LMFDB - Embedded newform 396.2.w.a.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(71,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 4]))

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

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

chi := DirichletCharacter("396.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.w (of order $10$, degree $4$, 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:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			71.4
Character	$\chi$	$=$	396.71
Dual form			396.2.w.a.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22090 + 0.713732i) q^{2} +(0.981175 - 1.74278i) q^{4} +(1.96829 + 0.639537i) q^{5} +(-2.79916 - 3.85272i) q^{7} +(0.0459679 + 2.82805i) q^{8} +O(q^{10})$	\(q+(-1.22090 + 0.713732i) q^{2} +(0.981175 - 1.74278i) q^{4} +(1.96829 + 0.639537i) q^{5} +(-2.79916 - 3.85272i) q^{7} +(0.0459679 + 2.82805i) q^{8} +(-2.85954 + 0.624025i) q^{10} +(1.63619 - 2.88494i) q^{11} +(-0.325879 - 1.00295i) q^{13} +(6.16729 + 2.70592i) q^{14} +(-2.07459 - 3.41995i) q^{16} +(-4.94627 - 1.60714i) q^{17} +(0.702088 - 0.966341i) q^{19} +(3.04582 - 2.80281i) q^{20} +(0.0614562 + 4.69001i) q^{22} -5.86457 q^{23} +(-0.579913 - 0.421331i) q^{25} +(1.11370 + 0.991909i) q^{26} +(-9.46092 + 1.09815i) q^{28} +(2.49060 + 3.42802i) q^{29} +(9.27709 - 3.01431i) q^{31} +(4.97379 + 2.69470i) q^{32} +(7.18594 - 1.56816i) q^{34} +(-3.04562 - 9.37345i) q^{35} +(7.27013 - 5.28206i) q^{37} +(-0.167468 + 1.68090i) q^{38} +(-1.71817 + 5.59584i) q^{40} +(2.36345 - 3.25300i) q^{41} -4.02485i q^{43} +(-3.42244 - 5.68216i) q^{44} +(7.16003 - 4.18573i) q^{46} +(-2.70695 - 1.96672i) q^{47} +(-4.84500 + 14.9114i) q^{49} +(1.00873 + 0.100500i) q^{50} +(-2.06767 - 0.416134i) q^{52} +(11.3480 - 3.68719i) q^{53} +(5.06553 - 4.63201i) q^{55} +(10.7670 - 8.09328i) q^{56} +(-5.48745 - 2.40763i) q^{58} +(-2.36747 + 1.72007i) q^{59} +(-1.03139 + 3.17428i) q^{61} +(-9.17496 + 10.3015i) q^{62} +(-7.99577 + 0.259999i) q^{64} -2.18251i q^{65} +10.8004i q^{67} +(-7.65405 + 7.04339i) q^{68} +(10.4085 + 9.27025i) q^{70} +(-1.68186 + 5.17623i) q^{71} +(4.47693 - 3.25268i) q^{73} +(-5.10610 + 11.6378i) q^{74} +(-0.995253 - 2.17174i) q^{76} +(-15.6948 + 1.77164i) q^{77} +(-8.43148 + 2.73955i) q^{79} +(-1.89622 - 8.05825i) q^{80} +(-0.563750 + 5.65845i) q^{82} +(-0.544346 + 1.67532i) q^{83} +(-8.70788 - 6.32664i) q^{85} +(2.87266 + 4.91392i) q^{86} +(8.23398 + 4.49462i) q^{88} +2.66925i q^{89} +(-2.95190 + 4.06294i) q^{91} +(-5.75417 + 10.2207i) q^{92} +(4.70862 + 0.469119i) q^{94} +(1.99993 - 1.45303i) q^{95} +(-1.29790 - 3.99452i) q^{97} +(-4.72748 - 21.6633i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 16 q^{10} + 32 q^{16} + 60 q^{22} + 8 q^{25} - 12 q^{28} + 24 q^{34} + 16 q^{40} - 40 q^{46} + 40 q^{49} - 32 q^{52} - 80 q^{58} - 72 q^{64} - 48 q^{70} - 24 q^{73} - 136 q^{76} - 132 q^{82} - 48 q^{85} - 64 q^{88} - 80 q^{94} - 80 q^{97}+O(q^{100}) $ 96 * q - 16 * q^10 + 32 * q^16 + 60 * q^22 + 8 * q^25 - 12 * q^28 + 24 * q^34 + 16 * q^40 - 40 * q^46 + 40 * q^49 - 32 * q^52 - 80 * q^58 - 72 * q^64 - 48 * q^70 - 24 * q^73 - 136 * q^76 - 132 * q^82 - 48 * q^85 - 64 * q^88 - 80 * q^94 - 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.22090	+	0.713732i	−0.863304	+	0.504684i
$2$	−1.22090	+	0.713732i	−0.863304	+	0.504684i
$3$		0			0
$3$		0			0
$4$	0.981175	−	1.74278i	0.490587	−	0.871392i
$5$	1.96829	+	0.639537i	0.880248	+	0.286010i	0.714060	−	0.700084i	$-0.246854\pi$
$5$	1.96829	+	0.639537i	0.880248	+	0.286010i	0.166188	+	0.986094i	$0.446854\pi$
$6$		0			0
$7$	−2.79916	−	3.85272i	−1.05798	−	1.45619i	−0.881676	−	0.471855i	$-0.843585\pi$
$7$	−2.79916	−	3.85272i	−1.05798	−	1.45619i	−0.176308	−	0.984335i	$-0.556415\pi$
$8$	0.0459679	+	2.82805i	0.0162521	+	0.999868i
$9$		0			0
$10$	−2.85954	+	0.624025i	−0.904266	+	0.197334i
$11$	1.63619	−	2.88494i	0.493330	−	0.869842i
$11$	1.63619	−	2.88494i	0.493330	−	0.869842i
$12$		0			0
$13$	−0.325879	−	1.00295i	−0.0903824	−	0.278169i	0.895640	−	0.444779i	$-0.146718\pi$
$13$	−0.325879	−	1.00295i	−0.0903824	−	0.278169i	−0.986023	+	0.166610i	$0.946718\pi$
$14$	6.16729	+	2.70592i	1.64828	+	0.723187i
$15$		0			0
$16$	−2.07459	−	3.41995i	−0.518648	−	0.854988i
$17$	−4.94627	−	1.60714i	−1.19965	−	0.389788i	−0.360015	−	0.932946i	$-0.617228\pi$
$17$	−4.94627	−	1.60714i	−1.19965	−	0.389788i	−0.839631	+	0.543158i	$0.817228\pi$
$18$		0			0
$19$	0.702088	−	0.966341i	0.161070	−	0.221694i	−0.720852	−	0.693089i	$-0.756249\pi$
$19$	0.702088	−	0.966341i	0.161070	−	0.221694i	0.881922	+	0.471395i	$0.156249\pi$
$20$	3.04582	−	2.80281i	0.681065	−	0.626728i
$21$		0			0
$22$	0.0614562	+	4.69001i	0.0131025	+	0.999914i
$23$	−5.86457			−1.22285			−0.611424	−	0.791303i	$-0.709403\pi$
$23$	−5.86457			−1.22285			−0.611424	+	0.791303i	$0.709403\pi$
$24$		0			0
$25$	−0.579913	−	0.421331i	−0.115983	−	0.0842663i
$26$	1.11370	+	0.991909i	0.218415	+	0.194529i
$27$		0			0
$28$	−9.46092	+	1.09815i	−1.78795	+	0.207531i
$29$	2.49060	+	3.42802i	0.462493	+	0.636567i	0.975023	−	0.222102i	$-0.0712918\pi$
$29$	2.49060	+	3.42802i	0.462493	+	0.636567i	−0.512530	+	0.858669i	$0.671292\pi$
$30$		0			0
$31$	9.27709	−	3.01431i	1.66622	−	0.541386i	0.684055	−	0.729431i	$-0.260215\pi$
$31$	9.27709	−	3.01431i	1.66622	−	0.541386i	0.982160	+	0.188045i	$0.0602150\pi$
$32$	4.97379	+	2.69470i	0.879250	+	0.476361i
$33$		0			0
$34$	7.18594	−	1.56816i	1.23238	−	0.268937i
$35$	−3.04562	−	9.37345i	−0.514803	−	1.58440i
$36$		0			0
$37$	7.27013	−	5.28206i	1.19520	−	0.868365i	0.201397	−	0.979510i	$-0.435452\pi$
$37$	7.27013	−	5.28206i	1.19520	−	0.868365i	0.993804	+	0.111145i	$0.0354518\pi$
$38$	−0.167468	+	1.68090i	−0.0271669	+	0.272679i
$39$		0			0
$40$	−1.71817	+	5.59584i	−0.271666	+	0.884780i
$41$	2.36345	−	3.25300i	0.369108	−	0.508034i	−0.583550	−	0.812077i	$-0.698337\pi$
$41$	2.36345	−	3.25300i	0.369108	−	0.508034i	0.952658	+	0.304043i	$0.0983367\pi$
$42$		0			0
$43$		−	4.02485i		−	0.613784i	−0.951744	−	0.306892i	$-0.900711\pi$
$43$		−	4.02485i		−	0.613784i	0.951744	−	0.306892i	$-0.0992890\pi$
$44$	−3.42244	−	5.68216i	−0.515953	−	0.856617i
$45$		0			0
$46$	7.16003	−	4.18573i	1.05569	−	0.617152i
$47$	−2.70695	−	1.96672i	−0.394850	−	0.286875i	0.372590	−	0.927996i	$-0.378470\pi$
$47$	−2.70695	−	1.96672i	−0.394850	−	0.286875i	−0.767440	+	0.641121i	$0.778470\pi$
$48$		0			0
$49$	−4.84500	+	14.9114i	−0.692142	+	2.13020i
$50$	1.00873	+	0.100500i	0.142656	+	0.0142128i
$51$		0			0
$52$	−2.06767	−	0.416134i	−0.286734	−	0.0577074i
$53$	11.3480	−	3.68719i	1.55877	−	0.506474i	0.602289	−	0.798278i	$-0.294255\pi$
$53$	11.3480	−	3.68719i	1.55877	−	0.506474i	0.956478	+	0.291804i	$0.0942554\pi$
$54$		0			0
$55$	5.06553	−	4.63201i	0.683036	−	0.624580i
$56$	10.7670	−	8.09328i	1.43880	−	1.08151i
$57$		0			0
$58$	−5.48745	−	2.40763i	−0.720538	−	0.316138i
$59$	−2.36747	+	1.72007i	−0.308218	+	0.223934i	−0.731132	−	0.682236i	$-0.761008\pi$
$59$	−2.36747	+	1.72007i	−0.308218	+	0.223934i	0.422913	+	0.906170i	$0.361008\pi$
$60$		0			0
$61$	−1.03139	+	3.17428i	−0.132055	+	0.406425i	−0.995120	−	0.0986681i	$-0.968542\pi$
$61$	−1.03139	+	3.17428i	−0.132055	+	0.406425i	0.863065	+	0.505093i	$0.168542\pi$
$62$	−9.17496	+	10.3015i	−1.16522	+	1.30829i
$63$		0			0
$64$	−7.99577	+	0.259999i	−0.999472	+	0.0324999i
$65$		−	2.18251i		−	0.270707i
$66$		0			0
$67$			10.8004i			1.31948i	0.751493	+	0.659741i	$0.229334\pi$
$67$			10.8004i			1.31948i	−0.751493	+	0.659741i	$0.770666\pi$
$68$	−7.65405	+	7.04339i	−0.928189	+	0.854136i
$69$		0			0
$70$	10.4085	+	9.27025i	1.24405	+	1.10801i
$71$	−1.68186	+	5.17623i	−0.199600	+	0.614305i	0.800292	+	0.599610i	$0.204678\pi$
$71$	−1.68186	+	5.17623i	−0.199600	+	0.614305i	−0.999892	+	0.0146949i	$0.995322\pi$
$72$		0			0
$73$	4.47693	−	3.25268i	0.523985	−	0.380697i	−0.294118	−	0.955769i	$-0.595026\pi$
$73$	4.47693	−	3.25268i	0.523985	−	0.380697i	0.818103	+	0.575072i	$0.195026\pi$
$74$	−5.10610	+	11.6378i	−0.593572	+	1.35286i
$75$		0			0
$76$	−0.995253	−	2.17174i	−0.114163	−	0.249115i
$77$	−15.6948	+	1.77164i	−1.78859	+	0.201898i
$78$		0			0
$79$	−8.43148	+	2.73955i	−0.948615	+	0.308224i	−0.742153	−	0.670231i	$-0.766195\pi$
$79$	−8.43148	+	2.73955i	−0.948615	+	0.308224i	−0.206463	+	0.978455i	$0.566195\pi$
$80$	−1.89622	−	8.05825i	−0.212004	−	0.900939i
$81$		0			0
$82$	−0.563750	+	5.65845i	−0.0622558	+	0.624871i
$83$	−0.544346	+	1.67532i	−0.0597497	+	0.183891i	−0.976476	−	0.215624i	$-0.930821\pi$
$83$	−0.544346	+	1.67532i	−0.0597497	+	0.183891i	0.916727	+	0.399515i	$0.130821\pi$
$84$		0			0
$85$	−8.70788	−	6.32664i	−0.944502	−	0.686221i
$86$	2.87266	+	4.91392i	0.309767	+	0.529882i
$87$		0			0
$88$	8.23398	+	4.49462i	0.877745	+	0.479128i
$89$			2.66925i			0.282940i	0.989943	+	0.141470i	$0.0451828\pi$
$89$			2.66925i			0.282940i	−0.989943	+	0.141470i	$0.954817\pi$
$90$		0			0
$91$	−2.95190	+	4.06294i	−0.309443	+	0.425912i
$92$	−5.75417	+	10.2207i	−0.599913	+	1.06558i
$93$		0			0
$94$	4.70862	+	0.469119i	0.485657	+	0.0483859i
$95$	1.99993	−	1.45303i	0.205188	−	0.149078i
$96$		0			0
$97$	−1.29790	−	3.99452i	−0.131782	−	0.405582i	0.863294	−	0.504701i	$-0.168397\pi$
$97$	−1.29790	−	3.99452i	−0.131782	−	0.405582i	−0.995076	+	0.0991195i	$0.968397\pi$
$98$	−4.72748	−	21.6633i	−0.477547	−	2.18832i
$99$		0			0
$100$	−1.30329	+	0.597264i	−0.130329	+	0.0597264i
$101$	−0.303600	+	0.0986458i	−0.0302094	+	0.00981562i	−0.324083	−	0.946029i	$-0.605056\pi$
$101$	−0.303600	+	0.0986458i	−0.0302094	+	0.00981562i	0.293873	+	0.955844i	$0.405056\pi$
$102$		0			0
$103$	7.37709	+	10.1537i	0.726886	+	1.00047i	0.999267	+	0.0382830i	$0.0121888\pi$
$103$	7.37709	+	10.1537i	0.726886	+	1.00047i	−0.272381	+	0.962189i	$0.587811\pi$
$104$	2.82142	−	0.967705i	0.276663	−	0.0948913i
$105$		0			0
$106$	−11.2231	+	12.6011i	−1.09008	+	1.22393i
$107$	−4.46181	−	3.24169i	−0.431339	−	0.313386i	0.350845	−	0.936434i	$-0.385894\pi$
$107$	−4.46181	−	3.24169i	−0.431339	−	0.313386i	−0.782184	+	0.623047i	$0.785894\pi$
$108$		0			0
$109$	−0.600497			−0.0575172			−0.0287586	−	0.999586i	$-0.509155\pi$
$109$	−0.600497			−0.0575172			−0.0287586	+	0.999586i	$0.509155\pi$
$110$	−2.87847	+	9.27063i	−0.274452	+	0.883920i
$111$		0			0
$112$	−7.36898	+	17.5658i	−0.696303	+	1.65981i
$113$	−3.04947	+	4.19723i	−0.286870	+	0.394843i	−0.927994	−	0.372594i	$-0.878468\pi$
$113$	−3.04947	+	4.19723i	−0.286870	+	0.394843i	0.641124	+	0.767437i	$0.278468\pi$
$114$		0			0
$115$	−11.5432	−	3.75061i	−1.07641	−	0.349746i
$116$	8.41801	−	0.977096i	0.781593	−	0.0907211i
$117$		0			0
$118$	1.66277	−	3.78976i	0.153070	−	0.348876i
$119$	7.65355	+	23.5552i	0.701600	+	2.15930i
$120$		0			0
$121$	−5.64577	−	9.44062i	−0.513252	−	0.858238i
$122$	−1.00637	−	4.61160i	−0.0911123	−	0.417514i
$123$		0			0
$124$	3.84916	−	19.1255i	0.345664	−	1.71752i
$125$	−6.95434	−	9.57183i	−0.622015	−	0.856131i
$126$		0			0
$127$	9.65342	+	3.13659i	0.856602	+	0.278327i	0.704209	−	0.709993i	$-0.251302\pi$
$127$	9.65342	+	3.13659i	0.856602	+	0.278327i	0.152394	+	0.988320i	$0.451302\pi$
$128$	9.57644	−	6.02427i	0.846446	−	0.532475i
$129$		0			0
$130$	1.55773	+	2.66462i	0.136622	+	0.233703i
$131$	4.79732			0.419144			0.209572	−	0.977793i	$-0.432793\pi$
$131$	4.79732			0.419144			0.209572	+	0.977793i	$0.432793\pi$
$132$		0			0
$133$	−5.68830			−0.493238
$134$	−7.70861	−	13.1862i	−0.665922	−	1.13911i
$135$		0			0
$136$	4.31771	−	14.0622i	0.370240	−	1.20582i
$137$	−7.29506	−	2.37031i	−0.623259	−	0.202509i	−0.0196722	−	0.999806i	$-0.506262\pi$
$137$	−7.29506	−	2.37031i	−0.623259	−	0.202509i	−0.603587	+	0.797297i	$0.706262\pi$
$138$		0			0
$139$	0.810307	+	1.11529i	0.0687293	+	0.0945978i	0.841998	−	0.539481i	$-0.181380\pi$
$139$	0.810307	+	1.11529i	0.0687293	+	0.0945978i	−0.773269	+	0.634079i	$0.781380\pi$
$140$	−19.3242	−	3.88913i	−1.63319	−	0.328692i
$141$		0			0
$142$	−1.64106	−	7.52003i	−0.137715	−	0.631067i
$143$	−3.42665	−	0.700877i	−0.286551	−	0.0586103i
$144$		0			0
$145$	2.70989	+	8.34018i	0.225044	+	0.692614i
$146$	−3.14433	+	7.16651i	−0.260226	+	0.593105i
$147$		0			0
$148$	−2.07222	−	17.8529i	−0.170335	−	1.46750i
$149$	5.74778	+	1.86757i	0.470876	+	0.152997i	0.534837	−	0.844955i	$-0.320373\pi$
$149$	5.74778	+	1.86757i	0.470876	+	0.152997i	−0.0639605	+	0.997952i	$0.520373\pi$
$150$		0			0
$151$	3.79682	−	5.22587i	0.308980	−	0.425275i	−0.626082	−	0.779757i	$-0.715343\pi$
$151$	3.79682	−	5.22587i	0.308980	−	0.425275i	0.935063	+	0.354482i	$0.115343\pi$
$152$	2.76514	+	1.94112i	0.224282	+	0.157446i
$153$		0			0
$154$	17.8973	−	13.3649i	1.44220	−	1.07697i
$155$	20.1878			1.62152
$156$		0			0
$157$	17.4482	+	12.6769i	1.39252	+	1.01173i	0.995584	+	0.0938792i	$0.0299267\pi$
$157$	17.4482	+	12.6769i	1.39252	+	1.01173i	0.396937	+	0.917846i	$0.370073\pi$
$158$	8.33865	−	9.36252i	0.663388	−	0.744842i
$159$		0			0
$160$	8.06652	+	8.48489i	0.637714	+	0.670789i
$161$	16.4159	+	22.5945i	1.29375	+	1.78070i
$162$		0			0
$163$	−17.2335	+	5.59952i	−1.34983	+	0.438588i	−0.892637	−	0.450777i	$-0.851147\pi$
$163$	−17.2335	+	5.59952i	−1.34983	+	0.438588i	−0.457198	+	0.889365i	$0.651147\pi$
$164$	−3.35033	−	7.31074i	−0.261617	−	0.570873i
$165$		0			0
$166$	−0.531142	−	2.43391i	−0.0412246	−	0.188908i
$167$	5.44439	+	16.7561i	0.421300	+	1.29663i	0.906493	+	0.422221i	$0.138749\pi$
$167$	5.44439	+	16.7561i	0.421300	+	1.29663i	−0.485193	+	0.874407i	$0.661251\pi$
$168$		0			0
$169$	9.61751	−	6.98753i	0.739808	−	0.537502i
$170$	15.1469	+	1.50909i	1.16172	+	0.115742i
$171$		0			0
$172$	−7.01444	−	3.94908i	−0.534846	−	0.301115i
$173$	−3.24820	+	4.47076i	−0.246956	+	0.339905i	−0.914442	−	0.404717i	$-0.867370\pi$
$173$	−3.24820	+	4.47076i	−0.246956	+	0.339905i	0.667486	+	0.744622i	$0.267370\pi$
$174$		0			0
$175$			3.41362i			0.258045i
$176$	−13.2608	+	0.389391i	−0.999569	+	0.0293515i
$177$		0			0
$178$	−1.90513	−	3.25887i	−0.142795	−	0.244263i
$179$	2.14705	+	1.55993i	0.160478	+	0.116594i	0.665126	−	0.746731i	$-0.268378\pi$
$179$	2.14705	+	1.55993i	0.160478	+	0.116594i	−0.504648	+	0.863325i	$0.668378\pi$
$180$		0			0
$181$	−6.25053	+	19.2372i	−0.464599	+	1.42989i	0.394888	+	0.918729i	$0.370783\pi$
$181$	−6.25053	+	19.2372i	−0.464599	+	1.42989i	−0.859487	+	0.511158i	$0.829217\pi$
$182$	0.704113	−	7.06729i	0.0521923	−	0.523863i
$183$		0			0
$184$	−0.269582	−	16.5853i	−0.0198738	−	1.22269i
$185$	17.6878	−	5.74712i	1.30043	−	0.422537i
$186$		0			0
$187$	−12.7295	+	11.6401i	−0.930875	+	0.851208i
$188$	−6.08355	+	2.78794i	−0.443689	+	0.203332i
$189$		0			0
$190$	−1.40463	+	3.20141i	−0.101902	+	0.232255i
$191$	14.7865	−	10.7430i	1.06991	−	0.777335i	0.0940143	−	0.995571i	$-0.470030\pi$
$191$	14.7865	−	10.7430i	1.06991	−	0.777335i	0.975896	+	0.218235i	$0.0700300\pi$
$192$		0			0
$193$	1.17256	−	3.60876i	0.0844025	−	0.259764i	−0.899945	−	0.436004i	$-0.856393\pi$
$193$	1.17256	−	3.60876i	0.0844025	−	0.259764i	0.984347	+	0.176240i	$0.0563934\pi$
$194$	4.43561	+	3.95054i	0.318458	+	0.283632i
$195$		0			0
$196$	21.2335	+	23.0744i	1.51668	+	1.64817i
$197$		−	15.3473i		−	1.09345i	−0.837312	−	0.546725i	$-0.815874\pi$
$197$		−	15.3473i		−	1.09345i	0.837312	−	0.546725i	$-0.184126\pi$
$198$		0			0
$199$		−	17.5197i		−	1.24194i	−0.783834	−	0.620971i	$-0.786739\pi$
$199$		−	17.5197i		−	1.24194i	0.783834	−	0.620971i	$-0.213261\pi$
$200$	1.16489	−	1.65939i	0.0823702	−	0.117337i
$201$		0			0
$202$	0.300258	−	0.337125i	0.0211261	−	0.0237201i
$203$	6.23559	−	19.1912i	0.437653	−	1.34696i
$204$		0			0
$205$	6.73238	−	4.89136i	0.470209	−	0.341627i
$206$	−16.2537	−	7.13134i	−1.13245	−	0.496864i
$207$		0			0
$208$	−2.75398	+	3.19520i	−0.190954	+	0.221548i
$209$	−1.63909	−	3.60660i	−0.113378	−	0.249474i
$210$		0			0
$211$	1.66515	−	0.541041i	0.114634	−	0.0372468i	−0.251138	−	0.967951i	$-0.580805\pi$
$211$	1.66515	−	0.541041i	0.114634	−	0.0372468i	0.365772	+	0.930704i	$0.380805\pi$
$212$	4.70839	−	23.3949i	0.323374	−	1.60677i
$213$		0			0
$214$	7.76110	+	0.773237i	0.530538	+	0.0528574i
$215$	2.57404	−	7.92209i	0.175548	−	0.540282i
$216$		0			0
$217$	−37.5814	−	27.3045i	−2.55119	−	1.85355i
$218$	0.733144	−	0.428594i	0.0496548	−	0.0290280i
$219$		0			0
$220$	−3.10242	−	13.3729i	−0.209165	−	0.901603i
$221$			5.48459i			0.368934i
$222$		0			0
$223$	3.76360	−	5.18015i	0.252029	−	0.346889i	−0.664191	−	0.747563i	$-0.731224\pi$
$223$	3.76360	−	5.18015i	0.252029	−	0.346889i	0.916221	+	0.400674i	$0.131224\pi$
$224$	−3.54052	−	26.7055i	−0.236561	−	1.78434i
$225$		0			0
$226$	0.727387	−	7.30089i	0.0483850	−	0.485648i
$227$	−21.1291	+	15.3512i	−1.40239	+	1.01890i	−0.408014	+	0.912976i	$0.633779\pi$
$227$	−21.1291	+	15.3512i	−1.40239	+	1.01890i	−0.994375	+	0.105919i	$0.966221\pi$
$228$		0			0
$229$	−3.90383	−	12.0148i	−0.257973	−	0.793958i	−0.993229	−	0.116169i	$-0.962938\pi$
$229$	−3.90383	−	12.0148i	−0.257973	−	0.793958i	0.735257	−	0.677789i	$-0.237062\pi$
$230$	16.7700	−	3.65964i	1.10578	−	0.241309i
$231$		0			0
$232$	−9.58014	+	7.20113i	−0.628967	+	0.472778i
$233$	−0.737532	+	0.239639i	−0.0483173	+	0.0156992i	−0.333076	−	0.942900i	$-0.608087\pi$
$233$	−0.737532	+	0.239639i	−0.0483173	+	0.0156992i	0.284759	+	0.958599i	$0.408087\pi$
$234$		0			0
$235$	−4.07029	−	5.60227i	−0.265516	−	0.365452i
$236$	0.674806	+	5.81368i	0.0439261	+	0.378438i
$237$		0			0
$238$	−26.1563	−	23.2959i	−1.69546	−	1.51005i
$239$	17.7034	+	12.8623i	1.14514	+	0.831991i	0.987827	−	0.155558i	$-0.0497174\pi$
$239$	17.7034	+	12.8623i	1.14514	+	0.831991i	0.157311	+	0.987549i	$0.449717\pi$
$240$		0			0
$241$	29.4907			1.89966			0.949831	−	0.312763i	$-0.101255\pi$
$241$	29.4907			1.89966			0.949831	+	0.312763i	$0.101255\pi$
$242$	13.6310	+	7.49645i	0.876232	+	0.481890i
$243$		0			0
$244$	4.52011	+	4.91201i	0.289371	+	0.314459i
$245$	−19.0728	+	26.2514i	−1.21851	+	1.67714i
$246$		0			0
$247$	−1.19799	−	0.389250i	−0.0762262	−	0.0247674i
$248$	8.95108	+	26.0976i	0.568394	+	1.65720i
$249$		0			0
$250$	15.3223	+	6.72268i	0.969064	+	0.425180i
$251$	−6.20578	−	19.0994i	−0.391706	−	1.20555i	−0.931498	−	0.363748i	$-0.881497\pi$
$251$	−6.20578	−	19.0994i	−0.391706	−	1.20555i	0.539792	−	0.841798i	$-0.318503\pi$
$252$		0			0
$253$	−9.59555	+	16.9189i	−0.603267	+	1.06368i
$254$	−14.0245	+	3.06050i	−0.879975	+	0.192033i
$255$		0			0
$256$	−7.39213	+	14.1900i	−0.462008	+	0.886876i
$257$	−9.68734	−	13.3335i	−0.604279	−	0.831719i	0.391812	−	0.920045i	$-0.371848\pi$
$257$	−9.68734	−	13.3335i	−0.604279	−	0.831719i	−0.996092	+	0.0883260i	$0.971848\pi$
$258$		0			0
$259$	−40.7005	−	13.2244i	−2.52901	−	0.821725i
$260$	−3.80365	−	2.14143i	−0.235892	−	0.132806i
$261$		0			0
$262$	−5.85703	+	3.42400i	−0.361848	+	0.211535i
$263$	17.1003			1.05445			0.527224	−	0.849727i	$-0.323233\pi$
$263$	17.1003			1.05445			0.527224	+	0.849727i	$0.323233\pi$
$264$		0			0
$265$	24.6943			1.51696
$266$	6.94482	−	4.05992i	0.425814	−	0.248930i
$267$		0			0
$268$	18.8228	+	10.5971i	1.14979	+	0.647322i
$269$	−12.7129	−	4.13068i	−0.775120	−	0.251852i	−0.105365	−	0.994434i	$-0.533601\pi$
$269$	−12.7129	−	4.13068i	−0.775120	−	0.251852i	−0.669755	+	0.742582i	$0.733601\pi$
$270$		0			0
$271$	15.5154	+	21.3551i	0.942491	+	1.29723i	0.954783	+	0.297303i	$0.0960871\pi$
$271$	15.5154	+	21.3551i	0.942491	+	1.29723i	−0.0122924	+	0.999924i	$0.503913\pi$
$272$	4.76515	+	20.2501i	0.288930	+	1.22785i
$273$		0			0
$274$	10.5983	−	2.31281i	0.640265	−	0.139722i
$275$	−2.16436	+	0.983637i	−0.130516	+	0.0593155i
$276$		0			0
$277$	−6.44813	−	19.8453i	−0.387431	−	1.19239i	−0.934701	−	0.355434i	$-0.884333\pi$
$277$	−6.44813	−	19.8453i	−0.387431	−	1.19239i	0.547271	−	0.836956i	$-0.315667\pi$
$278$	−1.78532	−	0.783313i	−0.107076	−	0.0469800i
$279$		0			0
$280$	26.3686	−	9.04405i	1.57583	−	0.540485i
$281$	0.599850	+	0.194903i	0.0357840	+	0.0116269i	0.326854	−	0.945075i	$-0.394011\pi$
$281$	0.599850	+	0.194903i	0.0357840	+	0.0116269i	−0.291070	+	0.956702i	$0.594011\pi$
$282$		0			0
$283$	12.8240	−	17.6508i	0.762310	−	1.04923i	−0.234709	−	0.972066i	$-0.575414\pi$
$283$	12.8240	−	17.6508i	0.762310	−	1.04923i	0.997018	−	0.0771635i	$-0.0245863\pi$
$284$	7.37085	+	8.00990i	0.437379	+	0.475300i
$285$		0			0
$286$	4.68383	−	1.59001i	0.276960	−	0.0940194i
$287$	−19.1486			−1.13030
$288$		0			0
$289$	8.12936	+	5.90632i	0.478198	+	0.347431i
$290$	−9.26114	−	8.24836i	−0.543833	−	0.484361i
$291$		0			0
$292$	−1.27607	−	10.9938i	−0.0746763	−	0.643362i
$293$	8.19972	+	11.2860i	0.479033	+	0.659332i	0.978319	−	0.207105i	$-0.0664042\pi$
$293$	8.19972	+	11.2860i	0.479033	+	0.659332i	−0.499286	+	0.866437i	$0.666404\pi$
$294$		0			0
$295$	−5.75993	+	1.87151i	−0.335356	+	0.108964i
$296$	15.2721	+	20.3175i	0.887675	+	1.18093i
$297$		0			0
$298$	−8.35038	+	1.82227i	−0.483724	+	0.105561i
$299$	1.91114	+	5.88188i	0.110524	+	0.340158i
$300$		0			0
$301$	−15.5066	+	11.2662i	−0.893786	+	0.649374i
$302$	−0.905650	+	9.09015i	−0.0521143	+	0.523079i
$303$		0			0
$304$	−4.76139	−	0.396342i	−0.273084	−	0.0227318i
$305$	−4.06014	+	5.58830i	−0.232483	+	0.319985i
$306$		0			0
$307$			28.7263i			1.63950i	0.572723	+	0.819749i	$0.305887\pi$
$307$			28.7263i			1.63950i	−0.572723	+	0.819749i	$0.694113\pi$
$308$	−12.3118	+	29.0910i	−0.701528	+	1.65761i
$309$		0			0
$310$	−24.6472	+	14.4087i	−1.39987	+	0.818358i
$311$	4.63561	+	3.36797i	0.262861	+	0.190980i	0.711408	−	0.702780i	$-0.248058\pi$
$311$	4.63561	+	3.36797i	0.262861	+	0.190980i	−0.448546	+	0.893760i	$0.648058\pi$
$312$		0			0
$313$	−3.34836	+	10.3052i	−0.189260	+	0.582484i	−0.999996	−	0.00292926i	$-0.999068\pi$
$313$	−3.34836	+	10.3052i	−0.189260	+	0.582484i	0.810735	+	0.585413i	$0.199068\pi$
$314$	−30.3504	−	3.02380i	−1.71277	−	0.170643i
$315$		0			0
$316$	−3.49830	+	17.3822i	−0.196795	+	0.977827i
$317$	19.4506	−	6.31988i	1.09245	−	0.354960i	0.293260	−	0.956033i	$-0.405260\pi$
$317$	19.4506	−	6.31988i	1.09245	−	0.354960i	0.799194	+	0.601073i	$0.205260\pi$
$318$		0			0
$319$	13.9647	−	1.57635i	0.781875	−	0.0882587i
$320$	−15.9043	−	4.60184i	−0.889078	−	0.257251i
$321$		0			0
$322$	−36.1685	−	15.8690i	−2.01559	−	0.884347i
$323$	−5.02576	+	3.65143i	−0.279641	+	0.203171i
$324$		0			0
$325$	−0.233594	+	0.718927i	−0.0129574	+	0.0398789i
$326$	17.0438	−	19.1365i	0.943969	−	1.05988i
$327$		0			0
$328$	9.30831	+	6.53442i	0.513966	+	0.360803i
$329$			15.9343i			0.878485i
$330$		0			0
$331$		−	6.76556i		−	0.371869i	−0.982562	−	0.185934i	$-0.940469\pi$
$331$		−	6.76556i		−	0.371869i	0.982562	−	0.185934i	$-0.0595312\pi$
$332$	2.38563	+	2.59246i	0.130929	+	0.142280i
$333$		0			0
$334$	−18.6064	−	16.5716i	−1.01810	−	0.906760i
$335$	−6.90728	+	21.2584i	−0.377385	+	1.16147i
$336$		0			0
$337$	−8.03235	+	5.83584i	−0.437550	+	0.317899i	−0.784661	−	0.619926i	$-0.787163\pi$
$337$	−8.03235	+	5.83584i	−0.437550	+	0.317899i	0.347111	+	0.937824i	$0.387163\pi$
$338$	−6.75476	+	15.3954i	−0.367410	+	0.837397i
$339$		0			0
$340$	−19.5699	+	8.96841i	−1.06133	+	0.486380i
$341$	6.48297	−	31.6958i	0.351073	−	1.71643i
$342$		0			0
$343$	39.3072	−	12.7717i	2.12239	−	0.689607i
$344$	11.3825	−	0.185014i	0.613703	−	0.00997527i
$345$		0			0
$346$	0.774788	−	7.77667i	0.0416529	−	0.418076i
$347$	−3.93294	+	12.1043i	−0.211131	+	0.649795i	0.788274	+	0.615324i	$0.210975\pi$
$347$	−3.93294	+	12.1043i	−0.211131	+	0.649795i	−0.999406	+	0.0344715i	$0.989025\pi$
$348$		0			0
$349$	−4.86184	−	3.53233i	−0.260248	−	0.189081i	0.450008	−	0.893024i	$-0.351421\pi$
$349$	−4.86184	−	3.53233i	−0.260248	−	0.189081i	−0.710256	+	0.703943i	$0.751421\pi$
$350$	−2.43641	−	4.16767i	−0.130231	−	0.222771i
$351$		0			0
$352$	15.9121	−	9.94005i	0.848119	−	0.529806i
$353$		−	24.7207i		−	1.31575i	−0.753126	−	0.657876i	$-0.771455\pi$
$353$		−	24.7207i		−	1.31575i	0.753126	−	0.657876i	$-0.228545\pi$
$354$		0			0
$355$	−6.62078	+	9.11272i	−0.351395	+	0.483653i
$356$	4.65192	+	2.61900i	0.246551	+	0.138807i
$357$		0			0
$358$	−3.73470	−	0.372088i	−0.197385	−	0.0196654i
$359$	−13.5621	+	9.85348i	−0.715783	+	0.520047i	−0.885034	−	0.465526i	$-0.845865\pi$
$359$	−13.5621	+	9.85348i	−0.715783	+	0.520047i	0.169251	+	0.985573i	$0.445865\pi$
$360$		0			0
$361$	5.43043	+	16.7132i	0.285812	+	0.879640i
$362$	−6.09892	−	27.9478i	−0.320552	−	1.46890i
$363$		0			0
$364$	4.18450	+	9.13098i	0.219327	+	0.478593i
$365$	10.8921	−	3.53907i	0.570120	−	0.185243i
$366$		0			0
$367$	2.65667	+	3.65659i	0.138677	+	0.190873i	0.872707	−	0.488245i	$-0.162363\pi$
$367$	2.65667	+	3.65659i	0.138677	+	0.190873i	−0.734030	+	0.679117i	$0.762363\pi$
$368$	12.1666	+	20.0565i	0.634228	+	1.04552i
$369$		0			0
$370$	−17.4931	+	19.6410i	−0.909422	+	1.02109i
$371$	−45.9706	−	33.3996i	−2.38667	−	1.73402i
$372$		0			0
$373$	15.8324			0.819771			0.409886	−	0.912137i	$-0.365569\pi$
$373$	15.8324			0.819771			0.409886	+	0.912137i	$0.365569\pi$
$374$	7.23352	−	23.2968i	0.374037	−	1.20465i
$375$		0			0
$376$	5.43755	−	7.74581i	0.280420	−	0.399460i
$377$	2.62650	−	3.61507i	0.135272	−	0.186186i
$378$		0			0
$379$	9.87398	+	3.20825i	0.507192	+	0.164797i	0.551425	−	0.834225i	$-0.314084\pi$
$379$	9.87398	+	3.20825i	0.507192	+	0.164797i	−0.0442328	+	0.999021i	$0.514084\pi$
$380$	−0.570044	−	4.91112i	−0.0292426	−	0.251935i
$381$		0			0
$382$	−10.3851	+	23.6696i	−0.531349	+	1.21104i
$383$	−7.82601	−	24.0860i	−0.399890	−	1.23074i	−0.925087	−	0.379755i	$-0.876008\pi$
$383$	−7.82601	−	24.0860i	−0.399890	−	1.23074i	0.525197	−	0.850981i	$-0.323992\pi$
$384$		0			0
$385$	−32.0251	−	6.55031i	−1.63215	−	0.333835i
$386$	1.14412	+	5.24281i	0.0582340	+	0.266852i
$387$		0			0
$388$	−8.23505	−	1.65736i	−0.418071	−	0.0841399i
$389$	3.77725	+	5.19894i	0.191514	+	0.263597i	0.893966	−	0.448134i	$-0.147911\pi$
$389$	3.77725	+	5.19894i	0.191514	+	0.263597i	−0.702452	+	0.711731i	$0.747911\pi$
$390$		0			0
$391$	29.0077	+	9.42518i	1.46698	+	0.476652i
$392$	−42.3929	−	13.0165i	−2.14116	−	0.657431i
$393$		0			0
$394$	10.9539	+	18.7375i	0.551847	+	0.943980i
$395$	−18.3477			−0.923172
$396$		0			0
$397$	10.1361			0.508717			0.254358	−	0.967110i	$-0.418136\pi$
$397$	10.1361			0.508717			0.254358	+	0.967110i	$0.418136\pi$
$398$	12.5044	+	21.3898i	0.626789	+	1.07217i
$399$		0			0
$400$	−0.237849	+	2.85737i	−0.0118925	+	0.142868i
$401$	−24.4112	−	7.93169i	−1.21904	−	0.396090i	−0.372307	−	0.928110i	$-0.621433\pi$
$401$	−24.4112	−	7.93169i	−1.21904	−	0.396090i	−0.846732	+	0.532020i	$0.821433\pi$
$402$		0			0
$403$	−6.04641	−	8.32217i	−0.301193	−	0.414557i
$404$	−0.125967	+	0.625899i	−0.00626708	+	0.0311396i
$405$		0			0
$406$	6.08434	+	27.8810i	0.301961	+	1.38371i
$407$	−3.34312	−	29.6163i	−0.165712	−	1.46803i
$408$		0			0
$409$	−3.25514	−	10.0183i	−0.160956	−	0.495372i	0.837759	−	0.546040i	$-0.183865\pi$
$409$	−3.25514	−	10.0183i	−0.160956	−	0.495372i	−0.998716	+	0.0506673i	$0.983865\pi$
$410$	−4.72841	+	10.7769i	−0.233520	+	0.532235i
$411$		0			0
$412$	24.9339	−	2.89413i	1.22840	−	0.142583i
$413$	13.2539	+	4.30644i	0.652180	+	0.211906i
$414$		0			0
$415$	−2.14287	+	2.94940i	−0.105189	+	0.144780i
$416$	1.08180	−	5.86661i	0.0530398	−	0.287634i
$417$		0			0
$418$	4.57530	+	3.23341i	0.223785	+	0.158151i
$419$	7.95028			0.388397			0.194198	−	0.980962i	$-0.437789\pi$
$419$	7.95028			0.388397			0.194198	+	0.980962i	$0.437789\pi$
$420$		0			0
$421$	9.90559	+	7.19683i	0.482769	+	0.350752i	0.802397	−	0.596791i	$-0.203558\pi$
$421$	9.90559	+	7.19683i	0.482769	+	0.350752i	−0.319628	+	0.947543i	$0.603558\pi$
$422$	−1.64682	+	1.84903i	−0.0801659	+	0.0900091i
$423$		0			0
$424$	10.9492	+	31.9233i	0.531741	+	1.55033i
$425$	2.19127	+	3.01602i	0.106292	+	0.146298i
$426$		0			0
$427$	15.1166	−	4.91169i	0.731544	−	0.237693i
$428$	−10.0274	+	4.59530i	−0.484692	+	0.222122i
$429$		0			0
$430$	2.51161	+	11.5092i	0.121120	+	0.555024i
$431$	0.362172	+	1.11465i	0.0174452	+	0.0536908i	0.959400	−	0.282048i	$-0.0910139\pi$
$431$	0.362172	+	1.11465i	0.0174452	+	0.0536908i	−0.941955	+	0.335739i	$0.891014\pi$
$432$		0			0
$433$	−4.10230	+	2.98050i	−0.197144	+	0.143234i	−0.681978	−	0.731373i	$-0.738880\pi$
$433$	−4.10230	+	2.98050i	−0.197144	+	0.143234i	0.484834	+	0.874606i	$0.338880\pi$
$434$	65.3710	+	6.51290i	3.13791	+	0.312629i
$435$		0			0
$436$	−0.589192	+	1.04654i	−0.0282172	+	0.0501200i
$437$	−4.11744	+	5.66718i	−0.196964	+	0.271098i
$438$		0			0
$439$		−	10.6061i		−	0.506202i	−0.967440	−	0.253101i	$-0.918549\pi$
$439$		−	10.6061i		−	0.506202i	0.967440	−	0.253101i	$-0.0814505\pi$
$440$	13.3324	+	14.1127i	0.635598	+	0.672795i
$441$		0			0
$442$	−3.91453	−	6.69612i	−0.186195	−	0.318502i
$443$	−22.5447	−	16.3797i	−1.07113	−	0.778222i	−0.0950151	−	0.995476i	$-0.530290\pi$
$443$	−22.5447	−	16.3797i	−1.07113	−	0.778222i	−0.976115	+	0.217254i	$0.930290\pi$
$444$		0			0
$445$	−1.70708	+	5.25386i	−0.0809235	+	0.249057i
$446$	−0.897728	+	9.01063i	−0.0425086	+	0.426666i
$447$		0			0
$448$	23.3832	+	30.0777i	1.10475	+	1.42104i
$449$	−17.2796	+	5.61448i	−0.815475	+	0.264964i	−0.686915	−	0.726738i	$-0.741035\pi$
$449$	−17.2796	+	5.61448i	−0.815475	+	0.264964i	−0.128560	+	0.991702i	$0.541035\pi$
$450$		0			0
$451$	−5.51768	−	12.1409i	−0.259817	−	0.571694i
$452$	4.32281	+	9.43279i	0.203328	+	0.443681i
$453$		0			0
$454$	14.8398	−	33.8227i	0.696467	−	1.58738i
$455$	−8.40861	+	6.10921i	−0.394202	+	0.286404i
$456$		0			0
$457$	−11.7519	+	36.1686i	−0.549731	+	1.69190i	0.159737	+	0.987160i	$0.448935\pi$
$457$	−11.7519	+	36.1686i	−0.549731	+	1.69190i	−0.709468	+	0.704738i	$0.751065\pi$
$458$	13.3415	+	11.8825i	0.623407	+	0.555232i
$459$		0			0
$460$	−17.8624	+	16.4373i	−0.832839	+	0.766393i
$461$			15.5852i			0.725877i	0.931813	+	0.362939i	$0.118227\pi$
$461$			15.5852i			0.725877i	−0.931813	+	0.362939i	$0.881773\pi$
$462$		0			0
$463$			0.382281i			0.0177661i	0.999961	+	0.00888306i	$0.00282760\pi$
$463$			0.382281i			0.0177661i	−0.999961	+	0.00888306i	$0.997172\pi$
$464$	6.55667	−	15.6295i	0.304386	−	0.725580i
$465$		0			0
$466$	0.729412	−	0.818973i	0.0337894	−	0.0379382i
$467$	11.6108	−	35.7343i	0.537282	−	1.65358i	−0.201383	−	0.979513i	$-0.564544\pi$
$467$	11.6108	−	35.7343i	0.537282	−	1.65358i	0.738666	−	0.674072i	$-0.235456\pi$
$468$		0			0
$469$	41.6110	−	30.2322i	1.92142	−	1.39599i
$470$	8.96792	+	3.93470i	0.413659	+	0.181494i
$471$		0			0
$472$	−4.97327	−	6.61627i	−0.228913	−	0.304538i
$473$	−11.6115	−	6.58542i	−0.533895	−	0.302798i
$474$		0			0
$475$	−0.814300	+	0.264582i	−0.0373627	+	0.0121399i
$476$	48.5611	+	9.77328i	2.22579	+	0.447958i
$477$		0			0
$478$	−30.7942	−	3.06802i	−1.40850	−	0.140328i
$479$	1.77484	−	5.46240i	0.0810946	−	0.249584i	−0.902286	−	0.431137i	$-0.858113\pi$
$479$	1.77484	−	5.46240i	0.0810946	−	0.249584i	0.983381	+	0.181553i	$0.0581125\pi$
$480$		0			0
$481$	−7.66682	−	5.57027i	−0.349577	−	0.253983i
$482$	−36.0051	+	21.0484i	−1.63999	+	0.958730i
$483$		0			0
$484$	−21.9924	+	0.576461i	−0.999657	+	0.0262028i
$485$		−	8.69244i		−	0.394703i
$486$		0			0
$487$	9.81099	−	13.5037i	0.444578	−	0.611909i	−0.526644	−	0.850086i	$-0.676550\pi$
$487$	9.81099	−	13.5037i	0.444578	−	0.611909i	0.971222	+	0.238177i	$0.0765498\pi$
$488$	−9.02444	−	2.77090i	−0.408517	−	0.125433i
$489$		0			0
$490$	4.54940	−	45.6631i	0.205521	−	2.06285i
$491$	23.7681	−	17.2685i	1.07264	−	0.779317i	0.0962536	−	0.995357i	$-0.469314\pi$
$491$	23.7681	−	17.2685i	1.07264	−	0.779317i	0.976385	+	0.216040i	$0.0693140\pi$
$492$		0			0
$493$	−6.80987	−	20.9586i	−0.306701	−	0.943930i
$494$	1.74044	−	0.379808i	0.0783061	−	0.0170884i
$495$		0			0
$496$	−29.5550	−	25.4737i	−1.32706	−	1.14380i
$497$	24.6503	−	8.00938i	1.10572	−	0.359270i
$498$		0			0
$499$	−14.7968	−	20.3661i	−0.662396	−	0.911710i	0.337161	−	0.941447i	$-0.390533\pi$
$499$	−14.7968	−	20.3661i	−0.662396	−	0.911710i	−0.999558	+	0.0297365i	$0.990533\pi$
$500$	−23.5051	+	2.72828i	−1.05118	+	0.122012i
$501$		0			0
$502$	21.2085	+	18.8892i	0.946581	+	0.843065i
$503$	25.6613	+	18.6440i	1.14418	+	0.831295i	0.987696	−	0.156386i	$-0.0499843\pi$
$503$	25.6613	+	18.6440i	1.14418	+	0.831295i	0.156483	+	0.987681i	$0.449984\pi$
$504$		0			0
$505$	−0.660663			−0.0293991
$506$	−0.360414	−	27.5049i	−0.0160224	−	1.22274i
$507$		0			0
$508$	14.9381	−	13.7463i	0.662770	−	0.609893i
$509$	1.37237	−	1.88891i	0.0608293	−	0.0837243i	−0.777519	−	0.628860i	$-0.783522\pi$
$509$	1.37237	−	1.88891i	0.0608293	−	0.0837243i	0.838348	+	0.545136i	$0.183522\pi$
$510$		0			0
$511$	−25.0633	−	8.14356i	−1.10874	−	0.360250i
$512$	−1.10284	−	22.6005i	−0.0487391	−	0.998812i
$513$		0			0
$514$	21.3437	+	9.36463i	0.941432	+	0.413056i
$515$	8.02661	+	24.7034i	0.353695	+	1.08856i
$516$		0			0
$517$	−10.1029	+	4.59148i	−0.444327	+	0.201933i
$518$	59.1298	−	12.9036i	2.59801	−	0.566953i
$519$		0			0
$520$	6.17227	−	0.100325i	0.270672	−	0.00439956i
$521$	8.11064	+	11.1633i	0.355334	+	0.489075i	0.948841	−	0.315754i	$-0.102257\pi$
$521$	8.11064	+	11.1633i	0.355334	+	0.489075i	−0.593508	+	0.804828i	$0.702257\pi$
$522$		0			0
$523$	7.42752	+	2.41335i	0.324783	+	0.105528i	0.466870	−	0.884326i	$-0.345381\pi$
$523$	7.42752	+	2.41335i	0.324783	+	0.105528i	−0.142088	+	0.989854i	$0.545381\pi$
$524$	4.70701	−	8.36069i	0.205627	−	0.365238i
$525$		0			0
$526$	−20.8776	+	12.2050i	−0.910309	+	0.532163i
$527$	−50.7314			−2.20989
$528$		0			0
$529$	11.3932			0.495356
$530$	−30.1492	+	17.6251i	−1.30960	+	0.765585i
$531$		0			0
$532$	−5.58121	+	9.91348i	−0.241976	+	0.429804i
$533$	−4.03280	−	1.31034i	−0.174680	−	0.0567570i
$534$		0			0
$535$	−6.70896	−	9.23409i	−0.290054	−	0.399225i
$536$	−30.5442	+	0.496473i	−1.31931	+	0.0214444i
$537$		0			0
$538$	18.4693	−	4.03048i	0.796270	−	0.173766i
$539$	35.0911	+	38.3754i	1.51148	+	1.65294i
$540$		0			0
$541$	−9.00275	−	27.7076i	−0.387058	−	1.19124i	−0.934976	−	0.354711i	$-0.884579\pi$
$541$	−9.00275	−	27.7076i	−0.387058	−	1.19124i	0.547918	−	0.836532i	$-0.315421\pi$
$542$	−34.1844	−	14.9985i	−1.46835	−	0.644241i
$543$		0			0
$544$	−20.2709	−	21.3223i	−0.869109	−	0.914185i
$545$	−1.18195	−	0.384040i	−0.0506294	−	0.0164505i
$546$		0			0
$547$	−12.8675	+	17.7106i	−0.550175	+	0.757251i	−0.990036	−	0.140815i	$-0.955028\pi$
$547$	−12.8675	+	17.7106i	−0.550175	+	0.757251i	0.439861	+	0.898066i	$0.355028\pi$
$548$	−11.2887	+	10.3880i	−0.482228	+	0.443754i
$549$		0			0
$550$	1.94041	−	2.74569i	0.0827394	−	0.117077i
$551$	5.06126			0.215617
$552$		0			0
$553$	34.1558	+	24.8156i	1.45245	+	1.05527i
$554$	22.0367	+	19.6268i	0.936251	+	0.833864i
$555$		0			0
$556$	2.73876	−	0.317894i	0.116149	−	0.0134817i
$557$	13.9849	+	19.2486i	0.592561	+	0.815590i	0.995002	−	0.0998558i	$-0.0318381\pi$
$557$	13.9849	+	19.2486i	0.592561	+	0.815590i	−0.402441	+	0.915446i	$0.631838\pi$
$558$		0			0
$559$	−4.03673	+	1.31161i	−0.170735	+	0.0554753i
$560$	−25.7383	+	29.8620i	−1.08764	+	1.26190i
$561$		0			0
$562$	−0.871463	+	0.190175i	−0.0367604	+	0.00802207i
$563$	−11.0114	−	33.8897i	−0.464077	−	1.42828i	−0.860140	−	0.510058i	$-0.829624\pi$
$563$	−11.0114	−	33.8897i	−0.464077	−	1.42828i	0.396063	−	0.918223i	$-0.370376\pi$
$564$		0			0
$565$	−8.68654	+	6.31114i	−0.365445	+	0.265512i
$566$	−3.05890	+	30.7027i	−0.128575	+	1.29053i
$567$		0			0
$568$	−14.7160	−	4.51844i	−0.617468	−	0.189590i
$569$	23.1697	−	31.8903i	0.971323	−	1.33691i	0.0299479	−	0.999551i	$-0.490466\pi$
$569$	23.1697	−	31.8903i	0.971323	−	1.33691i	0.941376	−	0.337361i	$-0.109534\pi$
$570$		0			0
$571$		−	16.3027i		−	0.682245i	−0.940019	−	0.341123i	$-0.889193\pi$
$571$		−	16.3027i		−	0.682245i	0.940019	−	0.341123i	$-0.110807\pi$
$572$	−4.58362	+	5.28423i	−0.191651	+	0.220945i
$573$		0			0
$574$	23.3784	−	13.6669i	0.975797	−	0.570447i
$575$	3.40094	+	2.47093i	0.141829	+	0.103045i
$576$		0			0
$577$	−5.26806	+	16.2134i	−0.219312	+	0.674974i	0.779507	+	0.626393i	$0.215470\pi$
$577$	−5.26806	+	16.2134i	−0.219312	+	0.674974i	−0.998819	+	0.0485801i	$0.984530\pi$
$578$	−14.1406	−	1.40883i	−0.588173	−	0.0585996i
$579$		0			0
$580$	17.1940	+	3.46042i	0.713942	+	0.143686i
$581$	7.97827	−	2.59230i	0.330994	−	0.107547i
$582$		0			0
$583$	7.93015	−	38.7712i	0.328433	−	1.60574i
$584$	9.40455	+	12.5115i	0.389163	+	0.517729i
$585$		0			0
$586$	−18.0662	−	7.92657i	−0.746306	−	0.327444i
$587$	13.6279	−	9.90127i	0.562485	−	0.408669i	−0.269883	−	0.962893i	$-0.586985\pi$
$587$	13.6279	−	9.90127i	0.562485	−	0.408669i	0.832367	+	0.554224i	$0.186985\pi$
$588$		0			0
$589$	3.60048	−	11.0812i	0.148355	−	0.456591i
$590$	5.69651	−	6.39596i	0.234522	−	0.263318i
$591$		0			0
$592$	−33.1469	−	13.9054i	−1.36233	−	0.571507i
$593$			35.3389i			1.45119i	0.688120	+	0.725597i	$0.258436\pi$
$593$			35.3389i			1.45119i	−0.688120	+	0.725597i	$0.741564\pi$
$594$		0			0
$595$			51.2583i			2.10139i
$596$	8.89434	−	8.18473i	0.364326	−	0.335259i
$597$		0			0
$598$	−6.53138	−	5.81712i	−0.267088	−	0.237880i
$599$	−10.0745	+	31.0062i	−0.411634	+	1.26688i	0.503594	+	0.863941i	$0.332011\pi$
$599$	−10.0745	+	31.0062i	−0.411634	+	1.26688i	−0.915227	+	0.402938i	$0.867989\pi$
$600$		0			0
$601$	−0.650494	+	0.472612i	−0.0265342	+	0.0192782i	−0.600973	−	0.799269i	$-0.705220\pi$
$601$	−0.650494	+	0.472612i	−0.0265342	+	0.0192782i	0.574439	+	0.818547i	$0.305220\pi$
$602$	10.8909	−	24.8224i	0.443880	−	1.01169i
$603$		0			0
$604$	−5.38222	−	11.7445i	−0.219000	−	0.477878i
$605$	−5.07490	−	22.1926i	−0.206324	−	0.902257i
$606$		0			0
$607$	−29.8432	+	9.69664i	−1.21130	+	0.393574i	−0.843905	−	0.536492i	$-0.819749\pi$
$607$	−29.8432	+	9.69664i	−1.21130	+	0.393574i	−0.367392	+	0.930066i	$0.619749\pi$
$608$	6.09604	−	2.91446i	0.247227	−	0.118197i
$609$		0			0
$610$	0.968461	−	9.72059i	0.0392118	−	0.393575i
$611$	−1.09038	+	3.35585i	−0.0441121	+	0.135763i
$612$		0			0
$613$	16.5768	+	12.0437i	0.669530	+	0.486442i	0.869868	−	0.493285i	$-0.164204\pi$
$613$	16.5768	+	12.0437i	0.669530	+	0.486442i	−0.200338	+	0.979727i	$0.564204\pi$
$614$	−20.5029	−	35.0719i	−0.827429	−	1.41539i
$615$		0			0
$616$	−5.73176	−	44.3044i	−0.230939	−	1.78507i
$617$			20.3723i			0.820158i	0.912050	+	0.410079i	$0.134499\pi$
$617$			20.3723i			0.820158i	−0.912050	+	0.410079i	$0.865501\pi$
$618$		0			0
$619$	−11.5772	+	15.9347i	−0.465327	+	0.640468i	−0.975603	−	0.219543i	$-0.929543\pi$
$619$	−11.5772	+	15.9347i	−0.465327	+	0.640468i	0.510275	+	0.860011i	$0.329543\pi$
$620$	19.8078	−	35.1830i	0.795499	−	1.41298i
$621$		0			0
$622$	−8.06342	−	0.803358i	−0.323314	−	0.0322117i
$623$	10.2839	−	7.47166i	0.412014	−	0.299346i
$624$		0			0
$625$	−6.45911	−	19.8791i	−0.258364	−	0.795164i
$626$	−3.26714	−	14.9714i	−0.130581	−	0.598377i
$627$		0			0
$628$	39.2128	−	17.9703i	1.56476	−	0.717092i
$629$	−44.4490	+	14.4423i	−1.77230	+	0.575854i
$630$		0			0
$631$	−4.79695	−	6.60243i	−0.190963	−	0.262839i	0.702790	−	0.711398i	$-0.251937\pi$
$631$	−4.79695	−	6.60243i	−0.190963	−	0.262839i	−0.893753	+	0.448559i	$0.851937\pi$
$632$	−8.13518	−	23.7187i	−0.323600	−	0.943481i
$633$		0			0
$634$	−19.2365	+	21.5984i	−0.763977	+	0.857783i
$635$	16.9948	+	12.3474i	0.674418	+	0.489993i
$636$		0			0
$637$	16.5343			0.655111
$638$	−15.9244	+	11.8916i	−0.630453	+	0.470794i
$639$		0			0
$640$	22.7020	−	5.73304i	0.897375	−	0.226618i
$641$	−4.57557	+	6.29773i	−0.180724	+	0.248745i	−0.889762	−	0.456425i	$-0.849130\pi$
$641$	−4.57557	+	6.29773i	−0.180724	+	0.248745i	0.709038	+	0.705171i	$0.249130\pi$
$642$		0			0
$643$	29.0648	+	9.44371i	1.14620	+	0.372424i	0.819712	−	0.572777i	$-0.194134\pi$
$643$	29.0648	+	9.44371i	1.14620	+	0.372424i	0.326491	+	0.945200i	$0.394134\pi$
$644$	55.4842	−	6.44017i	2.18639	−	0.253778i
$645$		0			0
$646$	3.52979	−	8.04506i	0.138878	−	0.316529i
$647$	11.0611	+	34.0424i	0.434855	+	1.33835i	0.893235	+	0.449590i	$0.148430\pi$
$647$	11.0611	+	34.0424i	0.434855	+	1.33835i	−0.458380	+	0.888756i	$0.651570\pi$
$648$		0			0
$649$	1.08866	+	9.64437i	0.0427338	+	0.378575i
$650$	−0.227928	−	1.04446i	−0.00894005	−	0.0409670i
$651$		0			0
$652$	−7.15036	+	35.5284i	−0.280030	+	1.39140i
$653$	−13.3516	−	18.3768i	−0.522487	−	0.719141i	0.463476	−	0.886110i	$-0.346602\pi$
$653$	−13.3516	−	18.3768i	−0.522487	−	0.719141i	−0.985962	+	0.166969i	$0.946602\pi$
$654$		0			0
$655$	9.44253	+	3.06806i	0.368950	+	0.119879i
$656$	−16.0283	−	1.33421i	−0.625800	−	0.0520921i
$657$		0			0
$658$	−11.3728	−	19.4541i	−0.443358	−	0.758400i
$659$	25.0452			0.975624			0.487812	−	0.872949i	$-0.337795\pi$
$659$	25.0452			0.975624			0.487812	+	0.872949i	$0.337795\pi$
$660$		0			0
$661$	−45.1890			−1.75765			−0.878825	−	0.477144i	$-0.841672\pi$
$661$	−45.1890			−1.75765			−0.878825	+	0.477144i	$0.841672\pi$
$662$	4.82879	+	8.26004i	0.187676	+	0.321036i
$663$		0			0
$664$	−4.76293	−	1.46243i	−0.184838	−	0.0567532i
$665$	−11.1962	−	3.63788i	−0.434172	−	0.141071i
$666$		0			0
$667$	−14.6063	−	20.1039i	−0.565559	−	0.778425i
$668$	34.5442	+	6.95228i	1.33656	+	0.268992i
$669$		0			0
$670$	−6.73974	−	30.8843i	−0.260379	−	1.19316i
$671$	7.47007	+	8.16921i	0.288379	+	0.315369i
$672$		0			0
$673$	−10.2979	−	31.6938i	−0.396956	−	1.22171i	−0.927428	−	0.374003i	$-0.877985\pi$
$673$	−10.2979	−	31.6938i	−0.396956	−	1.22171i	0.530471	−	0.847703i	$-0.322015\pi$
$674$	5.64144	−	12.8579i	0.217300	−	0.495268i
$675$		0			0
$676$	−2.74130	−	23.6172i	−0.105435	−	0.908355i
$677$	4.72933	+	1.53665i	0.181763	+	0.0590583i	0.398484	−	0.917175i	$-0.369536\pi$
$677$	4.72933	+	1.53665i	0.181763	+	0.0590583i	−0.216721	+	0.976233i	$0.569536\pi$
$678$		0			0
$679$	−11.7567	+	16.1817i	−0.451182	+	0.620998i
$680$	17.4918	−	24.9172i	0.670780	−	0.955530i
$681$		0			0
$682$	14.7073	+	43.3244i	0.563171	+	1.65898i
$683$	11.2268			0.429581			0.214791	−	0.976660i	$-0.431093\pi$
$683$	11.2268			0.429581			0.214791	+	0.976660i	$0.431093\pi$
$684$		0			0
$685$	−12.8429	−	9.33093i	−0.490703	−	0.356516i
$686$	−38.8745	+	43.6477i	−1.48423	+	1.66648i
$687$		0			0
$688$	−13.7648	+	8.34993i	−0.524778	+	0.318338i
$689$	−7.39614	−	10.1799i	−0.281770	−	0.387824i
$690$		0			0
$691$	8.95981	−	2.91122i	0.340847	−	0.110748i	−0.133591	−	0.991036i	$-0.542651\pi$
$691$	8.95981	−	2.91122i	0.340847	−	0.110748i	0.474439	+	0.880288i	$0.342651\pi$
$692$	4.60452	+	10.0475i	0.175038	+	0.381948i
$693$		0			0
$694$	−3.83754	−	17.5852i	−0.145671	−	0.667526i
$695$	0.881651	+	2.71344i	0.0334429	+	0.102927i
$696$		0			0
$697$	−16.9183	+	12.2918i	−0.640825	+	0.465587i
$698$	8.45694	+	0.842563i	0.320100	+	0.0318915i
$699$		0			0
$700$	5.94920	+	3.34935i	0.224858	+	0.126594i
$701$	5.17700	−	7.12553i	0.195533	−	0.269128i	−0.699981	−	0.714161i	$-0.746808\pi$
$701$	5.17700	−	7.12553i	0.195533	−	0.269128i	0.895514	+	0.445034i	$0.146808\pi$
$702$		0			0
$703$		−	10.7339i		−	0.404836i
$704$	−12.3325	+	23.4927i	−0.464799	+	0.885416i
$705$		0			0
$706$	17.6440	+	30.1814i	0.664040	+	1.13589i
$707$	1.22988	+	0.893561i	0.0462544	+	0.0336058i
$708$		0			0
$709$	−5.34013	+	16.4352i	−0.200553	+	0.617238i	0.799314	+	0.600914i	$0.205196\pi$
$709$	−5.34013	+	16.4352i	−0.200553	+	0.617238i	−0.999867	+	0.0163245i	$0.994804\pi$
$710$	1.57925	−	15.8511i	0.0592681	−	0.594883i
$711$		0			0
$712$	−7.54878	+	0.122700i	−0.282902	+	0.00459836i
$713$	−54.4062	+	17.6776i	−2.03753	+	0.662033i
$714$		0			0
$715$	−6.29642	−	3.57101i	−0.235473	−	0.133548i
$716$	4.82525	−	2.21129i	0.180328	−	0.0826399i
$717$		0			0
$718$	9.52524	−	21.7098i	0.355479	−	0.810203i
$719$	15.6044	−	11.3372i	0.581945	−	0.422808i	−0.257480	−	0.966284i	$-0.582892\pi$
$719$	15.6044	−	11.3372i	0.581945	−	0.422808i	0.839425	+	0.543476i	$0.182892\pi$
$720$		0			0
$721$	18.4696	−	56.8436i	0.687845	−	2.11697i
$722$	−18.5587	−	16.5292i	−0.690684	−	0.615152i
$723$		0			0
$724$	27.3934	+	29.7684i	1.01807	+	1.10633i
$725$		−	3.03732i		−	0.112803i
$726$		0			0
$727$			2.59644i			0.0962965i	0.998840	+	0.0481482i	$0.0153320\pi$
$727$			2.59644i			0.0962965i	−0.998840	+	0.0481482i	$0.984668\pi$
$728$	−11.6259	−	8.16136i	−0.430885	−	0.302480i
$729$		0			0
$730$	−10.7722	+	12.0949i	−0.398697	+	0.447652i
$731$	−6.46849	+	19.9080i	−0.239246	+	0.736323i
$732$		0			0
$733$	26.3869	−	19.1712i	0.974621	−	0.708104i	0.0181212	−	0.999836i	$-0.494232\pi$
$733$	26.3869	−	19.1712i	0.974621	−	0.708104i	0.956500	+	0.291732i	$0.0942315\pi$
$734$	−5.85335	−	2.56817i	−0.216051	−	0.0947929i
$735$		0			0
$736$	−29.1691	−	15.8033i	−1.07519	−	0.582516i
$737$	31.1586	+	17.6716i	1.14774	+	0.650940i
$738$		0			0
$739$	−24.6991	+	8.02521i	−0.908570	+	0.295212i	−0.725770	−	0.687938i	$-0.758516\pi$
$739$	−24.6991	+	8.02521i	−0.908570	+	0.295212i	−0.182800	+	0.983150i	$0.558516\pi$
$740$	7.33885	−	36.4650i	0.269781	−	1.34048i
$741$		0			0
$742$	79.9637	+	7.96677i	2.93556	+	0.292469i
$743$	5.56858	−	17.1383i	0.204291	−	0.628744i	−0.795451	−	0.606019i	$-0.792766\pi$
$743$	5.56858	−	17.1383i	0.204291	−	0.628744i	0.999742	−	0.0227252i	$-0.00723427\pi$
$744$		0			0
$745$	10.1189	+	7.35184i	0.370729	+	0.269350i
$746$	−19.3297	+	11.3001i	−0.707712	+	0.413726i
$747$		0			0
$748$	7.79629	+	33.6058i	0.285061	+	1.22875i
$749$			26.2641i			0.959669i
$750$		0			0
$751$	−27.2751	+	37.5410i	−0.995283	+	1.36989i	−0.0671077	+	0.997746i	$0.521377\pi$
$751$	−27.2751	+	37.5410i	−0.995283	+	1.36989i	−0.928175	+	0.372144i	$0.878623\pi$
$752$	−1.11025	+	13.3378i	−0.0404866	+	0.486379i
$753$		0			0
$754$	−0.626497	+	6.28824i	−0.0228157	+	0.229004i
$755$	10.8154	−	7.85784i	0.393612	−	0.285976i
$756$		0			0
$757$	6.12214	+	18.8420i	0.222513	+	0.684824i	0.998535	+	0.0541179i	$0.0172347\pi$
$757$	6.12214	+	18.8420i	0.222513	+	0.684824i	−0.776022	+	0.630706i	$0.782765\pi$
$758$	−14.3449	+	3.13043i	−0.521031	+	0.113702i
$759$		0			0
$760$	4.20118	+	5.58911i	0.152393	+	0.202738i
$761$	45.0795	−	14.6472i	1.63413	−	0.530962i	0.658916	−	0.752217i	$-0.271015\pi$
$761$	45.0795	−	14.6472i	1.63413	−	0.530962i	0.975216	+	0.221255i	$0.0710154\pi$
$762$		0			0
$763$	1.68089	+	2.31354i	0.0608523	+	0.0837559i
$764$	−4.21462	−	36.3104i	−0.152480	−	1.31366i
$765$		0			0
$766$	26.7457	+	23.8208i	0.966360	+	0.860681i
$767$	2.49665	+	1.81392i	0.0901489	+	0.0654970i
$768$		0			0
$769$	−3.65298			−0.131730			−0.0658649	−	0.997829i	$-0.520981\pi$
$769$	−3.65298			−0.131730			−0.0658649	+	0.997829i	$0.520981\pi$
$770$	43.7744	−	14.8600i	1.57752	−	0.535519i
$771$		0			0
$772$	−5.13881	−	5.58434i	−0.184950	−	0.200985i
$773$	−4.03481	+	5.55344i	−0.145122	+	0.199743i	−0.875390	−	0.483418i	$-0.839395\pi$
$773$	−4.03481	+	5.55344i	−0.145122	+	0.199743i	0.730268	+	0.683161i	$0.239395\pi$
$774$		0			0
$775$	−6.64993	−	2.16069i	−0.238873	−	0.0776144i
$776$	11.2371	−	3.85414i	0.403387	−	0.138356i
$777$		0			0
$778$	−8.32228	−	3.65142i	−0.298368	−	0.130910i
$779$	−1.48417	−	4.56779i	−0.0531758	−	0.163658i
$780$		0			0
$781$	12.1813	+	13.3213i	0.435880	+	0.476675i
$782$	−42.1425	+	9.19656i	−1.50701	+	0.328868i
$783$		0			0
$784$	61.0475	−	14.3654i	2.18027	−	0.513049i
$785$	26.2359	+	36.1106i	0.936399	+	1.28884i
$786$		0			0
$787$	22.1364	+	7.19256i	0.789079	+	0.256387i	0.675712	−	0.737166i	$-0.263836\pi$
$787$	22.1364	+	7.19256i	0.789079	+	0.256387i	0.113367	+	0.993553i	$0.463836\pi$
$788$	−26.7470	−	15.0584i	−0.952824	−	0.536433i
$789$		0			0
$790$	22.4006	−	13.0953i	0.796978	−	0.465910i
$791$	24.7067			0.878470
$792$		0			0
$793$	3.51975			0.124990
$794$	−12.3751	+	7.23446i	−0.439177	+	0.256741i
$795$		0			0
$796$	−30.5331	−	17.1899i	−1.08222	−	0.609281i
$797$	32.3102	+	10.4982i	1.14449	+	0.371866i	0.819064	−	0.573703i	$-0.194493\pi$
$797$	32.3102	+	10.4982i	1.14449	+	0.371866i	0.325423	+	0.945569i	$0.394493\pi$
$798$		0			0
$799$	10.2285	+	14.0783i	0.361859	+	0.498056i
$800$	−1.74900	−	3.65831i	−0.0618366	−	0.129341i
$801$		0			0
$802$	35.4647	−	7.73930i	1.25230	−	0.273284i
$803$	−2.05868	−	18.2377i	−0.0726494	−	0.643594i
$804$		0			0
$805$	17.8612	+	54.9712i	0.629526	+	1.93748i
$806$	13.3218	+	5.84499i	0.469242	+	0.205881i
$807$		0			0
$808$	−0.292931	−	0.854064i	−0.0103053	−	0.0300459i
$809$	−48.7230	−	15.8311i	−1.71301	−	0.556591i	−0.722180	−	0.691705i	$-0.756860\pi$
$809$	−48.7230	−	15.8311i	−1.71301	−	0.556591i	−0.990830	+	0.135114i	$0.956860\pi$
$810$		0			0
$811$	17.2341	−	23.7207i	0.605172	−	0.832948i	−0.390998	−	0.920392i	$-0.627870\pi$
$811$	17.2341	−	23.7207i	0.605172	−	0.832948i	0.996169	+	0.0874441i	$0.0278699\pi$
$812$	−27.3279	−	29.6972i	−0.959020	−	1.04217i
$813$		0			0
$814$	25.2197	+	33.7724i	0.883950	+	1.18372i
$815$	−37.5018			−1.31363
$816$		0			0
$817$	−3.88938	−	2.82580i	−0.136072	−	0.0988622i
$818$	11.1245	+	9.90799i	0.388961	+	0.346425i
$819$		0			0
$820$	−1.91894	−	16.5324i	−0.0670124	−	0.577335i
$821$	−21.1733	−	29.1426i	−0.738955	−	1.01708i	−0.998678	−	0.0514011i	$-0.983631\pi$
$821$	−21.1733	−	29.1426i	−0.738955	−	1.01708i	0.259723	−	0.965683i	$-0.416369\pi$
$822$		0			0
$823$	15.1584	−	4.92528i	0.528390	−	0.171684i	−0.0326594	−	0.999467i	$-0.510398\pi$
$823$	15.1584	−	4.92528i	0.528390	−	0.171684i	0.561050	+	0.827782i	$0.310398\pi$
$824$	−28.3761	+	21.3295i	−0.988527	+	0.743050i
$825$		0			0
$826$	−19.2552	+	4.20199i	−0.669976	+	0.146206i
$827$	5.83560	+	17.9601i	0.202924	+	0.624535i	0.999792	+	0.0203825i	$0.00648840\pi$
$827$	5.83560	+	17.9601i	0.202924	+	0.624535i	−0.796868	+	0.604153i	$0.793512\pi$
$828$		0			0
$829$	−30.3345	+	22.0393i	−1.05356	+	0.765457i	−0.972886	−	0.231284i	$-0.925707\pi$
$829$	−30.3345	+	22.0393i	−1.05356	+	0.765457i	−0.0806743	+	0.996741i	$0.525707\pi$
$830$	0.511135	−	5.13034i	0.0177418	−	0.178077i
$831$		0			0
$832$	2.86642	+	7.93464i	0.0993751	+	0.275084i
$833$	47.9293	−	65.9690i	1.66065	−	2.28569i
$834$		0			0
$835$			36.4629i			1.26185i
$836$	−7.89376	−	0.682126i	−0.273011	−	0.0235918i
$837$		0			0
$838$	−9.70647	+	5.67437i	−0.335304	+	0.196018i
$839$	5.85228	+	4.25193i	0.202043	+	0.146793i	0.684206	−	0.729289i	$-0.260149\pi$
$839$	5.85228	+	4.25193i	0.202043	+	0.146793i	−0.482163	+	0.876081i	$0.660149\pi$
$840$		0			0
$841$	3.41327	−	10.5050i	0.117699	−	0.362240i
$842$	−17.2303	−	1.71665i	−0.593795	−	0.0591597i
$843$		0			0
$844$	0.690887	−	3.43285i	0.0237813	−	0.118164i
$845$	23.3989	−	7.60275i	0.804945	−	0.261543i
$846$		0			0
$847$	−20.5686	+	48.1774i	−0.706746	+	1.65539i
$848$	−36.1525	−	31.1602i	−1.24148	−	1.07005i
$849$		0			0
$850$	−4.82794	−	2.11827i	−0.165597	−	0.0726560i
$851$	−42.6362	+	30.9770i	−1.46155	+	1.06188i
$852$		0			0
$853$	−12.3212	+	37.9206i	−0.421869	+	1.29838i	0.484093	+	0.875017i	$0.339150\pi$
$853$	−12.3212	+	37.9206i	−0.421869	+	1.29838i	−0.905961	+	0.423361i	$0.860850\pi$
$854$	−14.9502	+	16.7859i	−0.511585	+	0.574400i
$855$		0			0
$856$	8.96258	−	12.7672i	0.306335	−	0.436375i
$857$		−	20.0319i		−	0.684276i	−0.939650	−	0.342138i	$-0.888849\pi$
$857$		−	20.0319i		−	0.684276i	0.939650	−	0.342138i	$-0.111151\pi$
$858$		0			0
$859$			1.44804i			0.0494065i	0.999695	+	0.0247032i	$0.00786408\pi$
$859$			1.44804i			0.0494065i	−0.999695	+	0.0247032i	$0.992136\pi$
$860$	−11.2809	−	12.2589i	−0.384676	−	0.418027i
$861$		0			0
$862$	−1.23774	−	1.10238i	−0.0421574	−	0.0375472i
$863$	0.892359	−	2.74640i	0.0303763	−	0.0934885i	−0.934719	−	0.355388i	$-0.884349\pi$
$863$	0.892359	−	2.74640i	0.0303763	−	0.0934885i	0.965095	+	0.261899i	$0.0843488\pi$
$864$		0			0
$865$	−9.25262	+	6.72242i	−0.314598	+	0.228569i
$866$	2.88121	−	6.56682i	0.0979075	−	0.223150i
$867$		0			0
$868$	−84.4597	+	38.7058i	−2.86675	+	1.31376i
$869$	−5.89205	+	28.8067i	−0.199874	+	0.977202i
$870$		0			0
$871$	10.8323	−	3.51963i	0.367039	−	0.119258i
$872$	−0.0276036	−	1.69824i	−0.000934775	−	0.0575096i
$873$		0			0
$874$	0.982130	−	9.85778i	0.0332210	−	0.333445i
$875$	−17.4112	+	53.5862i	−0.588607	+	1.81155i
$876$		0			0
$877$	−17.2616	−	12.5413i	−0.582882	−	0.423489i	0.256880	−	0.966443i	$-0.417306\pi$
$877$	−17.2616	−	12.5413i	−0.582882	−	0.423489i	−0.839762	+	0.542955i	$0.817306\pi$
$878$	7.56992	+	12.9490i	0.255472	+	0.437006i
$879$		0			0
$880$	−26.3501	−	7.71433i	−0.888263	−	0.260050i
$881$		−	6.88589i		−	0.231991i	−0.993250	−	0.115996i	$-0.962994\pi$
$881$		−	6.88589i		−	0.231991i	0.993250	−	0.115996i	$-0.0370059\pi$
$882$		0			0
$883$	−3.43359	+	4.72594i	−0.115550	+	0.159040i	−0.862874	−	0.505419i	$-0.831338\pi$
$883$	−3.43359	+	4.72594i	−0.115550	+	0.159040i	0.747325	+	0.664459i	$0.231338\pi$
$884$	9.55846	+	5.38134i	0.321486	+	0.180994i
$885$		0			0
$886$	39.2154	+	3.90702i	1.31747	+	0.131259i
$887$	26.2038	−	19.0381i	0.879836	−	0.639238i	−0.0533720	−	0.998575i	$-0.516997\pi$
$887$	26.2038	−	19.0381i	0.879836	−	0.639238i	0.933208	+	0.359336i	$0.116997\pi$
$888$		0			0
$889$	−14.9371	−	45.9717i	−0.500975	−	1.54184i
$890$	−1.66568	−	7.63282i	−0.0558336	−	0.255853i
$891$		0			0
$892$	−5.33514	−	11.6418i	−0.178634	−	0.389796i
$893$	−3.80104	+	1.23503i	−0.127197	+	0.0413288i
$894$		0			0
$895$	3.22840	+	4.44352i	0.107914	+	0.148530i
$896$	−50.0158	−	20.0324i	−1.67091	−	0.669236i
$897$		0			0
$898$	17.0894	−	19.1877i	0.570279	−	0.640302i
$899$	33.4387	+	24.2946i	1.11524	+	0.810271i
$900$		0			0
$901$	−62.0560			−2.06739
$902$	15.4019	+	10.8847i	0.512827	+	0.362420i
$903$		0			0
$904$	−12.0102	−	8.43112i	−0.399453	−	0.280415i
$905$	−24.6058	+	33.8669i	−0.817924	+	1.12578i
$906$		0			0
$907$	6.10592	+	1.98393i	0.202744	+	0.0658755i	0.408629	−	0.912701i	$-0.366007\pi$
$907$	6.10592	+	1.98393i	0.202744	+	0.0658755i	−0.205885	+	0.978576i	$0.566007\pi$
$908$	6.02248	+	51.8857i	0.199863	+	1.72189i
$909$		0			0
$910$	5.90570	−	13.4602i	0.195772	−	0.446201i
$911$	−14.9768	−	46.0938i	−0.496203	−	1.52716i	−0.815073	−	0.579358i	$-0.803303\pi$
$911$	−14.9768	−	46.0938i	−0.496203	−	1.52716i	0.318870	−	0.947798i	$-0.396697\pi$
$912$		0			0
$913$	3.94256	+	4.31155i	0.130480	+	0.142692i
$914$	−11.4668	−	52.5459i	−0.379290	−	1.73806i
$915$		0			0
$916$	−24.7695	−	4.98504i	−0.818407	−	0.164710i
$917$	−13.4285	−	18.4827i	−0.443447	−	0.610353i
$918$		0			0
$919$	−36.5068	−	11.8618i	−1.20425	−	0.391284i	−0.362927	−	0.931818i	$-0.618223\pi$
$919$	−36.5068	−	11.8618i	−1.20425	−	0.391284i	−0.841323	+	0.540533i	$0.818223\pi$
$920$	10.0763	−	32.8172i	0.332206	−	1.08195i
$921$		0			0
$922$	−11.1237	−	19.0280i	−0.366339	−	0.626653i
$923$	5.73958			0.188921
$924$		0			0
$925$	−6.44154			−0.211796
$926$	−0.272846	−	0.466726i	−0.00896628	−	0.0153376i
$927$		0			0
$928$	3.15024	+	23.7617i	0.103412	+	0.780015i
$929$	−26.7420	−	8.68901i	−0.877378	−	0.285077i	−0.164510	−	0.986375i	$-0.552604\pi$
$929$	−26.7420	−	8.68901i	−0.877378	−	0.285077i	−0.712868	+	0.701298i	$0.752604\pi$
$930$		0			0
$931$	11.0079	+	15.1510i	0.360768	+	0.496554i
$932$	−0.306009	+	1.52049i	−0.0100237	+	0.0498052i
$933$		0			0
$934$	11.3291	+	51.9148i	0.370701	+	1.69870i
$935$	−32.4997	+	14.7701i	−1.06285	+	0.483035i
$936$		0			0
$937$	13.2113	+	40.6602i	0.431595	+	1.32831i	0.896536	+	0.442970i	$0.146075\pi$
$937$	13.2113	+	40.6602i	0.431595	+	1.32831i	−0.464942	+	0.885341i	$0.653925\pi$
$938$	−29.2251	+	66.6094i	−0.954232	+	2.17488i
$939$		0			0
$940$	−13.7572	+	1.59683i	−0.448711	+	0.0520828i
$941$	−33.5854	−	10.9126i	−1.09485	−	0.355739i	−0.294733	−	0.955580i	$-0.595231\pi$
$941$	−33.5854	−	10.9126i	−1.09485	−	0.355739i	−0.800120	+	0.599840i	$0.795231\pi$
$942$		0			0
$943$	−13.8606	+	19.0775i	−0.451363	+	0.621248i
$944$	10.7941	+	4.52819i	0.351318	+	0.147380i
$945$		0			0
$946$	18.8766	−	0.247352i	0.613731	−	0.00804211i
$947$	−27.3997			−0.890372			−0.445186	−	0.895438i	$-0.646862\pi$
$947$	−27.3997			−0.890372			−0.445186	+	0.895438i	$0.646862\pi$
$948$		0			0
$949$	−4.72121	−	3.43016i	−0.153257	−	0.111348i
$950$	0.805335	−	0.904219i	0.0261285	−	0.0293367i
$951$		0			0
$952$	−66.2636	+	22.7274i	−2.14761	+	0.736600i
$953$	1.24663	+	1.71584i	0.0403824	+	0.0555816i	0.828731	−	0.559648i	$-0.189063\pi$
$953$	1.24663	+	1.71584i	0.0403824	+	0.0555816i	−0.788348	+	0.615229i	$0.789063\pi$
$954$		0			0
$955$	35.9746	−	11.6889i	1.16411	−	0.378243i
$956$	39.7863	−	18.2331i	1.28678	−	0.589700i
$957$		0			0
$958$	1.73179	+	7.93579i	0.0559516	+	0.256394i
$959$	11.2879	+	34.7407i	0.364506	+	1.12183i
$960$		0			0
$961$	51.8989	−	37.7067i	1.67416	−	1.21635i
$962$	13.3361	+	1.32867i	0.429972	+	0.0428381i
$963$		0			0
$964$	28.9355	−	51.3959i	0.931950	−	1.65535i
$965$	4.61588	−	6.35321i	0.148590	−	0.204517i
$966$		0			0
$967$			33.6610i			1.08247i	0.840873	+	0.541233i	$0.182042\pi$
$967$			33.6610i			1.08247i	−0.840873	+	0.541233i	$0.817958\pi$
$968$	26.4391	−	16.4005i	0.849783	−	0.527132i
$969$		0			0
$970$	6.20407	+	10.6126i	0.199201	+	0.340749i
$971$	34.9851	+	25.4182i	1.12273	+	0.815708i	0.984620	−	0.174709i	$-0.0558986\pi$
$971$	34.9851	+	25.4182i	1.12273	+	0.815708i	0.138106	+	0.990417i	$0.455899\pi$
$972$		0			0
$973$	2.02872	−	6.24376i	0.0650378	−	0.200166i
$974$	−2.34020	+	23.4890i	−0.0749850	+	0.752635i
$975$		0			0
$976$	12.9956	−	3.05805i	0.415979	−	0.0978858i
$977$	−15.5363	+	5.04806i	−0.497052	+	0.161502i	−0.546806	−	0.837260i	$-0.684156\pi$
$977$	−15.5363	+	5.04806i	−0.497052	+	0.161502i	0.0497539	+	0.998762i	$0.484156\pi$
$978$		0			0
$979$	7.70062	+	4.36740i	0.246113	+	0.139583i
$980$	27.0368	+	58.9969i	0.863659	+	1.88459i
$981$		0			0
$982$	−16.6933	+	38.0471i	−0.532703	+	1.21413i
$983$	−10.2504	+	7.44739i	−0.326939	+	0.237535i	−0.739130	−	0.673562i	$-0.764763\pi$
$983$	−10.2504	+	7.44739i	−0.326939	+	0.237535i	0.412192	+	0.911097i	$0.364763\pi$
$984$		0			0
$985$	9.81517	−	30.2080i	0.312737	−	0.962507i
$986$	23.2730	+	20.7279i	0.741163	+	0.660111i
$987$		0			0
$988$	−1.85381	+	1.70591i	−0.0589777	+	0.0542723i
$989$			23.6040i			0.750564i
$990$		0			0
$991$		−	51.6564i		−	1.64092i	−0.571704	−	0.820460i	$-0.693718\pi$
$991$		−	51.6564i		−	1.64092i	0.571704	−	0.820460i	$-0.306282\pi$
$992$	54.2650	+	10.0065i	1.72291	+	0.317705i
$993$		0			0
$994$	−24.3789	+	27.3723i	−0.773253	+	0.868198i
$995$	11.2045	−	34.4840i	0.355208	−	1.09322i
$996$		0			0
$997$	38.0171	−	27.6210i	1.20401	−	0.874766i	0.209339	−	0.977843i	$-0.432869\pi$
$997$	38.0171	−	27.6210i	1.20401	−	0.874766i	0.994673	+	0.103077i	$0.0328689\pi$
$998$	32.6013	+	14.3039i	1.03198	+	0.452782i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.w.a.71.4	yes	96
3.2	odd	2	inner	396.2.w.a.71.21	yes	96
4.3	odd	2	inner	396.2.w.a.71.2	✓	96
11.9	even	5	inner	396.2.w.a.251.23	yes	96
12.11	even	2	inner	396.2.w.a.71.23	yes	96
33.20	odd	10	inner	396.2.w.a.251.2	yes	96
44.31	odd	10	inner	396.2.w.a.251.21	yes	96
132.119	even	10	inner	396.2.w.a.251.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
396.2.w.a.71.2	✓	96	4.3	odd	2	inner
396.2.w.a.71.4	yes	96	1.1	even	1	trivial
396.2.w.a.71.21	yes	96	3.2	odd	2	inner
396.2.w.a.71.23	yes	96	12.11	even	2	inner
396.2.w.a.251.2	yes	96	33.20	odd	10	inner
396.2.w.a.251.4	yes	96	132.119	even	10	inner
396.2.w.a.251.21	yes	96	44.31	odd	10	inner
396.2.w.a.251.23	yes	96	11.9	even	5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22090 + 0.713732i) q^{2} +(0.981175 - 1.74278i) q^{4} +(1.96829 + 0.639537i) q^{5} +(-2.79916 - 3.85272i) q^{7} +(0.0459679 + 2.82805i) q^{8} +O(q^{10})\)	\(q+(-1.22090 + 0.713732i) q^{2} +(0.981175 - 1.74278i) q^{4} +(1.96829 + 0.639537i) q^{5} +(-2.79916 - 3.85272i) q^{7} +(0.0459679 + 2.82805i) q^{8} +(-2.85954 + 0.624025i) q^{10} +(1.63619 - 2.88494i) q^{11} +(-0.325879 - 1.00295i) q^{13} +(6.16729 + 2.70592i) q^{14} +(-2.07459 - 3.41995i) q^{16} +(-4.94627 - 1.60714i) q^{17} +(0.702088 - 0.966341i) q^{19} +(3.04582 - 2.80281i) q^{20} +(0.0614562 + 4.69001i) q^{22} -5.86457 q^{23} +(-0.579913 - 0.421331i) q^{25} +(1.11370 + 0.991909i) q^{26} +(-9.46092 + 1.09815i) q^{28} +(2.49060 + 3.42802i) q^{29} +(9.27709 - 3.01431i) q^{31} +(4.97379 + 2.69470i) q^{32} +(7.18594 - 1.56816i) q^{34} +(-3.04562 - 9.37345i) q^{35} +(7.27013 - 5.28206i) q^{37} +(-0.167468 + 1.68090i) q^{38} +(-1.71817 + 5.59584i) q^{40} +(2.36345 - 3.25300i) q^{41} -4.02485i q^{43} +(-3.42244 - 5.68216i) q^{44} +(7.16003 - 4.18573i) q^{46} +(-2.70695 - 1.96672i) q^{47} +(-4.84500 + 14.9114i) q^{49} +(1.00873 + 0.100500i) q^{50} +(-2.06767 - 0.416134i) q^{52} +(11.3480 - 3.68719i) q^{53} +(5.06553 - 4.63201i) q^{55} +(10.7670 - 8.09328i) q^{56} +(-5.48745 - 2.40763i) q^{58} +(-2.36747 + 1.72007i) q^{59} +(-1.03139 + 3.17428i) q^{61} +(-9.17496 + 10.3015i) q^{62} +(-7.99577 + 0.259999i) q^{64} -2.18251i q^{65} +10.8004i q^{67} +(-7.65405 + 7.04339i) q^{68} +(10.4085 + 9.27025i) q^{70} +(-1.68186 + 5.17623i) q^{71} +(4.47693 - 3.25268i) q^{73} +(-5.10610 + 11.6378i) q^{74} +(-0.995253 - 2.17174i) q^{76} +(-15.6948 + 1.77164i) q^{77} +(-8.43148 + 2.73955i) q^{79} +(-1.89622 - 8.05825i) q^{80} +(-0.563750 + 5.65845i) q^{82} +(-0.544346 + 1.67532i) q^{83} +(-8.70788 - 6.32664i) q^{85} +(2.87266 + 4.91392i) q^{86} +(8.23398 + 4.49462i) q^{88} +2.66925i q^{89} +(-2.95190 + 4.06294i) q^{91} +(-5.75417 + 10.2207i) q^{92} +(4.70862 + 0.469119i) q^{94} +(1.99993 - 1.45303i) q^{95} +(-1.29790 - 3.99452i) q^{97} +(-4.72748 - 21.6633i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 16 q^{10} + 32 q^{16} + 60 q^{22} + 8 q^{25} - 12 q^{28} + 24 q^{34} + 16 q^{40} - 40 q^{46} + 40 q^{49} - 32 q^{52} - 80 q^{58} - 72 q^{64} - 48 q^{70} - 24 q^{73} - 136 q^{76} - 132 q^{82} - 48 q^{85} - 64 q^{88} - 80 q^{94} - 80 q^{97}+O(q^{100}) \) 96 * q - 16 * q^10 + 32 * q^16 + 60 * q^22 + 8 * q^25 - 12 * q^28 + 24 * q^34 + 16 * q^40 - 40 * q^46 + 40 * q^49 - 32 * q^52 - 80 * q^58 - 72 * q^64 - 48 * q^70 - 24 * q^73 - 136 * q^76 - 132 * q^82 - 48 * q^85 - 64 * q^88 - 80 * q^94 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more