LMFDB - Embedded newform 192.2.s.a.107.1

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			107.1
Character	$\chi$	$=$	192.107
Dual form			192.2.s.a.131.1

$q$-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 $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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	0.634573	−	0.772863i	$-0.281176\pi$
$5$	−0.720684	−	1.07858i	−0.322300	−	0.482355i	−0.956873	+	0.290507i	$0.906176\pi$
$6$	2.44266	+	0.182801i	0.997211	+	0.0746280i
$7$	−0.767030	+	1.85177i	−0.289910	+	0.699905i	−0.999991	−	0.00421502i	$-0.998658\pi$
$7$	−0.767030	+	1.85177i	−0.289910	+	0.699905i	0.710081	+	0.704120i	$0.248658\pi$
$8$	−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	0.338850	−	0.940840i	$-0.389962\pi$
$11$	0.967998	+	0.192547i	0.291862	+	0.0580550i	−0.0469875	+	0.998895i	$0.514962\pi$
$12$	−3.40018	−	0.662398i	−0.981548	−	0.191218i
$13$	2.76775	+	1.84935i	0.767637	+	0.512919i	0.876654	−	0.481121i	$-0.159770\pi$
$13$	2.76775	+	1.84935i	0.767637	+	0.512919i	−0.109017	+	0.994040i	$0.534770\pi$
$14$	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	0.999813	+	0.0193250i	$0.00615171\pi$
$17$	4.20201	+	4.20201i	1.01914	+	1.01914i	0.0193250	+	0.999813i	$0.493848\pi$
$18$	−4.24051	−	0.134425i	−0.999498	−	0.0316842i
$19$	1.31593	+	0.879274i	0.301894	+	0.201719i	0.697285	−	0.716794i	$-0.254391\pi$
$19$	1.31593	+	0.879274i	0.301894	+	0.201719i	−0.395391	+	0.918513i	$0.629391\pi$
$20$	−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	0.692337	+	0.721574i	$0.256581\pi$
$23$	3.41948	+	8.25535i	0.713011	+	1.72136i	0.0206735	+	0.999786i	$0.493419\pi$
$24$	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	0.942370	−	0.334573i	$-0.108592\pi$
$29$	−0.303195	−	1.52426i	−0.0563019	−	0.283049i	−0.998672	+	0.0515242i	$0.983592\pi$
$30$	−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	0.417355	−	0.908743i	$-0.362957\pi$
$37$	−3.53974	−	5.29759i	−0.581929	−	0.870918i	−0.999284	+	0.0378252i	$0.987957\pi$
$38$	−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	−0.334859	−	0.942268i	$-0.608689\pi$
$41$	0.606016	−	0.251020i	0.0946437	−	0.0392027i	0.429503	+	0.903065i	$0.358689\pi$
$42$	−2.21210	+	4.38304i	−0.341334	+	0.676318i
$43$	−7.79176	−	1.54988i	−1.18823	−	0.236354i	−0.438892	−	0.898540i	$-0.644629\pi$
$43$	−7.79176	−	1.54988i	−1.18823	−	0.236354i	−0.749340	+	0.662185i	$0.769629\pi$
$44$	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	−0.917789	−	0.397068i	$-0.870028\pi$
$47$	−3.56988	+	3.56988i	−0.520721	+	0.520721i	0.397068	+	0.917789i	$0.370028\pi$
$48$	−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	0.916655	+	0.399679i	$0.130878\pi$
$53$	−0.605519	+	3.04415i	−0.0831744	+	0.418146i	−0.999829	+	0.0184666i	$0.994122\pi$
$54$	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	−0.0989555	−	0.995092i	$-0.531550\pi$
$59$	6.01066	−	4.01619i	0.782521	−	0.522864i	0.881476	+	0.472228i	$0.156550\pi$
$60$	1.73601	+	4.14475i	0.224117	+	0.535084i
$61$	2.31440	+	11.6353i	0.296328	+	1.48974i	0.786214	+	0.617955i	$0.212038\pi$
$61$	2.31440	+	11.6353i	0.296328	+	1.48974i	−0.489886	+	0.871787i	$0.662962\pi$
$62$	−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	0.622774	−	0.782402i	$-0.286006\pi$
$67$	12.2580	−	2.43827i	1.49755	−	0.297882i	0.874780	+	0.484520i	$0.161006\pi$
$68$	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	−0.318572	−	0.947899i	$-0.603203\pi$
$71$	−10.2302	−	4.23749i	−1.21410	−	0.502897i	−0.895530	+	0.445001i	$0.853203\pi$
$72$	−8.18440	−	2.23957i	−0.964540	−	0.263936i
$73$	−8.22378	+	3.40640i	−0.962521	+	0.398689i	−0.807923	−	0.589288i	$-0.799408\pi$
$73$	−8.22378	+	3.40640i	−0.962521	+	0.398689i	−0.154598	+	0.987977i	$0.549408\pi$
$74$	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	−0.428365	−	0.903606i	$-0.640910\pi$
$79$	4.22403	−	4.22403i	0.475241	−	0.475241i	0.903606	+	0.428365i	$0.140910\pi$
$80$	−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	0.0403648	−	0.999185i	$-0.487148\pi$
$83$	8.63710	−	12.9263i	0.948044	−	1.41885i	0.907680	−	0.419664i	$-0.137852\pi$
$84$	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	0.860056	−	0.510200i	$-0.170429\pi$
$89$	10.4476	+	4.32753i	1.10744	+	0.458717i	0.247385	+	0.968917i	$0.420429\pi$
$90$	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	$0.0654945\pi$
$97$			4.02440i			0.408616i	−0.978907	+	0.204308i	$0.934506\pi$
$98$	−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	−0.384079	+	0.923300i	$0.625481\pi$
$101$	−13.9098	+	9.29424i	−1.38408	+	0.924811i	−0.999999	+	0.00151063i	$0.999519\pi$
$102$	9.49596	+	11.0322i	0.940240	+	1.09235i
$103$	−3.57072	−	1.47904i	−0.351833	−	0.145734i	0.199765	−	0.979844i	$-0.435982\pi$
$103$	−3.57072	−	1.47904i	−0.351833	−	0.145734i	−0.551599	+	0.834110i	$0.685982\pi$
$104$	−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	−0.996813	−	0.0797738i	$-0.974580\pi$
$107$	−0.469101	+	2.35833i	−0.0453497	+	0.227989i	0.951463	+	0.307762i	$0.0995802\pi$
$108$	−10.3335	−	1.10352i	−0.994346	−	0.106186i
$109$	−6.70309	+	10.0319i	−0.642040	+	0.960881i	0.357595	+	0.933877i	$0.383597\pi$
$109$	−6.70309	+	10.0319i	−0.642040	+	0.960881i	−0.999635	+	0.0270042i	$0.991403\pi$
$110$	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	0.430958	−	0.902372i	$-0.358176\pi$
$113$	14.1735	−	14.1735i	1.33333	−	1.33333i	0.902372	−	0.430958i	$-0.141824\pi$
$114$	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	$-0.997806\pi$
$127$		−	0.155374i		−	0.0137873i	0.999976	−	0.00689363i	$-0.00219433\pi$
$128$	−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	0.785292	+	0.619125i	$0.212513\pi$
$131$	3.39595	+	17.0726i	0.296706	+	1.49164i	−0.488586	+	0.872516i	$0.662487\pi$
$132$	−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	−0.973114	−	0.230325i	$-0.926021\pi$
$137$	−5.24233	−	12.6561i	−0.447883	−	1.08128i	0.525231	−	0.850960i	$-0.323979\pi$
$138$	6.84354	+	20.7901i	0.582561	+	1.76977i
$139$	0.184246	−	0.926267i	0.0156275	−	0.0785649i	−0.972185	−	0.234216i	$-0.924748\pi$
$139$	0.184246	−	0.926267i	0.0156275	−	0.0785649i	0.987812	+	0.155651i	$0.0497476\pi$
$140$	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	0.693984	−	0.719990i	$-0.255854\pi$
$149$	12.9342	+	2.57278i	1.05961	+	0.210770i	0.365629	+	0.930761i	$0.380854\pi$
$150$	3.66112	−	7.25412i	0.298929	−	0.592297i
$151$	3.52819	−	1.46142i	0.287120	−	0.118929i	−0.234475	−	0.972122i	$-0.575337\pi$
$151$	3.52819	−	1.46142i	0.287120	−	0.118929i	0.521595	+	0.853193i	$0.325337\pi$
$152$	−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	−0.288341	−	0.957528i	$-0.593104\pi$
$157$	−2.35944	+	0.469323i	−0.188304	+	0.0374560i	0.100037	+	0.994984i	$0.468104\pi$
$158$	−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	−0.954694	−	0.297588i	$-0.903818\pi$
$163$	−2.38176	−	11.9739i	−0.186554	−	0.937869i	0.768141	−	0.640281i	$-0.221182\pi$
$164$	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	−0.540189	−	0.841544i	$-0.681647\pi$
$167$	5.64526	−	13.6289i	0.436843	−	1.05463i	0.977033	−	0.213090i	$-0.0683527\pi$
$168$	−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	0.796369	−	0.604811i	$-0.206751\pi$
$173$	7.13355	+	4.76648i	0.542354	+	0.362389i	−0.254015	+	0.967200i	$0.581751\pi$
$174$	−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	0.322019	−	0.946733i	$-0.395639\pi$
$179$	−5.74521	−	3.83883i	−0.429417	−	0.286928i	−0.751436	+	0.659806i	$0.770639\pi$
$180$	−3.31273	−	7.04299i	−0.246916	−	0.524954i
$181$	−20.4058	−	4.05897i	−1.51675	−	0.301701i	−0.634665	−	0.772788i	$-0.718862\pi$
$181$	−20.4058	−	4.05897i	−1.51675	−	0.301701i	−0.882087	+	0.471087i	$0.843862\pi$
$182$	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	0.781187	−	0.624297i	$-0.214615\pi$
$197$	−1.32687	−	1.98581i	−0.0945358	−	0.141483i	−0.875723	+	0.482814i	$0.839615\pi$
$198$	−4.07892	−	0.946620i	−0.289876	−	0.0672733i
$199$	7.94054	−	19.1702i	0.562890	−	1.35894i	−0.344555	−	0.938766i	$-0.611970\pi$
$199$	7.94054	−	19.1702i	0.562890	−	1.35894i	0.907445	−	0.420171i	$-0.138030\pi$
$200$	−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	0.631785	−	0.775143i	$-0.282322\pi$
$211$	2.28666	+	1.52790i	0.157420	+	0.105185i	−0.474365	+	0.880328i	$0.657322\pi$
$212$	−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	−0.353559	−	0.935412i	$-0.615029\pi$
$227$	−4.85500	+	0.965719i	−0.322238	+	0.0640970i	0.0313212	+	0.999509i	$0.490029\pi$
$228$	−3.89196	−	3.86136i	−0.257751	−	0.255725i
$229$	2.62485	+	3.92837i	0.173455	+	0.259594i	0.908004	−	0.418962i	$-0.137606\pi$
$229$	2.62485	+	3.92837i	0.173455	+	0.259594i	−0.734549	+	0.678556i	$0.762606\pi$
$230$	−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	−0.239842	−	0.970812i	$-0.577096\pi$
$233$	4.22871	−	1.75159i	0.277032	−	0.114751i	0.516874	+	0.856061i	$0.327096\pi$
$234$	−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	−0.0468626	−	0.998901i	$-0.514922\pi$
$239$	14.7182	−	14.7182i	0.952039	−	0.952039i	0.998901	+	0.0468626i	$0.0149223\pi$
$240$	1.44279	+	8.87068i	0.0931316	+	0.572600i
$241$	10.1915	+	10.1915i	0.656494	+	0.656494i	0.954549	−	0.298055i	$-0.0963379\pi$
$241$	10.1915	+	10.1915i	0.656494	+	0.656494i	−0.298055	+	0.954549i	$0.596338\pi$
$242$	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	−0.215852	−	0.976426i	$-0.569253\pi$
$251$	9.56353	−	6.39015i	0.603645	−	0.403343i	0.819497	+	0.573083i	$0.194253\pi$
$252$	−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	$0.0273919\pi$
$257$			2.75570i			0.171896i	−0.996300	+	0.0859479i	$0.972608\pi$
$258$	−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	0.240759	−	0.970585i	$-0.422604\pi$
$263$	−4.46471	−	1.84934i	−0.275306	−	0.114035i	−0.516065	+	0.856549i	$0.672604\pi$
$264$	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	−0.109961	−	0.993936i	$-0.535073\pi$
$269$	13.9475	−	20.8740i	0.850396	−	1.27271i	0.960357	−	0.278772i	$-0.0899273\pi$
$270$	−5.38529	−	7.86546i	−0.327738	−	0.478677i
$271$	−2.50752	+	2.50752i	−0.152321	+	0.152321i	−0.779154	−	0.626833i	$-0.784351\pi$
$271$	−2.50752	+	2.50752i	−0.152321	+	0.152321i	0.626833	+	0.779154i	$0.284351\pi$
$272$	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	−0.872570	−	0.488488i	$-0.837548\pi$
$277$	2.00578	−	10.0838i	0.120516	−	0.605875i	0.993086	−	0.117386i	$-0.0374515\pi$
$278$	−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	−0.452037	−	0.891999i	$-0.649302\pi$
$281$	−23.5087	−	9.73764i	−1.40241	−	0.580899i	−0.950377	+	0.311100i	$0.899302\pi$
$282$	−9.37258	+	8.06743i	−0.558129	+	0.480408i
$283$	−14.0073	+	9.35938i	−0.832648	+	0.556357i	−0.897234	−	0.441555i	$-0.854427\pi$
$283$	−14.0073	+	9.35938i	−0.832648	+	0.556357i	0.0645865	+	0.997912i	$0.479427\pi$
$284$	−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	−0.445595	−	0.895235i	$-0.647008\pi$
$293$	3.61126	−	2.41296i	0.210972	−	0.140967i	0.656567	+	0.754268i	$0.272008\pi$
$294$	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	−0.882271	−	0.470742i	$-0.843986\pi$
$307$	−1.92265	+	2.87744i	−0.109731	+	0.164224i	0.772540	+	0.634967i	$0.218986\pi$
$308$	−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	−0.819929	−	0.572465i	$-0.805987\pi$
$311$	−17.5455	+	7.26758i	−0.994913	+	0.412107i	−0.174984	+	0.984571i	$0.555987\pi$
$312$	10.1477	+	12.7655i	0.574498	+	0.722706i
$313$	12.3369	+	5.11012i	0.697324	+	0.288841i	0.703048	−	0.711143i	$-0.251822\pi$
$313$	12.3369	+	5.11012i	0.697324	+	0.288841i	−0.00572401	+	0.999984i	$0.501822\pi$
$314$	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	−0.585892	−	0.810390i	$-0.699256\pi$
$317$	−14.5474	+	2.89365i	−0.817062	+	0.162524i	−0.231171	+	0.972913i	$0.574256\pi$
$318$	−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	0.363766	+	0.931490i	$0.381491\pi$
$331$	−5.98155	+	30.0713i	−0.328776	+	1.65287i	−0.692542	+	0.721378i	$0.743509\pi$
$332$	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	−0.467723	−	0.883875i	$-0.654925\pi$
$337$	7.63954	−	7.63954i	0.416152	−	0.416152i	0.883875	+	0.467723i	$0.154925\pi$
$338$	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	0.768741	−	0.639561i	$-0.220884\pi$
$347$	−2.16682	−	3.24287i	−0.116321	−	0.174086i	−0.885061	+	0.465474i	$0.845884\pi$
$348$	0.0212479	+	5.38361i	0.00113901	+	0.288592i
$349$	13.8459	−	2.75411i	0.741151	−	0.147424i	0.189947	−	0.981794i	$-0.439168\pi$
$349$	13.8459	−	2.75411i	0.741151	−	0.147424i	0.551204	+	0.834370i	$0.314168\pi$
$350$	−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	0.0957787	−	0.995403i	$-0.469466\pi$
$359$	13.8677	−	33.4796i	0.731909	−	1.76698i	0.636130	−	0.771582i	$-0.280534\pi$
$360$	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	0.0764579	−	0.997073i	$-0.475639\pi$
$367$	−17.6364	−	17.6364i	−0.920615	−	0.920615i	−0.997073	+	0.0764579i	$0.975639\pi$
$368$	−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	0.684184	−	0.729309i	$-0.260158\pi$
$373$	20.0315	+	3.98452i	1.03719	+	0.206311i	0.353009	+	0.935620i	$0.385158\pi$
$374$	−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	−0.910747	−	0.412965i	$-0.864493\pi$
$379$	−18.3728	−	27.4969i	−0.943749	−	1.41242i	−0.0330024	−	0.999455i	$-0.510507\pi$
$380$	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	0.822372	−	0.568951i	$-0.192650\pi$
$389$	−0.354585	−	0.530674i	−0.0179782	−	0.0269062i	−0.840350	+	0.542044i	$0.817650\pi$
$390$	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	0.823434	−	0.567412i	$-0.192055\pi$
$397$	12.2404	+	8.17878i	0.614328	+	0.410481i	−0.209106	+	0.977893i	$0.567055\pi$
$398$	−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	0.121575	−	0.992582i	$-0.461205\pi$
$401$	−17.4419	−	17.4419i	−0.871007	−	0.871007i	−0.992582	+	0.121575i	$0.961205\pi$
$402$	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	−0.385816	−	0.922576i	$-0.626080\pi$
$409$	10.9078	−	26.3338i	0.539357	−	1.30212i	0.925173	−	0.379546i	$-0.123920\pi$
$410$	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	−0.0899675	−	0.995945i	$-0.528676\pi$
$419$	4.25857	−	0.847083i	0.208045	−	0.0413827i	0.298012	+	0.954562i	$0.403676\pi$
$420$	−9.00670	+	0.0355475i	−0.439482	+	0.00173454i
$421$	−11.3949	−	17.0536i	−0.555352	−	0.831143i	0.442492	−	0.896772i	$-0.354094\pi$
$421$	−11.3949	−	17.0536i	−0.555352	−	0.831143i	−0.997844	+	0.0656295i	$0.979094\pi$
$422$	−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	−0.766033	−	0.642802i	$-0.777772\pi$
$431$	−2.55834	+	2.55834i	−0.123231	+	0.123231i	0.642802	+	0.766033i	$0.277772\pi$
$432$	−19.5823	−	6.96661i	−0.942154	−	0.335181i
$433$	−19.0584	−	19.0584i	−0.915888	−	0.915888i	0.0808391	−	0.996727i	$-0.474240\pi$
$433$	−19.0584	−	19.0584i	−0.915888	−	0.915888i	−0.996727	+	0.0808391i	$0.974240\pi$
$434$	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	0.997613	+	0.0690583i	$0.0219994\pi$
$439$	7.14528	+	17.2502i	0.341026	+	0.823309i	−0.656587	+	0.754250i	$0.728001\pi$
$440$	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	0.151951	−	0.988388i	$-0.451444\pi$
$443$	23.6417	−	15.7969i	1.12325	−	0.750533i	0.971301	+	0.237855i	$0.0764442\pi$
$444$	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	$0.240824\pi$
$449$			29.0905i			1.37286i	−0.727194	+	0.686432i	$0.759176\pi$
$450$	−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	0.386202	−	0.922414i	$-0.373787\pi$
$457$	28.0374	−	11.6135i	1.31153	−	0.543255i	0.925331	+	0.379160i	$0.123787\pi$
$458$	−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	−0.629811	−	0.776748i	$-0.716868\pi$
$461$	7.06025	−	10.5664i	0.328829	−	0.492127i	0.958640	+	0.284621i	$0.0918678\pi$
$462$	−2.98525	+	3.81684i	−0.138886	+	0.177576i
$463$	1.39596	−	1.39596i	0.0648758	−	0.0648758i	−0.673924	−	0.738800i	$-0.735393\pi$
$463$	1.39596	−	1.39596i	0.0648758	−	0.0648758i	0.738800	+	0.673924i	$0.235393\pi$
$464$	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	−0.897620	−	0.440769i	$-0.854706\pi$
$467$	−3.17450	+	4.75097i	−0.146898	+	0.219849i	0.750722	+	0.660618i	$0.229706\pi$
$468$	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	$0.0360889\pi$
$479$			4.95212i			0.226268i	−0.993580	+	0.113134i	$0.963911\pi$
$480$	−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	0.950303	−	0.311325i	$-0.100773\pi$
$487$	30.9423	+	12.8167i	1.40213	+	0.580781i	0.451826	+	0.892106i	$0.350773\pi$
$488$	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	0.749662	+	0.661821i	$0.230216\pi$
$491$	−4.34757	+	21.8567i	−0.196203	+	0.986380i	−0.945865	+	0.324559i	$0.894784\pi$
$492$	−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	−0.971650	−	0.236422i	$-0.924025\pi$
$499$	−8.51962	+	12.7505i	−0.381390	+	0.570791i	0.590260	+	0.807213i	$0.299025\pi$
$500$	−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	−0.446929	−	0.894569i	$-0.647482\pi$
$503$	−2.92455	+	1.21139i	−0.130399	+	0.0540131i	0.316530	+	0.948583i	$0.397482\pi$
$504$	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	−0.645203	−	0.764011i	$-0.723227\pi$
$509$	−21.4086	+	4.25843i	−0.948919	+	0.188752i	−0.303716	+	0.952763i	$0.598227\pi$
$510$	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	0.970149	+	0.242509i	$0.0779705\pi$
$521$	10.3999	+	25.1077i	0.455630	+	1.09999i	−0.514519	+	0.857479i	$0.672030\pi$
$522$	1.08080	+	6.50441i	0.0473054	+	0.284690i
$523$	5.49571	−	27.6288i	0.240310	−	1.20812i	−0.652535	−	0.757759i	$-0.726294\pi$
$523$	5.49571	−	27.6288i	0.240310	−	1.20812i	0.892845	−	0.450363i	$-0.148706\pi$
$524$	−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	0.401856	−	0.915703i	$-0.368365\pi$
$541$	26.1330	−	5.19818i	1.12355	−	0.223487i	0.721691	+	0.692216i	$0.243365\pi$
$542$	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	0.963760	−	0.266769i	$-0.0859562\pi$
$547$	−0.671852	−	3.37763i	−0.0287263	−	0.144417i	−0.992487	+	0.122352i	$0.960956\pi$
$548$	−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	0.705408	−	0.708801i	$-0.250764\pi$
$557$	7.56429	+	5.05430i	0.320509	+	0.214157i	−0.384899	+	0.922959i	$0.625764\pi$
$558$	−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	0.945452	−	0.325762i	$-0.105621\pi$
$563$	23.8770	+	15.9541i	1.00630	+	0.672386i	0.0608444	+	0.998147i	$0.480621\pi$
$564$	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	−0.942860	−	0.333188i	$-0.891875\pi$
$569$	−0.967449	+	2.33563i	−0.0405576	+	0.0979147i	0.902303	+	0.431103i	$0.141875\pi$
$570$	0.375291	−	5.01480i	0.0157192	−	0.210047i
$571$	13.9993	+	20.9514i	0.585850	+	0.876787i	0.999433	−	0.0336797i	$-0.0107226\pi$
$571$	13.9993	+	20.9514i	0.585850	+	0.876787i	−0.413582	+	0.910467i	$0.635723\pi$
$572$	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	0.201057	−	0.979580i	$-0.435562\pi$
$587$	0.289296	+	0.0575446i	0.0119405	+	0.00237512i	−0.189116	+	0.981955i	$0.560562\pi$
$588$	−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	0.981593	−	0.190986i	$-0.0611684\pi$
$593$	19.2525	+	19.2525i	0.790607	+	0.790607i	−0.190986	+	0.981593i	$0.561168\pi$
$594$	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	0.976906	−	0.213670i	$-0.0685419\pi$
$599$	3.30506	+	7.97913i	0.135041	+	0.326018i	−0.841865	+	0.539689i	$0.818542\pi$
$600$	10.5042	−	12.4002i	0.428833	−	0.506237i
$601$	8.94164	−	21.5870i	0.364737	−	0.880553i	−0.629857	−	0.776711i	$-0.716886\pi$
$601$	8.94164	−	21.5870i	0.364737	−	0.880553i	0.994594	−	0.103842i	$-0.0331136\pi$
$602$	−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	0.649646	−	0.760237i	$-0.274917\pi$
$613$	−7.46059	−	11.1656i	−0.301330	−	0.450973i	−0.950976	+	0.309264i	$0.899917\pi$
$614$	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	−0.128346	−	0.991729i	$-0.540967\pi$
$617$	11.9765	−	4.96085i	0.482157	−	0.199716i	0.610504	+	0.792013i	$0.290967\pi$
$618$	−8.45168	−	4.26552i	−0.339976	−	0.171584i
$619$	−0.0735165	−	0.0146233i	−0.00295488	−	0.000587762i	0.193613	−	0.981078i	$-0.437979\pi$
$619$	−0.0735165	−	0.0146233i	−0.00295488	−	0.000587762i	−0.196568	+	0.980490i	$0.562979\pi$
$620$	−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	0.996114	+	0.0880725i	$0.0280707\pi$
$631$	8.89318	+	21.4700i	0.354032	+	0.854708i	−0.642082	+	0.766636i	$0.721929\pi$
$632$	−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	$0.0607967\pi$
$641$			9.61269i			0.379678i	−0.981815	+	0.189839i	$0.939203\pi$
$642$	−1.57696	+	5.67485i	−0.0622376	+	0.223968i
$643$	−25.0712	+	4.98697i	−0.988710	+	0.196667i	−0.662851	−	0.748751i	$-0.730654\pi$
$643$	−25.0712	+	4.98697i	−0.988710	+	0.196667i	−0.325860	+	0.945418i	$0.605654\pi$
$644$	−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	0.970115	−	0.242647i	$-0.0780156\pi$
$647$	37.7603	+	15.6408i	1.48451	+	0.614905i	0.514398	+	0.857552i	$0.328016\pi$
$648$	−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	−0.367340	−	0.930087i	$-0.619731\pi$
$653$	16.1634	−	24.1903i	0.632523	−	0.946638i	0.999863	−	0.0165511i	$-0.00526862\pi$
$654$	−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	−0.827845	−	0.560957i	$-0.810433\pi$
$659$	0.185192	−	0.277160i	0.00721407	−	0.0107966i	0.835059	+	0.550160i	$0.185433\pi$
$660$	0.882393	+	4.34637i	0.0343471	+	0.169182i
$661$	6.23540	−	31.3475i	0.242529	−	1.21928i	−0.647033	−	0.762462i	$-0.723991\pi$
$661$	6.23540	−	31.3475i	0.242529	−	1.21928i	0.889562	−	0.456814i	$-0.151009\pi$
$662$	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	$0.138390\pi$
$673$			21.8536i			0.842395i	−0.906969	+	0.421197i	$0.861610\pi$
$674$	−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	−0.971999	−	0.234984i	$-0.924496\pi$
$677$	−29.3203	+	19.5912i	−1.12687	+	0.752951i	−0.154871	+	0.987935i	$0.549496\pi$
$678$	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	−0.946074	−	0.323950i	$-0.894989\pi$
$683$	1.35779	−	6.82609i	0.0519545	−	0.261193i	0.998029	+	0.0627565i	$0.0199892\pi$
$684$	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	−0.754918	−	0.655819i	$-0.772324\pi$
$691$	3.67684	−	5.50279i	0.139874	−	0.209336i	0.894792	+	0.446483i	$0.147324\pi$
$692$	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	−0.507065	−	0.861908i	$-0.669270\pi$
$701$	−17.0957	+	3.40054i	−0.645695	+	0.128437i	−0.138630	+	0.990344i	$0.544270\pi$
$702$	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	−0.975884	−	0.218292i	$-0.929952\pi$
$709$	−30.5589	+	20.4188i	−1.14766	+	0.766844i	−0.171779	+	0.985135i	$0.554952\pi$
$710$	−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	0.685290	−	0.728270i	$-0.259676\pi$
$719$	−1.15249	−	1.15249i	−0.0429805	−	0.0429805i	−0.728270	+	0.685290i	$0.759676\pi$
$720$	−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	0.0397704	−	0.999209i	$-0.487337\pi$
$727$	20.8812	−	8.64926i	0.774440	−	0.320783i	0.734669	+	0.678425i	$0.237337\pi$
$728$	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	−0.282343	−	0.959314i	$-0.591112\pi$
$733$	−4.76718	+	0.948252i	−0.176080	+	0.0350245i	0.106263	+	0.994338i	$0.466112\pi$
$734$	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	0.959747	+	0.280867i	$0.0906221\pi$
$739$	4.90789	+	24.6736i	0.180540	+	0.907634i	−0.779207	+	0.626767i	$0.784378\pi$
$740$	−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	−0.978573	−	0.205902i	$-0.933987\pi$
$743$	−3.84400	+	9.28024i	−0.141023	+	0.340459i	0.837550	+	0.546361i	$0.183987\pi$
$744$	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	0.834950	−	0.550327i	$-0.185497\pi$
$751$	7.79992	+	7.79992i	0.284623	+	0.284623i	−0.550327	+	0.834950i	$0.685497\pi$
$752$	−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	0.703256	−	0.710937i	$-0.251729\pi$
$757$	29.7399	+	5.91564i	1.08092	+	0.215008i	0.377660	+	0.925944i	$0.376729\pi$
$758$	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	−0.924146	−	0.382039i	$-0.875222\pi$
$761$	−0.0147356	+	0.0355749i	−0.000534165	+	0.00128959i	0.923612	+	0.383328i	$0.125222\pi$
$762$	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	0.630354	−	0.776308i	$-0.282910\pi$
$773$	−9.12175	−	13.6517i	−0.328087	−	0.491016i	−0.958441	+	0.285291i	$0.907910\pi$
$774$	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	0.308159	−	0.951335i	$-0.400287\pi$
$787$	−12.7036	−	8.48825i	−0.452833	−	0.302574i	−0.760992	+	0.648762i	$0.775287\pi$
$788$	−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	−0.673407	−	0.739272i	$-0.735170\pi$
$797$	−9.43393	−	47.4276i	−0.334167	−	1.67997i	0.339240	−	0.940700i	$-0.389830\pi$
$798$	−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	−0.709908	−	0.704294i	$-0.751264\pi$
$809$	−20.3048	+	8.41051i	−0.713878	+	0.295698i	−0.00396971	+	0.999992i	$0.501264\pi$
$810$	9.90470	+	13.2097i	0.348016	+	0.464143i
$811$	10.6456	+	2.11755i	0.373819	+	0.0743572i	0.378424	−	0.925632i	$-0.376466\pi$
$811$	10.6456	+	2.11755i	0.373819	+	0.0743572i	−0.00460559	+	0.999989i	$0.501466\pi$
$812$	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	−0.454935	−	0.890524i	$-0.650338\pi$
$821$	8.77241	−	44.1019i	0.306159	−	1.53917i	0.761094	−	0.648641i	$-0.224662\pi$
$822$	−10.4917	−	31.8729i	−0.365940	−	1.11169i
$823$	1.14321	+	2.75996i	0.0398499	+	0.0962062i	0.942551	−	0.334061i	$-0.108419\pi$
$823$	1.14321	+	2.75996i	0.0398499	+	0.0962062i	−0.902701	+	0.430267i	$0.858419\pi$
$824$	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	−0.973429	−	0.228991i	$-0.926457\pi$
$827$	−32.6221	+	21.7974i	−1.13438	+	0.757971i	−0.160955	+	0.986962i	$0.551457\pi$
$828$	12.9160	+	52.0341i	0.448862	+	1.80831i
$829$	−1.57093	−	7.89760i	−0.0545607	−	0.274295i	0.943869	−	0.330321i	$-0.107157\pi$
$829$	−1.57093	−	7.89760i	−0.0545607	−	0.274295i	−0.998429	+	0.0560260i	$0.982157\pi$
$830$	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	−0.172732	−	0.984969i	$-0.555260\pi$
$839$	−28.7150	−	11.8941i	−0.991351	−	0.410631i	−0.818618	+	0.574338i	$0.805260\pi$
$840$	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	0.644168	+	0.764884i	$0.277204\pi$
$853$	−7.11679	+	35.7785i	−0.243674	+	1.22503i	−0.887842	+	0.460148i	$0.847796\pi$
$854$	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	0.220299	−	0.975432i	$-0.429297\pi$
$857$	−9.18228	−	3.80342i	−0.313661	−	0.129923i	−0.533960	+	0.845510i	$0.679297\pi$
$858$	5.24986	+	6.09919i	0.179227	+	0.208223i
$859$	12.6718	−	8.46703i	0.432356	−	0.288891i	−0.320286	−	0.947321i	$-0.603779\pi$
$859$	12.6718	−	8.46703i	0.432356	−	0.288891i	0.752642	+	0.658430i	$0.228779\pi$
$860$	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	$0.0264760\pi$
$863$			4.88131i			0.166162i	−0.996543	+	0.0830808i	$0.973524\pi$
$864$	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	−0.572520	−	0.819890i	$-0.694034\pi$
$877$	11.9657	−	17.9080i	0.404054	−	0.604709i	0.976574	+	0.215181i	$0.0690343\pi$
$878$	−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	−0.861770	−	0.507299i	$-0.830644\pi$
$881$	−10.5213	+	10.5213i	−0.354471	+	0.354471i	0.507299	+	0.861770i	$0.330644\pi$
$882$	−8.65979	−	9.22680i	−0.291590	−	0.310682i
$883$	6.61033	−	9.89306i	0.222455	−	0.332928i	−0.703408	−	0.710786i	$-0.748339\pi$
$883$	6.61033	−	9.89306i	0.222455	−	0.332928i	0.925863	+	0.377858i	$0.123339\pi$
$884$	−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	−0.656779	−	0.754083i	$-0.728082\pi$
$887$	−17.5114	+	7.25345i	−0.587975	+	0.243547i	0.0688044	+	0.997630i	$0.478082\pi$
$888$	−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	−0.943884	−	0.330278i	$-0.892858\pi$
$907$	1.64264	−	8.25812i	0.0545430	−	0.274206i	0.998427	+	0.0560716i	$0.0178575\pi$
$908$	−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	0.427293	−	0.904113i	$-0.359467\pi$
$911$	−14.3917	−	14.3917i	−0.476820	−	0.476820i	−0.904113	+	0.427293i	$0.859467\pi$
$912$	−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	−0.0992157	−	0.995066i	$-0.531633\pi$
$919$	16.1957	−	6.70847i	0.534246	−	0.221292i	0.633462	+	0.773774i	$0.281633\pi$
$920$	−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	0.898550	+	0.438872i	$0.144622\pi$
$937$	17.5554	+	42.3824i	0.573508	+	1.38457i	−0.325041	+	0.945700i	$0.605378\pi$
$938$	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	0.662593	−	0.748979i	$-0.269456\pi$
$941$	6.87719	+	4.59519i	0.224190	+	0.149799i	−0.438403	+	0.898778i	$0.644456\pi$
$942$	−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	0.141200	−	0.989981i	$-0.454904\pi$
$947$	−22.1380	−	14.7922i	−0.719389	−	0.480680i	−0.860589	+	0.509301i	$0.829904\pi$
$948$	−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	−0.691055	−	0.722802i	$-0.742854\pi$
$953$	9.52957	−	23.0064i	0.308693	−	0.745251i	0.999748	−	0.0224487i	$-0.00714623\pi$
$954$	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	−0.785865	−	0.618397i	$-0.787782\pi$
$967$	6.44006	−	15.5477i	0.207098	−	0.499980i	0.992964	+	0.118418i	$0.0377822\pi$
$968$	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	0.631521	−	0.775359i	$-0.282431\pi$
$971$	28.6135	+	5.69159i	0.918252	+	0.182652i	0.286732	+	0.958011i	$0.407431\pi$
$972$	−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	0.708366	−	0.705846i	$-0.249433\pi$
$977$	0.0787675	+	0.0787675i	0.00252000	+	0.00252000i	−0.705846	+	0.708366i	$0.749433\pi$
$978$	−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	0.814728	−	0.579843i	$-0.196886\pi$
$983$	−5.37333	−	12.9724i	−0.171383	−	0.413754i	−0.986111	+	0.166089i	$0.946886\pi$
$984$	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	0.999650	+	0.0264367i	$0.00841606\pi$
$997$	20.2564	+	30.3158i	0.641525	+	0.960110i	−0.358125	+	0.933674i	$0.616584\pi$
$998$	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.107.1	✓	240
3.2	odd	2	inner	192.2.s.a.107.30	yes	240
4.3	odd	2		768.2.s.a.335.30		240
12.11	even	2		768.2.s.a.335.27		240
64.3	odd	16	inner	192.2.s.a.131.30	yes	240
64.61	even	16		768.2.s.a.431.27		240
192.125	odd	16		768.2.s.a.431.30		240
192.131	even	16	inner	192.2.s.a.131.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.1	✓	240	1.1	even	1	trivial
192.2.s.a.107.30	yes	240	3.2	odd	2	inner
192.2.s.a.131.1	yes	240	192.131	even	16	inner
192.2.s.a.131.30	yes	240	64.3	odd	16	inner
768.2.s.a.335.27		240	12.11	even	2
768.2.s.a.335.30		240	4.3	odd	2
768.2.s.a.431.27		240	64.61	even	16
768.2.s.a.431.30		240	192.125	odd	16

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

Related objects

Downloads

Learn more