LMFDB - Embedded newform 552.2.f.d.277.5

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

$q$-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	$0.0867782\pi$
$5$			1.20415i			0.538514i	−0.963068	+	0.269257i	$0.913222\pi$
$6$	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	$-0.624661\pi$
$11$		−	6.13102i		−	1.84857i	0.381699	−	0.924287i	$-0.375339\pi$
$12$	−1.81512	+	0.839855i	−0.523979	+	0.242445i
$13$		−	3.14654i		−	0.872692i	−0.899779	−	0.436346i	$-0.856272\pi$
$13$		−	3.14654i		−	0.872692i	0.899779	−	0.436346i	$-0.143728\pi$
$14$	−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	$0.160496\pi$
$19$			4.21172i			0.966235i	−0.875555	+	0.483118i	$0.839504\pi$
$20$	−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	$0.0415971\pi$
$29$			1.40348i			0.260619i	−0.991473	+	0.130309i	$0.958403\pi$
$30$	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	$-0.859541\pi$
$37$		−	5.19569i		−	0.854166i	0.904212	−	0.427083i	$-0.140459\pi$
$38$	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	$0.220999\pi$
$43$			8.39142i			1.27968i	−0.768508	+	0.639840i	$0.779001\pi$
$44$	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	$-0.981683\pi$
$53$		−	0.837384i		−	0.115024i	0.998345	−	0.0575118i	$-0.0183167\pi$
$54$	−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	$0.222846\pi$
$59$			9.89772i			1.28857i	−0.764784	+	0.644286i	$0.777154\pi$
$60$	−1.01132	−	2.18568i	−0.130560	−	0.282170i
$61$		−	8.37304i		−	1.07206i	−0.844200	−	0.536029i	$-0.819924\pi$
$61$		−	8.37304i		−	1.07206i	0.844200	−	0.536029i	$-0.180076\pi$
$62$	−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	$0.191342\pi$
$67$			9.25869i			1.13113i	−0.824704	+	0.565565i	$0.808658\pi$
$68$	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	$-0.889870\pi$
$83$		−	6.17911i		−	0.678245i	0.940742	−	0.339123i	$-0.110130\pi$
$84$	−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	$-0.883561\pi$
$101$		−	7.18966i		−	0.715398i	0.933837	−	0.357699i	$-0.116439\pi$
$102$	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	$0.305420\pi$
$107$			16.9417i			1.63781i	−0.573926	+	0.818907i	$0.694580\pi$
$108$	1.81512	−	0.839855i	0.174660	−	0.0808151i
$109$			3.11251i			0.298125i	0.988828	+	0.149062i	$0.0476255\pi$
$109$			3.11251i			0.298125i	−0.988828	+	0.149062i	$0.952374\pi$
$110$	−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	$0.0147693\pi$
$131$			1.06175i			0.0927652i	−0.998924	+	0.0463826i	$0.985231\pi$
$132$	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	$-0.797606\pi$
$139$		−	14.0028i		−	1.18770i	0.804574	−	0.593852i	$-0.202394\pi$
$140$	−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	$0.0333364\pi$
$149$			2.55210i			0.209076i	−0.994521	+	0.104538i	$0.966664\pi$
$150$	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	$-0.935496\pi$
$157$		−	5.04360i		−	0.402523i	0.979538	−	0.201262i	$-0.0645042\pi$
$158$	−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	$-0.943156\pi$
$163$		−	4.53576i		−	0.355268i	0.984097	−	0.177634i	$-0.0568443\pi$
$164$	−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	$-0.795728\pi$
$173$		−	15.7464i		−	1.19718i	0.801057	−	0.598589i	$-0.204272\pi$
$174$	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	$0.0883363\pi$
$179$			7.33089i			0.547936i	−0.961739	+	0.273968i	$0.911664\pi$
$180$	2.18568	−	1.01132i	0.162911	−	0.0753790i
$181$		−	16.7273i		−	1.24333i	−0.783283	−	0.621665i	$-0.786456\pi$
$181$		−	16.7273i		−	1.24333i	0.783283	−	0.621665i	$-0.213544\pi$
$182$	−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	$0.120393\pi$
$197$			10.3660i			0.738546i	−0.929321	+	0.369273i	$0.879607\pi$
$198$	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	$-0.927417\pi$
$211$		−	6.56726i		−	0.452109i	0.974115	−	0.226055i	$-0.0725828\pi$
$212$	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	$0.341030\pi$
$227$			26.4526i			1.75572i	−0.478914	+	0.877862i	$0.658970\pi$
$228$	−3.53723	−	7.64476i	−0.234259	−	0.506287i
$229$		−	19.8062i		−	1.30883i	−0.756136	−	0.654415i	$-0.772915\pi$
$229$		−	19.8062i		−	1.30883i	0.756136	−	0.654415i	$-0.227085\pi$
$230$	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	$-0.934183\pi$
$251$		−	6.50511i		−	0.410599i	0.978699	−	0.205300i	$-0.0658169\pi$
$252$	−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	$0.160576\pi$
$269$			15.8547i			0.966678i	−0.875433	+	0.483339i	$0.839424\pi$
$270$	−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	$-0.929470\pi$
$277$		−	7.31533i		−	0.439536i	0.975552	−	0.219768i	$-0.0705300\pi$
$278$	−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	$-0.966990\pi$
$283$		−	3.48290i		−	0.207037i	0.994628	−	0.103518i	$-0.0330101\pi$
$284$	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	$-0.771734\pi$
$293$		−	22.4995i		−	1.31443i	0.753702	−	0.657216i	$-0.228266\pi$
$294$	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	$0.0889697\pi$
$307$			9.66767i			0.551763i	−0.961192	+	0.275882i	$0.911030\pi$
$308$	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	$0.321575\pi$
$317$			30.1597i			1.69394i	−0.531644	+	0.846968i	$0.678425\pi$
$318$	−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	$-0.954272\pi$
$331$		−	5.20937i		−	0.286333i	0.989699	−	0.143166i	$-0.0457284\pi$
$332$	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	$0.00384709\pi$
$347$			0.450264i			0.0241714i	−0.999927	+	0.0120857i	$0.996153\pi$
$348$	−1.17872	−	2.54747i	−0.0631858	−	0.136559i
$349$		−	23.3898i		−	1.25203i	−0.779812	−	0.626014i	$-0.784685\pi$
$349$		−	23.3898i		−	1.25203i	0.779812	−	0.626014i	$-0.215315\pi$
$350$	−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	$0.284395\pi$
$373$			30.0993i			1.55848i	−0.626726	+	0.779240i	$0.715605\pi$
$374$	−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	$0.212720\pi$
$379$			24.1260i			1.23927i	−0.784890	+	0.619636i	$0.787280\pi$
$380$	−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	$-0.950840\pi$
$389$		−	6.06797i		−	0.307658i	0.988097	−	0.153829i	$-0.0491605\pi$
$390$	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	$0.283566\pi$
$397$			30.9874i			1.55521i	−0.628751	+	0.777606i	$0.716434\pi$
$398$	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	$0.0840200\pi$
$419$			10.6811i			0.521805i	−0.965365	+	0.260902i	$0.915980\pi$
$420$	−3.91909	−	8.47004i	−0.191232	−	0.413296i
$421$			4.50730i			0.219673i	0.993950	+	0.109836i	$0.0350327\pi$
$421$			4.50730i			0.219673i	−0.993950	+	0.109836i	$0.964967\pi$
$422$	−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	$-0.792784\pi$
$443$		−	25.5085i		−	1.21195i	0.795485	−	0.605973i	$-0.207216\pi$
$444$	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	$-0.923245\pi$
$461$		−	10.2547i		−	0.477608i	0.971068	−	0.238804i	$-0.0767554\pi$
$462$	−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	$0.115344\pi$
$467$			15.3211i			0.708974i	−0.935061	+	0.354487i	$0.884656\pi$
$468$	−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	$0.201785\pi$
$491$			26.2495i			1.18462i	−0.805709	+	0.592312i	$0.798215\pi$
$492$	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	$-0.873377\pi$
$499$		−	17.3073i		−	0.774780i	0.921916	−	0.387390i	$-0.126623\pi$
$500$	−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	$0.297821\pi$
$509$			36.3221i			1.60995i	−0.593310	+	0.804974i	$0.702179\pi$
$510$	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	$-0.817623\pi$
$523$		−	24.7955i		−	1.08423i	0.840304	−	0.542116i	$-0.182377\pi$
$524$	−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	$0.225704\pi$
$541$			30.2897i			1.30225i	−0.758969	+	0.651127i	$0.774296\pi$
$542$	−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	$0.0503629\pi$
$547$			7.37006i			0.315121i	−0.987509	+	0.157560i	$0.949637\pi$
$548$	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	$0.0225082\pi$
$557$			3.33492i			0.141305i	−0.997501	+	0.0706525i	$0.977492\pi$
$558$	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	$-0.722127\pi$
$563$		−	36.3619i		−	1.53247i	0.642559	−	0.766236i	$-0.277873\pi$
$564$	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	$-0.763727\pi$
$571$		−	32.3052i		−	1.35193i	0.736933	−	0.675966i	$-0.236273\pi$
$572$	−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	$-0.874944\pi$
$587$		−	18.5512i		−	0.765690i	0.923813	−	0.382845i	$-0.125056\pi$
$588$	−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	$0.0122429\pi$
$613$			1.90409i			0.0769054i	−0.999260	+	0.0384527i	$0.987757\pi$
$614$	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	$-0.765850\pi$
$619$		−	33.3903i		−	1.34207i	0.741426	−	0.671034i	$-0.234150\pi$
$620$	−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	$0.327564\pi$
$643$			43.4536i			1.71364i	−0.515614	+	0.856821i	$0.672436\pi$
$644$	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	$-0.896900\pi$
$653$		−	16.2658i		−	0.636531i	0.948002	−	0.318266i	$-0.103100\pi$
$654$	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	$0.315119\pi$
$659$			42.9225i			1.67202i	−0.548711	+	0.836012i	$0.684881\pi$
$660$	−13.4005	+	6.20040i	−0.521612	+	0.241350i
$661$			25.2591i			0.982466i	0.871028	+	0.491233i	$0.163454\pi$
$661$			25.2591i			0.982466i	−0.871028	+	0.491233i	$0.836546\pi$
$662$	−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	$-0.975672\pi$
$677$		−	3.97333i		−	0.152707i	0.997081	−	0.0763537i	$-0.0243278\pi$
$678$	−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	$-0.924401\pi$
$683$		−	12.2975i		−	0.470552i	0.971929	−	0.235276i	$-0.0755994\pi$
$684$	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	$0.128729\pi$
$691$			20.6867i			0.786958i	−0.919334	+	0.393479i	$0.871271\pi$
$692$	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	$-0.981170\pi$
$701$		−	3.13058i		−	0.118241i	0.998251	−	0.0591203i	$-0.0188295\pi$
$702$	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	$-0.942537\pi$
$709$		−	9.56160i		−	0.359093i	0.983749	−	0.179547i	$-0.0574631\pi$
$710$	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	$0.0886700\pi$
$733$			14.8894i			0.549952i	−0.961451	+	0.274976i	$0.911330\pi$
$734$	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	$0.306169\pi$
$739$			44.5966i			1.64051i	−0.571997	+	0.820256i	$0.693831\pi$
$740$	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	$-0.985353\pi$
$757$		−	2.53120i		−	0.0919980i	0.998941	−	0.0459990i	$-0.0146471\pi$
$758$	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	$-0.957356\pi$
$773$		−	7.42724i		−	0.267139i	0.991039	−	0.133570i	$-0.0426440\pi$
$774$	−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	$0.000422392\pi$
$787$			0.0744530i			0.00265396i	−0.999999	+	0.00132698i	$0.999578\pi$
$788$	−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	$-0.862925\pi$
$797$		−	23.5701i		−	0.834894i	0.908701	−	0.417447i	$-0.137075\pi$
$798$	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	$0.0946895\pi$
$811$			16.6943i			0.586216i	−0.956079	+	0.293108i	$0.905310\pi$
$812$	−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	$0.0376404\pi$
$821$			6.76073i			0.235951i	−0.993017	+	0.117975i	$0.962360\pi$
$822$	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	$-0.678664\pi$
$827$		−	48.6906i		−	1.69314i	0.532279	−	0.846569i	$-0.321336\pi$
$828$	−0.839855	−	1.81512i	−0.0291870	−	0.0630796i
$829$		−	26.7182i		−	0.927962i	−0.885845	−	0.463981i	$-0.846421\pi$
$829$		−	26.7182i		−	0.927962i	0.885845	−	0.463981i	$-0.153579\pi$
$830$	−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	$0.238901\pi$
$853$			39.8387i			1.36405i	−0.731328	+	0.682026i	$0.761099\pi$
$854$	−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	$0.00363276\pi$
$859$			0.668965i			0.0228248i	−0.999935	+	0.0114124i	$0.996367\pi$
$860$	−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	$0.133221\pi$
$877$			24.0713i			0.812829i	−0.913689	+	0.406415i	$0.866779\pi$
$878$	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	$0.117378\pi$
$883$			21.4220i			0.720908i	−0.932777	+	0.360454i	$0.882622\pi$
$884$	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	$0.268796\pi$
$907$			45.0304i			1.49521i	−0.664143	+	0.747605i	$0.731204\pi$
$908$	−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	$-0.931842\pi$
$941$		−	13.0367i		−	0.424985i	0.977163	−	0.212492i	$-0.0681581\pi$
$942$	−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	$-0.951927\pi$
$947$		−	9.25988i		−	0.300906i	0.988617	−	0.150453i	$-0.0480732\pi$
$948$	−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	$-0.799742\pi$
$971$		−	36.6727i		−	1.17688i	0.808539	−	0.588442i	$-0.200258\pi$
$972$	−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	$-0.834982\pi$
$997$		−	31.2917i		−	0.991018i	0.868603	−	0.495509i	$-0.165018\pi$
$998$	−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.277.5	✓	20
4.3	odd	2		2208.2.f.d.1105.7		20
8.3	odd	2		2208.2.f.d.1105.14		20
8.5	even	2	inner	552.2.f.d.277.6	yes	20

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