LMFDB - Embedded newform 735.2.s.i.656.1

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			656.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	735.656
Dual form			735.2.s.i.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.686141 - 0.396143i) q^{2} +(-1.68614 - 0.396143i) q^{3} +(-0.686141 - 1.18843i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.00000 + 0.939764i) q^{6} +2.67181i q^{8} +(2.68614 + 1.33591i) q^{9} +(-0.686141 + 0.396143i) q^{10} +(2.18614 - 1.26217i) q^{11} +(0.686141 + 2.27567i) q^{12} +4.10891i q^{13} +(-1.18614 + 1.26217i) q^{15} +(-0.313859 + 0.543620i) q^{16} +(2.18614 + 3.78651i) q^{17} +(-1.31386 - 1.98072i) q^{18} +(-3.00000 - 1.73205i) q^{19} -1.37228 q^{20} -2.00000 q^{22} +(7.37228 + 4.25639i) q^{23} +(1.05842 - 4.50506i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.62772 - 2.81929i) q^{26} +(-4.00000 - 3.31662i) q^{27} -0.939764i q^{29} +(1.31386 - 0.396143i) q^{30} +(-3.00000 + 1.73205i) q^{31} +(5.05842 - 2.92048i) q^{32} +(-4.18614 + 1.26217i) q^{33} -3.46410i q^{34} +(-0.255437 - 4.10891i) q^{36} +(3.37228 - 5.84096i) q^{37} +(1.37228 + 2.37686i) q^{38} +(1.62772 - 6.92820i) q^{39} +(2.31386 + 1.33591i) q^{40} +6.00000 q^{41} +4.74456 q^{43} +(-3.00000 - 1.73205i) q^{44} +(2.50000 - 1.65831i) q^{45} +(-3.37228 - 5.84096i) q^{46} +(-0.813859 + 1.40965i) q^{47} +(0.744563 - 0.792287i) q^{48} +0.792287i q^{50} +(-2.18614 - 7.25061i) q^{51} +(4.88316 - 2.81929i) q^{52} +(1.62772 - 0.939764i) q^{53} +(1.43070 + 3.86025i) q^{54} -2.52434i q^{55} +(4.37228 + 4.10891i) q^{57} +(-0.372281 + 0.644810i) q^{58} +(-4.37228 - 7.57301i) q^{59} +(2.31386 + 0.543620i) q^{60} +(6.00000 + 3.46410i) q^{61} +2.74456 q^{62} -3.37228 q^{64} +(3.55842 + 2.05446i) q^{65} +(3.37228 + 0.792287i) q^{66} +(-2.37228 - 4.10891i) q^{67} +(3.00000 - 5.19615i) q^{68} +(-10.7446 - 10.0974i) q^{69} -0.294954i q^{71} +(-3.56930 + 7.17687i) q^{72} +(-6.00000 + 3.46410i) q^{73} +(-4.62772 + 2.67181i) q^{74} +(0.500000 + 1.65831i) q^{75} +4.75372i q^{76} +(-3.86141 + 4.10891i) q^{78} +(1.18614 - 2.05446i) q^{79} +(0.313859 + 0.543620i) q^{80} +(5.43070 + 7.17687i) q^{81} +(-4.11684 - 2.37686i) q^{82} +17.4891 q^{83} +4.37228 q^{85} +(-3.25544 - 1.87953i) q^{86} +(-0.372281 + 1.58457i) q^{87} +(3.37228 + 5.84096i) q^{88} +(7.37228 - 12.7692i) q^{89} +(-2.37228 + 0.147477i) q^{90} -11.6819i q^{92} +(5.74456 - 1.73205i) q^{93} +(1.11684 - 0.644810i) q^{94} +(-3.00000 + 1.73205i) q^{95} +(-9.68614 + 2.92048i) q^{96} +11.0371i q^{97} +(7.55842 - 0.469882i) 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} + 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}+ \cdots + 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

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 $

$2$	−0.686141	−	0.396143i	−0.485175	−	0.280116i	0.237396	−	0.971413i	$-0.423706\pi$
$2$	−0.686141	−	0.396143i	−0.485175	−	0.280116i	−0.722570	+	0.691297i	$0.757040\pi$
$3$	−1.68614	−	0.396143i	−0.973494	−	0.228714i
$3$	−1.68614	−	0.396143i	−0.973494	−	0.228714i
$4$	−0.686141	−	1.18843i	−0.343070	−	0.594215i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.00000	+	0.939764i	0.408248	+	0.383657i
$7$		0			0
$7$		0			0
$8$			2.67181i			0.944629i
$9$	2.68614	+	1.33591i	0.895380	+	0.445302i
$10$	−0.686141	+	0.396143i	−0.216977	+	0.125272i
$11$	2.18614	−	1.26217i	0.659146	−	0.380558i	−0.132805	−	0.991142i	$-0.542399\pi$
$11$	2.18614	−	1.26217i	0.659146	−	0.380558i	0.791952	+	0.610584i	$0.209065\pi$
$12$	0.686141	+	2.27567i	0.198072	+	0.656930i
$13$			4.10891i			1.13961i	0.821781	+	0.569804i	$0.192981\pi$
$13$			4.10891i			1.13961i	−0.821781	+	0.569804i	$0.807019\pi$
$14$		0			0
$15$	−1.18614	+	1.26217i	−0.306260	+	0.325891i
$16$	−0.313859	+	0.543620i	−0.0784648	+	0.135905i
$17$	2.18614	+	3.78651i	0.530217	+	0.918363i	0.999379	+	0.0352504i	$0.0112229\pi$
$17$	2.18614	+	3.78651i	0.530217	+	0.918363i	−0.469162	+	0.883112i	$0.655444\pi$
$18$	−1.31386	−	1.98072i	−0.309680	−	0.466860i
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−1.37228			−0.306851
$21$		0			0
$22$	−2.00000			−0.426401
$23$	7.37228	+	4.25639i	1.53723	+	0.887518i	0.999000	+	0.0447187i	$0.0142391\pi$
$23$	7.37228	+	4.25639i	1.53723	+	0.887518i	0.538227	+	0.842800i	$0.319094\pi$
$24$	1.05842	−	4.50506i	0.216049	−	0.919591i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.62772	−	2.81929i	0.319222	−	0.552909i
$27$	−4.00000	−	3.31662i	−0.769800	−	0.638285i
$28$		0			0
$29$		−	0.939764i		−	0.174510i	−0.996186	−	0.0872549i	$-0.972191\pi$
$29$		−	0.939764i		−	0.174510i	0.996186	−	0.0872549i	$-0.0278095\pi$
$30$	1.31386	−	0.396143i	0.239877	−	0.0723256i
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	−0.744599	−	0.667512i	$-0.767359\pi$
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	0.205783	+	0.978598i	$0.434026\pi$
$32$	5.05842	−	2.92048i	0.894211	−	0.516273i
$33$	−4.18614	+	1.26217i	−0.728714	+	0.219715i
$34$		−	3.46410i		−	0.594089i
$35$		0			0
$36$	−0.255437	−	4.10891i	−0.0425729	−	0.684819i
$37$	3.37228	−	5.84096i	0.554400	−	0.960248i	−0.443550	−	0.896249i	$-0.646281\pi$
$37$	3.37228	−	5.84096i	0.554400	−	0.960248i	0.997950	−	0.0639989i	$-0.0203854\pi$
$38$	1.37228	+	2.37686i	0.222613	+	0.385578i
$39$	1.62772	−	6.92820i	0.260644	−	1.10940i
$40$	2.31386	+	1.33591i	0.365853	+	0.211225i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	4.74456			0.723539			0.361770	−	0.932268i	$-0.382173\pi$
$43$	4.74456			0.723539			0.361770	+	0.932268i	$0.382173\pi$
$44$	−3.00000	−	1.73205i	−0.452267	−	0.261116i
$45$	2.50000	−	1.65831i	0.372678	−	0.247207i
$46$	−3.37228	−	5.84096i	−0.497216	−	0.861203i
$47$	−0.813859	+	1.40965i	−0.118714	+	0.205618i	−0.919258	−	0.393655i	$-0.871210\pi$
$47$	−0.813859	+	1.40965i	−0.118714	+	0.205618i	0.800545	+	0.599273i	$0.204544\pi$
$48$	0.744563	−	0.792287i	0.107468	−	0.114357i
$49$		0			0
$50$			0.792287i			0.112046i
$51$	−2.18614	−	7.25061i	−0.306121	−	1.01529i
$52$	4.88316	−	2.81929i	0.677172	−	0.390965i
$53$	1.62772	−	0.939764i	0.223584	−	0.129086i	−0.384024	−	0.923323i	$-0.625462\pi$
$53$	1.62772	−	0.939764i	0.223584	−	0.129086i	0.607609	+	0.794236i	$0.292129\pi$
$54$	1.43070	+	3.86025i	0.194694	+	0.525313i
$55$		−	2.52434i		−	0.340382i
$56$		0			0
$57$	4.37228	+	4.10891i	0.579123	+	0.544239i
$58$	−0.372281	+	0.644810i	−0.0488829	+	0.0846677i
$59$	−4.37228	−	7.57301i	−0.569223	−	0.985922i	−0.996643	−	0.0818694i	$-0.973911\pi$
$59$	−4.37228	−	7.57301i	−0.569223	−	0.985922i	0.427421	−	0.904053i	$-0.359422\pi$
$60$	2.31386	+	0.543620i	0.298718	+	0.0701811i
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	2.74456			0.348560
$63$		0			0
$64$	−3.37228			−0.421535
$65$	3.55842	+	2.05446i	0.441368	+	0.254824i
$66$	3.37228	+	0.792287i	0.415099	+	0.0975238i
$67$	−2.37228	−	4.10891i	−0.289820	−	0.501983i	0.683946	−	0.729532i	$-0.260262\pi$
$67$	−2.37228	−	4.10891i	−0.289820	−	0.501983i	−0.973767	+	0.227549i	$0.926929\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	−10.7446	−	10.0974i	−1.29349	−	1.21558i
$70$		0			0
$71$		−	0.294954i		−	0.0350046i	−0.999847	−	0.0175023i	$-0.994429\pi$
$71$		−	0.294954i		−	0.0350046i	0.999847	−	0.0175023i	$-0.00557143\pi$
$72$	−3.56930	+	7.17687i	−0.420646	+	0.845802i
$73$	−6.00000	+	3.46410i	−0.702247	+	0.405442i	−0.808184	−	0.588930i	$-0.799549\pi$
$73$	−6.00000	+	3.46410i	−0.702247	+	0.405442i	0.105937	+	0.994373i	$0.466216\pi$
$74$	−4.62772	+	2.67181i	−0.537961	+	0.310592i
$75$	0.500000	+	1.65831i	0.0577350	+	0.191485i
$76$			4.75372i			0.545289i
$77$		0			0
$78$	−3.86141	+	4.10891i	−0.437218	+	0.465243i
$79$	1.18614	−	2.05446i	0.133451	−	0.231144i	−0.791554	−	0.611100i	$-0.790727\pi$
$79$	1.18614	−	2.05446i	0.133451	−	0.231144i	0.925005	+	0.379956i	$0.124061\pi$
$80$	0.313859	+	0.543620i	0.0350905	+	0.0607786i
$81$	5.43070	+	7.17687i	0.603411	+	0.797430i
$82$	−4.11684	−	2.37686i	−0.454629	−	0.262480i
$83$	17.4891			1.91968			0.959840	−	0.280546i	$-0.0905157\pi$
$83$	17.4891			1.91968			0.959840	+	0.280546i	$0.0905157\pi$
$84$		0			0
$85$	4.37228			0.474240
$86$	−3.25544	−	1.87953i	−0.351043	−	0.202675i
$87$	−0.372281	+	1.58457i	−0.0399127	+	0.169884i
$88$	3.37228	+	5.84096i	0.359486	+	0.622649i
$89$	7.37228	−	12.7692i	0.781460	−	1.35353i	−0.149631	−	0.988742i	$-0.547808\pi$
$89$	7.37228	−	12.7692i	0.781460	−	1.35353i	0.931091	−	0.364787i	$-0.118858\pi$
$90$	−2.37228	+	0.147477i	−0.250060	+	0.0155454i
$91$		0			0
$92$		−	11.6819i		−	1.21792i
$93$	5.74456	−	1.73205i	0.595683	−	0.179605i
$94$	1.11684	−	0.644810i	0.115194	−	0.0665071i
$95$	−3.00000	+	1.73205i	−0.307794	+	0.177705i
$96$	−9.68614	+	2.92048i	−0.988588	+	0.298070i
$97$			11.0371i			1.12065i	0.828273	+	0.560325i	$0.189324\pi$
$97$			11.0371i			1.12065i	−0.828273	+	0.560325i	$0.810676\pi$
$98$		0			0
$99$	7.55842	−	0.469882i	0.759650	−	0.0472249i
$100$	−0.686141	+	1.18843i	−0.0686141	+	0.118843i
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$	−1.37228	+	5.84096i	−0.135876	+	0.578341i
$103$	−5.44158	−	3.14170i	−0.536175	−	0.309561i	0.207353	−	0.978266i	$-0.433515\pi$
$103$	−5.44158	−	3.14170i	−0.536175	−	0.309561i	−0.743527	+	0.668706i	$0.766849\pi$
$104$	−10.9783			−1.07651
$105$		0			0
$106$	−1.48913			−0.144637
$107$	−5.74456	−	3.31662i	−0.555348	−	0.320630i	0.195928	−	0.980618i	$-0.437228\pi$
$107$	−5.74456	−	3.31662i	−0.555348	−	0.320630i	−0.751276	+	0.659988i	$0.770561\pi$
$108$	−1.19702	+	7.02939i	−0.115183	+	0.676404i
$109$	8.55842	+	14.8236i	0.819748	+	1.41985i	0.905868	+	0.423561i	$0.139220\pi$
$109$	8.55842	+	14.8236i	0.819748	+	1.41985i	−0.0861196	+	0.996285i	$0.527447\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$	−8.00000	+	8.51278i	−0.759326	+	0.807997i
$112$		0			0
$113$			3.16915i			0.298128i	0.988828	+	0.149064i	$0.0476261\pi$
$113$			3.16915i			0.298128i	−0.988828	+	0.149064i	$0.952374\pi$
$114$	−1.37228	−	4.55134i	−0.128526	−	0.426272i
$115$	7.37228	−	4.25639i	0.687469	−	0.396910i
$116$	−1.11684	+	0.644810i	−0.103696	+	0.0598691i
$117$	−5.48913	+	11.0371i	−0.507470	+	1.02038i
$118$			6.92820i			0.637793i
$119$		0			0
$120$	−3.37228	−	3.16915i	−0.307846	−	0.289302i
$121$	−2.31386	+	4.00772i	−0.210351	+	0.364338i
$122$	−2.74456	−	4.75372i	−0.248481	−	0.430382i
$123$	−10.1168	−	2.37686i	−0.912205	−	0.214314i
$124$	4.11684	+	2.37686i	0.369704	+	0.213448i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.744563			−0.0660693			−0.0330346	−	0.999454i	$-0.510517\pi$
$127$	−0.744563			−0.0660693			−0.0330346	+	0.999454i	$0.510517\pi$
$128$	−7.80298	−	4.50506i	−0.689693	−	0.398194i
$129$	−8.00000	−	1.87953i	−0.704361	−	0.165483i
$130$	−1.62772	−	2.81929i	−0.142760	−	0.247268i
$131$	2.74456	−	4.75372i	0.239794	−	0.415335i	−0.720861	−	0.693079i	$-0.756254\pi$
$131$	2.74456	−	4.75372i	0.239794	−	0.415335i	0.960655	+	0.277745i	$0.0895869\pi$
$132$	4.37228	+	4.10891i	0.380558	+	0.357635i
$133$		0			0
$134$			3.75906i			0.324733i
$135$	−4.87228	+	1.80579i	−0.419339	+	0.155418i
$136$	−10.1168	+	5.84096i	−0.867512	+	0.500858i
$137$	−11.4891	+	6.63325i	−0.981582	+	0.566717i	−0.902747	−	0.430171i	$-0.858453\pi$
$137$	−11.4891	+	6.63325i	−0.981582	+	0.566717i	−0.0788348	+	0.996888i	$0.525120\pi$
$138$	3.37228	+	11.1846i	0.287068	+	0.952096i
$139$		−	18.6101i		−	1.57849i	−0.614078	−	0.789245i	$-0.710472\pi$
$139$		−	18.6101i		−	1.57849i	0.614078	−	0.789245i	$-0.289528\pi$
$140$		0			0
$141$	1.93070	−	2.05446i	0.162595	−	0.173016i
$142$	−0.116844	+	0.202380i	−0.00980533	+	0.0169833i
$143$	5.18614	+	8.98266i	0.433687	+	0.751168i
$144$	−1.56930	+	1.04095i	−0.130775	+	0.0867461i
$145$	−0.813859	−	0.469882i	−0.0675873	−	0.0390216i
$146$	5.48913			0.454283
$147$		0			0
$148$	−9.25544			−0.760792
$149$	−2.74456	−	1.58457i	−0.224843	−	0.129813i	0.383348	−	0.923604i	$-0.374771\pi$
$149$	−2.74456	−	1.58457i	−0.224843	−	0.129813i	−0.608191	+	0.793791i	$0.708104\pi$
$150$	0.313859	−	1.33591i	0.0256265	−	0.109076i
$151$	1.18614	+	2.05446i	0.0965268	+	0.167189i	0.910245	−	0.414071i	$-0.135893\pi$
$151$	1.18614	+	2.05446i	0.0965268	+	0.167189i	−0.813718	+	0.581260i	$0.802560\pi$
$152$	4.62772	−	8.01544i	0.375358	−	0.650138i
$153$	0.813859	+	13.0916i	0.0657966	+	1.05839i
$154$		0			0
$155$			3.46410i			0.278243i
$156$	−9.35053	+	2.81929i	−0.748642	+	0.225724i
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	−1.62772	+	0.939764i	−0.129494	+	0.0747636i
$159$	−3.11684	+	0.939764i	−0.247182	+	0.0745281i
$160$		−	5.84096i		−	0.461769i
$161$		0			0
$162$	−0.883156	−	7.07568i	−0.0693873	−	0.555918i
$163$	−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	$0.268103\pi$
$164$	−4.11684	−	7.13058i	−0.321472	−	0.556805i
$165$	−1.00000	+	4.25639i	−0.0778499	+	0.331359i
$166$	−12.0000	−	6.92820i	−0.931381	−	0.537733i
$167$	4.88316			0.377870			0.188935	−	0.981990i	$-0.439496\pi$
$167$	4.88316			0.377870			0.188935	+	0.981990i	$0.439496\pi$
$168$		0			0
$169$	−3.88316			−0.298704
$170$	−3.00000	−	1.73205i	−0.230089	−	0.132842i
$171$	−5.74456	−	8.66025i	−0.439298	−	0.662266i
$172$	−3.25544	−	5.63858i	−0.248225	−	0.429938i
$173$	−0.558422	+	0.967215i	−0.0424560	+	0.0735360i	−0.886473	−	0.462781i	$-0.846852\pi$
$173$	−0.558422	+	0.967215i	−0.0424560	+	0.0735360i	0.844017	+	0.536317i	$0.180185\pi$
$174$	0.883156	−	0.939764i	0.0669519	−	0.0712433i
$175$		0			0
$176$			1.58457i			0.119442i
$177$	4.37228	+	14.5012i	0.328641	+	1.08998i
$178$	−10.1168	+	5.84096i	−0.758290	+	0.437799i
$179$	5.74456	−	3.31662i	0.429369	−	0.247896i	−0.269709	−	0.962942i	$-0.586927\pi$
$179$	5.74456	−	3.31662i	0.429369	−	0.247896i	0.699078	+	0.715046i	$0.253594\pi$
$180$	−3.68614	−	1.83324i	−0.274749	−	0.136642i
$181$		−	1.28962i		−	0.0958567i	−0.998851	−	0.0479284i	$-0.984738\pi$
$181$		−	1.28962i		−	0.0958567i	0.998851	−	0.0479284i	$-0.0152619\pi$
$182$		0			0
$183$	−8.74456	−	8.21782i	−0.646417	−	0.607479i
$184$	−11.3723	+	19.6974i	−0.838376	+	1.45211i
$185$	−3.37228	−	5.84096i	−0.247935	−	0.429436i
$186$	−4.62772	−	1.08724i	−0.339321	−	0.0797204i
$187$	9.55842	+	5.51856i	0.698981	+	0.403557i
$188$	2.23369			0.162908
$189$		0			0
$190$	2.74456			0.199112
$191$	18.0475	+	10.4198i	1.30587	+	0.753947i	0.981405	−	0.191949i	$-0.0614808\pi$
$191$	18.0475	+	10.4198i	1.30587	+	0.753947i	0.324470	+	0.945896i	$0.394814\pi$
$192$	5.68614	+	1.33591i	0.410362	+	0.0964108i
$193$	6.11684	+	10.5947i	0.440300	+	0.762622i	0.997712	−	0.0676143i	$-0.0215387\pi$
$193$	6.11684	+	10.5947i	0.440300	+	0.762622i	−0.557411	+	0.830236i	$0.688205\pi$
$194$	4.37228	−	7.57301i	0.313912	−	0.543711i
$195$	−5.18614	−	4.87375i	−0.371387	−	0.349016i
$196$		0			0
$197$			15.7359i			1.12114i	0.828107	+	0.560569i	$0.189418\pi$
$197$			15.7359i			1.12114i	−0.828107	+	0.560569i	$0.810582\pi$
$198$	−5.37228	−	2.67181i	−0.381791	−	0.189878i
$199$	23.2337	−	13.4140i	1.64699	−	0.950892i	0.668734	−	0.743502i	$-0.266836\pi$
$199$	23.2337	−	13.4140i	1.64699	−	0.950892i	0.978258	−	0.207390i	$-0.0664969\pi$
$200$	2.31386	−	1.33591i	0.163615	−	0.0944629i
$201$	2.37228	+	7.86797i	0.167328	+	0.554964i
$202$		−	4.75372i		−	0.334471i
$203$		0			0
$204$	−7.11684	+	7.57301i	−0.498279	+	0.530217i
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	2.48913	+	4.31129i	0.173426	+	0.300382i
$207$	14.1168	+	21.2819i	0.981188	+	1.47920i
$208$	−2.23369	−	1.28962i	−0.154878	−	0.0894191i
$209$	−8.74456			−0.604874
$210$		0			0
$211$	−11.1168			−0.765315			−0.382658	−	0.923890i	$-0.624991\pi$
$211$	−11.1168			−0.765315			−0.382658	+	0.923890i	$0.624991\pi$
$212$	−2.23369	−	1.28962i	−0.153410	−	0.0885715i
$213$	−0.116844	+	0.497333i	−0.00800602	+	0.0340767i
$214$	2.62772	+	4.55134i	0.179627	+	0.311123i
$215$	2.37228	−	4.10891i	0.161788	−	0.280225i
$216$	8.86141	−	10.6873i	0.602942	−	0.727176i
$217$		0			0
$218$		−	13.5615i		−	0.918497i
$219$	11.4891	−	3.46410i	0.776363	−	0.234082i
$220$	−3.00000	+	1.73205i	−0.202260	+	0.116775i
$221$	−15.5584	+	8.98266i	−1.04657	+	0.604239i
$222$	8.86141	−	2.67181i	0.594739	−	0.179320i
$223$			8.86263i			0.593486i	0.954957	+	0.296743i	$0.0959004\pi$
$223$			8.86263i			0.593486i	−0.954957	+	0.296743i	$0.904100\pi$
$224$		0			0
$225$	−0.186141	−	2.99422i	−0.0124094	−	0.199615i
$226$	1.25544	−	2.17448i	0.0835105	−	0.144644i
$227$	12.3030	+	21.3094i	0.816578	+	1.41435i	0.908189	+	0.418559i	$0.137465\pi$
$227$	12.3030	+	21.3094i	0.816578	+	1.41435i	−0.0916117	+	0.995795i	$0.529202\pi$
$228$	1.88316	−	8.01544i	0.124715	−	0.530836i
$229$	13.1168	+	7.57301i	0.866785	+	0.500439i	0.866279	−	0.499561i	$-0.166505\pi$
$229$	13.1168	+	7.57301i	0.866785	+	0.500439i	0.000506770		1.00000i	$0.499839\pi$
$230$	−6.74456			−0.444723
$231$		0			0
$232$	2.51087			0.164847
$233$	−14.7446	−	8.51278i	−0.965948	−	0.557691i	−0.0679497	−	0.997689i	$-0.521646\pi$
$233$	−14.7446	−	8.51278i	−0.965948	−	0.557691i	−0.897999	+	0.439998i	$0.854979\pi$
$234$	8.13859	−	5.39853i	0.532036	−	0.352913i
$235$	0.813859	+	1.40965i	0.0530903	+	0.0919551i
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$	−2.81386	+	2.99422i	−0.182780	+	0.194495i
$238$		0			0
$239$		−	20.8395i		−	1.34800i	−0.738733	−	0.673998i	$-0.764576\pi$
$239$		−	20.8395i		−	1.34800i	0.738733	−	0.673998i	$-0.235424\pi$
$240$	−0.313859	−	1.04095i	−0.0202595	−	0.0671933i
$241$	14.2337	−	8.21782i	0.916872	−	0.529357i	0.0342365	−	0.999414i	$-0.489100\pi$
$241$	14.2337	−	8.21782i	0.916872	−	0.529357i	0.882636	+	0.470057i	$0.155767\pi$
$242$	3.17527	−	1.83324i	0.204114	−	0.117845i
$243$	−6.31386	−	14.2525i	−0.405034	−	0.914302i
$244$		−	9.50744i		−	0.608652i
$245$		0			0
$246$	6.00000	+	5.63858i	0.382546	+	0.359503i
$247$	7.11684	−	12.3267i	0.452834	−	0.784331i
$248$	−4.62772	−	8.01544i	−0.293860	−	0.508981i
$249$	−29.4891	−	6.92820i	−1.86880	−	0.439057i
$250$	0.686141	+	0.396143i	0.0433953	+	0.0250543i
$251$	5.48913			0.346471			0.173235	−	0.984880i	$-0.444578\pi$
$251$	5.48913			0.346471			0.173235	+	0.984880i	$0.444578\pi$
$252$		0			0
$253$	21.4891			1.35101
$254$	0.510875	+	0.294954i	0.0320551	+	0.0185070i
$255$	−7.37228	−	1.73205i	−0.461670	−	0.108465i
$256$	6.94158	+	12.0232i	0.433849	+	0.751448i
$257$	0.255437	−	0.442430i	0.0159337	−	0.0275981i	−0.857949	−	0.513736i	$-0.828261\pi$
$257$	0.255437	−	0.442430i	0.0159337	−	0.0275981i	0.873882	+	0.486137i	$0.161595\pi$
$258$	4.74456	+	4.45877i	0.295384	+	0.277591i
$259$		0			0
$260$		−	5.63858i		−	0.349690i
$261$	1.25544	−	2.52434i	0.0777096	−	0.156253i
$262$	−3.76631	+	2.17448i	−0.232684	+	0.134340i
$263$	−0.255437	+	0.147477i	−0.0157509	+	0.00909381i	−0.507855	−	0.861443i	$-0.669561\pi$
$263$	−0.255437	+	0.147477i	−0.0157509	+	0.00909381i	0.492104	+	0.870536i	$0.336228\pi$
$264$	−3.37228	−	11.1846i	−0.207550	−	0.688364i
$265$		−	1.87953i		−	0.115458i
$266$		0			0
$267$	−17.4891	+	18.6101i	−1.07032	+	1.13892i
$268$	−3.25544	+	5.63858i	−0.198857	+	0.344431i
$269$	1.37228	+	2.37686i	0.0836695	+	0.144920i	0.904823	−	0.425787i	$-0.140003\pi$
$269$	1.37228	+	2.37686i	0.0836695	+	0.144920i	−0.821154	+	0.570707i	$0.806669\pi$
$270$	4.05842	+	0.691097i	0.246988	+	0.0420588i
$271$	−4.11684	−	2.37686i	−0.250080	−	0.144384i	0.369721	−	0.929143i	$-0.379453\pi$
$271$	−4.11684	−	2.37686i	−0.250080	−	0.144384i	−0.619801	+	0.784759i	$0.712787\pi$
$272$	−2.74456			−0.166414
$273$		0			0
$274$	10.5109			0.634985
$275$	−2.18614	−	1.26217i	−0.131829	−	0.0761116i
$276$	−4.62772	+	19.6974i	−0.278556	+	1.18564i
$277$	−14.1168	−	24.4511i	−0.848199	−	1.46912i	−0.882814	−	0.469723i	$-0.844354\pi$
$277$	−14.1168	−	24.4511i	−0.848199	−	1.46912i	0.0346149	−	0.999401i	$-0.488980\pi$
$278$	−7.37228	+	12.7692i	−0.442160	+	0.765844i
$279$	−10.3723	+	0.644810i	−0.620972	+	0.0386038i
$280$		0			0
$281$			28.0627i			1.67408i	0.547143	+	0.837039i	$0.315715\pi$
$281$			28.0627i			1.67408i	−0.547143	+	0.837039i	$0.684285\pi$
$282$	−2.13859	+	0.644810i	−0.127351	+	0.0383979i
$283$	−0.558422	+	0.322405i	−0.0331947	+	0.0191650i	−0.516506	−	0.856284i	$-0.672767\pi$
$283$	−0.558422	+	0.322405i	−0.0331947	+	0.0191650i	0.483311	+	0.875449i	$0.339434\pi$
$284$	−0.350532	+	0.202380i	−0.0208002	+	0.0120090i
$285$	5.74456	−	1.73205i	0.340279	−	0.102598i
$286$		−	8.21782i		−	0.485930i
$287$		0			0
$288$	17.4891	−	1.08724i	1.03056	−	0.0640663i
$289$	−1.05842	+	1.83324i	−0.0622601	+	0.107838i
$290$	0.372281	+	0.644810i	0.0218611	+	0.0378646i
$291$	4.37228	−	18.6101i	0.256308	−	1.09095i
$292$	8.23369	+	4.75372i	0.481840	+	0.278191i
$293$	10.8832			0.635801			0.317900	−	0.948124i	$-0.397022\pi$
$293$	10.8832			0.635801			0.317900	+	0.948124i	$0.397022\pi$
$294$		0			0
$295$	−8.74456			−0.509128
$296$	15.6060	+	9.01011i	0.907079	+	0.523702i
$297$	−12.9307	−	2.20193i	−0.750316	−	0.127769i
$298$	1.25544	+	2.17448i	0.0727255	+	0.125964i
$299$	−17.4891	+	30.2921i	−1.01142	+	1.75183i
$300$	1.62772	−	1.73205i	0.0939764	−	0.100000i
$301$		0			0
$302$		−	1.87953i		−	0.108155i
$303$	−3.00000	−	9.94987i	−0.172345	−	0.571605i
$304$	1.88316	−	1.08724i	0.108006	−	0.0623575i
$305$	6.00000	−	3.46410i	0.343559	−	0.198354i
$306$	4.62772	−	9.30506i	0.264549	−	0.531935i
$307$		−	22.7190i		−	1.29664i	−0.761366	−	0.648322i	$-0.775471\pi$
$307$		−	22.7190i		−	1.29664i	0.761366	−	0.648322i	$-0.224529\pi$
$308$		0			0
$309$	7.93070	+	7.45299i	0.451162	+	0.423986i
$310$	1.37228	−	2.37686i	0.0779403	−	0.134997i
$311$	−7.11684	−	12.3267i	−0.403559	−	0.698985i	0.590593	−	0.806969i	$-0.298894\pi$
$311$	−7.11684	−	12.3267i	−0.403559	−	0.698985i	−0.994153	+	0.107984i	$0.965560\pi$
$312$	18.5109	+	4.34896i	1.04797	+	0.246212i
$313$	4.67527	+	2.69927i	0.264262	+	0.152572i	0.626277	−	0.779601i	$-0.284578\pi$
$313$	4.67527	+	2.69927i	0.264262	+	0.152572i	−0.362015	+	0.932172i	$0.617911\pi$
$314$		0			0
$315$		0			0
$316$	−3.25544			−0.183133
$317$	−1.62772	−	0.939764i	−0.0914218	−	0.0527824i	0.453592	−	0.891209i	$-0.350142\pi$
$317$	−1.62772	−	0.939764i	−0.0914218	−	0.0527824i	−0.545014	+	0.838427i	$0.683476\pi$
$318$	2.51087	+	0.589907i	0.140803	+	0.0330804i
$319$	−1.18614	−	2.05446i	−0.0664111	−	0.115027i
$320$	−1.68614	+	2.92048i	−0.0942581	+	0.163260i
$321$	8.37228	+	7.86797i	0.467295	+	0.439147i
$322$		0			0
$323$		−	15.1460i		−	0.842747i
$324$	4.80298	−	11.3784i	0.266832	−	0.632131i
$325$	3.55842	−	2.05446i	0.197386	−	0.113961i
$326$	5.48913	−	3.16915i	0.304015	−	0.175523i
$327$	−8.55842	−	28.3851i	−0.473282	−	1.56970i
$328$			16.0309i			0.885158i
$329$		0			0
$330$	2.37228	−	2.52434i	0.130590	−	0.138960i
$331$	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
$333$	16.8614	−	11.1846i	0.923999	−	0.612912i
$334$	−3.35053	−	1.93443i	−0.183333	−	0.105847i
$335$	−4.74456			−0.259223
$336$		0			0
$337$	16.2337			0.884305			0.442153	−	0.896940i	$-0.354215\pi$
$337$	16.2337			0.884305			0.442153	+	0.896940i	$0.354215\pi$
$338$	2.66439	+	1.53829i	0.144924	+	0.0836718i
$339$	1.25544	−	5.34363i	0.0681860	−	0.290226i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	−4.37228	+	7.57301i	−0.236772	+	0.410102i
$342$	0.510875	+	8.21782i	0.0276249	+	0.444369i
$343$		0			0
$344$			12.6766i			0.683476i
$345$	−14.1168	+	4.25639i	−0.760025	+	0.229156i
$346$	0.766312	−	0.442430i	0.0411972	−	0.0237852i
$347$	12.8614	−	7.42554i	0.690436	−	0.398624i	−0.113339	−	0.993556i	$-0.536155\pi$
$347$	12.8614	−	7.42554i	0.690436	−	0.398624i	0.803776	+	0.594933i	$0.202821\pi$
$348$	2.13859	−	0.644810i	0.114641	−	0.0345655i
$349$			15.1460i			0.810748i	0.914151	+	0.405374i	$0.132859\pi$
$349$			15.1460i			0.810748i	−0.914151	+	0.405374i	$0.867141\pi$
$350$		0			0
$351$	13.6277	−	16.4356i	0.727394	−	0.877270i
$352$	7.37228	−	12.7692i	0.392944	−	0.680599i
$353$	12.5584	+	21.7518i	0.668417	+	1.15773i	0.978347	+	0.206973i	$0.0663613\pi$
$353$	12.5584	+	21.7518i	0.668417	+	1.15773i	−0.309929	+	0.950760i	$0.600305\pi$
$354$	2.74456	−	11.6819i	0.145872	−	0.620887i
$355$	−0.255437	−	0.147477i	−0.0135572	−	0.00782726i
$356$	−20.2337			−1.07238
$357$		0			0
$358$	−5.25544			−0.277758
$359$	14.4891	+	8.36530i	0.764707	+	0.441504i	0.830983	−	0.556298i	$-0.187779\pi$
$359$	14.4891	+	8.36530i	0.764707	+	0.441504i	−0.0662763	+	0.997801i	$0.521112\pi$
$360$	4.43070	+	6.67954i	0.233519	+	0.352042i
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$	−0.510875	+	0.884861i	−0.0268510	+	0.0465073i
$363$	5.48913	−	5.84096i	0.288104	−	0.306571i
$364$		0			0
$365$			6.92820i			0.362639i
$366$	2.74456	+	9.10268i	0.143461	+	0.475805i
$367$	−30.5584	+	17.6429i	−1.59514	+	0.920953i	−0.602731	+	0.797944i	$0.705921\pi$
$367$	−30.5584	+	17.6429i	−1.59514	+	0.920953i	−0.992406	+	0.123008i	$0.960746\pi$
$368$	−4.62772	+	2.67181i	−0.241237	+	0.139278i
$369$	16.1168	+	8.01544i	0.839009	+	0.417267i
$370$			5.34363i			0.277802i
$371$		0			0
$372$	−6.00000	−	5.63858i	−0.311086	−	0.292347i
$373$	6.62772	−	11.4795i	0.343170	−	0.594388i	−0.641849	−	0.766831i	$-0.721833\pi$
$373$	6.62772	−	11.4795i	0.343170	−	0.594388i	0.985020	+	0.172442i	$0.0551659\pi$
$374$	−4.37228	−	7.57301i	−0.226085	−	0.391591i
$375$	1.68614	+	0.396143i	0.0870719	+	0.0204568i
$376$	−3.76631	−	2.17448i	−0.194233	−	0.112140i
$377$	3.86141			0.198873
$378$		0			0
$379$	−21.4891			−1.10382			−0.551911	−	0.833903i	$-0.686101\pi$
$379$	−21.4891			−1.10382			−0.551911	+	0.833903i	$0.686101\pi$
$380$	4.11684	+	2.37686i	0.211190	+	0.121930i
$381$	1.25544	+	0.294954i	0.0643180	+	0.0151109i
$382$	−8.25544	−	14.2988i	−0.422385	−	0.731592i
$383$	2.74456	−	4.75372i	0.140241	−	0.242904i	−0.787347	−	0.616511i	$-0.788546\pi$
$383$	2.74456	−	4.75372i	0.140241	−	0.242904i	0.927587	+	0.373607i	$0.121879\pi$
$384$	11.3723	+	10.6873i	0.580339	+	0.545382i
$385$		0			0
$386$		−	9.69259i		−	0.493340i
$387$	12.7446	+	6.33830i	0.647843	+	0.322194i
$388$	13.1168	−	7.57301i	0.665907	−	0.384462i
$389$	25.4198	−	14.6761i	1.28884	−	0.744110i	0.310390	−	0.950609i	$-0.399540\pi$
$389$	25.4198	−	14.6761i	1.28884	−	0.744110i	0.978447	+	0.206499i	$0.0662071\pi$
$390$	1.62772	+	5.39853i	0.0824227	+	0.273365i
$391$			37.2203i			1.88231i
$392$		0			0
$393$	−6.51087	+	6.92820i	−0.328430	+	0.349482i
$394$	6.23369	−	10.7971i	0.314049	−	0.543948i
$395$	−1.18614	−	2.05446i	−0.0596812	−	0.103371i
$396$	−5.74456	−	8.66025i	−0.288675	−	0.435194i
$397$	−22.6753	−	13.0916i	−1.13804	−	0.657047i	−0.192095	−	0.981376i	$-0.561528\pi$
$397$	−22.6753	−	13.0916i	−1.13804	−	0.657047i	−0.945944	+	0.324329i	$0.894861\pi$
$398$	−21.2554			−1.06544
$399$		0			0
$400$	0.627719			0.0313859
$401$	−5.18614	−	2.99422i	−0.258984	−	0.149524i	0.364887	−	0.931052i	$-0.381108\pi$
$401$	−5.18614	−	2.99422i	−0.258984	−	0.149524i	−0.623871	+	0.781528i	$0.714441\pi$
$402$	1.48913	−	6.33830i	0.0742708	−	0.316125i
$403$	−7.11684	−	12.3267i	−0.354515	−	0.614038i
$404$	4.11684	−	7.13058i	0.204821	−	0.354760i
$405$	8.93070	−	1.11469i	0.443770	−	0.0553895i
$406$		0			0
$407$		−	17.0256i		−	0.843925i
$408$	19.3723	−	5.84096i	0.959071	−	0.289171i
$409$	−21.3505	+	12.3267i	−1.05572	+	0.609518i	−0.924244	−	0.381802i	$-0.875304\pi$
$409$	−21.3505	+	12.3267i	−1.05572	+	0.609518i	−0.131472	+	0.991320i	$0.541970\pi$
$410$	−4.11684	+	2.37686i	−0.203316	+	0.117385i
$411$	22.0000	−	6.63325i	1.08518	−	0.327194i
$412$			8.62258i			0.424804i
$413$		0			0
$414$	−1.25544	−	20.1947i	−0.0617014	−	0.992515i
$415$	8.74456	−	15.1460i	0.429254	−	0.743489i
$416$	12.0000	+	20.7846i	0.588348	+	1.01905i
$417$	−7.37228	+	31.3793i	−0.361022	+	1.53665i
$418$	6.00000	+	3.46410i	0.293470	+	0.169435i
$419$	−8.74456			−0.427200			−0.213600	−	0.976921i	$-0.568519\pi$
$419$	−8.74456			−0.427200			−0.213600	+	0.976921i	$0.568519\pi$
$420$		0			0
$421$	14.6060			0.711851			0.355926	−	0.934514i	$-0.384166\pi$
$421$	14.6060			0.711851			0.355926	+	0.934514i	$0.384166\pi$
$422$	7.62772	+	4.40387i	0.371312	+	0.214377i
$423$	−4.06930	+	2.69927i	−0.197856	+	0.131243i
$424$	2.51087	+	4.34896i	0.121939	+	0.211204i
$425$	2.18614	−	3.78651i	0.106043	−	0.183673i
$426$	0.277187	−	0.294954i	0.0134297	−	0.0142906i
$427$		0			0
$428$			9.10268i			0.439995i
$429$	−5.18614	−	17.2005i	−0.250389	−	0.830447i
$430$	−3.25544	+	1.87953i	−0.156991	+	0.0906389i
$431$	13.0693	−	7.54556i	0.629526	−	0.363457i	−0.151043	−	0.988527i	$-0.548263\pi$
$431$	13.0693	−	7.54556i	0.629526	−	0.363457i	0.780568	+	0.625070i	$0.214930\pi$
$432$	3.05842	−	1.13353i	0.147148	−	0.0545369i
$433$		−	37.2203i		−	1.78869i	−0.447377	−	0.894346i	$-0.647642\pi$
$433$		−	37.2203i		−	1.78869i	0.447377	−	0.894346i	$-0.352358\pi$
$434$		0			0
$435$	1.18614	+	1.11469i	0.0568711	+	0.0534454i
$436$	11.7446	−	20.3422i	0.562463	−	0.974214i
$437$	−14.7446	−	25.5383i	−0.705328	−	1.22166i
$438$	−9.25544	−	2.17448i	−0.442242	−	0.103901i
$439$	−16.1168	−	9.30506i	−0.769215	−	0.444106i	0.0633795	−	0.997989i	$-0.479812\pi$
$439$	−16.1168	−	9.30506i	−0.769215	−	0.444106i	−0.832595	+	0.553883i	$0.813145\pi$
$440$	6.74456			0.321534
$441$		0			0
$442$	14.2337			0.677027
$443$	−5.74456	−	3.31662i	−0.272932	−	0.157578i	0.357287	−	0.933995i	$-0.383702\pi$
$443$	−5.74456	−	3.31662i	−0.272932	−	0.157578i	−0.630220	+	0.776417i	$0.717035\pi$
$444$	15.6060	+	3.66648i	0.740627	+	0.174004i
$445$	−7.37228	−	12.7692i	−0.349480	−	0.605317i
$446$	3.51087	−	6.08101i	0.166245	−	0.287944i
$447$	4.00000	+	3.75906i	0.189194	+	0.177797i
$448$		0			0
$449$			11.6270i			0.548713i	0.961628	+	0.274357i	$0.0884648\pi$
$449$			11.6270i			0.548713i	−0.961628	+	0.274357i	$0.911535\pi$
$450$	−1.05842	+	2.12819i	−0.0498945	+	0.100324i
$451$	13.1168	−	7.57301i	0.617648	−	0.356599i
$452$	3.76631	−	2.17448i	0.177152	−	0.102279i
$453$	−1.18614	−	3.93398i	−0.0557297	−	0.184835i
$454$		−	19.4950i		−	0.914945i
$455$		0			0
$456$	−10.9783	+	11.6819i	−0.514104	+	0.547056i
$457$	−6.48913	+	11.2395i	−0.303548	+	0.525761i	−0.976937	−	0.213527i	$-0.931505\pi$
$457$	−6.48913	+	11.2395i	−0.303548	+	0.525761i	0.673389	+	0.739289i	$0.264838\pi$
$458$	−6.00000	−	10.3923i	−0.280362	−	0.485601i
$459$	3.81386	−	22.3966i	0.178016	−	1.04539i
$460$	−10.1168	−	5.84096i	−0.471700	−	0.272336i
$461$	−2.74456			−0.127827			−0.0639135	−	0.997955i	$-0.520358\pi$
$461$	−2.74456			−0.127827			−0.0639135	+	0.997955i	$0.520358\pi$
$462$		0			0
$463$	−32.4674			−1.50889			−0.754443	−	0.656365i	$-0.772093\pi$
$463$	−32.4674			−1.50889			−0.754443	+	0.656365i	$0.772093\pi$
$464$	0.510875	+	0.294954i	0.0237168	+	0.0136929i
$465$	1.37228	−	5.84096i	0.0636380	−	0.270868i
$466$	6.74456	+	11.6819i	0.312436	+	0.541155i
$467$	−15.5584	+	26.9480i	−0.719958	+	1.24700i	0.241058	+	0.970511i	$0.422506\pi$
$467$	−15.5584	+	26.9480i	−0.719958	+	1.24700i	−0.961016	+	0.276493i	$0.910828\pi$
$468$	16.8832	−	1.04957i	0.780424	−	0.0485164i
$469$		0			0
$470$		−	1.28962i		−	0.0594858i
$471$		0			0
$472$	20.2337	−	11.6819i	0.931331	−	0.537704i
$473$	10.3723	−	5.98844i	0.476918	−	0.275349i
$474$	3.11684	−	0.939764i	0.143161	−	0.0431648i
$475$			3.46410i			0.158944i
$476$		0			0
$477$	5.62772	−	0.349857i	0.257676	−	0.0160188i
$478$	−8.25544	+	14.2988i	−0.377595	+	0.654014i
$479$	20.7446	+	35.9306i	0.947843	+	1.64171i	0.749956	+	0.661488i	$0.230075\pi$
$479$	20.7446	+	35.9306i	0.947843	+	1.64171i	0.197887	+	0.980225i	$0.436592\pi$
$480$	−2.31386	+	9.84868i	−0.105613	+	0.449529i
$481$	24.0000	+	13.8564i	1.09431	+	0.631798i
$482$	−13.0217			−0.593124
$483$		0			0
$484$	6.35053			0.288661
$485$	9.55842	+	5.51856i	0.434026	+	0.250585i
$486$	−1.31386	+	12.2804i	−0.0595979	+	0.557052i
$487$	−18.7446	−	32.4665i	−0.849397	−	1.47120i	−0.881747	−	0.471723i	$-0.843632\pi$
$487$	−18.7446	−	32.4665i	−0.849397	−	1.47120i	0.0323498	−	0.999477i	$-0.489701\pi$
$488$	−9.25544	+	16.0309i	−0.418974	+	0.725684i
$489$	9.48913	−	10.0974i	0.429113	−	0.456618i
$490$		0			0
$491$		−	5.69349i		−	0.256943i	−0.991713	−	0.128472i	$-0.958993\pi$
$491$		−	5.69349i		−	0.256943i	0.991713	−	0.128472i	$-0.0410072\pi$
$492$	4.11684	+	13.6540i	0.185602	+	0.615571i
$493$	3.55842	−	2.05446i	0.160263	−	0.0925280i
$494$	−9.76631	+	5.63858i	−0.439407	+	0.253692i
$495$	3.37228	−	6.78073i	0.151573	−	0.304771i
$496$		−	2.17448i		−	0.0976371i
$497$		0			0
$498$	17.4891	+	16.4356i	0.783706	+	0.736499i
$499$	−20.6753	+	35.8106i	−0.925552	+	1.60310i	−0.134881	+	0.990862i	$0.543065\pi$
$499$	−20.6753	+	35.8106i	−0.925552	+	1.60310i	−0.790671	+	0.612241i	$0.790268\pi$
$500$	0.686141	+	1.18843i	0.0306851	+	0.0531482i
$501$	−8.23369	−	1.93443i	−0.367854	−	0.0864240i
$502$	−3.76631	−	2.17448i	−0.168099	−	0.0970518i
$503$	−12.6060			−0.562072			−0.281036	−	0.959697i	$-0.590678\pi$
$503$	−12.6060			−0.562072			−0.281036	+	0.959697i	$0.590678\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$	−14.7446	−	8.51278i	−0.655476	−	0.378439i
$507$	6.54755	+	1.53829i	0.290787	+	0.0683177i
$508$	0.510875	+	0.884861i	0.0226664	+	0.0392594i
$509$	−1.88316	+	3.26172i	−0.0834694	+	0.144573i	−0.904738	−	0.425969i	$-0.859933\pi$
$509$	−1.88316	+	3.26172i	−0.0834694	+	0.144573i	0.821269	+	0.570542i	$0.193267\pi$
$510$	4.37228	+	4.10891i	0.193608	+	0.181946i
$511$		0			0
$512$			7.02078i			0.310277i
$513$	6.25544	+	16.8781i	0.276184	+	0.745185i
$514$	−0.350532	+	0.202380i	−0.0154613	+	0.00892659i
$515$	−5.44158	+	3.14170i	−0.239785	+	0.138440i
$516$	3.25544	+	10.7971i	0.143313	+	0.475314i
$517$			4.10891i			0.180710i
$518$		0			0
$519$	1.32473	−	1.40965i	0.0581494	−	0.0618766i
$520$	−5.48913	+	9.50744i	−0.240714	+	0.416929i
$521$	−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	$-0.439040\pi$
$522$	−1.86141	+	1.23472i	−0.0814716	+	0.0540421i
$523$	9.00000	+	5.19615i	0.393543	+	0.227212i	0.683694	−	0.729769i	$-0.260372\pi$
$523$	9.00000	+	5.19615i	0.393543	+	0.227212i	−0.290151	+	0.956981i	$0.593706\pi$
$524$	−7.53262			−0.329064
$525$		0			0
$526$	0.233688			0.0101893
$527$	−13.1168	−	7.57301i	−0.571379	−	0.329886i
$528$	0.627719	−	2.67181i	0.0273179	−	0.116276i
$529$	24.7337	+	42.8400i	1.07538	+	1.86261i
$530$	−0.744563	+	1.28962i	−0.0323417	+	0.0560175i
$531$	−1.62772	−	26.1831i	−0.0706370	−	1.13625i
$532$		0			0
$533$			24.6535i			1.06786i
$534$	19.3723	−	5.84096i	0.838321	−	0.252763i
$535$	−5.74456	+	3.31662i	−0.248359	+	0.143390i
$536$	10.9783	−	6.33830i	0.474188	−	0.273773i
$537$	−11.0000	+	3.31662i	−0.474685	+	0.143123i
$538$		−	2.17448i		−	0.0937485i
$539$		0			0
$540$	5.48913	+	4.55134i	0.236214	+	0.195859i
$541$	−12.1861	+	21.1070i	−0.523923	+	0.907461i	0.475689	+	0.879614i	$0.342199\pi$
$541$	−12.1861	+	21.1070i	−0.523923	+	0.907461i	−0.999612	+	0.0278479i	$0.991135\pi$
$542$	1.88316	+	3.26172i	0.0808885	+	0.140103i
$543$	−0.510875	+	2.17448i	−0.0219237	+	0.0933159i
$544$	22.1168	+	12.7692i	0.948252	+	0.547473i
$545$	17.1168			0.733205
$546$		0			0
$547$	−2.97825			−0.127341			−0.0636704	−	0.997971i	$-0.520281\pi$
$547$	−2.97825			−0.127341			−0.0636704	+	0.997971i	$0.520281\pi$
$548$	15.7663	+	9.10268i	0.673503	+	0.388847i
$549$	11.4891	+	17.3205i	0.490344	+	0.739221i
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	−1.62772	+	2.81929i	−0.0693431	+	0.120106i
$552$	26.9783	−	28.7075i	1.14827	−	1.22187i
$553$		0			0
$554$			22.3692i			0.950376i
$555$	3.37228	+	11.1846i	0.143145	+	0.474759i
$556$	−22.1168	+	12.7692i	−0.937963	+	0.541533i
$557$	−15.2554	+	8.80773i	−0.646394	+	0.373196i	−0.787073	−	0.616860i	$-0.788405\pi$
$557$	−15.2554	+	8.80773i	−0.646394	+	0.373196i	0.140680	+	0.990055i	$0.455071\pi$
$558$	7.37228	+	3.66648i	0.312094	+	0.155215i
$559$			19.4950i			0.824550i
$560$		0			0
$561$	−13.9307	−	13.0916i	−0.588155	−	0.552727i
$562$	11.1168	−	19.2549i	0.468936	−	0.812221i
$563$	−8.74456	−	15.1460i	−0.368539	−	0.638329i	0.620798	−	0.783971i	$-0.286809\pi$
$563$	−8.74456	−	15.1460i	−0.368539	−	0.638329i	−0.989337	+	0.145642i	$0.953475\pi$
$564$	−3.76631	−	0.884861i	−0.158590	−	0.0372594i
$565$	2.74456	+	1.58457i	0.115465	+	0.0666635i
$566$	0.510875			0.0214737
$567$		0			0
$568$	0.788061			0.0330663
$569$	−20.7446	−	11.9769i	−0.869657	−	0.502097i	−0.00242296	−	0.999997i	$-0.500771\pi$
$569$	−20.7446	−	11.9769i	−0.869657	−	0.502097i	−0.867234	+	0.497900i	$0.834105\pi$
$570$	−4.62772	−	1.08724i	−0.193834	−	0.0455395i
$571$	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	$0.806660\pi$
$572$	7.11684	−	12.3267i	0.297570	−	0.515407i
$573$	−26.3030	−	24.7186i	−1.09882	−	1.03263i
$574$		0			0
$575$		−	8.51278i		−	0.355007i
$576$	−9.05842	−	4.50506i	−0.377434	−	0.187711i
$577$	2.44158	−	1.40965i	0.101644	−	0.0586843i	−0.448316	−	0.893875i	$-0.647976\pi$
$577$	2.44158	−	1.40965i	0.101644	−	0.0586843i	0.549960	+	0.835191i	$0.314643\pi$
$578$	1.45245	−	0.838574i	0.0604141	−	0.0348801i
$579$	−6.11684	−	20.2873i	−0.254207	−	0.843110i
$580$			1.28962i			0.0535486i
$581$		0			0
$582$	−10.3723	+	11.0371i	−0.429945	+	0.457503i
$583$	2.37228	−	4.10891i	0.0982499	−	0.170174i
$584$	−9.25544	−	16.0309i	−0.382993	−	0.663363i
$585$	6.81386	+	10.2723i	0.281718	+	0.424706i
$586$	−7.46738	−	4.31129i	−0.308474	−	0.178098i
$587$	−17.4891			−0.721853			−0.360927	−	0.932594i	$-0.617540\pi$
$587$	−17.4891			−0.721853			−0.360927	+	0.932594i	$0.617540\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$	6.00000	+	3.46410i	0.247016	+	0.142615i
$591$	6.23369	−	26.5330i	0.256420	−	1.09142i
$592$	2.11684	+	3.66648i	0.0870018	+	0.150691i
$593$	2.18614	−	3.78651i	0.0897740	−	0.155493i	−0.817642	−	0.575728i	$-0.804719\pi$
$593$	2.18614	−	3.78651i	0.0897740	−	0.155493i	0.907416	+	0.420234i	$0.138052\pi$
$594$	8.00000	+	6.63325i	0.328244	+	0.272166i
$595$		0			0
$596$			4.34896i			0.178140i
$597$	−44.4891	+	13.4140i	−1.82082	+	0.548997i
$598$	24.0000	−	13.8564i	0.981433	−	0.566631i
$599$	−30.0475	+	17.3480i	−1.22771	+	0.708818i	−0.966550	−	0.256477i	$-0.917438\pi$
$599$	−30.0475	+	17.3480i	−1.22771	+	0.708818i	−0.261159	+	0.965296i	$0.584105\pi$
$600$	−4.43070	+	1.33591i	−0.180883	+	0.0545382i
$601$		−	22.0742i		−	0.900427i	−0.892921	−	0.450213i	$-0.851348\pi$
$601$		−	22.0742i		−	0.900427i	0.892921	−	0.450213i	$-0.148652\pi$
$602$		0			0
$603$	−0.883156	−	14.2063i	−0.0359649	−	0.578524i
$604$	1.62772	−	2.81929i	0.0662309	−	0.114715i
$605$	2.31386	+	4.00772i	0.0940718	+	0.162937i
$606$	−1.88316	+	8.01544i	−0.0764980	+	0.325605i
$607$	−7.67527	−	4.43132i	−0.311529	−	0.179862i	0.336081	−	0.941833i	$-0.390898\pi$
$607$	−7.67527	−	4.43132i	−0.311529	−	0.179862i	−0.647611	+	0.761971i	$0.724232\pi$
$608$	−20.2337			−0.820584
$609$		0			0
$610$	−5.48913			−0.222248
$611$	−5.79211	−	3.34408i	−0.234324	−	0.135287i
$612$	15.0000	−	9.94987i	0.606339	−	0.402200i
$613$	13.7446	+	23.8063i	0.555138	+	0.961527i	0.997893	+	0.0648841i	$0.0206678\pi$
$613$	13.7446	+	23.8063i	0.555138	+	0.961527i	−0.442755	+	0.896643i	$0.645999\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$	−7.11684	+	7.57301i	−0.286979	+	0.305373i
$616$		0			0
$617$		−	24.5437i		−	0.988091i	−0.869436	−	0.494045i	$-0.835518\pi$
$617$		−	24.5437i		−	0.988091i	0.869436	−	0.494045i	$-0.164482\pi$
$618$	−2.48913	−	8.25549i	−0.100127	−	0.332085i
$619$	−16.1168	+	9.30506i	−0.647791	+	0.374002i	−0.787609	−	0.616175i	$-0.788681\pi$
$619$	−16.1168	+	9.30506i	−0.647791	+	0.374002i	0.139819	+	0.990177i	$0.455348\pi$
$620$	4.11684	−	2.37686i	0.165336	−	0.0954570i
$621$	−15.3723	−	41.4766i	−0.616868	−	1.66440i
$622$			11.2772i			0.452173i
$623$		0			0
$624$	3.25544	+	3.05934i	0.130322	+	0.122472i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.13859	−	3.70415i	−0.0854754	−	0.148048i
$627$	14.7446	+	3.46410i	0.588841	+	0.138343i
$628$		0			0
$629$	29.4891			1.17581
$630$		0			0
$631$	−23.1168			−0.920267			−0.460134	−	0.887850i	$-0.652198\pi$
$631$	−23.1168			−0.920267			−0.460134	+	0.887850i	$0.652198\pi$
$632$	5.48913	+	3.16915i	0.218346	+	0.126062i
$633$	18.7446	+	4.40387i	0.745029	+	0.175038i
$634$	0.744563	+	1.28962i	0.0295704	+	0.0512174i
$635$	−0.372281	+	0.644810i	−0.0147735	+	0.0255885i
$636$	3.25544	+	3.05934i	0.129086	+	0.121311i
$637$		0			0
$638$			1.87953i			0.0744112i
$639$	0.394031	−	0.792287i	0.0155876	−	0.0313424i
$640$	−7.80298	+	4.50506i	−0.308440	+	0.178078i
$641$	−31.7228	+	18.3152i	−1.25298	+	0.723406i	−0.971699	−	0.236221i	$-0.924091\pi$
$641$	−31.7228	+	18.3152i	−1.25298	+	0.723406i	−0.281276	+	0.959627i	$0.590758\pi$
$642$	−2.62772	−	8.71516i	−0.103708	−	0.343960i
$643$			10.1523i			0.400366i	0.979759	+	0.200183i	$0.0641536\pi$
$643$			10.1523i			0.400366i	−0.979759	+	0.200183i	$0.935846\pi$
$644$		0			0
$645$	−5.62772	+	5.98844i	−0.221591	+	0.235795i
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	0.959529	−	0.281609i	$-0.0908680\pi$
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	−0.723645	+	0.690172i	$0.757535\pi$
$648$	−19.1753	+	14.5098i	−0.753276	+	0.570000i
$649$	−19.1168	−	11.0371i	−0.750402	−	0.433245i
$650$	−3.25544			−0.127689
$651$		0			0
$652$	10.9783			0.429941
$653$	34.3723	+	19.8448i	1.34509	+	0.776589i	0.987550	−	0.157308i	$-0.0502816\pi$
$653$	34.3723	+	19.8448i	1.34509	+	0.776589i	0.357542	+	0.933897i	$0.383615\pi$
$654$	−5.37228	+	22.8665i	−0.210073	+	0.894152i
$655$	−2.74456	−	4.75372i	−0.107239	−	0.185743i
$656$	−1.88316	+	3.26172i	−0.0735249	+	0.127349i
$657$	−20.7446	+	1.28962i	−0.809322	+	0.0503129i
$658$		0			0
$659$		−	35.9855i		−	1.40180i	−0.713261	−	0.700899i	$-0.752782\pi$
$659$		−	35.9855i		−	1.40180i	0.713261	−	0.700899i	$-0.247218\pi$
$660$	5.74456	−	1.73205i	0.223607	−	0.0674200i
$661$	6.00000	−	3.46410i	0.233373	−	0.134738i	−0.378754	−	0.925497i	$-0.623647\pi$
$661$	6.00000	−	3.46410i	0.233373	−	0.134738i	0.612127	+	0.790759i	$0.290314\pi$
$662$	−2.74456	+	1.58457i	−0.106670	+	0.0615862i
$663$	29.7921	−	8.98266i	1.15703	−	0.348858i
$664$			46.7277i			1.81339i
$665$		0			0
$666$	−16.0000	+	0.994667i	−0.619987	+	0.0385426i
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$	−3.35053	−	5.80329i	−0.129636	−	0.224536i
$669$	3.51087	−	14.9436i	0.135738	−	0.577755i
$670$	3.25544	+	1.87953i	0.125769	+	0.0726125i
$671$	17.4891			0.675160
$672$		0			0
$673$	−12.2337			−0.471574			−0.235787	−	0.971805i	$-0.575767\pi$
$673$	−12.2337			−0.471574			−0.235787	+	0.971805i	$0.575767\pi$
$674$	−11.1386	−	6.43087i	−0.429043	−	0.247708i
$675$	−0.872281	+	5.12241i	−0.0335741	+	0.197162i
$676$	2.66439	+	4.61486i	0.102477	+	0.177495i
$677$	−9.30298	+	16.1132i	−0.357543	+	0.619282i	−0.987550	−	0.157307i	$-0.949719\pi$
$677$	−9.30298	+	16.1132i	−0.357543	+	0.619282i	0.630007	+	0.776589i	$0.283052\pi$
$678$	−2.97825	+	3.16915i	−0.114379	+	0.121710i
$679$		0			0
$680$			11.6819i			0.447981i
$681$	−12.3030	−	40.8044i	−0.471451	−	1.56363i
$682$	6.00000	−	3.46410i	0.229752	−	0.132647i
$683$	−29.8397	+	17.2279i	−1.14178	+	0.659209i	−0.946871	−	0.321612i	$-0.895775\pi$
$683$	−29.8397	+	17.2279i	−1.14178	+	0.659209i	−0.194911	+	0.980821i	$0.562442\pi$
$684$	−6.35053	+	12.7692i	−0.242819	+	0.488241i
$685$			13.2665i			0.506887i
$686$		0			0
$687$	−19.1168	−	17.9653i	−0.729353	−	0.685420i
$688$	−1.48913	+	2.57924i	−0.0567724	+	0.0983326i
$689$	3.86141	+	6.68815i	0.147108	+	0.254798i
$690$	11.3723	+	2.67181i	0.432935	+	0.101714i
$691$	18.3505	+	10.5947i	0.698087	+	0.403041i	0.806635	−	0.591050i	$-0.201287\pi$
$691$	18.3505	+	10.5947i	0.698087	+	0.403041i	−0.108547	+	0.994091i	$0.534620\pi$
$692$	1.53262			0.0582616
$693$		0			0
$694$	−11.7663			−0.446643
$695$	−16.1168	−	9.30506i	−0.611347	−	0.352961i
$696$	−4.23369	−	0.994667i	−0.160478	−	0.0377027i
$697$	13.1168	+	22.7190i	0.496836	+	0.860545i
$698$	6.00000	−	10.3923i	0.227103	−	0.393355i
$699$	21.4891	+	20.1947i	0.812793	+	0.763834i
$700$		0			0
$701$		−	42.5090i		−	1.60554i	−0.596287	−	0.802771i	$-0.703358\pi$
$701$		−	42.5090i		−	1.60554i	0.596287	−	0.802771i	$-0.296642\pi$
$702$	−15.8614	+	5.87863i	−0.598650	+	0.221875i
$703$	−20.2337	+	11.6819i	−0.763128	+	0.440592i
$704$	−7.37228	+	4.25639i	−0.277853	+	0.160419i
$705$	−0.813859	−	2.69927i	−0.0306517	−	0.101660i
$706$		−	19.8997i		−	0.748937i
$707$		0			0
$708$	14.2337	−	15.1460i	0.534935	−	0.569223i
$709$	−3.44158	+	5.96099i	−0.129251	+	0.223870i	−0.923387	−	0.383871i	$-0.874591\pi$
$709$	−3.44158	+	5.96099i	−0.129251	+	0.223870i	0.794135	+	0.607741i	$0.207924\pi$
$710$	0.116844	+	0.202380i	0.00438508	+	0.00759517i
$711$	5.93070	−	3.93398i	0.222419	−	0.147536i
$712$	34.1168	+	19.6974i	1.27858	+	0.738190i
$713$	−29.4891			−1.10438
$714$		0			0
$715$	10.3723			0.387901
$716$	−7.88316	−	4.55134i	−0.294607	−	0.170092i
$717$	−8.25544	+	35.1383i	−0.308305	+	1.31227i
$718$	−6.62772	−	11.4795i	−0.247344	−	0.428413i
$719$	−14.2337	+	24.6535i	−0.530827	+	0.919419i	0.468526	+	0.883450i	$0.344785\pi$
$719$	−14.2337	+	24.6535i	−0.530827	+	0.919419i	−0.999353	+	0.0359696i	$0.988548\pi$
$720$	0.116844	+	1.87953i	0.00435452	+	0.0700459i
$721$		0			0
$722$			5.54601i			0.206401i
$723$	−27.2554	+	8.21782i	−1.01364	+	0.305624i
$724$	−1.53262	+	0.884861i	−0.0569595	+	0.0328856i
$725$	−0.813859	+	0.469882i	−0.0302260	+	0.0174510i
$726$	−6.08017	+	1.83324i	−0.225656	+	0.0680379i
$727$		−	3.46410i		−	0.128476i	−0.997935	−	0.0642382i	$-0.979538\pi$
$727$		−	3.46410i		−	0.128476i	0.997935	−	0.0642382i	$-0.0204617\pi$
$728$		0			0
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$	2.74456	−	4.75372i	0.101581	−	0.175943i
$731$	10.3723	+	17.9653i	0.383633	+	0.664471i
$732$	−3.76631	+	16.0309i	−0.139207	+	0.592519i
$733$	−34.6753	−	20.0198i	−1.28076	−	0.739447i	−0.303773	−	0.952744i	$-0.598246\pi$
$733$	−34.6753	−	20.0198i	−1.28076	−	0.739447i	−0.976987	+	0.213297i	$0.931580\pi$
$734$	27.9565			1.03189
$735$		0			0
$736$	49.7228			1.83281
$737$	−10.3723	−	5.98844i	−0.382068	−	0.220587i
$738$	−7.88316	−	11.8843i	−0.290183	−	0.437467i
$739$	7.18614	+	12.4468i	0.264346	+	0.457861i	0.967392	−	0.253283i	$-0.0815104\pi$
$739$	7.18614	+	12.4468i	0.264346	+	0.457861i	−0.703046	+	0.711145i	$0.748177\pi$
$740$	−4.62772	+	8.01544i	−0.170118	+	0.294654i
$741$	−16.8832	+	17.9653i	−0.620218	+	0.659972i
$742$		0			0
$743$			16.1407i			0.592145i	0.955166	+	0.296072i	$0.0956769\pi$
$743$			16.1407i			0.592145i	−0.955166	+	0.296072i	$0.904323\pi$
$744$	4.62772	+	15.3484i	0.169660	+	0.562700i
$745$	−2.74456	+	1.58457i	−0.100553	+	0.0580543i
$746$	−9.09509	+	5.25106i	−0.332995	+	0.192255i
$747$	46.9783	+	23.3639i	1.71884	+	0.854839i
$748$		−	15.1460i		−	0.553794i
$749$		0			0
$750$	−1.00000	−	0.939764i	−0.0365148	−	0.0343153i
$751$	−14.6753	+	25.4183i	−0.535508	+	0.927527i	0.463631	+	0.886029i	$0.346547\pi$
$751$	−14.6753	+	25.4183i	−0.535508	+	0.927527i	−0.999139	+	0.0414985i	$0.986787\pi$
$752$	−0.510875	−	0.884861i	−0.0186297	−	0.0322676i
$753$	−9.25544	−	2.17448i	−0.337287	−	0.0792425i
$754$	−2.64947	−	1.52967i	−0.0964879	−	0.0557073i
$755$	2.37228			0.0863362
$756$		0			0
$757$	−19.7663			−0.718419			−0.359209	−	0.933257i	$-0.616954\pi$
$757$	−19.7663			−0.718419			−0.359209	+	0.933257i	$0.616954\pi$
$758$	14.7446	+	8.51278i	0.535547	+	0.309198i
$759$	−36.2337	−	8.51278i	−1.31520	−	0.308994i
$760$	−4.62772	−	8.01544i	−0.167865	−	0.290751i
$761$	4.11684	−	7.13058i	0.149235	−	0.258483i	−0.781710	−	0.623643i	$-0.785652\pi$
$761$	4.11684	−	7.13058i	0.149235	−	0.258483i	0.930945	+	0.365159i	$0.118985\pi$
$762$	−0.744563	−	0.699713i	−0.0269727	−	0.0253479i
$763$		0			0
$764$		−	28.5977i		−	1.03463i
$765$	11.7446	+	5.84096i	0.424626	+	0.211180i
$766$	−3.76631	+	2.17448i	−0.136082	+	0.0785672i
$767$	31.1168	−	17.9653i	1.12356	−	0.648690i
$768$	−6.94158	−	23.0226i	−0.250483	−	0.830757i
$769$			38.5099i			1.38870i	0.719637	+	0.694351i	$0.244308\pi$
$769$			38.5099i			1.38870i	−0.719637	+	0.694351i	$0.755692\pi$
$770$		0			0
$771$	−0.605969	+	0.644810i	−0.0218234	+	0.0232223i
$772$	8.39403	−	14.5389i	0.302108	−	0.523266i
$773$	−26.1861	−	45.3557i	−0.941850	−	1.63133i	−0.761939	−	0.647649i	$-0.775752\pi$
$773$	−26.1861	−	45.3557i	−0.941850	−	1.63133i	−0.179911	−	0.983683i	$-0.557581\pi$
$774$	−6.23369	−	9.39764i	−0.224065	−	0.337791i
$775$	3.00000	+	1.73205i	0.107763	+	0.0622171i
$776$	−29.4891			−1.05860
$777$		0			0
$778$	−23.2554			−0.833748
$779$	−18.0000	−	10.3923i	−0.644917	−	0.372343i
$780$	−2.23369	+	9.50744i	−0.0799789	+	0.340421i
$781$	−0.372281	−	0.644810i	−0.0133213	−	0.0230731i
$782$	14.7446	−	25.5383i	0.527264	−	0.913249i
$783$	−3.11684	+	3.75906i	−0.111387	+	0.134338i
$784$		0			0
$785$		0			0
$786$	7.21194	−	2.17448i	0.257241	−	0.0775612i
$787$	−2.79211	+	1.61203i	−0.0995280	+	0.0574625i	−0.548938	−	0.835863i	$-0.684968\pi$
$787$	−2.79211	+	1.61203i	−0.0995280	+	0.0574625i	0.449410	+	0.893326i	$0.351634\pi$
$788$	18.7011	−	10.7971i	0.666198	−	0.384629i
$789$	0.489125	−	0.147477i	0.0174133	−	0.00525031i
$790$			1.87953i			0.0668706i
$791$		0			0
$792$	1.25544	+	20.1947i	0.0446100	+	0.717588i
$793$	−14.2337	+	24.6535i	−0.505453	+	0.875470i
$794$	10.3723	+	17.9653i	0.368098	+	0.637565i
$795$	−0.744563	+	3.16915i	−0.0264069	+	0.112398i
$796$	−31.8832	−	18.4077i	−1.13007	−	0.652445i
$797$	14.1386			0.500815			0.250407	−	0.968141i	$-0.419435\pi$
$797$	14.1386			0.500815			0.250407	+	0.968141i	$0.419435\pi$
$798$		0			0
$799$	−7.11684			−0.251776
$800$	−5.05842	−	2.92048i	−0.178842	−	0.103255i
$801$	36.8614	−	24.4511i	1.30243	−	0.863937i
$802$	2.37228	+	4.10891i	0.0837682	+	0.145091i
$803$	−8.74456	+	15.1460i	−0.308589	+	0.534492i
$804$	7.72281	−	8.21782i	0.272363	−	0.289820i
$805$		0			0
$806$			11.2772i			0.397221i
$807$	−1.37228	−	4.55134i	−0.0483066	−	0.160215i
$808$	−13.8832	+	8.01544i	−0.488408	+	0.281982i
$809$	−11.6970	+	6.75327i	−0.411245	+	0.237433i	−0.691325	−	0.722544i	$-0.742973\pi$
$809$	−11.6970	+	6.75327i	−0.411245	+	0.237433i	0.280079	+	0.959977i	$0.409639\pi$
$810$	−6.56930	−	2.77300i	−0.230822	−	0.0974334i
$811$		−	18.6101i		−	0.653490i	−0.945113	−	0.326745i	$-0.894048\pi$
$811$		−	18.6101i		−	0.653490i	0.945113	−	0.326745i	$-0.105952\pi$
$812$		0			0
$813$	6.00000	+	5.63858i	0.210429	+	0.197754i
$814$	−6.74456	+	11.6819i	−0.236397	+	0.409451i
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$	4.62772	+	1.08724i	0.162003	+	0.0380610i
$817$	−14.2337	−	8.21782i	−0.497974	−	0.287505i
$818$	19.5326			0.682942
$819$		0			0
$820$	−8.23369			−0.287533
$821$	−30.3030	−	17.4954i	−1.05758	−	0.610595i	−0.132819	−	0.991140i	$-0.542403\pi$
$821$	−30.3030	−	17.4954i	−1.05758	−	0.610595i	−0.924762	+	0.380545i	$0.875736\pi$
$822$	−17.7228	−	4.16381i	−0.618154	−	0.145230i
$823$	6.88316	+	11.9220i	0.239932	+	0.415574i	0.960694	−	0.277608i	$-0.0895416\pi$
$823$	6.88316	+	11.9220i	0.239932	+	0.415574i	−0.720763	+	0.693182i	$0.756208\pi$
$824$	8.39403	−	14.5389i	0.292420	−	0.506486i
$825$	3.18614	+	2.99422i	0.110927	+	0.104245i
$826$		0			0
$827$			14.8511i			0.516422i	0.966088	+	0.258211i	$0.0831330\pi$
$827$			14.8511i			0.516422i	−0.966088	+	0.258211i	$0.916867\pi$
$828$	15.6060	−	31.3793i	0.542345	−	1.09051i
$829$	−10.8832	+	6.28339i	−0.377988	+	0.218231i	−0.676942	−	0.736036i	$-0.736695\pi$
$829$	−10.8832	+	6.28339i	−0.377988	+	0.218231i	0.298955	+	0.954267i	$0.403362\pi$
$830$	−12.0000	+	6.92820i	−0.416526	+	0.240481i
$831$	14.1168	+	46.8203i	0.489708	+	1.62418i
$832$		−	13.8564i		−	0.480384i
$833$		0			0
$834$	17.4891	−	18.6101i	0.605599	−	0.644416i
$835$	2.44158	−	4.22894i	0.0844943	−	0.146348i
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	17.7446	+	3.02167i	0.613342	+	0.104444i
$838$	6.00000	+	3.46410i	0.207267	+	0.119665i
$839$	30.5109			1.05335			0.526676	−	0.850066i	$-0.323438\pi$
$839$	30.5109			1.05335			0.526676	+	0.850066i	$0.323438\pi$
$840$		0			0
$841$	28.1168			0.969546
$842$	−10.0217	−	5.78606i	−0.345372	−	0.199401i
$843$	11.1168	−	47.3176i	0.382884	−	1.62970i
$844$	7.62772	+	13.2116i	0.262557	+	0.454762i
$845$	−1.94158	+	3.36291i	−0.0667923	+	0.115688i
$846$	3.86141	−	0.240051i	0.132758	−	0.00825312i
$847$		0			0
$848$			1.17981i			0.0405150i
$849$	1.06930	−	0.322405i	0.0366982	−	0.0110649i
$850$	−3.00000	+	1.73205i	−0.102899	+	0.0594089i
$851$	49.7228	−	28.7075i	1.70448	−	0.984080i
$852$	0.671218	−	0.202380i	0.0229955	−	0.00693341i
$853$		−	32.8713i		−	1.12549i	−0.826630	−	0.562746i	$-0.809745\pi$
$853$		−	32.8713i		−	1.12549i	0.826630	−	0.562746i	$-0.190255\pi$
$854$		0			0
$855$	−10.3723	+	0.644810i	−0.354725	+	0.0220520i
$856$	8.86141	−	15.3484i	0.302877	−	0.524598i
$857$	23.2337	+	40.2419i	0.793648	+	1.37464i	0.923694	+	0.383130i	$0.125154\pi$
$857$	23.2337	+	40.2419i	0.793648	+	1.37464i	−0.130047	+	0.991508i	$0.541513\pi$
$858$	−3.25544	+	13.8564i	−0.111139	+	0.473050i
$859$	−12.3505	−	7.13058i	−0.421395	−	0.243292i	0.274279	−	0.961650i	$-0.411561\pi$
$859$	−12.3505	−	7.13058i	−0.421395	−	0.243292i	−0.695674	+	0.718358i	$0.744894\pi$
$860$	−6.51087			−0.222019
$861$		0			0
$862$	−11.9565			−0.407240
$863$	−35.7446	−	20.6371i	−1.21676	−	0.702496i	−0.252536	−	0.967588i	$-0.581265\pi$
$863$	−35.7446	−	20.6371i	−1.21676	−	0.702496i	−0.964223	+	0.265091i	$0.914598\pi$
$864$	−29.9198	−	5.09496i	−1.01789	−	0.173334i
$865$	0.558422	+	0.967215i	0.0189869	+	0.0328863i
$866$	−14.7446	+	25.5383i	−0.501041	+	0.867828i
$867$	2.51087	−	2.67181i	0.0852738	−	0.0907396i
$868$		0			0
$869$		−	5.98844i		−	0.203144i
$870$	−0.372281	−	1.23472i	−0.0126215	−	0.0418608i
$871$	16.8832	−	9.74749i	0.572064	−	0.330281i
$872$	−39.6060	+	22.8665i	−1.34123	+	0.774358i
$873$	−14.7446	+	29.6472i	−0.499028	+	1.00341i
$874$			23.3639i			0.790294i
$875$		0			0
$876$	−12.0000	−	11.2772i	−0.405442	−	0.381020i
$877$	19.2337	−	33.3137i	0.649475	−	1.12492i	−0.333773	−	0.942654i	$-0.608322\pi$
$877$	19.2337	−	33.3137i	0.649475	−	1.12492i	0.983248	−	0.182271i	$-0.0583448\pi$
$878$	7.37228	+	12.7692i	0.248802	+	0.430938i
$879$	−18.3505	−	4.31129i	−0.618948	−	0.145416i
$880$	1.37228	+	0.792287i	0.0462596	+	0.0267080i
$881$	−32.2337			−1.08598			−0.542990	−	0.839739i	$-0.682708\pi$
$881$	−32.2337			−1.08598			−0.542990	+	0.839739i	$0.682708\pi$
$882$		0			0
$883$	49.4891			1.66544			0.832721	−	0.553693i	$-0.186782\pi$
$883$	49.4891			1.66544			0.832721	+	0.553693i	$0.186782\pi$
$884$	21.3505	+	12.3267i	0.718096	+	0.414593i
$885$	14.7446	+	3.46410i	0.495633	+	0.116445i
$886$	2.62772	+	4.55134i	0.0882799	+	0.152905i
$887$	9.25544	−	16.0309i	0.310767	−	0.538265i	−0.667761	−	0.744375i	$-0.732747\pi$
$887$	9.25544	−	16.0309i	0.310767	−	0.538265i	0.978529	+	0.206111i	$0.0660807\pi$
$888$	−22.7446	−	21.3745i	−0.763258	−	0.717282i
$889$		0			0
$890$			11.6819i			0.391579i
$891$	20.9307	+	8.83518i	0.701205	+	0.295990i
$892$	10.5326	−	6.08101i	0.352658	−	0.203607i
$893$	4.88316	−	2.81929i	0.163409	−	0.0943440i
$894$	−1.25544	−	4.16381i	−0.0419881	−	0.139259i
$895$		−	6.63325i		−	0.221725i
$896$		0			0
$897$	41.4891	−	44.1485i	1.38528	−	1.47407i
$898$	4.60597	−	7.97777i	0.153703	−	0.266222i
$899$	1.62772	+	2.81929i	0.0542875	+	0.0940286i
$900$	−3.43070	+	2.27567i	−0.114357	+	0.0758557i
$901$	7.11684	+	4.10891i	0.237096	+	0.136888i
$902$	−12.0000			−0.399556
$903$		0			0
$904$	−8.46738			−0.281621
$905$	−1.11684	−	0.644810i	−0.0371251	−	0.0214342i
$906$	−0.744563	+	3.16915i	−0.0247364	+	0.105288i
$907$	−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	$0.875736\pi$
$908$	16.8832	−	29.2425i	0.560287	−	0.970446i
$909$	1.11684	+	17.9653i	0.0370434	+	0.595872i
$910$		0			0
$911$		−	2.87419i		−	0.0952263i	−0.998866	−	0.0476132i	$-0.984839\pi$
$911$		−	2.87419i		−	0.0952263i	0.998866	−	0.0476132i	$-0.0151615\pi$
$912$	−3.60597	+	1.08724i	−0.119406	+	0.0360021i
$913$	38.2337	−	22.0742i	1.26535	−	0.730550i
$914$	8.90491	−	5.14125i	0.294548	−	0.170057i
$915$	−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
$919$	2.81386	−	4.87375i	0.0928207	−	0.160770i	−0.815876	−	0.578226i	$-0.803745\pi$
$919$	2.81386	−	4.87375i	0.0928207	−	0.160770i	0.908697	+	0.417456i	$0.137078\pi$
$920$	11.3723	+	19.6974i	0.374933	+	0.649403i
$921$	−9.00000	+	38.3075i	−0.296560	+	1.26227i
$922$	1.88316	+	1.08724i	0.0620184	+	0.0358064i
$923$	1.21194			0.0398914
$924$		0			0
$925$	−6.74456			−0.221760
$926$	22.2772	+	12.8617i	0.732074	+	0.422663i
$927$	−10.4198	−	15.7085i	−0.342232	−	0.515934i
$928$	−2.74456	−	4.75372i	−0.0900947	−	0.156049i
$929$	26.4891	−	45.8805i	0.869080	−	1.50529i	0.00614188	−	0.999981i	$-0.498045\pi$
$929$	26.4891	−	45.8805i	0.869080	−	1.50529i	0.862938	−	0.505310i	$-0.168622\pi$
$930$	−3.25544	+	3.46410i	−0.106750	+	0.113592i
$931$		0			0
$932$			23.3639i			0.765308i
$933$	7.11684	+	23.6039i	0.232995	+	0.772757i
$934$	21.3505	−	12.3267i	0.698611	−	0.403343i
$935$	9.55842	−	5.51856i	0.312594	−	0.180476i
$936$	−29.4891	−	14.6659i	−0.963882	−	0.479371i
$937$			0.240051i			0.00784212i	0.999992	+	0.00392106i	$0.00124811\pi$
$937$			0.240051i			0.00784212i	−0.999992	+	0.00392106i	$0.998752\pi$
$938$		0			0
$939$	−6.81386	−	6.40342i	−0.222362	−	0.208968i
$940$	1.11684	−	1.93443i	0.0364274	−	0.0630942i
$941$	−19.3723	−	33.5538i	−0.631518	−	1.09382i	−0.987241	−	0.159230i	$-0.949099\pi$
$941$	−19.3723	−	33.5538i	−0.631518	−	1.09382i	0.355723	−	0.934591i	$-0.384235\pi$
$942$		0			0
$943$	44.2337	+	25.5383i	1.44045	+	0.831643i
$944$	5.48913			0.178656
$945$		0			0
$946$	−9.48913			−0.308518
$947$	30.2554	+	17.4680i	0.983170	+	0.567633i	0.903226	−	0.429166i	$-0.141193\pi$
$947$	30.2554	+	17.4680i	0.983170	+	0.567633i	0.0799440	+	0.996799i	$0.474526\pi$
$948$	5.48913	+	1.28962i	0.178279	+	0.0418849i
$949$	−14.2337	−	24.6535i	−0.462045	−	0.800286i
$950$	1.37228	−	2.37686i	0.0445227	−	0.0771156i
$951$	2.37228	+	2.22938i	0.0769265	+	0.0722927i
$952$		0			0
$953$		−	7.62792i		−	0.247092i	−0.992339	−	0.123546i	$-0.960573\pi$
$953$		−	7.62792i		−	0.247092i	0.992339	−	0.123546i	$-0.0394267\pi$
$954$	−4.00000	−	1.98933i	−0.129505	−	0.0644070i
$955$	18.0475	−	10.4198i	0.584005	−	0.337175i
$956$	−24.7663	+	14.2988i	−0.801000	+	0.462457i
$957$	1.18614	+	3.93398i	0.0383425	+	0.127168i
$958$		−	32.8713i		−	1.06202i
$959$		0			0
$960$	4.00000	−	4.25639i	0.129099	−	0.137374i
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	−10.9783	−	19.0149i	−0.353953	−	0.613065i
$963$	−11.0000	−	16.5831i	−0.354470	−	0.534384i
$964$	−19.5326	−	11.2772i	−0.629103	−	0.363213i
$965$	12.2337			0.393816
$966$		0			0
$967$	10.2337			0.329093			0.164547	−	0.986369i	$-0.447384\pi$
$967$	10.2337			0.329093			0.164547	+	0.986369i	$0.447384\pi$
$968$	−10.7079	−	6.18220i	−0.344165	−	0.198704i
$969$	−6.00000	+	25.5383i	−0.192748	+	0.820409i
$970$	−4.37228	−	7.57301i	−0.140385	−	0.243155i
$971$	18.6060	−	32.2265i	0.597094	−	1.03420i	−0.396154	−	0.918184i	$-0.629655\pi$
$971$	18.6060	−	32.2265i	0.597094	−	1.03420i	0.993248	−	0.116013i	$-0.0370114\pi$
$972$	−12.6060	+	17.2828i	−0.404337	+	0.554347i
$973$		0			0
$974$			29.7021i			0.951718i
$975$	−6.81386	+	2.05446i	−0.218218	+	0.0657952i
$976$	−3.76631	+	2.17448i	−0.120557	+	0.0696034i
$977$	−6.60597	+	3.81396i	−0.211344	+	0.122019i	−0.601936	−	0.798545i	$-0.705604\pi$
$977$	−6.60597	+	3.81396i	−0.211344	+	0.122019i	0.390592	+	0.920564i	$0.372270\pi$
$978$	−10.5109	+	3.16915i	−0.336101	+	0.101338i
$979$		−	37.2203i		−	1.18956i
$980$		0			0
$981$	3.18614	+	51.2516i	0.101726	+	1.63634i
$982$	−2.25544	+	3.90653i	−0.0719739	+	0.124662i
$983$	19.9307	+	34.5210i	0.635691	+	1.10105i	0.986368	+	0.164552i	$0.0526180\pi$
$983$	19.9307	+	34.5210i	0.635691	+	1.10105i	−0.350678	+	0.936496i	$0.614049\pi$
$984$	6.35053	−	27.0303i	0.202448	−	0.861696i
$985$	13.6277	+	7.86797i	0.434215	+	0.250694i
$986$	−3.25544			−0.103674
$987$		0			0
$988$	−19.5326			−0.621416
$989$	34.9783	+	20.1947i	1.11224	+	0.642154i
$990$	−5.00000	+	3.31662i	−0.158910	+	0.105409i
$991$	−12.7446	−	22.0742i	−0.404844	−	0.701211i	0.589459	−	0.807798i	$-0.299341\pi$
$991$	−12.7446	−	22.0742i	−0.404844	−	0.701211i	−0.994303	+	0.106587i	$0.966008\pi$
$992$	−10.1168	+	17.5229i	−0.321210	+	0.556352i
$993$	−4.74456	+	5.04868i	−0.150564	+	0.160215i
$994$		0			0
$995$		−	26.8280i		−	0.850503i
$996$	12.0000	+	39.7995i	0.380235	+	1.26110i
$997$	27.5584	−	15.9109i	0.872784	−	0.503902i	0.00451159	−	0.999990i	$-0.498564\pi$
$997$	27.5584	−	15.9109i	0.872784	−	0.503902i	0.868272	+	0.496088i	$0.165231\pi$
$998$	28.3723	−	16.3807i	0.898109	−	0.518523i
$999$	−32.8614	+	12.1793i	−1.03969	+	0.385335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.s.i.656.1		4
3.2	odd	2		735.2.s.g.656.2		4
7.2	even	3		105.2.b.c.41.3	yes	4
7.3	odd	6		735.2.s.g.521.2		4
7.4	even	3		735.2.s.h.521.2		4
7.5	odd	6		105.2.b.d.41.3	yes	4
7.6	odd	2		735.2.s.j.656.1		4
21.2	odd	6		105.2.b.d.41.2	yes	4
21.5	even	6		105.2.b.c.41.2	✓	4
21.11	odd	6		735.2.s.j.521.1		4
21.17	even	6	inner	735.2.s.i.521.1		4
21.20	even	2		735.2.s.h.656.2		4
28.19	even	6		1680.2.f.g.881.3		4
28.23	odd	6		1680.2.f.h.881.2		4
35.2	odd	12		525.2.g.e.524.3		8
35.9	even	6		525.2.b.g.251.2		4
35.12	even	12		525.2.g.d.524.4		8
35.19	odd	6		525.2.b.e.251.2		4
35.23	odd	12		525.2.g.e.524.6		8
35.33	even	12		525.2.g.d.524.5		8
84.23	even	6		1680.2.f.g.881.4		4
84.47	odd	6		1680.2.f.h.881.1		4
105.2	even	12		525.2.g.d.524.6		8
105.23	even	12		525.2.g.d.524.3		8
105.44	odd	6		525.2.b.e.251.3		4
105.47	odd	12		525.2.g.e.524.5		8
105.68	odd	12		525.2.g.e.524.4		8
105.89	even	6		525.2.b.g.251.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.b.c.41.2	✓	4	21.5	even	6
105.2.b.c.41.3	yes	4	7.2	even	3
105.2.b.d.41.2	yes	4	21.2	odd	6
105.2.b.d.41.3	yes	4	7.5	odd	6
525.2.b.e.251.2		4	35.19	odd	6
525.2.b.e.251.3		4	105.44	odd	6
525.2.b.g.251.2		4	35.9	even	6
525.2.b.g.251.3		4	105.89	even	6
525.2.g.d.524.3		8	105.23	even	12
525.2.g.d.524.4		8	35.12	even	12
525.2.g.d.524.5		8	35.33	even	12
525.2.g.d.524.6		8	105.2	even	12
525.2.g.e.524.3		8	35.2	odd	12
525.2.g.e.524.4		8	105.68	odd	12
525.2.g.e.524.5		8	105.47	odd	12
525.2.g.e.524.6		8	35.23	odd	12
735.2.s.g.521.2		4	7.3	odd	6
735.2.s.g.656.2		4	3.2	odd	2
735.2.s.h.521.2		4	7.4	even	3
735.2.s.h.656.2		4	21.20	even	2
735.2.s.i.521.1		4	21.17	even	6	inner
735.2.s.i.656.1		4	1.1	even	1	trivial
735.2.s.j.521.1		4	21.11	odd	6
735.2.s.j.656.1		4	7.6	odd	2
1680.2.f.g.881.3		4	28.19	even	6
1680.2.f.g.881.4		4	84.23	even	6
1680.2.f.h.881.1		4	84.47	odd	6
1680.2.f.h.881.2		4	28.23	odd	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+(-0.686141 - 0.396143i) q^{2} +(-1.68614 - 0.396143i) q^{3} +(-0.686141 - 1.18843i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.00000 + 0.939764i) q^{6} +2.67181i q^{8} +(2.68614 + 1.33591i) q^{9} +(-0.686141 + 0.396143i) q^{10} +(2.18614 - 1.26217i) q^{11} +(0.686141 + 2.27567i) q^{12} +4.10891i q^{13} +(-1.18614 + 1.26217i) q^{15} +(-0.313859 + 0.543620i) q^{16} +(2.18614 + 3.78651i) q^{17} +(-1.31386 - 1.98072i) q^{18} +(-3.00000 - 1.73205i) q^{19} -1.37228 q^{20} -2.00000 q^{22} +(7.37228 + 4.25639i) q^{23} +(1.05842 - 4.50506i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.62772 - 2.81929i) q^{26} +(-4.00000 - 3.31662i) q^{27} -0.939764i q^{29} +(1.31386 - 0.396143i) q^{30} +(-3.00000 + 1.73205i) q^{31} +(5.05842 - 2.92048i) q^{32} +(-4.18614 + 1.26217i) q^{33} -3.46410i q^{34} +(-0.255437 - 4.10891i) q^{36} +(3.37228 - 5.84096i) q^{37} +(1.37228 + 2.37686i) q^{38} +(1.62772 - 6.92820i) q^{39} +(2.31386 + 1.33591i) q^{40} +6.00000 q^{41} +4.74456 q^{43} +(-3.00000 - 1.73205i) q^{44} +(2.50000 - 1.65831i) q^{45} +(-3.37228 - 5.84096i) q^{46} +(-0.813859 + 1.40965i) q^{47} +(0.744563 - 0.792287i) q^{48} +0.792287i q^{50} +(-2.18614 - 7.25061i) q^{51} +(4.88316 - 2.81929i) q^{52} +(1.62772 - 0.939764i) q^{53} +(1.43070 + 3.86025i) q^{54} -2.52434i q^{55} +(4.37228 + 4.10891i) q^{57} +(-0.372281 + 0.644810i) q^{58} +(-4.37228 - 7.57301i) q^{59} +(2.31386 + 0.543620i) q^{60} +(6.00000 + 3.46410i) q^{61} +2.74456 q^{62} -3.37228 q^{64} +(3.55842 + 2.05446i) q^{65} +(3.37228 + 0.792287i) q^{66} +(-2.37228 - 4.10891i) q^{67} +(3.00000 - 5.19615i) q^{68} +(-10.7446 - 10.0974i) q^{69} -0.294954i q^{71} +(-3.56930 + 7.17687i) q^{72} +(-6.00000 + 3.46410i) q^{73} +(-4.62772 + 2.67181i) q^{74} +(0.500000 + 1.65831i) q^{75} +4.75372i q^{76} +(-3.86141 + 4.10891i) q^{78} +(1.18614 - 2.05446i) q^{79} +(0.313859 + 0.543620i) q^{80} +(5.43070 + 7.17687i) q^{81} +(-4.11684 - 2.37686i) q^{82} +17.4891 q^{83} +4.37228 q^{85} +(-3.25544 - 1.87953i) q^{86} +(-0.372281 + 1.58457i) q^{87} +(3.37228 + 5.84096i) q^{88} +(7.37228 - 12.7692i) q^{89} +(-2.37228 + 0.147477i) q^{90} -11.6819i q^{92} +(5.74456 - 1.73205i) q^{93} +(1.11684 - 0.644810i) q^{94} +(-3.00000 + 1.73205i) q^{95} +(-9.68614 + 2.92048i) q^{96} +11.0371i q^{97} +(7.55842 - 0.469882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} + 2 q^{5} + 4 q^{6} + 5 q^{9} + 3 q^{10} + 3 q^{11} - 3 q^{12} + q^{15} - 7 q^{16} + 3 q^{17} - 11 q^{18} - 12 q^{19} + 6 q^{20} - 8 q^{22} + 18 q^{23} - 13 q^{24} - 2 q^{25}+ \cdots + 13 q^{99}+O(q^{100}) \) 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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