LMFDB - Embedded newform 372.2.g.b.247.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(247,372)] 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("372.247"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} - x^{13} - 2 x^{12} + 5 x^{11} + 4 x^{10} - 10 x^{9} - 20 x^{7} + 16 x^{6} + 40 x^{5} + \cdots + 256 $ x^16 - x^14 - x^13 - 2x^12 + 5x^11 + 4x^10 - 10x^9 - 20x^7 + 16x^6 + 40x^5 - 32x^4 - 32x^3 - 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			247.3
Root			$-1.31420 + 0.522370i$ of defining polynomial
Character	$\chi$	$=$	372.247
Dual form			372.2.g.b.247.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31420 - 0.522370i) q^{2} +1.00000 q^{3} +(1.45426 + 1.37300i) q^{4} +3.41432 q^{5} +(-1.31420 - 0.522370i) q^{6} -2.57432i q^{7} +(-1.19398 - 2.56406i) q^{8} +1.00000 q^{9} +(-4.48711 - 1.78354i) q^{10} -0.618251 q^{11} +(1.45426 + 1.37300i) q^{12} -6.01558i q^{13} +(-1.34475 + 3.38318i) q^{14} +3.41432 q^{15} +(0.229736 + 3.99340i) q^{16} +6.56767i q^{17} +(-1.31420 - 0.522370i) q^{18} +0.164649i q^{19} +(4.96530 + 4.68787i) q^{20} -2.57432i q^{21} +(0.812507 + 0.322956i) q^{22} -6.90297 q^{23} +(-1.19398 - 2.56406i) q^{24} +6.65758 q^{25} +(-3.14236 + 7.90569i) q^{26} +1.00000 q^{27} +(3.53455 - 3.74373i) q^{28} +2.64515i q^{29} +(-4.48711 - 1.78354i) q^{30} +(5.56329 + 0.223126i) q^{31} +(1.78411 - 5.36814i) q^{32} -0.618251 q^{33} +(3.43076 - 8.63126i) q^{34} -8.78956i q^{35} +(1.45426 + 1.37300i) q^{36} +2.29489i q^{37} +(0.0860078 - 0.216382i) q^{38} -6.01558i q^{39} +(-4.07662 - 8.75453i) q^{40} +5.03933 q^{41} +(-1.34475 + 3.38318i) q^{42} -8.46494 q^{43} +(-0.899096 - 0.848859i) q^{44} +3.41432 q^{45} +(9.07191 + 3.60591i) q^{46} -8.40212i q^{47} +(0.229736 + 3.99340i) q^{48} +0.372864 q^{49} +(-8.74942 - 3.47772i) q^{50} +6.56767i q^{51} +(8.25940 - 8.74821i) q^{52} +4.86996i q^{53} +(-1.31420 - 0.522370i) q^{54} -2.11091 q^{55} +(-6.60073 + 3.07368i) q^{56} +0.164649i q^{57} +(1.38175 - 3.47627i) q^{58} +13.1432i q^{59} +(4.96530 + 4.68787i) q^{60} -6.27850i q^{61} +(-7.19474 - 3.19933i) q^{62} -2.57432i q^{63} +(-5.14884 + 6.12286i) q^{64} -20.5391i q^{65} +(0.812507 + 0.322956i) q^{66} -1.25147i q^{67} +(-9.01742 + 9.55110i) q^{68} -6.90297 q^{69} +(-4.59141 + 11.5513i) q^{70} +13.7892i q^{71} +(-1.19398 - 2.56406i) q^{72} +5.21502i q^{73} +(1.19878 - 3.01595i) q^{74} +6.65758 q^{75} +(-0.226064 + 0.239442i) q^{76} +1.59158i q^{77} +(-3.14236 + 7.90569i) q^{78} +2.23797 q^{79} +(0.784392 + 13.6347i) q^{80} +1.00000 q^{81} +(-6.62271 - 2.63240i) q^{82} +11.8591 q^{83} +(3.53455 - 3.74373i) q^{84} +22.4241i q^{85} +(11.1246 + 4.42183i) q^{86} +2.64515i q^{87} +(0.738176 + 1.58523i) q^{88} +4.47064i q^{89} +(-4.48711 - 1.78354i) q^{90} -15.4860 q^{91} +(-10.0387 - 9.47779i) q^{92} +(5.56329 + 0.223126i) q^{93} +(-4.38902 + 11.0421i) q^{94} +0.562165i q^{95} +(1.78411 - 5.36814i) q^{96} -9.71032 q^{97} +(-0.490019 - 0.194773i) q^{98} -0.618251 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 2 q^{4} + 3 q^{8} + 16 q^{9} - 5 q^{10} + 4 q^{11} + 2 q^{12} + 5 q^{14} + 10 q^{16} - q^{20} - 16 q^{23} + 3 q^{24} + 12 q^{25} - 10 q^{26} + 16 q^{27} + 3 q^{28} - 5 q^{30} - 6 q^{31}+ \cdots + 4 q^{99}+O(q^{100}) $ 16 * q + 16 * q^3 + 2 * q^4 + 3 * q^8 + 16 * q^9 - 5 * q^10 + 4 * q^11 + 2 * q^12 + 5 * q^14 + 10 * q^16 - q^20 - 16 * q^23 + 3 * q^24 + 12 * q^25 - 10 * q^26 + 16 * q^27 + 3 * q^28 - 5 * q^30 - 6 * q^31 - 20 * q^32 + 4 * q^33 + 28 * q^34 + 2 * q^36 + q^38 - 26 * q^40 + 5 * q^42 - 20 * q^43 - 14 * q^44 - 4 * q^46 + 10 * q^48 - 8 * q^49 - 11 * q^50 - 4 * q^52 + 8 * q^55 - 40 * q^56 + 36 * q^58 - q^60 - 26 * q^62 - 7 * q^64 - 6 * q^68 - 16 * q^69 + 9 * q^70 + 3 * q^72 - 52 * q^74 + 12 * q^75 - 3 * q^76 - 10 * q^78 - 12 * q^79 - 13 * q^80 + 16 * q^81 - 11 * q^82 - 28 * q^83 + 3 * q^84 + 8 * q^86 - 16 * q^88 - 5 * q^90 + 16 * q^91 - 6 * q^93 + 26 * q^94 - 20 * q^96 - 40 * q^97 - 15 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.31420	−	0.522370i	−0.929282	−	0.369372i
$2$	−1.31420	−	0.522370i	−0.929282	−	0.369372i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.45426	+	1.37300i	0.727129	+	0.686501i
$5$	3.41432			1.52693			0.763465	−	0.645849i	$-0.223496\pi$
$5$	3.41432			1.52693			0.763465	+	0.645849i	$0.223496\pi$
$6$	−1.31420	−	0.522370i	−0.536521	−	0.213257i
$7$		−	2.57432i		−	0.973002i	−0.873680	−	0.486501i	$-0.838273\pi$
$7$		−	2.57432i		−	0.973002i	0.873680	−	0.486501i	$-0.161727\pi$
$8$	−1.19398	−	2.56406i	−0.422134	−	0.906533i
$9$	1.00000			0.333333
$10$	−4.48711	−	1.78354i	−1.41895	−	0.564005i
$11$	−0.618251			−0.186410			−0.0932048	−	0.995647i	$-0.529711\pi$
$11$	−0.618251			−0.186410			−0.0932048	+	0.995647i	$0.529711\pi$
$12$	1.45426	+	1.37300i	0.419808	+	0.396351i
$13$		−	6.01558i		−	1.66842i	−0.551446	−	0.834211i	$-0.685924\pi$
$13$		−	6.01558i		−	1.66842i	0.551446	−	0.834211i	$-0.314076\pi$
$14$	−1.34475	+	3.38318i	−0.359399	+	0.904193i
$15$	3.41432			0.881574
$16$	0.229736	+	3.99340i	0.0574340	+	0.998349i
$17$			6.56767i			1.59289i	0.604708	+	0.796447i	$0.293290\pi$
$17$			6.56767i			1.59289i	−0.604708	+	0.796447i	$0.706710\pi$
$18$	−1.31420	−	0.522370i	−0.309761	−	0.123124i
$19$			0.164649i			0.0377731i	0.999822	+	0.0188866i	$0.00601214\pi$
$19$			0.164649i			0.0377731i	−0.999822	+	0.0188866i	$0.993988\pi$
$20$	4.96530	+	4.68787i	1.11028	+	1.04824i
$21$		−	2.57432i		−	0.561763i
$22$	0.812507	+	0.322956i	0.173227	+	0.0688544i
$23$	−6.90297			−1.43937			−0.719685	−	0.694301i	$-0.755714\pi$
$23$	−6.90297			−1.43937			−0.719685	+	0.694301i	$0.755714\pi$
$24$	−1.19398	−	2.56406i	−0.243719	−	0.523387i
$25$	6.65758			1.33152
$26$	−3.14236	+	7.90569i	−0.616268	+	1.55043i
$27$	1.00000			0.192450
$28$	3.53455	−	3.74373i	0.667967	−	0.707499i
$29$			2.64515i			0.491193i	0.969372	+	0.245596i	$0.0789838\pi$
$29$			2.64515i			0.491193i	−0.969372	+	0.245596i	$0.921016\pi$
$30$	−4.48711	−	1.78354i	−0.819230	−	0.325628i
$31$	5.56329	+	0.223126i	0.999197	+	0.0400746i
$31$	5.56329	+	0.223126i	0.999197	+	0.0400746i
$32$	1.78411	−	5.36814i	0.315389	−	0.948962i
$33$	−0.618251			−0.107624
$34$	3.43076	−	8.63126i	0.588370	−	1.48025i
$35$		−	8.78956i		−	1.48571i
$36$	1.45426	+	1.37300i	0.242376	+	0.228834i
$37$			2.29489i			0.377278i	0.982046	+	0.188639i	$0.0604076\pi$
$37$			2.29489i			0.377278i	−0.982046	+	0.188639i	$0.939592\pi$
$38$	0.0860078	−	0.216382i	0.0139523	−	0.0351019i
$39$		−	6.01558i		−	0.963264i
$40$	−4.07662	−	8.75453i	−0.644570	−	1.38421i
$41$	5.03933			0.787012			0.393506	−	0.919322i	$-0.371262\pi$
$41$	5.03933			0.787012			0.393506	+	0.919322i	$0.371262\pi$
$42$	−1.34475	+	3.38318i	−0.207499	+	0.522036i
$43$	−8.46494			−1.29089			−0.645445	−	0.763807i	$-0.723328\pi$
$43$	−8.46494			−1.29089			−0.645445	+	0.763807i	$0.723328\pi$
$44$	−0.899096	−	0.848859i	−0.135544	−	0.127970i
$45$	3.41432			0.508977
$46$	9.07191	+	3.60591i	1.33758	+	0.531662i
$47$		−	8.40212i		−	1.22557i	−0.790248	−	0.612787i	$-0.790048\pi$
$47$		−	8.40212i		−	1.22557i	0.790248	−	0.612787i	$-0.209952\pi$
$48$	0.229736	+	3.99340i	0.0331595	+	0.576397i
$49$	0.372864			0.0532663
$50$	−8.74942	−	3.47772i	−1.23735	−	0.491824i
$51$			6.56767i			0.919658i
$52$	8.25940	−	8.74821i	1.14537	−	1.21316i
$53$			4.86996i			0.668940i	0.942406	+	0.334470i	$0.108557\pi$
$53$			4.86996i			0.668940i	−0.942406	+	0.334470i	$0.891443\pi$
$54$	−1.31420	−	0.522370i	−0.178840	−	0.0710856i
$55$	−2.11091			−0.284634
$56$	−6.60073	+	3.07368i	−0.882059	+	0.410738i
$57$			0.164649i			0.0218083i
$58$	1.38175	−	3.47627i	0.181433	−	0.456456i
$59$			13.1432i			1.71110i	0.517716	+	0.855552i	$0.326782\pi$
$59$			13.1432i			1.71110i	−0.517716	+	0.855552i	$0.673218\pi$
$60$	4.96530	+	4.68787i	0.641018	+	0.605201i
$61$		−	6.27850i		−	0.803880i	−0.915666	−	0.401940i	$-0.868336\pi$
$61$		−	6.27850i		−	0.803880i	0.915666	−	0.401940i	$-0.131664\pi$
$62$	−7.19474	−	3.19933i	−0.913733	−	0.406315i
$63$		−	2.57432i		−	0.324334i
$64$	−5.14884	+	6.12286i	−0.643605	+	0.765358i
$65$		−	20.5391i		−	2.54756i
$66$	0.812507	+	0.322956i	0.100013	+	0.0397531i
$67$		−	1.25147i		−	0.152891i	−0.997074	−	0.0764454i	$-0.975643\pi$
$67$		−	1.25147i		−	0.152891i	0.997074	−	0.0764454i	$-0.0243571\pi$
$68$	−9.01742	+	9.55110i	−1.09352	+	1.15824i
$69$	−6.90297			−0.831020
$70$	−4.59141	+	11.5513i	−0.548778	+	1.38064i
$71$			13.7892i			1.63647i	0.574883	+	0.818236i	$0.305048\pi$
$71$			13.7892i			1.63647i	−0.574883	+	0.818236i	$0.694952\pi$
$72$	−1.19398	−	2.56406i	−0.140711	−	0.302178i
$73$			5.21502i			0.610372i	0.952293	+	0.305186i	$0.0987187\pi$
$73$			5.21502i			0.610372i	−0.952293	+	0.305186i	$0.901281\pi$
$74$	1.19878	−	3.01595i	0.139356	−	0.350598i
$75$	6.65758			0.768752
$76$	−0.226064	+	0.239442i	−0.0259313	+	0.0274659i
$77$			1.59158i			0.181377i
$78$	−3.14236	+	7.90569i	−0.355802	+	0.895143i
$79$	2.23797			0.251792			0.125896	−	0.992043i	$-0.459819\pi$
$79$	2.23797			0.251792			0.125896	+	0.992043i	$0.459819\pi$
$80$	0.784392	+	13.6347i	0.0876977	+	1.52441i
$81$	1.00000			0.111111
$82$	−6.62271	−	2.63240i	−0.731356	−	0.290700i
$83$	11.8591			1.30170			0.650852	−	0.759205i	$-0.274412\pi$
$83$	11.8591			1.30170			0.650852	+	0.759205i	$0.274412\pi$
$84$	3.53455	−	3.74373i	0.385651	−	0.408474i
$85$			22.4241i			2.43224i
$86$	11.1246	+	4.42183i	1.19960	+	0.476818i
$87$			2.64515i			0.283590i
$88$	0.738176	+	1.58523i	0.0786899	+	0.168986i
$89$			4.47064i			0.473887i	0.971523	+	0.236943i	$0.0761456\pi$
$89$			4.47064i			0.473887i	−0.971523	+	0.236943i	$0.923854\pi$
$90$	−4.48711	−	1.78354i	−0.472983	−	0.188002i
$91$	−15.4860			−1.62338
$92$	−10.0387	−	9.47779i	−1.04661	−	0.988128i
$93$	5.56329	+	0.223126i	0.576886	+	0.0231371i
$94$	−4.38902	+	11.0421i	−0.452693	+	1.13890i
$95$			0.562165i			0.0576769i
$96$	1.78411	−	5.36814i	0.182090	−	0.547884i
$97$	−9.71032			−0.985934			−0.492967	−	0.870048i	$-0.664088\pi$
$97$	−9.71032			−0.985934			−0.492967	+	0.870048i	$0.664088\pi$
$98$	−0.490019	−	0.194773i	−0.0494994	−	0.0196750i
$99$	−0.618251			−0.0621365
$100$	9.68185	+	9.14087i	0.968185	+	0.914087i
$101$	−5.59956			−0.557177			−0.278588	−	0.960411i	$-0.589867\pi$
$101$	−5.59956			−0.557177			−0.278588	+	0.960411i	$0.589867\pi$
$102$	3.43076	−	8.63126i	0.339696	−	0.854622i
$103$			9.05162i			0.891883i	0.895062	+	0.445941i	$0.147131\pi$
$103$			9.05162i			0.891883i	−0.895062	+	0.445941i	$0.852869\pi$
$104$	−15.4243	+	7.18246i	−1.51248	+	0.704298i
$105$		−	8.78956i		−	0.857773i
$106$	2.54392	−	6.40011i	0.247087	−	0.621634i
$107$		−	5.56176i		−	0.537676i	−0.963185	−	0.268838i	$-0.913360\pi$
$107$		−	5.56176i		−	0.537676i	0.963185	−	0.268838i	$-0.0866396\pi$
$108$	1.45426	+	1.37300i	0.139936	+	0.132117i
$109$	−1.25068			−0.119793			−0.0598966	−	0.998205i	$-0.519077\pi$
$109$	−1.25068			−0.119793			−0.0598966	+	0.998205i	$0.519077\pi$
$110$	2.77416	+	1.10267i	0.264506	+	0.105136i
$111$			2.29489i			0.217822i
$112$	10.2803	−	0.591415i	0.971396	−	0.0558834i
$113$	−16.1132			−1.51580			−0.757900	−	0.652370i	$-0.773775\pi$
$113$	−16.1132			−1.51580			−0.757900	+	0.652370i	$0.773775\pi$
$114$	0.0860078	−	0.216382i	0.00805537	−	0.0202661i
$115$	−23.5690			−2.19782
$116$	−3.63180	+	3.84674i	−0.337204	+	0.357161i
$117$		−	6.01558i		−	0.556141i
$118$	6.86564	−	17.2729i	0.632033	−	1.59010i
$119$	16.9073			1.54989
$120$	−4.07662	−	8.75453i	−0.372142	−	0.799176i
$121$	−10.6178			−0.965251
$122$	−3.27970	+	8.25123i	−0.296930	+	0.747031i
$123$	5.03933			0.454381
$124$	7.78411	+	7.96289i	0.699034	+	0.715089i
$125$	5.65953			0.506203
$126$	−1.34475	+	3.38318i	−0.119800	+	0.301398i
$127$	11.1482			0.989241			0.494620	−	0.869109i	$-0.335307\pi$
$127$	11.1482			0.989241			0.494620	+	0.869109i	$0.335307\pi$
$128$	9.96502	−	5.35708i	0.880792	−	0.473503i
$129$	−8.46494			−0.745296
$130$	−10.7290	+	26.9926i	−0.940998	+	2.36741i
$131$		−	9.20268i		−	0.804042i	−0.915631	−	0.402021i	$-0.868308\pi$
$131$		−	9.20268i		−	0.804042i	0.915631	−	0.402021i	$-0.131692\pi$
$132$	−0.899096	−	0.848859i	−0.0782563	−	0.0738837i
$133$	0.423860			0.0367533
$134$	−0.653728	+	1.64468i	−0.0564735	+	0.142079i
$135$	3.41432			0.293858
$136$	16.8399	−	7.84164i	1.44401	−	0.672415i
$137$		−	18.7908i		−	1.60541i	−0.596379	−	0.802703i	$-0.703394\pi$
$137$		−	18.7908i		−	1.60541i	0.596379	−	0.802703i	$-0.296606\pi$
$138$	9.07191	+	3.60591i	0.772252	+	0.306955i
$139$	−2.89057			−0.245175			−0.122587	−	0.992458i	$-0.539119\pi$
$139$	−2.89057			−0.245175			−0.122587	+	0.992458i	$0.539119\pi$
$140$	12.0681	−	12.7823i	1.01994	−	1.08030i
$141$		−	8.40212i		−	0.707586i
$142$	7.20305	−	18.1218i	0.604466	−	1.52074i
$143$			3.71914i			0.311010i
$144$	0.229736	+	3.99340i	0.0191447	+	0.332783i
$145$			9.03140i			0.750017i
$146$	2.72417	−	6.85360i	0.225454	−	0.567208i
$147$	0.372864			0.0307533
$148$	−3.15089	+	3.33737i	−0.259002	+	0.274330i
$149$	−11.1299			−0.911800			−0.455900	−	0.890031i	$-0.650682\pi$
$149$	−11.1299			−0.911800			−0.455900	+	0.890031i	$0.650682\pi$
$150$	−8.74942	−	3.47772i	−0.714387	−	0.283955i
$151$	−14.7964			−1.20411			−0.602057	−	0.798453i	$-0.705652\pi$
$151$	−14.7964			−1.20411			−0.602057	+	0.798453i	$0.705652\pi$
$152$	0.422171	−	0.196587i	0.0342426	−	0.0159453i
$153$			6.56767i			0.530965i
$154$	0.831392	−	2.09165i	0.0669955	−	0.168550i
$155$	18.9949	+	0.761824i	1.52570	+	0.0611912i
$156$	8.25940	−	8.74821i	0.661281	−	0.700417i
$157$	16.9165			1.35009			0.675043	−	0.737778i	$-0.264125\pi$
$157$	16.9165			1.35009			0.675043	+	0.737778i	$0.264125\pi$
$158$	−2.94115	−	1.16905i	−0.233985	−	0.0930047i
$159$			4.86996i			0.386213i
$160$	6.09153	−	18.3286i	0.481578	−	1.44900i
$161$			17.7705i			1.40051i
$162$	−1.31420	−	0.522370i	−0.103254	−	0.0410413i
$163$			24.2254i			1.89748i	0.316056	+	0.948741i	$0.397641\pi$
$163$			24.2254i			1.89748i	−0.316056	+	0.948741i	$0.602359\pi$
$164$	7.32849	+	6.91901i	0.572259	+	0.540284i
$165$	−2.11091			−0.164334
$166$	−15.5853	−	6.19484i	−1.20965	−	0.480813i
$167$	3.54747			0.274511			0.137256	−	0.990536i	$-0.456172\pi$
$167$	3.54747			0.274511			0.137256	+	0.990536i	$0.456172\pi$
$168$	−6.60073	+	3.07368i	−0.509257	+	0.237139i
$169$	−23.1872			−1.78363
$170$	11.7137	−	29.4699i	0.898400	−	2.26024i
$171$			0.164649i			0.0125910i
$172$	−12.3102	−	11.6224i	−0.938644	−	0.886197i
$173$	1.31424			0.0999199			0.0499599	−	0.998751i	$-0.484091\pi$
$173$	1.31424			0.0999199			0.0499599	+	0.998751i	$0.484091\pi$
$174$	1.38175	−	3.47627i	0.104750	−	0.263535i
$175$		−	17.1388i		−	1.29557i
$176$	−0.142034	−	2.46892i	−0.0107062	−	0.186102i
$177$			13.1432i			0.987907i
$178$	2.33533	−	5.87532i	0.175040	−	0.440374i
$179$	−11.7430			−0.877716			−0.438858	−	0.898557i	$-0.644617\pi$
$179$	−11.7430			−0.877716			−0.438858	+	0.898557i	$0.644617\pi$
$180$	4.96530	+	4.68787i	0.370092	+	0.349413i
$181$		−	9.34059i		−	0.694281i	−0.937813	−	0.347140i	$-0.887153\pi$
$181$		−	9.34059i		−	0.694281i	0.937813	−	0.347140i	$-0.112847\pi$
$182$	20.3518	+	8.08945i	1.50858	+	0.599630i
$183$		−	6.27850i		−	0.464120i
$184$	8.24198	+	17.6997i	0.607607	+	1.30484i
$185$			7.83550i			0.576077i
$186$	−7.19474	−	3.19933i	−0.527544	−	0.234586i
$187$		−	4.06047i		−	0.296931i
$188$	11.5361	−	12.2189i	0.841358	−	0.891151i
$189$		−	2.57432i		−	0.187254i
$190$	0.293658	−	0.738799i	0.0213042	−	0.0535981i
$191$			2.76140i			0.199808i	0.994997	+	0.0999039i	$0.0318535\pi$
$191$			2.76140i			0.199808i	−0.994997	+	0.0999039i	$0.968146\pi$
$192$	−5.14884	+	6.12286i	−0.371586	+	0.441879i
$193$	1.08692			0.0782380			0.0391190	−	0.999235i	$-0.487545\pi$
$193$	1.08692			0.0782380			0.0391190	+	0.999235i	$0.487545\pi$
$194$	12.7613	+	5.07238i	0.916210	+	0.364176i
$195$		−	20.5391i		−	1.47084i
$196$	0.542240	+	0.511942i	0.0387315	+	0.0365673i
$197$		−	14.7312i		−	1.04955i	−0.851240	−	0.524777i	$-0.824149\pi$
$197$		−	14.7312i		−	1.04955i	0.851240	−	0.524777i	$-0.175851\pi$
$198$	0.812507	+	0.322956i	0.0577423	+	0.0229515i
$199$	15.9168			1.12832			0.564158	−	0.825667i	$-0.309201\pi$
$199$	15.9168			1.12832			0.564158	+	0.825667i	$0.309201\pi$
$200$	−7.94900	−	17.0705i	−0.562079	−	1.20706i
$201$		−	1.25147i		−	0.0882716i
$202$	7.35895	+	2.92504i	0.517774	+	0.205805i
$203$	6.80948			0.477932
$204$	−9.01742	+	9.55110i	−0.631346	+	0.668710i
$205$	17.2059			1.20171
$206$	4.72830	−	11.8957i	0.329436	−	0.828810i
$207$	−6.90297			−0.479790
$208$	24.0226	−	1.38200i	1.66567	−	0.0958242i
$209$		−	0.101794i		−	0.00704127i
$210$	−4.59141	+	11.5513i	−0.316837	+	0.797113i
$211$		−	4.78985i		−	0.329747i	−0.986315	−	0.164874i	$-0.947278\pi$
$211$		−	4.78985i		−	0.329747i	0.986315	−	0.164874i	$-0.0527216\pi$
$212$	−6.68645	+	7.08218i	−0.459228	+	0.486406i
$213$			13.7892i			0.944817i
$214$	−2.90530	+	7.30928i	−0.198602	+	0.499652i
$215$	−28.9020			−1.97110
$216$	−1.19398	−	2.56406i	−0.0812398	−	0.174462i
$217$	0.574399	−	14.3217i	0.0389927	−	0.972221i
$218$	1.64364	+	0.653317i	0.111322	+	0.0442482i
$219$			5.21502i			0.352398i
$220$	−3.06980	−	2.89828i	−0.206966	−	0.195402i
$221$	39.5084			2.65762
$222$	1.19878	−	3.01595i	0.0804571	−	0.202418i
$223$	−1.54024			−0.103142			−0.0515710	−	0.998669i	$-0.516423\pi$
$223$	−1.54024			−0.103142			−0.0515710	+	0.998669i	$0.516423\pi$
$224$	−13.8193	−	4.59288i	−0.923343	−	0.306875i
$225$	6.65758			0.443839
$226$	21.1760	+	8.41705i	1.40861	+	0.559894i
$227$		−	6.94451i		−	0.460924i	−0.973081	−	0.230462i	$-0.925976\pi$
$227$		−	6.94451i		−	0.460924i	0.973081	−	0.230462i	$-0.0740237\pi$
$228$	−0.226064	+	0.239442i	−0.0149714	+	0.0158575i
$229$		−	27.0602i		−	1.78819i	−0.447882	−	0.894093i	$-0.647821\pi$
$229$		−	27.0602i		−	1.78819i	0.447882	−	0.894093i	$-0.352179\pi$
$230$	30.9744	+	12.3117i	2.04239	+	0.811811i
$231$			1.59158i			0.104718i
$232$	6.78234	−	3.15825i	0.445282	−	0.207349i
$233$	−19.3200			−1.26570			−0.632848	−	0.774276i	$-0.718114\pi$
$233$	−19.3200			−1.26570			−0.632848	+	0.774276i	$0.718114\pi$
$234$	−3.14236	+	7.90569i	−0.205423	+	0.516811i
$235$		−	28.6875i		−	1.87137i
$236$	−18.0457	+	19.1137i	−1.17467	+	1.24419i
$237$	2.23797			0.145372
$238$	−22.2196	−	8.83188i	−1.44029	−	0.572485i
$239$	−25.3977			−1.64284			−0.821421	−	0.570322i	$-0.806818\pi$
$239$	−25.3977			−1.64284			−0.821421	+	0.570322i	$0.806818\pi$
$240$	0.784392	+	13.6347i	0.0506323	+	0.880119i
$241$			11.8873i			0.765729i	0.923804	+	0.382865i	$0.125062\pi$
$241$			11.8873i			0.765729i	−0.923804	+	0.382865i	$0.874938\pi$
$242$	13.9539	+	5.54641i	0.896991	+	0.356536i
$243$	1.00000			0.0641500
$244$	8.62039	−	9.13057i	0.551864	−	0.584525i
$245$	1.27308			0.0813339
$246$	−6.62271	−	2.63240i	−0.422248	−	0.167836i
$247$	0.990460			0.0630215
$248$	−6.07033	−	14.5310i	−0.385466	−	0.922722i
$249$	11.8591			0.751539
$250$	−7.43776	−	2.95637i	−0.470406	−	0.186977i
$251$	20.5641			1.29800			0.648998	−	0.760790i	$-0.275188\pi$
$251$	20.5641			1.29800			0.648998	+	0.760790i	$0.275188\pi$
$252$	3.53455	−	3.74373i	0.222656	−	0.235833i
$253$	4.26777			0.268312
$254$	−14.6510	−	5.82348i	−0.919283	−	0.365397i
$255$			22.4241i			1.40425i
$256$	−15.8944	+	1.83485i	−0.993403	+	0.114678i
$257$	−13.0118			−0.811655			−0.405827	−	0.913950i	$-0.633017\pi$
$257$	−13.0118			−0.811655			−0.405827	+	0.913950i	$0.633017\pi$
$258$	11.1246	+	4.42183i	0.692590	+	0.275291i
$259$	5.90779			0.367092
$260$	28.2002	−	29.8692i	1.74890	−	1.85241i
$261$			2.64515i			0.163731i
$262$	−4.80721	+	12.0942i	−0.296990	+	0.747181i
$263$	−0.105475			−0.00650386			−0.00325193	−	0.999995i	$-0.501035\pi$
$263$	−0.105475			−0.00650386			−0.00325193	+	0.999995i	$0.501035\pi$
$264$	0.738176	+	1.58523i	0.0454316	+	0.0975644i
$265$			16.6276i			1.02142i
$266$	−0.557038	−	0.221412i	−0.0341542	−	0.0135756i
$267$			4.47064i			0.273599i
$268$	1.71826	−	1.81995i	0.104960	−	0.111171i
$269$		−	0.617529i		−	0.0376514i	−0.999823	−	0.0188257i	$-0.994007\pi$
$269$		−	0.617529i		−	0.0376514i	0.999823	−	0.0188257i	$-0.00599276\pi$
$270$	−4.48711	−	1.78354i	−0.273077	−	0.108543i
$271$	8.88861			0.539945			0.269972	−	0.962868i	$-0.412985\pi$
$271$	8.88861			0.539945			0.269972	+	0.962868i	$0.412985\pi$
$272$	−26.2273	+	1.50883i	−1.59027	+	0.0914863i
$273$	−15.4860			−0.937258
$274$	−9.81575	+	24.6949i	−0.592991	+	1.49187i
$275$	−4.11606			−0.248208
$276$	−10.0387	−	9.47779i	−0.604259	−	0.570496i
$277$			27.3650i			1.64420i	0.569340	+	0.822102i	$0.307199\pi$
$277$			27.3650i			1.64420i	−0.569340	+	0.822102i	$0.692801\pi$
$278$	3.79879	+	1.50995i	0.227836	+	0.0905605i
$279$	5.56329	+	0.223126i	0.333066	+	0.0133582i
$280$	−22.5370	+	10.4945i	−1.34684	+	0.627168i
$281$	−12.1221			−0.723145			−0.361572	−	0.932344i	$-0.617760\pi$
$281$	−12.1221			−0.723145			−0.361572	+	0.932344i	$0.617760\pi$
$282$	−4.38902	+	11.0421i	−0.261362	+	0.657547i
$283$			10.1449i			0.603053i	0.953458	+	0.301526i	$0.0974961\pi$
$283$			10.1449i			0.603053i	−0.953458	+	0.301526i	$0.902504\pi$
$284$	−18.9325	+	20.0530i	−1.12344	+	1.18993i
$285$			0.562165i			0.0332998i
$286$	1.94277	−	4.88770i	0.114878	−	0.289016i
$287$		−	12.9729i		−	0.765764i
$288$	1.78411	−	5.36814i	0.105130	−	0.316321i
$289$	−26.1343			−1.53731
$290$	4.71774	−	11.8691i	0.277035	−	0.696977i
$291$	−9.71032			−0.569229
$292$	−7.16023	+	7.58399i	−0.419021	+	0.443819i
$293$	10.5694			0.617473			0.308737	−	0.951148i	$-0.400094\pi$
$293$	10.5694			0.617473			0.308737	+	0.951148i	$0.400094\pi$
$294$	−0.490019	−	0.194773i	−0.0285785	−	0.0113594i
$295$			44.8753i			2.61274i
$296$	5.88425	−	2.74005i	0.342015	−	0.159262i
$297$	−0.618251			−0.0358745
$298$	14.6270	+	5.81395i	0.847319	+	0.336793i
$299$			41.5254i			2.40147i
$300$	9.68185	+	9.14087i	0.558982	+	0.527748i
$301$			21.7915i			1.25604i
$302$	19.4455	+	7.72920i	1.11896	+	0.444766i
$303$	−5.59956			−0.321686
$304$	−0.657510	+	0.0378259i	−0.0377108	+	0.00216946i
$305$		−	21.4368i		−	1.22747i
$306$	3.43076	−	8.63126i	0.196123	−	0.493416i
$307$		−	13.1387i		−	0.749866i	−0.927052	−	0.374933i	$-0.877666\pi$
$307$		−	13.1387i		−	0.749866i	0.927052	−	0.374933i	$-0.122334\pi$
$308$	−2.18524	+	2.31456i	−0.124515	+	0.131885i
$309$			9.05162i			0.514929i
$310$	−24.5651	−	10.9235i	−1.39521	−	0.620416i
$311$		−	18.1154i		−	1.02723i	−0.858021	−	0.513615i	$-0.828306\pi$
$311$		−	18.1154i		−	1.02723i	0.858021	−	0.513615i	$-0.171694\pi$
$312$	−15.4243	+	7.18246i	−0.873231	+	0.406627i
$313$			2.34613i			0.132611i	0.997799	+	0.0663056i	$0.0211212\pi$
$313$			2.34613i			0.132611i	−0.997799	+	0.0663056i	$0.978879\pi$
$314$	−22.2317	−	8.83669i	−1.25461	−	0.498683i
$315$		−	8.78956i		−	0.495236i
$316$	3.25459	+	3.07274i	0.183085	+	0.172855i
$317$	17.7785			0.998542			0.499271	−	0.866446i	$-0.333601\pi$
$317$	17.7785			0.998542			0.499271	+	0.866446i	$0.333601\pi$
$318$	2.54392	−	6.40011i	0.142656	−	0.358900i
$319$		−	1.63537i		−	0.0915630i
$320$	−17.5798	+	20.9054i	−0.982741	+	1.16865i
$321$		−	5.56176i		−	0.310427i
$322$	9.28277	−	23.3540i	0.517308	−	1.30147i
$323$	−1.08136			−0.0601686
$324$	1.45426	+	1.37300i	0.0807921	+	0.0762778i
$325$		−	40.0492i		−	2.22153i
$326$	12.6546	−	31.8371i	0.700876	−	1.76329i
$327$	−1.25068			−0.0691626
$328$	−6.01684	−	12.9212i	−0.332225	−	0.713452i
$329$	−21.6298			−1.19249
$330$	2.77416	+	1.10267i	0.152712	+	0.0607002i
$331$	−2.70580			−0.148724			−0.0743622	−	0.997231i	$-0.523692\pi$
$331$	−2.70580			−0.148724			−0.0743622	+	0.997231i	$0.523692\pi$
$332$	17.2462	+	16.2825i	0.946507	+	0.893621i
$333$			2.29489i			0.125759i
$334$	−4.66209	−	1.85309i	−0.255098	−	0.101397i
$335$		−	4.27290i		−	0.233454i
$336$	10.2803	−	0.591415i	0.560836	−	0.0322643i
$337$		−	11.1788i		−	0.608948i	−0.952521	−	0.304474i	$-0.901519\pi$
$337$		−	11.1788i		−	0.608948i	0.952521	−	0.304474i	$-0.0984807\pi$
$338$	30.4727	+	12.1123i	1.65750	+	0.658823i
$339$	−16.1132			−0.875148
$340$	−30.7884	+	32.6105i	−1.66973	+	1.76855i
$341$	−3.43951	−	0.137948i	−0.186260	−	0.00747030i
$342$	0.0860078	−	0.216382i	0.00465077	−	0.0117006i
$343$		−	18.9801i		−	1.02483i
$344$	10.1069	+	21.7046i	0.544929	+	1.17024i
$345$	−23.5690			−1.26891
$346$	−1.72718	−	0.686520i	−0.0928537	−	0.0369076i
$347$	29.7510			1.59712			0.798558	−	0.601918i	$-0.205597\pi$
$347$	29.7510			1.59712			0.798558	+	0.601918i	$0.205597\pi$
$348$	−3.63180	+	3.84674i	−0.194685	+	0.206207i
$349$	15.2367			0.815599			0.407800	−	0.913071i	$-0.366296\pi$
$349$	15.2367			0.815599			0.407800	+	0.913071i	$0.366296\pi$
$350$	−8.95278	+	22.5238i	−0.478546	+	1.20395i
$351$		−	6.01558i		−	0.321088i
$352$	−1.10303	+	3.31886i	−0.0587916	+	0.176896i
$353$		−	23.6247i		−	1.25741i	−0.777642	−	0.628707i	$-0.783584\pi$
$353$		−	23.6247i		−	1.25741i	0.777642	−	0.628707i	$-0.216416\pi$
$354$	6.86564	−	17.2729i	0.364905	−	0.918044i
$355$			47.0806i			2.49878i
$356$	−6.13819	+	6.50146i	−0.325323	+	0.344577i
$357$	16.9073			0.894830
$358$	15.4327	+	6.13421i	0.815645	+	0.324203i
$359$			18.4669i			0.974646i	0.873222	+	0.487323i	$0.162027\pi$
$359$			18.4669i			0.974646i	−0.873222	+	0.487323i	$0.837973\pi$
$360$	−4.07662	−	8.75453i	−0.214857	−	0.461404i
$361$	18.9729			0.998573
$362$	−4.87925	+	12.2754i	−0.256448	+	0.645183i
$363$	−10.6178			−0.557288
$364$	−22.5207	−	21.2624i	−1.18041	−	1.11445i
$365$			17.8058i			0.931996i
$366$	−3.27970	+	8.25123i	−0.171433	+	0.431298i
$367$	25.7959			1.34654			0.673268	−	0.739399i	$-0.264890\pi$
$367$	25.7959			1.34654			0.673268	+	0.739399i	$0.264890\pi$
$368$	−1.58586	−	27.5663i	−0.0826687	−	1.43699i
$369$	5.03933			0.262337
$370$	4.09303	−	10.2974i	0.212787	−	0.535338i
$371$	12.5368			0.650880
$372$	7.78411	+	7.96289i	0.403587	+	0.412857i
$373$	−19.3134			−1.00001			−0.500005	−	0.866023i	$-0.666668\pi$
$373$	−19.3134			−1.00001			−0.500005	+	0.866023i	$0.666668\pi$
$374$	−2.12107	+	5.33628i	−0.109678	+	0.275932i
$375$	5.65953			0.292257
$376$	−21.5436	+	10.0319i	−1.11102	+	0.517357i
$377$	15.9121			0.819516
$378$	−1.34475	+	3.38318i	−0.0691665	+	0.174012i
$379$			9.43037i			0.484405i	0.970226	+	0.242203i	$0.0778699\pi$
$379$			9.43037i			0.484405i	−0.970226	+	0.242203i	$0.922130\pi$
$380$	−0.771853	+	0.817533i	−0.0395952	+	0.0419386i
$381$	11.1482			0.571138
$382$	1.44247	−	3.62904i	0.0738033	−	0.185678i
$383$	−4.00388			−0.204589			−0.102294	−	0.994754i	$-0.532618\pi$
$383$	−4.00388			−0.204589			−0.102294	+	0.994754i	$0.532618\pi$
$384$	9.96502	−	5.35708i	0.508526	−	0.273377i
$385$			5.43415i			0.276950i
$386$	−1.42843	−	0.567773i	−0.0727052	−	0.0288989i
$387$	−8.46494			−0.430297
$388$	−14.1213	−	13.3323i	−0.716901	−	0.676844i
$389$		−	3.05571i		−	0.154931i	−0.996995	−	0.0774653i	$-0.975317\pi$
$389$		−	3.05571i		−	0.154931i	0.996995	−	0.0774653i	$-0.0246827\pi$
$390$	−10.7290	+	26.9926i	−0.543285	+	1.36682i
$391$		−	45.3365i		−	2.29276i
$392$	−0.445190	−	0.956047i	−0.0224855	−	0.0482876i
$393$		−	9.20268i		−	0.464214i
$394$	−7.69514	+	19.3598i	−0.387676	+	0.975332i
$395$	7.64116			0.384468
$396$	−0.899096	−	0.848859i	−0.0451813	−	0.0426568i
$397$	10.9743			0.550786			0.275393	−	0.961332i	$-0.411192\pi$
$397$	10.9743			0.550786			0.275393	+	0.961332i	$0.411192\pi$
$398$	−20.9180	−	8.31449i	−1.04852	−	0.416768i
$399$	0.423860			0.0212195
$400$	1.52949	+	26.5864i	0.0764744	+	1.32932i
$401$			23.7678i			1.18691i	0.804868	+	0.593454i	$0.202236\pi$
$401$			23.7678i			1.18691i	−0.804868	+	0.593454i	$0.797764\pi$
$402$	−0.653728	+	1.64468i	−0.0326050	+	0.0820291i
$403$	1.34223	−	33.4664i	0.0668614	−	1.66708i
$404$	−8.14320	−	7.68820i	−0.405140	−	0.382502i
$405$	3.41432			0.169659
$406$	−8.94903	−	3.55707i	−0.444133	−	0.176534i
$407$		−	1.41882i		−	0.0703282i
$408$	16.8399	−	7.84164i	0.833701	−	0.388219i
$409$		−	21.9791i		−	1.08680i	−0.839475	−	0.543399i	$-0.817137\pi$
$409$		−	21.9791i		−	1.08680i	0.839475	−	0.543399i	$-0.182863\pi$
$410$	−22.6120	−	8.98785i	−1.11673	−	0.443878i
$411$		−	18.7908i		−	0.926881i
$412$	−12.4279	+	13.1634i	−0.612278	+	0.648514i
$413$	33.8350			1.66491
$414$	9.07191	+	3.60591i	0.445860	+	0.177221i
$415$	40.4907			1.98761
$416$	−32.2925	−	10.7325i	−1.58327	−	0.526203i
$417$	−2.89057			−0.141552
$418$	−0.0531744	+	0.133779i	−0.00260085	+	0.00654332i
$419$		−	24.5238i		−	1.19807i	−0.800724	−	0.599034i	$-0.795552\pi$
$419$		−	24.5238i		−	1.19807i	0.800724	−	0.599034i	$-0.204448\pi$
$420$	12.0681	−	12.7823i	0.588862	−	0.623712i
$421$	40.5763			1.97757			0.988785	−	0.149346i	$-0.0477167\pi$
$421$	40.5763			1.97757			0.988785	+	0.149346i	$0.0477167\pi$
$422$	−2.50208	+	6.29484i	−0.121799	+	0.306428i
$423$		−	8.40212i		−	0.408525i
$424$	12.4869	−	5.81461i	0.606416	−	0.282382i
$425$			43.7248i			2.12097i
$426$	7.20305	−	18.1218i	0.348989	−	0.878002i
$427$	−16.1629			−0.782177
$428$	7.63630	−	8.08824i	0.369115	−	0.390960i
$429$			3.71914i			0.179562i
$430$	37.9831	+	15.0975i	1.83171	+	0.728068i
$431$		−	8.81621i		−	0.424662i	−0.977198	−	0.212331i	$-0.931895\pi$
$431$		−	8.81621i		−	0.424662i	0.977198	−	0.212331i	$-0.0681055\pi$
$432$	0.229736	+	3.99340i	0.0110532	+	0.192132i
$433$		−	16.1566i		−	0.776438i	−0.921567	−	0.388219i	$-0.873090\pi$
$433$		−	16.1566i		−	0.776438i	0.921567	−	0.388219i	$-0.126910\pi$
$434$	−8.23611	+	18.5216i	−0.395346	+	0.889064i
$435$			9.03140i			0.433023i
$436$	−1.81881	−	1.71718i	−0.0871051	−	0.0822381i
$437$		−	1.13657i		−	0.0543695i
$438$	2.72417	−	6.85360i	0.130166	−	0.327478i
$439$			9.76967i			0.466281i	0.972443	+	0.233141i	$0.0749002\pi$
$439$			9.76967i			0.466281i	−0.972443	+	0.233141i	$0.925100\pi$
$440$	2.52037	+	5.41250i	0.120154	+	0.258031i
$441$	0.372864			0.0177554
$442$	−51.9220	−	20.6380i	−2.46968	−	0.981649i
$443$		−	15.7031i		−	0.746079i	−0.927815	−	0.373039i	$-0.878316\pi$
$443$		−	15.7031i		−	0.746079i	0.927815	−	0.373039i	$-0.121684\pi$
$444$	−3.15089	+	3.33737i	−0.149535	+	0.158384i
$445$			15.2642i			0.723592i
$446$	2.02419	+	0.804575i	0.0958480	+	0.0380977i
$447$	−11.1299			−0.526428
$448$	15.7622	+	13.2548i	0.744695	+	0.626230i
$449$		−	4.44409i		−	0.209730i	−0.994486	−	0.104865i	$-0.966559\pi$
$449$		−	4.44409i		−	0.209730i	0.994486	−	0.104865i	$-0.0334410\pi$
$450$	−8.74942	−	3.47772i	−0.412451	−	0.163941i
$451$	−3.11557			−0.146707
$452$	−23.4327	−	22.1234i	−1.10218	−	1.04060i
$453$	−14.7964			−0.695196
$454$	−3.62761	+	9.12650i	−0.170252	+	0.428328i
$455$	−52.8743			−2.47879
$456$	0.422171	−	0.196587i	0.0197700	−	0.00920604i
$457$		−	26.7985i		−	1.25358i	−0.779189	−	0.626789i	$-0.784369\pi$
$457$		−	26.7985i		−	1.25358i	0.779189	−	0.626789i	$-0.215631\pi$
$458$	−14.1354	+	35.5625i	−0.660505	+	1.66173i
$459$			6.56767i			0.306553i
$460$	−34.2754	−	32.3602i	−1.59810	−	1.50880i
$461$		−	18.9732i		−	0.883672i	−0.897096	−	0.441836i	$-0.854327\pi$
$461$		−	18.9732i		−	0.883672i	0.897096	−	0.441836i	$-0.145673\pi$
$462$	0.831392	−	2.09165i	0.0386799	−	0.0973126i
$463$	−27.9926			−1.30093			−0.650464	−	0.759537i	$-0.725426\pi$
$463$	−27.9926			−1.30093			−0.650464	+	0.759537i	$0.725426\pi$
$464$	−10.5631	+	0.607687i	−0.490382	+	0.0282112i
$465$	18.9949	+	0.761824i	0.880866	+	0.0353288i
$466$	25.3904	+	10.0922i	1.17619	+	0.467512i
$467$			1.79665i			0.0831392i	0.999136	+	0.0415696i	$0.0132358\pi$
$467$			1.79665i			0.0831392i	−0.999136	+	0.0415696i	$0.986764\pi$
$468$	8.25940	−	8.74821i	0.381791	−	0.404386i
$469$	−3.22168			−0.148763
$470$	−14.9855	+	37.7012i	−0.691230	+	1.73903i
$471$	16.9165			0.779472
$472$	33.7001	−	15.6927i	1.55117	−	0.722316i
$473$	5.23345			0.240634
$474$	−2.94115	−	1.16905i	−0.135092	−	0.0536963i
$475$			1.09617i			0.0502955i
$476$	24.5876	+	23.2138i	1.12697	+	1.06400i
$477$			4.86996i			0.222980i
$478$	33.3778	+	13.2670i	1.52666	+	0.606819i
$479$		−	33.0395i		−	1.50961i	−0.655948	−	0.754806i	$-0.727731\pi$
$479$		−	33.0395i		−	1.50961i	0.655948	−	0.754806i	$-0.272269\pi$
$480$	6.09153	−	18.3286i	0.278039	−	0.836580i
$481$	13.8051			0.629459
$482$	6.20958	−	15.6223i	0.282839	−	0.711578i
$483$			17.7705i			0.808585i
$484$	−15.4410	−	14.5782i	−0.701863	−	0.662646i
$485$	−33.1542			−1.50545
$486$	−1.31420	−	0.522370i	−0.0596135	−	0.0236952i
$487$	−11.9539			−0.541682			−0.270841	−	0.962624i	$-0.587302\pi$
$487$	−11.9539			−0.541682			−0.270841	+	0.962624i	$0.587302\pi$
$488$	−16.0985	+	7.49638i	−0.728744	+	0.339345i
$489$			24.2254i			1.09551i
$490$	−1.67308	−	0.665017i	−0.0755821	−	0.0300424i
$491$	−7.87087			−0.355208			−0.177604	−	0.984102i	$-0.556835\pi$
$491$	−7.87087			−0.355208			−0.177604	+	0.984102i	$0.556835\pi$
$492$	7.32849	+	6.91901i	0.330394	+	0.311933i
$493$	−17.3725			−0.782418
$494$	−1.30167	−	0.517387i	−0.0585647	−	0.0232783i
$495$	−2.11091			−0.0948782
$496$	0.387057	+	22.2677i	0.0173794	+	0.999849i
$497$	35.4977			1.59229
$498$	−15.5853	−	6.19484i	−0.698392	−	0.277597i
$499$	42.9063			1.92075			0.960376	−	0.278708i	$-0.0899063\pi$
$499$	42.9063			1.92075			0.960376	+	0.278708i	$0.0899063\pi$
$500$	8.23041	+	7.77053i	0.368075	+	0.347509i
$501$	3.54747			0.158489
$502$	−27.0254	−	10.7421i	−1.20620	−	0.479443i
$503$			8.93560i			0.398419i	0.979957	+	0.199209i	$0.0638374\pi$
$503$			8.93560i			0.398419i	−0.979957	+	0.199209i	$0.936163\pi$
$504$	−6.60073	+	3.07368i	−0.294020	+	0.136913i
$505$	−19.1187			−0.850770
$506$	−5.60871	−	2.22935i	−0.249338	−	0.0991069i
$507$	−23.1872			−1.02978
$508$	16.2123	+	15.3065i	0.719306	+	0.679114i
$509$			32.8606i			1.45652i	0.685301	+	0.728260i	$0.259670\pi$
$509$			32.8606i			1.45652i	−0.685301	+	0.728260i	$0.740330\pi$
$510$	11.7137	−	29.4699i	0.518692	−	1.30495i
$511$	13.4251			0.593894
$512$	21.8470	+	5.89141i	0.965510	+	0.260366i
$513$			0.164649i			0.00726944i
$514$	17.1002	+	6.79698i	0.754256	+	0.299802i
$515$			30.9051i			1.36184i
$516$	−12.3102	−	11.6224i	−0.541927	−	0.511646i
$517$			5.19461i			0.228459i
$518$	−7.76404	−	3.08606i	−0.341132	−	0.135594i
$519$	1.31424			0.0576888
$520$	−52.6636	+	24.5232i	−2.30945	+	1.07541i
$521$	17.1677			0.752131			0.376066	−	0.926593i	$-0.377277\pi$
$521$	17.1677			0.752131			0.376066	+	0.926593i	$0.377277\pi$
$522$	1.38175	−	3.47627i	0.0604775	−	0.152152i
$523$	28.3950			1.24163			0.620814	−	0.783958i	$-0.286802\pi$
$523$	28.3950			1.24163			0.620814	+	0.783958i	$0.286802\pi$
$524$	12.6353	−	13.3831i	0.551975	−	0.584642i
$525$		−	17.1388i		−	0.747997i
$526$	0.138615	+	0.0550970i	0.00604392	+	0.00240234i
$527$	−1.46542	+	36.5379i	−0.0638347	+	1.59162i
$528$	−0.142034	−	2.46892i	−0.00618126	−	0.107446i
$529$	24.6510			1.07178
$530$	8.68576	−	21.8520i	0.377285	−	0.949191i
$531$			13.1432i			0.570368i
$532$	0.616402	+	0.581960i	0.0267244	+	0.0252312i
$533$		−	30.3145i		−	1.31307i
$534$	2.33533	−	5.87532i	0.101060	−	0.254250i
$535$		−	18.9896i		−	0.820993i
$536$	−3.20884	+	1.49422i	−0.138601	+	0.0645404i
$537$	−11.7430			−0.506749
$538$	−0.322579	+	0.811558i	−0.0139074	+	0.0349888i
$539$	−0.230523			−0.00992934
$540$	4.96530	+	4.68787i	0.213673	+	0.201734i
$541$	8.05633			0.346369			0.173184	−	0.984889i	$-0.444594\pi$
$541$	8.05633			0.346369			0.173184	+	0.984889i	$0.444594\pi$
$542$	−11.6814	−	4.64315i	−0.501761	−	0.199440i
$543$		−	9.34059i		−	0.400843i
$544$	35.2562	+	11.7175i	1.51160	+	0.502382i
$545$	−4.27021			−0.182916
$546$	20.3518	+	8.08945i	0.870977	+	0.346196i
$547$		−	35.8956i		−	1.53479i	−0.641177	−	0.767393i	$-0.721554\pi$
$547$		−	35.8956i		−	1.53479i	0.641177	−	0.767393i	$-0.278446\pi$
$548$	25.7998	−	27.3267i	1.10211	−	1.16734i
$549$		−	6.27850i		−	0.267960i
$550$	5.40933	+	2.15011i	0.230655	+	0.0916808i
$551$	−0.435522			−0.0185539
$552$	8.24198	+	17.6997i	0.350802	+	0.753347i
$553$		−	5.76127i		−	0.244994i
$554$	14.2947	−	35.9632i	0.607322	−	1.52793i
$555$			7.83550i			0.332598i
$556$	−4.20363	−	3.96875i	−0.178274	−	0.168313i
$557$			4.09133i			0.173355i	0.996236	+	0.0866777i	$0.0276250\pi$
$557$			4.09133i			0.173355i	−0.996236	+	0.0866777i	$0.972375\pi$
$558$	−7.19474	−	3.19933i	−0.304578	−	0.135438i
$559$			50.9215i			2.15375i
$560$	35.1002	−	2.01928i	1.48325	−	0.0853301i
$561$		−	4.06047i		−	0.171433i
$562$	15.9309	+	6.33223i	0.672005	+	0.267109i
$563$			0.838070i			0.0353204i	0.999844	+	0.0176602i	$0.00562171\pi$
$563$			0.838070i			0.0353204i	−0.999844	+	0.0176602i	$0.994378\pi$
$564$	11.5361	−	12.2189i	0.485758	−	0.514507i
$565$	−55.0156			−2.31452
$566$	5.29940	−	13.3325i	0.222751	−	0.560406i
$567$		−	2.57432i		−	0.108111i
$568$	35.3563	−	16.4639i	1.48352	−	0.690811i
$569$			40.3294i			1.69070i	0.534215	+	0.845348i	$0.320607\pi$
$569$			40.3294i			1.69070i	−0.534215	+	0.845348i	$0.679393\pi$
$570$	0.293658	−	0.738799i	0.0123000	−	0.0309449i
$571$	−33.4910			−1.40155			−0.700776	−	0.713381i	$-0.747163\pi$
$571$	−33.4910			−1.40155			−0.700776	+	0.713381i	$0.747163\pi$
$572$	−5.10638	+	5.40859i	−0.213508	+	0.226144i
$573$			2.76140i			0.115359i
$574$	−6.77664	+	17.0490i	−0.282852	+	0.711611i
$575$	−45.9571			−1.91654
$576$	−5.14884	+	6.12286i	−0.214535	+	0.255119i
$577$	15.3292			0.638164			0.319082	−	0.947727i	$-0.396625\pi$
$577$	15.3292			0.638164			0.319082	+	0.947727i	$0.396625\pi$
$578$	34.3458	+	13.6518i	1.42860	+	0.567840i
$579$	1.08692			0.0451707
$580$	−12.4001	+	13.1340i	−0.514887	+	0.545359i
$581$		−	30.5291i		−	1.26656i
$582$	12.7613	+	5.07238i	0.528974	+	0.210257i
$583$		−	3.01085i		−	0.124697i
$584$	13.3716	−	6.22661i	0.553323	−	0.257659i
$585$		−	20.5391i		−	0.849188i
$586$	−13.8904	−	5.52116i	−0.573807	−	0.228077i
$587$	−2.44784			−0.101033			−0.0505167	−	0.998723i	$-0.516087\pi$
$587$	−2.44784			−0.101033			−0.0505167	+	0.998723i	$0.516087\pi$
$588$	0.542240	+	0.511942i	0.0223616	+	0.0211122i
$589$	−0.0367375	+	0.915991i	−0.00151374	+	0.0377428i
$590$	23.4415	−	58.9752i	0.965071	−	2.42797i
$591$		−	14.7312i		−	0.605961i
$592$	−9.16442	+	0.527220i	−0.376655	+	0.0216686i
$593$	−12.3833			−0.508522			−0.254261	−	0.967136i	$-0.581832\pi$
$593$	−12.3833			−0.508522			−0.254261	+	0.967136i	$0.581832\pi$
$594$	0.812507	+	0.322956i	0.0333376	+	0.0132510i
$595$	57.7270			2.36658
$596$	−16.1858	−	15.2814i	−0.662996	−	0.625951i
$597$	15.9168			0.651433
$598$	21.6916	−	54.5728i	0.887036	−	2.23165i
$599$		−	20.3532i		−	0.831608i	−0.909454	−	0.415804i	$-0.863500\pi$
$599$		−	20.3532i		−	0.831608i	0.909454	−	0.415804i	$-0.136500\pi$
$600$	−7.94900	−	17.0705i	−0.324516	−	0.696899i
$601$			22.9772i			0.937259i	0.883395	+	0.468629i	$0.155252\pi$
$601$			22.9772i			0.937259i	−0.883395	+	0.468629i	$0.844748\pi$
$602$	11.3832	−	28.6384i	0.463945	−	1.16721i
$603$		−	1.25147i		−	0.0509636i
$604$	−21.5178	−	20.3155i	−0.875547	−	0.826625i
$605$	−36.2525			−1.47387
$606$	7.35895	+	2.92504i	0.298937	+	0.118822i
$607$			33.8896i			1.37554i	0.725930	+	0.687768i	$0.241409\pi$
$607$			33.8896i			1.37554i	−0.725930	+	0.687768i	$0.758591\pi$
$608$	0.883860	+	0.293753i	0.0358453	+	0.0119132i
$609$	6.80948			0.275934
$610$	−11.1980	+	28.1723i	−0.453392	+	1.14066i
$611$	−50.5436			−2.04478
$612$	−9.01742	+	9.55110i	−0.364508	+	0.386080i
$613$			34.9455i			1.41143i	0.708494	+	0.705717i	$0.249375\pi$
$613$			34.9455i			1.41143i	−0.708494	+	0.705717i	$0.750625\pi$
$614$	−6.86327	+	17.2669i	−0.276979	+	0.696837i
$615$	17.2059			0.693809
$616$	4.08090	−	1.90030i	0.164424	−	0.0765654i
$617$	−15.2775			−0.615049			−0.307525	−	0.951540i	$-0.599501\pi$
$617$	−15.2775			−0.615049			−0.307525	+	0.951540i	$0.599501\pi$
$618$	4.72830	−	11.8957i	0.190200	−	0.478514i
$619$	3.13328			0.125937			0.0629686	−	0.998016i	$-0.479943\pi$
$619$	3.13328			0.125937			0.0629686	+	0.998016i	$0.479943\pi$
$620$	26.5775	+	27.1879i	1.06738	+	1.09189i
$621$	−6.90297			−0.277007
$622$	−9.46294	+	23.8073i	−0.379429	+	0.954586i
$623$	11.5089			0.461093
$624$	24.0226	−	1.38200i	0.961674	−	0.0553241i
$625$	−13.9645			−0.558580
$626$	1.22555	−	3.08330i	0.0489828	−	0.123233i
$627$		−	0.101794i		−	0.00406528i
$628$	24.6010	+	23.2264i	0.981687	+	0.926835i
$629$	−15.0721			−0.600964
$630$	−4.59141	+	11.5513i	−0.182926	+	0.460214i
$631$	−25.5464			−1.01699			−0.508493	−	0.861066i	$-0.669797\pi$
$631$	−25.5464			−1.01699			−0.508493	+	0.861066i	$0.669797\pi$
$632$	−2.67209	−	5.73831i	−0.106290	−	0.228258i
$633$		−	4.78985i		−	0.190380i
$634$	−23.3646	−	9.28697i	−0.927926	−	0.368833i
$635$	38.0634			1.51050
$636$	−6.68645	+	7.08218i	−0.265135	+	0.280827i
$637$		−	2.24299i		−	0.0888706i
$638$	−0.854267	+	2.14920i	−0.0338208	+	0.0850878i
$639$			13.7892i			0.545491i
$640$	34.0238	−	18.2908i	1.34491	−	0.723007i
$641$		−	0.521818i		−	0.0206106i	−0.999947	−	0.0103053i	$-0.996720\pi$
$641$		−	0.521818i		−	0.0206106i	0.999947	−	0.0103053i	$-0.00328034\pi$
$642$	−2.90530	+	7.30928i	−0.114663	+	0.288474i
$643$	27.1894			1.07225			0.536123	−	0.844140i	$-0.319888\pi$
$643$	27.1894			1.07225			0.536123	+	0.844140i	$0.319888\pi$
$644$	−24.3989	+	25.8429i	−0.961451	+	1.01835i
$645$	−28.9020			−1.13802
$646$	1.42113	+	0.564871i	0.0559136	+	0.0222246i
$647$	−14.0585			−0.552698			−0.276349	−	0.961057i	$-0.589125\pi$
$647$	−14.0585			−0.552698			−0.276349	+	0.961057i	$0.589125\pi$
$648$	−1.19398	−	2.56406i	−0.0469038	−	0.100726i
$649$		−	8.12582i		−	0.318966i
$650$	−20.9205	+	52.6328i	−0.820571	+	2.06443i
$651$	0.574399	−	14.3217i	0.0225125	−	0.561312i
$652$	−33.2615	+	35.2300i	−1.30262	+	1.37971i
$653$	−14.4478			−0.565387			−0.282693	−	0.959210i	$-0.591228\pi$
$653$	−14.4478			−0.565387			−0.282693	+	0.959210i	$0.591228\pi$
$654$	1.64364	+	0.653317i	0.0642716	+	0.0255467i
$655$		−	31.4209i		−	1.22772i
$656$	1.15772	+	20.1241i	0.0452012	+	0.785713i
$657$			5.21502i			0.203457i
$658$	28.4259	+	11.2987i	1.10816	+	0.440471i
$659$			25.6200i			0.998013i	0.866598	+	0.499007i	$0.166302\pi$
$659$			25.6200i			0.998013i	−0.866598	+	0.499007i	$0.833698\pi$
$660$	−3.06980	−	2.89828i	−0.119492	−	0.112815i
$661$	−18.5928			−0.723176			−0.361588	−	0.932338i	$-0.617765\pi$
$661$	−18.5928			−0.723176			−0.361588	+	0.932338i	$0.617765\pi$
$662$	3.55597	+	1.41343i	0.138207	+	0.0549345i
$663$	39.5084			1.53438
$664$	−14.1595	−	30.4075i	−0.549494	−	1.18004i
$665$	1.44719			0.0561198
$666$	1.19878	−	3.01595i	0.0464519	−	0.116866i
$667$		−	18.2594i		−	0.707007i
$668$	5.15894	+	4.87068i	0.199605	+	0.188452i
$669$	−1.54024			−0.0595491
$670$	−2.23204	+	5.61546i	−0.0862311	+	0.216944i
$671$			3.88169i			0.149851i
$672$	−13.8193	−	4.59288i	−0.533092	−	0.177174i
$673$		−	5.48239i		−	0.211331i	−0.994402	−	0.105665i	$-0.966303\pi$
$673$		−	5.48239i		−	0.211331i	0.994402	−	0.105665i	$-0.0336972\pi$
$674$	−5.83947	+	14.6912i	−0.224928	+	0.565885i
$675$	6.65758			0.256251
$676$	−33.7202	−	31.8361i	−1.29693	−	1.22446i
$677$			23.0541i			0.886041i	0.896512	+	0.443020i	$0.146093\pi$
$677$			23.0541i			0.886041i	−0.896512	+	0.443020i	$0.853907\pi$
$678$	21.1760	+	8.41705i	0.813259	+	0.323255i
$679$			24.9975i			0.959316i
$680$	57.4969	−	26.7739i	2.20491	−	1.02673i
$681$		−	6.94451i		−	0.266114i
$682$	4.44815	+	1.97799i	0.170329	+	0.0757411i
$683$		−	27.6463i		−	1.05786i	−0.848666	−	0.528929i	$-0.822594\pi$
$683$		−	27.6463i		−	1.05786i	0.848666	−	0.528929i	$-0.177406\pi$
$684$	−0.226064	+	0.239442i	−0.00864375	+	0.00915531i
$685$		−	64.1578i		−	2.45134i
$686$	−9.91466	+	24.9437i	−0.378543	+	0.952356i
$687$		−	27.0602i		−	1.03241i
$688$	−1.94470	−	33.8038i	−0.0741410	−	1.28876i
$689$	29.2956			1.11607
$690$	30.9744	+	12.3117i	1.17917	+	0.468699i
$691$			21.0900i			0.802302i	0.916012	+	0.401151i	$0.131390\pi$
$691$			21.0900i			0.802302i	−0.916012	+	0.401151i	$0.868610\pi$
$692$	1.91125	+	1.80445i	0.0726547	+	0.0685951i
$693$			1.59158i			0.0604590i
$694$	−39.0988	−	15.5410i	−1.48417	−	0.589929i
$695$	−9.86932			−0.374365
$696$	6.78234	−	3.15825i	0.257084	−	0.119713i
$697$			33.0967i			1.25363i
$698$	−20.0241	−	7.95917i	−0.757922	−	0.301259i
$699$	−19.3200			−0.730750
$700$	23.5315	−	24.9242i	0.889409	−	0.942046i
$701$	28.6684			1.08279			0.541396	−	0.840768i	$-0.317896\pi$
$701$	28.6684			1.08279			0.541396	+	0.840768i	$0.317896\pi$
$702$	−3.14236	+	7.90569i	−0.118601	+	0.298381i
$703$	−0.377852			−0.0142510
$704$	3.18328	−	3.78546i	0.119974	−	0.142670i
$705$		−	28.6875i		−	1.08043i
$706$	−12.3408	+	31.0476i	−0.464453	+	1.16849i
$707$			14.4151i			0.542134i
$708$	−18.0457	+	19.1137i	−0.678199	+	0.718336i
$709$		−	14.8562i		−	0.557938i	−0.960300	−	0.278969i	$-0.910007\pi$
$709$		−	14.8562i		−	0.557938i	0.960300	−	0.278969i	$-0.0899926\pi$
$710$	24.5935	−	61.8735i	0.922978	−	2.32207i
$711$	2.23797			0.0839306
$712$	11.4630	−	5.33783i	0.429594	−	0.200044i
$713$	−38.4032	−	1.54023i	−1.43821	−	0.0576822i
$714$	−22.2196	−	8.83188i	−0.831549	−	0.330525i
$715$			12.6983i			0.474890i
$716$	−17.0774	−	16.1232i	−0.638213	−	0.602552i
$717$	−25.3977			−0.948495
$718$	9.64657	−	24.2693i	0.360007	−	0.905721i
$719$	−13.0734			−0.487555			−0.243777	−	0.969831i	$-0.578387\pi$
$719$	−13.0734			−0.487555			−0.243777	+	0.969831i	$0.578387\pi$
$720$	0.784392	+	13.6347i	0.0292326	+	0.508137i
$721$	23.3018			0.867804
$722$	−24.9342	−	9.91087i	−0.927956	−	0.368845i
$723$			11.8873i			0.442094i
$724$	12.8246	−	13.5836i	0.476624	−	0.504832i
$725$			17.6103i			0.654031i
$726$	13.9539	+	5.54641i	0.517878	+	0.205846i
$727$			4.31555i			0.160055i	0.996793	+	0.0800275i	$0.0255008\pi$
$727$			4.31555i			0.160055i	−0.996793	+	0.0800275i	$0.974499\pi$
$728$	18.4900	+	39.7072i	0.685284	+	1.47165i
$729$	1.00000			0.0370370
$730$	9.30120	−	23.4004i	0.344253	−	0.866087i
$731$		−	55.5949i		−	2.05625i
$732$	8.62039	−	9.13057i	0.318619	−	0.337475i
$733$	19.6738			0.726667			0.363333	−	0.931659i	$-0.381639\pi$
$733$	19.6738			0.726667			0.363333	+	0.931659i	$0.381639\pi$
$734$	−33.9011	−	13.4750i	−1.25131	−	0.497372i
$735$	1.27308			0.0469581
$736$	−12.3157	+	37.0561i	−0.453962	+	1.36591i
$737$			0.773719i			0.0285003i
$738$	−6.62271	−	2.63240i	−0.243785	−	0.0968999i
$739$	−12.1990			−0.448747			−0.224374	−	0.974503i	$-0.572034\pi$
$739$	−12.1990			−0.448747			−0.224374	+	0.974503i	$0.572034\pi$
$740$	−10.7581	+	11.3948i	−0.395477	+	0.418883i
$741$	0.990460			0.0363855
$742$	−16.4759	−	6.54887i	−0.604851	−	0.240417i
$743$	−33.3779			−1.22452			−0.612259	−	0.790657i	$-0.709739\pi$
$743$	−33.3779			−1.22452			−0.612259	+	0.790657i	$0.709739\pi$
$744$	−6.07033	−	14.5310i	−0.222549	−	0.532734i
$745$	−38.0012			−1.39225
$746$	25.3817	+	10.0887i	0.929291	+	0.369375i
$747$	11.8591			0.433901
$748$	5.57503	−	5.90497i	0.203843	−	0.215907i
$749$	−14.3178			−0.523160
$750$	−7.43776	−	2.95637i	−0.271589	−	0.107951i
$751$		−	44.2439i		−	1.61448i	−0.590222	−	0.807241i	$-0.700960\pi$
$751$		−	44.2439i		−	1.61448i	0.590222	−	0.807241i	$-0.299040\pi$
$752$	33.5530	−	1.93027i	1.22355	−	0.0703897i
$753$	20.5641			0.749399
$754$	−20.9118	−	8.31202i	−0.761562	−	0.302706i
$755$	−50.5197			−1.83860
$756$	3.53455	−	3.74373i	0.128550	−	0.136158i
$757$		−	4.75155i		−	0.172698i	−0.996265	−	0.0863491i	$-0.972480\pi$
$757$		−	4.75155i		−	0.172698i	0.996265	−	0.0863491i	$-0.0275200\pi$
$758$	4.92614	−	12.3934i	0.178926	−	0.450149i
$759$	4.26777			0.154910
$760$	1.44143	−	0.671212i	0.0522861	−	0.0243474i
$761$		−	20.8459i		−	0.755663i	−0.925874	−	0.377832i	$-0.876670\pi$
$761$		−	20.8459i		−	0.755663i	0.925874	−	0.377832i	$-0.123330\pi$
$762$	−14.6510	−	5.82348i	−0.530748	−	0.210962i
$763$			3.21965i			0.116559i
$764$	−3.79140	+	4.01579i	−0.137168	+	0.145286i
$765$			22.4241i			0.810747i
$766$	5.26191	+	2.09151i	0.190121	+	0.0755693i
$767$	79.0643			2.85484
$768$	−15.8944	+	1.83485i	−0.573541	+	0.0662096i
$769$	−1.44080			−0.0519565			−0.0259783	−	0.999663i	$-0.508270\pi$
$769$	−1.44080			−0.0519565			−0.0259783	+	0.999663i	$0.508270\pi$
$770$	2.83864	−	7.14158i	0.102297	−	0.257365i
$771$	−13.0118			−0.468609
$772$	1.58066	+	1.49234i	0.0568891	+	0.0537104i
$773$			54.3188i			1.95371i	0.213899	+	0.976856i	$0.431384\pi$
$773$			54.3188i			1.95371i	−0.213899	+	0.976856i	$0.568616\pi$
$774$	11.1246	+	4.42183i	0.399867	+	0.158939i
$775$	37.0381	+	1.48548i	1.33045	+	0.0533601i
$776$	11.5939	+	24.8979i	0.416196	+	0.893782i
$777$	5.90779			0.211941
$778$	−1.59621	+	4.01582i	−0.0572269	+	0.143974i
$779$			0.829722i			0.0297279i
$780$	28.2002	−	29.8692i	1.00973	−	1.06949i
$781$		−	8.52515i		−	0.305054i
$782$	−23.6824	+	59.5813i	−0.846882	+	2.13062i
$783$			2.64515i			0.0945301i
$784$	0.0856603	+	1.48899i	0.00305930	+	0.0531783i
$785$	57.7584			2.06149
$786$	−4.80721	+	12.0942i	−0.171467	+	0.431385i
$787$	−5.67370			−0.202245			−0.101123	−	0.994874i	$-0.532243\pi$
$787$	−5.67370			−0.202245			−0.101123	+	0.994874i	$0.532243\pi$
$788$	20.2260	−	21.4230i	0.720520	−	0.763162i
$789$	−0.105475			−0.00375501
$790$	−10.0420	−	3.99151i	−0.357280	−	0.142012i
$791$			41.4805i			1.47488i
$792$	0.738176	+	1.58523i	0.0262300	+	0.0563288i
$793$	−37.7688			−1.34121
$794$	−14.4225	−	5.73266i	−0.511835	−	0.203445i
$795$			16.6276i			0.589720i
$796$	23.1472	+	21.8539i	0.820431	+	0.774589i
$797$		−	36.2168i		−	1.28287i	−0.767179	−	0.641433i	$-0.778340\pi$
$797$		−	36.2168i		−	1.28287i	0.767179	−	0.641433i	$-0.221660\pi$
$798$	−0.557038	−	0.221412i	−0.0197189	−	0.00783790i
$799$	55.1824			1.95221
$800$	11.8779	−	35.7389i	0.419946	−	1.26356i
$801$			4.47064i			0.157962i
$802$	12.4156	−	31.2357i	0.438410	−	1.10297i
$803$		−	3.22419i		−	0.113779i
$804$	1.71826	−	1.81995i	0.0605985	−	0.0641848i
$805$			60.6741i			2.13848i
$806$	−19.2458	+	43.2805i	−0.677906	+	1.52449i
$807$		−	0.617529i		−	0.0217381i
$808$	6.68574	+	14.3576i	0.235203	+	0.505099i
$809$			29.6902i			1.04385i	0.852991	+	0.521926i	$0.174786\pi$
$809$			29.6902i			1.04385i	−0.852991	+	0.521926i	$0.825214\pi$
$810$	−4.48711	−	1.78354i	−0.157661	−	0.0626672i
$811$			31.6577i			1.11165i	0.831298	+	0.555827i	$0.187598\pi$
$811$			31.6577i			1.11165i	−0.831298	+	0.555827i	$0.812402\pi$
$812$	9.90274	+	9.34942i	0.347518	+	0.328100i
$813$	8.88861			0.311737
$814$	−0.741149	+	1.86462i	−0.0259773	+	0.0653547i
$815$			82.7133i			2.89732i
$816$	−26.2273	+	1.50883i	−0.918140	+	0.0528197i
$817$		−	1.39374i		−	0.0487610i
$818$	−11.4812	+	28.8850i	−0.401432	+	1.00994i
$819$	−15.4860			−0.541126
$820$	25.0218	+	23.6237i	0.873800	+	0.824976i
$821$		−	29.9748i		−	1.04613i	−0.852294	−	0.523064i	$-0.824789\pi$
$821$		−	29.9748i		−	1.04613i	0.852294	−	0.523064i	$-0.175211\pi$
$822$	−9.81575	+	24.6949i	−0.342364	+	0.861334i
$823$	−25.2645			−0.880666			−0.440333	−	0.897835i	$-0.645140\pi$
$823$	−25.2645			−0.880666			−0.440333	+	0.897835i	$0.645140\pi$
$824$	23.2089	−	10.8074i	0.808522	−	0.376494i
$825$	−4.11606			−0.143303
$826$	−44.4660	−	17.6744i	−1.54717	−	0.614970i
$827$	10.1261			0.352117			0.176059	−	0.984380i	$-0.443665\pi$
$827$	10.1261			0.352117			0.176059	+	0.984380i	$0.443665\pi$
$828$	−10.0387	−	9.47779i	−0.348869	−	0.329376i
$829$		−	56.0399i		−	1.94635i	−0.230073	−	0.973173i	$-0.573896\pi$
$829$		−	56.0399i		−	1.94635i	0.230073	−	0.973173i	$-0.426104\pi$
$830$	−53.2130	−	21.1512i	−1.84705	−	0.734167i
$831$			27.3650i			0.949282i
$832$	36.8326	+	30.9733i	1.27694	+	1.07381i
$833$			2.44885i			0.0848475i
$834$	3.79879	+	1.50995i	0.131541	+	0.0522852i
$835$	12.1122			0.419160
$836$	0.139764	−	0.148035i	0.00483384	−	0.00511991i
$837$	5.56329	+	0.223126i	0.192295	+	0.00771237i
$838$	−12.8105	+	32.2293i	−0.442532	+	1.11334i
$839$			0.194352i			0.00670976i	0.999994	+	0.00335488i	$0.00106789\pi$
$839$			0.194352i			0.00670976i	−0.999994	+	0.00335488i	$0.998932\pi$
$840$	−22.5370	+	10.4945i	−0.777600	+	0.362096i
$841$	22.0032			0.758730
$842$	−53.3256	−	21.1959i	−1.83772	−	0.730458i
$843$	−12.1221			−0.417508
$844$	6.57647	−	6.96568i	0.226372	−	0.239769i
$845$	−79.1686			−2.72348
$846$	−4.38902	+	11.0421i	−0.150898	+	0.379635i
$847$			27.3336i			0.939192i
$848$	−19.4477	+	1.11880i	−0.667836	+	0.0384199i
$849$			10.1449i			0.348173i
$850$	22.8406	−	57.4633i	0.783425	−	1.97098i
$851$		−	15.8416i		−	0.543042i
$852$	−18.9325	+	20.0530i	−0.648618	+	0.687004i
$853$	−41.3309			−1.41514			−0.707571	−	0.706643i	$-0.750209\pi$
$853$	−41.3309			−1.41514			−0.707571	+	0.706643i	$0.750209\pi$
$854$	21.2413	+	8.44301i	0.726863	+	0.288914i
$855$			0.562165i			0.0192256i
$856$	−14.2607	+	6.64061i	−0.487421	+	0.226971i
$857$	−55.3475			−1.89063			−0.945317	−	0.326154i	$-0.894247\pi$
$857$	−55.3475			−1.89063			−0.945317	+	0.326154i	$0.894247\pi$
$858$	1.94277	−	4.88770i	0.0663249	−	0.166863i
$859$	−24.7767			−0.845371			−0.422686	−	0.906276i	$-0.638913\pi$
$859$	−24.7767			−0.845371			−0.422686	+	0.906276i	$0.638913\pi$
$860$	−42.0310	−	39.6825i	−1.43324	−	1.35316i
$861$		−	12.9729i		−	0.442114i
$862$	−4.60532	+	11.5863i	−0.156858	+	0.394630i
$863$	−7.70341			−0.262227			−0.131114	−	0.991367i	$-0.541855\pi$
$863$	−7.70341			−0.262227			−0.131114	+	0.991367i	$0.541855\pi$
$864$	1.78411	−	5.36814i	0.0606967	−	0.182628i
$865$	4.48724			0.152571
$866$	−8.43974	+	21.2331i	−0.286794	+	0.721530i
$867$	−26.1343			−0.887569
$868$	20.4990	−	20.0388i	0.695783	−	0.680162i
$869$	−1.38363			−0.0469364
$870$	4.71774	−	11.8691i	0.159946	−	0.402400i
$871$	−7.52829			−0.255086
$872$	1.49328	+	3.20682i	0.0505688	+	0.108596i
$873$	−9.71032			−0.328645
$874$	−0.593710	+	1.49368i	−0.0200825	+	0.0505245i
$875$		−	14.5694i		−	0.492537i
$876$	−7.16023	+	7.58399i	−0.241922	+	0.256239i
$877$	4.97712			0.168065			0.0840327	−	0.996463i	$-0.473220\pi$
$877$	4.97712			0.168065			0.0840327	+	0.996463i	$0.473220\pi$
$878$	5.10339	−	12.8393i	0.172231	−	0.433307i
$879$	10.5694			0.356498
$880$	−0.484951	−	8.42969i	−0.0163477	−	0.284165i
$881$		−	5.23018i		−	0.176209i	−0.996111	−	0.0881046i	$-0.971919\pi$
$881$		−	5.23018i		−	0.176209i	0.996111	−	0.0881046i	$-0.0280810\pi$
$882$	−0.490019	−	0.194773i	−0.0164998	−	0.00655835i
$883$	−6.44779			−0.216985			−0.108493	−	0.994097i	$-0.534602\pi$
$883$	−6.44779			−0.216985			−0.108493	+	0.994097i	$0.534602\pi$
$884$	57.4554	+	54.2450i	1.93243	+	1.82446i
$885$			44.8753i			1.50847i
$886$	−8.20285	+	20.6371i	−0.275580	+	0.693317i
$887$			3.68993i			0.123896i	0.998079	+	0.0619478i	$0.0197312\pi$
$887$			3.68993i			0.123896i	−0.998079	+	0.0619478i	$0.980269\pi$
$888$	5.88425	−	2.74005i	0.197463	−	0.0919499i
$889$		−	28.6990i		−	0.962534i
$890$	7.97356	−	20.0602i	0.267274	−	0.672421i
$891$	−0.618251			−0.0207122
$892$	−2.23990	−	2.11475i	−0.0749976	−	0.0708070i
$893$	1.38340			0.0462938
$894$	14.6270	+	5.81395i	0.489200	+	0.194447i
$895$	−40.0945			−1.34021
$896$	−13.7908	−	25.6532i	−0.460720	−	0.857013i
$897$			41.5254i			1.38649i
$898$	−2.32146	+	5.84044i	−0.0774681	+	0.194898i
$899$	−0.590203	+	14.7158i	−0.0196844	+	0.490798i
$900$	9.68185	+	9.14087i	0.322728	+	0.304696i
$901$	−31.9843			−1.06555
$902$	4.09449	+	1.62748i	0.136332	+	0.0541892i
$903$			21.7915i			0.725175i
$904$	19.2387	+	41.3152i	0.639871	+	1.37412i
$905$		−	31.8918i		−	1.06012i
$906$	19.4455	+	7.72920i	0.646033	+	0.256786i
$907$			13.5441i			0.449723i	0.974391	+	0.224862i	$0.0721930\pi$
$907$			13.5441i			0.449723i	−0.974391	+	0.224862i	$0.927807\pi$
$908$	9.53483	−	10.0991i	0.316424	−	0.335151i
$909$	−5.59956			−0.185726
$910$	69.4876	+	27.6200i	2.30349	+	0.915593i
$911$	50.9840			1.68917			0.844587	−	0.535418i	$-0.179846\pi$
$911$	50.9840			1.68917			0.844587	+	0.535418i	$0.179846\pi$
$912$	−0.657510	+	0.0378259i	−0.0217723	+	0.00125254i
$913$	−7.33189			−0.242650
$914$	−13.9987	+	35.2186i	−0.463036	+	1.16493i
$915$		−	21.4368i		−	0.708679i
$916$	37.1536	−	39.3525i	1.22759	−	1.30024i
$917$	−23.6907			−0.782334
$918$	3.43076	−	8.63126i	0.113232	−	0.284874i
$919$		−	33.8651i		−	1.11711i	−0.829468	−	0.558554i	$-0.811357\pi$
$919$		−	33.8651i		−	1.11711i	0.829468	−	0.558554i	$-0.188643\pi$
$920$	28.1408	+	60.4323i	0.927774	+	1.99239i
$921$		−	13.1387i		−	0.432935i
$922$	−9.91105	+	24.9347i	−0.326403	+	0.821180i
$923$	82.9498			2.73033
$924$	−2.18524	+	2.31456i	−0.0718890	+	0.0761436i
$925$			15.2784i			0.502352i
$926$	36.7880	+	14.6225i	1.20893	+	0.480526i
$927$			9.05162i			0.297294i
$928$	14.1996	+	4.71925i	0.466123	+	0.154917i
$929$		−	4.01905i		−	0.131861i	−0.997824	−	0.0659303i	$-0.978998\pi$
$929$		−	4.01905i		−	0.131861i	0.997824	−	0.0659303i	$-0.0210015\pi$
$930$	−24.5651	−	10.9235i	−0.805523	−	0.358197i
$931$			0.0613917i			0.00201203i
$932$	−28.0963	−	26.5264i	−0.920325	−	0.868901i
$933$		−	18.1154i		−	0.593071i
$934$	0.938519	−	2.36117i	0.0307093	−	0.0772598i
$935$		−	13.8637i		−	0.453393i
$936$	−15.4243	+	7.18246i	−0.504160	+	0.234766i
$937$	−3.30441			−0.107950			−0.0539752	−	0.998542i	$-0.517189\pi$
$937$	−3.30441			−0.107950			−0.0539752	+	0.998542i	$0.517189\pi$
$938$	4.23393	+	1.68291i	0.138243	+	0.0549489i
$939$			2.34613i			0.0765632i
$940$	39.3880	−	41.7191i	1.28470	−	1.36073i
$941$			25.7782i			0.840347i	0.907444	+	0.420173i	$0.138031\pi$
$941$			25.7782i			0.840347i	−0.907444	+	0.420173i	$0.861969\pi$
$942$	−22.2317	−	8.83669i	−0.724350	−	0.287915i
$943$	−34.7864			−1.13280
$944$	−52.4862	+	3.01948i	−1.70828	+	0.0982756i
$945$		−	8.78956i		−	0.285924i
$946$	−6.87782	−	2.73380i	−0.223617	−	0.0888835i
$947$	1.14281			0.0371364			0.0185682	−	0.999828i	$-0.494089\pi$
$947$	1.14281			0.0371364			0.0185682	+	0.999828i	$0.494089\pi$
$948$	3.25459	+	3.07274i	0.105704	+	0.0997980i
$949$	31.3714			1.01836
$950$	0.572604	−	1.44058i	0.0185777	−	0.0467387i
$951$	17.7785			0.576508
$952$	−20.1869	−	43.3514i	−0.654262	−	1.40503i
$953$		−	1.88706i		−	0.0611279i	−0.999533	−	0.0305639i	$-0.990270\pi$
$953$		−	1.88706i		−	0.0611279i	0.999533	−	0.0305639i	$-0.00973031\pi$
$954$	2.54392	−	6.40011i	0.0823625	−	0.207211i
$955$			9.42830i			0.305093i
$956$	−36.9349	−	34.8711i	−1.19456	−	1.12781i
$957$		−	1.63537i		−	0.0528639i
$958$	−17.2588	+	43.4206i	−0.557608	+	1.40286i
$959$	−48.3736			−1.56206
$960$	−17.5798	+	20.9054i	−0.567386	+	0.674719i
$961$	30.9004	+	2.48263i	0.996788	+	0.0800849i
$962$	−18.1427	−	7.21138i	−0.584945	−	0.232504i
$963$		−	5.56176i		−	0.179225i
$964$	−16.3213	+	17.2872i	−0.525674	+	0.556784i
$965$	3.71108			0.119464
$966$	9.28277	−	23.3540i	0.298668	−	0.751403i
$967$	−19.2488			−0.619000			−0.309500	−	0.950899i	$-0.600162\pi$
$967$	−19.2488			−0.619000			−0.309500	+	0.950899i	$0.600162\pi$
$968$	12.6774	+	27.2246i	0.407466	+	0.875033i
$969$	−1.08136			−0.0347384
$970$	43.5713	+	17.3187i	1.39899	+	0.556071i
$971$		−	21.4054i		−	0.686932i	−0.939165	−	0.343466i	$-0.888399\pi$
$971$		−	21.4054i		−	0.686932i	0.939165	−	0.343466i	$-0.111601\pi$
$972$	1.45426	+	1.37300i	0.0466454	+	0.0440390i
$973$			7.44125i			0.238556i
$974$	15.7098	+	6.24435i	0.503375	+	0.200082i
$975$		−	40.0492i		−	1.28260i
$976$	25.0726	−	1.44240i	0.802553	−	0.0461700i
$977$	40.6587			1.30079			0.650393	−	0.759598i	$-0.274604\pi$
$977$	40.6587			1.30079			0.650393	+	0.759598i	$0.274604\pi$
$978$	12.6546	−	31.8371i	0.404651	−	1.01804i
$979$		−	2.76397i		−	0.0883370i
$980$	1.85138	+	1.74794i	0.0591402	+	0.0558358i
$981$	−1.25068			−0.0399311
$982$	10.3439	+	4.11151i	0.330088	+	0.131204i
$983$	37.7512			1.20408			0.602039	−	0.798467i	$-0.294355\pi$
$983$	37.7512			1.20408			0.602039	+	0.798467i	$0.294355\pi$
$984$	−6.01684	−	12.9212i	−0.191810	−	0.411912i
$985$		−	50.2970i		−	1.60260i
$986$	22.8310	+	9.07488i	0.727087	+	0.289003i
$987$	−21.6298			−0.688483
$988$	1.44039	+	1.35990i	0.0458248	+	0.0432643i
$989$	58.4332			1.85807
$990$	2.77416	+	1.10267i	0.0881685	+	0.0350453i
$991$	−48.6397			−1.54509			−0.772546	−	0.634959i	$-0.781017\pi$
$991$	−48.6397			−1.54509			−0.772546	+	0.634959i	$0.781017\pi$
$992$	11.1233	−	29.4665i	0.353165	−	0.935561i
$993$	−2.70580			−0.0858660
$994$	−46.6512	−	18.5430i	−1.47969	−	0.588147i
$995$	54.3452			1.72286
$996$	17.2462	+	16.2825i	0.546466	+	0.515932i
$997$	−9.44897			−0.299252			−0.149626	−	0.988743i	$-0.547807\pi$
$997$	−9.44897			−0.299252			−0.149626	+	0.988743i	$0.547807\pi$
$998$	−56.3876	−	22.4130i	−1.78492	−	0.709471i
$999$			2.29489i			0.0726072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.g.b.247.3	yes	16
3.2	odd	2		1116.2.g.i.991.14		16
4.3	odd	2		372.2.g.a.247.4	yes	16
12.11	even	2		1116.2.g.j.991.13		16
31.30	odd	2		372.2.g.a.247.3	✓	16
93.92	even	2		1116.2.g.j.991.14		16
124.123	even	2	inner	372.2.g.b.247.4	yes	16
372.371	odd	2		1116.2.g.i.991.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.g.a.247.3	✓	16	31.30	odd	2
372.2.g.a.247.4	yes	16	4.3	odd	2
372.2.g.b.247.3	yes	16	1.1	even	1	trivial
372.2.g.b.247.4	yes	16	124.123	even	2	inner
1116.2.g.i.991.13		16	372.371	odd	2
1116.2.g.i.991.14		16	3.2	odd	2
1116.2.g.j.991.13		16	12.11	even	2
1116.2.g.j.991.14		16	93.92	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31420 - 0.522370i) q^{2} +1.00000 q^{3} +(1.45426 + 1.37300i) q^{4} +3.41432 q^{5} +(-1.31420 - 0.522370i) q^{6} -2.57432i q^{7} +(-1.19398 - 2.56406i) q^{8} +1.00000 q^{9} +(-4.48711 - 1.78354i) q^{10} -0.618251 q^{11} +(1.45426 + 1.37300i) q^{12} -6.01558i q^{13} +(-1.34475 + 3.38318i) q^{14} +3.41432 q^{15} +(0.229736 + 3.99340i) q^{16} +6.56767i q^{17} +(-1.31420 - 0.522370i) q^{18} +0.164649i q^{19} +(4.96530 + 4.68787i) q^{20} -2.57432i q^{21} +(0.812507 + 0.322956i) q^{22} -6.90297 q^{23} +(-1.19398 - 2.56406i) q^{24} +6.65758 q^{25} +(-3.14236 + 7.90569i) q^{26} +1.00000 q^{27} +(3.53455 - 3.74373i) q^{28} +2.64515i q^{29} +(-4.48711 - 1.78354i) q^{30} +(5.56329 + 0.223126i) q^{31} +(1.78411 - 5.36814i) q^{32} -0.618251 q^{33} +(3.43076 - 8.63126i) q^{34} -8.78956i q^{35} +(1.45426 + 1.37300i) q^{36} +2.29489i q^{37} +(0.0860078 - 0.216382i) q^{38} -6.01558i q^{39} +(-4.07662 - 8.75453i) q^{40} +5.03933 q^{41} +(-1.34475 + 3.38318i) q^{42} -8.46494 q^{43} +(-0.899096 - 0.848859i) q^{44} +3.41432 q^{45} +(9.07191 + 3.60591i) q^{46} -8.40212i q^{47} +(0.229736 + 3.99340i) q^{48} +0.372864 q^{49} +(-8.74942 - 3.47772i) q^{50} +6.56767i q^{51} +(8.25940 - 8.74821i) q^{52} +4.86996i q^{53} +(-1.31420 - 0.522370i) q^{54} -2.11091 q^{55} +(-6.60073 + 3.07368i) q^{56} +0.164649i q^{57} +(1.38175 - 3.47627i) q^{58} +13.1432i q^{59} +(4.96530 + 4.68787i) q^{60} -6.27850i q^{61} +(-7.19474 - 3.19933i) q^{62} -2.57432i q^{63} +(-5.14884 + 6.12286i) q^{64} -20.5391i q^{65} +(0.812507 + 0.322956i) q^{66} -1.25147i q^{67} +(-9.01742 + 9.55110i) q^{68} -6.90297 q^{69} +(-4.59141 + 11.5513i) q^{70} +13.7892i q^{71} +(-1.19398 - 2.56406i) q^{72} +5.21502i q^{73} +(1.19878 - 3.01595i) q^{74} +6.65758 q^{75} +(-0.226064 + 0.239442i) q^{76} +1.59158i q^{77} +(-3.14236 + 7.90569i) q^{78} +2.23797 q^{79} +(0.784392 + 13.6347i) q^{80} +1.00000 q^{81} +(-6.62271 - 2.63240i) q^{82} +11.8591 q^{83} +(3.53455 - 3.74373i) q^{84} +22.4241i q^{85} +(11.1246 + 4.42183i) q^{86} +2.64515i q^{87} +(0.738176 + 1.58523i) q^{88} +4.47064i q^{89} +(-4.48711 - 1.78354i) q^{90} -15.4860 q^{91} +(-10.0387 - 9.47779i) q^{92} +(5.56329 + 0.223126i) q^{93} +(-4.38902 + 11.0421i) q^{94} +0.562165i q^{95} +(1.78411 - 5.36814i) q^{96} -9.71032 q^{97} +(-0.490019 - 0.194773i) q^{98} -0.618251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 2 q^{4} + 3 q^{8} + 16 q^{9} - 5 q^{10} + 4 q^{11} + 2 q^{12} + 5 q^{14} + 10 q^{16} - q^{20} - 16 q^{23} + 3 q^{24} + 12 q^{25} - 10 q^{26} + 16 q^{27} + 3 q^{28} - 5 q^{30} - 6 q^{31}+ \cdots + 4 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 2 * q^4 + 3 * q^8 + 16 * q^9 - 5 * q^10 + 4 * q^11 + 2 * q^12 + 5 * q^14 + 10 * q^16 - q^20 - 16 * q^23 + 3 * q^24 + 12 * q^25 - 10 * q^26 + 16 * q^27 + 3 * q^28 - 5 * q^30 - 6 * q^31 - 20 * q^32 + 4 * q^33 + 28 * q^34 + 2 * q^36 + q^38 - 26 * q^40 + 5 * q^42 - 20 * q^43 - 14 * q^44 - 4 * q^46 + 10 * q^48 - 8 * q^49 - 11 * q^50 - 4 * q^52 + 8 * q^55 - 40 * q^56 + 36 * q^58 - q^60 - 26 * q^62 - 7 * q^64 - 6 * q^68 - 16 * q^69 + 9 * q^70 + 3 * q^72 - 52 * q^74 + 12 * q^75 - 3 * q^76 - 10 * q^78 - 12 * q^79 - 13 * q^80 + 16 * q^81 - 11 * q^82 - 28 * q^83 + 3 * q^84 + 8 * q^86 - 16 * q^88 - 5 * q^90 + 16 * q^91 - 6 * q^93 + 26 * q^94 - 20 * q^96 - 40 * q^97 - 15 * q^98 + 4 * q^99

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