LMFDB - Embedded newform 504.2.cc.a.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{12} + 19x^{8} + 810x^{4} + 6561 $ x^16 + 10x^12 + 19x^8 + 810*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			293.1
Root			$-0.475594 + 1.66548i$ of defining polynomial
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.a.461.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-1.68014 - 0.420861i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.32070 + 1.91721i) q^{5} +(2.35534 - 0.672592i) q^{6} +(1.32288 + 2.29129i) q^{7} +2.82843i q^{8} +(2.64575 + 1.41421i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-1.68014 - 0.420861i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.32070 + 1.91721i) q^{5} +(2.35534 - 0.672592i) q^{6} +(1.32288 + 2.29129i) q^{7} +2.82843i q^{8} +(2.64575 + 1.41421i) q^{9} -5.42268 q^{10} +(-2.40909 + 2.48923i) q^{12} +(2.27533 - 3.94099i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(-4.77237 - 4.61873i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-4.24037 + 0.138778i) q^{18} -7.01226 q^{19} +(6.64140 - 3.83441i) q^{20} +(-1.25830 - 4.40644i) q^{21} +(7.74037 + 4.46890i) q^{23} +(1.19038 - 4.75216i) q^{24} +(4.85136 + 8.40280i) q^{25} +6.43560i q^{26} +(-3.85005 - 3.48957i) q^{27} +5.29150 q^{28} +(9.11087 + 2.28220i) q^{30} +(4.89898 + 2.82843i) q^{32} +10.1449i q^{35} +(5.09524 - 3.16836i) q^{36} +(8.58823 - 4.95842i) q^{38} +(-5.48148 + 5.66382i) q^{39} +(-5.42268 + 9.39235i) q^{40} +(4.65692 + 4.50700i) q^{42} +(6.07440 + 9.76863i) q^{45} -12.6400 q^{46} +(1.90238 + 6.66190i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-11.8834 - 6.86086i) q^{50} +(-4.55066 - 7.88197i) q^{52} +(7.18283 + 1.55144i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(11.7816 + 2.95119i) q^{57} +(4.58621 + 2.64785i) q^{59} +(-12.7722 + 3.64725i) q^{60} +(3.66740 + 6.35212i) q^{61} +(0.259630 + 7.93301i) q^{63} -8.00000 q^{64} +(15.1114 - 8.72455i) q^{65} +(-11.1241 - 10.7660i) q^{69} +(-7.17353 - 12.4249i) q^{70} +10.9193i q^{71} +(-4.00000 + 7.48331i) q^{72} +(-4.61456 - 16.1596i) q^{75} +(-7.01226 + 12.1456i) q^{76} +(2.70850 - 10.8127i) q^{78} +(-8.67134 - 15.0192i) q^{79} -15.3376i q^{80} +(5.00000 + 7.48331i) q^{81} +(15.7330 - 9.08345i) q^{83} +(-8.89047 - 2.22699i) q^{84} +(-14.3471 - 7.66882i) q^{90} +12.0399 q^{91} +(15.4807 - 8.93781i) q^{92} +(-23.2856 - 13.4439i) q^{95} +(-7.04060 - 6.81395i) q^{96} -9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4}+O(q^{10}) $ 16 * q + 16 * q^4	$ 16 q + 16 q^{4} - 16 q^{15} - 32 q^{16} - 16 q^{18} + 72 q^{23} + 40 q^{25} + 32 q^{30} - 40 q^{39} - 56 q^{49} - 144 q^{50} + 8 q^{57} - 16 q^{60} + 56 q^{63} - 128 q^{64} - 72 q^{65} - 64 q^{72} + 128 q^{78} + 80 q^{81} + 144 q^{92}+O(q^{100}) $ 16 * q + 16 * q^4 - 16 * q^15 - 32 * q^16 - 16 * q^18 + 72 * q^23 + 40 * q^25 + 32 * q^30 - 40 * q^39 - 56 * q^49 - 144 * q^50 + 8 * q^57 - 16 * q^60 + 56 * q^63 - 128 * q^64 - 72 * q^65 - 64 * q^72 + 128 * q^78 + 80 * q^81 + 144 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$3$	−1.68014	−	0.420861i	−0.970030	−	0.242984i
$3$	−1.68014	−	0.420861i	−0.970030	−	0.242984i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	3.32070	+	1.91721i	1.48506	+	0.857401i	0.999856	−	0.0169992i	$-0.00541128\pi$
$5$	3.32070	+	1.91721i	1.48506	+	0.857401i	0.485206	+	0.874400i	$0.338745\pi$
$6$	2.35534	−	0.672592i	0.961563	−	0.274584i
$7$	1.32288	+	2.29129i	0.500000	+	0.866025i
$7$	1.32288	+	2.29129i	0.500000	+	0.866025i
$8$			2.82843i			1.00000i
$9$	2.64575	+	1.41421i	0.881917	+	0.471405i
$10$	−5.42268			−1.71480
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−2.40909	+	2.48923i	−0.695446	+	0.718579i
$13$	2.27533	−	3.94099i	0.631063	−	1.09303i	−0.356272	−	0.934382i	$-0.615952\pi$
$13$	2.27533	−	3.94099i	0.631063	−	1.09303i	0.987335	−	0.158651i	$-0.0507143\pi$
$14$	−3.24037	−	1.87083i	−0.866025	−	0.500000i
$15$	−4.77237	−	4.61873i	−1.23222	−	1.19255i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−4.24037	+	0.138778i	−0.999465	+	0.0327103i
$19$	−7.01226			−1.60872			−0.804361	−	0.594140i	$-0.797492\pi$
$19$	−7.01226			−1.60872			−0.804361	+	0.594140i	$0.797492\pi$
$20$	6.64140	−	3.83441i	1.48506	−	0.857401i
$21$	−1.25830	−	4.40644i	−0.274584	−	0.961563i
$22$		0			0
$23$	7.74037	+	4.46890i	1.61398	+	0.931831i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	7.74037	+	4.46890i	1.61398	+	0.931831i	0.625543	+	0.780189i	$0.284877\pi$
$24$	1.19038	−	4.75216i	0.242984	−	0.970030i
$25$	4.85136	+	8.40280i	0.970272	+	1.68056i
$26$			6.43560i			1.26213i
$27$	−3.85005	−	3.48957i	−0.740942	−	0.671569i
$28$	5.29150			1.00000
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	9.11087	+	2.28220i	1.66341	+	0.416670i
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	4.89898	+	2.82843i	0.866025	+	0.500000i
$33$		0			0
$34$		0			0
$35$			10.1449i			1.71480i
$36$	5.09524	−	3.16836i	0.849207	−	0.528060i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	8.58823	−	4.95842i	1.39319	−	0.804361i
$39$	−5.48148	+	5.66382i	−0.877740	+	0.906936i
$40$	−5.42268	+	9.39235i	−0.857401	+	1.48506i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$	4.65692	+	4.50700i	0.718579	+	0.695446i
$43$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$43$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$44$		0			0
$45$	6.07440	+	9.76863i	0.905519	+	1.45622i
$46$	−12.6400			−1.86366
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	1.90238	+	6.66190i	0.274584	+	0.961563i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	−11.8834	−	6.86086i	−1.68056	−	0.970272i
$51$		0			0
$52$	−4.55066	−	7.88197i	−0.631063	−	1.09303i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	7.18283	+	1.55144i	0.977459	+	0.211124i
$55$		0			0
$56$	−6.48074	+	3.74166i	−0.866025	+	0.500000i
$57$	11.7816	+	2.95119i	1.56051	+	0.390895i
$58$		0			0
$59$	4.58621	+	2.64785i	0.597074	+	0.344721i	0.767890	−	0.640582i	$-0.221307\pi$
$59$	4.58621	+	2.64785i	0.597074	+	0.344721i	−0.170816	+	0.985303i	$0.554640\pi$
$60$	−12.7722	+	3.64725i	−1.64889	+	0.470858i
$61$	3.66740	+	6.35212i	0.469562	+	0.813306i	0.999394	−	0.0347968i	$-0.0110784\pi$
$61$	3.66740	+	6.35212i	0.469562	+	0.813306i	−0.529832	+	0.848103i	$0.677745\pi$
$62$		0			0
$63$	0.259630	+	7.93301i	0.0327103	+	0.999465i
$64$	−8.00000			−1.00000
$65$	15.1114	−	8.72455i	1.87433	−	1.08215i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	−11.1241	−	10.7660i	−1.33919	−	1.29608i
$70$	−7.17353	−	12.4249i	−0.857401	−	1.48506i
$71$			10.9193i			1.29588i	0.761690	+	0.647941i	$0.224370\pi$
$71$			10.9193i			1.29588i	−0.761690	+	0.647941i	$0.775630\pi$
$72$	−4.00000	+	7.48331i	−0.471405	+	0.881917i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−4.61456	−	16.1596i	−0.532843	−	1.86595i
$76$	−7.01226	+	12.1456i	−0.804361	+	1.39319i
$77$		0			0
$78$	2.70850	−	10.8127i	0.306677	−	1.22430i
$79$	−8.67134	−	15.0192i	−0.975603	−	1.68979i	−0.677932	−	0.735124i	$-0.737124\pi$
$79$	−8.67134	−	15.0192i	−0.975603	−	1.68979i	−0.297670	−	0.954669i	$-0.596210\pi$
$80$		−	15.3376i		−	1.71480i
$81$	5.00000	+	7.48331i	0.555556	+	0.831479i
$82$		0			0
$83$	15.7330	−	9.08345i	1.72692	−	0.997039i	0.825010	−	0.565118i	$-0.191170\pi$
$83$	15.7330	−	9.08345i	1.72692	−	0.997039i	0.901912	−	0.431920i	$-0.142164\pi$
$84$	−8.89047	−	2.22699i	−0.970030	−	0.242984i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	−14.3471	−	7.66882i	−1.51231	−	0.808365i
$91$	12.0399			1.26213
$92$	15.4807	−	8.93781i	1.61398	−	0.931831i
$93$		0			0
$94$		0			0
$95$	−23.2856	−	13.4439i	−2.38905	−	1.37932i
$96$	−7.04060	−	6.81395i	−0.718579	−	0.695446i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$		−	9.89949i		−	1.00000i
$99$		0			0
$100$	19.4054			1.94054
$101$	−17.3740	+	10.0309i	−1.72877	+	0.998109i	−0.833650	+	0.552294i	$0.813753\pi$
$101$	−17.3740	+	10.0309i	−1.72877	+	0.998109i	−0.895125	+	0.445815i	$0.852914\pi$
$102$		0			0
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	11.1468	+	6.43560i	1.09303	+	0.631063i
$105$	4.26960	−	17.0449i	0.416670	−	1.66341i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−9.89417	+	3.17891i	−0.952067	+	0.305890i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	5.29150	−	9.16515i	0.500000	−	0.866025i
$113$	−5.78216	−	3.33833i	−0.543940	−	0.314044i	0.202735	−	0.979234i	$-0.435017\pi$
$113$	−5.78216	−	3.33833i	−0.543940	−	0.314044i	−0.746674	+	0.665190i	$0.768350\pi$
$114$	−16.5162	+	4.71639i	−1.54689	+	0.441730i
$115$	17.1356	+	29.6798i	1.59791	+	2.76765i
$116$		0			0
$117$	11.5934	−	7.20907i	1.07181	−	0.666479i
$118$	−7.48925			−0.689442
$119$		0			0
$120$	13.0637	−	13.4983i	1.19255	−	1.23222i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−8.98326	−	5.18648i	−0.813306	−	0.469562i
$123$		0			0
$124$		0			0
$125$			18.0322i			1.61285i
$126$	−5.92746	−	9.53232i	−0.528060	−	0.849207i
$127$	18.4422			1.63648			0.818241	−	0.574875i	$-0.194949\pi$
$127$	18.4422			1.63648			0.818241	+	0.574875i	$0.194949\pi$
$128$	9.79796	−	5.65685i	0.866025	−	0.500000i
$129$		0			0
$130$	−12.3384	+	21.3707i	−1.08215	+	1.87433i
$131$	−8.39072	−	4.84438i	−0.733100	−	0.423256i	0.0864550	−	0.996256i	$-0.472446\pi$
$131$	−8.39072	−	4.84438i	−0.733100	−	0.423256i	−0.819555	+	0.573000i	$0.805779\pi$
$132$		0			0
$133$	−9.27635	−	16.0671i	−0.804361	−	1.39319i
$134$		0			0
$135$	−6.09462	−	18.9692i	−0.524541	−	1.63261i
$136$		0			0
$137$	−12.9615	+	7.48331i	−1.10737	+	0.639343i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−12.9615	+	7.48331i	−1.10737	+	0.639343i	−0.169226	+	0.985577i	$0.554127\pi$
$138$	21.2369	+	5.31968i	1.80781	+	0.452841i
$139$	−1.14233	+	1.97858i	−0.0968913	+	0.167821i	−0.910396	−	0.413737i	$-0.864223\pi$
$139$	−1.14233	+	1.97858i	−0.0968913	+	0.167821i	0.813505	+	0.581558i	$0.197557\pi$
$140$	17.5715	+	10.1449i	1.48506	+	0.857401i
$141$		0			0
$142$	−7.72111	−	13.3734i	−0.647941	−	1.12227i
$143$		0			0
$144$	−0.392523	−	11.9936i	−0.0327103	−	0.999465i
$145$		0			0
$146$		0			0
$147$	8.43183	−	8.71230i	0.695446	−	0.718579i
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$	17.0782	+	16.5285i	1.39443	+	1.34954i
$151$	−12.2211	−	21.1676i	−0.994540	−	1.72259i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	−12.2211	−	21.1676i	−0.994540	−	1.72259i	−0.406894	−	0.913475i	$-0.633388\pi$
$152$		−	19.8337i		−	1.60872i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	4.32853	+	15.1580i	0.346560	+	1.21361i
$157$	3.34486	−	5.79347i	0.266949	−	0.462369i	−0.701123	−	0.713040i	$-0.747318\pi$
$157$	3.34486	−	5.79347i	0.266949	−	0.462369i	0.968072	+	0.250671i	$0.0806511\pi$
$158$	21.2404	+	12.2631i	1.68979	+	0.975603i
$159$		0			0
$160$	10.8454	+	18.7847i	0.857401	+	1.48506i
$161$			23.6472i			1.86366i
$162$	−11.4152	−	5.62962i	−0.896865	−	0.442305i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$	−12.8459	+	22.2498i	−0.997039	+	1.72692i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$	12.4633	−	3.55902i	0.961563	−	0.274584i
$169$	−3.85425	−	6.67575i	−0.296481	−	0.513520i
$170$		0			0
$171$	−18.5527	−	9.91683i	−1.41876	−	0.758359i
$172$		0			0
$173$	−21.3064	+	12.3013i	−1.61990	+	0.935247i	−0.632950	+	0.774193i	$0.718156\pi$
$173$	−21.3064	+	12.3013i	−1.61990	+	0.935247i	−0.986945	+	0.161055i	$0.948510\pi$
$174$		0			0
$175$	−12.8355	+	22.2317i	−0.970272	+	1.68056i
$176$		0			0
$177$	−6.59111	−	6.37892i	−0.495418	−	0.479469i
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	22.9942	−	0.752548i	1.71388	−	0.0560916i
$181$	3.13802			0.233247			0.116623	−	0.993176i	$-0.462793\pi$
$181$	3.13802			0.233247			0.116623	+	0.993176i	$0.462793\pi$
$182$	−14.7458	+	8.51350i	−1.09303	+	0.631063i
$183$	−3.48839	−	12.2159i	−0.257869	−	0.903027i
$184$	−12.6400	+	21.8931i	−0.931831	+	1.61398i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.90248	−	13.4378i	0.211124	−	0.977459i
$190$	38.0252			2.75864
$191$	2.10792	−	1.21701i	0.152524	−	0.0880597i	−0.421796	−	0.906691i	$-0.638600\pi$
$191$	2.10792	−	1.21701i	0.152524	−	0.0880597i	0.574320	+	0.818631i	$0.305267\pi$
$192$	13.4411	+	3.36689i	0.970030	+	0.242984i
$193$	10.2886	−	17.8204i	0.740591	−	1.28274i	−0.211636	−	0.977349i	$-0.567879\pi$
$193$	10.2886	−	17.8204i	0.740591	−	1.28274i	0.952227	−	0.305392i	$-0.0987875\pi$
$194$		0			0
$195$	−29.0611	+	8.29869i	−2.08111	+	0.594282i
$196$	7.00000	+	12.1244i	0.500000	+	0.866025i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−23.7667	+	13.7217i	−1.68056	+	0.970272i
$201$		0			0
$202$	14.1858	−	24.5705i	0.998109	−	1.72877i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	14.1591	+	22.7701i	0.984126	+	1.58263i
$208$	−18.2026			−1.26213
$209$		0			0
$210$	6.82338	+	23.8947i	0.470858	+	1.64889i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	4.59551	−	18.3460i	0.314879	−	1.25705i
$214$		0			0
$215$		0			0
$216$	9.87000	−	10.8896i	0.671569	−	0.740942i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$223$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$224$			14.9666i			1.00000i
$225$	0.952135	+	29.0926i	0.0634757	+	1.93951i
$226$	9.44222			0.628087
$227$	−12.7602	+	7.36712i	−0.846926	+	0.488973i	−0.859612	−	0.510947i	$-0.829295\pi$
$227$	−12.7602	+	7.36712i	−0.846926	+	0.488973i	0.0126866	+	0.999920i	$0.495962\pi$
$228$	16.8932	−	17.4551i	1.11878	−	1.15599i
$229$	14.6990	−	25.4595i	0.971339	−	1.68241i	0.279817	−	0.960053i	$-0.409726\pi$
$229$	14.6990	−	25.4595i	0.971339	−	1.68241i	0.691522	−	0.722355i	$-0.256940\pi$
$230$	−41.9735	−	24.2334i	−2.76765	−	1.59791i
$231$		0			0
$232$		0			0
$233$		−	20.1628i		−	1.32091i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$		−	20.1628i		−	1.32091i	0.750867	−	0.660454i	$-0.229636\pi$
$234$	−9.10132	+	17.0270i	−0.594972	+	1.11309i
$235$		0			0
$236$	9.17242	−	5.29570i	0.597074	−	0.344721i
$237$	8.24808	+	28.8838i	0.535770	+	1.87621i
$238$		0			0
$239$	−19.2596	−	11.1196i	−1.24580	−	0.719264i	−0.275533	−	0.961292i	$-0.588854\pi$
$239$	−19.2596	−	11.1196i	−1.24580	−	0.719264i	−0.970269	+	0.242028i	$0.922188\pi$
$240$	−6.45503	+	25.7694i	−0.416670	+	1.66341i
$241$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$241$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$242$			15.5563i			1.00000i
$243$	−5.25127	−	14.6773i	−0.336869	−	0.941551i
$244$	14.6696			0.939125
$245$	−23.2449	+	13.4204i	−1.48506	+	0.857401i
$246$		0			0
$247$	−15.9552	+	27.6352i	−1.01521	+	1.75839i
$248$		0			0
$249$	−30.2566	+	8.64007i	−1.91743	+	0.547542i
$250$	−12.7507	−	22.0848i	−0.806423	−	1.39677i
$251$			7.06541i			0.445965i	0.974822	+	0.222982i	$0.0715793\pi$
$251$			7.06541i			0.445965i	−0.974822	+	0.222982i	$0.928421\pi$
$252$	14.0000	+	7.48331i	0.881917	+	0.471405i
$253$		0			0
$254$	−22.5870	+	13.0406i	−1.41724	+	0.818241i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$		0			0
$260$		−	34.8982i		−	2.16429i
$261$		0			0
$262$	13.7020			0.846511
$263$	24.1533	−	13.9449i	1.48936	−	0.859881i	0.489432	−	0.872041i	$-0.337204\pi$
$263$	24.1533	−	13.9449i	1.48936	−	0.859881i	0.999926	+	0.0121601i	$0.00387079\pi$
$264$		0			0
$265$		0			0
$266$	22.7223	+	13.1187i	1.39319	+	0.804361i
$267$		0			0
$268$		0			0
$269$		−	20.5179i		−	1.25100i	−0.780225	−	0.625498i	$-0.784896\pi$
$269$		−	20.5179i		−	1.25100i	0.780225	−	0.625498i	$-0.215104\pi$
$270$	20.8776	+	18.9228i	1.27057	+	1.15161i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	−20.2288	−	5.06713i	−1.22430	−	0.306677i
$274$	10.5830	−	18.3303i	0.639343	−	1.10737i
$275$		0			0
$276$	−29.7714	+	8.50154i	−1.79203	+	0.511733i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		−	3.23100i		−	0.193783i
$279$		0			0
$280$	−28.6941			−1.71480
$281$	28.9807	−	16.7320i	1.72885	−	0.998150i	0.834021	−	0.551733i	$-0.186033\pi$
$281$	28.9807	−	16.7320i	1.72885	−	0.998150i	0.894825	−	0.446417i	$-0.147300\pi$
$282$		0			0
$283$	3.82867	−	6.63145i	0.227591	−	0.394199i	−0.729503	−	0.683978i	$-0.760249\pi$
$283$	3.82867	−	6.63145i	0.227591	−	0.394199i	0.957094	+	0.289779i	$0.0935819\pi$
$284$	18.9128	+	10.9193i	1.12227	+	0.647941i
$285$	33.4651	+	32.3877i	1.98230	+	1.91848i
$286$		0			0
$287$		0			0
$288$	8.96148	+	14.4115i	0.528060	+	0.849207i
$289$	−17.0000			−1.00000
$290$		0			0
$291$		0			0
$292$		0			0
$293$	16.9789	+	9.80280i	0.991921	+	0.572686i	0.905848	−	0.423603i	$-0.139235\pi$
$293$	16.9789	+	9.80280i	0.991921	+	0.572686i	0.0860728	+	0.996289i	$0.472568\pi$
$294$	−4.16632	+	16.6326i	−0.242984	+	0.970030i
$295$	10.1530	+	17.5854i	0.591128	+	1.02386i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	35.2238	−	20.3365i	2.03704	−	1.17609i
$300$	−32.6039	−	8.16700i	−1.88239	−	0.471522i
$301$		0			0
$302$	29.9355	+	17.2833i	1.72259	+	0.994540i
$303$	33.4123	−	9.54124i	1.91949	−	0.548130i
$304$	14.0245	+	24.2912i	0.804361	+	1.39319i
$305$			28.1246i			1.61041i
$306$		0			0
$307$	34.8207			1.98732			0.993662	−	0.112409i	$-0.0358567\pi$
$307$	34.8207			1.98732			0.993662	+	0.112409i	$0.0358567\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	−16.0197	−	15.5040i	−0.906936	−	0.877740i
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$			9.46070i			0.533898i
$315$	−14.3471	+	26.8409i	−0.808365	+	1.51231i
$316$	−34.6854			−1.95121
$317$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$317$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$318$		0			0
$319$		0			0
$320$	−26.5656	−	15.3376i	−1.48506	−	0.857401i
$321$		0			0
$322$	−16.7211	−	28.9618i	−0.931831	−	1.61398i
$323$		0			0
$324$	17.9615	−	1.17694i	0.997860	−	0.0653855i
$325$	44.1538			2.44921
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$		−	36.3338i		−	1.99408i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−12.7477	+	13.1718i	−0.695446	+	0.718579i
$337$	−13.2288	+	22.9129i	−0.720616	+	1.24814i	0.240137	+	0.970739i	$0.422808\pi$
$337$	−13.2288	+	22.9129i	−0.720616	+	1.24814i	−0.960753	+	0.277405i	$0.910526\pi$
$338$	9.44094	+	5.45073i	0.513520	+	0.296481i
$339$	8.30987	+	8.04235i	0.451330	+	0.436801i
$340$		0			0
$341$		0			0
$342$	29.7346	−	0.973147i	1.60786	−	0.0526217i
$343$	−18.5203			−1.00000
$344$		0			0
$345$	−16.2992	−	57.0779i	−0.877520	−	3.07297i
$346$	17.3966	−	30.1318i	0.935247	−	1.61990i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	−14.3152	−	24.7947i	−0.766277	−	1.32723i	−0.939569	−	0.342361i	$-0.888774\pi$
$349$	−14.3152	−	24.7947i	−0.766277	−	1.32723i	0.173291	−	0.984871i	$-0.444560\pi$
$350$		−	36.3042i		−	1.94054i
$351$	−22.5125	+	7.23306i	−1.20163	+	0.386072i
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$	12.5830	+	3.15194i	0.668779	+	0.167524i
$355$	−20.9345	+	36.2597i	−1.11109	+	1.92447i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			13.5121i			0.713143i	0.934268	+	0.356572i	$0.116054\pi$
$359$			13.5121i			0.713143i	−0.934268	+	0.356572i	$0.883946\pi$
$360$	−27.6299	+	17.1810i	−1.45622	+	0.905519i
$361$	30.1718			1.58799
$362$	−3.84327	+	2.21891i	−0.201998	+	0.116623i
$363$	−13.2500	+	13.6908i	−0.695446	+	0.718579i
$364$	12.0399	−	20.8537i	0.631063	−	1.09303i
$365$		0			0
$366$	12.9103	+	12.4947i	0.674835	+	0.653110i
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$		−	35.7512i		−	1.86366i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	7.58904	−	30.2966i	0.391896	−	1.56451i
$376$		0			0
$377$		0			0
$378$	5.94719	+	18.5103i	0.305890	+	0.952067i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−46.5712	+	26.8879i	−2.38905	+	1.37932i
$381$	−30.9855	−	7.76162i	−1.58744	−	0.397640i
$382$	−1.72111	+	2.98105i	−0.0880597	+	0.152524i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$	−18.8427	+	5.38073i	−0.961563	+	0.274584i
$385$		0			0
$386$			29.1006i			1.48118i
$387$		0			0
$388$		0			0
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$	29.7243	−	30.7131i	1.50515	−	1.55522i
$391$		0			0
$392$	−17.1464	−	9.89949i	−0.866025	−	0.500000i
$393$	12.0588	+	11.6706i	0.608285	+	0.588703i
$394$		0			0
$395$		−	66.4990i		−	3.34593i
$396$		0			0
$397$	−37.7318			−1.89370			−0.946852	−	0.321668i	$-0.895756\pi$
$397$	−37.7318			−1.89370			−0.946852	+	0.321668i	$0.895756\pi$
$398$		0			0
$399$	8.82355	+	30.8991i	0.441730	+	1.54689i
$400$	19.4054	−	33.6112i	0.970272	−	1.68056i
$401$	−27.8276	−	16.0663i	−1.38964	−	0.802310i	−0.396368	−	0.918092i	$-0.629729\pi$
$401$	−27.8276	−	16.0663i	−1.38964	−	0.802310i	−0.993275	+	0.115782i	$0.963063\pi$
$402$		0			0
$403$		0			0
$404$			40.1235i			1.99622i
$405$	2.25644	+	34.4359i	0.112123	+	1.71113i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$409$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$	24.9266	−	7.11804i	1.22954	−	0.351107i
$412$		0			0
$413$			14.0111i			0.689442i
$414$	−33.4422	−	17.8756i	−1.64360	−	0.878539i
$415$	69.6594			3.41945
$416$	22.2936	−	12.8712i	1.09303	−	0.631063i
$417$	2.75198	−	2.84352i	0.134765	−	0.139248i
$418$		0			0
$419$	−7.16397	−	4.13612i	−0.349983	−	0.202063i	0.314695	−	0.949193i	$-0.398098\pi$
$419$	−7.16397	−	4.13612i	−0.349983	−	0.202063i	−0.664678	+	0.747130i	$0.731431\pi$
$420$	−25.2530	−	24.4400i	−1.23222	−	1.19255i
$421$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$421$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	7.34423	+	25.7187i	0.355829	+	1.24607i
$427$	−9.70302	+	16.8061i	−0.469562	+	0.813306i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	37.4166i		−	1.80229i	−0.433515	−	0.901146i	$-0.642727\pi$
$431$		−	37.4166i		−	1.80229i	0.433515	−	0.901146i	$-0.357273\pi$
$432$	−4.38814	+	20.3161i	−0.211124	+	0.977459i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−54.2775	−	31.3371i	−2.59644	−	1.49906i
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	−17.8333	+	11.0893i	−0.849207	+	0.528060i
$442$		0			0
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−10.5830	−	18.3303i	−0.500000	−	0.866025i
$449$			11.0141i			0.519789i	0.965637	+	0.259895i	$0.0836878\pi$
$449$			11.0141i			0.519789i	−0.965637	+	0.259895i	$0.916312\pi$
$450$	−21.7377	−	34.9577i	−1.02472	−	1.64792i
$451$		0			0
$452$	−11.5643	+	6.67666i	−0.543940	+	0.314044i
$453$	11.6246	+	40.7079i	0.546170	+	1.91263i
$454$	10.4187	−	18.0457i	0.488973	−	0.846926i
$455$	39.9809	+	23.0830i	1.87433	+	1.08215i
$456$	−8.34723	+	33.3234i	−0.390895	+	1.56051i
$457$	−19.6940	−	34.1111i	−0.921249	−	1.59565i	−0.797486	−	0.603338i	$-0.793837\pi$
$457$	−19.6940	−	34.1111i	−0.921249	−	1.59565i	−0.123763	−	0.992312i	$-0.539496\pi$
$458$			41.5751i			1.94268i
$459$		0			0
$460$	68.5425			3.19581
$461$	34.5504	−	19.9477i	1.60917	−	0.929057i	0.619619	−	0.784903i	$-0.287287\pi$
$461$	34.5504	−	19.9477i	1.60917	−	0.929057i	0.989555	−	0.144154i	$-0.0460461\pi$
$462$		0			0
$463$	21.3113	−	36.9123i	0.990421	−	1.71546i	0.375628	−	0.926770i	$-0.377427\pi$
$463$	21.3113	−	36.9123i	0.990421	−	1.71546i	0.614792	−	0.788689i	$-0.289240\pi$
$464$		0			0
$465$		0			0
$466$	14.2572	+	24.6943i	0.660454	+	1.14394i
$467$			41.6295i			1.92638i	0.268814	+	0.963192i	$0.413368\pi$
$467$			41.6295i			1.92638i	−0.268814	+	0.963192i	$0.586632\pi$
$468$	−0.893119	−	27.2893i	−0.0412845	−	1.26145i
$469$		0			0
$470$		0			0
$471$	−8.05809	+	8.32613i	−0.371297	+	0.383648i
$472$	−7.48925	+	12.9718i	−0.344721	+	0.597074i
$473$		0			0
$474$	−30.5257	−	29.5431i	−1.40209	−	1.35696i
$475$	−34.0190	−	58.9226i	−1.56090	−	2.70356i
$476$		0			0
$477$		0			0
$478$	31.4508			1.43853
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	−10.3160	−	36.1254i	−0.470858	−	1.64889i
$481$		0			0
$482$		0			0
$483$	9.95220	−	39.7307i	0.452841	−	1.80781i
$484$	−11.0000	−	19.0526i	−0.500000	−	0.866025i
$485$		0			0
$486$	16.8099	+	14.2628i	0.762513	+	0.646973i
$487$	0.442222			0.0200390			0.0100195	−	0.999950i	$-0.496811\pi$
$487$	0.442222			0.0200390			0.0100195	+	0.999950i	$0.496811\pi$
$488$	−17.9665	+	10.3730i	−0.813306	+	0.469562i
$489$		0			0
$490$	18.9794	−	32.8732i	0.857401	−	1.48506i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$		0			0
$494$		−	45.1281i		−	2.03041i
$495$		0			0
$496$		0			0
$497$	−25.0193	+	14.4449i	−1.12227	+	0.647941i
$498$	30.9471	−	31.9765i	1.38677	−	1.43290i
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	31.2326	+	18.0322i	1.39677	+	0.806423i
$501$		0			0
$502$	−4.99600	−	8.65333i	−0.222982	−	0.386217i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−22.4379	+	0.734344i	−0.999465	+	0.0327103i
$505$	−76.9250			−3.42312
$506$		0			0
$507$	3.66612	+	12.8383i	0.162818	+	0.570170i
$508$	18.4422	−	31.9429i	0.818241	−	1.41724i
$509$	−32.4532	−	18.7369i	−1.43846	−	0.830497i	−0.440719	−	0.897645i	$-0.645277\pi$
$509$	−32.4532	−	18.7369i	−1.43846	−	0.830497i	−0.997743	+	0.0671482i	$0.978610\pi$
$510$		0			0
$511$		0			0
$512$		−	22.6274i		−	1.00000i
$513$	26.9975	+	24.4698i	1.19197	+	1.08037i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	40.9749	−	11.7008i	1.79860	−	0.513609i
$520$	24.6768	+	42.7414i	1.08215	+	1.87433i
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	−45.6661			−1.99684			−0.998419	−	0.0562050i	$-0.982100\pi$
$523$	−45.6661			−1.99684			−0.998419	+	0.0562050i	$0.982100\pi$
$524$	−16.7814	+	9.68876i	−0.733100	+	0.423256i
$525$	30.9219	−	31.9505i	1.34954	−	1.39443i
$526$	−19.7211	+	34.1580i	−0.859881	+	1.48936i
$527$		0			0
$528$		0			0
$529$	28.4422	+	49.2634i	1.23662	+	2.14189i
$530$		0			0
$531$	8.38935	+	13.4914i	0.364067	+	0.585479i
$532$	−37.1054			−1.60872
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	14.5083	+	25.1292i	0.625498	+	1.08339i
$539$		0			0
$540$	−38.9502	−	8.41297i	−1.67615	−	0.362037i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−5.27231	−	1.32067i	−0.226257	−	0.0566754i
$544$		0			0
$545$		0			0
$546$	28.3581	−	8.09794i	1.21361	−	0.346560i
$547$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$547$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$548$			29.9333i			1.27869i
$549$	0.719769	+	21.9926i	0.0307190	+	0.938622i
$550$		0			0
$551$		0			0
$552$	30.4509	−	31.4638i	1.29608	−	1.33919i
$553$	22.9422	−	39.7371i	0.975603	−	1.68979i
$554$		0			0
$555$		0			0
$556$	2.28466	+	3.95715i	0.0968913	+	0.167821i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$	35.1430	−	20.2898i	1.48506	−	0.857401i
$561$		0			0
$562$	−23.6627	+	40.9850i	−0.998150	+	1.72885i
$563$	13.8054	+	7.97053i	0.581827	+	0.335918i	0.761859	−	0.647743i	$-0.224287\pi$
$563$	13.8054	+	7.97053i	0.581827	+	0.335918i	−0.180032	+	0.983661i	$0.557620\pi$
$564$		0			0
$565$	−12.8005	−	22.1712i	−0.538522	−	0.932748i
$566$			10.8291i			0.455181i
$567$	−10.5320	+	21.3559i	−0.442305	+	0.896865i
$568$	−30.8844			−1.29588
$569$	−2.44949	+	1.41421i	−0.102688	+	0.0592869i	−0.550464	−	0.834859i	$-0.685549\pi$
$569$	−2.44949	+	1.41421i	−0.102688	+	0.0592869i	0.447777	+	0.894146i	$0.352216\pi$
$570$	−63.8878	−	16.0034i	−2.67596	−	0.670307i
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$	−4.05380	+	1.15760i	−0.169350	+	0.0483596i
$574$		0			0
$575$			86.7210i			3.61652i
$576$	−21.1660	−	11.3137i	−0.881917	−	0.471405i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	20.8207	−	12.0208i	0.866025	−	0.500000i
$579$	−24.7862	+	25.6107i	−1.03008	+	1.06434i
$580$		0			0
$581$	41.6256	+	24.0326i	1.72692	+	0.997039i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	52.3193	−	1.71229i	2.16314	−	0.0707947i
$586$	−27.7265			−1.14537
$587$	7.99569	−	4.61631i	0.330017	−	0.190536i	−0.325831	−	0.945428i	$-0.605644\pi$
$587$	7.99569	−	4.61631i	0.330017	−	0.190536i	0.655849	+	0.754892i	$0.272311\pi$
$588$	−6.65832	−	23.3167i	−0.274584	−	0.961563i
$589$		0			0
$590$	−24.8696	−	14.3584i	−1.02386	−	0.591128i
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−28.7601	+	49.8140i	−1.17609	+	2.03704i
$599$	9.79796	+	5.65685i	0.400334	+	0.231133i	0.686628	−	0.727009i	$-0.259090\pi$
$599$	9.79796	+	5.65685i	0.400334	+	0.231133i	−0.286294	+	0.958142i	$0.592423\pi$
$600$	45.7064	−	13.0519i	1.86595	−	0.532843i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	−48.8844			−1.98908
$605$	36.5277	−	21.0893i	1.48506	−	0.857401i
$606$	−34.1749	+	35.3117i	−1.38826	+	1.43444i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	−34.3529	−	19.8337i	−1.39319	−	0.804361i
$609$		0			0
$610$	−19.8871	−	34.4455i	−0.805206	−	1.39466i
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	−42.6465	+	24.6220i	−1.72107	+	0.993662i
$615$		0			0
$616$		0			0
$617$	−12.2474	−	7.07107i	−0.493064	−	0.284670i	0.232781	−	0.972529i	$-0.425218\pi$
$617$	−12.2474	−	7.07107i	−0.493064	−	0.284670i	−0.725845	+	0.687859i	$0.758551\pi$
$618$		0			0
$619$	24.8654	+	43.0682i	0.999427	+	1.73106i	0.529034	+	0.848601i	$0.322554\pi$
$619$	24.8654	+	43.0682i	0.999427	+	1.73106i	0.470393	+	0.882457i	$0.344112\pi$
$620$		0			0
$621$	−14.2062	−	44.2161i	−0.570076	−	1.77433i
$622$		0			0
$623$		0			0
$624$	30.5830	+	7.66079i	1.22430	+	0.306677i
$625$	−10.3146	+	17.8654i	−0.412583	+	0.714615i
$626$		0			0
$627$		0			0
$628$	−6.68972	−	11.5869i	−0.266949	−	0.462369i
$629$		0			0
$630$	−1.40789	−	43.0181i	−0.0560916	−	1.71388i
$631$	−10.8736			−0.432872			−0.216436	−	0.976297i	$-0.569443\pi$
$631$	−10.8736			−0.432872			−0.216436	+	0.976297i	$0.569443\pi$
$632$	42.4807	−	24.5263i	1.68979	−	0.975603i
$633$		0			0
$634$		0			0
$635$	61.2411	+	35.3575i	2.43028	+	1.40312i
$636$		0			0
$637$	15.9273	+	27.5869i	0.631063	+	1.09303i
$638$		0			0
$639$	−15.4422	+	28.8898i	−0.610885	+	1.14286i
$640$	43.3814			1.71480
$641$	−8.91478	+	5.14695i	−0.352113	+	0.203292i	−0.665615	−	0.746295i	$-0.731831\pi$
$641$	−8.91478	+	5.14695i	−0.352113	+	0.203292i	0.313503	+	0.949587i	$0.398498\pi$
$642$		0			0
$643$	7.63202	−	13.2190i	0.300978	−	0.521308i	−0.675380	−	0.737470i	$-0.736020\pi$
$643$	7.63202	−	13.2190i	0.300978	−	0.521308i	0.976358	+	0.216161i	$0.0693537\pi$
$644$	40.9582	+	23.6472i	1.61398	+	0.931831i
$645$		0			0
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−21.1660	+	14.1421i	−0.831479	+	0.555556i
$649$		0			0
$650$	−54.0771	+	31.2214i	−2.12108	+	1.22460i
$651$		0			0
$652$		0			0
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$		0			0
$655$	−18.5754	−	32.1735i	−0.725799	−	1.25712i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	−25.5444	+	44.2442i	−0.993561	+	1.72090i	−0.398664	+	0.917097i	$0.630526\pi$
$661$	−25.5444	+	44.2442i	−0.993561	+	1.72090i	−0.594898	+	0.803801i	$0.702807\pi$
$662$		0			0
$663$		0			0
$664$	25.6919	+	44.4997i	0.997039	+	1.72692i
$665$		−	71.1387i		−	2.75864i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	6.29888	−	25.1461i	0.242984	−	0.970030i
$673$	25.9422	+	44.9332i	0.999999	+	1.73205i	0.501113	+	0.865382i	$0.332924\pi$
$673$	25.9422	+	44.9332i	0.999999	+	1.73205i	0.498886	+	0.866668i	$0.333743\pi$
$674$		−	37.4166i		−	1.44123i
$675$	10.6442	−	49.2804i	0.409696	−	1.89680i
$676$	−15.4170			−0.592961
$677$	−8.18524	+	4.72575i	−0.314584	+	0.181625i	−0.648976	−	0.760809i	$-0.724802\pi$
$677$	−8.18524	+	4.72575i	−0.314584	+	0.181625i	0.334392	+	0.942434i	$0.391469\pi$
$678$	−15.8643	−	3.97387i	−0.609264	−	0.152615i
$679$		0			0
$680$		0			0
$681$	24.5395	−	7.00752i	0.940356	−	0.268529i
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$	−35.7292	+	22.2174i	−1.36614	+	0.849503i
$685$	−57.3882			−2.19269
$686$	22.6826	−	13.0958i	0.866025	−	0.500000i
$687$	−35.4113	+	36.5892i	−1.35103	+	1.39597i
$688$		0			0
$689$		0			0
$690$	60.3226	+	58.3806i	2.29644	+	2.22251i
$691$	15.1257	+	26.1985i	0.575409	+	0.996637i	0.995997	+	0.0893857i	$0.0284904\pi$
$691$	15.1257	+	26.1985i	0.575409	+	0.996637i	−0.420588	+	0.907252i	$0.638176\pi$
$692$			49.2050i			1.87049i
$693$		0			0
$694$		0			0
$695$	−7.58667	+	4.38017i	−0.287779	+	0.166149i
$696$		0			0
$697$		0			0
$698$	35.0650	+	20.2448i	1.32723	+	0.766277i
$699$	−8.48574	+	33.8763i	−0.320960	+	1.28132i
$700$	25.6710	+	44.4634i	0.970272	+	1.68056i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	22.4575	−	24.7774i	0.847604	−	0.935162i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−45.9672	−	26.5392i	−1.72877	−	0.998109i
$708$	−17.6397	+	5.03721i	−0.662942	+	0.189310i
$709$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$709$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$710$		−	59.2118i		−	2.22218i
$711$	−1.70185	−	52.0002i	−0.0638244	−	1.95016i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	27.6791	+	26.7881i	1.03370	+	1.00042i
$718$	−9.55452	−	16.5489i	−0.356572	−	0.617600i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	21.6907	−	40.5796i	0.808365	−	1.51231i
$721$		0			0
$722$	−36.9527	+	21.3347i	−1.37524	+	0.793994i
$723$		0			0
$724$	3.13802	−	5.43520i	0.116623	−	0.201998i
$725$		0			0
$726$	6.54707	−	26.1369i	0.242984	−	0.970030i
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$			34.0540i			1.26213i
$729$	2.64575	+	26.8701i	0.0979908	+	0.995187i
$730$		0			0
$731$		0			0
$732$	−24.6470	−	6.17387i	−0.910979	−	0.228193i
$733$	25.0267	−	43.3475i	0.924383	−	1.60108i	0.131832	−	0.991272i	$-0.457914\pi$
$733$	25.0267	−	43.3475i	0.924383	−	1.60108i	0.792551	−	0.609806i	$-0.208753\pi$
$734$		0			0
$735$	44.7029	−	12.7654i	1.64889	−	0.470858i
$736$	25.2799	+	43.7861i	0.931831	+	1.61398i
$737$		0			0
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$	38.4376	−	39.7162i	1.41204	−	1.45901i
$742$		0			0
$743$	−6.48074	−	3.74166i	−0.237755	−	0.137268i	0.376389	−	0.926462i	$-0.377166\pi$
$743$	−6.48074	−	3.74166i	−0.237755	−	0.137268i	−0.614145	+	0.789193i	$0.710499\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	54.4716	−	1.78273i	1.99301	−	0.0652268i
$748$		0			0
$749$		0			0
$750$	12.1283	+	42.4718i	0.442862	+	1.55085i
$751$	2.77889	−	4.81318i	0.101403	−	0.175635i	−0.810860	−	0.585240i	$-0.801000\pi$
$751$	2.77889	−	4.81318i	0.101403	−	0.175635i	0.912263	+	0.409605i	$0.134333\pi$
$752$		0			0
$753$	2.97356	−	11.8709i	0.108363	−	0.432599i
$754$		0			0
$755$		−	93.7216i		−	3.41088i
$756$	−20.3725	−	18.4651i	−0.740942	−	0.671569i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	38.0252	−	65.8616i	1.37932	−	2.38905i
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$	43.4377	−	12.4041i	1.57358	−	0.449353i
$763$		0			0
$764$		−	4.86804i		−	0.176119i
$765$		0			0
$766$		0			0
$767$	20.8703	−	12.0495i	0.753582	−	0.435081i
$768$	19.2728	−	19.9138i	0.695446	−	0.718579i
$769$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$769$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$		0			0
$772$	−20.5772	−	35.6408i	−0.740591	−	1.28274i
$773$			40.8077i			1.46775i	0.679285	+	0.733875i	$0.262290\pi$
$773$			40.8077i			1.46775i	−0.679285	+	0.733875i	$0.737710\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−14.6873	+	58.6339i	−0.525890	+	2.09943i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	28.0000			1.00000
$785$	22.2146	−	12.8256i	0.792871	−	0.457764i
$786$	−23.0213	−	5.76664i	−0.821142	−	0.205689i
$787$	−22.6105	+	39.1626i	−0.805978	+	1.39600i	0.109650	+	0.993970i	$0.465027\pi$
$787$	−22.6105	+	39.1626i	−0.805978	+	1.39600i	−0.915629	+	0.402025i	$0.868306\pi$
$788$		0			0
$789$	−46.4499	+	13.2643i	−1.65366	+	0.472220i
$790$	47.0219	+	81.4443i	1.67296	+	2.89766i
$791$		−	17.6648i		−	0.628087i
$792$		0			0
$793$	33.3782			1.18529
$794$	46.2118	−	26.6804i	1.64000	−	0.946852i
$795$		0			0
$796$		0			0
$797$	18.1640	+	10.4870i	0.643403	+	0.371469i	0.785924	−	0.618323i	$-0.212188\pi$
$797$	18.1640	+	10.4870i	0.643403	+	0.371469i	−0.142521	+	0.989792i	$0.545521\pi$
$798$	−32.6555	−	31.6043i	−1.15599	−	1.11878i
$799$		0			0
$800$			54.8869i			1.94054i
$801$		0			0
$802$	45.4422			1.60462
$803$		0			0
$804$		0			0
$805$	−45.3366	+	78.5253i	−1.59791	+	2.76765i
$806$		0			0
$807$	−8.63518	+	34.4729i	−0.303973	+	1.21350i
$808$	−28.3716	−	49.1410i	−0.998109	−	1.72877i
$809$			31.1127i			1.09386i	0.837177	+	0.546932i	$0.184204\pi$
$809$			31.1127i			1.09386i	−0.837177	+	0.546932i	$0.815796\pi$
$810$	−27.1134	−	40.5796i	−0.952667	−	1.42582i
$811$	−48.4452			−1.70114			−0.850570	−	0.525861i	$-0.823743\pi$
$811$	−48.4452			−1.70114			−0.850570	+	0.525861i	$0.823743\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	31.8546	+	17.0270i	1.11309	+	0.594972i
$820$		0			0
$821$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$821$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$822$	−25.4955	+	26.3435i	−0.889256	+	0.918836i
$823$	−13.2288	+	22.9129i	−0.461125	+	0.798693i	−0.999017	−	0.0443211i	$-0.985888\pi$
$823$	−13.2288	+	22.9129i	−0.461125	+	0.798693i	0.537892	+	0.843014i	$0.319221\pi$
$824$		0			0
$825$		0			0
$826$	−9.90735	−	17.1600i	−0.344721	−	0.597074i
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	53.5982	−	1.75415i	1.86266	−	0.0609609i
$829$	1.32653			0.0460723			0.0230361	−	0.999735i	$-0.492667\pi$
$829$	1.32653			0.0460723			0.0230361	+	0.999735i	$0.492667\pi$
$830$	−85.3150	+	49.2566i	−2.96133	+	1.70972i
$831$		0			0
$832$	−18.2026	+	31.5279i	−0.631063	+	1.09303i
$833$		0			0
$834$	−1.35980	+	5.42854i	−0.0470861	+	0.187975i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	11.6987			0.404125
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$	48.2102	+	12.0762i	1.66341	+	0.416670i
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$		0			0
$843$	−55.7336	+	15.9153i	−1.91957	+	0.548153i
$844$		0			0
$845$		−	29.5576i		−	1.01681i
$846$		0			0
$847$	29.1033			1.00000
$848$		0			0
$849$	−9.22362	+	9.53043i	−0.316554	+	0.327084i
$850$		0			0
$851$		0			0
$852$	−27.1806	−	26.3056i	−0.931193	−	0.901216i
$853$	−17.8370	−	30.8947i	−0.610729	−	1.05781i	−0.991118	−	0.132987i	$-0.957543\pi$
$853$	−17.8370	−	30.8947i	−0.610729	−	1.05781i	0.380389	−	0.924827i	$-0.375790\pi$
$854$		−	27.4443i		−	0.939125i
$855$	−42.5953	−	68.5002i	−1.45673	−	2.34266i
$856$		0			0
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$	27.1612	−	47.0446i	0.926728	−	1.60514i	0.137969	−	0.990437i	$-0.455943\pi$
$859$	27.1612	−	47.0446i	0.926728	−	1.60514i	0.788759	−	0.614703i	$-0.210724\pi$
$860$		0			0
$861$		0			0
$862$	26.4575	+	45.8258i	0.901146	+	1.56083i
$863$		−	14.5365i		−	0.494830i	−0.968910	−	0.247415i	$-0.920419\pi$
$863$		−	14.5365i		−	0.494830i	0.968910	−	0.247415i	$-0.0795811\pi$
$864$	−8.99131	−	27.9849i	−0.305890	−	0.952067i
$865$	−94.3362			−3.20753
$866$		0			0
$867$	28.5624	+	7.15464i	0.970030	+	0.242984i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	88.6348			2.99812
$875$	−41.3169	+	23.8543i	−1.39677	+	0.806423i
$876$		0			0
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$		0			0
$879$	−24.4014	−	23.6159i	−0.823039	−	0.796544i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	14.0000	−	26.1916i	0.471405	−	0.881917i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$	−9.65737	−	33.8190i	−0.324629	−	1.13681i
$886$		0			0
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$	24.3968	+	42.2564i	0.818241	+	1.41724i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	25.9230	+	14.9666i	0.866025	+	0.500000i
$897$	−67.7398	+	19.3438i	−2.26177	+	0.645871i
$898$	−7.78817	−	13.4895i	−0.259895	−	0.450151i
$899$		0			0
$900$	51.3420	+	27.4434i	1.71140	+	0.914781i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	9.44222	−	16.3544i	0.314044	−	0.543940i
$905$	10.4204	+	6.01622i	0.346386	+	0.199986i
$906$	−43.0220	−	41.6370i	−1.42931	−	1.38330i
$907$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$907$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$908$			29.4685i			0.977946i
$909$	−60.1530	+	1.96867i	−1.99515	+	0.0652968i
$910$	−65.2886			−2.16429
$911$	−0.182592	+	0.105420i	−0.00604956	+	0.00349271i	−0.503022	−	0.864274i	$-0.667778\pi$
$911$	−0.182592	+	0.105420i	−0.00604956	+	0.00349271i	0.496972	+	0.867766i	$0.334445\pi$
$912$	−13.3400	−	46.7150i	−0.441730	−	1.54689i
$913$		0			0
$914$	48.2404	+	27.8516i	1.59565	+	0.921249i
$915$	11.8366	−	47.2534i	0.391305	−	1.56215i
$916$	−29.3981	−	50.9189i	−0.971339	−	1.68241i
$917$		−	25.6341i		−	0.846511i
$918$		0			0
$919$	−14.4063			−0.475221			−0.237610	−	0.971361i	$-0.576364\pi$
$919$	−14.4063			−0.475221			−0.237610	+	0.971361i	$0.576364\pi$
$920$	−83.9471	+	48.4669i	−2.76765	+	1.59791i
$921$	−58.5038	−	14.6547i	−1.92776	−	0.482889i
$922$	−28.2103	+	48.8617i	−0.929057	+	1.60917i
$923$	43.0328	+	24.8450i	1.41644	+	0.817783i
$924$		0			0
$925$		0			0
$926$			60.2775i			1.98084i
$927$		0			0
$928$		0			0
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$		0			0
$931$	24.5429	−	42.5096i	0.804361	−	1.39319i
$932$	−34.9230	−	20.1628i	−1.14394	−	0.660454i
$933$		0			0
$934$	−29.4365	−	50.9855i	−0.963192	−	1.66830i
$935$		0			0
$936$	20.3903	+	32.7910i	0.666479	+	1.07181i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−35.4825	−	20.4859i	−1.15670	−	0.667820i	−0.206187	−	0.978513i	$-0.566106\pi$
$941$	−35.4825	−	20.4859i	−1.15670	−	0.667820i	−0.950510	+	0.310693i	$0.899439\pi$
$942$	3.98164	−	15.8953i	0.129729	−	0.517897i
$943$		0			0
$944$		−	21.1828i		−	0.689442i
$945$	35.4014	−	39.0584i	1.15161	−	1.27057i
$946$		0			0
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$	58.2763	+	14.5977i	1.89273	+	0.474113i
$949$		0			0
$950$	83.3292	+	48.1101i	2.70356	+	1.56090i
$951$		0			0
$952$		0			0
$953$			29.9333i			0.969633i	0.874616	+	0.484817i	$0.161114\pi$
$953$			29.9333i			0.969633i	−0.874616	+	0.484817i	$0.838886\pi$
$954$		0			0
$955$	9.33303			0.302010
$956$	−38.5193	+	22.2391i	−1.24580	+	0.719264i
$957$		0			0
$958$		0			0
$959$	−34.2929	−	19.7990i	−1.10737	−	0.639343i
$960$	38.1789	+	36.9499i	1.23222	+	1.19255i
$961$	−15.5000	−	26.8468i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	68.3308	−	39.4508i	2.19965	−	1.26997i
$966$	15.9049	+	55.6972i	0.511733	+	1.79203i
$967$	−24.2211	+	41.9522i	−0.778898	+	1.34909i	0.153679	+	0.988121i	$0.450888\pi$
$967$	−24.2211	+	41.9522i	−0.778898	+	1.34909i	−0.932577	+	0.360971i	$0.882445\pi$
$968$	26.9444	+	15.5563i	0.866025	+	0.500000i
$969$		0			0
$970$		0			0
$971$			31.2787i			1.00378i	0.864931	+	0.501891i	$0.167362\pi$
$971$			31.2787i			1.00378i	−0.864931	+	0.501891i	$0.832638\pi$
$972$	−30.6732	−	5.58187i	−0.983842	−	0.179039i
$973$	−6.04465			−0.193783
$974$	−0.541609	+	0.312698i	−0.0173543	+	0.0100195i
$975$	−74.1846	−	18.5826i	−2.37581	−	0.595120i
$976$	14.6696	−	25.4085i	0.469562	−	0.813306i
$977$	51.8459	+	29.9333i	1.65870	+	0.957650i	0.973317	+	0.229465i	$0.0736978\pi$
$977$	51.8459	+	29.9333i	1.65870	+	0.957650i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$		0			0
$980$			53.6818i			1.71480i
$981$		0			0
$982$		0			0
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	31.9104	+	55.2704i	1.01521	+	1.75839i
$989$		0			0
$990$		0			0
$991$	−37.0405			−1.17663			−0.588315	−	0.808632i	$-0.700209\pi$
$991$	−37.0405			−1.17663			−0.588315	+	0.808632i	$0.700209\pi$
$992$		0			0
$993$		0			0
$994$	20.4281	−	35.3826i	0.647941	−	1.12227i
$995$		0			0
$996$	−15.2915	+	61.0460i	−0.484530	+	1.93432i
$997$	30.9671	+	53.6365i	0.980737	+	1.69869i	0.659533	+	0.751675i	$0.270754\pi$
$997$	30.9671	+	53.6365i	0.980737	+	1.69869i	0.321203	+	0.947010i	$0.395913\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.a.293.1	✓	16
7.6	odd	2	inner	504.2.cc.a.293.4	yes	16
8.5	even	2	inner	504.2.cc.a.293.4	yes	16
9.2	odd	6	inner	504.2.cc.a.461.1	yes	16
56.13	odd	2	CM	504.2.cc.a.293.1	✓	16
63.20	even	6	inner	504.2.cc.a.461.4	yes	16
72.29	odd	6	inner	504.2.cc.a.461.4	yes	16
504.461	even	6	inner	504.2.cc.a.461.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.a.293.1	✓	16	1.1	even	1	trivial
504.2.cc.a.293.1	✓	16	56.13	odd	2	CM
504.2.cc.a.293.4	yes	16	7.6	odd	2	inner
504.2.cc.a.293.4	yes	16	8.5	even	2	inner
504.2.cc.a.461.1	yes	16	9.2	odd	6	inner
504.2.cc.a.461.1	yes	16	504.461	even	6	inner
504.2.cc.a.461.4	yes	16	63.20	even	6	inner
504.2.cc.a.461.4	yes	16	72.29	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-1.68014 - 0.420861i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.32070 + 1.91721i) q^{5} +(2.35534 - 0.672592i) q^{6} +(1.32288 + 2.29129i) q^{7} +2.82843i q^{8} +(2.64575 + 1.41421i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-1.68014 - 0.420861i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.32070 + 1.91721i) q^{5} +(2.35534 - 0.672592i) q^{6} +(1.32288 + 2.29129i) q^{7} +2.82843i q^{8} +(2.64575 + 1.41421i) q^{9} -5.42268 q^{10} +(-2.40909 + 2.48923i) q^{12} +(2.27533 - 3.94099i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(-4.77237 - 4.61873i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-4.24037 + 0.138778i) q^{18} -7.01226 q^{19} +(6.64140 - 3.83441i) q^{20} +(-1.25830 - 4.40644i) q^{21} +(7.74037 + 4.46890i) q^{23} +(1.19038 - 4.75216i) q^{24} +(4.85136 + 8.40280i) q^{25} +6.43560i q^{26} +(-3.85005 - 3.48957i) q^{27} +5.29150 q^{28} +(9.11087 + 2.28220i) q^{30} +(4.89898 + 2.82843i) q^{32} +10.1449i q^{35} +(5.09524 - 3.16836i) q^{36} +(8.58823 - 4.95842i) q^{38} +(-5.48148 + 5.66382i) q^{39} +(-5.42268 + 9.39235i) q^{40} +(4.65692 + 4.50700i) q^{42} +(6.07440 + 9.76863i) q^{45} -12.6400 q^{46} +(1.90238 + 6.66190i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-11.8834 - 6.86086i) q^{50} +(-4.55066 - 7.88197i) q^{52} +(7.18283 + 1.55144i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(11.7816 + 2.95119i) q^{57} +(4.58621 + 2.64785i) q^{59} +(-12.7722 + 3.64725i) q^{60} +(3.66740 + 6.35212i) q^{61} +(0.259630 + 7.93301i) q^{63} -8.00000 q^{64} +(15.1114 - 8.72455i) q^{65} +(-11.1241 - 10.7660i) q^{69} +(-7.17353 - 12.4249i) q^{70} +10.9193i q^{71} +(-4.00000 + 7.48331i) q^{72} +(-4.61456 - 16.1596i) q^{75} +(-7.01226 + 12.1456i) q^{76} +(2.70850 - 10.8127i) q^{78} +(-8.67134 - 15.0192i) q^{79} -15.3376i q^{80} +(5.00000 + 7.48331i) q^{81} +(15.7330 - 9.08345i) q^{83} +(-8.89047 - 2.22699i) q^{84} +(-14.3471 - 7.66882i) q^{90} +12.0399 q^{91} +(15.4807 - 8.93781i) q^{92} +(-23.2856 - 13.4439i) q^{95} +(-7.04060 - 6.81395i) q^{96} -9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4}+O(q^{10}) \) 16 * q + 16 * q^4	\( 16 q + 16 q^{4} - 16 q^{15} - 32 q^{16} - 16 q^{18} + 72 q^{23} + 40 q^{25} + 32 q^{30} - 40 q^{39} - 56 q^{49} - 144 q^{50} + 8 q^{57} - 16 q^{60} + 56 q^{63} - 128 q^{64} - 72 q^{65} - 64 q^{72} + 128 q^{78} + 80 q^{81} + 144 q^{92}+O(q^{100}) \) 16 * q + 16 * q^4 - 16 * q^15 - 32 * q^16 - 16 * q^18 + 72 * q^23 + 40 * q^25 + 32 * q^30 - 40 * q^39 - 56 * q^49 - 144 * q^50 + 8 * q^57 - 16 * q^60 + 56 * q^63 - 128 * q^64 - 72 * q^65 - 64 * q^72 + 128 * q^78 + 80 * q^81 + 144 * q^92

Introduction

L-functions

Modular forms

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Database

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