LMFDB - Embedded newform 2058.2.e.l.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2058,2,Mod(361,2058)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2058, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("2058.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2058 = 2 \cdot 3 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2058.e (of order $3$, degree $2$, not 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:	$16.4332127360$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.2
Root			$-0.623490 + 1.07992i$ of defining polynomial
Character	$\chi$	$=$	2058.667
Dual form			2058.2.e.l.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.277479 - 0.480608i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.277479 - 0.480608i) q^{10} +(-2.27144 - 3.93425i) q^{11} +(0.500000 - 0.866025i) q^{12} +5.96077 q^{13} +0.554958 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.59299 - 6.22324i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.15399 + 1.99877i) q^{19} -0.554958 q^{20} -4.54288 q^{22} +(1.90097 - 3.29257i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.34601 + 4.06341i) q^{25} +(2.98039 - 5.16218i) q^{26} -1.00000 q^{27} -10.1588 q^{29} +(0.277479 - 0.480608i) q^{30} +(-1.51357 - 2.62159i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.27144 - 3.93425i) q^{33} -7.18598 q^{34} +1.00000 q^{36} +(0.0108851 - 0.0188536i) q^{37} +(1.15399 + 1.99877i) q^{38} +(2.98039 + 5.16218i) q^{39} +(-0.277479 + 0.480608i) q^{40} +1.77479 q^{41} +4.93900 q^{43} +(-2.27144 + 3.93425i) q^{44} +(0.277479 + 0.480608i) q^{45} +(-1.90097 - 3.29257i) q^{46} +(3.47434 - 6.01774i) q^{47} -1.00000 q^{48} +4.69202 q^{50} +(3.59299 - 6.22324i) q^{51} +(-2.98039 - 5.16218i) q^{52} +(2.81551 + 4.87661i) q^{53} +(-0.500000 + 0.866025i) q^{54} -2.52111 q^{55} -2.30798 q^{57} +(-5.07942 + 8.79781i) q^{58} +(-6.64795 - 11.5146i) q^{59} +(-0.277479 - 0.480608i) q^{60} +(5.86174 - 10.1528i) q^{61} -3.02715 q^{62} +1.00000 q^{64} +(1.65399 - 2.86479i) q^{65} +(-2.27144 - 3.93425i) q^{66} +(-6.64795 - 11.5146i) q^{67} +(-3.59299 + 6.22324i) q^{68} +3.80194 q^{69} -0.423272 q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.16637 - 12.4125i) q^{73} +(-0.0108851 - 0.0188536i) q^{74} +(-2.34601 + 4.06341i) q^{75} +2.30798 q^{76} +5.96077 q^{78} +(-7.12229 + 12.3362i) q^{79} +(0.277479 + 0.480608i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.887395 - 1.53701i) q^{82} +2.41789 q^{83} -3.98792 q^{85} +(2.46950 - 4.27730i) q^{86} +(-5.07942 - 8.79781i) q^{87} +(2.27144 + 3.93425i) q^{88} +(-2.41939 + 4.19050i) q^{89} +0.554958 q^{90} -3.80194 q^{92} +(1.51357 - 2.62159i) q^{93} +(-3.47434 - 6.01774i) q^{94} +(0.640416 + 1.10923i) q^{95} +(-0.500000 + 0.866025i) q^{96} +11.9051 q^{97} +4.54288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{8} - 3 q^{9} - 2 q^{10} + 5 q^{11} + 3 q^{12} + 10 q^{13} + 4 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} - 12 q^{19} - 4 q^{20} + 10 q^{22} + 7 q^{23}+ \cdots - 10 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^8 - 3 * q^9 - 2 * q^10 + 5 * q^11 + 3 * q^12 + 10 * q^13 + 4 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 - 12 * q^19 - 4 * q^20 + 10 * q^22 + 7 * q^23 - 3 * q^24 + 9 * q^25 + 5 * q^26 - 6 * q^27 - 44 * q^29 + 2 * q^30 - 3 * q^31 + 3 * q^32 - 5 * q^33 - 14 * q^34 + 6 * q^36 - 3 * q^37 + 12 * q^38 + 5 * q^39 - 2 * q^40 + 14 * q^41 + 10 * q^43 + 5 * q^44 + 2 * q^45 - 7 * q^46 - 11 * q^47 - 6 * q^48 + 18 * q^50 + 7 * q^51 - 5 * q^52 + 2 * q^53 - 3 * q^54 + 16 * q^55 - 24 * q^57 - 22 * q^58 - 26 * q^59 - 2 * q^60 + 5 * q^61 - 6 * q^62 + 6 * q^64 + 15 * q^65 + 5 * q^66 - 26 * q^67 - 7 * q^68 + 14 * q^69 - 8 * q^71 + 3 * q^72 - q^73 + 3 * q^74 - 9 * q^75 + 24 * q^76 + 10 * q^78 + 3 * q^79 + 2 * q^80 - 3 * q^81 + 7 * q^82 + 26 * q^83 + 14 * q^85 + 5 * q^86 - 22 * q^87 - 5 * q^88 + 18 * q^89 + 4 * q^90 - 14 * q^92 + 3 * q^93 + 11 * q^94 + 15 * q^95 - 3 * q^96 + 20 * q^97 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2058\mathbb{Z}\right)^\times$.

$n$	$1373$	$1375$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.277479	−	0.480608i	0.124092	−	0.214934i	−0.797285	−	0.603603i	$-0.793731\pi$
$5$	0.277479	−	0.480608i	0.124092	−	0.214934i	0.921378	+	0.388668i	$0.127065\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.277479	−	0.480608i	−0.0877466	−	0.151982i
$11$	−2.27144	−	3.93425i	−0.684864	−	1.18622i	−0.973479	−	0.228775i	$-0.926528\pi$
$11$	−2.27144	−	3.93425i	−0.684864	−	1.18622i	0.288615	−	0.957445i	$-0.406805\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	5.96077			1.65322			0.826610	−	0.562775i	$-0.190266\pi$
$13$	5.96077			1.65322			0.826610	+	0.562775i	$0.190266\pi$
$14$		0			0
$15$	0.554958			0.143290
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.59299	−	6.22324i	−0.871428	−	1.50936i	−0.860520	−	0.509417i	$-0.829861\pi$
$17$	−3.59299	−	6.22324i	−0.871428	−	1.50936i	−0.0109086	−	0.999940i	$-0.503472\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.15399	+	1.99877i	−0.264743	+	0.458549i	−0.967496	−	0.252885i	$-0.918621\pi$
$19$	−1.15399	+	1.99877i	−0.264743	+	0.458549i	0.702753	+	0.711434i	$0.251954\pi$
$20$	−0.554958			−0.124092
$21$		0			0
$22$	−4.54288			−0.968545
$23$	1.90097	−	3.29257i	0.396379	−	0.686549i	−0.596897	−	0.802318i	$-0.703600\pi$
$23$	1.90097	−	3.29257i	0.396379	−	0.686549i	0.993276	+	0.115769i	$0.0369332\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.34601	+	4.06341i	0.469202	+	0.812682i
$26$	2.98039	−	5.16218i	0.584502	−	1.01239i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−10.1588			−1.88645			−0.943224	−	0.332157i	$-0.892224\pi$
$29$	−10.1588			−1.88645			−0.943224	+	0.332157i	$0.892224\pi$
$30$	0.277479	−	0.480608i	0.0506605	−	0.0877466i
$31$	−1.51357	−	2.62159i	−0.271846	−	0.470851i	0.697489	−	0.716596i	$-0.254301\pi$
$31$	−1.51357	−	2.62159i	−0.271846	−	0.470851i	−0.969335	+	0.245745i	$0.920967\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.27144	−	3.93425i	0.395407	−	0.684864i
$34$	−7.18598			−1.23239
$35$		0			0
$36$	1.00000			0.166667
$37$	0.0108851	−	0.0188536i	0.00178950	−	0.00309951i	−0.865129	−	0.501549i	$-0.832764\pi$
$37$	0.0108851	−	0.0188536i	0.00178950	−	0.00309951i	0.866919	+	0.498449i	$0.166097\pi$
$38$	1.15399	+	1.99877i	0.187202	+	0.324243i
$39$	2.98039	+	5.16218i	0.477244	+	0.826610i
$40$	−0.277479	+	0.480608i	−0.0438733	+	0.0759908i
$41$	1.77479			0.277176			0.138588	−	0.990350i	$-0.455744\pi$
$41$	1.77479			0.277176			0.138588	+	0.990350i	$0.455744\pi$
$42$		0			0
$43$	4.93900			0.753191			0.376595	−	0.926378i	$-0.377095\pi$
$43$	4.93900			0.753191			0.376595	+	0.926378i	$0.377095\pi$
$44$	−2.27144	+	3.93425i	−0.342432	+	0.593110i
$45$	0.277479	+	0.480608i	0.0413641	+	0.0716448i
$46$	−1.90097	−	3.29257i	−0.280283	−	0.485464i
$47$	3.47434	−	6.01774i	0.506785	−	0.877778i	−0.493184	−	0.869925i	$-0.664167\pi$
$47$	3.47434	−	6.01774i	0.506785	−	0.877778i	0.999969	−	0.00785278i	$-0.00249964\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	4.69202			0.663552
$51$	3.59299	−	6.22324i	0.503119	−	0.871428i
$52$	−2.98039	−	5.16218i	−0.413305	−	0.715865i
$53$	2.81551	+	4.87661i	0.386740	+	0.669854i	0.992009	−	0.126167i	$-0.0402677\pi$
$53$	2.81551	+	4.87661i	0.386740	+	0.669854i	−0.605269	+	0.796021i	$0.706934\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−2.52111			−0.339946
$56$		0			0
$57$	−2.30798			−0.305699
$58$	−5.07942	+	8.79781i	−0.666960	+	1.15521i
$59$	−6.64795	−	11.5146i	−0.865489	−	1.49907i	−0.866561	−	0.499072i	$-0.833674\pi$
$59$	−6.64795	−	11.5146i	−0.865489	−	1.49907i	0.00107147	−	0.999999i	$-0.499659\pi$
$60$	−0.277479	−	0.480608i	−0.0358224	−	0.0620462i
$61$	5.86174	−	10.1528i	0.750519	−	1.29994i	−0.197053	−	0.980393i	$-0.563137\pi$
$61$	5.86174	−	10.1528i	0.750519	−	1.29994i	0.947571	−	0.319544i	$-0.103530\pi$
$62$	−3.02715			−0.384448
$63$		0			0
$64$	1.00000			0.125000
$65$	1.65399	−	2.86479i	0.205152	−	0.355334i
$66$	−2.27144	−	3.93425i	−0.279595	−	0.484272i
$67$	−6.64795	−	11.5146i	−0.812176	−	1.40673i	−0.911338	−	0.411659i	$-0.864949\pi$
$67$	−6.64795	−	11.5146i	−0.812176	−	1.40673i	0.0991618	−	0.995071i	$-0.468384\pi$
$68$	−3.59299	+	6.22324i	−0.435714	+	0.754679i
$69$	3.80194			0.457700
$70$		0			0
$71$	−0.423272			−0.0502331			−0.0251165	−	0.999685i	$-0.507996\pi$
$71$	−0.423272			−0.0502331			−0.0251165	+	0.999685i	$0.507996\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−7.16637	−	12.4125i	−0.838760	−	1.45277i	−0.890932	−	0.454136i	$-0.849948\pi$
$73$	−7.16637	−	12.4125i	−0.838760	−	1.45277i	0.0521724	−	0.998638i	$-0.483385\pi$
$74$	−0.0108851	−	0.0188536i	−0.00126537	−	0.00219169i
$75$	−2.34601	+	4.06341i	−0.270894	+	0.469202i
$76$	2.30798			0.264743
$77$		0			0
$78$	5.96077			0.674924
$79$	−7.12229	+	12.3362i	−0.801321	+	1.38793i	0.117427	+	0.993082i	$0.462536\pi$
$79$	−7.12229	+	12.3362i	−0.801321	+	1.38793i	−0.918747	+	0.394846i	$0.870798\pi$
$80$	0.277479	+	0.480608i	0.0310231	+	0.0537336i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.887395	−	1.53701i	0.0979964	−	0.169735i
$83$	2.41789			0.265398			0.132699	−	0.991156i	$-0.457636\pi$
$83$	2.41789			0.265398			0.132699	+	0.991156i	$0.457636\pi$
$84$		0			0
$85$	−3.98792			−0.432550
$86$	2.46950	−	4.27730i	0.266293	−	0.461233i
$87$	−5.07942	−	8.79781i	−0.544571	−	0.943224i
$88$	2.27144	+	3.93425i	0.242136	+	0.419392i
$89$	−2.41939	+	4.19050i	−0.256454	+	0.444192i	−0.965290	−	0.261182i	$-0.915888\pi$
$89$	−2.41939	+	4.19050i	−0.256454	+	0.444192i	0.708835	+	0.705374i	$0.249221\pi$
$90$	0.554958			0.0584977
$91$		0			0
$92$	−3.80194			−0.396379
$93$	1.51357	−	2.62159i	0.156950	−	0.271846i
$94$	−3.47434	−	6.01774i	−0.358351	−	0.620683i
$95$	0.640416	+	1.10923i	0.0657053	+	0.113805i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	11.9051			1.20878			0.604392	−	0.796687i	$-0.293416\pi$
$97$	11.9051			1.20878			0.604392	+	0.796687i	$0.293416\pi$
$98$		0			0
$99$	4.54288			0.456576
$100$	2.34601	−	4.06341i	0.234601	−	0.406341i
$101$	8.30947	+	14.3924i	0.826823	+	1.43210i	0.900518	+	0.434819i	$0.143188\pi$
$101$	8.30947	+	14.3924i	0.826823	+	1.43210i	−0.0736947	+	0.997281i	$0.523479\pi$
$102$	−3.59299	−	6.22324i	−0.355759	−	0.616193i
$103$	6.05376	−	10.4854i	0.596495	−	1.03316i	−0.396839	−	0.917888i	$-0.629893\pi$
$103$	6.05376	−	10.4854i	0.596495	−	1.03316i	0.993334	−	0.115271i	$-0.0367737\pi$
$104$	−5.96077			−0.584502
$105$		0			0
$106$	5.63102			0.546933
$107$	7.52326	−	13.0307i	0.727301	−	1.25972i	−0.230719	−	0.973021i	$-0.574108\pi$
$107$	7.52326	−	13.0307i	0.727301	−	1.25972i	0.958020	−	0.286702i	$-0.0925590\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	0.260553	+	0.451291i	0.0249565	+	0.0432259i	0.878234	−	0.478231i	$-0.158722\pi$
$109$	0.260553	+	0.451291i	0.0249565	+	0.0432259i	−0.853277	+	0.521457i	$0.825389\pi$
$110$	−1.26055	+	2.18334i	−0.120189	+	0.208173i
$111$	0.0217703			0.00206634
$112$		0			0
$113$	−5.41119			−0.509042			−0.254521	−	0.967067i	$-0.581918\pi$
$113$	−5.41119			−0.509042			−0.254521	+	0.967067i	$0.581918\pi$
$114$	−1.15399	+	1.99877i	−0.108081	+	0.187202i
$115$	−1.05496	−	1.82724i	−0.0983754	−	0.170391i
$116$	5.07942	+	8.79781i	0.471612	+	0.816856i
$117$	−2.98039	+	5.16218i	−0.275537	+	0.477244i
$118$	−13.2959			−1.22399
$119$		0			0
$120$	−0.554958			−0.0506605
$121$	−4.81886	+	8.34652i	−0.438079	+	0.758774i
$122$	−5.86174	−	10.1528i	−0.530697	−	0.919194i
$123$	0.887395	+	1.53701i	0.0800137	+	0.138588i
$124$	−1.51357	+	2.62159i	−0.135923	+	0.235425i
$125$	5.37867			0.481083
$126$		0			0
$127$	9.80731			0.870258			0.435129	−	0.900368i	$-0.356703\pi$
$127$	9.80731			0.870258			0.435129	+	0.900368i	$0.356703\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.46950	+	4.27730i	0.217427	+	0.376595i
$130$	−1.65399	−	2.86479i	−0.145064	−	0.251259i
$131$	−0.0941868	+	0.163136i	−0.00822914	+	0.0142533i	−0.870111	−	0.492856i	$-0.835953\pi$
$131$	−0.0941868	+	0.163136i	−0.00822914	+	0.0142533i	0.861882	+	0.507110i	$0.169286\pi$
$132$	−4.54288			−0.395407
$133$		0			0
$134$	−13.2959			−1.14859
$135$	−0.277479	+	0.480608i	−0.0238816	+	0.0413641i
$136$	3.59299	+	6.22324i	0.308096	+	0.533639i
$137$	−1.38135	−	2.39258i	−0.118017	−	0.204412i	0.800965	−	0.598712i	$-0.204320\pi$
$137$	−1.38135	−	2.39258i	−0.118017	−	0.204412i	−0.918982	+	0.394300i	$0.870987\pi$
$138$	1.90097	−	3.29257i	0.161821	−	0.280283i
$139$	3.45712			0.293229			0.146615	−	0.989194i	$-0.453162\pi$
$139$	3.45712			0.293229			0.146615	+	0.989194i	$0.453162\pi$
$140$		0			0
$141$	6.94869			0.585185
$142$	−0.211636	+	0.366564i	−0.0177601	+	0.0307614i
$143$	−13.5395	−	23.4511i	−1.13223	−	1.96108i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.81886	+	4.88242i	−0.234094	+	0.405463i
$146$	−14.3327			−1.18619
$147$		0			0
$148$	−0.0217703			−0.00178950
$149$	−4.87316	+	8.44056i	−0.399225	+	0.691477i	−0.993630	−	0.112688i	$-0.964054\pi$
$149$	−4.87316	+	8.44056i	−0.399225	+	0.691477i	0.594406	+	0.804165i	$0.297387\pi$
$150$	2.34601	+	4.06341i	0.191551	+	0.331776i
$151$	1.90850	+	3.30562i	0.155312	+	0.269008i	0.933172	−	0.359429i	$-0.117028\pi$
$151$	1.90850	+	3.30562i	0.155312	+	0.269008i	−0.777861	+	0.628437i	$0.783695\pi$
$152$	1.15399	−	1.99877i	0.0936009	−	0.162121i
$153$	7.18598			0.580952
$154$		0			0
$155$	−1.67994			−0.134936
$156$	2.98039	−	5.16218i	0.238622	−	0.413305i
$157$	−1.56369	−	2.70839i	−0.124796	−	0.216153i	0.796857	−	0.604168i	$-0.206494\pi$
$157$	−1.56369	−	2.70839i	−0.124796	−	0.216153i	−0.921653	+	0.388015i	$0.873161\pi$
$158$	7.12229	+	12.3362i	0.566619	+	0.981413i
$159$	−2.81551	+	4.87661i	−0.223285	+	0.386740i
$160$	0.554958			0.0438733
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−6.64526	+	11.5099i	−0.520497	+	0.901527i	0.479219	+	0.877695i	$0.340920\pi$
$163$	−6.64526	+	11.5099i	−0.520497	+	0.901527i	−0.999716	+	0.0238318i	$0.992413\pi$
$164$	−0.887395	−	1.53701i	−0.0692939	−	0.120021i
$165$	−1.26055	−	2.18334i	−0.0981339	−	0.169973i
$166$	1.20895	−	2.09396i	0.0938325	−	0.162523i
$167$	3.17629			0.245789			0.122894	−	0.992420i	$-0.460782\pi$
$167$	3.17629			0.245789			0.122894	+	0.992420i	$0.460782\pi$
$168$		0			0
$169$	22.5308			1.73314
$170$	−1.99396	+	3.45364i	−0.152930	+	0.264882i
$171$	−1.15399	−	1.99877i	−0.0882478	−	0.152850i
$172$	−2.46950	−	4.27730i	−0.188298	−	0.326141i
$173$	−6.97554	+	12.0820i	−0.530341	+	0.918577i	0.469033	+	0.883181i	$0.344603\pi$
$173$	−6.97554	+	12.0820i	−0.530341	+	0.918577i	−0.999373	+	0.0353961i	$0.988731\pi$
$174$	−10.1588			−0.770139
$175$		0			0
$176$	4.54288			0.342432
$177$	6.64795	−	11.5146i	0.499690	−	0.865489i
$178$	2.41939	+	4.19050i	0.181341	+	0.314091i
$179$	1.67845	+	2.90716i	0.125453	+	0.217291i	0.921910	−	0.387404i	$-0.126628\pi$
$179$	1.67845	+	2.90716i	0.125453	+	0.217291i	−0.796457	+	0.604695i	$0.793295\pi$
$180$	0.277479	−	0.480608i	0.0206821	−	0.0358224i
$181$	−23.4306			−1.74158			−0.870790	−	0.491655i	$-0.836392\pi$
$181$	−23.4306			−1.74158			−0.870790	+	0.491655i	$0.836392\pi$
$182$		0			0
$183$	11.7235			0.866625
$184$	−1.90097	+	3.29257i	−0.140141	+	0.242732i
$185$	−0.00604079	−	0.0104630i	−0.000444128	−	0.000769252i
$186$	−1.51357	−	2.62159i	−0.110981	−	0.192224i
$187$	−16.3225	+	28.2714i	−1.19362	+	2.06741i
$188$	−6.94869			−0.506785
$189$		0			0
$190$	1.28083			0.0929213
$191$	−1.85958	+	3.22089i	−0.134555	+	0.233056i	−0.925427	−	0.378925i	$-0.876294\pi$
$191$	−1.85958	+	3.22089i	−0.134555	+	0.233056i	0.790873	+	0.611981i	$0.209627\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	6.38016	+	11.0508i	0.459254	+	0.795451i	0.998922	−	0.0464271i	$-0.0147835\pi$
$193$	6.38016	+	11.0508i	0.459254	+	0.795451i	−0.539668	+	0.841878i	$0.681450\pi$
$194$	5.95257	−	10.3102i	0.427370	−	0.740226i
$195$	3.30798			0.236889
$196$		0			0
$197$	10.8901			0.775886			0.387943	−	0.921683i	$-0.373186\pi$
$197$	10.8901			0.775886			0.387943	+	0.921683i	$0.373186\pi$
$198$	2.27144	−	3.93425i	0.161424	−	0.279595i
$199$	0.420583	+	0.728471i	0.0298144	+	0.0516400i	0.880548	−	0.473958i	$-0.157175\pi$
$199$	0.420583	+	0.728471i	0.0298144	+	0.0516400i	−0.850733	+	0.525598i	$0.823842\pi$
$200$	−2.34601	−	4.06341i	−0.165888	−	0.287326i
$201$	6.64795	−	11.5146i	0.468910	−	0.812176i
$202$	16.6189			1.16930
$203$		0			0
$204$	−7.18598			−0.503119
$205$	0.492467	−	0.852978i	0.0343954	−	0.0595746i
$206$	−6.05376	−	10.4854i	−0.421786	−	0.730554i
$207$	1.90097	+	3.29257i	0.132126	+	0.228850i
$208$	−2.98039	+	5.16218i	−0.206653	+	0.357933i
$209$	10.4849			0.725253
$210$		0			0
$211$	−14.6571			−1.00904			−0.504518	−	0.863401i	$-0.668330\pi$
$211$	−14.6571			−1.00904			−0.504518	+	0.863401i	$0.668330\pi$
$212$	2.81551	−	4.87661i	0.193370	−	0.334927i
$213$	−0.211636	−	0.366564i	−0.0145010	−	0.0251165i
$214$	−7.52326	−	13.0307i	−0.514280	−	0.890758i
$215$	1.37047	−	2.37372i	0.0934652	−	0.161887i
$216$	1.00000			0.0680414
$217$		0			0
$218$	0.521106			0.0352938
$219$	7.16637	−	12.4125i	0.484258	−	0.838760i
$220$	1.26055	+	2.18334i	0.0849865	+	0.147201i
$221$	−21.4170	−	37.0953i	−1.44066	−	2.49530i
$222$	0.0108851	−	0.0188536i	0.000730562	−	0.00126537i
$223$	21.9530			1.47008			0.735041	−	0.678023i	$-0.237163\pi$
$223$	21.9530			1.47008			0.735041	+	0.678023i	$0.237163\pi$
$224$		0			0
$225$	−4.69202			−0.312801
$226$	−2.70560	+	4.68623i	−0.179974	+	0.311723i
$227$	3.47434	+	6.01774i	0.230600	+	0.399412i	0.957985	−	0.286818i	$-0.0925977\pi$
$227$	3.47434	+	6.01774i	0.230600	+	0.399412i	−0.727385	+	0.686230i	$0.759264\pi$
$228$	1.15399	+	1.99877i	0.0764248	+	0.132372i
$229$	−2.86443	+	4.96134i	−0.189287	+	0.327854i	−0.945013	−	0.327034i	$-0.893951\pi$
$229$	−2.86443	+	4.96134i	−0.189287	+	0.327854i	0.755726	+	0.654888i	$0.227284\pi$
$230$	−2.10992			−0.139124
$231$		0			0
$232$	10.1588			0.666960
$233$	7.40366	−	12.8235i	0.485030	−	0.840096i	−0.514822	−	0.857297i	$-0.672142\pi$
$233$	7.40366	−	12.8235i	0.485030	−	0.840096i	0.999852	+	0.0172008i	$0.00547545\pi$
$234$	2.98039	+	5.16218i	0.194834	+	0.337462i
$235$	−1.92812	−	3.33959i	−0.125776	−	0.217851i
$236$	−6.64795	+	11.5146i	−0.432745	+	0.749536i
$237$	−14.2446			−0.925285
$238$		0			0
$239$	−11.9444			−0.772618			−0.386309	−	0.922370i	$-0.626250\pi$
$239$	−11.9444			−0.772618			−0.386309	+	0.922370i	$0.626250\pi$
$240$	−0.277479	+	0.480608i	−0.0179112	+	0.0310231i
$241$	0.312823	+	0.541825i	0.0201507	+	0.0349020i	0.875925	−	0.482447i	$-0.160252\pi$
$241$	0.312823	+	0.541825i	0.0201507	+	0.0349020i	−0.855774	+	0.517349i	$0.826919\pi$
$242$	4.81886	+	8.34652i	0.309768	+	0.536534i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−11.7235			−0.750519
$245$		0			0
$246$	1.77479			0.113157
$247$	−6.87867	+	11.9142i	−0.437679	+	0.758082i
$248$	1.51357	+	2.62159i	0.0961120	+	0.166471i
$249$	1.20895	+	2.09396i	0.0766139	+	0.132699i
$250$	2.68933	−	4.65806i	0.170088	−	0.294602i
$251$	23.9608			1.51239			0.756195	−	0.654346i	$-0.227056\pi$
$251$	23.9608			1.51239			0.756195	+	0.654346i	$0.227056\pi$
$252$		0			0
$253$	−17.2717			−1.08586
$254$	4.90366	−	8.49338i	0.307683	−	0.532922i
$255$	−1.99396	−	3.45364i	−0.124867	−	0.216275i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.77963	+	8.27857i	−0.298145	+	0.516403i	−0.975712	−	0.219059i	$-0.929701\pi$
$257$	−4.77963	+	8.27857i	−0.298145	+	0.516403i	0.677566	+	0.735462i	$0.263035\pi$
$258$	4.93900			0.307489
$259$		0			0
$260$	−3.30798			−0.205152
$261$	5.07942	−	8.79781i	0.314408	−	0.544571i
$262$	0.0941868	+	0.163136i	0.00581888	+	0.0100786i
$263$	−3.68329	−	6.37965i	−0.227122	−	0.393386i	0.729832	−	0.683626i	$-0.239598\pi$
$263$	−3.68329	−	6.37965i	−0.227122	−	0.393386i	−0.956954	+	0.290240i	$0.906265\pi$
$264$	−2.27144	+	3.93425i	−0.139797	+	0.242136i
$265$	3.12498			0.191966
$266$		0			0
$267$	−4.83877			−0.296128
$268$	−6.64795	+	11.5146i	−0.406088	+	0.703365i
$269$	8.03199	+	13.9118i	0.489719	+	0.848218i	0.999930	−	0.0118309i	$-0.00376598\pi$
$269$	8.03199	+	13.9118i	0.489719	+	0.848218i	−0.510211	+	0.860049i	$0.670433\pi$
$270$	0.277479	+	0.480608i	0.0168868	+	0.0292489i
$271$	1.25518	−	2.17403i	0.0762465	−	0.132063i	−0.825381	−	0.564576i	$-0.809040\pi$
$271$	1.25518	−	2.17403i	0.0762465	−	0.132063i	0.901628	+	0.432513i	$0.142373\pi$
$272$	7.18598			0.435714
$273$		0			0
$274$	−2.76271			−0.166901
$275$	10.6576	−	18.4596i	0.642680	−	1.11315i
$276$	−1.90097	−	3.29257i	−0.114425	−	0.198190i
$277$	2.95862	+	5.12447i	0.177766	+	0.307900i	0.941115	−	0.338087i	$-0.109780\pi$
$277$	2.95862	+	5.12447i	0.177766	+	0.307900i	−0.763349	+	0.645986i	$0.776446\pi$
$278$	1.72856	−	2.99396i	0.103672	−	0.179566i
$279$	3.02715			0.181231
$280$		0			0
$281$	−19.7409			−1.17765			−0.588823	−	0.808262i	$-0.700408\pi$
$281$	−19.7409			−1.17765			−0.588823	+	0.808262i	$0.700408\pi$
$282$	3.47434	−	6.01774i	0.206894	−	0.358351i
$283$	−3.61596	−	6.26302i	−0.214946	−	0.372298i	0.738310	−	0.674462i	$-0.235624\pi$
$283$	−3.61596	−	6.26302i	−0.214946	−	0.372298i	−0.953256	+	0.302164i	$0.902291\pi$
$284$	0.211636	+	0.366564i	0.0125583	+	0.0217516i
$285$	−0.640416	+	1.10923i	−0.0379350	+	0.0657053i
$286$	−27.0790			−1.60122
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−17.3192	+	29.9977i	−1.01877	+	1.76457i
$290$	2.81886	+	4.88242i	0.165529	+	0.286705i
$291$	5.95257	+	10.3102i	0.348946	+	0.604392i
$292$	−7.16637	+	12.4125i	−0.419380	+	0.726387i
$293$	24.1250			1.40940			0.704698	−	0.709507i	$-0.251082\pi$
$293$	24.1250			1.40940			0.704698	+	0.709507i	$0.251082\pi$
$294$		0			0
$295$	−7.37867			−0.429603
$296$	−0.0108851	+	0.0188536i	−0.000632685	+	0.00109584i
$297$	2.27144	+	3.93425i	0.131802	+	0.228288i
$298$	4.87316	+	8.44056i	0.282294	+	0.488948i
$299$	11.3312	−	19.6263i	0.655303	−	1.13502i
$300$	4.69202			0.270894
$301$		0			0
$302$	3.81700			0.219644
$303$	−8.30947	+	14.3924i	−0.477367	+	0.826823i
$304$	−1.15399	−	1.99877i	−0.0661858	−	0.114637i
$305$	−3.25302	−	5.63440i	−0.186267	−	0.322625i
$306$	3.59299	−	6.22324i	0.205398	−	0.355759i
$307$	26.5730			1.51660			0.758301	−	0.651905i	$-0.226030\pi$
$307$	26.5730			1.51660			0.758301	+	0.651905i	$0.226030\pi$
$308$		0			0
$309$	12.1075			0.688773
$310$	−0.839970	+	1.45487i	−0.0477071	+	0.0826311i
$311$	12.5625	+	21.7589i	0.712354	+	1.23383i	0.963971	+	0.266006i	$0.0857040\pi$
$311$	12.5625	+	21.7589i	0.712354	+	1.23383i	−0.251618	+	0.967827i	$0.580963\pi$
$312$	−2.98039	−	5.16218i	−0.168731	−	0.292251i
$313$	−3.59515	+	6.22698i	−0.203210	+	0.351969i	−0.949561	−	0.313583i	$-0.898471\pi$
$313$	−3.59515	+	6.22698i	−0.203210	+	0.351969i	0.746351	+	0.665552i	$0.231804\pi$
$314$	−3.12737			−0.176488
$315$		0			0
$316$	14.2446			0.801321
$317$	−3.02715	+	5.24317i	−0.170022	+	0.294486i	−0.938427	−	0.345477i	$-0.887717\pi$
$317$	−3.02715	+	5.24317i	−0.170022	+	0.294486i	0.768406	+	0.639963i	$0.221050\pi$
$318$	2.81551	+	4.87661i	0.157886	+	0.273467i
$319$	23.0752	+	39.9674i	1.29196	+	2.23774i
$320$	0.277479	−	0.480608i	0.0155116	−	0.0268668i
$321$	15.0465			0.839815
$322$		0			0
$323$	16.5851			0.922819
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	13.9840	+	24.2211i	0.775695	+	1.34354i
$326$	6.64526	+	11.5099i	0.368047	+	0.637476i
$327$	−0.260553	+	0.451291i	−0.0144086	+	0.0249565i
$328$	−1.77479			−0.0979964
$329$		0			0
$330$	−2.52111			−0.138782
$331$	−1.56853	+	2.71678i	−0.0862143	+	0.149328i	−0.905908	−	0.423475i	$-0.860810\pi$
$331$	−1.56853	+	2.71678i	−0.0862143	+	0.149328i	0.819694	+	0.572802i	$0.194144\pi$
$332$	−1.20895	−	2.09396i	−0.0663496	−	0.114921i
$333$	0.0108851	+	0.0188536i	0.000596502	+	0.00103317i
$334$	1.58815	−	2.75075i	0.0868995	−	0.150514i
$335$	−7.37867			−0.403140
$336$		0			0
$337$	−15.8649			−0.864214			−0.432107	−	0.901822i	$-0.642230\pi$
$337$	−15.8649			−0.864214			−0.432107	+	0.901822i	$0.642230\pi$
$338$	11.2654	−	19.5122i	0.612757	−	1.06133i
$339$	−2.70560	−	4.68623i	−0.146948	−	0.254521i
$340$	1.99396	+	3.45364i	0.108138	+	0.187300i
$341$	−6.87598	+	11.9095i	−0.372355	+	0.644938i
$342$	−2.30798			−0.124801
$343$		0			0
$344$	−4.93900			−0.266293
$345$	1.05496	−	1.82724i	0.0567970	−	0.0983754i
$346$	6.97554	+	12.0820i	0.375007	+	0.649532i
$347$	−5.97703	−	10.3525i	−0.320864	−	0.555753i	0.659803	−	0.751439i	$-0.270640\pi$
$347$	−5.97703	−	10.3525i	−0.320864	−	0.555753i	−0.980667	+	0.195686i	$0.937307\pi$
$348$	−5.07942	+	8.79781i	−0.272285	+	0.471612i
$349$	12.3381			0.660444			0.330222	−	0.943903i	$-0.392876\pi$
$349$	12.3381			0.660444			0.330222	+	0.943903i	$0.392876\pi$
$350$		0			0
$351$	−5.96077			−0.318162
$352$	2.27144	−	3.93425i	0.121068	−	0.209696i
$353$	7.88500	+	13.6572i	0.419676	+	0.726901i	0.995907	−	0.0903865i	$-0.0288103\pi$
$353$	7.88500	+	13.6572i	0.419676	+	0.726901i	−0.576230	+	0.817287i	$0.695477\pi$
$354$	−6.64795	−	11.5146i	−0.353334	−	0.611993i
$355$	−0.117449	+	0.203428i	−0.00623355	+	0.0107968i
$356$	4.83877			0.256454
$357$		0			0
$358$	3.35690			0.177417
$359$	1.57942	−	2.73563i	0.0833584	−	0.144381i	−0.821332	−	0.570450i	$-0.806769\pi$
$359$	1.57942	−	2.73563i	0.0833584	−	0.144381i	0.904691	+	0.426069i	$0.140102\pi$
$360$	−0.277479	−	0.480608i	−0.0146244	−	0.0253303i
$361$	6.83662	+	11.8414i	0.359822	+	0.623230i
$362$	−11.7153	+	20.2915i	−0.615742	+	1.06650i
$363$	−9.63773			−0.505849
$364$		0			0
$365$	−7.95407			−0.416335
$366$	5.86174	−	10.1528i	0.306398	−	0.530697i
$367$	−4.71110	−	8.15987i	−0.245918	−	0.425942i	0.716472	−	0.697616i	$-0.245756\pi$
$367$	−4.71110	−	8.15987i	−0.245918	−	0.425942i	−0.962389	+	0.271674i	$0.912423\pi$
$368$	1.90097	+	3.29257i	0.0990949	+	0.171637i
$369$	−0.887395	+	1.53701i	−0.0461960	+	0.0800137i
$370$	−0.0120816			−0.000628092
$371$		0			0
$372$	−3.02715			−0.156950
$373$	−18.7005	+	32.3902i	−0.968276	+	1.67710i	−0.267732	+	0.963493i	$0.586274\pi$
$373$	−18.7005	+	32.3902i	−0.968276	+	1.67710i	−0.700543	+	0.713610i	$0.747059\pi$
$374$	16.3225	+	28.2714i	0.844017	+	1.46188i
$375$	2.68933	+	4.65806i	0.138877	+	0.240541i
$376$	−3.47434	+	6.01774i	−0.179176	+	0.310341i
$377$	−60.5545			−3.11871
$378$		0			0
$379$	24.5851			1.26285			0.631426	−	0.775436i	$-0.282470\pi$
$379$	24.5851			1.26285			0.631426	+	0.775436i	$0.282470\pi$
$380$	0.640416	−	1.10923i	0.0328526	−	0.0569024i
$381$	4.90366	+	8.49338i	0.251222	+	0.435129i
$382$	1.85958	+	3.22089i	0.0951446	+	0.164795i
$383$	−7.15495	+	12.3927i	−0.365601	+	0.633239i	−0.988872	−	0.148766i	$-0.952470\pi$
$383$	−7.15495	+	12.3927i	−0.365601	+	0.633239i	0.623272	+	0.782005i	$0.285803\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	12.7603			0.649483
$387$	−2.46950	+	4.27730i	−0.125532	+	0.217427i
$388$	−5.95257	−	10.3102i	−0.302196	−	0.523419i
$389$	−2.62833	−	4.55241i	−0.133262	−	0.230816i	0.791670	−	0.610949i	$-0.209212\pi$
$389$	−2.62833	−	4.55241i	−0.133262	−	0.230816i	−0.924932	+	0.380132i	$0.875878\pi$
$390$	1.65399	−	2.86479i	0.0837530	−	0.145064i
$391$	−27.3207			−1.38166
$392$		0			0
$393$	−0.188374			−0.00950219
$394$	5.44504	−	9.43109i	0.274317	−	0.475131i
$395$	3.95257	+	6.84606i	0.198876	+	0.344463i
$396$	−2.27144	−	3.93425i	−0.114144	−	0.197703i
$397$	16.0211	−	27.7494i	0.804076	−	1.39270i	−0.112837	−	0.993614i	$-0.535994\pi$
$397$	16.0211	−	27.7494i	0.804076	−	1.39270i	0.916913	−	0.399087i	$-0.130673\pi$
$398$	0.841166			0.0421639
$399$		0			0
$400$	−4.69202			−0.234601
$401$	−8.08211	+	13.9986i	−0.403601	+	0.699058i	−0.994158	−	0.107939i	$-0.965575\pi$
$401$	−8.08211	+	13.9986i	−0.403601	+	0.699058i	0.590556	+	0.806996i	$0.298908\pi$
$402$	−6.64795	−	11.5146i	−0.331570	−	0.574295i
$403$	−9.02207	−	15.6267i	−0.449421	−	0.778420i
$404$	8.30947	−	14.3924i	0.413412	−	0.716050i
$405$	−0.554958			−0.0275761
$406$		0			0
$407$	−0.0988996			−0.00490227
$408$	−3.59299	+	6.22324i	−0.177880	+	0.308096i
$409$	17.0097	+	29.4616i	0.841075	+	1.45678i	0.888987	+	0.457933i	$0.151410\pi$
$409$	17.0097	+	29.4616i	0.841075	+	1.45678i	−0.0479117	+	0.998852i	$0.515257\pi$
$410$	−0.492467	−	0.852978i	−0.0243212	−	0.0421256i
$411$	1.38135	−	2.39258i	0.0681372	−	0.118017i
$412$	−12.1075			−0.596495
$413$		0			0
$414$	3.80194			0.186855
$415$	0.670915	−	1.16206i	0.0329339	−	0.0570432i
$416$	2.98039	+	5.16218i	0.146125	+	0.253097i
$417$	1.72856	+	2.99396i	0.0846480	+	0.146615i
$418$	5.24243	−	9.08016i	0.256416	−	0.444125i
$419$	−15.8616			−0.774890			−0.387445	−	0.921893i	$-0.626642\pi$
$419$	−15.8616			−0.774890			−0.387445	+	0.921893i	$0.626642\pi$
$420$		0			0
$421$	−24.3696			−1.18770			−0.593850	−	0.804576i	$-0.702393\pi$
$421$	−24.3696			−1.18770			−0.593850	+	0.804576i	$0.702393\pi$
$422$	−7.32855	+	12.6934i	−0.356748	+	0.617906i
$423$	3.47434	+	6.01774i	0.168928	+	0.292593i
$424$	−2.81551	−	4.87661i	−0.136733	−	0.236829i
$425$	16.8584	−	29.1996i	0.817752	−	1.41639i
$426$	−0.423272			−0.0205076
$427$		0			0
$428$	−15.0465			−0.727301
$429$	13.5395	−	23.4511i	0.653694	−	1.13223i
$430$	−1.37047	−	2.37372i	−0.0660899	−	0.114471i
$431$	3.00216	+	5.19989i	0.144609	+	0.250470i	0.929227	−	0.369510i	$-0.120474\pi$
$431$	3.00216	+	5.19989i	0.144609	+	0.250470i	−0.784618	+	0.619979i	$0.787141\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	14.4233			0.693138			0.346569	−	0.938024i	$-0.387347\pi$
$433$	14.4233			0.693138			0.346569	+	0.938024i	$0.387347\pi$
$434$		0			0
$435$	−5.63773			−0.270308
$436$	0.260553	−	0.451291i	0.0124782	−	0.0216129i
$437$	4.38740	+	7.59919i	0.209878	+	0.363519i
$438$	−7.16637	−	12.4125i	−0.342422	−	0.593093i
$439$	9.06398	−	15.6993i	0.432600	−	0.749286i	−0.564496	−	0.825436i	$-0.690929\pi$
$439$	9.06398	−	15.6993i	0.432600	−	0.749286i	0.997096	+	0.0761501i	$0.0242628\pi$
$440$	2.52111			0.120189
$441$		0			0
$442$	−42.8340			−2.03741
$443$	9.41066	−	16.2997i	0.447114	−	0.774424i	−0.551083	−	0.834450i	$-0.685785\pi$
$443$	9.41066	−	16.2997i	0.447114	−	0.774424i	0.998197	+	0.0600266i	$0.0191186\pi$
$444$	−0.0108851	−	0.0188536i	−0.000516586	−	0.000894752i
$445$	1.34266	+	2.32555i	0.0636481	+	0.110242i
$446$	10.9765	−	19.0119i	0.519752	−	0.900238i
$447$	−9.74632			−0.460985
$448$		0			0
$449$	9.24027			0.436076			0.218038	−	0.975940i	$-0.430034\pi$
$449$	9.24027			0.436076			0.218038	+	0.975940i	$0.430034\pi$
$450$	−2.34601	+	4.06341i	−0.110592	+	0.191551i
$451$	−4.03133	−	6.98246i	−0.189828	−	0.328791i
$452$	2.70560	+	4.68623i	0.127260	+	0.220422i
$453$	−1.90850	+	3.30562i	−0.0896692	+	0.155312i
$454$	6.94869			0.326118
$455$		0			0
$456$	2.30798			0.108081
$457$	10.5489	−	18.2713i	0.493458	−	0.854694i	−0.506514	−	0.862232i	$-0.669066\pi$
$457$	10.5489	−	18.2713i	0.493458	−	0.854694i	0.999972	+	0.00753818i	$0.00239950\pi$
$458$	2.86443	+	4.96134i	0.133846	+	0.231828i
$459$	3.59299	+	6.22324i	0.167706	+	0.290476i
$460$	−1.05496	+	1.82724i	−0.0491877	+	0.0851956i
$461$	23.0320			1.07271			0.536355	−	0.843993i	$-0.319801\pi$
$461$	23.0320			1.07271			0.536355	+	0.843993i	$0.319801\pi$
$462$		0			0
$463$	0.0814412			0.00378489			0.00189245	−	0.999998i	$-0.499398\pi$
$463$	0.0814412			0.00378489			0.00189245	+	0.999998i	$0.499398\pi$
$464$	5.07942	−	8.79781i	0.235806	−	0.408428i
$465$	−0.839970	−	1.45487i	−0.0389527	−	0.0674680i
$466$	−7.40366	−	12.8235i	−0.342968	−	0.594038i
$467$	−11.8550	+	20.5335i	−0.548586	+	0.950178i	0.449786	+	0.893136i	$0.351500\pi$
$467$	−11.8550	+	20.5335i	−0.548586	+	0.950178i	−0.998372	+	0.0570419i	$0.981833\pi$
$468$	5.96077			0.275537
$469$		0			0
$470$	−3.85623			−0.177875
$471$	1.56369	−	2.70839i	0.0720509	−	0.124796i
$472$	6.64795	+	11.5146i	0.305997	+	0.530002i
$473$	−11.2186	−	19.4312i	−0.515833	−	0.893450i
$474$	−7.12229	+	12.3362i	−0.327138	+	0.566619i
$475$	−10.8291			−0.496872
$476$		0			0
$477$	−5.63102			−0.257827
$478$	−5.97219	+	10.3441i	−0.273162	+	0.473130i
$479$	−5.33609	−	9.24237i	−0.243812	−	0.422295i	0.717985	−	0.696059i	$-0.245065\pi$
$479$	−5.33609	−	9.24237i	−0.243812	−	0.422295i	−0.961797	+	0.273764i	$0.911731\pi$
$480$	0.277479	+	0.480608i	0.0126651	+	0.0219366i
$481$	0.0648838	−	0.112382i	0.00295845	−	0.00512418i
$482$	0.625646			0.0284974
$483$		0			0
$484$	9.63773			0.438079
$485$	3.30343	−	5.72171i	0.150001	−	0.259809i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−17.6039	−	30.4908i	−0.797708	−	1.38167i	−0.921106	−	0.389313i	$-0.872712\pi$
$487$	−17.6039	−	30.4908i	−0.797708	−	1.38167i	0.123398	−	0.992357i	$-0.460621\pi$
$488$	−5.86174	+	10.1528i	−0.265349	+	0.459597i
$489$	−13.2905			−0.601018
$490$		0			0
$491$	16.7399			0.755460			0.377730	−	0.925916i	$-0.376705\pi$
$491$	16.7399			0.755460			0.377730	+	0.925916i	$0.376705\pi$
$492$	0.887395	−	1.53701i	0.0400069	−	0.0692939i
$493$	36.5006	+	63.2209i	1.64390	+	2.84733i
$494$	6.87867	+	11.9142i	0.309486	+	0.536045i
$495$	1.26055	−	2.18334i	0.0566577	−	0.0981339i
$496$	3.02715			0.135923
$497$		0			0
$498$	2.41789			0.108348
$499$	−16.4949	+	28.5700i	−0.738414	+	1.27897i	0.214795	+	0.976659i	$0.431092\pi$
$499$	−16.4949	+	28.5700i	−0.738414	+	1.27897i	−0.953209	+	0.302311i	$0.902242\pi$
$500$	−2.68933	−	4.65806i	−0.120271	−	0.208315i
$501$	1.58815	+	2.75075i	0.0709531	+	0.122894i
$502$	11.9804	−	20.7506i	0.534711	−	0.926146i
$503$	29.4282			1.31214			0.656069	−	0.754701i	$-0.272218\pi$
$503$	29.4282			1.31214			0.656069	+	0.754701i	$0.272218\pi$
$504$		0			0
$505$	9.22282			0.410410
$506$	−8.63587	+	14.9578i	−0.383911	+	0.664954i
$507$	11.2654	+	19.5122i	0.500314	+	0.866569i
$508$	−4.90366	−	8.49338i	−0.217565	−	0.376833i
$509$	2.69322	−	4.66479i	0.119375	−	0.206763i	−0.800145	−	0.599806i	$-0.795244\pi$
$509$	2.69322	−	4.66479i	0.119375	−	0.206763i	0.919520	+	0.393043i	$0.128578\pi$
$510$	−3.98792			−0.176588
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	1.15399	−	1.99877i	0.0509499	−	0.0882478i
$514$	4.77963	+	8.27857i	0.210821	+	0.365152i
$515$	−3.35958	−	5.81897i	−0.148041	−	0.256414i
$516$	2.46950	−	4.27730i	0.108714	−	0.188298i
$517$	−31.5670			−1.38832
$518$		0			0
$519$	−13.9511			−0.612385
$520$	−1.65399	+	2.86479i	−0.0725322	+	0.125630i
$521$	1.97405	+	3.41915i	0.0864847	+	0.149796i	0.906023	−	0.423229i	$-0.139103\pi$
$521$	1.97405	+	3.41915i	0.0864847	+	0.149796i	−0.819538	+	0.573025i	$0.805770\pi$
$522$	−5.07942	−	8.79781i	−0.222320	−	0.385070i
$523$	18.5378	−	32.1084i	0.810601	−	1.40400i	−0.101843	−	0.994801i	$-0.532474\pi$
$523$	18.5378	−	32.1084i	0.810601	−	1.40400i	0.912444	−	0.409202i	$-0.134193\pi$
$524$	0.188374			0.00822914
$525$		0			0
$526$	−7.36658			−0.321198
$527$	−10.8765	+	18.8387i	−0.473788	+	0.820625i
$528$	2.27144	+	3.93425i	0.0988517	+	0.171216i
$529$	4.27263	+	7.40042i	0.185767	+	0.321757i
$530$	1.56249	−	2.70631i	0.0678703	−	0.117555i
$531$	13.2959			0.576993
$532$		0			0
$533$	10.5791			0.458233
$534$	−2.41939	+	4.19050i	−0.104697	+	0.181341i
$535$	−4.17510	−	7.23148i	−0.180505	−	0.312644i
$536$	6.64795	+	11.5146i	0.287148	+	0.497354i
$537$	−1.67845	+	2.90716i	−0.0724304	+	0.125453i
$538$	16.0640			0.692567
$539$		0			0
$540$	0.554958			0.0238816
$541$	11.3693	−	19.6922i	0.488803	−	0.846632i	−0.511114	−	0.859513i	$-0.670767\pi$
$541$	11.3693	−	19.6922i	0.488803	−	0.846632i	0.999917	+	0.0128810i	$0.00410027\pi$
$542$	−1.25518	−	2.17403i	−0.0539144	−	0.0933825i
$543$	−11.7153	−	20.2915i	−0.502751	−	0.870790i
$544$	3.59299	−	6.22324i	0.154048	−	0.266819i
$545$	0.289192			0.0123876
$546$		0			0
$547$	31.1704			1.33275			0.666376	−	0.745616i	$-0.267845\pi$
$547$	31.1704			1.33275			0.666376	+	0.745616i	$0.267845\pi$
$548$	−1.38135	+	2.39258i	−0.0590085	+	0.102206i
$549$	5.86174	+	10.1528i	0.250173	+	0.433312i
$550$	−10.6576	−	18.4596i	−0.454443	−	0.787119i
$551$	11.7232	−	20.3052i	0.499424	−	0.865029i
$552$	−3.80194			−0.161821
$553$		0			0
$554$	5.91723			0.251399
$555$	0.00604079	−	0.0104630i	0.000256417	−	0.000444128i
$556$	−1.72856	−	2.99396i	−0.0733073	−	0.126972i
$557$	9.77509	+	16.9309i	0.414184	+	0.717387i	0.995342	−	0.0964031i	$-0.0307338\pi$
$557$	9.77509	+	16.9309i	0.414184	+	0.717387i	−0.581159	+	0.813790i	$0.697400\pi$
$558$	1.51357	−	2.62159i	0.0640747	−	0.110981i
$559$	29.4403			1.24519
$560$		0			0
$561$	−32.6450			−1.37827
$562$	−9.87047	+	17.0962i	−0.416361	+	0.721158i
$563$	−23.4197	−	40.5641i	−0.987022	−	1.70957i	−0.632582	−	0.774493i	$-0.718005\pi$
$563$	−23.4197	−	40.5641i	−0.987022	−	1.70957i	−0.354440	−	0.935079i	$-0.615328\pi$
$564$	−3.47434	−	6.01774i	−0.146296	−	0.253393i
$565$	−1.50149	+	2.60066i	−0.0631682	+	0.109411i
$566$	−7.23191			−0.303980
$567$		0			0
$568$	0.423272			0.0177601
$569$	16.8364	−	29.1615i	0.705818	−	1.22251i	−0.260578	−	0.965453i	$-0.583913\pi$
$569$	16.8364	−	29.1615i	0.705818	−	1.22251i	0.966396	−	0.257059i	$-0.0827536\pi$
$570$	0.640416	+	1.10923i	0.0268241	+	0.0464606i
$571$	8.87047	+	15.3641i	0.371218	+	0.642968i	0.989753	−	0.142789i	$-0.0456071\pi$
$571$	8.87047	+	15.3641i	0.371218	+	0.642968i	−0.618536	+	0.785757i	$0.712274\pi$
$572$	−13.5395	+	23.4511i	−0.566116	+	0.980542i
$573$	−3.71917			−0.155370
$574$		0			0
$575$	17.8388			0.743928
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	9.64244	+	16.7012i	0.401420	+	0.695280i	0.993898	−	0.110307i	$-0.0351834\pi$
$577$	9.64244	+	16.7012i	0.401420	+	0.695280i	−0.592478	+	0.805587i	$0.701850\pi$
$578$	17.3192	+	29.9977i	0.720382	+	1.24774i
$579$	−6.38016	+	11.0508i	−0.265150	+	0.459254i
$580$	5.63773			0.234094
$581$		0			0
$582$	11.9051			0.493484
$583$	12.7905	−	22.1538i	0.529729	−	0.917518i
$584$	7.16637	+	12.4125i	0.296546	+	0.513633i
$585$	1.65399	+	2.86479i	0.0683840	+	0.118445i
$586$	12.0625	−	20.8928i	0.498297	−	0.863076i
$587$	−20.8122			−0.859012			−0.429506	−	0.903064i	$-0.641312\pi$
$587$	−20.8122			−0.859012			−0.429506	+	0.903064i	$0.641312\pi$
$588$		0			0
$589$	6.98659			0.287877
$590$	−3.68933	+	6.39011i	−0.151887	+	0.263077i
$591$	5.44504	+	9.43109i	0.223979	+	0.387943i
$592$	0.0108851	+	0.0188536i	0.000447376	+	0.000774878i
$593$	5.81282	−	10.0681i	0.238704	−	0.413447i	−0.721639	−	0.692270i	$-0.756611\pi$
$593$	5.81282	−	10.0681i	0.238704	−	0.413447i	0.960343	+	0.278822i	$0.0899441\pi$
$594$	4.54288			0.186396
$595$		0			0
$596$	9.74632			0.399225
$597$	−0.420583	+	0.728471i	−0.0172133	+	0.0298144i
$598$	−11.3312	−	19.6263i	−0.463369	−	0.802578i
$599$	−1.78554	−	3.09265i	−0.0729554	−	0.126362i	0.827240	−	0.561849i	$-0.189910\pi$
$599$	−1.78554	−	3.09265i	−0.0729554	−	0.126362i	−0.900195	+	0.435486i	$0.856576\pi$
$600$	2.34601	−	4.06341i	0.0957755	−	0.165888i
$601$	−14.6455			−0.597402			−0.298701	−	0.954347i	$-0.596553\pi$
$601$	−14.6455			−0.597402			−0.298701	+	0.954347i	$0.596553\pi$
$602$		0			0
$603$	13.2959			0.541451
$604$	1.90850	−	3.30562i	0.0776558	−	0.134504i
$605$	2.67427	+	4.63197i	0.108724	+	0.188316i
$606$	8.30947	+	14.3924i	0.337549	+	0.584652i
$607$	−19.2932	+	33.4168i	−0.783087	+	1.35635i	0.147048	+	0.989129i	$0.453023\pi$
$607$	−19.2932	+	33.4168i	−0.783087	+	1.35635i	−0.930135	+	0.367217i	$0.880310\pi$
$608$	−2.30798			−0.0936009
$609$		0			0
$610$	−6.50604			−0.263422
$611$	20.7098	−	35.8704i	0.837828	−	1.45116i
$612$	−3.59299	−	6.22324i	−0.145238	−	0.251560i
$613$	6.01424	+	10.4170i	0.242913	+	0.420737i	0.961543	−	0.274655i	$-0.0885638\pi$
$613$	6.01424	+	10.4170i	0.242913	+	0.420737i	−0.718630	+	0.695393i	$0.755230\pi$
$614$	13.2865	−	23.0129i	0.536200	−	0.928725i
$615$	0.984935			0.0397164
$616$		0			0
$617$	32.7356			1.31788			0.658942	−	0.752194i	$-0.271004\pi$
$617$	32.7356			1.31788			0.658942	+	0.752194i	$0.271004\pi$
$618$	6.05376	−	10.4854i	0.243518	−	0.421786i
$619$	−16.9373	−	29.3362i	−0.680766	−	1.17912i	−0.974747	−	0.223311i	$-0.928314\pi$
$619$	−16.9373	−	29.3362i	−0.680766	−	1.17912i	0.293981	−	0.955811i	$-0.405020\pi$
$620$	0.839970	+	1.45487i	0.0337340	+	0.0584290i
$621$	−1.90097	+	3.29257i	−0.0762833	+	0.132126i
$622$	25.1250			1.00742
$623$		0			0
$624$	−5.96077			−0.238622
$625$	−10.2376	+	17.7320i	−0.409503	+	0.709281i
$626$	3.59515	+	6.22698i	0.143691	+	0.248880i
$627$	5.24243	+	9.08016i	0.209363	+	0.362627i
$628$	−1.56369	+	2.70839i	−0.0623979	+	0.108076i
$629$	−0.156441			−0.00623770
$630$		0			0
$631$	12.6890			0.505143			0.252571	−	0.967578i	$-0.418724\pi$
$631$	12.6890			0.505143			0.252571	+	0.967578i	$0.418724\pi$
$632$	7.12229	−	12.3362i	0.283310	−	0.490707i
$633$	−7.32855	−	12.6934i	−0.291284	−	0.504518i
$634$	3.02715	+	5.24317i	0.120223	+	0.208233i
$635$	2.72132	−	4.71347i	0.107992	−	0.187048i
$636$	5.63102			0.223285
$637$		0			0
$638$	46.1503			1.82711
$639$	0.211636	−	0.366564i	0.00837218	−	0.0145010i
$640$	−0.277479	−	0.480608i	−0.0109683	−	0.0189977i
$641$	12.5152	+	21.6770i	0.494321	+	0.856188i	0.999979	−	0.00654568i	$-0.00208357\pi$
$641$	12.5152	+	21.6770i	0.494321	+	0.856188i	−0.505658	+	0.862734i	$0.668750\pi$
$642$	7.52326	−	13.0307i	0.296919	−	0.514280i
$643$	−13.4644			−0.530985			−0.265492	−	0.964113i	$-0.585535\pi$
$643$	−13.4644			−0.530985			−0.265492	+	0.964113i	$0.585535\pi$
$644$		0			0
$645$	2.74094			0.107924
$646$	8.29254	−	14.3631i	0.326266	−	0.565109i
$647$	9.80439	+	16.9817i	0.385450	+	0.667620i	0.991832	−	0.127555i	$-0.0407128\pi$
$647$	9.80439	+	16.9817i	0.385450	+	0.667620i	−0.606381	+	0.795174i	$0.707379\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−30.2008	+	52.3093i	−1.18549	+	2.05332i
$650$	27.9681			1.09700
$651$		0			0
$652$	13.2905			0.520497
$653$	−4.12737	+	7.14882i	−0.161517	+	0.279755i	−0.935413	−	0.353557i	$-0.884972\pi$
$653$	−4.12737	+	7.14882i	−0.161517	+	0.279755i	0.773896	+	0.633313i	$0.218305\pi$
$654$	0.260553	+	0.451291i	0.0101884	+	0.0176469i
$655$	0.0522697	+	0.0905338i	0.00204235	+	0.00353745i
$656$	−0.887395	+	1.53701i	−0.0346470	+	0.0600103i
$657$	14.3327			0.559173
$658$		0			0
$659$	11.0164			0.429138			0.214569	−	0.976709i	$-0.431165\pi$
$659$	11.0164			0.429138			0.214569	+	0.976709i	$0.431165\pi$
$660$	−1.26055	+	2.18334i	−0.0490670	+	0.0849865i
$661$	−2.43027	−	4.20935i	−0.0945266	−	0.163725i	0.814884	−	0.579624i	$-0.196800\pi$
$661$	−2.43027	−	4.20935i	−0.0945266	−	0.163725i	−0.909411	+	0.415899i	$0.863467\pi$
$662$	1.56853	+	2.71678i	0.0609627	+	0.105591i
$663$	21.4170	−	37.0953i	0.831767	−	1.44066i
$664$	−2.41789			−0.0938325
$665$		0			0
$666$	0.0217703			0.000843581
$667$	−19.3116	+	33.4487i	−0.747749	+	1.29514i
$668$	−1.58815	−	2.75075i	−0.0614472	−	0.106430i
$669$	10.9765	+	19.0119i	0.424376	+	0.735041i
$670$	−3.68933	+	6.39011i	−0.142531	+	0.246872i
$671$	−53.2583			−2.05601
$672$		0			0
$673$	−45.5918			−1.75743			−0.878717	−	0.477343i	$-0.841600\pi$
$673$	−45.5918			−1.75743			−0.878717	+	0.477343i	$0.841600\pi$
$674$	−7.93243	+	13.7394i	−0.305546	+	0.529221i
$675$	−2.34601	−	4.06341i	−0.0902980	−	0.156401i
$676$	−11.2654	−	19.5122i	−0.433285	−	0.750471i
$677$	−4.27844	+	7.41047i	−0.164434	+	0.284808i	−0.936454	−	0.350790i	$-0.885913\pi$
$677$	−4.27844	+	7.41047i	−0.164434	+	0.284808i	0.772020	+	0.635598i	$0.219246\pi$
$678$	−5.41119			−0.207816
$679$		0			0
$680$	3.98792			0.152930
$681$	−3.47434	+	6.01774i	−0.133137	+	0.230600i
$682$	6.87598	+	11.9095i	0.263295	+	0.456040i
$683$	−3.09365	−	5.35837i	−0.118375	−	0.205032i	0.800749	−	0.599001i	$-0.204435\pi$
$683$	−3.09365	−	5.35837i	−0.118375	−	0.205032i	−0.919124	+	0.393968i	$0.871102\pi$
$684$	−1.15399	+	1.99877i	−0.0441239	+	0.0764248i
$685$	−1.53319			−0.0585801
$686$		0			0
$687$	−5.72886			−0.218570
$688$	−2.46950	+	4.27730i	−0.0941488	+	0.163071i
$689$	16.7826	+	29.0683i	0.639367	+	1.10742i
$690$	−1.05496	−	1.82724i	−0.0401616	−	0.0695619i
$691$	5.43512	−	9.41390i	0.206762	−	0.358122i	−0.743931	−	0.668256i	$-0.767041\pi$
$691$	5.43512	−	9.41390i	0.206762	−	0.358122i	0.950693	+	0.310135i	$0.100374\pi$
$692$	13.9511			0.530341
$693$		0			0
$694$	−11.9541			−0.453770
$695$	0.959279	−	1.66152i	0.0363875	−	0.0630251i
$696$	5.07942	+	8.79781i	0.192535	+	0.333480i
$697$	−6.37681	−	11.0450i	−0.241539	−	0.418357i
$698$	6.16905	−	10.6851i	0.233502	−	0.404438i
$699$	14.8073			0.560064
$700$		0			0
$701$	−19.2198			−0.725923			−0.362962	−	0.931804i	$-0.618234\pi$
$701$	−19.2198			−0.725923			−0.362962	+	0.931804i	$0.618234\pi$
$702$	−2.98039	+	5.16218i	−0.112487	+	0.194834i
$703$	0.0251227	+	0.0435137i	0.000947519	+	0.00164115i
$704$	−2.27144	−	3.93425i	−0.0856081	−	0.148277i
$705$	1.92812	−	3.33959i	0.0726170	−	0.125776i
$706$	15.7700			0.593512
$707$		0			0
$708$	−13.2959			−0.499690
$709$	9.97853	−	17.2833i	0.374751	−	0.649088i	−0.615538	−	0.788107i	$-0.711061\pi$
$709$	9.97853	−	17.2833i	0.374751	−	0.649088i	0.990290	+	0.139018i	$0.0443947\pi$
$710$	0.117449	+	0.203428i	0.00440778	+	0.00763450i
$711$	−7.12229	−	12.3362i	−0.267107	−	0.462643i
$712$	2.41939	−	4.19050i	0.0906704	−	0.157046i
$713$	−11.5090			−0.431016
$714$		0			0
$715$	−15.0277			−0.562006
$716$	1.67845	−	2.90716i	0.0627265	−	0.108646i
$717$	−5.97219	−	10.3441i	−0.223035	−	0.386309i
$718$	−1.57942	−	2.73563i	−0.0589433	−	0.102093i
$719$	3.30141	−	5.71820i	0.123122	−	0.213253i	−0.797876	−	0.602822i	$-0.794043\pi$
$719$	3.30141	−	5.71820i	0.123122	−	0.213253i	0.920997	+	0.389569i	$0.127376\pi$
$720$	−0.554958			−0.0206821
$721$		0			0
$722$	13.6732			0.508865
$723$	−0.312823	+	0.541825i	−0.0116340	+	0.0201507i
$724$	11.7153	+	20.2915i	0.435395	+	0.754126i
$725$	−23.8327	−	41.2795i	−0.885125	−	1.53308i
$726$	−4.81886	+	8.34652i	−0.178845	+	0.309768i
$727$	−34.3889			−1.27542			−0.637708	−	0.770278i	$-0.720117\pi$
$727$	−34.3889			−1.27542			−0.637708	+	0.770278i	$0.720117\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−3.97703	+	6.88842i	−0.147197	+	0.254952i
$731$	−17.7458	−	30.7366i	−0.656351	−	1.13683i
$732$	−5.86174	−	10.1528i	−0.216656	−	0.375259i
$733$	2.32036	−	4.01897i	0.0857043	−	0.148444i	−0.819987	−	0.572382i	$-0.806019\pi$
$733$	2.32036	−	4.01897i	0.0857043	−	0.148444i	0.905691	+	0.423938i	$0.139353\pi$
$734$	−9.42221			−0.347780
$735$		0			0
$736$	3.80194			0.140141
$737$	−30.2008	+	52.3093i	−1.11246	+	1.92684i
$738$	0.887395	+	1.53701i	0.0326655	+	0.0565783i
$739$	16.9393	+	29.3397i	0.623122	+	1.07928i	0.988901	+	0.148577i	$0.0474694\pi$
$739$	16.9393	+	29.3397i	0.623122	+	1.07928i	−0.365779	+	0.930702i	$0.619197\pi$
$740$	−0.00604079	+	0.0104630i	−0.000222064	+	0.000384626i
$741$	−13.7573			−0.505388
$742$		0			0
$743$	−23.1631			−0.849773			−0.424887	−	0.905247i	$-0.639686\pi$
$743$	−23.1631			−0.849773			−0.424887	+	0.905247i	$0.639686\pi$
$744$	−1.51357	+	2.62159i	−0.0554903	+	0.0961120i
$745$	2.70440	+	4.68416i	0.0990815	+	0.171614i
$746$	18.7005	+	32.3902i	0.684674	+	1.18589i
$747$	−1.20895	+	2.09396i	−0.0442331	+	0.0766139i
$748$	32.6450			1.19362
$749$		0			0
$750$	5.37867			0.196401
$751$	8.80798	−	15.2559i	0.321408	−	0.556694i	−0.659371	−	0.751818i	$-0.729177\pi$
$751$	8.80798	−	15.2559i	0.321408	−	0.556694i	0.980779	+	0.195123i	$0.0625107\pi$
$752$	3.47434	+	6.01774i	0.126696	+	0.219444i
$753$	11.9804	+	20.7506i	0.436590	+	0.756195i
$754$	−30.2772	+	52.4417i	−1.10263	+	1.90981i
$755$	2.11828			0.0770920
$756$		0			0
$757$	37.7622			1.37249			0.686246	−	0.727370i	$-0.259257\pi$
$757$	37.7622			1.37249			0.686246	+	0.727370i	$0.259257\pi$
$758$	12.2925	−	21.2913i	0.446485	−	0.773335i
$759$	−8.63587	−	14.9578i	−0.313462	−	0.542932i
$760$	−0.640416	−	1.10923i	−0.0232303	−	0.0402361i
$761$	24.8605	−	43.0597i	0.901194	−	1.56091i	0.0752478	−	0.997165i	$-0.476025\pi$
$761$	24.8605	−	43.0597i	0.901194	−	1.56091i	0.825946	−	0.563749i	$-0.190641\pi$
$762$	9.80731			0.355282
$763$		0			0
$764$	3.71917			0.134555
$765$	1.99396	−	3.45364i	0.0720917	−	0.124867i
$766$	7.15495	+	12.3927i	0.258519	+	0.447768i
$767$	−39.6269	−	68.6358i	−1.43084	−	2.47830i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−25.2573			−0.910800			−0.455400	−	0.890287i	$-0.650504\pi$
$769$	−25.2573			−0.910800			−0.455400	+	0.890287i	$0.650504\pi$
$770$		0			0
$771$	−9.55927			−0.344269
$772$	6.38016	−	11.0508i	0.229627	−	0.397725i
$773$	12.3393	+	21.3723i	0.443814	+	0.768708i	0.997969	−	0.0637053i	$-0.0202918\pi$
$773$	12.3393	+	21.3723i	0.443814	+	0.768708i	−0.554155	+	0.832414i	$0.686958\pi$
$774$	2.46950	+	4.27730i	0.0887644	+	0.153744i
$775$	7.10172	−	12.3005i	0.255101	−	0.441848i
$776$	−11.9051			−0.427370
$777$		0			0
$778$	−5.25667			−0.188461
$779$	−2.04809	+	3.54739i	−0.0733804	+	0.127099i
$780$	−1.65399	−	2.86479i	−0.0592223	−	0.102576i
$781$	0.961435	+	1.66525i	0.0344029	+	0.0595875i
$782$	−13.6603	+	23.6604i	−0.488492	+	0.846093i
$783$	10.1588			0.363047
$784$		0			0
$785$	−1.73556			−0.0619449
$786$	−0.0941868	+	0.163136i	−0.00335953	+	0.00581888i
$787$	2.53737	+	4.39485i	0.0904474	+	0.156660i	0.907699	−	0.419621i	$-0.137837\pi$
$787$	2.53737	+	4.39485i	0.0904474	+	0.156660i	−0.817252	+	0.576280i	$0.804504\pi$
$788$	−5.44504	−	9.43109i	−0.193972	−	0.335969i
$789$	3.68329	−	6.37965i	0.131129	−	0.227122i
$790$	7.90515			0.281253
$791$		0			0
$792$	−4.54288			−0.161424
$793$	34.9405	−	60.5187i	1.24077	−	2.14908i
$794$	−16.0211	−	27.7494i	−0.568568	−	0.984788i
$795$	1.56249	+	2.70631i	0.0554158	+	0.0959831i
$796$	0.420583	−	0.728471i	0.0149072	−	0.0258200i
$797$	42.5023			1.50551			0.752755	−	0.658301i	$-0.228725\pi$
$797$	42.5023			1.50551			0.752755	+	0.658301i	$0.228725\pi$
$798$		0			0
$799$	−49.9332			−1.76651
$800$	−2.34601	+	4.06341i	−0.0829440	+	0.143663i
$801$	−2.41939	−	4.19050i	−0.0854848	−	0.148064i
$802$	8.08211	+	13.9986i	0.285389	+	0.494308i
$803$	−32.5559	+	56.3885i	−1.14887	+	1.98991i
$804$	−13.2959			−0.468910
$805$		0			0
$806$	−18.0441			−0.635577
$807$	−8.03199	+	13.9118i	−0.282739	+	0.489719i
$808$	−8.30947	−	14.3924i	−0.292326	−	0.506324i
$809$	6.88769	+	11.9298i	0.242158	+	0.419431i	0.961329	−	0.275403i	$-0.0888113\pi$
$809$	6.88769	+	11.9298i	0.242158	+	0.419431i	−0.719171	+	0.694834i	$0.755478\pi$
$810$	−0.277479	+	0.480608i	−0.00974962	+	0.0168868i
$811$	−28.9028			−1.01491			−0.507457	−	0.861677i	$-0.669414\pi$
$811$	−28.9028			−1.01491			−0.507457	+	0.861677i	$0.669414\pi$
$812$		0			0
$813$	2.51035			0.0880419
$814$	−0.0494498	+	0.0856496i	−0.00173321	+	0.00300202i
$815$	3.68784	+	6.38753i	0.129179	+	0.223745i
$816$	3.59299	+	6.22324i	0.125780	+	0.217857i
$817$	−5.69955	+	9.87192i	−0.199402	+	0.345375i
$818$	34.0194			1.18946
$819$		0			0
$820$	−0.984935			−0.0343954
$821$	−27.0182	+	46.7969i	−0.942941	+	1.63322i	−0.183119	+	0.983091i	$0.558619\pi$
$821$	−27.0182	+	46.7969i	−0.942941	+	1.63322i	−0.759822	+	0.650131i	$0.774714\pi$
$822$	−1.38135	−	2.39258i	−0.0481803	−	0.0834507i
$823$	−15.2290	−	26.3774i	−0.530849	−	0.919458i	−0.999352	−	0.0359957i	$-0.988540\pi$
$823$	−15.2290	−	26.3774i	−0.530849	−	0.919458i	0.468503	−	0.883462i	$-0.344794\pi$
$824$	−6.05376	+	10.4854i	−0.210893	+	0.365277i
$825$	21.3153			0.742103
$826$		0			0
$827$	−37.3840			−1.29997			−0.649985	−	0.759947i	$-0.725225\pi$
$827$	−37.3840			−1.29997			−0.649985	+	0.759947i	$0.725225\pi$
$828$	1.90097	−	3.29257i	0.0660632	−	0.114425i
$829$	−21.8225	−	37.7977i	−0.757927	−	1.31277i	−0.943906	−	0.330215i	$-0.892879\pi$
$829$	−21.8225	−	37.7977i	−0.757927	−	1.31277i	0.185979	−	0.982554i	$-0.440454\pi$
$830$	−0.670915	−	1.16206i	−0.0232878	−	0.0403357i
$831$	−2.95862	+	5.12447i	−0.102633	+	0.177766i
$832$	5.96077			0.206653
$833$		0			0
$834$	3.45712			0.119710
$835$	0.881355	−	1.52655i	0.0305005	−	0.0528285i
$836$	−5.24243	−	9.08016i	−0.181313	−	0.314044i
$837$	1.51357	+	2.62159i	0.0523168	+	0.0906153i
$838$	−7.93080	+	13.7366i	−0.273965	+	0.474521i
$839$	−20.0640			−0.692686			−0.346343	−	0.938108i	$-0.612577\pi$
$839$	−20.0640			−0.692686			−0.346343	+	0.938108i	$0.612577\pi$
$840$		0			0
$841$	74.2019			2.55869
$842$	−12.1848	+	21.1047i	−0.419915	+	0.727315i
$843$	−9.87047	−	17.0962i	−0.339957	−	0.588823i
$844$	7.32855	+	12.6934i	0.252259	+	0.436926i
$845$	6.25182	−	10.8285i	0.215069	−	0.372511i
$846$	6.94869			0.238901
$847$		0			0
$848$	−5.63102			−0.193370
$849$	3.61596	−	6.26302i	0.124099	−	0.214946i
$850$	−16.8584	−	29.1996i	−0.578238	−	1.00154i
$851$	−0.0413846	−	0.0716802i	−0.00141865	−	0.00245717i
$852$	−0.211636	+	0.366564i	−0.00725052	+	0.0125583i
$853$	30.2543			1.03589			0.517943	−	0.855415i	$-0.326698\pi$
$853$	30.2543			1.03589			0.517943	+	0.855415i	$0.326698\pi$
$854$		0			0
$855$	−1.28083			−0.0438035
$856$	−7.52326	+	13.0307i	−0.257140	+	0.445379i
$857$	5.89546	+	10.2112i	0.201385	+	0.348809i	0.948975	−	0.315351i	$-0.102122\pi$
$857$	5.89546	+	10.2112i	0.201385	+	0.348809i	−0.747590	+	0.664161i	$0.768789\pi$
$858$	−13.5395	−	23.4511i	−0.462232	−	0.800609i
$859$	0.410658	−	0.711280i	0.0140115	−	0.0242686i	−0.858935	−	0.512085i	$-0.828873\pi$
$859$	0.410658	−	0.711280i	0.0140115	−	0.0242686i	0.872946	+	0.487817i	$0.162207\pi$
$860$	−2.74094			−0.0934652
$861$		0			0
$862$	6.00431			0.204508
$863$	20.2729	−	35.1137i	0.690099	−	1.19529i	−0.281707	−	0.959501i	$-0.590900\pi$
$863$	20.2729	−	35.1137i	0.690099	−	1.19529i	0.971805	−	0.235785i	$-0.0757662\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	3.87113	+	6.70500i	0.131622	+	0.227977i
$866$	7.21164	−	12.4909i	0.245061	−	0.424459i
$867$	−34.6383			−1.17638
$868$		0			0
$869$	64.7114			2.19518
$870$	−2.81886	+	4.88242i	−0.0955684	+	0.165529i
$871$	−39.6269	−	68.6358i	−1.34271	−	2.32564i
$872$	−0.260553	−	0.451291i	−0.00882344	−	0.0152827i
$873$	−5.95257	+	10.3102i	−0.201464	+	0.348946i
$874$	8.77479			0.296812
$875$		0			0
$876$	−14.3327			−0.484258
$877$	25.3784	−	43.9567i	0.856969	−	1.48431i	−0.0178379	−	0.999841i	$-0.505678\pi$
$877$	25.3784	−	43.9567i	0.856969	−	1.48431i	0.874807	−	0.484472i	$-0.160988\pi$
$878$	−9.06398	−	15.6993i	−0.305895	−	0.529825i
$879$	12.0625	+	20.8928i	0.406858	+	0.704698i
$880$	1.26055	−	2.18334i	0.0424932	−	0.0736004i
$881$	1.44504			0.0486847			0.0243423	−	0.999704i	$-0.492251\pi$
$881$	1.44504			0.0486847			0.0243423	+	0.999704i	$0.492251\pi$
$882$		0			0
$883$	−55.8133			−1.87827			−0.939133	−	0.343553i	$-0.888369\pi$
$883$	−55.8133			−1.87827			−0.939133	+	0.343553i	$0.888369\pi$
$884$	−21.4170	+	37.0953i	−0.720331	+	1.24765i
$885$	−3.68933	−	6.39011i	−0.124016	−	0.214801i
$886$	−9.41066	−	16.2997i	−0.316157	−	0.547600i
$887$	5.76218	−	9.98038i	0.193475	−	0.335108i	−0.752925	−	0.658107i	$-0.771358\pi$
$887$	5.76218	−	9.98038i	0.193475	−	0.335108i	0.946400	+	0.322998i	$0.104691\pi$
$888$	−0.0217703			−0.000730562
$889$		0			0
$890$	2.68532			0.0900120
$891$	−2.27144	+	3.93425i	−0.0760960	+	0.131802i
$892$	−10.9765	−	19.0119i	−0.367520	−	0.636564i
$893$	8.01871	+	13.8888i	0.268336	+	0.464772i
$894$	−4.87316	+	8.44056i	−0.162983	+	0.282294i
$895$	1.86294			0.0622711
$896$		0			0
$897$	22.6625			0.756678
$898$	4.62014	−	8.00231i	0.154176	−	0.267041i
$899$	15.3761	+	26.6323i	0.512823	+	0.888236i
$900$	2.34601	+	4.06341i	0.0782004	+	0.135447i
$901$	20.2322	−	35.0432i	0.674033	−	1.16746i
$902$	−8.06265			−0.268457
$903$		0			0
$904$	5.41119			0.179974
$905$	−6.50149	+	11.2609i	−0.216117	+	0.374325i
$906$	1.90850	+	3.30562i	0.0634057	+	0.109822i
$907$	18.8817	+	32.7040i	0.626955	+	1.08592i	0.988159	+	0.153431i	$0.0490323\pi$
$907$	18.8817	+	32.7040i	0.626955	+	1.08592i	−0.361204	+	0.932487i	$0.617634\pi$
$908$	3.47434	−	6.01774i	0.115300	−	0.199706i
$909$	−16.6189			−0.551215
$910$		0			0
$911$	44.6510			1.47935			0.739677	−	0.672962i	$-0.234978\pi$
$911$	44.6510			1.47935			0.739677	+	0.672962i	$0.234978\pi$
$912$	1.15399	−	1.99877i	0.0382124	−	0.0661858i
$913$	−5.49210	−	9.51259i	−0.181762	−	0.314821i
$914$	−10.5489	−	18.2713i	−0.348927	−	0.604360i
$915$	3.25302	−	5.63440i	0.107542	−	0.186267i
$916$	5.72886			0.189287
$917$		0			0
$918$	7.18598			0.237173
$919$	19.4937	−	33.7641i	0.643039	−	1.11378i	−0.341712	−	0.939805i	$-0.611007\pi$
$919$	19.4937	−	33.7641i	0.643039	−	1.11378i	0.984751	−	0.173971i	$-0.0556598\pi$
$920$	1.05496	+	1.82724i	0.0347809	+	0.0602424i
$921$	13.2865	+	23.0129i	0.437805	+	0.758301i
$922$	11.5160	−	19.9463i	0.379260	−	0.656898i
$923$	−2.52303			−0.0830464
$924$		0			0
$925$	0.102147			0.00335856
$926$	0.0407206	−	0.0705302i	0.00133816	−	0.00231777i
$927$	6.05376	+	10.4854i	0.198832	+	0.344386i
$928$	−5.07942	−	8.79781i	−0.166740	−	0.288802i
$929$	−19.6265	+	33.9940i	−0.643924	+	1.11531i	0.340625	+	0.940199i	$0.389361\pi$
$929$	−19.6265	+	33.9940i	−0.643924	+	1.11531i	−0.984549	+	0.175109i	$0.943972\pi$
$930$	−1.67994			−0.0550874
$931$		0			0
$932$	−14.8073			−0.485030
$933$	−12.5625	+	21.7589i	−0.411277	+	0.712354i
$934$	11.8550	+	20.5335i	0.387909	+	0.671877i
$935$	9.05831	+	15.6895i	0.296238	+	0.513100i
$936$	2.98039	−	5.16218i	0.0974170	−	0.168731i
$937$	28.5007			0.931076			0.465538	−	0.885028i	$-0.345861\pi$
$937$	28.5007			0.931076			0.465538	+	0.885028i	$0.345861\pi$
$938$		0			0
$939$	−7.19029			−0.234646
$940$	−1.92812	+	3.33959i	−0.0628882	+	0.108926i
$941$	−24.7313	−	42.8359i	−0.806218	−	1.39641i	−0.915466	−	0.402395i	$-0.868178\pi$
$941$	−24.7313	−	42.8359i	−0.806218	−	1.39641i	0.109248	−	0.994014i	$-0.465156\pi$
$942$	−1.56369	−	2.70839i	−0.0509477	−	0.0882440i
$943$	3.37382	−	5.84363i	0.109867	−	0.190295i
$944$	13.2959			0.432745
$945$		0			0
$946$	−22.4373			−0.729499
$947$	−13.7599	+	23.8328i	−0.447136	+	0.774463i	−0.998198	−	0.0600015i	$-0.980889\pi$
$947$	−13.7599	+	23.8328i	−0.447136	+	0.774463i	0.551062	+	0.834464i	$0.314223\pi$
$948$	7.12229	+	12.3362i	0.231321	+	0.400660i
$949$	−42.7171	−	73.9881i	−1.38665	−	2.40176i
$950$	−5.41454	+	9.37826i	−0.175671	+	0.304271i
$951$	−6.05429			−0.196324
$952$		0			0
$953$	31.4196			1.01778			0.508890	−	0.860832i	$-0.330056\pi$
$953$	31.4196			1.01778			0.508890	+	0.860832i	$0.330056\pi$
$954$	−2.81551	+	4.87661i	−0.0911555	+	0.157886i
$955$	1.03199	+	1.78746i	0.0333945	+	0.0578409i
$956$	5.97219	+	10.3441i	0.193154	+	0.334553i
$957$	−23.0752	+	39.9674i	−0.745914	+	1.29196i
$958$	−10.6722			−0.344802
$959$		0			0
$960$	0.554958			0.0179112
$961$	10.9182	−	18.9109i	0.352200	−	0.610028i
$962$	−0.0648838	−	0.112382i	−0.00209194	−	0.00362334i
$963$	7.52326	+	13.0307i	0.242434	+	0.419908i
$964$	0.312823	−	0.541825i	0.0100753	−	0.0174510i
$965$	7.08144			0.227960
$966$		0			0
$967$	2.02848			0.0652314			0.0326157	−	0.999468i	$-0.489616\pi$
$967$	2.02848			0.0652314			0.0326157	+	0.999468i	$0.489616\pi$
$968$	4.81886	−	8.34652i	0.154884	−	0.268267i
$969$	8.29254	+	14.3631i	0.266395	+	0.461410i
$970$	−3.30343	−	5.72171i	−0.106067	−	0.183713i
$971$	−18.7424	+	32.4628i	−0.601473	+	1.04178i	0.391125	+	0.920338i	$0.372086\pi$
$971$	−18.7424	+	32.4628i	−0.601473	+	1.04178i	−0.992598	+	0.121445i	$0.961247\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−35.2078			−1.12813
$975$	−13.9840	+	24.2211i	−0.447847	+	0.775695i
$976$	5.86174	+	10.1528i	0.187630	+	0.324984i
$977$	−0.175760	−	0.304424i	−0.00562305	−	0.00973940i	0.863200	−	0.504862i	$-0.168457\pi$
$977$	−0.175760	−	0.304424i	−0.00562305	−	0.00973940i	−0.868823	+	0.495122i	$0.835123\pi$
$978$	−6.64526	+	11.5099i	−0.212492	+	0.368047i
$979$	21.9820			0.702546
$980$		0			0
$981$	−0.521106			−0.0166376
$982$	8.36994	−	14.4972i	0.267095	−	0.462623i
$983$	−21.7860	−	37.7344i	−0.694865	−	1.20354i	−0.970226	−	0.242200i	$-0.922131\pi$
$983$	−21.7860	−	37.7344i	−0.694865	−	1.20354i	0.275362	−	0.961341i	$-0.411202\pi$
$984$	−0.887395	−	1.53701i	−0.0282891	−	0.0489982i
$985$	3.02177	−	5.23386i	0.0962816	−	0.166765i
$986$	73.0012			2.32483
$987$		0			0
$988$	13.7573			0.437679
$989$	9.38889	−	16.2620i	0.298549	−	0.517102i
$990$	−1.26055	−	2.18334i	−0.0400630	−	0.0693912i
$991$	9.18718	+	15.9127i	0.291840	+	0.505482i	0.974245	−	0.225492i	$-0.0723991\pi$
$991$	9.18718	+	15.9127i	0.291840	+	0.505482i	−0.682405	+	0.730975i	$0.739066\pi$
$992$	1.51357	−	2.62159i	0.0480560	−	0.0832354i
$993$	−3.13706			−0.0995517
$994$		0			0
$995$	0.466812			0.0147989
$996$	1.20895	−	2.09396i	0.0383070	−	0.0663496i
$997$	17.9629	+	31.1127i	0.568892	+	0.985349i	0.996676	+	0.0814683i	$0.0259609\pi$
$997$	17.9629	+	31.1127i	0.568892	+	0.985349i	−0.427784	+	0.903881i	$0.640706\pi$
$998$	16.4949	+	28.5700i	0.522138	+	0.904369i
$999$	−0.0108851	+	0.0188536i	−0.000344390	+	0.000596502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2058.2.e.l.667.2		6
7.2	even	3		2058.2.a.a.1.2	✓	3
7.3	odd	6		2058.2.e.g.361.2		6
7.4	even	3	inner	2058.2.e.l.361.2		6
7.5	odd	6		2058.2.a.f.1.2	yes	3
7.6	odd	2		2058.2.e.g.667.2		6
21.2	odd	6		6174.2.a.o.1.2		3
21.5	even	6		6174.2.a.j.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2058.2.a.a.1.2	✓	3	7.2	even	3
2058.2.a.f.1.2	yes	3	7.5	odd	6
2058.2.e.g.361.2		6	7.3	odd	6
2058.2.e.g.667.2		6	7.6	odd	2
2058.2.e.l.361.2		6	7.4	even	3	inner
2058.2.e.l.667.2		6	1.1	even	1	trivial
6174.2.a.j.1.2		3	21.5	even	6
6174.2.a.o.1.2		3	21.2	odd	6

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:	\( N \)	\(=\)	\( 2058 = 2 \cdot 3 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2058.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.277479 - 0.480608i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.277479 - 0.480608i) q^{10} +(-2.27144 - 3.93425i) q^{11} +(0.500000 - 0.866025i) q^{12} +5.96077 q^{13} +0.554958 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.59299 - 6.22324i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.15399 + 1.99877i) q^{19} -0.554958 q^{20} -4.54288 q^{22} +(1.90097 - 3.29257i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.34601 + 4.06341i) q^{25} +(2.98039 - 5.16218i) q^{26} -1.00000 q^{27} -10.1588 q^{29} +(0.277479 - 0.480608i) q^{30} +(-1.51357 - 2.62159i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.27144 - 3.93425i) q^{33} -7.18598 q^{34} +1.00000 q^{36} +(0.0108851 - 0.0188536i) q^{37} +(1.15399 + 1.99877i) q^{38} +(2.98039 + 5.16218i) q^{39} +(-0.277479 + 0.480608i) q^{40} +1.77479 q^{41} +4.93900 q^{43} +(-2.27144 + 3.93425i) q^{44} +(0.277479 + 0.480608i) q^{45} +(-1.90097 - 3.29257i) q^{46} +(3.47434 - 6.01774i) q^{47} -1.00000 q^{48} +4.69202 q^{50} +(3.59299 - 6.22324i) q^{51} +(-2.98039 - 5.16218i) q^{52} +(2.81551 + 4.87661i) q^{53} +(-0.500000 + 0.866025i) q^{54} -2.52111 q^{55} -2.30798 q^{57} +(-5.07942 + 8.79781i) q^{58} +(-6.64795 - 11.5146i) q^{59} +(-0.277479 - 0.480608i) q^{60} +(5.86174 - 10.1528i) q^{61} -3.02715 q^{62} +1.00000 q^{64} +(1.65399 - 2.86479i) q^{65} +(-2.27144 - 3.93425i) q^{66} +(-6.64795 - 11.5146i) q^{67} +(-3.59299 + 6.22324i) q^{68} +3.80194 q^{69} -0.423272 q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.16637 - 12.4125i) q^{73} +(-0.0108851 - 0.0188536i) q^{74} +(-2.34601 + 4.06341i) q^{75} +2.30798 q^{76} +5.96077 q^{78} +(-7.12229 + 12.3362i) q^{79} +(0.277479 + 0.480608i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.887395 - 1.53701i) q^{82} +2.41789 q^{83} -3.98792 q^{85} +(2.46950 - 4.27730i) q^{86} +(-5.07942 - 8.79781i) q^{87} +(2.27144 + 3.93425i) q^{88} +(-2.41939 + 4.19050i) q^{89} +0.554958 q^{90} -3.80194 q^{92} +(1.51357 - 2.62159i) q^{93} +(-3.47434 - 6.01774i) q^{94} +(0.640416 + 1.10923i) q^{95} +(-0.500000 + 0.866025i) q^{96} +11.9051 q^{97} +4.54288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{8} - 3 q^{9} - 2 q^{10} + 5 q^{11} + 3 q^{12} + 10 q^{13} + 4 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} - 12 q^{19} - 4 q^{20} + 10 q^{22} + 7 q^{23}+ \cdots - 10 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^8 - 3 * q^9 - 2 * q^10 + 5 * q^11 + 3 * q^12 + 10 * q^13 + 4 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 - 12 * q^19 - 4 * q^20 + 10 * q^22 + 7 * q^23 - 3 * q^24 + 9 * q^25 + 5 * q^26 - 6 * q^27 - 44 * q^29 + 2 * q^30 - 3 * q^31 + 3 * q^32 - 5 * q^33 - 14 * q^34 + 6 * q^36 - 3 * q^37 + 12 * q^38 + 5 * q^39 - 2 * q^40 + 14 * q^41 + 10 * q^43 + 5 * q^44 + 2 * q^45 - 7 * q^46 - 11 * q^47 - 6 * q^48 + 18 * q^50 + 7 * q^51 - 5 * q^52 + 2 * q^53 - 3 * q^54 + 16 * q^55 - 24 * q^57 - 22 * q^58 - 26 * q^59 - 2 * q^60 + 5 * q^61 - 6 * q^62 + 6 * q^64 + 15 * q^65 + 5 * q^66 - 26 * q^67 - 7 * q^68 + 14 * q^69 - 8 * q^71 + 3 * q^72 - q^73 + 3 * q^74 - 9 * q^75 + 24 * q^76 + 10 * q^78 + 3 * q^79 + 2 * q^80 - 3 * q^81 + 7 * q^82 + 26 * q^83 + 14 * q^85 + 5 * q^86 - 22 * q^87 - 5 * q^88 + 18 * q^89 + 4 * q^90 - 14 * q^92 + 3 * q^93 + 11 * q^94 + 15 * q^95 - 3 * q^96 + 20 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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