LMFDB - Embedded newform 222.2.e.c.121.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [222,2,Mod(121,222)] 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("222.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(222, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 222 = 2 \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	222.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.77267892487$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	222.121
Dual form			222.2.e.c.211.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.68614 - 2.92048i) q^{5} +1.00000 q^{6} +(-2.18614 - 3.78651i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -3.37228 q^{10} +2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(2.18614 + 3.78651i) q^{13} -4.37228 q^{14} +(1.68614 - 2.92048i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.68614 - 6.38458i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.37228 + 5.84096i) q^{19} +(-1.68614 + 2.92048i) q^{20} +(2.18614 - 3.78651i) q^{21} +(1.00000 - 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{24} +(-3.18614 + 5.51856i) q^{25} +4.37228 q^{26} -1.00000 q^{27} +(-2.18614 + 3.78651i) q^{28} -1.37228 q^{29} +(-1.68614 - 2.92048i) q^{30} -3.62772 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(-3.68614 - 6.38458i) q^{34} +(-7.37228 + 12.7692i) q^{35} +1.00000 q^{36} +(6.05842 - 0.543620i) q^{37} +6.74456 q^{38} +(-2.18614 + 3.78651i) q^{39} +(1.68614 + 2.92048i) q^{40} +(-0.686141 - 1.18843i) q^{41} +(-2.18614 - 3.78651i) q^{42} -3.62772 q^{43} +(-1.00000 - 1.73205i) q^{44} +3.37228 q^{45} +2.00000 q^{47} -1.00000 q^{48} +(-6.05842 + 10.4935i) q^{49} +(3.18614 + 5.51856i) q^{50} +7.37228 q^{51} +(2.18614 - 3.78651i) q^{52} +(5.74456 - 9.94987i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.37228 - 5.84096i) q^{55} +(2.18614 + 3.78651i) q^{56} +(-3.37228 + 5.84096i) q^{57} +(-0.686141 + 1.18843i) q^{58} +(2.00000 - 3.46410i) q^{59} -3.37228 q^{60} +(-4.05842 - 7.02939i) q^{61} +(-1.81386 + 3.14170i) q^{62} +4.37228 q^{63} +1.00000 q^{64} +(7.37228 - 12.7692i) q^{65} +2.00000 q^{66} +(6.55842 + 11.3595i) q^{67} -7.37228 q^{68} +(7.37228 + 12.7692i) q^{70} +(5.74456 + 9.94987i) q^{71} +(0.500000 - 0.866025i) q^{72} +8.37228 q^{73} +(2.55842 - 5.51856i) q^{74} -6.37228 q^{75} +(3.37228 - 5.84096i) q^{76} +(-4.37228 - 7.57301i) q^{77} +(2.18614 + 3.78651i) q^{78} +(2.18614 + 3.78651i) q^{79} +3.37228 q^{80} +(-0.500000 - 0.866025i) q^{81} -1.37228 q^{82} +(-4.00000 + 6.92820i) q^{83} -4.37228 q^{84} -24.8614 q^{85} +(-1.81386 + 3.14170i) q^{86} +(-0.686141 - 1.18843i) q^{87} -2.00000 q^{88} +(-4.68614 + 8.11663i) q^{89} +(1.68614 - 2.92048i) q^{90} +(9.55842 - 16.5557i) q^{91} +(-1.81386 - 3.14170i) q^{93} +(1.00000 - 1.73205i) q^{94} +(11.3723 - 19.6974i) q^{95} +(-0.500000 + 0.866025i) q^{96} -5.74456 q^{97} +(6.05842 + 10.4935i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + 4 q^{6} - 3 q^{7} - 4 q^{8} - 2 q^{9} - 2 q^{10} + 8 q^{11} + 2 q^{12} + 3 q^{13} - 6 q^{14} + q^{15} - 2 q^{16} + 9 q^{17} + 2 q^{18} + 2 q^{19} - q^{20}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + 4 * q^6 - 3 * q^7 - 4 * q^8 - 2 * q^9 - 2 * q^10 + 8 * q^11 + 2 * q^12 + 3 * q^13 - 6 * q^14 + q^15 - 2 * q^16 + 9 * q^17 + 2 * q^18 + 2 * q^19 - q^20 + 3 * q^21 + 4 * q^22 - 2 * q^24 - 7 * q^25 + 6 * q^26 - 4 * q^27 - 3 * q^28 + 6 * q^29 - q^30 - 26 * q^31 + 2 * q^32 + 4 * q^33 - 9 * q^34 - 18 * q^35 + 4 * q^36 + 7 * q^37 + 4 * q^38 - 3 * q^39 + q^40 + 3 * q^41 - 3 * q^42 - 26 * q^43 - 4 * q^44 + 2 * q^45 + 8 * q^47 - 4 * q^48 - 7 * q^49 + 7 * q^50 + 18 * q^51 + 3 * q^52 - 2 * q^54 - 2 * q^55 + 3 * q^56 - 2 * q^57 + 3 * q^58 + 8 * q^59 - 2 * q^60 + q^61 - 13 * q^62 + 6 * q^63 + 4 * q^64 + 18 * q^65 + 8 * q^66 + 9 * q^67 - 18 * q^68 + 18 * q^70 + 2 * q^72 + 22 * q^73 - 7 * q^74 - 14 * q^75 + 2 * q^76 - 6 * q^77 + 3 * q^78 + 3 * q^79 + 2 * q^80 - 2 * q^81 + 6 * q^82 - 16 * q^83 - 6 * q^84 - 42 * q^85 - 13 * q^86 + 3 * q^87 - 8 * q^88 - 13 * q^89 + q^90 + 21 * q^91 - 13 * q^93 + 4 * q^94 + 34 * q^95 - 2 * q^96 + 7 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/222\mathbb{Z}\right)^\times$.

$n$	$149$	$187$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.68614	−	2.92048i	−0.754065	−	1.30608i	−0.945838	−	0.324640i	$-0.894757\pi$
$5$	−1.68614	−	2.92048i	−0.754065	−	1.30608i	0.191773	−	0.981439i	$-0.438576\pi$
$6$	1.00000			0.408248
$7$	−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
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−3.37228			−1.06641
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	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
$15$	1.68614	−	2.92048i	0.435360	−	0.754065i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.68614	−	6.38458i	0.894020	−	1.54849i	0.0590081	−	0.998258i	$-0.481206\pi$
$17$	3.68614	−	6.38458i	0.894020	−	1.54849i	0.835012	−	0.550231i	$-0.185460\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	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
$21$	2.18614	−	3.78651i	0.477055	−	0.826284i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−3.18614	+	5.51856i	−0.637228	+	1.10371i
$26$	4.37228			0.857475
$27$	−1.00000			−0.192450
$28$	−2.18614	+	3.78651i	−0.413142	+	0.715583i
$29$	−1.37228			−0.254826			−0.127413	−	0.991850i	$-0.540667\pi$
$29$	−1.37228			−0.254826			−0.127413	+	0.991850i	$0.540667\pi$
$30$	−1.68614	−	2.92048i	−0.307846	−	0.533204i
$31$	−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
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$	−3.68614	−	6.38458i	−0.632168	−	1.09495i
$35$	−7.37228	+	12.7692i	−1.24614	+	2.15838i
$36$	1.00000			0.166667
$37$	6.05842	−	0.543620i	0.995998	−	0.0893706i
$37$	6.05842	−	0.543620i	0.995998	−	0.0893706i
$38$	6.74456			1.09411
$39$	−2.18614	+	3.78651i	−0.350063	+	0.606326i
$40$	1.68614	+	2.92048i	0.266602	+	0.461769i
$41$	−0.686141	−	1.18843i	−0.107157	−	0.185602i	0.807460	−	0.589922i	$-0.200841\pi$
$41$	−0.686141	−	1.18843i	−0.107157	−	0.185602i	−0.914617	+	0.404320i	$0.867508\pi$
$42$	−2.18614	−	3.78651i	−0.337329	−	0.584271i
$43$	−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
$45$	3.37228			0.502710
$46$		0			0
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	−1.00000			−0.144338
$49$	−6.05842	+	10.4935i	−0.865489	+	1.49907i
$50$	3.18614	+	5.51856i	0.450588	+	0.780442i
$51$	7.37228			1.03233
$52$	2.18614	−	3.78651i	0.303163	−	0.525094i
$53$	5.74456	−	9.94987i	0.789076	−	1.36672i	−0.137457	−	0.990508i	$-0.543893\pi$
$53$	5.74456	−	9.94987i	0.789076	−	1.36672i	0.926533	−	0.376213i	$-0.122774\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−3.37228	−	5.84096i	−0.454718	−	0.787595i
$56$	2.18614	+	3.78651i	0.292135	+	0.505993i
$57$	−3.37228	+	5.84096i	−0.446670	+	0.773654i
$58$	−0.686141	+	1.18843i	−0.0900947	+	0.156049i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	−3.37228			−0.435360
$61$	−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
$63$	4.37228			0.550856
$64$	1.00000			0.125000
$65$	7.37228	−	12.7692i	0.914419	−	1.58382i
$66$	2.00000			0.246183
$67$	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	$0.0721160\pi$
$71$	5.74456	+	9.94987i	0.681754	+	1.18083i	−0.292691	+	0.956207i	$0.594551\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	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
$75$	−6.37228			−0.735808
$76$	3.37228	−	5.84096i	0.386827	−	0.670004i
$77$	−4.37228	−	7.57301i	−0.498268	−	0.863025i
$78$	2.18614	+	3.78651i	0.247532	+	0.428737i
$79$	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
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.37228			−0.151543
$83$	−4.00000	+	6.92820i	−0.439057	+	0.760469i	−0.997617	−	0.0689950i	$-0.978021\pi$
$83$	−4.00000	+	6.92820i	−0.439057	+	0.760469i	0.558560	+	0.829464i	$0.311354\pi$
$84$	−4.37228			−0.477055
$85$	−24.8614			−2.69660
$86$	−1.81386	+	3.14170i	−0.195593	+	0.338778i
$87$	−0.686141	−	1.18843i	−0.0735620	−	0.127413i
$88$	−2.00000			−0.213201
$89$	−4.68614	+	8.11663i	−0.496730	+	0.860361i	−0.999993	−	0.00377186i	$-0.998799\pi$
$89$	−4.68614	+	8.11663i	−0.496730	+	0.860361i	0.503263	+	0.864133i	$0.332133\pi$
$90$	1.68614	−	2.92048i	0.177735	−	0.307846i
$91$	9.55842	−	16.5557i	1.00199	−	1.73551i
$92$		0			0
$93$	−1.81386	−	3.14170i	−0.188088	−	0.325779i
$94$	1.00000	−	1.73205i	0.103142	−	0.178647i
$95$	11.3723	−	19.6974i	1.16677	−	2.02091i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−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
$99$	−1.00000	+	1.73205i	−0.100504	+	0.174078i
$100$	6.37228			0.637228
$101$	−14.8614			−1.47877			−0.739383	−	0.673285i	$-0.764883\pi$
$101$	−14.8614			−1.47877			−0.739383	+	0.673285i	$0.764883\pi$
$102$	3.68614	−	6.38458i	0.364982	−	0.632168i
$103$	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
$105$	−14.7446			−1.43892
$106$	−5.74456	−	9.94987i	−0.557961	−	0.966417i
$107$	3.37228	+	5.84096i	0.326011	+	0.564667i	0.981716	−	0.190349i	$-0.0609621\pi$
$107$	3.37228	+	5.84096i	0.326011	+	0.564667i	−0.655706	+	0.755017i	$0.727629\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	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
$111$	3.50000	+	4.97494i	0.332205	+	0.472200i
$112$	4.37228			0.413142
$113$	−3.74456	+	6.48577i	−0.352259	+	0.610130i	−0.986645	−	0.162886i	$-0.947920\pi$
$113$	−3.74456	+	6.48577i	−0.352259	+	0.610130i	0.634386	+	0.773016i	$0.281253\pi$
$114$	3.37228	+	5.84096i	0.315843	+	0.547056i
$115$		0			0
$116$	0.686141	+	1.18843i	0.0637066	+	0.110343i
$117$	−4.37228			−0.404218
$118$	−2.00000	−	3.46410i	−0.184115	−	0.318896i
$119$	−32.2337			−2.95486
$120$	−1.68614	+	2.92048i	−0.153923	+	0.266602i
$121$	−7.00000			−0.636364
$122$	−8.11684			−0.734865
$123$	0.686141	−	1.18843i	0.0618672	−	0.107157i
$124$	1.81386	+	3.14170i	0.162889	+	0.282133i
$125$	4.62772			0.413916
$126$	2.18614	−	3.78651i	0.194757	−	0.337329i
$127$	−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
$129$	−1.81386	−	3.14170i	−0.159701	−	0.276611i
$130$	−7.37228	−	12.7692i	−0.646592	−	1.11993i
$131$	0.372281	−	0.644810i	0.0325264	−	0.0563373i	−0.849304	−	0.527904i	$-0.822978\pi$
$131$	0.372281	−	0.644810i	0.0325264	−	0.0563373i	0.881830	+	0.471567i	$0.156311\pi$
$132$	1.00000	−	1.73205i	0.0870388	−	0.150756i
$133$	14.7446	−	25.5383i	1.27852	−	2.21445i
$134$	13.1168			1.13312
$135$	1.68614	+	2.92048i	0.145120	+	0.251355i
$136$	−3.68614	+	6.38458i	−0.316084	+	0.547473i
$137$	4.62772			0.395373			0.197686	−	0.980265i	$-0.436657\pi$
$137$	4.62772			0.395373			0.197686	+	0.980265i	$0.436657\pi$
$138$		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
$141$	1.00000	+	1.73205i	0.0842152	+	0.145865i
$142$	11.4891			0.964146
$143$	4.37228	+	7.57301i	0.365629	+	0.633287i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.31386	+	4.00772i	0.192156	+	0.332823i
$146$	4.18614	−	7.25061i	0.346447	−	0.600065i
$147$	−12.1168			−0.999380
$148$	−3.50000	−	4.97494i	−0.287698	−	0.408937i
$149$	7.37228			0.603961			0.301980	−	0.953314i	$-0.402352\pi$
$149$	7.37228			0.603961			0.301980	+	0.953314i	$0.402352\pi$
$150$	−3.18614	+	5.51856i	−0.260147	+	0.450588i
$151$	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
$153$	3.68614	+	6.38458i	0.298007	+	0.516163i
$154$	−8.74456			−0.704657
$155$	6.11684	+	10.5947i	0.491317	+	0.850986i
$156$	4.37228			0.350063
$157$	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
$159$	11.4891			0.911147
$160$	1.68614	−	2.92048i	0.133301	−	0.230884i
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−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
$165$	3.37228	−	5.84096i	0.262532	−	0.454718i
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	−10.7446	−	18.6101i	−0.831439	−	1.44009i	−0.896897	−	0.442240i	$-0.854184\pi$
$167$	−10.7446	−	18.6101i	−0.831439	−	1.44009i	0.0654577	−	0.997855i	$-0.479149\pi$
$168$	−2.18614	+	3.78651i	−0.168664	+	0.292135i
$169$	−3.05842	+	5.29734i	−0.235263	+	0.407488i
$170$	−12.4307	+	21.5306i	−0.953391	+	1.65132i
$171$	−6.74456			−0.515770
$172$	1.81386	+	3.14170i	0.138305	+	0.239552i
$173$	−2.94158	+	5.09496i	−0.223644	+	0.387363i	−0.955912	−	0.293654i	$-0.905129\pi$
$173$	−2.94158	+	5.09496i	−0.223644	+	0.387363i	0.732268	+	0.681017i	$0.238462\pi$
$174$	−1.37228			−0.104032
$175$	27.8614			2.10612
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	4.00000			0.300658
$178$	4.68614	+	8.11663i	0.351241	+	0.608367i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	−1.68614	−	2.92048i	−0.125678	−	0.217680i
$181$	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
$183$	4.05842	−	7.02939i	0.300007	−	0.519628i
$184$		0			0
$185$	−11.8030	−	16.7769i	−0.867773	−	1.23346i
$186$	−3.62772			−0.265997
$187$	7.37228	−	12.7692i	0.539115	−	0.933774i
$188$	−1.00000	−	1.73205i	−0.0729325	−	0.126323i
$189$	2.18614	+	3.78651i	0.159018	+	0.275428i
$190$	−11.3723	−	19.6974i	−0.825032	−	1.42900i
$191$	−11.2554			−0.814415			−0.407207	−	0.913336i	$-0.633497\pi$
$191$	−11.2554			−0.814415			−0.407207	+	0.913336i	$0.633497\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	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
$195$	14.7446			1.05588
$196$	12.1168			0.865489
$197$	−9.68614	+	16.7769i	−0.690109	+	1.19530i	0.281693	+	0.959505i	$0.409104\pi$
$197$	−9.68614	+	16.7769i	−0.690109	+	1.19530i	−0.971802	+	0.235799i	$0.924229\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	−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
$201$	−6.55842	+	11.3595i	−0.462595	+	0.801239i
$202$	−7.43070	+	12.8704i	−0.522822	+	0.905555i
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$	−3.68614	−	6.38458i	−0.258081	−	0.447010i
$205$	−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
$210$	−7.37228	+	12.7692i	−0.508736	+	0.881156i
$211$	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
$213$	−5.74456	+	9.94987i	−0.393611	+	0.681754i
$214$	6.74456			0.461049
$215$	6.11684	+	10.5947i	0.417165	+	0.722551i
$216$	1.00000			0.0680414
$217$	7.93070	+	13.7364i	0.538371	+	0.932486i
$218$	−7.87228	−	13.6352i	−0.533178	−	0.923492i
$219$	4.18614	+	7.25061i	0.282873	+	0.489951i
$220$	−3.37228	+	5.84096i	−0.227359	+	0.393798i
$221$	32.2337			2.16827
$222$	6.05842	−	0.543620i	0.406615	−	0.0364854i
$223$	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
$225$	−3.18614	−	5.51856i	−0.212409	−	0.367904i
$226$	3.74456	+	6.48577i	0.249085	+	0.431427i
$227$	−5.74456	−	9.94987i	−0.381280	−	0.660396i	0.609965	−	0.792428i	$-0.291183\pi$
$227$	−5.74456	−	9.94987i	−0.381280	−	0.660396i	−0.991246	+	0.132032i	$0.957850\pi$
$228$	6.74456			0.446670
$229$	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
$231$	4.37228	−	7.57301i	0.287675	−	0.498268i
$232$	1.37228			0.0900947
$233$	11.6060			0.760332			0.380166	−	0.924918i	$-0.375867\pi$
$233$	11.6060			0.760332			0.380166	+	0.924918i	$0.375867\pi$
$234$	−2.18614	+	3.78651i	−0.142912	+	0.247532i
$235$	−3.37228	−	5.84096i	−0.219983	−	0.381022i
$236$	−4.00000			−0.260378
$237$	−2.18614	+	3.78651i	−0.142005	+	0.245960i
$238$	−16.1168	+	27.9152i	−1.04470	+	1.80947i
$239$	−6.11684	+	10.5947i	−0.395666	+	0.685313i	−0.993186	−	0.116541i	$-0.962819\pi$
$239$	−6.11684	+	10.5947i	−0.395666	+	0.685313i	0.597520	+	0.801854i	$0.296153\pi$
$240$	1.68614	+	2.92048i	0.108840	+	0.188516i
$241$	−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
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.05842	+	7.02939i	−0.259814	+	0.450011i
$245$	40.8614			2.61054
$246$	−0.686141	−	1.18843i	−0.0437467	−	0.0757716i
$247$	−14.7446	+	25.5383i	−0.938174	+	1.62497i
$248$	3.62772			0.230360
$249$	−8.00000			−0.506979
$250$	2.31386	−	4.00772i	0.146341	−	0.253471i
$251$	−1.25544			−0.0792425			−0.0396213	−	0.999215i	$-0.512615\pi$
$251$	−1.25544			−0.0792425			−0.0396213	+	0.999215i	$0.512615\pi$
$252$	−2.18614	−	3.78651i	−0.137714	−	0.238528i
$253$		0			0
$254$	7.18614	+	12.4468i	0.450899	+	0.780979i
$255$	−12.4307	−	21.5306i	−0.778441	−	1.34830i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.43070	−	7.67420i	0.276380	−	0.478704i	−0.694103	−	0.719876i	$-0.744199\pi$
$257$	4.43070	−	7.67420i	0.276380	−	0.478704i	0.970482	+	0.241172i	$0.0775319\pi$
$258$	−3.62772			−0.225852
$259$	−15.3030	−	21.7518i	−0.950881	−	1.35159i
$260$	−14.7446			−0.914419
$261$	0.686141	−	1.18843i	0.0424710	−	0.0735620i
$262$	−0.372281	−	0.644810i	−0.0229996	−	0.0398365i
$263$	7.62772	+	13.2116i	0.470345	+	0.814662i	0.999425	−	0.0339103i	$-0.0107960\pi$
$263$	7.62772	+	13.2116i	0.470345	+	0.814662i	−0.529080	+	0.848572i	$0.677463\pi$
$264$	−1.00000	−	1.73205i	−0.0615457	−	0.106600i
$265$	−38.7446			−2.38006
$266$	−14.7446	−	25.5383i	−0.904047	−	1.56586i
$267$	−9.37228			−0.573574
$268$	6.55842	−	11.3595i	0.400619	−	0.693893i
$269$	2.00000			0.121942			0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000			0.121942			0.0609711	+	0.998140i	$0.480580\pi$
$270$	3.37228			0.205231
$271$	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
$273$	19.1168			1.15700
$274$	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
$279$	1.81386	−	3.14170i	0.108593	−	0.188088i
$280$	7.37228	−	12.7692i	0.440578	−	0.763104i
$281$	−5.05842	+	8.76144i	−0.301760	+	0.522664i	−0.976535	−	0.215360i	$-0.930908\pi$
$281$	−5.05842	+	8.76144i	−0.301760	+	0.522664i	0.674775	+	0.738024i	$0.264241\pi$
$282$	2.00000			0.119098
$283$	−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
$285$	22.7446			1.34727
$286$	8.74456			0.517077
$287$	−3.00000	+	5.19615i	−0.177084	+	0.306719i
$288$	−1.00000			−0.0589256
$289$	−18.6753	−	32.3465i	−1.09855	−	1.90274i
$290$	4.62772			0.271749
$291$	−2.87228	−	4.97494i	−0.168376	−	0.291636i
$292$	−4.18614	−	7.25061i	−0.244975	−	0.424310i
$293$	7.94158	+	13.7552i	0.463952	+	0.803588i	0.999154	−	0.0411360i	$-0.0130977\pi$
$293$	7.94158	+	13.7552i	0.463952	+	0.803588i	−0.535202	+	0.844724i	$0.679764\pi$
$294$	−6.05842	+	10.4935i	−0.353334	+	0.611993i
$295$	−13.4891			−0.785367
$296$	−6.05842	+	0.543620i	−0.352139	+	0.0315973i
$297$	−2.00000			−0.116052
$298$	3.68614	−	6.38458i	0.213532	−	0.369849i
$299$		0			0
$300$	3.18614	+	5.51856i	0.183952	+	0.318614i
$301$	7.93070	+	13.7364i	0.457118	+	0.791752i
$302$	13.6277			0.784187
$303$	−7.43070	−	12.8704i	−0.426883	−	0.739383i
$304$	−6.74456			−0.386827
$305$	−13.6861	+	23.7051i	−0.783666	+	1.35735i
$306$	7.37228			0.421445
$307$	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
$309$	0.627719	+	1.08724i	0.0357097	+	0.0618510i
$310$	12.2337			0.694827
$311$	−8.48913	+	14.7036i	−0.481374	+	0.833764i	−0.999772	−	0.0213754i	$-0.993195\pi$
$311$	−8.48913	+	14.7036i	−0.481374	+	0.833764i	0.518397	+	0.855140i	$0.326529\pi$
$312$	2.18614	−	3.78651i	0.123766	−	0.214369i
$313$	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
$315$	−7.37228	−	12.7692i	−0.415381	−	0.719461i
$316$	2.18614	−	3.78651i	0.122980	−	0.213008i
$317$	15.0584	−	26.0820i	0.845765	−	1.46491i	−0.0391897	−	0.999232i	$-0.512478\pi$
$317$	15.0584	−	26.0820i	0.845765	−	1.46491i	0.884955	−	0.465677i	$-0.154189\pi$
$318$	5.74456	−	9.94987i	0.322139	−	0.557961i
$319$	−2.74456			−0.153666
$320$	−1.68614	−	2.92048i	−0.0942581	−	0.163260i
$321$	−3.37228	+	5.84096i	−0.188222	+	0.326011i
$322$		0			0
$323$	49.7228			2.76665
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−27.8614			−1.54547
$326$	6.62772	+	11.4795i	0.367075	+	0.635793i
$327$	15.7446			0.870676
$328$	0.686141	+	1.18843i	0.0378858	+	0.0656201i
$329$	−4.37228	−	7.57301i	−0.241052	−	0.417514i
$330$	−3.37228	−	5.84096i	−0.185638	−	0.321534i
$331$	−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
$333$	−2.55842	+	5.51856i	−0.140201	+	0.302415i
$334$	−21.4891			−1.17583
$335$	22.1168	−	38.3075i	1.20837	−	2.09296i
$336$	2.18614	+	3.78651i	0.119264	+	0.206571i
$337$	−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
$339$	−7.48913			−0.406753
$340$	12.4307	+	21.5306i	0.674150	+	1.16766i
$341$	−7.25544			−0.392904
$342$	−3.37228	+	5.84096i	−0.182352	+	0.315843i
$343$	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	$-0.365711\pi$
$347$	15.2554			0.818955			0.409477	+	0.912320i	$0.365711\pi$
$348$	−0.686141	+	1.18843i	−0.0367810	+	0.0637066i
$349$	−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
$351$	−2.18614	−	3.78651i	−0.116688	−	0.202109i
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	4.80298	−	8.31901i	0.255637	−	0.442776i	−0.709431	−	0.704775i	$-0.751048\pi$
$353$	4.80298	−	8.31901i	0.255637	−	0.442776i	0.965068	+	0.261998i	$0.0843815\pi$
$354$	2.00000	−	3.46410i	0.106299	−	0.184115i
$355$	19.3723	−	33.5538i	1.02817	−	1.78085i
$356$	9.37228			0.496730
$357$	−16.1168	−	27.9152i	−0.852994	−	1.47743i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	−22.2337			−1.17345			−0.586725	−	0.809787i	$-0.699583\pi$
$359$	−22.2337			−1.17345			−0.586725	+	0.809787i	$0.699583\pi$
$360$	−3.37228			−0.177735
$361$	−13.2446	+	22.9403i	−0.697082	+	1.20738i
$362$	15.7446			0.827516
$363$	−3.50000	−	6.06218i	−0.183702	−	0.318182i
$364$	−19.1168			−1.00199
$365$	−14.1168	−	24.4511i	−0.738909	−	1.27983i
$366$	−4.05842	−	7.02939i	−0.212137	−	0.367432i
$367$	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
$369$	1.37228			0.0714381
$370$	−20.4307	+	1.83324i	−1.06214	+	0.0953056i
$371$	−50.2337			−2.60800
$372$	−1.81386	+	3.14170i	−0.0940442	+	0.162889i
$373$	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
$375$	2.31386	+	4.00772i	0.119487	+	0.206958i
$376$	−2.00000			−0.103142
$377$	−3.00000	−	5.19615i	−0.154508	−	0.267615i
$378$	4.37228			0.224886
$379$	−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
$381$	−14.3723			−0.736314
$382$	−5.62772	+	9.74749i	−0.287939	+	0.498725i
$383$	−14.1168	−	24.4511i	−0.721337	−	1.24939i	−0.960464	−	0.278404i	$-0.910195\pi$
$383$	−14.1168	−	24.4511i	−0.721337	−	1.24939i	0.239127	−	0.970988i	$-0.423139\pi$
$384$	1.00000			0.0510310
$385$	−14.7446	+	25.5383i	−0.751452	+	1.30155i
$386$	2.24456	−	3.88770i	0.114245	−	0.197879i
$387$	1.81386	−	3.14170i	0.0922037	−	0.159701i
$388$	2.87228	+	4.97494i	0.145818	+	0.252564i
$389$	−12.0584	−	20.8858i	−0.611386	−	1.05895i	−0.991007	−	0.133810i	$-0.957279\pi$
$389$	−12.0584	−	20.8858i	−0.611386	−	1.05895i	0.379621	−	0.925142i	$-0.376054\pi$
$390$	7.37228	−	12.7692i	0.373310	−	0.646592i
$391$		0			0
$392$	6.05842	−	10.4935i	0.305997	−	0.530002i
$393$	0.744563			0.0375582
$394$	9.68614	+	16.7769i	0.487981	+	0.845207i
$395$	7.37228	−	12.7692i	0.370940	−	0.642486i
$396$	2.00000			0.100504
$397$	−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
$399$	29.4891			1.47630
$400$	−3.18614	−	5.51856i	−0.159307	−	0.275928i
$401$	−14.7446			−0.736308			−0.368154	−	0.929765i	$-0.620010\pi$
$401$	−14.7446			−0.736308			−0.368154	+	0.929765i	$0.620010\pi$
$402$	6.55842	+	11.3595i	0.327104	+	0.566561i
$403$	−7.93070	−	13.7364i	−0.395056	−	0.684258i
$404$	7.43070	+	12.8704i	0.369691	+	0.640324i
$405$	−1.68614	+	2.92048i	−0.0837850	+	0.145120i
$406$	6.00000			0.297775
$407$	12.1168	−	1.08724i	0.600610	−	0.0538925i
$408$	−7.37228			−0.364982
$409$	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
$411$	2.31386	+	4.00772i	0.114134	+	0.197686i
$412$	−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
$417$	14.3723			0.703814
$418$	13.4891			0.659775
$419$	1.74456	−	3.02167i	0.0852275	−	0.147618i	−0.820261	−	0.571990i	$-0.806172\pi$
$419$	1.74456	−	3.02167i	0.0852275	−	0.147618i	0.905488	+	0.424372i	$0.139505\pi$
$420$	7.37228	+	12.7692i	0.359730	+	0.623071i
$421$	−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
$423$	−1.00000	+	1.73205i	−0.0486217	+	0.0842152i
$424$	−5.74456	+	9.94987i	−0.278981	+	0.483209i
$425$	23.4891	+	40.6844i	1.13939	+	1.97348i
$426$	5.74456	+	9.94987i	0.278325	+	0.482073i
$427$	−17.7446	+	30.7345i	−0.858720	+	1.48735i
$428$	3.37228	−	5.84096i	0.163005	−	0.282334i
$429$	−4.37228	+	7.57301i	−0.211096	+	0.365629i
$430$	12.2337			0.589961
$431$	18.4891	+	32.0241i	0.890590	+	1.54255i	0.839170	+	0.543870i	$0.183041\pi$
$431$	18.4891	+	32.0241i	0.890590	+	1.54255i	0.0514202	+	0.998677i	$0.483625\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	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
$435$	−2.31386	+	4.00772i	−0.110941	+	0.192156i
$436$	−15.7446			−0.754028
$437$		0			0
$438$	8.37228			0.400043
$439$	−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
$441$	−6.05842	−	10.4935i	−0.288496	−	0.499690i
$442$	16.1168	−	27.9152i	0.766600	−	1.32779i
$443$	17.4891			0.830933			0.415467	−	0.909608i	$-0.363618\pi$
$443$	17.4891			0.830933			0.415467	+	0.909608i	$0.363618\pi$
$444$	2.55842	−	5.51856i	0.121417	−	0.261899i
$445$	31.6060			1.49827
$446$	0.441578	−	0.764836i	0.0209093	−	0.0362160i
$447$	3.68614	+	6.38458i	0.174348	+	0.301980i
$448$	−2.18614	−	3.78651i	−0.103285	−	0.178896i
$449$	10.4891	+	18.1677i	0.495012	+	0.857387i	0.999983	−	0.00574961i	$-0.00183017\pi$
$449$	10.4891	+	18.1677i	0.495012	+	0.857387i	−0.504971	+	0.863136i	$0.668497\pi$
$450$	−6.37228			−0.300392
$451$	−1.37228	−	2.37686i	−0.0646182	−	0.111922i
$452$	7.48913			0.352259
$453$	−6.81386	+	11.8020i	−0.320143	+	0.554504i
$454$	−11.4891			−0.539211
$455$	−64.4674			−3.02228
$456$	3.37228	−	5.84096i	0.157922	−	0.273528i
$457$	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
$459$	−3.68614	+	6.38458i	−0.172054	+	0.298007i
$460$		0			0
$461$	−12.4891	+	21.6318i	−0.581677	+	1.00749i	0.413604	+	0.910457i	$0.364270\pi$
$461$	−12.4891	+	21.6318i	−0.581677	+	1.00749i	−0.995281	+	0.0970366i	$0.969064\pi$
$462$	−4.37228	−	7.57301i	−0.203417	−	0.352328i
$463$	−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
$465$	−6.11684	+	10.5947i	−0.283662	+	0.491317i
$466$	5.80298	−	10.0511i	0.268818	−	0.465607i
$467$	3.25544			0.150644			0.0753218	−	0.997159i	$-0.476002\pi$
$467$	3.25544			0.150644			0.0753218	+	0.997159i	$0.476002\pi$
$468$	2.18614	+	3.78651i	0.101054	+	0.175031i
$469$	28.6753	−	49.6670i	1.32410	−	2.29341i
$470$	−6.74456			−0.311103
$471$	16.4891			0.759779
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	−7.25544			−0.333605
$474$	2.18614	+	3.78651i	0.100413	+	0.173920i
$475$	−42.9783			−1.97198
$476$	16.1168	+	27.9152i	0.738714	+	1.27949i
$477$	5.74456	+	9.94987i	0.263025	+	0.455573i
$478$	6.11684	+	10.5947i	0.279778	+	0.484590i
$479$	−17.1168	+	29.6472i	−0.782089	+	1.35462i	0.148634	+	0.988892i	$0.452512\pi$
$479$	−17.1168	+	29.6472i	−0.782089	+	1.35462i	−0.930723	+	0.365725i	$0.880821\pi$
$480$	3.37228			0.153923
$481$	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
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−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
$489$	−13.2554			−0.599432
$490$	20.4307	−	35.3870i	0.922965	−	1.59862i
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$	−1.37228			−0.0618672
$493$	−5.05842	+	8.76144i	−0.227820	+	0.394596i
$494$	14.7446	+	25.5383i	0.663389	+	1.14902i
$495$	6.74456			0.303146
$496$	1.81386	−	3.14170i	0.0814447	−	0.141066i
$497$	25.1168	−	43.5036i	1.12664	−	1.95141i
$498$	−4.00000	+	6.92820i	−0.179244	+	0.310460i
$499$	−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
$501$	10.7446	−	18.6101i	0.480032	−	0.831439i
$502$	−0.627719	+	1.08724i	−0.0280165	+	0.0485259i
$503$	11.0000	−	19.0526i	0.490466	−	0.849512i	−0.509474	−	0.860486i	$-0.670160\pi$
$503$	11.0000	−	19.0526i	0.490466	−	0.849512i	0.999940	+	0.0109744i	$0.00349334\pi$
$504$	−4.37228			−0.194757
$505$	25.0584	+	43.4025i	1.11509	+	1.93138i
$506$		0			0
$507$	−6.11684			−0.271659
$508$	14.3723			0.637667
$509$	0.686141	−	1.18843i	0.0304127	−	0.0526763i	−0.850418	−	0.526107i	$-0.823651\pi$
$509$	0.686141	−	1.18843i	0.0304127	−	0.0526763i	0.880831	+	0.473431i	$0.156985\pi$
$510$	−24.8614			−1.10088
$511$	−18.3030	−	31.7017i	−0.809676	−	1.40240i
$512$	−1.00000			−0.0441942
$513$	−3.37228	−	5.84096i	−0.148890	−	0.257885i
$514$	−4.43070	−	7.67420i	−0.195430	−	0.338495i
$515$	−2.11684	−	3.66648i	−0.0932793	−	0.161564i
$516$	−1.81386	+	3.14170i	−0.0798507	+	0.138305i
$517$	4.00000			0.175920
$518$	−26.4891	+	2.37686i	−1.16387	+	0.104433i
$519$	−5.88316			−0.258242
$520$	−7.37228	+	12.7692i	−0.323296	+	0.559965i
$521$	−4.62772	−	8.01544i	−0.202744	−	0.351163i	0.746668	−	0.665197i	$-0.231653\pi$
$521$	−4.62772	−	8.01544i	−0.202744	−	0.351163i	−0.949412	+	0.314034i	$0.898319\pi$
$522$	−0.686141	−	1.18843i	−0.0300316	−	0.0520162i
$523$	−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
$525$	13.9307	+	24.1287i	0.607986	+	1.05306i
$526$	15.2554			0.665169
$527$	−13.3723	+	23.1615i	−0.582506	+	1.00893i
$528$	−2.00000			−0.0870388
$529$	−23.0000			−1.00000
$530$	−19.3723	+	33.5538i	−0.841478	+	1.45748i
$531$	2.00000	+	3.46410i	0.0867926	+	0.150329i
$532$	−29.4891			−1.27852
$533$	3.00000	−	5.19615i	0.129944	−	0.225070i
$534$	−4.68614	+	8.11663i	−0.202789	+	0.351241i
$535$	11.3723	−	19.6974i	0.491667	−	0.851592i
$536$	−6.55842	−	11.3595i	−0.283281	−	0.490657i
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$	1.00000	−	1.73205i	0.0431131	−	0.0746740i
$539$	−12.1168	+	20.9870i	−0.521909	+	0.903974i
$540$	1.68614	−	2.92048i	0.0725599	−	0.125678i
$541$	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
$543$	−7.87228	+	13.6352i	−0.337832	+	0.585142i
$544$	7.37228			0.316084
$545$	−53.0951			−2.27434
$546$	9.55842	−	16.5557i	0.409063	−	0.708517i
$547$	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
$549$	8.11684			0.346418
$550$	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
$555$	8.62772	−	18.6101i	0.366226	−	0.789956i
$556$	−14.3723			−0.609520
$557$	7.05842	−	12.2255i	0.299075	−	0.518013i	−0.676850	−	0.736121i	$-0.736655\pi$
$557$	7.05842	−	12.2255i	0.299075	−	0.518013i	0.975925	+	0.218108i	$0.0699886\pi$
$558$	−1.81386	−	3.14170i	−0.0767868	−	0.132999i
$559$	−7.93070	−	13.7364i	−0.335433	−	0.580987i
$560$	−7.37228	−	12.7692i	−0.311536	−	0.539596i
$561$	14.7446			0.622516
$562$	5.05842	+	8.76144i	0.213377	+	0.369579i
$563$	24.7446			1.04286			0.521429	−	0.853294i	$-0.325399\pi$
$563$	24.7446			1.04286			0.521429	+	0.853294i	$0.325399\pi$
$564$	1.00000	−	1.73205i	0.0421076	−	0.0729325i
$565$	25.2554			1.06250
$566$	−17.1168			−0.719475
$567$	−2.18614	+	3.78651i	−0.0918093	+	0.159018i
$568$	−5.74456	−	9.94987i	−0.241036	−	0.417487i
$569$	21.3723			0.895973			0.447986	−	0.894040i	$-0.352141\pi$
$569$	21.3723			0.895973			0.447986	+	0.894040i	$0.352141\pi$
$570$	11.3723	−	19.6974i	0.476332	−	0.825032i
$571$	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
$573$	−5.62772	−	9.74749i	−0.235101	−	0.407207i
$574$	3.00000	+	5.19615i	0.125218	+	0.216883i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−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
$579$	2.24456	+	3.88770i	0.0932808	+	0.161567i
$580$	2.31386	−	4.00772i	0.0960778	−	0.166412i
$581$	34.9783			1.45114
$582$	−5.74456			−0.238120
$583$	11.4891	−	19.8997i	0.475831	−	0.824163i
$584$	−8.37228			−0.346447
$585$	7.37228	+	12.7692i	0.304806	+	0.527940i
$586$	15.8832			0.656127
$587$	−4.37228	−	7.57301i	−0.180463	−	0.312572i	0.761575	−	0.648077i	$-0.224426\pi$
$587$	−4.37228	−	7.57301i	−0.180463	−	0.312572i	−0.942038	+	0.335505i	$0.891093\pi$
$588$	6.05842	+	10.4935i	0.249845	+	0.432744i
$589$	−12.2337	−	21.1894i	−0.504080	−	0.873093i
$590$	−6.74456	+	11.6819i	−0.277669	+	0.480937i
$591$	−19.3723			−0.796869
$592$	−2.55842	+	5.51856i	−0.105150	+	0.226811i
$593$	8.62772			0.354298			0.177149	−	0.984184i	$-0.443313\pi$
$593$	8.62772			0.354298			0.177149	+	0.984184i	$0.443313\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	54.3505	+	94.1379i	2.22815	+	3.85928i
$596$	−3.68614	−	6.38458i	−0.150990	−	0.261523i
$597$	−6.18614	−	10.7147i	−0.253182	−	0.438524i
$598$		0			0
$599$	−9.37228	−	16.2333i	−0.382941	−	0.663273i	0.608540	−	0.793523i	$-0.291755\pi$
$599$	−9.37228	−	16.2333i	−0.382941	−	0.663273i	−0.991481	+	0.130250i	$0.958422\pi$
$600$	6.37228			0.260147
$601$	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
$603$	−13.1168			−0.534159
$604$	6.81386	−	11.8020i	0.277252	−	0.480215i
$605$	11.8030	+	20.4434i	0.479860	+	0.831141i
$606$	−14.8614			−0.603703
$607$	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
$609$	−3.00000	+	5.19615i	−0.121566	+	0.210559i
$610$	13.6861	+	23.7051i	0.554136	+	0.959791i
$611$	4.37228	+	7.57301i	0.176884	+	0.306371i
$612$	3.68614	−	6.38458i	0.149003	−	0.258081i
$613$	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
$615$	−4.62772			−0.186608
$616$	4.37228	+	7.57301i	0.176164	+	0.305125i
$617$	−16.8614	+	29.2048i	−0.678815	+	1.17574i	0.296523	+	0.955026i	$0.404173\pi$
$617$	−16.8614	+	29.2048i	−0.678815	+	1.17574i	−0.975338	+	0.220716i	$0.929161\pi$
$618$	1.25544			0.0505011
$619$	−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
$624$	−2.18614	−	3.78651i	−0.0875157	−	0.151582i
$625$	8.12772	+	14.0776i	0.325109	+	0.563105i
$626$	−8.50000	−	14.7224i	−0.339728	−	0.588427i
$627$	−6.74456	+	11.6819i	−0.269352	+	0.466531i
$628$	−16.4891			−0.657988
$629$	18.8614	−	40.6844i	0.752054	−	1.62219i
$630$	−14.7446			−0.587437
$631$	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
$633$	3.81386	+	6.60580i	0.151587	+	0.262557i
$634$	−15.0584	−	26.0820i	−0.598046	−	1.03585i
$635$	48.4674			1.92337
$636$	−5.74456	−	9.94987i	−0.227787	−	0.394538i
$637$	−52.9783			−2.09907
$638$	−1.37228	+	2.37686i	−0.0543291	+	0.0941008i
$639$	−11.4891			−0.454503
$640$	−3.37228			−0.133301
$641$	−1.05842	+	1.83324i	−0.0418052	+	0.0724087i	−0.886171	−	0.463359i	$-0.846644\pi$
$641$	−1.05842	+	1.83324i	−0.0418052	+	0.0724087i	0.844366	+	0.535767i	$0.179978\pi$
$642$	3.37228	+	5.84096i	0.133093	+	0.230524i
$643$	−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
$645$	−6.11684	+	10.5947i	−0.240850	+	0.417165i
$646$	24.8614	−	43.0612i	0.978159	−	1.69422i
$647$	−8.86141	−	15.3484i	−0.348378	−	0.603408i	0.637584	−	0.770381i	$-0.279934\pi$
$647$	−8.86141	−	15.3484i	−0.348378	−	0.603408i	−0.985961	+	0.166973i	$0.946601\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	4.00000	−	6.92820i	0.157014	−	0.271956i
$650$	−13.9307	+	24.1287i	−0.546407	+	0.946405i
$651$	−7.93070	+	13.7364i	−0.310829	+	0.538371i
$652$	13.2554			0.519123
$653$	−23.9198	−	41.4304i	−0.936055	−	1.62130i	−0.772741	−	0.634721i	$-0.781115\pi$
$653$	−23.9198	−	41.4304i	−0.936055	−	1.62130i	−0.163314	−	0.986574i	$-0.552218\pi$
$654$	7.87228	−	13.6352i	0.307831	−	0.533178i
$655$	−2.51087			−0.0981080
$656$	1.37228			0.0535786
$657$	−4.18614	+	7.25061i	−0.163317	+	0.282873i
$658$	−8.74456			−0.340899
$659$	−21.1168	−	36.5754i	−0.822595	−	1.42478i	−0.903743	−	0.428075i	$-0.859192\pi$
$659$	−21.1168	−	36.5754i	−0.822595	−	1.42478i	0.0811477	−	0.996702i	$-0.474141\pi$
$660$	−6.74456			−0.262532
$661$	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
$663$	16.1168	+	27.9152i	0.625926	+	1.08414i
$664$	4.00000	−	6.92820i	0.155230	−	0.268866i
$665$	−99.4456			−3.85634
$666$	3.50000	+	4.97494i	0.135622	+	0.192775i
$667$		0			0
$668$	−10.7446	+	18.6101i	−0.415720	+	0.720047i
$669$	0.441578	+	0.764836i	0.0170724	+	0.0295703i
$670$	−22.1168	−	38.3075i	−0.854448	−	1.47995i
$671$	−8.11684	−	14.0588i	−0.313347	−	0.542733i
$672$	4.37228			0.168664
$673$	−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
$675$	3.18614	−	5.51856i	0.122635	−	0.212409i
$676$	6.11684			0.235263
$677$	−11.8832			−0.456707			−0.228353	−	0.973578i	$-0.573334\pi$
$677$	−11.8832			−0.456707			−0.228353	+	0.973578i	$0.573334\pi$
$678$	−3.74456	+	6.48577i	−0.143809	+	0.249085i
$679$	12.5584	+	21.7518i	0.481948	+	0.834758i
$680$	24.8614			0.953391
$681$	5.74456	−	9.94987i	0.220132	−	0.381280i
$682$	−3.62772	+	6.28339i	−0.138913	+	0.240604i
$683$	10.1168	−	17.5229i	0.387110	−	0.670495i	−0.604949	−	0.796264i	$-0.706807\pi$
$683$	10.1168	−	17.5229i	0.387110	−	0.670495i	0.992060	+	0.125769i	$0.0401399\pi$
$684$	3.37228	+	5.84096i	0.128942	+	0.223335i
$685$	−7.80298	−	13.5152i	−0.298137	−	0.516388i
$686$	11.1861	−	19.3750i	0.427089	−	0.739740i
$687$	−1.12772	+	1.95327i	−0.0430252	+	0.0745217i
$688$	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
$693$	8.74456			0.332178
$694$	7.62772	−	13.2116i	0.289544	−	0.501505i
$695$	−48.4674			−1.83847
$696$	0.686141	+	1.18843i	0.0260081	+	0.0450473i
$697$	−10.1168			−0.383203
$698$	4.05842	+	7.02939i	0.153614	+	0.266066i
$699$	5.80298	+	10.0511i	0.219489	+	0.380166i
$700$	−13.9307	−	24.1287i	−0.526531	−	0.911979i
$701$	−3.88316	+	6.72582i	−0.146665	+	0.254031i	−0.929993	−	0.367578i	$-0.880187\pi$
$701$	−3.88316	+	6.72582i	−0.146665	+	0.254031i	0.783328	+	0.621609i	$0.213521\pi$
$702$	−4.37228			−0.165021
$703$	23.6060	+	33.5538i	0.890316	+	1.26550i
$704$	2.00000			0.0753778
$705$	3.37228	−	5.84096i	0.127007	−	0.219983i
$706$	−4.80298	−	8.31901i	−0.180763	−	0.313090i
$707$	32.4891	+	56.2728i	1.22188	+	2.11636i
$708$	−2.00000	−	3.46410i	−0.0751646	−	0.130189i
$709$	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
$711$	−4.37228			−0.163973
$712$	4.68614	−	8.11663i	0.175621	−	0.304184i
$713$		0			0
$714$	−32.2337			−1.20632
$715$	14.7446	−	25.5383i	0.551415	−	0.955079i
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$	−12.2337			−0.456875
$718$	−11.1168	+	19.2549i	−0.414877	+	0.718588i
$719$	−18.6060	+	32.2265i	−0.693886	+	1.20185i	0.276669	+	0.960965i	$0.410769\pi$
$719$	−18.6060	+	32.2265i	−0.693886	+	1.20185i	−0.970555	+	0.240880i	$0.922564\pi$
$720$	−1.68614	+	2.92048i	−0.0628388	+	0.108840i
$721$	−2.74456	−	4.75372i	−0.102213	−	0.177038i
$722$	13.2446	+	22.9403i	0.492912	+	0.853748i
$723$	3.44158	−	5.96099i	0.127994	−	0.221692i
$724$	7.87228	−	13.6352i	0.292571	−	0.506748i
$725$	4.37228	−	7.57301i	0.162382	−	0.281255i
$726$	−7.00000			−0.259794
$727$	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
$729$	1.00000			0.0370370
$730$	−28.2337			−1.04498
$731$	−13.3723	+	23.1615i	−0.494592	+	0.856658i
$732$	−8.11684			−0.300007
$733$	−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
$735$	20.4307	+	35.3870i	0.753598	+	1.30527i
$736$		0			0
$737$	13.1168	+	22.7190i	0.483165	+	0.836867i
$738$	0.686141	−	1.18843i	0.0252572	−	0.0437467i
$739$	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
$741$	−29.4891			−1.08331
$742$	−25.1168	+	43.5036i	−0.922068	+	1.59707i
$743$	−17.7446	−	30.7345i	−0.650985	−	1.12754i	−0.982884	−	0.184224i	$-0.941023\pi$
$743$	−17.7446	−	30.7345i	−0.650985	−	1.12754i	0.331899	−	0.943315i	$-0.392311\pi$
$744$	1.81386	+	3.14170i	0.0664993	+	0.115180i
$745$	−12.4307	−	21.5306i	−0.455426	−	0.788821i
$746$	31.0000			1.13499
$747$	−4.00000	−	6.92820i	−0.146352	−	0.253490i
$748$	−14.7446			−0.539115
$749$	14.7446	−	25.5383i	0.538755	−	0.933150i
$750$	4.62772			0.168980
$751$	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
$753$	−0.627719	−	1.08724i	−0.0228753	−	0.0396213i
$754$	−6.00000			−0.218507
$755$	22.9783	−	39.7995i	0.836264	−	1.44845i
$756$	2.18614	−	3.78651i	0.0795092	−	0.137714i
$757$	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	−0.818601	−	0.574363i	$-0.805250\pi$
$761$	2.43070	−	4.21010i	0.0881129	−	0.152616i	0.906713	+	0.421747i	$0.138583\pi$
$762$	−7.18614	+	12.4468i	−0.260326	+	0.450899i
$763$	−68.8397			−2.49216
$764$	5.62772	+	9.74749i	0.203604	+	0.352652i
$765$	12.4307	−	21.5306i	0.449433	−	0.778441i
$766$	−28.2337			−1.02012
$767$	17.4891			0.631496
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	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
$771$	8.86141			0.319136
$772$	−2.24456	−	3.88770i	−0.0807836	−	0.139921i
$773$	−16.4307	−	28.4588i	−0.590971	−	1.02359i	−0.994102	−	0.108450i	$-0.965411\pi$
$773$	−16.4307	−	28.4588i	−0.590971	−	1.02359i	0.403131	−	0.915142i	$-0.367922\pi$
$774$	−1.81386	−	3.14170i	−0.0651978	−	0.112926i
$775$	11.5584	−	20.0198i	0.415191	−	0.719132i
$776$	5.74456			0.206218
$777$	11.1861	−	24.1287i	0.401301	−	0.865612i
$778$	−24.1168			−0.864631
$779$	4.62772	−	8.01544i	0.165805	−	0.287183i
$780$	−7.37228	−	12.7692i	−0.263970	−	0.457209i
$781$	11.4891	+	19.8997i	0.411113	+	0.712069i
$782$		0			0
$783$	1.37228			0.0490413
$784$	−6.05842	−	10.4935i	−0.216372	−	0.374768i
$785$	−55.6060			−1.98466
$786$	0.372281	−	0.644810i	0.0132788	−	0.0229996i
$787$	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
$789$	−7.62772	+	13.2116i	−0.271554	+	0.470345i
$790$	−7.37228	−	12.7692i	−0.262294	−	0.454307i
$791$	32.7446			1.16426
$792$	1.00000	−	1.73205i	0.0355335	−	0.0615457i
$793$	17.7446	−	30.7345i	0.630128	−	1.09141i
$794$	−9.50000	+	16.4545i	−0.337142	+	0.583948i
$795$	−19.3723	−	33.5538i	−0.687064	−	1.19003i
$796$	6.18614	+	10.7147i	0.219262	+	0.379773i
$797$	−19.6060	+	33.9585i	−0.694479	+	1.20287i	0.275877	+	0.961193i	$0.411032\pi$
$797$	−19.6060	+	33.9585i	−0.694479	+	1.20287i	−0.970356	+	0.241680i	$0.922302\pi$
$798$	14.7446	−	25.5383i	0.521952	−	0.904047i
$799$	7.37228	−	12.7692i	0.260813	−	0.451741i
$800$	−6.37228			−0.225294
$801$	−4.68614	−	8.11663i	−0.165577	−	0.286787i
$802$	−7.37228	+	12.7692i	−0.260324	+	0.450895i
$803$	16.7446			0.590903
$804$	13.1168			0.462595
$805$		0			0
$806$	−15.8614			−0.558694
$807$	1.00000	+	1.73205i	0.0352017	+	0.0609711i
$808$	14.8614			0.522822
$809$	3.51087	+	6.08101i	0.123436	+	0.213797i	0.921120	−	0.389278i	$-0.127275\pi$
$809$	3.51087	+	6.08101i	0.123436	+	0.213797i	−0.797685	+	0.603075i	$0.793942\pi$
$810$	1.68614	+	2.92048i	0.0592449	+	0.102615i
$811$	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
$813$	9.86141			0.345855
$814$	5.11684	−	11.0371i	0.179345	−	0.386851i
$815$	44.7011			1.56581
$816$	−3.68614	+	6.38458i	−0.129041	+	0.223505i
$817$	−12.2337	−	21.1894i	−0.428003	−	0.741322i
$818$	−6.12772	−	10.6135i	−0.214251	−	0.371093i
$819$	9.55842	+	16.5557i	0.333998	+	0.578502i
$820$	4.62772			0.161607
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$	4.62772			0.161410
$823$	−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
$825$	−12.7446			−0.443709
$826$	−8.74456	+	15.1460i	−0.304262	+	0.526998i
$827$	−16.0000	−	27.7128i	−0.556375	−	0.963669i	−0.997795	−	0.0663686i	$-0.978859\pi$
$827$	−16.0000	−	27.7128i	−0.556375	−	0.963669i	0.441421	−	0.897300i	$-0.354475\pi$
$828$		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
$831$	−15.4307	+	26.7268i	−0.535285	+	0.927141i
$832$	2.18614	+	3.78651i	0.0757908	+	0.131274i
$833$	44.6644	+	77.3610i	1.54753	+	2.68040i
$834$	7.18614	−	12.4468i	0.248836	−	0.430996i
$835$	−36.2337	+	62.7586i	−1.25392	+	2.17185i
$836$	6.74456	−	11.6819i	0.233266	−	0.404028i
$837$	3.62772			0.125392
$838$	−1.74456	−	3.02167i	−0.0602649	−	0.104382i
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	−0.898482	−	0.439010i	$-0.855329\pi$
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	0.829435	+	0.558604i	$0.188663\pi$
$840$	14.7446			0.508736
$841$	−27.1168			−0.935064
$842$	−8.68614	+	15.0448i	−0.299344	+	0.518479i
$843$	−10.1168			−0.348443
$844$	−3.81386	−	6.60580i	−0.131278	−	0.227381i
$845$	20.6277			0.709615
$846$	1.00000	+	1.73205i	0.0343807	+	0.0595491i
$847$	15.3030	+	26.5055i	0.525817	+	0.910741i
$848$	5.74456	+	9.94987i	0.197269	+	0.341680i
$849$	8.55842	−	14.8236i	0.293724	−	0.508745i
$850$	46.9783			1.61134
$851$		0			0
$852$	11.4891			0.393611
$853$	−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
$855$	11.3723	+	19.6974i	0.388924	+	0.673636i
$856$	−3.37228	−	5.84096i	−0.115262	−	0.199640i
$857$	−43.8397			−1.49753			−0.748767	−	0.662833i	$-0.769354\pi$
$857$	−43.8397			−1.49753			−0.748767	+	0.662833i	$0.769354\pi$
$858$	4.37228	+	7.57301i	0.149267	+	0.258538i
$859$	−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
$861$	−6.00000			−0.204479
$862$	36.9783			1.25948
$863$	7.62772	−	13.2116i	0.259651	−	0.449728i	−0.706498	−	0.707715i	$-0.749726\pi$
$863$	7.62772	−	13.2116i	0.259651	−	0.449728i	0.966148	+	0.257987i	$0.0830593\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	19.8397			0.674569
$866$	6.68614	−	11.5807i	0.227204	−	0.393529i
$867$	18.6753	−	32.3465i	0.634245	−	1.09855i
$868$	7.93070	−	13.7364i	0.269186	−	0.466243i
$869$	4.37228	+	7.57301i	0.148319	+	0.256897i
$870$	2.31386	+	4.00772i	0.0784472	+	0.135874i
$871$	−28.6753	+	49.6670i	−0.971624	+	1.68290i
$872$	−7.87228	+	13.6352i	−0.266589	+	0.461746i
$873$	2.87228	−	4.97494i	0.0972120	−	0.168376i
$874$		0			0
$875$	−10.1168	−	17.5229i	−0.342012	−	0.592382i
$876$	4.18614	−	7.25061i	0.141437	−	0.244975i
$877$	−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
$879$	−7.94158	+	13.7552i	−0.267863	+	0.463952i
$880$	6.74456			0.227359
$881$	−5.05842	−	8.76144i	−0.170423	−	0.295181i	0.768145	−	0.640276i	$-0.221180\pi$
$881$	−5.05842	−	8.76144i	−0.170423	−	0.295181i	−0.938568	+	0.345095i	$0.887847\pi$
$882$	−12.1168			−0.407995
$883$	−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
$885$	−6.74456	−	11.6819i	−0.226716	−	0.392684i
$886$	8.74456	−	15.1460i	0.293779	−	0.508841i
$887$	−20.0000			−0.671534			−0.335767	−	0.941945i	$-0.608996\pi$
$887$	−20.0000			−0.671534			−0.335767	+	0.941945i	$0.608996\pi$
$888$	−3.50000	−	4.97494i	−0.117452	−	0.166948i
$889$	62.8397			2.10757
$890$	15.8030	−	27.3716i	0.529717	−	0.917497i
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	−0.441578	−	0.764836i	−0.0147851	−	0.0256086i
$893$	6.74456	+	11.6819i	0.225698	+	0.390921i
$894$	7.37228			0.246566
$895$	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
$900$	−3.18614	+	5.51856i	−0.106205	+	0.183952i
$901$	−42.3505	−	73.3533i	−1.41090	−	2.44375i
$902$	−2.74456			−0.0913839
$903$	−7.93070	+	13.7364i	−0.263917	+	0.457118i
$904$	3.74456	−	6.48577i	0.124542	−	0.215714i
$905$	26.5475	−	45.9817i	0.882470	−	1.52848i
$906$	6.81386	+	11.8020i	0.226375	+	0.392094i
$907$	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
$909$	7.43070	−	12.8704i	0.246461	−	0.426883i
$910$	−32.2337	+	55.8304i	−1.06854	+	1.85076i
$911$	−35.7228			−1.18355			−0.591775	−	0.806103i	$-0.701573\pi$
$911$	−35.7228			−1.18355			−0.591775	+	0.806103i	$0.701573\pi$
$912$	−3.37228	−	5.84096i	−0.111667	−	0.193414i
$913$	−8.00000	+	13.8564i	−0.264761	+	0.458580i
$914$	39.0951			1.29315
$915$	−27.3723			−0.904900
$916$	1.12772	−	1.95327i	0.0372609	−	0.0645377i
$917$	−3.25544			−0.107504
$918$	3.68614	+	6.38458i	0.121661	+	0.210723i
$919$	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
$921$	4.55842	+	7.89542i	0.150205	+	0.260163i
$922$	12.4891	+	21.6318i	0.411307	+	0.712405i
$923$	−25.1168	+	43.5036i	−0.826731	+	1.43194i
$924$	−8.74456			−0.287675
$925$	−16.3030	+	35.1658i	−0.536039	+	1.15624i
$926$	−17.1168			−0.562494
$927$	−0.627719	+	1.08724i	−0.0206170	+	0.0357097i
$928$	−0.686141	−	1.18843i	−0.0225237	−	0.0390121i
$929$	24.8030	+	42.9600i	0.813760	+	1.40947i	0.910215	+	0.414136i	$0.135916\pi$
$929$	24.8030	+	42.9600i	0.813760	+	1.40947i	−0.0964557	+	0.995337i	$0.530751\pi$
$930$	6.11684	+	10.5947i	0.200579	+	0.347413i
$931$	−81.7228			−2.67836
$932$	−5.80298	−	10.0511i	−0.190083	−	0.329234i
$933$	−16.9783			−0.555843
$934$	1.62772	−	2.81929i	0.0532606	−	0.0922500i
$935$	−49.7228			−1.62611
$936$	4.37228			0.142912
$937$	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
$939$	17.0000			0.554774
$940$	−3.37228	+	5.84096i	−0.109992	+	0.190511i
$941$	−20.6644	+	35.7918i	−0.673640	+	1.16678i	0.303225	+	0.952919i	$0.401937\pi$
$941$	−20.6644	+	35.7918i	−0.673640	+	1.16678i	−0.976864	+	0.213859i	$0.931397\pi$
$942$	8.24456	−	14.2800i	0.268622	−	0.465268i
$943$		0			0
$944$	2.00000	+	3.46410i	0.0650945	+	0.112747i
$945$	7.37228	−	12.7692i	0.239820	−	0.415381i
$946$	−3.62772	+	6.28339i	−0.117947	+	0.204291i
$947$	18.6060	−	32.2265i	0.604613	−	1.04722i	−0.387500	−	0.921870i	$-0.626661\pi$
$947$	18.6060	−	32.2265i	0.604613	−	1.04722i	0.992113	−	0.125350i	$-0.0400055\pi$
$948$	4.37228			0.142005
$949$	18.3030	+	31.7017i	0.594140	+	1.02908i
$950$	−21.4891	+	37.2203i	−0.697199	+	1.20758i
$951$	30.1168			0.976606
$952$	32.2337			1.04470
$953$	−2.86141	+	4.95610i	−0.0926901	+	0.160544i	−0.908642	−	0.417576i	$-0.862880\pi$
$953$	−2.86141	+	4.95610i	−0.0926901	+	0.160544i	0.815952	+	0.578119i	$0.196213\pi$
$954$	11.4891			0.371974
$955$	18.9783	+	32.8713i	0.614122	+	1.06369i
$956$	12.2337			0.395666
$957$	−1.37228	−	2.37686i	−0.0443596	−	0.0768330i
$958$	17.1168	+	29.6472i	0.553020	+	0.957859i
$959$	−10.1168	−	17.5229i	−0.326690	−	0.565844i
$960$	1.68614	−	2.92048i	0.0544200	−	0.0942581i
$961$	−17.8397			−0.575473
$962$	26.4891	−	2.37686i	0.854044	−	0.0766331i
$963$	−6.74456			−0.217340
$964$	−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
$969$	24.8614	+	43.0612i	0.798663	+	1.38333i
$970$	19.3723			0.622006
$971$	22.9783	−	39.7995i	0.737407	−	1.27723i	−0.216252	−	0.976338i	$-0.569383\pi$
$971$	22.9783	−	39.7995i	0.737407	−	1.27723i	0.953659	−	0.300889i	$-0.0972834\pi$
$972$	−1.00000			−0.0320750
$973$	−62.8397			−2.01455
$974$	−7.25544	+	12.5668i	−0.232479	+	0.402666i
$975$	−13.9307	−	24.1287i	−0.446140	−	0.772736i
$976$	8.11684			0.259814
$977$	7.37228	−	12.7692i	0.235860	−	0.408522i	−0.723662	−	0.690154i	$-0.757543\pi$
$977$	7.37228	−	12.7692i	0.235860	−	0.408522i	0.959522	+	0.281633i	$0.0908759\pi$
$978$	−6.62772	+	11.4795i	−0.211931	+	0.367075i
$979$	−9.37228	+	16.2333i	−0.299539	+	0.518817i
$980$	−20.4307	−	35.3870i	−0.652635	−	1.13040i
$981$	7.87228	+	13.6352i	0.251343	+	0.435338i
$982$	3.00000	−	5.19615i	0.0957338	−	0.165816i
$983$	4.62772	−	8.01544i	0.147601	−	0.255653i	−0.782739	−	0.622350i	$-0.786178\pi$
$983$	4.62772	−	8.01544i	0.147601	−	0.255653i	0.930340	+	0.366697i	$0.119511\pi$
$984$	−0.686141	+	1.18843i	−0.0218734	+	0.0378858i
$985$	65.3288			2.08155
$986$	5.05842	+	8.76144i	0.161093	+	0.279021i
$987$	4.37228	−	7.57301i	0.139171	−	0.241052i
$988$	29.4891			0.938174
$989$		0			0
$990$	3.37228	−	5.84096i	0.107178	−	0.185638i
$991$	−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
$993$	−4.60597			−0.146166
$994$	−25.1168	−	43.5036i	−0.796658	−	1.37985i
$995$	20.8614	+	36.1330i	0.661351	+	1.14549i
$996$	4.00000	+	6.92820i	0.126745	+	0.219529i
$997$	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
$999$	−6.05842	+	0.543620i	−0.191680	+	0.0171994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.2.e.c.121.1	✓	4
3.2	odd	2		666.2.f.g.343.2		4
4.3	odd	2		1776.2.q.h.1009.1		4
37.10	even	3		8214.2.a.m.1.2		2
37.26	even	3	inner	222.2.e.c.211.1	yes	4
37.27	even	6		8214.2.a.o.1.1		2
111.26	odd	6		666.2.f.g.433.2		4
148.63	odd	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	1.1	even	1	trivial
222.2.e.c.211.1	yes	4	37.26	even	3	inner
666.2.f.g.343.2		4	3.2	odd	2
666.2.f.g.433.2		4	111.26	odd	6
1776.2.q.h.433.1		4	148.63	odd	6
1776.2.q.h.1009.1		4	4.3	odd	2
8214.2.a.m.1.2		2	37.10	even	3
8214.2.a.o.1.1		2	37.27	even	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:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	222.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.68614 - 2.92048i) q^{5} +1.00000 q^{6} +(-2.18614 - 3.78651i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -3.37228 q^{10} +2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(2.18614 + 3.78651i) q^{13} -4.37228 q^{14} +(1.68614 - 2.92048i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.68614 - 6.38458i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.37228 + 5.84096i) q^{19} +(-1.68614 + 2.92048i) q^{20} +(2.18614 - 3.78651i) q^{21} +(1.00000 - 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{24} +(-3.18614 + 5.51856i) q^{25} +4.37228 q^{26} -1.00000 q^{27} +(-2.18614 + 3.78651i) q^{28} -1.37228 q^{29} +(-1.68614 - 2.92048i) q^{30} -3.62772 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(-3.68614 - 6.38458i) q^{34} +(-7.37228 + 12.7692i) q^{35} +1.00000 q^{36} +(6.05842 - 0.543620i) q^{37} +6.74456 q^{38} +(-2.18614 + 3.78651i) q^{39} +(1.68614 + 2.92048i) q^{40} +(-0.686141 - 1.18843i) q^{41} +(-2.18614 - 3.78651i) q^{42} -3.62772 q^{43} +(-1.00000 - 1.73205i) q^{44} +3.37228 q^{45} +2.00000 q^{47} -1.00000 q^{48} +(-6.05842 + 10.4935i) q^{49} +(3.18614 + 5.51856i) q^{50} +7.37228 q^{51} +(2.18614 - 3.78651i) q^{52} +(5.74456 - 9.94987i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.37228 - 5.84096i) q^{55} +(2.18614 + 3.78651i) q^{56} +(-3.37228 + 5.84096i) q^{57} +(-0.686141 + 1.18843i) q^{58} +(2.00000 - 3.46410i) q^{59} -3.37228 q^{60} +(-4.05842 - 7.02939i) q^{61} +(-1.81386 + 3.14170i) q^{62} +4.37228 q^{63} +1.00000 q^{64} +(7.37228 - 12.7692i) q^{65} +2.00000 q^{66} +(6.55842 + 11.3595i) q^{67} -7.37228 q^{68} +(7.37228 + 12.7692i) q^{70} +(5.74456 + 9.94987i) q^{71} +(0.500000 - 0.866025i) q^{72} +8.37228 q^{73} +(2.55842 - 5.51856i) q^{74} -6.37228 q^{75} +(3.37228 - 5.84096i) q^{76} +(-4.37228 - 7.57301i) q^{77} +(2.18614 + 3.78651i) q^{78} +(2.18614 + 3.78651i) q^{79} +3.37228 q^{80} +(-0.500000 - 0.866025i) q^{81} -1.37228 q^{82} +(-4.00000 + 6.92820i) q^{83} -4.37228 q^{84} -24.8614 q^{85} +(-1.81386 + 3.14170i) q^{86} +(-0.686141 - 1.18843i) q^{87} -2.00000 q^{88} +(-4.68614 + 8.11663i) q^{89} +(1.68614 - 2.92048i) q^{90} +(9.55842 - 16.5557i) q^{91} +(-1.81386 - 3.14170i) q^{93} +(1.00000 - 1.73205i) q^{94} +(11.3723 - 19.6974i) q^{95} +(-0.500000 + 0.866025i) q^{96} -5.74456 q^{97} +(6.05842 + 10.4935i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + 4 q^{6} - 3 q^{7} - 4 q^{8} - 2 q^{9} - 2 q^{10} + 8 q^{11} + 2 q^{12} + 3 q^{13} - 6 q^{14} + q^{15} - 2 q^{16} + 9 q^{17} + 2 q^{18} + 2 q^{19} - q^{20}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + 4 * q^6 - 3 * q^7 - 4 * q^8 - 2 * q^9 - 2 * q^10 + 8 * q^11 + 2 * q^12 + 3 * q^13 - 6 * q^14 + q^15 - 2 * q^16 + 9 * q^17 + 2 * q^18 + 2 * q^19 - q^20 + 3 * q^21 + 4 * q^22 - 2 * q^24 - 7 * q^25 + 6 * q^26 - 4 * q^27 - 3 * q^28 + 6 * q^29 - q^30 - 26 * q^31 + 2 * q^32 + 4 * q^33 - 9 * q^34 - 18 * q^35 + 4 * q^36 + 7 * q^37 + 4 * q^38 - 3 * q^39 + q^40 + 3 * q^41 - 3 * q^42 - 26 * q^43 - 4 * q^44 + 2 * q^45 + 8 * q^47 - 4 * q^48 - 7 * q^49 + 7 * q^50 + 18 * q^51 + 3 * q^52 - 2 * q^54 - 2 * q^55 + 3 * q^56 - 2 * q^57 + 3 * q^58 + 8 * q^59 - 2 * q^60 + q^61 - 13 * q^62 + 6 * q^63 + 4 * q^64 + 18 * q^65 + 8 * q^66 + 9 * q^67 - 18 * q^68 + 18 * q^70 + 2 * q^72 + 22 * q^73 - 7 * q^74 - 14 * q^75 + 2 * q^76 - 6 * q^77 + 3 * q^78 + 3 * q^79 + 2 * q^80 - 2 * q^81 + 6 * q^82 - 16 * q^83 - 6 * q^84 - 42 * q^85 - 13 * q^86 + 3 * q^87 - 8 * q^88 - 13 * q^89 + q^90 + 21 * q^91 - 13 * q^93 + 4 * q^94 + 34 * q^95 - 2 * q^96 + 7 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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