i
$391$		−	32.7017i		−	1.65380i
$392$	−5.34193	+	4.52369i	−0.269808	+	0.228481i
$393$	−4.42606			−0.223265
$394$	−22.8699	+	13.2040i	−1.15217	+	0.665206i
$395$	1.71624	+	6.40508i	0.0863532	+	0.322274i
$396$	1.13497	−	0.304114i	0.0570343	−	0.0152823i
$397$	0.466352	−	1.74045i	0.0234055	−	0.0873507i	−0.953235	−	0.302230i	$-0.902269\pi$
$397$	0.466352	−	1.74045i	0.0234055	−	0.0873507i	0.976641	+	0.214879i	$0.0689357\pi$
$398$	−13.8829	−	13.8829i	−0.695887	−	0.695887i
$399$	11.6508	−	10.7245i	0.583272	−	0.536898i
$400$		−	3.89006i		−	0.194503i
$401$	24.2870	+	6.50768i	1.21283	+	0.324978i	0.807873	−	0.589356i	$-0.200619\pi$
$401$	24.2870	+	6.50768i	1.21283	+	0.324978i	0.404961	+	0.914334i	$0.367285\pi$
$402$	5.94160	−	10.2912i	0.296340	−	0.513276i
$403$	13.8532	−	2.89193i	0.690077	−	0.144057i
$404$	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
$408$	1.31203	−	4.89655i	0.0649550	−	0.242415i
$409$	6.53829	+	24.4012i	0.323298	+	1.20656i	0.916012	+	0.401150i	$0.131390\pi$
$409$	6.53829	+	24.4012i	0.323298	+	1.20656i	−0.592715	+	0.805413i	$0.701944\pi$
$410$	0.794131	+	2.96374i	0.0392193	+	0.146368i
$411$	0.601316	−	2.24414i	0.0296607	−	0.110695i
$412$			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
$416$	−0.736795	−	3.52947i	−0.0361243	−	0.173046i
$417$	−11.2287	+	19.4487i	−0.549872	+	0.952406i
$418$	6.79300	+	1.82018i	0.332257	+	0.0890279i
$419$		−	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	0.162107	−	0.986773i	$-0.448171\pi$
$421$	−16.9207	−	16.9207i	−0.824667	−	0.824667i	−0.986773	+	0.162107i	$0.948171\pi$
$422$	−5.30710	+	19.8064i	−0.258346	+	0.964160i
$423$	−6.63638	+	1.77821i	−0.322672	+	0.0864596i
$424$	0.229526	+	0.856602i	0.0111468	+	0.0416003i
$425$	17.0779	−	9.85992i	0.828399	−	0.478276i
$426$	6.53563			0.316652
$427$	13.7835	+	26.3326i	0.667032	+	1.27432i
$428$		−	0.962927i		−	0.0465448i
$429$	4.02440	+	1.32382i	0.194300	+	0.0639147i
$430$	1.63165	+	0.942035i	0.0786852	+	0.0454289i
$431$	−29.3977	+	7.87709i	−1.41604	+	0.379426i	−0.884076	−	0.467342i	$-0.845212\pi$
$431$	−29.3977	+	7.87709i	−1.41604	+	0.379426i	−0.531962	+	0.846768i	$0.678545\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−3.38394			−0.162622			−0.0813108	−	0.996689i	$-0.525911\pi$
$433$	−3.38394			−0.162622			−0.0813108	+	0.996689i	$0.525911\pi$
$434$	0.429539	−	10.3757i	0.0206185	−	0.498051i
$435$	2.32961	+	2.32961i	0.111696	+	0.111696i
$436$	5.11304	+	1.37003i	0.244870	+	0.0656127i
$437$	37.2946	−	9.99306i	1.78404	−	0.478033i
$438$	−4.47907	+	7.75798i	−0.214018	+	0.370691i
$439$	17.7101	+	30.6749i	0.845259	+	1.46403i	0.885396	+	0.464837i	$0.153887\pi$
$439$	17.7101	+	30.6749i	0.845259	+	1.46403i	−0.0401377	+	0.999194i	$0.512780\pi$
$440$	−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	$0.692274\pi$
$444$	0.363278	+	1.35577i	0.0172404	+	0.0643420i
$445$	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
$448$	−2.64349	−	0.109436i	−0.124893	−	0.00517038i
$449$	−25.5364	+	25.5364i	−1.20514	+	1.20514i	−0.232554	+	0.972584i	$0.574708\pi$
$449$	−25.5364	+	25.5364i	−1.20514	+	1.20514i	−0.972584	+	0.232554i	$0.925292\pi$
$450$	3.75751	+	1.00682i	0.177131	+	0.0474621i
$451$	−2.96358	−	1.71103i	−0.139550	−	0.0805691i
$452$	5.00905	+	2.89197i	0.235606	+	0.136027i
$453$	−1.57989	+	5.89624i	−0.0742298	+	0.277029i
$454$	15.2512			0.715775
$455$	−9.40876	−	3.53261i	−0.441090	−	0.165611i
$456$	5.98519			0.280282
$457$	−1.27462	+	4.75695i	−0.0596242	+	0.222521i	−0.989309	−	0.145836i	$-0.953413\pi$
$457$	−1.27462	+	4.75695i	−0.0596242	+	0.222521i	0.929685	+	0.368357i	$0.120079\pi$
$458$	−4.09564	−	2.36462i	−0.191377	−	0.110491i
$459$	4.39013	+	2.53464i	0.204914	+	0.118307i
$460$	−6.56473	−	1.75901i	−0.306082	−	0.0820145i
$461$	26.3259	−	26.3259i	1.22612	−	1.22612i	0.260702	−	0.965419i	$-0.416046\pi$
$461$	26.3259	−	26.3259i	1.22612	−	1.22612i	0.965419	−	0.260702i	$-0.0839541\pi$
$462$	1.66442	−	2.62568i	0.0774357	−	0.122158i
$463$	−11.5245	+	11.5245i	−0.535588	+	0.535588i	−0.922230	−	0.386642i	$-0.873635\pi$
$463$	−11.5245	+	11.5245i	−0.535588	+	0.535588i	0.386642	+	0.922230i	$0.373635\pi$
$464$	1.56358	+	2.70820i	0.0725873	+	0.125725i
$465$	2.06757	−	3.58114i	0.0958813	−	0.166071i
$466$	−2.51229	−	9.37600i	−0.116380	−	0.434335i
$467$	17.0885	+	29.5981i	0.790760	+	1.36964i	0.925497	+	0.378756i	$0.123648\pi$
$467$	17.0885	+	29.5981i	0.790760	+	1.36964i	−0.134736	+	0.990882i	$0.543019\pi$
$468$	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
$473$	−2.02970	+	0.543856i	−0.0933257	+	0.0250065i
$474$	−6.07960	−	1.62903i	−0.279246	−	0.0748236i
$475$	16.4634	+	16.4634i	0.755393	+	0.755393i
$476$	−6.21985	−	11.8826i	−0.285086	−	0.544639i
$477$	−0.886819			−0.0406047
$478$	15.7152	−	9.07318i	0.718797	−	0.414997i
$479$	−18.7141	+	5.01443i	−0.855069	+	0.229115i	−0.659620	−	0.751599i	$-0.729283\pi$
$479$	−18.7141	+	5.01443i	−0.855069	+	0.229115i	−0.195449	+	0.980714i	$0.562616\pi$
$480$	−0.912388	−	0.526768i	−0.0416446	−	0.0240435i
$481$	−1.58136	+	4.80733i	−0.0721039	+	0.219195i
$482$			21.9513i			0.999852i
$483$	0.705969	−	17.0530i	0.0321227	−	0.775939i
$484$	−9.61936			−0.437244
$485$	−2.05956	+	1.18909i	−0.0935197	+	0.0539936i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	16.4552	−	4.40916i	0.745657	−	0.199798i	0.134066	−	0.990972i	$-0.457197\pi$
$487$	16.4552	−	4.40916i	0.745657	−	0.199798i	0.611591	+	0.791174i	$0.290530\pi$
$488$	−2.90753	+	10.8510i	−0.131617	+	0.491203i
$489$	−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	$-0.896543\pi$
$491$		−	14.1517i		−	0.638657i	0.947644	−	0.319329i	$-0.103457\pi$
$492$	−2.81313	−	0.753777i	−0.126826	−	0.0339829i
$493$	−7.92622	+	13.7286i	−0.356979	+	0.618306i
$494$	18.0555	+	11.8191i	0.812357	+	0.531765i
$495$	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
$499$	8.15988	−	30.4531i	0.365286	−	1.36327i	−0.501746	−	0.865015i	$-0.667309\pi$
$499$	8.15988	−	30.4531i	0.365286	−	1.36327i	0.867032	−	0.498252i	$-0.166024\pi$
$500$	−2.42410	−	9.04686i	−0.108409	−	0.404588i
$501$	−0.663952	−	2.47790i	−0.0296632	−	0.110704i
$502$	1.07434	−	4.00951i	0.0479503	−	0.178953i
$503$			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
$507$	10.4613	+	7.71756i	0.464603	+	0.342749i
$508$	4.67355	−	8.09482i	0.207355	−	0.359150i
$509$	28.1581	+	7.54493i	1.24808	+	0.334423i	0.821596	−	0.570070i	$-0.193084\pi$
$509$	28.1581	+	7.54493i	1.24808	+	0.334423i	0.426488	+	0.904493i	$0.359751\pi$
$510$		−	5.34067i		−	0.236489i
$511$	5.18208	+	23.1276i	0.229242	+	1.02310i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.54908	+	5.78125i	−0.0683936	+	0.255249i
$514$	16.5235	−	4.42746i	0.728820	−	0.195287i
$515$	3.35424	+	12.5182i	0.147806	+	0.551618i
$516$	−1.54874	+	0.894166i	−0.0681795	+	0.0393634i
$517$	−8.07286			−0.355044
$518$	3.13649	+	1.98822i	0.137809	+	0.0873574i
$519$			19.5871i			0.859780i
$520$	−1.71219	−	3.39081i	−0.0750843	−	0.148697i
$521$	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	$0.548850\pi$
$522$	−3.02060	+	0.809368i	−0.132208	+	0.0354251i
$523$	−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
$525$	9.11849	−	4.77299i	0.397963	−	0.208310i
$526$	−22.2456	−	22.2456i	−0.969953	−	0.969953i
$527$	19.2190	+	5.14973i	0.837194	+	0.224326i
$528$	1.13497	−	0.304114i	0.0493932	−	0.0132349i
$529$	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
$535$	−0.262566	−	0.979910i	−0.0113517	−	0.0423652i
$536$	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
$539$	−1.46483	−	8.09355i	−0.0630949	−	0.348614i
$540$	0.744962	−	0.744962i	0.0320580	−	0.0320580i
$541$	1.93821	+	0.519341i	0.0833300	+	0.0223282i	0.300243	−	0.953863i	$-0.402932\pi$
$541$	1.93821	+	0.519341i	0.0833300	+	0.0223282i	−0.216913	+	0.976191i	$0.569599\pi$
$542$	6.79084	+	3.92069i	0.291692	+	0.168408i
$543$	13.2245	+	7.63515i	0.567516	+	0.327656i
$544$	1.31203	−	4.89655i	0.0562527	−	0.209938i
$545$	5.57679			0.238883
$546$	7.36920	−	6.05763i	0.315373	−	0.259242i
$547$	−22.4682			−0.960673			−0.480336	−	0.877084i	$-0.659485\pi$
$547$	−22.4682			−0.960673			−0.480336	+	0.877084i	$0.659485\pi$
$548$	0.601316	−	2.24414i	0.0256869	−	0.0958650i
$549$	−9.72877	−	5.61691i	−0.415214	−	0.239724i
$550$	3.95847	+	2.28542i	0.168790	+	0.0974508i
$551$	−18.0789	−	4.84422i	−0.770186	−	0.206371i
$552$	4.56151	−	4.56151i	0.194151	−	0.194151i
$553$	−14.7536	+	7.72263i	−0.627386	+	0.328400i
$554$	−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
$557$	−7.09929	−	26.4949i	−0.300807	−	1.12263i	−0.936495	−	0.350680i	$-0.885950\pi$
$557$	−7.09929	−	26.4949i	−0.300807	−	1.12263i	0.635689	−	0.771946i	$-0.280716\pi$
$558$	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	$-0.573282\pi$
$563$	17.2993	−	29.9633i	0.729079	−	1.26280i	0.957273	−	0.289187i	$-0.0933849\pi$
$564$	−6.63638	+	1.77821i	−0.279442	+	0.0748762i
$565$	5.88596	+	1.57714i	0.247624	+	0.0663507i
$566$	−20.1185	−	20.1185i	−0.845643	−	0.845643i
$567$	2.23461	+	1.41652i	0.0938447	+	0.0594882i
$568$	6.53563			0.274229
$569$	16.5652	−	9.56394i	0.694450	−	0.400941i	−0.110827	−	0.993840i	$-0.535350\pi$
$569$	16.5652	−	9.56394i	0.694450	−	0.400941i	0.805277	+	0.592899i	$0.202017\pi$
$570$	6.09075	−	1.63201i	0.255114	−	0.0683575i
$571$	25.1326	+	14.5103i	1.05177	+	0.607239i	0.923144	−	0.384455i	$-0.125610\pi$
$571$	25.1326	+	14.5103i	1.05177	+	0.607239i	0.128625	+	0.991693i	$0.458944\pi$
$572$	4.02440	+	1.32382i	0.168269	+	0.0553517i
$573$			26.6536i			1.11347i
$574$	−6.82673	+	3.57339i	−0.284942	+	0.149150i
$575$	25.0946			1.04652
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	0.918717	+	3.42870i	0.0382467	+	0.142739i	0.982409	−	0.186742i	$-0.0597929\pi$
$577$	0.918717	+	3.42870i	0.0382467	+	0.142739i	−0.944162	+	0.329481i	$0.893126\pi$
$578$	8.40127	−	2.25111i	0.349447	−	0.0936339i
$579$	−1.53842	+	5.74146i	−0.0639346	+	0.238607i
$580$	2.32961	+	2.32961i	0.0967319	+	0.0967319i
$581$	−24.8511	−	26.9975i	−1.03100	−	1.12005i
$582$		−	2.25733i		−	0.0935692i
$583$	−1.00651	−	0.269694i	−0.0416855	−	0.0111696i
$584$	−4.47907	+	7.75798i	−0.185345	+	0.321027i
$585$	3.71842	−	0.776239i	0.153738	−	0.0320935i
$586$	5.65560	−	3.26526i	0.233631	−	0.134887i
$587$	8.10224	−	8.10224i	0.334415	−	0.334415i	−0.519845	−	0.854260i	$-0.674010\pi$
$587$	8.10224	−	8.10224i	0.334415	−	0.334415i	0.854260	+	0.519845i	$0.174010\pi$
$588$	−2.98695	−	6.33073i	−0.123180	−	0.261075i
$589$			23.4920i			0.967970i
$590$	−1.86598	+	6.96392i	−0.0768210	+	0.286700i
$591$	−6.83488	−	25.5081i	−0.281149	−	1.04926i
$592$	0.363278	+	1.35577i	0.0149306	+	0.0557218i
$593$	3.40618	−	12.7120i	0.139875	−	0.522020i	−0.860055	−	0.510201i	$-0.829571\pi$
$593$	3.40618	−	12.7120i	0.139875	−	0.522020i	0.999930	−	0.0118192i	$-0.00376226\pi$
$594$			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
$598$	22.7684	−	4.75303i	0.931070	−	0.194366i
$599$	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	$0.133826\pi$
$600$	3.75751	+	1.00682i	0.153400	+	0.0411034i
$601$			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
$604$	−1.57989	+	5.89624i	−0.0642849	+	0.239914i
$605$	−9.78901	+	2.62296i	−0.397980	+	0.106638i
$606$	0.901648	+	3.36500i	0.0366269	+	0.136694i
$607$	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
$609$	−4.42968	+	6.98797i	−0.179500	+	0.283167i
$610$			11.8352i			0.479194i
$611$	−23.5314	−	7.74063i	−0.951980	−	0.313152i
$612$	4.39013	+	2.53464i	0.177460	+	0.102457i
$613$	9.73830	−	2.60937i	0.393326	−	0.105391i	−0.0567348	−	0.998389i	$-0.518069\pi$
$613$	9.73830	−	2.60937i	0.393326	−	0.105391i	0.450061	+	0.892998i	$0.351402\pi$
$614$	−4.34240	+	2.50709i	−0.175245	+	0.101178i
$615$	−3.06828			−0.123725
$616$	1.66442	−	2.62568i	0.0670613	−	0.105792i
$617$	−27.0273	−	27.0273i	−1.08808	−	1.08808i	−0.995726	−	0.0923529i	$-0.970561\pi$
$617$	−27.0273	−	27.0273i	−1.08808	−	1.08808i	−0.0923529	−	0.995726i	$-0.529439\pi$
$618$	−11.8821	−	3.18380i	−0.477968	−	0.128071i
$619$	6.57252	−	1.76110i	0.264172	−	0.0707847i	−0.124302	−	0.992244i	$-0.539669\pi$
$619$	6.57252	−	1.76110i	0.264172	−	0.0707847i	0.388474	+	0.921460i	$0.373002\pi$
$620$	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
$626$	−2.53597	−	9.46438i	−0.101358	−	0.378273i
$627$	−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
$630$	0.115295	−	2.78501i	0.00459346	−	0.110957i
$631$	11.0014	−	11.0014i	0.437958	−	0.437958i	−0.453366	−	0.891324i	$-0.649777\pi$
$631$	11.0014	−	11.0014i	0.437958	−	0.437958i	0.891324	+	0.453366i	$0.149777\pi$
$632$	−6.07960	−	1.62903i	−0.241834	−	0.0647991i
$633$	−17.7579	−	10.2525i	−0.705814	−	0.407502i
$634$	−24.8434	−	14.3433i	−0.986656	−	0.569646i
$635$	2.54872	−	9.51195i	0.101143	−	0.377470i
$636$	−0.886819			−0.0351647
$637$	3.49065	−	24.9963i	0.138305	−	0.990390i
$638$	−3.67443			−0.145472
$639$	−1.69155	+	6.31294i	−0.0669165	+	0.249736i
$640$	−0.912388	−	0.526768i	−0.0360653	−	0.0208223i
$641$	19.3404	+	11.1662i	0.763901	+	0.441039i	0.830695	−	0.556728i	$-0.187944\pi$
$641$	19.3404	+	11.1662i	0.763901	+	0.441039i	−0.0667935	+	0.997767i	$0.521277\pi$
$642$	0.930116	+	0.249224i	0.0367088	+	0.00983608i
$643$	−11.0313	+	11.0313i	−0.435031	+	0.435031i	−0.890336	−	0.455305i	$-0.849530\pi$
$643$	−11.0313	+	11.0313i	−0.435031	+	0.435031i	0.455305	+	0.890336i	$0.349530\pi$
$644$	0.705969	−	17.0530i	0.0278191	−	0.671983i
$645$	−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	$0.345170\pi$
$647$	−13.5282	+	23.4316i	−0.531850	+	0.921192i	−0.999309	+	0.0371765i	$0.988164\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	−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
$655$	−4.50412	+	1.20688i	−0.175991	+	0.0471565i
$656$	−2.81313	−	0.753777i	−0.109834	−	0.0294301i
$657$	−6.33436	−	6.33436i	−0.247127	−	0.247127i
$658$	−9.73217	+	15.3528i	−0.379399	+	0.598516i
$659$	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
$661$	12.4840	−	3.34507i	0.485570	−	0.130108i	−0.00772513	−	0.999970i	$-0.502459\pi$
$661$	12.4840	−	3.34507i	0.485570	−	0.130108i	0.493295	+	0.869862i	$0.335792\pi$
$662$	10.7175	+	6.18774i	0.416547	+	0.240493i
$663$	8.23851	+	16.3155i	0.319957	+	0.633642i
$664$		−	13.8690i		−	0.538221i
$665$	8.93201	−	14.0906i	0.346369	−	0.546409i
$666$	−1.40360			−0.0543883
$667$	−17.4705	+	10.0866i	−0.676459	+	0.390554i
$668$	−0.663952	−	2.47790i	−0.0256891	−	0.0958729i
$669$	−9.36807	+	2.51017i	−0.362190	+	0.0970486i
$670$	3.24025	−	12.0928i	0.125182	−	0.467185i
$671$	−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	$-0.981494\pi$
$673$		−	3.01477i		−	0.116211i	0.998310	−	0.0581055i	$-0.0185060\pi$
$674$	−13.6145	−	3.64800i	−0.524411	−	0.140516i
$675$	−1.94503	+	3.36889i	−0.0748643	+	0.129669i
$676$	10.4613	+	7.71756i	0.402358	+	0.296829i
$677$	−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
$681$	−3.94730	+	14.7315i	−0.151261	+	0.564514i
$682$	1.19365	+	4.45477i	0.0457073	+	0.170582i
$683$	9.56199	+	35.6858i	0.365880	+	1.36548i	0.866225	+	0.499655i	$0.166540\pi$
$683$	9.56199	+	35.6858i	0.365880	+	1.36548i	−0.500345	+	0.865826i	$0.666794\pi$
$684$	−1.54908	+	5.78125i	−0.0592306	+	0.221052i
$685$		−	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
$689$	−2.67527	−	1.75122i	−0.101920	−	0.0667161i
$690$	3.39815	−	5.88578i	0.129366	−	0.224068i
$691$	−27.9303	−	7.48390i	−1.06252	−	0.284701i	−0.315103	−	0.949058i	$-0.602039\pi$
$691$	−27.9303	−	7.48390i	−1.06252	−	0.284701i	−0.747416	+	0.664357i	$0.768706\pi$
$692$			19.5871i			0.744591i
$693$	2.10543	+	2.28728i	0.0799786	+	0.0868865i
$694$	−22.9941	−	22.9941i	−0.872844	−	0.872844i
$695$	−6.12357	+	22.8535i	−0.232280	+	0.866882i
$696$	−3.02060	+	0.809368i	−0.114496	+	0.0306790i
$697$	−3.82111	−	14.2606i	−0.144735	−	0.540158i
$698$	−4.53298	+	2.61711i	−0.171576	+	0.0990593i
$699$	9.70675			0.367143
$700$	9.11849	−	4.77299i	0.344646	−	0.180402i
$701$			40.8735i			1.54377i	0.635762	+	0.771885i	$0.280686\pi$
$701$			40.8735i			1.54377i	−0.635762	+	0.771885i	$0.719314\pi$
$702$	−1.12665	+	3.42501i	−0.0425227	+	0.129268i
$703$	−7.27530	−	4.20040i	−0.274393	−	0.158421i
$704$	1.13497	−	0.304114i	0.0427757	−	0.0114617i
$705$	−6.26855	+	3.61915i	−0.236087	+	0.136305i
$706$	−17.5504			−0.660516
$707$	7.78471	+	4.93472i	0.292774	+	0.185589i
$708$	−4.83889	−	4.83889i	−0.181857	−	0.181857i
$709$	30.4853	+	8.16850i	1.14490	+	0.306775i	0.780919	−	0.624633i	$-0.214751\pi$
$709$	30.4853	+	8.16850i	1.14490	+	0.306775i	0.363979	+	0.931407i	$0.381418\pi$
$710$	6.65090	−	1.78210i	0.249604	−	0.0668812i
$711$	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
$717$	4.69662	+	17.5280i	0.175399	+	0.654596i
$718$	9.16965	−	15.8823i	0.342208	−	0.592722i
$719$	−8.82429	−	15.2841i	−0.329091	−	0.570002i	0.653241	−	0.757150i	$-0.273409\pi$
$719$	−8.82429	−	15.2841i	−0.329091	−	0.570002i	−0.982332	+	0.187148i	$0.940075\pi$
$720$	0.744962	−	0.744962i	0.0277631	−	0.0277631i
$721$	−28.8347	+	15.0933i	−1.07386	+	0.562102i
$722$	−11.8953	+	11.8953i	−0.442698	+	0.442698i
$723$	−21.2033	−	5.68140i	−0.788559	−	0.211294i
$724$	13.2245	+	7.63515i	0.491484	+	0.283758i
$725$	−10.5351	−	6.08242i	−0.391262	−	0.225895i
$726$	2.48967	−	9.29159i	0.0924005	−	0.344843i
$727$	−45.8265			−1.69961			−0.849805	−	0.527098i	$-0.823280\pi$
$727$	−45.8265			−1.69961			−0.849805	+	0.527098i	$0.823280\pi$
$728$	7.36920	−	6.05763i	0.273121	−	0.224511i
$729$	−1.00000			−0.0370370
$730$	−2.44266	+	9.11613i	−0.0904069	+	0.337403i
$731$	−7.85100	−	4.53278i	−0.290380	−	0.167651i
$732$	−9.72877	−	5.61691i	−0.359586	−	0.207607i
$733$	−10.6483	−	2.85321i	−0.393305	−	0.105386i	0.0567460	−	0.998389i	$-0.481927\pi$
$733$	−10.6483	−	2.85321i	−0.393305	−	0.105386i	−0.450051	+	0.893003i	$0.648594\pi$
$734$	−13.3003	+	13.3003i	−0.490923	+	0.490923i
$735$	−4.76586	−	5.62791i	−0.175792	−	0.207589i
$736$	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
$739$	−10.9818	−	40.9848i	−0.403974	−	1.50765i	−0.805941	−	0.591996i	$-0.798340\pi$
$739$	−10.9818	−	40.9848i	−0.403974	−	1.50765i	0.401967	−	0.915654i	$-0.368327\pi$
$740$	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	0.150541	−	0.988604i	$-0.451898\pi$
$743$	−22.8439	−	22.8439i	−0.838063	−	0.838063i	−0.988604	+	0.150541i	$0.951898\pi$
$744$	1.96251	+	3.39916i	0.0719490	+	0.124619i
$745$	−6.24004	+	10.8081i	−0.228617	+	0.395977i
$746$	9.04643	−	2.42398i	0.331213	−	0.0887483i
$747$	13.3964	+	3.58956i	0.490149	+	0.131335i
$748$	4.21184	+	4.21184i	0.154000	+	0.154000i
$749$	2.25714	−	1.18148i	0.0824743	−	0.0431704i
$750$	9.36599			0.341998
$751$	−26.0921	+	15.0643i	−0.952115	+	0.549704i	−0.893737	−	0.448591i	$-0.851926\pi$
$751$	−26.0921	+	15.0643i	−0.952115	+	0.549704i	−0.0583777	+	0.998295i	$0.518593\pi$
$752$	−6.63638	+	1.77821i	−0.242004	+	0.0648447i
$753$	3.59483	+	2.07547i	0.131003	+	0.0756344i
$754$	−10.7105	−	3.52321i	−0.390055	−	0.128308i
$755$			6.43102i			0.234049i
$756$	2.23461	+	1.41652i	0.0812719	+	0.0515183i
$757$	−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
$759$	1.96183	+	7.32163i	0.0712098	+	0.265758i
$760$	6.09075	−	1.63201i	0.220935	−	0.0591993i
$761$	1.04451	−	3.89815i	0.0378633	−	0.141308i	−0.944407	−	0.328780i	$-0.893363\pi$
$761$	1.04451	−	3.89815i	0.0378633	−	0.141308i	0.982270	+	0.187472i	$0.0600293\pi$
$762$	6.60939	+	6.60939i	0.239433	+	0.239433i
$763$	3.06212	+	13.6662i	0.110856	+	0.494749i
$764$			26.6536i			0.964292i
$765$	5.15869	+	1.38227i	0.186513	+	0.0499759i
$766$	7.21610	−	12.4987i	0.260728	−	0.451595i
$767$	−5.04205	−	24.1529i	−0.182058	−	0.872112i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−6.16074	+	6.16074i	−0.222162	+	0.222162i	−0.809408	−	0.587246i	$-0.800212\pi$
$769$	−6.16074	+	6.16074i	−0.222162	+	0.222162i	0.587246	+	0.809408i	$0.300212\pi$
$770$	0.977815	−	3.12583i	0.0352380	−	0.112647i
$771$			17.1064i			0.616071i
$772$	−1.53842	+	5.74146i	−0.0553689	+	0.206640i
$773$	11.8750	+	44.3180i	0.427113	+	1.59401i	0.759264	+	0.650783i	$0.225559\pi$
$773$	11.8750	+	44.3180i	0.427113	+	1.59401i	−0.332150	+	0.943226i	$0.607774\pi$
$774$	−0.462854	−	1.72740i	−0.0166369	−	0.0620899i
$775$	−3.95179	+	14.7483i	−0.141953	+	0.529774i
$776$		−	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
$780$	3.71842	−	0.776239i	0.133141	−	0.0277938i
$781$	−3.83970	+	6.65056i	−0.137395	+	0.237976i
$782$	31.5874	+	8.46383i	1.12956	+	0.302666i
$783$		−	3.12716i		−	0.111756i
$784$	−2.98695	−	6.33073i	−0.106677	−	0.226097i
$785$	−16.2642	−	16.2642i	−0.580494	−	0.580494i
$786$	1.14555	−	4.27524i	0.0408604	−	0.152493i
$787$	33.2511	−	8.90961i	1.18527	−	0.317593i	0.388258	−	0.921551i	$-0.373077\pi$
$787$	33.2511	−	8.90961i	1.18527	−	0.317593i	0.797017	+	0.603957i	$0.206410\pi$
$788$	−6.83488	−	25.5081i	−0.243482	−	0.908688i
$789$	27.2451	−	15.7300i	0.969953	−	0.560002i
$790$	−6.63102			−0.235921
$791$	−0.632974	+	15.2898i	−0.0225060	+	0.543642i
$792$			1.17501i			0.0417520i
$793$	−18.2570	−	36.1561i	−0.648325	−	1.28394i
$794$	1.56044	+	0.900923i	0.0553781	+	0.0319726i
$795$	−0.902460	+	0.241813i	−0.0320070	+	0.00857624i
$796$	17.0030	−	9.81669i	0.602656	−	0.347943i
$797$	22.0319			0.780409			0.390204	−	0.920728i	$-0.372404\pi$
$797$	22.0319			0.780409			0.390204	+	0.920728i	$0.372404\pi$
$798$	7.34364	+	14.0296i	0.259962	+	0.496641i
$799$	−24.6274	−	24.6274i	−0.871255	−	0.871255i
$800$	3.75751	+	1.00682i	0.132848	+	0.0355966i
$801$	−7.08351	+	1.89802i	−0.250284	+	0.0670633i
$802$	−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
$808$	0.901648	+	3.36500i	0.0317199	+	0.118380i
$809$	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	$-0.953882\pi$
$811$	−24.0681	+	24.0681i	−0.845144	+	0.845144i	0.144379	+	0.989523i	$0.453882\pi$
$812$	−4.42968	+	6.98797i	−0.155451	+	0.245230i
$813$	−5.54470	+	5.54470i	−0.194461	+	0.194461i
$814$	−1.59304	−	0.426853i	−0.0558360	−	0.0149612i
$815$	−20.3482	−	11.7481i	−0.712768	−	0.411517i
$816$	4.39013	+	2.53464i	0.153685	+	0.0887302i
$817$	2.77027	−	10.3388i	0.0969195	−	0.361709i
$818$	−25.2620			−0.883265
$819$	3.94393	+	8.68593i	0.137812	+	0.303511i
$820$	−3.06828			−0.107149
$821$	−9.74742	+	36.3779i	−0.340187	+	1.26960i	0.557948	+	0.829876i	$0.311589\pi$
$821$	−9.74742	+	36.3779i	−0.340187	+	1.26960i	−0.898135	+	0.439720i	$0.855078\pi$
$822$	2.01204	+	1.16165i	0.0701780	+	0.0405173i
$823$	−25.5124	−	14.7296i	−0.889305	−	0.513441i	−0.0155900	−	0.999878i	$-0.504963\pi$
$823$	−25.5124	−	14.7296i	−0.889305	−	0.513441i	−0.873715	+	0.486438i	$0.838296\pi$
$824$	−11.8821	−	3.18380i	−0.413932	−	0.110913i
$825$	−3.23208	+	3.23208i	−0.112526	+	0.112526i
$826$	−18.0900	−	0.748897i	−0.629431	−	0.0260575i
$827$	7.78910	−	7.78910i	0.270854	−	0.270854i	−0.558590	−	0.829444i	$-0.688658\pi$
$827$	7.78910	−	7.78910i	0.270854	−	0.270854i	0.829444	+	0.558590i	$0.188658\pi$
$828$	3.22548	+	5.58669i	0.112093	+	0.194151i
$829$	−9.99718	+	17.3156i	−0.347216	+	0.601396i	−0.985754	−	0.168194i	$-0.946206\pi$
$829$	−9.99718	+	17.3156i	−0.347216	+	0.601396i	0.638537	+	0.769591i	$0.279540\pi$
$830$	−3.78172	−	14.1136i	−0.131266	−	0.489890i
$831$	−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
$837$	−3.79127	+	1.01587i	−0.131046	+	0.0351136i
$838$	1.15275	+	0.308877i	0.0398210	+	0.0106700i
$839$	6.26481	+	6.26481i	0.216285	+	0.216285i	0.806931	−	0.590646i	$-0.201127\pi$
$839$	6.26481	+	6.26481i	0.216285	+	0.216285i	−0.590646	+	0.806931i	$0.701127\pi$
$840$	0.115295	−	2.78501i	0.00397806	−	0.0960918i
$841$	−19.2209			−0.662789
$842$	20.7236	−	11.9648i	0.714182	−	0.412333i
$843$	5.71023	−	1.53005i	0.196671	−	0.0526977i
$844$	−17.7579	−	10.2525i	−0.611253	−	0.352907i
$845$	12.7502	+	5.00114i	0.438621	+	0.172044i
$846$		−	6.87048i		−	0.236212i
$847$	−11.8027	−	22.5482i	−0.405544	−	0.774766i
$848$	−0.886819			−0.0304535
$849$	24.6400	−	14.2259i	0.845643	−	0.488232i
$850$	5.10387	+	19.0479i	0.175061	+	0.653338i
$851$	−8.74602	+	2.34349i	−0.299810	+	0.0803337i
$852$	−1.69155	+	6.31294i	−0.0579514	+	0.216278i
$853$	19.1027	+	19.1027i	0.654063	+	0.654063i	0.953969	−	0.299906i	$-0.0969552\pi$
$853$	19.1027	+	19.1027i	0.654063	+	0.654063i	−0.299906	+	0.953969i	$0.596955\pi$
$854$	−29.0027	+	6.49851i	−0.992454	+	0.222374i
$855$			6.30561i			0.215647i
$856$	0.930116	+	0.249224i	0.0317907	+	0.00851830i
$857$	20.3680	−	35.2784i	0.695757	−	1.20509i	−0.274167	−	0.961682i	$-0.588402\pi$
$857$	20.3680	−	35.2784i	0.695757	−	1.20509i	0.969925	−	0.243405i	$-0.0782645\pi$
$858$	−2.32030	+	3.54464i	−0.0792139	+	0.121012i
$859$	−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
$863$	−8.97921	+	33.5109i	−0.305656	+	1.14072i	0.626723	+	0.779242i	$0.284396\pi$
$863$	−8.97921	+	33.5109i	−0.305656	+	1.14072i	−0.932379	+	0.361481i	$0.882271\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	5.34092	+	19.9326i	0.181597	+	0.677728i
$866$	0.875828	−	3.26863i	0.0297618	−	0.111073i
$867$			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
$871$	8.75548	+	41.9414i	0.296668	+	1.42113i
$872$	−2.64670	+	4.58422i	−0.0896287	+	0.155241i
$873$	2.18041	+	0.584239i	0.0737957	+	0.0197735i
$874$			38.6102i			1.30601i
$875$	18.2319	−	16.7824i	0.616352	−	0.567349i
$876$	−6.33436	−	6.33436i	−0.214018	−	0.214018i
$877$	−10.2848	+	38.3833i	−0.347292	+	1.29611i	0.542619	+	0.839979i	$0.317433\pi$
$877$	−10.2848	+	38.3833i	−0.347292	+	1.29611i	−0.889911	+	0.456134i	$0.849234\pi$
$878$	−34.2134	+	9.16744i	−1.15464	+	0.309386i
$879$	1.69023	+	6.30801i	0.0570099	+	0.212764i
$880$	1.07206	−	0.618955i	0.0361392	−	0.0208650i
$881$	−19.0788			−0.642781			−0.321391	−	0.946947i	$-0.604150\pi$
$881$	−19.0788			−0.642781			−0.321391	+	0.946947i	$0.604150\pi$
$882$	6.88809	−	1.24666i	0.231934	−	0.0419773i
$883$			20.8870i			0.702902i	0.936206	+	0.351451i	$0.114312\pi$
$883$			20.8870i			0.702902i	−0.936206	+	0.351451i	$0.885688\pi$
$884$	8.23851	+	16.3155i	0.277091	+	0.548750i
$885$	−6.24368	−	3.60479i	−0.209879	−	0.121174i
$886$	−17.4349	+	4.67167i	−0.585737	+	0.156948i
$887$	−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
$889$	24.7089	+	1.02291i	0.828711	+	0.0343074i
$890$	5.46310	+	5.46310i	0.183123	+	0.183123i
$891$	−1.13497	−	0.304114i	−0.0380229	−	0.0101882i
$892$	−9.36807	+	2.51017i	−0.313666	+	0.0840466i
$893$	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
$899$	−3.17678	−	11.8559i	−0.105952	−	0.395417i
$900$	−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
$903$	−3.99622	−	2.53320i	−0.132986	−	0.0842997i
$904$	−4.08987	+	4.08987i	−0.136027	+	0.136027i
$905$	15.5396	+	4.16383i	0.516554	+	0.138410i
$906$	−5.28642	−	3.05212i	−0.175630	−	0.101400i
$907$	−20.0127	−	11.5543i	−0.664509	−	0.383655i	0.129484	−	0.991582i	$-0.458668\pi$
$907$	−20.0127	−	11.5543i	−0.664509	−	0.383655i	−0.793993	+	0.607927i	$0.792001\pi$
$908$	−3.94730	+	14.7315i	−0.130996	+	0.488883i
$909$	−3.48370			−0.115547
$910$	5.84741	−	8.17386i	0.193840	−	0.270961i
$911$	−35.1881			−1.16583			−0.582917	−	0.812532i	$-0.698089\pi$
$911$	−35.1881			−1.16583			−0.582917	+	0.812532i	$0.698089\pi$
$912$	−1.54908	+	5.78125i	−0.0512952	+	0.191436i
$913$	14.1129	+	8.14807i	0.467068	+	0.269662i
$914$	−4.26496	−	2.46238i	−0.141072	−	0.0814482i
$915$	−11.4319	−	3.06318i	−0.377928	−	0.101266i
$916$	3.34408	−	3.34408i	0.110491	−	0.110491i
$917$	−5.43064	−	10.3749i	−0.179335	−	0.342609i
$918$	−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
$921$	−1.29776	−	4.84332i	−0.0427627	−	0.159593i
$922$	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
$928$	−3.02060	+	0.809368i	−0.0991561	+	0.0265688i
$929$	40.8860	+	10.9554i	1.34143	+	0.359434i	0.856964	−	0.515377i	$-0.172348\pi$
$929$	40.8860	+	10.9554i	1.34143	+	0.359434i	0.484464	+	0.874811i	$0.339015\pi$
$930$	2.92399	+	2.92399i	0.0958813	+	0.0958813i
$931$	39.4340	+	14.1514i	1.29240	+	0.463794i
$932$	9.70675			0.317955
$933$	0.302124	−	0.174431i	0.00989109	−	0.00571063i
$934$	−33.0124	+	8.84565i	−1.08020	+	0.289438i
$935$	5.43458	+	3.13766i	0.177730	+	0.102612i
$936$	−1.12665	+	3.42501i	−0.0368257	+	0.111950i
$937$		−	16.6317i		−	0.543332i	−0.962392	−	0.271666i	$-0.912425\pi$
$937$		−	16.6317i		−	0.543332i	0.962392	−	0.271666i	$-0.0875747\pi$
$938$	31.4131	+	1.30045i	1.02567	+	0.0424613i
$939$	9.79825			0.319754
$940$	−6.26855	+	3.61915i	−0.204457	+	0.118044i
$941$	2.21830	+	8.27880i	0.0723145	+	0.269881i	0.992611	−	0.121340i	$-0.0387193\pi$
$941$	2.21830	+	8.27880i	0.0723145	+	0.269881i	−0.920296	+	0.391222i	$0.872053\pi$
$942$	21.0883	−	5.65060i	0.687095	−	0.184107i
$943$	4.86258	−	18.1474i	0.158347	−	0.590961i
$944$	−4.83889	−	4.83889i	−0.157493	−	0.157493i
$945$	2.66027	+	0.832179i	0.0865386	+	0.0270708i
$946$		−	2.10130i		−	0.0683191i
$947$	54.3838	+	14.5721i	1.76724	+	0.473530i	0.988164	−	0.153403i	$-0.0490231\pi$
$947$	54.3838	+	14.5721i	1.76724	+	0.473530i	0.779074	+	0.626932i	$0.215690\pi$
$948$	3.14704	−	5.45082i	0.102211	−	0.177035i
$949$	−6.60031	−	31.6175i	−0.214255	−	1.02635i
$950$	−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	$-0.763117\pi$
$953$		−	41.8221i		−	1.35475i	0.735638	−	0.677375i	$-0.236883\pi$
$954$	0.229526	−	0.856602i	0.00743117	−	0.0277335i
$955$	7.26776	+	27.1236i	0.235179	+	0.877700i
$956$	4.69662	+	17.5280i	0.151900	+	0.566897i
$957$	0.951012	−	3.54923i	0.0307419	−	0.114730i
$958$		−	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
$962$	−4.23423	−	2.77171i	−0.136517	−	0.0893634i
$963$	−0.481464	+	0.833919i	−0.0155149	+	0.0268727i
$964$	−21.2033	−	5.68140i	−0.682912	−	0.182986i
$965$			6.26221i			0.201588i
$966$	16.2892	+	5.09556i	0.524097	+	0.163947i
$967$	−36.8456	−	36.8456i	−1.18487	−	1.18487i	−0.978466	−	0.206408i	$-0.933823\pi$
$967$	−36.8456	−	36.8456i	−1.18487	−	1.18487i	−0.206408	−	0.978466i	$-0.566177\pi$
$968$	2.48967	−	9.29159i	0.0800212	−	0.298643i
$969$	−29.3068	+	7.85273i	−0.941470	+	0.252266i
$970$	−0.615516	−	2.29714i	−0.0197630	−	0.0737567i
$971$	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
$973$	−59.3658	−	2.45765i	−1.90318	−	0.0787888i
$974$			17.0357i			0.545859i
$975$	−12.5202	+	6.32206i	−0.400967	+	0.202468i
$976$	−9.72877	−	5.61691i	−0.311410	−	0.179793i
$977$	12.3916	−	3.32031i	0.396441	−	0.106226i	−0.0550902	−	0.998481i	$-0.517545\pi$
$977$	12.3916	−	3.32031i	0.396441	−	0.106226i	0.451531	+	0.892255i	$0.350878\pi$
$978$	19.3142	−	11.1511i	0.617601	−	0.356572i
$979$	−8.61678			−0.275393
$980$	−4.76586	−	5.62791i	−0.152240	−	0.179777i
$981$	−3.74300	−	3.74300i	−0.119505	−	0.119505i
$982$	13.6695	+	3.66273i	0.436211	+	0.116882i
$983$	−6.31014	+	1.69080i	−0.201262	+	0.0539281i	−0.358042	−	0.933706i	$-0.616555\pi$
$983$	−6.31014	+	1.69080i	−0.201262	+	0.0539281i	0.156779	+	0.987634i	$0.449889\pi$
$984$	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
$990$	0.320395	+	1.19573i	0.0101828	+	0.0380028i
$991$	−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
$994$	8.01902	+	15.3198i	0.254348	+	0.485915i
$995$	14.6261	−	14.6261i	0.463679	−	0.463679i
$996$	13.3964	+	3.58956i	0.424481	+	0.113739i
$997$	−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
$999$	0.363278	−	1.35577i	0.0114936	−	0.0428947i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.73.2	✓	40	1.1	even	1	trivial
546.2.bz.a.187.2	yes	40	91.5	even	12	inner
546.2.bz.b.31.7	yes	40	13.5	odd	4
546.2.bz.b.229.7	yes	40	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.01764 - 0.272675i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.109436 - 2.64349i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.01764 - 0.272675i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.109436 - 2.64349i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.526768 - 0.912388i) q^{10} +(0.304114 + 1.13497i) 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} +(-0.965926 + 0.258819i) q^{18} +(-5.78125 - 1.54908i) q^{19} +(0.744962 + 0.744962i) q^{20} +(-1.41652 + 2.23461i) q^{21} -1.17501 q^{22} +(-5.58669 + 3.22548i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(-3.36889 - 1.94503i) q^{25} +(-3.42501 - 1.12665i) q^{26} -1.00000i q^{27} +(-1.41652 + 2.23461i) q^{28} +3.12716 q^{29} +(-0.912388 + 0.526768i) q^{30} +(-1.01587 - 3.79127i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.304114 - 1.13497i) q^{33} +(-3.58452 - 3.58452i) q^{34} +(-0.832179 + 2.66027i) q^{35} -1.00000i q^{36} +(1.35577 + 0.363278i) q^{37} +(2.99260 - 5.18333i) q^{38} +(1.97472 - 3.01670i) q^{39} +(-0.912388 + 0.526768i) q^{40} +(-2.05936 + 2.05936i) q^{41} +(-1.79184 - 1.94661i) q^{42} +1.78833i q^{43} +(0.304114 - 1.13497i) q^{44} +(-0.272675 - 1.01764i) q^{45} +(-1.66963 - 6.23115i) q^{46} +(-1.77821 + 6.63638i) q^{47} -1.00000i q^{48} +(-6.97605 - 0.578587i) q^{49} +(2.75069 - 2.75069i) q^{50} +(4.39013 - 2.53464i) q^{51} +(1.97472 - 3.01670i) q^{52} +(-0.443410 + 0.768008i) q^{53} +(0.965926 + 0.258819i) q^{54} -1.23791i q^{55} +(-1.79184 - 1.94661i) q^{56} +(4.23217 + 4.23217i) q^{57} +(-0.809368 + 3.02060i) q^{58} +(-6.61005 + 1.77116i) q^{59} +(-0.272675 - 1.01764i) q^{60} +(-9.72877 + 5.61691i) q^{61} +3.92502 q^{62} +(2.34405 - 1.22697i) q^{63} -1.00000i q^{64} +(1.18697 - 3.60836i) q^{65} +(1.01758 + 0.587503i) q^{66} +(11.4783 - 3.07560i) q^{67} +(4.39013 - 2.53464i) q^{68} +6.45096 q^{69} +(-2.35424 - 1.49235i) q^{70} +(4.62139 + 4.62139i) q^{71} +(0.965926 + 0.258819i) q^{72} +(-8.65290 + 2.31854i) 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} +(-0.272675 - 1.01764i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.45619 - 2.52219i) q^{82} +(9.80685 - 9.80685i) q^{83} +(2.34405 - 1.22697i) q^{84} +(3.77642 - 3.77642i) q^{85} +(-1.72740 - 0.462854i) q^{86} +(-2.70820 - 1.56358i) q^{87} +(1.01758 + 0.587503i) q^{88} +(-1.89802 + 7.08351i) q^{89} +1.05354 q^{90} +(9.49420 + 0.927426i) q^{91} +6.45096 q^{92} +(-1.01587 + 3.79127i) q^{93} +(-5.95001 - 3.43524i) q^{94} +(5.46082 + 3.15280i) q^{95} +(0.965926 + 0.258819i) q^{96} +(1.59617 - 1.59617i) q^{97} +(2.36441 - 6.58860i) 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	\( 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * 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 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * 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 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * 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 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

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