LMFDB - Embedded newform 756.2.bj.b.451.4

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			451.4
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36675 + 0.363308i) q^{2} +(1.73601 - 0.993103i) q^{4} +(-1.43430 - 0.828095i) q^{5} +(0.375983 + 2.61890i) q^{7} +(-2.01190 + 1.98803i) q^{8} +O(q^{10})$	\(q+(-1.36675 + 0.363308i) q^{2} +(1.73601 - 0.993103i) q^{4} +(-1.43430 - 0.828095i) q^{5} +(0.375983 + 2.61890i) q^{7} +(-2.01190 + 1.98803i) q^{8} +(2.26119 + 0.610706i) q^{10} +(2.34869 - 1.35602i) q^{11} +(-4.25755 + 2.45810i) q^{13} +(-1.46534 - 3.44279i) q^{14} +(2.02749 - 3.44808i) q^{16} +(2.86290 + 1.65289i) q^{17} +(-0.756379 - 1.31009i) q^{19} +(-3.31235 - 0.0131756i) q^{20} +(-2.71742 + 2.70664i) q^{22} +(-3.45097 - 1.99242i) q^{23} +(-1.12852 - 1.95465i) q^{25} +(4.92596 - 4.90641i) q^{26} +(3.25355 + 4.17306i) q^{28} +(-3.66717 + 6.35172i) q^{29} -6.31513 q^{31} +(-1.51836 + 5.44927i) q^{32} +(-4.51337 - 1.21898i) q^{34} +(1.62942 - 4.06764i) q^{35} +(4.46089 + 7.72649i) q^{37} +(1.50975 + 1.51576i) q^{38} +(4.53195 - 1.18540i) q^{40} +(-0.879545 + 0.507805i) q^{41} +(5.68989 + 3.28506i) q^{43} +(2.73070 - 4.68656i) q^{44} +(5.44047 + 1.46937i) q^{46} -1.95291 q^{47} +(-6.71727 + 1.96932i) q^{49} +(2.25254 + 2.26152i) q^{50} +(-4.95003 + 8.49548i) q^{52} +(-5.20840 + 9.02122i) q^{53} -4.49164 q^{55} +(-5.96289 - 4.52149i) q^{56} +(2.70447 - 10.0135i) q^{58} -6.50576 q^{59} +11.3099i q^{61} +(8.63121 - 2.29434i) q^{62} +(0.0954627 - 7.99943i) q^{64} +8.14215 q^{65} +4.23288i q^{67} +(6.61152 + 0.0262988i) q^{68} +(-0.749211 + 6.15144i) q^{70} -2.11040i q^{71} +(-4.56368 - 2.63484i) q^{73} +(-8.90403 - 8.93951i) q^{74} +(-2.61414 - 1.52317i) q^{76} +(4.43434 + 5.64115i) q^{77} -15.2086i q^{79} +(-5.76338 + 3.26663i) q^{80} +(1.01763 - 1.01359i) q^{82} +(-7.30362 + 12.6502i) q^{83} +(-2.73751 - 4.74150i) q^{85} +(-8.97016 - 2.42268i) q^{86} +(-2.02952 + 7.39744i) q^{88} +(-4.61689 + 2.66556i) q^{89} +(-8.03827 - 10.2259i) q^{91} +(-7.96961 - 0.0317009i) q^{92} +(2.66914 - 0.709507i) q^{94} +2.50541i q^{95} +(-4.20504 - 2.42778i) q^{97} +(8.46537 - 5.13201i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.36675	+	0.363308i	−0.966439	+	0.256897i
$2$	−1.36675	+	0.363308i	−0.966439	+	0.256897i
$3$		0			0
$3$		0			0
$4$	1.73601	−	0.993103i	0.868007	−	0.496551i
$5$	−1.43430	−	0.828095i	−0.641439	−	0.370335i	0.143729	−	0.989617i	$-0.454091\pi$
$5$	−1.43430	−	0.828095i	−0.641439	−	0.370335i	−0.785169	+	0.619282i	$0.787424\pi$
$6$		0			0
$7$	0.375983	+	2.61890i	0.142108	+	0.989851i
$7$	0.375983	+	2.61890i	0.142108	+	0.989851i
$8$	−2.01190	+	1.98803i	−0.711313	+	0.702875i
$9$		0			0
$10$	2.26119	+	0.610706i	0.715050	+	0.193122i
$11$	2.34869	−	1.35602i	0.708157	−	0.408855i	−0.102221	−	0.994762i	$-0.532595\pi$
$11$	2.34869	−	1.35602i	0.708157	−	0.408855i	0.810378	+	0.585907i	$0.199262\pi$
$12$		0			0
$13$	−4.25755	+	2.45810i	−1.18083	+	0.681753i	−0.956207	−	0.292692i	$-0.905449\pi$
$13$	−4.25755	+	2.45810i	−1.18083	+	0.681753i	−0.224625	+	0.974445i	$0.572116\pi$
$14$	−1.46534	−	3.44279i	−0.391629	−	0.920123i
$15$		0			0
$16$	2.02749	−	3.44808i	0.506874	−	0.862020i
$17$	2.86290	+	1.65289i	0.694354	+	0.400886i	0.805241	−	0.592947i	$-0.202036\pi$
$17$	2.86290	+	1.65289i	0.694354	+	0.400886i	−0.110887	+	0.993833i	$0.535369\pi$
$18$		0			0
$19$	−0.756379	−	1.31009i	−0.173525	−	0.300555i	0.766125	−	0.642692i	$-0.222182\pi$
$19$	−0.756379	−	1.31009i	−0.173525	−	0.300555i	−0.939650	+	0.342137i	$0.888849\pi$
$20$	−3.31235	−	0.0131756i	−0.740665	−	0.00294616i
$21$		0			0
$22$	−2.71742	+	2.70664i	−0.579356	+	0.577057i
$23$	−3.45097	−	1.99242i	−0.719577	−	0.415448i	0.0950202	−	0.995475i	$-0.469708\pi$
$23$	−3.45097	−	1.99242i	−0.719577	−	0.415448i	−0.814597	+	0.580028i	$0.803042\pi$
$24$		0			0
$25$	−1.12852	−	1.95465i	−0.225704	−	0.390930i
$26$	4.92596	−	4.90641i	0.966061	−	0.962226i
$27$		0			0
$28$	3.25355	+	4.17306i	0.614863	+	0.788634i
$29$	−3.66717	+	6.35172i	−0.680976	+	1.17948i	0.293708	+	0.955895i	$0.405111\pi$
$29$	−3.66717	+	6.35172i	−0.680976	+	1.17948i	−0.974683	+	0.223589i	$0.928223\pi$
$30$		0			0
$31$	−6.31513			−1.13423			−0.567116	−	0.823638i	$-0.691941\pi$
$31$	−6.31513			−1.13423			−0.567116	+	0.823638i	$0.691941\pi$
$32$	−1.51836	+	5.44927i	−0.268412	+	0.963304i
$33$		0			0
$34$	−4.51337	−	1.21898i	−0.774037	−	0.209054i
$35$	1.62942	−	4.06764i	0.275423	−	0.687557i
$36$		0			0
$37$	4.46089	+	7.72649i	0.733366	+	1.27023i	0.955436	+	0.295197i	$0.0953853\pi$
$37$	4.46089	+	7.72649i	0.733366	+	1.27023i	−0.222070	+	0.975031i	$0.571281\pi$
$38$	1.50975	+	1.51576i	0.244913	+	0.245889i
$39$		0			0
$40$	4.53195	−	1.18540i	0.716564	−	0.187428i
$41$	−0.879545	+	0.507805i	−0.137362	+	0.0793059i	−0.567106	−	0.823645i	$-0.691937\pi$
$41$	−0.879545	+	0.507805i	−0.137362	+	0.0793059i	0.429744	+	0.902951i	$0.358604\pi$
$42$		0			0
$43$	5.68989	+	3.28506i	0.867701	+	0.500967i	0.866584	−	0.499032i	$-0.166311\pi$
$43$	5.68989	+	3.28506i	0.867701	+	0.500967i	0.00111731	+	0.999999i	$0.499644\pi$
$44$	2.73070	−	4.68656i	0.411668	−	0.706525i
$45$		0			0
$46$	5.44047	+	1.46937i	0.802154	+	0.216647i
$47$	−1.95291			−0.284861			−0.142430	−	0.989805i	$-0.545492\pi$
$47$	−1.95291			−0.284861			−0.142430	+	0.989805i	$0.545492\pi$
$48$		0			0
$49$	−6.71727	+	1.96932i	−0.959611	+	0.281332i
$50$	2.25254	+	2.26152i	0.318558	+	0.319827i
$51$		0			0
$52$	−4.95003	+	8.49548i	−0.686445	+	1.17811i
$53$	−5.20840	+	9.02122i	−0.715429	+	1.23916i	0.247365	+	0.968922i	$0.420435\pi$
$53$	−5.20840	+	9.02122i	−0.715429	+	1.23916i	−0.962794	+	0.270237i	$0.912898\pi$
$54$		0			0
$55$	−4.49164			−0.605653
$56$	−5.96289	−	4.52149i	−0.796825	−	0.604210i
$57$		0			0
$58$	2.70447	−	10.0135i	0.355115	−	1.31484i
$59$	−6.50576			−0.846978			−0.423489	−	0.905901i	$-0.639195\pi$
$59$	−6.50576			−0.846978			−0.423489	+	0.905901i	$0.639195\pi$
$60$		0			0
$61$			11.3099i			1.44809i	0.689755	+	0.724043i	$0.257718\pi$
$61$			11.3099i			1.44809i	−0.689755	+	0.724043i	$0.742282\pi$
$62$	8.63121	−	2.29434i	1.09617	−	0.291381i
$63$		0			0
$64$	0.0954627	−	7.99943i	0.0119328	−	0.999929i
$65$	8.14215			1.00991
$66$		0			0
$67$			4.23288i			0.517128i	0.965994	+	0.258564i	$0.0832493\pi$
$67$			4.23288i			0.517128i	−0.965994	+	0.258564i	$0.916751\pi$
$68$	6.61152	+	0.0262988i	0.801765	+	0.00318920i
$69$		0			0
$70$	−0.749211	+	6.15144i	−0.0895478	+	0.735237i
$71$		−	2.11040i		−	0.250459i	−0.992128	−	0.125229i	$-0.960033\pi$
$71$		−	2.11040i		−	0.250459i	0.992128	−	0.125229i	$-0.0399666\pi$
$72$		0			0
$73$	−4.56368	−	2.63484i	−0.534139	−	0.308385i	0.208561	−	0.978009i	$-0.433122\pi$
$73$	−4.56368	−	2.63484i	−0.534139	−	0.308385i	−0.742700	+	0.669624i	$0.766455\pi$
$74$	−8.90403	−	8.93951i	−1.03507	−	1.03920i
$75$		0			0
$76$	−2.61414	−	1.52317i	−0.299862	−	0.174719i
$77$	4.43434	+	5.64115i	0.505340	+	0.642868i
$78$		0			0
$79$		−	15.2086i		−	1.71110i	−0.517717	−	0.855552i	$-0.673218\pi$
$79$		−	15.2086i		−	1.71110i	0.517717	−	0.855552i	$-0.326782\pi$
$80$	−5.76338	+	3.26663i	−0.644365	+	0.365221i
$81$		0			0
$82$	1.01763	−	1.01359i	0.112378	−	0.111932i
$83$	−7.30362	+	12.6502i	−0.801676	+	1.38854i	0.116836	+	0.993151i	$0.462725\pi$
$83$	−7.30362	+	12.6502i	−0.801676	+	1.38854i	−0.918512	+	0.395393i	$0.870609\pi$
$84$		0			0
$85$	−2.73751	−	4.74150i	−0.296924	−	0.514288i
$86$	−8.97016	−	2.42268i	−0.967277	−	0.261244i
$87$		0			0
$88$	−2.02952	+	7.39744i	−0.216348	+	0.788570i
$89$	−4.61689	+	2.66556i	−0.489389	+	0.282549i	−0.724321	−	0.689463i	$-0.757847\pi$
$89$	−4.61689	+	2.66556i	−0.489389	+	0.282549i	0.234932	+	0.972012i	$0.424513\pi$
$90$		0			0
$91$	−8.03827	−	10.2259i	−0.842640	−	1.07196i
$92$	−7.96961	−	0.0317009i	−0.830889	−	0.00330505i
$93$		0			0
$94$	2.66914	−	0.709507i	0.275301	−	0.0731800i
$95$			2.50541i			0.257050i
$96$		0			0
$97$	−4.20504	−	2.42778i	−0.426957	−	0.246504i	0.271092	−	0.962553i	$-0.412615\pi$
$97$	−4.20504	−	2.42778i	−0.426957	−	0.246504i	−0.698049	+	0.716050i	$0.745948\pi$
$98$	8.46537	−	5.13201i	0.855131	−	0.518411i
$99$		0			0
$100$	−3.90029	−	2.27257i	−0.390029	−	0.227257i
$101$	−2.44236	+	1.41010i	−0.243024	+	0.140310i	−0.616566	−	0.787303i	$-0.711477\pi$
$101$	−2.44236	+	1.41010i	−0.243024	+	0.140310i	0.373542	+	0.927613i	$0.378143\pi$
$102$		0			0
$103$	−0.797304	+	1.38097i	−0.0785607	+	0.136071i	−0.902629	−	0.430419i	$-0.858366\pi$
$103$	−0.797304	+	1.38097i	−0.0785607	+	0.136071i	0.824068	+	0.566490i	$0.191699\pi$
$104$	3.67898	−	13.4096i	0.360753	−	1.31492i
$105$		0			0
$106$	3.84111	−	14.2220i	0.373081	−	1.38136i
$107$	4.75730	−	2.74663i	0.459906	−	0.265527i	−0.252099	−	0.967701i	$-0.581121\pi$
$107$	4.75730	−	2.74663i	0.459906	−	0.265527i	0.712005	+	0.702175i	$0.247787\pi$
$108$		0			0
$109$	−6.81189	+	11.7985i	−0.652461	+	1.13010i	0.330063	+	0.943959i	$0.392930\pi$
$109$	−6.81189	+	11.7985i	−0.652461	+	1.13010i	−0.982524	+	0.186136i	$0.940403\pi$
$110$	6.13896	−	1.63185i	0.585326	−	0.155591i
$111$		0			0
$112$	9.79248	+	4.01339i	0.925303	+	0.379229i
$113$	0.261159	+	0.452340i	0.0245677	+	0.0425526i	0.878048	−	0.478573i	$-0.158846\pi$
$113$	0.261159	+	0.452340i	0.0245677	+	0.0425526i	−0.853480	+	0.521125i	$0.825512\pi$
$114$		0			0
$115$	3.29982	+	5.71546i	0.307710	+	0.532969i
$116$	−0.0583475	+	14.6686i	−0.00541743	+	1.36194i
$117$		0			0
$118$	8.89175	−	2.36359i	0.818552	−	0.217586i
$119$	−3.25236	+	8.11910i	−0.298144	+	0.744276i
$120$		0			0
$121$	−1.82244	+	3.15655i	−0.165676	+	0.286959i
$122$	−4.10898	−	15.4578i	−0.372010	−	1.39949i
$123$		0			0
$124$	−10.9632	+	6.27158i	−0.984521	+	0.563204i
$125$			12.0190i			1.07501i
$126$		0			0
$127$		−	8.34549i		−	0.740543i	−0.928924	−	0.370271i	$-0.879265\pi$
$127$		−	8.34549i		−	0.740543i	0.928924	−	0.370271i	$-0.120735\pi$
$128$	2.77578	+	10.9679i	0.245347	+	0.969435i
$129$		0			0
$130$	−11.1283	+	2.95811i	−0.976015	+	0.259443i
$131$	8.56896	−	14.8419i	0.748673	−	1.29674i	−0.199786	−	0.979840i	$-0.564025\pi$
$131$	8.56896	−	14.8419i	0.748673	−	1.29674i	0.948459	−	0.316900i	$-0.102642\pi$
$132$		0			0
$133$	3.14660	−	2.47345i	0.272845	−	0.214475i
$134$	−1.53784	−	5.78529i	−0.132849	−	0.499773i
$135$		0			0
$136$	−9.04586	+	2.36607i	−0.775676	+	0.202889i
$137$	−0.0749253	−	0.129774i	−0.00640130	−	0.0110874i	0.862807	−	0.505533i	$-0.168704\pi$
$137$	−0.0749253	−	0.129774i	−0.00640130	−	0.0110874i	−0.869208	+	0.494446i	$0.835371\pi$
$138$		0			0
$139$	6.06467	+	10.5043i	0.514399	+	0.890965i	0.999860	+	0.0167067i	$0.00531816\pi$
$139$	6.06467	+	10.5043i	0.514399	+	0.890965i	−0.485462	+	0.874258i	$0.661349\pi$
$140$	−1.21088	−	8.67967i	−0.102338	−	0.733566i
$141$		0			0
$142$	0.766725	+	2.88439i	0.0643422	+	0.242053i
$143$	−6.66644	+	11.5466i	−0.557476	+	0.965577i
$144$		0			0
$145$	10.5197	−	6.07352i	0.873609	−	0.504379i
$146$	7.19468	+	1.94315i	0.595436	+	0.160816i
$147$		0			0
$148$	15.4174	+	8.98318i	1.26730	+	0.738413i
$149$	8.27619	−	14.3348i	0.678012	−	1.17435i	−0.297567	−	0.954701i	$-0.596175\pi$
$149$	8.27619	−	14.3348i	0.678012	−	1.17435i	0.975579	−	0.219650i	$-0.0704916\pi$
$150$		0			0
$151$	14.7206	−	8.49894i	1.19794	−	0.691634i	0.237848	−	0.971302i	$-0.423558\pi$
$151$	14.7206	−	8.49894i	1.19794	−	0.691634i	0.960097	+	0.279669i	$0.0902246\pi$
$152$	4.12625	+	1.13206i	0.334683	+	0.0918218i
$153$		0			0
$154$	−8.11011	−	6.09901i	−0.653531	−	0.491472i
$155$	9.05781	+	5.22953i	0.727541	+	0.420046i
$156$		0			0
$157$		−	15.1129i		−	1.20614i	−0.797687	−	0.603071i	$-0.793943\pi$
$157$		−	15.1129i		−	1.20614i	0.797687	−	0.603071i	$-0.206057\pi$
$158$	5.52541	+	20.7864i	0.439578	+	1.65368i
$159$		0			0
$160$	6.69031	−	6.55855i	0.528915	−	0.518499i
$161$	3.92044	−	9.78686i	0.308974	−	0.771312i
$162$		0			0
$163$	5.13064	−	2.96218i	0.401863	−	0.232015i	−0.285425	−	0.958401i	$-0.592135\pi$
$163$	5.13064	−	2.96218i	0.401863	−	0.232015i	0.687287	+	0.726386i	$0.258801\pi$
$164$	−1.02260	+	1.75504i	−0.0798516	+	0.137045i
$165$		0			0
$166$	5.38629	−	19.9432i	0.418057	−	1.54789i
$167$	8.25628	+	14.3003i	0.638890	+	1.10659i	0.985677	+	0.168646i	$0.0539394\pi$
$167$	8.25628	+	14.3003i	0.638890	+	1.10659i	−0.346787	+	0.937944i	$0.612727\pi$
$168$		0			0
$169$	5.58448	−	9.67261i	0.429576	−	0.744047i
$170$	5.46411	+	5.48589i	0.419078	+	0.420748i
$171$		0			0
$172$	13.1401	+	0.0522679i	1.00193	+	0.00398539i
$173$		−	16.2245i		−	1.23353i	−0.787148	−	0.616764i	$-0.788443\pi$
$173$		−	16.2245i		−	1.23353i	0.787148	−	0.616764i	$-0.211557\pi$
$174$		0			0
$175$	4.69473	−	3.69039i	0.354888	−	0.278967i
$176$	0.0863005	−	10.8478i	0.00650514	−	0.817683i
$177$		0			0
$178$	5.34172	−	5.32051i	0.400379	−	0.398789i
$179$	15.1520	+	8.74799i	1.13251	+	0.653855i	0.944565	−	0.328324i	$-0.106484\pi$
$179$	15.1520	+	8.74799i	1.13251	+	0.653855i	0.187945	+	0.982180i	$0.439817\pi$
$180$		0			0
$181$		−	9.17571i		−	0.682025i	−0.940059	−	0.341013i	$-0.889230\pi$
$181$		−	9.17571i		−	0.682025i	0.940059	−	0.341013i	$-0.110770\pi$
$182$	14.7015	+	11.0559i	1.08975	+	0.819516i
$183$		0			0
$184$	10.9040	−	2.85209i	0.803852	−	0.210259i
$185$		−	14.7762i		−	1.08637i
$186$		0			0
$187$	8.96541			0.655616
$188$	−3.39028	+	1.93944i	−0.247261	+	0.141448i
$189$		0			0
$190$	−0.910237	−	3.42428i	−0.0660355	−	0.248423i
$191$			0.746176i			0.0539914i	0.999636	+	0.0269957i	$0.00859404\pi$
$191$			0.746176i			0.0539914i	−0.999636	+	0.0269957i	$0.991406\pi$
$192$		0			0
$193$	5.27175			0.379469			0.189734	−	0.981835i	$-0.439237\pi$
$193$	5.27175			0.379469			0.189734	+	0.981835i	$0.439237\pi$
$194$	6.62927	+	1.79045i	0.475954	+	0.128547i
$195$		0			0
$196$	−9.70555	+	10.0897i	−0.693254	+	0.720694i
$197$	12.9993			0.926162			0.463081	−	0.886316i	$-0.346744\pi$
$197$	12.9993			0.926162			0.463081	+	0.886316i	$0.346744\pi$
$198$		0			0
$199$	−4.92545	+	8.53113i	−0.349156	+	0.604756i	−0.986100	−	0.166154i	$-0.946865\pi$
$199$	−4.92545	+	8.53113i	−0.349156	+	0.604756i	0.636944	+	0.770910i	$0.280198\pi$
$200$	6.15637	+	1.68903i	0.435321	+	0.119432i
$201$		0			0
$202$	2.82580	−	2.81458i	0.198822	−	0.198033i
$203$	−18.0133	−	7.21581i	−1.26429	−	0.506450i
$204$		0			0
$205$	1.68204			0.117479
$206$	0.587998	−	2.17711i	0.0409678	−	0.151686i
$207$		0			0
$208$	−0.156440	+	19.6642i	−0.0108471	+	1.36346i
$209$	−3.55300	−	2.05133i	−0.245766	−	0.141893i
$210$		0			0
$211$	−20.4282	+	11.7942i	−1.40633	+	0.811946i	−0.995032	−	0.0995535i	$-0.968259\pi$
$211$	−20.4282	+	11.7942i	−1.40633	+	0.811946i	−0.411300	+	0.911500i	$0.634925\pi$
$212$	−0.0828697	+	20.8334i	−0.00569152	+	1.43085i
$213$		0			0
$214$	−5.50417	+	5.48232i	−0.376258	+	0.374764i
$215$	−5.44069	−	9.42354i	−0.371052	−	0.642680i
$216$		0			0
$217$	−2.37438	−	16.5387i	−0.161183	−	1.12272i
$218$	5.02365	−	18.6005i	0.340245	−	1.25978i
$219$		0			0
$220$	−7.79756	+	4.46066i	−0.525711	+	0.300738i
$221$	−16.2519			−1.09322
$222$		0			0
$223$	−2.37545	+	4.11440i	−0.159072	+	0.275520i	−0.934534	−	0.355873i	$-0.884183\pi$
$223$	−2.37545	+	4.11440i	−0.159072	+	0.275520i	0.775462	+	0.631394i	$0.217517\pi$
$224$	−14.8420	−	1.92761i	−0.991671	−	0.128794i
$225$		0			0
$226$	−0.521277	−	0.523355i	−0.0346749	−	0.0348131i
$227$	−13.8419	−	23.9749i	−0.918720	−	1.59127i	−0.801361	−	0.598180i	$-0.795891\pi$
$227$	−13.8419	−	23.9749i	−0.918720	−	1.59127i	−0.117359	−	0.993090i	$-0.537443\pi$
$228$		0			0
$229$	8.76512	+	5.06054i	0.579215	+	0.334410i	0.760822	−	0.648961i	$-0.224796\pi$
$229$	8.76512	+	5.06054i	0.579215	+	0.334410i	−0.181606	+	0.983371i	$0.558130\pi$
$230$	−6.58650	−	6.61276i	−0.434301	−	0.436032i
$231$		0			0
$232$	−5.24945	−	20.0694i	−0.344643	−	1.31762i
$233$	−6.75115	−	11.6933i	−0.442283	−	0.766056i	0.555576	−	0.831466i	$-0.312498\pi$
$233$	−6.75115	−	11.6933i	−0.442283	−	0.766056i	−0.997858	+	0.0654097i	$0.979165\pi$
$234$		0			0
$235$	2.80106	+	1.61719i	0.182721	+	0.105494i
$236$	−11.2941	+	6.46088i	−0.735183	+	0.420568i
$237$		0			0
$238$	1.49544	−	12.2784i	0.0969349	−	0.795890i
$239$	21.6423	−	12.4952i	1.39992	−	0.808246i	0.405540	−	0.914077i	$-0.367084\pi$
$239$	21.6423	−	12.4952i	1.39992	−	0.808246i	0.994384	+	0.105831i	$0.0337503\pi$
$240$		0			0
$241$	−9.04255	+	5.22072i	−0.582482	+	0.336296i	−0.762119	−	0.647437i	$-0.775841\pi$
$241$	−9.04255	+	5.22072i	−0.582482	+	0.336296i	0.179637	+	0.983733i	$0.442508\pi$
$242$	1.34401	−	4.97632i	0.0863966	−	0.319890i
$243$		0			0
$244$	11.2319	+	19.6342i	0.719049	+	1.25695i
$245$	11.2654	+	2.73794i	0.719719	+	0.174920i
$246$		0			0
$247$	6.44064	+	3.71851i	0.409808	+	0.236603i
$248$	12.7054	−	12.5547i	0.806794	−	0.797223i
$249$		0			0
$250$	−4.36661	−	16.4270i	−0.276168	−	1.03894i
$251$	4.59012			0.289726			0.144863	−	0.989452i	$-0.453726\pi$
$251$	4.59012			0.289726			0.144863	+	0.989452i	$0.453726\pi$
$252$		0			0
$253$	−10.8070			−0.679431
$254$	3.03198	+	11.4062i	0.190244	+	0.715689i
$255$		0			0
$256$	−7.77853	−	13.9819i	−0.486158	−	0.873871i
$257$	22.6947	+	13.1028i	1.41566	+	0.817331i	0.995914	−	0.0903116i	$-0.0287863\pi$
$257$	22.6947	+	13.1028i	1.41566	+	0.817331i	0.419745	+	0.907642i	$0.362120\pi$
$258$		0			0
$259$	−18.5577	+	14.5877i	−1.15312	+	0.906433i
$260$	14.1349	−	8.08599i	0.876609	−	0.501472i
$261$		0			0
$262$	−6.31946	+	23.3983i	−0.390418	+	1.44555i
$263$	5.13861	−	2.96678i	0.316860	−	0.182939i	−0.333132	−	0.942880i	$-0.608105\pi$
$263$	5.13861	−	2.96678i	0.316860	−	0.182939i	0.649992	+	0.759941i	$0.274772\pi$
$264$		0			0
$265$	14.9408	−	8.62610i	0.917809	−	0.529897i
$266$	−3.40200	+	4.52378i	−0.208590	+	0.277371i
$267$		0			0
$268$	4.20368	+	7.34834i	0.256781	+	0.448871i
$269$	1.49698	+	0.864283i	0.0912726	+	0.0526963i	0.544942	−	0.838474i	$-0.316552\pi$
$269$	1.49698	+	0.864283i	0.0912726	+	0.0526963i	−0.453669	+	0.891170i	$0.649885\pi$
$270$		0			0
$271$	3.37150	+	5.83961i	0.204804	+	0.354731i	0.950070	−	0.312036i	$-0.101011\pi$
$271$	3.37150	+	5.83961i	0.204804	+	0.354731i	−0.745266	+	0.666767i	$0.767678\pi$
$272$	11.5038	−	6.52026i	0.697521	−	0.395349i
$273$		0			0
$274$	0.149552	+	0.150148i	0.00903478	+	0.00907079i
$275$	−5.30108	−	3.06058i	−0.319667	−	0.184560i
$276$		0			0
$277$	3.53023	+	6.11454i	0.212111	+	0.367387i	0.952375	−	0.304929i	$-0.0986328\pi$
$277$	3.53023	+	6.11454i	0.212111	+	0.367387i	−0.740264	+	0.672316i	$0.765300\pi$
$278$	−12.1052	−	12.1534i	−0.726021	−	0.728915i
$279$		0			0
$280$	4.80837	+	11.4230i	0.287355	+	0.682657i
$281$	−0.814975	+	1.41158i	−0.0486174	+	0.0842077i	−0.889310	−	0.457305i	$-0.848815\pi$
$281$	−0.814975	+	1.41158i	−0.0486174	+	0.0842077i	0.840693	+	0.541513i	$0.182148\pi$
$282$		0			0
$283$	25.1027			1.49220			0.746101	−	0.665833i	$-0.231924\pi$
$283$	25.1027			1.49220			0.746101	+	0.665833i	$0.231924\pi$
$284$	−2.09584	−	3.66369i	−0.124366	−	0.217400i
$285$		0			0
$286$	4.91639	−	18.2033i	0.290712	−	1.07638i
$287$	−1.66058	−	2.11251i	−0.0980212	−	0.124698i
$288$		0			0
$289$	−3.03589	−	5.25831i	−0.178581	−	0.309312i
$290$	−12.1712	+	12.1229i	−0.714716	+	0.711879i
$291$		0			0
$292$	−10.5393	−	0.0419224i	−0.616765	−	0.00245332i
$293$	−17.8533	+	10.3076i	−1.04300	+	0.602175i	−0.920681	−	0.390316i	$-0.872366\pi$
$293$	−17.8533	+	10.3076i	−1.04300	+	0.602175i	−0.122317	+	0.992491i	$0.539033\pi$
$294$		0			0
$295$	9.33122	+	5.38738i	0.543285	+	0.313666i
$296$	−24.3354	−	6.67652i	−1.41446	−	0.388065i
$297$		0			0
$298$	−6.10355	+	22.5989i	−0.353569	+	1.30912i
$299$	19.5902			1.13293
$300$		0			0
$301$	−6.46395	+	16.1364i	−0.372576	+	0.930086i
$302$	−17.0316	+	16.9640i	−0.980061	+	0.976171i
$303$		0			0
$304$	−6.05084	−	0.0481380i	−0.347040	−	0.00276090i
$305$	9.36568	−	16.2218i	0.536277	−	0.928860i
$306$		0			0
$307$	−28.7340			−1.63993			−0.819967	−	0.572410i	$-0.806008\pi$
$307$	−28.7340			−1.63993			−0.819967	+	0.572410i	$0.806008\pi$
$308$	13.3003	+	5.38936i	0.757856	+	0.307087i
$309$		0			0
$310$	−14.2797	−	3.85669i	−0.811032	−	0.219045i
$311$	−10.2429			−0.580824			−0.290412	−	0.956902i	$-0.593792\pi$
$311$	−10.2429			−0.580824			−0.290412	+	0.956902i	$0.593792\pi$
$312$		0			0
$313$			0.107424i			0.00607194i	0.999995	+	0.00303597i	$0.000966381\pi$
$313$			0.107424i			0.00607194i	−0.999995	+	0.00303597i	$0.999034\pi$
$314$	5.49064	+	20.6556i	0.309855	+	1.16566i
$315$		0			0
$316$	−15.1037	−	26.4024i	−0.849651	−	1.48525i
$317$	−14.3346			−0.805113			−0.402556	−	0.915395i	$-0.631878\pi$
$317$	−14.3346			−0.805113			−0.402556	+	0.915395i	$0.631878\pi$
$318$		0			0
$319$			19.8910i			1.11368i
$320$	−6.76121	+	11.3945i	−0.377963	+	0.636975i
$321$		0			0
$322$	−1.80262	+	14.8005i	−0.100456	+	0.824801i
$323$		−	5.00086i		−	0.278255i
$324$		0			0
$325$	9.60944	+	5.54801i	0.533036	+	0.307748i
$326$	−5.93612	+	5.91256i	−0.328771	+	0.327466i
$327$		0			0
$328$	0.760021	−	2.77021i	0.0419651	−	0.152959i
$329$	−0.734259	−	5.11447i	−0.0404810	−	0.281970i
$330$		0			0
$331$		−	13.9762i		−	0.768202i	−0.923291	−	0.384101i	$-0.874511\pi$
$331$		−	13.9762i		−	0.768202i	0.923291	−	0.384101i	$-0.125489\pi$
$332$	−0.116206	+	29.2142i	−0.00637765	+	1.60334i
$333$		0			0
$334$	−16.4797	−	16.5454i	−0.901728	−	0.905322i
$335$	3.50522	−	6.07123i	0.191511	−	0.331706i
$336$		0			0
$337$	8.48571	+	14.6977i	0.462246	+	0.800634i	0.999073	−	0.0430591i	$-0.0137104\pi$
$337$	8.48571	+	14.6977i	0.462246	+	0.800634i	−0.536827	+	0.843693i	$0.680377\pi$
$338$	−4.11846	+	15.2489i	−0.224015	+	0.829432i
$339$		0			0
$340$	−9.46114	−	5.51269i	−0.513103	−	0.298967i
$341$	−14.8323	+	8.56343i	−0.803214	+	0.463736i
$342$		0			0
$343$	−7.68303	−	16.8514i	−0.414845	−	0.909892i
$344$	−17.9783	+	4.70248i	−0.969325	+	0.253541i
$345$		0			0
$346$	5.89449	+	22.1749i	0.316890	+	1.19213i
$347$			17.6139i			0.945561i	0.881180	+	0.472781i	$0.156750\pi$
$347$			17.6139i			0.945561i	−0.881180	+	0.472781i	$0.843250\pi$
$348$		0			0
$349$	24.0589	+	13.8904i	1.28785	+	0.743538i	0.978270	−	0.207337i	$-0.0664796\pi$
$349$	24.0589	+	13.8904i	1.28785	+	0.743538i	0.309576	+	0.950875i	$0.399813\pi$
$350$	−5.07578	+	6.74948i	−0.271312	+	0.360775i
$351$		0			0
$352$	3.82314	+	14.8576i	0.203774	+	0.791912i
$353$	−17.6109	+	10.1677i	−0.937335	+	0.541170i	−0.889124	−	0.457667i	$-0.848685\pi$
$353$	−17.6109	+	10.1677i	−0.937335	+	0.541170i	−0.0482109	+	0.998837i	$0.515352\pi$
$354$		0			0
$355$	−1.74761	+	3.02695i	−0.0927536	+	0.160654i
$356$	−5.36781	+	9.21250i	−0.284493	+	0.488261i
$357$		0			0
$358$	−23.8872	−	6.45149i	−1.26248	−	0.340972i
$359$	9.00180	−	5.19719i	0.475097	−	0.274297i	−0.243274	−	0.969958i	$-0.578221\pi$
$359$	9.00180	−	5.19719i	0.475097	−	0.274297i	0.718371	+	0.695660i	$0.244888\pi$
$360$		0			0
$361$	8.35578	−	14.4726i	0.439778	−	0.761718i
$362$	3.33361	+	12.5409i	0.175211	+	0.659136i
$363$		0			0
$364$	−24.1099	−	9.76947i	−1.26370	−	0.512059i
$365$	4.36380	+	7.55833i	0.228412	+	0.395621i
$366$		0			0
$367$	−6.21836	−	10.7705i	−0.324596	−	0.562216i	0.656835	−	0.754034i	$-0.271895\pi$
$367$	−6.21836	−	10.7705i	−0.324596	−	0.562216i	−0.981430	+	0.191818i	$0.938562\pi$
$368$	−13.8668	+	7.85960i	−0.722859	+	0.409710i
$369$		0			0
$370$	5.36830	+	20.1953i	0.279085	+	1.04991i
$371$	−25.5839	−	10.2485i	−1.32825	−	0.532074i
$372$		0			0
$373$	−3.52422	+	6.10412i	−0.182477	+	0.316059i	−0.942723	−	0.333575i	$-0.891745\pi$
$373$	−3.52422	+	6.10412i	−0.182477	+	0.316059i	0.760246	+	0.649635i	$0.225078\pi$
$374$	−12.2535	+	3.25720i	−0.633612	+	0.168426i
$375$		0			0
$376$	3.92905	−	3.88244i	0.202625	−	0.200222i
$377$		−	36.0570i		−	1.85703i
$378$		0			0
$379$			5.49479i			0.282248i	0.989992	+	0.141124i	$0.0450717\pi$
$379$			5.49479i			0.282248i	−0.989992	+	0.141124i	$0.954928\pi$
$380$	2.48813	+	4.34944i	0.127639	+	0.223121i
$381$		0			0
$382$	−0.271092	−	1.01984i	−0.0138703	−	0.0521794i
$383$	−14.9307	+	25.8607i	−0.762923	+	1.32142i	0.178414	+	0.983955i	$0.442903\pi$
$383$	−14.9307	+	25.8607i	−0.762923	+	1.32142i	−0.941338	+	0.337466i	$0.890430\pi$
$384$		0			0
$385$	−1.68878	−	11.7632i	−0.0860682	−	0.599506i
$386$	−7.20517	+	1.91527i	−0.366733	+	0.0974846i
$387$		0			0
$388$	−9.71105	−	0.0386279i	−0.493004	−	0.00196103i
$389$	−1.85969	−	3.22107i	−0.0942899	−	0.163315i	0.815022	−	0.579430i	$-0.196725\pi$
$389$	−1.85969	−	3.22107i	−0.0942899	−	0.163315i	−0.909312	+	0.416115i	$0.863391\pi$
$390$		0			0
$391$	−6.58651	−	11.4082i	−0.333094	−	0.576936i
$392$	9.59939	−	17.3162i	0.484843	−	0.874601i
$393$		0			0
$394$	−17.7668	+	4.72275i	−0.895079	+	0.237929i
$395$	−12.5942	+	21.8138i	−0.633682	+	1.09757i
$396$		0			0
$397$	15.9038	−	9.18206i	0.798189	−	0.460834i	−0.0446487	−	0.999003i	$-0.514217\pi$
$397$	15.9038	−	9.18206i	0.798189	−	0.460834i	0.842837	+	0.538168i	$0.180884\pi$
$398$	3.63244	−	13.4494i	0.182078	−	0.674157i
$399$		0			0
$400$	−9.02786	−	0.0718219i	−0.451393	−	0.00359109i
$401$	−12.0156	+	20.8116i	−0.600029	+	1.03928i	0.392787	+	0.919629i	$0.371511\pi$
$401$	−12.0156	+	20.8116i	−0.600029	+	1.03928i	−0.992816	+	0.119651i	$0.961822\pi$
$402$		0			0
$403$	26.8870	−	15.5232i	1.33934	−	0.773266i
$404$	−2.83960	+	4.87346i	−0.141276	+	0.242464i
$405$		0			0
$406$	27.2413	+	3.31783i	1.35196	+	0.164661i
$407$	20.9545	+	12.0981i	1.03868	+	0.599680i
$408$		0			0
$409$		−	3.31574i		−	0.163953i	−0.996634	−	0.0819764i	$-0.973877\pi$
$409$		−	3.31574i		−	0.163953i	0.996634	−	0.0819764i	$-0.0261232\pi$
$410$	−2.29893	+	0.611100i	−0.113536	+	0.0301801i
$411$		0			0
$412$	−0.0126857	+	3.18919i	−0.000624981	+	0.157120i
$413$	−2.44605	−	17.0379i	−0.120362	−	0.838382i
$414$		0			0
$415$	20.9512	−	12.0962i	1.02845	−	0.593778i
$416$	−6.93033	−	26.9328i	−0.339787	−	1.32049i
$417$		0			0
$418$	5.60133	+	1.51282i	0.273970	+	0.0739944i
$419$	1.19685	+	2.07300i	0.0584698	+	0.101273i	0.893779	−	0.448508i	$-0.148045\pi$
$419$	1.19685	+	2.07300i	0.0584698	+	0.101273i	−0.835309	+	0.549781i	$0.814711\pi$
$420$		0			0
$421$	−3.27117	+	5.66583i	−0.159427	+	0.276135i	−0.934662	−	0.355537i	$-0.884298\pi$
$421$	−3.27117	+	5.66583i	−0.159427	+	0.276135i	0.775235	+	0.631673i	$0.217631\pi$
$422$	23.6353	−	23.5414i	1.15055	−	1.14598i
$423$		0			0
$424$	−7.45569	−	28.5042i	−0.362080	−	1.38429i
$425$		−	7.46128i		−	0.361925i
$426$		0			0
$427$	−29.6195	+	4.25233i	−1.43339	+	0.205785i
$428$	5.53106	−	9.49268i	0.267354	−	0.458846i
$429$		0			0
$430$	10.8597	+	10.9030i	0.523702	+	0.525789i
$431$	−19.2653	−	11.1228i	−0.927978	−	0.535768i	−0.0418066	−	0.999126i	$-0.513311\pi$
$431$	−19.2653	−	11.1228i	−0.927978	−	0.535768i	−0.886172	+	0.463357i	$0.846645\pi$
$432$		0			0
$433$		−	5.03561i		−	0.241996i	−0.992653	−	0.120998i	$-0.961391\pi$
$433$		−	5.03561i		−	0.241996i	0.992653	−	0.120998i	$-0.0386094\pi$
$434$	9.25383	+	21.7417i	0.444198	+	1.04363i
$435$		0			0
$436$	−0.108383	+	27.2473i	−0.00519058	+	1.30491i
$437$			6.02809i			0.288363i
$438$		0			0
$439$	−16.4591			−0.785551			−0.392776	−	0.919634i	$-0.628485\pi$
$439$	−16.4591			−0.785551			−0.392776	+	0.919634i	$0.628485\pi$
$440$	9.03672	−	8.92953i	0.430809	−	0.425698i
$441$		0			0
$442$	22.2123	−	5.90444i	1.05653	−	0.280846i
$443$		−	26.8092i		−	1.27374i	−0.770969	−	0.636872i	$-0.780228\pi$
$443$		−	26.8092i		−	1.27374i	0.770969	−	0.636872i	$-0.219772\pi$
$444$		0			0
$445$	8.82935			0.418551
$446$	1.75185	−	6.48638i	0.0829526	−	0.307139i
$447$		0			0
$448$	20.9856	−	2.75764i	0.991476	−	0.130286i
$449$	7.27030			0.343107			0.171553	−	0.985175i	$-0.445121\pi$
$449$	7.27030			0.343107			0.171553	+	0.985175i	$0.445121\pi$
$450$		0			0
$451$	−1.37719	+	2.38535i	−0.0648491	+	0.112322i
$452$	0.902595	+	0.525912i	0.0424545	+	0.0247368i
$453$		0			0
$454$	27.6287	+	27.7388i	1.29668	+	1.30185i
$455$	3.06131	+	21.3235i	0.143516	+	0.999660i
$456$		0			0
$457$	9.18531			0.429670			0.214835	−	0.976650i	$-0.431079\pi$
$457$	9.18531			0.429670			0.214835	+	0.976650i	$0.431079\pi$
$458$	−13.8183	−	3.73207i	−0.645685	−	0.174388i
$459$		0			0
$460$	11.4046	+	6.64506i	0.531741	+	0.309827i
$461$	−19.8154	−	11.4404i	−0.922894	−	0.532833i	−0.0383369	−	0.999265i	$-0.512206\pi$
$461$	−19.8154	−	11.4404i	−0.922894	−	0.532833i	−0.884557	+	0.466432i	$0.845539\pi$
$462$		0			0
$463$	8.96359	−	5.17513i	0.416573	−	0.240509i	−0.277037	−	0.960859i	$-0.589352\pi$
$463$	8.96359	−	5.17513i	0.416573	−	0.240509i	0.693610	+	0.720351i	$0.256019\pi$
$464$	14.4661	+	25.5228i	0.671571	+	1.18486i
$465$		0			0
$466$	13.4754	+	13.5291i	0.624237	+	0.626725i
$467$	−2.05702	−	3.56287i	−0.0951876	−	0.164870i	0.814499	−	0.580165i	$-0.197012\pi$
$467$	−2.05702	−	3.56287i	−0.0951876	−	0.164870i	−0.909687	+	0.415295i	$0.863678\pi$
$468$		0			0
$469$	−11.0855	+	1.59149i	−0.511880	+	0.0734881i
$470$	−4.41589	−	1.19265i	−0.203690	−	0.0550129i
$471$		0			0
$472$	13.0889	−	12.9337i	0.602466	−	0.595320i
$473$	17.8184			0.819291
$474$		0			0
$475$	−1.70718	+	2.95691i	−0.0783306	+	0.135673i
$476$	2.41694	+	17.3248i	0.110780	+	0.794081i
$477$		0			0
$478$	−25.0400	+	24.9406i	−1.14530	+	1.14076i
$479$	4.35898	+	7.54998i	0.199167	+	0.344967i	0.948259	−	0.317499i	$-0.102843\pi$
$479$	4.35898	+	7.54998i	0.199167	+	0.344967i	−0.749092	+	0.662466i	$0.769510\pi$
$480$		0			0
$481$	−37.9849	−	21.9306i	−1.73196	−	0.999950i
$482$	10.4622	−	10.4206i	0.476539	−	0.474648i
$483$		0			0
$484$	−0.0289964	+	7.28968i	−0.00131802	+	0.331349i
$485$	4.02087	+	6.96434i	0.182578	+	0.316235i
$486$		0			0
$487$	29.6495	+	17.1181i	1.34355	+	0.775697i	0.987326	−	0.158704i	$-0.0507316\pi$
$487$	29.6495	+	17.1181i	1.34355	+	0.775697i	0.356221	+	0.934402i	$0.384065\pi$
$488$	−22.4845	−	22.7544i	−1.01782	−	1.03004i
$489$		0			0
$490$	−16.3917	+	0.350726i	−0.740501	+	0.0158442i
$491$	34.6007	−	19.9767i	1.56151	−	0.901537i	0.564403	−	0.825499i	$-0.309106\pi$
$491$	34.6007	−	19.9767i	1.56151	−	0.901537i	0.997105	−	0.0760381i	$-0.0242271\pi$
$492$		0			0
$493$	−20.9974	+	12.1229i	−0.945677	+	0.545987i
$494$	−10.1537	−	2.74234i	−0.456837	−	0.123384i
$495$		0			0
$496$	−12.8039	+	21.7751i	−0.574912	+	0.977731i
$497$	5.52693	−	0.793474i	0.247917	−	0.0355922i
$498$		0			0
$499$	−13.4941	−	7.79083i	−0.604080	−	0.348766i	0.166565	−	0.986030i	$-0.446732\pi$
$499$	−13.4941	−	7.79083i	−0.604080	−	0.348766i	−0.770645	+	0.637265i	$0.780066\pi$
$500$	11.9361	+	20.8652i	0.533800	+	0.933121i
$501$		0			0
$502$	−6.27355	+	1.66763i	−0.280002	+	0.0744299i
$503$	−9.03852			−0.403008			−0.201504	−	0.979488i	$-0.564583\pi$
$503$	−9.03852			−0.403008			−0.201504	+	0.979488i	$0.564583\pi$
$504$		0			0
$505$	4.67078			0.207847
$506$	14.7705	−	3.92627i	0.656628	−	0.174544i
$507$		0			0
$508$	−8.28793	−	14.4879i	−0.367717	−	0.642797i
$509$	−13.0489	−	7.53379i	−0.578382	−	0.333929i	0.182108	−	0.983279i	$-0.441708\pi$
$509$	−13.0489	−	7.53379i	−0.578382	−	0.333929i	−0.760490	+	0.649349i	$0.775041\pi$
$510$		0			0
$511$	5.18453	−	12.9425i	0.229350	−	0.572542i
$512$	15.7111	+	16.2838i	0.694337	+	0.719650i
$513$		0			0
$514$	−35.7784	−	9.66310i	−1.57812	−	0.426221i
$515$	2.28715	−	1.32049i	0.100784	−	0.0581876i
$516$		0			0
$517$	−4.58678	+	2.64818i	−0.201726	+	0.116467i
$518$	20.0639	−	26.6799i	0.881559	−	1.17225i
$519$		0			0
$520$	−16.3812	+	16.1868i	−0.718362	+	0.709840i
$521$	9.24459	+	5.33737i	0.405013	+	0.233834i	0.688645	−	0.725099i	$-0.258206\pi$
$521$	9.24459	+	5.33737i	0.405013	+	0.233834i	−0.283632	+	0.958933i	$0.591539\pi$
$522$		0			0
$523$	−5.88205	−	10.1880i	−0.257204	−	0.445490i	0.708288	−	0.705924i	$-0.249468\pi$
$523$	−5.88205	−	10.1880i	−0.257204	−	0.445490i	−0.965492	+	0.260433i	$0.916135\pi$
$524$	0.136339	−	34.2756i	0.00595599	−	1.49733i
$525$		0			0
$526$	−5.94535	+	5.92175i	−0.259229	+	0.258200i
$527$	−18.0796	−	10.4382i	−0.787558	−	0.454697i
$528$		0			0
$529$	−3.56054	−	6.16704i	−0.154806	−	0.268132i
$530$	−17.2865	+	17.2179i	−0.750877	+	0.747896i
$531$		0			0
$532$	3.00616	−	7.41885i	0.130333	−	0.321648i
$533$	2.49647	−	4.32401i	0.108134	−	0.187294i
$534$		0			0
$535$	−9.09788			−0.393336
$536$	−8.41509	−	8.51612i	−0.363477	−	0.367840i
$537$		0			0
$538$	−2.36000	−	0.637394i	−0.101747	−	0.0274800i
$539$	−13.1064	+	13.7341i	−0.564531	+	0.591568i
$540$		0			0
$541$	7.31831	+	12.6757i	0.314639	+	0.544970i	0.979361	−	0.202120i	$-0.0647833\pi$
$541$	7.31831	+	12.6757i	0.314639	+	0.544970i	−0.664722	+	0.747091i	$0.731450\pi$
$542$	−6.72958	−	6.75640i	−0.289060	−	0.290212i
$543$		0			0
$544$	−13.3540	+	13.0910i	−0.572547	+	0.561272i
$545$	19.5406	−	11.2818i	0.837028	−	0.483258i
$546$		0			0
$547$	28.3730	+	16.3812i	1.21314	+	0.700408i	0.963442	−	0.267916i	$-0.0863349\pi$
$547$	28.3730	+	16.3812i	1.21314	+	0.700408i	0.249699	+	0.968323i	$0.419668\pi$
$548$	−0.258951	−	0.150882i	−0.0110618	−	0.00644535i
$549$		0			0
$550$	8.35719	+	2.25713i	0.356352	+	0.0962442i
$551$	11.0951			0.472666
$552$		0			0
$553$	39.8299	−	5.71818i	1.69374	−	0.243162i
$554$	−7.04640	−	7.07449i	−0.299373	−	0.300566i
$555$		0			0
$556$	20.9602	+	12.2128i	0.888911	+	0.517939i
$557$	−7.70165	+	13.3397i	−0.326330	+	0.565219i	−0.981781	−	0.190018i	$-0.939145\pi$
$557$	−7.70165	+	13.3397i	−0.326330	+	0.565219i	0.655451	+	0.755238i	$0.272479\pi$
$558$		0			0
$559$	−32.3000			−1.36614
$560$	−10.7219	−	13.8655i	−0.453084	−	0.585925i
$561$		0			0
$562$	0.601030	−	2.22536i	0.0253529	−	0.0938713i
$563$	30.9832			1.30579			0.652893	−	0.757450i	$-0.273555\pi$
$563$	30.9832			1.30579			0.652893	+	0.757450i	$0.273555\pi$
$564$		0			0
$565$		−	0.865056i		−	0.0363932i
$566$	−34.3092	+	9.12001i	−1.44212	+	0.383343i
$567$		0			0
$568$	4.19554	+	4.24591i	0.176041	+	0.178154i
$569$	38.2081			1.60177			0.800884	−	0.598820i	$-0.204363\pi$
$569$	38.2081			1.60177			0.800884	+	0.598820i	$0.204363\pi$
$570$		0			0
$571$		−	10.2007i		−	0.426886i	−0.976955	−	0.213443i	$-0.931532\pi$
$571$		−	10.2007i		−	0.426886i	0.976955	−	0.213443i	$-0.0684678\pi$
$572$	−0.106068	+	26.6656i	−0.00443494	+	1.11494i
$573$		0			0
$574$	3.03710	+	2.28398i	0.126766	+	0.0953313i
$575$			8.99392i			0.375072i
$576$		0			0
$577$	28.2579	+	16.3147i	1.17639	+	0.679191i	0.955177	−	0.296035i	$-0.0956643\pi$
$577$	28.2579	+	16.3147i	1.17639	+	0.679191i	0.221215	+	0.975225i	$0.428998\pi$
$578$	6.05968	+	6.08383i	0.252050	+	0.253054i
$579$		0			0
$580$	12.2306	−	20.9908i	0.507850	−	0.871596i
$581$	−35.8757	−	14.3712i	−1.48838	−	0.596217i
$582$		0			0
$583$			28.2507i			1.17003i
$584$	14.4198	−	3.77171i	0.596696	−	0.156074i
$585$		0			0
$586$	20.6561	−	20.5741i	0.853297	−	0.849909i
$587$	−17.3247	+	30.0073i	−0.715067	+	1.23853i	0.247867	+	0.968794i	$0.420271\pi$
$587$	−17.3247	+	30.0073i	−0.715067	+	1.23853i	−0.962934	+	0.269738i	$0.913063\pi$
$588$		0			0
$589$	4.77664	+	8.27338i	0.196818	+	0.340898i
$590$	−14.7107	−	3.97310i	−0.605631	−	0.163570i
$591$		0			0
$592$	35.6860	+	0.283903i	1.46669	+	0.0116683i
$593$	−4.42792	+	2.55646i	−0.181833	+	0.104981i	−0.588153	−	0.808749i	$-0.700145\pi$
$593$	−4.42792	+	2.55646i	−0.181833	+	0.104981i	0.406321	+	0.913731i	$0.366812\pi$
$594$		0			0
$595$	11.3883	−	8.95197i	0.466873	−	0.366995i
$596$	0.131681	−	33.1045i	0.00539385	−	1.35601i
$597$		0			0
$598$	−26.7750	+	7.11728i	−1.09491	+	0.291047i
$599$		−	23.2794i		−	0.951171i	−0.879669	−	0.475586i	$-0.842236\pi$
$599$		−	23.2794i		−	0.951171i	0.879669	−	0.475586i	$-0.157764\pi$
$600$		0			0
$601$	−35.2417	−	20.3468i	−1.43754	−	0.829964i	−0.439862	−	0.898066i	$-0.644973\pi$
$601$	−35.2417	−	20.3468i	−1.43754	−	0.829964i	−0.997678	+	0.0681014i	$0.978306\pi$
$602$	2.97213	−	24.4028i	0.121135	−	0.994585i
$603$		0			0
$604$	17.1148	−	29.3733i	0.696393	−	1.19518i
$605$	5.22785	−	3.01830i	0.212542	−	0.122711i
$606$		0			0
$607$	2.67342	−	4.63049i	0.108511	−	0.187946i	−0.806656	−	0.591021i	$-0.798725\pi$
$607$	2.67342	−	4.63049i	0.108511	−	0.187946i	0.915167	+	0.403075i	$0.132059\pi$
$608$	8.28748	−	2.13253i	0.336102	−	0.0864853i
$609$		0			0
$610$	−6.90703	+	25.5738i	−0.279657	+	1.03545i
$611$	8.31460	−	4.80044i	0.336373	−	0.194205i
$612$		0			0
$613$	−21.3074	+	36.9055i	−0.860597	+	1.49060i	0.0107566	+	0.999942i	$0.496576\pi$
$613$	−21.3074	+	36.9055i	−0.860597	+	1.49060i	−0.871354	+	0.490656i	$0.836757\pi$
$614$	39.2722	−	10.4393i	1.58490	−	0.421295i
$615$		0			0
$616$	−20.1362	−	2.53380i	−0.811311	−	0.102090i
$617$	3.10687	+	5.38126i	0.125078	+	0.216641i	0.921763	−	0.387753i	$-0.126749\pi$
$617$	3.10687	+	5.38126i	0.125078	+	0.216641i	−0.796685	+	0.604394i	$0.793415\pi$
$618$		0			0
$619$	−1.91636	−	3.31923i	−0.0770249	−	0.133411i	0.824940	−	0.565220i	$-0.191209\pi$
$619$	−1.91636	−	3.31923i	−0.0770249	−	0.133411i	−0.901965	+	0.431809i	$0.857875\pi$
$620$	20.9180	+	0.0832059i	0.840085	+	0.00334163i
$621$		0			0
$622$	13.9995	−	3.72134i	0.561331	−	0.149212i
$623$	−8.71671	−	11.0890i	−0.349228	−	0.444270i
$624$		0			0
$625$	4.31030	−	7.46567i	0.172412	−	0.298627i
$626$	−0.0390279	−	0.146821i	−0.00155987	−	0.00586816i
$627$		0			0
$628$	−15.0087	−	26.2363i	−0.598912	−	1.04694i
$629$			29.4935i			1.17598i
$630$		0			0
$631$			31.3249i			1.24703i	0.781813	+	0.623513i	$0.214295\pi$
$631$			31.3249i			1.24703i	−0.781813	+	0.623513i	$0.785705\pi$
$632$	30.2352	+	30.5982i	1.20269	+	1.21713i
$633$		0			0
$634$	19.5919	−	5.20788i	0.778092	−	0.206831i
$635$	−6.91086	+	11.9700i	−0.274249	+	0.475013i
$636$		0			0
$637$	23.7583	−	24.8962i	0.941340	−	0.986423i
$638$	−7.22654	−	27.1860i	−0.286102	−	1.07630i
$639$		0			0
$640$	5.10116	−	18.0299i	0.201641	−	0.712695i
$641$	10.2056	+	17.6766i	0.403097	+	0.698185i	0.994098	−	0.108486i	$-0.0346002\pi$
$641$	10.2056	+	17.6766i	0.403097	+	0.698185i	−0.591001	+	0.806671i	$0.701267\pi$
$642$		0			0
$643$	7.30287	+	12.6489i	0.287997	+	0.498826i	0.973332	−	0.229403i	$-0.0736773\pi$
$643$	7.30287	+	12.6489i	0.287997	+	0.498826i	−0.685334	+	0.728228i	$0.740344\pi$
$644$	−2.91341	−	20.8835i	−0.114805	−	0.822926i
$645$		0			0
$646$	1.81685	+	6.83492i	0.0714830	+	0.268917i
$647$	16.1015	−	27.8887i	0.633017	−	1.09642i	−0.353915	−	0.935278i	$-0.615150\pi$
$647$	16.1015	−	27.8887i	0.633017	−	1.09642i	0.986932	−	0.161140i	$-0.0515170\pi$
$648$		0			0
$649$	−15.2800	+	8.82192i	−0.599793	+	0.346291i
$650$	−15.1493	−	4.09157i	−0.594206	−	0.160484i
$651$		0			0
$652$	5.96512	−	10.2376i	0.233612	−	0.400937i
$653$	−17.9103	+	31.0215i	−0.700883	+	1.21397i	0.267274	+	0.963621i	$0.413877\pi$
$653$	−17.9103	+	31.0215i	−0.700883	+	1.21397i	−0.968157	+	0.250344i	$0.919456\pi$
$654$		0			0
$655$	−24.5809	+	14.1918i	−0.960457	+	0.554520i
$656$	−0.0323181	+	4.06231i	−0.00126181	+	0.158607i
$657$		0			0
$658$	2.86168	+	6.72344i	0.111560	+	0.262107i
$659$	−0.326746	−	0.188647i	−0.0127282	−	0.00734865i	0.493622	−	0.869676i	$-0.335673\pi$
$659$	−0.326746	−	0.188647i	−0.0127282	−	0.00734865i	−0.506351	+	0.862328i	$0.669006\pi$
$660$		0			0
$661$		−	39.3987i		−	1.53243i	−0.642584	−	0.766216i	$-0.722137\pi$
$661$		−	39.3987i		−	1.53243i	0.642584	−	0.766216i	$-0.277863\pi$
$662$	5.07767	+	19.1020i	0.197349	+	0.742420i
$663$		0			0
$664$	−10.4549	−	39.9708i	−0.405730	−	1.55117i
$665$	−6.56143	+	0.941992i	−0.254441	+	0.0365289i
$666$		0			0
$667$	25.3106	−	14.6131i	0.980029	−	0.565820i
$668$	28.5347	+	16.6262i	1.10404	+	0.643287i
$669$		0			0
$670$	−2.58504	+	9.57133i	−0.0998689	+	0.369773i
$671$	15.3364	+	26.5635i	0.592057	+	1.02547i
$672$		0			0
$673$	−16.6511	+	28.8406i	−0.641853	+	1.11172i	0.343166	+	0.939275i	$0.388501\pi$
$673$	−16.6511	+	28.8406i	−0.641853	+	1.11172i	−0.985019	+	0.172447i	$0.944833\pi$
$674$	−16.9376	−	17.0051i	−0.652413	−	0.655013i
$675$		0			0
$676$	0.0888535	−	22.3378i	0.00341744	−	0.859144i
$677$			9.32909i			0.358546i	0.983799	+	0.179273i	$0.0573745\pi$
$677$			9.32909i			0.358546i	−0.983799	+	0.179273i	$0.942625\pi$
$678$		0			0
$679$	4.77709	−	11.9254i	0.183328	−	0.457654i
$680$	14.9338	+	4.09716i	0.572686	+	0.157119i
$681$		0			0
$682$	17.1609	−	17.0928i	0.657124	−	0.654516i
$683$	1.57689	+	0.910416i	0.0603379	+	0.0348361i	0.529865	−	0.848082i	$-0.322242\pi$
$683$	1.57689	+	0.910416i	0.0603379	+	0.0348361i	−0.469528	+	0.882918i	$0.655576\pi$
$684$		0			0
$685$			0.248181i			0.00948251i
$686$	16.6231	+	20.2404i	0.634671	+	0.772782i
$687$		0			0
$688$	22.8634	−	12.9588i	0.871659	−	0.494049i
$689$		−	51.2110i		−	1.95098i
$690$		0			0
$691$	−2.82516			−0.107474			−0.0537371	−	0.998555i	$-0.517113\pi$
$691$	−2.82516			−0.107474			−0.0537371	+	0.998555i	$0.517113\pi$
$692$	−16.1126	−	28.1660i	−0.612509	−	1.07071i
$693$		0			0
$694$	−6.39925	−	24.0737i	−0.242912	−	0.913827i
$695$		−	20.0885i		−	0.762000i
$696$		0			0
$697$	−3.35739			−0.127170
$698$	−37.9291	−	10.2440i	−1.43564	−	0.387740i
$699$		0			0
$700$	4.48519	−	11.0689i	0.169524	−	0.418366i
$701$	−21.7145			−0.820146			−0.410073	−	0.912053i	$-0.634497\pi$
$701$	−21.7145			−0.820146			−0.410073	+	0.912053i	$0.634497\pi$
$702$		0			0
$703$	6.74825	−	11.6883i	0.254515	−	0.440833i
$704$	−10.6232	−	18.9176i	−0.400375	−	0.712985i
$705$		0			0
$706$	20.3757	−	20.2949i	0.766851	−	0.763807i
$707$	−4.61119	−	5.86613i	−0.173422	−	0.220618i
$708$		0			0
$709$	18.2252			0.684460			0.342230	−	0.939616i	$-0.388818\pi$
$709$	18.2252			0.684460			0.342230	+	0.939616i	$0.388818\pi$
$710$	1.28883	−	4.77201i	0.0483691	−	0.179090i
$711$		0			0
$712$	3.98949	−	14.5414i	0.149512	−	0.544960i
$713$	21.7933	+	12.5824i	0.816167	+	0.471214i
$714$		0			0
$715$	19.1234	−	11.0409i	0.715174	−	0.412906i
$716$	34.9917	+	0.139187i	1.30770	+	0.00520167i
$717$		0			0
$718$	−10.4150	+	10.3737i	−0.388686	+	0.387143i
$719$	0.946279	+	1.63900i	0.0352903	+	0.0611245i	0.883131	−	0.469126i	$-0.155431\pi$
$719$	0.946279	+	1.63900i	0.0352903	+	0.0611245i	−0.847841	+	0.530251i	$0.822098\pi$
$720$		0			0
$721$	−3.91640	−	1.56884i	−0.145854	−	0.0584266i
$722$	−6.16225	+	22.8162i	−0.229335	+	0.849131i
$723$		0			0
$724$	−9.11242	−	15.9292i	−0.338660	−	0.592003i
$725$	16.5539			0.614795
$726$		0			0
$727$	−16.6125	+	28.7738i	−0.616125	+	1.06716i	0.374061	+	0.927404i	$0.377965\pi$
$727$	−16.6125	+	28.7738i	−0.616125	+	1.06716i	−0.990186	+	0.139756i	$0.955368\pi$
$728$	36.5016	+	4.59311i	1.35284	+	0.170232i
$729$		0			0
$730$	−8.71023	−	8.74494i	−0.322380	−	0.323665i
$731$	10.8597	+	18.8096i	0.401661	+	0.695698i
$732$		0			0
$733$	−7.05539	−	4.07343i	−0.260597	−	0.150456i	0.364010	−	0.931395i	$-0.381407\pi$
$733$	−7.05539	−	4.07343i	−0.260597	−	0.150456i	−0.624607	+	0.780939i	$0.714741\pi$
$734$	12.4120	+	12.4614i	0.458134	+	0.459960i
$735$		0			0
$736$	16.0971	−	15.7801i	0.593345	−	0.581660i
$737$	5.73985	+	9.94172i	0.211430	+	0.366208i
$738$		0			0
$739$	−4.33522	−	2.50294i	−0.159474	−	0.0920722i	0.418139	−	0.908383i	$-0.362682\pi$
$739$	−4.33522	−	2.50294i	−0.159474	−	0.0920722i	−0.577613	+	0.816311i	$0.696016\pi$
$740$	−14.6743	−	25.6517i	−0.539436	−	0.942973i
$741$		0			0
$742$	38.6902	+	4.71225i	1.42036	+	0.172992i
$743$	−23.9292	+	13.8155i	−0.877877	+	0.506842i	−0.869958	−	0.493126i	$-0.835854\pi$
$743$	−23.9292	+	13.8155i	−0.877877	+	0.506842i	−0.00791898	+	0.999969i	$0.502521\pi$
$744$		0			0
$745$	−23.7411	+	13.7069i	−0.869807	+	0.502184i
$746$	2.59905	−	9.62318i	0.0951579	−	0.352330i
$747$		0			0
$748$	15.5641	−	8.90357i	0.569079	−	0.325547i
$749$	8.98181	+	11.4262i	0.328188	+	0.417505i
$750$		0			0
$751$	28.3094	+	16.3445i	1.03303	+	0.596418i	0.917850	−	0.396927i	$-0.129923\pi$
$751$	28.3094	+	16.3445i	1.03303	+	0.596418i	0.115176	+	0.993345i	$0.463257\pi$
$752$	−3.95951	+	6.73379i	−0.144388	+	0.245556i
$753$		0			0
$754$	13.0998	+	49.2809i	0.477066	+	1.79471i
$755$	−28.1517			−1.02455
$756$		0			0
$757$	−19.8021			−0.719720			−0.359860	−	0.933006i	$-0.617176\pi$
$757$	−19.8021			−0.719720			−0.359860	+	0.933006i	$0.617176\pi$
$758$	−1.99630	−	7.51001i	−0.0725089	−	0.272776i
$759$		0			0
$760$	−4.98084	−	5.04064i	−0.180674	−	0.182843i
$761$	41.0380	+	23.6933i	1.48763	+	0.858881i	0.999900	−	0.0141164i	$-0.00449353\pi$
$761$	41.0380	+	23.6933i	1.48763	+	0.858881i	0.487725	+	0.872997i	$0.337827\pi$
$762$		0			0
$763$	−33.4603	−	13.4036i	−1.21135	−	0.485243i
$764$	0.741029	+	1.29537i	0.0268095	+	0.0468649i
$765$		0			0
$766$	11.0111	−	40.7696i	0.397849	−	1.47307i
$767$	27.6986	−	15.9918i	1.00014	−	0.577430i
$768$		0			0
$769$	−41.6592	+	24.0520i	−1.50227	+	0.867336i	−0.502273	+	0.864709i	$0.667503\pi$
$769$	−41.6592	+	24.0520i	−1.50227	+	0.867336i	−0.999997	+	0.00262643i	$0.999164\pi$
$770$	6.58179	+	15.4638i	0.237191	+	0.557275i
$771$		0			0
$772$	9.15184	−	5.23539i	0.329382	−	0.188426i
$773$	0.506957	+	0.292692i	0.0182340	+	0.0105274i	0.509089	−	0.860714i	$-0.329982\pi$
$773$	0.506957	+	0.292692i	0.0182340	+	0.0105274i	−0.490855	+	0.871241i	$0.663316\pi$
$774$		0			0
$775$	7.12674	+	12.3439i	0.256000	+	0.443405i
$776$	13.2866	−	3.47530i	0.476962	−	0.124756i
$777$		0			0
$778$	3.71197	+	3.72676i	0.133081	+	0.133611i
$779$	1.33054	+	0.768187i	0.0476715	+	0.0275231i
$780$		0			0
$781$	−2.86174	−	4.95668i	−0.102401	−	0.177364i
$782$	13.1468	+	13.1992i	0.470128	+	0.472002i
$783$		0			0
$784$	−6.82886	+	27.1545i	−0.243888	+	0.969803i
$785$	−12.5149	+	21.6765i	−0.446677	+	0.773667i
$786$		0			0
$787$	1.22833			0.0437851			0.0218926	−	0.999760i	$-0.493031\pi$
$787$	1.22833			0.0437851			0.0218926	+	0.999760i	$0.493031\pi$
$788$	22.5670	−	12.9096i	0.803915	−	0.459887i
$789$		0			0
$790$	9.28800	−	34.3895i	0.330452	−	1.22352i
$791$	−1.08644	+	0.854020i	−0.0386294	+	0.0303655i
$792$		0			0
$793$	−27.8009	−	48.1525i	−0.987238	−	1.70995i
$794$	−18.4006	+	18.3276i	−0.653013	+	0.650421i
$795$		0			0
$796$	−0.0783678	+	19.7016i	−0.00277767	+	0.698306i
$797$	10.3748	−	5.98989i	0.367494	−	0.212173i	−0.304869	−	0.952394i	$-0.598613\pi$
$797$	10.3748	−	5.98989i	0.367494	−	0.212173i	0.672363	+	0.740222i	$0.265279\pi$
$798$		0			0
$799$	−5.59097	−	3.22795i	−0.197794	−	0.114197i
$800$	12.3649	−	3.18173i	0.437166	−	0.112491i
$801$		0			0
$802$	8.86128	−	32.8096i	0.312903	−	1.15855i
$803$	−14.2916			−0.504339
$804$		0			0
$805$	−13.7275	+	10.7908i	−0.483832	+	0.380326i
$806$	−31.1081	+	30.9846i	−1.09574	+	1.09139i
$807$		0			0
$808$	2.11046	−	7.69246i	0.0742458	−	0.270620i
$809$	3.43996	−	5.95818i	0.120943	−	0.209479i	−0.799197	−	0.601069i	$-0.794742\pi$
$809$	3.43996	−	5.95818i	0.120943	−	0.209479i	0.920140	+	0.391590i	$0.128075\pi$
$810$		0			0
$811$	12.6994			0.445938			0.222969	−	0.974826i	$-0.428425\pi$
$811$	12.6994			0.445938			0.222969	+	0.974826i	$0.428425\pi$
$812$	−38.4374	+	5.36231i	−1.34889	+	0.188180i
$813$		0			0
$814$	−33.0349	−	8.92214i	−1.15787	−	0.312721i
$815$	−9.81185			−0.343694
$816$		0			0
$817$		−	9.93901i		−	0.347722i
$818$	1.20464	+	4.53179i	0.0421191	+	0.158450i
$819$		0			0
$820$	2.92005	−	1.67044i	0.101973	−	0.0583344i
$821$	40.0401			1.39741			0.698704	−	0.715411i	$-0.253761\pi$
$821$	40.0401			1.39741			0.698704	+	0.715411i	$0.253761\pi$
$822$		0			0
$823$		−	35.4514i		−	1.23576i	−0.786274	−	0.617878i	$-0.787992\pi$
$823$		−	35.4514i		−	1.23576i	0.786274	−	0.617878i	$-0.212008\pi$
$824$	−1.14132	−	4.36344i	−0.0397598	−	0.152008i
$825$		0			0
$826$	9.53316	+	22.3979i	0.331701	+	0.779324i
$827$			51.5618i			1.79298i	0.443064	+	0.896490i	$0.353891\pi$
$827$			51.5618i			1.79298i	−0.443064	+	0.896490i	$0.646109\pi$
$828$		0			0
$829$	35.0577	+	20.2406i	1.21760	+	0.702984i	0.964405	−	0.264431i	$-0.0851840\pi$
$829$	35.0577	+	20.2406i	1.21760	+	0.702984i	0.253199	+	0.967414i	$0.418517\pi$
$830$	−24.2404	+	24.1442i	−0.841397	+	0.838057i
$831$		0			0
$832$	19.2569	+	34.2926i	0.667614	+	1.18888i
$833$	−22.4859	−	5.46498i	−0.779091	−	0.189350i
$834$		0			0
$835$		−	27.3479i		−	0.946414i
$836$	−8.20524	−	0.0326382i	−0.283784	−	0.00112882i
$837$		0			0
$838$	−2.38893	−	2.39845i	−0.0825242	−	0.0828531i
$839$	3.71303	−	6.43115i	0.128188	−	0.222028i	−0.794787	−	0.606889i	$-0.792417\pi$
$839$	3.71303	−	6.43115i	0.128188	−	0.222028i	0.922975	+	0.384861i	$0.125751\pi$
$840$		0			0
$841$	−12.3962	−	21.4709i	−0.427456	−	0.740375i
$842$	2.41243	−	8.93221i	0.0831378	−	0.307824i
$843$		0			0
$844$	−23.7507	+	40.7622i	−0.817534	+	1.40309i
$845$	−16.0197	+	9.24896i	−0.551093	+	0.318174i
$846$		0			0
$847$	−8.95189	−	3.58597i	−0.307591	−	0.123215i
$848$	20.5459	+	36.2495i	0.705548	+	1.24481i
$849$		0			0
$850$	2.71074	+	10.1977i	0.0929777	+	0.349779i
$851$		−	35.5519i		−	1.21870i
$852$		0			0
$853$	8.86973	+	5.12094i	0.303694	+	0.175338i	0.644101	−	0.764940i	$-0.277232\pi$
$853$	8.86973	+	5.12094i	0.303694	+	0.175338i	−0.340407	+	0.940278i	$0.610565\pi$
$854$	38.9376	−	16.5729i	1.33242	−	0.567112i
$855$		0			0
$856$	−4.11082	+	14.9836i	−0.140505	+	0.512129i
$857$	15.5246	−	8.96315i	0.530311	−	0.306175i	−0.210832	−	0.977522i	$-0.567617\pi$
$857$	15.5246	−	8.96315i	0.530311	−	0.306175i	0.741143	+	0.671347i	$0.234284\pi$
$858$		0			0
$859$	17.5755	−	30.4417i	0.599670	−	1.03866i	−0.393200	−	0.919453i	$-0.628632\pi$
$859$	17.5755	−	30.4417i	0.599670	−	1.03866i	0.992870	−	0.119205i	$-0.0380346\pi$
$860$	−18.8037	−	10.9563i	−0.641199	−	0.373605i
$861$		0			0
$862$	30.3719	+	8.20291i	1.03447	+	0.279392i
$863$	−13.3132	+	7.68639i	−0.453187	+	0.261648i	−0.709175	−	0.705032i	$-0.750932\pi$
$863$	−13.3132	+	7.68639i	−0.453187	+	0.261648i	0.255988	+	0.966680i	$0.417599\pi$
$864$		0			0
$865$	−13.4354	+	23.2709i	−0.456819	+	0.791233i
$866$	1.82948	+	6.88242i	0.0621681	+	0.233874i
$867$		0			0
$868$	−20.5466	−	26.3534i	−0.697397	−	0.894494i
$869$	−20.6232	−	35.7204i	−0.699593	−	1.21173i
$870$		0			0
$871$	−10.4048	−	18.0217i	−0.352554	−	0.610641i
$872$	−9.75104	−	37.2797i	−0.330212	−	1.26245i
$873$		0			0
$874$	−2.19005	−	8.23890i	−0.0740797	−	0.278685i
$875$	−31.4766	+	4.51894i	−1.06410	+	0.152768i
$876$		0			0
$877$	−11.2020	+	19.4025i	−0.378265	+	0.655174i	−0.990810	−	0.135261i	$-0.956813\pi$
$877$	−11.2020	+	19.4025i	−0.378265	+	0.655174i	0.612545	+	0.790436i	$0.290146\pi$
$878$	22.4955	−	5.97973i	0.759187	−	0.201806i
$879$		0			0
$880$	−9.10678	+	15.4875i	−0.306990	+	0.522085i
$881$			29.1250i			0.981247i	0.871372	+	0.490624i	$0.163231\pi$
$881$			29.1250i			0.981247i	−0.871372	+	0.490624i	$0.836769\pi$
$882$		0			0
$883$			20.8057i			0.700168i	0.936718	+	0.350084i	$0.113847\pi$
$883$			20.8057i			0.700168i	−0.936718	+	0.350084i	$0.886153\pi$
$884$	−28.2135	+	16.1398i	−0.948924	+	0.542840i
$885$		0			0
$886$	9.74000	+	36.6415i	0.327222	+	1.23100i
$887$	6.23363	−	10.7970i	0.209305	−	0.362526i	−0.742191	−	0.670188i	$-0.766213\pi$
$887$	6.23363	−	10.7970i	0.209305	−	0.362526i	0.951496	+	0.307662i	$0.0995466\pi$
$888$		0			0
$889$	21.8560	−	3.13776i	0.733027	−	0.105237i
$890$	−12.0675	+	3.20777i	−0.404504	+	0.107525i
$891$		0			0
$892$	−0.0377952	+	9.50172i	−0.00126548	+	0.318141i
$893$	1.47714	+	2.55848i	0.0494306	+	0.0856162i
$894$		0			0
$895$	−14.4883	−	25.0945i	−0.484291	−	0.838817i
$896$	−27.6802	+	11.3932i	−0.924731	+	0.380621i
$897$		0			0
$898$	−9.93668	+	2.64136i	−0.331591	+	0.0881432i
$899$	23.1586	−	40.1120i	0.772384	−	1.33781i
$900$		0			0
$901$	−29.8222	+	17.2179i	−0.993522	+	0.573610i
$902$	1.01565	−	3.76053i	0.0338175	−	0.125212i
$903$		0			0
$904$	−1.42469	−	0.390870i	−0.0473845	−	0.0130001i
$905$	−7.59836	+	13.1607i	−0.252578	+	0.437478i
$906$		0			0
$907$	−23.9315	+	13.8169i	−0.794634	+	0.458782i	−0.841591	−	0.540115i	$-0.818381\pi$
$907$	−23.9315	+	13.8169i	−0.794634	+	0.458782i	0.0469575	+	0.998897i	$0.485047\pi$
$908$	−47.8393	−	27.8743i	−1.58760	−	0.925043i
$909$		0			0
$910$	−11.9310	−	28.0317i	−0.395510	−	0.929241i
$911$	−16.9835	−	9.80544i	−0.562689	−	0.324869i	0.191535	−	0.981486i	$-0.438653\pi$
$911$	−16.9835	−	9.80544i	−0.562689	−	0.324869i	−0.754224	+	0.656617i	$0.771987\pi$
$912$		0			0
$913$			39.6153i			1.31108i
$914$	−12.5540	+	3.33709i	−0.415250	+	0.110381i
$915$		0			0
$916$	20.2420	+	0.0805172i	0.668815	+	0.00266036i
$917$	42.0911	+	16.8610i	1.38997	+	0.556798i
$918$		0			0
$919$	−26.8847	+	15.5219i	−0.886843	+	0.512019i	−0.872908	−	0.487884i	$-0.837769\pi$
$919$	−26.8847	+	15.5219i	−0.886843	+	0.512019i	−0.0139343	+	0.999903i	$0.504436\pi$
$920$	−18.0014	−	4.93877i	−0.593489	−	0.162826i
$921$		0			0
$922$	31.2391	+	8.43711i	1.02880	+	0.277861i
$923$	5.18757	+	8.98514i	0.170751	+	0.295749i
$924$		0			0
$925$	10.0684	−	17.4390i	0.331047	−	0.573390i
$926$	−10.3708	+	10.3297i	−0.340806	+	0.339453i
$927$		0			0
$928$	−29.0441	−	29.6276i	−0.953421	−	0.972574i
$929$		−	8.72104i		−	0.286128i	−0.989713	−	0.143064i	$-0.954305\pi$
$929$		−	8.72104i		−	0.286128i	0.989713	−	0.143064i	$-0.0456955\pi$
$930$		0			0
$931$	7.66079	+	7.31066i	0.251072	+	0.239597i
$932$	−23.3328	−	13.5952i	−0.764291	−	0.445326i
$933$		0			0
$934$	4.10585	+	4.12222i	0.134348	+	0.134883i
$935$	−12.8591	−	7.42421i	−0.420538	−	0.242798i
$936$		0			0
$937$		−	15.0809i		−	0.492672i	−0.969185	−	0.246336i	$-0.920773\pi$
$937$		−	15.0809i		−	0.492672i	0.969185	−	0.246336i	$-0.0792266\pi$
$938$	14.5729	−	6.20261i	0.475822	−	0.202522i
$939$		0			0
$940$	6.46872	+	0.0257308i	0.210986	+	0.000839246i
$941$			52.4732i			1.71058i	0.518151	+	0.855289i	$0.326620\pi$
$941$			52.4732i			1.71058i	−0.518151	+	0.855289i	$0.673380\pi$
$942$		0			0
$943$	4.04704			0.131790
$944$	−13.1904	+	22.4324i	−0.429311	+	0.730112i
$945$		0			0
$946$	−24.3533	+	6.47357i	−0.791795	+	0.210474i
$947$			44.4680i			1.44501i	0.691363	+	0.722507i	$0.257010\pi$
$947$			44.4680i			1.44501i	−0.691363	+	0.722507i	$0.742990\pi$
$948$		0			0
$949$	25.9068			0.840971
$950$	1.25901	−	4.66159i	0.0408478	−	0.151242i
$951$		0			0
$952$	−9.59760	−	22.8006i	−0.311060	−	0.738971i
$953$	−13.0081			−0.421374			−0.210687	−	0.977554i	$-0.567570\pi$
$953$	−13.0081			−0.421374			−0.210687	+	0.977554i	$0.567570\pi$
$954$		0			0
$955$	0.617905	−	1.07024i	0.0199949	−	0.0346322i
$956$	25.1623	−	43.1848i	0.813808	−	1.39670i
$957$		0			0
$958$	−8.70061	−	8.73529i	−0.281104	−	0.282224i
$959$	0.311696	−	0.245015i	0.0100652	−	0.00791194i
$960$		0			0
$961$	8.88091			0.286481
$962$	59.8835	+	16.1735i	1.93072	+	0.521453i
$963$		0			0
$964$	−10.5133	+	18.0434i	−0.338610	+	0.581139i
$965$	−7.56128	−	4.36551i	−0.243406	−	0.140531i
$966$		0			0
$967$	−24.2347	+	13.9919i	−0.779335	+	0.449949i	−0.836194	−	0.548433i	$-0.815225\pi$
$967$	−24.2347	+	13.9919i	−0.779335	+	0.449949i	0.0568598	+	0.998382i	$0.481891\pi$
$968$	−2.60877	−	9.97371i	−0.0838490	−	0.320567i
$969$		0			0
$970$	−8.02572	−	8.05771i	−0.257690	−	0.258717i
$971$	4.21204	+	7.29547i	0.135171	+	0.234123i	0.925663	−	0.378350i	$-0.123508\pi$
$971$	4.21204	+	7.29547i	0.135171	+	0.234123i	−0.790492	+	0.612473i	$0.790175\pi$
$972$		0			0
$973$	−25.2295	+	19.8322i	−0.808822	+	0.635791i
$974$	−46.7426	−	12.6243i	−1.49773	−	0.404510i
$975$		0			0
$976$	38.9975	+	22.9308i	1.24828	+	0.733997i
$977$	−0.704020			−0.0225236			−0.0112618	−	0.999937i	$-0.503585\pi$
$977$	−0.704020			−0.0225236			−0.0112618	+	0.999937i	$0.503585\pi$
$978$		0			0
$979$	−7.22910	+	12.5212i	−0.231043	+	0.400178i
$980$	22.2759	−	6.43458i	0.711578	−	0.205545i
$981$		0			0
$982$	−40.0328	+	39.8739i	−1.27750	+	1.27243i
$983$	−15.3077	−	26.5137i	−0.488240	−	0.845656i	0.511669	−	0.859183i	$-0.329028\pi$
$983$	−15.3077	−	26.5137i	−0.488240	−	0.845656i	−0.999909	+	0.0135267i	$0.995694\pi$
$984$		0			0
$985$	−18.6449	−	10.7647i	−0.594077	−	0.342990i
$986$	24.2939	−	24.1975i	0.773676	−	0.770605i
$987$		0			0
$988$	14.8739	+	0.0591644i	0.473202	+	0.00188227i
$989$	−13.0904	−	22.6733i	−0.416252	−	0.720969i
$990$		0			0
$991$	−38.1803	−	22.0434i	−1.21284	−	0.700232i	−0.249460	−	0.968385i	$-0.580253\pi$
$991$	−38.1803	−	22.0434i	−1.21284	−	0.700232i	−0.963376	+	0.268153i	$0.913587\pi$
$992$	9.58868	−	34.4129i	0.304441	−	1.09261i
$993$		0			0
$994$	−7.26566	+	3.09246i	−0.230453	+	0.0980868i
$995$	14.1292	−	8.15748i	0.447925	−	0.258609i
$996$		0			0
$997$	6.37914	−	3.68300i	0.202030	−	0.116642i	−0.395572	−	0.918435i	$-0.629454\pi$
$997$	6.37914	−	3.68300i	0.202030	−	0.116642i	0.597602	+	0.801793i	$0.296120\pi$
$998$	21.2736	+	5.74561i	0.673403	+	0.181874i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bj.b.451.4		84
3.2	odd	2		252.2.bj.b.115.39	yes	84
4.3	odd	2	inner	756.2.bj.b.451.3		84
7.5	odd	6		756.2.n.b.19.32		84
9.4	even	3		756.2.n.b.199.26		84
9.5	odd	6		252.2.n.b.31.17	yes	84
12.11	even	2		252.2.bj.b.115.40	yes	84
21.5	even	6		252.2.n.b.187.11	yes	84
28.19	even	6		756.2.n.b.19.26		84
36.23	even	6		252.2.n.b.31.11	✓	84
36.31	odd	6		756.2.n.b.199.32		84
63.5	even	6		252.2.bj.b.103.39	yes	84
63.40	odd	6	inner	756.2.bj.b.523.4		84
84.47	odd	6		252.2.n.b.187.17	yes	84
252.103	even	6	inner	756.2.bj.b.523.3		84
252.131	odd	6		252.2.bj.b.103.40	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.11	✓	84	36.23	even	6
252.2.n.b.31.17	yes	84	9.5	odd	6
252.2.n.b.187.11	yes	84	21.5	even	6
252.2.n.b.187.17	yes	84	84.47	odd	6
252.2.bj.b.103.39	yes	84	63.5	even	6
252.2.bj.b.103.40	yes	84	252.131	odd	6
252.2.bj.b.115.39	yes	84	3.2	odd	2
252.2.bj.b.115.40	yes	84	12.11	even	2
756.2.n.b.19.26		84	28.19	even	6
756.2.n.b.19.32		84	7.5	odd	6
756.2.n.b.199.26		84	9.4	even	3
756.2.n.b.199.32		84	36.31	odd	6
756.2.bj.b.451.3		84	4.3	odd	2	inner
756.2.bj.b.451.4		84	1.1	even	1	trivial
756.2.bj.b.523.3		84	252.103	even	6	inner
756.2.bj.b.523.4		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)

\(f(q)\)	\(=\)	\(q+(-1.36675 + 0.363308i) q^{2} +(1.73601 - 0.993103i) q^{4} +(-1.43430 - 0.828095i) q^{5} +(0.375983 + 2.61890i) q^{7} +(-2.01190 + 1.98803i) q^{8} +O(q^{10})\)	\(q+(-1.36675 + 0.363308i) q^{2} +(1.73601 - 0.993103i) q^{4} +(-1.43430 - 0.828095i) q^{5} +(0.375983 + 2.61890i) q^{7} +(-2.01190 + 1.98803i) q^{8} +(2.26119 + 0.610706i) q^{10} +(2.34869 - 1.35602i) q^{11} +(-4.25755 + 2.45810i) q^{13} +(-1.46534 - 3.44279i) q^{14} +(2.02749 - 3.44808i) q^{16} +(2.86290 + 1.65289i) q^{17} +(-0.756379 - 1.31009i) q^{19} +(-3.31235 - 0.0131756i) q^{20} +(-2.71742 + 2.70664i) q^{22} +(-3.45097 - 1.99242i) q^{23} +(-1.12852 - 1.95465i) q^{25} +(4.92596 - 4.90641i) q^{26} +(3.25355 + 4.17306i) q^{28} +(-3.66717 + 6.35172i) q^{29} -6.31513 q^{31} +(-1.51836 + 5.44927i) q^{32} +(-4.51337 - 1.21898i) q^{34} +(1.62942 - 4.06764i) q^{35} +(4.46089 + 7.72649i) q^{37} +(1.50975 + 1.51576i) q^{38} +(4.53195 - 1.18540i) q^{40} +(-0.879545 + 0.507805i) q^{41} +(5.68989 + 3.28506i) q^{43} +(2.73070 - 4.68656i) q^{44} +(5.44047 + 1.46937i) q^{46} -1.95291 q^{47} +(-6.71727 + 1.96932i) q^{49} +(2.25254 + 2.26152i) q^{50} +(-4.95003 + 8.49548i) q^{52} +(-5.20840 + 9.02122i) q^{53} -4.49164 q^{55} +(-5.96289 - 4.52149i) q^{56} +(2.70447 - 10.0135i) q^{58} -6.50576 q^{59} +11.3099i q^{61} +(8.63121 - 2.29434i) q^{62} +(0.0954627 - 7.99943i) q^{64} +8.14215 q^{65} +4.23288i q^{67} +(6.61152 + 0.0262988i) q^{68} +(-0.749211 + 6.15144i) q^{70} -2.11040i q^{71} +(-4.56368 - 2.63484i) q^{73} +(-8.90403 - 8.93951i) q^{74} +(-2.61414 - 1.52317i) q^{76} +(4.43434 + 5.64115i) q^{77} -15.2086i q^{79} +(-5.76338 + 3.26663i) q^{80} +(1.01763 - 1.01359i) q^{82} +(-7.30362 + 12.6502i) q^{83} +(-2.73751 - 4.74150i) q^{85} +(-8.97016 - 2.42268i) q^{86} +(-2.02952 + 7.39744i) q^{88} +(-4.61689 + 2.66556i) q^{89} +(-8.03827 - 10.2259i) q^{91} +(-7.96961 - 0.0317009i) q^{92} +(2.66914 - 0.709507i) q^{94} +2.50541i q^{95} +(-4.20504 - 2.42778i) q^{97} +(8.46537 - 5.13201i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 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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