LMFDB - Embedded newform 756.2.bj.b.451.16

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			451.16
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.667137 + 1.24697i) q^{2} +(-1.10986 - 1.66380i) q^{4} +(0.627749 + 0.362431i) q^{5} +(-2.64477 + 0.0721413i) q^{7} +(2.81513 - 0.273973i) q^{8} +O(q^{10})$	\(q+(-0.667137 + 1.24697i) q^{2} +(-1.10986 - 1.66380i) q^{4} +(0.627749 + 0.362431i) q^{5} +(-2.64477 + 0.0721413i) q^{7} +(2.81513 - 0.273973i) q^{8} +(-0.870735 + 0.540991i) q^{10} +(0.501838 - 0.289736i) q^{11} +(-3.35535 + 1.93721i) q^{13} +(1.67447 - 3.34607i) q^{14} +(-1.53644 + 3.69315i) q^{16} +(3.20279 + 1.84913i) q^{17} +(-2.04363 - 3.53967i) q^{19} +(-0.0936991 - 1.44669i) q^{20} +(0.0264969 + 0.819070i) q^{22} +(-4.47089 - 2.58127i) q^{23} +(-2.23729 - 3.87510i) q^{25} +(-0.177162 - 5.47641i) q^{26} +(3.05534 + 4.32029i) q^{28} +(-4.56967 + 7.91490i) q^{29} -0.848671 q^{31} +(-3.58022 - 4.37973i) q^{32} +(-4.44251 + 2.76015i) q^{34} +(-1.68640 - 0.913260i) q^{35} +(-1.73892 - 3.01190i) q^{37} +(5.77724 - 0.186894i) q^{38} +(1.86649 + 0.848304i) q^{40} +(0.854749 - 0.493490i) q^{41} +(-10.9509 - 6.32252i) q^{43} +(-1.03903 - 0.513391i) q^{44} +(6.20145 - 3.85299i) q^{46} -11.5806 q^{47} +(6.98959 - 0.381594i) q^{49} +(6.32470 - 0.204604i) q^{50} +(6.94709 + 3.43260i) q^{52} +(2.70941 - 4.69284i) q^{53} +0.420038 q^{55} +(-7.42559 + 0.927681i) q^{56} +(-6.82102 - 10.9786i) q^{58} +0.387839 q^{59} +0.891401i q^{61} +(0.566180 - 1.05827i) q^{62} +(7.84988 - 1.54254i) q^{64} -2.80843 q^{65} +3.15867i q^{67} +(-0.478055 - 7.38106i) q^{68} +(2.26386 - 1.49361i) q^{70} +7.56506i q^{71} +(-10.1955 - 5.88637i) q^{73} +(4.91584 - 0.159027i) q^{74} +(-3.62116 + 7.32871i) q^{76} +(-1.30634 + 0.802489i) q^{77} +3.39987i q^{79} +(-2.30301 + 1.76152i) q^{80} +(0.0451305 + 1.39507i) q^{82} +(3.46587 - 6.00306i) q^{83} +(1.34037 + 2.32158i) q^{85} +(15.1897 - 9.43746i) q^{86} +(1.33336 - 0.953134i) q^{88} +(2.37662 - 1.37214i) q^{89} +(8.73438 - 5.36554i) q^{91} +(0.667333 + 10.3035i) q^{92} +(7.72586 - 14.4406i) q^{94} -2.96270i q^{95} +(9.32750 + 5.38523i) q^{97} +(-4.18718 + 8.97037i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$10$	−0.870735	+	0.540991i	−0.275351	+	0.171077i
$11$	0.501838	−	0.289736i	0.151310	−	0.0873588i	−0.422434	−	0.906394i	$-0.638824\pi$
$11$	0.501838	−	0.289736i	0.151310	−	0.0873588i	0.573743	+	0.819035i	$0.305491\pi$
$12$		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	$0.513884\pi$
$14$	1.67447	−	3.34607i	0.447520	−	0.894274i
$15$		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	0.530525	−	0.847670i	$-0.321995\pi$
$19$	−2.04363	−	3.53967i	−0.468841	−	0.812057i	−0.999366	+	0.0356130i	$0.988662\pi$
$20$	−0.0936991	−	1.44669i	−0.0209517	−	0.323491i
$21$		0			0
$22$	0.0264969	+	0.819070i	0.00564915	+	0.174626i
$23$	−4.47089	−	2.58127i	−0.932244	−	0.538231i	−0.0447236	−	0.998999i	$-0.514241\pi$
$23$	−4.47089	−	2.58127i	−0.932244	−	0.538231i	−0.887521	+	0.460768i	$0.847574\pi$
$24$		0			0
$25$	−2.23729	−	3.87510i	−0.447457	−	0.775019i
$26$	−0.177162	−	5.47641i	−0.0347442	−	1.07401i
$27$		0			0
$28$	3.05534	+	4.32029i	0.577405	+	0.816458i
$29$	−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	$-0.524283\pi$
$31$	−0.848671			−0.152426			−0.0762129	+	0.997092i	$0.524283\pi$
$32$	−3.58022	−	4.37973i	−0.632899	−	0.774234i
$33$		0			0
$34$	−4.44251	+	2.76015i	−0.761884	+	0.473362i
$35$	−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	$0.925618\pi$
$38$	5.77724	−	0.186894i	0.937192	−	0.0303181i
$39$		0			0
$40$	1.86649	+	0.848304i	0.295118	+	0.134129i
$41$	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	$-0.918793\pi$
$43$	−10.9509	−	6.32252i	−1.67000	−	0.964175i	−0.702367	−	0.711815i	$-0.747874\pi$
$44$	−1.03903	−	0.513391i	−0.156640	−	0.0773966i
$45$		0			0
$46$	6.20145	−	3.85299i	0.914354	−	0.568092i
$47$	−11.5806			−1.68921			−0.844603	−	0.535394i	$-0.820163\pi$
$47$	−11.5806			−1.68921			−0.844603	+	0.535394i	$0.820163\pi$
$48$		0			0
$49$	6.98959	−	0.381594i	0.998513	−	0.0545134i
$50$	6.32470	−	0.204604i	0.894447	−	0.0289353i
$51$		0			0
$52$	6.94709	+	3.43260i	0.963388	+	0.476016i
$53$	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
$56$	−7.42559	+	0.927681i	−0.992286	+	0.123967i
$57$		0			0
$58$	−6.82102	−	10.9786i	−0.895644	−	1.44155i
$59$	0.387839			0.0504924			0.0252462	−	0.999681i	$-0.491963\pi$
$59$	0.387839			0.0504924			0.0252462	+	0.999681i	$0.491963\pi$
$60$		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	$0.0618044\pi$
$67$			3.15867i			0.385893i	−0.981209	+	0.192947i	$0.938196\pi$
$68$	−0.478055	−	7.38106i	−0.0579726	−	0.895085i
$69$		0			0
$70$	2.26386	−	1.49361i	0.270583	−	0.178521i
$71$			7.56506i			0.897807i	0.893580	+	0.448904i	$0.148185\pi$
$71$			7.56506i			0.897807i	−0.893580	+	0.448904i	$0.851815\pi$
$72$		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	$0.908593\pi$
$74$	4.91584	−	0.159027i	0.571454	−	0.0184865i
$75$		0			0
$76$	−3.62116	+	7.32871i	−0.415376	+	0.840661i
$77$	−1.30634	+	0.802489i	−0.148872	+	0.0914521i
$78$		0			0
$79$			3.39987i			0.382515i	0.981540	+	0.191257i	$0.0612565\pi$
$79$			3.39987i			0.382515i	−0.981540	+	0.191257i	$0.938743\pi$
$80$	−2.30301	+	1.76152i	−0.257485	+	0.196944i
$81$		0			0
$82$	0.0451305	+	1.39507i	0.00498383	+	0.154060i
$83$	3.46587	−	6.00306i	0.380428	−	0.658921i	−0.610695	−	0.791866i	$-0.709110\pi$
$83$	3.46587	−	6.00306i	0.380428	−	0.658921i	0.991123	+	0.132945i	$0.0424433\pi$
$84$		0			0
$85$	1.34037	+	2.32158i	0.145383	+	0.251811i
$86$	15.1897	−	9.43746i	1.63795	−	1.01767i
$87$		0			0
$88$	1.33336	−	0.953134i	0.142136	−	0.101604i
$89$	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
$92$	0.667333	+	10.3035i	0.0695743	+	1.07421i
$93$		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	$0.482517\pi$
$98$	−4.18718	+	8.97037i	−0.422969	+	0.906144i
$99$		0			0
$100$	−3.96431	+	8.02319i	−0.396431	+	0.802319i
$101$	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	$-0.656573\pi$
$103$	5.35055	−	9.26743i	0.527206	−	0.913147i	0.999497	−	0.0317044i	$-0.0100935\pi$
$104$	−8.91500	+	6.37278i	−0.874188	+	0.624903i
$105$		0			0
$106$	4.04427	+	6.50932i	0.392814	+	0.632241i
$107$	1.37590	−	0.794374i	0.133013	−	0.0767950i	−0.432017	−	0.901865i	$-0.642198\pi$
$107$	1.37590	−	0.794374i	0.133013	−	0.0767950i	0.565030	+	0.825070i	$0.308865\pi$
$108$		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
$112$	3.79710	−	9.87836i	0.358792	−	0.933417i
$113$	−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
$116$	18.2405	−	1.18139i	1.69358	−	0.109690i
$117$		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	$0.133952\pi$
$127$			9.20736i			0.817021i	−0.912754	+	0.408511i	$0.866048\pi$
$128$	−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	$0.415730\pi$
$131$	−8.06936	+	13.9765i	−0.705023	+	1.22114i	−0.966683	+	0.255976i	$0.917603\pi$
$132$		0			0
$133$	5.66029	+	9.21418i	0.490809	+	0.798971i
$134$	−3.93876	−	2.10727i	−0.340257	−	0.182040i
$135$		0			0
$136$	9.52287	+	4.32806i	0.816580	+	0.371128i
$137$	−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	0.684726	−	0.728801i	$-0.259922\pi$
$139$	−3.40486	−	5.89740i	−0.288797	−	0.500211i	−0.973523	+	0.228590i	$0.926589\pi$
$140$	0.352179	+	3.81941i	0.0297645	+	0.322799i
$141$		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
$146$	14.1419	−	8.78642i	1.17039	−	0.727169i
$147$		0			0
$148$	−3.08124	+	6.23598i	−0.253276	+	0.512594i
$149$	−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	0.0696928	−	0.997568i	$-0.477798\pi$
$151$	11.9006	−	6.87083i	0.968459	−	0.559140i	0.898766	+	0.438428i	$0.144465\pi$
$152$	−6.72285	−	9.40473i	−0.545295	−	0.762824i
$153$		0			0
$154$	−0.129167	−	2.16434i	−0.0104086	−	0.174407i
$155$	−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
$160$	−0.660129	−	4.04695i	−0.0521878	−	0.319940i
$161$	12.0107	+	6.50432i	0.946573	+	0.512612i
$162$		0			0
$163$	−4.96214	+	2.86489i	−0.388665	+	0.224396i	−0.681582	−	0.731742i	$-0.738708\pi$
$163$	−4.96214	+	2.86489i	−0.388665	+	0.224396i	0.292917	+	0.956138i	$0.405374\pi$
$164$	−1.76971	−	0.874427i	−0.138192	−	0.0682813i
$165$		0			0
$166$	5.17341	+	8.32668i	0.401534	+	0.646276i
$167$	4.19478	+	7.26556i	0.324601	+	0.562226i	0.981432	−	0.191812i	$-0.0614365\pi$
$167$	4.19478	+	7.26556i	0.324601	+	0.562226i	−0.656830	+	0.754039i	$0.728103\pi$
$168$		0			0
$169$	1.00560	−	1.74175i	0.0773539	−	0.133981i
$170$	−3.78915	+	0.122579i	−0.290614	+	0.00940136i
$171$		0			0
$172$	1.63456	+	25.2372i	0.124634	+	1.92432i
$173$			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
$176$	0.298995	+	2.29853i	0.0225376	+	0.173258i
$177$		0			0
$178$	0.125484	+	3.87897i	0.00940546	+	0.290741i
$179$	21.7765	+	12.5727i	1.62765	+	0.939727i	0.984790	+	0.173747i	$0.0555874\pi$
$179$	21.7765	+	12.5727i	1.62765	+	0.939727i	0.642864	+	0.765980i	$0.277746\pi$
$180$		0			0
$181$		−	21.3865i		−	1.58965i	−0.606841	−	0.794824i	$-0.707563\pi$
$181$		−	21.3865i		−	1.58965i	0.606841	−	0.794824i	$-0.292437\pi$
$182$	0.863626	+	14.4710i	0.0640162	+	1.07266i
$183$		0			0
$184$	−13.2933	−	6.04169i	−0.979996	−	0.445400i
$185$		−	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	$0.00459532\pi$
$191$			0.399022i			0.0288722i	−0.999896	+	0.0144361i	$0.995405\pi$
$192$		0			0
$193$	−16.1954			−1.16577			−0.582885	−	0.812554i	$-0.698076\pi$
$193$	−16.1954			−1.16577			−0.582885	+	0.812554i	$0.698076\pi$
$194$	−12.9379	+	8.03840i	−0.928890	+	0.577123i
$195$		0			0
$196$	−8.39233	−	11.2057i	−0.599452	−	0.800411i
$197$	−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	−0.997160	−	0.0753071i	$-0.976006\pi$
$199$	−6.11333	+	10.5886i	−0.433362	+	0.750606i	0.563798	+	0.825913i	$0.309340\pi$
$200$	−7.35992	−	10.2959i	−0.520425	−	0.728032i
$201$		0			0
$202$	0.437691	+	13.5299i	0.0307959	+	0.951959i
$203$	11.5147	−	21.2627i	0.808175	−	1.49235i
$204$		0			0
$205$	0.715424			0.0499674
$206$	7.98663	+	12.8546i	0.556455	+	0.895623i
$207$		0			0
$208$	−1.99912	−	15.3682i	−0.138614	−	1.06560i
$209$	−2.05114	−	1.18423i	−0.141881	−	0.0819148i
$210$		0			0
$211$	−11.8107	+	6.81891i	−0.813082	+	0.469433i	−0.848025	−	0.529956i	$-0.822208\pi$
$211$	−11.8107	+	6.81891i	−0.813082	+	0.469433i	0.0349433	+	0.999389i	$0.488875\pi$
$212$	−10.8150	+	0.700462i	−0.742776	+	0.0481079i
$213$		0			0
$214$	0.0726469	+	2.24565i	0.00496604	+	0.153510i
$215$	−4.58296	−	7.93791i	−0.312555	−	0.541361i
$216$		0			0
$217$	2.24454	−	0.0612242i	0.152369	−	0.00415617i
$218$	−6.54376	−	10.5323i	−0.443199	−	0.713337i
$219$		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	$-0.643789\pi$
$223$	8.37599	−	14.5076i	0.560898	−	0.971504i	0.997418	−	0.0718094i	$-0.0228773\pi$
$224$	9.78481	+	11.3251i	0.653775	+	0.756689i
$225$		0			0
$226$	9.35809	−	0.302734i	0.622491	−	0.0201376i
$227$	10.9841	+	19.0249i	0.729037	+	1.26273i	0.957291	+	0.289128i	$0.0933652\pi$
$227$	10.9841	+	19.0249i	0.729037	+	1.26273i	−0.228253	+	0.973602i	$0.573301\pi$
$228$		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	$0.626650\pi$
$230$	5.28940	−	0.171112i	0.348773	−	0.0112828i
$231$		0			0
$232$	−10.6957	+	23.5334i	−0.702209	+	1.54504i
$233$	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
$238$	11.5503	−	7.62045i	0.748694	−	0.493960i
$239$	−0.874254	+	0.504751i	−0.0565508	+	0.0326496i	−0.528009	−	0.849239i	$-0.677061\pi$
$239$	−0.874254	+	0.504751i	−0.0565508	+	0.0326496i	0.471458	+	0.881888i	$0.343728\pi$
$240$		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	$0.0168544\pi$
$242$	−7.95909	−	12.8103i	−0.511630	−	0.823477i
$243$		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	$-0.697468\pi$
$251$	−18.4201			−1.16266			−0.581332	+	0.813666i	$0.697468\pi$
$252$		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
$262$	−12.0449	−	19.3865i	−0.744137	−	1.19770i
$263$	8.60780	−	4.96972i	0.530780	−	0.306446i	−0.210554	−	0.977582i	$-0.567527\pi$
$263$	8.60780	−	4.96972i	0.530780	−	0.306446i	0.741334	+	0.671136i	$0.234194\pi$
$264$		0			0
$265$	3.40166	−	1.96395i	0.208962	−	0.120645i
$266$	−15.2660	+	0.911067i	−0.936017	+	0.0558611i
$267$		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	0.944915	−	0.327316i	$-0.106144\pi$
$271$	3.11123	+	5.38881i	0.188994	+	0.327347i	−0.755921	+	0.654663i	$0.772811\pi$
$272$	−11.7500	+	8.98730i	−0.712450	+	0.544935i
$273$		0			0
$274$	3.24750	−	0.105057i	0.196189	−	0.00634670i
$275$	−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	$-0.455617\pi$
$278$	9.62537	−	0.311381i	0.577291	−	0.0186754i
$279$		0			0
$280$	−4.99763	−	2.10891i	−0.298666	−	0.126032i
$281$	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	$-0.174515\pi$
$283$	28.7140			1.70687			0.853435	+	0.521200i	$0.174515\pi$
$284$	12.5867	−	8.39612i	0.746885	−	0.498218i
$285$		0			0
$286$	−1.67562	−	2.69694i	−0.0990815	−	0.159473i
$287$	−2.22501	+	1.36683i	−0.131338	+	0.0806813i
$288$		0			0
$289$	−1.66142	−	2.87767i	−0.0977307	−	0.169275i
$290$	−0.302923	−	9.36393i	−0.0177882	−	0.549869i
$291$		0			0
$292$	1.52180	+	23.4962i	0.0890565	+	1.37501i
$293$	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
$296$	−5.72046	−	8.00246i	−0.332495	−	0.465133i
$297$		0			0
$298$	−8.87419	−	14.2832i	−0.514068	−	0.827402i
$299$	20.0019			1.15674
$300$		0			0
$301$	29.4188	+	15.9316i	1.69567	+	0.918281i
$302$	0.628349	+	19.4235i	0.0361574	+	1.11770i
$303$		0			0
$304$	16.2125	−	2.10893i	0.929848	−	0.120956i
$305$	−0.323072	+	0.559576i	−0.0184990	+	0.0320412i
$306$		0			0
$307$	−12.4459			−0.710323			−0.355161	−	0.934805i	$-0.615574\pi$
$307$	−12.4459			−0.710323			−0.355161	+	0.934805i	$0.615574\pi$
$308$	2.78503	+	1.28284i	0.158692	+	0.0730968i
$309$		0			0
$310$	0.738967	−	0.459124i	0.0419705	−	0.0260765i
$311$	27.7490			1.57350			0.786752	−	0.617269i	$-0.211761\pi$
$311$	27.7490			1.57350			0.786752	+	0.617269i	$0.211761\pi$
$312$		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
$320$	5.48682	+	1.87672i	0.306722	+	0.104912i
$321$		0			0
$322$	−16.1234	+	10.6376i	−0.898524	+	0.592813i
$323$		−	15.1158i		−	0.841064i
$324$		0			0
$325$	15.0138	+	8.66821i	0.832815	+	0.480826i
$326$	−0.261999	−	8.09891i	−0.0145108	−	0.448557i
$327$		0			0
$328$	2.27102	−	1.62341i	0.125396	−	0.0896380i
$329$	30.6280	−	0.835440i	1.68858	−	0.0460593i
$330$		0			0
$331$			7.75625i			0.426322i	0.977017	+	0.213161i	$0.0683759\pi$
$331$			7.75625i			0.426322i	−0.977017	+	0.213161i	$0.931624\pi$
$332$	−13.8345	+	0.896028i	−0.759265	+	0.0491759i
$333$		0			0
$334$	−11.8584	+	0.383619i	−0.648863	+	0.0209907i
$335$	−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	$-0.537004\pi$
$338$	1.50103	+	2.41594i	0.0816455	+	0.131410i
$339$		0			0
$340$	2.37503	−	4.80672i	0.128804	−	0.260681i
$341$	−0.425895	+	0.245891i	−0.0230635	+	0.0133157i
$342$		0			0
$343$	−18.4583	+	1.51347i	−0.996655	+	0.0817195i
$344$	−32.5604	−	14.7984i	−1.75554	−	0.797878i
$345$		0			0
$346$	−22.2817	−	11.9209i	−1.19787	−	0.640872i
$347$			0.861953i			0.0462721i	0.999732	+	0.0231360i	$0.00736509\pi$
$347$			0.861953i			0.0462721i	−0.999732	+	0.0231360i	$0.992635\pi$
$348$		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	$0.295232\pi$
$350$	−16.7126	+	0.997401i	−0.893325	+	0.0533133i
$351$		0			0
$352$	−3.06566	−	1.16060i	−0.163400	−	0.0618599i
$353$	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
$356$	−4.92066	−	2.43133i	−0.260795	−	0.128860i
$357$		0			0
$358$	−30.2057	+	18.7669i	−1.59642	+	0.991863i
$359$	20.6811	−	11.9402i	1.09150	−	0.630181i	0.157528	−	0.987515i	$-0.449648\pi$
$359$	20.6811	−	11.9402i	1.09150	−	0.630181i	0.933977	+	0.357334i	$0.116314\pi$
$360$		0			0
$361$	1.14715	−	1.98692i	0.0603761	−	0.104574i
$362$	26.6683	+	14.2677i	1.40165	+	0.749896i
$363$		0			0
$364$	−18.6211	−	8.57726i	−0.976009	−	0.449570i
$365$	−4.26680	−	7.39032i	−0.223335	−	0.386827i
$366$		0			0
$367$	0.770528	+	1.33459i	0.0402212	+	0.0696652i	0.885435	−	0.464763i	$-0.153860\pi$
$367$	0.770528	+	1.33459i	0.0402212	+	0.0696652i	−0.845214	+	0.534428i	$0.820527\pi$
$368$	16.4023	−	12.5457i	0.855027	−	0.653989i
$369$		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	$0.186117\pi$
$379$			21.4907i			1.10390i	−0.833876	+	0.551951i	$0.813883\pi$
$380$	−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	−0.806529	−	0.591195i	$-0.798656\pi$
$383$	2.12781	−	3.68547i	0.108726	−	0.188319i	0.915254	+	0.402877i	$0.131990\pi$
$384$		0			0
$385$	−1.11090	+	0.0303021i	−0.0566168	+	0.00154434i
$386$	10.8046	−	20.1951i	0.549938	−	1.02791i
$387$		0			0
$388$	−1.39224	−	21.4959i	−0.0706803	−	1.09129i
$389$	−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
$392$	19.5720	−	2.98919i	0.988537	−	0.150977i
$393$		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	$0.389798\pi$
$398$	−9.12520	−	14.6872i	−0.457405	−	0.736201i
$399$		0			0
$400$	17.7488	−	2.30878i	0.887438	−	0.115439i
$401$	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
$404$	−17.1633	−	8.48050i	−0.853907	−	0.421921i
$405$		0			0
$406$	18.8320	+	28.5436i	0.934618	+	1.41660i
$407$	−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
$412$	−21.3575	+	1.38327i	−1.05221	+	0.0681490i
$413$	−1.02574	+	0.0279792i	−0.0504736	+	0.00137677i
$414$		0			0
$415$	4.35139	−	2.51228i	0.213601	−	0.123323i
$416$	20.4974	+	7.75989i	1.00497	+	0.380460i
$417$		0			0
$418$	2.84509	−	1.76767i	0.139158	−	0.0864594i
$419$	−7.60902	−	13.1792i	−0.371725	−	0.643847i	0.618106	−	0.786095i	$-0.287900\pi$
$419$	−7.60902	−	13.1792i	−0.371725	−	0.643847i	−0.989831	+	0.142248i	$0.954567\pi$
$420$		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	$0.220888\pi$
$422$	−0.623601	−	19.2767i	−0.0303564	−	0.938375i
$423$		0			0
$424$	6.34163	−	13.9532i	0.307977	−	0.677629i
$425$		−	16.5482i		−	0.802704i
$426$		0			0
$427$	−0.0643068	−	2.35755i	−0.00311203	−	0.114090i
$428$	−2.84872	−	1.40757i	−0.137698	−	0.0680375i
$429$		0			0
$430$	12.9558	−	0.419119i	0.624783	−	0.0202117i
$431$	−27.3227	−	15.7748i	−1.31609	−	0.759845i	−0.332993	−	0.942929i	$-0.608059\pi$
$431$	−27.3227	−	15.7748i	−1.31609	−	0.759845i	−0.983097	+	0.183084i	$0.941392\pi$
$432$		0			0
$433$		−	9.13238i		−	0.438874i	−0.975627	−	0.219437i	$-0.929578\pi$
$433$		−	9.13238i		−	0.438874i	0.975627	−	0.219437i	$-0.0704221\pi$
$434$	−1.42107	+	2.83971i	−0.0682136	+	0.136310i
$435$		0			0
$436$	17.4990	−	1.13337i	0.838051	−	0.0542786i
$437$			21.1006i			1.00938i
$438$		0			0
$439$	−22.1491			−1.05712			−0.528560	−	0.848896i	$-0.677268\pi$
$439$	−22.1491			−1.05712			−0.528560	+	0.848896i	$0.677268\pi$
$440$	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	$0.0958716\pi$
$443$			12.4878i			0.593313i	−0.954984	+	0.296656i	$0.904128\pi$
$444$		0			0
$445$	1.98922			0.0942983
$446$	12.5026	+	20.1232i	0.592016	+	0.952860i
$447$		0			0
$448$	−20.6498	+	4.64595i	−0.975612	+	0.219500i
$449$	−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
$452$	−5.86563	+	11.8712i	−0.275896	+	0.558374i
$453$		0			0
$454$	−31.0514	+	1.00451i	−1.45731	+	0.0471440i
$455$	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	$0.539708\pi$
$458$	−4.55857	+	2.83226i	−0.213008	+	0.132343i
$459$		0			0
$460$	−3.31539	+	6.70986i	−0.154581	+	0.312849i
$461$	−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	−0.511356	−	0.859369i	$-0.670856\pi$
$463$	−0.490550	+	0.283219i	−0.0227978	+	0.0131623i	0.488558	+	0.872532i	$0.337523\pi$
$464$	−22.2099	−	29.0372i	−1.03107	−	1.34802i
$465$		0			0
$466$	−29.3972	+	0.951000i	−1.36180	+	0.0440542i
$467$	−4.77345	−	8.26785i	−0.220889	−	0.382591i	0.734189	−	0.678945i	$-0.237562\pi$
$467$	−4.77345	−	8.26785i	−0.220889	−	0.382591i	−0.955078	+	0.296354i	$0.904229\pi$
$468$		0			0
$469$	−0.227871	−	8.35395i	−0.0105221	−	0.385750i
$470$	10.0836	−	6.26501i	0.465124	−	0.288983i
$471$		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
$476$	1.79682	+	19.4867i	0.0823572	+	0.893172i
$477$		0			0
$478$	−0.0461603	−	1.42690i	−0.00211132	−	0.0652651i
$479$	−11.9617	−	20.7183i	−0.546545	−	0.946644i	−0.998508	−	0.0546071i	$-0.982609\pi$
$479$	−11.9617	−	20.7183i	−0.546545	−	0.946644i	0.451963	−	0.892037i	$-0.350724\pi$
$480$		0			0
$481$	11.6694	+	6.73732i	0.532078	+	0.307195i
$482$	1.19021	+	36.7918i	0.0542128	+	1.67582i
$483$		0			0
$484$	21.2838	−	1.37851i	0.967447	−	0.0626593i
$485$	3.90355	+	6.76115i	0.177251	+	0.307008i
$486$		0			0
$487$	−13.0207	−	7.51748i	−0.590022	−	0.340650i	0.175084	−	0.984553i	$-0.443980\pi$
$487$	−13.0207	−	7.51748i	−0.590022	−	0.340650i	−0.765106	+	0.643904i	$0.777314\pi$
$488$	0.244220	+	2.50941i	0.0110553	+	0.113596i
$489$		0			0
$490$	−5.87964	+	4.11358i	−0.265615	+	0.185832i
$491$	−13.4272	+	7.75218i	−0.605960	+	0.349851i	−0.771383	−	0.636372i	$-0.780434\pi$
$491$	−13.4272	+	7.75218i	−0.605960	+	0.349851i	0.165423	+	0.986223i	$0.447101\pi$
$492$		0			0
$493$	−29.2714	+	16.8998i	−1.31832	+	0.761130i
$494$	−19.0226	+	11.8188i	−0.855869	+	0.531755i
$495$		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	0.491558	−	0.870845i	$-0.336428\pi$
$499$	−0.376114	−	0.217150i	−0.0168372	−	0.00972096i	−0.508395	+	0.861124i	$0.669761\pi$
$500$	−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	$-0.621070\pi$
$503$	−16.6525			−0.742496			−0.371248	+	0.928534i	$0.621070\pi$
$504$		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
$514$	15.0943	−	9.37817i	0.665782	−	0.413653i
$515$	6.71761	−	3.87841i	0.296013	−	0.170903i
$516$		0			0
$517$	−5.81159	+	3.35532i	−0.255593	+	0.147567i
$518$	−12.9898	+	0.775225i	−0.570738	+	0.0340614i
$519$		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	$0.00509259\pi$
$523$	11.7500	+	20.3516i	0.513791	+	0.889912i	−0.486081	+	0.873914i	$0.661574\pi$
$524$	32.2099	−	2.08616i	1.40710	−	0.0911345i
$525$		0			0
$526$	0.454489	+	14.0491i	0.0198167	+	0.612571i
$527$	−2.71812	−	1.56930i	−0.118403	−	0.0683600i
$528$		0			0
$529$	1.82588	+	3.16252i	0.0793862	+	0.137501i
$530$	0.179607	+	5.55199i	0.00780161	+	0.241163i
$531$		0			0
$532$	9.04843	−	19.6440i	0.392299	−	0.851674i
$533$	−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
$538$	8.60185	−	5.34437i	0.370852	−	0.230412i
$539$	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	$0.780548\pi$
$542$	−8.79529	+	0.284527i	−0.377790	+	0.0122215i
$543$		0			0
$544$	−3.36799	−	20.6477i	−0.144402	−	0.885261i
$545$	−5.50400	+	3.17774i	−0.235766	+	0.136119i
$546$		0			0
$547$	3.76933	+	2.17622i	0.161165	+	0.0930485i	0.578413	−	0.815744i	$-0.303672\pi$
$547$	3.76933	+	2.17622i	0.161165	+	0.0930485i	−0.417248	+	0.908792i	$0.637006\pi$
$548$	−2.03553	+	4.11961i	−0.0869534	+	0.175981i
$549$		0			0
$550$	3.11469	−	1.93517i	0.132811	−	0.0825160i
$551$	37.3549			1.59137
$552$		0			0
$553$	−0.245271	−	8.99186i	−0.0104300	−	0.382373i
$554$	37.0813	−	1.19958i	1.57544	−	0.0509653i
$555$		0			0
$556$	−6.03316	+	12.2103i	−0.255863	+	0.517830i
$557$	−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
$560$	5.96385	−	4.82495i	0.252019	−	0.203891i
$561$		0			0
$562$	6.40487	+	10.3088i	0.270173	+	0.434848i
$563$	−15.0531			−0.634411			−0.317205	−	0.948357i	$-0.602744\pi$
$563$	−15.0531			−0.634411			−0.317205	+	0.948357i	$0.602744\pi$
$564$		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	$-0.993466\pi$
$571$		−	0.980970i		−	0.0410523i	0.999789	−	0.0205262i	$-0.00653414\pi$
$572$	4.48086	−	0.290215i	0.187354	−	0.0121345i
$573$		0			0
$574$	−0.220002	−	3.68638i	−0.00918270	−	0.153867i
$575$			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	$0.718283\pi$
$578$	4.69675	−	0.151940i	0.195359	−	0.00631986i
$579$		0			0
$580$	11.8786	+	5.86929i	0.493232	+	0.243709i
$581$	−8.73334	+	16.1267i	−0.362320	+	0.669049i
$582$		0			0
$583$		−	3.14006i		−	0.130048i
$584$	−30.3143	−	13.7776i	−1.25441	−	0.570120i
$585$		0			0
$586$	1.08734	+	33.6118i	0.0449176	+	1.38849i
$587$	−9.68642	+	16.7774i	−0.399801	+	0.692476i	−0.993701	−	0.112063i	$-0.964254\pi$
$587$	−9.68642	+	16.7774i	−0.399801	+	0.692476i	0.593900	+	0.804539i	$0.297588\pi$
$588$		0			0
$589$	1.73437	+	3.00402i	0.0714635	+	0.123778i
$590$	−0.337705	+	0.209818i	−0.0139031	+	0.00863806i
$591$		0			0
$592$	13.7951	−	1.79449i	0.566976	−	0.0737529i
$593$	−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
$596$	23.7309	−	1.53700i	0.972058	−	0.0629580i
$597$		0			0
$598$	−13.3440	+	24.9417i	−0.545677	+	1.01994i
$599$			30.9174i			1.26325i	0.775274	+	0.631625i	$0.217612\pi$
$599$			30.9174i			1.26325i	−0.775274	+	0.631625i	$0.782388\pi$
$600$		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	$0.564701\pi$
$602$	−39.4925	+	26.0557i	−1.60960	+	1.06195i
$603$		0			0
$604$	−24.6396	−	12.1746i	−1.00257	−	0.495377i
$605$	−6.69445	+	3.86504i	−0.272168	+	0.157136i
$606$		0			0
$607$	−4.56330	+	7.90387i	−0.185219	+	0.320808i	−0.943650	−	0.330945i	$-0.892633\pi$
$607$	−4.56330	+	7.90387i	−0.185219	+	0.320808i	0.758432	+	0.651753i	$0.225966\pi$
$608$	−8.18616	+	21.6234i	−0.331993	+	0.876943i
$609$		0			0
$610$	−0.482240	−	0.776174i	−0.0195253	−	0.0314264i
$611$	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
$616$	−3.45766	+	2.61701i	−0.139313	+	0.105442i
$617$	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	0.599954	−	0.800034i	$-0.295185\pi$
$619$	−9.77457	−	16.9300i	−0.392873	−	0.680476i	−0.992827	+	0.119558i	$0.961852\pi$
$620$	0.0795197	+	1.22777i	0.00319359	+	0.0493083i
$621$		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	$-0.601696\pi$
$631$		−	47.6971i		−	1.89879i	0.314080	−	0.949396i	$-0.398304\pi$
$632$	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
$640$	−6.00066	+	5.58986i	−0.237197	+	0.220958i
$641$	−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	$-0.859841\pi$
$643$	−20.8295	−	36.0777i	−0.821435	−	1.42277i	0.0831794	−	0.996535i	$-0.473493\pi$
$644$	−2.50825	−	27.2022i	−0.0988388	−	1.07192i
$645$		0			0
$646$	18.8489	+	10.0843i	0.741599	+	0.396761i
$647$	−9.38911	+	16.2624i	−0.369124	+	0.639342i	−0.989429	−	0.145019i	$-0.953676\pi$
$647$	−9.38911	+	16.2624i	−0.369124	+	0.639342i	0.620305	+	0.784361i	$0.287009\pi$
$648$		0			0
$649$	0.194632	−	0.112371i	0.00763999	−	0.00441095i
$650$	−20.8252	+	12.9388i	−0.816833	+	0.507502i
$651$		0			0
$652$	10.2739	+	5.07638i	0.402355	+	0.198806i
$653$	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
$656$	0.509259	+	3.91493i	0.0198832	+	0.152852i
$657$		0			0
$658$	−19.3913	+	38.7495i	−0.755953	+	1.51061i
$659$	−11.5880	−	6.69033i	−0.451404	−	0.260618i	0.257019	−	0.966406i	$-0.417260\pi$
$659$	−11.5880	−	6.69033i	−0.451404	−	0.260618i	−0.708423	+	0.705788i	$0.750593\pi$
$660$		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
$664$	8.11218	−	17.8489i	0.314814	−	0.692672i
$665$	0.213733	+	7.83566i	0.00828822	+	0.303854i
$666$		0			0
$667$	40.8609	−	23.5911i	1.58214	−	0.913450i
$668$	7.43283	−	15.0430i	0.287585	−	0.582030i
$669$		0			0
$670$	−1.70881	−	2.75037i	−0.0660173	−	0.106256i
$671$	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	$0.00441883\pi$
$674$	47.6495	−	1.54146i	1.83539	−	0.0593748i
$675$		0			0
$676$	−4.01399	+	0.259977i	−0.154384	+	0.00999913i
$677$			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
$680$	4.40935	+	6.16833i	0.169091	+	0.236544i
$681$		0			0
$682$	−0.0224871	−	0.695121i	−0.000861077	−	0.0266175i
$683$	−5.67586	−	3.27696i	−0.217181	−	0.125389i	0.387463	−	0.921885i	$-0.373351\pi$
$683$	−5.67586	−	3.27696i	−0.217181	−	0.125389i	−0.604644	+	0.796496i	$0.706685\pi$
$684$		0			0
$685$		−	1.66539i		−	0.0636314i
$686$	10.4270	−	24.0266i	0.398104	−	0.917340i
$687$		0			0
$688$	40.1755	−	30.7292i	1.53168	−	1.17154i
$689$			20.9948i			0.799840i
$690$		0			0
$691$	0.410768			0.0156264			0.00781318	−	0.999969i	$-0.497513\pi$
$691$	0.410768			0.0156264			0.00781318	+	0.999969i	$0.497513\pi$
$692$	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
$698$	−41.2707	+	25.6417i	−1.56212	+	0.970551i
$699$		0			0
$700$	9.90587	−	21.5055i	0.374407	−	0.812830i
$701$	−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
$704$	3.49244	−	3.04850i	0.131626	−	0.114895i
$705$		0			0
$706$	1.21169	+	37.4558i	0.0456027	+	1.40967i
$707$	−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	$0.602433\pi$
$710$	−4.09263	−	6.58716i	−0.153594	−	0.247212i
$711$		0			0
$712$	6.31454	−	4.51387i	0.236648	−	0.169165i
$713$	3.79431	+	2.19065i	0.142098	+	0.0820404i
$714$		0			0
$715$	−1.40938	+	0.813704i	−0.0527077	+	0.0304308i
$716$	−3.25041	−	50.1856i	−0.121473	−	1.87552i
$717$		0			0
$718$	1.09195	+	33.7544i	0.0407513	+	1.25970i
$719$	15.7871	+	27.3440i	0.588759	+	1.01976i	0.994395	+	0.105726i	$0.0337166\pi$
$719$	15.7871	+	27.3440i	0.588759	+	1.01976i	−0.405636	+	0.914035i	$0.632950\pi$
$720$		0			0
$721$	−13.4824	+	24.8962i	−0.502111	+	0.927182i
$722$	1.71231	+	2.75600i	0.0637258	+	0.102568i
$723$		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	$0.352154\pi$
$727$	−14.8377	+	25.6997i	−0.550301	+	0.953150i	−0.998253	+	0.0590918i	$0.981180\pi$
$728$	23.1184	−	17.4977i	0.856824	−	0.648507i
$729$		0			0
$730$	12.0620	−	0.390207i	0.446436	−	0.0144422i
$731$	−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	$0.761326\pi$
$734$	−2.17824	+	0.0704661i	−0.0804004	+	0.00260095i
$735$		0			0
$736$	4.70150	+	28.8228i	0.173300	+	1.06242i
$737$	0.915182	+	1.58514i	0.0337112	+	0.0583894i
$738$		0			0
$739$	0.242332	+	0.139910i	0.00891432	+	0.00514668i	0.504451	−	0.863441i	$-0.331695\pi$
$739$	0.242332	+	0.139910i	0.00891432	+	0.00514668i	−0.495536	+	0.868587i	$0.665028\pi$
$740$	−4.19436	+	2.79790i	−0.154188	+	0.102853i
$741$		0			0
$742$	−11.1657	−	16.9239i	−0.409907	−	0.621295i
$743$	−8.28791	+	4.78503i	−0.304054	+	0.175546i	−0.644263	−	0.764804i	$-0.722836\pi$
$743$	−8.28791	+	4.78503i	−0.304054	+	0.175546i	0.340209	+	0.940350i	$0.389502\pi$
$744$		0			0
$745$	−7.46415	+	4.30943i	−0.273465	+	0.157885i
$746$	−23.5461	−	37.8978i	−0.862084	−	1.38754i
$747$		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	−0.0443332	−	0.999017i	$-0.514116\pi$
$751$	−25.5319	−	14.7409i	−0.931674	−	0.537902i	−0.887341	+	0.461115i	$0.847450\pi$
$752$	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
$766$	3.17612	+	5.11202i	0.114758	+	0.184705i
$767$	−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	$0.0101398\pi$
$770$	0.703339	−	1.40548i	0.0253466	−	0.0506498i
$771$		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
$776$	27.7335	+	12.6046i	0.995575	+	0.452480i
$777$		0			0
$778$	13.1823	−	0.426448i	0.472609	−	0.0152889i
$779$	−3.49358	−	2.01702i	−0.125171	−	0.0722673i
$780$		0			0
$781$	2.19187	+	3.79643i	0.0784314	+	0.135847i
$782$	26.9866	−	0.873017i	0.965040	−	0.0312190i
$783$		0			0
$784$	−9.32981	+	26.3999i	−0.333208	+	0.942853i
$785$	−4.46549	+	7.73445i	−0.159380	+	0.276055i
$786$		0			0
$787$	31.0153			1.10558			0.552788	−	0.833322i	$-0.313564\pi$
$787$	31.0153			1.10558			0.552788	+	0.833322i	$0.313564\pi$
$788$	25.9836	+	38.9522i	0.925626	+	1.38762i
$789$		0			0
$790$	−1.83930	−	2.96038i	−0.0654393	−	0.105326i
$791$	9.16864	+	14.9253i	0.325999	+	0.530683i
$792$		0			0
$793$	−1.72684	−	2.99097i	−0.0613217	−	0.106212i
$794$	−0.321540	−	9.93942i	−0.0114110	−	0.352737i
$795$		0			0
$796$	24.4022	−	1.58047i	0.864913	−	0.0560184i
$797$	−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
$800$	−8.96189	+	23.6724i	−0.316851	+	0.836946i
$801$		0			0
$802$	4.32988	+	6.96902i	0.152893	+	0.246085i
$803$	−6.82198			−0.240742
$804$		0			0
$805$	5.18232	+	8.43612i	0.182653	+	0.297334i
$806$	0.150352	+	4.64767i	0.00529592	+	0.163707i
$807$		0			0
$808$	22.0252	−	15.7444i	0.774844	−	0.553888i
$809$	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	$-0.544371\pi$
$811$	−7.91368			−0.277887			−0.138943	+	0.990300i	$0.544371\pi$
$812$	−48.1565	+	4.44040i	−1.68996	+	0.155827i
$813$		0			0
$814$	2.42088	−	1.50410i	0.0848517	−	0.0527188i
$815$	−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	$0.205478\pi$
$823$			34.5185i			1.20324i	−0.798783	+	0.601619i	$0.794522\pi$
$824$	12.5235	−	27.5549i	0.436275	−	0.959920i
$825$		0			0
$826$	0.649423	−	1.29774i	0.0225963	−	0.0451540i
$827$			22.6614i			0.788016i	0.919107	+	0.394008i	$0.128912\pi$
$827$			22.6614i			0.788016i	−0.919107	+	0.394008i	$0.871088\pi$
$828$		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	$0.617503\pi$
$830$	0.229752	+	7.10207i	0.00797480	+	0.246517i
$831$		0			0
$832$	−23.3509	+	20.3827i	−0.809547	+	0.706641i
$833$	23.0918	+	11.7025i	0.800084	+	0.405468i
$834$		0			0
$835$			6.08127i			0.210451i
$836$	0.306158	+	4.72701i	0.0105887	+	0.163487i
$837$		0			0
$838$	21.5103	−	0.695858i	0.743061	−	0.0240380i
$839$	15.4881	−	26.8261i	0.534707	−	0.926140i	−0.464470	−	0.885589i	$-0.653755\pi$
$839$	15.4881	−	26.8261i	0.534707	−	0.926140i	0.999177	−	0.0405511i	$-0.0129114\pi$
$840$		0			0
$841$	−27.2637	−	47.2222i	−0.940129	−	1.62835i
$842$	−5.19187	−	8.35640i	−0.178924	−	0.287981i
$843$		0			0
$844$	24.4534	+	12.0826i	0.841722	+	0.415900i
$845$	1.26253	−	0.728922i	0.0434324	−	0.0250757i
$846$		0			0
$847$	13.4359	−	24.8104i	0.461664	−	0.852494i
$848$	13.1685	+	17.2165i	0.452208	+	0.591218i
$849$		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	$0.714358\pi$
$854$	2.98269	+	1.49262i	0.102065	+	0.0510764i
$855$		0			0
$856$	3.65569	−	2.61322i	0.124949	−	0.0893181i
$857$	−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	$0.342801\pi$
$859$	−15.4027	+	26.6783i	−0.525534	+	0.910252i	−0.999558	+	0.0297395i	$0.990532\pi$
$860$	−8.12066	+	16.4350i	−0.276912	+	0.560430i
$861$		0			0
$862$	37.8987	−	23.5466i	1.29083	−	0.802001i
$863$	−12.2843	+	7.09233i	−0.418161	+	0.241426i	−0.694290	−	0.719695i	$-0.744282\pi$
$863$	−12.2843	+	7.09233i	−0.418161	+	0.241426i	0.276129	+	0.961121i	$0.410948\pi$
$864$		0			0
$865$	−6.47619	+	11.2171i	−0.220197	+	0.381392i
$866$	11.3878	+	6.09255i	0.386973	+	0.207033i
$867$		0			0
$868$	−2.59298	−	3.66651i	−0.0880114	−	0.124449i
$869$	0.985065	+	1.70618i	0.0334160	+	0.0578783i
$870$		0			0
$871$	−6.11903	−	10.5985i	−0.207335	−	0.359115i
$872$	−10.2610	+	22.5768i	−0.347480	+	0.764547i
$873$		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	$-0.993104\pi$
$883$		−	1.28738i		−	0.0433239i	0.999765	−	0.0216620i	$-0.00689576\pi$
$884$	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	−0.820783	−	0.571240i	$-0.806463\pi$
$887$	2.51116	−	4.34946i	0.0843165	−	0.146040i	0.905100	+	0.425199i	$0.139796\pi$
$888$		0			0
$889$	−0.664231	−	24.3513i	−0.0222776	−	0.816718i
$890$	−1.32709	+	2.48050i	−0.0444840	+	0.0831465i
$891$		0			0
$892$	−33.4339	+	2.16544i	−1.11945	+	0.0725043i
$893$	23.6665	+	40.9916i	0.791969	+	1.37173i
$894$		0			0
$895$	9.11347	+	15.7850i	0.304630	+	0.527634i
$896$	7.98292	−	28.8491i	0.266691	−	0.963782i
$897$		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
$902$	0.426851	+	0.687023i	0.0142126	+	0.0228754i
$903$		0			0
$904$	−10.8898	−	15.2340i	−0.362190	−	0.506674i
$905$	7.75114	−	13.4254i	0.257657	−	0.446274i
$906$		0			0
$907$	23.9555	−	13.8307i	0.795430	−	0.459242i	−0.0464409	−	0.998921i	$-0.514788\pi$
$907$	23.9555	−	13.8307i	0.795430	−	0.459242i	0.841871	+	0.539680i	$0.181455\pi$
$908$	19.4629	−	39.3902i	0.645900	−	1.30721i
$909$		0			0
$910$	−4.70262	+	9.39719i	−0.155890	+	0.311514i
$911$	9.94522	+	5.74187i	0.329500	+	0.190237i	0.655619	−	0.755092i	$-0.272408\pi$
$911$	9.94522	+	5.74187i	0.329500	+	0.190237i	−0.326119	+	0.945329i	$0.605741\pi$
$912$		0			0
$913$		−	4.01675i		−	0.132935i
$914$	3.54900	−	6.63354i	0.117390	−	0.219418i
$915$		0			0
$916$	−0.490544	−	7.57390i	−0.0162080	−	0.250249i
$917$	20.3333	−	37.5468i	0.671464	−	1.23991i
$918$		0			0
$919$	−23.5746	+	13.6108i	−0.777656	+	0.448980i	−0.835599	−	0.549340i	$-0.814879\pi$
$919$	−23.5746	+	13.6108i	−0.777656	+	0.448980i	0.0579432	+	0.998320i	$0.481546\pi$
$920$	−6.15517	−	8.61058i	−0.202930	−	0.283882i
$921$		0			0
$922$	10.9327	−	6.79254i	0.360050	−	0.223701i
$923$	−14.6551	−	25.3835i	−0.482380	−	0.835507i
$924$		0			0
$925$	−7.78093	+	13.4770i	−0.255835	+	0.443120i
$926$	−0.0259009	−	0.800646i	−0.000851156	−	0.0263109i
$927$		0			0
$928$	51.0255	−	8.32316i	1.67499	−	0.273221i
$929$		−	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
$932$	18.4261	−	37.2918i	0.603568	−	1.22153i
$933$		0			0
$934$	13.4943	−	0.436540i	0.441547	−	0.0142840i
$935$	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	$-0.0381361\pi$
$938$	10.5691	+	5.28909i	0.345094	+	0.172695i
$939$		0			0
$940$	1.08509	+	16.7536i	0.0353918	+	0.546442i
$941$		−	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	$0.220593\pi$
$947$			39.3196i			1.27772i	−0.769324	+	0.638858i	$0.779407\pi$
$948$		0			0
$949$	45.6126			1.48065
$950$	−13.6496	−	21.9692i	−0.442851	−	0.712775i
$951$		0			0
$952$	−25.4980	−	10.7597i	−0.826396	−	0.348725i
$953$	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
$956$	1.81010	+	0.894381i	0.0585428	+	0.0289263i
$957$		0			0
$958$	33.8152	−	1.09392i	1.09252	−	0.0353430i
$959$	3.18176	+	5.17947i	0.102744	+	0.167254i
$960$		0			0
$961$	−30.2798			−0.976766
$962$	−16.1863	+	10.0566i	−0.521867	+	0.324239i
$963$		0			0
$964$	−46.6722	−	23.0610i	−1.50321	−	0.742746i
$965$	−10.1667	−	5.86972i	−0.327276	−	0.188953i
$966$		0			0
$967$	17.2860	−	9.98006i	0.555879	−	0.320937i	−0.195611	−	0.980682i	$-0.562669\pi$
$967$	17.2860	−	9.98006i	0.555879	−	0.320937i	0.751490	+	0.659745i	$0.229336\pi$
$968$	−12.4803	+	27.4599i	−0.401132	+	0.882594i
$969$		0			0
$970$	−11.0351	+	0.356987i	−0.354317	+	0.0114621i
$971$	−26.7791	−	46.3827i	−0.859381	−	1.48849i	−0.872520	−	0.488578i	$-0.837516\pi$
$971$	−26.7791	−	46.3827i	−0.859381	−	1.48849i	0.0131389	−	0.999914i	$-0.495818\pi$
$972$		0			0
$973$	9.43052	+	15.3516i	0.302329	+	0.492150i
$974$	18.0606	−	11.2211i	0.578700	−	0.359549i
$975$		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
$980$	−1.20697	−	10.0760i	−0.0385552	−	0.321867i
$981$		0			0
$982$	−0.708950	−	21.9150i	−0.0226235	−	0.699336i
$983$	−14.9059	−	25.8179i	−0.475426	−	0.823462i	0.524178	−	0.851609i	$-0.324373\pi$
$983$	−14.9059	−	25.8179i	−0.475426	−	0.823462i	−0.999604	+	0.0281471i	$0.991039\pi$
$984$		0			0
$985$	−14.6966	−	8.48511i	−0.468274	−	0.270358i
$986$	−1.54552	−	47.7750i	−0.0492193	−	1.52147i
$987$		0			0
$988$	−2.04701	−	31.6054i	−0.0651240	−	1.00550i
$989$	32.6402	+	56.5345i	1.03790	+	1.79769i
$990$		0			0
$991$	−34.7638	−	20.0709i	−1.10431	−	0.637574i	−0.166960	−	0.985964i	$-0.553395\pi$
$991$	−34.7638	−	20.0709i	−1.10431	−	0.637574i	−0.937350	+	0.348390i	$0.886729\pi$
$992$	3.03843	+	3.71695i	0.0964702	+	0.118013i
$993$		0			0
$994$	25.3132	+	12.6674i	0.802886	+	0.401787i
$995$	−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	$0.590113\pi$
$998$	0.521699	−	0.324134i	0.0165141	−	0.0102603i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.667137 + 1.24697i) q^{2} +(-1.10986 - 1.66380i) q^{4} +(0.627749 + 0.362431i) q^{5} +(-2.64477 + 0.0721413i) q^{7} +(2.81513 - 0.273973i) q^{8} +O(q^{10})\)	\(q+(-0.667137 + 1.24697i) q^{2} +(-1.10986 - 1.66380i) q^{4} +(0.627749 + 0.362431i) q^{5} +(-2.64477 + 0.0721413i) q^{7} +(2.81513 - 0.273973i) q^{8} +(-0.870735 + 0.540991i) q^{10} +(0.501838 - 0.289736i) q^{11} +(-3.35535 + 1.93721i) q^{13} +(1.67447 - 3.34607i) q^{14} +(-1.53644 + 3.69315i) q^{16} +(3.20279 + 1.84913i) q^{17} +(-2.04363 - 3.53967i) q^{19} +(-0.0936991 - 1.44669i) q^{20} +(0.0264969 + 0.819070i) q^{22} +(-4.47089 - 2.58127i) q^{23} +(-2.23729 - 3.87510i) q^{25} +(-0.177162 - 5.47641i) q^{26} +(3.05534 + 4.32029i) q^{28} +(-4.56967 + 7.91490i) q^{29} -0.848671 q^{31} +(-3.58022 - 4.37973i) q^{32} +(-4.44251 + 2.76015i) q^{34} +(-1.68640 - 0.913260i) q^{35} +(-1.73892 - 3.01190i) q^{37} +(5.77724 - 0.186894i) q^{38} +(1.86649 + 0.848304i) q^{40} +(0.854749 - 0.493490i) q^{41} +(-10.9509 - 6.32252i) q^{43} +(-1.03903 - 0.513391i) q^{44} +(6.20145 - 3.85299i) q^{46} -11.5806 q^{47} +(6.98959 - 0.381594i) q^{49} +(6.32470 - 0.204604i) q^{50} +(6.94709 + 3.43260i) q^{52} +(2.70941 - 4.69284i) q^{53} +0.420038 q^{55} +(-7.42559 + 0.927681i) q^{56} +(-6.82102 - 10.9786i) q^{58} +0.387839 q^{59} +0.891401i q^{61} +(0.566180 - 1.05827i) q^{62} +(7.84988 - 1.54254i) q^{64} -2.80843 q^{65} +3.15867i q^{67} +(-0.478055 - 7.38106i) q^{68} +(2.26386 - 1.49361i) q^{70} +7.56506i q^{71} +(-10.1955 - 5.88637i) q^{73} +(4.91584 - 0.159027i) q^{74} +(-3.62116 + 7.32871i) q^{76} +(-1.30634 + 0.802489i) q^{77} +3.39987i q^{79} +(-2.30301 + 1.76152i) q^{80} +(0.0451305 + 1.39507i) q^{82} +(3.46587 - 6.00306i) q^{83} +(1.34037 + 2.32158i) q^{85} +(15.1897 - 9.43746i) q^{86} +(1.33336 - 0.953134i) q^{88} +(2.37662 - 1.37214i) q^{89} +(8.73438 - 5.36554i) q^{91} +(0.667333 + 10.3035i) q^{92} +(7.72586 - 14.4406i) q^{94} -2.96270i q^{95} +(9.32750 + 5.38523i) q^{97} +(-4.18718 + 8.97037i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 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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