LMFDB - Embedded newform 567.2.f.j.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(190,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("567.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			190.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	567.190
Dual form			567.2.f.j.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.73205 q^{8} +O(q^{10})$	\(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.73205 q^{8} -6.00000 q^{10} +(1.73205 + 3.00000i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(0.866025 - 1.50000i) q^{14} +(2.50000 + 4.33013i) q^{16} -3.46410 q^{17} -4.00000 q^{19} +(-1.73205 - 3.00000i) q^{20} +(-3.00000 + 5.19615i) q^{22} +(-1.73205 + 3.00000i) q^{23} +(-3.50000 - 6.06218i) q^{25} -3.46410 q^{26} +1.00000 q^{28} +(2.00000 - 3.46410i) q^{31} +(-2.59808 + 4.50000i) q^{32} +(-3.00000 - 5.19615i) q^{34} +3.46410 q^{35} +2.00000 q^{37} +(-3.46410 - 6.00000i) q^{38} +(-3.00000 + 5.19615i) q^{40} +(5.19615 - 9.00000i) q^{41} +(2.00000 + 3.46410i) q^{43} -3.46410 q^{44} -6.00000 q^{46} +(3.46410 + 6.00000i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(6.06218 - 10.5000i) q^{50} +(-1.00000 - 1.73205i) q^{52} +6.92820 q^{53} -12.0000 q^{55} +(-0.866025 - 1.50000i) q^{56} +(-3.46410 + 6.00000i) q^{59} +(5.00000 + 8.66025i) q^{61} +6.92820 q^{62} +1.00000 q^{64} +(-3.46410 - 6.00000i) q^{65} +(2.00000 - 3.46410i) q^{67} +(1.73205 - 3.00000i) q^{68} +(3.00000 + 5.19615i) q^{70} +10.3923 q^{71} +14.0000 q^{73} +(1.73205 + 3.00000i) q^{74} +(2.00000 - 3.46410i) q^{76} +(1.73205 - 3.00000i) q^{77} +(-4.00000 - 6.92820i) q^{79} -17.3205 q^{80} +18.0000 q^{82} +(6.00000 - 10.3923i) q^{85} +(-3.46410 + 6.00000i) q^{86} +(3.00000 + 5.19615i) q^{88} +3.46410 q^{89} +2.00000 q^{91} +(-1.73205 - 3.00000i) q^{92} +(-6.00000 + 10.3923i) q^{94} +(6.92820 - 12.0000i) q^{95} +(-7.00000 - 12.1244i) q^{97} -1.73205 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} - 2 q^{7}+O(q^{10}) $ 4 * q - 2 * q^4 - 2 * q^7	$ 4 q - 2 q^{4} - 2 q^{7} - 24 q^{10} - 4 q^{13} + 10 q^{16} - 16 q^{19} - 12 q^{22} - 14 q^{25} + 4 q^{28} + 8 q^{31} - 12 q^{34} + 8 q^{37} - 12 q^{40} + 8 q^{43} - 24 q^{46} - 2 q^{49} - 4 q^{52} - 48 q^{55} + 20 q^{61} + 4 q^{64} + 8 q^{67} + 12 q^{70} + 56 q^{73} + 8 q^{76} - 16 q^{79} + 72 q^{82} + 24 q^{85} + 12 q^{88} + 8 q^{91} - 24 q^{94} - 28 q^{97}+O(q^{100}) $ 4 * q - 2 * q^4 - 2 * q^7 - 24 * q^10 - 4 * q^13 + 10 * q^16 - 16 * q^19 - 12 * q^22 - 14 * q^25 + 4 * q^28 + 8 * q^31 - 12 * q^34 + 8 * q^37 - 12 * q^40 + 8 * q^43 - 24 * q^46 - 2 * q^49 - 4 * q^52 - 48 * q^55 + 20 * q^61 + 4 * q^64 + 8 * q^67 + 12 * q^70 + 56 * q^73 + 8 * q^76 - 16 * q^79 + 72 * q^82 + 24 * q^85 + 12 * q^88 + 8 * q^91 - 24 * q^94 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	0.990839	+	0.135045i	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.73205	+	3.00000i	−0.774597	+	1.34164i	0.160424	+	0.987048i	$0.448714\pi$
$5$	−1.73205	+	3.00000i	−0.774597	+	1.34164i	−0.935021	+	0.354593i	$0.884620\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	1.73205			0.612372
$9$		0			0
$10$	−6.00000			−1.89737
$11$	1.73205	+	3.00000i	0.522233	+	0.904534i	0.999665	+	0.0258656i	$0.00823419\pi$
$11$	1.73205	+	3.00000i	0.522233	+	0.904534i	−0.477432	+	0.878668i	$0.658432\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	0.866025	−	1.50000i	0.231455	−	0.400892i
$15$		0			0
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−3.46410			−0.840168			−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410			−0.840168			−0.420084	+	0.907485i	$0.637999\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.73205	−	3.00000i	−0.387298	−	0.670820i
$21$		0			0
$22$	−3.00000	+	5.19615i	−0.639602	+	1.10782i
$23$	−1.73205	+	3.00000i	−0.361158	+	0.625543i	−0.988152	−	0.153481i	$-0.950952\pi$
$23$	−1.73205	+	3.00000i	−0.361158	+	0.625543i	0.626994	+	0.779024i	$0.284285\pi$
$24$		0			0
$25$	−3.50000	−	6.06218i	−0.700000	−	1.21244i
$26$	−3.46410			−0.679366
$27$		0			0
$28$	1.00000			0.188982
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$		0			0
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$	3.46410			0.585540
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−3.46410	−	6.00000i	−0.561951	−	0.973329i
$39$		0			0
$40$	−3.00000	+	5.19615i	−0.474342	+	0.821584i
$41$	5.19615	−	9.00000i	0.811503	−	1.40556i	−0.100309	−	0.994956i	$-0.531983\pi$
$41$	5.19615	−	9.00000i	0.811503	−	1.40556i	0.911812	−	0.410608i	$-0.134683\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	−3.46410			−0.522233
$45$		0			0
$46$	−6.00000			−0.884652
$47$	3.46410	+	6.00000i	0.505291	+	0.875190i	0.999981	+	0.00612051i	$0.00194823\pi$
$47$	3.46410	+	6.00000i	0.505291	+	0.875190i	−0.494690	+	0.869069i	$0.664718\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	6.06218	−	10.5000i	0.857321	−	1.48492i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	6.92820			0.951662			0.475831	−	0.879537i	$-0.342147\pi$
$53$	6.92820			0.951662			0.475831	+	0.879537i	$0.342147\pi$
$54$		0			0
$55$	−12.0000			−1.61808
$56$	−0.866025	−	1.50000i	−0.115728	−	0.200446i
$57$		0			0
$58$		0			0
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	−0.998448	−	0.0556984i	$-0.982261\pi$
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	0.547460	+	0.836832i	$0.315595\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	6.92820			0.879883
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.46410	−	6.00000i	−0.429669	−	0.744208i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	1.73205	−	3.00000i	0.210042	−	0.363803i
$69$		0			0
$70$	3.00000	+	5.19615i	0.358569	+	0.621059i
$71$	10.3923			1.23334			0.616670	−	0.787222i	$-0.288481\pi$
$71$	10.3923			1.23334			0.616670	+	0.787222i	$0.288481\pi$
$72$		0			0
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$	1.73205	+	3.00000i	0.201347	+	0.348743i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	1.73205	−	3.00000i	0.197386	−	0.341882i
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−17.3205			−1.93649
$81$		0			0
$82$	18.0000			1.98777
$83$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$83$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$84$		0			0
$85$	6.00000	−	10.3923i	0.650791	−	1.12720i
$86$	−3.46410	+	6.00000i	−0.373544	+	0.646997i
$87$		0			0
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	3.46410			0.367194			0.183597	−	0.983002i	$-0.441226\pi$
$89$	3.46410			0.367194			0.183597	+	0.983002i	$0.441226\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$	−1.73205	−	3.00000i	−0.180579	−	0.312772i
$93$		0			0
$94$	−6.00000	+	10.3923i	−0.618853	+	1.07188i
$95$	6.92820	−	12.0000i	0.710819	−	1.23117i
$96$		0			0
$97$	−7.00000	−	12.1244i	−0.710742	−	1.23104i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−7.00000	−	12.1244i	−0.710742	−	1.23104i	0.253837	−	0.967247i	$-0.418307\pi$
$98$	−1.73205			−0.174964
$99$		0			0
$100$	7.00000			0.700000
$101$	1.73205	+	3.00000i	0.172345	+	0.298511i	0.939239	−	0.343263i	$-0.111532\pi$
$101$	1.73205	+	3.00000i	0.172345	+	0.298511i	−0.766894	+	0.641774i	$0.778199\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$		0			0
$106$	6.00000	+	10.3923i	0.582772	+	1.00939i
$107$	−17.3205			−1.67444			−0.837218	−	0.546869i	$-0.815820\pi$
$107$	−17.3205			−1.67444			−0.837218	+	0.546869i	$0.815820\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	−10.3923	−	18.0000i	−0.990867	−	1.71623i
$111$		0			0
$112$	2.50000	−	4.33013i	0.236228	−	0.409159i
$113$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$113$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$114$		0			0
$115$	−6.00000	−	10.3923i	−0.559503	−	0.969087i
$116$		0			0
$117$		0			0
$118$	−12.0000			−1.10469
$119$	1.73205	+	3.00000i	0.158777	+	0.275010i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−8.66025	+	15.0000i	−0.784063	+	1.35804i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	6.92820			0.619677
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$		0			0
$130$	6.00000	−	10.3923i	0.526235	−	0.911465i
$131$	−6.92820	+	12.0000i	−0.605320	+	1.04844i	0.386681	+	0.922214i	$0.373621\pi$
$131$	−6.92820	+	12.0000i	−0.605320	+	1.04844i	−0.992001	+	0.126231i	$0.959712\pi$
$132$		0			0
$133$	2.00000	+	3.46410i	0.173422	+	0.300376i
$134$	6.92820			0.598506
$135$		0			0
$136$	−6.00000			−0.514496
$137$	−3.46410	−	6.00000i	−0.295958	−	0.512615i	0.679249	−	0.733908i	$-0.262306\pi$
$137$	−3.46410	−	6.00000i	−0.295958	−	0.512615i	−0.975207	+	0.221293i	$0.928972\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$	−1.73205	+	3.00000i	−0.146385	+	0.253546i
$141$		0			0
$142$	9.00000	+	15.5885i	0.755263	+	1.30815i
$143$	−6.92820			−0.579365
$144$		0			0
$145$		0			0
$146$	12.1244	+	21.0000i	1.00342	+	1.73797i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	3.46410	−	6.00000i	0.283790	−	0.491539i	−0.688525	−	0.725213i	$-0.741741\pi$
$149$	3.46410	−	6.00000i	0.283790	−	0.491539i	0.972315	+	0.233674i	$0.0750747\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	−6.92820			−0.561951
$153$		0			0
$154$	6.00000			0.483494
$155$	6.92820	+	12.0000i	0.556487	+	0.963863i
$156$		0			0
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	−0.594565	−	0.804048i	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$	6.92820	−	12.0000i	0.551178	−	0.954669i
$159$		0			0
$160$	−9.00000	−	15.5885i	−0.711512	−	1.23238i
$161$	3.46410			0.273009
$162$		0			0
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$	5.19615	+	9.00000i	0.405751	+	0.702782i
$165$		0			0
$166$		0			0
$167$	−10.3923	+	18.0000i	−0.804181	+	1.39288i	0.112662	+	0.993633i	$0.464062\pi$
$167$	−10.3923	+	18.0000i	−0.804181	+	1.39288i	−0.916843	+	0.399248i	$0.869271\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	20.7846			1.59411
$171$		0			0
$172$	−4.00000			−0.304997
$173$	8.66025	+	15.0000i	0.658427	+	1.14043i	0.981023	+	0.193892i	$0.0621112\pi$
$173$	8.66025	+	15.0000i	0.658427	+	1.14043i	−0.322596	+	0.946537i	$0.604555\pi$
$174$		0			0
$175$	−3.50000	+	6.06218i	−0.264575	+	0.458258i
$176$	−8.66025	+	15.0000i	−0.652791	+	1.13067i
$177$		0			0
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	17.3205			1.29460			0.647298	−	0.762237i	$-0.275899\pi$
$179$	17.3205			1.29460			0.647298	+	0.762237i	$0.275899\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	1.73205	+	3.00000i	0.128388	+	0.222375i
$183$		0			0
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	−3.46410	+	6.00000i	−0.254686	+	0.441129i
$186$		0			0
$187$	−6.00000	−	10.3923i	−0.438763	−	0.759961i
$188$	−6.92820			−0.505291
$189$		0			0
$190$	24.0000			1.74114
$191$	−12.1244	−	21.0000i	−0.877288	−	1.51951i	−0.854306	−	0.519771i	$-0.826017\pi$
$191$	−12.1244	−	21.0000i	−0.877288	−	1.51951i	−0.0229818	−	0.999736i	$-0.507316\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	12.1244	−	21.0000i	0.870478	−	1.50771i
$195$		0			0
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	−20.7846			−1.48084			−0.740421	−	0.672143i	$-0.765374\pi$
$197$	−20.7846			−1.48084			−0.740421	+	0.672143i	$0.765374\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−6.06218	−	10.5000i	−0.428661	−	0.742462i
$201$		0			0
$202$	−3.00000	+	5.19615i	−0.211079	+	0.365600i
$203$		0			0
$204$		0			0
$205$	18.0000	+	31.1769i	1.25717	+	2.17749i
$206$	6.92820			0.482711
$207$		0			0
$208$	−10.0000			−0.693375
$209$	−6.92820	−	12.0000i	−0.479234	−	0.830057i
$210$		0			0
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	0.283918	+	0.958849i	$0.408366\pi$
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	−0.972346	+	0.233544i	$0.924968\pi$
$212$	−3.46410	+	6.00000i	−0.237915	+	0.412082i
$213$		0			0
$214$	−15.0000	−	25.9808i	−1.02538	−	1.77601i
$215$	−13.8564			−0.944999
$216$		0			0
$217$	−4.00000			−0.271538
$218$	1.73205	+	3.00000i	0.117309	+	0.203186i
$219$		0			0
$220$	6.00000	−	10.3923i	0.404520	−	0.700649i
$221$	3.46410	−	6.00000i	0.233021	−	0.403604i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$	5.19615			0.347183
$225$		0			0
$226$		0			0
$227$	−3.46410	−	6.00000i	−0.229920	−	0.398234i	0.727864	−	0.685722i	$-0.240513\pi$
$227$	−3.46410	−	6.00000i	−0.229920	−	0.398234i	−0.957784	+	0.287488i	$0.907180\pi$
$228$		0			0
$229$	11.0000	−	19.0526i	0.726900	−	1.25903i	−0.231287	−	0.972886i	$-0.574293\pi$
$229$	11.0000	−	19.0526i	0.726900	−	1.25903i	0.958187	−	0.286143i	$-0.0923732\pi$
$230$	10.3923	−	18.0000i	0.685248	−	1.18688i
$231$		0			0
$232$		0			0
$233$	−6.92820			−0.453882			−0.226941	−	0.973909i	$-0.572872\pi$
$233$	−6.92820			−0.453882			−0.226941	+	0.973909i	$0.572872\pi$
$234$		0			0
$235$	−24.0000			−1.56559
$236$	−3.46410	−	6.00000i	−0.225494	−	0.390567i
$237$		0			0
$238$	−3.00000	+	5.19615i	−0.194461	+	0.336817i
$239$	5.19615	−	9.00000i	0.336111	−	0.582162i	−0.647586	−	0.761992i	$-0.724222\pi$
$239$	5.19615	−	9.00000i	0.336111	−	0.582162i	0.983698	+	0.179830i	$0.0575549\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	−1.73205			−0.111340
$243$		0			0
$244$	−10.0000			−0.640184
$245$	−1.73205	−	3.00000i	−0.110657	−	0.191663i
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$	3.46410	−	6.00000i	0.219971	−	0.381000i
$249$		0			0
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	−20.7846			−1.31191			−0.655956	−	0.754799i	$-0.727735\pi$
$251$	−20.7846			−1.31191			−0.655956	+	0.754799i	$0.727735\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	6.92820	+	12.0000i	0.434714	+	0.752947i
$255$		0			0
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−1.73205	+	3.00000i	−0.108042	+	0.187135i	−0.914977	−	0.403506i	$-0.867792\pi$
$257$	−1.73205	+	3.00000i	−0.108042	+	0.187135i	0.806935	+	0.590641i	$0.201125\pi$
$258$		0			0
$259$	−1.00000	−	1.73205i	−0.0621370	−	0.107624i
$260$	6.92820			0.429669
$261$		0			0
$262$	−24.0000			−1.48272
$263$	−8.66025	−	15.0000i	−0.534014	−	0.924940i	−0.999210	−	0.0397320i	$-0.987350\pi$
$263$	−8.66025	−	15.0000i	−0.534014	−	0.924940i	0.465196	−	0.885208i	$-0.345984\pi$
$264$		0			0
$265$	−12.0000	+	20.7846i	−0.737154	+	1.27679i
$266$	−3.46410	+	6.00000i	−0.212398	+	0.367884i
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	17.3205			1.05605			0.528025	−	0.849229i	$-0.322933\pi$
$269$	17.3205			1.05605			0.528025	+	0.849229i	$0.322933\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	−8.66025	−	15.0000i	−0.525105	−	0.909509i
$273$		0			0
$274$	6.00000	−	10.3923i	0.362473	−	0.627822i
$275$	12.1244	−	21.0000i	0.731126	−	1.26635i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	27.7128			1.66210
$279$		0			0
$280$	6.00000			0.358569
$281$	−10.3923	−	18.0000i	−0.619953	−	1.07379i	−0.989494	−	0.144575i	$-0.953818\pi$
$281$	−10.3923	−	18.0000i	−0.619953	−	1.07379i	0.369541	−	0.929214i	$-0.379515\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	−5.19615	+	9.00000i	−0.308335	+	0.534052i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$	−10.3923			−0.613438
$288$		0			0
$289$	−5.00000			−0.294118
$290$		0			0
$291$		0			0
$292$	−7.00000	+	12.1244i	−0.409644	+	0.709524i
$293$	−5.19615	+	9.00000i	−0.303562	+	0.525786i	−0.976940	−	0.213513i	$-0.931509\pi$
$293$	−5.19615	+	9.00000i	−0.303562	+	0.525786i	0.673378	+	0.739299i	$0.264843\pi$
$294$		0			0
$295$	−12.0000	−	20.7846i	−0.698667	−	1.21013i
$296$	3.46410			0.201347
$297$		0			0
$298$	12.0000			0.695141
$299$	−3.46410	−	6.00000i	−0.200334	−	0.346989i
$300$		0			0
$301$	2.00000	−	3.46410i	0.115278	−	0.199667i
$302$	6.92820	−	12.0000i	0.398673	−	0.690522i
$303$		0			0
$304$	−10.0000	−	17.3205i	−0.573539	−	0.993399i
$305$	−34.6410			−1.98354
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	1.73205	+	3.00000i	0.0986928	+	0.170941i
$309$		0			0
$310$	−12.0000	+	20.7846i	−0.681554	+	1.18049i
$311$	17.3205	−	30.0000i	0.982156	−	1.70114i	0.328206	−	0.944606i	$-0.393556\pi$
$311$	17.3205	−	30.0000i	0.982156	−	1.70114i	0.653950	−	0.756538i	$-0.273111\pi$
$312$		0			0
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	0.836379	−	0.548151i	$-0.184668\pi$
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	−0.892903	+	0.450250i	$0.851335\pi$
$314$	17.3205			0.977453
$315$		0			0
$316$	8.00000			0.450035
$317$	3.46410	+	6.00000i	0.194563	+	0.336994i	0.946757	−	0.321948i	$-0.104338\pi$
$317$	3.46410	+	6.00000i	0.194563	+	0.336994i	−0.752194	+	0.658942i	$0.771004\pi$
$318$		0			0
$319$		0			0
$320$	−1.73205	+	3.00000i	−0.0968246	+	0.167705i
$321$		0			0
$322$	3.00000	+	5.19615i	0.167183	+	0.289570i
$323$	13.8564			0.770991
$324$		0			0
$325$	14.0000			0.776580
$326$	17.3205	+	30.0000i	0.959294	+	1.66155i
$327$		0			0
$328$	9.00000	−	15.5885i	0.496942	−	0.860729i
$329$	3.46410	−	6.00000i	0.190982	−	0.330791i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$		0			0
$333$		0			0
$334$	−36.0000			−1.96983
$335$	6.92820	+	12.0000i	0.378528	+	0.655630i
$336$		0			0
$337$	−7.00000	+	12.1244i	−0.381314	+	0.660456i	−0.991250	−	0.131995i	$-0.957862\pi$
$337$	−7.00000	+	12.1244i	−0.381314	+	0.660456i	0.609936	+	0.792451i	$0.291195\pi$
$338$	−7.79423	+	13.5000i	−0.423950	+	0.734303i
$339$		0			0
$340$	6.00000	+	10.3923i	0.325396	+	0.563602i
$341$	13.8564			0.750366
$342$		0			0
$343$	1.00000			0.0539949
$344$	3.46410	+	6.00000i	0.186772	+	0.323498i
$345$		0			0
$346$	−15.0000	+	25.9808i	−0.806405	+	1.39673i
$347$	−8.66025	+	15.0000i	−0.464907	+	0.805242i	−0.999197	−	0.0400587i	$-0.987246\pi$
$347$	−8.66025	+	15.0000i	−0.464907	+	0.805242i	0.534291	+	0.845301i	$0.320579\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	−12.1244			−0.648074
$351$		0			0
$352$	−18.0000			−0.959403
$353$	1.73205	+	3.00000i	0.0921878	+	0.159674i	0.908431	−	0.418034i	$-0.137281\pi$
$353$	1.73205	+	3.00000i	0.0921878	+	0.159674i	−0.816244	+	0.577708i	$0.803947\pi$
$354$		0			0
$355$	−18.0000	+	31.1769i	−0.955341	+	1.65470i
$356$	−1.73205	+	3.00000i	−0.0917985	+	0.159000i
$357$		0			0
$358$	15.0000	+	25.9808i	0.792775	+	1.37313i
$359$	24.2487			1.27980			0.639899	−	0.768459i	$-0.278976\pi$
$359$	24.2487			1.27980			0.639899	+	0.768459i	$0.278976\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	1.73205	+	3.00000i	0.0910346	+	0.157676i
$363$		0			0
$364$	−1.00000	+	1.73205i	−0.0524142	+	0.0907841i
$365$	−24.2487	+	42.0000i	−1.26924	+	2.19838i
$366$		0			0
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	0.995697	−	0.0926670i	$-0.0295392\pi$
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	−0.578101	+	0.815966i	$0.696206\pi$
$368$	−17.3205			−0.902894
$369$		0			0
$370$	−12.0000			−0.623850
$371$	−3.46410	−	6.00000i	−0.179847	−	0.311504i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	10.3923	−	18.0000i	0.537373	−	0.930758i
$375$		0			0
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$		0			0
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	6.92820	+	12.0000i	0.355409	+	0.615587i
$381$		0			0
$382$	21.0000	−	36.3731i	1.07445	−	1.86101i
$383$	−6.92820	+	12.0000i	−0.354015	+	0.613171i	−0.986949	−	0.161034i	$-0.948517\pi$
$383$	−6.92820	+	12.0000i	−0.354015	+	0.613171i	0.632934	+	0.774206i	$0.281850\pi$
$384$		0			0
$385$	6.00000	+	10.3923i	0.305788	+	0.529641i
$386$	−24.2487			−1.23423
$387$		0			0
$388$	14.0000			0.710742
$389$	6.92820	+	12.0000i	0.351274	+	0.608424i	0.986473	−	0.163924i	$-0.0524153\pi$
$389$	6.92820	+	12.0000i	0.351274	+	0.608424i	−0.635199	+	0.772348i	$0.719082\pi$
$390$		0			0
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$	−0.866025	+	1.50000i	−0.0437409	+	0.0757614i
$393$		0			0
$394$	−18.0000	−	31.1769i	−0.906827	−	1.57067i
$395$	27.7128			1.39438
$396$		0			0
$397$	38.0000			1.90717			0.953583	−	0.301131i	$-0.0973643\pi$
$397$	38.0000			1.90717			0.953583	+	0.301131i	$0.0973643\pi$
$398$	−13.8564	−	24.0000i	−0.694559	−	1.20301i
$399$		0			0
$400$	17.5000	−	30.3109i	0.875000	−	1.51554i
$401$	3.46410	−	6.00000i	0.172989	−	0.299626i	−0.766475	−	0.642275i	$-0.777991\pi$
$401$	3.46410	−	6.00000i	0.172989	−	0.299626i	0.939463	+	0.342649i	$0.111324\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	−3.46410			−0.172345
$405$		0			0
$406$		0			0
$407$	3.46410	+	6.00000i	0.171709	+	0.297409i
$408$		0			0
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$	−31.1769	+	54.0000i	−1.53972	+	2.66687i
$411$		0			0
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$	6.92820			0.340915
$414$		0			0
$415$		0			0
$416$	−5.19615	−	9.00000i	−0.254762	−	0.441261i
$417$		0			0
$418$	12.0000	−	20.7846i	0.586939	−	1.01661i
$419$	10.3923	−	18.0000i	0.507697	−	0.879358i	−0.492263	−	0.870447i	$-0.663830\pi$
$419$	10.3923	−	18.0000i	0.507697	−	0.879358i	0.999960	−	0.00891102i	$-0.00283650\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	−34.6410			−1.68630
$423$		0			0
$424$	12.0000			0.582772
$425$	12.1244	+	21.0000i	0.588118	+	1.01865i
$426$		0			0
$427$	5.00000	−	8.66025i	0.241967	−	0.419099i
$428$	8.66025	−	15.0000i	0.418609	−	0.725052i
$429$		0			0
$430$	−12.0000	−	20.7846i	−0.578691	−	1.00232i
$431$	−3.46410			−0.166860			−0.0834300	−	0.996514i	$-0.526587\pi$
$431$	−3.46410			−0.166860			−0.0834300	+	0.996514i	$0.526587\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	−3.46410	−	6.00000i	−0.166282	−	0.288009i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	6.92820	−	12.0000i	0.331421	−	0.574038i
$438$		0			0
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	−20.7846			−0.990867
$441$		0			0
$442$	12.0000			0.570782
$443$	−1.73205	−	3.00000i	−0.0822922	−	0.142534i	0.821942	−	0.569571i	$-0.192891\pi$
$443$	−1.73205	−	3.00000i	−0.0822922	−	0.142534i	−0.904234	+	0.427037i	$0.859557\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	6.92820	−	12.0000i	0.328060	−	0.568216i
$447$		0			0
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−41.5692			−1.96177			−0.980886	−	0.194581i	$-0.937665\pi$
$449$	−41.5692			−1.96177			−0.980886	+	0.194581i	$0.937665\pi$
$450$		0			0
$451$	36.0000			1.69517
$452$		0			0
$453$		0			0
$454$	6.00000	−	10.3923i	0.281594	−	0.487735i
$455$	−3.46410	+	6.00000i	−0.162400	+	0.281284i
$456$		0			0
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	38.1051			1.78054
$459$		0			0
$460$	12.0000			0.559503
$461$	15.5885	+	27.0000i	0.726027	+	1.25752i	0.958550	+	0.284925i	$0.0919685\pi$
$461$	15.5885	+	27.0000i	0.726027	+	1.25752i	−0.232523	+	0.972591i	$0.574698\pi$
$462$		0			0
$463$	−16.0000	+	27.7128i	−0.743583	+	1.28792i	0.207271	+	0.978284i	$0.433542\pi$
$463$	−16.0000	+	27.7128i	−0.743583	+	1.28792i	−0.950854	+	0.309640i	$0.899791\pi$
$464$		0			0
$465$		0			0
$466$	−6.00000	−	10.3923i	−0.277945	−	0.481414i
$467$	−6.92820			−0.320599			−0.160300	−	0.987068i	$-0.551246\pi$
$467$	−6.92820			−0.320599			−0.160300	+	0.987068i	$0.551246\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$	−20.7846	−	36.0000i	−0.958723	−	1.66056i
$471$		0			0
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−6.92820	+	12.0000i	−0.318559	+	0.551761i
$474$		0			0
$475$	14.0000	+	24.2487i	0.642364	+	1.11261i
$476$	−3.46410			−0.158777
$477$		0			0
$478$	18.0000			0.823301
$479$	−3.46410	−	6.00000i	−0.158279	−	0.274147i	0.775969	−	0.630771i	$-0.217261\pi$
$479$	−3.46410	−	6.00000i	−0.158279	−	0.274147i	−0.934248	+	0.356624i	$0.883928\pi$
$480$		0			0
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$	−8.66025	+	15.0000i	−0.394464	+	0.683231i
$483$		0			0
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	48.4974			2.20215
$486$		0			0
$487$	−40.0000			−1.81257			−0.906287	−	0.422664i	$-0.861095\pi$
$487$	−40.0000			−1.81257			−0.906287	+	0.422664i	$0.861095\pi$
$488$	8.66025	+	15.0000i	0.392031	+	0.679018i
$489$		0			0
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	5.19615	−	9.00000i	0.234499	−	0.406164i	−0.724628	−	0.689140i	$-0.757988\pi$
$491$	5.19615	−	9.00000i	0.234499	−	0.406164i	0.959127	+	0.282976i	$0.0913217\pi$
$492$		0			0
$493$		0			0
$494$	13.8564			0.623429
$495$		0			0
$496$	20.0000			0.898027
$497$	−5.19615	−	9.00000i	−0.233079	−	0.403705i
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	−3.46410	+	6.00000i	−0.154919	+	0.268328i
$501$		0			0
$502$	−18.0000	−	31.1769i	−0.803379	−	1.39149i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	−12.0000			−0.533993
$506$	−10.3923	−	18.0000i	−0.461994	−	0.800198i
$507$		0			0
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	−0.901855	−	0.432038i	$-0.857795\pi$
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	0.825084	+	0.565011i	$0.191128\pi$
$510$		0			0
$511$	−7.00000	−	12.1244i	−0.309662	−	0.536350i
$512$	−8.66025			−0.382733
$513$		0			0
$514$	−6.00000			−0.264649
$515$	6.92820	+	12.0000i	0.305293	+	0.528783i
$516$		0			0
$517$	−12.0000	+	20.7846i	−0.527759	+	0.914106i
$518$	1.73205	−	3.00000i	0.0761019	−	0.131812i
$519$		0			0
$520$	−6.00000	−	10.3923i	−0.263117	−	0.455733i
$521$	−3.46410			−0.151765			−0.0758825	−	0.997117i	$-0.524177\pi$
$521$	−3.46410			−0.151765			−0.0758825	+	0.997117i	$0.524177\pi$
$522$		0			0
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	−6.92820	−	12.0000i	−0.302660	−	0.524222i
$525$		0			0
$526$	15.0000	−	25.9808i	0.654031	−	1.13282i
$527$	−6.92820	+	12.0000i	−0.301797	+	0.522728i
$528$		0			0
$529$	5.50000	+	9.52628i	0.239130	+	0.414186i
$530$	−41.5692			−1.80565
$531$		0			0
$532$	−4.00000			−0.173422
$533$	10.3923	+	18.0000i	0.450141	+	0.779667i
$534$		0			0
$535$	30.0000	−	51.9615i	1.29701	−	2.24649i
$536$	3.46410	−	6.00000i	0.149626	−	0.259161i
$537$		0			0
$538$	15.0000	+	25.9808i	0.646696	+	1.12011i
$539$	−3.46410			−0.149209
$540$		0			0
$541$	14.0000			0.601907			0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000			0.601907			0.300954	+	0.953639i	$0.402695\pi$
$542$	17.3205	+	30.0000i	0.743980	+	1.28861i
$543$		0			0
$544$	9.00000	−	15.5885i	0.385872	−	0.668350i
$545$	−3.46410	+	6.00000i	−0.148386	+	0.257012i
$546$		0			0
$547$	2.00000	+	3.46410i	0.0855138	+	0.148114i	0.905610	−	0.424111i	$-0.139413\pi$
$547$	2.00000	+	3.46410i	0.0855138	+	0.148114i	−0.820096	+	0.572226i	$0.806080\pi$
$548$	6.92820			0.295958
$549$		0			0
$550$	42.0000			1.79089
$551$		0			0
$552$		0			0
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	−8.66025	+	15.0000i	−0.367939	+	0.637289i
$555$		0			0
$556$	8.00000	+	13.8564i	0.339276	+	0.587643i
$557$	6.92820			0.293557			0.146779	−	0.989169i	$-0.453109\pi$
$557$	6.92820			0.293557			0.146779	+	0.989169i	$0.453109\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$	8.66025	+	15.0000i	0.365963	+	0.633866i
$561$		0			0
$562$	18.0000	−	31.1769i	0.759284	−	1.31512i
$563$	17.3205	−	30.0000i	0.729972	−	1.26435i	−0.226922	−	0.973913i	$-0.572866\pi$
$563$	17.3205	−	30.0000i	0.729972	−	1.26435i	0.956894	−	0.290436i	$-0.0938004\pi$
$564$		0			0
$565$		0			0
$566$	6.92820			0.291214
$567$		0			0
$568$	18.0000			0.755263
$569$	3.46410	+	6.00000i	0.145223	+	0.251533i	0.929456	−	0.368933i	$-0.120277\pi$
$569$	3.46410	+	6.00000i	0.145223	+	0.251533i	−0.784233	+	0.620466i	$0.786943\pi$
$570$		0			0
$571$	14.0000	−	24.2487i	0.585882	−	1.01478i	−0.408883	−	0.912587i	$-0.634082\pi$
$571$	14.0000	−	24.2487i	0.585882	−	1.01478i	0.994765	−	0.102190i	$-0.0325850\pi$
$572$	3.46410	−	6.00000i	0.144841	−	0.250873i
$573$		0			0
$574$	−9.00000	−	15.5885i	−0.375653	−	0.650650i
$575$	24.2487			1.01124
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	−4.33013	−	7.50000i	−0.180110	−	0.311959i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$	24.2487			1.00342
$585$		0			0
$586$	−18.0000			−0.743573
$587$	−10.3923	−	18.0000i	−0.428936	−	0.742940i	0.567843	−	0.823137i	$-0.307778\pi$
$587$	−10.3923	−	18.0000i	−0.428936	−	0.742940i	−0.996779	+	0.0801976i	$0.974445\pi$
$588$		0			0
$589$	−8.00000	+	13.8564i	−0.329634	+	0.570943i
$590$	20.7846	−	36.0000i	0.855689	−	1.48210i
$591$		0			0
$592$	5.00000	+	8.66025i	0.205499	+	0.355934i
$593$	24.2487			0.995775			0.497888	−	0.867242i	$-0.334109\pi$
$593$	24.2487			0.995775			0.497888	+	0.867242i	$0.334109\pi$
$594$		0			0
$595$	−12.0000			−0.491952
$596$	3.46410	+	6.00000i	0.141895	+	0.245770i
$597$		0			0
$598$	6.00000	−	10.3923i	0.245358	−	0.424973i
$599$	22.5167	−	39.0000i	0.920006	−	1.59350i	0.120603	−	0.992701i	$-0.461517\pi$
$599$	22.5167	−	39.0000i	0.920006	−	1.59350i	0.799402	−	0.600796i	$-0.205150\pi$
$600$		0			0
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	0.998302	−	0.0582563i	$-0.0185541\pi$
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	−0.549602	+	0.835426i	$0.685221\pi$
$602$	6.92820			0.282372
$603$		0			0
$604$	8.00000			0.325515
$605$	−1.73205	−	3.00000i	−0.0704179	−	0.121967i
$606$		0			0
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$	10.3923	−	18.0000i	0.421464	−	0.729996i
$609$		0			0
$610$	−30.0000	−	51.9615i	−1.21466	−	2.10386i
$611$	−13.8564			−0.560570
$612$		0			0
$613$	38.0000			1.53481			0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000			1.53481			0.767403	+	0.641165i	$0.221549\pi$
$614$	−24.2487	−	42.0000i	−0.978598	−	1.69498i
$615$		0			0
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	−10.3923	+	18.0000i	−0.418378	+	0.724653i	−0.995777	−	0.0918100i	$-0.970735\pi$
$617$	−10.3923	+	18.0000i	−0.418378	+	0.724653i	0.577398	+	0.816463i	$0.304068\pi$
$618$		0			0
$619$	−4.00000	−	6.92820i	−0.160774	−	0.278468i	0.774373	−	0.632730i	$-0.218066\pi$
$619$	−4.00000	−	6.92820i	−0.160774	−	0.278468i	−0.935146	+	0.354262i	$0.884732\pi$
$620$	−13.8564			−0.556487
$621$		0			0
$622$	60.0000			2.40578
$623$	−1.73205	−	3.00000i	−0.0693932	−	0.120192i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	1.73205	−	3.00000i	0.0692267	−	0.119904i
$627$		0			0
$628$	5.00000	+	8.66025i	0.199522	+	0.345582i
$629$	−6.92820			−0.276246
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−6.92820	−	12.0000i	−0.275589	−	0.477334i
$633$		0			0
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$	−13.8564	+	24.0000i	−0.549875	+	0.952411i
$636$		0			0
$637$	−1.00000	−	1.73205i	−0.0396214	−	0.0686264i
$638$		0			0
$639$		0			0
$640$	−42.0000			−1.66020
$641$	−24.2487	−	42.0000i	−0.957767	−	1.65890i	−0.727906	−	0.685677i	$-0.759506\pi$
$641$	−24.2487	−	42.0000i	−0.957767	−	1.65890i	−0.229860	−	0.973224i	$-0.573827\pi$
$642$		0			0
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	−0.993019	−	0.117951i	$-0.962368\pi$
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	0.598658	+	0.801005i	$0.295701\pi$
$644$	−1.73205	+	3.00000i	−0.0682524	+	0.118217i
$645$		0			0
$646$	12.0000	+	20.7846i	0.472134	+	0.817760i
$647$	6.92820			0.272376			0.136188	−	0.990683i	$-0.456515\pi$
$647$	6.92820			0.272376			0.136188	+	0.990683i	$0.456515\pi$
$648$		0			0
$649$	−24.0000			−0.942082
$650$	12.1244	+	21.0000i	0.475556	+	0.823688i
$651$		0			0
$652$	−10.0000	+	17.3205i	−0.391630	+	0.678323i
$653$	13.8564	−	24.0000i	0.542243	−	0.939193i	−0.456532	−	0.889707i	$-0.650909\pi$
$653$	13.8564	−	24.0000i	0.542243	−	0.939193i	0.998775	−	0.0494855i	$-0.0157581\pi$
$654$		0			0
$655$	−24.0000	−	41.5692i	−0.937758	−	1.62424i
$656$	51.9615			2.02876
$657$		0			0
$658$	12.0000			0.467809
$659$	−5.19615	−	9.00000i	−0.202413	−	0.350590i	0.746892	−	0.664945i	$-0.231545\pi$
$659$	−5.19615	−	9.00000i	−0.202413	−	0.350590i	−0.949306	+	0.314355i	$0.898212\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	17.3205	−	30.0000i	0.673181	−	1.16598i
$663$		0			0
$664$		0			0
$665$	−13.8564			−0.537328
$666$		0			0
$667$		0			0
$668$	−10.3923	−	18.0000i	−0.402090	−	0.696441i
$669$		0			0
$670$	−12.0000	+	20.7846i	−0.463600	+	0.802980i
$671$	−17.3205	+	30.0000i	−0.668651	+	1.15814i
$672$		0			0
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	0.946156	−	0.323711i	$-0.104931\pi$
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	−0.753420	+	0.657539i	$0.771597\pi$
$674$	−24.2487			−0.934025
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−12.1244	−	21.0000i	−0.465977	−	0.807096i	0.533268	−	0.845946i	$-0.320964\pi$
$677$	−12.1244	−	21.0000i	−0.465977	−	0.807096i	−0.999245	+	0.0388507i	$0.987630\pi$
$678$		0			0
$679$	−7.00000	+	12.1244i	−0.268635	+	0.465290i
$680$	10.3923	−	18.0000i	0.398527	−	0.690268i
$681$		0			0
$682$	12.0000	+	20.7846i	0.459504	+	0.795884i
$683$	−24.2487			−0.927851			−0.463926	−	0.885874i	$-0.653559\pi$
$683$	−24.2487			−0.927851			−0.463926	+	0.885874i	$0.653559\pi$
$684$		0			0
$685$	24.0000			0.916993
$686$	0.866025	+	1.50000i	0.0330650	+	0.0572703i
$687$		0			0
$688$	−10.0000	+	17.3205i	−0.381246	+	0.660338i
$689$	−6.92820	+	12.0000i	−0.263944	+	0.457164i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	−17.3205			−0.658427
$693$		0			0
$694$	−30.0000			−1.13878
$695$	27.7128	+	48.0000i	1.05121	+	1.82074i
$696$		0			0
$697$	−18.0000	+	31.1769i	−0.681799	+	1.18091i
$698$	12.1244	−	21.0000i	0.458914	−	0.794862i
$699$		0			0
$700$	−3.50000	−	6.06218i	−0.132288	−	0.229129i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−8.00000			−0.301726
$704$	1.73205	+	3.00000i	0.0652791	+	0.113067i
$705$		0			0
$706$	−3.00000	+	5.19615i	−0.112906	+	0.195560i
$707$	1.73205	−	3.00000i	0.0651405	−	0.112827i
$708$		0			0
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	0.511683	−	0.859174i	$-0.329022\pi$
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	−0.999908	+	0.0135434i	$0.995689\pi$
$710$	−62.3538			−2.34010
$711$		0			0
$712$	6.00000			0.224860
$713$	6.92820	+	12.0000i	0.259463	+	0.449404i
$714$		0			0
$715$	12.0000	−	20.7846i	0.448775	−	0.777300i
$716$	−8.66025	+	15.0000i	−0.323649	+	0.560576i
$717$		0			0
$718$	21.0000	+	36.3731i	0.783713	+	1.35743i
$719$	−27.7128			−1.03351			−0.516757	−	0.856132i	$-0.672861\pi$
$719$	−27.7128			−1.03351			−0.516757	+	0.856132i	$0.672861\pi$
$720$		0			0
$721$	−4.00000			−0.148968
$722$	−2.59808	−	4.50000i	−0.0966904	−	0.167473i
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$		0			0
$726$		0			0
$727$	2.00000	+	3.46410i	0.0741759	+	0.128476i	0.900728	−	0.434384i	$-0.143034\pi$
$727$	2.00000	+	3.46410i	0.0741759	+	0.128476i	−0.826552	+	0.562861i	$0.809701\pi$
$728$	3.46410			0.128388
$729$		0			0
$730$	−84.0000			−3.10898
$731$	−6.92820	−	12.0000i	−0.256249	−	0.443836i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	−13.8564	+	24.0000i	−0.511449	+	0.885856i
$735$		0			0
$736$	−9.00000	−	15.5885i	−0.331744	−	0.574598i
$737$	13.8564			0.510407
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	−3.46410	−	6.00000i	−0.127343	−	0.220564i
$741$		0			0
$742$	6.00000	−	10.3923i	0.220267	−	0.381514i
$743$	−5.19615	+	9.00000i	−0.190628	+	0.330178i	−0.945459	−	0.325742i	$-0.894386\pi$
$743$	−5.19615	+	9.00000i	−0.190628	+	0.330178i	0.754830	+	0.655920i	$0.227719\pi$
$744$		0			0
$745$	12.0000	+	20.7846i	0.439646	+	0.761489i
$746$	17.3205			0.634149
$747$		0			0
$748$	12.0000			0.438763
$749$	8.66025	+	15.0000i	0.316439	+	0.548088i
$750$		0			0
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$	−17.3205	+	30.0000i	−0.631614	+	1.09399i
$753$		0			0
$754$		0			0
$755$	27.7128			1.00857
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	−24.2487	−	42.0000i	−0.880753	−	1.52551i
$759$		0			0
$760$	12.0000	−	20.7846i	0.435286	−	0.753937i
$761$	19.0526	−	33.0000i	0.690655	−	1.19625i	−0.280969	−	0.959717i	$-0.590656\pi$
$761$	19.0526	−	33.0000i	0.690655	−	1.19625i	0.971624	−	0.236532i	$-0.0760109\pi$
$762$		0			0
$763$	−1.00000	−	1.73205i	−0.0362024	−	0.0627044i
$764$	24.2487			0.877288
$765$		0			0
$766$	−24.0000			−0.867155
$767$	−6.92820	−	12.0000i	−0.250163	−	0.433295i
$768$		0			0
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	−0.596643	−	0.802507i	$-0.703499\pi$
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	0.993313	+	0.115454i	$0.0368323\pi$
$770$	−10.3923	+	18.0000i	−0.374513	+	0.648675i
$771$		0			0
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	−45.0333			−1.61974			−0.809868	−	0.586612i	$-0.800461\pi$
$773$	−45.0333			−1.61974			−0.809868	+	0.586612i	$0.800461\pi$
$774$		0			0
$775$	−28.0000			−1.00579
$776$	−12.1244	−	21.0000i	−0.435239	−	0.753856i
$777$		0			0
$778$	−12.0000	+	20.7846i	−0.430221	+	0.745164i
$779$	−20.7846	+	36.0000i	−0.744686	+	1.28983i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$	20.7846			0.743256
$783$		0			0
$784$	−5.00000			−0.178571
$785$	17.3205	+	30.0000i	0.618195	+	1.07075i
$786$		0			0
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$	10.3923	−	18.0000i	0.370211	−	0.641223i
$789$		0			0
$790$	24.0000	+	41.5692i	0.853882	+	1.47897i
$791$		0			0
$792$		0			0
$793$	−20.0000			−0.710221
$794$	32.9090	+	57.0000i	1.16790	+	2.02285i
$795$		0			0
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	15.5885	−	27.0000i	0.552171	−	0.956389i	−0.445946	−	0.895060i	$-0.647133\pi$
$797$	15.5885	−	27.0000i	0.552171	−	0.956389i	0.998118	−	0.0613293i	$-0.0195340\pi$
$798$		0			0
$799$	−12.0000	−	20.7846i	−0.424529	−	0.735307i
$800$	36.3731			1.28598
$801$		0			0
$802$	12.0000			0.423735
$803$	24.2487	+	42.0000i	0.855718	+	1.48215i
$804$		0			0
$805$	−6.00000	+	10.3923i	−0.211472	+	0.366281i
$806$	−6.92820	+	12.0000i	−0.244036	+	0.422682i
$807$		0			0
$808$	3.00000	+	5.19615i	0.105540	+	0.182800i
$809$	27.7128			0.974331			0.487165	−	0.873310i	$-0.338031\pi$
$809$	27.7128			0.974331			0.487165	+	0.873310i	$0.338031\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$		0			0
$813$		0			0
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$	−34.6410	+	60.0000i	−1.21342	+	2.10171i
$816$		0			0
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$	−24.2487			−0.847836
$819$		0			0
$820$	−36.0000			−1.25717
$821$	3.46410	+	6.00000i	0.120898	+	0.209401i	0.920122	−	0.391632i	$-0.128089\pi$
$821$	3.46410	+	6.00000i	0.120898	+	0.209401i	−0.799224	+	0.601033i	$0.794756\pi$
$822$		0			0
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$	3.46410	−	6.00000i	0.120678	−	0.209020i
$825$		0			0
$826$	6.00000	+	10.3923i	0.208767	+	0.361595i
$827$	10.3923			0.361376			0.180688	−	0.983540i	$-0.442168\pi$
$827$	10.3923			0.361376			0.180688	+	0.983540i	$0.442168\pi$
$828$		0			0
$829$	50.0000			1.73657			0.868286	−	0.496064i	$-0.165222\pi$
$829$	50.0000			1.73657			0.868286	+	0.496064i	$0.165222\pi$
$830$		0			0
$831$		0			0
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	1.73205	−	3.00000i	0.0600120	−	0.103944i
$834$		0			0
$835$	−36.0000	−	62.3538i	−1.24583	−	2.15784i
$836$	13.8564			0.479234
$837$		0			0
$838$	36.0000			1.24360
$839$	10.3923	+	18.0000i	0.358782	+	0.621429i	0.987758	−	0.155996i	$-0.0498587\pi$
$839$	10.3923	+	18.0000i	0.358782	+	0.621429i	−0.628975	+	0.777425i	$0.716525\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	−8.66025	+	15.0000i	−0.298452	+	0.516934i
$843$		0			0
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	−31.1769			−1.07252
$846$		0			0
$847$	1.00000			0.0343604
$848$	17.3205	+	30.0000i	0.594789	+	1.03020i
$849$		0			0
$850$	−21.0000	+	36.3731i	−0.720294	+	1.24759i
$851$	−3.46410	+	6.00000i	−0.118748	+	0.205677i
$852$		0			0
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$	17.3205			0.592696
$855$		0			0
$856$	−30.0000			−1.02538
$857$	−8.66025	−	15.0000i	−0.295829	−	0.512390i	0.679349	−	0.733816i	$-0.262262\pi$
$857$	−8.66025	−	15.0000i	−0.295829	−	0.512390i	−0.975177	+	0.221425i	$0.928929\pi$
$858$		0			0
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$	6.92820	−	12.0000i	0.236250	−	0.409197i
$861$		0			0
$862$	−3.00000	−	5.19615i	−0.102180	−	0.176982i
$863$	−38.1051			−1.29711			−0.648557	−	0.761166i	$-0.724627\pi$
$863$	−38.1051			−1.29711			−0.648557	+	0.761166i	$0.724627\pi$
$864$		0			0
$865$	−60.0000			−2.04006
$866$	22.5167	+	39.0000i	0.765147	+	1.32527i
$867$		0			0
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	13.8564	−	24.0000i	0.470046	−	0.814144i
$870$		0			0
$871$	4.00000	+	6.92820i	0.135535	+	0.234753i
$872$	3.46410			0.117309
$873$		0			0
$874$	24.0000			0.811812
$875$	−3.46410	−	6.00000i	−0.117108	−	0.202837i
$876$		0			0
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	−0.959671	−	0.281126i	$-0.909292\pi$
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	0.723298	+	0.690536i	$0.242625\pi$
$878$	−13.8564	+	24.0000i	−0.467631	+	0.809961i
$879$		0			0
$880$	−30.0000	−	51.9615i	−1.01130	−	1.75162i
$881$	51.9615			1.75063			0.875314	−	0.483555i	$-0.160655\pi$
$881$	51.9615			1.75063			0.875314	+	0.483555i	$0.160655\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$	3.46410	+	6.00000i	0.116510	+	0.201802i
$885$		0			0
$886$	3.00000	−	5.19615i	0.100787	−	0.174568i
$887$	3.46410	−	6.00000i	0.116313	−	0.201460i	−0.801991	−	0.597336i	$-0.796226\pi$
$887$	3.46410	−	6.00000i	0.116313	−	0.201460i	0.918304	+	0.395876i	$0.129559\pi$
$888$		0			0
$889$	−4.00000	−	6.92820i	−0.134156	−	0.232364i
$890$	−20.7846			−0.696702
$891$		0			0
$892$	8.00000			0.267860
$893$	−13.8564	−	24.0000i	−0.463687	−	0.803129i
$894$		0			0
$895$	−30.0000	+	51.9615i	−1.00279	+	1.73688i
$896$	6.06218	−	10.5000i	0.202523	−	0.350780i
$897$		0			0
$898$	−36.0000	−	62.3538i	−1.20134	−	2.08077i
$899$		0			0
$900$		0			0
$901$	−24.0000			−0.799556
$902$	31.1769	+	54.0000i	1.03808	+	1.79800i
$903$		0			0
$904$		0			0
$905$	−3.46410	+	6.00000i	−0.115151	+	0.199447i
$906$		0			0
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	6.92820			0.229920
$909$		0			0
$910$	−12.0000			−0.397796
$911$	15.5885	+	27.0000i	0.516469	+	0.894550i	0.999817	+	0.0191219i	$0.00608706\pi$
$911$	15.5885	+	27.0000i	0.516469	+	0.894550i	−0.483349	+	0.875428i	$0.660580\pi$
$912$		0			0
$913$		0			0
$914$	−8.66025	+	15.0000i	−0.286456	+	0.496156i
$915$		0			0
$916$	11.0000	+	19.0526i	0.363450	+	0.629514i
$917$	13.8564			0.457579
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$	−10.3923	−	18.0000i	−0.342624	−	0.593442i
$921$		0			0
$922$	−27.0000	+	46.7654i	−0.889198	+	1.54014i
$923$	−10.3923	+	18.0000i	−0.342067	+	0.592477i
$924$		0			0
$925$	−7.00000	−	12.1244i	−0.230159	−	0.398646i
$926$	−55.4256			−1.82140
$927$		0			0
$928$		0			0
$929$	−22.5167	−	39.0000i	−0.738748	−	1.27955i	−0.953059	−	0.302783i	$-0.902084\pi$
$929$	−22.5167	−	39.0000i	−0.738748	−	1.27955i	0.214312	−	0.976765i	$-0.431249\pi$
$930$		0			0
$931$	2.00000	−	3.46410i	0.0655474	−	0.113531i
$932$	3.46410	−	6.00000i	0.113470	−	0.196537i
$933$		0			0
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	41.5692			1.35946
$936$		0			0
$937$	−46.0000			−1.50275			−0.751377	−	0.659873i	$-0.770610\pi$
$937$	−46.0000			−1.50275			−0.751377	+	0.659873i	$0.770610\pi$
$938$	−3.46410	−	6.00000i	−0.113107	−	0.195907i
$939$		0			0
$940$	12.0000	−	20.7846i	0.391397	−	0.677919i
$941$	−8.66025	+	15.0000i	−0.282316	+	0.488986i	−0.971955	−	0.235168i	$-0.924436\pi$
$941$	−8.66025	+	15.0000i	−0.282316	+	0.488986i	0.689639	+	0.724154i	$0.257769\pi$
$942$		0			0
$943$	18.0000	+	31.1769i	0.586161	+	1.01526i
$944$	−34.6410			−1.12747
$945$		0			0
$946$	−24.0000			−0.780307
$947$	−12.1244	−	21.0000i	−0.393989	−	0.682408i	0.598983	−	0.800762i	$-0.295572\pi$
$947$	−12.1244	−	21.0000i	−0.393989	−	0.682408i	−0.992972	+	0.118354i	$0.962238\pi$
$948$		0			0
$949$	−14.0000	+	24.2487i	−0.454459	+	0.787146i
$950$	−24.2487	+	42.0000i	−0.786732	+	1.36266i
$951$		0			0
$952$	3.00000	+	5.19615i	0.0972306	+	0.168408i
$953$	41.5692			1.34656			0.673280	−	0.739388i	$-0.264885\pi$
$953$	41.5692			1.34656			0.673280	+	0.739388i	$0.264885\pi$
$954$		0			0
$955$	84.0000			2.71818
$956$	5.19615	+	9.00000i	0.168056	+	0.291081i
$957$		0			0
$958$	6.00000	−	10.3923i	0.193851	−	0.335760i
$959$	−3.46410	+	6.00000i	−0.111862	+	0.193750i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−6.92820			−0.223374
$963$		0			0
$964$	−10.0000			−0.322078
$965$	−24.2487	−	42.0000i	−0.780594	−	1.35203i
$966$		0			0
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	−0.708245	−	0.705967i	$-0.750513\pi$
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	0.965508	+	0.260375i	$0.0838461\pi$
$968$	−0.866025	+	1.50000i	−0.0278351	+	0.0482118i
$969$		0			0
$970$	42.0000	+	72.7461i	1.34854	+	2.33574i
$971$	−27.7128			−0.889346			−0.444673	−	0.895693i	$-0.646680\pi$
$971$	−27.7128			−0.889346			−0.444673	+	0.895693i	$0.646680\pi$
$972$		0			0
$973$	−16.0000			−0.512936
$974$	−34.6410	−	60.0000i	−1.10997	−	1.92252i
$975$		0			0
$976$	−25.0000	+	43.3013i	−0.800230	+	1.38604i
$977$	17.3205	−	30.0000i	0.554132	−	0.959785i	−0.443838	−	0.896107i	$-0.646384\pi$
$977$	17.3205	−	30.0000i	0.554132	−	0.959785i	0.997970	−	0.0636782i	$-0.0202831\pi$
$978$		0			0
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$	3.46410			0.110657
$981$		0			0
$982$	18.0000			0.574403
$983$	6.92820	+	12.0000i	0.220975	+	0.382741i	0.955104	−	0.296269i	$-0.0957426\pi$
$983$	6.92820	+	12.0000i	0.220975	+	0.382741i	−0.734129	+	0.679010i	$0.762409\pi$
$984$		0			0
$985$	36.0000	−	62.3538i	1.14706	−	1.98676i
$986$		0			0
$987$		0			0
$988$	4.00000	+	6.92820i	0.127257	+	0.220416i
$989$	−13.8564			−0.440608
$990$		0			0
$991$	56.0000			1.77890			0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000			1.77890			0.889449	+	0.457034i	$0.151088\pi$
$992$	10.3923	+	18.0000i	0.329956	+	0.571501i
$993$		0			0
$994$	9.00000	−	15.5885i	0.285463	−	0.494436i
$995$	27.7128	−	48.0000i	0.878555	−	1.52170i
$996$		0			0
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	0.934274	−	0.356555i	$-0.116049\pi$
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	−0.775923	+	0.630828i	$0.782715\pi$
$998$	6.92820			0.219308
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.j.190.2		4
3.2	odd	2	inner	567.2.f.j.190.1		4
9.2	odd	6	inner	567.2.f.j.379.1		4
9.4	even	3		63.2.a.b.1.1	✓	2
9.5	odd	6		63.2.a.b.1.2	yes	2
9.7	even	3	inner	567.2.f.j.379.2		4
36.23	even	6		1008.2.a.n.1.1		2
36.31	odd	6		1008.2.a.n.1.2		2
45.4	even	6		1575.2.a.q.1.2		2
45.13	odd	12		1575.2.d.i.1324.3		4
45.14	odd	6		1575.2.a.q.1.1		2
45.22	odd	12		1575.2.d.i.1324.2		4
45.23	even	12		1575.2.d.i.1324.1		4
45.32	even	12		1575.2.d.i.1324.4		4
63.4	even	3		441.2.e.j.226.2		4
63.5	even	6		441.2.e.i.361.1		4
63.13	odd	6		441.2.a.g.1.1		2
63.23	odd	6		441.2.e.j.361.1		4
63.31	odd	6		441.2.e.i.226.2		4
63.32	odd	6		441.2.e.j.226.1		4
63.40	odd	6		441.2.e.i.361.2		4
63.41	even	6		441.2.a.g.1.2		2
63.58	even	3		441.2.e.j.361.2		4
63.59	even	6		441.2.e.i.226.1		4
72.5	odd	6		4032.2.a.bt.1.2		2
72.13	even	6		4032.2.a.bt.1.1		2
72.59	even	6		4032.2.a.bq.1.2		2
72.67	odd	6		4032.2.a.bq.1.1		2
99.32	even	6		7623.2.a.bi.1.1		2
99.76	odd	6		7623.2.a.bi.1.2		2
252.139	even	6		7056.2.a.cm.1.1		2
252.167	odd	6		7056.2.a.cm.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.a.b.1.1	✓	2	9.4	even	3
63.2.a.b.1.2	yes	2	9.5	odd	6
441.2.a.g.1.1		2	63.13	odd	6
441.2.a.g.1.2		2	63.41	even	6
441.2.e.i.226.1		4	63.59	even	6
441.2.e.i.226.2		4	63.31	odd	6
441.2.e.i.361.1		4	63.5	even	6
441.2.e.i.361.2		4	63.40	odd	6
441.2.e.j.226.1		4	63.32	odd	6
441.2.e.j.226.2		4	63.4	even	3
441.2.e.j.361.1		4	63.23	odd	6
441.2.e.j.361.2		4	63.58	even	3
567.2.f.j.190.1		4	3.2	odd	2	inner
567.2.f.j.190.2		4	1.1	even	1	trivial
567.2.f.j.379.1		4	9.2	odd	6	inner
567.2.f.j.379.2		4	9.7	even	3	inner
1008.2.a.n.1.1		2	36.23	even	6
1008.2.a.n.1.2		2	36.31	odd	6
1575.2.a.q.1.1		2	45.14	odd	6
1575.2.a.q.1.2		2	45.4	even	6
1575.2.d.i.1324.1		4	45.23	even	12
1575.2.d.i.1324.2		4	45.22	odd	12
1575.2.d.i.1324.3		4	45.13	odd	12
1575.2.d.i.1324.4		4	45.32	even	12
4032.2.a.bq.1.1		2	72.67	odd	6
4032.2.a.bq.1.2		2	72.59	even	6
4032.2.a.bt.1.1		2	72.13	even	6
4032.2.a.bt.1.2		2	72.5	odd	6
7056.2.a.cm.1.1		2	252.139	even	6
7056.2.a.cm.1.2		2	252.167	odd	6
7623.2.a.bi.1.1		2	99.32	even	6
7623.2.a.bi.1.2		2	99.76	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.73205 q^{8} +O(q^{10})\)	\(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.73205 q^{8} -6.00000 q^{10} +(1.73205 + 3.00000i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(0.866025 - 1.50000i) q^{14} +(2.50000 + 4.33013i) q^{16} -3.46410 q^{17} -4.00000 q^{19} +(-1.73205 - 3.00000i) q^{20} +(-3.00000 + 5.19615i) q^{22} +(-1.73205 + 3.00000i) q^{23} +(-3.50000 - 6.06218i) q^{25} -3.46410 q^{26} +1.00000 q^{28} +(2.00000 - 3.46410i) q^{31} +(-2.59808 + 4.50000i) q^{32} +(-3.00000 - 5.19615i) q^{34} +3.46410 q^{35} +2.00000 q^{37} +(-3.46410 - 6.00000i) q^{38} +(-3.00000 + 5.19615i) q^{40} +(5.19615 - 9.00000i) q^{41} +(2.00000 + 3.46410i) q^{43} -3.46410 q^{44} -6.00000 q^{46} +(3.46410 + 6.00000i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(6.06218 - 10.5000i) q^{50} +(-1.00000 - 1.73205i) q^{52} +6.92820 q^{53} -12.0000 q^{55} +(-0.866025 - 1.50000i) q^{56} +(-3.46410 + 6.00000i) q^{59} +(5.00000 + 8.66025i) q^{61} +6.92820 q^{62} +1.00000 q^{64} +(-3.46410 - 6.00000i) q^{65} +(2.00000 - 3.46410i) q^{67} +(1.73205 - 3.00000i) q^{68} +(3.00000 + 5.19615i) q^{70} +10.3923 q^{71} +14.0000 q^{73} +(1.73205 + 3.00000i) q^{74} +(2.00000 - 3.46410i) q^{76} +(1.73205 - 3.00000i) q^{77} +(-4.00000 - 6.92820i) q^{79} -17.3205 q^{80} +18.0000 q^{82} +(6.00000 - 10.3923i) q^{85} +(-3.46410 + 6.00000i) q^{86} +(3.00000 + 5.19615i) q^{88} +3.46410 q^{89} +2.00000 q^{91} +(-1.73205 - 3.00000i) q^{92} +(-6.00000 + 10.3923i) q^{94} +(6.92820 - 12.0000i) q^{95} +(-7.00000 - 12.1244i) q^{97} -1.73205 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} - 2 q^{7}+O(q^{10}) \) 4 * q - 2 * q^4 - 2 * q^7	\( 4 q - 2 q^{4} - 2 q^{7} - 24 q^{10} - 4 q^{13} + 10 q^{16} - 16 q^{19} - 12 q^{22} - 14 q^{25} + 4 q^{28} + 8 q^{31} - 12 q^{34} + 8 q^{37} - 12 q^{40} + 8 q^{43} - 24 q^{46} - 2 q^{49} - 4 q^{52} - 48 q^{55} + 20 q^{61} + 4 q^{64} + 8 q^{67} + 12 q^{70} + 56 q^{73} + 8 q^{76} - 16 q^{79} + 72 q^{82} + 24 q^{85} + 12 q^{88} + 8 q^{91} - 24 q^{94} - 28 q^{97}+O(q^{100}) \) 4 * q - 2 * q^4 - 2 * q^7 - 24 * q^10 - 4 * q^13 + 10 * q^16 - 16 * q^19 - 12 * q^22 - 14 * q^25 + 4 * q^28 + 8 * q^31 - 12 * q^34 + 8 * q^37 - 12 * q^40 + 8 * q^43 - 24 * q^46 - 2 * q^49 - 4 * q^52 - 48 * q^55 + 20 * q^61 + 4 * q^64 + 8 * q^67 + 12 * q^70 + 56 * q^73 + 8 * q^76 - 16 * q^79 + 72 * q^82 + 24 * q^85 + 12 * q^88 + 8 * q^91 - 24 * q^94 - 28 * q^97

Introduction

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