LMFDB - Embedded newform 324.2.p.a.23.49

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			23.49
Character	$\chi$	$=$	324.23
Dual form			324.2.p.a.155.49

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37299 - 0.338962i) q^{2} +(-1.19533 - 1.25347i) q^{3} +(1.77021 - 0.930784i) q^{4} +(2.32883 - 3.54082i) q^{5} +(-2.06605 - 1.31583i) q^{6} +(-1.95981 + 1.84899i) q^{7} +(2.11498 - 1.87799i) q^{8} +(-0.142379 + 2.99662i) q^{9} +O(q^{10})$	\(q+(1.37299 - 0.338962i) q^{2} +(-1.19533 - 1.25347i) q^{3} +(1.77021 - 0.930784i) q^{4} +(2.32883 - 3.54082i) q^{5} +(-2.06605 - 1.31583i) q^{6} +(-1.95981 + 1.84899i) q^{7} +(2.11498 - 1.87799i) q^{8} +(-0.142379 + 2.99662i) q^{9} +(1.99727 - 5.65090i) q^{10} +(-2.16538 - 1.08750i) q^{11} +(-3.28269 - 1.10631i) q^{12} +(-1.41601 + 3.28267i) q^{13} +(-2.06407 + 3.20295i) q^{14} +(-7.22204 + 1.31332i) q^{15} +(2.26728 - 3.29536i) q^{16} +(0.283793 - 0.338211i) q^{17} +(0.820255 + 4.16259i) q^{18} +(4.04034 + 4.81510i) q^{19} +(0.826787 - 8.43563i) q^{20} +(4.66027 + 0.246420i) q^{21} +(-3.34167 - 0.759141i) q^{22} +(4.73909 - 5.02315i) q^{23} +(-4.88211 - 0.406251i) q^{24} +(-5.13354 - 11.9009i) q^{25} +(-0.831463 + 4.98705i) q^{26} +(3.92636 - 3.40348i) q^{27} +(-1.74827 + 5.09726i) q^{28} +(-0.676913 + 5.79136i) q^{29} +(-9.47063 + 4.25117i) q^{30} +(-0.147962 + 0.624300i) q^{31} +(1.99596 - 5.29303i) q^{32} +(1.22520 + 4.01416i) q^{33} +(0.275004 - 0.560556i) q^{34} +(1.98285 + 11.2453i) q^{35} +(2.53716 + 5.43717i) q^{36} +(0.533400 - 3.02506i) q^{37} +(7.17949 + 5.24156i) q^{38} +(5.80733 - 2.14895i) q^{39} +(-1.72419 - 11.8623i) q^{40} +(-2.82019 + 2.09956i) q^{41} +(6.48204 - 1.24132i) q^{42} +(3.43227 - 0.199907i) q^{43} +(-4.84541 + 0.0904070i) q^{44} +(10.2789 + 7.48277i) q^{45} +(4.80408 - 8.50311i) q^{46} +(-2.24434 + 0.531918i) q^{47} +(-6.84079 + 1.09707i) q^{48} +(0.0150955 - 0.259180i) q^{49} +(-11.0823 - 14.5997i) q^{50} +(-0.763163 + 0.0485474i) q^{51} +(0.548829 + 7.12901i) q^{52} +(10.1282 + 5.84749i) q^{53} +(4.23721 - 6.00383i) q^{54} +(-8.89345 + 5.13464i) q^{55} +(-0.672584 + 7.59109i) q^{56} +(1.20604 - 10.8201i) q^{57} +(1.03365 + 8.18093i) q^{58} +(-0.765520 + 0.384459i) q^{59} +(-11.5621 + 9.04700i) q^{60} +(-1.96293 + 6.55663i) q^{61} +(0.00846371 + 0.907313i) q^{62} +(-5.26168 - 6.13607i) q^{63} +(0.946296 - 7.94384i) q^{64} +(8.32571 + 12.6586i) q^{65} +(3.04284 + 5.09611i) q^{66} +(0.666987 + 5.70644i) q^{67} +(0.187571 - 0.862854i) q^{68} +(-11.9611 + 0.0639941i) q^{69} +(6.53418 + 14.7676i) q^{70} +(0.181994 - 0.0662404i) q^{71} +(5.32650 + 6.60518i) q^{72} +(-10.7793 - 3.92333i) q^{73} +(-0.293028 - 4.33419i) q^{74} +(-8.78115 + 20.6602i) q^{75} +(11.6341 + 4.76304i) q^{76} +(6.25451 - 1.87248i) q^{77} +(7.24500 - 4.91895i) q^{78} +(-4.29936 - 3.20076i) q^{79} +(-6.38817 - 15.7024i) q^{80} +(-8.95946 - 0.853310i) q^{81} +(-3.16043 + 3.83861i) q^{82} +(-4.40395 + 5.91553i) q^{83} +(8.47902 - 3.90149i) q^{84} +(-0.536638 - 1.79250i) q^{85} +(4.64472 - 1.43788i) q^{86} +(8.06843 - 6.07408i) q^{87} +(-6.62206 + 1.76654i) q^{88} +(-0.733774 + 2.01603i) q^{89} +(16.6492 + 6.78961i) q^{90} +(-3.29451 - 9.05160i) q^{91} +(3.71373 - 13.3031i) q^{92} +(0.959406 - 0.560778i) q^{93} +(-2.90116 + 1.49106i) q^{94} +(26.4587 - 3.09258i) q^{95} +(-9.02048 + 3.82504i) q^{96} +(5.05121 - 3.32223i) q^{97} +(-0.0671263 - 0.360969i) q^{98} +(3.56712 - 6.33400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{54}\right)$

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 $

$2$	1.37299	−	0.338962i	0.970851	−	0.239682i
$2$	1.37299	−	0.338962i	0.970851	−	0.239682i
$3$	−1.19533	−	1.25347i	−0.690123	−	0.723692i
$3$	−1.19533	−	1.25347i	−0.690123	−	0.723692i
$4$	1.77021	−	0.930784i	0.885105	−	0.465392i
$5$	2.32883	−	3.54082i	1.04149	−	1.58350i	0.253967	−	0.967213i	$-0.418265\pi$
$5$	2.32883	−	3.54082i	1.04149	−	1.58350i	0.787519	−	0.616290i	$-0.211365\pi$
$6$	−2.06605	−	1.31583i	−0.843463	−	0.537187i
$7$	−1.95981	+	1.84899i	−0.740739	+	0.698852i	−0.960987	−	0.276592i	$-0.910795\pi$
$7$	−1.95981	+	1.84899i	−0.740739	+	0.698852i	0.220248	+	0.975444i	$0.429313\pi$
$8$	2.11498	−	1.87799i	0.747759	−	0.663970i
$9$	−0.142379	+	2.99662i	−0.0474596	+	0.998873i
$10$	1.99727	−	5.65090i	0.631591	−	1.78697i
$11$	−2.16538	−	1.08750i	−0.652888	−	0.327893i	0.0913387	−	0.995820i	$-0.470885\pi$
$11$	−2.16538	−	1.08750i	−0.652888	−	0.327893i	−0.744227	+	0.667927i	$0.767182\pi$
$12$	−3.28269	−	1.10631i	−0.947632	−	0.319365i
$13$	−1.41601	+	3.28267i	−0.392729	+	0.910449i	0.601063	+	0.799201i	$0.294744\pi$
$13$	−1.41601	+	3.28267i	−0.392729	+	0.910449i	−0.993793	+	0.111248i	$0.964515\pi$
$14$	−2.06407	+	3.20295i	−0.551646	+	0.856023i
$15$	−7.22204	+	1.31332i	−1.86472	+	0.339097i
$16$	2.26728	−	3.29536i	0.566821	−	0.823841i
$17$	0.283793	−	0.338211i	0.0688298	−	0.0820282i	−0.730531	−	0.682880i	$-0.760727\pi$
$17$	0.283793	−	0.338211i	0.0688298	−	0.0820282i	0.799361	+	0.600852i	$0.205172\pi$
$18$	0.820255	+	4.16259i	0.193336	+	0.981133i
$19$	4.04034	+	4.81510i	0.926919	+	1.10466i	0.994267	+	0.106929i	$0.0341018\pi$
$19$	4.04034	+	4.81510i	0.926919	+	1.10466i	−0.0673480	+	0.997730i	$0.521454\pi$
$20$	0.826787	−	8.43563i	0.184875	−	1.88627i
$21$	4.66027	+	0.246420i	1.01695	+	0.0537732i
$22$	−3.34167	−	0.759141i	−0.712447	−	0.161849i
$23$	4.73909	−	5.02315i	0.988170	−	1.04740i	−0.0107037	−	0.999943i	$-0.503407\pi$
$23$	4.73909	−	5.02315i	0.988170	−	1.04740i	0.998873	−	0.0474559i	$-0.0151113\pi$
$24$	−4.88211	−	0.406251i	−0.996556	−	0.0829256i
$25$	−5.13354	−	11.9009i	−1.02671	−	2.38018i
$26$	−0.831463	+	4.98705i	−0.163063	+	0.978041i
$27$	3.92636	−	3.40348i	0.755629	−	0.655000i
$28$	−1.74827	+	5.09726i	−0.330392	+	0.963291i
$29$	−0.676913	+	5.79136i	−0.125699	+	1.07543i	0.772247	+	0.635323i	$0.219133\pi$
$29$	−0.676913	+	5.79136i	−0.125699	+	1.07543i	−0.897946	+	0.440105i	$0.854941\pi$
$30$	−9.47063	+	4.25117i	−1.72909	+	0.776154i
$31$	−0.147962	+	0.624300i	−0.0265747	+	0.112128i	−0.984716	−	0.174169i	$-0.944276\pi$
$31$	−0.147962	+	0.624300i	−0.0265747	+	0.112128i	0.958141	+	0.286297i	$0.0924243\pi$
$32$	1.99596	−	5.29303i	0.352839	−	0.935684i
$33$	1.22520	+	4.01416i	0.213280	+	0.698776i
$34$	0.275004	−	0.560556i	0.0471628	−	0.0961345i
$35$	1.98285	+	11.2453i	0.335164	+	1.90081i
$36$	2.53716	+	5.43717i	0.422861	+	0.906195i
$37$	0.533400	−	3.02506i	0.0876905	−	0.497317i	−0.909053	−	0.416680i	$-0.863193\pi$
$37$	0.533400	−	3.02506i	0.0876905	−	0.497317i	0.996744	−	0.0806370i	$-0.0256955\pi$
$38$	7.17949	+	5.24156i	1.16467	+	0.850293i
$39$	5.80733	−	2.14895i	0.929916	−	0.344107i
$40$	−1.72419	−	11.8623i	−0.272618	−	1.87559i
$41$	−2.82019	+	2.09956i	−0.440440	+	0.327895i	−0.794432	−	0.607353i	$-0.792231\pi$
$41$	−2.82019	+	2.09956i	−0.440440	+	0.327895i	0.353992	+	0.935248i	$0.384824\pi$
$42$	6.48204	−	1.24132i	1.00020	−	0.191540i
$43$	3.43227	−	0.199907i	0.523417	−	0.0304856i	0.205597	−	0.978637i	$-0.434086\pi$
$43$	3.43227	−	0.199907i	0.523417	−	0.0304856i	0.317820	+	0.948151i	$0.397049\pi$
$44$	−4.84541	+	0.0904070i	−0.730473	+	0.0136294i
$45$	10.2789	+	7.48277i	1.53229	+	1.11547i
$46$	4.80408	−	8.50311i	0.708323	−	1.25372i
$47$	−2.24434	+	0.531918i	−0.327370	+	0.0775882i	−0.391015	−	0.920384i	$-0.627876\pi$
$47$	−2.24434	+	0.531918i	−0.327370	+	0.0775882i	0.0636443	+	0.997973i	$0.479728\pi$
$48$	−6.84079	+	1.09707i	−0.987383	+	0.158348i
$49$	0.0150955	−	0.259180i	0.00215651	−	0.0370258i
$50$	−11.0823	−	14.5997i	−1.56727	−	2.06471i
$51$	−0.763163	+	0.0485474i	−0.106864	+	0.00679799i
$52$	0.548829	+	7.12901i	0.0761089	+	0.988616i
$53$	10.1282	+	5.84749i	1.39121	+	0.803215i	0.993449	−	0.114274i	$-0.0364543\pi$
$53$	10.1282	+	5.84749i	1.39121	+	0.803215i	0.397760	+	0.917490i	$0.369788\pi$
$54$	4.23721	−	6.00383i	0.576612	−	0.817018i
$55$	−8.89345	+	5.13464i	−1.19919	+	0.692354i
$56$	−0.672584	+	7.59109i	−0.0898779	+	1.01440i
$57$	1.20604	−	10.8201i	0.159744	−	1.43315i
$58$	1.03365	+	8.18093i	0.135726	+	1.07421i
$59$	−0.765520	+	0.384459i	−0.0996623	+	0.0500523i	−0.497932	−	0.867216i	$-0.665907\pi$
$59$	−0.765520	+	0.384459i	−0.0996623	+	0.0500523i	0.398270	+	0.917268i	$0.369611\pi$
$60$	−11.5621	+	9.04700i	−1.49266	+	1.16796i
$61$	−1.96293	+	6.55663i	−0.251327	+	0.839490i	0.735474	+	0.677553i	$0.236959\pi$
$61$	−1.96293	+	6.55663i	−0.251327	+	0.839490i	−0.986801	+	0.161938i	$0.948226\pi$
$62$	0.00846371	+	0.907313i	0.00107489	+	0.115229i
$63$	−5.26168	−	6.13607i	−0.662909	−	0.773072i
$64$	0.946296	−	7.94384i	0.118287	−	0.992979i
$65$	8.32571	+	12.6586i	1.03268	+	1.57011i
$66$	3.04284	+	5.09611i	0.374547	+	0.627288i
$67$	0.666987	+	5.70644i	0.0814855	+	0.697153i	0.970806	+	0.239868i	$0.0771040\pi$
$67$	0.666987	+	5.70644i	0.0814855	+	0.697153i	−0.889320	+	0.457285i	$0.848822\pi$
$68$	0.187571	−	0.862854i	0.0227464	−	0.104636i
$69$	−11.9611	+	0.0639941i	−1.43995	+	0.00770399i
$70$	6.53418	+	14.7676i	0.780984	+	1.76507i
$71$	0.181994	−	0.0662404i	0.0215987	−	0.00786128i	−0.331198	−	0.943561i	$-0.607453\pi$
$71$	0.181994	−	0.0662404i	0.0215987	−	0.00786128i	0.352797	+	0.935700i	$0.385231\pi$
$72$	5.32650	+	6.60518i	0.627734	+	0.778428i
$73$	−10.7793	−	3.92333i	−1.26162	−	0.459191i	−0.377305	−	0.926089i	$-0.623149\pi$
$73$	−10.7793	−	3.92333i	−1.26162	−	0.459191i	−0.884311	+	0.466898i	$0.845372\pi$
$74$	−0.293028	−	4.33419i	−0.0340638	−	0.503839i
$75$	−8.78115	+	20.6602i	−1.01396	+	2.38564i
$76$	11.6341	+	4.76304i	1.33452	+	0.546358i
$77$	6.25451	−	1.87248i	0.712768	−	0.213389i
$78$	7.24500	−	4.91895i	0.820334	−	0.556961i
$79$	−4.29936	−	3.20076i	−0.483716	−	0.360113i	0.327508	−	0.944848i	$-0.393791\pi$
$79$	−4.29936	−	3.20076i	−0.483716	−	0.360113i	−0.811224	+	0.584735i	$0.801198\pi$
$80$	−6.38817	−	15.7024i	−0.714219	−	1.75558i
$81$	−8.95946	−	0.853310i	−0.995495	−	0.0948122i
$82$	−3.16043	+	3.83861i	−0.349011	+	0.423903i
$83$	−4.40395	+	5.91553i	−0.483396	+	0.649313i	−0.975183	−	0.221402i	$-0.928937\pi$
$83$	−4.40395	+	5.91553i	−0.483396	+	0.649313i	0.491787	+	0.870716i	$0.336344\pi$
$84$	8.47902	−	3.90149i	0.925137	−	0.425687i
$85$	−0.536638	−	1.79250i	−0.0582066	−	0.194424i
$86$	4.64472	−	1.43788i	0.500853	−	0.155051i
$87$	8.06843	−	6.07408i	0.865027	−	0.651210i
$88$	−6.62206	+	1.76654i	−0.705914	+	0.188313i
$89$	−0.733774	+	2.01603i	−0.0777799	+	0.213698i	−0.972488	−	0.232953i	$-0.925161\pi$
$89$	−0.733774	+	2.01603i	−0.0777799	+	0.213698i	0.894708	+	0.446651i	$0.147383\pi$
$90$	16.6492	+	6.78961i	1.75498	+	0.715688i
$91$	−3.29451	−	9.05160i	−0.345359	−	0.948865i
$92$	3.71373	−	13.3031i	0.387183	−	1.38694i
$93$	0.959406	−	0.560778i	0.0994857	−	0.0581500i
$94$	−2.90116	+	1.49106i	−0.299232	+	0.153792i
$95$	26.4587	−	3.09258i	2.71460	−	0.317292i
$96$	−9.02048	+	3.82504i	−0.920649	+	0.390391i
$97$	5.05121	−	3.32223i	0.512872	−	0.337321i	−0.266549	−	0.963821i	$-0.585883\pi$
$97$	5.05121	−	3.32223i	0.512872	−	0.337321i	0.779421	+	0.626500i	$0.215513\pi$
$98$	−0.0671263	−	0.360969i	−0.00678078	−	0.0364634i
$99$	3.56712	−	6.33400i	0.358509	−	0.636591i
$100$	−20.1646	−	16.2888i	−2.01646	−	1.62888i
$101$	−9.86726	−	2.95406i	−0.981829	−	0.293940i	−0.244631	−	0.969616i	$-0.578667\pi$
$101$	−9.86726	−	2.95406i	−0.981829	−	0.293940i	−0.737199	+	0.675676i	$0.763852\pi$
$102$	−1.03136	+	0.325338i	−0.102120	+	0.0322133i
$103$	2.65792	+	5.29235i	0.261892	+	0.521471i	0.985696	−	0.168536i	$-0.0539039\pi$
$103$	2.65792	+	5.29235i	0.261892	+	0.521471i	−0.723803	+	0.690007i	$0.757608\pi$
$104$	3.17000	+	9.60204i	0.310844	+	0.941557i
$105$	11.7255	−	15.9273i	1.14429	−	1.55435i
$106$	15.8879	+	4.59550i	1.54317	+	0.446354i
$107$	−0.376903	−	0.652815i	−0.0364366	−	0.0631100i	0.847232	−	0.531223i	$-0.178267\pi$
$107$	−0.376903	−	0.652815i	−0.0364366	−	0.0631100i	−0.883669	+	0.468113i	$0.844934\pi$
$108$	3.78259	−	9.67946i	0.363980	−	0.931407i
$109$	5.31966	−	9.21391i	0.509531	−	0.882533i	−0.490408	−	0.871493i	$-0.663152\pi$
$109$	5.31966	−	9.21391i	0.509531	−	0.882533i	0.999939	−	0.0110402i	$-0.00351428\pi$
$110$	−10.4702	+	10.0644i	−0.998293	+	0.959598i
$111$	−4.42942	+	2.94734i	−0.420422	+	0.279749i
$112$	1.64964	+	10.6505i	0.155876	+	1.00638i
$113$	−7.35894	−	0.428609i	−0.692270	−	0.0403202i	−0.291597	−	0.956541i	$-0.594187\pi$
$113$	−7.35894	−	0.428609i	−0.692270	−	0.0403202i	−0.400673	+	0.916221i	$0.631224\pi$
$114$	−2.01171	−	15.2647i	−0.188414	−	1.42967i
$115$	−6.74950	−	28.4784i	−0.629394	−	2.65562i
$116$	4.19222	+	10.8820i	0.389238	+	1.01037i
$117$	−9.63531	−	4.71061i	−0.890784	−	0.435496i
$118$	−0.920736	+	0.787341i	−0.0847606	+	0.0724806i
$119$	0.0691674	+	1.18756i	0.00634057	+	0.108863i
$120$	−12.8081	+	16.3406i	−1.16921	+	1.49168i
$121$	−3.06251	−	4.11366i	−0.278410	−	0.373969i
$122$	−0.472632	+	9.66755i	−0.0427901	+	0.875259i
$123$	6.00279	+	1.02537i	0.541253	+	0.0924545i
$124$	0.319165	+	1.24286i	0.0286619	+	0.111612i
$125$	−33.2259	−	5.85861i	−2.97181	−	0.524010i
$126$	−9.30413	−	6.64126i	−0.828878	−	0.591650i
$127$	−9.25450	+	1.63182i	−0.821204	+	0.144800i	−0.568437	−	0.822727i	$-0.692452\pi$
$127$	−9.25450	+	1.63182i	−0.821204	+	0.144800i	−0.252767	+	0.967527i	$0.581341\pi$
$128$	−1.39340	−	11.2276i	−0.123161	−	0.992387i
$129$	−4.35327	−	4.06330i	−0.383284	−	0.357754i
$130$	15.7219	+	14.5581i	1.37890	+	1.27683i
$131$	9.00201	+	2.13352i	0.786510	+	0.186406i	0.604198	−	0.796835i	$-0.293494\pi$
$131$	9.00201	+	2.13352i	0.786510	+	0.186406i	0.182312	+	0.983241i	$0.441642\pi$
$132$	5.90518	+	5.96551i	0.513980	+	0.519231i
$133$	−16.8214	−	1.96614i	−1.45860	−	0.170486i
$134$	2.85003	+	7.60881i	0.246205	+	0.657301i
$135$	−2.90725	−	21.8287i	−0.250216	−	1.87871i
$136$	−0.0349409	−	1.24827i	−0.00299616	−	0.107038i
$137$	16.0001	−	6.90179i	1.36698	−	0.589659i	0.419003	−	0.907985i	$-0.362380\pi$
$137$	16.0001	−	6.90179i	1.36698	−	0.589659i	0.947981	+	0.318325i	$0.103120\pi$
$138$	−16.4009	+	4.14224i	−1.39613	+	0.352611i
$139$	7.79886	+	7.35785i	0.661491	+	0.624084i	0.941939	−	0.335785i	$-0.109001\pi$
$139$	7.79886	+	7.35785i	0.661491	+	0.624084i	−0.280448	+	0.959869i	$0.590483\pi$
$140$	13.9770	+	18.0610i	1.18128	+	1.52643i
$141$	3.34947	+	2.17740i	0.282076	+	0.183370i
$142$	0.227423	−	0.152636i	0.0190849	−	0.0128090i
$143$	6.63609	−	5.56834i	0.554938	−	0.465648i
$144$	9.55214	+	7.26338i	0.796012	+	0.605281i
$145$	18.9297	+	15.8839i	1.57203	+	1.31909i
$146$	−16.1297	−	1.73294i	−1.33490	−	0.143419i
$147$	−0.342919	+	0.290884i	−0.0282835	+	0.0239917i
$148$	−1.87145	−	5.85148i	−0.153832	−	0.480988i
$149$	14.6030	+	6.29913i	1.19633	+	0.516045i	0.898669	−	0.438628i	$-0.144536\pi$
$149$	14.6030	+	6.29913i	1.19633	+	0.516045i	0.297657	+	0.954673i	$0.403795\pi$
$150$	−5.05341	+	31.3428i	−0.412609	+	2.55913i
$151$	−10.4825	+	20.8724i	−0.853054	+	1.69857i	−0.148508	+	0.988911i	$0.547447\pi$
$151$	−10.4825	+	20.8724i	−0.853054	+	1.69857i	−0.704546	+	0.709659i	$0.748849\pi$
$152$	17.5880	+	2.59611i	1.42657	+	0.210572i
$153$	0.973084	+	0.898573i	0.0786691	+	0.0726453i
$154$	7.95269	−	4.69094i	0.640846	−	0.378007i
$155$	1.86596	+	1.97780i	0.149877	+	0.158861i
$156$	8.27998	−	9.20945i	0.662929	−	0.737346i
$157$	−9.75582	−	6.41650i	−0.778599	−	0.512093i	0.0969108	−	0.995293i	$-0.469104\pi$
$157$	−9.75582	−	6.41650i	−0.778599	−	0.512093i	−0.875510	+	0.483201i	$0.839474\pi$
$158$	−6.98792	−	2.93729i	−0.555929	−	0.233678i
$159$	−4.77681	−	19.6850i	−0.378826	−	1.56112i
$160$	−14.0934	−	19.3939i	−1.11418	−	1.53322i
$161$			18.6070i			1.46643i
$162$	−12.5905	+	1.86533i	−0.989203	+	0.146554i
$163$		−	19.3521i		−	1.51577i	−0.652388	−	0.757885i	$-0.726233\pi$
$163$		−	19.3521i		−	1.51577i	0.652388	−	0.757885i	$-0.273767\pi$
$164$	−3.03810	+	6.34164i	−0.237236	+	0.495199i
$165$	17.0667	+	5.01010i	1.32864	+	0.390036i
$166$	−4.04144	+	9.61474i	−0.313677	+	0.746248i
$167$	−10.2700	−	6.75472i	−0.794720	−	0.522696i	0.0860211	−	0.996293i	$-0.472585\pi$
$167$	−10.2700	−	6.75472i	−0.794720	−	0.522696i	−0.880741	+	0.473598i	$0.842955\pi$
$168$	10.3192	−	8.23078i	0.796141	−	0.635018i
$169$	0.150284	+	0.159292i	0.0115603	+	0.0122532i
$170$	−1.34439	−	2.27918i	−0.103110	−	0.174805i
$171$	−15.0043	+	11.4218i	−1.14741	+	0.873448i
$172$	5.88977	−	3.54858i	0.449091	−	0.270577i
$173$	−4.27319	+	8.50863i	−0.324885	+	0.646899i	−0.995485	−	0.0949201i	$-0.969740\pi$
$173$	−4.27319	+	8.50863i	−0.324885	+	0.646899i	0.670600	+	0.741819i	$0.266037\pi$
$174$	9.01900	−	11.0746i	0.683729	−	0.839560i
$175$	32.0654	+	13.8316i	2.42391	+	1.04557i
$176$	−8.49324	+	4.67007i	−0.640202	+	0.352019i
$177$	1.39696	+	0.500003i	0.105002	+	0.0375825i
$178$	−0.324108	+	3.01671i	−0.0242930	+	0.226112i
$179$	−8.70936	−	7.30802i	−0.650968	−	0.546227i	0.256396	−	0.966572i	$-0.417465\pi$
$179$	−8.70936	−	7.30802i	−0.650968	−	0.546227i	−0.907365	+	0.420344i	$0.861909\pi$
$180$	25.1607	+	3.67862i	1.87537	+	0.274188i
$181$	−16.0159	+	13.4390i	−1.19046	+	0.998911i	−0.190604	+	0.981667i	$0.561045\pi$
$181$	−16.0159	+	13.4390i	−1.19046	+	0.998911i	−0.999851	+	0.0172439i	$0.994511\pi$
$182$	−7.59148	−	11.3110i	−0.562718	−	0.838431i
$183$	10.5649	−	5.37686i	0.780979	−	0.397469i
$184$	0.589672	−	19.5238i	0.0434712	−	1.43932i
$185$	−9.46901	−	8.93355i	−0.696175	−	0.656807i
$186$	1.12717	−	1.09515i	0.0826483	−	0.0803000i
$187$	−0.982324	+	0.423733i	−0.0718346	+	0.0309864i
$188$	−3.47785	+	3.03060i	−0.253648	+	0.221029i
$189$	−1.40195	+	13.9300i	−0.101977	+	1.01326i
$190$	35.2793	−	13.2146i	2.55943	−	0.958685i
$191$	−22.2613	−	2.60197i	−1.61077	−	0.188272i	−0.737445	−	0.675407i	$-0.763968\pi$
$191$	−22.2613	−	2.60197i	−1.61077	−	0.188272i	−0.873327	+	0.487135i	$0.838042\pi$
$192$	−11.0885	+	8.30934i	−0.800244	+	0.599675i
$193$	11.3546	+	2.69108i	0.817319	+	0.193708i	0.617951	−	0.786217i	$-0.287963\pi$
$193$	11.3546	+	2.69108i	0.817319	+	0.193708i	0.199368	+	0.979925i	$0.436111\pi$
$194$	5.80915	−	6.27356i	0.417073	−	0.450415i
$195$	5.91526	−	25.5672i	0.423600	−	1.83091i
$196$	−0.214519	−	0.472854i	−0.0153228	−	0.0337753i
$197$	−15.6130	+	2.75300i	−1.11238	+	0.196143i	−0.699494	−	0.714638i	$-0.746591\pi$
$197$	−15.6130	+	2.75300i	−1.11238	+	0.196143i	−0.412889	+	0.910781i	$0.635480\pi$
$198$	2.75064	−	9.90564i	0.195479	−	0.703963i
$199$	−13.9606	−	2.46164i	−0.989644	−	0.174501i	−0.344685	−	0.938718i	$-0.612014\pi$
$199$	−13.9606	−	2.46164i	−0.989644	−	0.174501i	−0.644959	+	0.764218i	$0.723125\pi$
$200$	−33.2071	−	15.5294i	−2.34810	−	1.09810i
$201$	6.35559	−	7.65712i	0.448289	−	0.540092i
$202$	−14.5490	−	0.711277i	−1.02366	−	0.0500453i
$203$	−9.38153	−	12.6016i	−0.658454	−	0.884457i
$204$	−1.30577	+	0.796279i	−0.0914223	+	0.0557507i
$205$	0.866388	+	14.8753i	0.0605112	+	1.03894i
$206$	5.44320	+	6.36542i	0.379246	+	0.443500i
$207$	14.3777	+	14.9165i	0.999320	+	1.03677i
$208$	7.60711	+	12.1090i	0.527458	+	0.839608i
$209$	−3.51250	−	14.8204i	−0.242965	−	1.02515i
$210$	10.7003	−	25.8426i	0.738390	−	1.78331i
$211$	−0.720919	−	0.0419888i	−0.0496301	−	0.00289063i	0.0333118	−	0.999445i	$-0.489395\pi$
$211$	−0.720919	−	0.0419888i	−0.0496301	−	0.00289063i	−0.0829419	+	0.996554i	$0.526432\pi$
$212$	23.3717	+	0.924167i	1.60518	+	0.0634720i
$213$	−0.300573	−	0.148945i	−0.0205949	−	0.0102055i
$214$	−0.738764	−	0.768553i	−0.0505008	−	0.0525372i
$215$	7.28536	−	12.6186i	0.496857	−	0.860582i
$216$	1.91249	−	14.5720i	0.130128	−	0.991497i
$217$	−0.864346	−	1.49709i	−0.0586756	−	0.101629i
$218$	4.18067	−	14.4538i	0.283151	−	0.978934i
$219$	7.96698	+	18.2012i	0.538358	+	1.22992i
$220$	−10.9640	+	17.3673i	−0.739195	+	1.17090i
$221$	0.708383	+	1.41051i	0.0476510	+	0.0948810i
$222$	−5.08251	+	5.54808i	−0.341116	+	0.372363i
$223$	21.3043	+	6.37810i	1.42664	+	0.427109i	0.904765	−	0.425910i	$-0.140046\pi$
$223$	21.3043	+	6.37810i	1.42664	+	0.427109i	0.521879	+	0.853020i	$0.325231\pi$
$224$	5.87504	+	14.0638i	0.392543	+	0.939680i
$225$	36.3933	−	13.6888i	2.42622	−	0.912589i
$226$	−10.2490	+	1.90592i	−0.681756	+	0.126780i
$227$	7.46820	−	4.91191i	0.495682	−	0.326015i	−0.276934	−	0.960889i	$-0.589318\pi$
$227$	7.46820	−	4.91191i	0.495682	−	0.326015i	0.772616	+	0.634874i	$0.218948\pi$
$228$	−7.93620	−	20.2764i	−0.525588	−	1.34284i
$229$	−4.54920	+	0.531725i	−0.300620	+	0.0351374i	−0.265066	−	0.964230i	$-0.585394\pi$
$229$	−4.54920	+	0.531725i	−0.300620	+	0.0351374i	−0.0355539	+	0.999368i	$0.511320\pi$
$230$	−18.9201	−	36.8127i	−1.24755	−	2.42736i
$231$	−9.82330	−	5.60162i	−0.646326	−	0.368560i
$232$	9.44446	+	13.5198i	0.620059	+	0.887622i
$233$	−5.98028	−	16.4307i	−0.391781	−	1.07641i	−0.966188	−	0.257840i	$-0.916989\pi$
$233$	−5.98028	−	16.4307i	−0.391781	−	1.07641i	0.574406	−	0.818570i	$-0.305233\pi$
$234$	−14.8259	−	3.20163i	−0.969200	−	0.209297i
$235$	−3.34327	+	9.18555i	−0.218091	+	0.599199i
$236$	−0.997284	+	1.39311i	−0.0649176	+	0.0906835i
$237$	1.12710	+	9.21508i	0.0732127	+	0.598584i
$238$	0.497504	+	1.60706i	0.0322484	+	0.104170i
$239$	−0.908258	−	3.03379i	−0.0587503	−	0.196240i	0.923576	−	0.383415i	$-0.125252\pi$
$239$	−0.908258	−	3.03379i	−0.0587503	−	0.196240i	−0.982327	+	0.187175i	$0.940067\pi$
$240$	−12.0465	+	26.7769i	−0.777601	+	1.72844i
$241$	−6.16193	+	8.27691i	−0.396925	+	0.533162i	−0.954991	−	0.296634i	$-0.904136\pi$
$241$	−6.16193	+	8.27691i	−0.396925	+	0.533162i	0.558067	+	0.829796i	$0.311543\pi$
$242$	−5.59917	−	4.60994i	−0.359928	−	0.296338i
$243$	9.63990	+	12.2504i	0.618400	+	0.785864i
$244$	2.62801	+	13.4337i	0.168241	+	0.860002i
$245$	−0.882556	−	0.657039i	−0.0563844	−	0.0419767i
$246$	8.58934	−	0.626893i	0.547636	−	0.0399692i
$247$	−21.5275	+	6.44492i	−1.36976	+	0.410080i
$248$	0.859494	+	1.59826i	0.0545779	+	0.101489i
$249$	12.6791	−	1.55078i	0.803506	−	0.0982767i
$250$	−47.6046	+	3.21848i	−3.01078	+	0.203554i
$251$	−10.5117	−	3.82596i	−0.663495	−	0.241492i	−0.0117502	−	0.999931i	$-0.503740\pi$
$251$	−10.5117	−	3.82596i	−0.663495	−	0.241492i	−0.651744	+	0.758439i	$0.725963\pi$
$252$	−15.0256	−	5.96464i	−0.946525	−	0.375737i
$253$	−15.7246	+	5.72329i	−0.988598	+	0.359820i
$254$	−12.1532	+	5.37739i	−0.762561	+	0.337408i
$255$	−1.60538	+	2.81528i	−0.100533	+	0.176300i
$256$	−5.71885	−	14.9431i	−0.357428	−	0.933941i
$257$	−2.87632	−	24.6085i	−0.179420	−	1.53504i	−0.720137	−	0.693832i	$-0.755921\pi$
$257$	−2.87632	−	24.6085i	−0.179420	−	1.53504i	0.540717	−	0.841205i	$-0.318153\pi$
$258$	−7.35431	−	4.10328i	−0.457859	−	0.255459i
$259$	4.54794	+	6.91481i	0.282595	+	0.429665i
$260$	26.5207	+	14.6590i	1.64474	+	0.909111i
$261$	−17.2581	−	2.85302i	−1.06825	−	0.176597i
$262$	13.0829	−	0.122041i	0.808262	−	0.00753974i
$263$	−3.12233	+	10.4293i	−0.192531	+	0.643099i	0.806148	+	0.591714i	$0.201549\pi$
$263$	−3.12233	+	10.4293i	−0.192531	+	0.643099i	−0.998679	+	0.0513847i	$0.983637\pi$
$264$	10.1298	+	6.18896i	0.623448	+	0.380904i
$265$	44.2917	−	22.2441i	2.72082	−	1.36645i
$266$	−23.7620	+	3.00232i	−1.45694	+	0.184084i
$267$	3.40413	−	1.49005i	0.208330	−	0.0911896i
$268$	6.49217	+	9.48077i	0.396572	+	0.579130i
$269$	4.98899	−	2.88040i	0.304184	−	0.175621i	−0.340137	−	0.940376i	$-0.610473\pi$
$269$	4.98899	−	2.88040i	0.304184	−	0.175621i	0.644321	+	0.764755i	$0.277140\pi$
$270$	−11.3907	−	28.9851i	−0.693217	−	1.76398i
$271$	4.04771	+	2.33695i	0.245881	+	0.141960i	0.617877	−	0.786275i	$-0.287993\pi$
$271$	4.04771	+	2.33695i	0.245881	+	0.141960i	−0.371996	+	0.928234i	$0.621326\pi$
$272$	−0.471090	−	1.70202i	−0.0285640	−	0.103200i
$273$	−7.40789	+	14.9492i	−0.448346	+	0.904767i
$274$	19.6286	−	14.8995i	1.18581	−	0.900114i
$275$	−1.82609	+	31.3527i	−0.110117	+	1.89064i
$276$	−21.1142	+	11.2465i	−1.27092	+	0.676961i
$277$	8.24059	−	1.95306i	0.495129	−	0.117348i	0.0245375	−	0.999699i	$-0.492189\pi$
$277$	8.24059	−	1.95306i	0.495129	−	0.117348i	0.470592	+	0.882351i	$0.344041\pi$
$278$	13.2018	+	7.45874i	0.791791	+	0.447346i
$279$	−1.84972	−	0.532273i	−0.110740	−	0.0318663i
$280$	25.3123	+	20.0599i	1.51270	+	1.19881i
$281$	8.20007	−	0.477599i	0.489175	−	0.0284912i	0.188215	−	0.982128i	$-0.439730\pi$
$281$	8.20007	−	0.477599i	0.489175	−	0.0284912i	0.300960	+	0.953637i	$0.402693\pi$
$282$	5.33684	+	1.85420i	0.317804	+	0.110416i
$283$	15.0730	−	11.2214i	0.895995	−	0.667044i	−0.0473424	−	0.998879i	$-0.515075\pi$
$283$	15.0730	−	11.2214i	0.895995	−	0.667044i	0.943337	+	0.331835i	$0.107668\pi$
$284$	0.260512	−	0.286656i	0.0154585	−	0.0170099i
$285$	−35.5033	−	29.4685i	−2.10303	−	1.74557i
$286$	7.22384	−	9.89467i	0.427155	−	0.585084i
$287$	1.64500	−	9.32923i	0.0971010	−	0.550687i
$288$	15.5770	+	6.73474i	0.917884	+	0.396848i
$289$	2.91817	+	16.5498i	0.171657	+	0.973516i
$290$	31.3744	+	15.3920i	1.84237	+	0.903852i
$291$	−10.2022	−	2.36038i	−0.598062	−	0.138368i
$292$	−22.7333	+	3.08804i	−1.33037	+	0.180714i
$293$	−1.28324	+	5.41443i	−0.0749679	+	0.316314i	−0.997589	−	0.0693921i	$-0.977894\pi$
$293$	−1.28324	+	5.41443i	−0.0749679	+	0.316314i	0.922622	+	0.385706i	$0.126042\pi$
$294$	−0.372226	+	0.515618i	−0.0217087	+	0.0300714i
$295$	−0.421471	+	3.60591i	−0.0245390	+	0.209944i
$296$	−4.55291	−	7.39968i	−0.264633	−	0.430097i
$297$	−12.2034	+	3.09993i	−0.708111	+	0.179876i
$298$	22.1850	+	3.69878i	1.28514	+	0.214264i
$299$	9.77875	+	22.6697i	0.565520	+	1.31102i
$300$	3.68572	+	44.7463i	0.212795	+	2.58343i
$301$	−6.35698	+	6.73801i	−0.366411	+	0.388372i
$302$	−7.31744	+	32.2108i	−0.421071	+	1.85352i
$303$	8.09179	+	15.8994i	0.464861	+	0.913397i
$304$	25.0281	−	2.39722i	1.43546	−	0.137490i
$305$	18.6445	+	22.2197i	1.06758	+	1.27229i
$306$	1.64062	+	0.903894i	0.0937878	+	0.0516722i
$307$	5.70960	−	6.80444i	0.325864	−	0.388350i	−0.578094	−	0.815970i	$-0.696203\pi$
$307$	5.70960	−	6.80444i	0.325864	−	0.388350i	0.903959	+	0.427620i	$0.140648\pi$
$308$	9.32893	−	9.13628i	0.531565	−	0.520588i
$309$	3.45672	−	9.65772i	0.196646	−	0.549408i
$310$	3.23234	+	2.08301i	0.183585	+	0.118307i
$311$	−5.43040	+	12.5891i	−0.307930	+	0.713861i	−0.999968	−	0.00799973i	$-0.997454\pi$
$311$	−5.43040	+	12.5891i	−0.307930	+	0.713861i	0.692038	+	0.721861i	$0.256713\pi$
$312$	8.24668	−	15.4511i	0.466876	−	0.874746i
$313$	−8.26464	−	4.15066i	−0.467145	−	0.234609i	0.199625	−	0.979872i	$-0.436027\pi$
$313$	−8.26464	−	4.15066i	−0.467145	−	0.234609i	−0.666770	+	0.745263i	$0.732324\pi$
$314$	−15.5696	−	5.50295i	−0.878643	−	0.310549i
$315$	−33.9803	+	4.34077i	−1.91457	+	0.244574i
$316$	−10.5900	−	1.66423i	−0.595733	−	0.0936204i
$317$	12.6337	−	11.9193i	0.709582	−	0.669456i	−0.244279	−	0.969705i	$-0.578551\pi$
$317$	12.6337	−	11.9193i	0.709582	−	0.669456i	0.953861	+	0.300249i	$0.0970699\pi$
$318$	−13.2310	−	25.4082i	−0.741957	−	1.42482i
$319$	7.76386	−	11.8044i	0.434693	−	0.660918i
$320$	−25.9239	−	21.8505i	−1.44919	−	1.22148i
$321$	−0.367762	+	1.25276i	−0.0205265	+	0.0699225i
$322$	6.30705	+	25.5472i	0.351478	+	1.42369i
$323$	2.77514			0.154413
$324$	−16.6544	+	6.82878i	−0.925242	+	0.379377i
$325$	46.3358			2.57025
$326$	−6.55961	−	26.5702i	−0.363303	−	1.47159i
$327$	−17.9081	+	4.34562i	−0.990321	+	0.240313i
$328$	−2.02171	+	9.73682i	−0.111630	+	0.537626i
$329$	3.41497	−	5.19221i	0.188274	−	0.286256i
$330$	25.1307	+	1.09386i	1.38340	+	0.0602151i
$331$	−10.6116	+	10.0115i	−0.583265	+	0.550282i	−0.920302	−	0.391210i	$-0.872057\pi$
$331$	−10.6116	+	10.0115i	−0.583265	+	0.550282i	0.337037	+	0.941491i	$0.390575\pi$
$332$	−2.28983	+	14.5708i	−0.125671	+	0.799679i
$333$	8.98902	+	2.02910i	0.492595	+	0.111194i
$334$	−16.3903	−	5.79301i	−0.896836	−	0.316979i
$335$	21.7588	+	10.9277i	1.18881	+	0.597042i
$336$	11.3782	−	14.7986i	0.620732	−	0.807329i
$337$	1.03035	−	2.38863i	0.0561269	−	0.130117i	−0.887845	−	0.460143i	$-0.847798\pi$
$337$	1.03035	−	2.38863i	0.0561269	−	0.130117i	0.943972	+	0.330026i	$0.107058\pi$
$338$	0.260333	+	0.167766i	0.0141602	+	0.00912525i
$339$	8.25910	+	9.73654i	0.448573	+	0.528816i
$340$	−2.61839	−	2.67360i	−0.142002	−	0.144996i
$341$	0.999319	−	1.19094i	0.0541162	−	0.0644931i
$342$	−16.7292	+	20.7679i	−0.904610	+	1.12300i
$343$	−11.6737	−	13.9122i	−0.630321	−	0.751187i
$344$	6.88377	−	6.86858i	0.371148	−	0.370329i
$345$	−27.6289	+	42.5013i	−1.48749	+	2.28819i
$346$	−2.98296	+	13.1307i	−0.160365	+	0.705912i
$347$	22.0987	−	23.4232i	1.18632	−	1.25742i	0.227381	−	0.973806i	$-0.426984\pi$
$347$	22.0987	−	23.4232i	1.18632	−	1.25742i	0.958937	−	0.283618i	$-0.0915347\pi$
$348$	8.62915	−	18.2624i	0.462571	−	0.978966i
$349$	6.89851	+	15.9925i	0.369269	+	0.856061i	0.996983	+	0.0776174i	$0.0247312\pi$
$349$	6.89851	+	15.9925i	0.369269	+	0.856061i	−0.627715	+	0.778444i	$0.716009\pi$
$350$	48.7139	+	8.12179i	2.60387	+	0.434128i
$351$	5.61274	+	17.7083i	0.299586	+	0.945200i
$352$	−10.0782	+	9.29084i	−0.537168	+	0.495204i
$353$	0.425622	−	3.64143i	0.0226536	−	0.193814i	−0.977173	−	0.212446i	$-0.931857\pi$
$353$	0.425622	−	3.64143i	0.0226536	−	0.193814i	0.999826	+	0.0186322i	$0.00593114\pi$
$354$	2.08749	+	0.212984i	0.110949	+	0.0113200i
$355$	0.189288	−	0.798670i	0.0100464	−	0.0423890i
$356$	0.577552	+	4.25178i	0.0306102	+	0.225344i
$357$	1.40589	−	1.50622i	0.0744078	−	0.0797178i
$358$	−14.4350	−	7.08171i	−0.762915	−	0.374280i
$359$	0.601828	+	3.41313i	0.0317633	+	0.180138i	0.996562	−	0.0828512i	$-0.0264026\pi$
$359$	0.601828	+	3.41313i	0.0317633	+	0.180138i	−0.964799	+	0.262990i	$0.915292\pi$
$360$	35.7923	−	3.47780i	1.88642	−	0.183296i
$361$	−3.56144	+	20.1979i	−0.187444	+	1.06305i
$362$	−17.4344	+	23.8804i	−0.916334	+	1.25513i
$363$	−1.49565	+	8.75594i	−0.0785013	+	0.459567i
$364$	−14.2571	−	12.9567i	−0.747273	−	0.679118i
$365$	−38.9949	+	29.0306i	−2.04109	+	1.51953i
$366$	12.6829	−	10.9635i	0.662948	−	0.573070i
$367$	−25.3191	+	1.47467i	−1.32165	+	0.0769772i	−0.704406	−	0.709797i	$-0.748787\pi$
$367$	−25.3191	+	1.47467i	−1.32165	+	0.0769772i	−0.617241	+	0.786774i	$0.711750\pi$
$368$	−5.80823	−	27.0059i	−0.302775	−	1.40778i
$369$	−5.89003	−	8.74997i	−0.306623	−	0.455505i
$370$	−16.0290	−	9.05605i	−0.833308	−	0.470802i
$371$	−30.6612	+	7.26684i	−1.59185	+	0.377276i
$372$	1.17639	−	1.88569i	0.0609928	−	0.0977687i
$373$	0.431879	−	7.41507i	0.0223618	−	0.383938i	−0.968496	−	0.249029i	$-0.919889\pi$
$373$	0.431879	−	7.41507i	0.0223618	−	0.383938i	0.990858	−	0.134909i	$-0.0430743\pi$
$374$	−1.20509	+	0.914752i	−0.0623138	+	0.0473007i
$375$	32.3722	+	48.6506i	1.67169	+	2.51231i
$376$	−3.74780	+	5.33985i	−0.193278	+	0.275382i
$377$	−18.0526	−	10.4227i	−0.929757	−	0.536795i
$378$	2.79687	+	19.6009i	0.143855	+	1.00816i
$379$	10.2416	−	5.91301i	0.526078	−	0.303731i	−0.213340	−	0.976978i	$-0.568434\pi$
$379$	10.2416	−	5.91301i	0.526078	−	0.303731i	0.739418	+	0.673247i	$0.235101\pi$
$380$	43.9589	−	30.1018i	2.25504	−	1.54419i
$381$	13.1076	+	9.64969i	0.671523	+	0.494368i
$382$	−31.4466	+	3.97325i	−1.60895	+	0.203289i
$383$	−11.1897	+	5.61970i	−0.571769	+	0.287153i	−0.711098	−	0.703093i	$-0.751802\pi$
$383$	−11.1897	+	5.61970i	−0.571769	+	0.287153i	0.139329	+	0.990246i	$0.455505\pi$
$384$	−12.4079	+	15.1672i	−0.633186	+	0.774000i
$385$	7.93562	−	26.5068i	0.404436	−	1.35091i
$386$	16.5019	−	0.153935i	0.839923	−	0.00783508i
$387$	0.110363	+	10.3137i	0.00561007	+	0.524274i
$388$	5.84942	−	10.5826i	0.296959	−	0.537251i
$389$	10.1035	+	15.3616i	0.512267	+	0.778865i	0.995310	−	0.0967318i	$-0.0308389\pi$
$389$	10.1035	+	15.3616i	0.512267	+	0.778865i	−0.483043	+	0.875597i	$0.660469\pi$
$390$	−0.544726	−	37.1086i	−0.0275833	−	1.87907i
$391$	−0.353963	−	3.02835i	−0.0179007	−	0.153150i
$392$	−0.454812	−	0.576511i	−0.0229715	−	0.0291182i
$393$	−8.08606	−	13.8340i	−0.407888	−	0.697834i
$394$	−20.5034	+	9.07208i	−1.03295	+	0.457045i
$395$	−21.3458	+	7.76924i	−1.07402	+	0.390913i
$396$	0.418968	−	14.5327i	0.0210539	−	0.730296i
$397$	16.5868	+	6.03710i	0.832468	+	0.302994i	0.722871	−	0.690983i	$-0.242822\pi$
$397$	16.5868	+	6.03710i	0.832468	+	0.302994i	0.109597	+	0.993976i	$0.465044\pi$
$398$	−20.0022	+	1.35232i	−1.00262	+	0.0677857i
$399$	17.6426	+	23.4353i	0.883233	+	1.17323i
$400$	−50.8569	−	10.0658i	−2.54285	−	0.503290i
$401$	9.40006	−	2.81419i	0.469417	−	0.140534i	−0.0433539	−	0.999060i	$-0.513804\pi$
$401$	9.40006	−	2.81419i	0.469417	−	0.140534i	0.512771	+	0.858526i	$0.328619\pi$
$402$	6.13069	−	12.6675i	0.305771	−	0.631796i
$403$	−1.83986	−	1.36972i	−0.0916499	−	0.0682308i
$404$	−20.2167	+	3.95497i	−1.00582	+	0.196767i
$405$	−23.8865	+	29.7366i	−1.18693	+	1.47762i
$406$	−17.1522	−	14.1219i	−0.851250	−	0.700857i
$407$	−4.44476	+	5.97035i	−0.220319	+	0.295939i
$408$	−1.52290	+	1.53589i	−0.0753950	+	0.0760379i
$409$	−5.10598	−	17.0552i	−0.252474	−	0.843323i	−0.986438	−	0.164134i	$-0.947517\pi$
$409$	−5.10598	−	17.0552i	−0.252474	−	0.843323i	0.733964	−	0.679189i	$-0.237668\pi$
$410$	6.23171	+	20.1300i	0.307762	+	0.994150i
$411$	−27.7766	−	11.8058i	−1.37012	−	0.582338i
$412$	9.63110	+	6.89462i	0.474490	+	0.339674i
$413$	0.789417	−	2.16890i	0.0388447	−	0.106725i
$414$	24.7966	+	15.6067i	1.21869	+	0.767025i
$415$	10.6898	+	29.3699i	0.524739	+	1.44171i
$416$	14.5490	+	14.0470i	0.713323	+	0.688712i
$417$	−0.0993563	−	18.5707i	−0.00486550	−	0.909411i
$418$	−9.84618	−	19.1577i	−0.481592	−	0.937032i
$419$	19.8813	−	2.32379i	0.971265	−	0.113525i	0.384363	−	0.923182i	$-0.374421\pi$
$419$	19.8813	−	2.32379i	0.971265	−	0.113525i	0.586903	+	0.809658i	$0.300347\pi$
$420$	5.93176	−	39.1086i	0.289440	−	1.90831i
$421$	15.2430	−	10.0255i	0.742900	−	0.488613i	−0.120764	−	0.992681i	$-0.538534\pi$
$421$	15.2430	−	10.0255i	0.742900	−	0.488613i	0.863664	+	0.504068i	$0.168164\pi$
$422$	−1.00405	+	0.186714i	−0.0488763	+	0.00908910i
$423$	−1.27441	−	6.80116i	−0.0619639	−	0.330684i
$424$	32.4024	−	6.65325i	1.57360	−	0.323110i
$425$	−5.48187	−	1.64116i	−0.265910	−	0.0796082i
$426$	−0.463171	−	0.102617i	−0.0224407	−	0.00497183i
$427$	−8.27616	−	16.4792i	−0.400511	−	0.797484i
$428$	−1.27483	−	0.804804i	−0.0616211	−	0.0389017i
$429$	−14.9121	−	1.66215i	−0.719961	−	0.0802493i
$430$	5.72550	−	19.7947i	0.276108	−	0.954585i
$431$	−12.4206	−	21.5131i	−0.598278	−	1.03625i	−0.993075	−	0.117480i	$-0.962518\pi$
$431$	−12.4206	−	21.5131i	−0.598278	−	1.03625i	0.394797	−	0.918768i	$-0.370815\pi$
$432$	−2.31352	−	20.6555i	−0.111309	−	0.993786i
$433$	3.10432	−	5.37684i	0.149184	−	0.258394i	−0.781742	−	0.623602i	$-0.785669\pi$
$433$	3.10432	−	5.37684i	0.149184	−	0.258394i	0.930926	+	0.365208i	$0.119002\pi$
$434$	−1.69420	−	1.76251i	−0.0813241	−	0.0846033i
$435$	−2.71721	−	42.7144i	−0.130280	−	2.04800i
$436$	0.840745	−	21.2620i	0.0402644	−	1.01827i
$437$	43.3345	+	2.52395i	2.07297	+	0.120737i
$438$	17.1081	+	22.2895i	0.817456	+	1.06503i
$439$	−4.27913	−	18.0551i	−0.204232	−	0.861721i	−0.974570	−	0.224085i	$-0.928061\pi$
$439$	−4.27913	−	18.0551i	−0.204232	−	0.861721i	0.770338	−	0.637636i	$-0.220088\pi$
$440$	−9.16668	+	27.5615i	−0.437004	+	1.31394i
$441$	0.774516	+	0.0821373i	0.0368817	+	0.00391130i
$442$	1.45071	+	1.69650i	0.0690033	+	0.0806942i
$443$	−0.750479	−	12.8852i	−0.0356563	−	0.612195i	−0.968051	−	0.250754i	$-0.919322\pi$
$443$	−0.750479	−	12.8852i	−0.0356563	−	0.612195i	0.932395	−	0.361442i	$-0.117715\pi$
$444$	−5.09766	+	9.34025i	−0.241924	+	0.443268i
$445$	5.42955	+	7.29315i	0.257385	+	0.345729i
$446$	31.4126	+	1.53571i	1.48743	+	0.0727182i
$447$	−9.55963	−	25.8340i	−0.452155	−	1.22191i
$448$	12.8335	+	17.3181i	0.606325	+	0.818204i
$449$	31.7939	+	5.60612i	1.50045	+	0.264569i	0.862715	−	0.505691i	$-0.168762\pi$
$449$	31.7939	+	5.60612i	1.50045	+	0.264569i	0.637730	+	0.770260i	$0.279873\pi$
$450$	45.3277	−	31.1306i	2.13677	−	1.46751i
$451$	8.39006	−	1.47939i	0.395072	−	0.0696619i
$452$	−13.4258	+	6.09085i	−0.631497	+	0.286489i
$453$	38.6929	−	11.8098i	1.81795	−	0.554875i
$454$	8.58882	−	9.27545i	0.403093	−	0.435318i
$455$	−39.7225	−	9.41439i	−1.86222	−	0.441354i
$456$	−17.7693	−	25.1492i	−0.832122	−	1.17772i
$457$	−36.5333	−	4.27013i	−1.70896	−	0.199748i	−0.795294	−	0.606223i	$-0.792684\pi$
$457$	−36.5333	−	4.27013i	−1.70896	−	0.199748i	−0.913662	+	0.406475i	$0.866758\pi$
$458$	−6.06578	+	2.27206i	−0.283435	+	0.106166i
$459$	−0.0368198	−	2.29382i	−0.00171860	−	0.107066i
$460$	−38.4552	−	44.1303i	−1.79298	−	2.05759i
$461$	8.92515	−	3.84993i	0.415686	−	0.179309i	−0.177957	−	0.984038i	$-0.556949\pi$
$461$	8.92515	−	3.84993i	0.415686	−	0.179309i	0.593642	+	0.804729i	$0.297689\pi$
$462$	−15.3860	−	4.36126i	−0.715823	−	0.202904i
$463$	1.27702	+	1.20481i	0.0593484	+	0.0559923i	0.715345	−	0.698772i	$-0.246270\pi$
$463$	1.27702	+	1.20481i	0.0593484	+	0.0559923i	−0.655996	+	0.754764i	$0.727751\pi$
$464$	17.5499	+	15.3613i	0.814733	+	0.713131i
$465$	0.248681	−	4.70304i	0.0115323	−	0.218098i
$466$	−13.7803	−	20.5321i	−0.638358	−	0.951131i
$467$	9.34654	−	7.84268i	0.432506	−	0.362916i	−0.400390	−	0.916345i	$-0.631125\pi$
$467$	9.34654	−	7.84268i	0.432506	−	0.362916i	0.832896	+	0.553429i	$0.186681\pi$
$468$	−21.4411	+	0.629613i	−0.991114	+	0.0291039i
$469$	−11.8583	−	9.95030i	−0.547566	−	0.459462i
$470$	−1.47672	+	13.7449i	−0.0681162	+	0.634006i
$471$	3.61851	+	19.8985i	0.166732	+	0.916873i
$472$	−0.897051	+	2.25076i	−0.0412901	+	0.103600i
$473$	−7.64959	−	3.29971i	−0.351728	−	0.151721i
$474$	4.67105	+	12.2702i	0.214549	+	0.563588i
$475$	36.5626	−	72.8022i	1.67761	−	3.34039i
$476$	1.22780	+	2.03785i	0.0562762	+	0.0934046i
$477$	−18.9647	+	29.5177i	−0.868336	+	1.35152i
$478$	−2.27537	−	3.85751i	−0.104073	−	0.176438i
$479$	−22.8277	−	24.1960i	−1.04303	−	1.10554i	−0.994288	−	0.106731i	$-0.965962\pi$
$479$	−22.8277	−	24.1960i	−1.04303	−	1.10554i	−0.0487381	−	0.998812i	$-0.515520\pi$
$480$	−7.46345	+	40.8478i	−0.340658	+	1.86444i
$481$	9.17499	+	6.03449i	0.418344	+	0.275149i
$482$	−5.65472	+	13.4528i	−0.257565	+	0.612757i
$483$	23.3233	−	22.2414i	1.06125	−	1.01202i
$484$	−9.25020	−	4.43151i	−0.420464	−	0.201432i
$485$		−	25.6223i		−	1.16345i
$486$	17.3879	+	13.5521i	0.788732	+	0.614737i
$487$			24.0231i			1.08859i	0.838894	+	0.544295i	$0.183203\pi$
$487$			24.0231i			1.08859i	−0.838894	+	0.544295i	$0.816797\pi$
$488$	8.16174	+	17.5535i	0.369465	+	0.794610i
$489$	−24.2572	+	23.1321i	−1.09695	+	1.04607i
$490$	−1.43445	−	0.602955i	−0.0648020	−	0.0272387i
$491$	28.0028	+	18.4178i	1.26375	+	0.831181i	0.991381	−	0.131011i	$-0.0418225\pi$
$491$	28.0028	+	18.4178i	1.26375	+	0.831181i	0.272369	+	0.962193i	$0.412193\pi$
$492$	11.5806	−	3.77218i	0.522093	−	0.170063i
$493$	1.76660	+	1.87248i	0.0795636	+	0.0843324i
$494$	−27.3725	+	16.1458i	−1.23155	+	0.726435i
$495$	−14.1203	−	27.3814i	−0.634661	−	1.23070i
$496$	1.72183	+	1.90305i	0.0773123	+	0.0854497i
$497$	−0.234196	+	0.466323i	−0.0105051	+	0.0209174i
$498$	16.8826	−	6.42694i	0.756529	−	0.287998i
$499$	−5.03451	−	2.17168i	−0.225376	−	0.0972176i	0.280398	−	0.959884i	$-0.409534\pi$
$499$	−5.03451	−	2.17168i	−0.225376	−	0.0972176i	−0.505774	+	0.862666i	$0.668793\pi$
$500$	−64.2698	+	20.5551i	−2.87423	+	0.919252i
$501$	3.80924	+	20.9473i	0.170184	+	0.935857i
$502$	−15.7294	−	1.68993i	−0.702036	−	0.0754252i
$503$	25.6199	+	21.4977i	1.14234	+	0.958533i	0.999513	−	0.0312154i	$-0.00993779\pi$
$503$	25.6199	+	21.4977i	1.14234	+	0.958533i	0.142822	+	0.989748i	$0.454382\pi$
$504$	−22.6518	−	3.09629i	−1.00899	−	0.137920i
$505$	−33.4390	+	28.0587i	−1.48802	+	1.24859i
$506$	−19.6498	+	13.1881i	−0.873539	+	0.586282i
$507$	0.0200288	−	0.378783i	0.000889510	−	0.0168223i
$508$	−14.8635	+	11.5026i	−0.659463	+	0.510345i
$509$	4.08301	+	3.85213i	0.180976	+	0.170742i	0.771399	−	0.636352i	$-0.219557\pi$
$509$	4.08301	+	3.85213i	0.180976	+	0.170742i	−0.590422	+	0.807094i	$0.701039\pi$
$510$	−1.24990	+	4.40952i	−0.0553466	+	0.195257i
$511$	28.3795	−	12.2417i	1.25544	−	0.541542i
$512$	−12.9171	−	18.5782i	−0.570859	−	0.821048i
$513$	32.2519	+	5.15460i	1.42396	+	0.227581i
$514$	−12.2905	−	32.8123i	−0.542111	−	1.44729i
$515$	24.9291	+	2.91379i	1.09851	+	0.128397i
$516$	−11.4883	−	3.14094i	−0.505742	−	0.138272i
$517$	5.43831	+	1.28890i	0.239177	+	0.0566859i
$518$	8.58814	+	7.95239i	0.377341	+	0.349408i
$519$	15.7732	−	4.81428i	0.692366	−	0.211324i
$520$	41.3815	+	11.1371i	1.81470	+	0.488396i
$521$	40.9886	−	7.22740i	1.79574	−	0.316638i	0.826536	−	0.562883i	$-0.190308\pi$
$521$	40.9886	−	7.22740i	1.79574	−	0.316638i	0.969208	+	0.246245i	$0.0791969\pi$
$522$	−24.6623	+	1.93268i	−1.07944	+	0.0845911i
$523$	−32.6689	−	5.76041i	−1.42851	−	0.251885i	−0.594707	−	0.803943i	$-0.702732\pi$
$523$	−32.6689	−	5.76041i	−1.42851	−	0.251885i	−0.833806	+	0.552057i	$0.813843\pi$
$524$	17.9213	−	4.60216i	0.782895	−	0.201046i
$525$	−20.9911	−	56.7264i	−0.916126	−	2.47574i
$526$	−0.751793	+	15.3777i	−0.0327797	+	0.670500i
$527$	0.169155	+	0.227214i	0.00736850	+	0.00989761i
$528$	16.0060	+	5.06376i	0.696572	+	0.220372i
$529$	−1.43566	−	24.6493i	−0.0624198	−	1.07171i
$530$	53.2722	−	45.5542i	2.31400	−	1.97875i
$531$	−1.04308	−	2.34871i	−0.0452659	−	0.101925i
$532$	−31.6074	+	12.1766i	−1.37035	+	0.527922i
$533$	−2.89874	−	12.2307i	−0.125558	−	0.529772i
$534$	4.16877	−	3.19970i	0.180400	−	0.138464i
$535$	−3.18924	−	0.185752i	−0.137883	−	0.00803077i
$536$	12.1273	+	10.8164i	0.523820	+	0.467198i
$537$	1.25016	+	19.6524i	0.0539482	+	0.848065i
$538$	5.87350	−	5.64584i	0.253225	−	0.243409i
$539$	−0.314545	+	0.544809i	−0.0135484	+	0.0234666i
$540$	−25.4642	−	35.9353i	−1.09581	−	1.54641i
$541$	−0.411783	−	0.713230i	−0.0177039	−	0.0306641i	0.857038	−	0.515254i	$-0.172302\pi$
$541$	−0.411783	−	0.713230i	−0.0177039	−	0.0306641i	−0.874742	+	0.484590i	$0.838969\pi$
$542$	6.34961	+	1.83659i	0.272739	+	0.0788882i
$543$	35.9897	+	4.01153i	1.54446	+	0.172151i
$544$	−1.22372	−	2.17718i	−0.0524667	−	0.0933457i
$545$	−20.2362	−	40.2936i	−0.866824	−	1.72599i
$546$	−5.10375	+	23.0361i	−0.218420	+	0.985855i
$547$	31.9841	+	9.57542i	1.36754	+	0.409416i	0.884647	−	0.466262i	$-0.154400\pi$
$547$	31.9841	+	9.57542i	1.36754	+	0.409416i	0.482896	+	0.875677i	$0.339585\pi$
$548$	21.8995	−	27.1103i	0.935502	−	1.15809i
$549$	−19.3682	−	6.81567i	−0.826617	−	0.290886i
$550$	8.12017	+	43.6660i	0.346245	+	1.86192i
$551$	−30.6209	+	20.1397i	−1.30449	+	0.857979i
$552$	−25.1774	+	22.5983i	−1.07162	+	0.961846i
$553$	14.3441	−	1.67658i	0.609973	−	0.0712956i
$554$	10.6522	−	5.47478i	0.452571	−	0.232601i
$555$	0.120634	+	22.5476i	0.00512062	+	0.957094i
$556$	20.6542	+	5.76588i	0.875933	+	0.244528i
$557$	−7.62859	−	20.9594i	−0.323234	−	0.888077i	−0.989779	−	0.142612i	$-0.954450\pi$
$557$	−7.62859	−	20.9594i	−0.323234	−	0.888077i	0.666545	−	0.745465i	$-0.267772\pi$
$558$	−2.72008	−	0.103819i	−0.115150	−	0.00439503i
$559$	−4.20389	+	11.5501i	−0.177806	+	0.488517i
$560$	41.5531	+	18.9621i	1.75594	+	0.801296i
$561$	1.70534	+	0.724814i	0.0719994	+	0.0306017i
$562$	11.0967	−	3.43525i	0.468087	−	0.144907i
$563$	8.53386	+	28.5051i	0.359659	+	1.20135i	0.926111	+	0.377251i	$0.123131\pi$
$563$	8.53386	+	28.5051i	0.359659	+	1.20135i	−0.566452	+	0.824095i	$0.691684\pi$
$564$	7.95594	+	0.736819i	0.335006	+	0.0310257i
$565$	−18.6554	+	25.0585i	−0.784837	+	1.05422i
$566$	16.8914	−	20.5161i	0.709999	−	0.862354i
$567$	19.1366	−	14.8936i	0.803662	−	0.625472i
$568$	0.260515	−	0.481880i	0.0109310	−	0.0202192i
$569$	1.85908	+	1.38403i	0.0779365	+	0.0580216i	0.635422	−	0.772165i	$-0.280826\pi$
$569$	1.85908	+	1.38403i	0.0779365	+	0.0580216i	−0.557485	+	0.830187i	$0.688234\pi$
$570$	−58.7344	−	28.4258i	−2.46011	−	1.19063i
$571$	−0.884876	+	0.264915i	−0.0370309	+	0.0110863i	−0.305265	−	0.952267i	$-0.598745\pi$
$571$	−0.884876	+	0.264915i	−0.0370309	+	0.0110863i	0.268234	+	0.963354i	$0.413560\pi$
$572$	6.56435	−	16.0339i	0.274469	−	0.670411i
$573$	23.3481	+	31.0141i	0.975380	+	1.29563i
$574$	−0.903691	−	13.3665i	−0.0377193	−	0.557909i
$575$	−84.1082	−	30.6129i	−3.50756	−	1.27665i
$576$	23.6699	+	3.96672i	0.986247	+	0.165280i
$577$	10.0700	−	3.66516i	0.419218	−	0.152583i	−0.123794	−	0.992308i	$-0.539506\pi$
$577$	10.0700	−	3.66516i	0.419218	−	0.152583i	0.543012	+	0.839725i	$0.317284\pi$
$578$	9.61637	+	21.7335i	0.399988	+	0.903996i
$579$	−10.1992	−	17.4493i	−0.423866	−	0.725169i
$580$	48.2941	+	10.4984i	2.00530	+	0.435922i
$581$	−2.30683	−	19.7362i	−0.0957033	−	0.818794i
$582$	−14.8076	+	0.217364i	−0.613794	+	0.00901002i
$583$	−15.5722	−	23.6764i	−0.644935	−	0.980577i
$584$	−30.1659	+	11.9456i	−1.24827	+	0.494312i
$585$	−39.1185	+	23.1467i	−1.61735	+	0.956996i
$586$	0.0734040	+	7.86893i	0.00303229	+	0.325063i
$587$	3.84221	−	12.8339i	0.158585	−	0.529711i	−0.841357	−	0.540480i	$-0.818243\pi$
$587$	3.84221	−	12.8339i	0.158585	−	0.529711i	0.999942	+	0.0107690i	$0.00342796\pi$
$588$	−0.336289	+	0.834109i	−0.0138683	+	0.0343981i
$589$	−3.60388	+	1.80994i	−0.148495	+	0.0745772i
$590$	0.643591	+	5.09375i	0.0264962	+	0.209706i
$591$	22.1135	+	16.2798i	0.909629	+	0.669660i
$592$	−8.75932	−	8.61643i	−0.360006	−	0.354133i
$593$	6.07819	−	3.50924i	0.249601	−	0.144107i	−0.369980	−	0.929040i	$-0.620636\pi$
$593$	6.07819	−	3.50924i	0.249601	−	0.144107i	0.619582	+	0.784932i	$0.287302\pi$
$594$	−15.7043	+	8.39265i	−0.644357	+	0.344355i
$595$	4.36601	+	2.52072i	0.178989	+	0.103339i
$596$	31.7135	−	2.44148i	1.29904	−	0.100007i
$597$	13.6020	+	20.4417i	0.556691	+	0.836624i
$598$	21.1103	+	27.8107i	0.863265	+	1.13726i
$599$	0.690439	−	11.8544i	0.0282106	−	0.484357i	−0.954383	−	0.298586i	$-0.903485\pi$
$599$	0.690439	−	11.8544i	0.0282106	−	0.484357i	0.982593	−	0.185770i	$-0.0594781\pi$
$600$	20.2277	+	60.1869i	0.825794	+	2.45712i
$601$	−14.0803	+	3.33709i	−0.574347	+	0.136123i	−0.507517	−	0.861642i	$-0.669437\pi$
$601$	−14.0803	+	3.33709i	−0.574347	+	0.136123i	−0.0668299	+	0.997764i	$0.521288\pi$
$602$	−6.44415	+	11.4060i	−0.262644	+	0.464874i
$603$	−17.1950	+	1.18623i	−0.700234	+	0.0483071i
$604$	0.871443	+	46.7054i	0.0354585	+	1.90042i
$605$	−21.6978	+	1.26375i	−0.882141	+	0.0513788i
$606$	16.4992	+	19.0869i	0.670236	+	0.775354i
$607$	−6.02530	+	4.48567i	−0.244560	+	0.182068i	−0.712459	−	0.701714i	$-0.752418\pi$
$607$	−6.02530	+	4.48567i	−0.244560	+	0.182068i	0.467899	+	0.883782i	$0.345011\pi$
$608$	33.5508	−	11.7749i	1.36066	−	0.477537i
$609$	−4.58170	+	26.8225i	−0.185660	+	1.08690i
$610$	33.1304	+	24.1876i	1.34141	+	0.979328i
$611$	1.43189	−	8.12063i	0.0579279	−	0.328525i
$612$	2.55894	+	0.684932i	0.103439	+	0.0276867i
$613$	−5.90584	−	33.4937i	−0.238535	−	1.35280i	−0.835041	−	0.550188i	$-0.814556\pi$
$613$	−5.90584	−	33.4937i	−0.238535	−	1.35280i	0.596506	−	0.802608i	$-0.296555\pi$
$614$	5.53279	−	11.2778i	0.223285	−	0.455134i
$615$	17.6101	−	18.8669i	0.710110	−	0.760786i
$616$	9.71168	−	15.7062i	0.391295	−	0.632820i
$617$	10.0198	−	42.2770i	0.403383	−	1.70201i	−0.270124	−	0.962825i	$-0.587065\pi$
$617$	10.0198	−	42.2770i	0.403383	−	1.70201i	0.673507	−	0.739181i	$-0.264787\pi$
$618$	1.47245	−	14.4317i	0.0592305	−	0.580527i
$619$	−0.404161	+	3.45782i	−0.0162446	+	0.138982i	−0.998927	−	0.0463177i	$-0.985251\pi$
$619$	−0.404161	+	3.45782i	−0.0162446	+	0.138982i	0.982682	+	0.185299i	$0.0593254\pi$
$620$	5.14404	+	1.76432i	0.206590	+	0.0708566i
$621$	1.51125	−	35.8521i	0.0606442	−	1.43870i
$622$	−3.18867	+	19.1254i	−0.127854	+	0.766858i
$623$	−2.28955	−	5.30777i	−0.0917289	−	0.212651i
$624$	6.08529	−	24.0095i	0.243606	−	0.961150i
$625$	−53.6503	+	56.8660i	−2.14601	+	2.27464i
$626$	−12.7542	−	2.89742i	−0.509760	−	0.115804i
$627$	−14.3783	+	22.1181i	−0.574216	+	0.883310i
$628$	−23.2422	−	2.27800i	−0.927465	−	0.0909020i
$629$	−0.871735	−	1.03889i	−0.0347583	−	0.0414234i
$630$	−45.1833	+	17.4779i	−1.80014	+	0.696335i
$631$	−6.18544	+	7.37152i	−0.246238	+	0.293455i	−0.874980	−	0.484159i	$-0.839126\pi$
$631$	−6.18544	+	7.37152i	−0.246238	+	0.293455i	0.628742	+	0.777614i	$0.283570\pi$
$632$	−15.1041	+	1.30462i	−0.600807	+	0.0518951i
$633$	0.809104	+	0.953842i	0.0321590	+	0.0379118i
$634$	13.3058	−	20.6475i	0.528442	−	0.820016i
$635$	−15.7742	+	36.5687i	−0.625981	+	1.45119i
$636$	−26.7785	−	30.4004i	−1.06183	−	1.20546i
$637$	0.829429	+	0.416555i	0.0328632	+	0.0165045i
$638$	6.65847	−	18.8390i	0.263612	−	0.745841i
$639$	0.172585	+	0.554798i	0.00682736	+	0.0219475i
$640$	−42.9998	−	21.2134i	−1.69972	−	0.838532i
$641$	6.03407	−	5.69285i	0.238331	−	0.224854i	−0.557804	−	0.829973i	$-0.688356\pi$
$641$	6.03407	−	5.69285i	0.238331	−	0.224854i	0.796135	+	0.605119i	$0.206874\pi$
$642$	−0.0802938	+	1.84469i	−0.00316894	+	0.0728042i
$643$	−27.0510	+	41.1290i	−1.06679	+	1.62197i	−0.332535	+	0.943091i	$0.607904\pi$
$643$	−27.0510	+	41.1290i	−1.06679	+	1.62197i	−0.734251	+	0.678878i	$0.762466\pi$
$644$	17.3190	+	32.9382i	0.682466	+	1.29795i
$645$	−24.5255	+	5.95140i	−0.965689	+	0.234336i
$646$	3.81024	−	0.940666i	0.149912	−	0.0370100i
$647$	7.85538			0.308827			0.154414	−	0.988006i	$-0.450651\pi$
$647$	7.85538			0.308827			0.154414	+	0.988006i	$0.450651\pi$
$648$	−20.5516	+	15.0210i	−0.807343	+	0.590083i
$649$	2.07574			0.0814801
$650$	63.6187	−	15.7061i	2.49533	−	0.616043i
$651$	−0.843383	+	2.87295i	−0.0330548	+	0.112600i
$652$	−18.0126	−	34.2572i	−0.705427	−	1.34162i
$653$	−8.26209	+	12.5619i	−0.323320	+	0.491585i	−0.960175	−	0.279399i	$-0.909865\pi$
$653$	−8.26209	+	12.5619i	−0.323320	+	0.491585i	0.636855	+	0.770984i	$0.280235\pi$
$654$	−23.1147	+	12.0367i	−0.903855	+	0.470671i
$655$	28.5186	−	26.9059i	1.11431	−	1.05130i
$656$	0.524624	+	14.0538i	0.0204831	+	0.548711i
$657$	13.2915	−	31.7427i	0.518549	−	1.23840i
$658$	2.92876	−	8.28641i	0.114175	−	0.323038i
$659$	−7.54862	−	3.79106i	−0.294052	−	0.147679i	0.295657	−	0.955294i	$-0.404461\pi$
$659$	−7.54862	−	3.79106i	−0.294052	−	0.147679i	−0.589709	+	0.807616i	$0.700758\pi$
$660$	34.8750	−	7.01648i	1.35751	−	0.273116i
$661$	−2.19968	+	5.09943i	−0.0855576	+	0.198345i	−0.955624	−	0.294590i	$-0.904817\pi$
$661$	−2.19968	+	5.09943i	−0.0855576	+	0.198345i	0.870066	+	0.492935i	$0.164076\pi$
$662$	−11.1761	+	17.3426i	−0.434370	+	0.674040i
$663$	0.921279	−	2.57396i	0.0357795	−	0.0999642i
$664$	1.79504	+	20.7818i	0.0696612	+	0.806490i
$665$	−46.1359	+	54.9826i	−1.78907	+	2.13214i
$666$	13.0296	−	0.260996i	0.504888	−	0.0101134i
$667$	25.8829	+	30.8460i	1.00219	+	1.19436i
$668$	−24.4673	−	2.39807i	−0.946669	−	0.0927842i
$669$	−17.4709	−	34.3283i	−0.675465	−	1.32721i
$670$	33.5787	+	7.62820i	1.29726	+	0.294703i
$671$	11.3808	−	12.0629i	0.439351	−	0.465685i
$672$	10.6060	−	24.1751i	0.409136	−	0.932575i
$673$	11.6649	+	27.0422i	0.449647	+	1.04240i	0.980781	+	0.195111i	$0.0625068\pi$
$673$	11.6649	+	27.0422i	0.449647	+	1.04240i	−0.531134	+	0.847288i	$0.678234\pi$
$674$	0.605012	−	3.62881i	0.0233042	−	0.139777i
$675$	−60.6606	−	29.2553i	−2.33483	−	1.12604i
$676$	0.414301	+	0.142098i	0.0159346	+	0.00546530i
$677$	−5.59889	+	47.9016i	−0.215183	+	1.84101i	0.265499	+	0.964111i	$0.414463\pi$
$677$	−5.59889	+	47.9016i	−0.215183	+	1.84101i	−0.480682	+	0.876895i	$0.659611\pi$
$678$	14.6400	+	10.5687i	0.562245	+	0.405887i
$679$	−3.75665	+	15.8506i	−0.144167	+	0.608289i
$680$	−4.50127	−	2.78329i	−0.172616	−	0.106734i
$681$	−15.0839	−	3.48982i	−0.578016	−	0.133730i
$682$	0.968372	−	1.97388i	0.0370809	−	0.0755839i
$683$	−7.95172	−	45.0965i	−0.304264	−	1.72557i	−0.626948	−	0.779062i	$-0.715696\pi$
$683$	−7.95172	−	45.0965i	−0.304264	−	1.72557i	0.322683	−	0.946507i	$-0.395415\pi$
$684$	−15.9295	+	34.1847i	−0.609078	+	1.30709i
$685$	12.8237	−	72.7267i	0.489968	−	2.77875i
$686$	−20.7436	−	15.1444i	−0.791994	−	0.578214i
$687$	6.10429	+	5.06670i	0.232893	+	0.193307i
$688$	7.12317	−	11.7638i	0.271568	−	0.448492i
$689$	−33.5369	+	24.9673i	−1.27766	+	0.951179i
$690$	−23.5280	+	67.7191i	−0.895694	+	2.57802i
$691$	−24.7748	+	1.44297i	−0.942478	+	0.0548931i	−0.522498	−	0.852640i	$-0.675000\pi$
$691$	−24.7748	+	1.44297i	−0.942478	+	0.0548931i	−0.419980	+	0.907533i	$0.637963\pi$
$692$	0.355244	+	19.0395i	0.0135044	+	0.723772i
$693$	4.72060	+	19.0090i	0.179321	+	0.722092i
$694$	22.4017	−	39.6505i	0.850356	−	1.50511i
$695$	44.2151	−	10.4792i	1.67717	−	0.397497i
$696$	5.65750	−	27.9990i	0.214447	−	1.06130i
$697$	−0.0902573	+	1.54966i	−0.00341874	+	0.0586975i
$698$	14.8925	+	19.6193i	0.563688	+	0.742601i
$699$	−13.4470	+	27.1362i	−0.508612	+	1.02638i
$700$	69.6367	−	5.36100i	2.63202	−	0.202627i
$701$	15.8626	+	9.15829i	0.599123	+	0.345904i	0.768696	−	0.639614i	$-0.220906\pi$
$701$	15.8626	+	9.15829i	0.599123	+	0.345904i	−0.169574	+	0.985518i	$0.554239\pi$
$702$	13.7087	+	22.4108i	0.517401	+	0.845843i
$703$	16.7211	−	9.65393i	0.630648	−	0.364105i
$704$	−10.6880	+	16.1724i	−0.402819	+	0.609519i
$705$	15.5101	−	6.78906i	0.584145	−	0.255691i
$706$	−0.649931	−	5.14392i	−0.0244605	−	0.193594i
$707$	24.8000	−	12.4550i	0.932700	−	0.468420i
$708$	2.93830	−	0.415154i	0.110428	−	0.0156025i
$709$	−2.55933	+	8.54877i	−0.0961178	+	0.321056i	−0.992503	−	0.122220i	$-0.960999\pi$
$709$	−2.55933	+	8.54877i	−0.0961178	+	0.321056i	0.896385	+	0.443276i	$0.146184\pi$
$710$	−0.0108277	−	1.16073i	−0.000406355	−	0.0435614i
$711$	10.2036	−	12.4278i	0.382664	−	0.466080i
$712$	2.23416	+	5.64188i	0.0837288	+	0.211438i
$713$	2.43475	+	3.70185i	0.0911820	+	0.138636i
$714$	1.41973	−	2.54458i	0.0531319	−	0.0952283i
$715$	−4.26214	−	36.4650i	−0.159395	−	1.36371i
$716$	−22.2196	−	4.83020i	−0.830385	−	0.180513i
$717$	−2.71710	+	4.76485i	−0.101472	+	0.177947i
$718$	1.98323	+	4.48221i	0.0740134	+	0.167274i
$719$	−9.48610	+	3.45266i	−0.353772	+	0.128762i	−0.512792	−	0.858513i	$-0.671389\pi$
$719$	−9.48610	+	3.45266i	−0.353772	+	0.128762i	0.159020	+	0.987275i	$0.449167\pi$
$720$	47.9637	−	16.9072i	1.78750	−	0.630095i
$721$	−14.9945	−	5.45755i	−0.558425	−	0.203250i
$722$	1.95651	+	28.9388i	0.0728136	+	1.07699i
$723$	17.7404	−	2.16983i	0.659772	−	0.0806967i
$724$	−15.8428	+	38.6972i	−0.588793	+	1.43817i
$725$	72.3972	−	21.6743i	2.68877	−	0.804964i
$726$	0.914414	+	12.5288i	0.0339371	+	0.464987i
$727$	35.5552	+	26.4699i	1.31867	+	0.981713i	0.999420	+	0.0340415i	$0.0108378\pi$
$727$	35.5552	+	26.4699i	1.31867	+	0.981713i	0.319248	+	0.947671i	$0.396570\pi$
$728$	−23.9667	−	12.9569i	−0.888263	−	0.480215i
$729$	3.83268	−	26.7266i	0.141951	−	0.989874i
$730$	−43.6994	+	53.0766i	−1.61739	+	1.96445i
$731$	0.906443	−	1.21756i	0.0335260	−	0.0450333i
$732$	13.6974	−	19.3518i	0.506269	−	0.715263i
$733$	−7.16999	−	23.9494i	−0.264830	−	0.884592i	−0.982190	−	0.187890i	$-0.939835\pi$
$733$	−7.16999	−	23.9494i	−0.264830	−	0.884592i	0.717360	−	0.696702i	$-0.245350\pi$
$734$	−34.2631	+	10.6069i	−1.26467	+	0.391509i
$735$	0.231366	+	1.89164i	0.00853405	+	0.0697740i
$736$	−17.1286	−	35.1102i	−0.631370	−	1.29418i
$737$	4.76145	−	13.0820i	0.175390	−	0.481881i
$738$	−11.0529	−	10.0171i	−0.406862	−	0.368736i
$739$	4.43971	+	12.1980i	0.163318	+	0.448711i	0.994175	−	0.107773i	$-0.0343721\pi$
$739$	4.43971	+	12.1980i	0.163318	+	0.448711i	−0.830858	+	0.556485i	$0.812150\pi$
$740$	−25.0773	−	7.00065i	−0.921861	−	0.257349i
$741$	33.8110	+	19.2803i	1.24208	+	0.708281i
$742$	−39.6344	+	20.3703i	−1.45503	+	0.747817i
$743$	17.3746	−	2.03080i	0.637413	−	0.0745029i	0.208752	−	0.977969i	$-0.433060\pi$
$743$	17.3746	−	2.03080i	0.637413	−	0.0745029i	0.428661	+	0.903466i	$0.358986\pi$
$744$	0.975989	−	2.98779i	0.0357815	−	0.109538i
$745$	56.3121	−	37.0370i	2.06311	−	1.35693i
$746$	−1.92046	−	10.3272i	−0.0703131	−	0.378106i
$747$	−17.0996	−	14.0392i	−0.625640	−	0.513667i
$748$	−1.34451	+	1.66443i	−0.0491603	+	0.0608575i
$749$	1.94571	+	0.582506i	0.0710945	+	0.0212843i
$750$	60.9375	+	55.8239i	2.22512	+	2.03840i
$751$	−12.2196	−	24.3312i	−0.445899	−	0.887857i	−0.998518	−	0.0544232i	$-0.982668\pi$
$751$	−12.2196	−	24.3312i	−0.445899	−	0.887857i	0.552619	−	0.833434i	$-0.313628\pi$
$752$	−3.33569	+	8.60192i	−0.121640	+	0.313680i
$753$	7.76925	+	17.7494i	0.283127	+	0.646825i
$754$	−28.3190	−	8.19110i	−1.03132	−	0.298302i
$755$	49.4933	+	85.7250i	1.80125	+	3.11985i
$756$	10.4840	+	25.9639i	0.381301	+	0.944298i
$757$	−10.5104	+	18.2045i	−0.382007	+	0.661655i	−0.991349	−	0.131252i	$-0.958100\pi$
$757$	−10.5104	+	18.2045i	−0.382007	+	0.661655i	0.609342	+	0.792907i	$0.291433\pi$
$758$	12.0574	−	11.5900i	0.437944	−	0.420969i
$759$	25.9701	+	12.8691i	0.942654	+	0.467120i
$760$	50.1518	−	56.2299i	1.81920	−	2.03967i
$761$	−17.4653	−	1.01724i	−0.633115	−	0.0368748i	−0.261414	−	0.965227i	$-0.584189\pi$
$761$	−17.4653	−	1.01724i	−0.633115	−	0.0368748i	−0.371702	+	0.928352i	$0.621226\pi$
$762$	21.2675	+	8.80595i	0.770440	+	0.319006i
$763$	6.61089	+	27.8935i	0.239330	+	1.00981i
$764$	−41.8291	+	16.1144i	−1.51332	+	0.583000i
$765$	5.44783	−	1.35289i	0.196967	−	0.0489137i
$766$	−13.4586	+	11.5087i	−0.486277	+	0.415826i
$767$	−0.178070	−	3.05735i	−0.00642974	−	0.110394i
$768$	−11.8948	+	25.0303i	−0.429216	+	0.903202i
$769$	−27.9417	−	37.5323i	−1.00760	−	1.35345i	−0.934437	−	0.356128i	$-0.884097\pi$
$769$	−27.9417	−	37.5323i	−1.00760	−	1.35345i	−0.0731677	−	0.997320i	$-0.523311\pi$
$770$	1.91073	−	39.0835i	0.0688580	−	1.40847i
$771$	−27.4079	+	33.0206i	−0.987071	+	1.18921i
$772$	22.6047	−	5.80486i	0.813563	−	0.208921i
$773$	−43.2085	−	7.61882i	−1.55410	−	0.274030i	−0.670371	−	0.742026i	$-0.733865\pi$
$773$	−43.2085	−	7.61882i	−1.55410	−	0.274030i	−0.883731	+	0.467996i	$0.844976\pi$
$774$	3.64747	+	14.1232i	0.131106	+	0.507647i
$775$	8.18930	−	1.44399i	0.294168	−	0.0518698i
$776$	4.44409	−	16.5126i	0.159533	−	0.592767i
$777$	3.23123	−	13.9662i	0.115920	−	0.501034i
$778$	19.0790	+	17.6667i	0.684016	+	0.633381i
$779$	−21.5041	−	5.09657i	−0.770465	−	0.182603i
$780$	−13.3263	−	50.7652i	−0.477159	−	1.81769i
$781$	−0.466123	−	0.0544819i	−0.0166792	−	0.00194952i
$782$	−1.51248	−	4.03791i	−0.0540863	−	0.144395i
$783$	17.0529	+	25.0428i	0.609423	+	0.894958i
$784$	−0.819868	−	0.637381i	−0.0292810	−	0.0227636i
$785$	−45.4394	+	19.6006i	−1.62180	+	0.699576i
$786$	−15.7913	−	16.2531i	−0.563257	−	0.579729i
$787$	8.48721	+	8.00727i	0.302536	+	0.285428i	0.822506	−	0.568756i	$-0.192575\pi$
$787$	8.48721	+	8.00727i	0.302536	+	0.285428i	−0.519970	+	0.854185i	$0.674057\pi$
$788$	−25.0759	+	19.4058i	−0.893293	+	0.691302i
$789$	16.8051	−	8.55270i	0.598276	−	0.304484i
$790$	−26.6741	+	17.9025i	−0.949023	+	0.636943i
$791$	15.2146	−	12.7666i	0.540970	−	0.453928i
$792$	−4.35080	−	20.0953i	−0.154599	−	0.714056i
$793$	−18.7437	−	15.7279i	−0.665610	−	0.558513i
$794$	24.8199	+	2.66659i	0.880825	+	0.0946339i
$795$	−80.8255	−	28.9293i	−2.86659	−	1.02602i
$796$	−27.0045	+	8.63672i	−0.957150	+	0.306120i
$797$	−6.86242	−	2.96016i	−0.243079	−	0.104854i	0.271055	−	0.962564i	$-0.412627\pi$
$797$	−6.86242	−	2.96016i	−0.243079	−	0.104854i	−0.514134	+	0.857710i	$0.671887\pi$
$798$	32.1668	+	26.1963i	1.13869	+	0.927338i
$799$	−0.457026	+	0.910014i	−0.0161684	+	0.0321940i
$800$	−73.2381	+	3.41832i	−2.58936	+	0.120856i
$801$	−5.93679	−	2.48588i	−0.209766	−	0.0878343i
$802$	11.9523	−	7.05013i	0.422050	−	0.248949i
$803$	19.0746	+	20.2179i	0.673129	+	0.713475i
$804$	4.12360	−	19.4704i	0.145428	−	0.686668i
$805$	65.8839	+	43.3325i	2.32210	+	1.52727i
$806$	−2.99039	−	1.25698i	−0.105332	−	0.0442751i
$807$	−9.57398	−	2.81054i	−0.337020	−	0.0989356i
$808$	−26.4168	+	12.2828i	−0.929339	+	0.432109i
$809$			26.7857i			0.941735i	0.882204	+	0.470868i	$0.156059\pi$
$809$			26.7857i			0.941735i	−0.882204	+	0.470868i	$0.843941\pi$
$810$	−22.7164	+	48.9247i	−0.798172	+	1.71904i
$811$		−	5.38255i		−	0.189007i	−0.995525	−	0.0945034i	$-0.969874\pi$
$811$		−	5.38255i		−	0.189007i	0.995525	−	0.0945034i	$-0.0301263\pi$
$812$	−28.3366	−	13.5753i	−0.994420	−	0.476398i
$813$	−1.90905	−	7.86711i	−0.0669533	−	0.275912i
$814$	−4.07890	+	9.70385i	−0.142965	+	0.340120i
$815$	−68.5222	−	45.0677i	−2.40023	−	1.57865i
$816$	−1.57033	+	2.62497i	−0.0549724	+	0.0918924i
$817$	14.8301	+	15.7190i	0.518841	+	0.549939i
$818$	−12.7915	−	21.6858i	−0.447245	−	0.758228i
$819$	27.5933	−	8.58364i	0.964187	−	0.299937i
$820$	15.3794	+	25.5260i	0.537071	+	0.891406i
$821$	−1.51207	+	3.01078i	−0.0527716	+	0.105077i	−0.918473	−	0.395484i	$-0.870577\pi$
$821$	−1.51207	+	3.01078i	−0.0527716	+	0.105077i	0.865701	+	0.500561i	$0.166873\pi$
$822$	−42.1388	−	6.79405i	−1.46976	−	0.236970i
$823$	−35.8317	−	15.4563i	−1.24901	−	0.538772i	−0.334145	−	0.942522i	$-0.608448\pi$
$823$	−35.8317	−	15.4563i	−1.24901	−	0.538772i	−0.914870	+	0.403749i	$0.867707\pi$
$824$	15.5604	+	6.20168i	0.542073	+	0.216046i
$825$	41.4825	−	35.1878i	1.44423	−	1.22508i
$826$	0.348686	−	3.24547i	0.0121323	−	0.112924i
$827$	41.1980	+	34.5692i	1.43259	+	1.20209i	0.944159	+	0.329489i	$0.106877\pi$
$827$	41.1980	+	34.5692i	1.43259	+	1.20209i	0.488435	+	0.872600i	$0.337568\pi$
$828$	39.3356	+	13.0227i	1.36701	+	0.452570i
$829$	33.1178	−	27.7891i	1.15023	−	0.965156i	0.150504	−	0.988609i	$-0.451910\pi$
$829$	33.1178	−	27.7891i	1.15023	−	0.965156i	0.999725	+	0.0234531i	$0.00746605\pi$
$830$	24.6322	+	36.7011i	0.854996	+	1.27392i
$831$	−12.2983	−	7.99480i	−0.426624	−	0.277336i
$832$	24.7370	+	14.3549i	0.857603	+	0.497667i
$833$	−0.0833736	−	0.0786590i	−0.00288873	−	0.00272537i
$834$	−6.43117	−	25.4637i	−0.222693	−	0.881737i
$835$	−47.8345	+	20.6338i	−1.65538	+	0.714061i
$836$	−20.0124	−	22.9658i	−0.692145	−	0.794290i
$837$	1.54384	+	2.95482i	0.0533629	+	0.102133i
$838$	26.5092	−	9.92955i	0.915744	−	0.343011i
$839$	46.6508	+	5.45269i	1.61056	+	0.188248i	0.873239	−	0.487291i	$-0.162015\pi$
$839$	46.6508	+	5.45269i	1.61056	+	0.188248i	0.737324	+	0.675539i	$0.236089\pi$
$840$	−5.11208	−	55.7064i	−0.176384	−	1.92205i
$841$	−4.86330	−	1.15262i	−0.167700	−	0.0397456i
$842$	17.5303	−	18.9317i	0.604133	−	0.652430i
$843$	−10.4004	−	9.70766i	−0.358210	−	0.334349i
$844$	−1.31526	+	0.596691i	−0.0452731	+	0.0205390i
$845$	0.914010	−	0.161165i	0.0314429	−	0.00554423i
$846$	−4.05509	−	8.90596i	−0.139417	−	0.306193i
$847$	13.6080	+	2.39946i	0.467578	+	0.0824466i
$848$	42.2330	−	20.1180i	1.45029	−	0.690856i
$849$	−32.0829	−	5.48026i	−1.10108	−	0.188082i
$850$	−8.08285	−	0.395158i	−0.277240	−	0.0135538i
$851$	−12.6675	−	17.0154i	−0.434237	−	0.583281i
$852$	−0.670713	+	0.0161044i	−0.0229782	+	0.000551727i
$853$	1.58615	+	27.2332i	0.0543088	+	0.932447i	0.909909	+	0.414809i	$0.136152\pi$
$853$	1.58615	+	27.2332i	0.0543088	+	0.932447i	−0.855600	+	0.517638i	$0.826811\pi$
$854$	−16.9489	−	19.8205i	−0.579980	−	0.678243i
$855$	5.50012	+	79.7269i	0.188100	+	2.72660i
$856$	−2.02312	−	0.672871i	−0.0691489	−	0.0229983i
$857$	1.09856	+	4.63518i	0.0375260	+	0.158335i	0.988582	−	0.150684i	$-0.0481476\pi$
$857$	1.09856	+	4.63518i	0.0375260	+	0.158335i	−0.951056	+	0.309019i	$0.899999\pi$
$858$	−21.0375	+	2.77251i	−0.718210	+	0.0946518i
$859$	22.3222	+	1.30012i	0.761623	+	0.0443595i	0.434560	−	0.900643i	$-0.356904\pi$
$859$	22.3222	+	1.30012i	0.761623	+	0.0443595i	0.327063	+	0.945003i	$0.393941\pi$
$860$	1.15141	−	29.1187i	0.0392629	−	0.992939i
$861$	−13.6602	+	9.08955i	−0.465540	+	0.309771i
$862$	−24.3455	−	25.3272i	−0.829210	−	0.862647i
$863$	3.35974	−	5.81924i	0.114367	−	0.198089i	−0.803160	−	0.595764i	$-0.796849\pi$
$863$	3.35974	−	5.81924i	0.114367	−	0.198089i	0.917526	+	0.397675i	$0.130183\pi$
$864$	−10.1779	−	27.5756i	−0.346257	−	0.938140i
$865$	20.1760	+	34.9458i	0.686003	+	1.18819i
$866$	2.43966	−	8.43459i	0.0829029	−	0.286619i
$867$	17.2565	−	23.4403i	0.586061	−	0.796073i
$868$	−2.92354	−	1.84565i	−0.0992315	−	0.0626453i
$869$	5.82896	+	11.6064i	0.197734	+	0.393720i
$870$	−18.2093	−	57.7255i	−0.617352	−	1.95708i
$871$	−19.6768	−	5.89086i	−0.666724	−	0.199604i
$872$	−6.05268	−	29.4775i	−0.204970	−	0.998235i
$873$	9.23628	+	15.6096i	0.312601	+	0.528303i
$874$	60.3534	−	11.2234i	2.04148	−	0.379637i
$875$	75.9489	−	49.9524i	2.56754	−	1.68870i
$876$	31.0446	+	24.8043i	1.04890	+	0.838060i
$877$	−22.8228	+	2.66761i	−0.770672	+	0.0900786i	−0.492336	−	0.870405i	$-0.663857\pi$
$877$	−22.8228	+	2.66761i	−0.770672	+	0.0900786i	−0.278336	+	0.960484i	$0.589783\pi$
$878$	−11.9952	−	23.3390i	−0.404818	−	0.787652i
$879$	8.32072	−	4.86351i	0.280651	−	0.164042i
$880$	−3.24348	+	40.9488i	−0.109338	+	1.38038i
$881$	0.121603	+	0.334102i	0.00409691	+	0.0112562i	0.941724	−	0.336386i	$-0.109205\pi$
$881$	0.121603	+	0.334102i	0.00409691	+	0.0112562i	−0.937627	+	0.347642i	$0.886982\pi$
$882$	1.09124	−	0.149758i	0.0367441	−	0.00504260i
$883$	17.6201	−	48.4109i	0.592964	−	1.62915i	−0.172011	−	0.985095i	$-0.555027\pi$
$883$	17.6201	−	48.4109i	0.592964	−	1.62915i	0.764975	−	0.644060i	$-0.222751\pi$
$884$	2.56686	+	1.83754i	0.0863330	+	0.0618032i
$885$	5.02370	−	3.78195i	0.168870	−	0.127129i
$886$	−5.39800	−	17.4369i	−0.181349	−	0.585805i
$887$	−5.34281	−	17.8462i	−0.179394	−	0.599218i	−0.999630	−	0.0271929i	$-0.991343\pi$
$887$	−5.34281	−	17.8462i	−0.179394	−	0.599218i	0.820236	−	0.572025i	$-0.193842\pi$
$888$	−3.83305	+	14.5520i	−0.128629	+	0.488333i
$889$	15.1199	−	20.3095i	0.507104	−	0.681159i
$890$	9.92683	+	8.17303i	0.332748	+	0.273960i
$891$	18.4727	+	11.5911i	0.618859	+	0.388317i
$892$	43.6498	−	8.53916i	1.46150	−	0.285912i
$893$	−11.6291	−	8.65757i	−0.389154	−	0.289715i
$894$	−21.8820	−	32.2295i	−0.731844	−	1.07791i
$895$	−46.1591	+	13.8191i	−1.54293	+	0.461922i
$896$	23.4905	+	19.4276i	0.784761	+	0.649029i
$897$	16.7270	−	39.3551i	0.558498	−	1.31403i
$898$	45.5530	−	3.07976i	1.52012	−	0.102773i
$899$	−3.51539	−	1.27950i	−0.117245	−	0.0426736i
$900$	51.6825	−	58.1064i	1.72275	−	1.93688i
$901$	4.85198	−	1.76598i	0.161643	−	0.0588332i
$902$	11.0180	−	4.87511i	0.366860	−	0.162323i
$903$	16.0446	−	0.0858412i	0.533930	−	0.00285662i
$904$	−16.3689	+	12.9135i	−0.544423	+	0.429497i
$905$	10.2865	+	88.0067i	0.341935	+	2.92544i
$906$	49.1220	−	29.3302i	1.63197	−	0.974432i
$907$	17.4435	+	26.5216i	0.579203	+	0.880636i	0.999644	−	0.0266843i	$-0.00849489\pi$
$907$	17.4435	+	26.5216i	0.579203	+	0.880636i	−0.420441	+	0.907320i	$0.638125\pi$
$908$	8.64835	−	15.6464i	0.287006	−	0.519244i
$909$	10.2571	−	29.1478i	0.340206	−	0.966773i
$910$	−57.7297	+	0.538522i	−1.91372	+	0.0178518i
$911$	13.3291	−	44.5224i	0.441614	−	1.47509i	−0.390560	−	0.920577i	$-0.627719\pi$
$911$	13.3291	−	44.5224i	0.441614	−	1.47509i	0.832174	−	0.554515i	$-0.187096\pi$
$912$	−32.9217	−	28.5065i	−1.09014	−	0.943945i
$913$	15.9694	−	8.02011i	0.528508	−	0.265427i
$914$	−51.6073	+	6.52055i	−1.70702	+	0.215681i
$915$	5.56538	−	49.9302i	0.183986	−	1.65064i
$916$	−7.55811	+	5.17559i	−0.249727	+	0.171006i
$917$	−21.5871	+	12.4633i	−0.712869	+	0.411575i
$918$	−0.828072	−	3.13692i	−0.0273304	−	0.103534i
$919$	−27.2642	−	15.7410i	−0.899362	−	0.519247i	−0.0223690	−	0.999750i	$-0.507121\pi$
$919$	−27.2642	−	15.7410i	−0.899362	−	0.519247i	−0.876993	+	0.480503i	$0.840454\pi$
$920$	−67.7572	−	47.5557i	−2.23389	−	1.56787i
$921$	−15.3540	+	0.976720i	−0.505932	+	0.0321840i
$922$	10.9492	−	8.31121i	0.360592	−	0.273715i
$923$	−0.0402591	+	0.691223i	−0.00132515	+	0.0227519i
$924$	−22.6032	−	0.772684i	−0.743591	−	0.0254194i
$925$	−38.7392	+	9.18135i	−1.27374	+	0.301881i
$926$	2.16173	+	1.22133i	0.0710388	+	0.0401355i
$927$	−16.2376	+	7.21125i	−0.533312	+	0.236849i
$928$	29.3027	+	15.1422i	0.961909	+	0.497068i
$929$	29.7547	−	1.73302i	0.976221	−	0.0568584i	0.437390	−	0.899272i	$-0.355903\pi$
$929$	29.7547	−	1.73302i	0.976221	−	0.0568584i	0.538831	+	0.842414i	$0.318866\pi$
$930$	−1.25272	−	6.54153i	−0.0410782	−	0.214505i
$931$	1.30897	−	0.974491i	0.0428997	−	0.0319377i
$932$	−25.8798	−	23.5194i	−0.847720	−	0.770404i
$933$	22.2711	−	8.24124i	0.729125	−	0.269806i
$934$	10.1743	−	13.9360i	0.332915	−	0.456001i
$935$	−0.787306	+	4.46504i	−0.0257477	+	0.146022i
$936$	−29.2250	+	8.13216i	−0.955249	+	0.265808i
$937$	7.30906	+	41.4518i	0.238777	+	1.35417i	0.834512	+	0.550989i	$0.185750\pi$
$937$	7.30906	+	41.4518i	0.238777	+	1.35417i	−0.595735	+	0.803181i	$0.703139\pi$
$938$	−19.6541	−	9.64216i	−0.641730	−	0.314828i
$939$	4.67623	+	15.3209i	0.152603	+	0.499978i
$940$	2.63148	+	19.3722i	0.0858293	+	0.631852i
$941$	−1.68865	+	7.12498i	−0.0550485	+	0.232268i	−0.993614	−	0.112834i	$-0.964007\pi$
$941$	−1.68865	+	7.12498i	−0.0550485	+	0.232268i	0.938565	+	0.345101i	$0.112155\pi$
$942$	11.7130	+	26.0939i	0.381630	+	0.850184i
$943$	−2.81878	+	24.1162i	−0.0917922	+	0.785332i
$944$	−0.468720	+	3.39435i	−0.0152555	+	0.110477i
$945$	46.0586	+	37.4047i	1.49829	+	1.21677i
$946$	−11.6213	−	1.93755i	−0.377841	−	0.0629953i
$947$	16.5516	+	38.3710i	0.537856	+	1.24689i	0.943047	+	0.332658i	$0.107946\pi$
$947$	16.5516	+	38.3710i	0.537856	+	1.24689i	−0.405191	+	0.914232i	$0.632795\pi$
$948$	10.5724	+	15.2635i	0.343377	+	0.495737i
$949$	28.1425	−	29.8293i	0.913544	−	0.968300i
$950$	25.5230	−	112.350i	0.828075	−	3.64512i
$951$	−30.0420	−	1.58852i	−0.974178	−	0.0515114i
$952$	2.37651	+	2.38177i	0.0770233	+	0.0771936i
$953$	−29.6266	−	35.3076i	−0.959700	−	1.14373i	−0.989553	−	0.144172i	$-0.953948\pi$
$953$	−29.6266	−	35.3076i	−0.959700	−	1.14373i	0.0298524	−	0.999554i	$-0.490496\pi$
$954$	−16.0331	+	46.9558i	−0.519090	+	1.52025i
$955$	−61.0560	+	72.7637i	−1.97573	+	2.35458i
$956$	−4.43161	−	4.52506i	−0.143329	−	0.146351i
$957$	−24.0768	+	4.37833i	−0.778292	+	0.141531i
$958$	−39.5438	−	25.4831i	−1.27760	−	0.823323i
$959$	−18.5960	+	43.1103i	−0.600495	+	1.39210i
$960$	3.59860	+	58.6135i	0.116144	+	1.89174i
$961$	27.3348	+	13.7280i	0.881766	+	0.442840i
$962$	14.6426	+	5.17532i	0.472098	+	0.166859i
$963$	2.00990	−	1.03649i	0.0647681	−	0.0334003i
$964$	−3.20389	+	20.3873i	−0.103191	+	0.656630i
$965$	35.9715	−	33.9374i	1.15796	−	1.09248i
$966$	24.4837	−	38.4430i	0.787749	−	1.23688i
$967$	28.2762	−	42.9918i	0.909301	−	1.38252i	−0.0146008	−	0.999893i	$-0.504648\pi$
$967$	28.2762	−	42.9918i	0.909301	−	1.38252i	0.923901	−	0.382631i	$-0.124982\pi$
$968$	−14.2026	−	2.94895i	−0.456488	−	0.0947830i
$969$	−3.31720	−	3.47856i	−0.106564	−	0.111747i
$970$	−8.68500	−	35.1792i	−0.278858	−	1.12954i
$971$	−16.1639			−0.518726			−0.259363	−	0.965780i	$-0.583513\pi$
$971$	−16.1639			−0.518726			−0.259363	+	0.965780i	$0.583513\pi$
$972$	28.4671	+	12.7131i	0.913083	+	0.407774i
$973$	−28.8889			−0.926135
$974$	8.14291	+	32.9835i	0.260916	+	1.05686i
$975$	−55.3865	−	58.0806i	−1.77379	−	1.86007i
$976$	17.1560	+	21.3343i	0.549149	+	0.682894i
$977$	−10.5281	+	16.0073i	−0.336825	+	0.512118i	−0.963695	−	0.267006i	$-0.913965\pi$
$977$	−10.5281	+	16.0073i	−0.336825	+	0.512118i	0.626870	+	0.779124i	$0.284336\pi$
$978$	−25.4641	+	39.9824i	−0.814252	+	1.27850i
$979$	3.78133	−	3.56750i	0.120852	−	0.114018i
$980$	−2.17387	−	0.341627i	−0.0694417	−	0.0109129i
$981$	26.8532	+	17.2529i	0.857356	+	0.550841i
$982$	44.6906	+	15.7955i	1.42613	+	0.504055i
$983$	−42.8532	−	21.5217i	−1.36681	−	0.686436i	−0.394228	−	0.919013i	$-0.628988\pi$
$983$	−42.8532	−	21.5217i	−1.36681	−	0.686436i	−0.972578	+	0.232577i	$0.925284\pi$
$984$	14.6214	−	9.10454i	0.466114	−	0.290242i
$985$	−26.6123	+	61.6943i	−0.847939	+	1.96574i
$986$	3.06022	+	1.97209i	0.0974574	+	0.0628043i
$987$	−10.5903	+	1.92583i	−0.337093	+	0.0612999i
$988$	−32.1094	+	31.4463i	−1.02154	+	1.00044i
$989$	15.2617	−	18.1882i	0.485294	−	0.578351i
$990$	−28.6683	−	32.8081i	−0.911138	−	1.04271i
$991$	9.06144	+	10.7990i	0.287846	+	0.343042i	0.890518	−	0.454947i	$-0.150342\pi$
$991$	9.06144	+	10.7990i	0.287846	+	0.343042i	−0.602672	+	0.797989i	$0.705897\pi$
$992$	3.00911	+	2.02924i	0.0955395	+	0.0644286i
$993$	25.2334	+	1.33426i	0.800759	+	0.0423415i
$994$	−0.163484	+	0.719641i	−0.00518538	+	0.0228256i
$995$	−41.2282	+	43.6994i	−1.30702	+	1.38536i
$996$	21.0012	−	14.5467i	0.665449	−	0.460930i
$997$	−2.70740	−	6.27647i	−0.0857444	−	0.198778i	0.869949	−	0.493142i	$-0.164152\pi$
$997$	−2.70740	−	6.27647i	−0.0857444	−	0.198778i	−0.955693	+	0.294364i	$0.904892\pi$
$998$	−7.64846	−	1.27518i	−0.242108	−	0.0403653i
$999$	−8.20141	−	13.6929i	−0.259481	−	0.433225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.23.49	yes	936
3.2	odd	2		972.2.p.a.503.4		936
4.3	odd	2	inner	324.2.p.a.23.29	✓	936
12.11	even	2		972.2.p.a.503.24		936
81.7	even	27		972.2.p.a.143.24		936
81.74	odd	54	inner	324.2.p.a.155.29	yes	936
324.7	odd	54		972.2.p.a.143.4		936
324.155	even	54	inner	324.2.p.a.155.49	yes	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.23.29	✓	936	4.3	odd	2	inner
324.2.p.a.23.49	yes	936	1.1	even	1	trivial
324.2.p.a.155.29	yes	936	81.74	odd	54	inner
324.2.p.a.155.49	yes	936	324.155	even	54	inner
972.2.p.a.143.4		936	324.7	odd	54
972.2.p.a.143.24		936	81.7	even	27
972.2.p.a.503.4		936	3.2	odd	2
972.2.p.a.503.24		936	12.11	even	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37299 - 0.338962i) q^{2} +(-1.19533 - 1.25347i) q^{3} +(1.77021 - 0.930784i) q^{4} +(2.32883 - 3.54082i) q^{5} +(-2.06605 - 1.31583i) q^{6} +(-1.95981 + 1.84899i) q^{7} +(2.11498 - 1.87799i) q^{8} +(-0.142379 + 2.99662i) q^{9} +O(q^{10})\)	\(q+(1.37299 - 0.338962i) q^{2} +(-1.19533 - 1.25347i) q^{3} +(1.77021 - 0.930784i) q^{4} +(2.32883 - 3.54082i) q^{5} +(-2.06605 - 1.31583i) q^{6} +(-1.95981 + 1.84899i) q^{7} +(2.11498 - 1.87799i) q^{8} +(-0.142379 + 2.99662i) q^{9} +(1.99727 - 5.65090i) q^{10} +(-2.16538 - 1.08750i) q^{11} +(-3.28269 - 1.10631i) q^{12} +(-1.41601 + 3.28267i) q^{13} +(-2.06407 + 3.20295i) q^{14} +(-7.22204 + 1.31332i) q^{15} +(2.26728 - 3.29536i) q^{16} +(0.283793 - 0.338211i) q^{17} +(0.820255 + 4.16259i) q^{18} +(4.04034 + 4.81510i) q^{19} +(0.826787 - 8.43563i) q^{20} +(4.66027 + 0.246420i) q^{21} +(-3.34167 - 0.759141i) q^{22} +(4.73909 - 5.02315i) q^{23} +(-4.88211 - 0.406251i) q^{24} +(-5.13354 - 11.9009i) q^{25} +(-0.831463 + 4.98705i) q^{26} +(3.92636 - 3.40348i) q^{27} +(-1.74827 + 5.09726i) q^{28} +(-0.676913 + 5.79136i) q^{29} +(-9.47063 + 4.25117i) q^{30} +(-0.147962 + 0.624300i) q^{31} +(1.99596 - 5.29303i) q^{32} +(1.22520 + 4.01416i) q^{33} +(0.275004 - 0.560556i) q^{34} +(1.98285 + 11.2453i) q^{35} +(2.53716 + 5.43717i) q^{36} +(0.533400 - 3.02506i) q^{37} +(7.17949 + 5.24156i) q^{38} +(5.80733 - 2.14895i) q^{39} +(-1.72419 - 11.8623i) q^{40} +(-2.82019 + 2.09956i) q^{41} +(6.48204 - 1.24132i) q^{42} +(3.43227 - 0.199907i) q^{43} +(-4.84541 + 0.0904070i) q^{44} +(10.2789 + 7.48277i) q^{45} +(4.80408 - 8.50311i) q^{46} +(-2.24434 + 0.531918i) q^{47} +(-6.84079 + 1.09707i) q^{48} +(0.0150955 - 0.259180i) q^{49} +(-11.0823 - 14.5997i) q^{50} +(-0.763163 + 0.0485474i) q^{51} +(0.548829 + 7.12901i) q^{52} +(10.1282 + 5.84749i) q^{53} +(4.23721 - 6.00383i) q^{54} +(-8.89345 + 5.13464i) q^{55} +(-0.672584 + 7.59109i) q^{56} +(1.20604 - 10.8201i) q^{57} +(1.03365 + 8.18093i) q^{58} +(-0.765520 + 0.384459i) q^{59} +(-11.5621 + 9.04700i) q^{60} +(-1.96293 + 6.55663i) q^{61} +(0.00846371 + 0.907313i) q^{62} +(-5.26168 - 6.13607i) q^{63} +(0.946296 - 7.94384i) q^{64} +(8.32571 + 12.6586i) q^{65} +(3.04284 + 5.09611i) q^{66} +(0.666987 + 5.70644i) q^{67} +(0.187571 - 0.862854i) q^{68} +(-11.9611 + 0.0639941i) q^{69} +(6.53418 + 14.7676i) q^{70} +(0.181994 - 0.0662404i) q^{71} +(5.32650 + 6.60518i) q^{72} +(-10.7793 - 3.92333i) q^{73} +(-0.293028 - 4.33419i) q^{74} +(-8.78115 + 20.6602i) q^{75} +(11.6341 + 4.76304i) q^{76} +(6.25451 - 1.87248i) q^{77} +(7.24500 - 4.91895i) q^{78} +(-4.29936 - 3.20076i) q^{79} +(-6.38817 - 15.7024i) q^{80} +(-8.95946 - 0.853310i) q^{81} +(-3.16043 + 3.83861i) q^{82} +(-4.40395 + 5.91553i) q^{83} +(8.47902 - 3.90149i) q^{84} +(-0.536638 - 1.79250i) q^{85} +(4.64472 - 1.43788i) q^{86} +(8.06843 - 6.07408i) q^{87} +(-6.62206 + 1.76654i) q^{88} +(-0.733774 + 2.01603i) q^{89} +(16.6492 + 6.78961i) q^{90} +(-3.29451 - 9.05160i) q^{91} +(3.71373 - 13.3031i) q^{92} +(0.959406 - 0.560778i) q^{93} +(-2.90116 + 1.49106i) q^{94} +(26.4587 - 3.09258i) q^{95} +(-9.02048 + 3.82504i) q^{96} +(5.05121 - 3.32223i) q^{97} +(-0.0671263 - 0.360969i) q^{98} +(3.56712 - 6.33400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

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