LMFDB - Embedded newform 756.2.bj.b.451.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(451,756)]

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, 1]))

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

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

chi := DirichletCharacter("756.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bj (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			451.15
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.667137 - 1.24697i) q^{2} +(-1.10986 + 1.66380i) q^{4} +(0.627749 + 0.362431i) q^{5} +(2.64477 - 0.0721413i) q^{7} +(2.81513 + 0.273973i) q^{8} +O(q^{10})$	\(q+(-0.667137 - 1.24697i) q^{2} +(-1.10986 + 1.66380i) q^{4} +(0.627749 + 0.362431i) q^{5} +(2.64477 - 0.0721413i) q^{7} +(2.81513 + 0.273973i) q^{8} +(0.0331449 - 1.02457i) q^{10} +(-0.501838 + 0.289736i) q^{11} +(-3.35535 + 1.93721i) q^{13} +(-1.85438 - 3.24981i) q^{14} +(-1.53644 - 3.69315i) q^{16} +(3.20279 + 1.84913i) q^{17} +(2.04363 + 3.53967i) q^{19} +(-1.29972 + 0.642201i) q^{20} +(0.696087 + 0.432482i) q^{22} +(4.47089 + 2.58127i) q^{23} +(-2.23729 - 3.87510i) q^{25} +(4.65413 + 2.89163i) q^{26} +(-2.81528 + 4.48042i) q^{28} +(-4.56967 + 7.91490i) q^{29} +0.848671 q^{31} +(-3.58022 + 4.37973i) q^{32} +(0.169106 - 5.22740i) q^{34} +(1.68640 + 0.913260i) q^{35} +(-1.73892 - 3.01190i) q^{37} +(3.05047 - 4.90979i) q^{38} +(1.66790 + 1.19228i) q^{40} +(0.854749 - 0.493490i) q^{41} +(10.9509 + 6.32252i) q^{43} +(0.0749053 - 1.15652i) q^{44} +(0.236061 - 7.29711i) q^{46} +11.5806 q^{47} +(6.98959 - 0.381594i) q^{49} +(-3.33954 + 5.37505i) q^{50} +(0.500827 - 7.73266i) q^{52} +(2.70941 - 4.69284i) q^{53} -0.420038 q^{55} +(7.46512 + 0.521507i) q^{56} +(12.9182 + 0.417904i) q^{58} -0.387839 q^{59} +0.891401i q^{61} +(-0.566180 - 1.05827i) q^{62} +(7.84988 + 1.54254i) q^{64} -2.80843 q^{65} -3.15867i q^{67} +(-6.63122 + 3.27652i) q^{68} +(0.0137466 - 2.71215i) q^{70} -7.56506i q^{71} +(-10.1955 - 5.88637i) q^{73} +(-2.59564 + 4.17773i) q^{74} +(-8.15743 - 0.528338i) q^{76} +(-1.30634 + 0.802489i) q^{77} -3.39987i q^{79} +(0.374013 - 2.87523i) q^{80} +(-1.18560 - 0.736619i) q^{82} +(-3.46587 + 6.00306i) q^{83} +(1.34037 + 2.32158i) q^{85} +(0.578205 - 17.8734i) q^{86} +(-1.49212 + 0.678155i) q^{88} +(2.37662 - 1.37214i) q^{89} +(-8.73438 + 5.36554i) q^{91} +(-9.25674 + 4.57381i) q^{92} +(-7.72586 - 14.4406i) q^{94} +2.96270i q^{95} +(9.32750 + 5.38523i) q^{97} +(-5.13885 - 8.46122i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37} - 33 q^{38} + 6 q^{40} - 6 q^{41} + 13 q^{44} + 10 q^{46} - 28 q^{49} + 17 q^{50} - 27 q^{52} + 2 q^{53} - 58 q^{56} - 13 q^{58} - 8 q^{64} + 100 q^{65} + 18 q^{68} - 19 q^{70} + 30 q^{73} + 23 q^{74} + 2 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} + 9 q^{86} + q^{88} + 102 q^{89} - 28 q^{92} + 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.667137	−	1.24697i	−0.471737	−	0.881739i
$2$	−0.667137	−	1.24697i	−0.471737	−	0.881739i
$3$		0			0
$3$		0			0
$4$	−1.10986	+	1.66380i	−0.554928	+	0.831899i
$5$	0.627749	+	0.362431i	0.280738	+	0.162084i	0.633757	−	0.773532i	$-0.281512\pi$
$5$	0.627749	+	0.362431i	0.280738	+	0.162084i	−0.353019	+	0.935616i	$0.614845\pi$
$6$		0			0
$7$	2.64477	−	0.0721413i	0.999628	−	0.0272668i
$7$	2.64477	−	0.0721413i	0.999628	−	0.0272668i
$8$	2.81513	+	0.273973i	0.995298	+	0.0968640i
$9$		0			0
$10$	0.0331449	−	1.02457i	0.0104814	−	0.323999i
$11$	−0.501838	+	0.289736i	−0.151310	+	0.0873588i	−0.573743	−	0.819035i	$-0.694509\pi$
$11$	−0.501838	+	0.289736i	−0.151310	+	0.0873588i	0.422434	+	0.906394i	$0.361176\pi$
$12$		0			0
$13$	−3.35535	+	1.93721i	−0.930608	+	0.537287i	−0.887004	−	0.461762i	$-0.847217\pi$
$13$	−3.35535	+	1.93721i	−0.930608	+	0.537287i	−0.0436041	+	0.999049i	$0.513884\pi$
$14$	−1.85438	−	3.24981i	−0.495604	−	0.868549i
$15$		0			0
$16$	−1.53644	−	3.69315i	−0.384110	−	0.923287i
$17$	3.20279	+	1.84913i	0.776791	+	0.448480i	0.835292	−	0.549807i	$-0.185299\pi$
$17$	3.20279	+	1.84913i	0.776791	+	0.448480i	−0.0585009	+	0.998287i	$0.518632\pi$
$18$		0			0
$19$	2.04363	+	3.53967i	0.468841	+	0.812057i	0.999366	−	0.0356130i	$-0.0113384\pi$
$19$	2.04363	+	3.53967i	0.468841	+	0.812057i	−0.530525	+	0.847670i	$0.678005\pi$
$20$	−1.29972	+	0.642201i	−0.290627	+	0.143601i
$21$		0			0
$22$	0.696087	+	0.432482i	0.148406	+	0.0922054i
$23$	4.47089	+	2.58127i	0.932244	+	0.538231i	0.887521	−	0.460768i	$-0.152426\pi$
$23$	4.47089	+	2.58127i	0.932244	+	0.538231i	0.0447236	+	0.998999i	$0.485759\pi$
$24$		0			0
$25$	−2.23729	−	3.87510i	−0.447457	−	0.775019i
$26$	4.65413	+	2.89163i	0.912749	+	0.567095i
$27$		0			0
$28$	−2.81528	+	4.48042i	−0.532038	+	0.846720i
$29$	−4.56967	+	7.91490i	−0.848566	+	1.46976i	0.0339219	+	0.999424i	$0.489200\pi$
$29$	−4.56967	+	7.91490i	−0.848566	+	1.46976i	−0.882488	+	0.470335i	$0.844133\pi$
$30$		0			0
$31$	0.848671			0.152426			0.0762129	−	0.997092i	$-0.475717\pi$
$31$	0.848671			0.152426			0.0762129	+	0.997092i	$0.475717\pi$
$32$	−3.58022	+	4.37973i	−0.632899	+	0.774234i
$33$		0			0
$34$	0.169106	−	5.22740i	0.0290015	−	0.896492i
$35$	1.68640	+	0.913260i	0.285053	+	0.154369i
$36$		0			0
$37$	−1.73892	−	3.01190i	−0.285877	−	0.495153i	0.686945	−	0.726710i	$-0.258951\pi$
$37$	−1.73892	−	3.01190i	−0.285877	−	0.495153i	−0.972821	+	0.231557i	$0.925618\pi$
$38$	3.05047	−	4.90979i	0.494852	−	0.796473i
$39$		0			0
$40$	1.66790	+	1.19228i	0.263718	+	0.188515i
$41$	0.854749	−	0.493490i	0.133489	−	0.0770701i	−0.431768	−	0.901985i	$-0.642110\pi$
$41$	0.854749	−	0.493490i	0.133489	−	0.0770701i	0.565258	+	0.824914i	$0.308777\pi$
$42$		0			0
$43$	10.9509	+	6.32252i	1.67000	+	0.964175i	0.967633	+	0.252360i	$0.0812069\pi$
$43$	10.9509	+	6.32252i	1.67000	+	0.964175i	0.702367	+	0.711815i	$0.252126\pi$
$44$	0.0749053	−	1.15652i	0.0112924	−	0.174352i
$45$		0			0
$46$	0.236061	−	7.29711i	0.0348053	−	1.07590i
$47$	11.5806			1.68921			0.844603	−	0.535394i	$-0.179837\pi$
$47$	11.5806			1.68921			0.844603	+	0.535394i	$0.179837\pi$
$48$		0			0
$49$	6.98959	−	0.381594i	0.998513	−	0.0545134i
$50$	−3.33954	+	5.37505i	−0.472282	+	0.760146i
$51$		0			0
$52$	0.500827	−	7.73266i	0.0694522	−	1.07233i
$53$	2.70941	−	4.69284i	0.372166	−	0.644611i	−0.617732	−	0.786388i	$-0.711948\pi$
$53$	2.70941	−	4.69284i	0.372166	−	0.644611i	0.989899	+	0.141778i	$0.0452818\pi$
$54$		0			0
$55$	−0.420038			−0.0566379
$56$	7.46512	+	0.521507i	0.997569	+	0.0696893i
$57$		0			0
$58$	12.9182	+	0.417904i	1.69624	+	0.0548735i
$59$	−0.387839			−0.0504924			−0.0252462	−	0.999681i	$-0.508037\pi$
$59$	−0.387839			−0.0504924			−0.0252462	+	0.999681i	$0.508037\pi$
$60$		0			0
$61$			0.891401i			0.114132i	0.998370	+	0.0570661i	$0.0181746\pi$
$61$			0.891401i			0.114132i	−0.998370	+	0.0570661i	$0.981825\pi$
$62$	−0.566180	−	1.05827i	−0.0719050	−	0.134400i
$63$		0			0
$64$	7.84988	+	1.54254i	0.981235	+	0.192817i
$65$	−2.80843			−0.348343
$66$		0			0
$67$		−	3.15867i		−	0.385893i	−0.981209	−	0.192947i	$-0.938196\pi$
$67$		−	3.15867i		−	0.385893i	0.981209	−	0.192947i	$-0.0618044\pi$
$68$	−6.63122	+	3.27652i	−0.804153	+	0.397337i
$69$		0			0
$70$	0.0137466	−	2.71215i	0.00164303	−	0.324164i
$71$		−	7.56506i		−	0.897807i	−0.893580	−	0.448904i	$-0.851815\pi$
$71$		−	7.56506i		−	0.897807i	0.893580	−	0.448904i	$-0.148185\pi$
$72$		0			0
$73$	−10.1955	−	5.88637i	−1.19329	−	0.688947i	−0.234240	−	0.972179i	$-0.575260\pi$
$73$	−10.1955	−	5.88637i	−1.19329	−	0.688947i	−0.959051	+	0.283232i	$0.908593\pi$
$74$	−2.59564	+	4.17773i	−0.301737	+	0.485651i
$75$		0			0
$76$	−8.15743	−	0.528338i	−0.935722	−	0.0606046i
$77$	−1.30634	+	0.802489i	−0.148872	+	0.0914521i
$78$		0			0
$79$		−	3.39987i		−	0.382515i	−0.981540	−	0.191257i	$-0.938743\pi$
$79$		−	3.39987i		−	0.382515i	0.981540	−	0.191257i	$-0.0612565\pi$
$80$	0.374013	−	2.87523i	0.0418159	−	0.321460i
$81$		0			0
$82$	−1.18560	−	0.736619i	−0.130928	−	0.0813460i
$83$	−3.46587	+	6.00306i	−0.380428	+	0.658921i	−0.991123	−	0.132945i	$-0.957557\pi$
$83$	−3.46587	+	6.00306i	−0.380428	+	0.658921i	0.610695	+	0.791866i	$0.290890\pi$
$84$		0			0
$85$	1.34037	+	2.32158i	0.145383	+	0.251811i
$86$	0.578205	−	17.8734i	0.0623495	−	1.92734i
$87$		0			0
$88$	−1.49212	+	0.678155i	−0.159060	+	0.0722915i
$89$	2.37662	−	1.37214i	0.251921	−	0.145446i	−0.368723	−	0.929539i	$-0.620205\pi$
$89$	2.37662	−	1.37214i	0.251921	−	0.145446i	0.620643	+	0.784093i	$0.286871\pi$
$90$		0			0
$91$	−8.73438	+	5.36554i	−0.915612	+	0.562462i
$92$	−9.25674	+	4.57381i	−0.965082	+	0.476853i
$93$		0			0
$94$	−7.72586	−	14.4406i	−0.796861	−	1.48944i
$95$			2.96270i			0.303967i
$96$		0			0
$97$	9.32750	+	5.38523i	0.947064	+	0.546788i	0.892168	−	0.451704i	$-0.149184\pi$
$97$	9.32750	+	5.38523i	0.947064	+	0.546788i	0.0548963	+	0.998492i	$0.482517\pi$
$98$	−5.13885	−	8.46122i	−0.519102	−	0.854712i
$99$		0			0
$100$	8.93044	+	0.578404i	0.893044	+	0.0578404i
$101$	8.28966	−	4.78604i	0.824852	−	0.476229i	−0.0272346	−	0.999629i	$-0.508670\pi$
$101$	8.28966	−	4.78604i	0.824852	−	0.476229i	0.852087	+	0.523400i	$0.175337\pi$
$102$		0			0
$103$	−5.35055	+	9.26743i	−0.527206	+	0.913147i	0.472292	+	0.881442i	$0.343427\pi$
$103$	−5.35055	+	9.26743i	−0.527206	+	0.913147i	−0.999497	+	0.0317044i	$0.989906\pi$
$104$	−9.97649	+	4.53423i	−0.978275	+	0.444618i
$105$		0			0
$106$	−7.65937	−	0.247780i	−0.743943	−	0.0240665i
$107$	−1.37590	+	0.794374i	−0.133013	+	0.0767950i	−0.565030	−	0.825070i	$-0.691135\pi$
$107$	−1.37590	+	0.794374i	−0.133013	+	0.0767950i	0.432017	+	0.901865i	$0.357802\pi$
$108$		0			0
$109$	−4.38392	+	7.59317i	−0.419903	+	0.727294i	−0.995929	−	0.0901375i	$-0.971269\pi$
$109$	−4.38392	+	7.59317i	−0.419903	+	0.727294i	0.576026	+	0.817431i	$0.304603\pi$
$110$	0.280223	+	0.523774i	0.0267182	+	0.0499399i
$111$		0			0
$112$	−4.32996	−	9.65668i	−0.409143	−	0.912470i
$113$	−3.31031	−	5.73363i	−0.311408	−	0.539375i	0.667259	−	0.744825i	$-0.267467\pi$
$113$	−3.31031	−	5.73363i	−0.311408	−	0.539375i	−0.978667	+	0.205451i	$0.934134\pi$
$114$		0			0
$115$	1.87106	+	3.24078i	0.174478	+	0.302204i
$116$	−8.09711	−	16.3874i	−0.751798	−	1.52153i
$117$		0			0
$118$	0.258742	+	0.483623i	0.0238191	+	0.0445211i
$119$	8.60404	+	4.65947i	0.788731	+	0.427133i
$120$		0			0
$121$	−5.33211	+	9.23548i	−0.484737	+	0.839589i
$122$	1.11155	−	0.594687i	0.100635	−	0.0538404i
$123$		0			0
$124$	−0.941902	+	1.41202i	−0.0845853	+	0.126803i
$125$		−	6.86776i		−	0.614271i
$126$		0			0
$127$		−	9.20736i		−	0.817021i	−0.912754	−	0.408511i	$-0.866048\pi$
$127$		−	9.20736i		−	0.817021i	0.912754	−	0.408511i	$-0.133952\pi$
$128$	−3.31345	−	10.8176i	−0.292871	−	0.956152i
$129$		0			0
$130$	1.87361	+	3.50202i	0.164326	+	0.307147i
$131$	8.06936	−	13.9765i	0.705023	−	1.22114i	−0.261660	−	0.965160i	$-0.584270\pi$
$131$	8.06936	−	13.9765i	0.705023	−	1.22114i	0.966683	−	0.255976i	$-0.0823967\pi$
$132$		0			0
$133$	5.66029	+	9.21418i	0.490809	+	0.798971i
$134$	−3.93876	+	2.10727i	−0.340257	+	0.182040i
$135$		0			0
$136$	8.50965	+	6.08302i	0.729696	+	0.521615i
$137$	−1.14877	−	1.98972i	−0.0981457	−	0.169993i	0.812771	−	0.582583i	$-0.197958\pi$
$137$	−1.14877	−	1.98972i	−0.0981457	−	0.169993i	−0.910917	+	0.412589i	$0.864624\pi$
$138$		0			0
$139$	3.40486	+	5.89740i	0.288797	+	0.500211i	0.973523	−	0.228590i	$-0.0734115\pi$
$139$	3.40486	+	5.89740i	0.288797	+	0.500211i	−0.684726	+	0.728801i	$0.740078\pi$
$140$	−3.39114	+	1.79224i	−0.286603	+	0.151472i
$141$		0			0
$142$	−9.43338	+	5.04693i	−0.791632	+	0.423529i
$143$	1.12256	−	1.94434i	0.0938734	−	0.162594i
$144$		0			0
$145$	−5.73721	+	3.31238i	−0.476449	+	0.275078i
$146$	−0.538318	+	16.6405i	−0.0445515	+	1.37717i
$147$		0			0
$148$	6.94114	+	0.449562i	0.570558	+	0.0369537i
$149$	−5.94517	+	10.2973i	−0.487047	+	0.843590i	−0.999889	−	0.0148927i	$-0.995259\pi$
$149$	−5.94517	+	10.2973i	−0.487047	+	0.843590i	0.512842	+	0.858483i	$0.328593\pi$
$150$		0			0
$151$	−11.9006	+	6.87083i	−0.968459	+	0.559140i	−0.898766	−	0.438428i	$-0.855535\pi$
$151$	−11.9006	+	6.87083i	−0.968459	+	0.559140i	−0.0696928	+	0.997568i	$0.522202\pi$
$152$	4.78331	+	10.5245i	0.387977	+	0.853652i
$153$		0			0
$154$	1.87219	+	1.09360i	0.150865	+	0.0881246i
$155$	0.532753	+	0.307585i	0.0427917	+	0.0247058i
$156$		0			0
$157$			12.3209i			0.983317i	0.870788	+	0.491659i	$0.163609\pi$
$157$			12.3209i			0.983317i	−0.870788	+	0.491659i	$0.836391\pi$
$158$	−4.23952	+	2.26818i	−0.337278	+	0.180447i
$159$		0			0
$160$	−3.83483	+	1.45179i	−0.303170	+	0.114774i
$161$	12.0107	+	6.50432i	0.946573	+	0.512612i
$162$		0			0
$163$	4.96214	−	2.86489i	0.388665	−	0.224396i	−0.292917	−	0.956138i	$-0.594626\pi$
$163$	4.96214	−	2.86489i	0.388665	−	0.224396i	0.681582	+	0.731742i	$0.261292\pi$
$164$	−0.127581	+	1.96983i	−0.00996244	+	0.153818i
$165$		0			0
$166$	9.79782	+	0.316959i	0.760459	+	0.0246008i
$167$	−4.19478	−	7.26556i	−0.324601	−	0.562226i	0.656830	−	0.754039i	$-0.271897\pi$
$167$	−4.19478	−	7.26556i	−0.324601	−	0.562226i	−0.981432	+	0.191812i	$0.938564\pi$
$168$		0			0
$169$	1.00560	−	1.74175i	0.0773539	−	0.133981i
$170$	2.00073	−	3.22021i	0.153449	−	0.246979i
$171$		0			0
$172$	−22.6733	+	11.2030i	−1.72883	+	0.854223i
$173$			17.8687i			1.35853i	0.733891	+	0.679267i	$0.237702\pi$
$173$			17.8687i			1.35853i	−0.733891	+	0.679267i	$0.762298\pi$
$174$		0			0
$175$	−6.19666	−	10.0873i	−0.468423	−	0.762530i
$176$	1.84108	+	1.40820i	0.138777	+	0.106147i
$177$		0			0
$178$	−3.29654	−	2.04816i	−0.247086	−	0.153516i
$179$	−21.7765	−	12.5727i	−1.62765	−	0.939727i	−0.984790	−	0.173747i	$-0.944413\pi$
$179$	−21.7765	−	12.5727i	−1.62765	−	0.939727i	−0.642864	−	0.765980i	$-0.722254\pi$
$180$		0			0
$181$		−	21.3865i		−	1.58965i	−0.606841	−	0.794824i	$-0.707563\pi$
$181$		−	21.3865i		−	1.58965i	0.606841	−	0.794824i	$-0.292437\pi$
$182$	12.5177	+	7.31193i	0.927873	+	0.541997i
$183$		0			0
$184$	11.8789	+	8.49150i	0.875725	+	0.626001i
$185$		−	2.52096i		−	0.185344i
$186$		0			0
$187$	−2.14304			−0.156715
$188$	−12.8528	+	19.2678i	−0.937387	+	1.40525i
$189$		0			0
$190$	3.69439	−	1.97653i	0.268019	−	0.143393i
$191$		−	0.399022i		−	0.0288722i	−0.999896	−	0.0144361i	$-0.995405\pi$
$191$		−	0.399022i		−	0.0288722i	0.999896	−	0.0144361i	$-0.00459532\pi$
$192$		0			0
$193$	−16.1954			−1.16577			−0.582885	−	0.812554i	$-0.698076\pi$
$193$	−16.1954			−1.16577			−0.582885	+	0.812554i	$0.698076\pi$
$194$	0.492489	−	15.2238i	0.0353586	−	1.09300i
$195$		0			0
$196$	−7.12254	+	12.0528i	−0.508753	+	0.860913i
$197$	−23.4117			−1.66801			−0.834006	−	0.551756i	$-0.813958\pi$
$197$	−23.4117			−1.66801			−0.834006	+	0.551756i	$0.813958\pi$
$198$		0			0
$199$	6.11333	−	10.5886i	0.433362	−	0.750606i	−0.563798	−	0.825913i	$-0.690660\pi$
$199$	6.11333	−	10.5886i	0.433362	−	0.750606i	0.997160	+	0.0753071i	$0.0239937\pi$
$200$	−5.23658	−	11.5218i	−0.370282	−	0.814717i
$201$		0			0
$202$	−11.4984	−	7.14399i	−0.809023	−	0.502650i
$203$	−11.5147	+	21.2627i	−0.808175	+	1.49235i
$204$		0			0
$205$	0.715424			0.0499674
$206$	15.1257	+	0.489317i	1.05386	+	0.0340923i
$207$		0			0
$208$	12.3097	+	9.41541i	0.853526	+	0.652841i
$209$	−2.05114	−	1.18423i	−0.141881	−	0.0819148i
$210$		0			0
$211$	11.8107	−	6.81891i	0.813082	−	0.469433i	−0.0349433	−	0.999389i	$-0.511125\pi$
$211$	11.8107	−	6.81891i	0.813082	−	0.469433i	0.848025	+	0.529956i	$0.177792\pi$
$212$	4.80087	+	9.71628i	0.329725	+	0.667317i
$213$		0			0
$214$	1.90847	+	1.18574i	0.130460	+	0.0810556i
$215$	4.58296	+	7.93791i	0.312555	+	0.541361i
$216$		0			0
$217$	2.24454	−	0.0612242i	0.152369	−	0.00415617i
$218$	12.3931	+	0.400917i	0.839368	+	0.0271535i
$219$		0			0
$220$	0.466181	−	0.698858i	0.0314299	−	0.0471170i
$221$	−14.3287			−0.963850
$222$		0			0
$223$	−8.37599	+	14.5076i	−0.560898	+	0.971504i	0.436520	+	0.899694i	$0.356211\pi$
$223$	−8.37599	+	14.5076i	−0.560898	+	0.971504i	−0.997418	+	0.0718094i	$0.977123\pi$
$224$	−9.15289	+	11.8416i	−0.611553	+	0.791203i
$225$		0			0
$226$	−4.94122	+	7.95297i	−0.328685	+	0.529024i
$227$	−10.9841	−	19.0249i	−0.729037	−	1.26273i	−0.957291	−	0.289128i	$-0.906635\pi$
$227$	−10.9841	−	19.0249i	−0.729037	−	1.26273i	0.228253	−	0.973602i	$-0.426699\pi$
$228$		0			0
$229$	3.28647	+	1.89744i	0.217176	+	0.125386i	0.604642	−	0.796497i	$-0.293316\pi$
$229$	3.28647	+	1.89744i	0.217176	+	0.125386i	−0.387466	+	0.921884i	$0.626650\pi$
$230$	2.79289	−	4.49520i	0.184158	−	0.296405i
$231$		0			0
$232$	−15.0327	+	21.0295i	−0.986943	+	1.38065i
$233$	10.3989	+	18.0115i	0.681256	+	1.17997i	0.974598	+	0.223963i	$0.0718995\pi$
$233$	10.3989	+	18.0115i	0.681256	+	1.17997i	−0.293341	+	0.956008i	$0.594767\pi$
$234$		0			0
$235$	7.26972	+	4.19717i	0.474224	+	0.273793i
$236$	0.430446	−	0.645286i	0.0280196	−	0.0420045i
$237$		0			0
$238$	0.0701353	−	13.8375i	0.00454620	−	0.896949i
$239$	0.874254	−	0.504751i	0.0565508	−	0.0326496i	−0.471458	−	0.881888i	$-0.656272\pi$
$239$	0.874254	−	0.504751i	0.0565508	−	0.0326496i	0.528009	+	0.849239i	$0.322939\pi$
$240$		0			0
$241$	22.5421	−	13.0147i	1.45206	−	0.838349i	0.453465	−	0.891274i	$-0.350188\pi$
$241$	22.5421	−	13.0147i	1.45206	−	0.838349i	0.998598	+	0.0529249i	$0.0168544\pi$
$242$	15.0736	+	0.487630i	0.968967	+	0.0313461i
$243$		0			0
$244$	−1.48311	−	0.989326i	−0.0949464	−	0.0633351i
$245$	4.52601	+	2.29370i	0.289156	+	0.146539i
$246$		0			0
$247$	−13.7142	−	7.91790i	−0.872614	−	0.503804i
$248$	2.38912	+	0.232513i	0.151709	+	0.0147646i
$249$		0			0
$250$	−8.56388	+	4.58174i	−0.541627	+	0.289775i
$251$	18.4201			1.16266			0.581332	−	0.813666i	$-0.302532\pi$
$251$	18.4201			1.16266			0.581332	+	0.813666i	$0.302532\pi$
$252$		0			0
$253$	−2.99155			−0.188077
$254$	−11.4813	+	6.14258i	−0.720400	+	0.385419i
$255$		0			0
$256$	−11.2787	+	11.3486i	−0.704919	+	0.709288i
$257$	−10.8821	−	6.28280i	−0.678809	−	0.391910i	0.120597	−	0.992702i	$-0.461519\pi$
$257$	−10.8821	−	6.28280i	−0.678809	−	0.391910i	−0.799406	+	0.600791i	$0.794852\pi$
$258$		0			0
$259$	−4.81632	−	7.84032i	−0.299272	−	0.487174i
$260$	3.11695	−	4.67265i	0.193305	−	0.289786i
$261$		0			0
$262$	−22.8117	−	0.737956i	−1.40931	−	0.0455911i
$263$	−8.60780	+	4.96972i	−0.530780	+	0.306446i	−0.741334	−	0.671136i	$-0.765806\pi$
$263$	−8.60780	+	4.96972i	−0.530780	+	0.306446i	0.210554	+	0.977582i	$0.432473\pi$
$264$		0			0
$265$	3.40166	−	1.96395i	0.208962	−	0.120645i
$266$	7.71360	−	13.2053i	0.472951	−	0.809670i
$267$		0			0
$268$	5.25539	+	3.50567i	0.321024	+	0.214143i
$269$	−6.20144	−	3.58040i	−0.378108	−	0.218301i	0.298887	−	0.954289i	$-0.403385\pi$
$269$	−6.20144	−	3.58040i	−0.378108	−	0.218301i	−0.676995	+	0.735988i	$0.736718\pi$
$270$		0			0
$271$	−3.11123	−	5.38881i	−0.188994	−	0.327347i	0.755921	−	0.654663i	$-0.227189\pi$
$271$	−3.11123	−	5.38881i	−0.188994	−	0.327347i	−0.944915	+	0.327316i	$0.893856\pi$
$272$	1.90822	−	14.6695i	0.115703	−	0.889467i
$273$		0			0
$274$	−1.71473	+	2.75989i	−0.103591	+	0.166731i
$275$	2.24551	+	1.29645i	0.135409	+	0.0781787i
$276$		0			0
$277$	−13.1171	−	22.7195i	−0.788130	−	1.36508i	−0.927111	−	0.374786i	$-0.877716\pi$
$277$	−13.1171	−	22.7195i	−0.788130	−	1.36508i	0.138982	−	0.990295i	$-0.455617\pi$
$278$	5.08235	−	8.18013i	0.304819	−	0.490611i
$279$		0			0
$280$	4.49721	+	3.03297i	0.268760	+	0.181255i
$281$	4.29087	−	7.43201i	0.255972	−	0.443357i	−0.709187	−	0.705020i	$-0.750938\pi$
$281$	4.29087	−	7.43201i	0.255972	−	0.443357i	0.965159	+	0.261664i	$0.0842712\pi$
$282$		0			0
$283$	−28.7140			−1.70687			−0.853435	−	0.521200i	$-0.825485\pi$
$283$	−28.7140			−1.70687			−0.853435	+	0.521200i	$0.825485\pi$
$284$	12.5867	+	8.39612i	0.746885	+	0.498218i
$285$		0			0
$286$	−3.17343	−	0.102660i	−0.187649	−	0.00607043i
$287$	2.22501	−	1.36683i	0.131338	−	0.0806813i
$288$		0			0
$289$	−1.66142	−	2.87767i	−0.0977307	−	0.169275i
$290$	7.95794	+	4.94430i	0.467306	+	0.290339i
$291$		0			0
$292$	21.1092	−	10.4302i	1.23532	−	0.610381i
$293$	20.5937	−	11.8898i	1.20310	−	0.694609i	0.241855	−	0.970312i	$-0.422244\pi$
$293$	20.5937	−	11.8898i	1.20310	−	0.694609i	0.961243	+	0.275704i	$0.0889109\pi$
$294$		0			0
$295$	−0.243466	−	0.140565i	−0.0141751	−	0.00818401i
$296$	−4.07010	−	8.95529i	−0.236570	−	0.520516i
$297$		0			0
$298$	16.8067	+	0.543696i	0.973585	+	0.0314954i
$299$	−20.0019			−1.15674
$300$		0			0
$301$	29.4188	+	15.9316i	1.69567	+	0.918281i
$302$	16.5070	+	10.2559i	0.949874	+	0.590161i
$303$		0			0
$304$	9.93262	−	12.9859i	0.569675	−	0.744794i
$305$	−0.323072	+	0.559576i	−0.0184990	+	0.0320412i
$306$		0			0
$307$	12.4459			0.710323			0.355161	−	0.934805i	$-0.384426\pi$
$307$	12.4459			0.710323			0.355161	+	0.934805i	$0.384426\pi$
$308$	0.114674	−	3.06414i	0.00653416	−	0.174595i
$309$		0			0
$310$	0.0281292	−	0.869527i	0.00159763	−	0.0493858i
$311$	−27.7490			−1.57350			−0.786752	−	0.617269i	$-0.788239\pi$
$311$	−27.7490			−1.57350			−0.786752	+	0.617269i	$0.788239\pi$
$312$		0			0
$313$		−	25.0450i		−	1.41563i	−0.706400	−	0.707813i	$-0.749682\pi$
$313$		−	25.0450i		−	1.41563i	0.706400	−	0.707813i	$-0.250318\pi$
$314$	15.3638	−	8.21975i	0.867029	−	0.463867i
$315$		0			0
$316$	5.65669	+	3.77336i	0.318214	+	0.212268i
$317$	−19.1683			−1.07660			−0.538300	−	0.842754i	$-0.680933\pi$
$317$	−19.1683			−1.07660			−0.538300	+	0.842754i	$0.680933\pi$
$318$		0			0
$319$		−	5.29600i		−	0.296519i
$320$	4.36869	+	3.81337i	0.244217	+	0.213174i
$321$		0			0
$322$	0.0979043	−	19.3162i	0.00545599	−	1.07645i
$323$			15.1158i			0.841064i
$324$		0			0
$325$	15.0138	+	8.66821i	0.832815	+	0.480826i
$326$	−6.88286	−	4.27635i	−0.381206	−	0.236845i
$327$		0			0
$328$	2.54143	−	1.15506i	0.140327	−	0.0637774i
$329$	30.6280	−	0.835440i	1.68858	−	0.0460593i
$330$		0			0
$331$		−	7.75625i		−	0.426322i	−0.977017	−	0.213161i	$-0.931624\pi$
$331$		−	7.75625i		−	0.426322i	0.977017	−	0.213161i	$-0.0683759\pi$
$332$	−6.14126	−	12.4290i	−0.337045	−	0.682131i
$333$		0			0
$334$	−6.26143	+	10.0779i	−0.342610	+	0.551437i
$335$	1.14480	−	1.98285i	0.0625472	−	0.108335i
$336$		0			0
$337$	−16.8555	−	29.1945i	−0.918175	−	1.59033i	−0.802185	−	0.597076i	$-0.796329\pi$
$337$	−16.8555	−	29.1945i	−0.918175	−	1.59033i	−0.115990	−	0.993250i	$-0.537004\pi$
$338$	−2.84278	−	0.0919639i	−0.154627	−	0.00500218i
$339$		0			0
$340$	−5.35025	−	0.346524i	−0.290158	−	0.0187929i
$341$	−0.425895	+	0.245891i	−0.0230635	+	0.0133157i
$342$		0			0
$343$	18.4583	−	1.51347i	0.996655	−	0.0817195i
$344$	29.0960	+	20.7989i	1.56875	+	1.12140i
$345$		0			0
$346$	22.2817	−	11.9209i	1.19787	−	0.640872i
$347$		−	0.861953i		−	0.0462721i	−0.999732	−	0.0231360i	$-0.992635\pi$
$347$		−	0.861953i		−	0.0462721i	0.999732	−	0.0231360i	$-0.00736509\pi$
$348$		0			0
$349$	29.7538	+	17.1783i	1.59268	+	0.919535i	0.992845	+	0.119414i	$0.0381015\pi$
$349$	29.7538	+	17.1783i	1.59268	+	0.919535i	0.599838	+	0.800122i	$0.295232\pi$
$350$	−8.44454	+	14.4567i	−0.451380	+	0.772741i
$351$		0			0
$352$	0.527723	−	3.23523i	0.0281278	−	0.172439i
$353$	22.9489	−	13.2495i	1.22145	−	0.705202i	0.256220	−	0.966619i	$-0.417523\pi$
$353$	22.9489	−	13.2495i	1.22145	−	0.705202i	0.965226	+	0.261416i	$0.0841896\pi$
$354$		0			0
$355$	2.74181	−	4.74896i	0.145520	−	0.252049i
$356$	−0.354738	+	5.47708i	−0.0188011	+	0.290285i
$357$		0			0
$358$	−1.14979	+	35.5423i	−0.0607685	+	1.87847i
$359$	−20.6811	+	11.9402i	−1.09150	+	0.630181i	−0.933977	−	0.357334i	$-0.883686\pi$
$359$	−20.6811	+	11.9402i	−1.09150	+	0.630181i	−0.157528	+	0.987515i	$0.550352\pi$
$360$		0			0
$361$	1.14715	−	1.98692i	0.0603761	−	0.104574i
$362$	−26.6683	+	14.2677i	−1.40165	+	0.749896i
$363$		0			0
$364$	0.766726	−	20.4872i	0.0401874	−	1.07382i
$365$	−4.26680	−	7.39032i	−0.223335	−	0.386827i
$366$		0			0
$367$	−0.770528	−	1.33459i	−0.0402212	−	0.0696652i	0.845214	−	0.534428i	$-0.179473\pi$
$367$	−0.770528	−	1.33459i	−0.0402212	−	0.0696652i	−0.885435	+	0.464763i	$0.846140\pi$
$368$	2.66375	−	20.4776i	0.138858	−	1.06747i
$369$		0			0
$370$	−3.14355	+	1.68182i	−0.163425	+	0.0874338i
$371$	6.82722	−	12.6069i	0.354451	−	0.654519i
$372$		0			0
$373$	−15.7744	+	27.3221i	−0.816770	+	1.41469i	0.0912800	+	0.995825i	$0.470904\pi$
$373$	−15.7744	+	27.3221i	−0.816770	+	1.41469i	−0.908050	+	0.418862i	$0.862429\pi$
$374$	1.42970	+	2.67230i	0.0739282	+	0.138182i
$375$		0			0
$376$	32.6009	+	3.17277i	1.68126	+	0.163623i
$377$		−	35.4097i		−	1.82369i
$378$		0			0
$379$		−	21.4907i		−	1.10390i	−0.833876	−	0.551951i	$-0.813883\pi$
$379$		−	21.4907i		−	1.10390i	0.833876	−	0.551951i	$-0.186117\pi$
$380$	−4.92934	−	3.28817i	−0.252870	−	0.168680i
$381$		0			0
$382$	−0.497567	+	0.266202i	−0.0254578	+	0.0136201i
$383$	−2.12781	+	3.68547i	−0.108726	+	0.188319i	−0.915254	−	0.402877i	$-0.868010\pi$
$383$	−2.12781	+	3.68547i	−0.108726	+	0.188319i	0.806529	+	0.591195i	$0.201344\pi$
$384$		0			0
$385$	−1.11090	+	0.0303021i	−0.0566168	+	0.00154434i
$386$	10.8046	+	20.1951i	0.549938	+	1.02791i
$387$		0			0
$388$	−19.3121	+	9.54223i	−0.980424	+	0.484433i
$389$	−4.66309	−	8.07672i	−0.236428	−	0.409506i	0.723259	−	0.690577i	$-0.242643\pi$
$389$	−4.66309	−	8.07672i	−0.236428	−	0.409506i	−0.959687	+	0.281072i	$0.909310\pi$
$390$		0			0
$391$	9.54621	+	16.5345i	0.482773	+	0.836187i
$392$	19.7811	+	0.840722i	0.999098	+	0.0424629i
$393$		0			0
$394$	15.6188	+	29.1936i	0.786863	+	1.47075i
$395$	1.23222	−	2.13426i	0.0619996	−	0.107386i
$396$		0			0
$397$	−6.08981	+	3.51595i	−0.305639	+	0.176461i	−0.644973	−	0.764205i	$-0.723131\pi$
$397$	−6.08981	+	3.51595i	−0.305639	+	0.176461i	0.339334	+	0.940666i	$0.389798\pi$
$398$	−17.2821	−	0.559074i	−0.866272	−	0.0280239i
$399$		0			0
$400$	−10.8738	+	14.2165i	−0.543692	+	0.710825i
$401$	2.90076	−	5.02426i	0.144857	−	0.250899i	−0.784463	−	0.620176i	$-0.787061\pi$
$401$	2.90076	−	5.02426i	0.144857	−	0.250899i	0.929320	+	0.369277i	$0.120395\pi$
$402$		0			0
$403$	−2.84759	+	1.64406i	−0.141849	+	0.0818964i
$404$	−1.23733	+	19.1041i	−0.0615595	+	0.950466i
$405$		0			0
$406$	34.1958	+	0.173322i	1.69711	+	0.00860182i
$407$	1.74531	+	1.00766i	0.0865119	+	0.0499477i
$408$		0			0
$409$		−	23.0535i		−	1.13992i	−0.821671	−	0.569961i	$-0.806958\pi$
$409$		−	23.0535i		−	1.13992i	0.821671	−	0.569961i	$-0.193042\pi$
$410$	−0.477286	−	0.892111i	−0.0235715	−	0.0440582i
$411$		0			0
$412$	−9.48078	−	19.1877i	−0.467084	−	0.945312i
$413$	−1.02574	+	0.0279792i	−0.0504736	+	0.00137677i
$414$		0			0
$415$	−4.35139	+	2.51228i	−0.213601	+	0.123323i
$416$	3.52843	−	21.6312i	0.172995	−	1.06056i
$417$		0			0
$418$	−0.108300	+	3.34775i	−0.00529711	+	0.163744i
$419$	7.60902	+	13.1792i	0.371725	+	0.643847i	0.989831	−	0.142248i	$-0.0454331\pi$
$419$	7.60902	+	13.1792i	0.371725	+	0.643847i	−0.618106	+	0.786095i	$0.712100\pi$
$420$		0			0
$421$	−3.47824	+	6.02448i	−0.169519	+	0.293615i	−0.938251	−	0.345956i	$-0.887555\pi$
$421$	−3.47824	+	6.02448i	−0.169519	+	0.293615i	0.768732	+	0.639571i	$0.220888\pi$
$422$	−16.3823	−	10.1784i	−0.797478	−	0.495477i
$423$		0			0
$424$	8.91305	−	12.4686i	0.432856	−	0.605530i
$425$		−	16.5482i		−	0.802704i
$426$		0			0
$427$	0.0643068	+	2.35755i	0.00311203	+	0.114090i
$428$	0.205369	−	3.17085i	0.00992688	−	0.153269i
$429$		0			0
$430$	6.84086	−	11.0105i	0.329896	−	0.530972i
$431$	27.3227	+	15.7748i	1.31609	+	0.759845i	0.983097	−	0.183084i	$-0.0586081\pi$
$431$	27.3227	+	15.7748i	1.31609	+	0.759845i	0.332993	+	0.942929i	$0.391941\pi$
$432$		0			0
$433$		−	9.13238i		−	0.438874i	−0.975627	−	0.219437i	$-0.929578\pi$
$433$		−	9.13238i		−	0.438874i	0.975627	−	0.219437i	$-0.0704221\pi$
$434$	−1.57376	−	2.75802i	−0.0755429	−	0.132389i
$435$		0			0
$436$	−7.76798	−	15.7213i	−0.372019	−	0.752913i
$437$			21.1006i			1.00938i
$438$		0			0
$439$	22.1491			1.05712			0.528560	−	0.848896i	$-0.322732\pi$
$439$	22.1491			1.05712			0.528560	+	0.848896i	$0.322732\pi$
$440$	−1.18246	−	0.115079i	−0.0563716	−	0.00548617i
$441$		0			0
$442$	9.55919	+	17.8674i	0.454684	+	0.849864i
$443$		−	12.4878i		−	0.593313i	−0.954984	−	0.296656i	$-0.904128\pi$
$443$		−	12.4878i		−	0.593313i	0.954984	−	0.296656i	$-0.0958716\pi$
$444$		0			0
$445$	1.98922			0.0942983
$446$	23.6785	+	0.765999i	1.12121	+	0.0362711i
$447$		0			0
$448$	20.8724	+	3.51335i	0.986127	+	0.165990i
$449$	−23.2620			−1.09780			−0.548901	−	0.835888i	$-0.684953\pi$
$449$	−23.2620			−1.09780			−0.548901	+	0.835888i	$0.684953\pi$
$450$		0			0
$451$	−0.285964	+	0.495304i	−0.0134655	+	0.0233229i
$452$	13.2136	+	0.855813i	0.621514	+	0.0402541i
$453$		0			0
$454$	−16.3956	+	26.3890i	−0.769484	+	1.23850i
$455$	−7.42764	+	0.202604i	−0.348213	+	0.00949821i
$456$		0			0
$457$	−5.31974			−0.248847			−0.124423	−	0.992229i	$-0.539708\pi$
$457$	−5.31974			−0.248847			−0.124423	+	0.992229i	$0.539708\pi$
$458$	0.173524	−	5.36397i	0.00810826	−	0.250642i
$459$		0			0
$460$	−7.46861	−	0.483725i	−0.348226	−	0.0225538i
$461$	−7.88185	−	4.55059i	−0.367094	−	0.211942i	0.305094	−	0.952322i	$-0.401312\pi$
$461$	−7.88185	−	4.55059i	−0.367094	−	0.211942i	−0.672188	+	0.740380i	$0.734645\pi$
$462$		0			0
$463$	0.490550	−	0.283219i	0.0227978	−	0.0131623i	−0.488558	−	0.872532i	$-0.662477\pi$
$463$	0.490550	−	0.283219i	0.0227978	−	0.0131623i	0.511356	+	0.859369i	$0.329144\pi$
$464$	36.2519	+	4.71569i	1.68295	+	0.218920i
$465$		0			0
$466$	15.5222	−	24.9833i	0.719052	−	1.15733i
$467$	4.77345	+	8.26785i	0.220889	+	0.382591i	0.955078	−	0.296354i	$-0.0957709\pi$
$467$	4.77345	+	8.26785i	0.220889	+	0.382591i	−0.734189	+	0.678945i	$0.762438\pi$
$468$		0			0
$469$	−0.227871	−	8.35395i	−0.0105221	−	0.385750i
$470$	0.383839	−	11.8652i	0.0177052	−	0.547300i
$471$		0			0
$472$	−1.09182	−	0.106257i	−0.0502549	−	0.00489089i
$473$	−7.32745			−0.336917
$474$		0			0
$475$	9.14438	−	15.8385i	0.419573	−	0.726722i
$476$	−17.3017	+	9.14403i	−0.793020	+	0.419116i
$477$		0			0
$478$	−1.21266	−	0.753428i	−0.0554655	−	0.0344610i
$479$	11.9617	+	20.7183i	0.546545	+	0.946644i	0.998508	+	0.0546071i	$0.0173906\pi$
$479$	11.9617	+	20.7183i	0.546545	+	0.946644i	−0.451963	+	0.892037i	$0.649276\pi$
$480$		0			0
$481$	11.6694	+	6.73732i	0.532078	+	0.307195i
$482$	−31.2675	−	19.4267i	−1.42420	−	0.884861i
$483$		0			0
$484$	−9.44809	−	19.1216i	−0.429459	−	0.869163i
$485$	3.90355	+	6.76115i	0.177251	+	0.307008i
$486$		0			0
$487$	13.0207	+	7.51748i	0.590022	+	0.340650i	0.765106	−	0.643904i	$-0.222686\pi$
$487$	13.0207	+	7.51748i	0.590022	+	0.340650i	−0.175084	+	0.984553i	$0.556020\pi$
$488$	−0.244220	+	2.50941i	−0.0110553	+	0.113596i
$489$		0			0
$490$	−0.159302	−	7.17400i	−0.00719652	−	0.324088i
$491$	13.4272	−	7.75218i	0.605960	−	0.349851i	−0.165423	−	0.986223i	$-0.552899\pi$
$491$	13.4272	−	7.75218i	0.605960	−	0.349851i	0.771383	+	0.636372i	$0.219566\pi$
$492$		0			0
$493$	−29.2714	+	16.8998i	−1.31832	+	0.761130i
$494$	−0.724106	+	22.3835i	−0.0325791	+	1.00708i
$495$		0			0
$496$	−1.30393	−	3.13427i	−0.0585483	−	0.140733i
$497$	−0.545753	−	20.0078i	−0.0244804	−	0.897474i
$498$		0			0
$499$	0.376114	+	0.217150i	0.0168372	+	0.00972096i	0.508395	−	0.861124i	$-0.330239\pi$
$499$	0.376114	+	0.217150i	0.0168372	+	0.00972096i	−0.491558	+	0.870845i	$0.663572\pi$
$500$	11.4266	+	7.62222i	0.511011	+	0.340876i
$501$		0			0
$502$	−12.2887	−	22.9692i	−0.548472	−	1.02517i
$503$	16.6525			0.742496			0.371248	−	0.928534i	$-0.378930\pi$
$503$	16.6525			0.742496			0.371248	+	0.928534i	$0.378930\pi$
$504$		0			0
$505$	6.93844			0.308756
$506$	1.99577	+	3.73036i	0.0887229	+	0.165835i
$507$		0			0
$508$	15.3192	+	10.2188i	0.679679	+	0.453388i
$509$	9.83654	+	5.67913i	0.435997	+	0.251723i	0.701898	−	0.712277i	$-0.252336\pi$
$509$	9.83654	+	5.67913i	0.435997	+	0.251723i	−0.265901	+	0.964000i	$0.585670\pi$
$510$		0			0
$511$	−27.3893	−	14.8326i	−1.21163	−	0.656154i
$512$	21.6758	+	6.49309i	0.957944	+	0.286957i
$513$		0			0
$514$	−0.574573	+	17.7612i	−0.0253433	+	0.783411i
$515$	−6.71761	+	3.87841i	−0.296013	+	0.170903i
$516$		0			0
$517$	−5.81159	+	3.35532i	−0.255593	+	0.147567i
$518$	−6.56348	+	11.2364i	−0.288383	+	0.493698i
$519$		0			0
$520$	−7.90608	−	0.769433i	−0.346705	−	0.0337418i
$521$	30.1497	+	17.4069i	1.32088	+	0.762612i	0.983869	−	0.178888i	$-0.0572499\pi$
$521$	30.1497	+	17.4069i	1.32088	+	0.762612i	0.337013	+	0.941500i	$0.390583\pi$
$522$		0			0
$523$	−11.7500	−	20.3516i	−0.513791	−	0.889912i	−0.999872	−	0.0159982i	$-0.994907\pi$
$523$	−11.7500	−	20.3516i	−0.513791	−	0.889912i	0.486081	−	0.873914i	$-0.338426\pi$
$524$	14.2983	+	28.9377i	0.624624	+	1.26415i
$525$		0			0
$526$	11.9397	+	7.41816i	0.520594	+	0.323447i
$527$	2.71812	+	1.56930i	0.118403	+	0.0683600i
$528$		0			0
$529$	1.82588	+	3.16252i	0.0793862	+	0.137501i
$530$	−4.71836	−	2.93154i	−0.204952	−	0.127338i
$531$		0			0
$532$	−21.6126	−	0.808844i	−0.937026	−	0.0350678i
$533$	−1.91199	+	3.31167i	−0.0828175	+	0.143444i
$534$		0			0
$535$	−1.15162			−0.0497890
$536$	0.865390	−	8.89206i	0.0373791	−	0.384079i
$537$		0			0
$538$	−0.327434	+	10.1216i	−0.0141167	+	0.436374i
$539$	−3.39708	+	2.21664i	−0.146323	+	0.0954773i
$540$		0			0
$541$	3.83947	+	6.65016i	0.165072	+	0.285913i	0.936681	−	0.350184i	$-0.113881\pi$
$541$	3.83947	+	6.65016i	0.165072	+	0.285913i	−0.771609	+	0.636097i	$0.780548\pi$
$542$	−4.64405	+	7.47468i	−0.199479	+	0.321065i
$543$		0			0
$544$	−19.5654	+	7.40706i	−0.838859	+	0.317575i
$545$	−5.50400	+	3.17774i	−0.235766	+	0.136119i
$546$		0			0
$547$	−3.76933	−	2.17622i	−0.161165	−	0.0930485i	0.417248	−	0.908792i	$-0.362994\pi$
$547$	−3.76933	−	2.17622i	−0.161165	−	0.0930485i	−0.578413	+	0.815744i	$0.696328\pi$
$548$	4.58545	+	0.296989i	0.195881	+	0.0126868i
$549$		0			0
$550$	0.118562	−	3.66499i	0.00505551	−	0.156276i
$551$	−37.3549			−1.59137
$552$		0			0
$553$	−0.245271	−	8.99186i	−0.0104300	−	0.382373i
$554$	−19.5795	+	31.5136i	−0.831855	+	1.33888i
$555$		0			0
$556$	−13.5910	−	0.880257i	−0.576386	−	0.0373312i
$557$	−16.1918	+	28.0450i	−0.686068	+	1.18830i	0.287032	+	0.957921i	$0.407331\pi$
$557$	−16.1918	+	28.0450i	−0.686068	+	1.18830i	−0.973100	+	0.230384i	$0.926002\pi$
$558$		0			0
$559$	−48.9923			−2.07215
$560$	0.781754	−	7.63129i	0.0330351	−	0.322481i
$561$		0			0
$562$	−12.1301	−	0.392408i	−0.511676	−	0.0165527i
$563$	15.0531			0.634411			0.317205	−	0.948357i	$-0.397256\pi$
$563$	15.0531			0.634411			0.317205	+	0.948357i	$0.397256\pi$
$564$		0			0
$565$		−	4.79904i		−	0.201897i
$566$	19.1562	+	35.8054i	0.805194	+	1.50501i
$567$		0			0
$568$	2.07262	−	21.2966i	0.0869652	−	0.893586i
$569$	31.4512			1.31850			0.659252	−	0.751922i	$-0.270873\pi$
$569$	31.4512			1.31850			0.659252	+	0.751922i	$0.270873\pi$
$570$		0			0
$571$			0.980970i			0.0410523i	0.999789	+	0.0205262i	$0.00653414\pi$
$571$			0.980970i			0.0410523i	−0.999789	+	0.0205262i	$0.993466\pi$
$572$	1.98910	+	4.02565i	0.0831684	+	0.168321i
$573$		0			0
$574$	−3.18878	−	1.86266i	−0.133097	−	0.0777457i
$575$		−	23.1001i		−	0.963343i
$576$		0			0
$577$	−6.71704	−	3.87808i	−0.279634	−	0.161447i	0.353624	−	0.935388i	$-0.384949\pi$
$577$	−6.71704	−	3.87808i	−0.279634	−	0.161447i	−0.633258	+	0.773941i	$0.718283\pi$
$578$	−2.47996	+	3.99154i	−0.103153	+	0.166026i
$579$		0			0
$580$	0.856347	−	13.2218i	0.0355579	−	0.549006i
$581$	−8.73334	+	16.1267i	−0.362320	+	0.669049i
$582$		0			0
$583$			3.14006i			0.130048i
$584$	−27.0889	−	19.3641i	−1.12095	−	0.801294i
$585$		0			0
$586$	−28.5650	−	17.7476i	−1.18001	−	0.733145i
$587$	9.68642	−	16.7774i	0.399801	−	0.692476i	−0.593900	−	0.804539i	$-0.702412\pi$
$587$	9.68642	−	16.7774i	0.399801	−	0.692476i	0.993701	+	0.112063i	$0.0357458\pi$
$588$		0			0
$589$	1.73437	+	3.00402i	0.0714635	+	0.123778i
$590$	−0.0128549	+	0.397370i	−0.000529228	+	0.0163595i
$591$		0			0
$592$	−8.45164	+	11.0497i	−0.347360	+	0.454140i
$593$	−8.54276	+	4.93217i	−0.350809	+	0.202540i	−0.665042	−	0.746806i	$-0.731586\pi$
$593$	−8.54276	+	4.93217i	−0.350809	+	0.202540i	0.314232	+	0.949346i	$0.398253\pi$
$594$		0			0
$595$	3.71244	+	6.04335i	0.152195	+	0.247753i
$596$	−10.5344	−	21.3201i	−0.431506	−	0.873305i
$597$		0			0
$598$	13.3440	+	24.9417i	0.545677	+	1.01994i
$599$		−	30.9174i		−	1.26325i	−0.775274	−	0.631625i	$-0.782388\pi$
$599$		−	30.9174i		−	1.26325i	0.775274	−	0.631625i	$-0.217612\pi$
$600$		0			0
$601$	13.3705	+	7.71949i	0.545396	+	0.314885i	0.747263	−	0.664528i	$-0.231368\pi$
$601$	13.3705	+	7.71949i	0.545396	+	0.314885i	−0.201867	+	0.979413i	$0.564701\pi$
$602$	0.239805	−	47.3128i	0.00977374	−	1.92833i
$603$		0			0
$604$	1.77631	−	27.4258i	0.0722770	−	1.11594i
$605$	−6.69445	+	3.86504i	−0.272168	+	0.157136i
$606$		0			0
$607$	4.56330	−	7.90387i	0.185219	−	0.320808i	−0.758432	−	0.651753i	$-0.774034\pi$
$607$	4.56330	−	7.90387i	0.185219	−	0.320808i	0.943650	+	0.330945i	$0.107367\pi$
$608$	−22.8195	−	3.72225i	−0.925451	−	0.150957i
$609$		0			0
$610$	0.913306	+	0.0295454i	0.0369787	+	0.00119626i
$611$	−38.8570	+	22.4341i	−1.57199	+	0.907587i
$612$		0			0
$613$	−10.5959	+	18.3526i	−0.427963	+	0.741253i	−0.996692	−	0.0812716i	$-0.974102\pi$
$613$	−10.5959	+	18.3526i	−0.427963	+	0.741253i	0.568729	+	0.822525i	$0.307435\pi$
$614$	−8.30309	−	15.5196i	−0.335086	−	0.626319i
$615$		0			0
$616$	−3.89738	+	1.90120i	−0.157030	+	0.0766017i
$617$	1.36130	+	2.35785i	0.0548040	+	0.0949233i	0.892126	−	0.451787i	$-0.149213\pi$
$617$	1.36130	+	2.35785i	0.0548040	+	0.0949233i	−0.837322	+	0.546710i	$0.815880\pi$
$618$		0			0
$619$	9.77457	+	16.9300i	0.392873	+	0.680476i	0.992827	−	0.119558i	$-0.0381478\pi$
$619$	9.77457	+	16.9300i	0.392873	+	0.680476i	−0.599954	+	0.800034i	$0.704815\pi$
$620$	−1.10304	+	0.545017i	−0.0442990	+	0.0218884i
$621$		0			0
$622$	18.5124	+	34.6022i	0.742281	+	1.38742i
$623$	6.18661	−	3.80044i	0.247861	−	0.152262i
$624$		0			0
$625$	−8.69734	+	15.0642i	−0.347894	+	0.602570i
$626$	−31.2303	+	16.7084i	−1.24821	+	0.667803i
$627$		0			0
$628$	−20.4995	−	13.6745i	−0.818020	−	0.545670i
$629$		−	12.8620i		−	0.512840i
$630$		0			0
$631$			47.6971i			1.89879i	0.314080	+	0.949396i	$0.398304\pi$
$631$			47.6971i			1.89879i	−0.314080	+	0.949396i	$0.601696\pi$
$632$	0.931471	−	9.57106i	0.0370519	−	0.380716i
$633$		0			0
$634$	12.7879	+	23.9023i	0.507872	+	0.949280i
$635$	3.33704	−	5.77992i	0.132426	−	0.229369i
$636$		0			0
$637$	−22.7133	+	14.8207i	−0.899935	+	0.587218i
$638$	−6.60393	+	3.53316i	−0.261452	+	0.139879i
$639$		0			0
$640$	1.84063	−	7.99166i	0.0727571	−	0.315898i
$641$	−3.91165	−	6.77517i	−0.154501	−	0.267603i	0.778376	−	0.627798i	$-0.216044\pi$
$641$	−3.91165	−	6.77517i	−0.154501	−	0.267603i	−0.932877	+	0.360195i	$0.882710\pi$
$642$		0			0
$643$	20.8295	+	36.0777i	0.821435	+	1.42277i	0.904614	+	0.426232i	$0.140159\pi$
$643$	20.8295	+	36.0777i	0.821435	+	1.42277i	−0.0831794	+	0.996535i	$0.526507\pi$
$644$	−24.1520	+	12.7645i	−0.951721	+	0.502990i
$645$		0			0
$646$	18.8489	−	10.0843i	0.741599	−	0.396761i
$647$	9.38911	−	16.2624i	0.369124	−	0.639342i	−0.620305	−	0.784361i	$-0.712991\pi$
$647$	9.38911	−	16.2624i	0.369124	−	0.639342i	0.989429	+	0.145019i	$0.0463244\pi$
$648$		0			0
$649$	0.194632	−	0.112371i	0.00763999	−	0.00441095i
$650$	0.792723	−	24.5046i	0.0310931	−	0.961149i
$651$		0			0
$652$	−0.740659	+	11.4356i	−0.0290064	+	0.447853i
$653$	0.450392	−	0.780101i	0.0176252	−	0.0305277i	−0.857078	−	0.515186i	$-0.827723\pi$
$653$	0.450392	−	0.780101i	0.0176252	−	0.0305277i	0.874703	+	0.484658i	$0.161056\pi$
$654$		0			0
$655$	10.1311	−	5.84917i	0.395854	−	0.228546i
$656$	−3.13580	−	2.39850i	−0.122433	−	0.0936456i
$657$		0			0
$658$	−21.4749	−	37.6348i	−0.837177	−	1.46716i
$659$	11.5880	+	6.69033i	0.451404	+	0.260618i	0.708423	−	0.705788i	$-0.249407\pi$
$659$	11.5880	+	6.69033i	0.451404	+	0.260618i	−0.257019	+	0.966406i	$0.582740\pi$
$660$		0			0
$661$			1.69061i			0.0657571i	0.999459	+	0.0328785i	$0.0104674\pi$
$661$			1.69061i			0.0657571i	−0.999459	+	0.0328785i	$0.989533\pi$
$662$	−9.67179	+	5.17449i	−0.375905	+	0.201112i
$663$		0			0
$664$	−11.4015	+	15.9498i	−0.442465	+	0.618973i
$665$	0.213733	+	7.83566i	0.00828822	+	0.303854i
$666$		0			0
$667$	−40.8609	+	23.5911i	−1.58214	+	0.913450i
$668$	16.7440	+	1.08447i	0.647845	+	0.0419595i
$669$		0			0
$670$	−3.23629	−	0.104694i	−0.125029	−	0.00404468i
$671$	−0.258271	−	0.447339i	−0.00997045	−	0.0172693i
$672$		0			0
$673$	12.6580	−	21.9243i	0.487930	−	0.845119i	−0.511974	−	0.859001i	$-0.671085\pi$
$673$	12.6580	−	21.9243i	0.487930	−	0.845119i	0.999904	+	0.0138817i	$0.00441883\pi$
$674$	−25.1597	+	40.4949i	−0.969115	+	1.55981i
$675$		0			0
$676$	1.78185	+	3.60621i	0.0685327	+	0.138700i
$677$			32.9850i			1.26772i	0.773449	+	0.633859i	$0.218530\pi$
$677$			32.9850i			1.26772i	−0.773449	+	0.633859i	$0.781470\pi$
$678$		0			0
$679$	25.0576	+	13.5698i	0.961621	+	0.520761i
$680$	3.13725	+	6.90277i	0.120308	+	0.264709i
$681$		0			0
$682$	0.590749	+	0.367035i	0.0226209	+	0.0140545i
$683$	5.67586	+	3.27696i	0.217181	+	0.125389i	0.604644	−	0.796496i	$-0.293315\pi$
$683$	5.67586	+	3.27696i	0.217181	+	0.125389i	−0.387463	+	0.921885i	$0.626649\pi$
$684$		0			0
$685$		−	1.66539i		−	0.0636314i
$686$	−14.2015	−	22.0072i	−0.542215	−	0.840240i
$687$		0			0
$688$	6.52455	−	50.1576i	0.248746	−	1.91224i
$689$			20.9948i			0.799840i
$690$		0			0
$691$	−0.410768			−0.0156264			−0.00781318	−	0.999969i	$-0.502487\pi$
$691$	−0.410768			−0.0156264			−0.00781318	+	0.999969i	$0.502487\pi$
$692$	−29.7299	−	19.8317i	−1.13016	−	0.753889i
$693$		0			0
$694$	−1.07483	+	0.575041i	−0.0407999	+	0.0218283i
$695$			4.93611i			0.187237i
$696$		0			0
$697$	3.65011			0.138258
$698$	1.57099	−	48.5623i	0.0594628	−	1.83811i
$699$		0			0
$700$	23.6607	+	0.885491i	0.894289	+	0.0334684i
$701$	−17.5496			−0.662841			−0.331420	−	0.943483i	$-0.607528\pi$
$701$	−17.5496			−0.662841			−0.331420	+	0.943483i	$0.607528\pi$
$702$		0			0
$703$	7.10742	−	12.3104i	0.268061	−	0.464296i
$704$	−4.38630	+	1.50029i	−0.165315	+	0.0565444i
$705$		0			0
$706$	−31.8318	−	19.7772i	−1.19801	−	0.744326i
$707$	21.5790	−	13.2560i	0.811560	−	0.498543i
$708$		0			0
$709$	−16.8431			−0.632557			−0.316279	−	0.948666i	$-0.602433\pi$
$709$	−16.8431			−0.632557			−0.316279	+	0.948666i	$0.602433\pi$
$710$	−7.75097	−	0.250744i	−0.290889	−	0.00941024i
$711$		0			0
$712$	7.06640	−	3.21162i	0.264825	−	0.120361i
$713$	3.79431	+	2.19065i	0.142098	+	0.0820404i
$714$		0			0
$715$	1.40938	−	0.813704i	0.0527077	−	0.0304308i
$716$	45.0872	−	22.2779i	1.68499	−	0.832563i
$717$		0			0
$718$	28.6862	+	17.8228i	1.07056	+	0.665143i
$719$	−15.7871	−	27.3440i	−0.588759	−	1.01976i	−0.994395	−	0.105726i	$-0.966283\pi$
$719$	−15.7871	−	27.3440i	−0.588759	−	1.01976i	0.405636	−	0.914035i	$-0.367050\pi$
$720$		0			0
$721$	−13.4824	+	24.8962i	−0.502111	+	0.927182i
$722$	−3.24292	−	0.104908i	−0.120689	−	0.00390429i
$723$		0			0
$724$	35.5828	+	23.7359i	1.32243	+	0.882139i
$725$	40.8946			1.51879
$726$		0			0
$727$	14.8377	−	25.6997i	0.550301	−	0.953150i	−0.447951	−	0.894058i	$-0.647846\pi$
$727$	14.8377	−	25.6997i	0.550301	−	0.953150i	0.998253	−	0.0590918i	$-0.0188205\pi$
$728$	−26.0584	+	12.7117i	−0.965788	+	0.471127i
$729$		0			0
$730$	−6.36895	+	10.2509i	−0.235725	+	0.379404i
$731$	23.3823	+	40.4994i	0.864827	+	1.49792i
$732$		0			0
$733$	−13.7406	−	7.93312i	−0.507519	−	0.293016i	0.224294	−	0.974522i	$-0.427992\pi$
$733$	−13.7406	−	7.93312i	−0.507519	−	0.293016i	−0.731813	+	0.681505i	$0.761326\pi$
$734$	−1.15015	+	1.85118i	−0.0424527	+	0.0683283i
$735$		0			0
$736$	−27.3120	+	10.3398i	−1.00673	+	0.381129i
$737$	0.915182	+	1.58514i	0.0337112	+	0.0583894i
$738$		0			0
$739$	−0.242332	−	0.139910i	−0.00891432	−	0.00514668i	0.495536	−	0.868587i	$-0.334972\pi$
$739$	−0.242332	−	0.139910i	−0.00891432	−	0.00514668i	−0.504451	+	0.863441i	$0.668305\pi$
$740$	4.19436	+	2.79790i	0.154188	+	0.102853i
$741$		0			0
$742$	−20.2751	−	0.102765i	−0.744323	−	0.00377261i
$743$	8.28791	−	4.78503i	0.304054	−	0.175546i	−0.340209	−	0.940350i	$-0.610498\pi$
$743$	8.28791	−	4.78503i	0.304054	−	0.175546i	0.644263	+	0.764804i	$0.277164\pi$
$744$		0			0
$745$	−7.46415	+	4.30943i	−0.273465	+	0.157885i
$746$	44.5936	+	1.44260i	1.63269	+	0.0528173i
$747$		0			0
$748$	2.37847	−	3.56559i	0.0869654	−	0.130371i
$749$	−3.58162	+	2.20019i	−0.130870	+	0.0803933i
$750$		0			0
$751$	25.5319	+	14.7409i	0.931674	+	0.537902i	0.887341	−	0.461115i	$-0.152550\pi$
$751$	25.5319	+	14.7409i	0.931674	+	0.537902i	0.0443332	+	0.999017i	$0.485884\pi$
$752$	−17.7929	−	42.7689i	−0.648841	−	1.55962i
$753$		0			0
$754$	−44.1548	+	23.6231i	−1.60802	+	0.860304i
$755$	−9.96081			−0.362511
$756$		0			0
$757$	27.0636			0.983643			0.491821	−	0.870696i	$-0.336331\pi$
$757$	27.0636			0.983643			0.491821	+	0.870696i	$0.336331\pi$
$758$	−26.7982	+	14.3372i	−0.973354	+	0.520752i
$759$		0			0
$760$	−0.811699	+	8.34038i	−0.0294434	+	0.302537i
$761$	−30.1287	−	17.3948i	−1.09216	−	0.630561i	−0.158012	−	0.987437i	$-0.550509\pi$
$761$	−30.1287	−	17.3948i	−1.09216	−	0.630561i	−0.934152	+	0.356876i	$0.883842\pi$
$762$		0			0
$763$	−11.0467	+	20.3984i	−0.399916	+	0.738473i
$764$	0.663892	+	0.442857i	0.0240188	+	0.0160220i
$765$		0			0
$766$	6.01520	+	0.194591i	0.217338	+	0.00703087i
$767$	1.30134	−	0.751328i	0.0469886	−	0.0271289i
$768$		0			0
$769$	40.8103	−	23.5618i	1.47166	−	0.849661i	0.472164	−	0.881511i	$-0.343473\pi$
$769$	40.8103	−	23.5618i	1.47166	−	0.849661i	0.999493	+	0.0318496i	$0.0101398\pi$
$770$	0.778910	+	1.36504i	0.0280700	+	0.0491928i
$771$		0			0
$772$	17.9746	−	26.9459i	0.646919	−	0.969803i
$773$	−34.1954	−	19.7427i	−1.22992	−	0.710096i	−0.262909	−	0.964821i	$-0.584682\pi$
$773$	−34.1954	−	19.7427i	−1.22992	−	0.710096i	−0.967014	+	0.254724i	$0.918015\pi$
$774$		0			0
$775$	−1.89872	−	3.28868i	−0.0682041	−	0.118133i
$776$	24.7827	+	17.7156i	0.889647	+	0.635953i
$777$		0			0
$778$	−6.96048	+	11.2030i	−0.249545	+	0.401647i
$779$	3.49358	+	2.01702i	0.125171	+	0.0722673i
$780$		0			0
$781$	2.19187	+	3.79643i	0.0784314	+	0.135847i
$782$	14.2494	−	22.9346i	0.509557	−	0.820140i
$783$		0			0
$784$	−12.1484	−	25.2273i	−0.433871	−	0.900975i
$785$	−4.46549	+	7.73445i	−0.159380	+	0.276055i
$786$		0			0
$787$	−31.0153			−1.10558			−0.552788	−	0.833322i	$-0.686436\pi$
$787$	−31.0153			−1.10558			−0.552788	+	0.833322i	$0.686436\pi$
$788$	25.9836	−	38.9522i	0.925626	−	1.38762i
$789$		0			0
$790$	−3.48342	−	0.112688i	−0.123934	−	0.00400927i
$791$	−9.16864	−	14.9253i	−0.325999	−	0.530683i
$792$		0			0
$793$	−1.72684	−	2.99097i	−0.0613217	−	0.106212i
$794$	8.44702	+	5.24817i	0.299773	+	0.186251i
$795$		0			0
$796$	10.8324	+	21.9232i	0.383943	+	0.777045i
$797$	−8.30567	+	4.79528i	−0.294202	+	0.169857i	−0.639835	−	0.768512i	$-0.720997\pi$
$797$	−8.30567	+	4.79528i	−0.294202	+	0.169857i	0.345633	+	0.938370i	$0.387664\pi$
$798$		0			0
$799$	37.0903	+	21.4141i	1.31216	+	0.757575i
$800$	24.9818	+	4.07498i	0.883242	+	0.144072i
$801$		0			0
$802$	−8.20029	−	0.265279i	−0.289562	−	0.00936733i
$803$	6.82198			0.240742
$804$		0			0
$805$	5.18232	+	8.43612i	0.182653	+	0.297334i
$806$	3.94982	+	2.45404i	0.139127	+	0.0864399i
$807$		0			0
$808$	24.6477	−	11.2022i	0.867103	−	0.394091i
$809$	7.65189	−	13.2535i	0.269026	−	0.465967i	−0.699584	−	0.714550i	$-0.746632\pi$
$809$	7.65189	−	13.2535i	0.269026	−	0.465967i	0.968611	+	0.248583i	$0.0799648\pi$
$810$		0			0
$811$	7.91368			0.277887			0.138943	−	0.990300i	$-0.455629\pi$
$811$	7.91368			0.277887			0.138943	+	0.990300i	$0.455629\pi$
$812$	−22.5972	−	42.7567i	−0.793006	−	1.50047i
$813$		0			0
$814$	0.0921519	−	2.84859i	0.00322992	−	0.0998431i
$815$	4.15331			0.145484
$816$		0			0
$817$			51.6836i			1.80818i
$818$	−28.7470	+	15.3799i	−1.00511	+	0.537744i
$819$		0			0
$820$	−0.794018	+	1.19032i	−0.0277283	+	0.0415678i
$821$	−25.0583			−0.874541			−0.437271	−	0.899330i	$-0.644055\pi$
$821$	−25.0583			−0.874541			−0.437271	+	0.899330i	$0.644055\pi$
$822$		0			0
$823$		−	34.5185i		−	1.20324i	−0.798783	−	0.601619i	$-0.794522\pi$
$823$		−	34.5185i		−	1.20324i	0.798783	−	0.601619i	$-0.205478\pi$
$824$	−17.6015	+	24.6231i	−0.613177	+	0.857786i
$825$		0			0
$826$	0.719202	+	1.26040i	0.0250242	+	0.0438551i
$827$		−	22.6614i		−	0.788016i	−0.919107	−	0.394008i	$-0.871088\pi$
$827$		−	22.6614i		−	0.788016i	0.919107	−	0.394008i	$-0.128912\pi$
$828$		0			0
$829$	7.67197	+	4.42941i	0.266458	+	0.153840i	0.627277	−	0.778796i	$-0.284169\pi$
$829$	7.67197	+	4.42941i	0.266458	+	0.153840i	−0.360819	+	0.932636i	$0.617503\pi$
$830$	6.03570	+	3.75001i	0.209502	+	0.130165i
$831$		0			0
$832$	−29.3273	+	10.0311i	−1.01674	+	0.347767i
$833$	23.0918	+	11.7025i	0.800084	+	0.405468i
$834$		0			0
$835$		−	6.08127i		−	0.210451i
$836$	4.24679	−	2.09836i	0.146878	−	0.0725734i
$837$		0			0
$838$	11.3578	−	18.2805i	0.392348	−	0.631491i
$839$	−15.4881	+	26.8261i	−0.534707	+	0.926140i	0.464470	+	0.885589i	$0.346245\pi$
$839$	−15.4881	+	26.8261i	−0.534707	+	0.926140i	−0.999177	+	0.0405511i	$0.987089\pi$
$840$		0			0
$841$	−27.2637	−	47.2222i	−0.940129	−	1.62835i
$842$	9.83279	+	0.318091i	0.338860	+	0.0109621i
$843$		0			0
$844$	−1.76289	+	27.2186i	−0.0606811	+	0.936903i
$845$	1.26253	−	0.728922i	0.0434324	−	0.0250757i
$846$		0			0
$847$	−13.4359	+	24.8104i	−0.461664	+	0.852494i
$848$	−21.4942	−	2.79599i	−0.738114	−	0.0960147i
$849$		0			0
$850$	−20.6350	+	11.0399i	−0.707775	+	0.378665i
$851$		−	17.9545i		−	0.615471i
$852$		0			0
$853$	−7.55084	−	4.35948i	−0.258536	−	0.149266i	0.365131	−	0.930956i	$-0.381024\pi$
$853$	−7.55084	−	4.35948i	−0.258536	−	0.149266i	−0.623666	+	0.781691i	$0.714358\pi$
$854$	2.89688	−	1.65300i	0.0991294	−	0.0565644i
$855$		0			0
$856$	−4.09096	+	1.85931i	−0.139826	+	0.0635498i
$857$	−39.9949	+	23.0911i	−1.36620	+	0.788776i	−0.990440	−	0.137941i	$-0.955952\pi$
$857$	−39.9949	+	23.0911i	−1.36620	+	0.788776i	−0.375760	+	0.926717i	$0.622618\pi$
$858$		0			0
$859$	15.4027	−	26.6783i	0.525534	−	0.910252i	−0.474024	−	0.880512i	$-0.657199\pi$
$859$	15.4027	−	26.6783i	0.525534	−	0.910252i	0.999558	−	0.0297395i	$-0.00946777\pi$
$860$	−18.2935	−	1.18483i	−0.623803	−	0.0404023i
$861$		0			0
$862$	1.44263	−	44.5945i	0.0491362	−	1.51890i
$863$	12.2843	−	7.09233i	0.418161	−	0.241426i	−0.276129	−	0.961121i	$-0.589052\pi$
$863$	12.2843	−	7.09233i	0.418161	−	0.241426i	0.694290	+	0.719695i	$0.255718\pi$
$864$		0			0
$865$	−6.47619	+	11.2171i	−0.220197	+	0.381392i
$866$	−11.3878	+	6.09255i	−0.386973	+	0.207033i
$867$		0			0
$868$	−2.38925	+	3.80241i	−0.0810964	+	0.129062i
$869$	0.985065	+	1.70618i	0.0334160	+	0.0578783i
$870$		0			0
$871$	6.11903	+	10.5985i	0.207335	+	0.359115i
$872$	−14.4216	+	20.1747i	−0.488377	+	0.683200i
$873$		0			0
$874$	26.3118	−	14.0770i	0.890010	−	0.476162i
$875$	−0.495449	−	18.1636i	−0.0167492	−	0.614043i
$876$		0			0
$877$	17.4251	−	30.1812i	0.588405	−	1.01915i	−0.406037	−	0.913857i	$-0.633089\pi$
$877$	17.4251	−	30.1812i	0.588405	−	1.01915i	0.994442	−	0.105290i	$-0.0335772\pi$
$878$	−14.7765	−	27.6192i	−0.498683	−	0.932103i
$879$		0			0
$880$	0.645364	+	1.55126i	0.0217552	+	0.0522931i
$881$			23.0498i			0.776567i	0.921540	+	0.388283i	$0.126932\pi$
$881$			23.0498i			0.776567i	−0.921540	+	0.388283i	$0.873068\pi$
$882$		0			0
$883$			1.28738i			0.0433239i	0.999765	+	0.0216620i	$0.00689576\pi$
$883$			1.28738i			0.0433239i	−0.999765	+	0.0216620i	$0.993104\pi$
$884$	15.9027	−	23.8400i	0.534867	−	0.801825i
$885$		0			0
$886$	−15.5719	+	8.33107i	−0.523147	+	0.279888i
$887$	−2.51116	+	4.34946i	−0.0843165	+	0.146040i	−0.905100	−	0.425199i	$-0.860204\pi$
$887$	−2.51116	+	4.34946i	−0.0843165	+	0.146040i	0.820783	+	0.571240i	$0.193537\pi$
$888$		0			0
$889$	−0.664231	−	24.3513i	−0.0222776	−	0.816718i
$890$	−1.32709	−	2.48050i	−0.0444840	−	0.0831465i
$891$		0			0
$892$	−14.8416	−	30.0373i	−0.496935	−	1.00572i
$893$	23.6665	+	40.9916i	0.791969	+	1.37173i
$894$		0			0
$895$	−9.11347	−	15.7850i	−0.304630	−	0.527634i
$896$	−9.54372	−	28.3711i	−0.318833	−	0.947811i
$897$		0			0
$898$	15.5189	+	29.0069i	0.517874	+	0.967974i
$899$	−3.87815	+	6.71714i	−0.129343	+	0.224029i
$900$		0			0
$901$	17.3554	−	10.0201i	0.578191	−	0.333819i
$902$	0.808405	+	0.0261519i	0.0269169	+	0.000870762i
$903$		0			0
$904$	−7.74810	−	17.0478i	−0.257698	−	0.567003i
$905$	7.75114	−	13.4254i	0.257657	−	0.446274i
$906$		0			0
$907$	−23.9555	+	13.8307i	−0.795430	+	0.459242i	−0.841871	−	0.539680i	$-0.818545\pi$
$907$	−23.9555	+	13.8307i	−0.795430	+	0.459242i	0.0464409	+	0.998921i	$0.485212\pi$
$908$	43.8443	+	2.83970i	1.45503	+	0.0942387i
$909$		0			0
$910$	5.20790	+	9.12686i	0.172640	+	0.302552i
$911$	−9.94522	−	5.74187i	−0.329500	−	0.190237i	0.326119	−	0.945329i	$-0.394259\pi$
$911$	−9.94522	−	5.74187i	−0.329500	−	0.190237i	−0.655619	+	0.755092i	$0.727592\pi$
$912$		0			0
$913$		−	4.01675i		−	0.132935i
$914$	3.54900	+	6.63354i	0.117390	+	0.219418i
$915$		0			0
$916$	−6.80446	+	3.36213i	−0.224826	+	0.111088i
$917$	20.3333	−	37.5468i	0.671464	−	1.23991i
$918$		0			0
$919$	23.5746	−	13.6108i	0.777656	−	0.448980i	−0.0579432	−	0.998320i	$-0.518454\pi$
$919$	23.5746	−	13.6108i	0.777656	−	0.448980i	0.835599	+	0.549340i	$0.185121\pi$
$920$	4.37940	+	9.63582i	0.144384	+	0.317684i
$921$		0			0
$922$	−0.416159	+	12.8643i	−0.0137055	+	0.423662i
$923$	14.6551	+	25.3835i	0.482380	+	0.835507i
$924$		0			0
$925$	−7.78093	+	13.4770i	−0.255835	+	0.443120i
$926$	−0.680430	−	0.422754i	−0.0223603	−	0.0138926i
$927$		0			0
$928$	−18.3047	−	48.3510i	−0.600881	−	1.58720i
$929$		−	28.0193i		−	0.919284i	−0.888104	−	0.459642i	$-0.847978\pi$
$929$		−	28.0193i		−	0.919284i	0.888104	−	0.459642i	$-0.152022\pi$
$930$		0			0
$931$	15.6349	+	23.9610i	0.512412	+	0.785291i
$932$	−41.5087	−	2.68843i	−1.35966	−	0.0880623i
$933$		0			0
$934$	7.12520	−	11.4681i	0.233144	−	0.375248i
$935$	−1.34529	−	0.776706i	−0.0439958	−	0.0254010i
$936$		0			0
$937$		−	7.31723i		−	0.239043i	−0.992832	−	0.119522i	$-0.961864\pi$
$937$		−	7.31723i		−	0.239043i	0.992832	−	0.119522i	$-0.0381361\pi$
$938$	−10.2651	+	5.85738i	−0.335167	+	0.191250i
$939$		0			0
$940$	−15.0516	+	7.43708i	−0.490928	+	0.242571i
$941$		−	17.3706i		−	0.566266i	−0.959081	−	0.283133i	$-0.908626\pi$
$941$		−	17.3706i		−	0.566266i	0.959081	−	0.283133i	$-0.0913738\pi$
$942$		0			0
$943$	5.09532			0.165926
$944$	0.595892	+	1.43235i	0.0193946	+	0.0466190i
$945$		0			0
$946$	4.88842	+	9.13710i	0.158936	+	0.297073i
$947$		−	39.3196i		−	1.27772i	−0.769324	−	0.638858i	$-0.779407\pi$
$947$		−	39.3196i		−	1.27772i	0.769324	−	0.638858i	$-0.220593\pi$
$948$		0			0
$949$	45.6126			1.48065
$950$	−25.8507	−	0.836269i	−0.838707	−	0.0271321i
$951$		0			0
$952$	22.9449	+	15.4743i	0.743648	+	0.501524i
$953$	33.5157			1.08568			0.542840	−	0.839836i	$-0.317349\pi$
$953$	33.5157			1.08568			0.542840	+	0.839836i	$0.317349\pi$
$954$		0			0
$955$	0.144618	−	0.250486i	0.00467973	−	0.00810553i
$956$	−0.130493	+	2.01478i	−0.00422044	+	0.0651627i
$957$		0			0
$958$	17.8550	−	28.7378i	0.576867	−	0.928478i
$959$	−3.18176	−	5.17947i	−0.102744	−	0.167254i
$960$		0			0
$961$	−30.2798			−0.976766
$962$	0.616140	−	19.0461i	0.0198651	−	0.614070i
$963$		0			0
$964$	−3.36467	+	51.9499i	−0.108369	+	1.67319i
$965$	−10.1667	−	5.86972i	−0.327276	−	0.188953i
$966$		0			0
$967$	−17.2860	+	9.98006i	−0.555879	+	0.320937i	−0.751490	−	0.659745i	$-0.770664\pi$
$967$	−17.2860	+	9.98006i	−0.555879	+	0.320937i	0.195611	+	0.980682i	$0.437331\pi$
$968$	−17.5408	+	24.5382i	−0.563783	+	0.788687i
$969$		0			0
$970$	5.82673	−	9.37822i	0.187085	−	0.301117i
$971$	26.7791	+	46.3827i	0.859381	+	1.48849i	0.872520	+	0.488578i	$0.162484\pi$
$971$	26.7791	+	46.3827i	0.859381	+	1.48849i	−0.0131389	+	0.999914i	$0.504182\pi$
$972$		0			0
$973$	9.43052	+	15.3516i	0.302329	+	0.492150i
$974$	0.687486	−	21.2515i	0.0220285	−	0.680943i
$975$		0			0
$976$	3.29208	−	1.36959i	0.105377	−	0.0438394i
$977$	−46.1501			−1.47647			−0.738236	−	0.674543i	$-0.764341\pi$
$977$	−46.1501			−1.47647			−0.738236	+	0.674543i	$0.764341\pi$
$978$		0			0
$979$	−0.795117	+	1.37718i	−0.0254121	+	0.0440150i
$980$	−8.83947	+	4.98469i	−0.282367	+	0.159230i
$981$		0			0
$982$	−18.6245	−	11.5715i	−0.594331	−	0.369261i
$983$	14.9059	+	25.8179i	0.475426	+	0.823462i	0.999604	−	0.0281471i	$-0.00896069\pi$
$983$	14.9059	+	25.8179i	0.475426	+	0.823462i	−0.524178	+	0.851609i	$0.675627\pi$
$984$		0			0
$985$	−14.6966	−	8.48511i	−0.468274	−	0.270358i
$986$	40.6016	+	25.2259i	1.29302	+	0.803358i
$987$		0			0
$988$	28.3946	−	14.0299i	0.903352	−	0.446352i
$989$	32.6402	+	56.5345i	1.03790	+	1.79769i
$990$		0			0
$991$	34.7638	+	20.0709i	1.10431	+	0.637574i	0.937350	−	0.348390i	$-0.113271\pi$
$991$	34.7638	+	20.0709i	1.10431	+	0.637574i	0.166960	+	0.985964i	$0.446605\pi$
$992$	−3.03843	+	3.71695i	−0.0964702	+	0.118013i
$993$		0			0
$994$	−24.5850	+	14.0285i	−0.779789	+	0.444957i
$995$	7.67527	−	4.43132i	0.243323	−	0.140482i
$996$		0			0
$997$	−39.4866	+	22.7976i	−1.25055	+	0.722007i	−0.971219	−	0.238187i	$-0.923447\pi$
$997$	−39.4866	+	22.7976i	−1.25055	+	0.722007i	−0.279333	+	0.960194i	$0.590113\pi$
$998$	0.0198587	−	0.613871i	0.000628616	−	0.0194317i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bj.b.451.15		84
3.2	odd	2		252.2.bj.b.115.28	yes	84
4.3	odd	2	inner	756.2.bj.b.451.16		84
7.5	odd	6		756.2.n.b.19.13		84
9.4	even	3		756.2.n.b.199.42		84
9.5	odd	6		252.2.n.b.31.1	✓	84
12.11	even	2		252.2.bj.b.115.27	yes	84
21.5	even	6		252.2.n.b.187.30	yes	84
28.19	even	6		756.2.n.b.19.42		84
36.23	even	6		252.2.n.b.31.30	yes	84
36.31	odd	6		756.2.n.b.199.13		84
63.5	even	6		252.2.bj.b.103.28	yes	84
63.40	odd	6	inner	756.2.bj.b.523.15		84
84.47	odd	6		252.2.n.b.187.1	yes	84
252.103	even	6	inner	756.2.bj.b.523.16		84
252.131	odd	6		252.2.bj.b.103.27	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.1	✓	84	9.5	odd	6
252.2.n.b.31.30	yes	84	36.23	even	6
252.2.n.b.187.1	yes	84	84.47	odd	6
252.2.n.b.187.30	yes	84	21.5	even	6
252.2.bj.b.103.27	yes	84	252.131	odd	6
252.2.bj.b.103.28	yes	84	63.5	even	6
252.2.bj.b.115.27	yes	84	12.11	even	2
252.2.bj.b.115.28	yes	84	3.2	odd	2
756.2.n.b.19.13		84	7.5	odd	6
756.2.n.b.19.42		84	28.19	even	6
756.2.n.b.199.13		84	36.31	odd	6
756.2.n.b.199.42		84	9.4	even	3
756.2.bj.b.451.15		84	1.1	even	1	trivial
756.2.bj.b.451.16		84	4.3	odd	2	inner
756.2.bj.b.523.15		84	63.40	odd	6	inner
756.2.bj.b.523.16		84	252.103	even	6	inner

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.bj (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.667137 - 1.24697i) q^{2} +(-1.10986 + 1.66380i) q^{4} +(0.627749 + 0.362431i) q^{5} +(2.64477 - 0.0721413i) q^{7} +(2.81513 + 0.273973i) q^{8} +O(q^{10})\)	\(q+(-0.667137 - 1.24697i) q^{2} +(-1.10986 + 1.66380i) q^{4} +(0.627749 + 0.362431i) q^{5} +(2.64477 - 0.0721413i) q^{7} +(2.81513 + 0.273973i) q^{8} +(0.0331449 - 1.02457i) q^{10} +(-0.501838 + 0.289736i) q^{11} +(-3.35535 + 1.93721i) q^{13} +(-1.85438 - 3.24981i) q^{14} +(-1.53644 - 3.69315i) q^{16} +(3.20279 + 1.84913i) q^{17} +(2.04363 + 3.53967i) q^{19} +(-1.29972 + 0.642201i) q^{20} +(0.696087 + 0.432482i) q^{22} +(4.47089 + 2.58127i) q^{23} +(-2.23729 - 3.87510i) q^{25} +(4.65413 + 2.89163i) q^{26} +(-2.81528 + 4.48042i) q^{28} +(-4.56967 + 7.91490i) q^{29} +0.848671 q^{31} +(-3.58022 + 4.37973i) q^{32} +(0.169106 - 5.22740i) q^{34} +(1.68640 + 0.913260i) q^{35} +(-1.73892 - 3.01190i) q^{37} +(3.05047 - 4.90979i) q^{38} +(1.66790 + 1.19228i) q^{40} +(0.854749 - 0.493490i) q^{41} +(10.9509 + 6.32252i) q^{43} +(0.0749053 - 1.15652i) q^{44} +(0.236061 - 7.29711i) q^{46} +11.5806 q^{47} +(6.98959 - 0.381594i) q^{49} +(-3.33954 + 5.37505i) q^{50} +(0.500827 - 7.73266i) q^{52} +(2.70941 - 4.69284i) q^{53} -0.420038 q^{55} +(7.46512 + 0.521507i) q^{56} +(12.9182 + 0.417904i) q^{58} -0.387839 q^{59} +0.891401i q^{61} +(-0.566180 - 1.05827i) q^{62} +(7.84988 + 1.54254i) q^{64} -2.80843 q^{65} -3.15867i q^{67} +(-6.63122 + 3.27652i) q^{68} +(0.0137466 - 2.71215i) q^{70} -7.56506i q^{71} +(-10.1955 - 5.88637i) q^{73} +(-2.59564 + 4.17773i) q^{74} +(-8.15743 - 0.528338i) q^{76} +(-1.30634 + 0.802489i) q^{77} -3.39987i q^{79} +(0.374013 - 2.87523i) q^{80} +(-1.18560 - 0.736619i) q^{82} +(-3.46587 + 6.00306i) q^{83} +(1.34037 + 2.32158i) q^{85} +(0.578205 - 17.8734i) q^{86} +(-1.49212 + 0.678155i) q^{88} +(2.37662 - 1.37214i) q^{89} +(-8.73438 + 5.36554i) q^{91} +(-9.25674 + 4.57381i) q^{92} +(-7.72586 - 14.4406i) q^{94} +2.96270i q^{95} +(9.32750 + 5.38523i) q^{97} +(-5.13885 - 8.46122i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37} - 33 q^{38} + 6 q^{40} - 6 q^{41} + 13 q^{44} + 10 q^{46} - 28 q^{49} + 17 q^{50} - 27 q^{52} + 2 q^{53} - 58 q^{56} - 13 q^{58} - 8 q^{64} + 100 q^{65} + 18 q^{68} - 19 q^{70} + 30 q^{73} + 23 q^{74} + 2 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} + 9 q^{86} + q^{88} + 102 q^{89} - 28 q^{92} + 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

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