LMFDB - Embedded newform 576.2.bd.a.253.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [576,2,Mod(37,576)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("576.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(576, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 9, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,8,0,-8,8,0,-8,8,0,-8,8,0,-8,8,0,-8,8,0,-8,8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(22)] == traces)

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			253.5
Character	$\chi$	$=$	576.253
Dual form			576.2.bd.a.469.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.887839 - 1.10079i) q^{2} +(-0.423482 - 1.95465i) q^{4} +(-0.649649 - 0.434082i) q^{5} +(-3.64486 + 1.50975i) q^{7} +(-2.52765 - 1.26925i) q^{8} +(-1.05462 + 0.329733i) q^{10} +(-5.80194 + 1.15408i) q^{11} +(2.03484 - 1.35963i) q^{13} +(-1.57413 + 5.35264i) q^{14} +(-3.64133 + 1.65552i) q^{16} +(-0.960477 - 0.960477i) q^{17} +(0.435978 + 0.652487i) q^{19} +(-0.573364 + 1.45366i) q^{20} +(-3.88079 + 7.41136i) q^{22} +(-0.421603 + 1.01784i) q^{23} +(-1.67980 - 4.05540i) q^{25} +(0.309935 - 3.44707i) q^{26} +(4.49456 + 6.48507i) q^{28} +(1.43977 + 0.286388i) q^{29} -6.88004i q^{31} +(-1.41053 + 5.47818i) q^{32} +(-1.91003 + 0.204535i) q^{34} +(3.02323 + 0.601358i) q^{35} +(-1.07856 + 1.61417i) q^{37} +(1.10533 + 0.0993831i) q^{38} +(1.09113 + 1.92177i) q^{40} +(2.79324 - 6.74347i) q^{41} +(-1.20307 - 6.04824i) q^{43} +(4.71284 + 10.8520i) q^{44} +(0.746114 + 1.36778i) q^{46} +(6.30014 + 6.30014i) q^{47} +(6.05588 - 6.05588i) q^{49} +(-5.95554 - 1.75143i) q^{50} +(-3.51933 - 3.40161i) q^{52} +(-10.2655 + 2.04194i) q^{53} +(4.27019 + 1.76877i) q^{55} +(11.1292 + 0.810126i) q^{56} +(1.59354 - 1.33062i) q^{58} +(-4.21278 - 2.81489i) q^{59} +(-2.08276 + 10.4707i) q^{61} +(-7.57348 - 6.10837i) q^{62} +(4.77800 + 6.41644i) q^{64} -1.91212 q^{65} +(1.42195 - 7.14864i) q^{67} +(-1.47065 + 2.28414i) q^{68} +(3.34611 - 2.79404i) q^{70} +(-2.49385 + 1.03299i) q^{71} +(-1.90488 - 0.789026i) q^{73} +(0.819282 + 2.62039i) q^{74} +(1.09076 - 1.12850i) q^{76} +(19.4049 - 12.9659i) q^{77} +(-6.20432 + 6.20432i) q^{79} +(3.08422 + 0.505126i) q^{80} +(-4.94320 - 9.06188i) q^{82} +(-1.13685 - 1.70141i) q^{83} +(0.207047 + 1.04090i) q^{85} +(-7.72599 - 4.04554i) q^{86} +(16.1301 + 4.44702i) q^{88} +(-1.15743 - 2.79429i) q^{89} +(-5.36398 + 8.02776i) q^{91} +(2.16806 + 0.393050i) q^{92} +(12.5287 - 1.34163i) q^{94} -0.613137i q^{95} -13.1193i q^{97} +(-1.28961 - 12.0429i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32}+ \cdots - 128 q^{98}+O(q^{100}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$	0.887839	−	1.10079i	0.627797	−	0.778377i
$2$	0.887839	−	1.10079i	0.627797	−	0.778377i
$3$		0			0
$3$		0			0
$4$	−0.423482	−	1.95465i	−0.211741	−	0.977326i
$5$	−0.649649	−	0.434082i	−0.290532	−	0.194127i	0.401760	−	0.915745i	$-0.368399\pi$
$5$	−0.649649	−	0.434082i	−0.290532	−	0.194127i	−0.692292	+	0.721618i	$0.743399\pi$
$6$		0			0
$7$	−3.64486	+	1.50975i	−1.37763	+	0.570631i	−0.943845	−	0.330387i	$-0.892821\pi$
$7$	−3.64486	+	1.50975i	−1.37763	+	0.570631i	−0.433780	+	0.901019i	$0.642821\pi$
$8$	−2.52765	−	1.26925i	−0.893658	−	0.448748i
$9$		0			0
$10$	−1.05462	+	0.329733i	−0.333499	+	0.104271i
$11$	−5.80194	+	1.15408i	−1.74935	+	0.347968i	−0.962936	−	0.269730i	$-0.913065\pi$
$11$	−5.80194	+	1.15408i	−1.74935	+	0.347968i	−0.786415	+	0.617698i	$0.788065\pi$
$12$		0			0
$13$	2.03484	−	1.35963i	0.564362	−	0.377095i	−0.240417	−	0.970670i	$-0.577284\pi$
$13$	2.03484	−	1.35963i	0.564362	−	0.377095i	0.804779	+	0.593575i	$0.202284\pi$
$14$	−1.57413	+	5.35264i	−0.420704	+	1.43055i
$15$		0			0
$16$	−3.64133	+	1.65552i	−0.910331	+	0.413880i
$17$	−0.960477	−	0.960477i	−0.232950	−	0.232950i	0.580973	−	0.813923i	$-0.302672\pi$
$17$	−0.960477	−	0.960477i	−0.232950	−	0.232950i	−0.813923	+	0.580973i	$0.802672\pi$
$18$		0			0
$19$	0.435978	+	0.652487i	0.100020	+	0.149691i	0.878104	−	0.478469i	$-0.158808\pi$
$19$	0.435978	+	0.652487i	0.100020	+	0.149691i	−0.778084	+	0.628160i	$0.783808\pi$
$20$	−0.573364	+	1.45366i	−0.128208	+	0.325049i
$21$		0			0
$22$	−3.88079	+	7.41136i	−0.827388	+	1.58011i
$23$	−0.421603	+	1.01784i	−0.0879104	+	0.212234i	−0.961720	−	0.274033i	$-0.911642\pi$
$23$	−0.421603	+	1.01784i	−0.0879104	+	0.212234i	0.873810	+	0.486268i	$0.161642\pi$
$24$		0			0
$25$	−1.67980	−	4.05540i	−0.335960	−	0.811079i
$26$	0.309935	−	3.44707i	0.0607832	−	0.676025i
$27$		0			0
$28$	4.49456	+	6.48507i	0.849393	+	1.22556i
$29$	1.43977	+	0.286388i	0.267358	+	0.0531809i	0.326949	−	0.945042i	$-0.393980\pi$
$29$	1.43977	+	0.286388i	0.267358	+	0.0531809i	−0.0595906	+	0.998223i	$0.518980\pi$
$30$		0			0
$31$		−	6.88004i		−	1.23569i	−0.786300	−	0.617845i	$-0.788006\pi$
$31$		−	6.88004i		−	1.23569i	0.786300	−	0.617845i	$-0.211994\pi$
$32$	−1.41053	+	5.47818i	−0.249349	+	0.968414i
$33$		0			0
$34$	−1.91003	+	0.204535i	−0.327568	+	0.0350775i
$35$	3.02323	+	0.601358i	0.511019	+	0.101648i
$36$		0			0
$37$	−1.07856	+	1.61417i	−0.177313	+	0.265368i	−0.909471	−	0.415767i	$-0.863513\pi$
$37$	−1.07856	+	1.61417i	−0.177313	+	0.265368i	0.732158	+	0.681135i	$0.238513\pi$
$38$	1.10533	+	0.0993831i	0.179308	+	0.0161221i
$39$		0			0
$40$	1.09113	+	1.92177i	0.172522	+	0.303859i
$41$	2.79324	−	6.74347i	0.436230	−	1.05315i	−0.541010	−	0.841016i	$-0.681958\pi$
$41$	2.79324	−	6.74347i	0.436230	−	1.05315i	0.977240	−	0.212136i	$-0.0680421\pi$
$42$		0			0
$43$	−1.20307	−	6.04824i	−0.183467	−	0.922349i	−0.957330	−	0.288996i	$-0.906678\pi$
$43$	−1.20307	−	6.04824i	−0.183467	−	0.922349i	0.773864	−	0.633352i	$-0.218322\pi$
$44$	4.71284	+	10.8520i	0.710487	+	1.63601i
$45$		0			0
$46$	0.746114	+	1.36778i	0.110008	+	0.201668i
$47$	6.30014	+	6.30014i	0.918970	+	0.918970i	0.996955	−	0.0779845i	$-0.0248485\pi$
$47$	6.30014	+	6.30014i	0.918970	+	0.918970i	−0.0779845	+	0.996955i	$0.524848\pi$
$48$		0			0
$49$	6.05588	−	6.05588i	0.865126	−	0.865126i
$50$	−5.95554	−	1.75143i	−0.842240	−	0.247690i
$51$		0			0
$52$	−3.51933	−	3.40161i	−0.488043	−	0.471719i
$53$	−10.2655	+	2.04194i	−1.41008	+	0.280482i	−0.840660	−	0.541564i	$-0.817832\pi$
$53$	−10.2655	+	2.04194i	−1.41008	+	0.280482i	−0.569421	+	0.822046i	$0.692832\pi$
$54$		0			0
$55$	4.27019	+	1.76877i	0.575792	+	0.238501i
$56$	11.1292	+	0.810126i	1.48720	+	0.108258i
$57$		0			0
$58$	1.59354	−	1.33062i	0.209242	−	0.174719i
$59$	−4.21278	−	2.81489i	−0.548458	−	0.366468i	0.250255	−	0.968180i	$-0.419485\pi$
$59$	−4.21278	−	2.81489i	−0.548458	−	0.366468i	−0.798713	+	0.601712i	$0.794485\pi$
$60$		0			0
$61$	−2.08276	+	10.4707i	−0.266670	+	1.34064i	0.582633	+	0.812736i	$0.302023\pi$
$61$	−2.08276	+	10.4707i	−0.266670	+	1.34064i	−0.849303	+	0.527906i	$0.822977\pi$
$62$	−7.57348	−	6.10837i	−0.961833	−	0.775763i
$63$		0			0
$64$	4.77800	+	6.41644i	0.597250	+	0.802055i
$65$	−1.91212			−0.237169
$66$		0			0
$67$	1.42195	−	7.14864i	0.173719	−	0.873345i	−0.791353	−	0.611360i	$-0.790623\pi$
$67$	1.42195	−	7.14864i	0.173719	−	0.873345i	0.965072	−	0.261985i	$-0.0843771\pi$
$68$	−1.47065	+	2.28414i	−0.178343	+	0.276993i
$69$		0			0
$70$	3.34611	−	2.79404i	0.399937	−	0.333951i
$71$	−2.49385	+	1.03299i	−0.295965	+	0.122593i	−0.525725	−	0.850655i	$-0.676206\pi$
$71$	−2.49385	+	1.03299i	−0.295965	+	0.122593i	0.229760	+	0.973247i	$0.426206\pi$
$72$		0			0
$73$	−1.90488	−	0.789026i	−0.222949	−	0.0923485i	0.268413	−	0.963304i	$-0.413501\pi$
$73$	−1.90488	−	0.789026i	−0.222949	−	0.0923485i	−0.491362	+	0.870955i	$0.663501\pi$
$74$	0.819282	+	2.62039i	0.0952396	+	0.304614i
$75$		0			0
$76$	1.09076	−	1.12850i	0.125118	−	0.129448i
$77$	19.4049	−	12.9659i	2.21139	−	1.47760i
$78$		0			0
$79$	−6.20432	+	6.20432i	−0.698040	+	0.698040i	−0.963988	−	0.265947i	$-0.914315\pi$
$79$	−6.20432	+	6.20432i	−0.698040	+	0.698040i	0.265947	+	0.963988i	$0.414315\pi$
$80$	3.08422	+	0.505126i	0.344826	+	0.0564748i
$81$		0			0
$82$	−4.94320	−	9.06188i	−0.545885	−	1.00072i
$83$	−1.13685	−	1.70141i	−0.124785	−	0.186755i	0.763817	−	0.645433i	$-0.223323\pi$
$83$	−1.13685	−	1.70141i	−0.124785	−	0.186755i	−0.888602	+	0.458678i	$0.848323\pi$
$84$		0			0
$85$	0.207047	+	1.04090i	0.0224575	+	0.112901i
$86$	−7.72599	−	4.04554i	−0.833115	−	0.436242i
$87$		0			0
$88$	16.1301	+	4.44702i	1.71947	+	0.474054i
$89$	−1.15743	−	2.79429i	−0.122688	−	0.296194i	0.850589	−	0.525832i	$-0.176246\pi$
$89$	−1.15743	−	2.79429i	−0.122688	−	0.296194i	−0.973276	+	0.229638i	$0.926246\pi$
$90$		0			0
$91$	−5.36398	+	8.02776i	−0.562298	+	0.841538i
$92$	2.16806	+	0.393050i	0.226036	+	0.0409783i
$93$		0			0
$94$	12.5287	−	1.34163i	1.29223	−	0.138378i
$95$		−	0.613137i		−	0.0629066i
$96$		0			0
$97$		−	13.1193i		−	1.33207i	−0.745922	−	0.666034i	$-0.767991\pi$
$97$		−	13.1193i		−	1.33207i	0.745922	−	0.666034i	$-0.232009\pi$
$98$	−1.28961	−	12.0429i	−0.130270	−	1.21652i
$99$		0			0
$100$	−7.21552	+	5.00081i	−0.721552	+	0.500081i
$101$	2.49376	−	3.73217i	0.248138	−	0.371365i	−0.686402	−	0.727222i	$-0.740811\pi$
$101$	2.49376	−	3.73217i	0.248138	−	0.371365i	0.934540	+	0.355857i	$0.115811\pi$
$102$		0			0
$103$	4.09230	+	9.87970i	0.403227	+	0.973476i	0.986878	+	0.161471i	$0.0516237\pi$
$103$	4.09230	+	9.87970i	0.403227	+	0.973476i	−0.583651	+	0.812005i	$0.698376\pi$
$104$	−6.86906	+	0.853956i	−0.673567	+	0.0837373i
$105$		0			0
$106$	−6.86640	+	13.1131i	−0.666924	+	1.27366i
$107$	−0.745466	−	3.74771i	−0.0720669	−	0.362305i	0.927877	−	0.372886i	$-0.121632\pi$
$107$	−0.745466	−	3.74771i	−0.0720669	−	0.362305i	−0.999944	+	0.0105812i	$0.996632\pi$
$108$		0			0
$109$	−5.47688	−	8.19674i	−0.524590	−	0.785105i	0.470674	−	0.882307i	$-0.344011\pi$
$109$	−5.47688	−	8.19674i	−0.524590	−	0.785105i	−0.995265	+	0.0972021i	$0.969011\pi$
$110$	5.73829	−	3.13020i	0.547125	−	0.298453i
$111$		0			0
$112$	10.7727	−	11.5316i	1.01792	−	1.08964i
$113$	3.26239	−	3.26239i	0.306900	−	0.306900i	−0.536806	−	0.843706i	$-0.680369\pi$
$113$	3.26239	−	3.26239i	0.306900	−	0.306900i	0.843706	+	0.536806i	$0.180369\pi$
$114$		0			0
$115$	0.715720	−	0.478229i	0.0667412	−	0.0445951i
$116$	−0.0499280	−	2.93552i	−0.00463569	−	0.272557i
$117$		0			0
$118$	−6.83888	+	2.13822i	−0.629570	+	0.196839i
$119$	4.95088	+	2.05072i	0.453846	+	0.187989i
$120$		0			0
$121$	22.1680	−	9.18227i	2.01527	−	0.834752i
$122$	9.67695	+	11.5890i	0.876109	+	1.04922i
$123$		0			0
$124$	−13.4481	+	2.91357i	−1.20767	+	0.261646i
$125$	−1.43124	+	7.19532i	−0.128014	+	0.643569i
$126$		0			0
$127$	6.57619			0.583543			0.291771	−	0.956488i	$-0.405755\pi$
$127$	6.57619			0.583543			0.291771	+	0.956488i	$0.405755\pi$
$128$	11.3053	+	0.437187i	0.999253	+	0.0386422i
$129$		0			0
$130$	−1.69766	+	2.10485i	−0.148894	+	0.184607i
$131$	−0.948444	+	4.76815i	−0.0828659	+	0.416595i	0.916978	+	0.398937i	$0.130621\pi$
$131$	−0.948444	+	4.76815i	−0.0828659	+	0.416595i	−0.999844	+	0.0176578i	$0.994379\pi$
$132$		0			0
$133$	−2.57417	−	1.72000i	−0.223209	−	0.149143i
$134$	−6.60669	−	7.91211i	−0.570731	−	0.683502i
$135$		0			0
$136$	1.20866	+	3.64683i	0.103642	+	0.312713i
$137$	19.4588	+	8.06010i	1.66248	+	0.688621i	0.998263	−	0.0589215i	$-0.0187662\pi$
$137$	19.4588	+	8.06010i	1.66248	+	0.688621i	0.664214	+	0.747542i	$0.268766\pi$
$138$		0			0
$139$	−18.8196	+	3.74344i	−1.59625	+	0.317515i	−0.911513	−	0.411272i	$-0.865085\pi$
$139$	−18.8196	+	3.74344i	−1.59625	+	0.317515i	−0.684741	+	0.728786i	$0.740085\pi$
$140$	−0.104839	−	6.16403i	−0.00886051	−	0.520956i
$141$		0			0
$142$	−1.07704	+	3.66233i	−0.0903828	+	0.307336i
$143$	−10.2369	+	10.2369i	−0.856050	+	0.856050i
$144$		0			0
$145$	−0.811028	−	0.811028i	−0.0673522	−	0.0673522i
$146$	−2.55978	+	1.39634i	−0.211849	+	0.115562i
$147$		0			0
$148$	3.61189	+	1.42463i	0.296896	+	0.117104i
$149$	−0.183778	−	0.923914i	−0.0150557	−	0.0756900i	0.972527	−	0.232790i	$-0.0747855\pi$
$149$	−0.183778	−	0.923914i	−0.0150557	−	0.0756900i	−0.987583	+	0.157100i	$0.949785\pi$
$150$		0			0
$151$	4.16374	−	10.0522i	0.338841	−	0.818034i	−0.658987	−	0.752154i	$-0.729015\pi$
$151$	4.16374	−	10.0522i	0.338841	−	0.818034i	0.997828	−	0.0658792i	$-0.0209852\pi$
$152$	−0.273828	−	2.20262i	−0.0222104	−	0.178656i
$153$		0			0
$154$	2.95564	−	32.8724i	0.238172	−	2.64893i
$155$	−2.98650	+	4.46961i	−0.239881	+	0.359008i
$156$		0			0
$157$	2.16776	+	0.431195i	0.173006	+	0.0344131i	0.280833	−	0.959757i	$-0.409389\pi$
$157$	2.16776	+	0.431195i	0.173006	+	0.0344131i	−0.107827	+	0.994170i	$0.534389\pi$
$158$	1.32122	+	12.3381i	0.105111	+	0.981567i
$159$		0			0
$160$	3.29433	−	2.94661i	0.260439	−	0.232950i
$161$		−	4.34640i		−	0.342544i
$162$		0			0
$163$	−10.1978	−	2.02847i	−0.798753	−	0.158882i	−0.221193	−	0.975230i	$-0.570995\pi$
$163$	−10.1978	−	2.02847i	−0.798753	−	0.158882i	−0.577560	+	0.816348i	$0.695995\pi$
$164$	−14.3640	−	2.60406i	−1.12164	−	0.203343i
$165$		0			0
$166$	−2.88224	−	0.259150i	−0.223705	−	0.0201139i
$167$	−5.67541	−	13.7016i	−0.439176	−	1.06027i	−0.976234	−	0.216720i	$-0.930464\pi$
$167$	−5.67541	−	13.7016i	−0.439176	−	1.06027i	0.537058	−	0.843546i	$-0.319536\pi$
$168$		0			0
$169$	−2.68293	+	6.47717i	−0.206379	+	0.498244i
$170$	1.32964	+	0.696234i	0.101978	+	0.0533987i
$171$		0			0
$172$	−11.3127	+	4.91291i	−0.862588	+	0.374606i
$173$	−2.81628	−	4.21486i	−0.214118	−	0.320450i	0.708827	−	0.705382i	$-0.249225\pi$
$173$	−2.81628	−	4.21486i	−0.214118	−	0.320450i	−0.922945	+	0.384933i	$0.874225\pi$
$174$		0			0
$175$	12.2453	+	12.2453i	0.925654	+	0.925654i
$176$	19.2162	−	13.8076i	1.44847	−	1.04079i
$177$		0			0
$178$	−4.10354	−	1.20679i	−0.307574	−	0.0904526i
$179$	−2.53753	+	1.69552i	−0.189664	+	0.126729i	−0.646777	−	0.762679i	$-0.723883\pi$
$179$	−2.53753	+	1.69552i	−0.189664	+	0.126729i	0.457113	+	0.889409i	$0.348883\pi$
$180$		0			0
$181$	−6.51424	+	1.29576i	−0.484200	+	0.0963133i	−0.431153	−	0.902279i	$-0.641893\pi$
$181$	−6.51424	+	1.29576i	−0.484200	+	0.0963133i	−0.0530464	+	0.998592i	$0.516893\pi$
$182$	4.07454	+	13.0320i	0.302025	+	0.965995i
$183$		0			0
$184$	2.35756	−	2.03762i	0.173802	−	0.150215i
$185$	1.40136	−	0.580464i	0.103030	−	0.0426766i
$186$		0			0
$187$	6.68109	+	4.46416i	0.488570	+	0.326452i
$188$	9.64658	−	14.9826i	0.703549	−	1.09272i
$189$		0			0
$190$	−0.674936	−	0.544367i	−0.0489650	−	0.0394926i
$191$	1.58154			0.114436			0.0572181	−	0.998362i	$-0.481777\pi$
$191$	1.58154			0.114436			0.0572181	+	0.998362i	$0.481777\pi$
$192$		0			0
$193$	−16.3932			−1.18001			−0.590004	−	0.807401i	$-0.700874\pi$
$193$	−16.3932			−1.18001			−0.590004	+	0.807401i	$0.700874\pi$
$194$	−14.4417	−	11.6479i	−1.03685	−	0.836269i
$195$		0			0
$196$	−14.4017	−	9.27258i	−1.02869	−	0.662327i
$197$	2.24425	+	1.49956i	0.159896	+	0.106839i	0.632944	−	0.774197i	$-0.281846\pi$
$197$	2.24425	+	1.49956i	0.159896	+	0.106839i	−0.473048	+	0.881037i	$0.656846\pi$
$198$		0			0
$199$	12.1675	−	5.03992i	0.862528	−	0.357271i	0.0928322	−	0.995682i	$-0.470408\pi$
$199$	12.1675	−	5.03992i	0.862528	−	0.357271i	0.769696	+	0.638411i	$0.220408\pi$
$200$	−0.901375	+	12.3827i	−0.0637369	+	0.875589i
$201$		0			0
$202$	−1.89428	−	6.05867i	−0.133281	−	0.426287i
$203$	−5.68012	+	1.12985i	−0.398666	+	0.0792996i
$204$		0			0
$205$	−4.74184	+	3.16839i	−0.331184	+	0.221290i
$206$	14.5088	+	4.26681i	1.01088	+	0.297283i
$207$		0			0
$208$	−5.15860	+	8.31958i	−0.357684	+	0.576859i
$209$	−3.28254	−	3.28254i	−0.227058	−	0.227058i
$210$		0			0
$211$	3.81684	+	5.71230i	0.262762	+	0.393251i	0.939267	−	0.343187i	$-0.111506\pi$
$211$	3.81684	+	5.71230i	0.262762	+	0.393251i	−0.676505	+	0.736438i	$0.736506\pi$
$212$	8.33856	+	19.2008i	0.572695	+	1.31872i
$213$		0			0
$214$	−4.78730	−	2.50676i	−0.327253	−	0.171359i
$215$	−1.84386	+	4.45147i	−0.125750	+	0.303588i
$216$		0			0
$217$	10.3871	+	25.0767i	0.705124	+	1.70232i
$218$	−13.8855	−	1.24848i	−0.940444	−	0.0845578i
$219$		0			0
$220$	1.64898	−	9.09578i	0.111174	−	0.613237i
$221$	−3.26031	−	0.648516i	−0.219312	−	0.0436239i
$222$		0			0
$223$			3.88311i			0.260032i	0.991512	+	0.130016i	$0.0415029\pi$
$223$			3.88311i			0.260032i	−0.991512	+	0.130016i	$0.958497\pi$
$224$	−3.12949	−	22.0967i	−0.209098	−	1.47640i
$225$		0			0
$226$	−0.694732	−	6.48769i	−0.0462129	−	0.431555i
$227$	−22.5337	−	4.48224i	−1.49562	−	0.297497i	−0.621577	−	0.783353i	$-0.713508\pi$
$227$	−22.5337	−	4.48224i	−1.49562	−	0.297497i	−0.874039	+	0.485856i	$0.838508\pi$
$228$		0			0
$229$	−3.41606	+	5.11250i	−0.225740	+	0.337844i	−0.927000	−	0.375062i	$-0.877621\pi$
$229$	−3.41606	+	5.11250i	−0.225740	+	0.337844i	0.701260	+	0.712906i	$0.252621\pi$
$230$	0.109014	−	1.21245i	0.00718820	−	0.0799465i
$231$		0			0
$232$	−3.27573	−	2.55131i	−0.215062	−	0.167502i
$233$	−0.733834	+	1.77163i	−0.0480751	+	0.116064i	−0.946093	−	0.323896i	$-0.895007\pi$
$233$	−0.733834	+	1.77163i	−0.0480751	+	0.116064i	0.898018	+	0.439960i	$0.145007\pi$
$234$		0			0
$235$	−1.35811	−	6.82766i	−0.0885930	−	0.445387i
$236$	−3.71809	+	9.42658i	−0.242027	+	0.613618i
$237$		0			0
$238$	6.65300	−	3.62917i	0.431250	−	0.235244i
$239$	6.09870	+	6.09870i	0.394492	+	0.394492i	0.876285	−	0.481793i	$-0.160014\pi$
$239$	6.09870	+	6.09870i	0.394492	+	0.394492i	−0.481793	+	0.876285i	$0.660014\pi$
$240$		0			0
$241$	5.21549	−	5.21549i	0.335959	−	0.335959i	−0.518885	−	0.854844i	$-0.673653\pi$
$241$	5.21549	−	5.21549i	0.335959	−	0.335959i	0.854844	+	0.518885i	$0.173653\pi$
$242$	9.57383	−	32.5547i	0.615429	−	2.09269i
$243$		0			0
$244$	21.3487	−	0.363102i	1.36671	−	0.0232452i
$245$	−6.56295	+	1.30545i	−0.419291	+	0.0834022i
$246$		0			0
$247$	1.77429	+	0.734933i	0.112895	+	0.0467627i
$248$	−8.73249	+	17.3903i	−0.554514	+	1.10429i
$249$		0			0
$250$	6.64984	+	7.96379i	0.420573	+	0.503674i
$251$	−3.73150	−	2.49331i	−0.235530	−	0.157376i	0.432204	−	0.901776i	$-0.357736\pi$
$251$	−3.73150	−	2.49331i	−0.235530	−	0.157376i	−0.667735	+	0.744399i	$0.732736\pi$
$252$		0			0
$253$	1.27145	−	6.39201i	0.0799354	−	0.401862i
$254$	5.83860	−	7.23901i	0.366347	−	0.454216i
$255$		0			0
$256$	10.5185	−	12.0566i	0.657407	−	0.753536i
$257$	5.86891			0.366092			0.183046	−	0.983104i	$-0.441404\pi$
$257$	5.86891			0.366092			0.183046	+	0.983104i	$0.441404\pi$
$258$		0			0
$259$	1.49418	−	7.51177i	0.0928441	−	0.466759i
$260$	0.809749	+	3.73753i	0.0502185	+	0.231792i
$261$		0			0
$262$	4.40667	+	5.27739i	0.272245	+	0.326038i
$263$	27.1667	−	11.2528i	1.67517	−	0.693877i	0.676090	−	0.736819i	$-0.263673\pi$
$263$	27.1667	−	11.2528i	1.67517	−	0.693877i	0.999078	+	0.0429417i	$0.0136730\pi$
$264$		0			0
$265$	7.55537	+	3.12954i	0.464123	+	0.192246i
$266$	−4.17881	+	1.30653i	−0.256219	+	0.0801087i
$267$		0			0
$268$	−14.5753	+	0.247899i	−0.890326	+	0.0151428i
$269$	−9.18707	+	6.13860i	−0.560145	+	0.374277i	−0.803176	−	0.595741i	$-0.796858\pi$
$269$	−9.18707	+	6.13860i	−0.560145	+	0.374277i	0.243031	+	0.970019i	$0.421858\pi$
$270$		0			0
$271$	−17.2217	+	17.2217i	−1.04614	+	1.04614i	−0.0472600	+	0.998883i	$0.515049\pi$
$271$	−17.2217	+	17.2217i	−1.04614	+	1.04614i	−0.998883	+	0.0472600i	$0.984951\pi$
$272$	5.08750	+	1.90732i	0.308475	+	0.115648i
$273$		0			0
$274$	26.1488	−	14.2640i	1.57970	−	0.861720i
$275$	14.4263	+	21.5906i	0.869941	+	1.30196i
$276$		0			0
$277$	5.36979	+	26.9957i	0.322639	+	1.62202i	0.712868	+	0.701299i	$0.247396\pi$
$277$	5.36979	+	26.9957i	0.322639	+	1.62202i	−0.390228	+	0.920718i	$0.627604\pi$
$278$	−12.5880	+	24.0400i	−0.754978	+	1.44182i
$279$		0			0
$280$	−6.87839	−	5.35726i	−0.411062	−	0.320158i
$281$	6.20216	+	14.9733i	0.369990	+	0.893234i	0.993751	+	0.111619i	$0.0356037\pi$
$281$	6.20216	+	14.9733i	0.369990	+	0.893234i	−0.623762	+	0.781615i	$0.714396\pi$
$282$		0			0
$283$	−4.95606	+	7.41727i	−0.294607	+	0.440911i	−0.949015	−	0.315231i	$-0.897918\pi$
$283$	−4.95606	+	7.41727i	−0.294607	+	0.440911i	0.654408	+	0.756142i	$0.272918\pi$
$284$	3.07523	+	4.43715i	0.182481	+	0.263297i
$285$		0			0
$286$	2.17996	+	20.3574i	0.128904	+	1.20376i
$287$			28.7960i			1.69978i
$288$		0			0
$289$		−	15.1550i		−	0.891469i
$290$	−1.61284	+	0.172710i	−0.0947090	+	0.0101419i
$291$		0			0
$292$	−0.735589	+	4.05751i	−0.0430471	+	0.237448i
$293$	−13.5525	+	20.2828i	−0.791747	+	1.18493i	0.187500	+	0.982265i	$0.439961\pi$
$293$	−13.5525	+	20.2828i	−0.791747	+	1.18493i	−0.979247	+	0.202669i	$0.935039\pi$
$294$		0			0
$295$	1.51494	+	3.65738i	0.0882031	+	0.212941i
$296$	4.77500	−	2.71110i	0.277541	−	0.157579i
$297$		0			0
$298$	−1.18020	−	0.617986i	−0.0683673	−	0.0357990i
$299$	0.525997	+	2.64436i	0.0304192	+	0.152928i
$300$		0			0
$301$	13.5163	+	20.2286i	0.779069	+	1.16596i
$302$	−7.36860	−	13.5081i	−0.424015	−	0.777305i
$303$		0			0
$304$	−2.66774	−	1.65415i	−0.153005	−	0.0948718i
$305$	5.89822	−	5.89822i	0.337731	−	0.337731i
$306$		0			0
$307$	8.15880	−	5.45154i	0.465647	−	0.311136i	−0.300521	−	0.953775i	$-0.597161\pi$
$307$	8.15880	−	5.45154i	0.465647	−	0.311136i	0.766169	+	0.642639i	$0.222161\pi$
$308$	−33.5615	−	32.4389i	−1.91234	−	1.84838i
$309$		0			0
$310$	2.26858	+	7.25580i	0.128846	+	0.412102i
$311$	−28.3647	−	11.7490i	−1.60842	−	0.666227i	−0.615841	−	0.787870i	$-0.711184\pi$
$311$	−28.3647	−	11.7490i	−1.60842	−	0.666227i	−0.992574	+	0.121643i	$0.961184\pi$
$312$		0			0
$313$	−22.4586	+	9.30264i	−1.26943	+	0.525816i	−0.912792	−	0.408425i	$-0.866078\pi$
$313$	−22.4586	+	9.30264i	−1.26943	+	0.525816i	−0.356641	+	0.934242i	$0.616078\pi$
$314$	2.39928	−	2.00342i	0.135399	−	0.113060i
$315$		0			0
$316$	14.7547	+	9.49986i	0.830017	+	0.534409i
$317$	−1.29802	+	6.52557i	−0.0729039	+	0.366513i	−0.999965	−	0.00839833i	$-0.997327\pi$
$317$	−1.29802	+	6.52557i	−0.0729039	+	0.366513i	0.927061	+	0.374911i	$0.122327\pi$
$318$		0			0
$319$	−8.68396			−0.486209
$320$	−0.318766	−	6.24248i	−0.0178195	−	0.348965i
$321$		0			0
$322$	−4.78447	−	3.85890i	−0.266628	−	0.215048i
$323$	0.207952	−	1.04544i	0.0115707	−	0.0581701i
$324$		0			0
$325$	−8.93197	−	5.96815i	−0.495457	−	0.331054i
$326$	−11.2869	+	9.42469i	−0.625125	+	0.521985i
$327$		0			0
$328$	−15.6195	+	13.4998i	−0.862441	+	0.745401i
$329$	−32.4747	−	13.4515i	−1.79039	−	0.741604i
$330$		0			0
$331$	3.84304	−	0.764428i	0.211233	−	0.0420168i	−0.0883396	−	0.996090i	$-0.528156\pi$
$331$	3.84304	−	0.764428i	0.211233	−	0.0420168i	0.299572	+	0.954074i	$0.403156\pi$
$332$	−2.84424	+	2.94266i	−0.156098	+	0.161500i
$333$		0			0
$334$	−20.1215	−	5.91742i	−1.10100	−	0.323787i
$335$	−4.02686	+	4.02686i	−0.220011	+	0.220011i
$336$		0			0
$337$	13.8621	+	13.8621i	0.755119	+	0.755119i	0.975430	−	0.220311i	$-0.0707072\pi$
$337$	13.8621	+	13.8621i	0.755119	+	0.755119i	−0.220311	+	0.975430i	$0.570707\pi$
$338$	4.74800	+	8.70404i	0.258257	+	0.473437i
$339$		0			0
$340$	1.94691	−	0.845507i	0.105586	−	0.0458541i
$341$	7.94010	+	39.9176i	0.429980	+	2.16166i
$342$		0			0
$343$	−2.36172	+	5.70170i	−0.127521	+	0.307863i
$344$	−4.63580	+	16.8148i	−0.249946	+	0.906595i
$345$		0			0
$346$	−7.14008	−	0.641984i	−0.383853	−	0.0345132i
$347$	13.7444	−	20.5699i	0.737836	−	1.10425i	−0.252773	−	0.967526i	$-0.581343\pi$
$347$	13.7444	−	20.5699i	0.737836	−	1.10425i	0.990609	−	0.136724i	$-0.0436574\pi$
$348$		0			0
$349$	−34.6278	−	6.88789i	−1.85358	−	0.368700i	−0.862953	−	0.505284i	$-0.831388\pi$
$349$	−34.6278	−	6.88789i	−1.85358	−	0.368700i	−0.990628	+	0.136584i	$0.956388\pi$
$350$	24.3513	−	2.60765i	1.30163	−	0.139385i
$351$		0			0
$352$	1.86158	−	33.4119i	0.0992224	−	1.78086i
$353$		−	16.3511i		−	0.870283i	−0.900362	−	0.435141i	$-0.856698\pi$
$353$		−	16.3511i		−	0.870283i	0.900362	−	0.435141i	$-0.143302\pi$
$354$		0			0
$355$	2.06853	+	0.411455i	0.109786	+	0.0218378i
$356$	−4.97171	+	3.44571i	−0.263500	+	0.182622i
$357$		0			0
$358$	−0.386502	+	4.29864i	−0.0204272	+	0.227190i
$359$	0.837827	+	2.02269i	0.0442188	+	0.106754i	0.944446	−	0.328667i	$-0.106599\pi$
$359$	0.837827	+	2.02269i	0.0442188	+	0.106754i	−0.900227	+	0.435421i	$0.856599\pi$
$360$		0			0
$361$	7.03532	−	16.9848i	0.370280	−	0.893935i
$362$	−4.35723	+	8.32125i	−0.229011	+	0.437355i
$363$		0			0
$364$	17.9630	+	7.08509i	0.941518	+	0.371360i
$365$	0.895000	+	1.33946i	0.0468464	+	0.0701106i
$366$		0			0
$367$	20.9060	+	20.9060i	1.09129	+	1.09129i	0.995392	+	0.0958935i	$0.0305708\pi$
$367$	20.9060	+	20.9060i	1.09129	+	1.09129i	0.0958935	+	0.995392i	$0.469429\pi$
$368$	−0.149860	−	4.40426i	−0.00781201	−	0.229588i
$369$		0			0
$370$	0.605217	−	2.05797i	0.0314637	−	0.106989i
$371$	34.3336	−	22.9410i	1.78251	−	1.19104i
$372$		0			0
$373$	23.8329	−	4.74066i	1.23402	−	0.245462i	0.465362	−	0.885121i	$-0.345924\pi$
$373$	23.8329	−	4.74066i	1.23402	−	0.245462i	0.768659	+	0.639659i	$0.220924\pi$
$374$	10.8459	−	3.39103i	0.560826	−	0.175346i
$375$		0			0
$376$	−7.92807	−	23.9210i	−0.408859	−	1.23363i
$377$	3.31907	−	1.37481i	0.170941	−	0.0708061i
$378$		0			0
$379$	−20.7596	−	13.8712i	−1.06635	−	0.712513i	−0.106867	−	0.994273i	$-0.534082\pi$
$379$	−20.7596	−	13.8712i	−1.06635	−	0.712513i	−0.959485	+	0.281760i	$0.909082\pi$
$380$	−1.19847	+	0.259653i	−0.0614802	+	0.0133199i
$381$		0			0
$382$	1.40415	−	1.74094i	0.0718427	−	0.0890744i
$383$	24.5463			1.25426			0.627128	−	0.778916i	$-0.284230\pi$
$383$	24.5463			1.25426			0.627128	+	0.778916i	$0.284230\pi$
$384$		0			0
$385$	−18.2346			−0.929323
$386$	−14.5545	+	18.0455i	−0.740806	+	0.918491i
$387$		0			0
$388$	−25.6437	+	5.55581i	−1.30186	+	0.282053i
$389$	−19.0280	−	12.7141i	−0.964758	−	0.644630i	−0.0298624	−	0.999554i	$-0.509507\pi$
$389$	−19.0280	−	12.7141i	−0.964758	−	0.644630i	−0.934895	+	0.354924i	$0.884507\pi$
$390$		0			0
$391$	1.38255	−	0.572672i	0.0699187	−	0.0289613i
$392$	−22.9936	+	7.62070i	−1.16135	+	0.384903i
$393$		0			0
$394$	3.64324	−	1.13908i	0.183544	−	0.0573862i
$395$	6.72381	−	1.33745i	0.338312	−	0.0672944i
$396$		0			0
$397$	20.2490	−	13.5300i	1.01627	−	0.679050i	0.0683838	−	0.997659i	$-0.478216\pi$
$397$	20.2490	−	13.5300i	1.01627	−	0.679050i	0.947886	+	0.318609i	$0.103216\pi$
$398$	5.25484	−	17.8685i	0.263401	−	0.895665i
$399$		0			0
$400$	12.8305	+	11.9861i	0.641524	+	0.599304i
$401$	−13.4688	−	13.4688i	−0.672599	−	0.672599i	0.285716	−	0.958314i	$-0.407769\pi$
$401$	−13.4688	−	13.4688i	−0.672599	−	0.672599i	−0.958314	+	0.285716i	$0.907769\pi$
$402$		0			0
$403$	−9.35433	−	13.9997i	−0.465972	−	0.697377i
$404$	−8.35115	−	3.29392i	−0.415485	−	0.163878i
$405$		0			0
$406$	−3.79931	+	7.25575i	−0.188557	+	0.360097i
$407$	4.39483	−	10.6101i	0.217844	−	0.525922i
$408$		0			0
$409$	−3.05166	−	7.36736i	−0.150895	−	0.364293i	0.830299	−	0.557319i	$-0.188170\pi$
$409$	−3.05166	−	7.36736i	−0.150895	−	0.364293i	−0.981194	+	0.193026i	$0.938170\pi$
$410$	−0.722250	+	8.03280i	−0.0356694	+	0.396712i
$411$		0			0
$412$	17.5783	−	12.1829i	0.866023	−	0.600209i
$413$	19.6048	+	3.89963i	0.964688	+	0.191888i
$414$		0			0
$415$			1.59881i			0.0784824i
$416$	4.57811	+	13.0650i	0.224460	+	0.640564i
$417$		0			0
$418$	−6.52775	+	0.699022i	−0.319283	+	0.0341903i
$419$	12.5395	+	2.49426i	0.612593	+	0.121852i	0.491629	−	0.870805i	$-0.336402\pi$
$419$	12.5395	+	2.49426i	0.612593	+	0.121852i	0.120964	+	0.992657i	$0.461402\pi$
$420$		0			0
$421$	−10.8903	+	16.2984i	−0.530759	+	0.794337i	−0.995858	−	0.0909215i	$-0.971019\pi$
$421$	−10.8903	+	16.2984i	−0.530759	+	0.794337i	0.465099	+	0.885259i	$0.346019\pi$
$422$	9.67679	+	0.870065i	0.471059	+	0.0423541i
$423$		0			0
$424$	28.5394	+	7.86824i	1.38600	+	0.382115i
$425$	−2.28170	+	5.50852i	−0.110679	+	0.267203i
$426$		0			0
$427$	−8.21683	−	41.3088i	−0.397640	−	1.99907i
$428$	−7.00978	+	3.04422i	−0.338830	+	0.147148i
$429$		0			0
$430$	3.26309	+	5.98189i	0.157360	+	0.288472i
$431$	−18.4810	−	18.4810i	−0.890199	−	0.890199i	0.104343	−	0.994541i	$-0.466726\pi$
$431$	−18.4810	−	18.4810i	−0.890199	−	0.890199i	−0.994541	+	0.104343i	$0.966726\pi$
$432$		0			0
$433$	6.00332	−	6.00332i	0.288501	−	0.288501i	−0.547986	−	0.836487i	$-0.684605\pi$
$433$	6.00332	−	6.00332i	0.288501	−	0.288501i	0.836487	+	0.547986i	$0.184605\pi$
$434$	36.8263	+	10.8301i	1.76772	+	0.519860i
$435$		0			0
$436$	−13.7024	+	14.1766i	−0.656226	+	0.678935i
$437$	−0.847937	+	0.168665i	−0.0405623	+	0.00806835i
$438$		0			0
$439$	−19.8680	−	8.22958i	−0.948246	−	0.392777i	−0.145675	−	0.989333i	$-0.546535\pi$
$439$	−19.8680	−	8.22958i	−0.948246	−	0.392777i	−0.802571	+	0.596556i	$0.796535\pi$
$440$	−8.54852	−	9.89077i	−0.407535	−	0.471524i
$441$		0			0
$442$	−3.60851	+	3.01314i	−0.171639	+	0.143320i
$443$	−15.5336	−	10.3792i	−0.738023	−	0.493131i	0.128848	−	0.991664i	$-0.458872\pi$
$443$	−15.5336	−	10.3792i	−0.738023	−	0.493131i	−0.866871	+	0.498533i	$0.833872\pi$
$444$		0			0
$445$	−0.461025	+	2.31773i	−0.0218547	+	0.109871i
$446$	4.27449	+	3.44757i	0.202403	+	0.163247i
$447$		0			0
$448$	−27.1023	−	16.1734i	−1.28047	−	0.764122i
$449$	−32.6778			−1.54216			−0.771081	−	0.636737i	$-0.780284\pi$
$449$	−32.6778			−1.54216			−0.771081	+	0.636737i	$0.780284\pi$
$450$		0			0
$451$	−8.42370	+	42.3488i	−0.396657	+	1.99413i
$452$	−7.75840	−	4.99527i	−0.364925	−	0.234958i
$453$		0			0
$454$	−24.9403	+	20.8254i	−1.17051	+	0.977386i
$455$	6.96941	−	2.88682i	0.326731	−	0.135336i
$456$		0			0
$457$	−23.3834	−	9.68573i	−1.09383	−	0.453079i	−0.238489	−	0.971145i	$-0.576652\pi$
$457$	−23.3834	−	9.68573i	−1.09383	−	0.453079i	−0.855341	+	0.518066i	$0.826652\pi$
$458$	2.59488	+	8.29945i	0.121251	+	0.387808i
$459$		0			0
$460$	−1.23787	−	1.19646i	−0.0577158	−	0.0557853i
$461$	−2.39596	+	1.60093i	−0.111591	+	0.0745627i	−0.610113	−	0.792314i	$-0.708876\pi$
$461$	−2.39596	+	1.60093i	−0.111591	+	0.0745627i	0.498522	+	0.866877i	$0.333876\pi$
$462$		0			0
$463$	24.5897	−	24.5897i	1.14278	−	1.14278i	0.154840	−	0.987940i	$-0.450514\pi$
$463$	24.5897	−	24.5897i	1.14278	−	1.14278i	0.987940	−	0.154840i	$-0.0494863\pi$
$464$	−5.71678	+	1.34073i	−0.265395	+	0.0622420i
$465$		0			0
$466$	1.29867	+	2.38072i	0.0601598	+	0.110285i
$467$	7.08500	+	10.6035i	0.327855	+	0.490670i	0.958379	−	0.285500i	$-0.0921598\pi$
$467$	7.08500	+	10.6035i	0.327855	+	0.490670i	−0.630524	+	0.776170i	$0.717160\pi$
$468$		0			0
$469$	5.60983	+	28.2025i	0.259038	+	1.30227i
$470$	−8.72160	−	4.56687i	−0.402298	−	0.210654i
$471$		0			0
$472$	7.07563	+	12.4621i	0.325682	+	0.573616i
$473$	13.9603	+	33.7031i	0.641895	+	1.54967i
$474$		0			0
$475$	1.91374	−	2.86411i	0.0878082	−	0.131414i
$476$	1.91184	−	10.5457i	0.0876288	−	0.483361i
$477$		0			0
$478$	12.1281	−	1.29873i	0.554724	−	0.0594024i
$479$			8.39981i			0.383797i	0.981415	+	0.191899i	$0.0614644\pi$
$479$			8.39981i			0.383797i	−0.981415	+	0.191899i	$0.938536\pi$
$480$		0			0
$481$			4.75101i			0.216628i
$482$	−1.11065	−	10.3717i	−0.0505886	−	0.472417i
$483$		0			0
$484$	−27.3359	−	39.4421i	−1.24254	−	1.79282i
$485$	−5.69487	+	8.52297i	−0.258591	+	0.387008i
$486$		0			0
$487$	−6.40268	−	15.4574i	−0.290133	−	0.700443i	0.709859	−	0.704343i	$-0.248758\pi$
$487$	−6.40268	−	15.4574i	−0.290133	−	0.700443i	−0.999992	+	0.00390038i	$0.998758\pi$
$488$	18.5545	−	23.8228i	0.839922	−	1.07841i
$489$		0			0
$490$	−4.38982	+	8.38347i	−0.198312	+	0.378726i
$491$	−1.85105	−	9.30587i	−0.0835368	−	0.419968i	−0.999811	−	0.0194174i	$-0.993819\pi$
$491$	−1.85105	−	9.30587i	−0.0835368	−	0.419968i	0.916275	−	0.400551i	$-0.131181\pi$
$492$		0			0
$493$	−1.10779	−	1.65793i	−0.0498926	−	0.0746695i
$494$	2.38429	−	1.30062i	0.107274	−	0.0585174i
$495$		0			0
$496$	11.3900	+	25.0524i	0.511428	+	1.12489i
$497$	7.53017	−	7.53017i	0.337774	−	0.337774i
$498$		0			0
$499$	12.4453	−	8.31569i	0.557129	−	0.372261i	−0.244899	−	0.969549i	$-0.578755\pi$
$499$	12.4453	−	8.31569i	0.557129	−	0.372261i	0.802027	+	0.597287i	$0.203755\pi$
$500$	14.6705	−	0.249518i	0.656083	−	0.0111588i
$501$		0			0
$502$	−6.05759	+	1.89395i	−0.270363	+	0.0845309i
$503$	−7.01440	−	2.90546i	−0.312757	−	0.129548i	0.220783	−	0.975323i	$-0.429139\pi$
$503$	−7.01440	−	2.90546i	−0.312757	−	0.129548i	−0.533540	+	0.845775i	$0.679139\pi$
$504$		0			0
$505$	−3.24013	+	1.34211i	−0.144184	+	0.0597230i
$506$	−5.90743	−	7.07468i	−0.262617	−	0.314508i
$507$		0			0
$508$	−2.78490	−	12.8542i	−0.123560	−	0.570311i
$509$	6.73996	−	33.8841i	0.298743	−	1.50188i	−0.481521	−	0.876435i	$-0.659915\pi$
$509$	6.73996	−	33.8841i	0.298743	−	1.50188i	0.780264	−	0.625450i	$-0.215085\pi$
$510$		0			0
$511$	8.13423			0.359837
$512$	−3.93303	−	22.2830i	−0.173817	−	0.984778i
$513$		0			0
$514$	5.21065	−	6.46044i	0.229832	−	0.284958i
$515$	1.63003	−	8.19473i	0.0718279	−	0.361103i
$516$		0			0
$517$	−43.8239	−	29.2822i	−1.92737	−	1.28783i
$518$	−6.94230	−	8.31403i	−0.305027	−	0.365298i
$519$		0			0
$520$	4.83317	+	2.42696i	0.211948	+	0.106429i
$521$	35.4201	+	14.6715i	1.55178	+	0.642770i	0.983638	−	0.180158i	$-0.0576610\pi$
$521$	35.4201	+	14.6715i	1.55178	+	0.642770i	0.568146	+	0.822928i	$0.307661\pi$
$522$		0			0
$523$	−3.91974	+	0.779685i	−0.171398	+	0.0340933i	−0.280043	−	0.959987i	$-0.590349\pi$
$523$	−3.91974	+	0.779685i	−0.171398	+	0.0340933i	0.108645	+	0.994081i	$0.465349\pi$
$524$	9.72172	−	0.165349i	0.424695	−	0.00722330i
$525$		0			0
$526$	11.7326	−	39.8955i	0.511568	−	1.73953i
$527$	−6.60811	+	6.60811i	−0.287854	+	0.287854i
$528$		0			0
$529$	15.4052	+	15.4052i	0.669792	+	0.669792i
$530$	10.1529	−	5.53836i	0.441015	−	0.240571i
$531$		0			0
$532$	−2.27189	+	5.75999i	−0.0984990	+	0.249727i
$533$	−3.48487	−	17.5196i	−0.150946	−	0.758859i
$534$		0			0
$535$	−1.14252	+	2.75829i	−0.0493955	+	0.119251i
$536$	−12.6676	+	16.2644i	−0.547157	+	0.702516i
$537$		0			0
$538$	−1.39932	+	15.5631i	−0.0603291	+	0.670974i
$539$	−28.1469	+	42.1248i	−1.21237	+	1.81445i
$540$		0			0
$541$	37.1103	+	7.38169i	1.59550	+	0.317364i	0.911239	−	0.411878i	$-0.135127\pi$
$541$	37.1103	+	7.38169i	1.59550	+	0.317364i	0.684256	+	0.729242i	$0.260127\pi$
$542$	3.66739	+	34.2476i	0.157528	+	1.47106i
$543$		0			0
$544$	6.61644	−	3.90688i	0.283678	−	0.167506i
$545$			7.70242i			0.329935i
$546$		0			0
$547$	6.05489	+	1.20439i	0.258888	+	0.0514961i	0.322828	−	0.946458i	$-0.395366\pi$
$547$	6.05489	+	1.20439i	0.258888	+	0.0514961i	−0.0639395	+	0.997954i	$0.520366\pi$
$548$	7.51423	−	41.4485i	0.320992	−	1.77059i
$549$		0			0
$550$	36.5750	+	3.28855i	1.55956	+	0.140224i
$551$	0.440842	+	1.06429i	0.0187805	+	0.0453402i
$552$		0			0
$553$	13.2469	−	31.9808i	0.563315	−	1.35996i
$554$	34.4842	+	18.0569i	1.46509	+	0.767163i
$555$		0			0
$556$	15.2869	+	35.2004i	0.648308	+	1.49283i
$557$	−10.4706	−	15.6704i	−0.443653	−	0.663974i	0.540490	−	0.841351i	$-0.318239\pi$
$557$	−10.4706	−	15.6704i	−0.443653	−	0.663974i	−0.984143	+	0.177377i	$0.943239\pi$
$558$		0			0
$559$	−10.6714	−	10.6714i	−0.451354	−	0.451354i
$560$	−12.0041	+	2.81528i	−0.507267	+	0.118967i
$561$		0			0
$562$	21.9890	+	6.46663i	0.927551	+	0.272778i
$563$	31.7318	−	21.2025i	1.33733	−	0.893578i	0.338458	−	0.940981i	$-0.390095\pi$
$563$	31.7318	−	21.2025i	1.33733	−	0.893578i	0.998876	+	0.0474033i	$0.0150946\pi$
$564$		0			0
$565$	−3.53555	+	0.703266i	−0.148742	+	0.0295866i
$566$	3.76468	+	12.0409i	0.158241	+	0.506118i
$567$		0			0
$568$	7.61469	+	0.554297i	0.319505	+	0.0232578i
$569$	−5.70005	+	2.36104i	−0.238958	+	0.0989798i	−0.498949	−	0.866631i	$-0.666281\pi$
$569$	−5.70005	+	2.36104i	−0.238958	+	0.0989798i	0.259991	+	0.965611i	$0.416281\pi$
$570$		0			0
$571$	25.4415	+	16.9994i	1.06469	+	0.711405i	0.959118	−	0.283007i	$-0.0913319\pi$
$571$	25.4415	+	16.9994i	1.06469	+	0.711405i	0.105574	+	0.994411i	$0.466332\pi$
$572$	24.3447	+	15.6744i	1.01790	+	0.655379i
$573$		0			0
$574$	31.6984	+	25.5663i	1.32307	+	1.06712i
$575$	4.83596			0.201673
$576$		0			0
$577$	13.1957			0.549345			0.274673	−	0.961538i	$-0.411431\pi$
$577$	13.1957			0.549345			0.274673	+	0.961538i	$0.411431\pi$
$578$	−16.6825	−	13.4552i	−0.693899	−	0.559662i
$579$		0			0
$580$	−1.24182	+	1.92873i	−0.0515638	+	0.0800863i
$581$	6.71236	+	4.48506i	0.278476	+	0.186071i
$582$		0			0
$583$	57.2035	−	23.6945i	2.36913	−	0.981324i
$584$	3.81338	+	4.41215i	0.157799	+	0.182576i
$585$		0			0
$586$	10.2946	+	32.9264i	0.425268	+	1.36018i
$587$	−28.1626	+	5.60188i	−1.16239	+	0.231215i	−0.738344	−	0.674424i	$-0.764392\pi$
$587$	−28.1626	+	5.60188i	−1.16239	+	0.231215i	−0.424050	+	0.905639i	$0.639392\pi$
$588$		0			0
$589$	4.48913	−	2.99954i	0.184971	−	0.123594i
$590$	5.37104	+	1.57954i	0.221122	+	0.0650286i
$591$		0			0
$592$	1.25508	−	7.66330i	0.0515833	−	0.314960i
$593$	−8.50593	−	8.50593i	−0.349297	−	0.349297i	0.510551	−	0.859848i	$-0.329441\pi$
$593$	−8.50593	−	8.50593i	−0.349297	−	0.349297i	−0.859848	+	0.510551i	$0.829441\pi$
$594$		0			0
$595$	−2.32615	−	3.48133i	−0.0953630	−	0.142721i
$596$	−1.72810	+	0.750483i	−0.0707859	+	0.0307410i
$597$		0			0
$598$	3.37789	+	1.76876i	0.138132	+	0.0723299i
$599$	17.7398	−	42.8278i	0.724831	−	1.74990i	0.0657345	−	0.997837i	$-0.479061\pi$
$599$	17.7398	−	42.8278i	0.724831	−	1.74990i	0.659096	−	0.752059i	$-0.270939\pi$
$600$		0			0
$601$	9.36011	+	22.5973i	0.381807	+	0.921763i	0.991617	+	0.129215i	$0.0412459\pi$
$601$	9.36011	+	22.5973i	0.381807	+	0.921763i	−0.609810	+	0.792548i	$0.708754\pi$
$602$	34.2679	+	3.08111i	1.39665	+	0.125577i
$603$		0			0
$604$	−21.4117	−	3.88175i	−0.871232	−	0.157946i
$605$	−18.3872	−	3.65745i	−0.747548	−	0.148697i
$606$		0			0
$607$		−	19.9552i		−	0.809956i	−0.914326	−	0.404978i	$-0.867279\pi$
$607$		−	19.9552i		−	0.809956i	0.914326	−	0.404978i	$-0.132721\pi$
$608$	−4.18940	+	1.46801i	−0.169902	+	0.0595356i
$609$		0			0
$610$	−1.25604	−	11.7294i	−0.0508554	−	0.474909i
$611$	21.3856	+	4.25387i	0.865170	+	0.172093i
$612$		0			0
$613$	15.7066	−	23.5066i	0.634384	−	0.949423i	−0.365443	−	0.930834i	$-0.619083\pi$
$613$	15.7066	−	23.5066i	0.634384	−	0.949423i	0.999827	−	0.0185890i	$-0.00591740\pi$
$614$	1.24270	−	13.8212i	0.0501514	−	0.557779i
$615$		0			0
$616$	−65.5057	+	8.14361i	−2.63930	+	0.328116i
$617$	7.93425	−	19.1550i	0.319421	−	0.771150i	−0.679864	−	0.733338i	$-0.737961\pi$
$617$	7.93425	−	19.1550i	0.319421	−	0.771150i	0.999285	−	0.0378118i	$-0.0120387\pi$
$618$		0			0
$619$	−1.06040	−	5.33101i	−0.0426212	−	0.214271i	0.953606	−	0.301059i	$-0.0973400\pi$
$619$	−1.06040	−	5.33101i	−0.0426212	−	0.214271i	−0.996227	+	0.0867872i	$0.972340\pi$
$620$	10.0013	+	3.94476i	0.401660	+	0.158425i
$621$		0			0
$622$	−38.1166	+	20.7924i	−1.52833	+	0.833697i
$623$	8.43735	+	8.43735i	0.338035	+	0.338035i
$624$		0			0
$625$	−11.4662	+	11.4662i	−0.458647	+	0.458647i
$626$	−9.69933	+	32.9814i	−0.387663	+	1.31820i
$627$		0			0
$628$	−0.0751732	−	4.41982i	−0.00299974	−	0.176370i
$629$	2.58630	−	0.514447i	0.103123	−	0.0205124i
$630$		0			0
$631$	−35.9213	−	14.8791i	−1.43000	−	0.592327i	−0.472652	−	0.881249i	$-0.656703\pi$
$631$	−35.9213	−	14.8791i	−1.43000	−	0.592327i	−0.957353	+	0.288922i	$0.906703\pi$
$632$	23.5572	−	7.80749i	0.937054	−	0.310565i
$633$		0			0
$634$	6.03086	+	7.22250i	0.239516	+	0.286842i
$635$	−4.27222	−	2.85460i	−0.169538	−	0.113282i
$636$		0			0
$637$	4.08894	−	20.5565i	0.162010	−	0.814479i
$638$	−7.70997	+	9.55923i	−0.305240	+	0.378454i
$639$		0			0
$640$	−7.15468	−	5.19142i	−0.282813	−	0.205209i
$641$	−2.72233			−0.107526			−0.0537629	−	0.998554i	$-0.517122\pi$
$641$	−2.72233			−0.107526			−0.0537629	+	0.998554i	$0.517122\pi$
$642$		0			0
$643$	0.135549	−	0.681448i	0.00534551	−	0.0268737i	−0.978020	−	0.208509i	$-0.933139\pi$
$643$	0.135549	−	0.681448i	0.00534551	−	0.0268737i	0.983366	+	0.181635i	$0.0581390\pi$
$644$	−8.49569	+	1.84062i	−0.334777	+	0.0725306i
$645$		0			0
$646$	−0.966188	−	1.15710i	−0.0380142	−	0.0455254i
$647$	29.4862	−	12.2136i	1.15922	−	0.480165i	0.281606	−	0.959530i	$-0.409133\pi$
$647$	29.4862	−	12.2136i	1.15922	−	0.480165i	0.877616	+	0.479365i	$0.159133\pi$
$648$		0			0
$649$	27.6909	+	11.4700i	1.08696	+	0.450235i
$650$	−14.4998	+	4.53347i	−0.568731	+	0.177817i
$651$		0			0
$652$	0.353637	+	20.7922i	0.0138495	+	0.814284i
$653$	35.6443	−	23.8167i	1.39487	−	0.932021i	0.394956	−	0.918700i	$-0.370760\pi$
$653$	35.6443	−	23.8167i	1.39487	−	0.932021i	0.999911	−	0.0133207i	$-0.00424022\pi$
$654$		0			0
$655$	2.68592	−	2.68592i	0.104948	−	0.104948i
$656$	0.992865	+	29.1794i	0.0387649	+	1.13926i
$657$		0			0
$658$	−43.6396	+	23.8051i	−1.70125	+	0.928021i
$659$	−19.0570	−	28.5207i	−0.742354	−	1.11101i	−0.989849	−	0.142122i	$-0.954608\pi$
$659$	−19.0570	−	28.5207i	−0.742354	−	1.11101i	0.247496	−	0.968889i	$-0.420392\pi$
$660$		0			0
$661$	−2.62496	−	13.1966i	−0.102099	−	0.513287i	−0.997661	−	0.0683508i	$-0.978226\pi$
$661$	−2.62496	−	13.1966i	−0.102099	−	0.513287i	0.895562	−	0.444936i	$-0.146774\pi$
$662$	2.57053	−	4.90907i	0.0999064	−	0.190797i
$663$		0			0
$664$	0.714030	+	5.74352i	0.0277097	+	0.222892i
$665$	0.925683	+	2.23480i	0.0358965	+	0.0866617i
$666$		0			0
$667$	−0.898508	+	1.34471i	−0.0347904	+	0.0520675i
$668$	−24.3785	+	16.8958i	−0.943233	+	0.653720i
$669$		0			0
$670$	0.857527	+	8.00794i	0.0331292	+	0.309374i
$671$		−	63.1543i		−	2.43805i
$672$		0			0
$673$			23.6665i			0.912275i	0.889909	+	0.456137i	$0.150767\pi$
$673$			23.6665i			0.912275i	−0.889909	+	0.456137i	$0.849233\pi$
$674$	27.5667	−	2.95197i	1.06183	−	0.113705i
$675$		0			0
$676$	13.7968	+	2.50123i	0.530646	+	0.0962012i
$677$	−14.9427	+	22.3633i	−0.574294	+	0.859491i	−0.998948	−	0.0458647i	$-0.985396\pi$
$677$	−14.9427	+	22.3633i	−0.574294	+	0.859491i	0.424654	+	0.905356i	$0.360396\pi$
$678$		0			0
$679$	19.8069	+	47.8181i	0.760120	+	1.83509i
$680$	0.797818	−	2.89382i	0.0305949	−	0.110973i
$681$		0			0
$682$	50.9904	+	26.7000i	1.95252	+	1.02240i
$683$	−4.84474	−	24.3562i	−0.185379	−	0.931963i	−0.955708	−	0.294316i	$-0.904908\pi$
$683$	−4.84474	−	24.3562i	−0.185379	−	0.931963i	0.770329	−	0.637647i	$-0.220092\pi$
$684$		0			0
$685$	−9.14265	−	13.6829i	−0.349323	−	0.522798i
$686$	4.17955	+	7.66195i	0.159576	+	0.292535i
$687$		0			0
$688$	14.3938	+	20.0319i	0.548757	+	0.763710i
$689$	−18.1124	+	18.1124i	−0.690027	+	0.690027i
$690$		0			0
$691$	11.5361	−	7.70819i	0.438855	−	0.293233i	−0.316448	−	0.948610i	$-0.602490\pi$
$691$	11.5361	−	7.70819i	0.438855	−	0.293233i	0.755302	+	0.655377i	$0.227490\pi$
$692$	−7.04594	+	7.28976i	−0.267846	+	0.277115i
$693$		0			0
$694$	−10.4404	−	33.3924i	−0.396311	−	1.26756i
$695$	13.8511	+	5.73730i	0.525401	+	0.217628i
$696$		0			0
$697$	−9.15978	+	3.79410i	−0.346951	+	0.143712i
$698$	−38.3260	+	32.0026i	−1.45066	+	1.21132i
$699$		0			0
$700$	18.7496	−	29.1209i	0.708667	−	1.10067i
$701$	−7.20549	+	36.2244i	−0.272148	+	1.36818i	0.566750	+	0.823890i	$0.308200\pi$
$701$	−7.20549	+	36.2244i	−0.272148	+	1.36818i	−0.838898	+	0.544289i	$0.816800\pi$
$702$		0			0
$703$	−1.52345			−0.0574581
$704$	−35.1268	−	31.7136i	−1.32389	−	1.19525i
$705$		0			0
$706$	−17.9992	−	14.5172i	−0.677408	−	0.546361i
$707$	−3.45474	+	17.3682i	−0.129929	+	0.653197i
$708$		0			0
$709$	−20.0441	−	13.3930i	−0.752770	−	0.502985i	0.119003	−	0.992894i	$-0.462030\pi$
$709$	−20.0441	−	13.3930i	−0.752770	−	0.502985i	−0.871774	+	0.489909i	$0.837030\pi$
$710$	2.28945	−	1.91171i	0.0859214	−	0.0717452i
$711$		0			0
$712$	−0.621074	+	8.53205i	−0.0232757	+	0.319752i
$713$	7.00278	+	2.90065i	0.262256	+	0.108630i
$714$		0			0
$715$	11.0940	−	2.20674i	0.414893	−	0.0825273i
$716$	4.38875	+	4.24196i	0.164015	+	0.158529i
$717$		0			0
$718$	2.97042	+	0.873555i	0.110855	+	0.0326008i
$719$	−5.08606	+	5.08606i	−0.189678	+	0.189678i	−0.795557	−	0.605879i	$-0.792822\pi$
$719$	−5.08606	+	5.08606i	−0.189678	+	0.189678i	0.605879	+	0.795557i	$0.292822\pi$
$720$		0			0
$721$	−29.8317	−	29.8317i	−1.11099	−	1.11099i
$722$	−12.4504	−	22.8242i	−0.463358	−	0.849428i
$723$		0			0
$724$	5.29143	+	12.1843i	0.196654	+	0.452827i
$725$	−1.25711	−	6.31990i	−0.0466878	−	0.234715i
$726$		0			0
$727$	16.1339	−	38.9506i	0.598372	−	1.44460i	−0.276867	−	0.960908i	$-0.589296\pi$
$727$	16.1339	−	38.9506i	0.598372	−	1.44460i	0.875240	−	0.483690i	$-0.160704\pi$
$728$	23.7475	−	13.4831i	0.880140	−	0.499717i
$729$		0			0
$730$	2.26908	+	0.204019i	0.0839826	+	0.00755109i
$731$	−4.65368	+	6.96472i	−0.172122	+	0.257599i
$732$		0			0
$733$	−32.2035	−	6.40567i	−1.18946	−	0.236599i	−0.439601	−	0.898193i	$-0.644880\pi$
$733$	−32.2035	−	6.40567i	−1.18946	−	0.236599i	−0.749862	+	0.661595i	$0.769880\pi$
$734$	41.5743	−	4.45197i	1.53454	−	0.164325i
$735$		0			0
$736$	−4.98122	−	3.74531i	−0.183610	−	0.138054i
$737$			43.1170i			1.58824i
$738$		0			0
$739$	−1.11174	−	0.221139i	−0.0408961	−	0.00813474i	0.174600	−	0.984639i	$-0.444137\pi$
$739$	−1.11174	−	0.221139i	−0.0408961	−	0.00813474i	−0.215496	+	0.976505i	$0.569137\pi$
$740$	−1.72806	−	2.49336i	−0.0635247	−	0.0916579i
$741$		0			0
$742$	5.22950	−	58.1620i	0.191981	−	2.13519i
$743$	11.1248	+	26.8577i	0.408130	+	0.985313i	0.985629	+	0.168922i	$0.0540285\pi$
$743$	11.1248	+	26.8577i	0.408130	+	0.985313i	−0.577500	+	0.816391i	$0.695972\pi$
$744$		0			0
$745$	−0.281663	+	0.679995i	−0.0103193	+	0.0249131i
$746$	15.9413	−	30.4440i	0.583653	−	1.11463i
$747$		0			0
$748$	5.89656	−	14.9497i	0.215600	−	0.546615i
$749$	8.37522	+	12.5344i	0.306024	+	0.457997i
$750$		0			0
$751$	−19.2670	−	19.2670i	−0.703061	−	0.703061i	0.262005	−	0.965066i	$-0.415616\pi$
$751$	−19.2670	−	19.2670i	−0.703061	−	0.703061i	−0.965066	+	0.262005i	$0.915616\pi$
$752$	−33.3709	−	12.5109i	−1.21691	−	0.456224i
$753$		0			0
$754$	1.43343	−	4.87421i	0.0522025	−	0.177508i
$755$	−7.06843	+	4.72298i	−0.257247	+	0.171887i
$756$		0			0
$757$	3.81457	−	0.758766i	0.138643	−	0.0275778i	−0.125281	−	0.992121i	$-0.539983\pi$
$757$	3.81457	−	0.758766i	0.138643	−	0.0275778i	0.263924	+	0.964544i	$0.414983\pi$
$758$	−33.7005	+	10.5367i	−1.22406	+	0.382709i
$759$		0			0
$760$	−0.778225	+	1.54979i	−0.0282292	+	0.0562170i
$761$	−14.1327	+	5.85394i	−0.512309	+	0.212205i	−0.623835	−	0.781556i	$-0.714426\pi$
$761$	−14.1327	+	5.85394i	−0.512309	+	0.212205i	0.111526	+	0.993762i	$0.464426\pi$
$762$		0			0
$763$	32.3375	+	21.6072i	1.17069	+	0.782233i
$764$	−0.669753	−	3.09136i	−0.0242308	−	0.111841i
$765$		0			0
$766$	21.7932	−	27.0203i	0.787419	−	0.976285i
$767$	−12.3995			−0.447722
$768$		0			0
$769$	−47.4209			−1.71004			−0.855020	−	0.518595i	$-0.826455\pi$
$769$	−47.4209			−1.71004			−0.855020	+	0.518595i	$0.826455\pi$
$770$	−16.1894	+	20.0725i	−0.583426	+	0.723363i
$771$		0			0
$772$	6.94222	+	32.0430i	0.249856	+	1.15325i
$773$	−18.9615	−	12.6697i	−0.681998	−	0.455697i	0.165699	−	0.986176i	$-0.447012\pi$
$773$	−18.9615	−	12.6697i	−0.681998	−	0.455697i	−0.847698	+	0.530480i	$0.822012\pi$
$774$		0			0
$775$	−27.9013	+	11.5571i	−1.00224	+	0.415143i
$776$	−16.6517	+	33.1611i	−0.597763	+	1.19041i
$777$		0			0
$778$	−30.8894	+	9.65777i	−1.10744	+	0.346248i
$779$	5.61781	−	1.11745i	0.201279	−	0.0400369i
$780$		0			0
$781$	13.2770	−	8.87142i	0.475089	−	0.317444i
$782$	0.597092	−	2.03034i	0.0213520	−	0.0726049i
$783$		0			0
$784$	−12.0258	+	32.0771i	−0.429493	+	1.14561i
$785$	−1.22111	−	1.22111i	−0.0435833	−	0.0435833i
$786$		0			0
$787$	8.45960	+	12.6607i	0.301552	+	0.451305i	0.951040	−	0.309067i	$-0.100017\pi$
$787$	8.45960	+	12.6607i	0.301552	+	0.451305i	−0.649488	+	0.760372i	$0.725017\pi$
$788$	1.98072	−	5.02177i	0.0705603	−	0.178893i
$789$		0			0
$790$	4.49741	−	8.58895i	0.160011	−	0.305581i
$791$	−6.96556	+	16.8163i	−0.247667	+	0.597920i
$792$		0			0
$793$	9.99830	+	24.1380i	0.355050	+	0.857167i
$794$	3.08422	−	34.3024i	0.109455	−	1.21735i
$795$		0			0
$796$	−15.0040	−	21.6488i	−0.531802	−	0.767322i
$797$	−1.21865	−	0.242404i	−0.0431668	−	0.00858640i	0.173460	−	0.984841i	$-0.444505\pi$
$797$	−1.21865	−	0.242404i	−0.0431668	−	0.00858640i	−0.216626	+	0.976255i	$0.569505\pi$
$798$		0			0
$799$		−	12.1023i		−	0.428148i
$800$	24.5856	−	3.48198i	0.869232	−	0.123107i
$801$		0			0
$802$	−26.7844	+	2.86820i	−0.945791	+	0.101280i
$803$	11.9626	+	2.37950i	0.422150	+	0.0839709i
$804$		0			0
$805$	−1.88669	+	2.82363i	−0.0664971	+	0.0995200i
$806$	−23.7159	−	2.13236i	−0.835358	−	0.0751092i
$807$		0			0
$808$	−11.0404	+	6.26840i	−0.388400	+	0.220522i
$809$	−11.5600	+	27.9083i	−0.406428	+	0.981203i	0.579642	+	0.814871i	$0.303192\pi$
$809$	−11.5600	+	27.9083i	−0.406428	+	0.981203i	−0.986070	+	0.166332i	$0.946808\pi$
$810$		0			0
$811$	1.27743	+	6.42210i	0.0448568	+	0.225510i	0.996711	−	0.0810417i	$-0.0258247\pi$
$811$	1.27743	+	6.42210i	0.0448568	+	0.225510i	−0.951854	+	0.306552i	$0.900825\pi$
$812$	4.61388	+	10.6242i	0.161916	+	0.372836i
$813$		0			0
$814$	−7.77756	−	14.2578i	−0.272603	−	0.499737i
$815$	5.74447	+	5.74447i	0.201220	+	0.201220i
$816$		0			0
$817$	3.42189	−	3.42189i	0.119717	−	0.119717i
$818$	−10.8193	−	3.18179i	−0.378288	−	0.111249i
$819$		0			0
$820$	8.20119	+	7.92688i	0.286398	+	0.276819i
$821$	−0.732994	+	0.145802i	−0.0255817	+	0.00508851i	−0.207865	−	0.978158i	$-0.566651\pi$
$821$	−0.732994	+	0.145802i	−0.0255817	+	0.00508851i	0.182283	+	0.983246i	$0.441651\pi$
$822$		0			0
$823$	−40.6921	−	16.8552i	−1.41844	−	0.587535i	−0.463969	−	0.885852i	$-0.653575\pi$
$823$	−40.6921	−	16.8552i	−1.41844	−	0.587535i	−0.954467	+	0.298316i	$0.903575\pi$
$824$	2.19592	−	30.1666i	0.0764984	−	1.05090i
$825$		0			0
$826$	21.6986	−	18.1185i	0.754990	−	0.630423i
$827$	17.5797	+	11.7464i	0.611308	+	0.408463i	0.822324	−	0.569020i	$-0.192677\pi$
$827$	17.5797	+	11.7464i	0.611308	+	0.408463i	−0.211016	+	0.977483i	$0.567677\pi$
$828$		0			0
$829$	−8.12158	+	40.8299i	−0.282074	+	1.41808i	0.536607	+	0.843833i	$0.319706\pi$
$829$	−8.12158	+	40.8299i	−0.282074	+	1.41808i	−0.818681	+	0.574249i	$0.805294\pi$
$830$	1.75995	+	1.41948i	0.0610889	+	0.0492710i
$831$		0			0
$832$	18.4465	+	6.56007i	0.639516	+	0.227429i
$833$	−11.6331			−0.403062
$834$		0			0
$835$	−2.26061	+	11.3649i	−0.0782316	+	0.393297i
$836$	−5.02612	+	7.80631i	−0.173832	+	0.269987i
$837$		0			0
$838$	13.8787	−	11.5888i	0.479431	−	0.400330i
$839$	−33.4505	+	13.8556i	−1.15484	+	0.478350i	−0.876154	−	0.482032i	$-0.839899\pi$
$839$	−33.4505	+	13.8556i	−1.15484	+	0.478350i	−0.278686	+	0.960382i	$0.589899\pi$
$840$		0			0
$841$	−24.8016	−	10.2732i	−0.855227	−	0.354247i
$842$	8.27236	+	26.4583i	0.285085	+	0.911813i
$843$		0			0
$844$	9.54919	−	9.87964i	0.328697	−	0.340071i
$845$	4.55459	−	3.04328i	0.156683	−	0.104692i
$846$		0			0
$847$	−66.9361	+	66.9361i	−2.29995	+	2.29995i
$848$	33.9997	−	24.4302i	1.16755	−	0.838936i
$849$		0			0
$850$	4.03794	+	7.40236i	0.138500	+	0.253899i
$851$	−1.18825	−	1.77834i	−0.0407326	−	0.0609606i
$852$		0			0
$853$	−2.29019	−	11.5136i	−0.0784145	−	0.394217i	−0.999982	−	0.00599829i	$-0.998091\pi$
$853$	−2.29019	−	11.5136i	−0.0784145	−	0.394217i	0.921567	−	0.388218i	$-0.126909\pi$
$854$	−52.7676	−	27.6306i	−1.80567	−	0.945498i
$855$		0			0
$856$	−2.87251	+	10.4191i	−0.0981805	+	0.356117i
$857$	3.96261	+	9.56660i	0.135360	+	0.326789i	0.976996	−	0.213257i	$-0.0684071\pi$
$857$	3.96261	+	9.56660i	0.135360	+	0.326789i	−0.841636	+	0.540045i	$0.818407\pi$
$858$		0			0
$859$	−22.7757	+	34.0863i	−0.777098	+	1.16301i	0.205753	+	0.978604i	$0.434036\pi$
$859$	−22.7757	+	34.0863i	−0.777098	+	1.16301i	−0.982850	+	0.184405i	$0.940964\pi$
$860$	9.48191	+	1.71898i	0.323330	+	0.0586168i
$861$		0			0
$862$	−36.7519	+	3.93556i	−1.25177	+	0.134046i
$863$			22.4117i			0.762902i	0.924389	+	0.381451i	$0.124576\pi$
$863$			22.4117i			0.762902i	−0.924389	+	0.381451i	$0.875424\pi$
$864$		0			0
$865$			3.96067i			0.134667i
$866$	−1.27842	−	11.9384i	−0.0434424	−	0.405683i
$867$		0			0
$868$	44.6175	−	30.9228i	1.51442	−	1.04959i
$869$	28.8368	−	43.1574i	0.978223	−	1.46401i
$870$		0			0
$871$	−6.82609	−	16.4796i	−0.231293	−	0.558391i
$872$	3.43991	+	27.6700i	0.116490	+	0.937024i
$873$		0			0
$874$	−0.567167	+	1.08315i	−0.0191847	+	0.0366381i
$875$	−5.64647	−	28.3867i	−0.190886	−	0.959646i
$876$		0			0
$877$	22.8368	+	34.1777i	0.771145	+	1.15410i	0.984200	+	0.177060i	$0.0566587\pi$
$877$	22.8368	+	34.1777i	0.771145	+	1.15410i	−0.213055	+	0.977040i	$0.568341\pi$
$878$	−26.6986	+	14.5639i	−0.901035	+	0.491509i
$879$		0			0
$880$	−18.4774	+	0.628716i	−0.622873	+	0.0211940i
$881$	19.2835	−	19.2835i	0.649677	−	0.649677i	−0.303238	−	0.952915i	$-0.598068\pi$
$881$	19.2835	−	19.2835i	0.649677	−	0.649677i	0.952915	+	0.303238i	$0.0980676\pi$
$882$		0			0
$883$	43.0348	−	28.7549i	1.44824	−	0.967681i	0.451068	−	0.892490i	$-0.351043\pi$
$883$	43.0348	−	28.7549i	1.44824	−	0.967681i	0.997169	−	0.0751915i	$-0.0239568\pi$
$884$	0.113060	+	6.64740i	0.00380263	+	0.223576i
$885$		0			0
$886$	−25.2167	+	7.88416i	−0.847171	+	0.264874i
$887$	2.36214	+	0.978431i	0.0793129	+	0.0328525i	0.421987	−	0.906602i	$-0.361333\pi$
$887$	2.36214	+	0.978431i	0.0793129	+	0.0328525i	−0.342674	+	0.939454i	$0.611333\pi$
$888$		0			0
$889$	−23.9693	+	9.92840i	−0.803904	+	0.332988i
$890$	2.14202	+	2.56526i	0.0718006	+	0.0859878i
$891$		0			0
$892$	7.59012	−	1.64443i	0.254136	−	0.0550595i
$893$	−1.36404	+	6.85748i	−0.0456458	+	0.229477i
$894$		0			0
$895$	2.38450			0.0797049
$896$	−41.8661	+	15.4746i	−1.39865	+	0.516971i
$897$		0			0
$898$	−29.0127	+	35.9715i	−0.968165	+	1.20038i
$899$	1.97036	−	9.90565i	0.0657151	−	0.330372i
$900$		0			0
$901$	11.8210	+	7.89857i	0.393816	+	0.263140i
$902$	39.1383	+	46.8717i	1.30316	+	1.56066i
$903$		0			0
$904$	−12.3870	+	4.10538i	−0.411985	+	0.136543i
$905$	4.79444	+	1.98592i	0.159372	+	0.0660142i
$906$		0			0
$907$	21.3347	−	4.24373i	0.708405	−	0.140911i	0.172279	−	0.985048i	$-0.444887\pi$
$907$	21.3347	−	4.24373i	0.708405	−	0.140911i	0.536127	+	0.844138i	$0.319887\pi$
$908$	0.781420	+	45.9437i	0.0259323	+	1.52470i
$909$		0			0
$910$	3.00993	−	10.2349i	0.0997781	−	0.339284i
$911$	−1.38797	+	1.38797i	−0.0459856	+	0.0459856i	−0.729726	−	0.683740i	$-0.760352\pi$
$911$	−1.38797	+	1.38797i	−0.0459856	+	0.0459856i	0.683740	+	0.729726i	$0.260352\pi$
$912$		0			0
$913$	8.55950	+	8.55950i	0.283278	+	0.283278i
$914$	−31.4227	+	17.1409i	−1.03937	+	0.566970i
$915$		0			0
$916$	11.4398	+	4.51216i	0.377982	+	0.149086i
$917$	−3.74177	−	18.8111i	−0.123564	−	0.621198i
$918$		0			0
$919$	1.63873	−	3.95625i	0.0540568	−	0.130505i	−0.894544	−	0.446980i	$-0.852499\pi$
$919$	1.63873	−	3.95625i	0.0540568	−	0.130505i	0.948601	+	0.316475i	$0.102499\pi$
$920$	−2.41608	+	0.300365i	−0.0796558	+	0.00990275i
$921$		0			0
$922$	−0.364939	+	4.05882i	−0.0120186	+	0.133670i
$923$	−3.67009	+	5.49268i	−0.120802	+	0.180794i
$924$		0			0
$925$	8.35786	+	1.66248i	0.274805	+	0.0546621i
$926$	−5.23641	−	48.8998i	−0.172079	−	1.60695i
$927$		0			0
$928$	−3.59972	+	7.48334i	−0.118167	+	0.245653i
$929$		−	53.4969i		−	1.75518i	−0.479415	−	0.877589i	$-0.659151\pi$
$929$		−	53.4969i		−	1.75518i	0.479415	−	0.877589i	$-0.340849\pi$
$930$		0			0
$931$	6.59161	+	1.31115i	0.216031	+	0.0429713i
$932$	3.77369	+	0.684136i	0.123611	+	0.0224096i
$933$		0			0
$934$	17.9625	+	1.61506i	0.587752	+	0.0528463i
$935$	−2.40255	−	5.80028i	−0.0785719	−	0.189689i
$936$		0			0
$937$	9.69070	−	23.3954i	0.316582	−	0.764295i	−0.682849	−	0.730559i	$-0.739259\pi$
$937$	9.69070	−	23.3954i	0.316582	−	0.764295i	0.999431	−	0.0337361i	$-0.0107406\pi$
$938$	36.0257	+	18.8641i	1.17628	+	0.615934i
$939$		0			0
$940$	−12.7706	+	5.54601i	−0.416530	+	0.180891i
$941$	14.9326	+	22.3482i	0.486788	+	0.728529i	0.990825	−	0.135153i	$-0.0431525\pi$
$941$	14.9326	+	22.3482i	0.486788	+	0.728529i	−0.504037	+	0.863682i	$0.668153\pi$
$942$		0			0
$943$	5.68614	+	5.68614i	0.185166	+	0.185166i
$944$	20.0002	+	3.27559i	0.650952	+	0.106611i
$945$		0			0
$946$	49.4946	+	14.5556i	1.60921	+	0.473243i
$947$	−15.6970	+	10.4884i	−0.510083	+	0.340827i	−0.783830	−	0.620975i	$-0.786737\pi$
$947$	−15.6970	+	10.4884i	−0.510083	+	0.340827i	0.273747	+	0.961802i	$0.411737\pi$
$948$		0			0
$949$	−4.94890	+	0.984397i	−0.160648	+	0.0319549i
$950$	−1.45369	−	4.64949i	−0.0471641	−	0.150849i
$951$		0			0
$952$	−9.91119	−	11.4674i	−0.321224	−	0.371661i
$953$	−31.0836	+	12.8753i	−1.00690	+	0.417070i	−0.824322	−	0.566122i	$-0.808443\pi$
$953$	−31.0836	+	12.8753i	−1.00690	+	0.417070i	−0.182575	+	0.983192i	$0.558443\pi$
$954$		0			0
$955$	−1.02745	−	0.686517i	−0.0332473	−	0.0222152i
$956$	9.33814	−	14.5035i	0.302017	−	0.469077i
$957$		0			0
$958$	9.24643	+	7.45768i	0.298739	+	0.240947i
$959$	−83.0932			−2.68322
$960$		0			0
$961$	−16.3349			−0.526932
$962$	5.22988	+	4.21814i	0.168618	+	0.135998i
$963$		0			0
$964$	−12.4031	−	7.98580i	−0.399478	−	0.257205i
$965$	10.6498	+	7.11598i	0.342830	+	0.229072i
$966$		0			0
$967$	−39.0826	+	16.1886i	−1.25681	+	0.520589i	−0.908930	−	0.416949i	$-0.863099\pi$
$967$	−39.0826	+	16.1886i	−1.25681	+	0.520589i	−0.347883	+	0.937538i	$0.613099\pi$
$968$	−67.6874	−	4.92718i	−2.17555	−	0.158365i
$969$		0			0
$970$	4.32588	+	13.8359i	0.138896	+	0.444244i
$971$	−15.9123	+	3.16514i	−0.510649	+	0.101574i	−0.443688	−	0.896181i	$-0.646330\pi$
$971$	−15.9123	+	3.16514i	−0.510649	+	0.101574i	−0.0669606	+	0.997756i	$0.521330\pi$
$972$		0			0
$973$	62.9429	−	42.0571i	2.01786	−	1.34829i
$974$	−22.7000	−	6.67571i	−0.727353	−	0.213903i
$975$		0			0
$976$	−9.75052	−	41.5754i	−0.312106	−	1.33080i
$977$	14.4085	+	14.4085i	0.460970	+	0.460970i	0.898973	−	0.438004i	$-0.144314\pi$
$977$	14.4085	+	14.4085i	0.460970	+	0.460970i	−0.438004	+	0.898973i	$0.644314\pi$
$978$		0			0
$979$	9.94018	+	14.8765i	0.317690	+	0.475456i
$980$	5.33099	+	12.2754i	0.170292	+	0.392125i
$981$		0			0
$982$	−11.8873	−	6.22450i	−0.379338	−	0.198632i
$983$	−14.2810	+	34.4773i	−0.455492	+	1.09966i	0.514711	+	0.857364i	$0.327899\pi$
$983$	−14.2810	+	34.4773i	−0.455492	+	1.09966i	−0.970203	+	0.242292i	$0.922101\pi$
$984$		0			0
$985$	−0.807045	−	1.94838i	−0.0257146	−	0.0620805i
$986$	−2.80858	−	0.252527i	−0.0894434	−	0.00804209i
$987$		0			0
$988$	0.685160	−	3.77934i	0.0217978	−	0.120237i
$989$	6.66337	+	1.32543i	0.211883	+	0.0421461i
$990$		0			0
$991$			5.17247i			0.164309i	0.996620	+	0.0821544i	$0.0261801\pi$
$991$			5.17247i			0.164309i	−0.996620	+	0.0821544i	$0.973820\pi$
$992$	37.6900	+	9.70450i	1.19666	+	0.308118i
$993$		0			0
$994$	−1.60356	−	14.9747i	−0.0508619	−	0.474969i
$995$	−10.0923	−	2.00749i	−0.319948	−	0.0636416i
$996$		0			0
$997$	−11.3818	+	17.0341i	−0.360466	+	0.539476i	−0.966734	−	0.255785i	$-0.917666\pi$
$997$	−11.3818	+	17.0341i	−0.360466	+	0.539476i	0.606267	+	0.795261i	$0.292666\pi$
$998$	1.89560	−	21.0827i	0.0600041	−	0.667361i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.a.253.5		56
3.2	odd	2		64.2.i.a.61.3	yes	56
12.11	even	2		256.2.i.a.81.6		56
24.5	odd	2		512.2.i.b.417.6		56
24.11	even	2		512.2.i.a.417.2		56
64.21	even	16	inner	576.2.bd.a.469.5		56
192.11	even	16		512.2.i.a.97.2		56
192.53	odd	16		512.2.i.b.97.6		56
192.107	even	16		256.2.i.a.177.6		56
192.149	odd	16		64.2.i.a.21.3	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.3	✓	56	192.149	odd	16
64.2.i.a.61.3	yes	56	3.2	odd	2
256.2.i.a.81.6		56	12.11	even	2
256.2.i.a.177.6		56	192.107	even	16
512.2.i.a.97.2		56	192.11	even	16
512.2.i.a.417.2		56	24.11	even	2
512.2.i.b.97.6		56	192.53	odd	16
512.2.i.b.417.6		56	24.5	odd	2
576.2.bd.a.253.5		56	1.1	even	1	trivial
576.2.bd.a.469.5		56	64.21	even	16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.887839 - 1.10079i) q^{2} +(-0.423482 - 1.95465i) q^{4} +(-0.649649 - 0.434082i) q^{5} +(-3.64486 + 1.50975i) q^{7} +(-2.52765 - 1.26925i) q^{8} +(-1.05462 + 0.329733i) q^{10} +(-5.80194 + 1.15408i) q^{11} +(2.03484 - 1.35963i) q^{13} +(-1.57413 + 5.35264i) q^{14} +(-3.64133 + 1.65552i) q^{16} +(-0.960477 - 0.960477i) q^{17} +(0.435978 + 0.652487i) q^{19} +(-0.573364 + 1.45366i) q^{20} +(-3.88079 + 7.41136i) q^{22} +(-0.421603 + 1.01784i) q^{23} +(-1.67980 - 4.05540i) q^{25} +(0.309935 - 3.44707i) q^{26} +(4.49456 + 6.48507i) q^{28} +(1.43977 + 0.286388i) q^{29} -6.88004i q^{31} +(-1.41053 + 5.47818i) q^{32} +(-1.91003 + 0.204535i) q^{34} +(3.02323 + 0.601358i) q^{35} +(-1.07856 + 1.61417i) q^{37} +(1.10533 + 0.0993831i) q^{38} +(1.09113 + 1.92177i) q^{40} +(2.79324 - 6.74347i) q^{41} +(-1.20307 - 6.04824i) q^{43} +(4.71284 + 10.8520i) q^{44} +(0.746114 + 1.36778i) q^{46} +(6.30014 + 6.30014i) q^{47} +(6.05588 - 6.05588i) q^{49} +(-5.95554 - 1.75143i) q^{50} +(-3.51933 - 3.40161i) q^{52} +(-10.2655 + 2.04194i) q^{53} +(4.27019 + 1.76877i) q^{55} +(11.1292 + 0.810126i) q^{56} +(1.59354 - 1.33062i) q^{58} +(-4.21278 - 2.81489i) q^{59} +(-2.08276 + 10.4707i) q^{61} +(-7.57348 - 6.10837i) q^{62} +(4.77800 + 6.41644i) q^{64} -1.91212 q^{65} +(1.42195 - 7.14864i) q^{67} +(-1.47065 + 2.28414i) q^{68} +(3.34611 - 2.79404i) q^{70} +(-2.49385 + 1.03299i) q^{71} +(-1.90488 - 0.789026i) q^{73} +(0.819282 + 2.62039i) q^{74} +(1.09076 - 1.12850i) q^{76} +(19.4049 - 12.9659i) q^{77} +(-6.20432 + 6.20432i) q^{79} +(3.08422 + 0.505126i) q^{80} +(-4.94320 - 9.06188i) q^{82} +(-1.13685 - 1.70141i) q^{83} +(0.207047 + 1.04090i) q^{85} +(-7.72599 - 4.04554i) q^{86} +(16.1301 + 4.44702i) q^{88} +(-1.15743 - 2.79429i) q^{89} +(-5.36398 + 8.02776i) q^{91} +(2.16806 + 0.393050i) q^{92} +(12.5287 - 1.34163i) q^{94} -0.613137i q^{95} -13.1193i q^{97} +(-1.28961 - 12.0429i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32}+ \cdots - 128 q^{98}+O(q^{100}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Introduction

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