LMFDB - Embedded newform 756.2.bj.b.451.7

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			451.7
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26364 - 0.634994i) q^{2} +(1.19357 + 1.60481i) q^{4} +(0.104850 + 0.0605350i) q^{5} +(-2.60650 + 0.454031i) q^{7} +(-0.489193 - 2.78580i) q^{8} +O(q^{10})$	\(q+(-1.26364 - 0.634994i) q^{2} +(1.19357 + 1.60481i) q^{4} +(0.104850 + 0.0605350i) q^{5} +(-2.60650 + 0.454031i) q^{7} +(-0.489193 - 2.78580i) q^{8} +(-0.0940527 - 0.143073i) q^{10} +(0.682250 - 0.393897i) q^{11} +(1.37544 - 0.794110i) q^{13} +(3.58198 + 1.08138i) q^{14} +(-1.15080 + 3.83088i) q^{16} +(1.88990 + 1.09114i) q^{17} +(-2.93511 - 5.08375i) q^{19} +(0.0279980 + 0.240516i) q^{20} +(-1.11224 + 0.0645191i) q^{22} +(0.0763898 + 0.0441037i) q^{23} +(-2.49267 - 4.31743i) q^{25} +(-2.24231 + 0.130073i) q^{26} +(-3.83966 - 3.64101i) q^{28} +(3.56388 - 6.17283i) q^{29} +5.68486 q^{31} +(3.88679 - 4.11010i) q^{32} +(-1.69529 - 2.57888i) q^{34} +(-0.300776 - 0.110180i) q^{35} +(4.04368 + 7.00386i) q^{37} +(0.480761 + 8.28780i) q^{38} +(0.117347 - 0.321704i) q^{40} +(6.59809 - 3.80941i) q^{41} +(-2.85304 - 1.64720i) q^{43} +(1.44644 + 0.624737i) q^{44} +(-0.0685235 - 0.104238i) q^{46} +1.07641 q^{47} +(6.58771 - 2.36687i) q^{49} +(0.408291 + 7.03851i) q^{50} +(2.91607 + 1.25949i) q^{52} +(2.79216 - 4.83615i) q^{53} +0.0953783 q^{55} +(2.53992 + 7.03909i) q^{56} +(-8.42317 + 5.53718i) q^{58} -9.64548 q^{59} -9.10250i q^{61} +(-7.18360 - 3.60985i) q^{62} +(-7.52138 + 2.72559i) q^{64} +0.192286 q^{65} -3.47336i q^{67} +(0.504661 + 4.33527i) q^{68} +(0.310108 + 0.330218i) q^{70} -13.4226i q^{71} +(8.22990 + 4.75153i) q^{73} +(-0.662341 - 11.4181i) q^{74} +(4.65520 - 10.7781i) q^{76} +(-1.59944 + 1.33646i) q^{77} -15.0525i q^{79} +(-0.352564 + 0.332003i) q^{80} +(-10.7566 + 0.623969i) q^{82} +(1.15290 - 1.99689i) q^{83} +(0.132104 + 0.228811i) q^{85} +(2.55925 + 3.89313i) q^{86} +(-1.43107 - 1.70792i) q^{88} +(-15.2992 + 8.83298i) q^{89} +(-3.22453 + 2.69434i) q^{91} +(0.0203984 + 0.175231i) q^{92} +(-1.36019 - 0.683513i) q^{94} -0.710706i q^{95} +(0.600098 + 0.346467i) q^{97} +(-9.82743 - 1.19229i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.26364	−	0.634994i	−0.893527	−	0.449009i
$2$	−1.26364	−	0.634994i	−0.893527	−	0.449009i
$3$		0			0
$3$		0			0
$4$	1.19357	+	1.60481i	0.596783	+	0.802403i
$5$	0.104850	+	0.0605350i	0.0468902	+	0.0270721i	0.523262	−	0.852172i	$-0.324715\pi$
$5$	0.104850	+	0.0605350i	0.0468902	+	0.0270721i	−0.476372	+	0.879244i	$0.658048\pi$
$6$		0			0
$7$	−2.60650	+	0.454031i	−0.985165	+	0.171608i
$7$	−2.60650	+	0.454031i	−0.985165	+	0.171608i
$8$	−0.489193	−	2.78580i	−0.172956	−	0.984930i
$9$		0			0
$10$	−0.0940527	−	0.143073i	−0.0297421	−	0.0452437i
$11$	0.682250	−	0.393897i	0.205706	−	0.118764i	−0.393608	−	0.919278i	$-0.628773\pi$
$11$	0.682250	−	0.393897i	0.205706	−	0.118764i	0.599314	+	0.800514i	$0.295440\pi$
$12$		0			0
$13$	1.37544	−	0.794110i	0.381478	−	0.220246i	−0.296983	−	0.954883i	$-0.595981\pi$
$13$	1.37544	−	0.794110i	0.381478	−	0.220246i	0.678461	+	0.734636i	$0.262647\pi$
$14$	3.58198	+	1.08138i	0.957326	+	0.289011i
$15$		0			0
$16$	−1.15080	+	3.83088i	−0.287701	+	0.957720i
$17$	1.88990	+	1.09114i	0.458369	+	0.264640i	0.711358	−	0.702830i	$-0.248080\pi$
$17$	1.88990	+	1.09114i	0.458369	+	0.264640i	−0.252989	+	0.967469i	$0.581414\pi$
$18$		0			0
$19$	−2.93511	−	5.08375i	−0.673359	−	1.16629i	−0.976946	−	0.213489i	$-0.931517\pi$
$19$	−2.93511	−	5.08375i	−0.673359	−	1.16629i	0.303586	−	0.952804i	$-0.401816\pi$
$20$	0.0279980	+	0.240516i	0.00626055	+	0.0537810i
$21$		0			0
$22$	−1.11224	+	0.0645191i	−0.237130	+	0.0137555i
$23$	0.0763898	+	0.0441037i	0.0159284	+	0.00919625i	0.507943	−	0.861391i	$-0.330406\pi$
$23$	0.0763898	+	0.0441037i	0.0159284	+	0.00919625i	−0.492015	+	0.870587i	$0.663739\pi$
$24$		0			0
$25$	−2.49267	−	4.31743i	−0.498534	−	0.863487i
$26$	−2.24231	+	0.130073i	−0.439754	+	0.0255093i
$27$		0			0
$28$	−3.83966	−	3.64101i	−0.725628	−	0.688087i
$29$	3.56388	−	6.17283i	0.661796	−	1.14626i	−0.318347	−	0.947974i	$-0.603128\pi$
$29$	3.56388	−	6.17283i	0.661796	−	1.14626i	0.980143	−	0.198291i	$-0.0635390\pi$
$30$		0			0
$31$	5.68486			1.02103			0.510515	−	0.859869i	$-0.329455\pi$
$31$	5.68486			1.02103			0.510515	+	0.859869i	$0.329455\pi$
$32$	3.88679	−	4.11010i	0.687093	−	0.726569i
$33$		0			0
$34$	−1.69529	−	2.57888i	−0.290740	−	0.442274i
$35$	−0.300776	−	0.110180i	−0.0508404	−	0.0186237i
$36$		0			0
$37$	4.04368	+	7.00386i	0.664777	+	1.15143i	0.979346	+	0.202193i	$0.0648067\pi$
$37$	4.04368	+	7.00386i	0.664777	+	1.15143i	−0.314569	+	0.949235i	$0.601860\pi$
$38$	0.480761	+	8.28780i	0.0779897	+	1.34446i
$39$		0			0
$40$	0.117347	−	0.321704i	0.0185542	−	0.0508658i
$41$	6.59809	−	3.80941i	1.03045	−	0.594930i	0.113335	−	0.993557i	$-0.463847\pi$
$41$	6.59809	−	3.80941i	1.03045	−	0.594930i	0.917113	+	0.398627i	$0.130513\pi$
$42$		0			0
$43$	−2.85304	−	1.64720i	−0.435084	−	0.251196i	0.266426	−	0.963855i	$-0.414157\pi$
$43$	−2.85304	−	1.64720i	−0.435084	−	0.251196i	−0.701510	+	0.712659i	$0.747491\pi$
$44$	1.44644	+	0.624737i	0.218059	+	0.0941826i
$45$		0			0
$46$	−0.0685235	−	0.104238i	−0.0101032	−	0.0153691i
$47$	1.07641			0.157010			0.0785052	−	0.996914i	$-0.474985\pi$
$47$	1.07641			0.157010			0.0785052	+	0.996914i	$0.474985\pi$
$48$		0			0
$49$	6.58771	−	2.36687i	0.941102	−	0.338124i
$50$	0.408291	+	7.03851i	0.0577411	+	0.995395i
$51$		0			0
$52$	2.91607	+	1.25949i	0.404386	+	0.174660i
$53$	2.79216	−	4.83615i	0.383532	−	0.664297i	−0.608032	−	0.793912i	$-0.708041\pi$
$53$	2.79216	−	4.83615i	0.383532	−	0.664297i	0.991564	+	0.129615i	$0.0413742\pi$
$54$		0			0
$55$	0.0953783			0.0128608
$56$	2.53992	+	7.03909i	0.339412	+	0.940638i
$57$		0			0
$58$	−8.42317	+	5.53718i	−1.10602	+	0.727067i
$59$	−9.64548			−1.25574			−0.627868	−	0.778320i	$-0.716072\pi$
$59$	−9.64548			−1.25574			−0.627868	+	0.778320i	$0.716072\pi$
$60$		0			0
$61$		−	9.10250i		−	1.16546i	−0.812667	−	0.582728i	$-0.801985\pi$
$61$		−	9.10250i		−	1.16546i	0.812667	−	0.582728i	$-0.198015\pi$
$62$	−7.18360	−	3.60985i	−0.912319	−	0.458451i
$63$		0			0
$64$	−7.52138	+	2.72559i	−0.940173	+	0.340699i
$65$	0.192286			0.0238501
$66$		0			0
$67$		−	3.47336i		−	0.424339i	−0.977233	−	0.212169i	$-0.931947\pi$
$67$		−	3.47336i		−	0.424339i	0.977233	−	0.212169i	$-0.0680529\pi$
$68$	0.504661	+	4.33527i	0.0611992	+	0.525729i
$69$		0			0
$70$	0.310108	+	0.330218i	0.0370651	+	0.0394686i
$71$		−	13.4226i		−	1.59297i	−0.604658	−	0.796485i	$-0.706690\pi$
$71$		−	13.4226i		−	1.59297i	0.604658	−	0.796485i	$-0.293310\pi$
$72$		0			0
$73$	8.22990	+	4.75153i	0.963237	+	0.556125i	0.897168	−	0.441690i	$-0.145621\pi$
$73$	8.22990	+	4.75153i	0.963237	+	0.556125i	0.0660689	+	0.997815i	$0.478954\pi$
$74$	−0.662341	−	11.4181i	−0.0769956	−	1.32732i
$75$		0			0
$76$	4.65520	−	10.7781i	0.533988	−	1.23633i
$77$	−1.59944	+	1.33646i	−0.182274	+	0.152303i
$78$		0			0
$79$		−	15.0525i		−	1.69354i	−0.531963	−	0.846768i	$-0.678545\pi$
$79$		−	15.0525i		−	1.69354i	0.531963	−	0.846768i	$-0.321455\pi$
$80$	−0.352564	+	0.332003i	−0.0394178	+	0.0371190i
$81$		0			0
$82$	−10.7566	+	0.623969i	−1.18786	+	0.0689058i
$83$	1.15290	−	1.99689i	0.126548	−	0.219187i	−0.795789	−	0.605574i	$-0.792944\pi$
$83$	1.15290	−	1.99689i	0.126548	−	0.219187i	0.922337	+	0.386387i	$0.126277\pi$
$84$		0			0
$85$	0.132104	+	0.228811i	0.0143287	+	0.0248180i
$86$	2.55925	+	3.89313i	0.275971	+	0.419807i
$87$		0			0
$88$	−1.43107	−	1.70792i	−0.152553	−	0.182065i
$89$	−15.2992	+	8.83298i	−1.62171	+	0.936294i	−0.635247	+	0.772309i	$0.719102\pi$
$89$	−15.2992	+	8.83298i	−1.62171	+	0.936294i	−0.986463	+	0.163985i	$0.947565\pi$
$90$		0			0
$91$	−3.22453	+	2.69434i	−0.338023	+	0.282444i
$92$	0.0203984	+	0.175231i	0.00212668	+	0.0182691i
$93$		0			0
$94$	−1.36019	−	0.683513i	−0.140293	−	0.0704990i
$95$		−	0.710706i		−	0.0729169i
$96$		0			0
$97$	0.600098	+	0.346467i	0.0609307	+	0.0351784i	0.530156	−	0.847900i	$-0.322133\pi$
$97$	0.600098	+	0.346467i	0.0609307	+	0.0351784i	−0.469225	+	0.883079i	$0.655467\pi$
$98$	−9.82743	−	1.19229i	−0.992721	−	0.120440i
$99$		0			0
$100$	3.95348	−	9.15339i	0.395348	−	0.915339i
$101$	14.8433	−	8.56979i	1.47696	−	0.852726i	0.477303	−	0.878739i	$-0.341614\pi$
$101$	14.8433	−	8.56979i	1.47696	−	0.852726i	0.999662	+	0.0260130i	$0.00828112\pi$
$102$		0			0
$103$	−2.82344	+	4.89035i	−0.278202	+	0.481860i	−0.970938	−	0.239331i	$-0.923072\pi$
$103$	−2.82344	+	4.89035i	−0.278202	+	0.481860i	0.692736	+	0.721191i	$0.256405\pi$
$104$	−2.88509	−	3.44323i	−0.282906	−	0.337636i
$105$		0			0
$106$	−6.59920	+	4.33815i	−0.640971	+	0.421358i
$107$	−7.99717	+	4.61717i	−0.773116	+	0.446359i	−0.833985	−	0.551787i	$-0.813946\pi$
$107$	−7.99717	+	4.61717i	−0.773116	+	0.446359i	0.0608692	+	0.998146i	$0.480613\pi$
$108$		0			0
$109$	2.86498	−	4.96229i	0.274415	−	0.475301i	−0.695572	−	0.718456i	$-0.744849\pi$
$109$	2.86498	−	4.96229i	0.274415	−	0.475301i	0.969987	+	0.243155i	$0.0781824\pi$
$110$	−0.120524	−	0.0605646i	−0.0114915	−	0.00577461i
$111$		0			0
$112$	1.26023	−	10.5077i	0.119081	−	0.992885i
$113$	−3.13541	−	5.43069i	−0.294955	−	0.510877i	0.680020	−	0.733194i	$-0.261971\pi$
$113$	−3.13541	−	5.43069i	−0.294955	−	0.510877i	−0.974974	+	0.222317i	$0.928638\pi$
$114$		0			0
$115$	0.00533963	+	0.00924851i	0.000497923	+	0.000862428i
$116$	14.1599	−	1.64833i	1.31471	−	0.153044i
$117$		0			0
$118$	12.1884	+	6.12482i	1.12203	+	0.563836i
$119$	−5.42145	−	1.98598i	−0.496984	−	0.182054i
$120$		0			0
$121$	−5.18969	+	8.98881i	−0.471790	+	0.817164i
$122$	−5.78003	+	11.5023i	−0.523300	+	1.04137i
$123$		0			0
$124$	6.78525	+	9.12309i	0.609333	+	0.819278i
$125$		−	1.20893i		−	0.108130i
$126$		0			0
$127$			16.2397i			1.44104i	0.693436	+	0.720519i	$0.256096\pi$
$127$			16.2397i			1.44104i	−0.693436	+	0.720519i	$0.743904\pi$
$128$	11.2350	+	1.33187i	0.993047	+	0.117722i
$129$		0			0
$130$	−0.242980	−	0.122100i	−0.0213107	−	0.0107089i
$131$	0.268437	−	0.464947i	0.0234535	−	0.0406226i	−0.854060	−	0.520174i	$-0.825867\pi$
$131$	0.268437	−	0.464947i	0.0234535	−	0.0406226i	0.877514	+	0.479551i	$0.159201\pi$
$132$		0			0
$133$	9.95854	+	11.9182i	0.863515	+	1.03344i
$134$	−2.20556	+	4.38908i	−0.190532	+	0.379158i
$135$		0			0
$136$	2.11516	−	5.79868i	0.181374	−	0.497232i
$137$	−6.58790	−	11.4106i	−0.562842	−	0.974872i	−0.997247	−	0.0741537i	$-0.976374\pi$
$137$	−6.58790	−	11.4106i	−0.562842	−	0.974872i	0.434404	−	0.900718i	$-0.356959\pi$
$138$		0			0
$139$	6.07703	+	10.5257i	0.515447	+	0.892780i	0.999839	+	0.0179295i	$0.00570745\pi$
$139$	6.07703	+	10.5257i	0.515447	+	0.892780i	−0.484392	+	0.874851i	$0.660959\pi$
$140$	−0.182179	−	0.614193i	−0.0153969	−	0.0519088i
$141$		0			0
$142$	−8.52327	+	16.9613i	−0.715257	+	1.42336i
$143$	0.625595	−	1.08356i	0.0523149	−	0.0906121i
$144$		0			0
$145$	0.747344	−	0.431479i	0.0620635	−	0.0358324i
$146$	−7.38242	−	11.2302i	−0.610973	−	0.929414i
$147$		0			0
$148$	−6.41344	+	14.8489i	−0.527181	+	1.22057i
$149$	−6.88184	+	11.9197i	−0.563783	+	0.976500i	0.433379	+	0.901212i	$0.357321\pi$
$149$	−6.88184	+	11.9197i	−0.563783	+	0.976500i	−0.997162	+	0.0752885i	$0.976012\pi$
$150$		0			0
$151$	11.6781	−	6.74236i	0.950352	−	0.548686i	0.0571616	−	0.998365i	$-0.481795\pi$
$151$	11.6781	−	6.74236i	0.950352	−	0.548686i	0.893190	+	0.449679i	$0.148462\pi$
$152$	−12.7265	+	10.6636i	−1.03225	+	0.864929i
$153$		0			0
$154$	2.86976	−	0.673161i	0.231252	−	0.0542449i
$155$	0.596055	+	0.344133i	0.0478763	+	0.0276414i
$156$		0			0
$157$		−	12.6437i		−	1.00908i	−0.863389	−	0.504539i	$-0.831663\pi$
$157$		−	12.6437i		−	1.00908i	0.863389	−	0.504539i	$-0.168337\pi$
$158$	−9.55823	+	19.0209i	−0.760412	+	1.51322i
$159$		0			0
$160$	0.656333	−	0.195656i	0.0518877	−	0.0154679i
$161$	−0.219135	−	0.0802730i	−0.0172702	−	0.00632640i
$162$		0			0
$163$	−2.17260	+	1.25435i	−0.170171	+	0.0982486i	−0.582667	−	0.812711i	$-0.697991\pi$
$163$	−2.17260	+	1.25435i	−0.170171	+	0.0982486i	0.412495	+	0.910960i	$0.364657\pi$
$164$	13.9886	+	6.04188i	1.09233	+	0.471791i
$165$		0			0
$166$	−2.72487	+	1.79126i	−0.211491	+	0.139029i
$167$	6.67408	+	11.5598i	0.516456	+	0.894527i	0.999817	+	0.0191068i	$0.00608225\pi$
$167$	6.67408	+	11.5598i	0.516456	+	0.894527i	−0.483362	+	0.875421i	$0.660584\pi$
$168$		0			0
$169$	−5.23878	+	9.07383i	−0.402983	+	0.697987i
$170$	−0.0216382	−	0.373019i	−0.00165957	−	0.0286093i
$171$		0			0
$172$	−0.761847	−	6.54462i	−0.0580903	−	0.499022i
$173$			11.6566i			0.886236i	0.896463	+	0.443118i	$0.146128\pi$
$173$			11.6566i			0.886236i	−0.896463	+	0.443118i	$0.853872\pi$
$174$		0			0
$175$	8.45740	+	10.1216i	0.639320	+	0.765125i
$176$	0.723837	+	3.06692i	0.0545613	+	0.231178i
$177$		0			0
$178$	24.9415	−	1.44681i	1.86945	−	0.108443i
$179$	13.7381	+	7.93170i	1.02683	+	0.592843i	0.916076	−	0.401004i	$-0.131339\pi$
$179$	13.7381	+	7.93170i	1.02683	+	0.592843i	0.110759	+	0.993847i	$0.464672\pi$
$180$		0			0
$181$			1.00851i			0.0749616i	0.999297	+	0.0374808i	$0.0119333\pi$
$181$			1.00851i			0.0749616i	−0.999297	+	0.0374808i	$0.988067\pi$
$182$	5.78554	−	1.35711i	0.428852	−	0.100596i
$183$		0			0
$184$	0.0854947	−	0.234382i	0.00630276	−	0.0172789i
$185$			0.979136i			0.0719875i
$186$		0			0
$187$	1.71918			0.125719
$188$	1.28476	+	1.72743i	0.0937011	+	0.125986i
$189$		0			0
$190$	−0.451294	+	0.898076i	−0.0327403	+	0.0651533i
$191$		−	6.77218i		−	0.490017i	−0.969521	−	0.245009i	$-0.921209\pi$
$191$		−	6.77218i		−	0.490017i	0.969521	−	0.245009i	$-0.0787908\pi$
$192$		0			0
$193$	−1.10276			−0.0793785			−0.0396892	−	0.999212i	$-0.512637\pi$
$193$	−1.10276			−0.0793785			−0.0396892	+	0.999212i	$0.512637\pi$
$194$	−0.538302	−	0.818867i	−0.0386479	−	0.0587912i
$195$		0			0
$196$	11.6612	+	7.74699i	0.832945	+	0.553356i
$197$	−9.04425			−0.644376			−0.322188	−	0.946676i	$-0.604418\pi$
$197$	−9.04425			−0.644376			−0.322188	+	0.946676i	$0.604418\pi$
$198$		0			0
$199$	−3.45279	+	5.98040i	−0.244761	+	0.423939i	−0.962065	−	0.272822i	$-0.912043\pi$
$199$	−3.45279	+	5.98040i	−0.244761	+	0.423939i	0.717303	+	0.696761i	$0.245376\pi$
$200$	−10.8081	+	9.05614i	−0.764249	+	0.640366i
$201$		0			0
$202$	−24.1983	+	1.40370i	−1.70259	+	0.0987642i
$203$	−6.48661	+	17.7076i	−0.455271	+	1.24283i
$204$		0			0
$205$	0.922410			0.0644239
$206$	6.67315	−	4.38676i	0.464940	−	0.305640i
$207$		0			0
$208$	1.45928	+	6.18301i	0.101183	+	0.428714i
$209$	−4.00495	−	2.31226i	−0.277028	−	0.159942i
$210$		0			0
$211$	24.4873	−	14.1377i	1.68577	−	0.973281i	0.728079	−	0.685494i	$-0.240414\pi$
$211$	24.4873	−	14.1377i	1.68577	−	0.973281i	0.957694	−	0.287788i	$-0.0929198\pi$
$212$	11.0937	−	1.29140i	0.761919	−	0.0886936i
$213$		0			0
$214$	13.0374	−	0.756277i	0.891219	−	0.0516980i
$215$	−0.199427	−	0.345417i	−0.0136008	−	0.0235573i
$216$		0			0
$217$	−14.8176	+	2.58110i	−1.00588	+	0.175217i
$218$	−6.77132	+	4.45130i	−0.458612	+	0.301480i
$219$		0			0
$220$	0.113840	+	0.153064i	0.00767510	+	0.0103195i
$221$	3.46593			0.233144
$222$		0			0
$223$	−8.22688	+	14.2494i	−0.550913	+	0.954209i	0.447296	+	0.894386i	$0.352387\pi$
$223$	−8.22688	+	14.2494i	−0.550913	+	0.954209i	−0.998209	+	0.0598231i	$0.980946\pi$
$224$	−8.26481	+	12.4777i	−0.552216	+	0.833701i
$225$		0			0
$226$	0.513570	+	8.85340i	0.0341622	+	0.588920i
$227$	11.9528	+	20.7028i	0.793332	+	1.37409i	0.923893	+	0.382651i	$0.124989\pi$
$227$	11.9528	+	20.7028i	0.793332	+	1.37409i	−0.130561	+	0.991440i	$0.541678\pi$
$228$		0			0
$229$	−16.8919	−	9.75257i	−1.11625	−	0.644468i	−0.175810	−	0.984424i	$-0.556254\pi$
$229$	−16.8919	−	9.75257i	−1.11625	−	0.644468i	−0.940441	+	0.339956i	$0.889588\pi$
$230$	−0.000874614	−	0.0150774i	−5.76703e−5	−	0.000994175i
$231$		0			0
$232$	−18.9397	−	6.90857i	−1.24345	−	0.453570i
$233$	−4.78357	−	8.28538i	−0.313382	−	0.542793i	0.665710	−	0.746210i	$-0.268129\pi$
$233$	−4.78357	−	8.28538i	−0.313382	−	0.542793i	−0.979092	+	0.203417i	$0.934795\pi$
$234$		0			0
$235$	0.112861	+	0.0651604i	0.00736225	+	0.00425060i
$236$	−11.5125	−	15.4791i	−0.749401	−	1.00761i
$237$		0			0
$238$	5.58967	+	5.95214i	0.362325	+	0.385820i
$239$	10.1872	−	5.88159i	0.658956	−	0.380449i	−0.132923	−	0.991126i	$-0.542436\pi$
$239$	10.1872	−	5.88159i	0.658956	−	0.380449i	0.791879	+	0.610678i	$0.209103\pi$
$240$		0			0
$241$	−17.5765	+	10.1478i	−1.13220	+	0.653677i	−0.944488	−	0.328547i	$-0.893441\pi$
$241$	−17.5765	+	10.1478i	−1.13220	+	0.653677i	−0.187714	+	0.982224i	$0.560108\pi$
$242$	12.2657	−	8.06318i	0.788471	−	0.518321i
$243$		0			0
$244$	14.6077	−	10.8644i	0.935165	−	0.695524i
$245$	0.833998	+	0.150622i	0.0532822	+	0.00962286i
$246$		0			0
$247$	−8.07411	−	4.66159i	−0.513744	−	0.296610i
$248$	−2.78099	−	15.8369i	−0.176593	−	1.00564i
$249$		0			0
$250$	−0.767660	+	1.52764i	−0.0485511	+	0.0966167i
$251$	14.5706			0.919691			0.459845	−	0.887999i	$-0.347905\pi$
$251$	14.5706			0.919691			0.459845	+	0.887999i	$0.347905\pi$
$252$		0			0
$253$	0.0694893			0.00436875
$254$	10.3121	−	20.5211i	0.647038	−	1.28761i
$255$		0			0
$256$	−13.3513	−	8.81719i	−0.834456	−	0.551074i
$257$	10.8730	+	6.27755i	0.678241	+	0.391583i	0.799192	−	0.601076i	$-0.205261\pi$
$257$	10.8730	+	6.27755i	0.678241	+	0.391583i	−0.120951	+	0.992659i	$0.538594\pi$
$258$		0			0
$259$	−13.7198	−	16.4196i	−0.852509	−	1.02027i
$260$	0.229506	+	0.308581i	0.0142333	+	0.0191374i
$261$		0			0
$262$	−0.634447	+	0.417069i	−0.0391963	+	0.0257666i
$263$	2.93339	−	1.69360i	0.180881	−	0.104432i	−0.406826	−	0.913506i	$-0.633364\pi$
$263$	2.93339	−	1.69360i	0.180881	−	0.104432i	0.587706	+	0.809074i	$0.300031\pi$
$264$		0			0
$265$	0.585513	−	0.338046i	0.0359678	−	0.0207660i
$266$	−5.01603	−	21.3839i	−0.307552	−	1.31113i
$267$		0			0
$268$	5.57407	−	4.14568i	0.340491	−	0.253238i
$269$	25.3711	+	14.6480i	1.54690	+	0.893104i	0.998376	+	0.0569705i	$0.0181441\pi$
$269$	25.3711	+	14.6480i	1.54690	+	0.893104i	0.548526	+	0.836134i	$0.315189\pi$
$270$		0			0
$271$	−0.767688	−	1.32967i	−0.0466337	−	0.0807720i	0.841766	−	0.539842i	$-0.181516\pi$
$271$	−0.767688	−	1.32967i	−0.0466337	−	0.0807720i	−0.888400	+	0.459070i	$0.848183\pi$
$272$	−6.35493	+	5.98431i	−0.385324	+	0.362852i
$273$		0			0
$274$	1.07908	+	18.6021i	0.0651894	+	1.12380i
$275$	−3.40125	−	1.96371i	−0.205103	−	0.118416i
$276$		0			0
$277$	−10.1485	−	17.5778i	−0.609767	−	1.05615i	−0.991279	−	0.131783i	$-0.957930\pi$
$277$	−10.1485	−	17.5778i	−0.609767	−	1.05615i	0.381512	−	0.924364i	$-0.375404\pi$
$278$	−0.995398	−	17.1596i	−0.0597000	−	1.02916i
$279$		0			0
$280$	−0.159801	+	0.891801i	−0.00954994	+	0.0532953i
$281$	−13.9539	+	24.1689i	−0.832421	+	1.44180i	0.0636914	+	0.997970i	$0.479713\pi$
$281$	−13.9539	+	24.1689i	−0.832421	+	1.44180i	−0.896113	+	0.443826i	$0.853621\pi$
$282$		0			0
$283$	−9.58069			−0.569513			−0.284756	−	0.958600i	$-0.591913\pi$
$283$	−9.58069			−0.569513			−0.284756	+	0.958600i	$0.591913\pi$
$284$	21.5407	−	16.0208i	1.27820	−	0.950657i
$285$		0			0
$286$	−1.47858	+	0.971983i	−0.0874304	+	0.0574745i
$287$	−15.4683	+	12.9250i	−0.913068	+	0.762937i
$288$		0			0
$289$	−6.11884	−	10.5981i	−0.359932	−	0.623420i
$290$	−1.21836	+	0.0706749i	−0.0715445	+	0.00415017i
$291$		0			0
$292$	2.19763	+	18.8787i	0.128607	+	1.10479i
$293$	3.48475	−	2.01192i	0.203581	−	0.117538i	−0.394743	−	0.918791i	$-0.629167\pi$
$293$	3.48475	−	2.01192i	0.203581	−	0.117538i	0.598325	+	0.801254i	$0.295833\pi$
$294$		0			0
$295$	−1.01133	−	0.583889i	−0.0588817	−	0.0339953i
$296$	17.5332	−	14.6911i	1.01910	−	0.853904i
$297$		0			0
$298$	16.2651	−	10.6923i	0.942212	−	0.619386i
$299$	0.140093			0.00810177
$300$		0			0
$301$	8.18433	+	2.99807i	0.471737	+	0.172806i
$302$	−19.0383	+	1.10438i	−1.09553	+	0.0635498i
$303$		0			0
$304$	22.8530	−	5.39364i	1.31071	−	0.309346i
$305$	0.551020	−	0.954394i	0.0315513	−	0.0546484i
$306$		0			0
$307$	−9.06875			−0.517581			−0.258790	−	0.965934i	$-0.583324\pi$
$307$	−9.06875			−0.517581			−0.258790	+	0.965934i	$0.583324\pi$
$308$	−4.05380	−	0.971650i	−0.230986	−	0.0553649i
$309$		0			0
$310$	−0.534676	−	0.813351i	−0.0303676	−	0.0461952i
$311$	−9.01424			−0.511151			−0.255575	−	0.966789i	$-0.582265\pi$
$311$	−9.01424			−0.511151			−0.255575	+	0.966789i	$0.582265\pi$
$312$		0			0
$313$			26.2481i			1.48363i	0.670606	+	0.741814i	$0.266034\pi$
$313$			26.2481i			1.48363i	−0.670606	+	0.741814i	$0.733966\pi$
$314$	−8.02868	+	15.9771i	−0.453084	+	0.901638i
$315$		0			0
$316$	24.1563	−	17.9661i	1.35890	−	1.01067i
$317$	−11.1800			−0.627934			−0.313967	−	0.949434i	$-0.601658\pi$
$317$	−11.1800			−0.627934			−0.313967	+	0.949434i	$0.601658\pi$
$318$		0			0
$319$		−	5.61521i		−	0.314392i
$320$	−0.953608	−	0.169530i	−0.0533083	−	0.00947699i
$321$		0			0
$322$	0.225934	+	0.240585i	0.0125908	+	0.0134073i
$323$		−	12.8104i		−	0.712790i
$324$		0			0
$325$	−6.85703	−	3.95891i	−0.380360	−	0.219601i
$326$	3.54189	−	0.205459i	0.196167	−	0.0113793i
$327$		0			0
$328$	−13.8400	−	16.5174i	−0.764186	−	0.912023i
$329$	−2.80566	+	0.488724i	−0.154681	+	0.0269442i
$330$		0			0
$331$		−	16.4048i		−	0.901689i	−0.892602	−	0.450845i	$-0.851123\pi$
$331$		−	16.4048i		−	0.901689i	0.892602	−	0.450845i	$-0.148877\pi$
$332$	4.58068	−	0.533229i	0.251398	−	0.0292647i
$333$		0			0
$334$	−1.09319	−	18.8455i	−0.0598168	−	1.03118i
$335$	0.210260	−	0.364181i	0.0114877	−	0.0198973i
$336$		0			0
$337$	3.97568	+	6.88607i	0.216569	+	0.375108i	0.953757	−	0.300580i	$-0.0971801\pi$
$337$	3.97568	+	6.88607i	0.216569	+	0.375108i	−0.737188	+	0.675688i	$0.763847\pi$
$338$	12.3818	−	8.13945i	0.673479	−	0.442728i
$339$		0			0
$340$	−0.209522	+	0.485102i	−0.0113629	+	0.0263083i
$341$	3.87849	−	2.23925i	0.210032	−	0.121262i
$342$		0			0
$343$	−16.0963	+	9.16028i	−0.869116	+	0.494608i
$344$	−3.19309	+	8.75380i	−0.172160	+	0.471973i
$345$		0			0
$346$	7.40188	−	14.7298i	0.397928	−	0.791876i
$347$		−	36.3652i		−	1.95218i	−0.217358	−	0.976092i	$-0.569744\pi$
$347$		−	36.3652i		−	1.95218i	0.217358	−	0.976092i	$-0.430256\pi$
$348$		0			0
$349$	1.38047	+	0.797016i	0.0738950	+	0.0426633i	0.536492	−	0.843905i	$-0.319749\pi$
$349$	1.38047	+	0.797016i	0.0738950	+	0.0426633i	−0.462597	+	0.886569i	$0.653082\pi$
$350$	−4.25992	−	18.1605i	−0.227702	−	0.970720i
$351$		0			0
$352$	1.03281	−	4.33511i	0.0550487	−	0.231062i
$353$	−20.6529	+	11.9239i	−1.09924	+	0.634647i	−0.936022	−	0.351943i	$-0.885521\pi$
$353$	−20.6529	+	11.9239i	−1.09924	+	0.634647i	−0.163220	+	0.986590i	$0.552188\pi$
$354$		0			0
$355$	0.812537	−	1.40736i	0.0431250	−	0.0746947i
$356$	−32.4358	−	14.0095i	−1.71909	−	0.742500i
$357$		0			0
$358$	−12.3234	−	18.7464i	−0.651313	−	0.990779i
$359$	−19.5420	+	11.2826i	−1.03139	+	0.595472i	−0.917382	−	0.398008i	$-0.869702\pi$
$359$	−19.5420	+	11.2826i	−1.03139	+	0.595472i	−0.114006	+	0.993480i	$0.536368\pi$
$360$		0			0
$361$	−7.72969	+	13.3882i	−0.406826	+	0.704643i
$362$	0.640395	−	1.27439i	0.0336584	−	0.0669803i
$363$		0			0
$364$	−8.17259	−	1.95888i	−0.428360	−	0.102673i
$365$	0.575268	+	0.996393i	0.0301109	+	0.0521536i
$366$		0			0
$367$	8.96237	+	15.5233i	0.467832	+	0.810309i	0.999324	−	0.0367544i	$-0.0117019\pi$
$367$	8.96237	+	15.5233i	0.467832	+	0.810309i	−0.531492	+	0.847063i	$0.678369\pi$
$368$	−0.256866	+	0.241886i	−0.0133900	+	0.0126092i
$369$		0			0
$370$	0.621746	−	1.23727i	0.0323230	−	0.0643228i
$371$	−5.08199	+	13.8732i	−0.263844	+	0.720259i
$372$		0			0
$373$	8.61803	−	14.9269i	0.446225	−	0.772884i	−0.551912	−	0.833903i	$-0.686101\pi$
$373$	8.61803	−	14.9269i	0.446225	−	0.772884i	0.998137	+	0.0610184i	$0.0194348\pi$
$374$	−2.17243	−	1.09167i	−0.112333	−	0.0564490i
$375$		0			0
$376$	−0.526572	−	2.99866i	−0.0271559	−	0.154644i
$377$		−	11.3205i		−	0.583033i
$378$		0			0
$379$		−	0.579373i		−	0.0297604i	−0.999889	−	0.0148802i	$-0.995263\pi$
$379$		−	0.579373i		−	0.0297604i	0.999889	−	0.0148802i	$-0.00473669\pi$
$380$	1.14055	−	0.848274i	0.0585088	−	0.0435156i
$381$		0			0
$382$	−4.30029	+	8.55758i	−0.220022	+	0.437844i
$383$	15.8996	−	27.5389i	0.812430	−	1.40717i	−0.0987285	−	0.995114i	$-0.531478\pi$
$383$	15.8996	−	27.5389i	0.812430	−	1.40717i	0.911159	−	0.412056i	$-0.135189\pi$
$384$		0			0
$385$	−0.248604	+	0.0433047i	−0.0126700	+	0.00220701i
$386$	1.39349	+	0.700247i	0.0709268	+	0.0356416i
$387$		0			0
$388$	0.160244	+	1.37657i	0.00813516	+	0.0698848i
$389$	5.29509	+	9.17137i	0.268472	+	0.465007i	0.968467	−	0.249140i	$-0.0801480\pi$
$389$	5.29509	+	9.17137i	0.268472	+	0.465007i	−0.699996	+	0.714147i	$0.746815\pi$
$390$		0			0
$391$	0.0962463	+	0.166703i	0.00486738	+	0.00843056i
$392$	−9.81629	−	17.1942i	−0.495797	−	0.868438i
$393$		0			0
$394$	11.4287	+	5.74304i	0.575768	+	0.289330i
$395$	0.911201	−	1.57825i	0.0458475	−	0.0794102i
$396$		0			0
$397$	16.0213	−	9.24988i	0.804084	−	0.464238i	−0.0408132	−	0.999167i	$-0.512995\pi$
$397$	16.0213	−	9.24988i	0.804084	−	0.464238i	0.844897	+	0.534929i	$0.179662\pi$
$398$	8.16059	−	5.36457i	0.409053	−	0.268901i
$399$		0			0
$400$	19.4081	−	4.58061i	0.970407	−	0.229030i
$401$	−3.86517	+	6.69467i	−0.193017	+	0.334316i	−0.946249	−	0.323440i	$-0.895161\pi$
$401$	−3.86517	+	6.69467i	−0.193017	+	0.334316i	0.753231	+	0.657756i	$0.228494\pi$
$402$		0			0
$403$	7.81917	−	4.51440i	0.389501	−	0.224878i
$404$	31.4693	+	13.5920i	1.56566	+	0.676229i
$405$		0			0
$406$	19.4410	−	18.2570i	0.964838	−	0.906082i
$407$	5.51760	+	3.18559i	0.273497	+	0.157904i
$408$		0			0
$409$		−	14.9130i		−	0.737401i	−0.929548	−	0.368701i	$-0.879803\pi$
$409$		−	14.9130i		−	0.737401i	0.929548	−	0.368701i	$-0.120197\pi$
$410$	−1.16559	−	0.585725i	−0.0575645	−	0.0289269i
$411$		0			0
$412$	−11.2180	+	1.30587i	−0.552672	+	0.0643355i
$413$	25.1410	−	4.37935i	1.23711	−	0.215494i
$414$		0			0
$415$	0.241763	−	0.139582i	0.0118677	−	0.00685181i
$416$	2.08217	−	8.73972i	0.102087	−	0.428500i
$417$		0			0
$418$	3.59254	+	5.46498i	0.175717	+	0.267301i
$419$	10.7579	+	18.6332i	0.525556	+	0.910289i	0.999557	+	0.0297650i	$0.00947588\pi$
$419$	10.7579	+	18.6332i	0.525556	+	0.910289i	−0.474001	+	0.880524i	$0.657191\pi$
$420$		0			0
$421$	6.84725	−	11.8598i	0.333715	−	0.578011i	−0.649522	−	0.760342i	$-0.725031\pi$
$421$	6.84725	−	11.8598i	0.333715	−	0.578011i	0.983237	+	0.182332i	$0.0583645\pi$
$422$	−39.9204	+	2.31571i	−1.94330	+	0.112727i
$423$		0			0
$424$	−14.8385	−	5.41258i	−0.720620	−	0.262858i
$425$		−	10.8794i		−	0.527728i
$426$		0			0
$427$	4.13282	+	23.7257i	0.200001	+	1.14817i
$428$	−16.9548	−	7.32302i	−0.819542	−	0.353971i
$429$		0			0
$430$	0.0326655	+	0.563117i	0.00157527	+	0.0271559i
$431$	−14.9098	−	8.60820i	−0.718181	−	0.414642i	0.0959016	−	0.995391i	$-0.469427\pi$
$431$	−14.9098	−	8.60820i	−0.718181	−	0.414642i	−0.814083	+	0.580749i	$0.802760\pi$
$432$		0			0
$433$		−	13.4777i		−	0.647695i	−0.946109	−	0.323848i	$-0.895023\pi$
$433$		−	13.4777i		−	0.647695i	0.946109	−	0.323848i	$-0.104977\pi$
$434$	20.3631	+	6.14750i	0.977458	+	0.295089i
$435$		0			0
$436$	11.3831	−	1.32508i	0.545149	−	0.0634599i
$437$		−	0.517796i		−	0.0247695i
$438$		0			0
$439$	8.89840			0.424697			0.212349	−	0.977194i	$-0.431889\pi$
$439$	8.89840			0.424697			0.212349	+	0.977194i	$0.431889\pi$
$440$	−0.0466584	−	0.265705i	−0.00222435	−	0.0126670i
$441$		0			0
$442$	−4.37968	−	2.20084i	−0.208320	−	0.104684i
$443$		−	24.6632i		−	1.17178i	−0.810390	−	0.585891i	$-0.800745\pi$
$443$		−	24.6632i		−	1.17178i	0.810390	−	0.585891i	$-0.199255\pi$
$444$		0			0
$445$	−2.13882			−0.101390
$446$	19.4441	−	12.7820i	0.920704	−	0.605247i
$447$		0			0
$448$	18.3670	−	10.5192i	0.867759	−	0.496985i
$449$	−27.3526			−1.29085			−0.645425	−	0.763824i	$-0.723320\pi$
$449$	−27.3526			−1.29085			−0.645425	+	0.763824i	$0.723320\pi$
$450$		0			0
$451$	3.00103	−	5.19794i	0.141313	−	0.244761i
$452$	4.97289	−	11.5136i	0.233905	−	0.541555i
$453$		0			0
$454$	−1.95782	−	33.7508i	−0.0918851	−	1.58400i
$455$	−0.501193	+	0.0873038i	−0.0234963	+	0.00409286i
$456$		0			0
$457$	−36.7556			−1.71935			−0.859677	−	0.510837i	$-0.829335\pi$
$457$	−36.7556			−1.71935			−0.859677	+	0.510837i	$0.829335\pi$
$458$	15.1525	+	23.0500i	0.708029	+	1.07706i
$459$		0			0
$460$	−0.00846887	+	0.0196078i	−0.000394863	+	0.000914217i
$461$	4.64718	+	2.68305i	0.216441	+	0.124962i	0.604301	−	0.796756i	$-0.293452\pi$
$461$	4.64718	+	2.68305i	0.216441	+	0.124962i	−0.387860	+	0.921718i	$0.626786\pi$
$462$		0			0
$463$	4.42338	−	2.55384i	0.205572	−	0.118687i	−0.393680	−	0.919248i	$-0.628798\pi$
$463$	4.42338	−	2.55384i	0.205572	−	0.118687i	0.599252	+	0.800561i	$0.295465\pi$
$464$	19.5460	+	20.7565i	0.907402	+	0.963597i
$465$		0			0
$466$	0.783532	+	13.5073i	0.0362964	+	0.625712i
$467$	0.342427	+	0.593101i	0.0158456	+	0.0274455i	0.873839	−	0.486214i	$-0.161623\pi$
$467$	0.342427	+	0.593101i	0.0158456	+	0.0274455i	−0.857994	+	0.513660i	$0.828289\pi$
$468$		0			0
$469$	1.57702	+	9.05333i	0.0728198	+	0.418044i
$470$	−0.101239	−	0.154005i	−0.00466982	−	0.00710374i
$471$		0			0
$472$	4.71850	+	26.8704i	0.217187	+	1.23681i
$473$	−2.59531			−0.119333
$474$		0			0
$475$	−14.6325	+	25.3442i	−0.671385	+	1.16287i
$476$	−3.28375	−	11.0708i	−0.150510	−	0.507428i
$477$		0			0
$478$	−16.6077	+	0.963386i	−0.759620	+	0.0440642i
$479$	−6.62396	−	11.4730i	−0.302656	−	0.524216i	0.674080	−	0.738658i	$-0.264540\pi$
$479$	−6.62396	−	11.4730i	−0.302656	−	0.524216i	−0.976737	+	0.214442i	$0.931207\pi$
$480$		0			0
$481$	11.1237	+	6.42225i	0.507195	+	0.292829i
$482$	28.6541	−	1.66218i	1.30516	−	0.0757100i
$483$		0			0
$484$	−20.6195	+	2.40028i	−0.937251	+	0.109104i
$485$	0.0419467	+	0.0726538i	0.00190470	+	0.00329904i
$486$		0			0
$487$	6.29077	+	3.63198i	0.285062	+	0.164581i	0.635713	−	0.771926i	$-0.280706\pi$
$487$	6.29077	+	3.63198i	0.285062	+	0.164581i	−0.350651	+	0.936506i	$0.614040\pi$
$488$	−25.3578	+	4.45288i	−1.14789	+	0.201572i
$489$		0			0
$490$	−0.958228	−	0.719915i	−0.0432883	−	0.0325224i
$491$	23.9003	−	13.7989i	1.07861	−	0.622734i	0.148086	−	0.988974i	$-0.452689\pi$
$491$	23.9003	−	13.7989i	1.07861	−	0.622734i	0.930520	+	0.366241i	$0.119355\pi$
$492$		0			0
$493$	13.4708	−	7.77737i	0.606694	−	0.350275i
$494$	7.24268	+	11.0176i	0.325864	+	0.495704i
$495$		0			0
$496$	−6.54216	+	21.7780i	−0.293752	+	0.977861i
$497$	6.09428	+	34.9860i	0.273366	+	1.56934i
$498$		0			0
$499$	−12.8699	−	7.43045i	−0.576137	−	0.332633i	0.183460	−	0.983027i	$-0.441270\pi$
$499$	−12.8699	−	7.43045i	−0.576137	−	0.332633i	−0.759597	+	0.650394i	$0.774604\pi$
$500$	1.94009	−	1.44293i	0.0867635	−	0.0645298i
$501$		0			0
$502$	−18.4120	−	9.25227i	−0.821769	−	0.412949i
$503$	36.3565			1.62106			0.810529	−	0.585698i	$-0.199180\pi$
$503$	36.3565			1.62106			0.810529	+	0.585698i	$0.199180\pi$
$504$		0			0
$505$	2.07509			0.0923402
$506$	−0.0878093	−	0.0441253i	−0.00390360	−	0.00196161i
$507$		0			0
$508$	−26.0615	+	19.3831i	−1.15629	+	0.859986i
$509$	−1.79178	−	1.03449i	−0.0794193	−	0.0458528i	0.459764	−	0.888041i	$-0.347934\pi$
$509$	−1.79178	−	1.03449i	−0.0794193	−	0.0458528i	−0.539184	+	0.842188i	$0.681267\pi$
$510$		0			0
$511$	−23.6086	−	8.64825i	−1.04438	−	0.382576i
$512$	11.2724	+	19.6197i	0.498172	+	0.867078i
$513$		0			0
$514$	−9.75338	−	14.8369i	−0.430203	−	0.654426i
$515$	−0.592074	+	0.341834i	−0.0260899	+	0.0150630i
$516$		0			0
$517$	0.734380	−	0.423995i	0.0322980	−	0.0186473i
$518$	6.91055	+	29.4605i	0.303632	+	1.29442i
$519$		0			0
$520$	−0.0940648	−	0.535670i	−0.00412501	−	0.0234907i
$521$	−8.99770	−	5.19483i	−0.394196	−	0.227589i	0.289780	−	0.957093i	$-0.406418\pi$
$521$	−8.99770	−	5.19483i	−0.394196	−	0.227589i	−0.683977	+	0.729504i	$0.739751\pi$
$522$		0			0
$523$	6.36621	+	11.0266i	0.278375	+	0.482160i	0.970981	−	0.239156i	$-0.0768708\pi$
$523$	6.36621	+	11.0266i	0.278375	+	0.482160i	−0.692606	+	0.721316i	$0.743537\pi$
$524$	1.06655	−	0.124155i	0.0465924	−	0.00542373i
$525$		0			0
$526$	−4.78217	+	0.277405i	−0.208513	+	0.0120954i
$527$	10.7438	+	6.20296i	0.468009	+	0.270205i
$528$		0			0
$529$	−11.4961	−	19.9118i	−0.499831	−	0.865732i
$530$	−0.954534	+	0.0553708i	−0.0414623	+	0.00240516i
$531$		0			0
$532$	−7.24020	+	30.2067i	−0.313902	+	1.30962i
$533$	6.05018	−	10.4792i	0.262062	−	0.453905i
$534$		0			0
$535$	−1.11800			−0.0483354
$536$	−9.67610	+	1.69914i	−0.417944	+	0.0733919i
$537$		0			0
$538$	−22.7585	−	34.6203i	−0.981188	−	1.49259i
$539$	3.56216	−	4.20968i	0.153433	−	0.181324i
$540$		0			0
$541$	−4.02354	−	6.96897i	−0.172985	−	0.299620i	0.766477	−	0.642272i	$-0.222008\pi$
$541$	−4.02354	−	6.96897i	−0.172985	−	0.299620i	−0.939462	+	0.342652i	$0.888675\pi$
$542$	0.125745	+	2.16770i	0.00540120	+	0.0931109i
$543$		0			0
$544$	11.8303	−	3.52667i	0.507221	−	0.151205i
$545$	0.600784	−	0.346863i	0.0257348	−	0.0148580i
$546$		0			0
$547$	21.1399	+	12.2051i	0.903876	+	0.521853i	0.878456	−	0.477824i	$-0.158574\pi$
$547$	21.1399	+	12.2051i	0.903876	+	0.521853i	0.0254202	+	0.999677i	$0.491908\pi$
$548$	10.4487	−	24.1916i	0.446345	−	1.03341i
$549$		0			0
$550$	3.05100	+	4.64120i	0.130095	+	0.197901i
$551$	−41.8415			−1.78251
$552$		0			0
$553$	6.83430	+	39.2343i	0.290624	+	1.66841i
$554$	1.66230	+	28.6562i	0.0706243	+	1.21749i
$555$		0			0
$556$	−9.63842	+	22.3156i	−0.408760	+	0.946392i
$557$	2.86442	−	4.96132i	0.121369	−	0.210218i	−0.798939	−	0.601413i	$-0.794605\pi$
$557$	2.86442	−	4.96132i	0.121369	−	0.210218i	0.920308	+	0.391195i	$0.127938\pi$
$558$		0			0
$559$	−5.23224			−0.221300
$560$	0.768219	−	1.02544i	0.0324632	−	0.0433328i
$561$		0			0
$562$	32.9798	−	21.6801i	1.39117	−	0.914520i
$563$	−10.5164			−0.443215			−0.221608	−	0.975136i	$-0.571130\pi$
$563$	−10.5164			−0.443215			−0.221608	+	0.975136i	$0.571130\pi$
$564$		0			0
$565$		−	0.759209i		−	0.0319401i
$566$	12.1065	+	6.08368i	0.508875	+	0.255716i
$567$		0			0
$568$	−37.3927	+	6.56624i	−1.56896	+	0.275513i
$569$	11.6739			0.489397			0.244698	−	0.969599i	$-0.421311\pi$
$569$	11.6739			0.489397			0.244698	+	0.969599i	$0.421311\pi$
$570$		0			0
$571$		−	13.0475i		−	0.546021i	−0.962011	−	0.273010i	$-0.911981\pi$
$571$		−	13.0475i		−	0.546021i	0.962011	−	0.273010i	$-0.0880193\pi$
$572$	2.48560	−	0.289344i	0.103928	−	0.0120981i
$573$		0			0
$574$	27.7537	−	6.51019i	1.15842	−	0.271730i
$575$		−	0.439744i		−	0.0183386i
$576$		0			0
$577$	15.9806	+	9.22642i	0.665282	+	0.384101i	0.794287	−	0.607543i	$-0.207845\pi$
$577$	15.9806	+	9.22642i	0.665282	+	0.384101i	−0.129004	+	0.991644i	$0.541178\pi$
$578$	1.00225	+	17.2776i	0.0416879	+	0.718655i
$579$		0			0
$580$	1.58444	+	0.684343i	0.0657904	+	0.0284158i
$581$	−2.09840	+	5.72835i	−0.0870562	+	0.237652i
$582$		0			0
$583$		−	4.39929i		−	0.182200i
$584$	9.21082	−	25.2513i	0.381147	−	1.04491i
$585$		0			0
$586$	−5.68103	+	0.329546i	−0.234681	+	0.0136134i
$587$	−19.0791	+	33.0459i	−0.787478	+	1.36395i	0.140030	+	0.990147i	$0.455280\pi$
$587$	−19.0791	+	33.0459i	−0.787478	+	1.36395i	−0.927508	+	0.373804i	$0.878053\pi$
$588$		0			0
$589$	−16.6857	−	28.9004i	−0.687520	−	1.19082i
$590$	0.907184	+	1.38001i	0.0373482	+	0.0568141i
$591$		0			0
$592$	−31.4844	+	7.43078i	−1.29400	+	0.305403i
$593$	14.3641	−	8.29312i	0.589863	−	0.340558i	−0.175180	−	0.984536i	$-0.556051\pi$
$593$	14.3641	−	8.29312i	0.589863	−	0.340558i	0.765043	+	0.643979i	$0.222717\pi$
$594$		0			0
$595$	−0.448216	−	0.536416i	−0.0183751	−	0.0219909i
$596$	−27.3427	+	3.18292i	−1.12000	+	0.130377i
$597$		0			0
$598$	−0.177026	−	0.0889580i	−0.00723915	−	0.00363776i
$599$			33.5411i			1.37045i	0.728330	+	0.685227i	$0.240297\pi$
$599$			33.5411i			1.37045i	−0.728330	+	0.685227i	$0.759703\pi$
$600$		0			0
$601$	31.5568	+	18.2193i	1.28723	+	0.743182i	0.978159	−	0.207858i	$-0.0666491\pi$
$601$	31.5568	+	18.2193i	1.28723	+	0.743182i	0.309069	+	0.951040i	$0.399982\pi$
$602$	−8.43829	−	8.98548i	−0.343919	−	0.366221i
$603$		0			0
$604$	24.7588	+	10.6937i	1.00742	+	0.435119i
$605$	−1.08827	+	0.628316i	−0.0442447	+	0.0255447i
$606$		0			0
$607$	−6.34967	+	10.9979i	−0.257725	+	0.446393i	−0.965632	−	0.259913i	$-0.916306\pi$
$607$	−6.34967	+	10.9979i	−0.257725	+	0.446393i	0.707907	+	0.706306i	$0.249640\pi$
$608$	−32.3028	−	7.69590i	−1.31005	−	0.312110i
$609$		0			0
$610$	−1.30232	+	0.856115i	−0.0527296	+	0.0346631i
$611$	1.48053	−	0.854787i	0.0598960	−	0.0345810i
$612$		0			0
$613$	−18.5394	+	32.1112i	−0.748799	+	1.29696i	0.199600	+	0.979877i	$0.436036\pi$
$613$	−18.5394	+	32.1112i	−0.748799	+	1.29696i	−0.948399	+	0.317080i	$0.897298\pi$
$614$	11.4596	+	5.75860i	0.462473	+	0.232398i
$615$		0			0
$616$	4.50554	+	3.80195i	0.181533	+	0.153185i
$617$	−21.2232	−	36.7597i	−0.854414	−	1.47989i	−0.877188	−	0.480148i	$-0.840583\pi$
$617$	−21.2232	−	36.7597i	−0.854414	−	1.47989i	0.0227735	−	0.999741i	$-0.492750\pi$
$618$		0			0
$619$	−4.95757	−	8.58676i	−0.199261	−	0.345131i	0.749028	−	0.662539i	$-0.230521\pi$
$619$	−4.95757	−	8.58676i	−0.199261	−	0.345131i	−0.948289	+	0.317408i	$0.897188\pi$
$620$	0.159165	+	1.36730i	0.00639221	+	0.0549120i
$621$		0			0
$622$	11.3907	+	5.72399i	0.456727	+	0.229511i
$623$	35.8669	−	29.9695i	1.43698	−	1.20070i
$624$		0			0
$625$	−12.3902	+	21.4604i	−0.495607	+	0.858416i
$626$	16.6674	−	33.1681i	0.666162	−	1.32566i
$627$		0			0
$628$	20.2907	−	15.0911i	0.809687	−	0.602200i
$629$			17.6488i			0.703705i
$630$		0			0
$631$		−	1.68031i		−	0.0668920i	−0.999441	−	0.0334460i	$-0.989352\pi$
$631$		−	1.68031i		−	0.0668920i	0.999441	−	0.0334460i	$-0.0106482\pi$
$632$	−41.9332	+	7.36356i	−1.66801	+	0.292907i
$633$		0			0
$634$	14.1275	+	7.09926i	0.561076	+	0.281948i
$635$	−0.983068	+	1.70272i	−0.0390119	+	0.0675705i
$636$		0			0
$637$	7.18144	−	8.48685i	0.284539	−	0.336261i
$638$	−3.56563	+	7.09560i	−0.141165	+	0.280918i
$639$		0			0
$640$	1.09737	+	0.819759i	0.0433772	+	0.0324038i
$641$	0.577484	+	1.00023i	0.0228092	+	0.0395067i	0.877205	−	0.480117i	$-0.159406\pi$
$641$	0.577484	+	1.00023i	0.0228092	+	0.0395067i	−0.854395	+	0.519623i	$0.826072\pi$
$642$		0			0
$643$	5.50859	+	9.54116i	0.217238	+	0.376267i	0.953962	−	0.299926i	$-0.0969620\pi$
$643$	5.50859	+	9.54116i	0.217238	+	0.376267i	−0.736725	+	0.676193i	$0.763629\pi$
$644$	−0.132729	−	0.447480i	−0.00523025	−	0.0176332i
$645$		0			0
$646$	−8.13453	+	16.1877i	−0.320049	+	0.636898i
$647$	−12.3459	+	21.3838i	−0.485368	+	0.840683i	−0.999859	−	0.0168136i	$-0.994648\pi$
$647$	−12.3459	+	21.3838i	−0.485368	+	0.840683i	0.514490	+	0.857496i	$0.327981\pi$
$648$		0			0
$649$	−6.58063	+	3.79933i	−0.258312	+	0.149137i
$650$	6.15093	+	9.35680i	0.241259	+	0.367004i
$651$		0			0
$652$	−4.60614	−	1.98946i	−0.180390	−	0.0779131i
$653$	−0.943231	+	1.63372i	−0.0369115	+	0.0639326i	−0.883891	−	0.467693i	$-0.845085\pi$
$653$	−0.943231	+	1.63372i	−0.0369115	+	0.0639326i	0.846980	+	0.531626i	$0.178419\pi$
$654$		0			0
$655$	0.0562912	−	0.0324997i	0.00219948	−	0.00126987i
$656$	7.00028	+	29.6604i	0.273315	+	1.15804i
$657$		0			0
$658$	3.85568	+	1.16401i	0.150310	+	0.0453778i
$659$	6.59789	+	3.80929i	0.257017	+	0.148389i	0.622973	−	0.782243i	$-0.285925\pi$
$659$	6.59789	+	3.80929i	0.257017	+	0.148389i	−0.365956	+	0.930632i	$0.619258\pi$
$660$		0			0
$661$		−	0.524205i		−	0.0203892i	−0.999948	−	0.0101946i	$-0.996755\pi$
$661$		−	0.524205i		−	0.0203892i	0.999948	−	0.0101946i	$-0.00324510\pi$
$662$	−10.4170	+	20.7297i	−0.404866	+	0.805684i
$663$		0			0
$664$	−6.12693	−	2.23490i	−0.237771	−	0.0867309i
$665$	0.322683	+	1.85246i	0.0125131	+	0.0718352i
$666$		0			0
$667$	0.544489	−	0.314361i	0.0210827	−	0.0121721i
$668$	−10.5854	+	24.5080i	−0.409560	+	0.948244i
$669$		0			0
$670$	−0.496945	+	0.326679i	−0.0191987	+	0.0126207i
$671$	−3.58545	−	6.21018i	−0.138415	−	0.239741i
$672$		0			0
$673$	3.99861	−	6.92580i	0.154135	−	0.266970i	−0.778609	−	0.627510i	$-0.784074\pi$
$673$	3.99861	−	6.92580i	0.154135	−	0.266970i	0.932744	+	0.360540i	$0.117408\pi$
$674$	−0.651203	−	11.2260i	−0.0250834	−	0.432411i
$675$		0			0
$676$	−20.8146	+	2.42299i	−0.800560	+	0.0931917i
$677$		−	43.1867i		−	1.65980i	−0.557912	−	0.829900i	$-0.688397\pi$
$677$		−	43.1867i		−	1.65980i	0.557912	−	0.829900i	$-0.311603\pi$
$678$		0			0
$679$	−1.72146	−	0.630603i	−0.0660637	−	0.0242003i
$680$	0.572797	−	0.479948i	0.0219658	−	0.0184052i
$681$		0			0
$682$	−6.32292	+	0.366782i	−0.242117	+	0.0140448i
$683$	−8.19378	−	4.73068i	−0.313526	−	0.181015i	0.334977	−	0.942226i	$-0.391271\pi$
$683$	−8.19378	−	4.73068i	−0.313526	−	0.181015i	−0.648503	+	0.761212i	$0.724605\pi$
$684$		0			0
$685$		−	1.59519i		−	0.0609492i
$686$	26.1566	−	1.35425i	0.998662	−	0.0517057i
$687$		0			0
$688$	9.59353	−	9.03404i	0.365750	−	0.344420i
$689$		−	8.86911i		−	0.337886i
$690$		0			0
$691$	28.4459			1.08213			0.541067	−	0.840980i	$-0.318021\pi$
$691$	28.4459			1.08213			0.541067	+	0.840980i	$0.318021\pi$
$692$	−18.7066	+	13.9129i	−0.711119	+	0.528890i
$693$		0			0
$694$	−23.0917	+	45.9524i	−0.876547	+	1.74433i
$695$			1.47149i			0.0558169i
$696$		0			0
$697$	16.6263			0.629768
$698$	−1.23832	−	1.88373i	−0.0468710	−	0.0713003i
$699$		0			0
$700$	−6.14882	+	25.6533i	−0.232404	+	0.969605i
$701$	33.5350			1.26660			0.633300	−	0.773906i	$-0.281700\pi$
$701$	33.5350			1.26660			0.633300	+	0.773906i	$0.281700\pi$
$702$		0			0
$703$	23.7373	−	41.1141i	0.895267	−	1.55065i
$704$	−4.05786	+	4.82218i	−0.152936	+	0.181743i
$705$		0			0
$706$	33.6694	−	1.95310i	1.26716	−	0.0735059i
$707$	−34.7982	+	29.0765i	−1.30872	+	1.09353i
$708$		0			0
$709$	27.8888			1.04739			0.523693	−	0.851907i	$-0.324554\pi$
$709$	27.8888			1.04739			0.523693	+	0.851907i	$0.324554\pi$
$710$	−1.92042	+	1.26243i	−0.0720719	+	0.0473783i
$711$		0			0
$712$	32.0912	+	38.2994i	1.20267	+	1.43533i
$713$	0.434265	+	0.250723i	0.0162634	+	0.00938965i
$714$		0			0
$715$	0.131187	−	0.0757408i	0.00490611	−	0.00283255i
$716$	3.66849	+	31.5140i	0.137098	+	1.17773i
$717$		0			0
$718$	31.8584	−	1.84805i	1.18895	−	0.0689686i
$719$	22.0843	+	38.2510i	0.823604	+	1.42652i	0.902982	+	0.429679i	$0.141373\pi$
$719$	22.0843	+	38.2510i	0.823604	+	1.42652i	−0.0793781	+	0.996845i	$0.525293\pi$
$720$		0			0
$721$	5.13894	−	14.0286i	0.191384	−	0.522453i
$722$	18.2690	−	12.0096i	0.679901	−	0.446949i
$723$		0			0
$724$	−1.61846	+	1.20372i	−0.0601494	+	0.0447358i
$725$	−35.5343			−1.31971
$726$		0			0
$727$	6.96878	−	12.0703i	0.258458	−	0.447662i	−0.707371	−	0.706842i	$-0.750119\pi$
$727$	6.96878	−	12.0703i	0.258458	−	0.447662i	0.965829	+	0.259180i	$0.0834524\pi$
$728$	9.08332	+	7.66486i	0.336650	+	0.284078i
$729$		0			0
$730$	−0.0942270	−	1.62437i	−0.00348750	−	0.0601207i
$731$	−3.59465	−	6.22611i	−0.132953	−	0.230281i
$732$		0			0
$733$	14.8947	+	8.59943i	0.550147	+	0.317627i	0.749181	−	0.662365i	$-0.230447\pi$
$733$	14.8947	+	8.59943i	0.550147	+	0.317627i	−0.199035	+	0.979992i	$0.563781\pi$
$734$	−1.46801	−	25.3069i	−0.0541851	−	0.934094i
$735$		0			0
$736$	0.478181	−	0.142548i	0.0176260	−	0.00525438i
$737$	−1.36815	−	2.36970i	−0.0503964	−	0.0872891i
$738$		0			0
$739$	8.40583	+	4.85311i	0.309214	+	0.178525i	0.646574	−	0.762851i	$-0.276201\pi$
$739$	8.40583	+	4.85311i	0.309214	+	0.178525i	−0.337361	+	0.941375i	$0.609534\pi$
$740$	−1.57132	+	1.16866i	−0.0577630	+	0.0429609i
$741$		0			0
$742$	15.2312	−	14.3036i	0.559154	−	0.525103i
$743$	−1.44066	+	0.831764i	−0.0528526	+	0.0305145i	−0.526193	−	0.850365i	$-0.676381\pi$
$743$	−1.44066	+	0.831764i	−0.0528526	+	0.0305145i	0.473341	+	0.880879i	$0.343048\pi$
$744$		0			0
$745$	−1.44312	+	0.833185i	−0.0528718	+	0.0305255i
$746$	−20.3686	+	13.3898i	−0.745746	+	0.490234i
$747$		0			0
$748$	2.05196	+	2.75896i	0.0750270	+	0.100877i
$749$	18.7483	−	15.6656i	0.685048	−	0.572410i
$750$		0			0
$751$	13.7319	+	7.92810i	0.501083	+	0.289300i	0.729161	−	0.684343i	$-0.239911\pi$
$751$	13.7319	+	7.92810i	0.501083	+	0.289300i	−0.228078	+	0.973643i	$0.573244\pi$
$752$	−1.23874	+	4.12360i	−0.0451721	+	0.150372i
$753$		0			0
$754$	−7.18842	+	14.3050i	−0.261787	+	0.520956i
$755$	1.63260			0.0594162
$756$		0			0
$757$	−1.10758			−0.0402555			−0.0201278	−	0.999797i	$-0.506407\pi$
$757$	−1.10758			−0.0402555			−0.0201278	+	0.999797i	$0.506407\pi$
$758$	−0.367898	+	0.732118i	−0.0133627	+	0.0265917i
$759$		0			0
$760$	−1.97989	+	0.347672i	−0.0718180	+	0.0126114i
$761$	−21.7341	−	12.5482i	−0.787862	−	0.454872i	0.0513475	−	0.998681i	$-0.483648\pi$
$761$	−21.7341	−	12.5482i	−0.787862	−	0.454872i	−0.839209	+	0.543809i	$0.816982\pi$
$762$		0			0
$763$	−5.21454	+	14.2350i	−0.188779	+	0.515342i
$764$	10.8680	−	8.08303i	0.393191	−	0.292434i
$765$		0			0
$766$	−37.5783	+	24.7030i	−1.35776	+	0.892557i
$767$	−13.2668	+	7.65957i	−0.479035	+	0.276571i
$768$		0			0
$769$	−10.1877	+	5.88189i	−0.367379	+	0.212106i	−0.672313	−	0.740267i	$-0.734699\pi$
$769$	−10.1877	+	5.88189i	−0.367379	+	0.212106i	0.304934	+	0.952374i	$0.401366\pi$
$770$	0.341643	+	0.103140i	0.0123120	+	0.00371692i
$771$		0			0
$772$	−1.31622	−	1.76972i	−0.0473717	−	0.0636935i
$773$	4.03375	+	2.32889i	0.145084	+	0.0837642i	0.570785	−	0.821100i	$-0.306639\pi$
$773$	4.03375	+	2.32889i	0.145084	+	0.0837642i	−0.425701	+	0.904864i	$0.639972\pi$
$774$		0			0
$775$	−14.1705	−	24.5440i	−0.509018	−	0.881646i
$776$	0.671624	−	1.84124i	0.0241099	−	0.0660967i
$777$		0			0
$778$	−0.867319	−	14.9516i	−0.0310949	−	0.536043i
$779$	−38.7322	−	22.3620i	−1.38772	−	0.801203i
$780$		0			0
$781$	−5.28713	−	9.15757i	−0.189188	−	0.327684i
$782$	−0.0157648	−	0.271769i	−0.000563749	−	0.00971843i
$783$		0			0
$784$	1.48602	+	27.9605i	0.0530723	+	0.998591i
$785$	0.765386	−	1.32569i	0.0273178	−	0.0473158i
$786$		0			0
$787$	−37.8242			−1.34829			−0.674143	−	0.738600i	$-0.735487\pi$
$787$	−37.8242			−1.34829			−0.674143	+	0.738600i	$0.735487\pi$
$788$	−10.7949	−	14.5143i	−0.384552	−	0.517049i
$789$		0			0
$790$	−2.15361	+	1.41573i	−0.0766219	+	0.0503693i
$791$	10.6382	+	12.7315i	0.378250	+	0.452681i
$792$		0			0
$793$	−7.22838	−	12.5199i	−0.256687	−	0.444596i
$794$	−26.1187	+	1.51510i	−0.926918	+	0.0537689i
$795$		0			0
$796$	−13.7185	+	1.59695i	−0.486240	+	0.0566023i
$797$	40.7370	−	23.5195i	1.44298	−	0.833104i	0.444931	−	0.895565i	$-0.353228\pi$
$797$	40.7370	−	23.5195i	1.44298	−	0.833104i	0.998047	+	0.0624614i	$0.0198950\pi$
$798$		0			0
$799$	2.03431	+	1.17451i	0.0719687	+	0.0415512i
$800$	−27.4335	−	6.53583i	−0.969922	−	0.231076i
$801$		0			0
$802$	9.13526	−	6.00529i	0.322577	−	0.212054i
$803$	7.48646			0.264192
$804$		0			0
$805$	−0.0181169	−	0.0216819i	−0.000638536	−	0.000764187i
$806$	−12.7472	+	0.739444i	−0.449002	+	0.0260458i
$807$		0			0
$808$	−31.1350	−	37.1582i	−1.09532	−	1.30722i
$809$	−25.6159	+	44.3680i	−0.900606	+	1.55989i	−0.0738961	+	0.997266i	$0.523543\pi$
$809$	−25.6159	+	44.3680i	−0.900606	+	1.55989i	−0.826710	+	0.562629i	$0.809790\pi$
$810$		0			0
$811$	35.2639			1.23828			0.619141	−	0.785280i	$-0.287481\pi$
$811$	35.2639			1.23828			0.619141	+	0.785280i	$0.287481\pi$
$812$	−36.1595	+	10.7254i	−1.26895	+	0.376388i
$813$		0			0
$814$	−4.94942	−	7.52908i	−0.173477	−	0.263894i
$815$	−0.303729			−0.0106392
$816$		0			0
$817$			19.3389i			0.676581i
$818$	−9.46968	+	18.8447i	−0.331100	+	0.658888i
$819$		0			0
$820$	1.10096	+	1.48029i	0.0384471	+	0.0516939i
$821$	28.0829			0.980101			0.490050	−	0.871694i	$-0.336978\pi$
$821$	28.0829			0.980101			0.490050	+	0.871694i	$0.336978\pi$
$822$		0			0
$823$		−	35.2419i		−	1.22846i	−0.789129	−	0.614228i	$-0.789468\pi$
$823$		−	35.2419i		−	1.22846i	0.789129	−	0.614228i	$-0.210532\pi$
$824$	15.0047	+	5.47323i	0.522715	+	0.190669i
$825$		0			0
$826$	−34.5500	−	10.4305i	−1.20215	−	0.362922i
$827$		−	18.2748i		−	0.635478i	−0.948178	−	0.317739i	$-0.897076\pi$
$827$		−	18.2748i		−	0.635478i	0.948178	−	0.317739i	$-0.102924\pi$
$828$		0			0
$829$	37.2925	+	21.5308i	1.29522	+	0.747797i	0.979575	−	0.201079i	$-0.0644449\pi$
$829$	37.2925	+	21.5308i	1.29522	+	0.747797i	0.315648	+	0.948876i	$0.397778\pi$
$830$	−0.394135	+	0.0228631i	−0.0136806	+	0.000793589i
$831$		0			0
$832$	−8.18078	+	9.72168i	−0.283618	+	0.337039i
$833$	15.0327	+	2.71494i	0.520853	+	0.0940671i
$834$		0			0
$835$			1.61606i			0.0559261i
$836$	−1.06944	−	9.18700i	−0.0369874	−	0.317739i
$837$		0			0
$838$	−1.76210	−	30.3767i	−0.0608708	−	1.04935i
$839$	9.15093	−	15.8499i	0.315925	−	0.547199i	−0.663708	−	0.747991i	$-0.731018\pi$
$839$	9.15093	−	15.8499i	0.315925	−	0.547199i	0.979634	+	0.200793i	$0.0643518\pi$
$840$		0			0
$841$	−10.9025	−	18.8837i	−0.375949	−	0.651162i
$842$	−16.1833	+	10.6385i	−0.557715	+	0.366628i
$843$		0			0
$844$	51.9155	+	22.4230i	1.78700	+	0.771832i
$845$	−1.09857	+	0.634259i	−0.0377919	+	0.0218192i
$846$		0			0
$847$	9.44574	−	25.7856i	0.324559	−	0.886005i
$848$	15.3135	+	16.2619i	0.525868	+	0.558435i
$849$		0			0
$850$	−6.90834	+	13.7476i	−0.236954	+	0.471539i
$851$			0.713365i			0.0244538i
$852$		0			0
$853$	37.5921	+	21.7038i	1.28713	+	0.743125i	0.978141	−	0.207941i	$-0.0666762\pi$
$853$	37.5921	+	21.7038i	1.28713	+	0.743125i	0.308989	+	0.951066i	$0.400009\pi$
$854$	9.84328	−	32.6050i	0.336830	−	1.11572i
$855$		0			0
$856$	16.7747	+	20.0198i	0.573347	+	0.684264i
$857$	−33.3399	+	19.2488i	−1.13887	+	0.657527i	−0.946150	−	0.323727i	$-0.895064\pi$
$857$	−33.3399	+	19.2488i	−1.13887	+	0.657527i	−0.192719	+	0.981254i	$0.561731\pi$
$858$		0			0
$859$	−1.25279	+	2.16989i	−0.0427445	+	0.0740357i	−0.886606	−	0.462525i	$-0.846943\pi$
$859$	−1.25279	+	2.16989i	−0.0427445	+	0.0740357i	0.843862	+	0.536561i	$0.180277\pi$
$860$	0.316299	−	0.732319i	0.0107857	−	0.0249719i
$861$		0			0
$862$	13.3745	+	20.3453i	0.455537	+	0.692964i
$863$	−23.9226	+	13.8117i	−0.814335	+	0.470157i	−0.848459	−	0.529261i	$-0.822469\pi$
$863$	−23.9226	+	13.8117i	−0.814335	+	0.470157i	0.0341239	+	0.999418i	$0.489136\pi$
$864$		0			0
$865$	−0.705633	+	1.22219i	−0.0239922	+	0.0415558i
$866$	−8.55824	+	17.0309i	−0.290821	+	0.578734i
$867$		0			0
$868$	−21.8279	−	20.6986i	−0.740888	−	0.702558i
$869$	−5.92913	−	10.2696i	−0.201132	−	0.348371i
$870$		0			0
$871$	−2.75823	−	4.77740i	−0.0934591	−	0.161876i
$872$	−15.2255	−	5.55375i	−0.515600	−	0.188074i
$873$		0			0
$874$	−0.328797	+	0.654307i	−0.0111217	+	0.0221323i
$875$	0.548890	+	3.15107i	0.0185559	+	0.106525i
$876$		0			0
$877$	−8.69270	+	15.0562i	−0.293532	+	0.508412i	−0.974642	−	0.223769i	$-0.928164\pi$
$877$	−8.69270	+	15.0562i	−0.293532	+	0.508412i	0.681111	+	0.732181i	$0.261497\pi$
$878$	−11.2444	−	5.65043i	−0.379479	−	0.190693i
$879$		0			0
$880$	−0.109762	+	0.365383i	−0.00370007	+	0.0123170i
$881$		−	25.8969i		−	0.872489i	−0.899828	−	0.436244i	$-0.856308\pi$
$881$		−	25.8969i		−	0.872489i	0.899828	−	0.436244i	$-0.143692\pi$
$882$		0			0
$883$			1.97128i			0.0663387i	0.999450	+	0.0331694i	$0.0105601\pi$
$883$			1.97128i			0.0663387i	−0.999450	+	0.0331694i	$0.989440\pi$
$884$	4.13681	+	5.56215i	0.139136	+	0.187075i
$885$		0			0
$886$	−15.6610	+	31.1653i	−0.526140	+	1.04702i
$887$	0.393262	−	0.681150i	0.0132045	−	0.0228708i	−0.859348	−	0.511392i	$-0.829130\pi$
$887$	0.393262	−	0.681150i	0.0132045	−	0.0228708i	0.872552	+	0.488521i	$0.162463\pi$
$888$		0			0
$889$	−7.37332	−	42.3287i	−0.247293	−	1.41966i
$890$	2.70269	+	1.35814i	0.0905945	+	0.0455248i
$891$		0			0
$892$	−32.6868	+	3.80501i	−1.09444	+	0.127401i
$893$	−3.15937	−	5.47220i	−0.105724	−	0.183120i
$894$		0			0
$895$	0.960291	+	1.66327i	0.0320990	+	0.0555971i
$896$	−29.8889	+	1.62953i	−0.998517	+	0.0544388i
$897$		0			0
$898$	34.5638	+	17.3687i	1.15341	+	0.579603i
$899$	20.2602	−	35.0916i	0.675714	−	1.17037i
$900$		0			0
$901$	10.5538	−	6.09325i	0.351599	−	0.202996i
$902$	−7.09288	+	4.66268i	−0.236167	+	0.155250i
$903$		0			0
$904$	−13.5950	+	11.3913i	−0.452163	+	0.378869i
$905$	−0.0610499	+	0.105741i	−0.00202937	+	0.00351497i
$906$		0			0
$907$	−29.5840	+	17.0803i	−0.982320	+	0.567143i	−0.902970	−	0.429704i	$-0.858618\pi$
$907$	−29.5840	+	17.0803i	−0.982320	+	0.567143i	−0.0793500	+	0.996847i	$0.525284\pi$
$908$	−18.9576	+	43.8920i	−0.629128	+	1.45661i
$909$		0			0
$910$	0.688764	+	0.207934i	0.0228323	+	0.00689295i
$911$	−24.1673	−	13.9530i	−0.800699	−	0.462284i	0.0430164	−	0.999074i	$-0.486303\pi$
$911$	−24.1673	−	13.9530i	−0.800699	−	0.462284i	−0.843716	+	0.536790i	$0.819637\pi$
$912$		0			0
$913$		−	1.81650i		−	0.0601175i
$914$	46.4458	+	23.3396i	1.53629	+	0.772005i
$915$		0			0
$916$	−4.51066	−	38.7486i	−0.149036	−	1.28029i
$917$	−0.488582	+	1.33377i	−0.0161344	+	0.0440448i
$918$		0			0
$919$	28.7012	−	16.5707i	0.946767	−	0.546616i	0.0546916	−	0.998503i	$-0.482582\pi$
$919$	28.7012	−	16.5707i	0.946767	−	0.546616i	0.892075	+	0.451887i	$0.149249\pi$
$920$	0.0231524	−	0.0193995i	0.000763312	−	0.000639581i
$921$		0			0
$922$	−4.16863	−	6.34134i	−0.137287	−	0.208841i
$923$	−10.6590	−	18.4620i	−0.350846	−	0.607683i
$924$		0			0
$925$	20.1591	−	34.9166i	0.662828	−	1.14805i
$926$	−7.21123	+	0.418311i	−0.236976	+	0.0137465i
$927$		0			0
$928$	−11.5188	−	38.6404i	−0.378125	−	1.26843i
$929$		−	41.7300i		−	1.36912i	−0.728958	−	0.684559i	$-0.759995\pi$
$929$		−	41.7300i		−	1.36912i	0.728958	−	0.684559i	$-0.240005\pi$
$930$		0			0
$931$	−31.3682	−	26.5433i	−1.02805	−	0.869921i
$932$	7.58693	−	17.5658i	0.248518	−	0.575388i
$933$		0			0
$934$	−0.0560884	−	0.966905i	−0.00183527	−	0.0316381i
$935$	0.180256	+	0.104071i	0.00589499	+	0.00340348i
$936$		0			0
$937$			11.0320i			0.360400i	0.983630	+	0.180200i	$0.0576745\pi$
$937$			11.0320i			0.360400i	−0.983630	+	0.180200i	$0.942326\pi$
$938$	3.75603	−	12.4415i	0.122639	−	0.406230i
$939$		0			0
$940$	0.0301373	+	0.258893i	0.000982971	+	0.00844417i
$941$		−	10.9832i		−	0.358042i	−0.983845	−	0.179021i	$-0.942707\pi$
$941$		−	10.9832i		−	0.358042i	0.983845	−	0.179021i	$-0.0572931\pi$
$942$		0			0
$943$	0.672036			0.0218845
$944$	11.1001	−	36.9507i	0.361276	−	1.20264i
$945$		0			0
$946$	3.27954	+	1.64801i	0.106627	+	0.0535814i
$947$		−	28.5971i		−	0.929282i	−0.885499	−	0.464641i	$-0.846183\pi$
$947$		−	28.5971i		−	0.929282i	0.885499	−	0.464641i	$-0.153817\pi$
$948$		0			0
$949$	15.0930			0.489938
$950$	34.5836	−	22.7344i	1.12204	−	0.737602i
$951$		0			0
$952$	−2.88040	+	16.0746i	−0.0933542	+	0.520981i
$953$	16.5382			0.535726			0.267863	−	0.963457i	$-0.413682\pi$
$953$	16.5382			0.535726			0.267863	+	0.963457i	$0.413682\pi$
$954$		0			0
$955$	0.409954	−	0.710060i	0.0132658	−	0.0229770i
$956$	21.5979	+	9.32844i	0.698527	+	0.301703i
$957$		0			0
$958$	1.08498	+	18.7039i	0.0350542	+	0.604297i
$959$	22.3521	+	26.7506i	0.721788	+	0.863822i
$960$		0			0
$961$	1.31759			0.0425027
$962$	−9.97820	−	15.1789i	−0.321710	−	0.489386i
$963$		0			0
$964$	−37.2639	−	16.0948i	−1.20019	−	0.518379i
$965$	−0.115624	−	0.0667556i	−0.00372207	−	0.00214894i
$966$		0			0
$967$	3.27690	−	1.89192i	0.105378	−	0.0608401i	−0.446385	−	0.894841i	$-0.647289\pi$
$967$	3.27690	−	1.89192i	0.105378	−	0.0608401i	0.551763	+	0.834001i	$0.313955\pi$
$968$	27.5798	+	10.0602i	0.886448	+	0.323347i
$969$		0			0
$970$	−0.00687073	−	0.118444i	−0.000220606	−	0.00380301i
$971$	−9.98069	−	17.2871i	−0.320296	−	0.554768i	0.660253	−	0.751043i	$-0.270449\pi$
$971$	−9.98069	−	17.2871i	−0.320296	−	0.554768i	−0.980549	+	0.196275i	$0.937116\pi$
$972$		0			0
$973$	−20.6188	−	24.6762i	−0.661009	−	0.791082i
$974$	−5.64297	−	8.58410i	−0.180813	−	0.275052i
$975$		0			0
$976$	34.8706	+	10.4752i	1.11618	+	0.335303i
$977$	37.8238			1.21009			0.605045	−	0.796192i	$-0.293155\pi$
$977$	37.8238			1.21009			0.605045	+	0.796192i	$0.293155\pi$
$978$		0			0
$979$	−6.95858	+	12.0526i	−0.222397	+	0.385203i
$980$	0.753712	+	1.51818i	0.0240764	+	0.0484965i
$981$		0			0
$982$	−38.9636	+	2.26021i	−1.24338	+	0.0721261i
$983$	11.7577	+	20.3649i	0.375011	+	0.649539i	0.990329	−	0.138741i	$-0.0443054\pi$
$983$	11.7577	+	20.3649i	0.375011	+	0.649539i	−0.615317	+	0.788280i	$0.710972\pi$
$984$		0			0
$985$	−0.948287	−	0.547494i	−0.0302149	−	0.0174446i
$986$	−21.9608	+	1.27391i	−0.699374	+	0.0405695i
$987$		0			0
$988$	−2.15603	−	18.5213i	−0.0685925	−	0.589241i
$989$	−0.145295	−	0.251659i	−0.00462012	−	0.00800229i
$990$		0			0
$991$	20.3738	+	11.7628i	0.647194	+	0.373658i	0.787380	−	0.616468i	$-0.211437\pi$
$991$	20.3738	+	11.7628i	0.647194	+	0.373658i	−0.140186	+	0.990125i	$0.544770\pi$
$992$	22.0958	−	23.3653i	0.701543	−	0.741849i
$993$		0			0
$994$	14.5150	−	48.0796i	0.460387	−	1.52499i
$995$	−0.724047	+	0.418029i	−0.0229538	+	0.0132524i
$996$		0			0
$997$	−44.9837	+	25.9713i	−1.42465	+	0.822520i	−0.996691	−	0.0812795i	$-0.974099\pi$
$997$	−44.9837	+	25.9713i	−1.42465	+	0.822520i	−0.427956	+	0.903800i	$0.640766\pi$
$998$	11.5446	+	17.5617i	0.365439	+	0.555907i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bj.b.451.7		84
3.2	odd	2		252.2.bj.b.115.36	yes	84
4.3	odd	2	inner	756.2.bj.b.451.8		84
7.5	odd	6		756.2.n.b.19.21		84
9.4	even	3		756.2.n.b.199.35		84
9.5	odd	6		252.2.n.b.31.8	✓	84
12.11	even	2		252.2.bj.b.115.35	yes	84
21.5	even	6		252.2.n.b.187.22	yes	84
28.19	even	6		756.2.n.b.19.35		84
36.23	even	6		252.2.n.b.31.22	yes	84
36.31	odd	6		756.2.n.b.199.21		84
63.5	even	6		252.2.bj.b.103.36	yes	84
63.40	odd	6	inner	756.2.bj.b.523.7		84
84.47	odd	6		252.2.n.b.187.8	yes	84
252.103	even	6	inner	756.2.bj.b.523.8		84
252.131	odd	6		252.2.bj.b.103.35	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.8	✓	84	9.5	odd	6
252.2.n.b.31.22	yes	84	36.23	even	6
252.2.n.b.187.8	yes	84	84.47	odd	6
252.2.n.b.187.22	yes	84	21.5	even	6
252.2.bj.b.103.35	yes	84	252.131	odd	6
252.2.bj.b.103.36	yes	84	63.5	even	6
252.2.bj.b.115.35	yes	84	12.11	even	2
252.2.bj.b.115.36	yes	84	3.2	odd	2
756.2.n.b.19.21		84	7.5	odd	6
756.2.n.b.19.35		84	28.19	even	6
756.2.n.b.199.21		84	36.31	odd	6
756.2.n.b.199.35		84	9.4	even	3
756.2.bj.b.451.7		84	1.1	even	1	trivial
756.2.bj.b.451.8		84	4.3	odd	2	inner
756.2.bj.b.523.7		84	63.40	odd	6	inner
756.2.bj.b.523.8		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)

\(f(q)\)	\(=\)	\(q+(-1.26364 - 0.634994i) q^{2} +(1.19357 + 1.60481i) q^{4} +(0.104850 + 0.0605350i) q^{5} +(-2.60650 + 0.454031i) q^{7} +(-0.489193 - 2.78580i) q^{8} +O(q^{10})\)	\(q+(-1.26364 - 0.634994i) q^{2} +(1.19357 + 1.60481i) q^{4} +(0.104850 + 0.0605350i) q^{5} +(-2.60650 + 0.454031i) q^{7} +(-0.489193 - 2.78580i) q^{8} +(-0.0940527 - 0.143073i) q^{10} +(0.682250 - 0.393897i) q^{11} +(1.37544 - 0.794110i) q^{13} +(3.58198 + 1.08138i) q^{14} +(-1.15080 + 3.83088i) q^{16} +(1.88990 + 1.09114i) q^{17} +(-2.93511 - 5.08375i) q^{19} +(0.0279980 + 0.240516i) q^{20} +(-1.11224 + 0.0645191i) q^{22} +(0.0763898 + 0.0441037i) q^{23} +(-2.49267 - 4.31743i) q^{25} +(-2.24231 + 0.130073i) q^{26} +(-3.83966 - 3.64101i) q^{28} +(3.56388 - 6.17283i) q^{29} +5.68486 q^{31} +(3.88679 - 4.11010i) q^{32} +(-1.69529 - 2.57888i) q^{34} +(-0.300776 - 0.110180i) q^{35} +(4.04368 + 7.00386i) q^{37} +(0.480761 + 8.28780i) q^{38} +(0.117347 - 0.321704i) q^{40} +(6.59809 - 3.80941i) q^{41} +(-2.85304 - 1.64720i) q^{43} +(1.44644 + 0.624737i) q^{44} +(-0.0685235 - 0.104238i) q^{46} +1.07641 q^{47} +(6.58771 - 2.36687i) q^{49} +(0.408291 + 7.03851i) q^{50} +(2.91607 + 1.25949i) q^{52} +(2.79216 - 4.83615i) q^{53} +0.0953783 q^{55} +(2.53992 + 7.03909i) q^{56} +(-8.42317 + 5.53718i) q^{58} -9.64548 q^{59} -9.10250i q^{61} +(-7.18360 - 3.60985i) q^{62} +(-7.52138 + 2.72559i) q^{64} +0.192286 q^{65} -3.47336i q^{67} +(0.504661 + 4.33527i) q^{68} +(0.310108 + 0.330218i) q^{70} -13.4226i q^{71} +(8.22990 + 4.75153i) q^{73} +(-0.662341 - 11.4181i) q^{74} +(4.65520 - 10.7781i) q^{76} +(-1.59944 + 1.33646i) q^{77} -15.0525i q^{79} +(-0.352564 + 0.332003i) q^{80} +(-10.7566 + 0.623969i) q^{82} +(1.15290 - 1.99689i) q^{83} +(0.132104 + 0.228811i) q^{85} +(2.55925 + 3.89313i) q^{86} +(-1.43107 - 1.70792i) q^{88} +(-15.2992 + 8.83298i) q^{89} +(-3.22453 + 2.69434i) q^{91} +(0.0203984 + 0.175231i) q^{92} +(-1.36019 - 0.683513i) q^{94} -0.710706i q^{95} +(0.600098 + 0.346467i) q^{97} +(-9.82743 - 1.19229i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 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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