LMFDB - Embedded newform 495.2.n.a.91.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$0.418926 - 1.28932i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.a.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90578 + 1.38463i) q^{2} +(1.09676 - 3.37549i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.0598032 - 0.184055i) q^{7} +(1.12773 + 3.47080i) q^{8} +O(q^{10})$	\(q+(-1.90578 + 1.38463i) q^{2} +(1.09676 - 3.37549i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.0598032 - 0.184055i) q^{7} +(1.12773 + 3.47080i) q^{8} -2.35567 q^{10} +(1.96213 - 2.67395i) q^{11} +(-0.787747 + 0.572331i) q^{13} +(0.140877 + 0.433574i) q^{14} +(-1.21225 - 0.880754i) q^{16} +(-2.16469 - 1.57274i) q^{17} +(-1.71480 - 5.27760i) q^{19} +(2.87136 - 2.08617i) q^{20} +(-0.0369604 + 7.81280i) q^{22} +4.80040 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.708805 - 2.18148i) q^{26} +(-0.555687 - 0.403730i) q^{28} +(3.12657 - 9.62260i) q^{29} +(2.02685 - 1.47259i) q^{31} -3.76902 q^{32} +6.30309 q^{34} +(0.156567 - 0.113752i) q^{35} +(1.76516 - 5.43260i) q^{37} +(10.5756 + 7.68359i) q^{38} +(-1.12773 + 3.47080i) q^{40} +(2.55823 + 7.87342i) q^{41} +5.11353 q^{43} +(-6.87391 - 9.55586i) q^{44} +(-9.14851 + 6.64678i) q^{46} +(3.35354 + 10.3211i) q^{47} +(5.63282 + 4.09248i) q^{49} +(-1.90578 - 1.38463i) q^{50} +(1.06793 + 3.28674i) q^{52} +(-7.51479 + 5.45981i) q^{53} +(3.15911 - 1.00996i) q^{55} +0.706260 q^{56} +(7.36518 + 22.6677i) q^{58} +(3.46656 - 10.6690i) q^{59} +(-0.975693 - 0.708883i) q^{61} +(-1.82374 + 5.61288i) q^{62} +(9.60743 - 6.98021i) q^{64} -0.973708 q^{65} +3.25922 q^{67} +(-7.68293 + 5.58197i) q^{68} +(-0.140877 + 0.433574i) q^{70} +(4.84664 + 3.52129i) q^{71} +(1.02168 - 3.14442i) q^{73} +(4.15814 + 12.7974i) q^{74} -19.6952 q^{76} +(-0.374813 - 0.521052i) q^{77} +(-8.21389 + 5.96774i) q^{79} +(-0.463040 - 1.42509i) q^{80} +(-15.7772 - 11.4628i) q^{82} +(6.72704 + 4.88748i) q^{83} +(-0.826838 - 2.54475i) q^{85} +(-9.74527 + 7.08035i) q^{86} +(11.4935 + 3.79468i) q^{88} -7.34270 q^{89} +(0.0582308 + 0.179216i) q^{91} +(5.26490 - 16.2037i) q^{92} +(-20.6821 - 15.0264i) q^{94} +(1.71480 - 5.27760i) q^{95} +(12.8248 - 9.31774i) q^{97} -16.4015 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8	$ 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} - 3 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{19} + 3 q^{20} + 9 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} - 11 q^{28} - 10 q^{29} + 19 q^{31} - 12 q^{32} - 6 q^{34} - 3 q^{35} - q^{37} + 20 q^{38} - q^{40} + 9 q^{41} - 17 q^{44} - 22 q^{46} + 19 q^{47} + q^{49} - 4 q^{50} - 2 q^{52} - 25 q^{53} + 3 q^{55} + 16 q^{56} - 12 q^{58} - 13 q^{59} + 13 q^{61} - 35 q^{62} + 39 q^{64} + 14 q^{65} + 2 q^{67} - 19 q^{68} - 4 q^{70} + 11 q^{71} - 7 q^{73} + 43 q^{74} - 38 q^{76} + 7 q^{77} - 22 q^{79} - 13 q^{80} - 35 q^{82} + 21 q^{83} + 10 q^{85} - 20 q^{86} + 59 q^{88} + 20 q^{89} - 11 q^{91} + 28 q^{92} - 35 q^{94} - 2 q^{95} + 31 q^{97} - 22 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8 - 6 * q^10 - 3 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^19 + 3 * q^20 + 9 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 - 11 * q^28 - 10 * q^29 + 19 * q^31 - 12 * q^32 - 6 * q^34 - 3 * q^35 - q^37 + 20 * q^38 - q^40 + 9 * q^41 - 17 * q^44 - 22 * q^46 + 19 * q^47 + q^49 - 4 * q^50 - 2 * q^52 - 25 * q^53 + 3 * q^55 + 16 * q^56 - 12 * q^58 - 13 * q^59 + 13 * q^61 - 35 * q^62 + 39 * q^64 + 14 * q^65 + 2 * q^67 - 19 * q^68 - 4 * q^70 + 11 * q^71 - 7 * q^73 + 43 * q^74 - 38 * q^76 + 7 * q^77 - 22 * q^79 - 13 * q^80 - 35 * q^82 + 21 * q^83 + 10 * q^85 - 20 * q^86 + 59 * q^88 + 20 * q^89 - 11 * q^91 + 28 * q^92 - 35 * q^94 - 2 * q^95 + 31 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−1.90578	+	1.38463i	−1.34759	+	0.979082i	−0.348463	+	0.937323i	$0.613296\pi$
$2$	−1.90578	+	1.38463i	−1.34759	+	0.979082i	−0.999128	+	0.0417590i	$0.986704\pi$
$3$		0			0
$3$		0			0
$4$	1.09676	−	3.37549i	0.548382	−	1.68775i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	0.0598032	−	0.184055i	0.0226035	−	0.0695663i	−0.939119	−	0.343593i	$-0.888356\pi$
$7$	0.0598032	−	0.184055i	0.0226035	−	0.0695663i	0.961722	+	0.274027i	$0.0883558\pi$
$8$	1.12773	+	3.47080i	0.398713	+	1.22711i
$9$		0			0
$10$	−2.35567			−0.744930
$11$	1.96213	−	2.67395i	0.591606	−	0.806227i
$11$	1.96213	−	2.67395i	0.591606	−	0.806227i
$12$		0			0
$13$	−0.787747	+	0.572331i	−0.218482	+	0.158736i	−0.691643	−	0.722240i	$-0.743113\pi$
$13$	−0.787747	+	0.572331i	−0.218482	+	0.158736i	0.473161	+	0.880976i	$0.343113\pi$
$14$	0.140877	+	0.433574i	0.0376509	+	0.115878i
$15$		0			0
$16$	−1.21225	−	0.880754i	−0.303063	−	0.220188i
$17$	−2.16469	−	1.57274i	−0.525015	−	0.381446i	0.293475	−	0.955967i	$-0.405188\pi$
$17$	−2.16469	−	1.57274i	−0.525015	−	0.381446i	−0.818490	+	0.574521i	$0.805188\pi$
$18$		0			0
$19$	−1.71480	−	5.27760i	−0.393402	−	1.21077i	−0.930199	−	0.367055i	$-0.880366\pi$
$19$	−1.71480	−	5.27760i	−0.393402	−	1.21077i	0.536798	−	0.843711i	$-0.319634\pi$
$20$	2.87136	−	2.08617i	0.642057	−	0.466481i
$21$		0			0
$22$	−0.0369604	+	7.81280i	−0.00787998	+	1.66569i
$23$	4.80040			1.00095			0.500476	−	0.865750i	$-0.333158\pi$
$23$	4.80040			1.00095			0.500476	+	0.865750i	$0.333158\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.708805	−	2.18148i	0.139008	−	0.427823i
$27$		0			0
$28$	−0.555687	−	0.403730i	−0.105015	−	0.0762978i
$29$	3.12657	−	9.62260i	0.580590	−	1.78687i	−0.0357132	−	0.999362i	$-0.511370\pi$
$29$	3.12657	−	9.62260i	0.580590	−	1.78687i	0.616303	−	0.787509i	$-0.288630\pi$
$30$		0			0
$31$	2.02685	−	1.47259i	0.364033	−	0.264486i	−0.390699	−	0.920518i	$-0.627767\pi$
$31$	2.02685	−	1.47259i	0.364033	−	0.264486i	0.754732	+	0.656033i	$0.227767\pi$
$32$	−3.76902			−0.666275
$33$		0			0
$34$	6.30309			1.08097
$35$	0.156567	−	0.113752i	0.0264646	−	0.0192277i
$36$		0			0
$37$	1.76516	−	5.43260i	0.290190	−	0.893114i	−0.694604	−	0.719392i	$-0.744421\pi$
$37$	1.76516	−	5.43260i	0.290190	−	0.893114i	0.984795	−	0.173722i	$-0.0555794\pi$
$38$	10.5756	+	7.68359i	1.71558	+	1.24644i
$39$		0			0
$40$	−1.12773	+	3.47080i	−0.178310	+	0.548781i
$41$	2.55823	+	7.87342i	0.399529	+	1.22962i	0.925378	+	0.379045i	$0.123747\pi$
$41$	2.55823	+	7.87342i	0.399529	+	1.22962i	−0.525850	+	0.850577i	$0.676253\pi$
$42$		0			0
$43$	5.11353			0.779807			0.389903	−	0.920856i	$-0.372508\pi$
$43$	5.11353			0.779807			0.389903	+	0.920856i	$0.372508\pi$
$44$	−6.87391	−	9.55586i	−1.03628	−	1.44060i
$45$		0			0
$46$	−9.14851	+	6.64678i	−1.34887	+	0.980014i
$47$	3.35354	+	10.3211i	0.489164	+	1.50549i	0.825857	+	0.563879i	$0.190692\pi$
$47$	3.35354	+	10.3211i	0.489164	+	1.50549i	−0.336693	+	0.941614i	$0.609308\pi$
$48$		0			0
$49$	5.63282	+	4.09248i	0.804688	+	0.584640i
$50$	−1.90578	−	1.38463i	−0.269518	−	0.195816i
$51$		0			0
$52$	1.06793	+	3.28674i	0.148095	+	0.455789i
$53$	−7.51479	+	5.45981i	−1.03224	+	0.749963i	−0.968755	−	0.248020i	$-0.920220\pi$
$53$	−7.51479	+	5.45981i	−1.03224	+	0.749963i	−0.0634803	+	0.997983i	$0.520220\pi$
$54$		0			0
$55$	3.15911	−	1.00996i	0.425974	−	0.136183i
$56$	0.706260			0.0943780
$57$		0			0
$58$	7.36518	+	22.6677i	0.967096	+	2.97642i
$59$	3.46656	−	10.6690i	0.451307	−	1.38898i	−0.424109	−	0.905611i	$-0.639413\pi$
$59$	3.46656	−	10.6690i	0.451307	−	1.38898i	0.875416	−	0.483369i	$-0.160587\pi$
$60$		0			0
$61$	−0.975693	−	0.708883i	−0.124925	−	0.0907631i	0.523568	−	0.851984i	$-0.324600\pi$
$61$	−0.975693	−	0.708883i	−0.124925	−	0.0907631i	−0.648493	+	0.761221i	$0.724600\pi$
$62$	−1.82374	+	5.61288i	−0.231615	+	0.712836i
$63$		0			0
$64$	9.60743	−	6.98021i	1.20093	−	0.872526i
$65$	−0.973708			−0.120774
$66$		0			0
$67$	3.25922			0.398176			0.199088	−	0.979982i	$-0.436202\pi$
$67$	3.25922			0.398176			0.199088	+	0.979982i	$0.436202\pi$
$68$	−7.68293	+	5.58197i	−0.931692	+	0.676914i
$69$		0			0
$70$	−0.140877	+	0.433574i	−0.0168380	+	0.0518220i
$71$	4.84664	+	3.52129i	0.575191	+	0.417901i	0.836987	−	0.547222i	$-0.184315\pi$
$71$	4.84664	+	3.52129i	0.575191	+	0.417901i	−0.261796	+	0.965123i	$0.584315\pi$
$72$		0			0
$73$	1.02168	−	3.14442i	0.119579	−	0.368026i	−0.873296	−	0.487191i	$-0.838022\pi$
$73$	1.02168	−	3.14442i	0.119579	−	0.368026i	0.992875	+	0.119165i	$0.0380216\pi$
$74$	4.15814	+	12.7974i	0.483374	+	1.48767i
$75$		0			0
$76$	−19.6952			−2.25920
$77$	−0.374813	−	0.521052i	−0.0427139	−	0.0593794i
$78$		0			0
$79$	−8.21389	+	5.96774i	−0.924135	+	0.671423i	−0.944550	−	0.328368i	$-0.893501\pi$
$79$	−8.21389	+	5.96774i	−0.924135	+	0.671423i	0.0204147	+	0.999792i	$0.493501\pi$
$80$	−0.463040	−	1.42509i	−0.0517694	−	0.159330i
$81$		0			0
$82$	−15.7772	−	11.4628i	−1.74230	−	1.26586i
$83$	6.72704	+	4.88748i	0.738388	+	0.536471i	0.892206	−	0.451629i	$-0.149157\pi$
$83$	6.72704	+	4.88748i	0.738388	+	0.536471i	−0.153818	+	0.988099i	$0.549157\pi$
$84$		0			0
$85$	−0.826838	−	2.54475i	−0.0896832	−	0.276017i
$86$	−9.74527	+	7.08035i	−1.05086	+	0.763494i
$87$		0			0
$88$	11.4935	+	3.79468i	1.22521	+	0.404514i
$89$	−7.34270			−0.778325			−0.389163	−	0.921169i	$-0.627236\pi$
$89$	−7.34270			−0.778325			−0.389163	+	0.921169i	$0.627236\pi$
$90$		0			0
$91$	0.0582308	+	0.179216i	0.00610425	+	0.0187869i
$92$	5.26490	−	16.2037i	0.548904	−	1.68935i
$93$		0			0
$94$	−20.6821	−	15.0264i	−2.13319	−	1.54986i
$95$	1.71480	−	5.27760i	0.175935	−	0.541471i
$96$		0			0
$97$	12.8248	−	9.31774i	1.30216	−	0.946074i	0.302184	−	0.953250i	$-0.402284\pi$
$97$	12.8248	−	9.31774i	1.30216	−	0.946074i	0.999974	+	0.00717602i	$0.00228422\pi$
$98$	−16.4015			−1.65680
$99$		0			0
$100$	3.54920			0.354920
$101$	10.6460	−	7.73475i	1.05931	−	0.769636i	0.0853519	−	0.996351i	$-0.472799\pi$
$101$	10.6460	−	7.73475i	1.05931	−	0.769636i	0.973961	+	0.226715i	$0.0727985\pi$
$102$		0			0
$103$	1.23525	−	3.80172i	0.121713	−	0.374595i	−0.871575	−	0.490263i	$-0.836901\pi$
$103$	1.23525	−	3.80172i	0.121713	−	0.374595i	0.993288	+	0.115668i	$0.0369009\pi$
$104$	−2.87481	−	2.08867i	−0.281899	−	0.204811i
$105$		0			0
$106$	6.76171	−	20.8104i	0.656755	−	2.02129i
$107$	−1.51011	−	4.64764i	−0.145988	−	0.449304i	0.851149	−	0.524924i	$-0.175906\pi$
$107$	−1.51011	−	4.64764i	−0.145988	−	0.449304i	−0.997137	+	0.0756201i	$0.975906\pi$
$108$		0			0
$109$	−7.51977			−0.720263			−0.360131	−	0.932902i	$-0.617268\pi$
$109$	−7.51977			−0.720263			−0.360131	+	0.932902i	$0.617268\pi$
$110$	−4.62215	+	6.29896i	−0.440705	+	0.600583i
$111$		0			0
$112$	−0.234604	+	0.170450i	−0.0221680	+	0.0161060i
$113$	−6.24947	−	19.2339i	−0.587901	−	1.80937i	−0.587296	−	0.809372i	$-0.699808\pi$
$113$	−6.24947	−	19.2339i	−0.587901	−	1.80937i	−0.000604375	−	1.00000i	$-0.500192\pi$
$114$		0			0
$115$	3.88361	+	2.82160i	0.362148	+	0.263116i
$116$	−29.0519	−	21.1074i	−2.69740	−	1.95978i
$117$		0			0
$118$	8.16608	+	25.1326i	0.751748	+	2.31364i
$119$	−0.418926	+	0.304368i	−0.0384029	+	0.0279014i
$120$		0			0
$121$	−3.30005	−	10.4933i	−0.300005	−	0.953938i
$122$	2.84100			0.257212
$123$		0			0
$124$	−2.74775	−	8.45670i	−0.246755	−	0.759434i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	−5.74419	−	4.17340i	−0.509715	−	0.370329i	0.303001	−	0.952990i	$-0.402012\pi$
$127$	−5.74419	−	4.17340i	−0.509715	−	0.370329i	−0.812715	+	0.582661i	$0.802012\pi$
$128$	−6.31526	+	19.4364i	−0.558196	+	1.71795i
$129$		0			0
$130$	1.85567	−	1.34823i	0.162753	−	0.118247i
$131$	2.50024			0.218447			0.109223	−	0.994017i	$-0.465164\pi$
$131$	2.50024			0.218447			0.109223	+	0.994017i	$0.465164\pi$
$132$		0			0
$133$	−1.07392			−0.0931207
$134$	−6.21135	+	4.51281i	−0.536579	+	0.389847i
$135$		0			0
$136$	3.01748	−	9.28684i	0.258746	−	0.796340i
$137$	−12.3734	−	8.98981i	−1.05713	−	0.768052i	−0.0835766	−	0.996501i	$-0.526634\pi$
$137$	−12.3734	−	8.98981i	−1.05713	−	0.768052i	−0.973556	+	0.228450i	$0.926634\pi$
$138$		0			0
$139$	−6.07484	+	18.6964i	−0.515261	+	1.58581i	0.267544	+	0.963546i	$0.413788\pi$
$139$	−6.07484	+	18.6964i	−0.515261	+	1.58581i	−0.782806	+	0.622266i	$0.786212\pi$
$140$	−0.212253	−	0.653249i	−0.0179387	−	0.0552096i
$141$		0			0
$142$	−14.1123			−1.18428
$143$	−0.0152774	+	3.22939i	−0.00127756	+	0.270055i
$144$		0			0
$145$	8.18547	−	5.94709i	0.679766	−	0.493879i
$146$	2.40675	+	7.40722i	0.199184	+	0.613026i
$147$		0			0
$148$	−16.4017	−	11.9166i	−1.34821	−	0.979535i
$149$	−8.19771	−	5.95599i	−0.671583	−	0.487933i	0.198972	−	0.980005i	$-0.436240\pi$
$149$	−8.19771	−	5.95599i	−0.671583	−	0.487933i	−0.870555	+	0.492072i	$0.836240\pi$
$150$		0			0
$151$	3.69682	+	11.3776i	0.300843	+	0.925899i	0.981196	+	0.193015i	$0.0618264\pi$
$151$	3.69682	+	11.3776i	0.300843	+	0.925899i	−0.680353	+	0.732884i	$0.738174\pi$
$152$	16.3837	−	11.9034i	1.32889	−	0.965496i
$153$		0			0
$154$	1.43578	+	0.474033i	0.115698	+	0.0381987i
$155$	2.50533			0.201233
$156$		0			0
$157$	−0.811494	−	2.49752i	−0.0647643	−	0.199324i	0.913438	−	0.406978i	$-0.133417\pi$
$157$	−0.811494	−	2.49752i	−0.0647643	−	0.199324i	−0.978202	+	0.207654i	$0.933417\pi$
$158$	7.39076	−	22.7464i	0.587977	−	1.80961i
$159$		0			0
$160$	−3.04920	−	2.21537i	−0.241061	−	0.175141i
$161$	0.287079	−	0.883539i	0.0226250	−	0.0696326i
$162$		0			0
$163$	−19.1927	+	13.9443i	−1.50329	+	1.09220i	−0.534238	+	0.845334i	$0.679402\pi$
$163$	−19.1927	+	13.9443i	−1.50329	+	1.09220i	−0.969049	+	0.246868i	$0.920598\pi$
$164$	29.3825			2.29438
$165$		0			0
$166$	−19.5876			−1.52029
$167$	2.82488	−	2.05240i	0.218596	−	0.158819i	−0.473098	−	0.881010i	$-0.656865\pi$
$167$	2.82488	−	2.05240i	0.218596	−	0.158819i	0.691694	+	0.722190i	$0.256865\pi$
$168$		0			0
$169$	−3.72424	+	11.4620i	−0.286480	+	0.881695i
$170$	5.09931	+	3.70486i	0.391099	+	0.284150i
$171$		0			0
$172$	5.60834	−	17.2607i	0.427632	−	1.31612i
$173$	6.29145	+	19.3631i	0.478330	+	1.47215i	0.841413	+	0.540392i	$0.181724\pi$
$173$	6.29145	+	19.3631i	0.478330	+	1.47215i	−0.363083	+	0.931757i	$0.618276\pi$
$174$		0			0
$175$	0.193527			0.0146293
$176$	−4.73370	+	1.51335i	−0.356816	+	0.114073i
$177$		0			0
$178$	13.9936	−	10.1669i	1.04886	−	0.762044i
$179$	−1.19008	−	3.66268i	−0.0889506	−	0.273762i	0.896679	−	0.442681i	$-0.145972\pi$
$179$	−1.19008	−	3.66268i	−0.0889506	−	0.273762i	−0.985630	+	0.168919i	$0.945972\pi$
$180$		0			0
$181$	14.2509	+	10.3539i	1.05926	+	0.769599i	0.973952	−	0.226755i	$-0.0728117\pi$
$181$	14.2509	+	10.3539i	1.05926	+	0.769599i	0.0853107	+	0.996354i	$0.472812\pi$
$182$	−0.359123	−	0.260918i	−0.0266200	−	0.0193406i
$183$		0			0
$184$	5.41356	+	16.6612i	0.399093	+	1.22828i
$185$	4.62125	−	3.35753i	0.339761	−	0.246851i
$186$		0			0
$187$	−8.45285	+	2.70236i	−0.618134	+	0.197616i
$188$	38.5170			2.80914
$189$		0			0
$190$	4.03950	+	12.4323i	0.293056	+	0.901935i
$191$	−0.128891	+	0.396685i	−0.00932620	+	0.0287031i	−0.955611	−	0.294630i	$-0.904804\pi$
$191$	−0.128891	+	0.396685i	−0.00932620	+	0.0287031i	0.946285	+	0.323333i	$0.104804\pi$
$192$		0			0
$193$	−9.46269	−	6.87505i	−0.681140	−	0.494877i	0.192596	−	0.981278i	$-0.438309\pi$
$193$	−9.46269	−	6.87505i	−0.681140	−	0.494877i	−0.873736	+	0.486401i	$0.838309\pi$
$194$	−11.5396	+	35.5151i	−0.828493	+	2.54984i
$195$		0			0
$196$	19.9920	−	14.5250i	1.42800	−	1.03750i
$197$	−21.5958			−1.53864			−0.769320	−	0.638863i	$-0.779405\pi$
$197$	−21.5958			−1.53864			−0.769320	+	0.638863i	$0.779405\pi$
$198$		0			0
$199$	7.76028			0.550111			0.275056	−	0.961428i	$-0.411304\pi$
$199$	7.76028			0.550111			0.275056	+	0.961428i	$0.411304\pi$
$200$	−2.95244	+	2.14507i	−0.208769	+	0.151679i
$201$		0			0
$202$	−9.57911	+	29.4815i	−0.673984	+	2.07431i
$203$	−1.58411	−	1.15092i	−0.111183	−	0.0807790i
$204$		0			0
$205$	−2.55823	+	7.87342i	−0.178675	+	0.549904i
$206$	2.90986	+	8.95561i	0.202739	+	0.623967i
$207$		0			0
$208$	1.45903			0.101166
$209$	−17.4767	−	5.77008i	−1.20889	−	0.399125i
$210$		0			0
$211$	10.1173	−	7.35065i	0.696504	−	0.506040i	−0.182288	−	0.983245i	$-0.558350\pi$
$211$	10.1173	−	7.35065i	0.696504	−	0.506040i	0.878792	+	0.477205i	$0.158350\pi$
$212$	10.1876	+	31.3542i	0.699687	+	2.15342i
$213$		0			0
$214$	9.31320	+	6.76644i	0.636637	+	0.462544i
$215$	4.13694	+	3.00566i	0.282137	+	0.204984i
$216$		0			0
$217$	−0.149826	−	0.461118i	−0.0101709	−	0.0313027i
$218$	14.3310	−	10.4121i	0.970619	−	0.705196i
$219$		0			0
$220$	0.0556868	−	11.7712i	0.00375440	−	0.793617i
$221$	2.60536			0.175255
$222$		0			0
$223$	−1.66118	−	5.11257i	−0.111241	−	0.342363i	0.879904	−	0.475152i	$-0.157607\pi$
$223$	−1.66118	−	5.11257i	−0.111241	−	0.342363i	−0.991144	+	0.132789i	$0.957607\pi$
$224$	−0.225399	+	0.693708i	−0.0150601	+	0.0463503i
$225$		0			0
$226$	38.5419	+	28.0024i	2.56377	+	1.86269i
$227$	6.72202	−	20.6882i	0.446156	−	1.37313i	−0.435055	−	0.900404i	$-0.643271\pi$
$227$	6.72202	−	20.6882i	0.446156	−	1.37313i	0.881211	−	0.472723i	$-0.156729\pi$
$228$		0			0
$229$	−2.16068	+	1.56983i	−0.142782	+	0.103737i	−0.656883	−	0.753992i	$-0.728126\pi$
$229$	−2.16068	+	1.56983i	−0.142782	+	0.103737i	0.514101	+	0.857730i	$0.328126\pi$
$230$	−11.3082			−0.745639
$231$		0			0
$232$	36.9240			2.42418
$233$	−4.63323	+	3.36624i	−0.303533	+	0.220530i	−0.729117	−	0.684389i	$-0.760069\pi$
$233$	−4.63323	+	3.36624i	−0.303533	+	0.220530i	0.425584	+	0.904919i	$0.360069\pi$
$234$		0			0
$235$	−3.35354	+	10.3211i	−0.218761	+	0.673277i
$236$	−32.2110	−	23.4027i	−2.09676	−	1.52338i
$237$		0			0
$238$	0.376945	−	1.16012i	0.0244337	−	0.0751992i
$239$	7.53013	+	23.1754i	0.487084	+	1.49909i	0.828940	+	0.559337i	$0.188944\pi$
$239$	7.53013	+	23.1754i	0.487084	+	1.49909i	−0.341857	+	0.939752i	$0.611056\pi$
$240$		0			0
$241$	−16.7082			−1.07627			−0.538135	−	0.842859i	$-0.680871\pi$
$241$	−16.7082			−1.07627			−0.538135	+	0.842859i	$0.680871\pi$
$242$	20.8185	+	15.4286i	1.33827	+	0.991788i
$243$		0			0
$244$	−3.46293	+	2.51597i	−0.221691	+	0.161068i
$245$	2.15155	+	6.62178i	0.137457	+	0.423050i
$246$		0			0
$247$	4.37136	+	3.17598i	0.278143	+	0.202083i
$248$	7.39682	+	5.37410i	0.469698	+	0.341256i
$249$		0			0
$250$	−0.727943	−	2.24038i	−0.0460392	−	0.141694i
$251$	−13.0239	+	9.46240i	−0.822060	+	0.597262i	−0.917302	−	0.398193i	$-0.869638\pi$
$251$	−13.0239	+	9.46240i	−0.822060	+	0.597262i	0.0952418	+	0.995454i	$0.469638\pi$
$252$		0			0
$253$	9.41903	−	12.8360i	0.592169	−	0.806995i
$254$	16.7258			1.04947
$255$		0			0
$256$	−7.53728	−	23.1974i	−0.471080	−	1.44984i
$257$	−1.84445	+	5.67662i	−0.115053	+	0.354098i	−0.991958	−	0.126566i	$-0.959604\pi$
$257$	−1.84445	+	5.67662i	−0.115053	+	0.354098i	0.876905	+	0.480664i	$0.159604\pi$
$258$		0			0
$259$	−0.894336	−	0.649773i	−0.0555713	−	0.0403749i
$260$	−1.06793	+	3.28674i	−0.0662301	+	0.203835i
$261$		0			0
$262$	−4.76490	+	3.46191i	−0.294377	+	0.213877i
$263$	0.451149			0.0278190			0.0139095	−	0.999903i	$-0.495572\pi$
$263$	0.451149			0.0278190			0.0139095	+	0.999903i	$0.495572\pi$
$264$		0			0
$265$	−9.28879			−0.570606
$266$	2.04666	−	1.48698i	0.125489	−	0.0911728i
$267$		0			0
$268$	3.57459	−	11.0015i	0.218353	−	0.672021i
$269$	11.9085	+	8.65203i	0.726074	+	0.527524i	0.888319	−	0.459227i	$-0.151873\pi$
$269$	11.9085	+	8.65203i	0.726074	+	0.527524i	−0.162245	+	0.986751i	$0.551873\pi$
$270$		0			0
$271$	1.36829	−	4.21115i	0.0831175	−	0.255809i	−0.900858	−	0.434114i	$-0.857061\pi$
$271$	1.36829	−	4.21115i	0.0831175	−	0.255809i	0.983975	+	0.178305i	$0.0570614\pi$
$272$	1.23896	+	3.81312i	0.0751228	+	0.231204i
$273$		0			0
$274$	36.0286			2.17657
$275$	3.14941	+	1.03980i	0.189917	+	0.0627025i
$276$		0			0
$277$	0.0746965	−	0.0542702i	0.00448808	−	0.00326078i	−0.585539	−	0.810644i	$-0.699117\pi$
$277$	0.0746965	−	0.0542702i	0.00448808	−	0.00326078i	0.590027	+	0.807383i	$0.299117\pi$
$278$	−14.3104	−	44.0427i	−0.858278	−	2.64151i
$279$		0			0
$280$	0.571377	+	0.415129i	0.0341463	+	0.0248087i
$281$	4.19314	+	3.04650i	0.250142	+	0.181739i	0.705790	−	0.708421i	$-0.250592\pi$
$281$	4.19314	+	3.04650i	0.250142	+	0.181739i	−0.455648	+	0.890160i	$0.650592\pi$
$282$		0			0
$283$	0.483496	+	1.48805i	0.0287408	+	0.0884552i	0.964398	−	0.264455i	$-0.0851921\pi$
$283$	0.483496	+	1.48805i	0.0287408	+	0.0884552i	−0.935657	+	0.352910i	$0.885192\pi$
$284$	17.2017	−	12.4978i	1.02073	−	0.741607i
$285$		0			0
$286$	−4.44240	−	6.17566i	−0.262684	−	0.365174i
$287$	1.60214			0.0945710
$288$		0			0
$289$	−3.04091	−	9.35897i	−0.178877	−	0.550527i
$290$	−7.36518	+	22.6677i	−0.432498	+	1.33109i
$291$		0			0
$292$	−9.49341	−	6.89736i	−0.555560	−	0.403638i
$293$	7.15592	−	22.0236i	0.418053	−	1.28664i	−0.491438	−	0.870912i	$-0.663529\pi$
$293$	7.15592	−	22.0236i	0.418053	−	1.28664i	0.909491	−	0.415723i	$-0.136471\pi$
$294$		0			0
$295$	9.07556	−	6.59378i	0.528400	−	0.383905i
$296$	20.8461			1.21165
$297$		0			0
$298$	23.8699			1.38274
$299$	−3.78150	+	2.74742i	−0.218690	+	0.158887i
$300$		0			0
$301$	0.305805	−	0.941172i	0.0176263	−	0.0542483i
$302$	−22.7991	−	16.5646i	−1.31194	−	0.953183i
$303$		0			0
$304$	−2.56950	+	7.90811i	−0.147371	+	0.453561i
$305$	−0.372682	−	1.14700i	−0.0213397	−	0.0656768i
$306$		0			0
$307$	−7.72480			−0.440878			−0.220439	−	0.975401i	$-0.570749\pi$
$307$	−7.72480			−0.440878			−0.220439	+	0.975401i	$0.570749\pi$
$308$	−2.16989	+	0.693708i	−0.123641	+	0.0395277i
$309$		0			0
$310$	−4.77460	+	3.46895i	−0.271179	+	0.197023i
$311$	5.90867	+	18.1850i	0.335050	+	1.03118i	0.966697	+	0.255922i	$0.0823790\pi$
$311$	5.90867	+	18.1850i	0.335050	+	1.03118i	−0.631647	+	0.775256i	$0.717621\pi$
$312$		0			0
$313$	−2.34863	−	1.70638i	−0.132752	−	0.0964503i	0.519427	−	0.854515i	$-0.326145\pi$
$313$	−2.34863	−	1.70638i	−0.132752	−	0.0964503i	−0.652180	+	0.758064i	$0.726145\pi$
$314$	5.00468	+	3.63611i	0.282430	+	0.205198i
$315$		0			0
$316$	11.1354	+	34.2711i	0.626413	+	1.92790i
$317$	1.82962	−	1.32930i	0.102762	−	0.0746607i	−0.535218	−	0.844714i	$-0.679770\pi$
$317$	1.82962	−	1.32930i	0.102762	−	0.0746607i	0.637979	+	0.770053i	$0.279770\pi$
$318$		0			0
$319$	−19.5956	−	27.2411i	−1.09714	−	1.52521i
$320$	11.8754			0.663857
$321$		0			0
$322$	0.676265	+	2.08133i	0.0376868	+	0.115988i
$323$	−4.58829	+	14.1213i	−0.255299	+	0.785731i
$324$		0			0
$325$	−0.787747	−	0.572331i	−0.0436963	−	0.0317472i
$326$	17.2693	−	53.1496i	0.956460	−	2.94368i
$327$		0			0
$328$	−24.4421	+	17.7582i	−1.34959	+	0.980533i
$329$	2.10021			0.115788
$330$		0			0
$331$	6.02336			0.331074			0.165537	−	0.986204i	$-0.447064\pi$
$331$	6.02336			0.331074			0.165537	+	0.986204i	$0.447064\pi$
$332$	23.8756	−	17.3466i	1.31034	−	0.952021i
$333$		0			0
$334$	−2.54179	+	7.82284i	−0.139081	+	0.428047i
$335$	2.63676	+	1.91572i	0.144062	+	0.104667i
$336$		0			0
$337$	−4.50076	+	13.8519i	−0.245172	+	0.754562i	0.750436	+	0.660943i	$0.229843\pi$
$337$	−4.50076	+	13.8519i	−0.245172	+	0.754562i	−0.995608	+	0.0936187i	$0.970157\pi$
$338$	−8.77310	−	27.0008i	−0.477193	−	1.46865i
$339$		0			0
$340$	−9.49662			−0.515026
$341$	0.0393084	−	8.30913i	0.00212867	−	0.449965i
$342$		0			0
$343$	2.18607	−	1.58827i	0.118037	−	0.0857587i
$344$	5.76669	+	17.7480i	0.310919	+	0.956911i
$345$		0			0
$346$	−38.8009	−	28.1905i	−2.08595	−	1.51553i
$347$	23.3281	+	16.9489i	1.25232	+	0.909863i	0.998354	−	0.0573506i	$-0.0182653\pi$
$347$	23.3281	+	16.9489i	1.25232	+	0.909863i	0.253965	+	0.967213i	$0.418265\pi$
$348$		0			0
$349$	−0.504421	−	1.55245i	−0.0270010	−	0.0831006i	0.936648	−	0.350272i	$-0.113911\pi$
$349$	−0.504421	−	1.55245i	−0.0270010	−	0.0831006i	−0.963649	+	0.267172i	$0.913911\pi$
$350$	−0.368820	+	0.267964i	−0.0197143	+	0.0143233i
$351$		0			0
$352$	−7.39533	+	10.0782i	−0.394172	+	0.537169i
$353$	−24.9297			−1.32687			−0.663437	−	0.748232i	$-0.730903\pi$
$353$	−24.9297			−1.32687			−0.663437	+	0.748232i	$0.730903\pi$
$354$		0			0
$355$	1.85125	+	5.69757i	0.0982543	+	0.302396i
$356$	−8.05321	+	24.7852i	−0.426819	+	1.31361i
$357$		0			0
$358$	7.33949	+	5.33245i	0.387904	+	0.281829i
$359$	−8.78874	+	27.0489i	−0.463852	+	1.42759i	0.396569	+	0.918005i	$0.370201\pi$
$359$	−8.78874	+	27.0489i	−0.463852	+	1.42759i	−0.860421	+	0.509584i	$0.829799\pi$
$360$		0			0
$361$	−9.54125	+	6.93213i	−0.502171	+	0.364849i
$362$	−41.4955			−2.18095
$363$		0			0
$364$	0.668808			0.0350550
$365$	2.67480	−	1.94336i	0.140005	−	0.101720i
$366$		0			0
$367$	−3.22653	+	9.93023i	−0.168423	+	0.518354i	−0.999272	−	0.0381442i	$-0.987855\pi$
$367$	−3.22653	+	9.93023i	−0.168423	+	0.518354i	0.830849	+	0.556498i	$0.187855\pi$
$368$	−5.81930	−	4.22797i	−0.303352	−	0.220398i
$369$		0			0
$370$	−4.15814	+	12.7974i	−0.216171	+	0.665307i
$371$	0.555499	+	1.70965i	0.0288401	+	0.0887606i
$372$		0			0
$373$	−2.81747			−0.145883			−0.0729416	−	0.997336i	$-0.523239\pi$
$373$	−2.81747			−0.145883			−0.0729416	+	0.997336i	$0.523239\pi$
$374$	12.3675	−	16.8542i	0.639509	−	0.871508i
$375$		0			0
$376$	−32.0407	+	23.2789i	−1.65237	+	1.20052i
$377$	3.04437	+	9.36960i	0.156793	+	0.482559i
$378$		0			0
$379$	−7.22711	−	5.25080i	−0.371231	−	0.269715i	0.386490	−	0.922294i	$-0.373687\pi$
$379$	−7.22711	−	5.25080i	−0.371231	−	0.269715i	−0.757721	+	0.652578i	$0.773687\pi$
$380$	−15.9338	−	11.5766i	−0.817386	−	0.593865i
$381$		0			0
$382$	−0.303625	−	0.934460i	−0.0155348	−	0.0478111i
$383$	−6.90317	+	5.01545i	−0.352736	+	0.256278i	−0.750016	−	0.661420i	$-0.769954\pi$
$383$	−6.90317	+	5.01545i	−0.352736	+	0.256278i	0.397280	+	0.917697i	$0.369954\pi$
$384$		0			0
$385$	0.00303643	−	0.641850i	0.000154751	−	0.0327117i
$386$	27.5532			1.40242
$387$		0			0
$388$	−17.3862	−	53.5093i	−0.882651	−	2.71652i
$389$	−3.63890	+	11.1994i	−0.184500	+	0.567832i	−0.999939	−	0.0110104i	$-0.996495\pi$
$389$	−3.63890	+	11.1994i	−0.184500	+	0.567832i	0.815440	+	0.578842i	$0.196495\pi$
$390$		0			0
$391$	−10.3914	−	7.54978i	−0.525515	−	0.381809i
$392$	−7.85188	+	24.1656i	−0.396580	+	1.22055i
$393$		0			0
$394$	41.1569	−	29.9023i	2.07346	−	1.50645i
$395$	−10.1529			−0.510849
$396$		0			0
$397$	−1.41214			−0.0708735			−0.0354368	−	0.999372i	$-0.511282\pi$
$397$	−1.41214			−0.0708735			−0.0354368	+	0.999372i	$0.511282\pi$
$398$	−14.7894	+	10.7451i	−0.741325	+	0.538604i
$399$		0			0
$400$	0.463040	−	1.42509i	0.0231520	−	0.0712545i
$401$	6.84361	+	4.97217i	0.341753	+	0.248298i	0.745401	−	0.666616i	$-0.232258\pi$
$401$	6.84361	+	4.97217i	0.341753	+	0.248298i	−0.403648	+	0.914914i	$0.632258\pi$
$402$		0			0
$403$	−0.753833	+	2.32006i	−0.0375511	+	0.115570i
$404$	−14.4325	−	44.4185i	−0.718042	−	2.20991i
$405$		0			0
$406$	4.61257			0.228918
$407$	−11.0630	−	15.3794i	−0.548375	−	0.762331i
$408$		0			0
$409$	−8.19172	+	5.95163i	−0.405054	+	0.294289i	−0.771597	−	0.636112i	$-0.780542\pi$
$409$	−8.19172	+	5.95163i	−0.405054	+	0.294289i	0.366542	+	0.930401i	$0.380542\pi$
$410$	−6.02636	−	18.5472i	−0.297621	−	0.915982i
$411$		0			0
$412$	−11.4779	−	8.33918i	−0.565475	−	0.410842i
$413$	−1.75637	−	1.27608i	−0.0864252	−	0.0627915i
$414$		0			0
$415$	2.56950	+	7.90811i	0.126132	+	0.388194i
$416$	2.96903	−	2.15713i	0.145569	−	0.105762i
$417$		0			0
$418$	41.2962	−	13.2023i	2.01987	−	0.645746i
$419$	−32.8019			−1.60248			−0.801240	−	0.598343i	$-0.795826\pi$
$419$	−32.8019			−1.60248			−0.801240	+	0.598343i	$0.795826\pi$
$420$		0			0
$421$	−4.36619	−	13.4377i	−0.212795	−	0.654915i	−0.999303	−	0.0373351i	$-0.988113\pi$
$421$	−4.36619	−	13.4377i	−0.212795	−	0.654915i	0.786508	−	0.617580i	$-0.211887\pi$
$422$	−9.10342	+	28.0175i	−0.443148	+	1.36387i
$423$		0			0
$424$	−27.4246	−	19.9251i	−1.33185	−	0.967649i
$425$	0.826838	−	2.54475i	0.0401076	−	0.123438i
$426$		0			0
$427$	−0.188823	+	0.137188i	−0.00913779	+	0.00663899i
$428$	−17.3443			−0.838368
$429$		0			0
$430$	−12.0458			−0.580901
$431$	15.4569	−	11.2301i	0.744531	−	0.540933i	−0.149596	−	0.988747i	$-0.547797\pi$
$431$	15.4569	−	11.2301i	0.744531	−	0.540933i	0.894127	+	0.447814i	$0.147797\pi$
$432$		0			0
$433$	4.67235	−	14.3800i	0.224539	−	0.691059i	−0.773799	−	0.633431i	$-0.781646\pi$
$433$	4.67235	−	14.3800i	0.224539	−	0.691059i	0.998338	−	0.0576283i	$-0.0183538\pi$
$434$	0.924015	+	0.671336i	0.0443541	+	0.0322252i
$435$		0			0
$436$	−8.24740	+	25.3829i	−0.394979	+	1.21562i
$437$	−8.23171	−	25.3346i	−0.393776	−	1.21192i
$438$		0			0
$439$	37.1642			1.77375			0.886876	−	0.462008i	$-0.152871\pi$
$439$	37.1642			1.77375			0.886876	+	0.462008i	$0.152871\pi$
$440$	7.06799	+	9.82567i	0.336953	+	0.468421i
$441$		0			0
$442$	−4.96524	+	3.60746i	−0.236172	+	0.171589i
$443$	0.853040	+	2.62539i	0.0405291	+	0.124736i	0.969274	−	0.245984i	$-0.0791110\pi$
$443$	0.853040	+	2.62539i	0.0405291	+	0.124736i	−0.928745	+	0.370720i	$0.879111\pi$
$444$		0			0
$445$	−5.94037	−	4.31593i	−0.281601	−	0.204595i
$446$	10.2449	+	7.44333i	0.485108	+	0.352452i
$447$		0			0
$448$	−0.710189	−	2.18574i	−0.0335533	−	0.103266i
$449$	−14.4540	+	10.5015i	−0.682127	+	0.495594i	−0.874063	−	0.485813i	$-0.838524\pi$
$449$	−14.4540	+	10.5015i	−0.682127	+	0.495594i	0.191936	+	0.981408i	$0.438524\pi$
$450$		0			0
$451$	26.0728	+	8.60813i	1.22772	+	0.405341i
$452$	−71.7780			−3.37615
$453$		0			0
$454$	15.8349	+	48.7348i	0.743168	+	2.28724i
$455$	−0.0582308	+	0.179216i	−0.00272990	+	0.00840178i
$456$		0			0
$457$	17.1205	+	12.4388i	0.800864	+	0.581862i	0.911167	−	0.412036i	$-0.135182\pi$
$457$	17.1205	+	12.4388i	0.800864	+	0.581862i	−0.110304	+	0.993898i	$0.535182\pi$
$458$	1.94416	−	5.98350i	0.0908444	−	0.279590i
$459$		0			0
$460$	13.7837	−	10.0144i	0.642668	−	0.466926i
$461$	34.3476			1.59973			0.799864	−	0.600181i	$-0.204905\pi$
$461$	34.3476			1.59973			0.799864	+	0.600181i	$0.204905\pi$
$462$		0			0
$463$	10.4516			0.485727			0.242864	−	0.970060i	$-0.421913\pi$
$463$	10.4516			0.485727			0.242864	+	0.970060i	$0.421913\pi$
$464$	−12.2653	+	8.91129i	−0.569404	+	0.413696i
$465$		0			0
$466$	4.16892	−	12.8306i	0.193122	−	0.594367i
$467$	23.9820	+	17.4239i	1.10975	+	0.806284i	0.982625	−	0.185602i	$-0.0594236\pi$
$467$	23.9820	+	17.4239i	1.10975	+	0.806284i	0.127129	+	0.991886i	$0.459424\pi$
$468$		0			0
$469$	0.194911	−	0.599875i	0.00900017	−	0.0276997i
$470$	−7.89985	−	24.3133i	−0.364393	−	1.12149i
$471$		0			0
$472$	40.9392			1.88438
$473$	10.0334	−	13.6734i	0.461338	−	0.628701i
$474$		0			0
$475$	4.48940	−	3.26174i	0.205988	−	0.149659i
$476$	0.567928	+	1.74790i	0.0260309	+	0.0801150i
$477$		0			0
$478$	−46.4401	−	33.7407i	−2.12412	−	1.54326i
$479$	−10.6941	−	7.76971i	−0.488625	−	0.355007i	0.316030	−	0.948749i	$-0.397650\pi$
$479$	−10.6941	−	7.76971i	−0.488625	−	0.355007i	−0.804655	+	0.593742i	$0.797650\pi$
$480$		0			0
$481$	1.71875	+	5.28977i	0.0783682	+	0.241193i
$482$	31.8422	−	23.1347i	1.45037	−	1.05376i
$483$		0			0
$484$	−39.0395	−	0.369380i	−1.77452	−	0.0167900i
$485$	15.8523			0.719816
$486$		0			0
$487$	−13.1325	−	40.4176i	−0.595089	−	1.83150i	−0.554282	−	0.832329i	$-0.687007\pi$
$487$	−13.1325	−	40.4176i	−0.595089	−	1.83150i	−0.0408075	−	0.999167i	$-0.512993\pi$
$488$	1.36007	−	4.18586i	0.0615675	−	0.189485i
$489$		0			0
$490$	−13.2691	−	9.64056i	−0.599436	−	0.435516i
$491$	4.86568	−	14.9750i	0.219585	−	0.675813i	−0.779211	−	0.626761i	$-0.784380\pi$
$491$	4.86568	−	14.9750i	0.219585	−	0.675813i	0.998796	−	0.0490515i	$-0.0156198\pi$
$492$		0			0
$493$	−21.9019	+	15.9127i	−0.986412	+	0.716670i
$494$	−12.7284			−0.572679
$495$		0			0
$496$	−3.75405			−0.168562
$497$	0.937957	−	0.681466i	0.0420731	−	0.0305679i
$498$		0			0
$499$	−10.3607	+	31.8869i	−0.463808	+	1.42746i	0.396666	+	0.917963i	$0.370167\pi$
$499$	−10.3607	+	31.8869i	−0.463808	+	1.42746i	−0.860475	+	0.509493i	$0.829833\pi$
$500$	2.87136	+	2.08617i	0.128411	+	0.0932963i
$501$		0			0
$502$	11.7187	−	36.0665i	0.523032	−	1.60973i
$503$	7.05063	+	21.6996i	0.314372	+	0.967537i	0.976012	+	0.217716i	$0.0698606\pi$
$503$	7.05063	+	21.6996i	0.314372	+	0.967537i	−0.661640	+	0.749821i	$0.730139\pi$
$504$		0			0
$505$	13.1591			0.585574
$506$	−0.177425	+	37.5046i	−0.00788749	+	1.66728i
$507$		0			0
$508$	−20.3873	+	14.8122i	−0.904540	+	0.657187i
$509$	−12.2731	−	37.7727i	−0.543996	−	1.67425i	−0.723365	−	0.690465i	$-0.757406\pi$
$509$	−12.2731	−	37.7727i	−0.543996	−	1.67425i	0.179370	−	0.983782i	$-0.442594\pi$
$510$		0			0
$511$	−0.517646	−	0.376092i	−0.0228993	−	0.0166373i
$512$	13.4170	+	9.74805i	0.592955	+	0.430807i
$513$		0			0
$514$	−4.34491	−	13.3723i	−0.191646	−	0.589826i
$515$	3.23394	−	2.34959i	0.142504	−	0.103535i
$516$		0			0
$517$	34.1784	+	11.2843i	1.50316	+	0.496281i
$518$	2.60410			0.114418
$519$		0			0
$520$	−1.09808	−	3.37955i	−0.0481540	−	0.148203i
$521$	−7.88005	+	24.2523i	−0.345231	+	1.06251i	0.616229	+	0.787567i	$0.288660\pi$
$521$	−7.88005	+	24.2523i	−0.345231	+	1.06251i	−0.961460	+	0.274945i	$0.911340\pi$
$522$		0			0
$523$	12.4835	+	9.06977i	0.545864	+	0.396593i	0.826258	−	0.563291i	$-0.190465\pi$
$523$	12.4835	+	9.06977i	0.545864	+	0.396593i	−0.280394	+	0.959885i	$0.590465\pi$
$524$	2.74217	−	8.43953i	0.119792	−	0.368683i
$525$		0			0
$526$	−0.859791	+	0.624675i	−0.0374887	+	0.0272371i
$527$	−6.70351			−0.292010
$528$		0			0
$529$	0.0438407			0.00190612
$530$	17.7024	−	12.8615i	0.768943	−	0.558669i
$531$		0			0
$532$	−1.17784	+	3.62501i	−0.0510657	+	0.157164i
$533$	−6.52145	−	4.73811i	−0.282475	−	0.205230i
$534$		0			0
$535$	1.51011	−	4.64764i	0.0652877	−	0.200935i
$536$	3.67552	+	11.3121i	0.158758	+	0.488607i
$537$		0			0
$538$	−34.6749			−1.49494
$539$	21.9955	−	7.03189i	0.947411	−	0.302885i
$540$		0			0
$541$	−22.3294	+	16.2233i	−0.960018	+	0.697494i	−0.953155	−	0.302483i	$-0.902185\pi$
$541$	−22.3294	+	16.2233i	−0.960018	+	0.697494i	−0.00686309	+	0.999976i	$0.502185\pi$
$542$	3.22324	+	9.92010i	0.138450	+	0.426105i
$543$		0			0
$544$	8.15877	+	5.92769i	0.349804	+	0.254148i
$545$	−6.08362	−	4.42001i	−0.260594	−	0.189332i
$546$		0			0
$547$	9.50800	+	29.2626i	0.406533	+	1.25118i	0.919608	+	0.392836i	$0.128506\pi$
$547$	9.50800	+	29.2626i	0.406533	+	1.25118i	−0.513076	+	0.858343i	$0.671494\pi$
$548$	−43.9157	+	31.9067i	−1.87599	+	1.36298i
$549$		0			0
$550$	−7.44184	+	2.37914i	−0.317321	+	0.101447i
$551$	−56.1457			−2.39189
$552$		0			0
$553$	0.607177	+	1.86870i	0.0258198	+	0.0794652i
$554$	−0.0672109	+	0.206854i	−0.00285552	+	0.00878838i
$555$		0			0
$556$	56.4470	+	41.0112i	2.39389	+	1.73926i
$557$	4.30642	−	13.2538i	0.182469	−	0.561582i	−0.817427	−	0.576033i	$-0.804600\pi$
$557$	4.30642	−	13.2538i	0.182469	−	0.561582i	0.999896	+	0.0144509i	$0.00460003\pi$
$558$		0			0
$559$	−4.02817	+	2.92664i	−0.170373	+	0.123783i
$560$	−0.289986			−0.0122542
$561$		0			0
$562$	−12.2095			−0.515026
$563$	4.72456	−	3.43259i	0.199117	−	0.144667i	−0.483759	−	0.875201i	$-0.660729\pi$
$563$	4.72456	−	3.43259i	0.199117	−	0.144667i	0.682876	+	0.730534i	$0.260729\pi$
$564$		0			0
$565$	6.24947	−	19.2339i	0.262917	−	0.809176i
$566$	−2.98183	−	2.16643i	−0.125336	−	0.0910618i
$567$		0			0
$568$	−6.75599	+	20.7928i	−0.283475	+	0.872447i
$569$	1.68536	+	5.18701i	0.0706540	+	0.217451i	0.980148	−	0.198266i	$-0.0635309\pi$
$569$	1.68536	+	5.18701i	0.0706540	+	0.217451i	−0.909494	+	0.415716i	$0.863531\pi$
$570$		0			0
$571$	40.2894			1.68606			0.843030	−	0.537866i	$-0.180770\pi$
$571$	40.2894			1.68606			0.843030	+	0.537866i	$0.180770\pi$
$572$	10.8840	+	3.59344i	0.455084	+	0.150249i
$573$		0			0
$574$	−3.05332	+	2.21837i	−0.127443	+	0.0925928i
$575$	1.48341	+	4.56545i	0.0618623	+	0.190392i
$576$		0			0
$577$	19.2737	+	14.0032i	0.802374	+	0.582959i	0.911610	−	0.411057i	$-0.134840\pi$
$577$	19.2737	+	14.0032i	0.802374	+	0.582959i	−0.109236	+	0.994016i	$0.534840\pi$
$578$	18.7540	+	13.6256i	0.780065	+	0.566750i
$579$		0			0
$580$	−11.0968	−	34.1525i	−0.460771	−	1.41811i
$581$	1.30186	−	0.945860i	0.0540104	−	0.0392409i
$582$		0			0
$583$	−0.145740	+	30.8071i	−0.00603595	+	1.27590i
$584$	12.0658			0.499287
$585$		0			0
$586$	16.8570	+	51.8805i	0.696357	+	2.14317i
$587$	−6.05919	+	18.6483i	−0.250090	+	0.769697i	0.744668	+	0.667435i	$0.232608\pi$
$587$	−6.05919	+	18.6483i	−0.250090	+	0.769697i	−0.994758	+	0.102262i	$0.967392\pi$
$588$		0			0
$589$	−11.2474	−	8.17172i	−0.463441	−	0.336710i
$590$	−8.16608	+	25.1326i	−0.336192	+	1.03469i
$591$		0			0
$592$	−6.92460	+	5.03102i	−0.284599	+	0.206774i
$593$	−3.31095			−0.135964			−0.0679822	−	0.997687i	$-0.521656\pi$
$593$	−3.31095			−0.135964			−0.0679822	+	0.997687i	$0.521656\pi$
$594$		0			0
$595$	−0.517822			−0.0212286
$596$	−29.0953	+	21.1390i	−1.19179	+	0.865887i
$597$		0			0
$598$	3.40255	−	10.4720i	0.139140	−	0.428230i
$599$	25.9460	+	18.8509i	1.06012	+	0.770225i	0.974111	−	0.226069i	$-0.0725875\pi$
$599$	25.9460	+	18.8509i	1.06012	+	0.770225i	0.0860126	+	0.996294i	$0.472587\pi$
$600$		0			0
$601$	−9.05125	+	27.8569i	−0.369208	+	1.13631i	0.578095	+	0.815969i	$0.303796\pi$
$601$	−9.05125	+	27.8569i	−0.369208	+	1.13631i	−0.947304	+	0.320337i	$0.896204\pi$
$602$	0.720378	+	2.21710i	0.0293604	+	0.0903621i
$603$		0			0
$604$	42.4596			1.72766
$605$	3.49802	−	10.4290i	0.142215	−	0.423999i
$606$		0			0
$607$	31.6169	−	22.9710i	1.28329	−	0.932364i	0.283642	−	0.958930i	$-0.408457\pi$
$607$	31.6169	−	22.9710i	1.28329	−	0.932364i	0.999647	+	0.0265657i	$0.00845712\pi$
$608$	6.46311	+	19.8914i	0.262114	+	0.806703i
$609$		0			0
$610$	2.29842	+	1.66990i	0.0930601	+	0.0676121i
$611$	−8.54886	−	6.21111i	−0.345850	−	0.251275i
$612$		0			0
$613$	−3.93452	−	12.1092i	−0.158914	−	0.489086i	0.839623	−	0.543170i	$-0.182776\pi$
$613$	−3.93452	−	12.1092i	−0.158914	−	0.489086i	−0.998536	+	0.0540840i	$0.982776\pi$
$614$	14.7218	−	10.6960i	0.594123	−	0.431655i
$615$		0			0
$616$	1.38578	−	1.88851i	0.0558346	−	0.0760901i
$617$	8.97789			0.361436			0.180718	−	0.983535i	$-0.442158\pi$
$617$	8.97789			0.361436			0.180718	+	0.983535i	$0.442158\pi$
$618$		0			0
$619$	−6.86392	−	21.1250i	−0.275884	−	0.849084i	−0.988984	−	0.148022i	$-0.952710\pi$
$619$	−6.86392	−	21.1250i	−0.275884	−	0.849084i	0.713100	−	0.701062i	$-0.247290\pi$
$620$	2.74775	−	8.45670i	0.110352	−	0.339629i
$621$		0			0
$622$	−36.4402	−	26.4753i	−1.46112	−	1.06156i
$623$	−0.439117	+	1.35146i	−0.0175928	+	0.0541452i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	6.83868			0.273329
$627$		0			0
$628$	−9.32038			−0.371924
$629$	−12.3651	+	8.98377i	−0.493029	+	0.358206i
$630$		0			0
$631$	8.27153	−	25.4572i	0.329285	−	1.01343i	−0.640185	−	0.768221i	$-0.721142\pi$
$631$	8.27153	−	25.4572i	0.329285	−	1.01343i	0.969469	−	0.245213i	$-0.0788578\pi$
$632$	−29.9759	−	21.7788i	−1.19238	−	0.866313i
$633$		0			0
$634$	−1.64627	+	5.06670i	−0.0653817	+	0.201224i
$635$	−2.19409	−	6.75270i	−0.0870697	−	0.267973i
$636$		0			0
$637$	−6.77949			−0.268613
$638$	75.0639	+	24.7829i	2.97181	+	0.981166i
$639$		0			0
$640$	−16.5336	+	12.0123i	−0.653547	+	0.474830i
$641$	−4.65770	−	14.3349i	−0.183968	−	0.566195i	0.815961	−	0.578107i	$-0.196208\pi$
$641$	−4.65770	−	14.3349i	−0.183968	−	0.566195i	−0.999929	+	0.0119117i	$0.996208\pi$
$642$		0			0
$643$	31.7840	+	23.0925i	1.25344	+	0.910678i	0.998416	−	0.0562569i	$-0.0179166\pi$
$643$	31.7840	+	23.0925i	1.25344	+	0.910678i	0.255024	+	0.966935i	$0.417917\pi$
$644$	−2.66752	−	1.93807i	−0.105115	−	0.0763705i
$645$		0			0
$646$	−10.8085	−	33.2652i	−0.425256	−	1.30880i
$647$	19.2656	−	13.9973i	0.757408	−	0.550289i	−0.140706	−	0.990051i	$-0.544937\pi$
$647$	19.2656	−	13.9973i	0.757408	−	0.550289i	0.898114	+	0.439762i	$0.144937\pi$
$648$		0			0
$649$	−21.7265	−	30.2033i	−0.852838	−	1.18559i
$650$	2.29374			0.0899679
$651$		0			0
$652$	26.0190	+	80.0784i	1.01898	+	3.13611i
$653$	−2.13331	+	6.56566i	−0.0834829	+	0.256934i	−0.984081	−	0.177718i	$-0.943129\pi$
$653$	−2.13331	+	6.56566i	−0.0834829	+	0.256934i	0.900599	+	0.434652i	$0.143129\pi$
$654$		0			0
$655$	2.02273	+	1.46960i	0.0790348	+	0.0574221i
$656$	3.83332	−	11.7978i	0.149666	−	0.460625i
$657$		0			0
$658$	−4.00254	+	2.90802i	−0.156035	+	0.113366i
$659$	20.3718			0.793571			0.396786	−	0.917911i	$-0.370126\pi$
$659$	20.3718			0.793571			0.396786	+	0.917911i	$0.370126\pi$
$660$		0			0
$661$	−19.7451			−0.767994			−0.383997	−	0.923334i	$-0.625453\pi$
$661$	−19.7451			−0.767994			−0.383997	+	0.923334i	$0.625453\pi$
$662$	−11.4792	+	8.34013i	−0.446152	+	0.324148i
$663$		0			0
$664$	−9.37717	+	28.8600i	−0.363905	+	1.11998i
$665$	−0.868820	−	0.631235i	−0.0336914	−	0.0244782i
$666$		0			0
$667$	15.0088	−	46.1923i	0.581143	−	1.78857i
$668$	−3.82962	−	11.7864i	−0.148172	−	0.456028i
$669$		0			0
$670$	−7.67765			−0.296613
$671$	−3.80996	+	1.21803i	−0.147082	+	0.0470217i
$672$		0			0
$673$	−29.6207	+	21.5207i	−1.14180	+	0.829563i	−0.987368	−	0.158441i	$-0.949353\pi$
$673$	−29.6207	+	21.5207i	−1.14180	+	0.829563i	−0.154427	+	0.988004i	$0.549353\pi$
$674$	−10.6023	−	32.6306i	−0.408386	−	1.25688i
$675$		0			0
$676$	34.6054	+	25.1423i	1.33098	+	0.967011i
$677$	5.96357	+	4.33279i	0.229199	+	0.166523i	0.696458	−	0.717598i	$-0.254758\pi$
$677$	5.96357	+	4.33279i	0.229199	+	0.166523i	−0.467259	+	0.884120i	$0.654758\pi$
$678$		0			0
$679$	−0.948017	−	2.91770i	−0.0363816	−	0.111971i
$680$	7.89985	−	5.73958i	0.302946	−	0.220103i
$681$		0			0
$682$	11.4302	+	15.8898i	0.437684	+	0.608452i
$683$	−24.5651			−0.939959			−0.469979	−	0.882677i	$-0.655739\pi$
$683$	−24.5651			−0.939959			−0.469979	+	0.882677i	$0.655739\pi$
$684$		0			0
$685$	−4.72622	−	14.5458i	−0.180580	−	0.555767i
$686$	−1.96700	+	6.05380i	−0.0751004	+	0.231135i
$687$		0			0
$688$	−6.19890	−	4.50376i	−0.236331	−	0.171704i
$689$	2.79492	−	8.60189i	0.106478	−	0.327706i
$690$		0			0
$691$	−24.1439	+	17.5416i	−0.918479	+	0.667314i	−0.943145	−	0.332382i	$-0.892148\pi$
$691$	−24.1439	+	17.5416i	−0.918479	+	0.667314i	0.0246662	+	0.999696i	$0.492148\pi$
$692$	72.2602			2.74692
$693$		0			0
$694$	−67.9262			−2.57844
$695$	−15.9041	+	11.5550i	−0.603279	+	0.438308i
$696$		0			0
$697$	6.84507	−	21.0670i	0.259276	−	0.797968i
$698$	3.11088	+	2.26019i	0.117749	+	0.0855494i
$699$		0			0
$700$	0.212253	−	0.653249i	0.00802243	−	0.0246905i
$701$	4.45569	+	13.7132i	0.168289	+	0.517940i	0.999264	−	0.0383701i	$-0.0122166\pi$
$701$	4.45569	+	13.7132i	0.168289	+	0.517940i	−0.830975	+	0.556310i	$0.812217\pi$
$702$		0			0
$703$	−31.6980			−1.19551
$704$	0.186325	−	39.3859i	0.00702238	−	1.48441i
$705$		0			0
$706$	47.5106	−	34.5184i	1.78808	−	1.29912i
$707$	−0.786958	−	2.42201i	−0.0295966	−	0.0910890i
$708$		0			0
$709$	36.0084	+	26.1616i	1.35232	+	0.982520i	0.998892	+	0.0470585i	$0.0149847\pi$
$709$	36.0084	+	26.1616i	1.35232	+	0.982520i	0.353430	+	0.935461i	$0.385015\pi$
$710$	−11.4171	−	8.29502i	−0.428477	−	0.311307i
$711$		0			0
$712$	−8.28059	−	25.4850i	−0.310328	−	0.955093i
$713$	9.72970	−	7.06904i	0.364380	−	0.264738i
$714$		0			0
$715$	−1.91055	+	2.60365i	−0.0714504	+	0.0973710i
$716$	−13.6686			−0.510819
$717$		0			0
$718$	−20.7034	−	63.7185i	−0.772644	−	2.37795i
$719$	−1.11044	+	3.41758i	−0.0414124	+	0.127454i	−0.969625	−	0.244595i	$-0.921345\pi$
$719$	−1.11044	+	3.41758i	−0.0414124	+	0.127454i	0.928213	+	0.372050i	$0.121345\pi$
$720$		0			0
$721$	−0.625854	−	0.454710i	−0.0233080	−	0.0169343i
$722$	8.58510	−	26.4222i	0.319504	−	0.983333i
$723$		0			0
$724$	50.5794	−	36.7481i	1.87977	−	1.36573i
$725$	10.1178			0.375766
$726$		0			0
$727$	−39.0846			−1.44957			−0.724784	−	0.688976i	$-0.758060\pi$
$727$	−39.0846			−1.44957			−0.724784	+	0.688976i	$0.758060\pi$
$728$	−0.556354	+	0.404215i	−0.0206199	+	0.0149812i
$729$		0			0
$730$	−2.40675	+	7.40722i	−0.0890779	+	0.274154i
$731$	−11.0692	−	8.04226i	−0.409410	−	0.297454i
$732$		0			0
$733$	11.6519	−	35.8610i	0.430374	−	1.32455i	−0.467379	−	0.884057i	$-0.654802\pi$
$733$	11.6519	−	35.8610i	0.430374	−	1.32455i	0.897753	−	0.440498i	$-0.145198\pi$
$734$	−7.60065	−	23.3924i	−0.280545	−	0.863429i
$735$		0			0
$736$	−18.0928			−0.666910
$737$	6.39502	−	8.71499i	0.235564	−	0.321021i
$738$		0			0
$739$	−12.0806	+	8.77706i	−0.444392	+	0.322869i	−0.787377	−	0.616471i	$-0.788562\pi$
$739$	−12.0806	+	8.77706i	−0.444392	+	0.322869i	0.342986	+	0.939341i	$0.388562\pi$
$740$	−6.26490	−	19.2814i	−0.230302	−	0.708798i
$741$		0			0
$742$	−3.42589	−	2.48906i	−0.125768	−	0.0913761i
$743$	10.8149	+	7.85749i	0.396760	+	0.288263i	0.768220	−	0.640186i	$-0.221143\pi$
$743$	10.8149	+	7.85749i	0.396760	+	0.288263i	−0.371460	+	0.928449i	$0.621143\pi$
$744$		0			0
$745$	−3.13125	−	9.63699i	−0.114720	−	0.353072i
$746$	5.36949	−	3.90116i	0.196591	−	0.142832i
$747$		0			0
$748$	−0.149001	+	31.4964i	−0.00544803	+	1.15162i
$749$	−0.945731			−0.0345563
$750$		0			0
$751$	12.5045	+	38.4849i	0.456296	+	1.40434i	0.869606	+	0.493745i	$0.164373\pi$
$751$	12.5045	+	38.4849i	0.456296	+	1.40434i	−0.413310	+	0.910590i	$0.635627\pi$
$752$	5.02504	−	15.4655i	0.183244	−	0.563968i
$753$		0			0
$754$	−18.7753	−	13.6411i	−0.683757	−	0.496779i
$755$	−3.69682	+	11.3776i	−0.134541	+	0.414075i
$756$		0			0
$757$	6.90704	−	5.01826i	0.251040	−	0.182392i	−0.455147	−	0.890416i	$-0.650413\pi$
$757$	6.90704	−	5.01826i	0.251040	−	0.182392i	0.706188	+	0.708025i	$0.250413\pi$
$758$	21.0437			0.764341
$759$		0			0
$760$	20.2513			0.734593
$761$	−17.2162	+	12.5083i	−0.624089	+	0.453427i	−0.854347	−	0.519703i	$-0.826043\pi$
$761$	−17.2162	+	12.5083i	−0.624089	+	0.453427i	0.230259	+	0.973129i	$0.426043\pi$
$762$		0			0
$763$	−0.449706	+	1.38405i	−0.0162804	+	0.0501060i
$764$	1.19764	+	0.870139i	0.0433292	+	0.0314805i
$765$		0			0
$766$	6.21139	−	19.1167i	0.224427	−	0.690714i
$767$	3.37541	+	10.3885i	0.121879	+	0.375105i
$768$		0			0
$769$	−24.4717			−0.882471			−0.441235	−	0.897391i	$-0.645460\pi$
$769$	−24.4717			−0.882471			−0.441235	+	0.897391i	$0.645460\pi$
$770$	0.882938	+	1.22743i	0.0318189	+	0.0442335i
$771$		0			0
$772$	−33.5850	+	24.4009i	−1.20875	+	0.878209i
$773$	−4.21721	−	12.9792i	−0.151682	−	0.466830i	0.846127	−	0.532981i	$-0.178928\pi$
$773$	−4.21721	−	12.9792i	−0.151682	−	0.466830i	−0.997810	+	0.0661505i	$0.978928\pi$
$774$		0			0
$775$	2.02685	+	1.47259i	0.0728066	+	0.0528971i
$776$	46.8029	+	34.0043i	1.68013	+	1.22068i
$777$		0			0
$778$	−8.57207	−	26.3821i	−0.307324	−	0.945845i
$779$	37.1660	−	27.0027i	1.33161	−	0.967471i
$780$		0			0
$781$	18.9255	−	6.05045i	0.677209	−	0.216502i
$782$	30.2574			1.08200
$783$		0			0
$784$	−3.22394	−	9.92225i	−0.115141	−	0.354366i
$785$	0.811494	−	2.49752i	0.0289635	−	0.0891404i
$786$		0			0
$787$	6.03291	+	4.38317i	0.215050	+	0.156243i	0.690096	−	0.723718i	$-0.257568\pi$
$787$	6.03291	+	4.38317i	0.215050	+	0.156243i	−0.475046	+	0.879961i	$0.657568\pi$
$788$	−23.6855	+	72.8966i	−0.843762	+	2.59683i
$789$		0			0
$790$	19.3493	−	14.0581i	0.688416	−	0.500163i
$791$	−3.91383			−0.139160
$792$		0			0
$793$	1.17431			0.0417011
$794$	2.69124	−	1.95530i	0.0955085	−	0.0693910i
$795$		0			0
$796$	8.51119	−	26.1947i	0.301671	−	0.928448i
$797$	9.73624	+	7.07379i	0.344875	+	0.250567i	0.746716	−	0.665143i	$-0.231629\pi$
$797$	9.73624	+	7.07379i	0.344875	+	0.250567i	−0.401841	+	0.915710i	$0.631629\pi$
$798$		0			0
$799$	8.97309	−	27.6163i	0.317445	−	0.976996i
$800$	−1.16469	−	3.58455i	−0.0411781	−	0.126733i
$801$		0			0
$802$	−19.9270			−0.703648
$803$	−6.40334	−	8.90170i	−0.225969	−	0.314134i
$804$		0			0
$805$	0.751583	−	0.546057i	0.0264898	−	0.0192460i
$806$	−1.77579	−	5.46531i	−0.0625494	−	0.192507i
$807$		0			0
$808$	38.8515	+	28.2273i	1.36679	+	0.993033i
$809$	−40.4782	−	29.4091i	−1.42314	−	1.03397i	−0.991244	−	0.132044i	$-0.957846\pi$
$809$	−40.4782	−	29.4091i	−1.42314	−	1.03397i	−0.431892	−	0.901925i	$-0.642154\pi$
$810$		0			0
$811$	−3.46678	−	10.6697i	−0.121735	−	0.374663i	0.871557	−	0.490294i	$-0.163111\pi$
$811$	−3.46678	−	10.6697i	−0.121735	−	0.374663i	−0.993292	+	0.115632i	$0.963111\pi$
$812$	−5.62233	+	4.08486i	−0.197305	+	0.143350i
$813$		0			0
$814$	42.3786	+	13.9916i	1.48537	+	0.490406i
$815$	−23.7235			−0.830997
$816$		0			0
$817$	−8.76867	−	26.9872i	−0.306777	−	0.944163i
$818$	7.37080	−	22.6850i	0.257714	−	0.793163i
$819$		0			0
$820$	23.7709	+	17.2706i	0.830116	+	0.603114i
$821$	−2.27969	+	7.01616i	−0.0795617	+	0.244866i	−0.982924	−	0.184013i	$-0.941091\pi$
$821$	−2.27969	+	7.01616i	−0.0795617	+	0.244866i	0.903362	+	0.428879i	$0.141091\pi$
$822$		0			0
$823$	−28.8318	+	20.9475i	−1.00501	+	0.730184i	−0.963157	−	0.268939i	$-0.913327\pi$
$823$	−28.8318	+	20.9475i	−1.00501	+	0.730184i	−0.0418554	+	0.999124i	$0.513327\pi$
$824$	14.5880			0.508198
$825$		0			0
$826$	5.11414			0.177944
$827$	−40.8789	+	29.7003i	−1.42150	+	1.03278i	−0.429977	+	0.902840i	$0.641478\pi$
$827$	−40.8789	+	29.7003i	−1.42150	+	1.03278i	−0.991522	+	0.129940i	$0.958522\pi$
$828$		0			0
$829$	−1.89888	+	5.84416i	−0.0659509	+	0.202976i	−0.978602	−	0.205765i	$-0.934032\pi$
$829$	−1.89888	+	5.84416i	−0.0659509	+	0.202976i	0.912651	+	0.408741i	$0.134032\pi$
$830$	−15.8467	−	11.5133i	−0.550047	−	0.399633i
$831$		0			0
$832$	−3.57323	+	10.9973i	−0.123879	+	0.381262i
$833$	−5.75690	−	17.7179i	−0.199465	−	0.613890i
$834$		0			0
$835$	3.49175			0.120837
$836$	−38.6447	+	52.6641i	−1.33655	+	1.82143i
$837$		0			0
$838$	62.5133	−	45.4186i	2.15949	−	1.56896i
$839$	11.5953	+	35.6865i	0.400312	+	1.23204i	0.924746	+	0.380584i	$0.124277\pi$
$839$	11.5953	+	35.6865i	0.400312	+	1.23204i	−0.524434	+	0.851451i	$0.675723\pi$
$840$		0			0
$841$	−59.3574	−	43.1257i	−2.04681	−	1.48709i
$842$	26.9273	+	19.5638i	0.927976	+	0.674214i
$843$		0			0
$844$	−13.7158	−	42.2128i	−0.472116	−	1.45302i
$845$	−9.75019	+	7.08392i	−0.335417	+	0.243694i
$846$		0			0
$847$	−2.12870	−	0.0201412i	−0.0731431	−	0.000692058i
$848$	13.9186			0.477966
$849$		0			0
$850$	1.94776	+	5.99460i	0.0668077	+	0.205613i
$851$	8.47347	−	26.0787i	0.290467	−	0.893965i
$852$		0			0
$853$	21.8533	+	15.8774i	0.748244	+	0.543631i	0.895282	−	0.445500i	$-0.146974\pi$
$853$	21.8533	+	15.8774i	0.748244	+	0.543631i	−0.147038	+	0.989131i	$0.546974\pi$
$854$	0.169901	−	0.522900i	0.00581388	−	0.0178933i
$855$		0			0
$856$	14.4280	−	10.4826i	0.493140	−	0.358287i
$857$	2.51515			0.0859159			0.0429580	−	0.999077i	$-0.486322\pi$
$857$	2.51515			0.0859159			0.0429580	+	0.999077i	$0.486322\pi$
$858$		0			0
$859$	6.70885			0.228903			0.114451	−	0.993429i	$-0.463489\pi$
$859$	6.70885			0.228903			0.114451	+	0.993429i	$0.463489\pi$
$860$	14.6828	−	10.6677i	0.500680	−	0.363765i
$861$		0			0
$862$	−13.9079	+	42.8041i	−0.473705	+	1.45791i
$863$	−2.67577	−	1.94406i	−0.0910844	−	0.0661767i	0.541311	−	0.840822i	$-0.317928\pi$
$863$	−2.67577	−	1.94406i	−0.0910844	−	0.0661767i	−0.632395	+	0.774646i	$0.717928\pi$
$864$		0			0
$865$	−6.29145	+	19.3631i	−0.213916	+	0.658365i
$866$	11.0065	+	33.8746i	0.374017	+	1.15111i
$867$		0			0
$868$	−1.72082			−0.0584086
$869$	−0.159299	+	33.6731i	−0.00540384	+	1.14228i
$870$		0			0
$871$	−2.56744	+	1.86535i	−0.0869942	+	0.0632050i
$872$	−8.48027	−	26.0996i	−0.287178	−	0.883844i
$873$		0			0
$874$	50.7669	+	36.8843i	1.71722	+	1.24763i
$875$	0.156567	+	0.113752i	0.00529292	+	0.00384553i
$876$		0			0
$877$	9.91956	+	30.5293i	0.334960	+	1.03090i	0.966742	+	0.255754i	$0.0823238\pi$
$877$	9.91956	+	30.5293i	0.334960	+	1.03090i	−0.631782	+	0.775146i	$0.717676\pi$
$878$	−70.8269	+	51.4587i	−2.39029	+	1.73665i
$879$		0			0
$880$	−4.71917	−	1.55807i	−0.159083	−	0.0525226i
$881$	35.2547			1.18776			0.593881	−	0.804553i	$-0.297595\pi$
$881$	35.2547			1.18776			0.593881	+	0.804553i	$0.297595\pi$
$882$		0			0
$883$	−0.140866	−	0.433541i	−0.00474052	−	0.0145898i	0.948658	−	0.316303i	$-0.102442\pi$
$883$	−0.140866	−	0.433541i	−0.00474052	−	0.0145898i	−0.953399	+	0.301713i	$0.902442\pi$
$884$	2.85746	−	8.79436i	0.0961068	−	0.295786i
$885$		0			0
$886$	−5.26090	−	3.82226i	−0.176743	−	0.128411i
$887$	0.556725	−	1.71342i	0.0186930	−	0.0575312i	−0.941275	−	0.337641i	$-0.890371\pi$
$887$	0.556725	−	1.71342i	0.0186930	−	0.0575312i	0.959968	+	0.280110i	$0.0903710\pi$
$888$		0			0
$889$	−1.11166	+	0.807666i	−0.0372838	+	0.0270882i
$890$	17.2970			0.579797
$891$		0			0
$892$	−19.0794			−0.638824
$893$	48.7203	−	35.3973i	1.63036	−	1.18453i
$894$		0			0
$895$	1.19008	−	3.66268i	0.0397799	−	0.122430i
$896$	3.19970	+	2.32471i	0.106894	+	0.0776633i
$897$		0			0
$898$	13.0055	−	40.0269i	0.434001	−	1.33572i
$899$	−7.83308	−	24.1077i	−0.261248	−	0.804038i
$900$		0			0
$901$	24.8541			0.828009
$902$	−61.6080	+	19.6959i	−2.05132	+	0.655803i
$903$		0			0
$904$	59.7092	−	43.3813i	1.98590	−	1.44284i
$905$	5.44337	+	16.7530i	0.180944	+	0.556887i
$906$		0			0
$907$	28.5962	+	20.7764i	0.949522	+	0.689868i	0.950694	−	0.310131i	$-0.100373\pi$
$907$	28.5962	+	20.7764i	0.949522	+	0.689868i	−0.00117159	+	0.999999i	$0.500373\pi$
$908$	−62.4605	−	45.3802i	−2.07282	−	1.50600i
$909$		0			0
$910$	−0.137173	−	0.422175i	−0.00454724	−	0.0139950i
$911$	−1.33388	+	0.969123i	−0.0441935	+	0.0321085i	−0.609663	−	0.792661i	$-0.708695\pi$
$911$	−1.33388	+	0.969123i	−0.0441935	+	0.0321085i	0.565469	+	0.824769i	$0.308695\pi$
$912$		0			0
$913$	26.2682	−	8.39789i	0.869352	−	0.277930i
$914$	−49.8511			−1.64893
$915$		0			0
$916$	2.92918	+	9.01510i	0.0967829	+	0.297867i
$917$	0.149522	−	0.460182i	0.00493765	−	0.0151965i
$918$		0			0
$919$	0.258068	+	0.187498i	0.00851288	+	0.00618497i	0.592034	−	0.805913i	$-0.298325\pi$
$919$	0.258068	+	0.187498i	0.00851288	+	0.00618497i	−0.583521	+	0.812098i	$0.698325\pi$
$920$	−5.41356	+	16.6612i	−0.178480	+	0.549304i
$921$		0			0
$922$	−65.4590	+	47.5588i	−2.15578	+	1.56626i
$923$	−5.83327			−0.192005
$924$		0			0
$925$	5.71217			0.187815
$926$	−19.9185	+	14.4716i	−0.654561	+	0.475567i
$927$		0			0
$928$	−11.7841	+	36.2678i	−0.386832	+	1.19055i
$929$	45.4270	+	33.0046i	1.49041	+	1.08285i	0.974011	+	0.226500i	$0.0727283\pi$
$929$	45.4270	+	33.0046i	1.49041	+	1.08285i	0.516400	+	0.856347i	$0.327272\pi$
$930$		0			0
$931$	11.9394	−	36.7456i	0.391297	−	1.20429i
$932$	6.28115	+	19.3314i	0.205746	+	0.633221i
$933$		0			0
$934$	−69.8301			−2.28491
$935$	−8.42690	−	2.78221i	−0.275589	−	0.0909880i
$936$		0			0
$937$	−29.8061	+	21.6554i	−0.973724	+	0.707452i	−0.956297	−	0.292396i	$-0.905547\pi$
$937$	−29.8061	+	21.6554i	−0.973724	+	0.707452i	−0.0174269	+	0.999848i	$0.505547\pi$
$938$	0.459148	+	1.41311i	0.0149917	+	0.0461397i
$939$		0			0
$940$	31.1609	+	22.6397i	1.01636	+	0.738426i
$941$	−12.3865	−	8.99929i	−0.403787	−	0.293368i	0.367295	−	0.930105i	$-0.380284\pi$
$941$	−12.3865	−	8.99929i	−0.403787	−	0.293368i	−0.771082	+	0.636736i	$0.780284\pi$
$942$		0			0
$943$	12.2805	+	37.7956i	0.399909	+	1.23079i
$944$	−13.5991	+	9.88030i	−0.442612	+	0.321576i
$945$		0			0
$946$	−0.188998	+	39.9510i	−0.00614486	+	1.29892i
$947$	22.6654			0.736526			0.368263	−	0.929722i	$-0.379953\pi$
$947$	22.6654			0.736526			0.368263	+	0.929722i	$0.379953\pi$
$948$		0			0
$949$	0.994821	+	3.06174i	0.0322933	+	0.0993884i
$950$	−4.03950	+	12.4323i	−0.131059	+	0.403358i
$951$		0			0
$952$	−1.52884	−	1.11076i	−0.0495499	−	0.0360001i
$953$	−12.1544	+	37.4074i	−0.393719	+	1.21174i	0.536235	+	0.844069i	$0.319846\pi$
$953$	−12.1544	+	37.4074i	−0.393719	+	1.21174i	−0.929955	+	0.367675i	$0.880154\pi$
$954$		0			0
$955$	−0.337440	+	0.245165i	−0.0109193	+	0.00793334i
$956$	86.4870			2.79719
$957$		0			0
$958$	31.1388			1.00605
$959$	−2.39459	+	1.73977i	−0.0773254	+	0.0561802i
$960$		0			0
$961$	−7.63993	+	23.5133i	−0.246449	+	0.758493i
$962$	−10.5999	−	7.70130i	−0.341756	−	0.248300i
$963$		0			0
$964$	−18.3249	+	56.3984i	−0.590207	+	1.81647i
$965$	−3.61443	−	11.1241i	−0.116353	−	0.358096i
$966$		0			0
$967$	3.06103			0.0984360			0.0492180	−	0.998788i	$-0.484327\pi$
$967$	3.06103			0.0984360			0.0492180	+	0.998788i	$0.484327\pi$
$968$	32.6986	−	23.2875i	1.05097	−	0.748487i
$969$		0			0
$970$	−30.2110	+	21.9496i	−0.970016	+	0.704758i
$971$	−9.90043	−	30.4704i	−0.317720	−	0.977841i	−0.974620	−	0.223864i	$-0.928133\pi$
$971$	−9.90043	−	30.4704i	−0.317720	−	0.977841i	0.656900	−	0.753977i	$-0.271867\pi$
$972$		0			0
$973$	3.07788	+	2.23621i	0.0986724	+	0.0716897i
$974$	80.9911	+	58.8434i	2.59512	+	1.88547i
$975$		0			0
$976$	0.558436	+	1.71869i	0.0178751	+	0.0550139i
$977$	−43.0366	+	31.2679i	−1.37686	+	1.00035i	−0.379697	+	0.925111i	$0.623972\pi$
$977$	−43.0366	+	31.2679i	−1.37686	+	1.00035i	−0.997166	+	0.0752388i	$0.976028\pi$
$978$		0			0
$979$	−14.4074	+	19.6340i	−0.460462	+	0.627507i
$980$	24.7115			0.789379
$981$		0			0
$982$	11.4619	+	35.2762i	0.365765	+	1.12571i
$983$	7.57104	−	23.3013i	0.241479	−	0.743195i	−0.754717	−	0.656051i	$-0.772226\pi$
$983$	7.57104	−	23.3013i	0.241479	−	0.743195i	0.996196	−	0.0871446i	$-0.0277742\pi$
$984$		0			0
$985$	−17.4714	−	12.6937i	−0.556685	−	0.404456i
$986$	19.7071	−	60.6521i	0.627601	−	1.93156i
$987$		0			0
$988$	15.5149	−	11.2722i	0.493593	−	0.358616i
$989$	24.5470			0.780549
$990$		0			0
$991$	−6.34819			−0.201657			−0.100828	−	0.994904i	$-0.532149\pi$
$991$	−6.34819			−0.201657			−0.100828	+	0.994904i	$0.532149\pi$
$992$	−7.63924	+	5.55023i	−0.242546	+	0.176220i
$993$		0			0
$994$	−0.843962	+	2.59745i	−0.0267689	+	0.0823861i
$995$	6.27820	+	4.56138i	0.199032	+	0.144605i
$996$		0			0
$997$	−8.01777	+	24.6761i	−0.253925	+	0.781501i	0.740114	+	0.672481i	$0.234771\pi$
$997$	−8.01777	+	24.6761i	−0.253925	+	0.781501i	−0.994040	+	0.109020i	$0.965229\pi$
$998$	−24.4064	−	75.1152i	−0.772572	−	2.37773i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.a.91.1		8
3.2	odd	2		165.2.m.d.91.2	✓	8
11.2	odd	10		5445.2.a.bf.1.1		4
11.4	even	5	inner	495.2.n.a.136.1		8
11.9	even	5		5445.2.a.bt.1.4		4
15.2	even	4		825.2.bx.f.124.4		16
15.8	even	4		825.2.bx.f.124.1		16
15.14	odd	2		825.2.n.g.751.1		8
33.2	even	10		1815.2.a.w.1.4		4
33.20	odd	10		1815.2.a.p.1.1		4
33.26	odd	10		165.2.m.d.136.2	yes	8
165.59	odd	10		825.2.n.g.301.1		8
165.92	even	20		825.2.bx.f.499.1		16
165.119	odd	10		9075.2.a.di.1.4		4
165.134	even	10		9075.2.a.cm.1.1		4
165.158	even	20		825.2.bx.f.499.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.91.2	✓	8	3.2	odd	2
165.2.m.d.136.2	yes	8	33.26	odd	10
495.2.n.a.91.1		8	1.1	even	1	trivial
495.2.n.a.136.1		8	11.4	even	5	inner
825.2.n.g.301.1		8	165.59	odd	10
825.2.n.g.751.1		8	15.14	odd	2
825.2.bx.f.124.1		16	15.8	even	4
825.2.bx.f.124.4		16	15.2	even	4
825.2.bx.f.499.1		16	165.92	even	20
825.2.bx.f.499.4		16	165.158	even	20
1815.2.a.p.1.1		4	33.20	odd	10
1815.2.a.w.1.4		4	33.2	even	10
5445.2.a.bf.1.1		4	11.2	odd	10
5445.2.a.bt.1.4		4	11.9	even	5
9075.2.a.cm.1.1		4	165.134	even	10
9075.2.a.di.1.4		4	165.119	odd	10

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)

\(f(q)\)	\(=\)	\(q+(-1.90578 + 1.38463i) q^{2} +(1.09676 - 3.37549i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.0598032 - 0.184055i) q^{7} +(1.12773 + 3.47080i) q^{8} +O(q^{10})\)	\(q+(-1.90578 + 1.38463i) q^{2} +(1.09676 - 3.37549i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.0598032 - 0.184055i) q^{7} +(1.12773 + 3.47080i) q^{8} -2.35567 q^{10} +(1.96213 - 2.67395i) q^{11} +(-0.787747 + 0.572331i) q^{13} +(0.140877 + 0.433574i) q^{14} +(-1.21225 - 0.880754i) q^{16} +(-2.16469 - 1.57274i) q^{17} +(-1.71480 - 5.27760i) q^{19} +(2.87136 - 2.08617i) q^{20} +(-0.0369604 + 7.81280i) q^{22} +4.80040 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.708805 - 2.18148i) q^{26} +(-0.555687 - 0.403730i) q^{28} +(3.12657 - 9.62260i) q^{29} +(2.02685 - 1.47259i) q^{31} -3.76902 q^{32} +6.30309 q^{34} +(0.156567 - 0.113752i) q^{35} +(1.76516 - 5.43260i) q^{37} +(10.5756 + 7.68359i) q^{38} +(-1.12773 + 3.47080i) q^{40} +(2.55823 + 7.87342i) q^{41} +5.11353 q^{43} +(-6.87391 - 9.55586i) q^{44} +(-9.14851 + 6.64678i) q^{46} +(3.35354 + 10.3211i) q^{47} +(5.63282 + 4.09248i) q^{49} +(-1.90578 - 1.38463i) q^{50} +(1.06793 + 3.28674i) q^{52} +(-7.51479 + 5.45981i) q^{53} +(3.15911 - 1.00996i) q^{55} +0.706260 q^{56} +(7.36518 + 22.6677i) q^{58} +(3.46656 - 10.6690i) q^{59} +(-0.975693 - 0.708883i) q^{61} +(-1.82374 + 5.61288i) q^{62} +(9.60743 - 6.98021i) q^{64} -0.973708 q^{65} +3.25922 q^{67} +(-7.68293 + 5.58197i) q^{68} +(-0.140877 + 0.433574i) q^{70} +(4.84664 + 3.52129i) q^{71} +(1.02168 - 3.14442i) q^{73} +(4.15814 + 12.7974i) q^{74} -19.6952 q^{76} +(-0.374813 - 0.521052i) q^{77} +(-8.21389 + 5.96774i) q^{79} +(-0.463040 - 1.42509i) q^{80} +(-15.7772 - 11.4628i) q^{82} +(6.72704 + 4.88748i) q^{83} +(-0.826838 - 2.54475i) q^{85} +(-9.74527 + 7.08035i) q^{86} +(11.4935 + 3.79468i) q^{88} -7.34270 q^{89} +(0.0582308 + 0.179216i) q^{91} +(5.26490 - 16.2037i) q^{92} +(-20.6821 - 15.0264i) q^{94} +(1.71480 - 5.27760i) q^{95} +(12.8248 - 9.31774i) q^{97} -16.4015 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8	\( 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} - 3 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{19} + 3 q^{20} + 9 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} - 11 q^{28} - 10 q^{29} + 19 q^{31} - 12 q^{32} - 6 q^{34} - 3 q^{35} - q^{37} + 20 q^{38} - q^{40} + 9 q^{41} - 17 q^{44} - 22 q^{46} + 19 q^{47} + q^{49} - 4 q^{50} - 2 q^{52} - 25 q^{53} + 3 q^{55} + 16 q^{56} - 12 q^{58} - 13 q^{59} + 13 q^{61} - 35 q^{62} + 39 q^{64} + 14 q^{65} + 2 q^{67} - 19 q^{68} - 4 q^{70} + 11 q^{71} - 7 q^{73} + 43 q^{74} - 38 q^{76} + 7 q^{77} - 22 q^{79} - 13 q^{80} - 35 q^{82} + 21 q^{83} + 10 q^{85} - 20 q^{86} + 59 q^{88} + 20 q^{89} - 11 q^{91} + 28 q^{92} - 35 q^{94} - 2 q^{95} + 31 q^{97} - 22 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8 - 6 * q^10 - 3 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^19 + 3 * q^20 + 9 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 - 11 * q^28 - 10 * q^29 + 19 * q^31 - 12 * q^32 - 6 * q^34 - 3 * q^35 - q^37 + 20 * q^38 - q^40 + 9 * q^41 - 17 * q^44 - 22 * q^46 + 19 * q^47 + q^49 - 4 * q^50 - 2 * q^52 - 25 * q^53 + 3 * q^55 + 16 * q^56 - 12 * q^58 - 13 * q^59 + 13 * q^61 - 35 * q^62 + 39 * q^64 + 14 * q^65 + 2 * q^67 - 19 * q^68 - 4 * q^70 + 11 * q^71 - 7 * q^73 + 43 * q^74 - 38 * q^76 + 7 * q^77 - 22 * q^79 - 13 * q^80 - 35 * q^82 + 21 * q^83 + 10 * q^85 - 20 * q^86 + 59 * q^88 + 20 * q^89 - 11 * q^91 + 28 * q^92 - 35 * q^94 - 2 * q^95 + 31 * q^97 - 22 * q^98

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