LMFDB - Embedded newform 756.2.bj.b.451.3

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			451.3
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36675 - 0.363308i) q^{2} +(1.73601 + 0.993103i) q^{4} +(-1.43430 - 0.828095i) q^{5} +(-0.375983 - 2.61890i) q^{7} +(-2.01190 - 1.98803i) q^{8} +O(q^{10})$	\(q+(-1.36675 - 0.363308i) q^{2} +(1.73601 + 0.993103i) q^{4} +(-1.43430 - 0.828095i) q^{5} +(-0.375983 - 2.61890i) q^{7} +(-2.01190 - 1.98803i) q^{8} +(1.65948 + 1.65289i) q^{10} +(-2.34869 + 1.35602i) q^{11} +(-4.25755 + 2.45810i) q^{13} +(-0.437592 + 3.71598i) q^{14} +(2.02749 + 3.44808i) q^{16} +(2.86290 + 1.65289i) q^{17} +(0.756379 + 1.31009i) q^{19} +(-1.66759 - 2.86199i) q^{20} +(3.70273 - 1.00004i) q^{22} +(3.45097 + 1.99242i) q^{23} +(-1.12852 - 1.95465i) q^{25} +(6.71205 - 1.81280i) q^{26} +(1.94812 - 4.91984i) q^{28} +(-3.66717 + 6.35172i) q^{29} +6.31513 q^{31} +(-1.51836 - 5.44927i) q^{32} +(-3.31236 - 3.29921i) q^{34} +(-1.62942 + 4.06764i) q^{35} +(4.46089 + 7.72649i) q^{37} +(-0.557817 - 2.06536i) q^{38} +(1.23939 + 4.51748i) q^{40} +(-0.879545 + 0.507805i) q^{41} +(-5.68989 - 3.28506i) q^{43} +(-5.42403 + 0.0215753i) q^{44} +(-3.99275 - 3.97690i) q^{46} +1.95291 q^{47} +(-6.71727 + 1.96932i) q^{49} +(0.832263 + 3.08152i) q^{50} +(-9.83231 + 0.0391102i) q^{52} +(-5.20840 + 9.02122i) q^{53} +4.49164 q^{55} +(-4.45002 + 6.01642i) q^{56} +(7.31973 - 7.34891i) q^{58} +6.50576 q^{59} +11.3099i q^{61} +(-8.63121 - 2.29434i) q^{62} +(0.0954627 + 7.99943i) q^{64} +8.14215 q^{65} -4.23288i q^{67} +(3.32854 + 5.71260i) q^{68} +(3.70482 - 4.96747i) q^{70} +2.11040i q^{71} +(-4.56368 - 2.63484i) q^{73} +(-3.28983 - 12.1809i) q^{74} +(0.0120346 + 3.02549i) q^{76} +(4.43434 + 5.64115i) q^{77} +15.2086i q^{79} +(-0.0527021 - 6.62455i) q^{80} +(1.38661 - 0.374498i) q^{82} +(7.30362 - 12.6502i) q^{83} +(-2.73751 - 4.74150i) q^{85} +(6.58318 + 6.55704i) q^{86} +(7.42113 + 1.94110i) q^{88} +(-4.61689 + 2.66556i) q^{89} +(8.03827 + 10.2259i) q^{91} +(4.01226 + 6.88603i) q^{92} +(-2.66914 - 0.709507i) q^{94} -2.50541i q^{95} +(-4.20504 - 2.42778i) q^{97} +(9.89631 - 0.251133i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$10$	1.65948	+	1.65289i	0.524774	+	0.522690i
$11$	−2.34869	+	1.35602i	−0.708157	+	0.408855i	−0.810378	−	0.585907i	$-0.800738\pi$
$11$	−2.34869	+	1.35602i	−0.708157	+	0.408855i	0.102221	+	0.994762i	$0.467405\pi$
$12$		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	$0.572116\pi$
$14$	−0.437592	+	3.71598i	−0.116952	+	0.993138i
$15$		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	0.939650	−	0.342137i	$-0.111151\pi$
$19$	0.756379	+	1.31009i	0.173525	+	0.300555i	−0.766125	+	0.642692i	$0.777818\pi$
$20$	−1.66759	−	2.86199i	−0.372884	−	0.639961i
$21$		0			0
$22$	3.70273	−	1.00004i	0.789424	−	0.213209i
$23$	3.45097	+	1.99242i	0.719577	+	0.415448i	0.814597	−	0.580028i	$-0.196958\pi$
$23$	3.45097	+	1.99242i	0.719577	+	0.415448i	−0.0950202	+	0.995475i	$0.530292\pi$
$24$		0			0
$25$	−1.12852	−	1.95465i	−0.225704	−	0.390930i
$26$	6.71205	−	1.81280i	1.31634	−	0.355520i
$27$		0			0
$28$	1.94812	−	4.91984i	0.368161	−	0.929762i
$29$	−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	$-0.308059\pi$
$31$	6.31513			1.13423			0.567116	+	0.823638i	$0.308059\pi$
$32$	−1.51836	−	5.44927i	−0.268412	−	0.963304i
$33$		0			0
$34$	−3.31236	−	3.29921i	−0.568064	−	0.565809i
$35$	−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	$0.571281\pi$
$38$	−0.557817	−	2.06536i	−0.0904898	−	0.335046i
$39$		0			0
$40$	1.23939	+	4.51748i	0.195965	+	0.714276i
$41$	−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	−0.00111731	−	0.999999i	$-0.500356\pi$
$43$	−5.68989	−	3.28506i	−0.867701	−	0.500967i	−0.866584	+	0.499032i	$0.833689\pi$
$44$	−5.42403	+	0.0215753i	−0.817703	+	0.00325260i
$45$		0			0
$46$	−3.99275	−	3.97690i	−0.588699	−	0.586362i
$47$	1.95291			0.284861			0.142430	−	0.989805i	$-0.454508\pi$
$47$	1.95291			0.284861			0.142430	+	0.989805i	$0.454508\pi$
$48$		0			0
$49$	−6.71727	+	1.96932i	−0.959611	+	0.281332i
$50$	0.832263	+	3.08152i	0.117700	+	0.435793i
$51$		0			0
$52$	−9.83231	+	0.0391102i	−1.36350	+	0.00542362i
$53$	−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
$56$	−4.45002	+	6.01642i	−0.594659	+	0.803978i
$57$		0			0
$58$	7.31973	−	7.34891i	0.961128	−	0.964959i
$59$	6.50576			0.846978			0.423489	−	0.905901i	$-0.360805\pi$
$59$	6.50576			0.846978			0.423489	+	0.905901i	$0.360805\pi$
$60$		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	$-0.916751\pi$
$67$		−	4.23288i		−	0.517128i	0.965994	−	0.258564i	$-0.0832493\pi$
$68$	3.32854	+	5.71260i	0.403644	+	0.692754i
$69$		0			0
$70$	3.70482	−	4.96747i	0.442811	−	0.593726i
$71$			2.11040i			0.250459i	0.992128	+	0.125229i	$0.0399666\pi$
$71$			2.11040i			0.250459i	−0.992128	+	0.125229i	$0.960033\pi$
$72$		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	$0.766455\pi$
$74$	−3.28983	−	12.1809i	−0.382435	−	1.41600i
$75$		0			0
$76$	0.0120346	+	3.02549i	0.00138046	+	0.347048i
$77$	4.43434	+	5.64115i	0.505340	+	0.642868i
$78$		0			0
$79$			15.2086i			1.71110i	0.517717	+	0.855552i	$0.326782\pi$
$79$			15.2086i			1.71110i	−0.517717	+	0.855552i	$0.673218\pi$
$80$	−0.0527021	−	6.62455i	−0.00589228	−	0.740647i
$81$		0			0
$82$	1.38661	−	0.374498i	0.153125	−	0.0413564i
$83$	7.30362	−	12.6502i	0.801676	−	1.38854i	−0.116836	−	0.993151i	$-0.537275\pi$
$83$	7.30362	−	12.6502i	0.801676	−	1.38854i	0.918512	−	0.395393i	$-0.129391\pi$
$84$		0			0
$85$	−2.73751	−	4.74150i	−0.296924	−	0.514288i
$86$	6.58318	+	6.55704i	0.709882	+	0.707064i
$87$		0			0
$88$	7.42113	+	1.94110i	0.791095	+	0.206922i
$89$	−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
$92$	4.01226	+	6.88603i	0.418307	+	0.717918i
$93$		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	$0.745948\pi$
$98$	9.89631	−	0.251133i	0.999678	−	0.0253683i
$99$		0			0
$100$	−0.0179556	−	4.51404i	−0.00179556	−	0.451404i
$101$	−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	−0.824068	−	0.566490i	$-0.808301\pi$
$103$	0.797304	−	1.38097i	0.0785607	−	0.136071i	0.902629	+	0.430419i	$0.141634\pi$
$104$	13.4525	+	3.51870i	1.31913	+	0.345037i
$105$		0			0
$106$	10.3961	−	10.4375i	1.00976	−	1.01378i
$107$	−4.75730	+	2.74663i	−0.459906	+	0.265527i	−0.712005	−	0.702175i	$-0.752213\pi$
$107$	−4.75730	+	2.74663i	−0.459906	+	0.265527i	0.252099	+	0.967701i	$0.418879\pi$
$108$		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
$112$	8.26788	−	6.60622i	0.781241	−	0.624230i
$113$	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
$116$	−12.6742	+	7.38481i	−1.17677	+	0.685662i
$117$		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	$0.120735\pi$
$127$			8.34549i			0.740543i	−0.928924	+	0.370271i	$0.879265\pi$
$128$	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	$0.435975\pi$
$131$	−8.56896	+	14.8419i	−0.748673	+	1.29674i	−0.948459	+	0.316900i	$0.897358\pi$
$132$		0			0
$133$	3.14660	−	2.47345i	0.272845	−	0.214475i
$134$	−1.53784	+	5.78529i	−0.132849	+	0.499773i
$135$		0			0
$136$	−2.47385	−	9.01698i	−0.212131	−	0.773200i
$137$	−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	$-0.994682\pi$
$139$	−6.06467	−	10.5043i	−0.514399	−	0.890965i	0.485462	−	0.874258i	$-0.338651\pi$
$140$	−6.86829	+	5.44330i	−0.580477	+	0.460043i
$141$		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
$146$	5.28016	+	5.25920i	0.436989	+	0.435254i
$147$		0			0
$148$	0.0709763	+	17.8434i	0.00583422	+	1.46672i
$149$	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	−0.960097	−	0.279669i	$-0.909775\pi$
$151$	−14.7206	+	8.49894i	−1.19794	+	0.691634i	−0.237848	+	0.971302i	$0.576442\pi$
$152$	1.08274	−	4.13947i	0.0878216	−	0.335755i
$153$		0			0
$154$	−4.01116	−	9.32107i	−0.323229	−	0.751113i
$155$	−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
$160$	−2.33472	+	9.07325i	−0.184576	+	0.717304i
$161$	3.92044	−	9.78686i	0.308974	−	0.771312i
$162$		0			0
$163$	−5.13064	+	2.96218i	−0.401863	+	0.232015i	−0.687287	−	0.726386i	$-0.741199\pi$
$163$	−5.13064	+	2.96218i	−0.401863	+	0.232015i	0.285425	+	0.958401i	$0.407865\pi$
$164$	−2.03121	+	0.00807958i	−0.158610	+	0.000630909i
$165$		0			0
$166$	−14.5782	+	14.6363i	−1.13148	+	1.13599i
$167$	−8.25628	−	14.3003i	−0.638890	−	1.10659i	−0.985677	−	0.168646i	$-0.946061\pi$
$167$	−8.25628	−	14.3003i	−0.638890	−	1.10659i	0.346787	−	0.937944i	$-0.387273\pi$
$168$		0			0
$169$	5.58448	−	9.67261i	0.429576	−	0.744047i
$170$	2.01886	+	7.47500i	0.154840	+	0.573307i
$171$		0			0
$172$	−6.61534	−	11.3536i	−0.504415	−	0.865701i
$173$		−	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
$176$	−9.43762	−	5.34916i	−0.711387	−	0.403208i
$177$		0			0
$178$	7.27856	−	1.96581i	0.545551	−	0.147343i
$179$	−15.1520	−	8.74799i	−1.13251	−	0.653855i	−0.187945	−	0.982180i	$-0.560183\pi$
$179$	−15.1520	−	8.74799i	−1.13251	−	0.653855i	−0.944565	+	0.328324i	$0.893516\pi$
$180$		0			0
$181$		−	9.17571i		−	0.682025i	−0.940059	−	0.341013i	$-0.889230\pi$
$181$		−	9.17571i		−	0.682025i	0.940059	−	0.341013i	$-0.110770\pi$
$182$	−7.27117	−	16.8966i	−0.538975	−	1.25246i
$183$		0			0
$184$	−2.98201	−	10.8692i	−0.219836	−	0.801286i
$185$		−	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	$-0.991406\pi$
$191$		−	0.746176i		−	0.0539914i	0.999636	−	0.0269957i	$-0.00859404\pi$
$192$		0			0
$193$	5.27175			0.379469			0.189734	−	0.981835i	$-0.439237\pi$
$193$	5.27175			0.379469			0.189734	+	0.981835i	$0.439237\pi$
$194$	4.86521	+	4.84590i	0.349302	+	0.347915i
$195$		0			0
$196$	−13.6170	−	3.25217i	−0.972645	−	0.232298i
$197$	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	−0.636944	−	0.770910i	$-0.719802\pi$
$199$	4.92545	−	8.53113i	0.349156	−	0.604756i	0.986100	+	0.166154i	$0.0531350\pi$
$200$	−1.61544	+	6.17609i	−0.114229	+	0.436715i
$201$		0			0
$202$	3.85040	−	1.03992i	0.270913	−	0.0731687i
$203$	18.0133	+	7.21581i	1.26429	+	0.506450i
$204$		0			0
$205$	1.68204			0.117479
$206$	−1.59143	+	1.59778i	−0.110880	+	0.111322i
$207$		0			0
$208$	−17.1079	−	9.69660i	−1.18622	−	0.672338i
$209$	−3.55300	−	2.05133i	−0.245766	−	0.141893i
$210$		0			0
$211$	20.4282	−	11.7942i	1.40633	−	0.811946i	0.411300	−	0.911500i	$-0.365075\pi$
$211$	20.4282	−	11.7942i	1.40633	−	0.811946i	0.995032	+	0.0995535i	$0.0317414\pi$
$212$	−18.0009	+	10.4885i	−1.23630	+	0.720352i
$213$		0			0
$214$	7.49992	−	2.02559i	0.512684	−	0.138467i
$215$	5.44069	+	9.42354i	0.371052	+	0.642680i
$216$		0			0
$217$	−2.37438	−	16.5387i	−0.161183	−	1.12272i
$218$	13.5967	−	13.6508i	0.920882	−	0.924552i
$219$		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	−0.775462	−	0.631394i	$-0.782483\pi$
$223$	2.37545	−	4.11440i	0.159072	−	0.275520i	0.934534	+	0.355873i	$0.115817\pi$
$224$	−13.7002	+	6.02528i	−0.915384	+	0.402581i
$225$		0			0
$226$	−0.192600	−	0.713117i	−0.0128116	−	0.0474358i
$227$	13.8419	+	23.9749i	0.918720	+	1.59127i	0.801361	+	0.598180i	$0.204109\pi$
$227$	13.8419	+	23.9749i	0.918720	+	1.59127i	0.117359	+	0.993090i	$0.462557\pi$
$228$		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	$0.558130\pi$
$230$	2.43356	+	9.01046i	0.160464	+	0.594132i
$231$		0			0
$232$	20.0054	−	5.48856i	1.31342	−	0.360342i
$233$	−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
$238$	−7.39490	+	9.91517i	−0.479340	+	0.642705i
$239$	−21.6423	+	12.4952i	−1.39992	+	0.808246i	−0.994384	−	0.105831i	$-0.966250\pi$
$239$	−21.6423	+	12.4952i	−1.39992	+	0.808246i	−0.405540	+	0.914077i	$0.632916\pi$
$240$		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	$0.442508\pi$
$242$	3.63761	−	3.65211i	0.233835	−	0.234767i
$243$		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	$-0.546274\pi$
$251$	−4.59012			−0.289726			−0.144863	+	0.989452i	$0.546274\pi$
$252$		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
$262$	17.1038	−	17.1720i	1.05668	−	1.06089i
$263$	−5.13861	+	2.96678i	−0.316860	+	0.182939i	−0.649992	−	0.759941i	$-0.725228\pi$
$263$	−5.13861	+	2.96678i	−0.316860	+	0.182939i	0.333132	+	0.942880i	$0.391895\pi$
$264$		0			0
$265$	14.9408	−	8.62610i	0.917809	−	0.529897i
$266$	−5.19924	+	2.23741i	−0.318786	+	0.137184i
$267$		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	0.745266	−	0.666767i	$-0.232322\pi$
$271$	−3.37150	−	5.83961i	−0.204804	−	0.354731i	−0.950070	+	0.312036i	$0.898989\pi$
$272$	0.105194	+	13.2227i	0.00637835	+	0.801746i
$273$		0			0
$274$	0.0552561	+	0.204590i	0.00333814	+	0.0123597i
$275$	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	$0.765300\pi$
$278$	4.47259	+	16.5601i	0.268248	+	0.993210i
$279$		0			0
$280$	11.3648	−	4.94433i	0.679179	−	0.295480i
$281$	−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	$-0.768076\pi$
$283$	−25.1027			−1.49220			−0.746101	+	0.665833i	$0.768076\pi$
$284$	−2.09584	+	3.66369i	−0.124366	+	0.217400i
$285$		0			0
$286$	−13.3063	+	13.3594i	−0.786821	+	0.789957i
$287$	1.66058	+	2.11251i	0.0980212	+	0.124698i
$288$		0			0
$289$	−3.03589	−	5.25831i	−0.178581	−	0.309312i
$290$	−16.5843	+	4.47912i	−0.973864	+	0.263023i
$291$		0			0
$292$	−5.30595	−	9.10633i	−0.310507	−	0.532908i
$293$	−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
$296$	6.38565	−	24.4133i	0.371159	−	1.41899i
$297$		0			0
$298$	−16.5194	+	16.5853i	−0.956945	+	0.960759i
$299$	−19.5902			−1.13293
$300$		0			0
$301$	−6.46395	+	16.1364i	−0.372576	+	0.930086i
$302$	23.2071	−	6.26782i	1.33542	−	0.360673i
$303$		0			0
$304$	−2.98373	+	5.26425i	−0.171129	+	0.301926i
$305$	9.36568	−	16.2218i	0.536277	−	0.928860i
$306$		0			0
$307$	28.7340			1.63993			0.819967	−	0.572410i	$-0.193992\pi$
$307$	28.7340			1.63993			0.819967	+	0.572410i	$0.193992\pi$
$308$	2.09584	+	14.1969i	0.119422	+	0.808942i
$309$		0			0
$310$	10.4798	+	10.4382i	0.595215	+	0.592852i
$311$	10.2429			0.580824			0.290412	−	0.956902i	$-0.406208\pi$
$311$	10.2429			0.580824			0.290412	+	0.956902i	$0.406208\pi$
$312$		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
$320$	6.48736	−	11.5527i	0.362655	−	0.645813i
$321$		0			0
$322$	−8.91390	+	11.9519i	−0.496752	+	0.666051i
$323$			5.00086i			0.278255i
$324$		0			0
$325$	9.60944	+	5.54801i	0.533036	+	0.307748i
$326$	8.08848	−	2.18455i	0.447980	−	0.120991i
$327$		0			0
$328$	2.77909	+	0.726910i	0.153449	+	0.0401369i
$329$	−0.734259	−	5.11447i	−0.0404810	−	0.281970i
$330$		0			0
$331$			13.9762i			0.768202i	0.923291	+	0.384101i	$0.125489\pi$
$331$			13.9762i			0.768202i	−0.923291	+	0.384101i	$0.874511\pi$
$332$	25.2422	−	14.7078i	1.38534	−	0.807193i
$333$		0			0
$334$	6.08886	+	22.5445i	0.333168	+	1.23358i
$335$	−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	$0.680377\pi$
$338$	−11.1467	+	11.1912i	−0.606302	+	0.608719i
$339$		0			0
$340$	−0.0435559	−	10.9499i	−0.00236215	−	0.593844i
$341$	−14.8323	+	8.56343i	−0.803214	+	0.463736i
$342$		0			0
$343$	7.68303	+	16.8514i	0.414845	+	0.909892i
$344$	4.91668	+	17.9209i	0.265090	+	0.966230i
$345$		0			0
$346$	−5.89449	+	22.1749i	−0.316890	+	1.19213i
$347$		−	17.6139i		−	0.945561i	−0.881180	−	0.472781i	$-0.843250\pi$
$347$		−	17.6139i		−	0.945561i	0.881180	−	0.472781i	$-0.156750\pi$
$348$		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	$0.399813\pi$
$350$	7.75727	−	3.33821i	0.414644	−	0.178435i
$351$		0			0
$352$	10.9555	+	10.7397i	0.583929	+	0.572429i
$353$	−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
$356$	−10.6622	+	0.0424112i	−0.565094	+	0.00224779i
$357$		0			0
$358$	17.5307	+	17.4611i	0.926528	+	0.922850i
$359$	−9.00180	+	5.19719i	−0.475097	+	0.274297i	−0.718371	−	0.695660i	$-0.755112\pi$
$359$	−9.00180	+	5.19719i	−0.475097	+	0.274297i	0.243274	+	0.969958i	$0.421779\pi$
$360$		0			0
$361$	8.35578	−	14.4726i	0.439778	−	0.761718i
$362$	−3.33361	+	12.5409i	−0.175211	+	0.659136i
$363$		0			0
$364$	3.79920	+	25.7351i	0.199132	+	1.34889i
$365$	4.36380	+	7.55833i	0.228412	+	0.395621i
$366$		0			0
$367$	6.21836	+	10.7705i	0.324596	+	0.562216i	0.981430	−	0.191818i	$-0.0614385\pi$
$367$	6.21836	+	10.7705i	0.324596	+	0.562216i	−0.656835	+	0.754034i	$0.728105\pi$
$368$	0.126803	+	15.9388i	0.00661005	+	0.830869i
$369$		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	$-0.954928\pi$
$379$		−	5.49479i		−	0.282248i	0.989992	−	0.141124i	$-0.0450717\pi$
$380$	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	$-0.557097\pi$
$383$	14.9307	−	25.8607i	0.762923	−	1.32142i	0.941338	−	0.337466i	$-0.109570\pi$
$384$		0			0
$385$	−1.68878	−	11.7632i	−0.0860682	−	0.599506i
$386$	−7.20517	−	1.91527i	−0.366733	−	0.0974846i
$387$		0			0
$388$	−4.88898	−	8.39070i	−0.248200	−	0.425973i
$389$	−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
$392$	17.4295	+	9.39208i	0.880325	+	0.474372i
$393$		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	$0.180884\pi$
$398$	−9.83129	+	9.87047i	−0.492798	+	0.494762i
$399$		0			0
$400$	4.45173	−	7.85427i	0.222586	−	0.392713i
$401$	−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
$404$	−5.64035	+	0.0224358i	−0.280618	+	0.00111622i
$405$		0			0
$406$	−21.9981	−	16.4066i	−1.09175	−	0.814245i
$407$	−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
$412$	2.75558	−	1.60558i	0.135758	−	0.0791013i
$413$	−2.44605	−	17.0379i	−0.120362	−	0.838382i
$414$		0			0
$415$	−20.9512	+	12.0962i	−1.02845	+	0.593778i
$416$	19.8594	+	19.4683i	0.973685	+	0.954510i
$417$		0			0
$418$	4.11080	+	4.09448i	0.201066	+	0.200268i
$419$	−1.19685	−	2.07300i	−0.0584698	−	0.101273i	0.835309	−	0.549781i	$-0.185289\pi$
$419$	−1.19685	−	2.07300i	−0.0584698	−	0.101273i	−0.893779	+	0.448508i	$0.851955\pi$
$420$		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	$0.217631\pi$
$422$	−32.2051	+	8.69802i	−1.56772	+	0.423413i
$423$		0			0
$424$	28.4132	−	7.79530i	1.37987	−	0.378573i
$425$		−	7.46128i		−	0.361925i
$426$		0			0
$427$	29.6195	−	4.25233i	1.43339	−	0.205785i
$428$	−10.9864	+	0.0437010i	−0.531049	+	0.00211237i
$429$		0			0
$430$	−4.01241	−	14.8563i	−0.193496	−	0.716433i
$431$	19.2653	+	11.1228i	0.927978	+	0.535768i	0.886172	−	0.463357i	$-0.153355\pi$
$431$	19.2653	+	11.1228i	0.927978	+	0.535768i	0.0418066	+	0.999126i	$0.486689\pi$
$432$		0			0
$433$		−	5.03561i		−	0.241996i	−0.992653	−	0.120998i	$-0.961391\pi$
$433$		−	5.03561i		−	0.241996i	0.992653	−	0.120998i	$-0.0386094\pi$
$434$	−2.76346	+	23.4669i	−0.132650	+	1.12645i
$435$		0			0
$436$	−23.5427	+	13.7175i	−1.12749	+	0.656951i
$437$			6.02809i			0.288363i
$438$		0			0
$439$	16.4591			0.785551			0.392776	−	0.919634i	$-0.371515\pi$
$439$	16.4591			0.785551			0.392776	+	0.919634i	$0.371515\pi$
$440$	−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	$0.219772\pi$
$443$			26.8092i			1.27374i	−0.770969	+	0.636872i	$0.780228\pi$
$444$		0			0
$445$	8.82935			0.418551
$446$	−4.74144	+	4.76034i	−0.224514	+	0.225408i
$447$		0			0
$448$	20.9138	−	3.25765i	0.988085	−	0.153910i
$449$	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
$452$	0.00415524	+	1.04463i	0.000195446	+	0.0491351i
$453$		0			0
$454$	−10.2082	−	37.7966i	−0.479093	−	1.77388i
$455$	−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	$0.431079\pi$
$458$	−10.1412	−	10.1009i	−0.473867	−	0.471986i
$459$		0			0
$460$	−0.0525027	−	13.1992i	−0.00244795	−	0.615415i
$461$	−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	−0.693610	−	0.720351i	$-0.743981\pi$
$463$	−8.96359	+	5.17513i	−0.416573	+	0.240509i	0.277037	+	0.960859i	$0.410648\pi$
$464$	−29.3364	+	0.233388i	−1.36191	+	0.0108348i
$465$		0			0
$466$	4.97886	+	18.4346i	0.230641	+	0.853968i
$467$	2.05702	+	3.56287i	0.0951876	+	0.164870i	0.909687	−	0.415295i	$-0.136322\pi$
$467$	2.05702	+	3.56287i	0.0951876	+	0.164870i	−0.814499	+	0.580165i	$0.802988\pi$
$468$		0			0
$469$	−11.0855	+	1.59149i	−0.511880	+	0.0734881i
$470$	3.24081	+	3.22795i	0.149488	+	0.148894i
$471$		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
$476$	13.7092	−	10.8649i	0.628362	−	0.497994i
$477$		0			0
$478$	34.1192	−	9.21499i	1.56058	−	0.421484i
$479$	−4.35898	−	7.54998i	−0.199167	−	0.344967i	0.749092	−	0.662466i	$-0.230490\pi$
$479$	−4.35898	−	7.54998i	−0.199167	−	0.344967i	−0.948259	+	0.317499i	$0.897157\pi$
$480$		0			0
$481$	−37.9849	−	21.9306i	−1.73196	−	0.999950i
$482$	14.2556	−	3.85019i	0.649326	−	0.175371i
$483$		0			0
$484$	−6.29855	+	3.66995i	−0.286298	+	0.166816i
$485$	4.02087	+	6.96434i	0.182578	+	0.316235i
$486$		0			0
$487$	−29.6495	−	17.1181i	−1.34355	−	0.775697i	−0.356221	−	0.934402i	$-0.615935\pi$
$487$	−29.6495	−	17.1181i	−1.34355	−	0.775697i	−0.987326	+	0.158704i	$0.949268\pi$
$488$	22.4845	−	22.7544i	1.01782	−	1.03004i
$489$		0			0
$490$	−14.4023	−	7.83488i	−0.650628	−	0.353944i
$491$	−34.6007	+	19.9767i	−1.56151	+	0.901537i	−0.564403	+	0.825499i	$0.690894\pi$
$491$	−34.6007	+	19.9767i	−1.56151	+	0.901537i	−0.997105	+	0.0760381i	$0.975773\pi$
$492$		0			0
$493$	−20.9974	+	12.1229i	−0.945677	+	0.545987i
$494$	7.45179	+	7.42221i	0.335272	+	0.333941i
$495$		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	0.770645	−	0.637265i	$-0.219934\pi$
$499$	13.4941	+	7.79083i	0.604080	+	0.348766i	−0.166565	+	0.986030i	$0.553268\pi$
$500$	−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	$-0.435417\pi$
$503$	9.03852			0.403008			0.201504	+	0.979488i	$0.435417\pi$
$504$		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
$514$	−26.2577	−	26.1534i	−1.15818	−	1.15358i
$515$	−2.28715	+	1.32049i	−0.100784	+	0.0581876i
$516$		0			0
$517$	−4.58678	+	2.64818i	−0.201726	+	0.116467i
$518$	−30.6636	+	13.1955i	−1.34728	+	0.579779i
$519$		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	0.965492	−	0.260433i	$-0.0838654\pi$
$523$	5.88205	+	10.1880i	0.257204	+	0.445490i	−0.708288	+	0.705924i	$0.750532\pi$
$524$	−29.6153	+	17.2558i	−1.29375	+	0.753825i
$525$		0			0
$526$	8.10106	−	2.18795i	0.353223	−	0.0953991i
$527$	18.0796	+	10.4382i	0.787558	+	0.454697i
$528$		0			0
$529$	−3.56054	−	6.16704i	−0.154806	−	0.268132i
$530$	−23.5543	+	6.36160i	−1.02314	+	0.276330i
$531$		0			0
$532$	7.91894	−	1.16905i	0.343329	−	0.0506847i
$533$	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
$538$	−1.73200	−	1.72512i	−0.0746718	−	0.0743754i
$539$	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	$0.731450\pi$
$542$	2.48643	+	9.20619i	0.106801	+	0.395440i
$543$		0			0
$544$	4.66015	−	18.1104i	0.199802	−	0.776477i
$545$	19.5406	−	11.2818i	0.837028	−	0.483258i
$546$		0			0
$547$	−28.3730	−	16.3812i	−1.21314	−	0.700408i	−0.249699	−	0.968323i	$-0.580332\pi$
$547$	−28.3730	−	16.3812i	−1.21314	−	0.700408i	−0.963442	+	0.267916i	$0.913665\pi$
$548$	−0.00119212	−	0.299699i	−5.09248e−5	−	0.0128025i
$549$		0			0
$550$	−6.13332	−	6.10897i	−0.261526	−	0.260487i
$551$	−11.0951			−0.472666
$552$		0			0
$553$	39.8299	−	5.71818i	1.69374	−	0.243162i
$554$	−2.60348	−	9.63961i	−0.110611	−	0.409548i
$555$		0			0
$556$	−0.0964937	−	24.2585i	−0.00409224	−	1.02879i
$557$	−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
$560$	−17.3292	+	2.62874i	−0.732293	+	0.111084i
$561$		0			0
$562$	1.62671	−	1.63319i	0.0686184	−	0.0688919i
$563$	−30.9832			−1.30579			−0.652893	−	0.757450i	$-0.726445\pi$
$563$	−30.9832			−1.30579			−0.652893	+	0.757450i	$0.726445\pi$
$564$		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	$0.0684678\pi$
$571$			10.2007i			0.426886i	−0.976955	+	0.213443i	$0.931532\pi$
$572$	23.0400	−	13.4246i	0.963352	−	0.561312i
$573$		0			0
$574$	−1.50211	−	3.49058i	−0.0626970	−	0.145694i
$575$		−	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	$0.428998\pi$
$578$	2.23891	+	8.28976i	0.0931265	+	0.344808i
$579$		0			0
$580$	24.2939	−	0.0966345i	1.00875	−	0.00401253i
$581$	−35.8757	−	14.3712i	−1.48838	−	0.596217i
$582$		0			0
$583$		−	28.2507i		−	1.17003i
$584$	3.94351	+	14.3738i	0.163184	+	0.594791i
$585$		0			0
$586$	28.1458	−	7.60167i	1.16269	−	0.314022i
$587$	17.3247	−	30.0073i	0.715067	−	1.23853i	−0.247867	−	0.968794i	$-0.579729\pi$
$587$	17.3247	−	30.0073i	0.715067	−	1.23853i	0.962934	−	0.269738i	$-0.0869372\pi$
$588$		0			0
$589$	4.77664	+	8.27338i	0.196818	+	0.340898i
$590$	10.7962	+	10.7533i	0.444472	+	0.442707i
$591$		0			0
$592$	−17.5971	+	31.0470i	−0.723238	+	1.27602i
$593$	−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
$596$	28.6035	−	16.6663i	1.17165	−	0.682678i
$597$		0			0
$598$	26.7750	+	7.11728i	1.09491	+	0.291047i
$599$			23.2794i			0.951171i	0.879669	+	0.475586i	$0.157764\pi$
$599$			23.2794i			0.951171i	−0.879669	+	0.475586i	$0.842236\pi$
$600$		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	$0.978306\pi$
$602$	14.6971	−	19.7060i	0.599008	−	0.803157i
$603$		0			0
$604$	−33.9955	+	0.135225i	−1.38326	+	0.00550222i
$605$	5.22785	−	3.01830i	0.212542	−	0.122711i
$606$		0			0
$607$	−2.67342	+	4.63049i	−0.108511	+	0.187946i	−0.915167	−	0.403075i	$-0.867941\pi$
$607$	−2.67342	+	4.63049i	−0.108511	+	0.187946i	0.806656	+	0.591021i	$0.201275\pi$
$608$	5.99056	−	6.11091i	0.242949	−	0.247830i
$609$		0			0
$610$	−18.6941	+	18.7686i	−0.756901	+	0.759917i
$611$	−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
$616$	2.29334	−	20.1650i	0.0924013	−	0.812472i
$617$	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	0.901965	−	0.431809i	$-0.142125\pi$
$619$	1.91636	+	3.31923i	0.0770249	+	0.133411i	−0.824940	+	0.565220i	$0.808791\pi$
$620$	−10.5310	−	18.0739i	−0.422937	−	0.725864i
$621$		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	$-0.785705\pi$
$631$		−	31.3249i		−	1.24703i	0.781813	−	0.623513i	$-0.214295\pi$
$632$	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
$640$	−13.0638	+	13.4327i	−0.516391	+	0.530974i
$641$	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	0.685334	−	0.728228i	$-0.259656\pi$
$643$	−7.30287	−	12.6489i	−0.287997	−	0.498826i	−0.973332	+	0.229403i	$0.926323\pi$
$644$	16.5253	−	13.0967i	0.651188	−	0.516083i
$645$		0			0
$646$	1.81685	−	6.83492i	0.0714830	−	0.268917i
$647$	−16.1015	+	27.8887i	−0.633017	+	1.09642i	0.353915	+	0.935278i	$0.384850\pi$
$647$	−16.1015	+	27.8887i	−0.633017	+	1.09642i	−0.986932	+	0.161140i	$0.948483\pi$
$648$		0			0
$649$	−15.2800	+	8.82192i	−0.599793	+	0.346291i
$650$	−11.1181	−	11.0739i	−0.436087	−	0.434356i
$651$		0			0
$652$	−11.8486	+	0.0471305i	−0.464027	+	0.00184577i
$653$	−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
$656$	−3.53423	−	2.00317i	−0.137988	−	0.0782106i
$657$		0			0
$658$	−0.854578	+	7.25697i	−0.0333149	+	0.282906i
$659$	0.326746	+	0.188647i	0.0127282	+	0.00734865i	0.506351	−	0.862328i	$-0.330994\pi$
$659$	0.326746	+	0.188647i	0.0127282	+	0.00734865i	−0.493622	+	0.869676i	$0.664327\pi$
$660$		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
$664$	−39.8432	+	10.9312i	−1.54622	+	0.424211i
$665$	−6.56143	+	0.941992i	−0.254441	+	0.0365289i
$666$		0			0
$667$	−25.3106	+	14.6131i	−0.980029	+	0.565820i
$668$	−0.131364	−	33.0248i	−0.00508262	−	1.27777i
$669$		0			0
$670$	6.99649	−	7.02438i	0.270298	−	0.271375i
$671$	−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	$0.944833\pi$
$674$	−6.25807	−	23.1710i	−0.241052	−	0.892513i
$675$		0			0
$676$	19.3006	−	11.2458i	0.742332	−	0.432532i
$677$			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
$680$	−3.91867	+	14.9817i	−0.150274	+	0.574520i
$681$		0			0
$682$	23.3832	−	6.31538i	0.895389	−	0.241829i
$683$	−1.57689	−	0.910416i	−0.0603379	−	0.0348361i	0.469528	−	0.882918i	$-0.344424\pi$
$683$	−1.57689	−	0.910416i	−0.0603379	−	0.0348361i	−0.529865	+	0.848082i	$0.677758\pi$
$684$		0			0
$685$			0.248181i			0.00948251i
$686$	−4.37853	−	25.8230i	−0.167173	−	0.985928i
$687$		0			0
$688$	−0.209070	−	26.2797i	−0.00797072	−	1.00190i
$689$		−	51.2110i		−	1.95098i
$690$		0			0
$691$	2.82516			0.107474			0.0537371	−	0.998555i	$-0.482887\pi$
$691$	2.82516			0.107474			0.0537371	+	0.998555i	$0.482887\pi$
$692$	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
$698$	−27.8361	−	27.7256i	−1.05361	−	1.04943i
$699$		0			0
$700$	−11.8151	+	1.74422i	−0.446567	+	0.0659254i
$701$	−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
$704$	−11.0716	−	18.6587i	−0.417276	−	0.703228i
$705$		0			0
$706$	27.7637	−	7.49848i	1.04490	−	0.282209i
$707$	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	$0.388818\pi$
$710$	−3.48827	+	3.50217i	−0.130912	+	0.131434i
$711$		0			0
$712$	14.5879	+	3.81568i	0.546706	+	0.142999i
$713$	21.7933	+	12.5824i	0.816167	+	0.471214i
$714$		0			0
$715$	−19.1234	+	11.0409i	−0.715174	+	0.412906i
$716$	−17.6164	−	30.2341i	−0.658355	−	1.12990i
$717$		0			0
$718$	14.1914	−	3.83284i	0.529618	−	0.143040i
$719$	−0.946279	−	1.63900i	−0.0352903	−	0.0611245i	0.847841	−	0.530251i	$-0.177902\pi$
$719$	−0.946279	−	1.63900i	−0.0352903	−	0.0611245i	−0.883131	+	0.469126i	$0.844569\pi$
$720$		0			0
$721$	−3.91640	−	1.56884i	−0.145854	−	0.0584266i
$722$	−16.6783	+	16.7448i	−0.620702	+	0.623176i
$723$		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	$-0.622035\pi$
$727$	16.6125	−	28.7738i	0.616125	−	1.06716i	0.990186	−	0.139756i	$-0.0446317\pi$
$728$	4.15721	−	36.5538i	0.154077	−	1.35477i
$729$		0			0
$730$	−3.21823	−	11.9157i	−0.119112	−	0.441022i
$731$	−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	$0.714741\pi$
$734$	−4.58593	−	16.9798i	−0.169270	−	0.626735i
$735$		0			0
$736$	5.61740	−	21.8305i	0.207060	−	0.804682i
$737$	5.73985	+	9.94172i	0.211430	+	0.366208i
$738$		0			0
$739$	4.33522	+	2.50294i	0.159474	+	0.0920722i	0.577613	−	0.816311i	$-0.303984\pi$
$739$	4.33522	+	2.50294i	0.159474	+	0.0920722i	−0.418139	+	0.908383i	$0.637318\pi$
$740$	14.6743	−	25.6517i	0.539436	−	0.942973i
$741$		0			0
$742$	−31.2435	−	23.3019i	−1.14699	−	0.855441i
$743$	23.9292	−	13.8155i	0.877877	−	0.506842i	0.00791898	−	0.999969i	$-0.497479\pi$
$743$	23.9292	−	13.8155i	0.877877	−	0.506842i	0.869958	+	0.493126i	$0.164146\pi$
$744$		0			0
$745$	−23.7411	+	13.7069i	−0.869807	+	0.502184i
$746$	7.03440	−	7.06243i	0.257548	−	0.258574i
$747$		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	−0.115176	−	0.993345i	$-0.536743\pi$
$751$	−28.3094	−	16.3445i	−1.03303	−	0.596418i	−0.917850	+	0.396927i	$0.870077\pi$
$752$	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
$766$	−29.8020	+	29.9207i	−1.07679	+	1.08108i
$767$	−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	$0.999164\pi$
$770$	−1.96551	+	16.6909i	−0.0708320	+	0.601497i
$771$		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
$776$	3.63360	+	13.2442i	0.130439	+	0.475439i
$777$		0			0
$778$	1.37149	+	5.07804i	0.0491702	+	0.182057i
$779$	−1.33054	−	0.768187i	−0.0476715	−	0.0275231i
$780$		0			0
$781$	−2.86174	−	4.95668i	−0.102401	−	0.177364i
$782$	−4.85744	−	17.9851i	−0.173702	−	0.643144i
$783$		0			0
$784$	−20.4096	−	19.1689i	−0.728915	−	0.684604i
$785$	−12.5149	+	21.6765i	−0.446677	+	0.773667i
$786$		0			0
$787$	−1.22833			−0.0437851			−0.0218926	−	0.999760i	$-0.506969\pi$
$787$	−1.22833			−0.0437851			−0.0218926	+	0.999760i	$0.506969\pi$
$788$	22.5670	+	12.9096i	0.803915	+	0.459887i
$789$		0			0
$790$	−25.1382	+	25.2384i	−0.894378	+	0.897942i
$791$	1.08644	−	0.854020i	0.0386294	−	0.0303655i
$792$		0			0
$793$	−27.8009	−	48.1525i	−0.987238	−	1.70995i
$794$	−25.0724	+	6.77161i	−0.889788	+	0.240316i
$795$		0			0
$796$	17.0229	−	9.91869i	0.603362	−	0.351559i
$797$	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
$800$	−8.93792	+	9.11747i	−0.316003	+	0.322351i
$801$		0			0
$802$	23.9833	−	24.0789i	0.846880	−	0.850255i
$803$	14.2916			0.504339
$804$		0			0
$805$	−13.7275	+	10.7908i	−0.483832	+	0.380326i
$806$	42.3875	−	11.4481i	1.49304	−	0.403242i
$807$		0			0
$808$	7.71710	+	2.01852i	0.271487	+	0.0710112i
$809$	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	$-0.571575\pi$
$811$	−12.6994			−0.445938			−0.222969	+	0.974826i	$0.571575\pi$
$812$	24.1053	+	30.4158i	0.845931	+	1.06739i
$813$		0			0
$814$	24.2443	+	24.1480i	0.849761	+	0.846388i
$815$	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	$0.212008\pi$
$823$			35.4514i			1.23576i	−0.786274	+	0.617878i	$0.787992\pi$
$824$	−4.34951	+	1.19331i	−0.151522	+	0.0415708i
$825$		0			0
$826$	−2.84687	+	24.1753i	−0.0990553	+	0.841165i
$827$		−	51.5618i		−	1.79298i	−0.443064	−	0.896490i	$-0.646109\pi$
$827$		−	51.5618i		−	1.79298i	0.443064	−	0.896490i	$-0.353891\pi$
$828$		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	$0.418517\pi$
$830$	33.0297	−	8.92072i	1.14648	−	0.309643i
$831$		0			0
$832$	−20.0698	−	33.8233i	−0.695796	−	1.17261i
$833$	−22.4859	−	5.46498i	−0.779091	−	0.189350i
$834$		0			0
$835$			27.3479i			0.946414i
$836$	−4.13089	−	7.08963i	−0.142870	−	0.245200i
$837$		0			0
$838$	0.882654	+	3.26810i	0.0304908	+	0.112895i
$839$	−3.71303	+	6.43115i	−0.128188	+	0.222028i	−0.922975	−	0.384861i	$-0.874249\pi$
$839$	−3.71303	+	6.43115i	−0.128188	+	0.222028i	0.794787	+	0.606889i	$0.207583\pi$
$840$		0			0
$841$	−12.3962	−	21.4709i	−0.427456	−	0.740375i
$842$	6.52931	−	6.55533i	0.225015	−	0.225912i
$843$		0			0
$844$	47.1764	−	0.187655i	1.62388	−	0.00645935i
$845$	−16.0197	+	9.24896i	−0.551093	+	0.318174i
$846$		0			0
$847$	8.95189	+	3.58597i	0.307591	+	0.123215i
$848$	−41.6659	+	0.331476i	−1.43081	+	0.0113829i
$849$		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	$0.610565\pi$
$854$	−42.0274	−	4.94913i	−1.43815	−	0.169356i
$855$		0			0
$856$	15.0316	+	3.93173i	0.513769	+	0.134384i
$857$	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	$0.371368\pi$
$859$	−17.5755	+	30.4417i	−0.599670	+	1.03866i	−0.992870	+	0.119205i	$0.961965\pi$
$860$	0.0865656	+	21.7626i	0.00295186	+	0.742098i
$861$		0			0
$862$	−22.2899	−	22.2014i	−0.759196	−	0.756183i
$863$	13.3132	−	7.68639i	0.453187	−	0.261648i	−0.255988	−	0.966680i	$-0.582401\pi$
$863$	13.3132	−	7.68639i	0.453187	−	0.261648i	0.709175	+	0.705032i	$0.249068\pi$
$864$		0			0
$865$	−13.4354	+	23.2709i	−0.456819	+	0.791233i
$866$	−1.82948	+	6.88242i	−0.0621681	+	0.233874i
$867$		0			0
$868$	12.3027	−	31.0694i	0.417580	−	1.05457i
$869$	−20.6232	−	35.7204i	−0.699593	−	1.21173i
$870$		0			0
$871$	10.4048	+	18.0217i	0.352554	+	0.610641i
$872$	37.1607	−	10.1952i	1.25842	−	0.345253i
$873$		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	$-0.886153\pi$
$883$		−	20.8057i		−	0.700168i	0.936718	−	0.350084i	$-0.113847\pi$
$884$	−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	−0.951496	−	0.307662i	$-0.900453\pi$
$887$	−6.23363	+	10.7970i	−0.209305	+	0.362526i	0.742191	+	0.670188i	$0.233787\pi$
$888$		0			0
$889$	21.8560	−	3.13776i	0.733027	−	0.105237i
$890$	−12.0675	−	3.20777i	−0.404504	−	0.107525i
$891$		0			0
$892$	8.20983	−	4.78359i	0.274886	−	0.160166i
$893$	1.47714	+	2.55848i	0.0494306	+	0.0856162i
$894$		0			0
$895$	14.4883	+	25.0945i	0.484291	+	0.838817i
$896$	−29.7675	−	3.14575i	−0.994462	−	0.105092i
$897$		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
$902$	−2.74889	+	2.75984i	−0.0915279	+	0.0918927i
$903$		0			0
$904$	0.373842	−	1.42925i	0.0124338	−	0.0475363i
$905$	−7.59836	+	13.1607i	−0.252578	+	0.437478i
$906$		0			0
$907$	23.9315	−	13.8169i	0.794634	−	0.458782i	−0.0469575	−	0.998897i	$-0.514953\pi$
$907$	23.9315	−	13.8169i	0.794634	−	0.458782i	0.841591	+	0.540115i	$0.181619\pi$
$908$	0.220236	+	55.3672i	0.00730878	+	1.83743i
$909$		0			0
$910$	−3.56294	+	30.2561i	−0.118110	+	1.00298i
$911$	16.9835	+	9.80544i	0.562689	+	0.324869i	0.754224	−	0.656617i	$-0.228013\pi$
$911$	16.9835	+	9.80544i	0.562689	+	0.324869i	−0.191535	+	0.981486i	$0.561347\pi$
$912$		0			0
$913$			39.6153i			1.31108i
$914$	−12.5540	−	3.33709i	−0.415250	−	0.110381i
$915$		0			0
$916$	10.1907	+	17.4898i	0.336711	+	0.577881i
$917$	42.0911	+	16.8610i	1.38997	+	0.556798i
$918$		0			0
$919$	26.8847	−	15.5219i	0.886843	−	0.512019i	0.0139343	−	0.999903i	$-0.495564\pi$
$919$	26.8847	−	15.5219i	0.886843	−	0.512019i	0.872908	+	0.487884i	$0.162231\pi$
$920$	−4.72361	+	18.0591i	−0.155733	+	0.595390i
$921$		0			0
$922$	22.9263	+	22.8353i	0.755037	+	0.752040i
$923$	−5.18757	−	8.98514i	−0.170751	−	0.295749i
$924$		0			0
$925$	10.0684	−	17.4390i	0.331047	−	0.573390i
$926$	14.1312	−	3.81657i	0.464378	−	0.125420i
$927$		0			0
$928$	40.1803	+	10.3392i	1.31898	+	0.339400i
$929$		−	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
$932$	−0.107416	−	27.0044i	−0.00351853	−	0.884558i
$933$		0			0
$934$	−1.51702	−	5.61688i	−0.0496384	−	0.183790i
$935$	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	$-0.0792266\pi$
$938$	15.7293	+	1.85228i	0.513580	+	0.0604789i
$939$		0			0
$940$	−3.25664	−	5.58921i	−0.106220	−	0.182300i
$941$			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	$-0.742990\pi$
$947$		−	44.4680i		−	1.44501i	0.691363	−	0.722507i	$-0.257010\pi$
$948$		0			0
$949$	25.9068			0.840971
$950$	−3.40755	+	3.42113i	−0.110556	+	0.110996i
$951$		0			0
$952$	−22.6844	+	9.86899i	−0.735207	+	0.319856i
$953$	−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
$956$	−49.9803	+	0.198808i	−1.61648	+	0.00642992i
$957$		0			0
$958$	3.21468	+	11.9026i	0.103861	+	0.384555i
$959$	−0.311696	+	0.245015i	−0.0100652	+	0.00791194i
$960$		0			0
$961$	8.88091			0.286481
$962$	43.9484	+	43.7739i	1.41695	+	1.41133i
$963$		0			0
$964$	−20.8827	+	0.0830657i	−0.672587	+	0.00267537i
$965$	−7.56128	−	4.36551i	−0.243406	−	0.140531i
$966$		0			0
$967$	24.2347	−	13.9919i	0.779335	−	0.449949i	−0.0568598	−	0.998382i	$-0.518109\pi$
$967$	24.2347	−	13.9919i	0.779335	−	0.449949i	0.836194	+	0.548433i	$0.184775\pi$
$968$	9.94187	−	2.72760i	0.319544	−	0.0876683i
$969$		0			0
$970$	−2.96532	−	10.9793i	−0.0952107	−	0.352525i
$971$	−4.21204	−	7.29547i	−0.135171	−	0.234123i	0.790492	−	0.612473i	$-0.209825\pi$
$971$	−4.21204	−	7.29547i	−0.135171	−	0.234123i	−0.925663	+	0.378350i	$0.876492\pi$
$972$		0			0
$973$	−25.2295	+	19.8322i	−0.808822	+	0.635791i
$974$	34.3043	+	34.1681i	1.09918	+	1.09482i
$975$		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
$980$	16.8378	+	15.9408i	0.537865	+	0.509210i
$981$		0			0
$982$	54.5483	−	14.7325i	1.74070	−	0.470133i
$983$	15.3077	+	26.5137i	0.488240	+	0.845656i	0.999909	−	0.0135267i	$-0.00430580\pi$
$983$	15.3077	+	26.5137i	0.488240	+	0.845656i	−0.511669	+	0.859183i	$0.670972\pi$
$984$		0			0
$985$	−18.6449	−	10.7647i	−0.594077	−	0.342990i
$986$	33.1026	−	8.94041i	1.05420	−	0.284721i
$987$		0			0
$988$	−7.48819	−	12.8516i	−0.238231	−	0.408864i
$989$	−13.0904	−	22.6733i	−0.416252	−	0.720969i
$990$		0			0
$991$	38.1803	+	22.0434i	1.21284	+	0.700232i	0.963376	−	0.268153i	$-0.0864134\pi$
$991$	38.1803	+	22.0434i	1.21284	+	0.700232i	0.249460	+	0.968385i	$0.419747\pi$
$992$	−9.58868	−	34.4129i	−0.304441	−	1.09261i
$993$		0			0
$994$	−7.84221	−	0.923496i	−0.248740	−	0.0292915i
$995$	−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	$0.296120\pi$
$998$	−15.6126	−	15.5506i	−0.494209	−	0.492247i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.36675 - 0.363308i) q^{2} +(1.73601 + 0.993103i) q^{4} +(-1.43430 - 0.828095i) q^{5} +(-0.375983 - 2.61890i) q^{7} +(-2.01190 - 1.98803i) q^{8} +O(q^{10})\)	\(q+(-1.36675 - 0.363308i) q^{2} +(1.73601 + 0.993103i) q^{4} +(-1.43430 - 0.828095i) q^{5} +(-0.375983 - 2.61890i) q^{7} +(-2.01190 - 1.98803i) q^{8} +(1.65948 + 1.65289i) q^{10} +(-2.34869 + 1.35602i) q^{11} +(-4.25755 + 2.45810i) q^{13} +(-0.437592 + 3.71598i) q^{14} +(2.02749 + 3.44808i) q^{16} +(2.86290 + 1.65289i) q^{17} +(0.756379 + 1.31009i) q^{19} +(-1.66759 - 2.86199i) q^{20} +(3.70273 - 1.00004i) q^{22} +(3.45097 + 1.99242i) q^{23} +(-1.12852 - 1.95465i) q^{25} +(6.71205 - 1.81280i) q^{26} +(1.94812 - 4.91984i) q^{28} +(-3.66717 + 6.35172i) q^{29} +6.31513 q^{31} +(-1.51836 - 5.44927i) q^{32} +(-3.31236 - 3.29921i) q^{34} +(-1.62942 + 4.06764i) q^{35} +(4.46089 + 7.72649i) q^{37} +(-0.557817 - 2.06536i) q^{38} +(1.23939 + 4.51748i) q^{40} +(-0.879545 + 0.507805i) q^{41} +(-5.68989 - 3.28506i) q^{43} +(-5.42403 + 0.0215753i) q^{44} +(-3.99275 - 3.97690i) q^{46} +1.95291 q^{47} +(-6.71727 + 1.96932i) q^{49} +(0.832263 + 3.08152i) q^{50} +(-9.83231 + 0.0391102i) q^{52} +(-5.20840 + 9.02122i) q^{53} +4.49164 q^{55} +(-4.45002 + 6.01642i) q^{56} +(7.31973 - 7.34891i) q^{58} +6.50576 q^{59} +11.3099i q^{61} +(-8.63121 - 2.29434i) q^{62} +(0.0954627 + 7.99943i) q^{64} +8.14215 q^{65} -4.23288i q^{67} +(3.32854 + 5.71260i) q^{68} +(3.70482 - 4.96747i) q^{70} +2.11040i q^{71} +(-4.56368 - 2.63484i) q^{73} +(-3.28983 - 12.1809i) q^{74} +(0.0120346 + 3.02549i) q^{76} +(4.43434 + 5.64115i) q^{77} +15.2086i q^{79} +(-0.0527021 - 6.62455i) q^{80} +(1.38661 - 0.374498i) q^{82} +(7.30362 - 12.6502i) q^{83} +(-2.73751 - 4.74150i) q^{85} +(6.58318 + 6.55704i) q^{86} +(7.42113 + 1.94110i) q^{88} +(-4.61689 + 2.66556i) q^{89} +(8.03827 + 10.2259i) q^{91} +(4.01226 + 6.88603i) q^{92} +(-2.66914 - 0.709507i) q^{94} -2.50541i q^{95} +(-4.20504 - 2.42778i) q^{97} +(9.89631 - 0.251133i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 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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