LMFDB - Embedded newform 156.2.p.b.35.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(35,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("156.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$156 = 2^{2} \cdot 3 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	156.p (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.20
Character	$\chi$	$=$	156.35
Dual form			156.2.p.b.107.20

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40167 + 0.187933i) q^{2} +(-1.64588 - 0.539506i) q^{3} +(1.92936 + 0.526840i) q^{4} -1.98084i q^{5} +(-2.20560 - 1.06553i) q^{6} +(2.42516 - 1.40017i) q^{7} +(2.60532 + 1.10105i) q^{8} +(2.41787 + 1.77593i) q^{9} +(0.372266 - 2.77649i) q^{10} +(-2.01615 + 3.49208i) q^{11} +(-2.89127 - 1.90802i) q^{12} +(0.235350 - 3.59786i) q^{13} +(3.66242 - 1.50681i) q^{14} +(-1.06868 + 3.26024i) q^{15} +(3.44488 + 2.03293i) q^{16} +(-6.77232 + 3.91000i) q^{17} +(3.05530 + 2.94366i) q^{18} +(-3.36616 + 1.94345i) q^{19} +(1.04359 - 3.82176i) q^{20} +(-4.74693 + 0.996124i) q^{21} +(-3.48226 + 4.51584i) q^{22} +(0.939991 - 1.62811i) q^{23} +(-3.69403 - 3.21778i) q^{24} +1.07626 q^{25} +(1.00604 - 4.99879i) q^{26} +(-3.02140 - 4.22742i) q^{27} +(5.41668 - 1.42376i) q^{28} +(-1.74420 - 1.00701i) q^{29} +(-2.11064 + 4.36894i) q^{30} +4.09815i q^{31} +(4.44653 + 3.49691i) q^{32} +(5.20235 - 4.65983i) q^{33} +(-10.2274 + 4.20779i) q^{34} +(-2.77351 - 4.80386i) q^{35} +(3.72931 + 4.70024i) q^{36} +(-2.61536 + 4.52993i) q^{37} +(-5.08348 + 2.09147i) q^{38} +(-2.32843 + 5.79469i) q^{39} +(2.18100 - 5.16073i) q^{40} +(3.61265 + 2.08577i) q^{41} +(-6.84084 + 0.504133i) q^{42} +(2.06494 - 1.19219i) q^{43} +(-5.72966 + 5.67529i) q^{44} +(3.51784 - 4.78941i) q^{45} +(1.62353 - 2.10542i) q^{46} +2.72193 q^{47} +(-4.57309 - 5.20450i) q^{48} +(0.420938 - 0.729086i) q^{49} +(1.50856 + 0.202265i) q^{50} +(13.2559 - 2.78170i) q^{51} +(2.34957 - 6.81759i) q^{52} -1.24793i q^{53} +(-3.44054 - 6.49328i) q^{54} +(6.91726 + 3.99368i) q^{55} +(7.85997 - 0.977669i) q^{56} +(6.58881 - 1.38263i) q^{57} +(-2.25554 - 1.73929i) q^{58} +(-0.420977 - 0.729153i) q^{59} +(-3.77949 + 5.72716i) q^{60} +(-1.28690 - 2.22897i) q^{61} +(-0.770178 + 5.74426i) q^{62} +(8.35031 + 0.921494i) q^{63} +(5.57539 + 5.73716i) q^{64} +(-7.12680 - 0.466192i) q^{65} +(8.16772 - 5.55385i) q^{66} +(-6.50853 - 3.75770i) q^{67} +(-15.1262 + 3.97588i) q^{68} +(-2.42549 + 2.17255i) q^{69} +(-2.98475 - 7.25467i) q^{70} +(-7.46100 - 12.9228i) q^{71} +(4.34394 + 7.28905i) q^{72} +2.63433 q^{73} +(-4.51719 + 5.85796i) q^{74} +(-1.77140 - 0.580649i) q^{75} +(-7.51843 + 1.97620i) q^{76} +11.2918i q^{77} +(-4.35270 + 7.68466i) q^{78} -7.13890i q^{79} +(4.02692 - 6.82377i) q^{80} +(2.69216 + 8.58791i) q^{81} +(4.67177 + 3.60249i) q^{82} +13.6116 q^{83} +(-9.68335 - 0.578990i) q^{84} +(7.74510 + 13.4149i) q^{85} +(3.11842 - 1.28299i) q^{86} +(2.32746 + 2.59843i) q^{87} +(-9.09767 + 6.87811i) q^{88} +(-2.80518 - 1.61957i) q^{89} +(5.83094 - 6.05207i) q^{90} +(-4.46685 - 9.05493i) q^{91} +(2.67134 - 2.64599i) q^{92} +(2.21098 - 6.74508i) q^{93} +(3.81526 + 0.511541i) q^{94} +(3.84967 + 6.66783i) q^{95} +(-5.43187 - 8.15443i) q^{96} +(-6.30978 - 10.9289i) q^{97} +(0.727036 - 0.942831i) q^{98} +(-11.0765 + 4.86284i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q + 6 q^{4} + 2 q^{6} - 10 q^{9} + 6 q^{10} - 16 q^{12} + 16 q^{13} + 18 q^{16} - 20 q^{18} - 60 q^{21} + 20 q^{22} - 20 q^{24} - 32 q^{25} - 24 q^{28} - 26 q^{30} - 2 q^{33} - 28 q^{34} + 6 q^{36} + 16 q^{37}+ \cdots - 56 q^{97}+O(q^{100})$ 40 * q + 6 * q^4 + 2 * q^6 - 10 * q^9 + 6 * q^10 - 16 * q^12 + 16 * q^13 + 18 * q^16 - 20 * q^18 - 60 * q^21 + 20 * q^22 - 20 * q^24 - 32 * q^25 - 24 * q^28 - 26 * q^30 - 2 * q^33 - 28 * q^34 + 6 * q^36 + 16 * q^37 + 20 * q^40 - 4 * q^42 + 28 * q^45 + 48 * q^46 - 24 * q^48 - 28 * q^49 + 12 * q^52 - 4 * q^54 + 44 * q^57 - 50 * q^58 - 12 * q^60 - 12 * q^61 + 12 * q^64 + 24 * q^66 - 6 * q^69 + 48 * q^72 - 16 * q^73 + 30 * q^78 - 14 * q^81 - 2 * q^82 - 6 * q^84 + 52 * q^85 - 12 * q^88 + 156 * q^90 + 40 * q^93 - 8 * q^94 + 128 * q^96 - 56 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$ .

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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

)

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

$2$	1.40167	+	0.187933i	0.991131	+	0.132889i
$2$	1.40167	+	0.187933i	0.991131	+	0.132889i
$3$	−1.64588	−	0.539506i	−0.950251	−	0.311484i
$3$	−1.64588	−	0.539506i	−0.950251	−	0.311484i
$4$	1.92936	+	0.526840i	0.964681	+	0.263420i
$5$		−	1.98084i		−	0.885860i	−0.896556	−	0.442930i	$-0.853939\pi$
$5$		−	1.98084i		−	0.885860i	0.896556	−	0.442930i	$-0.146061\pi$
$6$	−2.20560	−	1.06553i	−0.900431	−	0.434999i
$7$	2.42516	−	1.40017i	0.916625	−	0.529214i	0.0340681	−	0.999420i	$-0.489154\pi$
$7$	2.42516	−	1.40017i	0.916625	−	0.529214i	0.882557	+	0.470206i	$0.155820\pi$
$8$	2.60532	+	1.10105i	0.921120	+	0.389279i
$9$	2.41787	+	1.77593i	0.805956	+	0.591976i
$10$	0.372266	−	2.77649i	0.117721	−	0.878003i
$11$	−2.01615	+	3.49208i	−0.607893	+	1.05290i	0.383694	+	0.923460i	$0.374652\pi$
$11$	−2.01615	+	3.49208i	−0.607893	+	1.05290i	−0.991587	+	0.129441i	$0.958682\pi$
$12$	−2.89127	−	1.90802i	−0.834639	−	0.550798i
$13$	0.235350	−	3.59786i	0.0652744	−	0.997867i
$13$	0.235350	−	3.59786i	0.0652744	−	0.997867i
$14$	3.66242	−	1.50681i	0.978822	−	0.402711i
$15$	−1.06868	+	3.26024i	−0.275931	+	0.841790i
$16$	3.44488	+	2.03293i	0.861220	+	0.508233i
$17$	−6.77232	+	3.91000i	−1.64253	+	0.948314i	−0.662598	+	0.748975i	$0.730546\pi$
$17$	−6.77232	+	3.91000i	−1.64253	+	0.948314i	−0.979931	+	0.199339i	$0.936120\pi$
$18$	3.05530	+	2.94366i	0.720141	+	0.693828i
$19$	−3.36616	+	1.94345i	−0.772250	+	0.445858i	−0.833677	−	0.552253i	$-0.813768\pi$
$19$	−3.36616	+	1.94345i	−0.772250	+	0.445858i	0.0614269	+	0.998112i	$0.480435\pi$
$20$	1.04359	−	3.82176i	0.233353	−	0.854573i
$21$	−4.74693	+	0.996124i	−1.03587	+	0.217372i
$22$	−3.48226	+	4.51584i	−0.742420	+	0.962781i
$23$	0.939991	−	1.62811i	0.196002	−	0.339485i	−0.751227	−	0.660044i	$-0.770538\pi$
$23$	0.939991	−	1.62811i	0.196002	−	0.339485i	0.947228	+	0.320559i	$0.103871\pi$
$24$	−3.69403	−	3.21778i	−0.754041	−	0.656827i
$25$	1.07626			0.215252
$26$	1.00604	−	4.99879i	0.197301	−	0.980343i
$27$	−3.02140	−	4.22742i	−0.581469	−	0.813568i
$28$	5.41668	−	1.42376i	1.02366	−	0.269065i
$29$	−1.74420	−	1.00701i	−0.323889	−	0.186998i	0.329236	−	0.944248i	$-0.393209\pi$
$29$	−1.74420	−	1.00701i	−0.323889	−	0.186998i	−0.653125	+	0.757250i	$0.726542\pi$
$30$	−2.11064	+	4.36894i	−0.385348	+	0.797656i
$31$			4.09815i			0.736050i	0.929816	+	0.368025i	$0.119966\pi$
$31$			4.09815i			0.736050i	−0.929816	+	0.368025i	$0.880034\pi$
$32$	4.44653	+	3.49691i	0.786043	+	0.618171i
$33$	5.20235	−	4.65983i	0.905613	−	0.811172i
$34$	−10.2274	+	4.20779i	−1.75398	+	0.721630i
$35$	−2.77351	−	4.80386i	−0.468809	−	0.812001i
$36$	3.72931	+	4.70024i	0.621552	+	0.783373i
$37$	−2.61536	+	4.52993i	−0.429962	+	0.744716i	−0.996869	−	0.0790655i	$-0.974806\pi$
$37$	−2.61536	+	4.52993i	−0.429962	+	0.744716i	0.566907	+	0.823782i	$0.308140\pi$
$38$	−5.08348	+	2.09147i	−0.824650	+	0.339281i
$39$	−2.32843	+	5.79469i	−0.372847	+	0.927893i
$40$	2.18100	−	5.16073i	0.344847	−	0.815983i
$41$	3.61265	+	2.08577i	0.564202	+	0.325742i	0.754830	−	0.655920i	$-0.227719\pi$
$41$	3.61265	+	2.08577i	0.564202	+	0.325742i	−0.190629	+	0.981662i	$0.561053\pi$
$42$	−6.84084	+	0.504133i	−1.05556	+	0.0777895i
$43$	2.06494	−	1.19219i	0.314900	−	0.181808i	−0.334217	−	0.942496i	$-0.608472\pi$
$43$	2.06494	−	1.19219i	0.314900	−	0.181808i	0.649117	+	0.760688i	$0.275138\pi$
$44$	−5.72966	+	5.67529i	−0.863778	+	0.855583i
$45$	3.51784	−	4.78941i	0.524408	−	0.713964i
$46$	1.62353	−	2.10542i	0.239377	−	0.310427i
$47$	2.72193			0.397035			0.198518	−	0.980097i	$-0.436387\pi$
$47$	2.72193			0.397035			0.198518	+	0.980097i	$0.436387\pi$
$48$	−4.57309	−	5.20450i	−0.660069	−	0.751205i
$49$	0.420938	−	0.729086i	0.0601340	−	0.104155i
$50$	1.50856	+	0.202265i	0.213343	+	0.0286045i
$51$	13.2559	−	2.78170i	1.85620	−	0.389516i
$52$	2.34957	−	6.81759i	0.325827	−	0.945429i
$53$		−	1.24793i		−	0.171417i	−0.996320	−	0.0857084i	$-0.972685\pi$
$53$		−	1.24793i		−	0.171417i	0.996320	−	0.0857084i	$-0.0273153\pi$
$54$	−3.44054	−	6.49328i	−0.468198	−	0.883623i
$55$	6.91726	+	3.99368i	0.932723	+	0.538508i
$56$	7.85997	−	0.977669i	1.05033	−	0.130646i
$57$	6.58881	−	1.38263i	0.872709	−	0.183134i
$58$	−2.25554	−	1.73929i	−0.296167	−	0.228380i
$59$	−0.420977	−	0.729153i	−0.0548065	−	0.0949276i	0.837321	−	0.546712i	$-0.184121\pi$
$59$	−0.420977	−	0.729153i	−0.0548065	−	0.0949276i	−0.892127	+	0.451785i	$0.850788\pi$
$60$	−3.77949	+	5.72716i	−0.487930	+	0.739373i
$61$	−1.28690	−	2.22897i	−0.164770	−	0.285391i	0.771803	−	0.635861i	$-0.219355\pi$
$61$	−1.28690	−	2.22897i	−0.164770	−	0.285391i	−0.936574	+	0.350471i	$0.886022\pi$
$62$	−0.770178	+	5.74426i	−0.0978127	+	0.729522i
$63$	8.35031	+	0.921494i	1.05204	+	0.116097i
$64$	5.57539	+	5.73716i	0.696924	+	0.717145i
$65$	−7.12680	−	0.466192i	−0.883971	−	0.0578240i
$66$	8.16772	−	5.55385i	1.00538	−	0.683632i
$67$	−6.50853	−	3.75770i	−0.795144	−	0.459076i	0.0466265	−	0.998912i	$-0.485153\pi$
$67$	−6.50853	−	3.75770i	−0.795144	−	0.459076i	−0.841770	+	0.539836i	$0.818486\pi$
$68$	−15.1262	+	3.97588i	−1.83432	+	0.482146i
$69$	−2.42549	+	2.17255i	−0.291995	+	0.261545i
$70$	−2.98475	−	7.25467i	−0.356746	−	0.867099i
$71$	−7.46100	−	12.9228i	−0.885458	−	1.53366i	−0.845188	−	0.534469i	$-0.820511\pi$
$71$	−7.46100	−	12.9228i	−0.885458	−	1.53366i	−0.0402702	−	0.999189i	$-0.512822\pi$
$72$	4.34394	+	7.28905i	0.511938	+	0.859022i
$73$	2.63433			0.308325			0.154162	−	0.988046i	$-0.450732\pi$
$73$	2.63433			0.308325			0.154162	+	0.988046i	$0.450732\pi$
$74$	−4.51719	+	5.85796i	−0.525113	+	0.680974i
$75$	−1.77140	−	0.580649i	−0.204544	−	0.0670476i
$76$	−7.51843	+	1.97620i	−0.862423	+	0.226685i
$77$			11.2918i			1.28682i
$78$	−4.35270	+	7.68466i	−0.492846	+	0.870116i
$79$		−	7.13890i		−	0.803188i	−0.915818	−	0.401594i	$-0.868456\pi$
$79$		−	7.13890i		−	0.803188i	0.915818	−	0.401594i	$-0.131544\pi$
$80$	4.02692	−	6.82377i	0.450223	−	0.762920i
$81$	2.69216	+	8.58791i	0.299129	+	0.954213i
$82$	4.67177	+	3.60249i	0.515910	+	0.397829i
$83$	13.6116			1.49407			0.747035	−	0.664784i	$-0.231477\pi$
$83$	13.6116			1.49407			0.747035	+	0.664784i	$0.231477\pi$
$84$	−9.68335	−	0.578990i	−1.05654	−	0.0631729i
$85$	7.74510	+	13.4149i	0.840074	+	1.45505i
$86$	3.11842	−	1.28299i	0.336268	−	0.138349i
$87$	2.32746	+	2.59843i	0.249529	+	0.278581i
$88$	−9.09767	+	6.87811i	−0.969814	+	0.733208i
$89$	−2.80518	−	1.61957i	−0.297349	−	0.171675i	0.343902	−	0.939005i	$-0.388251\pi$
$89$	−2.80518	−	1.61957i	−0.297349	−	0.171675i	−0.641251	+	0.767331i	$0.721584\pi$
$90$	5.83094	−	6.05207i	0.614635	−	0.637944i
$91$	−4.46685	−	9.05493i	−0.468253	−	0.949214i
$92$	2.67134	−	2.64599i	0.278506	−	0.275864i
$93$	2.21098	−	6.74508i	0.229268	−	0.699433i
$94$	3.81526	+	0.511541i	0.393514	+	0.0527614i
$95$	3.84967	+	6.66783i	0.394968	+	0.684105i
$96$	−5.43187	−	8.15443i	−0.554388	−	0.832258i
$97$	−6.30978	−	10.9289i	−0.640661	−	1.10966i	−0.985286	−	0.170916i	$-0.945327\pi$
$97$	−6.30978	−	10.9289i	−0.640661	−	1.10966i	0.344625	−	0.938740i	$-0.388006\pi$
$98$	0.727036	−	0.942831i	0.0734417	−	0.0952403i
$99$	−11.0765	+	4.86284i	−1.11323	+	0.488734i
$100$	2.07650	+	0.567017i	0.207650	+	0.0567017i
$101$	4.54040	+	2.62140i	0.451787	+	0.260839i	0.708584	−	0.705626i	$-0.249334\pi$
$101$	4.54040	+	2.62140i	0.451787	+	0.260839i	−0.256798	+	0.966465i	$0.582667\pi$
$102$	19.1032	−	1.40780i	1.89150	−	0.139393i
$103$			4.31171i			0.424845i	0.977178	+	0.212423i	$0.0681353\pi$
$103$			4.31171i			0.424845i	−0.977178	+	0.212423i	$0.931865\pi$
$104$	4.57458	−	9.11445i	0.448574	−	0.893746i
$105$	1.97317	+	9.40293i	0.192561	+	0.917632i
$106$	0.234528	−	1.74919i	0.0227793	−	0.169896i
$107$	6.91701	−	11.9806i	0.668692	−	1.15821i	−0.309578	−	0.950874i	$-0.600188\pi$
$107$	6.91701	−	11.9806i	0.668692	−	1.15821i	0.978270	−	0.207335i	$-0.0664789\pi$
$108$	−3.60221	−	9.74803i	−0.346622	−	0.938005i
$109$	−9.47620			−0.907656			−0.453828	−	0.891089i	$-0.649942\pi$
$109$	−9.47620			−0.907656			−0.453828	+	0.891089i	$0.649942\pi$
$110$	8.94518	+	6.89781i	0.852889	+	0.657680i
$111$	6.74850	−	6.04474i	0.640539	−	0.573741i
$112$	11.2008	+	0.106777i	1.05838	+	0.0100895i
$113$	10.6484	−	6.14784i	1.00171	−	0.578340i	0.0929592	−	0.995670i	$-0.470367\pi$
$113$	10.6484	−	6.14784i	1.00171	−	0.578340i	0.908755	+	0.417330i	$0.137034\pi$
$114$	9.49518	−	0.699744i	0.889305	−	0.0655371i
$115$	−3.22503	−	1.86197i	−0.300736	−	0.173630i
$116$	−2.83465	−	2.86180i	−0.263191	−	0.265712i
$117$	6.95859	−	8.28119i	0.643322	−	0.765596i
$118$	−0.453039	−	1.10115i	−0.0417056	−	0.101369i
$119$	−10.9493	+	18.9648i	−1.00372	+	1.73850i
$120$	−6.37392	+	7.31730i	−0.581857	+	0.667975i
$121$	−2.62974	−	4.55484i	−0.239067	−	0.414077i
$122$	−1.38491	−	3.36614i	−0.125384	−	0.304756i
$123$	−4.82072	−	5.38198i	−0.434670	−	0.485276i
$124$	−2.15907	+	7.90682i	−0.193890	+	0.710054i
$125$		−	12.0361i		−	1.07654i
$126$	11.5312	+	2.86093i	1.02728	+	0.254872i
$127$	6.70906	+	3.87348i	0.595333	+	0.343716i	0.767203	−	0.641404i	$-0.221648\pi$
$127$	6.70906	+	3.87348i	0.595333	+	0.343716i	−0.171870	+	0.985120i	$0.554981\pi$
$128$	6.73666	+	9.08941i	0.595442	+	0.803398i
$129$	−4.04185	+	0.848165i	−0.355865	+	0.0746768i
$130$	−9.90182	−	1.99281i	−0.868447	−	0.174781i
$131$	−11.4093			−0.996839			−0.498420	−	0.866936i	$-0.666086\pi$
$131$	−11.4093			−0.996839			−0.498420	+	0.866936i	$0.666086\pi$
$132$	12.4922	−	6.24969i	1.08731	−	0.543966i
$133$	−5.44232	+	9.42637i	−0.471909	+	0.817370i
$134$	−8.41662	−	6.49023i	−0.727086	−	0.560670i
$135$	−8.37387	+	5.98493i	−0.720708	+	0.515100i
$136$	−21.9492	+	2.73016i	−1.88212	+	0.234110i
$137$	−4.71225	+	2.72062i	−0.402595	+	0.232438i	−0.687603	−	0.726087i	$-0.741337\pi$
$137$	−4.71225	+	2.72062i	−0.402595	+	0.232438i	0.285008	+	0.958525i	$0.408004\pi$
$138$	−3.80803	+	2.58937i	−0.324161	+	0.220422i
$139$	−3.44882	+	1.99118i	−0.292525	+	0.168889i	−0.639080	−	0.769140i	$-0.720685\pi$
$139$	−3.44882	+	1.99118i	−0.292525	+	0.168889i	0.346555	+	0.938030i	$0.387351\pi$
$140$	−2.82024	−	10.7296i	−0.238354	−	0.906816i
$141$	−4.47999	−	1.46850i	−0.377283	−	0.123670i
$142$	−8.02924	−	19.5157i	−0.673799	−	1.63772i
$143$	12.0895	+	8.07570i	1.01098	+	0.675324i
$144$	4.71892	+	11.0332i	0.393243	+	0.919434i
$145$	−1.99473	+	3.45498i	−0.165654	+	0.286920i
$146$	3.69246	+	0.495077i	0.305590	+	0.0409728i
$147$	−1.08616	+	0.972892i	−0.0895851	+	0.0802428i
$148$	−7.43252	+	7.36200i	−0.610949	+	0.605153i
$149$	−0.634052	+	0.366070i	−0.0519435	+	0.0299896i	−0.525747	−	0.850641i	$-0.676214\pi$
$149$	−0.634052	+	0.366070i	−0.0519435	+	0.0299896i	0.473803	+	0.880631i	$0.342881\pi$
$150$	−2.37380	−	1.14678i	−0.193820	−	0.0936344i
$151$			12.7204i			1.03517i	0.855631	+	0.517587i	$0.173170\pi$
$151$			12.7204i			1.03517i	−0.855631	+	0.517587i	$0.826830\pi$
$152$	−10.9098	+	1.35702i	−0.884898	+	0.110069i
$153$	−23.3184	−	2.57329i	−1.88518	−	0.208038i
$154$	−2.12210	+	15.8274i	−0.171004	+	1.27541i
$155$	8.11780			0.652037
$156$	−7.54525	+	9.95335i	−0.604104	+	0.796906i
$157$	17.1422			1.36810			0.684048	−	0.729437i	$-0.260218\pi$
$157$	17.1422			1.36810			0.684048	+	0.729437i	$0.260218\pi$
$158$	1.34163	−	10.0064i	0.106735	−	0.796065i
$159$	−0.673267	+	2.05395i	−0.0533936	+	0.162889i
$160$	6.92682	−	8.80788i	0.547613	−	0.696324i
$161$		−	5.26458i		−	0.414907i
$162$	2.15957	+	12.5434i	0.169672	+	0.985501i
$163$	−13.8016	+	7.96836i	−1.08102	+	0.624130i	−0.931173	−	0.364579i	$-0.881213\pi$
$163$	−13.8016	+	7.96836i	−1.08102	+	0.624130i	−0.149852	+	0.988708i	$0.547880\pi$
$164$	5.87125	+	5.92749i	0.458468	+	0.462859i
$165$	−9.23039	−	10.3050i	−0.718585	−	0.802246i
$166$	19.0790	+	2.55807i	1.48082	+	0.198545i
$167$	−9.26053	+	16.0397i	−0.716601	+	1.24119i	0.245738	+	0.969336i	$0.420970\pi$
$167$	−9.26053	+	16.0397i	−0.716601	+	1.24119i	−0.962339	+	0.271853i	$0.912363\pi$
$168$	−13.4641	−	2.63137i	−1.03877	−	0.203015i
$169$	−12.8892	−	1.69352i	−0.991478	−	0.130270i
$170$	8.33498	+	20.2588i	0.639263	+	1.55378i
$171$	−11.5904	−	1.27905i	−0.886336	−	0.0978111i
$172$	4.61211	−	1.21228i	0.351670	−	0.0924355i
$173$	12.1103	−	6.99189i	0.920730	−	0.531584i	0.0368619	−	0.999320i	$-0.488264\pi$
$173$	12.1103	−	6.99189i	0.920730	−	0.531584i	0.883868	+	0.467737i	$0.154930\pi$
$174$	2.77400	+	4.07955i	0.210296	+	0.309270i
$175$	2.61010	−	1.50694i	0.197305	−	0.113914i
$176$	−14.0446	+	7.93109i	−1.05865	+	0.597828i
$177$	0.299496	+	1.42722i	0.0225115	+	0.107276i
$178$	−3.62757	−	2.79730i	−0.271898	−	0.209666i
$179$	−8.30296	+	14.3811i	−0.620592	+	1.07490i	0.368784	+	0.929515i	$0.379774\pi$
$179$	−8.30296	+	14.3811i	−0.620592	+	1.07490i	−0.989376	+	0.145382i	$0.953559\pi$
$180$	9.31043	−	7.38718i	0.693959	−	0.550608i
$181$	10.2752			0.763750			0.381875	−	0.924214i	$-0.375278\pi$
$181$	10.2752			0.763750			0.381875	+	0.924214i	$0.375278\pi$
$182$	−4.55933	−	13.5315i	−0.337960	−	1.00302i
$183$	0.915540	+	4.36292i	0.0676787	+	0.322516i
$184$	4.24160	−	3.20678i	0.312695	−	0.236407i
$185$	8.97308	+	5.18061i	0.659714	+	0.380886i
$186$	4.36669	−	9.03887i	0.320181	−	0.662762i
$187$		−	31.5326i		−	2.30589i
$188$	5.25160	+	1.43402i	0.383012	+	0.104587i
$189$	−13.2465	−	6.02172i	−0.963541	−	0.438015i
$190$	4.14287	+	10.0696i	0.300555	+	0.730524i
$191$	−10.0558	−	17.4171i	−0.727611	−	1.26026i	−0.957890	−	0.287134i	$-0.907297\pi$
$191$	−10.0558	−	17.4171i	−0.727611	−	1.26026i	0.230280	−	0.973124i	$-0.426036\pi$
$192$	−6.08121	−	12.4507i	−0.438874	−	0.898549i
$193$	3.99386	−	6.91758i	0.287485	−	0.497938i	−0.685724	−	0.727862i	$-0.740514\pi$
$193$	3.99386	−	6.91758i	0.287485	−	0.497938i	0.973209	+	0.229924i	$0.0738476\pi$
$194$	−6.79034	−	16.5045i	−0.487518	−	1.18495i
$195$	11.4784	+	4.61225i	0.821983	+	0.330290i
$196$	1.19625	−	1.18490i	0.0854467	−	0.0846360i
$197$	−13.2446	−	7.64680i	−0.943642	−	0.544812i	−0.0525419	−	0.998619i	$-0.516732\pi$
$197$	−13.2446	−	7.64680i	−0.943642	−	0.544812i	−0.891100	+	0.453807i	$0.850066\pi$
$198$	−16.4394	+	4.73447i	−1.16830	+	0.336464i
$199$	2.39424	−	1.38231i	0.169723	−	0.0979896i	−0.412732	−	0.910852i	$-0.635425\pi$
$199$	2.39424	−	1.38231i	0.169723	−	0.0979896i	0.582455	+	0.812863i	$0.302092\pi$
$200$	2.80400	+	1.18501i	0.198273	+	0.0837931i
$201$	8.68498	+	9.69613i	0.612592	+	0.683913i
$202$	5.87150	+	4.52763i	0.413117	+	0.318563i
$203$	−5.63994			−0.395846
$204$	27.0410	+	1.61684i	1.89325	+	0.113202i
$205$	4.13158	−	7.15610i	0.288562	−	0.499804i
$206$	−0.810312	+	6.04360i	−0.0564571	+	0.421077i
$207$	5.16418	−	2.26720i	0.358935	−	0.157581i
$208$	8.12496	−	11.9157i	0.563364	−	0.826208i
$209$		−	15.6732i		−	1.08414i
$210$	0.998609	+	13.5506i	0.0689106	+	0.935083i
$211$	17.9842	+	10.3832i	1.23808	+	0.714808i	0.968702	−	0.248226i	$-0.0798475\pi$
$211$	17.9842	+	10.3832i	1.23808	+	0.714808i	0.269381	+	0.963034i	$0.413181\pi$
$212$	0.657461	−	2.40772i	0.0451546	−	0.165363i
$213$	5.30800	+	25.2947i	0.363698	+	1.73317i
$214$	11.9469	−	15.4929i	0.816674	−	1.05908i
$215$	−2.36155	−	4.09032i	−0.161056	−	0.278958i
$216$	−3.21713	−	14.3405i	−0.218898	−	0.975748i
$217$	5.73810	+	9.93868i	0.389528	+	0.674682i
$218$	−13.2825	−	1.78089i	−0.899606	−	0.120617i
$219$	−4.33580	−	1.42123i	−0.292986	−	0.0960382i
$220$	11.2419	+	11.3495i	0.757927	+	0.765186i
$221$	12.4738	+	25.2861i	0.839077	+	1.70093i
$222$	10.5952	−	7.20447i	0.711102	−	0.483532i
$223$	0.964251	+	0.556711i	0.0645710	+	0.0372801i	0.531938	−	0.846783i	$-0.321464\pi$
$223$	0.964251	+	0.556711i	0.0645710	+	0.0372801i	−0.467367	+	0.884063i	$0.654797\pi$
$224$	15.6798	+	2.25467i	1.04765	+	0.150647i
$225$	2.60225	+	1.91136i	0.173484	+	0.127424i
$226$	16.0809	−	6.61607i	1.06968	−	0.440094i
$227$	−1.97871	−	3.42722i	−0.131331	−	0.227473i	0.792859	−	0.609406i	$-0.208592\pi$
$227$	−1.97871	−	3.42722i	−0.131331	−	0.227473i	−0.924190	+	0.381933i	$0.875259\pi$
$228$	13.4406	+	0.803646i	0.890127	+	0.0532227i
$229$	−3.59696			−0.237694			−0.118847	−	0.992913i	$-0.537920\pi$
$229$	−3.59696			−0.237694			−0.118847	+	0.992913i	$0.537920\pi$
$230$	−4.17051	−	3.21596i	−0.274995	−	0.212054i
$231$	6.09200	−	18.5850i	0.400824	−	1.22280i
$232$	−3.43542	−	4.54403i	−0.225547	−	0.298330i
$233$			0.850018i			0.0556865i	0.999612	+	0.0278433i	$0.00886393\pi$
$233$			0.850018i			0.0556865i	−0.999612	+	0.0278433i	$0.991136\pi$
$234$	11.3100	−	10.2997i	0.739355	−	0.673316i
$235$		−	5.39173i		−	0.351717i
$236$	−0.428070	−	1.62859i	−0.0278650	−	0.106012i
$237$	−3.85148	+	11.7498i	−0.250180	+	0.763231i
$238$	−18.9114	+	24.5246i	−1.22585	+	1.58969i
$239$	2.44269			0.158005			0.0790023	−	0.996874i	$-0.474827\pi$
$239$	2.44269			0.158005			0.0790023	+	0.996874i	$0.474827\pi$
$240$	−10.3093	+	9.05858i	−0.665462	+	0.584729i
$241$	−6.95115	−	12.0397i	−0.447763	−	0.775548i	0.550477	−	0.834850i	$-0.314446\pi$
$241$	−6.95115	−	12.0397i	−0.447763	−	0.775548i	−0.998240	+	0.0593022i	$0.981112\pi$
$242$	−2.83003	−	6.87861i	−0.181921	−	0.442174i
$243$	0.202251	−	15.5871i	0.0129744	−	0.999916i
$244$	−1.30858	−	4.97848i	−0.0837733	−	0.318715i
$245$	−1.44421	−	0.833812i	−0.0922669	−	0.0532703i
$246$	−5.74562	−	8.44973i	−0.366327	−	0.538735i
$247$	6.20005	+	12.5684i	0.394499	+	0.799706i
$248$	−4.51226	+	10.6770i	−0.286529	+	0.677990i
$249$	−22.4032	−	7.34356i	−1.41974	−	0.465379i
$250$	2.26198	−	16.8707i	0.143060	−	1.06700i
$251$	9.31600	+	16.1358i	0.588021	+	1.01848i	0.994491	+	0.104818i	$0.0334260\pi$
$251$	9.31600	+	16.1358i	0.588021	+	1.01848i	−0.406471	+	0.913664i	$0.633241\pi$
$252$	15.6253	+	6.17718i	0.984301	+	0.389125i
$253$	3.79033	+	6.56504i	0.238296	+	0.412741i
$254$	8.67594	+	6.69019i	0.544377	+	0.419780i
$255$	−5.51011	−	26.2579i	−0.345056	−	1.64433i
$256$	7.73438	+	14.0064i	0.483399	+	0.875400i
$257$	24.1583	+	13.9478i	1.50695	+	0.870039i	0.999967	+	0.00808340i	$0.00257305\pi$
$257$	24.1583	+	13.9478i	1.50695	+	0.870039i	0.506984	+	0.861955i	$0.330760\pi$
$258$	−5.82474	+	0.429252i	−0.362632	+	0.0267241i
$259$			14.6477i			0.910167i
$260$	−13.5046	−	4.65414i	−0.837518	−	0.288637i
$261$	−2.42885	−	5.53239i	−0.150342	−	0.342446i
$262$	−15.9921	−	2.14419i	−0.987998	−	0.132469i
$263$	14.0576	−	24.3485i	0.866828	−	1.50139i	0.00160803	−	0.999999i	$-0.499488\pi$
$263$	14.0576	−	24.3485i	0.866828	−	1.50139i	0.865220	−	0.501392i	$-0.167179\pi$
$264$	18.6845	−	6.41232i	1.14995	−	0.394651i
$265$	−2.47196			−0.151851
$266$	−9.39986	+	12.1899i	−0.576343	+	0.747409i
$267$	3.74324	+	4.17904i	0.229082	+	0.255753i
$268$	−10.5776	−	10.6789i	−0.646130	−	0.652319i
$269$	5.29540	−	3.05730i	0.322866	−	0.186407i	−0.329803	−	0.944050i	$-0.606982\pi$
$269$	5.29540	−	3.05730i	0.322866	−	0.186407i	0.652669	+	0.757643i	$0.273649\pi$
$270$	−12.8622	+	6.81517i	−0.782767	+	0.414758i
$271$	−5.91118	−	3.41282i	−0.359079	−	0.207314i	0.309598	−	0.950868i	$-0.399806\pi$
$271$	−5.91118	−	3.41282i	−0.359079	−	0.207314i	−0.668677	+	0.743553i	$0.733139\pi$
$272$	−31.2786	−	0.298178i	−1.89654	−	0.0180797i
$273$	2.46672	+	17.3132i	0.149293	+	1.04785i
$274$	−7.11632	+	2.92783i	−0.429913	+	0.176877i
$275$	−2.16990	+	3.75839i	−0.130850	+	0.226639i
$276$	−5.82424	+	2.91379i	−0.350578	+	0.175390i
$277$	10.8046	+	18.7141i	0.649186	+	1.12442i	0.983318	+	0.181897i	$0.0582236\pi$
$277$	10.8046	+	18.7141i	0.649186	+	1.12442i	−0.334132	+	0.942526i	$0.608443\pi$
$278$	−5.20831	+	2.14283i	−0.312374	+	0.128518i
$279$	−7.27803	+	9.90879i	−0.435724	+	0.593224i
$280$	−1.93661	−	15.5694i	−0.115735	−	0.930448i
$281$		−	0.713464i		−	0.0425617i	−0.999774	−	0.0212808i	$-0.993226\pi$
$281$		−	0.713464i		−	0.0425617i	0.999774	−	0.0212808i	$-0.00677441\pi$
$282$	−6.00349	−	2.90029i	−0.357503	−	0.172710i
$283$	−1.60203	−	0.924935i	−0.0952310	−	0.0549817i	0.451628	−	0.892206i	$-0.350843\pi$
$283$	−1.60203	−	0.924935i	−0.0952310	−	0.0549817i	−0.546859	+	0.837225i	$0.684177\pi$
$284$	−7.58671	−	28.8636i	−0.450188	−	1.71274i
$285$	−2.73878	−	13.0514i	−0.162231	−	0.773098i
$286$	15.4278	+	13.5915i	0.912267	+	0.803682i
$287$	11.6817			0.689548
$288$	4.54087	+	16.3518i	0.267573	+	0.963538i
$289$	22.0762	−	38.2371i	1.29860	−	2.24924i
$290$	−3.44526	+	4.46787i	−0.202313	+	0.262362i
$291$	4.48898	+	21.3918i	0.263148	+	1.25401i
$292$	5.08257	+	1.38787i	0.297435	+	0.0812189i
$293$	−5.46613	+	3.15587i	−0.319335	+	0.184368i	−0.651096	−	0.758995i	$-0.725690\pi$
$293$	−5.46613	+	3.15587i	−0.319335	+	0.184368i	0.331761	+	0.943363i	$0.392357\pi$
$294$	−1.70528	+	1.15955i	−0.0994539	+	0.0676263i
$295$	−1.44434	+	0.833889i	−0.0840926	+	0.0485509i
$296$	−11.8015	+	8.92229i	−0.685949	+	0.518598i
$297$	20.8541	−	2.02785i	1.21008	−	0.117668i
$298$	−0.957528	+	0.393950i	−0.0554681	+	0.0228209i
$299$	−5.63649	−	3.76513i	−0.325967	−	0.217743i
$300$	−3.11176	−	2.05353i	−0.179658	−	0.118560i
$301$	3.33854	−	5.78252i	0.192430	−	0.333299i
$302$	−2.39059	+	17.8299i	−0.137563	+	1.02599i
$303$	−6.05871	−	6.76409i	−0.348064	−	0.388587i
$304$	−15.5469	−	0.148208i	−0.891676	−	0.00850033i
$305$	−4.41524	+	2.54914i	−0.252816	+	0.145963i
$306$	−32.2012	−	7.98921i	−1.84082	−	0.456713i
$307$			2.21488i			0.126410i	0.998001	+	0.0632050i	$0.0201322\pi$
$307$			2.21488i			0.126410i	−0.998001	+	0.0632050i	$0.979868\pi$
$308$	−5.94897	+	21.7860i	−0.338974	+	1.24137i
$309$	2.32619	−	7.09657i	0.132332	−	0.403710i
$310$	11.3785	+	1.52560i	0.646254	+	0.0866483i
$311$	25.4362			1.44235			0.721177	−	0.692750i	$-0.243601\pi$
$311$	25.4362			1.44235			0.721177	+	0.692750i	$0.243601\pi$
$312$	−12.4465	+	12.5333i	−0.704646	+	0.709559i
$313$	−27.4174			−1.54972			−0.774861	−	0.632131i	$-0.782180\pi$
$313$	−27.4174			−1.54972			−0.774861	+	0.632131i	$0.782180\pi$
$314$	24.0277	+	3.22158i	1.35596	+	0.181804i
$315$	1.82533	−	16.5407i	0.102846	−	0.931961i
$316$	3.76106	−	13.7735i	0.211576	−	0.774821i
$317$		−	13.2937i		−	0.746646i	−0.927701	−	0.373323i	$-0.878218\pi$
$317$		−	13.2937i		−	0.746646i	0.927701	−	0.373323i	$-0.121782\pi$
$318$	−1.32970	+	2.75244i	−0.0745661	+	0.154349i
$319$	7.03313	−	4.06058i	0.393780	−	0.227349i
$320$	11.3644	−	11.0440i	0.635290	−	0.617377i
$321$	−17.8482	+	15.9869i	−0.996189	+	0.892303i
$322$	0.989387	−	7.37921i	0.0551364	−	0.411227i
$323$	15.1978	−	26.3234i	0.845628	−	1.46467i
$324$	0.669692	+	17.9875i	0.0372051	+	0.999308i
$325$	0.253298	−	3.87224i	0.0140505	−	0.214793i
$326$	−20.8428	+	8.57524i	−1.15438	+	0.474939i
$327$	15.5967	+	5.11247i	0.862501	+	0.282720i
$328$	7.11559	+	9.41179i	0.392893	+	0.519679i
$329$	6.60113	−	3.81116i	0.363932	−	0.210116i
$330$	−11.0013	−	16.1790i	−0.605602	−	0.890623i
$331$	28.0738	−	16.2084i	1.54307	−	0.890894i	0.544432	−	0.838805i	$-0.316745\pi$
$331$	28.0738	−	16.2084i	1.54307	−	0.890894i	0.998642	−	0.0520889i	$-0.0165879\pi$
$332$	26.2618	+	7.17115i	1.44130	+	0.393568i
$333$	−14.3684	+	6.30808i	−0.787384	+	0.345681i
$334$	−15.9946	+	20.7420i	−0.875186	+	1.13495i
$335$	−7.44342	+	12.8924i	−0.406677	+	0.704386i
$336$	−18.3777	−	6.21866i	−1.00258	−	0.339256i
$337$	−23.3411			−1.27147			−0.635736	−	0.771906i	$-0.719303\pi$
$337$	−23.3411			−1.27147			−0.635736	+	0.771906i	$0.719303\pi$
$338$	−17.7482	−	4.79606i	−0.965374	−	0.260871i
$339$	−20.8428	+	4.37377i	−1.13202	+	0.237551i
$340$	7.87559	+	29.9626i	0.427114	+	1.62495i
$341$	−14.3111	−	8.26250i	−0.774988	−	0.447440i
$342$	−16.0055	−	3.97101i	−0.865477	−	0.214728i
$343$			17.2448i			0.931132i
$344$	6.69249	−	0.832451i	0.360835	−	0.0448827i
$345$	4.30348	+	4.80452i	0.231692	+	0.258667i
$346$	18.2887	−	7.52440i	0.983205	−	0.404514i
$347$	4.49629	+	7.78780i	0.241374	+	0.418071i	0.961106	−	0.276181i	$-0.0890688\pi$
$347$	4.49629	+	7.78780i	0.241374	+	0.418071i	−0.719732	+	0.694252i	$0.755735\pi$
$348$	3.12155	+	6.23951i	0.167333	+	0.334473i
$349$	−13.8208	+	23.9383i	−0.739809	+	1.28139i	0.212772	+	0.977102i	$0.431751\pi$
$349$	−13.8208	+	23.9383i	−0.739809	+	1.28139i	−0.952581	+	0.304285i	$0.901582\pi$
$350$	3.94171	−	1.62172i	0.210693	−	0.0866844i
$351$	−15.9208	+	9.87567i	−0.849788	+	0.527124i
$352$	−21.1764	+	8.47734i	−1.12870	+	0.451844i
$353$	−1.88888	−	1.09054i	−0.100535	−	0.0580438i	0.448890	−	0.893587i	$-0.351820\pi$
$353$	−1.88888	−	1.09054i	−0.100535	−	0.0580438i	−0.549424	+	0.835543i	$0.685153\pi$
$354$	0.151574	+	2.05678i	0.00805605	+	0.109317i
$355$	−25.5981	+	14.7791i	−1.35861	+	0.784392i
$356$	−4.55896	−	4.60263i	−0.241624	−	0.243939i
$357$	28.2529	−	25.3066i	1.49530	−	1.33937i
$358$	−14.3407	+	18.5972i	−0.757930	+	0.982894i
$359$	−3.58192			−0.189046			−0.0945231	−	0.995523i	$-0.530133\pi$
$359$	−3.58192			−0.189046			−0.0945231	+	0.995523i	$0.530133\pi$
$360$	14.4385	−	8.60466i	0.760974	−	0.453505i
$361$	−1.94599	+	3.37055i	−0.102420	+	0.177397i
$362$	14.4025	+	1.93105i	0.756977	+	0.101494i
$363$	1.87088	+	8.91550i	0.0981958	+	0.467943i
$364$	−3.84767	−	19.8235i	−0.201673	−	1.03904i
$365$		−	5.21819i		−	0.273132i
$366$	0.463350	+	6.28744i	0.0242197	+	0.328650i
$367$	−29.3819	−	16.9636i	−1.53372	−	0.885495i	−0.999186	−	0.0403498i	$-0.987153\pi$
$367$	−29.3819	−	16.9636i	−1.53372	−	0.885495i	−0.534537	−	0.845145i	$-0.679514\pi$
$368$	6.54799	−	3.69771i	0.341338	−	0.192757i
$369$	5.03074	+	11.4589i	0.261890	+	0.596527i
$370$	11.6037	+	8.94785i	0.603248	+	0.465177i
$371$	−1.74732	−	3.02644i	−0.0907161	−	0.157125i
$372$	7.81936	−	11.8489i	0.405415	−	0.614336i
$373$	1.94382	+	3.36679i	0.100647	+	0.174326i	0.911951	−	0.410298i	$-0.134575\pi$
$373$	1.94382	+	3.36679i	0.100647	+	0.174326i	−0.811304	+	0.584624i	$0.801242\pi$
$374$	5.92602	−	44.1984i	0.306427	−	2.28544i
$375$	−6.49356	+	19.8101i	−0.335326	+	1.02299i
$376$	7.09151	+	2.99698i	0.365717	+	0.154557i
$377$	−4.03359	+	6.03838i	−0.207740	+	0.310992i
$378$	−17.4355	−	10.9299i	−0.896788	−	0.562174i
$379$	15.2264	+	8.79094i	0.782125	+	0.451560i	0.837183	−	0.546923i	$-0.184201\pi$
$379$	15.2264	+	8.79094i	0.782125	+	0.451560i	−0.0550576	+	0.998483i	$0.517534\pi$
$380$	3.91454	+	14.8928i	0.200811	+	0.763986i
$381$	−8.95257	−	9.99487i	−0.458654	−	0.512053i
$382$	−10.8216	−	26.3029i	−0.553683	−	1.34577i
$383$	−5.29523	−	9.17162i	−0.270574	−	0.468648i	0.698435	−	0.715673i	$-0.253880\pi$
$383$	−5.29523	−	9.17162i	−0.270574	−	0.468648i	−0.969009	+	0.247026i	$0.920547\pi$
$384$	−6.18397	−	18.5946i	−0.315575	−	0.948901i
$385$	22.3673			1.13994
$386$	6.89812	−	8.94559i	0.351105	−	0.455318i
$387$	7.11000	+	0.784620i	0.361422	+	0.0398845i
$388$	−6.41609	−	24.4100i	−0.325727	−	1.23923i
$389$			13.7221i			0.695737i	0.937543	+	0.347868i	$0.113094\pi$
$389$			13.7221i			0.695737i	−0.937543	+	0.347868i	$0.886906\pi$
$390$	15.2221	+	8.62202i	0.770801	+	0.436593i
$391$			14.7015i			0.743485i
$392$	1.89944	−	1.43603i	0.0959360	−	0.0725305i
$393$	18.7785	+	6.15541i	0.947248	+	0.310499i
$394$	−17.1275	−	13.2074i	−0.862873	−	0.665379i
$395$	−14.1410			−0.711513
$396$	−23.9325	+	3.54665i	−1.20265	+	0.178226i
$397$	3.61632	+	6.26365i	0.181498	+	0.314364i	0.942391	−	0.334514i	$-0.108572\pi$
$397$	3.61632	+	6.26365i	0.181498	+	0.314364i	−0.760893	+	0.648878i	$0.775239\pi$
$398$	3.61571	−	1.48759i	0.181239	−	0.0745663i
$399$	14.0430	−	12.5785i	0.703030	−	0.629715i
$400$	3.70759	+	2.18796i	0.185379	+	0.109398i
$401$	−8.45838	−	4.88345i	−0.422391	−	0.243868i	0.273709	−	0.961813i	$-0.411750\pi$
$401$	−8.45838	−	4.88345i	−0.422391	−	0.243868i	−0.696100	+	0.717945i	$0.745083\pi$
$402$	10.3513	+	15.2230i	0.516274	+	0.759253i
$403$	14.7446	+	0.964502i	0.734480	+	0.0480453i
$404$	7.37902	+	7.44970i	0.367120	+	0.370636i
$405$	17.0113	−	5.33274i	0.845299	−	0.264986i
$406$	−7.90535	−	1.05993i	−0.392336	−	0.0526035i
$407$	−10.5459	−	18.2661i	−0.522742	−	0.905415i
$408$	37.5987	+	7.34817i	1.86141	+	0.363789i
$409$	13.0347	+	22.5767i	0.644524	+	1.11635i	0.984411	+	0.175882i	$0.0562777\pi$
$409$	13.0347	+	22.5767i	0.644524	+	1.11635i	−0.339887	+	0.940466i	$0.610389\pi$
$410$	7.13598	−	9.25404i	0.352421	−	0.457024i
$411$	9.22361	−	1.93554i	0.454967	−	0.0954730i
$412$	−2.27158	+	8.31885i	−0.111913	+	0.409840i
$413$	−2.04187	−	1.17888i	−0.100474	−	0.0580087i
$414$	7.66456	−	2.20735i	0.376693	−	0.108485i
$415$		−	26.9625i		−	1.32354i
$416$	13.6279	−	15.1750i	0.668162	−	0.744016i
$417$	6.75060	−	1.41659i	0.330578	−	0.0693705i
$418$	2.94551	−	21.9686i	0.144069	−	1.07452i
$419$	−14.5467	+	25.1957i	−0.710655	+	1.23089i	0.253956	+	0.967216i	$0.418268\pi$
$419$	−14.5467	+	25.1957i	−0.710655	+	1.23089i	−0.964612	+	0.263675i	$0.915065\pi$
$420$	−1.14689	+	19.1812i	−0.0559624	+	0.935947i
$421$	−15.6745			−0.763927			−0.381964	−	0.924177i	$-0.624752\pi$
$421$	−15.6745			−0.763927			−0.381964	+	0.924177i	$0.624752\pi$
$422$	23.2566	+	17.9336i	1.13211	+	0.872995i
$423$	6.58128	+	4.83396i	0.319993	+	0.235035i
$424$	1.37403	−	3.25127i	0.0667289	−	0.157895i
$425$	−7.28878	+	4.20818i	−0.353558	+	0.204127i
$426$	2.68635	+	36.4524i	0.130154	+	1.76613i
$427$	−6.24187	−	3.60374i	−0.302065	−	0.174397i
$428$	19.6573	−	19.4708i	0.950170	−	0.941155i
$429$	−15.5410	−	19.8140i	−0.750329	−	0.956630i
$430$	−2.54141	−	6.17710i	−0.122558	−	0.297886i
$431$	−3.63631	+	6.29827i	−0.175155	+	0.303377i	−0.940215	−	0.340582i	$-0.889376\pi$
$431$	−3.63631	+	6.29827i	−0.175155	+	0.303377i	0.765060	+	0.643959i	$0.222709\pi$
$432$	−1.81431	−	20.7053i	−0.0872910	−	0.996183i
$433$	−6.50796	−	11.2721i	−0.312753	−	0.541704i	0.666205	−	0.745769i	$-0.267918\pi$
$433$	−6.50796	−	11.2721i	−0.312753	−	0.541704i	−0.978957	+	0.204066i	$0.934584\pi$
$434$	6.17512	+	15.0091i	0.296415	+	0.720462i
$435$	5.14708	−	4.61032i	0.246784	−	0.221048i
$436$	−18.2830	−	4.99244i	−0.875598	−	0.239095i
$437$			7.30731i			0.349556i
$438$	−5.81026	−	2.80694i	−0.277625	−	0.134121i
$439$	−23.4044	−	13.5125i	−1.11703	−	0.644918i	−0.176390	−	0.984320i	$-0.556442\pi$
$439$	−23.4044	−	13.5125i	−1.11703	−	0.644918i	−0.940641	+	0.339402i	$0.889775\pi$
$440$	13.6244	+	18.0210i	0.649520	+	0.859120i
$441$	2.31258	−	1.01528i	0.110123	−	0.0483465i
$442$	12.7320	+	37.7870i	0.605601	+	1.79734i
$443$	7.59619			0.360906			0.180453	−	0.983584i	$-0.442244\pi$
$443$	7.59619			0.360906			0.180453	+	0.983584i	$0.442244\pi$
$444$	16.2049	−	8.10711i	0.769051	−	0.384747i
$445$	−3.20812	+	5.55663i	−0.152080	+	0.263410i
$446$	1.24694	+	0.961540i	0.0590443	+	0.0455302i
$447$	1.24107	−	0.260434i	0.0587007	−	0.0123181i
$448$	21.5542	+	6.10706i	1.01834	+	0.288531i
$449$	6.82867	−	3.94253i	0.322265	−	0.186060i	−0.330137	−	0.943933i	$-0.607095\pi$
$449$	6.82867	−	3.94253i	0.322265	−	0.186060i	0.652402	+	0.757873i	$0.273762\pi$
$450$	3.28830	+	3.16815i	0.155012	+	0.149348i
$451$	−14.5673	+	8.41044i	−0.685948	+	0.396032i
$452$	23.7835	−	6.25142i	1.11868	−	0.294042i
$453$	6.86275	−	20.9363i	0.322440	−	0.983675i
$454$	−2.12941	−	5.17570i	−0.0999380	−	0.242908i
$455$	−17.9364	+	8.84812i	−0.840871	+	0.414806i
$456$	18.6883	+	3.65238i	0.875160	+	0.171038i
$457$	7.82778	−	13.5581i	0.366168	−	0.634222i	−0.622795	−	0.782385i	$-0.714003\pi$
$457$	7.82778	−	13.5581i	0.366168	−	0.634222i	0.988963	+	0.148164i	$0.0473362\pi$
$458$	−5.04175	−	0.675987i	−0.235586	−	0.0315868i
$459$	36.9911	+	16.8158i	1.72660	+	0.784893i
$460$	−5.24130	−	5.29150i	−0.244377	−	0.246717i
$461$	−34.1273	+	19.7034i	−1.58947	+	0.917679i	−0.596072	+	0.802931i	$0.703273\pi$
$461$	−34.1273	+	19.7034i	−1.58947	+	0.917679i	−0.993395	+	0.114749i	$0.963394\pi$
$462$	12.0317	−	24.9052i	0.559766	−	1.15869i
$463$		−	34.9373i		−	1.62367i	−0.583884	−	0.811837i	$-0.698468\pi$
$463$		−	34.9373i		−	1.62367i	0.583884	−	0.811837i	$-0.301532\pi$
$464$	−3.96136	−	7.01487i	−0.183902	−	0.325657i
$465$	−13.3610	−	4.37960i	−0.619599	−	0.203099i
$466$	−0.159746	+	1.19145i	−0.00740011	+	0.0551926i
$467$	−22.6893			−1.04994			−0.524969	−	0.851121i	$-0.675923\pi$
$467$	−22.6893			−1.04994			−0.524969	+	0.851121i	$0.675923\pi$
$468$	17.7885	−	12.3113i	0.822274	−	0.569092i
$469$	−21.0457			−0.971798
$470$	1.01328	−	7.55743i	0.0467392	−	0.348598i
$471$	−28.2140	−	9.24831i	−1.30003	−	0.426140i
$472$	−0.293948	−	2.36319i	−0.0135300	−	0.108775i
$473$			9.61458i			0.442079i
$474$	−7.60667	+	15.7455i	−0.349386	+	0.723216i
$475$	−3.62286	+	2.09166i	−0.166228	+	0.0959720i
$476$	−31.1166	+	30.8214i	−1.42623	+	1.41269i
$477$	2.21624	−	3.01734i	0.101475	−	0.138154i
$478$	3.42385	+	0.459062i	0.156603	+	0.0209970i
$479$	−3.31239	+	5.73723i	−0.151347	+	0.262141i	−0.931723	−	0.363170i	$-0.881694\pi$
$479$	−3.31239	+	5.73723i	−0.151347	+	0.262141i	0.780376	+	0.625311i	$0.215028\pi$
$480$	−16.1526	+	10.7597i	−0.737264	+	0.491110i
$481$	15.6825	+	10.4758i	0.715062	+	0.477656i
$482$	−7.48056	−	18.1821i	−0.340730	−	0.828172i
$483$	−2.84027	+	8.66488i	−0.129237	+	0.394266i
$484$	−2.67405	−	10.1734i	−0.121548	−	0.462427i
$485$	−21.6483	+	12.4987i	−0.983001	+	0.567536i
$486$	3.21283	−	21.8100i	0.145737	−	0.989323i
$487$	−2.69276	+	1.55467i	−0.122021	+	0.0704487i	−0.559768	−	0.828649i	$-0.689110\pi$
$487$	−2.69276	+	1.55467i	−0.122021	+	0.0704487i	0.437747	+	0.899098i	$0.355776\pi$
$488$	−0.898578	−	7.22412i	−0.0406767	−	0.327021i
$489$	27.0148	−	5.66894i	1.22165	−	0.256359i
$490$	−1.86760	−	1.44014i	−0.0843696	−	0.0650591i
$491$	2.24938	−	3.89604i	0.101513	−	0.175826i	−0.810795	−	0.585330i	$-0.800965\pi$
$491$	2.24938	−	3.89604i	0.101513	−	0.175826i	0.912308	+	0.409504i	$0.134298\pi$
$492$	−6.46548	−	12.9235i	−0.291486	−	0.582638i
$493$	15.7497			0.709330
$494$	6.32842	+	18.7819i	0.284729	+	0.845038i
$495$	9.63252	+	21.9407i	0.432950	+	0.986163i
$496$	−8.33126	+	14.1176i	−0.374085	+	0.633901i
$497$	−36.1883	−	20.8933i	−1.62327	−	0.937193i
$498$	−30.0218	−	14.5035i	−1.34531	−	0.649919i
$499$		−	6.63001i		−	0.296800i	−0.988927	−	0.148400i	$-0.952588\pi$
$499$		−	6.63001i		−	0.296800i	0.988927	−	0.148400i	$-0.0474123\pi$
$500$	6.34111	−	23.2220i	0.283583	−	1.03852i
$501$	23.8953	−	21.4034i	1.06756	−	0.956232i
$502$	10.0255	+	24.3678i	0.447461	+	1.08759i
$503$	21.1482	+	36.6298i	0.942952	+	1.63324i	0.759800	+	0.650157i	$0.225297\pi$
$503$	21.1482	+	36.6298i	0.942952	+	1.63324i	0.183152	+	0.983085i	$0.441370\pi$
$504$	20.7406	+	11.5949i	0.923861	+	0.516477i
$505$	5.19258	−	8.99382i	0.231067	−	0.400220i
$506$	4.07901	+	9.91436i	0.181334	+	0.440747i
$507$	20.3005	+	9.74114i	0.901577	+	0.432619i
$508$	10.9035	+	11.0079i	0.483765	+	0.488399i
$509$	12.2759	+	7.08748i	0.544118	+	0.314147i	0.746746	−	0.665109i	$-0.231615\pi$
$509$	12.2759	+	7.08748i	0.544118	+	0.314147i	−0.202628	+	0.979256i	$0.564948\pi$
$510$	−2.78864	−	37.8405i	−0.123483	−	1.67560i
$511$	6.38867	−	3.68850i	0.282618	−	0.163170i
$512$	8.20880	+	21.0859i	0.362781	+	0.931874i
$513$	18.3863	+	8.35823i	0.811776	+	0.369025i
$514$	31.2407	+	24.0903i	1.37797	+	1.06258i
$515$	8.54082			0.376353
$516$	−8.24504	−	0.492990i	−0.362967	−	0.0217027i
$517$	−5.48784	+	9.50521i	−0.241355	+	0.418039i
$518$	−2.75279	+	20.5313i	−0.120951	+	0.902095i
$519$	−23.7043	+	4.97425i	−1.04050	+	0.218346i
$520$	−18.0543	−	9.06152i	−0.791733	−	0.397374i
$521$		−	33.0887i		−	1.44964i	−0.688938	−	0.724820i	$-0.741923\pi$
$521$		−	33.0887i		−	1.44964i	0.688938	−	0.724820i	$-0.258077\pi$
$522$	−2.36474	−	8.21105i	−0.103502	−	0.359388i
$523$	24.6943	+	14.2572i	1.07981	+	0.623426i	0.930844	−	0.365417i	$-0.119074\pi$
$523$	24.6943	+	14.2572i	1.07981	+	0.623426i	0.148961	+	0.988843i	$0.452407\pi$
$524$	−22.0128	−	6.01090i	−0.961632	−	0.262587i
$525$	−5.10893	+	1.07209i	−0.222972	+	0.0467898i
$526$	24.2800	−	31.4867i	1.05866	−	1.37288i
$527$	−16.0238	−	27.7540i	−0.698007	−	1.20898i
$528$	27.3946	−	5.47653i	1.19220	−	0.238335i
$529$	9.73284	+	16.8578i	0.423167	+	0.732946i
$530$	−3.46487	−	0.464562i	−0.150504	−	0.0201793i
$531$	0.277058	−	2.51062i	0.0120233	−	0.108952i
$532$	−15.4664	+	15.3197i	−0.670553	+	0.664191i
$533$	8.35454	−	12.5069i	0.361875	−	0.541736i
$534$	4.46141	+	6.56112i	0.193064	+	0.283928i
$535$	−23.7317	−	13.7015i	−1.02601	−	0.592368i
$536$	−12.8194	−	16.9562i	−0.553714	−	0.732397i
$537$	21.4244	−	19.1902i	0.924532	−	0.828118i
$538$	7.99697	−	3.29015i	0.344774	−	0.141848i
$539$	1.69735	+	2.93990i	0.0731101	+	0.126630i
$540$	−19.3093	+	7.13541i	−0.830941	+	0.307059i
$541$	9.76861			0.419985			0.209993	−	0.977703i	$-0.432656\pi$
$541$	9.76861			0.419985			0.209993	+	0.977703i	$0.432656\pi$
$542$	−7.64415	−	5.89456i	−0.328345	−	0.253193i
$543$	−16.9118	−	5.54354i	−0.725755	−	0.237896i
$544$	−43.7862	−	6.29622i	−1.87732	−	0.269948i
$545$			18.7709i			0.804056i
$546$	0.203808	+	24.7310i	0.00872220	+	1.05839i
$547$			18.5829i			0.794549i	0.917700	+	0.397275i	$0.130044\pi$
$547$			18.5829i			0.794549i	−0.917700	+	0.397275i	$0.869956\pi$
$548$	−10.5250	+	2.76646i	−0.449605	+	0.118177i
$549$	0.846947	−	7.67480i	0.0361468	−	0.327552i
$550$	−3.74782	+	4.86022i	−0.159807	+	0.207241i
$551$	7.82832			0.333498
$552$	−8.71126	+	2.98961i	−0.370776	+	0.127246i
$553$	−9.99565	−	17.3130i	−0.425058	−	0.736222i
$554$	11.6275	+	28.2616i	0.494005	+	1.20072i
$555$	−11.9737	−	13.3677i	−0.508254	−	0.567428i
$556$	−7.70305	+	2.02472i	−0.326682	+	0.0858674i
$557$	−16.0205	−	9.24946i	−0.678812	−	0.391912i	0.120595	−	0.992702i	$-0.461520\pi$
$557$	−16.0205	−	9.24946i	−0.678812	−	0.391912i	−0.799407	+	0.600790i	$0.794853\pi$
$558$	−12.0636	+	12.5211i	−0.510692	+	0.530060i
$559$	−3.80336	−	7.70995i	−0.160865	−	0.326096i
$560$	0.211509	−	22.1871i	0.00893789	−	0.937576i
$561$	−17.0120	+	51.8990i	−0.718249	+	2.19118i
$562$	0.134083	−	1.00004i	0.00565596	−	0.0421842i
$563$	−9.52361	−	16.4954i	−0.401372	−	0.695198i	0.592519	−	0.805556i	$-0.298133\pi$
$563$	−9.52361	−	16.4954i	−0.401372	−	0.695198i	−0.993892	+	0.110359i	$0.964800\pi$
$564$	−7.86986	−	5.19351i	−0.331381	−	0.218686i
$565$	−12.1779	−	21.0927i	−0.512328	−	0.887379i
$566$	−2.07170	−	1.59753i	−0.0870800	−	0.0671491i
$567$	18.5534	+	17.0576i	0.779171	+	0.716352i
$568$	−5.20965	−	41.8830i	−0.218592	−	1.75737i
$569$	16.6680	+	9.62328i	0.698759	+	0.403429i	0.806885	−	0.590708i	$-0.201152\pi$
$569$	16.6680	+	9.62328i	0.698759	+	0.403429i	−0.108126	+	0.994137i	$0.534485\pi$
$570$	−1.38608	−	18.8085i	−0.0580567	−	0.787800i
$571$			14.9433i			0.625357i	0.949859	+	0.312678i	$0.101226\pi$
$571$			14.9433i			0.625357i	−0.949859	+	0.312678i	$0.898774\pi$
$572$	19.0705	+	21.9502i	0.797376	+	0.917784i
$573$	7.15400	+	34.0917i	0.298863	+	1.42420i
$574$	16.3739	+	2.19537i	0.683433	+	0.0916331i
$575$	1.01167	−	1.75227i	0.0421898	−	0.0730748i
$576$	3.29177	+	23.7732i	0.137157	+	0.990549i
$577$	−10.5158			−0.437777			−0.218889	−	0.975750i	$-0.570243\pi$
$577$	−10.5158			−0.437777			−0.218889	+	0.975750i	$0.570243\pi$
$578$	38.1296	−	49.4470i	1.58598	−	2.05672i
$579$	−10.3055	+	9.23081i	−0.428282	+	0.383619i
$580$	−5.66879	+	5.61500i	−0.235384	+	0.233150i
$581$	33.0104	−	19.0586i	1.36950	−	0.790683i
$582$	2.27185	+	30.8279i	0.0941712	+	1.27786i
$583$	4.35788	+	2.51602i	0.180485	+	0.104203i
$584$	6.86327	+	2.90052i	0.284004	+	0.120024i
$585$	−16.4037	−	13.7839i	−0.678211	−	0.569893i
$586$	−8.25480	+	3.39623i	−0.341003	+	0.140297i
$587$	10.4007	−	18.0146i	0.429284	−	0.743542i	−0.567526	−	0.823356i	$-0.692099\pi$
$587$	10.4007	−	18.0146i	0.429284	−	0.743542i	0.996810	+	0.0798138i	$0.0254326\pi$
$588$	−2.60816	+	1.30483i	−0.107559	+	0.0538102i
$589$	−7.96457	−	13.7950i	−0.328174	−	0.568414i
$590$	−2.18120	+	0.897399i	−0.0897986	+	0.0369453i
$591$	17.6737	+	19.7313i	0.726997	+	0.811638i
$592$	−18.2186	+	10.2882i	−0.748781	+	0.422843i
$593$			33.8531i			1.39018i	0.718922	+	0.695090i	$0.244636\pi$
$593$			33.8531i			1.39018i	−0.718922	+	0.695090i	$0.755364\pi$
$594$	29.6117	+	1.07680i	1.21498	+	0.0441816i
$595$	37.5662	+	21.6889i	1.54006	+	0.889157i
$596$	−1.41618	+	0.372238i	−0.0580088	+	0.0152475i
$597$	−4.68640	+	0.983422i	−0.191802	+	0.0402488i
$598$	−7.19292	−	6.33676i	−0.294140	−	0.259129i
$599$	−13.5256			−0.552642			−0.276321	−	0.961065i	$-0.589115\pi$
$599$	−13.5256			−0.552642			−0.276321	+	0.961065i	$0.589115\pi$
$600$	−3.97574	−	3.46317i	−0.162309	−	0.141383i
$601$	4.97195	−	8.61168i	0.202810	−	0.351278i	−0.746623	−	0.665248i	$-0.768326\pi$
$601$	4.97195	−	8.61168i	0.202810	−	0.351278i	0.949433	+	0.313970i	$0.101659\pi$
$602$	5.76626	−	7.47777i	0.235015	−	0.304771i
$603$	−9.06335	−	20.6443i	−0.369088	−	0.840701i
$604$	−6.70163	+	24.5423i	−0.272686	+	0.998613i
$605$	−9.02243	+	5.20910i	−0.366814	+	0.211780i
$606$	−7.22112	−	10.6197i	−0.293338	−	0.431394i
$607$	20.0249	−	11.5614i	0.812786	−	0.469262i	−0.0351367	−	0.999383i	$-0.511187\pi$
$607$	20.0249	−	11.5614i	0.812786	−	0.469262i	0.847922	+	0.530121i	$0.177853\pi$
$608$	−21.7638	−	3.12951i	−0.882639	−	0.126919i
$609$	9.28269	+	3.04278i	0.376154	+	0.123300i
$610$	−6.66779	+	2.74329i	−0.269971	+	0.111073i
$611$	0.640608	−	9.79315i	0.0259162	−	0.396188i
$612$	−43.6340	−	17.2499i	−1.76380	−	0.697286i
$613$	−13.2467	+	22.9439i	−0.535029	+	0.926697i	0.464133	+	0.885765i	$0.346366\pi$
$613$	−13.2467	+	22.9439i	−0.535029	+	0.926697i	−0.999162	+	0.0409317i	$0.986967\pi$
$614$	−0.416249	+	3.10453i	−0.0167984	+	0.125289i
$615$	−10.6609	+	9.54910i	−0.429887	+	0.385057i
$616$	−12.4328	+	29.4188i	−0.500932	+	1.18532i
$617$	−29.4281	+	16.9903i	−1.18473	+	0.684003i	−0.957104	−	0.289745i	$-0.906429\pi$
$617$	−29.4281	+	16.9903i	−1.18473	+	0.684003i	−0.227625	+	0.973749i	$0.573096\pi$
$618$	4.59423	−	9.50989i	0.184807	−	0.382544i
$619$			13.2158i			0.531187i	0.964085	+	0.265593i	$0.0855678\pi$
$619$			13.2158i			0.531187i	−0.964085	+	0.265593i	$0.914432\pi$
$620$	15.6622	+	4.27678i	0.629008	+	0.171760i
$621$	−9.72281	+	0.945443i	−0.390163	+	0.0379393i
$622$	35.6532	+	4.78030i	1.42956	+	0.191673i
$623$	−9.07070			−0.363410
$624$	−19.8014	+	15.2285i	−0.792689	+	0.609627i
$625$	−18.4604			−0.738414
$626$	−38.4302	−	5.15263i	−1.53598	−	0.205940i
$627$	−8.45577	+	25.7962i	−0.337691	+	1.03020i
$628$	33.0735	+	9.03119i	1.31978	+	0.360384i
$629$		−	40.9042i		−	1.63096i
$630$	5.66705	−	22.8415i	0.225781	−	0.910028i
$631$	−7.34162	+	4.23869i	−0.292265	+	0.168739i	−0.638963	−	0.769238i	$-0.720636\pi$
$631$	−7.34162	+	4.23869i	−0.292265	+	0.168739i	0.346698	+	0.937977i	$0.387303\pi$
$632$	7.86026	−	18.5991i	0.312664	−	0.739833i
$633$	−23.9981	−	26.7921i	−0.953839	−	1.06489i
$634$	2.49831	−	18.6333i	0.0992207	−	0.740024i
$635$	7.67275	−	13.2896i	0.304484	−	0.527382i
$636$	−2.38108	+	3.60812i	−0.0944160	+	0.143071i
$637$	−2.52408	−	1.68607i	−0.100008	−	0.0668044i
$638$	10.6213	−	4.36984i	0.420499	−	0.173004i
$639$	4.91032	−	44.4959i	0.194249	−	1.76023i
$640$	18.0047	−	13.3443i	0.711698	−	0.527479i
$641$	−12.4529	+	7.18968i	−0.491860	+	0.283975i	−0.725346	−	0.688385i	$-0.758320\pi$
$641$	−12.4529	+	7.18968i	−0.491860	+	0.283975i	0.233486	+	0.972360i	$0.424987\pi$
$642$	−28.0218	+	19.0541i	−1.10593	+	0.752007i
$643$	−7.39212	+	4.26784i	−0.291517	+	0.168307i	−0.638626	−	0.769518i	$-0.720497\pi$
$643$	−7.39212	+	4.26784i	−0.291517	+	0.168307i	0.347109	+	0.937825i	$0.387163\pi$
$644$	2.77359	−	10.1573i	0.109295	−	0.400253i
$645$	1.68008	+	8.00627i	0.0661532	+	0.315246i
$646$	26.2493	−	34.0405i	1.03277	−	1.33931i
$647$	16.2864	−	28.2089i	0.640285	−	1.10901i	−0.345084	−	0.938572i	$-0.612149\pi$
$647$	16.2864	−	28.2089i	0.640285	−	1.10901i	0.985369	−	0.170435i	$-0.0545172\pi$
$648$	−2.44176	+	25.3385i	−0.0959215	+	0.995389i
$649$	3.39501			0.133266
$650$	1.08276	−	5.38000i	0.0424694	−	0.211021i
$651$	−4.08227	−	19.4537i	−0.159997	−	0.762449i
$652$	−30.8263	+	8.10261i	−1.20725	+	0.317323i
$653$	33.8257	+	19.5293i	1.32370	+	0.764240i	0.984317	−	0.176407i	$-0.0564474\pi$
$653$	33.8257	+	19.5293i	1.32370	+	0.764240i	0.339386	+	0.940647i	$0.389781\pi$
$654$	20.9007	+	10.0971i	0.817281	+	0.394829i
$655$			22.6001i			0.883060i
$656$	8.20493	+	14.5295i	0.320349	+	0.567281i
$657$	6.36945	+	4.67837i	0.248496	+	0.182521i
$658$	9.96886	−	4.10143i	0.388626	−	0.159890i
$659$	6.42459	+	11.1277i	0.250266	+	0.433474i	0.963599	−	0.267351i	$-0.0861485\pi$
$659$	6.42459	+	11.1277i	0.250266	+	0.433474i	−0.713333	+	0.700826i	$0.752815\pi$
$660$	−12.3797	−	24.7451i	−0.481878	−	0.963201i
$661$	11.7808	−	20.4049i	0.458219	−	0.793658i	−0.540648	−	0.841249i	$-0.681821\pi$
$661$	11.7808	−	20.4049i	0.458219	−	0.793658i	0.998867	+	0.0475909i	$0.0151544\pi$
$662$	42.3963	−	17.4429i	1.64778	−	0.677936i
$663$	−6.88839	−	48.3476i	−0.267523	−	1.87767i
$664$	35.4627	+	14.9870i	1.37622	+	0.581610i
$665$	18.6722	+	10.7804i	0.724075	+	0.418045i
$666$	−21.3253	+	6.14156i	−0.826338	+	0.237981i
$667$	−3.27906	+	1.89316i	−0.126966	+	0.0733036i
$668$	−26.3173	+	26.0676i	−1.01825	+	1.00859i
$669$	−1.28670	−	1.43650i	−0.0497466	−	0.0555383i
$670$	−12.8561	+	16.6720i	−0.496676	+	0.644096i
$671$	10.3783			0.400651
$672$	−24.5907	−	12.1703i	−0.948608	−	0.469479i
$673$	11.7674	−	20.3818i	0.453602	−	0.785661i	−0.545005	−	0.838433i	$-0.683472\pi$
$673$	11.7674	−	20.3818i	0.453602	−	0.785661i	0.998607	+	0.0527718i	$0.0168056\pi$
$674$	−32.7166	−	4.38657i	−1.26020	−	0.168964i
$675$	−3.25182	−	4.54981i	−0.125162	−	0.175122i
$676$	−23.9758	−	10.0580i	−0.922145	−	0.386845i
$677$			28.4274i			1.09255i	0.837605	+	0.546276i	$0.183955\pi$
$677$			28.4274i			1.09255i	−0.837605	+	0.546276i	$0.816045\pi$
$678$	−30.0367	+	2.21354i	−1.15355	+	0.0850106i
$679$	−30.6044	−	17.6695i	−1.17449	−	0.678093i
$680$	5.40802	+	43.4778i	0.207388	+	1.66730i
$681$	1.40771	+	6.70833i	0.0539438	+	0.257064i
$682$	−18.5066	−	14.2708i	−0.708655	−	0.546458i
$683$	12.6467	+	21.9047i	0.483911	+	0.838158i	0.999829	−	0.0184794i	$-0.00588250\pi$
$683$	12.6467	+	21.9047i	0.483911	+	0.838158i	−0.515918	+	0.856638i	$0.672549\pi$
$684$	−21.6881	−	8.57401i	−0.829267	−	0.327835i
$685$	5.38912	+	9.33424i	0.205908	+	0.356643i
$686$	−3.24087	+	24.1715i	−0.123737	+	0.922874i
$687$	5.92018	+	1.94058i	0.225869	+	0.0740378i
$688$	9.53712	+	0.0909171i	0.363599	+	0.00346618i
$689$	−4.48989	−	0.293701i	−0.171051	−	0.0111891i
$690$	5.12914	+	7.54312i	0.195263	+	0.287162i
$691$	35.7171	+	20.6213i	1.35874	+	0.784471i	0.989455	−	0.144843i	$-0.0462677\pi$
$691$	35.7171	+	20.6213i	1.35874	+	0.784471i	0.369290	+	0.929314i	$0.379601\pi$
$692$	27.0488	−	7.10969i	1.02824	−	0.270270i
$693$	−20.0534	+	27.3021i	−0.761767	+	1.03712i
$694$	4.83874	+	11.7609i	0.183676	+	0.446439i
$695$	3.94421	+	6.83157i	0.149612	+	0.259136i
$696$	3.20278	+	9.33238i	0.121401	+	0.353743i
$697$	−32.6214			−1.23562
$698$	−23.8710	+	30.9562i	−0.903529	+	1.17171i
$699$	0.458590	−	1.39903i	0.0173455	−	0.0529162i
$700$	5.82976	−	1.53233i	0.220344	−	0.0579168i
$701$		−	17.2824i		−	0.652747i	−0.945241	−	0.326374i	$-0.894173\pi$
$701$		−	17.2824i		−	0.652747i	0.945241	−	0.326374i	$-0.105827\pi$
$702$	−24.1717	+	10.8504i	−0.912300	+	0.409522i
$703$		−	20.3313i		−	0.766809i
$704$	−31.2755	+	7.90271i	−1.17874	+	0.297845i
$705$	−2.90887	+	8.87415i	−0.109554	+	0.334220i
$706$	−2.44264	−	1.88357i	−0.0919298	−	0.0708889i
$707$	14.6816			0.552158
$708$	−0.174080	+	2.91141i	−0.00654233	+	0.109418i
$709$	16.5524	+	28.6696i	0.621639	+	1.07671i	0.989181	+	0.146703i	$0.0468661\pi$
$709$	16.5524	+	28.6696i	0.621639	+	1.07671i	−0.367542	+	0.930007i	$0.619801\pi$
$710$	−38.6576	+	15.9047i	−1.45079	+	0.596892i
$711$	12.6782	−	17.2609i	0.475468	−	0.647334i
$712$	−5.52518	−	7.30815i	−0.207065	−	0.273884i
$713$	6.67225	+	3.85223i	0.249878	+	0.144267i
$714$	44.3572	−	30.1618i	1.66003	−	1.12878i
$715$	15.9967	−	23.9474i	0.598242	−	0.895583i
$716$	−23.5960	+	23.3721i	−0.881823	+	0.873456i
$717$	−4.02039	−	1.31785i	−0.150144	−	0.0492159i
$718$	−5.02067	−	0.673160i	−0.187370	−	0.0251221i
$719$	−0.122727	−	0.212570i	−0.00457695	−	0.00792751i	0.863728	−	0.503959i	$-0.168124\pi$
$719$	−0.122727	−	0.212570i	−0.00457695	−	0.00792751i	−0.868305	+	0.496031i	$0.834790\pi$
$720$	21.8551	−	9.34744i	0.814490	−	0.348358i
$721$	6.03711	+	10.4566i	0.224834	+	0.389424i
$722$	−3.36107	+	4.35869i	−0.125086	+	0.162214i
$723$	4.94527	+	23.5662i	0.183917	+	0.876436i
$724$	19.8246	+	5.41339i	0.736776	+	0.201187i
$725$	−1.87721	−	1.08381i	−0.0697178	−	0.0402516i
$726$	0.946844	+	12.8482i	0.0351407	+	0.476841i
$727$			22.0505i			0.817806i	0.912578	+	0.408903i	$0.134089\pi$
$727$			22.0505i			0.817806i	−0.912578	+	0.408903i	$0.865911\pi$
$728$	−1.66767	−	28.5092i	−0.0618080	−	1.05662i
$729$	−8.74224	+	25.5455i	−0.323787	+	0.946130i
$730$	0.980669	−	7.31418i	0.0362962	−	0.270710i
$731$	−9.32296	+	16.1478i	−0.344822	+	0.597249i
$732$	−0.532151	+	8.89999i	−0.0196689	+	0.328953i
$733$	53.3800			1.97164			0.985818	−	0.167818i	$-0.0536722\pi$
$733$	53.3800			1.97164			0.985818	+	0.167818i	$0.0536722\pi$
$734$	−37.9957	−	29.2993i	−1.40245	−	1.08146i
$735$	1.92715	+	2.15152i	0.0710839	+	0.0793598i
$736$	9.87305	−	3.95239i	0.363926	−	0.145687i
$737$	26.2444	−	15.1522i	0.966724	−	0.558139i
$738$	4.89794	+	17.0071i	0.180296	+	0.626039i
$739$	−23.7188	−	13.6941i	−0.872510	−	0.503744i	−0.00432869	−	0.999991i	$-0.501378\pi$
$739$	−23.7188	−	13.6941i	−0.872510	−	0.503744i	−0.868182	+	0.496247i	$0.834711\pi$
$740$	14.5830	+	14.7227i	0.536081	+	0.541216i
$741$	−3.42385	−	24.0310i	−0.125778	−	0.882802i
$742$	−1.88039	−	4.57045i	−0.0690314	−	0.167786i
$743$	15.7175	−	27.2235i	0.576619	−	0.998733i	−0.419245	−	0.907873i	$-0.637705\pi$
$743$	15.7175	−	27.2235i	0.576619	−	0.998733i	0.995864	−	0.0908602i	$-0.0289616\pi$
$744$	13.1870	−	15.1387i	0.483457	−	0.555012i
$745$	0.725127	+	1.25596i	0.0265666	+	0.0460147i
$746$	2.09186	+	5.08443i	0.0765884	+	0.186154i
$747$	32.9111	+	24.1733i	1.20415	+	0.884454i
$748$	16.6126	−	60.8379i	0.607419	−	2.22445i
$749$		−	38.7399i		−	1.41552i
$750$	−12.8248	+	26.5468i	−0.468295	+	0.969353i
$751$	17.5626	+	10.1398i	0.640868	+	0.370005i	0.784949	−	0.619561i	$-0.212689\pi$
$751$	17.5626	+	10.1398i	0.640868	+	0.370005i	−0.144081	+	0.989566i	$0.546023\pi$
$752$	9.37674	+	5.53351i	0.341934	+	0.201786i
$753$	−6.62770	−	31.5837i	−0.241527	−	1.15097i
$754$	−6.78857	+	7.70577i	−0.247225	+	0.280628i
$755$	25.1972			0.917019
$756$	−22.3848	−	18.5969i	−0.814128	−	0.676361i
$757$	−4.57964	+	7.93216i	−0.166450	+	0.288299i	−0.937169	−	0.348875i	$-0.886564\pi$
$757$	−4.57964	+	7.93216i	−0.166450	+	0.288299i	0.770719	+	0.637175i	$0.219897\pi$
$758$	19.6902	+	15.1835i	0.715182	+	0.551491i
$759$	−2.69656	−	12.8502i	−0.0978790	−	0.466433i
$760$	2.68804	+	21.6105i	0.0975055	+	0.783896i
$761$	3.99740	−	2.30790i	0.144905	−	0.0836612i	−0.425794	−	0.904820i	$-0.640005\pi$
$761$	3.99740	−	2.30790i	0.144905	−	0.0836612i	0.570700	+	0.821159i	$0.306672\pi$
$762$	−10.6702	−	15.6920i	−0.386540	−	0.568461i
$763$	−22.9813	+	13.2683i	−0.831980	+	0.480344i
$764$	−10.2252	−	38.9017i	−0.369935	−	1.40742i
$765$	−5.09729	+	46.1902i	−0.184293	+	1.67001i
$766$	−5.69853	−	13.8507i	−0.205896	−	0.500447i
$767$	−2.72247	+	1.34301i	−0.0983027	+	0.0484933i
$768$	−5.17336	−	27.2257i	−0.186678	−	0.982421i
$769$	6.18090	−	10.7056i	0.222889	−	0.386055i	−0.732795	−	0.680450i	$-0.761785\pi$
$769$	6.18090	−	10.7056i	0.222889	−	0.386055i	0.955684	+	0.294394i	$0.0951179\pi$
$770$	31.3516	+	4.20355i	1.12983	+	0.151485i
$771$	−32.2368	−	35.9900i	−1.16098	−	1.29615i
$772$	11.3501	−	11.2424i	0.408498	−	0.404622i
$773$	2.81129	−	1.62310i	0.101115	−	0.0583788i	−0.448590	−	0.893738i	$-0.648074\pi$
$773$	2.81129	−	1.62310i	0.101115	−	0.0583788i	0.549705	+	0.835359i	$0.314740\pi$
$774$	9.81843	+	2.43598i	0.352916	+	0.0875596i
$775$			4.41068i			0.158436i
$776$	−4.40581	−	35.4205i	−0.158159	−	1.27152i
$777$	7.90255	−	24.1085i	0.283502	−	0.864887i
$778$	−2.57883	+	19.2338i	−0.0924555	+	0.689566i
$779$	−16.2143			−0.580939
$780$	19.7160	+	14.9460i	0.705947	+	0.535151i
$781$	60.1701			2.15305
$782$	−2.76289	+	20.6066i	−0.0988006	+	0.736891i
$783$	1.01285	+	10.4161i	0.0361964	+	0.372239i
$784$	2.93226	−	1.65588i	0.104724	−	0.0591384i
$785$		−	33.9560i		−	1.21194i
$786$	25.1644	+	12.1569i	0.897585	+	0.433624i
$787$	−1.24966	+	0.721491i	−0.0445455	+	0.0257184i	−0.522107	−	0.852880i	$-0.674854\pi$
$787$	−1.24966	+	0.721491i	−0.0445455	+	0.0257184i	0.477562	+	0.878598i	$0.341521\pi$
$788$	−21.5251	−	21.7313i	−0.766799	−	0.774144i
$789$	−36.2733	+	32.4906i	−1.29136	+	1.15670i
$790$	−19.8211	−	2.65756i	−0.705202	−	0.0945519i
$791$	17.2160	−	29.8190i	0.612131	−	1.06024i
$792$	−34.2120	+	0.473541i	−1.21567	+	0.0168266i
$793$	−8.32241	+	4.10549i	−0.295537	+	0.145790i
$794$	3.89175	+	9.45921i	0.138113	+	0.335695i
$795$	4.06856	+	1.33364i	0.144297	+	0.0472992i
$796$	5.34761	−	1.40560i	0.189541	−	0.0498203i
$797$	−2.03875	+	1.17707i	−0.0722162	+	0.0416940i	−0.535673	−	0.844425i	$-0.679942\pi$
$797$	−2.03875	+	1.17707i	−0.0722162	+	0.0416940i	0.463457	+	0.886119i	$0.346609\pi$
$798$	22.0476	−	14.9918i	0.780476	−	0.530705i
$799$	−18.4338	+	10.6428i	−0.652141	+	0.376514i
$800$	4.78563	+	3.76358i	0.169197	+	0.133063i
$801$	−3.90631	−	8.89772i	−0.138023	−	0.314385i
$802$	−10.9381	−	8.43459i	−0.386238	−	0.297836i
$803$	−5.31120	+	9.19927i	−0.187428	+	0.324635i
$804$	11.6482	+	23.2830i	0.410799	+	0.821127i
$805$	−10.4283			−0.367549
$806$	20.4858	+	4.12291i	0.721582	+	0.145223i
$807$	−10.3650	+	2.17506i	−0.364867	+	0.0765657i
$808$	8.94291	+	11.8288i	0.314610	+	0.416135i
$809$	−9.09309	−	5.24990i	−0.319696	−	0.184577i	0.331561	−	0.943434i	$-0.392425\pi$
$809$	−9.09309	−	5.24990i	−0.319696	−	0.184577i	−0.651257	+	0.758857i	$0.725758\pi$
$810$	24.8465	−	4.27777i	0.873016	−	0.150305i
$811$		−	38.1116i		−	1.33828i	−0.743137	−	0.669139i	$-0.766663\pi$
$811$		−	38.1116i		−	1.33828i	0.743137	−	0.669139i	$-0.233337\pi$
$812$	−10.8815	−	2.97135i	−0.381866	−	0.104274i
$813$	7.88788	+	8.80623i	0.276640	+	0.308848i
$814$	−11.3491	−	27.5849i	−0.397786	−	0.966851i
$815$	15.7841	+	27.3388i	0.552892	+	0.957636i
$816$	51.3200	+	17.3657i	1.79656	+	0.607923i
$817$	−4.63394	+	8.02623i	−0.162121	+	0.280802i
$818$	14.0274	+	34.0948i	0.490458	+	1.19210i
$819$	5.28066	−	29.8264i	0.184521	−	1.04222i
$820$	11.7414	−	11.6300i	0.410028	−	0.406138i
$821$	48.0908	+	27.7652i	1.67838	+	0.969013i	0.962694	+	0.270591i	$0.0872190\pi$
$821$	48.0908	+	27.7652i	1.67838	+	0.969013i	0.715686	+	0.698422i	$0.246114\pi$
$822$	13.2922	−	0.979566i	0.463619	−	0.0341663i
$823$	40.4499	−	23.3538i	1.40999	−	0.814061i	0.414607	−	0.910000i	$-0.363919\pi$
$823$	40.4499	−	23.3538i	1.40999	−	0.814061i	0.995387	+	0.0959396i	$0.0305856\pi$
$824$	−4.74739	+	11.2334i	−0.165383	+	0.391333i
$825$	5.59908	−	5.01519i	0.194935	−	0.174606i
$826$	−2.64048	−	2.03613i	−0.0918742	−	0.0708461i
$827$	−22.0817			−0.767857			−0.383928	−	0.923363i	$-0.625429\pi$
$827$	−22.0817			−0.767857			−0.383928	+	0.923363i	$0.625429\pi$
$828$	11.1580	−	1.65355i	0.387768	−	0.0574650i
$829$	−0.0585429	+	0.101399i	−0.00203328	+	0.00352174i	−0.867040	−	0.498238i	$-0.833981\pi$
$829$	−0.0585429	+	0.101399i	−0.00203328	+	0.00352174i	0.865007	+	0.501760i	$0.167314\pi$
$830$	5.06714	−	37.7926i	0.175883	−	1.31180i
$831$	−7.68674	−	36.6304i	−0.266650	−	1.27070i
$832$	21.9537	−	18.7092i	0.761107	−	0.648626i
$833$			6.58347i			0.228104i
$834$	9.72835	−	0.716927i	0.336865	−	0.0248252i
$835$	31.7721	+	18.3437i	1.09952	+	0.634808i
$836$	8.25726	−	30.2392i	0.285583	−	1.04585i
$837$	17.3246	−	12.3822i	0.598827	−	0.427991i
$838$	−25.1249	+	32.5823i	−0.867924	+	1.12554i
$839$	21.6203	+	37.4475i	0.746416	+	1.29283i	0.949530	+	0.313676i	$0.101561\pi$
$839$	21.6203	+	37.4475i	0.746416	+	1.29283i	−0.203114	+	0.979155i	$0.565106\pi$
$840$	−5.21234	+	26.6702i	−0.179843	+	0.920209i
$841$	−12.4719	−	21.6019i	−0.430064	−	0.744892i
$842$	−21.9705	−	2.94575i	−0.757152	−	0.101517i
$843$	−0.384918	+	1.17428i	−0.0132573	+	0.0404443i
$844$	29.2278	+	29.5077i	1.00606	+	1.01570i
$845$	−3.35459	+	25.5315i	−0.115401	+	0.878311i
$846$	8.31632	+	8.01246i	0.285921	+	0.275474i
$847$	−12.7551	−	7.36415i	−0.438270	−	0.253035i
$848$	2.53696	−	4.29898i	0.0871196	−	0.147628i
$849$	2.13775	+	2.38664i	0.0733675	+	0.0819093i
$850$	−11.0073	+	4.52868i	−0.377548	+	0.155332i
$851$	4.91682	+	8.51619i	0.168546	+	0.291931i
$852$	−3.08523	+	51.5992i	−0.105698	+	1.76776i
$853$	−25.9640			−0.888990			−0.444495	−	0.895781i	$-0.646617\pi$
$853$	−25.9640			−0.888990			−0.444495	+	0.895781i	$0.646617\pi$
$854$	−8.07178	−	6.22432i	−0.276211	−	0.212992i
$855$	−2.53359	+	22.9587i	−0.0866470	+	0.785170i
$856$	31.2122	−	23.5974i	1.06681	−	0.806541i
$857$		−	33.7371i		−	1.15244i	−0.817296	−	0.576218i	$-0.804528\pi$
$857$		−	33.7371i		−	1.15244i	0.817296	−	0.576218i	$-0.195472\pi$
$858$	−18.0597	−	30.6934i	−0.616549	−	1.04786i
$859$		−	9.97263i		−	0.340262i	−0.985421	−	0.170131i	$-0.945581\pi$
$859$		−	9.97263i		−	0.340262i	0.985421	−	0.170131i	$-0.0544191\pi$
$860$	−2.40134	−	9.13587i	−0.0818850	−	0.311531i
$861$	−19.2267	−	6.30234i	−0.655244	−	0.214783i
$862$	−6.28056	+	8.14473i	−0.213917	+	0.277410i
$863$	−19.5813			−0.666554			−0.333277	−	0.942829i	$-0.608154\pi$
$863$	−19.5813			−0.666554			−0.333277	+	0.942829i	$0.608154\pi$
$864$	1.34814	−	29.3629i	0.0458646	−	0.998948i
$865$	−13.8498	−	23.9886i	−0.470909	−	0.815638i
$866$	−7.00362	−	17.0229i	−0.237993	−	0.578460i
$867$	−56.9640	+	51.0236i	−1.93460	+	1.73285i
$868$	5.83478	+	22.1984i	0.198045	+	0.753462i
$869$	24.9296	+	14.3931i	0.845678	+	0.488252i
$870$	8.08095	−	5.49485i	0.273970	−	0.186293i
$871$	−15.0515	+	22.5324i	−0.510000	+	0.763482i
$872$	−24.6885	−	10.4337i	−0.836060	−	0.353331i
$873$	4.15266	−	37.6302i	0.140546	−	1.27359i
$874$	−1.37328	+	10.2424i	−0.0464520	+	0.346456i
$875$	−16.8526	−	29.1895i	−0.569721	−	0.986786i
$876$	−7.61656	−	5.02635i	−0.257340	−	0.169825i
$877$	−17.0141	−	29.4693i	−0.574525	−	0.995106i	−0.996093	−	0.0883096i	$-0.971854\pi$
$877$	−17.0141	−	29.4693i	−0.574525	−	0.995106i	0.421568	−	0.906797i	$-0.361480\pi$
$878$	−30.2658	−	23.3386i	−1.02142	−	0.787639i
$879$	10.6992	−	2.24519i	0.360876	−	0.0757283i
$880$	15.7102	+	27.8201i	0.529592	+	0.937814i
$881$	15.0990	+	8.71742i	0.508699	+	0.293697i	0.732299	−	0.680984i	$-0.238448\pi$
$881$	15.0990	+	8.71742i	0.508699	+	0.293697i	−0.223600	+	0.974681i	$0.571781\pi$
$882$	3.43228	−	0.988475i	0.115571	−	0.0332837i
$883$		−	24.3615i		−	0.819829i	−0.912124	−	0.409914i	$-0.865559\pi$
$883$		−	24.3615i		−	0.819829i	0.912124	−	0.409914i	$-0.134441\pi$
$884$	10.7447	+	55.3577i	0.361384	+	1.86188i
$885$	2.82710	−	0.593255i	0.0950319	−	0.0199421i
$886$	10.6474	+	1.42757i	0.357705	+	0.0479603i
$887$	−23.0104	+	39.8552i	−0.772613	+	1.33821i	0.163513	+	0.986541i	$0.447717\pi$
$887$	−23.0104	+	39.8552i	−0.772613	+	1.33821i	−0.936126	+	0.351664i	$0.885616\pi$
$888$	24.2375	−	8.31807i	0.813359	−	0.279136i
$889$	21.6941			0.727596
$890$	−5.54100	+	7.18566i	−0.185735	+	0.240864i
$891$	−35.4175	−	7.91332i	−1.18653	−	0.265106i
$892$	1.56709	+	1.58210i	0.0524701	+	0.0529727i
$893$	−9.16246	+	5.28995i	−0.306610	+	0.177021i
$894$	1.78852	−	0.131804i	0.0598170	−	0.00440820i
$895$	28.4868	+	16.4469i	0.952208	+	0.549758i
$896$	29.0642	+	12.6108i	0.970966	+	0.421298i
$897$	7.24570	+	9.23789i	0.241927	+	0.308444i
$898$	10.3125	−	4.24280i	0.344132	−	0.141584i
$899$	4.12689	−	7.14799i	0.137640	−	0.238399i
$900$	4.01371	+	5.05868i	0.133790	+	0.168623i
$901$	4.87942	+	8.45140i	0.162557	+	0.281557i
$902$	−21.9992	+	9.05100i	−0.732493	+	0.301365i
$903$	−8.61456	+	7.71620i	−0.286675	+	0.256779i
$904$	34.5115	−	4.29274i	1.14783	−	0.142774i
$905$		−	20.3536i		−	0.676576i
$906$	13.5539	−	28.0561i	0.450300	−	0.932103i
$907$	−45.0566	−	26.0134i	−1.49608	−	0.863762i	−0.496089	−	0.868271i	$-0.665231\pi$
$907$	−45.0566	−	26.0134i	−1.49608	−	0.863762i	−0.999990	+	0.00450965i	$0.998565\pi$
$908$	−2.01204	−	7.65481i	−0.0667720	−	0.254034i
$909$	6.32266	+	14.4016i	0.209709	+	0.477672i
$910$	−26.8038	+	9.03132i	−0.888536	+	0.299385i
$911$	20.2998			0.672564			0.336282	−	0.941761i	$-0.390831\pi$
$911$	20.2998			0.672564			0.336282	+	0.941761i	$0.390831\pi$
$912$	25.5084	+	8.63158i	0.844669	+	0.285820i
$913$	−27.4431	+	47.5329i	−0.908235	+	1.57311i
$914$	13.5200	−	17.5329i	0.447201	−	0.579937i
$915$	8.64226	−	1.81354i	0.285704	−	0.0599538i
$916$	−6.93984	−	1.89502i	−0.229299	−	0.0626133i
$917$	−27.6695	+	15.9750i	−0.913728	+	0.527541i
$918$	48.6892	+	30.5220i	1.60698	+	1.00738i
$919$	5.11593	−	2.95368i	0.168759	−	0.0974330i	−0.413242	−	0.910621i	$-0.635603\pi$
$919$	5.11593	−	2.95368i	0.168759	−	0.0974330i	0.582001	+	0.813188i	$0.302270\pi$
$920$	−6.35213	−	8.40195i	−0.209423	−	0.277004i
$921$	1.19494	−	3.64544i	0.0393747	−	0.120121i
$922$	−51.5382	+	21.2041i	−1.69732	+	0.698318i
$923$	−48.2505	+	23.8023i	−1.58819	+	0.783461i
$924$	21.5450	−	32.6477i	0.708778	−	1.07403i
$925$	−2.81480	+	4.87538i	−0.0925502	+	0.160302i
$926$	6.56586	−	48.9706i	0.215768	−	1.60927i
$927$	−7.65728	+	10.4251i	−0.251498	+	0.342406i
$928$	−4.23420	−	10.5770i	−0.138994	−	0.347207i
$929$	−11.5057	+	6.64281i	−0.377489	+	0.217943i	−0.676725	−	0.736236i	$-0.736601\pi$
$929$	−11.5057	+	6.64281i	−0.377489	+	0.217943i	0.299236	+	0.954179i	$0.403268\pi$
$930$	−17.9046	−	8.64972i	−0.587115	−	0.283636i
$931$			3.27229i			0.107245i
$932$	−0.447824	+	1.63999i	−0.0146689	+	0.0537198i
$933$	−41.8650	−	13.7230i	−1.37060	−	0.449270i
$934$	−31.8030	−	4.26407i	−1.04063	−	0.139525i
$935$	−62.4612			−2.04270
$936$	27.2473	−	13.9134i	0.890607	−	0.454774i
$937$	−35.4819			−1.15914			−0.579572	−	0.814921i	$-0.696780\pi$
$937$	−35.4819			−1.15914			−0.579572	+	0.814921i	$0.696780\pi$
$938$	−29.4991	−	3.95517i	−0.963179	−	0.129141i
$939$	45.1258	+	14.7918i	1.47263	+	0.482714i
$940$	2.84058	−	10.4026i	0.0926494	−	0.339295i
$941$			6.71658i			0.218954i	0.993989	+	0.109477i	$0.0349177\pi$
$941$			6.71658i			0.218954i	−0.993989	+	0.109477i	$0.965082\pi$
$942$	−37.8087	−	18.2654i	−1.23188	−	0.595120i
$943$	6.79172	−	3.92120i	0.221169	−	0.127692i
$944$	0.0321038	−	3.36766i	0.00104489	−	0.109608i
$945$	−11.9281	+	26.2392i	−0.388020	+	0.853562i
$946$	−1.80690	+	13.4765i	−0.0587472	+	0.438158i
$947$	−17.9692	+	31.1236i	−0.583921	+	1.01138i	0.411087	+	0.911596i	$0.365149\pi$
$947$	−17.9692	+	31.1236i	−0.583921	+	1.01138i	−0.995009	+	0.0997857i	$0.968184\pi$
$948$	−13.6212	+	20.6405i	−0.442395	+	0.670372i
$949$	0.619990	−	9.47794i	0.0201257	−	0.307667i
$950$	−5.47115	+	2.25096i	−0.177508	+	0.0730309i
$951$	−7.17201	+	21.8798i	−0.232568	+	0.709501i
$952$	−49.4076	+	37.3536i	−1.60131	+	1.21064i
$953$	7.45821	−	4.30600i	0.241595	−	0.139485i	−0.374314	−	0.927302i	$-0.622122\pi$
$953$	7.45821	−	4.30600i	0.241595	−	0.139485i	0.615910	+	0.787817i	$0.288789\pi$
$954$	3.67349	−	3.81281i	0.118934	−	0.123444i
$955$	−34.5006	+	19.9189i	−1.11641	+	0.644561i
$956$	4.71284	+	1.28691i	0.152424	+	0.0416216i
$957$	−13.7664	+	2.88883i	−0.445005	+	0.0933825i
$958$	−5.72110	+	7.41920i	−0.184840	+	0.239703i
$959$	−7.61865	+	13.1959i	−0.246019	+	0.426117i
$960$	−24.6628	+	12.0459i	−0.795988	+	0.388781i
$961$	14.2051			0.458230
$962$	20.0130	+	17.6309i	0.645245	+	0.568443i
$963$	38.0011	−	16.6834i	1.22457	−	0.537615i
$964$	−7.06827	−	26.8912i	−0.227654	−	0.866106i
$965$	−13.7026	−	7.91122i	−0.441103	−	0.254671i
$966$	−5.60954	+	11.6115i	−0.180484	+	0.373595i
$967$			39.9079i			1.28335i	0.766975	+	0.641676i	$0.221761\pi$
$967$			39.9079i			1.28335i	−0.766975	+	0.641676i	$0.778239\pi$
$968$	−1.83622	−	14.7623i	−0.0590183	−	0.474478i
$969$	−39.2154	+	35.1259i	−1.25978	+	1.12841i
$970$	−32.6928	+	13.4506i	−1.04970	+	0.431873i
$971$	4.39573	+	7.61362i	0.141066	+	0.244333i	0.927898	−	0.372834i	$-0.121614\pi$
$971$	4.39573	+	7.61362i	0.141066	+	0.244333i	−0.786833	+	0.617167i	$0.788280\pi$
$972$	8.60215	−	29.9667i	0.275914	−	0.961182i
$973$	−5.57596	+	9.65784i	−0.178757	+	0.309616i
$974$	−4.06654	+	1.67307i	−0.130300	+	0.0536088i
$975$	−2.50599	+	6.23659i	−0.0802560	+	0.199731i
$976$	0.0981393	−	10.2947i	0.00314136	−	0.329526i
$977$	−27.1638	−	15.6830i	−0.869047	−	0.501745i	−0.00201588	−	0.999998i	$-0.500642\pi$
$977$	−27.1638	−	15.6830i	−0.869047	−	0.501745i	−0.867032	+	0.498253i	$0.833975\pi$
$978$	38.9312	−	2.86902i	1.24488	−	0.0917413i
$979$	11.3114	−	6.53062i	0.361513	−	0.208719i
$980$	−2.34711	−	2.36959i	−0.0749757	−	0.0756938i
$981$	−22.9122	−	16.8291i	−0.731530	−	0.537310i
$982$	3.88509	−	5.03824i	0.123978	−	0.160777i
$983$	−25.0538			−0.799092			−0.399546	−	0.916713i	$-0.630832\pi$
$983$	−25.0538			−0.799092			−0.399546	+	0.916713i	$0.630832\pi$
$984$	−6.63372	−	19.3296i	−0.211475	−	0.616206i
$985$	−15.1471	+	26.2356i	−0.482627	+	0.835935i
$986$	22.0759	+	2.95988i	0.703039	+	0.0942618i
$987$	−12.9208	+	2.71138i	−0.411275	+	0.0863043i
$988$	5.34062	+	27.5154i	0.169908	+	0.875380i
$989$		−	4.48260i		−	0.142539i
$990$	9.37823	+	32.5640i	0.298060	+	1.03495i
$991$	−9.47381	−	5.46971i	−0.300945	−	0.173751i	0.341922	−	0.939728i	$-0.388922\pi$
$991$	−9.47381	−	5.46971i	−0.300945	−	0.173751i	−0.642868	+	0.765977i	$0.722255\pi$
$992$	−14.3309	+	18.2226i	−0.455005	+	0.578567i
$993$	−54.9507	+	11.5312i	−1.74381	+	0.365931i
$994$	−46.7975	−	36.0865i	−1.48433	−	1.14459i
$995$	−2.73815	−	4.74261i	−0.0868050	−	0.150351i
$996$	−39.3549	−	25.9713i	−1.24701	−	0.822931i
$997$	−17.0806	−	29.5845i	−0.540948	−	0.936950i	−0.998850	−	0.0479470i	$-0.984732\pi$
$997$	−17.0806	−	29.5845i	−0.540948	−	0.936950i	0.457902	−	0.889003i	$-0.348601\pi$
$998$	1.24600	−	9.29309i	0.0394413	−	0.294168i
$999$	27.0520	−	2.63053i	0.855887	−	0.0832262i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.p.b.35.20	yes	40
3.2	odd	2	inner	156.2.p.b.35.1	✓	40
4.3	odd	2	inner	156.2.p.b.35.14	yes	40
12.11	even	2	inner	156.2.p.b.35.7	yes	40
13.3	even	3	inner	156.2.p.b.107.7	yes	40
39.29	odd	6	inner	156.2.p.b.107.14	yes	40
52.3	odd	6	inner	156.2.p.b.107.1	yes	40
156.107	even	6	inner	156.2.p.b.107.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.p.b.35.1	✓	40	3.2	odd	2	inner
156.2.p.b.35.7	yes	40	12.11	even	2	inner
156.2.p.b.35.14	yes	40	4.3	odd	2	inner
156.2.p.b.35.20	yes	40	1.1	even	1	trivial
156.2.p.b.107.1	yes	40	52.3	odd	6	inner
156.2.p.b.107.7	yes	40	13.3	even	3	inner
156.2.p.b.107.14	yes	40	39.29	odd	6	inner
156.2.p.b.107.20	yes	40	156.107	even	6	inner

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	156.2.p.b.35.20

Level	$156$
Weight	$2$
Character	156.35
Analytic conductor	$1.246$
Analytic rank	$0$
Dimension	$40$
Inner twists	$8$