LMFDB - Embedded newform 630.2.ce.a.233.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(53,630)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ce (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.22986704741655040229376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 $ x^16 - 31x^12 + 880x^8 - 2511*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.3
Root			$-2.22431 - 0.596002i$ of defining polynomial
Character	$\chi$	$=$	630.233
Dual form			630.2.ce.a.557.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.19067 - 0.448288i) q^{5} +(-2.30278 - 1.30278i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.19067 - 0.448288i) q^{5} +(-2.30278 - 1.30278i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.23205 + 0.133975i) q^{10} +(-3.21189 + 1.85439i) q^{11} +(-4.62250 - 4.62250i) q^{13} +(-2.56149 - 0.662382i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.35751 + 5.06628i) q^{17} +(0.866025 + 0.500000i) q^{19} +(-2.12132 + 0.707107i) q^{20} +(-2.62250 + 2.62250i) q^{22} +(-1.09869 - 4.10035i) q^{23} +(4.59808 + 1.96410i) q^{25} +(-5.66138 - 3.26860i) q^{26} +(-2.64565 + 0.0231510i) q^{28} +2.82843 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.258819 - 0.965926i) q^{32} +5.24500i q^{34} +(4.46060 + 3.88626i) q^{35} +(-2.79003 - 10.4125i) q^{37} +(0.965926 + 0.258819i) q^{38} +(-1.86603 + 1.23205i) q^{40} +0.880347i q^{41} +(3.00000 + 3.00000i) q^{43} +(-1.85439 + 3.21189i) q^{44} +(-2.12250 - 3.67628i) q^{46} +(-8.69333 + 2.32937i) q^{47} +(3.60555 + 6.00000i) q^{49} +(4.94975 + 0.707107i) q^{50} +(-6.31445 - 1.69195i) q^{52} +(2.16850 + 0.581048i) q^{53} +(7.86750 - 2.62250i) q^{55} +(-2.54951 + 0.707107i) q^{56} +(2.73205 - 0.732051i) q^{58} +(-5.83009 - 10.0980i) q^{59} +(1.62250 - 2.81025i) q^{61} +(-2.82843 - 2.82843i) q^{62} -1.00000i q^{64} +(8.05416 + 12.1986i) q^{65} +(9.56218 + 2.56218i) q^{67} +(1.35751 + 5.06628i) q^{68} +(5.31445 + 2.59935i) q^{70} +10.2460i q^{71} +(3.74993 - 13.9949i) q^{73} +(-5.38992 - 9.33562i) q^{74} +1.00000 q^{76} +(9.81212 - 0.0858619i) q^{77} +(-2.38590 - 1.37750i) q^{79} +(-1.48356 + 1.67303i) q^{80} +(0.227850 + 0.850349i) q^{82} +(6.53720 - 6.53720i) q^{83} +(5.24500 - 10.4900i) q^{85} +(3.67423 + 2.12132i) q^{86} +(-0.959901 + 3.58240i) q^{88} +(-4.94975 + 8.57321i) q^{89} +(4.62250 + 16.6667i) q^{91} +(-3.00167 - 3.00167i) q^{92} +(-7.79423 + 4.50000i) q^{94} +(-1.67303 - 1.48356i) q^{95} +(-9.24500 + 9.24500i) q^{97} +(5.03561 + 4.86237i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 8 q^{10} - 24 q^{13} + 8 q^{16} + 8 q^{22} + 32 q^{25} + 4 q^{28} - 32 q^{31} + 36 q^{37} - 16 q^{40} + 48 q^{43} + 16 q^{46} - 12 q^{52} - 24 q^{55} + 16 q^{58} - 24 q^{61} + 56 q^{67} - 4 q^{70} - 32 q^{73} + 16 q^{76} + 20 q^{82} - 16 q^{85} - 4 q^{88} + 24 q^{91} - 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 8 * q^10 - 24 * q^13 + 8 * q^16 + 8 * q^22 + 32 * q^25 + 4 * q^28 - 32 * q^31 + 36 * q^37 - 16 * q^40 + 48 * q^43 + 16 * q^46 - 12 * q^52 - 24 * q^55 + 16 * q^58 - 24 * q^61 + 56 * q^67 - 4 * q^70 - 32 * q^73 + 16 * q^76 + 20 * q^82 - 16 * q^85 - 4 * q^88 + 24 * q^91 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.19067	−	0.448288i	−0.979698	−	0.200480i
$5$	−2.19067	−	0.448288i	−0.979698	−	0.200480i
$6$		0			0
$7$	−2.30278	−	1.30278i	−0.870367	−	0.492403i
$7$	−2.30278	−	1.30278i	−0.870367	−	0.492403i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−2.23205	+	0.133975i	−0.705836	+	0.0423665i
$11$	−3.21189	+	1.85439i	−0.968422	+	0.559119i	−0.898755	−	0.438452i	$-0.855527\pi$
$11$	−3.21189	+	1.85439i	−0.968422	+	0.559119i	−0.0696671	+	0.997570i	$0.522194\pi$
$12$		0			0
$13$	−4.62250	−	4.62250i	−1.28205	−	1.28205i	−0.939499	−	0.342551i	$-0.888709\pi$
$13$	−4.62250	−	4.62250i	−1.28205	−	1.28205i	−0.342551	−	0.939499i	$-0.611291\pi$
$14$	−2.56149	−	0.662382i	−0.684588	−	0.177029i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.35751	+	5.06628i	−0.329243	+	1.22875i	0.580733	+	0.814094i	$0.302766\pi$
$17$	−1.35751	+	5.06628i	−0.329243	+	1.22875i	−0.909977	+	0.414659i	$0.863901\pi$
$18$		0			0
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i	0.596040	−	0.802955i	$-0.296740\pi$
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i	−0.397360	+	0.917663i	$0.630073\pi$
$20$	−2.12132	+	0.707107i	−0.474342	+	0.158114i
$21$		0			0
$22$	−2.62250	+	2.62250i	−0.559119	+	0.559119i
$23$	−1.09869	−	4.10035i	−0.229092	−	0.854983i	−0.980724	−	0.195400i	$-0.937400\pi$
$23$	−1.09869	−	4.10035i	−0.229092	−	0.854983i	0.751632	−	0.659583i	$-0.229267\pi$
$24$		0			0
$25$	4.59808	+	1.96410i	0.919615	+	0.392820i
$26$	−5.66138	−	3.26860i	−1.11029	−	0.641025i
$27$		0			0
$28$	−2.64565	+	0.0231510i	−0.499981	+	0.00437513i
$29$	2.82843			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$		0			0
$34$			5.24500i			0.899510i
$35$	4.46060	+	3.88626i	0.753980	+	0.656898i
$36$		0			0
$37$	−2.79003	−	10.4125i	−0.458678	−	1.71181i	−0.677044	−	0.735942i	$-0.736740\pi$
$37$	−2.79003	−	10.4125i	−0.458678	−	1.71181i	0.218367	−	0.975867i	$-0.429927\pi$
$38$	0.965926	+	0.258819i	0.156694	+	0.0419860i
$39$		0			0
$40$	−1.86603	+	1.23205i	−0.295045	+	0.194804i
$41$			0.880347i			0.137487i	0.997634	+	0.0687435i	$0.0218990\pi$
$41$			0.880347i			0.137487i	−0.997634	+	0.0687435i	$0.978101\pi$
$42$		0			0
$43$	3.00000	+	3.00000i	0.457496	+	0.457496i	0.897833	−	0.440337i	$-0.145141\pi$
$43$	3.00000	+	3.00000i	0.457496	+	0.457496i	−0.440337	+	0.897833i	$0.645141\pi$
$44$	−1.85439	+	3.21189i	−0.279559	+	0.484211i
$45$		0			0
$46$	−2.12250	−	3.67628i	−0.312945	−	0.542037i
$47$	−8.69333	+	2.32937i	−1.26805	+	0.339774i	−0.829285	−	0.558827i	$-0.811252\pi$
$47$	−8.69333	+	2.32937i	−1.26805	+	0.339774i	−0.438768	+	0.898600i	$0.644585\pi$
$48$		0			0
$49$	3.60555	+	6.00000i	0.515079	+	0.857143i
$50$	4.94975	+	0.707107i	0.700000	+	0.100000i
$51$		0			0
$52$	−6.31445	−	1.69195i	−0.875657	−	0.234632i
$53$	2.16850	+	0.581048i	0.297867	+	0.0798131i	0.404657	−	0.914468i	$-0.367391\pi$
$53$	2.16850	+	0.581048i	0.297867	+	0.0798131i	−0.106791	+	0.994282i	$0.534057\pi$
$54$		0			0
$55$	7.86750	−	2.62250i	1.06085	−	0.353618i
$56$	−2.54951	+	0.707107i	−0.340693	+	0.0944911i
$57$		0			0
$58$	2.73205	−	0.732051i	0.358736	−	0.0961230i
$59$	−5.83009	−	10.0980i	−0.759014	−	1.31465i	−0.943354	−	0.331788i	$-0.892348\pi$
$59$	−5.83009	−	10.0980i	−0.759014	−	1.31465i	0.184341	−	0.982862i	$-0.440985\pi$
$60$		0			0
$61$	1.62250	−	2.81025i	0.207740	−	0.359816i	−0.743262	−	0.669000i	$-0.766723\pi$
$61$	1.62250	−	2.81025i	0.207740	−	0.359816i	0.951002	+	0.309184i	$0.100056\pi$
$62$	−2.82843	−	2.82843i	−0.359211	−	0.359211i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	8.05416	+	12.1986i	0.998996	+	1.51305i
$66$		0			0
$67$	9.56218	+	2.56218i	1.16821	+	0.313020i	0.790239	−	0.612799i	$-0.209957\pi$
$67$	9.56218	+	2.56218i	1.16821	+	0.313020i	0.377967	+	0.925819i	$0.376623\pi$
$68$	1.35751	+	5.06628i	0.164622	+	0.614377i
$69$		0			0
$70$	5.31445	+	2.59935i	0.635198	+	0.310682i
$71$			10.2460i			1.21597i	0.793947	+	0.607987i	$0.208023\pi$
$71$			10.2460i			1.21597i	−0.793947	+	0.607987i	$0.791977\pi$
$72$		0			0
$73$	3.74993	−	13.9949i	0.438896	−	1.63798i	−0.292671	−	0.956213i	$-0.594544\pi$
$73$	3.74993	−	13.9949i	0.438896	−	1.63798i	0.731567	−	0.681769i	$-0.238789\pi$
$74$	−5.38992	−	9.33562i	−0.626566	−	1.08524i
$75$		0			0
$76$	1.00000			0.114708
$77$	9.81212	−	0.0858619i	1.11819	−	0.00978487i
$78$		0			0
$79$	−2.38590	−	1.37750i	−0.268435	−	0.154981i	0.359741	−	0.933052i	$-0.382865\pi$
$79$	−2.38590	−	1.37750i	−0.268435	−	0.154981i	−0.628176	+	0.778071i	$0.716198\pi$
$80$	−1.48356	+	1.67303i	−0.165867	+	0.187051i
$81$		0			0
$82$	0.227850	+	0.850349i	0.0251619	+	0.0939054i
$83$	6.53720	−	6.53720i	0.717551	−	0.717551i	−0.250552	−	0.968103i	$-0.580612\pi$
$83$	6.53720	−	6.53720i	0.717551	−	0.717551i	0.968103	+	0.250552i	$0.0806121\pi$
$84$		0			0
$85$	5.24500	−	10.4900i	0.568900	−	1.13780i
$86$	3.67423	+	2.12132i	0.396203	+	0.228748i
$87$		0			0
$88$	−0.959901	+	3.58240i	−0.102326	+	0.381885i
$89$	−4.94975	+	8.57321i	−0.524672	+	0.908759i	0.474915	+	0.880032i	$0.342479\pi$
$89$	−4.94975	+	8.57321i	−0.524672	+	0.908759i	−0.999587	+	0.0287273i	$0.990855\pi$
$90$		0			0
$91$	4.62250	+	16.6667i	0.484570	+	1.74714i
$92$	−3.00167	−	3.00167i	−0.312945	−	0.312945i
$93$		0			0
$94$	−7.79423	+	4.50000i	−0.803913	+	0.464140i
$95$	−1.67303	−	1.48356i	−0.171650	−	0.152210i
$96$		0			0
$97$	−9.24500	+	9.24500i	−0.938687	+	0.938687i	−0.998226	−	0.0595387i	$-0.981037\pi$
$97$	−9.24500	+	9.24500i	−0.938687	+	0.938687i	0.0595387	+	0.998226i	$0.481037\pi$
$98$	5.03561	+	4.86237i	0.508673	+	0.491174i
$99$		0			0
$100$	4.96410	−	0.598076i	0.496410	−	0.0598076i
$101$	1.52480	−	0.880347i	0.151724	−	0.0875978i	−0.422216	−	0.906495i	$-0.638748\pi$
$101$	1.52480	−	0.880347i	0.151724	−	0.0875978i	0.573940	+	0.818897i	$0.305414\pi$
$102$		0			0
$103$	−5.79878	+	1.55378i	−0.571370	+	0.153098i	−0.532925	−	0.846162i	$-0.678907\pi$
$103$	−5.79878	+	1.55378i	−0.571370	+	0.153098i	−0.0384453	+	0.999261i	$0.512241\pi$
$104$	−6.53720			−0.641025
$105$		0			0
$106$	2.24500			0.218053
$107$	−6.99813	+	1.87514i	−0.676535	+	0.181277i	−0.580697	−	0.814120i	$-0.697220\pi$
$107$	−6.99813	+	1.87514i	−0.676535	+	0.181277i	−0.0958381	+	0.995397i	$0.530553\pi$
$108$		0			0
$109$	3.46410	−	2.00000i	0.331801	−	0.191565i	−0.324840	−	0.945769i	$-0.605310\pi$
$109$	3.46410	−	2.00000i	0.331801	−	0.191565i	0.656640	+	0.754204i	$0.271977\pi$
$110$	6.92067	−	4.56940i	0.659860	−	0.435675i
$111$		0			0
$112$	−2.27962	+	1.34287i	−0.215404	+	0.126890i
$113$	7.41755	−	7.41755i	0.697784	−	0.697784i	−0.266148	−	0.963932i	$-0.585751\pi$
$113$	7.41755	−	7.41755i	0.697784	−	0.697784i	0.963932	+	0.266148i	$0.0857510\pi$
$114$		0			0
$115$	0.568722	+	9.47505i	0.0530336	+	0.883553i
$116$	2.44949	−	1.41421i	0.227429	−	0.131306i
$117$		0			0
$118$	−8.24500	−	8.24500i	−0.759014	−	0.759014i
$119$	9.72626	−	9.89798i	0.891604	−	0.907346i
$120$		0			0
$121$	1.37750	−	2.38590i	0.125227	−	0.216900i
$122$	0.839867	−	3.13443i	0.0760380	−	0.283778i
$123$		0			0
$124$	−3.46410	−	2.00000i	−0.311086	−	0.179605i
$125$	−9.19239	−	6.36396i	−0.822192	−	0.569210i
$126$		0			0
$127$	−14.6225	+	14.6225i	−1.29754	+	1.29754i	−0.367522	+	0.930015i	$0.619794\pi$
$127$	−14.6225	+	14.6225i	−1.29754	+	1.29754i	−0.930015	+	0.367522i	$0.880206\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$		0			0
$130$	10.9370	+	9.69836i	0.959234	+	0.850602i
$131$	−0.462342	−	0.266934i	−0.0403950	−	0.0233221i	0.479666	−	0.877451i	$-0.340758\pi$
$131$	−0.462342	−	0.266934i	−0.0403950	−	0.0233221i	−0.520062	+	0.854129i	$0.674091\pi$
$132$		0			0
$133$	−1.34287	−	2.27962i	−0.116442	−	0.197669i
$134$	9.89949			0.855186
$135$		0			0
$136$	2.62250	+	4.54230i	0.224877	+	0.389499i
$137$	5.49861	−	20.5211i	0.469778	−	1.75324i	−0.170764	−	0.985312i	$-0.554624\pi$
$137$	5.49861	−	20.5211i	0.469778	−	1.75324i	0.640542	−	0.767923i	$-0.278710\pi$
$138$		0			0
$139$		−	8.00000i		−	0.678551i	−0.940687	−	0.339276i	$-0.889818\pi$
$139$		−	8.00000i		−	0.678551i	0.940687	−	0.339276i	$-0.110182\pi$
$140$	5.80613	+	1.13530i	0.490707	+	0.0959500i
$141$		0			0
$142$	2.65185	+	9.89685i	0.222539	+	0.830525i
$143$	23.4189	+	6.27507i	1.95838	+	0.524747i
$144$		0			0
$145$	−6.19615	−	1.26795i	−0.514562	−	0.105297i
$146$		−	14.4886i		−	1.19909i
$147$		0			0
$148$	−7.62250	−	7.62250i	−0.626566	−	0.626566i
$149$	4.41588	−	7.64853i	0.361763	−	0.626592i	−0.626488	−	0.779431i	$-0.715508\pi$
$149$	4.41588	−	7.64853i	0.361763	−	0.626592i	0.988251	+	0.152839i	$0.0488416\pi$
$150$		0			0
$151$	7.24500	+	12.5487i	0.589590	+	1.02120i	0.994286	+	0.106748i	$0.0340438\pi$
$151$	7.24500	+	12.5487i	0.589590	+	1.02120i	−0.404697	+	0.914451i	$0.632623\pi$
$152$	0.965926	−	0.258819i	0.0783469	−	0.0209930i
$153$		0			0
$154$	9.45555	−	2.62250i	0.761950	−	0.211327i
$155$	2.82843	+	8.48528i	0.227185	+	0.681554i
$156$		0			0
$157$	10.4125	+	2.79003i	0.831010	+	0.222668i	0.649154	−	0.760657i	$-0.275123\pi$
$157$	10.4125	+	2.79003i	0.831010	+	0.222668i	0.181856	+	0.983325i	$0.441790\pi$
$158$	−2.66113	−	0.713047i	−0.211708	−	0.0567270i
$159$		0			0
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	−2.81181	+	10.8735i	−0.221602	+	0.856955i
$162$		0			0
$163$	−7.16480	+	1.91980i	−0.561190	+	0.150371i	−0.528253	−	0.849087i	$-0.677153\pi$
$163$	−7.16480	+	1.91980i	−0.561190	+	0.150371i	−0.0329373	+	0.999457i	$0.510486\pi$
$164$	0.440173	+	0.762402i	0.0343718	+	0.0595336i
$165$		0			0
$166$	4.62250	−	8.00640i	0.358776	−	0.621417i
$167$	−7.24431	−	7.24431i	−0.560581	−	0.560581i	0.368891	−	0.929473i	$-0.379737\pi$
$167$	−7.24431	−	7.24431i	−0.560581	−	0.560581i	−0.929473	+	0.368891i	$0.879737\pi$
$168$		0			0
$169$			29.7350i			2.28731i
$170$	2.35127	−	11.4901i	0.180334	−	0.881248i
$171$		0			0
$172$	4.09808	+	1.09808i	0.312475	+	0.0837275i
$173$	2.00714	+	7.49076i	0.152600	+	0.569512i	0.999299	+	0.0374391i	$0.0119200\pi$
$173$	2.00714	+	7.49076i	0.152600	+	0.569512i	−0.846699	+	0.532073i	$0.821413\pi$
$174$		0			0
$175$	−8.02955	−	10.5131i	−0.606977	−	0.794719i
$176$			3.70877i			0.279559i
$177$		0			0
$178$	−2.56218	+	9.56218i	−0.192043	+	0.716716i
$179$	−8.21835	−	14.2346i	−0.614268	−	1.06394i	−0.990512	−	0.137423i	$-0.956118\pi$
$179$	−8.21835	−	14.2346i	−0.614268	−	1.06394i	0.376244	−	0.926521i	$-0.377215\pi$
$180$		0			0
$181$	11.2450			0.835834			0.417917	−	0.908485i	$-0.362760\pi$
$181$	11.2450			0.835834			0.417917	+	0.908485i	$0.362760\pi$
$182$	8.77864	+	14.9024i	0.650716	+	1.10464i
$183$		0			0
$184$	−3.67628	−	2.12250i	−0.271019	−	0.156473i
$185$	1.44422	+	24.0612i	0.106182	+	1.76901i
$186$		0			0
$187$	−5.03468	−	18.7897i	−0.368172	−	1.37404i
$188$	−6.36396	+	6.36396i	−0.464140	+	0.464140i
$189$		0			0
$190$	−2.00000	−	1.00000i	−0.145095	−	0.0725476i
$191$	10.0980	+	5.83009i	0.730667	+	0.421851i	0.818666	−	0.574270i	$-0.194714\pi$
$191$	10.0980	+	5.83009i	0.730667	+	0.421851i	−0.0879991	+	0.996121i	$0.528047\pi$
$192$		0			0
$193$	4.57166	−	17.0617i	0.329075	−	1.22812i	−0.581076	−	0.813849i	$-0.697368\pi$
$193$	4.57166	−	17.0617i	0.329075	−	1.22812i	0.910151	−	0.414276i	$-0.135965\pi$
$194$	−6.53720	+	11.3228i	−0.469344	+	0.812927i
$195$		0			0
$196$	6.12250	+	3.39338i	0.437321	+	0.242384i
$197$	−6.71044	−	6.71044i	−0.478099	−	0.478099i	0.426424	−	0.904523i	$-0.359773\pi$
$197$	−6.71044	−	6.71044i	−0.478099	−	0.478099i	−0.904523	+	0.426424i	$0.859773\pi$
$198$		0			0
$199$	−2.81025	+	1.62250i	−0.199213	+	0.115016i	−0.596289	−	0.802770i	$-0.703359\pi$
$199$	−2.81025	+	1.62250i	−0.199213	+	0.115016i	0.397075	+	0.917786i	$0.370025\pi$
$200$	4.64016	−	1.86250i	0.328109	−	0.131699i
$201$		0			0
$202$	1.24500	−	1.24500i	0.0875978	−	0.0875978i
$203$	−6.51323	−	3.68481i	−0.457139	−	0.258623i
$204$		0			0
$205$	0.394649	−	1.92855i	0.0275635	−	0.134696i
$206$	−5.19904	+	3.00167i	−0.362234	+	0.209136i
$207$		0			0
$208$	−6.31445	+	1.69195i	−0.437828	+	0.117316i
$209$	−3.70877			−0.256541
$210$		0			0
$211$	−28.2450			−1.94447			−0.972233	−	0.234015i	$-0.924813\pi$
$211$	−28.2450			−1.94447			−0.972233	+	0.234015i	$0.924813\pi$
$212$	2.16850	−	0.581048i	0.148933	−	0.0399066i
$213$		0			0
$214$	−6.27435	+	3.62250i	−0.428906	+	0.247629i
$215$	−5.22715	−	7.91688i	−0.356489	−	0.539926i
$216$		0			0
$217$	0.0926041	+	10.5826i	0.00628637	+	0.718394i
$218$	2.82843	−	2.82843i	0.191565	−	0.191565i
$219$		0			0
$220$	5.50220	−	6.20490i	0.370958	−	0.418334i
$221$	29.6939	−	17.1438i	1.99743	−	1.15322i
$222$		0			0
$223$	−5.75500	−	5.75500i	−0.385383	−	0.385383i	0.487654	−	0.873037i	$-0.337853\pi$
$223$	−5.75500	−	5.75500i	−0.385383	−	0.385383i	−0.873037	+	0.487654i	$0.837853\pi$
$224$	−1.85439	+	1.88713i	−0.123901	+	0.126089i
$225$		0			0
$226$	5.24500	−	9.08460i	0.348892	−	0.604299i
$227$	1.35751	−	5.06628i	0.0901008	−	0.336261i	−0.906130	−	0.422998i	$-0.860978\pi$
$227$	1.35751	−	5.06628i	0.0901008	−	0.336261i	0.996231	+	0.0867377i	$0.0276442\pi$
$228$		0			0
$229$	8.00640	+	4.62250i	0.529078	+	0.305463i	0.740641	−	0.671901i	$-0.234522\pi$
$229$	8.00640	+	4.62250i	0.529078	+	0.305463i	−0.211563	+	0.977364i	$0.567855\pi$
$230$	3.00167	+	9.00500i	0.197924	+	0.593772i
$231$		0			0
$232$	2.00000	−	2.00000i	0.131306	−	0.131306i
$233$	−3.81888	−	14.2522i	−0.250183	−	0.933695i	−0.970707	−	0.240265i	$-0.922765\pi$
$233$	−3.81888	−	14.2522i	−0.250183	−	0.933695i	0.720524	−	0.693430i	$-0.243901\pi$
$234$		0			0
$235$	20.0885	−	1.20577i	1.31043	−	0.0786559i
$236$	−10.0980	−	5.83009i	−0.657325	−	0.379507i
$237$		0			0
$238$	6.83306	−	12.0781i	0.442921	−	0.782904i
$239$	−17.3170			−1.12015			−0.560073	−	0.828443i	$-0.689227\pi$
$239$	−17.3170			−1.12015			−0.560073	+	0.828443i	$0.689227\pi$
$240$		0			0
$241$	−5.12250	−	8.87243i	−0.329969	−	0.571523i	0.652536	−	0.757758i	$-0.273705\pi$
$241$	−5.12250	−	8.87243i	−0.329969	−	0.571523i	−0.982505	+	0.186234i	$0.940372\pi$
$242$	0.713047	−	2.66113i	0.0458364	−	0.171064i
$243$		0			0
$244$		−	3.24500i		−	0.207740i
$245$	−5.20885	−	14.7603i	−0.332781	−	0.943004i
$246$		0			0
$247$	−1.69195	−	6.31445i	−0.107656	−	0.401779i
$248$	−3.86370	−	1.03528i	−0.245345	−	0.0657401i
$249$		0			0
$250$	−10.5263	−	3.76795i	−0.665740	−	0.238306i
$251$			19.6116i			1.23787i	0.785441	+	0.618937i	$0.212436\pi$
$251$			19.6116i			1.23787i	−0.785441	+	0.618937i	$0.787564\pi$
$252$		0			0
$253$	11.1325	+	11.1325i	0.699894	+	0.699894i
$254$	−10.3397	+	17.9088i	−0.648768	+	1.12370i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.8618	+	2.91042i	−0.677543	+	0.181547i	−0.581150	−	0.813796i	$-0.697397\pi$
$257$	−10.8618	+	2.91042i	−0.677543	+	0.181547i	−0.0963925	+	0.995343i	$0.530730\pi$
$258$		0			0
$259$	−7.14038	+	27.6125i	−0.443681	+	1.71576i
$260$	13.0744	+	6.53720i	0.810840	+	0.405420i
$261$		0			0
$262$	−0.515676	−	0.138175i	−0.0318586	−	0.00853648i
$263$	−21.7237	−	5.82084i	−1.33954	−	0.358928i	−0.483276	−	0.875468i	$-0.660553\pi$
$263$	−21.7237	−	5.82084i	−1.33954	−	0.358928i	−0.856263	+	0.516540i	$0.827220\pi$
$264$		0			0
$265$	−4.49000	−	2.24500i	−0.275818	−	0.137909i
$266$	−1.88713	−	1.85439i	−0.115707	−	0.113700i
$267$		0			0
$268$	9.56218	−	2.56218i	0.584103	−	0.156510i
$269$	4.94975	+	8.57321i	0.301791	+	0.522718i	0.976542	−	0.215328i	$-0.0690820\pi$
$269$	4.94975	+	8.57321i	0.301791	+	0.522718i	−0.674750	+	0.738046i	$0.735749\pi$
$270$		0			0
$271$	−3.24500	+	5.62050i	−0.197120	+	0.341421i	−0.947593	−	0.319479i	$-0.896492\pi$
$271$	−3.24500	+	5.62050i	−0.197120	+	0.341421i	0.750474	+	0.660900i	$0.229825\pi$
$272$	3.70877	+	3.70877i	0.224877	+	0.224877i
$273$		0			0
$274$		−	21.2450i		−	1.28346i
$275$	−18.4107	+	2.21813i	−1.11021	+	0.133758i
$276$		0			0
$277$	−12.9636	−	3.47358i	−0.778906	−	0.208707i	−0.152604	−	0.988287i	$-0.548766\pi$
$277$	−12.9636	−	3.47358i	−0.778906	−	0.208707i	−0.626302	+	0.779580i	$0.715432\pi$
$278$	−2.07055	−	7.72741i	−0.124183	−	0.463459i
$279$		0			0
$280$	5.90212	−	0.406124i	0.352719	−	0.0242706i
$281$			1.94808i			0.116213i	0.998310	+	0.0581064i	$0.0185063\pi$
$281$			1.94808i			0.116213i	−0.998310	+	0.0581064i	$0.981494\pi$
$282$		0			0
$283$	−3.66025	+	13.6603i	−0.217580	+	0.812018i	0.767663	+	0.640854i	$0.221419\pi$
$283$	−3.66025	+	13.6603i	−0.217580	+	0.812018i	−0.985243	+	0.171164i	$0.945247\pi$
$284$	5.12299	+	8.87327i	0.303993	+	0.526532i
$285$		0			0
$286$	24.2450			1.43364
$287$	1.14689	−	2.02724i	0.0676990	−	0.119664i
$288$		0			0
$289$	−9.10193	−	5.25500i	−0.535408	−	0.309118i
$290$	−6.31319	+	0.378937i	−0.370723	+	0.0222520i
$291$		0			0
$292$	−3.74993	−	13.9949i	−0.219448	−	0.818991i
$293$	15.1957	−	15.1957i	0.887744	−	0.887744i	−0.106562	−	0.994306i	$-0.533984\pi$
$293$	15.1957	−	15.1957i	0.887744	−	0.887744i	0.994306	+	0.106562i	$0.0339844\pi$
$294$		0			0
$295$	8.24500	+	24.7350i	0.480042	+	1.44013i
$296$	−9.33562	−	5.38992i	−0.542622	−	0.313283i
$297$		0			0
$298$	2.28583	−	8.53083i	0.132414	−	0.494177i
$299$	−13.8752	+	24.0326i	−0.802424	+	1.38984i
$300$		0			0
$301$	−3.00000	−	10.8167i	−0.172917	−	0.623462i
$302$	10.2460	+	10.2460i	0.589590	+	0.589590i
$303$		0			0
$304$	0.866025	−	0.500000i	0.0496700	−	0.0286770i
$305$	−4.81416	+	5.42899i	−0.275658	+	0.310863i
$306$		0			0
$307$	−6.24500	+	6.24500i	−0.356421	+	0.356421i	−0.862492	−	0.506071i	$-0.831097\pi$
$307$	−6.24500	+	6.24500i	−0.356421	+	0.356421i	0.506071	+	0.862492i	$0.331097\pi$
$308$	8.45461	−	4.98042i	0.481746	−	0.283786i
$309$		0			0
$310$	4.92820	+	7.46410i	0.279903	+	0.423932i
$311$	−21.4208	+	12.3673i	−1.21466	+	0.701285i	−0.963771	−	0.266731i	$-0.914057\pi$
$311$	−21.4208	+	12.3673i	−1.21466	+	0.701285i	−0.250890	+	0.968016i	$0.580723\pi$
$312$		0			0
$313$	21.1597	−	5.66973i	1.19602	−	0.320472i	0.394756	−	0.918786i	$-0.370829\pi$
$313$	21.1597	−	5.66973i	1.19602	−	0.320472i	0.801262	+	0.598314i	$0.204162\pi$
$314$	10.7798			0.608342
$315$		0			0
$316$	−2.75500			−0.154981
$317$	−11.5911	+	3.10583i	−0.651022	+	0.174441i	−0.569191	−	0.822206i	$-0.692743\pi$
$317$	−11.5911	+	3.10583i	−0.651022	+	0.174441i	−0.0818309	+	0.996646i	$0.526077\pi$
$318$		0			0
$319$	−9.08460	+	5.24500i	−0.508640	+	0.293664i
$320$	−0.448288	+	2.19067i	−0.0250600	+	0.122462i
$321$		0			0
$322$	0.0982760	+	11.2308i	0.00547671	+	0.625867i
$323$	−3.70877	+	3.70877i	−0.206362	+	0.206362i
$324$		0			0
$325$	−12.1755	−	30.3337i	−0.675378	−	1.68261i
$326$	−6.42378	+	3.70877i	−0.355781	+	0.205410i
$327$		0			0
$328$	0.622499	+	0.622499i	0.0343718	+	0.0343718i
$329$	23.0534	+	5.96144i	1.27098	+	0.328665i
$330$		0			0
$331$	−3.50000	+	6.06218i	−0.192377	+	0.333207i	−0.946038	−	0.324057i	$-0.894953\pi$
$331$	−3.50000	+	6.06218i	−0.192377	+	0.333207i	0.753660	+	0.657264i	$0.228286\pi$
$332$	2.39278	−	8.92998i	0.131321	−	0.490096i
$333$		0			0
$334$	−8.87243	−	5.12250i	−0.485478	−	0.280291i
$335$	−19.7990	−	9.89949i	−1.08173	−	0.540867i
$336$		0			0
$337$	6.24500	−	6.24500i	0.340187	−	0.340187i	−0.516251	−	0.856437i	$-0.672673\pi$
$337$	6.24500	−	6.24500i	0.340187	−	0.340187i	0.856437	+	0.516251i	$0.172673\pi$
$338$	7.69598	+	28.7218i	0.418606	+	1.56226i
$339$		0			0
$340$	−0.702696	−	11.7071i	−0.0381091	−	0.634907i
$341$	12.8476	+	7.41755i	0.695735	+	0.401683i
$342$		0			0
$343$	−0.486122	−	18.5139i	−0.0262481	−	0.999655i
$344$	4.24264			0.228748
$345$		0			0
$346$	3.87750	+	6.71603i	0.208456	+	0.361056i
$347$	−2.91042	+	10.8618i	−0.156240	+	0.583094i	0.842757	+	0.538295i	$0.180931\pi$
$347$	−2.91042	+	10.8618i	−0.156240	+	0.583094i	−0.998996	+	0.0447988i	$0.985735\pi$
$348$		0			0
$349$		−	9.51000i		−	0.509059i	−0.967065	−	0.254529i	$-0.918079\pi$
$349$		−	9.51000i		−	0.509059i	0.967065	−	0.254529i	$-0.0819206\pi$
$350$	−10.4770	−	8.07672i	−0.560017	−	0.431719i
$351$		0			0
$352$	0.959901	+	3.58240i	0.0511629	+	0.190943i
$353$	−6.26885	−	1.67973i	−0.333657	−	0.0894033i	0.0881008	−	0.996112i	$-0.471920\pi$
$353$	−6.26885	−	1.67973i	−0.333657	−	0.0894033i	−0.421758	+	0.906708i	$0.638587\pi$
$354$		0			0
$355$	4.59314	−	22.4456i	0.243779	−	1.19129i
$356$			9.89949i			0.524672i
$357$		0			0
$358$	−11.6225	−	11.6225i	−0.614268	−	0.614268i
$359$	5.65685	−	9.79796i	0.298557	−	0.517116i	−0.677249	−	0.735754i	$-0.736828\pi$
$359$	5.65685	−	9.79796i	0.298557	−	0.517116i	0.975806	+	0.218638i	$0.0701613\pi$
$360$		0			0
$361$	−9.00000	−	15.5885i	−0.473684	−	0.820445i
$362$	10.8618	−	2.91042i	0.570885	−	0.152968i
$363$		0			0
$364$	12.3365	+	12.1225i	0.646610	+	0.635392i
$365$	−14.4886	+	28.9772i	−0.758369	+	1.51674i
$366$		0			0
$367$	−1.18502	−	0.317526i	−0.0618577	−	0.0165747i	0.227757	−	0.973718i	$-0.426861\pi$
$367$	−1.18502	−	0.317526i	−0.0618577	−	0.0165747i	−0.289615	+	0.957143i	$0.593527\pi$
$368$	−4.10035	−	1.09869i	−0.213746	−	0.0572730i
$369$		0			0
$370$	7.62250	+	22.8675i	0.396275	+	1.18882i
$371$	−4.23660	−	4.16309i	−0.219953	−	0.216137i
$372$		0			0
$373$	11.2629	−	3.01788i	0.583170	−	0.156260i	0.0448400	−	0.998994i	$-0.485722\pi$
$373$	11.2629	−	3.01788i	0.583170	−	0.156260i	0.538330	+	0.842734i	$0.319056\pi$
$374$	−9.72626	−	16.8464i	−0.502933	−	0.871105i
$375$		0			0
$376$	−4.50000	+	7.79423i	−0.232070	+	0.401957i
$377$	−13.0744	−	13.0744i	−0.673366	−	0.673366i
$378$		0			0
$379$		−	4.73499i		−	0.243220i	−0.992578	−	0.121610i	$-0.961194\pi$
$379$		−	4.73499i		−	0.243220i	0.992578	−	0.121610i	$-0.0388058\pi$
$380$	−2.19067	−	0.448288i	−0.112379	−	0.0229967i
$381$		0			0
$382$	11.2629	+	3.01788i	0.576259	+	0.154408i
$383$	−5.68884	−	21.2310i	−0.290686	−	1.08486i	−0.944583	−	0.328272i	$-0.893534\pi$
$383$	−5.68884	−	21.2310i	−0.290686	−	1.08486i	0.653897	−	0.756584i	$-0.273133\pi$
$384$		0			0
$385$	−21.5336	−	4.21056i	−1.09745	−	0.214590i
$386$		−	17.6635i		−	0.899050i
$387$		0			0
$388$	−3.38390	+	12.6289i	−0.171792	+	0.641135i
$389$	0.346479	+	0.600120i	0.0175672	+	0.0304273i	0.874675	−	0.484709i	$-0.161075\pi$
$389$	0.346479	+	0.600120i	0.0175672	+	0.0304273i	−0.857108	+	0.515136i	$0.827741\pi$
$390$		0			0
$391$	22.2650			1.12599
$392$	6.79215	+	1.69313i	0.343055	+	0.0855160i
$393$		0			0
$394$	−8.21858	−	4.74500i	−0.414046	−	0.239050i
$395$	4.60921	+	4.08722i	0.231914	+	0.205650i
$396$		0			0
$397$	−5.39338	−	20.1284i	−0.270686	−	1.01021i	−0.958677	−	0.284495i	$-0.908174\pi$
$397$	−5.39338	−	20.1284i	−0.270686	−	1.01021i	0.687991	−	0.725719i	$-0.258493\pi$
$398$	−2.29456	+	2.29456i	−0.115016	+	0.115016i
$399$		0			0
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$	−13.3099	−	7.68448i	−0.664665	−	0.383745i	0.129387	−	0.991594i	$-0.458699\pi$
$401$	−13.3099	−	7.68448i	−0.664665	−	0.383745i	−0.794052	+	0.607850i	$0.792032\pi$
$402$		0			0
$403$	−6.76781	+	25.2578i	−0.337129	+	1.25818i
$404$	0.880347	−	1.52480i	0.0437989	−	0.0758619i
$405$		0			0
$406$	−7.24500	−	1.87350i	−0.359563	−	0.0929803i
$407$	28.2701	+	28.2701i	1.40130	+	1.40130i
$408$		0			0
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$	−0.117944	−	1.96498i	−0.00582484	−	0.0970434i
$411$		0			0
$412$	−4.24500	+	4.24500i	−0.209136	+	0.209136i
$413$	0.269945	+	30.8488i	0.0132831	+	1.51797i
$414$		0			0
$415$	−17.2514	+	11.3903i	−0.846838	+	0.559128i
$416$	−5.66138	+	3.26860i	−0.277572	+	0.160256i
$417$		0			0
$418$	−3.58240	+	0.959901i	−0.175221	+	0.0469503i
$419$	23.1613			1.13150			0.565751	−	0.824576i	$-0.308586\pi$
$419$	23.1613			1.13150			0.565751	+	0.824576i	$0.308586\pi$
$420$		0			0
$421$	4.75500			0.231745			0.115872	−	0.993264i	$-0.463034\pi$
$421$	4.75500			0.231745			0.115872	+	0.993264i	$0.463034\pi$
$422$	−27.2826	+	7.31034i	−1.32809	+	0.355862i
$423$		0			0
$424$	1.94423	−	1.12250i	0.0944199	−	0.0545134i
$425$	−16.1926	+	20.6289i	−0.785456	+	1.00065i
$426$		0			0
$427$	−7.39738	+	4.35762i	−0.357984	+	0.210880i
$428$	−5.12299	+	5.12299i	−0.247629	+	0.247629i
$429$		0			0
$430$	−7.09808	−	6.29423i	−0.342300	−	0.303535i
$431$	10.0980	−	5.83009i	0.486404	−	0.280826i	−0.236677	−	0.971588i	$-0.576058\pi$
$431$	10.0980	−	5.83009i	0.486404	−	0.280826i	0.723082	+	0.690763i	$0.242725\pi$
$432$		0			0
$433$	−19.2450	−	19.2450i	−0.924856	−	0.924856i	0.0725120	−	0.997368i	$-0.476898\pi$
$433$	−19.2450	−	19.2450i	−0.924856	−	0.924856i	−0.997368	+	0.0725120i	$0.976898\pi$
$434$	2.82843	+	10.1980i	0.135769	+	0.489522i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	1.09869	−	4.10035i	0.0525573	−	0.196146i
$438$		0			0
$439$	17.3205	+	10.0000i	0.826663	+	0.477274i	0.852709	−	0.522387i	$-0.174958\pi$
$439$	17.3205	+	10.0000i	0.826663	+	0.477274i	−0.0260459	+	0.999661i	$0.508292\pi$
$440$	3.70877	−	7.41755i	0.176809	−	0.353618i
$441$		0			0
$442$	24.2450	−	24.2450i	1.15322	−	1.15322i
$443$	−10.2842	−	38.3811i	−0.488616	−	1.82354i	−0.563195	−	0.826324i	$-0.690428\pi$
$443$	−10.2842	−	38.3811i	−0.488616	−	1.82354i	0.0745793	−	0.997215i	$-0.476239\pi$
$444$		0			0
$445$	14.6865	−	16.5622i	0.696208	−	0.785123i
$446$	−7.04841	−	4.06940i	−0.333752	−	0.192692i
$447$		0			0
$448$	−1.30278	+	2.30278i	−0.0615504	+	0.108796i
$449$	9.71211			0.458343			0.229171	−	0.973386i	$-0.426398\pi$
$449$	9.71211			0.458343			0.229171	+	0.973386i	$0.426398\pi$
$450$		0			0
$451$	−1.63250	−	2.82758i	−0.0768716	−	0.133145i
$452$	2.71501	−	10.1326i	0.127703	−	0.476595i
$453$		0			0
$454$		−	5.24500i		−	0.246160i
$455$	−2.65492	−	38.5834i	−0.124464	−	1.80882i
$456$		0			0
$457$	8.96396	+	33.4540i	0.419316	+	1.56491i	0.776030	+	0.630696i	$0.217231\pi$
$457$	8.96396	+	33.4540i	0.419316	+	1.56491i	−0.356713	+	0.934214i	$0.616103\pi$
$458$	8.92998	+	2.39278i	0.417271	+	0.111807i
$459$		0			0
$460$	5.23005	+	7.92127i	0.243852	+	0.369331i
$461$			6.72459i			0.313195i	0.987662	+	0.156598i	$0.0500526\pi$
$461$			6.72459i			0.313195i	−0.987662	+	0.156598i	$0.949947\pi$
$462$		0			0
$463$	12.8675	+	12.8675i	0.598003	+	0.598003i	0.939781	−	0.341778i	$-0.111029\pi$
$463$	12.8675	+	12.8675i	0.598003	+	0.598003i	−0.341778	+	0.939781i	$0.611029\pi$
$464$	1.41421	−	2.44949i	0.0656532	−	0.113715i
$465$		0			0
$466$	−7.37750	−	12.7782i	−0.341756	−	0.591939i
$467$	−6.99813	+	1.87514i	−0.323835	+	0.0867713i	−0.417074	−	0.908872i	$-0.636944\pi$
$467$	−6.99813	+	1.87514i	−0.323835	+	0.0867713i	0.0932393	+	0.995644i	$0.470278\pi$
$468$		0			0
$469$	−18.6816	−	18.3575i	−0.862636	−	0.847670i
$470$	19.0919	−	6.36396i	0.880643	−	0.293548i
$471$		0			0
$472$	−11.2629	−	3.01788i	−0.518416	−	0.138909i
$473$	−15.1988	−	4.07252i	−0.698843	−	0.187254i
$474$		0			0
$475$	3.00000	+	4.00000i	0.137649	+	0.183533i
$476$	3.47419	−	13.4350i	0.159239	−	0.615794i
$477$		0			0
$478$	−16.7270	+	4.48198i	−0.765074	+	0.205001i
$479$	9.53887	+	16.5218i	0.435842	+	0.754900i	0.997364	−	0.0725614i	$-0.0231173\pi$
$479$	9.53887	+	16.5218i	0.435842	+	0.754900i	−0.561522	+	0.827462i	$0.689784\pi$
$480$		0			0
$481$	−35.2350	+	61.0288i	−1.60658	+	2.78267i
$482$	−7.24431	−	7.24431i	−0.329969	−	0.329969i
$483$		0			0
$484$		−	2.75500i		−	0.125227i
$485$	24.3972	−	16.1083i	1.10782	−	0.731441i
$486$		0			0
$487$	21.1597	+	5.66973i	0.958839	+	0.256920i	0.704109	−	0.710092i	$-0.251347\pi$
$487$	21.1597	+	5.66973i	0.958839	+	0.256920i	0.254730	+	0.967012i	$0.418013\pi$
$488$	−0.839867	−	3.13443i	−0.0380190	−	0.141889i
$489$		0			0
$490$	−8.85162	−	12.9093i	−0.399875	−	0.583181i
$491$		−	37.8090i		−	1.70630i	−0.521669	−	0.853148i	$-0.674690\pi$
$491$		−	37.8090i		−	1.70630i	0.521669	−	0.853148i	$-0.325310\pi$
$492$		0			0
$493$	−3.83961	+	14.3296i	−0.172927	+	0.645373i
$494$	−3.26860	−	5.66138i	−0.147061	−	0.254718i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	13.3482	−	23.5942i	0.598749	−	1.05834i
$498$		0			0
$499$	−14.2808	−	8.24500i	−0.639294	−	0.369097i	0.145048	−	0.989425i	$-0.453666\pi$
$499$	−14.2808	−	8.24500i	−0.639294	−	0.369097i	−0.784343	+	0.620328i	$0.787000\pi$
$500$	−11.1428	−	0.915158i	−0.498322	−	0.0409271i
$501$		0			0
$502$	5.07586	+	18.9434i	0.226547	+	0.845483i
$503$	−30.3914	+	30.3914i	−1.35509	+	1.35509i	−0.475221	+	0.879866i	$0.657632\pi$
$503$	−30.3914	+	30.3914i	−1.35509	+	1.35509i	−0.879866	+	0.475221i	$0.842368\pi$
$504$		0			0
$505$	−3.73499	+	1.24500i	−0.166205	+	0.0554017i
$506$	13.6345	+	7.87187i	0.606126	+	0.349947i
$507$		0			0
$508$	−5.35221	+	19.9747i	−0.237466	+	0.886234i
$509$	9.71211	−	16.8219i	0.430482	−	0.745616i	−0.566433	−	0.824108i	$-0.691677\pi$
$509$	9.71211	−	16.8219i	0.430482	−	0.745616i	0.996915	+	0.0784917i	$0.0250104\pi$
$510$		0			0
$511$	−26.8675	+	27.3419i	−1.18855	+	1.20953i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−9.73845	+	5.62250i	−0.429545	+	0.247998i
$515$	13.3997	−	0.804294i	0.590463	−	0.0354414i
$516$		0			0
$517$	23.6025	−	23.6025i	1.03804	−	1.03804i
$518$	0.249564	+	28.5197i	0.0109652	+	1.25308i
$519$		0			0
$520$	14.3209	+	2.93055i	0.628011	+	0.128513i
$521$	17.5843	−	10.1523i	0.770381	−	0.444779i	−0.0626297	−	0.998037i	$-0.519949\pi$
$521$	17.5843	−	10.1523i	0.770381	−	0.444779i	0.833010	+	0.553257i	$0.186615\pi$
$522$		0			0
$523$	33.1193	−	8.87429i	1.44821	−	0.388045i	0.552806	−	0.833310i	$-0.313557\pi$
$523$	33.1193	−	8.87429i	1.44821	−	0.388045i	0.895399	+	0.445265i	$0.146890\pi$
$524$	−0.533867			−0.0233221
$525$		0			0
$526$	−22.4900			−0.980610
$527$	20.2651	−	5.43002i	0.882762	−	0.236535i
$528$		0			0
$529$	4.31280	−	2.49000i	0.187513	−	0.108261i
$530$	−4.91805	−	1.00641i	−0.213626	−	0.0437154i
$531$		0			0
$532$	−2.30278	−	1.30278i	−0.0998380	−	0.0564825i
$533$	4.06940	−	4.06940i	0.176265	−	0.176265i
$534$		0			0
$535$	16.1712	−	0.970646i	0.699142	−	0.0419647i
$536$	8.57321	−	4.94975i	0.370306	−	0.213797i
$537$		0			0
$538$	7.00000	+	7.00000i	0.301791	+	0.301791i
$539$	−22.7070	−	12.5853i	−0.978058	−	0.542086i
$540$		0			0
$541$	−3.37750	+	5.85000i	−0.145210	+	0.251511i	−0.929451	−	0.368945i	$-0.879719\pi$
$541$	−3.37750	+	5.85000i	−0.145210	+	0.251511i	0.784241	+	0.620456i	$0.213052\pi$
$542$	−1.67973	+	6.26885i	−0.0721508	+	0.269270i
$543$		0			0
$544$	4.54230	+	2.62250i	0.194750	+	0.112439i
$545$	−8.48528	+	2.82843i	−0.363470	+	0.121157i
$546$		0			0
$547$	6.24500	−	6.24500i	0.267017	−	0.267017i	−0.560880	−	0.827897i	$-0.689537\pi$
$547$	6.24500	−	6.24500i	0.267017	−	0.267017i	0.827897	+	0.560880i	$0.189537\pi$
$548$	−5.49861	−	20.5211i	−0.234889	−	0.876618i
$549$		0			0
$550$	−17.2093	+	6.90760i	−0.733807	+	0.294541i
$551$	2.44949	+	1.41421i	0.104352	+	0.0602475i
$552$		0			0
$553$	3.69962	+	6.28037i	0.157324	+	0.267069i
$554$	−13.4209			−0.570199
$555$		0			0
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	−4.59533	+	17.1500i	−0.194710	+	0.726669i	0.797631	+	0.603146i	$0.206086\pi$
$557$	−4.59533	+	17.1500i	−0.194710	+	0.726669i	−0.992342	+	0.123524i	$0.960580\pi$
$558$		0			0
$559$		−	27.7350i		−	1.17307i
$560$	5.59590	−	1.91987i	0.236470	−	0.0811292i
$561$		0			0
$562$	0.504200	+	1.88170i	0.0212684	+	0.0793748i
$563$	17.8600	+	4.78556i	0.752708	+	0.201687i	0.614719	−	0.788746i	$-0.289269\pi$
$563$	17.8600	+	4.78556i	0.752708	+	0.201687i	0.137989	+	0.990434i	$0.455936\pi$
$564$		0			0
$565$	−19.5746	+	12.9242i	−0.823510	+	0.543726i
$566$			14.1421i			0.594438i
$567$		0			0
$568$	7.24500	+	7.24500i	0.303993	+	0.303993i
$569$	−14.7555	+	25.5574i	−0.618585	+	1.07142i	0.371159	+	0.928569i	$0.378960\pi$
$569$	−14.7555	+	25.5574i	−0.618585	+	1.07142i	−0.989744	+	0.142851i	$0.954373\pi$
$570$		0			0
$571$	−22.4900	−	38.9538i	−0.941177	−	1.63017i	−0.763231	−	0.646126i	$-0.776388\pi$
$571$	−22.4900	−	38.9538i	−0.941177	−	1.63017i	−0.177947	−	0.984040i	$-0.556945\pi$
$572$	23.4189	−	6.27507i	0.979192	−	0.262374i
$573$		0			0
$574$	0.583126	−	2.25500i	0.0243392	−	0.0941220i
$575$	3.00167	−	21.0117i	0.125178	−	0.876247i
$576$		0			0
$577$	32.0879	+	8.59794i	1.33584	+	0.357937i	0.854889	−	0.518812i	$-0.173625\pi$
$577$	32.0879	+	8.59794i	1.33584	+	0.357937i	0.480949	+	0.876748i	$0.340292\pi$
$578$	−10.1519	−	2.72019i	−0.422263	−	0.113145i
$579$		0			0
$580$	−6.00000	+	2.00000i	−0.249136	+	0.0830455i
$581$	−23.5702	+	6.53720i	−0.977857	+	0.271209i
$582$		0			0
$583$	−8.04248	+	2.15498i	−0.333086	+	0.0892500i
$584$	−7.24431	−	12.5475i	−0.299772	−	0.519220i
$585$		0			0
$586$	10.7450	−	18.6109i	0.443872	−	0.768808i
$587$	30.3914	+	30.3914i	1.25439	+	1.25439i	0.953732	+	0.300657i	$0.0972058\pi$
$587$	30.3914	+	30.3914i	1.25439	+	1.25439i	0.300657	+	0.953732i	$0.402794\pi$
$588$		0			0
$589$		−	4.00000i		−	0.164817i
$590$	14.3659	+	21.7582i	0.591437	+	0.895771i
$591$		0			0
$592$	−10.4125	−	2.79003i	−0.427952	−	0.114669i
$593$	7.82280	+	29.1951i	0.321244	+	1.19890i	0.918034	+	0.396502i	$0.129776\pi$
$593$	7.82280	+	29.1951i	0.321244	+	1.19890i	−0.596790	+	0.802397i	$0.703557\pi$
$594$		0			0
$595$	−25.7442	+	17.3231i	−1.05541	+	0.710176i
$596$		−	8.83176i		−	0.361763i
$597$		0			0
$598$	−7.18233	+	26.8048i	−0.293707	+	1.09613i
$599$	4.60327	+	7.97309i	0.188084	+	0.325772i	0.944612	−	0.328191i	$-0.106439\pi$
$599$	4.60327	+	7.97309i	0.188084	+	0.325772i	−0.756527	+	0.653962i	$0.773105\pi$
$600$		0			0
$601$	38.9800			1.59003			0.795014	−	0.606592i	$-0.207464\pi$
$601$	38.9800			1.59003			0.795014	+	0.606592i	$0.207464\pi$
$602$	−5.69733	−	9.67163i	−0.232206	−	0.394186i
$603$		0			0
$604$	12.5487	+	7.24500i	0.510600	+	0.294795i
$605$	−4.08722	+	4.60921i	−0.166169	+	0.187391i
$606$		0			0
$607$	−1.60228	−	5.97978i	−0.0650344	−	0.242712i	0.925755	−	0.378124i	$-0.123431\pi$
$607$	−1.60228	−	5.97978i	−0.0650344	−	0.242712i	−0.990789	+	0.135412i	$0.956764\pi$
$608$	0.707107	−	0.707107i	0.0286770	−	0.0286770i
$609$		0			0
$610$	−3.24500	+	6.49000i	−0.131386	+	0.262772i
$611$	50.9524	+	29.4174i	2.06131	+	1.19010i
$612$		0			0
$613$	−7.36168	+	27.4742i	−0.297336	+	1.10967i	0.642009	+	0.766697i	$0.278101\pi$
$613$	−7.36168	+	27.4742i	−0.297336	+	1.10967i	−0.939345	+	0.342975i	$0.888566\pi$
$614$	−4.41588	+	7.64853i	−0.178210	+	0.308670i
$615$		0			0
$616$	6.87750	−	6.99893i	0.277102	−	0.281995i
$617$	−10.7798	−	10.7798i	−0.433980	−	0.433980i	0.456000	−	0.889980i	$-0.349282\pi$
$617$	−10.7798	−	10.7798i	−0.433980	−	0.433980i	−0.889980	+	0.456000i	$0.849282\pi$
$618$		0			0
$619$	42.6301	−	24.6125i	1.71345	−	0.989260i	0.783640	−	0.621216i	$-0.213361\pi$
$619$	42.6301	−	24.6125i	1.71345	−	0.989260i	0.929808	−	0.368044i	$-0.119972\pi$
$620$	6.69213	+	5.93426i	0.268762	+	0.238325i
$621$		0			0
$622$	−17.4900	+	17.4900i	−0.701285	+	0.701285i
$623$	22.5671	−	13.2938i	0.904133	−	0.532604i
$624$		0			0
$625$	17.2846	+	18.0622i	0.691384	+	0.722487i
$626$	18.9713	−	10.9531i	0.758245	−	0.437773i
$627$		0			0
$628$	10.4125	−	2.79003i	0.415505	−	0.111334i
$629$	56.5402			2.25441
$630$		0			0
$631$	34.9800			1.39253			0.696266	−	0.717784i	$-0.254844\pi$
$631$	34.9800			1.39253			0.696266	+	0.717784i	$0.254844\pi$
$632$	−2.66113	+	0.713047i	−0.105854	+	0.0283635i
$633$		0			0
$634$	−10.3923	+	6.00000i	−0.412731	+	0.238290i
$635$	38.5882	−	25.4780i	1.53132	−	1.01106i
$636$		0			0
$637$	11.0683	−	44.4017i	0.438543	−	1.75926i
$638$	−7.41755	+	7.41755i	−0.293664	+	0.293664i
$639$		0			0
$640$	0.133975	+	2.23205i	0.00529581	+	0.0882296i
$641$	36.5801	−	21.1195i	1.44483	−	0.834170i	0.446659	−	0.894704i	$-0.352614\pi$
$641$	36.5801	−	21.1195i	1.44483	−	0.834170i	0.998166	+	0.0605336i	$0.0192802\pi$
$642$		0			0
$643$	9.73499	+	9.73499i	0.383911	+	0.383911i	0.872509	−	0.488598i	$-0.162492\pi$
$643$	9.73499	+	9.73499i	0.383911	+	0.383911i	−0.488598	+	0.872509i	$0.662492\pi$
$644$	3.00167	+	10.8227i	0.118282	+	0.426473i
$645$		0			0
$646$	−2.62250	+	4.54230i	−0.103181	+	0.178714i
$647$	2.72019	−	10.1519i	0.106942	−	0.399112i	−0.891617	−	0.452791i	$-0.850428\pi$
$647$	2.72019	−	10.1519i	0.106942	−	0.399112i	0.998558	+	0.0536795i	$0.0170949\pi$
$648$		0			0
$649$	37.4513	+	21.6225i	1.47009	+	0.848757i
$650$	−19.6116	−	26.1488i	−0.769230	−	1.02564i
$651$		0			0
$652$	−5.24500	+	5.24500i	−0.205410	+	0.205410i
$653$	−0.649637	−	2.42448i	−0.0254223	−	0.0948771i	0.952049	−	0.305945i	$-0.0989725\pi$
$653$	−0.649637	−	2.42448i	−0.0254223	−	0.0948771i	−0.977471	+	0.211068i	$0.932306\pi$
$654$		0			0
$655$	0.893177	+	0.792026i	0.0348993	+	0.0309470i
$656$	0.762402	+	0.440173i	0.0297668	+	0.0171859i
$657$		0			0
$658$	23.8109	−	0.208359i	0.928244	−	0.00812269i
$659$	−32.5269			−1.26707			−0.633534	−	0.773715i	$-0.718396\pi$
$659$	−32.5269			−1.26707			−0.633534	+	0.773715i	$0.718396\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	−1.81173	+	6.76148i	−0.0704150	+	0.262792i
$663$		0			0
$664$		−	9.24500i		−	0.358776i
$665$	1.91987	+	5.59590i	0.0744493	+	0.217000i
$666$		0			0
$667$	−3.10755	−	11.5976i	−0.120325	−	0.449059i
$668$	−9.89591	−	2.65160i	−0.382884	−	0.102594i
$669$		0			0
$670$	−21.6865	−	4.43782i	−0.837824	−	0.171448i
$671$			12.0350i			0.464605i
$672$		0			0
$673$	31.2450	+	31.2450i	1.20441	+	1.20441i	0.972813	+	0.231594i	$0.0743939\pi$
$673$	31.2450	+	31.2450i	1.20441	+	1.20441i	0.231594	+	0.972813i	$0.425606\pi$
$674$	4.41588	−	7.64853i	0.170093	−	0.294610i
$675$		0			0
$676$	14.8675	+	25.7513i	0.571827	+	0.990433i
$677$	11.5718	−	3.10065i	0.444740	−	0.119168i	−0.0294973	−	0.999565i	$-0.509391\pi$
$677$	11.5718	−	3.10065i	0.444740	−	0.119168i	0.474237	+	0.880397i	$0.342724\pi$
$678$		0			0
$679$	33.3333	−	9.24500i	1.27922	−	0.354790i
$680$	−3.70877	−	11.1263i	−0.142225	−	0.426675i
$681$		0			0
$682$	14.3296	+	3.83961i	0.548709	+	0.147026i
$683$	12.5377	+	3.35947i	0.479742	+	0.128547i	0.490583	−	0.871395i	$-0.336784\pi$
$683$	12.5377	+	3.35947i	0.479742	+	0.128547i	−0.0108404	+	0.999941i	$0.503451\pi$
$684$		0			0
$685$	−21.2450	+	42.4900i	−0.811730	+	1.62346i
$686$	−5.26130	−	17.7572i	−0.200877	−	0.677974i
$687$		0			0
$688$	4.09808	−	1.09808i	0.156238	−	0.0418638i
$689$	−7.33800	−	12.7098i	−0.279556	−	0.484204i
$690$		0			0
$691$	12.4900	−	21.6333i	0.475142	−	0.822970i	−0.524453	−	0.851440i	$-0.675730\pi$
$691$	12.4900	−	21.6333i	0.475142	−	0.822970i	0.999595	+	0.0284697i	$0.00906341\pi$
$692$	5.48361	+	5.48361i	0.208456	+	0.208456i
$693$		0			0
$694$			11.2450i			0.426854i
$695$	−3.58630	+	17.5254i	−0.136036	+	0.664775i
$696$		0			0
$697$	−4.46008	−	1.19508i	−0.168938	−	0.0452667i
$698$	−2.46137	−	9.18596i	−0.0931642	−	0.347694i
$699$		0			0
$700$	−12.2104	−	5.08988i	−0.461509	−	0.192379i
$701$			21.1849i			0.800143i	0.916484	+	0.400071i	$0.131015\pi$
$701$			21.1849i			0.800143i	−0.916484	+	0.400071i	$0.868985\pi$
$702$		0			0
$703$	2.79003	−	10.4125i	0.105228	−	0.392716i
$704$	1.85439	+	3.21189i	0.0698898	+	0.121053i
$705$		0			0
$706$	−6.49000			−0.244254
$707$	−4.65818	+	0.0407618i	−0.175189	+	0.00153301i
$708$		0			0
$709$	−39.3782	−	22.7350i	−1.47888	−	0.853831i	−0.479164	−	0.877726i	$-0.659060\pi$
$709$	−39.3782	−	22.7350i	−1.47888	−	0.853831i	−0.999714	+	0.0238950i	$0.992393\pi$
$710$	−1.37270	−	22.8695i	−0.0515165	−	0.858278i
$711$		0			0
$712$	2.56218	+	9.56218i	0.0960217	+	0.358358i
$713$	−12.0067	+	12.0067i	−0.449653	+	0.449653i
$714$		0			0
$715$	−48.4900	−	24.2450i	−1.81342	−	0.906712i
$716$	−14.2346	−	8.21835i	−0.531972	−	0.307134i
$717$		0			0
$718$	2.92820	−	10.9282i	0.109280	−	0.407837i
$719$	15.5563	−	26.9444i	0.580154	−	1.00486i	−0.415307	−	0.909681i	$-0.636326\pi$
$719$	15.5563	−	26.9444i	0.580154	−	1.00486i	0.995461	−	0.0951746i	$-0.0303409\pi$
$720$		0			0
$721$	15.3775	+	3.97650i	0.572688	+	0.148093i
$722$	−12.7279	−	12.7279i	−0.473684	−	0.473684i
$723$		0			0
$724$	9.73845	−	5.62250i	0.361927	−	0.208959i
$725$	13.0053	+	5.55532i	0.483006	+	0.206319i
$726$		0			0
$727$	−10.3775	+	10.3775i	−0.384880	+	0.384880i	−0.872857	−	0.487977i	$-0.837735\pi$
$727$	−10.3775	+	10.3775i	−0.384880	+	0.384880i	0.487977	+	0.872857i	$0.337735\pi$
$728$	15.0537	+	8.51651i	0.557927	+	0.315643i
$729$		0			0
$730$	−6.49507	+	31.7398i	−0.240393	+	1.17474i
$731$	−19.2714	+	11.1263i	−0.712777	+	0.411522i
$732$		0			0
$733$	−7.01113	+	1.87863i	−0.258962	+	0.0693887i	−0.385964	−	0.922514i	$-0.626131\pi$
$733$	−7.01113	+	1.87863i	−0.258962	+	0.0693887i	0.127002	+	0.991902i	$0.459464\pi$
$734$	−1.22683			−0.0452830
$735$		0			0
$736$	−4.24500			−0.156473
$737$	−35.4640	+	9.50254i	−1.30633	+	0.350030i
$738$		0			0
$739$	17.3032	−	9.99000i	0.636508	−	0.367488i	−0.146760	−	0.989172i	$-0.546885\pi$
$739$	17.3032	−	9.99000i	0.636508	−	0.367488i	0.783268	+	0.621684i	$0.213551\pi$
$740$	13.2813	+	20.1155i	0.488231	+	0.739459i
$741$		0			0
$742$	−5.16973	−	2.92473i	−0.189787	−	0.107370i
$743$	−12.3673	+	12.3673i	−0.453712	+	0.453712i	−0.896585	−	0.442873i	$-0.853959\pi$
$743$	−12.3673	+	12.3673i	−0.453712	+	0.453712i	0.442873	+	0.896585i	$0.353959\pi$
$744$		0			0
$745$	−13.1025	+	14.7758i	−0.480038	+	0.541344i
$746$	10.0980	−	5.83009i	0.369715	−	0.213455i
$747$		0			0
$748$	−13.7550	−	13.7550i	−0.502933	−	0.502933i
$749$	18.5580	+	4.79896i	0.678095	+	0.175350i
$750$		0			0
$751$	7.13250	−	12.3539i	0.260269	−	0.450799i	−0.706045	−	0.708167i	$-0.749522\pi$
$751$	7.13250	−	12.3539i	0.260269	−	0.450799i	0.966313	+	0.257369i	$0.0828555\pi$
$752$	−2.32937	+	8.69333i	−0.0849434	+	0.317013i
$753$		0			0
$754$	−16.0128	−	9.24500i	−0.583152	−	0.336683i
$755$	−10.2460	−	30.7379i	−0.372889	−	1.11867i
$756$		0			0
$757$	9.00000	−	9.00000i	0.327111	−	0.327111i	−0.524376	−	0.851487i	$-0.675701\pi$
$757$	9.00000	−	9.00000i	0.327111	−	0.327111i	0.851487	+	0.524376i	$0.175701\pi$
$758$	−1.22551	−	4.57365i	−0.0445124	−	0.166123i
$759$		0			0
$760$	−2.23205	+	0.133975i	−0.0809650	+	0.00485977i
$761$	−16.3595	−	9.44517i	−0.593032	−	0.342387i	0.173263	−	0.984876i	$-0.444569\pi$
$761$	−16.3595	−	9.44517i	−0.593032	−	0.342387i	−0.766296	+	0.642488i	$0.777902\pi$
$762$		0			0
$763$	−10.5826	+	0.0926041i	−0.383116	+	0.00335249i
$764$	11.6602			0.421851
$765$		0			0
$766$	−10.9900	−	19.0352i	−0.397085	−	0.687771i
$767$	−19.7285	+	73.6277i	−0.712354	+	2.65854i
$768$		0			0
$769$			22.7350i			0.819845i	0.912120	+	0.409922i	$0.134444\pi$
$769$			22.7350i			0.819845i	−0.912120	+	0.409922i	$0.865556\pi$
$770$	−21.8896	+	1.50622i	−0.788848	+	0.0542805i
$771$		0			0
$772$	−4.57166	−	17.0617i	−0.164537	−	0.614062i
$773$	−32.8222	−	8.79467i	−1.18053	−	0.316322i	−0.385394	−	0.922752i	$-0.625934\pi$
$773$	−32.8222	−	8.79467i	−1.18053	−	0.316322i	−0.795137	+	0.606430i	$0.792601\pi$
$774$		0			0
$775$	−2.39230	−	19.8564i	−0.0859341	−	0.713263i
$776$			13.0744i			0.469344i
$777$		0			0
$778$	0.489996	+	0.489996i	0.0175672	+	0.0175672i
$779$	−0.440173	+	0.762402i	−0.0157708	+	0.0273159i
$780$		0			0
$781$	−19.0000	−	32.9090i	−0.679873	−	1.17758i
$782$	21.5063	−	5.76261i	0.769065	−	0.206070i
$783$		0			0
$784$	6.99893	−	0.122499i	0.249962	−	0.00437496i
$785$	−21.5597	−	10.7798i	−0.769498	−	0.384749i
$786$		0			0
$787$	31.0839	+	8.32891i	1.10802	+	0.296894i	0.766027	−	0.642808i	$-0.222231\pi$
$787$	31.0839	+	8.32891i	1.10802	+	0.296894i	0.341995	+	0.939702i	$0.388898\pi$
$788$	−9.16663	−	2.45619i	−0.326548	−	0.0874982i
$789$		0			0
$790$	5.51000	+	2.75500i	0.196037	+	0.0980186i
$791$	−26.7443	+	7.41755i	−0.950920	+	0.263738i
$792$		0			0
$793$	−20.4904	+	5.49038i	−0.727635	+	0.194969i
$794$	−10.4192	−	18.0466i	−0.369764	−	0.640450i
$795$		0			0
$796$	−1.62250	+	2.81025i	−0.0575080	+	0.0996067i
$797$	13.4209	+	13.4209i	0.475392	+	0.475392i	0.903654	−	0.428262i	$-0.140874\pi$
$797$	13.4209	+	13.4209i	0.475392	+	0.475392i	−0.428262	+	0.903654i	$0.640874\pi$
$798$		0			0
$799$		−	47.2050i		−	1.66999i
$800$	3.08725	−	3.93305i	0.109151	−	0.139054i
$801$		0			0
$802$	−14.8453	−	3.97778i	−0.524205	−	0.140460i
$803$	13.9076	+	51.9040i	0.490790	+	1.83165i
$804$		0			0
$805$	11.0342	−	22.5598i	0.388905	−	0.795130i
$806$			26.1488i			0.921052i
$807$		0			0
$808$	0.455701	−	1.70070i	0.0160315	−	0.0598304i
$809$	−0.0795460	−	0.137778i	−0.00279669	−	0.00484400i	0.864624	−	0.502420i	$-0.167557\pi$
$809$	−0.0795460	−	0.137778i	−0.00279669	−	0.00484400i	−0.867420	+	0.497576i	$0.834224\pi$
$810$		0			0
$811$	−17.2250			−0.604851			−0.302426	−	0.953173i	$-0.597796\pi$
$811$	−17.2250			−0.604851			−0.302426	+	0.953173i	$0.597796\pi$
$812$	−7.48303	+	0.0654810i	−0.262603	+	0.00229793i
$813$		0			0
$814$	34.6237	+	19.9900i	1.21356	+	0.700649i
$815$	16.5563	−	0.993763i	0.579943	−	0.0348100i
$816$		0			0
$817$	1.09808	+	4.09808i	0.0384168	+	0.143374i
$818$		0			0
$819$		0			0
$820$	−0.622499	−	1.86750i	−0.0217386	−	0.0652158i
$821$	−14.3724	−	8.29789i	−0.501599	−	0.289598i	0.227774	−	0.973714i	$-0.426855\pi$
$821$	−14.3724	−	8.29789i	−0.501599	−	0.289598i	−0.729374	+	0.684115i	$0.760188\pi$
$822$		0			0
$823$	−11.3468	+	42.3468i	−0.395524	+	1.47612i	0.425361	+	0.905024i	$0.360147\pi$
$823$	−11.3468	+	42.3468i	−0.395524	+	1.47612i	−0.820886	+	0.571093i	$0.806520\pi$
$824$	−3.00167	+	5.19904i	−0.104568	+	0.181117i
$825$		0			0
$826$	8.24500	+	29.7278i	0.286880	+	1.03436i
$827$	−25.4558	−	25.4558i	−0.885186	−	0.885186i	0.108870	−	0.994056i	$-0.465277\pi$
$827$	−25.4558	−	25.4558i	−0.885186	−	0.885186i	−0.994056	+	0.108870i	$0.965277\pi$
$828$		0			0
$829$	10.6218	−	6.13250i	0.368911	−	0.212991i	−0.304072	−	0.952649i	$-0.598346\pi$
$829$	10.6218	−	6.13250i	0.368911	−	0.212991i	0.672982	+	0.739658i	$0.265013\pi$
$830$	−13.7155	+	15.4672i	−0.476074	+	0.536874i
$831$		0			0
$832$	−4.62250	+	4.62250i	−0.160256	+	0.160256i
$833$	−35.2922	+	10.1217i	−1.22280	+	0.350696i
$834$		0			0
$835$	12.6224	+	19.1174i	0.436815	+	0.661586i
$836$	−3.21189	+	1.85439i	−0.111086	+	0.0641353i
$837$		0			0
$838$	22.3721	−	5.99458i	0.772831	−	0.207079i
$839$	18.3848			0.634713			0.317356	−	0.948306i	$-0.397205\pi$
$839$	18.3848			0.634713			0.317356	+	0.948306i	$0.397205\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	4.59298	−	1.23069i	0.158285	−	0.0424122i
$843$		0			0
$844$	−24.4609	+	14.1225i	−0.841978	+	0.486116i
$845$	13.3298	−	65.1396i	0.458560	−	2.24087i
$846$		0			0
$847$	−6.28037	+	3.69962i	−0.215796	+	0.127121i
$848$	1.58745	−	1.58745i	0.0545134	−	0.0545134i
$849$		0			0
$850$	−10.3017	+	24.1169i	−0.353346	+	0.827203i
$851$	−39.6297	+	22.8802i	−1.35849	+	0.784323i
$852$		0			0
$853$	−30.8675	−	30.8675i	−1.05688	−	1.05688i	−0.998281	−	0.0586015i	$-0.981336\pi$
$853$	−30.8675	−	30.8675i	−1.05688	−	1.05688i	−0.0586015	−	0.998281i	$-0.518664\pi$
$854$	−6.01748	+	6.12372i	−0.205914	+	0.209550i
$855$		0			0
$856$	−3.62250	+	6.27435i	−0.123814	+	0.214453i
$857$	0.713047	−	2.66113i	0.0243572	−	0.0909024i	−0.952677	−	0.303984i	$-0.901683\pi$
$857$	0.713047	−	2.66113i	0.0243572	−	0.0909024i	0.977035	+	0.213081i	$0.0683499\pi$
$858$		0			0
$859$	−19.4769	−	11.2450i	−0.664544	−	0.383674i	0.129462	−	0.991584i	$-0.458675\pi$
$859$	−19.4769	−	11.2450i	−0.664544	−	0.383674i	−0.794006	+	0.607910i	$0.792008\pi$
$860$	−8.48528	−	4.24264i	−0.289346	−	0.144673i
$861$		0			0
$862$	8.24500	−	8.24500i	0.280826	−	0.280826i
$863$	0.707869	+	2.64180i	0.0240961	+	0.0899280i	0.976927	−	0.213574i	$-0.0685106\pi$
$863$	0.707869	+	2.64180i	0.0240961	+	0.0899280i	−0.952831	+	0.303502i	$0.901844\pi$
$864$		0			0
$865$	−1.03897	−	17.3096i	−0.0353262	−	0.588543i
$866$	−23.5702	−	13.6083i	−0.800948	−	0.462428i
$867$		0			0
$868$	5.37150	+	9.11850i	0.182321	+	0.309502i
$869$	10.2177			0.346611
$870$		0			0
$871$	−32.3575	−	56.0448i	−1.09639	−	1.89901i
$872$	1.03528	−	3.86370i	0.0350589	−	0.130842i
$873$		0			0
$874$		−	4.24500i		−	0.143589i
$875$	12.8772	+	26.6304i	0.435329	+	0.900272i
$876$		0			0
$877$	−1.69195	−	6.31445i	−0.0571332	−	0.213224i	0.931458	−	0.363850i	$-0.118538\pi$
$877$	−1.69195	−	6.31445i	−0.0571332	−	0.213224i	−0.988591	+	0.150626i	$0.951871\pi$
$878$	19.3185	+	5.17638i	0.651968	+	0.174694i
$879$		0			0
$880$	1.66260	−	8.12470i	0.0560462	−	0.273884i
$881$		−	34.1002i		−	1.14887i	−0.818552	−	0.574433i	$-0.805223\pi$
$881$		−	34.1002i		−	1.14887i	0.818552	−	0.574433i	$-0.194777\pi$
$882$		0			0
$883$	28.7350	+	28.7350i	0.967010	+	0.967010i	0.999473	−	0.0324634i	$-0.0103352\pi$
$883$	28.7350	+	28.7350i	0.967010	+	0.967010i	−0.0324634	+	0.999473i	$0.510335\pi$
$884$	17.1438	−	29.6939i	0.576608	−	0.998715i
$885$		0			0
$886$	−19.8675	−	34.4115i	−0.667462	−	1.15608i
$887$	11.1178	−	2.97901i	0.373300	−	0.100025i	−0.0672912	−	0.997733i	$-0.521436\pi$
$887$	11.1178	−	2.97901i	0.373300	−	0.100025i	0.440591	+	0.897708i	$0.354769\pi$
$888$		0			0
$889$	52.7222	−	14.6225i	1.76824	−	0.490423i
$890$	9.89949	−	19.7990i	0.331832	−	0.663664i
$891$		0			0
$892$	−7.86148	−	2.10648i	−0.263222	−	0.0705301i
$893$	−8.69333	−	2.32937i	−0.290911	−	0.0779494i
$894$		0			0
$895$	11.6225	+	34.8675i	0.388497	+	1.16549i
$896$	−0.662382	+	2.56149i	−0.0221286	+	0.0855735i
$897$		0			0
$898$	9.38118	−	2.51368i	0.313054	−	0.0838825i
$899$	−5.65685	−	9.79796i	−0.188667	−	0.326780i
$900$		0			0
$901$	−5.88751	+	10.1975i	−0.196141	+	0.339727i
$902$	−2.30871	−	2.30871i	−0.0768716	−	0.0768716i
$903$		0			0
$904$		−	10.4900i		−	0.348892i
$905$	−24.6341	−	5.04099i	−0.818865	−	0.167568i
$906$		0			0
$907$	−2.03537	−	0.545376i	−0.0675834	−	0.0181089i	0.224869	−	0.974389i	$-0.427805\pi$
$907$	−2.03537	−	0.545376i	−0.0675834	−	0.0181089i	−0.292452	+	0.956280i	$0.594471\pi$
$908$	−1.35751	−	5.06628i	−0.0450504	−	0.168130i
$909$		0			0
$910$	−12.5506	−	36.5815i	−0.416047	−	1.21267i
$911$		−	32.1804i		−	1.06619i	−0.846057	−	0.533093i	$-0.821030\pi$
$911$		−	32.1804i		−	1.06619i	0.846057	−	0.533093i	$-0.178970\pi$
$912$		0			0
$913$	−8.87429	+	33.1193i	−0.293696	+	1.09609i
$914$	17.3170	+	29.9940i	0.572797	+	0.992113i
$915$		0			0
$916$	9.24500			0.305463
$917$	0.716916	+	1.21702i	0.0236747	+	0.0401894i
$918$		0			0
$919$	−3.03975	−	1.75500i	−0.100272	−	0.0578922i	0.449025	−	0.893519i	$-0.351771\pi$
$919$	−3.03975	−	1.75500i	−0.100272	−	0.0578922i	−0.549298	+	0.835627i	$0.685105\pi$
$920$	7.10202	+	6.29773i	0.234147	+	0.207630i
$921$		0			0
$922$	1.74045	+	6.49545i	0.0573187	+	0.213916i
$923$	47.3620	−	47.3620i	1.55894	−	1.55894i
$924$		0			0
$925$	7.62250	−	53.3575i	0.250626	−	1.75438i
$926$	15.7594	+	9.09869i	0.517886	+	0.299002i
$927$		0			0
$928$	0.732051	−	2.73205i	0.0240307	−	0.0896840i
$929$	14.5823	−	25.2573i	0.478430	−	0.828665i	−0.521264	−	0.853395i	$-0.674539\pi$
$929$	14.5823	−	25.2573i	0.478430	−	0.828665i	0.999694	+	0.0247303i	$0.00787269\pi$
$930$		0			0
$931$	0.122499	+	6.99893i	0.00401474	+	0.229381i
$932$	−10.4334	−	10.4334i	−0.341756	−	0.341756i
$933$		0			0
$934$	−6.27435	+	3.62250i	−0.205303	+	0.118532i
$935$	2.60614	+	43.4190i	0.0852300	+	1.41995i
$936$		0			0
$937$	−17.0000	+	17.0000i	−0.555366	+	0.555366i	−0.927985	−	0.372619i	$-0.878460\pi$
$937$	−17.0000	+	17.0000i	−0.555366	+	0.555366i	0.372619	+	0.927985i	$0.378460\pi$
$938$	−22.7963	−	12.8968i	−0.744326	−	0.421096i
$939$		0			0
$940$	16.7942	−	11.0885i	0.547767	−	0.361666i
$941$	3.07411	−	1.77484i	0.100213	−	0.0578582i	−0.449056	−	0.893504i	$-0.648240\pi$
$941$	3.07411	−	1.77484i	0.100213	−	0.0578582i	0.549269	+	0.835646i	$0.314906\pi$
$942$		0			0
$943$	3.60973	−	0.967225i	0.117549	−	0.0314972i
$944$	−11.6602			−0.379507
$945$		0			0
$946$	−15.7350			−0.511589
$947$	19.0625	−	5.10779i	0.619449	−	0.165981i	0.0645719	−	0.997913i	$-0.479432\pi$
$947$	19.0625	−	5.10779i	0.619449	−	0.165981i	0.554877	+	0.831932i	$0.312765\pi$
$948$		0			0
$949$	−82.0256	+	47.3575i	−2.66266	+	1.53729i
$950$	3.93305	+	3.08725i	0.127605	+	0.100163i
$951$		0			0
$952$	−0.121427	−	13.8764i	−0.00393547	−	0.449738i
$953$	−25.8023	+	25.8023i	−0.835819	+	0.835819i	−0.988306	−	0.152486i	$-0.951272\pi$
$953$	−25.8023	+	25.8023i	−0.835819	+	0.835819i	0.152486	+	0.988306i	$0.451272\pi$
$954$		0			0
$955$	−19.5079	−	17.2986i	−0.631260	−	0.559771i
$956$	−14.9970	+	8.65852i	−0.485038	+	0.280037i
$957$		0			0
$958$	13.4900	+	13.4900i	0.435842	+	0.435842i
$959$	−39.3964	+	40.0920i	−1.27218	+	1.29464i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−18.2390	+	68.0688i	−0.588048	+	2.19463i
$963$		0			0
$964$	−8.87243	−	5.12250i	−0.285762	−	0.164985i
$965$	−17.6635	+	35.3270i	−0.568609	+	1.13722i
$966$		0			0
$967$	−26.7350	+	26.7350i	−0.859739	+	0.859739i	−0.991307	−	0.131568i	$-0.957999\pi$
$967$	−26.7350	+	26.7350i	−0.859739	+	0.859739i	0.131568	+	0.991307i	$0.457999\pi$
$968$	−0.713047	−	2.66113i	−0.0229182	−	0.0855319i
$969$		0			0
$970$	19.3967	−	21.8739i	0.622791	−	0.702329i
$971$	7.81081	+	4.50957i	0.250661	+	0.144719i	0.620067	−	0.784549i	$-0.287105\pi$
$971$	7.81081	+	4.50957i	0.250661	+	0.144719i	−0.369406	+	0.929268i	$0.620439\pi$
$972$		0			0
$973$	−10.4222	+	18.4222i	−0.334121	+	0.590589i
$974$	21.9062			0.701919
$975$		0			0
$976$	−1.62250	−	2.81025i	−0.0519349	−	0.0899539i
$977$	−14.1030	+	52.6333i	−0.451197	+	1.68389i	0.247839	+	0.968801i	$0.420280\pi$
$977$	−14.1030	+	52.6333i	−0.451197	+	1.68389i	−0.699035	+	0.715087i	$0.746387\pi$
$978$		0			0
$979$		−	36.7150i		−	1.17342i
$980$	−11.8912	−	10.1784i	−0.379849	−	0.325137i
$981$		0			0
$982$	−9.78569	−	36.5207i	−0.312274	−	1.16542i
$983$	4.82963	+	1.29410i	0.154041	+	0.0412752i	0.335016	−	0.942213i	$-0.391258\pi$
$983$	4.82963	+	1.29410i	0.154041	+	0.0412752i	−0.180974	+	0.983488i	$0.557925\pi$
$984$		0			0
$985$	11.6922	+	17.7086i	0.372543	+	0.564242i
$986$			14.8351i			0.472446i
$987$		0			0
$988$	−4.62250	−	4.62250i	−0.147061	−	0.147061i
$989$	9.00500	−	15.5971i	0.286342	−	0.495960i
$990$		0			0
$991$	−13.1125	−	22.7115i	−0.416532	−	0.721455i	0.579056	−	0.815288i	$-0.303421\pi$
$991$	−13.1125	−	22.7115i	−0.416532	−	0.721455i	−0.995588	+	0.0938331i	$0.970088\pi$
$992$	−3.86370	+	1.03528i	−0.122673	+	0.0328701i
$993$		0			0
$994$	6.78675	−	26.2450i	0.215263	−	0.832441i
$995$	6.88368	−	2.29456i	0.218227	−	0.0727424i
$996$		0			0
$997$	23.2224	+	6.22243i	0.735462	+	0.197066i	0.607060	−	0.794656i	$-0.292349\pi$
$997$	23.2224	+	6.22243i	0.735462	+	0.197066i	0.128402	+	0.991722i	$0.459015\pi$
$998$	−15.9281	−	4.26793i	−0.504196	−	0.135099i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ce.a.233.3	yes	16
3.2	odd	2	inner	630.2.ce.a.233.1	yes	16
5.2	odd	4	inner	630.2.ce.a.107.4	yes	16
7.4	even	3	inner	630.2.ce.a.53.2	✓	16
15.2	even	4	inner	630.2.ce.a.107.2	yes	16
21.11	odd	6	inner	630.2.ce.a.53.4	yes	16
35.32	odd	12	inner	630.2.ce.a.557.1	yes	16
105.32	even	12	inner	630.2.ce.a.557.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.a.53.2	✓	16	7.4	even	3	inner
630.2.ce.a.53.4	yes	16	21.11	odd	6	inner
630.2.ce.a.107.2	yes	16	15.2	even	4	inner
630.2.ce.a.107.4	yes	16	5.2	odd	4	inner
630.2.ce.a.233.1	yes	16	3.2	odd	2	inner
630.2.ce.a.233.3	yes	16	1.1	even	1	trivial
630.2.ce.a.557.1	yes	16	35.32	odd	12	inner
630.2.ce.a.557.3	yes	16	105.32	even	12	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.19067 - 0.448288i) q^{5} +(-2.30278 - 1.30278i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.19067 - 0.448288i) q^{5} +(-2.30278 - 1.30278i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.23205 + 0.133975i) q^{10} +(-3.21189 + 1.85439i) q^{11} +(-4.62250 - 4.62250i) q^{13} +(-2.56149 - 0.662382i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.35751 + 5.06628i) q^{17} +(0.866025 + 0.500000i) q^{19} +(-2.12132 + 0.707107i) q^{20} +(-2.62250 + 2.62250i) q^{22} +(-1.09869 - 4.10035i) q^{23} +(4.59808 + 1.96410i) q^{25} +(-5.66138 - 3.26860i) q^{26} +(-2.64565 + 0.0231510i) q^{28} +2.82843 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.258819 - 0.965926i) q^{32} +5.24500i q^{34} +(4.46060 + 3.88626i) q^{35} +(-2.79003 - 10.4125i) q^{37} +(0.965926 + 0.258819i) q^{38} +(-1.86603 + 1.23205i) q^{40} +0.880347i q^{41} +(3.00000 + 3.00000i) q^{43} +(-1.85439 + 3.21189i) q^{44} +(-2.12250 - 3.67628i) q^{46} +(-8.69333 + 2.32937i) q^{47} +(3.60555 + 6.00000i) q^{49} +(4.94975 + 0.707107i) q^{50} +(-6.31445 - 1.69195i) q^{52} +(2.16850 + 0.581048i) q^{53} +(7.86750 - 2.62250i) q^{55} +(-2.54951 + 0.707107i) q^{56} +(2.73205 - 0.732051i) q^{58} +(-5.83009 - 10.0980i) q^{59} +(1.62250 - 2.81025i) q^{61} +(-2.82843 - 2.82843i) q^{62} -1.00000i q^{64} +(8.05416 + 12.1986i) q^{65} +(9.56218 + 2.56218i) q^{67} +(1.35751 + 5.06628i) q^{68} +(5.31445 + 2.59935i) q^{70} +10.2460i q^{71} +(3.74993 - 13.9949i) q^{73} +(-5.38992 - 9.33562i) q^{74} +1.00000 q^{76} +(9.81212 - 0.0858619i) q^{77} +(-2.38590 - 1.37750i) q^{79} +(-1.48356 + 1.67303i) q^{80} +(0.227850 + 0.850349i) q^{82} +(6.53720 - 6.53720i) q^{83} +(5.24500 - 10.4900i) q^{85} +(3.67423 + 2.12132i) q^{86} +(-0.959901 + 3.58240i) q^{88} +(-4.94975 + 8.57321i) q^{89} +(4.62250 + 16.6667i) q^{91} +(-3.00167 - 3.00167i) q^{92} +(-7.79423 + 4.50000i) q^{94} +(-1.67303 - 1.48356i) q^{95} +(-9.24500 + 9.24500i) q^{97} +(5.03561 + 4.86237i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 8 q^{10} - 24 q^{13} + 8 q^{16} + 8 q^{22} + 32 q^{25} + 4 q^{28} - 32 q^{31} + 36 q^{37} - 16 q^{40} + 48 q^{43} + 16 q^{46} - 12 q^{52} - 24 q^{55} + 16 q^{58} - 24 q^{61} + 56 q^{67} - 4 q^{70} - 32 q^{73} + 16 q^{76} + 20 q^{82} - 16 q^{85} - 4 q^{88} + 24 q^{91} - 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 8 * q^10 - 24 * q^13 + 8 * q^16 + 8 * q^22 + 32 * q^25 + 4 * q^28 - 32 * q^31 + 36 * q^37 - 16 * q^40 + 48 * q^43 + 16 * q^46 - 12 * q^52 - 24 * q^55 + 16 * q^58 - 24 * q^61 + 56 * q^67 - 4 * q^70 - 32 * q^73 + 16 * q^76 + 20 * q^82 - 16 * q^85 - 4 * q^88 + 24 * q^91 - 48 * q^97

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