LMFDB - Embedded newform 450.2.l.a.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.2
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	450.289
Dual form			450.2.l.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-0.530249 + 2.17229i) q^{5} -0.273457i q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-0.530249 + 2.17229i) q^{5} -0.273457i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.06909 + 0.847859i) q^{10} +(-3.87811 + 2.81761i) q^{11} +(-1.01869 + 1.40211i) q^{13} +(0.221232 - 0.160734i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.79892 - 0.584503i) q^{17} +(0.930333 + 2.86327i) q^{19} +(-1.90211 - 1.17557i) q^{20} +(-4.55899 - 1.48131i) q^{22} +(2.73076 + 3.75856i) q^{23} +(-4.43767 - 2.30371i) q^{25} -1.73311 q^{26} +(0.260074 + 0.0845030i) q^{28} +(2.80808 - 8.64240i) q^{29} +(1.18474 + 3.64625i) q^{31} -1.00000i q^{32} +(1.53025 + 1.11179i) q^{34} +(0.594028 + 0.145000i) q^{35} +(-5.29563 + 7.28881i) q^{37} +(-1.76960 + 2.43564i) q^{38} +(-0.166977 - 2.22982i) q^{40} +(-6.13287 - 4.45579i) q^{41} +2.88963i q^{43} +(-1.48131 - 4.55899i) q^{44} +(-1.43564 + 4.41846i) q^{46} +(1.12991 + 0.367130i) q^{47} +6.92522 q^{49} +(-0.744661 - 4.94424i) q^{50} +(-1.01869 - 1.40211i) q^{52} +(11.0465 + 3.58924i) q^{53} +(-4.06430 - 9.91840i) q^{55} +(0.0845030 + 0.260074i) q^{56} +(8.64240 - 2.80808i) q^{58} +(11.5604 + 8.39915i) q^{59} +(4.16750 - 3.02786i) q^{61} +(-2.25351 + 3.10169i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-2.50563 - 2.95637i) q^{65} +(5.98215 - 1.94372i) q^{67} +1.89149i q^{68} +(0.231853 + 0.565808i) q^{70} +(0.433294 - 1.33354i) q^{71} +(-1.04691 - 1.44095i) q^{73} -9.00947 q^{74} -3.01062 q^{76} +(0.770497 + 1.06050i) q^{77} +(4.96261 - 15.2733i) q^{79} +(1.70582 - 1.44575i) q^{80} -7.58064i q^{82} +(-14.3983 + 4.67828i) q^{83} +(0.315836 + 4.21769i) q^{85} +(-2.33776 + 1.69848i) q^{86} +(2.81761 - 3.87811i) q^{88} +(11.9956 - 8.71529i) q^{89} +(0.383418 + 0.278570i) q^{91} +(-4.41846 + 1.43564i) q^{92} +(0.367130 + 1.12991i) q^{94} +(-6.71316 + 0.502706i) q^{95} +(5.59789 + 1.81886i) q^{97} +(4.07054 + 5.60262i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4}+O(q^{10}) $ 8 * q + 2 * q^4	$ 8 q + 2 q^{4} - 10 q^{11} - 20 q^{13} + 2 q^{14} - 2 q^{16} - 10 q^{17} - 8 q^{19} + 10 q^{23} - 10 q^{25} - 4 q^{26} - 10 q^{28} + 22 q^{29} + 24 q^{31} + 8 q^{34} - 10 q^{35} - 20 q^{37} + 10 q^{38} - 22 q^{41} + 10 q^{46} - 10 q^{47} + 8 q^{49} + 20 q^{50} - 20 q^{52} + 30 q^{53} + 10 q^{55} - 2 q^{56} + 30 q^{58} + 20 q^{59} - 10 q^{62} + 2 q^{64} - 20 q^{65} + 10 q^{67} - 10 q^{70} - 20 q^{71} - 20 q^{73} + 4 q^{74} - 12 q^{76} + 20 q^{77} + 16 q^{79} - 70 q^{83} + 20 q^{85} + 18 q^{86} + 10 q^{88} + 34 q^{89} - 24 q^{91} - 30 q^{92} + 30 q^{94} - 30 q^{95} + 60 q^{97} - 20 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 - 10 * q^11 - 20 * q^13 + 2 * q^14 - 2 * q^16 - 10 * q^17 - 8 * q^19 + 10 * q^23 - 10 * q^25 - 4 * q^26 - 10 * q^28 + 22 * q^29 + 24 * q^31 + 8 * q^34 - 10 * q^35 - 20 * q^37 + 10 * q^38 - 22 * q^41 + 10 * q^46 - 10 * q^47 + 8 * q^49 + 20 * q^50 - 20 * q^52 + 30 * q^53 + 10 * q^55 - 2 * q^56 + 30 * q^58 + 20 * q^59 - 10 * q^62 + 2 * q^64 - 20 * q^65 + 10 * q^67 - 10 * q^70 - 20 * q^71 - 20 * q^73 + 4 * q^74 - 12 * q^76 + 20 * q^77 + 16 * q^79 - 70 * q^83 + 20 * q^85 + 18 * q^86 + 10 * q^88 + 34 * q^89 - 24 * q^91 - 30 * q^92 + 30 * q^94 - 30 * q^95 + 60 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−0.530249	+	2.17229i	−0.237134	+	0.971477i
$5$	−0.530249	+	2.17229i	−0.237134	+	0.971477i
$6$		0			0
$7$		−	0.273457i		−	0.103357i	−0.998664	−	0.0516786i	$-0.983543\pi$
$7$		−	0.273457i		−	0.103357i	0.998664	−	0.0516786i	$-0.0164571\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$		0			0
$10$	−2.06909	+	0.847859i	−0.654304	+	0.268116i
$11$	−3.87811	+	2.81761i	−1.16929	+	0.849541i	−0.990924	−	0.134422i	$-0.957082\pi$
$11$	−3.87811	+	2.81761i	−1.16929	+	0.849541i	−0.178369	+	0.983964i	$0.557082\pi$
$12$		0			0
$13$	−1.01869	+	1.40211i	−0.282535	+	0.388876i	−0.926572	−	0.376119i	$-0.877259\pi$
$13$	−1.01869	+	1.40211i	−0.282535	+	0.388876i	0.644036	+	0.764995i	$0.277259\pi$
$14$	0.221232	−	0.160734i	0.0591267	−	0.0429580i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.79892	−	0.584503i	0.436301	−	0.141763i	−0.0826274	−	0.996581i	$-0.526331\pi$
$17$	1.79892	−	0.584503i	0.436301	−	0.141763i	0.518928	+	0.854818i	$0.326331\pi$
$18$		0			0
$19$	0.930333	+	2.86327i	0.213433	+	0.656879i	0.999261	+	0.0384344i	$0.0122371\pi$
$19$	0.930333	+	2.86327i	0.213433	+	0.656879i	−0.785828	+	0.618445i	$0.787763\pi$
$20$	−1.90211	−	1.17557i	−0.425325	−	0.262866i
$21$		0			0
$22$	−4.55899	−	1.48131i	−0.971980	−	0.315815i
$23$	2.73076	+	3.75856i	0.569402	+	0.783715i	0.992484	−	0.122377i	$-0.0390516\pi$
$23$	2.73076	+	3.75856i	0.569402	+	0.783715i	−0.423081	+	0.906092i	$0.639052\pi$
$24$		0			0
$25$	−4.43767	−	2.30371i	−0.887535	−	0.460741i
$26$	−1.73311			−0.339890
$27$		0			0
$28$	0.260074	+	0.0845030i	0.0491493	+	0.0159696i
$29$	2.80808	−	8.64240i	0.521448	−	1.60485i	−0.249786	−	0.968301i	$-0.580360\pi$
$29$	2.80808	−	8.64240i	0.521448	−	1.60485i	0.771234	−	0.636552i	$-0.219640\pi$
$30$		0			0
$31$	1.18474	+	3.64625i	0.212786	+	0.654887i	0.999303	+	0.0373190i	$0.0118818\pi$
$31$	1.18474	+	3.64625i	0.212786	+	0.654887i	−0.786518	+	0.617568i	$0.788118\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	1.53025	+	1.11179i	0.262435	+	0.190671i
$35$	0.594028	+	0.145000i	0.100409	+	0.0245096i
$36$		0			0
$37$	−5.29563	+	7.28881i	−0.870597	+	1.19827i	0.108341	+	0.994114i	$0.465446\pi$
$37$	−5.29563	+	7.28881i	−0.870597	+	1.19827i	−0.978938	+	0.204160i	$0.934554\pi$
$38$	−1.76960	+	2.43564i	−0.287067	+	0.395114i
$39$		0			0
$40$	−0.166977	−	2.22982i	−0.0264015	−	0.352566i
$41$	−6.13287	−	4.45579i	−0.957793	−	0.695878i	−0.00515619	−	0.999987i	$-0.501641\pi$
$41$	−6.13287	−	4.45579i	−0.957793	−	0.695878i	−0.952637	+	0.304109i	$0.901641\pi$
$42$		0			0
$43$			2.88963i			0.440664i	0.975425	+	0.220332i	$0.0707141\pi$
$43$			2.88963i			0.440664i	−0.975425	+	0.220332i	$0.929286\pi$
$44$	−1.48131	−	4.55899i	−0.223315	−	0.687293i
$45$		0			0
$46$	−1.43564	+	4.41846i	−0.211674	+	0.651466i
$47$	1.12991	+	0.367130i	0.164814	+	0.0535514i	0.390262	−	0.920704i	$-0.372384\pi$
$47$	1.12991	+	0.367130i	0.164814	+	0.0535514i	−0.225448	+	0.974255i	$0.572384\pi$
$48$		0			0
$49$	6.92522			0.989317
$50$	−0.744661	−	4.94424i	−0.105311	−	0.699221i
$51$		0			0
$52$	−1.01869	−	1.40211i	−0.141268	−	0.194438i
$53$	11.0465	+	3.58924i	1.51736	+	0.493020i	0.945024	−	0.327001i	$-0.106038\pi$
$53$	11.0465	+	3.58924i	1.51736	+	0.493020i	0.572334	+	0.820020i	$0.306038\pi$
$54$		0			0
$55$	−4.06430	−	9.91840i	−0.548030	−	1.33740i
$56$	0.0845030	+	0.260074i	0.0112922	+	0.0347538i
$57$		0			0
$58$	8.64240	−	2.80808i	1.13480	−	0.368720i
$59$	11.5604	+	8.39915i	1.50504	+	1.09348i	0.968319	+	0.249718i	$0.0803378\pi$
$59$	11.5604	+	8.39915i	1.50504	+	1.09348i	0.536723	+	0.843759i	$0.319662\pi$
$60$		0			0
$61$	4.16750	−	3.02786i	0.533593	−	0.387678i	−0.288107	−	0.957598i	$-0.593026\pi$
$61$	4.16750	−	3.02786i	0.533593	−	0.387678i	0.821700	+	0.569920i	$0.193026\pi$
$62$	−2.25351	+	3.10169i	−0.286196	+	0.393915i
$63$		0			0
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−2.50563	−	2.95637i	−0.310785	−	0.366692i
$66$		0			0
$67$	5.98215	−	1.94372i	0.730836	−	0.237463i	0.0801208	−	0.996785i	$-0.474469\pi$
$67$	5.98215	−	1.94372i	0.730836	−	0.237463i	0.650715	+	0.759322i	$0.274469\pi$
$68$			1.89149i			0.229377i
$69$		0			0
$70$	0.231853	+	0.565808i	0.0277118	+	0.0676270i
$71$	0.433294	−	1.33354i	0.0514226	−	0.158262i	−0.922048	−	0.387077i	$-0.873485\pi$
$71$	0.433294	−	1.33354i	0.0514226	−	0.158262i	0.973470	+	0.228814i	$0.0734849\pi$
$72$		0			0
$73$	−1.04691	−	1.44095i	−0.122532	−	0.168651i	0.743344	−	0.668909i	$-0.233238\pi$
$73$	−1.04691	−	1.44095i	−0.122532	−	0.168651i	−0.865876	+	0.500258i	$0.833238\pi$
$74$	−9.00947			−1.04733
$75$		0			0
$76$	−3.01062			−0.345342
$77$	0.770497	+	1.06050i	0.0878062	+	0.120855i
$78$		0			0
$79$	4.96261	−	15.2733i	0.558337	−	1.71839i	−0.128626	−	0.991693i	$-0.541057\pi$
$79$	4.96261	−	15.2733i	0.558337	−	1.71839i	0.686963	−	0.726692i	$-0.258943\pi$
$80$	1.70582	−	1.44575i	0.190716	−	0.161639i
$81$		0			0
$82$		−	7.58064i		−	0.837142i
$83$	−14.3983	+	4.67828i	−1.58041	+	0.513508i	−0.962163	−	0.272474i	$-0.912158\pi$
$83$	−14.3983	+	4.67828i	−1.58041	+	0.513508i	−0.618250	+	0.785981i	$0.712158\pi$
$84$		0			0
$85$	0.315836	+	4.21769i	0.0342573	+	0.457473i
$86$	−2.33776	+	1.69848i	−0.252087	+	0.183152i
$87$		0			0
$88$	2.81761	−	3.87811i	0.300358	−	0.413408i
$89$	11.9956	−	8.71529i	1.27153	−	0.923819i	0.272265	−	0.962222i	$-0.412227\pi$
$89$	11.9956	−	8.71529i	1.27153	−	0.923819i	0.999262	+	0.0384036i	$0.0122272\pi$
$90$		0			0
$91$	0.383418	+	0.278570i	0.0401932	+	0.0292020i
$92$	−4.41846	+	1.43564i	−0.460656	+	0.149676i
$93$		0			0
$94$	0.367130	+	1.12991i	0.0378665	+	0.116541i
$95$	−6.71316	+	0.502706i	−0.688756	+	0.0515765i
$96$		0			0
$97$	5.59789	+	1.81886i	0.568379	+	0.184678i	0.579088	−	0.815265i	$-0.303409\pi$
$97$	5.59789	+	1.81886i	0.568379	+	0.184678i	−0.0107087	+	0.999943i	$0.503409\pi$
$98$	4.07054	+	5.60262i	0.411187	+	0.565950i
$99$		0			0
$100$	3.56227	−	3.50859i	0.356227	−	0.350859i
$101$	−4.83576			−0.481176			−0.240588	−	0.970627i	$-0.577340\pi$
$101$	−4.83576			−0.481176			−0.240588	+	0.970627i	$0.577340\pi$
$102$		0			0
$103$	−0.0694118	−	0.0225533i	−0.00683935	−	0.00222224i	0.305595	−	0.952161i	$-0.401145\pi$
$103$	−0.0694118	−	0.0225533i	−0.00683935	−	0.00222224i	−0.312435	+	0.949939i	$0.601145\pi$
$104$	0.535560	−	1.64828i	0.0525159	−	0.161627i
$105$		0			0
$106$	3.58924	+	11.0465i	0.348618	+	1.07293i
$107$			5.84754i			0.565303i	0.959223	+	0.282651i	$0.0912140\pi$
$107$			5.84754i			0.565303i	−0.959223	+	0.282651i	$0.908786\pi$
$108$		0			0
$109$	−7.93329	−	5.76388i	−0.759872	−	0.552079i	0.138999	−	0.990292i	$-0.455611\pi$
$109$	−7.93329	−	5.76388i	−0.759872	−	0.552079i	−0.898871	+	0.438213i	$0.855611\pi$
$110$	5.63522	−	9.11798i	0.537297	−	0.869365i
$111$		0			0
$112$	−0.160734	+	0.221232i	−0.0151880	+	0.0209044i
$113$	10.1858	−	14.0196i	0.958201	−	1.31885i	0.0104140	−	0.999946i	$-0.496685\pi$
$113$	10.1858	−	14.0196i	0.958201	−	1.31885i	0.947787	−	0.318905i	$-0.103315\pi$
$114$		0			0
$115$	−9.61267	+	3.93902i	−0.896386	+	0.367315i
$116$	7.35166	+	5.34129i	0.682585	+	0.495927i
$117$		0			0
$118$			14.2895i			1.31545i
$119$	−0.159837	−	0.491927i	−0.0146522	−	0.0450949i
$120$		0			0
$121$	3.70160	−	11.3924i	0.336510	−	1.03567i
$122$	4.89919	+	1.59184i	0.443552	+	0.144119i
$123$		0			0
$124$	−3.83390			−0.344294
$125$	7.35738	−	8.41837i	0.658064	−	0.752962i
$126$		0			0
$127$	10.7963	+	14.8598i	0.958013	+	1.31859i	0.947875	+	0.318643i	$0.103227\pi$
$127$	10.7963	+	14.8598i	0.958013	+	1.31859i	0.0101377	+	0.999949i	$0.496773\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$		0			0
$130$	0.918978	−	3.76481i	0.0805997	−	0.330196i
$131$	2.34036	+	7.20289i	0.204478	+	0.629320i	0.999734	+	0.0230460i	$0.00733641\pi$
$131$	2.34036	+	7.20289i	0.204478	+	0.629320i	−0.795256	+	0.606274i	$0.792664\pi$
$132$		0			0
$133$	0.782983	−	0.254407i	0.0678932	−	0.0220598i
$134$	5.08872	+	3.69717i	0.439598	+	0.319387i
$135$		0			0
$136$	−1.53025	+	1.11179i	−0.131218	+	0.0953353i
$137$	−11.5262	+	15.8644i	−0.984747	+	1.35539i	−0.0505148	+	0.998723i	$0.516086\pi$
$137$	−11.5262	+	15.8644i	−0.984747	+	1.35539i	−0.934232	+	0.356665i	$0.883914\pi$
$138$		0			0
$139$	7.73836	−	5.62225i	0.656359	−	0.476873i	−0.209072	−	0.977900i	$-0.567044\pi$
$139$	7.73836	−	5.62225i	0.656359	−	0.476873i	0.865431	+	0.501027i	$0.167044\pi$
$140$	−0.321469	+	0.520147i	−0.0271691	+	0.0439604i
$141$		0			0
$142$	1.33354	−	0.433294i	0.111908	−	0.0363612i
$143$		−	8.30783i		−	0.694736i
$144$		0			0
$145$	17.2848	+	10.6826i	1.43542	+	0.887141i
$146$	0.550396	−	1.69394i	0.0455511	−	0.140192i
$147$		0			0
$148$	−5.29563	−	7.28881i	−0.435298	−	0.599137i
$149$	−4.64398			−0.380449			−0.190225	−	0.981741i	$-0.560922\pi$
$149$	−4.64398			−0.380449			−0.190225	+	0.981741i	$0.560922\pi$
$150$		0			0
$151$	−16.7881			−1.36619			−0.683097	−	0.730327i	$-0.739368\pi$
$151$	−16.7881			−1.36619			−0.683097	+	0.730327i	$0.739368\pi$
$152$	−1.76960	−	2.43564i	−0.143533	−	0.197557i
$153$		0			0
$154$	−0.405074	+	1.24669i	−0.0326418	+	0.100461i
$155$	−8.54892	+	0.640175i	−0.686666	+	0.0514201i
$156$		0			0
$157$		−	5.57763i		−	0.445143i	−0.974916	−	0.222572i	$-0.928555\pi$
$157$		−	5.57763i		−	0.445143i	0.974916	−	0.222572i	$-0.0714451\pi$
$158$	15.2733	−	4.96261i	1.21508	−	0.394804i
$159$		0			0
$160$	2.17229	+	0.530249i	0.171734	+	0.0419198i
$161$	1.02781	−	0.746746i	0.0810026	−	0.0588518i
$162$		0			0
$163$	−10.8007	+	14.8659i	−0.845978	+	1.16439i	0.138757	+	0.990327i	$0.455689\pi$
$163$	−10.8007	+	14.8659i	−0.845978	+	1.16439i	−0.984735	+	0.174062i	$0.944311\pi$
$164$	6.13287	−	4.45579i	0.478897	−	0.347939i
$165$		0			0
$166$	−12.2479	−	8.89861i	−0.950620	−	0.690666i
$167$	−8.50651	+	2.76393i	−0.658253	+	0.213879i	−0.619050	−	0.785352i	$-0.712482\pi$
$167$	−8.50651	+	2.76393i	−0.658253	+	0.213879i	−0.0392036	+	0.999231i	$0.512482\pi$
$168$		0			0
$169$	3.08904	+	9.50708i	0.237618	+	0.731314i
$170$	−3.22654	+	2.73462i	−0.247465	+	0.209735i
$171$		0			0
$172$	−2.74820	−	0.892944i	−0.209548	−	0.0680863i
$173$	7.00354	+	9.63954i	0.532469	+	0.732881i	0.987504	−	0.157593i	$-0.0503733\pi$
$173$	7.00354	+	9.63954i	0.532469	+	0.732881i	−0.455035	+	0.890473i	$0.650373\pi$
$174$		0			0
$175$	−0.629966	+	1.21351i	−0.0476209	+	0.0917331i
$176$	4.79360			0.361332
$177$		0			0
$178$	14.1016	+	4.58190i	1.05696	+	0.343428i
$179$	−1.16073	+	3.57237i	−0.0867574	+	0.267012i	−0.985018	−	0.172451i	$-0.944831\pi$
$179$	−1.16073	+	3.57237i	−0.0867574	+	0.267012i	0.898261	+	0.439463i	$0.144831\pi$
$180$		0			0
$181$	−5.58164	−	17.1785i	−0.414880	−	1.27687i	−0.912358	−	0.409393i	$-0.865740\pi$
$181$	−5.58164	−	17.1785i	−0.414880	−	1.27687i	0.497478	−	0.867477i	$-0.334260\pi$
$182$			0.473931i			0.0351301i
$183$		0			0
$184$	−3.75856	−	2.73076i	−0.277085	−	0.201314i
$185$	−13.0254	−	15.3685i	−0.957647	−	1.12992i
$186$		0			0
$187$	−5.32949	+	7.33541i	−0.389731	+	0.536418i
$188$	−0.698322	+	0.961158i	−0.0509304	+	0.0700997i
$189$		0			0
$190$	−4.35259	−	5.13558i	−0.315770	−	0.372574i
$191$	−13.4303	−	9.75767i	−0.971781	−	0.706040i	−0.0159240	−	0.999873i	$-0.505069\pi$
$191$	−13.4303	−	9.75767i	−0.971781	−	0.706040i	−0.955857	+	0.293833i	$0.905069\pi$
$192$		0			0
$193$			3.84858i			0.277027i	0.990361	+	0.138513i	$0.0442324\pi$
$193$			3.84858i			0.277027i	−0.990361	+	0.138513i	$0.955768\pi$
$194$	1.81886	+	5.59789i	0.130587	+	0.401905i
$195$		0			0
$196$	−2.14001	+	6.58628i	−0.152858	+	0.470448i
$197$	10.2174	+	3.31984i	0.727960	+	0.236529i	0.649471	−	0.760386i	$-0.274990\pi$
$197$	10.2174	+	3.31984i	0.727960	+	0.236529i	0.0784892	+	0.996915i	$0.474990\pi$
$198$		0			0
$199$	−2.49808			−0.177084			−0.0885421	−	0.996072i	$-0.528221\pi$
$199$	−2.49808			−0.177084			−0.0885421	+	0.996072i	$0.528221\pi$
$200$	4.93236	+	0.819639i	0.348771	+	0.0579572i
$201$		0			0
$202$	−2.84239	−	3.91221i	−0.199990	−	0.275262i
$203$	−2.36333	−	0.767892i	−0.165873	−	0.0538954i
$204$		0			0
$205$	12.9312	−	10.9597i	0.903155	−	0.765458i
$206$	−0.0225533	−	0.0694118i	−0.00157136	−	0.00483615i
$207$		0			0
$208$	1.64828	−	0.535560i	0.114288	−	0.0371344i
$209$	−11.6755	−	8.48276i	−0.807612	−	0.586765i
$210$		0			0
$211$	−19.6381	+	14.2679i	−1.35194	+	0.982245i	−0.353032	+	0.935611i	$0.614849\pi$
$211$	−19.6381	+	14.2679i	−1.35194	+	0.982245i	−0.998912	+	0.0466338i	$0.985151\pi$
$212$	−6.82714	+	9.39675i	−0.468890	+	0.645371i
$213$		0			0
$214$	−4.73076	+	3.43710i	−0.323388	+	0.234955i
$215$	−6.27710	−	1.53222i	−0.428095	−	0.104497i
$216$		0			0
$217$	0.997095	−	0.323976i	0.0676872	−	0.0219929i
$218$		−	9.80609i		−	0.664152i
$219$		0			0
$220$	10.6889	−	0.800424i	0.720645	−	0.0539646i
$221$	−1.01301	+	3.11771i	−0.0681422	+	0.209720i
$222$		0			0
$223$	−7.67291	−	10.5609i	−0.513816	−	0.707207i	0.470741	−	0.882271i	$-0.343987\pi$
$223$	−7.67291	−	10.5609i	−0.513816	−	0.707207i	−0.984557	+	0.175064i	$0.943987\pi$
$224$	−0.273457			−0.0182711
$225$		0			0
$226$	17.3291			1.15272
$227$	−4.15067	−	5.71290i	−0.275489	−	0.379179i	0.648744	−	0.761007i	$-0.275295\pi$
$227$	−4.15067	−	5.71290i	−0.275489	−	0.379179i	−0.924233	+	0.381828i	$0.875295\pi$
$228$		0			0
$229$	3.88654	−	11.9615i	0.256830	−	0.790441i	−0.736634	−	0.676292i	$-0.763586\pi$
$229$	3.88654	−	11.9615i	0.256830	−	0.790441i	0.993464	−	0.114149i	$-0.0364143\pi$
$230$	−8.83692	−	5.46151i	−0.582689	−	0.360122i
$231$		0			0
$232$			9.08715i			0.596601i
$233$	−9.32536	+	3.02999i	−0.610925	+	0.198501i	−0.598107	−	0.801416i	$-0.704080\pi$
$233$	−9.32536	+	3.02999i	−0.610925	+	0.198501i	−0.0128179	+	0.999918i	$0.504080\pi$
$234$		0			0
$235$	−1.39664	+	2.25982i	−0.0911071	+	0.147414i
$236$	−11.5604	+	8.39915i	−0.752521	+	0.546738i
$237$		0			0
$238$	0.304027	−	0.418458i	0.0197072	−	0.0271246i
$239$	−4.07768	+	2.96261i	−0.263763	+	0.191635i	−0.711805	−	0.702378i	$-0.752122\pi$
$239$	−4.07768	+	2.96261i	−0.263763	+	0.191635i	0.448041	+	0.894013i	$0.352122\pi$
$240$		0			0
$241$	−5.53446	−	4.02102i	−0.356506	−	0.259017i	0.395087	−	0.918644i	$-0.370714\pi$
$241$	−5.53446	−	4.02102i	−0.356506	−	0.259017i	−0.751593	+	0.659627i	$0.770714\pi$
$242$	11.3924	−	3.70160i	0.732329	−	0.237948i
$243$		0			0
$244$	1.59184	+	4.89919i	0.101907	+	0.313638i
$245$	−3.67209	+	15.0436i	−0.234601	+	0.961099i
$246$		0			0
$247$	−4.96236	−	1.61237i	−0.315747	−	0.102592i
$248$	−2.25351	−	3.10169i	−0.143098	−	0.196957i
$249$		0			0
$250$	11.1352	+	1.00406i	0.704250	+	0.0635021i
$251$	7.07549			0.446601			0.223301	−	0.974750i	$-0.428317\pi$
$251$	7.07549			0.446601			0.223301	+	0.974750i	$0.428317\pi$
$252$		0			0
$253$	−21.1803	−	6.88191i	−1.33160	−	0.432662i
$254$	−5.67593	+	17.4687i	−0.356139	+	1.09608i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			4.47318i			0.279029i	0.990220	+	0.139515i	$0.0445542\pi$
$257$			4.47318i			0.279029i	−0.990220	+	0.139515i	$0.955446\pi$
$258$		0			0
$259$	1.99318	+	1.44813i	0.123850	+	0.0899824i
$260$	3.58596	−	1.46943i	0.222392	−	0.0911302i
$261$		0			0
$262$	−4.45163	+	6.12715i	−0.275023	+	0.378536i
$263$	−1.47083	+	2.02442i	−0.0906950	+	0.124831i	−0.851953	−	0.523618i	$-0.824582\pi$
$263$	−1.47083	+	2.02442i	−0.0906950	+	0.124831i	0.761258	+	0.648449i	$0.224582\pi$
$264$		0			0
$265$	−13.6543	+	22.0931i	−0.838775	+	1.35717i
$266$	0.666045	+	0.483910i	0.0408378	+	0.0296704i
$267$		0			0
$268$			6.29000i			0.384223i
$269$	1.91241	+	5.88580i	0.116602	+	0.358864i	0.992278	−	0.124036i	$-0.0395837\pi$
$269$	1.91241	+	5.88580i	0.116602	+	0.358864i	−0.875676	+	0.482899i	$0.839584\pi$
$270$		0			0
$271$	4.06941	−	12.5244i	0.247199	−	0.760801i	−0.748068	−	0.663622i	$-0.769018\pi$
$271$	4.06941	−	12.5244i	0.247199	−	0.760801i	0.995267	−	0.0971785i	$-0.0309818\pi$
$272$	−1.79892	−	0.584503i	−0.109075	−	0.0354407i
$273$		0			0
$274$	−19.6095			−1.18465
$275$	23.7007	−	3.56961i	1.42921	−	0.215256i
$276$		0			0
$277$	−3.03717	−	4.18031i	−0.182486	−	0.251170i	0.707967	−	0.706245i	$-0.249612\pi$
$277$	−3.03717	−	4.18031i	−0.182486	−	0.251170i	−0.890453	+	0.455075i	$0.849612\pi$
$278$	9.09699	+	2.95579i	0.545601	+	0.177277i
$279$		0			0
$280$	−0.609762	+	0.0456612i	−0.0364403	+	0.00272878i
$281$	0.0145149	+	0.0446724i	0.000865889	+	0.00266493i	0.951489	−	0.307684i	$-0.0995540\pi$
$281$	0.0145149	+	0.0446724i	0.000865889	+	0.00266493i	−0.950623	+	0.310349i	$0.899554\pi$
$282$		0			0
$283$	20.8007	−	6.75856i	1.23647	−	0.401755i	0.383419	−	0.923575i	$-0.374747\pi$
$283$	20.8007	−	6.75856i	1.23647	−	0.401755i	0.853056	+	0.521820i	$0.174747\pi$
$284$	1.13438	+	0.824175i	0.0673130	+	0.0489058i
$285$		0			0
$286$	6.72118	−	4.88322i	0.397431	−	0.288751i
$287$	−1.21847	+	1.67708i	−0.0719240	+	0.0989949i
$288$		0			0
$289$	−10.8588	+	7.88941i	−0.638755	+	0.464083i
$290$	1.51735	+	20.2628i	0.0891018	+	1.18987i
$291$		0			0
$292$	1.69394	−	0.550396i	0.0991306	−	0.0322095i
$293$		−	8.35289i		−	0.487981i	−0.969778	−	0.243991i	$-0.921543\pi$
$293$		−	8.35289i		−	0.487981i	0.969778	−	0.243991i	$-0.0784566\pi$
$294$		0			0
$295$	−24.3753	+	20.6590i	−1.41918	+	1.20281i
$296$	2.78408	−	8.56851i	0.161821	−	0.498035i
$297$		0			0
$298$	−2.72966	−	3.75706i	−0.158125	−	0.217640i
$299$	−8.05174			−0.465644
$300$		0			0
$301$	0.790190			0.0455458
$302$	−9.86779	−	13.5818i	−0.567827	−	0.781547i
$303$		0			0
$304$	0.930333	−	2.86327i	0.0533583	−	0.164220i
$305$	4.36758	+	10.6585i	0.250087	+	0.610305i
$306$		0			0
$307$			2.28918i			0.130650i	0.997864	+	0.0653251i	$0.0208084\pi$
$307$			2.28918i			0.130650i	−0.997864	+	0.0653251i	$0.979192\pi$
$308$	−1.24669	+	0.405074i	−0.0710367	+	0.0230812i
$309$		0			0
$310$	−5.54284	−	6.53994i	−0.314812	−	0.371444i
$311$	20.7653	−	15.0869i	1.17749	−	0.855497i	0.185604	−	0.982625i	$-0.440576\pi$
$311$	20.7653	−	15.0869i	1.17749	−	0.855497i	0.991886	+	0.127128i	$0.0405758\pi$
$312$		0			0
$313$	17.7576	−	24.4412i	1.00372	−	1.38150i	0.0807005	−	0.996738i	$-0.474284\pi$
$313$	17.7576	−	24.4412i	1.00372	−	1.38150i	0.923017	−	0.384760i	$-0.125716\pi$
$314$	4.51240	−	3.27845i	0.254649	−	0.185013i
$315$		0			0
$316$	12.9923	+	9.43945i	0.730873	+	0.531010i
$317$	24.5955	−	7.99157i	1.38142	−	0.448851i	0.478286	−	0.878204i	$-0.341258\pi$
$317$	24.5955	−	7.99157i	1.38142	−	0.448851i	0.903137	+	0.429353i	$0.141258\pi$
$318$		0			0
$319$	13.4608	+	41.4282i	0.753663	+	2.31954i
$320$	0.847859	+	2.06909i	0.0473967	+	0.115666i
$321$		0			0
$322$	1.20826	+	0.392588i	0.0673337	+	0.0218781i
$323$	3.34718	+	4.60700i	0.186242	+	0.256340i
$324$		0			0
$325$	7.75069	−	3.87535i	0.429931	−	0.214965i
$326$	−18.3753			−1.01771
$327$		0			0
$328$	7.20962	+	2.34255i	0.398085	+	0.129346i
$329$	0.100394	−	0.308982i	0.00553492	−	0.0170347i
$330$		0			0
$331$	4.48366	+	13.7993i	0.246444	+	0.758477i	0.995396	+	0.0958519i	$0.0305575\pi$
$331$	4.48366	+	13.7993i	0.246444	+	0.758477i	−0.748952	+	0.662625i	$0.769442\pi$
$332$		−	15.1392i		−	0.830873i
$333$		0			0
$334$	−7.23607	−	5.25731i	−0.395940	−	0.287667i
$335$	1.05029	+	14.0256i	0.0573834	+	0.766300i
$336$		0			0
$337$	−6.50536	+	8.95385i	−0.354369	+	0.487747i	−0.948569	−	0.316570i	$-0.897469\pi$
$337$	−6.50536	+	8.95385i	−0.354369	+	0.487747i	0.594200	+	0.804317i	$0.297469\pi$
$338$	−5.87570	+	8.08721i	−0.319596	+	0.439886i
$339$		0			0
$340$	−4.10886	−	1.00296i	−0.222834	−	0.0543932i
$341$	−14.8683	−	10.8024i	−0.805162	−	0.584984i
$342$		0			0
$343$		−	3.80796i		−	0.205610i
$344$	−0.892944	−	2.74820i	−0.0481443	−	0.148173i
$345$		0			0
$346$	−3.68198	+	11.3320i	−0.197944	+	0.609210i
$347$	0.961158	+	0.312299i	0.0515977	+	0.0167651i	0.334702	−	0.942324i	$-0.391364\pi$
$347$	0.961158	+	0.312299i	0.0515977	+	0.0167651i	−0.283104	+	0.959089i	$0.591364\pi$
$348$		0			0
$349$	−30.4268			−1.62871			−0.814356	−	0.580366i	$-0.802910\pi$
$349$	−30.4268			−1.62871			−0.814356	+	0.580366i	$0.802910\pi$
$350$	−1.35204	+	0.203633i	−0.0722695	+	0.0108846i
$351$		0			0
$352$	2.81761	+	3.87811i	0.150179	+	0.206704i
$353$	−14.8932	−	4.83911i	−0.792687	−	0.257560i	−0.115439	−	0.993315i	$-0.536828\pi$
$353$	−14.8932	−	4.83911i	−0.792687	−	0.257560i	−0.677248	+	0.735755i	$0.736828\pi$
$354$		0			0
$355$	2.66708	+	1.64835i	0.141554	+	0.0874853i
$356$	4.58190	+	14.1016i	0.242840	+	0.747385i
$357$		0			0
$358$	−3.57237	+	1.16073i	−0.188806	+	0.0613467i
$359$	−3.53800	−	2.57051i	−0.186729	−	0.135666i	0.490494	−	0.871445i	$-0.336816\pi$
$359$	−3.53800	−	2.57051i	−0.186729	−	0.135666i	−0.677222	+	0.735778i	$0.736816\pi$
$360$		0			0
$361$	8.03852	−	5.84033i	0.423080	−	0.307386i
$362$	10.6169	−	14.6129i	0.558013	−	0.768039i
$363$		0			0
$364$	−0.383418	+	0.278570i	−0.0200966	+	0.0146010i
$365$	3.68529	−	1.51014i	0.192897	−	0.0790442i
$366$		0			0
$367$	20.7648	−	6.74689i	1.08391	−	0.352185i	0.288022	−	0.957624i	$-0.407003\pi$
$367$	20.7648	−	6.74689i	1.08391	−	0.352185i	0.795892	+	0.605439i	$0.207003\pi$
$368$		−	4.64584i		−	0.242181i
$369$		0			0
$370$	4.77726	−	19.5712i	0.248358	−	1.01746i
$371$	0.981504	−	3.02076i	0.0509571	−	0.156830i
$372$		0			0
$373$	0.833899	+	1.14776i	0.0431776	+	0.0594289i	0.830060	−	0.557674i	$-0.188306\pi$
$373$	0.833899	+	1.14776i	0.0431776	+	0.0594289i	−0.786882	+	0.617103i	$0.788306\pi$
$374$	−9.06706			−0.468847
$375$		0			0
$376$	−1.18806			−0.0612694
$377$	9.25703	+	12.7412i	0.476762	+	0.656206i
$378$		0			0
$379$	8.05934	−	24.8041i	0.413981	−	1.27410i	−0.499179	−	0.866499i	$-0.666365\pi$
$379$	8.05934	−	24.8041i	0.413981	−	1.27410i	0.913159	−	0.407603i	$-0.133635\pi$
$380$	1.59638	−	6.53994i	0.0818925	−	0.335492i
$381$		0			0
$382$		−	16.6007i		−	0.849367i
$383$	−31.1609	+	10.1248i	−1.59225	+	0.517353i	−0.965175	−	0.261607i	$-0.915748\pi$
$383$	−31.1609	+	10.1248i	−1.59225	+	0.517353i	−0.627074	+	0.778960i	$0.715748\pi$
$384$		0			0
$385$	−2.71226	+	1.11141i	−0.138230	+	0.0566429i
$386$	−3.11356	+	2.26214i	−0.158476	+	0.115140i
$387$		0			0
$388$	−3.45968	+	4.76185i	−0.175639	+	0.241746i
$389$	3.60929	−	2.62231i	0.182998	−	0.132956i	−0.492515	−	0.870304i	$-0.663922\pi$
$389$	3.60929	−	2.62231i	0.182998	−	0.132956i	0.675513	+	0.737348i	$0.263922\pi$
$390$		0			0
$391$	7.10929	+	5.16520i	0.359532	+	0.261216i
$392$	−6.58628	+	2.14001i	−0.332657	+	0.108087i
$393$		0			0
$394$	3.31984	+	10.2174i	0.167251	+	0.514746i
$395$	30.5467	+	18.8789i	1.53697	+	0.949900i
$396$		0			0
$397$	2.01364	+	0.654271i	0.101062	+	0.0328369i	0.359111	−	0.933295i	$-0.383080\pi$
$397$	2.01364	+	0.654271i	0.101062	+	0.0328369i	−0.258050	+	0.966132i	$0.583080\pi$
$398$	−1.46833	−	2.02099i	−0.0736009	−	0.101303i
$399$		0			0
$400$	2.23607	+	4.47214i	0.111803	+	0.223607i
$401$	28.6530			1.43086			0.715431	−	0.698683i	$-0.246230\pi$
$401$	28.6530			1.43086			0.715431	+	0.698683i	$0.246230\pi$
$402$		0			0
$403$	−6.31935	−	2.05328i	−0.314789	−	0.102281i
$404$	1.49433	−	4.59908i	0.0743458	−	0.228813i
$405$		0			0
$406$	−0.767892	−	2.36333i	−0.0381098	−	0.117290i
$407$		−	43.1878i		−	2.14074i
$408$		0			0
$409$	31.8385	+	23.1320i	1.57431	+	1.14381i	0.922872	+	0.385107i	$0.125835\pi$
$409$	31.8385	+	23.1320i	1.57431	+	1.14381i	0.651442	+	0.758699i	$0.274165\pi$
$410$	16.4673	+	4.01963i	0.813264	+	0.198515i
$411$		0			0
$412$	0.0428988	−	0.0590452i	0.00211347	−	0.00290895i
$413$	2.29681	−	3.16129i	0.113019	−	0.155557i
$414$		0			0
$415$	−2.52791	−	33.7578i	−0.124090	−	1.65711i
$416$	1.40211	+	1.01869i	0.0687442	+	0.0499456i
$417$		0			0
$418$		−	14.4317i		−	0.705879i
$419$	4.35926	+	13.4164i	0.212964	+	0.655434i	0.999292	+	0.0376256i	$0.0119794\pi$
$419$	4.35926	+	13.4164i	0.212964	+	0.655434i	−0.786328	+	0.617809i	$0.788021\pi$
$420$		0			0
$421$	5.03839	−	15.5066i	0.245556	−	0.755744i	−0.749988	−	0.661451i	$-0.769941\pi$
$421$	5.03839	−	15.5066i	0.245556	−	0.755744i	0.995545	−	0.0942928i	$-0.0300590\pi$
$422$	−23.0860	−	7.50110i	−1.12381	−	0.365148i
$423$		0			0
$424$	−11.6150			−0.564075
$425$	−9.32952	−	1.55034i	−0.452548	−	0.0752025i
$426$		0			0
$427$	−0.827992	−	1.13963i	−0.0400693	−	0.0551507i
$428$	−5.56134	−	1.80699i	−0.268817	−	0.0873441i
$429$		0			0
$430$	−2.45000	−	5.97890i	−0.118149	−	0.288328i
$431$	0.612525	+	1.88516i	0.0295043	+	0.0908048i	0.964724	−	0.263262i	$-0.0847985\pi$
$431$	0.612525	+	1.88516i	0.0295043	+	0.0908048i	−0.935220	+	0.354067i	$0.884798\pi$
$432$		0			0
$433$	4.26971	−	1.38731i	0.205189	−	0.0666699i	−0.204619	−	0.978842i	$-0.565596\pi$
$433$	4.26971	−	1.38731i	0.205189	−	0.0666699i	0.409808	+	0.912172i	$0.365596\pi$
$434$	0.848180	+	0.616239i	0.0407139	+	0.0295804i
$435$		0			0
$436$	7.93329	−	5.76388i	0.379936	−	0.276040i
$437$	−8.22128	+	11.3156i	−0.393277	+	0.541299i
$438$		0			0
$439$	20.8045	−	15.1154i	0.992946	−	0.721417i	0.0323816	−	0.999476i	$-0.489691\pi$
$439$	20.8045	−	15.1154i	0.992946	−	0.721417i	0.960564	+	0.278058i	$0.0896908\pi$
$440$	6.93033	+	8.17702i	0.330391	+	0.389824i
$441$		0			0
$442$	−3.11771	+	1.01301i	−0.148294	+	0.0481838i
$443$			29.1477i			1.38485i	0.721491	+	0.692423i	$0.243457\pi$
$443$			29.1477i			1.38485i	−0.721491	+	0.692423i	$0.756543\pi$
$444$		0			0
$445$	12.5715	+	30.6791i	0.595946	+	1.45433i
$446$	4.03389	−	12.4150i	0.191010	−	0.587869i
$447$		0			0
$448$	−0.160734	−	0.221232i	−0.00759398	−	0.0104522i
$449$	−5.14037			−0.242589			−0.121295	−	0.992617i	$-0.538705\pi$
$449$	−5.14037			−0.242589			−0.121295	+	0.992617i	$0.538705\pi$
$450$		0			0
$451$	36.3386			1.71112
$452$	10.1858	+	14.0196i	0.479100	+	0.659425i
$453$		0			0
$454$	2.18213	−	6.71592i	0.102413	−	0.315194i
$455$	−0.808441	+	0.685184i	−0.0379003	+	0.0321219i
$456$		0			0
$457$		−	20.8445i		−	0.975066i	−0.873105	−	0.487533i	$-0.837897\pi$
$457$		−	20.8445i		−	0.975066i	0.873105	−	0.487533i	$-0.162103\pi$
$458$	11.9615	−	3.88654i	0.558926	−	0.181606i
$459$		0			0
$460$	−0.775751	−	10.3594i	−0.0361696	−	0.483010i
$461$	−4.02072	+	2.92123i	−0.187264	+	0.136055i	−0.677467	−	0.735553i	$-0.736922\pi$
$461$	−4.02072	+	2.92123i	−0.187264	+	0.136055i	0.490204	+	0.871608i	$0.336922\pi$
$462$		0			0
$463$	4.17718	−	5.74940i	0.194130	−	0.267197i	−0.700845	−	0.713314i	$-0.747193\pi$
$463$	4.17718	−	5.74940i	0.194130	−	0.267197i	0.894975	+	0.446117i	$0.147193\pi$
$464$	−7.35166	+	5.34129i	−0.341292	+	0.247963i
$465$		0			0
$466$	−7.93263	−	5.76339i	−0.367472	−	0.266984i
$467$	28.7049	−	9.32679i	1.32831	−	0.431592i	0.442966	−	0.896538i	$-0.353926\pi$
$467$	28.7049	−	9.32679i	1.32831	−	0.431592i	0.885339	+	0.464946i	$0.153926\pi$
$468$		0			0
$469$	−0.531524	−	1.63586i	−0.0245435	−	0.0755371i
$470$	−2.64916	+	0.198379i	−0.122197	+	0.00915053i
$471$		0			0
$472$	−13.5901	−	4.41570i	−0.625536	−	0.203249i
$473$	−8.14184	−	11.2063i	−0.374362	−	0.515265i
$474$		0			0
$475$	2.46762	−	14.8495i	0.113222	−	0.681341i
$476$	0.517242			0.0237078
$477$		0			0
$478$	−4.79360	−	1.55754i	−0.219254	−	0.0712401i
$479$	8.60350	−	26.4788i	0.393104	−	1.20985i	−0.537325	−	0.843376i	$-0.680565\pi$
$479$	8.60350	−	26.4788i	0.393104	−	1.20985i	0.930428	−	0.366474i	$-0.119435\pi$
$480$		0			0
$481$	−4.82511	−	14.8502i	−0.220006	−	0.677109i
$482$		−	6.84097i		−	0.311598i
$483$		0			0
$484$	9.69093	+	7.04087i	0.440497	+	0.320040i
$485$	−6.91937	+	11.1958i	−0.314192	+	0.508374i
$486$		0			0
$487$	0.763835	−	1.05133i	0.0346127	−	0.0476402i	−0.791360	−	0.611351i	$-0.790627\pi$
$487$	0.763835	−	1.05133i	0.0346127	−	0.0476402i	0.825973	+	0.563710i	$0.190627\pi$
$488$	−3.02786	+	4.16750i	−0.137065	+	0.188654i
$489$		0			0
$490$	−14.3289	+	5.87161i	−0.647314	+	0.265252i
$491$	15.5048	+	11.2649i	0.699723	+	0.508379i	0.879842	−	0.475266i	$-0.157648\pi$
$491$	15.5048	+	11.2649i	0.699723	+	0.508379i	−0.180119	+	0.983645i	$0.557648\pi$
$492$		0			0
$493$		−	17.1883i		−	0.774121i
$494$	−1.61237	−	4.96236i	−0.0725438	−	0.223267i
$495$		0			0
$496$	1.18474	−	3.64625i	0.0531964	−	0.163722i
$497$	−0.364667	−	0.118488i	−0.0163576	−	0.00531489i
$498$		0			0
$499$	−6.41339			−0.287103			−0.143551	−	0.989643i	$-0.545852\pi$
$499$	−6.41339			−0.287103			−0.143551	+	0.989643i	$0.545852\pi$
$500$	5.73279	+	9.59871i	0.256378	+	0.429267i
$501$		0			0
$502$	4.15887	+	5.72419i	0.185619	+	0.255483i
$503$	−34.0189	−	11.0534i	−1.51683	−	0.492848i	−0.571956	−	0.820284i	$-0.693815\pi$
$503$	−34.0189	−	11.0534i	−1.51683	−	0.492848i	−0.944873	+	0.327436i	$0.893815\pi$
$504$		0			0
$505$	2.56416	−	10.5047i	0.114104	−	0.467452i
$506$	−6.88191	−	21.1803i	−0.305938	−	0.941581i
$507$		0			0
$508$	−17.4687	+	5.67593i	−0.775049	+	0.251829i
$509$	−9.75570	−	7.08793i	−0.432414	−	0.314167i	0.350200	−	0.936675i	$-0.386114\pi$
$509$	−9.75570	−	7.08793i	−0.432414	−	0.314167i	−0.782613	+	0.622508i	$0.786114\pi$
$510$		0			0
$511$	−0.394040	+	0.286287i	−0.0174313	+	0.0126646i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$		0			0
$514$	−3.61888	+	2.62927i	−0.159622	+	0.115972i
$515$	0.0857977	−	0.138824i	0.00378070	−	0.00611730i
$516$		0			0
$517$	−5.41634	+	1.75987i	−0.238210	+	0.0773992i
$518$			2.46371i			0.108249i
$519$		0			0
$520$	3.29657	+	2.03739i	0.144564	+	0.0893454i
$521$	−1.08563	+	3.34124i	−0.0475625	+	0.146382i	−0.972017	−	0.234909i	$-0.924521\pi$
$521$	−1.08563	+	3.34124i	−0.0475625	+	0.146382i	0.924455	+	0.381292i	$0.124521\pi$
$522$		0			0
$523$	14.3695	+	19.7779i	0.628333	+	0.864826i	0.997926	−	0.0643677i	$-0.0205030\pi$
$523$	14.3695	+	19.7779i	0.628333	+	0.864826i	−0.369593	+	0.929194i	$0.620503\pi$
$524$	−7.57357			−0.330853
$525$		0			0
$526$	−2.50232			−0.109106
$527$	4.26249	+	5.86682i	0.185677	+	0.255563i
$528$		0			0
$529$	0.437616	−	1.34684i	0.0190268	−	0.0585584i
$530$	−25.8995	+	1.93945i	−1.12500	+	0.0842442i
$531$		0			0
$532$			0.823277i			0.0356936i
$533$	12.4950	−	4.05989i	0.541220	−	0.175853i
$534$		0			0
$535$	−12.7025	−	3.10065i	−0.549179	−	0.134053i
$536$	−5.08872	+	3.69717i	−0.219799	+	0.159693i
$537$		0			0
$538$	−3.63763	+	5.00676i	−0.156829	+	0.215857i
$539$	−26.8568	+	19.5126i	−1.15680	+	0.840466i
$540$		0			0
$541$	31.3407	+	22.7703i	1.34744	+	0.978974i	0.999135	+	0.0415933i	$0.0132434\pi$
$541$	31.3407	+	22.7703i	1.34744	+	0.978974i	0.348307	+	0.937380i	$0.386757\pi$
$542$	12.5244	−	4.06941i	0.537967	−	0.174796i
$543$		0			0
$544$	−0.584503	−	1.79892i	−0.0250604	−	0.0771279i
$545$	16.7274	−	14.1771i	0.716524	−	0.607281i
$546$		0			0
$547$	−28.8377	−	9.36994i	−1.23301	−	0.400630i	−0.381207	−	0.924490i	$-0.624491\pi$
$547$	−28.8377	−	9.36994i	−1.23301	−	0.400630i	−0.851804	+	0.523860i	$0.824491\pi$
$548$	−11.5262	−	15.8644i	−0.492374	−	0.677694i
$549$		0			0
$550$	16.8188	+	17.0761i	0.717156	+	0.728128i
$551$	27.3580			1.16549
$552$		0			0
$553$	−4.17661	−	1.35706i	−0.177608	−	0.0577082i
$554$	1.59673	−	4.91424i	0.0678387	−	0.208786i
$555$		0			0
$556$	2.95579	+	9.09699i	0.125353	+	0.385798i
$557$		−	25.7254i		−	1.09002i	−0.838430	−	0.545010i	$-0.816526\pi$
$557$		−	25.7254i		−	1.09002i	0.838430	−	0.545010i	$-0.183474\pi$
$558$		0			0
$559$	−4.05158	−	2.94365i	−0.171364	−	0.124503i
$560$	−0.395350	−	0.466469i	−0.0167066	−	0.0197119i
$561$		0			0
$562$	−0.0276091	+	0.0380006i	−0.00116462	+	0.00160296i
$563$	18.0058	−	24.7829i	0.758854	−	1.04447i	−0.238454	−	0.971154i	$-0.576641\pi$
$563$	18.0058	−	24.7829i	0.758854	−	1.04447i	0.997308	−	0.0733197i	$-0.0233593\pi$
$564$		0			0
$565$	25.0535	+	29.5604i	1.05401	+	1.24361i
$566$	17.6942	+	12.8556i	0.743741	+	0.540359i
$567$		0			0
$568$			1.40217i			0.0588337i
$569$	3.85826	+	11.8745i	0.161747	+	0.497805i	0.998782	−	0.0493440i	$-0.0157131\pi$
$569$	3.85826	+	11.8745i	0.161747	+	0.497805i	−0.837035	+	0.547149i	$0.815713\pi$
$570$		0			0
$571$	−7.52655	+	23.1644i	−0.314976	+	0.969398i	0.660788	+	0.750573i	$0.270222\pi$
$571$	−7.52655	+	23.1644i	−0.314976	+	0.969398i	−0.975764	+	0.218825i	$0.929778\pi$
$572$	7.90122	+	2.56726i	0.330366	+	0.107343i
$573$		0			0
$574$	−2.07298			−0.0865247
$575$	−3.45958	−	22.9701i	−0.144274	−	0.957921i
$576$		0			0
$577$	−1.88827	−	2.59898i	−0.0786098	−	0.108197i	0.767901	−	0.640568i	$-0.221301\pi$
$577$	−1.88827	−	2.59898i	−0.0786098	−	0.108197i	−0.846511	+	0.532371i	$0.821301\pi$
$578$	−12.7653	−	4.14771i	−0.530968	−	0.172522i
$579$		0			0
$580$	−15.5010	+	13.1377i	−0.643646	+	0.545514i
$581$	1.27931	+	3.93731i	0.0530747	+	0.163347i
$582$		0			0
$583$	−52.9527	+	17.2054i	−2.19308	+	0.712574i
$584$	1.44095	+	1.04691i	0.0596271	+	0.0433216i
$585$		0			0
$586$	6.75763	−	4.90971i	0.279155	−	0.202818i
$587$	8.92797	−	12.2883i	0.368497	−	0.507192i	−0.583995	−	0.811757i	$-0.698511\pi$
$587$	8.92797	−	12.2883i	0.368497	−	0.507192i	0.952491	+	0.304565i	$0.0985112\pi$
$588$		0			0
$589$	−9.33801	+	6.78446i	−0.384766	+	0.279549i
$590$	−31.0409	−	7.57698i	−1.27793	−	0.311940i
$591$		0			0
$592$	8.56851	−	2.78408i	0.352164	−	0.114425i
$593$		−	4.96989i		−	0.204089i	−0.994780	−	0.102044i	$-0.967462\pi$
$593$		−	4.96989i		−	0.204089i	0.994780	−	0.102044i	$-0.0325384\pi$
$594$		0			0
$595$	1.15336	−	0.0863678i	0.0472832	−	0.00354074i
$596$	1.43507	−	4.41668i	0.0587827	−	0.180914i
$597$		0			0
$598$	−4.73269	−	6.51400i	−0.193534	−	0.266377i
$599$	−3.23524			−0.132188			−0.0660942	−	0.997813i	$-0.521054\pi$
$599$	−3.23524			−0.132188			−0.0660942	+	0.997813i	$0.521054\pi$
$600$		0			0
$601$	−8.78152			−0.358205			−0.179103	−	0.983830i	$-0.557319\pi$
$601$	−8.78152			−0.358205			−0.179103	+	0.983830i	$0.557319\pi$
$602$	0.464462	+	0.639277i	0.0189301	+	0.0260550i
$603$		0			0
$604$	5.18780	−	15.9664i	0.211089	−	0.649664i
$605$	22.7847	+	14.0817i	0.926331	+	0.572504i
$606$		0			0
$607$		−	39.5692i		−	1.60606i	−0.595937	−	0.803031i	$-0.703219\pi$
$607$		−	39.5692i		−	1.60606i	0.595937	−	0.803031i	$-0.296781\pi$
$608$	2.86327	−	0.930333i	0.116121	−	0.0377300i
$609$		0			0
$610$	−6.05573	+	9.79837i	−0.245189	+	0.396725i
$611$	−1.66579	+	1.21027i	−0.0673907	+	0.0489622i
$612$		0			0
$613$	−27.5582	+	37.9307i	−1.11307	+	1.53201i	−0.296248	+	0.955111i	$0.595736\pi$
$613$	−27.5582	+	37.9307i	−1.11307	+	1.53201i	−0.816819	+	0.576894i	$0.804264\pi$
$614$	−1.85198	+	1.34554i	−0.0747399	+	0.0543017i
$615$		0			0
$616$	−1.06050	−	0.770497i	−0.0427287	−	0.0310442i
$617$	−13.4594	+	4.37322i	−0.541854	+	0.176059i	−0.567140	−	0.823621i	$-0.691950\pi$
$617$	−13.4594	+	4.37322i	−0.541854	+	0.176059i	0.0252863	+	0.999680i	$0.491950\pi$
$618$		0			0
$619$	2.02304	+	6.22627i	0.0813128	+	0.250255i	0.983446	−	0.181203i	$-0.0579992\pi$
$619$	2.02304	+	6.22627i	0.0813128	+	0.250255i	−0.902133	+	0.431458i	$0.857999\pi$
$620$	2.03292	−	8.32833i	0.0816440	−	0.334474i
$621$		0			0
$622$	24.4110	+	7.93163i	0.978794	+	0.318029i
$623$	−2.38326	−	3.28028i	−0.0954833	−	0.131422i
$624$		0			0
$625$	14.3859	+	20.4462i	0.575435	+	0.817848i
$626$	30.2110			1.20747
$627$		0			0
$628$	5.30464	+	1.72358i	0.211678	+	0.0687784i
$629$	−5.26606	+	16.2073i	−0.209972	+	0.646226i
$630$		0			0
$631$	1.86919	+	5.75279i	0.0744114	+	0.229015i	0.981344	−	0.192262i	$-0.0615822\pi$
$631$	1.86919	+	5.75279i	0.0744114	+	0.229015i	−0.906932	+	0.421276i	$0.861582\pi$
$632$			16.0593i			0.638806i
$633$		0			0
$634$	20.9222	+	15.2009i	0.830927	+	0.603704i
$635$	−38.0044	+	15.5732i	−1.50816	+	0.618004i
$636$		0			0
$637$	−7.05469	+	9.70994i	−0.279517	+	0.384722i
$638$	−25.6041	+	35.2410i	−1.01367	+	1.39520i
$639$		0			0
$640$	−1.17557	+	1.90211i	−0.0464685	+	0.0751876i
$641$	26.1185	+	18.9762i	1.03162	+	0.749515i	0.968632	−	0.248499i	$-0.0799374\pi$
$641$	26.1185	+	18.9762i	1.03162	+	0.749515i	0.0629869	+	0.998014i	$0.479937\pi$
$642$		0			0
$643$		−	12.1187i		−	0.477914i	−0.971030	−	0.238957i	$-0.923194\pi$
$643$		−	12.1187i		−	0.477914i	0.971030	−	0.238957i	$-0.0768056\pi$
$644$	0.392588	+	1.20826i	0.0154701	+	0.0476121i
$645$		0			0
$646$	−1.75972	+	5.41585i	−0.0692352	+	0.213084i
$647$	−19.2386	−	6.25100i	−0.756348	−	0.245752i	−0.0946373	−	0.995512i	$-0.530169\pi$
$647$	−19.2386	−	6.25100i	−0.756348	−	0.245752i	−0.661710	+	0.749760i	$0.730169\pi$
$648$		0			0
$649$	−68.4982			−2.68879
$650$	7.69096	+	3.99257i	0.301664	+	0.156601i
$651$		0			0
$652$	−10.8007	−	14.8659i	−0.422989	−	0.582194i
$653$	31.7499	+	10.3162i	1.24247	+	0.403702i	0.855216	−	0.518271i	$-0.173424\pi$
$653$	31.7499	+	10.3162i	1.24247	+	0.403702i	0.387252	+	0.921974i	$0.373424\pi$
$654$		0			0
$655$	−16.8877	+	1.26462i	−0.659858	+	0.0494126i
$656$	2.34255	+	7.20962i	0.0914611	+	0.281488i
$657$		0			0
$658$	0.308982	−	0.100394i	0.0120454	−	0.00391378i
$659$	24.5894	+	17.8653i	0.957869	+	0.695932i	0.952655	−	0.304054i	$-0.0983403\pi$
$659$	24.5894	+	17.8653i	0.957869	+	0.695932i	0.00521401	+	0.999986i	$0.498340\pi$
$660$		0			0
$661$	−20.1744	+	14.6576i	−0.784694	+	0.570114i	−0.906384	−	0.422455i	$-0.861169\pi$
$661$	−20.1744	+	14.6576i	−0.784694	+	0.570114i	0.121690	+	0.992568i	$0.461169\pi$
$662$	−8.52842	+	11.7384i	−0.331466	+	0.456224i
$663$		0			0
$664$	12.2479	−	8.89861i	0.475310	−	0.345333i
$665$	0.137469	+	1.83576i	0.00533081	+	0.0711879i
$666$		0			0
$667$	40.1512	−	13.0459i	1.55466	−	0.505140i
$668$		−	8.94427i		−	0.346064i
$669$		0			0
$670$	−10.7296	+	9.09374i	−0.414521	+	0.351322i
$671$	−7.63066	+	23.4848i	−0.294578	+	0.906619i
$672$		0			0
$673$	27.0791	+	37.2711i	1.04382	+	1.43670i	0.894045	+	0.447977i	$0.147855\pi$
$673$	27.0791	+	37.2711i	1.04382	+	1.43670i	0.149777	+	0.988720i	$0.452145\pi$
$674$	−11.0676			−0.426307
$675$		0			0
$676$	−9.99634			−0.384475
$677$	−16.8060	−	23.1315i	−0.645908	−	0.889016i	0.353006	−	0.935621i	$-0.385160\pi$
$677$	−16.8060	−	23.1315i	−0.645908	−	0.889016i	−0.998913	+	0.0466053i	$0.985160\pi$
$678$		0			0
$679$	0.497382	−	1.53078i	0.0190878	−	0.0587461i
$680$	−1.60372	−	3.91367i	−0.0614998	−	0.150082i
$681$		0			0
$682$		−	18.3782i		−	0.703737i
$683$	8.49047	−	2.75872i	0.324879	−	0.105560i	−0.142037	−	0.989861i	$-0.545365\pi$
$683$	8.49047	−	2.75872i	0.324879	−	0.105560i	0.466916	+	0.884302i	$0.345365\pi$
$684$		0			0
$685$	−28.3503	−	33.4502i	−1.08321	−	1.27807i
$686$	3.08070	−	2.23826i	0.117622	−	0.0854572i
$687$		0			0
$688$	1.69848	−	2.33776i	0.0647539	−	0.0891262i
$689$	−16.2856	+	11.8322i	−0.620431	+	0.450769i
$690$		0			0
$691$	1.06206	+	0.771634i	0.0404028	+	0.0293543i	0.607803	−	0.794088i	$-0.292051\pi$
$691$	1.06206	+	0.771634i	0.0404028	+	0.0293543i	−0.567401	+	0.823442i	$0.692051\pi$
$692$	−11.3320	+	3.68198i	−0.430777	+	0.139968i
$693$		0			0
$694$	0.312299	+	0.961158i	0.0118547	+	0.0364851i
$695$	8.10989	+	19.7911i	0.307626	+	0.750721i
$696$		0			0
$697$	−13.6369	−	4.43091i	−0.516536	−	0.167833i
$698$	−17.8845	−	24.6158i	−0.676936	−	0.931723i
$699$		0			0
$700$	−0.959451	−	0.974130i	−0.0362638	−	0.0368186i
$701$	−22.5267			−0.850822			−0.425411	−	0.905000i	$-0.639870\pi$
$701$	−22.5267			−0.850822			−0.425411	+	0.905000i	$0.639870\pi$
$702$		0			0
$703$	−25.7966	−	8.38181i	−0.972935	−	0.316126i
$704$	−1.48131	+	4.55899i	−0.0558288	+	0.171823i
$705$		0			0
$706$	−4.83911	−	14.8932i	−0.182122	−	0.560515i
$707$			1.32238i			0.0497331i
$708$		0			0
$709$	−5.57914	−	4.05348i	−0.209529	−	0.152232i	0.478072	−	0.878321i	$-0.341336\pi$
$709$	−5.57914	−	4.05348i	−0.209529	−	0.152232i	−0.687600	+	0.726089i	$0.741336\pi$
$710$	0.234131	+	3.12659i	0.00878677	+	0.117339i
$711$		0			0
$712$	−8.71529	+	11.9956i	−0.326619	+	0.449553i
$713$	−10.4694	+	14.4100i	−0.392084	+	0.539657i
$714$		0			0
$715$	18.0470	+	4.40522i	0.674920	+	0.164746i
$716$	−3.03884	−	2.20785i	−0.113567	−	0.0825111i
$717$		0			0
$718$		−	4.37321i		−	0.163207i
$719$	8.75827	+	26.9552i	0.326628	+	1.00526i	0.970700	+	0.240293i	$0.0772437\pi$
$719$	8.75827	+	26.9552i	0.326628	+	1.00526i	−0.644072	+	0.764965i	$0.722756\pi$
$720$		0			0
$721$	−0.00616736	+	0.0189812i	−0.000229684	+	0.000706896i
$722$	9.44985	+	3.07044i	0.351687	+	0.114270i
$723$		0			0
$724$	18.0626			0.671290
$725$	−32.3709	+	31.8831i	−1.20223	+	1.18411i
$726$		0			0
$727$	10.0395	+	13.8182i	0.372344	+	0.512487i	0.953536	−	0.301279i	$-0.0974135\pi$
$727$	10.0395	+	13.8182i	0.372344	+	0.512487i	−0.581192	+	0.813766i	$0.697414\pi$
$728$	−0.450735	−	0.146453i	−0.0167054	−	0.00542790i
$729$		0			0
$730$	3.38789	+	2.09383i	0.125391	+	0.0774961i
$731$	1.68900	+	5.19819i	0.0624698	+	0.192262i
$732$		0			0
$733$	11.3102	−	3.67491i	0.417753	−	0.135736i	−0.0925958	−	0.995704i	$-0.529516\pi$
$733$	11.3102	−	3.67491i	0.417753	−	0.135736i	0.510348	+	0.859968i	$0.329516\pi$
$734$	17.6636	+	12.8333i	0.651975	+	0.473687i
$735$		0			0
$736$	3.75856	−	2.73076i	0.138543	−	0.100657i
$737$	−17.7228	+	24.3933i	−0.652827	+	0.898539i
$738$		0			0
$739$	9.27173	−	6.73631i	0.341066	−	0.247799i	−0.404045	−	0.914739i	$-0.632396\pi$
$739$	9.27173	−	6.73631i	0.341066	−	0.247799i	0.745112	+	0.666940i	$0.232396\pi$
$740$	18.6414	−	7.63876i	0.685272	−	0.280806i
$741$		0			0
$742$	3.02076	−	0.981504i	0.110896	−	0.0360321i
$743$		−	8.64114i		−	0.317013i	−0.987358	−	0.158506i	$-0.949332\pi$
$743$		−	8.64114i		−	0.317013i	0.987358	−	0.158506i	$-0.0506678\pi$
$744$		0			0
$745$	2.46246	−	10.0881i	0.0902177	−	0.369598i
$746$	−0.438406	+	1.34928i	−0.0160512	+	0.0494005i
$747$		0			0
$748$	−5.32949	−	7.33541i	−0.194865	−	0.268209i
$749$	1.59905			0.0584281
$750$		0			0
$751$	−8.45998			−0.308709			−0.154354	−	0.988016i	$-0.549330\pi$
$751$	−8.45998			−0.308709			−0.154354	+	0.988016i	$0.549330\pi$
$752$	−0.698322	−	0.961158i	−0.0254652	−	0.0350498i
$753$		0			0
$754$	−4.86671	+	14.9782i	−0.177235	+	0.545474i
$755$	8.90186	−	36.4685i	0.323972	−	1.32723i
$756$		0			0
$757$			53.6675i			1.95058i	0.220932	+	0.975289i	$0.429090\pi$
$757$			53.6675i			1.95058i	−0.220932	+	0.975289i	$0.570910\pi$
$758$	24.8041	−	8.05934i	0.900926	−	0.292729i
$759$		0			0
$760$	6.22925	−	2.55258i	0.225959	−	0.0925919i
$761$	9.52327	−	6.91906i	0.345218	−	0.250816i	−0.401642	−	0.915797i	$-0.631560\pi$
$761$	9.52327	−	6.91906i	0.345218	−	0.250816i	0.746860	+	0.664981i	$0.231560\pi$
$762$		0			0
$763$	−1.57617	+	2.16942i	−0.0570614	+	0.0785382i
$764$	13.4303	−	9.75767i	0.485890	−	0.353020i
$765$		0			0
$766$	−26.5071	−	19.2585i	−0.957739	−	0.695838i
$767$	−23.5531	+	7.65287i	−0.850454	+	0.276329i
$768$		0			0
$769$	−1.57472	−	4.84650i	−0.0567859	−	0.174769i	0.918641	−	0.395094i	$-0.129288\pi$
$769$	−1.57472	−	4.84650i	−0.0567859	−	0.174769i	−0.975426	+	0.220325i	$0.929288\pi$
$770$	−2.49338	−	1.54099i	−0.0898551	−	0.0555335i
$771$		0			0
$772$	−3.66021	−	1.18928i	−0.131734	−	0.0428030i
$773$	−7.41916	−	10.2116i	−0.266849	−	0.367285i	0.654474	−	0.756084i	$-0.272890\pi$
$773$	−7.41916	−	10.2116i	−0.266849	−	0.367285i	−0.921323	+	0.388799i	$0.872890\pi$
$774$		0			0
$775$	3.14241	−	18.9102i	0.112879	−	0.679274i
$776$	−5.88597			−0.211294
$777$		0			0
$778$	4.24298	+	1.37863i	0.152118	+	0.0494262i
$779$	7.05253	−	21.7054i	0.252683	−	0.777678i
$780$		0			0
$781$	2.07704	+	6.39247i	0.0743224	+	0.228741i
$782$			8.78757i			0.314243i
$783$		0			0
$784$	−5.60262	−	4.07054i	−0.200094	−	0.145377i
$785$	12.1162	+	2.95753i	0.432446	+	0.105559i
$786$		0			0
$787$	25.9859	−	35.7665i	0.926296	−	1.27494i	−0.0349910	−	0.999388i	$-0.511140\pi$
$787$	25.9859	−	35.7665i	0.926296	−	1.27494i	0.961287	−	0.275549i	$-0.0888597\pi$
$788$	−6.31471	+	8.69145i	−0.224952	+	0.309620i
$789$		0			0
$790$	2.68155	+	35.8095i	0.0954052	+	1.27405i
$791$	−3.83376	−	2.78539i	−0.136313	−	0.0990370i
$792$		0			0
$793$			8.92777i			0.317034i
$794$	0.654271	+	2.01364i	0.0232192	+	0.0714614i
$795$		0			0
$796$	0.771949	−	2.37581i	0.0273610	−	0.0842085i
$797$	−44.0719	−	14.3198i	−1.56111	−	0.507235i	−0.604004	−	0.796981i	$-0.706429\pi$
$797$	−44.0719	−	14.3198i	−1.56111	−	0.507235i	−0.957103	+	0.289746i	$0.906429\pi$
$798$		0			0
$799$	2.24720			0.0795002
$800$	−2.30371	+	4.43767i	−0.0814483	+	0.156895i
$801$		0			0
$802$	16.8418	+	23.1808i	0.594705	+	0.818541i
$803$	8.12010	+	2.63838i	0.286552	+	0.0931064i
$804$		0			0
$805$	1.07715	+	2.62866i	0.0379647	+	0.0926479i
$806$	−2.05328	−	6.31935i	−0.0723237	−	0.222590i
$807$		0			0
$808$	4.59908	−	1.49433i	0.161795	−	0.0525705i
$809$	−40.0393	−	29.0902i	−1.40771	−	1.02276i	−0.993651	−	0.112507i	$-0.964112\pi$
$809$	−40.0393	−	29.0902i	−1.40771	−	1.02276i	−0.414056	−	0.910252i	$-0.635888\pi$
$810$		0			0
$811$	2.27136	−	1.65024i	0.0797583	−	0.0579478i	−0.547192	−	0.837007i	$-0.684303\pi$
$811$	2.27136	−	1.65024i	0.0797583	−	0.0579478i	0.626950	+	0.779060i	$0.284303\pi$
$812$	1.46062	−	2.01037i	0.0512576	−	0.0705500i
$813$		0			0
$814$	34.9397	−	25.3852i	1.22464	−	0.889750i
$815$	−26.5660	−	31.3449i	−0.930566	−	1.09796i
$816$		0			0
$817$	−8.27378	+	2.68832i	−0.289463	+	0.0940523i
$818$			39.3546i			1.37600i
$819$		0			0
$820$	6.42732	+	15.6850i	0.224452	+	0.547745i
$821$	11.5462	−	35.5356i	0.402965	−	1.24020i	−0.519617	−	0.854399i	$-0.673925\pi$
$821$	11.5462	−	35.5356i	0.402965	−	1.24020i	0.922582	−	0.385800i	$-0.126075\pi$
$822$		0			0
$823$	13.4238	+	18.4763i	0.467925	+	0.644044i	0.976129	−	0.217193i	$-0.0696902\pi$
$823$	13.4238	+	18.4763i	0.467925	+	0.644044i	−0.508203	+	0.861237i	$0.669690\pi$
$824$	0.0729839			0.00254251
$825$		0			0
$826$	3.90757			0.135962
$827$	−6.29560	−	8.66515i	−0.218919	−	0.301317i	0.685405	−	0.728162i	$-0.259625\pi$
$827$	−6.29560	−	8.66515i	−0.218919	−	0.301317i	−0.904325	+	0.426845i	$0.859625\pi$
$828$		0			0
$829$	8.52760	−	26.2453i	0.296176	−	0.911536i	−0.686648	−	0.726990i	$-0.740919\pi$
$829$	8.52760	−	26.2453i	0.296176	−	0.911536i	0.982824	−	0.184546i	$-0.0590814\pi$
$830$	25.8248	−	21.8875i	0.896391	−	0.759725i
$831$		0			0
$832$			1.73311i			0.0600847i
$833$	12.4579	−	4.04781i	0.431640	−	0.140248i
$834$		0			0
$835$	−1.49349	−	19.9442i	−0.0516844	−	0.690196i
$836$	11.6755	−	8.48276i	0.403806	−	0.293382i
$837$		0			0
$838$	−8.29180	+	11.4127i	−0.286435	+	0.394244i
$839$	8.03884	−	5.84056i	0.277532	−	0.201639i	−0.440308	−	0.897847i	$-0.645131\pi$
$839$	8.03884	−	5.84056i	0.277532	−	0.201639i	0.717840	+	0.696208i	$0.245131\pi$
$840$		0			0
$841$	−43.3442	−	31.4914i	−1.49463	−	1.08591i
$842$	15.5066	−	5.03839i	0.534392	−	0.173634i
$843$		0			0
$844$	−7.50110	−	23.0860i	−0.258198	−	0.794653i
$845$	−22.2901	+	1.66916i	−0.766802	+	0.0574210i
$846$		0			0
$847$	−3.11533	−	1.01223i	−0.107044	−	0.0347807i
$848$	−6.82714	−	9.39675i	−0.234445	−	0.322686i
$849$		0			0
$850$	−4.22950	−	8.45901i	−0.145071	−	0.290142i
$851$	−41.8566			−1.43482
$852$		0			0
$853$	42.8052	+	13.9083i	1.46562	+	0.476210i	0.929782	−	0.368110i	$-0.119995\pi$
$853$	42.8052	+	13.9083i	1.46562	+	0.476210i	0.535840	+	0.844319i	$0.319995\pi$
$854$	0.435301	−	1.33972i	0.0148957	−	0.0458442i
$855$		0			0
$856$	−1.80699	−	5.56134i	−0.0617616	−	0.190083i
$857$			24.6986i			0.843686i	0.906669	+	0.421843i	$0.138617\pi$
$857$			24.6986i			0.843686i	−0.906669	+	0.421843i	$0.861383\pi$
$858$		0			0
$859$	−14.0283	−	10.1922i	−0.478641	−	0.347753i	0.322159	−	0.946686i	$-0.395592\pi$
$859$	−14.0283	−	10.1922i	−0.478641	−	0.347753i	−0.800799	+	0.598933i	$0.795592\pi$
$860$	3.39696	−	5.49640i	0.115835	−	0.187426i
$861$		0			0
$862$	−1.16509	+	1.60361i	−0.0396832	+	0.0546192i
$863$	15.2158	−	20.9428i	0.517954	−	0.712902i	−0.467282	−	0.884109i	$-0.654767\pi$
$863$	15.2158	−	20.9428i	0.517954	−	0.712902i	0.985235	+	0.171207i	$0.0547666\pi$
$864$		0			0
$865$	−24.6535	+	10.1023i	−0.838243	+	0.343490i
$866$	3.63203	+	2.63882i	0.123421	+	0.0896709i
$867$		0			0
$868$			1.04841i			0.0355853i
$869$	23.7888	+	73.2144i	0.806979	+	2.48363i
$870$		0			0
$871$	−3.36867	+	10.3677i	−0.114143	+	0.351296i
$872$	9.32615	+	3.03025i	0.315823	+	0.102617i
$873$		0			0
$874$	−13.9869			−0.473113
$875$	−2.30207	−	2.01193i	−0.0778240	−	0.0680157i
$876$		0			0
$877$	11.8673	+	16.3339i	0.400729	+	0.551557i	0.960927	−	0.276802i	$-0.0892748\pi$
$877$	11.8673	+	16.3339i	0.400729	+	0.551557i	−0.560198	+	0.828359i	$0.689275\pi$
$878$	24.4572	+	7.94662i	0.825390	+	0.268185i
$879$		0			0
$880$	−2.54180	+	10.4131i	−0.0856842	+	0.351025i
$881$	−7.34633	−	22.6097i	−0.247504	−	0.761739i	−0.995215	−	0.0977143i	$-0.968847\pi$
$881$	−7.34633	−	22.6097i	−0.247504	−	0.761739i	0.747710	−	0.664025i	$-0.231153\pi$
$882$		0			0
$883$	−30.9842	+	10.0674i	−1.04270	+	0.338794i	−0.779800	−	0.626029i	$-0.784679\pi$
$883$	−30.9842	+	10.0674i	−1.04270	+	0.338794i	−0.262900	+	0.964823i	$0.584679\pi$
$884$	−2.65208	−	1.92685i	−0.0891993	−	0.0648071i
$885$		0			0
$886$	−23.5809	+	17.1326i	−0.792217	+	0.575580i
$887$	33.1027	−	45.5619i	1.11148	−	1.52982i	0.292261	−	0.956339i	$-0.405592\pi$
$887$	33.1027	−	45.5619i	1.11148	−	1.52982i	0.819218	−	0.573482i	$-0.194408\pi$
$888$		0			0
$889$	4.06351	−	2.95232i	0.136286	−	0.0990175i
$890$	−17.4306	+	28.2033i	−0.584274	+	0.945376i
$891$		0			0
$892$	12.4150	−	4.03389i	0.415686	−	0.135065i
$893$			3.57679i			0.119693i
$894$		0			0
$895$	−7.14475	−	4.41570i	−0.238823	−	0.147600i
$896$	0.0845030	−	0.260074i	0.00282305	−	0.00868845i
$897$		0			0
$898$	−3.02144	−	4.15865i	−0.100827	−	0.138776i
$899$	34.8392			1.16195
$900$		0			0
$901$	21.9697			0.731917
$902$	21.3593	+	29.3986i	0.711187	+	0.978865i
$903$		0			0
$904$	−5.35500	+	16.4810i	−0.178105	+	0.548150i
$905$	40.2764	−	3.01604i	1.33883	−	0.100257i
$906$		0			0
$907$		−	46.7617i		−	1.55270i	−0.630304	−	0.776349i	$-0.717070\pi$
$907$		−	46.7617i		−	1.55270i	0.630304	−	0.776349i	$-0.282930\pi$
$908$	6.71592	−	2.18213i	0.222876	−	0.0724167i
$909$		0			0
$910$	−1.02951	−	0.251301i	−0.0341281	−	0.00833056i
$911$	−13.5487	+	9.84374i	−0.448890	+	0.326138i	−0.789157	−	0.614191i	$-0.789482\pi$
$911$	−13.5487	+	9.84374i	−0.448890	+	0.326138i	0.340268	+	0.940329i	$0.389482\pi$
$912$		0			0
$913$	42.6564	−	58.7115i	1.41172	−	1.94307i
$914$	16.8636	−	12.2521i	0.557797	−	0.405263i
$915$		0			0
$916$	10.1751	+	7.39264i	0.336195	+	0.244260i
$917$	1.96968	−	0.639989i	0.0650447	−	0.0211343i
$918$		0			0
$919$	1.58373	+	4.87423i	0.0522426	+	0.160786i	0.973774	−	0.227518i	$-0.0730610\pi$
$919$	1.58373	+	4.87423i	0.0522426	+	0.160786i	−0.921531	+	0.388304i	$0.873061\pi$
$920$	7.92497	−	6.71671i	0.261278	−	0.221443i
$921$		0			0
$922$	−4.72664	−	1.53578i	−0.155664	−	0.0505782i
$923$	1.42838	+	1.96600i	0.0470158	+	0.0647117i
$924$		0			0
$925$	40.2916	−	20.1458i	1.32478	−	0.662389i
$926$	7.10664			0.233539
$927$		0			0
$928$	−8.64240	−	2.80808i	−0.283701	−	0.0921799i
$929$	14.0119	−	43.1241i	0.459715	−	1.41486i	−0.405795	−	0.913964i	$-0.633005\pi$
$929$	14.0119	−	43.1241i	0.459715	−	1.41486i	0.865510	−	0.500892i	$-0.166995\pi$
$930$		0			0
$931$	6.44276	+	19.8288i	0.211153	+	0.649862i
$932$		−	9.80527i		−	0.321182i
$933$		0			0
$934$	24.4179	+	17.7406i	0.798977	+	0.580491i
$935$	−13.1087	−	15.4668i	−0.428699	−	0.505817i
$936$		0			0
$937$	−18.2283	+	25.0891i	−0.595493	+	0.819626i	−0.995286	−	0.0969794i	$-0.969082\pi$
$937$	−18.2283	+	25.0891i	−0.595493	+	0.819626i	0.399793	+	0.916605i	$0.369082\pi$
$938$	1.01102	−	1.39155i	0.0330109	−	0.0454356i
$939$		0			0
$940$	−1.71763	−	2.02661i	−0.0560229	−	0.0661007i
$941$	−39.0847	−	28.3967i	−1.27412	−	0.925705i	−0.274765	−	0.961512i	$-0.588600\pi$
$941$	−39.0847	−	28.3967i	−1.27412	−	0.925705i	−0.999359	+	0.0358067i	$0.988600\pi$
$942$		0			0
$943$		−	35.2185i		−	1.14687i
$944$	−4.41570	−	13.5901i	−0.143719	−	0.442321i
$945$		0			0
$946$	4.28042	−	13.1738i	0.139168	−	0.428316i
$947$	31.7532	+	10.3172i	1.03184	+	0.335265i	0.775517	−	0.631327i	$-0.217489\pi$
$947$	31.7532	+	10.3172i	1.03184	+	0.335265i	0.256322	+	0.966591i	$0.417489\pi$
$948$		0			0
$949$	3.08687			0.100204
$950$	13.4639	−	6.73195i	0.436827	−	0.218413i
$951$		0			0
$952$	0.304027	+	0.418458i	0.00985359	+	0.0135623i
$953$	−20.7830	−	6.75280i	−0.673226	−	0.218745i	−0.0475990	−	0.998867i	$-0.515157\pi$
$953$	−20.7830	−	6.75280i	−0.673226	−	0.218745i	−0.625627	+	0.780122i	$0.715157\pi$
$954$		0			0
$955$	28.3179	−	24.0004i	0.916344	−	0.776636i
$956$	−1.55754	−	4.79360i	−0.0503743	−	0.155036i
$957$		0			0
$958$	26.4788	−	8.60350i	0.855493	−	0.277966i
$959$	4.33824	+	3.15192i	0.140089	+	0.101781i
$960$		0			0
$961$	13.1880	−	9.58162i	0.425418	−	0.309084i
$962$	9.17790	−	12.6323i	0.295907	−	0.407282i
$963$		0			0
$964$	5.53446	−	4.02102i	0.178253	−	0.129508i
$965$	−8.36022	−	2.04070i	−0.269125	−	0.0656926i
$966$		0			0
$967$	−30.6435	+	9.95669i	−0.985430	+	0.320186i	−0.757029	−	0.653382i	$-0.773350\pi$
$967$	−30.6435	+	9.95669i	−0.985430	+	0.320186i	−0.228401	+	0.973567i	$0.573350\pi$
$968$			11.9786i			0.385008i
$969$		0			0
$970$	−13.1247	+	0.982824i	−0.421408	+	0.0315566i
$971$	−11.0045	+	33.8684i	−0.353152	+	1.08689i	0.603922	+	0.797044i	$0.293604\pi$
$971$	−11.0045	+	33.8684i	−0.353152	+	1.08689i	−0.957073	+	0.289845i	$0.906396\pi$
$972$		0			0
$973$	−1.53745	−	2.11611i	−0.0492883	−	0.0678395i
$974$	1.29951			0.0416391
$975$		0			0
$976$	−5.15131			−0.164889
$977$	5.79486	+	7.97594i	0.185394	+	0.255173i	0.891590	−	0.452843i	$-0.149590\pi$
$977$	5.79486	+	7.97594i	0.185394	+	0.255173i	−0.706196	+	0.708016i	$0.749590\pi$
$978$		0			0
$979$	−21.9638	+	67.5976i	−0.701966	+	2.16043i
$980$	−13.1726	−	8.14109i	−0.420782	−	0.260057i
$981$		0			0
$982$			19.1650i			0.611580i
$983$	28.9244	−	9.39810i	0.922544	−	0.299753i	0.191034	−	0.981583i	$-0.438816\pi$
$983$	28.9244	−	9.39810i	0.922544	−	0.299753i	0.731510	+	0.681831i	$0.238816\pi$
$984$		0			0
$985$	−12.6294	+	20.4348i	−0.402406	+	0.651107i
$986$	13.9056	−	10.1030i	0.442845	−	0.321745i
$987$		0			0
$988$	3.06690	−	4.22123i	0.0975712	−	0.134295i
$989$	−10.8608	+	7.89087i	−0.345355	+	0.250915i
$990$		0			0
$991$	33.1759	+	24.1037i	1.05387	+	0.765680i	0.972944	−	0.231040i	$-0.0742128\pi$
$991$	33.1759	+	24.1037i	1.05387	+	0.765680i	0.0809242	+	0.996720i	$0.474213\pi$
$992$	3.64625	−	1.18474i	0.115769	−	0.0376155i
$993$		0			0
$994$	−0.118488	−	0.364667i	−0.00375820	−	0.0115665i
$995$	1.32460	−	5.42655i	0.0419927	−	0.172033i
$996$		0			0
$997$	−7.61617	−	2.47464i	−0.241206	−	0.0783727i	0.185919	−	0.982565i	$-0.440474\pi$
$997$	−7.61617	−	2.47464i	−0.241206	−	0.0783727i	−0.427126	+	0.904192i	$0.640474\pi$
$998$	−3.76970	−	5.18854i	−0.119328	−	0.164240i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.a.289.2		8
3.2	odd	2		150.2.h.a.139.1	yes	8
15.2	even	4		750.2.g.e.301.1		8
15.8	even	4		750.2.g.c.301.2		8
15.14	odd	2		750.2.h.c.199.2		8
25.9	even	10	inner	450.2.l.a.109.2		8
75.29	odd	10		3750.2.c.e.1249.2		8
75.38	even	20		750.2.g.c.451.2		8
75.41	odd	10		750.2.h.c.49.2		8
75.47	even	20		3750.2.a.m.1.2		4
75.53	even	20		3750.2.a.o.1.3		4
75.59	odd	10		150.2.h.a.109.1	✓	8
75.62	even	20		750.2.g.e.451.1		8
75.71	odd	10		3750.2.c.e.1249.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.109.1	✓	8	75.59	odd	10
150.2.h.a.139.1	yes	8	3.2	odd	2
450.2.l.a.109.2		8	25.9	even	10	inner
450.2.l.a.289.2		8	1.1	even	1	trivial
750.2.g.c.301.2		8	15.8	even	4
750.2.g.c.451.2		8	75.38	even	20
750.2.g.e.301.1		8	15.2	even	4
750.2.g.e.451.1		8	75.62	even	20
750.2.h.c.49.2		8	75.41	odd	10
750.2.h.c.199.2		8	15.14	odd	2
3750.2.a.m.1.2		4	75.47	even	20
3750.2.a.o.1.3		4	75.53	even	20
3750.2.c.e.1249.2		8	75.29	odd	10
3750.2.c.e.1249.7		8	75.71	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-0.530249 + 2.17229i) q^{5} -0.273457i q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-0.530249 + 2.17229i) q^{5} -0.273457i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.06909 + 0.847859i) q^{10} +(-3.87811 + 2.81761i) q^{11} +(-1.01869 + 1.40211i) q^{13} +(0.221232 - 0.160734i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.79892 - 0.584503i) q^{17} +(0.930333 + 2.86327i) q^{19} +(-1.90211 - 1.17557i) q^{20} +(-4.55899 - 1.48131i) q^{22} +(2.73076 + 3.75856i) q^{23} +(-4.43767 - 2.30371i) q^{25} -1.73311 q^{26} +(0.260074 + 0.0845030i) q^{28} +(2.80808 - 8.64240i) q^{29} +(1.18474 + 3.64625i) q^{31} -1.00000i q^{32} +(1.53025 + 1.11179i) q^{34} +(0.594028 + 0.145000i) q^{35} +(-5.29563 + 7.28881i) q^{37} +(-1.76960 + 2.43564i) q^{38} +(-0.166977 - 2.22982i) q^{40} +(-6.13287 - 4.45579i) q^{41} +2.88963i q^{43} +(-1.48131 - 4.55899i) q^{44} +(-1.43564 + 4.41846i) q^{46} +(1.12991 + 0.367130i) q^{47} +6.92522 q^{49} +(-0.744661 - 4.94424i) q^{50} +(-1.01869 - 1.40211i) q^{52} +(11.0465 + 3.58924i) q^{53} +(-4.06430 - 9.91840i) q^{55} +(0.0845030 + 0.260074i) q^{56} +(8.64240 - 2.80808i) q^{58} +(11.5604 + 8.39915i) q^{59} +(4.16750 - 3.02786i) q^{61} +(-2.25351 + 3.10169i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-2.50563 - 2.95637i) q^{65} +(5.98215 - 1.94372i) q^{67} +1.89149i q^{68} +(0.231853 + 0.565808i) q^{70} +(0.433294 - 1.33354i) q^{71} +(-1.04691 - 1.44095i) q^{73} -9.00947 q^{74} -3.01062 q^{76} +(0.770497 + 1.06050i) q^{77} +(4.96261 - 15.2733i) q^{79} +(1.70582 - 1.44575i) q^{80} -7.58064i q^{82} +(-14.3983 + 4.67828i) q^{83} +(0.315836 + 4.21769i) q^{85} +(-2.33776 + 1.69848i) q^{86} +(2.81761 - 3.87811i) q^{88} +(11.9956 - 8.71529i) q^{89} +(0.383418 + 0.278570i) q^{91} +(-4.41846 + 1.43564i) q^{92} +(0.367130 + 1.12991i) q^{94} +(-6.71316 + 0.502706i) q^{95} +(5.59789 + 1.81886i) q^{97} +(4.07054 + 5.60262i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4}+O(q^{10}) \) 8 * q + 2 * q^4	\( 8 q + 2 q^{4} - 10 q^{11} - 20 q^{13} + 2 q^{14} - 2 q^{16} - 10 q^{17} - 8 q^{19} + 10 q^{23} - 10 q^{25} - 4 q^{26} - 10 q^{28} + 22 q^{29} + 24 q^{31} + 8 q^{34} - 10 q^{35} - 20 q^{37} + 10 q^{38} - 22 q^{41} + 10 q^{46} - 10 q^{47} + 8 q^{49} + 20 q^{50} - 20 q^{52} + 30 q^{53} + 10 q^{55} - 2 q^{56} + 30 q^{58} + 20 q^{59} - 10 q^{62} + 2 q^{64} - 20 q^{65} + 10 q^{67} - 10 q^{70} - 20 q^{71} - 20 q^{73} + 4 q^{74} - 12 q^{76} + 20 q^{77} + 16 q^{79} - 70 q^{83} + 20 q^{85} + 18 q^{86} + 10 q^{88} + 34 q^{89} - 24 q^{91} - 30 q^{92} + 30 q^{94} - 30 q^{95} + 60 q^{97} - 20 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 - 10 * q^11 - 20 * q^13 + 2 * q^14 - 2 * q^16 - 10 * q^17 - 8 * q^19 + 10 * q^23 - 10 * q^25 - 4 * q^26 - 10 * q^28 + 22 * q^29 + 24 * q^31 + 8 * q^34 - 10 * q^35 - 20 * q^37 + 10 * q^38 - 22 * q^41 + 10 * q^46 - 10 * q^47 + 8 * q^49 + 20 * q^50 - 20 * q^52 + 30 * q^53 + 10 * q^55 - 2 * q^56 + 30 * q^58 + 20 * q^59 - 10 * q^62 + 2 * q^64 - 20 * q^65 + 10 * q^67 - 10 * q^70 - 20 * q^71 - 20 * q^73 + 4 * q^74 - 12 * q^76 + 20 * q^77 + 16 * q^79 - 70 * q^83 + 20 * q^85 + 18 * q^86 + 10 * q^88 + 34 * q^89 - 24 * q^91 - 30 * q^92 + 30 * q^94 - 30 * q^95 + 60 * q^97 - 20 * q^98

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