LMFDB - Embedded newform 222.2.e.c.121.2

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			121.2
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	222.121
Dual form			222.2.e.c.211.2

$q$-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^{3} +(-0.500000 - 0.866025i) q^{4} +(1.18614 + 2.05446i) q^{5} +1.00000 q^{6} +(0.686141 + 1.18843i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +2.37228 q^{10} +2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.686141 - 1.18843i) q^{13} +1.37228 q^{14} +(-1.18614 + 2.05446i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.813859 - 1.40965i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.37228 - 4.10891i) q^{19} +(1.18614 - 2.05446i) q^{20} +(-0.686141 + 1.18843i) q^{21} +(1.00000 - 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{24} +(-0.313859 + 0.543620i) q^{25} -1.37228 q^{26} -1.00000 q^{27} +(0.686141 - 1.18843i) q^{28} +4.37228 q^{29} +(1.18614 + 2.05446i) q^{30} -9.37228 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(-0.813859 - 1.40965i) q^{34} +(-1.62772 + 2.81929i) q^{35} +1.00000 q^{36} +(-2.55842 - 5.51856i) q^{37} -4.74456 q^{38} +(0.686141 - 1.18843i) q^{39} +(-1.18614 - 2.05446i) q^{40} +(2.18614 + 3.78651i) q^{41} +(0.686141 + 1.18843i) q^{42} -9.37228 q^{43} +(-1.00000 - 1.73205i) q^{44} -2.37228 q^{45} +2.00000 q^{47} -1.00000 q^{48} +(2.55842 - 4.43132i) q^{49} +(0.313859 + 0.543620i) q^{50} +1.62772 q^{51} +(-0.686141 + 1.18843i) q^{52} +(-5.74456 + 9.94987i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.37228 + 4.10891i) q^{55} +(-0.686141 - 1.18843i) q^{56} +(2.37228 - 4.10891i) q^{57} +(2.18614 - 3.78651i) q^{58} +(2.00000 - 3.46410i) q^{59} +2.37228 q^{60} +(4.55842 + 7.89542i) q^{61} +(-4.68614 + 8.11663i) q^{62} -1.37228 q^{63} +1.00000 q^{64} +(1.62772 - 2.81929i) q^{65} +2.00000 q^{66} +(-2.05842 - 3.56529i) q^{67} -1.62772 q^{68} +(1.62772 + 2.81929i) q^{70} +(-5.74456 - 9.94987i) q^{71} +(0.500000 - 0.866025i) q^{72} +2.62772 q^{73} +(-6.05842 - 0.543620i) q^{74} -0.627719 q^{75} +(-2.37228 + 4.10891i) q^{76} +(1.37228 + 2.37686i) q^{77} +(-0.686141 - 1.18843i) q^{78} +(-0.686141 - 1.18843i) q^{79} -2.37228 q^{80} +(-0.500000 - 0.866025i) q^{81} +4.37228 q^{82} +(-4.00000 + 6.92820i) q^{83} +1.37228 q^{84} +3.86141 q^{85} +(-4.68614 + 8.11663i) q^{86} +(2.18614 + 3.78651i) q^{87} -2.00000 q^{88} +(-1.81386 + 3.14170i) q^{89} +(-1.18614 + 2.05446i) q^{90} +(0.941578 - 1.63086i) q^{91} +(-4.68614 - 8.11663i) q^{93} +(1.00000 - 1.73205i) q^{94} +(5.62772 - 9.74749i) q^{95} +(-0.500000 + 0.866025i) q^{96} +5.74456 q^{97} +(-2.55842 - 4.43132i) 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
$5$	1.18614	+	2.05446i	0.530458	+	0.918781i	0.999368	+	0.0355348i	$0.0113134\pi$
$5$	1.18614	+	2.05446i	0.530458	+	0.918781i	−0.468910	+	0.883246i	$0.655353\pi$
$6$	1.00000			0.408248
$7$	0.686141	+	1.18843i	0.259337	+	0.449185i	0.966064	−	0.258301i	$-0.0831627\pi$
$7$	0.686141	+	1.18843i	0.259337	+	0.449185i	−0.706728	+	0.707486i	$0.749829\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.37228			0.750181
$11$	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
$13$	−0.686141	−	1.18843i	−0.190301	−	0.329611i	0.755049	−	0.655669i	$-0.227613\pi$
$13$	−0.686141	−	1.18843i	−0.190301	−	0.329611i	−0.945350	+	0.326057i	$0.894280\pi$
$14$	1.37228			0.366758
$15$	−1.18614	+	2.05446i	−0.306260	+	0.530458i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.813859	−	1.40965i	0.197390	−	0.341889i	−0.750291	−	0.661107i	$-0.770087\pi$
$17$	0.813859	−	1.40965i	0.197390	−	0.341889i	0.947681	+	0.319218i	$0.103420\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−2.37228	−	4.10891i	−0.544239	−	0.942649i	−0.998654	−	0.0518593i	$-0.983485\pi$
$19$	−2.37228	−	4.10891i	−0.544239	−	0.942649i	0.454416	−	0.890790i	$-0.349848\pi$
$20$	1.18614	−	2.05446i	0.265229	−	0.459390i
$21$	−0.686141	+	1.18843i	−0.149728	+	0.259337i
$22$	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
$25$	−0.313859	+	0.543620i	−0.0627719	+	0.108724i
$26$	−1.37228			−0.269127
$27$	−1.00000			−0.192450
$28$	0.686141	−	1.18843i	0.129668	−	0.224592i
$29$	4.37228			0.811912			0.405956	−	0.913893i	$-0.366939\pi$
$29$	4.37228			0.811912			0.405956	+	0.913893i	$0.366939\pi$
$30$	1.18614	+	2.05446i	0.216559	+	0.375091i
$31$	−9.37228			−1.68331			−0.841656	−	0.540015i	$-0.818419\pi$
$31$	−9.37228			−1.68331			−0.841656	+	0.540015i	$0.818419\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$	−0.813859	−	1.40965i	−0.139576	−	0.241752i
$35$	−1.62772	+	2.81929i	−0.275135	+	0.476547i
$36$	1.00000			0.166667
$37$	−2.55842	−	5.51856i	−0.420602	−	0.907245i
$37$	−2.55842	−	5.51856i	−0.420602	−	0.907245i
$38$	−4.74456			−0.769670
$39$	0.686141	−	1.18843i	0.109870	−	0.190301i
$40$	−1.18614	−	2.05446i	−0.187545	−	0.324838i
$41$	2.18614	+	3.78651i	0.341418	+	0.591353i	0.984696	−	0.174279i	$-0.0557596\pi$
$41$	2.18614	+	3.78651i	0.341418	+	0.591353i	−0.643278	+	0.765632i	$0.722426\pi$
$42$	0.686141	+	1.18843i	0.105874	+	0.183379i
$43$	−9.37228			−1.42926			−0.714630	−	0.699503i	$-0.753405\pi$
$43$	−9.37228			−1.42926			−0.714630	+	0.699503i	$0.753405\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$	−2.37228			−0.353639
$46$		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
$49$	2.55842	−	4.43132i	0.365489	−	0.633045i
$50$	0.313859	+	0.543620i	0.0443864	+	0.0768795i
$51$	1.62772			0.227926
$52$	−0.686141	+	1.18843i	−0.0951506	+	0.164806i
$53$	−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	$0.877226\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	2.37228	+	4.10891i	0.319878	+	0.554046i
$56$	−0.686141	−	1.18843i	−0.0916894	−	0.158811i
$57$	2.37228	−	4.10891i	0.314216	−	0.544239i
$58$	2.18614	−	3.78651i	0.287054	−	0.497193i
$59$	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	$0.0828195\pi$
$60$	2.37228			0.306260
$61$	4.55842	+	7.89542i	0.583646	+	1.01090i	0.995043	+	0.0994483i	$0.0317078\pi$
$61$	4.55842	+	7.89542i	0.583646	+	1.01090i	−0.411397	+	0.911456i	$0.634959\pi$
$62$	−4.68614	+	8.11663i	−0.595140	+	1.03081i
$63$	−1.37228			−0.172891
$64$	1.00000			0.125000
$65$	1.62772	−	2.81929i	0.201894	−	0.349690i
$66$	2.00000			0.246183
$67$	−2.05842	−	3.56529i	−0.251476	−	0.435570i	0.712456	−	0.701717i	$-0.247583\pi$
$67$	−2.05842	−	3.56529i	−0.251476	−	0.435570i	−0.963932	+	0.266147i	$0.914249\pi$
$68$	−1.62772			−0.197390
$69$		0			0
$70$	1.62772	+	2.81929i	0.194550	+	0.336970i
$71$	−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	$-0.405449\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	2.62772			0.307551			0.153776	−	0.988106i	$-0.450857\pi$
$73$	2.62772			0.307551			0.153776	+	0.988106i	$0.450857\pi$
$74$	−6.05842	−	0.543620i	−0.704277	−	0.0631946i
$75$	−0.627719			−0.0724827
$76$	−2.37228	+	4.10891i	−0.272119	+	0.471325i
$77$	1.37228	+	2.37686i	0.156386	+	0.270868i
$78$	−0.686141	−	1.18843i	−0.0776901	−	0.134563i
$79$	−0.686141	−	1.18843i	−0.0771969	−	0.133709i	0.824843	−	0.565362i	$-0.191264\pi$
$79$	−0.686141	−	1.18843i	−0.0771969	−	0.133709i	−0.902039	+	0.431653i	$0.857930\pi$
$80$	−2.37228			−0.265229
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.37228			0.482838
$83$	−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	$0.311354\pi$
$84$	1.37228			0.149728
$85$	3.86141			0.418828
$86$	−4.68614	+	8.11663i	−0.505320	+	0.875239i
$87$	2.18614	+	3.78651i	0.234379	+	0.405956i
$88$	−2.00000			−0.213201
$89$	−1.81386	+	3.14170i	−0.192269	+	0.333019i	−0.946002	−	0.324162i	$-0.894918\pi$
$89$	−1.81386	+	3.14170i	−0.192269	+	0.333019i	0.753733	+	0.657181i	$0.228251\pi$
$90$	−1.18614	+	2.05446i	−0.125030	+	0.216559i
$91$	0.941578	−	1.63086i	0.0987042	−	0.170961i
$92$		0			0
$93$	−4.68614	−	8.11663i	−0.485930	−	0.841656i
$94$	1.00000	−	1.73205i	0.103142	−	0.178647i
$95$	5.62772	−	9.74749i	0.577392	−	1.00007i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	5.74456			0.583272			0.291636	−	0.956529i	$-0.405800\pi$
$97$	5.74456			0.583272			0.291636	+	0.956529i	$0.405800\pi$
$98$	−2.55842	−	4.43132i	−0.258440	−	0.447631i
$99$	−1.00000	+	1.73205i	−0.100504	+	0.174078i
$100$	0.627719			0.0627719
$101$	13.8614			1.37926			0.689631	−	0.724161i	$-0.257773\pi$
$101$	13.8614			1.37926			0.689631	+	0.724161i	$0.257773\pi$
$102$	0.813859	−	1.40965i	0.0805841	−	0.139576i
$103$	12.7446			1.25576			0.627880	−	0.778311i	$-0.283923\pi$
$103$	12.7446			1.25576			0.627880	+	0.778311i	$0.283923\pi$
$104$	0.686141	+	1.18843i	0.0672816	+	0.116535i
$105$	−3.25544			−0.317698
$106$	5.74456	+	9.94987i	0.557961	+	0.966417i
$107$	−2.37228	−	4.10891i	−0.229337	−	0.397223i	0.728275	−	0.685285i	$-0.240322\pi$
$107$	−2.37228	−	4.10891i	−0.229337	−	0.397223i	−0.957612	+	0.288062i	$0.906989\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	2.12772	−	3.68532i	0.203798	−	0.352989i	−0.745951	−	0.666001i	$-0.768005\pi$
$109$	2.12772	−	3.68532i	0.203798	−	0.352989i	0.949749	+	0.313012i	$0.101338\pi$
$110$	4.74456			0.452376
$111$	3.50000	−	4.97494i	0.332205	−	0.472200i
$112$	−1.37228			−0.129668
$113$	7.74456	−	13.4140i	0.728547	−	1.26188i	−0.228950	−	0.973438i	$-0.573529\pi$
$113$	7.74456	−	13.4140i	0.728547	−	1.26188i	0.957497	−	0.288443i	$-0.0931374\pi$
$114$	−2.37228	−	4.10891i	−0.222185	−	0.384835i
$115$		0			0
$116$	−2.18614	−	3.78651i	−0.202978	−	0.351568i
$117$	1.37228			0.126867
$118$	−2.00000	−	3.46410i	−0.184115	−	0.318896i
$119$	2.23369			0.204762
$120$	1.18614	−	2.05446i	0.108279	−	0.187545i
$121$	−7.00000			−0.636364
$122$	9.11684			0.825400
$123$	−2.18614	+	3.78651i	−0.197118	+	0.341418i
$124$	4.68614	+	8.11663i	0.420828	+	0.728895i
$125$	10.3723			0.927725
$126$	−0.686141	+	1.18843i	−0.0611263	+	0.105874i
$127$	−4.31386	+	7.47182i	−0.382793	+	0.663017i	−0.991460	−	0.130408i	$-0.958371\pi$
$127$	−4.31386	+	7.47182i	−0.382793	+	0.663017i	0.608667	+	0.793426i	$0.291704\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.68614	−	8.11663i	−0.412592	−	0.714630i
$130$	−1.62772	−	2.81929i	−0.142760	−	0.247268i
$131$	−5.37228	+	9.30506i	−0.469378	+	0.812987i	−0.999387	−	0.0350049i	$-0.988855\pi$
$131$	−5.37228	+	9.30506i	−0.469378	+	0.812987i	0.530009	+	0.847992i	$0.322189\pi$
$132$	1.00000	−	1.73205i	0.0870388	−	0.150756i
$133$	3.25544	−	5.63858i	0.282282	−	0.488927i
$134$	−4.11684			−0.355641
$135$	−1.18614	−	2.05446i	−0.102087	−	0.176819i
$136$	−0.813859	+	1.40965i	−0.0697879	+	0.120876i
$137$	10.3723			0.886164			0.443082	−	0.896481i	$-0.353885\pi$
$137$	10.3723			0.886164			0.443082	+	0.896481i	$0.353885\pi$
$138$		0			0
$139$	4.31386	−	7.47182i	0.365897	−	0.633752i	−0.623023	−	0.782204i	$-0.714096\pi$
$139$	4.31386	−	7.47182i	0.365897	−	0.633752i	0.988920	+	0.148452i	$0.0474290\pi$
$140$	3.25544			0.275135
$141$	1.00000	+	1.73205i	0.0842152	+	0.145865i
$142$	−11.4891			−0.964146
$143$	−1.37228	−	2.37686i	−0.114756	−	0.198763i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	5.18614	+	8.98266i	0.430686	+	0.745969i
$146$	1.31386	−	2.27567i	0.108736	−	0.188336i
$147$	5.11684			0.422030
$148$	−3.50000	+	4.97494i	−0.287698	+	0.408937i
$149$	1.62772			0.133348			0.0666740	−	0.997775i	$-0.478761\pi$
$149$	1.62772			0.133348			0.0666740	+	0.997775i	$0.478761\pi$
$150$	−0.313859	+	0.543620i	−0.0256265	+	0.0443864i
$151$	9.68614	+	16.7769i	0.788247	+	1.36528i	0.927040	+	0.374962i	$0.122344\pi$
$151$	9.68614	+	16.7769i	0.788247	+	1.36528i	−0.138793	+	0.990321i	$0.544322\pi$
$152$	2.37228	+	4.10891i	0.192417	+	0.333277i
$153$	0.813859	+	1.40965i	0.0657966	+	0.113963i
$154$	2.74456			0.221163
$155$	−11.1168	−	19.2549i	−0.892926	−	1.54659i
$156$	−1.37228			−0.109870
$157$	−3.24456	+	5.61975i	−0.258944	+	0.448505i	−0.965959	−	0.258694i	$-0.916708\pi$
$157$	−3.24456	+	5.61975i	−0.258944	+	0.448505i	0.707015	+	0.707198i	$0.250041\pi$
$158$	−1.37228			−0.109173
$159$	−11.4891			−0.911147
$160$	−1.18614	+	2.05446i	−0.0937727	+	0.162419i
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−12.3723	+	21.4294i	−0.969072	+	1.67848i	−0.270819	+	0.962630i	$0.587295\pi$
$163$	−12.3723	+	21.4294i	−0.969072	+	1.67848i	−0.698253	+	0.715852i	$0.746039\pi$
$164$	2.18614	−	3.78651i	0.170709	−	0.295676i
$165$	−2.37228	+	4.10891i	−0.184682	+	0.319878i
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	0.744563	+	1.28962i	0.0576160	+	0.0997938i	0.893395	−	0.449273i	$-0.148317\pi$
$167$	0.744563	+	1.28962i	0.0576160	+	0.0997938i	−0.835779	+	0.549066i	$0.814983\pi$
$168$	0.686141	−	1.18843i	0.0529369	−	0.0916894i
$169$	5.55842	−	9.62747i	0.427571	−	0.740575i
$170$	1.93070	−	3.34408i	0.148078	−	0.256479i
$171$	4.74456			0.362826
$172$	4.68614	+	8.11663i	0.357315	+	0.618888i
$173$	−11.5584	+	20.0198i	−0.878771	+	1.52208i	−0.0260794	+	0.999660i	$0.508302\pi$
$173$	−11.5584	+	20.0198i	−0.878771	+	1.52208i	−0.852691	+	0.522415i	$0.825031\pi$
$174$	4.37228			0.331462
$175$	−0.861407			−0.0651162
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	4.00000			0.300658
$178$	1.81386	+	3.14170i	0.135955	+	0.235480i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.18614	+	2.05446i	0.0884097	+	0.153130i
$181$	2.12772	+	3.68532i	0.158152	+	0.273927i	0.934202	−	0.356744i	$-0.116113\pi$
$181$	2.12772	+	3.68532i	0.158152	+	0.273927i	−0.776050	+	0.630671i	$0.782780\pi$
$182$	−0.941578	−	1.63086i	−0.0697944	−	0.120887i
$183$	−4.55842	+	7.89542i	−0.336968	+	0.583646i
$184$		0			0
$185$	8.30298	−	11.8020i	0.610448	−	0.867697i
$186$	−9.37228			−0.687209
$187$	1.62772	−	2.81929i	0.119031	−	0.206167i
$188$	−1.00000	−	1.73205i	−0.0729325	−	0.126323i
$189$	−0.686141	−	1.18843i	−0.0499094	−	0.0864456i
$190$	−5.62772	−	9.74749i	−0.408278	−	0.707158i
$191$	−22.7446			−1.64574			−0.822869	−	0.568231i	$-0.807628\pi$
$191$	−22.7446			−1.64574			−0.822869	+	0.568231i	$0.807628\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−18.4891			−1.33088			−0.665438	−	0.746453i	$-0.731755\pi$
$193$	−18.4891			−1.33088			−0.665438	+	0.746453i	$0.731755\pi$
$194$	2.87228	−	4.97494i	0.206218	−	0.357180i
$195$	3.25544			0.233127
$196$	−5.11684			−0.365489
$197$	−6.81386	+	11.8020i	−0.485467	+	0.840854i	−0.999861	−	0.0167003i	$-0.994684\pi$
$197$	−6.81386	+	11.8020i	−0.485467	+	0.840854i	0.514393	+	0.857554i	$0.328017\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	−6.62772			−0.469827			−0.234913	−	0.972016i	$-0.575481\pi$
$199$	−6.62772			−0.469827			−0.234913	+	0.972016i	$0.575481\pi$
$200$	0.313859	−	0.543620i	0.0221932	−	0.0384398i
$201$	2.05842	−	3.56529i	0.145190	−	0.251476i
$202$	6.93070	−	12.0043i	0.487643	−	0.844622i
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$	−0.813859	−	1.40965i	−0.0569816	−	0.0986949i
$205$	−5.18614	+	8.98266i	−0.362216	+	0.627376i
$206$	6.37228	−	11.0371i	0.443978	−	0.768992i
$207$		0			0
$208$	1.37228			0.0951506
$209$	−4.74456	−	8.21782i	−0.328188	−	0.568439i
$210$	−1.62772	+	2.81929i	−0.112323	+	0.194550i
$211$	13.3723			0.920586			0.460293	−	0.887767i	$-0.347744\pi$
$211$	13.3723			0.920586			0.460293	+	0.887767i	$0.347744\pi$
$212$	11.4891			0.789076
$213$	5.74456	−	9.94987i	0.393611	−	0.681754i
$214$	−4.74456			−0.324332
$215$	−11.1168	−	19.2549i	−0.758162	−	1.31318i
$216$	1.00000			0.0680414
$217$	−6.43070	−	11.1383i	−0.436545	−	0.756117i
$218$	−2.12772	−	3.68532i	−0.144107	−	0.249601i
$219$	1.31386	+	2.27567i	0.0887824	+	0.153776i
$220$	2.37228	−	4.10891i	0.159939	−	0.277023i
$221$	−2.23369			−0.150254
$222$	−2.55842	−	5.51856i	−0.171710	−	0.370381i
$223$	18.1168			1.21319			0.606597	−	0.795010i	$-0.292534\pi$
$223$	18.1168			1.21319			0.606597	+	0.795010i	$0.292534\pi$
$224$	−0.686141	+	1.18843i	−0.0458447	+	0.0794054i
$225$	−0.313859	−	0.543620i	−0.0209240	−	0.0362414i
$226$	−7.74456	−	13.4140i	−0.515161	−	0.892284i
$227$	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	$0.708817\pi$
$228$	−4.74456			−0.314216
$229$	6.87228	+	11.9031i	0.454133	+	0.786582i	0.998638	−	0.0521761i	$-0.0166157\pi$
$229$	6.87228	+	11.9031i	0.454133	+	0.786582i	−0.544505	+	0.838758i	$0.683282\pi$
$230$		0			0
$231$	−1.37228	+	2.37686i	−0.0902895	+	0.156386i
$232$	−4.37228			−0.287054
$233$	−28.6060			−1.87404			−0.937020	−	0.349277i	$-0.886427\pi$
$233$	−28.6060			−1.87404			−0.937020	+	0.349277i	$0.886427\pi$
$234$	0.686141	−	1.18843i	0.0448544	−	0.0776901i
$235$	2.37228	+	4.10891i	0.154751	+	0.268036i
$236$	−4.00000			−0.260378
$237$	0.686141	−	1.18843i	0.0445696	−	0.0771969i
$238$	1.11684	−	1.93443i	0.0723942	−	0.125391i
$239$	11.1168	−	19.2549i	0.719089	−	1.24550i	−0.242272	−	0.970208i	$-0.577893\pi$
$239$	11.1168	−	19.2549i	0.719089	−	1.24550i	0.961361	−	0.275290i	$-0.0887739\pi$
$240$	−1.18614	−	2.05446i	−0.0765651	−	0.132615i
$241$	−12.0584	−	20.8858i	−0.776751	−	1.34537i	−0.933805	−	0.357783i	$-0.883533\pi$
$241$	−12.0584	−	20.8858i	−0.776751	−	1.34537i	0.157054	−	0.987590i	$-0.449800\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.55842	−	7.89542i	0.291823	−	0.505452i
$245$	12.1386			0.775506
$246$	2.18614	+	3.78651i	0.139383	+	0.241419i
$247$	−3.25544	+	5.63858i	−0.207139	+	0.358774i
$248$	9.37228			0.595140
$249$	−8.00000			−0.506979
$250$	5.18614	−	8.98266i	0.328000	−	0.568113i
$251$	−12.7446			−0.804430			−0.402215	−	0.915545i	$-0.631760\pi$
$251$	−12.7446			−0.804430			−0.402215	+	0.915545i	$0.631760\pi$
$252$	0.686141	+	1.18843i	0.0432228	+	0.0748641i
$253$		0			0
$254$	4.31386	+	7.47182i	0.270676	+	0.468824i
$255$	1.93070	+	3.34408i	0.120905	+	0.209414i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.93070	+	17.2005i	−0.619460	+	1.07294i	0.370124	+	0.928982i	$0.379315\pi$
$257$	−9.93070	+	17.2005i	−0.619460	+	1.07294i	−0.989584	+	0.143954i	$0.954018\pi$
$258$	−9.37228			−0.583493
$259$	4.80298	−	6.82701i	0.298443	−	0.424210i
$260$	−3.25544			−0.201894
$261$	−2.18614	+	3.78651i	−0.135319	+	0.234379i
$262$	5.37228	+	9.30506i	0.331901	+	0.574869i
$263$	13.3723	+	23.1615i	0.824570	+	1.42820i	0.902247	+	0.431219i	$0.141916\pi$
$263$	13.3723	+	23.1615i	0.824570	+	1.42820i	−0.0776771	+	0.996979i	$0.524750\pi$
$264$	−1.00000	−	1.73205i	−0.0615457	−	0.106600i
$265$	−27.2554			−1.67429
$266$	−3.25544	−	5.63858i	−0.199604	−	0.345724i
$267$	−3.62772			−0.222013
$268$	−2.05842	+	3.56529i	−0.125738	+	0.217785i
$269$	2.00000			0.121942			0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000			0.121942			0.0609711	+	0.998140i	$0.480580\pi$
$270$	−2.37228			−0.144372
$271$	−9.43070	+	16.3345i	−0.572874	+	0.992248i	0.423395	+	0.905945i	$0.360838\pi$
$271$	−9.43070	+	16.3345i	−0.572874	+	0.992248i	−0.996269	+	0.0863022i	$0.972495\pi$
$272$	0.813859	+	1.40965i	0.0493475	+	0.0854723i
$273$	1.88316			0.113974
$274$	5.18614	−	8.98266i	0.313306	−	0.542662i
$275$	−0.627719	+	1.08724i	−0.0378529	+	0.0655631i
$276$		0			0
$277$	1.06930	+	1.85208i	0.0642478	+	0.111280i	0.896360	−	0.443327i	$-0.146202\pi$
$277$	1.06930	+	1.85208i	0.0642478	+	0.111280i	−0.832112	+	0.554607i	$0.812869\pi$
$278$	−4.31386	−	7.47182i	−0.258728	−	0.448130i
$279$	4.68614	−	8.11663i	0.280552	−	0.485930i
$280$	1.62772	−	2.81929i	0.0972748	−	0.168485i
$281$	3.55842	−	6.16337i	0.212278	−	0.367676i	−0.740149	−	0.672443i	$-0.765245\pi$
$281$	3.55842	−	6.16337i	0.212278	−	0.367676i	0.952427	+	0.304767i	$0.0985785\pi$
$282$	2.00000			0.119098
$283$	0.0584220	+	0.101190i	0.00347283	+	0.00601511i	0.867757	−	0.496989i	$-0.165561\pi$
$283$	0.0584220	+	0.101190i	0.00347283	+	0.00601511i	−0.864284	+	0.503005i	$0.832228\pi$
$284$	−5.74456	+	9.94987i	−0.340877	+	0.590416i
$285$	11.2554			0.666715
$286$	−2.74456			−0.162289
$287$	−3.00000	+	5.19615i	−0.177084	+	0.306719i
$288$	−1.00000			−0.0589256
$289$	7.17527	+	12.4279i	0.422074	+	0.731054i
$290$	10.3723			0.609081
$291$	2.87228	+	4.97494i	0.168376	+	0.291636i
$292$	−1.31386	−	2.27567i	−0.0768878	−	0.133174i
$293$	16.5584	+	28.6800i	0.967353	+	1.67551i	0.703155	+	0.711037i	$0.251774\pi$
$293$	16.5584	+	28.6800i	0.967353	+	1.67551i	0.264199	+	0.964468i	$0.414893\pi$
$294$	2.55842	−	4.43132i	0.149210	−	0.258440i
$295$	9.48913			0.552478
$296$	2.55842	+	5.51856i	0.148705	+	0.320760i
$297$	−2.00000			−0.116052
$298$	0.813859	−	1.40965i	0.0471456	−	0.0816586i
$299$		0			0
$300$	0.313859	+	0.543620i	0.0181207	+	0.0313859i
$301$	−6.43070	−	11.1383i	−0.370660	−	0.642001i
$302$	19.3723			1.11475
$303$	6.93070	+	12.0043i	0.398159	+	0.689631i
$304$	4.74456			0.272119
$305$	−10.8139	+	18.7302i	−0.619200	+	1.07249i
$306$	1.62772			0.0930505
$307$	−8.11684			−0.463253			−0.231626	−	0.972805i	$-0.574405\pi$
$307$	−8.11684			−0.463253			−0.231626	+	0.972805i	$0.574405\pi$
$308$	1.37228	−	2.37686i	0.0781930	−	0.135434i
$309$	6.37228	+	11.0371i	0.362506	+	0.627880i
$310$	−22.2337			−1.26279
$311$	14.4891	−	25.0959i	0.821603	−	1.42306i	−0.0828852	−	0.996559i	$-0.526413\pi$
$311$	14.4891	−	25.0959i	0.821603	−	1.42306i	0.904488	−	0.426499i	$-0.140253\pi$
$312$	−0.686141	+	1.18843i	−0.0388451	+	0.0672816i
$313$	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	$0.00714060\pi$
$314$	3.24456	+	5.61975i	0.183101	+	0.317141i
$315$	−1.62772	−	2.81929i	−0.0917116	−	0.158849i
$316$	−0.686141	+	1.18843i	−0.0385984	+	0.0668544i
$317$	6.44158	−	11.1571i	0.361795	−	0.626647i	−0.626461	−	0.779453i	$-0.715497\pi$
$317$	6.44158	−	11.1571i	0.361795	−	0.626647i	0.988256	+	0.152805i	$0.0488307\pi$
$318$	−5.74456	+	9.94987i	−0.322139	+	0.557961i
$319$	8.74456			0.489602
$320$	1.18614	+	2.05446i	0.0663073	+	0.114848i
$321$	2.37228	−	4.10891i	0.132408	−	0.229337i
$322$		0			0
$323$	−7.72281			−0.429709
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	0.861407			0.0477822
$326$	12.3723	+	21.4294i	0.685237	+	1.18687i
$327$	4.25544			0.235326
$328$	−2.18614	−	3.78651i	−0.120709	−	0.209075i
$329$	1.37228	+	2.37686i	0.0756563	+	0.131041i
$330$	2.37228	+	4.10891i	0.130590	+	0.226188i
$331$	17.8030	−	30.8357i	0.978541	−	1.69488i	0.310822	−	0.950468i	$-0.399396\pi$
$331$	17.8030	−	30.8357i	0.978541	−	1.69488i	0.667719	−	0.744414i	$-0.267271\pi$
$332$	8.00000			0.439057
$333$	6.05842	+	0.543620i	0.331999	+	0.0297902i
$334$	1.48913			0.0814813
$335$	4.88316	−	8.45787i	0.266795	−	0.462103i
$336$	−0.686141	−	1.18843i	−0.0374320	−	0.0648342i
$337$	−14.8723	−	25.7595i	−0.810145	−	1.40321i	−0.912762	−	0.408491i	$-0.866055\pi$
$337$	−14.8723	−	25.7595i	−0.810145	−	1.40321i	0.102618	−	0.994721i	$-0.467278\pi$
$338$	−5.55842	−	9.62747i	−0.302338	−	0.523665i
$339$	15.4891			0.841254
$340$	−1.93070	−	3.34408i	−0.104707	−	0.181358i
$341$	−18.7446			−1.01507
$342$	2.37228	−	4.10891i	0.128278	−	0.222185i
$343$	16.6277			0.897812
$344$	9.37228			0.505320
$345$		0			0
$346$	11.5584	+	20.0198i	0.621385	+	1.07627i
$347$	26.7446			1.43572			0.717862	−	0.696186i	$-0.245121\pi$
$347$	26.7446			1.43572			0.717862	+	0.696186i	$0.245121\pi$
$348$	2.18614	−	3.78651i	0.117189	−	0.202978i
$349$	4.55842	−	7.89542i	0.244007	−	0.422632i	−0.717845	−	0.696203i	$-0.754871\pi$
$349$	4.55842	−	7.89542i	0.244007	−	0.422632i	0.961852	+	0.273571i	$0.0882048\pi$
$350$	−0.430703	+	0.746000i	−0.0230221	+	0.0398754i
$351$	0.686141	+	1.18843i	0.0366235	+	0.0634337i
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	−15.3030	+	26.5055i	−0.814496	+	1.41075i	0.0951938	+	0.995459i	$0.469653\pi$
$353$	−15.3030	+	26.5055i	−0.814496	+	1.41075i	−0.909689	+	0.415289i	$0.863680\pi$
$354$	2.00000	−	3.46410i	0.106299	−	0.184115i
$355$	13.6277	−	23.6039i	0.723284	−	1.25276i
$356$	3.62772			0.192269
$357$	1.11684	+	1.93443i	0.0591097	+	0.102381i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	12.2337			0.645669			0.322835	−	0.946455i	$-0.395364\pi$
$359$	12.2337			0.645669			0.322835	+	0.946455i	$0.395364\pi$
$360$	2.37228			0.125030
$361$	−1.75544	+	3.04051i	−0.0923914	+	0.160027i
$362$	4.25544			0.223661
$363$	−3.50000	−	6.06218i	−0.183702	−	0.318182i
$364$	−1.88316			−0.0987042
$365$	3.11684	+	5.39853i	0.163143	+	0.282572i
$366$	4.55842	+	7.89542i	0.238273	+	0.412700i
$367$	−3.05842	−	5.29734i	−0.159648	−	0.276519i	0.775094	−	0.631846i	$-0.217703\pi$
$367$	−3.05842	−	5.29734i	−0.159648	−	0.276519i	−0.934742	+	0.355327i	$0.884369\pi$
$368$		0			0
$369$	−4.37228			−0.227612
$370$	−6.06930	−	13.0916i	−0.315528	−	0.680598i
$371$	−15.7663			−0.818546
$372$	−4.68614	+	8.11663i	−0.242965	+	0.420828i
$373$	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	$0.536804\pi$
$374$	−1.62772	−	2.81929i	−0.0841673	−	0.145782i
$375$	5.18614	+	8.98266i	0.267811	+	0.463863i
$376$	−2.00000			−0.103142
$377$	−3.00000	−	5.19615i	−0.154508	−	0.267615i
$378$	−1.37228			−0.0705825
$379$	13.8614	−	24.0087i	0.712013	−	1.23324i	−0.252088	−	0.967704i	$-0.581117\pi$
$379$	13.8614	−	24.0087i	0.712013	−	1.23324i	0.964100	−	0.265538i	$-0.0855495\pi$
$380$	−11.2554			−0.577392
$381$	−8.62772			−0.442011
$382$	−11.3723	+	19.6974i	−0.581857	+	1.00781i
$383$	3.11684	+	5.39853i	0.159263	+	0.275852i	0.934603	−	0.355692i	$-0.115755\pi$
$383$	3.11684	+	5.39853i	0.159263	+	0.275852i	−0.775340	+	0.631544i	$0.782421\pi$
$384$	1.00000			0.0510310
$385$	−3.25544	+	5.63858i	−0.165912	+	0.287369i
$386$	−9.24456	+	16.0121i	−0.470536	+	0.814992i
$387$	4.68614	−	8.11663i	0.238210	−	0.412592i
$388$	−2.87228	−	4.97494i	−0.145818	−	0.252564i
$389$	−3.44158	−	5.96099i	−0.174495	−	0.302234i	0.765491	−	0.643446i	$-0.222496\pi$
$389$	−3.44158	−	5.96099i	−0.174495	−	0.302234i	−0.939986	+	0.341212i	$0.889163\pi$
$390$	1.62772	−	2.81929i	0.0824227	−	0.142760i
$391$		0			0
$392$	−2.55842	+	4.43132i	−0.129220	+	0.223815i
$393$	−10.7446			−0.541991
$394$	6.81386	+	11.8020i	0.343277	+	0.594574i
$395$	1.62772	−	2.81929i	0.0818994	−	0.141854i
$396$	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	$0.658200\pi$
$398$	−3.31386	+	5.73977i	−0.166109	+	0.287709i
$399$	6.51087			0.325951
$400$	−0.313859	−	0.543620i	−0.0156930	−	0.0271810i
$401$	−3.25544			−0.162569			−0.0812844	−	0.996691i	$-0.525902\pi$
$401$	−3.25544			−0.162569			−0.0812844	+	0.996691i	$0.525902\pi$
$402$	−2.05842	−	3.56529i	−0.102665	−	0.177821i
$403$	6.43070	+	11.1383i	0.320336	+	0.554838i
$404$	−6.93070	−	12.0043i	−0.344815	−	0.597238i
$405$	1.18614	−	2.05446i	0.0589398	−	0.102087i
$406$	6.00000			0.297775
$407$	−5.11684	−	11.0371i	−0.253633	−	0.547089i
$408$	−1.62772			−0.0805841
$409$	11.8723	−	20.5634i	0.587047	−	1.01679i	−0.407570	−	0.913174i	$-0.633624\pi$
$409$	11.8723	−	20.5634i	0.587047	−	1.01679i	0.994617	−	0.103621i	$-0.0330428\pi$
$410$	5.18614	+	8.98266i	0.256125	+	0.443622i
$411$	5.18614	+	8.98266i	0.255813	+	0.443082i
$412$	−6.37228	−	11.0371i	−0.313940	−	0.543760i
$413$	5.48913			0.270102
$414$		0			0
$415$	−18.9783			−0.931606
$416$	0.686141	−	1.18843i	0.0336408	−	0.0582676i
$417$	8.62772			0.422501
$418$	−9.48913			−0.464128
$419$	−9.74456	+	16.8781i	−0.476053	+	0.824548i	−0.999624	−	0.0274343i	$-0.991266\pi$
$419$	−9.74456	+	16.8781i	−0.476053	+	0.824548i	0.523571	+	0.851982i	$0.324600\pi$
$420$	1.62772	+	2.81929i	0.0794245	+	0.137567i
$421$	−11.6277			−0.566700			−0.283350	−	0.959017i	$-0.591446\pi$
$421$	−11.6277			−0.566700			−0.283350	+	0.959017i	$0.591446\pi$
$422$	6.68614	−	11.5807i	0.325476	−	0.563741i
$423$	−1.00000	+	1.73205i	−0.0486217	+	0.0842152i
$424$	5.74456	−	9.94987i	0.278981	−	0.483209i
$425$	0.510875	+	0.884861i	0.0247811	+	0.0429221i
$426$	−5.74456	−	9.94987i	−0.278325	−	0.482073i
$427$	−6.25544	+	10.8347i	−0.302722	+	0.524330i
$428$	−2.37228	+	4.10891i	−0.114669	+	0.198612i
$429$	1.37228	−	2.37686i	0.0662544	−	0.114756i
$430$	−22.2337			−1.07220
$431$	−4.48913	−	7.77539i	−0.216234	−	0.374528i	0.737420	−	0.675435i	$-0.236044\pi$
$431$	−4.48913	−	7.77539i	−0.216234	−	0.374528i	−0.953653	+	0.300907i	$0.902711\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	7.62772			0.366565			0.183282	−	0.983060i	$-0.441328\pi$
$433$	7.62772			0.366565			0.183282	+	0.983060i	$0.441328\pi$
$434$	−12.8614			−0.617367
$435$	−5.18614	+	8.98266i	−0.248656	+	0.430686i
$436$	−4.25544			−0.203798
$437$		0			0
$438$	2.62772			0.125557
$439$	−4.31386	−	7.47182i	−0.205889	−	0.356611i	0.744526	−	0.667593i	$-0.232675\pi$
$439$	−4.31386	−	7.47182i	−0.205889	−	0.356611i	−0.950416	+	0.310982i	$0.899342\pi$
$440$	−2.37228	−	4.10891i	−0.113094	−	0.195885i
$441$	2.55842	+	4.43132i	0.121830	+	0.211015i
$442$	−1.11684	+	1.93443i	−0.0531229	+	0.0920115i
$443$	−5.48913			−0.260796			−0.130398	−	0.991462i	$-0.541626\pi$
$443$	−5.48913			−0.260796			−0.130398	+	0.991462i	$0.541626\pi$
$444$	−6.05842	−	0.543620i	−0.287520	−	0.0257991i
$445$	−8.60597			−0.407962
$446$	9.05842	−	15.6896i	0.428929	−	0.742926i
$447$	0.813859	+	1.40965i	0.0384942	+	0.0666740i
$448$	0.686141	+	1.18843i	0.0324171	+	0.0561481i
$449$	−12.4891	−	21.6318i	−0.589398	−	1.02087i	−0.994311	−	0.106513i	$-0.966032\pi$
$449$	−12.4891	−	21.6318i	−0.589398	−	1.02087i	0.404913	−	0.914355i	$-0.367302\pi$
$450$	−0.627719			−0.0295909
$451$	4.37228	+	7.57301i	0.205883	+	0.356599i
$452$	−15.4891			−0.728547
$453$	−9.68614	+	16.7769i	−0.455095	+	0.788247i
$454$	11.4891			0.539211
$455$	4.46738			0.209434
$456$	−2.37228	+	4.10891i	−0.111092	+	0.192417i
$457$	−12.0475	−	20.8670i	−0.563560	−	0.976115i	−0.997182	−	0.0750203i	$-0.976098\pi$
$457$	−12.0475	−	20.8670i	−0.563560	−	0.976115i	0.433622	−	0.901095i	$-0.357235\pi$
$458$	13.7446			0.642241
$459$	−0.813859	+	1.40965i	−0.0379877	+	0.0657966i
$460$		0			0
$461$	10.4891	−	18.1677i	0.488527	−	0.846154i	−0.511386	−	0.859351i	$-0.670868\pi$
$461$	10.4891	−	18.1677i	0.488527	−	0.846154i	0.999913	+	0.0131973i	$0.00420095\pi$
$462$	1.37228	+	2.37686i	0.0638443	+	0.110582i
$463$	0.0584220	+	0.101190i	0.00271510	+	0.00470269i	0.867380	−	0.497647i	$-0.165802\pi$
$463$	0.0584220	+	0.101190i	0.00271510	+	0.00470269i	−0.864665	+	0.502350i	$0.832469\pi$
$464$	−2.18614	+	3.78651i	−0.101489	+	0.175784i
$465$	11.1168	−	19.2549i	0.515531	−	0.892926i
$466$	−14.3030	+	24.7735i	−0.662573	+	1.14761i
$467$	14.7446			0.682297			0.341148	−	0.940009i	$-0.389184\pi$
$467$	14.7446			0.682297			0.341148	+	0.940009i	$0.389184\pi$
$468$	−0.686141	−	1.18843i	−0.0317169	−	0.0549352i
$469$	2.82473	−	4.89258i	0.130434	−	0.225918i
$470$	4.74456			0.218850
$471$	−6.48913			−0.299003
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	−18.7446			−0.861876
$474$	−0.686141	−	1.18843i	−0.0315155	−	0.0545864i
$475$	2.97825			0.136652
$476$	−1.11684	−	1.93443i	−0.0511905	−	0.0886645i
$477$	−5.74456	−	9.94987i	−0.263025	−	0.455573i
$478$	−11.1168	−	19.2549i	−0.508473	−	0.880700i
$479$	0.116844	−	0.202380i	0.00533874	−	0.00924696i	−0.863344	−	0.504616i	$-0.831634\pi$
$479$	0.116844	−	0.202380i	0.00533874	−	0.00924696i	0.868682	+	0.495369i	$0.164967\pi$
$480$	−2.37228			−0.108279
$481$	−4.80298	+	6.82701i	−0.218997	+	0.311285i
$482$	−24.1168			−1.09849
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	6.81386	+	11.8020i	0.309401	+	0.535899i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−37.4891			−1.69879			−0.849397	−	0.527754i	$-0.823034\pi$
$487$	−37.4891			−1.69879			−0.849397	+	0.527754i	$0.823034\pi$
$488$	−4.55842	−	7.89542i	−0.206350	−	0.357409i
$489$	−24.7446			−1.11899
$490$	6.06930	−	10.5123i	0.274183	−	0.474899i
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$	4.37228			0.197118
$493$	3.55842	−	6.16337i	0.160263	−	0.277584i
$494$	3.25544	+	5.63858i	0.146469	+	0.253692i
$495$	−4.74456			−0.213252
$496$	4.68614	−	8.11663i	0.210414	−	0.364448i
$497$	7.88316	−	13.6540i	0.353608	−	0.612467i
$498$	−4.00000	+	6.92820i	−0.179244	+	0.310460i
$499$	13.1168	+	22.7190i	0.587191	+	1.01704i	0.994598	+	0.103798i	$0.0330994\pi$
$499$	13.1168	+	22.7190i	0.587191	+	1.01704i	−0.407408	+	0.913246i	$0.633567\pi$
$500$	−5.18614	−	8.98266i	−0.231931	−	0.401717i
$501$	−0.744563	+	1.28962i	−0.0332646	+	0.0576160i
$502$	−6.37228	+	11.0371i	−0.284409	+	0.492611i
$503$	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	$0.00349334\pi$
$504$	1.37228			0.0611263
$505$	16.4416	+	28.4776i	0.731641	+	1.26724i
$506$		0			0
$507$	11.1168			0.493716
$508$	8.62772			0.382793
$509$	−2.18614	+	3.78651i	−0.0968990	+	0.167834i	−0.910400	−	0.413730i	$-0.864226\pi$
$509$	−2.18614	+	3.78651i	−0.0968990	+	0.167834i	0.813501	+	0.581564i	$0.197559\pi$
$510$	3.86141			0.170986
$511$	1.80298	+	3.12286i	0.0797593	+	0.138147i
$512$	−1.00000			−0.0441942
$513$	2.37228	+	4.10891i	0.104739	+	0.181413i
$514$	9.93070	+	17.2005i	0.438025	+	0.758681i
$515$	15.1168	+	26.1831i	0.666128	+	1.15377i
$516$	−4.68614	+	8.11663i	−0.206296	+	0.357315i
$517$	4.00000			0.175920
$518$	−3.51087	−	7.57301i	−0.154259	−	0.332739i
$519$	−23.1168			−1.01472
$520$	−1.62772	+	2.81929i	−0.0713802	+	0.123634i
$521$	−10.3723	−	17.9653i	−0.454418	−	0.787075i	0.544237	−	0.838932i	$-0.316819\pi$
$521$	−10.3723	−	17.9653i	−0.454418	−	0.787075i	−0.998655	+	0.0518569i	$0.983486\pi$
$522$	2.18614	+	3.78651i	0.0956848	+	0.165731i
$523$	−0.941578	−	1.63086i	−0.0411723	−	0.0713126i	0.844705	−	0.535232i	$-0.179776\pi$
$523$	−0.941578	−	1.63086i	−0.0411723	−	0.0713126i	−0.885877	+	0.463920i	$0.846443\pi$
$524$	10.7446			0.469378
$525$	−0.430703	−	0.746000i	−0.0187974	−	0.0325581i
$526$	26.7446			1.16612
$527$	−7.62772	+	13.2116i	−0.332269	+	0.575506i
$528$	−2.00000			−0.0870388
$529$	−23.0000			−1.00000
$530$	−13.6277	+	23.6039i	−0.591950	+	1.02529i
$531$	2.00000	+	3.46410i	0.0867926	+	0.150329i
$532$	−6.51087			−0.282282
$533$	3.00000	−	5.19615i	0.129944	−	0.225070i
$534$	−1.81386	+	3.14170i	−0.0784934	+	0.135955i
$535$	5.62772	−	9.74749i	0.243307	−	0.421421i
$536$	2.05842	+	3.56529i	0.0889103	+	0.153997i
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$	1.00000	−	1.73205i	0.0431131	−	0.0746740i
$539$	5.11684	−	8.86263i	0.220398	−	0.381741i
$540$	−1.18614	+	2.05446i	−0.0510434	+	0.0884097i
$541$	−5.74456			−0.246978			−0.123489	−	0.992346i	$-0.539408\pi$
$541$	−5.74456			−0.246978			−0.123489	+	0.992346i	$0.539408\pi$
$542$	9.43070	+	16.3345i	0.405083	+	0.701625i
$543$	−2.12772	+	3.68532i	−0.0913091	+	0.158152i
$544$	1.62772			0.0697879
$545$	10.0951			0.432426
$546$	0.941578	−	1.63086i	0.0402958	−	0.0697944i
$547$	−39.0951			−1.67159			−0.835793	−	0.549045i	$-0.814992\pi$
$547$	−39.0951			−1.67159			−0.835793	+	0.549045i	$0.814992\pi$
$548$	−5.18614	−	8.98266i	−0.221541	−	0.383720i
$549$	−9.11684			−0.389097
$550$	0.627719	+	1.08724i	0.0267660	+	0.0463601i
$551$	−10.3723	−	17.9653i	−0.441874	−	0.765348i
$552$		0			0
$553$	0.941578	−	1.63086i	0.0400400	−	0.0693513i
$554$	2.13859			0.0908601
$555$	14.3723	+	1.28962i	0.610069	+	0.0547413i
$556$	−8.62772			−0.365897
$557$	−1.55842	+	2.69927i	−0.0660325	+	0.114372i	−0.897152	−	0.441723i	$-0.854367\pi$
$557$	−1.55842	+	2.69927i	−0.0660325	+	0.114372i	0.831119	+	0.556095i	$0.187701\pi$
$558$	−4.68614	−	8.11663i	−0.198380	−	0.343605i
$559$	6.43070	+	11.1383i	0.271990	+	0.471100i
$560$	−1.62772	−	2.81929i	−0.0687837	−	0.119137i
$561$	3.25544			0.137445
$562$	−3.55842	−	6.16337i	−0.150103	−	0.259986i
$563$	13.2554			0.558650			0.279325	−	0.960197i	$-0.409889\pi$
$563$	13.2554			0.558650			0.279325	+	0.960197i	$0.409889\pi$
$564$	1.00000	−	1.73205i	0.0421076	−	0.0729325i
$565$	36.7446			1.54586
$566$	0.116844			0.00491132
$567$	0.686141	−	1.18843i	0.0288152	−	0.0499094i
$568$	5.74456	+	9.94987i	0.241036	+	0.417487i
$569$	15.6277			0.655148			0.327574	−	0.944826i	$-0.393769\pi$
$569$	15.6277			0.655148			0.327574	+	0.944826i	$0.393769\pi$
$570$	5.62772	−	9.74749i	0.235719	−	0.408278i
$571$	−17.9198	+	31.0381i	−0.749921	+	1.29890i	0.197938	+	0.980214i	$0.436575\pi$
$571$	−17.9198	+	31.0381i	−0.749921	+	1.29890i	−0.947860	+	0.318688i	$0.896758\pi$
$572$	−1.37228	+	2.37686i	−0.0573780	+	0.0993815i
$573$	−11.3723	−	19.6974i	−0.475084	−	0.822869i
$574$	3.00000	+	5.19615i	0.125218	+	0.216883i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	6.48913	−	11.2395i	0.270146	−	0.467906i	−0.698753	−	0.715363i	$-0.746261\pi$
$577$	6.48913	−	11.2395i	0.270146	−	0.467906i	0.968899	+	0.247457i	$0.0795948\pi$
$578$	14.3505			0.596903
$579$	−9.24456	−	16.0121i	−0.384191	−	0.665438i
$580$	5.18614	−	8.98266i	0.215343	−	0.372985i
$581$	−10.9783			−0.455455
$582$	5.74456			0.238120
$583$	−11.4891	+	19.8997i	−0.475831	+	0.824163i
$584$	−2.62772			−0.108736
$585$	1.62772	+	2.81929i	0.0672979	+	0.116563i
$586$	33.1168			1.36804
$587$	1.37228	+	2.37686i	0.0566401	+	0.0981036i	0.892955	−	0.450146i	$-0.148628\pi$
$587$	1.37228	+	2.37686i	0.0566401	+	0.0981036i	−0.836315	+	0.548249i	$0.815295\pi$
$588$	−2.55842	−	4.43132i	−0.105508	−	0.182744i
$589$	22.2337	+	38.5099i	0.916123	+	1.58677i
$590$	4.74456	−	8.21782i	0.195331	−	0.338322i
$591$	−13.6277			−0.560569
$592$	6.05842	+	0.543620i	0.249000	+	0.0223427i
$593$	14.3723			0.590199			0.295099	−	0.955467i	$-0.404647\pi$
$593$	14.3723			0.590199			0.295099	+	0.955467i	$0.404647\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	2.64947	+	4.58901i	0.108618	+	0.188131i
$596$	−0.813859	−	1.40965i	−0.0333370	−	0.0577413i
$597$	−3.31386	−	5.73977i	−0.135627	−	0.234913i
$598$		0			0
$599$	−3.62772	−	6.28339i	−0.148225	−	0.256732i	0.782347	−	0.622843i	$-0.214023\pi$
$599$	−3.62772	−	6.28339i	−0.148225	−	0.256732i	−0.930571	+	0.366111i	$0.880689\pi$
$600$	0.627719			0.0256265
$601$	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	$0.0539613\pi$
$602$	−12.8614			−0.524192
$603$	4.11684			0.167651
$604$	9.68614	−	16.7769i	0.394123	−	0.682642i
$605$	−8.30298	−	14.3812i	−0.337564	−	0.584679i
$606$	13.8614			0.563081
$607$	−23.8614	+	41.3292i	−0.968505	+	1.67750i	−0.268616	+	0.963247i	$0.586566\pi$
$607$	−23.8614	+	41.3292i	−0.968505	+	1.67750i	−0.699889	+	0.714252i	$0.746767\pi$
$608$	2.37228	−	4.10891i	0.0962087	−	0.166638i
$609$	−3.00000	+	5.19615i	−0.121566	+	0.210559i
$610$	10.8139	+	18.7302i	0.437840	+	0.758362i
$611$	−1.37228	−	2.37686i	−0.0555166	−	0.0961575i
$612$	0.813859	−	1.40965i	0.0328983	−	0.0569816i
$613$	−8.93070	+	15.4684i	−0.360708	+	0.624764i	−0.988077	−	0.153957i	$-0.950798\pi$
$613$	−8.93070	+	15.4684i	−0.360708	+	0.624764i	0.627370	+	0.778721i	$0.284131\pi$
$614$	−4.05842	+	7.02939i	−0.163785	+	0.283683i
$615$	−10.3723			−0.418251
$616$	−1.37228	−	2.37686i	−0.0552908	−	0.0957665i
$617$	11.8614	−	20.5446i	0.477522	−	0.827093i	−0.522146	−	0.852856i	$-0.674868\pi$
$617$	11.8614	−	20.5446i	0.477522	−	0.827093i	0.999668	+	0.0257634i	$0.00820166\pi$
$618$	12.7446			0.512661
$619$	33.8397			1.36013			0.680065	−	0.733152i	$-0.261951\pi$
$619$	33.8397			1.36013			0.680065	+	0.733152i	$0.261951\pi$
$620$	−11.1168	+	19.2549i	−0.446463	+	0.773297i
$621$		0			0
$622$	−14.4891	−	25.0959i	−0.580961	−	1.00625i
$623$	−4.97825			−0.199449
$624$	0.686141	+	1.18843i	0.0274676	+	0.0475753i
$625$	13.8723	+	24.0275i	0.554891	+	0.961100i
$626$	−8.50000	−	14.7224i	−0.339728	−	0.588427i
$627$	4.74456	−	8.21782i	0.189480	−	0.328188i
$628$	6.48913			0.258944
$629$	−9.86141	−	0.884861i	−0.393200	−	0.0352817i
$630$	−3.25544			−0.129700
$631$	21.0584	−	36.4743i	0.838323	−	1.45202i	−0.0529738	−	0.998596i	$-0.516870\pi$
$631$	21.0584	−	36.4743i	0.838323	−	1.45202i	0.891296	−	0.453421i	$-0.149797\pi$
$632$	0.686141	+	1.18843i	0.0272932	+	0.0472732i
$633$	6.68614	+	11.5807i	0.265750	+	0.460293i
$634$	−6.44158	−	11.1571i	−0.255828	−	0.443107i
$635$	−20.4674			−0.812223
$636$	5.74456	+	9.94987i	0.227787	+	0.394538i
$637$	−7.02175			−0.278212
$638$	4.37228	−	7.57301i	0.173100	−	0.299818i
$639$	11.4891			0.454503
$640$	2.37228			0.0937727
$641$	7.55842	−	13.0916i	0.298540	−	0.517086i	−0.677262	−	0.735742i	$-0.736834\pi$
$641$	7.55842	−	13.0916i	0.298540	−	0.517086i	0.975802	+	0.218656i	$0.0701671\pi$
$642$	−2.37228	−	4.10891i	−0.0936265	−	0.162166i
$643$	17.6060			0.694312			0.347156	−	0.937807i	$-0.387147\pi$
$643$	17.6060			0.694312			0.347156	+	0.937807i	$0.387147\pi$
$644$		0			0
$645$	11.1168	−	19.2549i	0.437725	−	0.758162i
$646$	−3.86141	+	6.68815i	−0.151925	+	0.263142i
$647$	19.8614	+	34.4010i	0.780832	+	1.35244i	0.931457	+	0.363851i	$0.118538\pi$
$647$	19.8614	+	34.4010i	0.780832	+	1.35244i	−0.150625	+	0.988591i	$0.548129\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	4.00000	−	6.92820i	0.157014	−	0.271956i
$650$	0.430703	−	0.746000i	0.0168936	−	0.0292605i
$651$	6.43070	−	11.1383i	0.252039	−	0.436545i
$652$	24.7446			0.969072
$653$	13.4198	+	23.2438i	0.525158	+	0.909601i	0.999571	+	0.0292984i	$0.00932729\pi$
$653$	13.4198	+	23.2438i	0.525158	+	0.909601i	−0.474412	+	0.880303i	$0.657339\pi$
$654$	2.12772	−	3.68532i	0.0832004	−	0.144107i
$655$	−25.4891			−0.995943
$656$	−4.37228			−0.170709
$657$	−1.31386	+	2.27567i	−0.0512585	+	0.0887824i
$658$	2.74456			0.106994
$659$	−3.88316	−	6.72582i	−0.151266	−	0.262001i	0.780427	−	0.625247i	$-0.215002\pi$
$659$	−3.88316	−	6.72582i	−0.151266	−	0.262001i	−0.931693	+	0.363246i	$0.881668\pi$
$660$	4.74456			0.184682
$661$	−9.98913	−	17.3017i	−0.388532	−	0.672957i	0.603720	−	0.797196i	$-0.293684\pi$
$661$	−9.98913	−	17.3017i	−0.388532	−	0.672957i	−0.992252	+	0.124239i	$0.960351\pi$
$662$	−17.8030	−	30.8357i	−0.691933	−	1.19846i
$663$	−1.11684	−	1.93443i	−0.0433746	−	0.0751271i
$664$	4.00000	−	6.92820i	0.155230	−	0.268866i
$665$	15.4456			0.598956
$666$	3.50000	−	4.97494i	0.135622	−	0.192775i
$667$		0			0
$668$	0.744563	−	1.28962i	0.0288080	−	0.0498969i
$669$	9.05842	+	15.6896i	0.350219	+	0.606597i
$670$	−4.88316	−	8.45787i	−0.188653	−	0.326756i
$671$	9.11684	+	15.7908i	0.351952	+	0.609598i
$672$	−1.37228			−0.0529369
$673$	6.48913	+	11.2395i	0.250137	+	0.433251i	0.963563	−	0.267480i	$-0.0861909\pi$
$673$	6.48913	+	11.2395i	0.250137	+	0.433251i	−0.713426	+	0.700731i	$0.752858\pi$
$674$	−29.7446			−1.14572
$675$	0.313859	−	0.543620i	0.0120805	−	0.0209240i
$676$	−11.1168			−0.427571
$677$	−29.1168			−1.11905			−0.559526	−	0.828813i	$-0.689017\pi$
$677$	−29.1168			−1.11905			−0.559526	+	0.828813i	$0.689017\pi$
$678$	7.74456	−	13.4140i	0.297428	−	0.515161i
$679$	3.94158	+	6.82701i	0.151264	+	0.261997i
$680$	−3.86141			−0.148078
$681$	−5.74456	+	9.94987i	−0.220132	+	0.381280i
$682$	−9.37228	+	16.2333i	−0.358883	+	0.621604i
$683$	−7.11684	+	12.3267i	−0.272318	+	0.471669i	−0.969455	−	0.245269i	$-0.921124\pi$
$683$	−7.11684	+	12.3267i	−0.272318	+	0.471669i	0.697137	+	0.716938i	$0.254457\pi$
$684$	−2.37228	−	4.10891i	−0.0907064	−	0.157108i
$685$	12.3030	+	21.3094i	0.470073	+	0.814190i
$686$	8.31386	−	14.4000i	0.317425	−	0.549796i
$687$	−6.87228	+	11.9031i	−0.262194	+	0.454133i
$688$	4.68614	−	8.11663i	0.178657	−	0.309444i
$689$	15.7663			0.600649
$690$		0			0
$691$	7.31386	−	12.6680i	0.278232	−	0.481913i	−0.692713	−	0.721213i	$-0.743585\pi$
$691$	7.31386	−	12.6680i	0.278232	−	0.481913i	0.970946	+	0.239301i	$0.0769182\pi$
$692$	23.1168			0.878771
$693$	−2.74456			−0.104257
$694$	13.3723	−	23.1615i	0.507605	−	0.879197i
$695$	20.4674			0.776372
$696$	−2.18614	−	3.78651i	−0.0828654	−	0.143527i
$697$	7.11684			0.269570
$698$	−4.55842	−	7.89542i	−0.172539	−	0.298846i
$699$	−14.3030	−	24.7735i	−0.540989	−	0.937020i
$700$	0.430703	+	0.746000i	0.0162791	+	0.0281962i
$701$	−21.1168	+	36.5754i	−0.797572	+	1.38144i	0.123621	+	0.992330i	$0.460549\pi$
$701$	−21.1168	+	36.5754i	−0.797572	+	1.38144i	−0.921193	+	0.389106i	$0.872784\pi$
$702$	1.37228			0.0517934
$703$	−16.6060	+	23.6039i	−0.626306	+	0.890238i
$704$	2.00000			0.0753778
$705$	−2.37228	+	4.10891i	−0.0893453	+	0.154751i
$706$	15.3030	+	26.5055i	0.575935	+	0.997549i
$707$	9.51087	+	16.4733i	0.357693	+	0.619543i
$708$	−2.00000	−	3.46410i	−0.0751646	−	0.130189i
$709$	−21.6060			−0.811429			−0.405715	−	0.914000i	$-0.632977\pi$
$709$	−21.6060			−0.811429			−0.405715	+	0.914000i	$0.632977\pi$
$710$	−13.6277	−	23.6039i	−0.511439	−	0.885839i
$711$	1.37228			0.0514646
$712$	1.81386	−	3.14170i	0.0679773	−	0.117740i
$713$		0			0
$714$	2.23369			0.0835937
$715$	3.25544	−	5.63858i	0.121746	−	0.210871i
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$	22.2337			0.830332
$718$	6.11684	−	10.5947i	0.228279	−	0.395390i
$719$	21.6060	−	37.4226i	0.805767	−	1.39563i	−0.110006	−	0.993931i	$-0.535087\pi$
$719$	21.6060	−	37.4226i	0.805767	−	1.39563i	0.915772	−	0.401698i	$-0.131580\pi$
$720$	1.18614	−	2.05446i	0.0442049	−	0.0765651i
$721$	8.74456	+	15.1460i	0.325665	+	0.564068i
$722$	1.75544	+	3.04051i	0.0653306	+	0.113156i
$723$	12.0584	−	20.8858i	0.448458	−	0.776751i
$724$	2.12772	−	3.68532i	0.0790760	−	0.136964i
$725$	−1.37228	+	2.37686i	−0.0509652	+	0.0882744i
$726$	−7.00000			−0.259794
$727$	−14.5475	−	25.1971i	−0.539539	−	0.934508i	−0.998929	−	0.0462738i	$-0.985265\pi$
$727$	−14.5475	−	25.1971i	−0.539539	−	0.934508i	0.459390	−	0.888235i	$-0.348068\pi$
$728$	−0.941578	+	1.63086i	−0.0348972	+	0.0604437i
$729$	1.00000			0.0370370
$730$	6.23369			0.230719
$731$	−7.62772	+	13.2116i	−0.282121	+	0.488649i
$732$	9.11684			0.336968
$733$	−4.68614	−	8.11663i	−0.173087	−	0.299795i	0.766411	−	0.642351i	$-0.222041\pi$
$733$	−4.68614	−	8.11663i	−0.173087	−	0.299795i	−0.939497	+	0.342556i	$0.888707\pi$
$734$	−6.11684			−0.225777
$735$	6.06930	+	10.5123i	0.223869	+	0.387753i
$736$		0			0
$737$	−4.11684	−	7.13058i	−0.151646	−	0.262658i
$738$	−2.18614	+	3.78651i	−0.0804729	+	0.139383i
$739$	−24.4674			−0.900047			−0.450023	−	0.893017i	$-0.648584\pi$
$739$	−24.4674			−0.900047			−0.450023	+	0.893017i	$0.648584\pi$
$740$	−14.3723	−	1.28962i	−0.528336	−	0.0474074i
$741$	−6.51087			−0.239183
$742$	−7.88316	+	13.6540i	−0.289400	+	0.501255i
$743$	−6.25544	−	10.8347i	−0.229490	−	0.397488i	0.728167	−	0.685399i	$-0.240372\pi$
$743$	−6.25544	−	10.8347i	−0.229490	−	0.397488i	−0.957657	+	0.287912i	$0.907039\pi$
$744$	4.68614	+	8.11663i	0.171802	+	0.297570i
$745$	1.93070	+	3.34408i	0.0707355	+	0.122517i
$746$	31.0000			1.13499
$747$	−4.00000	−	6.92820i	−0.146352	−	0.253490i
$748$	−3.25544			−0.119031
$749$	3.25544	−	5.63858i	0.118951	−	0.206029i
$750$	10.3723			0.378742
$751$	15.8832			0.579585			0.289792	−	0.957090i	$-0.406414\pi$
$751$	15.8832			0.579585			0.289792	+	0.957090i	$0.406414\pi$
$752$	−1.00000	+	1.73205i	−0.0364662	+	0.0631614i
$753$	−6.37228	−	11.0371i	−0.232219	−	0.402215i
$754$	−6.00000			−0.218507
$755$	−22.9783	+	39.7995i	−0.836264	+	1.44845i
$756$	−0.686141	+	1.18843i	−0.0249547	+	0.0432228i
$757$	10.1277	−	17.5417i	0.368098	−	0.637565i	−0.621170	−	0.783676i	$-0.713342\pi$
$757$	10.1277	−	17.5417i	0.368098	−	0.637565i	0.989268	+	0.146111i	$0.0466757\pi$
$758$	−13.8614	−	24.0087i	−0.503469	−	0.872034i
$759$		0			0
$760$	−5.62772	+	9.74749i	−0.204139	+	0.353579i
$761$	−11.9307	+	20.6646i	−0.432488	+	0.749091i	−0.997087	−	0.0762746i	$-0.975697\pi$
$761$	−11.9307	+	20.6646i	−0.432488	+	0.749091i	0.564599	+	0.825365i	$0.309031\pi$
$762$	−4.31386	+	7.47182i	−0.156275	+	0.270676i
$763$	5.83966			0.211410
$764$	11.3723	+	19.6974i	0.411435	+	0.712626i
$765$	−1.93070	+	3.34408i	−0.0698047	+	0.120905i
$766$	6.23369			0.225232
$767$	−5.48913			−0.198201
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	3.88316			0.140030			0.0700151	−	0.997546i	$-0.477695\pi$
$769$	3.88316			0.140030			0.0700151	+	0.997546i	$0.477695\pi$
$770$	3.25544	+	5.63858i	0.117318	+	0.203200i
$771$	−19.8614			−0.715291
$772$	9.24456	+	16.0121i	0.332719	+	0.576286i
$773$	−2.06930	−	3.58413i	−0.0744274	−	0.128912i	0.826410	−	0.563069i	$-0.190380\pi$
$773$	−2.06930	−	3.58413i	−0.0744274	−	0.128912i	−0.900837	+	0.434157i	$0.857046\pi$
$774$	−4.68614	−	8.11663i	−0.168440	−	0.291746i
$775$	2.94158	−	5.09496i	0.105665	−	0.183016i
$776$	−5.74456			−0.206218
$777$	8.31386	+	0.746000i	0.298258	+	0.0267626i
$778$	−6.88316			−0.246773
$779$	10.3723	−	17.9653i	0.371626	−	0.643674i
$780$	−1.62772	−	2.81929i	−0.0582817	−	0.100947i
$781$	−11.4891	−	19.8997i	−0.411113	−	0.712069i
$782$		0			0
$783$	−4.37228			−0.156253
$784$	2.55842	+	4.43132i	0.0913722	+	0.158261i
$785$	−15.3940			−0.549437
$786$	−5.37228	+	9.30506i	−0.191623	+	0.331901i
$787$	−6.11684			−0.218042			−0.109021	−	0.994039i	$-0.534772\pi$
$787$	−6.11684			−0.218042			−0.109021	+	0.994039i	$0.534772\pi$
$788$	13.6277			0.485467
$789$	−13.3723	+	23.1615i	−0.476066	+	0.824570i
$790$	−1.62772	−	2.81929i	−0.0579116	−	0.100306i
$791$	21.2554			0.755756
$792$	1.00000	−	1.73205i	0.0355335	−	0.0615457i
$793$	6.25544	−	10.8347i	0.222137	−	0.384753i
$794$	−9.50000	+	16.4545i	−0.337142	+	0.583948i
$795$	−13.6277	−	23.6039i	−0.483325	−	0.837144i
$796$	3.31386	+	5.73977i	0.117457	+	0.203441i
$797$	20.6060	−	35.6906i	0.729901	−	1.26423i	−0.227024	−	0.973889i	$-0.572900\pi$
$797$	20.6060	−	35.6906i	0.729901	−	1.26423i	0.956925	−	0.290336i	$-0.0937671\pi$
$798$	3.25544	−	5.63858i	0.115241	−	0.199604i
$799$	1.62772	−	2.81929i	0.0575845	−	0.0997394i
$800$	−0.627719			−0.0221932
$801$	−1.81386	−	3.14170i	−0.0640896	−	0.111006i
$802$	−1.62772	+	2.81929i	−0.0574767	+	0.0995526i
$803$	5.25544			0.185460
$804$	−4.11684			−0.145190
$805$		0			0
$806$	12.8614			0.453024
$807$	1.00000	+	1.73205i	0.0352017	+	0.0609711i
$808$	−13.8614			−0.487643
$809$	26.4891	+	45.8805i	0.931308	+	1.61307i	0.781089	+	0.624420i	$0.214665\pi$
$809$	26.4891	+	45.8805i	0.931308	+	1.61307i	0.150219	+	0.988653i	$0.452002\pi$
$810$	−1.18614	−	2.05446i	−0.0416767	−	0.0721862i
$811$	−5.48913	−	9.50744i	−0.192749	−	0.333852i	0.753411	−	0.657550i	$-0.228407\pi$
$811$	−5.48913	−	9.50744i	−0.192749	−	0.333852i	−0.946160	+	0.323698i	$0.895074\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$	−18.8614			−0.661498
$814$	−12.1168	−	1.08724i	−0.424695	−	0.0381078i
$815$	−58.7011			−2.05621
$816$	−0.813859	+	1.40965i	−0.0284908	+	0.0493475i
$817$	22.2337	+	38.5099i	0.777858	+	1.34729i
$818$	−11.8723	−	20.5634i	−0.415105	−	0.718982i
$819$	0.941578	+	1.63086i	0.0329014	+	0.0569869i
$820$	10.3723			0.362216
$821$	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	$0.707913\pi$
$822$	10.3723			0.361775
$823$	23.9198	−	41.4304i	0.833793	−	1.44417i	−0.0612167	−	0.998124i	$-0.519498\pi$
$823$	23.9198	−	41.4304i	0.833793	−	1.44417i	0.895010	−	0.446047i	$-0.147169\pi$
$824$	−12.7446			−0.443978
$825$	−1.25544			−0.0437087
$826$	2.74456	−	4.75372i	0.0954955	−	0.165403i
$827$	−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
$829$	−19.4307	+	33.6550i	−0.674856	+	1.16889i	0.301655	+	0.953417i	$0.402461\pi$
$829$	−19.4307	+	33.6550i	−0.674856	+	1.16889i	−0.976511	+	0.215468i	$0.930872\pi$
$830$	−9.48913	+	16.4356i	−0.329372	+	0.570490i
$831$	−1.06930	+	1.85208i	−0.0370935	+	0.0642478i
$832$	−0.686141	−	1.18843i	−0.0237876	−	0.0412014i
$833$	−4.16439	−	7.21294i	−0.144288	−	0.249913i
$834$	4.31386	−	7.47182i	0.149377	−	0.258728i
$835$	−1.76631	+	3.05934i	−0.0611257	+	0.105873i
$836$	−4.74456	+	8.21782i	−0.164094	+	0.284219i
$837$	9.37228			0.323953
$838$	9.74456	+	16.8781i	0.336620	+	0.583044i
$839$	−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	$0.188663\pi$
$840$	3.25544			0.112323
$841$	−9.88316			−0.340798
$842$	−5.81386	+	10.0699i	−0.200359	+	0.347032i
$843$	7.11684			0.245117
$844$	−6.68614	−	11.5807i	−0.230146	−	0.398625i
$845$	26.3723			0.907234
$846$	1.00000	+	1.73205i	0.0343807	+	0.0595491i
$847$	−4.80298	−	8.31901i	−0.165033	−	0.285845i
$848$	−5.74456	−	9.94987i	−0.197269	−	0.341680i
$849$	−0.0584220	+	0.101190i	−0.00200504	+	0.00347283i
$850$	1.02175			0.0350457
$851$		0			0
$852$	−11.4891			−0.393611
$853$	17.3030	−	29.9696i	0.592443	−	1.02614i	−0.401459	−	0.915877i	$-0.631497\pi$
$853$	17.3030	−	29.9696i	0.592443	−	1.02614i	0.993902	−	0.110264i	$-0.0351698\pi$
$854$	6.25544	+	10.8347i	0.214057	+	0.370757i
$855$	5.62772	+	9.74749i	0.192464	+	0.333357i
$856$	2.37228	+	4.10891i	0.0810829	+	0.140440i
$857$	30.8397			1.05346			0.526731	−	0.850032i	$-0.323417\pi$
$857$	30.8397			1.05346			0.526731	+	0.850032i	$0.323417\pi$
$858$	−1.37228	−	2.37686i	−0.0468489	−	0.0811447i
$859$	37.6060			1.28310			0.641550	−	0.767082i	$-0.278292\pi$
$859$	37.6060			1.28310			0.641550	+	0.767082i	$0.278292\pi$
$860$	−11.1168	+	19.2549i	−0.379081	+	0.656588i
$861$	−6.00000			−0.204479
$862$	−8.97825			−0.305800
$863$	13.3723	−	23.1615i	0.455198	−	0.788426i	−0.543502	−	0.839408i	$-0.682902\pi$
$863$	13.3723	−	23.1615i	0.455198	−	0.788426i	0.998700	+	0.0509824i	$0.0162352\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−54.8397			−1.86460
$866$	3.81386	−	6.60580i	0.129600	−	0.224474i
$867$	−7.17527	+	12.4279i	−0.243685	+	0.422074i
$868$	−6.43070	+	11.1383i	−0.218272	+	0.378059i
$869$	−1.37228	−	2.37686i	−0.0465515	−	0.0806295i
$870$	5.18614	+	8.98266i	0.175827	+	0.304541i
$871$	−2.82473	+	4.89258i	−0.0957125	+	0.165779i
$872$	−2.12772	+	3.68532i	−0.0720536	+	0.124801i
$873$	−2.87228	+	4.97494i	−0.0972120	+	0.168376i
$874$		0			0
$875$	7.11684	+	12.3267i	0.240593	+	0.416720i
$876$	1.31386	−	2.27567i	0.0443912	−	0.0768878i
$877$	−47.0000			−1.58708			−0.793539	−	0.608520i	$-0.791764\pi$
$877$	−47.0000			−1.58708			−0.793539	+	0.608520i	$0.791764\pi$
$878$	−8.62772			−0.291171
$879$	−16.5584	+	28.6800i	−0.558502	+	0.967353i
$880$	−4.74456			−0.159939
$881$	3.55842	+	6.16337i	0.119886	+	0.207649i	0.919722	−	0.392569i	$-0.128414\pi$
$881$	3.55842	+	6.16337i	0.119886	+	0.207649i	−0.799836	+	0.600218i	$0.795080\pi$
$882$	5.11684			0.172293
$883$	3.48913	+	6.04334i	0.117418	+	0.203375i	0.918744	−	0.394854i	$-0.129205\pi$
$883$	3.48913	+	6.04334i	0.117418	+	0.203375i	−0.801325	+	0.598229i	$0.795871\pi$
$884$	1.11684	+	1.93443i	0.0375635	+	0.0650619i
$885$	4.74456	+	8.21782i	0.159487	+	0.276239i
$886$	−2.74456	+	4.75372i	−0.0922054	+	0.159704i
$887$	−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
$889$	−11.8397			−0.397089
$890$	−4.30298	+	7.45299i	−0.144236	+	0.249825i
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	−9.05842	−	15.6896i	−0.303298	−	0.525328i
$893$	−4.74456	−	8.21782i	−0.158771	−	0.274999i
$894$	1.62772			0.0544391
$895$	−14.2337	−	24.6535i	−0.475780	−	0.824075i
$896$	1.37228			0.0458447
$897$		0			0
$898$	−24.9783			−0.833535
$899$	−40.9783			−1.36670
$900$	−0.313859	+	0.543620i	−0.0104620	+	0.0181207i
$901$	9.35053	+	16.1956i	0.311511	+	0.539554i
$902$	8.74456			0.291162
$903$	6.43070	−	11.1383i	0.214000	−	0.370660i
$904$	−7.74456	+	13.4140i	−0.257580	+	0.446142i
$905$	−5.04755	+	8.74261i	−0.167786	+	0.290614i
$906$	9.68614	+	16.7769i	0.321800	+	0.557375i
$907$	−10.1753	−	17.6241i	−0.337864	−	0.585198i	0.646167	−	0.763196i	$-0.276371\pi$
$907$	−10.1753	−	17.6241i	−0.337864	−	0.585198i	−0.984031	+	0.177998i	$0.943038\pi$
$908$	5.74456	−	9.94987i	0.190640	−	0.330198i
$909$	−6.93070	+	12.0043i	−0.229877	+	0.398159i
$910$	2.23369	−	3.86886i	0.0740460	−	0.128251i
$911$	21.7228			0.719709			0.359854	−	0.933008i	$-0.382826\pi$
$911$	21.7228			0.719709			0.359854	+	0.933008i	$0.382826\pi$
$912$	2.37228	+	4.10891i	0.0785541	+	0.136060i
$913$	−8.00000	+	13.8564i	−0.264761	+	0.458580i
$914$	−24.0951			−0.796995
$915$	−21.6277			−0.714990
$916$	6.87228	−	11.9031i	0.227067	−	0.393291i
$917$	−14.7446			−0.486908
$918$	0.813859	+	1.40965i	0.0268614	+	0.0465252i
$919$	−23.6060			−0.778689			−0.389345	−	0.921092i	$-0.627298\pi$
$919$	−23.6060			−0.778689			−0.389345	+	0.921092i	$0.627298\pi$
$920$		0			0
$921$	−4.05842	−	7.02939i	−0.133730	−	0.231626i
$922$	−10.4891	−	18.1677i	−0.345441	−	0.598321i
$923$	−7.88316	+	13.6540i	−0.259477	+	0.449428i
$924$	2.74456			0.0902895
$925$	3.80298	+	0.341241i	0.125041	+	0.0112199i
$926$	0.116844			0.00383973
$927$	−6.37228	+	11.0371i	−0.209293	+	0.362506i
$928$	2.18614	+	3.78651i	0.0717636	+	0.124298i
$929$	4.69702	+	8.13547i	0.154104	+	0.266916i	0.932732	−	0.360569i	$-0.117418\pi$
$929$	4.69702	+	8.13547i	0.154104	+	0.266916i	−0.778628	+	0.627485i	$0.784084\pi$
$930$	−11.1168	−	19.2549i	−0.364536	−	0.631394i
$931$	−24.2772			−0.795653
$932$	14.3030	+	24.7735i	0.468510	+	0.811483i
$933$	28.9783			0.948705
$934$	7.37228	−	12.7692i	0.241228	−	0.417820i
$935$	7.72281			0.252563
$936$	−1.37228			−0.0448544
$937$	23.9891	−	41.5504i	0.783691	−	1.35739i	−0.146088	−	0.989272i	$-0.546668\pi$
$937$	23.9891	−	41.5504i	0.783691	−	1.35739i	0.929778	−	0.368120i	$-0.119999\pi$
$938$	−2.82473	−	4.89258i	−0.0922308	−	0.159748i
$939$	17.0000			0.554774
$940$	2.37228	−	4.10891i	0.0773753	−	0.134018i
$941$	28.1644	−	48.7822i	0.918133	−	1.59025i	0.115884	−	0.993263i	$-0.463030\pi$
$941$	28.1644	−	48.7822i	0.918133	−	1.59025i	0.802249	−	0.596990i	$-0.203637\pi$
$942$	−3.24456	+	5.61975i	−0.105714	+	0.183101i
$943$		0			0
$944$	2.00000	+	3.46410i	0.0650945	+	0.112747i
$945$	1.62772	−	2.81929i	0.0529497	−	0.0917116i
$946$	−9.37228	+	16.2333i	−0.304719	+	0.527789i
$947$	−21.6060	+	37.4226i	−0.702100	+	1.21607i	0.265628	+	0.964075i	$0.414421\pi$
$947$	−21.6060	+	37.4226i	−0.702100	+	1.21607i	−0.967728	+	0.251997i	$0.918913\pi$
$948$	−1.37228			−0.0445696
$949$	−1.80298	−	3.12286i	−0.0585274	−	0.101372i
$950$	1.48913	−	2.57924i	0.0483136	−	0.0836816i
$951$	12.8832			0.417765
$952$	−2.23369			−0.0723942
$953$	25.8614	−	44.7933i	0.837733	−	1.45100i	−0.0540525	−	0.998538i	$-0.517214\pi$
$953$	25.8614	−	44.7933i	0.837733	−	1.45100i	0.891786	−	0.452458i	$-0.149453\pi$
$954$	−11.4891			−0.371974
$955$	−26.9783	−	46.7277i	−0.872996	−	1.51207i
$956$	−22.2337			−0.719089
$957$	4.37228	+	7.57301i	0.141336	+	0.244801i
$958$	−0.116844	−	0.202380i	−0.00377506	−	0.00653859i
$959$	7.11684	+	12.3267i	0.229815	+	0.398051i
$960$	−1.18614	+	2.05446i	−0.0382825	+	0.0663073i
$961$	56.8397			1.83354
$962$	3.51087	+	7.57301i	0.113195	+	0.244164i
$963$	4.74456			0.152891
$964$	−12.0584	+	20.8858i	−0.388376	+	0.672686i
$965$	−21.9307	−	37.9851i	−0.705974	−	1.22278i
$966$		0			0
$967$	3.80298	+	6.58696i	0.122296	+	0.211822i	0.920673	−	0.390336i	$-0.127641\pi$
$967$	3.80298	+	6.58696i	0.122296	+	0.211822i	−0.798377	+	0.602158i	$0.794308\pi$
$968$	7.00000			0.224989
$969$	−3.86141	−	6.68815i	−0.124046	−	0.214854i
$970$	13.6277			0.437560
$971$	−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	$0.902717\pi$
$972$	−1.00000			−0.0320750
$973$	11.8397			0.379562
$974$	−18.7446	+	32.4665i	−0.600615	+	1.04029i
$975$	0.430703	+	0.746000i	0.0137935	+	0.0238911i
$976$	−9.11684			−0.291823
$977$	1.62772	−	2.81929i	0.0520753	−	0.0901971i	−0.838813	−	0.544420i	$-0.816750\pi$
$977$	1.62772	−	2.81929i	0.0520753	−	0.0901971i	0.890888	+	0.454223i	$0.150083\pi$
$978$	−12.3723	+	21.4294i	−0.395622	+	0.685237i
$979$	−3.62772	+	6.28339i	−0.115942	+	0.200818i
$980$	−6.06930	−	10.5123i	−0.193877	−	0.335804i
$981$	2.12772	+	3.68532i	0.0679328	+	0.117663i
$982$	3.00000	−	5.19615i	0.0957338	−	0.165816i
$983$	10.3723	−	17.9653i	0.330824	−	0.573005i	−0.651849	−	0.758348i	$-0.726007\pi$
$983$	10.3723	−	17.9653i	0.330824	−	0.573005i	0.982674	+	0.185344i	$0.0593399\pi$
$984$	2.18614	−	3.78651i	0.0696916	−	0.120709i
$985$	−32.3288			−1.03008
$986$	−3.55842	−	6.16337i	−0.113323	−	0.196282i
$987$	−1.37228	+	2.37686i	−0.0436802	+	0.0756563i
$988$	6.51087			0.207139
$989$		0			0
$990$	−2.37228	+	4.10891i	−0.0753960	+	0.130590i
$991$	−17.7663			−0.564366			−0.282183	−	0.959361i	$-0.591058\pi$
$991$	−17.7663			−0.564366			−0.282183	+	0.959361i	$0.591058\pi$
$992$	−4.68614	−	8.11663i	−0.148785	−	0.257703i
$993$	35.6060			1.12992
$994$	−7.88316	−	13.6540i	−0.250039	−	0.433079i
$995$	−7.86141	−	13.6164i	−0.249223	−	0.431667i
$996$	4.00000	+	6.92820i	0.126745	+	0.219529i
$997$	26.4891	−	45.8805i	0.838919	−	1.45305i	−0.0518802	−	0.998653i	$-0.516521\pi$
$997$	26.4891	−	45.8805i	0.838919	−	1.45305i	0.890799	−	0.454397i	$-0.150145\pi$
$998$	26.2337			0.830413
$999$	2.55842	+	5.51856i	0.0809449	+	0.174599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.2.e.c.121.2	✓	4
3.2	odd	2		666.2.f.g.343.1		4
4.3	odd	2		1776.2.q.h.1009.2		4
37.10	even	3		8214.2.a.m.1.1		2
37.26	even	3	inner	222.2.e.c.211.2	yes	4
37.27	even	6		8214.2.a.o.1.2		2
111.26	odd	6		666.2.f.g.433.1		4
148.63	odd	6		1776.2.q.h.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.e.c.121.2	✓	4	1.1	even	1	trivial
222.2.e.c.211.2	yes	4	37.26	even	3	inner
666.2.f.g.343.1		4	3.2	odd	2
666.2.f.g.433.1		4	111.26	odd	6
1776.2.q.h.433.2		4	148.63	odd	6
1776.2.q.h.1009.2		4	4.3	odd	2
8214.2.a.m.1.1		2	37.10	even	3
8214.2.a.o.1.2		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} +(1.18614 + 2.05446i) q^{5} +1.00000 q^{6} +(0.686141 + 1.18843i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +2.37228 q^{10} +2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.686141 - 1.18843i) q^{13} +1.37228 q^{14} +(-1.18614 + 2.05446i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.813859 - 1.40965i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.37228 - 4.10891i) q^{19} +(1.18614 - 2.05446i) q^{20} +(-0.686141 + 1.18843i) q^{21} +(1.00000 - 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{24} +(-0.313859 + 0.543620i) q^{25} -1.37228 q^{26} -1.00000 q^{27} +(0.686141 - 1.18843i) q^{28} +4.37228 q^{29} +(1.18614 + 2.05446i) q^{30} -9.37228 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(-0.813859 - 1.40965i) q^{34} +(-1.62772 + 2.81929i) q^{35} +1.00000 q^{36} +(-2.55842 - 5.51856i) q^{37} -4.74456 q^{38} +(0.686141 - 1.18843i) q^{39} +(-1.18614 - 2.05446i) q^{40} +(2.18614 + 3.78651i) q^{41} +(0.686141 + 1.18843i) q^{42} -9.37228 q^{43} +(-1.00000 - 1.73205i) q^{44} -2.37228 q^{45} +2.00000 q^{47} -1.00000 q^{48} +(2.55842 - 4.43132i) q^{49} +(0.313859 + 0.543620i) q^{50} +1.62772 q^{51} +(-0.686141 + 1.18843i) q^{52} +(-5.74456 + 9.94987i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.37228 + 4.10891i) q^{55} +(-0.686141 - 1.18843i) q^{56} +(2.37228 - 4.10891i) q^{57} +(2.18614 - 3.78651i) q^{58} +(2.00000 - 3.46410i) q^{59} +2.37228 q^{60} +(4.55842 + 7.89542i) q^{61} +(-4.68614 + 8.11663i) q^{62} -1.37228 q^{63} +1.00000 q^{64} +(1.62772 - 2.81929i) q^{65} +2.00000 q^{66} +(-2.05842 - 3.56529i) q^{67} -1.62772 q^{68} +(1.62772 + 2.81929i) q^{70} +(-5.74456 - 9.94987i) q^{71} +(0.500000 - 0.866025i) q^{72} +2.62772 q^{73} +(-6.05842 - 0.543620i) q^{74} -0.627719 q^{75} +(-2.37228 + 4.10891i) q^{76} +(1.37228 + 2.37686i) q^{77} +(-0.686141 - 1.18843i) q^{78} +(-0.686141 - 1.18843i) q^{79} -2.37228 q^{80} +(-0.500000 - 0.866025i) q^{81} +4.37228 q^{82} +(-4.00000 + 6.92820i) q^{83} +1.37228 q^{84} +3.86141 q^{85} +(-4.68614 + 8.11663i) q^{86} +(2.18614 + 3.78651i) q^{87} -2.00000 q^{88} +(-1.81386 + 3.14170i) q^{89} +(-1.18614 + 2.05446i) q^{90} +(0.941578 - 1.63086i) q^{91} +(-4.68614 - 8.11663i) q^{93} +(1.00000 - 1.73205i) q^{94} +(5.62772 - 9.74749i) q^{95} +(-0.500000 + 0.866025i) q^{96} +5.74456 q^{97} +(-2.55842 - 4.43132i) 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

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Database

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