LMFDB - Embedded newform 552.2.f.d.277.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 2x^17 + x^16 - 4x^15 + 16x^14 - 24x^13 + 32x^12 - 16x^11 - 16x^10 - 32x^9 + 128x^8 - 192x^7 + 256x^6 - 128x^5 + 64x^4 - 256x^3 + 512x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.6
Root			$1.19161 - 0.761625i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.d.277.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19161 + 0.761625i) q^{2} -1.00000i q^{3} +(0.839855 - 1.81512i) q^{4} -1.20415i q^{5} +(0.761625 + 1.19161i) q^{6} +3.87524 q^{7} +(0.381661 + 2.80256i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.19161 + 0.761625i) q^{2} -1.00000i q^{3} +(0.839855 - 1.81512i) q^{4} -1.20415i q^{5} +(0.761625 + 1.19161i) q^{6} +3.87524 q^{7} +(0.381661 + 2.80256i) q^{8} -1.00000 q^{9} +(0.917114 + 1.43488i) q^{10} +6.13102i q^{11} +(-1.81512 - 0.839855i) q^{12} +3.14654i q^{13} +(-4.61777 + 2.95148i) q^{14} -1.20415 q^{15} +(-2.58929 - 3.04887i) q^{16} +3.86545 q^{17} +(1.19161 - 0.761625i) q^{18} -4.21172i q^{19} +(-2.18568 - 1.01132i) q^{20} -3.87524i q^{21} +(-4.66954 - 7.30577i) q^{22} +1.00000 q^{23} +(2.80256 - 0.381661i) q^{24} +3.55001 q^{25} +(-2.39648 - 3.74943i) q^{26} +1.00000i q^{27} +(3.25464 - 7.03401i) q^{28} -1.40348i q^{29} +(1.43488 - 0.917114i) q^{30} +4.44998 q^{31} +(5.40751 + 1.66098i) q^{32} +6.13102 q^{33} +(-4.60610 + 2.94402i) q^{34} -4.66639i q^{35} +(-0.839855 + 1.81512i) q^{36} +5.19569i q^{37} +(3.20775 + 5.01872i) q^{38} +3.14654 q^{39} +(3.37471 - 0.459578i) q^{40} -8.51623 q^{41} +(2.95148 + 4.61777i) q^{42} -8.39142i q^{43} +(11.1285 + 5.14917i) q^{44} +1.20415i q^{45} +(-1.19161 + 0.761625i) q^{46} -0.0559777 q^{47} +(-3.04887 + 2.58929i) q^{48} +8.01751 q^{49} +(-4.23022 + 2.70378i) q^{50} -3.86545i q^{51} +(5.71132 + 2.64263i) q^{52} +0.837384i q^{53} +(-0.761625 - 1.19161i) q^{54} +7.38270 q^{55} +(1.47903 + 10.8606i) q^{56} -4.21172 q^{57} +(1.06892 + 1.67239i) q^{58} -9.89772i q^{59} +(-1.01132 + 2.18568i) q^{60} +8.37304i q^{61} +(-5.30262 + 3.38921i) q^{62} -3.87524 q^{63} +(-7.70867 + 2.13925i) q^{64} +3.78892 q^{65} +(-7.30577 + 4.66954i) q^{66} -9.25869i q^{67} +(3.24642 - 7.01624i) q^{68} -1.00000i q^{69} +(3.55404 + 5.56051i) q^{70} +4.54537 q^{71} +(-0.381661 - 2.80256i) q^{72} -11.6784 q^{73} +(-3.95717 - 6.19122i) q^{74} -3.55001i q^{75} +(-7.64476 - 3.53723i) q^{76} +23.7592i q^{77} +(-3.74943 + 2.39648i) q^{78} +9.67513 q^{79} +(-3.67131 + 3.11790i) q^{80} +1.00000 q^{81} +(10.1480 - 6.48617i) q^{82} +6.17911i q^{83} +(-7.03401 - 3.25464i) q^{84} -4.65460i q^{85} +(6.39112 + 9.99928i) q^{86} -1.40348 q^{87} +(-17.1826 + 2.33997i) q^{88} +9.45216 q^{89} +(-0.917114 - 1.43488i) q^{90} +12.1936i q^{91} +(0.839855 - 1.81512i) q^{92} -4.44998i q^{93} +(0.0667035 - 0.0426341i) q^{94} -5.07157 q^{95} +(1.66098 - 5.40751i) q^{96} +9.73827 q^{97} +(-9.55373 + 6.10634i) q^{98} -6.13102i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−1.19161	+	0.761625i	−0.842593	+	0.538550i
$2$	−1.19161	+	0.761625i	−0.842593	+	0.538550i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.839855	−	1.81512i	0.419927	−	0.907558i
$5$		−	1.20415i		−	0.538514i	−0.963068	−	0.269257i	$-0.913222\pi$
$5$		−	1.20415i		−	0.538514i	0.963068	−	0.269257i	$-0.0867782\pi$
$6$	0.761625	+	1.19161i	0.310932	+	0.486472i
$7$	3.87524			1.46470			0.732352	−	0.680926i	$-0.238422\pi$
$7$	3.87524			1.46470			0.732352	+	0.680926i	$0.238422\pi$
$8$	0.381661	+	2.80256i	0.134937	+	0.990854i
$9$	−1.00000			−0.333333
$10$	0.917114	+	1.43488i	0.290017	+	0.453749i
$11$			6.13102i			1.84857i	0.381699	+	0.924287i	$0.375339\pi$
$11$			6.13102i			1.84857i	−0.381699	+	0.924287i	$0.624661\pi$
$12$	−1.81512	−	0.839855i	−0.523979	−	0.242445i
$13$			3.14654i			0.872692i	0.899779	+	0.436346i	$0.143728\pi$
$13$			3.14654i			0.872692i	−0.899779	+	0.436346i	$0.856272\pi$
$14$	−4.61777	+	2.95148i	−1.23415	+	0.788817i
$15$	−1.20415			−0.310911
$16$	−2.58929	−	3.04887i	−0.647322	−	0.762217i
$17$	3.86545			0.937509			0.468755	−	0.883328i	$-0.344703\pi$
$17$	3.86545			0.937509			0.468755	+	0.883328i	$0.344703\pi$
$18$	1.19161	−	0.761625i	0.280864	−	0.179517i
$19$		−	4.21172i		−	0.966235i	−0.875555	−	0.483118i	$-0.839504\pi$
$19$		−	4.21172i		−	0.966235i	0.875555	−	0.483118i	$-0.160496\pi$
$20$	−2.18568	−	1.01132i	−0.488733	−	0.226137i
$21$		−	3.87524i		−	0.845647i
$22$	−4.66954	−	7.30577i	−0.995549	−	1.55760i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	2.80256	−	0.381661i	0.572070	−	0.0779061i
$25$	3.55001			0.710002
$26$	−2.39648	−	3.74943i	−0.469988	−	0.735324i
$27$			1.00000i			0.192450i
$28$	3.25464	−	7.03401i	0.615069	−	1.32930i
$29$		−	1.40348i		−	0.260619i	−0.991473	−	0.130309i	$-0.958403\pi$
$29$		−	1.40348i		−	0.260619i	0.991473	−	0.130309i	$-0.0415971\pi$
$30$	1.43488	−	0.917114i	0.261972	−	0.167441i
$31$	4.44998			0.799239			0.399620	−	0.916681i	$-0.369142\pi$
$31$	4.44998			0.799239			0.399620	+	0.916681i	$0.369142\pi$
$32$	5.40751	+	1.66098i	0.955921	+	0.293623i
$33$	6.13102			1.06727
$34$	−4.60610	+	2.94402i	−0.789939	+	0.504896i
$35$		−	4.66639i		−	0.788764i
$36$	−0.839855	+	1.81512i	−0.139976	+	0.302519i
$37$			5.19569i			0.854166i	0.904212	+	0.427083i	$0.140459\pi$
$37$			5.19569i			0.854166i	−0.904212	+	0.427083i	$0.859541\pi$
$38$	3.20775	+	5.01872i	0.520366	+	0.814144i
$39$	3.14654			0.503849
$40$	3.37471	−	0.459578i	0.533589	−	0.0726657i
$41$	−8.51623			−1.33001			−0.665006	−	0.746838i	$-0.731571\pi$
$41$	−8.51623			−1.33001			−0.665006	+	0.746838i	$0.731571\pi$
$42$	2.95148	+	4.61777i	0.455424	+	0.712537i
$43$		−	8.39142i		−	1.27968i	−0.768508	−	0.639840i	$-0.779001\pi$
$43$		−	8.39142i		−	1.27968i	0.768508	−	0.639840i	$-0.220999\pi$
$44$	11.1285	+	5.14917i	1.67769	+	0.776266i
$45$			1.20415i			0.179505i
$46$	−1.19161	+	0.761625i	−0.175693	+	0.112295i
$47$	−0.0559777			−0.00816519			−0.00408260	−	0.999992i	$-0.501300\pi$
$47$	−0.0559777			−0.00816519			−0.00408260	+	0.999992i	$0.501300\pi$
$48$	−3.04887	+	2.58929i	−0.440066	+	0.373732i
$49$	8.01751			1.14536
$50$	−4.23022	+	2.70378i	−0.598243	+	0.382372i
$51$		−	3.86545i		−	0.541271i
$52$	5.71132	+	2.64263i	0.792018	+	0.366467i
$53$			0.837384i			0.115024i	0.998345	+	0.0575118i	$0.0183167\pi$
$53$			0.837384i			0.115024i	−0.998345	+	0.0575118i	$0.981683\pi$
$54$	−0.761625	−	1.19161i	−0.103644	−	0.162157i
$55$	7.38270			0.995483
$56$	1.47903	+	10.8606i	0.197643	+	1.45131i
$57$	−4.21172			−0.557856
$58$	1.06892	+	1.67239i	0.140356	+	0.219596i
$59$		−	9.89772i		−	1.28857i	−0.764784	−	0.644286i	$-0.777154\pi$
$59$		−	9.89772i		−	1.28857i	0.764784	−	0.644286i	$-0.222846\pi$
$60$	−1.01132	+	2.18568i	−0.130560	+	0.282170i
$61$			8.37304i			1.07206i	0.844200	+	0.536029i	$0.180076\pi$
$61$			8.37304i			1.07206i	−0.844200	+	0.536029i	$0.819924\pi$
$62$	−5.30262	+	3.38921i	−0.673434	+	0.430431i
$63$	−3.87524			−0.488235
$64$	−7.70867	+	2.13925i	−0.963584	+	0.267407i
$65$	3.78892			0.469957
$66$	−7.30577	+	4.66954i	−0.899278	+	0.574781i
$67$		−	9.25869i		−	1.13113i	−0.824704	−	0.565565i	$-0.808658\pi$
$67$		−	9.25869i		−	1.13113i	0.824704	−	0.565565i	$-0.191342\pi$
$68$	3.24642	−	7.01624i	0.393686	−	0.850844i
$69$		−	1.00000i		−	0.120386i
$70$	3.55404	+	5.56051i	0.424789	+	0.664608i
$71$	4.54537			0.539436			0.269718	−	0.962939i	$-0.413070\pi$
$71$	4.54537			0.539436			0.269718	+	0.962939i	$0.413070\pi$
$72$	−0.381661	−	2.80256i	−0.0449791	−	0.330285i
$73$	−11.6784			−1.36685			−0.683425	−	0.730020i	$-0.739511\pi$
$73$	−11.6784			−1.36685			−0.683425	+	0.730020i	$0.739511\pi$
$74$	−3.95717	−	6.19122i	−0.460011	−	0.719715i
$75$		−	3.55001i		−	0.409920i
$76$	−7.64476	−	3.53723i	−0.876914	−	0.405749i
$77$			23.7592i			2.70761i
$78$	−3.74943	+	2.39648i	−0.424540	+	0.271348i
$79$	9.67513			1.08854			0.544269	−	0.838911i	$-0.316807\pi$
$79$	9.67513			1.08854			0.544269	+	0.838911i	$0.316807\pi$
$80$	−3.67131	+	3.11790i	−0.410465	+	0.348592i
$81$	1.00000			0.111111
$82$	10.1480	−	6.48617i	1.12066	−	0.716278i
$83$			6.17911i			0.678245i	0.940742	+	0.339123i	$0.110130\pi$
$83$			6.17911i			0.678245i	−0.940742	+	0.339123i	$0.889870\pi$
$84$	−7.03401	−	3.25464i	−0.767474	−	0.355111i
$85$		−	4.65460i		−	0.504862i
$86$	6.39112	+	9.99928i	0.689172	+	1.07825i
$87$	−1.40348			−0.150468
$88$	−17.1826	+	2.33997i	−1.83167	+	0.249442i
$89$	9.45216			1.00193			0.500963	−	0.865469i	$-0.332979\pi$
$89$	9.45216			1.00193			0.500963	+	0.865469i	$0.332979\pi$
$90$	−0.917114	−	1.43488i	−0.0966723	−	0.151250i
$91$			12.1936i			1.27824i
$92$	0.839855	−	1.81512i	0.0875609	−	0.189239i
$93$		−	4.44998i		−	0.461441i
$94$	0.0667035	−	0.0426341i	0.00687994	−	0.00439737i
$95$	−5.07157			−0.520332
$96$	1.66098	−	5.40751i	0.169523	−	0.551901i
$97$	9.73827			0.988772			0.494386	−	0.869243i	$-0.335393\pi$
$97$	9.73827			0.988772			0.494386	+	0.869243i	$0.335393\pi$
$98$	−9.55373	+	6.10634i	−0.965072	+	0.616833i
$99$		−	6.13102i		−	0.616191i
$100$	2.98149	−	6.44368i	0.298149	−	0.644368i
$101$			7.18966i			0.715398i	0.933837	+	0.357699i	$0.116439\pi$
$101$			7.18966i			0.715398i	−0.933837	+	0.357699i	$0.883561\pi$
$102$	2.94402	+	4.60610i	0.291502	+	0.456072i
$103$	3.87162			0.381482			0.190741	−	0.981640i	$-0.438911\pi$
$103$	3.87162			0.381482			0.190741	+	0.981640i	$0.438911\pi$
$104$	−8.81835	+	1.20091i	−0.864710	+	0.117759i
$105$	−4.66639			−0.455393
$106$	−0.637773	−	0.997833i	−0.0619460	−	0.0969181i
$107$		−	16.9417i		−	1.63781i	−0.573926	−	0.818907i	$-0.694580\pi$
$107$		−	16.9417i		−	1.63781i	0.573926	−	0.818907i	$-0.305420\pi$
$108$	1.81512	+	0.839855i	0.174660	+	0.0808151i
$109$		−	3.11251i		−	0.298125i	−0.988828	−	0.149062i	$-0.952374\pi$
$109$		−	3.11251i		−	0.298125i	0.988828	−	0.149062i	$-0.0476255\pi$
$110$	−8.79728	+	5.62285i	−0.838788	+	0.536118i
$111$	5.19569			0.493153
$112$	−10.0341	−	11.8151i	−0.948135	−	1.11642i
$113$	−16.6444			−1.56577			−0.782887	−	0.622165i	$-0.786253\pi$
$113$	−16.6444			−1.56577			−0.782887	+	0.622165i	$0.786253\pi$
$114$	5.01872	−	3.20775i	0.470046	−	0.300434i
$115$		−	1.20415i		−	0.112288i
$116$	−2.54747	−	1.17872i	−0.236527	−	0.109441i
$117$		−	3.14654i		−	0.290897i
$118$	7.53835	+	11.7942i	0.693961	+	1.08574i
$119$	14.9796			1.37317
$120$	−0.459578	−	3.37471i	−0.0419536	−	0.308068i
$121$	−26.5894			−2.41722
$122$	−6.37711	−	9.97737i	−0.577357	−	0.903309i
$123$			8.51623i			0.767883i
$124$	3.73733	−	8.07722i	0.335622	−	0.725356i
$125$		−	10.2955i		−	0.920861i
$126$	4.61777	−	2.95148i	0.411383	−	0.262939i
$127$	−20.1152			−1.78493			−0.892466	−	0.451114i	$-0.851027\pi$
$127$	−20.1152			−1.78493			−0.892466	+	0.451114i	$0.851027\pi$
$128$	7.55640	−	8.42026i	0.667898	−	0.744253i
$129$	−8.39142			−0.738823
$130$	−4.51490	+	2.88573i	−0.395983	+	0.253095i
$131$		−	1.06175i		−	0.0927652i	−0.998924	−	0.0463826i	$-0.985231\pi$
$131$		−	1.06175i		−	0.0927652i	0.998924	−	0.0463826i	$-0.0147693\pi$
$132$	5.14917	−	11.1285i	0.448178	−	0.968613i
$133$		−	16.3215i		−	1.41525i
$134$	7.05165	+	11.0327i	0.609170	+	0.953082i
$135$	1.20415			0.103637
$136$	1.47529	+	10.8331i	0.126505	+	0.928935i
$137$	2.15811			0.184380			0.0921898	−	0.995741i	$-0.470613\pi$
$137$	2.15811			0.184380			0.0921898	+	0.995741i	$0.470613\pi$
$138$	0.761625	+	1.19161i	0.0648338	+	0.101436i
$139$			14.0028i			1.18770i	0.804574	+	0.593852i	$0.202394\pi$
$139$			14.0028i			1.18770i	−0.804574	+	0.593852i	$0.797606\pi$
$140$	−8.47004	−	3.91909i	−0.715849	−	0.331224i
$141$			0.0559777i			0.00471418i
$142$	−5.41629	+	3.46187i	−0.454525	+	0.290513i
$143$	−19.2915			−1.61323
$144$	2.58929	+	3.04887i	0.215774	+	0.254072i
$145$	−1.69000			−0.140347
$146$	13.9160	−	8.89455i	1.15170	−	0.736118i
$147$		−	8.01751i		−	0.661273i
$148$	9.43078	+	4.36363i	0.775205	+	0.358688i
$149$		−	2.55210i		−	0.209076i	−0.994521	−	0.104538i	$-0.966664\pi$
$149$		−	2.55210i		−	0.209076i	0.994521	−	0.104538i	$-0.0333364\pi$
$150$	2.70378	+	4.23022i	0.220763	+	0.345396i
$151$	−5.48163			−0.446088			−0.223044	−	0.974808i	$-0.571599\pi$
$151$	−5.48163			−0.446088			−0.223044	+	0.974808i	$0.571599\pi$
$152$	11.8036	−	1.60745i	0.957398	−	0.130381i
$153$	−3.86545			−0.312503
$154$	−18.0956	−	28.3116i	−1.45819	−	2.28142i
$155$		−	5.35846i		−	0.430402i
$156$	2.64263	−	5.71132i	0.211580	−	0.457272i
$157$			5.04360i			0.402523i	0.979538	+	0.201262i	$0.0645042\pi$
$157$			5.04360i			0.402523i	−0.979538	+	0.201262i	$0.935496\pi$
$158$	−11.5290	+	7.36882i	−0.917194	+	0.586232i
$159$	0.837384			0.0664089
$160$	2.00008	−	6.51148i	0.158120	−	0.514777i
$161$	3.87524			0.305412
$162$	−1.19161	+	0.761625i	−0.0936215	+	0.0598389i
$163$			4.53576i			0.355268i	0.984097	+	0.177634i	$0.0568443\pi$
$163$			4.53576i			0.355268i	−0.984097	+	0.177634i	$0.943156\pi$
$164$	−7.15239	+	15.4579i	−0.558508	+	1.20706i
$165$		−	7.38270i		−	0.574742i
$166$	−4.70616	−	7.36307i	−0.365269	−	0.571485i
$167$	−19.2122			−1.48668			−0.743342	−	0.668911i	$-0.766761\pi$
$167$	−19.2122			−1.48668			−0.743342	+	0.668911i	$0.766761\pi$
$168$	10.8606	−	1.47903i	0.837913	−	0.114109i
$169$	3.09932			0.238409
$170$	3.54506	+	5.54645i	0.271894	+	0.425394i
$171$			4.21172i			0.322078i
$172$	−15.2314	−	7.04757i	−1.16138	−	0.537373i
$173$			15.7464i			1.19718i	0.801057	+	0.598589i	$0.204272\pi$
$173$			15.7464i			1.19718i	−0.801057	+	0.598589i	$0.795728\pi$
$174$	1.67239	−	1.06892i	0.126784	−	0.0810348i
$175$	13.7572			1.03994
$176$	18.6927	−	15.8750i	1.40901	−	1.19662i
$177$	−9.89772			−0.743958
$178$	−11.2633	+	7.19900i	−0.844217	+	0.539588i
$179$		−	7.33089i		−	0.547936i	−0.961739	−	0.273968i	$-0.911664\pi$
$179$		−	7.33089i		−	0.547936i	0.961739	−	0.273968i	$-0.0883363\pi$
$180$	2.18568	+	1.01132i	0.162911	+	0.0753790i
$181$			16.7273i			1.24333i	0.783283	+	0.621665i	$0.213544\pi$
$181$			16.7273i			1.24333i	−0.783283	+	0.621665i	$0.786456\pi$
$182$	−9.28694	−	14.5300i	−0.688394	−	1.07703i
$183$	8.37304			0.618953
$184$	0.381661	+	2.80256i	0.0281364	+	0.206607i
$185$	6.25642			0.459981
$186$	3.38921	+	5.30262i	0.248509	+	0.388807i
$187$			23.6992i			1.73305i
$188$	−0.0470132	+	0.101606i	−0.00342879	+	0.00741038i
$189$			3.87524i			0.281882i
$190$	6.04331	−	3.86263i	0.438428	−	0.280225i
$191$	−6.95847			−0.503497			−0.251749	−	0.967793i	$-0.581006\pi$
$191$	−6.95847			−0.503497			−0.251749	+	0.967793i	$0.581006\pi$
$192$	2.13925	+	7.70867i	0.154387	+	0.556325i
$193$	−21.6923			−1.56145			−0.780724	−	0.624876i	$-0.785149\pi$
$193$	−21.6923			−1.56145			−0.780724	+	0.624876i	$0.785149\pi$
$194$	−11.6042	+	7.41691i	−0.833133	+	0.532503i
$195$		−	3.78892i		−	0.271330i
$196$	6.73355	−	14.5527i	0.480968	−	1.03948i
$197$		−	10.3660i		−	0.738546i	−0.929321	−	0.369273i	$-0.879607\pi$
$197$		−	10.3660i		−	0.738546i	0.929321	−	0.369273i	$-0.120393\pi$
$198$	4.66954	+	7.30577i	0.331850	+	0.519199i
$199$	−20.3489			−1.44249			−0.721246	−	0.692679i	$-0.756430\pi$
$199$	−20.3489			−1.44249			−0.721246	+	0.692679i	$0.756430\pi$
$200$	1.35490	+	9.94912i	0.0958058	+	0.703509i
$201$	−9.25869			−0.653058
$202$	−5.47582	−	8.56725i	−0.385278	−	0.602789i
$203$		−	5.43881i		−	0.381730i
$204$	−7.01624	−	3.24642i	−0.491235	−	0.227295i
$205$			10.2549i			0.716230i
$206$	−4.61345	+	2.94872i	−0.321434	+	0.205447i
$207$	−1.00000			−0.0695048
$208$	9.59337	−	8.14729i	0.665180	−	0.564913i
$209$	25.8222			1.78616
$210$	5.56051	−	3.55404i	0.383711	−	0.245252i
$211$			6.56726i			0.452109i	0.974115	+	0.226055i	$0.0725828\pi$
$211$			6.56726i			0.452109i	−0.974115	+	0.226055i	$0.927417\pi$
$212$	1.51995	+	0.703281i	0.104391	+	0.0483015i
$213$		−	4.54537i		−	0.311443i
$214$	12.9032	+	20.1878i	0.882045	+	1.38001i
$215$	−10.1046			−0.689126
$216$	−2.80256	+	0.381661i	−0.190690	+	0.0259687i
$217$	17.2447			1.17065
$218$	2.37057	+	3.70889i	0.160555	+	0.251198i
$219$			11.6784i			0.789152i
$220$	6.20040	−	13.4005i	0.418031	−	0.903458i
$221$			12.1628i			0.818157i
$222$	−6.19122	+	3.95717i	−0.415528	+	0.265588i
$223$	27.0078			1.80858			0.904289	−	0.426921i	$-0.140402\pi$
$223$	27.0078			1.80858			0.904289	+	0.426921i	$0.140402\pi$
$224$	20.9554	+	6.43672i	1.40014	+	0.430071i
$225$	−3.55001			−0.236667
$226$	19.8336	−	12.6768i	1.31931	−	0.843247i
$227$		−	26.4526i		−	1.75572i	−0.478914	−	0.877862i	$-0.658970\pi$
$227$		−	26.4526i		−	1.75572i	0.478914	−	0.877862i	$-0.341030\pi$
$228$	−3.53723	+	7.64476i	−0.234259	+	0.506287i
$229$			19.8062i			1.30883i	0.756136	+	0.654415i	$0.227085\pi$
$229$			19.8062i			1.30883i	−0.756136	+	0.654415i	$0.772915\pi$
$230$	0.917114	+	1.43488i	0.0604727	+	0.0946131i
$231$	23.7592			1.56324
$232$	3.93332	−	0.535651i	0.258235	−	0.0351672i
$233$	5.80023			0.379986			0.189993	−	0.981785i	$-0.439153\pi$
$233$	5.80023			0.379986			0.189993	+	0.981785i	$0.439153\pi$
$234$	2.39648	+	3.74943i	0.156663	+	0.245108i
$235$			0.0674059i			0.00439707i
$236$	−17.9655	−	8.31264i	−1.16945	−	0.541107i
$237$		−	9.67513i		−	0.628467i
$238$	−17.8497	+	11.4088i	−1.15703	+	0.739523i
$239$	26.3096			1.70183			0.850914	−	0.525305i	$-0.176049\pi$
$239$	26.3096			1.70183			0.850914	+	0.525305i	$0.176049\pi$
$240$	3.11790	+	3.67131i	0.201260	+	0.236982i
$241$	−11.2269			−0.723191			−0.361595	−	0.932335i	$-0.617768\pi$
$241$	−11.2269			−0.723191			−0.361595	+	0.932335i	$0.617768\pi$
$242$	31.6842	−	20.2512i	2.03674	−	1.30180i
$243$		−	1.00000i		−	0.0641500i
$244$	15.1980	+	7.03213i	0.972954	+	0.450186i
$245$		−	9.65433i		−	0.616792i
$246$	−6.48617	−	10.1480i	−0.413543	−	0.647013i
$247$	13.2523			0.843226
$248$	1.69838	+	12.4713i	0.107847	+	0.791930i
$249$	6.17911			0.391585
$250$	7.84134	+	12.2682i	0.495930	+	0.775911i
$251$			6.50511i			0.410599i	0.978699	+	0.205300i	$0.0658169\pi$
$251$			6.50511i			0.410599i	−0.978699	+	0.205300i	$0.934183\pi$
$252$	−3.25464	+	7.03401i	−0.205023	+	0.443101i
$253$			6.13102i			0.385454i
$254$	23.9694	−	15.3202i	1.50397	−	0.961276i
$255$	−4.65460			−0.291482
$256$	−2.59117	+	15.7888i	−0.161948	+	0.986799i
$257$	−4.82215			−0.300797			−0.150399	−	0.988625i	$-0.548056\pi$
$257$	−4.82215			−0.300797			−0.150399	+	0.988625i	$0.548056\pi$
$258$	9.99928	−	6.39112i	0.622528	−	0.397894i
$259$			20.1346i			1.25110i
$260$	3.18214	−	6.87732i	0.197348	−	0.426513i
$261$			1.40348i			0.0868730i
$262$	0.808653	+	1.26518i	0.0499587	+	0.0781634i
$263$	−28.9590			−1.78569			−0.892845	−	0.450364i	$-0.851294\pi$
$263$	−28.9590			−1.78569			−0.892845	+	0.450364i	$0.851294\pi$
$264$	2.33997	+	17.1826i	0.144015	+	1.05751i
$265$	1.00834			0.0619418
$266$	12.4308	+	19.4488i	0.762183	+	1.19248i
$267$		−	9.45216i		−	0.578463i
$268$	−16.8056	−	7.77596i	−1.02657	−	0.474992i
$269$		−	15.8547i		−	0.966678i	−0.875433	−	0.483339i	$-0.839424\pi$
$269$		−	15.8547i		−	0.966678i	0.875433	−	0.483339i	$-0.160576\pi$
$270$	−1.43488	+	0.917114i	−0.0873240	+	0.0558138i
$271$	23.3998			1.42144			0.710719	−	0.703476i	$-0.248370\pi$
$271$	23.3998			1.42144			0.710719	+	0.703476i	$0.248370\pi$
$272$	−10.0088	−	11.7852i	−0.606870	−	0.714585i
$273$	12.1936			0.737990
$274$	−2.57162	+	1.64367i	−0.155357	+	0.0992977i
$275$			21.7652i			1.31249i
$276$	−1.81512	−	0.839855i	−0.109257	−	0.0505533i
$277$			7.31533i			0.439536i	0.975552	+	0.219768i	$0.0705300\pi$
$277$			7.31533i			0.439536i	−0.975552	+	0.219768i	$0.929470\pi$
$278$	−10.6649	−	16.6859i	−0.639638	−	1.00075i
$279$	−4.44998			−0.266413
$280$	13.0778	−	1.78098i	0.781550	−	0.106434i
$281$	−20.4449			−1.21964			−0.609821	−	0.792539i	$-0.708759\pi$
$281$	−20.4449			−1.21964			−0.609821	+	0.792539i	$0.708759\pi$
$282$	−0.0426341	−	0.0667035i	−0.00253882	−	0.00397213i
$283$			3.48290i			0.207037i	0.994628	+	0.103518i	$0.0330101\pi$
$283$			3.48290i			0.207037i	−0.994628	+	0.103518i	$0.966990\pi$
$284$	3.81745	−	8.25037i	0.226524	−	0.489569i
$285$			5.07157i			0.300414i
$286$	22.9879	−	14.6929i	1.35930	−	0.868808i
$287$	−33.0025			−1.94807
$288$	−5.40751	−	1.66098i	−0.318640	−	0.0978744i
$289$	−2.05830			−0.121077
$290$	2.01382	−	1.28715i	0.118256	−	0.0755839i
$291$		−	9.73827i		−	0.570868i
$292$	−9.80814	+	21.1976i	−0.573978	+	1.24050i
$293$			22.4995i			1.31443i	0.753702	+	0.657216i	$0.228266\pi$
$293$			22.4995i			1.31443i	−0.753702	+	0.657216i	$0.771734\pi$
$294$	6.10634	+	9.55373i	0.356129	+	0.557185i
$295$	−11.9184			−0.693915
$296$	−14.5612	+	1.98299i	−0.846354	+	0.115259i
$297$	−6.13102			−0.355758
$298$	1.94374	+	3.04110i	0.112598	+	0.176166i
$299$			3.14654i			0.181969i
$300$	−6.44368	−	2.98149i	−0.372026	−	0.172137i
$301$		−	32.5188i		−	1.87435i
$302$	6.53194	−	4.17494i	0.375871	−	0.240241i
$303$	7.18966			0.413035
$304$	−12.8410	+	10.9054i	−0.736481	+	0.625465i
$305$	10.0824			0.577318
$306$	4.60610	−	2.94402i	0.263313	−	0.168299i
$307$		−	9.66767i		−	0.551763i	−0.961192	−	0.275882i	$-0.911030\pi$
$307$		−	9.66767i		−	0.551763i	0.961192	−	0.275882i	$-0.0889697\pi$
$308$	43.1257	+	19.9543i	2.45732	+	1.13700i
$309$		−	3.87162i		−	0.220249i
$310$	4.08114	+	6.38518i	0.231793	+	0.362654i
$311$	12.6510			0.717370			0.358685	−	0.933459i	$-0.383225\pi$
$311$	12.6510			0.717370			0.358685	+	0.933459i	$0.383225\pi$
$312$	1.20091	+	8.81835i	0.0679880	+	0.499241i
$313$	16.9933			0.960519			0.480260	−	0.877126i	$-0.340542\pi$
$313$	16.9933			0.960519			0.480260	+	0.877126i	$0.340542\pi$
$314$	−3.84133	−	6.00999i	−0.216779	−	0.339164i
$315$			4.66639i			0.262921i
$316$	8.12570	−	17.5615i	0.457106	−	0.987910i
$317$		−	30.1597i		−	1.69394i	−0.531644	−	0.846968i	$-0.678425\pi$
$317$		−	30.1597i		−	1.69394i	0.531644	−	0.846968i	$-0.321575\pi$
$318$	−0.997833	+	0.637773i	−0.0559557	+	0.0357645i
$319$	8.60475			0.481773
$320$	2.57599	+	9.28243i	0.144002	+	0.518904i
$321$	−16.9417			−0.945593
$322$	−4.61777	+	2.95148i	−0.257338	+	0.164480i
$323$		−	16.2802i		−	0.905854i
$324$	0.839855	−	1.81512i	0.0466586	−	0.100840i
$325$			11.1702i			0.619613i
$326$	−3.45455	−	5.40484i	−0.191330	−	0.299347i
$327$	−3.11251			−0.172122
$328$	−3.25031	−	23.8672i	−0.179468	−	1.31785i
$329$	−0.216927			−0.0119596
$330$	5.62285	+	8.79728i	0.309528	+	0.484274i
$331$			5.20937i			0.286333i	0.989699	+	0.143166i	$0.0457284\pi$
$331$			5.20937i			0.286333i	−0.989699	+	0.143166i	$0.954272\pi$
$332$	11.2158	+	5.18955i	0.615547	+	0.284814i
$333$		−	5.19569i		−	0.284722i
$334$	22.8934	−	14.6325i	1.25267	−	0.800654i
$335$	−11.1489			−0.609129
$336$	−11.8151	+	10.0341i	−0.644567	+	0.547406i
$337$	−26.3728			−1.43662			−0.718309	−	0.695724i	$-0.755084\pi$
$337$	−26.3728			−1.43662			−0.718309	+	0.695724i	$0.755084\pi$
$338$	−3.69317	+	2.36052i	−0.200882	+	0.128395i
$339$			16.6444i			0.903999i
$340$	−8.44863	−	3.90919i	−0.458192	−	0.212005i
$341$			27.2829i			1.47745i
$342$	−3.20775	−	5.01872i	−0.173455	−	0.271381i
$343$	3.94311			0.212908
$344$	23.5175	−	3.20267i	1.26798	−	0.172677i
$345$	−1.20415			−0.0648295
$346$	−11.9929	−	18.7635i	−0.644740	−	1.00873i
$347$		−	0.450264i		−	0.0241714i	−0.999927	−	0.0120857i	$-0.996153\pi$
$347$		−	0.450264i		−	0.0241714i	0.999927	−	0.0120857i	$-0.00384709\pi$
$348$	−1.17872	+	2.54747i	−0.0631858	+	0.136559i
$349$			23.3898i			1.25203i	0.779812	+	0.626014i	$0.215315\pi$
$349$			23.3898i			1.25203i	−0.779812	+	0.626014i	$0.784685\pi$
$350$	−16.3931	+	10.4778i	−0.876250	+	0.560062i
$351$	−3.14654			−0.167950
$352$	−10.1835	+	33.1536i	−0.542784	+	1.76709i
$353$	0.490804			0.0261228			0.0130614	−	0.999915i	$-0.495842\pi$
$353$	0.490804			0.0261228			0.0130614	+	0.999915i	$0.495842\pi$
$354$	11.7942	−	7.53835i	0.626854	−	0.400659i
$355$		−	5.47333i		−	0.290494i
$356$	7.93844	−	17.1568i	0.420736	−	0.909306i
$357$		−	14.9796i		−	0.792802i
$358$	5.58339	+	8.73554i	0.295091	+	0.461688i
$359$	27.8781			1.47135			0.735674	−	0.677335i	$-0.236865\pi$
$359$	27.8781			1.47135			0.735674	+	0.677335i	$0.236865\pi$
$360$	−3.37471	+	0.459578i	−0.177863	+	0.0242219i
$361$	1.26139			0.0663892
$362$	−12.7399	−	19.9324i	−0.669596	−	1.04762i
$363$			26.5894i			1.39558i
$364$	22.1328	+	10.2408i	1.16007	+	0.536766i
$365$			14.0626i			0.736069i
$366$	−9.97737	+	6.37711i	−0.521525	+	0.333337i
$367$	−29.9938			−1.56567			−0.782833	−	0.622232i	$-0.786226\pi$
$367$	−29.9938			−1.56567			−0.782833	+	0.622232i	$0.786226\pi$
$368$	−2.58929	−	3.04887i	−0.134976	−	0.158933i
$369$	8.51623			0.443337
$370$	−7.45519	+	4.76504i	−0.387577	+	0.247723i
$371$			3.24507i			0.168476i
$372$	−8.07722	−	3.73733i	−0.418784	−	0.193772i
$373$		−	30.0993i		−	1.55848i	−0.626726	−	0.779240i	$-0.715605\pi$
$373$		−	30.0993i		−	1.55848i	0.626726	−	0.779240i	$-0.284395\pi$
$374$	−18.0499	−	28.2401i	−0.933337	−	1.46026i
$375$	−10.2955			−0.531659
$376$	−0.0213645	−	0.156881i	−0.00110179	−	0.00809052i
$377$	4.41609			0.227440
$378$	−2.95148	−	4.61777i	−0.151808	−	0.237512i
$379$		−	24.1260i		−	1.23927i	−0.784890	−	0.619636i	$-0.787280\pi$
$379$		−	24.1260i		−	1.23927i	0.784890	−	0.619636i	$-0.212720\pi$
$380$	−4.25938	+	9.20548i	−0.218501	+	0.472231i
$381$			20.1152i			1.03053i
$382$	8.29176	−	5.29975i	0.424243	−	0.271159i
$383$	−32.8068			−1.67635			−0.838174	−	0.545403i	$-0.816377\pi$
$383$	−32.8068			−1.67635			−0.838174	+	0.545403i	$0.816377\pi$
$384$	−8.42026	−	7.55640i	−0.429695	−	0.385611i
$385$	28.6098			1.45809
$386$	25.8487	−	16.5214i	1.31567	−	0.840918i
$387$			8.39142i			0.426560i
$388$	8.17873	−	17.6761i	0.415212	−	0.897368i
$389$			6.06797i			0.307658i	0.988097	+	0.153829i	$0.0491605\pi$
$389$			6.06797i			0.307658i	−0.988097	+	0.153829i	$0.950840\pi$
$390$	2.88573	+	4.51490i	0.146125	+	0.228621i
$391$	3.86545			0.195484
$392$	3.05997	+	22.4696i	0.154552	+	1.13488i
$393$	−1.06175			−0.0535580
$394$	7.89499	+	12.3522i	0.397744	+	0.622294i
$395$		−	11.6504i		−	0.586193i
$396$	−11.1285	−	5.14917i	−0.559229	−	0.258755i
$397$		−	30.9874i		−	1.55521i	−0.628751	−	0.777606i	$-0.716434\pi$
$397$		−	30.9874i		−	1.55521i	0.628751	−	0.777606i	$-0.283566\pi$
$398$	24.2478	−	15.4982i	1.21543	−	0.776855i
$399$	−16.3215			−0.817095
$400$	−9.19200	−	10.8235i	−0.459600	−	0.541176i
$401$	31.9875			1.59738			0.798691	−	0.601741i	$-0.205526\pi$
$401$	31.9875			1.59738			0.798691	+	0.601741i	$0.205526\pi$
$402$	11.0327	−	7.05165i	0.550262	−	0.351704i
$403$			14.0020i			0.697490i
$404$	13.0501	+	6.03827i	0.649265	+	0.300415i
$405$		−	1.20415i		−	0.0598349i
$406$	4.14234	+	6.48093i	0.205581	+	0.321643i
$407$	−31.8549			−1.57899
$408$	10.8331	−	1.47529i	0.536321	−	0.0730377i
$409$	9.91934			0.490480			0.245240	−	0.969462i	$-0.421133\pi$
$409$	9.91934			0.490480			0.245240	+	0.969462i	$0.421133\pi$
$410$	−7.81036	−	12.2198i	−0.385726	−	0.603491i
$411$		−	2.15811i		−	0.106452i
$412$	3.25160	−	7.02744i	0.160195	−	0.346217i
$413$		−	38.3561i		−	1.88738i
$414$	1.19161	−	0.761625i	0.0585643	−	0.0374318i
$415$	7.44060			0.365245
$416$	−5.22635	+	17.0149i	−0.256243	+	0.834225i
$417$	14.0028			0.685721
$418$	−30.7699	+	19.6668i	−1.50500	+	0.961935i
$419$		−	10.6811i		−	0.521805i	−0.965365	−	0.260902i	$-0.915980\pi$
$419$		−	10.6811i		−	0.521805i	0.965365	−	0.260902i	$-0.0840200\pi$
$420$	−3.91909	+	8.47004i	−0.191232	+	0.413296i
$421$		−	4.50730i		−	0.219673i	−0.993950	−	0.109836i	$-0.964967\pi$
$421$		−	4.50730i		−	0.219673i	0.993950	−	0.109836i	$-0.0350327\pi$
$422$	−5.00179	−	7.82560i	−0.243483	−	0.380944i
$423$	0.0559777			0.00272173
$424$	−2.34682	+	0.319596i	−0.113972	+	0.0155210i
$425$	13.7224			0.665634
$426$	3.46187	+	5.41629i	0.167728	+	0.262420i
$427$			32.4476i			1.57025i
$428$	−30.7511	−	14.2286i	−1.48641	−	0.687763i
$429$			19.2915i			0.931401i
$430$	12.0407	−	7.69589i	0.580653	−	0.371129i
$431$	15.0499			0.724927			0.362464	−	0.931998i	$-0.381936\pi$
$431$	15.0499			0.724927			0.362464	+	0.931998i	$0.381936\pi$
$432$	3.04887	−	2.58929i	0.146689	−	0.124577i
$433$	−1.08877			−0.0523229			−0.0261615	−	0.999658i	$-0.508328\pi$
$433$	−1.08877			−0.0523229			−0.0261615	+	0.999658i	$0.508328\pi$
$434$	−20.5490	+	13.1340i	−0.986381	+	0.630453i
$435$			1.69000i			0.0810294i
$436$	−5.64957	−	2.61406i	−0.270565	−	0.125191i
$437$		−	4.21172i		−	0.201474i
$438$	−8.89455	−	13.9160i	−0.424998	−	0.664934i
$439$	−26.1726			−1.24915			−0.624574	−	0.780966i	$-0.714727\pi$
$439$	−26.1726			−1.24915			−0.624574	+	0.780966i	$0.714727\pi$
$440$	2.81769	+	20.6905i	0.134328	+	0.986379i
$441$	−8.01751			−0.381786
$442$	−9.26347	−	14.4932i	−0.440618	−	0.689373i
$443$			25.5085i			1.21195i	0.795485	+	0.605973i	$0.207216\pi$
$443$			25.5085i			1.21195i	−0.795485	+	0.605973i	$0.792784\pi$
$444$	4.36363	−	9.43078i	0.207089	−	0.447565i
$445$		−	11.3819i		−	0.539552i
$446$	−32.1827	+	20.5698i	−1.52390	+	0.974010i
$447$	−2.55210			−0.120710
$448$	−29.8730	+	8.29012i	−1.41137	+	0.391671i
$449$	−7.93209			−0.374338			−0.187169	−	0.982328i	$-0.559931\pi$
$449$	−7.93209			−0.374338			−0.187169	+	0.982328i	$0.559931\pi$
$450$	4.23022	−	2.70378i	0.199414	−	0.127457i
$451$		−	52.2132i		−	2.45862i
$452$	−13.9789	+	30.2115i	−0.657511	+	1.42103i
$453$			5.48163i			0.257549i
$454$	20.1470	+	31.5211i	0.945545	+	1.47936i
$455$	14.6830			0.688348
$456$	−1.60745	−	11.8036i	−0.0752757	−	0.552754i
$457$	0.512744			0.0239852			0.0119926	−	0.999928i	$-0.496183\pi$
$457$	0.512744			0.0239852			0.0119926	+	0.999928i	$0.496183\pi$
$458$	−15.0849	−	23.6012i	−0.704870	−	1.10281i
$459$			3.86545i			0.180424i
$460$	−2.18568	−	1.01132i	−0.101908	−	0.0471528i
$461$			10.2547i			0.477608i	0.971068	+	0.238804i	$0.0767554\pi$
$461$			10.2547i			0.477608i	−0.971068	+	0.238804i	$0.923245\pi$
$462$	−28.3116	+	18.0956i	−1.31718	+	0.841884i
$463$	14.6611			0.681360			0.340680	−	0.940179i	$-0.389343\pi$
$463$	14.6611			0.681360			0.340680	+	0.940179i	$0.389343\pi$
$464$	−4.27901	+	3.63400i	−0.198648	+	0.168704i
$465$	−5.35846			−0.248493
$466$	−6.91160	+	4.41760i	−0.320174	+	0.204641i
$467$		−	15.3211i		−	0.708974i	−0.935061	−	0.354487i	$-0.884656\pi$
$467$		−	15.3211i		−	0.708974i	0.935061	−	0.354487i	$-0.115344\pi$
$468$	−5.71132	−	2.64263i	−0.264006	−	0.122156i
$469$		−	35.8797i		−	1.65677i
$470$	−0.0513380	−	0.0803213i	−0.00236805	−	0.00370495i
$471$	5.04360			0.232397
$472$	27.7389	−	3.77757i	1.27679	−	0.173877i
$473$	51.4480			2.36558
$474$	7.36882	+	11.5290i	0.338461	+	0.529542i
$475$		−	14.9517i		−	0.686029i
$476$	12.5807	−	27.1896i	0.576633	−	1.24623i
$477$		−	0.837384i		−	0.0383412i
$478$	−31.3507	+	20.0381i	−1.43395	+	0.916520i
$479$	−12.9617			−0.592234			−0.296117	−	0.955152i	$-0.595692\pi$
$479$	−12.9617			−0.592234			−0.296117	+	0.955152i	$0.595692\pi$
$480$	−6.51148	−	2.00008i	−0.297207	−	0.0912908i
$481$	−16.3484			−0.745424
$482$	13.3781	−	8.55072i	0.609356	−	0.389474i
$483$		−	3.87524i		−	0.176330i
$484$	−22.3313	+	48.2629i	−1.01506	+	2.19377i
$485$		−	11.7264i		−	0.532468i
$486$	0.761625	+	1.19161i	0.0345480	+	0.0540524i
$487$	−26.9256			−1.22012			−0.610058	−	0.792357i	$-0.708854\pi$
$487$	−26.9256			−1.22012			−0.610058	+	0.792357i	$0.708854\pi$
$488$	−23.4659	+	3.19566i	−1.06225	+	0.144661i
$489$	4.53576			0.205114
$490$	7.35298	+	11.5042i	0.332174	+	0.519705i
$491$		−	26.2495i		−	1.18462i	−0.805709	−	0.592312i	$-0.798215\pi$
$491$		−	26.2495i		−	1.18462i	0.805709	−	0.592312i	$-0.201785\pi$
$492$	15.4579	+	7.15239i	0.696898	+	0.322455i
$493$		−	5.42507i		−	0.244333i
$494$	−15.7916	+	10.0933i	−0.710496	+	0.454119i
$495$	−7.38270			−0.331828
$496$	−11.5223	−	13.5674i	−0.517365	−	0.609193i
$497$	17.6144			0.790114
$498$	−7.36307	+	4.70616i	−0.329947	+	0.210888i
$499$			17.3073i			0.774780i	0.921916	+	0.387390i	$0.126623\pi$
$499$			17.3073i			0.774780i	−0.921916	+	0.387390i	$0.873377\pi$
$500$	−18.6876	−	8.64675i	−0.835734	−	0.386695i
$501$			19.2122i			0.858338i
$502$	−4.95446	−	7.75154i	−0.221128	−	0.345968i
$503$	4.62184			0.206078			0.103039	−	0.994677i	$-0.467143\pi$
$503$	4.62184			0.206078			0.103039	+	0.994677i	$0.467143\pi$
$504$	−1.47903	−	10.8606i	−0.0658811	−	0.483769i
$505$	8.65746			0.385252
$506$	−4.66954	−	7.30577i	−0.207586	−	0.324781i
$507$		−	3.09932i		−	0.137645i
$508$	−16.8938	+	36.5114i	−0.749542	+	1.61993i
$509$		−	36.3221i		−	1.60995i	−0.593310	−	0.804974i	$-0.702179\pi$
$509$		−	36.3221i		−	1.60995i	0.593310	−	0.804974i	$-0.297821\pi$
$510$	5.54645	−	3.54506i	0.245601	−	0.156978i
$511$	−45.2566			−2.00203
$512$	−8.93747	−	20.7875i	−0.394984	−	0.918688i
$513$	4.21172			0.185952
$514$	5.74611	−	3.67267i	0.253450	−	0.161995i
$515$		−	4.66203i		−	0.205434i
$516$	−7.04757	+	15.2314i	−0.310252	+	0.670525i
$517$		−	0.343201i		−	0.0150940i
$518$	−15.3350	−	23.9925i	−0.673781	−	1.05417i
$519$	15.7464			0.691191
$520$	1.44608	+	10.6187i	0.0634148	+	0.465659i
$521$	−15.3424			−0.672165			−0.336082	−	0.941833i	$-0.609102\pi$
$521$	−15.3424			−0.672165			−0.336082	+	0.941833i	$0.609102\pi$
$522$	−1.06892	−	1.67239i	−0.0467855	−	0.0731986i
$523$			24.7955i			1.08423i	0.840304	+	0.542116i	$0.182377\pi$
$523$			24.7955i			1.08423i	−0.840304	+	0.542116i	$0.817623\pi$
$524$	−1.92719	−	0.891713i	−0.0841898	−	0.0389547i
$525$		−	13.7572i		−	0.600412i
$526$	34.5078	−	22.0559i	1.50461	−	0.961684i
$527$	17.2012			0.749294
$528$	−15.8750	−	18.6927i	−0.690870	−	0.813494i
$529$	1.00000			0.0434783
$530$	−1.20155	+	0.767977i	−0.0521918	+	0.0333588i
$531$			9.89772i			0.429524i
$532$	−29.6253	−	13.7076i	−1.28442	−	0.594302i
$533$		−	26.7966i		−	1.16069i
$534$	7.19900	+	11.2633i	0.311531	+	0.487409i
$535$	−20.4004			−0.881987
$536$	25.9480	−	3.53368i	1.12078	−	0.152632i
$537$	−7.33089			−0.316351
$538$	12.0753	+	18.8926i	0.520605	+	0.814517i
$539$			49.1556i			2.11728i
$540$	1.01132	−	2.18568i	0.0435201	−	0.0940567i
$541$		−	30.2897i		−	1.30225i	−0.758969	−	0.651127i	$-0.774296\pi$
$541$		−	30.2897i		−	1.30225i	0.758969	−	0.651127i	$-0.225704\pi$
$542$	−27.8834	+	17.8219i	−1.19769	+	0.765516i
$543$	16.7273			0.717837
$544$	20.9024	+	6.42045i	0.896185	+	0.275275i
$545$	−3.74795			−0.160544
$546$	−14.5300	+	9.28694i	−0.621825	+	0.397444i
$547$		−	7.37006i		−	0.315121i	−0.987509	−	0.157560i	$-0.949637\pi$
$547$		−	7.37006i		−	0.315121i	0.987509	−	0.157560i	$-0.0503629\pi$
$548$	1.81250	−	3.91722i	0.0774261	−	0.167335i
$549$		−	8.37304i		−	0.357352i
$550$	−16.5769	−	25.9356i	−0.706842	−	1.10590i
$551$	−5.91105			−0.251819
$552$	2.80256	−	0.381661i	0.119285	−	0.0162446i
$553$	37.4935			1.59439
$554$	−5.57154	−	8.71700i	−0.236712	−	0.370350i
$555$		−	6.25642i		−	0.265570i
$556$	25.4167	+	11.7603i	1.07791	+	0.498749i
$557$		−	3.33492i		−	0.141305i	−0.997501	−	0.0706525i	$-0.977492\pi$
$557$		−	3.33492i		−	0.141305i	0.997501	−	0.0706525i	$-0.0225082\pi$
$558$	5.30262	−	3.38921i	0.224478	−	0.143477i
$559$	26.4039			1.11677
$560$	−14.2272	+	12.0826i	−0.601209	+	0.510585i
$561$	23.6992			1.00058
$562$	24.3623	−	15.5714i	1.02766	−	0.656838i
$563$			36.3619i			1.53247i	0.642559	+	0.766236i	$0.277873\pi$
$563$			36.3619i			1.53247i	−0.642559	+	0.766236i	$0.722127\pi$
$564$	0.101606	+	0.0470132i	0.00427839	+	0.00197961i
$565$			20.0424i			0.843191i
$566$	−2.65266	−	4.15024i	−0.111500	−	0.174448i
$567$	3.87524			0.162745
$568$	1.73479	+	12.7387i	0.0727901	+	0.534502i
$569$	−38.6962			−1.62223			−0.811115	−	0.584887i	$-0.801139\pi$
$569$	−38.6962			−1.62223			−0.811115	+	0.584887i	$0.801139\pi$
$570$	−3.86263	−	6.04331i	−0.161788	−	0.253127i
$571$			32.3052i			1.35193i	0.736933	+	0.675966i	$0.236273\pi$
$571$			32.3052i			1.35193i	−0.736933	+	0.675966i	$0.763727\pi$
$572$	−16.2020	+	35.0163i	−0.677441	+	1.46410i
$573$			6.95847i			0.290694i
$574$	39.3260	−	25.1355i	1.64143	−	1.04914i
$575$	3.55001			0.148046
$576$	7.70867	−	2.13925i	0.321195	−	0.0891355i
$577$	−13.1887			−0.549052			−0.274526	−	0.961580i	$-0.588521\pi$
$577$	−13.1887			−0.549052			−0.274526	+	0.961580i	$0.588521\pi$
$578$	2.45269	−	1.56765i	0.102018	−	0.0652058i
$579$			21.6923i			0.901502i
$580$	−1.41936	+	3.06755i	−0.0589356	+	0.127373i
$581$			23.9456i			0.993429i
$582$	7.41691	+	11.6042i	0.307441	+	0.481009i
$583$	−5.13402			−0.212629
$584$	−4.45718	−	32.7293i	−0.184439	−	1.35435i
$585$	−3.78892			−0.156652
$586$	−17.1362	−	26.8105i	−0.707888	−	1.10753i
$587$			18.5512i			0.765690i	0.923813	+	0.382845i	$0.125056\pi$
$587$			18.5512i			0.765690i	−0.923813	+	0.382845i	$0.874944\pi$
$588$	−14.5527	−	6.73355i	−0.600144	−	0.277687i
$589$		−	18.7421i		−	0.772253i
$590$	14.2020	−	9.07734i	0.584688	−	0.373708i
$591$	−10.3660			−0.426400
$592$	15.8410	−	13.4531i	0.651060	−	0.552921i
$593$	19.7287			0.810162			0.405081	−	0.914281i	$-0.367243\pi$
$593$	19.7287			0.810162			0.405081	+	0.914281i	$0.367243\pi$
$594$	7.30577	−	4.66954i	0.299759	−	0.191594i
$595$		−	18.0377i		−	0.739474i
$596$	−4.63236	−	2.14339i	−0.189749	−	0.0877968i
$597$			20.3489i			0.832823i
$598$	−2.39648	−	3.74943i	−0.0979993	−	0.153326i
$599$	40.0926			1.63814			0.819069	−	0.573694i	$-0.194490\pi$
$599$	40.0926			1.63814			0.819069	+	0.573694i	$0.194490\pi$
$600$	9.94912	−	1.35490i	0.406171	−	0.0553135i
$601$	−21.9112			−0.893777			−0.446889	−	0.894590i	$-0.647468\pi$
$601$	−21.9112			−0.893777			−0.446889	+	0.894590i	$0.647468\pi$
$602$	24.7671	+	38.7496i	1.00943	+	1.57932i
$603$			9.25869i			0.377043i
$604$	−4.60377	+	9.94978i	−0.187325	+	0.404851i
$605$			32.0178i			1.30171i
$606$	−8.56725	+	5.47582i	−0.348021	+	0.222440i
$607$	26.7808			1.08700			0.543500	−	0.839409i	$-0.317099\pi$
$607$	26.7808			1.08700			0.543500	+	0.839409i	$0.317099\pi$
$608$	6.99560	−	22.7749i	0.283709	−	0.923645i
$609$	−5.43881			−0.220392
$610$	−12.0143	+	7.67903i	−0.486445	+	0.310915i
$611$		−	0.176136i		−	0.00712570i
$612$	−3.24642	+	7.01624i	−0.131229	+	0.283615i
$613$		−	1.90409i		−	0.0769054i	−0.999260	−	0.0384527i	$-0.987757\pi$
$613$		−	1.90409i		−	0.0769054i	0.999260	−	0.0384527i	$-0.0122429\pi$
$614$	7.36314	+	11.5201i	0.297152	+	0.464912i
$615$	10.2549			0.413516
$616$	−66.5866	+	9.06795i	−2.68285	+	0.365358i
$617$	−34.1544			−1.37501			−0.687503	−	0.726181i	$-0.741293\pi$
$617$	−34.1544			−1.37501			−0.687503	+	0.726181i	$0.741293\pi$
$618$	2.94872	+	4.61345i	0.118615	+	0.185580i
$619$			33.3903i			1.34207i	0.741426	+	0.671034i	$0.234150\pi$
$619$			33.3903i			1.34207i	−0.741426	+	0.671034i	$0.765850\pi$
$620$	−9.72622	−	4.50033i	−0.390615	−	0.180738i
$621$			1.00000i			0.0401286i
$622$	−15.0750	+	9.63528i	−0.604451	+	0.386340i
$623$	36.6294			1.46753
$624$	−8.14729	−	9.59337i	−0.326152	−	0.384042i
$625$	5.35264			0.214105
$626$	−20.2494	+	12.9425i	−0.809327	+	0.517288i
$627$		−	25.8222i		−	1.03124i
$628$	9.15472	+	4.23589i	0.365313	+	0.169031i
$629$			20.0837i			0.800789i
$630$	−3.55404	−	5.56051i	−0.141596	−	0.221536i
$631$	−9.21448			−0.366823			−0.183411	−	0.983036i	$-0.558714\pi$
$631$	−9.21448			−0.366823			−0.183411	+	0.983036i	$0.558714\pi$
$632$	3.69261	+	27.1151i	0.146884	+	1.07858i
$633$	6.56726			0.261025
$634$	22.9704	+	35.9385i	0.912270	+	1.42730i
$635$			24.2218i			0.961212i
$636$	0.703281	−	1.51995i	0.0278869	−	0.0602699i
$637$			25.2274i			0.999545i
$638$	−10.2535	+	6.55359i	−0.405939	+	0.259459i
$639$	−4.54537			−0.179812
$640$	−10.1393	−	9.09907i	−0.400791	−	0.359672i
$641$	−27.3601			−1.08066			−0.540329	−	0.841454i	$-0.681700\pi$
$641$	−27.3601			−1.08066			−0.540329	+	0.841454i	$0.681700\pi$
$642$	20.1878	−	12.9032i	0.796750	−	0.509249i
$643$		−	43.4536i		−	1.71364i	−0.515614	−	0.856821i	$-0.672436\pi$
$643$		−	43.4536i		−	1.71364i	0.515614	−	0.856821i	$-0.327564\pi$
$644$	3.25464	−	7.03401i	0.128251	−	0.277179i
$645$			10.1046i			0.397867i
$646$	12.3994	+	19.3996i	0.487848	+	0.763267i
$647$	22.8797			0.899494			0.449747	−	0.893156i	$-0.351514\pi$
$647$	22.8797			0.899494			0.449747	+	0.893156i	$0.351514\pi$
$648$	0.381661	+	2.80256i	0.0149930	+	0.110095i
$649$	60.6831			2.38202
$650$	−8.50753	−	13.3105i	−0.333693	−	0.522082i
$651$		−	17.2447i		−	0.675875i
$652$	8.23293	+	3.80938i	0.322426	+	0.149187i
$653$			16.2658i			0.636531i	0.948002	+	0.318266i	$0.103100\pi$
$653$			16.2658i			0.636531i	−0.948002	+	0.318266i	$0.896900\pi$
$654$	3.70889	−	2.37057i	0.145029	−	0.0926966i
$655$	−1.27851			−0.0499554
$656$	22.0510	+	25.9648i	0.860946	+	1.01376i
$657$	11.6784			0.455617
$658$	0.258492	−	0.165217i	0.0100771	−	0.00644084i
$659$		−	42.9225i		−	1.67202i	−0.548711	−	0.836012i	$-0.684881\pi$
$659$		−	42.9225i		−	1.67202i	0.548711	−	0.836012i	$-0.315119\pi$
$660$	−13.4005	−	6.20040i	−0.521612	−	0.241350i
$661$		−	25.2591i		−	0.982466i	−0.871028	−	0.491233i	$-0.836546\pi$
$661$		−	25.2591i		−	0.982466i	0.871028	−	0.491233i	$-0.163454\pi$
$662$	−3.96759	−	6.20752i	−0.154205	−	0.241262i
$663$	12.1628			0.472363
$664$	−17.3173	+	2.35832i	−0.672042	+	0.0915206i
$665$	−19.6536			−0.762132
$666$	3.95717	+	6.19122i	0.153337	+	0.239905i
$667$		−	1.40348i		−	0.0543428i
$668$	−16.1355	+	34.8724i	−0.624299	+	1.34925i
$669$		−	27.0078i		−	1.04418i
$670$	13.2851	−	8.49128i	0.513248	−	0.328047i
$671$	−51.3353			−1.98178
$672$	6.43672	−	20.9554i	0.248302	−	0.808372i
$673$	−21.2323			−0.818443			−0.409222	−	0.912435i	$-0.634200\pi$
$673$	−21.2323			−0.818443			−0.409222	+	0.912435i	$0.634200\pi$
$674$	31.4260	−	20.0862i	1.21049	−	0.773691i
$675$			3.55001i			0.136640i
$676$	2.60298	−	5.62562i	0.100114	−	0.216370i
$677$			3.97333i			0.152707i	0.997081	+	0.0763537i	$0.0243278\pi$
$677$			3.97333i			0.152707i	−0.997081	+	0.0763537i	$0.975672\pi$
$678$	−12.6768	−	19.8336i	−0.486849	−	0.761704i
$679$	37.7382			1.44826
$680$	13.0448	−	1.77648i	0.500245	−	0.0681248i
$681$	−26.4526			−1.01367
$682$	−20.7793	−	32.5105i	−0.795682	−	1.24489i
$683$			12.2975i			0.470552i	0.971929	+	0.235276i	$0.0755994\pi$
$683$			12.2975i			0.470552i	−0.971929	+	0.235276i	$0.924401\pi$
$684$	7.64476	+	3.53723i	0.292305	+	0.135250i
$685$		−	2.59870i		−	0.0992911i
$686$	−4.69864	+	3.00317i	−0.179395	+	0.114662i
$687$	19.8062			0.755653
$688$	−25.5843	+	21.7278i	−0.975393	+	0.828365i
$689$	−2.63486			−0.100380
$690$	1.43488	−	0.917114i	0.0546249	−	0.0349139i
$691$		−	20.6867i		−	0.786958i	−0.919334	−	0.393479i	$-0.871271\pi$
$691$		−	20.6867i		−	0.786958i	0.919334	−	0.393479i	$-0.128729\pi$
$692$	28.5815	+	13.2247i	1.08651	+	0.502727i
$693$		−	23.7592i		−	0.902538i
$694$	0.342932	+	0.536537i	0.0130175	+	0.0203667i
$695$	16.8616			0.639596
$696$	−0.535651	−	3.93332i	−0.0203038	−	0.149092i
$697$	−32.9191			−1.24690
$698$	−17.8143	−	27.8715i	−0.674280	−	1.05495i
$699$		−	5.80023i		−	0.219385i
$700$	11.5540	−	24.9708i	0.436701	−	0.943809i
$701$			3.13058i			0.118241i	0.998251	+	0.0591203i	$0.0188295\pi$
$701$			3.13058i			0.118241i	−0.998251	+	0.0591203i	$0.981170\pi$
$702$	3.74943	−	2.39648i	0.141513	−	0.0904493i
$703$	21.8828			0.825326
$704$	−13.1158	−	47.2620i	−0.494320	−	1.78126i
$705$	0.0674059			0.00253865
$706$	−0.584845	+	0.373808i	−0.0220109	+	0.0140685i
$707$			27.8617i			1.04785i
$708$	−8.31264	+	17.9655i	−0.312408	+	0.675185i
$709$			9.56160i			0.359093i	0.983749	+	0.179547i	$0.0574631\pi$
$709$			9.56160i			0.359093i	−0.983749	+	0.179547i	$0.942537\pi$
$710$	4.16862	+	6.52205i	0.156446	+	0.244768i
$711$	−9.67513			−0.362846
$712$	3.60752	+	26.4902i	0.135197	+	0.992763i
$713$	4.44998			0.166653
$714$	11.4088	+	17.8497i	0.426964	+	0.668010i
$715$			23.2299i			0.868750i
$716$	−13.3064	−	6.15688i	−0.497284	−	0.230093i
$717$		−	26.3096i		−	0.982551i
$718$	−33.2197	+	21.2326i	−1.23975	+	0.792395i
$719$	−8.90669			−0.332163			−0.166082	−	0.986112i	$-0.553112\pi$
$719$	−8.90669			−0.332163			−0.166082	+	0.986112i	$0.553112\pi$
$720$	3.67131	−	3.11790i	0.136822	−	0.116197i
$721$	15.0035			0.558758
$722$	−1.50309	+	0.960710i	−0.0559391	+	0.0357539i
$723$			11.2269i			0.417534i
$724$	30.3620	+	14.0485i	1.12839	+	0.522109i
$725$		−	4.98236i		−	0.185040i
$726$	−20.2512	−	31.6842i	−0.751592	−	1.17591i
$727$	9.97324			0.369887			0.184944	−	0.982749i	$-0.440790\pi$
$727$	9.97324			0.369887			0.184944	+	0.982749i	$0.440790\pi$
$728$	−34.1733	+	4.65381i	−1.26655	+	0.172482i
$729$	−1.00000			−0.0370370
$730$	−10.7104	−	16.7571i	−0.396410	−	0.620207i
$731$		−	32.4366i		−	1.19971i
$732$	7.03213	−	15.1980i	0.259915	−	0.561735i
$733$		−	14.8894i		−	0.549952i	−0.961451	−	0.274976i	$-0.911330\pi$
$733$		−	14.8894i		−	0.549952i	0.961451	−	0.274976i	$-0.0886700\pi$
$734$	35.7409	−	22.8441i	1.31922	−	0.843190i
$735$	−9.65433			−0.356105
$736$	5.40751	+	1.66098i	0.199323	+	0.0612247i
$737$	56.7653			2.09098
$738$	−10.1480	+	6.48617i	−0.373553	+	0.238759i
$739$		−	44.5966i		−	1.64051i	−0.571997	−	0.820256i	$-0.693831\pi$
$739$		−	44.5966i		−	1.64051i	0.571997	−	0.820256i	$-0.306169\pi$
$740$	5.25448	−	11.3561i	0.193159	−	0.417459i
$741$		−	13.2523i		−	0.486837i
$742$	−2.47152	−	3.86685i	−0.0907325	−	0.141956i
$743$	−36.9224			−1.35455			−0.677276	−	0.735729i	$-0.736840\pi$
$743$	−36.9224			−1.35455			−0.677276	+	0.735729i	$0.736840\pi$
$744$	12.4713	−	1.69838i	0.457221	−	0.0622656i
$745$	−3.07312			−0.112591
$746$	22.9243	+	35.8665i	0.839320	+	1.31317i
$747$		−	6.17911i		−	0.226082i
$748$	43.0167	+	19.9039i	1.57285	+	0.727757i
$749$		−	65.6532i		−	2.39891i
$750$	12.2682	−	7.84134i	0.447973	−	0.286325i
$751$	45.9248			1.67582			0.837911	−	0.545807i	$-0.183777\pi$
$751$	45.9248			1.67582			0.837911	+	0.545807i	$0.183777\pi$
$752$	0.144943	+	0.170669i	0.00528551	+	0.00622365i
$753$	6.50511			0.237060
$754$	−5.26224	+	3.36340i	−0.191639	+	0.122488i
$755$			6.60073i			0.240225i
$756$	7.03401	+	3.25464i	0.255825	+	0.118370i
$757$			2.53120i			0.0919980i	0.998941	+	0.0459990i	$0.0146471\pi$
$757$			2.53120i			0.0919980i	−0.998941	+	0.0459990i	$0.985353\pi$
$758$	18.3750	+	28.7487i	0.667410	+	1.04420i
$759$	6.13102			0.222542
$760$	−1.93562	−	14.2134i	−0.0702122	−	0.515573i
$761$	22.3946			0.811805			0.405903	−	0.913916i	$-0.366957\pi$
$761$	22.3946			0.811805			0.405903	+	0.913916i	$0.366957\pi$
$762$	−15.3202	−	23.9694i	−0.554993	−	0.868319i
$763$		−	12.0618i		−	0.436665i
$764$	−5.84410	+	12.6304i	−0.211432	+	0.456953i
$765$			4.65460i			0.168287i
$766$	39.0928	−	24.9865i	1.41248	−	0.902798i
$767$	31.1435			1.12453
$768$	15.7888	+	2.59117i	0.569729	+	0.0935009i
$769$	−14.1205			−0.509199			−0.254600	−	0.967047i	$-0.581944\pi$
$769$	−14.1205			−0.509199			−0.254600	+	0.967047i	$0.581944\pi$
$770$	−34.0916	+	21.7899i	−1.22858	+	0.785254i
$771$			4.82215i			0.173665i
$772$	−18.2184	+	39.3741i	−0.655694	+	1.41710i
$773$			7.42724i			0.267139i	0.991039	+	0.133570i	$0.0426440\pi$
$773$			7.42724i			0.267139i	−0.991039	+	0.133570i	$0.957356\pi$
$774$	−6.39112	−	9.99928i	−0.229724	−	0.359417i
$775$	15.7975			0.567462
$776$	3.71671	+	27.2921i	0.133422	+	0.979729i
$777$	20.1346			0.722324
$778$	−4.62151	−	7.23063i	−0.165689	−	0.259231i
$779$			35.8680i			1.28510i
$780$	−6.87732	−	3.18214i	−0.246248	−	0.113939i
$781$			27.8678i			0.997187i
$782$	−4.60610	+	2.94402i	−0.164714	+	0.105278i
$783$	1.40348			0.0501561
$784$	−20.7597	−	24.4443i	−0.741416	−	0.873012i
$785$	6.07328			0.216765
$786$	1.26518	−	0.808653i	0.0451276	−	0.0288437i
$787$		−	0.0744530i		−	0.00265396i	−0.999999	−	0.00132698i	$-0.999578\pi$
$787$		−	0.0744530i		−	0.00265396i	0.999999	−	0.00132698i	$-0.000422392\pi$
$788$	−18.8155	−	8.70592i	−0.670273	−	0.310136i
$789$			28.9590i			1.03097i
$790$	8.87320	+	13.8826i	0.315694	+	0.493922i
$791$	−64.5011			−2.29339
$792$	17.1826	−	2.33997i	0.610555	−	0.0831472i
$793$	−26.3461			−0.935576
$794$	23.6008	+	36.9248i	0.837560	+	1.31041i
$795$		−	1.00834i		−	0.0357621i
$796$	−17.0901	+	36.9355i	−0.605742	+	1.30915i
$797$			23.5701i			0.834894i	0.908701	+	0.417447i	$0.137075\pi$
$797$			23.5701i			0.834894i	−0.908701	+	0.417447i	$0.862925\pi$
$798$	19.4488	−	12.4308i	0.688478	−	0.440046i
$799$	−0.216379			−0.00765494
$800$	19.1967	+	5.89651i	0.678706	+	0.208473i
$801$	−9.45216			−0.333976
$802$	−38.1166	+	24.3625i	−1.34594	+	0.860270i
$803$		−	71.6004i		−	2.52672i
$804$	−7.77596	+	16.8056i	−0.274237	+	0.592688i
$805$		−	4.66639i		−	0.164469i
$806$	−10.6643	−	16.6849i	−0.375633	−	0.587700i
$807$	−15.8547			−0.558112
$808$	−20.1494	+	2.74401i	−0.708855	+	0.0965339i
$809$	2.81346			0.0989158			0.0494579	−	0.998776i	$-0.484251\pi$
$809$	2.81346			0.0989158			0.0494579	+	0.998776i	$0.484251\pi$
$810$	0.917114	+	1.43488i	0.0322241	+	0.0504165i
$811$		−	16.6943i		−	0.586216i	−0.956079	−	0.293108i	$-0.905310\pi$
$811$		−	16.6943i		−	0.586216i	0.956079	−	0.293108i	$-0.0946895\pi$
$812$	−9.87207	−	4.56781i	−0.346442	−	0.160299i
$813$		−	23.3998i		−	0.820668i
$814$	37.9585	−	24.2615i	1.33045	−	0.850365i
$815$	5.46176			0.191317
$816$	−11.7852	+	10.0088i	−0.412566	+	0.350377i
$817$	−35.3423			−1.23647
$818$	−11.8200	+	7.55481i	−0.413275	+	0.264148i
$819$		−	12.1936i		−	0.426079i
$820$	18.6138	+	8.61259i	0.650020	+	0.300765i
$821$		−	6.76073i		−	0.235951i	−0.993017	−	0.117975i	$-0.962360\pi$
$821$		−	6.76073i		−	0.235951i	0.993017	−	0.117975i	$-0.0376404\pi$
$822$	1.64367	+	2.57162i	0.0573296	+	0.0896955i
$823$	−15.5558			−0.542241			−0.271120	−	0.962545i	$-0.587394\pi$
$823$	−15.5558			−0.542241			−0.271120	+	0.962545i	$0.587394\pi$
$824$	1.47764	+	10.8504i	0.0514762	+	0.377993i
$825$	21.7652			0.757767
$826$	29.2129	+	45.7054i	1.01645	+	1.59029i
$827$			48.6906i			1.69314i	0.532279	+	0.846569i	$0.321336\pi$
$827$			48.6906i			1.69314i	−0.532279	+	0.846569i	$0.678664\pi$
$828$	−0.839855	+	1.81512i	−0.0291870	+	0.0630796i
$829$			26.7182i			0.927962i	0.885845	+	0.463981i	$0.153579\pi$
$829$			26.7182i			0.927962i	−0.885845	+	0.463981i	$0.846421\pi$
$830$	−8.86627	+	5.66695i	−0.307753	+	0.196703i
$831$	7.31533			0.253766
$832$	−6.73123	−	24.2556i	−0.233363	−	0.840912i
$833$	30.9913			1.07378
$834$	−16.6859	+	10.6649i	−0.577784	+	0.369295i
$835$			23.1345i			0.800601i
$836$	21.6869	−	46.8702i	0.750056	−	1.62104i
$837$			4.44998i			0.153814i
$838$	8.13497	+	12.7276i	0.281018	+	0.439669i
$839$	−2.48150			−0.0856708			−0.0428354	−	0.999082i	$-0.513639\pi$
$839$	−2.48150			−0.0856708			−0.0428354	+	0.999082i	$0.513639\pi$
$840$	−1.78098	−	13.0778i	−0.0614496	−	0.451228i
$841$	27.0303			0.932078
$842$	3.43288	+	5.37094i	0.118305	+	0.185095i
$843$			20.4449i			0.704160i
$844$	11.9203	+	5.51555i	0.410315	+	0.189853i
$845$		−	3.73206i		−	0.128387i
$846$	−0.0667035	+	0.0426341i	−0.00229331	+	0.00146579i
$847$	−103.041			−3.54052
$848$	2.55307	−	2.16823i	0.0876729	−	0.0744573i
$849$	3.48290			0.119533
$850$	−16.3517	+	10.4513i	−0.560859	+	0.358477i
$851$			5.19569i			0.178106i
$852$	−8.25037	−	3.81745i	−0.282653	−	0.130784i
$853$		−	39.8387i		−	1.36405i	−0.731328	−	0.682026i	$-0.761099\pi$
$853$		−	39.8387i		−	1.36405i	0.731328	−	0.682026i	$-0.238901\pi$
$854$	−24.7129	−	38.6647i	−0.845657	−	1.32308i
$855$	5.07157			0.173444
$856$	47.4801	−	6.46597i	1.62284	−	0.221002i
$857$	−1.26069			−0.0430645			−0.0215322	−	0.999768i	$-0.506854\pi$
$857$	−1.26069			−0.0430645			−0.0215322	+	0.999768i	$0.506854\pi$
$858$	−14.6929	−	22.9879i	−0.501606	−	0.784793i
$859$		−	0.668965i		−	0.0228248i	−0.999935	−	0.0114124i	$-0.996367\pi$
$859$		−	0.668965i		−	0.0228248i	0.999935	−	0.0114124i	$-0.00363276\pi$
$860$	−8.48637	+	18.3410i	−0.289383	+	0.625422i
$861$			33.0025i			1.12472i
$862$	−17.9335	+	11.4624i	−0.610819	+	0.390410i
$863$	32.4496			1.10460			0.552299	−	0.833646i	$-0.313751\pi$
$863$	32.4496			1.10460			0.552299	+	0.833646i	$0.313751\pi$
$864$	−1.66098	+	5.40751i	−0.0565078	+	0.183967i
$865$	18.9611			0.644697
$866$	1.29739	−	0.829234i	0.0440870	−	0.0281785i
$867$			2.05830i			0.0699036i
$868$	14.4831	−	31.3012i	0.491588	−	1.06243i
$869$			59.3184i			2.01224i
$870$	−1.28715	−	2.01382i	−0.0436384	−	0.0682749i
$871$	29.1328			0.987127
$872$	8.72300	−	1.18792i	0.295398	−	0.0402282i
$873$	−9.73827			−0.329591
$874$	3.20775	+	5.01872i	0.108504	+	0.169761i
$875$		−	39.8977i		−	1.34879i
$876$	21.1976	+	9.80814i	0.716201	+	0.331386i
$877$		−	24.0713i		−	0.812829i	−0.913689	−	0.406415i	$-0.866779\pi$
$877$		−	24.0713i		−	0.812829i	0.913689	−	0.406415i	$-0.133221\pi$
$878$	31.1874	−	19.9337i	1.05252	−	0.672729i
$879$	22.4995			0.758888
$880$	−19.1159	−	22.5089i	−0.644398	−	0.758774i
$881$	22.1444			0.746065			0.373032	−	0.927818i	$-0.378318\pi$
$881$	22.1444			0.746065			0.373032	+	0.927818i	$0.378318\pi$
$882$	9.55373	−	6.10634i	0.321691	−	0.205611i
$883$		−	21.4220i		−	0.720908i	−0.932777	−	0.360454i	$-0.882622\pi$
$883$		−	21.4220i		−	0.720908i	0.932777	−	0.360454i	$-0.117378\pi$
$884$	22.0768	+	10.2150i	0.742524	+	0.343566i
$885$			11.9184i			0.400632i
$886$	−19.4279	−	30.3961i	−0.652694	−	1.02118i
$887$	5.15429			0.173064			0.0865320	−	0.996249i	$-0.472422\pi$
$887$	5.15429			0.173064			0.0865320	+	0.996249i	$0.472422\pi$
$888$	1.98299	+	14.5612i	0.0665448	+	0.488643i
$889$	−77.9512			−2.61440
$890$	8.66871	+	13.5627i	0.290576	+	0.454623i
$891$			6.13102i			0.205397i
$892$	22.6827	−	49.0223i	0.759471	−	1.64139i
$893$			0.235763i			0.00788950i
$894$	3.04110	−	1.94374i	0.101710	−	0.0650085i
$895$	−8.82752			−0.295072
$896$	29.2829	−	32.6306i	0.978273	−	1.09011i
$897$	3.14654			0.105060
$898$	9.45193	−	6.04128i	0.315415	−	0.201600i
$899$		−	6.24544i		−	0.208297i
$900$	−2.98149	+	6.44368i	−0.0993831	+	0.214789i
$901$			3.23687i			0.107836i
$902$	39.7669	+	62.2176i	1.32409	+	2.07162i
$903$	−32.5188			−1.08216
$904$	−6.35251	−	46.6469i	−0.211281	−	1.55145i
$905$	20.1423			0.669551
$906$	−4.17494	−	6.53194i	−0.138703	−	0.217009i
$907$		−	45.0304i		−	1.49521i	−0.664143	−	0.747605i	$-0.731204\pi$
$907$		−	45.0304i		−	1.49521i	0.664143	−	0.747605i	$-0.268796\pi$
$908$	−48.0146	−	22.2164i	−1.59342	−	0.737276i
$909$		−	7.18966i		−	0.238466i
$910$	−17.4963	+	11.1829i	−0.579998	+	0.370710i
$911$	3.67588			0.121787			0.0608937	−	0.998144i	$-0.480605\pi$
$911$	3.67588			0.121787			0.0608937	+	0.998144i	$0.480605\pi$
$912$	10.9054	+	12.8410i	0.361113	+	0.425207i
$913$	−37.8843			−1.25379
$914$	−0.610989	+	0.390519i	−0.0202097	+	0.0129172i
$915$		−	10.0824i		−	0.333315i
$916$	35.9505	+	16.6343i	1.18784	+	0.549613i
$917$		−	4.11453i		−	0.135874i
$918$	−2.94402	−	4.60610i	−0.0971672	−	0.152024i
$919$	−53.8386			−1.77597			−0.887985	−	0.459872i	$-0.847895\pi$
$919$	−53.8386			−1.77597			−0.887985	+	0.459872i	$0.847895\pi$
$920$	3.37471	−	0.459578i	0.111261	−	0.0151518i
$921$	−9.66767			−0.318561
$922$	−7.81022	−	12.2196i	−0.257216	−	0.402429i
$923$			14.3022i			0.470761i
$924$	19.9543	−	43.1257i	0.656448	−	1.41873i
$925$			18.4448i			0.606460i
$926$	−17.4703	+	11.1663i	−0.574109	+	0.366947i
$927$	−3.87162			−0.127161
$928$	2.33115	−	7.58931i	0.0765238	−	0.249131i
$929$	−1.36611			−0.0448206			−0.0224103	−	0.999749i	$-0.507134\pi$
$929$	−1.36611			−0.0448206			−0.0224103	+	0.999749i	$0.507134\pi$
$930$	6.38518	−	4.08114i	0.209378	−	0.133826i
$931$		−	33.7675i		−	1.10669i
$932$	4.87135	−	10.5281i	0.159566	−	0.344859i
$933$		−	12.6510i		−	0.414174i
$934$	11.6689	+	18.2567i	0.381818	+	0.597377i
$935$	28.5375			0.933275
$936$	8.81835	−	1.20091i	0.288237	−	0.0392529i
$937$	21.8381			0.713419			0.356710	−	0.934215i	$-0.383899\pi$
$937$	21.8381			0.713419			0.356710	+	0.934215i	$0.383899\pi$
$938$	27.3269	+	42.7545i	0.892254	+	1.39598i
$939$		−	16.9933i		−	0.554556i
$940$	0.122349	+	0.0566111i	0.00399060	+	0.00184645i
$941$			13.0367i			0.424985i	0.977163	+	0.212492i	$0.0681581\pi$
$941$			13.0367i			0.424985i	−0.977163	+	0.212492i	$0.931842\pi$
$942$	−6.00999	+	3.84133i	−0.195816	+	0.125157i
$943$	−8.51623			−0.277327
$944$	−30.1768	+	25.6280i	−0.982172	+	0.834122i
$945$	4.66639			0.151798
$946$	−61.3058	+	39.1841i	−1.99322	+	1.27398i
$947$			9.25988i			0.300906i	0.988617	+	0.150453i	$0.0480732\pi$
$947$			9.25988i			0.300906i	−0.988617	+	0.150453i	$0.951927\pi$
$948$	−17.5615	−	8.12570i	−0.570370	−	0.263911i
$949$		−	36.7464i		−	1.19284i
$950$	11.3876	+	17.8165i	0.369461	+	0.578044i
$951$	−30.1597			−0.977994
$952$	5.71711	+	41.9811i	0.185292	+	1.36061i
$953$	9.76517			0.316325			0.158162	−	0.987413i	$-0.449443\pi$
$953$	9.76517			0.316325			0.158162	+	0.987413i	$0.449443\pi$
$954$	0.637773	+	0.997833i	0.0206487	+	0.0323060i
$955$			8.37908i			0.271141i
$956$	22.0963	−	47.7550i	0.714644	−	1.54451i
$957$		−	8.60475i		−	0.278152i
$958$	15.4452	−	9.87194i	0.499013	−	0.318948i
$959$	8.36320			0.270062
$960$	9.28243	−	2.57599i	0.299589	−	0.0831397i
$961$	−11.1977			−0.361217
$962$	19.4809	−	12.4514i	0.628089	−	0.401448i
$963$			16.9417i			0.545938i
$964$	−9.42900	+	20.3782i	−0.303688	+	0.656337i
$965$			26.1209i			0.840862i
$966$	2.95148	+	4.61777i	0.0949624	+	0.148574i
$967$	33.9258			1.09098			0.545489	−	0.838118i	$-0.316344\pi$
$967$	33.9258			1.09098			0.545489	+	0.838118i	$0.316344\pi$
$968$	−10.1481	−	74.5185i	−0.326174	−	2.39511i
$969$	−16.2802			−0.522995
$970$	8.93111	+	13.9732i	0.286761	+	0.448654i
$971$			36.6727i			1.17688i	0.808539	+	0.588442i	$0.200258\pi$
$971$			36.6727i			1.17688i	−0.808539	+	0.588442i	$0.799742\pi$
$972$	−1.81512	−	0.839855i	−0.0582199	−	0.0269384i
$973$			54.2643i			1.73964i
$974$	32.0848	−	20.5072i	1.02806	−	0.657094i
$975$	11.1702			0.357734
$976$	25.5283	−	21.6802i	0.817140	−	0.693966i
$977$	−17.4349			−0.557790			−0.278895	−	0.960322i	$-0.589968\pi$
$977$	−17.4349			−0.557790			−0.278895	+	0.960322i	$0.589968\pi$
$978$	−5.40484	+	3.45455i	−0.172828	+	0.110464i
$979$			57.9514i			1.85213i
$980$	−17.5237	−	8.10823i	−0.559775	−	0.259008i
$981$			3.11251i			0.0993749i
$982$	19.9923	+	31.2791i	0.637979	+	0.998156i
$983$	−43.0964			−1.37456			−0.687281	−	0.726391i	$-0.741196\pi$
$983$	−43.0964			−1.37456			−0.687281	+	0.726391i	$0.741196\pi$
$984$	−23.8672	+	3.25031i	−0.760860	+	0.103616i
$985$	−12.4822			−0.397717
$986$	4.13187	+	6.46455i	0.131585	+	0.205873i
$987$			0.216927i			0.00690488i
$988$	11.1300	−	24.0545i	0.354094	−	0.765276i
$989$		−	8.39142i		−	0.266832i
$990$	8.79728	−	5.62285i	0.279596	−	0.178706i
$991$	24.5220			0.778968			0.389484	−	0.921033i	$-0.372653\pi$
$991$	24.5220			0.778968			0.389484	+	0.921033i	$0.372653\pi$
$992$	24.0633	+	7.39134i	0.764010	+	0.234675i
$993$	5.20937			0.165314
$994$	−20.9894	+	13.4156i	−0.665745	+	0.425516i
$995$			24.5032i			0.776803i
$996$	5.18955	−	11.2158i	0.164437	−	0.355386i
$997$			31.2917i			0.991018i	0.868603	+	0.495509i	$0.165018\pi$
$997$			31.2917i			0.991018i	−0.868603	+	0.495509i	$0.834982\pi$
$998$	−13.1817	−	20.6235i	−0.417258	−	0.652824i
$999$	−5.19569			−0.164384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.d.277.6	yes	20
4.3	odd	2		2208.2.f.d.1105.14		20
8.3	odd	2		2208.2.f.d.1105.7		20
8.5	even	2	inner	552.2.f.d.277.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.d.277.5	✓	20	8.5	even	2	inner
552.2.f.d.277.6	yes	20	1.1	even	1	trivial
2208.2.f.d.1105.7		20	8.3	odd	2
2208.2.f.d.1105.14		20	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19161 + 0.761625i) q^{2} -1.00000i q^{3} +(0.839855 - 1.81512i) q^{4} -1.20415i q^{5} +(0.761625 + 1.19161i) q^{6} +3.87524 q^{7} +(0.381661 + 2.80256i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.19161 + 0.761625i) q^{2} -1.00000i q^{3} +(0.839855 - 1.81512i) q^{4} -1.20415i q^{5} +(0.761625 + 1.19161i) q^{6} +3.87524 q^{7} +(0.381661 + 2.80256i) q^{8} -1.00000 q^{9} +(0.917114 + 1.43488i) q^{10} +6.13102i q^{11} +(-1.81512 - 0.839855i) q^{12} +3.14654i q^{13} +(-4.61777 + 2.95148i) q^{14} -1.20415 q^{15} +(-2.58929 - 3.04887i) q^{16} +3.86545 q^{17} +(1.19161 - 0.761625i) q^{18} -4.21172i q^{19} +(-2.18568 - 1.01132i) q^{20} -3.87524i q^{21} +(-4.66954 - 7.30577i) q^{22} +1.00000 q^{23} +(2.80256 - 0.381661i) q^{24} +3.55001 q^{25} +(-2.39648 - 3.74943i) q^{26} +1.00000i q^{27} +(3.25464 - 7.03401i) q^{28} -1.40348i q^{29} +(1.43488 - 0.917114i) q^{30} +4.44998 q^{31} +(5.40751 + 1.66098i) q^{32} +6.13102 q^{33} +(-4.60610 + 2.94402i) q^{34} -4.66639i q^{35} +(-0.839855 + 1.81512i) q^{36} +5.19569i q^{37} +(3.20775 + 5.01872i) q^{38} +3.14654 q^{39} +(3.37471 - 0.459578i) q^{40} -8.51623 q^{41} +(2.95148 + 4.61777i) q^{42} -8.39142i q^{43} +(11.1285 + 5.14917i) q^{44} +1.20415i q^{45} +(-1.19161 + 0.761625i) q^{46} -0.0559777 q^{47} +(-3.04887 + 2.58929i) q^{48} +8.01751 q^{49} +(-4.23022 + 2.70378i) q^{50} -3.86545i q^{51} +(5.71132 + 2.64263i) q^{52} +0.837384i q^{53} +(-0.761625 - 1.19161i) q^{54} +7.38270 q^{55} +(1.47903 + 10.8606i) q^{56} -4.21172 q^{57} +(1.06892 + 1.67239i) q^{58} -9.89772i q^{59} +(-1.01132 + 2.18568i) q^{60} +8.37304i q^{61} +(-5.30262 + 3.38921i) q^{62} -3.87524 q^{63} +(-7.70867 + 2.13925i) q^{64} +3.78892 q^{65} +(-7.30577 + 4.66954i) q^{66} -9.25869i q^{67} +(3.24642 - 7.01624i) q^{68} -1.00000i q^{69} +(3.55404 + 5.56051i) q^{70} +4.54537 q^{71} +(-0.381661 - 2.80256i) q^{72} -11.6784 q^{73} +(-3.95717 - 6.19122i) q^{74} -3.55001i q^{75} +(-7.64476 - 3.53723i) q^{76} +23.7592i q^{77} +(-3.74943 + 2.39648i) q^{78} +9.67513 q^{79} +(-3.67131 + 3.11790i) q^{80} +1.00000 q^{81} +(10.1480 - 6.48617i) q^{82} +6.17911i q^{83} +(-7.03401 - 3.25464i) q^{84} -4.65460i q^{85} +(6.39112 + 9.99928i) q^{86} -1.40348 q^{87} +(-17.1826 + 2.33997i) q^{88} +9.45216 q^{89} +(-0.917114 - 1.43488i) q^{90} +12.1936i q^{91} +(0.839855 - 1.81512i) q^{92} -4.44998i q^{93} +(0.0667035 - 0.0426341i) q^{94} -5.07157 q^{95} +(1.66098 - 5.40751i) q^{96} +9.73827 q^{97} +(-9.55373 + 6.10634i) q^{98} -6.13102i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Introduction

L-functions

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