LMFDB - Embedded newform 441.2.u.d.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.2
Character	$\chi$	$=$	441.127
Dual form			441.2.u.d.316.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54657 - 0.744788i) q^{2} +(0.590184 + 0.740067i) q^{4} +(-0.580458 - 2.54315i) q^{5} +(2.64218 + 0.137475i) q^{7} +(0.402375 + 1.76292i) q^{8} +O(q^{10})$	\(q+(-1.54657 - 0.744788i) q^{2} +(0.590184 + 0.740067i) q^{4} +(-0.580458 - 2.54315i) q^{5} +(2.64218 + 0.137475i) q^{7} +(0.402375 + 1.76292i) q^{8} +(-0.996391 + 4.36547i) q^{10} +(4.78563 + 2.30464i) q^{11} +(2.79932 + 1.34808i) q^{13} +(-3.98392 - 2.18048i) q^{14} +(1.11197 - 4.87186i) q^{16} +(1.56639 - 1.96419i) q^{17} -7.74408 q^{19} +(1.53953 - 1.93050i) q^{20} +(-5.68483 - 7.12855i) q^{22} +(1.61774 + 2.02859i) q^{23} +(-1.62584 + 0.782964i) q^{25} +(-3.32531 - 4.16980i) q^{26} +(1.45763 + 2.03652i) q^{28} +(3.80345 - 4.76938i) q^{29} +2.25866 q^{31} +(-3.09338 + 3.87897i) q^{32} +(-3.88544 + 1.87113i) q^{34} +(-1.18405 - 6.79925i) q^{35} +(6.33364 - 7.94214i) q^{37} +(11.9767 + 5.76770i) q^{38} +(4.24981 - 2.04660i) q^{40} +(0.261037 + 1.14368i) q^{41} +(-0.464819 + 2.03651i) q^{43} +(1.11881 + 4.90184i) q^{44} +(-0.991084 - 4.34222i) q^{46} +(-10.4372 - 5.02627i) q^{47} +(6.96220 + 0.726468i) q^{49} +3.09761 q^{50} +(0.654443 + 2.86730i) q^{52} +(-5.52071 - 6.92275i) q^{53} +(3.08318 - 13.5083i) q^{55} +(0.820788 + 4.71326i) q^{56} +(-9.43447 + 4.54340i) q^{58} +(-1.55399 + 6.80849i) q^{59} +(-3.28315 + 4.11694i) q^{61} +(-3.49318 - 1.68223i) q^{62} +(-1.33142 + 0.641176i) q^{64} +(1.80349 - 7.90160i) q^{65} -3.66376 q^{67} +2.37809 q^{68} +(-3.23279 + 11.3974i) q^{70} +(-0.0227312 - 0.0285040i) q^{71} +(-4.18971 + 2.01766i) q^{73} +(-15.7106 + 7.56583i) q^{74} +(-4.57043 - 5.73114i) q^{76} +(12.3276 + 6.74716i) q^{77} +13.3648 q^{79} -13.0353 q^{80} +(0.448086 - 1.96319i) q^{82} +(5.75678 - 2.77232i) q^{83} +(-5.90446 - 2.84344i) q^{85} +(2.23564 - 2.80340i) q^{86} +(-2.13727 + 9.36400i) q^{88} +(7.45728 - 3.59123i) q^{89} +(7.21098 + 3.94671i) q^{91} +(-0.546524 + 2.39448i) q^{92} +(12.3983 + 15.5469i) q^{94} +(4.49511 + 19.6944i) q^{95} -1.62118 q^{97} +(-10.2265 - 6.30890i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

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 $

$2$	−1.54657	−	0.744788i	−1.09359	−	0.526645i	−0.201952	−	0.979395i	$-0.564728\pi$
$2$	−1.54657	−	0.744788i	−1.09359	−	0.526645i	−0.891637	+	0.452751i	$0.850443\pi$
$3$		0			0
$3$		0			0
$4$	0.590184	+	0.740067i	0.295092	+	0.370034i
$5$	−0.580458	−	2.54315i	−0.259589	−	1.13733i	−0.921693	−	0.387920i	$-0.873194\pi$
$5$	−0.580458	−	2.54315i	−0.259589	−	1.13733i	0.662104	−	0.749412i	$-0.269663\pi$
$6$		0			0
$7$	2.64218	+	0.137475i	0.998649	+	0.0519608i
$7$	2.64218	+	0.137475i	0.998649	+	0.0519608i
$8$	0.402375	+	1.76292i	0.142261	+	0.623286i
$9$		0			0
$10$	−0.996391	+	4.36547i	−0.315086	+	1.38048i
$11$	4.78563	+	2.30464i	1.44292	+	0.694874i	0.981350	−	0.192230i	$-0.0615719\pi$
$11$	4.78563	+	2.30464i	1.44292	+	0.694874i	0.461570	+	0.887104i	$0.347286\pi$
$12$		0			0
$13$	2.79932	+	1.34808i	0.776392	+	0.373891i	0.779740	−	0.626104i	$-0.215351\pi$
$13$	2.79932	+	1.34808i	0.776392	+	0.373891i	−0.00334765	+	0.999994i	$0.501066\pi$
$14$	−3.98392	−	2.18048i	−1.06475	−	0.582757i
$15$		0			0
$16$	1.11197	−	4.87186i	0.277992	−	1.21796i
$17$	1.56639	−	1.96419i	0.379906	−	0.476387i	−0.554711	−	0.832043i	$-0.687171\pi$
$17$	1.56639	−	1.96419i	0.379906	−	0.476387i	0.934617	+	0.355656i	$0.115743\pi$
$18$		0			0
$19$	−7.74408			−1.77661			−0.888307	−	0.459251i	$-0.848118\pi$
$19$	−7.74408			−1.77661			−0.888307	+	0.459251i	$0.848118\pi$
$20$	1.53953	−	1.93050i	0.344248	−	0.431674i
$21$		0			0
$22$	−5.68483	−	7.12855i	−1.21201	−	1.51981i
$23$	1.61774	+	2.02859i	0.337323	+	0.422989i	0.921344	−	0.388749i	$-0.127093\pi$
$23$	1.61774	+	2.02859i	0.337323	+	0.422989i	−0.584021	+	0.811739i	$0.698521\pi$
$24$		0			0
$25$	−1.62584	+	0.782964i	−0.325168	+	0.156593i
$26$	−3.32531	−	4.16980i	−0.652146	−	0.817765i
$27$		0			0
$28$	1.45763	+	2.03652i	0.275466	+	0.384867i
$29$	3.80345	−	4.76938i	0.706283	−	0.885651i	−0.291192	−	0.956665i	$-0.594052\pi$
$29$	3.80345	−	4.76938i	0.706283	−	0.885651i	0.997475	+	0.0710132i	$0.0226233\pi$
$30$		0			0
$31$	2.25866			0.405668			0.202834	−	0.979213i	$-0.434985\pi$
$31$	2.25866			0.405668			0.202834	+	0.979213i	$0.434985\pi$
$32$	−3.09338	+	3.87897i	−0.546837	+	0.685712i
$33$		0			0
$34$	−3.88544	+	1.87113i	−0.666347	+	0.320896i
$35$	−1.18405	−	6.79925i	−0.200141	−	1.14928i
$36$		0			0
$37$	6.33364	−	7.94214i	1.04124	−	1.30568i	0.0904353	−	0.995902i	$-0.471174\pi$
$37$	6.33364	−	7.94214i	1.04124	−	1.30568i	0.950809	−	0.309777i	$-0.100254\pi$
$38$	11.9767	+	5.76770i	1.94288	+	0.935644i
$39$		0			0
$40$	4.24981	−	2.04660i	0.671954	−	0.323596i
$41$	0.261037	+	1.14368i	0.0407672	+	0.178613i	0.991213	−	0.132279i	$-0.0422295\pi$
$41$	0.261037	+	1.14368i	0.0407672	+	0.178613i	−0.950445	+	0.310892i	$0.899372\pi$
$42$		0			0
$43$	−0.464819	+	2.03651i	−0.0708843	+	0.310564i	−0.997924	−	0.0643982i	$-0.979487\pi$
$43$	−0.464819	+	2.03651i	−0.0708843	+	0.310564i	0.927040	+	0.374962i	$0.122344\pi$
$44$	1.11881	+	4.90184i	0.168668	+	0.738981i
$45$		0			0
$46$	−0.991084	−	4.34222i	−0.146127	−	0.640226i
$47$	−10.4372	−	5.02627i	−1.52242	−	0.733157i	−0.529097	−	0.848561i	$-0.677469\pi$
$47$	−10.4372	−	5.02627i	−1.52242	−	0.733157i	−0.993319	+	0.115405i	$0.963184\pi$
$48$		0			0
$49$	6.96220	+	0.726468i	0.994600	+	0.103781i
$50$	3.09761			0.438069
$51$		0			0
$52$	0.654443	+	2.86730i	0.0907549	+	0.397623i
$53$	−5.52071	−	6.92275i	−0.758328	−	0.950913i	0.241482	−	0.970405i	$-0.422366\pi$
$53$	−5.52071	−	6.92275i	−0.758328	−	0.950913i	−0.999810	+	0.0194925i	$0.993795\pi$
$54$		0			0
$55$	3.08318	−	13.5083i	0.415736	−	1.82146i
$56$	0.820788	+	4.71326i	0.109682	+	0.629836i
$57$		0			0
$58$	−9.43447	+	4.54340i	−1.23881	+	0.596578i
$59$	−1.55399	+	6.80849i	−0.202313	+	0.886390i	0.767211	+	0.641394i	$0.221644\pi$
$59$	−1.55399	+	6.80849i	−0.202313	+	0.886390i	−0.969524	+	0.244996i	$0.921213\pi$
$60$		0			0
$61$	−3.28315	+	4.11694i	−0.420365	+	0.527121i	−0.946251	−	0.323434i	$-0.895162\pi$
$61$	−3.28315	+	4.11694i	−0.420365	+	0.527121i	0.525886	+	0.850555i	$0.323734\pi$
$62$	−3.49318	−	1.68223i	−0.443634	−	0.213643i
$63$		0			0
$64$	−1.33142	+	0.641176i	−0.166427	+	0.0801470i
$65$	1.80349	−	7.90160i	0.223695	−	0.980073i
$66$		0			0
$67$	−3.66376			−0.447600			−0.223800	−	0.974635i	$-0.571846\pi$
$67$	−3.66376			−0.447600			−0.223800	+	0.974635i	$0.571846\pi$
$68$	2.37809			0.288386
$69$		0			0
$70$	−3.23279	+	11.3974i	−0.386392	+	1.36225i
$71$	−0.0227312	−	0.0285040i	−0.00269770	−	0.00338281i	0.780481	−	0.625180i	$-0.214974\pi$
$71$	−0.0227312	−	0.0285040i	−0.00269770	−	0.00338281i	−0.783179	+	0.621797i	$0.786403\pi$
$72$		0			0
$73$	−4.18971	+	2.01766i	−0.490368	+	0.236149i	−0.662693	−	0.748891i	$-0.730587\pi$
$73$	−4.18971	+	2.01766i	−0.490368	+	0.236149i	0.172325	+	0.985040i	$0.444872\pi$
$74$	−15.7106	+	7.56583i	−1.82632	+	0.879510i
$75$		0			0
$76$	−4.57043	−	5.73114i	−0.524264	−	0.657407i
$77$	12.3276	+	6.74716i	1.40487	+	0.768910i
$78$		0			0
$79$	13.3648			1.50366			0.751829	−	0.659359i	$-0.229172\pi$
$79$	13.3648			1.50366			0.751829	+	0.659359i	$0.229172\pi$
$80$	−13.0353			−1.45739
$81$		0			0
$82$	0.448086	−	1.96319i	0.0494828	−	0.216798i
$83$	5.75678	−	2.77232i	0.631889	−	0.304302i	−0.0903868	−	0.995907i	$-0.528810\pi$
$83$	5.75678	−	2.77232i	0.631889	−	0.304302i	0.722276	+	0.691605i	$0.243096\pi$
$84$		0			0
$85$	−5.90446	−	2.84344i	−0.640429	−	0.308414i
$86$	2.23564	−	2.80340i	0.241075	−	0.302299i
$87$		0			0
$88$	−2.13727	+	9.36400i	−0.227834	+	0.998206i
$89$	7.45728	−	3.59123i	0.790470	−	0.380670i	0.00532759	−	0.999986i	$-0.498304\pi$
$89$	7.45728	−	3.59123i	0.790470	−	0.380670i	0.785142	+	0.619316i	$0.212590\pi$
$90$		0			0
$91$	7.21098	+	3.94671i	0.755916	+	0.413728i
$92$	−0.546524	+	2.39448i	−0.0569791	+	0.249642i
$93$		0			0
$94$	12.3983	+	15.5469i	1.27878	+	1.60354i
$95$	4.49511	+	19.6944i	0.461188	+	2.02060i
$96$		0			0
$97$	−1.62118			−0.164606			−0.0823028	−	0.996607i	$-0.526227\pi$
$97$	−1.62118			−0.164606			−0.0823028	+	0.996607i	$0.526227\pi$
$98$	−10.2265	−	6.30890i	−1.03303	−	0.637295i
$99$		0			0
$100$	−1.53899	−	0.741139i	−0.153899	−	0.0741139i
$101$	0.394614	+	1.72892i	0.0392656	+	0.172034i	0.990759	−	0.135636i	$-0.0433078\pi$
$101$	0.394614	+	1.72892i	0.0392656	+	0.172034i	−0.951493	+	0.307670i	$0.900451\pi$
$102$		0			0
$103$	−0.984963	−	4.31540i	−0.0970513	−	0.425209i	0.902938	−	0.429770i	$-0.141405\pi$
$103$	−0.984963	−	4.31540i	−0.0970513	−	0.425209i	−0.999990	+	0.00456072i	$0.998548\pi$
$104$	−1.25018	+	5.47742i	−0.122591	+	0.537105i
$105$		0			0
$106$	3.38217	+	14.8183i	0.328505	+	1.43928i
$107$	−6.07016	+	2.92323i	−0.586824	+	0.282600i	−0.703643	−	0.710554i	$-0.748445\pi$
$107$	−6.07016	+	2.92323i	−0.586824	+	0.282600i	0.116819	+	0.993153i	$0.462730\pi$
$108$		0			0
$109$	−1.17257	−	0.564681i	−0.112312	−	0.0540866i	0.376884	−	0.926260i	$-0.376995\pi$
$109$	−1.17257	−	0.564681i	−0.112312	−	0.0540866i	−0.489196	+	0.872174i	$0.662710\pi$
$110$	−14.8292	+	18.5952i	−1.41391	+	1.77298i
$111$		0			0
$112$	3.60778	−	12.7194i	0.340903	−	1.20187i
$113$	1.50922	−	0.726801i	0.141975	−	0.0683717i	−0.361547	−	0.932354i	$-0.617751\pi$
$113$	1.50922	−	0.726801i	0.141975	−	0.0683717i	0.503522	+	0.863982i	$0.332037\pi$
$114$		0			0
$115$	4.21997	−	5.29167i	0.393514	−	0.493451i
$116$	5.77440			0.536139
$117$		0			0
$118$	7.47424	−	9.37240i	0.688060	−	0.862800i
$119$	4.40871	−	4.97440i	0.404146	−	0.456003i
$120$		0			0
$121$	10.7325	+	13.4581i	0.975680	+	1.22346i
$122$	8.14387	−	3.92188i	0.737311	−	0.355070i
$123$		0			0
$124$	1.33303	+	1.67156i	0.119709	+	0.150111i
$125$	−5.19710	−	6.51696i	−0.464843	−	0.582895i
$126$		0			0
$127$	−9.74258	+	12.2168i	−0.864514	+	1.08407i	0.131180	+	0.991359i	$0.458124\pi$
$127$	−9.74258	+	12.2168i	−0.864514	+	1.08407i	−0.995693	+	0.0927074i	$0.970448\pi$
$128$	12.4595			1.10127
$129$		0			0
$130$	−8.67424	+	10.8771i	−0.760781	+	0.953989i
$131$	−2.95354	+	12.9403i	−0.258052	+	1.13060i	0.665278	+	0.746595i	$0.268313\pi$
$131$	−2.95354	+	12.9403i	−0.258052	+	1.13060i	−0.923331	+	0.384006i	$0.874544\pi$
$132$		0			0
$133$	−20.4612	−	1.06462i	−1.77421	−	0.0923142i
$134$	5.66626	+	2.72873i	0.489490	+	0.235726i
$135$		0			0
$136$	4.09299	+	1.97108i	0.350971	+	0.169019i
$137$	−3.55123	+	15.5589i	−0.303402	+	1.32929i	0.561553	+	0.827441i	$0.310204\pi$
$137$	−3.55123	+	15.5589i	−0.303402	+	1.32929i	−0.864955	+	0.501849i	$0.832653\pi$
$138$		0			0
$139$	0.781405	+	3.42356i	0.0662779	+	0.290382i	0.997195	−	0.0748483i	$-0.0238473\pi$
$139$	0.781405	+	3.42356i	0.0662779	+	0.290382i	−0.930917	+	0.365231i	$0.880990\pi$
$140$	4.33310	−	4.88909i	0.366213	−	0.413203i
$141$		0			0
$142$	0.0139259	+	0.0610134i	0.00116864	+	0.00512013i
$143$	10.2897	+	12.9028i	0.860465	+	1.07899i
$144$		0			0
$145$	−14.3370	−	6.90433i	−1.19062	−	0.573374i
$146$	7.98240			0.660628
$147$		0			0
$148$	9.61573			0.790408
$149$	10.2821	+	4.95158i	0.842340	+	0.405649i	0.804728	−	0.593643i	$-0.202311\pi$
$149$	10.2821	+	4.95158i	0.842340	+	0.405649i	0.0376111	+	0.999292i	$0.488025\pi$
$150$		0			0
$151$	8.55043	+	10.7219i	0.695825	+	0.872536i	0.996704	−	0.0811259i	$-0.0258516\pi$
$151$	8.55043	+	10.7219i	0.695825	+	0.872536i	−0.300879	+	0.953662i	$0.597280\pi$
$152$	−3.11602	−	13.6522i	−0.252743	−	1.10734i
$153$		0			0
$154$	−14.0403	−	19.6164i	−1.13140	−	1.58074i
$155$	−1.31106	−	5.74412i	−0.105307	−	0.461379i
$156$		0			0
$157$	1.56797	−	6.86972i	0.125138	−	0.548263i	−0.873025	−	0.487675i	$-0.837845\pi$
$157$	1.56797	−	6.86972i	0.125138	−	0.548263i	0.998163	−	0.0605884i	$-0.0192977\pi$
$158$	−20.6696	−	9.95394i	−1.64438	−	0.791893i
$159$		0			0
$160$	11.6604	+	5.61535i	0.921835	+	0.443932i
$161$	3.99548	+	5.58228i	0.314888	+	0.439946i
$162$		0			0
$163$	0.883948	−	3.87283i	0.0692361	−	0.303343i	−0.928440	−	0.371483i	$-0.878849\pi$
$163$	0.883948	−	3.87283i	0.0692361	−	0.303343i	0.997676	+	0.0681399i	$0.0217064\pi$
$164$	−0.692339	+	0.868166i	−0.0540626	+	0.0677923i
$165$		0			0
$166$	−10.9680			−0.851286
$167$	4.77982	−	5.99371i	0.369874	−	0.463807i	−0.561710	−	0.827334i	$-0.689856\pi$
$167$	4.77982	−	5.99371i	0.369874	−	0.463807i	0.931584	+	0.363527i	$0.118428\pi$
$168$		0			0
$169$	−2.08649	−	2.61638i	−0.160499	−	0.201260i
$170$	7.01389	+	8.79514i	0.537941	+	0.674556i
$171$		0			0
$172$	−1.78148	+	0.857915i	−0.135837	+	0.0654154i
$173$	−1.59733	−	2.00299i	−0.121443	−	0.152285i	0.717393	−	0.696668i	$-0.245335\pi$
$173$	−1.59733	−	2.00299i	−0.121443	−	0.152285i	−0.838836	+	0.544383i	$0.816764\pi$
$174$		0			0
$175$	−4.40340	+	1.84522i	−0.332866	+	0.139485i
$176$	16.5493	−	20.7522i	1.24745	−	1.56426i
$177$		0			0
$178$	−14.2079			−1.06493
$179$	4.85586	−	6.08906i	0.362944	−	0.455118i	−0.566510	−	0.824055i	$-0.691707\pi$
$179$	4.85586	−	6.08906i	0.362944	−	0.455118i	0.929454	+	0.368937i	$0.120278\pi$
$180$		0			0
$181$	−11.9004	+	5.73095i	−0.884553	+	0.425978i	−0.820285	−	0.571955i	$-0.806185\pi$
$181$	−11.9004	+	5.73095i	−0.884553	+	0.425978i	−0.0642673	+	0.997933i	$0.520471\pi$
$182$	−8.21280	−	11.4745i	−0.608774	−	0.850547i
$183$		0			0
$184$	−2.92530	+	3.66821i	−0.215656	+	0.270424i
$185$	−23.8745	−	11.4973i	−1.75529	−	0.845301i
$186$		0			0
$187$	12.0229	−	5.78993i	0.879202	−	0.423401i
$188$	−2.44006	−	10.6906i	−0.177960	−	0.779694i
$189$		0			0
$190$	7.71613	−	33.8066i	0.559787	−	2.45259i
$191$	0.0983165	+	0.430753i	0.00711393	+	0.0311682i	0.978360	−	0.206908i	$-0.0663402\pi$
$191$	0.0983165	+	0.430753i	0.00711393	+	0.0311682i	−0.971246	+	0.238077i	$0.923483\pi$
$192$		0			0
$193$	−4.70319	−	20.6060i	−0.338543	−	1.48325i	−0.802102	−	0.597187i	$-0.796285\pi$
$193$	−4.70319	−	20.6060i	−0.338543	−	1.48325i	0.463559	−	0.886066i	$-0.346572\pi$
$194$	2.50726	+	1.20743i	0.180011	+	0.0866887i
$195$		0			0
$196$	3.57134	+	5.58125i	0.255096	+	0.398660i
$197$	−9.72368			−0.692783			−0.346392	−	0.938090i	$-0.612593\pi$
$197$	−9.72368			−0.692783			−0.346392	+	0.938090i	$0.612593\pi$
$198$		0			0
$199$	−3.66797	−	16.0704i	−0.260015	−	1.13920i	−0.921234	−	0.389008i	$-0.872818\pi$
$199$	−3.66797	−	16.0704i	−0.260015	−	1.13920i	0.661219	−	0.750193i	$-0.270039\pi$
$200$	−2.03450	−	2.55118i	−0.143861	−	0.180396i
$201$		0			0
$202$	0.677380	−	2.96779i	0.0476603	−	0.208813i
$203$	10.7051	−	12.0787i	0.751348	−	0.847756i
$204$		0			0
$205$	2.75703	−	1.32771i	0.192559	−	0.0927315i
$206$	−1.69075	+	7.40765i	−0.117800	+	0.516116i
$207$		0			0
$208$	9.68043	−	12.1389i	0.671217	−	0.841679i
$209$	−37.0603	−	17.8473i	−2.56351	−	1.23452i
$210$		0			0
$211$	13.3485	−	6.42831i	0.918950	−	0.442543i	0.0862540	−	0.996273i	$-0.472510\pi$
$211$	13.3485	−	6.42831i	0.918950	−	0.442543i	0.832696	+	0.553730i	$0.186796\pi$
$212$	1.86507	−	8.17139i	0.128093	−	0.561213i
$213$		0			0
$214$	11.5651			0.790574
$215$	5.44895			0.371615
$216$		0			0
$217$	5.96779	+	0.310510i	0.405120	+	0.0210788i
$218$	1.39289	+	1.74663i	0.0943387	+	0.118297i
$219$		0			0
$220$	11.8167	−	5.69062i	0.796682	−	0.383662i
$221$	7.03272	−	3.38678i	0.473072	−	0.227820i
$222$		0			0
$223$	11.6457	+	14.6033i	0.779855	+	0.977907i	0.999997	+	0.00243896i	$0.000776345\pi$
$223$	11.6457	+	14.6033i	0.779855	+	0.977907i	−0.220142	+	0.975468i	$0.570652\pi$
$224$	−8.70651	+	9.82367i	−0.581728	+	0.656372i
$225$		0			0
$226$	−2.87542			−0.191270
$227$	8.19861			0.544161			0.272081	−	0.962274i	$-0.412288\pi$
$227$	8.19861			0.544161			0.272081	+	0.962274i	$0.412288\pi$
$228$		0			0
$229$	−0.894228	+	3.91787i	−0.0590922	+	0.258900i	−0.995842	−	0.0911007i	$-0.970961\pi$
$229$	−0.894228	+	3.91787i	−0.0590922	+	0.258900i	0.936749	+	0.350001i	$0.113819\pi$
$230$	−10.4676	+	5.04095i	−0.690216	+	0.332391i
$231$		0			0
$232$	9.93845	+	4.78610i	0.652491	+	0.314223i
$233$	−11.0328	+	13.8347i	−0.722786	+	0.906344i	−0.998492	−	0.0548974i	$-0.982517\pi$
$233$	−11.0328	+	13.8347i	−0.722786	+	0.906344i	0.275706	+	0.961242i	$0.411088\pi$
$234$		0			0
$235$	−6.72423	+	29.4608i	−0.438641	+	1.92181i
$236$	−5.95589	+	2.86820i	−0.387695	+	0.186704i
$237$		0			0
$238$	−10.5232	+	4.40970i	−0.682121	+	0.285838i
$239$	−4.88801	+	21.4158i	−0.316179	+	1.38527i	0.528017	+	0.849234i	$0.322936\pi$
$239$	−4.88801	+	21.4158i	−0.316179	+	1.38527i	−0.844195	+	0.536036i	$0.819921\pi$
$240$		0			0
$241$	4.41845	+	5.54056i	0.284617	+	0.356899i	0.903503	−	0.428583i	$-0.140987\pi$
$241$	4.41845	+	5.54056i	0.284617	+	0.356899i	−0.618885	+	0.785481i	$0.712415\pi$
$242$	−6.57508	−	28.8073i	−0.422662	−	1.85180i
$243$		0			0
$244$	−4.98448			−0.319099
$245$	−2.19374	−	18.1276i	−0.140153	−	1.15813i
$246$		0			0
$247$	−21.6782	−	10.4397i	−1.37935	−	0.664259i
$248$	0.908830	+	3.98184i	0.0577107	+	0.252847i
$249$		0			0
$250$	3.18392	+	13.9497i	0.201369	+	0.882254i
$251$	1.70200	−	7.45696i	0.107429	−	0.470679i	−0.892382	−	0.451280i	$-0.850968\pi$
$251$	1.70200	−	7.45696i	0.107429	−	0.470679i	0.999812	−	0.0193991i	$-0.00617533\pi$
$252$		0			0
$253$	3.06676	+	13.4364i	0.192806	+	0.844737i
$254$	24.1665	−	11.6380i	1.51634	−	0.730231i
$255$		0			0
$256$	−16.6066	−	7.99730i	−1.03791	−	0.499831i
$257$	0.779607	−	0.977596i	0.0486305	−	0.0609808i	−0.756921	−	0.653506i	$-0.773297\pi$
$257$	0.779607	−	0.977596i	0.0486305	−	0.0609808i	0.805552	+	0.592525i	$0.201869\pi$
$258$		0			0
$259$	17.8265	−	20.1138i	1.10768	−	1.24981i
$260$	6.91211	−	3.32870i	0.428671	−	0.206437i
$261$		0			0
$262$	14.2056	−	17.8133i	0.877628	−	1.10051i
$263$	31.6443			1.95127			0.975637	−	0.219391i	$-0.0704072\pi$
$263$	31.6443			1.95127			0.975637	+	0.219391i	$0.0704072\pi$
$264$		0			0
$265$	−14.4011	+	18.0584i	−0.884650	+	1.10932i
$266$	30.8518	+	16.8858i	1.89164	+	1.03533i
$267$		0			0
$268$	−2.16229	−	2.71143i	−0.132083	−	0.165627i
$269$	−1.24141	+	0.597831i	−0.0756900	+	0.0364504i	−0.471346	−	0.881948i	$-0.656232\pi$
$269$	−1.24141	+	0.597831i	−0.0756900	+	0.0364504i	0.395656	+	0.918399i	$0.370517\pi$
$270$		0			0
$271$	18.4367	+	23.1188i	1.11995	+	1.40437i	0.903771	+	0.428015i	$0.140787\pi$
$271$	18.4367	+	23.1188i	1.11995	+	1.40437i	0.216176	+	0.976354i	$0.430642\pi$
$272$	−7.82748	−	9.81535i	−0.474611	−	0.595143i
$273$		0			0
$274$	17.0803	−	21.4180i	1.03186	−	1.29391i
$275$	−9.58511			−0.578004
$276$		0			0
$277$	−5.34327	+	6.70025i	−0.321046	+	0.402579i	−0.915998	−	0.401182i	$-0.868600\pi$
$277$	−5.34327	+	6.70025i	−0.321046	+	0.402579i	0.594952	+	0.803761i	$0.297171\pi$
$278$	1.34133	−	5.87674i	0.0804475	−	0.352464i
$279$		0			0
$280$	11.5101	−	4.82324i	0.687861	−	0.288244i
$281$	−13.7316	−	6.61279i	−0.819159	−	0.394486i	−0.0231209	−	0.999733i	$-0.507360\pi$
$281$	−13.7316	−	6.61279i	−0.819159	−	0.394486i	−0.796038	+	0.605247i	$0.793075\pi$
$282$		0			0
$283$	−27.3965	−	13.1935i	−1.62856	−	0.784271i	−0.999979	−	0.00652285i	$-0.997924\pi$
$283$	−27.3965	−	13.1935i	−1.62856	−	0.784271i	−0.628576	−	0.777748i	$-0.716362\pi$
$284$	0.00767931	−	0.0336453i	0.000455683	−	0.00199648i
$285$		0			0
$286$	−6.30380	−	27.6187i	−0.372751	−	1.63313i
$287$	0.532479	+	3.05769i	0.0314312	+	0.180490i
$288$		0			0
$289$	2.37839	+	10.4204i	0.139905	+	0.612964i
$290$	17.0309	+	21.3560i	1.00009	+	1.25407i
$291$		0			0
$292$	−3.96590	−	1.90988i	−0.232087	−	0.111767i
$293$	0.459582			0.0268491			0.0134245	−	0.999910i	$-0.495727\pi$
$293$	0.459582			0.0268491			0.0134245	+	0.999910i	$0.495727\pi$
$294$		0			0
$295$	18.2171			1.06064
$296$	16.5499	+	7.96999i	0.961941	+	0.463246i
$297$		0			0
$298$	−12.2140	−	15.3159i	−0.707540	−	0.887227i
$299$	1.79388	+	7.85952i	0.103743	+	0.454528i
$300$		0			0
$301$	−1.50810	+	5.31691i	−0.0869257	+	0.306461i
$302$	−5.23828	−	22.9504i	−0.301429	−	1.32065i
$303$		0			0
$304$	−8.61118	+	37.7280i	−0.493885	+	2.16385i
$305$	12.3757	+	5.95984i	0.708633	+	0.341260i
$306$		0			0
$307$	−28.0826	−	13.5239i	−1.60276	−	0.771849i	−0.603095	−	0.797669i	$-0.706066\pi$
$307$	−28.0826	−	13.5239i	−1.60276	−	0.771849i	−0.999667	+	0.0258203i	$0.991780\pi$
$308$	2.28222	+	13.1053i	0.130042	+	0.746747i
$309$		0			0
$310$	−2.25051	+	9.86013i	−0.127820	+	0.560018i
$311$	−0.877798	+	1.10072i	−0.0497754	+	0.0624163i	−0.806096	−	0.591785i	$-0.798424\pi$
$311$	−0.877798	+	1.10072i	−0.0497754	+	0.0624163i	0.756321	+	0.654201i	$0.226995\pi$
$312$		0			0
$313$	−21.9818			−1.24248			−0.621241	−	0.783619i	$-0.713371\pi$
$313$	−21.9818			−1.24248			−0.621241	+	0.783619i	$0.713371\pi$
$314$	−7.54145	+	9.45668i	−0.425589	+	0.533671i
$315$		0			0
$316$	7.88769	+	9.89085i	0.443717	+	0.556404i
$317$	−9.27168	−	11.6263i	−0.520749	−	0.652999i	0.450019	−	0.893019i	$-0.351417\pi$
$317$	−9.27168	−	11.6263i	−0.520749	−	0.652999i	−0.970768	+	0.240020i	$0.922846\pi$
$318$		0			0
$319$	29.1936	−	14.0589i	1.63453	−	0.787147i
$320$	2.40344	+	3.01382i	0.134356	+	0.168477i
$321$		0			0
$322$	−2.02167	−	11.6092i	−0.112663	−	0.646954i
$323$	−12.1303	+	15.2109i	−0.674945	+	0.846355i
$324$		0			0
$325$	−5.60675			−0.311007
$326$	−4.25152	+	5.33124i	−0.235470	+	0.295270i
$327$		0			0
$328$	−1.91118	+	0.920375i	−0.105527	+	0.0508192i
$329$	−26.8858	−	14.7151i	−1.48226	−	0.811272i
$330$		0			0
$331$	−16.6140	+	20.8333i	−0.913190	+	1.14510i	0.0758006	+	0.997123i	$0.475849\pi$
$331$	−16.6140	+	20.8333i	−0.913190	+	1.14510i	−0.988990	+	0.147981i	$0.952723\pi$
$332$	5.44927	+	2.62423i	0.299067	+	0.144023i
$333$		0			0
$334$	−11.8564	+	5.70972i	−0.648751	+	0.312422i
$335$	2.12666	+	9.31751i	0.116192	+	0.509070i
$336$		0			0
$337$	1.18060	−	5.17253i	0.0643111	−	0.281765i	−0.932539	−	0.361068i	$-0.882412\pi$
$337$	1.18060	−	5.17253i	0.0643111	−	0.281765i	0.996851	+	0.0793026i	$0.0252693\pi$
$338$	1.27825	+	5.60040i	0.0695278	+	0.304621i
$339$		0			0
$340$	−1.38038	−	6.04785i	−0.0748617	−	0.327991i
$341$	10.8091	+	5.20540i	0.585347	+	0.281888i
$342$		0			0
$343$	18.2955	+	2.87659i	0.987864	+	0.155321i
$344$	−3.77723			−0.203655
$345$		0			0
$346$	0.978581	+	4.28744i	0.0526088	+	0.230494i
$347$	−15.5319	−	19.4763i	−0.833794	−	1.04554i	−0.998248	−	0.0591602i	$-0.981158\pi$
$347$	−15.5319	−	19.4763i	−0.833794	−	1.04554i	0.164454	−	0.986385i	$-0.447414\pi$
$348$		0			0
$349$	−7.18254	+	31.4688i	−0.384473	+	1.68448i	0.298796	+	0.954317i	$0.403415\pi$
$349$	−7.18254	+	31.4688i	−0.384473	+	1.68448i	−0.683268	+	0.730167i	$0.739442\pi$
$350$	8.18445	+	0.425845i	0.437477	+	0.0227624i
$351$		0			0
$352$	−23.7434	+	11.4342i	−1.26553	+	0.609445i
$353$	−3.49150	+	15.2973i	−0.185834	+	0.814190i	0.792949	+	0.609288i	$0.208545\pi$
$353$	−3.49150	+	15.2973i	−0.185834	+	0.814190i	−0.978782	+	0.204902i	$0.934312\pi$
$354$		0			0
$355$	−0.0592956	+	0.0743543i	−0.00314708	+	0.00394632i
$356$	7.05892	+	3.39940i	0.374122	+	0.180168i
$357$		0			0
$358$	−12.0450	+	5.80056i	−0.636597	+	0.306569i
$359$	−1.15824	+	5.07457i	−0.0611294	+	0.267826i	−0.996252	−	0.0864990i	$-0.972432\pi$
$359$	−1.15824	+	5.07457i	−0.0611294	+	0.267826i	0.935123	+	0.354325i	$0.115289\pi$
$360$		0			0
$361$	40.9707			2.15636
$362$	22.6732			1.19168
$363$		0			0
$364$	1.33497	+	7.66589i	0.0699715	+	0.401802i
$365$	7.56316	+	9.48390i	0.395874	+	0.496410i
$366$		0			0
$367$	−21.7414	+	10.4701i	−1.13489	+	0.546534i	−0.904462	−	0.426555i	$-0.859727\pi$
$367$	−21.7414	+	10.4701i	−1.13489	+	0.546534i	−0.230429	+	0.973089i	$0.574013\pi$
$368$	11.6819	−	5.62569i	0.608959	−	0.293259i
$369$		0			0
$370$	28.3604	+	35.5628i	1.47439	+	1.84882i
$371$	−13.6350	−	19.0501i	−0.707893	−	0.989031i
$372$		0			0
$373$	20.6990			1.07175			0.535876	−	0.844297i	$-0.319981\pi$
$373$	20.6990			1.07175			0.535876	+	0.844297i	$0.319981\pi$
$374$	−22.9065			−1.18447
$375$		0			0
$376$	4.66126	−	20.4223i	0.240386	−	1.05320i
$377$	17.0766	−	8.22366i	0.879490	−	0.423540i
$378$		0			0
$379$	−13.2389	−	6.37552i	−0.680036	−	0.327488i	0.0617815	−	0.998090i	$-0.480322\pi$
$379$	−13.2389	−	6.37552i	−0.680036	−	0.327488i	−0.741818	+	0.670601i	$0.766036\pi$
$380$	−11.9222	+	14.9500i	−0.611596	+	0.766918i
$381$		0			0
$382$	0.168766	−	0.739413i	0.00863484	−	0.0378317i
$383$	−21.0326	+	10.1288i	−1.07472	+	0.517556i	−0.885624	−	0.464403i	$-0.846269\pi$
$383$	−21.0326	+	10.1288i	−1.07472	+	0.517556i	−0.189093	+	0.981959i	$0.560555\pi$
$384$		0			0
$385$	10.0034	−	35.2675i	0.509819	−	1.79740i
$386$	−8.07331	+	35.3715i	−0.410920	+	1.80036i
$387$		0			0
$388$	−0.956793	−	1.19978i	−0.0485738	−	0.0609096i
$389$	2.21818	+	9.71850i	0.112466	+	0.492747i	0.999517	+	0.0310753i	$0.00989318\pi$
$389$	2.21818	+	9.71850i	0.112466	+	0.492747i	−0.887051	+	0.461672i	$0.847250\pi$
$390$		0			0
$391$	6.51855			0.329657
$392$	1.52071	+	12.5661i	0.0768075	+	0.634685i
$393$		0			0
$394$	15.0383	+	7.24208i	0.757620	+	0.364851i
$395$	−7.75770	−	33.9887i	−0.390332	−	1.71016i
$396$		0			0
$397$	−6.32003	−	27.6899i	−0.317193	−	1.38971i	−0.842452	−	0.538771i	$-0.818889\pi$
$397$	−6.32003	−	27.6899i	−0.317193	−	1.38971i	0.525259	−	0.850942i	$-0.323968\pi$
$398$	−6.29629	+	27.5858i	−0.315604	+	1.38275i
$399$		0			0
$400$	2.00660	+	8.79150i	0.100330	+	0.439575i
$401$	−14.4779	+	6.97217i	−0.722990	+	0.348173i	−0.758923	−	0.651181i	$-0.774274\pi$
$401$	−14.4779	+	6.97217i	−0.722990	+	0.348173i	0.0359331	+	0.999354i	$0.488560\pi$
$402$		0			0
$403$	6.32273	+	3.04486i	0.314957	+	0.151675i
$404$	−1.04662	+	1.31242i	−0.0520713	+	0.0652954i
$405$		0			0
$406$	−25.5522	+	10.7075i	−1.26813	+	0.531403i
$407$	48.6142	−	23.4114i	2.40972	−	1.16046i
$408$		0			0
$409$	13.0317	−	16.3412i	0.644375	−	0.808021i	−0.347167	−	0.937803i	$-0.612856\pi$
$409$	13.0317	−	16.3412i	0.644375	−	0.808021i	0.991543	+	0.129782i	$0.0414278\pi$
$410$	−5.25279			−0.259417
$411$		0			0
$412$	2.61238	−	3.27582i	0.128703	−	0.161388i
$413$	−5.04193	+	17.7756i	−0.248097	+	0.874681i
$414$		0			0
$415$	−10.3920	−	13.0312i	−0.510123	−	0.639674i
$416$	−13.8885	+	6.68837i	−0.680941	+	0.327924i
$417$		0			0
$418$	44.0238	+	55.2041i	2.15327	+	2.70012i
$419$	19.8170	+	24.8497i	0.968122	+	1.21399i	0.976828	+	0.214025i	$0.0686573\pi$
$419$	19.8170	+	24.8497i	0.968122	+	1.21399i	−0.00870603	+	0.999962i	$0.502771\pi$
$420$		0			0
$421$	−9.93634	+	12.4598i	−0.484268	+	0.607252i	−0.962600	−	0.270927i	$-0.912670\pi$
$421$	−9.93634	+	12.4598i	−0.484268	+	0.607252i	0.478332	+	0.878179i	$0.341241\pi$
$422$	−25.4321			−1.23802
$423$		0			0
$424$	9.98286	−	12.5181i	0.484810	−	0.607933i
$425$	−1.00881	+	4.41989i	−0.0489345	+	0.214396i
$426$		0			0
$427$	−9.24065	+	10.4263i	−0.447186	+	0.504566i
$428$	−5.74590	−	2.76708i	−0.277738	−	0.133752i
$429$		0			0
$430$	−8.42717	−	4.05831i	−0.406394	−	0.195709i
$431$	−0.749085	+	3.28195i	−0.0360821	+	0.158086i	−0.989759	−	0.142745i	$-0.954407\pi$
$431$	−0.749085	+	3.28195i	−0.0360821	+	0.158086i	0.953677	+	0.300831i	$0.0972642\pi$
$432$		0			0
$433$	0.988195	+	4.32956i	0.0474896	+	0.208066i	0.993106	−	0.117218i	$-0.0373975\pi$
$433$	0.988195	+	4.32956i	0.0474896	+	0.208066i	−0.945617	+	0.325283i	$0.894540\pi$
$434$	−8.99833	−	4.92496i	−0.431934	−	0.236406i
$435$		0			0
$436$	−0.274131	−	1.20105i	−0.0131285	−	0.0575197i
$437$	−12.5279	−	15.7095i	−0.599292	−	0.751489i
$438$		0			0
$439$	−21.3307	−	10.2723i	−1.01806	−	0.490270i	−0.151028	−	0.988529i	$-0.548259\pi$
$439$	−21.3307	−	10.2723i	−1.01806	−	0.490270i	−0.867028	+	0.498259i	$0.833973\pi$
$440$	25.0547			1.19443
$441$		0			0
$442$	−13.3990			−0.637326
$443$	11.8142	+	5.68943i	0.561311	+	0.270313i	0.692951	−	0.720984i	$-0.256310\pi$
$443$	11.8142	+	5.68943i	0.561311	+	0.270313i	−0.131640	+	0.991298i	$0.542024\pi$
$444$		0			0
$445$	−13.4617	−	16.8804i	−0.638145	−	0.800209i
$446$	−7.13455	−	31.2585i	−0.337831	−	1.48013i
$447$		0			0
$448$	−3.60598	+	1.51106i	−0.170367	+	0.0713911i
$449$	7.88563	+	34.5492i	0.372146	+	1.63048i	0.720742	+	0.693204i	$0.243801\pi$
$449$	7.88563	+	34.5492i	0.372146	+	1.63048i	−0.348596	+	0.937273i	$0.613341\pi$
$450$		0			0
$451$	−1.38654	+	6.07481i	−0.0652894	+	0.286052i
$452$	1.42860	+	0.687976i	0.0671956	+	0.0323597i
$453$		0			0
$454$	−12.6797	−	6.10623i	−0.595088	−	0.286580i
$455$	5.85141	−	20.6295i	0.274318	−	0.967126i
$456$		0			0
$457$	−3.51391	+	15.3954i	−0.164374	+	0.720169i	0.823806	+	0.566871i	$0.191846\pi$
$457$	−3.51391	+	15.3954i	−0.164374	+	0.720169i	−0.988180	+	0.153297i	$0.951011\pi$
$458$	4.30096	−	5.39324i	0.200971	−	0.252009i
$459$		0			0
$460$	6.40675			0.298716
$461$	−15.2819	+	19.1630i	−0.711751	+	0.892508i	−0.997840	−	0.0656953i	$-0.979073\pi$
$461$	−15.2819	+	19.1630i	−0.711751	+	0.892508i	0.286088	+	0.958203i	$0.407645\pi$
$462$		0			0
$463$	18.2675	+	22.9068i	0.848965	+	1.06457i	0.997138	+	0.0756068i	$0.0240894\pi$
$463$	18.2675	+	22.9068i	0.848965	+	1.06457i	−0.148173	+	0.988961i	$0.547339\pi$
$464$	−19.0064	−	23.8333i	−0.882350	−	1.10643i
$465$		0			0
$466$	27.3670	−	13.1792i	1.26775	−	0.610517i
$467$	−1.97732	−	2.47948i	−0.0914993	−	0.114737i	0.733974	−	0.679177i	$-0.237663\pi$
$467$	−1.97732	−	2.47948i	−0.0914993	−	0.114737i	−0.825474	+	0.564441i	$0.809092\pi$
$468$		0			0
$469$	−9.68032	−	0.503677i	−0.446995	−	0.0232576i
$470$	32.3415	−	40.5550i	1.49180	−	1.87066i
$471$		0			0
$472$	−12.6281			−0.581256
$473$	−6.91785	+	8.67472i	−0.318083	+	0.398864i
$474$		0			0
$475$	12.5906	−	6.06333i	0.577698	−	0.278205i
$476$	6.28334	+	0.326929i	0.287997	+	0.0149848i
$477$		0			0
$478$	23.5098	−	29.4804i	1.07531	−	1.34840i
$479$	−5.65635	−	2.72395i	−0.258445	−	0.124461i	0.300175	−	0.953884i	$-0.402955\pi$
$479$	−5.65635	−	2.72395i	−0.258445	−	0.124461i	−0.558620	+	0.829423i	$0.688669\pi$
$480$		0			0
$481$	28.4366	−	13.6943i	1.29660	−	0.624408i
$482$	−2.70689	−	11.8597i	−0.123295	−	0.540193i
$483$		0			0
$484$	−3.62576	+	15.8855i	−0.164807	+	0.722069i
$485$	0.941025	+	4.12290i	0.0427297	+	0.187211i
$486$		0			0
$487$	−0.787907	−	3.45205i	−0.0357035	−	0.156427i	0.953934	−	0.300017i	$-0.0969925\pi$
$487$	−0.787907	−	3.45205i	−0.0357035	−	0.156427i	−0.989637	+	0.143590i	$0.954135\pi$
$488$	−8.57890	−	4.13138i	−0.388349	−	0.187019i
$489$		0			0
$490$	−10.1084	+	29.6695i	−0.456653	+	1.34033i
$491$	−32.5769			−1.47018			−0.735088	−	0.677971i	$-0.762859\pi$
$491$	−32.5769			−1.47018			−0.735088	+	0.677971i	$0.762859\pi$
$492$		0			0
$493$	−3.41028	−	14.9414i	−0.153591	−	0.672928i
$494$	25.7514	+	32.2913i	1.15861	+	1.45285i
$495$		0			0
$496$	2.51157	−	11.0039i	0.112773	−	0.494089i
$497$	−0.0561413	−	0.0784377i	−0.00251828	−	0.00351841i
$498$		0			0
$499$	10.1964	−	4.91035i	0.456455	−	0.219817i	−0.191505	−	0.981492i	$-0.561337\pi$
$499$	10.1964	−	4.91035i	0.456455	−	0.219817i	0.647960	+	0.761674i	$0.275622\pi$
$500$	1.75574	−	7.69241i	0.0785192	−	0.344015i
$501$		0			0
$502$	−8.18612	+	10.2651i	−0.365364	+	0.458152i
$503$	21.6285	+	10.4158i	0.964369	+	0.464415i	0.848701	−	0.528873i	$-0.177385\pi$
$503$	21.6285	+	10.4158i	0.964369	+	0.464415i	0.115667	+	0.993288i	$0.463099\pi$
$504$		0			0
$505$	4.16784	−	2.00713i	0.185467	−	0.0893160i
$506$	5.26428	−	23.0643i	0.234026	−	1.02533i
$507$		0			0
$508$	−14.7912			−0.656252
$509$	−0.837443			−0.0371190			−0.0185595	−	0.999828i	$-0.505908\pi$
$509$	−0.837443			−0.0371190			−0.0185595	+	0.999828i	$0.505908\pi$
$510$		0			0
$511$	−11.3473	+	4.75503i	−0.501976	+	0.210350i
$512$	4.19020	+	5.25434i	0.185182	+	0.232211i
$513$		0			0
$514$	−1.93382	+	0.931277i	−0.0852970	+	0.0410769i
$515$	−10.4030	+	5.00982i	−0.458411	+	0.220759i
$516$		0			0
$517$	−38.3646	−	48.1077i	−1.68727	−	2.11577i
$518$	−42.5504	+	17.8305i	−1.86956	+	0.783425i
$519$		0			0
$520$	14.6556			0.642689
$521$	−0.933671			−0.0409049			−0.0204524	−	0.999791i	$-0.506511\pi$
$521$	−0.933671			−0.0409049			−0.0204524	+	0.999791i	$0.506511\pi$
$522$		0			0
$523$	−1.46116	+	6.40175i	−0.0638920	+	0.279929i	−0.996775	−	0.0802513i	$-0.974428\pi$
$523$	−1.46116	+	6.40175i	−0.0638920	+	0.279929i	0.932883	+	0.360180i	$0.117285\pi$
$524$	−11.3198	+	5.45135i	−0.494509	+	0.238143i
$525$		0			0
$526$	−48.9401	−	23.5683i	−2.13389	−	1.02763i
$527$	3.53795	−	4.43645i	0.154116	−	0.193255i
$528$		0			0
$529$	3.61991	−	15.8599i	0.157388	−	0.689560i
$530$	35.7219	−	17.2027i	1.55166	−	0.747239i
$531$		0			0
$532$	−11.2880	−	15.7710i	−0.489397	−	0.683760i
$533$	−0.811046	+	3.55342i	−0.0351303	+	0.153916i
$534$		0			0
$535$	10.9577	+	13.7405i	0.473742	+	0.594054i
$536$	−1.47421	−	6.45893i	−0.0636761	−	0.278983i
$537$		0			0
$538$	2.36518			0.101970
$539$	31.6442	+	19.5219i	1.36301	+	0.840870i
$540$		0			0
$541$	−9.63793	−	4.64138i	−0.414367	−	0.199549i	0.215073	−	0.976598i	$-0.431001\pi$
$541$	−9.63793	−	4.64138i	−0.414367	−	0.199549i	−0.629439	+	0.777050i	$0.716715\pi$
$542$	−11.2949	−	49.4863i	−0.485158	−	2.12562i
$543$		0			0
$544$	2.77361	+	12.1520i	0.118917	+	0.521012i
$545$	−0.755440	+	3.30980i	−0.0323595	+	0.141776i
$546$		0			0
$547$	−1.31163	−	5.74663i	−0.0560813	−	0.245708i	0.939116	−	0.343601i	$-0.111647\pi$
$547$	−1.31163	−	5.74663i	−0.0560813	−	0.245708i	−0.995197	+	0.0978930i	$0.968790\pi$
$548$	−13.6105	+	6.55449i	−0.581413	+	0.279994i
$549$		0			0
$550$	14.8240	+	7.13887i	0.632099	+	0.304403i
$551$	−29.4542	+	36.9344i	−1.25479	+	1.57346i
$552$		0			0
$553$	35.3122	+	1.83733i	1.50163	+	0.0781312i
$554$	13.2540	−	6.38279i	0.563109	−	0.271179i
$555$		0			0
$556$	−2.07249	+	2.59882i	−0.0878932	+	0.110215i
$557$	−24.8938			−1.05479			−0.527393	−	0.849621i	$-0.676830\pi$
$557$	−24.8938			−1.05479			−0.527393	+	0.849621i	$0.676830\pi$
$558$		0			0
$559$	−4.04656	+	5.07422i	−0.171151	+	0.214617i
$560$	−34.4416	−	1.79203i	−1.45542	−	0.0757273i
$561$		0			0
$562$	16.3117	+	20.4543i	0.688069	+	0.862811i
$563$	35.6045	−	17.1462i	1.50055	−	0.722626i	0.510050	−	0.860145i	$-0.329627\pi$
$563$	35.6045	−	17.1462i	1.50055	−	0.722626i	0.990499	+	0.137519i	$0.0439127\pi$
$564$		0			0
$565$	−2.72440	−	3.41629i	−0.114616	−	0.143724i
$566$	32.5443	+	40.8092i	1.36794	+	1.71534i
$567$		0			0
$568$	0.0411039	−	0.0515426i	0.00172468	−	0.00216268i
$569$	5.62587			0.235849			0.117924	−	0.993023i	$-0.462376\pi$
$569$	5.62587			0.235849			0.117924	+	0.993023i	$0.462376\pi$
$570$		0			0
$571$	−25.5245	+	32.0068i	−1.06817	+	1.33944i	−0.130681	+	0.991424i	$0.541716\pi$
$571$	−25.5245	+	32.0068i	−1.06817	+	1.33944i	−0.937488	+	0.348017i	$0.886855\pi$
$572$	−3.47617	+	15.2301i	−0.145346	+	0.636802i
$573$		0			0
$574$	1.45381	−	5.12551i	0.0606810	−	0.213934i
$575$	−4.21850	−	2.03152i	−0.175924	−	0.0847204i
$576$		0			0
$577$	29.6299	+	14.2690i	1.23351	+	0.594026i	0.933042	−	0.359767i	$-0.117144\pi$
$577$	29.6299	+	14.2690i	1.23351	+	0.594026i	0.300465	+	0.953793i	$0.402858\pi$
$578$	4.08264	−	17.8872i	0.169816	−	0.744011i
$579$		0			0
$580$	−3.35179	−	14.6852i	−0.139176	−	0.609768i
$581$	15.5916	−	6.53355i	0.646847	−	0.271057i
$582$		0			0
$583$	−10.4656	−	45.8529i	−0.433442	−	1.89903i
$584$	−5.24280	−	6.57427i	−0.216949	−	0.272045i
$585$		0			0
$586$	−0.710775	−	0.342291i	−0.0293618	−	0.0141399i
$587$	−19.3209			−0.797461			−0.398730	−	0.917068i	$-0.630549\pi$
$587$	−19.3209			−0.797461			−0.398730	+	0.917068i	$0.630549\pi$
$588$		0			0
$589$	−17.4913			−0.720715
$590$	−28.1739	−	13.5678i	−1.15990	−	0.558579i
$591$		0			0
$592$	−31.6501	−	39.6880i	−1.30081	−	1.63117i
$593$	−8.30801	−	36.3998i	−0.341169	−	1.49476i	−0.796610	−	0.604493i	$-0.793376\pi$
$593$	−8.30801	−	36.3998i	−0.341169	−	1.49476i	0.455441	−	0.890266i	$-0.349481\pi$
$594$		0			0
$595$	−15.2097	−	8.32458i	−0.623538	−	0.341275i
$596$	2.40381	+	10.5318i	0.0984637	+	0.431398i
$597$		0			0
$598$	3.07931	−	13.4913i	0.125922	−	0.551702i
$599$	11.7124	+	5.64039i	0.478555	+	0.230460i	0.657580	−	0.753385i	$-0.271580\pi$
$599$	11.7124	+	5.64039i	0.478555	+	0.230460i	−0.179025	+	0.983844i	$0.557294\pi$
$600$		0			0
$601$	2.76898	+	1.33347i	0.112949	+	0.0543933i	0.489505	−	0.872001i	$-0.337178\pi$
$601$	2.76898	+	1.33347i	0.112949	+	0.0543933i	−0.376556	+	0.926394i	$0.622892\pi$
$602$	6.29235	−	7.09974i	0.256457	−	0.289364i
$603$		0			0
$604$	−2.88860	+	12.6558i	−0.117536	+	0.514957i
$605$	27.9962	−	35.1062i	1.13821	−	1.42727i
$606$		0			0
$607$	29.7313			1.20676			0.603379	−	0.797455i	$-0.293821\pi$
$607$	29.7313			1.20676			0.603379	+	0.797455i	$0.293821\pi$
$608$	23.9554	−	30.0391i	0.971518	−	1.21825i
$609$		0			0
$610$	−14.7011	−	18.4346i	−0.595230	−	0.746395i
$611$	−22.4411	−	28.1403i	−0.907871	−	1.13843i
$612$		0			0
$613$	−32.1843	+	15.4991i	−1.29991	+	0.626005i	−0.950430	−	0.310939i	$-0.899357\pi$
$613$	−32.1843	+	15.4991i	−1.29991	+	0.626005i	−0.349482	+	0.936943i	$0.613642\pi$
$614$	33.3593	+	41.8312i	1.34627	+	1.68817i
$615$		0			0
$616$	−6.93437	+	24.4475i	−0.279394	+	0.985019i
$617$	−19.1872	+	24.0599i	−0.772446	+	0.968617i	−0.999987	−	0.00515160i	$-0.998360\pi$
$617$	−19.1872	+	24.0599i	−0.772446	+	0.968617i	0.227540	+	0.973769i	$0.426932\pi$
$618$		0			0
$619$	20.0927			0.807593			0.403796	−	0.914849i	$-0.367690\pi$
$619$	20.0927			0.807593			0.403796	+	0.914849i	$0.367690\pi$
$620$	3.47727	−	4.36036i	0.139651	−	0.175116i
$621$		0			0
$622$	2.17738	−	1.04857i	0.0873050	−	0.0420439i
$623$	20.1972	−	8.46349i	0.809182	−	0.339082i
$624$		0			0
$625$	−19.1825	+	24.0541i	−0.767300	+	0.962164i
$626$	33.9963	+	16.3717i	1.35876	+	0.654347i
$627$		0			0
$628$	6.00944	−	2.89400i	0.239803	−	0.115483i
$629$	−5.67892	−	24.8810i	−0.226433	−	0.992070i
$630$		0			0
$631$	−8.46250	+	37.0766i	−0.336887	+	1.47600i	0.468614	+	0.883403i	$0.344754\pi$
$631$	−8.46250	+	37.0766i	−0.336887	+	1.47600i	−0.805501	+	0.592595i	$0.798104\pi$
$632$	5.37766	+	23.5611i	0.213912	+	0.937209i
$633$		0			0
$634$	5.68014	+	24.8863i	0.225587	+	0.988362i
$635$	36.7243	+	17.6855i	1.45736	+	0.701828i
$636$		0			0
$637$	18.5101	+	11.4192i	0.733397	+	0.452447i
$638$	−55.6207			−2.20205
$639$		0			0
$640$	−7.23218	−	31.6863i	−0.285877	−	1.25251i
$641$	−2.02577	−	2.54024i	−0.0800132	−	0.100333i	0.740214	−	0.672372i	$-0.234724\pi$
$641$	−2.02577	−	2.54024i	−0.0800132	−	0.100333i	−0.820227	+	0.572038i	$0.806153\pi$
$642$		0			0
$643$	2.25734	−	9.89003i	0.0890206	−	0.390025i	−0.910715	−	0.413036i	$-0.864468\pi$
$643$	2.25734	−	9.89003i	0.0890206	−	0.390025i	0.999735	+	0.0230114i	$0.00732541\pi$
$644$	−1.77319	+	6.25150i	−0.0698737	+	0.246344i
$645$		0			0
$646$	30.0891	−	14.4902i	1.18384	−	0.570108i
$647$	−3.46337	+	15.1740i	−0.136159	+	0.596552i	0.860099	+	0.510127i	$0.170401\pi$
$647$	−3.46337	+	15.1740i	−0.136159	+	0.596552i	−0.996258	+	0.0864252i	$0.972456\pi$
$648$		0			0
$649$	−23.1279	+	29.0015i	−0.907851	+	1.13841i
$650$	8.67122	+	4.17584i	0.340113	+	0.163790i
$651$		0			0
$652$	3.38785	−	1.63150i	0.132678	−	0.0638945i
$653$	−1.43941	+	6.30645i	−0.0563284	+	0.246791i	−0.995252	−	0.0973361i	$-0.968968\pi$
$653$	−1.43941	+	6.30645i	−0.0563284	+	0.246791i	0.938923	+	0.344127i	$0.111825\pi$
$654$		0			0
$655$	34.6236			1.35286
$656$	5.86210			0.228877
$657$		0			0
$658$	30.6211	+	42.7822i	1.19373	+	1.66782i
$659$	−0.0676060	−	0.0847752i	−0.00263355	−	0.00330237i	0.780513	−	0.625140i	$-0.214958\pi$
$659$	−0.0676060	−	0.0847752i	−0.00263355	−	0.00330237i	−0.783147	+	0.621837i	$0.786387\pi$
$660$		0			0
$661$	17.3427	−	8.35180i	0.674552	−	0.324847i	−0.0650590	−	0.997881i	$-0.520724\pi$
$661$	17.3427	−	8.35180i	0.674552	−	0.324847i	0.739611	+	0.673034i	$0.235009\pi$
$662$	41.2111	−	19.8462i	1.60172	−	0.771346i
$663$		0			0
$664$	7.20377	+	9.03324i	0.279560	+	0.350558i
$665$	9.16939	+	52.6540i	0.355574	+	2.04183i
$666$		0			0
$667$	15.8281			0.612867
$668$	7.25672			0.280771
$669$		0			0
$670$	3.65054	−	15.9941i	0.141033	−	0.617905i
$671$	−25.2000	+	12.1357i	−0.972835	+	0.468493i
$672$		0			0
$673$	−17.5251	−	8.43967i	−0.675545	−	0.325325i	0.0644663	−	0.997920i	$-0.479465\pi$
$673$	−17.5251	−	8.43967i	−0.675545	−	0.325325i	−0.740011	+	0.672595i	$0.765180\pi$
$674$	−5.67831	+	7.12037i	−0.218720	+	0.274266i
$675$		0			0
$676$	0.704881	−	3.08829i	0.0271108	−	0.118780i
$677$	23.3158	−	11.2283i	0.896100	−	0.431539i	0.0716215	−	0.997432i	$-0.477183\pi$
$677$	23.3158	−	11.2283i	0.896100	−	0.431539i	0.824479	+	0.565893i	$0.191468\pi$
$678$		0			0
$679$	−4.28344	−	0.222872i	−0.164383	−	0.00855304i
$680$	2.63695	−	11.5532i	0.101122	−	0.443046i
$681$		0			0
$682$	−12.8401	−	16.1010i	−0.491674	−	0.616539i
$683$	−9.52497	−	41.7316i	−0.364463	−	1.59682i	−0.741722	−	0.670708i	$-0.765990\pi$
$683$	−9.52497	−	41.7316i	−0.364463	−	1.59682i	0.377259	−	0.926108i	$-0.376867\pi$
$684$		0			0
$685$	41.6301			1.59060
$686$	−26.1528	−	18.0751i	−0.998518	−	0.690111i
$687$		0			0
$688$	9.40470	+	4.52907i	0.358551	+	0.172669i
$689$	−6.12180	−	26.8214i	−0.233222	−	1.02181i
$690$		0			0
$691$	0.601911	+	2.63715i	0.0228978	+	0.100322i	0.985086	−	0.172065i	$-0.0550440\pi$
$691$	0.601911	+	2.63715i	0.0228978	+	0.100322i	−0.962188	+	0.272387i	$0.912187\pi$
$692$	0.539629	−	2.36427i	0.0205136	−	0.0898761i
$693$		0			0
$694$	9.51534	+	41.6894i	0.361197	+	1.58251i
$695$	8.25305	−	3.97446i	0.313056	−	0.150760i
$696$		0			0
$697$	2.65529	+	1.27872i	0.100576	+	0.0484350i
$698$	34.5458	−	43.3191i	1.30758	−	1.63965i
$699$		0			0
$700$	−3.96440	−	2.16979i	−0.149840	−	0.0820105i
$701$	6.21145	−	2.99127i	0.234603	−	0.112979i	−0.312889	−	0.949790i	$-0.601297\pi$
$701$	6.21145	−	2.99127i	0.234603	−	0.112979i	0.547492	+	0.836811i	$0.315583\pi$
$702$		0			0
$703$	−49.0482	+	61.5045i	−1.84989	+	2.31969i
$704$	−7.84934			−0.295833
$705$		0			0
$706$	16.7930	−	21.0578i	0.632015	−	0.792521i
$707$	0.804958	+	4.62236i	0.0302736	+	0.173842i
$708$		0			0
$709$	−16.8019	−	21.0689i	−0.631007	−	0.791258i	0.358839	−	0.933399i	$-0.383173\pi$
$709$	−16.8019	−	21.0689i	−0.631007	−	0.791258i	−0.989846	+	0.142142i	$0.954601\pi$
$710$	0.147083	−	0.0708314i	0.00551992	−	0.00265825i
$711$		0			0
$712$	9.33168	+	11.7016i	0.349720	+	0.438534i
$713$	3.65394	+	4.58189i	0.136841	+	0.171593i
$714$		0			0
$715$	26.8411	−	33.6577i	1.00380	−	1.25873i
$716$	7.37217			0.275511
$717$		0			0
$718$	5.57077	−	6.98553i	0.207899	−	0.260698i
$719$	6.10467	−	26.7463i	0.227666	−	0.997469i	−0.723871	−	0.689935i	$-0.757639\pi$
$719$	6.10467	−	26.7463i	0.227666	−	0.997469i	0.951537	−	0.307534i	$-0.0995038\pi$
$720$		0			0
$721$	−2.00919	−	11.5375i	−0.0748260	−	0.429678i
$722$	−63.3640	−	30.5145i	−2.35817	−	1.13563i
$723$		0			0
$724$	−11.2647	−	5.42481i	−0.418651	−	0.201611i
$725$	−2.44956	+	10.7322i	−0.0909743	+	0.398584i
$726$		0			0
$727$	6.95280	+	30.4622i	0.257865	+	1.12978i	0.923529	+	0.383529i	$0.125291\pi$
$727$	6.95280	+	30.4622i	0.257865	+	1.12978i	−0.665663	+	0.746252i	$0.731851\pi$
$728$	−4.05622	+	14.3004i	−0.150333	+	0.530009i
$729$		0			0
$730$	−4.63344	−	20.3004i	−0.171491	−	0.751353i
$731$	3.27200	+	4.10296i	0.121019	+	0.151753i
$732$		0			0
$733$	30.4834	+	14.6801i	1.12593	+	0.542220i	0.901720	−	0.432320i	$-0.142305\pi$
$733$	30.4834	+	14.6801i	1.12593	+	0.542220i	0.224212	+	0.974540i	$0.428019\pi$
$734$	41.4225			1.52893
$735$		0			0
$736$	−12.8731			−0.474510
$737$	−17.5334	−	8.44364i	−0.645851	−	0.311026i
$738$		0			0
$739$	−14.8068	−	18.5672i	−0.544678	−	0.683005i	0.430965	−	0.902369i	$-0.358173\pi$
$739$	−14.8068	−	18.5672i	−0.544678	−	0.683005i	−0.975643	+	0.219364i	$0.929602\pi$
$740$	−5.58152	−	24.4543i	−0.205181	−	0.898956i
$741$		0			0
$742$	6.89915	+	39.6174i	0.253276	+	1.45440i
$743$	7.23529	+	31.6999i	0.265437	+	1.16296i	0.915258	+	0.402868i	$0.131987\pi$
$743$	7.23529	+	31.6999i	0.265437	+	1.16296i	−0.649821	+	0.760087i	$0.725156\pi$
$744$		0			0
$745$	6.62432	−	29.0230i	0.242696	−	1.06332i
$746$	−32.0124	−	15.4163i	−1.17206	−	0.564432i
$747$		0			0
$748$	11.3807	+	5.48064i	0.416118	+	0.200392i
$749$	−16.4403	+	6.88920i	−0.600715	+	0.251726i
$750$		0			0
$751$	5.19281	−	22.7512i	0.189488	−	0.830202i	−0.787399	−	0.616444i	$-0.788573\pi$
$751$	5.19281	−	22.7512i	0.189488	−	0.830202i	0.976887	−	0.213758i	$-0.0685703\pi$
$752$	−36.0931	+	45.2593i	−1.31618	+	1.65044i
$753$		0			0
$754$	−32.5350			−1.18486
$755$	22.3043	−	27.9687i	0.811735	−	1.01788i
$756$		0			0
$757$	−14.6895	−	18.4200i	−0.533898	−	0.669487i	0.439597	−	0.898195i	$-0.355121\pi$
$757$	−14.6895	−	18.4200i	−0.533898	−	0.669487i	−0.973495	+	0.228708i	$0.926550\pi$
$758$	15.7264	+	19.7203i	0.571210	+	0.716275i
$759$		0			0
$760$	−32.9109	+	15.8490i	−1.19380	+	0.574905i
$761$	−9.82010	−	12.3140i	−0.355978	−	0.446383i	0.571308	−	0.820736i	$-0.306436\pi$
$761$	−9.82010	−	12.3140i	−0.355978	−	0.446383i	−0.927286	+	0.374353i	$0.877865\pi$
$762$		0			0
$763$	−3.02051	−	1.65319i	−0.109350	−	0.0598494i
$764$	−0.260761	+	0.326984i	−0.00943401	+	0.0118299i
$765$		0			0
$766$	40.0722			1.44787
$767$	−13.5285	+	16.9643i	−0.488487	+	0.612544i
$768$		0			0
$769$	23.5179	−	11.3256i	0.848076	−	0.408412i	0.0412127	−	0.999150i	$-0.486878\pi$
$769$	23.5179	−	11.3256i	0.848076	−	0.408412i	0.806863	+	0.590739i	$0.201164\pi$
$770$	−41.7377	+	47.0932i	−1.50412	+	1.69712i
$771$		0			0
$772$	12.4741	−	15.6420i	0.448952	−	0.562968i
$773$	−10.9731	−	5.28436i	−0.394675	−	0.190065i	0.226011	−	0.974125i	$-0.427431\pi$
$773$	−10.9731	−	5.28436i	−0.394675	−	0.190065i	−0.620686	+	0.784059i	$0.713146\pi$
$774$		0			0
$775$	−3.67223	+	1.76845i	−0.131910	+	0.0635246i
$776$	−0.652322	−	2.85801i	−0.0234170	−	0.102596i
$777$		0			0
$778$	3.80765	−	16.6824i	0.136511	−	0.598093i
$779$	−2.02149	−	8.85674i	−0.0724275	−	0.317325i
$780$		0			0
$781$	−0.0430917	−	0.188797i	−0.00154194	−	0.00675568i
$782$	−10.0814	−	4.85494i	−0.360510	−	0.173612i
$783$		0			0
$784$	11.2810	−	33.1110i	0.402893	−	1.18254i
$785$	−18.3809			−0.656041
$786$		0			0
$787$	−4.36470	−	19.1230i	−0.155585	−	0.681661i	−0.991203	−	0.132351i	$-0.957747\pi$
$787$	−4.36470	−	19.1230i	−0.155585	−	0.681661i	0.835618	−	0.549311i	$-0.185110\pi$
$788$	−5.73876	−	7.19617i	−0.204435	−	0.256353i
$789$		0			0
$790$	−13.3166	+	58.3437i	−0.473782	+	2.07577i
$791$	4.08754	−	1.71286i	0.145336	−	0.0609022i
$792$		0			0
$793$	−14.7406	+	7.09869i	−0.523453	+	0.252082i
$794$	−10.8487	+	47.5313i	−0.385006	+	1.68682i
$795$		0			0
$796$	9.72841	−	12.1990i	0.344814	−	0.432384i
$797$	−23.2265	−	11.1853i	−0.822725	−	0.396203i	−0.0253432	−	0.999679i	$-0.508068\pi$
$797$	−23.2265	−	11.1853i	−0.822725	−	0.396203i	−0.797382	+	0.603475i	$0.793782\pi$
$798$		0			0
$799$	−26.2212	+	12.6275i	−0.927640	+	0.446728i
$800$	1.99224	−	8.72859i	0.0704365	−	0.308602i
$801$		0			0
$802$	27.5838			0.974017
$803$	−24.7003			−0.871656
$804$		0			0
$805$	11.8774	−	13.4014i	0.418623	−	0.472337i
$806$	−7.51075	−	9.41818i	−0.264555	−	0.331741i
$807$		0			0
$808$	−2.88916	+	1.39135i	−0.101640	+	0.0489474i
$809$	14.6923	−	7.07544i	0.516554	−	0.248759i	−0.157397	−	0.987535i	$-0.550310\pi$
$809$	14.6923	−	7.07544i	0.516554	−	0.248759i	0.673951	+	0.738776i	$0.264596\pi$
$810$		0			0
$811$	6.36229	+	7.97806i	0.223410	+	0.280148i	0.880886	−	0.473328i	$-0.156947\pi$
$811$	6.36229	+	7.97806i	0.223410	+	0.280148i	−0.657476	+	0.753475i	$0.728376\pi$
$812$	15.2570	+	0.793837i	0.535415	+	0.0278582i
$813$		0			0
$814$	−92.6216			−3.24639
$815$	−10.3623			−0.362975
$816$		0			0
$817$	3.59960	−	15.7709i	0.125934	−	0.551753i
$818$	−32.3251	+	15.5670i	−1.13022	+	0.544286i
$819$		0			0
$820$	2.60975	+	1.25679i	0.0911364	+	0.0438890i
$821$	25.6113	−	32.1156i	0.893841	−	1.12084i	−0.0982301	−	0.995164i	$-0.531318\pi$
$821$	25.6113	−	32.1156i	0.893841	−	1.12084i	0.992071	−	0.125677i	$-0.0401105\pi$
$822$		0			0
$823$	−8.87754	+	38.8951i	−0.309452	+	1.35580i	0.545944	+	0.837822i	$0.316171\pi$
$823$	−8.87754	+	38.8951i	−0.309452	+	1.35580i	−0.855396	+	0.517975i	$0.826686\pi$
$824$	7.21139	−	3.47282i	0.251221	−	0.120981i
$825$		0			0
$826$	21.0367	−	23.7360i	0.731962	−	0.825882i
$827$	2.75040	−	12.0503i	0.0956409	−	0.419030i	−0.904329	−	0.426837i	$-0.859628\pi$
$827$	2.75040	−	12.0503i	0.0956409	−	0.419030i	0.999970	+	0.00780675i	$0.00248499\pi$
$828$		0			0
$829$	4.31957	+	5.41656i	0.150025	+	0.188125i	0.851165	−	0.524898i	$-0.175897\pi$
$829$	4.31957	+	5.41656i	0.150025	+	0.188125i	−0.701140	+	0.713023i	$0.747325\pi$
$830$	6.36649	+	27.8934i	0.220984	+	0.968194i
$831$		0			0
$832$	−4.59142			−0.159179
$833$	12.3325	−	12.5372i	0.427294	−	0.434387i
$834$		0			0
$835$	−18.0174	−	8.67671i	−0.623517	−	0.300270i
$836$	−8.66418	−	37.9603i	−0.299657	−	1.31288i
$837$		0			0
$838$	−12.1405	−	53.1912i	−0.419388	−	1.83746i
$839$	3.38458	−	14.8288i	0.116849	−	0.511947i	−0.882300	−	0.470688i	$-0.844006\pi$
$839$	3.38458	−	14.8288i	0.116849	−	0.511947i	0.999148	−	0.0412596i	$-0.0131371\pi$
$840$		0			0
$841$	−1.82761	−	8.00730i	−0.0630212	−	0.276114i
$842$	24.6471	−	11.8694i	0.849396	−	0.409047i
$843$		0			0
$844$	12.6355	+	6.08492i	0.434931	+	0.209452i
$845$	−5.44272	+	6.82495i	−0.187235	+	0.234786i
$846$		0			0
$847$	26.5070	+	37.0341i	0.910790	+	1.27251i
$848$	−39.8655	+	19.1982i	−1.36899	+	0.659269i
$849$		0			0
$850$	4.85208	−	6.08431i	0.166425	−	0.208690i
$851$	26.3575			0.903524
$852$		0			0
$853$	12.5969	−	15.7960i	0.431309	−	0.540844i	−0.517921	−	0.855429i	$-0.673294\pi$
$853$	12.5969	−	15.7960i	0.431309	−	0.540844i	0.949229	+	0.314585i	$0.101865\pi$
$854$	22.0567	−	9.24272i	0.754765	−	0.316280i
$855$		0			0
$856$	−7.59591	−	9.52496i	−0.259623	−	0.325557i
$857$	37.7467	−	18.1779i	1.28940	−	0.620944i	0.341615	−	0.939840i	$-0.389026\pi$
$857$	37.7467	−	18.1779i	1.28940	−	0.620944i	0.947790	+	0.318896i	$0.103312\pi$
$858$		0			0
$859$	−25.0271	−	31.3830i	−0.853914	−	1.07077i	−0.996712	−	0.0810223i	$-0.974182\pi$
$859$	−25.0271	−	31.3830i	−0.853914	−	1.07077i	0.142798	−	0.989752i	$-0.454390\pi$
$860$	3.21588	+	4.03259i	0.109661	+	0.137510i
$861$		0			0
$862$	3.60287	−	4.51786i	0.122714	−	0.153879i
$863$	−35.7427			−1.21670			−0.608349	−	0.793670i	$-0.708168\pi$
$863$	−35.7427			−1.21670			−0.608349	+	0.793670i	$0.708168\pi$
$864$		0			0
$865$	−4.16673	+	5.22492i	−0.141673	+	0.177653i
$866$	1.69630	−	7.43196i	0.0576425	−	0.252548i
$867$		0			0
$868$	3.29229	+	4.59982i	0.111748	+	0.156128i
$869$	63.9589	+	30.8010i	2.16966	+	1.04485i
$870$		0			0
$871$	−10.2561	−	4.93906i	−0.347513	−	0.167354i
$872$	0.523674	−	2.29436i	0.0177338	−	0.0776970i
$873$		0			0
$874$	7.67503	+	33.6265i	0.259612	+	1.13743i
$875$	−12.8357	−	17.9334i	−0.433928	−	0.606261i
$876$		0			0
$877$	5.06744	+	22.2019i	0.171115	+	0.749705i	0.985541	+	0.169437i	$0.0541950\pi$
$877$	5.06744	+	22.2019i	0.171115	+	0.749705i	−0.814426	+	0.580268i	$0.802948\pi$
$878$	25.3386	+	31.7736i	0.855137	+	1.07231i
$879$		0			0
$880$	−62.3822	−	30.0417i	−2.10290	−	1.01270i
$881$	−13.6397			−0.459533			−0.229767	−	0.973246i	$-0.573796\pi$
$881$	−13.6397			−0.459533			−0.229767	+	0.973246i	$0.573796\pi$
$882$		0			0
$883$	21.0423			0.708129			0.354064	−	0.935221i	$-0.384799\pi$
$883$	21.0423			0.708129			0.354064	+	0.935221i	$0.384799\pi$
$884$	6.65705	+	3.20586i	0.223901	+	0.107825i
$885$		0			0
$886$	−14.0341	−	17.5982i	−0.471485	−	0.591223i
$887$	5.92616	+	25.9642i	0.198981	+	0.871792i	0.971545	+	0.236855i	$0.0761168\pi$
$887$	5.92616	+	25.9642i	0.198981	+	0.871792i	−0.772564	+	0.634937i	$0.781026\pi$
$888$		0			0
$889$	−27.4211	+	30.9396i	−0.919675	+	1.03768i
$890$	8.24708	+	36.1328i	0.276443	+	1.21117i
$891$		0			0
$892$	−3.93428	+	17.2372i	−0.131730	+	0.577145i
$893$	80.8261	+	38.9238i	2.70474	+	1.30254i
$894$		0			0
$895$	−18.3040	−	8.81475i	−0.611836	−	0.294645i
$896$	32.9201	+	1.71287i	1.09978	+	0.0572228i
$897$		0			0
$898$	13.5362	−	59.3058i	0.451707	−	1.97906i
$899$	8.59072	−	10.7724i	0.286517	−	0.359280i
$900$		0			0
$901$	−22.2452			−0.741095
$902$	6.66882	−	8.36244i	0.222047	−	0.278439i
$903$		0			0
$904$	1.88856	+	2.36818i	0.0628127	+	0.0787646i
$905$	21.4824	+	26.9380i	0.714098	+	0.895451i
$906$		0			0
$907$	14.0178	−	6.75063i	0.465455	−	0.224151i	−0.186432	−	0.982468i	$-0.559692\pi$
$907$	14.0178	−	6.75063i	0.465455	−	0.224151i	0.651886	+	0.758317i	$0.273978\pi$
$908$	4.83869	+	6.06753i	0.160578	+	0.201358i
$909$		0			0
$910$	−24.4142	+	27.5469i	−0.809323	+	0.913170i
$911$	20.9846	−	26.3138i	0.695250	−	0.871816i	−0.301409	−	0.953495i	$-0.597457\pi$
$911$	20.9846	−	26.3138i	0.695250	−	0.871816i	0.996659	+	0.0816794i	$0.0260283\pi$
$912$		0			0
$913$	33.9390			1.12322
$914$	16.9008	−	21.1930i	0.559030	−	0.701002i
$915$		0			0
$916$	−3.42724	+	1.65047i	−0.113239	+	0.0545332i
$917$	−9.58276	+	33.7846i	−0.316451	+	1.11567i
$918$		0			0
$919$	16.6888	−	20.9271i	0.550513	−	0.690321i	−0.426260	−	0.904601i	$-0.640169\pi$
$919$	16.6888	−	20.9271i	0.550513	−	0.690321i	0.976772	+	0.214280i	$0.0687404\pi$
$920$	11.0268	+	5.31023i	0.363543	+	0.175073i
$921$		0			0
$922$	37.9069	−	18.2550i	1.24840	−	0.601197i
$923$	−0.0252062	−	0.110436i	−0.000829672	−	0.00363503i
$924$		0			0
$925$	−4.07909	+	17.8717i	−0.134120	+	0.587617i
$926$	−11.1913	−	49.0323i	−0.367769	−	1.61130i
$927$		0			0
$928$	6.73478	+	29.5070i	0.221080	+	0.968614i
$929$	−9.72168	−	4.68172i	−0.318958	−	0.153602i	0.267553	−	0.963543i	$-0.413785\pi$
$929$	−9.72168	−	4.68172i	−0.318958	−	0.153602i	−0.586511	+	0.809941i	$0.699499\pi$
$930$		0			0
$931$	−53.9158	−	5.62582i	−1.76702	−	0.184379i
$932$	−16.7500			−0.548666
$933$		0			0
$934$	1.21137	+	5.30736i	0.0396373	+	0.173662i
$935$	−21.7034	−	27.2153i	−0.709779	−	0.890034i
$936$		0			0
$937$	−1.42642	+	6.24958i	−0.0465993	+	0.204165i	−0.992868	−	0.119215i	$-0.961962\pi$
$937$	−1.42642	+	6.24958i	−0.0465993	+	0.204165i	0.946269	+	0.323380i	$0.104819\pi$
$938$	14.5961	+	7.98875i	0.476581	+	0.260842i
$939$		0			0
$940$	−25.7715	+	12.4109i	−0.840574	+	0.404799i
$941$	6.44346	−	28.2306i	0.210051	−	0.920292i	−0.754480	−	0.656323i	$-0.772111\pi$
$941$	6.44346	−	28.2306i	0.210051	−	0.920292i	0.964531	−	0.263969i	$-0.0850318\pi$
$942$		0			0
$943$	−1.89776	+	2.37971i	−0.0617995	+	0.0774942i
$944$	31.4420	+	15.1417i	1.02335	+	0.492820i
$945$		0			0
$946$	17.1598	−	8.26370i	0.557912	−	0.268676i
$947$	−10.9966	+	48.1791i	−0.357340	+	1.56561i	0.402450	+	0.915442i	$0.368159\pi$
$947$	−10.9966	+	48.1791i	−0.357340	+	1.56561i	−0.759790	+	0.650168i	$0.774698\pi$
$948$		0			0
$949$	−14.4483			−0.469012
$950$	−23.9882			−0.778279
$951$		0			0
$952$	10.5434	+	5.77063i	0.341715	+	0.187027i
$953$	−26.6549	−	33.4242i	−0.863436	−	1.08272i	−0.995804	−	0.0915143i	$-0.970829\pi$
$953$	−26.6549	−	33.4242i	−0.863436	−	1.08272i	0.132367	−	0.991201i	$-0.457742\pi$
$954$		0			0
$955$	1.03840	−	0.500067i	0.0336019	−	0.0161818i
$956$	−18.7339	+	9.02178i	−0.605898	+	0.291785i
$957$		0			0
$958$	6.71916	+	8.42556i	0.217086	+	0.272217i
$959$	−11.5219	+	40.6213i	−0.372063	+	1.31173i
$960$		0			0
$961$	−25.8984			−0.835434
$962$	−54.1784			−1.74678
$963$		0			0
$964$	−1.49269	+	6.53990i	−0.0480763	+	0.210636i
$965$	−49.6742	+	23.9218i	−1.59907	+	0.770071i
$966$		0			0
$967$	−20.1534	−	9.70535i	−0.648089	−	0.312103i	0.0808049	−	0.996730i	$-0.474251\pi$
$967$	−20.1534	−	9.70535i	−0.648089	−	0.312103i	−0.728894	+	0.684627i	$0.759965\pi$
$968$	−19.4071	+	24.3357i	−0.623767	+	0.782179i
$969$		0			0
$970$	1.61533	−	7.07721i	0.0518650	−	0.227235i
$971$	−9.37522	+	4.51487i	−0.300865	+	0.144889i	−0.578226	−	0.815877i	$-0.696255\pi$
$971$	−9.37522	+	4.51487i	−0.300865	+	0.144889i	0.277360	+	0.960766i	$0.410540\pi$
$972$		0			0
$973$	1.59396	+	9.15307i	0.0510999	+	0.293434i
$974$	−1.35249	+	5.92565i	−0.0433366	+	0.189870i
$975$		0			0
$976$	16.4064	+	20.5730i	0.525156	+	0.658525i
$977$	−5.45012	−	23.8785i	−0.174365	−	0.763942i	−0.984168	−	0.177240i	$-0.943283\pi$
$977$	−5.45012	−	23.8785i	−0.174365	−	0.763942i	0.809803	−	0.586702i	$-0.199574\pi$
$978$		0			0
$979$	43.9642			1.40510
$980$	12.1209	−	12.3221i	0.387189	−	0.393616i
$981$		0			0
$982$	50.3825	+	24.2629i	1.60777	+	0.774261i
$983$	9.27014	+	40.6151i	0.295672	+	1.29542i	0.876502	+	0.481398i	$0.159871\pi$
$983$	9.27014	+	40.6151i	0.295672	+	1.29542i	−0.580831	+	0.814024i	$0.697272\pi$
$984$		0			0
$985$	5.64418	+	24.7288i	0.179839	+	0.787924i
$986$	−5.85396	+	25.6479i	−0.186428	+	0.816794i
$987$		0			0
$988$	−5.06806	−	22.2046i	−0.161236	−	0.706423i
$989$	−4.88319	+	2.35162i	−0.155276	+	0.0747771i
$990$		0			0
$991$	−9.07534	−	4.37045i	−0.288288	−	0.138832i	0.284151	−	0.958780i	$-0.408288\pi$
$991$	−9.07534	−	4.37045i	−0.288288	−	0.138832i	−0.572439	+	0.819948i	$0.694003\pi$
$992$	−6.98690	+	8.76129i	−0.221834	+	0.278171i
$993$		0			0
$994$	0.0284069	+	0.163123i	0.000901012	+	0.00517394i
$995$	−38.7404	+	18.6564i	−1.22815	+	0.591447i
$996$		0			0
$997$	25.9595	−	32.5522i	0.822147	−	1.03094i	−0.176762	−	0.984254i	$-0.556562\pi$
$997$	25.9595	−	32.5522i	0.822147	−	1.03094i	0.998910	−	0.0466864i	$-0.0148661\pi$
$998$	−19.4267			−0.614940
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.127.2		36
3.2	odd	2		147.2.i.b.127.5	yes	36
49.22	even	7	inner	441.2.u.d.316.2		36
147.62	even	14		7203.2.a.g.1.4		18
147.71	odd	14		147.2.i.b.22.5	✓	36
147.134	odd	14		7203.2.a.h.1.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.22.5	✓	36	147.71	odd	14
147.2.i.b.127.5	yes	36	3.2	odd	2
441.2.u.d.127.2		36	1.1	even	1	trivial
441.2.u.d.316.2		36	49.22	even	7	inner
7203.2.a.g.1.4		18	147.62	even	14
7203.2.a.h.1.4		18	147.134	odd	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54657 - 0.744788i) q^{2} +(0.590184 + 0.740067i) q^{4} +(-0.580458 - 2.54315i) q^{5} +(2.64218 + 0.137475i) q^{7} +(0.402375 + 1.76292i) q^{8} +O(q^{10})\)	\(q+(-1.54657 - 0.744788i) q^{2} +(0.590184 + 0.740067i) q^{4} +(-0.580458 - 2.54315i) q^{5} +(2.64218 + 0.137475i) q^{7} +(0.402375 + 1.76292i) q^{8} +(-0.996391 + 4.36547i) q^{10} +(4.78563 + 2.30464i) q^{11} +(2.79932 + 1.34808i) q^{13} +(-3.98392 - 2.18048i) q^{14} +(1.11197 - 4.87186i) q^{16} +(1.56639 - 1.96419i) q^{17} -7.74408 q^{19} +(1.53953 - 1.93050i) q^{20} +(-5.68483 - 7.12855i) q^{22} +(1.61774 + 2.02859i) q^{23} +(-1.62584 + 0.782964i) q^{25} +(-3.32531 - 4.16980i) q^{26} +(1.45763 + 2.03652i) q^{28} +(3.80345 - 4.76938i) q^{29} +2.25866 q^{31} +(-3.09338 + 3.87897i) q^{32} +(-3.88544 + 1.87113i) q^{34} +(-1.18405 - 6.79925i) q^{35} +(6.33364 - 7.94214i) q^{37} +(11.9767 + 5.76770i) q^{38} +(4.24981 - 2.04660i) q^{40} +(0.261037 + 1.14368i) q^{41} +(-0.464819 + 2.03651i) q^{43} +(1.11881 + 4.90184i) q^{44} +(-0.991084 - 4.34222i) q^{46} +(-10.4372 - 5.02627i) q^{47} +(6.96220 + 0.726468i) q^{49} +3.09761 q^{50} +(0.654443 + 2.86730i) q^{52} +(-5.52071 - 6.92275i) q^{53} +(3.08318 - 13.5083i) q^{55} +(0.820788 + 4.71326i) q^{56} +(-9.43447 + 4.54340i) q^{58} +(-1.55399 + 6.80849i) q^{59} +(-3.28315 + 4.11694i) q^{61} +(-3.49318 - 1.68223i) q^{62} +(-1.33142 + 0.641176i) q^{64} +(1.80349 - 7.90160i) q^{65} -3.66376 q^{67} +2.37809 q^{68} +(-3.23279 + 11.3974i) q^{70} +(-0.0227312 - 0.0285040i) q^{71} +(-4.18971 + 2.01766i) q^{73} +(-15.7106 + 7.56583i) q^{74} +(-4.57043 - 5.73114i) q^{76} +(12.3276 + 6.74716i) q^{77} +13.3648 q^{79} -13.0353 q^{80} +(0.448086 - 1.96319i) q^{82} +(5.75678 - 2.77232i) q^{83} +(-5.90446 - 2.84344i) q^{85} +(2.23564 - 2.80340i) q^{86} +(-2.13727 + 9.36400i) q^{88} +(7.45728 - 3.59123i) q^{89} +(7.21098 + 3.94671i) q^{91} +(-0.546524 + 2.39448i) q^{92} +(12.3983 + 15.5469i) q^{94} +(4.49511 + 19.6944i) q^{95} -1.62118 q^{97} +(-10.2265 - 6.30890i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

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