LMFDB - Embedded newform 756.2.bj.b.451.8

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			451.8
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26364 + 0.634994i) q^{2} +(1.19357 - 1.60481i) q^{4} +(0.104850 + 0.0605350i) q^{5} +(2.60650 - 0.454031i) q^{7} +(-0.489193 + 2.78580i) q^{8} +O(q^{10})$	\(q+(-1.26364 + 0.634994i) q^{2} +(1.19357 - 1.60481i) q^{4} +(0.104850 + 0.0605350i) q^{5} +(2.60650 - 0.454031i) q^{7} +(-0.489193 + 2.78580i) q^{8} +(-0.170931 - 0.00991543i) q^{10} +(-0.682250 + 0.393897i) q^{11} +(1.37544 - 0.794110i) q^{13} +(-3.00537 + 2.22885i) q^{14} +(-1.15080 - 3.83088i) q^{16} +(1.88990 + 1.09114i) q^{17} +(2.93511 + 5.08375i) q^{19} +(0.222292 - 0.0960109i) q^{20} +(0.611995 - 0.930968i) q^{22} +(-0.0763898 - 0.0441037i) q^{23} +(-2.49267 - 4.31743i) q^{25} +(-1.23380 + 1.87686i) q^{26} +(2.38240 - 4.72485i) q^{28} +(3.56388 - 6.17283i) q^{29} -5.68486 q^{31} +(3.88679 + 4.11010i) q^{32} +(-3.08102 - 0.178725i) q^{34} +(0.300776 + 0.110180i) q^{35} +(4.04368 + 7.00386i) q^{37} +(-6.93706 - 4.56025i) q^{38} +(-0.219930 + 0.262477i) q^{40} +(6.59809 - 3.80941i) q^{41} +(2.85304 + 1.64720i) q^{43} +(-0.182181 + 1.56502i) q^{44} +(0.124535 + 0.00722404i) q^{46} -1.07641 q^{47} +(6.58771 - 2.36687i) q^{49} +(5.89138 + 3.87284i) q^{50} +(0.367283 - 3.15513i) q^{52} +(2.79216 - 4.83615i) q^{53} -0.0953783 q^{55} +(-0.0102409 + 7.48331i) q^{56} +(-0.583752 + 10.0633i) q^{58} +9.64548 q^{59} -9.10250i q^{61} +(7.18360 - 3.60985i) q^{62} +(-7.52138 - 2.72559i) q^{64} +0.192286 q^{65} +3.47336i q^{67} +(4.00679 - 1.73059i) q^{68} +(-0.450035 + 0.0517637i) q^{70} +13.4226i q^{71} +(8.22990 + 4.75153i) q^{73} +(-9.55716 - 6.28263i) q^{74} +(11.6617 + 1.35751i) q^{76} +(-1.59944 + 1.33646i) q^{77} +15.0525i q^{79} +(0.111241 - 0.471331i) q^{80} +(-5.91865 + 9.00346i) q^{82} +(-1.15290 + 1.99689i) q^{83} +(0.132104 + 0.228811i) q^{85} +(-4.65117 - 0.269806i) q^{86} +(-0.763568 - 2.09330i) q^{88} +(-15.2992 + 8.83298i) q^{89} +(3.22453 - 2.69434i) q^{91} +(-0.161954 + 0.0699502i) q^{92} +(1.36019 - 0.683513i) q^{94} +0.710706i q^{95} +(0.600098 + 0.346467i) q^{97} +(-6.82154 + 7.17402i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$10$	−0.170931	−	0.00991543i	−0.0540533	−	0.00313553i
$11$	−0.682250	+	0.393897i	−0.205706	+	0.118764i	−0.599314	−	0.800514i	$-0.704560\pi$
$11$	−0.682250	+	0.393897i	−0.205706	+	0.118764i	0.393608	+	0.919278i	$0.371227\pi$
$12$		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	$0.262647\pi$
$14$	−3.00537	+	2.22885i	−0.803219	+	0.595684i
$15$		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	$0.0684826\pi$
$19$	2.93511	+	5.08375i	0.673359	+	1.16629i	−0.303586	+	0.952804i	$0.598184\pi$
$20$	0.222292	−	0.0960109i	0.0497060	−	0.0214687i
$21$		0			0
$22$	0.611995	−	0.930968i	0.130478	−	0.198483i
$23$	−0.0763898	−	0.0441037i	−0.0159284	−	0.00919625i	0.492015	−	0.870587i	$-0.336261\pi$
$23$	−0.0763898	−	0.0441037i	−0.0159284	−	0.00919625i	−0.507943	+	0.861391i	$0.669594\pi$
$24$		0			0
$25$	−2.49267	−	4.31743i	−0.498534	−	0.863487i
$26$	−1.23380	+	1.87686i	−0.241969	+	0.368083i
$27$		0			0
$28$	2.38240	−	4.72485i	0.450231	−	0.892912i
$29$	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	$-0.670545\pi$
$31$	−5.68486			−1.02103			−0.510515	+	0.859869i	$0.670545\pi$
$32$	3.88679	+	4.11010i	0.687093	+	0.726569i
$33$		0			0
$34$	−3.08102	−	0.178725i	−0.528391	−	0.0306510i
$35$	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	$0.601860\pi$
$38$	−6.93706	−	4.56025i	−1.12534	−	0.739770i
$39$		0			0
$40$	−0.219930	+	0.262477i	−0.0347740	+	0.0415013i
$41$	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	0.701510	−	0.712659i	$-0.252509\pi$
$43$	2.85304	+	1.64720i	0.435084	+	0.251196i	−0.266426	+	0.963855i	$0.585843\pi$
$44$	−0.182181	+	1.56502i	−0.0274649	+	0.235936i
$45$		0			0
$46$	0.124535	+	0.00722404i	0.0183616	+	0.00106513i
$47$	−1.07641			−0.157010			−0.0785052	−	0.996914i	$-0.525015\pi$
$47$	−1.07641			−0.157010			−0.0785052	+	0.996914i	$0.525015\pi$
$48$		0			0
$49$	6.58771	−	2.36687i	0.941102	−	0.338124i
$50$	5.89138	+	3.87284i	0.833167	+	0.547703i
$51$		0			0
$52$	0.367283	−	3.15513i	0.0509330	−	0.437538i
$53$	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
$56$	−0.0102409	+	7.48331i	−0.00136849	+	0.999999i
$57$		0			0
$58$	−0.583752	+	10.0633i	−0.0766504	+	1.32137i
$59$	9.64548			1.25574			0.627868	−	0.778320i	$-0.283928\pi$
$59$	9.64548			1.25574			0.627868	+	0.778320i	$0.283928\pi$
$60$		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	$0.0680529\pi$
$67$			3.47336i			0.424339i	−0.977233	+	0.212169i	$0.931947\pi$
$68$	4.00679	−	1.73059i	0.485894	−	0.209865i
$69$		0			0
$70$	−0.450035	+	0.0517637i	−0.0537895	+	0.00618694i
$71$			13.4226i			1.59297i	0.604658	+	0.796485i	$0.293310\pi$
$71$			13.4226i			1.59297i	−0.604658	+	0.796485i	$0.706690\pi$
$72$		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	$0.478954\pi$
$74$	−9.55716	−	6.28263i	−1.11100	−	0.730341i
$75$		0			0
$76$	11.6617	+	1.35751i	1.33769	+	0.155718i
$77$	−1.59944	+	1.33646i	−0.182274	+	0.152303i
$78$		0			0
$79$			15.0525i			1.69354i	0.531963	+	0.846768i	$0.321455\pi$
$79$			15.0525i			1.69354i	−0.531963	+	0.846768i	$0.678545\pi$
$80$	0.111241	−	0.471331i	0.0124371	−	0.0526964i
$81$		0			0
$82$	−5.91865	+	9.00346i	−0.653606	+	0.994266i
$83$	−1.15290	+	1.99689i	−0.126548	+	0.219187i	−0.922337	−	0.386387i	$-0.873723\pi$
$83$	−1.15290	+	1.99689i	−0.126548	+	0.219187i	0.795789	+	0.605574i	$0.207056\pi$
$84$		0			0
$85$	0.132104	+	0.228811i	0.0143287	+	0.0248180i
$86$	−4.65117	−	0.269806i	−0.501549	−	0.0290940i
$87$		0			0
$88$	−0.763568	−	2.09330i	−0.0813966	−	0.223147i
$89$	−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
$92$	−0.161954	+	0.0699502i	−0.0168849	+	0.00729281i
$93$		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	$0.655467\pi$
$98$	−6.82154	+	7.17402i	−0.689079	+	0.724686i
$99$		0			0
$100$	−9.90381	−	1.15288i	−0.990381	−	0.115288i
$101$	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	−0.692736	−	0.721191i	$-0.743595\pi$
$103$	2.82344	−	4.89035i	0.278202	−	0.481860i	0.970938	+	0.239331i	$0.0769282\pi$
$104$	1.53938	+	4.22017i	0.150948	+	0.413822i
$105$		0			0
$106$	−0.457346	+	7.88415i	−0.0444214	+	0.765777i
$107$	7.99717	−	4.61717i	0.773116	−	0.446359i	−0.0608692	−	0.998146i	$-0.519387\pi$
$107$	7.99717	−	4.61717i	0.773116	−	0.446359i	0.833985	+	0.551787i	$0.186054\pi$
$108$		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
$112$	−4.73892	−	9.46270i	−0.447785	−	0.894141i
$113$	−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
$116$	−5.65246	−	13.0870i	−0.524818	−	1.21510i
$117$		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	$-0.743904\pi$
$127$		−	16.2397i		−	1.44104i	0.693436	−	0.720519i	$-0.256096\pi$
$128$	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	−0.877514	−	0.479551i	$-0.840799\pi$
$131$	−0.268437	+	0.464947i	−0.0234535	+	0.0406226i	0.854060	+	0.520174i	$0.174133\pi$
$132$		0			0
$133$	9.95854	+	11.9182i	0.863515	+	1.03344i
$134$	−2.20556	−	4.38908i	−0.190532	−	0.379158i
$135$		0			0
$136$	−3.96422	+	4.73112i	−0.339929	+	0.405690i
$137$	−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	$-0.994293\pi$
$139$	−6.07703	−	10.5257i	−0.515447	−	0.892780i	0.484392	−	0.874851i	$-0.339041\pi$
$140$	0.535812	−	0.351180i	0.0452844	−	0.0296801i
$141$		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
$146$	−13.4168	−	0.778286i	−1.11038	−	0.0644114i
$147$		0			0
$148$	16.0662	+	1.87024i	1.32064	+	0.153733i
$149$	−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	−0.893190	−	0.449679i	$-0.851538\pi$
$151$	−11.6781	+	6.74236i	−0.950352	+	0.548686i	−0.0571616	+	0.998365i	$0.518205\pi$
$152$	−15.5982	+	5.68969i	−1.26518	+	0.461495i
$153$		0			0
$154$	1.17248	−	2.70444i	0.0944810	−	0.217930i
$155$	−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
$160$	0.158724	+	0.666229i	0.0125482	+	0.0526700i
$161$	−0.219135	−	0.0802730i	−0.0172702	−	0.00632640i
$162$		0			0
$163$	2.17260	−	1.25435i	0.170171	−	0.0982486i	−0.412495	−	0.910960i	$-0.635343\pi$
$163$	2.17260	−	1.25435i	0.170171	−	0.0982486i	0.582667	+	0.812711i	$0.302009\pi$
$164$	1.76189	−	15.1354i	0.137580	−	1.18188i
$165$		0			0
$166$	0.188842	−	3.25543i	0.0146570	−	0.252671i
$167$	−6.67408	−	11.5598i	−0.516456	−	0.894527i	−0.999817	−	0.0191068i	$-0.993918\pi$
$167$	−6.67408	−	11.5598i	−0.516456	−	0.894527i	0.483362	−	0.875421i	$-0.339416\pi$
$168$		0			0
$169$	−5.23878	+	9.07383i	−0.402983	+	0.697987i
$170$	−0.312225	−	0.205249i	−0.0239466	−	0.0157419i
$171$		0			0
$172$	6.04873	−	2.61253i	0.461211	−	0.199204i
$173$			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
$176$	2.29411	+	2.16032i	0.172925	+	0.162840i
$177$		0			0
$178$	13.7237	−	20.8766i	1.02864	−	1.56477i
$179$	−13.7381	−	7.93170i	−1.02683	−	0.592843i	−0.110759	−	0.993847i	$-0.535328\pi$
$179$	−13.7381	−	7.93170i	−1.02683	−	0.592843i	−0.916076	+	0.401004i	$0.868661\pi$
$180$		0			0
$181$			1.00851i			0.0749616i	0.999297	+	0.0374808i	$0.0119333\pi$
$181$			1.00851i			0.0749616i	−0.999297	+	0.0374808i	$0.988067\pi$
$182$	−2.36375	+	5.45223i	−0.175213	+	0.404146i
$183$		0			0
$184$	0.160233	−	0.191232i	0.0118126	−	0.0140978i
$185$			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	$0.0787908\pi$
$191$			6.77218i			0.490017i	−0.969521	+	0.245009i	$0.921209\pi$
$192$		0			0
$193$	−1.10276			−0.0793785			−0.0396892	−	0.999212i	$-0.512637\pi$
$193$	−1.10276			−0.0793785			−0.0396892	+	0.999212i	$0.512637\pi$
$194$	−0.978311	−	0.0567501i	−0.0702386	−	0.00407442i
$195$		0			0
$196$	4.06450	−	13.3970i	0.290321	−	0.956929i
$197$	−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	−0.717303	−	0.696761i	$-0.754624\pi$
$199$	3.45279	−	5.98040i	0.244761	−	0.423939i	0.962065	+	0.272822i	$0.0879570\pi$
$200$	13.2469	−	4.83203i	0.936698	−	0.341676i
$201$		0			0
$202$	−13.3148	+	20.2545i	−0.936827	+	1.42510i
$203$	6.48661	−	17.7076i	0.455271	−	1.24283i
$204$		0			0
$205$	0.922410			0.0644239
$206$	−0.462471	+	7.97250i	−0.0322218	+	0.555470i
$207$		0			0
$208$	−4.62500	−	4.35528i	−0.320686	−	0.301984i
$209$	−4.00495	−	2.31226i	−0.277028	−	0.159942i
$210$		0			0
$211$	−24.4873	+	14.1377i	−1.68577	+	0.973281i	−0.728079	+	0.685494i	$0.759586\pi$
$211$	−24.4873	+	14.1377i	−1.68577	+	0.973281i	−0.957694	+	0.287788i	$0.907080\pi$
$212$	−4.42847	−	10.2531i	−0.304149	−	0.704188i
$213$		0			0
$214$	−7.17366	+	10.9126i	−0.490381	+	0.745969i
$215$	0.199427	+	0.345417i	0.0136008	+	0.0235573i
$216$		0			0
$217$	−14.8176	+	2.58110i	−1.00588	+	0.175217i
$218$	−0.469274	+	8.08979i	−0.0317833	+	0.547910i
$219$		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	$-0.647613\pi$
$223$	8.22688	−	14.2494i	0.550913	−	0.954209i	0.998209	−	0.0598231i	$-0.0190537\pi$
$224$	11.9970	+	8.94825i	0.801586	+	0.597880i
$225$		0			0
$226$	7.41049	+	4.87147i	0.492938	+	0.324045i
$227$	−11.9528	−	20.7028i	−0.793332	−	1.37409i	−0.923893	−	0.382651i	$-0.875011\pi$
$227$	−11.9528	−	20.7028i	−0.793332	−	1.37409i	0.130561	−	0.991440i	$-0.458322\pi$
$228$		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	$0.889588\pi$
$230$	0.0126201	+	0.00829614i	0.000832146	+	0.000547032i
$231$		0			0
$232$	15.4528	+	12.9480i	1.01453	+	0.850076i
$233$	−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
$238$	−8.11184	+	0.933035i	−0.525812	+	0.0604797i
$239$	−10.1872	+	5.88159i	−0.658956	+	0.380449i	−0.791879	−	0.610678i	$-0.790897\pi$
$239$	−10.1872	+	5.88159i	−0.658956	+	0.380449i	0.132923	+	0.991126i	$0.457564\pi$
$240$		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	$0.560108\pi$
$242$	0.850054	−	14.6540i	0.0546435	−	0.941996i
$243$		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	$-0.652095\pi$
$251$	−14.5706			−0.919691			−0.459845	+	0.887999i	$0.652095\pi$
$252$		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
$262$	0.0439692	−	0.757982i	0.00271642	−	0.0468283i
$263$	−2.93339	+	1.69360i	−0.180881	+	0.104432i	−0.587706	−	0.809074i	$-0.699969\pi$
$263$	−2.93339	+	1.69360i	−0.180881	+	0.104432i	0.406826	+	0.913506i	$0.366636\pi$
$264$		0			0
$265$	0.585513	−	0.338046i	0.0359678	−	0.0207660i
$266$	−20.1520	−	8.73666i	−1.23560	−	0.535679i
$267$		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	0.888400	−	0.459070i	$-0.151817\pi$
$271$	0.767688	+	1.32967i	0.0466337	+	0.0807720i	−0.841766	+	0.539842i	$0.818484\pi$
$272$	2.00511	−	8.49568i	0.121577	−	0.515127i
$273$		0			0
$274$	15.5704	+	10.2356i	0.940641	+	0.618353i
$275$	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	$-0.375404\pi$
$278$	14.3629	+	9.44184i	0.861432	+	0.566284i
$279$		0			0
$280$	−0.454076	+	0.784002i	−0.0271362	+	0.0468531i
$281$	−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	$-0.408087\pi$
$283$	9.58069			0.569513			0.284756	+	0.958600i	$0.408087\pi$
$284$	21.5407	+	16.0208i	1.27820	+	0.950657i
$285$		0			0
$286$	0.102470	−	1.76648i	0.00605920	−	0.104454i
$287$	15.4683	−	12.9250i	0.913068	−	0.762937i
$288$		0			0
$289$	−6.11884	−	10.5981i	−0.359932	−	0.623420i
$290$	−0.670386	+	1.01979i	−0.0393664	+	0.0598843i
$291$		0			0
$292$	17.4482	−	7.53612i	1.02108	−	0.441018i
$293$	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
$296$	−21.4895	+	7.83865i	−1.24905	+	0.455612i
$297$		0			0
$298$	1.12722	−	19.4321i	0.0652983	−	1.12567i
$299$	−0.140093			−0.00810177
$300$		0			0
$301$	8.18433	+	2.99807i	0.471737	+	0.172806i
$302$	10.4756	−	15.9354i	0.602801	−	0.916982i
$303$		0			0
$304$	16.0975	−	17.0944i	0.923256	−	0.980434i
$305$	0.551020	−	0.954394i	0.0315513	−	0.0546484i
$306$		0			0
$307$	9.06875			0.517581			0.258790	−	0.965934i	$-0.416676\pi$
$307$	9.06875			0.517581			0.258790	+	0.965934i	$0.416676\pi$
$308$	0.235713	+	4.16195i	0.0134310	+	0.237149i
$309$		0			0
$310$	0.971721	+	0.0563678i	0.0551900	+	0.00320148i
$311$	9.01424			0.511151			0.255575	−	0.966789i	$-0.417735\pi$
$311$	9.01424			0.511151			0.255575	+	0.966789i	$0.417735\pi$
$312$		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
$320$	−0.623621	−	0.741084i	−0.0348615	−	0.0414278i
$321$		0			0
$322$	0.327880	−	0.0377132i	0.0182720	−	0.00210167i
$323$			12.8104i			0.712790i
$324$		0			0
$325$	−6.85703	−	3.95891i	−0.380360	−	0.219601i
$326$	−1.94888	+	2.96464i	−0.107938	+	0.164196i
$327$		0			0
$328$	7.38452	+	20.2445i	0.407742	+	1.11782i
$329$	−2.80566	+	0.488724i	−0.154681	+	0.0269442i
$330$		0			0
$331$			16.4048i			0.901689i	0.892602	+	0.450845i	$0.148877\pi$
$331$			16.4048i			0.901689i	−0.892602	+	0.450845i	$0.851123\pi$
$332$	1.82855	+	4.23360i	0.100355	+	0.232349i
$333$		0			0
$334$	15.7741	+	10.3695i	0.863118	+	0.567392i
$335$	−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	$0.763847\pi$
$338$	0.858095	−	14.7926i	0.0466742	−	0.804613i
$339$		0			0
$340$	0.524871	+	0.0610993i	0.0284651	+	0.00331358i
$341$	3.87849	−	2.23925i	0.210032	−	0.121262i
$342$		0			0
$343$	16.0963	−	9.16028i	0.869116	−	0.494608i
$344$	−5.98447	+	7.14220i	−0.322661	+	0.385082i
$345$		0			0
$346$	−7.40188	−	14.7298i	−0.397928	−	0.791876i
$347$			36.3652i			1.95218i	0.217358	+	0.976092i	$0.430256\pi$
$347$			36.3652i			1.95218i	−0.217358	+	0.976092i	$0.569744\pi$
$348$		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	$0.653082\pi$
$350$	17.1143	+	7.41971i	0.914797	+	0.396600i
$351$		0			0
$352$	−4.27072	−	1.27312i	−0.227630	−	0.0678574i
$353$	−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
$356$	−4.08534	+	35.0950i	−0.216523	+	1.86003i
$357$		0			0
$358$	22.3966	+	1.29919i	1.18370	+	0.0686642i
$359$	19.5420	−	11.2826i	1.03139	−	0.595472i	0.114006	−	0.993480i	$-0.463632\pi$
$359$	19.5420	−	11.2826i	1.03139	−	0.595472i	0.917382	+	0.398008i	$0.130298\pi$
$360$		0			0
$361$	−7.72969	+	13.3882i	−0.406826	+	0.704643i
$362$	−0.640395	−	1.27439i	−0.0336584	−	0.0669803i
$363$		0			0
$364$	−0.475205	−	8.39062i	−0.0249075	−	0.439788i
$365$	0.575268	+	0.996393i	0.0301109	+	0.0521536i
$366$		0			0
$367$	−8.96237	−	15.5233i	−0.467832	−	0.810309i	0.531492	−	0.847063i	$-0.321631\pi$
$367$	−8.96237	−	15.5233i	−0.467832	−	0.810309i	−0.999324	+	0.0367544i	$0.988298\pi$
$368$	−0.0810462	+	0.343395i	−0.00422483	+	0.0179007i
$369$		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	$0.00473669\pi$
$379$			0.579373i			0.0297604i	−0.999889	+	0.0148802i	$0.995263\pi$
$380$	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	$0.468522\pi$
$383$	−15.8996	+	27.5389i	−0.812430	+	1.40717i	−0.911159	+	0.412056i	$0.864811\pi$
$384$		0			0
$385$	−0.248604	+	0.0433047i	−0.0126700	+	0.00220701i
$386$	1.39349	−	0.700247i	0.0709268	−	0.0356416i
$387$		0			0
$388$	1.27227	−	0.549510i	0.0645896	−	0.0278971i
$389$	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
$392$	3.37096	+	19.5099i	0.170259	+	0.985399i
$393$		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	$0.179662\pi$
$398$	−0.565555	+	9.74956i	−0.0283487	+	0.488701i
$399$		0			0
$400$	−13.6710	+	14.5176i	−0.683550	+	0.725882i
$401$	−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
$404$	3.96361	−	34.0492i	0.197197	−	1.69401i
$405$		0			0
$406$	3.04749	+	26.4950i	0.151244	+	1.31492i
$407$	−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
$412$	−4.47809	−	10.3680i	−0.220620	−	0.510796i
$413$	25.1410	−	4.37935i	1.23711	−	0.215494i
$414$		0			0
$415$	−0.241763	+	0.139582i	−0.0118677	+	0.00685181i
$416$	8.60990	+	2.56665i	0.422135	+	0.125840i
$417$		0			0
$418$	6.52908	+	0.378741i	0.319348	+	0.0185248i
$419$	−10.7579	−	18.6332i	−0.525556	−	0.910289i	−0.999557	−	0.0297650i	$-0.990524\pi$
$419$	−10.7579	−	18.6332i	−0.525556	−	0.910289i	0.474001	−	0.880524i	$-0.342809\pi$
$420$		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	$0.0583645\pi$
$422$	21.9657	−	33.4142i	1.06927	−	1.62658i
$423$		0			0
$424$	12.1067	+	10.1442i	0.587952	+	0.492646i
$425$		−	10.8794i		−	0.527728i
$426$		0			0
$427$	−4.13282	−	23.7257i	−0.200001	−	1.14817i
$428$	2.13549	−	18.3448i	0.103223	−	0.886730i
$429$		0			0
$430$	−0.471341	−	0.309848i	−0.0227301	−	0.0149422i
$431$	14.9098	+	8.60820i	0.718181	+	0.414642i	0.814083	−	0.580749i	$-0.197240\pi$
$431$	14.9098	+	8.60820i	0.718181	+	0.414642i	−0.0959016	+	0.995391i	$0.530573\pi$
$432$		0			0
$433$		−	13.4777i		−	0.647695i	−0.946109	−	0.323848i	$-0.895023\pi$
$433$		−	13.4777i		−	0.647695i	0.946109	−	0.323848i	$-0.104977\pi$
$434$	17.0851	−	12.6707i	0.820111	−	0.608211i
$435$		0			0
$436$	−4.54397	−	10.5206i	−0.217617	−	0.503843i
$437$		−	0.517796i		−	0.0247695i
$438$		0			0
$439$	−8.89840			−0.424697			−0.212349	−	0.977194i	$-0.568111\pi$
$439$	−8.89840			−0.424697			−0.212349	+	0.977194i	$0.568111\pi$
$440$	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	$0.199255\pi$
$443$			24.6632i			1.17178i	−0.810390	+	0.585891i	$0.800745\pi$
$444$		0			0
$445$	−2.13882			−0.101390
$446$	−1.34754	+	23.2301i	−0.0638077	+	1.09998i
$447$		0			0
$448$	−20.8420	−	3.68931i	−0.984692	−	0.174303i
$449$	−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
$452$	−12.4575	−	1.45016i	−0.585953	−	0.0682097i
$453$		0			0
$454$	28.2501	+	18.5709i	1.32584	+	0.871576i
$455$	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	$0.829335\pi$
$458$	27.5381	+	1.59744i	1.28677	+	0.0746434i
$459$		0			0
$460$	−0.0212153	−	0.00246963i	−0.000989167	−	0.000115147i
$461$	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	−0.599252	−	0.800561i	$-0.704535\pi$
$463$	−4.42338	+	2.55384i	−0.205572	+	0.118687i	0.393680	+	0.919248i	$0.371202\pi$
$464$	−27.7487	−	6.54909i	−1.28820	−	0.304034i
$465$		0			0
$466$	11.3059	+	7.43219i	0.523734	+	0.344289i
$467$	−0.342427	−	0.593101i	−0.0158456	−	0.0274455i	0.857994	−	0.513660i	$-0.171711\pi$
$467$	−0.342427	−	0.593101i	−0.0158456	−	0.0274455i	−0.873839	+	0.486214i	$0.838377\pi$
$468$		0			0
$469$	1.57702	+	9.05333i	0.0728198	+	0.418044i
$470$	0.183992	+	0.0106731i	0.00848693	+	0.000492312i
$471$		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
$476$	9.65796	−	6.32999i	0.442672	−	0.290134i
$477$		0			0
$478$	9.13819	−	13.9010i	0.417971	−	0.635818i
$479$	6.62396	+	11.4730i	0.302656	+	0.524216i	0.976737	−	0.214442i	$-0.0687932\pi$
$479$	6.62396	+	11.4730i	0.302656	+	0.524216i	−0.674080	+	0.738658i	$0.735460\pi$
$480$		0			0
$481$	11.1237	+	6.42225i	0.507195	+	0.292829i
$482$	15.7666	−	23.9841i	0.718147	−	1.09245i
$483$		0			0
$484$	8.23106	+	19.0572i	0.374139	+	0.866235i
$485$	0.0419467	+	0.0726538i	0.00190470	+	0.00329904i
$486$		0			0
$487$	−6.29077	−	3.63198i	−0.285062	−	0.164581i	0.350651	−	0.936506i	$-0.385960\pi$
$487$	−6.29077	−	3.63198i	−0.285062	−	0.164581i	−0.635713	+	0.771926i	$0.719294\pi$
$488$	25.3578	+	4.45288i	1.14789	+	0.201572i
$489$		0			0
$490$	−1.14952	+	0.339252i	−0.0519298	+	0.0153259i
$491$	−23.9003	+	13.7989i	−1.07861	+	0.622734i	−0.930520	−	0.366241i	$-0.880645\pi$
$491$	−23.9003	+	13.7989i	−1.07861	+	0.622734i	−0.148086	+	0.988974i	$0.547311\pi$
$492$		0			0
$493$	13.4708	−	7.77737i	0.606694	−	0.350275i
$494$	−13.1628	−	0.763553i	−0.592224	−	0.0343539i
$495$		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	0.759597	−	0.650394i	$-0.225396\pi$
$499$	12.8699	+	7.43045i	0.576137	+	0.332633i	−0.183460	+	0.983027i	$0.558730\pi$
$500$	−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	$-0.800820\pi$
$503$	−36.3565			−1.62106			−0.810529	+	0.585698i	$0.800820\pi$
$504$		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
$514$	−17.7258	−	1.02824i	−0.781851	−	0.0453538i
$515$	0.592074	−	0.341834i	0.0260899	−	0.0150630i
$516$		0			0
$517$	0.734380	−	0.423995i	0.0322980	−	0.0186473i
$518$	−27.7633	−	12.0365i	−1.21985	−	0.528851i
$519$		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	0.692606	−	0.721316i	$-0.256463\pi$
$523$	−6.36621	−	11.0266i	−0.278375	−	0.482160i	−0.970981	+	0.239156i	$0.923129\pi$
$524$	0.425753	+	0.985735i	0.0185991	+	0.0430620i
$525$		0			0
$526$	2.63133	−	4.00278i	0.114731	−	0.174529i
$527$	−10.7438	−	6.20296i	−0.468009	−	0.270205i
$528$		0			0
$529$	−11.4961	−	19.9118i	−0.499831	−	0.865732i
$530$	−0.525220	+	0.798966i	−0.0228141	+	0.0347048i
$531$		0			0
$532$	31.0125	−	1.75640i	1.34456	−	0.0761497i
$533$	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
$538$	−41.3613	−	2.39929i	−1.78321	−	0.103441i
$539$	−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	$0.888675\pi$
$542$	−1.81442	−	1.19275i	−0.0779358	−	0.0512330i
$543$		0			0
$544$	2.86098	+	12.0087i	0.122664	+	0.514869i
$545$	0.600784	−	0.346863i	0.0257348	−	0.0148580i
$546$		0			0
$547$	−21.1399	−	12.2051i	−0.903876	−	0.521853i	−0.0254202	−	0.999677i	$-0.508092\pi$
$547$	−21.1399	−	12.2051i	−0.903876	−	0.521853i	−0.878456	+	0.477824i	$0.841426\pi$
$548$	−26.1749	−	3.04697i	−1.11813	−	0.130160i
$549$		0			0
$550$	−5.54490	−	0.321650i	−0.236435	−	0.0137152i
$551$	41.8415			1.78251
$552$		0			0
$553$	6.83430	+	39.2343i	0.290624	+	1.66841i
$554$	23.9859	+	15.7677i	1.01906	+	0.669906i
$555$		0			0
$556$	−24.1451	−	2.81068i	−1.02398	−	0.119200i
$557$	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
$560$	0.0759507	−	1.27903i	0.00320950	−	0.0540489i
$561$		0			0
$562$	2.28561	−	39.4014i	0.0964125	−	1.66205i
$563$	10.5164			0.443215			0.221608	−	0.975136i	$-0.428870\pi$
$563$	10.5164			0.443215			0.221608	+	0.975136i	$0.428870\pi$
$564$		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	$0.0880193\pi$
$571$			13.0475i			0.546021i	−0.962011	+	0.273010i	$0.911981\pi$
$572$	0.992219	+	2.29726i	0.0414868	+	0.0960533i
$573$		0			0
$574$	−11.3391	+	26.1548i	−0.473286	+	1.09168i
$575$			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	$0.541178\pi$
$578$	14.4618	+	9.50680i	0.601530	+	0.395431i
$579$		0			0
$580$	0.199563	−	1.71434i	0.00828641	−	0.0711841i
$581$	−2.09840	+	5.72835i	−0.0870562	+	0.237652i
$582$		0			0
$583$			4.39929i			0.182200i
$584$	−17.2628	+	20.6024i	−0.714341	+	0.852535i
$585$		0			0
$586$	−3.12591	+	4.75514i	−0.129130	+	0.196433i
$587$	19.0791	−	33.0459i	0.787478	−	1.36395i	−0.140030	−	0.990147i	$-0.544720\pi$
$587$	19.0791	−	33.0459i	0.787478	−	1.36395i	0.927508	−	0.373804i	$-0.121947\pi$
$588$		0			0
$589$	−16.6857	−	28.9004i	−0.687520	−	1.19082i
$590$	−1.64872	−	0.0956391i	−0.0678766	−	0.00393740i
$591$		0			0
$592$	22.1775	−	23.5509i	0.911488	−	0.967937i
$593$	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
$596$	10.9149	+	25.2710i	0.447091	+	1.03514i
$597$		0			0
$598$	0.177026	−	0.0889580i	0.00723915	−	0.00363776i
$599$		−	33.5411i		−	1.37045i	−0.728330	−	0.685227i	$-0.759703\pi$
$599$		−	33.5411i		−	1.37045i	0.728330	−	0.685227i	$-0.240297\pi$
$600$		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	$0.399982\pi$
$602$	−12.2458	+	1.40853i	−0.499101	+	0.0574073i
$603$		0			0
$604$	−3.11841	+	26.7886i	−0.126886	+	1.09001i
$605$	−1.08827	+	0.628316i	−0.0442447	+	0.0255447i
$606$		0			0
$607$	6.34967	−	10.9979i	0.257725	−	0.446393i	−0.707907	−	0.706306i	$-0.750360\pi$
$607$	6.34967	−	10.9979i	0.257725	−	0.446393i	0.965632	+	0.259913i	$0.0836938\pi$
$608$	−9.48657	+	31.8230i	−0.384731	+	1.29059i
$609$		0			0
$610$	−0.0902552	+	1.55590i	−0.00365433	+	0.0629967i
$611$	−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
$616$	−2.94067	−	5.10952i	−0.118483	−	0.205868i
$617$	−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	0.948289	−	0.317408i	$-0.102812\pi$
$619$	4.95757	+	8.58676i	0.199261	+	0.345131i	−0.749028	+	0.662539i	$0.769479\pi$
$620$	−1.26370	+	0.545808i	−0.0507513	+	0.0219202i
$621$		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	$0.0106482\pi$
$631$			1.68031i			0.0668920i	−0.999441	+	0.0334460i	$0.989352\pi$
$632$	−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
$640$	1.25862	+	0.540467i	0.0497511	+	0.0213638i
$641$	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	0.736725	−	0.676193i	$-0.236371\pi$
$643$	−5.50859	−	9.54116i	−0.217238	−	0.376267i	−0.953962	+	0.299926i	$0.903038\pi$
$644$	−0.390374	+	0.255858i	−0.0153829	+	0.0100822i
$645$		0			0
$646$	−8.13453	−	16.1877i	−0.320049	−	0.636898i
$647$	12.3459	−	21.3838i	0.485368	−	0.840683i	−0.514490	−	0.857496i	$-0.672019\pi$
$647$	12.3459	−	21.3838i	0.485368	−	0.840683i	0.999859	+	0.0168136i	$0.00535217\pi$
$648$		0			0
$649$	−6.58063	+	3.79933i	−0.258312	+	0.149137i
$650$	11.1787	+	0.648456i	0.438464	+	0.0254345i
$651$		0			0
$652$	0.580150	−	4.98376i	0.0227204	−	0.195179i
$653$	−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
$656$	−22.1865	−	20.8926i	−0.866237	−	0.815720i
$657$		0			0
$658$	3.23501	−	2.39915i	0.126114	−	0.0935286i
$659$	−6.59789	−	3.80929i	−0.257017	−	0.148389i	0.365956	−	0.930632i	$-0.380742\pi$
$659$	−6.59789	−	3.80929i	−0.257017	−	0.148389i	−0.622973	+	0.782243i	$0.714075\pi$
$660$		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
$664$	−4.99894	−	4.18863i	−0.193997	−	0.162550i
$665$	0.322683	+	1.85246i	0.0125131	+	0.0718352i
$666$		0			0
$667$	−0.544489	+	0.314361i	−0.0210827	+	0.0121721i
$668$	−26.5173	−	3.08682i	−1.02598	−	0.119433i
$669$		0			0
$670$	0.0344399	−	0.593707i	0.00133053	−	0.0229369i
$671$	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	$0.117408\pi$
$674$	−9.39643	−	6.17698i	−0.361937	−	0.237928i
$675$		0			0
$676$	8.30892	+	19.2374i	0.319574	+	0.739901i
$677$		−	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
$680$	−0.702045	+	0.256083i	−0.0269222	+	0.00982033i
$681$		0			0
$682$	−3.47910	+	5.29242i	−0.133222	+	0.202657i
$683$	8.19378	+	4.73068i	0.313526	+	0.181015i	0.648503	−	0.761212i	$-0.275395\pi$
$683$	8.19378	+	4.73068i	0.313526	+	0.181015i	−0.334977	+	0.942226i	$0.608729\pi$
$684$		0			0
$685$		−	1.59519i		−	0.0609492i
$686$	−14.5231	+	21.7963i	−0.554496	+	0.832187i
$687$		0			0
$688$	3.02695	−	12.8253i	0.115401	−	0.488958i
$689$		−	8.86911i		−	0.337886i
$690$		0			0
$691$	−28.4459			−1.08213			−0.541067	−	0.840980i	$-0.681979\pi$
$691$	−28.4459			−1.08213			−0.541067	+	0.840980i	$0.681979\pi$
$692$	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
$698$	−2.25052	−	0.130549i	−0.0851834	−	0.00494134i
$699$		0			0
$700$	−26.3377	+	1.49164i	−0.995473	+	0.0563789i
$701$	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
$704$	6.20506	−	1.10312i	0.233862	−	0.0415753i
$705$		0			0
$706$	18.5261	−	28.1820i	0.697240	−	1.06064i
$707$	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	$0.324554\pi$
$710$	0.133091	−	2.29435i	0.00499481	−	0.0861052i
$711$		0			0
$712$	−17.1227	−	46.9415i	−0.641700	−	1.75921i
$713$	0.434265	+	0.250723i	0.0162634	+	0.00938965i
$714$		0			0
$715$	−0.131187	+	0.0757408i	−0.00490611	+	0.00283255i
$716$	−29.1262	+	12.5800i	−1.08850	+	0.470137i
$717$		0			0
$718$	−17.5297	+	26.6662i	−0.654201	+	0.995173i
$719$	−22.0843	−	38.2510i	−0.823604	−	1.42652i	−0.902982	−	0.429679i	$-0.858627\pi$
$719$	−22.0843	−	38.2510i	−0.823604	−	1.42652i	0.0793781	−	0.996845i	$-0.474707\pi$
$720$		0			0
$721$	5.13894	−	14.0286i	0.191384	−	0.522453i
$722$	1.26610	−	21.8262i	0.0471193	−	0.812286i
$723$		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	−0.965829	−	0.259180i	$-0.916548\pi$
$727$	−6.96878	+	12.0703i	−0.258458	+	0.447662i	0.707371	+	0.706842i	$0.249881\pi$
$728$	5.92848	+	10.3010i	0.219724	+	0.381779i
$729$		0			0
$730$	−1.35963	−	0.893789i	−0.0503223	−	0.0330806i
$731$	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	$0.563781\pi$
$734$	21.1824	+	13.9248i	0.781856	+	0.513972i
$735$		0			0
$736$	−0.115641	−	0.485391i	−0.00426257	−	0.0178918i
$737$	−1.36815	−	2.36970i	−0.0503964	−	0.0872891i
$738$		0			0
$739$	−8.40583	−	4.85311i	−0.309214	−	0.178525i	0.337361	−	0.941375i	$-0.390466\pi$
$739$	−8.40583	−	4.85311i	−0.309214	−	0.178525i	−0.646574	+	0.762851i	$0.723799\pi$
$740$	1.57132	+	1.16866i	0.0577630	+	0.0429609i
$741$		0			0
$742$	2.38758	+	20.7577i	0.0876508	+	0.762040i
$743$	1.44066	−	0.831764i	0.0528526	−	0.0305145i	−0.473341	−	0.880879i	$-0.656952\pi$
$743$	1.44066	−	0.831764i	0.0528526	−	0.0305145i	0.526193	+	0.850365i	$0.323619\pi$
$744$		0			0
$745$	−1.44312	+	0.833185i	−0.0528718	+	0.0305255i
$746$	−1.41161	+	24.3346i	−0.0516825	+	0.890952i
$747$		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	0.228078	−	0.973643i	$-0.426756\pi$
$751$	−13.7319	−	7.92810i	−0.501083	−	0.289300i	−0.729161	+	0.684343i	$0.760089\pi$
$752$	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
$766$	2.60430	−	44.8953i	0.0940971	−	1.62213i
$767$	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	$0.401366\pi$
$770$	0.286647	−	0.212583i	0.0103300	−	0.00766097i
$771$		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
$776$	−1.25875	+	1.50226i	−0.0451865	+	0.0539281i
$777$		0			0
$778$	−12.5148	−	8.22694i	−0.448679	−	0.294950i
$779$	38.7322	+	22.3620i	1.38772	+	0.801203i
$780$		0			0
$781$	−5.28713	−	9.15757i	−0.189188	−	0.327684i
$782$	0.227476	+	0.149537i	0.00813453	+	0.00534744i
$783$		0			0
$784$	−16.6484	−	22.5129i	−0.594584	−	0.804033i
$785$	0.765386	−	1.32569i	0.0273178	−	0.0473158i
$786$		0			0
$787$	37.8242			1.34829			0.674143	−	0.738600i	$-0.264513\pi$
$787$	37.8242			1.34829			0.674143	+	0.738600i	$0.264513\pi$
$788$	−10.7949	+	14.5143i	−0.384552	+	0.517049i
$789$		0			0
$790$	0.149252	−	2.57294i	0.00531014	−	0.0915411i
$791$	−10.6382	−	12.7315i	−0.378250	−	0.452681i
$792$		0			0
$793$	−7.22838	−	12.5199i	−0.256687	−	0.444596i
$794$	−14.3715	+	21.8619i	−0.510024	+	0.775850i
$795$		0			0
$796$	−5.47626	−	12.6790i	−0.194101	−	0.449397i
$797$	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
$800$	8.05658	−	27.0261i	0.284843	−	0.955515i
$801$		0			0
$802$	0.633102	−	10.9140i	0.0223556	−	0.385387i
$803$	−7.48646			−0.264192
$804$		0			0
$805$	−0.0181169	−	0.0216819i	−0.000638536	−	0.000764187i
$806$	7.01399	−	10.6697i	0.247057	−	0.375824i
$807$		0			0
$808$	16.6125	+	45.5428i	0.584425	+	1.60219i
$809$	−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	$-0.712519\pi$
$811$	−35.2639			−1.23828			−0.619141	+	0.785280i	$0.712519\pi$
$812$	−20.6751	−	31.5449i	−0.725553	−	1.10701i
$813$		0			0
$814$	8.99508	+	0.521789i	0.315278	+	0.0182887i
$815$	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	$0.210532\pi$
$823$			35.2419i			1.22846i	−0.789129	+	0.614228i	$0.789468\pi$
$824$	12.2423	+	10.2579i	0.426482	+	0.357350i
$825$		0			0
$826$	−28.9882	+	21.4983i	−1.00863	+	0.748021i
$827$			18.2748i			0.635478i	0.948178	+	0.317739i	$0.102924\pi$
$827$			18.2748i			0.635478i	−0.948178	+	0.317739i	$0.897076\pi$
$828$		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	$0.397778\pi$
$830$	0.216868	−	0.329899i	0.00752758	−	0.0114510i
$831$		0			0
$832$	−12.5096	+	2.22392i	−0.433693	+	0.0771007i
$833$	15.0327	+	2.71494i	0.520853	+	0.0940671i
$834$		0			0
$835$		−	1.61606i		−	0.0559261i
$836$	−8.49090	+	3.66734i	−0.293664	+	0.126838i
$837$		0			0
$838$	25.4260	+	16.7144i	0.878326	+	0.577389i
$839$	−9.15093	+	15.8499i	−0.315925	+	0.547199i	−0.979634	−	0.200793i	$-0.935648\pi$
$839$	−9.15093	+	15.8499i	−0.315925	+	0.547199i	0.663708	+	0.747991i	$0.268982\pi$
$840$		0			0
$841$	−10.9025	−	18.8837i	−0.375949	−	0.651162i
$842$	−1.12156	+	19.3345i	−0.0386514	+	0.666309i
$843$		0			0
$844$	−6.53883	+	56.1716i	−0.225076	+	1.93351i
$845$	−1.09857	+	0.634259i	−0.0377919	+	0.0218192i
$846$		0			0
$847$	−9.44574	+	25.7856i	−0.324559	+	0.886005i
$848$	−21.7400	−	5.13095i	−0.746553	−	0.176197i
$849$		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	$0.400009\pi$
$854$	20.2881	+	27.3564i	0.694243	+	0.936116i
$855$		0			0
$856$	8.95036	+	24.5372i	0.305917	+	0.838665i
$857$	−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	−0.843862	−	0.536561i	$-0.819723\pi$
$859$	1.25279	−	2.16989i	0.0427445	−	0.0740357i	0.886606	+	0.462525i	$0.153057\pi$
$860$	0.792357	+	0.0922368i	0.0270191	+	0.00314525i
$861$		0			0
$862$	−24.3068	−	1.40999i	−0.827893	−	0.0480246i
$863$	23.9226	−	13.8117i	0.814335	−	0.470157i	−0.0341239	−	0.999418i	$-0.510864\pi$
$863$	23.9226	−	13.8117i	0.814335	−	0.470157i	0.848459	+	0.529261i	$0.177531\pi$
$864$		0			0
$865$	−0.705633	+	1.22219i	−0.0239922	+	0.0415558i
$866$	8.55824	+	17.0309i	0.290821	+	0.578734i
$867$		0			0
$868$	−13.5436	+	26.8601i	−0.459699	+	0.911690i
$869$	−5.92913	−	10.2696i	−0.201132	−	0.348371i
$870$		0			0
$871$	2.75823	+	4.77740i	0.0934591	+	0.161876i
$872$	12.4224	+	10.4088i	0.420677	+	0.352486i
$873$		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	$-0.989440\pi$
$883$		−	1.97128i		−	0.0663387i	0.999450	−	0.0331694i	$-0.0105601\pi$
$884$	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	−0.872552	−	0.488521i	$-0.837537\pi$
$887$	−0.393262	+	0.681150i	−0.0132045	+	0.0228708i	0.859348	+	0.511392i	$0.170870\pi$
$888$		0			0
$889$	−7.37332	−	42.3287i	−0.247293	−	1.41966i
$890$	2.70269	−	1.35814i	0.0905945	−	0.0455248i
$891$		0			0
$892$	−13.0482	−	30.2101i	−0.436885	−	1.01151i
$893$	−3.15937	−	5.47220i	−0.105724	−	0.183120i
$894$		0			0
$895$	−0.960291	−	1.66327i	−0.0320990	−	0.0555971i
$896$	28.6794	−	8.57259i	0.958113	−	0.286390i
$897$		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
$902$	0.491559	−	8.47395i	0.0163671	−	0.282152i
$903$		0			0
$904$	16.6627	−	6.07798i	0.554192	−	0.202151i
$905$	−0.0610499	+	0.105741i	−0.00202937	+	0.00351497i
$906$		0			0
$907$	29.5840	−	17.0803i	0.982320	−	0.567143i	0.0793500	−	0.996847i	$-0.474716\pi$
$907$	29.5840	−	17.0803i	0.982320	−	0.567143i	0.902970	+	0.429704i	$0.141382\pi$
$908$	−47.4903	−	5.52826i	−1.57602	−	0.183462i
$909$		0			0
$910$	−0.577890	+	0.428575i	−0.0191569	+	0.0142071i
$911$	24.1673	+	13.9530i	0.800699	+	0.462284i	0.843716	−	0.536790i	$-0.180363\pi$
$911$	24.1673	+	13.9530i	0.800699	+	0.462284i	−0.0430164	+	0.999074i	$0.513697\pi$
$912$		0			0
$913$		−	1.81650i		−	0.0601175i
$914$	46.4458	−	23.3396i	1.53629	−	0.772005i
$915$		0			0
$916$	−35.8126	+	15.4680i	−1.18328	+	0.511076i
$917$	−0.488582	+	1.33377i	−0.0161344	+	0.0440448i
$918$		0			0
$919$	−28.7012	+	16.5707i	−0.946767	+	0.546616i	−0.892075	−	0.451887i	$-0.850751\pi$
$919$	−28.7012	+	16.5707i	−0.946767	+	0.546616i	−0.0546916	+	0.998503i	$0.517418\pi$
$920$	0.0283766	−	0.0103508i	0.000935550	−	0.000341257i
$921$		0			0
$922$	−7.57607	−	0.439475i	−0.249505	−	0.0144733i
$923$	10.6590	+	18.4620i	0.350846	+	0.607683i
$924$		0			0
$925$	20.1591	−	34.9166i	0.662828	−	1.14805i
$926$	3.96788	−	6.03595i	0.130393	−	0.198354i
$927$		0			0
$928$	39.2230	−	9.34456i	1.28756	−	0.306750i
$929$		−	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
$932$	−19.0059	−	2.21244i	−0.622560	−	0.0724710i
$933$		0			0
$934$	0.809320	+	0.532026i	0.0264818	+	0.0174084i
$935$	−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	$0.942326\pi$
$938$	−7.74159	−	10.4387i	−0.252772	−	0.340837i
$939$		0			0
$940$	−0.239277	+	0.103347i	−0.00780435	+	0.00337081i
$941$		−	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	$0.153817\pi$
$947$			28.5971i			0.929282i	−0.885499	+	0.464641i	$0.846183\pi$
$948$		0			0
$949$	15.0930			0.489938
$950$	−2.39676	+	41.3175i	−0.0777610	+	1.34052i
$951$		0			0
$952$	−8.18467	+	14.1316i	−0.265267	+	0.458007i
$953$	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
$956$	−2.72029	+	23.3686i	−0.0879806	+	0.755794i
$957$		0			0
$958$	−15.6556	−	10.2916i	−0.505809	−	0.332506i
$959$	−22.3521	−	26.7506i	−0.721788	−	0.863822i
$960$		0			0
$961$	1.31759			0.0425027
$962$	−18.1344	−	1.05194i	−0.584676	−	0.0339160i
$963$		0			0
$964$	−4.69345	+	40.3189i	−0.151166	+	1.29859i
$965$	−0.115624	−	0.0667556i	−0.00372207	−	0.00214894i
$966$		0			0
$967$	−3.27690	+	1.89192i	−0.105378	+	0.0608401i	−0.551763	−	0.834001i	$-0.686045\pi$
$967$	−3.27690	+	1.89192i	−0.105378	+	0.0608401i	0.446385	+	0.894841i	$0.352711\pi$
$968$	−22.5023	−	18.8547i	−0.723250	−	0.606013i
$969$		0			0
$970$	−0.0991402	−	0.0651723i	−0.00318320	−	0.00209256i
$971$	9.98069	+	17.2871i	0.320296	+	0.554768i	0.980549	−	0.196275i	$-0.0628844\pi$
$971$	9.98069	+	17.2871i	0.320296	+	0.554768i	−0.660253	+	0.751043i	$0.729551\pi$
$972$		0			0
$973$	−20.6188	−	24.6762i	−0.661009	−	0.791082i
$974$	10.2555	+	0.594906i	0.328609	+	0.0190620i
$975$		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
$980$	1.23715	−	1.15863i	0.0395193	−	0.0370110i
$981$		0			0
$982$	21.4392	−	32.6133i	0.684152	−	1.04073i
$983$	−11.7577	−	20.3649i	−0.375011	−	0.649539i	0.615317	−	0.788280i	$-0.289028\pi$
$983$	−11.7577	−	20.3649i	−0.375011	−	0.649539i	−0.990329	+	0.138741i	$0.955695\pi$
$984$		0			0
$985$	−0.948287	−	0.547494i	−0.0302149	−	0.0174446i
$986$	−12.0836	+	18.3817i	−0.384821	+	0.585391i
$987$		0			0
$988$	17.1179	−	7.39347i	0.544594	−	0.235218i
$989$	−0.145295	−	0.251659i	−0.00462012	−	0.00800229i
$990$		0			0
$991$	−20.3738	−	11.7628i	−0.647194	−	0.373658i	0.140186	−	0.990125i	$-0.455230\pi$
$991$	−20.3738	−	11.7628i	−0.647194	−	0.373658i	−0.787380	+	0.616468i	$0.788563\pi$
$992$	−22.0958	−	23.3653i	−0.701543	−	0.741849i
$993$		0			0
$994$	−29.9169	−	40.3399i	−0.948907	−	1.27950i
$995$	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	$0.640766\pi$
$998$	−20.9812	−	1.21708i	−0.664149	−	0.0385261i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.26364 + 0.634994i) q^{2} +(1.19357 - 1.60481i) q^{4} +(0.104850 + 0.0605350i) q^{5} +(2.60650 - 0.454031i) q^{7} +(-0.489193 + 2.78580i) q^{8} +O(q^{10})\)	\(q+(-1.26364 + 0.634994i) q^{2} +(1.19357 - 1.60481i) q^{4} +(0.104850 + 0.0605350i) q^{5} +(2.60650 - 0.454031i) q^{7} +(-0.489193 + 2.78580i) q^{8} +(-0.170931 - 0.00991543i) q^{10} +(-0.682250 + 0.393897i) q^{11} +(1.37544 - 0.794110i) q^{13} +(-3.00537 + 2.22885i) q^{14} +(-1.15080 - 3.83088i) q^{16} +(1.88990 + 1.09114i) q^{17} +(2.93511 + 5.08375i) q^{19} +(0.222292 - 0.0960109i) q^{20} +(0.611995 - 0.930968i) q^{22} +(-0.0763898 - 0.0441037i) q^{23} +(-2.49267 - 4.31743i) q^{25} +(-1.23380 + 1.87686i) q^{26} +(2.38240 - 4.72485i) q^{28} +(3.56388 - 6.17283i) q^{29} -5.68486 q^{31} +(3.88679 + 4.11010i) q^{32} +(-3.08102 - 0.178725i) q^{34} +(0.300776 + 0.110180i) q^{35} +(4.04368 + 7.00386i) q^{37} +(-6.93706 - 4.56025i) q^{38} +(-0.219930 + 0.262477i) q^{40} +(6.59809 - 3.80941i) q^{41} +(2.85304 + 1.64720i) q^{43} +(-0.182181 + 1.56502i) q^{44} +(0.124535 + 0.00722404i) q^{46} -1.07641 q^{47} +(6.58771 - 2.36687i) q^{49} +(5.89138 + 3.87284i) q^{50} +(0.367283 - 3.15513i) q^{52} +(2.79216 - 4.83615i) q^{53} -0.0953783 q^{55} +(-0.0102409 + 7.48331i) q^{56} +(-0.583752 + 10.0633i) q^{58} +9.64548 q^{59} -9.10250i q^{61} +(7.18360 - 3.60985i) q^{62} +(-7.52138 - 2.72559i) q^{64} +0.192286 q^{65} +3.47336i q^{67} +(4.00679 - 1.73059i) q^{68} +(-0.450035 + 0.0517637i) q^{70} +13.4226i q^{71} +(8.22990 + 4.75153i) q^{73} +(-9.55716 - 6.28263i) q^{74} +(11.6617 + 1.35751i) q^{76} +(-1.59944 + 1.33646i) q^{77} +15.0525i q^{79} +(0.111241 - 0.471331i) q^{80} +(-5.91865 + 9.00346i) q^{82} +(-1.15290 + 1.99689i) q^{83} +(0.132104 + 0.228811i) q^{85} +(-4.65117 - 0.269806i) q^{86} +(-0.763568 - 2.09330i) q^{88} +(-15.2992 + 8.83298i) q^{89} +(3.22453 - 2.69434i) q^{91} +(-0.161954 + 0.0699502i) q^{92} +(1.36019 - 0.683513i) q^{94} +0.710706i q^{95} +(0.600098 + 0.346467i) q^{97} +(-6.82154 + 7.17402i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 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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