LMFDB - Embedded newform 1690.2.e.s.191.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(191,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.191"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,-2,-4,8,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.22581504.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.3
Root			$1.40994 + 0.109843i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.s.991.3

$q$-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} +(0.300098 - 0.519785i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(0.300098 + 0.519785i) q^{6} +(-0.719687 - 1.24653i) q^{7} +1.00000 q^{8} +(1.31988 + 2.28610i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.38581 + 2.40029i) q^{11} -0.600196 q^{12} +1.43937 q^{14} +(0.300098 - 0.519785i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.25184 + 3.90029i) q^{17} -2.63977 q^{18} +(-2.16612 - 3.75184i) q^{19} +(-0.500000 - 0.866025i) q^{20} -0.863906 q^{21} +(-1.38581 - 2.40029i) q^{22} +(-2.21969 + 3.84461i) q^{23} +(0.300098 - 0.519785i) q^{24} +1.00000 q^{25} +3.38496 q^{27} +(-0.719687 + 1.24653i) q^{28} +(-3.93244 + 6.81119i) q^{29} +(0.300098 + 0.519785i) q^{30} +4.16082 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.831757 + 1.44065i) q^{33} -4.50367 q^{34} +(-0.719687 - 1.24653i) q^{35} +(1.31988 - 2.28610i) q^{36} +(0.287734 - 0.498370i) q^{37} +4.33225 q^{38} +1.00000 q^{40} +(-2.11256 + 3.65906i) q^{41} +(0.431953 - 0.748164i) q^{42} +(-1.30752 - 2.26469i) q^{43} +2.77162 q^{44} +(1.31988 + 2.28610i) q^{45} +(-2.21969 - 3.84461i) q^{46} -12.7684 q^{47} +(0.300098 + 0.519785i) q^{48} +(2.46410 - 4.26795i) q^{49} +(-0.500000 + 0.866025i) q^{50} +2.70308 q^{51} +9.57123 q^{53} +(-1.69248 + 2.93146i) q^{54} +(-1.38581 + 2.40029i) q^{55} +(-0.719687 - 1.24653i) q^{56} -2.60020 q^{57} +(-3.93244 - 6.81119i) q^{58} +(1.73205 + 3.00000i) q^{59} -0.600196 q^{60} +(6.25184 + 10.8285i) q^{61} +(-2.08041 + 3.60338i) q^{62} +(1.89980 - 3.29056i) q^{63} +1.00000 q^{64} -1.66351 q^{66} +(-2.66449 + 4.61504i) q^{67} +(2.25184 - 3.90029i) q^{68} +(1.33225 + 2.30752i) q^{69} +1.43937 q^{70} +(3.00000 + 5.19615i) q^{71} +(1.31988 + 2.28610i) q^{72} -1.66351 q^{73} +(0.287734 + 0.498370i) q^{74} +(0.300098 - 0.519785i) q^{75} +(-2.16612 + 3.75184i) q^{76} +3.98940 q^{77} +12.7288 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-2.94383 + 5.09886i) q^{81} +(-2.11256 - 3.65906i) q^{82} +10.0469 q^{83} +(0.431953 + 0.748164i) q^{84} +(2.25184 + 3.90029i) q^{85} +2.61504 q^{86} +(2.36023 + 4.08805i) q^{87} +(-1.38581 + 2.40029i) q^{88} +(-2.97859 + 5.15906i) q^{89} -2.63977 q^{90} +4.43937 q^{92} +(1.24865 - 2.16273i) q^{93} +(6.38418 - 11.0577i) q^{94} +(-2.16612 - 3.75184i) q^{95} -0.600196 q^{96} +(0.793166 + 1.37380i) q^{97} +(2.46410 + 4.26795i) q^{98} -7.31643 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 2 q^{6} + 8 q^{8} - 4 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} - 2 q^{15} - 4 q^{16} - 6 q^{17} + 8 q^{18} - 6 q^{19} - 4 q^{20} + 12 q^{21} + 6 q^{22} - 12 q^{23}+ \cdots - 84 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 2 * q^6 + 8 * q^8 - 4 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 - 2 * q^15 - 4 * q^16 - 6 * q^17 + 8 * q^18 - 6 * q^19 - 4 * q^20 + 12 * q^21 + 6 * q^22 - 12 * q^23 - 2 * q^24 + 8 * q^25 + 40 * q^27 - 2 * q^30 + 36 * q^31 - 4 * q^32 + 6 * q^33 + 12 * q^34 - 4 * q^36 + 6 * q^37 + 12 * q^38 + 8 * q^40 - 6 * q^42 - 4 * q^43 - 12 * q^44 - 4 * q^45 - 12 * q^46 - 2 * q^48 - 8 * q^49 - 4 * q^50 + 60 * q^53 - 20 * q^54 + 6 * q^55 - 12 * q^57 + 4 * q^60 + 26 * q^61 - 18 * q^62 + 24 * q^63 + 8 * q^64 - 12 * q^66 + 24 * q^67 - 6 * q^68 - 12 * q^69 + 24 * q^71 - 4 * q^72 - 12 * q^73 + 6 * q^74 - 2 * q^75 - 6 * q^76 + 60 * q^77 + 20 * q^79 - 4 * q^80 - 28 * q^81 - 36 * q^83 - 6 * q^84 - 6 * q^85 + 8 * q^86 + 48 * q^87 + 6 * q^88 + 8 * q^90 + 24 * q^92 + 12 * q^93 - 6 * q^95 + 4 * q^96 - 18 * q^97 - 8 * q^98 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.300098	−	0.519785i	0.173262	−	0.300098i	−0.766297	−	0.642487i	$-0.777903\pi$
$3$	0.300098	−	0.519785i	0.173262	−	0.300098i	0.939558	+	0.342389i	$0.111236\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.300098	+	0.519785i	0.122514	+	0.212201i
$7$	−0.719687	−	1.24653i	−0.272016	−	0.471146i	0.697362	−	0.716719i	$-0.254357\pi$
$7$	−0.719687	−	1.24653i	−0.272016	−	0.471146i	−0.969378	+	0.245574i	$0.921024\pi$
$8$	1.00000			0.353553
$9$	1.31988	+	2.28610i	0.439961	+	0.762035i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−1.38581	+	2.40029i	−0.417837	+	0.723716i	−0.995722	−	0.0924030i	$-0.970545\pi$
$11$	−1.38581	+	2.40029i	−0.417837	+	0.723716i	0.577884	+	0.816119i	$0.303879\pi$
$12$	−0.600196			−0.173262
$13$		0			0
$13$		0			0
$14$	1.43937			0.384689
$15$	0.300098	−	0.519785i	0.0774849	−	0.134208i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.25184	+	3.90029i	0.546150	+	0.945960i	0.998534	+	0.0541365i	$0.0172406\pi$
$17$	2.25184	+	3.90029i	0.546150	+	0.945960i	−0.452383	+	0.891824i	$0.649426\pi$
$18$	−2.63977			−0.622199
$19$	−2.16612	−	3.75184i	−0.496943	−	0.860730i	0.503051	−	0.864257i	$-0.332211\pi$
$19$	−2.16612	−	3.75184i	−0.496943	−	0.860730i	−0.999994	+	0.00352661i	$0.998877\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−0.863906			−0.188520
$22$	−1.38581	−	2.40029i	−0.295456	−	0.511744i
$23$	−2.21969	+	3.84461i	−0.462837	+	0.801657i	−0.999101	−	0.0423934i	$-0.986502\pi$
$23$	−2.21969	+	3.84461i	−0.462837	+	0.801657i	0.536264	+	0.844050i	$0.319835\pi$
$24$	0.300098	−	0.519785i	0.0612572	−	0.106101i
$25$	1.00000			0.200000
$26$		0			0
$27$	3.38496			0.651436
$28$	−0.719687	+	1.24653i	−0.136008	+	0.235573i
$29$	−3.93244	+	6.81119i	−0.730236	+	1.26481i	0.226546	+	0.974000i	$0.427257\pi$
$29$	−3.93244	+	6.81119i	−0.730236	+	1.26481i	−0.956782	+	0.290806i	$0.906077\pi$
$30$	0.300098	+	0.519785i	0.0547901	+	0.0948993i
$31$	4.16082			0.747306			0.373653	−	0.927569i	$-0.378105\pi$
$31$	4.16082			0.747306			0.373653	+	0.927569i	$0.378105\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.831757	+	1.44065i	0.144790	+	0.250784i
$34$	−4.50367			−0.772373
$35$	−0.719687	−	1.24653i	−0.121649	−	0.210703i
$36$	1.31988	−	2.28610i	0.219980	−	0.381017i
$37$	0.287734	−	0.498370i	0.0473032	−	0.0819315i	−0.841404	−	0.540406i	$-0.818271\pi$
$37$	0.287734	−	0.498370i	0.0473032	−	0.0819315i	0.888708	+	0.458475i	$0.151604\pi$
$38$	4.33225			0.702783
$39$		0			0
$40$	1.00000			0.158114
$41$	−2.11256	+	3.65906i	−0.329926	+	0.571449i	−0.982497	−	0.186279i	$-0.940357\pi$
$41$	−2.11256	+	3.65906i	−0.329926	+	0.571449i	0.652571	+	0.757728i	$0.273691\pi$
$42$	0.431953	−	0.748164i	0.0666518	−	0.115444i
$43$	−1.30752	−	2.26469i	−0.199395	−	0.345362i	0.748938	−	0.662641i	$-0.230564\pi$
$43$	−1.30752	−	2.26469i	−0.199395	−	0.345362i	−0.948332	+	0.317279i	$0.897231\pi$
$44$	2.77162			0.417837
$45$	1.31988	+	2.28610i	0.196756	+	0.340792i
$46$	−2.21969	−	3.84461i	−0.327275	−	0.566857i
$47$	−12.7684			−1.86246			−0.931228	−	0.364436i	$-0.881262\pi$
$47$	−12.7684			−1.86246			−0.931228	+	0.364436i	$0.881262\pi$
$48$	0.300098	+	0.519785i	0.0433154	+	0.0750245i
$49$	2.46410	−	4.26795i	0.352015	−	0.609707i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	2.70308			0.378507
$52$		0			0
$53$	9.57123			1.31471			0.657355	−	0.753581i	$-0.271675\pi$
$53$	9.57123			1.31471			0.657355	+	0.753581i	$0.271675\pi$
$54$	−1.69248	+	2.93146i	−0.230318	+	0.398922i
$55$	−1.38581	+	2.40029i	−0.186863	+	0.323656i
$56$	−0.719687	−	1.24653i	−0.0961722	−	0.166575i
$57$	−2.60020			−0.344404
$58$	−3.93244	−	6.81119i	−0.516355	−	0.894353i
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	0.956467	−	0.291839i	$-0.0942671\pi$
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	−0.730974	+	0.682406i	$0.760934\pi$
$60$	−0.600196			−0.0774849
$61$	6.25184	+	10.8285i	0.800466	+	1.38645i	0.919310	+	0.393534i	$0.128748\pi$
$61$	6.25184	+	10.8285i	0.800466	+	1.38645i	−0.118845	+	0.992913i	$0.537919\pi$
$62$	−2.08041	+	3.60338i	−0.264212	+	0.457629i
$63$	1.89980	−	3.29056i	0.239353	−	0.414571i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.66351			−0.204764
$67$	−2.66449	+	4.61504i	−0.325520	+	0.563817i	−0.981617	−	0.190859i	$-0.938873\pi$
$67$	−2.66449	+	4.61504i	−0.325520	+	0.563817i	0.656098	+	0.754676i	$0.272206\pi$
$68$	2.25184	−	3.90029i	0.273075	−	0.472980i
$69$	1.33225	+	2.30752i	0.160384	+	0.277793i
$70$	1.43937			0.172038
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	1.31988	+	2.28610i	0.155550	+	0.269420i
$73$	−1.66351			−0.194700			−0.0973498	−	0.995250i	$-0.531037\pi$
$73$	−1.66351			−0.194700			−0.0973498	+	0.995250i	$0.531037\pi$
$74$	0.287734	+	0.498370i	0.0334484	+	0.0579343i
$75$	0.300098	−	0.519785i	0.0346523	−	0.0600196i
$76$	−2.16612	+	3.75184i	−0.248471	+	0.430365i
$77$	3.98940			0.454634
$78$		0			0
$79$	12.7288			1.43210			0.716050	−	0.698049i	$-0.245948\pi$
$79$	12.7288			1.43210			0.716050	+	0.698049i	$0.245948\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−2.94383	+	5.09886i	−0.327092	+	0.566540i
$82$	−2.11256	−	3.65906i	−0.233293	−	0.404076i
$83$	10.0469			1.10279			0.551396	−	0.834244i	$-0.314095\pi$
$83$	10.0469			1.10279			0.551396	+	0.834244i	$0.314095\pi$
$84$	0.431953	+	0.748164i	0.0471299	+	0.0816314i
$85$	2.25184	+	3.90029i	0.244246	+	0.423046i
$86$	2.61504			0.281987
$87$	2.36023	+	4.08805i	0.253044	+	0.438285i
$88$	−1.38581	+	2.40029i	−0.147728	+	0.255872i
$89$	−2.97859	+	5.15906i	−0.315729	+	0.546859i	−0.979592	−	0.200995i	$-0.935583\pi$
$89$	−2.97859	+	5.15906i	−0.315729	+	0.546859i	0.663863	+	0.747854i	$0.268916\pi$
$90$	−2.63977			−0.278256
$91$		0			0
$92$	4.43937			0.462837
$93$	1.24865	−	2.16273i	0.129479	−	0.224265i
$94$	6.38418	−	11.0577i	0.658478	−	1.14052i
$95$	−2.16612	−	3.75184i	−0.222240	−	0.384930i
$96$	−0.600196			−0.0612572
$97$	0.793166	+	1.37380i	0.0805338	+	0.139489i	0.903479	−	0.428632i	$-0.141004\pi$
$97$	0.793166	+	1.37380i	0.0805338	+	0.139489i	−0.822946	+	0.568120i	$0.807671\pi$
$98$	2.46410	+	4.26795i	0.248912	+	0.431128i
$99$	−7.31643			−0.735329
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−6.87676	+	11.9109i	−0.684263	+	1.18518i	0.289405	+	0.957207i	$0.406543\pi$
$101$	−6.87676	+	11.9109i	−0.684263	+	1.18518i	−0.973668	+	0.227972i	$0.926791\pi$
$102$	−1.35154	+	2.34094i	−0.133823	+	0.231788i
$103$	5.73205			0.564796			0.282398	−	0.959297i	$-0.408870\pi$
$103$	5.73205			0.564796			0.282398	+	0.959297i	$0.408870\pi$
$104$		0			0
$105$	−0.863906			−0.0843086
$106$	−4.78561	+	8.28893i	−0.464820	+	0.805092i
$107$	−2.33967	+	4.05242i	−0.226184	+	0.391762i	−0.956674	−	0.291161i	$-0.905958\pi$
$107$	−2.33967	+	4.05242i	−0.226184	+	0.391762i	0.730490	+	0.682924i	$0.239292\pi$
$108$	−1.69248	−	2.93146i	−0.162859	−	0.282080i
$109$	2.32164			0.222373			0.111187	−	0.993800i	$-0.464535\pi$
$109$	2.32164			0.222373			0.111187	+	0.993800i	$0.464535\pi$
$110$	−1.38581	−	2.40029i	−0.132132	−	0.228859i
$111$	−0.172697	−	0.299119i	−0.0163916	−	0.0283912i
$112$	1.43937			0.136008
$113$	−3.86814	−	6.69982i	−0.363884	−	0.630266i	0.624712	−	0.780855i	$-0.285216\pi$
$113$	−3.86814	−	6.69982i	−0.363884	−	0.630266i	−0.988596	+	0.150589i	$0.951883\pi$
$114$	1.30010	−	2.25184i	0.121765	−	0.210904i
$115$	−2.21969	+	3.84461i	−0.206987	+	0.358512i
$116$	7.86488			0.730236
$117$		0			0
$118$	−3.46410			−0.318896
$119$	3.24123	−	5.61398i	0.297123	−	0.514633i
$120$	0.300098	−	0.519785i	0.0273951	−	0.0474496i
$121$	1.65906	+	2.87358i	0.150824	+	0.261234i
$122$	−12.5037			−1.13203
$123$	1.26795	+	2.19615i	0.114327	+	0.198020i
$124$	−2.08041	−	3.60338i	−0.186826	−	0.323593i
$125$	1.00000			0.0894427
$126$	1.89980	+	3.29056i	0.169248	+	0.293146i
$127$	8.06218	−	13.9641i	0.715403	−	1.23911i	−0.247401	−	0.968913i	$-0.579577\pi$
$127$	8.06218	−	13.9641i	0.715403	−	1.23911i	0.962804	−	0.270201i	$-0.0870900\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.56953			−0.138190
$130$		0			0
$131$	−19.7609			−1.72651			−0.863257	−	0.504764i	$-0.831579\pi$
$131$	−19.7609			−1.72651			−0.863257	+	0.504764i	$0.831579\pi$
$132$	0.831757	−	1.44065i	0.0723952	−	0.125392i
$133$	−3.11786	+	5.40029i	−0.270353	+	0.468265i
$134$	−2.66449	−	4.61504i	−0.230177	−	0.398678i
$135$	3.38496			0.291331
$136$	2.25184	+	3.90029i	0.193093	+	0.334447i
$137$	8.63234	+	14.9517i	0.737511	+	1.27741i	0.953613	+	0.301036i	$0.0973323\pi$
$137$	8.63234	+	14.9517i	0.737511	+	1.27741i	−0.216102	+	0.976371i	$0.569334\pi$
$138$	−2.66449			−0.226817
$139$	−1.47328	−	2.55180i	−0.124962	−	0.216441i	0.796756	−	0.604301i	$-0.206548\pi$
$139$	−1.47328	−	2.55180i	−0.124962	−	0.216441i	−0.921718	+	0.387860i	$0.873214\pi$
$140$	−0.719687	+	1.24653i	−0.0608246	+	0.105351i
$141$	−3.83176	+	6.63680i	−0.322692	+	0.558919i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	−2.63977			−0.219980
$145$	−3.93244	+	6.81119i	−0.326572	+	0.565639i
$146$	0.831757	−	1.44065i	0.0688367	−	0.119229i
$147$	−1.47894	−	2.56160i	−0.121981	−	0.211278i
$148$	−0.575468			−0.0473032
$149$	−3.53264	−	6.11871i	−0.289405	−	0.501264i	0.684263	−	0.729235i	$-0.260124\pi$
$149$	−3.53264	−	6.11871i	−0.289405	−	0.501264i	−0.973668	+	0.227971i	$0.926791\pi$
$150$	0.300098	+	0.519785i	0.0245029	+	0.0424402i
$151$	−15.8327			−1.28844			−0.644222	−	0.764839i	$-0.722819\pi$
$151$	−15.8327			−1.28844			−0.644222	+	0.764839i	$0.722819\pi$
$152$	−2.16612	−	3.75184i	−0.175696	−	0.304314i
$153$	−5.94432	+	10.2959i	−0.480570	+	0.832371i
$154$	−1.99470	+	3.45492i	−0.160737	+	0.278405i
$155$	4.16082			0.334205
$156$		0			0
$157$	12.6280			1.00783			0.503913	−	0.863754i	$-0.331893\pi$
$157$	12.6280			1.00783			0.503913	+	0.863754i	$0.331893\pi$
$158$	−6.36440	+	11.0235i	−0.506324	+	0.876979i
$159$	2.87231	−	4.97498i	0.227789	−	0.394541i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	6.38992			0.503596
$162$	−2.94383	−	5.09886i	−0.231289	−	0.400604i
$163$	9.18428	+	15.9076i	0.719368	+	1.24598i	0.961250	+	0.275677i	$0.0889019\pi$
$163$	9.18428	+	15.9076i	0.719368	+	1.24598i	−0.241882	+	0.970306i	$0.577765\pi$
$164$	4.22512			0.329926
$165$	0.831757	+	1.44065i	0.0647522	+	0.112154i
$166$	−5.02346	+	8.70088i	−0.389896	+	0.675319i
$167$	10.8043	−	18.7135i	0.836059	−	1.44810i	−0.0571070	−	0.998368i	$-0.518188\pi$
$167$	10.8043	−	18.7135i	0.836059	−	1.44810i	0.893166	−	0.449728i	$-0.148479\pi$
$168$	−0.863906			−0.0666518
$169$		0			0
$170$	−4.50367			−0.345416
$171$	5.71806	−	9.90396i	0.437271	−	0.757375i
$172$	−1.30752	+	2.26469i	−0.0996974	+	0.172681i
$173$	−1.99470	−	3.45492i	−0.151654	−	0.262673i	0.780182	−	0.625553i	$-0.215127\pi$
$173$	−1.99470	−	3.45492i	−0.151654	−	0.262673i	−0.931836	+	0.362880i	$0.881793\pi$
$174$	−4.72047			−0.357858
$175$	−0.719687	−	1.24653i	−0.0544032	−	0.0942291i
$176$	−1.38581	−	2.40029i	−0.104459	−	0.180929i
$177$	2.07914			0.156278
$178$	−2.97859	−	5.15906i	−0.223254	−	0.386688i
$179$	−6.23996	+	10.8079i	−0.466397	+	0.807823i	−0.999263	−	0.0383766i	$-0.987781\pi$
$179$	−6.23996	+	10.8079i	−0.466397	+	0.807823i	0.532867	+	0.846199i	$0.321115\pi$
$180$	1.31988	−	2.28610i	0.0983782	−	0.170396i
$181$	−19.4319			−1.44436			−0.722180	−	0.691705i	$-0.756860\pi$
$181$	−19.4319			−1.44436			−0.722180	+	0.691705i	$0.756860\pi$
$182$		0			0
$183$	7.50465			0.554760
$184$	−2.21969	+	3.84461i	−0.163637	+	0.283428i
$185$	0.287734	−	0.498370i	0.0211546	−	0.0366409i
$186$	1.24865	+	2.16273i	0.0915557	+	0.158579i
$187$	−12.4825			−0.912808
$188$	6.38418	+	11.0577i	0.465614	+	0.806467i
$189$	−2.43611	−	4.21947i	−0.177201	−	0.306921i
$190$	4.33225			0.314294
$191$	9.16074	+	15.8669i	0.662848	+	1.14809i	0.979864	+	0.199666i	$0.0639858\pi$
$191$	9.16074	+	15.8669i	0.662848	+	1.14809i	−0.317016	+	0.948420i	$0.602681\pi$
$192$	0.300098	−	0.519785i	0.0216577	−	0.0375122i
$193$	2.37182	−	4.10811i	0.170727	−	0.295708i	−0.767947	−	0.640513i	$-0.778722\pi$
$193$	2.37182	−	4.10811i	0.170727	−	0.295708i	0.938674	+	0.344805i	$0.112055\pi$
$194$	−1.58633			−0.113892
$195$		0			0
$196$	−4.92820			−0.352015
$197$	5.40029	−	9.35358i	0.384755	−	0.666415i	−0.606980	−	0.794717i	$-0.707619\pi$
$197$	5.40029	−	9.35358i	0.384755	−	0.666415i	0.991735	+	0.128302i	$0.0409526\pi$
$198$	3.65821	−	6.33621i	0.259978	−	0.450295i
$199$	−5.50367	−	9.53264i	−0.390145	−	0.675751i	0.602323	−	0.798252i	$-0.294242\pi$
$199$	−5.50367	−	9.53264i	−0.390145	−	0.675751i	−0.992468	+	0.122501i	$0.960908\pi$
$200$	1.00000			0.0707107
$201$	1.59922	+	2.76993i	0.112800	+	0.195375i
$202$	−6.87676	−	11.9109i	−0.483847	−	0.838048i
$203$	11.3205			0.794544
$204$	−1.35154	−	2.34094i	−0.0946269	−	0.163899i
$205$	−2.11256	+	3.65906i	−0.147548	+	0.255560i
$206$	−2.86603	+	4.96410i	−0.199685	+	0.345865i
$207$	−11.7189			−0.814520
$208$		0			0
$209$	12.0073			0.830565
$210$	0.431953	−	0.748164i	0.0298076	−	0.0516283i
$211$	−13.1291	+	22.7402i	−0.903843	+	1.56550i	−0.0813811	+	0.996683i	$0.525933\pi$
$211$	−13.1291	+	22.7402i	−0.903843	+	1.56550i	−0.822462	+	0.568820i	$0.807400\pi$
$212$	−4.78561	−	8.28893i	−0.328677	−	0.569286i
$213$	3.60117			0.246748
$214$	−2.33967	−	4.05242i	−0.159936	−	0.277018i
$215$	−1.30752	−	2.26469i	−0.0891720	−	0.154450i
$216$	3.38496			0.230318
$217$	−2.99449	−	5.18661i	−0.203279	−	0.352090i
$218$	−1.16082	+	2.01060i	−0.0786208	+	0.136175i
$219$	−0.499217	+	0.864669i	−0.0337340	+	0.0584289i
$220$	2.77162			0.186863
$221$		0			0
$222$	0.345393			0.0231813
$223$	11.1021	−	19.2294i	0.743452	−	1.28770i	−0.207463	−	0.978243i	$-0.566521\pi$
$223$	11.1021	−	19.2294i	0.743452	−	1.28770i	0.950915	−	0.309454i	$-0.100146\pi$
$224$	−0.719687	+	1.24653i	−0.0480861	+	0.0832876i
$225$	1.31988	+	2.28610i	0.0879922	+	0.152407i
$226$	7.73629			0.514610
$227$	1.03957	+	1.80059i	0.0689986	+	0.119509i	0.898461	−	0.439054i	$-0.144686\pi$
$227$	1.03957	+	1.80059i	0.0689986	+	0.119509i	−0.829462	+	0.558563i	$0.811353\pi$
$228$	1.30010	+	2.25184i	0.0861011	+	0.149131i
$229$	−4.67933			−0.309219			−0.154610	−	0.987976i	$-0.549412\pi$
$229$	−4.67933			−0.309219			−0.154610	+	0.987976i	$0.549412\pi$
$230$	−2.21969	−	3.84461i	−0.146362	−	0.253506i
$231$	1.19721	−	2.07363i	0.0787706	−	0.136435i
$232$	−3.93244	+	6.81119i	−0.258177	+	0.447177i
$233$	−0.611060			−0.0400319			−0.0200160	−	0.999800i	$-0.506372\pi$
$233$	−0.611060			−0.0400319			−0.0200160	+	0.999800i	$0.506372\pi$
$234$		0			0
$235$	−12.7684			−0.832916
$236$	1.73205	−	3.00000i	0.112747	−	0.195283i
$237$	3.81988	−	6.61623i	0.248128	−	0.429770i
$238$	3.24123	+	5.61398i	0.210098	+	0.363900i
$239$	−25.6481			−1.65904			−0.829518	−	0.558479i	$-0.811385\pi$
$239$	−25.6481			−1.65904			−0.829518	+	0.558479i	$0.811385\pi$
$240$	0.300098	+	0.519785i	0.0193712	+	0.0335520i
$241$	−13.5466	−	23.4633i	−0.872610	−	1.51141i	−0.859287	−	0.511494i	$-0.829092\pi$
$241$	−13.5466	−	23.4633i	−0.872610	−	1.51141i	−0.0133234	−	0.999911i	$-0.504241\pi$
$242$	−3.31812			−0.213297
$243$	6.84432	+	11.8547i	0.439063	+	0.760480i
$244$	6.25184	−	10.8285i	0.400233	−	0.693223i
$245$	2.46410	−	4.26795i	0.157426	−	0.272669i
$246$	−2.53590			−0.161683
$247$		0			0
$248$	4.16082			0.264212
$249$	3.01506	−	5.22223i	0.191071	−	0.330945i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−0.751836	−	1.30222i	−0.0474554	−	0.0821952i	0.841322	−	0.540534i	$-0.181778\pi$
$251$	−0.751836	−	1.30222i	−0.0474554	−	0.0821952i	−0.888777	+	0.458339i	$0.848445\pi$
$252$	−3.79961			−0.239353
$253$	−6.15213	−	10.6558i	−0.386781	−	0.669924i
$254$	8.06218	+	13.9641i	0.505866	+	0.876186i
$255$	2.70308			0.169274
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.1724	−	17.6191i	0.634537	−	1.09905i	−0.352076	−	0.935971i	$-0.614524\pi$
$257$	10.1724	−	17.6191i	0.634537	−	1.09905i	0.986613	−	0.163079i	$-0.0521425\pi$
$258$	0.784767	−	1.35926i	0.0488575	−	0.0846236i
$259$	−0.828313			−0.0514689
$260$		0			0
$261$	−20.7614			−1.28510
$262$	9.88043	−	17.1134i	0.610415	−	1.05727i
$263$	8.56466	−	14.8344i	0.528119	−	0.914729i	−0.471343	−	0.881950i	$-0.656231\pi$
$263$	8.56466	−	14.8344i	0.528119	−	0.914729i	0.999463	−	0.0327796i	$-0.0104359\pi$
$264$	0.831757	+	1.44065i	0.0511911	+	0.0886656i
$265$	9.57123			0.587956
$266$	−3.11786	−	5.40029i	−0.191168	−	0.331113i
$267$	1.78773	+	3.09645i	0.109408	+	0.189499i
$268$	5.32899			0.325520
$269$	−9.69121	−	16.7857i	−0.590883	−	1.02344i	−0.994114	−	0.108342i	$-0.965446\pi$
$269$	−9.69121	−	16.7857i	−0.590883	−	1.02344i	0.403230	−	0.915099i	$-0.367887\pi$
$270$	−1.69248	+	2.93146i	−0.103001	+	0.178403i
$271$	−9.18555	+	15.9098i	−0.557982	+	0.966454i	0.439682	+	0.898153i	$0.355091\pi$
$271$	−9.18555	+	15.9098i	−0.557982	+	0.966454i	−0.997665	+	0.0683006i	$0.978242\pi$
$272$	−4.50367			−0.273075
$273$		0			0
$274$	−17.2647			−1.04300
$275$	−1.38581	+	2.40029i	−0.0835675	+	0.144743i
$276$	1.33225	−	2.30752i	0.0801918	−	0.138896i
$277$	13.6171	+	23.5855i	0.818171	+	1.41711i	0.907028	+	0.421069i	$0.138345\pi$
$277$	13.6171	+	23.5855i	0.818171	+	1.41711i	−0.0888576	+	0.996044i	$0.528322\pi$
$278$	2.94657			0.176723
$279$	5.49180	+	9.51207i	0.328785	+	0.569473i
$280$	−0.719687	−	1.24653i	−0.0430095	−	0.0744947i
$281$	30.0815			1.79451			0.897257	−	0.441509i	$-0.145557\pi$
$281$	30.0815			1.79451			0.897257	+	0.441509i	$0.145557\pi$
$282$	−3.83176	−	6.63680i	−0.228178	−	0.395216i
$283$	12.7394	−	22.0653i	0.757278	−	1.31164i	−0.186955	−	0.982368i	$-0.559862\pi$
$283$	12.7394	−	22.0653i	0.757278	−	1.31164i	0.944234	−	0.329276i	$-0.106805\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	−2.60020			−0.154022
$286$		0			0
$287$	6.08153			0.358981
$288$	1.31988	−	2.28610i	0.0777748	−	0.134710i
$289$	−1.64153	+	2.84321i	−0.0965604	+	0.167247i
$290$	−3.93244	−	6.81119i	−0.230921	−	0.399967i
$291$	0.952110			0.0558137
$292$	0.831757	+	1.44065i	0.0486749	+	0.0843074i
$293$	8.28893	+	14.3568i	0.484244	+	0.838736i	0.999836	−	0.0180985i	$-0.00576126\pi$
$293$	8.28893	+	14.3568i	0.484244	+	0.838736i	−0.515592	+	0.856834i	$0.672428\pi$
$294$	2.95789			0.172507
$295$	1.73205	+	3.00000i	0.100844	+	0.174667i
$296$	0.287734	−	0.498370i	0.0167242	−	0.0289672i
$297$	−4.69092	+	8.12490i	−0.272195	+	0.471455i
$298$	7.06528			0.409280
$299$		0			0
$300$	−0.600196			−0.0346523
$301$	−1.88201	+	3.25973i	−0.108477	+	0.187888i
$302$	7.91633	−	13.7115i	0.455534	−	0.789007i
$303$	4.12740	+	7.14887i	0.237113	+	0.410692i
$304$	4.33225			0.248471
$305$	6.25184	+	10.8285i	0.357979	+	0.620038i
$306$	−5.94432	−	10.2959i	−0.339814	−	0.588575i
$307$	−16.2722			−0.928703			−0.464351	−	0.885651i	$-0.653713\pi$
$307$	−16.2722			−0.928703			−0.464351	+	0.885651i	$0.653713\pi$
$308$	−1.99470	−	3.45492i	−0.113659	−	0.196862i
$309$	1.72018	−	2.97943i	0.0978574	−	0.169494i
$310$	−2.08041	+	3.60338i	−0.118159	+	0.204658i
$311$	16.1053			0.913246			0.456623	−	0.889660i	$-0.349059\pi$
$311$	16.1053			0.913246			0.456623	+	0.889660i	$0.349059\pi$
$312$		0			0
$313$	−10.2162			−0.577454			−0.288727	−	0.957411i	$-0.593232\pi$
$313$	−10.2162			−0.577454			−0.288727	+	0.957411i	$0.593232\pi$
$314$	−6.31401	+	10.9362i	−0.356320	+	0.617165i
$315$	1.89980	−	3.29056i	0.107042	−	0.185402i
$316$	−6.36440	−	11.0235i	−0.358025	−	0.620118i
$317$	−0.204368			−0.0114785			−0.00573923	−	0.999984i	$-0.501827\pi$
$317$	−0.204368			−0.0114785			−0.00573923	+	0.999984i	$0.501827\pi$
$318$	2.87231	+	4.97498i	0.161071	+	0.278983i
$319$	−10.8992	−	18.8780i	−0.610240	−	1.05697i
$320$	1.00000			0.0559017
$321$	1.40426	+	2.43225i	0.0783781	+	0.135755i
$322$	−3.19496	+	5.53383i	−0.178048	+	0.308388i
$323$	9.75551	−	16.8970i	0.542811	−	0.940176i
$324$	5.88766			0.327092
$325$		0			0
$326$	−18.3686			−1.01734
$327$	0.696720	−	1.20676i	0.0385287	−	0.0667337i
$328$	−2.11256	+	3.65906i	−0.116647	+	0.202038i
$329$	9.18922	+	15.9162i	0.506618	+	0.877488i
$330$	−1.66351			−0.0915735
$331$	9.53264	+	16.5110i	0.523961	+	0.907527i	0.999611	+	0.0278926i	$0.00887964\pi$
$331$	9.53264	+	16.5110i	0.523961	+	0.907527i	−0.475650	+	0.879635i	$0.657787\pi$
$332$	−5.02346	−	8.70088i	−0.275698	−	0.477523i
$333$	1.51910			0.0832462
$334$	10.8043	+	18.7135i	0.591183	+	1.02396i
$335$	−2.66449	+	4.61504i	−0.145577	+	0.252146i
$336$	0.431953	−	0.748164i	0.0235650	−	0.0408157i
$337$	−19.8609			−1.08189			−0.540946	−	0.841057i	$-0.681934\pi$
$337$	−19.8609			−1.08189			−0.540946	+	0.841057i	$0.681934\pi$
$338$		0			0
$339$	−4.64329			−0.252189
$340$	2.25184	−	3.90029i	0.122123	−	0.211523i
$341$	−5.76611	+	9.98719i	−0.312252	+	0.540837i
$342$	5.71806	+	9.90396i	0.309197	+	0.535545i
$343$	−17.1691			−0.927047
$344$	−1.30752	−	2.26469i	−0.0704967	−	0.122104i
$345$	1.33225	+	2.30752i	0.0717257	+	0.124233i
$346$	3.98940			0.214471
$347$	−8.52522	−	14.7661i	−0.457658	−	0.792686i	0.541179	−	0.840907i	$-0.317978\pi$
$347$	−8.52522	−	14.7661i	−0.457658	−	0.792686i	−0.998837	+	0.0482211i	$0.984645\pi$
$348$	2.36023	−	4.08805i	0.126522	−	0.219142i
$349$	10.6185	−	18.3917i	0.568394	−	0.984488i	−0.428331	−	0.903622i	$-0.640898\pi$
$349$	10.6185	−	18.3917i	0.568394	−	0.984488i	0.996725	−	0.0808657i	$-0.0257685\pi$
$350$	1.43937			0.0769378
$351$		0			0
$352$	2.77162			0.147728
$353$	−8.00840	+	13.8710i	−0.426244	+	0.738276i	−0.996536	−	0.0831659i	$-0.973497\pi$
$353$	−8.00840	+	13.8710i	−0.426244	+	0.738276i	0.570292	+	0.821442i	$0.306830\pi$
$354$	−1.03957	+	1.80059i	−0.0552525	+	0.0957001i
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	5.95717			0.315729
$357$	−1.94537	−	3.36949i	−0.102960	−	0.178332i
$358$	−6.23996	−	10.8079i	−0.329792	−	0.571217i
$359$	24.2487			1.27980			0.639899	−	0.768459i	$-0.278976\pi$
$359$	24.2487			1.27980			0.639899	+	0.768459i	$0.278976\pi$
$360$	1.31988	+	2.28610i	0.0695639	+	0.120488i
$361$	0.115820	−	0.200606i	0.00609580	−	0.0105582i
$362$	9.71594	−	16.8285i	0.510658	−	0.884486i
$363$	1.99152			0.104528
$364$		0			0
$365$	−1.66351			−0.0870723
$366$	−3.75232	+	6.49922i	−0.196137	+	0.339720i
$367$	14.8854	−	25.7822i	0.777010	−	1.34582i	−0.156648	−	0.987655i	$-0.550069\pi$
$367$	14.8854	−	25.7822i	0.777010	−	1.34582i	0.933658	−	0.358167i	$-0.116598\pi$
$368$	−2.21969	−	3.84461i	−0.115709	−	0.200414i
$369$	−11.1533			−0.580619
$370$	0.287734	+	0.498370i	0.0149586	+	0.0259090i
$371$	−6.88829	−	11.9309i	−0.357622	−	0.619420i
$372$	−2.49731			−0.129479
$373$	−14.1929	−	24.5828i	−0.734880	−	1.27285i	−0.954776	−	0.297326i	$-0.903905\pi$
$373$	−14.1929	−	24.5828i	−0.734880	−	1.27285i	0.219896	−	0.975523i	$-0.429428\pi$
$374$	6.24123	−	10.8101i	0.322726	−	0.558979i
$375$	0.300098	−	0.519785i	0.0154970	−	0.0268416i
$376$	−12.7684			−0.658478
$377$		0			0
$378$	4.87223			0.250600
$379$	14.2069	−	24.6070i	0.729759	−	1.26398i	−0.227226	−	0.973842i	$-0.572966\pi$
$379$	14.2069	−	24.6070i	0.729759	−	1.26398i	0.956985	−	0.290137i	$-0.0937009\pi$
$380$	−2.16612	+	3.75184i	−0.111120	+	0.192465i
$381$	−4.83888	−	8.38119i	−0.247904	−	0.429382i
$382$	−18.3215			−0.937409
$383$	−4.69863	−	8.13827i	−0.240089	−	0.415846i	0.720651	−	0.693298i	$-0.243843\pi$
$383$	−4.69863	−	8.13827i	−0.240089	−	0.415846i	−0.960739	+	0.277452i	$0.910510\pi$
$384$	0.300098	+	0.519785i	0.0153143	+	0.0265252i
$385$	3.98940			0.203319
$386$	2.37182	+	4.10811i	0.120722	+	0.209097i
$387$	3.45154	−	5.97825i	0.175452	−	0.303891i
$388$	0.793166	−	1.37380i	0.0402669	−	0.0697443i
$389$	−11.6461			−0.590482			−0.295241	−	0.955423i	$-0.595400\pi$
$389$	−11.6461			−0.590482			−0.295241	+	0.955423i	$0.595400\pi$
$390$		0			0
$391$	−19.9935			−1.01111
$392$	2.46410	−	4.26795i	0.124456	−	0.215564i
$393$	−5.93019	+	10.2714i	−0.299139	+	0.518123i
$394$	5.40029	+	9.35358i	0.272063	+	0.471227i
$395$	12.7288			0.640455
$396$	3.65821	+	6.33621i	0.183832	+	0.318407i
$397$	0.199902	+	0.346241i	0.0100328	+	0.0173773i	0.870998	−	0.491286i	$-0.163473\pi$
$397$	0.199902	+	0.346241i	0.0100328	+	0.0173773i	−0.860965	+	0.508663i	$0.830140\pi$
$398$	11.0073			0.551748
$399$	1.87133	+	3.24123i	0.0936835	+	0.162265i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	4.25388	−	7.36793i	0.212428	−	0.367937i	−0.740046	−	0.672557i	$-0.765196\pi$
$401$	4.25388	−	7.36793i	0.212428	−	0.367937i	0.952474	+	0.304620i	$0.0985294\pi$
$402$	−3.19843			−0.159523
$403$		0			0
$404$	13.7535			0.684263
$405$	−2.94383	+	5.09886i	−0.146280	+	0.253364i
$406$	−5.66025	+	9.80385i	−0.280914	+	0.486557i
$407$	0.797489	+	1.38129i	0.0395301	+	0.0684681i
$408$	2.70308			0.133823
$409$	−7.00657	−	12.1357i	−0.346453	−	0.600074i	0.639164	−	0.769071i	$-0.279281\pi$
$409$	−7.00657	−	12.1357i	−0.346453	−	0.600074i	−0.985617	+	0.168997i	$0.945947\pi$
$410$	−2.11256	−	3.65906i	−0.104332	−	0.180708i
$411$	10.3622			0.511129
$412$	−2.86603	−	4.96410i	−0.141199	−	0.244564i
$413$	2.49307	−	4.31812i	0.122676	−	0.212481i
$414$	5.85945	−	10.1489i	0.287976	−	0.498790i
$415$	10.0469			0.493183
$416$		0			0
$417$	−1.76852			−0.0866047
$418$	−6.00367	+	10.3987i	−0.293649	+	0.508615i
$419$	12.0977	−	20.9539i	0.591012	−	1.02366i	−0.403084	−	0.915163i	$-0.632062\pi$
$419$	12.0977	−	20.9539i	0.591012	−	1.02366i	0.994096	−	0.108500i	$-0.0346048\pi$
$420$	0.431953	+	0.748164i	0.0210771	+	0.0365067i
$421$	35.6392			1.73695			0.868474	−	0.495735i	$-0.165101\pi$
$421$	35.6392			1.73695			0.868474	+	0.495735i	$0.165101\pi$
$422$	−13.1291	−	22.7402i	−0.639114	−	1.10698i
$423$	−16.8527	−	29.1898i	−0.819408	−	1.41926i
$424$	9.57123			0.464820
$425$	2.25184	+	3.90029i	0.109230	+	0.189192i
$426$	−1.80059	+	3.11871i	−0.0872387	+	0.151102i
$427$	8.99873	−	15.5863i	0.435479	−	0.754272i
$428$	4.67933			0.226184
$429$		0			0
$430$	2.61504			0.126108
$431$	−2.48022	+	4.29586i	−0.119468	+	0.206924i	−0.919557	−	0.392957i	$-0.871452\pi$
$431$	−2.48022	+	4.29586i	−0.119468	+	0.206924i	0.800089	+	0.599881i	$0.204785\pi$
$432$	−1.69248	+	2.93146i	−0.0814295	+	0.141040i
$433$	−2.10811	−	3.65135i	−0.101309	−	0.175472i	0.810915	−	0.585164i	$-0.198970\pi$
$433$	−2.10811	−	3.65135i	−0.101309	−	0.175472i	−0.912224	+	0.409691i	$0.865636\pi$
$434$	5.98898			0.287480
$435$	2.36023	+	4.08805i	0.113165	+	0.196007i
$436$	−1.16082	−	2.01060i	−0.0555933	−	0.0962904i
$437$	19.2325			0.920013
$438$	−0.499217	−	0.864669i	−0.0238535	−	0.0413155i
$439$	7.37500	−	12.7739i	0.351989	−	0.609664i	−0.634608	−	0.772834i	$-0.718839\pi$
$439$	7.37500	−	12.7739i	0.351989	−	0.609664i	0.986598	+	0.163170i	$0.0521720\pi$
$440$	−1.38581	+	2.40029i	−0.0660659	+	0.114430i
$441$	13.0093			0.619490
$442$		0			0
$443$	−12.2374			−0.581417			−0.290709	−	0.956812i	$-0.593891\pi$
$443$	−12.2374			−0.581417			−0.290709	+	0.956812i	$0.593891\pi$
$444$	−0.172697	+	0.299119i	−0.00819582	+	0.0141956i
$445$	−2.97859	+	5.15906i	−0.141198	+	0.244563i
$446$	11.1021	+	19.2294i	0.525700	+	0.910539i
$447$	−4.24055			−0.200571
$448$	−0.719687	−	1.24653i	−0.0340020	−	0.0588932i
$449$	9.53569	+	16.5163i	0.450017	+	0.779452i	0.998386	−	0.0567839i	$-0.0180846\pi$
$449$	9.53569	+	16.5163i	0.450017	+	0.779452i	−0.548370	+	0.836236i	$0.684751\pi$
$450$	−2.63977			−0.124440
$451$	−5.85521	−	10.1415i	−0.275711	−	0.477546i
$452$	−3.86814	+	6.69982i	−0.181942	+	0.315133i
$453$	−4.75135	+	8.22957i	−0.223238	+	0.386659i
$454$	−2.07914			−0.0975788
$455$		0			0
$456$	−2.60020			−0.121765
$457$	−8.05688	+	13.9549i	−0.376885	+	0.652784i	−0.990607	−	0.136738i	$-0.956338\pi$
$457$	−8.05688	+	13.9549i	−0.376885	+	0.652784i	0.613722	+	0.789522i	$0.289671\pi$
$458$	2.33967	−	4.05242i	0.109325	−	0.189357i
$459$	7.62238	+	13.2023i	0.355782	+	0.616233i
$460$	4.43937			0.206987
$461$	2.42233	+	4.19560i	0.112819	+	0.195408i	0.916906	−	0.399104i	$-0.130679\pi$
$461$	2.42233	+	4.19560i	0.112819	+	0.195408i	−0.804087	+	0.594512i	$0.797345\pi$
$462$	1.19721	+	2.07363i	0.0556992	+	0.0964739i
$463$	−8.23164			−0.382557			−0.191278	−	0.981536i	$-0.561263\pi$
$463$	−8.23164			−0.382557			−0.191278	+	0.981536i	$0.561263\pi$
$464$	−3.93244	−	6.81119i	−0.182559	−	0.316202i
$465$	1.24865	−	2.16273i	0.0579049	−	0.100294i
$466$	0.305530	−	0.529194i	0.0141534	−	0.0245144i
$467$	33.4873			1.54961			0.774803	−	0.632203i	$-0.217849\pi$
$467$	33.4873			1.54961			0.774803	+	0.632203i	$0.217849\pi$
$468$		0			0
$469$	7.67040			0.354186
$470$	6.38418	−	11.0577i	0.294480	−	0.510055i
$471$	3.78964	−	6.56386i	0.174618	−	0.302446i
$472$	1.73205	+	3.00000i	0.0797241	+	0.138086i
$473$	7.24789			0.333258
$474$	3.81988	+	6.61623i	0.175453	+	0.303894i
$475$	−2.16612	−	3.75184i	−0.0993886	−	0.172146i
$476$	−6.48247			−0.297123
$477$	12.6329	+	21.8808i	0.578421	+	1.00185i
$478$	12.8240	−	22.2119i	0.586558	−	1.01595i
$479$	4.02672	−	6.97448i	0.183985	−	0.318672i	−0.759249	−	0.650800i	$-0.774433\pi$
$479$	4.02672	−	6.97448i	0.183985	−	0.318672i	0.943234	+	0.332128i	$0.107767\pi$
$480$	−0.600196			−0.0273951
$481$		0			0
$482$	27.0931			1.23406
$483$	1.91760	−	3.32138i	0.0872538	−	0.151128i
$484$	1.65906	−	2.87358i	0.0754118	−	0.130617i
$485$	0.793166	+	1.37380i	0.0360158	+	0.0623812i
$486$	−13.6886			−0.620929
$487$	−0.811758	−	1.40601i	−0.0367842	−	0.0637122i	0.847047	−	0.531518i	$-0.178378\pi$
$487$	−0.811758	−	1.40601i	−0.0367842	−	0.0637122i	−0.883831	+	0.467806i	$0.845045\pi$
$488$	6.25184	+	10.8285i	0.283007	+	0.490183i
$489$	11.0247			0.498555
$490$	2.46410	+	4.26795i	0.111317	+	0.192806i
$491$	−5.16033	+	8.93796i	−0.232883	+	0.403364i	−0.958655	−	0.284570i	$-0.908149\pi$
$491$	−5.16033	+	8.93796i	−0.232883	+	0.403364i	0.725773	+	0.687935i	$0.241482\pi$
$492$	1.26795	−	2.19615i	0.0571636	−	0.0990102i
$493$	−35.4209			−1.59527
$494$		0			0
$495$	−7.31643			−0.328849
$496$	−2.08041	+	3.60338i	−0.0934132	+	0.161796i
$497$	4.31812	−	7.47921i	0.193694	−	0.335488i
$498$	3.01506	+	5.22223i	0.135108	+	0.234014i
$499$	−13.9807			−0.625860			−0.312930	−	0.949776i	$-0.601311\pi$
$499$	−13.9807			−0.625860			−0.312930	+	0.949776i	$0.601311\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−6.48467	−	11.2318i	−0.289714	−	0.501799i
$502$	1.50367			0.0671121
$503$	−11.8924	−	20.5983i	−0.530258	−	0.918434i	−0.999377	−	0.0352988i	$-0.988762\pi$
$503$	−11.8924	−	20.5983i	−0.530258	−	0.918434i	0.469119	−	0.883135i	$-0.344572\pi$
$504$	1.89980	−	3.29056i	0.0846240	−	0.146573i
$505$	−6.87676	+	11.9109i	−0.306012	+	0.530028i
$506$	12.3043			0.546991
$507$		0			0
$508$	−16.1244			−0.715403
$509$	12.8185	−	22.2023i	0.568171	−	0.984102i	−0.428575	−	0.903506i	$-0.640984\pi$
$509$	12.8185	−	22.2023i	0.568171	−	0.984102i	0.996747	−	0.0805958i	$-0.0256823\pi$
$510$	−1.35154	+	2.34094i	−0.0598473	+	0.103659i
$511$	1.19721	+	2.07363i	0.0529614	+	0.0917319i
$512$	1.00000			0.0441942
$513$	−7.33225	−	12.6998i	−0.323727	−	0.560711i
$514$	10.1724	+	17.6191i	0.448685	+	0.777146i
$515$	5.73205			0.252584
$516$	0.784767	+	1.35926i	0.0345474	+	0.0598379i
$517$	17.6945	−	30.6478i	0.778204	−	1.34789i
$518$	0.414157	−	0.717340i	0.0181970	−	0.0315181i
$519$	−2.39442			−0.105103
$520$		0			0
$521$	−8.53476			−0.373915			−0.186957	−	0.982368i	$-0.559863\pi$
$521$	−8.53476			−0.373915			−0.186957	+	0.982368i	$0.559863\pi$
$522$	10.3807	−	17.9799i	0.454352	−	0.786961i
$523$	6.34383	−	10.9878i	0.277396	−	0.480464i	−0.693341	−	0.720610i	$-0.743862\pi$
$523$	6.34383	−	10.9878i	0.277396	−	0.480464i	0.970737	+	0.240146i	$0.0771952\pi$
$524$	9.88043	+	17.1134i	0.431629	+	0.747603i
$525$	−0.863906			−0.0377039
$526$	8.56466	+	14.8344i	0.373437	+	0.646811i
$527$	9.36949	+	16.2284i	0.408141	+	0.706921i
$528$	−1.66351			−0.0723952
$529$	1.64598	+	2.85092i	0.0715644	+	0.123953i
$530$	−4.78561	+	8.28893i	−0.207874	+	0.360048i
$531$	−4.57221	+	7.91930i	−0.198417	+	0.343668i
$532$	6.23572			0.270353
$533$		0			0
$534$	−3.57547			−0.154726
$535$	−2.33967	+	4.05242i	−0.101153	+	0.175202i
$536$	−2.66449	+	4.61504i	−0.115089	+	0.199339i
$537$	3.74520	+	6.48687i	0.161617	+	0.279929i
$538$	19.3824			0.835635
$539$	6.82955	+	11.8291i	0.294170	+	0.509517i
$540$	−1.69248	−	2.93146i	−0.0728328	−	0.126150i
$541$	42.0507			1.80790			0.903951	−	0.427636i	$-0.140653\pi$
$541$	42.0507			1.80790			0.903951	+	0.427636i	$0.140653\pi$
$542$	−9.18555	−	15.9098i	−0.394553	−	0.683386i
$543$	−5.83146	+	10.1004i	−0.250252	+	0.433449i
$544$	2.25184	−	3.90029i	0.0965467	−	0.167224i
$545$	2.32164			0.0994483
$546$		0			0
$547$	24.6297			1.05309			0.526545	−	0.850147i	$-0.323487\pi$
$547$	24.6297			1.05309			0.526545	+	0.850147i	$0.323487\pi$
$548$	8.63234	−	14.9517i	0.368755	−	0.638703i
$549$	−16.5034	+	28.5847i	−0.704347	+	1.21996i
$550$	−1.38581	−	2.40029i	−0.0590911	−	0.102349i
$551$	34.0726			1.45154
$552$	1.33225	+	2.30752i	0.0567042	+	0.0982145i
$553$	−9.16074	−	15.8669i	−0.389554	−	0.674728i
$554$	−27.2342			−1.15707
$555$	−0.172697	−	0.299119i	−0.00733056	−	0.0126969i
$556$	−1.47328	+	2.55180i	−0.0624811	+	0.108221i
$557$	3.95244	−	6.84583i	0.167470	−	0.290067i	−0.770059	−	0.637972i	$-0.779773\pi$
$557$	3.95244	−	6.84583i	0.167470	−	0.290067i	0.937530	+	0.347905i	$0.113107\pi$
$558$	−10.9836			−0.464973
$559$		0			0
$560$	1.43937			0.0608246
$561$	−3.74596	+	6.48819i	−0.158155	+	0.273932i
$562$	−15.0408	+	26.0514i	−0.634456	+	1.09891i
$563$	−6.63553	−	11.4931i	−0.279654	−	0.484375i	0.691645	−	0.722238i	$-0.256886\pi$
$563$	−6.63553	−	11.4931i	−0.279654	−	0.484375i	−0.971299	+	0.237863i	$0.923553\pi$
$564$	7.66351			0.322692
$565$	−3.86814	−	6.69982i	−0.162734	−	0.281864i
$566$	12.7394	+	22.0653i	0.535477	+	0.927473i
$567$	8.47454			0.355897
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−21.1323	+	36.6022i	−0.885911	+	1.53444i	−0.0412443	+	0.999149i	$0.513132\pi$
$569$	−21.1323	+	36.6022i	−0.885911	+	1.53444i	−0.844666	+	0.535293i	$0.820201\pi$
$570$	1.30010	−	2.25184i	0.0544551	−	0.0943190i
$571$	−1.64965			−0.0690358			−0.0345179	−	0.999404i	$-0.510990\pi$
$571$	−1.64965			−0.0690358			−0.0345179	+	0.999404i	$0.510990\pi$
$572$		0			0
$573$	10.9965			0.459384
$574$	−3.04076	+	5.26676i	−0.126919	+	0.219830i
$575$	−2.21969	+	3.84461i	−0.0925673	+	0.160331i
$576$	1.31988	+	2.28610i	0.0549951	+	0.0952543i
$577$	−28.4651			−1.18502			−0.592508	−	0.805564i	$-0.701862\pi$
$577$	−28.4651			−1.18502			−0.592508	+	0.805564i	$0.701862\pi$
$578$	−1.64153	−	2.84321i	−0.0682785	−	0.118262i
$579$	−1.42355	−	2.46567i	−0.0591609	−	0.102470i
$580$	7.86488			0.326572
$581$	−7.23063	−	12.5238i	−0.299977	−	0.519576i
$582$	−0.476055	+	0.824551i	−0.0197331	+	0.0341788i
$583$	−13.2639	+	22.9738i	−0.549335	+	0.951476i
$584$	−1.66351			−0.0688367
$585$		0			0
$586$	−16.5779			−0.684825
$587$	−11.0848	+	19.1994i	−0.457518	+	0.792445i	−0.998829	−	0.0483779i	$-0.984595\pi$
$587$	−11.0848	+	19.1994i	−0.457518	+	0.792445i	0.541311	+	0.840822i	$0.317928\pi$
$588$	−1.47894	+	2.56160i	−0.0609906	+	0.105639i
$589$	−9.01285	−	15.6107i	−0.371368	−	0.643228i
$590$	−3.46410			−0.142615
$591$	−3.24123	−	5.61398i	−0.133327	−	0.230928i
$592$	0.287734	+	0.498370i	0.0118258	+	0.0204829i
$593$	9.68683			0.397791			0.198895	−	0.980021i	$-0.436265\pi$
$593$	9.68683			0.397791			0.198895	+	0.980021i	$0.436265\pi$
$594$	−4.69092	−	8.12490i	−0.192471	−	0.333369i
$595$	3.24123	−	5.61398i	0.132878	−	0.230151i
$596$	−3.53264	+	6.11871i	−0.144702	+	0.250632i
$597$	−6.60656			−0.270388
$598$		0			0
$599$	8.33012			0.340360			0.170180	−	0.985413i	$-0.445565\pi$
$599$	8.33012			0.340360			0.170180	+	0.985413i	$0.445565\pi$
$600$	0.300098	−	0.519785i	0.0122514	−	0.0212201i
$601$	6.10117	−	10.5675i	0.248872	−	0.431059i	−0.714341	−	0.699798i	$-0.753273\pi$
$601$	6.10117	−	10.5675i	0.248872	−	0.431059i	0.963213	+	0.268739i	$0.0866068\pi$
$602$	−1.88201	−	3.25973i	−0.0767049	−	0.132857i
$603$	−14.0673			−0.572864
$604$	7.91633	+	13.7115i	0.322111	+	0.557912i
$605$	1.65906	+	2.87358i	0.0674504	+	0.116828i
$606$	−8.25480			−0.335328
$607$	4.91946	+	8.52075i	0.199675	+	0.345847i	0.948423	−	0.317008i	$-0.102678\pi$
$607$	4.91946	+	8.52075i	0.199675	+	0.345847i	−0.748748	+	0.662854i	$0.769345\pi$
$608$	−2.16612	+	3.75184i	−0.0878479	+	0.152157i
$609$	3.39726	−	5.88423i	0.137664	−	0.238441i
$610$	−12.5037			−0.506259
$611$		0			0
$612$	11.8886			0.480570
$613$	−7.60586	+	13.1737i	−0.307198	+	0.532082i	−0.977748	−	0.209782i	$-0.932725\pi$
$613$	−7.60586	+	13.1737i	−0.307198	+	0.532082i	0.670551	+	0.741864i	$0.266058\pi$
$614$	8.13609	−	14.0921i	0.328346	−	0.568712i
$615$	1.26795	+	2.19615i	0.0511286	+	0.0885574i
$616$	3.98940			0.160737
$617$	−12.2357	−	21.1929i	−0.492592	−	0.853194i	0.507372	−	0.861727i	$-0.330617\pi$
$617$	−12.2357	−	21.1929i	−0.492592	−	0.853194i	−0.999964	+	0.00853345i	$0.997284\pi$
$618$	1.72018	+	2.97943i	0.0691956	+	0.119850i
$619$	−42.4157			−1.70483			−0.852416	−	0.522864i	$-0.824864\pi$
$619$	−42.4157			−1.70483			−0.852416	+	0.522864i	$0.824864\pi$
$620$	−2.08041	−	3.60338i	−0.0835513	−	0.144715i
$621$	−7.51356	+	13.0139i	−0.301509	+	0.522228i
$622$	−8.05264	+	13.9476i	−0.322881	+	0.559247i
$623$	8.57459			0.343534
$624$		0			0
$625$	1.00000			0.0400000
$626$	5.10811	−	8.84750i	0.204161	−	0.353617i
$627$	3.60338	−	6.24123i	0.143905	−	0.249251i
$628$	−6.31401	−	10.9362i	−0.251957	−	0.436402i
$629$	2.59172			0.103339
$630$	1.89980	+	3.29056i	0.0756900	+	0.131099i
$631$	0.0141253	+	0.0244657i	0.000562318	+	0.000973964i	0.866306	−	0.499513i	$-0.166488\pi$
$631$	0.0141253	+	0.0244657i	0.000562318	+	0.000973964i	−0.865744	+	0.500487i	$0.833154\pi$
$632$	12.7288			0.506324
$633$	7.88002	+	13.6486i	0.313203	+	0.542483i
$634$	0.102184	−	0.176988i	0.00405825	−	0.00702909i
$635$	8.06218	−	13.9641i	0.319938	−	0.554148i
$636$	−5.74461			−0.227789
$637$		0			0
$638$	21.7985			0.863010
$639$	−7.91930	+	13.7166i	−0.313282	+	0.542621i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−8.10465	−	14.0377i	−0.320114	−	0.554454i	0.660397	−	0.750917i	$-0.270388\pi$
$641$	−8.10465	−	14.0377i	−0.320114	−	0.554454i	−0.980511	+	0.196462i	$0.937055\pi$
$642$	−2.80852			−0.110843
$643$	9.10586	+	15.7718i	0.359100	+	0.621979i	0.987811	−	0.155660i	$-0.0497504\pi$
$643$	9.10586	+	15.7718i	0.359100	+	0.621979i	−0.628711	+	0.777639i	$0.716417\pi$
$644$	−3.19496	−	5.53383i	−0.125899	−	0.218064i
$645$	−1.56953			−0.0618003
$646$	9.75551	+	16.8970i	0.383825	+	0.664805i
$647$	3.56139	−	6.16852i	0.140013	−	0.242509i	−0.787488	−	0.616330i	$-0.788619\pi$
$647$	3.56139	−	6.16852i	0.140013	−	0.242509i	0.927501	+	0.373820i	$0.121952\pi$
$648$	−2.94383	+	5.09886i	−0.115644	+	0.200302i
$649$	−9.60117			−0.376879
$650$		0			0
$651$	−3.59456			−0.140882
$652$	9.18428	−	15.9076i	0.359684	−	0.622991i
$653$	8.03546	−	13.9178i	0.314452	−	0.544647i	−0.664869	−	0.746960i	$-0.731513\pi$
$653$	8.03546	−	13.9178i	0.314452	−	0.544647i	0.979321	+	0.202313i	$0.0648459\pi$
$654$	0.696720	+	1.20676i	0.0272439	+	0.0471879i
$655$	−19.7609			−0.772121
$656$	−2.11256	−	3.65906i	−0.0824816	−	0.142862i
$657$	−2.19564	−	3.80297i	−0.0856602	−	0.148368i
$658$	−18.3784			−0.716466
$659$	−22.5988	−	39.1423i	−0.880326	−	1.52477i	−0.850979	−	0.525200i	$-0.823990\pi$
$659$	−22.5988	−	39.1423i	−0.880326	−	1.52477i	−0.0293473	−	0.999569i	$-0.509343\pi$
$660$	0.831757	−	1.44065i	0.0323761	−	0.0560771i
$661$	−4.40723	+	7.63354i	−0.171421	+	0.296910i	−0.938917	−	0.344144i	$-0.888169\pi$
$661$	−4.40723	+	7.63354i	−0.171421	+	0.296910i	0.767496	+	0.641054i	$0.221503\pi$
$662$	−19.0653			−0.740993
$663$		0			0
$664$	10.0469			0.389896
$665$	−3.11786	+	5.40029i	−0.120905	+	0.209414i
$666$	−0.759550	+	1.31558i	−0.0294320	+	0.0509777i
$667$	−17.4576	−	30.2374i	−0.675960	−	1.17080i
$668$	−21.6085			−0.836059
$669$	−6.66344	−	11.5414i	−0.257623	−	0.446217i
$670$	−2.66449	−	4.61504i	−0.102938	−	0.178294i
$671$	−34.6554			−1.33786
$672$	0.431953	+	0.748164i	0.0166629	+	0.0288611i
$673$	−20.7199	+	35.8879i	−0.798693	+	1.38338i	0.121775	+	0.992558i	$0.461141\pi$
$673$	−20.7199	+	35.8879i	−0.798693	+	1.38338i	−0.920468	+	0.390819i	$0.872192\pi$
$674$	9.93045	−	17.2001i	0.382507	−	0.662521i
$675$	3.38496			0.130287
$676$		0			0
$677$	−18.8510			−0.724504			−0.362252	−	0.932080i	$-0.617992\pi$
$677$	−18.8510			−0.724504			−0.362252	+	0.932080i	$0.617992\pi$
$678$	2.32164	−	4.02121i	0.0891622	−	0.154433i
$679$	1.14166	−	1.97742i	0.0438130	−	0.0758863i
$680$	2.25184	+	3.90029i	0.0863540	+	0.149569i
$681$	1.24789			0.0478193
$682$	−5.76611	−	9.98719i	−0.220796	−	0.382429i
$683$	−11.3332	−	19.6297i	−0.433654	−	0.751110i	0.563531	−	0.826095i	$-0.309443\pi$
$683$	−11.3332	−	19.6297i	−0.433654	−	0.751110i	−0.997185	+	0.0749846i	$0.976109\pi$
$684$	−11.4361			−0.437271
$685$	8.63234	+	14.9517i	0.329825	+	0.571274i
$686$	8.58457	−	14.8689i	0.327760	−	0.567698i
$687$	−1.40426	+	2.43225i	−0.0535758	+	0.0927960i
$688$	2.61504			0.0996974
$689$		0			0
$690$	−2.66449			−0.101436
$691$	−15.9196	+	27.5736i	−0.605612	+	1.04895i	0.386343	+	0.922355i	$0.373738\pi$
$691$	−15.9196	+	27.5736i	−0.605612	+	1.04895i	−0.991954	+	0.126595i	$0.959595\pi$
$692$	−1.99470	+	3.45492i	−0.0758271	+	0.131336i
$693$	5.26554	+	9.12018i	0.200021	+	0.346447i
$694$	17.0504			0.647226
$695$	−1.47328	−	2.55180i	−0.0558848	−	0.0967954i
$696$	2.36023	+	4.08805i	0.0894645	+	0.154957i
$697$	−19.0285			−0.720758
$698$	10.6185	+	18.3917i	0.401915	+	0.696138i
$699$	−0.183378	+	0.317620i	−0.00693599	+	0.0120135i
$700$	−0.719687	+	1.24653i	−0.0272016	+	0.0471146i
$701$	−0.611060			−0.0230794			−0.0115397	−	0.999933i	$-0.503673\pi$
$701$	−0.611060			−0.0230794			−0.0115397	+	0.999933i	$0.503673\pi$
$702$		0			0
$703$	−2.49307			−0.0940279
$704$	−1.38581	+	2.40029i	−0.0522297	+	0.0904645i
$705$	−3.83176	+	6.63680i	−0.144312	+	0.249956i
$706$	−8.00840	−	13.8710i	−0.301400	−	0.522040i
$707$	19.7965			0.744522
$708$	−1.03957	−	1.80059i	−0.0390694	−	0.0676702i
$709$	−6.48212	−	11.2274i	−0.243441	−	0.421653i	0.718251	−	0.695784i	$-0.244943\pi$
$709$	−6.48212	−	11.2274i	−0.243441	−	0.421653i	−0.961692	+	0.274131i	$0.911610\pi$
$710$	−6.00000			−0.225176
$711$	16.8005	+	29.0993i	0.630068	+	1.09131i
$712$	−2.97859	+	5.15906i	−0.111627	+	0.193344i
$713$	−9.23572	+	15.9967i	−0.345881	+	0.599083i
$714$	3.89075			0.145608
$715$		0			0
$716$	12.4799			0.466397
$717$	−7.69694	+	13.3315i	−0.287447	+	0.497873i
$718$	−12.1244	+	21.0000i	−0.452477	+	0.783713i
$719$	−17.8616	−	30.9372i	−0.666126	−	1.15376i	−0.978979	−	0.203963i	$-0.934618\pi$
$719$	−17.8616	−	30.9372i	−0.666126	−	1.15376i	0.312853	−	0.949802i	$-0.398715\pi$
$720$	−2.63977			−0.0983782
$721$	−4.12528	−	7.14520i	−0.153634	−	0.266101i
$722$	0.115820	+	0.200606i	0.00431038	+	0.00746580i
$723$	−16.2612			−0.604759
$724$	9.71594	+	16.8285i	0.361090	+	0.625426i
$725$	−3.93244	+	6.81119i	−0.146047	+	0.252961i
$726$	−0.995761	+	1.72471i	−0.0369562	+	0.0640099i
$727$	51.7313			1.91861			0.959304	−	0.282375i	$-0.0911224\pi$
$727$	51.7313			1.91861			0.959304	+	0.282375i	$0.0911224\pi$
$728$		0			0
$729$	−9.44711			−0.349893
$730$	0.831757	−	1.44065i	0.0307847	−	0.0533207i
$731$	5.88863	−	10.1994i	0.217799	−	0.377239i
$732$	−3.75232	−	6.49922i	−0.138690	−	0.240218i
$733$	−26.4319			−0.976284			−0.488142	−	0.872764i	$-0.662325\pi$
$733$	−26.4319			−0.976284			−0.488142	+	0.872764i	$0.662325\pi$
$734$	14.8854	+	25.7822i	0.549429	+	0.951639i
$735$	−1.47894	−	2.56160i	−0.0545516	−	0.0944862i
$736$	4.43937			0.163637
$737$	−7.38496	−	12.7911i	−0.272029	−	0.471167i
$738$	5.57666	−	9.65906i	0.205280	−	0.355555i
$739$	−13.7051	+	23.7380i	−0.504151	+	0.873215i	0.495837	+	0.868415i	$0.334861\pi$
$739$	−13.7051	+	23.7380i	−0.504151	+	0.873215i	−0.999988	+	0.00480000i	$0.998472\pi$
$740$	−0.575468			−0.0211546
$741$		0			0
$742$	13.7766			0.505754
$743$	21.0909	−	36.5306i	0.773751	−	1.34018i	−0.161742	−	0.986833i	$-0.551711\pi$
$743$	21.0909	−	36.5306i	0.773751	−	1.34018i	0.935494	−	0.353344i	$-0.114955\pi$
$744$	1.24865	−	2.16273i	0.0457779	−	0.0792896i
$745$	−3.53264	−	6.11871i	−0.129426	−	0.224172i
$746$	28.3858			1.03928
$747$	13.2607	+	22.9683i	0.485185	+	0.840365i
$748$	6.24123	+	10.8101i	0.228202	+	0.395258i
$749$	6.73531			0.246103
$750$	0.300098	+	0.519785i	0.0109580	+	0.0189799i
$751$	−9.66351	+	16.7377i	−0.352627	+	0.610767i	−0.986709	−	0.162498i	$-0.948045\pi$
$751$	−9.66351	+	16.7377i	−0.352627	+	0.610767i	0.634082	+	0.773266i	$0.281378\pi$
$752$	6.38418	−	11.0577i	0.232807	−	0.403234i
$753$	−0.902497			−0.0328888
$754$		0			0
$755$	−15.8327			−0.576209
$756$	−2.43611	+	4.21947i	−0.0886006	+	0.153461i
$757$	10.1513	−	17.5825i	0.368955	−	0.639048i	−0.620448	−	0.784248i	$-0.713049\pi$
$757$	10.1513	−	17.5825i	0.368955	−	0.639048i	0.989402	+	0.145200i	$0.0463824\pi$
$758$	14.2069	+	24.6070i	0.516017	+	0.893768i
$759$	−7.38496			−0.268057
$760$	−2.16612	−	3.75184i	−0.0785735	−	0.136093i
$761$	22.1348	+	38.3386i	0.802386	+	1.38977i	0.918042	+	0.396484i	$0.129770\pi$
$761$	22.1348	+	38.3386i	0.802386	+	1.38977i	−0.115656	+	0.993289i	$0.536897\pi$
$762$	9.67777			0.350589
$763$	−1.67086	−	2.89401i	−0.0604891	−	0.104770i
$764$	9.16074	−	15.8669i	0.331424	−	0.574043i
$765$	−5.94432	+	10.2959i	−0.214917	+	0.372248i
$766$	9.39726			0.339537
$767$		0			0
$768$	−0.600196			−0.0216577
$769$	−1.87005	+	3.23903i	−0.0674359	+	0.116802i	−0.897772	−	0.440461i	$-0.854815\pi$
$769$	−1.87005	+	3.23903i	−0.0674359	+	0.116802i	0.830336	+	0.557263i	$0.188148\pi$
$770$	−1.99470	+	3.45492i	−0.0718840	+	0.124507i
$771$	−6.10543	−	10.5749i	−0.219882	−	0.380846i
$772$	−4.74363			−0.170727
$773$	2.24045	+	3.88057i	0.0805834	+	0.139575i	0.903501	−	0.428587i	$-0.140988\pi$
$773$	2.24045	+	3.88057i	0.0805834	+	0.139575i	−0.822917	+	0.568161i	$0.807655\pi$
$774$	3.45154	+	5.97825i	0.124063	+	0.214884i
$775$	4.16082			0.149461
$776$	0.793166	+	1.37380i	0.0284730	+	0.0493167i
$777$	−0.248575	+	0.430545i	−0.00891758	+	0.0154457i
$778$	5.82306	−	10.0858i	0.208767	−	0.361595i
$779$	18.3043			0.655818
$780$		0			0
$781$	−16.6297			−0.595058
$782$	9.99674	−	17.3149i	0.357483	−	0.619178i
$783$	−13.3112	+	23.0556i	−0.475702	+	0.823941i
$784$	2.46410	+	4.26795i	0.0880036	+	0.152427i
$785$	12.6280			0.450714
$786$	−5.93019	−	10.2714i	−0.211523	−	0.366368i
$787$	16.0482	+	27.7963i	0.572056	+	0.990830i	0.996355	+	0.0853077i	$0.0271873\pi$
$787$	16.0482	+	27.7963i	0.572056	+	0.990830i	−0.424299	+	0.905522i	$0.639479\pi$
$788$	−10.8006			−0.384755
$789$	−5.14047	−	8.90355i	−0.183006	−	0.316975i
$790$	−6.36440	+	11.0235i	−0.226435	+	0.392197i
$791$	−5.56771	+	9.64355i	−0.197965	+	0.342885i
$792$	−7.31643			−0.259978
$793$		0			0
$794$	−0.399804			−0.0141885
$795$	2.87231	−	4.97498i	0.101870	−	0.176444i
$796$	−5.50367	+	9.53264i	−0.195072	+	0.337875i
$797$	−11.1083	−	19.2402i	−0.393477	−	0.681522i	0.599429	−	0.800428i	$-0.295395\pi$
$797$	−11.1083	−	19.2402i	−0.393477	−	0.681522i	−0.992905	+	0.118906i	$0.962061\pi$
$798$	−3.74265			−0.132488
$799$	−28.7522	−	49.8004i	−1.01718	−	1.76181i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−15.7255			−0.555634
$802$	4.25388	+	7.36793i	0.150210	+	0.260171i
$803$	2.30532	−	3.99292i	0.0813528	−	0.140907i
$804$	1.59922	−	2.76993i	0.0564000	−	0.0976877i
$805$	6.38992			0.225215
$806$		0			0
$807$	−11.6332			−0.409510
$808$	−6.87676	+	11.9109i	−0.241924	+	0.419024i
$809$	5.27410	−	9.13501i	0.185427	−	0.321170i	−0.758293	−	0.651914i	$-0.773966\pi$
$809$	5.27410	−	9.13501i	0.185427	−	0.321170i	0.943720	+	0.330744i	$0.107300\pi$
$810$	−2.94383	−	5.09886i	−0.103436	−	0.179156i
$811$	−41.6434			−1.46230			−0.731149	−	0.682218i	$-0.761016\pi$
$811$	−41.6434			−1.46230			−0.731149	+	0.682218i	$0.761016\pi$
$812$	−5.66025	−	9.80385i	−0.198636	−	0.344048i
$813$	5.51313	+	9.54902i	0.193354	+	0.334899i
$814$	−1.59498			−0.0559040
$815$	9.18428	+	15.9076i	0.321711	+	0.557220i
$816$	−1.35154	+	2.34094i	−0.0473134	+	0.0819493i
$817$	−5.66449	+	9.81119i	−0.198176	+	0.343250i
$818$	14.0131			0.489958
$819$		0			0
$820$	4.22512			0.147548
$821$	−11.6140	+	20.1160i	−0.405331	+	0.702053i	−0.994360	−	0.106058i	$-0.966177\pi$
$821$	−11.6140	+	20.1160i	−0.405331	+	0.702053i	0.589029	+	0.808112i	$0.299510\pi$
$822$	−5.18110	+	8.97392i	−0.180711	+	0.313001i
$823$	0.499427	+	0.865033i	0.0174089	+	0.0301531i	0.874599	−	0.484848i	$-0.161125\pi$
$823$	0.499427	+	0.865033i	0.0174089	+	0.0301531i	−0.857190	+	0.515001i	$0.827792\pi$
$824$	5.73205			0.199685
$825$	0.831757	+	1.44065i	0.0289581	+	0.0501569i
$826$	2.49307	+	4.31812i	0.0867449	+	0.150247i
$827$	−29.8030			−1.03635			−0.518175	−	0.855274i	$-0.673389\pi$
$827$	−29.8030			−1.03635			−0.518175	+	0.855274i	$0.673389\pi$
$828$	5.85945	+	10.1489i	0.203630	+	0.352698i
$829$	−11.8508	+	20.5261i	−0.411594	+	0.712902i	−0.995064	−	0.0992329i	$-0.968361\pi$
$829$	−11.8508	+	20.5261i	−0.411594	+	0.712902i	0.583470	+	0.812134i	$0.301694\pi$
$830$	−5.02346	+	8.70088i	−0.174367	+	0.302012i
$831$	16.3458			0.567030
$832$		0			0
$833$	22.1950			0.769011
$834$	0.884259	−	1.53158i	0.0306194	−	0.0530343i
$835$	10.8043	−	18.7135i	0.373897	−	0.647608i
$836$	−6.00367	−	10.3987i	−0.207641	−	0.359645i
$837$	14.0842			0.486822
$838$	12.0977	+	20.9539i	0.417909	+	0.723839i
$839$	12.2971	+	21.2991i	0.424541	+	0.735327i	0.996377	−	0.0850406i	$-0.0271020\pi$
$839$	12.2971	+	21.2991i	0.424541	+	0.735327i	−0.571836	+	0.820368i	$0.693769\pi$
$840$	−0.863906			−0.0298076
$841$	−16.4282	−	28.4545i	−0.566490	−	0.981189i
$842$	−17.8196	+	30.8644i	−0.614104	+	1.06366i
$843$	9.02740	−	15.6359i	0.310920	−	0.538530i
$844$	26.2582			0.903843
$845$		0			0
$846$	33.7055			1.15882
$847$	2.38801	−	4.13615i	0.0820529	−	0.142120i
$848$	−4.78561	+	8.28893i	−0.164339	+	0.284643i
$849$	−7.64613	−	13.2435i	−0.262414	−	0.454515i
$850$	−4.50367			−0.154475
$851$	1.27736	+	2.21245i	0.0437873	+	0.0758418i
$852$	−1.80059	−	3.11871i	−0.0616871	−	0.106845i
$853$	−41.7449			−1.42932			−0.714659	−	0.699473i	$-0.753418\pi$
$853$	−41.7449			−1.42932			−0.714659	+	0.699473i	$0.753418\pi$
$854$	8.99873	+	15.5863i	0.307930	+	0.533351i
$855$	5.71806	−	9.90396i	0.195553	−	0.338708i
$856$	−2.33967	+	4.05242i	−0.0799682	+	0.138509i
$857$	−18.7543			−0.640636			−0.320318	−	0.947310i	$-0.603790\pi$
$857$	−18.7543			−0.640636			−0.320318	+	0.947310i	$0.603790\pi$
$858$		0			0
$859$	13.8357			0.472066			0.236033	−	0.971745i	$-0.424153\pi$
$859$	13.8357			0.472066			0.236033	+	0.971745i	$0.424153\pi$
$860$	−1.30752	+	2.26469i	−0.0445860	+	0.0772252i
$861$	1.82505	−	3.16108i	0.0621976	−	0.107729i
$862$	−2.48022	−	4.29586i	−0.0844765	−	0.146318i
$863$	8.00891			0.272626			0.136313	−	0.990666i	$-0.456475\pi$
$863$	8.00891			0.272626			0.136313	+	0.990666i	$0.456475\pi$
$864$	−1.69248	−	2.93146i	−0.0575794	−	0.0997304i
$865$	−1.99470	−	3.45492i	−0.0678218	−	0.117471i
$866$	4.21621			0.143273
$867$	0.985237	+	1.70648i	0.0334604	+	0.0579551i
$868$	−2.99449	+	5.18661i	−0.101640	+	0.176045i
$869$	−17.6397	+	30.5528i	−0.598385	+	1.03643i
$870$	−4.72047			−0.160039
$871$		0			0
$872$	2.32164			0.0786208
$873$	−2.09377	+	3.62652i	−0.0708635	+	0.122739i
$874$	−9.61623	+	16.6558i	−0.325274	+	0.563391i
$875$	−0.719687	−	1.24653i	−0.0243299	−	0.0421405i
$876$	0.998434			0.0337340
$877$	18.7658	+	32.5033i	0.633677	+	1.09756i	0.986794	+	0.161981i	$0.0517883\pi$
$877$	18.7658	+	32.5033i	0.633677	+	1.09756i	−0.353117	+	0.935579i	$0.614878\pi$
$878$	7.37500	+	12.7739i	0.248894	+	0.431097i
$879$	9.94996			0.335604
$880$	−1.38581	−	2.40029i	−0.0467156	−	0.0809139i
$881$	−6.05808	+	10.4929i	−0.204102	+	0.353515i	−0.949846	−	0.312717i	$-0.898761\pi$
$881$	−6.05808	+	10.4929i	−0.204102	+	0.353515i	0.745744	+	0.666232i	$0.232094\pi$
$882$	−6.50465	+	11.2664i	−0.219023	+	0.379359i
$883$	−44.4026			−1.49427			−0.747133	−	0.664675i	$-0.768570\pi$
$883$	−44.4026			−1.49427			−0.747133	+	0.664675i	$0.768570\pi$
$884$		0			0
$885$	2.07914			0.0698895
$886$	6.11871	−	10.5979i	0.205562	−	0.356044i
$887$	3.25714	−	5.64153i	0.109364	−	0.189424i	−0.806149	−	0.591713i	$-0.798452\pi$
$887$	3.25714	−	5.64153i	0.109364	−	0.189424i	0.915513	+	0.402289i	$0.131785\pi$
$888$	−0.172697	−	0.299119i	−0.00579532	−	0.0100378i
$889$	−23.2090			−0.778404
$890$	−2.97859	−	5.15906i	−0.0998424	−	0.172932i
$891$	−8.15917	−	14.1321i	−0.273343	−	0.473443i
$892$	−22.2042			−0.743452
$893$	27.6578	+	47.9048i	0.925534	+	1.60307i
$894$	2.12027	−	3.67242i	0.0709126	−	0.122824i
$895$	−6.23996	+	10.8079i	−0.208579	+	0.361269i
$896$	1.43937			0.0480861
$897$		0			0
$898$	−19.0714			−0.636420
$899$	−16.3622	+	28.3401i	−0.545710	+	0.945197i
$900$	1.31988	−	2.28610i	0.0439961	−	0.0762035i
$901$	21.5528	+	37.3306i	0.718029	+	1.24366i
$902$	11.7104			0.389915
$903$	1.12957	+	1.95648i	0.0375898	+	0.0651075i
$904$	−3.86814	−	6.69982i	−0.128653	−	0.222833i
$905$	−19.4319			−0.645937
$906$	−4.75135	−	8.22957i	−0.157853	−	0.273409i
$907$	2.96883	−	5.14216i	0.0985784	−	0.170743i	−0.812518	−	0.582936i	$-0.801904\pi$
$907$	2.96883	−	5.14216i	0.0985784	−	0.170743i	0.911096	+	0.412193i	$0.135237\pi$
$908$	1.03957	−	1.80059i	0.0344993	−	0.0597546i
$909$	−36.3061			−1.20420
$910$		0			0
$911$	48.7860			1.61635			0.808177	−	0.588940i	$-0.200455\pi$
$911$	48.7860			1.61635			0.808177	+	0.588940i	$0.200455\pi$
$912$	1.30010	−	2.25184i	0.0430505	−	0.0745657i
$913$	−13.9231	+	24.1155i	−0.460788	+	0.798108i
$914$	−8.05688	−	13.9549i	−0.266498	−	0.461588i
$915$	7.50465			0.248096
$916$	2.33967	+	4.05242i	0.0773048	+	0.133896i
$917$	14.2216	+	24.6326i	0.469640	+	0.813440i
$918$	−15.2448			−0.503152
$919$	14.8564	+	25.7321i	0.490068	+	0.848822i	0.999935	−	0.0114312i	$-0.00363874\pi$
$919$	14.8564	+	25.7321i	0.490068	+	0.848822i	−0.509867	+	0.860253i	$0.670305\pi$
$920$	−2.21969	+	3.84461i	−0.0731809	+	0.126753i
$921$	−4.88325	+	8.45803i	−0.160909	+	0.278702i
$922$	−4.84466			−0.159550
$923$		0			0
$924$	−2.39442			−0.0787706
$925$	0.287734	−	0.498370i	0.00946063	−	0.0163863i
$926$	4.11582	−	7.12881i	0.135254	−	0.234267i
$927$	7.56563	+	13.1041i	0.248488	+	0.430394i
$928$	7.86488			0.258177
$929$	9.00734	+	15.6012i	0.295521	+	0.511858i	0.975106	−	0.221739i	$-0.0711733\pi$
$929$	9.00734	+	15.6012i	0.295521	+	0.511858i	−0.679585	+	0.733597i	$0.737840\pi$
$930$	1.24865	+	2.16273i	0.0409450	+	0.0709188i
$931$	−21.3502			−0.699724
$932$	0.305530	+	0.529194i	0.0100080	+	0.0173343i
$933$	4.83316	−	8.37128i	0.158231	−	0.274063i
$934$	−16.7436	+	29.0008i	−0.547868	+	0.948936i
$935$	−12.4825			−0.408220
$936$		0			0
$937$	28.9796			0.946723			0.473361	−	0.880868i	$-0.343040\pi$
$937$	28.9796			0.946723			0.473361	+	0.880868i	$0.343040\pi$
$938$	−3.83520	+	6.64276i	−0.125224	+	0.216894i
$939$	−3.06586	+	5.31023i	−0.100051	+	0.173293i
$940$	6.38418	+	11.0577i	0.208229	+	0.360663i
$941$	−4.61504			−0.150446			−0.0752230	−	0.997167i	$-0.523967\pi$
$941$	−4.61504			−0.150446			−0.0752230	+	0.997167i	$0.523967\pi$
$942$	3.78964	+	6.56386i	0.123473	+	0.213862i
$943$	−9.37844	−	16.2439i	−0.305404	−	0.528975i
$944$	−3.46410			−0.112747
$945$	−2.43611	−	4.21947i	−0.0792468	−	0.137259i
$946$	−3.62395	+	6.27686i	−0.117825	+	0.204078i
$947$	5.30031	−	9.18041i	0.172237	−	0.298323i	−0.766965	−	0.641689i	$-0.778234\pi$
$947$	5.30031	−	9.18041i	0.172237	−	0.298323i	0.939202	+	0.343366i	$0.111567\pi$
$948$	−7.63977			−0.248128
$949$		0			0
$950$	4.33225			0.140557
$951$	−0.0613304	+	0.106227i	−0.00198878	+	0.00344466i
$952$	3.24123	−	5.61398i	0.105049	−	0.181950i
$953$	−14.3705	−	24.8905i	−0.465508	−	0.806283i	0.533717	−	0.845663i	$-0.320795\pi$
$953$	−14.3705	−	24.8905i	−0.465508	−	0.806283i	−0.999224	+	0.0393806i	$0.987462\pi$
$954$	−25.2658			−0.818010
$955$	9.16074	+	15.8669i	0.296435	+	0.513440i
$956$	12.8240	+	22.2119i	0.414759	+	0.718384i
$957$	−13.0833			−0.422925
$958$	4.02672	+	6.97448i	0.130097	+	0.225335i
$959$	12.4252	−	21.5210i	0.401230	−	0.694950i
$960$	0.300098	−	0.519785i	0.00968562	−	0.0167760i
$961$	−13.6876			−0.441534
$962$		0			0
$963$	−12.3523			−0.398049
$964$	−13.5466	+	23.4633i	−0.436305	+	0.755703i
$965$	2.37182	−	4.10811i	0.0763515	−	0.132245i
$966$	1.91760	+	3.32138i	0.0616978	+	0.106864i
$967$	8.08648			0.260044			0.130022	−	0.991511i	$-0.458495\pi$
$967$	8.08648			0.260044			0.130022	+	0.991511i	$0.458495\pi$
$968$	1.65906	+	2.87358i	0.0533242	+	0.0923603i
$969$	−5.85521	−	10.1415i	−0.188097	−	0.325793i
$970$	−1.58633			−0.0509341
$971$	−0.302790	−	0.524448i	−0.00971701	−	0.0168304i	0.861126	−	0.508392i	$-0.169760\pi$
$971$	−0.302790	−	0.524448i	−0.00971701	−	0.0168304i	−0.870843	+	0.491561i	$0.836426\pi$
$972$	6.84432	−	11.8547i	0.219532	−	0.380240i
$973$	−2.12061	+	3.67300i	−0.0679835	+	0.117751i
$974$	1.62352			0.0520208
$975$		0			0
$976$	−12.5037			−0.400233
$977$	−24.5216	+	42.4727i	−0.784516	+	1.35882i	0.144772	+	0.989465i	$0.453755\pi$
$977$	−24.5216	+	42.4727i	−0.784516	+	1.35882i	−0.929288	+	0.369356i	$0.879578\pi$
$978$	−5.51236	+	9.54769i	−0.176266	+	0.305302i
$979$	−8.25551	−	14.2990i	−0.263847	−	0.456997i
$980$	−4.92820			−0.157426
$981$	3.06430	+	5.30752i	0.0978355	+	0.169456i
$982$	−5.16033	−	8.93796i	−0.164673	−	0.285222i
$983$	30.7684			0.981358			0.490679	−	0.871340i	$-0.336749\pi$
$983$	30.7684			0.981358			0.490679	+	0.871340i	$0.336749\pi$
$984$	1.26795	+	2.19615i	0.0404207	+	0.0700108i
$985$	5.40029	−	9.35358i	0.172068	−	0.298030i
$986$	17.7104	−	30.6754i	0.564015	−	0.976902i
$987$	11.0307			0.351110
$988$		0			0
$989$	11.6091			0.369149
$990$	3.65821	−	6.33621i	0.116266	−	0.201378i
$991$	−7.74435	+	13.4136i	−0.246007	+	0.426097i	−0.962414	−	0.271585i	$-0.912452\pi$
$991$	−7.74435	+	13.4136i	−0.246007	+	0.426097i	0.716407	+	0.697683i	$0.245785\pi$
$992$	−2.08041	−	3.60338i	−0.0660531	−	0.114407i
$993$	11.4429			0.363129
$994$	4.31812	+	7.47921i	0.136962	+	0.237226i
$995$	−5.50367	−	9.53264i	−0.174478	−	0.302205i
$996$	−6.03011			−0.191071
$997$	3.91111	+	6.77423i	0.123866	+	0.214542i	0.921289	−	0.388878i	$-0.127137\pi$
$997$	3.91111	+	6.77423i	0.123866	+	0.214542i	−0.797423	+	0.603421i	$0.793804\pi$
$998$	6.99033	−	12.1076i	0.221275	−	0.383260i
$999$	0.973969	−	1.68696i	0.0308150	−	0.0533731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.s.191.3		8
13.2	odd	12		1690.2.l.j.361.2		8
13.3	even	3	inner	1690.2.e.s.991.3		8
13.4	even	6		1690.2.a.t.1.2		4
13.5	odd	4		130.2.l.b.121.4	yes	8
13.6	odd	12		1690.2.d.k.1351.2		8
13.7	odd	12		1690.2.d.k.1351.6		8
13.8	odd	4		1690.2.l.j.1161.2		8
13.9	even	3		1690.2.a.u.1.2		4
13.10	even	6		1690.2.e.t.991.3		8
13.11	odd	12		130.2.l.b.101.4	✓	8
13.12	even	2		1690.2.e.t.191.3		8
39.5	even	4		1170.2.bs.g.901.2		8
39.11	even	12		1170.2.bs.g.361.2		8
52.11	even	12		1040.2.da.d.881.2		8
52.31	even	4		1040.2.da.d.641.2		8
65.4	even	6		8450.2.a.cm.1.3		4
65.9	even	6		8450.2.a.ci.1.3		4
65.18	even	4		650.2.n.e.199.3		8
65.24	odd	12		650.2.m.c.101.1		8
65.37	even	12		650.2.n.e.49.3		8
65.44	odd	4		650.2.m.c.251.1		8
65.57	even	4		650.2.n.d.199.2		8
65.63	even	12		650.2.n.d.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.4	✓	8	13.11	odd	12
130.2.l.b.121.4	yes	8	13.5	odd	4
650.2.m.c.101.1		8	65.24	odd	12
650.2.m.c.251.1		8	65.44	odd	4
650.2.n.d.49.2		8	65.63	even	12
650.2.n.d.199.2		8	65.57	even	4
650.2.n.e.49.3		8	65.37	even	12
650.2.n.e.199.3		8	65.18	even	4
1040.2.da.d.641.2		8	52.31	even	4
1040.2.da.d.881.2		8	52.11	even	12
1170.2.bs.g.361.2		8	39.11	even	12
1170.2.bs.g.901.2		8	39.5	even	4
1690.2.a.t.1.2		4	13.4	even	6
1690.2.a.u.1.2		4	13.9	even	3
1690.2.d.k.1351.2		8	13.6	odd	12
1690.2.d.k.1351.6		8	13.7	odd	12
1690.2.e.s.191.3		8	1.1	even	1	trivial
1690.2.e.s.991.3		8	13.3	even	3	inner
1690.2.e.t.191.3		8	13.12	even	2
1690.2.e.t.991.3		8	13.10	even	6
1690.2.l.j.361.2		8	13.2	odd	12
1690.2.l.j.1161.2		8	13.8	odd	4
8450.2.a.ci.1.3		4	65.9	even	6
8450.2.a.cm.1.3		4	65.4	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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.300098 - 0.519785i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(0.300098 + 0.519785i) q^{6} +(-0.719687 - 1.24653i) q^{7} +1.00000 q^{8} +(1.31988 + 2.28610i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.38581 + 2.40029i) q^{11} -0.600196 q^{12} +1.43937 q^{14} +(0.300098 - 0.519785i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.25184 + 3.90029i) q^{17} -2.63977 q^{18} +(-2.16612 - 3.75184i) q^{19} +(-0.500000 - 0.866025i) q^{20} -0.863906 q^{21} +(-1.38581 - 2.40029i) q^{22} +(-2.21969 + 3.84461i) q^{23} +(0.300098 - 0.519785i) q^{24} +1.00000 q^{25} +3.38496 q^{27} +(-0.719687 + 1.24653i) q^{28} +(-3.93244 + 6.81119i) q^{29} +(0.300098 + 0.519785i) q^{30} +4.16082 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.831757 + 1.44065i) q^{33} -4.50367 q^{34} +(-0.719687 - 1.24653i) q^{35} +(1.31988 - 2.28610i) q^{36} +(0.287734 - 0.498370i) q^{37} +4.33225 q^{38} +1.00000 q^{40} +(-2.11256 + 3.65906i) q^{41} +(0.431953 - 0.748164i) q^{42} +(-1.30752 - 2.26469i) q^{43} +2.77162 q^{44} +(1.31988 + 2.28610i) q^{45} +(-2.21969 - 3.84461i) q^{46} -12.7684 q^{47} +(0.300098 + 0.519785i) q^{48} +(2.46410 - 4.26795i) q^{49} +(-0.500000 + 0.866025i) q^{50} +2.70308 q^{51} +9.57123 q^{53} +(-1.69248 + 2.93146i) q^{54} +(-1.38581 + 2.40029i) q^{55} +(-0.719687 - 1.24653i) q^{56} -2.60020 q^{57} +(-3.93244 - 6.81119i) q^{58} +(1.73205 + 3.00000i) q^{59} -0.600196 q^{60} +(6.25184 + 10.8285i) q^{61} +(-2.08041 + 3.60338i) q^{62} +(1.89980 - 3.29056i) q^{63} +1.00000 q^{64} -1.66351 q^{66} +(-2.66449 + 4.61504i) q^{67} +(2.25184 - 3.90029i) q^{68} +(1.33225 + 2.30752i) q^{69} +1.43937 q^{70} +(3.00000 + 5.19615i) q^{71} +(1.31988 + 2.28610i) q^{72} -1.66351 q^{73} +(0.287734 + 0.498370i) q^{74} +(0.300098 - 0.519785i) q^{75} +(-2.16612 + 3.75184i) q^{76} +3.98940 q^{77} +12.7288 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-2.94383 + 5.09886i) q^{81} +(-2.11256 - 3.65906i) q^{82} +10.0469 q^{83} +(0.431953 + 0.748164i) q^{84} +(2.25184 + 3.90029i) q^{85} +2.61504 q^{86} +(2.36023 + 4.08805i) q^{87} +(-1.38581 + 2.40029i) q^{88} +(-2.97859 + 5.15906i) q^{89} -2.63977 q^{90} +4.43937 q^{92} +(1.24865 - 2.16273i) q^{93} +(6.38418 - 11.0577i) q^{94} +(-2.16612 - 3.75184i) q^{95} -0.600196 q^{96} +(0.793166 + 1.37380i) q^{97} +(2.46410 + 4.26795i) q^{98} -7.31643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 2 q^{6} + 8 q^{8} - 4 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} - 2 q^{15} - 4 q^{16} - 6 q^{17} + 8 q^{18} - 6 q^{19} - 4 q^{20} + 12 q^{21} + 6 q^{22} - 12 q^{23}+ \cdots - 84 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 2 * q^6 + 8 * q^8 - 4 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 - 2 * q^15 - 4 * q^16 - 6 * q^17 + 8 * q^18 - 6 * q^19 - 4 * q^20 + 12 * q^21 + 6 * q^22 - 12 * q^23 - 2 * q^24 + 8 * q^25 + 40 * q^27 - 2 * q^30 + 36 * q^31 - 4 * q^32 + 6 * q^33 + 12 * q^34 - 4 * q^36 + 6 * q^37 + 12 * q^38 + 8 * q^40 - 6 * q^42 - 4 * q^43 - 12 * q^44 - 4 * q^45 - 12 * q^46 - 2 * q^48 - 8 * q^49 - 4 * q^50 + 60 * q^53 - 20 * q^54 + 6 * q^55 - 12 * q^57 + 4 * q^60 + 26 * q^61 - 18 * q^62 + 24 * q^63 + 8 * q^64 - 12 * q^66 + 24 * q^67 - 6 * q^68 - 12 * q^69 + 24 * q^71 - 4 * q^72 - 12 * q^73 + 6 * q^74 - 2 * q^75 - 6 * q^76 + 60 * q^77 + 20 * q^79 - 4 * q^80 - 28 * q^81 - 36 * q^83 - 6 * q^84 - 6 * q^85 + 8 * q^86 + 48 * q^87 + 6 * q^88 + 8 * q^90 + 24 * q^92 + 12 * q^93 - 6 * q^95 + 4 * q^96 - 18 * q^97 - 8 * q^98 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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