LMFDB - Embedded newform 512.2.o.a.149.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			149.23
Character	$\chi$	$=$	512.149
Dual form			512.2.o.a.189.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.777462 + 1.18134i) q^{2} +(-3.02508 - 0.524902i) q^{3} +(-0.791106 - 1.83689i) q^{4} +(-0.967631 + 2.92906i) q^{5} +(2.97197 - 3.16555i) q^{6} +(0.196816 - 4.00628i) q^{7} +(2.78503 + 0.493547i) q^{8} +(6.05098 + 2.16508i) q^{9} +O(q^{10})$	\(q+(-0.777462 + 1.18134i) q^{2} +(-3.02508 - 0.524902i) q^{3} +(-0.791106 - 1.83689i) q^{4} +(-0.967631 + 2.92906i) q^{5} +(2.97197 - 3.16555i) q^{6} +(0.196816 - 4.00628i) q^{7} +(2.78503 + 0.493547i) q^{8} +(6.05098 + 2.16508i) q^{9} +(-2.70791 - 3.42033i) q^{10} +(-3.73704 - 1.65652i) q^{11} +(1.42898 + 5.97199i) q^{12} +(1.89136 - 1.63150i) q^{13} +(4.57974 + 3.34723i) q^{14} +(4.46464 - 8.35275i) q^{15} +(-2.74830 + 2.90634i) q^{16} +(2.32811 - 1.24440i) q^{17} +(-7.26209 + 5.46498i) q^{18} +(-0.0744722 + 0.0421880i) q^{19} +(6.14585 - 0.539771i) q^{20} +(-2.69829 + 12.0160i) q^{21} +(4.86231 - 3.12682i) q^{22} +(1.71953 + 6.86475i) q^{23} +(-8.16590 - 2.95489i) q^{24} +(-3.62705 - 2.69000i) q^{25} +(0.456887 + 3.50276i) q^{26} +(-9.15404 - 5.18570i) q^{27} +(-7.51478 + 2.80786i) q^{28} +(-6.06531 + 0.148895i) q^{29} +(6.39631 + 11.7682i) q^{30} +(0.434748 - 0.290489i) q^{31} +(-1.29667 - 5.50624i) q^{32} +(10.4354 + 6.97268i) q^{33} +(-0.339962 + 3.71775i) q^{34} +(11.5442 + 4.45308i) q^{35} +(-0.809973 - 12.8278i) q^{36} +(-3.63236 - 0.448009i) q^{37} +(0.00806113 - 0.120776i) q^{38} +(-6.57791 + 3.94265i) q^{39} +(-4.14051 + 7.67996i) q^{40} +(-4.93172 + 3.65761i) q^{41} +(-12.0971 - 12.5296i) q^{42} +(-4.92449 + 6.99223i) q^{43} +(-0.0864348 + 8.17500i) q^{44} +(-12.1968 + 15.6287i) q^{45} +(-9.44645 - 3.30574i) q^{46} +(1.17717 + 11.9520i) q^{47} +(9.83939 - 7.34935i) q^{48} +(-9.04524 - 0.890878i) q^{49} +(5.99769 - 2.19339i) q^{50} +(-7.69591 + 2.54239i) q^{51} +(-4.49315 - 2.18353i) q^{52} +(12.3110 + 0.302217i) q^{53} +(13.2430 - 6.78230i) q^{54} +(8.46811 - 9.34312i) q^{55} +(2.52542 - 11.0605i) q^{56} +(0.247429 - 0.0885316i) q^{57} +(4.53965 - 7.28092i) q^{58} +(-1.40771 + 1.63193i) q^{59} +(-18.8750 - 1.59312i) q^{60} +(7.97061 - 1.78986i) q^{61} +(0.00516536 + 0.739428i) q^{62} +(9.86483 - 23.8158i) q^{63} +(7.51282 + 2.74909i) q^{64} +(2.94862 + 7.11860i) q^{65} +(-16.3502 + 6.90666i) q^{66} +(12.6913 + 8.03670i) q^{67} +(-4.12760 - 3.29202i) q^{68} +(-1.59841 - 21.6690i) q^{69} +(-14.2357 + 10.1755i) q^{70} +(-3.53041 - 1.66976i) q^{71} +(15.7836 + 9.01625i) q^{72} +(-0.170356 - 3.46768i) q^{73} +(3.35327 - 3.94273i) q^{74} +(9.56014 + 10.0413i) q^{75} +(0.136410 + 0.103422i) q^{76} +(-7.37197 + 14.6456i) q^{77} +(0.456485 - 10.8360i) q^{78} +(-0.300227 - 0.365828i) q^{79} +(-5.85352 - 10.8622i) q^{80} +(10.0661 + 8.26106i) q^{81} +(-0.486643 - 8.66966i) q^{82} +(8.57479 - 1.05760i) q^{83} +(24.2067 - 4.54950i) q^{84} +(1.39217 + 8.02329i) q^{85} +(-4.43157 - 11.2537i) q^{86} +(18.4262 + 2.73327i) q^{87} +(-9.59021 - 6.45786i) q^{88} +(1.08200 - 4.31957i) q^{89} +(-8.98022 - 26.5592i) q^{90} +(-6.16399 - 7.89843i) q^{91} +(11.2494 - 8.58933i) q^{92} +(-1.46763 + 0.650555i) q^{93} +(-15.0345 - 7.90160i) q^{94} +(-0.0515095 - 0.258956i) q^{95} +(1.03230 + 17.3375i) q^{96} +(-3.48428 + 17.5167i) q^{97} +(8.08475 - 9.99283i) q^{98} +(-19.0263 - 18.1145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{77}{128}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.777462	+	1.18134i	−0.549748	+	0.835330i
$2$	−0.777462	+	1.18134i	−0.549748	+	0.835330i
$3$	−3.02508	−	0.524902i	−1.74653	−	0.303052i	−0.794097	−	0.607791i	$-0.792056\pi$
$3$	−3.02508	−	0.524902i	−1.74653	−	0.303052i	−0.952436	+	0.304738i	$0.901431\pi$
$4$	−0.791106	−	1.83689i	−0.395553	−	0.918443i
$5$	−0.967631	+	2.92906i	−0.432738	+	1.30992i	0.471115	+	0.882072i	$0.343852\pi$
$5$	−0.967631	+	2.92906i	−0.432738	+	1.30992i	−0.903853	+	0.427844i	$0.859273\pi$
$6$	2.97197	−	3.16555i	1.21330	−	1.29233i
$7$	0.196816	−	4.00628i	0.0743894	−	1.51423i	−0.614241	−	0.789118i	$-0.710538\pi$
$7$	0.196816	−	4.00628i	0.0743894	−	1.51423i	0.688631	−	0.725112i	$-0.258212\pi$
$8$	2.78503	+	0.493547i	0.984658	+	0.174495i
$9$	6.05098	+	2.16508i	2.01699	+	0.721692i
$10$	−2.70791	−	3.42033i	−0.856315	−	1.08160i
$11$	−3.73704	−	1.65652i	−1.12676	−	0.499458i	−0.244231	−	0.969717i	$-0.578536\pi$
$11$	−3.73704	−	1.65652i	−1.12676	−	0.499458i	−0.882529	+	0.470259i	$0.844161\pi$
$12$	1.42898	+	5.97199i	0.412511	+	1.72396i
$13$	1.89136	−	1.63150i	0.524570	−	0.452497i	−0.350452	−	0.936581i	$-0.613972\pi$
$13$	1.89136	−	1.63150i	0.524570	−	0.452497i	0.875022	+	0.484084i	$0.160847\pi$
$14$	4.57974	+	3.34723i	1.22399	+	0.894586i
$15$	4.46464	−	8.35275i	1.15276	−	2.15667i
$16$	−2.74830	+	2.90634i	−0.687075	+	0.726586i
$17$	2.32811	−	1.24440i	0.564649	−	0.301811i	−0.164265	−	0.986416i	$-0.552525\pi$
$17$	2.32811	−	1.24440i	0.564649	−	0.301811i	0.728914	+	0.684605i	$0.240025\pi$
$18$	−7.26209	+	5.46498i	−1.71169	+	1.28811i
$19$	−0.0744722	+	0.0421880i	−0.0170851	+	0.00967858i	−0.501417	−	0.865206i	$-0.667188\pi$
$19$	−0.0744722	+	0.0421880i	−0.0170851	+	0.00967858i	0.484332	+	0.874884i	$0.339063\pi$
$20$	6.14585	−	0.539771i	1.37425	−	0.120696i
$21$	−2.69829	+	12.0160i	−0.588815	+	2.62211i
$22$	4.86231	−	3.12682i	1.03665	−	0.666640i
$23$	1.71953	+	6.86475i	0.358547	+	1.43140i	0.834051	+	0.551687i	$0.186016\pi$
$23$	1.71953	+	6.86475i	0.358547	+	1.43140i	−0.475504	+	0.879713i	$0.657734\pi$
$24$	−8.16590	−	2.95489i	−1.66686	−	0.603164i
$25$	−3.62705	−	2.69000i	−0.725410	−	0.538001i
$26$	0.456887	+	3.50276i	0.0896029	+	0.686948i
$27$	−9.15404	−	5.18570i	−1.76170	−	0.997988i
$28$	−7.51478	+	2.80786i	−1.42016	+	0.530636i
$29$	−6.06531	+	0.148895i	−1.12630	+	0.0276491i	−0.583426	−	0.812166i	$-0.698288\pi$
$29$	−6.06531	+	0.148895i	−1.12630	+	0.0276491i	−0.542873	+	0.839815i	$0.682663\pi$
$30$	6.39631	+	11.7682i	1.16780	+	2.14856i
$31$	0.434748	−	0.290489i	0.0780831	−	0.0521734i	−0.515916	−	0.856639i	$-0.672548\pi$
$31$	0.434748	−	0.290489i	0.0780831	−	0.0521734i	0.593999	+	0.804466i	$0.297548\pi$
$32$	−1.29667	−	5.50624i	−0.229221	−	0.973374i
$33$	10.4354	+	6.97268i	1.81656	+	1.21379i
$34$	−0.339962	+	3.71775i	−0.0583029	+	0.637589i
$35$	11.5442	+	4.45308i	1.95132	+	0.752709i
$36$	−0.809973	−	12.8278i	−0.134995	−	2.13796i
$37$	−3.63236	−	0.448009i	−0.597156	−	0.0736522i	−0.181838	−	0.983328i	$-0.558205\pi$
$37$	−3.63236	−	0.448009i	−0.597156	−	0.0736522i	−0.415318	+	0.909676i	$0.636330\pi$
$38$	0.00806113	−	0.120776i	0.00130769	−	0.0195925i
$39$	−6.57791	+	3.94265i	−1.05331	+	0.631329i
$40$	−4.14051	+	7.67996i	−0.654673	+	1.21431i
$41$	−4.93172	+	3.65761i	−0.770205	+	0.571223i	−0.907868	−	0.419256i	$-0.862291\pi$
$41$	−4.93172	+	3.65761i	−0.770205	+	0.571223i	0.137663	+	0.990479i	$0.456041\pi$
$42$	−12.0971	−	12.5296i	−1.86663	−	1.93336i
$43$	−4.92449	+	6.99223i	−0.750977	+	1.06631i	0.244345	+	0.969688i	$0.421427\pi$
$43$	−4.92449	+	6.99223i	−0.750977	+	1.06631i	−0.995322	+	0.0966170i	$0.969198\pi$
$44$	−0.0864348	+	8.17500i	−0.0130305	+	1.23243i
$45$	−12.1968	+	15.6287i	−1.81819	+	2.32979i
$46$	−9.44645	−	3.30574i	−1.39280	−	0.487405i
$47$	1.17717	+	11.9520i	0.171708	+	1.74338i	0.566009	+	0.824399i	$0.308487\pi$
$47$	1.17717	+	11.9520i	0.171708	+	1.74338i	−0.394301	+	0.918982i	$0.629013\pi$
$48$	9.83939	−	7.34935i	1.42019	−	1.06079i
$49$	−9.04524	−	0.890878i	−1.29218	−	0.127268i
$50$	5.99769	−	2.19339i	0.848201	−	0.310192i
$51$	−7.69591	+	2.54239i	−1.07764	+	0.356005i
$52$	−4.49315	−	2.18353i	−0.623088	−	0.302801i
$53$	12.3110	+	0.302217i	1.69104	+	0.0415127i	0.858613	−	0.512624i	$-0.171326\pi$
$53$	12.3110	+	0.302217i	1.69104	+	0.0415127i	0.832426	+	0.554136i	$0.186951\pi$
$54$	13.2430	−	6.78230i	1.80214	−	0.922955i
$55$	8.46811	−	9.34312i	1.14184	−	1.25983i
$56$	2.52542	−	11.0605i	0.337474	−	1.47802i
$57$	0.247429	−	0.0885316i	0.0327728	−	0.0117263i
$58$	4.53965	−	7.28092i	0.596085	−	0.956032i
$59$	−1.40771	+	1.63193i	−0.183269	+	0.212459i	−0.841355	−	0.540483i	$-0.818241\pi$
$59$	−1.40771	+	1.63193i	−0.183269	+	0.212459i	0.658086	+	0.752943i	$0.271366\pi$
$60$	−18.8750	−	1.59312i	−2.43676	−	0.205670i
$61$	7.97061	−	1.78986i	1.02053	−	0.229168i	0.323515	−	0.946223i	$-0.395135\pi$
$61$	7.97061	−	1.78986i	1.02053	−	0.229168i	0.697017	+	0.717055i	$0.254510\pi$
$62$	0.00516536	+	0.739428i	0.000656002	+	0.0939074i
$63$	9.86483	−	23.8158i	1.24285	−	3.00051i
$64$	7.51282	+	2.74909i	0.939103	+	0.343636i
$65$	2.94862	+	7.11860i	0.365732	+	0.882954i
$66$	−16.3502	+	6.90666i	−2.01257	+	0.850151i
$67$	12.6913	+	8.03670i	1.55049	+	0.981839i	0.987898	+	0.155106i	$0.0495718\pi$
$67$	12.6913	+	8.03670i	1.55049	+	0.981839i	0.562595	+	0.826733i	$0.309803\pi$
$68$	−4.12760	−	3.29202i	−0.500545	−	0.399216i
$69$	−1.59841	−	21.6690i	−0.192425	−	2.60865i
$70$	−14.2357	+	10.1755i	−1.70150	+	1.21620i
$71$	−3.53041	−	1.66976i	−0.418983	−	0.198164i	0.206425	−	0.978462i	$-0.433817\pi$
$71$	−3.53041	−	1.66976i	−0.418983	−	0.198164i	−0.625407	+	0.780298i	$0.715067\pi$
$72$	15.7836	+	9.01625i	1.86012	+	1.06258i
$73$	−0.170356	−	3.46768i	−0.0199387	−	0.405862i	−0.987932	−	0.154887i	$-0.950499\pi$
$73$	−0.170356	−	3.46768i	−0.0199387	−	0.405862i	0.967994	−	0.250975i	$-0.0807512\pi$
$74$	3.35327	−	3.94273i	0.389810	−	0.458333i
$75$	9.56014	+	10.0413i	1.10391	+	1.15947i
$76$	0.136410	+	0.103422i	0.0156473	+	0.0118633i
$77$	−7.37197	+	14.6456i	−0.840114	+	1.66902i
$78$	0.456485	−	10.8360i	0.0516867	−	1.22693i
$79$	−0.300227	−	0.365828i	−0.0337782	−	0.0411589i	0.755847	−	0.654748i	$-0.227225\pi$
$79$	−0.300227	−	0.365828i	−0.0337782	−	0.0411589i	−0.789626	+	0.613589i	$0.789725\pi$
$80$	−5.85352	−	10.8622i	−0.654443	−	1.21443i
$81$	10.0661	+	8.26106i	1.11846	+	0.917895i
$82$	−0.486643	−	8.66966i	−0.0537408	−	0.957404i
$83$	8.57479	−	1.05760i	0.941205	−	0.116087i	0.362828	−	0.931856i	$-0.381811\pi$
$83$	8.57479	−	1.05760i	0.941205	−	0.116087i	0.578377	+	0.815769i	$0.303686\pi$
$84$	24.2067	−	4.54950i	2.64117	−	0.496392i
$85$	1.39217	+	8.02329i	0.151002	+	0.870248i
$86$	−4.43157	−	11.2537i	−0.477869	−	1.21351i
$87$	18.4262	+	2.73327i	1.97550	+	0.293037i
$88$	−9.59021	−	6.45786i	−1.02232	−	0.688410i
$89$	1.08200	−	4.31957i	0.114691	−	0.457873i	−0.885283	−	0.465053i	$-0.846035\pi$
$89$	1.08200	−	4.31957i	0.114691	−	0.457873i	0.999974	+	0.00717958i	$0.00228535\pi$
$90$	−8.98022	−	26.5592i	−0.946599	−	2.79958i
$91$	−6.16399	−	7.89843i	−0.646162	−	0.827980i
$92$	11.2494	−	8.58933i	1.17284	−	0.895500i
$93$	−1.46763	+	0.650555i	−0.152186	+	0.0674594i
$94$	−15.0345	−	7.90160i	−1.55070	−	0.814988i
$95$	−0.0515095	−	0.258956i	−0.00528477	−	0.0265683i
$96$	1.03230	+	17.3375i	0.105358	+	1.76950i
$97$	−3.48428	+	17.5167i	−0.353776	+	1.77855i	0.236791	+	0.971561i	$0.423904\pi$
$97$	−3.48428	+	17.5167i	−0.353776	+	1.77855i	−0.590566	+	0.806989i	$0.701096\pi$
$98$	8.08475	−	9.99283i	0.816683	−	1.00943i
$99$	−19.0263	−	18.1145i	−1.91221	−	1.82058i
$100$	−2.07185	+	8.79055i	−0.207185	+	0.879055i
$101$	3.72855	−	1.03183i	0.371005	−	0.102671i	−0.0762234	−	0.997091i	$-0.524286\pi$
$101$	3.72855	−	1.03183i	0.371005	−	0.102671i	0.447228	+	0.894420i	$0.352411\pi$
$102$	2.97987	−	11.0681i	0.295051	−	1.09590i
$103$	−1.28198	−	8.64239i	−0.126317	−	0.851560i	−0.956009	−	0.293338i	$-0.905234\pi$
$103$	−1.28198	−	8.64239i	−0.126317	−	0.851560i	0.829692	−	0.558222i	$-0.188516\pi$
$104$	6.07273	−	3.61031i	0.595480	−	0.354020i
$105$	−32.5847	−	19.5305i	−3.17994	−	1.90598i
$106$	−9.92831	+	14.3084i	−0.964323	+	1.38975i
$107$	−2.85196	+	1.80599i	−0.275710	+	0.174591i	−0.665682	−	0.746235i	$-0.731859\pi$
$107$	−2.85196	+	1.80599i	−0.275710	+	0.174591i	0.389973	+	0.920826i	$0.372484\pi$
$108$	−2.28372	+	20.9174i	−0.219751	+	2.01277i
$109$	−3.27066	+	11.8186i	−0.313272	+	1.13202i	0.623426	+	0.781883i	$0.285740\pi$
$109$	−3.27066	+	11.8186i	−0.313272	+	1.13202i	−0.936698	+	0.350138i	$0.886135\pi$
$110$	4.45373	+	17.2676i	0.424646	+	1.64640i
$111$	10.7530	+	3.26190i	1.02063	+	0.309606i
$112$	11.1027	+	11.5825i	1.04911	+	1.09444i
$113$	1.65865	+	5.46785i	0.156033	+	0.514372i	0.999749	−	0.0224185i	$-0.00713662\pi$
$113$	1.65865	+	5.46785i	0.156033	+	0.514372i	−0.843716	+	0.536790i	$0.819637\pi$
$114$	−0.0877813	+	0.361127i	−0.00822147	+	0.0338226i
$115$	−21.7712	−	1.60594i	−2.03017	−	0.149754i
$116$	5.07181	+	11.0235i	0.470905	+	1.02350i
$117$	14.9769	−	5.77724i	1.38462	−	0.534106i
$118$	−0.833415	−	2.93175i	−0.0767221	−	0.269889i
$119$	−4.52720	−	9.57196i	−0.415008	−	0.877460i
$120$	16.5566	−	21.0592i	1.51141	−	1.92243i
$121$	3.83428	+	4.23047i	0.348571	+	0.384588i
$122$	−4.08242	+	10.8075i	−0.369605	+	0.978466i
$123$	16.8388	−	8.47591i	1.51830	−	0.764248i
$124$	−0.877528	−	0.568775i	−0.0788044	−	0.0510775i
$125$	−1.22141	+	0.860217i	−0.109247	+	0.0769401i
$126$	20.4649	+	30.1695i	1.82316	+	2.68772i
$127$	10.3982	+	10.3982i	0.922689	+	0.922689i	0.997219	−	0.0745295i	$-0.0237455\pi$
$127$	10.3982	+	10.3982i	0.922689	+	0.922689i	−0.0745295	+	0.997219i	$0.523746\pi$
$128$	−9.08853	+	6.73785i	−0.803320	+	0.595548i
$129$	18.5672	−	18.5672i	1.63475	−	1.63475i
$130$	−10.7019	−	2.05113i	−0.938619	−	0.179896i
$131$	−5.83274	−	8.28186i	−0.509609	−	0.723589i	0.478373	−	0.878157i	$-0.341227\pi$
$131$	−5.83274	−	8.28186i	−0.509609	−	0.723589i	−0.987982	+	0.154567i	$0.950602\pi$
$132$	4.55255	−	24.6847i	0.396248	−	2.14853i
$133$	0.154359	+	0.306660i	0.0133847	+	0.0265908i
$134$	−19.3611	+	8.74449i	−1.67254	+	0.755409i
$135$	24.0470	−	21.7949i	2.06963	−	1.87581i
$136$	7.09803	−	2.31666i	0.608651	−	0.198652i
$137$	−13.8625	+	6.55647i	−1.18435	+	0.560157i	−0.915223	−	0.402947i	$-0.867986\pi$
$137$	−13.8625	+	6.55647i	−1.18435	+	0.560157i	−0.269130	+	0.963104i	$0.586736\pi$
$138$	26.8411	+	14.9586i	2.28487	+	1.27336i
$139$	3.38638	+	8.77886i	0.287229	+	0.744613i	0.999105	+	0.0423077i	$0.0134710\pi$
$139$	3.38638	+	8.77886i	0.287229	+	0.744613i	−0.711876	+	0.702306i	$0.752154\pi$
$140$	−0.952871	−	24.7282i	−0.0805323	−	2.08992i
$141$	2.71260	−	36.7738i	0.228442	−	3.09691i
$142$	4.71731	−	2.87242i	0.395867	−	0.241048i
$143$	−9.77070	+	2.96391i	−0.817067	+	0.247855i
$144$	−22.9224	+	11.6360i	−1.91020	+	0.969663i
$145$	5.43286	−	17.9097i	0.451174	−	1.48732i
$146$	4.22894	+	2.49474i	0.349990	+	0.206466i
$147$	26.8950	+	7.44284i	2.21826	+	0.613875i
$148$	2.05064	+	7.02666i	0.168562	+	0.577588i
$149$	7.42464	+	11.7248i	0.608250	+	0.960531i	0.999195	+	0.0401175i	$0.0127732\pi$
$149$	7.42464	+	11.7248i	0.608250	+	0.960531i	−0.390945	+	0.920414i	$0.627852\pi$
$150$	−19.2948	+	3.48698i	−1.57542	+	0.284711i
$151$	−3.28069	+	5.47350i	−0.266979	+	0.445427i	−0.961799	−	0.273756i	$-0.911734\pi$
$151$	−3.28069	+	5.47350i	−0.266979	+	0.445427i	0.694820	+	0.719183i	$0.255484\pi$
$152$	−0.228229	+	0.0807394i	−0.0185118	+	0.00654883i
$153$	16.7816	−	2.48931i	1.35671	−	0.201249i
$154$	−11.5699	−	20.0952i	−0.932332	−	1.61931i
$155$	0.430185	+	1.55449i	0.0345533	+	0.124860i
$156$	12.4460	+	8.96382i	0.996479	+	0.717680i
$157$	7.83762	−	8.23211i	0.625510	−	0.656994i	−0.332709	−	0.943030i	$-0.607963\pi$
$157$	7.83762	−	8.23211i	0.625510	−	0.656994i	0.958219	+	0.286036i	$0.0923376\pi$
$158$	0.665581	−	0.0702518i	0.0529508	−	0.00558893i
$159$	−37.0830	−	7.37627i	−2.94088	−	0.584977i
$160$	17.3828	+	1.52998i	1.37423	+	0.120956i
$161$	27.8405	−	5.53783i	2.19414	−	0.436442i
$162$	−17.5851	+	5.46882i	−1.38162	+	0.429671i
$163$	7.62673	+	17.2056i	0.597372	+	1.34765i	0.916537	+	0.399950i	$0.130973\pi$
$163$	7.62673	+	17.2056i	0.597372	+	1.34765i	−0.319165	+	0.947699i	$0.603402\pi$
$164$	10.6201	+	6.16544i	0.829293	+	0.481440i
$165$	−30.5210	+	23.8188i	−2.37606	+	1.85429i
$166$	−5.41719	+	10.9519i	−0.420456	+	0.850036i
$167$	−13.3896	−	3.35392i	−1.03612	−	0.259534i	−0.312633	−	0.949874i	$-0.601211\pi$
$167$	−13.3896	−	3.35392i	−1.03612	−	0.259534i	−0.723485	+	0.690340i	$0.757461\pi$
$168$	−13.4453	+	32.1333i	−1.03733	+	2.47914i
$169$	−0.992038	+	6.68778i	−0.0763106	+	0.514444i
$170$	−10.5606	−	4.59318i	−0.809957	−	0.352281i
$171$	−0.541970	+	0.0940407i	−0.0414455	+	0.00719147i
$172$	16.7397	+	3.51412i	1.27639	+	0.267949i
$173$	−1.97340	−	15.9999i	−0.150035	−	1.21645i	−0.859286	−	0.511496i	$-0.829092\pi$
$173$	−1.97340	−	15.9999i	−0.150035	−	1.21645i	0.709251	−	0.704956i	$-0.249033\pi$
$174$	−17.5546	+	19.6425i	−1.33081	+	1.48910i
$175$	−11.4908	+	14.0015i	−0.868620	+	1.05842i
$176$	15.0849	−	6.30852i	1.13707	−	0.475523i
$177$	5.11506	−	4.19782i	0.384471	−	0.315527i
$178$	4.26165	+	4.63650i	0.319424	+	0.347520i
$179$	9.33392	+	4.69830i	0.697650	+	0.351168i	0.762734	−	0.646712i	$-0.223857\pi$
$179$	9.33392	+	4.69830i	0.697650	+	0.351168i	−0.0650839	+	0.997880i	$0.520732\pi$
$180$	38.3571	+	10.0401i	2.85897	+	0.748344i
$181$	−2.27652	+	2.16743i	−0.169213	+	0.161104i	−0.769426	−	0.638736i	$-0.779457\pi$
$181$	−2.27652	+	2.16743i	−0.169213	+	0.161104i	0.600213	+	0.799840i	$0.295082\pi$
$182$	14.1230	−	1.14102i	1.04686	−	0.0845779i
$183$	−25.0513	+	1.23069i	−1.85184	+	0.0909752i
$184$	1.40088	+	19.9672i	0.103274	+	1.47200i
$185$	4.82703	−	10.2059i	0.354890	−	0.750352i
$186$	0.372502	−	2.23954i	0.0273131	−	0.164211i
$187$	−10.7616	+	0.793823i	−0.786966	+	0.0580501i
$188$	21.0232	−	11.6176i	1.53328	−	0.847304i
$189$	−22.5770	+	35.6530i	−1.64224	+	2.59337i
$190$	0.345960	+	0.140478i	0.0250986	+	0.0101914i
$191$	−20.7875	+	8.61048i	−1.50413	+	0.623032i	−0.974337	−	0.225093i	$-0.927732\pi$
$191$	−20.7875	+	8.61048i	−1.50413	+	0.623032i	−0.529796	+	0.848125i	$0.677732\pi$
$192$	−21.2839	−	12.2597i	−1.53603	−	0.884769i
$193$	6.96990	+	2.88703i	0.501704	+	0.207813i	0.619159	−	0.785265i	$-0.287474\pi$
$193$	6.96990	+	2.88703i	0.501704	+	0.207813i	−0.117455	+	0.993078i	$0.537474\pi$
$194$	−17.9842	−	17.7347i	−1.29119	−	1.27327i
$195$	−5.18326	−	23.0821i	−0.371181	−	1.65295i
$196$	5.51930	+	17.3198i	0.394236	+	1.23713i
$197$	−2.00247	−	1.72734i	−0.142670	−	0.123068i	0.578933	−	0.815375i	$-0.303469\pi$
$197$	−2.00247	−	1.72734i	−0.142670	−	0.123068i	−0.721603	+	0.692307i	$0.756594\pi$
$198$	36.1915	−	8.39307i	2.57202	−	0.596470i
$199$	−3.28285	−	9.17495i	−0.232715	−	0.650395i	−0.999959	−	0.00903987i	$-0.997122\pi$
$199$	−3.28285	−	9.17495i	−0.232715	−	0.650395i	0.767244	−	0.641355i	$-0.221628\pi$
$200$	−8.77381	−	9.28187i	−0.620402	−	0.656327i
$201$	−34.1739	−	30.9734i	−2.41044	−	2.18469i
$202$	−1.67987	+	5.20688i	−0.118195	+	0.366355i
$203$	−0.597234	+	24.3286i	−0.0419176	+	1.70753i
$204$	10.7584	+	12.1252i	0.753236	+	0.848935i
$205$	−5.94128	−	17.9845i	−0.414957	−	1.25609i
$206$	11.2063	+	5.20468i	0.780776	+	0.362627i
$207$	−4.45786	+	45.2614i	−0.309843	+	3.14589i
$208$	−0.456331	+	9.98081i	−0.0316409	+	0.692044i
$209$	0.348191	−	0.0342938i	0.0240848	−	0.00237215i
$210$	48.4055	−	23.3092i	3.34029	−	1.60849i
$211$	11.7766	+	9.19054i	0.810734	+	0.632703i	0.933033	−	0.359791i	$-0.117152\pi$
$211$	11.7766	+	9.19054i	0.810734	+	0.632703i	−0.122300	+	0.992493i	$0.539027\pi$
$212$	−9.18413	−	22.8529i	−0.630769	−	1.56954i
$213$	9.80333	+	6.90428i	0.671713	+	0.473074i
$214$	0.0838175	−	4.77321i	0.00572965	−	0.326290i
$215$	−15.7156	−	21.1900i	−1.07179	−	1.44515i
$216$	−22.9349	−	18.9603i	−1.56052	−	1.29008i
$217$	−1.07822	−	1.79890i	−0.0731941	−	0.122117i
$218$	−11.4190	−	13.0523i	−0.773390	−	0.884013i
$219$	−1.30485	+	10.5795i	−0.0881737	+	0.714894i
$220$	−23.8614	−	8.16355i	−1.60874	−	0.550387i
$221$	2.37306	−	6.15192i	0.159629	−	0.413823i
$222$	−12.2135	+	10.1669i	−0.819715	+	0.682361i
$223$	10.0840	−	15.0917i	0.675272	−	1.01062i	−0.322671	−	0.946511i	$-0.604581\pi$
$223$	10.0840	−	15.0917i	0.675272	−	1.01062i	0.997943	−	0.0641052i	$-0.0204193\pi$
$224$	−22.3147	+	4.11110i	−1.49097	+	0.274684i
$225$	−16.1232	−	24.1300i	−1.07488	−	1.60867i
$226$	−7.74890	−	2.29162i	−0.515449	−	0.152436i
$227$	0.176370	+	7.18453i	0.0117061	+	0.476854i	0.976703	+	0.214594i	$0.0688428\pi$
$227$	0.176370	+	7.18453i	0.0117061	+	0.476854i	−0.964997	+	0.262260i	$0.915532\pi$
$228$	−0.358365	−	0.384461i	−0.0237333	−	0.0254616i
$229$	−7.77901	+	13.7319i	−0.514052	+	0.907428i	0.485399	+	0.874293i	$0.338674\pi$
$229$	−7.77901	+	13.7319i	−0.514052	+	0.907428i	−0.999451	+	0.0331355i	$0.989451\pi$
$230$	18.8234	−	24.4705i	1.24118	−	1.61354i
$231$	29.9883	−	40.4346i	1.97309	−	2.66040i
$232$	−16.9656	−	2.57883i	−1.11384	−	0.169309i
$233$	18.8450	−	4.72042i	1.23457	−	0.309245i	0.429854	−	0.902899i	$-0.358565\pi$
$233$	18.8450	−	4.72042i	1.23457	−	0.309245i	0.804721	+	0.593654i	$0.202315\pi$
$234$	−4.81913	+	22.1844i	−0.315037	+	1.45024i
$235$	−36.1473	−	8.11714i	−2.35799	−	0.529504i
$236$	4.11132	+	1.29478i	0.267624	+	0.0842829i
$237$	0.716189	+	1.26425i	0.0465215	+	0.0821219i
$238$	14.8274	+	2.09369i	0.961119	+	0.135714i
$239$	0.430491	+	0.805391i	0.0278461	+	0.0520964i	0.895460	−	0.445143i	$-0.146847\pi$
$239$	0.430491	+	0.805391i	0.0278461	+	0.0520964i	−0.867613	+	0.497239i	$0.834347\pi$
$240$	12.0058	+	35.9316i	0.774971	+	2.31938i
$241$	5.61315	+	3.00029i	0.361575	+	0.193266i	0.642173	−	0.766559i	$-0.278033\pi$
$241$	5.61315	+	3.00029i	0.361575	+	0.193266i	−0.280599	+	0.959825i	$0.590533\pi$
$242$	−7.97861	+	1.24054i	−0.512885	+	0.0797447i
$243$	−5.49888	−	6.37473i	−0.352753	−	0.408939i
$244$	−9.59337	−	13.2251i	−0.614152	−	0.846652i
$245$	11.3619	−	25.6320i	0.725884	−	1.63757i
$246$	−3.07859	+	26.4819i	−0.196284	+	1.68843i
$247$	−0.0720242	+	0.201294i	−0.00458279	+	0.0128080i
$248$	1.35416	−	0.594454i	0.0859891	−	0.0377479i
$249$	−26.4946	−	1.30160i	−1.67903	−	0.0824853i
$250$	−0.0666018	−	2.11168i	−0.00421227	−	0.133555i
$251$	7.65286	+	2.52816i	0.483044	+	0.159576i	0.544887	−	0.838510i	$-0.316573\pi$
$251$	7.65286	+	2.52816i	0.483044	+	0.159576i	−0.0618425	+	0.998086i	$0.519698\pi$
$252$	−51.5510	+	0.720268i	−3.24741	+	0.0453726i
$253$	4.94562	−	28.5023i	0.310928	−	1.79192i
$254$	−20.3679	+	4.19955i	−1.27800	+	0.263503i
$255$		−	25.0019i		−	1.56568i
$256$	−0.893680	−	15.9750i	−0.0558550	−	0.998439i
$257$			5.50575i			0.343439i	0.985146	+	0.171720i	$0.0549323\pi$
$257$			5.50575i			0.343439i	−0.985146	+	0.171720i	$0.945068\pi$
$258$	7.49881	+	36.3694i	0.466856	+	2.26426i
$259$	−2.50975	+	14.4641i	−0.155949	+	0.898754i
$260$	10.7434	−	11.0479i	0.666277	−	0.685159i
$261$	−37.0234	−	12.2309i	−2.29169	−	0.757073i
$262$	14.3184	−	0.451597i	0.884593	−	0.0278998i
$263$	−10.9841	−	0.539616i	−0.677311	−	0.0332742i	−0.292495	−	0.956267i	$-0.594485\pi$
$263$	−10.9841	−	0.539616i	−0.677311	−	0.0332742i	−0.384817	+	0.922993i	$0.625735\pi$
$264$	25.6215	+	24.5695i	1.57689	+	1.51215i
$265$	−12.7977	+	35.7671i	−0.786155	+	2.19715i
$266$	−0.482276	−	0.0560658i	−0.0295703	−	0.00343761i
$267$	−5.54048	+	12.4991i	−0.339072	+	0.764933i
$268$	4.72230	−	29.6704i	0.288461	−	1.81241i
$269$	−9.34743	−	10.8363i	−0.569923	−	0.660699i	0.396386	−	0.918084i	$-0.370264\pi$
$269$	−9.34743	−	10.8363i	−0.569923	−	0.660699i	−0.966309	+	0.257385i	$0.917139\pi$
$270$	7.05148	+	45.3522i	0.429140	+	2.76005i
$271$	−16.4506	−	8.79301i	−0.999301	−	0.534138i	−0.111206	−	0.993797i	$-0.535471\pi$
$271$	−16.4506	−	8.79301i	−0.999301	−	0.534138i	−0.888095	+	0.459660i	$0.847971\pi$
$272$	−2.78169	+	10.1863i	−0.168665	+	0.617633i
$273$	14.5007	+	27.1289i	0.877623	+	1.64192i
$274$	3.03217	−	21.4737i	0.183180	−	1.29727i
$275$	9.09840	+	16.0609i	0.548654	+	0.968510i
$276$	−38.5391	+	20.0786i	−2.31978	+	1.20859i
$277$	−12.9006	−	2.89692i	−0.775120	−	0.174059i	−0.186485	−	0.982458i	$-0.559710\pi$
$277$	−12.9006	−	2.89692i	−0.775120	−	0.174059i	−0.588635	+	0.808399i	$0.700335\pi$
$278$	−13.0036	−	2.82478i	−0.779902	−	0.169419i
$279$	3.25959	−	0.816484i	0.195146	−	0.0488816i
$280$	29.9531	+	18.0996i	1.79004	+	1.08166i
$281$	7.10136	−	9.57507i	0.423631	−	0.571201i	−0.538900	−	0.842369i	$-0.681160\pi$
$281$	7.10136	−	9.57507i	0.423631	−	0.571201i	0.962532	+	0.271169i	$0.0874101\pi$
$282$	41.3332	+	31.7947i	2.46136	+	1.89335i
$283$	7.85548	−	13.8669i	0.466960	−	0.824300i	−0.532799	−	0.846242i	$-0.678860\pi$
$283$	7.85548	−	13.8669i	0.466960	−	0.824300i	0.999759	+	0.0219419i	$0.00698489\pi$
$284$	−0.274228	+	7.80592i	−0.0162725	+	0.463196i
$285$	0.0198942	+	0.810401i	0.00117843	+	0.0480040i
$286$	4.09498	−	13.8468i	0.242141	−	0.818779i
$287$	13.6828	+	20.4777i	0.807668	+	1.20876i
$288$	4.07530	−	36.1255i	0.240140	−	2.12872i
$289$	−5.57314	+	8.34079i	−0.327832	+	0.490635i
$290$	16.9336	+	20.3421i	0.994372	+	1.19453i
$291$	19.7348	−	51.1605i	1.15687	−	2.99908i
$292$	−6.23497	+	3.05623i	−0.364874	+	0.178852i
$293$	2.01771	−	16.3592i	0.117876	−	0.955714i	−0.810929	−	0.585145i	$-0.801038\pi$
$293$	2.01771	−	16.3592i	0.117876	−	0.955714i	0.928805	−	0.370569i	$-0.120837\pi$
$294$	−29.7023	+	25.9855i	−1.73227	+	1.51550i
$295$	−3.41788	−	5.70239i	−0.198997	−	0.332006i
$296$	−9.89513	−	3.04046i	−0.575143	−	0.176723i
$297$	25.6188	+	34.5430i	1.48655	+	2.00439i
$298$	−19.6233	−	0.344584i	−1.13675	−	0.0199612i
$299$	14.4521	+	10.1783i	0.835787	+	0.588628i
$300$	10.8817	−	25.5047i	0.628255	−	1.47251i
$301$	27.0436	+	21.1050i	1.55877	+	1.21647i
$302$	−3.91543	−	8.13103i	−0.225307	−	0.467888i
$303$	−11.8208	+	1.16425i	−0.679087	+	0.0668842i
$304$	0.0820592	−	0.332387i	0.00470642	−	0.0190637i
$305$	−2.47000	+	25.0783i	−0.141432	+	1.43598i
$306$	−10.1063	+	21.7600i	−0.577739	+	1.24394i
$307$	−5.75216	−	17.4120i	−0.328293	−	0.993757i	−0.973291	−	0.229573i	$-0.926267\pi$
$307$	−5.75216	−	17.4120i	−0.328293	−	0.993757i	0.644999	−	0.764184i	$-0.276858\pi$
$308$	32.7343	+	1.95525i	1.86521	+	0.111411i
$309$	−0.658317	+	26.8169i	−0.0374504	+	1.52556i
$310$	−2.17083	−	0.700364i	−0.123295	−	0.0397780i
$311$	23.9853	+	21.7390i	1.36008	+	1.23271i	0.946686	+	0.322157i	$0.104408\pi$
$311$	23.9853	+	21.7390i	1.36008	+	1.23271i	0.413397	+	0.910551i	$0.364342\pi$
$312$	−20.2656	+	7.73390i	−1.14731	+	0.437846i
$313$	3.88037	+	10.8449i	0.219331	+	0.612990i	0.999927	−	0.0120458i	$-0.00383439\pi$
$313$	3.88037	+	10.8449i	0.219331	+	0.612990i	−0.780596	+	0.625036i	$0.785084\pi$
$314$	3.63143	+	15.6590i	0.204934	+	0.883689i
$315$	60.2124	+	51.9396i	3.39259	+	2.92646i
$316$	−0.434473	+	0.840892i	−0.0244410	+	0.0473039i
$317$	−2.19491	−	9.77437i	−0.123278	−	0.548983i	−0.997935	−	0.0642395i	$-0.979538\pi$
$317$	−2.19491	−	9.77437i	−0.123278	−	0.548983i	0.874656	−	0.484744i	$-0.161087\pi$
$318$	37.5445	−	38.0727i	2.10539	−	2.13501i
$319$	22.9129	+	9.49085i	1.28288	+	0.531386i
$320$	−15.3219	+	19.3454i	−0.856520	+	1.08144i
$321$	9.57540	−	3.96626i	0.534447	−	0.221375i
$322$	−15.1029	+	37.1945i	−0.841653	+	2.07277i
$323$	−0.120881	+	0.190891i	−0.00672597	+	0.0106215i
$324$	7.21124	−	25.0257i	0.400625	−	1.39032i
$325$	−11.2488	+	0.829762i	−0.623971	+	0.0460269i
$326$	−26.2551	−	4.36699i	−1.45414	−	0.241865i
$327$	16.0977	−	34.0356i	0.890202	−	1.88217i
$328$	−15.5402	+	7.75254i	−0.858064	+	0.428062i
$329$	48.1148	−	2.36373i	2.65265	−	0.130317i
$330$	−4.40910	−	54.5737i	−0.242713	−	3.00418i
$331$	5.87528	−	5.59373i	0.322934	−	0.307459i	−0.510718	−	0.859748i	$-0.670620\pi$
$331$	5.87528	−	5.59373i	0.322934	−	0.307459i	0.833653	+	0.552289i	$0.186245\pi$
$332$	−8.72626	−	14.9142i	−0.478916	−	0.818525i
$333$	−21.0094	−	10.5752i	−1.15131	−	0.579519i
$334$	14.3720	−	13.2101i	0.786401	−	0.722822i
$335$	−35.8205	+	29.3971i	−1.95708	+	1.60614i
$336$	−27.5070	−	40.8658i	−1.50063	−	2.22941i
$337$	−3.55220	+	4.32837i	−0.193501	+	0.235781i	−0.860718	−	0.509082i	$-0.829985\pi$
$337$	−3.55220	+	4.32837i	−0.193501	+	0.235781i	0.667218	+	0.744863i	$0.267485\pi$
$338$	−7.12924	−	6.37142i	−0.387779	−	0.346560i
$339$	−2.14748	−	17.4113i	−0.116635	−	0.945654i
$340$	13.6365	−	8.90454i	0.739543	−	0.482916i
$341$	−2.10587	+	0.365403i	−0.114039	+	0.0197877i
$342$	0.310267	−	0.713362i	0.0167773	−	0.0385742i
$343$	−1.22949	+	8.28852i	−0.0663860	+	0.447538i
$344$	−17.1659	+	17.0431i	−0.925521	+	0.918904i
$345$	65.0166	+	16.2858i	3.50038	+	0.876799i
$346$	20.4355	+	10.1081i	1.09862	+	0.543414i
$347$	−0.449697	+	0.350947i	−0.0241410	+	0.0188398i	−0.627230	−	0.778834i	$-0.715811\pi$
$347$	−0.449697	+	0.350947i	−0.0241410	+	0.0188398i	0.603089	+	0.797674i	$0.293936\pi$
$348$	−9.55639	−	36.0092i	−0.512276	−	1.93029i
$349$	−4.45929	−	10.0600i	−0.238700	−	0.538499i	0.754311	−	0.656517i	$-0.227971\pi$
$349$	−4.45929	−	10.0600i	−0.238700	−	0.538499i	−0.993011	+	0.118018i	$0.962346\pi$
$350$	−7.60688	−	24.4601i	−0.406605	−	1.30745i
$351$	−25.7741	+	5.12678i	−1.37572	+	0.273647i
$352$	−4.27547	+	22.7250i	−0.227883	+	1.21125i
$353$	19.5997	+	3.89863i	1.04319	+	0.207503i	0.686809	−	0.726838i	$-0.259011\pi$
$353$	19.5997	+	3.89863i	1.04319	+	0.207503i	0.356380	+	0.934341i	$0.384011\pi$
$354$	0.982271	+	9.30624i	0.0522071	+	0.494621i
$355$	8.30696	−	8.72507i	0.440888	−	0.463079i
$356$	−8.79053	+	1.42974i	−0.465897	+	0.0757758i
$357$	8.67083	+	31.3323i	0.458909	+	1.65828i
$358$	−12.8070	+	7.37374i	−0.676873	+	0.389714i
$359$	−11.2082	+	1.66258i	−0.591546	+	0.0877475i	−0.435790	−	0.900048i	$-0.643531\pi$
$359$	−11.2082	+	1.66258i	−0.591546	+	0.0877475i	−0.155755	+	0.987796i	$0.549781\pi$
$360$	−41.6819	+	37.5068i	−2.19683	+	1.97678i
$361$	−9.76419	+	16.2906i	−0.513905	+	0.857398i
$362$	−0.790553	−	4.37443i	−0.0415505	−	0.229915i
$363$	−9.37843	−	14.8102i	−0.492240	−	0.777332i
$364$	−9.63214	+	17.5711i	−0.504861	+	0.920973i
$365$	10.3219	+	2.85645i	0.540273	+	0.149514i
$366$	18.0225	−	30.5508i	0.942053	−	1.59691i
$367$	3.38944	−	11.1735i	0.176927	−	0.583252i	−0.822958	−	0.568103i	$-0.807678\pi$
$367$	3.38944	−	11.1735i	0.176927	−	0.583252i	0.999885	−	0.0151491i	$-0.00482230\pi$
$368$	−24.6771	−	13.8689i	−1.28638	−	0.722964i
$369$	−37.7607	+	11.4546i	−1.96575	+	0.596303i
$370$	8.30376	+	13.6370i	0.431692	+	0.708956i
$371$	3.63375	−	49.2616i	0.188655	−	2.55754i
$372$	2.35605	+	2.18121i	0.122155	+	0.113090i
$373$	−7.45053	−	19.3148i	−0.385774	−	1.00008i	−0.980564	−	0.196200i	$-0.937140\pi$
$373$	−7.45053	−	19.3148i	−0.385774	−	1.00008i	0.594790	−	0.803881i	$-0.297235\pi$
$374$	7.42896	−	13.3302i	0.384142	−	0.689289i
$375$	4.14641	−	1.96111i	0.214120	−	0.101271i
$376$	−2.62042	+	33.8678i	−0.135138	+	1.74660i
$377$	−11.2288	+	10.1772i	−0.578311	+	0.524151i
$378$	−24.5654	−	54.3898i	−1.26351	−	2.79751i
$379$	−0.492680	−	0.978787i	−0.0253073	−	0.0502769i	0.880217	−	0.474572i	$-0.157397\pi$
$379$	−0.492680	−	0.978787i	−0.0253073	−	0.0502769i	−0.905524	+	0.424295i	$0.860522\pi$
$380$	−0.434923	+	0.299479i	−0.0223111	+	0.0153629i
$381$	−25.9974	−	36.9134i	−1.33188	−	1.89113i
$382$	5.98965	−	31.2514i	0.306457	−	1.59896i
$383$	16.3549	−	16.3549i	0.835696	−	0.835696i	−0.152593	−	0.988289i	$-0.548762\pi$
$383$	16.3549	−	16.3549i	0.835696	−	0.835696i	0.988289	+	0.152593i	$0.0487623\pi$
$384$	31.0303	−	15.6120i	1.58351	−	0.796696i
$385$	−35.7645	−	35.7645i	−1.82273	−	1.82273i
$386$	−8.82938	+	5.98924i	−0.449403	+	0.304844i
$387$	−44.9367	+	31.6480i	−2.28426	+	1.60876i
$388$	34.9326	−	7.45733i	1.77343	−	0.378588i
$389$	−1.20073	+	0.604398i	−0.0608795	+	0.0306442i	−0.479790	−	0.877383i	$-0.659287\pi$
$389$	−1.20073	+	0.604398i	−0.0608795	+	0.0306442i	0.418910	+	0.908028i	$0.362412\pi$
$390$	31.2975	+	11.8223i	1.58481	+	0.598645i
$391$	12.5457	+	13.8421i	0.634466	+	0.700025i
$392$	−24.7516	−	6.94537i	−1.25014	−	0.350794i
$393$	13.2974	+	28.1149i	0.670764	+	1.41821i
$394$	3.59742	−	1.02265i	0.181235	−	0.0515202i
$395$	1.36204	−	0.525397i	0.0685317	−	0.0264356i
$396$	−18.2225	+	49.2796i	−0.915716	+	2.47640i
$397$	−3.80612	−	0.280756i	−0.191023	−	0.0140907i	−0.0222853	−	0.999752i	$-0.507094\pi$
$397$	−3.80612	−	0.280756i	−0.191023	−	0.0140907i	−0.168738	+	0.985661i	$0.553969\pi$
$398$	13.3910	+	3.25503i	0.671230	+	0.163160i
$399$	−0.305984	−	1.00869i	−0.0153184	−	0.0504979i
$400$	17.7863	−	3.14852i	0.889315	−	0.157426i
$401$	22.6988	+	6.88560i	1.13352	+	0.343850i	0.800656	−	0.599124i	$-0.204484\pi$
$401$	22.6988	+	6.88560i	1.13352	+	0.343850i	0.332866	+	0.942974i	$0.391984\pi$
$402$	63.1588	−	16.2902i	3.15008	−	0.812480i
$403$	0.348333	−	1.25871i	0.0173517	−	0.0627009i
$404$	−4.84503	−	6.03264i	−0.241049	−	0.300135i
$405$	−33.9374	+	21.4906i	−1.68636	+	1.06788i
$406$	−28.2759	−	19.6201i	−1.40331	−	0.973729i
$407$	12.8321	+	7.69129i	0.636066	+	0.381243i
$408$	−22.6882	+	3.28234i	−1.12323	+	0.162500i
$409$	−1.38506	−	9.33732i	−0.0684868	−	0.461701i	−0.996105	−	0.0881716i	$-0.971898\pi$
$409$	−1.38506	−	9.33732i	−0.0684868	−	0.461701i	0.927618	−	0.373529i	$-0.121852\pi$
$410$	25.8649	+	6.96363i	1.27737	+	0.343909i
$411$	45.3767	−	12.5574i	2.23827	−	0.619412i
$412$	−14.8609	+	9.19190i	−0.732144	+	0.452852i
$413$	6.26091	+	5.96088i	0.308079	+	0.293316i
$414$	−50.0031	−	40.4553i	−2.45752	−	1.98827i
$415$	−5.19946	+	26.1394i	−0.255231	+	1.28313i
$416$	−11.4359	−	8.29877i	−0.560691	−	0.406881i
$417$	−5.63605	−	28.3343i	−0.275998	−	1.38754i
$418$	−0.230192	+	0.437992i	−0.0112591	+	0.0214229i
$419$	−32.3910	+	14.3579i	−1.58240	+	0.701431i	−0.994226	−	0.107302i	$-0.965779\pi$
$419$	−32.3910	+	14.3579i	−1.58240	+	0.701431i	−0.588176	+	0.808733i	$0.700154\pi$
$420$	−10.0974	+	75.3051i	−0.492701	+	3.67451i
$421$	4.25461	+	5.45178i	0.207357	+	0.265704i	0.880750	−	0.473581i	$-0.157039\pi$
$421$	4.25461	+	5.45178i	0.207357	+	0.265704i	−0.673393	+	0.739285i	$0.735164\pi$
$422$	−20.0130	+	6.76681i	−0.974215	+	0.329403i
$423$	−18.7540	+	74.8701i	−0.911850	+	3.64031i
$424$	34.1373	+	6.91771i	1.65785	+	0.335954i
$425$	−11.7916	−	1.74912i	−0.571976	−	0.0848447i
$426$	−15.7780	+	6.21320i	−0.764446	+	0.301031i
$427$	−5.60193	−	32.2847i	−0.271097	−	1.56237i
$428$	5.57360	+	3.81000i	0.269410	+	0.184164i
$429$	31.1130	−	3.83742i	1.50215	−	0.185272i
$430$	37.2508	−	2.09095i	1.79639	−	0.100835i
$431$	15.1039	+	12.3954i	0.727529	+	0.597068i	0.923526	−	0.383537i	$-0.125294\pi$
$431$	15.1039	+	12.3954i	0.727529	+	0.597068i	−0.195997	+	0.980605i	$0.562794\pi$
$432$	40.2295	−	12.3529i	1.93554	−	0.594330i
$433$	2.09852	+	2.55706i	0.100849	+	0.122884i	0.820989	−	0.570944i	$-0.193423\pi$
$433$	2.09852	+	2.55706i	0.100849	+	0.122884i	−0.720140	+	0.693828i	$0.755923\pi$
$434$	2.96337	+	0.124837i	0.142246	+	0.00599238i
$435$	−25.8357	+	51.3267i	−1.23873	+	2.46093i
$436$	24.2969	−	3.34198i	1.16361	−	0.160052i
$437$	−0.417667	−	0.438690i	−0.0199797	−	0.0209854i
$438$	−11.4834	−	9.76659i	−0.548699	−	0.466666i
$439$	−0.371033	−	7.55255i	−0.0177084	−	0.360463i	−0.991254	−	0.131970i	$-0.957870\pi$
$439$	−0.371033	−	7.55255i	−0.0177084	−	0.360463i	0.973545	−	0.228494i	$-0.0733801\pi$
$440$	28.1952	−	21.8415i	1.34416	−	1.04125i
$441$	−52.8038	−	24.9743i	−2.51446	−	1.18925i
$442$	5.42252	+	7.58626i	0.257923	+	0.360841i
$443$	1.79429	+	24.3246i	0.0852492	+	1.15570i	0.855447	+	0.517890i	$0.173282\pi$
$443$	1.79429	+	24.3246i	0.0852492	+	1.15570i	−0.770198	+	0.637805i	$0.779843\pi$
$444$	−2.51506	−	22.3326i	−0.119360	−	1.05986i
$445$	11.6053	+	7.34898i	0.550144	+	0.348375i
$446$	9.98849	+	23.6458i	0.472969	+	1.11966i
$447$	−16.3058	−	39.3657i	−0.771237	−	1.86193i
$448$	12.4923	−	29.5574i	0.590204	−	1.39646i
$449$	−1.99830	+	4.82431i	−0.0943054	+	0.227673i	−0.963992	−	0.265931i	$-0.914321\pi$
$449$	−1.99830	+	4.82431i	−0.0943054	+	0.227673i	0.869687	+	0.493604i	$0.164321\pi$
$450$	41.0408	−	0.286695i	1.93468	−	0.0135149i
$451$	24.4889	−	5.49917i	1.15314	−	0.258946i
$452$	8.73164	−	7.37241i	0.410702	−	0.346769i
$453$	12.7974	−	14.8358i	0.601275	−	0.697045i
$454$	−8.62446	−	5.37735i	−0.404766	−	0.252371i
$455$	29.0994	−	10.4119i	1.36420	−	0.488120i
$456$	0.732793	−	0.124446i	0.0343162	−	0.00582770i
$457$	8.07824	−	8.91296i	0.377884	−	0.416931i	−0.522079	−	0.852897i	$-0.674843\pi$
$457$	8.07824	−	8.91296i	0.377884	−	0.416931i	0.899963	+	0.435966i	$0.143593\pi$
$458$	−10.1741	−	19.8656i	−0.475403	−	0.928260i
$459$	−27.7647	−	0.681584i	−1.29594	−	0.0318136i
$460$	14.2734	+	41.2616i	0.665500	+	1.92383i
$461$	−27.1352	+	8.96426i	−1.26381	+	0.417507i	−0.866039	−	0.499977i	$-0.833342\pi$
$461$	−27.1352	+	8.96426i	−1.26381	+	0.417507i	−0.397773	+	0.917484i	$0.630217\pi$
$462$	24.4520	+	66.8627i	1.13761	+	3.11073i
$463$	−15.7643	−	1.55265i	−0.732631	−	0.0721578i	−0.275180	−	0.961393i	$-0.588737\pi$
$463$	−15.7643	−	1.55265i	−0.732631	−	0.0721578i	−0.457451	+	0.889235i	$0.651237\pi$
$464$	16.2365	−	18.0371i	0.753763	−	0.837350i
$465$	−0.485392	−	4.92827i	−0.0225095	−	0.228543i
$466$	−9.07484	+	25.9322i	−0.420384	+	1.20128i
$467$	−18.7797	+	24.0640i	−0.869021	+	1.11355i	0.123605	+	0.992331i	$0.460554\pi$
$467$	−18.7797	+	24.0640i	−0.869021	+	1.11355i	−0.992626	+	0.121216i	$0.961321\pi$
$468$	−22.4605	−	22.9405i	−1.03824	−	1.06042i
$469$	34.6951	−	49.2632i	1.60207	−	2.27477i
$470$	37.6922	−	36.3913i	1.73861	−	1.67860i
$471$	−28.0305	+	20.7888i	−1.29158	+	0.957899i
$472$	−4.72597	+	3.85021i	−0.217530	+	0.177220i
$473$	29.9857	−	17.9728i	1.37875	−	0.826389i
$474$	−2.05031	−	0.136847i	−0.0941740	−	0.00628559i
$475$	0.383600	+	0.0473125i	0.0176008	+	0.00217085i
$476$	−14.0011	+	15.8884i	−0.641740	+	0.728243i
$477$	73.8390	+	28.4829i	3.38086	+	1.30414i
$478$	−1.28613	−	0.117607i	−0.0588261	−	0.00537923i
$479$	−15.1822	−	10.1444i	−0.693693	−	0.463511i	0.158077	−	0.987427i	$-0.449471\pi$
$479$	−15.1822	−	10.1444i	−0.693693	−	0.463511i	−0.851770	+	0.523916i	$0.824471\pi$
$480$	−51.7814	−	13.7526i	−2.36348	−	0.627717i
$481$	−7.60104	+	5.07885i	−0.346577	+	0.231576i
$482$	−7.90836	+	4.29840i	−0.360216	+	0.195787i
$483$	−87.1268	+	2.13884i	−3.96441	+	0.0973208i
$484$	4.73758	−	10.3899i	0.215344	−	0.472268i
$485$	−47.9359	−	27.1554i	−2.17666	−	1.23306i
$486$	11.8059	−	1.53991i	0.535525	−	0.0698519i
$487$	0.531994	+	0.394553i	0.0241069	+	0.0178789i	0.607686	−	0.794178i	$-0.292098\pi$
$487$	0.531994	+	0.394553i	0.0241069	+	0.0178789i	−0.583579	+	0.812057i	$0.698348\pi$
$488$	23.0818	−	1.05095i	1.04486	−	0.0475743i
$489$	−14.0402	−	56.0518i	−0.634922	−	2.53475i
$490$	21.4466	+	33.3501i	0.968857	+	1.50660i
$491$	7.48304	−	33.3235i	0.337705	−	1.50387i	−0.452912	−	0.891555i	$-0.649615\pi$
$491$	7.48304	−	33.3235i	0.337705	−	1.50387i	0.790616	−	0.612312i	$-0.209760\pi$
$492$	−28.8905	−	24.2255i	−1.30249	−	1.09217i
$493$	−13.9354	+	7.89431i	−0.627619	+	0.355542i
$494$	−0.181800	−	0.241583i	−0.00817956	−	0.0108693i
$495$	71.4690	−	38.2010i	3.21229	−	1.71701i
$496$	−0.350557	+	2.06188i	−0.0157405	+	0.0925812i
$497$	−7.38436	+	13.8152i	−0.331234	+	0.619695i
$498$	22.1362	−	30.2871i	0.991945	−	1.35720i
$499$	26.2745	−	22.6646i	1.17621	−	1.01461i	0.176670	−	0.984270i	$-0.443467\pi$
$499$	26.2745	−	22.6646i	1.17621	−	1.01461i	0.999540	−	0.0303356i	$-0.00965761\pi$
$500$	2.54639	+	1.56307i	0.113878	+	0.0699028i
$501$	38.7442	+	17.1741i	1.73096	+	0.767283i
$502$	−8.93641	+	7.07504i	−0.398852	+	0.315775i
$503$	38.9573	+	13.9391i	1.73702	+	0.621516i	0.998604	−	0.0528300i	$-0.0168242\pi$
$503$	38.9573	+	13.9391i	1.73702	+	0.621516i	0.738416	+	0.674346i	$0.235574\pi$
$504$	39.2281	−	61.4591i	1.74736	−	2.73760i
$505$	−0.585571	+	11.9196i	−0.0260576	+	0.530414i
$506$	29.8257	+	28.0019i	1.32592	+	1.24484i
$507$	6.51143	−	19.7104i	0.289183	−	0.875368i
$508$	10.8742	−	27.3263i	0.482465	−	1.21241i
$509$	7.78127	+	1.35018i	0.344899	+	0.0598456i	0.340772	−	0.940146i	$-0.389311\pi$
$509$	7.78127	+	1.35018i	0.344899	+	0.0598456i	0.00412652	+	0.999991i	$0.498686\pi$
$510$	29.5356	+	19.4380i	1.30786	+	0.860729i
$511$	−13.9260			−0.616052
$512$	19.5667	+	11.3642i	0.864732	+	0.502233i
$513$	0.900495			0.0397578
$514$	−6.50413	−	4.28051i	−0.286885	−	0.188805i
$515$	26.5546	+	4.60765i	1.17013	+	0.203038i
$516$	−48.7945	−	19.4172i	−2.14806	−	0.854796i
$517$	15.3996	−	46.6152i	0.677273	−	2.05013i
$518$	−15.1357	−	14.2101i	−0.665024	−	0.624357i
$519$	−2.42868	+	49.4370i	−0.106607	+	2.17004i
$520$	4.69865	+	21.2808i	0.206049	+	0.933226i
$521$	−3.13259	−	1.12086i	−0.137241	−	0.0491058i	0.267373	−	0.963593i	$-0.413844\pi$
$521$	−3.13259	−	1.12086i	−0.137241	−	0.0491058i	−0.404615	+	0.914487i	$0.632594\pi$
$522$	43.2331	−	34.2280i	1.89226	−	1.49812i
$523$	14.6950	+	6.51385i	0.642568	+	0.284831i	0.700676	−	0.713479i	$-0.252882\pi$
$523$	14.6950	+	6.51385i	0.642568	+	0.284831i	−0.0581079	+	0.998310i	$0.518507\pi$
$524$	−10.5985	+	17.2659i	−0.462998	+	0.754265i
$525$	42.1100	−	36.3243i	1.83783	−	1.58532i
$526$	9.17722	−	12.5564i	0.400146	−	0.547486i
$527$	0.650656	−	1.21729i	0.0283430	−	0.0530260i
$528$	−48.9445	+	11.1657i	−2.13004	+	0.485925i
$529$	−23.8839	+	12.7662i	−1.03843	+	0.555052i
$530$	−32.3032	−	42.9259i	−1.40316	−	1.86458i
$531$	−12.0513	+	6.82698i	−0.522982	+	0.296266i
$532$	0.441184	−	0.526141i	0.0191277	−	0.0228111i
$533$	−3.36027	+	14.9640i	−0.145549	+	0.648161i
$534$	−10.4581	−	16.2627i	−0.452568	−	0.703758i
$535$	−2.53019	−	10.1011i	−0.109390	−	0.436709i
$536$	31.3793	+	28.6462i	1.35538	+	1.23733i
$537$	−25.7698	−	19.1122i	−1.11205	−	0.824750i
$538$	20.0685	−	2.61766i	0.865216	−	0.112856i
$539$	32.3267	+	18.3128i	1.39241	+	0.788789i
$540$	−59.0584	−	26.9294i	−2.54147	−	1.15886i
$541$	−32.7755	+	0.804593i	−1.40913	+	0.0345921i	−0.721974	−	0.691920i	$-0.756765\pi$
$541$	−32.7755	+	0.804593i	−1.40913	+	0.0345921i	−0.687154	+	0.726512i	$0.741140\pi$
$542$	23.1772	−	12.5974i	0.995545	−	0.541105i
$543$	8.02437	−	5.36171i	0.344359	−	0.230093i
$544$	−9.87074	−	11.2055i	−0.423205	−	0.480433i
$545$	−31.4527	−	21.0160i	−1.34729	−	0.900228i
$546$	−43.3221	−	3.96150i	−1.85401	−	0.169536i
$547$	−7.97408	−	3.07594i	−0.340947	−	0.131518i	0.183363	−	0.983045i	$-0.441302\pi$
$547$	−7.97408	−	3.07594i	−0.340947	−	0.131518i	−0.524310	+	0.851528i	$0.675677\pi$
$548$	23.0102	+	20.2770i	0.982947	+	0.866189i
$549$	52.1052	+	6.42656i	2.22380	+	0.274279i
$550$	−26.0470	−	1.73849i	−1.11065	−	0.0741295i
$551$	0.445415	−	0.266971i	0.0189753	−	0.0113734i
$552$	6.24308	−	61.1379i	0.265723	−	2.60220i
$553$	−1.52470	+	1.13079i	−0.0648368	+	0.0480862i
$554$	13.4519	−	12.9877i	0.571518	−	0.551793i
$555$	−19.9593	+	28.3400i	−0.847224	+	1.20297i
$556$	13.4468	−	13.1654i	0.570271	−	0.558338i
$557$	−25.1744	+	32.2580i	−1.06667	+	1.36682i	−0.140343	+	0.990103i	$0.544820\pi$
$557$	−25.1744	+	32.2580i	−1.06667	+	1.36682i	−0.926330	+	0.376712i	$0.877055\pi$
$558$	−1.56966	+	4.48545i	−0.0664491	+	0.189884i
$559$	2.09384	+	21.2591i	0.0885601	+	0.899166i
$560$	−44.6691	+	21.3130i	−1.88761	+	0.900637i
$561$	32.9714	+	3.24740i	1.39205	+	0.137105i
$562$	5.79034	+	15.8333i	0.244251	+	0.667889i
$563$	−17.4359	+	5.76004i	−0.734835	+	0.242757i	−0.656664	−	0.754183i	$-0.728033\pi$
$563$	−17.4359	+	5.76004i	−0.734835	+	0.242757i	−0.0781710	+	0.996940i	$0.524908\pi$
$564$	−69.6952	+	24.1092i	−2.93470	+	1.01518i
$565$	−17.6206	−	0.432562i	−0.741305	−	0.0181980i
$566$	10.2741	+	20.0609i	0.431852	+	0.843223i
$567$	35.0773	−	38.7018i	1.47311	−	1.62532i
$568$	−9.00821	−	6.39276i	−0.377976	−	0.268234i
$569$	−14.5250	+	5.19712i	−0.608918	+	0.217874i	−0.623250	−	0.782023i	$-0.714188\pi$
$569$	−14.5250	+	5.19712i	−0.608918	+	0.217874i	0.0143315	+	0.999897i	$0.495438\pi$
$570$	−0.972822	−	0.606554i	−0.0407470	−	0.0254058i
$571$	−9.80765	+	11.3698i	−0.410437	+	0.475811i	−0.924083	−	0.382191i	$-0.875170\pi$
$571$	−9.80765	+	11.3698i	−0.410437	+	0.475811i	0.513646	+	0.858002i	$0.328295\pi$
$572$	13.1740	+	15.6029i	0.550834	+	0.652390i
$573$	67.4037	−	15.1360i	2.81583	−	0.632316i
$574$	−34.8289	+	0.243301i	−1.45373	+	0.0101552i
$575$	12.2294	−	29.5243i	0.510001	−	1.23125i
$576$	39.5080	+	32.9005i	1.64617	+	1.37086i
$577$	15.3375	+	37.0280i	0.638509	+	1.54150i	0.828666	+	0.559743i	$0.189100\pi$
$577$	15.3375	+	37.0280i	0.638509	+	1.54150i	−0.190157	+	0.981754i	$0.560900\pi$
$578$	−5.52037	−	13.0684i	−0.229617	−	0.543574i
$579$	−19.5691	−	12.3920i	−0.813265	−	0.514995i
$580$	−37.1961	+	4.18896i	−1.54448	+	0.173937i
$581$	−2.54938	−	34.5611i	−0.105766	−	1.43384i
$582$	45.0947	+	63.0888i	1.86924	+	2.61511i
$583$	−45.5059	−	21.5227i	−1.88466	−	0.891379i
$584$	1.23702	−	9.74170i	0.0511881	−	0.403114i
$585$	2.42974	+	49.4586i	0.100458	+	2.04486i
$586$	17.7570	+	15.1022i	0.733535	+	0.623868i
$587$	2.06128	+	2.16503i	0.0850782	+	0.0893605i	0.765407	−	0.643547i	$-0.222538\pi$
$587$	2.06128	+	2.16503i	0.0850782	+	0.0893605i	−0.680328	+	0.732907i	$0.738163\pi$
$588$	−7.60514	−	55.2911i	−0.313631	−	2.28017i
$589$	−0.0201215	+	0.0399745i	−0.000829091	+	0.00164712i
$590$	9.39370	+	0.395726i	0.386733	+	0.0162918i
$591$	5.15096	+	6.27646i	0.211882	+	0.258179i
$592$	11.2849	−	9.32563i	0.463806	−	0.383281i
$593$	−14.1652	−	11.6251i	−0.581697	−	0.477386i	0.296927	−	0.954900i	$-0.404038\pi$
$593$	−14.1652	−	11.6251i	−0.581697	−	0.477386i	−0.878624	+	0.477514i	$0.841538\pi$
$594$	−60.7245	+	3.40857i	−2.49156	+	0.139855i
$595$	32.4175	−	3.99832i	1.32899	−	0.163915i
$596$	15.6634	−	22.9138i	0.641598	−	0.938584i
$597$	5.11495	+	29.4782i	0.209341	+	1.20646i
$598$	−23.2600	+	9.15953i	−0.951171	+	0.374561i
$599$	−15.2824	−	2.26693i	−0.624422	−	0.0926242i	−0.172981	−	0.984925i	$-0.555340\pi$
$599$	−15.2824	−	2.26693i	−0.624422	−	0.0926242i	−0.451441	+	0.892301i	$0.649090\pi$
$600$	21.6694	+	32.6838i	0.884652	+	1.33431i
$601$	−0.0171076	+	0.0682976i	−0.000697836	+	0.00278592i	−0.970379	−	0.241587i	$-0.922332\pi$
$601$	−0.0171076	+	0.0682976i	−0.000697836	+	0.00278592i	0.969681	+	0.244373i	$0.0785821\pi$
$602$	−45.9575	+	15.5392i	−1.87309	+	0.633331i
$603$	59.3950	+	76.1076i	2.41875	+	3.09934i
$604$	12.6496	+	1.69613i	0.514703	+	0.0690146i
$605$	−16.1015	+	7.13729i	−0.654618	+	0.290172i
$606$	7.81485	−	14.8695i	0.317456	−	0.604031i
$607$	−1.40786	−	7.07778i	−0.0571432	−	0.287278i	0.941638	−	0.336626i	$-0.109286\pi$
$607$	−1.40786	−	7.07778i	−0.0571432	−	0.287278i	−0.998782	+	0.0493476i	$0.984286\pi$
$608$	0.328863	+	0.355358i	0.0133371	+	0.0144117i
$609$	14.5768	−	73.2826i	0.590682	−	2.96956i
$610$	−27.7056	−	22.4153i	−1.12177	−	0.907570i
$611$	21.7262	+	20.6850i	0.878947	+	0.836827i
$612$	−17.8486	−	28.8565i	−0.721486	−	1.16646i
$613$	−32.7216	+	9.05530i	−1.32161	+	0.365740i	−0.854957	−	0.518698i	$-0.826417\pi$
$613$	−32.7216	+	9.05530i	−1.32161	+	0.365740i	−0.466657	+	0.884438i	$0.654542\pi$
$614$	25.0415	+	6.74196i	1.01059	+	0.272083i
$615$	8.53277	+	57.5233i	0.344075	+	2.31956i
$616$	−27.7595	+	37.1501i	−1.11846	+	1.49682i
$617$	4.69216	+	2.81237i	0.188899	+	0.113222i	0.605426	−	0.795902i	$-0.293003\pi$
$617$	4.69216	+	2.81237i	0.188899	+	0.113222i	−0.416527	+	0.909123i	$0.636753\pi$
$618$	−31.1679	−	21.6268i	−1.25376	−	0.869957i
$619$	−4.21937	+	2.67188i	−0.169591	+	0.107392i	−0.617091	−	0.786891i	$-0.711689\pi$
$619$	−4.21937	+	2.67188i	−0.169591	+	0.107392i	0.447501	+	0.894284i	$0.352314\pi$
$620$	2.51510	−	2.01997i	0.101009	−	0.0811239i
$621$	19.8579	−	71.7572i	0.796869	−	2.87952i
$622$	−44.3288	+	11.4335i	−1.77742	+	0.458440i
$623$	−17.0924	−	5.18493i	−0.684794	−	0.207730i
$624$	6.61938	−	29.9533i	0.264987	−	1.19909i
$625$	−7.89195	−	26.0163i	−0.315678	−	1.04065i
$626$	−15.8283	−	3.84748i	−0.632626	−	0.153776i
$627$	−1.07131	−	0.0790243i	−0.0427839	−	0.00315593i
$628$	−21.3218	−	7.88434i	−0.850834	−	0.314619i
$629$	−9.01403	+	3.47709i	−0.359413	+	0.138641i
$630$	−108.171	+	30.7500i	−4.30963	+	1.22511i
$631$	2.60114	+	5.49964i	0.103550	+	0.218937i	0.949112	−	0.314940i	$-0.101984\pi$
$631$	2.60114	+	5.49964i	0.103550	+	0.218937i	−0.845562	+	0.533877i	$0.820734\pi$
$632$	−0.655590	−	1.16702i	−0.0260780	−	0.0464215i
$633$	−30.8010	−	33.9837i	−1.22423	−	1.35073i
$634$	13.2533	+	5.00628i	0.526354	+	0.198825i
$635$	−40.5185	+	20.3953i	−1.60793	+	0.809363i
$636$	15.7873	+	73.9527i	0.626005	+	2.93242i
$637$	−18.5613	+	13.0723i	−0.735425	+	0.517945i
$638$	−29.0258	+	19.6891i	−1.14914	+	0.779499i
$639$	−17.7473	−	17.7473i	−0.702072	−	0.702072i
$640$	−10.9412	−	33.1406i	−0.432490	−	1.31000i
$641$	−21.7008	+	21.7008i	−0.857129	+	0.857129i	−0.990999	−	0.133870i	$-0.957259\pi$
$641$	−21.7008	+	21.7008i	−0.857129	+	0.857129i	0.133870	+	0.990999i	$0.457259\pi$
$642$	−2.75902	+	14.3954i	−0.108890	+	0.568140i
$643$	17.1301	+	24.3228i	0.675544	+	0.959199i	0.999912	+	0.0132680i	$0.00422347\pi$
$643$	17.1301	+	24.3228i	0.675544	+	0.959199i	−0.324368	+	0.945931i	$0.605152\pi$
$644$	−32.1972	−	46.7589i	−1.26875	−	1.84256i
$645$	36.4183	+	72.3507i	1.43397	+	2.84881i
$646$	−0.131527	−	0.291211i	−0.00517484	−	0.0114575i
$647$	−9.45045	+	8.56539i	−0.371536	+	0.336740i	−0.835878	−	0.548916i	$-0.815041\pi$
$647$	−9.45045	+	8.56539i	−0.371536	+	0.336740i	0.464342	+	0.885656i	$0.346291\pi$
$648$	23.9573	+	27.9754i	0.941131	+	1.09898i
$649$	7.96401	−	3.76669i	0.312615	−	0.147856i
$650$	7.76529	−	13.9337i	0.304580	−	0.546525i
$651$	2.31745	+	6.00777i	0.0908281	+	0.235463i
$652$	25.5712	−	27.6209i	1.00145	−	1.08172i
$653$	−0.142303	+	1.92915i	−0.00556873	+	0.0754935i	−0.999360	−	0.0357651i	$-0.988613\pi$
$653$	−0.142303	+	1.92915i	−0.00556873	+	0.0754935i	0.993791	+	0.111259i	$0.0354882\pi$
$654$	27.6922	+	45.4781i	1.08285	+	1.77834i
$655$	29.9020	−	9.07067i	1.16837	−	0.354421i
$656$	2.92357	−	24.3855i	0.114146	−	0.952093i
$657$	6.47698	−	21.3517i	0.252691	−	0.833011i
$658$	−34.6151	+	58.6774i	−1.34944	+	2.28748i
$659$	−27.4774	−	7.60401i	−1.07037	−	0.296210i	−0.313371	−	0.949631i	$-0.601458\pi$
$659$	−27.4774	−	7.60401i	−1.07037	−	0.296210i	−0.756995	+	0.653420i	$0.773333\pi$
$660$	67.8978	+	37.2204i	2.64292	+	1.44880i
$661$	6.84470	+	10.8090i	0.266228	+	0.420420i	0.951398	−	0.307963i	$-0.0996473\pi$
$661$	6.84470	+	10.8090i	0.266228	+	0.420420i	−0.685170	+	0.728383i	$0.740272\pi$
$662$	2.04027	+	11.2896i	0.0792972	+	0.438782i
$663$	−10.4079	+	17.3645i	−0.404207	+	0.674379i
$664$	24.4030	+	1.28661i	0.947022	+	0.0499301i
$665$	−1.04759	+	0.155395i	−0.0406237	+	0.00602596i
$666$	28.8269	−	16.5973i	1.11702	−	0.643132i
$667$	−11.4516	−	41.3808i	−0.443408	−	1.60227i
$668$	4.43183	+	27.2485i	0.171473	+	1.05427i
$669$	−38.4265	+	40.3606i	−1.48566	+	1.56043i
$670$	−6.87879	−	65.1711i	−0.265751	−	2.51778i
$671$	−32.7514	−	6.51466i	−1.26435	−	0.251496i
$672$	69.6619	−	0.723385i	2.68726	−	0.0279052i
$673$	33.3462	−	6.63297i	1.28540	−	0.255682i	0.495334	−	0.868703i	$-0.335046\pi$
$673$	33.3462	−	6.63297i	1.28540	−	0.255682i	0.790067	+	0.613021i	$0.210046\pi$
$674$	−2.35156	−	7.56148i	−0.0905785	−	0.291257i
$675$	19.2526	+	43.4332i	0.741033	+	1.67174i
$676$	13.0695	−	3.46848i	0.502673	−	0.133403i
$677$	16.2953	−	12.7170i	0.626278	−	0.488752i	−0.251476	−	0.967864i	$-0.580916\pi$
$677$	16.2953	−	12.7170i	0.626278	−	0.488752i	0.877754	+	0.479111i	$0.159041\pi$
$678$	22.2382	+	10.9997i	0.854053	+	0.422443i
$679$	69.4909	+	17.4066i	2.66682	+	0.668003i
$680$	−0.0826207	+	23.0322i	−0.00316836	+	0.883245i
$681$	3.23764	−	21.8264i	0.124067	−	0.836389i
$682$	1.20557	−	2.77183i	0.0461637	−	0.106139i
$683$	−42.2327	+	7.32806i	−1.61599	+	0.280401i	−0.905830	−	0.423642i	$-0.860752\pi$
$683$	−42.2327	+	7.32806i	−1.61599	+	0.280401i	−0.710158	+	0.704042i	$0.751377\pi$
$684$	0.601498	+	0.921141i	0.0229989	+	0.0352207i
$685$	−5.79052	−	46.9483i	−0.221245	−	1.79380i
$686$	−8.83565	−	7.89644i	−0.337347	−	0.301488i
$687$	30.7401	−	37.4569i	1.17281	−	1.42907i
$688$	−6.78787	−	33.5290i	−0.258785	−	1.27828i
$689$	23.7775	−	19.5137i	0.905852	−	0.743413i
$690$	−69.7869	+	64.1448i	−2.65674	+	2.44195i
$691$	−32.3665	−	16.2919i	−1.23128	−	0.619775i	−0.289879	−	0.957063i	$-0.593615\pi$
$691$	−32.3665	−	16.2919i	−1.23128	−	0.619775i	−0.941401	+	0.337289i	$0.890490\pi$
$692$	−27.8289	+	16.2826i	−1.05790	+	0.618970i
$693$	−76.3165	+	72.6594i	−2.89903	+	2.76010i
$694$	−0.0649639	−	0.804092i	−0.00246600	−	0.0305229i
$695$	−28.9906	+	1.42422i	−1.09968	+	0.0540236i
$696$	49.9686	+	16.7065i	1.89406	+	0.633256i
$697$	−6.93004	+	14.6523i	−0.262494	+	0.554997i
$698$	15.3512	+	2.55335i	0.581050	+	0.0966455i
$699$	−59.4854	+	4.38790i	−2.24994	+	0.165966i
$700$	34.8096	+	10.0305i	1.31568	+	0.379118i
$701$	14.6876	−	23.1942i	0.554742	−	0.876033i	−0.445069	−	0.895496i	$-0.646821\pi$
$701$	14.6876	−	23.1942i	0.554742	−	0.876033i	0.999811	+	0.0194634i	$0.00619578\pi$
$702$	13.9819	−	34.4337i	0.527713	−	1.29962i
$703$	0.289410	−	0.119878i	0.0109153	−	0.00452127i
$704$	−23.5218	−	22.7186i	−0.886512	−	0.856238i
$705$	105.088	+	43.5288i	3.95784	+	1.63939i
$706$	−19.8436	+	20.1228i	−0.746825	+	0.757332i
$707$	−3.39996	−	15.1407i	−0.127869	−	0.569424i
$708$	−11.7575	−	6.07486i	−0.441873	−	0.228307i
$709$	18.7146	+	16.1433i	0.702840	+	0.606274i	0.929990	−	0.367586i	$-0.119816\pi$
$709$	18.7146	+	16.1433i	0.702840	+	0.606274i	−0.227149	+	0.973860i	$0.572941\pi$
$710$	3.84889	+	16.5967i	0.144446	+	0.622864i
$711$	−1.02462	−	2.86363i	−0.0384264	−	0.107395i
$712$	5.14530	−	11.4961i	0.192828	−	0.430835i
$713$	2.74170	+	2.48493i	0.102678	+	0.0930615i
$714$	−43.7552	−	14.1165i	−1.63750	−	0.528298i
$715$	0.772961	−	31.4870i	0.0289071	−	1.17755i
$716$	1.24612	−	20.8622i	0.0465697	−	0.779657i
$717$	−0.879519	−	2.66234i	−0.0328462	−	0.0994270i
$718$	6.74988	−	14.5332i	0.251903	−	0.542375i
$719$	−2.63929	+	26.7972i	−0.0984289	+	0.999366i	0.811430	+	0.584449i	$0.198689\pi$
$719$	−2.63929	+	26.7972i	−0.0984289	+	0.999366i	−0.909859	+	0.414917i	$0.863811\pi$
$720$	−11.9020	−	78.4004i	−0.443562	−	2.92181i
$721$	−34.8761	+	3.43500i	−1.29886	+	0.127926i
$722$	−11.6533	−	24.2001i	−0.433692	−	0.900633i
$723$	−15.4054	−	12.0225i	−0.572933	−	0.447121i
$724$	5.78230	+	2.46705i	0.214897	+	0.0916871i
$725$	22.3997	+	15.7756i	0.831904	+	0.585893i
$726$	24.7871	+	0.435262i	0.919937	+	0.0161541i
$727$	−21.9899	−	29.6500i	−0.815561	−	1.09966i	−0.993298	−	0.115578i	$-0.963128\pi$
$727$	−21.9899	−	29.6500i	−0.815561	−	1.09966i	0.177738	−	0.984078i	$-0.443122\pi$
$728$	−13.2687	−	25.0396i	−0.491770	−	0.928030i
$729$	−6.79543	−	11.3375i	−0.251683	−	0.419907i
$730$	−11.3993	+	9.97284i	−0.421907	+	0.369111i
$731$	−2.76360	+	22.4067i	−0.102216	+	0.828742i
$732$	22.0788	+	45.0427i	0.816058	+	1.66483i
$733$	2.35717	−	6.11072i	0.0870639	−	0.225705i	−0.882611	−	0.470105i	$-0.844216\pi$
$733$	2.35717	−	6.11072i	0.0870639	−	0.225705i	0.969674	+	0.244400i	$0.0785911\pi$
$734$	10.5645	+	12.6910i	0.389942	+	0.468435i
$735$	−47.8250	+	71.5751i	−1.76405	+	2.64009i
$736$	35.5693	−	18.3695i	1.31110	−	0.677107i
$737$	−34.1151	−	51.0568i	−1.25665	−	1.88070i
$738$	15.8258	−	53.5136i	0.582556	−	1.96986i
$739$	0.911244	+	37.1200i	0.0335206	+	1.36548i	0.747010	+	0.664813i	$0.231489\pi$
$739$	0.911244	+	37.1200i	0.0335206	+	1.36548i	−0.713489	+	0.700667i	$0.752886\pi$
$740$	−22.5658	−	0.792754i	−0.829534	−	0.0291422i
$741$	0.323539	−	0.571126i	0.0118855	−	0.0209808i
$742$	55.3694	+	42.5917i	2.03267	+	1.56359i
$743$	20.4912	−	27.6292i	0.751749	−	1.01362i	−0.247254	−	0.968951i	$-0.579528\pi$
$743$	20.4912	−	27.6292i	0.751749	−	1.01362i	0.999002	−	0.0446647i	$-0.0142219\pi$
$744$	−4.40847	+	1.08747i	−0.161623	+	0.0398687i
$745$	−41.5269	+	10.4019i	−1.52143	+	0.381098i
$746$	28.6097	+	6.21492i	1.04748	+	0.227544i
$747$	54.1757	+	12.1656i	1.98218	+	0.445114i
$748$	9.97173	+	19.1398i	0.364603	+	0.699822i
$749$	6.67397	+	11.7812i	0.243862	+	0.430476i
$750$	−0.906951	+	6.42298i	−0.0331172	+	0.234534i
$751$	5.02576	+	9.40254i	0.183393	+	0.343103i	0.956772	−	0.290841i	$-0.0939349\pi$
$751$	5.02576	+	9.40254i	0.183393	+	0.343103i	−0.773379	+	0.633944i	$0.781435\pi$
$752$	−37.9719	−	29.4265i	−1.38469	−	1.07307i
$753$	−21.8235	−	11.6649i	−0.795293	−	0.425093i
$754$	−3.29270	−	21.1773i	−0.119913	−	0.771232i
$755$	−12.8577	−	14.9057i	−0.467940	−	0.542472i
$756$	83.3513	+	13.2661i	3.03146	+	0.482483i
$757$	1.88485	−	4.25216i	0.0685062	−	0.154548i	−0.876685	−	0.481065i	$-0.840250\pi$
$757$	1.88485	−	4.25216i	0.0685062	−	0.154548i	0.945191	+	0.326517i	$0.105875\pi$
$758$	1.53932	+	0.178949i	0.0559105	+	0.00649973i
$759$	−29.9218	+	83.6259i	−1.08609	+	3.03543i
$760$	−0.0156489	−	0.746623i	−0.000567646	−	0.0270829i
$761$	−19.5287	−	0.959382i	−0.707914	−	0.0347776i	−0.308074	−	0.951363i	$-0.599684\pi$
$761$	−19.5287	−	0.959382i	−0.707914	−	0.0347776i	−0.399840	+	0.916585i	$0.630934\pi$
$762$	63.8191	−	2.01283i	2.31192	−	0.0729172i
$763$	46.7051	+	15.4293i	1.69084	+	0.558577i
$764$	32.2616	+	31.3725i	1.16718	+	1.13502i
$765$	−8.94702	+	51.5629i	−0.323480	+	1.86426i
$766$	6.60531	+	32.0359i	0.238660	+	1.15751i
$767$			5.38326i			0.194378i
$768$	−5.68186	+	48.7949i	−0.205027	+	1.76073i
$769$			16.8082i			0.606120i	0.952972	+	0.303060i	$0.0980082\pi$
$769$			16.8082i			0.606120i	−0.952972	+	0.303060i	$0.901992\pi$
$770$	70.0554	−	14.4443i	2.52462	−	0.520538i
$771$	2.88998	−	16.6553i	0.104080	−	0.599828i
$772$	−0.210792	−	15.0869i	−0.00758659	−	0.542988i
$773$	−4.74629	−	1.56796i	−0.170712	−	0.0563957i	0.227056	−	0.973882i	$-0.427090\pi$
$773$	−4.74629	−	1.56796i	−0.170712	−	0.0563957i	−0.397768	+	0.917486i	$0.630215\pi$
$774$	−2.45033	−	77.6904i	−0.0880753	−	2.79252i
$775$	−2.35827	−	0.115854i	−0.0847116	−	0.00416161i
$776$	−18.3492	+	47.0649i	−0.658696	+	1.68953i
$777$	15.1844	−	42.4377i	0.544739	−	1.52244i
$778$	0.219527	−	1.88836i	0.00787042	−	0.0677011i
$779$	0.212969	−	0.480449i	0.00763039	−	0.0172139i
$780$	−38.2987	+	27.7815i	−1.37131	+	0.994737i
$781$	10.4273	+	12.0881i	0.373118	+	0.432548i
$782$	−26.1060	+	4.05903i	−0.933549	+	0.145151i
$783$	56.2942	+	30.0899i	2.01179	+	1.07532i
$784$	27.4482	−	23.8402i	0.980294	−	0.851435i
$785$	16.5284	+	30.9225i	0.589925	+	1.10367i
$786$	−43.5514	−	6.14963i	−1.55343	−	0.219350i
$787$	0.566683	+	1.00034i	0.0202001	+	0.0356581i	0.880004	−	0.474966i	$-0.157540\pi$
$787$	0.566683	+	1.00034i	0.0202001	+	0.0356581i	−0.859804	+	0.510624i	$0.829415\pi$
$788$	−1.58877	+	5.04482i	−0.0565974	+	0.179714i
$789$	32.9447	+	7.39798i	1.17286	+	0.263375i
$790$	−0.438265	+	2.01750i	−0.0155928	+	0.0717796i
$791$	22.2322	−	5.56887i	0.790485	−	0.198006i
$792$	−44.0485	−	59.8399i	−1.56519	−	2.12632i
$793$	12.1551	−	16.3893i	0.431642	−	0.582002i
$794$	3.29078	−	4.27802i	0.116785	−	0.151821i
$795$	57.4882	−	101.481i	2.03890	−	3.59916i
$796$	−14.2563	+	13.2886i	−0.505300	+	0.471001i
$797$	0.912135	+	37.1563i	0.0323095	+	1.31614i	0.768710	+	0.639597i	$0.220899\pi$
$797$	0.912135	+	37.1563i	0.0323095	+	1.31614i	−0.736401	+	0.676546i	$0.763476\pi$
$798$	1.42950	+	0.422752i	0.0506037	+	0.0149652i
$799$	17.6137	+	26.3607i	0.623127	+	0.932575i
$800$	−10.1087	+	23.4594i	−0.357397	+	0.829416i
$801$	15.8993	−	23.7950i	0.561775	−	0.840756i
$802$	−25.7816	+	21.4616i	−0.910381	+	0.757835i
$803$	−5.10765	+	13.2411i	−0.180245	+	0.467267i
$804$	−29.8594	+	87.2767i	−1.05306	+	3.07801i
$805$	−10.7187	+	86.9052i	−0.377786	+	3.06301i
$806$	1.21615	+	1.39010i	0.0428369	+	0.0489641i
$807$	22.5888	+	37.6871i	0.795163	+	1.32665i
$808$	10.8934	−	1.03346i	0.383228	−	0.0363571i
$809$	21.6135	+	29.1424i	0.759890	+	1.02459i	0.998568	+	0.0534942i	$0.0170359\pi$
$809$	21.6135	+	29.1424i	0.759890	+	1.02459i	−0.238678	+	0.971099i	$0.576714\pi$
$810$	0.997401	−	56.7996i	0.0350451	−	1.99574i
$811$	22.7197	+	16.0010i	0.797795	+	0.561871i	0.901521	−	0.432735i	$-0.142451\pi$
$811$	22.7197	+	16.0010i	0.797795	+	0.561871i	−0.103726	+	0.994606i	$0.533076\pi$
$812$	45.1614	−	18.1495i	1.58485	−	0.636921i
$813$	45.1489	+	35.2345i	1.58344	+	1.23573i
$814$	−19.0625	+	9.17938i	−0.668140	+	0.321737i
$815$	−57.7762	+	5.69046i	−2.02381	+	0.199328i
$816$	13.7616	−	29.3542i	0.481753	−	1.02760i
$817$	0.0717491	−	0.728481i	0.00251018	−	0.0254863i
$818$	12.1073	+	5.62319i	0.423323	+	0.196610i
$819$	−20.1975	−	61.1388i	−0.705759	−	2.13636i
$820$	−28.3353	+	25.1411i	−0.989512	+	0.877966i
$821$	1.00524	−	40.9491i	0.0350832	−	1.42913i	−0.681595	−	0.731729i	$-0.738714\pi$
$821$	1.00524	−	40.9491i	0.0350832	−	1.42913i	0.716679	−	0.697404i	$-0.245661\pi$
$822$	−20.4441	+	63.3681i	−0.713071	+	2.21021i
$823$	−22.1891	−	20.1110i	−0.773464	−	0.701027i	0.186096	−	0.982532i	$-0.440417\pi$
$823$	−22.1891	−	20.1110i	−0.773464	−	0.701027i	−0.959560	+	0.281505i	$0.909167\pi$
$824$	0.695074	−	24.7021i	0.0242140	−	0.860537i
$825$	−19.0930	−	53.3614i	−0.664733	−	1.85781i
$826$	−11.9094	+	2.76188i	−0.414382	+	0.0960980i
$827$	2.55917	+	2.20755i	0.0889909	+	0.0767641i	0.696540	−	0.717518i	$-0.254722\pi$
$827$	2.55917	+	2.20755i	0.0889909	+	0.0767641i	−0.607549	+	0.794282i	$0.707847\pi$
$828$	86.6667	−	27.6180i	3.01188	−	0.959793i
$829$	−0.229418	−	1.02165i	−0.00796803	−	0.0354833i	0.971557	−	0.236807i	$-0.0761008\pi$
$829$	−0.229418	−	1.02165i	−0.00796803	−	0.0354833i	−0.979525	+	0.201323i	$0.935476\pi$
$830$	−26.8371	−	26.4647i	−0.931528	−	0.918604i
$831$	37.5047	+	15.5350i	1.30102	+	0.538902i
$832$	18.6946	−	7.05765i	0.648119	−	0.244680i
$833$	−22.1669	+	9.18183i	−0.768037	+	0.318131i
$834$	37.8541	+	15.3708i	1.31078	+	0.532247i
$835$	22.7800	−	35.9736i	0.788335	−	1.24492i
$836$	−0.338450	−	0.612456i	−0.0117055	−	0.0211822i
$837$	−5.48609	+	0.404678i	−0.189627	+	0.0139877i
$838$	8.22121	−	49.4273i	0.283997	−	1.70744i
$839$	2.04890	−	4.33203i	0.0707358	−	0.149558i	−0.865523	−	0.500869i	$-0.833014\pi$
$839$	2.04890	−	4.33203i	0.0707358	−	0.149558i	0.936259	+	0.351311i	$0.114264\pi$
$840$	−81.1103	−	70.4752i	−2.79857	−	2.43163i
$841$	7.80070	−	0.383224i	0.268990	−	0.0132146i
$842$	−9.74819	+	0.787572i	−0.335945	+	0.0271415i
$843$	−26.5082	+	25.2379i	−0.912990	+	0.869239i
$844$	7.56544	−	28.9029i	0.260413	−	0.994880i
$845$	−18.6290	−	9.37704i	−0.640856	−	0.322580i
$846$	−73.8662	−	80.3634i	−2.53957	−	2.76295i
$847$	17.7031	−	14.5286i	0.608286	−	0.499207i
$848$	−34.7125	+	34.9493i	−1.19203	+	1.20016i
$849$	−31.0423	+	37.8251i	−1.06537	+	1.29815i
$850$	11.2338	−	12.5700i	0.385317	−	0.431146i
$851$	−3.17049	−	25.7056i	−0.108683	−	0.881178i
$852$	4.92691	−	23.4696i	0.168793	−	0.804056i
$853$	15.7291	−	2.72926i	0.538554	−	0.0934480i	0.104824	−	0.994491i	$-0.466572\pi$
$853$	15.7291	−	2.72926i	0.538554	−	0.0934480i	0.433730	+	0.901043i	$0.357197\pi$
$854$	42.4944	+	18.4824i	1.45413	+	0.632454i
$855$	0.248976	−	1.67846i	0.00851480	−	0.0574021i
$856$	−8.83415	+	3.62215i	−0.301945	+	0.123803i
$857$	−32.7098	−	8.19339i	−1.11735	−	0.279881i	−0.360038	−	0.932938i	$-0.617236\pi$
$857$	−32.7098	−	8.19339i	−1.11735	−	0.279881i	−0.757309	+	0.653057i	$0.773486\pi$
$858$	−19.6559	+	39.7383i	−0.671040	+	1.35664i
$859$	26.0883	−	20.3595i	0.890120	−	0.694657i	−0.0627517	−	0.998029i	$-0.519988\pi$
$859$	26.0883	−	20.3595i	0.890120	−	0.694657i	0.952872	+	0.303372i	$0.0981126\pi$
$860$	−26.4909	+	45.6313i	−0.903334	+	1.55601i
$861$	−30.6427	−	69.1289i	−1.04430	−	2.35591i
$862$	−26.3859	+	8.20578i	−0.898707	+	0.279490i
$863$	7.82075	−	1.55564i	0.266221	−	0.0529547i	−0.0601745	−	0.998188i	$-0.519166\pi$
$863$	7.82075	−	1.55564i	0.266221	−	0.0529547i	0.326396	+	0.945233i	$0.394166\pi$
$864$	−16.6839	+	57.1284i	−0.567599	+	1.94355i
$865$	48.7743	+	9.70181i	1.65838	+	0.329871i
$866$	−4.65226	+	0.491045i	−0.158090	+	0.0166864i
$867$	21.2373	−	22.3063i	0.721257	−	0.757560i
$868$	−2.45138	+	3.40368i	−0.0832053	+	0.115528i
$869$	0.515962	+	1.86445i	0.0175028	+	0.0632470i
$870$	−40.5478	−	70.4252i	−1.37470	−	2.38764i
$871$	37.1158	−	5.50560i	1.25762	−	0.186550i
$872$	−14.9419	+	31.3011i	−0.505998	+	1.05999i
$873$	−59.0083	+	98.4494i	−1.99713	+	3.33201i
$874$	0.842960	−	0.152341i	0.0285135	−	0.00515300i
$875$	3.20587	+	5.06263i	0.108378	+	0.171148i
$876$	20.4655	−	5.97261i	0.691466	−	0.201796i
$877$	−20.9809	−	5.80619i	−0.708474	−	0.196061i	−0.106193	−	0.994345i	$-0.533866\pi$
$877$	−20.9809	−	5.80619i	−0.708474	−	0.196061i	−0.602281	+	0.798284i	$0.705741\pi$
$878$	9.21056	+	5.43350i	0.310841	+	0.183372i
$879$	−14.6907	+	48.4288i	−0.495506	+	1.63346i
$880$	3.88141	+	50.2890i	0.130842	+	1.69524i
$881$	−17.6170	+	5.34405i	−0.593531	+	0.180046i	−0.572738	−	0.819738i	$-0.694119\pi$
$881$	−17.6170	+	5.34405i	−0.593531	+	0.180046i	−0.0207924	+	0.999784i	$0.506619\pi$
$882$	70.5559	−	42.9624i	2.37574	−	1.44662i
$883$	1.93282	−	26.2026i	0.0650446	−	0.881789i	−0.862017	−	0.506879i	$-0.830799\pi$
$883$	1.93282	−	26.2026i	0.0650446	−	0.881789i	0.927062	−	0.374909i	$-0.122326\pi$
$884$	−13.1777	+	0.507787i	−0.443214	+	0.0170787i
$885$	7.34618	+	19.0443i	0.246939	+	0.640166i
$886$	−30.1305	−	16.7918i	−1.01225	−	0.564131i
$887$	18.2114	−	8.61334i	0.611478	−	0.289208i	−0.0966203	−	0.995321i	$-0.530803\pi$
$887$	18.2114	−	8.61334i	0.611478	−	0.289208i	0.708099	+	0.706114i	$0.249553\pi$
$888$	28.3377	+	14.3916i	0.950950	+	0.482951i
$889$	43.7045	−	39.6115i	1.46580	−	1.32853i
$890$	−17.7043	+	7.99620i	−0.593449	+	0.268033i
$891$	−23.9329	−	47.5466i	−0.801784	−	1.59287i
$892$	−35.6993	−	6.58394i	−1.19530	−	0.220447i
$893$	−0.591898	−	0.840430i	−0.0198071	−	0.0281239i
$894$	59.1812	+	11.3427i	1.97931	+	0.379356i
$895$	−22.7934	+	22.7934i	−0.761899	+	0.761899i
$896$	25.2049	+	37.7373i	0.842038	+	1.26071i
$897$	−38.3762	−	38.3762i	−1.28134	−	1.28134i
$898$	−4.14553	−	6.11138i	−0.138338	−	0.203939i
$899$	−2.59363	+	1.82664i	−0.0865024	+	0.0609218i
$900$	−31.5689	+	48.7058i	−1.05230	+	1.62353i
$901$	29.0373	−	14.6161i	0.967373	−	0.486934i
$902$	−12.5428	+	33.2050i	−0.417631	+	1.10561i
$903$	−70.7311	−	78.0398i	−2.35378	−	2.59700i
$904$	1.92077	+	16.0468i	0.0638838	+	0.533707i
$905$	−4.14570	−	8.76535i	−0.137808	−	0.291370i
$906$	7.57650	+	26.6523i	0.251712	+	0.885462i
$907$	−7.97406	+	3.07593i	−0.264774	+	0.102135i	−0.488641	−	0.872485i	$-0.662507\pi$
$907$	−7.97406	+	3.07593i	−0.264774	+	0.102135i	0.223866	+	0.974620i	$0.428132\pi$
$908$	13.0576	−	6.00770i	0.433333	−	0.199373i
$909$	24.7954	+	1.82902i	0.822411	+	0.0606647i
$910$	−10.3237	+	42.4711i	−0.342227	+	1.40790i
$911$	−9.97757	−	32.8916i	−0.330572	−	1.08975i	−0.951954	−	0.306241i	$-0.900929\pi$
$911$	−9.97757	−	32.8916i	−0.330572	−	1.08975i	0.621382	−	0.783508i	$-0.286571\pi$
$912$	−0.422707	+	0.962426i	−0.0139972	+	0.0318691i
$913$	−33.7963	−	10.2520i	−1.11849	−	0.339291i
$914$	4.24867	+	16.4726i	0.140534	+	0.544865i
$915$	20.6356	−	74.5675i	0.682192	−	2.46513i
$916$	31.3779	+	3.42578i	1.03676	+	0.113191i
$917$	−34.3274	+	21.7376i	−1.13359	+	0.717838i
$918$	22.3911	−	32.2695i	0.739018	−	1.06505i
$919$	28.6222	+	17.1555i	0.944159	+	0.565907i	0.901310	−	0.433174i	$-0.142606\pi$
$919$	28.6222	+	17.1555i	0.944159	+	0.565907i	0.0428492	+	0.999082i	$0.486356\pi$
$920$	−59.8408	−	15.2177i	−1.97289	−	0.501712i
$921$	8.26115	+	55.6922i	0.272214	+	1.83512i
$922$	10.5068	−	39.0251i	0.346023	−	1.28522i
$923$	−9.40150	+	2.60175i	−0.309454	+	0.0856375i
$924$	−97.9977	−	23.0971i	−3.22389	−	0.759839i
$925$	11.9696	+	11.3960i	0.393558	+	0.374699i
$926$	14.0904	−	17.4158i	0.463038	−	0.572320i
$927$	10.9542	−	55.0705i	0.359784	−	1.80875i
$928$	8.68454	+	33.2039i	0.285084	+	1.08997i
$929$	8.02134	+	40.3260i	0.263172	+	1.32305i	0.855687	+	0.517494i	$0.173135\pi$
$929$	8.02134	+	40.3260i	0.263172	+	1.32305i	−0.592515	+	0.805559i	$0.701865\pi$
$930$	6.19931	+	3.25813i	0.203284	+	0.106838i
$931$	0.711203	−	0.315254i	0.0233087	−	0.0103320i
$932$	−23.5792	−	30.8817i	−0.772364	−	1.01156i
$933$	−61.1468	−	78.3524i	−2.00186	−	2.56514i
$934$	−13.8271	−	40.8939i	−0.452437	−	1.33809i
$935$	8.08810	−	32.2895i	0.264509	−	1.05598i
$936$	44.5626	−	8.69799i	1.45657	−	0.284303i
$937$	13.9846	+	2.07442i	0.456856	+	0.0677682i	0.371193	−	0.928556i	$-0.378949\pi$
$937$	13.9846	+	2.07442i	0.456856	+	0.0677682i	0.0856637	+	0.996324i	$0.472699\pi$
$938$	31.2223	+	79.2868i	1.01944	+	2.58881i
$939$	−6.04593	−	34.8435i	−0.197301	−	1.13708i
$940$	13.6861	+	72.8199i	0.446390	+	2.37512i
$941$	22.1651	−	2.73380i	0.722560	−	0.0891193i	0.247268	−	0.968947i	$-0.420467\pi$
$941$	22.1651	−	2.73380i	0.722560	−	0.0891193i	0.475293	+	0.879828i	$0.342342\pi$
$942$	−2.76595	−	49.2760i	−0.0901194	−	1.60550i
$943$	−33.5888	−	27.5657i	−1.09380	−	0.897661i
$944$	−0.874134	−	8.57634i	−0.0284506	−	0.279136i
$945$	−82.5836	−	100.628i	−2.68644	−	3.27344i
$946$	−2.08091	+	49.3964i	−0.0676562	+	1.60601i
$947$	−18.4208	+	36.5958i	−0.598594	+	1.18920i	0.367260	+	0.930118i	$0.380296\pi$
$947$	−18.4208	+	36.5958i	−0.598594	+	1.18920i	−0.965855	+	0.259085i	$0.916579\pi$
$948$	1.75570	−	2.31571i	0.0570226	−	0.0752109i
$949$	−5.97973	−	6.28071i	−0.194110	−	0.203880i
$950$	−0.354126	+	0.416376i	−0.0114894	+	0.0135090i
$951$	1.50920	+	30.7204i	0.0489391	+	0.996178i
$952$	−7.88420	−	28.8926i	−0.255528	−	0.936415i
$953$	32.5150	+	15.3785i	1.05327	+	0.498157i	0.874143	−	0.485669i	$-0.161424\pi$
$953$	32.5150	+	15.3785i	1.05327	+	0.498157i	0.179123	+	0.983827i	$0.442674\pi$
$954$	−91.0548	+	65.0843i	−2.94801	+	2.10718i
$955$	−5.10595	−	69.2197i	−0.165225	−	2.23990i
$956$	1.13885	−	1.42791i	0.0368330	−	0.0461820i
$957$	−64.3318	−	40.7377i	−2.07955	−	1.31686i
$958$	23.7876	−	10.0484i	0.768541	−	0.324648i
$959$	23.5387	+	56.8274i	0.760104	+	1.83505i
$960$	56.5045	−	50.4790i	1.82367	−	1.62920i
$961$	−11.7586	+	28.3877i	−0.379309	+	0.915732i
$962$	−0.0903100	−	12.9280i	−0.00291171	−	0.416815i
$963$	−21.1673	+	4.75327i	−0.682106	+	0.153172i
$964$	1.07059	−	12.6843i	0.0344815	−	0.408533i
$965$	−15.2006	+	17.6217i	−0.489324	+	0.567262i
$966$	65.2111	−	104.589i	2.09813	−	3.36509i
$967$	−9.87180	+	3.53218i	−0.317456	+	0.113587i	−0.490796	−	0.871275i	$-0.663294\pi$
$967$	−9.87180	+	3.53218i	−0.317456	+	0.113587i	0.173340	+	0.984862i	$0.444544\pi$
$968$	8.59066	+	13.6744i	0.276114	+	0.439512i
$969$	0.465873	−	0.514012i	0.0149660	−	0.0165124i
$970$	69.3479	−	35.5161i	2.22663	−	1.14035i
$971$	53.2238	+	1.30657i	1.70803	+	0.0419299i	0.866774	−	0.498701i	$-0.166189\pi$
$971$	53.2238	+	1.30657i	1.70803	+	0.0419299i	0.841260	+	0.540631i	$0.181814\pi$
$972$	−7.35946	+	15.1439i	−0.236055	+	0.485741i
$973$	35.8371	−	11.8390i	1.14888	−	0.379540i
$974$	−0.879704	+	0.321713i	−0.0281875	+	0.0103083i
$975$	34.4641	+	3.39442i	1.10374	+	0.108708i
$976$	−16.7037	+	28.0844i	−0.534672	+	0.898960i
$977$	−0.278498	−	2.82764i	−0.00890995	−	0.0904643i	0.989701	−	0.143148i	$-0.0457225\pi$
$977$	−0.278498	−	2.82764i	−0.00890995	−	0.0904643i	−0.998611	+	0.0526837i	$0.983222\pi$
$978$	77.1317	+	26.9919i	2.46640	+	0.863106i
$979$	−11.1989	+	14.3501i	−0.357918	+	0.458630i
$980$	−56.0715	−	0.592848i	−1.79114	−	0.0189378i
$981$	−45.3790	+	64.4332i	−1.44884	+	2.05719i
$982$	33.5484	+	34.7477i	1.07057	+	1.10884i
$983$	−4.69661	+	3.48325i	−0.149799	+	0.111098i	−0.668003	−	0.744159i	$-0.732851\pi$
$983$	−4.69661	+	3.48325i	−0.149799	+	0.111098i	0.518204	+	0.855257i	$0.326601\pi$
$984$	51.0797	−	15.2950i	1.62836	−	0.487587i
$985$	6.99714	−	4.19393i	0.222948	−	0.133630i
$986$	1.50842	−	22.5999i	0.0480378	−	0.719727i
$987$	−146.792	−	18.1051i	−4.67244	−	0.576291i
$988$	0.426733	−	0.0269448i	0.0135762	−	0.000857229i
$989$	−56.4678	−	21.7820i	−1.79557	−	0.692628i
$990$	−10.4362	+	114.129i	−0.331686	+	3.62725i
$991$	−36.5910	−	24.4494i	−1.16235	−	0.776659i	−0.183862	−	0.982952i	$-0.558860\pi$
$991$	−36.5910	−	24.4494i	−1.16235	−	0.776659i	−0.978490	+	0.206293i	$0.933860\pi$
$992$	−2.16323	−	2.01716i	−0.0686826	−	0.0640448i
$993$	−20.7094	+	13.8376i	−0.657192	+	0.439122i
$994$	−10.5793	−	19.4642i	−0.335555	−	0.617366i
$995$	30.0506	−	0.737700i	0.952667	−	0.0233867i
$996$	18.5692	+	49.6973i	0.588386	+	1.57472i
$997$	27.3426	+	15.4894i	0.865949	+	0.490554i	0.860512	−	0.509431i	$-0.170144\pi$
$997$	27.3426	+	15.4894i	0.865949	+	0.490554i	0.00543786	+	0.999985i	$0.498269\pi$
$998$	6.34701	+	48.6599i	0.200911	+	1.54030i
$999$	30.9275	+	22.9374i	0.978503	+	0.725708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.149.23	✓	4032
512.189	even	128	inner	512.2.o.a.189.23	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.149.23	✓	4032	1.1	even	1	trivial
512.2.o.a.189.23	yes	4032	512.189	even	128	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.777462 + 1.18134i) q^{2} +(-3.02508 - 0.524902i) q^{3} +(-0.791106 - 1.83689i) q^{4} +(-0.967631 + 2.92906i) q^{5} +(2.97197 - 3.16555i) q^{6} +(0.196816 - 4.00628i) q^{7} +(2.78503 + 0.493547i) q^{8} +(6.05098 + 2.16508i) q^{9} +O(q^{10})\)	\(q+(-0.777462 + 1.18134i) q^{2} +(-3.02508 - 0.524902i) q^{3} +(-0.791106 - 1.83689i) q^{4} +(-0.967631 + 2.92906i) q^{5} +(2.97197 - 3.16555i) q^{6} +(0.196816 - 4.00628i) q^{7} +(2.78503 + 0.493547i) q^{8} +(6.05098 + 2.16508i) q^{9} +(-2.70791 - 3.42033i) q^{10} +(-3.73704 - 1.65652i) q^{11} +(1.42898 + 5.97199i) q^{12} +(1.89136 - 1.63150i) q^{13} +(4.57974 + 3.34723i) q^{14} +(4.46464 - 8.35275i) q^{15} +(-2.74830 + 2.90634i) q^{16} +(2.32811 - 1.24440i) q^{17} +(-7.26209 + 5.46498i) q^{18} +(-0.0744722 + 0.0421880i) q^{19} +(6.14585 - 0.539771i) q^{20} +(-2.69829 + 12.0160i) q^{21} +(4.86231 - 3.12682i) q^{22} +(1.71953 + 6.86475i) q^{23} +(-8.16590 - 2.95489i) q^{24} +(-3.62705 - 2.69000i) q^{25} +(0.456887 + 3.50276i) q^{26} +(-9.15404 - 5.18570i) q^{27} +(-7.51478 + 2.80786i) q^{28} +(-6.06531 + 0.148895i) q^{29} +(6.39631 + 11.7682i) q^{30} +(0.434748 - 0.290489i) q^{31} +(-1.29667 - 5.50624i) q^{32} +(10.4354 + 6.97268i) q^{33} +(-0.339962 + 3.71775i) q^{34} +(11.5442 + 4.45308i) q^{35} +(-0.809973 - 12.8278i) q^{36} +(-3.63236 - 0.448009i) q^{37} +(0.00806113 - 0.120776i) q^{38} +(-6.57791 + 3.94265i) q^{39} +(-4.14051 + 7.67996i) q^{40} +(-4.93172 + 3.65761i) q^{41} +(-12.0971 - 12.5296i) q^{42} +(-4.92449 + 6.99223i) q^{43} +(-0.0864348 + 8.17500i) q^{44} +(-12.1968 + 15.6287i) q^{45} +(-9.44645 - 3.30574i) q^{46} +(1.17717 + 11.9520i) q^{47} +(9.83939 - 7.34935i) q^{48} +(-9.04524 - 0.890878i) q^{49} +(5.99769 - 2.19339i) q^{50} +(-7.69591 + 2.54239i) q^{51} +(-4.49315 - 2.18353i) q^{52} +(12.3110 + 0.302217i) q^{53} +(13.2430 - 6.78230i) q^{54} +(8.46811 - 9.34312i) q^{55} +(2.52542 - 11.0605i) q^{56} +(0.247429 - 0.0885316i) q^{57} +(4.53965 - 7.28092i) q^{58} +(-1.40771 + 1.63193i) q^{59} +(-18.8750 - 1.59312i) q^{60} +(7.97061 - 1.78986i) q^{61} +(0.00516536 + 0.739428i) q^{62} +(9.86483 - 23.8158i) q^{63} +(7.51282 + 2.74909i) q^{64} +(2.94862 + 7.11860i) q^{65} +(-16.3502 + 6.90666i) q^{66} +(12.6913 + 8.03670i) q^{67} +(-4.12760 - 3.29202i) q^{68} +(-1.59841 - 21.6690i) q^{69} +(-14.2357 + 10.1755i) q^{70} +(-3.53041 - 1.66976i) q^{71} +(15.7836 + 9.01625i) q^{72} +(-0.170356 - 3.46768i) q^{73} +(3.35327 - 3.94273i) q^{74} +(9.56014 + 10.0413i) q^{75} +(0.136410 + 0.103422i) q^{76} +(-7.37197 + 14.6456i) q^{77} +(0.456485 - 10.8360i) q^{78} +(-0.300227 - 0.365828i) q^{79} +(-5.85352 - 10.8622i) q^{80} +(10.0661 + 8.26106i) q^{81} +(-0.486643 - 8.66966i) q^{82} +(8.57479 - 1.05760i) q^{83} +(24.2067 - 4.54950i) q^{84} +(1.39217 + 8.02329i) q^{85} +(-4.43157 - 11.2537i) q^{86} +(18.4262 + 2.73327i) q^{87} +(-9.59021 - 6.45786i) q^{88} +(1.08200 - 4.31957i) q^{89} +(-8.98022 - 26.5592i) q^{90} +(-6.16399 - 7.89843i) q^{91} +(11.2494 - 8.58933i) q^{92} +(-1.46763 + 0.650555i) q^{93} +(-15.0345 - 7.90160i) q^{94} +(-0.0515095 - 0.258956i) q^{95} +(1.03230 + 17.3375i) q^{96} +(-3.48428 + 17.5167i) q^{97} +(8.08475 - 9.99283i) q^{98} +(-19.0263 - 18.1145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

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