LMFDB - Embedded newform 756.2.n.b.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(19,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 5]))

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

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

chi := DirichletCharacter("756.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.n (of order $6$, degree $2$, not 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27769 - 0.606229i) q^{2} +(1.26497 + 1.54914i) q^{4} -0.139892i q^{5} +(-1.99326 - 1.73980i) q^{7} +(-0.677105 - 2.74618i) q^{8} +O(q^{10})$	\(q+(-1.27769 - 0.606229i) q^{2} +(1.26497 + 1.54914i) q^{4} -0.139892i q^{5} +(-1.99326 - 1.73980i) q^{7} +(-0.677105 - 2.74618i) q^{8} +(-0.0848066 + 0.178738i) q^{10} +5.54332i q^{11} +(-0.0343058 + 0.0198065i) q^{13} +(1.49204 + 3.43130i) q^{14} +(-0.799688 + 3.91925i) q^{16} +(2.38588 - 1.37749i) q^{17} +(1.16353 - 2.01529i) q^{19} +(0.216713 - 0.176960i) q^{20} +(3.36052 - 7.08263i) q^{22} +5.33791i q^{23} +4.98043 q^{25} +(0.0558394 - 0.00450931i) q^{26} +(0.173788 - 5.28865i) q^{28} +(1.26196 - 2.18578i) q^{29} +(-3.87090 + 6.70459i) q^{31} +(3.39771 - 4.52278i) q^{32} +(-3.88348 + 0.313611i) q^{34} +(-0.243385 + 0.278841i) q^{35} +(1.58289 - 2.74164i) q^{37} +(-2.70835 + 1.86954i) q^{38} +(-0.384169 + 0.0947216i) q^{40} +(-0.965497 + 0.557430i) q^{41} +(7.88143 + 4.55034i) q^{43} +(-8.58739 + 7.01215i) q^{44} +(3.23600 - 6.82019i) q^{46} +(3.81582 + 6.60920i) q^{47} +(0.946160 + 6.93576i) q^{49} +(-6.36344 - 3.01928i) q^{50} +(-0.0740790 - 0.0280900i) q^{52} +(4.31672 + 7.47678i) q^{53} +0.775466 q^{55} +(-3.42818 + 6.65189i) q^{56} +(-2.93747 + 2.02770i) q^{58} +(3.58441 - 6.20838i) q^{59} +(-8.62902 + 4.98197i) q^{61} +(9.01032 - 6.21973i) q^{62} +(-7.08306 + 3.71891i) q^{64} +(0.00277077 + 0.00479911i) q^{65} +(-1.62278 - 0.936915i) q^{67} +(5.15200 + 1.95358i) q^{68} +(0.480011 - 0.208725i) q^{70} +6.76960i q^{71} +(11.0331 - 6.36998i) q^{73} +(-3.68450 + 2.54337i) q^{74} +(4.59379 - 0.746814i) q^{76} +(9.64429 - 11.0493i) q^{77} +(1.47070 - 0.849112i) q^{79} +(0.548271 + 0.111870i) q^{80} +(1.57153 - 0.126909i) q^{82} +(6.67089 - 11.5543i) q^{83} +(-0.192700 - 0.333765i) q^{85} +(-7.31145 - 10.5919i) q^{86} +(15.2230 - 3.75341i) q^{88} +(13.3763 + 7.72281i) q^{89} +(0.102840 + 0.0202060i) q^{91} +(-8.26919 + 6.75232i) q^{92} +(-0.868743 - 10.7578i) q^{94} +(-0.281922 - 0.162768i) q^{95} +(8.85713 + 5.11366i) q^{97} +(2.99576 - 9.43533i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) $ 84 * q + q^2 + q^4 + 16 * q^8	$ 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.27769	−	0.606229i	−0.903462	−	0.428669i
$2$	−1.27769	−	0.606229i	−0.903462	−	0.428669i
$3$		0			0
$3$		0			0
$4$	1.26497	+	1.54914i	0.632486	+	0.774571i
$5$		−	0.139892i		−	0.0625616i	−0.999511	−	0.0312808i	$-0.990041\pi$
$5$		−	0.139892i		−	0.0625616i	0.999511	−	0.0312808i	$-0.00995861\pi$
$6$		0			0
$7$	−1.99326	−	1.73980i	−0.753381	−	0.657584i
$7$	−1.99326	−	1.73980i	−0.753381	−	0.657584i
$8$	−0.677105	−	2.74618i	−0.239393	−	0.970923i
$9$		0			0
$10$	−0.0848066	+	0.178738i	−0.0268182	+	0.0565220i
$11$			5.54332i			1.67137i	0.549206	+	0.835687i	$0.314930\pi$
$11$			5.54332i			1.67137i	−0.549206	+	0.835687i	$0.685070\pi$
$12$		0			0
$13$	−0.0343058	+	0.0198065i	−0.00951473	+	0.00549333i	−0.504750	−	0.863266i	$-0.668415\pi$
$13$	−0.0343058	+	0.0198065i	−0.00951473	+	0.00549333i	0.495235	+	0.868759i	$0.335082\pi$
$14$	1.49204	+	3.43130i	0.398765	+	0.917053i
$15$		0			0
$16$	−0.799688	+	3.91925i	−0.199922	+	0.979812i
$17$	2.38588	−	1.37749i	0.578661	−	0.334090i	−0.181940	−	0.983310i	$-0.558238\pi$
$17$	2.38588	−	1.37749i	0.578661	−	0.334090i	0.760601	+	0.649220i	$0.224904\pi$
$18$		0			0
$19$	1.16353	−	2.01529i	0.266931	−	0.462338i	−0.701137	−	0.713027i	$-0.747324\pi$
$19$	1.16353	−	2.01529i	0.266931	−	0.462338i	0.968068	+	0.250689i	$0.0806570\pi$
$20$	0.216713	−	0.176960i	0.0484584	−	0.0395694i
$21$		0			0
$22$	3.36052	−	7.08263i	0.716466	−	1.51002i
$23$			5.33791i			1.11303i	0.830837	+	0.556516i	$0.187862\pi$
$23$			5.33791i			1.11303i	−0.830837	+	0.556516i	$0.812138\pi$
$24$		0			0
$25$	4.98043			0.996086
$26$	0.0558394	−	0.00450931i	0.0109510	−	0.000884349i
$27$		0			0
$28$	0.173788	−	5.28865i	0.0328429	−	0.999461i
$29$	1.26196	−	2.18578i	0.234340	−	0.405888i	−0.724741	−	0.689022i	$-0.758041\pi$
$29$	1.26196	−	2.18578i	0.234340	−	0.405888i	0.959081	+	0.283133i	$0.0913739\pi$
$30$		0			0
$31$	−3.87090	+	6.70459i	−0.695234	+	1.20418i	0.274868	+	0.961482i	$0.411366\pi$
$31$	−3.87090	+	6.70459i	−0.695234	+	1.20418i	−0.970102	+	0.242698i	$0.921967\pi$
$32$	3.39771	−	4.52278i	0.600636	−	0.799522i
$33$		0			0
$34$	−3.88348	+	0.313611i	−0.666012	+	0.0537838i
$35$	−0.243385	+	0.278841i	−0.0411395	+	0.0471327i
$36$		0			0
$37$	1.58289	−	2.74164i	0.260225	−	0.450724i	−0.706076	−	0.708136i	$-0.749536\pi$
$37$	1.58289	−	2.74164i	0.260225	−	0.450724i	0.966302	+	0.257412i	$0.0828698\pi$
$38$	−2.70835	+	1.86954i	−0.439352	+	0.303280i
$39$		0			0
$40$	−0.384169	+	0.0947216i	−0.0607425	+	0.0149768i
$41$	−0.965497	+	0.557430i	−0.150785	+	0.0870560i	−0.573494	−	0.819209i	$-0.694413\pi$
$41$	−0.965497	+	0.557430i	−0.150785	+	0.0870560i	0.422709	+	0.906265i	$0.361079\pi$
$42$		0			0
$43$	7.88143	+	4.55034i	1.20191	+	0.693921i	0.960979	−	0.276622i	$-0.0892151\pi$
$43$	7.88143	+	4.55034i	1.20191	+	0.693921i	0.240927	+	0.970543i	$0.422548\pi$
$44$	−8.58739	+	7.01215i	−1.29460	+	1.05712i
$45$		0			0
$46$	3.23600	−	6.82019i	0.477122	−	1.00558i
$47$	3.81582	+	6.60920i	0.556595	+	0.964051i	0.997778	+	0.0666333i	$0.0212258\pi$
$47$	3.81582	+	6.60920i	0.556595	+	0.964051i	−0.441183	+	0.897417i	$0.645441\pi$
$48$		0			0
$49$	0.946160	+	6.93576i	0.135166	+	0.990823i
$50$	−6.36344	−	3.01928i	−0.899926	−	0.426991i
$51$		0			0
$52$	−0.0740790	−	0.0280900i	−0.0102729	−	0.00389538i
$53$	4.31672	+	7.47678i	0.592947	+	1.02701i	0.993833	+	0.110887i	$0.0353690\pi$
$53$	4.31672	+	7.47678i	0.592947	+	1.02701i	−0.400886	+	0.916128i	$0.631298\pi$
$54$		0			0
$55$	0.775466			0.104564
$56$	−3.42818	+	6.65189i	−0.458110	+	0.888896i
$57$		0			0
$58$	−2.93747	+	2.02770i	−0.385709	+	0.266250i
$59$	3.58441	−	6.20838i	0.466651	−	0.808263i	−0.532624	−	0.846352i	$-0.678794\pi$
$59$	3.58441	−	6.20838i	0.466651	−	0.808263i	0.999274	+	0.0380895i	$0.0121272\pi$
$60$		0			0
$61$	−8.62902	+	4.98197i	−1.10483	+	0.637876i	−0.937486	−	0.348022i	$-0.886853\pi$
$61$	−8.62902	+	4.98197i	−1.10483	+	0.637876i	−0.167347	+	0.985898i	$0.553520\pi$
$62$	9.01032	−	6.21973i	1.14431	−	0.789906i
$63$		0			0
$64$	−7.08306	+	3.71891i	−0.885382	+	0.464864i
$65$	0.00277077	+	0.00479911i	0.000343671	+	0.000595256i
$66$		0			0
$67$	−1.62278	−	0.936915i	−0.198255	−	0.114462i	0.397587	−	0.917565i	$-0.369848\pi$
$67$	−1.62278	−	0.936915i	−0.198255	−	0.114462i	−0.595841	+	0.803102i	$0.703181\pi$
$68$	5.15200	+	1.95358i	0.624772	+	0.236907i
$69$		0			0
$70$	0.480011	−	0.208725i	0.0573723	−	0.0249474i
$71$			6.76960i			0.803404i	0.915770	+	0.401702i	$0.131581\pi$
$71$			6.76960i			0.803404i	−0.915770	+	0.401702i	$0.868419\pi$
$72$		0			0
$73$	11.0331	−	6.36998i	1.29133	−	0.745550i	0.312440	−	0.949937i	$-0.398854\pi$
$73$	11.0331	−	6.36998i	1.29133	−	0.745550i	0.978890	+	0.204387i	$0.0655202\pi$
$74$	−3.68450	+	2.54337i	−0.428315	+	0.295661i
$75$		0			0
$76$	4.59379	−	0.746814i	0.526944	−	0.0856655i
$77$	9.64429	−	11.0493i	1.09907	−	1.25918i
$78$		0			0
$79$	1.47070	−	0.849112i	0.165467	−	0.0955325i	−0.414980	−	0.909831i	$-0.636211\pi$
$79$	1.47070	−	0.849112i	0.165467	−	0.0955325i	0.580447	+	0.814298i	$0.302878\pi$
$80$	0.548271	+	0.111870i	0.0612986	+	0.0125074i
$81$		0			0
$82$	1.57153	−	0.126909i	0.173547	−	0.0140148i
$83$	6.67089	−	11.5543i	0.732225	−	1.26825i	−0.223705	−	0.974657i	$-0.571815\pi$
$83$	6.67089	−	11.5543i	0.732225	−	1.26825i	0.955930	−	0.293595i	$-0.0948516\pi$
$84$		0			0
$85$	−0.192700	−	0.333765i	−0.0209012	−	0.0362019i
$86$	−7.31145	−	10.5919i	−0.788414	−	1.14215i
$87$		0			0
$88$	15.2230	−	3.75341i	1.62277	−	0.400115i
$89$	13.3763	+	7.72281i	1.41789	+	0.818617i	0.996113	−	0.0880851i	$-0.0280748\pi$
$89$	13.3763	+	7.72281i	1.41789	+	0.818617i	0.421773	+	0.906702i	$0.361408\pi$
$90$		0			0
$91$	0.102840	+	0.0202060i	0.0107805	+	0.00211817i
$92$	−8.26919	+	6.75232i	−0.862123	+	0.703978i
$93$		0			0
$94$	−0.868743	−	10.7578i	−0.0896039	−	1.10958i
$95$	−0.281922	−	0.162768i	−0.0289246	−	0.0166996i
$96$		0			0
$97$	8.85713	+	5.11366i	0.899305	+	0.519214i	0.876975	−	0.480537i	$-0.159558\pi$
$97$	8.85713	+	5.11366i	0.899305	+	0.519214i	0.0223304	+	0.999751i	$0.492891\pi$
$98$	2.99576	−	9.43533i	0.302618	−	0.953112i
$99$		0			0
$100$	6.30011	+	7.71540i	0.630011	+	0.771540i
$101$		−	4.05869i		−	0.403855i	−0.979400	−	0.201927i	$-0.935280\pi$
$101$		−	4.05869i		−	0.403855i	0.979400	−	0.201927i	$-0.0647205\pi$
$102$		0			0
$103$	−8.20350			−0.808314			−0.404157	−	0.914690i	$-0.632435\pi$
$103$	−8.20350			−0.808314			−0.404157	+	0.914690i	$0.632435\pi$
$104$	0.0776209	+	0.0807991i	0.00761136	+	0.00792300i
$105$		0			0
$106$	−0.982781	−	12.1699i	−0.0954562	−	1.18205i
$107$	−1.91019	−	1.10285i	−0.184665	−	0.106617i	0.404818	−	0.914397i	$-0.367335\pi$
$107$	−1.91019	−	1.10285i	−0.184665	−	0.106617i	−0.589483	+	0.807781i	$0.700668\pi$
$108$		0			0
$109$	4.62412	+	8.00921i	0.442910	+	0.767143i	0.997904	−	0.0647113i	$-0.0206127\pi$
$109$	4.62412	+	8.00921i	0.442910	+	0.767143i	−0.554994	+	0.831855i	$0.687279\pi$
$110$	−0.990803	−	0.470110i	−0.0944694	−	0.0448232i
$111$		0			0
$112$	8.41271	−	6.42077i	0.794926	−	0.606706i
$113$	−1.75754	−	3.04415i	−0.165335	−	0.286369i	0.771439	−	0.636303i	$-0.219537\pi$
$113$	−1.75754	−	3.04415i	−0.165335	−	0.286369i	−0.936774	+	0.349934i	$0.886204\pi$
$114$		0			0
$115$	0.746731			0.0696330
$116$	4.98242	−	0.809993i	0.462606	−	0.0752060i
$117$		0			0
$118$	−8.34346	+	5.75940i	−0.768078	+	0.530196i
$119$	−7.15224	−	1.40527i	−0.655645	−	0.128821i
$120$		0			0
$121$	−19.7284			−1.79349
$122$	14.0454	−	1.13424i	1.27161	−	0.102689i
$123$		0			0
$124$	−15.2830	+	2.48455i	−1.37245	+	0.223119i
$125$		−	1.39618i		−	0.124878i
$126$		0			0
$127$			12.6596i			1.12336i	0.827355	+	0.561680i	$0.189845\pi$
$127$			12.6596i			1.12336i	−0.827355	+	0.561680i	$0.810155\pi$
$128$	11.3044	−	0.457653i	0.999182	−	0.0404512i
$129$		0			0
$130$	−0.000630817	−	0.00781149i	−5.53263e−5	−	0.000685113i
$131$	−16.5689			−1.44764			−0.723818	−	0.689991i	$-0.757614\pi$
$131$	−16.5689			−1.44764			−0.723818	+	0.689991i	$0.757614\pi$
$132$		0			0
$133$	−5.82541	+	1.99268i	−0.505127	+	0.172787i
$134$	1.50543	+	2.18086i	0.130049	+	0.188398i
$135$		0			0
$136$	−5.39833	−	5.61936i	−0.462903	−	0.481856i
$137$	−10.4266			−0.890809			−0.445404	−	0.895330i	$-0.646940\pi$
$137$	−10.4266			−0.890809			−0.445404	+	0.895330i	$0.646940\pi$
$138$		0			0
$139$	4.56708	+	7.91041i	0.387374	+	0.670952i	0.992096	−	0.125485i	$-0.0400487\pi$
$139$	4.56708	+	7.91041i	0.387374	+	0.670952i	−0.604721	+	0.796437i	$0.706715\pi$
$140$	−0.739839	−	0.0243116i	−0.0625278	−	0.00205470i
$141$		0			0
$142$	4.10393	−	8.64944i	0.344394	−	0.725845i
$143$	−0.109794	−	0.190168i	−0.00918141	−	0.0159027i
$144$		0			0
$145$	−0.305772	−	0.176538i	−0.0253930	−	0.0146607i
$146$	−17.9586	+	1.45024i	−1.48626	+	0.120023i
$147$		0			0
$148$	6.24951	−	1.01598i	0.513707	−	0.0835134i
$149$	−10.4960			−0.859867			−0.429933	−	0.902861i	$-0.641463\pi$
$149$	−10.4960			−0.859867			−0.429933	+	0.902861i	$0.641463\pi$
$150$		0			0
$151$			2.24225i			0.182472i	0.995829	+	0.0912360i	$0.0290818\pi$
$151$			2.24225i			0.182472i	−0.995829	+	0.0912360i	$0.970918\pi$
$152$	−6.32218	−	1.83070i	−0.512796	−	0.148489i
$153$		0			0
$154$	−19.0208	+	8.27087i	−1.53274	+	0.666486i
$155$	0.937919	+	0.541508i	0.0753354	+	0.0434949i
$156$		0			0
$157$	6.04801	+	3.49182i	0.482684	+	0.278678i	0.721534	−	0.692379i	$-0.243437\pi$
$157$	6.04801	+	3.49182i	0.482684	+	0.278678i	−0.238850	+	0.971056i	$0.576771\pi$
$158$	−2.39386	+	0.193316i	−0.190445	+	0.0153794i
$159$		0			0
$160$	−0.632701	−	0.475313i	−0.0500194	−	0.0375768i
$161$	9.28693	−	10.6398i	0.731912	−	0.838537i
$162$		0			0
$163$	−17.1344	−	9.89255i	−1.34207	−	0.774844i	−0.354959	−	0.934882i	$-0.615505\pi$
$163$	−17.1344	−	9.89255i	−1.34207	−	0.774844i	−0.987111	+	0.160038i	$0.948838\pi$
$164$	−2.08487	−	0.790559i	−0.162801	−	0.0617323i
$165$		0			0
$166$	−15.5279	+	10.7187i	−1.20520	+	0.831935i
$167$	−4.33186	−	7.50301i	−0.335210	−	0.580600i	0.648315	−	0.761372i	$-0.275474\pi$
$167$	−4.33186	−	7.50301i	−0.335210	−	0.580600i	−0.983525	+	0.180772i	$0.942140\pi$
$168$		0			0
$169$	−6.49922	+	11.2570i	−0.499940	+	0.865921i
$170$	0.0438716	+	0.543268i	0.00336480	+	0.0416668i
$171$		0			0
$172$	2.92066	+	17.9655i	0.222698	+	1.36986i
$173$	−6.74765	+	3.89576i	−0.513014	+	0.296189i	−0.734072	−	0.679072i	$-0.762382\pi$
$173$	−6.74765	+	3.89576i	−0.513014	+	0.296189i	0.221057	+	0.975261i	$0.429049\pi$
$174$		0			0
$175$	−9.92729	−	8.66498i	−0.750432	−	0.655011i
$176$	−21.7256	−	4.43292i	−1.63763	−	0.334144i
$177$		0			0
$178$	−12.4089	−	17.9764i	−0.930090	−	1.34739i
$179$	14.5262	−	8.38672i	1.08574	−	0.626853i	0.153302	−	0.988179i	$-0.451009\pi$
$179$	14.5262	−	8.38672i	1.08574	−	0.626853i	0.932439	+	0.361326i	$0.117676\pi$
$180$		0			0
$181$			4.24292i			0.315374i	0.987489	+	0.157687i	$0.0504037\pi$
$181$			4.24292i			0.315374i	−0.987489	+	0.157687i	$0.949596\pi$
$182$	−0.119148	−	0.0881615i	−0.00883182	−	0.00653496i
$183$		0			0
$184$	14.6589	−	3.61433i	1.08067	−	0.266452i
$185$	−0.383534	−	0.221433i	−0.0281980	−	0.0162801i
$186$		0			0
$187$	7.63586	+	13.2257i	0.558389	+	0.967159i
$188$	−5.41168	+	14.2717i	−0.394687	+	1.04087i
$189$		0			0
$190$	0.261534	+	0.378876i	0.0189737	+	0.0274866i
$191$	−0.756859	+	0.436973i	−0.0547644	+	0.0316182i	−0.527132	−	0.849783i	$-0.676733\pi$
$191$	−0.756859	+	0.436973i	−0.0547644	+	0.0316182i	0.472368	+	0.881402i	$0.343399\pi$
$192$		0			0
$193$	7.36614	−	12.7585i	0.530226	−	0.918379i	−0.469152	−	0.883118i	$-0.655440\pi$
$193$	7.36614	−	12.7585i	0.530226	−	0.918379i	0.999378	−	0.0352614i	$-0.0112264\pi$
$194$	−8.21659	−	11.9031i	−0.589917	−	0.854594i
$195$		0			0
$196$	−9.54762	+	10.2393i	−0.681973	+	0.731378i
$197$	−21.2951			−1.51722			−0.758608	−	0.651547i	$-0.774120\pi$
$197$	−21.2951			−1.51722			−0.758608	+	0.651547i	$0.774120\pi$
$198$		0			0
$199$	−13.2609	−	22.9685i	−0.940039	−	1.62820i	−0.765392	−	0.643564i	$-0.777455\pi$
$199$	−13.2609	−	22.9685i	−0.940039	−	1.62820i	−0.174647	−	0.984631i	$-0.555878\pi$
$200$	−3.37227	−	13.6772i	−0.238456	−	0.967123i
$201$		0			0
$202$	−2.46050	+	5.18574i	−0.173120	+	0.364867i
$203$	−6.31823	+	2.16126i	−0.443453	+	0.151690i
$204$		0			0
$205$	0.0779800	+	0.135065i	0.00544636	+	0.00943337i
$206$	10.4815	+	4.97320i	0.730281	+	0.346499i
$207$		0			0
$208$	−0.0501926	−	0.150292i	−0.00348023	−	0.0104209i
$209$	11.1714	+	6.44980i	0.772740	+	0.446142i
$210$		0			0
$211$	−4.58363	+	2.64636i	−0.315550	+	0.182183i	−0.649408	−	0.760441i	$-0.724983\pi$
$211$	−4.58363	+	2.64636i	−0.315550	+	0.182183i	0.333857	+	0.942624i	$0.391650\pi$
$212$	−6.12207	+	16.1451i	−0.420465	+	1.10885i
$213$		0			0
$214$	1.77205	+	2.56711i	0.121135	+	0.175484i
$215$	0.636556	−	1.10255i	0.0434128	−	0.0751932i
$216$		0			0
$217$	19.3804	−	6.62938i	1.31563	−	0.450032i
$218$	−1.05277	−	13.0365i	−0.0713023	−	0.882946i
$219$		0			0
$220$	0.980943	+	1.20131i	0.0661352	+	0.0809921i
$221$	−0.0545664	+	0.0945118i	−0.00367053	+	0.00635755i
$222$		0			0
$223$	12.4505	−	21.5649i	0.833746	−	1.44409i	−0.0613010	−	0.998119i	$-0.519525\pi$
$223$	12.4505	−	21.5649i	0.833746	−	1.44409i	0.895047	−	0.445971i	$-0.147142\pi$
$224$	−14.6413	+	3.10372i	−0.978261	+	0.207376i
$225$		0			0
$226$	0.400136	+	4.95494i	0.0266167	+	0.329598i
$227$	−7.94018			−0.527008			−0.263504	−	0.964658i	$-0.584878\pi$
$227$	−7.94018			−0.527008			−0.263504	+	0.964658i	$0.584878\pi$
$228$		0			0
$229$		−	10.5006i		−	0.693901i	−0.937883	−	0.346950i	$-0.887217\pi$
$229$		−	10.5006i		−	0.693901i	0.937883	−	0.346950i	$-0.112783\pi$
$230$	−0.954090	−	0.452690i	−0.0629108	−	0.0298495i
$231$		0			0
$232$	−6.85702	−	1.98557i	−0.450185	−	0.130359i
$233$	−4.22434	+	7.31676i	−0.276745	+	0.479337i	−0.970574	−	0.240803i	$-0.922589\pi$
$233$	−4.22434	+	7.31676i	−0.276745	+	0.479337i	0.693829	+	0.720140i	$0.255923\pi$
$234$		0			0
$235$	0.924574	−	0.533803i	0.0603125	−	0.0348215i
$236$	14.1519	−	2.30067i	0.921207	−	0.149761i
$237$		0			0
$238$	8.28641	+	6.13140i	0.537128	+	0.397439i
$239$	24.5953	−	14.2001i	1.59094	−	0.918529i	0.597792	−	0.801651i	$-0.296045\pi$
$239$	24.5953	−	14.2001i	1.59094	−	0.918529i	0.993146	−	0.116878i	$-0.0372886\pi$
$240$		0			0
$241$		−	20.6102i		−	1.32762i	−0.747902	−	0.663809i	$-0.768939\pi$
$241$		−	20.6102i		−	1.32762i	0.747902	−	0.663809i	$-0.231061\pi$
$242$	25.2067	+	11.9599i	1.62035	+	0.768813i
$243$		0			0
$244$	−18.6333	−	7.06553i	−1.19287	−	0.452325i
$245$	0.970257	−	0.132360i	0.0619875	−	0.00845618i
$246$		0			0
$247$			0.0921814i			0.00586536i
$248$	21.0331	+	6.09049i	1.33560	+	0.386746i
$249$		0			0
$250$	−0.846406	+	1.78388i	−0.0535314	+	0.112823i
$251$	−11.6339			−0.734327			−0.367164	−	0.930156i	$-0.619671\pi$
$251$	−11.6339			−0.734327			−0.367164	+	0.930156i	$0.619671\pi$
$252$		0			0
$253$	−29.5898			−1.86029
$254$	7.67463	−	16.1750i	0.481549	−	1.01491i
$255$		0			0
$256$	−14.7210	−	6.26835i	−0.920062	−	0.391772i
$257$			25.2591i			1.57562i	0.615917	+	0.787811i	$0.288786\pi$
$257$			25.2591i			1.57562i	−0.615917	+	0.787811i	$0.711214\pi$
$258$		0			0
$259$	−7.92503	+	2.71089i	−0.492438	+	0.168446i
$260$	−0.00392956	+	0.0103631i	−0.000243701	+	0.000642690i
$261$		0			0
$262$	21.1699	+	10.0446i	1.30788	+	0.620556i
$263$			5.96876i			0.368050i	0.982922	+	0.184025i	$0.0589127\pi$
$263$			5.96876i			0.368050i	−0.982922	+	0.184025i	$0.941087\pi$
$264$		0			0
$265$	1.04594	−	0.603875i	0.0642517	−	0.0370957i
$266$	8.65108	+	0.985513i	0.530432	+	0.0604257i
$267$		0			0
$268$	−0.601363	−	3.69910i	−0.0367341	−	0.225958i
$269$	0.753852	−	0.435237i	0.0459632	−	0.0265369i	−0.476842	−	0.878989i	$-0.658219\pi$
$269$	0.753852	−	0.435237i	0.0459632	−	0.0265369i	0.522806	+	0.852452i	$0.324885\pi$
$270$		0			0
$271$	8.58619	−	14.8717i	0.521574	−	0.903393i	−0.478111	−	0.878299i	$-0.658678\pi$
$271$	8.58619	−	14.8717i	0.521574	−	0.903393i	0.999685	−	0.0250933i	$-0.00798828\pi$
$272$	3.49076	+	10.4524i	0.211658	+	0.633771i
$273$		0			0
$274$	13.3220	+	6.32094i	0.804812	+	0.381862i
$275$			27.6081i			1.66483i
$276$		0			0
$277$	−11.9755			−0.719537			−0.359769	−	0.933042i	$-0.617144\pi$
$277$	−11.9755			−0.719537			−0.359769	+	0.933042i	$0.617144\pi$
$278$	−1.03978	−	12.8757i	−0.0623618	−	0.772235i
$279$		0			0
$280$	0.930545	+	0.479575i	0.0556107	+	0.0286601i
$281$	−10.9043	+	18.8867i	−0.650494	+	1.12669i	0.332510	+	0.943100i	$0.392105\pi$
$281$	−10.9043	+	18.8867i	−0.650494	+	1.12669i	−0.983003	+	0.183588i	$0.941229\pi$
$282$		0			0
$283$	−5.29112	+	9.16449i	−0.314525	+	0.544772i	−0.979336	−	0.202238i	$-0.935178\pi$
$283$	−5.29112	+	9.16449i	−0.314525	+	0.544772i	0.664812	+	0.747011i	$0.268512\pi$
$284$	−10.4871	+	8.56336i	−0.622294	+	0.508142i
$285$		0			0
$286$	0.0249966	+	0.309536i	0.00147808	+	0.0183032i
$287$	2.89431	+	0.568674i	0.170845	+	0.0335678i
$288$		0			0
$289$	−4.70505	+	8.14939i	−0.276768	+	0.479376i
$290$	0.283659	+	0.410928i	0.0166571	+	0.0241305i
$291$		0			0
$292$	23.8246	+	9.03404i	1.39423	+	0.528677i
$293$	0.652663	−	0.376815i	0.0381290	−	0.0220138i	−0.480814	−	0.876822i	$-0.659659\pi$
$293$	0.652663	−	0.376815i	0.0381290	−	0.0220138i	0.518943	+	0.854809i	$0.326326\pi$
$294$		0			0
$295$	−0.868503	−	0.501430i	−0.0505662	−	0.0291944i
$296$	−8.60084	−	2.49052i	−0.499914	−	0.144759i
$297$		0			0
$298$	13.4106	+	6.36299i	0.776857	+	0.368598i
$299$	−0.105725	−	0.183122i	−0.00611425	−	0.0105902i
$300$		0			0
$301$	−7.79301	−	22.7822i	−0.449182	−	1.31314i
$302$	1.35932	−	2.86490i	0.0782201	−	0.164857i
$303$		0			0
$304$	6.96795	+	6.17175i	0.399639	+	0.353974i
$305$	0.696937	+	1.20713i	0.0399065	+	0.0691201i
$306$		0			0
$307$	16.5771			0.946107			0.473053	−	0.881034i	$-0.343152\pi$
$307$	16.5771			0.946107			0.473053	+	0.881034i	$0.343152\pi$
$308$	29.3167	+	0.963363i	1.67047	+	0.0548927i
$309$		0			0
$310$	−0.870090	−	1.26047i	−0.0494178	−	0.0715900i
$311$	0.661515	−	1.14578i	0.0375111	−	0.0649711i	−0.846660	−	0.532134i	$-0.821390\pi$
$311$	0.661515	−	1.14578i	0.0375111	−	0.0649711i	0.884171	+	0.467163i	$0.154724\pi$
$312$		0			0
$313$	9.50131	−	5.48558i	0.537046	−	0.310063i	−0.206835	−	0.978376i	$-0.566316\pi$
$313$	9.50131	−	5.48558i	0.537046	−	0.310063i	0.743881	+	0.668312i	$0.232983\pi$
$314$	−5.61063	−	8.12794i	−0.316626	−	0.458686i
$315$		0			0
$316$	3.17580	+	1.20423i	0.178652	+	0.0677431i
$317$	−9.79131	−	16.9591i	−0.549935	−	0.952515i	−0.998278	−	0.0586540i	$-0.981319\pi$
$317$	−9.79131	−	16.9591i	−0.549935	−	0.952515i	0.448343	−	0.893861i	$-0.352014\pi$
$318$		0			0
$319$	12.1165	+	6.99544i	0.678391	+	0.391669i
$320$	0.520246	+	0.990863i	0.0290826	+	0.0553909i
$321$		0			0
$322$	−18.3160	+	7.96439i	−1.02071	+	0.443838i
$323$		−	6.41098i		−	0.356716i
$324$		0			0
$325$	−0.170858	+	0.0986448i	−0.00947749	+	0.00547183i
$326$	15.8953	+	23.0270i	0.880357	+	1.27535i
$327$		0			0
$328$	2.18455	+	2.27400i	0.120622	+	0.125560i
$329$	3.89279	−	19.8126i	0.214617	−	1.09231i
$330$		0			0
$331$	3.43396	−	1.98260i	0.188747	−	0.108973i	−0.402649	−	0.915355i	$-0.631910\pi$
$331$	3.43396	−	1.98260i	0.188747	−	0.108973i	0.591396	+	0.806381i	$0.298577\pi$
$332$	26.3378	−	4.28174i	1.44547	−	0.234991i
$333$		0			0
$334$	0.986229	+	12.2126i	0.0539640	+	0.668244i
$335$	−0.131067	+	0.227014i	−0.00716095	+	0.0124031i
$336$		0			0
$337$	−4.29338	−	7.43635i	−0.233875	−	0.405084i	0.725070	−	0.688675i	$-0.241807\pi$
$337$	−4.29338	−	7.43635i	−0.233875	−	0.405084i	−0.958945	+	0.283591i	$0.908474\pi$
$338$	15.1283	−	10.4429i	0.822869	−	0.568018i
$339$		0			0
$340$	0.273291	−	0.720723i	0.0148213	−	0.0390867i
$341$	−37.1657	−	21.4576i	−2.01264	−	1.16200i
$342$		0			0
$343$	10.1809	−	15.4709i	0.549718	−	0.835350i
$344$	7.15953	−	24.7249i	0.386016	−	1.33308i
$345$		0			0
$346$	10.9831	−	0.886941i	0.590456	−	0.0476823i
$347$	4.78952	+	2.76523i	0.257115	+	0.148445i	0.623018	−	0.782208i	$-0.285906\pi$
$347$	4.78952	+	2.76523i	0.257115	+	0.148445i	−0.365903	+	0.930653i	$0.619240\pi$
$348$		0			0
$349$	18.5119	+	10.6879i	0.990919	+	0.572108i	0.905549	−	0.424242i	$-0.139459\pi$
$349$	18.5119	+	10.6879i	0.990919	+	0.572108i	0.0853704	+	0.996349i	$0.472793\pi$
$350$	7.43101	+	17.0893i	0.397204	+	0.913464i
$351$		0			0
$352$	25.0712	+	18.8346i	1.33630	+	1.00389i
$353$			4.28880i			0.228270i	0.993465	+	0.114135i	$0.0364096\pi$
$353$			4.28880i			0.228270i	−0.993465	+	0.114135i	$0.963590\pi$
$354$		0			0
$355$	0.947013			0.0502622
$356$	4.95692	+	30.4910i	0.262716	+	1.61602i
$357$		0			0
$358$	−23.6443	+	1.90939i	−1.24964	+	0.100915i
$359$	−11.3279	−	6.54017i	−0.597864	−	0.345177i	0.170337	−	0.985386i	$-0.445515\pi$
$359$	−11.3279	−	6.54017i	−0.597864	−	0.345177i	−0.768201	+	0.640209i	$0.778848\pi$
$360$		0			0
$361$	6.79241	+	11.7648i	0.357496	+	0.619200i
$362$	2.57218	−	5.42113i	0.135191	−	0.284928i
$363$		0			0
$364$	0.0987876	+	0.184874i	0.00517788	+	0.00969001i
$365$	−0.891109	−	1.54345i	−0.0466428	−	0.0807877i
$366$		0			0
$367$	20.5981			1.07521			0.537605	−	0.843197i	$-0.319329\pi$
$367$	20.5981			1.07521			0.537605	+	0.843197i	$0.319329\pi$
$368$	−20.9206	−	4.26866i	−1.09056	−	0.222519i
$369$		0			0
$370$	0.355797	+	0.515432i	0.0184970	+	0.0267961i
$371$	4.40379	−	22.4134i	0.228634	−	1.16365i
$372$		0			0
$373$	10.6360			0.550713			0.275356	−	0.961342i	$-0.411204\pi$
$373$	10.6360			0.550713			0.275356	+	0.961342i	$0.411204\pi$
$374$	−1.73844	−	21.5274i	−0.0898928	−	1.11315i
$375$		0			0
$376$	15.5664	−	14.9541i	0.802774	−	0.771197i
$377$			0.0999798i			0.00514922i
$378$		0			0
$379$			10.1687i			0.522331i	0.965294	+	0.261165i	$0.0841068\pi$
$379$			10.1687i			0.522331i	−0.965294	+	0.261165i	$0.915893\pi$
$380$	−0.104473	−	0.642635i	−0.00535937	−	0.0329665i
$381$		0			0
$382$	1.23194	−	0.0994850i	0.0630313	−	0.00509009i
$383$	10.9369			0.558850			0.279425	−	0.960168i	$-0.409856\pi$
$383$	10.9369			0.558850			0.279425	+	0.960168i	$0.409856\pi$
$384$		0			0
$385$	−1.54570	−	1.34916i	−0.0787764	−	0.0687595i
$386$	−17.1462	+	11.8358i	−0.872719	+	0.602429i
$387$		0			0
$388$	3.28223	+	20.1896i	0.166630	+	1.02497i
$389$	−1.88575			−0.0956112			−0.0478056	−	0.998857i	$-0.515223\pi$
$389$	−1.88575			−0.0956112			−0.0478056	+	0.998857i	$0.515223\pi$
$390$		0			0
$391$	7.35292	+	12.7356i	0.371853	+	0.644068i
$392$	18.4062	−	7.29457i	0.929655	−	0.368431i
$393$		0			0
$394$	27.2085	+	12.9097i	1.37075	+	0.650383i
$395$	−0.118784	−	0.205740i	−0.00597667	−	0.0103519i
$396$		0			0
$397$	−30.4293	−	17.5684i	−1.52720	−	0.881730i	−0.999478	−	0.0323144i	$-0.989712\pi$
$397$	−30.4293	−	17.5684i	−1.52720	−	0.881730i	−0.527724	−	0.849416i	$-0.676954\pi$
$398$	3.01909	+	37.3857i	0.151333	+	1.87398i
$399$		0			0
$400$	−3.98279	+	19.5195i	−0.199139	+	0.975977i
$401$	18.7073			0.934197			0.467099	−	0.884205i	$-0.345299\pi$
$401$	18.7073			0.934197			0.467099	+	0.884205i	$0.345299\pi$
$402$		0			0
$403$		−	0.306676i		−	0.0152766i
$404$	6.28749	−	5.13413i	0.312814	−	0.255433i
$405$		0			0
$406$	9.38294	+	1.06889i	0.465668	+	0.0530479i
$407$	15.1978	+	8.77446i	0.753328	+	0.434934i
$408$		0			0
$409$	3.50923	+	2.02606i	0.173520	+	0.100182i	0.584245	−	0.811577i	$-0.301391\pi$
$409$	3.50923	+	2.02606i	0.173520	+	0.100182i	−0.410724	+	0.911760i	$0.634724\pi$
$410$	−0.0177536	−	0.219845i	−0.000876787	−	0.0108574i
$411$		0			0
$412$	−10.3772	−	12.7084i	−0.511248	−	0.626097i
$413$	−17.9460	+	6.13874i	−0.883067	+	0.302068i
$414$		0			0
$415$	−1.61636	−	0.933204i	−0.0793438	−	0.0458092i
$416$	−0.0269810	+	0.222455i	−0.00132285	+	0.0109067i
$417$		0			0
$418$	−10.3635	−	15.0132i	−0.506894	−	0.734322i
$419$	−4.42682	−	7.66747i	−0.216264	−	0.374580i	0.737399	−	0.675458i	$-0.236054\pi$
$419$	−4.42682	−	7.66747i	−0.216264	−	0.374580i	−0.953663	+	0.300877i	$0.902721\pi$
$420$		0			0
$421$	−15.1319	+	26.2092i	−0.737483	+	1.27736i	0.216142	+	0.976362i	$0.430653\pi$
$421$	−15.1319	+	26.2092i	−0.737483	+	1.27736i	−0.953625	+	0.300997i	$0.902681\pi$
$422$	7.46076	−	0.602493i	0.363184	−	0.0293289i
$423$		0			0
$424$	17.6097	−	16.9171i	0.855205	−	0.821566i
$425$	11.8827	−	6.86049i	0.576396	−	0.332782i
$426$		0			0
$427$	25.8675	+	5.08246i	1.25182	+	0.245958i
$428$	−0.707869	−	4.35423i	−0.0342161	−	0.210470i
$429$		0			0
$430$	−1.48172	+	1.02281i	−0.0714547	+	0.0493244i
$431$	−12.7886	+	7.38348i	−0.616003	+	0.355650i	−0.775311	−	0.631579i	$-0.782407\pi$
$431$	−12.7886	+	7.38348i	−0.616003	+	0.355650i	0.159308	+	0.987229i	$0.449074\pi$
$432$		0			0
$433$		−	8.47613i		−	0.407337i	−0.979040	−	0.203668i	$-0.934714\pi$
$433$		−	8.47613i		−	0.407337i	0.979040	−	0.203668i	$-0.0652864\pi$
$434$	−28.7810	−	3.27867i	−1.38153	−	0.157381i
$435$		0			0
$436$	−6.55803	+	17.2949i	−0.314072	+	0.828273i
$437$	10.7574	+	6.21080i	0.514597	+	0.297103i
$438$		0			0
$439$	15.0061	+	25.9914i	0.716203	+	1.24050i	0.962494	+	0.271304i	$0.0874550\pi$
$439$	15.0061	+	25.9914i	0.716203	+	1.24050i	−0.246290	+	0.969196i	$0.579212\pi$
$440$	−0.525072	−	2.12957i	−0.0250318	−	0.101523i
$441$		0			0
$442$	0.127015	−	0.0876768i	0.00604147	−	0.00417036i
$443$	−4.11180	+	2.37395i	−0.195358	+	0.112790i	−0.594488	−	0.804104i	$-0.702645\pi$
$443$	−4.11180	+	2.37395i	−0.195358	+	0.112790i	0.399131	+	0.916894i	$0.369312\pi$
$444$		0			0
$445$	1.08036	−	1.87124i	0.0512140	−	0.0887052i
$446$	−28.9811	+	20.0053i	−1.37229	+	0.947280i
$447$		0			0
$448$	20.5885	+	4.91038i	0.972717	+	0.231994i
$449$	11.0084			0.519517			0.259758	−	0.965674i	$-0.416357\pi$
$449$	11.0084			0.519517			0.259758	+	0.965674i	$0.416357\pi$
$450$		0			0
$451$	−3.09001	−	5.35206i	−0.145503	−	0.252019i
$452$	2.49258	−	6.57344i	0.117241	−	0.309189i
$453$		0			0
$454$	10.1451	+	4.81357i	0.476132	+	0.225912i
$455$	0.00282666	−	0.0143865i	0.000132516	−	0.000674448i
$456$		0			0
$457$	−6.55868	−	11.3600i	−0.306802	−	0.531397i	0.670859	−	0.741585i	$-0.265926\pi$
$457$	−6.55868	−	11.3600i	−0.306802	−	0.531397i	−0.977661	+	0.210188i	$0.932592\pi$
$458$	−6.36578	+	13.4165i	−0.297454	+	0.626913i
$459$		0			0
$460$	0.944595	+	1.15679i	0.0440420	+	0.0539358i
$461$	28.9043	+	16.6879i	1.34621	+	0.777234i	0.987710	−	0.156296i	$-0.0499555\pi$
$461$	28.9043	+	16.6879i	1.34621	+	0.777234i	0.358498	+	0.933530i	$0.383289\pi$
$462$		0			0
$463$	9.95524	−	5.74766i	0.462659	−	0.267116i	−0.250502	−	0.968116i	$-0.580596\pi$
$463$	9.95524	−	5.74766i	0.462659	−	0.267116i	0.713162	+	0.700999i	$0.247262\pi$
$464$	7.55742	+	6.69386i	0.350845	+	0.310755i
$465$		0			0
$466$	9.83302	−	6.78763i	0.455506	−	0.314431i
$467$	12.1346	−	21.0178i	0.561523	−	0.972586i	−0.435841	−	0.900024i	$-0.643549\pi$
$467$	12.1346	−	21.0178i	0.561523	−	0.972586i	0.997364	−	0.0725625i	$-0.0231177\pi$
$468$		0			0
$469$	1.60458	+	4.69084i	0.0740926	+	0.216603i
$470$	−1.50492	+	0.121530i	−0.0694169	+	0.00560577i
$471$		0			0
$472$	−19.4764	−	5.63973i	−0.896473	−	0.259589i
$473$	−25.2240	+	43.6893i	−1.15980	+	2.00883i
$474$		0			0
$475$	5.79486	−	10.0370i	0.265886	−	0.460529i
$476$	−6.87041	−	12.8575i	−0.314905	−	0.589321i
$477$		0			0
$478$	−40.0337	+	3.23292i	−1.83110	+	0.147870i
$479$	−38.4599			−1.75728			−0.878638	−	0.477488i	$-0.841547\pi$
$479$	−38.4599			−1.75728			−0.878638	+	0.477488i	$0.841547\pi$
$480$		0			0
$481$			0.125406i			0.00571802i
$482$	−12.4945	+	26.3334i	−0.569108	+	1.19945i
$483$		0			0
$484$	−24.9559	−	30.5621i	−1.13436	−	1.38919i
$485$	0.715361	−	1.23904i	0.0324829	−	0.0562620i
$486$		0			0
$487$	−4.45081	+	2.56967i	−0.201685	+	0.116443i	−0.597441	−	0.801913i	$-0.703816\pi$
$487$	−4.45081	+	2.56967i	−0.201685	+	0.116443i	0.395756	+	0.918356i	$0.370483\pi$
$488$	19.5242	+	20.3236i	0.883817	+	0.920005i
$489$		0			0
$490$	−1.31993	−	0.419083i	−0.0596282	−	0.0189322i
$491$	−5.48778	+	3.16837i	−0.247660	+	0.142987i	−0.618692	−	0.785633i	$-0.712337\pi$
$491$	−5.48778	+	3.16837i	−0.247660	+	0.142987i	0.371032	+	0.928620i	$0.379004\pi$
$492$		0			0
$493$		−	6.95333i		−	0.313162i
$494$	0.0558831	−	0.117779i	0.00251430	−	0.00529913i
$495$		0			0
$496$	−23.1814	−	20.5326i	−1.04088	−	0.921940i
$497$	11.7778	−	13.4936i	0.528306	−	0.605269i
$498$		0			0
$499$		−	4.76254i		−	0.213200i	−0.994302	−	0.106600i	$-0.966003\pi$
$499$		−	4.76254i		−	0.213200i	0.994302	−	0.106600i	$-0.0339965\pi$
$500$	2.16289	−	1.76613i	0.0967272	−	0.0789838i
$501$		0			0
$502$	14.8645	+	7.05283i	0.663437	+	0.314783i
$503$	40.5527			1.80815			0.904077	−	0.427369i	$-0.140559\pi$
$503$	40.5527			1.80815			0.904077	+	0.427369i	$0.140559\pi$
$504$		0			0
$505$	−0.567778			−0.0252658
$506$	37.8065	+	17.9382i	1.68070	+	0.797449i
$507$		0			0
$508$	−19.6116	+	16.0141i	−0.870122	+	0.710510i
$509$		−	41.2030i		−	1.82629i	−0.407635	−	0.913145i	$-0.633646\pi$
$509$		−	41.2030i		−	1.82629i	0.407635	−	0.913145i	$-0.366354\pi$
$510$		0			0
$511$	−33.0744	−	6.49847i	−1.46313	−	0.287476i
$512$	15.0088	+	16.9333i	0.663301	+	0.748353i
$513$		0			0
$514$	15.3128	−	32.2733i	0.675420	−	1.42351i
$515$			1.14760i			0.0505694i
$516$		0			0
$517$	−36.6369	+	21.1523i	−1.61129	+	0.930278i
$518$	11.7691	+	1.34072i	0.517106	+	0.0589076i
$519$		0			0
$520$	0.0113031	−	0.0108585i	0.000495676	−	0.000476179i
$521$	14.8622	−	8.58067i	0.651123	−	0.375926i	−0.137763	−	0.990465i	$-0.543991\pi$
$521$	14.8622	−	8.58067i	0.651123	−	0.375926i	0.788886	+	0.614539i	$0.210658\pi$
$522$		0			0
$523$	0.525714	−	0.910563i	0.0229879	−	0.0398161i	−0.854303	−	0.519776i	$-0.826015\pi$
$523$	0.525714	−	0.910563i	0.0229879	−	0.0398161i	0.877290	+	0.479960i	$0.159349\pi$
$524$	−20.9593	−	25.6677i	−0.915610	−	1.12130i
$525$		0			0
$526$	3.61844	−	7.62622i	0.157771	−	0.332519i
$527$			21.3285i			0.929083i
$528$		0			0
$529$	−5.49332			−0.238840
$530$	−1.70247	+	0.137483i	−0.0739507	+	0.00597189i
$531$		0			0
$532$	−10.4559	−	6.50371i	−0.453322	−	0.281972i
$533$	0.0220815	−	0.0382462i	0.000956454	−	0.00165663i
$534$		0			0
$535$	−0.154280	+	0.267220i	−0.00667010	+	0.0115529i
$536$	−1.47414	+	5.09085i	−0.0636734	+	0.219891i
$537$		0			0
$538$	−1.22704	+	0.0990897i	−0.0529015	+	0.00427206i
$539$	−38.4471	+	5.24487i	−1.65604	+	0.225912i
$540$		0			0
$541$	21.1107	−	36.5648i	0.907620	−	1.57204i	0.0902597	−	0.995918i	$-0.471230\pi$
$541$	21.1107	−	36.5648i	0.907620	−	1.57204i	0.817361	−	0.576126i	$-0.195436\pi$
$542$	−19.9861	+	13.7962i	−0.858478	+	0.592598i
$543$		0			0
$544$	1.87646	−	15.4711i	0.0804524	−	0.663319i
$545$	1.12042	−	0.646877i	0.0479937	−	0.0277092i
$546$		0			0
$547$	10.7150	+	6.18628i	0.458138	+	0.264506i	0.711261	−	0.702928i	$-0.248124\pi$
$547$	10.7150	+	6.18628i	0.458138	+	0.264506i	−0.253123	+	0.967434i	$0.581458\pi$
$548$	−13.1894	−	16.1524i	−0.563424	−	0.689995i
$549$		0			0
$550$	16.7368	−	35.2746i	0.713661	−	1.50411i
$551$	−2.93664	−	5.08641i	−0.125105	−	0.216688i
$552$		0			0
$553$	−4.40878	−	0.866239i	−0.187480	−	0.0368362i
$554$	15.3009	+	7.25989i	0.650074	+	0.308443i
$555$		0			0
$556$	−6.47713	+	17.0815i	−0.274691	+	0.724417i
$557$	−0.650577	−	1.12683i	−0.0275658	−	0.0477454i	0.851913	−	0.523683i	$-0.175442\pi$
$557$	−0.650577	−	1.12683i	−0.0275658	−	0.0477454i	−0.879479	+	0.475937i	$0.842109\pi$
$558$		0			0
$559$	−0.360505			−0.0152477
$560$	−0.898215	−	1.17687i	−0.0379565	−	0.0497319i
$561$		0			0
$562$	25.3819	−	17.5209i	1.07067	−	0.739073i
$563$	7.16053	−	12.4024i	0.301780	−	0.522699i	−0.674759	−	0.738038i	$-0.735752\pi$
$563$	7.16053	−	12.4024i	0.301780	−	0.522699i	0.976539	+	0.215339i	$0.0690858\pi$
$564$		0			0
$565$	−0.425851	+	0.245865i	−0.0179157	+	0.0103436i
$566$	12.3162	−	8.50173i	0.517688	−	0.357354i
$567$		0			0
$568$	18.5906	−	4.58373i	0.780043	−	0.192329i
$569$	0.509017	+	0.881643i	0.0213391	+	0.0369604i	0.876498	−	0.481406i	$-0.159874\pi$
$569$	0.509017	+	0.881643i	0.0213391	+	0.0369604i	−0.855159	+	0.518366i	$0.826540\pi$
$570$		0			0
$571$	−11.9720	−	6.91203i	−0.501012	−	0.289260i	0.228119	−	0.973633i	$-0.426742\pi$
$571$	−11.9720	−	6.91203i	−0.501012	−	0.289260i	−0.729131	+	0.684374i	$0.760076\pi$
$572$	0.155712	−	0.410644i	0.00651063	−	0.0171699i
$573$		0			0
$574$	−3.35327	−	2.48120i	−0.139963	−	0.103563i
$575$			26.5851i			1.10868i
$576$		0			0
$577$	1.25177	−	0.722708i	0.0521117	−	0.0300867i	−0.473718	−	0.880677i	$-0.657088\pi$
$577$	1.25177	−	0.722708i	0.0521117	−	0.0300867i	0.525830	+	0.850590i	$0.323755\pi$
$578$	10.9520	−	7.56003i	0.455542	−	0.314456i
$579$		0			0
$580$	−0.113312	−	0.697001i	−0.00470501	−	0.0289414i
$581$	−33.3991	+	11.4247i	−1.38563	+	0.473977i
$582$		0			0
$583$	−41.4462	+	23.9290i	−1.71653	+	0.991036i
$584$	−24.9637	−	25.9859i	−1.03301	−	1.07530i
$585$		0			0
$586$	−1.06234	+	0.0857889i	−0.0438847	+	0.00354391i
$587$	−4.13937	+	7.16959i	−0.170850	+	0.295921i	−0.938717	−	0.344688i	$-0.887985\pi$
$587$	−4.13937	+	7.16959i	−0.170850	+	0.295921i	0.767867	+	0.640609i	$0.221318\pi$
$588$		0			0
$589$	9.00778	+	15.6019i	0.371159	+	0.642867i
$590$	0.805694	+	1.16718i	0.0331699	+	0.0480522i
$591$		0			0
$592$	9.47937	+	8.39619i	0.389600	+	0.345081i
$593$	−4.44238	−	2.56481i	−0.182427	−	0.105324i	0.406006	−	0.913871i	$-0.366921\pi$
$593$	−4.44238	−	2.56481i	−0.182427	−	0.105324i	−0.588432	+	0.808546i	$0.700255\pi$
$594$		0			0
$595$	−0.196587	+	1.00054i	−0.00805927	+	0.0410182i
$596$	−13.2772	−	16.2598i	−0.543854	−	0.666028i
$597$		0			0
$598$	0.0240703	+	0.298066i	0.000984309	+	0.0121888i
$599$	10.1606	+	5.86623i	0.415151	+	0.239688i	0.693001	−	0.720937i	$-0.256288\pi$
$599$	10.1606	+	5.86623i	0.415151	+	0.239688i	−0.277850	+	0.960625i	$0.589622\pi$
$600$		0			0
$601$	22.2513	+	12.8468i	0.907651	+	0.524032i	0.879675	−	0.475576i	$-0.157760\pi$
$601$	22.2513	+	12.8468i	0.907651	+	0.524032i	0.0279762	+	0.999609i	$0.491094\pi$
$602$	−3.85416	+	33.8328i	−0.157084	+	1.37892i
$603$		0			0
$604$	−3.47357	+	2.83639i	−0.141338	+	0.115411i
$605$			2.75984i			0.112204i
$606$		0			0
$607$	−14.6996			−0.596640			−0.298320	−	0.954466i	$-0.596426\pi$
$607$	−14.6996			−0.596640			−0.298320	+	0.954466i	$0.596426\pi$
$608$	−5.16137	−	12.1097i	−0.209321	−	0.491115i
$609$		0			0
$610$	−0.158671	−	1.96484i	−0.00642439	−	0.0795541i
$611$	−0.261810	−	0.151156i	−0.0105917	−	0.00611512i
$612$		0			0
$613$	−0.915202	−	1.58518i	−0.0369647	−	0.0640247i	0.846951	−	0.531671i	$-0.178436\pi$
$613$	−0.915202	−	1.58518i	−0.0369647	−	0.0640247i	−0.883916	+	0.467646i	$0.845102\pi$
$614$	−21.1804	−	10.0495i	−0.854771	−	0.405566i
$615$		0			0
$616$	−36.8735	−	19.0035i	−1.48568	−	0.765672i
$617$	15.1569	+	26.2525i	0.610194	+	1.05689i	0.991207	+	0.132317i	$0.0422417\pi$
$617$	15.1569	+	26.2525i	0.610194	+	1.05689i	−0.381014	+	0.924569i	$0.624425\pi$
$618$		0			0
$619$	−18.4886			−0.743118			−0.371559	−	0.928409i	$-0.621177\pi$
$619$	−18.4886			−0.743118			−0.371559	+	0.928409i	$0.621177\pi$
$620$	0.347569	+	2.13796i	0.0139587	+	0.0858626i
$621$		0			0
$622$	−1.53981	+	1.06292i	−0.0617409	+	0.0426191i
$623$	−13.2262	−	38.6657i	−0.529898	−	1.54911i
$624$		0			0
$625$	24.7068			0.988273
$626$	−15.4652	+	1.24889i	−0.618115	+	0.0499159i
$627$		0			0
$628$	2.24124	+	13.7863i	0.0894352	+	0.550133i
$629$		−	8.72165i		−	0.347755i
$630$		0			0
$631$			36.1728i			1.44001i	0.693966	+	0.720007i	$0.255862\pi$
$631$			36.1728i			1.44001i	−0.693966	+	0.720007i	$0.744138\pi$
$632$	−3.32764	−	3.46389i	−0.132366	−	0.137786i
$633$		0			0
$634$	2.22917	+	27.6042i	0.0885318	+	1.09630i
$635$	1.77098			0.0702792
$636$		0			0
$637$	−0.169832	−	0.219197i	−0.00672898	−	0.00868490i
$638$	−11.2402	−	16.2833i	−0.445004	−	0.644663i
$639$		0			0
$640$	−0.0640220	−	1.58140i	−0.00253069	−	0.0625104i
$641$	15.4204			0.609070			0.304535	−	0.952501i	$-0.401499\pi$
$641$	15.4204			0.609070			0.304535	+	0.952501i	$0.401499\pi$
$642$		0			0
$643$	−22.4330	−	38.8551i	−0.884670	−	1.53229i	−0.846091	−	0.533038i	$-0.821050\pi$
$643$	−22.4330	−	38.8551i	−0.884670	−	1.53229i	−0.0385791	−	0.999256i	$-0.512283\pi$
$644$	28.2303	+	0.927666i	1.11243	+	0.0365551i
$645$		0			0
$646$	−3.88652	+	8.19123i	−0.152913	+	0.322279i
$647$	15.0162	+	26.0087i	0.590346	+	1.02251i	0.994186	+	0.107680i	$0.0343421\pi$
$647$	15.0162	+	26.0087i	0.590346	+	1.02251i	−0.403840	+	0.914830i	$0.632325\pi$
$648$		0			0
$649$	34.4151	+	19.8695i	1.35091	+	0.779948i
$650$	0.278104	−	0.0224583i	0.0109081	−	0.000880888i
$651$		0			0
$652$	−6.34957	−	39.0574i	−0.248669	−	1.52961i
$653$	−24.3252			−0.951920			−0.475960	−	0.879467i	$-0.657899\pi$
$653$	−24.3252			−0.951920			−0.475960	+	0.879467i	$0.657899\pi$
$654$		0			0
$655$			2.31786i			0.0905664i
$656$	−1.41261	−	4.22979i	−0.0551532	−	0.165146i
$657$		0			0
$658$	−16.9848	+	22.9544i	−0.662135	+	0.894857i
$659$	25.8393	+	14.9183i	1.00655	+	0.581135i	0.910181	−	0.414211i	$-0.135942\pi$
$659$	25.8393	+	14.9183i	1.00655	+	0.581135i	0.0963736	+	0.995345i	$0.469276\pi$
$660$		0			0
$661$	−16.4815	−	9.51561i	−0.641057	−	0.370115i	0.143964	−	0.989583i	$-0.454015\pi$
$661$	−16.4815	−	9.51561i	−0.641057	−	0.370115i	−0.785022	+	0.619468i	$0.787348\pi$
$662$	−5.58943	+	0.451375i	−0.217239	+	0.0175432i
$663$		0			0
$664$	−36.2472	−	10.4960i	−1.40666	−	0.407324i
$665$	0.278760	+	0.814928i	0.0108098	+	0.0316016i
$666$		0			0
$667$	11.6675	+	6.73622i	0.451767	+	0.260828i
$668$	6.14354	−	16.2018i	0.237701	−	0.626865i
$669$		0			0
$670$	0.305085	−	0.210597i	0.0117865	−	0.00813607i
$671$	−27.6166	−	47.8334i	−1.06613	−	1.84659i
$672$		0			0
$673$	17.5875	−	30.4624i	0.677948	−	1.17424i	−0.297650	−	0.954675i	$-0.596203\pi$
$673$	17.5875	−	30.4624i	0.677948	−	1.17424i	0.975598	−	0.219565i	$-0.0704638\pi$
$674$	0.977468	+	12.1041i	0.0376506	+	0.466233i
$675$		0			0
$676$	−25.6600	+	4.17155i	−0.986923	+	0.160444i
$677$	15.0720	−	8.70183i	0.579265	−	0.334439i	−0.181576	−	0.983377i	$-0.558120\pi$
$677$	15.0720	−	8.70183i	0.579265	−	0.334439i	0.760841	+	0.648938i	$0.224787\pi$
$678$		0			0
$679$	−8.75777	−	25.6025i	−0.336092	−	0.982535i
$680$	−0.786104	+	0.755183i	−0.0301457	+	0.0289599i
$681$		0			0
$682$	34.4779	+	49.9471i	1.32023	+	1.91257i
$683$	−6.86600	+	3.96409i	−0.262720	+	0.151682i	−0.625575	−	0.780164i	$-0.715135\pi$
$683$	−6.86600	+	3.96409i	−0.262720	+	0.151682i	0.362855	+	0.931846i	$0.381802\pi$
$684$		0			0
$685$			1.45860i			0.0557304i
$686$	−22.3870	+	13.5950i	−0.854738	+	0.519060i
$687$		0			0
$688$	−24.1366	+	27.2504i	−0.920199	+	1.03891i
$689$	−0.296177	−	0.170998i	−0.0112835	−	0.00651451i
$690$		0			0
$691$	−15.4618	−	26.7807i	−0.588196	−	1.01879i	−0.994469	−	0.105034i	$-0.966505\pi$
$691$	−15.4618	−	26.7807i	−0.588196	−	1.01879i	0.406272	−	0.913752i	$-0.366828\pi$
$692$	−14.5707	−	5.52505i	−0.553894	−	0.210031i
$693$		0			0
$694$	−4.44315	−	6.43665i	−0.168660	−	0.244332i
$695$	1.10660	−	0.638897i	0.0419758	−	0.0242348i
$696$		0			0
$697$	−1.53571	+	2.65992i	−0.0581691	+	0.100752i
$698$	−17.1731	−	24.8782i	−0.650013	−	0.941653i
$699$		0			0
$700$	0.865539	−	26.3397i	0.0327143	−	0.995549i
$701$	24.8836			0.939841			0.469921	−	0.882709i	$-0.344283\pi$
$701$	24.8836			0.939841			0.469921	+	0.882709i	$0.344283\pi$
$702$		0			0
$703$	−3.68347	−	6.37995i	−0.138925	−	0.240624i
$704$	−20.6151	−	39.2637i	−0.776961	−	1.47980i
$705$		0			0
$706$	2.59999	−	5.47974i	0.0978520	−	0.206233i
$707$	−7.06133	+	8.09002i	−0.265569	+	0.304256i
$708$		0			0
$709$	22.5345	+	39.0309i	0.846302	+	1.46584i	0.884486	+	0.466567i	$0.154509\pi$
$709$	22.5345	+	39.0309i	0.846302	+	1.46584i	−0.0381845	+	0.999271i	$0.512157\pi$
$710$	−1.20999	−	0.574107i	−0.0454100	−	0.0215458i
$711$		0			0
$712$	12.1511	−	41.9630i	0.455382	−	1.57263i
$713$	−35.7885	−	20.6625i	−1.34029	−	0.773818i
$714$		0			0
$715$	−0.0266030	+	0.0153593i	−0.000994896	+	0.000574404i
$716$	31.3675	+	11.8942i	1.17226	+	0.444508i
$717$		0			0
$718$	10.5087	+	15.2236i	0.392181	+	0.568140i
$719$	−5.12633	+	8.87906i	−0.191180	+	0.331133i	−0.945641	−	0.325211i	$-0.894565\pi$
$719$	−5.12633	+	8.87906i	−0.191180	+	0.331133i	0.754462	+	0.656344i	$0.227898\pi$
$720$		0			0
$721$	16.3517	+	14.2725i	0.608969	+	0.531535i
$722$	−1.54642	−	19.1495i	−0.0575517	−	0.712671i
$723$		0			0
$724$	−6.57289	+	5.36718i	−0.244280	+	0.199470i
$725$	6.28509	−	10.8861i	0.233423	−	0.404300i
$726$		0			0
$727$	12.2970	−	21.2990i	0.456069	−	0.789935i	−0.542680	−	0.839940i	$-0.682590\pi$
$727$	12.2970	−	21.2990i	0.456069	−	0.789935i	0.998749	+	0.0500046i	$0.0159236\pi$
$728$	−0.0141439	−	0.296099i	−0.000524209	−	0.0109741i
$729$		0			0
$730$	0.202878	+	2.51226i	0.00750883	+	0.0929829i
$731$	25.0722			0.927328
$732$		0			0
$733$			37.9554i			1.40192i	0.713203	+	0.700958i	$0.247244\pi$
$733$			37.9554i			1.40192i	−0.713203	+	0.700958i	$0.752756\pi$
$734$	−26.3179	−	12.4871i	−0.971411	−	0.460909i
$735$		0			0
$736$	24.1422	+	18.1367i	0.889894	+	0.668527i
$737$	5.19362	−	8.99561i	0.191309	−	0.331357i
$738$		0			0
$739$	−43.7280	+	25.2464i	−1.60856	+	0.928702i	−0.618866	+	0.785496i	$0.712408\pi$
$739$	−43.7280	+	25.2464i	−1.60856	+	0.928702i	−0.989693	+	0.143206i	$0.954259\pi$
$740$	−0.142128	−	0.874256i	−0.00522473	−	0.0321383i
$741$		0			0
$742$	−19.2143	+	25.9676i	−0.705380	+	0.953302i
$743$	4.15036	−	2.39621i	0.152262	−	0.0879084i	−0.421933	−	0.906627i	$-0.638648\pi$
$743$	4.15036	−	2.39621i	0.152262	−	0.0879084i	0.574195	+	0.818718i	$0.305315\pi$
$744$		0			0
$745$			1.46831i			0.0537946i
$746$	−13.5895	−	6.44787i	−0.497548	−	0.236073i
$747$		0			0
$748$	−10.8293	+	28.5592i	−0.395960	+	1.04423i
$749$	1.88876	+	5.52163i	0.0690139	+	0.201756i
$750$		0			0
$751$			19.0447i			0.694952i	0.937689	+	0.347476i	$0.112961\pi$
$751$			19.0447i			0.694952i	−0.937689	+	0.347476i	$0.887039\pi$
$752$	−28.9545	+	9.66986i	−1.05586	+	0.352623i
$753$		0			0
$754$	0.0606107	−	0.127743i	0.00220731	−	0.00465213i
$755$	0.313673			0.0114157
$756$		0			0
$757$	−8.47980			−0.308203			−0.154102	−	0.988055i	$-0.549248\pi$
$757$	−8.47980			−0.308203			−0.154102	+	0.988055i	$0.549248\pi$
$758$	6.16456	−	12.9924i	0.223907	−	0.471906i
$759$		0			0
$760$	−0.256100	+	0.884422i	−0.00928971	+	0.0320813i
$761$			25.2637i			0.915807i	0.889002	+	0.457904i	$0.151400\pi$
$761$			25.2637i			0.915807i	−0.889002	+	0.457904i	$0.848600\pi$
$762$		0			0
$763$	4.71740	−	24.0095i	0.170781	−	0.869202i
$764$	−1.63434	−	0.619724i	−0.0591283	−	0.0224208i
$765$		0			0
$766$	−13.9739	−	6.63027i	−0.504899	−	0.239561i
$767$			0.283978i			0.0102539i
$768$		0			0
$769$	−13.9907	+	8.07751i	−0.504516	+	0.291282i	−0.730577	−	0.682831i	$-0.760749\pi$
$769$	−13.9907	+	8.07751i	−0.504516	+	0.291282i	0.226061	+	0.974113i	$0.427415\pi$
$770$	1.15703	+	2.66086i	0.0416964	+	0.0958906i
$771$		0			0
$772$	29.0827	−	4.72799i	1.04671	−	0.170164i
$773$	3.05215	−	1.76216i	0.109778	−	0.0633805i	−0.444106	−	0.895974i	$-0.646479\pi$
$773$	3.05215	−	1.76216i	0.109778	−	0.0633805i	0.553884	+	0.832594i	$0.313145\pi$
$774$		0			0
$775$	−19.2787	+	33.3918i	−0.692513	+	1.19947i
$776$	8.04586	−	27.7858i	0.288830	−	0.997452i
$777$		0			0
$778$	2.40940	+	1.14319i	0.0863811	+	0.0409855i
$779$			2.59434i			0.0929518i
$780$		0			0
$781$	−37.5261			−1.34279
$782$	−1.67403	−	20.7297i	−0.0598631	−	0.741293i
$783$		0			0
$784$	−27.9396	−	1.83821i	−0.997843	−	0.0656503i
$785$	0.488478	−	0.846068i	0.0174345	−	0.0301975i
$786$		0			0
$787$	−2.39816	+	4.15374i	−0.0854852	+	0.148065i	−0.905598	−	0.424137i	$-0.860577\pi$
$787$	−2.39816	+	4.15374i	−0.0854852	+	0.148065i	0.820113	+	0.572202i	$0.193911\pi$
$788$	−26.9378	−	32.9892i	−0.959618	−	1.17519i
$789$		0			0
$790$	0.0270433	+	0.334881i	0.000962159	+	0.0119145i
$791$	−1.79299	+	9.12554i	−0.0637514	+	0.324467i
$792$		0			0
$793$	0.197351	−	0.341821i	0.00700812	−	0.0121384i
$794$	28.2287	+	40.8940i	1.00180	+	1.45127i
$795$		0			0
$796$	18.8069	−	49.5976i	0.666592	−	1.75794i
$797$	34.8677	−	20.1309i	1.23508	−	0.713073i	0.266994	−	0.963698i	$-0.413969\pi$
$797$	34.8677	−	20.1309i	1.23508	−	0.713073i	0.968084	+	0.250625i	$0.0806362\pi$
$798$		0			0
$799$	18.2082	+	10.5125i	0.644159	+	0.371906i
$800$	16.9221	−	22.5254i	0.598286	−	0.796393i
$801$		0			0
$802$	−23.9021	−	11.3409i	−0.844012	−	0.400461i
$803$	35.3108	+	61.1602i	1.24609	+	2.15830i
$804$		0			0
$805$	−1.48843	−	1.29917i	−0.0524602	−	0.0457896i
$806$	−0.185916	+	0.391836i	−0.00654860	+	0.0138018i
$807$		0			0
$808$	−11.1459	+	2.74816i	−0.392112	+	0.0966799i
$809$	−3.05446	−	5.29049i	−0.107389	−	0.186004i	0.807323	−	0.590110i	$-0.200916\pi$
$809$	−3.05446	−	5.29049i	−0.107389	−	0.186004i	−0.914712	+	0.404107i	$0.867582\pi$
$810$		0			0
$811$	39.5573			1.38904			0.694522	−	0.719471i	$-0.255616\pi$
$811$	39.5573			1.38904			0.694522	+	0.719471i	$0.255616\pi$
$812$	−11.3405	−	7.05391i	−0.397973	−	0.247544i
$813$		0			0
$814$	−14.0987	−	20.4244i	−0.494160	−	0.715874i
$815$	−1.38389	+	2.39696i	−0.0484755	+	0.0839620i
$816$		0			0
$817$	18.3405	−	10.5889i	0.641652	−	0.370458i
$818$	−3.25545	−	4.71607i	−0.113824	−	0.164893i
$819$		0			0
$820$	−0.110593	+	0.291656i	−0.00386207	+	0.0101851i
$821$	−15.0173	−	26.0107i	−0.524106	−	0.907778i	−0.999606	−	0.0280628i	$-0.991066\pi$
$821$	−15.0173	−	26.0107i	−0.524106	−	0.907778i	0.475500	−	0.879716i	$-0.342267\pi$
$822$		0			0
$823$	1.59605	+	0.921481i	0.0556349	+	0.0321208i	0.527559	−	0.849518i	$-0.323107\pi$
$823$	1.59605	+	0.921481i	0.0556349	+	0.0321208i	−0.471925	+	0.881639i	$0.656441\pi$
$824$	5.55463	+	22.5283i	0.193505	+	0.784811i
$825$		0			0
$826$	26.6509	+	3.03602i	0.927304	+	0.105636i
$827$		−	20.1939i		−	0.702212i	−0.936336	−	0.351106i	$-0.885806\pi$
$827$		−	20.1939i		−	0.702212i	0.936336	−	0.351106i	$-0.114194\pi$
$828$		0			0
$829$	−47.6406	+	27.5053i	−1.65463	+	0.955299i	−0.679494	+	0.733681i	$0.737801\pi$
$829$	−47.6406	+	27.5053i	−1.65463	+	0.955299i	−0.975134	+	0.221618i	$0.928866\pi$
$830$	1.49946	+	2.17223i	0.0520472	+	0.0753991i
$831$		0			0
$832$	0.169332	−	0.267871i	0.00587052	−	0.00928675i
$833$	11.8114	+	15.2446i	0.409239	+	0.528193i
$834$		0			0
$835$	−1.04961	+	0.605993i	−0.0363233	+	0.0209712i
$836$	4.13983	+	25.4649i	0.143179	+	0.880721i
$837$		0			0
$838$	1.00785	+	12.4803i	0.0348155	+	0.431125i
$839$	14.6061	−	25.2985i	0.504258	−	0.873400i	−0.495730	−	0.868477i	$-0.665099\pi$
$839$	14.6061	−	25.2985i	0.504258	−	0.873400i	0.999988	−	0.00492355i	$-0.00156722\pi$
$840$		0			0
$841$	11.3149	+	19.5980i	0.390170	+	0.675794i
$842$	35.2226	−	24.3138i	1.21385	−	0.837909i
$843$		0			0
$844$	−9.89777	−	3.75313i	−0.340695	−	0.129188i
$845$	1.57476	+	0.909188i	0.0541734	+	0.0312770i
$846$		0			0
$847$	39.3238	+	34.3236i	1.35118	+	1.17937i
$848$	−32.7554	+	10.9392i	−1.12482	+	0.375654i
$849$		0			0
$850$	−19.3414	+	1.56192i	−0.663405	+	0.0535733i
$851$	14.6347	+	8.44933i	0.501670	+	0.289639i
$852$		0			0
$853$	−22.5023	−	12.9917i	−0.770464	−	0.444827i	0.0625764	−	0.998040i	$-0.480068\pi$
$853$	−22.5023	−	12.9917i	−0.770464	−	0.444827i	−0.833040	+	0.553213i	$0.813402\pi$
$854$	−29.9695	−	22.1754i	−1.02553	−	0.758828i
$855$		0			0
$856$	−1.73523	+	5.99248i	−0.0593089	+	0.204819i
$857$		−	9.86217i		−	0.336885i	−0.985711	−	0.168443i	$-0.946126\pi$
$857$		−	9.86217i		−	0.336885i	0.985711	−	0.168443i	$-0.0538738\pi$
$858$		0			0
$859$	−21.0857			−0.719434			−0.359717	−	0.933061i	$-0.617127\pi$
$859$	−21.0857			−0.719434			−0.359717	+	0.933061i	$0.617127\pi$
$860$	2.51323	−	0.408577i	0.0857005	−	0.0139323i
$861$		0			0
$862$	20.8159	−	1.68099i	0.708991	−	0.0572546i
$863$	−43.2668	−	24.9801i	−1.47282	−	0.850332i	−0.473285	−	0.880909i	$-0.656932\pi$
$863$	−43.2668	−	24.9801i	−1.47282	−	0.850332i	−0.999532	+	0.0305776i	$0.990265\pi$
$864$		0			0
$865$	0.544985	+	0.943942i	0.0185301	+	0.0320950i
$866$	−5.13847	+	10.8298i	−0.174612	+	0.368013i
$867$		0			0
$868$	34.7855	+	21.6370i	1.18070	+	0.734408i
$869$	4.70690	+	8.15258i	0.159671	+	0.276557i
$870$		0			0
$871$	0.0742279			0.00251512
$872$	18.8638	−	18.1218i	0.638807	−	0.613680i
$873$		0			0
$874$	−9.97946	−	14.4569i	−0.337560	−	0.489013i
$875$	−2.42908	+	2.78295i	−0.0821180	+	0.0940809i
$876$		0			0
$877$	25.3137			0.854781			0.427391	−	0.904067i	$-0.359433\pi$
$877$	25.3137			0.854781			0.427391	+	0.904067i	$0.359433\pi$
$878$	−3.41642	−	42.3060i	−0.115299	−	1.42776i
$879$		0			0
$880$	−0.620130	+	3.03924i	−0.0209046	+	0.102453i
$881$			40.8595i			1.37659i	0.725430	+	0.688296i	$0.241641\pi$
$881$			40.8595i			1.37659i	−0.725430	+	0.688296i	$0.758359\pi$
$882$		0			0
$883$		−	9.44199i		−	0.317748i	−0.987299	−	0.158874i	$-0.949214\pi$
$883$		−	9.44199i		−	0.317748i	0.987299	−	0.158874i	$-0.0507864\pi$
$884$	−0.215437	+	0.0350237i	−0.00724594	+	0.00117797i
$885$		0			0
$886$	6.69276	−	0.540474i	0.224848	−	0.0181576i
$887$	−13.5607			−0.455324			−0.227662	−	0.973740i	$-0.573108\pi$
$887$	−13.5607			−0.455324			−0.227662	+	0.973740i	$0.573108\pi$
$888$		0			0
$889$	22.0253	−	25.2339i	0.738704	−	0.846318i
$890$	−2.51476	+	1.73591i	−0.0842950	+	0.0581879i
$891$		0			0
$892$	49.1566	−	7.99140i	1.64588	−	0.267572i
$893$	17.7592			0.594290
$894$		0			0
$895$	−1.17324	−	2.03210i	−0.0392169	−	0.0679257i
$896$	−23.3289	−	18.7553i	−0.779364	−	0.626571i
$897$		0			0
$898$	−14.0652	−	6.67359i	−0.469363	−	0.222700i
$899$	9.76982	+	16.9218i	0.325842	+	0.564375i
$900$		0			0
$901$	20.5984	+	11.8925i	0.686231	+	0.396195i
$902$	0.703499	+	8.71152i	0.0234239	+	0.290062i
$903$		0			0
$904$	−7.16975	+	6.88773i	−0.238462	+	0.229082i
$905$	0.593550			0.0197303
$906$		0			0
$907$		−	35.5393i		−	1.18006i	−0.807380	−	0.590031i	$-0.799115\pi$
$907$		−	35.5393i		−	1.18006i	0.807380	−	0.590031i	$-0.200885\pi$
$908$	−10.0441	−	12.3005i	−0.333325	−	0.408205i
$909$		0			0
$910$	−0.0123331	+	0.0166678i	−0.000408838	+	0.000552533i
$911$	−12.9375	−	7.46947i	−0.428638	−	0.247475i	0.270128	−	0.962824i	$-0.412934\pi$
$911$	−12.9375	−	7.46947i	−0.428638	−	0.247475i	−0.698766	+	0.715350i	$0.746267\pi$
$912$		0			0
$913$	64.0493	+	36.9789i	2.11972	+	1.22382i
$914$	1.49320	+	18.4905i	0.0493908	+	0.611613i
$915$		0			0
$916$	16.2670	−	13.2830i	0.537476	−	0.438883i
$917$	33.0262	+	28.8267i	1.09062	+	0.951943i
$918$		0			0
$919$	−16.9214	−	9.76960i	−0.558187	−	0.322269i	0.194231	−	0.980956i	$-0.437779\pi$
$919$	−16.9214	−	9.76960i	−0.558187	−	0.322269i	−0.752417	+	0.658687i	$0.771112\pi$
$920$	−0.505616	−	2.05066i	−0.0166697	−	0.0676083i
$921$		0			0
$922$	−26.8140	−	38.8446i	−0.883072	−	1.27928i
$923$	−0.134082	−	0.232237i	−0.00441336	−	0.00764417i
$924$		0			0
$925$	7.88347	−	13.6546i	0.259207	−	0.448959i
$926$	−16.2041	+	1.30856i	−0.532500	+	0.0430020i
$927$		0			0
$928$	−5.59801	−	13.1342i	−0.183764	−	0.431151i
$929$	3.48834	−	2.01400i	0.114449	−	0.0660771i	−0.441683	−	0.897171i	$-0.645618\pi$
$929$	3.48834	−	2.01400i	0.114449	−	0.0660771i	0.556132	+	0.831094i	$0.312285\pi$
$930$		0			0
$931$	15.0784	+	6.16316i	0.494175	+	0.201989i
$932$	−16.6784	+	2.71141i	−0.546319	+	0.0888151i
$933$		0			0
$934$	−28.2458	+	19.4978i	−0.924232	+	0.637987i
$935$	1.85017	−	1.06820i	0.0605070	−	0.0349337i
$936$		0			0
$937$			18.0167i			0.588578i	0.955716	+	0.294289i	$0.0950829\pi$
$937$			18.0167i			0.588578i	−0.955716	+	0.294289i	$0.904917\pi$
$938$	0.793571	−	6.96617i	0.0259110	−	0.227454i
$939$		0			0
$940$	1.99650	+	0.757051i	0.0651186	+	0.0246923i
$941$	−27.4256	−	15.8342i	−0.894049	−	0.516179i	−0.0187842	−	0.999824i	$-0.505980\pi$
$941$	−27.4256	−	15.8342i	−0.894049	−	0.516179i	−0.875265	+	0.483644i	$0.839313\pi$
$942$		0			0
$943$	−2.97551	−	5.15374i	−0.0968961	−	0.167829i
$944$	21.4658	+	19.0130i	0.698652	+	0.618819i
$945$		0			0
$946$	58.7141	−	40.5297i	1.90896	−	1.31773i
$947$	37.3188	−	21.5460i	1.21270	−	0.700151i	0.249351	−	0.968413i	$-0.419783\pi$
$947$	37.3188	−	21.5460i	1.21270	−	0.700151i	0.963346	+	0.268262i	$0.0864492\pi$
$948$		0			0
$949$	−0.252334	+	0.437055i	−0.00819110	+	0.0141874i
$950$	−13.4887	+	9.31113i	−0.437632	+	0.302093i
$951$		0			0
$952$	0.983674	+	20.5929i	0.0318810	+	0.667419i
$953$	30.6261			0.992076			0.496038	−	0.868301i	$-0.334788\pi$
$953$	30.6261			0.992076			0.496038	+	0.868301i	$0.334788\pi$
$954$		0			0
$955$	0.0611290	+	0.105879i	0.00197809	+	0.00342615i
$956$	53.1104	+	20.1389i	1.71771	+	0.651339i
$957$		0			0
$958$	49.1397	+	23.3155i	1.58763	+	0.753289i
$959$	20.7830	+	18.1403i	0.671118	+	0.585782i
$960$		0			0
$961$	−14.4677	−	25.0588i	−0.466700	−	0.808349i
$962$	0.0760247	−	0.160230i	0.00245113	−	0.00516601i
$963$		0			0
$964$	31.9281	−	26.0713i	1.02833	−	0.839700i
$965$	−1.78482	−	1.03046i	−0.0574552	−	0.0331718i
$966$		0			0
$967$	30.1593	−	17.4125i	0.969858	−	0.559948i	0.0706649	−	0.997500i	$-0.477488\pi$
$967$	30.1593	−	17.4125i	0.969858	−	0.559948i	0.899193	+	0.437552i	$0.144155\pi$
$968$	13.3582	+	54.1778i	0.429349	+	1.74134i
$969$		0			0
$970$	−1.66515	+	1.14944i	−0.0534647	+	0.0369061i
$971$	11.0289	−	19.1026i	0.353934	−	0.613032i	−0.633001	−	0.774151i	$-0.718177\pi$
$971$	11.0289	−	19.1026i	0.353934	−	0.613032i	0.986935	+	0.161119i	$0.0515103\pi$
$972$		0			0
$973$	4.65920	−	23.7133i	0.149367	−	0.760214i
$974$	7.24455	−	0.585034i	0.232130	−	0.0187457i
$975$		0			0
$976$	−12.6250	−	37.8033i	−0.404118	−	1.21005i
$977$	16.6197	−	28.7862i	0.531712	−	0.920952i	−0.467603	−	0.883939i	$-0.654882\pi$
$977$	16.6197	−	28.7862i	0.531712	−	0.920952i	0.999315	−	0.0370136i	$-0.0117845\pi$
$978$		0			0
$979$	−42.8100	+	74.1491i	−1.36821	+	2.36982i
$980$	1.43239	+	1.33564i	0.0457561	+	0.0426653i
$981$		0			0
$982$	8.93243	−	0.721339i	0.285045	−	0.0230188i
$983$	−18.3766			−0.586122			−0.293061	−	0.956094i	$-0.594674\pi$
$983$	−18.3766			−0.586122			−0.293061	+	0.956094i	$0.594674\pi$
$984$		0			0
$985$			2.97902i			0.0949194i
$986$	−4.21531	+	8.88419i	−0.134243	+	0.282930i
$987$		0			0
$988$	−0.142802	+	0.116607i	−0.00454314	+	0.00370976i
$989$	−24.2893	+	42.0704i	−0.772356	+	1.33776i
$990$		0			0
$991$	−11.9336	+	6.88984i	−0.379082	+	0.218863i	−0.677419	−	0.735598i	$-0.736901\pi$
$991$	−11.9336	+	6.88984i	−0.379082	+	0.218863i	0.298337	+	0.954461i	$0.403568\pi$
$992$	17.1712	+	40.2875i	0.545186	+	1.27913i
$993$		0			0
$994$	−23.2285	+	10.1005i	−0.736764	+	0.320369i
$995$	−3.21311	+	1.85509i	−0.101862	+	0.0588103i
$996$		0			0
$997$		−	24.6010i		−	0.779121i	−0.921001	−	0.389561i	$-0.872627\pi$
$997$		−	24.6010i		−	0.779121i	0.921001	−	0.389561i	$-0.127373\pi$
$998$	−2.88719	+	6.08504i	−0.0913924	+	0.192618i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.7		84
3.2	odd	2		252.2.n.b.187.36	yes	84
4.3	odd	2	inner	756.2.n.b.19.22		84
7.3	odd	6		756.2.bj.b.451.35		84
9.4	even	3		756.2.bj.b.523.35		84
9.5	odd	6		252.2.bj.b.103.8	yes	84
12.11	even	2		252.2.n.b.187.21	yes	84
21.17	even	6		252.2.bj.b.115.8	yes	84
28.3	even	6		756.2.bj.b.451.36		84
36.23	even	6		252.2.bj.b.103.7	yes	84
36.31	odd	6		756.2.bj.b.523.36		84
63.31	odd	6	inner	756.2.n.b.199.22		84
63.59	even	6		252.2.n.b.31.21	✓	84
84.59	odd	6		252.2.bj.b.115.7	yes	84
252.31	even	6	inner	756.2.n.b.199.7		84
252.59	odd	6		252.2.n.b.31.36	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.21	✓	84	63.59	even	6
252.2.n.b.31.36	yes	84	252.59	odd	6
252.2.n.b.187.21	yes	84	12.11	even	2
252.2.n.b.187.36	yes	84	3.2	odd	2
252.2.bj.b.103.7	yes	84	36.23	even	6
252.2.bj.b.103.8	yes	84	9.5	odd	6
252.2.bj.b.115.7	yes	84	84.59	odd	6
252.2.bj.b.115.8	yes	84	21.17	even	6
756.2.n.b.19.7		84	1.1	even	1	trivial
756.2.n.b.19.22		84	4.3	odd	2	inner
756.2.n.b.199.7		84	252.31	even	6	inner
756.2.n.b.199.22		84	63.31	odd	6	inner
756.2.bj.b.451.35		84	7.3	odd	6
756.2.bj.b.451.36		84	28.3	even	6
756.2.bj.b.523.35		84	9.4	even	3
756.2.bj.b.523.36		84	36.31	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.27769 - 0.606229i) q^{2} +(1.26497 + 1.54914i) q^{4} -0.139892i q^{5} +(-1.99326 - 1.73980i) q^{7} +(-0.677105 - 2.74618i) q^{8} +O(q^{10})\)	\(q+(-1.27769 - 0.606229i) q^{2} +(1.26497 + 1.54914i) q^{4} -0.139892i q^{5} +(-1.99326 - 1.73980i) q^{7} +(-0.677105 - 2.74618i) q^{8} +(-0.0848066 + 0.178738i) q^{10} +5.54332i q^{11} +(-0.0343058 + 0.0198065i) q^{13} +(1.49204 + 3.43130i) q^{14} +(-0.799688 + 3.91925i) q^{16} +(2.38588 - 1.37749i) q^{17} +(1.16353 - 2.01529i) q^{19} +(0.216713 - 0.176960i) q^{20} +(3.36052 - 7.08263i) q^{22} +5.33791i q^{23} +4.98043 q^{25} +(0.0558394 - 0.00450931i) q^{26} +(0.173788 - 5.28865i) q^{28} +(1.26196 - 2.18578i) q^{29} +(-3.87090 + 6.70459i) q^{31} +(3.39771 - 4.52278i) q^{32} +(-3.88348 + 0.313611i) q^{34} +(-0.243385 + 0.278841i) q^{35} +(1.58289 - 2.74164i) q^{37} +(-2.70835 + 1.86954i) q^{38} +(-0.384169 + 0.0947216i) q^{40} +(-0.965497 + 0.557430i) q^{41} +(7.88143 + 4.55034i) q^{43} +(-8.58739 + 7.01215i) q^{44} +(3.23600 - 6.82019i) q^{46} +(3.81582 + 6.60920i) q^{47} +(0.946160 + 6.93576i) q^{49} +(-6.36344 - 3.01928i) q^{50} +(-0.0740790 - 0.0280900i) q^{52} +(4.31672 + 7.47678i) q^{53} +0.775466 q^{55} +(-3.42818 + 6.65189i) q^{56} +(-2.93747 + 2.02770i) q^{58} +(3.58441 - 6.20838i) q^{59} +(-8.62902 + 4.98197i) q^{61} +(9.01032 - 6.21973i) q^{62} +(-7.08306 + 3.71891i) q^{64} +(0.00277077 + 0.00479911i) q^{65} +(-1.62278 - 0.936915i) q^{67} +(5.15200 + 1.95358i) q^{68} +(0.480011 - 0.208725i) q^{70} +6.76960i q^{71} +(11.0331 - 6.36998i) q^{73} +(-3.68450 + 2.54337i) q^{74} +(4.59379 - 0.746814i) q^{76} +(9.64429 - 11.0493i) q^{77} +(1.47070 - 0.849112i) q^{79} +(0.548271 + 0.111870i) q^{80} +(1.57153 - 0.126909i) q^{82} +(6.67089 - 11.5543i) q^{83} +(-0.192700 - 0.333765i) q^{85} +(-7.31145 - 10.5919i) q^{86} +(15.2230 - 3.75341i) q^{88} +(13.3763 + 7.72281i) q^{89} +(0.102840 + 0.0202060i) q^{91} +(-8.26919 + 6.75232i) q^{92} +(-0.868743 - 10.7578i) q^{94} +(-0.281922 - 0.162768i) q^{95} +(8.85713 + 5.11366i) q^{97} +(2.99576 - 9.43533i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 84 * q + q^2 + q^4 + 16 * q^8	\( 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

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