LMFDB - Embedded newform 330.2.m.f.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [330,2,Mod(31,330)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(330, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("330.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 330 = 2 \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	330.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.63506326670$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.2769390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 5x^{5} + 21x^{4} + 75x^{3} - 198x^{2} - 87x + 841 $ x^8 - x^7 - 2x^6 + 5x^5 + 21x^4 + 75x^3 - 198x^2 - 87x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$1.88778 - 1.74766i$ of defining polynomial
Character	$\chi$	$=$	330.91
Dual form			330.2.m.f.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.38778 + 4.27116i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.38778 + 4.27116i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.00000 q^{10} +(3.28475 + 0.458729i) q^{11} +1.00000 q^{12} +(1.88778 - 1.37155i) q^{13} +(1.38778 + 4.27116i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.17253 + 3.03152i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-1.85770 - 5.71740i) q^{19} +(0.809017 - 0.587785i) q^{20} -4.49096 q^{21} +(2.92705 - 1.55961i) q^{22} -8.88456 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.721069 - 2.21922i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(3.63326 + 2.63972i) q^{28} +(2.34270 - 7.21008i) q^{29} +(0.309017 + 0.951057i) q^{30} +(0.897194 - 0.651849i) q^{31} -1.00000 q^{32} +(0.578765 + 3.26574i) q^{33} +5.15753 q^{34} +(-3.63326 + 2.63972i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.45146 - 7.54482i) q^{37} +(-4.86351 - 3.53355i) q^{38} +(1.88778 + 1.37155i) q^{39} +(0.309017 - 0.951057i) q^{40} +(2.95728 + 9.10157i) q^{41} +(-3.63326 + 2.63972i) q^{42} -0.0785371 q^{43} +(1.45132 - 2.98223i) q^{44} -1.00000 q^{45} +(-7.18776 + 5.22221i) q^{46} +(0.896965 + 2.76058i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-10.6537 - 7.74037i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-1.59376 + 4.90510i) q^{51} +(-0.721069 - 2.21922i) q^{52} +(-0.602806 + 0.437964i) q^{53} -1.00000 q^{54} +(2.38778 + 2.30185i) q^{55} +4.49096 q^{56} +(4.86351 - 3.53355i) q^{57} +(-2.34270 - 7.21008i) q^{58} +(-1.64590 + 5.06555i) q^{59} +(0.809017 + 0.587785i) q^{60} +(-12.5026 - 9.08366i) q^{61} +(0.342697 - 1.05471i) q^{62} +(-1.38778 - 4.27116i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.33343 q^{65} +(2.38778 + 2.30185i) q^{66} -1.67821 q^{67} +(4.17253 - 3.03152i) q^{68} +(-2.74548 - 8.44972i) q^{69} +(-1.38778 + 4.27116i) q^{70} +(-7.72703 - 5.61401i) q^{71} +(0.809017 + 0.587785i) q^{72} +(3.38197 - 10.4086i) q^{73} +(-2.45146 - 7.54482i) q^{74} +(-0.809017 + 0.587785i) q^{75} -6.01163 q^{76} +(-6.51782 + 13.3931i) q^{77} +2.33343 q^{78} +(4.42742 - 3.21671i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(7.74225 + 5.62508i) q^{82} +(6.47214 + 4.70228i) q^{83} +(-1.38778 + 4.27116i) q^{84} +(1.59376 + 4.90510i) q^{85} +(-0.0635378 + 0.0461629i) q^{86} +7.58113 q^{87} +(-0.578765 - 3.26574i) q^{88} -7.41196 q^{89} +(-0.809017 + 0.587785i) q^{90} +(3.23829 + 9.96643i) q^{91} +(-2.74548 + 8.44972i) q^{92} +(0.897194 + 0.651849i) q^{93} +(2.34829 + 1.70613i) q^{94} +(1.85770 - 5.71740i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-4.64849 + 3.37733i) q^{97} -13.1687 q^{98} +(-2.92705 + 1.55961i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} - 3 q^{14} + 2 q^{15} - 2 q^{16} + 3 q^{17} + 2 q^{18} - 12 q^{19} + 2 q^{20} - 2 q^{21} + 10 q^{22} + 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + 27 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 5 q^{33} + 22 q^{34} + 2 q^{35} - 2 q^{36} - 4 q^{37} - 13 q^{38} + q^{39} - 2 q^{40} - 23 q^{41} + 2 q^{42} - 2 q^{43} + 10 q^{44} - 8 q^{45} - 5 q^{46} + 5 q^{47} - 2 q^{48} - 53 q^{49} + 2 q^{50} + 8 q^{51} + q^{52} - 18 q^{53} - 8 q^{54} + 5 q^{55} + 2 q^{56} + 13 q^{57} - 27 q^{58} - 40 q^{59} + 2 q^{60} - 20 q^{61} + 11 q^{62} + 3 q^{63} - 2 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 3 q^{68} - 5 q^{69} + 3 q^{70} - 10 q^{71} + 2 q^{72} + 36 q^{73} + 4 q^{74} - 2 q^{75} - 2 q^{76} + 50 q^{77} + 4 q^{78} - 11 q^{79} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 16 q^{83} + 3 q^{84} - 8 q^{85} - 13 q^{86} - 18 q^{87} + 5 q^{88} - 46 q^{89} - 2 q^{90} - 39 q^{91} - 5 q^{92} - 6 q^{93} + 15 q^{94} + 12 q^{95} + 2 q^{96} + 16 q^{97} - 62 q^{98} - 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^10 + 10 * q^11 + 8 * q^12 + q^13 - 3 * q^14 + 2 * q^15 - 2 * q^16 + 3 * q^17 + 2 * q^18 - 12 * q^19 + 2 * q^20 - 2 * q^21 + 10 * q^22 + 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + 27 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 5 * q^33 + 22 * q^34 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 13 * q^38 + q^39 - 2 * q^40 - 23 * q^41 + 2 * q^42 - 2 * q^43 + 10 * q^44 - 8 * q^45 - 5 * q^46 + 5 * q^47 - 2 * q^48 - 53 * q^49 + 2 * q^50 + 8 * q^51 + q^52 - 18 * q^53 - 8 * q^54 + 5 * q^55 + 2 * q^56 + 13 * q^57 - 27 * q^58 - 40 * q^59 + 2 * q^60 - 20 * q^61 + 11 * q^62 + 3 * q^63 - 2 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 3 * q^68 - 5 * q^69 + 3 * q^70 - 10 * q^71 + 2 * q^72 + 36 * q^73 + 4 * q^74 - 2 * q^75 - 2 * q^76 + 50 * q^77 + 4 * q^78 - 11 * q^79 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 16 * q^83 + 3 * q^84 - 8 * q^85 - 13 * q^86 - 18 * q^87 + 5 * q^88 - 46 * q^89 - 2 * q^90 - 39 * q^91 - 5 * q^92 - 6 * q^93 + 15 * q^94 + 12 * q^95 + 2 * q^96 + 16 * q^97 - 62 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	−1.38778	+	4.27116i	−0.524532	+	1.61434i	0.240706	+	0.970598i	$0.422621\pi$
$7$	−1.38778	+	4.27116i	−0.524532	+	1.61434i	−0.765239	+	0.643747i	$0.777379\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.00000			0.316228
$11$	3.28475	+	0.458729i	0.990389	+	0.138312i
$11$	3.28475	+	0.458729i	0.990389	+	0.138312i
$12$	1.00000			0.288675
$13$	1.88778	−	1.37155i	0.523577	−	0.380401i	−0.294373	−	0.955691i	$-0.595111\pi$
$13$	1.88778	−	1.37155i	0.523577	−	0.380401i	0.817950	+	0.575290i	$0.195111\pi$
$14$	1.38778	+	4.27116i	0.370900	+	1.14151i
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.17253	+	3.03152i	1.01199	+	0.735252i	0.964625	−	0.263626i	$-0.0849185\pi$
$17$	4.17253	+	3.03152i	1.01199	+	0.735252i	0.0473623	+	0.998878i	$0.484918\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	−1.85770	−	5.71740i	−0.426185	−	1.31166i	−0.901855	−	0.432038i	$-0.857794\pi$
$19$	−1.85770	−	5.71740i	−0.426185	−	1.31166i	0.475670	−	0.879624i	$-0.342206\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	−4.49096			−0.980007
$22$	2.92705	−	1.55961i	0.624049	−	0.332509i
$23$	−8.88456			−1.85256			−0.926279	−	0.376838i	$-0.877011\pi$
$23$	−8.88456			−1.85256			−0.926279	+	0.376838i	$0.877011\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.721069	−	2.21922i	0.141413	−	0.435225i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	3.63326	+	2.63972i	0.686622	+	0.498860i
$29$	2.34270	−	7.21008i	0.435028	−	1.33888i	−0.458030	−	0.888937i	$-0.651445\pi$
$29$	2.34270	−	7.21008i	0.435028	−	1.33888i	0.893058	−	0.449942i	$-0.148555\pi$
$30$	0.309017	+	0.951057i	0.0564185	+	0.173638i
$31$	0.897194	−	0.651849i	0.161141	−	0.117076i	−0.504293	−	0.863533i	$-0.668247\pi$
$31$	0.897194	−	0.651849i	0.161141	−	0.117076i	0.665433	+	0.746457i	$0.268247\pi$
$32$	−1.00000			−0.176777
$33$	0.578765	+	3.26574i	0.100750	+	0.568492i
$34$	5.15753			0.884509
$35$	−3.63326	+	2.63972i	−0.614133	+	0.446194i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	2.45146	−	7.54482i	0.403018	−	1.24036i	−0.519521	−	0.854457i	$-0.673890\pi$
$37$	2.45146	−	7.54482i	0.403018	−	1.24036i	0.922539	−	0.385904i	$-0.126110\pi$
$38$	−4.86351	−	3.53355i	−0.788966	−	0.573217i
$39$	1.88778	+	1.37155i	0.302287	+	0.219624i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	2.95728	+	9.10157i	0.461849	+	1.42143i	0.862902	+	0.505371i	$0.168644\pi$
$41$	2.95728	+	9.10157i	0.461849	+	1.42143i	−0.401053	+	0.916055i	$0.631356\pi$
$42$	−3.63326	+	2.63972i	−0.560624	+	0.407317i
$43$	−0.0785371			−0.0119768			−0.00598839	−	0.999982i	$-0.501906\pi$
$43$	−0.0785371			−0.0119768			−0.00598839	+	0.999982i	$0.501906\pi$
$44$	1.45132	−	2.98223i	0.218795	−	0.449587i
$45$	−1.00000			−0.149071
$46$	−7.18776	+	5.22221i	−1.05978	+	0.769973i
$47$	0.896965	+	2.76058i	0.130836	+	0.402671i	0.994919	−	0.100678i	$-0.0321011\pi$
$47$	0.896965	+	2.76058i	0.130836	+	0.402671i	−0.864083	+	0.503349i	$0.832101\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−10.6537	−	7.74037i	−1.52196	−	1.10577i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	−1.59376	+	4.90510i	−0.223172	+	0.686852i
$52$	−0.721069	−	2.21922i	−0.0999942	−	0.307751i
$53$	−0.602806	+	0.437964i	−0.0828018	+	0.0601590i	−0.628416	−	0.777877i	$-0.716296\pi$
$53$	−0.602806	+	0.437964i	−0.0828018	+	0.0601590i	0.545614	+	0.838036i	$0.316296\pi$
$54$	−1.00000			−0.136083
$55$	2.38778	+	2.30185i	0.321969	+	0.310381i
$56$	4.49096			0.600130
$57$	4.86351	−	3.53355i	0.644188	−	0.468030i
$58$	−2.34270	−	7.21008i	−0.307611	−	0.946730i
$59$	−1.64590	+	5.06555i	−0.214278	+	0.659479i	0.784926	+	0.619589i	$0.212701\pi$
$59$	−1.64590	+	5.06555i	−0.214278	+	0.659479i	−0.999204	+	0.0398899i	$0.987299\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	−12.5026	−	9.08366i	−1.60079	−	1.16304i	−0.885975	−	0.463734i	$-0.846509\pi$
$61$	−12.5026	−	9.08366i	−1.60079	−	1.16304i	−0.714818	−	0.699310i	$-0.753491\pi$
$62$	0.342697	−	1.05471i	0.0435226	−	0.133949i
$63$	−1.38778	−	4.27116i	−0.174844	−	0.538115i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.33343			0.289426
$66$	2.38778	+	2.30185i	0.293916	+	0.283338i
$67$	−1.67821			−0.205025			−0.102513	−	0.994732i	$-0.532688\pi$
$67$	−1.67821			−0.205025			−0.102513	+	0.994732i	$0.532688\pi$
$68$	4.17253	−	3.03152i	0.505994	−	0.367626i
$69$	−2.74548	−	8.44972i	−0.330517	−	1.01723i
$70$	−1.38778	+	4.27116i	−0.165872	+	0.510501i
$71$	−7.72703	−	5.61401i	−0.917029	−	0.666261i	0.0257535	−	0.999668i	$-0.491802\pi$
$71$	−7.72703	−	5.61401i	−0.917029	−	0.666261i	−0.942783	+	0.333408i	$0.891802\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	3.38197	−	10.4086i	0.395829	−	1.21824i	−0.532485	−	0.846440i	$-0.678742\pi$
$73$	3.38197	−	10.4086i	0.395829	−	1.21824i	0.928314	−	0.371797i	$-0.121258\pi$
$74$	−2.45146	−	7.54482i	−0.284977	−	0.877068i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	−6.01163			−0.689582
$77$	−6.51782	+	13.3931i	−0.742774	+	1.52628i
$78$	2.33343			0.264209
$79$	4.42742	−	3.21671i	0.498124	−	0.361908i	−0.310176	−	0.950679i	$-0.600388\pi$
$79$	4.42742	−	3.21671i	0.498124	−	0.361908i	0.808300	+	0.588771i	$0.200388\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	7.74225	+	5.62508i	0.854989	+	0.621186i
$83$	6.47214	+	4.70228i	0.710409	+	0.516143i	0.883306	−	0.468798i	$-0.155313\pi$
$83$	6.47214	+	4.70228i	0.710409	+	0.516143i	−0.172896	+	0.984940i	$0.555313\pi$
$84$	−1.38778	+	4.27116i	−0.151419	+	0.466021i
$85$	1.59376	+	4.90510i	0.172868	+	0.532033i
$86$	−0.0635378	+	0.0461629i	−0.00685146	+	0.00497788i
$87$	7.58113			0.812782
$88$	−0.578765	−	3.26574i	−0.0616966	−	0.348129i
$89$	−7.41196			−0.785667			−0.392833	−	0.919610i	$-0.628505\pi$
$89$	−7.41196			−0.785667			−0.392833	+	0.919610i	$0.628505\pi$
$90$	−0.809017	+	0.587785i	−0.0852779	+	0.0619580i
$91$	3.23829	+	9.96643i	0.339465	+	1.04477i
$92$	−2.74548	+	8.44972i	−0.286236	+	0.880944i
$93$	0.897194	+	0.651849i	0.0930346	+	0.0675936i
$94$	2.34829	+	1.70613i	0.242207	+	0.175974i
$95$	1.85770	−	5.71740i	0.190596	−	0.586593i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−4.64849	+	3.37733i	−0.471983	+	0.342915i	−0.798213	−	0.602375i	$-0.794221\pi$
$97$	−4.64849	+	3.37733i	−0.471983	+	0.342915i	0.326231	+	0.945290i	$0.394221\pi$
$98$	−13.1687			−1.33024
$99$	−2.92705	+	1.55961i	−0.294180	+	0.156746i
$100$	1.00000			0.100000
$101$	13.4086	−	9.74192i	1.33421	−	0.969357i	0.334570	−	0.942371i	$-0.391409\pi$
$101$	13.4086	−	9.74192i	1.33421	−	0.969357i	0.999636	−	0.0269859i	$-0.00859092\pi$
$102$	1.59376	+	4.90510i	0.157806	+	0.485678i
$103$	−0.337022	+	1.03725i	−0.0332078	+	0.102203i	−0.966287	−	0.257469i	$-0.917111\pi$
$103$	−0.337022	+	1.03725i	−0.0332078	+	0.102203i	0.933079	+	0.359672i	$0.117111\pi$
$104$	−1.88778	−	1.37155i	−0.185112	−	0.134492i
$105$	−3.63326	−	2.63972i	−0.354570	−	0.257610i
$106$	−0.230252	+	0.708641i	−0.0223640	+	0.0688293i
$107$	1.75674	+	5.40670i	0.169831	+	0.522685i	0.999360	−	0.0357784i	$-0.0113911\pi$
$107$	1.75674	+	5.40670i	0.169831	+	0.522685i	−0.829529	+	0.558464i	$0.811391\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−8.94427			−0.856706			−0.428353	−	0.903612i	$-0.640906\pi$
$109$	−8.94427			−0.856706			−0.428353	+	0.903612i	$0.640906\pi$
$110$	3.28475	+	0.458729i	0.313188	+	0.0437381i
$111$	7.93310			0.752976
$112$	3.63326	−	2.63972i	0.343311	−	0.249430i
$113$	1.19680	+	3.68337i	0.112585	+	0.346502i	0.991436	−	0.130595i	$-0.0416888\pi$
$113$	1.19680	+	3.68337i	0.112585	+	0.346502i	−0.878850	+	0.477098i	$0.841689\pi$
$114$	1.85770	−	5.71740i	0.173989	−	0.535484i
$115$	−7.18776	−	5.22221i	−0.670262	−	0.486974i
$116$	−6.13326	−	4.45608i	−0.569459	−	0.413736i
$117$	−0.721069	+	2.21922i	−0.0666628	+	0.205167i
$118$	1.64590	+	5.06555i	0.151517	+	0.466322i
$119$	−18.7387	+	13.6144i	−1.71777	+	1.24803i
$120$	1.00000			0.0912871
$121$	10.5791	+	3.01362i	0.961740	+	0.273965i
$122$	−15.4541			−1.39914
$123$	−7.74225	+	5.62508i	−0.698096	+	0.507196i
$124$	−0.342697	−	1.05471i	−0.0307751	−	0.0947161i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−3.63326	−	2.63972i	−0.323677	−	0.235165i
$127$	6.76615	+	4.91590i	0.600399	+	0.436215i	0.846020	−	0.533150i	$-0.178992\pi$
$127$	6.76615	+	4.91590i	0.600399	+	0.436215i	−0.245621	+	0.969366i	$0.578992\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−0.0242693	−	0.0746932i	−0.00213679	−	0.00657637i
$130$	1.88778	−	1.37155i	0.165569	−	0.120293i
$131$	7.40079			0.646610			0.323305	−	0.946295i	$-0.395206\pi$
$131$	7.40079			0.646610			0.323305	+	0.946295i	$0.395206\pi$
$132$	3.28475	+	0.458729i	0.285901	+	0.0399273i
$133$	26.9980			2.34102
$134$	−1.35770	+	0.986424i	−0.117287	+	0.0852141i
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$	1.59376	−	4.90510i	0.136664	−	0.420609i
$137$	3.59376	+	2.61102i	0.307036	+	0.223075i	0.730624	−	0.682780i	$-0.239229\pi$
$137$	3.59376	+	2.61102i	0.307036	+	0.223075i	−0.423588	+	0.905855i	$0.639229\pi$
$138$	−7.18776	−	5.22221i	−0.611863	−	0.444544i
$139$	6.15171	−	18.9330i	0.521782	−	1.60588i	−0.248812	−	0.968552i	$-0.580040\pi$
$139$	6.15171	−	18.9330i	0.521782	−	1.60588i	0.770594	−	0.637327i	$-0.219960\pi$
$140$	1.38778	+	4.27116i	0.117289	+	0.360979i
$141$	−2.34829	+	1.70613i	−0.197761	+	0.143682i
$142$	−9.55113			−0.801513
$143$	6.83006	−	3.63923i	0.571158	−	0.304328i
$144$	1.00000			0.0833333
$145$	6.13326	−	4.45608i	0.509340	−	0.370057i
$146$	−3.38197	−	10.4086i	−0.279893	−	0.861424i
$147$	4.06935	−	12.5242i	0.335635	−	1.03298i
$148$	−6.41801	−	4.66296i	−0.527557	−	0.383293i
$149$	7.53567	+	5.47499i	0.617346	+	0.448528i	0.851994	−	0.523552i	$-0.175393\pi$
$149$	7.53567	+	5.47499i	0.617346	+	0.448528i	−0.234647	+	0.972081i	$0.575393\pi$
$150$	−0.309017	+	0.951057i	−0.0252311	+	0.0776534i
$151$	4.29624	+	13.2225i	0.349623	+	1.07603i	0.959062	+	0.283196i	$0.0913947\pi$
$151$	4.29624	+	13.2225i	0.349623	+	1.07603i	−0.609439	+	0.792833i	$0.708605\pi$
$152$	−4.86351	+	3.53355i	−0.394483	+	0.286609i
$153$	−5.15753			−0.416962
$154$	2.59921	+	14.6663i	0.209450	+	1.18184i
$155$	1.10899			0.0890764
$156$	1.88778	−	1.37155i	0.151144	−	0.109812i
$157$	3.05672	+	9.40761i	0.243953	+	0.750809i	0.995807	+	0.0914797i	$0.0291597\pi$
$157$	3.05672	+	9.40761i	0.243953	+	0.750809i	−0.751854	+	0.659329i	$0.770840\pi$
$158$	1.69112	−	5.20475i	0.134539	−	0.414067i
$159$	−0.602806	−	0.437964i	−0.0478057	−	0.0347328i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	12.3298	−	37.9473i	0.971727	−	2.99067i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−5.20299	+	3.78019i	−0.407529	+	0.296087i	−0.772601	−	0.634892i	$-0.781045\pi$
$163$	−5.20299	+	3.78019i	−0.407529	+	0.296087i	0.365072	+	0.930979i	$0.381045\pi$
$164$	9.56995			0.747288
$165$	−1.45132	+	2.98223i	−0.112985	+	0.232166i
$166$	8.00000			0.620920
$167$	4.88778	−	3.55118i	0.378228	−	0.274799i	−0.382387	−	0.924002i	$-0.624898\pi$
$167$	4.88778	−	3.55118i	0.378228	−	0.274799i	0.760615	+	0.649204i	$0.224898\pi$
$168$	1.38778	+	4.27116i	0.107070	+	0.329527i
$169$	−2.33466	+	7.18534i	−0.179589	+	0.552719i
$170$	4.17253	+	3.03152i	0.320018	+	0.232507i
$171$	4.86351	+	3.53355i	0.371922	+	0.270217i
$172$	−0.0242693	+	0.0746932i	−0.00185052	+	0.00569530i
$173$	0.200253	+	0.616316i	0.0152250	+	0.0468576i	0.958380	−	0.285494i	$-0.0921578\pi$
$173$	0.200253	+	0.616316i	0.0152250	+	0.0468576i	−0.943155	+	0.332352i	$0.892158\pi$
$174$	6.13326	−	4.45608i	0.464961	−	0.337814i
$175$	−4.49096			−0.339485
$176$	−2.38778	−	2.30185i	−0.179986	−	0.173508i
$177$	−5.32624			−0.400345
$178$	−5.99641	+	4.35664i	−0.449450	+	0.326544i
$179$	0.482779	+	1.48584i	0.0360846	+	0.111057i	0.967476	−	0.252961i	$-0.0814045\pi$
$179$	0.482779	+	1.48584i	0.0360846	+	0.111057i	−0.931392	+	0.364018i	$0.881405\pi$
$180$	−0.309017	+	0.951057i	−0.0230328	+	0.0708876i
$181$	−14.9443	−	10.8576i	−1.11080	−	0.807043i	−0.128010	−	0.991773i	$-0.540859\pi$
$181$	−14.9443	−	10.8576i	−1.11080	−	0.807043i	−0.982789	+	0.184730i	$0.940859\pi$
$182$	8.47795	+	6.15959i	0.628428	+	0.456579i
$183$	4.77556	−	14.6977i	0.353020	−	1.08648i
$184$	2.74548	+	8.44972i	0.202399	+	0.622921i
$185$	6.41801	−	4.66296i	0.471861	−	0.342827i
$186$	1.10899			0.0813153
$187$	12.3151	+	11.8718i	0.900567	+	0.868155i
$188$	2.90264			0.211697
$189$	3.63326	−	2.63972i	0.264281	−	0.192011i
$190$	−1.85770	−	5.71740i	−0.134771	−	0.414784i
$191$	−5.46096	+	16.8071i	−0.395141	+	1.21612i	0.533710	+	0.845667i	$0.320797\pi$
$191$	−5.46096	+	16.8071i	−0.395141	+	1.21612i	−0.928852	+	0.370452i	$0.879203\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	8.49096	+	6.16904i	0.611193	+	0.444057i	0.849834	−	0.527050i	$-0.176702\pi$
$193$	8.49096	+	6.16904i	0.611193	+	0.444057i	−0.238642	+	0.971108i	$0.576702\pi$
$194$	−1.77556	+	5.46463i	−0.127478	+	0.392337i
$195$	0.721069	+	2.21922i	0.0516368	+	0.158922i
$196$	−10.6537	+	7.74037i	−0.760979	+	0.552884i
$197$	−10.0788			−0.718086			−0.359043	−	0.933321i	$-0.616897\pi$
$197$	−10.0788			−0.718086			−0.359043	+	0.933321i	$0.616897\pi$
$198$	−1.45132	+	2.98223i	−0.103141	+	0.211938i
$199$	−13.6906			−0.970499			−0.485250	−	0.874376i	$-0.661271\pi$
$199$	−13.6906			−0.970499			−0.485250	+	0.874376i	$0.661271\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	−0.518594	−	1.59607i	−0.0365788	−	0.112578i
$202$	5.12163	−	15.7628i	0.360357	−	1.10906i
$203$	27.5442	+	20.0120i	1.93323	+	1.40457i
$204$	4.17253	+	3.03152i	0.292136	+	0.212249i
$205$	−2.95728	+	9.10157i	−0.206545	+	0.635681i
$206$	0.337022	+	1.03725i	0.0234814	+	0.0722685i
$207$	7.18776	−	5.22221i	0.499584	−	0.362969i
$208$	−2.33343			−0.161794
$209$	−3.47933	−	19.6324i	−0.240670	−	1.35800i
$210$	−4.49096			−0.309906
$211$	−18.4845	+	13.4298i	−1.27253	+	0.924544i	−0.999300	−	0.0374057i	$-0.988091\pi$
$211$	−18.4845	+	13.4298i	−1.27253	+	0.924544i	−0.273226	+	0.961950i	$0.588091\pi$
$212$	0.230252	+	0.708641i	0.0158137	+	0.0486697i
$213$	2.95146	−	9.08366i	0.202231	−	0.622402i
$214$	4.59921	+	3.34152i	0.314396	+	0.228422i
$215$	−0.0635378	−	0.0461629i	−0.00433324	−	0.00314829i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	1.53904	+	4.73668i	0.104477	+	0.321547i
$218$	−7.23607	+	5.25731i	−0.490088	+	0.356070i
$219$	10.9443			0.739545
$220$	2.92705	−	1.55961i	0.197342	−	0.105149i
$221$	12.0347			0.809543
$222$	6.41801	−	4.66296i	0.430749	−	0.312957i
$223$	−0.151714	−	0.466929i	−0.0101596	−	0.0312679i	0.945848	−	0.324609i	$-0.105233\pi$
$223$	−0.151714	−	0.466929i	−0.0101596	−	0.0312679i	−0.956008	+	0.293341i	$0.905233\pi$
$224$	1.38778	−	4.27116i	0.0927251	−	0.285379i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	3.13326	+	2.27645i	0.208421	+	0.151427i
$227$	0.460503	−	1.41728i	0.0305647	−	0.0940684i	−0.934610	−	0.355673i	$-0.884252\pi$
$227$	0.460503	−	1.41728i	0.0305647	−	0.0940684i	0.965175	+	0.261605i	$0.0842517\pi$
$228$	−1.85770	−	5.71740i	−0.123029	−	0.378644i
$229$	6.64849	−	4.83041i	0.439345	−	0.319202i	−0.346030	−	0.938223i	$-0.612470\pi$
$229$	6.64849	−	4.83041i	0.439345	−	0.319202i	0.785374	+	0.619021i	$0.212470\pi$
$230$	−8.88456			−0.585830
$231$	−14.7517	−	2.06013i	−0.970588	−	0.135547i
$232$	−7.58113			−0.497725
$233$	−5.36933	+	3.90105i	−0.351756	+	0.255566i	−0.749606	−	0.661885i	$-0.769757\pi$
$233$	−5.36933	+	3.90105i	−0.351756	+	0.255566i	0.397849	+	0.917451i	$0.369757\pi$
$234$	0.721069	+	2.21922i	0.0471377	+	0.145075i
$235$	−0.896965	+	2.76058i	−0.0585116	+	0.180080i
$236$	4.30902	+	3.13068i	0.280493	+	0.203790i
$237$	4.42742	+	3.21671i	0.287592	+	0.208948i
$238$	−7.15753	+	22.0286i	−0.463954	+	1.42790i
$239$	−1.88427	−	5.79920i	−0.121884	−	0.375119i	0.871437	−	0.490508i	$-0.163189\pi$
$239$	−1.88427	−	5.79920i	−0.121884	−	0.375119i	−0.993320	+	0.115389i	$0.963189\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	5.70376			0.367412			0.183706	−	0.982981i	$-0.441191\pi$
$241$	5.70376			0.367412			0.183706	+	0.982981i	$0.441191\pi$
$242$	10.3301	−	3.78019i	0.664041	−	0.243000i
$243$	1.00000			0.0641500
$244$	−12.5026	+	9.08366i	−0.800396	+	0.581522i
$245$	−4.06935	−	12.5242i	−0.259982	−	0.800141i
$246$	−2.95728	+	9.10157i	−0.188549	+	0.580295i
$247$	−11.3487	−	8.24528i	−0.722098	−	0.524635i
$248$	−0.897194	−	0.651849i	−0.0569719	−	0.0413925i
$249$	−2.47214	+	7.60845i	−0.156665	+	0.482166i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	2.10922	−	1.53244i	0.133133	−	0.0967267i	−0.519226	−	0.854637i	$-0.673780\pi$
$251$	2.10922	−	1.53244i	0.133133	−	0.0967267i	0.652359	+	0.757910i	$0.273780\pi$
$252$	−4.49096			−0.282904
$253$	−29.1835	−	4.07561i	−1.83475	−	0.256231i
$254$	8.36343			0.524768
$255$	−4.17253	+	3.03152i	−0.261294	+	0.189841i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	5.69703	−	17.5336i	0.355371	−	1.09372i	−0.600423	−	0.799682i	$-0.705001\pi$
$257$	5.69703	−	17.5336i	0.355371	−	1.09372i	0.955794	−	0.294037i	$-0.0949988\pi$
$258$	−0.0635378	−	0.0461629i	−0.00395569	−	0.00287398i
$259$	28.8230	+	20.9411i	1.79097	+	1.30122i
$260$	0.721069	−	2.21922i	0.0447188	−	0.137630i
$261$	2.34270	+	7.21008i	0.145009	+	0.446293i
$262$	5.98736	−	4.35007i	0.369901	−	0.268748i
$263$	−24.4285			−1.50633			−0.753163	−	0.657834i	$-0.771473\pi$
$263$	−24.4285			−1.50633			−0.753163	+	0.657834i	$0.771473\pi$
$264$	2.92705	−	1.55961i	0.180148	−	0.0959871i
$265$	−0.745110			−0.0457717
$266$	21.8418	−	15.8690i	1.33921	−	0.972992i
$267$	−2.29042	−	7.04920i	−0.140172	−	0.431404i
$268$	−0.518594	+	1.59607i	−0.0316782	+	0.0974954i
$269$	8.90883	+	6.47264i	0.543181	+	0.394644i	0.825265	−	0.564746i	$-0.191026\pi$
$269$	8.90883	+	6.47264i	0.543181	+	0.394644i	−0.282084	+	0.959390i	$0.591026\pi$
$270$	−0.809017	−	0.587785i	−0.0492352	−	0.0357715i
$271$	−0.200166	+	0.616047i	−0.0121592	+	0.0374222i	−0.956952	−	0.290246i	$-0.906263\pi$
$271$	−0.200166	+	0.616047i	−0.0121592	+	0.0374222i	0.944793	+	0.327668i	$0.106263\pi$
$272$	−1.59376	−	4.90510i	−0.0966362	−	0.297416i
$273$	−8.47795	+	6.15959i	−0.513109	+	0.372796i
$274$	4.44214			0.268359
$275$	0.578765	+	3.26574i	0.0349009	+	0.196931i
$276$	−8.88456			−0.534788
$277$	−19.9264	+	14.4774i	−1.19726	+	0.869862i	−0.994013	−	0.109265i	$-0.965150\pi$
$277$	−19.9264	+	14.4774i	−1.19726	+	0.869862i	−0.203250	+	0.979127i	$0.565150\pi$
$278$	−6.15171	−	18.9330i	−0.368955	−	1.13553i
$279$	−0.342697	+	1.05471i	−0.0205168	+	0.0631441i
$280$	3.63326	+	2.63972i	0.217129	+	0.157753i
$281$	7.67894	+	5.57908i	0.458087	+	0.332820i	0.792781	−	0.609507i	$-0.208633\pi$
$281$	7.67894	+	5.57908i	0.458087	+	0.332820i	−0.334693	+	0.942327i	$0.608633\pi$
$282$	−0.896965	+	2.76058i	−0.0534135	+	0.164390i
$283$	6.24562	+	19.2220i	0.371264	+	1.14263i	0.945965	+	0.324269i	$0.105118\pi$
$283$	6.24562	+	19.2220i	0.371264	+	1.14263i	−0.574701	+	0.818363i	$0.694882\pi$
$284$	−7.72703	+	5.61401i	−0.458515	+	0.333130i
$285$	6.01163			0.356098
$286$	3.38655	−	6.95881i	0.200251	−	0.411483i
$287$	−42.9783			−2.53693
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	2.96660	+	9.13026i	0.174506	+	0.537074i
$290$	2.34270	−	7.21008i	0.137568	−	0.423391i
$291$	−4.64849	−	3.37733i	−0.272499	−	0.197982i
$292$	−8.85410	−	6.43288i	−0.518147	−	0.376456i
$293$	0.368960	−	1.13554i	0.0215549	−	0.0663391i	−0.939700	−	0.341999i	$-0.888896\pi$
$293$	0.368960	−	1.13554i	0.0215549	−	0.0663391i	0.961255	+	0.275659i	$0.0888962\pi$
$294$	−4.06935	−	12.5242i	−0.237330	−	0.730425i
$295$	−4.30902	+	3.13068i	−0.250881	+	0.182275i
$296$	−7.93310			−0.461102
$297$	−2.38778	−	2.30185i	−0.138553	−	0.133567i
$298$	9.31461			0.539581
$299$	−16.7721	+	12.1857i	−0.969956	+	0.704714i
$300$	0.309017	+	0.951057i	0.0178411	+	0.0549093i
$301$	0.108992	−	0.335444i	0.00628221	−	0.0193347i
$302$	11.2477	+	8.17193i	0.647232	+	0.470242i
$303$	13.4086	+	9.74192i	0.770304	+	0.559658i
$304$	−1.85770	+	5.71740i	−0.106546	+	0.327916i
$305$	−4.77556	−	14.6977i	−0.273448	−	0.841587i
$306$	−4.17253	+	3.03152i	−0.238528	+	0.173300i
$307$	11.3502			0.647793			0.323896	−	0.946093i	$-0.395007\pi$
$307$	11.3502			0.647793			0.323896	+	0.946093i	$0.395007\pi$
$308$	10.7234	+	10.3375i	0.611024	+	0.589033i
$309$	−1.09063			−0.0620436
$310$	0.897194	−	0.651849i	0.0509572	−	0.0370226i
$311$	−4.68984	−	14.4338i	−0.265936	−	0.818468i	−0.991476	−	0.130288i	$-0.958410\pi$
$311$	−4.68984	−	14.4338i	−0.265936	−	0.818468i	0.725540	−	0.688180i	$-0.241590\pi$
$312$	0.721069	−	2.21922i	0.0408225	−	0.125639i
$313$	−18.8962	−	13.7289i	−1.06808	−	0.776003i	−0.0925104	−	0.995712i	$-0.529489\pi$
$313$	−18.8962	−	13.7289i	−1.06808	−	0.776003i	−0.975565	+	0.219709i	$0.929489\pi$
$314$	8.00259	+	5.81422i	0.451612	+	0.328116i
$315$	1.38778	−	4.27116i	0.0781927	−	0.240652i
$316$	−1.69112	−	5.20475i	−0.0951332	−	0.292790i
$317$	−8.62745	+	6.26821i	−0.484566	+	0.352058i	−0.803091	−	0.595857i	$-0.796813\pi$
$317$	−8.62745	+	6.26821i	−0.484566	+	0.352058i	0.318525	+	0.947914i	$0.396813\pi$
$318$	−0.745110			−0.0417837
$319$	11.0026	−	22.6086i	0.616030	−	1.26584i
$320$	−1.00000			−0.0559017
$321$	−4.59921	+	3.34152i	−0.256703	+	0.186506i
$322$	−12.3298	−	37.9473i	−0.687115	−	2.11472i
$323$	9.58113	−	29.4877i	0.533108	−	1.64074i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	1.88778	+	1.37155i	0.104715	+	0.0760801i
$326$	−1.98736	+	6.11648i	−0.110070	+	0.338760i
$327$	−2.76393	−	8.50651i	−0.152846	−	0.470411i
$328$	7.74225	−	5.62508i	0.427494	−	0.310593i
$329$	−13.0356			−0.718678
$330$	0.578765	+	3.26574i	0.0318600	+	0.179773i
$331$	−2.42434			−0.133254			−0.0666268	−	0.997778i	$-0.521224\pi$
$331$	−2.42434			−0.133254			−0.0666268	+	0.997778i	$0.521224\pi$
$332$	6.47214	−	4.70228i	0.355205	−	0.258071i
$333$	2.45146	+	7.54482i	0.134339	+	0.413454i
$334$	1.86697	−	5.74593i	0.102156	−	0.314403i
$335$	−1.35770	−	0.986424i	−0.0741789	−	0.0538941i
$336$	3.63326	+	2.63972i	0.198211	+	0.144008i
$337$	0.363600	−	1.11905i	0.0198066	−	0.0609584i	−0.940665	−	0.339337i	$-0.889797\pi$
$337$	0.363600	−	1.11905i	0.0198066	−	0.0609584i	0.960471	+	0.278379i	$0.0897971\pi$
$338$	2.33466	+	7.18534i	0.126989	+	0.390831i
$339$	−3.13326	+	2.27645i	−0.170175	+	0.123640i
$340$	5.15753			0.279706
$341$	3.24608	−	1.72959i	0.175785	−	0.0936626i
$342$	6.01163			0.325072
$343$	22.4125	−	16.2837i	1.21016	−	0.879235i
$344$	0.0242693	+	0.0746932i	0.00130851	+	0.00402719i
$345$	2.74548	−	8.44972i	0.147812	−	0.454917i
$346$	0.524269	+	0.380904i	0.0281849	+	0.0204775i
$347$	−18.8962	−	13.7289i	−1.01440	−	0.737005i	−0.0492731	−	0.998785i	$-0.515690\pi$
$347$	−18.8962	−	13.7289i	−1.01440	−	0.737005i	−0.965128	+	0.261780i	$0.915690\pi$
$348$	2.34270	−	7.21008i	0.125582	−	0.386501i
$349$	0.115900	+	0.356702i	0.00620396	+	0.0190938i	0.954111	−	0.299455i	$-0.0968047\pi$
$349$	0.115900	+	0.356702i	0.00620396	+	0.0190938i	−0.947907	+	0.318548i	$0.896805\pi$
$350$	−3.63326	+	2.63972i	−0.194206	+	0.141099i
$351$	−2.33343			−0.124549
$352$	−3.28475	−	0.458729i	−0.175078	−	0.0244503i
$353$	2.07854			0.110629			0.0553147	−	0.998469i	$-0.482384\pi$
$353$	2.07854			0.110629			0.0553147	+	0.998469i	$0.482384\pi$
$354$	−4.30902	+	3.13068i	−0.229022	+	0.166394i
$355$	−2.95146	−	9.08366i	−0.156647	−	0.482111i
$356$	−2.29042	+	7.04920i	−0.121392	+	0.373607i
$357$	−18.7387	−	13.6144i	−0.991755	−	0.720552i
$358$	1.26393	+	0.918300i	0.0668009	+	0.0485337i
$359$	−0.0557281	+	0.171513i	−0.00294122	+	0.00905213i	−0.952516	−	0.304487i	$-0.901515\pi$
$359$	−0.0557281	+	0.171513i	−0.00294122	+	0.00905213i	0.949575	+	0.313540i	$0.101515\pi$
$360$	0.309017	+	0.951057i	0.0162866	+	0.0501251i
$361$	−13.8663	+	10.0745i	−0.729807	+	0.530236i
$362$	−18.4721			−0.970874
$363$	0.403010	+	10.9926i	0.0211525	+	0.576963i
$364$	10.4793			0.549266
$365$	8.85410	−	6.43288i	0.463445	−	0.336712i
$366$	−4.77556	−	14.6977i	−0.249623	−	0.768260i
$367$	3.60640	−	11.0994i	0.188253	−	0.579382i	−0.811737	−	0.584024i	$-0.801478\pi$
$367$	3.60640	−	11.0994i	0.188253	−	0.579382i	0.999989	+	0.00464173i	$0.00147752\pi$
$368$	7.18776	+	5.22221i	0.374688	+	0.272227i
$369$	−7.74225	−	5.62508i	−0.403046	−	0.292830i
$370$	2.45146	−	7.54482i	0.127445	−	0.392237i
$371$	−1.03405	−	3.18248i	−0.0536852	−	0.165226i
$372$	0.897194	−	0.651849i	0.0465173	−	0.0337968i
$373$	10.1687			0.526516			0.263258	−	0.964726i	$-0.415203\pi$
$373$	10.1687			0.526516			0.263258	+	0.964726i	$0.415203\pi$
$374$	16.9412	+	2.36591i	0.876008	+	0.122338i
$375$	−1.00000			−0.0516398
$376$	2.34829	−	1.70613i	0.121104	−	0.0879869i
$377$	−5.46651	−	16.8242i	−0.281540	−	0.866490i
$378$	1.38778	−	4.27116i	0.0713798	−	0.219685i
$379$	−8.96595	−	6.51414i	−0.460550	−	0.334609i	0.333197	−	0.942857i	$-0.391873\pi$
$379$	−8.96595	−	6.51414i	−0.460550	−	0.334609i	−0.793747	+	0.608248i	$0.791873\pi$
$380$	−4.86351	−	3.53355i	−0.249493	−	0.181267i
$381$	−2.58444	+	7.95409i	−0.132405	+	0.407500i
$382$	5.46096	+	16.8071i	0.279407	+	0.859926i
$383$	−17.2387	+	12.5246i	−0.880854	+	0.639978i	−0.933477	−	0.358636i	$-0.883242\pi$
$383$	−17.2387	+	12.5246i	−0.880854	+	0.639978i	0.0526230	+	0.998614i	$0.483242\pi$
$384$	−1.00000			−0.0510310
$385$	−13.1453	+	7.00413i	−0.669945	+	0.356963i
$386$	10.4954			0.534202
$387$	0.0635378	−	0.0461629i	0.00322981	−	0.00234659i
$388$	1.77556	+	5.46463i	0.0901407	+	0.277424i
$389$	−11.6611	+	35.8893i	−0.591243	+	1.81966i	−0.0186372	+	0.999826i	$0.505933\pi$
$389$	−11.6611	+	35.8893i	−0.591243	+	1.81966i	−0.572605	+	0.819831i	$0.694067\pi$
$390$	1.88778	+	1.37155i	0.0955916	+	0.0694513i
$391$	−37.0711	−	26.9337i	−1.87477	−	1.36210i
$392$	−4.06935	+	12.5242i	−0.205533	+	0.632567i
$393$	2.28697	+	7.03857i	0.115362	+	0.355049i
$394$	−8.15394	+	5.92418i	−0.410789	+	0.298456i
$395$	5.47259			0.275356
$396$	0.578765	+	3.26574i	0.0290841	+	0.164109i
$397$	−22.4348			−1.12597			−0.562985	−	0.826467i	$-0.690347\pi$
$397$	−22.4348			−1.12597			−0.562985	+	0.826467i	$0.690347\pi$
$398$	−11.0759	+	8.04712i	−0.555185	+	0.403366i
$399$	8.34284	+	25.6766i	0.417664	+	1.28544i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	20.9537	+	15.2237i	1.04638	+	0.760237i	0.971520	−	0.236957i	$-0.0761500\pi$
$401$	20.9537	+	15.2237i	1.04638	+	0.760237i	0.0748568	+	0.997194i	$0.476150\pi$
$402$	−1.35770	−	0.986424i	−0.0677158	−	0.0491984i
$403$	0.799660	−	2.46110i	0.0398339	−	0.122596i
$404$	−5.12163	−	15.7628i	−0.254811	−	0.784226i
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	34.0465			1.68970
$407$	11.5135	−	23.6583i	0.570701	−	1.17270i
$408$	5.15753			0.255336
$409$	−20.0572	+	14.5724i	−0.991766	+	0.720560i	−0.960307	−	0.278945i	$-0.910015\pi$
$409$	−20.0572	+	14.5724i	−0.991766	+	0.720560i	−0.0314590	+	0.999505i	$0.510015\pi$
$410$	2.95728	+	9.10157i	0.146050	+	0.449494i
$411$	−1.37270	+	4.22472i	−0.0677101	+	0.208390i
$412$	0.882336	+	0.641054i	0.0434696	+	0.0315825i
$413$	−19.3516	−	14.0598i	−0.952231	−	0.691836i
$414$	2.74548	−	8.44972i	0.134933	−	0.415281i
$415$	2.47214	+	7.60845i	0.121352	+	0.373484i
$416$	−1.88778	+	1.37155i	−0.0925561	+	0.0672460i
$417$	19.9074			0.974868
$418$	−14.3545	−	13.8379i	−0.702100	−	0.676832i
$419$	27.8969			1.36285			0.681427	−	0.731886i	$-0.261360\pi$
$419$	27.8969			1.36285			0.681427	+	0.731886i	$0.261360\pi$
$420$	−3.63326	+	2.63972i	−0.177285	+	0.128805i
$421$	7.72703	+	23.7813i	0.376592	+	1.15903i	0.942398	+	0.334493i	$0.108565\pi$
$421$	7.72703	+	23.7813i	0.376592	+	1.15903i	−0.565806	+	0.824538i	$0.691435\pi$
$422$	−7.06045	+	21.7298i	−0.343698	+	1.05779i
$423$	−2.34829	−	1.70613i	−0.114178	−	0.0829548i
$424$	0.602806	+	0.437964i	0.0292749	+	0.0212694i
$425$	−1.59376	+	4.90510i	−0.0773089	+	0.237932i
$426$	−2.95146	−	9.08366i	−0.142999	−	0.440105i
$427$	56.1486	−	40.7944i	2.71722	−	1.97418i
$428$	5.68494			0.274792
$429$	5.57172	+	5.37119i	0.269005	+	0.259324i
$430$	−0.0785371			−0.00378739
$431$	−14.5319	+	10.5580i	−0.699975	+	0.508561i	−0.879924	−	0.475115i	$-0.842407\pi$
$431$	−14.5319	+	10.5580i	−0.699975	+	0.508561i	0.179949	+	0.983676i	$0.442407\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−8.32669	+	25.6269i	−0.400155	+	1.23155i	0.524718	+	0.851276i	$0.324171\pi$
$433$	−8.32669	+	25.6269i	−0.400155	+	1.23155i	−0.924873	+	0.380276i	$0.875829\pi$
$434$	4.02926	+	2.92743i	0.193411	+	0.140521i
$435$	6.13326	+	4.45608i	0.294067	+	0.213652i
$436$	−2.76393	+	8.50651i	−0.132368	+	0.407388i
$437$	16.5048	+	50.7966i	0.789532	+	2.42993i
$438$	8.85410	−	6.43288i	0.423065	−	0.307375i
$439$	4.79393			0.228802			0.114401	−	0.993435i	$-0.463505\pi$
$439$	4.79393			0.228802			0.114401	+	0.993435i	$0.463505\pi$
$440$	1.45132	−	2.98223i	0.0691890	−	0.142172i
$441$	13.1687			0.627081
$442$	9.73630	−	7.07383i	0.463108	−	0.336468i
$443$	3.10871	+	9.56763i	0.147699	+	0.454572i	0.997348	−	0.0727771i	$-0.0231862\pi$
$443$	3.10871	+	9.56763i	0.147699	+	0.454572i	−0.849649	+	0.527349i	$0.823186\pi$
$444$	2.45146	−	7.54482i	0.116341	−	0.358061i
$445$	−5.99641	−	4.35664i	−0.284257	−	0.206525i
$446$	−0.397194	−	0.288578i	−0.0188077	−	0.0136646i
$447$	−2.87837	+	8.85872i	−0.136142	+	0.419003i
$448$	−1.38778	−	4.27116i	−0.0655666	−	0.201793i
$449$	0.403010	−	0.292804i	0.0190192	−	0.0138183i	−0.578235	−	0.815870i	$-0.696258\pi$
$449$	0.403010	−	0.292804i	0.0190192	−	0.0138183i	0.597254	+	0.802052i	$0.296258\pi$
$450$	−1.00000			−0.0471405
$451$	5.53876	+	31.2529i	0.260810	+	1.47164i
$452$	3.87292			0.182167
$453$	−11.2477	+	8.17193i	−0.528463	+	0.383951i
$454$	−0.460503	−	1.41728i	−0.0216125	−	0.0665164i
$455$	−3.23829	+	9.96643i	−0.151813	+	0.467233i
$456$	−4.86351	−	3.53355i	−0.227755	−	0.165474i
$457$	−1.50259	−	1.09170i	−0.0702883	−	0.0510674i	0.552086	−	0.833787i	$-0.313832\pi$
$457$	−1.50259	−	1.09170i	−0.0702883	−	0.0510674i	−0.622375	+	0.782720i	$0.713832\pi$
$458$	2.53950	−	7.81577i	0.118663	−	0.365207i
$459$	−1.59376	−	4.90510i	−0.0743906	−	0.228951i
$460$	−7.18776	+	5.22221i	−0.335131	+	0.243487i
$461$	22.1394			1.03114			0.515568	−	0.856848i	$-0.327581\pi$
$461$	22.1394			1.03114			0.515568	+	0.856848i	$0.327581\pi$
$462$	−13.1453	+	7.00413i	−0.611573	+	0.325862i
$463$	−22.1920			−1.03135			−0.515674	−	0.856785i	$-0.672459\pi$
$463$	−22.1920			−1.03135			−0.515674	+	0.856785i	$0.672459\pi$
$464$	−6.13326	+	4.45608i	−0.284730	+	0.206868i
$465$	0.342697	+	1.05471i	0.0158922	+	0.0489112i
$466$	−2.05090	+	6.31203i	−0.0950062	+	0.292399i
$467$	−25.6420	−	18.6300i	−1.18657	−	0.862095i	−0.193674	−	0.981066i	$-0.562041\pi$
$467$	−25.6420	−	18.6300i	−1.18657	−	0.862095i	−0.992898	+	0.118971i	$0.962041\pi$
$468$	1.88778	+	1.37155i	0.0872628	+	0.0634001i
$469$	2.32898	−	7.16788i	0.107542	−	0.330982i
$470$	0.896965	+	2.76058i	0.0413739	+	0.127336i
$471$	−8.00259	+	5.81422i	−0.368740	+	0.267905i
$472$	5.32624			0.245160
$473$	−0.257974	−	0.0360272i	−0.0118617	−	0.00165653i
$474$	5.47259			0.251365
$475$	4.86351	−	3.53355i	0.223153	−	0.162130i
$476$	7.15753	+	22.0286i	0.328065	+	1.00968i
$477$	0.230252	−	0.708641i	0.0105425	−	0.0324465i
$478$	−4.93310	−	3.58410i	−0.225635	−	0.163933i
$479$	18.7867	+	13.6494i	0.858388	+	0.623655i	0.927446	−	0.373957i	$-0.121999\pi$
$479$	18.7867	+	13.6494i	0.858388	+	0.623655i	−0.0690579	+	0.997613i	$0.521999\pi$
$480$	0.309017	−	0.951057i	0.0141046	−	0.0434096i
$481$	−5.72031	−	17.6053i	−0.260824	−	0.802732i
$482$	4.61444	−	3.35259i	0.210182	−	0.152706i
$483$	39.9002			1.81552
$484$	6.13525	−	9.13010i	0.278875	−	0.415004i
$485$	−5.74585			−0.260906
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−12.0233	−	37.0038i	−0.544826	−	1.67680i	−0.721403	−	0.692516i	$-0.756502\pi$
$487$	−12.0233	−	37.0038i	−0.544826	−	1.67680i	0.176577	−	0.984287i	$-0.443498\pi$
$488$	−4.77556	+	14.6977i	−0.216180	+	0.665333i
$489$	−5.20299	−	3.78019i	−0.235287	−	0.170946i
$490$	−10.6537	−	7.74037i	−0.481285	−	0.349674i
$491$	1.44045	−	4.43325i	0.0650065	−	0.200070i	−0.913278	−	0.407338i	$-0.866457\pi$
$491$	1.44045	−	4.43325i	0.0650065	−	0.200070i	0.978284	+	0.207268i	$0.0664572\pi$
$492$	2.95728	+	9.10157i	0.133324	+	0.410330i
$493$	31.6325	−	22.9823i	1.42466	−	1.03507i
$494$	−14.0277			−0.631136
$495$	−3.28475	−	0.458729i	−0.147638	−	0.0206183i
$496$	−1.10899			−0.0497952
$497$	34.7018	−	25.2123i	1.55659	−	1.13093i
$498$	2.47214	+	7.60845i	0.110779	+	0.340943i
$499$	5.06581	−	15.5910i	0.226777	−	0.697948i	−0.771329	−	0.636436i	$-0.780408\pi$
$499$	5.06581	−	15.5910i	0.226777	−	0.697948i	0.998106	−	0.0615116i	$-0.0195921\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	4.88778	+	3.55118i	0.218370	+	0.158655i
$502$	0.805651	−	2.47954i	0.0359579	−	0.110667i
$503$	−0.211570	−	0.651146i	−0.00943345	−	0.0290332i	0.946229	−	0.323498i	$-0.104859\pi$
$503$	−0.211570	−	0.651146i	−0.00943345	−	0.0290332i	−0.955662	+	0.294464i	$0.904859\pi$
$504$	−3.63326	+	2.63972i	−0.161838	+	0.117582i
$505$	16.5739			0.737531
$506$	−26.0056	+	13.8564i	−1.15609	+	0.615993i
$507$	−7.55512			−0.335534
$508$	6.76615	−	4.91590i	0.300200	−	0.218108i
$509$	1.66421	+	5.12191i	0.0737648	+	0.227025i	0.981141	−	0.193296i	$-0.0619177\pi$
$509$	1.66421	+	5.12191i	0.0737648	+	0.227025i	−0.907376	+	0.420320i	$0.861918\pi$
$510$	−1.59376	+	4.90510i	−0.0705731	+	0.217202i
$511$	39.7634	+	28.8898i	1.75903	+	1.27801i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−1.85770	+	5.71740i	−0.0820193	+	0.252429i
$514$	−5.69703	−	17.5336i	−0.251285	−	0.773376i
$515$	−0.882336	+	0.641054i	−0.0388804	+	0.0282482i
$516$	−0.0785371			−0.00345740
$517$	1.67995	+	9.47926i	0.0738840	+	0.416897i
$518$	35.6272			1.56537
$519$	−0.524269	+	0.380904i	−0.0230129	+	0.0167198i
$520$	−0.721069	−	2.21922i	−0.0316210	−	0.0973193i
$521$	2.35059	−	7.23439i	0.102981	−	0.316944i	−0.886270	−	0.463169i	$-0.846712\pi$
$521$	2.35059	−	7.23439i	0.102981	−	0.316944i	0.989251	+	0.146225i	$0.0467123\pi$
$522$	6.13326	+	4.45608i	0.268446	+	0.195037i
$523$	4.54024	+	3.29867i	0.198531	+	0.144241i	0.682609	−	0.730784i	$-0.260845\pi$
$523$	4.54024	+	3.29867i	0.198531	+	0.144241i	−0.484079	+	0.875025i	$0.660845\pi$
$524$	2.28697	−	7.03857i	0.0999067	−	0.307481i
$525$	−1.38778	−	4.27116i	−0.0605678	−	0.186408i
$526$	−19.7631	+	14.3587i	−0.861711	+	0.626070i
$527$	5.71966			0.249152
$528$	1.45132	−	2.98223i	0.0631606	−	0.129785i
$529$	55.9354			2.43197
$530$	−0.602806	+	0.437964i	−0.0261842	+	0.0190240i
$531$	−1.64590	−	5.06555i	−0.0714259	−	0.219826i
$532$	8.34284	−	25.6766i	0.361708	−	1.11322i
$533$	18.0660	+	13.1257i	0.782525	+	0.568538i
$534$	−5.99641	−	4.35664i	−0.259490	−	0.188530i
$535$	−1.75674	+	5.40670i	−0.0759506	+	0.233752i
$536$	0.518594	+	1.59607i	0.0223998	+	0.0689396i
$537$	−1.26393	+	0.918300i	−0.0545427	+	0.0396276i
$538$	11.0119			0.474757
$539$	−31.4440	−	30.3123i	−1.35439	−	1.30564i
$540$	−1.00000			−0.0430331
$541$	36.2712	−	26.3526i	1.55942	−	1.13299i	0.622942	−	0.782268i	$-0.285937\pi$
$541$	36.2712	−	26.3526i	1.55942	−	1.13299i	0.936481	−	0.350719i	$-0.114063\pi$
$542$	0.200166	+	0.616047i	0.00859786	+	0.0264615i
$543$	5.70820	−	17.5680i	0.244962	−	0.753917i
$544$	−4.17253	−	3.03152i	−0.178896	−	0.129975i
$545$	−7.23607	−	5.25731i	−0.309959	−	0.225198i
$546$	−3.23829	+	9.96643i	−0.138586	+	0.426524i
$547$	3.32433	+	10.2312i	0.142138	+	0.437456i	0.996632	−	0.0820054i	$-0.0261325\pi$
$547$	3.32433	+	10.2312i	0.142138	+	0.437456i	−0.854494	+	0.519462i	$0.826132\pi$
$548$	3.59376	−	2.61102i	0.153518	−	0.111537i
$549$	15.4541			0.659563
$550$	2.38778	+	2.30185i	0.101815	+	0.0981510i
$551$	−45.5750			−1.94156
$552$	−7.18776	+	5.22221i	−0.305931	+	0.222272i
$553$	7.59477	+	23.3743i	0.322962	+	0.993976i
$554$	−7.61121	+	23.4249i	−0.323369	+	0.995229i
$555$	6.41801	+	4.66296i	0.272429	+	0.197931i
$556$	−16.1054	−	11.7013i	−0.683021	−	0.496244i
$557$	−6.51292	+	20.0447i	−0.275961	+	0.849321i	0.713002	+	0.701162i	$0.247335\pi$
$557$	−6.51292	+	20.0447i	−0.275961	+	0.849321i	−0.988963	+	0.148160i	$0.952665\pi$
$558$	0.342697	+	1.05471i	0.0145075	+	0.0446496i
$559$	−0.148261	+	0.107718i	−0.00627077	+	0.00455598i
$560$	4.49096			0.189778
$561$	−7.48523	+	15.3809i	−0.316027	+	0.649383i
$562$	9.49170			0.400383
$563$	−21.3755	+	15.5302i	−0.900871	+	0.654521i	−0.938689	−	0.344764i	$-0.887959\pi$
$563$	−21.3755	+	15.5302i	−0.900871	+	0.654521i	0.0378189	+	0.999285i	$0.487959\pi$
$564$	0.896965	+	2.76058i	0.0377691	+	0.116241i
$565$	−1.19680	+	3.68337i	−0.0503497	+	0.154961i
$566$	16.3512	+	11.8799i	0.687294	+	0.499348i
$567$	3.63326	+	2.63972i	0.152583	+	0.110858i
$568$	−2.95146	+	9.08366i	−0.123841	+	0.381142i
$569$	9.91610	+	30.5186i	0.415705	+	1.27941i	0.911619	+	0.411036i	$0.134833\pi$
$569$	9.91610	+	30.5186i	0.415705	+	1.27941i	−0.495914	+	0.868371i	$0.665167\pi$
$570$	4.86351	−	3.53355i	0.203710	−	0.148004i
$571$	0.842187			0.0352444			0.0176222	−	0.999845i	$-0.494390\pi$
$571$	0.842187			0.0352444			0.0176222	+	0.999845i	$0.494390\pi$
$572$	−1.35051	−	7.62036i	−0.0564675	−	0.318623i
$573$	−17.6720			−0.738260
$574$	−34.7701	+	25.2620i	−1.45128	+	1.05441i
$575$	−2.74548	−	8.44972i	−0.114494	−	0.352378i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	12.5928	+	9.14918i	0.524244	+	0.380885i	0.818200	−	0.574934i	$-0.194972\pi$
$577$	12.5928	+	9.14918i	0.524244	+	0.380885i	−0.293957	+	0.955819i	$0.594972\pi$
$578$	7.76666	+	5.64281i	0.323051	+	0.234710i
$579$	−3.24326	+	9.98172i	−0.134785	+	0.414826i
$580$	−2.34270	−	7.21008i	−0.0972752	−	0.299382i
$581$	−29.0661	+	21.1178i	−1.20586	+	0.876112i
$582$	−5.74585			−0.238173
$583$	−2.18097	+	1.16208i	−0.0903267	+	0.0481283i
$584$	−10.9443			−0.452877
$585$	−1.88778	+	1.37155i	−0.0780502	+	0.0567068i
$586$	−0.368960	−	1.13554i	−0.0152416	−	0.0469088i
$587$	5.95146	−	18.3167i	0.245643	−	0.756012i	−0.749887	−	0.661566i	$-0.769892\pi$
$587$	5.95146	−	18.3167i	0.245643	−	0.756012i	0.995530	−	0.0944457i	$-0.0301079\pi$
$588$	−10.6537	−	7.74037i	−0.439352	−	0.319208i
$589$	−5.39360	−	3.91868i	−0.222239	−	0.161466i
$590$	−1.64590	+	5.06555i	−0.0677605	+	0.208546i
$591$	−3.11453	−	9.58553i	−0.128115	−	0.394296i
$592$	−6.41801	+	4.66296i	−0.263779	+	0.191646i
$593$	21.1332			0.867835			0.433918	−	0.900953i	$-0.357131\pi$
$593$	21.1332			0.867835			0.433918	+	0.900953i	$0.357131\pi$
$594$	−3.28475	−	0.458729i	−0.134775	−	0.0188219i
$595$	−23.1623			−0.949560
$596$	7.53567	−	5.47499i	0.308673	−	0.224264i
$597$	−4.23062	−	13.0205i	−0.173148	−	0.532894i
$598$	−6.40638	+	19.7168i	−0.261976	+	0.806280i
$599$	10.6966	+	7.77151i	0.437050	+	0.317535i	0.784462	−	0.620177i	$-0.212939\pi$
$599$	10.6966	+	7.77151i	0.437050	+	0.317535i	−0.347412	+	0.937713i	$0.612939\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	12.1170	−	37.2924i	0.494264	−	1.52119i	−0.323837	−	0.946113i	$-0.604973\pi$
$601$	12.1170	−	37.2924i	0.494264	−	1.52119i	0.818101	−	0.575075i	$-0.195027\pi$
$602$	−0.108992	−	0.335444i	−0.00444220	−	0.0136717i
$603$	1.35770	−	0.986424i	0.0552897	−	0.0401703i
$604$	13.9029			0.565702
$605$	6.78734	+	8.65633i	0.275945	+	0.351930i
$606$	16.5739			0.673270
$607$	−6.74631	+	4.90148i	−0.273824	+	0.198945i	−0.716219	−	0.697875i	$-0.754129\pi$
$607$	−6.74631	+	4.90148i	−0.273824	+	0.198945i	0.442395	+	0.896820i	$0.354129\pi$
$608$	1.85770	+	5.71740i	0.0753396	+	0.231871i
$609$	−10.5210	+	32.3802i	−0.426331	+	1.31211i
$610$	−12.5026	−	9.08366i	−0.506215	−	0.367787i
$611$	5.47955	+	3.98113i	0.221679	+	0.161059i
$612$	−1.59376	+	4.90510i	−0.0644241	+	0.198277i
$613$	−14.4610	−	44.5063i	−0.584073	−	1.79759i	−0.602963	−	0.797769i	$-0.706013\pi$
$613$	−14.4610	−	44.5063i	−0.584073	−	1.79759i	0.0188902	−	0.999822i	$-0.493987\pi$
$614$	9.18254	−	6.67151i	0.370577	−	0.269240i
$615$	−9.56995			−0.385898
$616$	14.7517	+	2.06013i	0.594362	+	0.0830052i
$617$	−18.5692			−0.747568			−0.373784	−	0.927516i	$-0.621940\pi$
$617$	−18.5692			−0.747568			−0.373784	+	0.927516i	$0.621940\pi$
$618$	−0.882336	+	0.641054i	−0.0354927	+	0.0257870i
$619$	−2.79781	−	8.61077i	−0.112453	−	0.346096i	0.878954	−	0.476907i	$-0.158242\pi$
$619$	−2.79781	−	8.61077i	−0.112453	−	0.346096i	−0.991407	+	0.130811i	$0.958242\pi$
$620$	0.342697	−	1.05471i	0.0137631	−	0.0423583i
$621$	7.18776	+	5.22221i	0.288435	+	0.209560i
$622$	−12.2782	−	8.92060i	−0.492309	−	0.357684i
$623$	10.2862	−	31.6577i	0.412108	−	1.26834i
$624$	−0.721069	−	2.21922i	−0.0288659	−	0.0888400i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−23.3570			−0.933532
$627$	17.5964	−	9.37578i	0.702731	−	0.374433i
$628$	9.89175			0.394724
$629$	33.1011	−	24.0493i	1.31983	−	0.958910i
$630$	−1.38778	−	4.27116i	−0.0552906	−	0.170167i
$631$	11.4405	−	35.2103i	0.455440	−	1.40170i	−0.415179	−	0.909740i	$-0.636281\pi$
$631$	11.4405	−	35.2103i	0.455440	−	1.40170i	0.870618	−	0.491959i	$-0.163719\pi$
$632$	−4.42742	−	3.21671i	−0.176113	−	0.127954i
$633$	−18.4845	−	13.4298i	−0.734693	−	0.533786i
$634$	−3.29539	+	10.1422i	−0.130877	+	0.402797i
$635$	2.58444	+	7.95409i	0.102560	+	0.315648i
$636$	−0.602806	+	0.437964i	−0.0239028	+	0.0173664i
$637$	−30.7282			−1.21750
$638$	−4.38770	−	24.7580i	−0.173711	−	0.980177i
$639$	9.55113			0.377837
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−3.35282	−	10.3189i	−0.132428	−	0.407572i	0.862753	−	0.505626i	$-0.168738\pi$
$641$	−3.35282	−	10.3189i	−0.132428	−	0.407572i	−0.995181	+	0.0980535i	$0.968738\pi$
$642$	−1.75674	+	5.40670i	−0.0693331	+	0.213385i
$643$	−23.8241	−	17.3092i	−0.939532	−	0.682610i	0.00877625	−	0.999961i	$-0.497206\pi$
$643$	−23.8241	−	17.3092i	−0.939532	−	0.682610i	−0.948308	+	0.317352i	$0.897206\pi$
$644$	−32.2799	−	23.4527i	−1.27201	−	0.924167i
$645$	0.0242693	−	0.0746932i	0.000955602	−	0.00294104i
$646$	−9.58113	−	29.4877i	−0.376964	−	1.16018i
$647$	27.4619	−	19.9522i	1.07964	−	0.784402i	0.102018	−	0.994783i	$-0.467470\pi$
$647$	27.4619	−	19.9522i	1.07964	−	0.784402i	0.977620	+	0.210380i	$0.0674702\pi$
$648$	−1.00000			−0.0392837
$649$	−7.73008	+	15.8840i	−0.303432	+	0.623503i
$650$	2.33343			0.0915246
$651$	−4.02926	+	2.92743i	−0.157919	+	0.114735i
$652$	1.98736	+	6.11648i	0.0778312	+	0.239540i
$653$	−5.89933	+	18.1563i	−0.230859	+	0.710510i	0.766785	+	0.641904i	$0.221855\pi$
$653$	−5.89933	+	18.1563i	−0.230859	+	0.710510i	−0.997644	+	0.0686059i	$0.978145\pi$
$654$	−7.23607	−	5.25731i	−0.282953	−	0.205577i
$655$	5.98736	+	4.35007i	0.233946	+	0.169971i
$656$	2.95728	−	9.10157i	0.115462	−	0.355356i
$657$	3.38197	+	10.4086i	0.131943	+	0.406079i
$658$	−10.5461	+	7.66216i	−0.411128	+	0.298702i
$659$	−9.56904			−0.372757			−0.186378	−	0.982478i	$-0.559675\pi$
$659$	−9.56904			−0.372757			−0.186378	+	0.982478i	$0.559675\pi$
$660$	2.38778	+	2.30185i	0.0929443	+	0.0895992i
$661$	16.7878			0.652968			0.326484	−	0.945203i	$-0.394136\pi$
$661$	16.7878			0.652968			0.326484	+	0.945203i	$0.394136\pi$
$662$	−1.96133	+	1.42499i	−0.0762292	+	0.0553838i
$663$	3.71893	+	11.4457i	0.144431	+	0.444514i
$664$	2.47214	−	7.60845i	0.0959375	−	0.295265i
$665$	21.8418	+	15.8690i	0.846990	+	0.615374i
$666$	6.41801	+	4.66296i	0.248693	+	0.180686i
$667$	−20.8138	+	64.0584i	−0.805915	+	2.48035i
$668$	−1.86697	−	5.74593i	−0.0722351	−	0.222317i
$669$	0.397194	−	0.288578i	0.0153564	−	0.0111571i
$670$	−1.67821			−0.0648347
$671$	−36.9009	−	35.5728i	−1.42454	−	1.37327i
$672$	4.49096			0.173242
$673$	−37.4476	+	27.2073i	−1.44350	+	1.04876i	−0.456202	+	0.889876i	$0.650791\pi$
$673$	−37.4476	+	27.2073i	−1.44350	+	1.04876i	−0.987297	+	0.158887i	$0.949209\pi$
$674$	−0.363600	−	1.11905i	−0.0140054	−	0.0431041i
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$	6.11222	+	4.44079i	0.235085	+	0.170799i
$677$	−22.0416	−	16.0142i	−0.847129	−	0.615475i	0.0772241	−	0.997014i	$-0.475394\pi$
$677$	−22.0416	−	16.0142i	−0.847129	−	0.615475i	−0.924353	+	0.381539i	$0.875394\pi$
$678$	−1.19680	+	3.68337i	−0.0459628	+	0.141459i
$679$	−7.97399	−	24.5414i	−0.306014	−	0.941813i
$680$	4.17253	−	3.03152i	0.160009	−	0.116254i
$681$	1.49022			0.0571053
$682$	1.60950	−	3.30727i	0.0616311	−	0.126642i
$683$	3.62551			0.138726			0.0693631	−	0.997591i	$-0.477903\pi$
$683$	3.62551			0.138726			0.0693631	+	0.997591i	$0.477903\pi$
$684$	4.86351	−	3.53355i	0.185961	−	0.135109i
$685$	1.37270	+	4.22472i	0.0524480	+	0.161418i
$686$	8.56082	−	26.3475i	0.326854	−	1.00595i
$687$	6.64849	+	4.83041i	0.253656	+	0.184292i
$688$	0.0635378	+	0.0461629i	0.00242236	+	0.00175994i
$689$	−0.537275	+	1.65356i	−0.0204686	+	0.0629957i
$690$	−2.74548	−	8.44972i	−0.104519	−	0.321675i
$691$	40.7474	−	29.6047i	1.55011	−	1.12622i	0.606530	−	0.795061i	$-0.292561\pi$
$691$	40.7474	−	29.6047i	1.55011	−	1.12622i	0.943576	−	0.331157i	$-0.107439\pi$
$692$	0.648032			0.0246345
$693$	−2.59921	−	14.6663i	−0.0987359	−	0.557126i
$694$	−23.3570			−0.886619
$695$	16.1054	−	11.7013i	0.610913	−	0.443854i
$696$	−2.34270	−	7.21008i	−0.0887997	−	0.273297i
$697$	−15.2523	+	46.9416i	−0.577720	+	1.77804i
$698$	0.303429	+	0.220454i	0.0114850	+	0.00834431i
$699$	−5.36933	−	3.90105i	−0.203087	−	0.147551i
$700$	−1.38778	+	4.27116i	−0.0524532	+	0.161434i
$701$	−5.29652	−	16.3010i	−0.200047	−	0.615681i	−0.999880	−	0.0154592i	$-0.995079\pi$
$701$	−5.29652	−	16.3010i	−0.200047	−	0.615681i	0.799834	−	0.600222i	$-0.204921\pi$
$702$	−1.88778	+	1.37155i	−0.0712498	+	0.0517660i
$703$	−47.6909			−1.79869
$704$	−2.92705	+	1.55961i	−0.110317	+	0.0587799i
$705$	−2.90264			−0.109320
$706$	1.68157	−	1.22173i	0.0632868	−	0.0459805i
$707$	23.0010	+	70.7899i	0.865042	+	2.66233i
$708$	−1.64590	+	5.06555i	−0.0618566	+	0.190375i
$709$	−23.5747	−	17.1280i	−0.885366	−	0.643256i	0.0492999	−	0.998784i	$-0.484301\pi$
$709$	−23.5747	−	17.1280i	−0.885366	−	0.643256i	−0.934666	+	0.355528i	$0.884301\pi$
$710$	−7.72703	−	5.61401i	−0.289990	−	0.210690i
$711$	−1.69112	+	5.20475i	−0.0634221	+	0.195193i
$712$	2.29042	+	7.04920i	0.0858372	+	0.264180i
$713$	−7.97117	+	5.79139i	−0.298523	+	0.216889i
$714$	−23.1623			−0.866826
$715$	7.66472	+	1.07041i	0.286644	+	0.0400311i
$716$	1.56231			0.0583861
$717$	4.93310	−	3.58410i	0.184230	−	0.133851i
$718$	0.0557281	+	0.171513i	0.00207975	+	0.00640082i
$719$	9.53703	−	29.3520i	0.355671	−	1.09464i	−0.599948	−	0.800039i	$-0.704812\pi$
$719$	9.53703	−	29.3520i	0.355671	−	1.09464i	0.955619	−	0.294605i	$-0.0951880\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	−3.96253	−	2.87895i	−0.147572	−	0.107218i
$722$	−5.29647	+	16.3009i	−0.197114	+	0.606655i
$723$	1.76256	+	5.42460i	0.0655503	+	0.201743i
$724$	−14.9443	+	10.8576i	−0.555399	+	0.403521i
$725$	7.58113			0.281556
$726$	6.78734	+	8.65633i	0.251902	+	0.321266i
$727$	−3.64376			−0.135140			−0.0675699	−	0.997715i	$-0.521525\pi$
$727$	−3.64376			−0.135140			−0.0675699	+	0.997715i	$0.521525\pi$
$728$	8.47795	−	6.15959i	0.314214	−	0.228290i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	3.38197	−	10.4086i	0.125172	−	0.385240i
$731$	−0.327698	−	0.238087i	−0.0121204	−	0.00880595i
$732$	−12.5026	−	9.08366i	−0.462109	−	0.335742i
$733$	−2.40652	+	7.40650i	−0.0888868	+	0.273565i	−0.985612	−	0.169022i	$-0.945939\pi$
$733$	−2.40652	+	7.40650i	−0.0888868	+	0.273565i	0.896726	+	0.442587i	$0.145939\pi$
$734$	−3.60640	−	11.0994i	−0.133115	−	0.409685i
$735$	10.6537	−	7.74037i	0.392968	−	0.285508i
$736$	8.88456			0.327489
$737$	−5.51248	−	0.769842i	−0.203055	−	0.0283575i
$738$	−9.56995			−0.352275
$739$	7.34147	−	5.33389i	0.270060	−	0.196210i	−0.444510	−	0.895774i	$-0.646622\pi$
$739$	7.34147	−	5.33389i	0.270060	−	0.196210i	0.714570	+	0.699564i	$0.246622\pi$
$740$	−2.45146	−	7.54482i	−0.0901175	−	0.277353i
$741$	4.33480	−	13.3411i	0.159243	−	0.490099i
$742$	−2.70718	−	1.96688i	−0.0993836	−	0.0722064i
$743$	−7.67516	−	5.57633i	−0.281574	−	0.204576i	0.438030	−	0.898961i	$-0.355677\pi$
$743$	−7.67516	−	5.57633i	−0.281574	−	0.204576i	−0.719604	+	0.694385i	$0.755677\pi$
$744$	0.342697	−	1.05471i	0.0125639	−	0.0386677i
$745$	2.87837	+	8.85872i	0.105455	+	0.324558i
$746$	8.22666	−	5.97702i	0.301199	−	0.218834i
$747$	−8.00000			−0.292705
$748$	15.0964	−	8.04372i	0.551977	−	0.294107i
$749$	−25.5308			−0.932876
$750$	−0.809017	+	0.587785i	−0.0295411	+	0.0214629i
$751$	15.2720	+	47.0023i	0.557282	+	1.71514i	0.689839	+	0.723963i	$0.257681\pi$
$751$	15.2720	+	47.0023i	0.557282	+	1.71514i	−0.132557	+	0.991175i	$0.542319\pi$
$752$	0.896965	−	2.76058i	0.0327090	−	0.100668i
$753$	2.10922	+	1.53244i	0.0768643	+	0.0558452i
$754$	−14.3115	−	10.3979i	−0.521195	−	0.378670i
$755$	−4.29624	+	13.2225i	−0.156356	+	0.481215i
$756$	−1.38778	−	4.27116i	−0.0504732	−	0.155340i
$757$	20.4496	−	14.8575i	0.743255	−	0.540006i	−0.150474	−	0.988614i	$-0.548080\pi$
$757$	20.4496	−	14.8575i	0.743255	−	0.540006i	0.893729	+	0.448608i	$0.148080\pi$
$758$	−11.0825			−0.402535
$759$	−5.14207	−	29.0146i	−0.186645	−	1.05316i
$760$	−6.01163			−0.218065
$761$	−18.3082	+	13.3017i	−0.663670	+	0.482185i	−0.867900	−	0.496738i	$-0.834531\pi$
$761$	−18.3082	+	13.3017i	−0.663670	+	0.482185i	0.204230	+	0.978923i	$0.434531\pi$
$762$	2.58444	+	7.95409i	0.0936244	+	0.288146i
$763$	12.4127	−	38.2024i	0.449370	−	1.38302i
$764$	14.2970	+	10.3874i	0.517247	+	0.375802i
$765$	−4.17253	−	3.03152i	−0.150858	−	0.109605i
$766$	−6.58458	+	20.2653i	−0.237911	+	0.732214i
$767$	3.84058	+	11.8201i	0.138675	+	0.426799i
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	11.4015			0.411150			0.205575	−	0.978641i	$-0.434094\pi$
$769$	11.4015			0.411150			0.205575	+	0.978641i	$0.434094\pi$
$770$	−6.51782	+	13.3931i	−0.234886	+	0.482652i
$771$	18.4360			0.663955
$772$	8.49096	−	6.16904i	0.305596	−	0.222029i
$773$	5.83722	+	17.9651i	0.209950	+	0.646160i	0.999474	+	0.0324398i	$0.0103277\pi$
$773$	5.83722	+	17.9651i	0.209950	+	0.646160i	−0.789524	+	0.613720i	$0.789672\pi$
$774$	0.0242693	−	0.0746932i	0.000872341	−	0.00268479i
$775$	0.897194	+	0.651849i	0.0322281	+	0.0234151i
$776$	4.64849	+	3.37733i	0.166871	+	0.121239i
$777$	−11.0094	+	33.8835i	−0.394960	+	1.21556i
$778$	11.6611	+	35.8893i	0.418072	+	1.28669i
$779$	46.5436	−	33.8159i	1.66760	−	1.21158i
$780$	2.33343			0.0835501
$781$	−22.8060	−	21.9852i	−0.816064	−	0.786693i
$782$	−45.8224			−1.63860
$783$	−6.13326	+	4.45608i	−0.219185	+	0.159247i
$784$	4.06935	+	12.5242i	0.145334	+	0.447292i
$785$	−3.05672	+	9.40761i	−0.109099	+	0.335772i
$786$	5.98736	+	4.35007i	0.213562	+	0.155162i
$787$	25.0494	+	18.1995i	0.892916	+	0.648742i	0.936637	−	0.350302i	$-0.113921\pi$
$787$	25.0494	+	18.1995i	0.892916	+	0.648742i	−0.0437206	+	0.999044i	$0.513921\pi$
$788$	−3.11453	+	9.58553i	−0.110950	+	0.341470i
$789$	−7.54882	−	23.2329i	−0.268745	−	0.827112i
$790$	4.42742	−	3.21671i	0.157521	−	0.114445i
$791$	−17.3931			−0.618429
$792$	2.38778	+	2.30185i	0.0848462	+	0.0817925i
$793$	−36.0609			−1.28056
$794$	−18.1501	+	13.1868i	−0.644123	+	0.467983i
$795$	−0.230252	−	0.708641i	−0.00816618	−	0.0251329i
$796$	−4.23062	+	13.0205i	−0.149950	+	0.461500i
$797$	6.42064	+	4.66487i	0.227431	+	0.165238i	0.695665	−	0.718366i	$-0.255110\pi$
$797$	6.42064	+	4.66487i	0.227431	+	0.165238i	−0.468235	+	0.883604i	$0.655110\pi$
$798$	21.8418	+	15.8690i	0.773193	+	0.561757i
$799$	−4.62613	+	14.2378i	−0.163661	+	0.503695i
$800$	−0.309017	−	0.951057i	−0.0109254	−	0.0336249i
$801$	5.99641	−	4.35664i	0.211873	−	0.153934i
$802$	25.9002			0.914567
$803$	15.8836	−	32.6383i	0.560522	−	1.15178i
$804$	−1.67821			−0.0591857
$805$	32.2799	−	23.4527i	1.13772	−	0.826600i
$806$	−0.799660	−	2.46110i	−0.0281668	−	0.0866885i
$807$	−3.40287	+	10.4730i	−0.119787	+	0.368665i
$808$	−13.4086	−	9.74192i	−0.471713	−	0.342719i
$809$	4.50037	+	3.26971i	0.158225	+	0.114957i	0.664080	−	0.747661i	$-0.268823\pi$
$809$	4.50037	+	3.26971i	0.158225	+	0.114957i	−0.505856	+	0.862618i	$0.668823\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	−9.92009	−	30.5309i	−0.348341	−	1.07208i	−0.959771	−	0.280786i	$-0.909405\pi$
$811$	−9.92009	−	30.5309i	−0.348341	−	1.07208i	0.611429	−	0.791299i	$-0.290595\pi$
$812$	27.5442	−	20.0120i	0.966613	−	0.702285i
$813$	−0.647750			−0.0227176
$814$	−4.59140	−	25.9074i	−0.160929	−	0.908054i
$815$	−6.43124			−0.225277
$816$	4.17253	−	3.03152i	0.146068	−	0.106124i
$817$	0.145898	+	0.449028i	0.00510433	+	0.0157095i
$818$	−7.66118	+	23.5787i	−0.267867	+	0.824409i
$819$	−8.47795	−	6.15959i	−0.296244	−	0.215234i
$820$	7.74225	+	5.62508i	0.270371	+	0.196436i
$821$	6.52815	−	20.0916i	0.227834	−	0.701201i	−0.770158	−	0.637854i	$-0.779823\pi$
$821$	6.52815	−	20.0916i	0.227834	−	0.701201i	0.997992	−	0.0633470i	$-0.0201775\pi$
$822$	1.37270	+	4.22472i	0.0478783	+	0.147354i
$823$	−4.00222	+	2.90778i	−0.139509	+	0.101359i	−0.655351	−	0.755325i	$-0.727479\pi$
$823$	−4.00222	+	2.90778i	−0.139509	+	0.101359i	0.515842	+	0.856684i	$0.327479\pi$
$824$	1.09063			0.0379938
$825$	−2.92705	+	1.55961i	−0.101907	+	0.0542985i
$826$	−23.9199			−0.832280
$827$	36.0461	−	26.1890i	1.25344	−	0.910681i	0.255028	−	0.966934i	$-0.417915\pi$
$827$	36.0461	−	26.1890i	1.25344	−	0.910681i	0.998417	+	0.0562526i	$0.0179152\pi$
$828$	−2.74548	−	8.44972i	−0.0954120	−	0.293648i
$829$	−6.69657	+	20.6099i	−0.232582	+	0.715812i	0.764851	+	0.644207i	$0.222812\pi$
$829$	−6.69657	+	20.6099i	−0.232582	+	0.715812i	−0.997433	+	0.0716057i	$0.977188\pi$
$830$	6.47214	+	4.70228i	0.224651	+	0.163219i
$831$	−19.9264	−	14.4774i	−0.691240	−	0.502215i
$832$	−0.721069	+	2.21922i	−0.0249986	+	0.0769377i
$833$	−20.9878	−	64.5939i	−0.727185	−	2.23804i
$834$	16.1054	−	11.7013i	0.557684	−	0.405181i
$835$	6.04163			0.209079
$836$	−19.7467	−	2.75771i	−0.682954	−	0.0953775i
$837$	−1.10899			−0.0383324
$838$	22.5691	−	16.3974i	0.779636	−	0.566439i
$839$	14.1278	+	43.4809i	0.487746	+	1.50113i	0.827964	+	0.560782i	$0.189499\pi$
$839$	14.1278	+	43.4809i	0.487746	+	1.50113i	−0.340217	+	0.940347i	$0.610501\pi$
$840$	−1.38778	+	4.27116i	−0.0478830	+	0.147369i
$841$	−23.0356	−	16.7363i	−0.794329	−	0.577114i
$842$	20.2296	+	14.6977i	0.697159	+	0.506515i
$843$	−2.93310	+	9.02714i	−0.101021	+	0.310911i
$844$	7.06045	+	21.7298i	0.243031	+	0.747972i
$845$	−6.11222	+	4.44079i	−0.210267	+	0.152768i
$846$	−2.90264			−0.0997948
$847$	−27.5532	+	41.0029i	−0.946738	+	1.40888i
$848$	0.745110			0.0255872
$849$	−16.3512	+	11.8799i	−0.561173	+	0.407716i
$850$	1.59376	+	4.90510i	0.0546657	+	0.168244i
$851$	−21.7801	+	67.0324i	−0.746614	+	2.29784i
$852$	−7.72703	−	5.61401i	−0.264724	−	0.192333i
$853$	2.65208	+	1.92685i	0.0908056	+	0.0659742i	0.632262	−	0.774755i	$-0.282127\pi$
$853$	2.65208	+	1.92685i	0.0908056	+	0.0659742i	−0.541456	+	0.840729i	$0.682127\pi$
$854$	21.4469	−	66.0067i	0.733897	−	2.25870i
$855$	1.85770	+	5.71740i	0.0635319	+	0.195531i
$856$	4.59921	−	3.34152i	0.157198	−	0.114211i
$857$	−0.297435			−0.0101602			−0.00508010	−	0.999987i	$-0.501617\pi$
$857$	−0.297435			−0.0101602			−0.00508010	+	0.999987i	$0.501617\pi$
$858$	7.66472	+	1.07041i	0.261669	+	0.0365432i
$859$	39.7745			1.35709			0.678544	−	0.734560i	$-0.262611\pi$
$859$	39.7745			1.35709			0.678544	+	0.734560i	$0.262611\pi$
$860$	−0.0635378	+	0.0461629i	−0.00216662	+	0.00157414i
$861$	−13.2810	−	40.8748i	−0.452616	−	1.39301i
$862$	−5.55067	+	17.0832i	−0.189057	+	0.581857i
$863$	12.1743	+	8.84514i	0.414418	+	0.301092i	0.775388	−	0.631485i	$-0.217554\pi$
$863$	12.1743	+	8.84514i	0.414418	+	0.301092i	−0.360970	+	0.932577i	$0.617554\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−0.200253	+	0.616316i	−0.00680881	+	0.0209554i
$866$	8.32669	+	25.6269i	0.282953	+	0.870839i
$867$	−7.76666	+	5.64281i	−0.263770	+	0.191640i
$868$	4.98044			0.169047
$869$	16.0186	−	8.53509i	0.543392	−	0.289533i
$870$	7.58113			0.257024
$871$	−3.16809	+	2.30175i	−0.107347	+	0.0779918i
$872$	2.76393	+	8.50651i	0.0935985	+	0.288067i
$873$	1.77556	−	5.46463i	0.0600938	−	0.184950i
$874$	43.2102	+	31.3940i	1.46161	+	1.06192i
$875$	−3.63326	−	2.63972i	−0.122827	−	0.0892388i
$876$	3.38197	−	10.4086i	0.114266	−	0.351675i
$877$	11.9236	+	36.6971i	0.402631	+	1.23917i	0.922857	+	0.385143i	$0.125848\pi$
$877$	11.9236	+	36.6971i	0.402631	+	1.23917i	−0.520226	+	0.854029i	$0.674152\pi$
$878$	3.87837	−	2.81780i	0.130889	−	0.0950962i
$879$	1.19398			0.0402719
$880$	−0.578765	−	3.26574i	−0.0195102	−	0.110088i
$881$	−14.2135			−0.478866			−0.239433	−	0.970913i	$-0.576962\pi$
$881$	−14.2135			−0.478866			−0.239433	+	0.970913i	$0.576962\pi$
$882$	10.6537	−	7.74037i	0.358729	−	0.260632i
$883$	−0.702757	−	2.16286i	−0.0236497	−	0.0727862i	0.938535	−	0.345184i	$-0.112183\pi$
$883$	−0.702757	−	2.16286i	−0.0236497	−	0.0727862i	−0.962185	+	0.272398i	$0.912183\pi$
$884$	3.71893	−	11.4457i	0.125081	−	0.384961i
$885$	−4.30902	−	3.13068i	−0.144846	−	0.105237i
$886$	8.13871	+	5.91312i	0.273425	+	0.198655i
$887$	16.1510	−	49.7076i	0.542297	−	1.66902i	−0.185033	−	0.982732i	$-0.559239\pi$
$887$	16.1510	−	49.7076i	0.542297	−	1.66902i	0.727331	−	0.686287i	$-0.240761\pi$
$888$	−2.45146	−	7.54482i	−0.0822657	−	0.253188i
$889$	−30.3865	+	22.0771i	−1.01913	+	0.740442i
$890$	−7.41196			−0.248450
$891$	1.45132	−	2.98223i	0.0486211	−	0.0999083i
$892$	−0.490958			−0.0164385
$893$	14.1170	−	10.2566i	0.472408	−	0.343225i
$894$	2.87837	+	8.85872i	0.0962671	+	0.296280i
$895$	−0.482779	+	1.48584i	−0.0161375	+	0.0496662i
$896$	−3.63326	−	2.63972i	−0.121379	−	0.0881868i
$897$	−16.7721	−	12.1857i	−0.560004	−	0.406867i
$898$	0.153936	−	0.473767i	0.00513692	−	0.0158098i
$899$	−2.59803	−	7.99593i	−0.0866493	−	0.266679i
$900$	−0.809017	+	0.587785i	−0.0269672	+	0.0195928i
$901$	−3.84293			−0.128026
$902$	22.8510	+	22.0286i	0.760854	+	0.733471i
$903$	0.352707			0.0117373
$904$	3.13326	−	2.27645i	0.104211	−	0.0757135i
$905$	−5.70820	−	17.5680i	−0.189747	−	0.583982i
$906$	−4.29624	+	13.2225i	−0.142733	+	0.439287i
$907$	42.9268	+	31.1882i	1.42536	+	1.03559i	0.990857	+	0.134916i	$0.0430764\pi$
$907$	42.9268	+	31.1882i	1.42536	+	1.03559i	0.434504	+	0.900670i	$0.356924\pi$
$908$	−1.20561	−	0.875929i	−0.0400097	−	0.0290687i
$909$	−5.12163	+	15.7628i	−0.169874	+	0.522817i
$910$	3.23829	+	9.96643i	0.107348	+	0.330384i
$911$	31.8405	−	23.1334i	1.05492	−	0.766445i	0.0817794	−	0.996650i	$-0.473940\pi$
$911$	31.8405	−	23.1334i	1.05492	−	0.766445i	0.973142	+	0.230205i	$0.0739397\pi$
$912$	−6.01163			−0.199065
$913$	19.1023	+	18.4148i	0.632193	+	0.609440i
$914$	−1.85730			−0.0614342
$915$	12.5026	−	9.08366i	0.413323	−	0.300297i
$916$	−2.53950	−	7.81577i	−0.0839073	−	0.258240i
$917$	−10.2707	+	31.6099i	−0.339168	+	1.04385i
$918$	−4.17253	−	3.03152i	−0.137714	−	0.100055i
$919$	6.02589	+	4.37807i	0.198776	+	0.144419i	0.682721	−	0.730679i	$-0.260797\pi$
$919$	6.02589	+	4.37807i	0.198776	+	0.144419i	−0.483945	+	0.875098i	$0.660797\pi$
$920$	−2.74548	+	8.44972i	−0.0905158	+	0.278579i
$921$	3.50742	+	10.7947i	0.115573	+	0.355698i
$922$	17.9112	−	13.0132i	0.589874	−	0.428568i
$923$	−22.2869			−0.733581
$924$	−6.51782	+	13.3931i	−0.214420	+	0.440599i
$925$	7.93310			0.260839
$926$	−17.9537	+	13.0441i	−0.589995	+	0.428656i
$927$	−0.337022	−	1.03725i	−0.0110693	−	0.0340677i
$928$	−2.34270	+	7.21008i	−0.0769028	+	0.236683i
$929$	−6.23247	−	4.52816i	−0.204481	−	0.148564i	0.480832	−	0.876813i	$-0.340335\pi$
$929$	−6.23247	−	4.52816i	−0.204481	−	0.148564i	−0.685313	+	0.728249i	$0.740335\pi$
$930$	0.897194	+	0.651849i	0.0294201	+	0.0213750i
$931$	−24.4635	+	75.2908i	−0.801758	+	2.46756i
$932$	2.05090	+	6.31203i	0.0671795	+	0.206757i
$933$	12.2782	−	8.92060i	0.401969	−	0.292047i
$934$	−31.6953			−1.03710
$935$	2.98500	+	16.8431i	0.0976200	+	0.550829i
$936$	2.33343			0.0762705
$937$	−19.2893	+	14.0145i	−0.630155	+	0.457834i	−0.856454	−	0.516223i	$-0.827337\pi$
$937$	−19.2893	+	14.0145i	−0.630155	+	0.457834i	0.226299	+	0.974058i	$0.427337\pi$
$938$	−2.32898	−	7.16788i	−0.0760440	−	0.234039i
$939$	7.21770	−	22.2138i	0.235541	−	0.724920i
$940$	2.34829	+	1.70613i	0.0765926	+	0.0556478i
$941$	16.5757	+	12.0429i	0.540352	+	0.392589i	0.824216	−	0.566276i	$-0.191616\pi$
$941$	16.5757	+	12.0429i	0.540352	+	0.392589i	−0.283864	+	0.958865i	$0.591616\pi$
$942$	−3.05672	+	9.40761i	−0.0995932	+	0.306517i
$943$	−26.2741	−	80.8634i	−0.855603	−	2.63327i
$944$	4.30902	−	3.13068i	0.140247	−	0.101895i
$945$	4.49096			0.146091
$946$	−0.229882	+	0.122487i	−0.00747411	+	0.00398239i
$947$	18.3389			0.595934			0.297967	−	0.954576i	$-0.403691\pi$
$947$	18.3389			0.595934			0.297967	+	0.954576i	$0.403691\pi$
$948$	4.42742	−	3.21671i	0.143796	−	0.104474i
$949$	−7.89157	−	24.2878i	−0.256171	−	0.788414i
$950$	1.85770	−	5.71740i	0.0602716	−	0.185497i
$951$	−8.62745	−	6.26821i	−0.279764	−	0.203261i
$952$	18.7387	+	13.6144i	0.607323	+	0.441246i
$953$	−13.4969	+	41.5391i	−0.437206	+	1.34558i	0.453603	+	0.891204i	$0.350139\pi$
$953$	−13.4969	+	41.5391i	−0.437206	+	1.34558i	−0.890809	+	0.454378i	$0.849861\pi$
$954$	−0.230252	−	0.708641i	−0.00745467	−	0.0229431i
$955$	−14.2970	+	10.3874i	−0.462639	+	0.336127i
$956$	−6.09764			−0.197212
$957$	24.9021	+	3.47768i	0.804970	+	0.112418i
$958$	23.2217			0.750259
$959$	−16.1394	+	11.7260i	−0.521170	+	0.378652i
$960$	−0.309017	−	0.951057i	−0.00997348	−	0.0306952i
$961$	−9.19948	+	28.3131i	−0.296757	+	0.913325i
$962$	−14.9760	−	10.8807i	−0.482844	−	0.350807i
$963$	−4.59921	−	3.34152i	−0.148208	−	0.107679i
$964$	1.76256	−	5.42460i	0.0567682	−	0.174715i
$965$	3.24326	+	9.98172i	0.104404	+	0.321323i
$966$	32.2799	−	23.4527i	1.03859	−	0.754579i
$967$	−44.2296			−1.42233			−0.711164	−	0.703026i	$-0.751832\pi$
$967$	−44.2296			−1.42233			−0.711164	+	0.703026i	$0.751832\pi$
$968$	−0.403010	−	10.9926i	−0.0129532	−	0.353316i
$969$	31.0052			0.996030
$970$	−4.64849	+	3.37733i	−0.149254	+	0.108439i
$971$	6.14470	+	18.9114i	0.197193	+	0.606897i	0.999944	+	0.0105829i	$0.00336871\pi$
$971$	6.14470	+	18.9114i	0.197193	+	0.606897i	−0.802751	+	0.596314i	$0.796631\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	72.3287	+	52.5499i	2.31875	+	1.68467i
$974$	−31.4773	−	22.8696i	−1.00860	−	0.732790i
$975$	−0.721069	+	2.21922i	−0.0230927	+	0.0710720i
$976$	4.77556	+	14.6977i	0.152862	+	0.470461i
$977$	27.3495	−	19.8706i	0.874988	−	0.635716i	−0.0569326	−	0.998378i	$-0.518132\pi$
$977$	27.3495	−	19.8706i	0.874988	−	0.635716i	0.931921	+	0.362662i	$0.118132\pi$
$978$	−6.43124			−0.205648
$979$	−24.3464	−	3.40008i	−0.778115	−	0.108667i
$980$	−13.1687			−0.420659
$981$	7.23607	−	5.25731i	0.231030	−	0.167853i
$982$	−1.44045	−	4.43325i	−0.0459666	−	0.141471i
$983$	−3.11463	+	9.58586i	−0.0993414	+	0.305741i	−0.988361	−	0.152128i	$-0.951387\pi$
$983$	−3.11463	+	9.58586i	−0.0993414	+	0.305741i	0.889019	+	0.457870i	$0.151387\pi$
$984$	7.74225	+	5.62508i	0.246814	+	0.179321i
$985$	−8.15394	−	5.92418i	−0.259806	−	0.188760i
$986$	12.0825	−	37.1862i	0.384786	−	1.18425i
$987$	−4.02823	−	12.3976i	−0.128220	−	0.394621i
$988$	−11.3487	+	8.24528i	−0.361049	+	0.262317i
$989$	0.697767			0.0221877
$990$	−2.92705	+	1.55961i	−0.0930278	+	0.0495675i
$991$	25.6906			0.816088			0.408044	−	0.912962i	$-0.366211\pi$
$991$	25.6906			0.816088			0.408044	+	0.912962i	$0.366211\pi$
$992$	−0.897194	+	0.651849i	−0.0284859	+	0.0206962i
$993$	−0.749161	−	2.30568i	−0.0237739	−	0.0731686i
$994$	13.2549	−	40.7944i	0.420420	−	1.29392i
$995$	−11.0759	−	8.04712i	−0.351130	−	0.255111i
$996$	6.47214	+	4.70228i	0.205077	+	0.148998i
$997$	13.2566	−	40.7997i	0.419842	−	1.29214i	−0.488006	−	0.872840i	$-0.662276\pi$
$997$	13.2566	−	40.7997i	0.419842	−	1.29214i	0.907848	−	0.419300i	$-0.137724\pi$
$998$	−5.06581	−	15.5910i	−0.160356	−	0.493524i
$999$	−6.41801	+	4.66296i	−0.203057	+	0.147529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	330.2.m.f.91.1	✓	8
3.2	odd	2		990.2.n.i.91.1		8
11.2	odd	10		3630.2.a.bs.1.4		4
11.4	even	5	inner	330.2.m.f.301.1	yes	8
11.9	even	5		3630.2.a.bq.1.1		4
33.26	odd	10		990.2.n.i.631.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.f.91.1	✓	8	1.1	even	1	trivial
330.2.m.f.301.1	yes	8	11.4	even	5	inner
990.2.n.i.91.1		8	3.2	odd	2
990.2.n.i.631.1		8	33.26	odd	10
3630.2.a.bq.1.1		4	11.9	even	5
3630.2.a.bs.1.4		4	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.38778 + 4.27116i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.38778 + 4.27116i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.00000 q^{10} +(3.28475 + 0.458729i) q^{11} +1.00000 q^{12} +(1.88778 - 1.37155i) q^{13} +(1.38778 + 4.27116i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.17253 + 3.03152i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-1.85770 - 5.71740i) q^{19} +(0.809017 - 0.587785i) q^{20} -4.49096 q^{21} +(2.92705 - 1.55961i) q^{22} -8.88456 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.721069 - 2.21922i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(3.63326 + 2.63972i) q^{28} +(2.34270 - 7.21008i) q^{29} +(0.309017 + 0.951057i) q^{30} +(0.897194 - 0.651849i) q^{31} -1.00000 q^{32} +(0.578765 + 3.26574i) q^{33} +5.15753 q^{34} +(-3.63326 + 2.63972i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.45146 - 7.54482i) q^{37} +(-4.86351 - 3.53355i) q^{38} +(1.88778 + 1.37155i) q^{39} +(0.309017 - 0.951057i) q^{40} +(2.95728 + 9.10157i) q^{41} +(-3.63326 + 2.63972i) q^{42} -0.0785371 q^{43} +(1.45132 - 2.98223i) q^{44} -1.00000 q^{45} +(-7.18776 + 5.22221i) q^{46} +(0.896965 + 2.76058i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-10.6537 - 7.74037i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-1.59376 + 4.90510i) q^{51} +(-0.721069 - 2.21922i) q^{52} +(-0.602806 + 0.437964i) q^{53} -1.00000 q^{54} +(2.38778 + 2.30185i) q^{55} +4.49096 q^{56} +(4.86351 - 3.53355i) q^{57} +(-2.34270 - 7.21008i) q^{58} +(-1.64590 + 5.06555i) q^{59} +(0.809017 + 0.587785i) q^{60} +(-12.5026 - 9.08366i) q^{61} +(0.342697 - 1.05471i) q^{62} +(-1.38778 - 4.27116i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.33343 q^{65} +(2.38778 + 2.30185i) q^{66} -1.67821 q^{67} +(4.17253 - 3.03152i) q^{68} +(-2.74548 - 8.44972i) q^{69} +(-1.38778 + 4.27116i) q^{70} +(-7.72703 - 5.61401i) q^{71} +(0.809017 + 0.587785i) q^{72} +(3.38197 - 10.4086i) q^{73} +(-2.45146 - 7.54482i) q^{74} +(-0.809017 + 0.587785i) q^{75} -6.01163 q^{76} +(-6.51782 + 13.3931i) q^{77} +2.33343 q^{78} +(4.42742 - 3.21671i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(7.74225 + 5.62508i) q^{82} +(6.47214 + 4.70228i) q^{83} +(-1.38778 + 4.27116i) q^{84} +(1.59376 + 4.90510i) q^{85} +(-0.0635378 + 0.0461629i) q^{86} +7.58113 q^{87} +(-0.578765 - 3.26574i) q^{88} -7.41196 q^{89} +(-0.809017 + 0.587785i) q^{90} +(3.23829 + 9.96643i) q^{91} +(-2.74548 + 8.44972i) q^{92} +(0.897194 + 0.651849i) q^{93} +(2.34829 + 1.70613i) q^{94} +(1.85770 - 5.71740i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-4.64849 + 3.37733i) q^{97} -13.1687 q^{98} +(-2.92705 + 1.55961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} - 3 q^{14} + 2 q^{15} - 2 q^{16} + 3 q^{17} + 2 q^{18} - 12 q^{19} + 2 q^{20} - 2 q^{21} + 10 q^{22} + 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + 27 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 5 q^{33} + 22 q^{34} + 2 q^{35} - 2 q^{36} - 4 q^{37} - 13 q^{38} + q^{39} - 2 q^{40} - 23 q^{41} + 2 q^{42} - 2 q^{43} + 10 q^{44} - 8 q^{45} - 5 q^{46} + 5 q^{47} - 2 q^{48} - 53 q^{49} + 2 q^{50} + 8 q^{51} + q^{52} - 18 q^{53} - 8 q^{54} + 5 q^{55} + 2 q^{56} + 13 q^{57} - 27 q^{58} - 40 q^{59} + 2 q^{60} - 20 q^{61} + 11 q^{62} + 3 q^{63} - 2 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 3 q^{68} - 5 q^{69} + 3 q^{70} - 10 q^{71} + 2 q^{72} + 36 q^{73} + 4 q^{74} - 2 q^{75} - 2 q^{76} + 50 q^{77} + 4 q^{78} - 11 q^{79} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 16 q^{83} + 3 q^{84} - 8 q^{85} - 13 q^{86} - 18 q^{87} + 5 q^{88} - 46 q^{89} - 2 q^{90} - 39 q^{91} - 5 q^{92} - 6 q^{93} + 15 q^{94} + 12 q^{95} + 2 q^{96} + 16 q^{97} - 62 q^{98} - 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^10 + 10 * q^11 + 8 * q^12 + q^13 - 3 * q^14 + 2 * q^15 - 2 * q^16 + 3 * q^17 + 2 * q^18 - 12 * q^19 + 2 * q^20 - 2 * q^21 + 10 * q^22 + 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + 27 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 5 * q^33 + 22 * q^34 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 13 * q^38 + q^39 - 2 * q^40 - 23 * q^41 + 2 * q^42 - 2 * q^43 + 10 * q^44 - 8 * q^45 - 5 * q^46 + 5 * q^47 - 2 * q^48 - 53 * q^49 + 2 * q^50 + 8 * q^51 + q^52 - 18 * q^53 - 8 * q^54 + 5 * q^55 + 2 * q^56 + 13 * q^57 - 27 * q^58 - 40 * q^59 + 2 * q^60 - 20 * q^61 + 11 * q^62 + 3 * q^63 - 2 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 3 * q^68 - 5 * q^69 + 3 * q^70 - 10 * q^71 + 2 * q^72 + 36 * q^73 + 4 * q^74 - 2 * q^75 - 2 * q^76 + 50 * q^77 + 4 * q^78 - 11 * q^79 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 16 * q^83 + 3 * q^84 - 8 * q^85 - 13 * q^86 - 18 * q^87 + 5 * q^88 - 46 * q^89 - 2 * q^90 - 39 * q^91 - 5 * q^92 - 6 * q^93 + 15 * q^94 + 12 * q^95 + 2 * q^96 + 16 * q^97 - 62 * q^98 - 10 * q^99

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