LMFDB - Embedded newform 192.2.s.a.131.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,2,Mod(11,192)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("192.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.1
Character	$\chi$	$=$	192.131
Dual form			192.2.s.a.107.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40443 + 0.166076i) q^{2} +(-1.73045 - 0.0744689i) q^{3} +(1.94484 - 0.466485i) q^{4} +(-0.720684 + 1.07858i) q^{5} +(2.44266 - 0.182801i) q^{6} +(-0.767030 - 1.85177i) q^{7} +(-2.65391 + 0.978136i) q^{8} +(2.98891 + 0.257729i) q^{9} +(0.833022 - 1.63448i) q^{10} +(0.967998 - 0.192547i) q^{11} +(-3.40018 + 0.662398i) q^{12} +(2.76775 - 1.84935i) q^{13} +(1.38477 + 2.47330i) q^{14} +(1.32743 - 1.81276i) q^{15} +(3.56478 - 1.81447i) q^{16} +(4.20201 - 4.20201i) q^{17} +(-4.24051 + 0.134425i) q^{18} +(1.31593 - 0.879274i) q^{19} +(-0.898472 + 2.43385i) q^{20} +(1.18941 + 3.26152i) q^{21} +(-1.32751 + 0.431180i) q^{22} +(3.41948 - 8.25535i) q^{23} +(4.66530 - 1.49498i) q^{24} +(1.26947 + 3.06477i) q^{25} +(-3.57998 + 3.05694i) q^{26} +(-5.15296 - 0.668568i) q^{27} +(-2.35557 - 3.24359i) q^{28} +(-0.303195 + 1.52426i) q^{29} +(-1.56322 + 2.76634i) q^{30} +1.85722 q^{31} +(-4.70514 + 3.14032i) q^{32} +(-1.68941 + 0.261107i) q^{33} +(-5.20357 + 6.59928i) q^{34} +(2.55007 + 0.507241i) q^{35} +(5.93317 - 0.893039i) q^{36} +(-3.53974 + 5.29759i) q^{37} +(-1.70210 + 1.45342i) q^{38} +(-4.92718 + 2.99410i) q^{39} +(0.857634 - 3.56738i) q^{40} +(0.606016 + 0.251020i) q^{41} +(-2.21210 - 4.38304i) q^{42} +(-7.79176 + 1.54988i) q^{43} +(1.79278 - 0.826028i) q^{44} +(-2.43204 + 3.03803i) q^{45} +(-3.43139 + 12.1619i) q^{46} +(-3.56988 - 3.56988i) q^{47} +(-6.30380 + 2.87439i) q^{48} +(2.10901 - 2.10901i) q^{49} +(-2.29186 - 4.09342i) q^{50} +(-7.58429 + 6.95845i) q^{51} +(4.52014 - 4.88781i) q^{52} +(-0.605519 - 3.04415i) q^{53} +(7.34800 + 0.0831709i) q^{54} +(-0.489944 + 1.18283i) q^{55} +(3.84692 + 4.16419i) q^{56} +(-2.34262 + 1.42354i) q^{57} +(0.172671 - 2.19107i) q^{58} +(6.01066 + 4.01619i) q^{59} +(1.73601 - 4.14475i) q^{60} +(2.31440 - 11.6353i) q^{61} +(-2.60833 + 0.308440i) q^{62} +(-1.81533 - 5.73247i) q^{63} +(6.08650 - 5.19177i) q^{64} +4.31804i q^{65} +(2.32929 - 0.647277i) q^{66} +(12.2580 + 2.43827i) q^{67} +(6.21206 - 10.1324i) q^{68} +(-6.53200 + 14.0308i) q^{69} +(-3.66563 - 0.288877i) q^{70} +(-10.2302 + 4.23749i) q^{71} +(-8.18440 + 2.23957i) q^{72} +(-8.22378 - 3.40640i) q^{73} +(4.09150 - 8.02795i) q^{74} +(-1.96852 - 5.39796i) q^{75} +(2.14909 - 2.32390i) q^{76} +(-1.09904 - 1.64482i) q^{77} +(6.42262 - 5.02329i) q^{78} +(4.22403 + 4.22403i) q^{79} +(-0.612028 + 5.15257i) q^{80} +(8.86715 + 1.54066i) q^{81} +(-0.892794 - 0.251894i) q^{82} +(8.63710 + 12.9263i) q^{83} +(3.83465 + 5.78829i) q^{84} +(1.50388 + 7.56053i) q^{85} +(10.6856 - 3.47072i) q^{86} +(0.638174 - 2.61508i) q^{87} +(-2.38064 + 1.45784i) q^{88} +(10.4476 - 4.32753i) q^{89} +(2.91108 - 4.67061i) q^{90} +(-5.54754 - 3.70675i) q^{91} +(2.79933 - 17.6505i) q^{92} +(-3.21382 - 0.138305i) q^{93} +(5.60652 + 4.42077i) q^{94} +2.05301i q^{95} +(8.37587 - 5.08379i) q^{96} -4.02440i q^{97} +(-2.61170 + 3.31222i) q^{98} +(2.94288 - 0.326023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40443	+	0.166076i	−0.993081	+	0.117434i
$2$	−1.40443	+	0.166076i	−0.993081	+	0.117434i
$3$	−1.73045	−	0.0744689i	−0.999075	−	0.0429946i
$3$	−1.73045	−	0.0744689i	−0.999075	−	0.0429946i
$4$	1.94484	−	0.466485i	0.972419	−	0.233242i
$5$	−0.720684	+	1.07858i	−0.322300	+	0.482355i	−0.956873	−	0.290507i	$-0.906176\pi$
$5$	−0.720684	+	1.07858i	−0.322300	+	0.482355i	0.634573	+	0.772863i	$0.281176\pi$
$6$	2.44266	−	0.182801i	0.997211	−	0.0746280i
$7$	−0.767030	−	1.85177i	−0.289910	−	0.699905i	0.710081	−	0.704120i	$-0.248658\pi$
$7$	−0.767030	−	1.85177i	−0.289910	−	0.699905i	−0.999991	+	0.00421502i	$0.998658\pi$
$8$	−2.65391	+	0.978136i	−0.938300	+	0.345823i
$9$	2.98891	+	0.257729i	0.996303	+	0.0859098i
$10$	0.833022	−	1.63448i	0.263425	−	0.516867i
$11$	0.967998	−	0.192547i	0.291862	−	0.0580550i	−0.0469875	−	0.998895i	$-0.514962\pi$
$11$	0.967998	−	0.192547i	0.291862	−	0.0580550i	0.338850	+	0.940840i	$0.389962\pi$
$12$	−3.40018	+	0.662398i	−0.981548	+	0.191218i
$13$	2.76775	−	1.84935i	0.767637	−	0.512919i	−0.109017	−	0.994040i	$-0.534770\pi$
$13$	2.76775	−	1.84935i	0.767637	−	0.512919i	0.876654	+	0.481121i	$0.159770\pi$
$14$	1.38477	+	2.47330i	0.370097	+	0.661017i
$15$	1.32743	−	1.81276i	0.342740	−	0.468052i
$16$	3.56478	−	1.81447i	0.891196	−	0.453618i
$17$	4.20201	−	4.20201i	1.01914	−	1.01914i	0.0193250	−	0.999813i	$-0.493848\pi$
$17$	4.20201	−	4.20201i	1.01914	−	1.01914i	0.999813	−	0.0193250i	$-0.00615171\pi$
$18$	−4.24051	+	0.134425i	−0.999498	+	0.0316842i
$19$	1.31593	−	0.879274i	0.301894	−	0.201719i	−0.395391	−	0.918513i	$-0.629391\pi$
$19$	1.31593	−	0.879274i	0.301894	−	0.201719i	0.697285	+	0.716794i	$0.254391\pi$
$20$	−0.898472	+	2.43385i	−0.200904	+	0.544225i
$21$	1.18941	+	3.26152i	0.259550	+	0.711722i
$22$	−1.32751	+	0.431180i	−0.283025	+	0.0919278i
$23$	3.41948	−	8.25535i	0.713011	−	1.72136i	0.0206735	−	0.999786i	$-0.493419\pi$
$23$	3.41948	−	8.25535i	0.713011	−	1.72136i	0.692337	−	0.721574i	$-0.256581\pi$
$24$	4.66530	−	1.49498i	0.952301	−	0.305162i
$25$	1.26947	+	3.06477i	0.253894	+	0.612954i
$26$	−3.57998	+	3.05694i	−0.702091	+	0.599516i
$27$	−5.15296	−	0.668568i	−0.991688	−	0.128666i
$28$	−2.35557	−	3.24359i	−0.445162	−	0.612981i
$29$	−0.303195	+	1.52426i	−0.0563019	+	0.283049i	−0.998672	−	0.0515242i	$-0.983592\pi$
$29$	−0.303195	+	1.52426i	−0.0563019	+	0.283049i	0.942370	+	0.334573i	$0.108592\pi$
$30$	−1.56322	+	2.76634i	−0.285404	+	0.505063i
$31$	1.85722			0.333566			0.166783	−	0.985994i	$-0.446662\pi$
$31$	1.85722			0.333566			0.166783	+	0.985994i	$0.446662\pi$
$32$	−4.70514	+	3.14032i	−0.831759	+	0.555136i
$33$	−1.68941	+	0.261107i	−0.294089	+	0.0454528i
$34$	−5.20357	+	6.59928i	−0.892405	+	1.13177i
$35$	2.55007	+	0.507241i	0.431041	+	0.0857394i
$36$	5.93317	−	0.893039i	0.988861	−	0.148840i
$37$	−3.53974	+	5.29759i	−0.581929	+	0.870918i	−0.999284	−	0.0378252i	$-0.987957\pi$
$37$	−3.53974	+	5.29759i	−0.581929	+	0.870918i	0.417355	+	0.908743i	$0.362957\pi$
$38$	−1.70210	+	1.45342i	−0.276117	+	0.235776i
$39$	−4.92718	+	2.99410i	−0.788980	+	0.479440i
$40$	0.857634	−	3.56738i	0.135604	−	0.564053i
$41$	0.606016	+	0.251020i	0.0946437	+	0.0392027i	0.429503	−	0.903065i	$-0.358689\pi$
$41$	0.606016	+	0.251020i	0.0946437	+	0.0392027i	−0.334859	+	0.942268i	$0.608689\pi$
$42$	−2.21210	−	4.38304i	−0.341334	−	0.676318i
$43$	−7.79176	+	1.54988i	−1.18823	+	0.236354i	−0.749340	−	0.662185i	$-0.769629\pi$
$43$	−7.79176	+	1.54988i	−1.18823	+	0.236354i	−0.438892	+	0.898540i	$0.644629\pi$
$44$	1.79278	−	0.826028i	0.270272	−	0.124528i
$45$	−2.43204	+	3.03803i	−0.362547	+	0.452883i
$46$	−3.43139	+	12.1619i	−0.505931	+	1.79318i
$47$	−3.56988	−	3.56988i	−0.520721	−	0.520721i	0.397068	−	0.917789i	$-0.370028\pi$
$47$	−3.56988	−	3.56988i	−0.520721	−	0.520721i	−0.917789	+	0.397068i	$0.870028\pi$
$48$	−6.30380	+	2.87439i	−0.909875	+	0.414882i
$49$	2.10901	−	2.10901i	0.301288	−	0.301288i
$50$	−2.29186	−	4.09342i	−0.324118	−	0.578897i
$51$	−7.58429	+	6.95845i	−1.06201	+	0.974378i
$52$	4.52014	−	4.88781i	0.626830	−	0.677817i
$53$	−0.605519	−	3.04415i	−0.0831744	−	0.418146i	−0.999829	−	0.0184666i	$-0.994122\pi$
$53$	−0.605519	−	3.04415i	−0.0831744	−	0.418146i	0.916655	−	0.399679i	$-0.130878\pi$
$54$	7.34800	+	0.0831709i	0.999936	+	0.0113181i
$55$	−0.489944	+	1.18283i	−0.0660640	+	0.159493i
$56$	3.84692	+	4.16419i	0.514066	+	0.556463i
$57$	−2.34262	+	1.42354i	−0.310288	+	0.188553i
$58$	0.172671	−	2.19107i	0.0226729	−	0.287702i
$59$	6.01066	+	4.01619i	0.782521	+	0.522864i	0.881476	−	0.472228i	$-0.156550\pi$
$59$	6.01066	+	4.01619i	0.782521	+	0.522864i	−0.0989555	+	0.995092i	$0.531550\pi$
$60$	1.73601	−	4.14475i	0.224117	−	0.535084i
$61$	2.31440	−	11.6353i	0.296328	−	1.48974i	−0.489886	−	0.871787i	$-0.662962\pi$
$61$	2.31440	−	11.6353i	0.296328	−	1.48974i	0.786214	−	0.617955i	$-0.212038\pi$
$62$	−2.60833	+	0.308440i	−0.331258	+	0.0391719i
$63$	−1.81533	−	5.73247i	−0.228710	−	0.722224i
$64$	6.08650	−	5.19177i	0.760813	−	0.648972i
$65$			4.31804i			0.535587i
$66$	2.32929	−	0.647277i	0.286716	−	0.0796742i
$67$	12.2580	+	2.43827i	1.49755	+	0.297882i	0.874780	−	0.484520i	$-0.161006\pi$
$67$	12.2580	+	2.43827i	1.49755	+	0.297882i	0.622774	+	0.782402i	$0.286006\pi$
$68$	6.21206	−	10.1324i	0.753323	−	1.22874i
$69$	−6.53200	+	14.0308i	−0.786361	+	1.68911i
$70$	−3.66563	−	0.288877i	−0.438127	−	0.0345274i
$71$	−10.2302	+	4.23749i	−1.21410	+	0.502897i	−0.895530	−	0.445001i	$-0.853203\pi$
$71$	−10.2302	+	4.23749i	−1.21410	+	0.502897i	−0.318572	+	0.947899i	$0.603203\pi$
$72$	−8.18440	+	2.23957i	−0.964540	+	0.263936i
$73$	−8.22378	−	3.40640i	−0.962521	−	0.398689i	−0.154598	−	0.987977i	$-0.549408\pi$
$73$	−8.22378	−	3.40640i	−0.962521	−	0.398689i	−0.807923	+	0.589288i	$0.799408\pi$
$74$	4.09150	−	8.02795i	0.475627	−	0.933230i
$75$	−1.96852	−	5.39796i	−0.227305	−	0.623303i
$76$	2.14909	−	2.32390i	0.246518	−	0.266570i
$77$	−1.09904	−	1.64482i	−0.125247	−	0.187445i
$78$	6.42262	−	5.02329i	0.727218	−	0.568775i
$79$	4.22403	+	4.22403i	0.475241	+	0.475241i	0.903606	−	0.428365i	$-0.140910\pi$
$79$	4.22403	+	4.22403i	0.475241	+	0.475241i	−0.428365	+	0.903606i	$0.640910\pi$
$80$	−0.612028	+	5.15257i	−0.0684268	+	0.576074i
$81$	8.86715	+	1.54066i	0.985239	+	0.171184i
$82$	−0.892794	−	0.251894i	−0.0985926	−	0.0278171i
$83$	8.63710	+	12.9263i	0.948044	+	1.41885i	0.907680	+	0.419664i	$0.137852\pi$
$83$	8.63710	+	12.9263i	0.948044	+	1.41885i	0.0403648	+	0.999185i	$0.487148\pi$
$84$	3.83465	+	5.78829i	0.418395	+	0.631554i
$85$	1.50388	+	7.56053i	0.163119	+	0.820055i
$86$	10.6856	−	3.47072i	1.15225	−	0.374257i
$87$	0.638174	−	2.61508i	0.0684194	−	0.280366i
$88$	−2.38064	+	1.45784i	−0.253778	+	0.155406i
$89$	10.4476	−	4.32753i	1.10744	−	0.458717i	0.247385	−	0.968917i	$-0.420429\pi$
$89$	10.4476	−	4.32753i	1.10744	−	0.458717i	0.860056	+	0.510200i	$0.170429\pi$
$90$	2.91108	−	4.67061i	0.306855	−	0.492325i
$91$	−5.54754	−	3.70675i	−0.581540	−	0.388573i
$92$	2.79933	−	17.6505i	0.291851	−	1.84019i
$93$	−3.21382	−	0.138305i	−0.333258	−	0.0143416i
$94$	5.60652	+	4.42077i	0.578268	+	0.455968i
$95$			2.05301i			0.210634i
$96$	8.37587	−	5.08379i	0.854858	−	0.518862i
$97$		−	4.02440i		−	0.408616i	−0.978907	−	0.204308i	$-0.934506\pi$
$97$		−	4.02440i		−	0.408616i	0.978907	−	0.204308i	$-0.0654945\pi$
$98$	−2.61170	+	3.31222i	−0.263822	+	0.334584i
$99$	2.94288	−	0.326023i	0.295771	−	0.0327666i
$100$	3.89858	+	5.36829i	0.389858	+	0.536829i
$101$	−13.9098	−	9.29424i	−1.38408	−	0.924811i	−0.999999	−	0.00151063i	$-0.999519\pi$
$101$	−13.9098	−	9.29424i	−1.38408	−	0.924811i	−0.384079	−	0.923300i	$-0.625481\pi$
$102$	9.49596	−	11.0322i	0.940240	−	1.09235i
$103$	−3.57072	+	1.47904i	−0.351833	+	0.145734i	−0.551599	−	0.834110i	$-0.685982\pi$
$103$	−3.57072	+	1.47904i	−0.351833	+	0.145734i	0.199765	+	0.979844i	$0.435982\pi$
$104$	−5.53646	+	7.61526i	−0.542894	+	0.746738i
$105$	−4.37500	−	1.06766i	−0.426956	−	0.104193i
$106$	1.35597	+	4.17472i	0.131703	+	0.405485i
$107$	−0.469101	−	2.35833i	−0.0453497	−	0.227989i	0.951463	−	0.307762i	$-0.0995802\pi$
$107$	−0.469101	−	2.35833i	−0.0453497	−	0.227989i	−0.996813	+	0.0797738i	$0.974580\pi$
$108$	−10.3335	+	1.10352i	−0.994346	+	0.106186i
$109$	−6.70309	−	10.0319i	−0.642040	−	0.960881i	−0.999635	−	0.0270042i	$-0.991403\pi$
$109$	−6.70309	−	10.0319i	−0.642040	−	0.960881i	0.357595	−	0.933877i	$-0.383597\pi$
$110$	0.491651	−	1.74257i	0.0468771	−	0.166147i
$111$	6.51984	−	8.90361i	0.618836	−	0.845093i
$112$	−6.09429	−	5.20942i	−0.575857	−	0.492244i
$113$	14.1735	+	14.1735i	1.33333	+	1.33333i	0.902372	+	0.430958i	$0.141824\pi$
$113$	14.1735	+	14.1735i	1.33333	+	1.33333i	0.430958	+	0.902372i	$0.358176\pi$
$114$	3.05363	−	2.38832i	0.285998	−	0.223686i
$115$	6.43969	+	9.63768i	0.600504	+	0.898718i
$116$	0.121381	+	3.10588i	0.0112699	+	0.288374i
$117$	8.74920	−	4.81422i	0.808864	−	0.445075i
$118$	−9.10853	−	4.64223i	−0.838508	−	0.427352i
$119$	−11.0043	−	4.55811i	−1.00876	−	0.417841i
$120$	−1.74975	+	6.10931i	−0.159730	+	0.557701i
$121$	−9.26273	+	3.83675i	−0.842066	+	0.348795i
$122$	−1.31806	+	16.7252i	−0.119332	+	1.51423i
$123$	−1.02999	−	0.479506i	−0.0928707	−	0.0432356i
$124$	3.61199	−	0.866363i	0.324366	−	0.0778017i
$125$	−10.5818	−	2.10486i	−0.946468	−	0.188264i
$126$	3.50152	+	7.74936i	0.311941	+	0.690368i
$127$			0.155374i			0.0137873i	0.999976	+	0.00689363i	$0.00219433\pi$
$127$			0.155374i			0.0137873i	−0.999976	+	0.00689363i	$0.997806\pi$
$128$	−7.68582	+	8.30230i	−0.679337	+	0.733826i
$129$	13.5987	−	2.10174i	1.19730	−	0.185048i
$130$	−0.717125	−	6.06438i	−0.0628960	−	0.531881i
$131$	3.39595	−	17.0726i	0.296706	−	1.49164i	−0.488586	−	0.872516i	$-0.662487\pi$
$131$	3.39595	−	17.0726i	0.296706	−	1.49164i	0.785292	−	0.619125i	$-0.212513\pi$
$132$	−3.16383	+	1.29589i	−0.275376	+	0.112793i
$133$	−2.63757	−	1.76237i	−0.228706	−	0.152817i
$134$	−17.6204	−	1.38861i	−1.52217	−	0.119958i
$135$	4.43476	−	5.07605i	0.381683	−	0.436877i
$136$	−7.04164	+	15.2619i	−0.603815	+	1.30870i
$137$	−5.24233	+	12.6561i	−0.447883	+	1.08128i	0.525231	+	0.850960i	$0.323979\pi$
$137$	−5.24233	+	12.6561i	−0.447883	+	1.08128i	−0.973114	+	0.230325i	$0.926021\pi$
$138$	6.84354	−	20.7901i	0.582561	−	1.76977i
$139$	0.184246	+	0.926267i	0.0156275	+	0.0785649i	0.987812	−	0.155651i	$-0.0497476\pi$
$139$	0.184246	+	0.926267i	0.0156275	+	0.0785649i	−0.972185	+	0.234216i	$0.924748\pi$
$140$	5.19610	−	0.203069i	0.439150	−	0.0171624i
$141$	5.91165	+	6.44335i	0.497851	+	0.542628i
$142$	13.6638	−	7.65024i	1.14664	−	0.641994i
$143$	2.32309	−	2.32309i	0.194267	−	0.194267i
$144$	11.1225	−	4.50455i	0.926871	−	0.375379i
$145$	−1.42553	−	1.42553i	−0.118384	−	0.118384i
$146$	12.1154	+	3.41827i	1.00268	+	0.282898i
$147$	−3.80660	+	3.49248i	−0.313963	+	0.288055i
$148$	−4.41297	+	11.9542i	−0.362743	+	0.982627i
$149$	12.9342	−	2.57278i	1.05961	−	0.210770i	0.365629	−	0.930761i	$-0.380854\pi$
$149$	12.9342	−	2.57278i	1.05961	−	0.210770i	0.693984	+	0.719990i	$0.255854\pi$
$150$	3.66112	+	7.25412i	0.298929	+	0.592297i
$151$	3.52819	+	1.46142i	0.287120	+	0.118929i	0.521595	−	0.853193i	$-0.325337\pi$
$151$	3.52819	+	1.46142i	0.287120	+	0.118929i	−0.234475	+	0.972122i	$0.575337\pi$
$152$	−2.63230	+	3.62067i	−0.213508	+	0.293675i
$153$	13.6424	−	11.4765i	1.10292	−	0.927816i
$154$	1.81668	+	2.12751i	0.146393	+	0.171440i
$155$	−1.33847	+	2.00316i	−0.107508	+	0.160897i
$156$	−8.18585	+	8.12149i	−0.655393	+	0.650240i
$157$	−2.35944	−	0.469323i	−0.188304	−	0.0374560i	0.100037	−	0.994984i	$-0.468104\pi$
$157$	−2.35944	−	0.469323i	−0.188304	−	0.0374560i	−0.288341	+	0.957528i	$0.593104\pi$
$158$	−6.63386	−	5.23084i	−0.527762	−	0.416143i
$159$	0.821125	+	5.31283i	0.0651194	+	0.421335i
$160$	0.00382993	−	7.33805i	0.000302782	−	0.580124i
$161$	−17.9099			−1.41150
$162$	−12.7091	−	0.691120i	−0.998525	−	0.0542995i
$163$	−2.38176	+	11.9739i	−0.186554	+	0.937869i	0.768141	+	0.640281i	$0.221182\pi$
$163$	−2.38176	+	11.9739i	−0.186554	+	0.937869i	−0.954694	+	0.297588i	$0.903818\pi$
$164$	1.29570	+	0.205496i	0.101177	+	0.0160465i
$165$	0.935906	−	2.01034i	0.0728602	−	0.156505i
$166$	−14.2769	−	16.7197i	−1.10811	−	1.29770i
$167$	5.64526	+	13.6289i	0.436843	+	1.05463i	0.977033	+	0.213090i	$0.0683527\pi$
$167$	5.64526	+	13.6289i	0.436843	+	1.05463i	−0.540189	+	0.841544i	$0.681647\pi$
$168$	−6.34679	−	7.49239i	−0.489666	−	0.578051i
$169$	−0.734533	+	1.77332i	−0.0565025	+	0.136409i
$170$	−3.36772	−	10.3685i	−0.258292	−	0.795225i
$171$	4.15980	−	2.28892i	0.318108	−	0.175038i
$172$	−14.4307	+	6.64900i	−1.10033	+	0.506981i
$173$	7.13355	−	4.76648i	0.542354	−	0.362389i	−0.254015	−	0.967200i	$-0.581751\pi$
$173$	7.13355	−	4.76648i	0.542354	−	0.362389i	0.796369	+	0.604811i	$0.206751\pi$
$174$	−0.461966	+	3.77868i	−0.0350215	+	0.286461i
$175$	4.70154	−	4.70154i	0.355403	−	0.355403i
$176$	3.10133	−	2.44279i	0.233772	−	0.184133i
$177$	−10.1021	−	7.39742i	−0.759317	−	0.556024i
$178$	−13.9542	+	7.81280i	−1.04591	+	0.585594i
$179$	−5.74521	+	3.83883i	−0.429417	+	0.286928i	−0.751436	−	0.659806i	$-0.770639\pi$
$179$	−5.74521	+	3.83883i	−0.429417	+	0.286928i	0.322019	+	0.946733i	$0.395639\pi$
$180$	−3.31273	+	7.04299i	−0.246916	+	0.524954i
$181$	−20.4058	+	4.05897i	−1.51675	+	0.301701i	−0.882087	−	0.471087i	$-0.843862\pi$
$181$	−20.4058	+	4.05897i	−1.51675	+	0.301701i	−0.634665	+	0.772788i	$0.718862\pi$
$182$	8.40672	+	4.28454i	0.623148	+	0.317592i
$183$	−4.87141	+	19.9619i	−0.360105	+	1.47562i
$184$	−1.00014	+	25.2537i	−0.0737314	+	1.86173i
$185$	−3.16284	−	7.63577i	−0.232537	−	0.561393i
$186$	4.53655	−	0.339500i	0.332636	−	0.0248934i
$187$	3.25846	−	4.87663i	0.238282	−	0.356614i
$188$	−8.60814	−	5.27754i	−0.627813	−	0.384905i
$189$	2.71444	+	10.0549i	0.197446	+	0.731389i
$190$	−0.340956	−	2.88330i	−0.0247356	−	0.209177i
$191$	−15.4616			−1.11876			−0.559382	−	0.828910i	$-0.688962\pi$
$191$	−15.4616			−1.11876			−0.559382	+	0.828910i	$0.688962\pi$
$192$	−10.9190	+	8.53084i	−0.788011	+	0.615661i
$193$	−4.44552			−0.319995			−0.159998	−	0.987117i	$-0.551149\pi$
$193$	−4.44552			−0.319995			−0.159998	+	0.987117i	$0.551149\pi$
$194$	0.668359	+	5.65199i	0.0479853	+	0.405789i
$195$	0.321560	−	7.47215i	0.0230274	−	0.535092i
$196$	3.11787	−	5.08551i	0.222705	−	0.363251i
$197$	−1.32687	+	1.98581i	−0.0945358	+	0.141483i	−0.875723	−	0.482814i	$-0.839615\pi$
$197$	−1.32687	+	1.98581i	−0.0945358	+	0.141483i	0.781187	+	0.624297i	$0.214615\pi$
$198$	−4.07892	+	0.946620i	−0.289876	+	0.0672733i
$199$	7.94054	+	19.1702i	0.562890	+	1.35894i	0.907445	+	0.420171i	$0.138030\pi$
$199$	7.94054	+	19.1702i	0.562890	+	1.35894i	−0.344555	+	0.938766i	$0.611970\pi$
$200$	−6.36682	−	6.89191i	−0.450202	−	0.487332i
$201$	−21.0303	−	5.13214i	−1.48336	−	0.361993i
$202$	21.0789	+	10.7430i	1.48310	+	0.755875i
$203$	3.05515	−	0.607708i	0.214430	−	0.0426527i
$204$	−11.5042	+	17.0710i	−0.805455	+	1.19521i
$205$	−0.707491	+	0.472730i	−0.0494133	+	0.0330169i
$206$	4.76919	−	2.67022i	0.332285	−	0.186043i
$207$	12.3482	−	23.7932i	0.858256	−	1.65374i
$208$	6.51084	−	11.6146i	0.451446	−	0.805325i
$209$	1.10451	−	1.10451i	0.0764007	−	0.0764007i
$210$	6.32168	+	0.772862i	0.436238	+	0.0533326i
$211$	2.28666	−	1.52790i	0.157420	−	0.105185i	−0.474365	−	0.880328i	$-0.657322\pi$
$211$	2.28666	−	1.52790i	0.157420	−	0.105185i	0.631785	+	0.775143i	$0.282322\pi$
$212$	−2.59768	−	5.63791i	−0.178410	−	0.387213i
$213$	18.0184	−	6.57093i	1.23460	−	0.450232i
$214$	1.05048	+	3.23420i	0.0718095	+	0.221085i
$215$	3.94373	−	9.52101i	0.268960	−	0.649327i
$216$	14.3295	−	3.26598i	0.974996	−	0.222221i
$217$	−1.42454	−	3.43915i	−0.0967042	−	0.233465i
$218$	11.0801	+	12.9758i	0.750437	+	0.878835i
$219$	13.9772	+	6.50702i	0.944489	+	0.439704i
$220$	−0.401089	+	2.52896i	−0.0270414	+	0.170502i
$221$	3.85913	−	19.4012i	0.259593	−	1.30506i
$222$	−7.67796	+	13.5873i	−0.515311	+	0.911918i
$223$	14.4098			0.964951			0.482476	−	0.875909i	$-0.339738\pi$
$223$	14.4098			0.964951			0.482476	+	0.875909i	$0.339738\pi$
$224$	9.42416	+	6.30414i	0.629678	+	0.421213i
$225$	3.00444	+	9.48749i	0.200296	+	0.632499i
$226$	−22.2595	−	17.5518i	−1.48068	−	1.16753i
$227$	−4.85500	−	0.965719i	−0.322238	−	0.0640970i	0.0313212	−	0.999509i	$-0.490029\pi$
$227$	−4.85500	−	0.965719i	−0.322238	−	0.0640970i	−0.353559	+	0.935412i	$0.615029\pi$
$228$	−3.89196	+	3.86136i	−0.257751	+	0.255725i
$229$	2.62485	−	3.92837i	0.173455	−	0.259594i	−0.734549	−	0.678556i	$-0.762606\pi$
$229$	2.62485	−	3.92837i	0.173455	−	0.259594i	0.908004	+	0.418962i	$0.137606\pi$
$230$	−10.6447	−	12.4660i	−0.701889	−	0.821980i
$231$	1.77934	+	2.92813i	0.117072	+	0.192657i
$232$	−0.686284	−	4.34183i	−0.0450568	−	0.285055i
$233$	4.22871	+	1.75159i	0.277032	+	0.114751i	0.516874	−	0.856061i	$-0.327096\pi$
$233$	4.22871	+	1.75159i	0.277032	+	0.114751i	−0.239842	+	0.970812i	$0.577096\pi$
$234$	−11.4881	+	8.21426i	−0.751000	+	0.536983i
$235$	6.42316	−	1.27765i	0.419001	−	0.0833444i
$236$	13.5632	+	5.00696i	0.882892	+	0.325925i
$237$	−6.99492	−	7.62403i	−0.454369	−	0.495234i
$238$	16.2117	+	4.57399i	1.05085	+	0.296488i
$239$	14.7182	+	14.7182i	0.952039	+	0.952039i	0.998901	−	0.0468626i	$-0.0149223\pi$
$239$	14.7182	+	14.7182i	0.952039	+	0.952039i	−0.0468626	+	0.998901i	$0.514922\pi$
$240$	1.44279	−	8.87068i	0.0931316	−	0.572600i
$241$	10.1915	−	10.1915i	0.656494	−	0.656494i	−0.298055	−	0.954549i	$-0.596338\pi$
$241$	10.1915	−	10.1915i	0.656494	−	0.656494i	0.954549	+	0.298055i	$0.0963379\pi$
$242$	12.3716	−	6.92676i	0.795279	−	0.445269i
$243$	−15.2294	−	3.32636i	−0.976968	−	0.213386i
$244$	−0.926544	−	23.7083i	−0.0593159	−	1.51777i
$245$	0.754807	+	3.79467i	0.0482229	+	0.242433i
$246$	1.52618	+	0.502376i	0.0973054	+	0.0320303i
$247$	2.01607	−	4.86723i	0.128280	−	0.309694i
$248$	−4.92889	+	1.81661i	−0.312985	+	0.115355i
$249$	−13.9834	−	23.0115i	−0.886165	−	1.45830i
$250$	15.2110	+	1.19873i	0.962028	+	0.0758143i
$251$	9.56353	+	6.39015i	0.603645	+	0.403343i	0.819497	−	0.573083i	$-0.194253\pi$
$251$	9.56353	+	6.39015i	0.603645	+	0.403343i	−0.215852	+	0.976426i	$0.569253\pi$
$252$	−6.20463	−	10.3019i	−0.390855	−	0.648959i
$253$	1.72051	−	8.64958i	0.108167	−	0.543794i
$254$	−0.0258040	−	0.218212i	−0.00161909	−	0.0136919i
$255$	−2.03937	−	13.1951i	−0.127710	−	0.826310i
$256$	9.41537	−	12.9364i	0.588461	−	0.808526i
$257$		−	2.75570i		−	0.171896i	−0.996300	−	0.0859479i	$-0.972608\pi$
$257$		−	2.75570i		−	0.171896i	0.996300	−	0.0859479i	$-0.0273919\pi$
$258$	−18.7493	+	5.21016i	−1.16728	+	0.324370i
$259$	12.5250	+	2.49138i	0.778267	+	0.154807i
$260$	2.01430	+	8.39789i	0.124922	+	0.520815i
$261$	−1.29907	+	4.47774i	−0.0804104	+	0.277165i
$262$	−1.93402	+	24.5412i	−0.119484	+	1.51616i
$263$	−4.46471	+	1.84934i	−0.275306	+	0.114035i	−0.516065	−	0.856549i	$-0.672604\pi$
$263$	−4.46471	+	1.84934i	−0.275306	+	0.114035i	0.240759	+	0.970585i	$0.422604\pi$
$264$	4.22815	−	2.34543i	0.260225	−	0.144351i
$265$	3.71974	+	1.54077i	0.228502	+	0.0946486i
$266$	3.99697	+	2.03708i	0.245070	+	0.124902i
$267$	−18.4013	+	6.71055i	−1.12614	+	0.410679i
$268$	24.9773	−	0.976136i	1.52573	−	0.0596270i
$269$	13.9475	+	20.8740i	0.850396	+	1.27271i	0.960357	+	0.278772i	$0.0899273\pi$
$269$	13.9475	+	20.8740i	0.850396	+	1.27271i	−0.109961	+	0.993936i	$0.535073\pi$
$270$	−5.38529	+	7.86546i	−0.327738	+	0.478677i
$271$	−2.50752	−	2.50752i	−0.152321	−	0.152321i	0.626833	−	0.779154i	$-0.284351\pi$
$271$	−2.50752	−	2.50752i	−0.152321	−	0.152321i	−0.779154	+	0.626833i	$0.784351\pi$
$272$	7.35483	−	22.6037i	0.445952	−	1.37055i
$273$	9.32369	+	6.82746i	0.564296	+	0.413216i
$274$	5.26060	−	18.6452i	0.317804	−	1.12640i
$275$	1.81895	+	2.72226i	0.109687	+	0.164158i
$276$	−6.15852	+	30.3348i	−0.370699	+	1.82594i
$277$	2.00578	+	10.0838i	0.120516	+	0.605875i	0.993086	+	0.117386i	$0.0374515\pi$
$277$	2.00578	+	10.0838i	0.120516	+	0.605875i	−0.872570	+	0.488488i	$0.837548\pi$
$278$	−0.412591	−	1.27028i	−0.0247456	−	0.0761861i
$279$	5.55105	+	0.478659i	0.332333	+	0.0286566i
$280$	−7.26382	+	1.14814i	−0.434096	+	0.0686148i
$281$	−23.5087	+	9.73764i	−1.40241	+	0.580899i	−0.950377	−	0.311100i	$-0.899302\pi$
$281$	−23.5087	+	9.73764i	−1.40241	+	0.580899i	−0.452037	+	0.891999i	$0.649302\pi$
$282$	−9.37258	−	8.06743i	−0.558129	−	0.480408i
$283$	−14.0073	−	9.35938i	−0.832648	−	0.556357i	0.0645865	−	0.997912i	$-0.479427\pi$
$283$	−14.0073	−	9.35938i	−0.832648	−	0.556357i	−0.897234	+	0.441555i	$0.854427\pi$
$284$	−17.9194	+	13.0135i	−1.06332	+	0.772207i
$285$	0.152885	−	3.55263i	0.00905615	−	0.210440i
$286$	−2.87681	+	3.64843i	−0.170109	+	0.215736i
$287$		−	1.31474i		−	0.0776069i
$288$	−14.8726	+	8.17349i	−0.876376	+	0.481628i
$289$		−	18.3139i		−	1.07729i
$290$	2.23881	+	1.76531i	0.131467	+	0.103663i
$291$	−0.299693	+	6.96403i	−0.0175683	+	0.408239i
$292$	−17.5830	−	2.78863i	−1.02896	−	0.163192i
$293$	3.61126	+	2.41296i	0.210972	+	0.140967i	0.656567	−	0.754268i	$-0.272008\pi$
$293$	3.61126	+	2.41296i	0.210972	+	0.140967i	−0.445595	+	0.895235i	$0.647008\pi$
$294$	4.76607	−	5.53713i	0.277963	−	0.322932i
$295$	−8.66357	+	3.58857i	−0.504412	+	0.208934i
$296$	4.21239	−	17.5217i	0.244840	−	1.01843i
$297$	−5.11679	+	0.345013i	−0.296906	+	0.0200197i
$298$	−17.7379	+	5.76135i	−1.02753	+	0.333746i
$299$	−5.80279	−	29.1726i	−0.335584	−	1.68710i
$300$	−6.34652	−	9.57987i	−0.366416	−	0.553094i
$301$	8.84654	+	13.2398i	0.509906	+	0.763128i
$302$	−5.19780	−	1.46652i	−0.299100	−	0.0843886i
$303$	23.3781	+	17.1191i	1.34304	+	0.983464i
$304$	3.09557	−	5.52213i	0.177543	−	0.316716i
$305$	10.8816	+	10.8816i	0.623078	+	0.623078i
$306$	−17.2538	+	18.3835i	−0.986336	+	1.05092i
$307$	−1.92265	−	2.87744i	−0.109731	−	0.164224i	0.772540	−	0.634967i	$-0.218986\pi$
$307$	−1.92265	−	2.87744i	−0.109731	−	0.164224i	−0.882271	+	0.470742i	$0.843986\pi$
$308$	−2.90473	−	2.68623i	−0.165513	−	0.153062i
$309$	6.28909	−	2.29350i	0.357774	−	0.130472i
$310$	1.54710	−	3.03558i	0.0878696	−	0.172409i
$311$	−17.5455	−	7.26758i	−0.994913	−	0.412107i	−0.174984	−	0.984571i	$-0.555987\pi$
$311$	−17.5455	−	7.26758i	−0.994913	−	0.412107i	−0.819929	+	0.572465i	$0.805987\pi$
$312$	10.1477	−	12.7655i	0.574498	−	0.722706i
$313$	12.3369	−	5.11012i	0.697324	−	0.288841i	−0.00572401	−	0.999984i	$-0.501822\pi$
$313$	12.3369	−	5.11012i	0.697324	−	0.288841i	0.703048	+	0.711143i	$0.251822\pi$
$314$	3.39161	+	0.267282i	0.191400	+	0.0150836i
$315$	7.49120	+	2.17333i	0.422082	+	0.122453i
$316$	10.1855	+	6.24461i	0.572979	+	0.351287i
$317$	−14.5474	−	2.89365i	−0.817062	−	0.162524i	−0.231171	−	0.972913i	$-0.574256\pi$
$317$	−14.5474	−	2.89365i	−0.817062	−	0.162524i	−0.585892	+	0.810390i	$0.699256\pi$
$318$	−2.03555	−	7.32512i	−0.114148	−	0.410773i
$319$			1.53386i			0.0858799i
$320$	1.21330	+	10.3064i	0.0678254	+	0.576145i
$321$	0.636134	+	4.11591i	0.0355055	+	0.229728i
$322$	25.1532	−	2.97441i	1.40173	−	0.165757i
$323$	1.83482	−	9.22426i	0.102092	−	0.513252i
$324$	17.9639	−	1.14006i	0.997992	−	0.0633367i
$325$	9.18142	+	6.13483i	0.509293	+	0.340299i
$326$	1.35643	−	17.2120i	0.0751254	−	0.953287i
$327$	10.8523	+	17.8588i	0.600134	+	0.987597i
$328$	−1.85384	−	0.0734192i	−0.102361	−	0.00405389i
$329$	−3.87241	+	9.34883i	−0.213493	+	0.515417i
$330$	−0.980543	+	2.97881i	−0.0539771	+	0.163978i
$331$	−5.98155	−	30.0713i	−0.328776	−	1.65287i	−0.692542	−	0.721378i	$-0.743509\pi$
$331$	−5.98155	−	30.0713i	−0.328776	−	1.65287i	0.363766	−	0.931490i	$-0.381491\pi$
$332$	22.8277	+	21.1105i	1.25283	+	1.15859i
$333$	−11.9453	+	14.9217i	−0.654598	+	0.817705i
$334$	−10.1918	−	18.2032i	−0.557670	−	0.996036i
$335$	−11.4640	+	11.4640i	−0.626346	+	0.626346i
$336$	10.1579	+	9.46847i	0.554160	+	0.516548i
$337$	7.63954	+	7.63954i	0.416152	+	0.416152i	0.883875	−	0.467723i	$-0.154925\pi$
$337$	7.63954	+	7.63954i	0.416152	+	0.416152i	−0.467723	+	0.883875i	$0.654925\pi$
$338$	0.737092	−	2.61249i	0.0400925	−	0.142101i
$339$	−23.4710	−	25.5820i	−1.27477	−	1.38942i
$340$	6.45168	+	14.0025i	0.349892	+	0.759390i
$341$	1.79778	−	0.357601i	0.0973554	−	0.0193652i
$342$	−5.46200	+	3.90546i	−0.295351	+	0.211183i
$343$	−18.4855	−	7.65695i	−0.998124	−	0.413437i
$344$	19.1627	−	11.7346i	1.03318	−	0.632689i
$345$	−10.4259	−	17.1571i	−0.561309	−	0.923706i
$346$	−9.22696	+	7.87890i	−0.496044	+	0.423572i
$347$	−2.16682	+	3.24287i	−0.116321	+	0.174086i	−0.885061	−	0.465474i	$-0.845884\pi$
$347$	−2.16682	+	3.24287i	−0.116321	+	0.174086i	0.768741	+	0.639561i	$0.220884\pi$
$348$	0.0212479	−	5.38361i	0.00113901	−	0.288592i
$349$	13.8459	+	2.75411i	0.741151	+	0.147424i	0.551204	−	0.834370i	$-0.314168\pi$
$349$	13.8459	+	2.75411i	0.741151	+	0.147424i	0.189947	+	0.981794i	$0.439168\pi$
$350$	−5.82216	+	7.38379i	−0.311207	+	0.394680i
$351$	−15.4986	+	7.67922i	−0.827251	+	0.409886i
$352$	−3.94991	+	3.94579i	−0.210531	+	0.210311i
$353$	−32.7904			−1.74526			−0.872628	−	0.488386i	$-0.837586\pi$
$353$	−32.7904			−1.74526			−0.872628	+	0.488386i	$0.837586\pi$
$354$	15.4161	+	8.71144i	0.819359	+	0.463008i
$355$	2.80227	−	14.0880i	0.148729	−	0.747712i
$356$	18.3001	−	13.2900i	0.969904	−	0.704367i
$357$	18.7029	+	8.70706i	0.989861	+	0.460826i
$358$	7.43120	−	6.34550i	0.392751	−	0.335370i
$359$	13.8677	+	33.4796i	0.731909	+	1.76698i	0.636130	+	0.771582i	$0.280534\pi$
$359$	13.8677	+	33.4796i	0.731909	+	1.76698i	0.0957787	+	0.995403i	$0.469466\pi$
$360$	3.48281	−	10.4415i	0.183560	−	0.550318i
$361$	−6.31245	+	15.2396i	−0.332234	+	0.802084i
$362$	27.9844	−	9.08945i	1.47083	−	0.477731i
$363$	16.3144	−	5.94951i	0.856284	−	0.312268i
$364$	−12.5182	−	4.62118i	−0.656132	−	0.242215i
$365$	9.60082	−	6.41506i	0.502530	−	0.335780i
$366$	3.52635	−	28.8440i	0.184325	−	1.50770i
$367$	−17.6364	+	17.6364i	−0.920615	+	0.920615i	−0.997073	−	0.0764579i	$-0.975639\pi$
$367$	−17.6364	+	17.6364i	−0.920615	+	0.920615i	0.0764579	+	0.997073i	$0.475639\pi$
$368$	−2.78942	−	35.6331i	−0.145408	−	1.85750i
$369$	1.74663	+	0.906463i	0.0909259	+	0.0471886i
$370$	5.71010	+	10.1986i	0.296854	+	0.530201i
$371$	−5.17262	+	3.45624i	−0.268549	+	0.179439i
$372$	−6.31487	+	1.23022i	−0.327411	+	0.0637838i
$373$	20.0315	−	3.98452i	1.03719	−	0.206311i	0.353009	−	0.935620i	$-0.385158\pi$
$373$	20.0315	−	3.98452i	1.03719	−	0.206311i	0.684184	+	0.729309i	$0.260158\pi$
$374$	−3.76638	+	7.39002i	−0.194755	+	0.382129i
$375$	18.1546	+	4.43037i	0.937499	+	0.228783i
$376$	12.9660	+	5.98232i	0.668670	+	0.308515i
$377$	1.97973	+	4.77950i	0.101962	+	0.246157i
$378$	−5.48212	−	13.6706i	−0.281970	−	0.703141i
$379$	−18.3728	+	27.4969i	−0.943749	+	1.41242i	−0.0330024	+	0.999455i	$0.510507\pi$
$379$	−18.3728	+	27.4969i	−0.943749	+	1.41242i	−0.910747	+	0.412965i	$0.864493\pi$
$380$	0.957697	+	3.99277i	0.0491288	+	0.204825i
$381$	0.0115706	−	0.268868i	0.000592778	−	0.0137745i
$382$	21.7148	−	2.56781i	1.11102	−	0.131381i
$383$	−12.1943			−0.623098			−0.311549	−	0.950230i	$-0.600848\pi$
$383$	−12.1943			−0.623098			−0.311549	+	0.950230i	$0.600848\pi$
$384$	13.9182	−	13.7943i	0.710260	−	0.703940i
$385$	2.56613			0.130782
$386$	6.24341	−	0.738296i	0.317781	−	0.0375783i
$387$	−23.6883	+	2.62428i	−1.20414	+	0.133400i
$388$	−1.87732	−	7.82681i	−0.0953066	−	0.397346i
$389$	−0.354585	+	0.530674i	−0.0179782	+	0.0269062i	−0.840350	−	0.542044i	$-0.817650\pi$
$389$	−0.354585	+	0.530674i	−0.0179782	+	0.0269062i	0.822372	+	0.568951i	$0.192650\pi$
$390$	0.789340	+	10.5475i	0.0399698	+	0.534094i
$391$	−20.3204	−	49.0578i	−1.02765	−	2.48096i
$392$	−3.53424	+	7.66004i	−0.178506	+	0.386890i
$393$	−7.14790	+	29.2904i	−0.360564	+	1.47750i
$394$	1.53370	−	3.00928i	0.0772668	−	0.151606i
$395$	−7.60015	+	1.51176i	−0.382405	+	0.0760651i
$396$	5.57134	−	2.00687i	0.279971	−	0.100849i
$397$	12.2404	−	8.17878i	0.614328	−	0.410481i	−0.209106	−	0.977893i	$-0.567055\pi$
$397$	12.2404	−	8.17878i	0.614328	−	0.410481i	0.823434	+	0.567412i	$0.192055\pi$
$398$	−14.3356	−	25.6044i	−0.718580	−	1.28343i
$399$	4.43294	+	3.24611i	0.221925	+	0.162509i
$400$	10.0863	+	8.62182i	0.504316	+	0.431091i
$401$	−17.4419	+	17.4419i	−0.871007	+	0.871007i	−0.992582	−	0.121575i	$-0.961205\pi$
$401$	−17.4419	+	17.4419i	−0.871007	+	0.871007i	0.121575	+	0.992582i	$0.461205\pi$
$402$	30.3879	+	3.71509i	1.51561	+	0.185292i
$403$	5.14032	−	3.43465i	0.256058	−	0.171092i
$404$	−31.3879	−	11.5871i	−1.56161	−	0.576478i
$405$	−8.05214	+	8.45360i	−0.400114	+	0.420063i
$406$	−4.18982	+	1.36087i	−0.207937	+	0.0675389i
$407$	−2.40642	+	5.80962i	−0.119282	+	0.287972i
$408$	13.3217	−	25.8856i	0.659524	−	1.28153i
$409$	10.9078	+	26.3338i	0.539357	+	1.30212i	0.925173	+	0.379546i	$0.123920\pi$
$409$	10.9078	+	26.3338i	0.539357	+	1.30212i	−0.385816	+	0.922576i	$0.626080\pi$
$410$	0.915110	−	0.781413i	0.0451941	−	0.0385912i
$411$	10.0141	−	21.5104i	0.493958	−	1.06103i
$412$	−6.25452	+	4.54218i	−0.308138	+	0.223777i
$413$	2.82673	−	14.2109i	0.139094	−	0.699274i
$414$	−13.3906	+	35.4666i	−0.658113	+	1.74309i
$415$	−20.1667			−0.989944
$416$	−7.21510	+	17.3931i	−0.353750	+	0.852768i
$417$	−0.249850	−	1.61658i	−0.0122352	−	0.0791642i
$418$	−1.36777	+	1.73464i	−0.0669001	+	0.0848441i
$419$	4.25857	+	0.847083i	0.208045	+	0.0413827i	0.298012	−	0.954562i	$-0.403676\pi$
$419$	4.25857	+	0.847083i	0.208045	+	0.0413827i	−0.0899675	+	0.995945i	$0.528676\pi$
$420$	−9.00670	−	0.0355475i	−0.439482	−	0.00173454i
$421$	−11.3949	+	17.0536i	−0.555352	+	0.831143i	−0.997844	−	0.0656295i	$-0.979094\pi$
$421$	−11.3949	+	17.0536i	−0.555352	+	0.831143i	0.442492	+	0.896772i	$0.354094\pi$
$422$	−2.95770	+	2.52558i	−0.143978	+	0.122943i
$423$	−9.74999	−	11.5901i	−0.474061	−	0.563531i
$424$	4.58458	+	7.48662i	0.222647	+	0.363582i
$425$	18.2125	+	7.54387i	0.883437	+	0.365932i
$426$	−24.2143	+	12.2208i	−1.17319	+	0.592101i
$427$	−23.3211	+	4.63885i	−1.12859	+	0.224490i
$428$	−2.01245	−	4.36774i	−0.0972755	−	0.211123i
$429$	−4.19299	+	3.84700i	−0.202440	+	0.185735i
$430$	−3.95747	+	14.0265i	−0.190846	+	0.676419i
$431$	−2.55834	−	2.55834i	−0.123231	−	0.123231i	0.642802	−	0.766033i	$-0.277772\pi$
$431$	−2.55834	−	2.55834i	−0.123231	−	0.123231i	−0.766033	+	0.642802i	$0.777772\pi$
$432$	−19.5823	+	6.96661i	−0.942154	+	0.335181i
$433$	−19.0584	+	19.0584i	−0.915888	+	0.915888i	−0.996727	−	0.0808391i	$-0.974240\pi$
$433$	−19.0584	+	19.0584i	−0.915888	+	0.915888i	0.0808391	+	0.996727i	$0.474240\pi$
$434$	2.57183	+	4.59345i	0.123452	+	0.220493i
$435$	2.36065	+	2.57297i	0.113185	+	0.123364i
$436$	−17.7162	−	16.3835i	−0.848450	−	0.784627i
$437$	−2.75893	−	13.8701i	−0.131978	−	0.663496i
$438$	−20.7106	−	6.81737i	−0.989590	−	0.325746i
$439$	7.14528	−	17.2502i	0.341026	−	0.823309i	−0.656587	−	0.754250i	$-0.728001\pi$
$439$	7.14528	−	17.2502i	0.341026	−	0.823309i	0.997613	−	0.0690583i	$-0.0219994\pi$
$440$	0.143300	−	3.61835i	0.00683158	−	0.172498i
$441$	6.84720	−	5.76009i	0.326057	−	0.274290i
$442$	−2.19780	+	27.8884i	−0.104539	+	1.32652i
$443$	23.6417	+	15.7969i	1.12325	+	0.750533i	0.971301	−	0.237855i	$-0.0764442\pi$
$443$	23.6417	+	15.7969i	1.12325	+	0.750533i	0.151951	+	0.988388i	$0.451444\pi$
$444$	8.52663	−	20.3575i	0.404656	−	0.966123i
$445$	−2.86182	+	14.3873i	−0.135663	+	0.682024i
$446$	−20.2375	+	2.39313i	−0.958275	+	0.113318i
$447$	−22.5736	+	3.48886i	−1.06770	+	0.165018i
$448$	−14.2825	−	7.28858i	−0.674786	−	0.344353i
$449$		−	29.0905i		−	1.37286i	−0.727194	−	0.686432i	$-0.759176\pi$
$449$		−	29.0905i		−	1.37286i	0.727194	−	0.686432i	$-0.240824\pi$
$450$	−5.79517	−	12.8255i	−0.273187	−	0.604601i
$451$	0.634955	+	0.126300i	0.0298989	+	0.00594725i
$452$	34.1769	+	20.9534i	1.60754	+	0.985566i
$453$	−5.99652	−	2.79166i	−0.281741	−	0.131164i
$454$	6.97888	+	0.549983i	0.327535	+	0.0258120i
$455$	7.99604	−	3.31207i	0.374860	−	0.155272i
$456$	4.82469	−	6.06936i	0.225937	−	0.284224i
$457$	28.0374	+	11.6135i	1.31153	+	0.543255i	0.925331	−	0.379160i	$-0.123787\pi$
$457$	28.0374	+	11.6135i	1.31153	+	0.543255i	0.386202	+	0.922414i	$0.373787\pi$
$458$	−3.03401	+	5.95303i	−0.141770	+	0.278167i
$459$	−24.4622	+	18.8435i	−1.14180	+	0.879539i
$460$	17.0200	+	15.7397i	0.793561	+	0.733868i
$461$	7.06025	+	10.5664i	0.328829	+	0.492127i	0.958640	−	0.284621i	$-0.0918678\pi$
$461$	7.06025	+	10.5664i	0.328829	+	0.492127i	−0.629811	+	0.776748i	$0.716868\pi$
$462$	−2.98525	−	3.81684i	−0.138886	−	0.177576i
$463$	1.39596	+	1.39596i	0.0648758	+	0.0648758i	0.738800	−	0.673924i	$-0.235393\pi$
$463$	1.39596	+	1.39596i	0.0648758	+	0.0648758i	−0.673924	+	0.738800i	$0.735393\pi$
$464$	1.68491	+	5.98381i	0.0782201	+	0.277791i
$465$	2.46532	−	3.36669i	0.114327	−	0.156126i
$466$	−6.22982	−	1.75769i	−0.288591	−	0.0814236i
$467$	−3.17450	−	4.75097i	−0.146898	−	0.219849i	0.750722	−	0.660618i	$-0.229706\pi$
$467$	−3.17450	−	4.75097i	−0.146898	−	0.219849i	−0.897620	+	0.440769i	$0.854706\pi$
$468$	14.7700	−	13.4442i	0.682744	−	0.621460i
$469$	−4.88714	−	24.5693i	−0.225667	−	1.13450i
$470$	−8.80868	+	2.86110i	−0.406314	+	0.131973i
$471$	4.04795	+	0.987844i	0.186520	+	0.0455175i
$472$	−19.8801	−	4.77938i	−0.915057	−	0.219989i
$473$	−7.24399	+	3.00056i	−0.333079	+	0.137966i
$474$	11.0900	+	9.54572i	0.509382	+	0.438449i
$475$	4.36530	+	2.91680i	0.200293	+	0.133832i
$476$	−23.5278	−	3.73147i	−1.07839	−	0.171032i
$477$	−1.02527	−	9.25474i	−0.0469441	−	0.423745i
$478$	−23.1149	−	18.2263i	−1.05725	−	0.833650i
$479$		−	4.95212i		−	0.226268i	−0.993580	−	0.113134i	$-0.963911\pi$
$479$		−	4.95212i		−	0.226268i	0.993580	−	0.113134i	$-0.0360889\pi$
$480$	−0.553084	+	12.6978i	−0.0252447	+	0.579574i
$481$			21.2086i			0.967031i
$482$	−12.6207	+	16.0058i	−0.574857	+	0.729046i
$483$	30.9922	+	1.33373i	1.41019	+	0.0606868i
$484$	−16.2247	+	11.7828i	−0.737487	+	0.535581i
$485$	4.34064	+	2.90032i	0.197098	+	0.131697i
$486$	21.9411	+	2.14238i	0.995267	+	0.0971805i
$487$	30.9423	−	12.8167i	1.40213	−	0.580781i	0.451826	−	0.892106i	$-0.350773\pi$
$487$	30.9423	−	12.8167i	1.40213	−	0.580781i	0.950303	+	0.311325i	$0.100773\pi$
$488$	5.23865	+	33.1427i	0.237143	+	1.50030i
$489$	5.01319	−	20.5429i	0.226704	−	0.928981i
$490$	−1.69028	−	5.20399i	−0.0763590	−	0.235092i
$491$	−4.34757	−	21.8567i	−0.196203	−	0.986380i	−0.945865	−	0.324559i	$-0.894784\pi$
$491$	−4.34757	−	21.8567i	−0.196203	−	0.986380i	0.749662	−	0.661821i	$-0.230216\pi$
$492$	−2.22684	−	0.452089i	−0.100394	−	0.0203818i
$493$	5.13095	+	7.67901i	0.231086	+	0.345845i
$494$	−2.02310	+	7.17049i	−0.0910234	+	0.322616i
$495$	−1.76925	+	3.40909i	−0.0795217	+	0.153227i
$496$	6.62058	−	3.36987i	0.297273	−	0.151312i
$497$	15.6937	+	15.6937i	0.703961	+	0.703961i
$498$	23.4604	+	29.9957i	1.05129	+	1.34414i
$499$	−8.51962	−	12.7505i	−0.381390	−	0.570791i	0.590260	−	0.807213i	$-0.299025\pi$
$499$	−8.51962	−	12.7505i	−0.381390	−	0.570791i	−0.971650	+	0.236422i	$0.924025\pi$
$500$	−21.5618	+	0.842659i	−0.964275	+	0.0376848i
$501$	−8.75391	−	24.0045i	−0.391096	−	1.07244i
$502$	−14.4926	−	7.38623i	−0.646834	−	0.329664i
$503$	−2.92455	−	1.21139i	−0.130399	−	0.0540131i	0.316530	−	0.948583i	$-0.397482\pi$
$503$	−2.92455	−	1.21139i	−0.130399	−	0.0540131i	−0.446929	+	0.894569i	$0.647482\pi$
$504$	10.4249	+	13.4378i	0.464360	+	0.598569i
$505$	20.0491	−	8.30463i	0.892175	−	0.369551i
$506$	−0.979839	+	12.4334i	−0.0435592	+	0.552734i
$507$	1.40313	−	3.01394i	0.0623152	−	0.133854i
$508$	0.0724798	+	0.302178i	0.00321577	+	0.0134070i
$509$	−21.4086	−	4.25843i	−0.948919	−	0.188752i	−0.303716	−	0.952763i	$-0.598227\pi$
$509$	−21.4086	−	4.25843i	−0.948919	−	0.188752i	−0.645203	+	0.764011i	$0.723227\pi$
$510$	5.05554	+	18.1929i	0.223863	+	0.805595i
$511$			17.8414i			0.789257i
$512$	−11.0748	+	19.7319i	−0.489441	+	0.872037i
$513$	−7.36877	+	3.65108i	−0.325339	+	0.161199i
$514$	0.457656	+	3.87018i	0.0201864	+	0.170706i
$515$	0.978097	−	4.91723i	0.0431001	−	0.216679i
$516$	25.4668	−	10.4311i	1.12111	−	0.459204i
$517$	−4.14301	−	2.76827i	−0.182209	−	0.121748i
$518$	−18.0043	−	1.41886i	−0.791062	−	0.0623410i
$519$	−12.6992	+	7.71693i	−0.557433	+	0.338736i
$520$	−4.22363	−	11.4597i	−0.185219	−	0.502541i
$521$	10.3999	−	25.1077i	0.455630	−	1.09999i	−0.514519	−	0.857479i	$-0.672030\pi$
$521$	10.3999	−	25.1077i	0.455630	−	1.09999i	0.970149	−	0.242509i	$-0.0779705\pi$
$522$	1.08080	−	6.50441i	0.0473054	−	0.284690i
$523$	5.49571	+	27.6288i	0.240310	+	1.20812i	0.892845	+	0.450363i	$0.148706\pi$
$523$	5.49571	+	27.6288i	0.240310	+	1.20812i	−0.652535	+	0.757759i	$0.726294\pi$
$524$	−1.35954	−	34.7876i	−0.0593916	−	1.51970i
$525$	−8.48589	+	7.78566i	−0.370355	+	0.339794i
$526$	5.96324	−	3.33875i	0.260009	−	0.145577i
$527$	7.80405	−	7.80405i	0.339950	−	0.339950i
$528$	−5.54861	+	3.99618i	−0.241472	+	0.173911i
$529$	−40.1946	−	40.1946i	−1.74759	−	1.74759i
$530$	−5.48000	−	1.54614i	−0.238036	−	0.0671599i
$531$	16.9302	+	13.5532i	0.734709	+	0.588157i
$532$	−5.95176	−	2.19713i	−0.258042	−	0.0952578i
$533$	2.14153	−	0.425976i	0.0927598	−	0.0184511i
$534$	24.7288	−	12.4805i	1.07012	−	0.540084i
$535$	2.88172	+	1.19365i	0.124588	+	0.0516059i
$536$	−34.9166	+	5.51905i	−1.50817	+	0.238386i
$537$	10.2277	−	6.21506i	0.441357	−	0.268200i
$538$	−23.0550	−	26.9996i	−0.993971	−	1.16404i
$539$	1.63544	−	2.44760i	0.0704433	−	0.105426i
$540$	6.25699	−	11.9408i	0.269258	−	0.513852i
$541$	26.1330	+	5.19818i	1.12355	+	0.223487i	0.721691	−	0.692216i	$-0.243365\pi$
$541$	26.1330	+	5.19818i	1.12355	+	0.223487i	0.401856	+	0.915703i	$0.368365\pi$
$542$	3.93807	+	3.10519i	0.169154	+	0.133379i
$543$	35.6135	−	5.50424i	1.52832	−	0.236209i
$544$	−6.57539	+	32.9668i	−0.281917	+	1.41344i
$545$	15.6510			0.670415
$546$	−14.2283	−	8.04023i	−0.608917	−	0.344090i
$547$	−0.671852	+	3.37763i	−0.0287263	+	0.144417i	−0.992487	−	0.122352i	$-0.960956\pi$
$547$	−0.671852	+	3.37763i	−0.0287263	+	0.144417i	0.963760	+	0.266769i	$0.0859562\pi$
$548$	−4.29160	+	27.0595i	−0.183328	+	1.15593i
$549$	9.91626	−	34.1802i	0.423216	−	1.45878i
$550$	−3.00669	−	3.52113i	−0.128206	−	0.150141i
$551$	0.941263	+	2.27241i	0.0400991	+	0.0968079i
$552$	3.61131	−	43.6258i	0.153708	−	1.85684i
$553$	4.58200	−	11.0619i	0.194846	−	0.470401i
$554$	−4.49166	−	13.8288i	−0.190832	−	0.587530i
$555$	4.90451	+	13.4488i	0.208185	+	0.570872i
$556$	0.790417	+	1.71549i	0.0335212	+	0.0727530i
$557$	7.56429	−	5.05430i	0.320509	−	0.214157i	−0.384899	−	0.922959i	$-0.625764\pi$
$557$	7.56429	−	5.05430i	0.320509	−	0.214157i	0.705408	+	0.708801i	$0.250764\pi$
$558$	−7.87555	+	0.249656i	−0.333399	+	0.0105688i
$559$	−18.6994	+	18.6994i	−0.790901	+	0.790901i
$560$	10.0108	−	2.81884i	0.423035	−	0.119118i
$561$	−6.00175	+	8.19610i	−0.253394	+	0.346040i
$562$	31.3991	−	17.5801i	1.32449	−	0.741570i
$563$	23.8770	−	15.9541i	1.00630	−	0.672386i	0.0608444	−	0.998147i	$-0.480621\pi$
$563$	23.8770	−	15.9541i	1.00630	−	0.672386i	0.945452	+	0.325762i	$0.105621\pi$
$564$	14.5029	+	9.77356i	0.610683	+	0.411541i
$565$	−25.5018	+	5.07263i	−1.07287	+	0.213407i
$566$	21.2266	+	10.8183i	0.892222	+	0.454727i
$567$	−3.94842	−	17.6017i	−0.165818	−	0.739202i
$568$	23.0052	−	21.2524i	0.965277	−	0.891733i
$569$	−0.967449	−	2.33563i	−0.0405576	−	0.0979147i	0.902303	−	0.431103i	$-0.141875\pi$
$569$	−0.967449	−	2.33563i	−0.0405576	−	0.0979147i	−0.942860	+	0.333188i	$0.891875\pi$
$570$	0.375291	+	5.01480i	0.0157192	+	0.210047i
$571$	13.9993	−	20.9514i	0.585850	−	0.876787i	−0.413582	−	0.910467i	$-0.635723\pi$
$571$	13.9993	−	20.9514i	0.585850	−	0.876787i	0.999433	+	0.0336797i	$0.0107226\pi$
$572$	3.43435	−	5.60173i	0.143597	−	0.234220i
$573$	26.7556	+	1.15141i	1.11773	+	0.0481009i
$574$	0.218348	+	1.84646i	0.00911367	+	0.0770699i
$575$	29.6417			1.23614
$576$	19.5301	−	13.9491i	0.813753	−	0.581211i
$577$	−23.0087			−0.957866			−0.478933	−	0.877852i	$-0.658976\pi$
$577$	−23.0087			−0.957866			−0.478933	+	0.877852i	$0.658976\pi$
$578$	3.04150	+	25.7205i	0.126510	+	1.06983i
$579$	7.69274	+	0.331053i	0.319700	+	0.0137581i
$580$	−3.43742	−	2.10744i	−0.142731	−	0.0875067i
$581$	17.3117	−	25.9088i	0.718212	−	1.07488i
$582$	−0.735663	−	9.83025i	−0.0304942	−	0.407477i
$583$	−1.17228	−	2.83014i	−0.0485509	−	0.117212i
$584$	25.1571	+	0.996316i	1.04101	+	0.0412279i
$585$	−1.11289	+	12.9062i	−0.0460122	+	0.533607i
$586$	−5.47249	−	2.78909i	−0.226066	−	0.115216i
$587$	0.289296	−	0.0575446i	0.0119405	−	0.00237512i	−0.189116	−	0.981955i	$-0.560562\pi$
$587$	0.289296	−	0.0575446i	0.0119405	−	0.00237512i	0.201057	+	0.979580i	$0.435562\pi$
$588$	−5.77402	+	8.56803i	−0.238117	+	0.353340i
$589$	2.44396	−	1.63300i	0.100702	−	0.0672867i
$590$	11.5714	−	6.47870i	0.476386	−	0.266724i
$591$	2.44397	−	3.33753i	0.100531	−	0.137287i
$592$	−3.00606	+	25.3075i	−0.123548	+	1.04013i
$593$	19.2525	−	19.2525i	0.790607	−	0.790607i	−0.190986	−	0.981593i	$-0.561168\pi$
$593$	19.2525	−	19.2525i	0.790607	−	0.790607i	0.981593	+	0.190986i	$0.0611684\pi$
$594$	7.12886	−	1.33432i	0.292501	−	0.0547480i
$595$	12.8469	−	8.58401i	0.526671	−	0.351910i
$596$	23.9548	−	11.0373i	0.981227	−	0.452104i
$597$	−12.3131	−	33.7643i	−0.503943	−	1.38188i
$598$	12.9945	+	40.0071i	0.531384	+	1.63601i
$599$	3.30506	−	7.97913i	0.135041	−	0.326018i	−0.841865	−	0.539689i	$-0.818542\pi$
$599$	3.30506	−	7.97913i	0.135041	−	0.326018i	0.976906	+	0.213670i	$0.0685419\pi$
$600$	10.5042	+	12.4002i	0.428833	+	0.506237i
$601$	8.94164	+	21.5870i	0.364737	+	0.880553i	0.994594	+	0.103842i	$0.0331136\pi$
$601$	8.94164	+	21.5870i	0.364737	+	0.880553i	−0.629857	+	0.776711i	$0.716886\pi$
$602$	−14.6231	−	17.1251i	−0.595995	−	0.697968i
$603$	36.0097	+	10.4470i	1.46643	+	0.425435i
$604$	7.54349	+	1.19639i	0.306940	+	0.0486802i
$605$	2.53726	−	12.7557i	0.103154	−	0.518592i
$606$	−35.6759	−	20.1599i	−1.44923	−	0.818941i
$607$	−16.1373			−0.654991			−0.327496	−	0.944853i	$-0.606205\pi$
$607$	−16.1373			−0.654991			−0.327496	+	0.944853i	$0.606205\pi$
$608$	−3.43041	+	8.26954i	−0.139122	+	0.335374i
$609$	−5.33204	+	0.824093i	−0.216065	+	0.0333940i
$610$	−17.0896	−	13.4752i	−0.691938	−	0.545597i
$611$	−16.4825	−	3.27858i	−0.666812	−	0.132637i
$612$	21.1787	−	28.6838i	0.856098	−	1.15947i
$613$	−7.46059	+	11.1656i	−0.301330	+	0.450973i	−0.950976	−	0.309264i	$-0.899917\pi$
$613$	−7.46059	+	11.1656i	−0.301330	+	0.450973i	0.649646	+	0.760237i	$0.274917\pi$
$614$	3.17809	+	3.72186i	0.128257	+	0.150202i
$615$	1.25948	−	0.765349i	0.0507871	−	0.0308619i
$616$	4.52561	+	3.29021i	0.182342	+	0.132566i
$617$	11.9765	+	4.96085i	0.482157	+	0.199716i	0.610504	−	0.792013i	$-0.290967\pi$
$617$	11.9765	+	4.96085i	0.482157	+	0.199716i	−0.128346	+	0.991729i	$0.540967\pi$
$618$	−8.45168	+	4.26552i	−0.339976	+	0.171584i
$619$	−0.0735165	+	0.0146233i	−0.00295488	+	0.000587762i	−0.196568	−	0.980490i	$-0.562979\pi$
$619$	−0.0735165	+	0.0146233i	−0.00295488	+	0.000587762i	0.193613	+	0.981078i	$0.437979\pi$
$620$	−1.66866	+	4.52019i	−0.0670149	+	0.181535i
$621$	−23.1397	+	40.2534i	−0.928565	+	1.61531i
$622$	25.8483	+	7.29290i	1.03642	+	0.292419i
$623$	−16.0272	−	16.0272i	−0.642117	−	0.642117i
$624$	−12.1316	+	19.6136i	−0.485653	+	0.785171i
$625$	−1.83194	+	1.83194i	−0.0732776	+	0.0732776i
$626$	−16.4776	+	9.22566i	−0.658579	+	0.368732i
$627$	−1.99355	+	1.82905i	−0.0796149	+	0.0730452i
$628$	−4.80767	+	0.187889i	−0.191847	+	0.00749757i
$629$	7.38652	+	37.1346i	0.294520	+	1.48065i
$630$	−10.8818	−	1.80817i	−0.433541	−	0.0720391i
$631$	8.89318	−	21.4700i	0.354032	−	0.854708i	−0.642082	−	0.766636i	$-0.721929\pi$
$631$	8.89318	−	21.4700i	0.354032	−	0.854708i	0.996114	−	0.0880725i	$-0.0280707\pi$
$632$	−15.3419	−	7.07853i	−0.610268	−	0.281569i
$633$	−4.07072	+	2.47366i	−0.161797	+	0.0983192i
$634$	20.9113	+	1.64795i	0.830494	+	0.0654485i
$635$	−0.167584	−	0.111976i	−0.00665036	−	0.00444363i
$636$	4.07531	+	9.94956i	0.161597	+	0.394526i
$637$	1.93692	−	9.73754i	0.0767435	−	0.385816i
$638$	−0.254739	−	2.15420i	−0.0100852	−	0.0852857i
$639$	−31.6693	+	10.0288i	−1.25282	+	0.396735i
$640$	−3.41564	−	14.2731i	−0.135015	−	0.564194i
$641$		−	9.61269i		−	0.379678i	−0.981815	−	0.189839i	$-0.939203\pi$
$641$		−	9.61269i		−	0.379678i	0.981815	−	0.189839i	$-0.0607967\pi$
$642$	−1.57696	−	5.67485i	−0.0622376	−	0.223968i
$643$	−25.0712	−	4.98697i	−0.988710	−	0.196667i	−0.325860	−	0.945418i	$-0.605654\pi$
$643$	−25.0712	−	4.98697i	−0.988710	−	0.196667i	−0.662851	+	0.748751i	$0.730654\pi$
$644$	−34.8318	+	8.35469i	−1.37257	+	0.329221i
$645$	−7.53344	+	16.1819i	−0.296629	+	0.637163i
$646$	−1.04494	+	13.2595i	−0.0411126	+	0.521689i
$647$	37.7603	−	15.6408i	1.48451	−	0.614905i	0.514398	−	0.857552i	$-0.328016\pi$
$647$	37.7603	−	15.6408i	1.48451	−	0.614905i	0.970115	+	0.242647i	$0.0780156\pi$
$648$	−25.0396	+	4.58450i	−0.983649	+	0.180096i
$649$	6.59161	+	2.73033i	0.258743	+	0.107175i
$650$	−13.9135	−	7.09111i	−0.545732	−	0.278136i
$651$	2.20899	+	6.05735i	0.0865770	+	0.237406i
$652$	0.953512	+	24.3983i	0.0373424	+	0.955513i
$653$	16.1634	+	24.1903i	0.632523	+	0.946638i	0.999863	+	0.0165511i	$0.00526862\pi$
$653$	16.1634	+	24.1903i	0.632523	+	0.946638i	−0.367340	+	0.930087i	$0.619731\pi$
$654$	−18.2072	−	23.2792i	−0.711958	−	0.910287i
$655$	15.9668	+	15.9668i	0.623873	+	0.623873i
$656$	2.61578	−	0.204768i	0.102129	−	0.00799483i
$657$	−23.7022	−	12.3009i	−0.924711	−	0.479905i
$658$	3.88590	−	13.7729i	0.151488	−	0.536922i
$659$	0.185192	+	0.277160i	0.00721407	+	0.0107966i	0.835059	−	0.550160i	$-0.185433\pi$
$659$	0.185192	+	0.277160i	0.00721407	+	0.0107966i	−0.827845	+	0.560957i	$0.810433\pi$
$660$	0.882393	−	4.34637i	0.0343471	−	0.169182i
$661$	6.23540	+	31.3475i	0.242529	+	1.21928i	0.889562	+	0.456814i	$0.151009\pi$
$661$	6.23540	+	31.3475i	0.242529	+	1.21928i	−0.647033	+	0.762462i	$0.723991\pi$
$662$	13.3948	+	41.2396i	0.520603	+	1.60282i
$663$	−8.12281	+	33.2853i	−0.315464	+	1.29270i
$664$	−35.5658	−	25.8571i	−1.38022	−	1.00345i
$665$	3.80171	−	1.57472i	0.147424	−	0.0610650i
$666$	14.2982	−	22.9403i	0.554042	−	0.888919i
$667$	11.5466	+	7.71517i	0.447085	+	0.298733i
$668$	17.3368	+	23.8725i	0.670780	+	0.923655i
$669$	−24.9354	−	1.07308i	−0.964059	−	0.0414877i
$670$	14.1965	−	18.0043i	0.548458	−	0.695567i
$671$		−	11.7085i		−	0.452003i
$672$	−15.8386	−	11.6108i	−0.610986	−	0.447896i
$673$		−	21.8536i		−	0.842395i	−0.906969	−	0.421197i	$-0.861610\pi$
$673$		−	21.8536i		−	0.842395i	0.906969	−	0.421197i	$-0.138390\pi$
$674$	−11.9979	−	9.46044i	−0.462143	−	0.364402i
$675$	−4.49252	−	16.6414i	−0.172917	−	0.640526i
$676$	−0.601321	+	3.79147i	−0.0231277	+	0.145826i
$677$	−29.3203	−	19.5912i	−1.12687	−	0.752951i	−0.154871	−	0.987935i	$-0.549496\pi$
$677$	−29.3203	−	19.5912i	−1.12687	−	0.752951i	−0.971999	+	0.234984i	$0.924496\pi$
$678$	37.2119	+	32.0301i	1.42912	+	1.23011i
$679$	−7.45229	+	3.08684i	−0.285993	+	0.118462i
$680$	−11.3864	−	18.5940i	−0.436649	−	0.713047i
$681$	8.32941	+	2.03267i	0.319184	+	0.0778923i
$682$	−2.46547	+	0.800794i	−0.0944076	+	0.0306640i
$683$	1.35779	+	6.82609i	0.0519545	+	0.261193i	0.998029	−	0.0627565i	$-0.0199892\pi$
$683$	1.35779	+	6.82609i	0.0519545	+	0.261193i	−0.946074	+	0.323950i	$0.894989\pi$
$684$	7.02238	−	6.39205i	0.268508	−	0.244406i
$685$	−9.87256	−	14.7753i	−0.377211	−	0.564536i
$686$	27.2332	+	7.68363i	1.03977	+	0.293362i
$687$	−4.83471	+	6.60237i	−0.184456	+	0.251896i
$688$	−24.9637	+	19.6629i	−0.951733	+	0.749642i
$689$	−7.30563	−	7.30563i	−0.278322	−	0.278322i
$690$	17.4917	+	22.3644i	0.665899	+	0.851398i
$691$	3.67684	+	5.50279i	0.139874	+	0.209336i	0.894792	−	0.446483i	$-0.147324\pi$
$691$	3.67684	+	5.50279i	0.139874	+	0.209336i	−0.754918	+	0.655819i	$0.772324\pi$
$692$	11.6501	−	12.5977i	0.442870	−	0.478894i
$693$	−2.86100	−	5.19949i	−0.108680	−	0.197512i
$694$	2.50457	−	4.91423i	0.0950723	−	0.186542i
$695$	−1.13184	−	0.468822i	−0.0429330	−	0.0177834i
$696$	0.864249	+	7.56442i	0.0327593	+	0.286729i
$697$	3.60128	−	1.49170i	0.136408	−	0.0565021i
$698$	−19.9029	−	1.56848i	−0.753336	−	0.0593679i
$699$	−7.18713	−	3.34595i	−0.271842	−	0.126555i
$700$	6.95053	−	11.3369i	0.262705	−	0.428495i
$701$	−17.0957	−	3.40054i	−0.645695	−	0.128437i	−0.138630	−	0.990344i	$-0.544270\pi$
$701$	−17.0957	−	3.40054i	−0.645695	−	0.128437i	−0.507065	+	0.861908i	$0.669270\pi$
$702$	20.4913	−	13.3589i	0.773393	−	0.504197i
$703$			10.0836i			0.380311i
$704$	4.89206	−	6.19756i	0.184376	−	0.233579i
$705$	−11.2101	+	1.73258i	−0.422197	+	0.0652526i
$706$	46.0517	−	5.44571i	1.73318	−	0.204952i
$707$	−6.54159	+	32.8868i	−0.246022	+	1.23683i
$708$	−23.0976	−	9.67433i	−0.868062	−	0.363584i
$709$	−30.5589	−	20.4188i	−1.14766	−	0.766844i	−0.171779	−	0.985135i	$-0.554952\pi$
$709$	−30.5589	−	20.4188i	−1.14766	−	0.766844i	−0.975884	+	0.218292i	$0.929952\pi$
$710$	−1.59591	+	20.2509i	−0.0598935	+	0.760004i
$711$	11.5366	+	13.7139i	0.432656	+	0.514312i
$712$	−23.4940	+	21.7040i	−0.880476	+	0.813393i
$713$	6.35072	−	15.3320i	0.237836	−	0.574187i
$714$	−27.7129	−	9.12233i	−1.03713	−	0.341395i
$715$	0.831425	+	4.17986i	0.0310935	+	0.156318i
$716$	−9.38275	+	10.1460i	−0.350650	+	0.379172i
$717$	−24.3730	−	26.5651i	−0.910226	−	0.992091i
$718$	−25.0363	−	44.7166i	−0.934348	−	1.66881i
$719$	−1.15249	+	1.15249i	−0.0429805	+	0.0429805i	−0.728270	−	0.685290i	$-0.759676\pi$
$719$	−1.15249	+	1.15249i	−0.0429805	+	0.0429805i	0.685290	+	0.728270i	$0.259676\pi$
$720$	−3.15726	+	15.2428i	−0.117664	+	0.568066i
$721$	5.47770	+	5.47770i	0.204000	+	0.204000i
$722$	6.33444	−	22.4513i	0.235743	−	0.835550i
$723$	−18.3949	+	16.8770i	−0.684112	+	0.627661i
$724$	−37.7925	+	17.4130i	−1.40455	+	0.647150i
$725$	−5.05641	+	1.00578i	−0.187790	+	0.0373538i
$726$	−21.9243	+	11.0651i	−0.813688	+	0.410664i
$727$	20.8812	+	8.64926i	0.774440	+	0.320783i	0.734669	−	0.678425i	$-0.237337\pi$
$727$	20.8812	+	8.64926i	0.774440	+	0.320783i	0.0397704	+	0.999209i	$0.487337\pi$
$728$	18.3484	+	4.41113i	0.680036	+	0.163487i
$729$	26.1060	+	6.89021i	0.966890	+	0.255193i
$730$	−12.4183	+	10.6040i	−0.459621	+	0.392470i
$731$	−26.2285	+	39.2537i	−0.970096	+	1.45185i
$732$	−0.162193	+	41.0950i	−0.00599483	+	1.51892i
$733$	−4.76718	−	0.948252i	−0.176080	−	0.0350245i	0.106263	−	0.994338i	$-0.466112\pi$
$733$	−4.76718	−	0.948252i	−0.176080	−	0.0350245i	−0.282343	+	0.959314i	$0.591112\pi$
$734$	21.8401	−	27.6981i	0.806134	−	1.02236i
$735$	−1.02357	−	6.62270i	−0.0377550	−	0.244282i
$736$	9.83535	+	49.5809i	0.362536	+	1.82758i
$737$	12.3352			0.454373
$738$	−2.60356	−	0.982989i	−0.0958383	−	0.0361843i
$739$	4.90789	−	24.6736i	0.180540	−	0.907634i	−0.779207	−	0.626767i	$-0.784378\pi$
$739$	4.90789	−	24.6736i	0.180540	−	0.907634i	0.959747	−	0.280867i	$-0.0906221\pi$
$740$	−9.71318	−	13.3749i	−0.357064	−	0.491672i
$741$	−3.85117	+	8.27235i	−0.141476	+	0.303892i
$742$	6.69058	−	5.71309i	0.245619	−	0.209734i
$743$	−3.84400	−	9.28024i	−0.141023	−	0.340459i	0.837550	−	0.546361i	$-0.183987\pi$
$743$	−3.84400	−	9.28024i	−0.141023	−	0.340459i	−0.978573	+	0.205902i	$0.933987\pi$
$744$	8.66448	−	2.77650i	0.317655	−	0.101792i
$745$	−6.54655	+	15.8048i	−0.239847	+	0.579042i
$746$	−27.4711	+	8.92273i	−1.00579	+	0.326684i
$747$	22.4840	+	40.8616i	0.822646	+	1.49505i
$748$	4.06230	−	11.0043i	0.148532	−	0.402356i
$749$	−4.00728	+	2.67758i	−0.146423	+	0.0978367i
$750$	−26.2326	−	3.20709i	−0.957879	−	0.117106i
$751$	7.79992	−	7.79992i	0.284623	−	0.284623i	−0.550327	−	0.834950i	$-0.685497\pi$
$751$	7.79992	−	7.79992i	0.284623	−	0.284623i	0.834950	+	0.550327i	$0.185497\pi$
$752$	−19.2033	−	6.24840i	−0.700273	−	0.227856i
$753$	−16.0733	−	11.7700i	−0.585745	−	0.428923i
$754$	−3.57416	−	6.38368i	−0.130163	−	0.232480i
$755$	−4.11897	+	2.75221i	−0.149905	+	0.100163i
$756$	9.96962	+	18.2890i	0.362591	+	0.665163i
$757$	29.7399	−	5.91564i	1.08092	−	0.215008i	0.377660	−	0.925944i	$-0.376729\pi$
$757$	29.7399	−	5.91564i	1.08092	−	0.215008i	0.703256	+	0.710937i	$0.251729\pi$
$758$	21.2367	−	41.6687i	0.771353	−	1.51348i
$759$	−3.62138	+	14.8395i	−0.131448	+	0.538641i
$760$	−2.00812	−	5.44851i	−0.0728422	−	0.197638i
$761$	−0.0147356	−	0.0355749i	−0.000534165	−	0.00128959i	0.923612	−	0.383328i	$-0.125222\pi$
$761$	−0.0147356	−	0.0355749i	−0.000534165	−	0.00128959i	−0.924146	+	0.382039i	$0.875222\pi$
$762$	0.0284025	+	0.379527i	0.00102892	+	0.0137488i
$763$	−13.4353	+	20.1074i	−0.486391	+	0.727936i
$764$	−30.0704	+	7.21262i	−1.08791	+	0.260943i
$765$	2.54640	+	22.9853i	0.0920653	+	0.831037i
$766$	17.1260	−	2.02518i	0.618787	−	0.0731727i
$767$	24.0634			0.868878
$768$	−17.2562	+	21.6847i	−0.622679	+	0.782478i
$769$	7.77174			0.280256			0.140128	−	0.990133i	$-0.455249\pi$
$769$	7.77174			0.280256			0.140128	+	0.990133i	$0.455249\pi$
$770$	−3.60395	+	0.426174i	−0.129877	+	0.0153582i
$771$	−0.205214	+	4.76860i	−0.00739060	+	0.171737i
$772$	−8.64581	+	2.07377i	−0.311170	+	0.0746365i
$773$	−9.12175	+	13.6517i	−0.328087	+	0.491016i	−0.958441	−	0.285291i	$-0.907910\pi$
$773$	−9.12175	+	13.6517i	−0.328087	+	0.491016i	0.630354	+	0.776308i	$0.282910\pi$
$774$	32.8327	−	7.61968i	1.18015	−	0.273884i
$775$	2.35768	+	5.69194i	0.0846903	+	0.204461i
$776$	3.93641	+	10.6804i	0.141309	+	0.383405i
$777$	−21.4884	−	5.24393i	−0.770892	−	0.188125i
$778$	0.409857	−	0.804182i	0.0146941	−	0.0288313i
$779$	1.01819	−	0.202530i	0.0364803	−	0.00725639i
$780$	−2.86026	−	14.6821i	−0.102414	−	0.525704i
$781$	−9.08690	+	6.07167i	−0.325155	+	0.217262i
$782$	36.6859	+	65.5234i	1.31189	+	2.34311i
$783$	2.58143	−	7.65177i	0.0922527	−	0.273452i
$784$	3.69143	−	11.3449i	0.131837	−	0.405176i
$785$	2.20662	−	2.20662i	0.0787575	−	0.0787575i
$786$	5.17427	−	42.3233i	0.184560	−	1.50962i
$787$	−12.7036	+	8.48825i	−0.452833	+	0.302574i	−0.760992	−	0.648762i	$-0.775287\pi$
$787$	−12.7036	+	8.48825i	−0.452833	+	0.302574i	0.308159	+	0.951335i	$0.400287\pi$
$788$	−1.65420	+	4.48104i	−0.0589286	+	0.159630i
$789$	7.86368	−	2.86771i	0.279954	−	0.102093i
$790$	10.4228	−	3.38537i	0.370826	−	0.120446i
$791$	15.3746	−	37.1176i	0.546658	−	1.31975i
$792$	−7.49126	+	3.74378i	−0.266190	+	0.133029i
$793$	−15.1120	−	36.4836i	−0.536644	−	1.29557i
$794$	−15.8325	+	13.5193i	−0.561873	+	0.479784i
$795$	−6.32209	−	2.94323i	−0.224221	−	0.104385i
$796$	24.3856	+	33.5787i	0.864326	+	1.19017i
$797$	−9.43393	+	47.4276i	−0.334167	+	1.67997i	0.339240	+	0.940700i	$0.389830\pi$
$797$	−9.43393	+	47.4276i	−0.334167	+	1.67997i	−0.673407	+	0.739272i	$0.735170\pi$
$798$	−6.76485	−	3.82272i	−0.239473	−	0.135323i
$799$	−30.0014			−1.06137
$800$	−15.5974	−	10.4336i	−0.551451	−	0.368884i
$801$	32.3422	−	10.2419i	1.14275	−	0.361881i
$802$	21.5992	−	27.3926i	0.762695	−	0.967266i
$803$	−8.61650	−	1.71393i	−0.304070	−	0.0604832i
$804$	−43.2946	−	0.170874i	−1.52688	−	0.00602627i
$805$	12.9074	−	19.3173i	0.454925	−	0.680844i
$806$	−6.64880	+	5.67741i	−0.234194	+	0.199978i
$807$	−22.5810	−	37.1600i	−0.794890	−	1.30809i
$808$	46.0064	+	11.0604i	1.61850	+	0.389104i
$809$	−20.3048	−	8.41051i	−0.713878	−	0.295698i	−0.00396971	−	0.999992i	$-0.501264\pi$
$809$	−20.3048	−	8.41051i	−0.713878	−	0.295698i	−0.709908	+	0.704294i	$0.751264\pi$
$810$	9.90470	−	13.2097i	0.348016	−	0.464143i
$811$	10.6456	−	2.11755i	0.373819	−	0.0743572i	−0.00460559	−	0.999989i	$-0.501466\pi$
$811$	10.6456	−	2.11755i	0.373819	−	0.0743572i	0.378424	+	0.925632i	$0.376466\pi$
$812$	5.65829	−	2.60707i	0.198567	−	0.0914904i
$813$	4.15240	+	4.52586i	0.145631	+	0.158729i
$814$	2.41481	−	8.55884i	0.0846390	−	0.299987i
$815$	−11.1983	−	11.1983i	−0.392260	−	0.392260i
$816$	−14.4104	+	38.5669i	−0.504466	+	1.35011i
$817$	−8.89061	+	8.89061i	−0.311043	+	0.311043i
$818$	−19.6927	−	35.1724i	−0.688538	−	1.22977i
$819$	−15.6257	−	12.5089i	−0.546008	−	0.437096i
$820$	−1.15543	+	1.24942i	−0.0403495	+	0.0436315i
$821$	8.77241	+	44.1019i	0.306159	+	1.53917i	0.761094	+	0.648641i	$0.224662\pi$
$821$	8.77241	+	44.1019i	0.306159	+	1.53917i	−0.454935	+	0.890524i	$0.650338\pi$
$822$	−10.4917	+	31.8729i	−0.365940	+	1.11169i
$823$	1.14321	−	2.75996i	0.0398499	−	0.0962062i	−0.902701	−	0.430267i	$-0.858419\pi$
$823$	1.14321	−	2.75996i	0.0398499	−	0.0962062i	0.942551	+	0.334061i	$0.108419\pi$
$824$	8.02967	−	7.41789i	0.279727	−	0.258415i
$825$	−2.94488	−	4.84618i	−0.102528	−	0.168722i
$826$	−1.60984	+	20.4277i	−0.0560134	+	0.710770i
$827$	−32.6221	−	21.7974i	−1.13438	−	0.757971i	−0.160955	−	0.986962i	$-0.551457\pi$
$827$	−32.6221	−	21.7974i	−1.13438	−	0.757971i	−0.973429	+	0.228991i	$0.926457\pi$
$828$	12.9160	−	52.0341i	0.448862	−	1.80831i
$829$	−1.57093	+	7.89760i	−0.0545607	+	0.274295i	−0.998429	−	0.0560260i	$-0.982157\pi$
$829$	−1.57093	+	7.89760i	−0.0545607	+	0.274295i	0.943869	+	0.330321i	$0.107157\pi$
$830$	28.3227	−	3.34921i	0.983094	−	0.116253i
$831$	−2.71998	−	17.5988i	−0.0943551	−	0.610496i
$832$	7.24451	−	25.6256i	0.251158	−	0.888409i
$833$		−	17.7242i		−	0.614108i
$834$	0.619372	+	2.22887i	0.0214471	+	0.0771796i
$835$	−18.7683	−	3.73324i	−0.649503	−	0.129194i
$836$	1.63286	−	2.66333i	0.0564736	−	0.0921134i
$837$	−9.57017	−	1.24168i	−0.330793	−	0.0429186i
$838$	−6.12154	−	0.482419i	−0.211465	−	0.0166649i
$839$	−28.7150	+	11.8941i	−0.991351	+	0.410631i	−0.818618	−	0.574338i	$-0.805260\pi$
$839$	−28.7150	+	11.8941i	−0.991351	+	0.410631i	−0.172732	+	0.984969i	$0.555260\pi$
$840$	12.6552	−	1.44588i	0.436645	−	0.0498875i
$841$	24.5611	+	10.1735i	0.846933	+	0.350811i
$842$	13.1711	−	25.8430i	0.453905	−	0.890609i
$843$	41.4058	−	15.0998i	1.42609	−	0.520065i
$844$	3.73444	−	4.03820i	0.128545	−	0.139000i
$845$	−1.38330	−	2.07026i	−0.0475870	−	0.0712189i
$846$	15.6180	+	14.6582i	0.536958	+	0.503961i
$847$	14.2096	+	14.2096i	0.488247	+	0.488247i
$848$	−7.68207	−	9.75303i	−0.263803	−	0.334920i
$849$	23.5419	+	17.2390i	0.807957	+	0.591642i
$850$	−26.8310	−	7.57016i	−0.920297	−	0.259654i
$851$	31.6294	+	47.3368i	1.08424	+	1.62268i
$852$	31.9776	−	21.1847i	1.09554	−	0.725776i
$853$	−7.11679	−	35.7785i	−0.243674	−	1.22503i	−0.887842	−	0.460148i	$-0.847796\pi$
$853$	−7.11679	−	35.7785i	−0.243674	−	1.22503i	0.644168	−	0.764884i	$-0.277204\pi$
$854$	31.9824	−	10.3880i	1.09441	−	0.355470i
$855$	−0.529121	+	6.13626i	−0.0180955	+	0.209856i
$856$	3.55172	+	5.79996i	0.121395	+	0.198239i
$857$	−9.18228	+	3.80342i	−0.313661	+	0.129923i	−0.533960	−	0.845510i	$-0.679297\pi$
$857$	−9.18228	+	3.80342i	−0.313661	+	0.129923i	0.220299	+	0.975432i	$0.429297\pi$
$858$	5.24986	−	6.09919i	0.179227	−	0.208223i
$859$	12.6718	+	8.46703i	0.432356	+	0.288891i	0.752642	−	0.658430i	$-0.228779\pi$
$859$	12.6718	+	8.46703i	0.432356	+	0.288891i	−0.320286	+	0.947321i	$0.603779\pi$
$860$	3.22851	−	20.3565i	0.110091	−	0.694151i
$861$	−0.0979075	+	2.27510i	−0.00333668	+	0.0775351i
$862$	4.01788	+	3.16812i	0.136850	+	0.107907i
$863$		−	4.88131i		−	0.166162i	−0.996543	−	0.0830808i	$-0.973524\pi$
$863$		−	4.88131i		−	0.166162i	0.996543	−	0.0830808i	$-0.0264760\pi$
$864$	26.3449	−	13.0363i	0.896273	−	0.443503i
$865$			11.1292i			0.378405i
$866$	23.6010	−	29.9313i	0.801995	−	1.01711i
$867$	−1.36381	+	31.6912i	−0.0463175	+	1.07629i
$868$	−4.37481	−	6.02406i	−0.148491	−	0.204470i
$869$	4.90218	+	3.27553i	0.166295	+	0.111115i
$870$	−3.74268	−	3.22150i	−0.126889	−	0.109219i
$871$	38.4364	−	15.9209i	1.30237	−	0.539458i
$872$	27.6020	+	20.0672i	0.934721	+	0.679562i
$873$	1.03721	−	12.0286i	0.0351041	−	0.407106i
$874$	6.17822	+	19.0214i	0.208981	+	0.643407i
$875$	4.21887	+	21.2097i	0.142624	+	0.717018i
$876$	30.2187	+	6.13496i	1.02100	+	0.207281i
$877$	11.9657	+	17.9080i	0.404054	+	0.604709i	0.976574	−	0.215181i	$-0.0690343\pi$
$877$	11.9657	+	17.9080i	0.404054	+	0.604709i	−0.572520	+	0.819890i	$0.694034\pi$
$878$	−7.17018	+	25.4134i	−0.241982	+	0.857660i
$879$	−6.06940	−	4.44444i	−0.204716	−	0.149907i
$880$	0.399668	+	5.10552i	0.0134728	+	0.172107i
$881$	−10.5213	−	10.5213i	−0.354471	−	0.354471i	0.507299	−	0.861770i	$-0.330644\pi$
$881$	−10.5213	−	10.5213i	−0.354471	−	0.354471i	−0.861770	+	0.507299i	$0.830644\pi$
$882$	−8.65979	+	9.22680i	−0.291590	+	0.310682i
$883$	6.61033	+	9.89306i	0.222455	+	0.332928i	0.925863	−	0.377858i	$-0.123339\pi$
$883$	6.61033	+	9.89306i	0.222455	+	0.332928i	−0.703408	+	0.710786i	$0.748339\pi$
$884$	−1.54496	−	39.5323i	−0.0519627	−	1.32962i
$885$	15.2591	−	5.56467i	0.512929	−	0.187054i
$886$	−35.8266	−	18.2593i	−1.20362	−	0.613432i
$887$	−17.5114	−	7.25345i	−0.587975	−	0.243547i	0.0688044	−	0.997630i	$-0.478082\pi$
$887$	−17.5114	−	7.25345i	−0.587975	−	0.243547i	−0.656779	+	0.754083i	$0.728082\pi$
$888$	−8.59414	+	30.0067i	−0.288400	+	1.00696i
$889$	0.287719	−	0.119177i	0.00964977	−	0.00399707i
$890$	1.62982	−	20.6812i	0.0546317	−	0.693237i
$891$	8.88003	−	0.215987i	0.297492	−	0.00723583i
$892$	28.0247	−	6.72195i	0.938337	−	0.225068i
$893$	−7.83660	−	1.55880i	−0.262242	−	0.0521632i
$894$	31.1236	−	8.64881i	1.04093	−	0.289259i
$895$		−	8.96325i		−	0.299608i
$896$	21.2692	+	7.86430i	0.710555	+	0.262728i
$897$	7.86899	+	50.9139i	0.262738	+	1.69996i
$898$	4.83124	+	40.8555i	0.161221	+	1.36337i
$899$	−0.563099	+	2.83089i	−0.0187804	+	0.0944154i
$900$	10.2689	+	17.0501i	0.342297	+	0.568337i
$901$	−15.3359	−	10.2472i	−0.510915	−	0.341382i
$902$	−0.912724	−	0.0719288i	−0.0303904	−	0.00239497i
$903$	−14.3225	−	23.5696i	−0.476624	−	0.784346i
$904$	−51.4788	−	23.7516i	−1.71216	−	0.789967i
$905$	10.3282	−	24.9345i	0.343322	−	0.828851i
$906$	8.88532	+	2.92481i	0.295195	+	0.0971702i
$907$	1.64264	+	8.25812i	0.0545430	+	0.274206i	0.998427	−	0.0560716i	$-0.0178575\pi$
$907$	1.64264	+	8.25812i	0.0545430	+	0.274206i	−0.943884	+	0.330278i	$0.892858\pi$
$908$	−9.89267	+	0.386616i	−0.328300	+	0.0128303i
$909$	−39.1797	−	31.3646i	−1.29951	−	1.04030i
$910$	−10.6798	+	5.97952i	−0.354032	+	0.198219i
$911$	−14.3917	+	14.3917i	−0.476820	+	0.476820i	−0.904113	−	0.427293i	$-0.859467\pi$
$911$	−14.3917	+	14.3917i	−0.476820	+	0.476820i	0.427293	+	0.904113i	$0.359467\pi$
$912$	−5.76796	+	9.32525i	−0.190996	+	0.308790i
$913$	10.8496	+	10.8496i	0.359070	+	0.359070i
$914$	−41.3052	−	11.6539i	−1.36625	−	0.385478i
$915$	−18.0197	−	19.6404i	−0.595713	−	0.649291i
$916$	3.27238	−	8.86449i	0.108123	−	0.292891i
$917$	−34.2194	+	6.80667i	−1.13002	+	0.224776i
$918$	31.2259	−	30.5269i	1.03061	−	1.00754i
$919$	16.1957	+	6.70847i	0.534246	+	0.221292i	0.633462	−	0.773774i	$-0.281633\pi$
$919$	16.1957	+	6.70847i	0.534246	+	0.221292i	−0.0992157	+	0.995066i	$0.531633\pi$
$920$	−26.5173	−	19.2787i	−0.874251	−	0.635599i
$921$	3.11276	+	5.12245i	0.102569	+	0.168790i
$922$	−11.6705	−	13.6672i	−0.384346	−	0.450106i
$923$	−20.4781	+	30.6476i	−0.674044	+	1.00878i
$924$	4.82645	+	4.86470i	0.158779	+	0.160037i
$925$	−20.7295	−	4.12335i	−0.681580	−	0.135575i
$926$	−2.19236	−	1.72869i	−0.0720455	−	0.0568083i
$927$	−11.0537	+	3.50044i	−0.363053	+	0.114969i
$928$	−3.36011	−	8.12401i	−0.110301	−	0.266684i
$929$	10.1436			0.332802			0.166401	−	0.986058i	$-0.446785\pi$
$929$	10.1436			0.332802			0.166401	+	0.986058i	$0.446785\pi$
$930$	−2.90324	+	5.13770i	−0.0952010	+	0.168472i
$931$	0.920906	−	4.62971i	0.0301815	−	0.151732i
$932$	9.04125	+	1.43393i	0.296156	+	0.0469699i
$933$	29.8204	+	13.8828i	0.976275	+	0.454501i
$934$	5.24738	+	6.14519i	0.171700	+	0.201077i
$935$	2.91151	+	7.02901i	0.0952166	+	0.229873i
$936$	−18.5106	+	21.3344i	−0.605039	+	0.697337i
$937$	17.5554	−	42.3824i	0.573508	−	1.38457i	−0.325041	−	0.945700i	$-0.605378\pi$
$937$	17.5554	−	42.3824i	0.573508	−	1.38457i	0.898550	−	0.438872i	$-0.144622\pi$
$938$	10.9440	+	33.6942i	0.357335	+	1.10015i
$939$	−21.7290	+	7.92408i	−0.709098	+	0.258593i
$940$	11.8960	−	5.48112i	0.388005	−	0.178774i
$941$	6.87719	−	4.59519i	0.224190	−	0.149799i	−0.438403	−	0.898778i	$-0.644456\pi$
$941$	6.87719	−	4.59519i	0.224190	−	0.149799i	0.662593	+	0.748979i	$0.269456\pi$
$942$	−5.84911	−	0.715088i	−0.190574	−	0.0232988i
$943$	4.14452	−	4.14452i	0.134964	−	0.134964i
$944$	28.7140	+	3.41068i	0.934560	+	0.111008i
$945$	−12.8013	−	4.31869i	−0.416426	−	0.140487i
$946$	9.67534	−	5.41712i	0.314572	−	0.176126i
$947$	−22.1380	+	14.7922i	−0.719389	+	0.480680i	−0.860589	−	0.509301i	$-0.829904\pi$
$947$	−22.1380	+	14.7922i	−0.719389	+	0.480680i	0.141200	+	0.989981i	$0.454904\pi$
$948$	−17.1605	−	11.5645i	−0.557346	−	0.375597i
$949$	−29.0610	+	5.78060i	−0.943362	+	0.187646i
$950$	−6.61515	−	3.37146i	−0.214624	−	0.109385i
$951$	24.9580	+	6.09065i	0.809319	+	0.197503i
$952$	33.6628	+	1.33317i	1.09102	+	0.0432084i
$953$	9.52957	+	23.0064i	0.308693	+	0.745251i	0.999748	+	0.0224487i	$0.00714623\pi$
$953$	9.52957	+	23.0064i	0.308693	+	0.745251i	−0.691055	+	0.722802i	$0.742854\pi$
$954$	2.97692	+	12.8273i	0.0963812	+	0.415301i
$955$	11.1430	−	16.6766i	0.360578	−	0.539642i
$956$	35.4902	+	21.7586i	1.14784	+	0.703724i
$957$	0.114225	−	2.65427i	0.00369237	−	0.0858005i
$958$	0.822430	+	6.95490i	0.0265715	+	0.224702i
$959$	27.4573			0.886642
$960$	−1.33204	−	17.9251i	−0.0429915	−	0.578529i
$961$	−27.5507			−0.888734
$962$	−3.52225	−	29.7860i	−0.113562	−	0.960340i
$963$	−0.794290	−	7.16974i	−0.0255956	−	0.231042i
$964$	15.0667	−	24.5750i	0.485265	−	0.791509i
$965$	3.20381	−	4.79485i	0.103134	−	0.154352i
$966$	−43.7478	+	3.27394i	−1.40756	+	0.105337i
$967$	6.44006	+	15.5477i	0.207098	+	0.499980i	0.992964	−	0.118418i	$-0.0377822\pi$
$967$	6.44006	+	15.5477i	0.207098	+	0.499980i	−0.785865	+	0.618397i	$0.787782\pi$
$968$	20.8296	−	19.2426i	0.669489	−	0.618481i
$969$	−3.86198	+	15.8255i	−0.124065	+	0.508388i
$970$	−6.57779	−	3.35242i	−0.211200	−	0.107640i
$971$	28.6135	−	5.69159i	0.918252	−	0.182652i	0.286732	−	0.958011i	$-0.407431\pi$
$971$	28.6135	−	5.69159i	0.918252	−	0.182652i	0.631521	+	0.775359i	$0.282431\pi$
$972$	−31.1704	+	0.635066i	−0.999793	+	0.0203698i
$973$	1.57391	−	1.05166i	0.0504574	−	0.0337146i
$974$	−41.3277	+	23.1389i	−1.32422	+	0.741420i
$975$	−15.4311	−	11.2997i	−0.494191	−	0.361881i
$976$	−12.8615	−	45.6766i	−0.411688	−	1.46207i
$977$	0.0787675	−	0.0787675i	0.00252000	−	0.00252000i	−0.705846	−	0.708366i	$-0.749433\pi$
$977$	0.0787675	−	0.0787675i	0.00252000	−	0.00252000i	0.708366	+	0.705846i	$0.249433\pi$
$978$	−3.62899	+	29.6836i	−0.116042	+	0.949175i
$979$	9.27998	−	6.20068i	0.296589	−	0.198175i
$980$	3.23813	+	7.02791i	0.103438	+	0.224498i
$981$	−17.4494	−	31.7120i	−0.557117	−	1.01249i
$982$	9.73574	+	29.9742i	0.310680	+	0.956514i
$983$	−5.37333	+	12.9724i	−0.171383	+	0.413754i	−0.986111	−	0.166089i	$-0.946886\pi$
$983$	−5.37333	+	12.9724i	−0.171383	+	0.413754i	0.814728	+	0.579843i	$0.196886\pi$
$984$	3.20251	+	0.265102i	0.102092	+	0.00845114i
$985$	−1.18559	−	2.86228i	−0.0377762	−	0.0911997i
$986$	−8.48135	−	9.93249i	−0.270101	−	0.316315i
$987$	7.39721	−	15.8893i	0.235456	−	0.505762i
$988$	1.65044	−	10.4064i	0.0525076	−	0.331073i
$989$	−13.8490	+	69.6235i	−0.440372	+	2.21390i
$990$	1.91861	−	5.08166i	0.0609774	−	0.161506i
$991$	47.6831			1.51471			0.757353	−	0.653006i	$-0.226492\pi$
$991$	47.6831			1.51471			0.757353	+	0.653006i	$0.226492\pi$
$992$	−8.73847	+	5.83226i	−0.277447	+	0.185175i
$993$	8.11140	+	52.4823i	0.257407	+	1.66548i
$994$	−24.6471	−	19.4344i	−0.781759	−	0.616421i
$995$	−26.3992	−	5.25112i	−0.836910	−	0.166472i
$996$	−37.9301	−	38.2307i	−1.20186	−	1.21138i
$997$	20.2564	−	30.3158i	0.641525	−	0.960110i	−0.358125	−	0.933674i	$-0.616584\pi$
$997$	20.2564	−	30.3158i	0.641525	−	0.960110i	0.999650	−	0.0264367i	$-0.00841606\pi$
$998$	14.0827	+	16.4923i	0.445782	+	0.522054i
$999$	21.7819	−	24.9317i	0.689149	−	0.788805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.131.1	yes	240
3.2	odd	2	inner	192.2.s.a.131.30	yes	240
4.3	odd	2		768.2.s.a.431.30		240
12.11	even	2		768.2.s.a.431.27		240
64.21	even	16		768.2.s.a.335.27		240
64.43	odd	16	inner	192.2.s.a.107.30	yes	240
192.107	even	16	inner	192.2.s.a.107.1	✓	240
192.149	odd	16		768.2.s.a.335.30		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.1	✓	240	192.107	even	16	inner
192.2.s.a.107.30	yes	240	64.43	odd	16	inner
192.2.s.a.131.1	yes	240	1.1	even	1	trivial
192.2.s.a.131.30	yes	240	3.2	odd	2	inner
768.2.s.a.335.27		240	64.21	even	16
768.2.s.a.335.30		240	192.149	odd	16
768.2.s.a.431.27		240	12.11	even	2
768.2.s.a.431.30		240	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40443 + 0.166076i) q^{2} +(-1.73045 - 0.0744689i) q^{3} +(1.94484 - 0.466485i) q^{4} +(-0.720684 + 1.07858i) q^{5} +(2.44266 - 0.182801i) q^{6} +(-0.767030 - 1.85177i) q^{7} +(-2.65391 + 0.978136i) q^{8} +(2.98891 + 0.257729i) q^{9} +(0.833022 - 1.63448i) q^{10} +(0.967998 - 0.192547i) q^{11} +(-3.40018 + 0.662398i) q^{12} +(2.76775 - 1.84935i) q^{13} +(1.38477 + 2.47330i) q^{14} +(1.32743 - 1.81276i) q^{15} +(3.56478 - 1.81447i) q^{16} +(4.20201 - 4.20201i) q^{17} +(-4.24051 + 0.134425i) q^{18} +(1.31593 - 0.879274i) q^{19} +(-0.898472 + 2.43385i) q^{20} +(1.18941 + 3.26152i) q^{21} +(-1.32751 + 0.431180i) q^{22} +(3.41948 - 8.25535i) q^{23} +(4.66530 - 1.49498i) q^{24} +(1.26947 + 3.06477i) q^{25} +(-3.57998 + 3.05694i) q^{26} +(-5.15296 - 0.668568i) q^{27} +(-2.35557 - 3.24359i) q^{28} +(-0.303195 + 1.52426i) q^{29} +(-1.56322 + 2.76634i) q^{30} +1.85722 q^{31} +(-4.70514 + 3.14032i) q^{32} +(-1.68941 + 0.261107i) q^{33} +(-5.20357 + 6.59928i) q^{34} +(2.55007 + 0.507241i) q^{35} +(5.93317 - 0.893039i) q^{36} +(-3.53974 + 5.29759i) q^{37} +(-1.70210 + 1.45342i) q^{38} +(-4.92718 + 2.99410i) q^{39} +(0.857634 - 3.56738i) q^{40} +(0.606016 + 0.251020i) q^{41} +(-2.21210 - 4.38304i) q^{42} +(-7.79176 + 1.54988i) q^{43} +(1.79278 - 0.826028i) q^{44} +(-2.43204 + 3.03803i) q^{45} +(-3.43139 + 12.1619i) q^{46} +(-3.56988 - 3.56988i) q^{47} +(-6.30380 + 2.87439i) q^{48} +(2.10901 - 2.10901i) q^{49} +(-2.29186 - 4.09342i) q^{50} +(-7.58429 + 6.95845i) q^{51} +(4.52014 - 4.88781i) q^{52} +(-0.605519 - 3.04415i) q^{53} +(7.34800 + 0.0831709i) q^{54} +(-0.489944 + 1.18283i) q^{55} +(3.84692 + 4.16419i) q^{56} +(-2.34262 + 1.42354i) q^{57} +(0.172671 - 2.19107i) q^{58} +(6.01066 + 4.01619i) q^{59} +(1.73601 - 4.14475i) q^{60} +(2.31440 - 11.6353i) q^{61} +(-2.60833 + 0.308440i) q^{62} +(-1.81533 - 5.73247i) q^{63} +(6.08650 - 5.19177i) q^{64} +4.31804i q^{65} +(2.32929 - 0.647277i) q^{66} +(12.2580 + 2.43827i) q^{67} +(6.21206 - 10.1324i) q^{68} +(-6.53200 + 14.0308i) q^{69} +(-3.66563 - 0.288877i) q^{70} +(-10.2302 + 4.23749i) q^{71} +(-8.18440 + 2.23957i) q^{72} +(-8.22378 - 3.40640i) q^{73} +(4.09150 - 8.02795i) q^{74} +(-1.96852 - 5.39796i) q^{75} +(2.14909 - 2.32390i) q^{76} +(-1.09904 - 1.64482i) q^{77} +(6.42262 - 5.02329i) q^{78} +(4.22403 + 4.22403i) q^{79} +(-0.612028 + 5.15257i) q^{80} +(8.86715 + 1.54066i) q^{81} +(-0.892794 - 0.251894i) q^{82} +(8.63710 + 12.9263i) q^{83} +(3.83465 + 5.78829i) q^{84} +(1.50388 + 7.56053i) q^{85} +(10.6856 - 3.47072i) q^{86} +(0.638174 - 2.61508i) q^{87} +(-2.38064 + 1.45784i) q^{88} +(10.4476 - 4.32753i) q^{89} +(2.91108 - 4.67061i) q^{90} +(-5.54754 - 3.70675i) q^{91} +(2.79933 - 17.6505i) q^{92} +(-3.21382 - 0.138305i) q^{93} +(5.60652 + 4.42077i) q^{94} +2.05301i q^{95} +(8.37587 - 5.08379i) q^{96} -4.02440i q^{97} +(-2.61170 + 3.31222i) q^{98} +(2.94288 - 0.326023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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