LMFDB - Embedded newform 504.2.cc.a.293.6

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			293.6
Root			$-1.66548 - 0.475594i$ of defining polynomial
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.a.461.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.420861 + 1.68014i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.99323 - 1.15079i) q^{5} +(0.672592 + 2.35534i) q^{6} +(-1.32288 - 2.29129i) q^{7} -2.82843i q^{8} +(-2.64575 - 1.41421i) q^{9} -3.25493 q^{10} +(2.48923 + 2.40909i) q^{12} +(2.79694 - 4.84444i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(2.77237 - 2.86458i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-4.24037 + 0.138778i) q^{18} -5.17960 q^{19} +(-3.98646 + 2.30158i) q^{20} +(4.40644 - 1.25830i) q^{21} +(7.74037 + 4.46890i) q^{23} +(4.75216 + 1.19038i) q^{24} +(0.148641 + 0.257454i) q^{25} -7.91094i q^{26} +(3.48957 - 3.85005i) q^{27} -5.29150 q^{28} +(1.36987 - 5.46874i) q^{30} +(-4.89898 - 2.82843i) q^{32} +6.08941i q^{35} +(-5.09524 + 3.16836i) q^{36} +(-6.34368 + 3.66253i) q^{38} +(6.96223 + 6.73809i) q^{39} +(-3.25493 + 5.63770i) q^{40} +(4.50700 - 4.65692i) q^{42} +(3.64612 + 5.86356i) q^{45} +12.6400 q^{46} +(6.66190 - 1.90238i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(0.364095 + 0.210210i) q^{50} +(-5.59388 - 9.68889i) q^{52} +(1.55144 - 7.18283i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(2.17989 - 8.70245i) q^{57} +(12.4887 + 7.21033i) q^{59} +(-2.18924 - 7.66646i) q^{60} +(-6.89566 - 11.9436i) q^{61} +(0.259630 + 7.93301i) q^{63} -8.00000 q^{64} +(-11.1499 + 6.43739i) q^{65} +(-10.7660 + 11.1241i) q^{69} +(4.30587 + 7.45798i) q^{70} -10.9193i q^{71} +(-4.00000 + 7.48331i) q^{72} +(-0.495116 + 0.141386i) q^{75} +(-5.17960 + 8.97132i) q^{76} +(13.2915 + 3.32941i) q^{78} +(8.67134 + 15.0192i) q^{79} +9.20633i q^{80} +(5.00000 + 7.48331i) q^{81} +(-1.21349 + 0.700610i) q^{83} +(2.22699 - 8.89047i) q^{84} +(8.61173 + 4.60317i) q^{90} -14.8000 q^{91} +(15.4807 - 8.93781i) q^{92} +(10.3241 + 5.96063i) q^{95} +(6.81395 - 7.04060i) q^{96} +9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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
$3$	−0.420861	+	1.68014i	−0.242984	+	0.970030i
$3$	−0.420861	+	1.68014i	−0.242984	+	0.970030i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−1.99323	−	1.15079i	−0.891399	−	0.514649i	−0.0169992	−	0.999856i	$-0.505411\pi$
$5$	−1.99323	−	1.15079i	−0.891399	−	0.514649i	−0.874400	+	0.485206i	$0.838745\pi$
$6$	0.672592	+	2.35534i	0.274584	+	0.961563i
$7$	−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
$10$	−3.25493			−1.02930
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	2.48923	+	2.40909i	0.718579	+	0.695446i
$13$	2.79694	−	4.84444i	0.775732	−	1.34361i	−0.158651	−	0.987335i	$-0.550714\pi$
$13$	2.79694	−	4.84444i	0.775732	−	1.34361i	0.934382	−	0.356272i	$-0.115952\pi$
$14$	−3.24037	−	1.87083i	−0.866025	−	0.500000i
$15$	2.77237	−	2.86458i	0.715822	−	0.739632i
$16$	−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
$19$	−5.17960			−1.18828			−0.594140	−	0.804361i	$-0.702508\pi$
$19$	−5.17960			−1.18828			−0.594140	+	0.804361i	$0.702508\pi$
$20$	−3.98646	+	2.30158i	−0.891399	+	0.514649i
$21$	4.40644	−	1.25830i	0.961563	−	0.274584i
$22$		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	$0.284877\pi$
$24$	4.75216	+	1.19038i	0.970030	+	0.242984i
$25$	0.148641	+	0.257454i	0.0297282	+	0.0514908i
$26$		−	7.91094i		−	1.55146i
$27$	3.48957	−	3.85005i	0.671569	−	0.740942i
$28$	−5.29150			−1.00000
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	1.36987	−	5.46874i	0.250104	−	0.998451i
$31$		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
$35$			6.08941i			1.02930i
$36$	−5.09524	+	3.16836i	−0.849207	+	0.528060i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−6.34368	+	3.66253i	−1.02908	+	0.594140i
$39$	6.96223	+	6.73809i	1.11485	+	1.07896i
$40$	−3.25493	+	5.63770i	−0.514649	+	0.891399i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$	4.50700	−	4.65692i	0.695446	−	0.718579i
$43$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$43$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$44$		0			0
$45$	3.64612	+	5.86356i	0.543532	+	0.874088i
$46$	12.6400			1.86366
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	6.66190	−	1.90238i	0.961563	−	0.274584i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	0.364095	+	0.210210i	0.0514908	+	0.0297282i
$51$		0			0
$52$	−5.59388	−	9.68889i	−0.775732	−	1.34361i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	1.55144	−	7.18283i	0.211124	−	0.977459i
$55$		0			0
$56$	−6.48074	+	3.74166i	−0.866025	+	0.500000i
$57$	2.17989	−	8.70245i	0.288734	−	1.15267i
$58$		0			0
$59$	12.4887	+	7.21033i	1.62589	+	0.938705i	0.985303	+	0.170816i	$0.0546403\pi$
$59$	12.4887	+	7.21033i	1.62589	+	0.938705i	0.640582	+	0.767890i	$0.278693\pi$
$60$	−2.18924	−	7.66646i	−0.282629	−	0.989736i
$61$	−6.89566	−	11.9436i	−0.882899	−	1.52923i	−0.848103	−	0.529832i	$-0.822255\pi$
$61$	−6.89566	−	11.9436i	−0.882899	−	1.52923i	−0.0347968	−	0.999394i	$-0.511078\pi$
$62$		0			0
$63$	0.259630	+	7.93301i	0.0327103	+	0.999465i
$64$	−8.00000			−1.00000
$65$	−11.1499	+	6.43739i	−1.38297	+	0.798460i
$66$		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
$69$	−10.7660	+	11.1241i	−1.29608	+	1.33919i
$70$	4.30587	+	7.45798i	0.514649	+	0.891399i
$71$		−	10.9193i		−	1.29588i	−0.761690	−	0.647941i	$-0.775630\pi$
$71$		−	10.9193i		−	1.29588i	0.761690	−	0.647941i	$-0.224370\pi$
$72$	−4.00000	+	7.48331i	−0.471405	+	0.881917i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−0.495116	+	0.141386i	−0.0571711	+	0.0163258i
$76$	−5.17960	+	8.97132i	−0.594140	+	1.02908i
$77$		0			0
$78$	13.2915	+	3.32941i	1.50497	+	0.376981i
$79$	8.67134	+	15.0192i	0.975603	+	1.68979i	0.677932	+	0.735124i	$0.262876\pi$
$79$	8.67134	+	15.0192i	0.975603	+	1.68979i	0.297670	+	0.954669i	$0.403790\pi$
$80$			9.20633i			1.02930i
$81$	5.00000	+	7.48331i	0.555556	+	0.831479i
$82$		0			0
$83$	−1.21349	+	0.700610i	−0.133198	+	0.0769020i	−0.565118	−	0.825010i	$-0.691170\pi$
$83$	−1.21349	+	0.700610i	−0.133198	+	0.0769020i	0.431920	+	0.901912i	$0.357836\pi$
$84$	2.22699	−	8.89047i	0.242984	−	0.970030i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	8.61173	+	4.60317i	0.907756	+	0.485216i
$91$	−14.8000			−1.55146
$92$	15.4807	−	8.93781i	1.61398	−	0.931831i
$93$		0			0
$94$		0			0
$95$	10.3241	+	5.96063i	1.05923	+	0.611548i
$96$	6.81395	−	7.04060i	0.695446	−	0.718579i
$97$		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
$100$	0.594564			0.0594564
$101$	1.07010	−	0.617820i	0.106478	−	0.0614754i	−0.445815	−	0.895125i	$-0.647086\pi$
$101$	1.07010	−	0.617820i	0.106478	−	0.0614754i	0.552294	+	0.833650i	$0.313753\pi$
$102$		0			0
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	−13.7022	−	7.91094i	−1.34361	−	0.775732i
$105$	−10.2311	−	2.56280i	−0.998451	−	0.250104i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−3.17891	−	9.89417i	−0.305890	−	0.952067i
$109$		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	0.746674	−	0.665190i	$-0.231650\pi$
$113$	5.78216	+	3.33833i	0.543940	+	0.314044i	−0.202735	+	0.979234i	$0.564983\pi$
$114$	−3.48375	−	12.1997i	−0.326283	−	1.14261i
$115$	−10.2856	−	17.8151i	−0.959133	−	1.66127i
$116$		0			0
$117$	−14.2511	+	8.86172i	−1.31751	+	0.819266i
$118$	20.3939			1.87741
$119$		0			0
$120$	−8.10226	−	7.84143i	−0.739632	−	0.715822i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−16.8909	−	9.75194i	−1.52923	−	0.882899i
$123$		0			0
$124$		0			0
$125$			10.8237i			0.968101i
$126$	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
$130$	−9.10384	+	15.7683i	−0.798460	+	1.38297i
$131$	17.9610	+	10.3698i	1.56926	+	0.906010i	0.996256	+	0.0864550i	$0.0275539\pi$
$131$	17.9610	+	10.3698i	1.56926	+	0.906010i	0.573000	+	0.819555i	$0.305779\pi$
$132$		0			0
$133$	6.85196	+	11.8679i	0.594140	+	1.02908i
$134$		0			0
$135$	−11.3861	+	3.65826i	−0.979961	+	0.314853i
$136$		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	$0.554127\pi$
$138$	−5.31968	+	21.2369i	−0.452841	+	1.80781i
$139$	11.7344	−	20.3245i	0.995295	−	1.72390i	0.413737	−	0.910396i	$-0.364223\pi$
$139$	11.7344	−	20.3245i	0.995295	−	1.72390i	0.581558	−	0.813505i	$-0.302443\pi$
$140$	10.5472	+	6.08941i	0.891399	+	0.514649i
$141$		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
$147$	−8.71230	−	8.43183i	−0.718579	−	0.695446i
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$	−0.506416	+	0.523261i	−0.0413487	+	0.0427241i
$151$	−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	$-0.633388\pi$
$152$			14.6501i			1.18828i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	18.6329	−	5.32083i	1.49183	−	0.426008i
$157$	12.0753	−	20.9150i	0.963711	−	1.66920i	0.250671	−	0.968072i	$-0.419349\pi$
$157$	12.0753	−	20.9150i	0.963711	−	1.66920i	0.713040	−	0.701123i	$-0.247318\pi$
$158$	21.2404	+	12.2631i	1.68979	+	0.975603i
$159$		0			0
$160$	6.50986	+	11.2754i	0.514649	+	0.891399i
$161$		−	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
$166$	−0.990812	+	1.71614i	−0.0769020	+	0.133198i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$	−3.55902	−	12.4633i	−0.274584	−	0.961563i
$169$	−9.14575	−	15.8409i	−0.703519	−	1.21853i
$170$		0			0
$171$	13.7039	+	7.32505i	1.04797	+	0.560161i
$172$		0			0
$173$	8.06457	−	4.65608i	0.613138	−	0.353995i	−0.161055	−	0.986945i	$-0.551490\pi$
$173$	8.06457	−	4.65608i	0.613138	−	0.353995i	0.774193	+	0.632950i	$0.218156\pi$
$174$		0			0
$175$	0.393267	−	0.681159i	0.0297282	−	0.0514908i
$176$		0			0
$177$	−17.3704	+	17.9482i	−1.30564	+	1.34907i
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	13.8021	−	0.451712i	1.02875	−	0.0336686i
$181$	26.7236			1.98635			0.993176	−	0.116623i	$-0.0372071\pi$
$181$	26.7236			1.98635			0.993176	+	0.116623i	$0.0372071\pi$
$182$	−18.1262	+	10.4652i	−1.34361	+	0.775732i
$183$	22.9691	−	6.55907i	1.69793	−	0.484861i
$184$	12.6400	−	21.8931i	0.931831	−	1.61398i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−13.4378	−	2.90248i	−0.977459	−	0.211124i
$190$	16.8592			1.22310
$191$	−2.10792	+	1.21701i	−0.152524	+	0.0880597i	−0.574320	−	0.818631i	$-0.694733\pi$
$191$	−2.10792	+	1.21701i	−0.152524	+	0.0880597i	0.421796	+	0.906691i	$0.361400\pi$
$192$	3.36689	−	13.4411i	0.242984	−	0.970030i
$193$	−10.2886	+	17.8204i	−0.740591	+	1.28274i	0.211636	+	0.977349i	$0.432121\pi$
$193$	−10.2886	+	17.8204i	−0.740591	+	1.28274i	−0.952227	+	0.305392i	$0.901213\pi$
$194$		0			0
$195$	−6.12317	−	21.4426i	−0.438489	−	1.53554i
$196$	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			$\pi$
$200$	0.728189	−	0.420420i	0.0514908	−	0.0297282i
$201$		0			0
$202$	0.873729	−	1.51334i	0.0614754	−	0.106478i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−14.1591	−	22.7701i	−0.984126	−	1.58263i
$208$	−22.3755			−1.55146
$209$		0			0
$210$	−14.3426	+	4.09569i	−0.989736	+	0.282629i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	18.3460	+	4.59551i	1.25705	+	0.314879i
$214$		0			0
$215$		0			0
$216$	−10.8896	−	9.87000i	−0.740942	−	0.671569i
$217$		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
$225$	−0.0291725	−	0.891369i	−0.00194483	−	0.0594246i
$226$	9.44222			0.628087
$227$	−22.7635	+	13.1425i	−1.51087	+	0.872299i	−0.510947	+	0.859612i	$0.670705\pi$
$227$	−22.7635	+	13.1425i	−1.51087	+	0.872299i	−0.999920	+	0.0126866i	$0.995962\pi$
$228$	−12.8932	−	12.4781i	−0.853873	−	0.826385i
$229$	−3.59703	+	6.23024i	−0.237699	+	0.411706i	−0.960053	−	0.279817i	$-0.909726\pi$
$229$	−3.59703	+	6.23024i	−0.237699	+	0.411706i	0.722355	+	0.691522i	$0.243060\pi$
$230$	−25.1944	−	14.5460i	−1.66127	−	0.959133i
$231$		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	$-0.229636\pi$
$234$	−11.1878	+	20.9304i	−0.731367	+	1.36826i
$235$		0			0
$236$	24.9773	−	14.4207i	1.62589	−	0.938705i
$237$	−28.8838	+	8.24808i	−1.87621	+	0.535770i
$238$		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	$0.922188\pi$
$240$	−15.4679	−	3.87459i	−0.998451	−	0.250104i
$241$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$241$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$242$		−	15.5563i		−	1.00000i
$243$	−14.6773	+	5.25127i	−0.941551	+	0.336869i
$244$	−27.5827			−1.76580
$245$	13.9526	−	8.05554i	0.891399	−	0.514649i
$246$		0			0
$247$	−14.4870	+	25.0923i	−0.921787	+	1.59658i
$248$		0			0
$249$	−0.666412	−	2.33370i	−0.0422322	−	0.147892i
$250$	7.65351	+	13.2563i	0.484050	+	0.838400i
$251$			30.8882i			1.94964i	0.222982	+	0.974822i	$0.428421\pi$
$251$			30.8882i			1.94964i	−0.222982	+	0.974822i	$0.571579\pi$
$252$	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
$260$			25.7496i			1.59692i
$261$		0			0
$262$	29.3301			1.81202
$263$	−24.1533	+	13.9449i	−1.48936	+	0.859881i	−0.999926	−	0.0121601i	$-0.996129\pi$
$263$	−24.1533	+	13.9449i	−1.48936	+	0.859881i	−0.489432	+	0.872041i	$0.662796\pi$
$264$		0			0
$265$		0			0
$266$	16.7838	+	9.69014i	1.02908	+	0.594140i
$267$		0			0
$268$		0			0
$269$		−	25.5933i		−	1.56045i	−0.625498	−	0.780225i	$-0.715104\pi$
$269$		−	25.5933i		−	1.56045i	0.625498	−	0.780225i	$-0.284896\pi$
$270$	−11.3583	+	12.5316i	−0.691245	+	0.762651i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	6.22876	−	24.8661i	0.376981	−	1.50497i
$274$	−10.5830	+	18.3303i	−0.639343	+	1.10737i
$275$		0			0
$276$	8.50154	+	29.7714i	0.511733	+	1.79203i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		−	33.1898i		−	1.99059i
$279$		0			0
$280$	17.2235			1.02930
$281$	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
$283$	−16.3811	+	28.3729i	−0.973757	+	1.68660i	−0.289779	+	0.957094i	$0.593582\pi$
$283$	−16.3811	+	28.3729i	−0.973757	+	1.68660i	−0.683978	+	0.729503i	$0.739751\pi$
$284$	−18.9128	−	10.9193i	−1.12227	−	0.647941i
$285$	−14.3597	+	14.8374i	−0.850597	+	0.878891i
$286$		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
$293$	−24.3046	−	14.0323i	−1.41989	−	0.819775i	−0.423603	−	0.905848i	$-0.639235\pi$
$293$	−24.3046	−	14.0323i	−1.41989	−	0.819775i	−0.996289	+	0.0860728i	$0.972568\pi$
$294$	−16.6326	−	4.16632i	−0.970030	−	0.242984i
$295$	−16.5952	−	28.7437i	−0.966208	−	1.67352i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	43.2987	−	24.9985i	2.50403	−	1.44570i
$300$	−0.250229	+	0.998952i	−0.0144470	+	0.0576745i
$301$		0			0
$302$	−29.9355	−	17.2833i	−1.72259	−	0.994540i
$303$	0.587663	+	2.05793i	0.0337603	+	0.118225i
$304$	10.3592	+	17.9426i	0.594140	+	1.02908i
$305$			31.7419i			1.81753i
$306$		0			0
$307$	−3.93913			−0.224818			−0.112409	−	0.993662i	$-0.535857\pi$
$307$	−3.93913			−0.224818			−0.112409	+	0.993662i	$0.535857\pi$
$308$		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	$0.166667\pi$
$312$	19.0582	−	19.6921i	1.07896	−	1.11485i
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$		−	34.1540i		−	1.92742i
$315$	8.61173	−	16.1111i	0.485216	−	0.907756i
$316$	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
$320$	15.9458	+	9.20633i	0.891399	+	0.514649i
$321$		0			0
$322$	−16.7211	−	28.9618i	−0.931831	−	1.61398i
$323$		0			0
$324$	17.9615	−	1.17694i	0.997860	−	0.0653855i
$325$	1.66296			0.0922445
$326$		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	$0.333333\pi$
$332$			2.80244i			0.153804i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−13.1718	−	12.7477i	−0.718579	−	0.695446i
$337$	13.2288	−	22.9129i	0.720616	−	1.24814i	−0.240137	−	0.970739i	$-0.577192\pi$
$337$	13.2288	−	22.9129i	0.720616	−	1.24814i	0.960753	−	0.277405i	$-0.0894744\pi$
$338$	−22.4024	−	12.9340i	−1.21853	−	0.703519i
$339$	−8.04235	+	8.30987i	−0.436801	+	0.451330i
$340$		0			0
$341$		0			0
$342$	21.9634	−	0.718813i	1.18764	−	0.0388690i
$343$	18.5203			1.00000
$344$		0			0
$345$	34.2607	−	9.78350i	1.84453	−	0.526726i
$346$	6.58469	−	11.4050i	0.353995	−	0.613138i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	12.0031	+	20.7899i	0.642510	+	1.11286i	0.984871	+	0.173291i	$0.0554402\pi$
$349$	12.0031	+	20.7899i	0.642510	+	1.11286i	−0.342361	+	0.939569i	$0.611226\pi$
$350$		−	1.11233i		−	0.0594564i
$351$	−8.89121	−	27.6734i	−0.474578	−	1.47710i
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$	−8.58301	+	34.2646i	−0.456182	+	1.82114i
$355$	−12.5658	+	21.7647i	−0.666925	+	1.15515i
$356$		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	$0.883946\pi$
$360$	16.5846	−	10.3128i	0.874088	−	0.543532i
$361$	7.82821			0.412011
$362$	32.7296	−	18.8965i	1.72023	−	0.993176i
$363$	13.6908	+	13.2500i	0.718579	+	0.695446i
$364$	−14.8000	+	25.6344i	−0.775732	+	1.34361i
$365$		0			0
$366$	23.4934	−	24.2748i	1.22802	−	1.26887i
$367$		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
$375$	−18.1853	−	4.55528i	−0.939087	−	0.235233i
$376$		0			0
$377$		0			0
$378$	−18.5103	+	5.94719i	−0.952067	+	0.305890i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	20.6482	−	11.9213i	1.05923	−	0.611548i
$381$	−7.76162	+	30.9855i	−0.397640	+	1.58744i
$382$	−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	$0.166667\pi$
$384$	−5.38073	−	18.8427i	−0.274584	−	0.961563i
$385$		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	$0.833333\pi$
$390$	−22.6616	−	21.9320i	−1.14751	−	1.11057i
$391$		0			0
$392$	17.1464	+	9.89949i	0.866025	+	0.500000i
$393$	−24.9817	+	25.8127i	−1.26016	+	1.30208i
$394$		0			0
$395$		−	39.9156i		−	2.00837i
$396$		0			0
$397$	12.8184			0.643337			0.321668	−	0.946852i	$-0.395756\pi$
$397$	12.8184			0.643337			0.321668	+	0.946852i	$0.395756\pi$
$398$		0			0
$399$	−22.8236	+	6.51750i	−1.14261	+	0.326283i
$400$	0.594564	−	1.02982i	0.0297282	−	0.0514908i
$401$	27.8276	+	16.0663i	1.38964	+	0.802310i	0.993275	−	0.115782i	$-0.0369373\pi$
$401$	27.8276	+	16.0663i	1.38964	+	0.802310i	0.396368	+	0.918092i	$0.370271\pi$
$402$		0			0
$403$		0			0
$404$		−	2.47128i		−	0.122951i
$405$	−1.35441	−	20.6699i	−0.0673012	−	1.02710i
$406$		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
$411$	−7.11804	−	24.9266i	−0.351107	−	1.22954i
$412$		0			0
$413$		−	38.1535i		−	1.87741i
$414$	−33.4422	−	17.8756i	−1.64360	−	0.878539i
$415$	3.22502			0.158310
$416$	−27.4043	+	15.8219i	−1.34361	+	0.775732i
$417$	29.2095	+	28.2692i	1.43040	+	1.38435i
$418$		0			0
$419$	34.7229	+	20.0473i	1.69632	+	0.979373i	0.949193	+	0.314695i	$0.101902\pi$
$419$	34.7229	+	20.0473i	1.69632	+	0.979373i	0.747130	+	0.664678i	$0.231431\pi$
$420$	−14.6700	+	15.1579i	−0.715822	+	0.739632i
$421$		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
$426$	25.7187	−	7.34423i	1.24607	−	0.355829i
$427$	−18.2442	+	31.5999i	−0.882899	+	1.52923i
$428$		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	$-0.357273\pi$
$432$	−20.3161	−	4.38814i	−0.977459	−	0.211124i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−40.0920	−	23.1471i	−1.91786	−	1.10728i
$438$		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	$0.916312\pi$
$450$	−0.666022	−	1.07107i	−0.0313966	−	0.0504908i
$451$		0			0
$452$	11.5643	−	6.67666i	0.543940	−	0.314044i
$453$	40.7079	−	11.6246i	1.91263	−	0.546170i
$454$	−18.5863	+	32.1924i	−0.872299	+	1.51087i
$455$	29.4998	+	17.0317i	1.38297	+	0.798460i
$456$	−24.6143	−	6.16567i	−1.15267	−	0.288734i
$457$	19.6940	+	34.1111i	0.921249	+	1.59565i	0.797486	+	0.603338i	$0.206163\pi$
$457$	19.6940	+	34.1111i	0.921249	+	1.59565i	0.123763	+	0.992312i	$0.460504\pi$
$458$			10.1739i			0.475397i
$459$		0			0
$460$	−41.1422			−1.91827
$461$	−13.7575	+	7.94287i	−0.640749	+	0.369937i	−0.784903	−	0.619619i	$-0.787287\pi$
$461$	−13.7575	+	7.94287i	−0.640749	+	0.369937i	0.144154	+	0.989555i	$0.453954\pi$
$462$		0			0
$463$	−21.3113	+	36.9123i	−0.990421	+	1.71546i	−0.375628	+	0.926770i	$0.622573\pi$
$463$	−21.3113	+	36.9123i	−0.990421	+	1.71546i	−0.614792	+	0.788689i	$0.710760\pi$
$464$		0			0
$465$		0			0
$466$	−14.2572	−	24.6943i	−0.660454	−	1.14394i
$467$			11.6182i			0.537627i	0.963192	+	0.268814i	$0.0866316\pi$
$467$			11.6182i			0.537627i	−0.963192	+	0.268814i	$0.913368\pi$
$468$	1.09786	+	33.5453i	0.0507488	+	1.55063i
$469$		0			0
$470$		0			0
$471$	30.0581	+	29.0904i	1.38500	+	1.34042i
$472$	20.3939	−	35.3233i	0.938705	−	1.62589i
$473$		0			0
$474$	−29.5431	+	30.5257i	−1.35696	+	1.40209i
$475$	−0.769900	−	1.33351i	−0.0353255	−	0.0611855i
$476$		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	$0.833333\pi$
$480$	−21.6840	+	6.19210i	−0.989736	+	0.282629i
$481$		0			0
$482$		0			0
$483$	39.7307	+	9.95220i	1.80781	+	0.452841i
$484$	−11.0000	−	19.0526i	−0.500000	−	0.866025i
$485$		0			0
$486$	−14.2628	+	16.8099i	−0.646973	+	0.762513i
$487$	0.442222			0.0200390			0.0100195	−	0.999950i	$-0.496811\pi$
$487$	0.442222			0.0200390			0.0100195	+	0.999950i	$0.496811\pi$
$488$	−33.7817	+	19.5039i	−1.52923	+	0.882899i
$489$		0			0
$490$	11.3923	−	19.7320i	0.514649	−	0.891399i
$491$		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
$494$			40.9755i			1.84357i
$495$		0			0
$496$		0			0
$497$	−25.0193	+	14.4449i	−1.12227	+	0.647941i
$498$	−2.46636	−	2.38696i	−0.110520	−	0.106962i
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	18.7472	+	10.8237i	0.838400	+	0.484050i
$501$		0			0
$502$	21.8412	+	37.8301i	0.974822	+	1.68844i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	22.4379	−	0.734344i	0.999465	−	0.0327103i
$505$	−2.84393			−0.126553
$506$		0			0
$507$	30.4641	−	8.69933i	1.35296	−	0.386351i
$508$	18.4422	−	31.9429i	0.818241	−	1.41724i
$509$	21.7667	+	12.5670i	0.964793	+	0.557024i	0.897645	−	0.440719i	$-0.145277\pi$
$509$	21.7667	+	12.5670i	0.964793	+	0.557024i	0.0671482	+	0.997743i	$0.478610\pi$
$510$		0			0
$511$		0			0
$512$			22.6274i			1.00000i
$513$	−18.0746	+	19.9417i	−0.798012	+	0.880447i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	4.42881	+	15.5092i	0.194403	+	0.680778i
$520$	18.2077	+	31.5366i	0.798460	+	1.38297i
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	−2.57072			−0.112410			−0.0562050	−	0.998419i	$-0.517900\pi$
$523$	−2.57072			−0.112410			−0.0562050	+	0.998419i	$0.517900\pi$
$524$	35.9219	−	20.7395i	1.56926	−	0.906010i
$525$	0.978932	+	0.947418i	0.0427241	+	0.0413487i
$526$	−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
$531$	−22.8449	−	36.7384i	−0.991386	−	1.59431i
$532$	27.4078			1.18828
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−18.0972	−	31.3453i	−0.780225	−	1.35139i
$539$		0			0
$540$	−5.04983	+	23.3796i	−0.217310	+	1.00610i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−11.2469	+	44.8995i	−0.482653	+	1.92682i
$544$		0			0
$545$		0			0
$546$	−9.95437	−	34.8591i	−0.426008	−	1.49183i
$547$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$547$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$548$			29.9333i			1.27869i
$549$	1.35335	+	41.3518i	0.0577597	+	1.76485i
$550$		0			0
$551$		0			0
$552$	31.4638	+	30.4509i	1.33919	+	1.29608i
$553$	22.9422	−	39.7371i	0.975603	−	1.68979i
$554$		0			0
$555$		0			0
$556$	−23.4687	−	40.6490i	−0.995295	−	1.72390i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$	21.0944	−	12.1788i	0.891399	−	0.514649i
$561$		0			0
$562$	23.6627	−	40.9850i	0.998150	−	1.72885i
$563$	−38.7093	−	22.3488i	−1.63140	−	0.941891i	−0.983661	−	0.180032i	$-0.942380\pi$
$563$	−38.7093	−	22.3488i	−1.63140	−	0.941891i	−0.647743	−	0.761859i	$-0.724287\pi$
$564$		0			0
$565$	−7.68344	−	13.3081i	−0.323245	−	0.559876i
$566$			46.3328i			1.94751i
$567$	10.5320	−	21.3559i	0.442305	−	0.896865i
$568$	−30.8844			−1.29588
$569$	2.44949	−	1.41421i	0.102688	−	0.0592869i	−0.447777	−	0.894146i	$-0.647784\pi$
$569$	2.44949	−	1.41421i	0.102688	−	0.0592869i	0.550464	+	0.834859i	$0.314451\pi$
$570$	−7.09539	+	28.3259i	−0.297193	+	1.18644i
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$	−1.15760	−	4.05380i	−0.0483596	−	0.169350i
$574$		0			0
$575$			2.65705i			0.110807i
$576$	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
$579$	−25.6107	−	24.7862i	−1.06434	−	1.03008i
$580$		0			0
$581$	3.21060	+	1.85364i	0.133198	+	0.0769020i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	38.6037	−	1.26341i	1.59607	−	0.0522357i
$586$	−39.6893			−1.63955
$587$	−41.1955	+	23.7842i	−1.70032	+	0.981680i	−0.754892	+	0.655849i	$0.772311\pi$
$587$	−41.1955	+	23.7842i	−1.70032	+	0.981680i	−0.945428	+	0.325831i	$0.894356\pi$
$588$	−23.3167	+	6.65832i	−0.961563	+	0.274584i
$589$		0			0
$590$	−40.6497	−	23.4691i	−1.67352	−	0.966208i
$591$		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
$598$	35.3532	−	61.2336i	1.44570	−	2.50403i
$599$	−9.79796	−	5.65685i	−0.400334	−	0.231133i	0.286294	−	0.958142i	$-0.407577\pi$
$599$	−9.79796	−	5.65685i	−0.400334	−	0.231133i	−0.686628	+	0.727009i	$0.740910\pi$
$600$	0.399899	+	1.40040i	0.0163258	+	0.0571711i
$601$		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
$605$	−21.9255	+	12.6587i	−0.891399	+	0.514649i
$606$	2.17491	+	2.10490i	0.0883497	+	0.0855056i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	25.3747	+	14.6501i	1.02908	+	0.594140i
$609$		0			0
$610$	22.4449	+	38.8757i	0.908767	+	1.57403i
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	−4.82443	+	2.78539i	−0.194698	+	0.112409i
$615$		0			0
$616$		0			0
$617$	12.2474	+	7.07107i	0.493064	+	0.284670i	0.725845	−	0.687859i	$-0.241449\pi$
$617$	12.2474	+	7.07107i	0.493064	+	0.284670i	−0.232781	+	0.972529i	$0.574782\pi$
$618$		0			0
$619$	−0.842340	−	1.45898i	−0.0338565	−	0.0586412i	0.848601	−	0.529034i	$-0.177446\pi$
$619$	−0.842340	−	1.45898i	−0.0338565	−	0.0586412i	−0.882457	+	0.470393i	$0.844112\pi$
$620$		0			0
$621$	44.2161	−	14.2062i	1.77433	−	0.570076i
$622$		0			0
$623$		0			0
$624$	9.41699	−	37.5940i	0.376981	−	1.50497i
$625$	13.1990	−	22.8614i	0.527961	−	0.914455i
$626$		0			0
$627$		0			0
$628$	−24.1505	−	41.8299i	−0.963711	−	1.66920i
$629$		0			0
$630$	−0.845076	−	25.8214i	−0.0336686	−	1.02875i
$631$	10.8736			0.432872			0.216436	−	0.976297i	$-0.430557\pi$
$631$	10.8736			0.432872			0.216436	+	0.976297i	$0.430557\pi$
$632$	42.4807	−	24.5263i	1.68979	−	0.975603i
$633$		0			0
$634$		0			0
$635$	−36.7596	−	21.2231i	−1.45876	−	0.842215i
$636$		0			0
$637$	19.5786	+	33.9111i	0.775732	+	1.34361i
$638$		0			0
$639$	−15.4422	+	28.8898i	−0.610885	+	1.14286i
$640$	26.0394			1.02930
$641$	8.91478	−	5.14695i	0.352113	−	0.203292i	−0.313503	−	0.949587i	$-0.601502\pi$
$641$	8.91478	−	5.14695i	0.352113	−	0.203292i	0.665615	+	0.746295i	$0.268169\pi$
$642$		0			0
$643$	24.1817	−	41.8838i	0.953631	−	1.65174i	0.216161	−	0.976358i	$-0.430646\pi$
$643$	24.1817	−	41.8838i	0.953631	−	1.65174i	0.737470	−	0.675380i	$-0.236020\pi$
$644$	−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
$650$	2.03670	−	1.17589i	0.0798860	−	0.0461222i
$651$		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
$655$	−23.8669	−	41.3386i	−0.932555	−	1.61523i
$656$		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
$661$	−2.91283	+	5.04516i	−0.113296	+	0.196234i	−0.917097	−	0.398664i	$-0.869474\pi$
$661$	−2.91283	+	5.04516i	−0.113296	+	0.196234i	0.803801	+	0.594898i	$0.202807\pi$
$662$		0			0
$663$		0			0
$664$	1.98162	+	3.43228i	0.0769020	+	0.133198i
$665$		−	31.5407i		−	1.22310i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−25.1461	−	6.29888i	−0.970030	−	0.242984i
$673$	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
$675$	1.50990	+	0.326129i	0.0581162	+	0.0125527i
$676$	−36.5830			−1.40704
$677$	−44.3171	+	25.5865i	−1.70324	+	0.983368i	−0.760809	+	0.648976i	$0.775198\pi$
$677$	−44.3171	+	25.5865i	−1.70324	+	0.983368i	−0.942434	+	0.334392i	$0.891469\pi$
$678$	−3.97387	+	15.8643i	−0.152615	+	0.609264i
$679$		0			0
$680$		0			0
$681$	−12.5010	−	43.7771i	−0.479039	−	1.67754i
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$	26.3913	−	16.4108i	1.00910	−	0.627484i
$685$	34.4469			1.31615
$686$	22.6826	−	13.0958i	0.866025	−	0.500000i
$687$	−8.95384	−	8.66559i	−0.341610	−	0.330613i
$688$		0			0
$689$		0			0
$690$	35.0426	−	36.2082i	1.33405	−	1.37842i
$691$	21.4991	+	37.2376i	0.817866	+	1.41659i	0.907252	+	0.420588i	$0.138176\pi$
$691$	21.4991	+	37.2376i	0.817866	+	1.41659i	−0.0893857	+	0.995997i	$0.528490\pi$
$692$		−	18.6243i		−	0.707991i
$693$		0			0
$694$		0			0
$695$	−46.7785	+	27.0076i	−1.77441	+	1.02446i
$696$		0			0
$697$		0			0
$698$	29.4014	+	16.9749i	1.11286	+	0.642510i
$699$	33.8763	+	8.48574i	1.28132	+	0.320960i
$700$	−0.786534	−	1.36232i	−0.0297282	−	0.0514908i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−30.4575	−	27.6058i	−1.14954	−	1.04191i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.83121	−	1.63460i	−0.106478	−	0.0614754i
$708$	13.7168	+	48.0345i	0.515508	+	1.80525i
$709$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$709$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$710$			35.5415i			1.33385i
$711$	−1.70185	−	52.0002i	−0.0638244	−	1.95016i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	26.7881	−	27.6791i	1.00042	−	1.03370i
$718$	9.55452	+	16.5489i	0.356572	+	0.617600i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	13.0197	−	24.3577i	0.485216	−	0.907756i
$721$		0			0
$722$	9.58756	−	5.53538i	0.356812	−	0.206006i
$723$		0			0
$724$	26.7236	−	46.2867i	0.993176	−	1.72023i
$725$		0			0
$726$	26.1369	+	6.54707i	0.970030	+	0.242984i
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$			41.8608i			1.55146i
$729$	−2.64575	−	26.8701i	−0.0979908	−	0.995187i
$730$		0			0
$731$		0			0
$732$	11.6085	−	46.3428i	0.429062	−	1.71288i
$733$	−10.3278	+	17.8883i	−0.381466	+	0.660719i	−0.991272	−	0.131832i	$-0.957914\pi$
$733$	−10.3278	+	17.8883i	−0.381466	+	0.660719i	0.609806	+	0.792551i	$0.291247\pi$
$734$		0			0
$735$	7.66233	+	26.8326i	0.282629	+	0.989736i
$736$	−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
$741$	−36.0615	−	34.9006i	−1.32475	−	1.28211i
$742$		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
$747$	4.20141	−	0.137503i	0.153722	−	0.00503097i
$748$		0			0
$749$		0			0
$750$	−25.4935	+	7.27993i	−0.930890	+	0.265825i
$751$	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
$753$	−51.8965	−	12.9996i	−1.89121	−	0.473733i
$754$		0			0
$755$			56.2558i			2.04736i
$756$	−18.4651	+	20.3725i	−0.671569	+	0.740942i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	16.8592	−	29.2010i	0.611548	−	1.05923i
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$	12.4041	+	43.4377i	0.449353	+	1.57358i
$763$		0			0
$764$			4.86804i			0.176119i
$765$		0			0
$766$		0			0
$767$	69.8601	−	40.3337i	2.52250	−	1.45637i
$768$	−19.9138	−	19.2728i	−0.718579	−	0.695446i
$769$		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
$773$			37.7721i			1.35857i	0.733875	+	0.679285i	$0.237710\pi$
$773$			37.7721i			1.35857i	−0.733875	+	0.679285i	$0.762290\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−43.2629	−	10.8370i	−1.54906	−	0.388027i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	28.0000			1.00000
$785$	−48.1375	+	27.7922i	−1.71810	+	0.991946i
$786$	−12.3439	+	49.2787i	−0.440293	+	1.75771i
$787$	16.6061	−	28.7627i	0.591945	−	1.02528i	−0.402025	−	0.915629i	$-0.631694\pi$
$787$	16.6061	−	28.7627i	0.591945	−	1.02528i	0.993970	−	0.109650i	$-0.0349731\pi$
$788$		0			0
$789$	−13.2643	−	46.4499i	−0.472220	−	1.65366i
$790$	−28.2246	−	48.8865i	−1.00419	−	1.73930i
$791$		−	17.6648i		−	0.628087i
$792$		0			0
$793$	−77.1470			−2.73957
$794$	15.6993	−	9.06397i	0.557146	−	0.321668i
$795$		0			0
$796$		0			0
$797$	45.3990	+	26.2111i	1.60811	+	0.928445i	0.989792	+	0.142521i	$0.0455210\pi$
$797$	45.3990	+	26.2111i	1.60811	+	0.928445i	0.618323	+	0.785924i	$0.287812\pi$
$798$	−23.3445	+	24.1210i	−0.826385	+	0.853873i
$799$		0			0
$800$		−	1.68168i		−	0.0594564i
$801$		0			0
$802$	45.4422			1.60462
$803$		0			0
$804$		0			0
$805$	−27.2130	+	47.1343i	−0.959133	+	1.66127i
$806$		0			0
$807$	43.0004	+	10.7712i	1.51368	+	0.379165i
$808$	−1.74746	−	3.02669i	−0.0614754	−	0.106478i
$809$		−	31.1127i		−	1.09386i	−0.837177	−	0.546932i	$-0.815796\pi$
$809$		−	31.1127i		−	1.09386i	0.837177	−	0.546932i	$-0.184204\pi$
$810$	−16.2746	−	24.3577i	−0.571833	−	0.855841i
$811$	−29.9510			−1.05172			−0.525861	−	0.850570i	$-0.676257\pi$
$811$	−29.9510			−1.05172			−0.525861	+	0.850570i	$0.676257\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	39.1572	+	20.9304i	1.36826	+	0.731367i
$820$		0			0
$821$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$821$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$822$	−26.3435	−	25.4955i	−0.918836	−	0.889256i
$823$	13.2288	−	22.9129i	0.461125	−	0.798693i	−0.537892	−	0.843014i	$-0.680779\pi$
$823$	13.2288	−	22.9129i	0.461125	−	0.798693i	0.999017	+	0.0443211i	$0.0141125\pi$
$824$		0			0
$825$		0			0
$826$	−26.9786	−	46.7283i	−0.938705	−	1.62589i
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	−53.5982	+	1.75415i	−1.86266	+	0.0609609i
$829$	−57.5694			−1.99947			−0.999735	−	0.0230361i	$-0.992667\pi$
$829$	−57.5694			−1.99947			−0.999735	+	0.0230361i	$0.992667\pi$
$830$	3.94983	−	2.28044i	0.137101	−	0.0791551i
$831$		0			0
$832$	−22.3755	+	38.7555i	−0.775732	+	1.34361i
$833$		0			0
$834$	55.7635	+	13.9683i	1.93093	+	0.483682i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	56.7022			1.95875
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$	−7.24869	+	28.9379i	−0.250104	+	0.998451i
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$		0			0
$843$	15.9153	+	55.7336i	0.548153	+	1.91957i
$844$		0			0
$845$			42.0994i			1.44826i
$846$		0			0
$847$	−29.1033			−1.00000
$848$		0			0
$849$	−40.7764	−	39.4637i	−1.39944	−	1.35439i
$850$		0			0
$851$		0			0
$852$	26.3056	−	27.1806i	0.901216	−	0.931193i
$853$	−23.1266	−	40.0565i	−0.791840	−	1.37151i	−0.924827	−	0.380389i	$-0.875790\pi$
$853$	−23.1266	−	40.0565i	−0.791840	−	1.37151i	0.132987	−	0.991118i	$-0.457543\pi$
$854$			51.6024i			1.76580i
$855$	−18.8854	−	30.3709i	−0.645869	−	1.03866i
$856$		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
$859$	−11.0123	+	19.0738i	−0.375734	+	0.650790i	−0.990437	−	0.137969i	$-0.955943\pi$
$859$	−11.0123	+	19.0738i	−0.375734	+	0.650790i	0.614703	+	0.788759i	$0.289276\pi$
$860$		0			0
$861$		0			0
$862$	−26.4575	−	45.8258i	−0.901146	−	1.56083i
$863$			14.5365i			0.494830i	0.968910	+	0.247415i	$0.0795811\pi$
$863$			14.5365i			0.494830i	−0.968910	+	0.247415i	$0.920419\pi$
$864$	−27.9849	+	8.99131i	−0.952067	+	0.305890i
$865$	−21.4327			−0.728734
$866$		0			0
$867$	7.15464	−	28.5624i	0.242984	−	0.970030i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−65.4699			−2.21455
$875$	24.8002	−	14.3184i	0.838400	−	0.484050i
$876$		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
$879$	33.8051	−	34.9296i	1.14022	−	1.17815i
$880$		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
$885$	55.2777	−	15.7851i	1.85814	−	0.530611i
$886$		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
$897$	23.7783	+	83.2689i	0.793934	+	2.78027i
$898$	7.78817	+	13.4895i	0.259895	+	0.450151i
$899$		0			0
$900$	−1.57307	−	0.840841i	−0.0524356	−	0.0280280i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	9.44222	−	16.3544i	0.314044	−	0.543940i
$905$	−53.2663	−	30.7533i	−1.77063	−	1.02228i
$906$	41.6370	−	43.0220i	1.38330	−	1.42931i
$907$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$907$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$908$			52.5700i			1.74460i
$909$	−3.70493	+	0.121254i	−0.122885	+	0.00402175i
$910$	48.1730			1.59692
$911$	−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	$0.334445\pi$
$912$	−34.5060	+	9.85354i	−1.14261	+	0.326283i
$913$		0			0
$914$	48.2404	+	27.8516i	1.59565	+	0.921249i
$915$	−53.3309	−	13.3589i	−1.76306	−	0.441633i
$916$	7.19406	+	12.4605i	0.237699	+	0.411706i
$917$		−	54.8716i		−	1.81202i
$918$		0			0
$919$	14.4063			0.475221			0.237610	−	0.971361i	$-0.423636\pi$
$919$	14.4063			0.475221			0.237610	+	0.971361i	$0.423636\pi$
$920$	−50.3887	+	29.0919i	−1.66127	+	0.959133i
$921$	1.65783	−	6.61830i	0.0546273	−	0.218080i
$922$	−11.2329	+	19.4560i	−0.369937	+	0.640749i
$923$	−52.8979	−	30.5406i	−1.74116	−	1.00526i
$924$		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
$931$	18.1286	−	31.3996i	0.594140	−	1.02908i
$932$	−34.9230	−	20.1628i	−1.14394	−	0.660454i
$933$		0			0
$934$	8.21532	+	14.2294i	0.268814	+	0.465599i
$935$		0			0
$936$	25.0647	+	40.3082i	0.819266	+	1.31751i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−39.5473	−	22.8326i	−1.28921	−	0.744323i	−0.310693	−	0.950510i	$-0.600561\pi$
$941$	−39.5473	−	22.8326i	−1.28921	−	0.744323i	−0.978513	+	0.206187i	$0.933894\pi$
$942$	57.3835	+	14.3741i	1.86966	+	0.468333i
$943$		0			0
$944$		−	57.6827i		−	1.87741i
$945$	23.4445	+	21.2495i	0.762651	+	0.691245i
$946$		0			0
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$	−14.5977	+	58.2763i	−0.474113	+	1.89273i
$949$		0			0
$950$	−1.88586	−	1.08880i	−0.0611855	−	0.0353255i
$951$		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
$955$	5.60209			0.181280
$956$	−38.5193	+	22.2391i	−1.24580	+	0.719264i
$957$		0			0
$958$		0			0
$959$	34.2929	+	19.7990i	1.10737	+	0.639343i
$960$	−22.1789	+	22.9167i	−0.715822	+	0.739632i
$961$	−15.5000	−	26.8468i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	41.0151	−	23.6801i	1.32032	−	0.762289i
$966$	55.6972	−	15.9049i	1.79203	−	0.511733i
$967$	−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
$971$		−	53.9040i		−	1.72986i	−0.501891	−	0.864931i	$-0.667362\pi$
$971$		−	53.9040i		−	1.72986i	0.501891	−	0.864931i	$-0.332638\pi$
$972$	−5.58187	+	30.6732i	−0.179039	+	0.983842i
$973$	−62.0924			−1.99059
$974$	0.541609	−	0.312698i	0.0173543	−	0.0100195i
$975$	−0.699876	+	2.79401i	−0.0224140	+	0.0894799i
$976$	−27.5827	+	47.7746i	−0.882899	+	1.52923i
$977$	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
$980$		−	32.2222i		−	1.02930i
$981$		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
$988$	28.9740	+	50.1845i	0.921787	+	1.59658i
$989$		0			0
$990$		0			0
$991$	37.0405			1.17663			0.588315	−	0.808632i	$-0.299791\pi$
$991$	37.0405			1.17663			0.588315	+	0.808632i	$0.299791\pi$
$992$		0			0
$993$		0			0
$994$	−20.4281	+	35.3826i	−0.647941	+	1.12227i
$995$		0			0
$996$	−4.70850	−	1.17944i	−0.149194	−	0.0373720i
$997$	6.16776	+	10.6829i	0.195335	+	0.338330i	0.947010	−	0.321203i	$-0.104087\pi$
$997$	6.16776	+	10.6829i	0.195335	+	0.338330i	−0.751675	+	0.659533i	$0.770754\pi$
$998$		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.293.6	✓	16
7.6	odd	2	inner	504.2.cc.a.293.7	yes	16
8.5	even	2	inner	504.2.cc.a.293.7	yes	16
9.2	odd	6	inner	504.2.cc.a.461.6	yes	16
56.13	odd	2	CM	504.2.cc.a.293.6	✓	16
63.20	even	6	inner	504.2.cc.a.461.7	yes	16
72.29	odd	6	inner	504.2.cc.a.461.7	yes	16
504.461	even	6	inner	504.2.cc.a.461.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.a.293.6	✓	16	1.1	even	1	trivial
504.2.cc.a.293.6	✓	16	56.13	odd	2	CM
504.2.cc.a.293.7	yes	16	7.6	odd	2	inner
504.2.cc.a.293.7	yes	16	8.5	even	2	inner
504.2.cc.a.461.6	yes	16	9.2	odd	6	inner
504.2.cc.a.461.6	yes	16	504.461	even	6	inner
504.2.cc.a.461.7	yes	16	63.20	even	6	inner
504.2.cc.a.461.7	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)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.420861 + 1.68014i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.99323 - 1.15079i) q^{5} +(0.672592 + 2.35534i) q^{6} +(-1.32288 - 2.29129i) q^{7} -2.82843i q^{8} +(-2.64575 - 1.41421i) q^{9} -3.25493 q^{10} +(2.48923 + 2.40909i) q^{12} +(2.79694 - 4.84444i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(2.77237 - 2.86458i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-4.24037 + 0.138778i) q^{18} -5.17960 q^{19} +(-3.98646 + 2.30158i) q^{20} +(4.40644 - 1.25830i) q^{21} +(7.74037 + 4.46890i) q^{23} +(4.75216 + 1.19038i) q^{24} +(0.148641 + 0.257454i) q^{25} -7.91094i q^{26} +(3.48957 - 3.85005i) q^{27} -5.29150 q^{28} +(1.36987 - 5.46874i) q^{30} +(-4.89898 - 2.82843i) q^{32} +6.08941i q^{35} +(-5.09524 + 3.16836i) q^{36} +(-6.34368 + 3.66253i) q^{38} +(6.96223 + 6.73809i) q^{39} +(-3.25493 + 5.63770i) q^{40} +(4.50700 - 4.65692i) q^{42} +(3.64612 + 5.86356i) q^{45} +12.6400 q^{46} +(6.66190 - 1.90238i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(0.364095 + 0.210210i) q^{50} +(-5.59388 - 9.68889i) q^{52} +(1.55144 - 7.18283i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(2.17989 - 8.70245i) q^{57} +(12.4887 + 7.21033i) q^{59} +(-2.18924 - 7.66646i) q^{60} +(-6.89566 - 11.9436i) q^{61} +(0.259630 + 7.93301i) q^{63} -8.00000 q^{64} +(-11.1499 + 6.43739i) q^{65} +(-10.7660 + 11.1241i) q^{69} +(4.30587 + 7.45798i) q^{70} -10.9193i q^{71} +(-4.00000 + 7.48331i) q^{72} +(-0.495116 + 0.141386i) q^{75} +(-5.17960 + 8.97132i) q^{76} +(13.2915 + 3.32941i) q^{78} +(8.67134 + 15.0192i) q^{79} +9.20633i q^{80} +(5.00000 + 7.48331i) q^{81} +(-1.21349 + 0.700610i) q^{83} +(2.22699 - 8.89047i) q^{84} +(8.61173 + 4.60317i) q^{90} -14.8000 q^{91} +(15.4807 - 8.93781i) q^{92} +(10.3241 + 5.96063i) q^{95} +(6.81395 - 7.04060i) q^{96} +9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 16 q^{15} - 32 q^{16} - 16 q^{18} + 72 q^{23} + 40 q^{25} + 32 q^{30} - 40 q^{39} - 56 q^{49} - 144 q^{50} + 8 q^{57} - 16 q^{60} + 56 q^{63} - 128 q^{64} - 72 q^{65} - 64 q^{72} + 128 q^{78}+ \cdots + 144 q^{92}+O(q^{100}) \) 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

Varieties

Fields

Representations

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Database

Properties

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