LMFDB - Embedded newform 630.2.ce.a.107.2

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			107.2
Root			$-0.337183 + 1.25838i$ of defining polynomial
Character	$\chi$	$=$	630.107
Dual form			630.2.ce.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.48356 + 1.67303i) q^{5} +(1.30278 - 2.30278i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.48356 + 1.67303i) q^{5} +(1.30278 - 2.30278i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.23205 - 1.86603i) q^{10} +(3.21189 - 1.85439i) q^{11} +(-4.62250 + 4.62250i) q^{13} +(-2.56149 - 0.662382i) q^{14} +(0.500000 - 0.866025i) q^{16} +(5.06628 + 1.35751i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(-2.12132 - 0.707107i) q^{20} +(-2.62250 - 2.62250i) q^{22} +(4.10035 - 1.09869i) q^{23} +(-0.598076 + 4.96410i) q^{25} +(5.66138 + 3.26860i) q^{26} +(0.0231510 + 2.64565i) q^{28} +2.82843 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.965926 - 0.258819i) q^{32} -5.24500i q^{34} +(5.78537 - 1.23673i) q^{35} +(10.4125 - 2.79003i) q^{37} +(-0.258819 + 0.965926i) q^{38} +(-0.133975 + 2.23205i) q^{40} -0.880347i q^{41} +(3.00000 - 3.00000i) q^{43} +(-1.85439 + 3.21189i) q^{44} +(-2.12250 - 3.67628i) q^{46} +(2.32937 + 8.69333i) q^{47} +(-3.60555 - 6.00000i) q^{49} +(4.94975 - 0.707107i) q^{50} +(1.69195 - 6.31445i) q^{52} +(-0.581048 + 2.16850i) q^{53} +(7.86750 + 2.62250i) q^{55} +(2.54951 - 0.707107i) q^{56} +(-0.732051 - 2.73205i) q^{58} +(-5.83009 - 10.0980i) q^{59} +(1.62250 - 2.81025i) q^{61} +(-2.82843 + 2.82843i) q^{62} +1.00000i q^{64} +(-14.5914 - 0.875819i) q^{65} +(-2.56218 + 9.56218i) q^{67} +(-5.06628 + 1.35751i) q^{68} +(-2.69195 - 5.26815i) q^{70} -10.2460i q^{71} +(-13.9949 - 3.74993i) q^{73} +(-5.38992 - 9.33562i) q^{74} +1.00000 q^{76} +(-0.0858619 - 9.81212i) q^{77} +(2.38590 + 1.37750i) q^{79} +(2.19067 - 0.448288i) q^{80} +(-0.850349 + 0.227850i) q^{82} +(6.53720 + 6.53720i) q^{83} +(5.24500 + 10.4900i) q^{85} +(-3.67423 - 2.12132i) q^{86} +(3.58240 + 0.959901i) q^{88} +(-4.94975 + 8.57321i) q^{89} +(4.62250 + 16.6667i) q^{91} +(-3.00167 + 3.00167i) q^{92} +(7.79423 - 4.50000i) q^{94} +(-0.448288 - 2.19067i) q^{95} +(-9.24500 - 9.24500i) q^{97} +(-4.86237 + 5.03561i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.48356	+	1.67303i	0.663470	+	0.748203i
$5$	1.48356	+	1.67303i	0.663470	+	0.748203i
$6$		0			0
$7$	1.30278	−	2.30278i	0.492403	−	0.870367i
$7$	1.30278	−	2.30278i	0.492403	−	0.870367i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.23205	−	1.86603i	0.389609	−	0.590089i
$11$	3.21189	−	1.85439i	0.968422	−	0.559119i	0.0696671	−	0.997570i	$-0.477806\pi$
$11$	3.21189	−	1.85439i	0.968422	−	0.559119i	0.898755	+	0.438452i	$0.144473\pi$
$12$		0			0
$13$	−4.62250	+	4.62250i	−1.28205	+	1.28205i	−0.342551	+	0.939499i	$0.611291\pi$
$13$	−4.62250	+	4.62250i	−1.28205	+	1.28205i	−0.939499	+	0.342551i	$0.888709\pi$
$14$	−2.56149	−	0.662382i	−0.684588	−	0.177029i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	5.06628	+	1.35751i	1.22875	+	0.329243i	0.814094	−	0.580733i	$-0.197234\pi$
$17$	5.06628	+	1.35751i	1.22875	+	0.329243i	0.414659	+	0.909977i	$0.363901\pi$
$18$		0			0
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	0.397360	−	0.917663i	$-0.369927\pi$
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	−0.596040	+	0.802955i	$0.703260\pi$
$20$	−2.12132	−	0.707107i	−0.474342	−	0.158114i
$21$		0			0
$22$	−2.62250	−	2.62250i	−0.559119	−	0.559119i
$23$	4.10035	−	1.09869i	0.854983	−	0.229092i	0.195400	−	0.980724i	$-0.437400\pi$
$23$	4.10035	−	1.09869i	0.854983	−	0.229092i	0.659583	+	0.751632i	$0.270733\pi$
$24$		0			0
$25$	−0.598076	+	4.96410i	−0.119615	+	0.992820i
$26$	5.66138	+	3.26860i	1.11029	+	0.641025i
$27$		0			0
$28$	0.0231510	+	2.64565i	0.00437513	+	0.499981i
$29$	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	$0.950287\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		0			0
$34$		−	5.24500i		−	0.899510i
$35$	5.78537	−	1.23673i	0.977906	−	0.209045i
$36$		0			0
$37$	10.4125	−	2.79003i	1.71181	−	0.458678i	0.735942	−	0.677044i	$-0.236740\pi$
$37$	10.4125	−	2.79003i	1.71181	−	0.458678i	0.975867	+	0.218367i	$0.0700729\pi$
$38$	−0.258819	+	0.965926i	−0.0419860	+	0.156694i
$39$		0			0
$40$	−0.133975	+	2.23205i	−0.0211832	+	0.352918i
$41$		−	0.880347i		−	0.137487i	−0.997634	−	0.0687435i	$-0.978101\pi$
$41$		−	0.880347i		−	0.137487i	0.997634	−	0.0687435i	$-0.0218990\pi$
$42$		0			0
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$	−1.85439	+	3.21189i	−0.279559	+	0.484211i
$45$		0			0
$46$	−2.12250	−	3.67628i	−0.312945	−	0.542037i
$47$	2.32937	+	8.69333i	0.339774	+	1.26805i	0.898600	+	0.438768i	$0.144585\pi$
$47$	2.32937	+	8.69333i	0.339774	+	1.26805i	−0.558827	+	0.829285i	$0.688748\pi$
$48$		0			0
$49$	−3.60555	−	6.00000i	−0.515079	−	0.857143i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$		0			0
$52$	1.69195	−	6.31445i	0.234632	−	0.875657i
$53$	−0.581048	+	2.16850i	−0.0798131	+	0.297867i	−0.994282	−	0.106791i	$-0.965943\pi$
$53$	−0.581048	+	2.16850i	−0.0798131	+	0.297867i	0.914468	+	0.404657i	$0.132609\pi$
$54$		0			0
$55$	7.86750	+	2.62250i	1.06085	+	0.353618i
$56$	2.54951	−	0.707107i	0.340693	−	0.0944911i
$57$		0			0
$58$	−0.732051	−	2.73205i	−0.0961230	−	0.358736i
$59$	−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
$65$	−14.5914	−	0.875819i	−1.80984	−	0.108632i
$66$		0			0
$67$	−2.56218	+	9.56218i	−0.313020	+	1.16821i	0.612799	+	0.790239i	$0.290043\pi$
$67$	−2.56218	+	9.56218i	−0.313020	+	1.16821i	−0.925819	+	0.377967i	$0.876623\pi$
$68$	−5.06628	+	1.35751i	−0.614377	+	0.164622i
$69$		0			0
$70$	−2.69195	−	5.26815i	−0.321750	−	0.629664i
$71$		−	10.2460i		−	1.21597i	−0.793947	−	0.607987i	$-0.791977\pi$
$71$		−	10.2460i		−	1.21597i	0.793947	−	0.607987i	$-0.208023\pi$
$72$		0			0
$73$	−13.9949	−	3.74993i	−1.63798	−	0.438896i	−0.681769	−	0.731567i	$-0.738789\pi$
$73$	−13.9949	−	3.74993i	−1.63798	−	0.438896i	−0.956213	+	0.292671i	$0.905456\pi$
$74$	−5.38992	−	9.33562i	−0.626566	−	1.08524i
$75$		0			0
$76$	1.00000			0.114708
$77$	−0.0858619	−	9.81212i	−0.00978487	−	1.11819i
$78$		0			0
$79$	2.38590	+	1.37750i	0.268435	+	0.154981i	0.628176	−	0.778071i	$-0.283802\pi$
$79$	2.38590	+	1.37750i	0.268435	+	0.154981i	−0.359741	+	0.933052i	$0.617135\pi$
$80$	2.19067	−	0.448288i	0.244924	−	0.0501201i
$81$		0			0
$82$	−0.850349	+	0.227850i	−0.0939054	+	0.0251619i
$83$	6.53720	+	6.53720i	0.717551	+	0.717551i	0.968103	−	0.250552i	$-0.0806121\pi$
$83$	6.53720	+	6.53720i	0.717551	+	0.717551i	−0.250552	+	0.968103i	$0.580612\pi$
$84$		0			0
$85$	5.24500	+	10.4900i	0.568900	+	1.13780i
$86$	−3.67423	−	2.12132i	−0.396203	−	0.228748i
$87$		0			0
$88$	3.58240	+	0.959901i	0.381885	+	0.102326i
$89$	−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
$95$	−0.448288	−	2.19067i	−0.0459934	−	0.224758i
$96$		0			0
$97$	−9.24500	−	9.24500i	−0.938687	−	0.938687i	0.0595387	−	0.998226i	$-0.481037\pi$
$97$	−9.24500	−	9.24500i	−0.938687	−	0.938687i	−0.998226	+	0.0595387i	$0.981037\pi$
$98$	−4.86237	+	5.03561i	−0.491174	+	0.508673i
$99$		0			0
$100$	−1.96410	−	4.59808i	−0.196410	−	0.459808i
$101$	−1.52480	+	0.880347i	−0.151724	+	0.0875978i	−0.573940	−	0.818897i	$-0.694586\pi$
$101$	−1.52480	+	0.880347i	−0.151724	+	0.0875978i	0.422216	+	0.906495i	$0.361252\pi$
$102$		0			0
$103$	1.55378	+	5.79878i	0.153098	+	0.571370i	0.999261	+	0.0384453i	$0.0122405\pi$
$103$	1.55378	+	5.79878i	0.153098	+	0.571370i	−0.846162	+	0.532925i	$0.821093\pi$
$104$	−6.53720			−0.641025
$105$		0			0
$106$	2.24500			0.218053
$107$	1.87514	+	6.99813i	0.181277	+	0.676535i	0.995397	+	0.0958381i	$0.0305531\pi$
$107$	1.87514	+	6.99813i	0.181277	+	0.676535i	−0.814120	+	0.580697i	$0.802780\pi$
$108$		0			0
$109$	−3.46410	+	2.00000i	−0.331801	+	0.191565i	−0.656640	−	0.754204i	$-0.728023\pi$
$109$	−3.46410	+	2.00000i	−0.331801	+	0.191565i	0.324840	+	0.945769i	$0.394690\pi$
$110$	0.496881	−	8.27817i	0.0473758	−	0.789293i
$111$		0			0
$112$	−1.34287	−	2.27962i	−0.126890	−	0.215404i
$113$	7.41755	+	7.41755i	0.697784	+	0.697784i	0.963932	−	0.266148i	$-0.0857510\pi$
$113$	7.41755	+	7.41755i	0.697784	+	0.697784i	−0.266148	+	0.963932i	$0.585751\pi$
$114$		0			0
$115$	7.92127	+	5.23005i	0.738663	+	0.487705i
$116$	−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
$122$	−3.13443	−	0.839867i	−0.283778	−	0.0760380i
$123$		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	−0.930015	−	0.367522i	$-0.880206\pi$
$127$	−14.6225	−	14.6225i	−1.29754	−	1.29754i	−0.367522	−	0.930015i	$-0.619794\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	2.93055	+	14.3209i	0.257026	+	1.25602i
$131$	0.462342	+	0.266934i	0.0403950	+	0.0233221i	0.520062	−	0.854129i	$-0.325909\pi$
$131$	0.462342	+	0.266934i	0.0403950	+	0.0233221i	−0.479666	+	0.877451i	$0.659242\pi$
$132$		0			0
$133$	−2.27962	+	1.34287i	−0.197669	+	0.116442i
$134$	9.89949			0.855186
$135$		0			0
$136$	2.62250	+	4.54230i	0.224877	+	0.389499i
$137$	−20.5211	−	5.49861i	−1.75324	−	0.469778i	−0.767923	−	0.640542i	$-0.778710\pi$
$137$	−20.5211	−	5.49861i	−1.75324	−	0.469778i	−0.985312	+	0.170764i	$0.945376\pi$
$138$		0			0
$139$			8.00000i			0.678551i	0.940687	+	0.339276i	$0.110182\pi$
$139$			8.00000i			0.678551i	−0.940687	+	0.339276i	$0.889818\pi$
$140$	−4.39191	+	3.96372i	−0.371184	+	0.334996i
$141$		0			0
$142$	−9.89685	+	2.65185i	−0.830525	+	0.222539i
$143$	−6.27507	+	23.4189i	−0.524747	+	1.95838i
$144$		0			0
$145$	4.19615	+	4.73205i	0.348471	+	0.392975i
$146$			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	$0.632623\pi$
$152$	−0.258819	−	0.965926i	−0.0209930	−	0.0783469i
$153$		0			0
$154$	−9.45555	+	2.62250i	−0.761950	+	0.211327i
$155$	2.82843	−	8.48528i	0.227185	−	0.681554i
$156$		0			0
$157$	−2.79003	+	10.4125i	−0.222668	+	0.831010i	0.760657	+	0.649154i	$0.224877\pi$
$157$	−2.79003	+	10.4125i	−0.222668	+	0.831010i	−0.983325	+	0.181856i	$0.941790\pi$
$158$	0.713047	−	2.66113i	0.0567270	−	0.211708i
$159$		0			0
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$	2.81181	−	10.8735i	0.221602	−	0.856955i
$162$		0			0
$163$	1.91980	+	7.16480i	0.150371	+	0.561190i	0.999457	+	0.0329373i	$0.0104862\pi$
$163$	1.91980	+	7.16480i	0.150371	+	0.561190i	−0.849087	+	0.528253i	$0.822847\pi$
$164$	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	−0.929473	−	0.368891i	$-0.879737\pi$
$167$	−7.24431	+	7.24431i	−0.560581	+	0.560581i	0.368891	+	0.929473i	$0.379737\pi$
$168$		0			0
$169$		−	29.7350i		−	2.28731i
$170$	8.77505	−	7.78129i	0.673016	−	0.596798i
$171$		0			0
$172$	−1.09808	+	4.09808i	−0.0837275	+	0.312475i
$173$	−7.49076	+	2.00714i	−0.569512	+	0.152600i	−0.532073	−	0.846699i	$-0.678587\pi$
$173$	−7.49076	+	2.00714i	−0.569512	+	0.152600i	−0.0374391	+	0.999299i	$0.511920\pi$
$174$		0			0
$175$	10.6521	+	7.84435i	0.805220	+	0.592977i
$176$		−	3.70877i		−	0.279559i
$177$		0			0
$178$	9.56218	+	2.56218i	0.716716	+	0.192043i
$179$	−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	$0.362760\pi$
$182$	14.9024	−	8.77864i	1.10464	−	0.650716i
$183$		0			0
$184$	3.67628	+	2.12250i	0.271019	+	0.156473i
$185$	20.1155	+	13.2813i	1.47892	+	0.976462i
$186$		0			0
$187$	18.7897	−	5.03468i	1.37404	−	0.368172i
$188$	−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	0.0879991	−	0.996121i	$-0.471953\pi$
$191$	−10.0980	−	5.83009i	−0.730667	−	0.421851i	−0.818666	+	0.574270i	$0.805286\pi$
$192$		0			0
$193$	−17.0617	−	4.57166i	−1.22812	−	0.329075i	−0.414276	−	0.910151i	$-0.635965\pi$
$193$	−17.0617	−	4.57166i	−1.22812	−	0.329075i	−0.813849	+	0.581076i	$0.802632\pi$
$194$	−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	−0.904523	−	0.426424i	$-0.859773\pi$
$197$	−6.71044	+	6.71044i	−0.478099	+	0.478099i	0.426424	+	0.904523i	$0.359773\pi$
$198$		0			0
$199$	2.81025	−	1.62250i	0.199213	−	0.115016i	−0.397075	−	0.917786i	$-0.629975\pi$
$199$	2.81025	−	1.62250i	0.199213	−	0.115016i	0.596289	+	0.802770i	$0.296641\pi$
$200$	−3.93305	+	3.08725i	−0.278109	+	0.218301i
$201$		0			0
$202$	1.24500	+	1.24500i	0.0875978	+	0.0875978i
$203$	3.68481	−	6.51323i	0.258623	−	0.457139i
$204$		0			0
$205$	1.47285	−	1.30605i	0.102868	−	0.0912185i
$206$	5.19904	−	3.00167i	0.362234	−	0.209136i
$207$		0			0
$208$	1.69195	+	6.31445i	0.117316	+	0.437828i
$209$	−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	$0.924813\pi$
$212$	−0.581048	−	2.16850i	−0.0399066	−	0.148933i
$213$		0			0
$214$	6.27435	−	3.62250i	0.428906	−	0.247629i
$215$	9.46979	+	0.568406i	0.645834	+	0.0387650i
$216$		0			0
$217$	−10.5826	+	0.0926041i	−0.718394	+	0.00628637i
$218$	2.82843	+	2.82843i	0.191565	+	0.191565i
$219$		0			0
$220$	−8.12470	+	1.66260i	−0.547767	+	0.112092i
$221$	−29.6939	+	17.1438i	−1.99743	+	1.15322i
$222$		0			0
$223$	−5.75500	+	5.75500i	−0.385383	+	0.385383i	−0.873037	−	0.487654i	$-0.837853\pi$
$223$	−5.75500	+	5.75500i	−0.385383	+	0.385383i	0.487654	+	0.873037i	$0.337853\pi$
$224$	−1.85439	+	1.88713i	−0.123901	+	0.126089i
$225$		0			0
$226$	5.24500	−	9.08460i	0.348892	−	0.604299i
$227$	−5.06628	−	1.35751i	−0.336261	−	0.0901008i	0.0867377	−	0.996231i	$-0.472356\pi$
$227$	−5.06628	−	1.35751i	−0.336261	−	0.0901008i	−0.422998	+	0.906130i	$0.639022\pi$
$228$		0			0
$229$	−8.00640	−	4.62250i	−0.529078	−	0.305463i	0.211563	−	0.977364i	$-0.432145\pi$
$229$	−8.00640	−	4.62250i	−0.529078	−	0.305463i	−0.740641	+	0.671901i	$0.765478\pi$
$230$	3.00167	−	9.00500i	0.197924	−	0.593772i
$231$		0			0
$232$	2.00000	+	2.00000i	0.131306	+	0.131306i
$233$	14.2522	−	3.81888i	0.933695	−	0.250183i	0.240265	−	0.970707i	$-0.422765\pi$
$233$	14.2522	−	3.81888i	0.933695	−	0.250183i	0.693430	+	0.720524i	$0.256099\pi$
$234$		0			0
$235$	−11.0885	+	16.7942i	−0.723331	+	1.09553i
$236$	10.0980	+	5.83009i	0.657325	+	0.379507i
$237$		0			0
$238$	−12.0781	−	6.83306i	−0.782904	−	0.442921i
$239$	−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	$0.940372\pi$
$242$	−2.66113	−	0.713047i	−0.171064	−	0.0458364i
$243$		0			0
$244$			3.24500i			0.207740i
$245$	4.68913	−	14.9336i	0.299578	−	0.954072i
$246$		0			0
$247$	6.31445	−	1.69195i	0.401779	−	0.107656i
$248$	1.03528	−	3.86370i	0.0657401	−	0.245345i
$249$		0			0
$250$	8.52628	+	7.23205i	0.539249	+	0.457395i
$251$		−	19.6116i		−	1.23787i	−0.785441	−	0.618937i	$-0.787564\pi$
$251$		−	19.6116i		−	1.23787i	0.785441	−	0.618937i	$-0.212436\pi$
$252$		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
$257$	2.91042	+	10.8618i	0.181547	+	0.677543i	0.995343	+	0.0963925i	$0.0307304\pi$
$257$	2.91042	+	10.8618i	0.181547	+	0.677543i	−0.813796	+	0.581150i	$0.802603\pi$
$258$		0			0
$259$	7.14038	−	27.6125i	0.443681	−	1.71576i
$260$	13.0744	−	6.53720i	0.810840	−	0.405420i
$261$		0			0
$262$	0.138175	−	0.515676i	0.00853648	−	0.0318586i
$263$	5.82084	−	21.7237i	0.358928	−	1.33954i	−0.516540	−	0.856263i	$-0.672780\pi$
$263$	5.82084	−	21.7237i	0.358928	−	1.33954i	0.875468	−	0.483276i	$-0.160553\pi$
$264$		0			0
$265$	−4.49000	+	2.24500i	−0.275818	+	0.137909i
$266$	1.88713	+	1.85439i	0.115707	+	0.113700i
$267$		0			0
$268$	−2.56218	−	9.56218i	−0.156510	−	0.584103i
$269$	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
$275$	7.28441	+	17.0532i	0.439266	+	1.02835i
$276$		0			0
$277$	3.47358	−	12.9636i	0.208707	−	0.778906i	−0.779580	−	0.626302i	$-0.784568\pi$
$277$	3.47358	−	12.9636i	0.208707	−	0.778906i	0.988287	−	0.152604i	$-0.0487657\pi$
$278$	7.72741	−	2.07055i	0.463459	−	0.124183i
$279$		0			0
$280$	4.96537	+	3.21637i	0.296738	+	0.192215i
$281$		−	1.94808i		−	0.116213i	−0.998310	−	0.0581064i	$-0.981494\pi$
$281$		−	1.94808i		−	0.116213i	0.998310	−	0.0581064i	$-0.0185063\pi$
$282$		0			0
$283$	13.6603	+	3.66025i	0.812018	+	0.217580i	0.640854	−	0.767663i	$-0.278581\pi$
$283$	13.6603	+	3.66025i	0.812018	+	0.217580i	0.171164	+	0.985243i	$0.445247\pi$
$284$	5.12299	+	8.87327i	0.303993	+	0.526532i
$285$		0			0
$286$	24.2450			1.43364
$287$	−2.02724	−	1.14689i	−0.119664	−	0.0676990i
$288$		0			0
$289$	9.10193	+	5.25500i	0.535408	+	0.309118i
$290$	3.48477	−	5.27792i	0.204633	−	0.309930i
$291$		0			0
$292$	13.9949	−	3.74993i	0.818991	−	0.219448i
$293$	15.1957	+	15.1957i	0.887744	+	0.887744i	0.994306	−	0.106562i	$-0.0339844\pi$
$293$	15.1957	+	15.1957i	0.887744	+	0.887744i	−0.106562	+	0.994306i	$0.533984\pi$
$294$		0			0
$295$	8.24500	−	24.7350i	0.480042	−	1.44013i
$296$	9.33562	+	5.38992i	0.542622	+	0.313283i
$297$		0			0
$298$	−8.53083	−	2.28583i	−0.494177	−	0.132414i
$299$	−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
$305$	7.10872	−	1.45469i	0.407044	−	0.0832955i
$306$		0			0
$307$	−6.24500	−	6.24500i	−0.356421	−	0.356421i	0.506071	−	0.862492i	$-0.331097\pi$
$307$	−6.24500	−	6.24500i	−0.356421	−	0.356421i	−0.862492	+	0.506071i	$0.831097\pi$
$308$	4.98042	+	8.45461i	0.283786	+	0.481746i
$309$		0			0
$310$	−8.92820	−	0.535898i	−0.507088	−	0.0304370i
$311$	21.4208	−	12.3673i	1.21466	−	0.701285i	0.250890	−	0.968016i	$-0.419277\pi$
$311$	21.4208	−	12.3673i	1.21466	−	0.701285i	0.963771	+	0.266731i	$0.0859434\pi$
$312$		0			0
$313$	−5.66973	−	21.1597i	−0.320472	−	1.19602i	−0.918786	−	0.394756i	$-0.870829\pi$
$313$	−5.66973	−	21.1597i	−0.320472	−	1.19602i	0.598314	−	0.801262i	$-0.295838\pi$
$314$	10.7798			0.608342
$315$		0			0
$316$	−2.75500			−0.154981
$317$	3.10583	+	11.5911i	0.174441	+	0.651022i	0.996646	+	0.0818309i	$0.0260767\pi$
$317$	3.10583	+	11.5911i	0.174441	+	0.651022i	−0.822206	+	0.569191i	$0.807257\pi$
$318$		0			0
$319$	9.08460	−	5.24500i	0.508640	−	0.293664i
$320$	−1.67303	+	1.48356i	−0.0935254	+	0.0829337i
$321$		0			0
$322$	−11.2308	+	0.0982760i	−0.625867	+	0.00547671i
$323$	−3.70877	−	3.70877i	−0.206362	−	0.206362i
$324$		0			0
$325$	−20.1819	−	25.7112i	−1.11949	−	1.42620i
$326$	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	$0.228286\pi$
$332$	−8.92998	−	2.39278i	−0.490096	−	0.131321i
$333$		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	0.856437	−	0.516251i	$-0.172673\pi$
$337$	6.24500	+	6.24500i	0.340187	+	0.340187i	−0.516251	+	0.856437i	$0.672673\pi$
$338$	−28.7218	+	7.69598i	−1.56226	+	0.418606i
$339$		0			0
$340$	−9.78730	−	6.46210i	−0.530791	−	0.350457i
$341$	−12.8476	−	7.41755i	−0.695735	−	0.401683i
$342$		0			0
$343$	−18.5139	+	0.486122i	−0.999655	+	0.0262481i
$344$	4.24264			0.228748
$345$		0			0
$346$	3.87750	+	6.71603i	0.208456	+	0.361056i
$347$	10.8618	+	2.91042i	0.583094	+	0.156240i	0.538295	−	0.842757i	$-0.319069\pi$
$347$	10.8618	+	2.91042i	0.583094	+	0.156240i	0.0447988	+	0.998996i	$0.485735\pi$
$348$		0			0
$349$			9.51000i			0.509059i	0.967065	+	0.254529i	$0.0819206\pi$
$349$			9.51000i			0.509059i	−0.967065	+	0.254529i	$0.918079\pi$
$350$	4.82010	−	12.3194i	0.257645	−	0.658497i
$351$		0			0
$352$	−3.58240	+	0.959901i	−0.190943	+	0.0511629i
$353$	1.67973	−	6.26885i	0.0894033	−	0.333657i	−0.906708	−	0.421758i	$-0.861413\pi$
$353$	1.67973	−	6.26885i	0.0894033	−	0.333657i	0.996112	+	0.0881008i	$0.0280798\pi$
$354$		0			0
$355$	17.1418	−	15.2006i	0.909795	−	0.806762i
$356$		−	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
$362$	−2.91042	−	10.8618i	−0.152968	−	0.570885i
$363$		0			0
$364$	−12.3365	−	12.1225i	−0.646610	−	0.635392i
$365$	−14.4886	−	28.9772i	−0.758369	−	1.51674i
$366$		0			0
$367$	0.317526	−	1.18502i	0.0165747	−	0.0618577i	−0.957143	−	0.289615i	$-0.906473\pi$
$367$	0.317526	−	1.18502i	0.0165747	−	0.0618577i	0.973718	+	0.227757i	$0.0731393\pi$
$368$	1.09869	−	4.10035i	0.0572730	−	0.213746i
$369$		0			0
$370$	7.62250	−	22.8675i	0.396275	−	1.18882i
$371$	4.23660	+	4.16309i	0.219953	+	0.216137i
$372$		0			0
$373$	−3.01788	−	11.2629i	−0.156260	−	0.583170i	−0.998994	−	0.0448400i	$-0.985722\pi$
$373$	−3.01788	−	11.2629i	−0.156260	−	0.583170i	0.842734	−	0.538330i	$-0.180944\pi$
$374$	−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	$0.0388058\pi$
$379$			4.73499i			0.243220i	−0.992578	+	0.121610i	$0.961194\pi$
$380$	1.48356	+	1.67303i	0.0761052	+	0.0858248i
$381$		0			0
$382$	−3.01788	+	11.2629i	−0.154408	+	0.576259i
$383$	21.2310	−	5.68884i	1.08486	−	0.290686i	0.328272	−	0.944583i	$-0.393534\pi$
$383$	21.2310	−	5.68884i	1.08486	−	0.290686i	0.756584	+	0.653897i	$0.226867\pi$
$384$		0			0
$385$	16.2886	−	14.7006i	0.830144	−	0.749210i
$386$			17.6635i			0.899050i
$387$		0			0
$388$	12.6289	+	3.38390i	0.641135	+	0.171792i
$389$	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
$392$	1.69313	−	6.79215i	0.0855160	−	0.343055i
$393$		0			0
$394$	8.21858	+	4.74500i	0.414046	+	0.239050i
$395$	1.23503	+	6.03530i	0.0621413	+	0.303669i
$396$		0			0
$397$	20.1284	−	5.39338i	1.01021	−	0.270686i	0.284495	−	0.958677i	$-0.408174\pi$
$397$	20.1284	−	5.39338i	1.01021	−	0.270686i	0.725719	+	0.687991i	$0.241507\pi$
$398$	−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	0.794052	−	0.607850i	$-0.207968\pi$
$401$	13.3099	+	7.68448i	0.664665	+	0.383745i	−0.129387	+	0.991594i	$0.541301\pi$
$402$		0			0
$403$	25.2578	+	6.76781i	1.25818	+	0.337129i
$404$	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	$0.333333\pi$
$410$	−1.64275	−	1.08463i	−0.0811296	−	0.0535661i
$411$		0			0
$412$	−4.24500	−	4.24500i	−0.209136	−	0.209136i
$413$	−30.8488	+	0.269945i	−1.51797	+	0.0132831i
$414$		0			0
$415$	−1.23859	+	20.6353i	−0.0608002	+	1.01295i
$416$	5.66138	−	3.26860i	0.277572	−	0.160256i
$417$		0			0
$418$	0.959901	+	3.58240i	0.0469503	+	0.175221i
$419$	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	$0.463034\pi$
$422$	7.31034	+	27.2826i	0.355862	+	1.32809i
$423$		0			0
$424$	−1.94423	+	1.12250i	−0.0944199	+	0.0545134i
$425$	−9.76882	+	24.3376i	−0.473857	+	1.18055i
$426$		0			0
$427$	−4.35762	−	7.39738i	−0.210880	−	0.357984i
$428$	−5.12299	−	5.12299i	−0.247629	−	0.247629i
$429$		0			0
$430$	−1.90192	−	9.29423i	−0.0917189	−	0.448208i
$431$	−10.0980	+	5.83009i	−0.486404	+	0.280826i	−0.723082	−	0.690763i	$-0.757275\pi$
$431$	−10.0980	+	5.83009i	−0.486404	+	0.280826i	0.236677	+	0.971588i	$0.423942\pi$
$432$		0			0
$433$	−19.2450	+	19.2450i	−0.924856	+	0.924856i	−0.997368	−	0.0725120i	$-0.976898\pi$
$433$	−19.2450	+	19.2450i	−0.924856	+	0.924856i	0.0725120	+	0.997368i	$0.476898\pi$
$434$	2.82843	+	10.1980i	0.135769	+	0.489522i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	−4.10035	−	1.09869i	−0.196146	−	0.0525573i
$438$		0			0
$439$	−17.3205	−	10.0000i	−0.826663	−	0.477274i	0.0260459	−	0.999661i	$-0.491708\pi$
$439$	−17.3205	−	10.0000i	−0.826663	−	0.477274i	−0.852709	+	0.522387i	$0.825042\pi$
$440$	3.70877	+	7.41755i	0.176809	+	0.353618i
$441$		0			0
$442$	24.2450	+	24.2450i	1.15322	+	1.15322i
$443$	38.3811	−	10.2842i	1.82354	−	0.488616i	0.826324	−	0.563195i	$-0.190428\pi$
$443$	38.3811	−	10.2842i	1.82354	−	0.488616i	0.997215	+	0.0745793i	$0.0237614\pi$
$444$		0			0
$445$	−21.6865	+	4.43782i	−1.02804	+	0.210373i
$446$	7.04841	+	4.06940i	0.333752	+	0.192692i
$447$		0			0
$448$	2.30278	+	1.30278i	0.108796	+	0.0615504i
$449$	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
$452$	−10.1326	−	2.71501i	−0.476595	−	0.127703i
$453$		0			0
$454$			5.24500i			0.246160i
$455$	−21.0261	+	32.4596i	−0.985718	+	1.52173i
$456$		0			0
$457$	−33.4540	+	8.96396i	−1.56491	+	0.419316i	−0.934214	−	0.356713i	$-0.883897\pi$
$457$	−33.4540	+	8.96396i	−1.56491	+	0.419316i	−0.630696	+	0.776030i	$0.717231\pi$
$458$	−2.39278	+	8.92998i	−0.111807	+	0.417271i
$459$		0			0
$460$	−9.47505	−	0.568722i	−0.441777	−	0.0265168i
$461$		−	6.72459i		−	0.313195i	−0.987662	−	0.156598i	$-0.949947\pi$
$461$		−	6.72459i		−	0.313195i	0.987662	−	0.156598i	$-0.0500526\pi$
$462$		0			0
$463$	12.8675	−	12.8675i	0.598003	−	0.598003i	−0.341778	−	0.939781i	$-0.611029\pi$
$463$	12.8675	−	12.8675i	0.598003	−	0.598003i	0.939781	+	0.341778i	$0.111029\pi$
$464$	1.41421	−	2.44949i	0.0656532	−	0.113715i
$465$		0			0
$466$	−7.37750	−	12.7782i	−0.341756	−	0.591939i
$467$	1.87514	+	6.99813i	0.0867713	+	0.323835i	0.995644	−	0.0932393i	$-0.0297222\pi$
$467$	1.87514	+	6.99813i	0.0867713	+	0.323835i	−0.908872	+	0.417074i	$0.863056\pi$
$468$		0			0
$469$	18.6816	+	18.3575i	0.862636	+	0.847670i
$470$	19.0919	+	6.36396i	0.880643	+	0.293548i
$471$		0			0
$472$	3.01788	−	11.2629i	0.138909	−	0.518416i
$473$	4.07252	−	15.1988i	0.187254	−	0.698843i
$474$		0			0
$475$	3.00000	−	4.00000i	0.137649	−	0.183533i
$476$	−3.47419	+	13.4350i	−0.159239	+	0.615794i
$477$		0			0
$478$	4.48198	+	16.7270i	0.205001	+	0.765074i
$479$	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
$485$	1.75164	−	29.1827i	0.0795378	−	1.32512i
$486$		0			0
$487$	−5.66973	+	21.1597i	−0.256920	+	0.958839i	0.710092	+	0.704109i	$0.248653\pi$
$487$	−5.66973	+	21.1597i	−0.256920	+	0.958839i	−0.967012	+	0.254730i	$0.918013\pi$
$488$	3.13443	−	0.839867i	0.141889	−	0.0380190i
$489$		0			0
$490$	−15.6384	−	0.664255i	−0.706470	−	0.0300080i
$491$			37.8090i			1.70630i	0.521669	+	0.853148i	$0.325310\pi$
$491$			37.8090i			1.70630i	−0.521669	+	0.853148i	$0.674690\pi$
$492$		0			0
$493$	14.3296	+	3.83961i	0.645373	+	0.172927i
$494$	−3.26860	−	5.66138i	−0.147061	−	0.254718i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−23.5942	−	13.3482i	−1.05834	−	0.598749i
$498$		0			0
$499$	14.2808	+	8.24500i	0.639294	+	0.369097i	0.784343	−	0.620328i	$-0.213000\pi$
$499$	14.2808	+	8.24500i	0.639294	+	0.369097i	−0.145048	+	0.989425i	$0.546334\pi$
$500$	4.77886	−	10.1075i	0.213717	−	0.452023i
$501$		0			0
$502$	−18.9434	+	5.07586i	−0.845483	+	0.226547i
$503$	−30.3914	−	30.3914i	−1.35509	−	1.35509i	−0.879866	−	0.475221i	$-0.842368\pi$
$503$	−30.3914	−	30.3914i	−1.35509	−	1.35509i	−0.475221	−	0.879866i	$-0.657632\pi$
$504$		0			0
$505$	−3.73499	−	1.24500i	−0.166205	−	0.0554017i
$506$	−13.6345	−	7.87187i	−0.606126	−	0.349947i
$507$		0			0
$508$	19.9747	+	5.35221i	0.886234	+	0.237466i
$509$	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
$515$	−7.39641	+	11.2024i	−0.325925	+	0.493636i
$516$		0			0
$517$	23.6025	+	23.6025i	1.03804	+	1.03804i
$518$	−28.5197	+	0.249564i	−1.25308	+	0.0109652i
$519$		0			0
$520$	−9.69836	−	10.9370i	−0.425301	−	0.479617i
$521$	−17.5843	+	10.1523i	−0.770381	+	0.444779i	−0.833010	−	0.553257i	$-0.813385\pi$
$521$	−17.5843	+	10.1523i	−0.770381	+	0.444779i	0.0626297	+	0.998037i	$0.480051\pi$
$522$		0			0
$523$	−8.87429	−	33.1193i	−0.388045	−	1.44821i	−0.833310	−	0.552806i	$-0.813557\pi$
$523$	−8.87429	−	33.1193i	−0.388045	−	1.44821i	0.445265	−	0.895399i	$-0.353110\pi$
$524$	−0.533867			−0.0233221
$525$		0			0
$526$	−22.4900			−0.980610
$527$	−5.43002	−	20.2651i	−0.236535	−	0.882762i
$528$		0			0
$529$	−4.31280	+	2.49000i	−0.187513	+	0.108261i
$530$	3.33060	+	3.75595i	0.144672	+	0.163148i
$531$		0			0
$532$	1.30278	−	2.30278i	0.0564825	−	0.0998380i
$533$	4.06940	+	4.06940i	0.176265	+	0.176265i
$534$		0			0
$535$	−8.92621	+	13.5194i	−0.385914	+	0.584492i
$536$	−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	$0.213052\pi$
$542$	6.26885	+	1.67973i	0.269270	+	0.0721508i
$543$		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	0.827897	−	0.560880i	$-0.189537\pi$
$547$	6.24500	+	6.24500i	0.267017	+	0.267017i	−0.560880	+	0.827897i	$0.689537\pi$
$548$	20.5211	−	5.49861i	0.876618	−	0.234889i
$549$		0			0
$550$	14.5868	−	11.4499i	0.621983	−	0.488225i
$551$	−2.44949	−	1.41421i	−0.104352	−	0.0602475i
$552$		0			0
$553$	6.28037	−	3.69962i	0.267069	−	0.157324i
$554$	−13.4209			−0.570199
$555$		0			0
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	17.1500	+	4.59533i	0.726669	+	0.194710i	0.603146	−	0.797631i	$-0.293914\pi$
$557$	17.1500	+	4.59533i	0.726669	+	0.194710i	0.123524	+	0.992342i	$0.460580\pi$
$558$		0			0
$559$			27.7350i			1.17307i
$560$	1.82165	−	5.62864i	0.0769786	−	0.237854i
$561$		0			0
$562$	−1.88170	+	0.504200i	−0.0793748	+	0.0212684i
$563$	−4.78556	+	17.8600i	−0.201687	+	0.752708i	0.788746	+	0.614719i	$0.210731\pi$
$563$	−4.78556	+	17.8600i	−0.201687	+	0.752708i	−0.990434	+	0.137989i	$0.955936\pi$
$564$		0			0
$565$	−1.40539	+	23.4142i	−0.0591253	+	0.985043i
$566$		−	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	$-0.556945\pi$
$572$	−6.27507	−	23.4189i	−0.262374	−	0.979192i
$573$		0			0
$574$	−0.583126	+	2.25500i	−0.0243392	+	0.0941220i
$575$	3.00167	+	21.0117i	0.125178	+	0.876247i
$576$		0			0
$577$	−8.59794	+	32.0879i	−0.357937	+	1.33584i	0.518812	+	0.854889i	$0.326375\pi$
$577$	−8.59794	+	32.0879i	−0.357937	+	1.33584i	−0.876748	+	0.480949i	$0.840292\pi$
$578$	2.72019	−	10.1519i	0.113145	−	0.422263i
$579$		0			0
$580$	−6.00000	−	2.00000i	−0.249136	−	0.0830455i
$581$	23.5702	−	6.53720i	0.977857	−	0.271209i
$582$		0			0
$583$	2.15498	+	8.04248i	0.0892500	+	0.333086i
$584$	−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	0.300657	−	0.953732i	$-0.402794\pi$
$587$	30.3914	−	30.3914i	1.25439	−	1.25439i	0.953732	−	0.300657i	$-0.0972058\pi$
$588$		0			0
$589$			4.00000i			0.164817i
$590$	−26.0261	−	1.56217i	−1.07148	−	0.0643135i
$591$		0			0
$592$	2.79003	−	10.4125i	0.114669	−	0.427952i
$593$	−29.1951	+	7.82280i	−1.19890	+	0.321244i	−0.802397	−	0.596790i	$-0.796443\pi$
$593$	−29.1951	+	7.82280i	−1.19890	+	0.321244i	−0.396502	+	0.918034i	$0.629776\pi$
$594$		0			0
$595$	30.9892	+	1.58806i	1.27043	+	0.0651040i
$596$			8.83176i			0.361763i
$597$		0			0
$598$	26.8048	+	7.18233i	1.09613	+	0.293707i
$599$	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	$0.207464\pi$
$602$	−9.67163	+	5.69733i	−0.394186	+	0.232206i
$603$		0			0
$604$	−12.5487	−	7.24500i	−0.510600	−	0.294795i
$605$	6.03530	−	1.23503i	0.245370	−	0.0502113i
$606$		0			0
$607$	5.97978	−	1.60228i	0.242712	−	0.0650344i	−0.135412	−	0.990789i	$-0.543236\pi$
$607$	5.97978	−	1.60228i	0.242712	−	0.0650344i	0.378124	+	0.925755i	$0.376569\pi$
$608$	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
$613$	27.4742	+	7.36168i	1.10967	+	0.297336i	0.766697	−	0.642009i	$-0.221899\pi$
$613$	27.4742	+	7.36168i	1.10967	+	0.297336i	0.342975	+	0.939345i	$0.388566\pi$
$614$	−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	−0.889980	−	0.456000i	$-0.849282\pi$
$617$	−10.7798	+	10.7798i	−0.433980	+	0.433980i	0.456000	+	0.889980i	$0.349282\pi$
$618$		0			0
$619$	−42.6301	+	24.6125i	−1.71345	+	0.989260i	−0.783640	+	0.621216i	$0.786639\pi$
$619$	−42.6301	+	24.6125i	−1.71345	+	0.989260i	−0.929808	+	0.368044i	$0.880028\pi$
$620$	1.79315	+	8.76268i	0.0720147	+	0.351918i
$621$		0			0
$622$	−17.4900	−	17.4900i	−0.701285	−	0.701285i
$623$	13.2938	+	22.5671i	0.532604	+	0.904133i
$624$		0			0
$625$	−24.2846	−	5.93782i	−0.971384	−	0.237513i
$626$	−18.9713	+	10.9531i	−0.758245	+	0.437773i
$627$		0			0
$628$	−2.79003	−	10.4125i	−0.111334	−	0.415505i
$629$	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	$0.254844\pi$
$632$	0.713047	+	2.66113i	0.0283635	+	0.105854i
$633$		0			0
$634$	10.3923	−	6.00000i	0.412731	−	0.238290i
$635$	2.77051	−	46.1573i	0.109944	−	1.83170i
$636$		0			0
$637$	44.4017	+	11.0683i	1.75926	+	0.438543i
$638$	−7.41755	−	7.41755i	−0.293664	−	0.293664i
$639$		0			0
$640$	1.86603	+	1.23205i	0.0737611	+	0.0487011i
$641$	−36.5801	+	21.1195i	−1.44483	+	0.834170i	−0.998166	−	0.0605336i	$-0.980720\pi$
$641$	−36.5801	+	21.1195i	−1.44483	+	0.834170i	−0.446659	+	0.894704i	$0.647386\pi$
$642$		0			0
$643$	9.73499	−	9.73499i	0.383911	−	0.383911i	−0.488598	−	0.872509i	$-0.662492\pi$
$643$	9.73499	−	9.73499i	0.383911	−	0.383911i	0.872509	+	0.488598i	$0.162492\pi$
$644$	3.00167	+	10.8227i	0.118282	+	0.426473i
$645$		0			0
$646$	−2.62250	+	4.54230i	−0.103181	+	0.178714i
$647$	−10.1519	−	2.72019i	−0.399112	−	0.106942i	0.0536795	−	0.998558i	$-0.482905\pi$
$647$	−10.1519	−	2.72019i	−0.399112	−	0.106942i	−0.452791	+	0.891617i	$0.649572\pi$
$648$		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
$653$	2.42448	−	0.649637i	0.0948771	−	0.0254223i	−0.211068	−	0.977471i	$-0.567694\pi$
$653$	2.42448	−	0.649637i	0.0948771	−	0.0254223i	0.305945	+	0.952049i	$0.401028\pi$
$654$		0			0
$655$	0.239326	+	1.16953i	0.00935124	+	0.0456972i
$656$	−0.762402	−	0.440173i	−0.0297668	−	0.0171859i
$657$		0			0
$658$	−0.208359	−	23.8109i	−0.00812269	−	0.928244i
$659$	−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	$0.771032\pi$
$662$	6.76148	+	1.81173i	0.262792	+	0.0704150i
$663$		0			0
$664$			9.24500i			0.358776i
$665$	−5.62864	−	1.82165i	−0.218269	−	0.0706404i
$666$		0			0
$667$	11.5976	−	3.10755i	0.449059	−	0.120325i
$668$	2.65160	−	9.89591i	0.102594	−	0.382884i
$669$		0			0
$670$	14.6865	+	16.5622i	0.567390	+	0.639853i
$671$		−	12.0350i		−	0.464605i
$672$		0			0
$673$	31.2450	−	31.2450i	1.20441	−	1.20441i	0.231594	−	0.972813i	$-0.425606\pi$
$673$	31.2450	−	31.2450i	1.20441	−	1.20441i	0.972813	−	0.231594i	$-0.0743939\pi$
$674$	4.41588	−	7.64853i	0.170093	−	0.294610i
$675$		0			0
$676$	14.8675	+	25.7513i	0.571827	+	0.990433i
$677$	−3.10065	−	11.5718i	−0.119168	−	0.444740i	0.880397	−	0.474237i	$-0.157276\pi$
$677$	−3.10065	−	11.5718i	−0.119168	−	0.444740i	−0.999565	+	0.0294973i	$0.990609\pi$
$678$		0			0
$679$	−33.3333	+	9.24500i	−1.27922	+	0.354790i
$680$	−3.70877	+	11.1263i	−0.142225	+	0.426675i
$681$		0			0
$682$	−3.83961	+	14.3296i	−0.147026	+	0.548709i
$683$	−3.35947	+	12.5377i	−0.128547	+	0.479742i	−0.999941	−	0.0108404i	$-0.996549\pi$
$683$	−3.35947	+	12.5377i	−0.128547	+	0.479742i	0.871395	+	0.490583i	$0.163216\pi$
$684$		0			0
$685$	−21.2450	−	42.4900i	−0.811730	−	1.62346i
$686$	5.26130	+	17.7572i	0.200877	+	0.677974i
$687$		0			0
$688$	−1.09808	−	4.09808i	−0.0418638	−	0.156238i
$689$	−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
$695$	−13.3843	+	11.8685i	−0.507694	+	0.450198i
$696$		0			0
$697$	1.19508	−	4.46008i	0.0452667	−	0.168938i
$698$	9.18596	−	2.46137i	0.347694	−	0.0931642i
$699$		0			0
$700$	−13.1471	−	1.46738i	−0.496914	−	0.0554616i
$701$		−	21.1849i		−	0.800143i	−0.916484	−	0.400071i	$-0.868985\pi$
$701$		−	21.1849i		−	0.800143i	0.916484	−	0.400071i	$-0.131015\pi$
$702$		0			0
$703$	−10.4125	−	2.79003i	−0.392716	−	0.105228i
$704$	1.85439	+	3.21189i	0.0698898	+	0.121053i
$705$		0			0
$706$	−6.49000			−0.244254
$707$	0.0407618	+	4.65818i	0.00153301	+	0.175189i
$708$		0			0
$709$	39.3782	+	22.7350i	1.47888	+	0.853831i	0.999714	−	0.0238950i	$-0.00760674\pi$
$709$	39.3782	+	22.7350i	1.47888	+	0.853831i	0.479164	+	0.877726i	$0.340940\pi$
$710$	−19.1192	−	12.6236i	−0.717533	−	0.473754i
$711$		0			0
$712$	−9.56218	+	2.56218i	−0.358358	+	0.0960217i
$713$	−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
$718$	−10.9282	−	2.92820i	−0.407837	−	0.109280i
$719$	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
$725$	−1.69161	+	14.0406i	−0.0628250	+	0.521455i
$726$		0			0
$727$	−10.3775	−	10.3775i	−0.384880	−	0.384880i	0.487977	−	0.872857i	$-0.337735\pi$
$727$	−10.3775	−	10.3775i	−0.384880	−	0.384880i	−0.872857	+	0.487977i	$0.837735\pi$
$728$	−8.51651	+	15.0537i	−0.315643	+	0.557927i
$729$		0			0
$730$	−24.2399	+	21.4948i	−0.897160	+	0.795558i
$731$	19.2714	−	11.1263i	0.712777	−	0.411522i
$732$		0			0
$733$	1.87863	+	7.01113i	0.0693887	+	0.258962i	0.991902	−	0.127002i	$-0.0405355\pi$
$733$	1.87863	+	7.01113i	0.0693887	+	0.258962i	−0.922514	+	0.385964i	$0.873869\pi$
$734$	−1.22683			−0.0452830
$735$		0			0
$736$	−4.24500			−0.156473
$737$	9.50254	+	35.4640i	0.350030	+	1.30633i
$738$		0			0
$739$	−17.3032	+	9.99000i	−0.636508	+	0.367488i	−0.783268	−	0.621684i	$-0.786449\pi$
$739$	−17.3032	+	9.99000i	−0.636508	+	0.367488i	0.146760	+	0.989172i	$0.453115\pi$
$740$	−24.0612	−	1.44422i	−0.884506	−	0.0530908i
$741$		0			0
$742$	2.92473	−	5.16973i	0.107370	−	0.189787i
$743$	−12.3673	−	12.3673i	−0.453712	−	0.453712i	0.442873	−	0.896585i	$-0.353959\pi$
$743$	−12.3673	−	12.3673i	−0.453712	−	0.453712i	−0.896585	+	0.442873i	$0.853959\pi$
$744$		0			0
$745$	19.3475	−	3.95917i	0.708837	−	0.145053i
$746$	−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	$0.0828555\pi$
$752$	8.69333	+	2.32937i	0.317013	+	0.0849434i
$753$		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	0.851487	−	0.524376i	$-0.175701\pi$
$757$	9.00000	+	9.00000i	0.327111	+	0.327111i	−0.524376	+	0.851487i	$0.675701\pi$
$758$	4.57365	−	1.22551i	0.166123	−	0.0445124i
$759$		0			0
$760$	1.23205	−	1.86603i	0.0446912	−	0.0676879i
$761$	16.3595	+	9.44517i	0.593032	+	0.342387i	0.766296	−	0.642488i	$-0.222098\pi$
$761$	16.3595	+	9.44517i	0.593032	+	0.342387i	−0.173263	+	0.984876i	$0.555431\pi$
$762$		0			0
$763$	0.0926041	+	10.5826i	0.00335249	+	0.383116i
$764$	11.6602			0.421851
$765$		0			0
$766$	−10.9900	−	19.0352i	−0.397085	−	0.687771i
$767$	73.6277	+	19.7285i	2.65854	+	0.712354i
$768$		0			0
$769$		−	22.7350i		−	0.819845i	−0.912120	−	0.409922i	$-0.865556\pi$
$769$		−	22.7350i		−	0.819845i	0.912120	−	0.409922i	$-0.134444\pi$
$770$	−18.4154	−	11.9288i	−0.663647	−	0.429884i
$771$		0			0
$772$	17.0617	−	4.57166i	0.614062	−	0.164537i
$773$	8.79467	−	32.8222i	0.316322	−	1.18053i	−0.606430	−	0.795137i	$-0.707399\pi$
$773$	8.79467	−	32.8222i	0.316322	−	1.18053i	0.922752	−	0.385394i	$-0.125934\pi$
$774$		0			0
$775$	18.3923	−	7.85641i	0.660671	−	0.282210i
$776$		−	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
$782$	−5.76261	−	21.5063i	−0.206070	−	0.769065i
$783$		0			0
$784$	−6.99893	+	0.122499i	−0.249962	+	0.00437496i
$785$	−21.5597	+	10.7798i	−0.769498	+	0.384749i
$786$		0			0
$787$	−8.32891	+	31.0839i	−0.296894	+	1.10802i	0.642808	+	0.766027i	$0.277769\pi$
$787$	−8.32891	+	31.0839i	−0.296894	+	1.10802i	−0.939702	+	0.341995i	$0.888898\pi$
$788$	2.45619	−	9.16663i	0.0874982	−	0.326548i
$789$		0			0
$790$	5.51000	−	2.75500i	0.196037	−	0.0980186i
$791$	26.7443	−	7.41755i	0.950920	−	0.263738i
$792$		0			0
$793$	5.49038	+	20.4904i	0.194969	+	0.727635i
$794$	−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	−0.428262	−	0.903654i	$-0.640874\pi$
$797$	13.4209	−	13.4209i	0.475392	−	0.475392i	0.903654	+	0.428262i	$0.140874\pi$
$798$		0			0
$799$			47.2050i			1.66999i
$800$	1.86250	−	4.64016i	0.0658494	−	0.164054i
$801$		0			0
$802$	3.97778	−	14.8453i	0.140460	−	0.524205i
$803$	−51.9040	+	13.9076i	−1.83165	+	0.490790i
$804$		0			0
$805$	22.3633	−	11.4273i	0.788202	−	0.402761i
$806$		−	26.1488i		−	0.921052i
$807$		0			0
$808$	−1.70070	−	0.455701i	−0.0598304	−	0.0160315i
$809$	−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	$0.597796\pi$
$812$	0.0654810	+	7.48303i	0.00229793	+	0.262603i
$813$		0			0
$814$	−34.6237	−	19.9900i	−1.21356	−	0.700649i
$815$	−9.13880	+	13.8413i	−0.320118	+	0.484841i
$816$		0			0
$817$	−4.09808	+	1.09808i	−0.143374	+	0.0384168i
$818$		0			0
$819$		0			0
$820$	−0.622499	+	1.86750i	−0.0217386	+	0.0652158i
$821$	14.3724	+	8.29789i	0.501599	+	0.289598i	0.729374	−	0.684115i	$-0.239812\pi$
$821$	14.3724	+	8.29789i	0.501599	+	0.289598i	−0.227774	+	0.973714i	$0.573145\pi$
$822$		0			0
$823$	42.3468	+	11.3468i	1.47612	+	0.395524i	0.905024	−	0.425361i	$-0.139853\pi$
$823$	42.3468	+	11.3468i	1.47612	+	0.395524i	0.571093	+	0.820886i	$0.306520\pi$
$824$	−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	−0.994056	−	0.108870i	$-0.965277\pi$
$827$	−25.4558	+	25.4558i	−0.885186	+	0.885186i	0.108870	+	0.994056i	$0.465277\pi$
$828$		0			0
$829$	−10.6218	+	6.13250i	−0.368911	+	0.212991i	−0.672982	−	0.739658i	$-0.734987\pi$
$829$	−10.6218	+	6.13250i	−0.368911	+	0.212991i	0.304072	+	0.952649i	$0.401654\pi$
$830$	20.2527	−	4.14442i	0.702983	−	0.143855i
$831$		0			0
$832$	−4.62250	−	4.62250i	−0.160256	−	0.160256i
$833$	−10.1217	−	35.2922i	−0.350696	−	1.22280i
$834$		0			0
$835$	−22.8674	−	1.37257i	−0.791357	−	0.0474997i
$836$	3.21189	−	1.85439i	0.111086	−	0.0641353i
$837$		0			0
$838$	−5.99458	−	22.3721i	−0.207079	−	0.772831i
$839$	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
$842$	−1.23069	−	4.59298i	−0.0424122	−	0.158285i
$843$		0			0
$844$	24.4609	−	14.1225i	0.841978	−	0.486116i
$845$	49.7476	−	44.1138i	1.71137	−	1.51756i
$846$		0			0
$847$	−3.69962	−	6.28037i	−0.127121	−	0.215796i
$848$	1.58745	+	1.58745i	0.0545134	+	0.0545134i
$849$		0			0
$850$	26.0367	+	3.13691i	0.893052	+	0.107595i
$851$	39.6297	−	22.8802i	1.35849	−	0.784323i
$852$		0			0
$853$	−30.8675	+	30.8675i	−1.05688	+	1.05688i	−0.0586015	+	0.998281i	$0.518664\pi$
$853$	−30.8675	+	30.8675i	−1.05688	+	1.05688i	−0.998281	+	0.0586015i	$0.981336\pi$
$854$	−6.01748	+	6.12372i	−0.205914	+	0.209550i
$855$		0			0
$856$	−3.62250	+	6.27435i	−0.123814	+	0.214453i
$857$	−2.66113	−	0.713047i	−0.0909024	−	0.0243572i	0.213081	−	0.977035i	$-0.431650\pi$
$857$	−2.66113	−	0.713047i	−0.0909024	−	0.0243572i	−0.303984	+	0.952677i	$0.598317\pi$
$858$		0			0
$859$	19.4769	+	11.2450i	0.664544	+	0.383674i	0.794006	−	0.607910i	$-0.207992\pi$
$859$	19.4769	+	11.2450i	0.664544	+	0.383674i	−0.129462	+	0.991584i	$0.541325\pi$
$860$	−8.48528	+	4.24264i	−0.289346	+	0.144673i
$861$		0			0
$862$	8.24500	+	8.24500i	0.280826	+	0.280826i
$863$	−2.64180	+	0.707869i	−0.0899280	+	0.0240961i	−0.303502	−	0.952831i	$-0.598156\pi$
$863$	−2.64180	+	0.707869i	−0.0899280	+	0.0240961i	0.213574	+	0.976927i	$0.431489\pi$
$864$		0			0
$865$	−14.4710	−	9.55456i	−0.492030	−	0.324865i
$866$	23.5702	+	13.6083i	0.800948	+	0.462428i
$867$		0			0
$868$	9.11850	−	5.37150i	0.309502	−	0.182321i
$869$	10.2177			0.346611
$870$		0			0
$871$	−32.3575	−	56.0448i	−1.09639	−	1.89901i
$872$	−3.86370	−	1.03528i	−0.130842	−	0.0350589i
$873$		0			0
$874$			4.24500i			0.143589i
$875$	2.67916	+	29.4588i	0.0905720	+	0.995890i
$876$		0			0
$877$	6.31445	−	1.69195i	0.213224	−	0.0571332i	−0.150626	−	0.988591i	$-0.548129\pi$
$877$	6.31445	−	1.69195i	0.213224	−	0.0571332i	0.363850	+	0.931458i	$0.381462\pi$
$878$	−5.17638	+	19.3185i	−0.174694	+	0.651968i
$879$		0			0
$880$	6.20490	−	5.50220i	0.209167	−	0.185479i
$881$			34.1002i			1.14887i	0.818552	+	0.574433i	$0.194777\pi$
$881$			34.1002i			1.14887i	−0.818552	+	0.574433i	$0.805223\pi$
$882$		0			0
$883$	28.7350	−	28.7350i	0.967010	−	0.967010i	−0.0324634	−	0.999473i	$-0.510335\pi$
$883$	28.7350	−	28.7350i	0.967010	−	0.967010i	0.999473	+	0.0324634i	$0.0103352\pi$
$884$	17.1438	−	29.6939i	0.576608	−	0.998715i
$885$		0			0
$886$	−19.8675	−	34.4115i	−0.667462	−	1.15608i
$887$	−2.97901	−	11.1178i	−0.100025	−	0.373300i	0.897708	−	0.440591i	$-0.145231\pi$
$887$	−2.97901	−	11.1178i	−0.100025	−	0.373300i	−0.997733	+	0.0672912i	$0.978564\pi$
$888$		0			0
$889$	−52.7222	+	14.6225i	−1.76824	+	0.490423i
$890$	9.89949	+	19.7990i	0.331832	+	0.663664i
$891$		0			0
$892$	2.10648	−	7.86148i	0.0705301	−	0.263222i
$893$	2.32937	−	8.69333i	0.0779494	−	0.290911i
$894$		0			0
$895$	11.6225	−	34.8675i	0.388497	−	1.16549i
$896$	0.662382	−	2.56149i	0.0221286	−	0.0855735i
$897$		0			0
$898$	−2.51368	−	9.38118i	−0.0838825	−	0.313054i
$899$	−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
$905$	16.6827	+	18.8132i	0.554551	+	0.625374i
$906$		0			0
$907$	0.545376	−	2.03537i	0.0181089	−	0.0675834i	−0.956280	−	0.292452i	$-0.905529\pi$
$907$	0.545376	−	2.03537i	0.0181089	−	0.0675834i	0.974389	+	0.224869i	$0.0721954\pi$
$908$	5.06628	−	1.35751i	0.168130	−	0.0450504i
$909$		0			0
$910$	36.7956	+	11.9085i	1.21976	+	0.394762i
$911$			32.1804i			1.06619i	0.846057	+	0.533093i	$0.178970\pi$
$911$			32.1804i			1.06619i	−0.846057	+	0.533093i	$0.821030\pi$
$912$		0			0
$913$	33.1193	+	8.87429i	1.09609	+	0.293696i
$914$	17.3170	+	29.9940i	0.572797	+	0.992113i
$915$		0			0
$916$	9.24500			0.305463
$917$	1.21702	−	0.716916i	0.0401894	−	0.0236747i
$918$		0			0
$919$	3.03975	+	1.75500i	0.100272	+	0.0578922i	0.549298	−	0.835627i	$-0.314895\pi$
$919$	3.03975	+	1.75500i	0.100272	+	0.0578922i	−0.449025	+	0.893519i	$0.648229\pi$
$920$	1.90298	+	9.29939i	0.0627394	+	0.306592i
$921$		0			0
$922$	−6.49545	+	1.74045i	−0.213916	+	0.0573187i
$923$	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
$928$	−2.73205	−	0.732051i	−0.0896840	−	0.0240307i
$929$	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
$935$	36.2989	+	23.9665i	1.18710	+	0.783788i
$936$		0			0
$937$	−17.0000	−	17.0000i	−0.555366	−	0.555366i	0.372619	−	0.927985i	$-0.378460\pi$
$937$	−17.0000	−	17.0000i	−0.555366	−	0.555366i	−0.927985	+	0.372619i	$0.878460\pi$
$938$	12.8968	−	22.7963i	0.421096	−	0.744326i
$939$		0			0
$940$	1.20577	−	20.0885i	0.0393279	−	0.655213i
$941$	−3.07411	+	1.77484i	−0.100213	+	0.0578582i	−0.549269	−	0.835646i	$-0.685094\pi$
$941$	−3.07411	+	1.77484i	−0.100213	+	0.0578582i	0.449056	+	0.893504i	$0.351760\pi$
$942$		0			0
$943$	−0.967225	−	3.60973i	−0.0314972	−	0.117549i
$944$	−11.6602			−0.379507
$945$		0			0
$946$	−15.7350			−0.511589
$947$	−5.10779	−	19.0625i	−0.165981	−	0.619449i	−0.997913	−	0.0645719i	$-0.979432\pi$
$947$	−5.10779	−	19.0625i	−0.165981	−	0.619449i	0.831932	−	0.554877i	$-0.187235\pi$
$948$		0			0
$949$	82.0256	−	47.3575i	2.66266	−	1.53729i
$950$	−4.64016	−	1.86250i	−0.150547	−	0.0604275i
$951$		0			0
$952$	13.8764	−	0.121427i	0.449738	−	0.00393547i
$953$	−25.8023	−	25.8023i	−0.835819	−	0.835819i	0.152486	−	0.988306i	$-0.451272\pi$
$953$	−25.8023	−	25.8023i	−0.835819	−	0.835819i	−0.988306	+	0.152486i	$0.951272\pi$
$954$		0			0
$955$	−5.22712	−	25.5436i	−0.169146	−	0.826573i
$956$	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
$962$	68.0688	+	18.2390i	2.19463	+	0.588048i
$963$		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	0.131568	−	0.991307i	$-0.457999\pi$
$967$	−26.7350	−	26.7350i	−0.859739	−	0.859739i	−0.991307	+	0.131568i	$0.957999\pi$
$968$	2.66113	−	0.713047i	0.0855319	−	0.0229182i
$969$		0			0
$970$	−28.6417	+	5.86109i	−0.919630	+	0.188188i
$971$	−7.81081	−	4.50957i	−0.250661	−	0.144719i	0.369406	−	0.929268i	$-0.379561\pi$
$971$	−7.81081	−	4.50957i	−0.250661	−	0.144719i	−0.620067	+	0.784549i	$0.712895\pi$
$972$		0			0
$973$	18.4222	+	10.4222i	0.590589	+	0.334121i
$974$	21.9062			0.701919
$975$		0			0
$976$	−1.62250	−	2.81025i	−0.0519349	−	0.0899539i
$977$	52.6333	+	14.1030i	1.68389	+	0.451197i	0.968801	−	0.247839i	$-0.0797204\pi$
$977$	52.6333	+	14.1030i	1.68389	+	0.451197i	0.715087	+	0.699035i	$0.246387\pi$
$978$		0			0
$979$			36.7150i			1.17342i
$980$	3.40589	+	15.2774i	0.108797	+	0.488020i
$981$		0			0
$982$	36.5207	−	9.78569i	1.16542	−	0.312274i
$983$	−1.29410	+	4.82963i	−0.0412752	+	0.154041i	−0.983488	−	0.180974i	$-0.942075\pi$
$983$	−1.29410	+	4.82963i	−0.0412752	+	0.154041i	0.942213	+	0.335016i	$0.108742\pi$
$984$		0			0
$985$	−21.1822	−	1.27142i	−0.674920	−	0.0405108i
$986$		−	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	$0.970088\pi$
$992$	1.03528	+	3.86370i	0.0328701	+	0.122673i
$993$		0			0
$994$	−6.78675	+	26.2450i	−0.215263	+	0.832441i
$995$	6.88368	+	2.29456i	0.218227	+	0.0727424i
$996$		0			0
$997$	−6.22243	+	23.2224i	−0.197066	+	0.735462i	0.794656	+	0.607060i	$0.207651\pi$
$997$	−6.22243	+	23.2224i	−0.197066	+	0.735462i	−0.991722	+	0.128402i	$0.959015\pi$
$998$	4.26793	−	15.9281i	0.135099	−	0.504196i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.a.53.2	✓	16	105.53	even	12	inner
630.2.ce.a.53.4	yes	16	35.18	odd	12	inner
630.2.ce.a.107.2	yes	16	1.1	even	1	trivial
630.2.ce.a.107.4	yes	16	3.2	odd	2	inner
630.2.ce.a.233.1	yes	16	5.3	odd	4	inner
630.2.ce.a.233.3	yes	16	15.8	even	4	inner
630.2.ce.a.557.1	yes	16	21.11	odd	6	inner
630.2.ce.a.557.3	yes	16	7.4	even	3	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)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.48356 + 1.67303i) q^{5} +(1.30278 - 2.30278i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.48356 + 1.67303i) q^{5} +(1.30278 - 2.30278i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.23205 - 1.86603i) q^{10} +(3.21189 - 1.85439i) q^{11} +(-4.62250 + 4.62250i) q^{13} +(-2.56149 - 0.662382i) q^{14} +(0.500000 - 0.866025i) q^{16} +(5.06628 + 1.35751i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(-2.12132 - 0.707107i) q^{20} +(-2.62250 - 2.62250i) q^{22} +(4.10035 - 1.09869i) q^{23} +(-0.598076 + 4.96410i) q^{25} +(5.66138 + 3.26860i) q^{26} +(0.0231510 + 2.64565i) q^{28} +2.82843 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.965926 - 0.258819i) q^{32} -5.24500i q^{34} +(5.78537 - 1.23673i) q^{35} +(10.4125 - 2.79003i) q^{37} +(-0.258819 + 0.965926i) q^{38} +(-0.133975 + 2.23205i) q^{40} -0.880347i q^{41} +(3.00000 - 3.00000i) q^{43} +(-1.85439 + 3.21189i) q^{44} +(-2.12250 - 3.67628i) q^{46} +(2.32937 + 8.69333i) q^{47} +(-3.60555 - 6.00000i) q^{49} +(4.94975 - 0.707107i) q^{50} +(1.69195 - 6.31445i) q^{52} +(-0.581048 + 2.16850i) q^{53} +(7.86750 + 2.62250i) q^{55} +(2.54951 - 0.707107i) q^{56} +(-0.732051 - 2.73205i) q^{58} +(-5.83009 - 10.0980i) q^{59} +(1.62250 - 2.81025i) q^{61} +(-2.82843 + 2.82843i) q^{62} +1.00000i q^{64} +(-14.5914 - 0.875819i) q^{65} +(-2.56218 + 9.56218i) q^{67} +(-5.06628 + 1.35751i) q^{68} +(-2.69195 - 5.26815i) q^{70} -10.2460i q^{71} +(-13.9949 - 3.74993i) q^{73} +(-5.38992 - 9.33562i) q^{74} +1.00000 q^{76} +(-0.0858619 - 9.81212i) q^{77} +(2.38590 + 1.37750i) q^{79} +(2.19067 - 0.448288i) q^{80} +(-0.850349 + 0.227850i) q^{82} +(6.53720 + 6.53720i) q^{83} +(5.24500 + 10.4900i) q^{85} +(-3.67423 - 2.12132i) q^{86} +(3.58240 + 0.959901i) q^{88} +(-4.94975 + 8.57321i) q^{89} +(4.62250 + 16.6667i) q^{91} +(-3.00167 + 3.00167i) q^{92} +(7.79423 - 4.50000i) q^{94} +(-0.448288 - 2.19067i) q^{95} +(-9.24500 - 9.24500i) q^{97} +(-4.86237 + 5.03561i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 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

Introduction

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