LMFDB - Embedded newform 495.2.n.g.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 5x^14 - 8x^13 + 47x^12 + 32x^11 + 171x^10 + 26x^9 + 360x^8 - 172x^7 + 471x^6 - 430x^5 + 383x^4 + 70x^3 + 17x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.3
Root			$-0.166559 + 0.121012i$ of defining polynomial
Character	$\chi$	$=$	495.181
Dual form			495.2.n.g.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.372637 + 1.14686i) q^{2} +(0.441609 - 0.320848i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-3.49122 + 2.53652i) q^{7} +(2.48368 + 1.80450i) q^{8} +O(q^{10})$	\(q+(0.372637 + 1.14686i) q^{2} +(0.441609 - 0.320848i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-3.49122 + 2.53652i) q^{7} +(2.48368 + 1.80450i) q^{8} +1.20588 q^{10} +(2.96210 - 1.49196i) q^{11} +(1.91048 + 5.87986i) q^{13} +(-4.20999 - 3.05873i) q^{14} +(-0.806633 + 2.48256i) q^{16} +(-0.248446 + 0.764638i) q^{17} +(1.51601 + 1.10144i) q^{19} +(-0.168680 - 0.519143i) q^{20} +(2.81486 + 2.84115i) q^{22} +8.08431 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-6.03145 + 4.38210i) q^{26} +(-0.727918 + 2.24030i) q^{28} +(0.857138 - 0.622747i) q^{29} +(-0.499089 - 1.53604i) q^{31} +2.99226 q^{32} -0.969511 q^{34} +(1.33353 + 4.10418i) q^{35} +(4.48304 - 3.25712i) q^{37} +(-0.698278 + 2.14908i) q^{38} +(2.48368 - 1.80450i) q^{40} +(-4.08714 - 2.96948i) q^{41} -9.87101 q^{43} +(0.829398 - 1.60925i) q^{44} +(3.01251 + 9.27156i) q^{46} +(-10.5056 - 7.63280i) q^{47} +(3.59157 - 11.0537i) q^{49} +(0.372637 - 1.14686i) q^{50} +(2.73023 + 1.98363i) q^{52} +(-0.823336 - 2.53397i) q^{53} +(-0.503601 - 3.27817i) q^{55} -13.2482 q^{56} +(1.03360 + 0.750957i) q^{58} +(-5.34734 + 3.88507i) q^{59} +(-1.65250 + 5.08587i) q^{61} +(1.57564 - 1.14477i) q^{62} +(2.72829 + 8.39682i) q^{64} +6.18245 q^{65} -7.49018 q^{67} +(0.135616 + 0.417384i) q^{68} +(-4.20999 + 3.05873i) q^{70} +(-1.80140 + 5.54415i) q^{71} +(-3.88448 + 2.82224i) q^{73} +(5.40600 + 3.92769i) q^{74} +1.02288 q^{76} +(-6.55696 + 12.7222i) q^{77} +(-4.31076 - 13.2672i) q^{79} +(2.11179 + 1.53431i) q^{80} +(1.88255 - 5.79391i) q^{82} +(3.72575 - 11.4667i) q^{83} +(0.650440 + 0.472572i) q^{85} +(-3.67830 - 11.3206i) q^{86} +(10.0491 + 1.63955i) q^{88} +12.7727 q^{89} +(-21.5843 - 15.6819i) q^{91} +(3.57011 - 2.59383i) q^{92} +(4.83894 - 14.8927i) q^{94} +(1.51601 - 1.10144i) q^{95} +(0.416434 + 1.28165i) q^{97} +14.0154 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8	$ 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8 + 8 * q^10 + 4 * q^11 + 2 * q^13 - 22 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 + 2 * q^20 - 28 * q^22 + 8 * q^23 - 4 * q^25 + 6 * q^26 - 2 * q^28 - 26 * q^29 - 10 * q^31 + 56 * q^32 - 4 * q^34 - 4 * q^35 + 22 * q^37 - 30 * q^38 - 6 * q^40 - 6 * q^41 + 28 * q^43 + 68 * q^44 + 16 * q^46 - 20 * q^47 + 10 * q^49 - 2 * q^50 + 30 * q^52 + 14 * q^53 - 6 * q^55 + 68 * q^56 - 6 * q^58 - 16 * q^59 - 38 * q^61 - 20 * q^62 + 10 * q^64 + 12 * q^65 + 20 * q^67 - 48 * q^68 - 22 * q^70 - 54 * q^71 + 2 * q^73 + 28 * q^74 - 44 * q^76 + 34 * q^77 - 12 * q^79 - 22 * q^80 + 30 * q^82 - 28 * q^83 - 4 * q^85 + 74 * q^86 + 46 * q^88 + 76 * q^89 - 34 * q^91 - 8 * q^92 - 10 * q^94 - 4 * q^95 - 18 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	0.372637	+	1.14686i	0.263494	+	0.810951i	0.992037	+	0.125950i	$0.0401980\pi$
$2$	0.372637	+	1.14686i	0.263494	+	0.810951i	−0.728543	+	0.685001i	$0.759802\pi$
$3$		0			0
$3$		0			0
$4$	0.441609	−	0.320848i	0.220805	−	0.160424i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$		0			0
$7$	−3.49122	+	2.53652i	−1.31956	+	0.958715i	−0.319620	+	0.947546i	$0.603555\pi$
$7$	−3.49122	+	2.53652i	−1.31956	+	0.958715i	−0.999938	+	0.0111694i	$0.996445\pi$
$8$	2.48368	+	1.80450i	0.878113	+	0.637986i
$9$		0			0
$10$	1.20588			0.381332
$11$	2.96210	−	1.49196i	0.893107	−	0.449844i
$11$	2.96210	−	1.49196i	0.893107	−	0.449844i
$12$		0			0
$13$	1.91048	+	5.87986i	0.529873	+	1.63078i	0.754474	+	0.656329i	$0.227892\pi$
$13$	1.91048	+	5.87986i	0.529873	+	1.63078i	−0.224602	+	0.974451i	$0.572108\pi$
$14$	−4.20999	−	3.05873i	−1.12517	−	0.817481i
$15$		0			0
$16$	−0.806633	+	2.48256i	−0.201658	+	0.620640i
$17$	−0.248446	+	0.764638i	−0.0602570	+	0.185452i	−0.976654	−	0.214819i	$-0.931084\pi$
$17$	−0.248446	+	0.764638i	−0.0602570	+	0.185452i	0.916397	+	0.400271i	$0.131084\pi$
$18$		0			0
$19$	1.51601	+	1.10144i	0.347795	+	0.252688i	0.747944	−	0.663762i	$-0.231041\pi$
$19$	1.51601	+	1.10144i	0.347795	+	0.252688i	−0.400148	+	0.916450i	$0.631041\pi$
$20$	−0.168680	−	0.519143i	−0.0377179	−	0.116084i
$21$		0			0
$22$	2.81486	+	2.84115i	0.600129	+	0.605735i
$23$	8.08431			1.68570			0.842848	−	0.538152i	$-0.180877\pi$
$23$	8.08431			1.68570			0.842848	+	0.538152i	$0.180877\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−6.03145	+	4.38210i	−1.18286	+	0.859401i
$27$		0			0
$28$	−0.727918	+	2.24030i	−0.137564	+	0.423377i
$29$	0.857138	−	0.622747i	0.159166	−	0.115641i	−0.505351	−	0.862914i	$-0.668637\pi$
$29$	0.857138	−	0.622747i	0.159166	−	0.115641i	0.664518	+	0.747273i	$0.268637\pi$
$30$		0			0
$31$	−0.499089	−	1.53604i	−0.0896391	−	0.275881i	0.896180	−	0.443690i	$-0.146331\pi$
$31$	−0.499089	−	1.53604i	−0.0896391	−	0.275881i	−0.985820	+	0.167809i	$0.946331\pi$
$32$	2.99226			0.528962
$33$		0			0
$34$	−0.969511			−0.166270
$35$	1.33353	+	4.10418i	0.225407	+	0.693733i
$36$		0			0
$37$	4.48304	−	3.25712i	0.737007	−	0.535467i	−0.154765	−	0.987951i	$-0.549462\pi$
$37$	4.48304	−	3.25712i	0.737007	−	0.535467i	0.891772	+	0.452484i	$0.149462\pi$
$38$	−0.698278	+	2.14908i	−0.113276	+	0.348627i
$39$		0			0
$40$	2.48368	−	1.80450i	0.392704	−	0.285316i
$41$	−4.08714	−	2.96948i	−0.638304	−	0.463755i	0.220963	−	0.975282i	$-0.429080\pi$
$41$	−4.08714	−	2.96948i	−0.638304	−	0.463755i	−0.859267	+	0.511527i	$0.829080\pi$
$42$		0			0
$43$	−9.87101			−1.50531			−0.752657	−	0.658412i	$-0.771228\pi$
$43$	−9.87101			−1.50531			−0.752657	+	0.658412i	$0.771228\pi$
$44$	0.829398	−	1.60925i	0.125037	−	0.242603i
$45$		0			0
$46$	3.01251	+	9.27156i	0.444171	+	1.36702i
$47$	−10.5056	−	7.63280i	−1.53241	−	1.11336i	−0.954883	−	0.296983i	$-0.904020\pi$
$47$	−10.5056	−	7.63280i	−1.53241	−	1.11336i	−0.577523	−	0.816375i	$-0.695980\pi$
$48$		0			0
$49$	3.59157	−	11.0537i	0.513082	−	1.57910i
$50$	0.372637	−	1.14686i	0.0526988	−	0.162190i
$51$		0			0
$52$	2.73023	+	1.98363i	0.378614	+	0.275079i
$53$	−0.823336	−	2.53397i	−0.113094	−	0.348067i	0.878451	−	0.477833i	$-0.158578\pi$
$53$	−0.823336	−	2.53397i	−0.113094	−	0.348067i	−0.991545	+	0.129766i	$0.958578\pi$
$54$		0			0
$55$	−0.503601	−	3.27817i	−0.0679055	−	0.442028i
$56$	−13.2482			−1.77037
$57$		0			0
$58$	1.03360	+	0.750957i	0.135719	+	0.0986054i
$59$	−5.34734	+	3.88507i	−0.696165	+	0.505793i	−0.878681	−	0.477410i	$-0.841576\pi$
$59$	−5.34734	+	3.88507i	−0.696165	+	0.505793i	0.182516	+	0.983203i	$0.441576\pi$
$60$		0			0
$61$	−1.65250	+	5.08587i	−0.211581	+	0.651178i	0.787798	+	0.615934i	$0.211221\pi$
$61$	−1.65250	+	5.08587i	−0.211581	+	0.651178i	−0.999379	+	0.0352447i	$0.988779\pi$
$62$	1.57564	−	1.14477i	0.200106	−	0.145386i
$63$		0			0
$64$	2.72829	+	8.39682i	0.341037	+	1.04960i
$65$	6.18245			0.766839
$66$		0			0
$67$	−7.49018			−0.915071			−0.457536	−	0.889191i	$-0.651268\pi$
$67$	−7.49018			−0.915071			−0.457536	+	0.889191i	$0.651268\pi$
$68$	0.135616	+	0.417384i	0.0164459	+	0.0506153i
$69$		0			0
$70$	−4.20999	+	3.05873i	−0.503190	+	0.365589i
$71$	−1.80140	+	5.54415i	−0.213787	+	0.657970i	0.785450	+	0.618925i	$0.212432\pi$
$71$	−1.80140	+	5.54415i	−0.213787	+	0.657970i	−0.999237	+	0.0390448i	$0.987568\pi$
$72$		0			0
$73$	−3.88448	+	2.82224i	−0.454643	+	0.330318i	−0.791426	−	0.611265i	$-0.790661\pi$
$73$	−3.88448	+	2.82224i	−0.454643	+	0.330318i	0.336783	+	0.941582i	$0.390661\pi$
$74$	5.40600	+	3.92769i	0.628435	+	0.456584i
$75$		0			0
$76$	1.02288			0.117332
$77$	−6.55696	+	12.7222i	−0.747235	+	1.44983i
$78$		0			0
$79$	−4.31076	−	13.2672i	−0.484998	−	1.49267i	−0.831983	−	0.554801i	$-0.812794\pi$
$79$	−4.31076	−	13.2672i	−0.484998	−	1.49267i	0.346985	−	0.937871i	$-0.387206\pi$
$80$	2.11179	+	1.53431i	0.236106	+	0.171541i
$81$		0			0
$82$	1.88255	−	5.79391i	0.207893	−	0.639830i
$83$	3.72575	−	11.4667i	0.408954	−	1.25863i	−0.508595	−	0.861006i	$-0.669835\pi$
$83$	3.72575	−	11.4667i	0.408954	−	1.25863i	0.917548	−	0.397624i	$-0.130165\pi$
$84$		0			0
$85$	0.650440	+	0.472572i	0.0705501	+	0.0512576i
$86$	−3.67830	−	11.3206i	−0.396641	−	1.22074i
$87$		0			0
$88$	10.0491	+	1.63955i	1.07124	+	0.174777i
$89$	12.7727			1.35390			0.676951	−	0.736028i	$-0.263301\pi$
$89$	12.7727			1.35390			0.676951	+	0.736028i	$0.263301\pi$
$90$		0			0
$91$	−21.5843	−	15.6819i	−2.26265	−	1.64391i
$92$	3.57011	−	2.59383i	0.372209	−	0.270426i
$93$		0			0
$94$	4.83894	−	14.8927i	0.499099	−	1.53607i
$95$	1.51601	−	1.10144i	0.155539	−	0.113006i
$96$		0			0
$97$	0.416434	+	1.28165i	0.0422825	+	0.130132i	0.969969	−	0.243227i	$-0.0782060\pi$
$97$	0.416434	+	1.28165i	0.0422825	+	0.130132i	−0.927687	+	0.373359i	$0.878206\pi$
$98$	14.0154			1.41577
$99$		0			0
$100$	−0.545859			−0.0545859
$101$	−2.60486	−	8.01692i	−0.259193	−	0.797713i	−0.992975	−	0.118328i	$-0.962247\pi$
$101$	−2.60486	−	8.01692i	−0.259193	−	0.797713i	0.733782	−	0.679385i	$-0.237753\pi$
$102$		0			0
$103$	8.00959	−	5.81931i	0.789208	−	0.573393i	−0.118520	−	0.992952i	$-0.537815\pi$
$103$	8.00959	−	5.81931i	0.789208	−	0.573393i	0.907728	+	0.419558i	$0.137815\pi$
$104$	−5.86517	+	18.0511i	−0.575127	+	1.77006i
$105$		0			0
$106$	2.59930	−	1.88850i	0.252466	−	0.183427i
$107$	−6.60758	−	4.80069i	−0.638779	−	0.464100i	0.220652	−	0.975353i	$-0.429182\pi$
$107$	−6.60758	−	4.80069i	−0.638779	−	0.464100i	−0.859430	+	0.511253i	$0.829182\pi$
$108$		0			0
$109$	13.4997			1.29303			0.646517	−	0.762900i	$-0.276225\pi$
$109$	13.4997			1.29303			0.646517	+	0.762900i	$0.276225\pi$
$110$	3.57193	−	1.79912i	0.340570	−	0.171540i
$111$		0			0
$112$	−3.48094	−	10.7132i	−0.328917	−	1.01230i
$113$	10.9303	+	7.94132i	1.02824	+	0.747057i	0.967955	−	0.251125i	$-0.0808004\pi$
$113$	10.9303	+	7.94132i	1.02824	+	0.747057i	0.0602808	+	0.998181i	$0.480800\pi$
$114$		0			0
$115$	2.49819	−	7.68864i	0.232957	−	0.716969i
$116$	0.178713	−	0.550022i	0.0165931	−	0.0510682i
$117$		0			0
$118$	−6.44824	−	4.68492i	−0.593609	−	0.431282i
$119$	−1.07214	−	3.29971i	−0.0982830	−	0.302484i
$120$		0			0
$121$	6.54810	−	8.83869i	0.595281	−	0.803517i
$122$	−6.44855			−0.583824
$123$		0			0
$124$	−0.713237	−	0.518197i	−0.0640506	−	0.0465355i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	−0.655154	+	2.01636i	−0.0581355	+	0.178923i	−0.975907	−	0.218186i	$-0.929986\pi$
$127$	−0.655154	+	2.01636i	−0.0581355	+	0.178923i	0.917772	+	0.397108i	$0.129986\pi$
$128$	−3.77172	+	2.74031i	−0.333376	+	0.242212i
$129$		0			0
$130$	2.30381	+	7.09039i	0.202057	+	0.621869i
$131$	8.72324			0.762153			0.381076	−	0.924544i	$-0.375553\pi$
$131$	8.72324			0.762153			0.381076	+	0.924544i	$0.375553\pi$
$132$		0			0
$133$	−8.08654			−0.701192
$134$	−2.79112	−	8.59017i	−0.241116	−	0.742078i
$135$		0			0
$136$	−1.99685	+	1.45079i	−0.171228	+	0.124405i
$137$	−0.477068	+	1.46826i	−0.0407587	+	0.125442i	−0.969365	−	0.245623i	$-0.921007\pi$
$137$	−0.477068	+	1.46826i	−0.0407587	+	0.125442i	0.928607	+	0.371065i	$0.121007\pi$
$138$		0			0
$139$	−13.1046	+	9.52107i	−1.11152	+	0.807566i	−0.982902	−	0.184128i	$-0.941054\pi$
$139$	−13.1046	+	9.52107i	−1.11152	+	0.807566i	−0.128617	+	0.991694i	$0.541054\pi$
$140$	1.90572	+	1.38458i	0.161062	+	0.117019i
$141$		0			0
$142$	−7.02962			−0.589913
$143$	14.4316	+	14.5664i	1.20683	+	1.21810i
$144$		0			0
$145$	−0.327397	−	1.00763i	−0.0271889	−	0.0836788i
$146$	−4.68420	−	3.40327i	−0.387667	−	0.281657i
$147$		0			0
$148$	0.934712	−	2.87675i	0.0768329	−	0.236467i
$149$	4.33189	−	13.3322i	0.354883	−	1.09222i	−0.601195	−	0.799102i	$-0.705308\pi$
$149$	4.33189	−	13.3322i	0.354883	−	1.09222i	0.956078	−	0.293114i	$-0.0946915\pi$
$150$		0			0
$151$	10.9906	+	7.98516i	0.894404	+	0.649823i	0.937023	−	0.349269i	$-0.113570\pi$
$151$	10.9906	+	7.98516i	0.894404	+	0.649823i	−0.0426183	+	0.999091i	$0.513570\pi$
$152$	1.77772	+	5.47126i	0.144192	+	0.443777i
$153$		0			0
$154$	−17.0339	−	2.77914i	−1.37263	−	0.223950i
$155$	−1.61509			−0.129727
$156$		0			0
$157$	3.54409	+	2.57493i	0.282849	+	0.205502i	0.720159	−	0.693809i	$-0.244069\pi$
$157$	3.54409	+	2.57493i	0.282849	+	0.205502i	−0.437310	+	0.899311i	$0.644069\pi$
$158$	13.6092	−	9.88766i	1.08269	−	0.786620i
$159$		0			0
$160$	0.924660	−	2.84581i	0.0731008	−	0.224981i
$161$	−28.2241	+	20.5060i	−2.22437	+	1.61610i
$162$		0			0
$163$	−1.44826	−	4.45729i	−0.113437	−	0.349122i	0.878181	−	0.478328i	$-0.158757\pi$
$163$	−1.44826	−	4.45729i	−0.113437	−	0.349122i	−0.991618	+	0.129206i	$0.958757\pi$
$164$	−2.75767			−0.215338
$165$		0			0
$166$	14.5390			1.12844
$167$	0.509622	+	1.56846i	0.0394358	+	0.121371i	0.968836	−	0.247702i	$-0.0796753\pi$
$167$	0.509622	+	1.56846i	0.0394358	+	0.121371i	−0.929401	+	0.369073i	$0.879675\pi$
$168$		0			0
$169$	−20.4056	+	14.8255i	−1.56966	+	1.14043i
$170$	−0.299595	+	0.922060i	−0.0229779	+	0.0707188i
$171$		0			0
$172$	−4.35913	+	3.16709i	−0.332380	+	0.241489i
$173$	13.4072	+	9.74090i	1.01933	+	0.740587i	0.966146	−	0.257998i	$-0.0830626\pi$
$173$	13.4072	+	9.74090i	1.01933	+	0.740587i	0.0531852	+	0.998585i	$0.483063\pi$
$174$		0			0
$175$	4.31539			0.326213
$176$	1.31456	+	8.55707i	0.0990886	+	0.645013i
$177$		0			0
$178$	4.75957	+	14.6485i	0.356745	+	1.09795i
$179$	−14.2383	−	10.3447i	−1.06422	−	0.773201i	−0.0893553	−	0.996000i	$-0.528481\pi$
$179$	−14.2383	−	10.3447i	−1.06422	−	0.773201i	−0.974864	+	0.222799i	$0.928481\pi$
$180$		0			0
$181$	2.59782	−	7.99527i	0.193094	−	0.594284i	−0.806899	−	0.590689i	$-0.798856\pi$
$181$	2.59782	−	7.99527i	0.193094	−	0.594284i	0.999994	−	0.00359434i	$-0.00114412\pi$
$182$	9.94183	−	30.5978i	0.736937	−	2.26806i
$183$		0			0
$184$	20.0788	+	14.5881i	1.48023	+	1.07545i
$185$	−1.71237	−	5.27013i	−0.125896	−	0.387468i
$186$		0			0
$187$	0.404889	+	2.63561i	0.0296084	+	0.192735i
$188$	−7.08835			−0.516971
$189$		0			0
$190$	1.82812	+	1.32820i	0.132626	+	0.0963581i
$191$	4.30212	−	3.12567i	0.311290	−	0.226166i	−0.421160	−	0.906987i	$-0.638377\pi$
$191$	4.30212	−	3.12567i	0.311290	−	0.226166i	0.732450	+	0.680821i	$0.238377\pi$
$192$		0			0
$193$	4.72401	−	14.5390i	0.340042	−	1.04654i	−0.624143	−	0.781310i	$-0.714552\pi$
$193$	4.72401	−	14.5390i	0.340042	−	1.04654i	0.964185	−	0.265231i	$-0.0854483\pi$
$194$	−1.31469	+	0.955181i	−0.0943895	+	0.0685780i
$195$		0			0
$196$	−1.96049	−	6.03378i	−0.140035	−	0.430984i
$197$	−1.69118			−0.120492			−0.0602458	−	0.998184i	$-0.519188\pi$
$197$	−1.69118			−0.120492			−0.0602458	+	0.998184i	$0.519188\pi$
$198$		0			0
$199$	3.44855			0.244461			0.122230	−	0.992502i	$-0.460995\pi$
$199$	3.44855			0.244461			0.122230	+	0.992502i	$0.460995\pi$
$200$	−0.948680	−	2.91974i	−0.0670818	−	0.206457i
$201$		0			0
$202$	8.22360	−	5.97480i	0.578611	−	0.420385i
$203$	−1.41285	+	4.34830i	−0.0991624	+	0.305191i
$204$		0			0
$205$	−4.08714	+	2.96948i	−0.285458	+	0.207398i
$206$	9.65858	+	7.01737i	0.672945	+	0.488923i
$207$		0			0
$208$	−16.1382			−1.11898
$209$	6.13387	+	1.00076i	0.424289	+	0.0692241i
$210$		0			0
$211$	−0.121891	−	0.375140i	−0.00839129	−	0.0258257i	0.946773	−	0.321901i	$-0.104322\pi$
$211$	−0.121891	−	0.375140i	−0.00839129	−	0.0258257i	−0.955164	+	0.296076i	$0.904322\pi$
$212$	−1.17661	−	0.854858i	−0.0808100	−	0.0587119i
$213$		0			0
$214$	3.04348	−	9.36687i	0.208048	−	0.640306i
$215$	−3.05031	+	9.38789i	−0.208029	+	0.640249i
$216$		0			0
$217$	5.63863	+	4.09670i	0.382775	+	0.278102i
$218$	5.03047	+	15.4822i	0.340707	+	1.04859i
$219$		0			0
$220$	−1.27419	−	1.28609i	−0.0859057	−	0.0867082i
$221$	−4.97062			−0.334360
$222$		0			0
$223$	6.28724	+	4.56795i	0.421025	+	0.305893i	0.778050	−	0.628202i	$-0.216209\pi$
$223$	6.28724	+	4.56795i	0.421025	+	0.305893i	−0.357025	+	0.934095i	$0.616209\pi$
$224$	−10.4467	+	7.58994i	−0.697996	+	0.507124i
$225$		0			0
$226$	−5.03454	+	15.4947i	−0.334893	+	1.03069i
$227$	−22.0993	+	16.0560i	−1.46678	+	1.06568i	−0.485248	+	0.874377i	$0.661271\pi$
$227$	−22.0993	+	16.0560i	−1.46678	+	1.06568i	−0.981531	+	0.191301i	$0.938729\pi$
$228$		0			0
$229$	4.81517	+	14.8196i	0.318195	+	0.979304i	0.974419	+	0.224738i	$0.0721526\pi$
$229$	4.81517	+	14.8196i	0.318195	+	0.979304i	−0.656224	+	0.754566i	$0.727847\pi$
$230$	9.74869			0.642810
$231$		0			0
$232$	3.25260			0.213544
$233$	−8.61681	−	26.5198i	−0.564506	−	1.73737i	−0.669414	−	0.742889i	$-0.733455\pi$
$233$	−8.61681	−	26.5198i	−0.564506	−	1.73737i	0.104908	−	0.994482i	$-0.466545\pi$
$234$		0			0
$235$	−10.5056	+	7.63280i	−0.685313	+	0.497909i
$236$	−1.11492	+	3.43137i	−0.0725750	+	0.223363i
$237$		0			0
$238$	3.38478	−	2.45919i	0.219403	−	0.159405i
$239$	−15.1657	−	11.0185i	−0.980988	−	0.712729i	−0.0230587	−	0.999734i	$-0.507340\pi$
$239$	−15.1657	−	11.0185i	−0.980988	−	0.712729i	−0.957929	+	0.287005i	$0.907340\pi$
$240$		0			0
$241$	−11.0049			−0.708886			−0.354443	−	0.935078i	$-0.615329\pi$
$241$	−11.0049			−0.708886			−0.354443	+	0.935078i	$0.615329\pi$
$242$	12.5768	+	4.21611i	0.808466	+	0.271022i
$243$		0			0
$244$	0.902031	+	2.77617i	0.0577466	+	0.177726i
$245$	−9.40286	−	6.83158i	−0.600727	−	0.436454i
$246$		0			0
$247$	−3.58003	+	11.0182i	−0.227792	+	0.701070i
$248$	1.53220	−	4.71563i	0.0972949	−	0.299443i
$249$		0			0
$250$	−0.975576	−	0.708797i	−0.0617008	−	0.0448283i
$251$	−7.20429	−	22.1725i	−0.454731	−	1.39952i	−0.871451	−	0.490482i	$-0.836821\pi$
$251$	−7.20429	−	22.1725i	−0.454731	−	1.39952i	0.416721	−	0.909035i	$-0.363179\pi$
$252$		0			0
$253$	23.9466	−	12.0615i	1.50551	−	0.758299i
$254$	−2.55661			−0.160416
$255$		0			0
$256$	9.73730	+	7.07456i	0.608581	+	0.442160i
$257$	−14.1360	+	10.2704i	−0.881779	+	0.640650i	−0.933721	−	0.358000i	$-0.883459\pi$
$257$	−14.1360	+	10.2704i	−0.881779	+	0.640650i	0.0519427	+	0.998650i	$0.483459\pi$
$258$		0			0
$259$	−7.38954	+	22.7427i	−0.459164	+	1.41316i
$260$	2.73023	−	1.98363i	0.169322	−	0.123019i
$261$		0			0
$262$	3.25060	+	10.0043i	0.200823	+	0.618069i
$263$	1.61187			0.0993921			0.0496961	−	0.998764i	$-0.484175\pi$
$263$	1.61187			0.0993921			0.0496961	+	0.998764i	$0.484175\pi$
$264$		0			0
$265$	−2.66437			−0.163671
$266$	−3.01334	−	9.27412i	−0.184760	−	0.568633i
$267$		0			0
$268$	−3.30773	+	2.40321i	−0.202052	+	0.146799i
$269$	2.52549	−	7.77266i	0.153982	−	0.473908i	−0.844074	−	0.536226i	$-0.819849\pi$
$269$	2.52549	−	7.77266i	0.153982	−	0.473908i	0.998056	+	0.0623184i	$0.0198494\pi$
$270$		0			0
$271$	−8.49430	+	6.17147i	−0.515992	+	0.374890i	−0.815092	−	0.579332i	$-0.803314\pi$
$271$	−8.49430	+	6.17147i	−0.515992	+	0.374890i	0.299100	+	0.954222i	$0.403314\pi$
$272$	−1.69786	−	1.23356i	−0.102948	−	0.0747958i
$273$		0			0
$274$	−1.86166			−0.112467
$275$	−3.27334	−	0.534057i	−0.197390	−	0.0322048i
$276$		0			0
$277$	2.75712	+	8.48554i	0.165659	+	0.509846i	0.999084	−	0.0427860i	$-0.0136234\pi$
$277$	2.75712	+	8.48554i	0.165659	+	0.509846i	−0.833425	+	0.552632i	$0.813623\pi$
$278$	−15.8026	−	11.4812i	−0.947775	−	0.688599i
$279$		0			0
$280$	−4.09392	+	12.5998i	−0.244659	+	0.752982i
$281$	1.35769	−	4.17854i	0.0809930	−	0.249271i	−0.902358	−	0.430987i	$-0.858165\pi$
$281$	1.35769	−	4.17854i	0.0809930	−	0.249271i	0.983351	+	0.181717i	$0.0581654\pi$
$282$		0			0
$283$	−10.5211	−	7.64404i	−0.625416	−	0.454391i	0.229393	−	0.973334i	$-0.426326\pi$
$283$	−10.5211	−	7.64404i	−0.625416	−	0.454391i	−0.854809	+	0.518943i	$0.826326\pi$
$284$	0.983313	+	3.02633i	0.0583489	+	0.179579i
$285$		0			0
$286$	−11.3278	+	21.9789i	−0.669829	+	1.29964i
$287$	21.8013			1.28689
$288$		0			0
$289$	13.2303	+	9.61241i	0.778255	+	0.565436i
$290$	1.03360	−	0.750957i	0.0606953	−	0.0440977i
$291$		0			0
$292$	−0.809912	+	2.49265i	−0.0473965	+	0.145871i
$293$	−12.5757	+	9.13679i	−0.734681	+	0.533777i	−0.891041	−	0.453923i	$-0.850024\pi$
$293$	−12.5757	+	9.13679i	−0.734681	+	0.533777i	0.156360	+	0.987700i	$0.450024\pi$
$294$		0			0
$295$	2.04250	+	6.28618i	0.118919	+	0.365996i
$296$	17.0119			0.988796
$297$		0			0
$298$	16.9044			0.979243
$299$	15.4449	+	47.5346i	0.893204	+	2.74900i
$300$		0			0
$301$	34.4619	−	25.0380i	1.98635	−	1.44317i
$302$	−5.06233	+	15.5802i	−0.291304	+	0.896542i
$303$		0			0
$304$	−3.95726	+	2.87512i	−0.226964	+	0.164899i
$305$	4.32630	+	3.14324i	0.247723	+	0.179981i
$306$		0			0
$307$	8.76859			0.500450			0.250225	−	0.968188i	$-0.419495\pi$
$307$	8.76859			0.500450			0.250225	+	0.968188i	$0.419495\pi$
$308$	1.18628	+	7.72203i	0.0675945	+	0.440004i
$309$		0			0
$310$	−0.601841	−	1.85228i	−0.0341823	−	0.105202i
$311$	1.41676	+	1.02934i	0.0803370	+	0.0583682i	0.627229	−	0.778835i	$-0.284189\pi$
$311$	1.41676	+	1.02934i	0.0803370	+	0.0583682i	−0.546892	+	0.837203i	$0.684189\pi$
$312$		0			0
$313$	−5.41621	+	16.6694i	−0.306142	+	0.942209i	0.673106	+	0.739546i	$0.264960\pi$
$313$	−5.41621	+	16.6694i	−0.306142	+	0.942209i	−0.979249	+	0.202663i	$0.935040\pi$
$314$	−1.63242	+	5.02408i	−0.0921230	+	0.283525i
$315$		0			0
$316$	−6.16041	−	4.47580i	−0.346550	−	0.251783i
$317$	−0.615520	−	1.89438i	−0.0345711	−	0.106399i	0.932282	−	0.361733i	$-0.117815\pi$
$317$	−0.615520	−	1.89438i	−0.0345711	−	0.106399i	−0.966853	+	0.255334i	$0.917815\pi$
$318$		0			0
$319$	1.60981	−	3.12346i	0.0901323	−	0.174880i
$320$	8.82894			0.493553
$321$		0			0
$322$	−34.0348	−	24.7278i	−1.89669	−	1.37802i
$323$	−1.21885	+	0.885546i	−0.0678186	+	0.0492731i
$324$		0			0
$325$	1.91048	−	5.87986i	0.105975	−	0.326156i
$326$	4.57220	−	3.32190i	0.253231	−	0.183983i
$327$		0			0
$328$	−4.79272	−	14.7505i	−0.264634	−	0.814458i
$329$	56.0383			3.08949
$330$		0			0
$331$	−10.3437			−0.568541			−0.284271	−	0.958744i	$-0.591751\pi$
$331$	−10.3437			−0.568541			−0.284271	+	0.958744i	$0.591751\pi$
$332$	−2.03373	−	6.25918i	−0.111616	−	0.343517i
$333$		0			0
$334$	−1.60889	+	1.16893i	−0.0880347	+	0.0639609i
$335$	−2.31459	+	7.12359i	−0.126460	+	0.389203i
$336$		0			0
$337$	16.6809	−	12.1194i	0.908667	−	0.660185i	−0.0320107	−	0.999488i	$-0.510191\pi$
$337$	16.6809	−	12.1194i	0.908667	−	0.660185i	0.940677	+	0.339303i	$0.110191\pi$
$338$	−24.6067	−	17.8778i	−1.33843	−	0.972423i
$339$		0			0
$340$	0.438864			0.0238007
$341$	−3.77007	−	3.80528i	−0.204161	−	0.206068i
$342$		0			0
$343$	6.16434	+	18.9719i	0.332843	+	1.02438i
$344$	−24.5164	−	17.8122i	−1.32184	−	0.960370i
$345$		0			0
$346$	−6.17542	+	19.0060i	−0.331992	+	1.02177i
$347$	0.922028	−	2.83771i	0.0494971	−	0.152336i	−0.923253	−	0.384193i	$-0.874480\pi$
$347$	0.922028	−	2.83771i	0.0494971	−	0.152336i	0.972750	+	0.231856i	$0.0744799\pi$
$348$		0			0
$349$	−9.13355	−	6.63591i	−0.488908	−	0.355212i	0.315857	−	0.948807i	$-0.397708\pi$
$349$	−9.13355	−	6.63591i	−0.488908	−	0.355212i	−0.804764	+	0.593595i	$0.797708\pi$
$350$	1.60807	+	4.94914i	0.0859551	+	0.264542i
$351$		0			0
$352$	8.86339	−	4.46434i	0.472420	−	0.237950i
$353$	−13.4952			−0.718275			−0.359137	−	0.933285i	$-0.616929\pi$
$353$	−13.4952			−0.718275			−0.359137	+	0.933285i	$0.616929\pi$
$354$		0			0
$355$	4.71614	+	3.42647i	0.250307	+	0.181858i
$356$	5.64054	−	4.09809i	0.298948	−	0.217198i
$357$		0			0
$358$	6.55822	−	20.1841i	0.346613	−	1.06676i
$359$	19.9818	−	14.5176i	1.05460	−	0.766211i	0.0815173	−	0.996672i	$-0.474023\pi$
$359$	19.9818	−	14.5176i	1.05460	−	0.766211i	0.973082	+	0.230461i	$0.0740234\pi$
$360$		0			0
$361$	−4.78623	−	14.7305i	−0.251907	−	0.775289i
$362$	10.1375			0.532814
$363$		0			0
$364$	−14.5633			−0.763327
$365$	1.48374	+	4.56647i	0.0776624	+	0.239020i
$366$		0			0
$367$	−5.13314	+	3.72944i	−0.267948	+	0.194675i	−0.713643	−	0.700509i	$-0.752956\pi$
$367$	−5.13314	+	3.72944i	−0.267948	+	0.194675i	0.445696	+	0.895184i	$0.352956\pi$
$368$	−6.52107	+	20.0698i	−0.339934	+	1.04621i
$369$		0			0
$370$	5.40600	−	3.92769i	0.281044	−	0.204191i
$371$	9.30191	+	6.75823i	0.482931	+	0.350870i
$372$		0			0
$373$	13.1832			0.682601			0.341301	−	0.939954i	$-0.389133\pi$
$373$	13.1832			0.682601			0.341301	+	0.939954i	$0.389133\pi$
$374$	−2.87179	+	1.44647i	−0.148497	+	0.0747954i
$375$		0			0
$376$	−12.3193	−	37.9148i	−0.635318	−	1.95531i
$377$	5.29921	+	3.85010i	0.272923	+	0.198290i
$378$		0			0
$379$	−5.72802	+	17.6290i	−0.294229	+	0.905543i	0.689251	+	0.724523i	$0.257940\pi$
$379$	−5.72802	+	17.6290i	−0.294229	+	0.905543i	−0.983479	+	0.181020i	$0.942060\pi$
$380$	0.316086	−	0.972814i	0.0162149	−	0.0499043i
$381$		0			0
$382$	5.18783	+	3.76918i	0.265432	+	0.192848i
$383$	−8.77123	−	26.9951i	−0.448189	−	1.37938i	−0.878949	−	0.476917i	$-0.841754\pi$
$383$	−8.77123	−	26.9951i	−0.448189	−	1.37938i	0.430760	−	0.902467i	$-0.358246\pi$
$384$		0			0
$385$	10.0733	+	10.1674i	0.513384	+	0.518180i
$386$	18.4345			0.938293
$387$		0			0
$388$	0.595116	+	0.432377i	0.0302125	+	0.0219506i
$389$	−15.5100	+	11.2687i	−0.786388	+	0.571344i	−0.906889	−	0.421369i	$-0.861550\pi$
$389$	−15.5100	+	11.2687i	−0.786388	+	0.571344i	0.120502	+	0.992713i	$0.461550\pi$
$390$		0			0
$391$	−2.00851	+	6.18157i	−0.101575	+	0.312615i
$392$	28.8667	−	20.9729i	1.45799	−	1.05929i
$393$		0			0
$394$	−0.630196	−	1.93954i	−0.0317488	−	0.0977127i
$395$	−13.9499			−0.701896
$396$		0			0
$397$	16.2455			0.815339			0.407670	−	0.913130i	$-0.366342\pi$
$397$	16.2455			0.815339			0.407670	+	0.913130i	$0.366342\pi$
$398$	1.28505	+	3.95499i	0.0644140	+	0.198246i
$399$		0			0
$400$	2.11179	−	1.53431i	0.105590	−	0.0767154i
$401$	−3.80853	+	11.7215i	−0.190189	+	0.585342i	−0.999999	−	0.00135034i	$-0.999570\pi$
$401$	−3.80853	+	11.7215i	−0.190189	+	0.585342i	0.809810	+	0.586692i	$0.199570\pi$
$402$		0			0
$403$	8.07820	−	5.86915i	0.402404	−	0.292363i
$404$	−3.72254	−	2.70458i	−0.185203	−	0.134558i
$405$		0			0
$406$	−5.51336			−0.273623
$407$	8.41972	−	16.3364i	0.417350	−	0.809768i
$408$		0			0
$409$	−0.604903	−	1.86170i	−0.0299106	−	0.0920552i	0.934987	−	0.354682i	$-0.115411\pi$
$409$	−0.604903	−	1.86170i	−0.0299106	−	0.0920552i	−0.964897	+	0.262627i	$0.915411\pi$
$410$	−4.92859	−	3.58083i	−0.243406	−	0.176845i
$411$		0			0
$412$	1.67000	−	5.13972i	0.0822748	−	0.253216i
$413$	8.81420	−	27.1273i	0.433718	−	1.33485i
$414$		0			0
$415$	−9.75413	−	7.08679i	−0.478811	−	0.347877i
$416$	5.71667	+	17.5941i	0.280283	+	0.862621i
$417$		0			0
$418$	1.13797	+	7.40760i	0.0556602	+	0.362318i
$419$	20.5776			1.00528			0.502640	−	0.864496i	$-0.332362\pi$
$419$	20.5776			1.00528			0.502640	+	0.864496i	$0.332362\pi$
$420$		0			0
$421$	13.8507	+	10.0632i	0.675044	+	0.490448i	0.871710	−	0.490022i	$-0.163011\pi$
$421$	13.8507	+	10.0632i	0.675044	+	0.490448i	−0.196666	+	0.980471i	$0.563011\pi$
$422$	0.384812	−	0.279582i	0.0187324	−	0.0136098i
$423$		0			0
$424$	2.52764	−	7.77927i	0.122753	−	0.377795i
$425$	0.650440	−	0.472572i	0.0315510	−	0.0229231i
$426$		0			0
$427$	−7.13117	−	21.9475i	−0.345101	−	1.06211i
$428$	−4.45826			−0.215498
$429$		0			0
$430$	−11.9032			−0.574025
$431$	3.27801	+	10.0887i	0.157896	+	0.485955i	0.998443	−	0.0557847i	$-0.0177660\pi$
$431$	3.27801	+	10.0887i	0.157896	+	0.485955i	−0.840547	+	0.541739i	$0.817766\pi$
$432$		0			0
$433$	−20.0848	+	14.5925i	−0.965215	+	0.701270i	−0.954356	−	0.298671i	$-0.903457\pi$
$433$	−20.0848	+	14.5925i	−0.965215	+	0.701270i	−0.0108592	+	0.999941i	$0.503457\pi$
$434$	−2.59718	+	7.99329i	−0.124668	+	0.383690i
$435$		0			0
$436$	5.96158	−	4.33134i	0.285508	−	0.207434i
$437$	12.2559	+	8.90440i	0.586277	+	0.425955i
$438$		0			0
$439$	6.78781			0.323965			0.161982	−	0.986794i	$-0.448211\pi$
$439$	6.78781			0.323965			0.161982	+	0.986794i	$0.448211\pi$
$440$	4.66466	−	9.05066i	0.222379	−	0.431473i
$441$		0			0
$442$	−1.85223	−	5.70059i	−0.0881018	−	0.271149i
$443$	12.2566	+	8.90495i	0.582329	+	0.423087i	0.839563	−	0.543262i	$-0.182811\pi$
$443$	12.2566	+	8.90495i	0.582329	+	0.423087i	−0.257234	+	0.966349i	$0.582811\pi$
$444$		0			0
$445$	3.94698	−	12.1476i	0.187105	−	0.575849i
$446$	−2.89593	+	8.91276i	−0.137126	+	0.422031i
$447$		0			0
$448$	−30.8238	−	22.3948i	−1.45629	−	1.05805i
$449$	−5.54099	−	17.0534i	−0.261495	−	0.804800i	−0.992480	−	0.122406i	$-0.960939\pi$
$449$	−5.54099	−	17.0534i	−0.261495	−	0.804800i	0.730985	−	0.682394i	$-0.239061\pi$
$450$		0			0
$451$	−16.5369	−	2.69805i	−0.778691	−	0.127046i
$452$	7.37488			0.346885
$453$		0			0
$454$	−26.6490	−	19.3616i	−1.25070	−	0.908686i
$455$	−21.5843	+	15.6819i	−1.01189	+	0.735180i
$456$		0			0
$457$	−12.7310	+	39.1820i	−0.595531	+	1.83286i	−0.0434679	+	0.999055i	$0.513841\pi$
$457$	−12.7310	+	39.1820i	−0.595531	+	1.83286i	−0.552063	+	0.833802i	$0.686159\pi$
$458$	−15.2016	+	11.0446i	−0.710325	+	0.516081i
$459$		0			0
$460$	−1.36366	−	4.19691i	−0.0635809	−	0.195682i
$461$	16.8145			0.783128			0.391564	−	0.920151i	$-0.371934\pi$
$461$	16.8145			0.783128			0.391564	+	0.920151i	$0.371934\pi$
$462$		0			0
$463$	−35.7050			−1.65935			−0.829676	−	0.558245i	$-0.811475\pi$
$463$	−35.7050			−1.65935			−0.829676	+	0.558245i	$0.811475\pi$
$464$	0.854612	+	2.63023i	0.0396744	+	0.122105i
$465$		0			0
$466$	27.2035	−	19.7645i	1.26018	−	0.915573i
$467$	−11.1095	+	34.1916i	−0.514087	+	1.58220i	0.270849	+	0.962622i	$0.412696\pi$
$467$	−11.1095	+	34.1916i	−0.514087	+	1.58220i	−0.784936	+	0.619576i	$0.787304\pi$
$468$		0			0
$469$	26.1499	−	18.9990i	1.20749	−	0.877293i
$470$	−12.6685	−	9.20422i	−0.584355	−	0.424559i
$471$		0			0
$472$	−20.2917			−0.934000
$473$	−29.2389	+	14.7272i	−1.34441	+	0.677156i
$474$		0			0
$475$	−0.579062	−	1.78217i	−0.0265692	−	0.0817716i
$476$	−1.53217	−	1.11319i	−0.0702270	−	0.0510229i
$477$		0			0
$478$	6.98539	−	21.4988i	0.319504	−	0.983333i
$479$	−4.29272	+	13.2116i	−0.196139	+	0.603655i	0.803822	+	0.594870i	$0.202796\pi$
$479$	−4.29272	+	13.2116i	−0.196139	+	0.603655i	−0.999961	+	0.00878522i	$0.997204\pi$
$480$		0			0
$481$	27.7162	+	20.1370i	1.26375	+	0.918167i
$482$	−4.10082	−	12.6210i	−0.186787	−	0.574872i
$483$		0			0
$484$	0.0558246	−	6.00419i	0.00253748	−	0.272918i
$485$	1.34761			0.0611918
$486$		0			0
$487$	11.3265	+	8.22916i	0.513251	+	0.372899i	0.814055	−	0.580787i	$-0.197255\pi$
$487$	11.3265	+	8.22916i	0.513251	+	0.372899i	−0.300804	+	0.953686i	$0.597255\pi$
$488$	−13.2817	+	9.64972i	−0.601234	+	0.436822i
$489$		0			0
$490$	4.33100	−	13.3294i	0.195655	−	0.602163i
$491$	20.4259	−	14.8403i	0.921806	−	0.669731i	−0.0221670	−	0.999754i	$-0.507057\pi$
$491$	20.4259	−	14.8403i	0.921806	−	0.669731i	0.943973	+	0.330023i	$0.107057\pi$
$492$		0			0
$493$	0.263224	+	0.810119i	0.0118550	+	0.0364859i
$494$	−13.9703			−0.628555
$495$		0			0
$496$	4.21590			0.189299
$497$	−7.77376	−	23.9252i	−0.348701	−	1.07319i
$498$		0			0
$499$	7.16997	−	5.20929i	0.320972	−	0.233200i	−0.415618	−	0.909539i	$-0.636435\pi$
$499$	7.16997	−	5.20929i	0.320972	−	0.233200i	0.736590	+	0.676340i	$0.236435\pi$
$500$	−0.168680	+	0.519143i	−0.00754359	+	0.0232168i
$501$		0			0
$502$	22.7441	−	16.5246i	1.01512	−	0.737528i
$503$	−0.534909	−	0.388634i	−0.0238504	−	0.0173283i	0.575796	−	0.817593i	$-0.304692\pi$
$503$	−0.534909	−	0.388634i	−0.0238504	−	0.0173283i	−0.599647	+	0.800265i	$0.704692\pi$
$504$		0			0
$505$	−8.42949			−0.375107
$506$	22.7562	+	22.9687i	1.01164	+	1.02108i
$507$		0			0
$508$	0.357621	+	1.10065i	0.0158669	+	0.0488333i
$509$	−31.3224	−	22.7570i	−1.38834	−	1.00869i	−0.996045	−	0.0888492i	$-0.971681\pi$
$509$	−31.3224	−	22.7570i	−1.38834	−	1.00869i	−0.392295	−	0.919839i	$-0.628319\pi$
$510$		0			0
$511$	6.40290	−	19.7061i	0.283248	−	0.871747i
$512$	−7.36638	+	22.6714i	−0.325551	+	1.00194i
$513$		0			0
$514$	−17.0463	−	12.3848i	−0.751879	−	0.546272i
$515$	−3.05939	−	9.41583i	−0.134813	−	0.414911i
$516$		0			0
$517$	−42.5066	−	6.93510i	−1.86944	−	0.305005i
$518$	−28.8362			−1.26699
$519$		0			0
$520$	15.3552	+	11.1562i	0.673371	+	0.489233i
$521$	19.8803	−	14.4439i	0.870971	−	0.632797i	−0.0598763	−	0.998206i	$-0.519071\pi$
$521$	19.8803	−	14.4439i	0.870971	−	0.632797i	0.930847	+	0.365408i	$0.119071\pi$
$522$		0			0
$523$	10.4121	−	32.0453i	0.455291	−	1.40124i	−0.415501	−	0.909593i	$-0.636394\pi$
$523$	10.4121	−	32.0453i	0.455291	−	1.40124i	0.870793	−	0.491650i	$-0.163606\pi$
$524$	3.85226	−	2.79883i	0.168287	−	0.122268i
$525$		0			0
$526$	0.600642	+	1.84859i	0.0261892	+	0.0806021i
$527$	1.29851			0.0565640
$528$		0			0
$529$	42.3561			1.84157
$530$	−0.992842	−	3.05565i	−0.0431263	−	0.132729i
$531$		0			0
$532$	−3.57109	+	2.59455i	−0.154826	+	0.112488i
$533$	9.65172	−	29.7050i	0.418063	−	1.28666i
$534$		0			0
$535$	−6.60758	+	4.80069i	−0.285671	+	0.207552i
$536$	−18.6032	−	13.5160i	−0.803536	−	0.583803i
$537$		0			0
$538$	9.85523			0.424889
$539$	−5.85314	−	38.1008i	−0.252113	−	1.64112i
$540$		0			0
$541$	−2.53653	−	7.80665i	−0.109054	−	0.335634i	0.881606	−	0.471985i	$-0.156462\pi$
$541$	−2.53653	−	7.80665i	−0.109054	−	0.335634i	−0.990661	+	0.136351i	$0.956462\pi$
$542$	−10.2431	−	7.44204i	−0.439978	−	0.319663i
$543$		0			0
$544$	−0.743415	+	2.28800i	−0.0318737	+	0.0980971i
$545$	4.17163	−	12.8390i	0.178693	−	0.549960i
$546$		0			0
$547$	−28.3770	−	20.6171i	−1.21331	−	0.881523i	−0.217785	−	0.975997i	$-0.569883\pi$
$547$	−28.3770	−	20.6171i	−1.21331	−	0.881523i	−0.995527	+	0.0944734i	$0.969883\pi$
$548$	0.260412	+	0.801465i	0.0111242	+	0.0342369i
$549$		0			0
$550$	−0.607281	−	3.95307i	−0.0258945	−	0.168559i
$551$	1.98534			0.0845785
$552$		0			0
$553$	48.7022	+	35.3843i	2.07103	+	1.50469i
$554$	−8.70430	+	6.32404i	−0.369810	+	0.268683i
$555$		0			0
$556$	−2.73231	+	8.40918i	−0.115876	+	0.356629i
$557$	−32.0476	+	23.2839i	−1.35790	+	0.986572i	−0.359325	+	0.933212i	$0.616993\pi$
$557$	−32.0476	+	23.2839i	−1.35790	+	0.986572i	−0.998575	+	0.0533600i	$0.983007\pi$
$558$		0			0
$559$	−18.8584	−	58.0402i	−0.797625	−	2.45484i
$560$	−11.2645			−0.476014
$561$		0			0
$562$	5.29812			0.223488
$563$	6.69959	+	20.6192i	0.282354	+	0.868996i	0.987179	+	0.159615i	$0.0510254\pi$
$563$	6.69959	+	20.6192i	0.282354	+	0.868996i	−0.704825	+	0.709381i	$0.748975\pi$
$564$		0			0
$565$	10.9303	−	7.94132i	0.459841	−	0.334094i
$566$	4.84607	−	14.9147i	0.203696	−	0.626911i
$567$		0			0
$568$	−14.4785	+	10.5193i	−0.607505	+	0.441378i
$569$	22.2187	+	16.1428i	0.931457	+	0.676743i	0.946349	−	0.323146i	$-0.104741\pi$
$569$	22.2187	+	16.1428i	0.931457	+	0.676743i	−0.0148922	+	0.999889i	$0.504741\pi$
$570$		0			0
$571$	23.8306			0.997281			0.498641	−	0.866809i	$-0.333833\pi$
$571$	23.8306			0.997281			0.498641	+	0.866809i	$0.333833\pi$
$572$	11.0467	+	1.80231i	0.461886	+	0.0753582i
$573$		0			0
$574$	8.12395	+	25.0029i	0.339087	+	1.04360i
$575$	−6.54034	−	4.75184i	−0.272751	−	0.198165i
$576$		0			0
$577$	−4.96685	+	15.2864i	−0.206773	+	0.636381i	0.792863	+	0.609400i	$0.208589\pi$
$577$	−4.96685	+	15.2864i	−0.206773	+	0.636381i	−0.999636	+	0.0269812i	$0.991411\pi$
$578$	−6.09395	+	18.7553i	−0.253475	+	0.780116i
$579$		0			0
$580$	−0.467876	−	0.339932i	−0.0194275	−	0.0141149i
$581$	16.0780	+	49.4831i	0.667030	+	2.05291i
$582$		0			0
$583$	−6.21939	−	6.27748i	−0.257581	−	0.259987i
$584$	−14.7405			−0.609966
$585$		0			0
$586$	−15.1648	−	11.0178i	−0.626451	−	0.455143i
$587$	14.3837	−	10.4504i	0.593680	−	0.431334i	−0.249950	−	0.968259i	$-0.580414\pi$
$587$	14.3837	−	10.4504i	0.593680	−	0.431334i	0.843630	+	0.536925i	$0.180414\pi$
$588$		0			0
$589$	0.935237	−	2.87836i	0.0385358	−	0.118601i
$590$	−6.44824	+	4.68492i	−0.265470	+	0.192875i
$591$		0			0
$592$	4.46983	+	13.7567i	0.183709	+	0.565398i
$593$	−20.2944			−0.833389			−0.416695	−	0.909046i	$-0.636812\pi$
$593$	−20.2944			−0.833389			−0.416695	+	0.909046i	$0.636812\pi$
$594$		0			0
$595$	−3.46952			−0.142236
$596$	−2.36460	−	7.27750i	−0.0968579	−	0.298098i
$597$		0			0
$598$	−48.7601	+	35.4263i	−1.99395	+	1.44869i
$599$	2.78334	−	8.56623i	0.113724	−	0.350007i	−0.877955	−	0.478744i	$-0.841092\pi$
$599$	2.78334	−	8.56623i	0.113724	−	0.350007i	0.991679	+	0.128737i	$0.0410923\pi$
$600$		0			0
$601$	−33.2571	+	24.1627i	−1.35659	+	0.985618i	−0.357933	+	0.933747i	$0.616519\pi$
$601$	−33.2571	+	24.1627i	−1.35659	+	0.985618i	−0.998654	+	0.0518711i	$0.983481\pi$
$602$	41.5568	+	30.1928i	1.69373	+	1.23057i
$603$		0			0
$604$	7.41558			0.301736
$605$	−6.38262	−	8.95891i	−0.259490	−	0.364232i
$606$		0			0
$607$	0.367905	+	1.13230i	0.0149328	+	0.0459585i	0.958245	−	0.285948i	$-0.0923083\pi$
$607$	0.367905	+	1.13230i	0.0149328	+	0.0459585i	−0.943312	+	0.331906i	$0.892308\pi$
$608$	4.53629	+	3.29580i	0.183971	+	0.133663i
$609$		0			0
$610$	−1.99271	+	6.13293i	−0.0806825	+	0.248315i
$611$	24.8089	−	76.3540i	1.00366	−	3.08895i
$612$		0			0
$613$	−0.110508	−	0.0802891i	−0.00446339	−	0.00324284i	0.585551	−	0.810635i	$-0.300878\pi$
$613$	−0.110508	−	0.0802891i	−0.00446339	−	0.00324284i	−0.590015	+	0.807392i	$0.700878\pi$
$614$	3.26750	+	10.0563i	0.131866	+	0.405840i
$615$		0			0
$616$	−39.2426	+	19.7658i	−1.58113	+	0.796389i
$617$	−17.7011			−0.712620			−0.356310	−	0.934368i	$-0.615965\pi$
$617$	−17.7011			−0.712620			−0.356310	+	0.934368i	$0.615965\pi$
$618$		0			0
$619$	5.73528	+	4.16693i	0.230521	+	0.167483i	0.697050	−	0.717023i	$-0.254496\pi$
$619$	5.73528	+	4.16693i	0.230521	+	0.167483i	−0.466529	+	0.884506i	$0.654496\pi$
$620$	−0.713237	+	0.518197i	−0.0286443	+	0.0208113i
$621$		0			0
$622$	−0.652565	+	2.00839i	−0.0261655	+	0.0805290i
$623$	−44.5923	+	32.3982i	−1.78655	+	1.29801i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−21.1357			−0.844752
$627$		0			0
$628$	2.39127			0.0954219
$629$	1.37672	+	4.23712i	0.0548936	+	0.168945i
$630$		0			0
$631$	−19.5299	+	14.1893i	−0.777473	+	0.564867i	−0.904220	−	0.427068i	$-0.859547\pi$
$631$	−19.5299	+	14.1893i	−0.777473	+	0.564867i	0.126746	+	0.991935i	$0.459547\pi$
$632$	13.2340	−	40.7301i	0.526421	−	1.62016i
$633$		0			0
$634$	1.94322	−	1.41183i	0.0771750	−	0.0560709i
$635$	1.71521	+	1.24618i	0.0680662	+	0.0494530i
$636$		0			0
$637$	71.8560			2.84704
$638$	4.18204	+	0.682313i	0.165568	+	0.0270130i
$639$		0			0
$640$	1.44067	+	4.43392i	0.0569474	+	0.175266i
$641$	34.6422	+	25.1690i	1.36828	+	0.994116i	0.997869	+	0.0652496i	$0.0207844\pi$
$641$	34.6422	+	25.1690i	1.36828	+	0.994116i	0.370415	+	0.928867i	$0.379216\pi$
$642$		0			0
$643$	−10.5810	+	32.5651i	−0.417275	+	1.28424i	0.492925	+	0.870072i	$0.335928\pi$
$643$	−10.5810	+	32.5651i	−0.417275	+	1.28424i	−0.910200	+	0.414169i	$0.864072\pi$
$644$	−5.88472	+	18.1113i	−0.231890	+	0.713685i
$645$		0			0
$646$	−1.46978	−	1.06786i	−0.0578279	−	0.0420144i
$647$	−3.36612	−	10.3598i	−0.132336	−	0.407287i	0.862830	−	0.505494i	$-0.168690\pi$
$647$	−3.36612	−	10.3598i	−0.132336	−	0.407287i	−0.995166	+	0.0982061i	$0.968690\pi$
$648$		0			0
$649$	−10.0430	+	19.4860i	−0.394222	+	0.764893i
$650$	7.45528			0.292420
$651$		0			0
$652$	−2.06968	−	1.50371i	−0.0810549	−	0.0588898i
$653$	34.0195	−	24.7166i	1.33129	−	0.967237i	0.331571	−	0.943430i	$-0.392421\pi$
$653$	34.0195	−	24.7166i	1.33129	−	0.967237i	0.999717	−	0.0238064i	$-0.00757854\pi$
$654$		0			0
$655$	2.69563	−	8.29629i	0.105327	−	0.324163i
$656$	10.6687	−	7.75129i	0.416544	−	0.302637i
$657$		0			0
$658$	20.8819	+	64.2679i	0.814062	+	2.50543i
$659$	0.425249			0.0165654			0.00828268	−	0.999966i	$-0.497364\pi$
$659$	0.425249			0.0165654			0.00828268	+	0.999966i	$0.497364\pi$
$660$		0			0
$661$	−7.08477			−0.275565			−0.137783	−	0.990462i	$-0.543998\pi$
$661$	−7.08477			−0.275565			−0.137783	+	0.990462i	$0.543998\pi$
$662$	−3.85444	−	11.8628i	−0.149807	−	0.461059i
$663$		0			0
$664$	29.9451	−	21.7564i	1.16210	−	0.844312i
$665$	−2.49888	+	7.69076i	−0.0969024	+	0.298235i
$666$		0			0
$667$	6.92937	−	5.03448i	0.268306	−	0.194936i
$668$	0.728290	+	0.529134i	0.0281784	+	0.0204728i
$669$		0			0
$670$	−9.03224			−0.348946
$671$	2.69305	+	17.5303i	0.103964	+	0.676750i
$672$		0			0
$673$	−3.79575	−	11.6821i	−0.146315	−	0.450313i	0.850862	−	0.525389i	$-0.176080\pi$
$673$	−3.79575	−	11.6821i	−0.146315	−	0.450313i	−0.997178	+	0.0750760i	$0.976080\pi$
$674$	20.1151	+	14.6145i	0.774806	+	0.562929i
$675$		0			0
$676$	−4.25456	+	13.0942i	−0.163637	+	0.503623i
$677$	−5.33859	+	16.4305i	−0.205179	+	0.631475i	0.794527	+	0.607228i	$0.207719\pi$
$677$	−5.33859	+	16.4305i	−0.205179	+	0.631475i	−0.999706	+	0.0242467i	$0.992281\pi$
$678$		0			0
$679$	−4.70480	−	3.41824i	−0.180554	−	0.131180i
$680$	0.762728	+	2.34743i	0.0292493	+	0.0900200i
$681$		0			0
$682$	2.95925	−	5.74172i	0.113316	−	0.219862i
$683$	−26.8858			−1.02876			−0.514379	−	0.857563i	$-0.671978\pi$
$683$	−26.8858			−1.02876			−0.514379	+	0.857563i	$0.671978\pi$
$684$		0			0
$685$	1.24898	+	0.907437i	0.0477211	+	0.0346714i
$686$	−19.4610	+	14.1392i	−0.743024	+	0.539838i
$687$		0			0
$688$	7.96228	−	24.5054i	0.303559	−	0.934259i
$689$	13.3264	−	9.68220i	0.507696	−	0.368862i
$690$		0			0
$691$	7.70472	+	23.7127i	0.293102	+	0.902074i	0.983853	+	0.178981i	$0.0572801\pi$
$691$	7.70472	+	23.7127i	0.293102	+	0.902074i	−0.690751	+	0.723093i	$0.742720\pi$
$692$	9.04609			0.343881
$693$		0			0
$694$	3.59803			0.136579
$695$	5.00552	+	15.4054i	0.189870	+	0.584361i
$696$		0			0
$697$	3.28601	−	2.38743i	0.124467	−	0.0904302i
$698$	4.20695	−	12.9477i	0.159235	−	0.490076i
$699$		0			0
$700$	1.90572	−	1.38458i	0.0720293	−	0.0523323i
$701$	16.2387	+	11.7981i	0.613325	+	0.445607i	0.850584	−	0.525840i	$-0.176249\pi$
$701$	16.2387	+	11.7981i	0.613325	+	0.445607i	−0.237258	+	0.971447i	$0.576249\pi$
$702$		0			0
$703$	10.3838			0.391634
$704$	20.6092	+	20.8017i	0.776740	+	0.783995i
$705$		0			0
$706$	−5.02879	−	15.4770i	−0.189261	−	0.582485i
$707$	29.4292	+	21.3816i	1.10680	+	0.804137i
$708$		0			0
$709$	−3.50289	+	10.7808i	−0.131554	+	0.404881i	−0.995038	−	0.0994949i	$-0.968277\pi$
$709$	−3.50289	+	10.7808i	−0.131554	+	0.404881i	0.863484	+	0.504376i	$0.168277\pi$
$710$	−2.17227	+	6.68557i	−0.0815240	+	0.250905i
$711$		0			0
$712$	31.7232	+	23.0483i	1.18888	+	0.863771i
$713$	−4.03479	−	12.4178i	−0.151104	−	0.465051i
$714$		0			0
$715$	18.3131	−	9.22399i	0.684869	−	0.344958i
$716$	−9.60684			−0.359025
$717$		0			0
$718$	24.0956	+	17.5065i	0.899240	+	0.653336i
$719$	3.75010	−	2.72460i	0.139855	−	0.101611i	−0.515658	−	0.856795i	$-0.672452\pi$
$719$	3.75010	−	2.72460i	0.139855	−	0.101611i	0.655513	+	0.755184i	$0.272452\pi$
$720$		0			0
$721$	−13.2025	+	40.6330i	−0.491685	+	1.51325i
$722$	15.1103	−	10.9782i	0.562345	−	0.408568i
$723$		0			0
$724$	−1.41804	−	4.36429i	−0.0527012	−	0.162198i
$725$	−1.05948			−0.0393481
$726$		0			0
$727$	−2.22651			−0.0825766			−0.0412883	−	0.999147i	$-0.513146\pi$
$727$	−2.22651			−0.0825766			−0.0412883	+	0.999147i	$0.513146\pi$
$728$	−25.3105	−	77.8977i	−0.938069	−	2.88708i
$729$		0			0
$730$	−4.68420	+	3.40327i	−0.173370	+	0.125961i
$731$	2.45241	−	7.54775i	0.0907057	−	0.279164i
$732$		0			0
$733$	24.6573	−	17.9145i	0.910737	−	0.661689i	−0.0304645	−	0.999536i	$-0.509699\pi$
$733$	24.6573	−	17.9145i	0.910737	−	0.661689i	0.941201	+	0.337847i	$0.109699\pi$
$734$	−6.18994	−	4.49725i	−0.228475	−	0.165997i
$735$		0			0
$736$	24.1904			0.891669
$737$	−22.1867	+	11.1751i	−0.817257	+	0.411639i
$738$		0			0
$739$	−2.84351	−	8.75141i	−0.104600	−	0.321926i	0.885036	−	0.465522i	$-0.154133\pi$
$739$	−2.84351	−	8.75141i	−0.104600	−	0.321926i	−0.989636	+	0.143596i	$0.954133\pi$
$740$	−2.44711	−	1.77793i	−0.0899575	−	0.0653579i
$741$		0			0
$742$	−4.28450	+	13.1863i	−0.157289	+	0.484086i
$743$	−0.534297	+	1.64440i	−0.0196014	+	0.0603270i	−0.960379	−	0.278698i	$-0.910097\pi$
$743$	−0.534297	+	1.64440i	−0.0196014	+	0.0603270i	0.940777	+	0.339025i	$0.110097\pi$
$744$		0			0
$745$	−11.3410	−	8.23975i	−0.415504	−	0.301881i
$746$	4.91255	+	15.1193i	0.179861	+	0.553556i
$747$		0			0
$748$	1.02443	+	1.03400i	0.0374569	+	0.0378068i
$749$	35.2456			1.28785
$750$		0			0
$751$	−27.4077	−	19.9129i	−1.00012	−	0.726631i	−0.0380072	−	0.999277i	$-0.512101\pi$
$751$	−27.4077	−	19.9129i	−1.00012	−	0.726631i	−0.962114	+	0.272647i	$0.912101\pi$
$752$	27.4231	−	19.9240i	1.00002	−	0.726555i
$753$		0			0
$754$	−2.44084	+	7.51213i	−0.0888901	+	0.273576i
$755$	10.9906	−	7.98516i	0.399990	−	0.290610i
$756$		0			0
$757$	−8.30257	−	25.5527i	−0.301762	−	0.928728i	−0.980866	−	0.194685i	$-0.937631\pi$
$757$	−8.30257	−	25.5527i	−0.301762	−	0.928728i	0.679104	−	0.734042i	$-0.262369\pi$
$758$	−22.3525			−0.811879
$759$		0			0
$760$	5.75282			0.208677
$761$	5.38966	+	16.5877i	0.195375	+	0.601303i	0.999972	+	0.00748151i	$0.00238146\pi$
$761$	5.38966	+	16.5877i	0.195375	+	0.601303i	−0.804597	+	0.593821i	$0.797619\pi$
$762$		0			0
$763$	−47.1304	+	34.2422i	−1.70623	+	1.23965i
$764$	0.896990	−	2.76065i	0.0324520	−	0.0998769i
$765$		0			0
$766$	27.6910	−	20.1187i	1.00052	−	0.726918i
$767$	−33.0597	−	24.0193i	−1.19372	−	0.867286i
$768$		0			0
$769$	−41.6485			−1.50188			−0.750942	−	0.660368i	$-0.770400\pi$
$769$	−41.6485			−1.50188			−0.750942	+	0.660368i	$0.770400\pi$
$770$	−7.90689	+	15.3414i	−0.284945	+	0.552867i
$771$		0			0
$772$	−2.57865	−	7.93626i	−0.0928075	−	0.285632i
$773$	17.9209	+	13.0203i	0.644570	+	0.468308i	0.861417	−	0.507898i	$-0.169577\pi$
$773$	17.9209	+	13.0203i	0.644570	+	0.468308i	−0.216847	+	0.976206i	$0.569577\pi$
$774$		0			0
$775$	−0.499089	+	1.53604i	−0.0179278	+	0.0551762i
$776$	−1.27845	+	3.93466i	−0.0458937	+	0.141246i
$777$		0			0
$778$	−18.7032	−	13.5886i	−0.670540	−	0.487176i
$779$	−2.92541	−	9.00350i	−0.104814	−	0.322584i
$780$		0			0
$781$	2.93572	+	19.1100i	0.105048	+	0.683809i
$782$	−7.83783			−0.280280
$783$		0			0
$784$	24.5445	+	17.8326i	0.876588	+	0.636879i
$785$	3.54409	−	2.57493i	0.126494	−	0.0919033i
$786$		0			0
$787$	−2.59956	+	8.00062i	−0.0926642	+	0.285191i	−0.986638	−	0.162928i	$-0.947906\pi$
$787$	−2.59956	+	8.00062i	−0.0926642	+	0.285191i	0.893974	+	0.448119i	$0.147906\pi$
$788$	−0.746840	+	0.542611i	−0.0266051	+	0.0193297i
$789$		0			0
$790$	−5.19825	−	15.9986i	−0.184945	−	0.569203i
$791$	−58.3034			−2.07303
$792$		0			0
$793$	−33.0612			−1.17404
$794$	6.05368	+	18.6313i	0.214837	+	0.661200i
$795$		0			0
$796$	1.52291	−	1.10646i	0.0539781	−	0.0392174i
$797$	12.6460	−	38.9205i	0.447945	−	1.37863i	−0.431276	−	0.902220i	$-0.641937\pi$
$797$	12.6460	−	38.9205i	0.447945	−	1.37863i	0.879221	−	0.476414i	$-0.158063\pi$
$798$		0			0
$799$	8.44641	−	6.13667i	0.298812	−	0.217100i
$800$	−2.42079	−	1.75881i	−0.0855879	−	0.0621832i
$801$		0			0
$802$	−14.8621			−0.524797
$803$	−7.29554	+	14.1552i	−0.257454	+	0.499528i
$804$		0			0
$805$	10.7807	+	33.1795i	0.379968	+	1.16942i
$806$	9.74132	+	7.07748i	0.343123	+	0.249294i
$807$		0			0
$808$	7.99689	−	24.6119i	0.281330	−	0.865844i
$809$	−6.69688	+	20.6109i	−0.235450	+	0.724640i	0.761612	+	0.648034i	$0.224408\pi$
$809$	−6.69688	+	20.6109i	−0.235450	+	0.724640i	−0.997061	+	0.0766060i	$0.975592\pi$
$810$		0			0
$811$	44.0939	+	32.0361i	1.54835	+	1.12494i	0.944816	+	0.327601i	$0.106240\pi$
$811$	44.0939	+	32.0361i	1.54835	+	1.12494i	0.603531	+	0.797339i	$0.293760\pi$
$812$	0.771215	+	2.37356i	0.0270644	+	0.0832955i
$813$		0			0
$814$	21.8731	+	3.56866i	0.766651	+	0.125082i
$815$	−4.68667			−0.164167
$816$		0			0
$817$	−14.9645	−	10.8723i	−0.523542	−	0.380375i
$818$	1.90970	−	1.38748i	0.0667710	−	0.0485120i
$819$		0			0
$820$	−0.852167	+	2.62270i	−0.0297590	+	0.0915886i
$821$	−14.5227	+	10.5513i	−0.506845	+	0.368244i	−0.811625	−	0.584178i	$-0.801417\pi$
$821$	−14.5227	+	10.5513i	−0.506845	+	0.368244i	0.304780	+	0.952423i	$0.401417\pi$
$822$		0			0
$823$	10.8883	+	33.5106i	0.379541	+	1.16811i	0.940363	+	0.340171i	$0.110485\pi$
$823$	10.8883	+	33.5106i	0.379541	+	1.16811i	−0.560822	+	0.827936i	$0.689515\pi$
$824$	30.3942			1.05883
$825$		0			0
$826$	34.3957			1.19678
$827$	12.3413	+	37.9826i	0.429149	+	1.32079i	0.898965	+	0.438021i	$0.144320\pi$
$827$	12.3413	+	37.9826i	0.429149	+	1.32079i	−0.469816	+	0.882765i	$0.655680\pi$
$828$		0			0
$829$	36.8359	−	26.7629i	1.27936	−	0.929512i	0.279830	−	0.960049i	$-0.409722\pi$
$829$	36.8359	−	26.7629i	1.27936	−	0.929512i	0.999534	+	0.0305372i	$0.00972181\pi$
$830$	4.49279	−	13.8274i	0.155947	−	0.479956i
$831$		0			0
$832$	−44.1598	+	32.0840i	−1.53097	+	1.11231i
$833$	7.55979	+	5.49251i	0.261931	+	0.190304i
$834$		0			0
$835$	1.64917			0.0570720
$836$	3.02987	−	1.52609i	0.104790	−	0.0527811i
$837$		0			0
$838$	7.66795	+	23.5995i	0.264885	+	0.815232i
$839$	14.5925	+	10.6021i	0.503789	+	0.366024i	0.810462	−	0.585791i	$-0.199216\pi$
$839$	14.5925	+	10.6021i	0.503789	+	0.366024i	−0.306673	+	0.951815i	$0.599216\pi$
$840$		0			0
$841$	−8.61462	+	26.5131i	−0.297056	+	0.914244i
$842$	−6.37971	+	19.6347i	−0.219859	+	0.676658i
$843$		0			0
$844$	−0.174191	−	0.126557i	−0.00599590	−	0.00435628i
$845$	7.79425	+	23.9882i	0.268130	+	0.825220i
$846$		0			0
$847$	−0.441331	+	47.4672i	−0.0151643	+	1.63099i
$848$	6.95486			0.238831
$849$		0			0
$850$	0.784351	+	0.569864i	0.0269030	+	0.0195462i
$851$	36.2423	−	26.3316i	1.24237	−	0.902635i
$852$		0			0
$853$	−0.366815	+	1.12894i	−0.0125595	+	0.0386542i	−0.957140	−	0.289626i	$-0.906469\pi$
$853$	−0.366815	+	1.12894i	−0.0125595	+	0.0386542i	0.944580	+	0.328280i	$0.106469\pi$
$854$	22.5133	−	16.3569i	0.770390	−	0.559721i
$855$		0			0
$856$	−7.74827	−	23.8467i	−0.264830	−	0.815064i
$857$	−5.59493			−0.191119			−0.0955597	−	0.995424i	$-0.530464\pi$
$857$	−5.59493			−0.191119			−0.0955597	+	0.995424i	$0.530464\pi$
$858$		0			0
$859$	−18.5783			−0.633882			−0.316941	−	0.948445i	$-0.602656\pi$
$859$	−18.5783			−0.633882			−0.316941	+	0.948445i	$0.602656\pi$
$860$	1.66504	+	5.12446i	0.0567774	+	0.174743i
$861$		0			0
$862$	−10.3488	+	7.51882i	−0.352481	+	0.256092i
$863$	−4.39573	+	13.5287i	−0.149632	+	0.460521i	−0.997578	−	0.0695631i	$-0.977839\pi$
$863$	−4.39573	+	13.5287i	−0.149632	+	0.460521i	0.847945	+	0.530084i	$0.177839\pi$
$864$		0			0
$865$	13.4072	−	9.74090i	0.455859	−	0.331201i
$866$	−24.2198	−	17.5968i	−0.823024	−	0.597962i
$867$		0			0
$868$	3.80449			0.129133
$869$	−32.5630	−	32.8672i	−1.10462	−	1.11494i
$870$		0			0
$871$	−14.3099	−	44.0412i	−0.484871	−	1.49228i
$872$	33.5288	+	24.3601i	1.13543	+	0.824938i
$873$		0			0
$874$	−5.64510	+	17.3738i	−0.190948	+	0.587679i
$875$	1.33353	−	4.10418i	0.0450815	−	0.138747i
$876$		0			0
$877$	15.0492	+	10.9339i	0.508177	+	0.369212i	0.812131	−	0.583475i	$-0.198307\pi$
$877$	15.0492	+	10.9339i	0.508177	+	0.369212i	−0.303955	+	0.952686i	$0.598307\pi$
$878$	2.52939	+	7.78466i	0.0853627	+	0.262719i
$879$		0			0
$880$	8.54448	+	1.39406i	0.288034	+	0.0469937i
$881$	30.5201			1.02825			0.514124	−	0.857716i	$-0.328117\pi$
$881$	30.5201			1.02825			0.514124	+	0.857716i	$0.328117\pi$
$882$		0			0
$883$	13.1770	+	9.57367i	0.443442	+	0.322180i	0.787001	−	0.616952i	$-0.211633\pi$
$883$	13.1770	+	9.57367i	0.443442	+	0.322180i	−0.343559	+	0.939131i	$0.611633\pi$
$884$	−2.19507	+	1.59481i	−0.0738282	+	0.0536393i
$885$		0			0
$886$	−5.64545	+	17.3749i	−0.189663	+	0.583721i
$887$	−4.28172	+	3.11085i	−0.143766	+	0.104452i	−0.657344	−	0.753591i	$-0.728320\pi$
$887$	−4.28172	+	3.11085i	−0.143766	+	0.104452i	0.513577	+	0.858043i	$0.328320\pi$
$888$		0			0
$889$	−2.82724	−	8.70136i	−0.0948226	−	0.291834i
$890$	15.4023			0.516286
$891$		0			0
$892$	4.24212			0.142037
$893$	−7.51952	−	23.1427i	−0.251631	−	0.774441i
$894$		0			0
$895$	−14.2383	+	10.3447i	−0.475934	+	0.345786i
$896$	6.21704	−	19.1341i	0.207697	−	0.639225i
$897$		0			0
$898$	17.4931	−	12.7095i	0.583751	−	0.424120i
$899$	−1.38435	−	1.00579i	−0.0461707	−	0.0335450i
$900$		0			0
$901$	2.14212			0.0713644
$902$	−3.06797	−	19.9708i	−0.102152	−	0.664956i
$903$		0			0
$904$	12.8172	+	39.4474i	0.426295	+	1.31200i
$905$	−6.80118	−	4.94135i	−0.226079	−	0.164256i
$906$		0			0
$907$	0.355631	−	1.09452i	0.0118085	−	0.0363429i	−0.944979	−	0.327132i	$-0.893918\pi$
$907$	0.355631	−	1.09452i	0.0118085	−	0.0363429i	0.956787	+	0.290789i	$0.0939178\pi$
$908$	−4.60769	+	14.1810i	−0.152911	+	0.470613i
$909$		0			0
$910$	−26.0280	−	18.9105i	−0.862821	−	0.626876i
$911$	−7.56155	−	23.2721i	−0.250525	−	0.771038i	−0.994678	−	0.103029i	$-0.967147\pi$
$911$	−7.56155	−	23.2721i	−0.250525	−	0.771038i	0.744153	−	0.668009i	$-0.232853\pi$
$912$		0			0
$913$	−6.07180	−	39.5241i	−0.200947	−	1.30806i
$914$	−49.6802			−1.64328
$915$		0			0
$916$	6.88125	+	4.99952i	0.227363	+	0.165189i
$917$	−30.4548	+	22.1267i	−1.00570	+	0.730687i
$918$		0			0
$919$	−8.37953	+	25.7896i	−0.276415	+	0.850719i	0.712426	+	0.701747i	$0.247596\pi$
$919$	−8.37953	+	25.7896i	−0.276415	+	0.850719i	−0.988841	+	0.148972i	$0.952404\pi$
$920$	20.0788	−	14.5881i	0.661979	−	0.480956i
$921$		0			0
$922$	6.26569	+	19.2838i	0.206349	+	0.635078i
$923$	−36.0404			−1.18628
$924$		0			0
$925$	−5.54134			−0.182198
$926$	−13.3050	−	40.9486i	−0.437229	−	1.34565i
$927$		0			0
$928$	2.56478	−	1.86342i	0.0841931	−	0.0611698i
$929$	−8.98153	+	27.6423i	−0.294674	+	0.906915i	0.688656	+	0.725088i	$0.258201\pi$
$929$	−8.98153	+	27.6423i	−0.294674	+	0.906915i	−0.983331	+	0.181827i	$0.941799\pi$
$930$		0			0
$931$	17.6199	−	12.8016i	0.577468	−	0.419555i
$932$	−12.3141	−	8.94671i	−0.403361	−	0.293059i
$933$		0			0
$934$	−43.3527			−1.41854
$935$	2.63173	+	0.429375i	0.0860667	+	0.0140421i
$936$		0			0
$937$	−18.4959	−	56.9244i	−0.604234	−	1.85964i	−0.501975	−	0.864882i	$-0.667393\pi$
$937$	−18.4959	−	56.9244i	−0.604234	−	1.85964i	−0.102258	−	0.994758i	$-0.532607\pi$
$938$	31.5336	+	22.9105i	1.02961	+	0.748054i
$939$		0			0
$940$	−2.19042	+	6.74143i	−0.0714437	+	0.219881i
$941$	−9.33822	+	28.7401i	−0.304417	+	0.936900i	0.675477	+	0.737381i	$0.263938\pi$
$941$	−9.33822	+	28.7401i	−0.304417	+	0.936900i	−0.979894	+	0.199519i	$0.936062\pi$
$942$		0			0
$943$	−33.0417	−	24.0062i	−1.07599	−	0.781750i
$944$	−5.33159	−	16.4089i	−0.173528	−	0.534065i
$945$		0			0
$946$	−27.7855	−	28.0450i	−0.903384	−	0.911822i
$947$	−38.6489			−1.25592			−0.627960	−	0.778245i	$-0.716110\pi$
$947$	−38.6489			−1.25592			−0.627960	+	0.778245i	$0.716110\pi$
$948$		0			0
$949$	−24.0156	−	17.4483i	−0.779579	−	0.566397i
$950$	1.82812	−	1.32820i	0.0593119	−	0.0430926i
$951$		0			0
$952$	3.29147	−	10.1301i	0.106677	−	0.328318i
$953$	36.1767	−	26.2839i	1.17188	−	0.851419i	0.180646	−	0.983548i	$-0.442181\pi$
$953$	36.1767	−	26.2839i	1.17188	−	0.851419i	0.991233	+	0.132129i	$0.0421813\pi$
$954$		0			0
$955$	−1.64326	−	5.05744i	−0.0531748	−	0.163655i
$956$	−10.2326			−0.330945
$957$		0			0
$958$	−16.7515			−0.541216
$959$	−2.05873	−	6.33613i	−0.0664800	−	0.204604i
$960$		0			0
$961$	22.9692	−	16.6881i	0.740942	−	0.538326i
$962$	−12.7662	+	39.2903i	−0.411599	+	1.26677i
$963$		0			0
$964$	−4.85985	+	3.53089i	−0.156525	+	0.113722i
$965$	−12.3676	−	8.98561i	−0.398128	−	0.289257i
$966$		0			0
$967$	−34.5876			−1.11226			−0.556131	−	0.831095i	$-0.687715\pi$
$967$	−34.5876			−1.11226			−0.556131	+	0.831095i	$0.687715\pi$
$968$	32.2128	−	10.1364i	1.03536	−	0.325797i
$969$		0			0
$970$	0.502168	+	1.54552i	0.0161237	+	0.0496235i
$971$	−5.59187	−	4.06273i	−0.179452	−	0.130379i	0.494433	−	0.869216i	$-0.335376\pi$
$971$	−5.59187	−	4.06273i	−0.179452	−	0.130379i	−0.673885	+	0.738836i	$0.735376\pi$
$972$		0			0
$973$	21.6008	−	66.4803i	0.692489	−	2.13126i
$974$	−5.21702	+	16.0563i	−0.167164	+	0.514478i
$975$		0			0
$976$	−11.2930	−	8.20486i	−0.361481	−	0.262631i
$977$	−3.79043	−	11.6658i	−0.121267	−	0.373220i	0.871936	−	0.489620i	$-0.162865\pi$
$977$	−3.79043	−	11.6658i	−0.121267	−	0.373220i	−0.993202	+	0.116400i	$0.962865\pi$
$978$		0			0
$979$	37.8340	−	19.0564i	1.20918	−	0.609044i
$980$	−6.34429			−0.202661
$981$		0			0
$982$	24.6311	+	17.8955i	0.786009	+	0.571069i
$983$	−0.130862	+	0.0950771i	−0.00417386	+	0.00303249i	−0.589870	−	0.807498i	$-0.700821\pi$
$983$	−0.130862	+	0.0950771i	−0.00417386	+	0.00303249i	0.585696	+	0.810531i	$0.300821\pi$
$984$		0			0
$985$	−0.522603	+	1.60841i	−0.0166515	+	0.0512481i
$986$	−0.831004	+	0.603760i	−0.0264646	+	0.0192276i
$987$		0			0
$988$	1.95419	+	6.01438i	0.0621710	+	0.191343i
$989$	−79.8003			−2.53750
$990$		0			0
$991$	43.1252			1.36992			0.684958	−	0.728582i	$-0.259820\pi$
$991$	43.1252			1.36992			0.684958	+	0.728582i	$0.259820\pi$
$992$	−1.49341	−	4.59623i	−0.0474157	−	0.145931i
$993$		0			0
$994$	24.5420	−	17.8308i	0.778424	−	0.565558i
$995$	1.06566	−	3.27976i	0.0337837	−	0.103975i
$996$		0			0
$997$	1.19110	−	0.865386i	0.0377226	−	0.0274070i	−0.568764	−	0.822501i	$-0.692578\pi$
$997$	1.19110	−	0.865386i	0.0377226	−	0.0274070i	0.606487	+	0.795094i	$0.292578\pi$
$998$	8.64610	+	6.28176i	0.273688	+	0.198846i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.g.181.3	✓	16
3.2	odd	2		495.2.n.h.181.2	yes	16
11.3	even	5		5445.2.a.cd.1.5		8
11.8	odd	10		5445.2.a.cb.1.4		8
11.9	even	5	inner	495.2.n.g.361.3	yes	16
33.8	even	10		5445.2.a.cc.1.5		8
33.14	odd	10		5445.2.a.ca.1.4		8
33.20	odd	10		495.2.n.h.361.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.181.3	✓	16	1.1	even	1	trivial
495.2.n.g.361.3	yes	16	11.9	even	5	inner
495.2.n.h.181.2	yes	16	3.2	odd	2
495.2.n.h.361.2	yes	16	33.20	odd	10
5445.2.a.ca.1.4		8	33.14	odd	10
5445.2.a.cb.1.4		8	11.8	odd	10
5445.2.a.cc.1.5		8	33.8	even	10
5445.2.a.cd.1.5		8	11.3	even	5

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.372637 + 1.14686i) q^{2} +(0.441609 - 0.320848i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-3.49122 + 2.53652i) q^{7} +(2.48368 + 1.80450i) q^{8} +O(q^{10})\)	\(q+(0.372637 + 1.14686i) q^{2} +(0.441609 - 0.320848i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-3.49122 + 2.53652i) q^{7} +(2.48368 + 1.80450i) q^{8} +1.20588 q^{10} +(2.96210 - 1.49196i) q^{11} +(1.91048 + 5.87986i) q^{13} +(-4.20999 - 3.05873i) q^{14} +(-0.806633 + 2.48256i) q^{16} +(-0.248446 + 0.764638i) q^{17} +(1.51601 + 1.10144i) q^{19} +(-0.168680 - 0.519143i) q^{20} +(2.81486 + 2.84115i) q^{22} +8.08431 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-6.03145 + 4.38210i) q^{26} +(-0.727918 + 2.24030i) q^{28} +(0.857138 - 0.622747i) q^{29} +(-0.499089 - 1.53604i) q^{31} +2.99226 q^{32} -0.969511 q^{34} +(1.33353 + 4.10418i) q^{35} +(4.48304 - 3.25712i) q^{37} +(-0.698278 + 2.14908i) q^{38} +(2.48368 - 1.80450i) q^{40} +(-4.08714 - 2.96948i) q^{41} -9.87101 q^{43} +(0.829398 - 1.60925i) q^{44} +(3.01251 + 9.27156i) q^{46} +(-10.5056 - 7.63280i) q^{47} +(3.59157 - 11.0537i) q^{49} +(0.372637 - 1.14686i) q^{50} +(2.73023 + 1.98363i) q^{52} +(-0.823336 - 2.53397i) q^{53} +(-0.503601 - 3.27817i) q^{55} -13.2482 q^{56} +(1.03360 + 0.750957i) q^{58} +(-5.34734 + 3.88507i) q^{59} +(-1.65250 + 5.08587i) q^{61} +(1.57564 - 1.14477i) q^{62} +(2.72829 + 8.39682i) q^{64} +6.18245 q^{65} -7.49018 q^{67} +(0.135616 + 0.417384i) q^{68} +(-4.20999 + 3.05873i) q^{70} +(-1.80140 + 5.54415i) q^{71} +(-3.88448 + 2.82224i) q^{73} +(5.40600 + 3.92769i) q^{74} +1.02288 q^{76} +(-6.55696 + 12.7222i) q^{77} +(-4.31076 - 13.2672i) q^{79} +(2.11179 + 1.53431i) q^{80} +(1.88255 - 5.79391i) q^{82} +(3.72575 - 11.4667i) q^{83} +(0.650440 + 0.472572i) q^{85} +(-3.67830 - 11.3206i) q^{86} +(10.0491 + 1.63955i) q^{88} +12.7727 q^{89} +(-21.5843 - 15.6819i) q^{91} +(3.57011 - 2.59383i) q^{92} +(4.83894 - 14.8927i) q^{94} +(1.51601 - 1.10144i) q^{95} +(0.416434 + 1.28165i) q^{97} +14.0154 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8	\( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8 + 8 * q^10 + 4 * q^11 + 2 * q^13 - 22 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 + 2 * q^20 - 28 * q^22 + 8 * q^23 - 4 * q^25 + 6 * q^26 - 2 * q^28 - 26 * q^29 - 10 * q^31 + 56 * q^32 - 4 * q^34 - 4 * q^35 + 22 * q^37 - 30 * q^38 - 6 * q^40 - 6 * q^41 + 28 * q^43 + 68 * q^44 + 16 * q^46 - 20 * q^47 + 10 * q^49 - 2 * q^50 + 30 * q^52 + 14 * q^53 - 6 * q^55 + 68 * q^56 - 6 * q^58 - 16 * q^59 - 38 * q^61 - 20 * q^62 + 10 * q^64 + 12 * q^65 + 20 * q^67 - 48 * q^68 - 22 * q^70 - 54 * q^71 + 2 * q^73 + 28 * q^74 - 44 * q^76 + 34 * q^77 - 12 * q^79 - 22 * q^80 + 30 * q^82 - 28 * q^83 - 4 * q^85 + 74 * q^86 + 46 * q^88 + 76 * q^89 - 34 * q^91 - 8 * q^92 - 10 * q^94 - 4 * q^95 - 18 * q^97 + 8 * q^98

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