LMFDB - Embedded newform 462.2.ba.b.61.6

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			61.6
Character	$\chi$	$=$	462.61
Dual form			462.2.ba.b.409.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.716223 + 0.644890i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(2.17783 + 1.50235i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.716223 + 0.644890i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(2.17783 + 1.50235i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(0.481886 + 0.834652i) q^{10} +(0.870641 - 3.20031i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.544440 - 1.67561i) q^{13} +(1.92232 - 1.81788i) q^{14} +(0.779709 - 0.566492i) q^{15} +(0.669131 + 0.743145i) q^{16} +(6.86988 - 1.46024i) q^{17} +(0.406737 - 0.913545i) q^{18} +(2.62462 - 1.16856i) q^{19} +(0.916603 - 0.297822i) q^{20} +(-2.00886 - 1.72176i) q^{21} +(-2.94936 - 1.51700i) q^{22} +(1.43322 - 2.48240i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.425550 + 4.04884i) q^{25} +(-1.75219 + 0.184163i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(-1.37849 - 2.25827i) q^{28} +(-6.05246 - 8.33049i) q^{29} +(-0.392002 - 0.880450i) q^{30} +(5.77486 + 5.19971i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.20040 + 3.09177i) q^{33} -7.02336i q^{34} +(-2.52866 + 0.328445i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-0.904640 - 8.60708i) q^{37} +(-0.597331 - 2.81022i) q^{38} +(0.366308 + 1.72334i) q^{39} +(-0.100742 - 0.958493i) q^{40} +(0.922748 + 0.670416i) q^{41} +(-2.10181 + 1.60699i) q^{42} -3.60525i q^{43} +(-2.09705 + 2.56951i) q^{44} +(-0.834652 + 0.481886i) q^{45} +(-2.13017 - 1.91802i) q^{46} +(0.759218 + 1.70523i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(2.48590 + 6.54372i) q^{49} +(3.87189 + 1.25805i) q^{50} +(-6.98488 + 0.734141i) q^{51} +(-0.184163 + 1.75219i) q^{52} +(2.60908 - 2.89768i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.44027 + 2.85360i) q^{55} +(-2.49552 + 0.878844i) q^{56} +(-2.73239 + 0.887808i) q^{57} +(-9.40683 + 4.18819i) q^{58} +(-3.59802 + 8.08128i) q^{59} +(-0.942712 + 0.200380i) q^{60} +(7.70182 + 8.55374i) q^{61} +(6.28674 - 4.56758i) q^{62} +(1.81788 + 1.92232i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(1.47053 + 0.849008i) q^{65} +(2.77463 + 1.81698i) q^{66} +(7.58406 + 13.1360i) q^{67} +(-6.86988 - 1.46024i) q^{68} +(-1.68485 + 2.31899i) q^{69} +(-0.204471 + 2.54169i) q^{70} +(3.16680 - 9.74640i) q^{71} +(-0.743145 + 0.669131i) q^{72} +(-6.84277 - 3.04660i) q^{73} +(-8.60708 - 0.904640i) q^{74} +(0.846438 - 3.98218i) q^{75} -2.87301 q^{76} +(6.70409 - 5.66173i) q^{77} +1.76184 q^{78} +(-1.42869 + 6.72144i) q^{79} +(-0.958493 - 0.100742i) q^{80} +(0.913545 + 0.406737i) q^{81} +(0.847616 - 0.763197i) q^{82} +(-0.368215 + 1.13325i) q^{83} +(1.13488 + 2.38999i) q^{84} +(-3.97867 + 5.47617i) q^{85} +(-3.52646 - 0.749573i) q^{86} +(5.14853 + 8.91751i) q^{87} +(2.07736 + 2.58546i) q^{88} +(-0.125384 - 0.0723905i) q^{89} +(0.297822 + 0.916603i) q^{90} +(1.33166 - 4.46714i) q^{91} +(-2.31899 + 1.68485i) q^{92} +(-5.19971 - 5.77486i) q^{93} +(1.82582 - 0.388090i) q^{94} +(-1.12622 + 2.52954i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-13.4066 + 4.35607i) q^{97} +(6.91757 - 1.07106i) q^{98} +(1.51700 - 2.94936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 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} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * 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 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * 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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$3$	−0.994522	−	0.104528i	−0.574187	−	0.0603495i
$3$	−0.994522	−	0.104528i	−0.574187	−	0.0603495i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	−0.716223	+	0.644890i	−0.320305	+	0.288404i	−0.813560	−	0.581481i	$-0.802473\pi$
$5$	−0.716223	+	0.644890i	−0.320305	+	0.288404i	0.493255	+	0.869885i	$0.335807\pi$
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	2.17783	+	1.50235i	0.823143	+	0.567834i
$7$	2.17783	+	1.50235i	0.823143	+	0.567834i
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.978148	+	0.207912i	0.326049	+	0.0693039i
$10$	0.481886	+	0.834652i	0.152386	+	0.263940i
$11$	0.870641	−	3.20031i	0.262508	−	0.964930i
$11$	0.870641	−	3.20031i	0.262508	−	0.964930i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−0.544440	−	1.67561i	−0.151000	−	0.464731i	0.846733	−	0.532018i	$-0.178566\pi$
$13$	−0.544440	−	1.67561i	−0.151000	−	0.464731i	−0.997734	+	0.0672862i	$0.978566\pi$
$14$	1.92232	−	1.81788i	0.513760	−	0.485850i
$15$	0.779709	−	0.566492i	0.201320	−	0.146267i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	6.86988	−	1.46024i	1.66619	−	0.354160i	0.724146	−	0.689647i	$-0.242234\pi$
$17$	6.86988	−	1.46024i	1.66619	−	0.354160i	0.942045	+	0.335487i	$0.108901\pi$
$18$	0.406737	−	0.913545i	0.0958687	−	0.215325i
$19$	2.62462	−	1.16856i	0.602129	−	0.268085i	−0.0829500	−	0.996554i	$-0.526434\pi$
$19$	2.62462	−	1.16856i	0.602129	−	0.268085i	0.685079	+	0.728468i	$0.259767\pi$
$20$	0.916603	−	0.297822i	0.204959	−	0.0665951i
$21$	−2.00886	−	1.72176i	−0.438370	−	0.375720i
$22$	−2.94936	−	1.51700i	−0.628805	−	0.323425i
$23$	1.43322	−	2.48240i	0.298846	−	0.517617i	−0.677026	−	0.735959i	$-0.736732\pi$
$23$	1.43322	−	2.48240i	0.298846	−	0.517617i	0.975872	+	0.218342i	$0.0700649\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.425550	+	4.04884i	−0.0851100	+	0.809768i
$26$	−1.75219	+	0.184163i	−0.343633	+	0.0361173i
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	−1.37849	−	2.25827i	−0.260510	−	0.426772i
$29$	−6.05246	−	8.33049i	−1.12391	−	1.54693i	−0.799143	−	0.601141i	$-0.794713\pi$
$29$	−6.05246	−	8.33049i	−1.12391	−	1.54693i	−0.324770	−	0.945793i	$-0.605287\pi$
$30$	−0.392002	−	0.880450i	−0.0715694	−	0.160748i
$31$	5.77486	+	5.19971i	1.03720	+	0.933895i	0.997864	−	0.0653316i	$-0.0208105\pi$
$31$	5.77486	+	5.19971i	1.03720	+	0.933895i	0.0393314	+	0.999226i	$0.487477\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.20040	+	3.09177i	−0.208962	+	0.538208i
$34$		−	7.02336i		−	1.20450i
$35$	−2.52866	+	0.328445i	−0.427422	+	0.0555173i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	−0.904640	−	8.60708i	−0.148722	−	1.41500i	−0.773304	−	0.634036i	$-0.781397\pi$
$37$	−0.904640	−	8.60708i	−0.148722	−	1.41500i	0.624582	−	0.780959i	$-0.285269\pi$
$38$	−0.597331	−	2.81022i	−0.0969000	−	0.455878i
$39$	0.366308	+	1.72334i	0.0586562	+	0.275956i
$40$	−0.100742	−	0.958493i	−0.0159287	−	0.151551i
$41$	0.922748	+	0.670416i	0.144109	+	0.104701i	0.657504	−	0.753451i	$-0.271612\pi$
$41$	0.922748	+	0.670416i	0.144109	+	0.104701i	−0.513395	+	0.858153i	$0.671612\pi$
$42$	−2.10181	+	1.60699i	−0.324316	+	0.247964i
$43$		−	3.60525i		−	0.549795i	−0.961474	−	0.274897i	$-0.911356\pi$
$43$		−	3.60525i		−	0.549795i	0.961474	−	0.274897i	$-0.0886439\pi$
$44$	−2.09705	+	2.56951i	−0.316143	+	0.387368i
$45$	−0.834652	+	0.481886i	−0.124423	+	0.0718354i
$46$	−2.13017	−	1.91802i	−0.314077	−	0.282796i
$47$	0.759218	+	1.70523i	0.110743	+	0.248733i	0.960412	−	0.278583i	$-0.0898648\pi$
$47$	0.759218	+	1.70523i	0.110743	+	0.248733i	−0.849669	+	0.527317i	$0.823198\pi$
$48$	−0.587785	−	0.809017i	−0.0848395	−	0.116772i
$49$	2.48590	+	6.54372i	0.355128	+	0.934818i
$50$	3.87189	+	1.25805i	0.547567	+	0.177915i
$51$	−6.98488	+	0.734141i	−0.978079	+	0.102800i
$52$	−0.184163	+	1.75219i	−0.0255388	+	0.242985i
$53$	2.60908	−	2.89768i	0.358385	−	0.398027i	−0.536809	−	0.843704i	$-0.680370\pi$
$53$	2.60908	−	2.89768i	0.358385	−	0.398027i	0.895194	+	0.445677i	$0.147037\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	1.44027	+	2.85360i	0.194207	+	0.384780i
$56$	−2.49552	+	0.878844i	−0.333478	+	0.117440i
$57$	−2.73239	+	0.887808i	−0.361914	+	0.117593i
$58$	−9.40683	+	4.18819i	−1.23518	+	0.549936i
$59$	−3.59802	+	8.08128i	−0.468422	+	1.05209i	0.512676	+	0.858582i	$0.328654\pi$
$59$	−3.59802	+	8.08128i	−0.468422	+	1.05209i	−0.981098	+	0.193511i	$0.938012\pi$
$60$	−0.942712	+	0.200380i	−0.121704	+	0.0258689i
$61$	7.70182	+	8.55374i	0.986118	+	1.09519i	0.995455	+	0.0952380i	$0.0303612\pi$
$61$	7.70182	+	8.55374i	0.986118	+	1.09519i	−0.00933701	+	0.999956i	$0.502972\pi$
$62$	6.28674	−	4.56758i	0.798417	−	0.580084i
$63$	1.81788	+	1.92232i	0.229032	+	0.242189i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	1.47053	+	0.849008i	0.182396	+	0.105307i
$66$	2.77463	+	1.81698i	0.341534	+	0.223655i
$67$	7.58406	+	13.1360i	0.926541	+	1.60482i	0.789064	+	0.614311i	$0.210566\pi$
$67$	7.58406	+	13.1360i	0.926541	+	1.60482i	0.137476	+	0.990505i	$0.456101\pi$
$68$	−6.86988	−	1.46024i	−0.833095	−	0.177080i
$69$	−1.68485	+	2.31899i	−0.202832	+	0.279174i
$70$	−0.204471	+	2.54169i	−0.0244389	+	0.303790i
$71$	3.16680	−	9.74640i	0.375830	−	1.15668i	−0.567087	−	0.823658i	$-0.691930\pi$
$71$	3.16680	−	9.74640i	0.375830	−	1.15668i	0.942917	−	0.333027i	$-0.108070\pi$
$72$	−0.743145	+	0.669131i	−0.0875805	+	0.0788578i
$73$	−6.84277	−	3.04660i	−0.800885	−	0.356577i	−0.0348638	−	0.999392i	$-0.511100\pi$
$73$	−6.84277	−	3.04660i	−0.800885	−	0.356577i	−0.766021	+	0.642815i	$0.777766\pi$
$74$	−8.60708	−	0.904640i	−1.00055	−	0.105162i
$75$	0.846438	−	3.98218i	0.0977382	−	0.459822i
$76$	−2.87301			−0.329556
$77$	6.70409	−	5.66173i	0.764002	−	0.645214i
$78$	1.76184			0.199489
$79$	−1.42869	+	6.72144i	−0.160740	+	0.756221i	0.821742	+	0.569860i	$0.193003\pi$
$79$	−1.42869	+	6.72144i	−0.160740	+	0.756221i	−0.982481	+	0.186361i	$0.940331\pi$
$80$	−0.958493	−	0.100742i	−0.107163	−	0.0112633i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	0.847616	−	0.763197i	0.0936035	−	0.0842810i
$83$	−0.368215	+	1.13325i	−0.0404168	+	0.124390i	−0.969229	−	0.246160i	$-0.920831\pi$
$83$	−0.368215	+	1.13325i	−0.0404168	+	0.124390i	0.928812	+	0.370551i	$0.120831\pi$
$84$	1.13488	+	2.38999i	0.123826	+	0.260769i
$85$	−3.97867	+	5.47617i	−0.431548	+	0.593974i
$86$	−3.52646	−	0.749573i	−0.380268	−	0.0808285i
$87$	5.14853	+	8.91751i	0.551980	+	0.956058i
$88$	2.07736	+	2.58546i	0.221447	+	0.275611i
$89$	−0.125384	−	0.0723905i	−0.0132907	−	0.00767338i	0.493340	−	0.869837i	$-0.335776\pi$
$89$	−0.125384	−	0.0723905i	−0.0132907	−	0.00767338i	−0.506631	+	0.862163i	$0.669109\pi$
$90$	0.297822	+	0.916603i	0.0313932	+	0.0966184i
$91$	1.33166	−	4.46714i	0.139596	−	0.468283i
$92$	−2.31899	+	1.68485i	−0.241772	+	0.175657i
$93$	−5.19971	−	5.77486i	−0.539184	−	0.598825i
$94$	1.82582	−	0.388090i	0.188319	−	0.0400284i
$95$	−1.12622	+	2.52954i	−0.115548	+	0.259525i
$96$	−0.913545	+	0.406737i	−0.0932383	+	0.0415124i
$97$	−13.4066	+	4.35607i	−1.36124	+	0.442292i	−0.896455	−	0.443134i	$-0.853867\pi$
$97$	−13.4066	+	4.35607i	−1.36124	+	0.442292i	−0.464780	+	0.885426i	$0.653867\pi$
$98$	6.91757	−	1.07106i	0.698781	−	0.108193i
$99$	1.51700	−	2.94936i	0.152464	−	0.296422i
$100$	2.03557	−	3.52571i	0.203557	−	0.352571i
$101$	7.65966	−	8.50691i	0.762165	−	0.846470i	−0.229767	−	0.973246i	$-0.573796\pi$
$101$	7.65966	−	8.50691i	0.762165	−	0.846470i	0.991931	+	0.126776i	$0.0404630\pi$
$102$	−0.734141	+	6.98488i	−0.0726908	+	0.691607i
$103$	−7.45326	+	0.783369i	−0.734391	+	0.0771876i	−0.464338	−	0.885658i	$-0.653708\pi$
$103$	−7.45326	+	0.783369i	−0.734391	+	0.0771876i	−0.270053	+	0.962845i	$0.587041\pi$
$104$	1.67561	+	0.544440i	0.164307	+	0.0533867i
$105$	2.54914	−	0.0623284i	0.248771	−	0.00608263i
$106$	−2.29190	−	3.15453i	−0.222609	−	0.306395i
$107$	6.07667	+	13.6484i	0.587454	+	1.31944i	0.925655	+	0.378369i	$0.123515\pi$
$107$	6.07667	+	13.6484i	0.587454	+	1.31944i	−0.338201	+	0.941074i	$0.609818\pi$
$108$	0.743145	+	0.669131i	0.0715091	+	0.0643871i
$109$	−2.64672	+	1.52808i	−0.253510	+	0.146364i	−0.621370	−	0.783517i	$-0.713424\pi$
$109$	−2.64672	+	1.52808i	−0.253510	+	0.146364i	0.367860	+	0.929881i	$0.380090\pi$
$110$	3.09069	−	0.815504i	0.294686	−	0.0777552i
$111$			8.65449i			0.821448i
$112$	0.340791	+	2.62371i	0.0322017	+	0.247917i
$113$	−15.2887	−	11.1079i	−1.43824	−	1.04494i	−0.988407	−	0.151831i	$-0.951483\pi$
$113$	−15.2887	−	11.1079i	−1.43824	−	1.04494i	−0.449834	−	0.893112i	$-0.648517\pi$
$114$	0.300311	+	2.85727i	0.0281267	+	0.267608i
$115$	0.574375	+	2.70222i	0.0535607	+	0.251983i
$116$	2.14088	+	10.0720i	0.198776	+	0.935166i
$117$	−0.184163	−	1.75219i	−0.0170259	−	0.161990i
$118$	7.15662	+	5.19959i	0.658820	+	0.478661i
$119$	17.1552	+	7.14081i	1.57262	+	0.654597i
$120$			0.963773i			0.0879800i
$121$	−9.48397	−	5.57264i	−0.862179	−	0.506604i
$122$	9.96812	−	5.75510i	0.902471	−	0.521042i
$123$	−0.847616	−	0.763197i	−0.0764269	−	0.0688151i
$124$	−3.16068	−	7.09901i	−0.283838	−	0.637510i
$125$	−5.13872	−	7.07285i	−0.459622	−	0.632615i
$126$	2.25827	−	1.37849i	0.201182	−	0.122805i
$127$	0.937326	+	0.304556i	0.0831742	+	0.0270249i	0.350309	−	0.936634i	$-0.386077\pi$
$127$	0.937326	+	0.304556i	0.0831742	+	0.0270249i	−0.267134	+	0.963659i	$0.586077\pi$
$128$	−0.994522	+	0.104528i	−0.0879041	+	0.00923910i
$129$	−0.376851	+	3.58550i	−0.0331799	+	0.315685i
$130$	1.13620	−	1.26187i	0.0996509	−	0.110674i
$131$	−0.800607	+	1.38669i	−0.0699494	+	0.121156i	−0.898879	−	0.438197i	$-0.855617\pi$
$131$	−0.800607	+	1.38669i	−0.0699494	+	0.121156i	0.828929	+	0.559353i	$0.188950\pi$
$132$	2.35415	−	2.33623i	0.204903	−	0.203343i
$133$	7.47156	+	1.39818i	0.647867	+	0.121237i
$134$	14.4257	−	4.68721i	1.24619	−	0.404913i
$135$	0.880450	−	0.392002i	0.0757771	−	0.0337381i
$136$	−2.85666	+	6.41616i	−0.244956	+	0.550181i
$137$	−21.7421	+	4.62142i	−1.85755	+	0.394834i	−0.993996	−	0.109421i	$-0.965100\pi$
$137$	−21.7421	+	4.62142i	−1.85755	+	0.394834i	−0.863555	+	0.504255i	$0.831767\pi$
$138$	1.91802	+	2.13017i	0.163272	+	0.181332i
$139$	3.97749	−	2.88981i	0.337366	−	0.245111i	−0.406184	−	0.913791i	$-0.633141\pi$
$139$	3.97749	−	2.88981i	0.337366	−	0.245111i	0.743550	+	0.668681i	$0.233141\pi$
$140$	2.44364	+	0.728450i	0.206525	+	0.0615653i
$141$	−0.576813	−	1.77525i	−0.0485765	−	0.149503i
$142$	−8.87500	−	5.12399i	−0.744774	−	0.429995i
$143$	−5.83649	+	0.283518i	−0.488072	+	0.0237089i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	9.70716	+	2.06332i	0.806136	+	0.171349i
$146$	−4.40271	+	6.05981i	−0.364371	+	0.501514i
$147$	−1.78827	−	6.76772i	−0.147494	−	0.558192i
$148$	−2.67438	+	8.23091i	−0.219833	+	0.676576i
$149$	5.55792	−	5.00437i	0.455322	−	0.409974i	−0.409297	−	0.912401i	$-0.634226\pi$
$149$	5.55792	−	5.00437i	0.455322	−	0.409974i	0.864620	+	0.502427i	$0.167559\pi$
$150$	−3.71917	−	1.65588i	−0.303669	−	0.135202i
$151$	−3.54713	−	0.372819i	−0.288662	−	0.0303396i	−0.0409089	−	0.999163i	$-0.513025\pi$
$151$	−3.54713	−	0.372819i	−0.288662	−	0.0303396i	−0.247753	+	0.968823i	$0.579692\pi$
$152$	−0.597331	+	2.81022i	−0.0484500	+	0.227939i
$153$	7.02336			0.567805
$154$	−4.14415	−	7.73473i	−0.333945	−	0.623282i
$155$	−7.48932			−0.601557
$156$	0.366308	−	1.72334i	0.0293281	−	0.137978i
$157$	3.89073	+	0.408932i	0.310514	+	0.0326363i	0.258504	−	0.966010i	$-0.416771\pi$
$157$	3.89073	+	0.408932i	0.310514	+	0.0326363i	0.0520101	+	0.998647i	$0.483437\pi$
$158$	6.27752	+	2.79493i	0.499413	+	0.222353i
$159$	−2.89768	+	2.60908i	−0.229801	+	0.206914i
$160$	−0.297822	+	0.916603i	−0.0235449	+	0.0724638i
$161$	6.85074	−	3.25306i	0.539914	−	0.256377i
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	−3.38186	−	0.718836i	−0.264888	−	0.0563036i	0.0735532	−	0.997291i	$-0.476566\pi$
$163$	−3.38186	−	0.718836i	−0.264888	−	0.0563036i	−0.338441	+	0.940988i	$0.609899\pi$
$164$	−0.570290	−	0.987771i	−0.0445321	−	0.0771319i
$165$	−1.13410	−	2.98852i	−0.0882897	−	0.232656i
$166$	1.03193	+	0.595784i	0.0800932	+	0.0462418i
$167$	6.59906	+	20.3098i	0.510650	+	1.57162i	0.791059	+	0.611739i	$0.209530\pi$
$167$	6.59906	+	20.3098i	0.510650	+	1.57162i	−0.280409	+	0.959881i	$0.590470\pi$
$168$	2.57372	−	0.613176i	0.198567	−	0.0473076i
$169$	8.00596	−	5.81667i	0.615843	−	0.447436i
$170$	4.52929	+	5.03029i	0.347381	+	0.385806i
$171$	2.81022	−	0.597331i	0.214903	−	0.0456791i
$172$	−1.46639	+	3.29356i	−0.111811	+	0.251131i
$173$	−15.5108	+	6.90586i	−1.17927	+	0.525043i	−0.900305	−	0.435260i	$-0.856656\pi$
$173$	−15.5108	+	6.90586i	−1.17927	+	0.525043i	−0.278960	+	0.960303i	$0.589990\pi$
$174$	9.79308	−	3.18197i	0.742412	−	0.241224i
$175$	−7.00955	+	8.17836i	−0.529872	+	0.618226i
$176$	2.96087	−	1.49441i	0.223184	−	0.112646i
$177$	4.42303	−	7.66092i	0.332456	−	0.575830i
$178$	−0.0968774	+	0.107593i	−0.00726127	+	0.00806446i
$179$	−0.902876	+	8.59029i	−0.0674841	+	0.642068i	0.907539	+	0.419967i	$0.137958\pi$
$179$	−0.902876	+	8.59029i	−0.0674841	+	0.642068i	−0.975024	+	0.222102i	$0.928708\pi$
$180$	0.958493	−	0.100742i	0.0714419	−	0.00750884i
$181$	−9.74270	−	3.16560i	−0.724169	−	0.235297i	−0.0763394	−	0.997082i	$-0.524323\pi$
$181$	−9.74270	−	3.16560i	−0.724169	−	0.235297i	−0.647830	+	0.761785i	$0.724323\pi$
$182$	−4.09265	−	2.23133i	−0.303368	−	0.165397i
$183$	−6.76552	−	9.31194i	−0.500122	−	0.688359i
$184$	1.16588	+	2.61862i	0.0859500	+	0.193047i
$185$	6.19854	+	5.58119i	0.455726	+	0.410337i
$186$	−6.72974	+	3.88542i	−0.493449	+	0.284893i
$187$	1.30799	−	23.2571i	0.0956495	−	1.70073i
$188$		−	1.86661i		−	0.136136i
$189$	−1.60699	−	2.10181i	−0.116891	−	0.152884i
$190$	2.24011	+	1.62753i	0.162514	+	0.118074i
$191$	−0.340172	−	3.23652i	−0.0246139	−	0.234186i	−0.999912	−	0.0132916i	$-0.995769\pi$
$191$	−0.340172	−	3.23652i	−0.0246139	−	0.234186i	0.975298	−	0.220894i	$-0.0708976\pi$
$192$	0.207912	+	0.978148i	0.0150047	+	0.0705917i
$193$	−3.21461	−	15.1236i	−0.231393	−	1.08862i	−0.928408	−	0.371562i	$-0.878822\pi$
$193$	−3.21461	−	15.1236i	−0.231393	−	1.08862i	0.697015	−	0.717056i	$-0.254511\pi$
$194$	1.47349	+	14.0193i	0.105790	+	1.00653i
$195$	−1.37372	−	0.998069i	−0.0983745	−	0.0714732i
$196$	0.390593	−	6.98909i	0.0278995	−	0.499221i
$197$		−	0.105970i		−	0.00755008i	−0.999993	−	0.00377504i	$-0.998798\pi$
$197$		−	0.105970i		−	0.00755008i	0.999993	−	0.00377504i	$-0.00120163\pi$
$198$	−2.56951	−	2.09705i	−0.182607	−	0.149031i
$199$	23.3037	−	13.4544i	1.65195	−	0.953756i	0.675687	−	0.737189i	$-0.263847\pi$
$199$	23.3037	−	13.4544i	1.65195	−	0.953756i	0.976268	−	0.216568i	$-0.0694862\pi$
$200$	−3.02545	−	2.72413i	−0.213931	−	0.192625i
$201$	−6.16943	−	13.8568i	−0.435158	−	0.977381i
$202$	−6.72849	−	9.26097i	−0.473415	−	0.651599i
$203$	−0.665924	−	27.2353i	−0.0467387	−	1.91154i
$204$	6.67961	+	2.17034i	0.467666	+	0.151954i
$205$	−1.09324	+	0.114904i	−0.0763550	+	0.00802524i
$206$	−0.783369	+	7.45326i	−0.0545799	+	0.519293i
$207$	1.91802	−	2.13017i	0.133311	−	0.148057i
$208$	0.880922	−	1.52580i	0.0610809	−	0.105795i
$209$	−1.45464	−	9.41700i	−0.100620	−	0.651387i
$210$	0.469030	−	2.50640i	0.0323661	−	0.172958i
$211$	−22.7672	+	7.39751i	−1.56736	+	0.509266i	−0.958761	−	0.284213i	$-0.908268\pi$
$211$	−22.7672	+	7.39751i	−1.56736	+	0.509266i	−0.608598	+	0.793479i	$0.708268\pi$
$212$	−3.56211	+	1.58595i	−0.244646	+	0.108924i
$213$	−4.16823	+	9.36199i	−0.285602	+	0.641473i
$214$	14.6136	−	3.10621i	0.998964	−	0.212336i
$215$	2.32499	+	2.58216i	0.158563	+	0.176102i
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	4.76489	+	19.9999i	0.323462	+	1.35768i
$218$	0.944408	+	2.90659i	0.0639634	+	0.196859i
$219$	6.48682	+	3.74517i	0.438339	+	0.253075i
$220$	−0.155091	−	3.19271i	−0.0104563	−	0.215252i
$221$	−6.18703	−	10.7162i	−0.416185	−	0.720853i
$222$	8.46537	+	1.79937i	0.568158	+	0.120766i
$223$	−0.650660	+	0.895557i	−0.0435714	+	0.0599709i	−0.830247	−	0.557396i	$-0.811801\pi$
$223$	−0.650660	+	0.895557i	−0.0435714	+	0.0599709i	0.786675	+	0.617367i	$0.211801\pi$
$224$	2.63723	+	0.212157i	0.176207	+	0.0141753i
$225$	−1.25805	+	3.87189i	−0.0838701	+	0.258126i
$226$	−14.0439	+	12.6451i	−0.934184	+	0.841143i
$227$	−1.82763	−	0.813713i	−0.121304	−	0.0540080i	0.345187	−	0.938534i	$-0.387815\pi$
$227$	−1.82763	−	0.813713i	−0.121304	−	0.0540080i	−0.466491	+	0.884526i	$0.654482\pi$
$228$	2.85727	+	0.300311i	0.189227	+	0.0198886i
$229$	2.31611	−	10.8965i	0.153053	−	0.720058i	−0.832952	−	0.553345i	$-0.813351\pi$
$229$	2.31611	−	10.8965i	0.153053	−	0.720058i	0.986005	−	0.166713i	$-0.0533154\pi$
$230$	2.76259			0.182160
$231$	−7.25918	+	4.92994i	−0.477619	+	0.324366i
$232$	10.2971			0.676035
$233$	−2.35647	+	11.0863i	−0.154377	+	0.726288i	0.831051	+	0.556196i	$0.187740\pi$
$233$	−2.35647	+	11.0863i	−0.154377	+	0.726288i	−0.985428	+	0.170092i	$0.945594\pi$
$234$	−1.75219	−	0.184163i	−0.114544	−	0.0120391i
$235$	−1.64346	−	0.731713i	−0.107207	−	0.0477317i
$236$	6.57391	−	5.91917i	0.427925	−	0.385305i
$237$	2.12344	−	6.53528i	0.137932	−	0.424512i
$238$	10.5515	−	15.2957i	0.683954	−	0.991472i
$239$	−1.62564	+	2.23750i	−0.105154	+	0.144732i	−0.858351	−	0.513063i	$-0.828511\pi$
$239$	−1.62564	+	2.23750i	−0.105154	+	0.144732i	0.753197	+	0.657795i	$0.228511\pi$
$240$	0.942712	+	0.200380i	0.0608518	+	0.0129345i
$241$	6.99153	+	12.1097i	0.450364	+	0.780053i	0.998408	−	0.0563958i	$-0.0179609\pi$
$241$	6.99153	+	12.1097i	0.450364	+	0.780053i	−0.548044	+	0.836449i	$0.684628\pi$
$242$	−7.42270	+	8.11810i	−0.477149	+	0.521851i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.55685	−	10.9468i	−0.227704	−	0.700800i
$245$	−6.00044	−	3.08363i	−0.383354	−	0.197006i
$246$	−0.922748	+	0.670416i	−0.0588323	+	0.0427441i
$247$	−3.38700	−	3.76164i	−0.215509	−	0.239347i
$248$	−7.60103	+	1.61565i	−0.482666	+	0.102594i
$249$	0.484654	−	1.08855i	0.0307137	−	0.0689842i
$250$	−7.98669	+	3.55590i	−0.505123	+	0.224895i
$251$	−10.5867	+	3.43984i	−0.668229	+	0.217121i	−0.623435	−	0.781876i	$-0.714263\pi$
$251$	−10.5867	+	3.43984i	−0.668229	+	0.217121i	−0.0447943	+	0.998996i	$0.514263\pi$
$252$	−0.878844	−	2.49552i	−0.0553620	−	0.157203i
$253$	−6.69664	−	6.74802i	−0.421014	−	0.424244i
$254$	0.492781	−	0.853522i	0.0309198	−	0.0535547i
$255$	4.52929	−	5.03029i	0.283635	−	0.315009i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−21.4316	+	2.25255i	−1.33686	+	0.140510i	−0.745830	−	0.666136i	$-0.767947\pi$
$257$	−21.4316	+	2.25255i	−1.33686	+	0.140510i	−0.591034	+	0.806646i	$0.701280\pi$
$258$	3.42879	+	1.11408i	0.213467	+	0.0693597i
$259$	10.9607	−	20.1038i	0.681064	−	1.24919i
$260$	−0.998069	−	1.37372i	−0.0618976	−	0.0851948i
$261$	−4.18819	−	9.40683i	−0.259242	−	0.582268i
$262$	1.18993	+	1.07142i	0.0735144	+	0.0661926i
$263$	1.15983	−	0.669631i	0.0715185	−	0.0412912i	−0.463814	−	0.885932i	$-0.653520\pi$
$263$	1.15983	−	0.669631i	0.0715185	−	0.0412912i	0.535333	+	0.844641i	$0.320186\pi$
$264$	−1.79572	−	2.78844i	−0.110519	−	0.171616i
$265$			3.75795i			0.230849i
$266$	2.92105	−	7.01759i	0.179101	−	0.430276i
$267$	0.117130	+	0.0851002i	0.00716826	+	0.00520805i
$268$	−1.58550	−	15.0850i	−0.0968499	−	0.921465i
$269$	−3.71362	−	17.4712i	−0.226423	−	1.06524i	−0.933632	−	0.358233i	$-0.883379\pi$
$269$	−3.71362	−	17.4712i	−0.226423	−	1.06524i	0.707209	−	0.707005i	$-0.249954\pi$
$270$	−0.200380	−	0.942712i	−0.0121947	−	0.0573716i
$271$	−1.49222	−	14.1975i	−0.0906458	−	0.862438i	−0.941495	−	0.337027i	$-0.890579\pi$
$271$	−1.49222	−	14.1975i	−0.0906458	−	0.862438i	0.850849	−	0.525410i	$-0.176088\pi$
$272$	5.68202	+	4.12823i	0.344523	+	0.250311i
$273$	−1.79131	+	4.30347i	−0.108415	+	0.260458i
$274$			22.2278i			1.34283i
$275$	12.5870	+	4.88698i	0.759027	+	0.294696i
$276$	2.48240	−	1.43322i	0.149423	−	0.0862695i
$277$	9.14890	+	8.23770i	0.549704	+	0.494956i	0.896536	−	0.442972i	$-0.146076\pi$
$277$	9.14890	+	8.23770i	0.549704	+	0.494956i	−0.346832	+	0.937927i	$0.612742\pi$
$278$	−1.99970	−	4.49140i	−0.119934	−	0.269376i
$279$	4.56758	+	6.28674i	0.273454	+	0.376377i
$280$	1.22059	−	2.23879i	0.0729444	−	0.133793i
$281$	27.2928	+	8.86795i	1.62815	+	0.529018i	0.973845	−	0.227214i	$-0.0729615\pi$
$281$	27.2928	+	8.86795i	1.62815	+	0.529018i	0.654304	+	0.756231i	$0.272962\pi$
$282$	−1.85638	+	0.195114i	−0.110546	+	0.0116188i
$283$	−1.78443	+	16.9777i	−0.106073	+	1.00922i	0.803960	+	0.594683i	$0.202723\pi$
$283$	−1.78443	+	16.9777i	−0.106073	+	1.00922i	−0.910033	+	0.414536i	$0.863944\pi$
$284$	−6.85723	+	7.61573i	−0.406902	+	0.451910i
$285$	1.38446	−	2.39796i	0.0820085	−	0.142043i
$286$	−0.936153	+	5.76790i	−0.0553559	+	0.341063i
$287$	1.00239	+	2.84634i	0.0591693	+	0.168014i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	29.5327	−	13.1488i	1.73722	−	0.773459i
$290$	4.03646	−	9.06605i	0.237029	−	0.532377i
$291$	13.7885	−	2.93084i	0.808297	−	0.171809i
$292$	5.01202	+	5.56641i	0.293306	+	0.325749i
$293$	−18.1582	+	13.1927i	−1.06081	+	0.770724i	−0.974238	−	0.225522i	$-0.927591\pi$
$293$	−18.1582	+	13.1927i	−1.06081	+	0.770724i	−0.0865723	+	0.996246i	$0.527591\pi$
$294$	−6.99164	+	0.342106i	−0.407760	+	0.0199520i
$295$	−2.63456	−	8.10833i	−0.153390	−	0.472085i
$296$	7.49501	+	4.32724i	0.435638	+	0.251516i
$297$	−1.81698	+	2.77463i	−0.105432	+	0.161001i
$298$	−3.73946	−	6.47693i	−0.216621	−	0.375199i
$299$	−4.93985	−	1.05000i	−0.285679	−	0.0607229i
$300$	−2.39296	+	3.29362i	−0.138157	+	0.190157i
$301$	5.41634	−	7.85162i	0.312193	−	0.452560i
$302$	−1.10216	+	3.39211i	−0.0634223	+	0.195194i
$303$	−8.50691	+	7.65966i	−0.488709	+	0.440036i
$304$	2.62462	+	1.16856i	0.150532	+	0.0670213i
$305$	−11.0324	−	1.15956i	−0.631716	−	0.0663960i
$306$	1.46024	−	6.86988i	0.0834763	−	0.392725i
$307$	−9.67780			−0.552341			−0.276171	−	0.961109i	$-0.589065\pi$
$307$	−9.67780			−0.552341			−0.276171	+	0.961109i	$0.589065\pi$
$308$	−8.42732	+	2.44545i	−0.480191	+	0.139342i
$309$	7.49431			0.426336
$310$	−1.55712	+	7.32566i	−0.0884383	+	0.416070i
$311$	1.00058	+	0.105165i	0.0567377	+	0.00596337i	0.132855	−	0.991136i	$-0.457586\pi$
$311$	1.00058	+	0.105165i	0.0567377	+	0.00596337i	−0.0761171	+	0.997099i	$0.524252\pi$
$312$	−1.60952	−	0.716606i	−0.0911214	−	0.0405698i
$313$	14.3888	−	12.9558i	0.813304	−	0.732303i	−0.153409	−	0.988163i	$-0.549025\pi$
$313$	14.3888	−	12.9558i	0.813304	−	0.732303i	0.966714	+	0.255860i	$0.0823586\pi$
$314$	1.20892	−	3.72068i	0.0682235	−	0.209970i
$315$	−2.54169	−	0.204471i	−0.143208	−	0.0115206i
$316$	4.03903	−	5.55924i	0.227213	−	0.312732i
$317$	3.64450	+	0.774663i	0.204696	+	0.0435094i	0.309118	−	0.951024i	$-0.399966\pi$
$317$	3.64450	+	0.774663i	0.204696	+	0.0435094i	−0.104423	+	0.994533i	$0.533299\pi$
$318$	1.94960	+	3.37681i	0.109328	+	0.189362i
$319$	−31.9297	+	12.1169i	−1.78772	+	0.678414i
$320$	0.834652	+	0.481886i	0.0466585	+	0.0269383i
$321$	−4.61673	−	14.2088i	−0.257681	−	0.793060i
$322$	−1.75763	−	7.37738i	−0.0979488	−	0.411125i
$323$	16.3245	−	11.8604i	0.908318	−	0.659931i
$324$	−0.669131	−	0.743145i	−0.0371739	−	0.0412858i
$325$	7.01597	−	1.49129i	0.389176	−	0.0827219i
$326$	−1.40626	+	3.15850i	−0.0778853	+	0.174933i
$327$	2.79195	−	1.24306i	0.154395	−	0.0687412i
$328$	−1.08476	+	0.352458i	−0.0598956	+	0.0194613i
$329$	−0.908404	+	4.85431i	−0.0500819	+	0.267627i
$330$	−3.15901	+	0.487971i	−0.173898	+	0.0268619i
$331$	5.99443	−	10.3827i	0.329484	−	0.570683i	−0.652926	−	0.757422i	$-0.726459\pi$
$331$	5.99443	−	10.3827i	0.329484	−	0.570683i	0.982410	+	0.186739i	$0.0597919\pi$
$332$	0.797315	−	0.885508i	0.0437583	−	0.0485985i
$333$	0.904640	−	8.60708i	0.0495740	−	0.471665i
$334$	21.2380	−	2.23220i	1.16209	−	0.122141i
$335$	−13.9031	−	4.51740i	−0.759610	−	0.246812i
$336$	−0.0646713	−	2.64496i	−0.00352811	−	0.144294i
$337$	4.61395	+	6.35056i	0.251338	+	0.345937i	0.915979	−	0.401225i	$-0.131416\pi$
$337$	4.61395	+	6.35056i	0.251338	+	0.345937i	−0.664641	+	0.747163i	$0.731416\pi$
$338$	−4.02503	−	9.04036i	−0.218933	−	0.491731i
$339$	14.0439	+	12.6451i	0.762758	+	0.686790i
$340$	5.86206	−	3.38446i	0.317915	−	0.183548i
$341$	21.6685	−	13.9543i	1.17341	−	0.755665i
$342$		−	2.87301i		−	0.155354i
$343$	−4.41709	+	17.9858i	−0.238501	+	0.971142i
$344$	2.91671	+	2.11911i	0.157258	+	0.114255i
$345$	−0.288769	−	2.74746i	−0.0155468	−	0.147918i
$346$	3.53007	+	16.6077i	0.189778	+	0.892834i
$347$	0.855037	+	4.02263i	0.0459008	+	0.215946i	0.995120	−	0.0986679i	$-0.0314582\pi$
$347$	0.855037	+	4.02263i	0.0459008	+	0.215946i	−0.949220	+	0.314614i	$0.898125\pi$
$348$	−1.07634	−	10.2406i	−0.0576976	−	0.548956i
$349$	15.9673	+	11.6010i	0.854712	+	0.620985i	0.926441	−	0.376439i	$-0.122852\pi$
$349$	15.9673	+	11.6010i	0.854712	+	0.620985i	−0.0717291	+	0.997424i	$0.522852\pi$
$350$	6.54228	+	8.55675i	0.349700	+	0.457377i
$351$			1.76184i			0.0940402i
$352$	−0.846158	−	3.20687i	−0.0451003	−	0.170927i
$353$	−8.47114	+	4.89082i	−0.450873	+	0.260312i	−0.708199	−	0.706013i	$-0.750492\pi$
$353$	−8.47114	+	4.89082i	−0.450873	+	0.260312i	0.257326	+	0.966325i	$0.417159\pi$
$354$	−6.57391	−	5.91917i	−0.349399	−	0.314601i
$355$	4.01722	+	9.02283i	0.213212	+	0.478882i
$356$	0.0851002	+	0.117130i	0.00451030	+	0.00620790i
$357$	−16.3148	−	8.89490i	−0.863473	−	0.470768i
$358$	8.21485	+	2.66917i	0.434168	+	0.141070i
$359$	−5.09356	+	0.535355i	−0.268828	+	0.0282550i	−0.237983	−	0.971269i	$-0.576486\pi$
$359$	−5.09356	+	0.535355i	−0.268828	+	0.0282550i	−0.0308446	+	0.999524i	$0.509820\pi$
$360$	0.100742	−	0.958493i	0.00530955	−	0.0505170i
$361$	−7.19037	+	7.98571i	−0.378440	+	0.420301i
$362$	−5.12204	+	8.87164i	−0.269209	+	0.466283i
$363$	8.84951	+	6.53346i	0.464479	+	0.342918i
$364$	−3.03348	+	3.53930i	−0.158997	+	0.185510i
$365$	6.86566	−	2.23079i	0.359365	−	0.116765i
$366$	−10.5151	+	4.68162i	−0.549632	+	0.244712i
$367$	6.36907	−	14.3052i	0.332463	−	0.746724i	−0.667535	−	0.744578i	$-0.732651\pi$
$367$	6.36907	−	14.3052i	0.332463	−	0.746724i	0.999998	−	0.00214513i	$-0.000682816\pi$
$368$	2.80379	−	0.595965i	0.146158	−	0.0310668i
$369$	0.763197	+	0.847616i	0.0397304	+	0.0441251i
$370$	6.74798	−	4.90269i	0.350811	−	0.254879i
$371$	10.0355	−	2.39090i	0.521015	−	0.124130i
$372$	2.40132	+	7.39051i	0.124503	+	0.383180i
$373$	16.0531	+	9.26824i	0.831196	+	0.479891i	0.854262	−	0.519843i	$-0.174009\pi$
$373$	16.0531	+	9.26824i	0.831196	+	0.479891i	−0.0230659	+	0.999734i	$0.507343\pi$
$374$	−22.4769	−	6.11483i	−1.16225	−	0.316190i
$375$	4.37126	+	7.57125i	0.225731	+	0.390977i
$376$	−1.82582	−	0.388090i	−0.0941594	−	0.0200142i
$377$	−10.6635	+	14.6770i	−0.549197	+	0.755905i
$378$	−2.38999	+	1.13488i	−0.122928	+	0.0583721i
$379$	−1.56078	+	4.80357i	−0.0801717	+	0.246743i	−0.983106	−	0.183034i	$-0.941408\pi$
$379$	−1.56078	+	4.80357i	−0.0801717	+	0.246743i	0.902935	+	0.429777i	$0.141408\pi$
$380$	2.05771	−	1.85277i	0.105558	−	0.0950452i
$381$	−0.900356	−	0.400864i	−0.0461266	−	0.0205369i
$382$	−3.23652	−	0.340172i	−0.165595	−	0.0174047i
$383$	−5.45574	+	25.6672i	−0.278775	+	1.31153i	0.586383	+	0.810034i	$0.300551\pi$
$383$	−5.45574	+	25.6672i	−0.278775	+	1.31153i	−0.865158	+	0.501500i	$0.832782\pi$
$384$	1.00000			0.0510310
$385$	−1.15043	+	8.37846i	−0.0586315	+	0.427006i
$386$	−15.4614			−0.786966
$387$	0.749573	−	3.52646i	0.0381029	−	0.179260i
$388$	14.0193	+	1.47349i	0.711724	+	0.0748052i
$389$	25.1572	+	11.2007i	1.27552	+	0.567899i	0.928978	−	0.370135i	$-0.120689\pi$
$389$	25.1572	+	11.2007i	1.27552	+	0.567899i	0.346544	+	0.938034i	$0.387355\pi$
$390$	−1.26187	+	1.13620i	−0.0638974	+	0.0575335i
$391$	6.22112	−	19.1467i	0.314616	−	0.968288i
$392$	−6.75516	−	1.83517i	−0.341187	−	0.0926902i
$393$	0.941170	−	1.29541i	0.0474758	−	0.0653448i
$394$	−0.103655	−	0.0220325i	−0.00522205	−	0.00110998i
$395$	−3.31133	−	5.73540i	−0.166611	−	0.288579i
$396$	−2.58546	+	2.07736i	−0.129924	+	0.104391i
$397$	−3.97407	−	2.29443i	−0.199453	−	0.115154i	0.396947	−	0.917841i	$-0.370070\pi$
$397$	−3.97407	−	2.29443i	−0.199453	−	0.115154i	−0.596400	+	0.802687i	$0.703403\pi$
$398$	−8.31527	−	25.5918i	−0.416807	−	1.28280i
$399$	−7.28448	−	2.17151i	−0.364680	−	0.108711i
$400$	−3.29362	+	2.39296i	−0.164681	+	0.119648i
$401$	18.2810	+	20.3031i	0.912910	+	1.01389i	0.999844	+	0.0176749i	$0.00562638\pi$
$401$	18.2810	+	20.3031i	0.912910	+	1.01389i	−0.0869341	+	0.996214i	$0.527707\pi$
$402$	−14.8367	+	3.15363i	−0.739986	+	0.157289i
$403$	5.56863	−	12.5073i	0.277393	−	0.623035i
$404$	−10.4575	+	4.65599i	−0.520281	+	0.231644i
$405$	−0.916603	+	0.297822i	−0.0455463	+	0.0147989i
$406$	−26.7786	−	5.01117i	−1.32900	−	0.248700i
$407$	−28.3329	−	4.59855i	−1.40441	−	0.227942i
$408$	3.51168	−	6.08241i	0.173854	−	0.301124i
$409$	−23.3096	+	25.8879i	−1.15259	+	1.28008i	−0.198648	+	0.980071i	$0.563655\pi$
$409$	−23.3096	+	25.8879i	−1.15259	+	1.28008i	−0.953938	+	0.300005i	$0.903012\pi$
$410$	−0.114904	+	1.09324i	−0.00567470	+	0.0539912i
$411$	22.1060	−	2.32344i	1.09041	−	0.114607i
$412$	7.12751	+	2.31587i	0.351147	+	0.114095i
$413$	−19.9768	+	12.1942i	−0.982993	+	0.600037i
$414$	−1.68485	−	2.31899i	−0.0828057	−	0.113972i
$415$	−0.467097	−	1.04912i	−0.0229289	−	0.0514991i
$416$	−1.30930	−	1.17890i	−0.0641939	−	0.0578005i
$417$	−4.25777	+	2.45822i	−0.208504	+	0.120380i
$418$	−9.51365	−	0.535051i	−0.465328	−	0.0261702i
$419$			20.1862i			0.986160i	0.869984	+	0.493080i	$0.164129\pi$
$419$			20.1862i			0.986160i	−0.869984	+	0.493080i	$0.835871\pi$
$420$	−2.35411	−	0.979889i	−0.114869	−	0.0478137i
$421$	−15.2891	−	11.1082i	−0.745145	−	0.541380i	0.149173	−	0.988811i	$-0.452339\pi$
$421$	−15.2891	−	11.1082i	−0.745145	−	0.541380i	−0.894318	+	0.447432i	$0.852339\pi$
$422$	2.50229	+	23.8077i	0.121810	+	1.15894i
$423$	0.388090	+	1.82582i	0.0188696	+	0.0887743i
$424$	0.810691	+	3.81400i	0.0393706	+	0.185224i
$425$	2.98879	+	28.4365i	0.144978	+	1.37937i
$426$	8.29078	+	6.02361i	0.401690	+	0.291845i
$427$	3.92257	+	30.1994i	0.189826	+	1.46145i
$428$		−	14.9401i		−	0.722155i
$429$	5.83415	+	0.328115i	0.281676	+	0.0158415i
$430$	3.00913	−	1.73732i	0.145113	−	0.0837810i
$431$	17.5381	+	15.7914i	0.844780	+	0.760644i	0.972927	−	0.231111i	$-0.0742362\pi$
$431$	17.5381	+	15.7914i	0.844780	+	0.760644i	−0.128147	+	0.991755i	$0.540903\pi$
$432$	−0.406737	−	0.913545i	−0.0195691	−	0.0439530i
$433$	8.48649	+	11.6806i	0.407835	+	0.561336i	0.962689	−	0.270612i	$-0.0872259\pi$
$433$	8.48649	+	11.6806i	0.407835	+	0.561336i	−0.554854	+	0.831948i	$0.687226\pi$
$434$	20.5536	−	0.502550i	0.986602	−	0.0241232i
$435$	−9.43831	−	3.06669i	−0.452532	−	0.147037i
$436$	3.03943	−	0.319457i	0.145562	−	0.0152992i
$437$	0.860821	−	8.19016i	0.0411786	−	0.391789i
$438$	5.01202	−	5.56641i	0.239483	−	0.265973i
$439$	19.5226	−	33.8141i	0.931761	−	1.61386i	0.151452	−	0.988465i	$-0.451605\pi$
$439$	19.5226	−	33.8141i	0.931761	−	1.61386i	0.780310	−	0.625393i	$-0.215061\pi$
$440$	−3.15519	−	0.512099i	−0.150418	−	0.0244134i
$441$	1.07106	+	6.91757i	0.0510027	+	0.329408i
$442$	−11.7684	+	3.82379i	−0.559767	+	0.181879i
$443$	−17.5523	+	7.81477i	−0.833933	+	0.371291i	−0.778865	−	0.627192i	$-0.784204\pi$
$443$	−17.5523	+	7.81477i	−0.833933	+	0.371291i	−0.0550680	+	0.998483i	$0.517538\pi$
$444$	3.52010	−	7.90627i	0.167056	−	0.375215i
$445$	0.136487	−	0.0290112i	0.00647010	−	0.00137526i
$446$	0.740707	+	0.822638i	0.0350735	+	0.0389531i
$447$	−6.05057	+	4.39600i	−0.286182	+	0.207923i
$448$	0.755832	−	2.53549i	0.0357097	−	0.119791i
$449$	−2.09813	−	6.45739i	−0.0990170	−	0.304743i	0.889263	−	0.457397i	$-0.151218\pi$
$449$	−2.09813	−	6.45739i	−0.0990170	−	0.304743i	−0.988280	+	0.152654i	$0.951218\pi$
$450$	3.52571	+	2.03557i	0.166204	+	0.0959577i
$451$	2.94892	−	2.36939i	0.138859	−	0.111570i
$452$	9.44894	+	16.3660i	0.444441	+	0.769794i
$453$	3.48873	+	0.741553i	0.163915	+	0.0348412i
$454$	−1.17592	+	1.61851i	−0.0551885	+	0.0759605i
$455$	1.92705	+	4.05824i	0.0903415	+	0.190253i
$456$	0.887808	−	2.73239i	0.0415754	−	0.127956i
$457$	−8.40822	+	7.57079i	−0.393320	+	0.354147i	−0.841936	−	0.539578i	$-0.818584\pi$
$457$	−8.40822	+	7.57079i	−0.393320	+	0.354147i	0.448616	+	0.893725i	$0.351917\pi$
$458$	−10.1768	−	4.53100i	−0.475530	−	0.211720i
$459$	−6.98488	−	0.734141i	−0.326026	−	0.0342668i
$460$	0.574375	−	2.70222i	0.0267804	−	0.125992i
$461$	−24.0471			−1.11999			−0.559993	−	0.828497i	$-0.689196\pi$
$461$	−24.0471			−1.11999			−0.559993	+	0.828497i	$0.689196\pi$
$462$	3.31294	+	8.12554i	0.154132	+	0.378034i
$463$	−7.00749			−0.325666			−0.162833	−	0.986654i	$-0.552063\pi$
$463$	−7.00749			−0.325666			−0.162833	+	0.986654i	$0.552063\pi$
$464$	2.14088	−	10.0720i	0.0993878	−	0.467583i
$465$	7.44830	+	0.782847i	0.345406	+	0.0363037i
$466$	10.3541	+	4.60994i	0.479644	+	0.213551i
$467$	−10.4679	+	9.42532i	−0.484396	+	0.436152i	−0.874795	−	0.484494i	$-0.839004\pi$
$467$	−10.4679	+	9.42532i	−0.484396	+	0.436152i	0.390399	+	0.920646i	$0.372337\pi$
$468$	−0.544440	+	1.67561i	−0.0251667	+	0.0774552i
$469$	−3.21802	+	40.0019i	−0.148594	+	1.84711i
$470$	−1.05742	+	1.45541i	−0.0487750	+	0.0671331i
$471$	−3.82667	−	0.813384i	−0.176324	−	0.0374787i
$472$	−4.42303	−	7.66092i	−0.203587	−	0.352622i
$473$	−11.5379	−	3.13888i	−0.530514	−	0.144326i
$474$	−5.95098	−	3.43580i	−0.273338	−	0.157812i
$475$	3.61439	+	11.1240i	0.165840	+	0.510402i
$476$	−12.7677	−	13.5011i	−0.585204	−	0.618822i
$477$	3.15453	−	2.29190i	0.144436	−	0.104939i
$478$	1.85062	+	2.05532i	0.0846453	+	0.0940081i
$479$	11.1425	−	2.36841i	0.509112	−	0.108215i	0.0538085	−	0.998551i	$-0.482864\pi$
$479$	11.1425	−	2.36841i	0.509112	−	0.108215i	0.455304	+	0.890336i	$0.349531\pi$
$480$	0.392002	−	0.880450i	0.0178924	−	0.0401869i
$481$	−13.9296	+	6.20186i	−0.635135	+	0.282781i
$482$	13.2987	−	4.32100i	0.605738	−	0.196816i
$483$	−7.15325	+	2.51915i	−0.325484	+	0.114625i
$484$	6.39744	+	8.94834i	0.290793	+	0.406743i
$485$	6.79294	−	11.7657i	0.308451	−	0.534253i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	2.52771	−	24.0496i	0.114542	−	1.08979i	−0.774693	−	0.632338i	$-0.782095\pi$
$487$	2.52771	−	24.0496i	0.114542	−	1.08979i	0.889234	−	0.457452i	$-0.151238\pi$
$488$	−11.4471	+	1.20314i	−0.518188	+	0.0544637i
$489$	3.28819	+	1.06840i	0.148697	+	0.0483147i
$490$	−4.26381	+	5.22819i	−0.192619	+	0.236186i
$491$	1.34703	+	1.85402i	0.0607904	+	0.0836708i	0.838330	−	0.545163i	$-0.183532\pi$
$491$	1.34703	+	1.85402i	0.0607904	+	0.0836708i	−0.777539	+	0.628834i	$0.783532\pi$
$492$	0.463915	+	1.04197i	0.0209149	+	0.0469757i
$493$	−53.7442	−	48.3915i	−2.42052	−	2.17944i
$494$	−4.38364	+	2.53089i	−0.197229	+	0.113870i
$495$	0.815504	+	3.09069i	0.0366542	+	0.138916i
$496$			7.77084i			0.348921i
$497$	21.5392	−	16.4684i	0.966167	−	0.738708i
$498$	−0.963999	−	0.700386i	−0.0431978	−	0.0313851i
$499$	−1.10843	−	10.5460i	−0.0496203	−	0.472106i	−0.990912	−	0.134511i	$-0.957054\pi$
$499$	−1.10843	−	10.5460i	−0.0496203	−	0.472106i	0.941292	−	0.337594i	$-0.109613\pi$
$500$	1.81767	+	8.55148i	0.0812888	+	0.382434i
$501$	−4.43995	−	20.8883i	−0.198362	−	0.933222i
$502$	1.16356	+	11.0706i	0.0519324	+	0.494104i
$503$	0.569387	+	0.413684i	0.0253877	+	0.0184453i	0.600407	−	0.799695i	$-0.295005\pi$
$503$	0.569387	+	0.413684i	0.0253877	+	0.0184453i	−0.575019	+	0.818140i	$0.695005\pi$
$504$	−2.62371	+	0.340791i	−0.116869	+	0.0151800i
$505$			11.0325i			0.490939i
$506$	−7.99287	+	5.14731i	−0.355326	+	0.228826i
$507$	−8.57011	+	4.94795i	−0.380612	+	0.219746i
$508$	−0.732416	−	0.659470i	−0.0324957	−	0.0292593i
$509$	2.47910	+	5.56816i	0.109884	+	0.246804i	0.960115	−	0.279607i	$-0.0902041\pi$
$509$	2.47910	+	5.56816i	0.109884	+	0.246804i	−0.850230	+	0.526411i	$0.823537\pi$
$510$	−3.97867	−	5.47617i	−0.176179	−	0.242489i
$511$	−10.3253	−	16.9152i	−0.456766	−	0.748284i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−2.85727	+	0.300311i	−0.126151	+	0.0132590i
$514$	−2.25255	+	21.4316i	−0.0993556	+	0.945306i
$515$	4.83301	−	5.36760i	0.212968	−	0.236525i
$516$	1.80262	−	3.12224i	0.0793561	−	0.137449i
$517$	6.11827	−	0.945088i	0.269081	−	0.0415649i
$518$	−17.3857	−	14.9010i	−0.763883	−	0.654712i
$519$	16.1477	−	5.24671i	0.708805	−	0.230305i
$520$	−1.55122	+	0.690646i	−0.0680253	+	0.0302868i
$521$	−9.96541	+	22.3827i	−0.436592	+	0.980603i	0.552528	+	0.833494i	$0.313663\pi$
$521$	−9.96541	+	22.3827i	−0.436592	+	0.980603i	−0.989120	+	0.147108i	$0.953003\pi$
$522$	−10.0720	+	2.14088i	−0.440841	+	0.0937037i
$523$	−12.0810	−	13.4173i	−0.528263	−	0.586696i	0.418665	−	0.908141i	$-0.362498\pi$
$523$	−12.0810	−	13.4173i	−0.528263	−	0.586696i	−0.946928	+	0.321445i	$0.895832\pi$
$524$	1.29541	−	0.941170i	0.0565902	−	0.0411152i
$525$	7.82602	−	7.40086i	0.341555	−	0.323000i
$526$	−0.413855	−	1.27371i	−0.0180449	−	0.0555365i
$527$	47.2654	+	27.2887i	2.05891	+	1.18871i
$528$	−3.10086	+	1.17673i	−0.134947	+	0.0512107i
$529$	7.39178	+	12.8029i	0.321382	+	0.556650i
$530$	3.67583	+	0.781322i	0.159668	+	0.0339385i
$531$	−5.19959	+	7.15662i	−0.225643	+	0.310571i
$532$	−6.25692	−	4.31626i	−0.271272	−	0.187133i
$533$	0.620977	−	1.91117i	0.0268975	−	0.0827819i
$534$	0.107593	−	0.0968774i	0.00465602	−	0.00419230i
$535$	−13.1540	−	5.85653i	−0.568696	−	0.253200i
$536$	−15.0850	−	1.58550i	−0.651574	−	0.0684832i
$537$	1.79586	−	8.44885i	0.0774971	−	0.364595i
$538$	−17.8615			−0.770065
$539$	23.1063	−	2.25840i	0.995257	−	0.0972763i
$540$	−0.963773			−0.0414742
$541$	−7.08073	+	33.3122i	−0.304424	+	1.43220i	0.514099	+	0.857731i	$0.328126\pi$
$541$	−7.08073	+	33.3122i	−0.304424	+	1.43220i	−0.818524	+	0.574473i	$0.805207\pi$
$542$	−14.1975	−	1.49222i	−0.609836	−	0.0640963i
$543$	9.35843	+	4.16664i	0.401609	+	0.178808i
$544$	5.21937	−	4.69954i	0.223779	−	0.201491i
$545$	0.910195	−	2.80129i	0.0389885	−	0.119994i
$546$	3.83700	+	2.64690i	0.164208	+	0.113277i
$547$	−7.76844	+	10.6923i	−0.332154	+	0.457171i	−0.942129	−	0.335249i	$-0.891179\pi$
$547$	−7.76844	+	10.6923i	−0.332154	+	0.457171i	0.609975	+	0.792421i	$0.291179\pi$
$548$	21.7421	+	4.62142i	0.928775	+	0.197417i
$549$	5.75510	+	9.96812i	0.245622	+	0.425429i
$550$	7.39718	−	11.2959i	0.315417	−	0.481660i
$551$	−25.6201	−	14.7918i	−1.09145	−	0.630150i
$552$	−0.885776	−	2.72614i	−0.0377011	−	0.116032i
$553$	−13.2094	+	12.4918i	−0.561720	+	0.531205i
$554$	9.95985	−	7.23626i	0.423154	−	0.307439i
$555$	−5.58119	−	6.19854i	−0.236908	−	0.263113i
$556$	−4.80901	+	1.02219i	−0.203947	+	0.0433504i
$557$	8.96711	−	20.1405i	0.379949	−	0.853379i	−0.617801	−	0.786334i	$-0.711976\pi$
$557$	8.96711	−	20.1405i	0.379949	−	0.853379i	0.997750	−	0.0670446i	$-0.0213570\pi$
$558$	7.09901	−	3.16068i	0.300525	−	0.133802i
$559$	−6.04100	+	1.96284i	−0.255507	+	0.0830192i
$560$	−1.93609	−	1.65939i	−0.0818146	−	0.0701220i
$561$	−3.73185	+	22.9930i	−0.157559	+	0.970764i
$562$	14.3487	−	24.8526i	0.605261	−	1.04834i
$563$	14.6665	−	16.2888i	0.618121	−	0.686493i	−0.350065	−	0.936725i	$-0.613840\pi$
$563$	14.6665	−	16.2888i	0.618121	−	0.686493i	0.968186	+	0.250233i	$0.0805071\pi$
$564$	−0.195114	+	1.85638i	−0.00821577	+	0.0781678i
$565$	18.1135	−	1.90380i	0.762040	−	0.0800937i
$566$	16.2357	+	5.27529i	0.682437	+	0.221737i
$567$	1.37849	+	2.25827i	0.0578910	+	0.0948383i
$568$	6.02361	+	8.29078i	0.252745	+	0.347874i
$569$	6.58033	+	14.7797i	0.275862	+	0.619596i	0.997344	−	0.0728373i	$-0.0232054\pi$
$569$	6.58033	+	14.7797i	0.275862	+	0.619596i	−0.721482	+	0.692433i	$0.756539\pi$
$570$	−2.05771	−	1.85277i	−0.0861881	−	0.0776041i
$571$	−1.86917	+	1.07917i	−0.0782223	+	0.0451617i	−0.538601	−	0.842561i	$-0.681047\pi$
$571$	−1.86917	+	1.07917i	−0.0782223	+	0.0451617i	0.460379	+	0.887723i	$0.347714\pi$
$572$	5.44722	+	2.11491i	0.227760	+	0.0884288i
$573$			3.25434i			0.135952i
$574$	2.99255	−	0.388699i	0.124907	−	0.0162240i
$575$	9.44095	+	6.85925i	0.393715	+	0.286050i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−6.88252	−	32.3797i	−0.286523	−	1.34798i	−0.852139	−	0.523316i	$-0.824695\pi$
$577$	−6.88252	−	32.3797i	−0.286523	−	1.34798i	0.565616	−	0.824669i	$-0.308639\pi$
$578$	−6.72128	−	31.6211i	−0.279568	−	1.31527i
$579$	1.61616	+	15.3767i	0.0671653	+	0.639035i
$580$	−8.02870	−	5.83320i	−0.333374	−	0.242210i
$581$	−2.50444	+	1.91484i	−0.103902	+	0.0794408i
$582$		−	14.0966i		−	0.584321i
$583$	−7.00189	−	10.8727i	−0.289989	−	0.450301i
$584$	6.48682	−	3.74517i	0.268427	−	0.154976i
$585$	1.26187	+	1.13620i	0.0521720	+	0.0469759i
$586$	9.12909	+	20.5043i	0.377119	+	0.847023i
$587$	−13.9702	−	19.2283i	−0.576612	−	0.793639i	0.416707	−	0.909041i	$-0.363184\pi$
$587$	−13.9702	−	19.2283i	−0.576612	−	0.793639i	−0.993319	+	0.115402i	$0.963184\pi$
$588$	−1.11901	+	6.90998i	−0.0461473	+	0.284963i
$589$	21.2330	+	6.89901i	0.874889	+	0.284269i
$590$	−8.47890	+	0.891168i	−0.349071	+	0.0366888i
$591$	−0.0110769	+	0.105390i	−0.000455644	+	0.00433516i
$592$	5.79098	−	6.43154i	0.238008	−	0.264335i
$593$	−0.526537	+	0.911990i	−0.0216223	+	0.0374509i	−0.876634	−	0.481158i	$-0.840216\pi$
$593$	−0.526537	+	0.911990i	−0.0216223	+	0.0374509i	0.855012	+	0.518609i	$0.173550\pi$
$594$	2.33623	+	2.35415i	0.0958566	+	0.0965920i
$595$	−16.8920	+	5.94883i	−0.692504	+	0.243878i
$596$	−7.11287	+	2.31111i	−0.291355	+	0.0946668i
$597$	−24.5824	+	10.9448i	−1.00609	+	0.447940i
$598$	−2.05410	+	4.61359i	−0.0839985	+	0.188664i
$599$	5.49874	−	1.16879i	0.224672	−	0.0477556i	−0.0941998	−	0.995553i	$-0.530029\pi$
$599$	5.49874	−	1.16879i	0.224672	−	0.0477556i	0.318872	+	0.947798i	$0.396696\pi$
$600$	2.72413	+	3.02545i	0.111212	+	0.123513i
$601$	30.3448	−	22.0468i	1.23779	−	0.899306i	0.240339	−	0.970689i	$-0.422741\pi$
$601$	30.3448	−	22.0468i	1.23779	−	0.899306i	0.997449	+	0.0713830i	$0.0227412\pi$
$602$	−6.55392	−	6.93042i	−0.267118	−	0.282463i
$603$	4.68721	+	14.4257i	0.190878	+	0.587462i
$604$	3.08883	+	1.78334i	0.125683	+	0.0725629i
$605$	10.3864	−	2.12486i	0.422266	−	0.0863879i
$606$	5.72359	+	9.91355i	0.232505	+	0.402710i
$607$	−12.1536	−	2.58332i	−0.493298	−	0.104854i	−0.0454559	−	0.998966i	$-0.514474\pi$
$607$	−12.1536	−	2.58332i	−0.493298	−	0.104854i	−0.447842	+	0.894113i	$0.647807\pi$
$608$	1.68871	−	2.32431i	0.0684862	−	0.0942632i
$609$	−2.18459	+	27.1557i	−0.0885240	+	1.10041i
$610$	−3.42799	+	10.5503i	−0.138795	+	0.427168i
$611$	2.44396	−	2.20055i	0.0988720	−	0.0890247i
$612$	−6.41616	−	2.85666i	−0.259358	−	0.115474i
$613$	21.8503	+	2.29656i	0.882525	+	0.0927571i	0.534939	−	0.844891i	$-0.320335\pi$
$613$	21.8503	+	2.29656i	0.882525	+	0.0927571i	0.347586	+	0.937648i	$0.387001\pi$
$614$	−2.01213	+	9.46631i	−0.0812028	+	0.382029i
$615$	1.09926			0.0443264
$616$	0.639868	+	8.75160i	0.0257810	+	0.352612i
$617$	9.52091			0.383298			0.191649	−	0.981464i	$-0.438617\pi$
$617$	9.52091			0.383298			0.191649	+	0.981464i	$0.438617\pi$
$618$	1.55816	−	7.33054i	0.0626782	−	0.294878i
$619$	38.8604	+	4.08440i	1.56193	+	0.164166i	0.845686	−	0.533681i	$-0.179192\pi$
$619$	38.8604	+	4.08440i	1.56193	+	0.164166i	0.716247	+	0.697847i	$0.245858\pi$
$620$	6.84184	+	3.04618i	0.274775	+	0.122338i
$621$	−2.13017	+	1.91802i	−0.0854810	+	0.0769674i
$622$	0.310900	−	0.956850i	0.0124659	−	0.0383662i
$623$	−0.164310	−	0.346025i	−0.00658292	−	0.0138632i
$624$	−1.03559	+	1.42536i	−0.0414566	+	0.0570601i
$625$	−11.6692	−	2.48037i	−0.466768	−	0.0992147i
$626$	−9.68104	−	16.7680i	−0.386932	−	0.670186i
$627$	0.462327	+	9.51746i	0.0184636	+	0.380091i
$628$	−3.38803	−	1.95608i	−0.135197	−	0.0780561i
$629$	−18.7832	−	57.8086i	−0.748934	−	2.30498i
$630$	−0.728450	+	2.44364i	−0.0290222	+	0.0973569i
$631$	16.0085	−	11.6308i	0.637288	−	0.463017i	−0.221630	−	0.975131i	$-0.571138\pi$
$631$	16.0085	−	11.6308i	0.637288	−	0.463017i	0.858917	+	0.512114i	$0.171138\pi$
$632$	−4.59800	−	5.10660i	−0.182899	−	0.203130i
$633$	23.4157	−	4.97717i	0.930692	−	0.197825i
$634$	1.51547	−	3.40380i	0.0601870	−	0.135182i
$635$	−0.867739	+	0.386342i	−0.0344352	+	0.0153315i
$636$	3.70837	−	1.20492i	0.147046	−	0.0477783i
$637$	9.61133	−	7.72806i	0.380815	−	0.306197i
$638$	5.21353	+	33.7512i	0.206406	+	1.33622i
$639$	5.12399	−	8.87500i	0.202702	−	0.351090i
$640$	0.644890	−	0.716223i	0.0254915	−	0.0283112i
$641$	5.03570	−	47.9115i	0.198898	−	1.89239i	−0.206803	−	0.978383i	$-0.566306\pi$
$641$	5.03570	−	47.9115i	0.198898	−	1.89239i	0.405701	−	0.914006i	$-0.367028\pi$
$642$	−14.8582	+	1.56166i	−0.586407	+	0.0616338i
$643$	13.8361	+	4.49561i	0.545642	+	0.177290i	0.568851	−	0.822441i	$-0.307388\pi$
$643$	13.8361	+	4.49561i	0.545642	+	0.177290i	−0.0232089	+	0.999731i	$0.507388\pi$
$644$	−7.58160	+	0.185376i	−0.298757	+	0.00730483i
$645$	−2.04234	−	2.81104i	−0.0804171	−	0.110685i
$646$	−8.20719	−	18.4337i	−0.322908	−	0.725263i
$647$	4.76162	+	4.28739i	0.187199	+	0.168555i	0.757401	−	0.652950i	$-0.226469\pi$
$647$	4.76162	+	4.28739i	0.187199	+	0.168555i	−0.570203	+	0.821504i	$0.693135\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	22.7300	+	18.5507i	0.892232	+	0.728178i
$650$		−	7.17271i		−	0.281337i
$651$	−2.64823	−	20.3884i	−0.103792	−	0.799086i
$652$	2.79710	+	2.03221i	0.109543	+	0.0795877i
$653$	−2.72082	−	25.8869i	−0.106474	−	1.01303i	−0.909108	−	0.416561i	$-0.863235\pi$
$653$	−2.72082	−	25.8869i	−0.106474	−	1.01303i	0.802634	−	0.596472i	$-0.203431\pi$
$654$	−0.635413	−	2.98939i	−0.0248466	−	0.116894i
$655$	−0.320851	−	1.50948i	−0.0125367	−	0.0589804i
$656$	0.119223	+	1.13433i	0.00465488	+	0.0442882i
$657$	−6.05981	−	4.40271i	−0.236416	−	0.171766i
$658$	4.55937	+	1.89782i	0.177743	+	0.0739848i
$659$			5.62340i			0.219057i	0.993984	+	0.109528i	$0.0349340\pi$
$659$			5.62340i			0.219057i	−0.993984	+	0.109528i	$0.965066\pi$
$660$	−0.179487	+	3.19143i	−0.00698653	+	0.124226i
$661$	−11.4724	+	6.62358i	−0.446224	+	0.257627i	−0.706234	−	0.707978i	$-0.749607\pi$
$661$	−11.4724	+	6.62358i	−0.446224	+	0.257627i	0.260010	+	0.965606i	$0.416274\pi$
$662$	−8.90947	−	8.02212i	−0.346276	−	0.311789i
$663$	5.03298	+	11.3043i	0.195465	+	0.439021i
$664$	−0.700386	−	0.963999i	−0.0271803	−	0.0374104i
$665$	−6.25297	+	3.81693i	−0.242480	+	0.148014i
$666$	−8.23091	−	2.67438i	−0.318941	−	0.103630i
$667$	−29.3541	+	3.08524i	−1.13660	+	0.119461i
$668$	2.23220	−	21.2380i	0.0863666	−	0.821723i
$669$	0.740707	−	0.822638i	0.0286374	−	0.0318050i
$670$	−7.30931	+	12.6601i	−0.282383	+	0.489102i
$671$	34.0802	−	17.2010i	1.31565	−	0.664037i
$672$	−2.60061	−	0.486660i	−0.100321	−	0.0187733i
$673$	−6.13976	+	1.99493i	−0.236671	+	0.0768989i	−0.424951	−	0.905216i	$-0.639709\pi$
$673$	−6.13976	+	1.99493i	−0.236671	+	0.0768989i	0.188280	+	0.982115i	$0.439709\pi$
$674$	7.17108	−	3.19277i	0.276220	−	0.122981i
$675$	1.65588	−	3.71917i	0.0637349	−	0.143151i
$676$	−9.67966	+	2.05747i	−0.372295	+	0.0791337i
$677$	−1.67035	−	1.85511i	−0.0641966	−	0.0712976i	0.710191	−	0.704009i	$-0.248609\pi$
$677$	−1.67035	−	1.85511i	−0.0641966	−	0.0712976i	−0.774388	+	0.632711i	$0.781942\pi$
$678$	15.2887	−	11.1079i	0.587159	−	0.426596i
$679$	−35.7417	−	10.6546i	−1.37164	−	0.408887i
$680$	−2.09171	−	6.43763i	−0.0802135	−	0.246872i
$681$	1.73256	+	1.00029i	0.0663919	+	0.0383314i
$682$	−9.14419	−	24.0962i	−0.350149	−	0.922693i
$683$	8.35011	+	14.4628i	0.319508	+	0.553404i	0.980385	−	0.197090i	$-0.0631490\pi$
$683$	8.35011	+	14.4628i	0.319508	+	0.553404i	−0.660877	+	0.750494i	$0.729816\pi$
$684$	−2.81022	−	0.597331i	−0.107452	−	0.0228395i
$685$	12.5919	−	17.3312i	0.481110	−	0.662191i
$686$	16.6744	+	8.06003i	0.636632	+	0.307733i
$687$	−3.44241	+	10.5947i	−0.131336	+	0.404212i
$688$	2.67922	−	2.41238i	0.102144	−	0.0919712i
$689$	−6.27587	−	2.79420i	−0.239092	−	0.106450i
$690$	−2.74746	−	0.288769i	−0.104594	−	0.0109933i
$691$	−2.52256	+	11.8677i	−0.0959625	+	0.451468i	0.903763	+	0.428034i	$0.140793\pi$
$691$	−2.52256	+	11.8677i	−0.0959625	+	0.451468i	−0.999725	+	0.0234347i	$0.992540\pi$
$692$	16.9787			0.645433
$693$	7.73473	−	4.14415i	0.293818	−	0.157423i
$694$	4.11250			0.156108
$695$	−0.985155	+	4.63479i	−0.0373691	+	0.175808i
$696$	−10.2406	−	1.07634i	−0.388171	−	0.0407984i
$697$	7.31814	+	3.25824i	0.277194	+	0.123415i
$698$	14.6672	−	13.2064i	0.555163	−	0.499871i
$699$	3.50239	−	10.7793i	0.132473	−	0.407709i
$700$	9.72998	−	4.62027i	0.367759	−	0.174630i
$701$	−9.23923	+	12.7167i	−0.348961	+	0.480303i	−0.947032	−	0.321140i	$-0.895934\pi$
$701$	−9.23923	+	12.7167i	−0.348961	+	0.480303i	0.598071	+	0.801443i	$0.295934\pi$
$702$	1.72334	+	0.366308i	0.0650434	+	0.0138254i
$703$	−12.4322	−	21.5332i	−0.468889	−	0.812140i
$704$	−3.31272	+	0.160921i	−0.124853	+	0.00606494i
$705$	1.55797	+	0.899493i	0.0586764	+	0.0338769i
$706$	3.02269	+	9.30289i	0.113760	+	0.350119i
$707$	29.4618	−	7.01914i	1.10802	−	0.263982i
$708$	−7.15662	+	5.19959i	−0.268962	+	0.195412i
$709$	5.76490	+	6.40257i	0.216505	+	0.240454i	0.841608	−	0.540089i	$-0.181609\pi$
$709$	5.76490	+	6.40257i	0.216505	+	0.240454i	−0.625102	+	0.780543i	$0.714943\pi$
$710$	9.66089	−	2.05349i	0.362567	−	0.0770659i
$711$	−2.79493	+	6.27752i	−0.104818	+	0.235426i
$712$	0.132264	−	0.0588878i	0.00495681	−	0.00220691i
$713$	21.1844	−	6.88322i	0.793361	−	0.257779i
$714$	−12.0926	+	14.1090i	−0.452553	+	0.528015i
$715$	3.99739	−	3.96696i	0.149494	−	0.148356i
$716$	4.31880	−	7.48039i	0.161401	−	0.279555i
$717$	1.85062	−	2.05532i	0.0691126	−	0.0767573i
$718$	−0.535355	+	5.09356i	−0.0199793	+	0.190090i
$719$	−33.7837	+	3.55081i	−1.25992	+	0.132423i	−0.710844	−	0.703350i	$-0.751687\pi$
$719$	−33.7837	+	3.55081i	−1.25992	+	0.132423i	−0.549076	+	0.835773i	$0.685020\pi$
$720$	−0.916603	−	0.297822i	−0.0341598	−	0.0110992i
$721$	−17.4088	−	9.49135i	−0.648339	−	0.353476i
$722$	6.31625	+	8.69357i	0.235066	+	0.323541i
$723$	−5.68742	−	12.7742i	−0.211518	−	0.475076i
$724$	7.61284	+	6.85463i	0.282929	+	0.254750i
$725$	36.3045	−	20.9604i	1.34831	−	0.778449i
$726$	8.23061	−	7.29775i	0.305466	−	0.270845i
$727$			2.77782i			0.103024i	0.998672	+	0.0515118i	$0.0164040\pi$
$727$			2.77782i			0.103024i	−0.998672	+	0.0515118i	$0.983596\pi$
$728$	2.83126	+	3.70305i	0.104934	+	0.137244i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−0.754590	−	7.17944i	−0.0279286	−	0.265723i
$731$	−5.26452	−	24.7676i	−0.194715	−	0.916063i
$732$	2.39310	+	11.2587i	0.0884517	+	0.416132i
$733$	4.43786	+	42.2234i	0.163916	+	1.55956i	0.699225	+	0.714902i	$0.253529\pi$
$733$	4.43786	+	42.2234i	0.163916	+	1.55956i	−0.535309	+	0.844656i	$0.679805\pi$
$734$	−12.6684	−	9.20410i	−0.467598	−	0.339730i
$735$	5.64524	+	3.69396i	0.208228	+	0.136254i
$736$		−	2.86643i		−	0.105658i
$737$	48.6422	−	12.8346i	1.79176	−	0.472769i
$738$	0.987771	−	0.570290i	0.0363603	−	0.0209927i
$739$	−23.6261	−	21.2730i	−0.869100	−	0.782541i	0.108260	−	0.994123i	$-0.465472\pi$
$739$	−23.6261	−	21.2730i	−0.869100	−	0.782541i	−0.977360	+	0.211581i	$0.932139\pi$
$740$	−3.39257	−	7.61985i	−0.124714	−	0.280111i
$741$	2.97524	+	4.09507i	0.109298	+	0.150436i
$742$	−0.252167	−	10.3133i	−0.00925734	−	0.378612i
$743$	−0.201536	−	0.0654830i	−0.00739364	−	0.00240234i	0.305318	−	0.952251i	$-0.401237\pi$
$743$	−0.201536	−	0.0654830i	−0.00739364	−	0.00240234i	−0.312711	+	0.949848i	$0.601237\pi$
$744$	7.72827	−	0.812274i	0.283332	−	0.0297794i
$745$	−0.753439	+	7.16849i	−0.0276039	+	0.262633i
$746$	12.4033	−	13.7753i	0.454118	−	0.504349i
$747$	−0.595784	+	1.03193i	−0.0217986	+	0.0377563i
$748$	−10.6544	+	20.7144i	−0.389564	+	0.757394i
$749$	−7.27073	+	38.8532i	−0.265667	+	1.41967i
$750$	8.31463	−	2.70159i	0.303607	−	0.0986480i
$751$	36.1205	−	16.0819i	1.31806	−	0.586836i	0.377353	−	0.926069i	$-0.376834\pi$
$751$	36.1205	−	16.0819i	1.31806	−	0.586836i	0.940702	+	0.339233i	$0.110168\pi$
$752$	−0.759218	+	1.70523i	−0.0276858	+	0.0621834i
$753$	10.8883	−	2.31438i	0.396792	−	0.0843407i
$754$	12.1392	+	13.4820i	0.442085	+	0.490985i
$755$	2.78096	−	2.02049i	0.101210	−	0.0735331i
$756$	0.613176	+	2.57372i	0.0223010	+	0.0936052i
$757$	−14.0754	−	43.3195i	−0.511578	−	1.57447i	−0.789423	−	0.613849i	$-0.789620\pi$
$757$	−14.0754	−	43.3195i	−0.511578	−	1.57447i	0.277845	−	0.960626i	$-0.410380\pi$
$758$	4.37410	+	2.52539i	0.158874	+	0.0917262i
$759$	5.95460	+	7.41104i	0.216138	+	0.269004i
$760$	−1.38446	−	2.39796i	−0.0502197	−	0.0869831i
$761$	28.0928	+	5.97131i	1.01836	+	0.216460i	0.686702	−	0.726939i	$-0.259058\pi$
$761$	28.0928	+	5.97131i	1.01836	+	0.216460i	0.331661	+	0.943399i	$0.392391\pi$
$762$	−0.579299	+	0.797337i	−0.0209858	+	0.0288845i
$763$	−8.05983	−	0.648387i	−0.291785	−	0.0234732i
$764$	−1.00565	+	3.09506i	−0.0363830	+	0.111976i
$765$	−5.03029	+	4.52929i	−0.181871	+	0.163757i
$766$	23.9720	+	10.6730i	0.866144	+	0.385632i
$767$	15.5000	+	1.62912i	0.559673	+	0.0588240i
$768$	0.207912	−	0.978148i	0.00750237	−	0.0352959i
$769$	−10.4652			−0.377385			−0.188692	−	0.982036i	$-0.560425\pi$
$769$	−10.4652			−0.377385			−0.188692	+	0.982036i	$0.560425\pi$
$770$	7.95618	+	2.86727i	0.286721	+	0.103329i
$771$	21.5496			0.776090
$772$	−3.21461	+	15.1236i	−0.115696	+	0.544309i
$773$	−44.8244	−	4.71124i	−1.61222	−	0.169451i	−0.744892	−	0.667185i	$-0.767499\pi$
$773$	−44.8244	−	4.71124i	−1.61222	−	0.169451i	−0.867330	+	0.497733i	$0.834166\pi$
$774$	−3.29356	−	1.46639i	−0.118384	−	0.0527082i
$775$	−23.5103	+	21.1687i	−0.844514	+	0.760403i
$776$	4.35607	−	13.4066i	0.156374	−	0.481269i
$777$	−13.0021	+	18.8480i	−0.466446	+	0.676169i
$778$	16.1864	−	22.2787i	0.580312	−	0.798731i
$779$	3.20528	+	0.681304i	0.114841	+	0.0244102i
$780$	0.849008	+	1.47053i	0.0303994	+	0.0526533i
$781$	−28.4344	−	18.6204i	−1.01746	−	0.666289i
$782$	−17.4348	−	10.0660i	−0.623467	−	0.359959i
$783$	3.18197	+	9.79308i	0.113714	+	0.349976i
$784$	−3.19955	+	6.22599i	−0.114269	+	0.222357i
$785$	−3.05034	+	2.21621i	−0.108871	+	0.0790998i
$786$	−1.07142	−	1.18993i	−0.0382163	−	0.0424435i
$787$	−40.6206	+	8.63419i	−1.44797	+	0.307775i	−0.863791	−	0.503850i	$-0.831917\pi$
$787$	−40.6206	+	8.63419i	−1.44797	+	0.307775i	−0.584178	+	0.811625i	$0.698583\pi$
$788$	−0.0431020	+	0.0968088i	−0.00153545	+	0.00344867i
$789$	−1.22348	+	0.544727i	−0.0435569	+	0.0193928i
$790$	−6.29853	+	2.04652i	−0.224092	+	0.0728118i
$791$	−16.6083	−	47.1601i	−0.590523	−	1.67682i
$792$	1.49441	+	2.96087i	0.0531016	+	0.105210i
$793$	10.1396	−	17.5623i	0.360067	−	0.623654i
$794$	−3.07055	+	3.41019i	−0.108970	+	0.121023i
$795$	0.392813	−	3.73737i	0.0139316	−	0.132551i
$796$	−26.7614	+	2.81273i	−0.948532	+	0.0996947i
$797$	19.7703	+	6.42376i	0.700300	+	0.227541i	0.637461	−	0.770482i	$-0.279985\pi$
$797$	19.7703	+	6.42376i	0.700300	+	0.227541i	0.0628387	+	0.998024i	$0.479985\pi$
$798$	−3.63859	+	6.67382i	−0.128805	+	0.236251i
$799$	7.70578	+	10.6061i	0.272611	+	0.375217i
$800$	1.65588	+	3.71917i	0.0585443	+	0.131493i
$801$	−0.107593	−	0.0968774i	−0.00380162	−	0.00342300i
$802$	23.6603	−	13.6603i	0.835473	−	0.482361i
$803$	−15.7076	+	19.2465i	−0.554311	+	0.679194i
$804$			15.1681i			0.534939i
$805$	−2.80879	+	6.74789i	−0.0989967	+	0.237832i
$806$	−11.0763	−	8.04737i	−0.390144	−	0.283456i
$807$	1.86704	+	17.7637i	0.0657228	+	0.625311i
$808$	2.38000	+	11.1970i	0.0837282	+	0.393910i
$809$	−6.43756	−	30.2863i	−0.226332	−	1.06481i	−0.933725	−	0.357990i	$-0.883462\pi$
$809$	−6.43756	−	30.2863i	−0.226332	−	1.06481i	0.707393	−	0.706820i	$-0.249871\pi$
$810$	0.100742	+	0.958493i	0.00353970	+	0.0336780i
$811$	16.7119	+	12.1419i	0.586833	+	0.426359i	0.841181	−	0.540754i	$-0.181861\pi$
$811$	16.7119	+	12.1419i	0.586833	+	0.426359i	−0.254348	+	0.967113i	$0.581861\pi$
$812$	−10.4692	+	25.1516i	−0.367399	+	0.882646i
$813$			14.2757i			0.500671i
$814$	−10.3888	+	26.7577i	−0.364128	+	0.937857i
$815$	2.88573	−	1.66608i	0.101083	−	0.0583602i
$816$	−5.21937	−	4.69954i	−0.182715	−	0.164517i
$817$	−4.21294	−	9.46241i	−0.147392	−	0.331048i
$818$	20.4759	+	28.1826i	0.715922	+	0.985383i
$819$	2.23133	−	4.09265i	0.0779689	−	0.143009i
$820$	1.04546	+	0.339690i	0.0365090	+	0.0118625i
$821$	2.86773	−	0.301410i	0.100084	−	0.0105193i	−0.0543538	−	0.998522i	$-0.517310\pi$
$821$	2.86773	−	0.301410i	0.100084	−	0.0105193i	0.154438	+	0.988002i	$0.450643\pi$
$822$	2.32344	−	22.1060i	0.0810392	−	0.771036i
$823$	5.41779	−	6.01707i	0.188852	−	0.209742i	−0.641282	−	0.767305i	$-0.721597\pi$
$823$	5.41779	−	6.01707i	0.188852	−	0.209742i	0.830134	+	0.557564i	$0.188264\pi$
$824$	3.74716	−	6.49026i	0.130538	−	0.226099i
$825$	−12.0073	−	6.17591i	−0.418039	−	0.215018i
$826$	7.77431	+	22.0756i	0.270503	+	0.768107i
$827$	−24.7944	+	8.05618i	−0.862185	+	0.280141i	−0.706541	−	0.707672i	$-0.749745\pi$
$827$	−24.7944	+	8.05618i	−0.862185	+	0.280141i	−0.155644	+	0.987813i	$0.549745\pi$
$828$	−2.61862	+	1.16588i	−0.0910032	+	0.0405172i
$829$	−19.8509	+	44.5858i	−0.689449	+	1.54853i	0.140127	+	0.990134i	$0.455249\pi$
$829$	−19.8509	+	44.5858i	−0.689449	+	1.54853i	−0.829576	+	0.558394i	$0.811418\pi$
$830$	−1.12331	+	0.238766i	−0.0389905	+	0.00828769i
$831$	−8.23770	−	9.14890i	−0.285763	−	0.317372i
$832$	−1.42536	+	1.03559i	−0.0494155	+	0.0359025i
$833$	26.6332	+	41.3246i	0.922786	+	1.43181i
$834$	1.51926	+	4.67582i	0.0526078	+	0.161910i
$835$	−17.8240	−	10.2907i	−0.616824	−	0.356124i
$836$	−2.50136	+	9.19451i	−0.0865113	+	0.317999i
$837$	−3.88542	−	6.72974i	−0.134300	−	0.232614i
$838$	19.7451	+	4.19694i	0.682082	+	0.144981i
$839$	−11.3423	+	15.6114i	−0.391580	+	0.538964i	−0.958606	−	0.284736i	$-0.908094\pi$
$839$	−11.3423	+	15.6114i	−0.391580	+	0.538964i	0.567026	+	0.823700i	$0.308094\pi$
$840$	−1.44792	+	2.09893i	−0.0499581	+	0.0724201i
$841$	−23.8034	+	73.2593i	−0.820807	+	2.52618i
$842$	−14.0442	+	12.6455i	−0.483996	+	0.435792i
$843$	−26.2163	−	11.6722i	−0.902937	−	0.402013i
$844$	23.8077	+	2.50229i	0.819495	+	0.0861324i
$845$	−1.98294	+	9.32899i	−0.0682152	+	0.320927i
$846$	1.86661			0.0641753
$847$	−12.2824	−	26.3845i	−0.422029	−	0.906582i
$848$	3.89921			0.133899
$849$	3.54930	−	16.6982i	0.121812	−	0.573079i
$850$	28.4365	+	2.98879i	0.975362	+	0.102515i
$851$	−22.6628	−	10.0901i	−0.776870	−	0.345885i
$852$	7.61573	−	6.85723i	0.260911	−	0.234925i
$853$	−2.83000	+	8.70984i	−0.0968973	+	0.298219i	−0.987743	−	0.156086i	$-0.950112\pi$
$853$	−2.83000	+	8.70984i	−0.0968973	+	0.298219i	0.890846	+	0.454305i	$0.150112\pi$
$854$	30.3550	+	2.44196i	1.03873	+	0.0835623i
$855$	−1.62753	+	2.24011i	−0.0556605	+	0.0766101i
$856$	−14.6136	−	3.10621i	−0.499482	−	0.106168i
$857$	11.7330	+	20.3222i	0.400793	+	0.694193i	0.993822	−	0.110988i	$-0.0354015\pi$
$857$	11.7330	+	20.3222i	0.400793	+	0.694193i	−0.593029	+	0.805181i	$0.702068\pi$
$858$	1.53393	−	5.63844i	0.0523676	−	0.192493i
$859$	−39.3882	−	22.7408i	−1.34391	−	0.775906i	−0.356529	−	0.934284i	$-0.616040\pi$
$859$	−39.3882	−	22.7408i	−1.34391	−	0.775906i	−0.987378	+	0.158379i	$0.949373\pi$
$860$	−1.07372	−	3.30458i	−0.0366136	−	0.112685i
$861$	−0.699376	−	2.93553i	−0.0238347	−	0.100043i
$862$	19.0927	−	13.8716i	0.650299	−	0.472470i
$863$	−31.4937	−	34.9772i	−1.07206	−	1.19064i	−0.980841	−	0.194808i	$-0.937592\pi$
$863$	−31.4937	−	34.9772i	−1.07206	−	1.19064i	−0.0912151	−	0.995831i	$-0.529075\pi$
$864$	−0.978148	+	0.207912i	−0.0332773	+	0.00707330i
$865$	6.65568	−	14.9489i	0.226300	−	0.508278i
$866$	13.1898	−	5.87249i	0.448209	−	0.199555i
$867$	−30.7453	+	9.98977i	−1.04417	+	0.339270i
$868$	3.78176	−	20.2089i	0.128361	−	0.685935i
$869$	20.2668	+	10.4242i	0.687505	+	0.353617i
$870$	−4.96201	+	8.59446i	−0.168228	+	0.291379i
$871$	17.8818	−	19.8597i	0.605900	−	0.672920i
$872$	0.319457	−	3.03943i	0.0108182	−	0.102928i
$873$	−14.0193	+	1.47349i	−0.474482	+	0.0498701i
$874$	−7.83221	−	2.54484i	−0.264929	−	0.0860805i
$875$	−0.565390	−	23.1236i	−0.0191137	−	0.781721i
$876$	−4.40271	−	6.05981i	−0.148754	−	0.204742i
$877$	−21.6320	−	48.5864i	−0.730462	−	1.64064i	−0.767272	−	0.641322i	$-0.778386\pi$
$877$	−21.6320	−	48.5864i	−0.730462	−	1.64064i	0.0368096	−	0.999322i	$-0.488280\pi$
$878$	−29.0162	−	26.1263i	−0.979249	−	0.881720i
$879$	19.4377	−	11.2224i	0.655617	−	0.378521i
$880$	−1.15691	+	2.97977i	−0.0389994	+	0.100448i
$881$			26.1280i			0.880274i	0.897931	+	0.440137i	$0.145070\pi$
$881$			26.1280i			0.880274i	−0.897931	+	0.440137i	$0.854930\pi$
$882$	6.98909	+	0.390593i	0.235335	+	0.0131519i
$883$	−13.2945	−	9.65899i	−0.447394	−	0.325051i	0.341172	−	0.940001i	$-0.389176\pi$
$883$	−13.2945	−	9.65899i	−0.447394	−	0.325051i	−0.788566	+	0.614950i	$0.789176\pi$
$884$	1.29344	+	12.3063i	0.0435031	+	0.413905i
$885$	1.77257	+	8.33929i	0.0595843	+	0.280322i
$886$	3.99468	+	18.7935i	0.134204	+	0.631379i
$887$	2.30304	+	21.9120i	0.0773285	+	0.735732i	0.962649	+	0.270751i	$0.0872720\pi$
$887$	2.30304	+	21.9120i	0.0773285	+	0.735732i	−0.885321	+	0.464981i	$0.846061\pi$
$888$	−7.00163	−	5.08698i	−0.234959	−	0.170708i
$889$	1.58379	+	2.07146i	0.0531186	+	0.0694746i
$890$		−	0.139536i		−	0.00467726i
$891$	2.09705	−	2.56951i	0.0702539	−	0.0860817i
$892$	0.958663	−	0.553485i	0.0320984	−	0.0185320i
$893$	3.98532	+	3.58840i	0.133364	+	0.120081i
$894$	3.04195	+	6.83233i	0.101738	+	0.228507i
$895$	−4.89313	−	6.73482i	−0.163559	−	0.225120i
$896$	−2.32294	−	1.26647i	−0.0776039	−	0.0423099i
$897$	4.80303	+	1.56060i	0.160369	+	0.0521069i
$898$	−6.75251	+	0.709717i	−0.225334	+	0.0236836i
$899$	8.36403	−	79.5784i	0.278956	−	2.65409i
$900$	2.72413	−	3.02545i	0.0908042	−	0.100848i
$901$	13.6928	−	23.7166i	0.456172	−	0.790114i
$902$	−1.70450	−	3.37710i	−0.0567535	−	0.112445i
$903$	−6.20738	+	7.24244i	−0.206569	+	0.241013i
$904$	17.9730	−	5.83977i	0.597771	−	0.194228i
$905$	9.01941	−	4.01570i	0.299815	−	0.133486i
$906$	1.45070	−	3.25832i	0.0481961	−	0.108250i
$907$	0.658980	−	0.140071i	0.0218811	−	0.00465097i	−0.196958	−	0.980412i	$-0.563106\pi$
$907$	0.658980	−	0.140071i	0.0218811	−	0.00465097i	0.218839	+	0.975761i	$0.429773\pi$
$908$	1.33866	+	1.48673i	0.0444248	+	0.0493388i
$909$	9.26097	−	6.72849i	0.307167	−	0.223170i
$910$	4.37021	−	1.04118i	0.144871	−	0.0345149i
$911$	−5.86870	−	18.0620i	−0.194439	−	0.598420i	−0.999983	−	0.00588464i	$-0.998127\pi$
$911$	−5.86870	−	18.0620i	−0.194439	−	0.598420i	0.805544	−	0.592536i	$-0.201873\pi$
$912$	−2.48810	−	1.43650i	−0.0823891	−	0.0475674i
$913$	3.30616	+	2.16505i	0.109418	+	0.0716528i
$914$	5.65718	+	9.79853i	0.187123	+	0.324107i
$915$	10.8508	+	2.30641i	0.358716	+	0.0762475i
$916$	−6.54786	+	9.01236i	−0.216347	+	0.297777i
$917$	−3.82688	+	1.81719i	−0.126375	+	0.0600089i
$918$	−2.17034	+	6.67961i	−0.0716318	+	0.220460i
$919$	−19.2113	+	17.2979i	−0.633722	+	0.570605i	−0.922120	−	0.386905i	$-0.873544\pi$
$919$	−19.2113	+	17.2979i	−0.633722	+	0.570605i	0.288398	+	0.957511i	$0.406877\pi$
$920$	−2.52375	−	1.12365i	−0.0832056	−	0.0370455i
$921$	9.62478	+	1.01161i	0.317147	+	0.0333335i
$922$	−4.99968	+	23.5217i	−0.164656	+	0.774644i
$923$	−18.0553			−0.594298
$924$	8.63678	−	1.55115i	0.284129	−	0.0510292i
$925$	35.2337			1.15848
$926$	−1.45694	+	6.85436i	−0.0478780	+	0.225248i
$927$	−7.45326	−	0.783369i	−0.244797	−	0.0257292i
$928$	−9.40683	−	4.18819i	−0.308794	−	0.137484i
$929$	−8.17223	+	7.35831i	−0.268122	+	0.241418i	−0.792214	−	0.610244i	$-0.791072\pi$
$929$	−8.17223	+	7.35831i	−0.268122	+	0.241418i	0.524092	+	0.851662i	$0.324405\pi$
$930$	2.31433	−	7.12277i	0.0758898	−	0.233565i
$931$	14.1712	+	14.2699i	0.464444	+	0.467677i
$932$	6.66194	−	9.16938i	0.218219	−	0.300353i
$933$	−0.984107	−	0.209178i	−0.0322182	−	0.00684819i
$934$	7.04296	+	12.1988i	0.230453	+	0.399156i
$935$	14.0615	+	17.5008i	0.459859	+	0.572336i
$936$	1.52580	+	0.880922i	0.0498724	+	0.0287938i
$937$	16.2496	+	50.0113i	0.530853	+	1.63380i	0.752443	+	0.658657i	$0.228875\pi$
$937$	16.2496	+	50.0113i	0.530853	+	1.63380i	−0.221590	+	0.975140i	$0.571125\pi$
$938$	38.4587	+	11.4646i	1.25572	+	0.374331i
$939$	−15.6642	+	11.3807i	−0.511183	+	0.371396i
$940$	1.20376	+	1.33691i	0.0392622	+	0.0436051i
$941$	−54.6653	+	11.6195i	−1.78204	+	0.378784i	−0.976797	−	0.214166i	$-0.931297\pi$
$941$	−54.6653	+	11.6195i	−1.78204	+	0.378784i	−0.805239	+	0.592950i	$0.797963\pi$
$942$	−1.59122	+	3.57394i	−0.0518447	+	0.116445i
$943$	2.98674	−	1.32978i	0.0972616	−	0.0433037i
$944$	−8.41311	+	2.73358i	−0.273823	+	0.0889706i
$945$	2.50640	+	0.469030i	0.0815331	+	0.0152575i
$946$	−5.46915	+	10.6332i	−0.177817	+	0.345714i
$947$	−1.66760	+	2.88837i	−0.0541898	+	0.0938595i	−0.891848	−	0.452336i	$-0.850591\pi$
$947$	−1.66760	+	2.88837i	−0.0541898	+	0.0938595i	0.837658	+	0.546195i	$0.183924\pi$
$948$	−4.59800	+	5.10660i	−0.149336	+	0.165855i
$949$	−1.37944	+	13.1245i	−0.0447786	+	0.426040i
$950$	11.6323	−	1.22261i	0.377403	−	0.0396666i
$951$	−3.54357	−	1.15137i	−0.114908	−	0.0373359i
$952$	−15.8606	+	9.68161i	−0.514046	+	0.313783i
$953$	−9.62041	−	13.2414i	−0.311636	−	0.428930i	0.624255	−	0.781221i	$-0.285403\pi$
$953$	−9.62041	−	13.2414i	−0.311636	−	0.428930i	−0.935890	+	0.352291i	$0.885403\pi$
$954$	−1.58595	−	3.56211i	−0.0513471	−	0.115327i
$955$	2.33084	+	2.09869i	0.0754241	+	0.0679121i
$956$	2.39517	−	1.38285i	0.0774653	−	0.0447246i
$957$	33.0213	−	8.71293i	1.06743	−	0.281649i
$958$		−	11.3914i		−	0.368039i
$959$	−54.2935	−	22.5995i	−1.75323	−	0.729776i
$960$	−0.779709	−	0.566492i	−0.0251650	−	0.0182834i
$961$	3.07166	+	29.2249i	0.0990859	+	0.942740i
$962$	3.17021	+	14.9147i	0.102212	+	0.480868i
$963$	3.10621	+	14.6136i	0.100096	+	0.470916i
$964$	−1.46163	−	13.9065i	−0.0470759	−	0.447897i
$965$	12.0554	+	8.75877i	0.388078	+	0.281955i
$966$	0.976854	+	7.52069i	0.0314297	+	0.241974i
$967$		−	30.9688i		−	0.995888i	−0.867209	−	0.497944i	$-0.834089\pi$
$967$		−	30.9688i		−	0.995888i	0.867209	−	0.497944i	$-0.165911\pi$
$968$	10.0829	−	4.39717i	0.324077	−	0.141330i
$969$	−17.4748	+	10.0891i	−0.561371	+	0.324108i
$970$	−10.0963	−	9.09072i	−0.324172	−	0.291886i
$971$	−4.69727	−	10.5502i	−0.150743	−	0.338573i	0.822352	−	0.568979i	$-0.192661\pi$
$971$	−4.69727	−	10.5502i	−0.150743	−	0.338573i	−0.973095	+	0.230406i	$0.925995\pi$
$972$	0.587785	+	0.809017i	0.0188532	+	0.0259492i
$973$	13.0038	−	0.317953i	0.416883	−	0.0101931i
$974$	−22.9985	−	7.47266i	−0.736919	−	0.239440i
$975$	−7.13342	+	0.749753i	−0.228452	+	0.0240113i
$976$	−1.20314	+	11.4471i	−0.0385117	+	0.366414i
$977$	5.87346	−	6.52314i	0.187909	−	0.208694i	−0.641828	−	0.766848i	$-0.721824\pi$
$977$	5.87346	−	6.52314i	0.187909	−	0.208694i	0.829737	+	0.558155i	$0.188490\pi$
$978$	1.72871	−	2.99421i	0.0552779	−	0.0957441i
$979$	−0.340837	+	0.338242i	−0.0108932	+	0.0108103i
$980$	4.22745	+	5.25764i	0.135041	+	0.167949i
$981$	−2.90659	+	0.944408i	−0.0928003	+	0.0301526i
$982$	2.09357	−	0.932117i	0.0668085	−	0.0297450i
$983$	−1.64893	+	3.70357i	−0.0525928	+	0.118125i	−0.937931	−	0.346823i	$-0.887260\pi$
$983$	−1.64893	+	3.70357i	−0.0525928	+	0.118125i	0.885338	+	0.464948i	$0.153927\pi$
$984$	1.11565	−	0.237140i	0.0355658	−	0.00755974i
$985$	0.0683392	+	0.0758984i	0.00217747	+	0.00241832i
$986$	−58.5080	+	42.5086i	−1.86328	+	1.35375i
$987$	1.41084	−	4.73277i	0.0449076	−	0.150646i
$988$	1.56418	+	4.81404i	0.0497631	+	0.153155i
$989$	−8.94968	−	5.16710i	−0.284583	−	0.164304i
$990$	3.19271	−	0.155091i	0.101471	−	0.00492913i
$991$	9.73826	+	16.8672i	0.309346	+	0.535803i	0.978219	−	0.207573i	$-0.0665566\pi$
$991$	9.73826	+	16.8672i	0.309346	+	0.535803i	−0.668874	+	0.743376i	$0.733223\pi$
$992$	7.60103	+	1.61565i	0.241333	+	0.0512969i
$993$	−7.04688	+	9.69920i	−0.223626	+	0.307795i
$994$	−11.6302	−	24.4925i	−0.368889	−	0.776856i
$995$	−8.01403	+	24.6647i	−0.254062	+	0.781922i
$996$	−0.885508	+	0.797315i	−0.0280584	+	0.0252639i
$997$	−18.5792	−	8.27198i	−0.588408	−	0.261976i	0.0908632	−	0.995863i	$-0.471037\pi$
$997$	−18.5792	−	8.27198i	−0.588408	−	0.261976i	−0.679271	+	0.733887i	$0.737704\pi$
$998$	−10.5460	−	1.10843i	−0.333829	−	0.0350868i
$999$	−1.79937	+	8.46537i	−0.0569295	+	0.267832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.b.61.6	yes	64
7.3	odd	6		462.2.ba.a.325.7	yes	64
11.2	odd	10		462.2.ba.a.145.7	✓	64
77.24	even	30	inner	462.2.ba.b.409.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.145.7	✓	64	11.2	odd	10
462.2.ba.a.325.7	yes	64	7.3	odd	6
462.2.ba.b.61.6	yes	64	1.1	even	1	trivial
462.2.ba.b.409.6	yes	64	77.24	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.716223 + 0.644890i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(2.17783 + 1.50235i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.716223 + 0.644890i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(2.17783 + 1.50235i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(0.481886 + 0.834652i) q^{10} +(0.870641 - 3.20031i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.544440 - 1.67561i) q^{13} +(1.92232 - 1.81788i) q^{14} +(0.779709 - 0.566492i) q^{15} +(0.669131 + 0.743145i) q^{16} +(6.86988 - 1.46024i) q^{17} +(0.406737 - 0.913545i) q^{18} +(2.62462 - 1.16856i) q^{19} +(0.916603 - 0.297822i) q^{20} +(-2.00886 - 1.72176i) q^{21} +(-2.94936 - 1.51700i) q^{22} +(1.43322 - 2.48240i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.425550 + 4.04884i) q^{25} +(-1.75219 + 0.184163i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(-1.37849 - 2.25827i) q^{28} +(-6.05246 - 8.33049i) q^{29} +(-0.392002 - 0.880450i) q^{30} +(5.77486 + 5.19971i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.20040 + 3.09177i) q^{33} -7.02336i q^{34} +(-2.52866 + 0.328445i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-0.904640 - 8.60708i) q^{37} +(-0.597331 - 2.81022i) q^{38} +(0.366308 + 1.72334i) q^{39} +(-0.100742 - 0.958493i) q^{40} +(0.922748 + 0.670416i) q^{41} +(-2.10181 + 1.60699i) q^{42} -3.60525i q^{43} +(-2.09705 + 2.56951i) q^{44} +(-0.834652 + 0.481886i) q^{45} +(-2.13017 - 1.91802i) q^{46} +(0.759218 + 1.70523i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(2.48590 + 6.54372i) q^{49} +(3.87189 + 1.25805i) q^{50} +(-6.98488 + 0.734141i) q^{51} +(-0.184163 + 1.75219i) q^{52} +(2.60908 - 2.89768i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.44027 + 2.85360i) q^{55} +(-2.49552 + 0.878844i) q^{56} +(-2.73239 + 0.887808i) q^{57} +(-9.40683 + 4.18819i) q^{58} +(-3.59802 + 8.08128i) q^{59} +(-0.942712 + 0.200380i) q^{60} +(7.70182 + 8.55374i) q^{61} +(6.28674 - 4.56758i) q^{62} +(1.81788 + 1.92232i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(1.47053 + 0.849008i) q^{65} +(2.77463 + 1.81698i) q^{66} +(7.58406 + 13.1360i) q^{67} +(-6.86988 - 1.46024i) q^{68} +(-1.68485 + 2.31899i) q^{69} +(-0.204471 + 2.54169i) q^{70} +(3.16680 - 9.74640i) q^{71} +(-0.743145 + 0.669131i) q^{72} +(-6.84277 - 3.04660i) q^{73} +(-8.60708 - 0.904640i) q^{74} +(0.846438 - 3.98218i) q^{75} -2.87301 q^{76} +(6.70409 - 5.66173i) q^{77} +1.76184 q^{78} +(-1.42869 + 6.72144i) q^{79} +(-0.958493 - 0.100742i) q^{80} +(0.913545 + 0.406737i) q^{81} +(0.847616 - 0.763197i) q^{82} +(-0.368215 + 1.13325i) q^{83} +(1.13488 + 2.38999i) q^{84} +(-3.97867 + 5.47617i) q^{85} +(-3.52646 - 0.749573i) q^{86} +(5.14853 + 8.91751i) q^{87} +(2.07736 + 2.58546i) q^{88} +(-0.125384 - 0.0723905i) q^{89} +(0.297822 + 0.916603i) q^{90} +(1.33166 - 4.46714i) q^{91} +(-2.31899 + 1.68485i) q^{92} +(-5.19971 - 5.77486i) q^{93} +(1.82582 - 0.388090i) q^{94} +(-1.12622 + 2.52954i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-13.4066 + 4.35607i) q^{97} +(6.91757 - 1.07106i) q^{98} +(1.51700 - 2.94936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * 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 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

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