LMFDB - Embedded newform 462.2.ba.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	462.19
Dual form			462.2.ba.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.716911 - 1.61021i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(1.87226 + 1.86939i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.716911 - 1.61021i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(1.87226 + 1.86939i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(0.881296 + 1.52645i) q^{10} +(3.30708 - 0.251417i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-4.51584 + 3.28095i) q^{13} +(-2.05741 - 1.66345i) q^{14} +(0.544671 - 1.67633i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.164901 - 1.56893i) q^{17} +(-0.207912 - 0.978148i) q^{18} +(8.01319 + 1.70326i) q^{19} +(-1.03603 - 1.42597i) q^{20} +(0.140496 + 2.64202i) q^{21} +(-3.26268 + 0.595724i) q^{22} +(1.59448 - 2.76172i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(1.26684 - 1.40697i) q^{25} +(4.14815 - 3.73501i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.22002 + 1.43928i) q^{28} +(3.68375 + 1.19692i) q^{29} +(-0.366464 + 1.72408i) q^{30} +(-2.22993 + 5.00850i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.62587 + 2.02603i) q^{33} +1.57757i q^{34} +(1.66786 - 4.35492i) q^{35} +(0.309017 + 0.951057i) q^{36} +(0.688318 + 0.764454i) q^{37} +(-8.14734 - 0.856320i) q^{38} +(-5.55130 - 0.583465i) q^{39} +(1.17940 + 1.30986i) q^{40} +(2.03783 + 6.27181i) q^{41} +(-0.415892 - 2.61286i) q^{42} -0.237804i q^{43} +(3.18254 - 0.933504i) q^{44} +(1.52645 - 0.881296i) q^{45} +(-1.29707 + 2.91326i) q^{46} +(0.287918 - 1.35455i) q^{47} +(0.951057 + 0.309017i) q^{48} +(0.0107455 + 6.99999i) q^{49} +(-1.11283 + 1.53168i) q^{50} +(1.17236 - 1.05560i) q^{51} +(-3.73501 + 4.14815i) q^{52} +(-6.91287 - 3.07781i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.77572 - 5.14485i) q^{55} +(-2.35830 - 1.19934i) q^{56} +(4.81526 + 6.62764i) q^{57} +(-3.78868 - 0.805309i) q^{58} +(1.40613 + 6.61530i) q^{59} +(0.184241 - 1.75294i) q^{60} +(4.88024 - 2.17282i) q^{61} +(1.69418 - 5.21415i) q^{62} +(-1.66345 + 2.05741i) q^{63} +(0.809017 - 0.587785i) q^{64} +(8.52046 + 4.91929i) q^{65} +(-2.82326 - 1.74045i) q^{66} +(-5.30356 - 9.18603i) q^{67} +(-0.164901 - 1.56893i) q^{68} +(3.03288 - 0.985443i) q^{69} +(-1.20351 + 4.50541i) q^{70} +(0.175328 + 0.127383i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(9.80345 - 2.08379i) q^{73} +(-0.764454 - 0.688318i) q^{74} +(1.88289 - 0.197900i) q^{75} +8.19221 q^{76} +(6.66173 + 5.71151i) q^{77} +5.58188 q^{78} +(1.57504 - 0.165543i) q^{79} +(-1.30986 - 1.17940i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-2.68225 - 6.02444i) q^{82} +(-8.61257 - 6.25740i) q^{83} +(0.686732 + 2.55507i) q^{84} +(-2.64452 + 0.859256i) q^{85} +(0.0248573 + 0.236502i) q^{86} +(1.93666 + 3.35439i) q^{87} +(-3.06753 + 1.26106i) q^{88} +(-6.84058 - 3.94941i) q^{89} +(-1.42597 + 1.03603i) q^{90} +(-14.5882 - 2.29907i) q^{91} +(0.985443 - 3.03288i) q^{92} +(-5.00850 + 2.22993i) q^{93} +(-0.144752 + 1.37722i) q^{94} +(-3.00215 - 14.1240i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-4.70842 - 6.48058i) q^{97} +(-0.742385 - 6.96052i) q^{98} +(0.595724 + 3.26268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.994522	+	0.104528i	−0.703233	+	0.0739128i
$2$	−0.994522	+	0.104528i	−0.703233	+	0.0739128i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$4$	0.978148	−	0.207912i	0.489074	−	0.103956i
$5$	−0.716911	−	1.61021i	−0.320612	−	0.720107i	0.679293	−	0.733867i	$-0.262287\pi$
$5$	−0.716911	−	1.61021i	−0.320612	−	0.720107i	−0.999905	+	0.0137600i	$0.995620\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	1.87226	+	1.86939i	0.707649	+	0.706564i
$7$	1.87226	+	1.86939i	0.707649	+	0.706564i
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	0.881296	+	1.52645i	0.278690	+	0.482706i
$11$	3.30708	−	0.251417i	0.997123	−	0.0758050i
$11$	3.30708	−	0.251417i	0.997123	−	0.0758050i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−4.51584	+	3.28095i	−1.25247	+	0.909971i	−0.998362	−	0.0572055i	$-0.981781\pi$
$13$	−4.51584	+	3.28095i	−1.25247	+	0.909971i	−0.254105	+	0.967177i	$0.581781\pi$
$14$	−2.05741	−	1.66345i	−0.549867	−	0.444575i
$15$	0.544671	−	1.67633i	0.140633	−	0.432825i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.164901	−	1.56893i	0.0399943	−	0.380520i	−0.956156	−	0.292858i	$-0.905394\pi$
$17$	0.164901	−	1.56893i	0.0399943	−	0.380520i	0.996150	−	0.0876624i	$-0.0279397\pi$
$18$	−0.207912	−	0.978148i	−0.0490053	−	0.230552i
$19$	8.01319	+	1.70326i	1.83835	+	0.390754i	0.990276	−	0.139119i	$-0.0444269\pi$
$19$	8.01319	+	1.70326i	1.83835	+	0.390754i	0.848077	+	0.529873i	$0.177760\pi$
$20$	−1.03603	−	1.42597i	−0.231662	−	0.318856i
$21$	0.140496	+	2.64202i	0.0306587	+	0.576536i
$22$	−3.26268	+	0.595724i	−0.695607	+	0.127009i
$23$	1.59448	−	2.76172i	0.332472	−	0.575859i	−0.650524	−	0.759486i	$-0.725451\pi$
$23$	1.59448	−	2.76172i	0.332472	−	0.575859i	0.982996	+	0.183627i	$0.0587839\pi$
$24$	−0.913545	−	0.406737i	−0.186477	−	0.0830248i
$25$	1.26684	−	1.40697i	0.253368	−	0.281394i
$26$	4.14815	−	3.73501i	0.813518	−	0.732495i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	2.22002	+	1.43928i	0.419544	+	0.271998i
$29$	3.68375	+	1.19692i	0.684055	+	0.222263i	0.630370	−	0.776295i	$-0.282903\pi$
$29$	3.68375	+	1.19692i	0.684055	+	0.222263i	0.0536851	+	0.998558i	$0.482903\pi$
$30$	−0.366464	+	1.72408i	−0.0669068	+	0.314772i
$31$	−2.22993	+	5.00850i	−0.400507	+	0.899553i	0.594898	+	0.803801i	$0.297192\pi$
$31$	−2.22993	+	5.00850i	−0.400507	+	0.899553i	−0.995405	+	0.0957521i	$0.969474\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.62587	+	2.02603i	0.457106	+	0.352687i
$34$			1.57757i			0.270551i
$35$	1.66786	−	4.35492i	0.281921	−	0.736117i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	0.688318	+	0.764454i	0.113159	+	0.125675i	0.797063	−	0.603896i	$-0.206386\pi$
$37$	0.688318	+	0.764454i	0.113159	+	0.125675i	−0.683904	+	0.729572i	$0.739719\pi$
$38$	−8.14734	−	0.856320i	−1.32167	−	0.138913i
$39$	−5.55130	−	0.583465i	−0.888920	−	0.0934292i
$40$	1.17940	+	1.30986i	0.186480	+	0.207107i
$41$	2.03783	+	6.27181i	0.318256	+	0.979492i	0.974393	+	0.224850i	$0.0721893\pi$
$41$	2.03783	+	6.27181i	0.318256	+	0.979492i	−0.656137	+	0.754642i	$0.727811\pi$
$42$	−0.415892	−	2.61286i	−0.0641736	−	0.403173i
$43$		−	0.237804i		−	0.0362648i	−0.999836	−	0.0181324i	$-0.994228\pi$
$43$		−	0.237804i		−	0.0362648i	0.999836	−	0.0181324i	$-0.00577204\pi$
$44$	3.18254	−	0.933504i	0.479786	−	0.140731i
$45$	1.52645	−	0.881296i	0.227550	−	0.131376i
$46$	−1.29707	+	2.91326i	−0.191242	+	0.429537i
$47$	0.287918	−	1.35455i	0.0419972	−	0.197581i	−0.952147	−	0.305639i	$-0.901130\pi$
$47$	0.287918	−	1.35455i	0.0419972	−	0.197581i	0.994145	+	0.108058i	$0.0344632\pi$
$48$	0.951057	+	0.309017i	0.137273	+	0.0446028i
$49$	0.0107455	+	6.99999i	0.00153506	+	0.999999i
$50$	−1.11283	+	1.53168i	−0.157378	+	0.216613i
$51$	1.17236	−	1.05560i	0.164163	−	0.147813i
$52$	−3.73501	+	4.14815i	−0.517952	+	0.575244i
$53$	−6.91287	−	3.07781i	−0.949556	−	0.422770i	−0.127286	−	0.991866i	$-0.540626\pi$
$53$	−6.91287	−	3.07781i	−0.949556	−	0.422770i	−0.822271	+	0.569096i	$0.807293\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−2.77572	−	5.14485i	−0.374278	−	0.693731i
$56$	−2.35830	−	1.19934i	−0.315141	−	0.160268i
$57$	4.81526	+	6.62764i	0.637797	+	0.877852i
$58$	−3.78868	−	0.805309i	−0.497478	−	0.105742i
$59$	1.40613	+	6.61530i	0.183062	+	0.861239i	0.969790	+	0.243940i	$0.0784399\pi$
$59$	1.40613	+	6.61530i	0.183062	+	0.861239i	−0.786728	+	0.617299i	$0.788227\pi$
$60$	0.184241	−	1.75294i	0.0237854	−	0.226303i
$61$	4.88024	−	2.17282i	0.624851	−	0.278202i	−0.0697860	−	0.997562i	$-0.522232\pi$
$61$	4.88024	−	2.17282i	0.624851	−	0.278202i	0.694637	+	0.719360i	$0.255565\pi$
$62$	1.69418	−	5.21415i	0.215161	−	0.662198i
$63$	−1.66345	+	2.05741i	−0.209575	+	0.259210i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	8.52046	+	4.91929i	1.05683	+	0.610163i
$66$	−2.82326	−	1.74045i	−0.347520	−	0.214235i
$67$	−5.30356	−	9.18603i	−0.647933	−	1.12225i	−0.983616	−	0.180277i	$-0.942301\pi$
$67$	−5.30356	−	9.18603i	−0.647933	−	1.12225i	0.335683	−	0.941975i	$-0.391033\pi$
$68$	−0.164901	−	1.56893i	−0.0199972	−	0.190260i
$69$	3.03288	−	0.985443i	0.365116	−	0.118633i
$70$	−1.20351	+	4.50541i	−0.143848	+	0.538499i
$71$	0.175328	+	0.127383i	0.0208075	+	0.0151176i	0.598140	−	0.801391i	$-0.295906\pi$
$71$	0.175328	+	0.127383i	0.0208075	+	0.0151176i	−0.577333	+	0.816509i	$0.695906\pi$
$72$	−0.406737	−	0.913545i	−0.0479344	−	0.107662i
$73$	9.80345	−	2.08379i	1.14741	−	0.243889i	0.405308	−	0.914180i	$-0.367164\pi$
$73$	9.80345	−	2.08379i	1.14741	−	0.243889i	0.742098	+	0.670291i	$0.233831\pi$
$74$	−0.764454	−	0.688318i	−0.0888660	−	0.0800153i
$75$	1.88289	−	0.197900i	0.217418	−	0.0228515i
$76$	8.19221			0.939711
$77$	6.66173	+	5.71151i	0.759174	+	0.650887i
$78$	5.58188			0.632024
$79$	1.57504	−	0.165543i	0.177206	−	0.0186251i	−0.0155098	−	0.999880i	$-0.504937\pi$
$79$	1.57504	−	0.165543i	0.177206	−	0.0186251i	0.192716	+	0.981255i	$0.438270\pi$
$80$	−1.30986	−	1.17940i	−0.146447	−	0.131861i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−2.68225	−	6.02444i	−0.296205	−	0.665288i
$83$	−8.61257	−	6.25740i	−0.945353	−	0.686839i	0.00435058	−	0.999991i	$-0.498615\pi$
$83$	−8.61257	−	6.25740i	−0.945353	−	0.686839i	−0.949703	+	0.313152i	$0.898615\pi$
$84$	0.686732	+	2.55507i	0.0749286	+	0.278781i
$85$	−2.64452	+	0.859256i	−0.286838	+	0.0931994i
$86$	0.0248573	+	0.236502i	0.00268043	+	0.0255026i
$87$	1.93666	+	3.35439i	0.207632	+	0.359629i
$88$	−3.06753	+	1.26106i	−0.327000	+	0.134429i
$89$	−6.84058	−	3.94941i	−0.725100	−	0.418637i	0.0915270	−	0.995803i	$-0.470825\pi$
$89$	−6.84058	−	3.94941i	−0.725100	−	0.418637i	−0.816627	+	0.577166i	$0.804159\pi$
$90$	−1.42597	+	1.03603i	−0.150310	+	0.109207i
$91$	−14.5882	−	2.29907i	−1.52926	−	0.241008i
$92$	0.985443	−	3.03288i	0.102740	−	0.316200i
$93$	−5.00850	+	2.22993i	−0.519357	+	0.231233i
$94$	−0.144752	+	1.37722i	−0.0149300	+	0.142050i
$95$	−3.00215	−	14.1240i	−0.308014	−	1.44909i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	−4.70842	−	6.48058i	−0.478068	−	0.658004i	0.500065	−	0.865988i	$-0.333310\pi$
$97$	−4.70842	−	6.48058i	−0.478068	−	0.658004i	−0.978132	+	0.207985i	$0.933310\pi$
$98$	−0.742385	−	6.96052i	−0.0749922	−	0.703119i
$99$	0.595724	+	3.26268i	0.0598725	+	0.327912i
$100$	0.946633	−	1.63962i	0.0946633	−	0.163962i
$101$	−17.1166	−	7.62082i	−1.70317	−	0.758300i	−0.998826	−	0.0484414i	$-0.984575\pi$
$101$	−17.1166	−	7.62082i	−1.70317	−	0.758300i	−0.704344	−	0.709859i	$-0.748759\pi$
$102$	−1.05560	+	1.17236i	−0.104520	+	0.116081i
$103$	−1.21705	+	1.09584i	−0.119920	+	0.107976i	−0.726909	−	0.686734i	$-0.759044\pi$
$103$	−1.21705	+	1.09584i	−0.119920	+	0.107976i	0.606989	+	0.794710i	$0.292377\pi$
$104$	3.28095	−	4.51584i	0.321723	−	0.442814i
$105$	4.15348	−	2.12032i	0.405338	−	0.206922i
$106$	7.19672	+	2.33836i	0.699008	+	0.227121i
$107$	0.390754	−	1.83835i	0.0377756	−	0.177720i	−0.955215	−	0.295912i	$-0.904376\pi$
$107$	0.390754	−	1.83835i	0.0377756	−	0.177720i	0.992991	+	0.118192i	$0.0377098\pi$
$108$	−0.406737	+	0.913545i	−0.0391383	+	0.0879060i
$109$	−3.51016	+	2.02659i	−0.336213	+	0.194112i	−0.658596	−	0.752497i	$-0.728849\pi$
$109$	−3.51016	+	2.02659i	−0.336213	+	0.194112i	0.322383	+	0.946609i	$0.395516\pi$
$110$	3.29829	+	4.82652i	0.314480	+	0.460191i
$111$			1.02867i			0.0976375i
$112$	2.47075	+	0.946256i	0.233464	+	0.0894128i
$113$	−5.52686	−	17.0099i	−0.519923	−	1.60016i	−0.774142	−	0.633012i	$-0.781818\pi$
$113$	−5.52686	−	17.0099i	−0.519923	−	1.60016i	0.254219	−	0.967147i	$-0.418182\pi$
$114$	−5.48166	−	6.08800i	−0.513405	−	0.570194i
$115$	−5.59005	−	0.587538i	−0.521275	−	0.0547882i
$116$	3.85210	+	0.404872i	0.357659	+	0.0375915i
$117$	−3.73501	−	4.14815i	−0.345302	−	0.383496i
$118$	−2.08991	−	6.43208i	−0.192392	−	0.592121i
$119$	3.24168	−	2.62918i	0.297164	−	0.241016i
$120$			1.76259i			0.160902i
$121$	10.8736	−	1.66291i	0.988507	−	0.151174i
$122$	−4.62639	+	2.67105i	−0.418853	+	0.241825i
$123$	−2.68225	+	6.02444i	−0.241851	+	0.543206i
$124$	−1.13987	+	5.36268i	−0.102364	+	0.481583i
$125$	−11.5554	−	3.75456i	−1.03354	−	0.335818i
$126$	1.43928	−	2.22002i	0.128221	−	0.197775i
$127$	−6.97399	+	9.59887i	−0.618841	+	0.851762i	−0.997268	−	0.0738693i	$-0.976465\pi$
$127$	−6.97399	+	9.59887i	−0.618841	+	0.851762i	0.378427	+	0.925631i	$0.376465\pi$
$128$	−0.743145	+	0.669131i	−0.0656853	+	0.0591433i
$129$	0.159122	−	0.176723i	0.0140099	−	0.0155596i
$130$	−8.98799	−	4.00171i	−0.788299	−	0.350973i
$131$	−9.26215	+	16.0425i	−0.809237	+	1.40164i	0.104155	+	0.994561i	$0.466786\pi$
$131$	−9.26215	+	16.0425i	−0.809237	+	1.40164i	−0.913393	+	0.407079i	$0.866547\pi$
$132$	2.98973	+	1.43581i	0.260222	+	0.124971i
$133$	11.8188	+	18.1688i	1.02482	+	1.57543i
$134$	6.23470	+	8.58133i	0.538596	+	0.741314i
$135$	1.72408	+	0.366464i	0.148385	+	0.0315402i
$136$	0.327995	+	1.54309i	0.0281253	+	0.132319i
$137$	0.947755	−	9.01729i	0.0809722	−	0.770399i	−0.876408	−	0.481569i	$-0.840067\pi$
$137$	0.947755	−	9.01729i	0.0809722	−	0.770399i	0.957380	−	0.288830i	$-0.0932662\pi$
$138$	−2.91326	+	1.29707i	−0.247993	+	0.110414i
$139$	3.43271	−	10.5648i	0.291159	−	0.896095i	−0.693326	−	0.720624i	$-0.743855\pi$
$139$	3.43271	−	10.5648i	0.291159	−	0.896095i	0.984485	−	0.175471i	$-0.0561447\pi$
$140$	0.725978	−	4.60653i	0.0613564	−	0.389323i
$141$	1.12033	−	0.813971i	0.0943492	−	0.0685487i
$142$	−0.187682	−	0.108358i	−0.0157499	−	0.00909323i
$143$	−14.1094	+	11.9857i	−1.17988	+	1.00230i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−0.713625	−	6.78969i	−0.0592633	−	0.563853i
$146$	−9.53193	+	3.09711i	−0.788868	+	0.256319i
$147$	−4.67592	+	5.20920i	−0.385664	+	0.429647i
$148$	0.832215	+	0.604640i	0.0684077	+	0.0497011i
$149$	5.36923	+	12.0595i	0.439864	+	0.987951i	0.988407	+	0.151828i	$0.0485161\pi$
$149$	5.36923	+	12.0595i	0.439864	+	0.987951i	−0.548543	+	0.836123i	$0.684817\pi$
$150$	−1.85189	+	0.393632i	−0.151206	+	0.0321399i
$151$	−15.2288	−	13.7120i	−1.23930	−	1.11587i	−0.989033	−	0.147693i	$-0.952815\pi$
$151$	−15.2288	−	13.7120i	−1.23930	−	1.11587i	−0.250266	−	0.968177i	$-0.580518\pi$
$152$	−8.14734	+	0.856320i	−0.660836	+	0.0694567i
$153$	1.57757			0.127539
$154$	−7.22225	−	4.98389i	−0.581985	−	0.401613i
$155$	9.66339			0.776182
$156$	−5.55130	+	0.583465i	−0.444460	+	0.0467146i
$157$	−8.65887	−	7.79648i	−0.691053	−	0.622227i	0.246879	−	0.969046i	$-0.420595\pi$
$157$	−8.65887	−	7.79648i	−0.691053	−	0.622227i	−0.937932	+	0.346819i	$0.887262\pi$
$158$	−1.54911	+	0.329273i	−0.123240	+	0.0261956i
$159$	−3.07781	−	6.91287i	−0.244086	−	0.548227i
$160$	1.42597	+	1.03603i	0.112733	+	0.0819051i
$161$	8.14803	−	2.18996i	0.642155	−	0.172593i
$162$	0.951057	−	0.309017i	0.0747221	−	0.0242787i
$163$	−1.93063	−	18.3687i	−0.151219	−	1.43875i	−0.762321	−	0.647199i	$-0.775940\pi$
$163$	−1.93063	−	18.3687i	−0.151219	−	1.43875i	0.611102	−	0.791551i	$-0.290726\pi$
$164$	3.29729	+	5.71107i	0.257475	+	0.445959i
$165$	1.37982	−	5.68069i	0.107419	−	0.442241i
$166$	9.21947	+	5.32286i	0.715569	+	0.413134i
$167$	−6.19748	+	4.50273i	−0.479575	+	0.348432i	−0.801161	−	0.598448i	$-0.795784\pi$
$167$	−6.19748	+	4.50273i	−0.479575	+	0.348432i	0.321586	+	0.946880i	$0.395784\pi$
$168$	−0.950048	−	2.46929i	−0.0732978	−	0.190510i
$169$	5.61094	−	17.2687i	0.431611	−	1.32836i
$170$	2.54021	−	1.13098i	0.194825	−	0.0867419i
$171$	−0.856320	+	8.14734i	−0.0654844	+	0.623042i
$172$	−0.0494423	−	0.232608i	−0.00376994	−	0.0177362i
$173$	25.4570	+	5.41105i	1.93546	+	0.411394i	0.997994	+	0.0633117i	$0.0201662\pi$
$173$	25.4570	+	5.41105i	1.93546	+	0.411394i	0.937464	+	0.348082i	$0.113167\pi$
$174$	−2.27668	−	3.13358i	−0.172595	−	0.237556i
$175$	5.00204	−	0.265996i	0.378119	−	0.0201074i
$176$	2.91891	−	1.57479i	0.220021	−	0.118704i
$177$	−3.38155	+	5.85701i	−0.254172	+	0.440240i
$178$	7.21593	+	3.21274i	0.540857	+	0.240805i
$179$	−7.88766	+	8.76013i	−0.589551	+	0.654763i	−0.961923	−	0.273321i	$-0.911878\pi$
$179$	−7.88766	+	8.76013i	−0.589551	+	0.654763i	0.372372	+	0.928084i	$0.378545\pi$
$180$	1.30986	−	1.17940i	0.0976313	−	0.0879077i
$181$	−10.3319	+	14.2206i	−0.767961	+	1.05701i	0.228549	+	0.973532i	$0.426602\pi$
$181$	−10.3319	+	14.2206i	−0.767961	+	1.05701i	−0.996510	+	0.0834747i	$0.973398\pi$
$182$	14.7486	+	0.761592i	1.09324	+	0.0564529i
$183$	5.08063	+	1.65080i	0.375571	+	0.122030i
$184$	−0.663022	+	3.11927i	−0.0488786	+	0.229956i
$185$	0.737468	−	1.65638i	0.0542197	−	0.121780i
$186$	4.74797	−	2.74124i	0.348138	−	0.200998i
$187$	0.150886	−	5.23002i	0.0110339	−	0.382457i
$188$		−	1.38481i		−	0.100998i
$189$	−2.61286	+	0.415892i	−0.190058	+	0.0302517i
$190$	4.46206	+	13.7328i	0.323712	+	0.996283i
$191$	1.65348	+	1.83637i	0.119642	+	0.132875i	0.799990	−	0.600014i	$-0.204838\pi$
$191$	1.65348	+	1.83637i	0.119642	+	0.132875i	−0.680348	+	0.732889i	$0.738171\pi$
$192$	0.994522	+	0.104528i	0.0717734	+	0.00754369i
$193$	21.5960	+	2.26983i	1.55451	+	0.163386i	0.842467	−	0.538749i	$-0.181103\pi$
$193$	21.5960	+	2.26983i	1.55451	+	0.163386i	0.712044	+	0.702134i	$0.247769\pi$
$194$	5.36003	+	5.95292i	0.384828	+	0.427395i
$195$	3.04029	+	9.35705i	0.217720	+	0.670072i
$196$	1.46589	+	6.84479i	0.104706	+	0.488914i
$197$			6.69661i			0.477114i	0.971128	+	0.238557i	$0.0766744\pi$
$197$			6.69661i			0.477114i	−0.971128	+	0.238557i	$0.923326\pi$
$198$	−0.933504	−	3.18254i	−0.0663412	−	0.226173i
$199$	10.7110	−	6.18401i	0.759284	−	0.438373i	−0.0697548	−	0.997564i	$-0.522222\pi$
$199$	10.7110	−	6.18401i	0.759284	−	0.438373i	0.829038	+	0.559192i	$0.188888\pi$
$200$	−0.770061	+	1.72958i	−0.0544515	+	0.122300i
$201$	2.20534	−	10.3753i	0.155553	−	0.731819i
$202$	17.8195	+	5.78990i	1.25377	+	0.407376i
$203$	4.65943	+	9.12732i	0.327028	+	0.640613i
$204$	0.927271	−	1.27628i	0.0649220	−	0.0893574i
$205$	8.63798	−	7.77767i	0.603303	−	0.543216i
$206$	1.09584	−	1.21705i	0.0763508	−	0.0847961i
$207$	2.91326	+	1.29707i	0.202486	+	0.0901524i
$208$	−2.79094	+	4.83405i	−0.193517	+	0.335181i
$209$	26.9285	+	3.61816i	1.86268	+	0.250273i
$210$	−3.90909	+	2.54286i	−0.269753	+	0.175474i
$211$	−13.5513	−	18.6518i	−0.932911	−	1.28404i	−0.958713	−	0.284375i	$-0.908214\pi$
$211$	−13.5513	−	18.6518i	−0.932911	−	1.28404i	0.0258019	−	0.999667i	$-0.491786\pi$
$212$	−7.40172	−	1.57329i	−0.508353	−	0.108054i
$213$	0.0450579	+	0.211981i	0.00308732	+	0.0145247i
$214$	−0.196453	+	1.86913i	−0.0134293	+	0.127771i
$215$	−0.382915	+	0.170485i	−0.0261146	+	0.0116270i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	−13.5379	+	5.20862i	−0.919010	+	0.353584i
$218$	3.27910	−	2.38240i	0.222089	−	0.161357i
$219$	8.67971	+	5.01123i	0.586520	+	0.338628i
$220$	−3.78474	−	4.45532i	−0.255167	−	0.300377i
$221$	4.40290	+	7.62604i	0.296171	+	0.512983i
$222$	−0.107526	−	1.02304i	−0.00721666	−	0.0686619i
$223$	19.4005	−	6.30361i	1.29916	−	0.422121i	0.423868	−	0.905724i	$-0.360672\pi$
$223$	19.4005	−	6.30361i	1.29916	−	0.422121i	0.875288	+	0.483603i	$0.160672\pi$
$224$	−2.55612	−	0.682809i	−0.170788	−	0.0456221i
$225$	1.53168	+	1.11283i	0.102112	+	0.0741889i
$226$	7.27460	+	16.3390i	0.483899	+	1.08686i
$227$	−8.82657	+	1.87615i	−0.585840	+	0.124524i	−0.491290	−	0.870996i	$-0.663475\pi$
$227$	−8.82657	+	1.87615i	−0.585840	+	0.124524i	−0.0945500	+	0.995520i	$0.530141\pi$
$228$	6.08800	+	5.48166i	0.403188	+	0.363032i
$229$	−6.86643	+	0.721691i	−0.453746	+	0.0476907i	−0.328645	−	0.944453i	$-0.606592\pi$
$229$	−6.86643	+	0.721691i	−0.453746	+	0.0476907i	−0.125101	+	0.992144i	$0.539925\pi$
$230$	5.62084			0.370627
$231$	1.12888	+	8.70205i	0.0742748	+	0.572553i
$232$	−3.87332			−0.254296
$233$	2.84315	−	0.298827i	0.186261	−	0.0195768i	−0.0109386	−	0.999940i	$-0.503482\pi$
$233$	2.84315	−	0.298827i	0.186261	−	0.0195768i	0.197200	+	0.980363i	$0.436815\pi$
$234$	4.14815	+	3.73501i	0.271173	+	0.244165i
$235$	−2.38752	+	0.507482i	−0.155744	+	0.0331045i
$236$	2.75080	+	6.17839i	0.179062	+	0.402179i
$237$	1.28125	+	0.930885i	0.0832264	+	0.0604675i
$238$	−2.94909	+	2.95362i	−0.191161	+	0.191455i
$239$	19.3686	−	6.29323i	1.25285	−	0.407075i	0.393908	−	0.919150i	$-0.371123\pi$
$239$	19.3686	−	6.29323i	1.25285	−	0.407075i	0.858941	+	0.512075i	$0.171123\pi$
$240$	−0.184241	−	1.75294i	−0.0118927	−	0.113152i
$241$	6.18718	+	10.7165i	0.398552	+	0.690311i	0.993547	−	0.113417i	$-0.0361797\pi$
$241$	6.18718	+	10.7165i	0.398552	+	0.690311i	−0.594996	+	0.803729i	$0.702846\pi$
$242$	−10.6402	+	2.79040i	−0.683977	+	0.179374i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	4.32184	−	3.14000i	0.276678	−	0.201018i
$245$	11.2637	−	5.03567i	0.719614	−	0.321717i
$246$	2.03783	−	6.27181i	0.129928	−	0.399876i
$247$	−41.7746	+	18.5992i	−2.65805	+	1.18344i
$248$	0.573076	−	5.45245i	0.0363903	−	0.346231i
$249$	−2.21337	−	10.4131i	−0.140267	−	0.659903i
$250$	11.8845	+	2.52613i	0.751643	+	0.159767i
$251$	2.10736	+	2.90053i	0.133016	+	0.183080i	0.870329	−	0.492470i	$-0.163906\pi$
$251$	2.10736	+	2.90053i	0.133016	+	0.183080i	−0.737314	+	0.675551i	$0.763906\pi$
$252$	−1.19934	+	2.35830i	−0.0755511	+	0.148559i
$253$	4.57873	−	9.53412i	0.287863	−	0.599405i
$254$	5.93243	−	10.2753i	0.372234	−	0.644728i
$255$	−2.54021	−	1.13098i	−0.159074	−	0.0708245i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−17.8810	+	16.1002i	−1.11539	+	1.00430i	−0.115449	+	0.993313i	$0.536831\pi$
$257$	−17.8810	+	16.1002i	−1.11539	+	1.00430i	−0.999940	+	0.0109869i	$0.996503\pi$
$258$	−0.139778	+	0.192388i	−0.00870219	+	0.0119775i
$259$	−0.140352	+	2.71800i	−0.00872107	+	0.168888i
$260$	9.35705	+	3.04029i	0.580300	+	0.188551i
$261$	−0.805309	+	3.78868i	−0.0498474	+	0.234513i
$262$	7.53451	−	16.9228i	0.465483	−	1.04549i
$263$	7.36346	−	4.25129i	0.454050	−	0.262146i	−0.255489	−	0.966812i	$-0.582236\pi$
$263$	7.36346	−	4.25129i	0.454050	−	0.262146i	0.709539	+	0.704666i	$0.248903\pi$
$264$	−3.12343	−	1.11543i	−0.192234	−	0.0686500i
$265$			13.3377i			0.819328i
$266$	−13.6532	−	16.8338i	−0.837129	−	1.03215i
$267$	−2.44087	−	7.51222i	−0.149379	−	0.459741i
$268$	−7.09754	−	7.88262i	−0.433551	−	0.481508i
$269$	−0.999386	−	0.105040i	−0.0609337	−	0.00640439i	0.0740126	−	0.997257i	$-0.476420\pi$
$269$	−0.999386	−	0.105040i	−0.0609337	−	0.00640439i	−0.134946	+	0.990853i	$0.543086\pi$
$270$	−1.75294	−	0.184241i	−0.106680	−	0.0112126i
$271$	−10.2471	−	11.3806i	−0.622468	−	0.691321i	0.346629	−	0.938002i	$-0.387326\pi$
$271$	−10.2471	−	11.3806i	−0.622468	−	0.691321i	−0.969097	+	0.246682i	$0.920660\pi$
$272$	−0.487495	−	1.50036i	−0.0295587	−	0.0909724i
$273$	−9.30278	−	11.4700i	−0.563030	−	0.694194i
$274$			9.06696i			0.547755i
$275$	3.83581	−	4.97147i	0.231308	−	0.299791i
$276$	2.76172	−	1.59448i	0.166236	−	0.0959764i
$277$	−3.28690	+	7.38251i	−0.197491	+	0.443572i	−0.984960	−	0.172782i	$-0.944724\pi$
$277$	−3.28690	+	7.38251i	−0.197491	+	0.443572i	0.787469	+	0.616354i	$0.211391\pi$
$278$	−2.30959	+	10.8657i	−0.138520	+	0.651684i
$279$	−5.21415	−	1.69418i	−0.312163	−	0.101428i
$280$	−0.240488	+	4.65718i	−0.0143719	+	0.278320i
$281$	−11.1060	+	15.2861i	−0.662529	+	0.911892i	−0.999562	−	0.0296004i	$-0.990577\pi$
$281$	−11.1060	+	15.2861i	−0.662529	+	0.911892i	0.337033	+	0.941493i	$0.390577\pi$
$282$	−1.02911	+	0.926619i	−0.0612829	+	0.0551793i
$283$	−16.8755	+	18.7421i	−1.00314	+	1.11410i	−0.00967847	+	0.999953i	$0.503081\pi$
$283$	−16.8755	+	18.7421i	−1.00314	+	1.11410i	−0.993464	+	0.114149i	$0.963586\pi$
$284$	0.197981	+	0.0881466i	0.0117480	+	0.00523054i
$285$	7.21977	−	12.5050i	0.427662	−	0.740733i
$286$	12.7792	−	13.3949i	0.755651	−	0.792056i
$287$	−7.90911	+	15.5520i	−0.466860	+	0.918005i
$288$	−0.587785	−	0.809017i	−0.0346356	−	0.0476718i
$289$	14.1942	+	3.01706i	0.834951	+	0.177474i
$290$	1.41943	+	6.67790i	0.0833519	+	0.392140i
$291$	0.837319	−	7.96656i	0.0490845	−	0.467008i
$292$	9.15597	−	4.07650i	0.535813	−	0.238559i
$293$	−6.28952	+	19.3572i	−0.367438	+	1.13086i	0.581003	+	0.813902i	$0.302661\pi$
$293$	−6.28952	+	19.3572i	−0.367438	+	1.13086i	−0.948440	+	0.316955i	$0.897339\pi$
$294$	4.10580	−	5.66943i	0.239455	−	0.330648i
$295$	9.64395	−	7.00674i	0.561492	−	0.407948i
$296$	−0.890858	−	0.514337i	−0.0517801	−	0.0298952i
$297$	−1.74045	+	2.82326i	−0.100991	+	0.163822i
$298$	−6.60037	−	11.4322i	−0.382349	−	0.662248i
$299$	1.86065	+	17.7029i	0.107604	+	1.02378i
$300$	1.80060	−	0.585051i	0.103958	−	0.0337780i
$301$	0.444550	−	0.445233i	0.0256234	−	0.0256628i
$302$	16.5786	+	12.0451i	0.953994	+	0.693117i
$303$	−7.62082	−	17.1166i	−0.437805	−	0.983326i
$304$	8.01319	−	1.70326i	0.459588	−	0.0976885i
$305$	−6.99740	−	6.30049i	−0.400670	−	0.360765i
$306$	−1.56893	+	0.164901i	−0.0896895	+	0.00942675i
$307$	−7.25267			−0.413932			−0.206966	−	0.978348i	$-0.566359\pi$
$307$	−7.25267			−0.413932			−0.206966	+	0.978348i	$0.566359\pi$
$308$	7.70364	+	4.20165i	0.438956	+	0.239411i
$309$	−1.63771			−0.0931659
$310$	−9.61045	+	1.01010i	−0.545837	+	0.0573698i
$311$	−2.51958	−	2.26864i	−0.142872	−	0.128643i	0.594596	−	0.804025i	$-0.297312\pi$
$311$	−2.51958	−	2.26864i	−0.142872	−	0.128643i	−0.737468	+	0.675382i	$0.763979\pi$
$312$	5.45990	−	1.16054i	0.309106	−	0.0657025i
$313$	7.26152	+	16.3096i	0.410445	+	0.921875i	0.993957	+	0.109771i	$0.0350116\pi$
$313$	7.26152	+	16.3096i	0.410445	+	0.921875i	−0.583512	+	0.812105i	$0.698322\pi$
$314$	9.42639	+	6.84868i	0.531962	+	0.386493i
$315$	4.50541	+	1.20351i	0.253851	+	0.0678104i
$316$	1.50620	−	0.489395i	0.0847306	−	0.0275306i
$317$	−1.64926	−	15.6917i	−0.0926319	−	0.881334i	−0.937880	−	0.346960i	$-0.887214\pi$
$317$	−1.64926	−	15.6917i	−0.0926319	−	0.881334i	0.845248	−	0.534374i	$-0.179453\pi$
$318$	3.78354	+	6.55329i	0.212170	+	0.367490i
$319$	12.4834	+	3.03216i	0.698935	+	0.169769i
$320$	−1.52645	−	0.881296i	−0.0853312	−	0.0492660i
$321$	1.52049	−	1.10470i	0.0848652	−	0.0616582i
$322$	−7.87448	+	3.02967i	−0.438828	+	0.168837i
$323$	3.99367	−	12.2912i	0.222213	−	0.683903i
$324$	−0.913545	+	0.406737i	−0.0507525	+	0.0225965i
$325$	−1.10466	+	10.5101i	−0.0612752	+	0.582995i
$326$	3.84011	+	18.0663i	0.212684	+	1.00060i
$327$	−3.96462	−	0.842705i	−0.219244	−	0.0466017i
$328$	−3.87619	−	5.33512i	−0.214027	−	0.294583i
$329$	3.07124	−	1.99784i	0.169323	−	0.110144i
$330$	−0.778464	+	5.79380i	−0.0428530	+	0.318938i
$331$	16.5386	−	28.6456i	0.909042	−	1.57451i	0.0936434	−	0.995606i	$-0.470149\pi$
$331$	16.5386	−	28.6456i	0.909042	−	1.57451i	0.815398	−	0.578900i	$-0.196518\pi$
$332$	−9.72535	−	4.33001i	−0.533748	−	0.237640i
$333$	−0.688318	+	0.764454i	−0.0377196	+	0.0418918i
$334$	5.69287	−	5.12588i	0.311500	−	0.280476i
$335$	−10.9892	+	15.1254i	−0.600407	+	0.826389i
$336$	1.20295	+	2.35646i	0.0656266	+	0.128555i
$337$	−6.97567	−	2.26653i	−0.379989	−	0.123466i	0.112794	−	0.993618i	$-0.464020\pi$
$337$	−6.97567	−	2.26653i	−0.379989	−	0.123466i	−0.492782	+	0.870153i	$0.664020\pi$
$338$	−3.77513	+	17.7606i	−0.205340	+	0.966050i
$339$	7.27460	−	16.3390i	0.395102	−	0.887414i
$340$	−2.40808	+	1.39030i	−0.130596	+	0.0753999i
$341$	−6.11533	+	17.1242i	−0.331164	+	0.927325i
$342$		−	8.19221i		−	0.442984i
$343$	−13.0656	+	13.1259i	−0.705477	+	0.708733i
$344$	0.0734856	+	0.226165i	0.00396208	+	0.0121940i
$345$	−3.76108	−	4.17710i	−0.202490	−	0.224887i
$346$	−25.8831	−	2.72043i	−1.39149	−	0.146251i
$347$	−6.73699	−	0.708086i	−0.361661	−	0.0380121i	−0.0780443	−	0.996950i	$-0.524868\pi$
$347$	−6.73699	−	0.708086i	−0.361661	−	0.0380121i	−0.283616	+	0.958938i	$0.591534\pi$
$348$	2.59176	+	2.87844i	0.138933	+	0.154301i
$349$	−9.52359	−	29.3106i	−0.509786	−	1.56896i	−0.792573	−	0.609777i	$-0.791259\pi$
$349$	−9.52359	−	29.3106i	−0.509786	−	1.56896i	0.282787	−	0.959183i	$-0.408741\pi$
$350$	−4.94684	+	0.787395i	−0.264420	+	0.0420880i
$351$		−	5.58188i		−	0.297939i
$352$	−2.73831	+	1.87127i	−0.145952	+	0.0997393i
$353$	6.71975	−	3.87965i	0.357656	−	0.206493i	−0.310396	−	0.950607i	$-0.600462\pi$
$353$	6.71975	−	3.87965i	0.357656	−	0.206493i	0.668052	+	0.744114i	$0.267128\pi$
$354$	2.75080	−	6.17839i	0.146203	−	0.328378i
$355$	0.0794188	−	0.373636i	0.00421511	−	0.0198305i
$356$	−7.51222	−	2.44087i	−0.398147	−	0.129366i
$357$	4.16830	+	0.215243i	0.220610	+	0.0113919i
$358$	6.92877	−	9.53663i	0.366197	−	0.504027i
$359$	26.8071	−	24.1372i	1.41482	−	1.27391i	0.502418	−	0.864625i	$-0.332444\pi$
$359$	26.8071	−	24.1372i	1.41482	−	1.27391i	0.912405	−	0.409288i	$-0.134223\pi$
$360$	−1.17940	+	1.30986i	−0.0621601	+	0.0690358i
$361$	43.9528	+	19.5691i	2.31331	+	1.02995i
$362$	8.78880	−	15.2226i	0.461929	−	0.800085i
$363$	9.19335	+	6.04006i	0.482526	+	0.317021i
$364$	−14.7474	+	0.784231i	−0.772975	+	0.0411049i
$365$	−10.3835	−	14.2917i	−0.543499	−	0.748062i
$366$	−5.22535	−	1.11068i	−0.273134	−	0.0580563i
$367$	4.32830	+	20.3630i	0.225935	+	1.06294i	0.934132	+	0.356927i	$0.116176\pi$
$367$	4.32830	+	20.3630i	0.225935	+	1.06294i	−0.708197	+	0.706015i	$0.750491\pi$
$368$	0.333337	−	3.17149i	0.0173764	−	0.165325i
$369$	−6.02444	+	2.68225i	−0.313620	+	0.139633i
$370$	−0.560289	+	1.72439i	−0.0291281	+	0.0896469i
$371$	−7.18909	−	18.6853i	−0.373239	−	0.970095i
$372$	−4.43542	+	3.22252i	−0.229966	+	0.167080i
$373$	−32.6736	−	18.8641i	−1.69177	−	0.976745i	−0.953088	−	0.302694i	$-0.902114\pi$
$373$	−32.6736	−	18.8641i	−1.69177	−	0.976745i	−0.738685	−	0.674051i	$-0.764553\pi$
$374$	0.396627	+	5.21715i	0.0205091	+	0.269772i
$375$	−6.07501	−	10.5222i	−0.313712	−	0.543366i
$376$	0.144752	+	1.37722i	0.00746502	+	0.0710249i
$377$	−20.5622	+	6.68108i	−1.05901	+	0.344093i
$378$	2.55507	−	0.686732i	0.131419	−	0.0353217i
$379$	−5.88551	−	4.27608i	−0.302319	−	0.219647i	0.426275	−	0.904594i	$-0.359826\pi$
$379$	−5.88551	−	4.27608i	−0.302319	−	0.219647i	−0.728593	+	0.684946i	$0.759826\pi$
$380$	−5.87309	−	13.1912i	−0.301283	−	0.676693i
$381$	−11.6056	+	2.46684i	−0.594572	+	0.126380i
$382$	−1.83637	−	1.65348i	−0.0939571	−	0.0845993i
$383$	−15.9000	+	1.67116i	−0.812452	+	0.0853921i	−0.501637	−	0.865078i	$-0.667269\pi$
$383$	−15.9000	+	1.67116i	−0.812452	+	0.0853921i	−0.310815	+	0.950470i	$0.600602\pi$
$384$	−1.00000			−0.0510310
$385$	4.42086	−	14.8214i	0.225308	−	0.755369i
$386$	−21.7149			−1.10526
$387$	0.236502	−	0.0248573i	0.0120221	−	0.00126357i
$388$	−5.95292	−	5.36003i	−0.302214	−	0.272114i
$389$	12.2529	−	2.60444i	0.621249	−	0.132051i	0.113475	−	0.993541i	$-0.463802\pi$
$389$	12.2529	−	2.60444i	0.621249	−	0.132051i	0.507774	+	0.861490i	$0.330469\pi$
$390$	−4.00171	−	8.98799i	−0.202635	−	0.455125i
$391$	−4.07000	−	2.95703i	−0.205829	−	0.149543i
$392$	−2.17334	−	6.65407i	−0.109770	−	0.336081i
$393$	−17.6176	+	5.72432i	−0.888693	+	0.288754i
$394$	−0.699987	−	6.65993i	−0.0352648	−	0.335522i
$395$	−1.39572	−	2.41746i	−0.0702265	−	0.121636i
$396$	1.26106	+	3.06753i	0.0633705	+	0.154149i
$397$	3.04579	+	1.75849i	0.152864	+	0.0882558i	0.574481	−	0.818518i	$-0.305204\pi$
$397$	3.04579	+	1.75849i	0.152864	+	0.0882558i	−0.421617	+	0.906774i	$0.638537\pi$
$398$	−10.0059	+	7.26974i	−0.501552	+	0.364399i
$399$	−3.37422	+	21.4103i	−0.168922	+	1.07186i
$400$	0.585051	−	1.80060i	0.0292526	−	0.0900301i
$401$	33.4422	−	14.8894i	1.67002	−	0.743543i	0.670025	−	0.742339i	$-0.266284\pi$
$401$	33.4422	−	14.8894i	1.67002	−	0.743543i	0.999999	−	0.00120359i	$-0.000383115\pi$
$402$	−1.10875	+	10.5490i	−0.0552992	+	0.526137i
$403$	−6.36263	−	29.9338i	−0.316945	−	1.49111i
$404$	−18.3271	−	3.89554i	−0.911806	−	0.193810i
$405$	1.03603	+	1.42597i	0.0514806	+	0.0708569i
$406$	−5.58797	−	8.59028i	−0.277326	−	0.426328i
$407$	2.46852	+	2.35506i	0.122360	+	0.116736i
$408$	−0.788784	+	1.36621i	−0.0390506	+	0.0676377i
$409$	19.9169	+	8.86758i	0.984827	+	0.438473i	0.835007	−	0.550240i	$-0.185464\pi$
$409$	19.9169	+	8.86758i	0.984827	+	0.438473i	0.149821	+	0.988713i	$0.452130\pi$
$410$	−7.77767	+	8.63798i	−0.384112	+	0.426599i
$411$	6.73806	−	6.06698i	0.332364	−	0.299262i
$412$	−0.962620	+	1.32493i	−0.0474249	+	0.0652747i
$413$	−9.73395	+	15.0142i	−0.478977	+	0.738800i
$414$	−3.03288	−	0.985443i	−0.149058	−	0.0484319i
$415$	−3.90127	+	18.3540i	−0.191506	+	0.900964i
$416$	2.27036	−	5.09930i	0.111313	−	0.250014i
$417$	9.62024	−	5.55425i	0.471105	−	0.271993i
$418$	−27.1592	−	0.783541i	−1.32840	−	0.0383243i
$419$		−	11.7175i		−	0.572435i	−0.958165	−	0.286218i	$-0.907602\pi$
$419$		−	11.7175i		−	0.572435i	0.958165	−	0.286218i	$-0.0923980\pi$
$420$	3.62188	−	2.93754i	0.176729	−	0.143337i
$421$	9.00812	+	27.7241i	0.439029	+	1.35119i	0.888901	+	0.458099i	$0.151470\pi$
$421$	9.00812	+	27.7241i	0.439029	+	1.35119i	−0.449872	+	0.893093i	$0.648530\pi$
$422$	15.4267	+	17.1331i	0.750961	+	0.834027i
$423$	1.37722	+	0.144752i	0.0669629	+	0.00703808i
$424$	7.52563	+	0.790976i	0.365477	+	0.0384132i
$425$	−1.99853	−	2.21959i	−0.0969429	−	0.107666i
$426$	−0.0669692	−	0.206110i	−0.00324467	−	0.00998606i
$427$	13.1990	+	5.05499i	0.638743	+	0.244628i
$428$		−	1.87942i		−	0.0908454i
$429$	−18.5053	−	0.533877i	−0.893445	−	0.0257758i
$430$	0.362997	−	0.209576i	0.0175053	−	0.0101067i
$431$	−15.1704	+	34.0732i	−0.730730	+	1.64125i	0.0360598	+	0.999350i	$0.488519\pi$
$431$	−15.1704	+	34.0732i	−0.730730	+	1.64125i	−0.766790	+	0.641898i	$0.778147\pi$
$432$	−0.207912	+	0.978148i	−0.0100032	+	0.0470611i
$433$	−5.20881	−	1.69245i	−0.250320	−	0.0813337i	0.181170	−	0.983452i	$-0.442012\pi$
$433$	−5.20881	−	1.69245i	−0.250320	−	0.0813337i	−0.431489	+	0.902118i	$0.642012\pi$
$434$	12.9193	−	6.59518i	0.620144	−	0.316579i
$435$	4.01286	−	5.52323i	0.192402	−	0.264819i
$436$	−3.01211	+	2.71211i	−0.144254	+	0.129887i
$437$	17.4808	−	19.4144i	0.836220	−	0.928717i
$438$	−9.15597	−	4.07650i	−0.437489	−	0.194783i
$439$	7.38776	−	12.7960i	0.352599	−	0.610719i	−0.634105	−	0.773247i	$-0.718631\pi$
$439$	7.38776	−	12.7960i	0.352599	−	0.610719i	0.986704	+	0.162528i	$0.0519648\pi$
$440$	4.22971	+	4.03530i	0.201644	+	0.192375i
$441$	−6.96052	+	0.742385i	−0.331453	+	0.0353517i
$442$	−5.17592	−	7.12404i	−0.246193	−	0.338856i
$443$	28.8102	+	6.12379i	1.36881	+	0.290950i	0.832947	−	0.553353i	$-0.186652\pi$
$443$	28.8102	+	6.12379i	1.36881	+	0.290950i	0.535866	+	0.844303i	$0.319985\pi$
$444$	0.213873	+	1.00620i	0.0101500	+	0.0477519i
$445$	−1.45529	+	13.8461i	−0.0689872	+	0.656370i
$446$	−18.6353	+	8.29699i	−0.882409	+	0.392874i
$447$	−4.07925	+	12.5547i	−0.192942	+	0.593815i
$448$	2.61349	+	0.411881i	0.123476	+	0.0194595i
$449$	5.29202	−	3.84488i	0.249746	−	0.181451i	−0.455868	−	0.890047i	$-0.650671\pi$
$449$	5.29202	−	3.84488i	0.249746	−	0.181451i	0.705614	+	0.708596i	$0.250671\pi$
$450$	−1.63962	−	0.946633i	−0.0772923	−	0.0446247i
$451$	8.31612	+	20.2290i	0.391591	+	0.952548i
$452$	−8.94265	−	15.4891i	−0.420627	−	0.728547i
$453$	−2.14203	−	20.3801i	−0.100641	−	0.957539i
$454$	8.58211	−	2.78850i	0.402778	−	0.130871i
$455$	6.75647	+	25.1383i	0.316748	+	1.17850i
$456$	−6.62764	−	4.81526i	−0.310368	−	0.225495i
$457$	3.16264	+	7.10340i	0.147942	+	0.332283i	0.972282	−	0.233812i	$-0.0751201\pi$
$457$	3.16264	+	7.10340i	0.147942	+	0.332283i	−0.824340	+	0.566095i	$0.808453\pi$
$458$	6.75338	−	1.43547i	0.315565	−	0.0670753i
$459$	1.17236	+	1.05560i	0.0547211	+	0.0492711i
$460$	−5.59005	+	0.587538i	−0.260637	+	0.0273941i
$461$	−27.8271			−1.29604			−0.648019	−	0.761625i	$-0.724402\pi$
$461$	−27.8271			−1.29604			−0.648019	+	0.761625i	$0.724402\pi$
$462$	−2.03231	−	8.53638i	−0.0945515	−	0.397148i
$463$	−37.6832			−1.75129			−0.875644	−	0.482958i	$-0.839563\pi$
$463$	−37.6832			−1.75129			−0.875644	+	0.482958i	$0.839563\pi$
$464$	3.85210	−	0.404872i	0.178829	−	0.0187957i
$465$	7.18130	+	6.46607i	0.333025	+	0.299857i
$466$	−2.79634	+	0.594380i	−0.129538	+	0.0275341i
$467$	3.09091	+	6.94231i	0.143030	+	0.321252i	0.970829	−	0.239774i	$-0.0770735\pi$
$467$	3.09091	+	6.94231i	0.143030	+	0.321252i	−0.827798	+	0.561026i	$0.810407\pi$
$468$	−4.51584	−	3.28095i	−0.208745	−	0.151662i
$469$	7.24263	−	27.1131i	0.334434	−	1.25197i
$470$	2.32139	−	0.754266i	0.107078	−	0.0347917i
$471$	−1.21793	−	11.5878i	−0.0561193	−	0.533939i
$472$	−3.38155	−	5.85701i	−0.155648	−	0.269591i
$473$	−0.0597880	−	0.786439i	−0.00274906	−	0.0361605i
$474$	−1.37154	−	0.791858i	−0.0629969	−	0.0363713i
$475$	12.5479	−	9.11657i	0.575737	−	0.418297i
$476$	2.62420	−	3.24571i	0.120280	−	0.148767i
$477$	2.33836	−	7.19672i	0.107066	−	0.329515i
$478$	−18.6046	+	8.28332i	−0.850957	+	0.378870i
$479$	3.76156	−	35.7889i	0.171870	−	1.63524i	−0.480258	−	0.877127i	$-0.659457\pi$
$479$	3.76156	−	35.7889i	0.171870	−	1.63524i	0.652128	−	0.758109i	$-0.273876\pi$
$480$	0.366464	+	1.72408i	0.0167267	+	0.0786929i
$481$	−5.61646	−	1.19382i	−0.256089	−	0.0544333i
$482$	−7.27347	−	10.0111i	−0.331297	−	0.455992i
$483$	7.52054	+	3.82464i	0.342196	+	0.174027i
$484$	10.2902	−	3.88732i	0.467738	−	0.176696i
$485$	−7.05957	+	12.2275i	−0.320559	+	0.555224i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	9.59059	−	10.6514i	0.434591	−	0.482662i	−0.485572	−	0.874196i	$-0.661389\pi$
$487$	9.59059	−	10.6514i	0.434591	−	0.482662i	0.920164	+	0.391534i	$0.128055\pi$
$488$	−3.96995	+	3.57456i	−0.179711	+	0.161813i
$489$	10.8563	−	14.9425i	0.490941	−	0.675722i
$490$	−10.6757	+	6.18547i	−0.482278	+	0.279431i
$491$	−26.4639	−	8.59865i	−1.19430	−	0.388052i	−0.356639	−	0.934242i	$-0.616078\pi$
$491$	−26.4639	−	8.59865i	−1.19430	−	0.388052i	−0.837661	+	0.546190i	$0.816078\pi$
$492$	−1.37109	+	6.45046i	−0.0618134	+	0.290809i
$493$	2.48533	−	5.58215i	0.111934	−	0.251408i
$494$	39.6016	−	22.8640i	1.78176	−	1.02870i
$495$	4.82652	−	3.29829i	0.216936	−	0.148247i
$496$			5.48249i			0.246171i
$497$	0.0901308	+	0.566250i	0.00404292	+	0.0253998i
$498$	3.28971	+	10.1247i	0.147415	+	0.453698i
$499$	13.8244	+	15.3536i	0.618867	+	0.687321i	0.968343	−	0.249624i	$-0.0803070\pi$
$499$	13.8244	+	15.3536i	0.618867	+	0.687321i	−0.349476	+	0.936945i	$0.613640\pi$
$500$	−12.0835	−	1.27002i	−0.540389	−	0.0567972i
$501$	−7.61854	−	0.800741i	−0.340371	−	0.0357745i
$502$	−2.39901	−	2.66437i	−0.107073	−	0.118916i
$503$	3.90081	+	12.0055i	0.173929	+	0.535298i	0.999583	−	0.0288790i	$-0.00919375\pi$
$503$	3.90081	+	12.0055i	0.173929	+	0.535298i	−0.825654	+	0.564177i	$0.809194\pi$
$504$	0.946256	−	2.47075i	0.0421496	−	0.110056i
$505$			33.0248i			1.46959i
$506$	−3.55706	+	9.96050i	−0.158131	+	0.442798i
$507$	15.7248	−	9.07870i	0.698361	−	0.403199i
$508$	−4.82587	+	10.8391i	−0.214113	+	0.480907i
$509$	5.64033	−	26.5357i	0.250003	−	1.17617i	−0.656617	−	0.754225i	$-0.728013\pi$
$509$	5.64033	−	26.5357i	0.250003	−	1.17617i	0.906620	−	0.421948i	$-0.138654\pi$
$510$	2.64452	+	0.859256i	0.117101	+	0.0380485i
$511$	22.2501	+	14.4251i	0.984284	+	0.638128i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−6.08800	+	5.48166i	−0.268792	+	0.242021i
$514$	16.1002	−	17.8810i	0.710148	−	0.788699i
$515$	2.63705	+	1.17409i	0.116202	+	0.0517366i
$516$	0.118902	−	0.205945i	0.00523438	−	0.00906621i
$517$	0.611613	−	4.55199i	0.0268987	−	0.200196i
$518$	−0.144524	−	2.71778i	−0.00635004	−	0.119412i
$519$	15.2975	+	21.0552i	0.671487	+	0.924222i
$520$	−9.62359	−	2.04556i	−0.422022	−	0.0897036i
$521$	−8.00913	−	37.6800i	−0.350886	−	1.65079i	−0.700320	−	0.713829i	$-0.746959\pi$
$521$	−8.00913	−	37.6800i	−0.350886	−	1.65079i	0.349434	−	0.936961i	$-0.386374\pi$
$522$	0.404872	−	3.85210i	0.0177208	−	0.168602i
$523$	17.2846	−	7.69561i	0.755804	−	0.336506i	0.00759710	−	0.999971i	$-0.497582\pi$
$523$	17.2846	−	7.69561i	0.755804	−	0.336506i	0.748207	+	0.663466i	$0.230915\pi$
$524$	−5.72432	+	17.6176i	−0.250068	+	0.769631i
$525$	3.89523	+	3.14935i	0.170002	+	0.137449i
$526$	−6.87874	+	4.99770i	−0.299927	+	0.217910i
$527$	7.49025	+	4.32450i	0.326280	+	0.188378i
$528$	3.22291	+	0.782833i	0.140259	+	0.0340684i
$529$	6.41526	+	11.1116i	0.278925	+	0.483112i
$530$	−1.39417	−	13.2646i	−0.0605588	−	0.576178i
$531$	−6.43208	+	2.08991i	−0.279129	+	0.0906944i
$532$	15.3380	+	15.3145i	0.664986	+	0.663966i
$533$	−29.7800	−	21.6364i	−1.28992	−	0.937178i
$534$	3.21274	+	7.21593i	0.139029	+	0.312264i
$535$	−3.24027	+	0.688741i	−0.140089	+	0.0297769i
$536$	7.88262	+	7.09754i	0.340477	+	0.306567i
$537$	−11.7233	+	1.23217i	−0.505900	+	0.0531722i
$538$	1.00489			0.0433239
$539$	1.79545	+	23.1468i	0.0773356	+	0.997005i
$540$	1.76259			0.0758499
$541$	−1.15068	+	0.120941i	−0.0494715	+	0.00519967i	−0.129232	−	0.991614i	$-0.541251\pi$
$541$	−1.15068	+	0.120941i	−0.0494715	+	0.00519967i	0.0797604	+	0.996814i	$0.474584\pi$
$542$	11.3806	+	10.2471i	0.488837	+	0.440151i
$543$	−17.1935	+	3.65459i	−0.737843	+	0.156833i
$544$	0.641655	+	1.44118i	0.0275107	+	0.0617901i
$545$	5.77971	+	4.19921i	0.247576	+	0.179874i
$546$	10.4508	+	10.4347i	0.447251	+	0.446565i
$547$	13.7848	−	4.47895i	0.589395	−	0.191506i	0.000890152	−	1.00000i	$-0.499717\pi$
$547$	13.7848	−	4.47895i	0.589395	−	0.191506i	0.588505	+	0.808493i	$0.299717\pi$
$548$	−0.947755	−	9.01729i	−0.0404861	−	0.385199i
$549$	2.67105	+	4.62639i	0.113997	+	0.197449i
$550$	−3.29514	+	5.34519i	−0.140505	+	0.227920i
$551$	27.4799	+	15.8655i	1.17068	+	0.675895i
$552$	−2.57992	+	1.87442i	−0.109809	+	0.0797808i
$553$	3.25836	+	2.63443i	0.138559	+	0.112027i
$554$	2.49722	−	7.68564i	0.106097	−	0.326532i
$555$	1.65638	−	0.737468i	0.0703094	−	0.0313038i
$556$	1.16115	−	11.0476i	0.0492439	−	0.468524i
$557$	0.470672	+	2.21434i	0.0199430	+	0.0938244i	0.986993	−	0.160760i	$-0.0513946\pi$
$557$	0.470672	+	2.21434i	0.0199430	+	0.0938244i	−0.967050	+	0.254585i	$0.918061\pi$
$558$	5.36268	+	1.13987i	0.227020	+	0.0482547i
$559$	0.780224	+	1.07389i	0.0329999	+	0.0454205i
$560$	−0.247637	−	4.65680i	−0.0104646	−	0.196786i
$561$	3.61170	−	3.78570i	0.152486	−	0.159833i
$562$	9.44733	−	16.3633i	0.398512	−	0.690242i
$563$	2.31898	+	1.03248i	0.0977335	+	0.0435138i	0.455021	−	0.890481i	$-0.349632\pi$
$563$	2.31898	+	1.03248i	0.0977335	+	0.0435138i	−0.357288	+	0.933994i	$0.616298\pi$
$564$	0.926619	−	1.02911i	0.0390177	−	0.0433335i
$565$	−23.4273	+	21.0940i	−0.985592	+	0.887431i
$566$	14.8239	−	20.4034i	0.623096	−	0.857619i
$567$	−2.22002	−	1.43928i	−0.0932320	−	0.0604439i
$568$	−0.206110	−	0.0669692i	−0.00864818	−	0.00280996i
$569$	−9.13198	+	42.9626i	−0.382833	+	1.80109i	0.190415	+	0.981704i	$0.439016\pi$
$569$	−9.13198	+	42.9626i	−0.382833	+	1.80109i	−0.573248	+	0.819382i	$0.694317\pi$
$570$	−5.87309	+	13.1912i	−0.245997	+	0.552518i
$571$	−33.0979	+	19.1091i	−1.38510	+	0.799689i	−0.992758	−	0.120130i	$-0.961669\pi$
$571$	−33.0979	+	19.1091i	−1.38510	+	0.799689i	−0.392344	+	0.919819i	$0.628336\pi$
$572$	−11.3091	+	14.6573i	−0.472856	+	0.612853i
$573$			2.47108i			0.103231i
$574$	6.24016	−	16.2935i	0.260459	−	0.680079i
$575$	−1.86571	−	5.74205i	−0.0778053	−	0.239460i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	25.7656	+	2.70808i	1.07264	+	0.112739i	0.624345	−	0.781149i	$-0.285366\pi$
$577$	25.7656	+	2.70808i	1.07264	+	0.112739i	0.448292	+	0.893887i	$0.352033\pi$
$578$	−14.4318	−	1.51684i	−0.600283	−	0.0630923i
$579$	14.5301	+	16.1373i	0.603851	+	0.670644i
$580$	−2.10969	−	6.49295i	−0.0876000	−	0.269605i
$581$	−4.42747	−	27.8158i	−0.183683	−	1.15399i
$582$			8.01044i			0.332043i
$583$	−23.6353	−	8.44056i	−0.978872	−	0.349572i
$584$	−8.67971	+	5.01123i	−0.359169	+	0.207366i
$585$	−4.00171	+	8.98799i	−0.165450	+	0.371608i
$586$	4.23169	−	19.9085i	0.174810	−	0.822414i
$587$	−3.04993	−	0.990983i	−0.125884	−	0.0409023i	0.245397	−	0.969423i	$-0.421082\pi$
$587$	−3.04993	−	0.990983i	−0.125884	−	0.0409023i	−0.371282	+	0.928520i	$0.621082\pi$
$588$	−3.49069	+	6.06754i	−0.143954	+	0.250221i
$589$	−26.3996	+	36.3359i	−1.08778	+	1.49720i
$590$	−8.85871	+	7.97642i	−0.364707	+	0.328384i
$591$	−4.48091	+	4.97655i	−0.184320	+	0.204708i
$592$	0.939741	+	0.418400i	0.0386231	+	0.0171961i
$593$	1.44076	−	2.49547i	0.0591650	−	0.102477i	−0.834926	−	0.550362i	$-0.814490\pi$
$593$	1.44076	−	2.49547i	0.0591650	−	0.102477i	0.894091	+	0.447886i	$0.147823\pi$
$594$	1.43581	−	2.98973i	0.0589119	−	0.122670i
$595$	−6.55752	−	3.33489i	−0.268832	−	0.136717i
$596$	7.75920	+	10.6796i	0.317829	+	0.437455i
$597$	12.0977	+	2.57145i	0.495128	+	0.105243i
$598$	−3.70091	−	17.4114i	−0.151342	−	0.712006i
$599$	2.15752	−	20.5274i	0.0881538	−	0.838727i	−0.857704	−	0.514145i	$-0.828110\pi$
$599$	2.15752	−	20.5274i	0.0881538	−	0.838727i	0.945857	−	0.324583i	$-0.105224\pi$
$600$	−1.72958	+	0.770061i	−0.0706100	+	0.0314376i
$601$	0.643933	−	1.98182i	0.0262666	−	0.0808402i	−0.937064	−	0.349158i	$-0.886468\pi$
$601$	0.643933	−	1.98182i	0.0262666	−	0.0808402i	0.963330	+	0.268318i	$0.0864677\pi$
$602$	−0.395575	+	0.489262i	−0.0161224	+	0.0199408i
$603$	8.58133	−	6.23470i	0.349459	−	0.253897i
$604$	−17.7469	−	10.2462i	−0.722110	−	0.416911i
$605$	−10.4730	−	16.3166i	−0.425789	−	0.663363i
$606$	9.36825	+	16.2263i	0.380559	+	0.659148i
$607$	−3.37834	−	32.1427i	−0.137122	−	1.30463i	−0.819266	−	0.573414i	$-0.805619\pi$
$607$	−3.37834	−	32.1427i	−0.137122	−	1.30463i	0.682143	−	0.731219i	$-0.261048\pi$
$608$	−7.79126	+	2.53153i	−0.315977	+	0.102667i
$609$	−2.64474	+	9.90069i	−0.107170	+	0.401196i
$610$	7.61765	+	5.53455i	0.308430	+	0.224087i
$611$	3.14401	+	7.06156i	0.127193	+	0.285680i
$612$	1.54309	−	0.327995i	0.0623759	−	0.0132584i
$613$	15.0653	+	13.5649i	0.608483	+	0.547880i	0.914727	−	0.404073i	$-0.132406\pi$
$613$	15.0653	+	13.5649i	0.608483	+	0.547880i	−0.306244	+	0.951953i	$0.599072\pi$
$614$	7.21294	−	0.758110i	0.291090	−	0.0305948i
$615$	11.6235			0.468707
$616$	−8.10063	−	3.37339i	−0.326384	−	0.135918i
$617$	3.63885			0.146495			0.0732473	−	0.997314i	$-0.476664\pi$
$617$	3.63885			0.146495			0.0732473	+	0.997314i	$0.476664\pi$
$618$	1.62873	−	0.171187i	0.0655173	−	0.00688615i
$619$	1.28363	+	1.15578i	0.0515934	+	0.0464549i	0.694524	−	0.719469i	$-0.255615\pi$
$619$	1.28363	+	1.15578i	0.0515934	+	0.0464549i	−0.642931	+	0.765924i	$0.722282\pi$
$620$	9.45222	−	2.00913i	0.379610	−	0.0806887i
$621$	1.29707	+	2.91326i	0.0520495	+	0.116905i
$622$	2.74292	+	1.99285i	0.109981	+	0.0799059i
$623$	−5.42437	−	20.1821i	−0.217323	−	0.808577i
$624$	−5.30868	+	1.72490i	−0.212517	+	0.0690511i
$625$	1.24903	+	11.8838i	0.0499613	+	0.475350i
$626$	−8.92656	−	15.4613i	−0.356777	−	0.617956i
$627$	17.5908	+	20.7075i	0.702508	+	0.826978i
$628$	−10.0906	−	5.82583i	−0.402660	−	0.232476i
$629$	1.31288	−	0.953860i	0.0523478	−	0.0380329i
$630$	−4.60653	−	0.725978i	−0.183528	−	0.0289237i
$631$	4.56321	−	14.0441i	0.181659	−	0.559088i	−0.818216	−	0.574911i	$-0.805037\pi$
$631$	4.56321	−	14.0441i	0.181659	−	0.559088i	0.999875	+	0.0158230i	$0.00503683\pi$
$632$	−1.44680	+	0.644156i	−0.0575505	+	0.0256231i
$633$	2.40989	−	22.9286i	0.0957846	−	0.911329i
$634$	3.28046	+	15.4333i	0.130284	+	0.612937i
$635$	20.4559	+	4.34804i	0.811768	+	0.172547i
$636$	−4.44782	−	6.12190i	−0.176368	−	0.242749i
$637$	−23.0151	−	31.5756i	−0.911893	−	1.25107i
$638$	−12.7319	−	1.71068i	−0.504062	−	0.0677266i
$639$	−0.108358	+	0.187682i	−0.00428659	+	0.00742459i
$640$	1.61021	+	0.716911i	0.0636491	+	0.0283384i
$641$	−16.9045	+	18.7744i	−0.667689	+	0.741544i	−0.977888	−	0.209128i	$-0.932938\pi$
$641$	−16.9045	+	18.7744i	−0.667689	+	0.741544i	0.310199	+	0.950672i	$0.399604\pi$
$642$	−1.39668	+	1.25758i	−0.0551227	+	0.0496327i
$643$	−9.93411	+	13.6731i	−0.391763	+	0.539216i	−0.958653	−	0.284578i	$-0.908147\pi$
$643$	−9.93411	+	13.6731i	−0.391763	+	0.539216i	0.566890	+	0.823794i	$0.308147\pi$
$644$	7.51466	−	3.83618i	0.296119	−	0.151167i
$645$	−0.398638	−	0.129525i	−0.0156963	−	0.00510005i
$646$	−2.68700	+	12.6414i	−0.105719	+	0.497368i
$647$	−1.72634	+	3.87743i	−0.0678696	+	0.152438i	−0.944295	−	0.329100i	$-0.893255\pi$
$647$	−1.72634	+	3.87743i	−0.0678696	+	0.152438i	0.876426	+	0.481537i	$0.159921\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	6.31337	+	21.5238i	0.247821	+	0.844884i
$650$		−	10.5680i		−	0.414510i
$651$	−13.5458	−	5.18784i	−0.530903	−	0.203327i
$652$	−5.70752	−	17.5659i	−0.223524	−	0.687935i
$653$	2.89569	+	3.21599i	0.113317	+	0.125852i	0.797135	−	0.603802i	$-0.206348\pi$
$653$	2.89569	+	3.21599i	0.113317	+	0.125852i	−0.683817	+	0.729653i	$0.739681\pi$
$654$	4.03098	+	0.423673i	0.157624	+	0.0165669i
$655$	32.4719	+	3.41294i	1.26878	+	0.133354i
$656$	4.41263	+	4.90072i	0.172284	+	0.191341i
$657$	3.09711	+	9.53193i	0.120830	+	0.371876i
$658$	−2.84558	+	2.30793i	−0.110932	+	0.0899724i
$659$		−	4.71642i		−	0.183726i	−0.995772	−	0.0918629i	$-0.970718\pi$
$659$		−	4.71642i		−	0.183726i	0.995772	−	0.0918629i	$-0.0292821\pi$
$660$	0.168583	−	5.84343i	0.00656207	−	0.227455i
$661$	−1.32891	+	0.767247i	−0.0516887	+	0.0298425i	−0.525622	−	0.850718i	$-0.676167\pi$
$661$	−1.32891	+	0.767247i	−0.0516887	+	0.0298425i	0.473933	+	0.880561i	$0.342834\pi$
$662$	−13.4537	+	30.2175i	−0.522892	+	1.17443i
$663$	−1.83083	+	8.61337i	−0.0711035	+	0.334515i
$664$	10.1247	+	3.28971i	0.392914	+	0.127665i
$665$	20.7825	−	32.0561i	0.805910	−	1.24308i
$666$	0.604640	−	0.832215i	0.0234293	−	0.0322477i
$667$	9.17923	−	8.26501i	0.355421	−	0.320023i
$668$	−5.12588	+	5.69287i	−0.198326	+	0.220264i
$669$	18.6353	+	8.29699i	0.720484	+	0.320780i
$670$	9.34801	−	16.1912i	0.361145	−	0.625522i
$671$	15.5931	−	8.41268i	0.601964	−	0.324768i
$672$	−1.44268	−	2.21781i	−0.0556527	−	0.0855538i
$673$	14.4958	+	19.9518i	0.558772	+	0.769084i	0.991170	−	0.132599i	$-0.0423323\pi$
$673$	14.4958	+	19.9518i	0.558772	+	0.769084i	−0.432398	+	0.901683i	$0.642332\pi$
$674$	7.17437	+	1.52496i	0.276346	+	0.0587392i
$675$	0.393632	+	1.85189i	0.0151509	+	0.0712794i
$676$	1.89796	−	18.0579i	0.0729986	−	0.694536i
$677$	−4.68527	+	2.08602i	−0.180069	+	0.0801721i	−0.494791	−	0.869012i	$-0.664755\pi$
$677$	−4.68527	+	2.08602i	−0.180069	+	0.0801721i	0.314722	+	0.949184i	$0.398089\pi$
$678$	−5.52686	+	17.0099i	−0.212258	+	0.653262i
$679$	3.29935	−	20.9352i	0.126617	−	0.803421i
$680$	2.24956	−	1.63440i	0.0862667	−	0.0626764i
$681$	−7.81481	−	4.51188i	−0.299464	−	0.172896i
$682$	4.29187	−	17.6696i	0.164344	−	0.676603i
$683$	12.5347	+	21.7107i	0.479627	+	0.830739i	0.999727	−	0.0233669i	$-0.00743860\pi$
$683$	12.5347	+	21.7107i	0.479627	+	0.830739i	−0.520100	+	0.854105i	$0.674105\pi$
$684$	0.856320	+	8.14734i	0.0327422	+	0.311521i
$685$	−15.1992	+	4.93851i	−0.580730	+	0.188691i
$686$	11.6220	−	14.4197i	0.443730	−	0.550548i
$687$	−5.58566	−	4.05822i	−0.213106	−	0.154831i
$688$	−0.0967238	−	0.217245i	−0.00368756	−	0.00828239i
$689$	41.3155	−	8.78189i	1.57400	−	0.334563i
$690$	4.17710	+	3.76108i	0.159019	+	0.143182i
$691$	−16.3307	+	1.71643i	−0.621249	+	0.0652959i	−0.409924	−	0.912120i	$-0.634445\pi$
$691$	−16.3307	+	1.71643i	−0.621249	+	0.0652959i	−0.211326	+	0.977416i	$0.567778\pi$
$692$	26.0257			0.989348
$693$	−4.98389	+	7.22225i	−0.189322	+	0.274351i
$694$	6.77410			0.257141
$695$	−19.4725	+	2.04664i	−0.738634	+	0.0776335i
$696$	−2.87844	−	2.59176i	−0.109107	−	0.0982403i
$697$	10.1760	−	2.16298i	0.385445	−	0.0819289i
$698$	12.5352	+	28.1545i	0.474465	+	1.06566i
$699$	2.31283	+	1.68037i	0.0874792	+	0.0635573i
$700$	4.83743	−	1.30017i	0.182838	−	0.0491417i
$701$	−31.5677	+	10.2570i	−1.19229	+	0.387400i	−0.836921	−	0.547324i	$-0.815646\pi$
$701$	−31.5677	+	10.2570i	−1.19229	+	0.387400i	−0.355374	+	0.934724i	$0.615646\pi$
$702$	0.583465	+	5.55130i	0.0220215	+	0.209520i
$703$	4.21356	+	7.29810i	0.158917	+	0.275253i
$704$	2.52771	−	2.14725i	0.0952665	−	0.0809277i
$705$	−2.11384	−	1.22043i	−0.0796119	−	0.0459640i
$706$	−6.27741	+	4.56080i	−0.236253	+	0.171648i
$707$	−17.8006	−	46.2659i	−0.669460	−	1.74001i
$708$	−2.08991	+	6.43208i	−0.0785436	+	0.241732i
$709$	−3.67697	+	1.63709i	−0.138092	+	0.0614823i	−0.474619	−	0.880191i	$-0.657414\pi$
$709$	−3.67697	+	1.63709i	−0.138092	+	0.0614823i	0.336527	+	0.941674i	$0.390748\pi$
$710$	−0.0399281	+	0.379891i	−0.00149848	+	0.0142570i
$711$	0.329273	+	1.54911i	0.0123487	+	0.0580961i
$712$	7.72621	+	1.64226i	0.289552	+	0.0615462i
$713$	10.2765	+	14.1444i	0.384858	+	0.529712i
$714$	−4.16796	+	0.221642i	−0.155982	+	0.00829473i
$715$	29.4147	+	14.1263i	1.10005	+	0.528294i
$716$	−5.89396	+	10.2086i	−0.220268	+	0.381515i
$717$	18.6046	+	8.28332i	0.694803	+	0.309346i
$718$	−24.1372	+	26.8071i	−0.900792	+	1.00043i
$719$	−14.1436	+	12.7350i	−0.527468	+	0.474934i	−0.889310	−	0.457305i	$-0.848815\pi$
$719$	−14.1436	+	12.7350i	−0.527468	+	0.474934i	0.361842	+	0.932239i	$0.382148\pi$
$720$	1.03603	−	1.42597i	0.0386104	−	0.0531427i
$721$	−4.32720	−	0.223449i	−0.161153	−	0.00832166i
$722$	−45.7576	−	14.8675i	−1.70292	−	0.553313i
$723$	−2.57278	+	12.1040i	−0.0956826	+	0.450151i
$724$	−7.14945	+	16.0579i	−0.265707	+	0.596788i
$725$	6.35076	−	3.66661i	0.235861	−	0.136175i
$726$	−9.77435	−	5.04601i	−0.362760	−	0.187275i
$727$			35.0199i			1.29882i	0.760440	+	0.649409i	$0.224983\pi$
$727$			35.0199i			1.29882i	−0.760440	+	0.649409i	$0.775017\pi$
$728$	14.5847	−	2.32146i	0.540544	−	0.0860391i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	11.8205	+	13.1280i	0.437498	+	0.485891i
$731$	−0.373097	−	0.0392141i	−0.0137995	−	0.00145039i
$732$	5.31283	+	0.558401i	0.196368	+	0.0206391i
$733$	−14.1345	−	15.6979i	−0.522069	−	0.579816i	0.423230	−	0.906022i	$-0.360896\pi$
$733$	−14.1345	−	15.6979i	−0.522069	−	0.579816i	−0.945299	+	0.326206i	$0.894230\pi$
$734$	−6.43311	−	19.7991i	−0.237450	−	0.730797i
$735$	11.7401	+	3.79468i	0.433041	+	0.139969i
$736$			3.18896i			0.117547i
$737$	−19.8488	−	29.0455i	−0.731141	−	1.06991i
$738$	5.71107	−	3.29729i	0.210227	−	0.121375i
$739$	15.2637	−	34.2828i	0.561484	−	1.26111i	−0.380291	−	0.924867i	$-0.624176\pi$
$739$	15.2637	−	34.2828i	0.561484	−	1.26111i	0.941774	−	0.336246i	$-0.109157\pi$
$740$	0.376972	−	1.77351i	0.0138578	−	0.0651956i
$741$	−43.4899	−	14.1307i	−1.59764	−	0.519105i
$742$	9.10286	+	17.8315i	0.334177	+	0.654616i
$743$	7.02101	−	9.66358i	0.257576	−	0.354523i	−0.660571	−	0.750764i	$-0.729686\pi$
$743$	7.02101	−	9.66358i	0.257576	−	0.354523i	0.918146	+	0.396241i	$0.129686\pi$
$744$	4.07428	−	3.66850i	0.149370	−	0.134494i
$745$	15.5690	−	17.2912i	0.570405	−	0.633499i
$746$	34.4664	+	15.3454i	1.26190	+	0.561836i
$747$	5.32286	−	9.21947i	0.194753	−	0.337323i
$748$	−0.939794	−	5.14711i	−0.0343623	−	0.188197i
$749$	4.16820	−	2.71141i	0.152303	−	0.0990728i
$750$	7.14160	+	9.82957i	0.260775	+	0.358925i
$751$	12.0666	+	2.56483i	0.440315	+	0.0935919i	0.422734	−	0.906254i	$-0.361070\pi$
$751$	12.0666	+	2.56483i	0.440315	+	0.0935919i	0.0175806	+	0.999845i	$0.494404\pi$
$752$	−0.287918	−	1.35455i	−0.0104993	−	0.0493953i
$753$	−0.374762	+	3.56562i	−0.0136571	+	0.129938i
$754$	19.7512	−	8.79382i	0.719298	−	0.320252i
$755$	−11.1616	+	34.3518i	−0.406212	+	1.25019i
$756$	−2.46929	+	0.950048i	−0.0898073	+	0.0345529i
$757$	1.37458	−	0.998690i	0.0499599	−	0.0362980i	−0.562525	−	0.826780i	$-0.690170\pi$
$757$	1.37458	−	0.998690i	0.0499599	−	0.0362980i	0.612485	+	0.790482i	$0.290170\pi$
$758$	6.30024	+	3.63745i	0.228835	+	0.132118i
$759$	9.78223	−	4.02146i	0.355072	−	0.145970i
$760$	7.21977	+	12.5050i	0.261889	+	0.453604i
$761$	−5.07578	−	48.2928i	−0.183997	−	1.75061i	−0.564134	−	0.825683i	$-0.690790\pi$
$761$	−5.07578	−	48.2928i	−0.183997	−	1.75061i	0.380138	−	0.924930i	$-0.375877\pi$
$762$	11.2841	−	3.66644i	0.408782	−	0.132821i
$763$	−10.3605	−	2.76755i	−0.375074	−	0.100192i
$764$	1.99915	+	1.45247i	0.0723267	+	0.0525484i
$765$	−1.13098	−	2.54021i	−0.0408905	−	0.0918416i
$766$	15.6382	−	3.32400i	0.565031	−	0.120101i
$767$	−28.0543	−	25.2602i	−1.01298	−	0.912093i
$768$	0.994522	−	0.104528i	0.0358867	−	0.00377185i
$769$	−26.3181			−0.949053			−0.474527	−	0.880241i	$-0.657381\pi$
$769$	−26.3181			−0.949053			−0.474527	+	0.880241i	$0.657381\pi$
$770$	−2.84739	+	15.2023i	−0.102613	+	0.547854i
$771$	−24.0613			−0.866547
$772$	21.5960	−	2.26983i	0.777256	−	0.0816928i
$773$	−17.5062	−	15.7626i	−0.629653	−	0.566942i	0.291292	−	0.956634i	$-0.405915\pi$
$773$	−17.5062	−	15.7626i	−0.629653	−	0.566942i	−0.920945	+	0.389692i	$0.872581\pi$
$774$	−0.232608	+	0.0494423i	−0.00836092	+	0.00177717i
$775$	4.22185	+	9.48242i	0.151653	+	0.340619i
$776$	6.48058	+	4.70842i	0.232639	+	0.169022i
$777$	−1.92300	+	1.92595i	−0.0689871	+	0.0690931i
$778$	−11.9136	+	3.87096i	−0.427123	+	0.138781i
$779$	5.64706	+	53.7282i	0.202327	+	1.92501i
$780$	4.91929	+	8.52046i	0.176139	+	0.305082i
$781$	0.611849	+	0.377185i	0.0218937	+	0.0134968i
$782$	4.35680	+	2.51540i	0.155799	+	0.0899505i
$783$	−3.13358	+	2.27668i	−0.111985	+	0.0813620i
$784$	2.85697	+	6.39044i	0.102035	+	0.228230i
$785$	−6.34632	+	19.5320i	−0.226510	+	0.697126i
$786$	16.9228	−	7.53451i	0.603616	−	0.268747i
$787$	−1.44053	+	13.7058i	−0.0513495	+	0.488558i	0.938380	+	0.345605i	$0.112326\pi$
$787$	−1.44053	+	13.7058i	−0.0513495	+	0.488558i	−0.989730	+	0.142953i	$0.954340\pi$
$788$	1.39230	+	6.55028i	0.0495988	+	0.233344i
$789$	8.31679	+	1.76779i	0.296085	+	0.0629349i
$790$	1.64077	+	2.25833i	0.0583760	+	0.0803477i
$791$	21.4505	−	42.1789i	0.762691	−	1.49971i
$792$	−1.57479	−	2.91891i	−0.0559578	−	0.103719i
$793$	−14.9095	+	25.8239i	−0.529450	+	0.917035i
$794$	−3.21291	−	1.43048i	−0.114022	−	0.0507659i
$795$	−8.92466	+	9.91183i	−0.316525	+	0.351537i
$796$	9.19123	−	8.27582i	0.325774	−	0.293329i
$797$	17.7045	−	24.3681i	0.627125	−	0.863163i	−0.370722	−	0.928744i	$-0.620890\pi$
$797$	17.7045	−	24.3681i	0.627125	−	0.863163i	0.997847	+	0.0655804i	$0.0208899\pi$
$798$	1.11775	−	21.6457i	0.0395678	−	0.766250i
$799$	−2.07771	−	0.675088i	−0.0735040	−	0.0238829i
$800$	−0.393632	+	1.85189i	−0.0139170	+	0.0654743i
$801$	3.21274	−	7.21593i	0.113517	−	0.254962i
$802$	−31.7026	+	18.3035i	−1.11946	+	0.646320i
$803$	31.8969	−	9.35600i	1.12562	−	0.330166i
$804$		−	10.6071i		−	0.374084i
$805$	−9.36771	−	11.5500i	−0.330168	−	0.407085i
$806$	9.45672	+	29.1048i	0.333099	+	1.02517i
$807$	−0.672404	−	0.746780i	−0.0236697	−	0.0262879i
$808$	18.6339	+	1.95850i	0.655537	+	0.0688997i
$809$	−5.45014	−	0.572832i	−0.191617	−	0.0201397i	0.00823400	−	0.999966i	$-0.497379\pi$
$809$	−5.45014	−	0.572832i	−0.191617	−	0.0201397i	−0.199851	+	0.979826i	$0.564046\pi$
$810$	−1.17940	−	1.30986i	−0.0414401	−	0.0460239i
$811$	−10.6960	−	32.9190i	−0.375589	−	1.15594i	−0.943081	−	0.332565i	$-0.892086\pi$
$811$	−10.6960	−	32.9190i	−0.375589	−	1.15594i	0.567492	−	0.823379i	$-0.307914\pi$
$812$	6.45529	+	7.95912i	0.226536	+	0.279310i
$813$		−	15.3141i		−	0.537088i
$814$	−2.70117	−	2.08413i	−0.0946759	−	0.0730486i
$815$	−28.1934	+	16.2775i	−0.987572	+	0.570175i
$816$	0.641655	−	1.44118i	0.0224624	−	0.0504514i
$817$	0.405042	−	1.90557i	0.0141706	−	0.0666676i
$818$	−20.7347	−	6.73712i	−0.724972	−	0.235558i
$819$	0.761592	−	14.7486i	0.0266122	−	0.515358i
$820$	6.83215	−	9.40365i	0.238589	−	0.328390i
$821$	−14.9968	+	13.5032i	−0.523392	+	0.471264i	−0.887965	−	0.459910i	$-0.847882\pi$
$821$	−14.9968	+	13.5032i	−0.523392	+	0.471264i	0.364573	+	0.931175i	$0.381215\pi$
$822$	−6.06698	+	6.73806i	−0.211610	+	0.235017i
$823$	48.2090	+	21.4640i	1.68046	+	0.748189i	0.999880	+	0.0155143i	$0.00493855\pi$
$823$	48.2090	+	21.4640i	1.68046	+	0.748189i	0.680579	+	0.732674i	$0.261728\pi$
$824$	0.818853	−	1.41830i	0.0285261	−	0.0494087i
$825$	6.17713	−	1.12786i	0.215060	−	0.0392672i
$826$	8.11122	−	15.9494i	0.282225	−	0.554951i
$827$	13.2624	+	18.2542i	0.461181	+	0.634761i	0.974753	−	0.223286i	$-0.0716783\pi$
$827$	13.2624	+	18.2542i	0.461181	+	0.634761i	−0.513573	+	0.858046i	$0.671678\pi$
$828$	3.11927	+	0.663022i	0.108402	+	0.0230416i
$829$	−0.842230	−	3.96238i	−0.0292518	−	0.137619i	0.961098	−	0.276206i	$-0.0890773\pi$
$829$	−0.842230	−	3.96238i	−0.0292518	−	0.137619i	−0.990350	+	0.138587i	$0.955744\pi$
$830$	1.96138	−	18.6613i	0.0680805	−	0.647743i
$831$	−7.38251	+	3.28690i	−0.256096	+	0.114021i
$832$	−1.72490	+	5.30868i	−0.0598000	+	0.184046i
$833$	10.9842	+	1.13744i	0.380581	+	0.0394101i
$834$	−8.98696	+	6.52941i	−0.311193	+	0.226095i
$835$	11.6934	+	6.75118i	0.404666	+	0.233634i
$836$	27.0923	−	2.05966i	0.937008	−	0.0712348i
$837$	−2.74124	−	4.74797i	−0.0947512	−	0.164114i
$838$	1.22481	+	11.6533i	0.0423103	+	0.402555i
$839$	36.4220	−	11.8342i	1.25743	−	0.408563i	0.396850	−	0.917883i	$-0.370103\pi$
$839$	36.4220	−	11.8342i	1.25743	−	0.408563i	0.860577	+	0.509320i	$0.170103\pi$
$840$	−3.29498	+	3.30004i	−0.113688	+	0.113862i
$841$	−11.3241	−	8.22745i	−0.390487	−	0.283705i
$842$	−11.8567	−	26.6307i	−0.408610	−	0.917753i
$843$	−18.4818	+	3.92842i	−0.636546	+	0.135302i
$844$	−17.1331	−	15.4267i	−0.589746	−	0.531010i
$845$	−31.8288	+	3.34534i	−1.09494	+	0.115083i
$846$	−1.38481			−0.0476107
$847$	23.4668	+	17.2136i	0.806330	+	0.591465i
$848$	−7.56708			−0.259855
$849$	−25.0818	+	2.63621i	−0.860806	+	0.0904744i
$850$	2.21959	+	1.99853i	0.0761314	+	0.0685490i
$851$	3.20872	−	0.682034i	0.109993	−	0.0233798i
$852$	0.0881466	+	0.197981i	0.00301985	+	0.00678270i
$853$	35.0928	+	25.4964i	1.20155	+	0.872981i	0.994437	−	0.105335i	$-0.0335915\pi$
$853$	35.0928	+	25.4964i	1.20155	+	0.872981i	0.207118	+	0.978316i	$0.433592\pi$
$854$	−13.6550	−	3.64763i	−0.467266	−	0.124819i
$855$	13.7328	−	4.46206i	0.469652	−	0.152599i
$856$	0.196453	+	1.86913i	0.00671463	+	0.0638855i
$857$	13.1525	+	22.7807i	0.449279	+	0.778175i	0.998339	−	0.0576082i	$-0.0183474\pi$
$857$	13.1525	+	22.7807i	0.449279	+	0.778175i	−0.549060	+	0.835783i	$0.685014\pi$
$858$	18.4597	−	1.40338i	0.630205	−	0.0479106i
$859$	−30.2125	−	17.4432i	−1.03084	−	0.595155i	−0.113614	−	0.993525i	$-0.536243\pi$
$859$	−30.2125	−	17.4432i	−1.03084	−	0.595155i	−0.917225	+	0.398370i	$0.869576\pi$
$860$	−0.339101	+	0.246372i	−0.0115633	+	0.00840120i
$861$	−16.2839	+	6.26516i	−0.554955	+	0.213516i
$862$	11.5256	−	35.4723i	0.392565	−	1.20819i
$863$	−6.42289	+	2.85965i	−0.218638	+	0.0973438i	−0.513133	−	0.858309i	$-0.671515\pi$
$863$	−6.42289	+	2.85965i	−0.218638	+	0.0973438i	0.294495	+	0.955653i	$0.404849\pi$
$864$	0.104528	−	0.994522i	0.00355613	−	0.0338343i
$865$	−9.53747	−	44.8703i	−0.324284	−	1.52564i
$866$	5.35719	+	1.13871i	0.182045	+	0.0386948i
$867$	8.52952	+	11.7399i	0.289678	+	0.398707i
$868$	−12.1591	+	7.90948i	−0.412707	+	0.268465i
$869$	5.16717	−	0.943458i	0.175284	−	0.0320046i
$870$	−3.41354	+	5.91243i	−0.115730	+	0.200450i
$871$	54.0889	+	24.0819i	1.83273	+	0.815985i
$872$	2.71211	−	3.01211i	0.0918437	−	0.102003i
$873$	5.95292	−	5.36003i	0.201476	−	0.181410i
$874$	−15.3557	+	21.1353i	−0.519414	+	0.714912i
$875$	−14.6159	−	28.6310i	−0.494109	−	0.967905i
$876$	9.53193	+	3.09711i	0.322054	+	0.104642i
$877$	−7.18454	+	33.8006i	−0.242605	+	1.14136i	0.673112	+	0.739540i	$0.264957\pi$
$877$	−7.18454	+	33.8006i	−0.242605	+	1.14136i	−0.915717	+	0.401825i	$0.868376\pi$
$878$	−6.00975	+	13.4981i	−0.202819	+	0.455539i
$879$	−17.6265	+	10.1767i	−0.594527	+	0.343250i
$880$	−4.62834	−	3.57107i	−0.156021	−	0.120381i
$881$			28.4742i			0.959321i	0.877454	+	0.479661i	$0.159240\pi$
$881$			28.4742i			0.959321i	−0.877454	+	0.479661i	$0.840760\pi$
$882$	6.84479	−	1.46589i	0.230476	−	0.0493591i
$883$	−3.09987	−	9.54041i	−0.104319	−	0.321060i	0.885251	−	0.465113i	$-0.153986\pi$
$883$	−3.09987	−	9.54041i	−0.104319	−	0.321060i	−0.989570	+	0.144053i	$0.953986\pi$
$884$	5.89223	+	6.54398i	0.198177	+	0.220098i
$885$	11.8553	+	1.24604i	0.398511	+	0.0418852i
$886$	−29.2925	−	3.07876i	−0.984099	−	0.103433i
$887$	17.8684	+	19.8449i	0.599963	+	0.666326i	0.964260	−	0.264956i	$-0.0853575\pi$
$887$	17.8684	+	19.8449i	0.599963	+	0.666326i	−0.364297	+	0.931283i	$0.618691\pi$
$888$	−0.317878	−	0.978328i	−0.0106673	−	0.0328305i
$889$	−31.0012	+	4.93450i	−1.03975	+	0.165498i
$890$		−	13.9224i		−	0.466680i
$891$	−3.18254	+	0.933504i	−0.106619	+	0.0312736i
$892$	17.6660	−	10.1995i	0.591501	−	0.341503i
$893$	4.61429	−	10.3639i	0.154411	−	0.346813i
$894$	2.74459	−	12.9123i	0.0917928	−	0.431851i
$895$	19.7604	+	6.42054i	0.660517	+	0.214615i
$896$	−2.64223	−	0.136440i	−0.0882707	−	0.00455814i
$897$	−10.4628	+	14.4008i	−0.349343	+	0.480830i
$898$	−4.86113	+	4.37698i	−0.162218	+	0.146062i
$899$	−14.2093	+	15.7810i	−0.473906	+	0.526326i
$900$	1.72958	+	0.770061i	0.0576528	+	0.0256687i
$901$	−5.96879	+	10.3383i	−0.198849	+	0.344417i
$902$	−10.3851	−	19.2490i	−0.345785	−	0.640920i
$903$	0.628284	−	0.0334105i	0.0209080	−	0.00111183i
$904$	10.5127	+	14.4695i	0.349648	+	0.481249i
$905$	30.3051	+	6.44155i	1.00738	+	0.214124i
$906$	4.26060	+	20.0445i	0.141549	+	0.665935i
$907$	−2.85779	+	27.1900i	−0.0948913	+	0.902830i	0.838725	+	0.544555i	$0.183302\pi$
$907$	−2.85779	+	27.1900i	−0.0948913	+	0.902830i	−0.933616	+	0.358275i	$0.883365\pi$
$908$	−8.24362	+	3.67030i	−0.273574	+	0.121803i
$909$	5.78990	−	17.8195i	0.192039	−	0.591035i
$910$	−9.34713	−	24.2943i	−0.309854	−	0.805350i
$911$	4.44954	−	3.23278i	0.147420	−	0.107107i	−0.511631	−	0.859206i	$-0.670958\pi$
$911$	4.44954	−	3.23278i	0.147420	−	0.107107i	0.659050	+	0.752099i	$0.270958\pi$
$912$	7.09467	+	4.09611i	0.234928	+	0.135636i
$913$	−30.0557	−	18.5284i	−0.994698	−	0.613200i
$914$	−3.88782	−	6.73390i	−0.128598	−	0.222737i
$915$	−0.984233	−	9.36435i	−0.0325377	−	0.309576i
$916$	−6.56633	+	2.13353i	−0.216958	+	0.0704938i
$917$	−47.3309	+	12.7212i	−1.56300	+	0.420092i
$918$	−1.27628	−	0.927271i	−0.0421235	−	0.0306045i
$919$	−18.7958	−	42.2160i	−0.620016	−	1.39258i	−0.901402	−	0.432984i	$-0.857461\pi$
$919$	−18.7958	−	42.2160i	−0.620016	−	1.39258i	0.281386	−	0.959595i	$-0.409206\pi$
$920$	5.49801	−	1.16864i	0.181264	−	0.0385289i
$921$	−5.38978	−	4.85298i	−0.177599	−	0.159911i
$922$	27.6747	−	2.90872i	0.911416	−	0.0957937i
$923$	−1.20969			−0.0398173
$924$	2.91347	+	8.27718i	0.0958460	+	0.272299i
$925$	1.94755			0.0640352
$926$	37.4768	−	3.93897i	1.23156	−	0.129443i
$927$	−1.21705	−	1.09584i	−0.0399733	−	0.0359921i
$928$	−3.78868	+	0.805309i	−0.124370	+	0.0264356i
$929$	2.41358	+	5.42100i	0.0791871	+	0.177857i	0.948800	−	0.315876i	$-0.102298\pi$
$929$	2.41358	+	5.42100i	0.0791871	+	0.177857i	−0.869613	+	0.493734i	$0.835632\pi$
$930$	−7.81785	−	5.68000i	−0.256357	−	0.186254i
$931$	−11.8367	+	56.1106i	−0.387932	+	1.83895i
$932$	2.71889	−	0.883421i	0.0890603	−	0.0289374i
$933$	−0.354397	−	3.37186i	−0.0116024	−	0.110390i
$934$	−3.79965	−	6.58119i	−0.124328	−	0.215343i
$935$	−8.52960	+	3.50650i	−0.278948	+	0.114675i
$936$	4.83405	+	2.79094i	0.158006	+	0.0912247i
$937$	16.2313	−	11.7927i	0.530253	−	0.385252i	−0.290199	−	0.956966i	$-0.593722\pi$
$937$	16.2313	−	11.7927i	0.530253	−	0.385252i	0.820453	+	0.571715i	$0.193722\pi$
$938$	−4.36887	+	27.7216i	−0.142649	+	0.905143i
$939$	−5.51692	+	16.9793i	−0.180038	+	0.554099i
$940$	−2.22983	+	0.992785i	−0.0727291	+	0.0323811i
$941$	3.45779	−	32.8987i	0.112721	−	1.07247i	−0.781212	−	0.624266i	$-0.785398\pi$
$941$	3.45779	−	32.8987i	0.112721	−	1.07247i	0.893933	−	0.448201i	$-0.147935\pi$
$942$	2.42252	+	11.3970i	0.0789299	+	0.371336i
$943$	20.5703	+	4.37235i	0.669860	+	0.142383i
$944$	3.97524	+	5.47145i	0.129383	+	0.178081i
$945$	2.54286	+	3.90909i	0.0827193	+	0.127163i
$946$	0.141666	+	0.775881i	0.00460595	+	0.0252261i
$947$	15.3745	−	26.6294i	0.499604	−	0.865339i	−0.500396	−	0.865796i	$-0.666812\pi$
$947$	15.3745	−	26.6294i	0.499604	−	0.865339i	1.00000		0.000457686i	$0.000145686\pi$
$948$	1.44680	+	0.644156i	0.0469898	+	0.0209212i
$949$	−37.4340	+	41.5746i	−1.21516	+	1.34957i
$950$	−11.5262	+	10.3782i	−0.373960	+	0.336715i
$951$	9.27416	−	12.7648i	0.300735	−	0.413926i
$952$	−2.27056	+	3.50223i	−0.0735891	+	0.113508i
$953$	−36.9208	−	11.9963i	−1.19598	−	0.388598i	−0.357702	−	0.933836i	$-0.616439\pi$
$953$	−36.9208	−	11.9963i	−1.19598	−	0.388598i	−0.838282	+	0.545238i	$0.816439\pi$
$954$	−1.57329	+	7.40172i	−0.0509370	+	0.239640i
$955$	1.77155	−	3.97896i	0.0573260	−	0.128756i
$956$	17.6369	−	10.1827i	0.570418	−	0.329331i
$957$	7.24805	+	10.6063i	0.234296	+	0.342855i
$958$			35.9860i			1.16266i
$959$	18.6313	−	15.1110i	0.601636	−	0.487960i
$960$	−0.544671	−	1.67633i	−0.0175792	−	0.0541032i
$961$	0.630559	+	0.700307i	0.0203406	+	0.0225905i
$962$	5.71048	+	0.600196i	0.184113	+	0.0193511i
$963$	1.86913	+	0.196453i	0.0602318	+	0.00633062i
$964$	8.28007	+	9.19595i	0.266683	+	0.296181i
$965$	−11.8275	−	36.4013i	−0.380740	−	1.17180i
$966$	−7.87912	−	3.01757i	−0.253507	−	0.0970889i
$967$		−	13.6406i		−	0.438653i	−0.975651	−	0.219327i	$-0.929614\pi$
$967$		−	13.6406i		−	0.438653i	0.975651	−	0.219327i	$-0.0703860\pi$
$968$	−9.82752	+	4.94164i	−0.315868	+	0.158830i
$969$	11.1923	−	6.46189i	0.359549	−	0.207586i
$970$	5.74277	−	12.8985i	0.184389	−	0.414145i
$971$	11.8314	−	55.6625i	0.379688	−	1.78629i	−0.208981	−	0.977920i	$-0.567015\pi$
$971$	11.8314	−	55.6625i	0.379688	−	1.78629i	0.588669	−	0.808374i	$-0.299652\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	26.1767	−	13.3630i	0.839187	−	0.428399i
$974$	−8.42468	+	11.5956i	−0.269944	+	0.371546i
$975$	−7.85354	+	7.07136i	−0.251515	+	0.226465i
$976$	3.57456	−	3.96995i	0.114419	−	0.127075i
$977$	−27.3631	−	12.1828i	−0.875424	−	0.389764i	−0.0807023	−	0.996738i	$-0.525716\pi$
$977$	−27.3631	−	12.1828i	−0.875424	−	0.389764i	−0.794721	+	0.606975i	$0.792383\pi$
$978$	−9.23496	+	15.9954i	−0.295301	+	0.511477i
$979$	−23.6153	−	11.3412i	−0.754748	−	0.362466i
$980$	9.97063	−	7.26750i	0.318500	−	0.232152i
$981$	−2.38240	−	3.27910i	−0.0760643	−	0.104694i
$982$	27.2178	+	5.78531i	0.868554	+	0.184617i
$983$	−3.56118	−	16.7540i	−0.113584	−	0.534370i	−0.997741	−	0.0671802i	$-0.978600\pi$
$983$	−3.56118	−	16.7540i	−0.113584	−	0.534370i	0.884157	−	0.467190i	$-0.154734\pi$
$984$	0.689320	−	6.55845i	0.0219747	−	0.209076i
$985$	10.7829	−	4.80088i	0.343573	−	0.152969i
$986$	−1.88823	+	5.81136i	−0.0601334	+	0.185071i
$987$	3.61919	+	0.570377i	0.115200	+	0.0181553i
$988$	−36.9947	+	26.8782i	−1.17696	+	0.855110i
$989$	−0.656749	−	0.379174i	−0.0208834	−	0.0120570i
$990$	−4.45532	+	3.78474i	−0.141599	+	0.120287i
$991$	−16.0095	−	27.7293i	−0.508560	−	0.880851i	−0.999951	−	0.00991210i	$-0.996845\pi$
$991$	−16.0095	−	27.7293i	−0.508560	−	0.880851i	0.491391	−	0.870939i	$-0.336489\pi$
$992$	−0.573076	−	5.45245i	−0.0181952	−	0.173116i
$993$	31.4582	−	10.2214i	0.998296	−	0.324366i
$994$	−0.148826	−	0.553727i	−0.00472048	−	0.0175632i
$995$	−17.6364	−	12.8136i	−0.559111	−	0.406218i
$996$	−4.33001	−	9.72535i	−0.137201	−	0.308160i
$997$	−34.2723	+	7.28480i	−1.08541	+	0.230712i	−0.715682	−	0.698426i	$-0.753884\pi$
$997$	−34.2723	+	7.28480i	−1.08541	+	0.230712i	−0.369733	+	0.929138i	$0.620551\pi$
$998$	−15.3536	−	13.8244i	−0.486010	−	0.437605i
$999$	−1.02304	+	0.107526i	−0.0323675	+	0.00340196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.a.19.2	✓	64
7.3	odd	6		462.2.ba.b.283.6	yes	64
11.7	odd	10		462.2.ba.b.271.6	yes	64
77.73	even	30	inner	462.2.ba.a.73.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.19.2	✓	64	1.1	even	1	trivial
462.2.ba.a.73.2	yes	64	77.73	even	30	inner
462.2.ba.b.271.6	yes	64	11.7	odd	10
462.2.ba.b.283.6	yes	64	7.3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.716911 - 1.61021i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(1.87226 + 1.86939i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.716911 - 1.61021i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(1.87226 + 1.86939i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(0.881296 + 1.52645i) q^{10} +(3.30708 - 0.251417i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-4.51584 + 3.28095i) q^{13} +(-2.05741 - 1.66345i) q^{14} +(0.544671 - 1.67633i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.164901 - 1.56893i) q^{17} +(-0.207912 - 0.978148i) q^{18} +(8.01319 + 1.70326i) q^{19} +(-1.03603 - 1.42597i) q^{20} +(0.140496 + 2.64202i) q^{21} +(-3.26268 + 0.595724i) q^{22} +(1.59448 - 2.76172i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(1.26684 - 1.40697i) q^{25} +(4.14815 - 3.73501i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.22002 + 1.43928i) q^{28} +(3.68375 + 1.19692i) q^{29} +(-0.366464 + 1.72408i) q^{30} +(-2.22993 + 5.00850i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.62587 + 2.02603i) q^{33} +1.57757i q^{34} +(1.66786 - 4.35492i) q^{35} +(0.309017 + 0.951057i) q^{36} +(0.688318 + 0.764454i) q^{37} +(-8.14734 - 0.856320i) q^{38} +(-5.55130 - 0.583465i) q^{39} +(1.17940 + 1.30986i) q^{40} +(2.03783 + 6.27181i) q^{41} +(-0.415892 - 2.61286i) q^{42} -0.237804i q^{43} +(3.18254 - 0.933504i) q^{44} +(1.52645 - 0.881296i) q^{45} +(-1.29707 + 2.91326i) q^{46} +(0.287918 - 1.35455i) q^{47} +(0.951057 + 0.309017i) q^{48} +(0.0107455 + 6.99999i) q^{49} +(-1.11283 + 1.53168i) q^{50} +(1.17236 - 1.05560i) q^{51} +(-3.73501 + 4.14815i) q^{52} +(-6.91287 - 3.07781i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.77572 - 5.14485i) q^{55} +(-2.35830 - 1.19934i) q^{56} +(4.81526 + 6.62764i) q^{57} +(-3.78868 - 0.805309i) q^{58} +(1.40613 + 6.61530i) q^{59} +(0.184241 - 1.75294i) q^{60} +(4.88024 - 2.17282i) q^{61} +(1.69418 - 5.21415i) q^{62} +(-1.66345 + 2.05741i) q^{63} +(0.809017 - 0.587785i) q^{64} +(8.52046 + 4.91929i) q^{65} +(-2.82326 - 1.74045i) q^{66} +(-5.30356 - 9.18603i) q^{67} +(-0.164901 - 1.56893i) q^{68} +(3.03288 - 0.985443i) q^{69} +(-1.20351 + 4.50541i) q^{70} +(0.175328 + 0.127383i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(9.80345 - 2.08379i) q^{73} +(-0.764454 - 0.688318i) q^{74} +(1.88289 - 0.197900i) q^{75} +8.19221 q^{76} +(6.66173 + 5.71151i) q^{77} +5.58188 q^{78} +(1.57504 - 0.165543i) q^{79} +(-1.30986 - 1.17940i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-2.68225 - 6.02444i) q^{82} +(-8.61257 - 6.25740i) q^{83} +(0.686732 + 2.55507i) q^{84} +(-2.64452 + 0.859256i) q^{85} +(0.0248573 + 0.236502i) q^{86} +(1.93666 + 3.35439i) q^{87} +(-3.06753 + 1.26106i) q^{88} +(-6.84058 - 3.94941i) q^{89} +(-1.42597 + 1.03603i) q^{90} +(-14.5882 - 2.29907i) q^{91} +(0.985443 - 3.03288i) q^{92} +(-5.00850 + 2.22993i) q^{93} +(-0.144752 + 1.37722i) q^{94} +(-3.00215 - 14.1240i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-4.70842 - 6.48058i) q^{97} +(-0.742385 - 6.96052i) q^{98} +(0.595724 + 3.26268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

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