LMFDB - Embedded newform 666.2.f.g.343.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(343,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.343"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,-2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 222)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			343.2
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	666.343
Dual form			666.2.f.g.433.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.68614 + 2.92048i) q^{5} +(-2.18614 - 3.78651i) q^{7} +1.00000 q^{8} -3.37228 q^{10} -2.00000 q^{11} +(2.18614 + 3.78651i) q^{13} +4.37228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.68614 + 6.38458i) q^{17} +(3.37228 + 5.84096i) q^{19} +(1.68614 - 2.92048i) q^{20} +(1.00000 - 1.73205i) q^{22} +(-3.18614 + 5.51856i) q^{25} -4.37228 q^{26} +(-2.18614 + 3.78651i) q^{28} +1.37228 q^{29} -3.62772 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.68614 - 6.38458i) q^{34} +(7.37228 - 12.7692i) q^{35} +(6.05842 - 0.543620i) q^{37} -6.74456 q^{38} +(1.68614 + 2.92048i) q^{40} +(0.686141 + 1.18843i) q^{41} -3.62772 q^{43} +(1.00000 + 1.73205i) q^{44} -2.00000 q^{47} +(-6.05842 + 10.4935i) q^{49} +(-3.18614 - 5.51856i) q^{50} +(2.18614 - 3.78651i) q^{52} +(-5.74456 + 9.94987i) q^{53} +(-3.37228 - 5.84096i) q^{55} +(-2.18614 - 3.78651i) q^{56} +(-0.686141 + 1.18843i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-4.05842 - 7.02939i) q^{61} +(1.81386 - 3.14170i) q^{62} +1.00000 q^{64} +(-7.37228 + 12.7692i) q^{65} +(6.55842 + 11.3595i) q^{67} +7.37228 q^{68} +(7.37228 + 12.7692i) q^{70} +(-5.74456 - 9.94987i) q^{71} +8.37228 q^{73} +(-2.55842 + 5.51856i) q^{74} +(3.37228 - 5.84096i) q^{76} +(4.37228 + 7.57301i) q^{77} +(2.18614 + 3.78651i) q^{79} -3.37228 q^{80} -1.37228 q^{82} +(4.00000 - 6.92820i) q^{83} -24.8614 q^{85} +(1.81386 - 3.14170i) q^{86} -2.00000 q^{88} +(4.68614 - 8.11663i) q^{89} +(9.55842 - 16.5557i) q^{91} +(1.00000 - 1.73205i) q^{94} +(-11.3723 + 19.6974i) q^{95} -5.74456 q^{97} +(-6.05842 - 10.4935i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + q^{5} - 3 q^{7} + 4 q^{8} - 2 q^{10} - 8 q^{11} + 3 q^{13} + 6 q^{14} - 2 q^{16} - 9 q^{17} + 2 q^{19} + q^{20} + 4 q^{22} - 7 q^{25} - 6 q^{26} - 3 q^{28} - 6 q^{29} - 26 q^{31}+ \cdots - 7 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + q^5 - 3 * q^7 + 4 * q^8 - 2 * q^10 - 8 * q^11 + 3 * q^13 + 6 * q^14 - 2 * q^16 - 9 * q^17 + 2 * q^19 + q^20 + 4 * q^22 - 7 * q^25 - 6 * q^26 - 3 * q^28 - 6 * q^29 - 26 * q^31 - 2 * q^32 - 9 * q^34 + 18 * q^35 + 7 * q^37 - 4 * q^38 + q^40 - 3 * q^41 - 26 * q^43 + 4 * q^44 - 8 * q^47 - 7 * q^49 - 7 * q^50 + 3 * q^52 - 2 * q^55 - 3 * q^56 + 3 * q^58 - 8 * q^59 + q^61 + 13 * q^62 + 4 * q^64 - 18 * q^65 + 9 * q^67 + 18 * q^68 + 18 * q^70 + 22 * q^73 + 7 * q^74 + 2 * q^76 + 6 * q^77 + 3 * q^79 - 2 * q^80 + 6 * q^82 + 16 * q^83 - 42 * q^85 + 13 * q^86 - 8 * q^88 + 13 * q^89 + 21 * q^91 + 4 * q^94 - 34 * q^95 - 7 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.68614	+	2.92048i	0.754065	+	1.30608i	0.945838	+	0.324640i	$0.105243\pi$
$5$	1.68614	+	2.92048i	0.754065	+	1.30608i	−0.191773	+	0.981439i	$0.561424\pi$
$6$		0			0
$7$	−2.18614	−	3.78651i	−0.826284	−	1.43117i	−0.900934	−	0.433955i	$-0.857118\pi$
$7$	−2.18614	−	3.78651i	−0.826284	−	1.43117i	0.0746509	−	0.997210i	$-0.476216\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−3.37228			−1.06641
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	2.18614	+	3.78651i	0.606326	+	1.05019i	0.991840	+	0.127486i	$0.0406908\pi$
$13$	2.18614	+	3.78651i	0.606326	+	1.05019i	−0.385514	+	0.922702i	$0.625976\pi$
$14$	4.37228			1.16854
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.68614	+	6.38458i	−0.894020	+	1.54849i	−0.0590081	+	0.998258i	$0.518794\pi$
$17$	−3.68614	+	6.38458i	−0.894020	+	1.54849i	−0.835012	+	0.550231i	$0.814540\pi$
$18$		0			0
$19$	3.37228	+	5.84096i	0.773654	+	1.34001i	0.935548	+	0.353200i	$0.114907\pi$
$19$	3.37228	+	5.84096i	0.773654	+	1.34001i	−0.161893	+	0.986808i	$0.551760\pi$
$20$	1.68614	−	2.92048i	0.377033	−	0.653039i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	−3.18614	+	5.51856i	−0.637228	+	1.10371i
$26$	−4.37228			−0.857475
$27$		0			0
$28$	−2.18614	+	3.78651i	−0.413142	+	0.715583i
$29$	1.37228			0.254826			0.127413	−	0.991850i	$-0.459333\pi$
$29$	1.37228			0.254826			0.127413	+	0.991850i	$0.459333\pi$
$30$		0			0
$31$	−3.62772			−0.651558			−0.325779	−	0.945446i	$-0.605626\pi$
$31$	−3.62772			−0.651558			−0.325779	+	0.945446i	$0.605626\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.68614	−	6.38458i	−0.632168	−	1.09495i
$35$	7.37228	−	12.7692i	1.24614	−	2.15838i
$36$		0			0
$37$	6.05842	−	0.543620i	0.995998	−	0.0893706i
$37$	6.05842	−	0.543620i	0.995998	−	0.0893706i
$38$	−6.74456			−1.09411
$39$		0			0
$40$	1.68614	+	2.92048i	0.266602	+	0.461769i
$41$	0.686141	+	1.18843i	0.107157	+	0.185602i	0.914617	−	0.404320i	$-0.132492\pi$
$41$	0.686141	+	1.18843i	0.107157	+	0.185602i	−0.807460	+	0.589922i	$0.799159\pi$
$42$		0			0
$43$	−3.62772			−0.553222			−0.276611	−	0.960982i	$-0.589211\pi$
$43$	−3.62772			−0.553222			−0.276611	+	0.960982i	$0.589211\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$		0			0
$47$	−2.00000			−0.291730			−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000			−0.291730			−0.145865	+	0.989305i	$0.546597\pi$
$48$		0			0
$49$	−6.05842	+	10.4935i	−0.865489	+	1.49907i
$50$	−3.18614	−	5.51856i	−0.450588	−	0.780442i
$51$		0			0
$52$	2.18614	−	3.78651i	0.303163	−	0.525094i
$53$	−5.74456	+	9.94987i	−0.789076	+	1.36672i	0.137457	+	0.990508i	$0.456107\pi$
$53$	−5.74456	+	9.94987i	−0.789076	+	1.36672i	−0.926533	+	0.376213i	$0.877226\pi$
$54$		0			0
$55$	−3.37228	−	5.84096i	−0.454718	−	0.787595i
$56$	−2.18614	−	3.78651i	−0.292135	−	0.505993i
$57$		0			0
$58$	−0.686141	+	1.18843i	−0.0900947	+	0.156049i
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−4.05842	−	7.02939i	−0.519628	−	0.900022i	−0.999740	−	0.0228144i	$-0.992737\pi$
$61$	−4.05842	−	7.02939i	−0.519628	−	0.900022i	0.480112	−	0.877207i	$-0.340596\pi$
$62$	1.81386	−	3.14170i	0.230360	−	0.398996i
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.37228	+	12.7692i	−0.914419	+	1.58382i
$66$		0			0
$67$	6.55842	+	11.3595i	0.801239	+	1.38779i	0.918801	+	0.394721i	$0.129159\pi$
$67$	6.55842	+	11.3595i	0.801239	+	1.38779i	−0.117562	+	0.993066i	$0.537508\pi$
$68$	7.37228			0.894020
$69$		0			0
$70$	7.37228	+	12.7692i	0.881156	+	1.52621i
$71$	−5.74456	−	9.94987i	−0.681754	−	1.18083i	−0.974445	−	0.224626i	$-0.927884\pi$
$71$	−5.74456	−	9.94987i	−0.681754	−	1.18083i	0.292691	−	0.956207i	$-0.405449\pi$
$72$		0			0
$73$	8.37228			0.979901			0.489951	−	0.871750i	$-0.337015\pi$
$73$	8.37228			0.979901			0.489951	+	0.871750i	$0.337015\pi$
$74$	−2.55842	+	5.51856i	−0.297411	+	0.641519i
$75$		0			0
$76$	3.37228	−	5.84096i	0.386827	−	0.670004i
$77$	4.37228	+	7.57301i	0.498268	+	0.863025i
$78$		0			0
$79$	2.18614	+	3.78651i	0.245960	+	0.426015i	0.962401	−	0.271632i	$-0.0875635\pi$
$79$	2.18614	+	3.78651i	0.245960	+	0.426015i	−0.716441	+	0.697648i	$0.754230\pi$
$80$	−3.37228			−0.377033
$81$		0			0
$82$	−1.37228			−0.151543
$83$	4.00000	−	6.92820i	0.439057	−	0.760469i	−0.558560	−	0.829464i	$-0.688646\pi$
$83$	4.00000	−	6.92820i	0.439057	−	0.760469i	0.997617	+	0.0689950i	$0.0219793\pi$
$84$		0			0
$85$	−24.8614			−2.69660
$86$	1.81386	−	3.14170i	0.195593	−	0.338778i
$87$		0			0
$88$	−2.00000			−0.213201
$89$	4.68614	−	8.11663i	0.496730	−	0.860361i	−0.503263	−	0.864133i	$-0.667867\pi$
$89$	4.68614	−	8.11663i	0.496730	−	0.860361i	0.999993	+	0.00377186i	$0.00120062\pi$
$90$		0			0
$91$	9.55842	−	16.5557i	1.00199	−	1.73551i
$92$		0			0
$93$		0			0
$94$	1.00000	−	1.73205i	0.103142	−	0.178647i
$95$	−11.3723	+	19.6974i	−1.16677	+	2.02091i
$96$		0			0
$97$	−5.74456			−0.583272			−0.291636	−	0.956529i	$-0.594200\pi$
$97$	−5.74456			−0.583272			−0.291636	+	0.956529i	$0.594200\pi$
$98$	−6.05842	−	10.4935i	−0.611993	−	1.06000i
$99$		0			0
$100$	6.37228			0.637228
$101$	14.8614			1.47877			0.739383	−	0.673285i	$-0.235117\pi$
$101$	14.8614			1.47877			0.739383	+	0.673285i	$0.235117\pi$
$102$		0			0
$103$	1.25544			0.123702			0.0618510	−	0.998085i	$-0.480300\pi$
$103$	1.25544			0.123702			0.0618510	+	0.998085i	$0.480300\pi$
$104$	2.18614	+	3.78651i	0.214369	+	0.371298i
$105$		0			0
$106$	−5.74456	−	9.94987i	−0.557961	−	0.966417i
$107$	−3.37228	−	5.84096i	−0.326011	−	0.564667i	0.655706	−	0.755017i	$-0.272371\pi$
$107$	−3.37228	−	5.84096i	−0.326011	−	0.564667i	−0.981716	+	0.190349i	$0.939038\pi$
$108$		0			0
$109$	7.87228	−	13.6352i	0.754028	−	1.30601i	−0.191828	−	0.981428i	$-0.561442\pi$
$109$	7.87228	−	13.6352i	0.754028	−	1.30601i	0.945856	−	0.324586i	$-0.105225\pi$
$110$	6.74456			0.643069
$111$		0			0
$112$	4.37228			0.413142
$113$	3.74456	−	6.48577i	0.352259	−	0.610130i	−0.634386	−	0.773016i	$-0.718747\pi$
$113$	3.74456	−	6.48577i	0.352259	−	0.610130i	0.986645	+	0.162886i	$0.0520803\pi$
$114$		0			0
$115$		0			0
$116$	−0.686141	−	1.18843i	−0.0637066	−	0.110343i
$117$		0			0
$118$	−2.00000	−	3.46410i	−0.184115	−	0.318896i
$119$	32.2337			2.95486
$120$		0			0
$121$	−7.00000			−0.636364
$122$	8.11684			0.734865
$123$		0			0
$124$	1.81386	+	3.14170i	0.162889	+	0.282133i
$125$	−4.62772			−0.413916
$126$		0			0
$127$	−7.18614	+	12.4468i	−0.637667	+	1.10447i	0.348277	+	0.937392i	$0.386767\pi$
$127$	−7.18614	+	12.4468i	−0.637667	+	1.10447i	−0.985943	+	0.167080i	$0.946566\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−7.37228	−	12.7692i	−0.646592	−	1.11993i
$131$	−0.372281	+	0.644810i	−0.0325264	+	0.0563373i	−0.881830	−	0.471567i	$-0.843689\pi$
$131$	−0.372281	+	0.644810i	−0.0325264	+	0.0563373i	0.849304	+	0.527904i	$0.177022\pi$
$132$		0			0
$133$	14.7446	−	25.5383i	1.27852	−	2.21445i
$134$	−13.1168			−1.13312
$135$		0			0
$136$	−3.68614	+	6.38458i	−0.316084	+	0.547473i
$137$	−4.62772			−0.395373			−0.197686	−	0.980265i	$-0.563343\pi$
$137$	−4.62772			−0.395373			−0.197686	+	0.980265i	$0.563343\pi$
$138$		0			0
$139$	7.18614	−	12.4468i	0.609520	−	1.05572i	−0.381799	−	0.924245i	$-0.624695\pi$
$139$	7.18614	−	12.4468i	0.609520	−	1.05572i	0.991319	−	0.131475i	$-0.0419713\pi$
$140$	−14.7446			−1.24614
$141$		0			0
$142$	11.4891			0.964146
$143$	−4.37228	−	7.57301i	−0.365629	−	0.633287i
$144$		0			0
$145$	2.31386	+	4.00772i	0.192156	+	0.332823i
$146$	−4.18614	+	7.25061i	−0.346447	+	0.600065i
$147$		0			0
$148$	−3.50000	−	4.97494i	−0.287698	−	0.408937i
$149$	−7.37228			−0.603961			−0.301980	−	0.953314i	$-0.597648\pi$
$149$	−7.37228			−0.603961			−0.301980	+	0.953314i	$0.597648\pi$
$150$		0			0
$151$	6.81386	+	11.8020i	0.554504	+	0.960429i	0.997942	+	0.0641240i	$0.0204253\pi$
$151$	6.81386	+	11.8020i	0.554504	+	0.960429i	−0.443438	+	0.896305i	$0.646241\pi$
$152$	3.37228	+	5.84096i	0.273528	+	0.473765i
$153$		0			0
$154$	−8.74456			−0.704657
$155$	−6.11684	−	10.5947i	−0.491317	−	0.850986i
$156$		0			0
$157$	8.24456	−	14.2800i	0.657988	−	1.13967i	−0.323148	−	0.946348i	$-0.604741\pi$
$157$	8.24456	−	14.2800i	0.657988	−	1.13967i	0.981136	−	0.193320i	$-0.0619255\pi$
$158$	−4.37228			−0.347840
$159$		0			0
$160$	1.68614	−	2.92048i	0.133301	−	0.230884i
$161$		0			0
$162$		0			0
$163$	−6.62772	+	11.4795i	−0.519123	+	0.899147i	0.480630	+	0.876923i	$0.340408\pi$
$163$	−6.62772	+	11.4795i	−0.519123	+	0.899147i	−0.999753	+	0.0222239i	$0.992925\pi$
$164$	0.686141	−	1.18843i	0.0535786	−	0.0928008i
$165$		0			0
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	10.7446	+	18.6101i	0.831439	+	1.44009i	0.896897	+	0.442240i	$0.145816\pi$
$167$	10.7446	+	18.6101i	0.831439	+	1.44009i	−0.0654577	+	0.997855i	$0.520851\pi$
$168$		0			0
$169$	−3.05842	+	5.29734i	−0.235263	+	0.407488i
$170$	12.4307	−	21.5306i	0.953391	−	1.65132i
$171$		0			0
$172$	1.81386	+	3.14170i	0.138305	+	0.239552i
$173$	2.94158	−	5.09496i	0.223644	−	0.387363i	−0.732268	−	0.681017i	$-0.761538\pi$
$173$	2.94158	−	5.09496i	0.223644	−	0.387363i	0.955912	+	0.293654i	$0.0948714\pi$
$174$		0			0
$175$	27.8614			2.10612
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$		0			0
$178$	4.68614	+	8.11663i	0.351241	+	0.608367i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	7.87228	+	13.6352i	0.585142	+	1.01350i	0.994858	+	0.101282i	$0.0322946\pi$
$181$	7.87228	+	13.6352i	0.585142	+	1.01350i	−0.409716	+	0.912213i	$0.634372\pi$
$182$	9.55842	+	16.5557i	0.708517	+	1.22719i
$183$		0			0
$184$		0			0
$185$	11.8030	+	16.7769i	0.867773	+	1.23346i
$186$		0			0
$187$	7.37228	−	12.7692i	0.539115	−	0.933774i
$188$	1.00000	+	1.73205i	0.0729325	+	0.126323i
$189$		0			0
$190$	−11.3723	−	19.6974i	−0.825032	−	1.42900i
$191$	11.2554			0.814415			0.407207	−	0.913336i	$-0.366503\pi$
$191$	11.2554			0.814415			0.407207	+	0.913336i	$0.366503\pi$
$192$		0			0
$193$	4.48913			0.323134			0.161567	−	0.986862i	$-0.448345\pi$
$193$	4.48913			0.323134			0.161567	+	0.986862i	$0.448345\pi$
$194$	2.87228	−	4.97494i	0.206218	−	0.357180i
$195$		0			0
$196$	12.1168			0.865489
$197$	9.68614	−	16.7769i	0.690109	−	1.19530i	−0.281693	−	0.959505i	$-0.590896\pi$
$197$	9.68614	−	16.7769i	0.690109	−	1.19530i	0.971802	−	0.235799i	$-0.0757707\pi$
$198$		0			0
$199$	−12.3723			−0.877048			−0.438524	−	0.898720i	$-0.644499\pi$
$199$	−12.3723			−0.877048			−0.438524	+	0.898720i	$0.644499\pi$
$200$	−3.18614	+	5.51856i	−0.225294	+	0.390221i
$201$		0			0
$202$	−7.43070	+	12.8704i	−0.522822	+	0.905555i
$203$	−3.00000	−	5.19615i	−0.210559	−	0.364698i
$204$		0			0
$205$	−2.31386	+	4.00772i	−0.161607	+	0.279911i
$206$	−0.627719	+	1.08724i	−0.0437352	+	0.0757516i
$207$		0			0
$208$	−4.37228			−0.303163
$209$	−6.74456	−	11.6819i	−0.466531	−	0.808056i
$210$		0			0
$211$	7.62772			0.525114			0.262557	−	0.964917i	$-0.415434\pi$
$211$	7.62772			0.525114			0.262557	+	0.964917i	$0.415434\pi$
$212$	11.4891			0.789076
$213$		0			0
$214$	6.74456			0.461049
$215$	−6.11684	−	10.5947i	−0.417165	−	0.722551i
$216$		0			0
$217$	7.93070	+	13.7364i	0.538371	+	0.932486i
$218$	7.87228	+	13.6352i	0.533178	+	0.923492i
$219$		0			0
$220$	−3.37228	+	5.84096i	−0.227359	+	0.393798i
$221$	−32.2337			−2.16827
$222$		0			0
$223$	0.883156			0.0591405			0.0295703	−	0.999563i	$-0.490586\pi$
$223$	0.883156			0.0591405			0.0295703	+	0.999563i	$0.490586\pi$
$224$	−2.18614	+	3.78651i	−0.146068	+	0.252997i
$225$		0			0
$226$	3.74456	+	6.48577i	0.249085	+	0.431427i
$227$	5.74456	+	9.94987i	0.381280	+	0.660396i	0.991246	−	0.132032i	$-0.0421500\pi$
$227$	5.74456	+	9.94987i	0.381280	+	0.660396i	−0.609965	+	0.792428i	$0.708817\pi$
$228$		0			0
$229$	1.12772	+	1.95327i	0.0745217	+	0.129075i	0.900878	−	0.434072i	$-0.142924\pi$
$229$	1.12772	+	1.95327i	0.0745217	+	0.129075i	−0.826356	+	0.563147i	$0.809590\pi$
$230$		0			0
$231$		0			0
$232$	1.37228			0.0900947
$233$	−11.6060			−0.760332			−0.380166	−	0.924918i	$-0.624133\pi$
$233$	−11.6060			−0.760332			−0.380166	+	0.924918i	$0.624133\pi$
$234$		0			0
$235$	−3.37228	−	5.84096i	−0.219983	−	0.381022i
$236$	4.00000			0.260378
$237$		0			0
$238$	−16.1168	+	27.9152i	−1.04470	+	1.80947i
$239$	6.11684	−	10.5947i	0.395666	−	0.685313i	−0.597520	−	0.801854i	$-0.703847\pi$
$239$	6.11684	−	10.5947i	0.395666	−	0.685313i	0.993186	+	0.116541i	$0.0371805\pi$
$240$		0			0
$241$	−3.44158	−	5.96099i	−0.221692	−	0.383981i	0.733630	−	0.679549i	$-0.237824\pi$
$241$	−3.44158	−	5.96099i	−0.221692	−	0.383981i	−0.955322	+	0.295568i	$0.904491\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$		0			0
$244$	−4.05842	+	7.02939i	−0.259814	+	0.450011i
$245$	−40.8614			−2.61054
$246$		0			0
$247$	−14.7446	+	25.5383i	−0.938174	+	1.62497i
$248$	−3.62772			−0.230360
$249$		0			0
$250$	2.31386	−	4.00772i	0.146341	−	0.253471i
$251$	1.25544			0.0792425			0.0396213	−	0.999215i	$-0.487385\pi$
$251$	1.25544			0.0792425			0.0396213	+	0.999215i	$0.487385\pi$
$252$		0			0
$253$		0			0
$254$	−7.18614	−	12.4468i	−0.450899	−	0.780979i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.43070	+	7.67420i	−0.276380	+	0.478704i	−0.970482	−	0.241172i	$-0.922468\pi$
$257$	−4.43070	+	7.67420i	−0.276380	+	0.478704i	0.694103	+	0.719876i	$0.255801\pi$
$258$		0			0
$259$	−15.3030	−	21.7518i	−0.950881	−	1.35159i
$260$	14.7446			0.914419
$261$		0			0
$262$	−0.372281	−	0.644810i	−0.0229996	−	0.0398365i
$263$	−7.62772	−	13.2116i	−0.470345	−	0.814662i	0.529080	−	0.848572i	$-0.322537\pi$
$263$	−7.62772	−	13.2116i	−0.470345	−	0.814662i	−0.999425	+	0.0339103i	$0.989204\pi$
$264$		0			0
$265$	−38.7446			−2.38006
$266$	14.7446	+	25.5383i	0.904047	+	1.56586i
$267$		0			0
$268$	6.55842	−	11.3595i	0.400619	−	0.693893i
$269$	−2.00000			−0.121942			−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000			−0.121942			−0.0609711	+	0.998140i	$0.519420\pi$
$270$		0			0
$271$	4.93070	−	8.54023i	0.299519	−	0.518782i	−0.676507	−	0.736436i	$-0.736507\pi$
$271$	4.93070	−	8.54023i	0.299519	−	0.518782i	0.976026	+	0.217654i	$0.0698405\pi$
$272$	−3.68614	−	6.38458i	−0.223505	−	0.387122i
$273$		0			0
$274$	2.31386	−	4.00772i	0.139785	−	0.242115i
$275$	6.37228	−	11.0371i	0.384263	−	0.665563i
$276$		0			0
$277$	15.4307	+	26.7268i	0.927141	+	1.60586i	0.788081	+	0.615572i	$0.211075\pi$
$277$	15.4307	+	26.7268i	0.927141	+	1.60586i	0.139060	+	0.990284i	$0.455592\pi$
$278$	7.18614	+	12.4468i	0.430996	+	0.746507i
$279$		0			0
$280$	7.37228	−	12.7692i	0.440578	−	0.763104i
$281$	5.05842	−	8.76144i	0.301760	−	0.522664i	−0.674775	−	0.738024i	$-0.735759\pi$
$281$	5.05842	−	8.76144i	0.301760	−	0.522664i	0.976535	+	0.215360i	$0.0690925\pi$
$282$		0			0
$283$	−8.55842	−	14.8236i	−0.508745	−	0.881173i	−0.999949	−	0.0101279i	$-0.996776\pi$
$283$	−8.55842	−	14.8236i	−0.508745	−	0.881173i	0.491203	−	0.871045i	$-0.336557\pi$
$284$	−5.74456	+	9.94987i	−0.340877	+	0.590416i
$285$		0			0
$286$	8.74456			0.517077
$287$	3.00000	−	5.19615i	0.177084	−	0.306719i
$288$		0			0
$289$	−18.6753	−	32.3465i	−1.09855	−	1.90274i
$290$	−4.62772			−0.271749
$291$		0			0
$292$	−4.18614	−	7.25061i	−0.244975	−	0.424310i
$293$	−7.94158	−	13.7552i	−0.463952	−	0.803588i	0.535202	−	0.844724i	$-0.320236\pi$
$293$	−7.94158	−	13.7552i	−0.463952	−	0.803588i	−0.999154	+	0.0411360i	$0.986902\pi$
$294$		0			0
$295$	−13.4891			−0.785367
$296$	6.05842	−	0.543620i	0.352139	−	0.0315973i
$297$		0			0
$298$	3.68614	−	6.38458i	0.213532	−	0.369849i
$299$		0			0
$300$		0			0
$301$	7.93070	+	13.7364i	0.457118	+	0.791752i
$302$	−13.6277			−0.784187
$303$		0			0
$304$	−6.74456			−0.386827
$305$	13.6861	−	23.7051i	0.783666	−	1.35735i
$306$		0			0
$307$	9.11684			0.520326			0.260163	−	0.965565i	$-0.416224\pi$
$307$	9.11684			0.520326			0.260163	+	0.965565i	$0.416224\pi$
$308$	4.37228	−	7.57301i	0.249134	−	0.431512i
$309$		0			0
$310$	12.2337			0.694827
$311$	8.48913	−	14.7036i	0.481374	−	0.833764i	−0.518397	−	0.855140i	$-0.673471\pi$
$311$	8.48913	−	14.7036i	0.481374	−	0.833764i	0.999772	+	0.0213754i	$0.00680452\pi$
$312$		0			0
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$	8.24456	+	14.2800i	0.465268	+	0.805867i
$315$		0			0
$316$	2.18614	−	3.78651i	0.122980	−	0.213008i
$317$	−15.0584	+	26.0820i	−0.845765	+	1.46491i	0.0391897	+	0.999232i	$0.487522\pi$
$317$	−15.0584	+	26.0820i	−0.845765	+	1.46491i	−0.884955	+	0.465677i	$0.845811\pi$
$318$		0			0
$319$	−2.74456			−0.153666
$320$	1.68614	+	2.92048i	0.0942581	+	0.163260i
$321$		0			0
$322$		0			0
$323$	−49.7228			−2.76665
$324$		0			0
$325$	−27.8614			−1.54547
$326$	−6.62772	−	11.4795i	−0.367075	−	0.635793i
$327$		0			0
$328$	0.686141	+	1.18843i	0.0378858	+	0.0656201i
$329$	4.37228	+	7.57301i	0.241052	+	0.417514i
$330$		0			0
$331$	−2.30298	+	3.98889i	−0.126583	+	0.219249i	−0.922351	−	0.386353i	$-0.873734\pi$
$331$	−2.30298	+	3.98889i	−0.126583	+	0.219249i	0.795767	+	0.605602i	$0.207068\pi$
$332$	−8.00000			−0.439057
$333$		0			0
$334$	−21.4891			−1.17583
$335$	−22.1168	+	38.3075i	−1.20837	+	2.09296i
$336$		0			0
$337$	−9.12772	−	15.8097i	−0.497219	−	0.861208i	0.502776	−	0.864417i	$-0.332312\pi$
$337$	−9.12772	−	15.8097i	−0.497219	−	0.861208i	−0.999995	+	0.00320880i	$0.998979\pi$
$338$	−3.05842	−	5.29734i	−0.166356	−	0.288137i
$339$		0			0
$340$	12.4307	+	21.5306i	0.674150	+	1.16766i
$341$	7.25544			0.392904
$342$		0			0
$343$	22.3723			1.20799
$344$	−3.62772			−0.195593
$345$		0			0
$346$	2.94158	+	5.09496i	0.158140	+	0.273907i
$347$	−15.2554			−0.818955			−0.409477	−	0.912320i	$-0.634289\pi$
$347$	−15.2554			−0.818955			−0.409477	+	0.912320i	$0.634289\pi$
$348$		0			0
$349$	−4.05842	+	7.02939i	−0.217242	+	0.376275i	−0.953964	−	0.299921i	$-0.903040\pi$
$349$	−4.05842	+	7.02939i	−0.217242	+	0.376275i	0.736722	+	0.676196i	$0.236373\pi$
$350$	−13.9307	+	24.1287i	−0.744627	+	1.28973i
$351$		0			0
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	−4.80298	+	8.31901i	−0.255637	+	0.442776i	−0.965068	−	0.261998i	$-0.915619\pi$
$353$	−4.80298	+	8.31901i	−0.255637	+	0.442776i	0.709431	+	0.704775i	$0.248952\pi$
$354$		0			0
$355$	19.3723	−	33.5538i	1.02817	−	1.78085i
$356$	−9.37228			−0.496730
$357$		0			0
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	22.2337			1.17345			0.586725	−	0.809787i	$-0.300417\pi$
$359$	22.2337			1.17345			0.586725	+	0.809787i	$0.300417\pi$
$360$		0			0
$361$	−13.2446	+	22.9403i	−0.697082	+	1.20738i
$362$	−15.7446			−0.827516
$363$		0			0
$364$	−19.1168			−1.00199
$365$	14.1168	+	24.4511i	0.738909	+	1.27983i
$366$		0			0
$367$	5.55842	+	9.62747i	0.290147	+	0.502550i	0.973844	−	0.227216i	$-0.0729624\pi$
$367$	5.55842	+	9.62747i	0.290147	+	0.502550i	−0.683697	+	0.729766i	$0.739629\pi$
$368$		0			0
$369$		0			0
$370$	−20.4307	+	1.83324i	−1.06214	+	0.0953056i
$371$	50.2337			2.60800
$372$		0			0
$373$	15.5000	+	26.8468i	0.802560	+	1.39007i	0.917926	+	0.396751i	$0.129862\pi$
$373$	15.5000	+	26.8468i	0.802560	+	1.39007i	−0.115367	+	0.993323i	$0.536804\pi$
$374$	7.37228	+	12.7692i	0.381212	+	0.660278i
$375$		0			0
$376$	−2.00000			−0.103142
$377$	3.00000	+	5.19615i	0.154508	+	0.267615i
$378$		0			0
$379$	−14.8614	+	25.7407i	−0.763379	+	1.32221i	0.177720	+	0.984081i	$0.443128\pi$
$379$	−14.8614	+	25.7407i	−0.763379	+	1.32221i	−0.941099	+	0.338130i	$0.890205\pi$
$380$	22.7446			1.16677
$381$		0			0
$382$	−5.62772	+	9.74749i	−0.287939	+	0.498725i
$383$	14.1168	+	24.4511i	0.721337	+	1.24939i	0.960464	+	0.278404i	$0.0898054\pi$
$383$	14.1168	+	24.4511i	0.721337	+	1.24939i	−0.239127	+	0.970988i	$0.576861\pi$
$384$		0			0
$385$	−14.7446	+	25.5383i	−0.751452	+	1.30155i
$386$	−2.24456	+	3.88770i	−0.114245	+	0.197879i
$387$		0			0
$388$	2.87228	+	4.97494i	0.145818	+	0.252564i
$389$	12.0584	+	20.8858i	0.611386	+	1.05895i	0.991007	+	0.133810i	$0.0427211\pi$
$389$	12.0584	+	20.8858i	0.611386	+	1.05895i	−0.379621	+	0.925142i	$0.623946\pi$
$390$		0			0
$391$		0			0
$392$	−6.05842	+	10.4935i	−0.305997	+	0.530002i
$393$		0			0
$394$	9.68614	+	16.7769i	0.487981	+	0.845207i
$395$	−7.37228	+	12.7692i	−0.370940	+	0.642486i
$396$		0			0
$397$	−19.0000			−0.953583			−0.476791	−	0.879017i	$-0.658200\pi$
$397$	−19.0000			−0.953583			−0.476791	+	0.879017i	$0.658200\pi$
$398$	6.18614	−	10.7147i	0.310083	−	0.537080i
$399$		0			0
$400$	−3.18614	−	5.51856i	−0.159307	−	0.275928i
$401$	14.7446			0.736308			0.368154	−	0.929765i	$-0.379990\pi$
$401$	14.7446			0.736308			0.368154	+	0.929765i	$0.379990\pi$
$402$		0			0
$403$	−7.93070	−	13.7364i	−0.395056	−	0.684258i
$404$	−7.43070	−	12.8704i	−0.369691	−	0.640324i
$405$		0			0
$406$	6.00000			0.297775
$407$	−12.1168	+	1.08724i	−0.600610	+	0.0538925i
$408$		0			0
$409$	6.12772	−	10.6135i	0.302996	−	0.524805i	−0.673817	−	0.738898i	$-0.735346\pi$
$409$	6.12772	−	10.6135i	0.302996	−	0.524805i	0.976813	+	0.214093i	$0.0686797\pi$
$410$	−2.31386	−	4.00772i	−0.114273	−	0.197927i
$411$		0			0
$412$	−0.627719	−	1.08724i	−0.0309255	−	0.0535645i
$413$	17.4891			0.860584
$414$		0			0
$415$	26.9783			1.32431
$416$	2.18614	−	3.78651i	0.107184	−	0.185649i
$417$		0			0
$418$	13.4891			0.659775
$419$	−1.74456	+	3.02167i	−0.0852275	+	0.147618i	−0.905488	−	0.424372i	$-0.860495\pi$
$419$	−1.74456	+	3.02167i	−0.0852275	+	0.147618i	0.820261	+	0.571990i	$0.193828\pi$
$420$		0			0
$421$	−17.3723			−0.846673			−0.423337	−	0.905972i	$-0.639141\pi$
$421$	−17.3723			−0.846673			−0.423337	+	0.905972i	$0.639141\pi$
$422$	−3.81386	+	6.60580i	−0.185656	+	0.321565i
$423$		0			0
$424$	−5.74456	+	9.94987i	−0.278981	+	0.483209i
$425$	−23.4891	−	40.6844i	−1.13939	−	1.97348i
$426$		0			0
$427$	−17.7446	+	30.7345i	−0.858720	+	1.48735i
$428$	−3.37228	+	5.84096i	−0.163005	+	0.282334i
$429$		0			0
$430$	12.2337			0.589961
$431$	−18.4891	−	32.0241i	−0.890590	−	1.54255i	−0.839170	−	0.543870i	$-0.816959\pi$
$431$	−18.4891	−	32.0241i	−0.890590	−	1.54255i	−0.0514202	−	0.998677i	$-0.516375\pi$
$432$		0			0
$433$	13.3723			0.642631			0.321315	−	0.946972i	$-0.395875\pi$
$433$	13.3723			0.642631			0.321315	+	0.946972i	$0.395875\pi$
$434$	−15.8614			−0.761372
$435$		0			0
$436$	−15.7446			−0.754028
$437$		0			0
$438$		0			0
$439$	−7.18614	−	12.4468i	−0.342976	−	0.594051i	0.642008	−	0.766698i	$-0.278102\pi$
$439$	−7.18614	−	12.4468i	−0.342976	−	0.594051i	−0.984984	+	0.172646i	$0.944768\pi$
$440$	−3.37228	−	5.84096i	−0.160767	−	0.278457i
$441$		0			0
$442$	16.1168	−	27.9152i	0.766600	−	1.32779i
$443$	−17.4891			−0.830933			−0.415467	−	0.909608i	$-0.636382\pi$
$443$	−17.4891			−0.830933			−0.415467	+	0.909608i	$0.636382\pi$
$444$		0			0
$445$	31.6060			1.49827
$446$	−0.441578	+	0.764836i	−0.0209093	+	0.0362160i
$447$		0			0
$448$	−2.18614	−	3.78651i	−0.103285	−	0.178896i
$449$	−10.4891	−	18.1677i	−0.495012	−	0.857387i	0.504971	−	0.863136i	$-0.331503\pi$
$449$	−10.4891	−	18.1677i	−0.495012	−	0.857387i	−0.999983	+	0.00574961i	$0.998170\pi$
$450$		0			0
$451$	−1.37228	−	2.37686i	−0.0646182	−	0.111922i
$452$	−7.48913			−0.352259
$453$		0			0
$454$	−11.4891			−0.539211
$455$	64.4674			3.02228
$456$		0			0
$457$	19.5475	+	33.8573i	0.914396	+	1.58378i	0.807784	+	0.589479i	$0.200667\pi$
$457$	19.5475	+	33.8573i	0.914396	+	1.58378i	0.106612	+	0.994301i	$0.466000\pi$
$458$	−2.25544			−0.105390
$459$		0			0
$460$		0			0
$461$	12.4891	−	21.6318i	0.581677	−	1.00749i	−0.413604	−	0.910457i	$-0.635730\pi$
$461$	12.4891	−	21.6318i	0.581677	−	1.00749i	0.995281	−	0.0970366i	$-0.0309364\pi$
$462$		0			0
$463$	−8.55842	−	14.8236i	−0.397744	−	0.688912i	0.595704	−	0.803204i	$-0.296873\pi$
$463$	−8.55842	−	14.8236i	−0.397744	−	0.688912i	−0.993447	+	0.114292i	$0.963540\pi$
$464$	−0.686141	+	1.18843i	−0.0318533	+	0.0551715i
$465$		0			0
$466$	5.80298	−	10.0511i	0.268818	−	0.465607i
$467$	−3.25544			−0.150644			−0.0753218	−	0.997159i	$-0.523998\pi$
$467$	−3.25544			−0.150644			−0.0753218	+	0.997159i	$0.523998\pi$
$468$		0			0
$469$	28.6753	−	49.6670i	1.32410	−	2.29341i
$470$	6.74456			0.311103
$471$		0			0
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	7.25544			0.333605
$474$		0			0
$475$	−42.9783			−1.97198
$476$	−16.1168	−	27.9152i	−0.738714	−	1.27949i
$477$		0			0
$478$	6.11684	+	10.5947i	0.279778	+	0.484590i
$479$	17.1168	−	29.6472i	0.782089	−	1.35462i	−0.148634	−	0.988892i	$-0.547488\pi$
$479$	17.1168	−	29.6472i	0.782089	−	1.35462i	0.930723	−	0.365725i	$-0.119179\pi$
$480$		0			0
$481$	15.3030	+	21.7518i	0.697756	+	0.991798i
$482$	6.88316			0.313519
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−9.68614	−	16.7769i	−0.439825	−	0.761799i
$486$		0			0
$487$	−14.5109			−0.657550			−0.328775	−	0.944408i	$-0.606636\pi$
$487$	−14.5109			−0.657550			−0.328775	+	0.944408i	$0.606636\pi$
$488$	−4.05842	−	7.02939i	−0.183716	−	0.318206i
$489$		0			0
$490$	20.4307	−	35.3870i	0.922965	−	1.59862i
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$		0			0
$493$	−5.05842	+	8.76144i	−0.227820	+	0.394596i
$494$	−14.7446	−	25.5383i	−0.663389	−	1.14902i
$495$		0			0
$496$	1.81386	−	3.14170i	0.0814447	−	0.141066i
$497$	−25.1168	+	43.5036i	−1.12664	+	1.95141i
$498$		0			0
$499$	−4.11684	−	7.13058i	−0.184295	−	0.319209i	0.759044	−	0.651040i	$-0.225667\pi$
$499$	−4.11684	−	7.13058i	−0.184295	−	0.319209i	−0.943339	+	0.331831i	$0.892334\pi$
$500$	2.31386	+	4.00772i	0.103479	+	0.179231i
$501$		0			0
$502$	−0.627719	+	1.08724i	−0.0280165	+	0.0485259i
$503$	−11.0000	+	19.0526i	−0.490466	+	0.849512i	−0.999940	−	0.0109744i	$-0.996507\pi$
$503$	−11.0000	+	19.0526i	−0.490466	+	0.849512i	0.509474	+	0.860486i	$0.329840\pi$
$504$		0			0
$505$	25.0584	+	43.4025i	1.11509	+	1.93138i
$506$		0			0
$507$		0			0
$508$	14.3723			0.637667
$509$	−0.686141	+	1.18843i	−0.0304127	+	0.0526763i	−0.880831	−	0.473431i	$-0.843015\pi$
$509$	−0.686141	+	1.18843i	−0.0304127	+	0.0526763i	0.850418	+	0.526107i	$0.176349\pi$
$510$		0			0
$511$	−18.3030	−	31.7017i	−0.809676	−	1.40240i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−4.43070	−	7.67420i	−0.195430	−	0.338495i
$515$	2.11684	+	3.66648i	0.0932793	+	0.161564i
$516$		0			0
$517$	4.00000			0.175920
$518$	26.4891	−	2.37686i	1.16387	−	0.104433i
$519$		0			0
$520$	−7.37228	+	12.7692i	−0.323296	+	0.559965i
$521$	4.62772	+	8.01544i	0.202744	+	0.351163i	0.949412	−	0.314034i	$-0.101681\pi$
$521$	4.62772	+	8.01544i	0.202744	+	0.351163i	−0.746668	+	0.665197i	$0.768347\pi$
$522$		0			0
$523$	−9.55842	−	16.5557i	−0.417961	−	0.723929i	0.577774	−	0.816197i	$-0.303922\pi$
$523$	−9.55842	−	16.5557i	−0.417961	−	0.723929i	−0.995734	+	0.0922681i	$0.970588\pi$
$524$	0.744563			0.0325264
$525$		0			0
$526$	15.2554			0.665169
$527$	13.3723	−	23.1615i	0.582506	−	1.00893i
$528$		0			0
$529$	−23.0000			−1.00000
$530$	19.3723	−	33.5538i	0.841478	−	1.45748i
$531$		0			0
$532$	−29.4891			−1.27852
$533$	−3.00000	+	5.19615i	−0.129944	+	0.225070i
$534$		0			0
$535$	11.3723	−	19.6974i	0.491667	−	0.851592i
$536$	6.55842	+	11.3595i	0.283281	+	0.490657i
$537$		0			0
$538$	1.00000	−	1.73205i	0.0431131	−	0.0746740i
$539$	12.1168	−	20.9870i	0.521909	−	0.903974i
$540$		0			0
$541$	5.74456			0.246978			0.123489	−	0.992346i	$-0.460592\pi$
$541$	5.74456			0.246978			0.123489	+	0.992346i	$0.460592\pi$
$542$	4.93070	+	8.54023i	0.211792	+	0.366834i
$543$		0			0
$544$	7.37228			0.316084
$545$	53.0951			2.27434
$546$		0			0
$547$	24.0951			1.03023			0.515116	−	0.857121i	$-0.327749\pi$
$547$	24.0951			1.03023			0.515116	+	0.857121i	$0.327749\pi$
$548$	2.31386	+	4.00772i	0.0988432	+	0.171201i
$549$		0			0
$550$	6.37228	+	11.0371i	0.271715	+	0.470624i
$551$	4.62772	+	8.01544i	0.197147	+	0.341469i
$552$		0			0
$553$	9.55842	−	16.5557i	0.406465	−	0.704019i
$554$	−30.8614			−1.31118
$555$		0			0
$556$	−14.3723			−0.609520
$557$	−7.05842	+	12.2255i	−0.299075	+	0.518013i	−0.975925	−	0.218108i	$-0.930011\pi$
$557$	−7.05842	+	12.2255i	−0.299075	+	0.518013i	0.676850	+	0.736121i	$0.263345\pi$
$558$		0			0
$559$	−7.93070	−	13.7364i	−0.335433	−	0.580987i
$560$	7.37228	+	12.7692i	0.311536	+	0.539596i
$561$		0			0
$562$	5.05842	+	8.76144i	0.213377	+	0.369579i
$563$	−24.7446			−1.04286			−0.521429	−	0.853294i	$-0.674601\pi$
$563$	−24.7446			−1.04286			−0.521429	+	0.853294i	$0.674601\pi$
$564$		0			0
$565$	25.2554			1.06250
$566$	17.1168			0.719475
$567$		0			0
$568$	−5.74456	−	9.94987i	−0.241036	−	0.417487i
$569$	−21.3723			−0.895973			−0.447986	−	0.894040i	$-0.647859\pi$
$569$	−21.3723			−0.895973			−0.447986	+	0.894040i	$0.647859\pi$
$570$		0			0
$571$	19.4198	−	33.6361i	0.812695	−	1.40763i	−0.0982770	−	0.995159i	$-0.531333\pi$
$571$	19.4198	−	33.6361i	0.812695	−	1.40763i	0.910972	−	0.412469i	$-0.135334\pi$
$572$	−4.37228	+	7.57301i	−0.182814	+	0.316644i
$573$		0			0
$574$	3.00000	+	5.19615i	0.125218	+	0.216883i
$575$		0			0
$576$		0			0
$577$	−16.4891	+	28.5600i	−0.686451	+	1.18897i	0.286527	+	0.958072i	$0.407499\pi$
$577$	−16.4891	+	28.5600i	−0.686451	+	1.18897i	−0.972978	+	0.230896i	$0.925834\pi$
$578$	37.3505			1.55358
$579$		0			0
$580$	2.31386	−	4.00772i	0.0960778	−	0.166412i
$581$	−34.9783			−1.45114
$582$		0			0
$583$	11.4891	−	19.8997i	0.475831	−	0.824163i
$584$	8.37228			0.346447
$585$		0			0
$586$	15.8832			0.656127
$587$	4.37228	+	7.57301i	0.180463	+	0.312572i	0.942038	−	0.335505i	$-0.108907\pi$
$587$	4.37228	+	7.57301i	0.180463	+	0.312572i	−0.761575	+	0.648077i	$0.775574\pi$
$588$		0			0
$589$	−12.2337	−	21.1894i	−0.504080	−	0.873093i
$590$	6.74456	−	11.6819i	0.277669	−	0.480937i
$591$		0			0
$592$	−2.55842	+	5.51856i	−0.105150	+	0.226811i
$593$	−8.62772			−0.354298			−0.177149	−	0.984184i	$-0.556687\pi$
$593$	−8.62772			−0.354298			−0.177149	+	0.984184i	$0.556687\pi$
$594$		0			0
$595$	54.3505	+	94.1379i	2.22815	+	3.85928i
$596$	3.68614	+	6.38458i	0.150990	+	0.261523i
$597$		0			0
$598$		0			0
$599$	9.37228	+	16.2333i	0.382941	+	0.663273i	0.991481	−	0.130250i	$-0.0415779\pi$
$599$	9.37228	+	16.2333i	0.382941	+	0.663273i	−0.608540	+	0.793523i	$0.708245\pi$
$600$		0			0
$601$	8.50000	−	14.7224i	0.346722	−	0.600541i	−0.638943	−	0.769254i	$-0.720628\pi$
$601$	8.50000	−	14.7224i	0.346722	−	0.600541i	0.985665	+	0.168714i	$0.0539613\pi$
$602$	−15.8614			−0.646463
$603$		0			0
$604$	6.81386	−	11.8020i	0.277252	−	0.480215i
$605$	−11.8030	−	20.4434i	−0.479860	−	0.831141i
$606$		0			0
$607$	4.86141	−	8.42020i	0.197318	−	0.341766i	−0.750340	−	0.661052i	$-0.770110\pi$
$607$	4.86141	−	8.42020i	0.197318	−	0.341766i	0.947658	+	0.319287i	$0.103443\pi$
$608$	3.37228	−	5.84096i	0.136764	−	0.236882i
$609$		0			0
$610$	13.6861	+	23.7051i	0.554136	+	0.959791i
$611$	−4.37228	−	7.57301i	−0.176884	−	0.306371i
$612$		0			0
$613$	5.43070	−	9.40625i	0.219344	−	0.379915i	−0.735264	−	0.677781i	$-0.762942\pi$
$613$	5.43070	−	9.40625i	0.219344	−	0.379915i	0.954608	+	0.297866i	$0.0962750\pi$
$614$	−4.55842	+	7.89542i	−0.183963	+	0.318633i
$615$		0			0
$616$	4.37228	+	7.57301i	0.176164	+	0.305125i
$617$	16.8614	−	29.2048i	0.678815	−	1.17574i	−0.296523	−	0.955026i	$-0.595827\pi$
$617$	16.8614	−	29.2048i	0.678815	−	1.17574i	0.975338	−	0.220716i	$-0.0708394\pi$
$618$		0			0
$619$	−40.8397			−1.64148			−0.820742	−	0.571299i	$-0.806440\pi$
$619$	−40.8397			−1.64148			−0.820742	+	0.571299i	$0.806440\pi$
$620$	−6.11684	+	10.5947i	−0.245658	+	0.425493i
$621$		0			0
$622$	8.48913	+	14.7036i	0.340383	+	0.589560i
$623$	−40.9783			−1.64176
$624$		0			0
$625$	8.12772	+	14.0776i	0.325109	+	0.563105i
$626$	8.50000	+	14.7224i	0.339728	+	0.588427i
$627$		0			0
$628$	−16.4891			−0.657988
$629$	−18.8614	+	40.6844i	−0.752054	+	1.62219i
$630$		0			0
$631$	12.4416	−	21.5494i	0.495291	−	0.857870i	−0.504694	−	0.863298i	$-0.668395\pi$
$631$	12.4416	−	21.5494i	0.495291	−	0.857870i	0.999985	+	0.00542852i	$0.00172796\pi$
$632$	2.18614	+	3.78651i	0.0869600	+	0.150619i
$633$		0			0
$634$	−15.0584	−	26.0820i	−0.598046	−	1.03585i
$635$	−48.4674			−1.92337
$636$		0			0
$637$	−52.9783			−2.09907
$638$	1.37228	−	2.37686i	0.0543291	−	0.0941008i
$639$		0			0
$640$	−3.37228			−0.133301
$641$	1.05842	−	1.83324i	0.0418052	−	0.0724087i	−0.844366	−	0.535767i	$-0.820022\pi$
$641$	1.05842	−	1.83324i	0.0418052	−	0.0724087i	0.886171	+	0.463359i	$0.153356\pi$
$642$		0			0
$643$	−22.6060			−0.891492			−0.445746	−	0.895159i	$-0.647062\pi$
$643$	−22.6060			−0.891492			−0.445746	+	0.895159i	$0.647062\pi$
$644$		0			0
$645$		0			0
$646$	24.8614	−	43.0612i	0.978159	−	1.69422i
$647$	8.86141	+	15.3484i	0.348378	+	0.603408i	0.985961	−	0.166973i	$-0.0533993\pi$
$647$	8.86141	+	15.3484i	0.348378	+	0.603408i	−0.637584	+	0.770381i	$0.720066\pi$
$648$		0			0
$649$	4.00000	−	6.92820i	0.157014	−	0.271956i
$650$	13.9307	−	24.1287i	0.546407	−	0.946405i
$651$		0			0
$652$	13.2554			0.519123
$653$	23.9198	+	41.4304i	0.936055	+	1.62130i	0.772741	+	0.634721i	$0.218885\pi$
$653$	23.9198	+	41.4304i	0.936055	+	1.62130i	0.163314	+	0.986574i	$0.447782\pi$
$654$		0			0
$655$	−2.51087			−0.0981080
$656$	−1.37228			−0.0535786
$657$		0			0
$658$	−8.74456			−0.340899
$659$	21.1168	+	36.5754i	0.822595	+	1.42478i	0.903743	+	0.428075i	$0.140808\pi$
$659$	21.1168	+	36.5754i	0.822595	+	1.42478i	−0.0811477	+	0.996702i	$0.525859\pi$
$660$		0			0
$661$	12.9891	+	22.4978i	0.505218	+	0.875064i	0.999982	+	0.00603623i	$0.00192140\pi$
$661$	12.9891	+	22.4978i	0.505218	+	0.875064i	−0.494763	+	0.869028i	$0.664745\pi$
$662$	−2.30298	−	3.98889i	−0.0895080	−	0.155032i
$663$		0			0
$664$	4.00000	−	6.92820i	0.155230	−	0.268866i
$665$	99.4456			3.85634
$666$		0			0
$667$		0			0
$668$	10.7446	−	18.6101i	0.415720	−	0.720047i
$669$		0			0
$670$	−22.1168	−	38.3075i	−0.854448	−	1.47995i
$671$	8.11684	+	14.0588i	0.313347	+	0.542733i
$672$		0			0
$673$	−16.4891	−	28.5600i	−0.635609	−	1.10091i	−0.986386	−	0.164448i	$-0.947416\pi$
$673$	−16.4891	−	28.5600i	−0.635609	−	1.10091i	0.350777	−	0.936459i	$-0.385918\pi$
$674$	18.2554			0.703173
$675$		0			0
$676$	6.11684			0.235263
$677$	11.8832			0.456707			0.228353	−	0.973578i	$-0.426666\pi$
$677$	11.8832			0.456707			0.228353	+	0.973578i	$0.426666\pi$
$678$		0			0
$679$	12.5584	+	21.7518i	0.481948	+	0.834758i
$680$	−24.8614			−0.953391
$681$		0			0
$682$	−3.62772	+	6.28339i	−0.138913	+	0.240604i
$683$	−10.1168	+	17.5229i	−0.387110	+	0.670495i	−0.992060	−	0.125769i	$-0.959860\pi$
$683$	−10.1168	+	17.5229i	−0.387110	+	0.670495i	0.604949	+	0.796264i	$0.293193\pi$
$684$		0			0
$685$	−7.80298	−	13.5152i	−0.298137	−	0.516388i
$686$	−11.1861	+	19.3750i	−0.427089	+	0.739740i
$687$		0			0
$688$	1.81386	−	3.14170i	0.0691527	−	0.119776i
$689$	−50.2337			−1.91375
$690$		0			0
$691$	10.1861	−	17.6429i	0.387499	−	0.671168i	−0.604613	−	0.796519i	$-0.706672\pi$
$691$	10.1861	−	17.6429i	0.387499	−	0.671168i	0.992112	+	0.125351i	$0.0400057\pi$
$692$	−5.88316			−0.223644
$693$		0			0
$694$	7.62772	−	13.2116i	0.289544	−	0.501505i
$695$	48.4674			1.83847
$696$		0			0
$697$	−10.1168			−0.383203
$698$	−4.05842	−	7.02939i	−0.153614	−	0.266066i
$699$		0			0
$700$	−13.9307	−	24.1287i	−0.526531	−	0.911979i
$701$	3.88316	−	6.72582i	0.146665	−	0.254031i	−0.783328	−	0.621609i	$-0.786479\pi$
$701$	3.88316	−	6.72582i	0.146665	−	0.254031i	0.929993	+	0.367578i	$0.119813\pi$
$702$		0			0
$703$	23.6060	+	33.5538i	0.890316	+	1.26550i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$	−4.80298	−	8.31901i	−0.180763	−	0.313090i
$707$	−32.4891	−	56.2728i	−1.22188	−	2.11636i
$708$		0			0
$709$	18.6060			0.698762			0.349381	−	0.936981i	$-0.386392\pi$
$709$	18.6060			0.698762			0.349381	+	0.936981i	$0.386392\pi$
$710$	19.3723	+	33.5538i	0.727029	+	1.25925i
$711$		0			0
$712$	4.68614	−	8.11663i	0.175621	−	0.304184i
$713$		0			0
$714$		0			0
$715$	14.7446	−	25.5383i	0.551415	−	0.955079i
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$		0			0
$718$	−11.1168	+	19.2549i	−0.414877	+	0.718588i
$719$	18.6060	−	32.2265i	0.693886	−	1.20185i	−0.276669	−	0.960965i	$-0.589231\pi$
$719$	18.6060	−	32.2265i	0.693886	−	1.20185i	0.970555	−	0.240880i	$-0.0774360\pi$
$720$		0			0
$721$	−2.74456	−	4.75372i	−0.102213	−	0.177038i
$722$	−13.2446	−	22.9403i	−0.492912	−	0.853748i
$723$		0			0
$724$	7.87228	−	13.6352i	0.292571	−	0.506748i
$725$	−4.37228	+	7.57301i	−0.162382	+	0.281255i
$726$		0			0
$727$	17.0475	+	29.5272i	0.632259	+	1.09510i	0.987089	+	0.160173i	$0.0512053\pi$
$727$	17.0475	+	29.5272i	0.632259	+	1.09510i	−0.354830	+	0.934931i	$0.615461\pi$
$728$	9.55842	−	16.5557i	0.354259	−	0.613594i
$729$		0			0
$730$	−28.2337			−1.04498
$731$	13.3723	−	23.1615i	0.494592	−	0.856658i
$732$		0			0
$733$	−1.81386	−	3.14170i	−0.0669964	−	0.116041i	0.830581	−	0.556897i	$-0.188008\pi$
$733$	−1.81386	−	3.14170i	−0.0669964	−	0.116041i	−0.897578	+	0.440856i	$0.854675\pi$
$734$	−11.1168			−0.410330
$735$		0			0
$736$		0			0
$737$	−13.1168	−	22.7190i	−0.483165	−	0.836867i
$738$		0			0
$739$	44.4674			1.63576			0.817879	−	0.575390i	$-0.195150\pi$
$739$	44.4674			1.63576			0.817879	+	0.575390i	$0.195150\pi$
$740$	8.62772	−	18.6101i	0.317161	−	0.684122i
$741$		0			0
$742$	−25.1168	+	43.5036i	−0.922068	+	1.59707i
$743$	17.7446	+	30.7345i	0.650985	+	1.12754i	0.982884	+	0.184224i	$0.0589772\pi$
$743$	17.7446	+	30.7345i	0.650985	+	1.12754i	−0.331899	+	0.943315i	$0.607689\pi$
$744$		0			0
$745$	−12.4307	−	21.5306i	−0.455426	−	0.788821i
$746$	−31.0000			−1.13499
$747$		0			0
$748$	−14.7446			−0.539115
$749$	−14.7446	+	25.5383i	−0.538755	+	0.933150i
$750$		0			0
$751$	33.1168			1.20845			0.604225	−	0.796813i	$-0.293483\pi$
$751$	33.1168			1.20845			0.604225	+	0.796813i	$0.293483\pi$
$752$	1.00000	−	1.73205i	0.0364662	−	0.0631614i
$753$		0			0
$754$	−6.00000			−0.218507
$755$	−22.9783	+	39.7995i	−0.836264	+	1.44845i
$756$		0			0
$757$	15.8723	−	27.4916i	0.576888	−	0.999199i	−0.418946	−	0.908011i	$-0.637600\pi$
$757$	15.8723	−	27.4916i	0.576888	−	0.999199i	0.995834	−	0.0911879i	$-0.0290664\pi$
$758$	−14.8614	−	25.7407i	−0.539791	−	0.934945i
$759$		0			0
$760$	−11.3723	+	19.6974i	−0.412516	+	0.714499i
$761$	−2.43070	+	4.21010i	−0.0881129	+	0.152616i	−0.906713	−	0.421747i	$-0.861417\pi$
$761$	−2.43070	+	4.21010i	−0.0881129	+	0.152616i	0.818601	+	0.574363i	$0.194750\pi$
$762$		0			0
$763$	−68.8397			−2.49216
$764$	−5.62772	−	9.74749i	−0.203604	−	0.352652i
$765$		0			0
$766$	−28.2337			−1.02012
$767$	−17.4891			−0.631496
$768$		0			0
$769$	21.1168			0.761493			0.380746	−	0.924679i	$-0.375667\pi$
$769$	21.1168			0.761493			0.380746	+	0.924679i	$0.375667\pi$
$770$	−14.7446	−	25.5383i	−0.531357	−	0.920338i
$771$		0			0
$772$	−2.24456	−	3.88770i	−0.0807836	−	0.139921i
$773$	16.4307	+	28.4588i	0.590971	+	1.02359i	0.994102	+	0.108450i	$0.0345887\pi$
$773$	16.4307	+	28.4588i	0.590971	+	1.02359i	−0.403131	+	0.915142i	$0.632078\pi$
$774$		0			0
$775$	11.5584	−	20.0198i	0.415191	−	0.719132i
$776$	−5.74456			−0.206218
$777$		0			0
$778$	−24.1168			−0.864631
$779$	−4.62772	+	8.01544i	−0.165805	+	0.287183i
$780$		0			0
$781$	11.4891	+	19.8997i	0.411113	+	0.712069i
$782$		0			0
$783$		0			0
$784$	−6.05842	−	10.4935i	−0.216372	−	0.374768i
$785$	55.6060			1.98466
$786$		0			0
$787$	11.1168			0.396273			0.198136	−	0.980174i	$-0.436511\pi$
$787$	11.1168			0.396273			0.198136	+	0.980174i	$0.436511\pi$
$788$	−19.3723			−0.690109
$789$		0			0
$790$	−7.37228	−	12.7692i	−0.262294	−	0.454307i
$791$	−32.7446			−1.16426
$792$		0			0
$793$	17.7446	−	30.7345i	0.630128	−	1.09141i
$794$	9.50000	−	16.4545i	0.337142	−	0.583948i
$795$		0			0
$796$	6.18614	+	10.7147i	0.219262	+	0.379773i
$797$	19.6060	−	33.9585i	0.694479	−	1.20287i	−0.275877	−	0.961193i	$-0.588968\pi$
$797$	19.6060	−	33.9585i	0.694479	−	1.20287i	0.970356	−	0.241680i	$-0.0776984\pi$
$798$		0			0
$799$	7.37228	−	12.7692i	0.260813	−	0.451741i
$800$	6.37228			0.225294
$801$		0			0
$802$	−7.37228	+	12.7692i	−0.260324	+	0.450895i
$803$	−16.7446			−0.590903
$804$		0			0
$805$		0			0
$806$	15.8614			0.558694
$807$		0			0
$808$	14.8614			0.522822
$809$	−3.51087	−	6.08101i	−0.123436	−	0.213797i	0.797685	−	0.603075i	$-0.206058\pi$
$809$	−3.51087	−	6.08101i	−0.123436	−	0.213797i	−0.921120	+	0.389278i	$0.872725\pi$
$810$		0			0
$811$	17.4891	+	30.2921i	0.614126	+	1.06370i	0.990537	+	0.137245i	$0.0438248\pi$
$811$	17.4891	+	30.2921i	0.614126	+	1.06370i	−0.376411	+	0.926453i	$0.622842\pi$
$812$	−3.00000	+	5.19615i	−0.105279	+	0.182349i
$813$		0			0
$814$	5.11684	−	11.0371i	0.179345	−	0.386851i
$815$	−44.7011			−1.56581
$816$		0			0
$817$	−12.2337	−	21.1894i	−0.428003	−	0.741322i
$818$	6.12772	+	10.6135i	0.214251	+	0.371093i
$819$		0			0
$820$	4.62772			0.161607
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	0.607714	−	0.794156i	$-0.292087\pi$
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	−0.991616	+	0.129217i	$0.958754\pi$
$822$		0			0
$823$	−13.4198	+	23.2438i	−0.467786	+	0.810229i	−0.999322	−	0.0368065i	$-0.988281\pi$
$823$	−13.4198	+	23.2438i	−0.467786	+	0.810229i	0.531537	+	0.847035i	$0.321615\pi$
$824$	1.25544			0.0437352
$825$		0			0
$826$	−8.74456	+	15.1460i	−0.304262	+	0.526998i
$827$	16.0000	+	27.7128i	0.556375	+	0.963669i	0.997795	+	0.0663686i	$0.0211413\pi$
$827$	16.0000	+	27.7128i	0.556375	+	0.963669i	−0.441421	+	0.897300i	$0.645525\pi$
$828$		0			0
$829$	−5.06930	+	8.78028i	−0.176064	+	0.304952i	−0.940529	−	0.339714i	$-0.889670\pi$
$829$	−5.06930	+	8.78028i	−0.176064	+	0.304952i	0.764465	+	0.644665i	$0.223003\pi$
$830$	−13.4891	+	23.3639i	−0.468214	+	0.810971i
$831$		0			0
$832$	2.18614	+	3.78651i	0.0757908	+	0.131274i
$833$	−44.6644	−	77.3610i	−1.54753	−	2.68040i
$834$		0			0
$835$	−36.2337	+	62.7586i	−1.25392	+	2.17185i
$836$	−6.74456	+	11.6819i	−0.233266	+	0.404028i
$837$		0			0
$838$	−1.74456	−	3.02167i	−0.0602649	−	0.104382i
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	−0.829435	−	0.558604i	$-0.811337\pi$
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	0.898482	+	0.439010i	$0.144671\pi$
$840$		0			0
$841$	−27.1168			−0.935064
$842$	8.68614	−	15.0448i	0.299344	−	0.518479i
$843$		0			0
$844$	−3.81386	−	6.60580i	−0.131278	−	0.227381i
$845$	−20.6277			−0.709615
$846$		0			0
$847$	15.3030	+	26.5055i	0.525817	+	0.910741i
$848$	−5.74456	−	9.94987i	−0.197269	−	0.341680i
$849$		0			0
$850$	46.9783			1.61134
$851$		0			0
$852$		0			0
$853$	−2.80298	+	4.85491i	−0.0959724	+	0.166229i	−0.910014	−	0.414577i	$-0.863929\pi$
$853$	−2.80298	+	4.85491i	−0.0959724	+	0.166229i	0.814042	+	0.580807i	$0.197263\pi$
$854$	−17.7446	−	30.7345i	−0.607206	−	1.05171i
$855$		0			0
$856$	−3.37228	−	5.84096i	−0.115262	−	0.199640i
$857$	43.8397			1.49753			0.748767	−	0.662833i	$-0.230646\pi$
$857$	43.8397			1.49753			0.748767	+	0.662833i	$0.230646\pi$
$858$		0			0
$859$	−2.60597			−0.0889145			−0.0444573	−	0.999011i	$-0.514156\pi$
$859$	−2.60597			−0.0889145			−0.0444573	+	0.999011i	$0.514156\pi$
$860$	−6.11684	+	10.5947i	−0.208583	+	0.361276i
$861$		0			0
$862$	36.9783			1.25948
$863$	−7.62772	+	13.2116i	−0.259651	+	0.449728i	−0.966148	−	0.257987i	$-0.916941\pi$
$863$	−7.62772	+	13.2116i	−0.259651	+	0.449728i	0.706498	+	0.707715i	$0.250274\pi$
$864$		0			0
$865$	19.8397			0.674569
$866$	−6.68614	+	11.5807i	−0.227204	+	0.393529i
$867$		0			0
$868$	7.93070	−	13.7364i	0.269186	−	0.466243i
$869$	−4.37228	−	7.57301i	−0.148319	−	0.256897i
$870$		0			0
$871$	−28.6753	+	49.6670i	−0.971624	+	1.68290i
$872$	7.87228	−	13.6352i	0.266589	−	0.461746i
$873$		0			0
$874$		0			0
$875$	10.1168	+	17.5229i	0.342012	+	0.592382i
$876$		0			0
$877$	−47.0000			−1.58708			−0.793539	−	0.608520i	$-0.791764\pi$
$877$	−47.0000			−1.58708			−0.793539	+	0.608520i	$0.791764\pi$
$878$	14.3723			0.485041
$879$		0			0
$880$	6.74456			0.227359
$881$	5.05842	+	8.76144i	0.170423	+	0.295181i	0.938568	−	0.345095i	$-0.112153\pi$
$881$	5.05842	+	8.76144i	0.170423	+	0.295181i	−0.768145	+	0.640276i	$0.778820\pi$
$882$		0			0
$883$	−19.4891	−	33.7562i	−0.655861	−	1.13599i	−0.981677	−	0.190552i	$-0.938972\pi$
$883$	−19.4891	−	33.7562i	−0.655861	−	1.13599i	0.325816	−	0.945433i	$-0.394361\pi$
$884$	16.1168	+	27.9152i	0.542068	+	0.938890i
$885$		0			0
$886$	8.74456	−	15.1460i	0.293779	−	0.508841i
$887$	20.0000			0.671534			0.335767	−	0.941945i	$-0.391004\pi$
$887$	20.0000			0.671534			0.335767	+	0.941945i	$0.391004\pi$
$888$		0			0
$889$	62.8397			2.10757
$890$	−15.8030	+	27.3716i	−0.529717	+	0.917497i
$891$		0			0
$892$	−0.441578	−	0.764836i	−0.0147851	−	0.0256086i
$893$	−6.74456	−	11.6819i	−0.225698	−	0.390921i
$894$		0			0
$895$	20.2337	+	35.0458i	0.676338	+	1.17145i
$896$	4.37228			0.146068
$897$		0			0
$898$	20.9783			0.700053
$899$	−4.97825			−0.166034
$900$		0			0
$901$	−42.3505	−	73.3533i	−1.41090	−	2.44375i
$902$	2.74456			0.0913839
$903$		0			0
$904$	3.74456	−	6.48577i	0.124542	−	0.215714i
$905$	−26.5475	+	45.9817i	−0.882470	+	1.52848i
$906$		0			0
$907$	15.6753	+	27.1504i	0.520489	+	0.901513i	0.999716	+	0.0238221i	$0.00758353\pi$
$907$	15.6753	+	27.1504i	0.520489	+	0.901513i	−0.479228	+	0.877691i	$0.659083\pi$
$908$	5.74456	−	9.94987i	0.190640	−	0.330198i
$909$		0			0
$910$	−32.2337	+	55.8304i	−1.06854	+	1.85076i
$911$	35.7228			1.18355			0.591775	−	0.806103i	$-0.298427\pi$
$911$	35.7228			1.18355			0.591775	+	0.806103i	$0.298427\pi$
$912$		0			0
$913$	−8.00000	+	13.8564i	−0.264761	+	0.458580i
$914$	−39.0951			−1.29315
$915$		0			0
$916$	1.12772	−	1.95327i	0.0372609	−	0.0645377i
$917$	3.25544			0.107504
$918$		0			0
$919$	16.6060			0.547780			0.273890	−	0.961761i	$-0.411690\pi$
$919$	16.6060			0.547780			0.273890	+	0.961761i	$0.411690\pi$
$920$		0			0
$921$		0			0
$922$	12.4891	+	21.6318i	0.411307	+	0.712405i
$923$	25.1168	−	43.5036i	0.826731	−	1.43194i
$924$		0			0
$925$	−16.3030	+	35.1658i	−0.536039	+	1.15624i
$926$	17.1168			0.562494
$927$		0			0
$928$	−0.686141	−	1.18843i	−0.0225237	−	0.0390121i
$929$	−24.8030	−	42.9600i	−0.813760	−	1.40947i	−0.910215	−	0.414136i	$-0.864084\pi$
$929$	−24.8030	−	42.9600i	−0.813760	−	1.40947i	0.0964557	−	0.995337i	$-0.469249\pi$
$930$		0			0
$931$	−81.7228			−2.67836
$932$	5.80298	+	10.0511i	0.190083	+	0.329234i
$933$		0			0
$934$	1.62772	−	2.81929i	0.0532606	−	0.0922500i
$935$	49.7228			1.62611
$936$		0			0
$937$	1.01087	−	1.75089i	0.0330238	−	0.0571990i	−0.849041	−	0.528327i	$-0.822820\pi$
$937$	1.01087	−	1.75089i	0.0330238	−	0.0571990i	0.882065	+	0.471128i	$0.156153\pi$
$938$	28.6753	+	49.6670i	0.936281	+	1.62169i
$939$		0			0
$940$	−3.37228	+	5.84096i	−0.109992	+	0.190511i
$941$	20.6644	−	35.7918i	0.673640	−	1.16678i	−0.303225	−	0.952919i	$-0.598063\pi$
$941$	20.6644	−	35.7918i	0.673640	−	1.16678i	0.976864	−	0.213859i	$-0.0686034\pi$
$942$		0			0
$943$		0			0
$944$	−2.00000	−	3.46410i	−0.0650945	−	0.112747i
$945$		0			0
$946$	−3.62772	+	6.28339i	−0.117947	+	0.204291i
$947$	−18.6060	+	32.2265i	−0.604613	+	1.04722i	0.387500	+	0.921870i	$0.373339\pi$
$947$	−18.6060	+	32.2265i	−0.604613	+	1.04722i	−0.992113	+	0.125350i	$0.959995\pi$
$948$		0			0
$949$	18.3030	+	31.7017i	0.594140	+	1.02908i
$950$	21.4891	−	37.2203i	0.697199	−	1.20758i
$951$		0			0
$952$	32.2337			1.04470
$953$	2.86141	−	4.95610i	0.0926901	−	0.160544i	−0.815952	−	0.578119i	$-0.803787\pi$
$953$	2.86141	−	4.95610i	0.0926901	−	0.160544i	0.908642	+	0.417576i	$0.137120\pi$
$954$		0			0
$955$	18.9783	+	32.8713i	0.614122	+	1.06369i
$956$	−12.2337			−0.395666
$957$		0			0
$958$	17.1168	+	29.6472i	0.553020	+	0.957859i
$959$	10.1168	+	17.5229i	0.326690	+	0.565844i
$960$		0			0
$961$	−17.8397			−0.575473
$962$	−26.4891	+	2.37686i	−0.854044	+	0.0766331i
$963$		0			0
$964$	−3.44158	+	5.96099i	−0.110846	+	0.191990i
$965$	7.56930	+	13.1104i	0.243664	+	0.422039i
$966$		0			0
$967$	−16.3030	−	28.2376i	−0.524269	−	0.908060i	−0.999601	−	0.0282535i	$-0.991005\pi$
$967$	−16.3030	−	28.2376i	−0.524269	−	0.908060i	0.475332	−	0.879806i	$-0.342328\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	19.3723			0.622006
$971$	−22.9783	+	39.7995i	−0.737407	+	1.27723i	0.216252	+	0.976338i	$0.430617\pi$
$971$	−22.9783	+	39.7995i	−0.737407	+	1.27723i	−0.953659	+	0.300889i	$0.902717\pi$
$972$		0			0
$973$	−62.8397			−2.01455
$974$	7.25544	−	12.5668i	0.232479	−	0.402666i
$975$		0			0
$976$	8.11684			0.259814
$977$	−7.37228	+	12.7692i	−0.235860	+	0.408522i	−0.959522	−	0.281633i	$-0.909124\pi$
$977$	−7.37228	+	12.7692i	−0.235860	+	0.408522i	0.723662	+	0.690154i	$0.242457\pi$
$978$		0			0
$979$	−9.37228	+	16.2333i	−0.299539	+	0.518817i
$980$	20.4307	+	35.3870i	0.652635	+	1.13040i
$981$		0			0
$982$	3.00000	−	5.19615i	0.0957338	−	0.165816i
$983$	−4.62772	+	8.01544i	−0.147601	+	0.255653i	−0.930340	−	0.366697i	$-0.880489\pi$
$983$	−4.62772	+	8.01544i	−0.147601	+	0.255653i	0.782739	+	0.622350i	$0.213822\pi$
$984$		0			0
$985$	65.3288			2.08155
$986$	−5.05842	−	8.76144i	−0.161093	−	0.279021i
$987$		0			0
$988$	29.4891			0.938174
$989$		0			0
$990$		0			0
$991$	−52.2337			−1.65926			−0.829629	−	0.558315i	$-0.811448\pi$
$991$	−52.2337			−1.65926			−0.829629	+	0.558315i	$0.811448\pi$
$992$	1.81386	+	3.14170i	0.0575901	+	0.0997490i
$993$		0			0
$994$	−25.1168	−	43.5036i	−0.796658	−	1.37985i
$995$	−20.8614	−	36.1330i	−0.661351	−	1.14549i
$996$		0			0
$997$	3.51087	−	6.08101i	0.111191	−	0.192588i	−0.805060	−	0.593193i	$-0.797867\pi$
$997$	3.51087	−	6.08101i	0.111191	−	0.192588i	0.916251	+	0.400606i	$0.131200\pi$
$998$	8.23369			0.260633
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.f.g.343.2		4
3.2	odd	2		222.2.e.c.121.1	✓	4
12.11	even	2		1776.2.q.h.1009.1		4
37.26	even	3	inner	666.2.f.g.433.2		4
111.26	odd	6		222.2.e.c.211.1	yes	4
111.47	odd	6		8214.2.a.m.1.2		2
111.101	odd	6		8214.2.a.o.1.1		2
444.359	even	6		1776.2.q.h.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.e.c.121.1	✓	4	3.2	odd	2
222.2.e.c.211.1	yes	4	111.26	odd	6
666.2.f.g.343.2		4	1.1	even	1	trivial
666.2.f.g.433.2		4	37.26	even	3	inner
1776.2.q.h.433.1		4	444.359	even	6
1776.2.q.h.1009.1		4	12.11	even	2
8214.2.a.m.1.2		2	111.47	odd	6
8214.2.a.o.1.1		2	111.101	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.68614 + 2.92048i) q^{5} +(-2.18614 - 3.78651i) q^{7} +1.00000 q^{8} -3.37228 q^{10} -2.00000 q^{11} +(2.18614 + 3.78651i) q^{13} +4.37228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.68614 + 6.38458i) q^{17} +(3.37228 + 5.84096i) q^{19} +(1.68614 - 2.92048i) q^{20} +(1.00000 - 1.73205i) q^{22} +(-3.18614 + 5.51856i) q^{25} -4.37228 q^{26} +(-2.18614 + 3.78651i) q^{28} +1.37228 q^{29} -3.62772 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.68614 - 6.38458i) q^{34} +(7.37228 - 12.7692i) q^{35} +(6.05842 - 0.543620i) q^{37} -6.74456 q^{38} +(1.68614 + 2.92048i) q^{40} +(0.686141 + 1.18843i) q^{41} -3.62772 q^{43} +(1.00000 + 1.73205i) q^{44} -2.00000 q^{47} +(-6.05842 + 10.4935i) q^{49} +(-3.18614 - 5.51856i) q^{50} +(2.18614 - 3.78651i) q^{52} +(-5.74456 + 9.94987i) q^{53} +(-3.37228 - 5.84096i) q^{55} +(-2.18614 - 3.78651i) q^{56} +(-0.686141 + 1.18843i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-4.05842 - 7.02939i) q^{61} +(1.81386 - 3.14170i) q^{62} +1.00000 q^{64} +(-7.37228 + 12.7692i) q^{65} +(6.55842 + 11.3595i) q^{67} +7.37228 q^{68} +(7.37228 + 12.7692i) q^{70} +(-5.74456 - 9.94987i) q^{71} +8.37228 q^{73} +(-2.55842 + 5.51856i) q^{74} +(3.37228 - 5.84096i) q^{76} +(4.37228 + 7.57301i) q^{77} +(2.18614 + 3.78651i) q^{79} -3.37228 q^{80} -1.37228 q^{82} +(4.00000 - 6.92820i) q^{83} -24.8614 q^{85} +(1.81386 - 3.14170i) q^{86} -2.00000 q^{88} +(4.68614 - 8.11663i) q^{89} +(9.55842 - 16.5557i) q^{91} +(1.00000 - 1.73205i) q^{94} +(-11.3723 + 19.6974i) q^{95} -5.74456 q^{97} +(-6.05842 - 10.4935i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + q^{5} - 3 q^{7} + 4 q^{8} - 2 q^{10} - 8 q^{11} + 3 q^{13} + 6 q^{14} - 2 q^{16} - 9 q^{17} + 2 q^{19} + q^{20} + 4 q^{22} - 7 q^{25} - 6 q^{26} - 3 q^{28} - 6 q^{29} - 26 q^{31}+ \cdots - 7 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + q^5 - 3 * q^7 + 4 * q^8 - 2 * q^10 - 8 * q^11 + 3 * q^13 + 6 * q^14 - 2 * q^16 - 9 * q^17 + 2 * q^19 + q^20 + 4 * q^22 - 7 * q^25 - 6 * q^26 - 3 * q^28 - 6 * q^29 - 26 * q^31 - 2 * q^32 - 9 * q^34 + 18 * q^35 + 7 * q^37 - 4 * q^38 + q^40 - 3 * q^41 - 26 * q^43 + 4 * q^44 - 8 * q^47 - 7 * q^49 - 7 * q^50 + 3 * q^52 - 2 * q^55 - 3 * q^56 + 3 * q^58 - 8 * q^59 + q^61 + 13 * q^62 + 4 * q^64 - 18 * q^65 + 9 * q^67 + 18 * q^68 + 18 * q^70 + 22 * q^73 + 7 * q^74 + 2 * q^76 + 6 * q^77 + 3 * q^79 - 2 * q^80 + 6 * q^82 + 16 * q^83 - 42 * q^85 + 13 * q^86 - 8 * q^88 + 13 * q^89 + 21 * q^91 + 4 * q^94 - 34 * q^95 - 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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