LMFDB - Embedded newform 495.2.n.b.91.2

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:	8.0.819390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 10x^{6} - 13x^{5} + 29x^{4} - 7x^{3} + 80x^{2} + 143x + 121 $ x^8 - 3x^7 + 10x^6 - 13x^5 + 29x^4 - 7x^3 + 80x^2 + 143*x + 121
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			91.2
Root			$-0.575405 + 1.77091i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.b.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50643 - 1.09448i) q^{2} +(0.453397 - 1.39541i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.812990 - 2.50213i) q^{7} +(0.306561 + 0.943499i) q^{8} +O(q^{10})$	\(q+(1.50643 - 1.09448i) q^{2} +(0.453397 - 1.39541i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.812990 - 2.50213i) q^{7} +(0.306561 + 0.943499i) q^{8} -1.86205 q^{10} +(-1.77282 - 2.80306i) q^{11} +(5.24250 - 3.80890i) q^{13} +(-1.51383 - 4.65908i) q^{14} +(3.86848 + 2.81061i) q^{16} +(-3.82187 - 2.77675i) q^{17} +(0.164637 + 0.506699i) q^{19} +(-1.18701 + 0.862413i) q^{20} +(-5.73852 - 2.28228i) q^{22} +4.54563 q^{23} +(0.309017 + 0.951057i) q^{25} +(3.72867 - 11.4757i) q^{26} +(-3.12289 - 2.26892i) q^{28} +(-3.28267 + 10.1030i) q^{29} +(-0.154234 + 0.112058i) q^{31} +6.91965 q^{32} -8.79650 q^{34} +(-2.12844 + 1.54640i) q^{35} +(-1.30656 + 4.02118i) q^{37} +(0.802588 + 0.583114i) q^{38} +(0.306561 - 0.943499i) q^{40} +(0.187010 + 0.575557i) q^{41} -9.24893 q^{43} +(-4.71521 + 1.20291i) q^{44} +(6.84767 - 4.97513i) q^{46} +(2.72773 + 8.39509i) q^{47} +(0.0634337 + 0.0460873i) q^{49} +(1.50643 + 1.09448i) q^{50} +(-2.93805 - 9.04240i) q^{52} +(5.41754 - 3.93607i) q^{53} +(-0.213356 + 3.30976i) q^{55} +2.60999 q^{56} +(6.11249 + 18.8123i) q^{58} +(1.83173 - 5.63748i) q^{59} +(2.60209 + 1.89053i) q^{61} +(-0.109698 + 0.337614i) q^{62} +(2.68701 - 1.95223i) q^{64} -6.48008 q^{65} +5.22812 q^{67} +(-5.60755 + 4.07412i) q^{68} +(-1.51383 + 4.65908i) q^{70} +(-2.21979 - 1.61277i) q^{71} +(-4.84404 + 14.9084i) q^{73} +(2.43288 + 7.48764i) q^{74} +0.781701 q^{76} +(-8.45488 + 2.15695i) q^{77} +(-0.979744 + 0.711826i) q^{79} +(-1.47763 - 4.54767i) q^{80} +(0.911655 + 0.662356i) q^{82} +(3.77227 + 2.74071i) q^{83} +(1.45983 + 4.49288i) q^{85} +(-13.9328 + 10.1228i) q^{86} +(2.10120 - 2.53196i) q^{88} -6.40768 q^{89} +(-5.26824 - 16.2140i) q^{91} +(2.06098 - 6.34304i) q^{92} +(13.2974 + 9.66115i) q^{94} +(0.164637 - 0.506699i) q^{95} +(5.92951 - 4.30804i) q^{97} +0.146000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8} - 2 q^{10} + 3 q^{11} + 10 q^{13} - 24 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{19} - 7 q^{20} - 7 q^{22} + 2 q^{23} - 2 q^{25} - 14 q^{26} + 13 q^{28} - 14 q^{29} - 5 q^{31} + 16 q^{32} - 70 q^{34} - q^{35} - 27 q^{37} + 16 q^{38} + 19 q^{40} - q^{41} - 28 q^{43} - 47 q^{44} + 42 q^{46} + 27 q^{47} - 15 q^{49} - 2 q^{50} + 22 q^{52} + q^{53} - 7 q^{55} + 24 q^{56} + 18 q^{58} - 13 q^{59} - 3 q^{61} - 15 q^{62} + 19 q^{64} - 30 q^{65} + 10 q^{67} + 33 q^{68} - 24 q^{70} - 9 q^{71} + 5 q^{73} + 17 q^{74} - 46 q^{76} - q^{77} - 10 q^{79} - 11 q^{80} - 33 q^{82} + 25 q^{83} - 8 q^{85} - 20 q^{86} + 29 q^{88} - 4 q^{89} - 43 q^{91} + 22 q^{92} + 57 q^{94} - 2 q^{95} + 13 q^{97} + 2 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8 - 2 * q^10 + 3 * q^11 + 10 * q^13 - 24 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^19 - 7 * q^20 - 7 * q^22 + 2 * q^23 - 2 * q^25 - 14 * q^26 + 13 * q^28 - 14 * q^29 - 5 * q^31 + 16 * q^32 - 70 * q^34 - q^35 - 27 * q^37 + 16 * q^38 + 19 * q^40 - q^41 - 28 * q^43 - 47 * q^44 + 42 * q^46 + 27 * q^47 - 15 * q^49 - 2 * q^50 + 22 * q^52 + q^53 - 7 * q^55 + 24 * q^56 + 18 * q^58 - 13 * q^59 - 3 * q^61 - 15 * q^62 + 19 * q^64 - 30 * q^65 + 10 * q^67 + 33 * q^68 - 24 * q^70 - 9 * q^71 + 5 * q^73 + 17 * q^74 - 46 * q^76 - q^77 - 10 * q^79 - 11 * q^80 - 33 * q^82 + 25 * q^83 - 8 * q^85 - 20 * q^86 + 29 * q^88 - 4 * q^89 - 43 * q^91 + 22 * q^92 + 57 * q^94 - 2 * q^95 + 13 * q^97 + 2 * 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 $

$2$	1.50643	−	1.09448i	1.06521	−	0.773918i	0.0901616	−	0.995927i	$-0.471262\pi$
$2$	1.50643	−	1.09448i	1.06521	−	0.773918i	0.975044	+	0.222010i	$0.0712616\pi$
$3$		0			0
$3$		0			0
$4$	0.453397	−	1.39541i	0.226699	−	0.697707i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	0.812990	−	2.50213i	0.307281	−	0.945715i	−0.671535	−	0.740973i	$-0.734365\pi$
$7$	0.812990	−	2.50213i	0.307281	−	0.945715i	0.978816	−	0.204742i	$-0.0656355\pi$
$8$	0.306561	+	0.943499i	0.108386	+	0.333577i
$9$		0			0
$10$	−1.86205			−0.588831
$11$	−1.77282	−	2.80306i	−0.534524	−	0.845153i
$11$	−1.77282	−	2.80306i	−0.534524	−	0.845153i
$12$		0			0
$13$	5.24250	−	3.80890i	1.45401	−	1.05640i	0.469133	−	0.883128i	$-0.344567\pi$
$13$	5.24250	−	3.80890i	1.45401	−	1.05640i	0.984874	−	0.173270i	$-0.0554334\pi$
$14$	−1.51383	−	4.65908i	−0.404587	−	1.24519i
$15$		0			0
$16$	3.86848	+	2.81061i	0.967119	+	0.702653i
$17$	−3.82187	−	2.77675i	−0.926941	−	0.673462i	0.0183011	−	0.999833i	$-0.494174\pi$
$17$	−3.82187	−	2.77675i	−0.926941	−	0.673462i	−0.945242	+	0.326371i	$0.894174\pi$
$18$		0			0
$19$	0.164637	+	0.506699i	0.0377702	+	0.116245i	0.968164	−	0.250317i	$-0.0805348\pi$
$19$	0.164637	+	0.506699i	0.0377702	+	0.116245i	−0.930394	+	0.366562i	$0.880535\pi$
$20$	−1.18701	+	0.862413i	−0.265423	+	0.192841i
$21$		0			0
$22$	−5.73852	−	2.28228i	−1.22346	−	0.486585i
$23$	4.54563			0.947830			0.473915	−	0.880571i	$-0.342840\pi$
$23$	4.54563			0.947830			0.473915	+	0.880571i	$0.342840\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	3.72867	−	11.4757i	0.731252	−	2.25056i
$27$		0			0
$28$	−3.12289	−	2.26892i	−0.590172	−	0.428785i
$29$	−3.28267	+	10.1030i	−0.609577	+	1.87608i	−0.147990	+	0.988989i	$0.547280\pi$
$29$	−3.28267	+	10.1030i	−0.609577	+	1.87608i	−0.461587	+	0.887095i	$0.652720\pi$
$30$		0			0
$31$	−0.154234	+	0.112058i	−0.0277013	+	0.0201262i	−0.601550	−	0.798835i	$-0.705450\pi$
$31$	−0.154234	+	0.112058i	−0.0277013	+	0.0201262i	0.573848	+	0.818962i	$0.305450\pi$
$32$	6.91965			1.22323
$33$		0			0
$34$	−8.79650			−1.50859
$35$	−2.12844	+	1.54640i	−0.359771	+	0.261389i
$36$		0			0
$37$	−1.30656	+	4.02118i	−0.214797	+	0.661078i	0.784371	+	0.620293i	$0.212986\pi$
$37$	−1.30656	+	4.02118i	−0.214797	+	0.661078i	−0.999168	+	0.0407858i	$0.987014\pi$
$38$	0.802588	+	0.583114i	0.130197	+	0.0945936i
$39$		0			0
$40$	0.306561	−	0.943499i	0.0484716	−	0.149180i
$41$	0.187010	+	0.575557i	0.0292060	+	0.0898869i	0.964597	−	0.263728i	$-0.0849522\pi$
$41$	0.187010	+	0.575557i	0.0292060	+	0.0898869i	−0.935391	+	0.353615i	$0.884952\pi$
$42$		0			0
$43$	−9.24893			−1.41045			−0.705224	−	0.708985i	$-0.749154\pi$
$43$	−9.24893			−1.41045			−0.705224	+	0.708985i	$0.749154\pi$
$44$	−4.71521	+	1.20291i	−0.710845	+	0.181346i
$45$		0			0
$46$	6.84767	−	4.97513i	1.00963	−	0.733542i
$47$	2.72773	+	8.39509i	0.397881	+	1.22455i	0.926695	+	0.375813i	$0.122637\pi$
$47$	2.72773	+	8.39509i	0.397881	+	1.22455i	−0.528815	+	0.848737i	$0.677363\pi$
$48$		0			0
$49$	0.0634337	+	0.0460873i	0.00906196	+	0.00658390i
$50$	1.50643	+	1.09448i	0.213041	+	0.154784i
$51$		0			0
$52$	−2.93805	−	9.04240i	−0.407435	−	1.25395i
$53$	5.41754	−	3.93607i	0.744156	−	0.540661i	−0.149854	−	0.988708i	$-0.547880\pi$
$53$	5.41754	−	3.93607i	0.744156	−	0.540661i	0.894010	+	0.448047i	$0.147880\pi$
$54$		0			0
$55$	−0.213356	+	3.30976i	−0.0287689	+	0.446287i
$56$	2.60999			0.348774
$57$		0			0
$58$	6.11249	+	18.8123i	0.802610	+	2.47018i
$59$	1.83173	−	5.63748i	0.238471	−	0.733938i	−0.758171	−	0.652056i	$-0.773907\pi$
$59$	1.83173	−	5.63748i	0.238471	−	0.733938i	0.996642	−	0.0818821i	$-0.0260931\pi$
$60$		0			0
$61$	2.60209	+	1.89053i	0.333163	+	0.242057i	0.741772	−	0.670652i	$-0.233986\pi$
$61$	2.60209	+	1.89053i	0.333163	+	0.242057i	−0.408608	+	0.912710i	$0.633986\pi$
$62$	−0.109698	+	0.337614i	−0.0139316	+	0.0428771i
$63$		0			0
$64$	2.68701	−	1.95223i	0.335876	−	0.244028i
$65$	−6.48008			−0.803755
$66$		0			0
$67$	5.22812			0.638717			0.319358	−	0.947634i	$-0.396533\pi$
$67$	5.22812			0.638717			0.319358	+	0.947634i	$0.396533\pi$
$68$	−5.60755	+	4.07412i	−0.680015	+	0.494060i
$69$		0			0
$70$	−1.51383	+	4.65908i	−0.180937	+	0.556867i
$71$	−2.21979	−	1.61277i	−0.263440	−	0.191400i	0.448222	−	0.893922i	$-0.352057\pi$
$71$	−2.21979	−	1.61277i	−0.263440	−	0.191400i	−0.711662	+	0.702522i	$0.752057\pi$
$72$		0			0
$73$	−4.84404	+	14.9084i	−0.566952	+	1.74490i	0.0951281	+	0.995465i	$0.469674\pi$
$73$	−4.84404	+	14.9084i	−0.566952	+	1.74490i	−0.662080	+	0.749433i	$0.730326\pi$
$74$	2.43288	+	7.48764i	0.282817	+	0.870420i
$75$		0			0
$76$	0.781701			0.0896673
$77$	−8.45488	+	2.15695i	−0.963523	+	0.245808i
$78$		0			0
$79$	−0.979744	+	0.711826i	−0.110230	+	0.0800866i	−0.641535	−	0.767094i	$-0.721702\pi$
$79$	−0.979744	+	0.711826i	−0.110230	+	0.0800866i	0.531305	+	0.847181i	$0.321702\pi$
$80$	−1.47763	−	4.54767i	−0.165204	−	0.508445i
$81$		0			0
$82$	0.911655	+	0.662356i	0.100675	+	0.0731450i
$83$	3.77227	+	2.74071i	0.414060	+	0.300832i	0.775244	−	0.631662i	$-0.217627\pi$
$83$	3.77227	+	2.74071i	0.414060	+	0.300832i	−0.361183	+	0.932495i	$0.617627\pi$
$84$		0			0
$85$	1.45983	+	4.49288i	0.158340	+	0.487322i
$86$	−13.9328	+	10.1228i	−1.50242	+	1.09157i
$87$		0			0
$88$	2.10120	−	2.53196i	0.223989	−	0.269908i
$89$	−6.40768			−0.679213			−0.339606	−	0.940568i	$-0.610294\pi$
$89$	−6.40768			−0.679213			−0.339606	+	0.940568i	$0.610294\pi$
$90$		0			0
$91$	−5.26824	−	16.2140i	−0.552262	−	1.69969i
$92$	2.06098	−	6.34304i	0.214872	−	0.661307i
$93$		0			0
$94$	13.2974	+	9.66115i	1.37153	+	0.996472i
$95$	0.164637	−	0.506699i	0.0168914	−	0.0519863i
$96$		0			0
$97$	5.92951	−	4.30804i	0.602050	−	0.437415i	−0.244556	−	0.969635i	$-0.578642\pi$
$97$	5.92951	−	4.30804i	0.602050	−	0.437415i	0.846606	+	0.532220i	$0.178642\pi$
$98$	0.146000			0.0147482
$99$		0			0
$100$	1.46722			0.146722
$101$	9.19035	−	6.67718i	0.914474	−	0.664404i	−0.0276682	−	0.999617i	$-0.508808\pi$
$101$	9.19035	−	6.67718i	0.914474	−	0.664404i	0.942142	+	0.335213i	$0.108808\pi$
$102$		0			0
$103$	−0.636773	+	1.95978i	−0.0627431	+	0.193103i	−0.977514	−	0.210869i	$-0.932371\pi$
$103$	−0.636773	+	1.95978i	−0.0627431	+	0.193103i	0.914771	+	0.403972i	$0.132371\pi$
$104$	5.20084	+	3.77863i	0.509984	+	0.370525i
$105$		0			0
$106$	3.85316	−	11.8588i	0.374252	−	1.15183i
$107$	−0.355281	−	1.09344i	−0.0343463	−	0.105707i	0.932414	−	0.361393i	$-0.117699\pi$
$107$	−0.355281	−	1.09344i	−0.0343463	−	0.105707i	−0.966760	+	0.255686i	$0.917699\pi$
$108$		0			0
$109$	−13.3402			−1.27776			−0.638879	−	0.769307i	$-0.720602\pi$
$109$	−13.3402			−1.27776			−0.638879	+	0.769307i	$0.720602\pi$
$110$	3.30107	+	5.21943i	0.314745	+	0.497653i
$111$		0			0
$112$	10.1775	−	7.39442i	0.961688	−	0.698707i
$113$	−1.94600	−	5.98917i	−0.183064	−	0.563414i	0.816845	−	0.576857i	$-0.195721\pi$
$113$	−1.94600	−	5.98917i	−0.183064	−	0.563414i	−0.999910	+	0.0134430i	$0.995721\pi$
$114$		0			0
$115$	−3.67749	−	2.67186i	−0.342928	−	0.249152i
$116$	12.6095	+	9.16137i	1.17077	+	0.850612i
$117$		0			0
$118$	−3.41077	−	10.4973i	−0.313987	−	0.966352i
$119$	−10.0549	+	7.30534i	−0.921735	+	0.669679i
$120$		0			0
$121$	−4.71424	+	9.93861i	−0.428568	+	0.903510i
$122$	5.98902			0.542220
$123$		0			0
$124$	0.0864376	+	0.266028i	0.00776233	+	0.0238900i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	8.16646	+	5.93328i	0.724656	+	0.526494i	0.887868	−	0.460097i	$-0.152186\pi$
$127$	8.16646	+	5.93328i	0.724656	+	0.526494i	−0.163212	+	0.986591i	$0.552186\pi$
$128$	−2.36547	+	7.28018i	−0.209080	+	0.643483i
$129$		0			0
$130$	−9.76178	+	7.09235i	−0.856165	+	0.622040i
$131$	4.64756			0.406060			0.203030	−	0.979173i	$-0.434921\pi$
$131$	4.64756			0.406060			0.203030	+	0.979173i	$0.434921\pi$
$132$		0			0
$133$	1.40167			0.121541
$134$	7.87579	−	5.72210i	0.680365	−	0.494314i
$135$		0			0
$136$	1.44823	−	4.45718i	0.124184	−	0.382200i
$137$	12.7562	+	9.26795i	1.08984	+	0.791815i	0.979372	−	0.202065i	$-0.0647653\pi$
$137$	12.7562	+	9.26795i	1.08984	+	0.791815i	0.110467	+	0.993880i	$0.464765\pi$
$138$		0			0
$139$	3.10209	−	9.54725i	0.263116	−	0.809787i	−0.729006	−	0.684508i	$-0.760017\pi$
$139$	3.10209	−	9.54725i	0.263116	−	0.809787i	0.992121	−	0.125280i	$-0.0399828\pi$
$140$	1.19284	+	3.67118i	0.100813	+	0.310272i
$141$		0			0
$142$	−5.10910			−0.428746
$143$	−19.9705	−	7.94254i	−1.67002	−	0.664188i
$144$		0			0
$145$	8.59414	−	6.24401i	0.713705	−	0.518537i
$146$	9.01983	+	27.7602i	0.746487	+	2.29745i
$147$		0			0
$148$	5.01882	+	3.64639i	0.412545	+	0.299731i
$149$	−8.46659	−	6.15134i	−0.693610	−	0.503937i	0.184235	−	0.982882i	$-0.441019\pi$
$149$	−8.46659	−	6.15134i	−0.693610	−	0.503937i	−0.877845	+	0.478945i	$0.841019\pi$
$150$		0			0
$151$	−4.83406	−	14.8777i	−0.393390	−	1.21073i	−0.930208	−	0.367032i	$-0.880374\pi$
$151$	−4.83406	−	14.8777i	−0.393390	−	1.21073i	0.536819	−	0.843698i	$-0.319626\pi$
$152$	−0.427599	+	0.310669i	−0.0346829	+	0.0251986i
$153$		0			0
$154$	−10.3759	+	12.5030i	−0.836116	+	1.00752i
$155$	0.190644			0.0153129
$156$		0			0
$157$	2.77797	+	8.54971i	0.221706	+	0.682341i	0.998609	+	0.0527210i	$0.0167894\pi$
$157$	2.77797	+	8.54971i	0.221706	+	0.682341i	−0.776903	+	0.629620i	$0.783211\pi$
$158$	−0.696832	+	2.14463i	−0.0554370	+	0.170618i
$159$		0			0
$160$	−5.59812	−	4.06727i	−0.442570	−	0.321546i
$161$	3.69556	−	11.3738i	0.291251	−	0.896377i
$162$		0			0
$163$	−16.0509	+	11.6616i	−1.25720	+	0.913411i	−0.998617	−	0.0525776i	$-0.983256\pi$
$163$	−16.0509	+	11.6616i	−1.25720	+	0.913411i	−0.258585	+	0.965988i	$0.583256\pi$
$164$	0.887929			0.0693356
$165$		0			0
$166$	8.68232			0.673879
$167$	9.31448	−	6.76736i	0.720776	−	0.523674i	−0.165856	−	0.986150i	$-0.553039\pi$
$167$	9.31448	−	6.76736i	0.720776	−	0.523674i	0.886632	+	0.462476i	$0.153039\pi$
$168$		0			0
$169$	8.95886	−	27.5725i	0.689143	−	2.12096i
$170$	7.11652	+	5.17045i	0.545812	+	0.396556i
$171$		0			0
$172$	−4.19344	+	12.9061i	−0.319747	+	0.984079i
$173$	2.31921	+	7.13779i	0.176326	+	0.542676i	0.999692	−	0.0248353i	$-0.00790614\pi$
$173$	2.31921	+	7.13779i	0.176326	+	0.542676i	−0.823365	+	0.567512i	$0.807906\pi$
$174$		0			0
$175$	2.63089			0.198877
$176$	1.02021	−	15.8263i	0.0769009	−	1.19295i
$177$		0			0
$178$	−9.65272	+	7.01311i	−0.723502	+	0.525655i
$179$	−2.02365	−	6.22815i	−0.151255	−	0.465514i	0.846507	−	0.532377i	$-0.178701\pi$
$179$	−2.02365	−	6.22815i	−0.151255	−	0.465514i	−0.997762	+	0.0668627i	$0.978701\pi$
$180$		0			0
$181$	6.50800	+	4.72834i	0.483736	+	0.351455i	0.802770	−	0.596289i	$-0.203359\pi$
$181$	6.50800	+	4.72834i	0.483736	+	0.351455i	−0.319035	+	0.947743i	$0.603359\pi$
$182$	−25.6822	−	18.6592i	−1.90369	−	1.38311i
$183$		0			0
$184$	1.39352	+	4.28880i	0.102731	+	0.316175i
$185$	3.42062	−	2.48523i	0.251489	−	0.182718i
$186$		0			0
$187$	−1.00791	+	15.6356i	−0.0737060	+	1.14339i
$188$	12.9514			0.944576
$189$		0			0
$190$	−0.306561	−	0.943499i	−0.0222403	−	0.0684486i
$191$	2.69720	−	8.30114i	0.195163	−	0.600649i	−0.804812	−	0.593530i	$-0.797734\pi$
$191$	2.69720	−	8.30114i	0.195163	−	0.600649i	0.999975	−	0.00711920i	$-0.00226613\pi$
$192$		0			0
$193$	−12.1848	−	8.85278i	−0.877082	−	0.637237i	0.0553960	−	0.998464i	$-0.482358\pi$
$193$	−12.1848	−	8.85278i	−0.877082	−	0.637237i	−0.932478	+	0.361227i	$0.882358\pi$
$194$	4.21730	−	12.9795i	0.302784	−	0.931874i
$195$		0			0
$196$	0.0930715	−	0.0676204i	0.00664797	−	0.00483003i
$197$	−13.0882			−0.932498			−0.466249	−	0.884654i	$-0.654395\pi$
$197$	−13.0882			−0.932498			−0.466249	+	0.884654i	$0.654395\pi$
$198$		0			0
$199$	7.16738			0.508082			0.254041	−	0.967193i	$-0.418240\pi$
$199$	7.16738			0.508082			0.254041	+	0.967193i	$0.418240\pi$
$200$	−0.802588	+	0.583114i	−0.0567515	+	0.0412324i
$201$		0			0
$202$	6.53654	−	20.1174i	0.459909	−	1.41546i
$203$	22.6103	+	16.4273i	1.58693	+	1.15297i
$204$		0			0
$205$	0.187010	−	0.575557i	0.0130613	−	0.0401986i
$206$	1.18570	+	3.64921i	0.0826117	+	0.254253i
$207$		0			0
$208$	30.9858			2.14848
$209$	1.12844	−	1.35977i	0.0780556	−	0.0940573i
$210$		0			0
$211$	−4.84459	+	3.51980i	−0.333515	+	0.242313i	−0.741921	−	0.670488i	$-0.766085\pi$
$211$	−4.84459	+	3.51980i	−0.333515	+	0.242313i	0.408406	+	0.912801i	$0.366085\pi$
$212$	−3.03615	−	9.34431i	−0.208524	−	0.641770i
$213$		0			0
$214$	−1.73196	−	1.25834i	−0.118394	−	0.0860186i
$215$	7.48254	+	5.43638i	0.510305	+	0.370758i
$216$		0			0
$217$	0.154992	+	0.477016i	0.0105215	+	0.0323820i
$218$	−20.0961	+	14.6006i	−1.36108	+	0.988880i
$219$		0			0
$220$	4.52174	+	1.79835i	0.304856	+	0.121245i
$221$	−30.6125			−2.05922
$222$		0			0
$223$	−0.0928665	−	0.285814i	−0.00621880	−	0.0191395i	0.947899	−	0.318571i	$-0.103203\pi$
$223$	−0.0928665	−	0.285814i	−0.00621880	−	0.0191395i	−0.954118	+	0.299432i	$0.903203\pi$
$224$	5.62561	−	17.3138i	0.375877	−	1.15683i
$225$		0			0
$226$	−9.48656	−	6.89239i	−0.631037	−	0.458475i
$227$	7.05112	−	21.7011i	0.468000	−	1.44035i	−0.387171	−	0.922008i	$-0.626548\pi$
$227$	7.05112	−	21.7011i	0.468000	−	1.44035i	0.855171	−	0.518347i	$-0.173452\pi$
$228$		0			0
$229$	−22.8231	+	16.5819i	−1.50819	+	1.09576i	−0.541219	+	0.840882i	$0.682037\pi$
$229$	−22.8231	+	16.5819i	−1.50819	+	1.09576i	−0.966972	+	0.254883i	$0.917963\pi$
$230$	−8.46419			−0.558112
$231$		0			0
$232$	−10.5385			−0.691888
$233$	−15.6824	+	11.3939i	−1.02739	+	0.746441i	−0.967784	−	0.251781i	$-0.918984\pi$
$233$	−15.6824	+	11.3939i	−1.02739	+	0.746441i	−0.0596042	+	0.998222i	$0.518984\pi$
$234$		0			0
$235$	2.72773	−	8.39509i	0.177938	−	0.547636i
$236$	−7.03612	−	5.11204i	−0.458012	−	0.332765i
$237$		0			0
$238$	−7.15147	+	22.0100i	−0.463561	+	1.42669i
$239$	4.71979	+	14.5260i	0.305298	+	0.939609i	0.979566	+	0.201123i	$0.0644590\pi$
$239$	4.71979	+	14.5260i	0.305298	+	0.939609i	−0.674269	+	0.738486i	$0.735541\pi$
$240$		0			0
$241$	−7.21213			−0.464574			−0.232287	−	0.972647i	$-0.574621\pi$
$241$	−7.21213			−0.464574			−0.232287	+	0.972647i	$0.574621\pi$
$242$	3.77598	+	20.1315i	0.242729	+	1.29410i
$243$		0			0
$244$	3.81785	−	2.77383i	0.244413	−	0.177576i
$245$	−0.0242295	−	0.0745708i	−0.00154797	−	0.00476415i
$246$		0			0
$247$	2.79307	+	2.02929i	0.177719	+	0.129120i
$248$	−0.153009	−	0.111167i	−0.00971607	−	0.00705914i
$249$		0			0
$250$	−0.575405	−	1.77091i	−0.0363918	−	0.112002i
$251$	15.4320	−	11.2120i	0.974057	−	0.707694i	0.0176843	−	0.999844i	$-0.494371\pi$
$251$	15.4320	−	11.2120i	0.974057	−	0.707694i	0.956373	+	0.292150i	$0.0943706\pi$
$252$		0			0
$253$	−8.05857	−	12.7417i	−0.506638	−	0.801061i
$254$	18.7961			1.17937
$255$		0			0
$256$	6.45732	+	19.8736i	0.403582	+	1.24210i
$257$	−8.06720	+	24.8283i	−0.503218	+	1.54875i	0.300528	+	0.953773i	$0.402837\pi$
$257$	−8.06720	+	24.8283i	−0.503218	+	1.54875i	−0.803746	+	0.594973i	$0.797163\pi$
$258$		0			0
$259$	8.99929	+	6.53836i	0.559188	+	0.406274i
$260$	−2.93805	+	9.04240i	−0.182210	+	0.560786i
$261$		0			0
$262$	7.00123	−	5.08669i	0.432537	−	0.314257i
$263$	−27.0086			−1.66542			−0.832710	−	0.553710i	$-0.813212\pi$
$263$	−27.0086			−1.66542			−0.832710	+	0.553710i	$0.813212\pi$
$264$		0			0
$265$	−6.69644			−0.411359
$266$	2.11152	−	1.53411i	0.129466	−	0.0940624i
$267$		0			0
$268$	2.37042	−	7.29539i	0.144796	−	0.445637i
$269$	−8.13280	−	5.90882i	−0.495866	−	0.360267i	0.311570	−	0.950223i	$-0.399145\pi$
$269$	−8.13280	−	5.90882i	−0.495866	−	0.360267i	−0.807436	+	0.589956i	$0.799145\pi$
$270$		0			0
$271$	9.04318	−	27.8320i	0.549334	−	1.69068i	−0.161122	−	0.986934i	$-0.551511\pi$
$271$	9.04318	−	27.8320i	0.549334	−	1.69068i	0.710456	−	0.703741i	$-0.248489\pi$
$272$	−6.98045	−	21.4836i	−0.423252	−	1.30264i
$273$		0			0
$274$	29.3600			1.77370
$275$	2.11803	−	2.55224i	0.127722	−	0.153906i
$276$		0			0
$277$	0.561916	−	0.408256i	0.0337623	−	0.0245297i	−0.570776	−	0.821106i	$-0.693358\pi$
$277$	0.561916	−	0.408256i	0.0337623	−	0.0245297i	0.604538	+	0.796576i	$0.293358\pi$
$278$	−5.77624	−	17.7774i	−0.346436	−	1.06622i
$279$		0			0
$280$	−2.11152	−	1.53411i	−0.126188	−	0.0916807i
$281$	−8.63123	−	6.27096i	−0.514896	−	0.374094i	0.299782	−	0.954008i	$-0.403086\pi$
$281$	−8.63123	−	6.27096i	−0.514896	−	0.374094i	−0.814678	+	0.579914i	$0.803086\pi$
$282$		0			0
$283$	−6.68160	−	20.5638i	−0.397180	−	1.22239i	−0.927251	−	0.374440i	$-0.877835\pi$
$283$	−6.68160	−	20.5638i	−0.397180	−	1.22239i	0.530071	−	0.847953i	$-0.322165\pi$
$284$	−3.25692	+	2.36629i	−0.193263	+	0.140414i
$285$		0			0
$286$	−38.7772	+	9.89258i	−2.29294	+	0.584961i
$287$	1.59215			0.0939818
$288$		0			0
$289$	1.64307	+	5.05686i	0.0966513	+	0.297462i
$290$	6.11249	−	18.8123i	0.358938	−	1.10470i
$291$		0			0
$292$	18.6071	+	13.5189i	1.08890	+	0.791132i
$293$	1.77951	−	5.47676i	0.103960	−	0.319956i	−0.885525	−	0.464592i	$-0.846201\pi$
$293$	1.77951	−	5.47676i	0.103960	−	0.319956i	0.989485	+	0.144636i	$0.0462011\pi$
$294$		0			0
$295$	−4.79553	+	3.48416i	−0.279206	+	0.202855i
$296$	−4.19452			−0.243802
$297$		0			0
$298$	−19.4869			−1.12884
$299$	23.8305	−	17.3138i	1.37815	−	1.00129i
$300$		0			0
$301$	−7.51929	+	23.1420i	−0.433404	+	1.33388i
$302$	−23.5656	−	17.1214i	−1.35605	−	0.985225i
$303$		0			0
$304$	−0.787243	+	2.42289i	−0.0451515	+	0.138962i
$305$	−0.993910	−	3.05894i	−0.0569111	−	0.175154i
$306$		0			0
$307$	−18.4941			−1.05552			−0.527758	−	0.849395i	$-0.676967\pi$
$307$	−18.4941			−1.05552			−0.527758	+	0.849395i	$0.676967\pi$
$308$	−0.823578	+	12.7760i	−0.0469277	+	0.727981i
$309$		0			0
$310$	0.287192	−	0.208657i	0.0163114	−	0.0118509i
$311$	3.49603	+	10.7597i	0.198241	+	0.610125i	0.999923	+	0.0123737i	$0.00393879\pi$
$311$	3.49603	+	10.7597i	0.198241	+	0.610125i	−0.801682	+	0.597751i	$0.796061\pi$
$312$		0			0
$313$	14.9993	+	10.8976i	0.847810	+	0.615970i	0.924541	−	0.381082i	$-0.124448\pi$
$313$	14.9993	+	10.8976i	0.847810	+	0.615970i	−0.0767315	+	0.997052i	$0.524448\pi$
$314$	13.5423	+	9.83908i	0.764238	+	0.555252i
$315$		0			0
$316$	0.549078	+	1.68989i	0.0308880	+	0.0950636i
$317$	−0.664554	+	0.482827i	−0.0373251	+	0.0271182i	−0.606291	−	0.795243i	$-0.707343\pi$
$317$	−0.664554	+	0.482827i	−0.0373251	+	0.0271182i	0.568966	+	0.822361i	$0.307343\pi$
$318$		0			0
$319$	34.1389	−	8.70929i	1.91141	−	0.487627i
$320$	−3.32133			−0.185668
$321$		0			0
$322$	−6.88130	−	21.1785i	−0.383480	−	1.18023i
$323$	0.777759	−	2.39370i	0.0432757	−	0.133189i
$324$		0			0
$325$	5.24250	+	3.80890i	0.290801	+	0.211280i
$326$	−11.4160	+	35.1349i	−0.632275	+	1.94594i
$327$		0			0
$328$	−0.485707	+	0.352887i	−0.0268187	+	0.0194849i
$329$	23.2232			1.28034
$330$		0			0
$331$	7.98217			0.438740			0.219370	−	0.975642i	$-0.429600\pi$
$331$	7.98217			0.438740			0.219370	+	0.975642i	$0.429600\pi$
$332$	5.53477	−	4.02124i	0.303760	−	0.220694i
$333$		0			0
$334$	6.62482	−	20.3891i	0.362494	−	1.11564i
$335$	−4.22964	−	3.07301i	−0.231090	−	0.167897i
$336$		0			0
$337$	−3.85313	+	11.8587i	−0.209893	+	0.645986i	0.789583	+	0.613643i	$0.210297\pi$
$337$	−3.85313	+	11.8587i	−0.209893	+	0.645986i	−0.999477	+	0.0323424i	$0.989703\pi$
$338$	−16.6818	−	51.3414i	−0.907372	−	2.79260i
$339$		0			0
$340$	6.93131			0.375903
$341$	0.587534	+	0.233670i	0.0318167	+	0.0126539i
$342$		0			0
$343$	15.0659	−	10.9460i	0.813484	−	0.591031i
$344$	−2.83536	−	8.72635i	−0.152873	−	0.470493i
$345$		0			0
$346$	11.3059	+	8.21424i	0.607811	+	0.441600i
$347$	16.9185	+	12.2920i	0.908231	+	0.659869i	0.940567	−	0.339608i	$-0.110295\pi$
$347$	16.9185	+	12.2920i	0.908231	+	0.659869i	−0.0323357	+	0.999477i	$0.510295\pi$
$348$		0			0
$349$	−2.37271	−	7.30245i	−0.127008	−	0.390891i	0.867253	−	0.497867i	$-0.165883\pi$
$349$	−2.37271	−	7.30245i	−0.127008	−	0.390891i	−0.994262	+	0.106976i	$0.965883\pi$
$350$	3.96325	−	2.87947i	0.211845	−	0.153914i
$351$		0			0
$352$	−12.2673	−	19.3962i	−0.653848	−	1.03382i
$353$	13.7984			0.734413			0.367207	−	0.930139i	$-0.380314\pi$
$353$	13.7984			0.734413			0.367207	+	0.930139i	$0.380314\pi$
$354$		0			0
$355$	0.847882	+	2.60951i	0.0450009	+	0.138499i
$356$	−2.90523	+	8.94137i	−0.153977	+	0.473891i
$357$		0			0
$358$	−9.86510	−	7.16742i	−0.521387	−	0.378810i
$359$	5.53641	−	17.0393i	0.292201	−	0.899301i	−0.691947	−	0.721948i	$-0.743247\pi$
$359$	5.53641	−	17.0393i	0.292201	−	0.899301i	0.984147	−	0.177352i	$-0.0567532\pi$
$360$		0			0
$361$	15.1417	−	11.0011i	0.796931	−	0.579004i
$362$	14.9789			0.787275
$363$		0			0
$364$	−25.0138			−1.31108
$365$	12.6819	−	9.21391i	0.663799	−	0.482278i
$366$		0			0
$367$	2.92590	−	9.00501i	0.152731	−	0.470057i	−0.845193	−	0.534461i	$-0.820515\pi$
$367$	2.92590	−	9.00501i	0.152731	−	0.470057i	0.997924	+	0.0644038i	$0.0205146\pi$
$368$	17.5847	+	12.7760i	0.916665	+	0.665996i
$369$		0			0
$370$	2.43288	−	7.48764i	0.126479	−	0.389264i
$371$	−5.44414	−	16.7553i	−0.282646	−	0.869894i
$372$		0			0
$373$	11.6402			0.602706			0.301353	−	0.953513i	$-0.402562\pi$
$373$	11.6402			0.602706			0.301353	+	0.953513i	$0.402562\pi$
$374$	15.5946	+	24.6571i	0.806376	+	1.27499i
$375$		0			0
$376$	−7.08455	+	5.14722i	−0.365358	+	0.265448i
$377$	21.2720	+	65.4684i	1.09556	+	3.37179i
$378$		0			0
$379$	5.34281	+	3.88178i	0.274442	+	0.199394i	0.716489	−	0.697598i	$-0.245748\pi$
$379$	5.34281	+	3.88178i	0.274442	+	0.199394i	−0.442048	+	0.896992i	$0.645748\pi$
$380$	−0.632409	−	0.459472i	−0.0324419	−	0.0235704i
$381$		0			0
$382$	−5.02232	−	15.4571i	−0.256964	−	0.790855i
$383$	15.9681	−	11.6015i	0.815931	−	0.592808i	−0.0996132	−	0.995026i	$-0.531761\pi$
$383$	15.9681	−	11.6015i	0.815931	−	0.592808i	0.915544	+	0.402218i	$0.131761\pi$
$384$		0			0
$385$	8.10797	+	3.22464i	0.413220	+	0.164343i
$386$	−28.0448			−1.42744
$387$		0			0
$388$	−3.32307	−	10.2274i	−0.168703	−	0.519216i
$389$	−7.83816	+	24.1234i	−0.397410	+	1.22310i	0.529658	+	0.848211i	$0.322320\pi$
$389$	−7.83816	+	24.1234i	−0.397410	+	1.22310i	−0.927068	+	0.374892i	$0.877680\pi$
$390$		0			0
$391$	−17.3728	−	12.6221i	−0.878582	−	0.638327i
$392$	−0.0240370	+	0.0739782i	−0.00121405	+	0.00373646i
$393$		0			0
$394$	−19.7165	+	14.3249i	−0.993302	+	0.721676i
$395$	1.21103			0.0609335
$396$		0			0
$397$	−39.2400			−1.96940			−0.984699	−	0.174264i	$-0.944245\pi$
$397$	−39.2400			−1.96940			−0.984699	+	0.174264i	$0.944245\pi$
$398$	10.7971	−	7.84459i	0.541212	−	0.393214i
$399$		0			0
$400$	−1.47763	+	4.54767i	−0.0738813	+	0.227383i
$401$	8.99848	+	6.53778i	0.449363	+	0.326481i	0.789344	−	0.613951i	$-0.210421\pi$
$401$	8.99848	+	6.53778i	0.449363	+	0.326481i	−0.339981	+	0.940432i	$0.610421\pi$
$402$		0			0
$403$	−0.381757	+	1.17493i	−0.0190167	+	0.0585272i
$404$	−5.15055	−	15.8518i	−0.256249	−	0.788655i
$405$		0			0
$406$	52.0402			2.58271
$407$	13.5879	−	3.46645i	0.673527	−	0.171826i
$408$		0			0
$409$	9.39356	−	6.82482i	0.464482	−	0.337466i	−0.330805	−	0.943699i	$-0.607320\pi$
$409$	9.39356	−	6.82482i	0.464482	−	0.337466i	0.795287	+	0.606233i	$0.207320\pi$
$410$	−0.348221	−	1.07171i	−0.0171974	−	0.0529282i
$411$		0			0
$412$	2.44600	+	1.77712i	0.120506	+	0.0875525i
$413$	−12.6165	−	9.16644i	−0.620818	−	0.451051i
$414$		0			0
$415$	−1.44088	−	4.43457i	−0.0707299	−	0.217684i
$416$	36.2763	−	26.3562i	1.77859	−	1.29222i
$417$		0			0
$418$	0.211661	−	3.28345i	0.0103527	−	0.160599i
$419$	−18.5499			−0.906220			−0.453110	−	0.891455i	$-0.649686\pi$
$419$	−18.5499			−0.906220			−0.453110	+	0.891455i	$0.649686\pi$
$420$		0			0
$421$	−6.17276	−	18.9978i	−0.300842	−	0.925896i	−0.981196	−	0.193013i	$-0.938174\pi$
$421$	−6.17276	−	18.9978i	−0.300842	−	0.925896i	0.680354	−	0.732883i	$-0.261826\pi$
$422$	−3.44566	+	10.6047i	−0.167732	+	0.516226i
$423$		0			0
$424$	5.37448	+	3.90479i	0.261008	+	0.189633i
$425$	1.45983	−	4.49288i	0.0708120	−	0.217937i
$426$		0			0
$427$	6.84582	−	4.97378i	0.331292	−	0.240698i
$428$	−1.68689			−0.0815388
$429$		0			0
$430$	17.2219			0.830516
$431$	−20.9993	+	15.2569i	−1.01150	+	0.734898i	−0.964523	−	0.263998i	$-0.914959\pi$
$431$	−20.9993	+	15.2569i	−1.01150	+	0.734898i	−0.0469769	+	0.998896i	$0.514959\pi$
$432$		0			0
$433$	−10.3764	+	31.9353i	−0.498659	+	1.53471i	0.312517	+	0.949912i	$0.398828\pi$
$433$	−10.3764	+	31.9353i	−0.498659	+	1.53471i	−0.811176	+	0.584803i	$0.801172\pi$
$434$	0.755571	+	0.548955i	0.0362686	+	0.0263507i
$435$		0			0
$436$	−6.04841	+	18.6151i	−0.289666	+	0.891501i
$437$	0.748378	+	2.30327i	0.0357998	+	0.110180i
$438$		0			0
$439$	−17.0280			−0.812703			−0.406351	−	0.913717i	$-0.633199\pi$
$439$	−17.0280			−0.812703			−0.406351	+	0.913717i	$0.633199\pi$
$440$	−3.18816	+	0.813342i	−0.151989	+	0.0387746i
$441$		0			0
$442$	−46.1156	+	33.5050i	−2.19350	+	1.59367i
$443$	−7.79180	−	23.9807i	−0.370199	−	1.13936i	−0.946661	−	0.322232i	$-0.895567\pi$
$443$	−7.79180	−	23.9807i	−0.370199	−	1.13936i	0.576461	−	0.817124i	$-0.304433\pi$
$444$		0			0
$445$	5.18392	+	3.76634i	0.245742	+	0.178542i
$446$	−0.452716	−	0.328917i	−0.0214367	−	0.0155747i
$447$		0			0
$448$	−2.70021	−	8.31038i	−0.127573	−	0.392629i
$449$	−21.5681	+	15.6701i	−1.01786	+	0.739518i	−0.965843	−	0.259128i	$-0.916565\pi$
$449$	−21.5681	+	15.6701i	−1.01786	+	0.739518i	−0.0520164	+	0.998646i	$0.516565\pi$
$450$		0			0
$451$	1.28178	−	1.54456i	0.0603568	−	0.0727303i
$452$	−9.23968			−0.434598
$453$		0			0
$454$	−13.1295	−	40.4086i	−0.616200	−	1.89647i
$455$	−5.26824	+	16.2140i	−0.246979	+	0.760123i
$456$		0			0
$457$	17.7564	+	12.9008i	0.830608	+	0.603472i	0.919731	−	0.392548i	$-0.128406\pi$
$457$	17.7564	+	12.9008i	0.830608	+	0.603472i	−0.0891231	+	0.996021i	$0.528406\pi$
$458$	−16.2327	+	49.9590i	−0.758502	+	2.33443i
$459$		0			0
$460$	−5.39571	+	3.92021i	−0.251576	+	0.182781i
$461$	4.32624			0.201493			0.100746	−	0.994912i	$-0.467877\pi$
$461$	4.32624			0.201493			0.100746	+	0.994912i	$0.467877\pi$
$462$		0			0
$463$	11.4573			0.532468			0.266234	−	0.963908i	$-0.414221\pi$
$463$	11.4573			0.532468			0.266234	+	0.963908i	$0.414221\pi$
$464$	−41.0946	+	29.8570i	−1.90777	+	1.38608i
$465$		0			0
$466$	−11.1539	+	34.3283i	−0.516696	+	1.59023i
$467$	−12.5837	−	9.14262i	−0.582306	−	0.423070i	0.257249	−	0.966345i	$-0.417184\pi$
$467$	−12.5837	−	9.14262i	−0.582306	−	0.423070i	−0.839555	+	0.543275i	$0.817184\pi$
$468$		0			0
$469$	4.25041	−	13.0814i	0.196266	−	0.604044i
$470$	−5.07917	−	15.6321i	−0.234285	−	0.721054i
$471$		0			0
$472$	5.88050			0.270672
$473$	16.3966	+	25.9253i	0.753919	+	1.19204i
$474$		0			0
$475$	−0.431024	+	0.313157i	−0.0197767	+	0.0143686i
$476$	5.63509	+	17.3430i	0.258284	+	0.794916i
$477$		0			0
$478$	23.0085	+	16.7167i	1.05238	+	0.764602i
$479$	8.08763	+	5.87601i	0.369533	+	0.268482i	0.757017	−	0.653395i	$-0.226656\pi$
$479$	8.08763	+	5.87601i	0.369533	+	0.268482i	−0.387484	+	0.921876i	$0.626656\pi$
$480$		0			0
$481$	8.46663	+	26.0576i	0.386045	+	1.18812i
$482$	−10.8646	+	7.89356i	−0.494867	+	0.359542i
$483$		0			0
$484$	11.7310	+	11.0845i	0.533229	+	0.503839i
$485$	−7.32927			−0.332805
$486$		0			0
$487$	12.2309	+	37.6428i	0.554234	+	1.70576i	0.697957	+	0.716140i	$0.254093\pi$
$487$	12.2309	+	37.6428i	0.554234	+	1.70576i	−0.143723	+	0.989618i	$0.545907\pi$
$488$	−0.986012	+	3.03463i	−0.0446347	+	0.137371i
$489$		0			0
$490$	−0.118117	−	0.0858168i	−0.00533597	−	0.00387681i
$491$	2.87093	−	8.83582i	0.129563	−	0.398755i	−0.865141	−	0.501528i	$-0.832771\pi$
$491$	2.87093	−	8.83582i	0.129563	−	0.398755i	0.994705	+	0.102773i	$0.0327715\pi$
$492$		0			0
$493$	40.5996	−	29.4973i	1.82851	−	1.32849i
$494$	6.42859			0.289236
$495$		0			0
$496$	−0.911604			−0.0409322
$497$	−5.84001	+	4.24302i	−0.261960	+	0.190325i
$498$		0			0
$499$	−7.21476	+	22.2048i	−0.322977	+	0.994021i	0.649368	+	0.760474i	$0.275033\pi$
$499$	−7.21476	+	22.2048i	−0.322977	+	0.994021i	−0.972345	+	0.233547i	$0.924967\pi$
$500$	−1.18701	−	0.862413i	−0.0530847	−	0.0385683i
$501$		0			0
$502$	10.9758	−	33.7801i	0.489875	−	1.50768i
$503$	−3.72423	−	11.4620i	−0.166055	−	0.511065i	0.833057	−	0.553186i	$-0.186588\pi$
$503$	−3.72423	−	11.4620i	−0.166055	−	0.511065i	−0.999112	+	0.0421216i	$0.986588\pi$
$504$		0			0
$505$	−11.3599			−0.505509
$506$	−26.0852	−	10.3744i	−1.15963	−	0.461199i
$507$		0			0
$508$	11.9820	−	8.70546i	0.531617	−	0.386242i
$509$	0.510193	+	1.57021i	0.0226139	+	0.0695984i	0.961727	−	0.274011i	$-0.0883504\pi$
$509$	0.510193	+	1.57021i	0.0226139	+	0.0695984i	−0.939113	+	0.343609i	$0.888350\pi$
$510$		0			0
$511$	33.3646	+	24.2408i	1.47596	+	1.07235i
$512$	19.0930	+	13.8719i	0.843801	+	0.613058i
$513$		0			0
$514$	15.0215	+	46.2315i	0.662571	+	2.03918i
$515$	1.66709	−	1.21121i	0.0734609	−	0.0533724i
$516$		0			0
$517$	18.6962	−	22.5289i	0.822256	−	0.990822i
$518$	20.7129			0.910074
$519$		0			0
$520$	−1.98654	−	6.11395i	−0.0871157	−	0.268114i
$521$	−6.60416	+	20.3255i	−0.289333	+	0.890476i	0.695733	+	0.718301i	$0.255080\pi$
$521$	−6.60416	+	20.3255i	−0.289333	+	0.890476i	−0.985066	+	0.172176i	$0.944920\pi$
$522$		0			0
$523$	9.83706	+	7.14704i	0.430145	+	0.312518i	0.781707	−	0.623646i	$-0.214349\pi$
$523$	9.83706	+	7.14704i	0.430145	+	0.312518i	−0.351562	+	0.936165i	$0.614349\pi$
$524$	2.10719	−	6.48527i	0.0920532	−	0.283311i
$525$		0			0
$526$	−40.6865	+	29.5605i	−1.77401	+	1.28890i
$527$	0.900622			0.0392317
$528$		0			0
$529$	−2.33722			−0.101618
$530$	−10.0877	+	7.32915i	−0.438182	+	0.318358i
$531$		0			0
$532$	0.635515	−	1.95592i	0.0275531	−	0.0847997i
$533$	3.17263	+	2.30505i	0.137422	+	0.0998430i
$534$		0			0
$535$	−0.355281	+	1.09344i	−0.0153601	+	0.0472736i
$536$	1.60274	+	4.93273i	0.0692278	+	0.213061i
$537$		0			0
$538$	−18.7186			−0.807016
$539$	0.0167289	−	0.259513i	0.000720565	−	0.0111780i
$540$		0			0
$541$	−16.6169	+	12.0729i	−0.714414	+	0.519052i	−0.884595	−	0.466360i	$-0.845565\pi$
$541$	−16.6169	+	12.0729i	−0.714414	+	0.519052i	0.170180	+	0.985413i	$0.445565\pi$
$542$	−16.8388	−	51.8246i	−0.723290	−	2.22606i
$543$		0			0
$544$	−26.4460	−	19.2142i	−1.13386	−	0.823801i
$545$	10.7924	+	7.84117i	0.462297	+	0.335879i
$546$		0			0
$547$	5.92794	+	18.2443i	0.253460	+	0.780071i	0.994129	+	0.108200i	$0.0345088\pi$
$547$	5.92794	+	18.2443i	0.253460	+	0.780071i	−0.740669	+	0.671870i	$0.765491\pi$
$548$	18.7163	−	13.5982i	0.799520	−	0.580885i
$549$		0			0
$550$	0.397279	−	6.16292i	0.0169401	−	0.262788i
$551$	−5.65964			−0.241109
$552$		0			0
$553$	0.984556	+	3.03015i	0.0418676	+	0.128855i
$554$	0.399657	−	1.23002i	0.0169798	−	0.0522584i
$555$		0			0
$556$	−11.9159	−	8.65740i	−0.505346	−	0.367155i
$557$	6.84064	−	21.0533i	0.289847	−	0.892059i	−0.695056	−	0.718955i	$-0.744621\pi$
$557$	6.84064	−	21.0533i	0.289847	−	0.892059i	0.984904	−	0.173103i	$-0.0553794\pi$
$558$		0			0
$559$	−48.4875	+	35.2282i	−2.05080	+	1.48999i
$560$	−12.5801			−0.531608
$561$		0			0
$562$	−19.8658			−0.837988
$563$	20.3261	−	14.7678i	0.856643	−	0.622388i	−0.0703265	−	0.997524i	$-0.522404\pi$
$563$	20.3261	−	14.7678i	0.856643	−	0.622388i	0.926970	+	0.375136i	$0.122404\pi$
$564$		0			0
$565$	−1.94600	+	5.98917i	−0.0818688	+	0.251966i
$566$	−32.5722	−	23.6651i	−1.36911	−	0.994717i
$567$		0			0
$568$	0.841145	−	2.58878i	0.0352936	−	0.108623i
$569$	7.93603	+	24.4246i	0.332696	+	1.02393i	0.967846	+	0.251544i	$0.0809382\pi$
$569$	7.93603	+	24.4246i	0.332696	+	1.02393i	−0.635150	+	0.772389i	$0.719062\pi$
$570$		0			0
$571$	13.3087			0.556953			0.278476	−	0.960443i	$-0.410171\pi$
$571$	13.3087			0.556953			0.278476	+	0.960443i	$0.410171\pi$
$572$	−20.1377	+	24.2660i	−0.842000	+	1.01461i
$573$		0			0
$574$	2.39847	−	1.74259i	0.100110	−	0.0727342i
$575$	1.40468	+	4.32315i	0.0585791	+	0.180288i
$576$		0			0
$577$	10.5985	+	7.70027i	0.441222	+	0.320566i	0.786120	−	0.618074i	$-0.212087\pi$
$577$	10.5985	+	7.70027i	0.441222	+	0.320566i	−0.344899	+	0.938640i	$0.612087\pi$
$578$	8.00982	+	5.81948i	0.333165	+	0.242058i
$579$		0			0
$580$	−4.81642	−	14.8234i	−0.199991	−	0.615508i
$581$	9.92443	−	7.21052i	0.411735	−	0.299143i
$582$		0			0
$583$	−20.6373	−	8.20772i	−0.854710	−	0.339929i
$584$	−15.5511			−0.643508
$585$		0			0
$586$	−3.31353	−	10.1980i	−0.136881	−	0.421275i
$587$	0.0888932	−	0.273585i	0.00366902	−	0.0112921i	−0.949205	−	0.314658i	$-0.898110\pi$
$587$	0.0888932	−	0.273585i	0.00366902	−	0.0112921i	0.952874	+	0.303366i	$0.0981103\pi$
$588$		0			0
$589$	−0.0821723	−	0.0597017i	−0.00338585	−	0.00245996i
$590$	−3.41077	+	10.4973i	−0.140419	+	0.432166i
$591$		0			0
$592$	−16.3564	+	11.8836i	−0.672244	+	0.488414i
$593$	31.8957			1.30980			0.654900	−	0.755716i	$-0.272711\pi$
$593$	31.8957			1.30980			0.654900	+	0.755716i	$0.272711\pi$
$594$		0			0
$595$	12.4286			0.509522
$596$	−12.4224	+	9.02540i	−0.508841	+	0.369695i
$597$		0			0
$598$	16.9492	−	52.1642i	0.693103	−	2.13315i
$599$	−27.1414	−	19.7194i	−1.10897	−	0.805712i	−0.126467	−	0.991971i	$-0.540364\pi$
$599$	−27.1414	−	19.7194i	−1.10897	−	0.805712i	−0.982501	+	0.186259i	$0.940364\pi$
$600$		0			0
$601$	−10.1457	+	31.2251i	−0.413850	+	1.27370i	0.499426	+	0.866357i	$0.333544\pi$
$601$	−10.1457	+	31.2251i	−0.413850	+	1.27370i	−0.913275	+	0.407342i	$0.866456\pi$
$602$	14.0013	+	43.0915i	0.570649	+	1.75628i
$603$		0			0
$604$	−22.9523			−0.933915
$605$	9.65567	−	5.26954i	0.392559	−	0.214237i
$606$		0			0
$607$	36.5025	−	26.5206i	1.48159	−	1.07644i	0.504549	−	0.863383i	$-0.331659\pi$
$607$	36.5025	−	26.5206i	1.48159	−	1.07644i	0.977040	−	0.213055i	$-0.0683414\pi$
$608$	1.13923	+	3.50618i	0.0462018	+	0.142195i
$609$		0			0
$610$	−4.84522	−	3.52026i	−0.196177	−	0.142531i
$611$	46.2762	+	33.6216i	1.87213	+	1.36018i
$612$		0			0
$613$	−14.3918	−	44.2933i	−0.581278	−	1.78899i	−0.613731	−	0.789515i	$-0.710332\pi$
$613$	−14.3918	−	44.2933i	−0.581278	−	1.78899i	0.0324534	−	0.999473i	$-0.489668\pi$
$614$	−27.8601	+	20.2416i	−1.12434	+	0.816883i
$615$		0			0
$616$	−4.62703	−	7.31593i	−0.186428	−	0.294767i
$617$	30.9597			1.24639			0.623195	−	0.782067i	$-0.285834\pi$
$617$	30.9597			1.24639			0.623195	+	0.782067i	$0.285834\pi$
$618$		0			0
$619$	−4.53714	−	13.9639i	−0.182363	−	0.561256i	0.817530	−	0.575886i	$-0.195343\pi$
$619$	−4.53714	−	13.9639i	−0.182363	−	0.561256i	−0.999893	+	0.0146305i	$0.995343\pi$
$620$	0.0864376	−	0.266028i	0.00347142	−	0.0106839i
$621$		0			0
$622$	17.0428	+	12.3823i	0.683354	+	0.496486i
$623$	−5.20938	+	16.0328i	−0.208710	+	0.642342i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	34.5226			1.37980
$627$		0			0
$628$	13.1899			0.526334
$629$	16.1594	−	11.7405i	0.644316	−	0.468123i
$630$		0			0
$631$	−3.94270	+	12.1344i	−0.156957	+	0.483063i	−0.998354	−	0.0573544i	$-0.981733\pi$
$631$	−3.94270	+	12.1344i	−0.156957	+	0.483063i	0.841397	+	0.540417i	$0.181733\pi$
$632$	−0.971958	−	0.706169i	−0.0386624	−	0.0280899i
$633$		0			0
$634$	−0.472657	+	1.45469i	−0.0187716	+	0.0577730i
$635$	−3.11931	−	9.60025i	−0.123786	−	0.380974i
$636$		0			0
$637$	0.508093			0.0201314
$638$	41.8956	−	50.4844i	1.65866	−	1.99870i
$639$		0			0
$640$	6.19289	−	4.49940i	0.244795	−	0.177854i
$641$	−5.04953	−	15.5408i	−0.199444	−	0.613826i	−0.999896	−	0.0144290i	$-0.995407\pi$
$641$	−5.04953	−	15.5408i	−0.199444	−	0.613826i	0.800452	−	0.599397i	$-0.204593\pi$
$642$		0			0
$643$	−4.80162	−	3.48858i	−0.189357	−	0.137576i	0.489068	−	0.872246i	$-0.337337\pi$
$643$	−4.80162	−	3.48858i	−0.189357	−	0.137576i	−0.678425	+	0.734670i	$0.737337\pi$
$644$	−14.1955	−	10.3137i	−0.559382	−	0.406415i
$645$		0			0
$646$	−1.44823	−	4.45718i	−0.0569797	−	0.175365i
$647$	−6.55138	+	4.75986i	−0.257561	+	0.187129i	−0.709071	−	0.705137i	$-0.750886\pi$
$647$	−6.55138	+	4.75986i	−0.257561	+	0.187129i	0.451510	+	0.892266i	$0.350886\pi$
$648$		0			0
$649$	−19.0495	+	4.85978i	−0.747758	+	0.190763i
$650$	12.0662			0.473276
$651$		0			0
$652$	8.99540	+	27.6850i	0.352287	+	1.08423i
$653$	−8.78282	+	27.0307i	−0.343698	+	1.05779i	0.618579	+	0.785723i	$0.287709\pi$
$653$	−8.78282	+	27.0307i	−0.343698	+	1.05779i	−0.962277	+	0.272072i	$0.912291\pi$
$654$		0			0
$655$	−3.75996	−	2.73177i	−0.146914	−	0.106739i
$656$	−0.894225	+	2.75214i	−0.0349136	+	0.107453i
$657$		0			0
$658$	34.9841	−	25.4174i	1.36382	−	0.990875i
$659$	−7.38736			−0.287771			−0.143885	−	0.989594i	$-0.545960\pi$
$659$	−7.38736			−0.287771			−0.143885	+	0.989594i	$0.545960\pi$
$660$		0			0
$661$	−31.4264			−1.22235			−0.611174	−	0.791497i	$-0.709302\pi$
$661$	−31.4264			−1.22235			−0.611174	+	0.791497i	$0.709302\pi$
$662$	12.0246	−	8.73636i	0.467348	−	0.339548i
$663$		0			0
$664$	−1.42943	+	4.39933i	−0.0554726	+	0.170727i
$665$	−1.13398	−	0.823883i	−0.0439738	−	0.0319488i
$666$		0			0
$667$	−14.9218	+	45.9246i	−0.577775	+	1.77821i
$668$	−5.22011	−	16.0659i	−0.201972	−	0.621606i
$669$		0			0
$670$	−9.73502			−0.376096
$671$	0.686230	−	10.6454i	0.0264916	−	0.410960i
$672$		0			0
$673$	12.6179	−	9.16742i	0.486383	−	0.353378i	−0.317408	−	0.948289i	$-0.602813\pi$
$673$	12.6179	−	9.16742i	0.486383	−	0.353378i	0.803792	+	0.594911i	$0.202813\pi$
$674$	7.17472	+	22.0815i	0.276360	+	0.850548i
$675$		0			0
$676$	−34.4132	−	25.0026i	−1.32358	−	0.961639i
$677$	−3.12823	−	2.27279i	−0.120228	−	0.0873504i	0.526047	−	0.850456i	$-0.323674\pi$
$677$	−3.12823	−	2.27279i	−0.120228	−	0.0873504i	−0.646274	+	0.763105i	$0.723674\pi$
$678$		0			0
$679$	−5.95863	−	18.3388i	−0.228671	−	0.703777i
$680$	−3.79150	+	2.75469i	−0.145398	+	0.105637i
$681$		0			0
$682$	1.14083	−	0.291040i	0.0436845	−	0.0111445i
$683$	−34.2736			−1.31144			−0.655722	−	0.755002i	$-0.727636\pi$
$683$	−34.2736			−1.31144			−0.655722	+	0.755002i	$0.727636\pi$
$684$		0			0
$685$	−4.87245	−	14.9959i	−0.186167	−	0.572962i
$686$	10.7155	−	32.9789i	0.409119	−	1.25914i
$687$		0			0
$688$	−35.7793	−	25.9952i	−1.36407	−	0.991056i
$689$	13.4093	−	41.2697i	0.510855	−	1.57225i
$690$		0			0
$691$	36.1869	−	26.2914i	1.37662	−	1.00017i	0.379429	−	0.925221i	$-0.376121\pi$
$691$	36.1869	−	26.2914i	1.37662	−	1.00017i	0.997187	−	0.0749493i	$-0.0238795\pi$
$692$	11.0117			0.418602
$693$		0			0
$694$	38.9399			1.47814
$695$	−8.12138	+	5.90053i	−0.308061	+	0.223820i
$696$		0			0
$697$	0.883452	−	2.71899i	0.0334631	−	0.102989i
$698$	−11.5667	−	8.40373i	−0.437808	−	0.318086i
$699$		0			0
$700$	1.19284	−	3.67118i	0.0450851	−	0.138758i
$701$	−3.44976	−	10.6173i	−0.130296	−	0.401009i	0.864533	−	0.502576i	$-0.167614\pi$
$701$	−3.44976	−	10.6173i	−0.130296	−	0.401009i	−0.994829	+	0.101567i	$0.967614\pi$
$702$		0			0
$703$	−2.25264			−0.0849599
$704$	−10.2358	−	4.07090i	−0.385775	−	0.153428i
$705$		0			0
$706$	20.7863	−	15.1021i	0.782302	−	0.568375i
$707$	−9.23549	−	28.4239i	−0.347336	−	1.06899i
$708$		0			0
$709$	−33.8056	−	24.5612i	−1.26960	−	0.922416i	−0.270410	−	0.962745i	$-0.587159\pi$
$709$	−33.8056	−	24.5612i	−1.26960	−	0.922416i	−0.999186	+	0.0403297i	$0.987159\pi$
$710$	4.13335	+	3.00305i	0.155122	+	0.112703i
$711$		0			0
$712$	−1.96435	−	6.04564i	−0.0736170	−	0.226570i
$713$	−0.701093	+	0.509374i	−0.0262561	+	0.0190762i
$714$		0			0
$715$	11.4880	+	18.1640i	0.429627	+	0.679296i
$716$	−9.60837			−0.359082
$717$		0			0
$718$	−10.3091	−	31.7280i	−0.384731	−	1.18408i
$719$	5.55930	−	17.1098i	0.207327	−	0.638087i	−0.792283	−	0.610154i	$-0.791108\pi$
$719$	5.55930	−	17.1098i	0.207327	−	0.638087i	0.999610	−	0.0279327i	$-0.00889240\pi$
$720$		0			0
$721$	4.38594	+	3.18657i	0.163341	+	0.118674i
$722$	10.7694	−	33.1447i	0.400794	−	1.23352i
$723$		0			0
$724$	9.54869	−	6.93753i	0.354874	−	0.257831i
$725$	−10.6229			−0.394526
$726$		0			0
$727$	23.9340			0.887664			0.443832	−	0.896110i	$-0.353619\pi$
$727$	23.9340			0.887664			0.443832	+	0.896110i	$0.353619\pi$
$728$	13.6828	−	9.94116i	0.507120	−	0.368444i
$729$		0			0
$730$	9.01983	−	27.7602i	0.333839	−	1.02745i
$731$	35.3482	+	25.6820i	1.30740	+	0.949883i
$732$		0			0
$733$	−2.28826	+	7.04254i	−0.0845188	+	0.260122i	−0.984381	−	0.176053i	$-0.943667\pi$
$733$	−2.28826	+	7.04254i	−0.0845188	+	0.260122i	0.899862	+	0.436175i	$0.143667\pi$
$734$	−5.44817	−	16.7678i	−0.201096	−	0.618909i
$735$		0			0
$736$	31.4542			1.15942
$737$	−9.26850	−	14.6547i	−0.341410	−	0.539813i
$738$		0			0
$739$	−25.0551	+	18.2036i	−0.921667	+	0.669630i	−0.943938	−	0.330122i	$-0.892910\pi$
$739$	−25.0551	+	18.2036i	−0.921667	+	0.669630i	0.0222712	+	0.999752i	$0.492910\pi$
$740$	−1.91702	−	5.89998i	−0.0704710	−	0.216888i
$741$		0			0
$742$	−26.5397	−	19.2822i	−0.974302	−	0.707872i
$743$	−40.2583	−	29.2494i	−1.47693	−	1.07306i	−0.978528	−	0.206112i	$-0.933919\pi$
$743$	−40.2583	−	29.2494i	−1.47693	−	1.07306i	−0.498406	−	0.866944i	$-0.666081\pi$
$744$		0			0
$745$	3.23395	+	9.95308i	0.118483	+	0.364653i
$746$	17.5351	−	12.7400i	0.642006	−	0.466445i
$747$		0			0
$748$	21.3611	+	8.49560i	0.781041	+	0.310630i
$749$	−3.02477			−0.110523
$750$		0			0
$751$	10.6418	+	32.7520i	0.388323	+	1.19514i	0.934041	+	0.357167i	$0.116257\pi$
$751$	10.6418	+	32.7520i	0.388323	+	1.19514i	−0.545717	+	0.837969i	$0.683743\pi$
$752$	−13.0432	+	40.1428i	−0.475636	+	1.46386i
$753$		0			0
$754$	103.699	+	75.3417i	3.77649	+	2.74378i
$755$	−4.83406	+	14.8777i	−0.175929	+	0.541455i
$756$		0			0
$757$	14.9533	−	10.8642i	0.543487	−	0.394867i	−0.281891	−	0.959446i	$-0.590962\pi$
$757$	14.9533	−	10.8642i	0.543487	−	0.394867i	0.825379	+	0.564580i	$0.190962\pi$
$758$	12.2971			0.446651
$759$		0			0
$760$	0.528542			0.0191722
$761$	−5.70368	+	4.14397i	−0.206758	+	0.150219i	−0.686346	−	0.727275i	$-0.740786\pi$
$761$	−5.70368	+	4.14397i	−0.206758	+	0.150219i	0.479587	+	0.877494i	$0.340786\pi$
$762$		0			0
$763$	−10.8454	+	33.3789i	−0.392632	+	1.20840i
$764$	−10.3606	−	7.52743i	−0.374834	−	0.272333i
$765$		0			0
$766$	11.3571	−	34.9536i	0.410350	−	1.26293i
$767$	−11.8698	−	36.5313i	−0.428592	−	1.31907i
$768$		0			0
$769$	−15.9027			−0.573465			−0.286732	−	0.958011i	$-0.592569\pi$
$769$	−15.9027			−0.573465			−0.286732	+	0.958011i	$0.592569\pi$
$770$	15.7434	−	4.01635i	0.567353	−	0.144739i
$771$		0			0
$772$	−17.8779	+	12.9890i	−0.643438	+	0.467485i
$773$	−5.29257	−	16.2889i	−0.190361	−	0.585870i	0.809639	−	0.586928i	$-0.199663\pi$
$773$	−5.29257	−	16.2889i	−0.190361	−	0.585870i	−0.999999	+	0.00105868i	$0.999663\pi$
$774$		0			0
$775$	−0.154234	−	0.112058i	−0.00554026	−	0.00402524i
$776$	5.88239	+	4.27380i	0.211165	+	0.153421i
$777$		0			0
$778$	14.5950	+	44.9189i	0.523257	+	1.61042i
$779$	−0.260846	+	0.189515i	−0.00934576	+	0.00679010i
$780$		0			0
$781$	−0.585408	+	9.08132i	−0.0209475	+	0.324955i
$782$	−39.9857			−1.42988
$783$		0			0
$784$	0.115858	+	0.356575i	0.00413780	+	0.0127348i
$785$	2.77797	−	8.54971i	0.0991500	−	0.305152i
$786$		0			0
$787$	−37.4288	−	27.1936i	−1.33419	−	0.969349i	−0.999636	−	0.0269735i	$-0.991413\pi$
$787$	−37.4288	−	27.1936i	−1.33419	−	0.969349i	−0.334558	−	0.942375i	$-0.608587\pi$
$788$	−5.93417	+	18.2635i	−0.211396	+	0.650610i
$789$		0			0
$790$	1.82433	−	1.32545i	0.0649068	−	0.0471575i
$791$	−16.5677			−0.589081
$792$		0			0
$793$	20.8423			0.740131
$794$	−59.1122	+	42.9476i	−2.09781	+	1.52415i
$795$		0			0
$796$	3.24967	−	10.0015i	0.115182	−	0.354492i
$797$	−3.16764	−	2.30143i	−0.112204	−	0.0815207i	0.530268	−	0.847830i	$-0.322091\pi$
$797$	−3.16764	−	2.30143i	−0.112204	−	0.0815207i	−0.642472	+	0.766309i	$0.722091\pi$
$798$		0			0
$799$	12.8861	−	39.6592i	0.455876	−	1.40304i
$800$	2.13829	+	6.58098i	0.0756000	+	0.232673i
$801$		0			0
$802$	20.7111			0.731333
$803$	50.3767	−	12.8518i	1.77776	−	0.453529i
$804$		0			0
$805$	−9.67509	+	7.02936i	−0.341002	+	0.247753i
$806$	0.710849	+	2.18777i	0.0250386	+	0.0770609i
$807$		0			0
$808$	9.11732	+	6.62412i	0.320746	+	0.233036i
$809$	5.46291	+	3.96904i	0.192066	+	0.139544i	0.679662	−	0.733525i	$-0.262126\pi$
$809$	5.46291	+	3.96904i	0.192066	+	0.139544i	−0.487597	+	0.873069i	$0.662126\pi$
$810$		0			0
$811$	−13.4196	−	41.3013i	−0.471227	−	1.45029i	−0.850980	−	0.525199i	$-0.823991\pi$
$811$	−13.4196	−	41.3013i	−0.471227	−	1.45029i	0.379753	−	0.925088i	$-0.376009\pi$
$812$	33.1743	−	24.1026i	1.16419	−	0.845834i
$813$		0			0
$814$	16.6752	−	20.0937i	0.584466	−	0.704284i
$815$	19.8400			0.694964
$816$		0			0
$817$	−1.52271	−	4.68643i	−0.0532729	−	0.163957i
$818$	6.68107	−	20.5622i	0.233598	−	0.718941i
$819$		0			0
$820$	−0.718350	−	0.521912i	−0.0250859	−	0.0182260i
$821$	2.20967	−	6.80067i	0.0771180	−	0.237345i	−0.905065	−	0.425274i	$-0.860178\pi$
$821$	2.20967	−	6.80067i	0.0771180	−	0.237345i	0.982183	+	0.187929i	$0.0601776\pi$
$822$		0			0
$823$	7.74935	−	5.63023i	0.270125	−	0.196257i	−0.444474	−	0.895792i	$-0.646609\pi$
$823$	7.74935	−	5.63023i	0.270125	−	0.196257i	0.714599	+	0.699534i	$0.246609\pi$
$824$	−2.04426			−0.0712153
$825$		0			0
$826$	−29.0384			−1.01038
$827$	4.94825	−	3.59511i	0.172067	−	0.125014i	−0.498419	−	0.866937i	$-0.666086\pi$
$827$	4.94825	−	3.59511i	0.172067	−	0.125014i	0.670486	+	0.741922i	$0.266086\pi$
$828$		0			0
$829$	10.6387	−	32.7426i	0.369498	−	1.13720i	−0.577618	−	0.816307i	$-0.696018\pi$
$829$	10.6387	−	32.7426i	0.369498	−	1.13720i	0.947116	−	0.320891i	$-0.103982\pi$
$830$	−7.02415	−	5.10334i	−0.243812	−	0.177140i
$831$		0			0
$832$	6.65081	−	20.4691i	0.230575	−	0.709638i
$833$	−0.114463	−	0.352280i	−0.00396589	−	0.0122058i
$834$		0			0
$835$	−11.5133			−0.398435
$836$	−1.38581	−	2.19115i	−0.0479293	−	0.0757826i
$837$		0			0
$838$	−27.9441	+	20.3025i	−0.965311	+	0.701340i
$839$	−2.90734	−	8.94788i	−0.100373	−	0.308915i	0.888244	−	0.459372i	$-0.151926\pi$
$839$	−2.90734	−	8.94788i	−0.100373	−	0.308915i	−0.988617	+	0.150457i	$0.951926\pi$
$840$		0			0
$841$	−67.8336	−	49.2840i	−2.33909	−	1.69945i
$842$	−30.0916	−	21.8629i	−1.03703	−	0.753444i
$843$		0			0
$844$	2.71505	+	8.35607i	0.0934559	+	0.287628i
$845$	−23.4546	+	17.0408i	−0.806862	+	0.586220i
$846$		0			0
$847$	21.0350	+	19.8756i	0.722772	+	0.682935i
$848$	32.0204			1.09958
$849$		0			0
$850$	−2.71827	−	8.36597i	−0.0932358	−	0.286950i
$851$	−5.93915	+	18.2788i	−0.203591	+	0.626590i
$852$		0			0
$853$	28.3918	+	20.6279i	0.972118	+	0.706285i	0.955933	−	0.293584i	$-0.0948480\pi$
$853$	28.3918	+	20.6279i	0.972118	+	0.706285i	0.0161846	+	0.999869i	$0.494848\pi$
$854$	4.86901	−	14.9853i	0.166614	−	0.512786i
$855$		0			0
$856$	0.922746	−	0.670414i	0.0315388	−	0.0229143i
$857$	−21.3605			−0.729661			−0.364831	−	0.931074i	$-0.618873\pi$
$857$	−21.3605			−0.729661			−0.364831	+	0.931074i	$0.618873\pi$
$858$		0			0
$859$	5.21468			0.177923			0.0889613	−	0.996035i	$-0.471645\pi$
$859$	5.21468			0.177923			0.0889613	+	0.996035i	$0.471645\pi$
$860$	10.9786	−	7.97639i	0.374366	−	0.271993i
$861$		0			0
$862$	−14.9355	+	45.9668i	−0.508706	+	1.56564i
$863$	3.52559	+	2.56149i	0.120012	+	0.0871941i	0.646172	−	0.763191i	$-0.276369\pi$
$863$	3.52559	+	2.56149i	0.120012	+	0.0871941i	−0.526160	+	0.850386i	$0.676369\pi$
$864$		0			0
$865$	2.31921	−	7.13779i	0.0788555	−	0.242692i
$866$	19.3214	+	59.4652i	0.656568	+	2.02071i
$867$		0			0
$868$	0.735908			0.0249783
$869$	3.73219	+	1.48434i	0.126606	+	0.0503528i
$870$		0			0
$871$	27.4084	−	19.9134i	0.928699	−	0.674739i
$872$	−4.08959	−	12.5865i	−0.138491	−	0.426231i
$873$		0			0
$874$	3.64827	+	2.65062i	0.123405	+	0.0896587i
$875$	−2.12844	−	1.54640i	−0.0719543	−	0.0522778i
$876$		0			0
$877$	−4.28638	−	13.1921i	−0.144741	−	0.445467i	0.852237	−	0.523156i	$-0.175246\pi$
$877$	−4.28638	−	13.1921i	−0.144741	−	0.445467i	−0.996978	+	0.0776898i	$0.975246\pi$
$878$	−25.6515	+	18.6369i	−0.865696	+	0.628965i
$879$		0			0
$880$	−10.1278	+	12.2041i	−0.341408	+	0.411398i
$881$	−40.9512			−1.37968			−0.689841	−	0.723961i	$-0.742319\pi$
$881$	−40.9512			−1.37968			−0.689841	+	0.723961i	$0.742319\pi$
$882$		0			0
$883$	−10.9972	−	33.8458i	−0.370084	−	1.13900i	−0.946736	−	0.322012i	$-0.895641\pi$
$883$	−10.9972	−	33.8458i	−0.370084	−	1.13900i	0.576651	−	0.816990i	$-0.304359\pi$
$884$	−13.8796	+	42.7172i	−0.466823	+	1.43673i
$885$		0			0
$886$	−37.9843	−	27.5972i	−1.27611	−	0.927146i
$887$	−9.96968	+	30.6835i	−0.334749	+	1.03025i	0.632096	+	0.774890i	$0.282195\pi$
$887$	−9.96968	+	30.6835i	−0.334749	+	1.03025i	−0.966846	+	0.255362i	$0.917805\pi$
$888$		0			0
$889$	21.4851	−	15.6098i	0.720586	−	0.523537i
$890$	11.9314			0.399942
$891$		0			0
$892$	−0.440934			−0.0147636
$893$	−3.80470	+	2.76428i	−0.127320	+	0.0925031i
$894$		0			0
$895$	−2.02365	+	6.22815i	−0.0676432	+	0.208184i
$896$	16.2928	+	11.8374i	0.544305	+	0.395461i
$897$		0			0
$898$	−15.3400	+	47.2118i	−0.511904	+	1.57548i
$899$	−0.625822	−	1.92608i	−0.0208723	−	0.0642385i
$900$		0			0
$901$	−31.6346			−1.05390
$902$	0.240424	−	3.72966i	0.00800525	−	0.124184i
$903$		0			0
$904$	5.05421	−	3.67210i	0.168100	−	0.122132i
$905$	−2.48583	−	7.65061i	−0.0826319	−	0.254315i
$906$		0			0
$907$	−11.7962	−	8.57041i	−0.391685	−	0.284576i	0.374461	−	0.927243i	$-0.377828\pi$
$907$	−11.7962	−	8.57041i	−0.391685	−	0.284576i	−0.766146	+	0.642667i	$0.777828\pi$
$908$	−27.0851	−	19.6785i	−0.898850	−	0.653053i
$909$		0			0
$910$	9.80973	+	30.1912i	0.325189	+	1.00083i
$911$	−27.1603	+	19.7331i	−0.899859	+	0.653786i	−0.938430	−	0.345470i	$-0.887720\pi$
$911$	−27.1603	+	19.7331i	−0.899859	+	0.653786i	0.0385704	+	0.999256i	$0.487720\pi$
$912$		0			0
$913$	0.994833	−	15.4327i	0.0329242	−	0.510747i
$914$	40.8684			1.35181
$915$		0			0
$916$	12.7907	+	39.3658i	0.422618	+	1.30068i
$917$	3.77842	−	11.6288i	0.124775	−	0.384017i
$918$		0			0
$919$	−29.3286	−	21.3085i	−0.967462	−	0.702902i	−0.0125900	−	0.999921i	$-0.504008\pi$
$919$	−29.3286	−	21.3085i	−0.967462	−	0.702902i	−0.954872	+	0.297019i	$0.904008\pi$
$920$	1.39352	−	4.28880i	0.0459428	−	0.141398i
$921$		0			0
$922$	6.51717	−	4.73500i	0.214632	−	0.155939i
$923$	−17.7801			−0.585239
$924$		0			0
$925$	−4.22812			−0.139020
$926$	17.2597	−	12.5399i	0.567188	−	0.412086i
$927$		0			0
$928$	−22.7149	+	69.9094i	−0.745654	+	2.29489i
$929$	19.5612	+	14.2120i	0.641782	+	0.466282i	0.860462	−	0.509515i	$-0.170175\pi$
$929$	19.5612	+	14.2120i	0.641782	+	0.466282i	−0.218680	+	0.975797i	$0.570175\pi$
$930$		0			0
$931$	−0.0129089	+	0.0397295i	−0.000423072	+	0.00130208i
$932$	8.78889	+	27.0494i	0.287890	+	0.886033i
$933$		0			0
$934$	−28.9630			−0.947697
$935$	10.0058	−	12.0570i	0.327225	−	0.394307i
$936$		0			0
$937$	13.2737	−	9.64389i	0.433632	−	0.315052i	−0.349468	−	0.936948i	$-0.613638\pi$
$937$	13.2737	−	9.64389i	0.433632	−	0.315052i	0.783100	+	0.621896i	$0.213638\pi$
$938$	−7.91447	−	24.3582i	−0.258417	−	0.795325i
$939$		0			0
$940$	−10.4779	−	7.61263i	−0.341751	−	0.248297i
$941$	6.49438	+	4.71844i	0.211711	+	0.153817i	0.688587	−	0.725153i	$-0.258231\pi$
$941$	6.49438	+	4.71844i	0.211711	+	0.153817i	−0.476877	+	0.878970i	$0.658231\pi$
$942$		0			0
$943$	0.850078	+	2.61627i	0.0276823	+	0.0851975i
$944$	22.9308	−	16.6602i	0.746333	−	0.542243i
$945$		0			0
$946$	53.0752	+	21.1087i	1.72562	+	0.686302i
$947$	−36.0500			−1.17147			−0.585733	−	0.810504i	$-0.699193\pi$
$947$	−36.0500			−1.17147			−0.585733	+	0.810504i	$0.699193\pi$
$948$		0			0
$949$	31.3898	+	96.6078i	1.01896	+	3.13602i
$950$	−0.306561	+	0.943499i	−0.00994616	+	0.0306111i
$951$		0			0
$952$	−9.97504	−	7.24729i	−0.323293	−	0.234886i
$953$	−2.16163	+	6.65281i	−0.0700221	+	0.215506i	−0.979944	−	0.199274i	$-0.936142\pi$
$953$	−2.16163	+	6.65281i	−0.0700221	+	0.215506i	0.909922	+	0.414780i	$0.136142\pi$
$954$		0			0
$955$	−7.06137	+	5.13038i	−0.228501	+	0.166015i
$956$	22.4097			0.724782
$957$		0			0
$958$	18.6146			0.601412
$959$	33.5603	−	24.3830i	1.08372	−	0.787367i
$960$		0			0
$961$	−9.56830	+	29.4482i	−0.308655	+	0.949941i
$962$	41.2740	+	29.9873i	1.33073	+	0.966830i
$963$		0			0
$964$	−3.26996	+	10.0639i	−0.105318	+	0.324136i
$965$	4.65418	+	14.3241i	0.149823	+	0.461109i
$966$		0			0
$967$	13.1569			0.423098			0.211549	−	0.977367i	$-0.432149\pi$
$967$	13.1569			0.423098			0.211549	+	0.977367i	$0.432149\pi$
$968$	−10.8223	−	1.40109i	−0.347841	−	0.0450327i
$969$		0			0
$970$	−11.0410	+	8.02178i	−0.354506	+	0.257564i
$971$	7.01971	+	21.6044i	0.225273	+	0.693319i	0.998264	+	0.0589020i	$0.0187600\pi$
$971$	7.01971	+	21.6044i	0.225273	+	0.693319i	−0.772991	+	0.634417i	$0.781240\pi$
$972$		0			0
$973$	−21.3665	−	15.5236i	−0.684977	−	0.497665i
$974$	59.6244	+	43.3197i	1.91049	+	1.38805i
$975$		0			0
$976$	4.75258	+	14.6269i	0.152126	+	0.468197i
$977$	−4.60907	+	3.34868i	−0.147457	+	0.107134i	−0.659068	−	0.752083i	$-0.729049\pi$
$977$	−4.60907	+	3.34868i	−0.147457	+	0.107134i	0.511611	+	0.859217i	$0.329049\pi$
$978$		0			0
$979$	11.3596	+	17.9611i	0.363056	+	0.574039i
$980$	−0.115043			−0.00367490
$981$		0			0
$982$	−5.34582	−	16.4527i	−0.170592	−	0.525028i
$983$	−5.23615	+	16.1152i	−0.167007	+	0.513995i	−0.999179	−	0.0405233i	$-0.987097\pi$
$983$	−5.23615	+	16.1152i	−0.167007	+	0.513995i	0.832171	+	0.554518i	$0.187097\pi$
$984$		0			0
$985$	10.5886	+	7.69307i	0.337381	+	0.245122i
$986$	28.8760	−	88.8712i	0.919599	−	2.83024i
$987$		0			0
$988$	4.09807	−	2.97742i	0.130377	−	0.0947243i
$989$	−42.0422			−1.33686
$990$		0			0
$991$	36.0516			1.14522			0.572609	−	0.819829i	$-0.305931\pi$
$991$	36.0516			1.14522			0.572609	+	0.819829i	$0.305931\pi$
$992$	−1.06725	+	0.775402i	−0.0338852	+	0.0246190i
$993$		0			0
$994$	−4.15365	+	12.7836i	−0.131746	+	0.405472i
$995$	−5.79853	−	4.21288i	−0.183826	−	0.133557i
$996$		0			0
$997$	5.76581	−	17.7453i	0.182605	−	0.562000i	−0.817294	−	0.576221i	$-0.804527\pi$
$997$	5.76581	−	17.7453i	0.182605	−	0.562000i	0.999899	+	0.0142207i	$0.00452675\pi$
$998$	13.4342	+	41.3463i	0.425253	+	1.30880i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.b.91.2		8
3.2	odd	2		165.2.m.b.91.1	✓	8
11.2	odd	10		5445.2.a.br.1.3		4
11.4	even	5	inner	495.2.n.b.136.2		8
11.9	even	5		5445.2.a.bk.1.2		4
15.2	even	4		825.2.bx.g.124.2		16
15.8	even	4		825.2.bx.g.124.3		16
15.14	odd	2		825.2.n.i.751.2		8
33.2	even	10		1815.2.a.r.1.2		4
33.20	odd	10		1815.2.a.v.1.3		4
33.26	odd	10		165.2.m.b.136.1	yes	8
165.59	odd	10		825.2.n.i.301.2		8
165.92	even	20		825.2.bx.g.499.3		16
165.119	odd	10		9075.2.a.cq.1.2		4
165.134	even	10		9075.2.a.dg.1.3		4
165.158	even	20		825.2.bx.g.499.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.b.91.1	✓	8	3.2	odd	2
165.2.m.b.136.1	yes	8	33.26	odd	10
495.2.n.b.91.2		8	1.1	even	1	trivial
495.2.n.b.136.2		8	11.4	even	5	inner
825.2.n.i.301.2		8	165.59	odd	10
825.2.n.i.751.2		8	15.14	odd	2
825.2.bx.g.124.2		16	15.2	even	4
825.2.bx.g.124.3		16	15.8	even	4
825.2.bx.g.499.2		16	165.158	even	20
825.2.bx.g.499.3		16	165.92	even	20
1815.2.a.r.1.2		4	33.2	even	10
1815.2.a.v.1.3		4	33.20	odd	10
5445.2.a.bk.1.2		4	11.9	even	5
5445.2.a.br.1.3		4	11.2	odd	10
9075.2.a.cq.1.2		4	165.119	odd	10
9075.2.a.dg.1.3		4	165.134	even	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)

\(f(q)\)	\(=\)	\(q+(1.50643 - 1.09448i) q^{2} +(0.453397 - 1.39541i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.812990 - 2.50213i) q^{7} +(0.306561 + 0.943499i) q^{8} +O(q^{10})\)	\(q+(1.50643 - 1.09448i) q^{2} +(0.453397 - 1.39541i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.812990 - 2.50213i) q^{7} +(0.306561 + 0.943499i) q^{8} -1.86205 q^{10} +(-1.77282 - 2.80306i) q^{11} +(5.24250 - 3.80890i) q^{13} +(-1.51383 - 4.65908i) q^{14} +(3.86848 + 2.81061i) q^{16} +(-3.82187 - 2.77675i) q^{17} +(0.164637 + 0.506699i) q^{19} +(-1.18701 + 0.862413i) q^{20} +(-5.73852 - 2.28228i) q^{22} +4.54563 q^{23} +(0.309017 + 0.951057i) q^{25} +(3.72867 - 11.4757i) q^{26} +(-3.12289 - 2.26892i) q^{28} +(-3.28267 + 10.1030i) q^{29} +(-0.154234 + 0.112058i) q^{31} +6.91965 q^{32} -8.79650 q^{34} +(-2.12844 + 1.54640i) q^{35} +(-1.30656 + 4.02118i) q^{37} +(0.802588 + 0.583114i) q^{38} +(0.306561 - 0.943499i) q^{40} +(0.187010 + 0.575557i) q^{41} -9.24893 q^{43} +(-4.71521 + 1.20291i) q^{44} +(6.84767 - 4.97513i) q^{46} +(2.72773 + 8.39509i) q^{47} +(0.0634337 + 0.0460873i) q^{49} +(1.50643 + 1.09448i) q^{50} +(-2.93805 - 9.04240i) q^{52} +(5.41754 - 3.93607i) q^{53} +(-0.213356 + 3.30976i) q^{55} +2.60999 q^{56} +(6.11249 + 18.8123i) q^{58} +(1.83173 - 5.63748i) q^{59} +(2.60209 + 1.89053i) q^{61} +(-0.109698 + 0.337614i) q^{62} +(2.68701 - 1.95223i) q^{64} -6.48008 q^{65} +5.22812 q^{67} +(-5.60755 + 4.07412i) q^{68} +(-1.51383 + 4.65908i) q^{70} +(-2.21979 - 1.61277i) q^{71} +(-4.84404 + 14.9084i) q^{73} +(2.43288 + 7.48764i) q^{74} +0.781701 q^{76} +(-8.45488 + 2.15695i) q^{77} +(-0.979744 + 0.711826i) q^{79} +(-1.47763 - 4.54767i) q^{80} +(0.911655 + 0.662356i) q^{82} +(3.77227 + 2.74071i) q^{83} +(1.45983 + 4.49288i) q^{85} +(-13.9328 + 10.1228i) q^{86} +(2.10120 - 2.53196i) q^{88} -6.40768 q^{89} +(-5.26824 - 16.2140i) q^{91} +(2.06098 - 6.34304i) q^{92} +(13.2974 + 9.66115i) q^{94} +(0.164637 - 0.506699i) q^{95} +(5.92951 - 4.30804i) q^{97} +0.146000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8} - 2 q^{10} + 3 q^{11} + 10 q^{13} - 24 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{19} - 7 q^{20} - 7 q^{22} + 2 q^{23} - 2 q^{25} - 14 q^{26} + 13 q^{28} - 14 q^{29} - 5 q^{31} + 16 q^{32} - 70 q^{34} - q^{35} - 27 q^{37} + 16 q^{38} + 19 q^{40} - q^{41} - 28 q^{43} - 47 q^{44} + 42 q^{46} + 27 q^{47} - 15 q^{49} - 2 q^{50} + 22 q^{52} + q^{53} - 7 q^{55} + 24 q^{56} + 18 q^{58} - 13 q^{59} - 3 q^{61} - 15 q^{62} + 19 q^{64} - 30 q^{65} + 10 q^{67} + 33 q^{68} - 24 q^{70} - 9 q^{71} + 5 q^{73} + 17 q^{74} - 46 q^{76} - q^{77} - 10 q^{79} - 11 q^{80} - 33 q^{82} + 25 q^{83} - 8 q^{85} - 20 q^{86} + 29 q^{88} - 4 q^{89} - 43 q^{91} + 22 q^{92} + 57 q^{94} - 2 q^{95} + 13 q^{97} + 2 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8 - 2 * q^10 + 3 * q^11 + 10 * q^13 - 24 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^19 - 7 * q^20 - 7 * q^22 + 2 * q^23 - 2 * q^25 - 14 * q^26 + 13 * q^28 - 14 * q^29 - 5 * q^31 + 16 * q^32 - 70 * q^34 - q^35 - 27 * q^37 + 16 * q^38 + 19 * q^40 - q^41 - 28 * q^43 - 47 * q^44 + 42 * q^46 + 27 * q^47 - 15 * q^49 - 2 * q^50 + 22 * q^52 + q^53 - 7 * q^55 + 24 * q^56 + 18 * q^58 - 13 * q^59 - 3 * q^61 - 15 * q^62 + 19 * q^64 - 30 * q^65 + 10 * q^67 + 33 * q^68 - 24 * q^70 - 9 * q^71 + 5 * q^73 + 17 * q^74 - 46 * q^76 - q^77 - 10 * q^79 - 11 * q^80 - 33 * q^82 + 25 * q^83 - 8 * q^85 - 20 * q^86 + 29 * q^88 - 4 * q^89 - 43 * q^91 + 22 * q^92 + 57 * q^94 - 2 * q^95 + 13 * q^97 + 2 * q^98

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