LMFDB - Embedded newform 735.2.s.j.656.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(521,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("735.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.s (of order $6$, degree $2$, not 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.2
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	735.656
Dual form			735.2.s.j.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18614 + 1.26217i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(2.18614 + 3.78651i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 4.25639i) q^{6} +5.98844i q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})$	\(q+(2.18614 + 1.26217i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(2.18614 + 3.78651i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 4.25639i) q^{6} +5.98844i q^{8} +(-0.186141 + 2.99422i) q^{9} +(-2.18614 + 1.26217i) q^{10} +(-0.686141 + 0.396143i) q^{11} +(2.18614 - 7.25061i) q^{12} +5.84096i q^{13} +(1.68614 - 0.396143i) q^{15} +(-3.18614 + 5.51856i) q^{16} +(0.686141 + 1.18843i) q^{17} +(-4.18614 + 6.31084i) q^{18} +(3.00000 + 1.73205i) q^{19} -4.37228 q^{20} -2.00000 q^{22} +(1.62772 + 0.939764i) q^{23} +(7.55842 - 7.10313i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-7.37228 + 12.7692i) q^{26} +(4.00000 - 3.31662i) q^{27} -4.25639i q^{29} +(4.18614 + 1.26217i) q^{30} +(3.00000 - 1.73205i) q^{31} +(-3.55842 + 2.05446i) q^{32} +(1.31386 + 0.396143i) q^{33} +3.46410i q^{34} +(-11.7446 + 5.84096i) q^{36} +(-2.37228 + 4.10891i) q^{37} +(4.37228 + 7.57301i) q^{38} +(7.37228 - 6.92820i) q^{39} +(-5.18614 - 2.99422i) q^{40} -6.00000 q^{41} -6.74456 q^{43} +(-3.00000 - 1.73205i) q^{44} +(-2.50000 - 1.65831i) q^{45} +(2.37228 + 4.10891i) q^{46} +(3.68614 - 6.38458i) q^{47} +(10.7446 - 2.52434i) q^{48} -2.52434i q^{50} +(0.686141 - 2.27567i) q^{51} +(-22.1168 + 12.7692i) q^{52} +(7.37228 - 4.25639i) q^{53} +(12.9307 - 2.20193i) q^{54} -0.792287i q^{55} +(-1.37228 - 5.84096i) q^{57} +(5.37228 - 9.30506i) q^{58} +(-1.37228 - 2.37686i) q^{59} +(5.18614 + 5.51856i) q^{60} +(-6.00000 - 3.46410i) q^{61} +8.74456 q^{62} +2.37228 q^{64} +(-5.05842 - 2.92048i) q^{65} +(2.37228 + 2.52434i) q^{66} +(3.37228 + 5.84096i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-0.744563 - 3.16915i) q^{69} -13.5615i q^{71} +(-17.9307 - 1.11469i) q^{72} +(6.00000 - 3.46410i) q^{73} +(-10.3723 + 5.98844i) q^{74} +(-0.500000 + 1.65831i) q^{75} +15.1460i q^{76} +(24.8614 - 5.84096i) q^{78} +(-1.68614 + 2.92048i) q^{79} +(-3.18614 - 5.51856i) q^{80} +(-8.93070 - 1.11469i) q^{81} +(-13.1168 - 7.57301i) q^{82} +5.48913 q^{83} -1.37228 q^{85} +(-14.7446 - 8.51278i) q^{86} +(-5.37228 + 5.04868i) q^{87} +(-2.37228 - 4.10891i) q^{88} +(-1.62772 + 2.81929i) q^{89} +(-3.37228 - 6.78073i) q^{90} +8.21782i q^{92} +(-5.74456 - 1.73205i) q^{93} +(16.1168 - 9.30506i) q^{94} +(-3.00000 + 1.73205i) q^{95} +(6.81386 + 2.05446i) q^{96} -1.08724i q^{97} +(-1.05842 - 2.12819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - 4 q^{6} + 5 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 - 4 * q^6 + 5 * q^9	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - 4 q^{6} + 5 q^{9} - 3 q^{10} + 3 q^{11} + 3 q^{12} + q^{15} - 7 q^{16} - 3 q^{17} - 11 q^{18} + 12 q^{19} - 6 q^{20} - 8 q^{22} + 18 q^{23} + 13 q^{24} - 2 q^{25} - 18 q^{26} + 16 q^{27} + 11 q^{30} + 12 q^{31} + 3 q^{32} + 11 q^{33} - 24 q^{36} + 2 q^{37} + 6 q^{38} + 18 q^{39} - 15 q^{40} - 24 q^{41} - 4 q^{43} - 12 q^{44} - 10 q^{45} - 2 q^{46} + 9 q^{47} + 20 q^{48} - 3 q^{51} - 54 q^{52} + 18 q^{53} + 23 q^{54} + 6 q^{57} + 10 q^{58} + 6 q^{59} + 15 q^{60} - 24 q^{61} + 12 q^{62} - 2 q^{64} - 3 q^{65} - 2 q^{66} + 2 q^{67} - 12 q^{68} + 20 q^{69} - 43 q^{72} + 24 q^{73} - 30 q^{74} - 2 q^{75} + 42 q^{78} - q^{79} - 7 q^{80} - 7 q^{81} - 18 q^{82} - 24 q^{83} + 6 q^{85} - 36 q^{86} - 10 q^{87} + 2 q^{88} - 18 q^{89} - 2 q^{90} + 30 q^{94} - 12 q^{95} + 33 q^{96} + 13 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 - 4 * q^6 + 5 * q^9 - 3 * q^10 + 3 * q^11 + 3 * q^12 + q^15 - 7 * q^16 - 3 * q^17 - 11 * q^18 + 12 * q^19 - 6 * q^20 - 8 * q^22 + 18 * q^23 + 13 * q^24 - 2 * q^25 - 18 * q^26 + 16 * q^27 + 11 * q^30 + 12 * q^31 + 3 * q^32 + 11 * q^33 - 24 * q^36 + 2 * q^37 + 6 * q^38 + 18 * q^39 - 15 * q^40 - 24 * q^41 - 4 * q^43 - 12 * q^44 - 10 * q^45 - 2 * q^46 + 9 * q^47 + 20 * q^48 - 3 * q^51 - 54 * q^52 + 18 * q^53 + 23 * q^54 + 6 * q^57 + 10 * q^58 + 6 * q^59 + 15 * q^60 - 24 * q^61 + 12 * q^62 - 2 * q^64 - 3 * q^65 - 2 * q^66 + 2 * q^67 - 12 * q^68 + 20 * q^69 - 43 * q^72 + 24 * q^73 - 30 * q^74 - 2 * q^75 + 42 * q^78 - q^79 - 7 * q^80 - 7 * q^81 - 18 * q^82 - 24 * q^83 + 6 * q^85 - 36 * q^86 - 10 * q^87 + 2 * q^88 - 18 * q^89 - 2 * q^90 + 30 * q^94 - 12 * q^95 + 33 * q^96 + 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	2.18614	+	1.26217i	1.54583	+	0.892488i	0.998453	+	0.0556054i	$0.0177089\pi$
$2$	2.18614	+	1.26217i	1.54583	+	0.892488i	0.547382	+	0.836883i	$0.315624\pi$
$3$	−1.18614	−	1.26217i	−0.684819	−	0.728714i
$3$	−1.18614	−	1.26217i	−0.684819	−	0.728714i
$4$	2.18614	+	3.78651i	1.09307	+	1.89325i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.00000	−	4.25639i	−0.408248	−	1.73766i
$7$		0			0
$7$		0			0
$8$			5.98844i			2.11723i
$9$	−0.186141	+	2.99422i	−0.0620469	+	0.998073i
$10$	−2.18614	+	1.26217i	−0.691318	+	0.399133i
$11$	−0.686141	+	0.396143i	−0.206879	+	0.119442i	−0.599860	−	0.800105i	$-0.704777\pi$
$11$	−0.686141	+	0.396143i	−0.206879	+	0.119442i	0.392981	+	0.919547i	$0.371444\pi$
$12$	2.18614	−	7.25061i	0.631084	−	2.09307i
$13$			5.84096i			1.61999i	0.586436	+	0.809996i	$0.300531\pi$
$13$			5.84096i			1.61999i	−0.586436	+	0.809996i	$0.699469\pi$
$14$		0			0
$15$	1.68614	−	0.396143i	0.435360	−	0.102284i
$16$	−3.18614	+	5.51856i	−0.796535	+	1.37964i
$17$	0.686141	+	1.18843i	0.166414	+	0.288237i	0.937156	−	0.348910i	$-0.113448\pi$
$17$	0.686141	+	1.18843i	0.166414	+	0.288237i	−0.770743	+	0.637146i	$0.780115\pi$
$18$	−4.18614	+	6.31084i	−0.986683	+	1.48748i
$19$	3.00000	+	1.73205i	0.688247	+	0.397360i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	3.00000	+	1.73205i	0.688247	+	0.397360i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−4.37228			−0.977672
$21$		0			0
$22$	−2.00000			−0.426401
$23$	1.62772	+	0.939764i	0.339403	+	0.195954i	0.660008	−	0.751259i	$-0.270553\pi$
$23$	1.62772	+	0.939764i	0.339403	+	0.195954i	−0.320605	+	0.947213i	$0.603886\pi$
$24$	7.55842	−	7.10313i	1.54286	−	1.44992i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−7.37228	+	12.7692i	−1.44582	+	2.50424i
$27$	4.00000	−	3.31662i	0.769800	−	0.638285i
$28$		0			0
$29$		−	4.25639i		−	0.790392i	−0.918597	−	0.395196i	$-0.870677\pi$
$29$		−	4.25639i		−	0.790392i	0.918597	−	0.395196i	$-0.129323\pi$
$30$	4.18614	+	1.26217i	0.764281	+	0.230439i
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	−0.205783	−	0.978598i	$-0.565974\pi$
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	0.744599	+	0.667512i	$0.232641\pi$
$32$	−3.55842	+	2.05446i	−0.629046	+	0.363180i
$33$	1.31386	+	0.396143i	0.228714	+	0.0689597i
$34$			3.46410i			0.594089i
$35$		0			0
$36$	−11.7446	+	5.84096i	−1.95743	+	0.973494i
$37$	−2.37228	+	4.10891i	−0.390001	+	0.675501i	−0.992449	−	0.122657i	$-0.960859\pi$
$37$	−2.37228	+	4.10891i	−0.390001	+	0.675501i	0.602448	+	0.798158i	$0.294192\pi$
$38$	4.37228	+	7.57301i	0.709278	+	1.22850i
$39$	7.37228	−	6.92820i	1.18051	−	1.10940i
$40$	−5.18614	−	2.99422i	−0.820001	−	0.473428i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−6.74456			−1.02854			−0.514268	−	0.857629i	$-0.671936\pi$
$43$	−6.74456			−1.02854			−0.514268	+	0.857629i	$0.671936\pi$
$44$	−3.00000	−	1.73205i	−0.452267	−	0.261116i
$45$	−2.50000	−	1.65831i	−0.372678	−	0.247207i
$46$	2.37228	+	4.10891i	0.349774	+	0.605826i
$47$	3.68614	−	6.38458i	0.537679	−	0.931287i	−0.461350	−	0.887218i	$-0.652635\pi$
$47$	3.68614	−	6.38458i	0.537679	−	0.931287i	0.999029	−	0.0440687i	$-0.0140321\pi$
$48$	10.7446	−	2.52434i	1.55084	−	0.364357i
$49$		0			0
$50$		−	2.52434i		−	0.356995i
$51$	0.686141	−	2.27567i	0.0960789	−	0.318658i
$52$	−22.1168	+	12.7692i	−3.06705	+	1.77076i
$53$	7.37228	−	4.25639i	1.01266	−	0.584660i	0.100691	−	0.994918i	$-0.467895\pi$
$53$	7.37228	−	4.25639i	1.01266	−	0.584660i	0.911970	+	0.410258i	$0.134561\pi$
$54$	12.9307	−	2.20193i	1.75965	−	0.299645i
$55$		−	0.792287i		−	0.106832i
$56$		0			0
$57$	−1.37228	−	5.84096i	−0.181763	−	0.773654i
$58$	5.37228	−	9.30506i	0.705415	−	1.22181i
$59$	−1.37228	−	2.37686i	−0.178656	−	0.309441i	0.762765	−	0.646676i	$-0.223842\pi$
$59$	−1.37228	−	2.37686i	−0.178656	−	0.309441i	−0.941420	+	0.337235i	$0.890508\pi$
$60$	5.18614	+	5.51856i	0.669528	+	0.712443i
$61$	−6.00000	−	3.46410i	−0.768221	−	0.443533i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	−6.00000	−	3.46410i	−0.768221	−	0.443533i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	8.74456			1.11056
$63$		0			0
$64$	2.37228			0.296535
$65$	−5.05842	−	2.92048i	−0.627420	−	0.362241i
$66$	2.37228	+	2.52434i	0.292008	+	0.310725i
$67$	3.37228	+	5.84096i	0.411990	+	0.713587i	0.995107	−	0.0988007i	$-0.0315006\pi$
$67$	3.37228	+	5.84096i	0.411990	+	0.713587i	−0.583118	+	0.812388i	$0.698167\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	−0.744563	−	3.16915i	−0.0896348	−	0.381521i
$70$		0			0
$71$		−	13.5615i		−	1.60945i	−0.593649	−	0.804724i	$-0.702313\pi$
$71$		−	13.5615i		−	1.60945i	0.593649	−	0.804724i	$-0.297687\pi$
$72$	−17.9307	−	1.11469i	−2.11315	−	0.131368i
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	−0.105937	−	0.994373i	$-0.533784\pi$
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	0.808184	+	0.588930i	$0.200451\pi$
$74$	−10.3723	+	5.98844i	−1.20575	+	0.696142i
$75$	−0.500000	+	1.65831i	−0.0577350	+	0.191485i
$76$			15.1460i			1.73737i
$77$		0			0
$78$	24.8614	−	5.84096i	2.81500	−	0.661359i
$79$	−1.68614	+	2.92048i	−0.189706	+	0.328580i	−0.945152	−	0.326631i	$-0.894087\pi$
$79$	−1.68614	+	2.92048i	−0.189706	+	0.328580i	0.755446	+	0.655210i	$0.227420\pi$
$80$	−3.18614	−	5.51856i	−0.356221	−	0.616993i
$81$	−8.93070	−	1.11469i	−0.992300	−	0.123855i
$82$	−13.1168	−	7.57301i	−1.44851	−	0.836299i
$83$	5.48913			0.602510			0.301255	−	0.953544i	$-0.402594\pi$
$83$	5.48913			0.602510			0.301255	+	0.953544i	$0.402594\pi$
$84$		0			0
$85$	−1.37228			−0.148845
$86$	−14.7446	−	8.51278i	−1.58995	−	0.917956i
$87$	−5.37228	+	5.04868i	−0.575969	+	0.541275i
$88$	−2.37228	−	4.10891i	−0.252886	−	0.438011i
$89$	−1.62772	+	2.81929i	−0.172538	+	0.298844i	−0.939306	−	0.343079i	$-0.888530\pi$
$89$	−1.62772	+	2.81929i	−0.172538	+	0.298844i	0.766769	+	0.641924i	$0.221863\pi$
$90$	−3.37228	−	6.78073i	−0.355470	−	0.714751i
$91$		0			0
$92$			8.21782i			0.856767i
$93$	−5.74456	−	1.73205i	−0.595683	−	0.179605i
$94$	16.1168	−	9.30506i	1.66233	−	0.959744i
$95$	−3.00000	+	1.73205i	−0.307794	+	0.177705i
$96$	6.81386	+	2.05446i	0.695437	+	0.209682i
$97$		−	1.08724i		−	0.110393i	−0.998476	−	0.0551963i	$-0.982422\pi$
$97$		−	1.08724i		−	0.110393i	0.998476	−	0.0551963i	$-0.0175785\pi$
$98$		0			0
$99$	−1.05842	−	2.12819i	−0.106375	−	0.213892i
$100$	2.18614	−	3.78651i	0.218614	−	0.378651i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	4.37228	−	4.10891i	0.432920	−	0.406843i
$103$	14.0584	+	8.11663i	1.38522	+	0.799756i	0.992772	−	0.120019i	$-0.0382957\pi$
$103$	14.0584	+	8.11663i	1.38522	+	0.799756i	0.392446	+	0.919775i	$0.371629\pi$
$104$	−34.9783			−3.42990
$105$		0			0
$106$	21.4891			2.08721
$107$	5.74456	+	3.31662i	0.555348	+	0.320630i	0.751276	−	0.659988i	$-0.229439\pi$
$107$	5.74456	+	3.31662i	0.555348	+	0.320630i	−0.195928	+	0.980618i	$0.562772\pi$
$108$	21.3030	+	7.89542i	2.04988	+	0.759737i
$109$	−0.0584220	−	0.101190i	−0.00559581	−	0.00969223i	0.863214	−	0.504838i	$-0.168448\pi$
$109$	−0.0584220	−	0.101190i	−0.00559581	−	0.00969223i	−0.868810	+	0.495146i	$0.835115\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$	8.00000	−	1.87953i	0.759326	−	0.178397i
$112$		0			0
$113$		−	10.0974i		−	0.949879i	−0.880018	−	0.474939i	$-0.842470\pi$
$113$		−	10.0974i		−	0.949879i	0.880018	−	0.474939i	$-0.157530\pi$
$114$	4.37228	−	14.5012i	0.409502	−	1.35816i
$115$	−1.62772	+	0.939764i	−0.151786	+	0.0876334i
$116$	16.1168	−	9.30506i	1.49641	−	0.863954i
$117$	−17.4891	−	1.08724i	−1.61687	−	0.100515i
$118$		−	6.92820i		−	0.637793i
$119$		0			0
$120$	2.37228	+	10.0974i	0.216559	+	0.921758i
$121$	−5.18614	+	8.98266i	−0.471467	+	0.816605i
$122$	−8.74456	−	15.1460i	−0.791696	−	1.37126i
$123$	7.11684	+	7.57301i	0.641704	+	0.682836i
$124$	13.1168	+	7.57301i	1.17793	+	0.680077i
$125$	1.00000			0.0894427
$126$		0			0
$127$	10.7446			0.953426			0.476713	−	0.879059i	$-0.341828\pi$
$127$	10.7446			0.953426			0.476713	+	0.879059i	$0.341828\pi$
$128$	12.3030	+	7.10313i	1.08744	+	0.627834i
$129$	8.00000	+	8.51278i	0.704361	+	0.749508i
$130$	−7.37228	−	12.7692i	−0.646592	−	1.11993i
$131$	8.74456	−	15.1460i	0.764016	−	1.32331i	−0.176749	−	0.984256i	$-0.556558\pi$
$131$	8.74456	−	15.1460i	0.764016	−	1.32331i	0.940765	−	0.339059i	$-0.110108\pi$
$132$	1.37228	+	5.84096i	0.119442	+	0.508391i
$133$		0			0
$134$			17.0256i			1.47078i
$135$	0.872281	+	5.12241i	0.0750740	+	0.440867i
$136$	−7.11684	+	4.10891i	−0.610264	+	0.352336i
$137$	11.4891	−	6.63325i	0.981582	−	0.566717i	0.0788348	−	0.996888i	$-0.474880\pi$
$137$	11.4891	−	6.63325i	0.981582	−	0.566717i	0.902747	+	0.430171i	$0.141547\pi$
$138$	2.37228	−	7.86797i	0.201942	−	0.669766i
$139$		−	1.28962i		−	0.109384i	−0.998503	−	0.0546921i	$-0.982582\pi$
$139$		−	1.28962i		−	0.109384i	0.998503	−	0.0546921i	$-0.0174177\pi$
$140$		0			0
$141$	−12.4307	+	2.92048i	−1.04685	+	0.245949i
$142$	17.1168	−	29.6472i	1.43641	−	2.48794i
$143$	−2.31386	−	4.00772i	−0.193495	−	0.335143i
$144$	−15.9307	−	10.5672i	−1.32756	−	0.880603i
$145$	3.68614	+	2.12819i	0.306117	+	0.176737i
$146$	17.4891			1.44741
$147$		0			0
$148$	−20.7446			−1.70519
$149$	8.74456	+	5.04868i	0.716382	+	0.413604i	0.813420	−	0.581677i	$-0.197603\pi$
$149$	8.74456	+	5.04868i	0.716382	+	0.413604i	−0.0970373	+	0.995281i	$0.530937\pi$
$150$	−3.18614	+	2.99422i	−0.260147	+	0.244477i
$151$	−1.68614	−	2.92048i	−0.137216	−	0.237665i	0.789226	−	0.614103i	$-0.210482\pi$
$151$	−1.68614	−	2.92048i	−0.137216	−	0.237665i	−0.926442	+	0.376438i	$0.877149\pi$
$152$	−10.3723	+	17.9653i	−0.841303	+	1.45718i
$153$	−3.68614	+	1.83324i	−0.298007	+	0.148209i
$154$		0			0
$155$			3.46410i			0.278243i
$156$	42.3505	+	12.7692i	3.39076	+	1.02235i
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	−7.37228	+	4.25639i	−0.586507	+	0.338620i
$159$	−14.1168	−	4.25639i	−1.11954	−	0.337554i
$160$		−	4.10891i		−	0.324838i
$161$		0			0
$162$	−18.1168	−	13.7089i	−1.42339	−	1.07708i
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$	−13.1168	−	22.7190i	−1.02425	−	1.77406i
$165$	−1.00000	+	0.939764i	−0.0778499	+	0.0731605i
$166$	12.0000	+	6.92820i	0.931381	+	0.537733i
$167$	−22.1168			−1.71145			−0.855726	−	0.517429i	$-0.826889\pi$
$167$	−22.1168			−1.71145			−0.855726	+	0.517429i	$0.826889\pi$
$168$		0			0
$169$	−21.1168			−1.62437
$170$	−3.00000	−	1.73205i	−0.230089	−	0.132842i
$171$	−5.74456	+	8.66025i	−0.439298	+	0.662266i
$172$	−14.7446	−	25.5383i	−1.12426	−	1.94728i
$173$	−8.05842	+	13.9576i	−0.612670	+	1.06118i	0.378118	+	0.925757i	$0.376571\pi$
$173$	−8.05842	+	13.9576i	−0.612670	+	1.06118i	−0.990788	+	0.135419i	$0.956762\pi$
$174$	−18.1168	+	4.25639i	−1.37343	+	0.322676i
$175$		0			0
$176$		−	5.04868i		−	0.380558i
$177$	−1.37228	+	4.55134i	−0.103147	+	0.342100i
$178$	−7.11684	+	4.10891i	−0.533430	+	0.307976i
$179$	−5.74456	+	3.31662i	−0.429369	+	0.247896i	−0.699078	−	0.715046i	$-0.746406\pi$
$179$	−5.74456	+	3.31662i	−0.429369	+	0.247896i	0.269709	+	0.962942i	$0.413073\pi$
$180$	0.813859	−	13.0916i	0.0606615	−	0.975788i
$181$		−	18.6101i		−	1.38328i	−0.722242	−	0.691640i	$-0.756889\pi$
$181$		−	18.6101i		−	1.38328i	0.722242	−	0.691640i	$-0.243111\pi$
$182$		0			0
$183$	2.74456	+	11.6819i	0.202884	+	0.863553i
$184$	−5.62772	+	9.74749i	−0.414881	+	0.718595i
$185$	−2.37228	−	4.10891i	−0.174414	−	0.302093i
$186$	−10.3723	−	11.0371i	−0.760533	−	0.809281i
$187$	−0.941578	−	0.543620i	−0.0688550	−	0.0397535i
$188$	32.2337			2.35088
$189$		0			0
$190$	−8.74456			−0.634397
$191$	−13.5475	−	7.82168i	−0.980266	−	0.565957i	−0.0779156	−	0.996960i	$-0.524826\pi$
$191$	−13.5475	−	7.82168i	−0.980266	−	0.565957i	−0.902350	+	0.431003i	$0.858160\pi$
$192$	−2.81386	−	2.99422i	−0.203073	−	0.216089i
$193$	−11.1168	−	19.2549i	−0.800208	−	1.38600i	−0.919479	−	0.393139i	$-0.871389\pi$
$193$	−11.1168	−	19.2549i	−0.800208	−	1.38600i	0.119271	−	0.992862i	$-0.461944\pi$
$194$	1.37228	−	2.37686i	0.0985241	−	0.170649i
$195$	2.31386	+	9.84868i	0.165699	+	0.705279i
$196$		0			0
$197$			22.3692i			1.59374i	0.604152	+	0.796869i	$0.293512\pi$
$197$			22.3692i			1.59374i	−0.604152	+	0.796869i	$0.706488\pi$
$198$	0.372281	−	5.98844i	0.0264569	−	0.425580i
$199$	11.2337	−	6.48577i	0.796335	−	0.459764i	−0.0458530	−	0.998948i	$-0.514601\pi$
$199$	11.2337	−	6.48577i	0.796335	−	0.459764i	0.842188	+	0.539184i	$0.181267\pi$
$200$	5.18614	−	2.99422i	0.366716	−	0.211723i
$201$	3.37228	−	11.1846i	0.237862	−	0.788900i
$202$		−	15.1460i		−	1.06567i
$203$		0			0
$204$	10.1168	−	2.37686i	0.708321	−	0.166414i
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	20.4891	+	35.4882i	1.42755	+	2.47258i
$207$	−3.11684	+	4.69882i	−0.216636	+	0.326591i
$208$	−32.2337	−	18.6101i	−2.23500	−	1.29038i
$209$	−2.74456			−0.189845
$210$		0			0
$211$	6.11684			0.421101			0.210550	−	0.977583i	$-0.432474\pi$
$211$	6.11684			0.421101			0.210550	+	0.977583i	$0.432474\pi$
$212$	32.2337	+	18.6101i	2.21382	+	1.27815i
$213$	−17.1168	+	16.0858i	−1.17283	+	1.10218i
$214$	8.37228	+	14.5012i	0.572317	+	0.991283i
$215$	3.37228	−	5.84096i	0.229988	−	0.398350i
$216$	19.8614	+	23.9538i	1.35140	+	1.62985i
$217$		0			0
$218$		−	0.294954i		−	0.0199768i
$219$	−11.4891	−	3.46410i	−0.776363	−	0.234082i
$220$	3.00000	−	1.73205i	0.202260	−	0.116775i
$221$	−6.94158	+	4.00772i	−0.466941	+	0.269589i
$222$	19.8614	+	5.98844i	1.33301	+	0.401918i
$223$			20.9870i			1.40539i	0.711490	+	0.702696i	$0.248021\pi$
$223$			20.9870i			1.40539i	−0.711490	+	0.702696i	$0.751979\pi$
$224$		0			0
$225$	2.68614	−	1.33591i	0.179076	−	0.0890605i
$226$	12.7446	−	22.0742i	0.847756	−	1.46836i
$227$	7.80298	+	13.5152i	0.517902	+	0.897033i	0.999784	+	0.0207966i	$0.00662025\pi$
$227$	7.80298	+	13.5152i	0.517902	+	0.897033i	−0.481881	+	0.876236i	$0.660046\pi$
$228$	19.1168	−	17.9653i	1.26604	−	1.18978i
$229$	4.11684	+	2.37686i	0.272049	+	0.157067i	0.629818	−	0.776743i	$-0.283129\pi$
$229$	4.11684	+	2.37686i	0.272049	+	0.157067i	−0.357770	+	0.933810i	$0.616463\pi$
$230$	−4.74456			−0.312847
$231$		0			0
$232$	25.4891			1.67344
$233$	−3.25544	−	1.87953i	−0.213271	−	0.123132i	0.389560	−	0.921001i	$-0.372627\pi$
$233$	−3.25544	−	1.87953i	−0.213271	−	0.123132i	−0.602831	+	0.797869i	$0.705961\pi$
$234$	−36.8614	−	24.4511i	−2.40971	−	1.59842i
$235$	3.68614	+	6.38458i	0.240457	+	0.416484i
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$	5.68614	−	1.33591i	0.369355	−	0.0867765i
$238$		0			0
$239$			15.6434i			1.01188i	0.862567	+	0.505942i	$0.168855\pi$
$239$			15.6434i			1.01188i	−0.862567	+	0.505942i	$0.831145\pi$
$240$	−3.18614	+	10.5672i	−0.205664	+	0.682112i
$241$	20.2337	−	11.6819i	1.30337	−	0.752499i	0.322386	−	0.946608i	$-0.395515\pi$
$241$	20.2337	−	11.6819i	1.30337	−	0.752499i	0.980980	+	0.194109i	$0.0621816\pi$
$242$	−22.6753	+	13.0916i	−1.45762	+	0.841558i
$243$	9.18614	+	12.5942i	0.589291	+	0.807921i
$244$		−	30.2921i		−	1.93925i
$245$		0			0
$246$	6.00000	+	25.5383i	0.382546	+	1.62826i
$247$	−10.1168	+	17.5229i	−0.643719	+	1.11495i
$248$	10.3723	+	17.9653i	0.658641	+	1.14080i
$249$	−6.51087	−	6.92820i	−0.412610	−	0.439057i
$250$	2.18614	+	1.26217i	0.138264	+	0.0798266i
$251$	17.4891			1.10390			0.551952	−	0.833876i	$-0.313883\pi$
$251$	17.4891			1.10390			0.551952	+	0.833876i	$0.313883\pi$
$252$		0			0
$253$	−1.48913			−0.0936205
$254$	23.4891	+	13.5615i	1.47384	+	0.850921i
$255$	1.62772	+	1.73205i	0.101932	+	0.108465i
$256$	15.5584	+	26.9480i	0.972401	+	1.68425i
$257$	−11.7446	+	20.3422i	−0.732606	+	1.26891i	0.223160	+	0.974782i	$0.428363\pi$
$257$	−11.7446	+	20.3422i	−0.732606	+	1.26891i	−0.955766	+	0.294128i	$0.904971\pi$
$258$	6.74456	+	28.7075i	0.419898	+	1.78725i
$259$		0			0
$260$		−	25.5383i		−	1.58382i
$261$	12.7446	+	0.792287i	0.788869	+	0.0490413i
$262$	38.2337	−	22.0742i	2.36209	−	1.36375i
$263$	−11.7446	+	6.78073i	−0.724201	+	0.418118i	−0.816297	−	0.577633i	$-0.803977\pi$
$263$	−11.7446	+	6.78073i	−0.724201	+	0.418118i	0.0920961	+	0.995750i	$0.470643\pi$
$264$	−2.37228	+	7.86797i	−0.146004	+	0.484240i
$265$			8.51278i			0.522936i
$266$		0			0
$267$	5.48913	−	1.28962i	0.335929	−	0.0789235i
$268$	−14.7446	+	25.5383i	−0.900668	+	1.56000i
$269$	4.37228	+	7.57301i	0.266583	+	0.461735i	0.967977	−	0.251039i	$-0.0807721\pi$
$269$	4.37228	+	7.57301i	0.266583	+	0.461735i	−0.701394	+	0.712773i	$0.747439\pi$
$270$	−4.55842	+	12.2993i	−0.277417	+	0.748511i
$271$	−13.1168	−	7.57301i	−0.796792	−	0.460028i	0.0455565	−	0.998962i	$-0.485494\pi$
$271$	−13.1168	−	7.57301i	−0.796792	−	0.460028i	−0.842348	+	0.538934i	$0.818827\pi$
$272$	−8.74456			−0.530217
$273$		0			0
$274$	33.4891			2.02315
$275$	0.686141	+	0.396143i	0.0413758	+	0.0238884i
$276$	10.3723	−	9.74749i	0.624338	−	0.586730i
$277$	3.11684	+	5.39853i	0.187273	+	0.324366i	0.944340	−	0.328971i	$-0.106702\pi$
$277$	3.11684	+	5.39853i	0.187273	+	0.324366i	−0.757067	+	0.653337i	$0.773368\pi$
$278$	1.62772	−	2.81929i	0.0976241	−	0.169090i
$279$	4.62772	+	9.30506i	0.277054	+	0.557080i
$280$		0			0
$281$			4.84630i			0.289106i	0.989497	+	0.144553i	$0.0461744\pi$
$281$			4.84630i			0.289106i	−0.989497	+	0.144553i	$0.953826\pi$
$282$	−30.8614	−	9.30506i	−1.83777	−	0.554109i
$283$	−8.05842	+	4.65253i	−0.479023	+	0.276564i	−0.720009	−	0.693964i	$-0.755863\pi$
$283$	−8.05842	+	4.65253i	−0.479023	+	0.276564i	0.240986	+	0.970529i	$0.422529\pi$
$284$	51.3505	−	29.6472i	3.04709	−	1.75924i
$285$	5.74456	+	1.73205i	0.340279	+	0.102598i
$286$		−	11.6819i		−	0.690767i
$287$		0			0
$288$	−5.48913	−	11.0371i	−0.323450	−	0.650368i
$289$	7.55842	−	13.0916i	0.444613	−	0.770092i
$290$	5.37228	+	9.30506i	0.315471	+	0.546412i
$291$	−1.37228	+	1.28962i	−0.0804446	+	0.0755989i
$292$	26.2337	+	15.1460i	1.53521	+	0.886354i
$293$	−28.1168			−1.64260			−0.821302	−	0.570494i	$-0.806752\pi$
$293$	−28.1168			−1.64260			−0.821302	+	0.570494i	$0.806752\pi$
$294$		0			0
$295$	2.74456			0.159795
$296$	−24.6060	−	14.2063i	−1.43019	−	0.825722i
$297$	−1.43070	+	3.86025i	−0.0830178	+	0.223994i
$298$	12.7446	+	22.0742i	0.738273	+	1.27873i
$299$	−5.48913	+	9.50744i	−0.317444	+	0.549830i
$300$	−7.37228	+	1.73205i	−0.425639	+	0.100000i
$301$		0			0
$302$		−	8.51278i		−	0.489855i
$303$	−3.00000	+	9.94987i	−0.172345	+	0.571605i
$304$	−19.1168	+	11.0371i	−1.09643	+	0.633022i
$305$	6.00000	−	3.46410i	0.343559	−	0.198354i
$306$	−10.3723	−	0.644810i	−0.592944	−	0.0368613i
$307$		−	7.13058i		−	0.406964i	−0.979079	−	0.203482i	$-0.934774\pi$
$307$		−	7.13058i		−	0.406964i	0.979079	−	0.203482i	$-0.0652258\pi$
$308$		0			0
$309$	−6.43070	−	27.3716i	−0.365830	−	1.55711i
$310$	−4.37228	+	7.57301i	−0.248329	+	0.430118i
$311$	−10.1168	−	17.5229i	−0.573674	−	0.993632i	−0.996184	−	0.0872739i	$-0.972184\pi$
$311$	−10.1168	−	17.5229i	−0.573674	−	0.993632i	0.422511	−	0.906358i	$-0.361149\pi$
$312$	41.4891	+	44.1485i	2.34886	+	2.49941i
$313$	21.1753	+	12.2255i	1.19690	+	0.691029i	0.959862	−	0.280472i	$-0.0904911\pi$
$313$	21.1753	+	12.2255i	1.19690	+	0.691029i	0.237035	+	0.971501i	$0.423824\pi$
$314$		0			0
$315$		0			0
$316$	−14.7446			−0.829446
$317$	−7.37228	−	4.25639i	−0.414069	−	0.239063i	0.278468	−	0.960446i	$-0.410173\pi$
$317$	−7.37228	−	4.25639i	−0.414069	−	0.239063i	−0.692536	+	0.721383i	$0.743507\pi$
$318$	−25.4891	−	27.1229i	−1.42936	−	1.52098i
$319$	1.68614	+	2.92048i	0.0944058	+	0.163516i
$320$	−1.18614	+	2.05446i	−0.0663073	+	0.114848i
$321$	−2.62772	−	11.1846i	−0.146665	−	0.624263i
$322$		0			0
$323$			4.75372i			0.264504i
$324$	−15.3030	−	36.2530i	−0.850166	−	2.01406i
$325$	5.05842	−	2.92048i	0.280591	−	0.161999i
$326$	−17.4891	+	10.0974i	−0.968633	+	0.559241i
$327$	−0.0584220	+	0.193764i	−0.00323074	+	0.0107152i
$328$		−	35.9306i		−	1.98394i
$329$		0			0
$330$	−3.37228	+	0.792287i	−0.185638	+	0.0436140i
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	12.0000	+	20.7846i	0.658586	+	1.14070i
$333$	−11.8614	−	7.86797i	−0.650001	−	0.431162i
$334$	−48.3505	−	27.9152i	−2.64562	−	1.52745i
$335$	−6.74456			−0.368495
$336$		0			0
$337$	−18.2337			−0.993252			−0.496626	−	0.867965i	$-0.665428\pi$
$337$	−18.2337			−0.993252			−0.496626	+	0.867965i	$0.665428\pi$
$338$	−46.1644	−	26.6530i	−2.51101	−	1.44973i
$339$	−12.7446	+	11.9769i	−0.692190	+	0.650495i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	−1.37228	+	2.37686i	−0.0743132	+	0.128714i
$342$	−23.4891	+	11.6819i	−1.27015	+	0.631686i
$343$		0			0
$344$		−	40.3894i		−	2.17765i
$345$	3.11684	+	0.939764i	0.167805	+	0.0505952i
$346$	−35.2337	+	20.3422i	−1.89417	+	1.09360i
$347$	−15.8614	+	9.15759i	−0.851485	+	0.491605i	−0.861152	−	0.508348i	$-0.830256\pi$
$347$	−15.8614	+	9.15759i	−0.851485	+	0.491605i	0.00966668	+	0.999953i	$0.496923\pi$
$348$	−30.8614	−	9.30506i	−1.65435	−	0.498804i
$349$			4.75372i			0.254461i	0.991873	+	0.127230i	$0.0406088\pi$
$349$			4.75372i			0.254461i	−0.991873	+	0.127230i	$0.959391\pi$
$350$		0			0
$351$	19.3723	+	23.3639i	1.03402	+	1.24707i
$352$	1.62772	−	2.81929i	0.0867577	−	0.150269i
$353$	−3.94158	−	6.82701i	−0.209789	−	0.363365i	0.741859	−	0.670556i	$-0.233944\pi$
$353$	−3.94158	−	6.82701i	−0.209789	−	0.363365i	−0.951648	+	0.307191i	$0.900611\pi$
$354$	−8.74456	+	8.21782i	−0.464768	+	0.436772i
$355$	11.7446	+	6.78073i	0.623337	+	0.359884i
$356$	−14.2337			−0.754384
$357$		0			0
$358$	−16.7446			−0.884978
$359$	−8.48913	−	4.90120i	−0.448039	−	0.258675i	0.258963	−	0.965887i	$-0.416619\pi$
$359$	−8.48913	−	4.90120i	−0.448039	−	0.258675i	−0.707002	+	0.707212i	$0.749953\pi$
$360$	9.93070	−	14.9711i	0.523394	−	0.789046i
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$	23.4891	−	40.6844i	1.23456	−	2.13832i
$363$	17.4891	−	4.10891i	0.917941	−	0.215662i
$364$		0			0
$365$			6.92820i			0.362639i
$366$	−8.74456	+	29.0024i	−0.457086	+	1.51598i
$367$	21.9416	−	12.6680i	1.14534	−	0.661263i	0.197593	−	0.980284i	$-0.436687\pi$
$367$	21.9416	−	12.6680i	1.14534	−	0.661263i	0.947748	+	0.319021i	$0.103354\pi$
$368$	−10.3723	+	5.98844i	−0.540693	+	0.312169i
$369$	1.11684	−	17.9653i	0.0581406	−	0.935237i
$370$		−	11.9769i		−	0.622648i
$371$		0			0
$372$	−6.00000	−	25.5383i	−0.311086	−	1.32410i
$373$	12.3723	−	21.4294i	0.640612	−	1.10957i	−0.344684	−	0.938719i	$-0.612014\pi$
$373$	12.3723	−	21.4294i	0.640612	−	1.10957i	0.985296	−	0.170854i	$-0.0546528\pi$
$374$	−1.37228	−	2.37686i	−0.0709590	−	0.122905i
$375$	−1.18614	−	1.26217i	−0.0612520	−	0.0651781i
$376$	38.2337	+	22.0742i	1.97175	+	1.13839i
$377$	24.8614			1.28043
$378$		0			0
$379$	1.48913			0.0764912			0.0382456	−	0.999268i	$-0.487823\pi$
$379$	1.48913			0.0764912			0.0382456	+	0.999268i	$0.487823\pi$
$380$	−13.1168	−	7.57301i	−0.672880	−	0.388487i
$381$	−12.7446	−	13.5615i	−0.652924	−	0.694774i
$382$	−19.7446	−	34.1986i	−1.01022	−	1.74975i
$383$	8.74456	−	15.1460i	0.446826	−	0.773926i	−0.551351	−	0.834273i	$-0.685888\pi$
$383$	8.74456	−	15.1460i	0.446826	−	0.773926i	0.998177	+	0.0603475i	$0.0192209\pi$
$384$	−5.62772	−	23.9538i	−0.287188	−	1.22239i
$385$		0			0
$386$		−	56.1253i		−	2.85670i
$387$	1.25544	−	20.1947i	0.0638175	−	1.02655i
$388$	4.11684	−	2.37686i	0.209001	−	0.120667i
$389$	−11.9198	+	6.88192i	−0.604359	+	0.348927i	−0.770755	−	0.637132i	$-0.780121\pi$
$389$	−11.9198	+	6.88192i	−0.604359	+	0.348927i	0.166395	+	0.986059i	$0.446787\pi$
$390$	−7.37228	+	24.4511i	−0.373310	+	1.23813i
$391$			2.57924i			0.130438i
$392$		0			0
$393$	−29.4891	+	6.92820i	−1.48753	+	0.349482i
$394$	−28.2337	+	48.9022i	−1.42239	+	2.46366i
$395$	−1.68614	−	2.92048i	−0.0848389	−	0.146945i
$396$	5.74456	−	8.66025i	0.288675	−	0.435194i
$397$	−3.17527	−	1.83324i	−0.159362	−	0.0920077i	0.418198	−	0.908356i	$-0.362662\pi$
$397$	−3.17527	−	1.83324i	−0.159362	−	0.0920077i	−0.577560	+	0.816348i	$0.695995\pi$
$398$	32.7446			1.64134
$399$		0			0
$400$	6.37228			0.318614
$401$	−2.31386	−	1.33591i	−0.115549	−	0.0667120i	0.441112	−	0.897452i	$-0.354584\pi$
$401$	−2.31386	−	1.33591i	−0.115549	−	0.0667120i	−0.556660	+	0.830740i	$0.687918\pi$
$402$	21.4891	−	20.1947i	1.07178	−	1.00722i
$403$	10.1168	+	17.5229i	0.503956	+	0.872877i
$404$	13.1168	−	22.7190i	0.652587	−	1.13031i
$405$	5.43070	−	7.17687i	0.269854	−	0.356622i
$406$		0			0
$407$		−	3.75906i		−	0.186329i
$408$	13.6277	+	4.10891i	0.674673	+	0.203421i
$409$	−30.3505	+	17.5229i	−1.50074	+	0.866451i	−0.500738	+	0.865599i	$0.666938\pi$
$409$	−30.3505	+	17.5229i	−1.50074	+	0.866451i	−1.00000		0.000851893i	$0.999729\pi$
$410$	13.1168	−	7.57301i	0.647795	−	0.374004i
$411$	−22.0000	−	6.63325i	−1.08518	−	0.327194i
$412$			70.9764i			3.49676i
$413$		0			0
$414$	−12.7446	+	6.33830i	−0.626361	+	0.311510i
$415$	−2.74456	+	4.75372i	−0.134725	+	0.233351i
$416$	−12.0000	−	20.7846i	−0.588348	−	1.01905i
$417$	−1.62772	+	1.52967i	−0.0797097	+	0.0749083i
$418$	−6.00000	−	3.46410i	−0.293470	−	0.169435i
$419$	−2.74456			−0.134081			−0.0670403	−	0.997750i	$-0.521356\pi$
$419$	−2.74456			−0.134081			−0.0670403	+	0.997750i	$0.521356\pi$
$420$		0			0
$421$	−25.6060			−1.24796			−0.623979	−	0.781441i	$-0.714485\pi$
$421$	−25.6060			−1.24796			−0.623979	+	0.781441i	$0.714485\pi$
$422$	13.3723	+	7.72049i	0.650952	+	0.375828i
$423$	18.4307	+	12.2255i	0.896131	+	0.594426i
$424$	25.4891	+	44.1485i	1.23786	+	2.14404i
$425$	0.686141	−	1.18843i	0.0332827	−	0.0576473i
$426$	−57.7228	+	13.5615i	−2.79668	+	0.657055i
$427$		0			0
$428$			29.0024i			1.40189i
$429$	−2.31386	+	7.67420i	−0.111714	+	0.370514i
$430$	14.7446	−	8.51278i	0.711046	−	0.410523i
$431$	27.4307	−	15.8371i	1.32129	−	0.762847i	0.337356	−	0.941377i	$-0.390467\pi$
$431$	27.4307	−	15.8371i	1.32129	−	0.762847i	0.983935	+	0.178530i	$0.0571341\pi$
$432$	5.55842	+	32.6415i	0.267430	+	1.57046i
$433$		−	2.57924i		−	0.123950i	−0.998078	−	0.0619752i	$-0.980260\pi$
$433$		−	2.57924i		−	0.123950i	0.998078	−	0.0619752i	$-0.0197400\pi$
$434$		0			0
$435$	−1.68614	−	7.17687i	−0.0808443	−	0.344105i
$436$	0.255437	−	0.442430i	0.0122332	−	0.0211886i
$437$	3.25544	+	5.63858i	0.155729	+	0.269730i
$438$	−20.7446	−	22.0742i	−0.991214	−	1.05475i
$439$	−1.11684	−	0.644810i	−0.0533041	−	0.0307751i	0.473111	−	0.881003i	$-0.343131\pi$
$439$	−1.11684	−	0.644810i	−0.0533041	−	0.0307751i	−0.526415	+	0.850228i	$0.676464\pi$
$440$	4.74456			0.226188
$441$		0			0
$442$	−20.2337			−0.962418
$443$	5.74456	+	3.31662i	0.272932	+	0.157578i	0.630220	−	0.776417i	$-0.282965\pi$
$443$	5.74456	+	3.31662i	0.272932	+	0.157578i	−0.357287	+	0.933995i	$0.616298\pi$
$444$	24.6060	+	26.1831i	1.16775	+	1.24260i
$445$	−1.62772	−	2.81929i	−0.0771613	−	0.133647i
$446$	−26.4891	+	45.8805i	−1.25430	+	2.17251i
$447$	−4.00000	−	17.0256i	−0.189194	−	0.805281i
$448$		0			0
$449$			28.2101i			1.33132i	0.746256	+	0.665660i	$0.231850\pi$
$449$			28.2101i			1.33132i	−0.746256	+	0.665660i	$0.768150\pi$
$450$	7.55842	+	0.469882i	0.356307	+	0.0221504i
$451$	4.11684	−	2.37686i	0.193855	−	0.111922i
$452$	38.2337	−	22.0742i	1.79836	−	1.03828i
$453$	−1.68614	+	5.59230i	−0.0792218	+	0.262749i
$454$			39.3947i			1.84889i
$455$		0			0
$456$	34.9783	−	8.21782i	1.63801	−	0.384835i
$457$	16.4891	−	28.5600i	0.771329	−	1.33598i	−0.165506	−	0.986209i	$-0.552926\pi$
$457$	16.4891	−	28.5600i	0.771329	−	1.33598i	0.936835	−	0.349772i	$-0.113741\pi$
$458$	6.00000	+	10.3923i	0.280362	+	0.485601i
$459$	6.68614	+	2.47805i	0.312082	+	0.115666i
$460$	−7.11684	−	4.10891i	−0.331825	−	0.191579i
$461$	−8.74456			−0.407275			−0.203637	−	0.979046i	$-0.565276\pi$
$461$	−8.74456			−0.407275			−0.203637	+	0.979046i	$0.565276\pi$
$462$		0			0
$463$	36.4674			1.69478			0.847391	−	0.530969i	$-0.178172\pi$
$463$	36.4674			1.69478			0.847391	+	0.530969i	$0.178172\pi$
$464$	23.4891	+	13.5615i	1.09046	+	0.629575i
$465$	4.37228	−	4.10891i	0.202760	−	0.190546i
$466$	−4.74456	−	8.21782i	−0.219788	−	0.380683i
$467$	6.94158	−	12.0232i	0.321218	−	0.556366i	−0.659522	−	0.751686i	$-0.729241\pi$
$467$	6.94158	−	12.0232i	0.321218	−	0.556366i	0.980740	+	0.195320i	$0.0625745\pi$
$468$	−34.1168	−	68.5996i	−1.57705	−	3.17102i
$469$		0			0
$470$			18.6101i			0.858421i
$471$		0			0
$472$	14.2337	−	8.21782i	0.655159	−	0.378256i
$473$	4.62772	−	2.67181i	0.212783	−	0.122850i
$474$	14.1168	+	4.25639i	0.648408	+	0.195502i
$475$		−	3.46410i		−	0.158944i
$476$		0			0
$477$	11.3723	+	22.8665i	0.520701	+	1.04699i
$478$	−19.7446	+	34.1986i	−0.903095	+	1.56421i
$479$	−9.25544	−	16.0309i	−0.422892	−	0.732470i	0.573329	−	0.819325i	$-0.305652\pi$
$479$	−9.25544	−	16.0309i	−0.422892	−	0.732470i	−0.996221	+	0.0868551i	$0.972318\pi$
$480$	−5.18614	+	4.87375i	−0.236714	+	0.222455i
$481$	−24.0000	−	13.8564i	−1.09431	−	0.631798i
$482$	58.9783			2.68639
$483$		0			0
$484$	−45.3505			−2.06139
$485$	0.941578	+	0.543620i	0.0427549	+	0.0246845i
$486$	4.18614	+	39.1272i	0.189887	+	1.77485i
$487$	−7.25544	−	12.5668i	−0.328775	−	0.569455i	0.653494	−	0.756932i	$-0.273303\pi$
$487$	−7.25544	−	12.5668i	−0.328775	−	0.569455i	−0.982269	+	0.187476i	$0.939969\pi$
$488$	20.7446	−	35.9306i	0.939062	−	1.62650i
$489$	13.4891	−	3.16915i	0.609999	−	0.143314i
$490$		0			0
$491$			10.8896i			0.491442i	0.969341	+	0.245721i	$0.0790248\pi$
$491$			10.8896i			0.491442i	−0.969341	+	0.245721i	$0.920975\pi$
$492$	−13.1168	+	43.5036i	−0.591353	+	1.96130i
$493$	5.05842	−	2.92048i	0.227820	−	0.131532i
$494$	−44.2337	+	25.5383i	−1.99017	+	1.14902i
$495$	2.37228	+	0.147477i	0.106626	+	0.00662859i
$496$			22.0742i			0.991162i
$497$		0			0
$498$	−5.48913	−	23.3639i	−0.245974	−	1.04696i
$499$	5.17527	−	8.96382i	0.231677	−	0.401276i	−0.726625	−	0.687034i	$-0.758912\pi$
$499$	5.17527	−	8.96382i	0.231677	−	0.401276i	0.958302	+	0.285758i	$0.0922455\pi$
$500$	2.18614	+	3.78651i	0.0977672	+	0.169338i
$501$	26.2337	+	27.9152i	1.17203	+	1.24716i
$502$	38.2337	+	22.0742i	1.70645	+	0.985221i
$503$	−27.6060			−1.23089			−0.615445	−	0.788180i	$-0.711024\pi$
$503$	−27.6060			−1.23089			−0.615445	+	0.788180i	$0.711024\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$	−3.25544	−	1.87953i	−0.144722	−	0.0835552i
$507$	25.0475	+	26.6530i	1.11240	+	1.18370i
$508$	23.4891	+	40.6844i	1.04216	+	1.80508i
$509$	19.1168	−	33.1113i	0.847339	−	1.46763i	−0.0362349	−	0.999343i	$-0.511536\pi$
$509$	19.1168	−	33.1113i	0.847339	−	1.46763i	0.883574	−	0.468291i	$-0.155130\pi$
$510$	1.37228	+	5.84096i	0.0607656	+	0.258642i
$511$		0			0
$512$			50.1369i			2.21576i
$513$	17.7446	−	3.02167i	0.783442	−	0.133410i
$514$	−51.3505	+	29.6472i	−2.26497	+	1.30768i
$515$	−14.0584	+	8.11663i	−0.619488	+	0.357662i
$516$	−14.7446	+	48.9022i	−0.649093	+	2.15280i
$517$			5.84096i			0.256885i
$518$		0			0
$519$	27.1753	−	6.38458i	1.19286	−	0.280252i
$520$	17.4891	−	30.2921i	0.766949	−	1.32839i
$521$	−17.2337	−	29.8496i	−0.755022	−	1.30774i	−0.945364	−	0.326018i	$-0.894293\pi$
$521$	−17.2337	−	29.8496i	−0.755022	−	1.30774i	0.190342	−	0.981718i	$-0.439040\pi$
$522$	26.8614	+	17.8178i	1.17569	+	0.779866i
$523$	−9.00000	−	5.19615i	−0.393543	−	0.227212i	0.290151	−	0.956981i	$-0.406294\pi$
$523$	−9.00000	−	5.19615i	−0.393543	−	0.227212i	−0.683694	+	0.729769i	$0.739628\pi$
$524$	76.4674			3.34049
$525$		0			0
$526$	−34.2337			−1.49266
$527$	4.11684	+	2.37686i	0.179333	+	0.103538i
$528$	−6.37228	+	5.98844i	−0.277318	+	0.260613i
$529$	−9.73369	−	16.8592i	−0.423204	−	0.733011i
$530$	−10.7446	+	18.6101i	−0.466714	+	0.808372i
$531$	7.37228	−	3.66648i	0.319930	−	0.159112i
$532$		0			0
$533$		−	35.0458i		−	1.51800i
$534$	13.6277	+	4.10891i	0.589729	+	0.177810i
$535$	−5.74456	+	3.31662i	−0.248359	+	0.143390i
$536$	−34.9783	+	20.1947i	−1.51083	+	0.872278i
$537$	11.0000	+	3.31662i	0.474685	+	0.143123i
$538$			22.0742i			0.951688i
$539$		0			0
$540$	−17.4891	+	14.5012i	−0.752612	+	0.624033i
$541$	−9.31386	+	16.1321i	−0.400434	+	0.693572i	−0.993778	−	0.111377i	$-0.964474\pi$
$541$	−9.31386	+	16.1321i	−0.400434	+	0.693572i	0.593344	+	0.804949i	$0.297807\pi$
$542$	−19.1168	−	33.1113i	−0.821139	−	1.42225i
$543$	−23.4891	+	22.0742i	−1.00801	+	0.947296i
$544$	−4.88316	−	2.81929i	−0.209364	−	0.120876i
$545$	0.116844			0.00500505
$546$		0			0
$547$	42.9783			1.83762			0.918809	−	0.394703i	$-0.129153\pi$
$547$	42.9783			1.83762			0.918809	+	0.394703i	$0.129153\pi$
$548$	50.2337	+	29.0024i	2.14588	+	1.23892i
$549$	11.4891	−	17.3205i	0.490344	−	0.739221i
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	7.37228	−	12.7692i	0.314070	−	0.543985i
$552$	18.9783	−	4.45877i	0.807768	−	0.189778i
$553$		0			0
$554$			15.7359i			0.668556i
$555$	−2.37228	+	7.86797i	−0.100698	+	0.333977i
$556$	4.88316	−	2.81929i	0.207092	−	0.119565i
$557$	−26.7446	+	15.4410i	−1.13320	+	0.654255i	−0.944739	−	0.327825i	$-0.893684\pi$
$557$	−26.7446	+	15.4410i	−1.13320	+	0.654255i	−0.188465	+	0.982080i	$0.560351\pi$
$558$	−1.62772	+	26.1831i	−0.0689068	+	1.10842i
$559$		−	39.3947i		−	1.66622i
$560$		0			0
$561$	0.430703	+	1.83324i	0.0181843	+	0.0773995i
$562$	−6.11684	+	10.5947i	−0.258023	+	0.446910i
$563$	−2.74456	−	4.75372i	−0.115670	−	0.200345i	0.802378	−	0.596817i	$-0.203568\pi$
$563$	−2.74456	−	4.75372i	−0.115670	−	0.200345i	−0.918047	+	0.396471i	$0.870235\pi$
$564$	−38.2337	−	40.6844i	−1.60993	−	1.71312i
$565$	8.74456	+	5.04868i	0.367887	+	0.212399i
$566$	−23.4891			−0.987322
$567$		0			0
$568$	81.2119			3.40758
$569$	−9.25544	−	5.34363i	−0.388008	−	0.224017i	0.293289	−	0.956024i	$-0.405250\pi$
$569$	−9.25544	−	5.34363i	−0.388008	−	0.224017i	−0.681297	+	0.732007i	$0.738584\pi$
$570$	10.3723	+	11.0371i	0.434447	+	0.462294i
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	10.1168	−	17.5229i	0.423006	−	0.732669i
$573$	6.19702	+	26.3769i	0.258884	+	1.10191i
$574$		0			0
$575$		−	1.87953i		−	0.0783817i
$576$	−0.441578	+	7.10313i	−0.0183991	+	0.295964i
$577$	−11.0584	+	6.38458i	−0.460368	+	0.265794i	−0.712199	−	0.701978i	$-0.752301\pi$
$577$	−11.0584	+	6.38458i	−0.460368	+	0.265794i	0.251831	+	0.967771i	$0.418967\pi$
$578$	33.0475	−	19.0800i	1.37460	−	0.793624i
$579$	−11.1168	+	36.8704i	−0.462000	+	1.53228i
$580$			18.6101i			0.772744i
$581$		0			0
$582$	−4.62772	+	1.08724i	−0.191825	+	0.0450676i
$583$	−3.37228	+	5.84096i	−0.139666	+	0.241908i
$584$	20.7446	+	35.9306i	0.858416	+	1.48682i
$585$	9.68614	−	14.6024i	0.400473	−	0.603735i
$586$	−61.4674	−	35.4882i	−2.53919	−	1.46600i
$587$	−5.48913			−0.226560			−0.113280	−	0.993563i	$-0.536136\pi$
$587$	−5.48913			−0.226560			−0.113280	+	0.993563i	$0.536136\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$	6.00000	+	3.46410i	0.247016	+	0.142615i
$591$	28.2337	−	26.5330i	1.16138	−	1.09142i
$592$	−15.1168	−	26.1831i	−0.621298	−	1.07612i
$593$	0.686141	−	1.18843i	0.0281764	−	0.0488030i	−0.851593	−	0.524203i	$-0.824363\pi$
$593$	0.686141	−	1.18843i	0.0281764	−	0.0488030i	0.879770	+	0.475400i	$0.157697\pi$
$594$	−8.00000	+	6.63325i	−0.328244	+	0.272166i
$595$		0			0
$596$			44.1485i			1.80839i
$597$	−21.5109	−	6.48577i	−0.880381	−	0.265445i
$598$	−24.0000	+	13.8564i	−0.981433	+	0.566631i
$599$	1.54755	−	0.893477i	0.0632311	−	0.0365065i	−0.468051	−	0.883701i	$-0.655044\pi$
$599$	1.54755	−	0.893477i	0.0632311	−	0.0365065i	0.531282	+	0.847195i	$0.321710\pi$
$600$	−9.93070	−	2.99422i	−0.405419	−	0.122239i
$601$			2.17448i			0.0886989i	0.999016	+	0.0443495i	$0.0141215\pi$
$601$			2.17448i			0.0886989i	−0.999016	+	0.0443495i	$0.985878\pi$
$602$		0			0
$603$	−18.1168	+	9.01011i	−0.737775	+	0.366920i
$604$	7.37228	−	12.7692i	0.299974	−	0.519570i
$605$	−5.18614	−	8.98266i	−0.210847	−	0.365197i
$606$	−19.1168	+	17.9653i	−0.776569	+	0.729791i
$607$	−18.1753	−	10.4935i	−0.737711	−	0.425918i	0.0835253	−	0.996506i	$-0.473382\pi$
$607$	−18.1753	−	10.4935i	−0.737711	−	0.425918i	−0.821237	+	0.570588i	$0.806715\pi$
$608$	−14.2337			−0.577252
$609$		0			0
$610$	17.4891			0.708114
$611$	37.2921	+	21.5306i	1.50868	+	0.871035i
$612$	−15.0000	−	9.94987i	−0.606339	−	0.402200i
$613$	2.25544	+	3.90653i	0.0910963	+	0.157783i	0.907973	−	0.419029i	$-0.137630\pi$
$613$	2.25544	+	3.90653i	0.0910963	+	0.157783i	−0.816876	+	0.576813i	$0.804296\pi$
$614$	9.00000	−	15.5885i	0.363210	−	0.629099i
$615$	−10.1168	+	2.37686i	−0.407951	+	0.0958443i
$616$		0			0
$617$		−	37.8102i		−	1.52218i	−0.648646	−	0.761090i	$-0.724665\pi$
$617$		−	37.8102i		−	1.52218i	0.648646	−	0.761090i	$-0.275335\pi$
$618$	20.4891	−	67.9547i	0.824193	−	2.73354i
$619$	−1.11684	+	0.644810i	−0.0448897	+	0.0259171i	−0.522277	−	0.852776i	$-0.674917\pi$
$619$	−1.11684	+	0.644810i	−0.0448897	+	0.0259171i	0.477387	+	0.878693i	$0.341584\pi$
$620$	−13.1168	+	7.57301i	−0.526785	+	0.304140i
$621$	9.62772	−	1.63948i	0.386347	−	0.0657899i
$622$		−	51.0767i		−	2.04799i
$623$		0			0
$624$	14.7446	+	62.7586i	0.590255	+	2.51235i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	30.8614	+	53.4535i	1.23347	+	2.13643i
$627$	3.25544	+	3.46410i	0.130010	+	0.138343i
$628$		0			0
$629$	−6.51087			−0.259606
$630$		0			0
$631$	−5.88316			−0.234205			−0.117102	−	0.993120i	$-0.537361\pi$
$631$	−5.88316			−0.234205			−0.117102	+	0.993120i	$0.537361\pi$
$632$	−17.4891	−	10.0974i	−0.695680	−	0.401651i
$633$	−7.25544	−	7.72049i	−0.288378	−	0.306862i
$634$	−10.7446	−	18.6101i	−0.426721	−	0.739103i
$635$	−5.37228	+	9.30506i	−0.213192	+	0.369260i
$636$	−14.7446	−	62.7586i	−0.584660	−	2.48854i
$637$		0			0
$638$			8.51278i			0.337024i
$639$	40.6060	+	2.52434i	1.60635	+	0.0998613i
$640$	−12.3030	+	7.10313i	−0.486318	+	0.280776i
$641$	25.7228	−	14.8511i	1.01599	−	0.586582i	0.103050	−	0.994676i	$-0.467140\pi$
$641$	25.7228	−	14.8511i	1.01599	−	0.586582i	0.912940	+	0.408094i	$0.133806\pi$
$642$	8.37228	−	27.7677i	0.330428	−	1.09590i
$643$			39.5971i			1.56156i	0.624807	+	0.780779i	$0.285178\pi$
$643$			39.5971i			1.56156i	−0.624807	+	0.780779i	$0.714822\pi$
$644$		0			0
$645$	−11.3723	+	2.67181i	−0.447783	+	0.105203i
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$	6.67527	−	53.4810i	0.262229	−	2.10093i
$649$	1.88316	+	1.08724i	0.0739203	+	0.0426779i
$650$	14.7446			0.578329
$651$		0			0
$652$	−34.9783			−1.36985
$653$	28.6277	+	16.5282i	1.12029	+	0.646799i	0.941475	−	0.337084i	$-0.109440\pi$
$653$	28.6277	+	16.5282i	1.12029	+	0.646799i	0.178814	+	0.983883i	$0.442774\pi$
$654$	−0.372281	+	0.349857i	−0.0145574	+	0.0136805i
$655$	8.74456	+	15.1460i	0.341678	+	0.591804i
$656$	19.1168	−	33.1113i	0.746387	−	1.29278i
$657$	9.25544	+	18.6101i	0.361089	+	0.726050i
$658$		0			0
$659$			20.3971i			0.794558i	0.917698	+	0.397279i	$0.130045\pi$
$659$			20.3971i			0.794558i	−0.917698	+	0.397279i	$0.869955\pi$
$660$	−5.74456	−	1.73205i	−0.223607	−	0.0674200i
$661$	−6.00000	+	3.46410i	−0.233373	+	0.134738i	−0.612127	−	0.790759i	$-0.709686\pi$
$661$	−6.00000	+	3.46410i	−0.233373	+	0.134738i	0.378754	+	0.925497i	$0.376353\pi$
$662$	8.74456	−	5.04868i	0.339867	−	0.196222i
$663$	13.2921	+	4.00772i	0.516223	+	0.155647i
$664$			32.8713i			1.27565i
$665$		0			0
$666$	−16.0000	−	32.1716i	−0.619987	−	1.24662i
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$	−48.3505	−	83.7456i	−1.87074	−	3.24021i
$669$	26.4891	−	24.8935i	1.02413	−	0.962439i
$670$	−14.7446	−	8.51278i	−0.569632	−	0.328877i
$671$	5.48913			0.211905
$672$		0			0
$673$	22.2337			0.857046			0.428523	−	0.903531i	$-0.359034\pi$
$673$	22.2337			0.857046			0.428523	+	0.903531i	$0.359034\pi$
$674$	−39.8614	−	23.0140i	−1.53540	−	0.886466i
$675$	−4.87228	−	1.80579i	−0.187534	−	0.0695049i
$676$	−46.1644	−	79.9591i	−1.77555	−	3.07535i
$677$	−10.8030	+	18.7113i	−0.415192	+	0.719134i	−0.995449	−	0.0952996i	$-0.969619\pi$
$677$	−10.8030	+	18.7113i	−0.415192	+	0.719134i	0.580256	+	0.814434i	$0.302952\pi$
$678$	−42.9783	+	10.0974i	−1.65057	+	0.387786i
$679$		0			0
$680$		−	8.21782i		−	0.315139i
$681$	7.80298	−	25.8796i	0.299011	−	0.991707i
$682$	−6.00000	+	3.46410i	−0.229752	+	0.132647i
$683$	44.8397	−	25.8882i	1.71574	−	0.990584i	0.789418	−	0.613856i	$-0.210383\pi$
$683$	44.8397	−	25.8882i	1.71574	−	0.990584i	0.926324	−	0.376728i	$-0.122951\pi$
$684$	−45.3505	−	2.81929i	−1.73402	−	0.107798i
$685$			13.2665i			0.506887i
$686$		0			0
$687$	−1.88316	−	8.01544i	−0.0718469	−	0.305808i
$688$	21.4891	−	37.2203i	0.819265	−	1.41901i
$689$	24.8614	+	43.0612i	0.947144	+	1.64050i
$690$	5.62772	+	5.98844i	0.214244	+	0.227976i
$691$	33.3505	+	19.2549i	1.26871	+	0.732492i	0.974745	−	0.223322i	$-0.0716903\pi$
$691$	33.3505	+	19.2549i	1.26871	+	0.732492i	0.293969	+	0.955815i	$0.405024\pi$
$692$	−70.4674			−2.67877
$693$		0			0
$694$	−46.2337			−1.75501
$695$	1.11684	+	0.644810i	0.0423643	+	0.0244590i
$696$	−30.2337	−	32.1716i	−1.14600	−	1.21946i
$697$	−4.11684	−	7.13058i	−0.155937	−	0.270090i
$698$	−6.00000	+	10.3923i	−0.227103	+	0.393355i
$699$	1.48913	+	6.33830i	0.0563239	+	0.239736i
$700$		0			0
$701$		−	45.8256i		−	1.73081i	−0.501074	−	0.865405i	$-0.667061\pi$
$701$		−	45.8256i		−	1.73081i	0.501074	−	0.865405i	$-0.332939\pi$
$702$	12.8614	+	75.5278i	0.485423	+	2.85061i
$703$	−14.2337	+	8.21782i	−0.536834	+	0.309941i
$704$	−1.62772	+	0.939764i	−0.0613470	+	0.0354187i
$705$	3.68614	−	12.2255i	0.138828	−	0.460441i
$706$		−	19.8997i		−	0.748937i
$707$		0			0
$708$	−20.2337	+	4.75372i	−0.760429	+	0.178656i
$709$	−12.0584	+	20.8858i	−0.452864	+	0.784383i	−0.998563	−	0.0535986i	$-0.982931\pi$
$709$	−12.0584	+	20.8858i	−0.452864	+	0.784383i	0.545699	+	0.837981i	$0.316264\pi$
$710$	17.1168	+	29.6472i	0.642384	+	1.11264i
$711$	−8.43070	−	5.59230i	−0.316176	−	0.209727i
$712$	−16.8832	−	9.74749i	−0.632723	−	0.365303i
$713$	6.51087			0.243834
$714$		0			0
$715$	4.62772			0.173067
$716$	−25.1168	−	14.5012i	−0.938661	−	0.541936i
$717$	19.7446	−	18.5552i	0.737374	−	0.692958i
$718$	−12.3723	−	21.4294i	−0.461729	−	0.799739i
$719$	−20.2337	+	35.0458i	−0.754589	+	1.30699i	0.190989	+	0.981592i	$0.438831\pi$
$719$	−20.2337	+	35.0458i	−0.754589	+	1.30699i	−0.945578	+	0.325395i	$0.894503\pi$
$720$	17.1168	−	8.51278i	0.637907	−	0.317252i
$721$		0			0
$722$		−	17.6704i		−	0.657623i
$723$	−38.7446	−	11.6819i	−1.44093	−	0.434455i
$724$	70.4674	−	40.6844i	2.61890	−	1.51202i
$725$	−3.68614	+	2.12819i	−0.136900	+	0.0790392i
$726$	43.4198	+	13.0916i	1.61146	+	0.485874i
$727$			3.46410i			0.128476i	0.997935	+	0.0642382i	$0.0204617\pi$
$727$			3.46410i			0.128476i	−0.997935	+	0.0642382i	$0.979538\pi$
$728$		0			0
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	−8.74456	+	15.1460i	−0.323651	+	0.560580i
$731$	−4.62772	−	8.01544i	−0.171162	−	0.296462i
$732$	−38.2337	+	35.9306i	−1.41316	+	1.32803i
$733$	8.82473	+	5.09496i	0.325949	+	0.188187i	0.654041	−	0.756459i	$-0.273072\pi$
$733$	8.82473	+	5.09496i	0.325949	+	0.188187i	−0.328092	+	0.944646i	$0.606406\pi$
$734$	63.9565			2.36068
$735$		0			0
$736$	−7.72281			−0.284667
$737$	−4.62772	−	2.67181i	−0.170464	−	0.0984176i
$738$	25.1168	−	37.8651i	0.924564	−	1.39383i
$739$	4.31386	+	7.47182i	0.158688	+	0.274855i	0.934396	−	0.356237i	$-0.115940\pi$
$739$	4.31386	+	7.47182i	0.158688	+	0.274855i	−0.775708	+	0.631092i	$0.782607\pi$
$740$	10.3723	−	17.9653i	0.381293	−	0.660418i
$741$	34.1168	−	8.01544i	1.25331	−	0.294455i
$742$		0			0
$743$		−	36.9253i		−	1.35466i	−0.735680	−	0.677329i	$-0.763137\pi$
$743$		−	36.9253i		−	1.35466i	0.735680	−	0.677329i	$-0.236863\pi$
$744$	10.3723	−	34.4010i	0.380266	−	1.26120i
$745$	−8.74456	+	5.04868i	−0.320376	+	0.184969i
$746$	54.0951	−	31.2318i	1.98056	−	1.14348i
$747$	−1.02175	+	16.4356i	−0.0373839	+	0.601349i
$748$		−	4.75372i		−	0.173813i
$749$		0			0
$750$	−1.00000	−	4.25639i	−0.0365148	−	0.155421i
$751$	11.1753	−	19.3561i	0.407791	−	0.706315i	−0.586851	−	0.809695i	$-0.699632\pi$
$751$	11.1753	−	19.3561i	0.407791	−	0.706315i	0.994642	+	0.103380i	$0.0329658\pi$
$752$	23.4891	+	40.6844i	0.856560	+	1.48361i
$753$	−20.7446	−	22.0742i	−0.755974	−	0.804430i
$754$	54.3505	+	31.3793i	1.97933	+	1.14277i
$755$	3.37228			0.122730
$756$		0			0
$757$	−54.2337			−1.97116			−0.985578	−	0.169219i	$-0.945875\pi$
$757$	−54.2337			−1.97116			−0.985578	+	0.169219i	$0.945875\pi$
$758$	3.25544	+	1.87953i	0.118243	+	0.0682675i
$759$	1.76631	+	1.87953i	0.0641131	+	0.0682225i
$760$	−10.3723	−	17.9653i	−0.376242	−	0.651671i
$761$	13.1168	−	22.7190i	0.475485	−	0.823565i	−0.524120	−	0.851644i	$-0.675606\pi$
$761$	13.1168	−	22.7190i	0.475485	−	0.823565i	0.999606	+	0.0280796i	$0.00893918\pi$
$762$	−10.7446	−	45.7330i	−0.389234	−	1.65673i
$763$		0			0
$764$		−	68.3972i		−	2.47452i
$765$	0.255437	−	4.10891i	0.00923536	−	0.148558i
$766$	38.2337	−	22.0742i	1.38144	−	0.797574i
$767$	13.8832	−	8.01544i	0.501292	−	0.289421i
$768$	15.5584	−	51.6014i	0.561416	−	1.86201i
$769$			21.1894i			0.764108i	0.924140	+	0.382054i	$0.124783\pi$
$769$			21.1894i			0.764108i	−0.924140	+	0.382054i	$0.875217\pi$
$770$		0			0
$771$	39.6060	−	9.30506i	1.42637	−	0.335114i
$772$	48.6060	−	84.1880i	1.74937	−	3.02999i
$773$	23.3139	+	40.3808i	0.838541	+	1.45240i	0.891114	+	0.453779i	$0.149924\pi$
$773$	23.3139	+	40.3808i	0.838541	+	1.45240i	−0.0525730	+	0.998617i	$0.516742\pi$
$774$	28.2337	−	42.5639i	1.01484	−	1.52993i
$775$	−3.00000	−	1.73205i	−0.107763	−	0.0622171i
$776$	6.51087			0.233727
$777$		0			0
$778$	−34.7446			−1.24565
$779$	−18.0000	−	10.3923i	−0.644917	−	0.372343i
$780$	−32.2337	+	30.2921i	−1.15415	+	1.08463i
$781$	5.37228	+	9.30506i	0.192235	+	0.332961i
$782$	−3.25544	+	5.63858i	−0.116414	+	0.201635i
$783$	−14.1168	−	17.0256i	−0.504495	−	0.608444i
$784$		0			0
$785$		0			0
$786$	−73.2119	−	22.0742i	−2.61138	−	0.787362i
$787$	−40.2921	+	23.2627i	−1.43626	+	0.829224i	−0.997587	−	0.0694233i	$-0.977884\pi$
$787$	−40.2921	+	23.2627i	−1.43626	+	0.829224i	−0.438671	+	0.898648i	$0.644551\pi$
$788$	−84.7011	+	48.9022i	−3.01735	+	1.74207i
$789$	22.4891	+	6.78073i	0.800634	+	0.241400i
$790$		−	8.51278i		−	0.302871i
$791$		0			0
$792$	12.7446	−	6.33830i	0.452858	−	0.225222i
$793$	20.2337	−	35.0458i	0.718519	−	1.24451i
$794$	−4.62772	−	8.01544i	−0.164232	−	0.284457i
$795$	10.7446	−	10.0974i	0.381070	−	0.358116i
$796$	49.1168	+	28.3576i	1.74090	+	1.00511i
$797$	−42.8614			−1.51823			−0.759114	−	0.650957i	$-0.774368\pi$
$797$	−42.8614			−1.51823			−0.759114	+	0.650957i	$0.774368\pi$
$798$		0			0
$799$	10.1168			0.357908
$800$	3.55842	+	2.05446i	0.125809	+	0.0726360i
$801$	−8.13859	−	5.39853i	−0.287563	−	0.190748i
$802$	−3.37228	−	5.84096i	−0.119079	−	0.206252i
$803$	−2.74456	+	4.75372i	−0.0968535	+	0.167755i
$804$	49.7228	−	11.6819i	1.75359	−	0.411990i
$805$		0			0
$806$			51.0767i			1.79910i
$807$	4.37228	−	14.5012i	0.153912	−	0.510467i
$808$	31.1168	−	17.9653i	1.09469	−	0.632018i
$809$	−31.8030	+	18.3615i	−1.11813	+	0.645555i	−0.940924	−	0.338619i	$-0.890040\pi$
$809$	−31.8030	+	18.3615i	−1.11813	+	0.645555i	−0.177210	+	0.984173i	$0.556707\pi$
$810$	20.9307	−	8.83518i	0.735430	−	0.310437i
$811$		−	1.28962i		−	0.0452847i	−0.999744	−	0.0226423i	$-0.992792\pi$
$811$		−	1.28962i		−	0.0452847i	0.999744	−	0.0226423i	$-0.00720790\pi$
$812$		0			0
$813$	6.00000	+	25.5383i	0.210429	+	0.895668i
$814$	4.74456	−	8.21782i	0.166297	−	0.288035i
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$	10.3723	+	11.0371i	0.363102	+	0.386376i
$817$	−20.2337	−	11.6819i	−0.707887	−	0.408699i
$818$	−88.4674			−3.09319
$819$		0			0
$820$	26.2337			0.916120
$821$	−10.1970	−	5.88725i	−0.355878	−	0.205466i	0.311393	−	0.950281i	$-0.399204\pi$
$821$	−10.1970	−	5.88725i	−0.355878	−	0.205466i	−0.667271	+	0.744815i	$0.732538\pi$
$822$	−39.7228	−	42.2689i	−1.38549	−	1.47430i
$823$	24.1168	+	41.7716i	0.840660	+	1.45607i	0.889337	+	0.457252i	$0.151166\pi$
$823$	24.1168	+	41.7716i	0.840660	+	1.45607i	−0.0486769	+	0.998815i	$0.515500\pi$
$824$	−48.6060	+	84.1880i	−1.69327	+	2.93283i
$825$	−0.313859	−	1.33591i	−0.0109272	−	0.0465103i
$826$		0			0
$827$		−	18.3152i		−	0.636881i	−0.947943	−	0.318441i	$-0.896841\pi$
$827$		−	18.3152i		−	0.636881i	0.947943	−	0.318441i	$-0.103159\pi$
$828$	−24.6060	−	1.52967i	−0.855117	−	0.0531597i
$829$	28.1168	−	16.2333i	0.976538	−	0.563805i	0.0753151	−	0.997160i	$-0.476004\pi$
$829$	28.1168	−	16.2333i	0.976538	−	0.563805i	0.901223	+	0.433355i	$0.142670\pi$
$830$	−12.0000	+	6.92820i	−0.416526	+	0.240481i
$831$	3.11684	−	10.3374i	0.108122	−	0.358601i
$832$			13.8564i			0.480384i
$833$		0			0
$834$	−5.48913	+	1.28962i	−0.190073	+	0.0446559i
$835$	11.0584	−	19.1537i	0.382692	−	0.662843i
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$	6.25544	−	16.8781i	0.216220	−	0.583392i
$838$	−6.00000	−	3.46410i	−0.207267	−	0.119665i
$839$	−53.4891			−1.84665			−0.923325	−	0.384020i	$-0.874539\pi$
$839$	−53.4891			−1.84665			−0.923325	+	0.384020i	$0.874539\pi$
$840$		0			0
$841$	10.8832			0.375281
$842$	−55.9783	−	32.3191i	−1.92914	−	1.11379i
$843$	6.11684	−	5.74839i	0.210675	−	0.197985i
$844$	13.3723	+	23.1615i	0.460293	+	0.797251i
$845$	10.5584	−	18.2877i	0.363221	−	0.629117i
$846$	24.8614	+	49.9894i	0.854753	+	1.71867i
$847$		0			0
$848$			54.2458i			1.86281i
$849$	15.4307	+	4.65253i	0.529580	+	0.159674i
$850$	3.00000	−	1.73205i	0.102899	−	0.0594089i
$851$	−7.72281	+	4.45877i	−0.264735	+	0.152845i
$852$	−98.3288	−	29.6472i	−3.36869	−	1.01570i
$853$		−	46.7277i		−	1.59993i	−0.600049	−	0.799963i	$-0.704852\pi$
$853$		−	46.7277i		−	1.59993i	0.600049	−	0.799963i	$-0.295148\pi$
$854$		0			0
$855$	−4.62772	−	9.30506i	−0.158265	−	0.318226i
$856$	−19.8614	+	34.4010i	−0.678849	+	1.17580i
$857$	11.2337	+	19.4573i	0.383735	+	0.664649i	0.991593	−	0.129397i	$-0.0413041\pi$
$857$	11.2337	+	19.4573i	0.383735	+	0.664649i	−0.607857	+	0.794046i	$0.707971\pi$
$858$	−14.7446	+	13.8564i	−0.503371	+	0.473050i
$859$	−39.3505	−	22.7190i	−1.34262	−	0.775164i	−0.355431	−	0.934702i	$-0.615666\pi$
$859$	−39.3505	−	22.7190i	−1.34262	−	0.775164i	−0.987192	+	0.159539i	$0.948999\pi$
$860$	29.4891			1.00557
$861$		0			0
$862$	79.9565			2.72333
$863$	−24.2554	−	14.0039i	−0.825665	−	0.476698i	0.0267013	−	0.999643i	$-0.491500\pi$
$863$	−24.2554	−	14.0039i	−0.825665	−	0.476698i	−0.852366	+	0.522946i	$0.824833\pi$
$864$	−7.41983	+	20.0198i	−0.252428	+	0.681087i
$865$	−8.05842	−	13.9576i	−0.273995	−	0.474573i
$866$	3.25544	−	5.63858i	0.110624	−	0.191607i
$867$	−25.4891	+	5.98844i	−0.865656	+	0.203378i
$868$		0			0
$869$		−	2.67181i		−	0.0906351i
$870$	5.37228	−	17.8178i	0.182137	−	0.604081i
$871$	−34.1168	+	19.6974i	−1.15601	+	0.667420i
$872$	0.605969	−	0.349857i	0.0205207	−	0.0118476i
$873$	3.25544	+	0.202380i	0.110180	+	0.00684951i
$874$			16.4356i			0.555944i
$875$		0			0
$876$	−12.0000	−	51.0767i	−0.405442	−	1.72572i
$877$	−15.2337	+	26.3855i	−0.514405	+	0.890976i	0.485455	+	0.874262i	$0.338654\pi$
$877$	−15.2337	+	26.3855i	−0.514405	+	0.890976i	−0.999860	+	0.0167142i	$0.994679\pi$
$878$	−1.62772	−	2.81929i	−0.0549328	−	0.0951465i
$879$	33.3505	+	35.4882i	1.12489	+	1.19699i
$880$	4.37228	+	2.52434i	0.147390	+	0.0850954i
$881$	−2.23369			−0.0752549			−0.0376274	−	0.999292i	$-0.511980\pi$
$881$	−2.23369			−0.0752549			−0.0376274	+	0.999292i	$0.511980\pi$
$882$		0			0
$883$	26.5109			0.892162			0.446081	−	0.894993i	$-0.352819\pi$
$883$	26.5109			0.892162			0.446081	+	0.894993i	$0.352819\pi$
$884$	−30.3505	−	17.5229i	−1.02080	−	0.589358i
$885$	−3.25544	−	3.46410i	−0.109430	−	0.116445i
$886$	8.37228	+	14.5012i	0.281272	+	0.487178i
$887$	−20.7446	+	35.9306i	−0.696534	+	1.20643i	0.273127	+	0.961978i	$0.411942\pi$
$887$	−20.7446	+	35.9306i	−0.696534	+	1.20643i	−0.969661	+	0.244455i	$0.921391\pi$
$888$	11.2554	+	47.9075i	0.377708	+	1.60767i
$889$		0			0
$890$		−	8.21782i		−	0.275462i
$891$	6.56930	−	2.77300i	0.220080	−	0.0928991i
$892$	−79.4674	+	45.8805i	−2.66076	+	1.53619i
$893$	22.1168	−	12.7692i	0.740112	−	0.427304i
$894$	12.7446	−	42.2689i	0.426242	−	1.41368i
$895$		−	6.63325i		−	0.221725i
$896$		0			0
$897$	18.5109	−	4.34896i	0.618060	−	0.145208i
$898$	−35.6060	+	61.6713i	−1.18819	+	2.05800i
$899$	−7.37228	−	12.7692i	−0.245879	−	0.425876i
$900$	10.9307	+	7.25061i	0.364357	+	0.241687i
$901$	10.1168	+	5.84096i	0.337041	+	0.194591i
$902$	12.0000			0.399556
$903$		0			0
$904$	60.4674			2.01112
$905$	16.1168	+	9.30506i	0.535742	+	0.309311i
$906$	−10.7446	+	10.0974i	−0.356964	+	0.335462i
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	0.791944	−	0.610594i	$-0.209069\pi$
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	−0.924762	+	0.380547i	$0.875736\pi$
$908$	−34.1168	+	59.0921i	−1.13221	+	1.96104i
$909$	16.1168	−	8.01544i	0.534562	−	0.265855i
$910$		0			0
$911$			23.6588i			0.783851i	0.919997	+	0.391926i	$0.128191\pi$
$911$			23.6588i			0.783851i	−0.919997	+	0.391926i	$0.871809\pi$
$912$	36.6060	+	11.0371i	1.21214	+	0.365475i
$913$	−3.76631	+	2.17448i	−0.124647	+	0.0719648i
$914$	72.0951	−	41.6241i	2.38469	−	1.37680i
$915$	−11.4891	−	3.46410i	−0.379819	−	0.114520i
$916$			20.7846i			0.686743i
$917$		0			0
$918$	11.4891	+	13.8564i	0.379198	+	0.457330i
$919$	5.68614	−	9.84868i	0.187568	−	0.324878i	−0.756871	−	0.653565i	$-0.773273\pi$
$919$	5.68614	−	9.84868i	0.187568	−	0.324878i	0.944439	+	0.328687i	$0.106606\pi$
$920$	−5.62772	−	9.74749i	−0.185540	−	0.321365i
$921$	−9.00000	+	8.45787i	−0.296560	+	0.278696i
$922$	−19.1168	−	11.0371i	−0.629580	−	0.363488i
$923$	79.2119			2.60729
$924$		0			0
$925$	4.74456			0.156000
$926$	79.7228	+	46.0280i	2.61985	+	1.51257i
$927$	−26.9198	+	40.5832i	−0.884163	+	1.33293i
$928$	8.74456	+	15.1460i	0.287054	+	0.497193i
$929$	−3.51087	+	6.08101i	−0.115188	+	0.199512i	−0.917855	−	0.396916i	$-0.870080\pi$
$929$	−3.51087	+	6.08101i	−0.115188	+	0.199512i	0.802667	+	0.596428i	$0.203414\pi$
$930$	14.7446	−	3.46410i	0.483493	−	0.113592i
$931$		0			0
$932$		−	16.4356i		−	0.538368i
$933$	−10.1168	+	33.5538i	−0.331211	+	1.09850i
$934$	30.3505	−	17.5229i	0.993100	−	0.573366i
$935$	0.941578	−	0.543620i	0.0307929	−	0.0177783i
$936$	6.51087	−	104.733i	0.212815	−	3.42329i
$937$		−	49.9894i		−	1.63308i	−0.577287	−	0.816542i	$-0.695888\pi$
$937$		−	49.9894i		−	1.63308i	0.577287	−	0.816542i	$-0.304112\pi$
$938$		0			0
$939$	−9.68614	−	41.2280i	−0.316095	−	1.34542i
$940$	−16.1168	+	27.9152i	−0.525673	+	0.910493i
$941$	13.6277	+	23.6039i	0.444251	+	0.769465i	0.998000	−	0.0632186i	$-0.0201365\pi$
$941$	13.6277	+	23.6039i	0.444251	+	0.769465i	−0.553749	+	0.832684i	$0.686803\pi$
$942$		0			0
$943$	−9.76631	−	5.63858i	−0.318035	−	0.183618i
$944$	17.4891			0.569223
$945$		0			0
$946$	13.4891			0.438569
$947$	41.7446	+	24.1012i	1.35652	+	0.783185i	0.989152	−	0.146893i	$-0.0469272\pi$
$947$	41.7446	+	24.1012i	1.35652	+	0.783185i	0.367364	+	0.930077i	$0.380260\pi$
$948$	17.4891	+	18.6101i	0.568020	+	0.604429i
$949$	20.2337	+	35.0458i	0.656813	+	1.13763i
$950$	4.37228	−	7.57301i	0.141856	−	0.245701i
$951$	3.37228	+	14.3537i	0.109354	+	0.465452i
$952$		0			0
$953$			38.8048i			1.25701i	0.777805	+	0.628506i	$0.216333\pi$
$953$			38.8048i			1.25701i	−0.777805	+	0.628506i	$0.783667\pi$
$954$	−4.00000	+	64.3432i	−0.129505	+	2.08319i
$955$	13.5475	−	7.82168i	0.438388	−	0.253104i
$956$	−59.2337	+	34.1986i	−1.91575	+	1.10606i
$957$	1.68614	−	5.59230i	0.0545052	−	0.180773i
$958$		−	46.7277i		−	1.50970i
$959$		0			0
$960$	4.00000	−	0.939764i	0.129099	−	0.0303307i
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	−34.9783	−	60.5841i	−1.12774	−	1.95331i
$963$	−11.0000	+	16.5831i	−0.354470	+	0.534384i
$964$	88.4674	+	51.0767i	2.84934	+	1.64507i
$965$	22.2337			0.715728
$966$		0			0
$967$	−24.2337			−0.779303			−0.389651	−	0.920962i	$-0.627405\pi$
$967$	−24.2337			−0.779303			−0.389651	+	0.920962i	$0.627405\pi$
$968$	−53.7921	−	31.0569i	−1.72894	−	0.998206i
$969$	6.00000	−	5.63858i	0.192748	−	0.181137i
$970$	1.37228	+	2.37686i	0.0440613	+	0.0763164i
$971$	21.6060	−	37.4226i	0.693369	−	1.20095i	−0.277359	−	0.960766i	$-0.589459\pi$
$971$	21.6060	−	37.4226i	0.693369	−	1.20095i	0.970728	−	0.240183i	$-0.0772075\pi$
$972$	−27.6060	+	62.3162i	−0.885462	+	1.99879i
$973$		0			0
$974$		−	36.6303i		−	1.17371i
$975$	−9.68614	−	2.92048i	−0.310205	−	0.0935303i
$976$	38.2337	−	22.0742i	1.22383	−	0.706579i
$977$	33.6060	−	19.4024i	1.07515	−	0.620738i	0.145566	−	0.989349i	$-0.453500\pi$
$977$	33.6060	−	19.4024i	1.07515	−	0.620738i	0.929584	+	0.368610i	$0.120166\pi$
$978$	33.4891	+	10.0974i	1.07086	+	0.322878i
$979$		−	2.57924i		−	0.0824329i
$980$		0			0
$981$	0.313859	−	0.156093i	0.0100208	−	0.00498366i
$982$	−13.7446	+	23.8063i	−0.438607	+	0.759689i
$983$	−5.56930	−	9.64630i	−0.177633	−	0.307669i	0.763436	−	0.645883i	$-0.223511\pi$
$983$	−5.56930	−	9.64630i	−0.177633	−	0.307669i	−0.941069	+	0.338214i	$0.890177\pi$
$984$	−45.3505	+	42.6188i	−1.44572	+	1.35864i
$985$	−19.3723	−	11.1846i	−0.617252	−	0.356371i
$986$	14.7446			0.469563
$987$		0			0
$988$	−88.4674			−2.81452
$989$	−10.9783	−	6.33830i	−0.349088	−	0.201546i
$990$	5.00000	+	3.31662i	0.158910	+	0.105409i
$991$	−1.25544	−	2.17448i	−0.0398803	−	0.0690747i	0.845396	−	0.534140i	$-0.179364\pi$
$991$	−1.25544	−	2.17448i	−0.0398803	−	0.0690747i	−0.885277	+	0.465065i	$0.846031\pi$
$992$	−7.11684	+	12.3267i	−0.225960	+	0.391374i
$993$	−6.74456	+	1.58457i	−0.214032	+	0.0502849i
$994$		0			0
$995$			12.9715i			0.411226i
$996$	12.0000	−	39.7995i	0.380235	−	1.26110i
$997$	−18.9416	+	10.9359i	−0.599886	+	0.346344i	−0.768997	−	0.639253i	$-0.779244\pi$
$997$	−18.9416	+	10.9359i	−0.599886	+	0.346344i	0.169111	+	0.985597i	$0.445910\pi$
$998$	22.6277	−	13.0641i	0.716268	−	0.413537i
$999$	4.13859	+	24.3036i	0.130939	+	0.768932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.s.j.656.2		4
3.2	odd	2		735.2.s.h.656.1		4
7.2	even	3		105.2.b.d.41.1	yes	4
7.3	odd	6		735.2.s.h.521.1		4
7.4	even	3		735.2.s.g.521.1		4
7.5	odd	6		105.2.b.c.41.1	✓	4
7.6	odd	2		735.2.s.i.656.2		4
21.2	odd	6		105.2.b.c.41.4	yes	4
21.5	even	6		105.2.b.d.41.4	yes	4
21.11	odd	6		735.2.s.i.521.2		4
21.17	even	6	inner	735.2.s.j.521.2		4
21.20	even	2		735.2.s.g.656.1		4
28.19	even	6		1680.2.f.h.881.3		4
28.23	odd	6		1680.2.f.g.881.2		4
35.2	odd	12		525.2.g.d.524.7		8
35.9	even	6		525.2.b.e.251.4		4
35.12	even	12		525.2.g.e.524.8		8
35.19	odd	6		525.2.b.g.251.4		4
35.23	odd	12		525.2.g.d.524.2		8
35.33	even	12		525.2.g.e.524.1		8
84.23	even	6		1680.2.f.h.881.4		4
84.47	odd	6		1680.2.f.g.881.1		4
105.2	even	12		525.2.g.e.524.2		8
105.23	even	12		525.2.g.e.524.7		8
105.44	odd	6		525.2.b.g.251.1		4
105.47	odd	12		525.2.g.d.524.1		8
105.68	odd	12		525.2.g.d.524.8		8
105.89	even	6		525.2.b.e.251.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.b.c.41.1	✓	4	7.5	odd	6
105.2.b.c.41.4	yes	4	21.2	odd	6
105.2.b.d.41.1	yes	4	7.2	even	3
105.2.b.d.41.4	yes	4	21.5	even	6
525.2.b.e.251.1		4	105.89	even	6
525.2.b.e.251.4		4	35.9	even	6
525.2.b.g.251.1		4	105.44	odd	6
525.2.b.g.251.4		4	35.19	odd	6
525.2.g.d.524.1		8	105.47	odd	12
525.2.g.d.524.2		8	35.23	odd	12
525.2.g.d.524.7		8	35.2	odd	12
525.2.g.d.524.8		8	105.68	odd	12
525.2.g.e.524.1		8	35.33	even	12
525.2.g.e.524.2		8	105.2	even	12
525.2.g.e.524.7		8	105.23	even	12
525.2.g.e.524.8		8	35.12	even	12
735.2.s.g.521.1		4	7.4	even	3
735.2.s.g.656.1		4	21.20	even	2
735.2.s.h.521.1		4	7.3	odd	6
735.2.s.h.656.1		4	3.2	odd	2
735.2.s.i.521.2		4	21.11	odd	6
735.2.s.i.656.2		4	7.6	odd	2
735.2.s.j.521.2		4	21.17	even	6	inner
735.2.s.j.656.2		4	1.1	even	1	trivial
1680.2.f.g.881.1		4	84.47	odd	6
1680.2.f.g.881.2		4	28.23	odd	6
1680.2.f.h.881.3		4	28.19	even	6
1680.2.f.h.881.4		4	84.23	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.18614 + 1.26217i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(2.18614 + 3.78651i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 4.25639i) q^{6} +5.98844i q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})\)	\(q+(2.18614 + 1.26217i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(2.18614 + 3.78651i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 4.25639i) q^{6} +5.98844i q^{8} +(-0.186141 + 2.99422i) q^{9} +(-2.18614 + 1.26217i) q^{10} +(-0.686141 + 0.396143i) q^{11} +(2.18614 - 7.25061i) q^{12} +5.84096i q^{13} +(1.68614 - 0.396143i) q^{15} +(-3.18614 + 5.51856i) q^{16} +(0.686141 + 1.18843i) q^{17} +(-4.18614 + 6.31084i) q^{18} +(3.00000 + 1.73205i) q^{19} -4.37228 q^{20} -2.00000 q^{22} +(1.62772 + 0.939764i) q^{23} +(7.55842 - 7.10313i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-7.37228 + 12.7692i) q^{26} +(4.00000 - 3.31662i) q^{27} -4.25639i q^{29} +(4.18614 + 1.26217i) q^{30} +(3.00000 - 1.73205i) q^{31} +(-3.55842 + 2.05446i) q^{32} +(1.31386 + 0.396143i) q^{33} +3.46410i q^{34} +(-11.7446 + 5.84096i) q^{36} +(-2.37228 + 4.10891i) q^{37} +(4.37228 + 7.57301i) q^{38} +(7.37228 - 6.92820i) q^{39} +(-5.18614 - 2.99422i) q^{40} -6.00000 q^{41} -6.74456 q^{43} +(-3.00000 - 1.73205i) q^{44} +(-2.50000 - 1.65831i) q^{45} +(2.37228 + 4.10891i) q^{46} +(3.68614 - 6.38458i) q^{47} +(10.7446 - 2.52434i) q^{48} -2.52434i q^{50} +(0.686141 - 2.27567i) q^{51} +(-22.1168 + 12.7692i) q^{52} +(7.37228 - 4.25639i) q^{53} +(12.9307 - 2.20193i) q^{54} -0.792287i q^{55} +(-1.37228 - 5.84096i) q^{57} +(5.37228 - 9.30506i) q^{58} +(-1.37228 - 2.37686i) q^{59} +(5.18614 + 5.51856i) q^{60} +(-6.00000 - 3.46410i) q^{61} +8.74456 q^{62} +2.37228 q^{64} +(-5.05842 - 2.92048i) q^{65} +(2.37228 + 2.52434i) q^{66} +(3.37228 + 5.84096i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-0.744563 - 3.16915i) q^{69} -13.5615i q^{71} +(-17.9307 - 1.11469i) q^{72} +(6.00000 - 3.46410i) q^{73} +(-10.3723 + 5.98844i) q^{74} +(-0.500000 + 1.65831i) q^{75} +15.1460i q^{76} +(24.8614 - 5.84096i) q^{78} +(-1.68614 + 2.92048i) q^{79} +(-3.18614 - 5.51856i) q^{80} +(-8.93070 - 1.11469i) q^{81} +(-13.1168 - 7.57301i) q^{82} +5.48913 q^{83} -1.37228 q^{85} +(-14.7446 - 8.51278i) q^{86} +(-5.37228 + 5.04868i) q^{87} +(-2.37228 - 4.10891i) q^{88} +(-1.62772 + 2.81929i) q^{89} +(-3.37228 - 6.78073i) q^{90} +8.21782i q^{92} +(-5.74456 - 1.73205i) q^{93} +(16.1168 - 9.30506i) q^{94} +(-3.00000 + 1.73205i) q^{95} +(6.81386 + 2.05446i) q^{96} -1.08724i q^{97} +(-1.05842 - 2.12819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - 4 q^{6} + 5 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 - 4 * q^6 + 5 * q^9	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - 4 q^{6} + 5 q^{9} - 3 q^{10} + 3 q^{11} + 3 q^{12} + q^{15} - 7 q^{16} - 3 q^{17} - 11 q^{18} + 12 q^{19} - 6 q^{20} - 8 q^{22} + 18 q^{23} + 13 q^{24} - 2 q^{25} - 18 q^{26} + 16 q^{27} + 11 q^{30} + 12 q^{31} + 3 q^{32} + 11 q^{33} - 24 q^{36} + 2 q^{37} + 6 q^{38} + 18 q^{39} - 15 q^{40} - 24 q^{41} - 4 q^{43} - 12 q^{44} - 10 q^{45} - 2 q^{46} + 9 q^{47} + 20 q^{48} - 3 q^{51} - 54 q^{52} + 18 q^{53} + 23 q^{54} + 6 q^{57} + 10 q^{58} + 6 q^{59} + 15 q^{60} - 24 q^{61} + 12 q^{62} - 2 q^{64} - 3 q^{65} - 2 q^{66} + 2 q^{67} - 12 q^{68} + 20 q^{69} - 43 q^{72} + 24 q^{73} - 30 q^{74} - 2 q^{75} + 42 q^{78} - q^{79} - 7 q^{80} - 7 q^{81} - 18 q^{82} - 24 q^{83} + 6 q^{85} - 36 q^{86} - 10 q^{87} + 2 q^{88} - 18 q^{89} - 2 q^{90} + 30 q^{94} - 12 q^{95} + 33 q^{96} + 13 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 - 4 * q^6 + 5 * q^9 - 3 * q^10 + 3 * q^11 + 3 * q^12 + q^15 - 7 * q^16 - 3 * q^17 - 11 * q^18 + 12 * q^19 - 6 * q^20 - 8 * q^22 + 18 * q^23 + 13 * q^24 - 2 * q^25 - 18 * q^26 + 16 * q^27 + 11 * q^30 + 12 * q^31 + 3 * q^32 + 11 * q^33 - 24 * q^36 + 2 * q^37 + 6 * q^38 + 18 * q^39 - 15 * q^40 - 24 * q^41 - 4 * q^43 - 12 * q^44 - 10 * q^45 - 2 * q^46 + 9 * q^47 + 20 * q^48 - 3 * q^51 - 54 * q^52 + 18 * q^53 + 23 * q^54 + 6 * q^57 + 10 * q^58 + 6 * q^59 + 15 * q^60 - 24 * q^61 + 12 * q^62 - 2 * q^64 - 3 * q^65 - 2 * q^66 + 2 * q^67 - 12 * q^68 + 20 * q^69 - 43 * q^72 + 24 * q^73 - 30 * q^74 - 2 * q^75 + 42 * q^78 - q^79 - 7 * q^80 - 7 * q^81 - 18 * q^82 - 24 * q^83 + 6 * q^85 - 36 * q^86 - 10 * q^87 + 2 * q^88 - 18 * q^89 - 2 * q^90 + 30 * q^94 - 12 * q^95 + 33 * q^96 + 13 * q^99

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