LMFDB - Embedded newform 189.2.ba.a.131.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(5,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([5, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			131.2
Character	$\chi$	$=$	189.131
Dual form			189.2.ba.a.101.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60395 - 1.91151i) q^{2} +(-1.44637 + 0.952904i) q^{3} +(-0.733927 + 4.16231i) q^{4} +(-0.273867 - 0.229802i) q^{5} +(4.14138 + 1.23633i) q^{6} +(2.61630 + 0.393657i) q^{7} +(4.81149 - 2.77792i) q^{8} +(1.18395 - 2.75650i) q^{9} +0.892090i q^{10} +(-2.21304 - 2.63740i) q^{11} +(-2.90475 - 6.71958i) q^{12} +(-0.362359 - 0.995572i) q^{13} +(-3.44393 - 5.63249i) q^{14} +(0.615091 + 0.0714084i) q^{15} +(-5.08414 - 1.85047i) q^{16} +5.82370 q^{17} +(-7.16806 + 2.15815i) q^{18} -4.08644i q^{19} +(1.15751 - 0.971262i) q^{20} +(-4.15925 + 1.92371i) q^{21} +(-1.49181 + 8.46049i) q^{22} +(0.737571 + 2.02646i) q^{23} +(-4.31209 + 8.60277i) q^{24} +(-0.846047 - 4.79817i) q^{25} +(-1.32184 + 2.28950i) q^{26} +(0.914255 + 5.11509i) q^{27} +(-3.55870 + 10.6009i) q^{28} +(2.91124 - 7.99857i) q^{29} +(-0.850076 - 1.29029i) q^{30} +(3.71733 + 0.655466i) q^{31} +(0.817075 + 2.24489i) q^{32} +(5.71405 + 1.70583i) q^{33} +(-9.34090 - 11.1321i) q^{34} +(-0.626056 - 0.709041i) q^{35} +(10.6045 + 6.95102i) q^{36} +(0.937031 + 1.62298i) q^{37} +(-7.81127 + 6.55443i) q^{38} +(1.47279 + 1.09467i) q^{39} +(-1.95608 - 0.344910i) q^{40} +(4.24450 - 1.54487i) q^{41} +(10.3484 + 4.86491i) q^{42} +(-1.24925 - 7.08485i) q^{43} +(12.6019 - 7.27569i) q^{44} +(-0.957692 + 0.482841i) q^{45} +(2.69057 - 4.66021i) q^{46} +(2.12948 + 12.0769i) q^{47} +(9.11684 - 2.16823i) q^{48} +(6.69007 + 2.05985i) q^{49} +(-7.81473 + 9.31324i) q^{50} +(-8.42319 + 5.54942i) q^{51} +(4.40982 - 0.777571i) q^{52} +(-7.91413 + 4.56923i) q^{53} +(8.31113 - 9.95194i) q^{54} +1.23086i q^{55} +(13.6819 - 5.37379i) q^{56} +(3.89398 + 5.91048i) q^{57} +(-19.9588 + 7.26442i) q^{58} +(-3.87534 + 1.41051i) q^{59} +(-0.748656 + 2.50779i) q^{60} +(13.0904 - 2.30819i) q^{61} +(-4.70948 - 8.15705i) q^{62} +(4.18268 - 6.74576i) q^{63} +(-2.42983 + 4.20859i) q^{64} +(-0.129546 + 0.355925i) q^{65} +(-5.90433 - 13.6585i) q^{66} +(3.53447 + 2.96577i) q^{67} +(-4.27417 + 24.2400i) q^{68} +(-2.99782 - 2.22817i) q^{69} +(-0.351177 + 2.33398i) q^{70} +(-7.24109 - 4.18065i) q^{71} +(-1.96076 - 16.5518i) q^{72} +(-6.45287 - 3.72557i) q^{73} +(1.59940 - 4.39433i) q^{74} +(5.79589 + 6.13370i) q^{75} +(17.0090 + 2.99915i) q^{76} +(-4.75175 - 7.77140i) q^{77} +(-0.269805 - 4.57104i) q^{78} +(-10.2764 + 8.62293i) q^{79} +(0.967136 + 1.67513i) q^{80} +(-6.19654 - 6.52709i) q^{81} +(-9.76098 - 5.63551i) q^{82} +(3.80912 + 1.38640i) q^{83} +(-4.95450 - 18.7239i) q^{84} +(-1.59492 - 1.33830i) q^{85} +(-11.5390 + 13.7517i) q^{86} +(3.41115 + 14.3430i) q^{87} +(-17.9745 - 6.54218i) q^{88} -11.5913 q^{89} +(2.45904 + 1.05619i) q^{90} +(-0.556126 - 2.74736i) q^{91} +(-8.97607 + 1.58272i) q^{92} +(-6.00122 + 2.59422i) q^{93} +(19.6695 - 23.4412i) q^{94} +(-0.939071 + 1.11914i) q^{95} +(-3.32096 - 2.46834i) q^{96} +(4.45675 - 0.785845i) q^{97} +(-6.79310 - 16.0920i) q^{98} +(-9.89010 + 2.97769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.60395	−	1.91151i	−1.13416	−	1.35164i	−0.927761	−	0.373174i	$-0.878269\pi$
$2$	−1.60395	−	1.91151i	−1.13416	−	1.35164i	−0.206401	−	0.978468i	$-0.566175\pi$
$3$	−1.44637	+	0.952904i	−0.835060	+	0.550159i
$3$	−1.44637	+	0.952904i	−0.835060	+	0.550159i
$4$	−0.733927	+	4.16231i	−0.366964	+	2.08115i
$5$	−0.273867	−	0.229802i	−0.122477	−	0.102771i	0.579492	−	0.814978i	$-0.303251\pi$
$5$	−0.273867	−	0.229802i	−0.122477	−	0.102771i	−0.701969	+	0.712208i	$0.747696\pi$
$6$	4.14138	+	1.23633i	1.69071	+	0.504731i
$7$	2.61630	+	0.393657i	0.988869	+	0.148788i
$7$	2.61630	+	0.393657i	0.988869	+	0.148788i
$8$	4.81149	−	2.77792i	1.70112	−	0.982141i
$9$	1.18395	−	2.75650i	0.394649	−	0.918832i
$10$			0.892090i			0.282104i
$11$	−2.21304	−	2.63740i	−0.667256	−	0.795205i	0.321151	−	0.947028i	$-0.395930\pi$
$11$	−2.21304	−	2.63740i	−0.667256	−	0.795205i	−0.988408	+	0.151823i	$0.951486\pi$
$12$	−2.90475	−	6.71958i	−0.838530	−	1.93978i
$13$	−0.362359	−	0.995572i	−0.100500	−	0.276122i	0.879245	−	0.476370i	$-0.158048\pi$
$13$	−0.362359	−	0.995572i	−0.100500	−	0.276122i	−0.979745	+	0.200248i	$0.935825\pi$
$14$	−3.44393	−	5.63249i	−0.920429	−	1.50535i
$15$	0.615091	+	0.0714084i	0.158816	+	0.0184376i
$16$	−5.08414	−	1.85047i	−1.27103	−	0.462619i
$17$	5.82370			1.41245			0.706227	−	0.707986i	$-0.250396\pi$
$17$	5.82370			1.41245			0.706227	+	0.707986i	$0.250396\pi$
$18$	−7.16806	+	2.15815i	−1.68953	+	0.508680i
$19$		−	4.08644i		−	0.937493i	−0.883333	−	0.468746i	$-0.844706\pi$
$19$		−	4.08644i		−	0.937493i	0.883333	−	0.468746i	$-0.155294\pi$
$20$	1.15751	−	0.971262i	0.258826	−	0.217181i
$21$	−4.15925	+	1.92371i	−0.907622	+	0.419789i
$22$	−1.49181	+	8.46049i	−0.318056	+	1.80378i
$23$	0.737571	+	2.02646i	0.153794	+	0.422546i	0.992531	−	0.121991i	$-0.0389278\pi$
$23$	0.737571	+	2.02646i	0.153794	+	0.422546i	−0.838737	+	0.544537i	$0.816706\pi$
$24$	−4.31209	+	8.60277i	−0.880201	+	1.75603i
$25$	−0.846047	−	4.79817i	−0.169209	−	0.959634i
$26$	−1.32184	+	2.28950i	−0.259235	+	0.449008i
$27$	0.914255	+	5.11509i	0.175948	+	0.984399i
$28$	−3.55870	+	10.6009i	−0.672530	+	2.00339i
$29$	2.91124	−	7.99857i	0.540604	−	1.48530i	−0.305455	−	0.952207i	$-0.598808\pi$
$29$	2.91124	−	7.99857i	0.540604	−	1.48530i	0.846058	−	0.533090i	$-0.178969\pi$
$30$	−0.850076	−	1.29029i	−0.155202	−	0.235573i
$31$	3.71733	+	0.655466i	0.667653	+	0.117725i	0.497194	−	0.867640i	$-0.334364\pi$
$31$	3.71733	+	0.655466i	0.667653	+	0.117725i	0.170459	+	0.985365i	$0.445475\pi$
$32$	0.817075	+	2.24489i	0.144440	+	0.396845i
$33$	5.71405	+	1.70583i	0.994689	+	0.296946i
$34$	−9.34090	−	11.1321i	−1.60195	−	1.90913i
$35$	−0.626056	−	0.709041i	−0.105823	−	0.119850i
$36$	10.6045	+	6.95102i	1.76741	+	1.15850i
$37$	0.937031	+	1.62298i	0.154047	+	0.266817i	0.932712	−	0.360623i	$-0.117436\pi$
$37$	0.937031	+	1.62298i	0.154047	+	0.266817i	−0.778665	+	0.627440i	$0.784103\pi$
$38$	−7.81127	+	6.55443i	−1.26715	+	1.06327i
$39$	1.47279	+	1.09467i	0.235835	+	0.175287i
$40$	−1.95608	−	0.344910i	−0.309283	−	0.0545350i
$41$	4.24450	−	1.54487i	0.662879	−	0.241268i	0.0114001	−	0.999935i	$-0.496371\pi$
$41$	4.24450	−	1.54487i	0.662879	−	0.241268i	0.651479	+	0.758667i	$0.274149\pi$
$42$	10.3484	+	4.86491i	1.59679	+	0.750671i
$43$	−1.24925	−	7.08485i	−0.190509	−	1.08043i	−0.918671	−	0.395024i	$-0.870736\pi$
$43$	−1.24925	−	7.08485i	−0.190509	−	1.08043i	0.728162	−	0.685405i	$-0.240375\pi$
$44$	12.6019	−	7.27569i	1.89980	−	1.09685i
$45$	−0.957692	+	0.482841i	−0.142764	+	0.0719776i
$46$	2.69057	−	4.66021i	0.396703	−	0.687110i
$47$	2.12948	+	12.0769i	0.310617	+	1.76159i	0.595811	+	0.803125i	$0.296831\pi$
$47$	2.12948	+	12.0769i	0.310617	+	1.76159i	−0.285194	+	0.958470i	$0.592058\pi$
$48$	9.11684	−	2.16823i	1.31590	−	0.312957i
$49$	6.69007	+	2.05985i	0.955724	+	0.294264i
$50$	−7.81473	+	9.31324i	−1.10517	+	1.31709i
$51$	−8.42319	+	5.54942i	−1.17948	+	0.777075i
$52$	4.40982	−	0.777571i	0.611533	−	0.107830i
$53$	−7.91413	+	4.56923i	−1.08709	+	0.627631i	−0.932800	−	0.360394i	$-0.882642\pi$
$53$	−7.91413	+	4.56923i	−1.08709	+	0.627631i	−0.154289	+	0.988026i	$0.549309\pi$
$54$	8.31113	−	9.95194i	1.13100	−	1.35429i
$55$			1.23086i			0.165969i
$56$	13.6819	−	5.37379i	1.82832	−	0.718103i
$57$	3.89398	+	5.91048i	0.515771	+	0.782862i
$58$	−19.9588	+	7.26442i	−2.62072	+	0.953865i
$59$	−3.87534	+	1.41051i	−0.504527	+	0.183633i	−0.581729	−	0.813383i	$-0.697624\pi$
$59$	−3.87534	+	1.41051i	−0.504527	+	0.183633i	0.0772021	+	0.997015i	$0.475401\pi$
$60$	−0.748656	+	2.50779i	−0.0966511	+	0.323754i
$61$	13.0904	−	2.30819i	1.67606	−	0.295534i	0.746822	−	0.665024i	$-0.231579\pi$
$61$	13.0904	−	2.30819i	1.67606	−	0.295534i	0.929235	+	0.369490i	$0.120468\pi$
$62$	−4.70948	−	8.15705i	−0.598104	−	1.03595i
$63$	4.18268	−	6.74576i	0.526968	−	0.849885i
$64$	−2.42983	+	4.20859i	−0.303729	+	0.526074i
$65$	−0.129546	+	0.355925i	−0.0160682	+	0.0441471i
$66$	−5.90433	−	13.6585i	−0.726773	−	1.68125i
$67$	3.53447	+	2.96577i	0.431804	+	0.362327i	0.832632	−	0.553827i	$-0.186833\pi$
$67$	3.53447	+	2.96577i	0.431804	+	0.362327i	−0.400828	+	0.916153i	$0.631277\pi$
$68$	−4.27417	+	24.2400i	−0.518319	+	2.93953i
$69$	−2.99782	−	2.22817i	−0.360895	−	0.268240i
$70$	−0.351177	+	2.33398i	−0.0419737	+	0.278964i
$71$	−7.24109	−	4.18065i	−0.859359	−	0.496151i	0.00443842	−	0.999990i	$-0.498587\pi$
$71$	−7.24109	−	4.18065i	−0.859359	−	0.496151i	−0.863798	+	0.503839i	$0.831921\pi$
$72$	−1.96076	−	16.5518i	−0.231078	−	1.95064i
$73$	−6.45287	−	3.72557i	−0.755251	−	0.436045i	0.0723368	−	0.997380i	$-0.476954\pi$
$73$	−6.45287	−	3.72557i	−0.755251	−	0.436045i	−0.827588	+	0.561336i	$0.810288\pi$
$74$	1.59940	−	4.39433i	0.185927	−	0.510830i
$75$	5.79589	+	6.13370i	0.669251	+	0.708259i
$76$	17.0090	+	2.99915i	1.95107	+	0.344026i
$77$	−4.75175	−	7.77140i	−0.541512	−	0.885634i
$78$	−0.269805	−	4.57104i	−0.0305494	−	0.517568i
$79$	−10.2764	+	8.62293i	−1.15619	+	0.970156i	−0.999846	−	0.0175477i	$-0.994414\pi$
$79$	−10.2764	+	8.62293i	−1.15619	+	0.970156i	−0.156340	+	0.987703i	$0.549970\pi$
$80$	0.967136	+	1.67513i	0.108129	+	0.187285i
$81$	−6.19654	−	6.52709i	−0.688504	−	0.725232i
$82$	−9.76098	−	5.63551i	−1.07792	−	0.622338i
$83$	3.80912	+	1.38640i	0.418105	+	0.152178i	0.542501	−	0.840055i	$-0.317477\pi$
$83$	3.80912	+	1.38640i	0.418105	+	0.152178i	−0.124397	+	0.992233i	$0.539700\pi$
$84$	−4.95450	−	18.7239i	−0.540581	−	2.04295i
$85$	−1.59492	−	1.33830i	−0.172993	−	0.145159i
$86$	−11.5390	+	13.7517i	−1.24429	+	1.48288i
$87$	3.41115	+	14.3430i	0.365714	+	1.53773i
$88$	−17.9745	−	6.54218i	−1.91609	−	0.697398i
$89$	−11.5913			−1.22867			−0.614337	−	0.789044i	$-0.710576\pi$
$89$	−11.5913			−1.22867			−0.614337	+	0.789044i	$0.710576\pi$
$90$	2.45904	+	1.05619i	0.259206	+	0.111332i
$91$	−0.556126	−	2.74736i	−0.0582978	−	0.288002i
$92$	−8.97607	+	1.58272i	−0.935820	+	0.165010i
$93$	−6.00122	+	2.59422i	−0.622298	+	0.269008i
$94$	19.6695	−	23.4412i	2.02876	−	2.41778i
$95$	−0.939071	+	1.11914i	−0.0963466	+	0.114821i
$96$	−3.32096	−	2.46834i	−0.338944	−	0.251924i
$97$	4.45675	−	0.785845i	0.452515	−	0.0797905i	0.0572541	−	0.998360i	$-0.481765\pi$
$97$	4.45675	−	0.785845i	0.452515	−	0.0797905i	0.395260	+	0.918569i	$0.370654\pi$
$98$	−6.79310	−	16.0920i	−0.686206	−	1.62554i
$99$	−9.89010	+	2.97769i	−0.993992	+	0.299269i
$100$	20.5924			2.05924
$101$	−2.02623	−	0.737486i	−0.201617	−	0.0733826i	0.239238	−	0.970961i	$-0.423102\pi$
$101$	−2.02623	−	0.737486i	−0.201617	−	0.0733826i	−0.440855	+	0.897578i	$0.645325\pi$
$102$	24.1181	+	7.20004i	2.38805	+	0.712910i
$103$	−2.87110	+	3.42164i	−0.282898	+	0.337144i	−0.888715	−	0.458459i	$-0.848402\pi$
$103$	−2.87110	+	3.42164i	−0.282898	+	0.337144i	0.605818	+	0.795603i	$0.292846\pi$
$104$	−4.50910	−	3.78359i	−0.442154	−	0.371011i
$105$	1.58115	+	0.428961i	0.154305	+	0.0418623i
$106$	21.4280	+	7.79914i	2.08127	+	0.757520i
$107$	4.17439	+	2.41009i	0.403554	+	0.232992i	0.688016	−	0.725695i	$-0.258482\pi$
$107$	4.17439	+	2.41009i	0.403554	+	0.232992i	−0.284463	+	0.958687i	$0.591815\pi$
$108$	−21.9616	+	0.0513086i	−2.11325	+	0.00493717i
$109$	−10.0905	−	17.4773i	−0.966494	−	1.67402i	−0.705545	−	0.708665i	$-0.749298\pi$
$109$	−10.0905	−	17.4773i	−0.966494	−	1.67402i	−0.260949	−	0.965353i	$-0.584036\pi$
$110$	2.35280	−	1.97423i	0.224330	−	0.188236i
$111$	−2.90184	−	1.45453i	−0.275430	−	0.138058i
$112$	−12.5732	−	6.84280i	−1.18805	−	0.646584i
$113$	12.4855	+	2.20154i	1.17454	+	0.207103i	0.726664	−	0.686993i	$-0.241070\pi$
$113$	12.4855	+	2.20154i	1.17454	+	0.207103i	0.447876	+	0.894096i	$0.352181\pi$
$114$	5.05220	−	16.9235i	0.473182	−	1.58503i
$115$	0.263688	−	0.724476i	0.0245890	−	0.0675578i
$116$	31.1559	+	17.9879i	2.89275	+	1.67013i
$117$	−3.17330	−	0.179865i	−0.293372	−	0.0166285i
$118$	8.91205	+	5.14538i	0.820421	+	0.473670i
$119$	15.2365	+	2.29254i	1.39673	+	0.210156i
$120$	3.15787	−	1.36509i	0.288273	−	0.124615i
$121$	−0.148193	+	0.840442i	−0.0134721	+	0.0764039i
$122$	−25.4085	−	21.3202i	−2.30038	−	1.93024i
$123$	−4.66698	+	6.27905i	−0.420807	+	0.566162i
$124$	−5.45651	+	14.9916i	−0.490009	+	1.34629i
$125$	−1.76469	+	3.05654i	−0.157839	+	0.273385i
$126$	−19.6034	+	2.82461i	−1.74641	+	0.251636i
$127$	3.72128	+	6.44544i	0.330210	+	0.571940i	0.982553	−	0.185984i	$-0.0595471\pi$
$127$	3.72128	+	6.44544i	0.330210	+	0.571940i	−0.652343	+	0.757924i	$0.726214\pi$
$128$	16.6474	−	2.93539i	1.47144	−	0.259454i
$129$	8.55805	+	9.05686i	0.753494	+	0.797412i
$130$	0.888140	−	0.323257i	0.0778951	−	0.0283515i
$131$	6.73738	−	2.45221i	0.588648	−	0.214250i	−0.0304869	−	0.999535i	$-0.509706\pi$
$131$	6.73738	−	2.45221i	0.588648	−	0.214250i	0.619134	+	0.785285i	$0.287484\pi$
$132$	−11.2939	+	22.5317i	−0.983006	+	1.96113i
$133$	1.60865	−	10.6914i	0.139488	−	0.927058i
$134$		−	11.5131i		−	0.994582i
$135$	0.925073	−	1.61095i	0.0796176	−	0.138649i
$136$	28.0207	−	16.1777i	2.40275	−	1.38723i
$137$	−3.66765	+	0.646705i	−0.313348	+	0.0552517i	−0.328111	−	0.944639i	$-0.606412\pi$
$137$	−3.66765	+	0.646705i	−0.313348	+	0.0552517i	0.0147625	+	0.999891i	$0.495301\pi$
$138$	0.549180	+	9.30423i	0.0467493	+	0.792028i
$139$	−8.88294	+	10.5863i	−0.753441	+	0.897916i	−0.997414	−	0.0718657i	$-0.977105\pi$
$139$	−8.88294	+	10.5863i	−0.753441	+	0.897916i	0.243973	+	0.969782i	$0.421549\pi$
$140$	3.41073	−	2.08546i	0.288259	−	0.176253i
$141$	−14.5881	−	15.4384i	−1.22854	−	1.30015i
$142$	3.62298	+	20.5470i	0.304034	+	1.72426i
$143$	−1.82381	+	3.15892i	−0.152514	+	0.264163i
$144$	−11.1202	+	11.8235i	−0.926681	+	0.985295i
$145$	−2.63538	+	1.52154i	−0.218856	+	0.126357i
$146$	3.22861	+	18.3103i	0.267201	+	1.51537i
$147$	−11.6391	+	3.39570i	−0.959979	+	0.280073i
$148$	−7.44308	+	2.70906i	−0.611817	+	0.222683i
$149$	9.28511	+	1.63721i	0.760666	+	0.134126i	0.540509	−	0.841339i	$-0.318232\pi$
$149$	9.28511	+	1.63721i	0.760666	+	0.134126i	0.220157	+	0.975464i	$0.429343\pi$
$150$	2.42834	−	20.9170i	0.198273	−	1.70787i
$151$	−3.54028	+	2.97065i	−0.288104	+	0.241748i	−0.775372	−	0.631504i	$-0.782438\pi$
$151$	−3.54028	+	2.97065i	−0.288104	+	0.241748i	0.487268	+	0.873252i	$0.337993\pi$
$152$	−11.3518	−	19.6619i	−0.920751	−	1.59479i
$153$	6.89495	−	16.0530i	0.557424	−	1.29781i
$154$	−7.23356	+	21.5479i	−0.582897	+	1.73638i
$155$	−0.867429	−	1.03376i	−0.0696735	−	0.0830337i
$156$	−5.63727	+	5.32679i	−0.451343	+	0.426485i
$157$	0.399278	+	1.09701i	0.0318659	+	0.0875508i	0.954605	−	0.297873i	$-0.0962773\pi$
$157$	0.399278	+	1.09701i	0.0318659	+	0.0875508i	−0.922739	+	0.385424i	$0.874055\pi$
$158$	32.9656	+	5.81273i	2.62261	+	0.462436i
$159$	7.09269	−	14.1502i	0.562487	−	1.12218i
$160$	0.292111	−	0.802568i	0.0230934	−	0.0634486i
$161$	1.13198	+	5.59218i	0.0892124	+	0.440726i
$162$	−2.53768	+	22.3139i	−0.199379	+	1.75314i
$163$	3.53124	−	6.11629i	0.276588	−	0.479065i	−0.693947	−	0.720027i	$-0.744130\pi$
$163$	3.53124	−	6.11629i	0.276588	−	0.479065i	0.970535	+	0.240962i	$0.0774629\pi$
$164$	3.31508	+	18.8007i	0.258864	+	1.46809i
$165$	−1.17289	−	1.78027i	−0.0913093	−	0.138594i
$166$	−3.45949	−	9.50488i	−0.268509	−	0.737722i
$167$	2.87826	−	16.3234i	0.222726	−	1.26314i	−0.644259	−	0.764808i	$-0.722834\pi$
$167$	2.87826	−	16.3234i	0.222726	−	1.26314i	0.866985	−	0.498335i	$-0.166055\pi$
$168$	−14.6683	+	20.8100i	−1.13168	+	1.60552i
$169$	9.09872	−	7.63473i	0.699901	−	0.587287i
$170$			5.19526i			0.398458i
$171$	−11.2642	−	4.83813i	−0.861398	−	0.369981i
$172$	30.4062			2.31845
$173$	3.04449	+	1.10810i	0.231468	+	0.0842475i	0.455150	−	0.890415i	$-0.349586\pi$
$173$	3.04449	+	1.10810i	0.231468	+	0.0842475i	−0.223682	+	0.974662i	$0.571808\pi$
$174$	21.9455	−	29.5258i	1.66368	−	2.23835i
$175$	−0.324682	−	12.8865i	−0.0245436	−	0.974128i
$176$	6.37096	+	17.5041i	0.480229	+	1.31942i
$177$	4.26108	−	5.73294i	0.320283	−	0.430914i
$178$	18.5918	+	22.1568i	1.39351	+	1.66073i
$179$			5.12037i			0.382714i	0.981520	+	0.191357i	$0.0612889\pi$
$179$			5.12037i			0.382714i	−0.981520	+	0.191357i	$0.938711\pi$
$180$	−1.30685	−	4.34058i	−0.0974072	−	0.323528i
$181$	−3.60530	+	2.08152i	−0.267980	+	0.154718i	−0.627969	−	0.778238i	$-0.716114\pi$
$181$	−3.60530	+	2.08152i	−0.267980	+	0.154718i	0.359990	+	0.932956i	$0.382780\pi$
$182$	−4.35961	+	5.46967i	−0.323156	+	0.405439i
$183$	−16.7340	+	15.8124i	−1.23702	+	1.16889i
$184$	9.17815	+	7.70138i	0.676622	+	0.567753i
$185$	0.116343	−	0.659814i	0.00855371	−	0.0485105i
$186$	14.5845	+	7.31040i	1.06939	+	0.536025i
$187$	−12.8881	−	15.3594i	−0.942469	−	1.12319i
$188$	−51.8306			−3.78014
$189$	0.378378	+	13.7425i	0.0275230	+	0.999621i
$190$	3.64547			0.264470
$191$	1.92952	+	2.29952i	0.139615	+	0.166387i	0.831321	−	0.555792i	$-0.187585\pi$
$191$	1.92952	+	2.29952i	0.139615	+	0.166387i	−0.691706	+	0.722179i	$0.743141\pi$
$192$	−0.495959	−	8.40256i	−0.0357928	−	0.606402i
$193$	−2.87016	+	16.2775i	−0.206599	+	1.17168i	0.688305	+	0.725422i	$0.258355\pi$
$193$	−2.87016	+	16.2775i	−0.206599	+	1.17168i	−0.894904	+	0.446259i	$0.852756\pi$
$194$	−8.65055	−	7.25867i	−0.621073	−	0.521142i
$195$	−0.151792	−	0.638243i	−0.0108700	−	0.0457056i
$196$	−13.4838	+	26.3344i	−0.963125	+	1.88103i
$197$	−2.93897	+	1.69681i	−0.209393	+	0.120893i	−0.601029	−	0.799227i	$-0.705242\pi$
$197$	−2.93897	+	1.69681i	−0.209393	+	0.120893i	0.391636	+	0.920120i	$0.371909\pi$
$198$	21.5551	+	14.1290i	1.53185	+	1.00410i
$199$			4.20709i			0.298232i	0.988820	+	0.149116i	$0.0476429\pi$
$199$			4.20709i			0.298232i	−0.988820	+	0.149116i	$0.952357\pi$
$200$	−17.3997	−	20.7361i	−1.23034	−	1.46626i
$201$	−7.93824	−	0.921581i	−0.559920	−	0.0650033i
$202$	1.84025	+	5.05604i	0.129479	+	0.355742i
$203$	10.7654	−	19.7806i	0.755581	−	1.38833i
$204$	−16.9164	−	39.1328i	−1.18439	−	2.73984i
$205$	−1.51744	−	0.552304i	−0.105983	−	0.0385746i
$206$	11.1456			0.776550
$207$	6.45917	+	0.366110i	0.448944	+	0.0254464i
$208$			5.73216i			0.397454i
$209$	−10.7776	+	9.04345i	−0.745499	+	0.625548i
$210$	−1.71613	−	3.71042i	−0.118424	−	0.256043i
$211$	−3.10714	+	17.6215i	−0.213905	+	1.21311i	0.668893	+	0.743359i	$0.266768\pi$
$211$	−3.10714	+	17.6215i	−0.213905	+	1.21311i	−0.882797	+	0.469754i	$0.844343\pi$
$212$	−13.2101	−	36.2945i	−0.907275	−	2.49272i
$213$	14.4570	−	0.853323i	0.990579	−	0.0584687i
$214$	−2.08860	−	11.8450i	−0.142774	−	0.809710i
$215$	−1.28598	+	2.22739i	−0.0877033	+	0.151907i
$216$	18.6082	+	22.0715i	1.26613	+	1.50177i
$217$	9.46764	+	3.17825i	0.642705	+	0.215754i
$218$	−17.2233	+	47.3207i	−1.16651	+	3.20496i
$219$	12.8833	−	0.760435i	0.870574	−	0.0513855i
$220$	−5.12321	−	0.903360i	−0.345407	−	0.0609045i
$221$	−2.11027	−	5.79791i	−0.141952	−	0.390010i
$222$	1.87405	+	7.87988i	0.125778	+	0.528863i
$223$	−8.41245	−	10.0256i	−0.563339	−	0.671361i	0.406911	−	0.913468i	$-0.366606\pi$
$223$	−8.41245	−	10.0256i	−0.563339	−	0.671361i	−0.970250	+	0.242107i	$0.922162\pi$
$224$	1.25400	+	6.19497i	0.0837861	+	0.413919i
$225$	−14.2278	−	3.34866i	−0.948520	−	0.223244i
$226$	−15.8179	−	27.3974i	−1.05219	−	1.82245i
$227$	0.859517	−	0.721220i	0.0570481	−	0.0478691i	−0.613818	−	0.789448i	$-0.710367\pi$
$227$	0.859517	−	0.721220i	0.0570481	−	0.0478691i	0.670866	+	0.741579i	$0.265923\pi$
$228$	−27.4592	+	11.8701i	−1.81853	+	0.786116i
$229$	1.25625	+	0.221510i	0.0830151	+	0.0146378i	0.215001	−	0.976614i	$-0.431024\pi$
$229$	1.25625	+	0.221510i	0.0830151	+	0.0146378i	−0.131986	+	0.991252i	$0.542136\pi$
$230$	−1.80778	+	0.657980i	−0.119202	+	0.0433859i
$231$	14.2782	+	6.71233i	0.939435	+	0.441639i
$232$	−8.21194	−	46.5722i	−0.539140	−	3.05762i
$233$	−16.2536	+	9.38404i	−1.06481	+	0.614769i	−0.926759	−	0.375656i	$-0.877417\pi$
$233$	−16.2536	+	9.38404i	−1.06481	+	0.614769i	−0.138052	+	0.990425i	$0.544084\pi$
$234$	4.74600	+	6.35430i	0.310256	+	0.415393i
$235$	2.19210	−	3.79682i	0.142997	−	0.247677i
$236$	−3.02676	−	17.1656i	−0.197025	−	1.11738i
$237$	6.64662	−	22.2643i	0.431744	−	1.44622i
$238$	−20.0564	−	32.8019i	−1.30006	−	2.12623i
$239$	8.01259	−	9.54904i	0.518292	−	0.617676i	−0.441884	−	0.897072i	$-0.645690\pi$
$239$	8.01259	−	9.54904i	0.518292	−	0.617676i	0.960176	+	0.279396i	$0.0901343\pi$
$240$	−2.99507	−	1.50126i	−0.193331	−	0.0969059i
$241$	−20.2909	+	3.57784i	−1.30705	+	0.230469i	−0.783429	−	0.621481i	$-0.786531\pi$
$241$	−20.2909	+	3.57784i	−1.30705	+	0.230469i	−0.523624	+	0.851950i	$0.675420\pi$
$242$	1.84421	−	1.06475i	0.118550	−	0.0684450i
$243$	15.1822	+	3.53586i	0.973935	+	0.226825i
$244$			56.1804i			3.59658i
$245$	−1.35883	−	2.10152i	−0.0868127	−	0.134261i
$246$	19.4881	−	1.15028i	1.24251	−	0.0733391i
$247$	−4.06834	+	1.48076i	−0.258862	+	0.0942182i
$248$	19.7067	−	7.17267i	1.25138	−	0.455465i
$249$	−6.83048	+	1.62447i	−0.432864	+	0.102947i
$250$	8.67309	−	1.52930i	0.548534	−	0.0967214i
$251$	4.73924	+	8.20860i	0.299138	+	0.518122i	0.975939	−	0.218044i	$-0.0699676\pi$
$251$	4.73924	+	8.20860i	0.299138	+	0.518122i	−0.676801	+	0.736166i	$0.736634\pi$
$252$	25.0081	+	22.3605i	1.57536	+	1.40858i
$253$	3.71231	−	6.42990i	0.233391	−	0.404245i
$254$	6.35179	−	17.4514i	0.398547	−	1.09500i
$255$	3.58210	+	0.415861i	0.224320	+	0.0260422i
$256$	−24.8672	−	20.8661i	−1.55420	−	1.30413i
$257$	−2.78746	+	15.8084i	−0.173877	+	0.986104i	0.765556	+	0.643370i	$0.222464\pi$
$257$	−2.78746	+	15.8084i	−0.173877	+	0.986104i	−0.939432	+	0.342734i	$0.888647\pi$
$258$	3.58562	−	30.8855i	0.223231	−	1.92285i
$259$	1.81266	+	4.61509i	0.112633	+	0.286767i
$260$	−1.38639	−	0.800435i	−0.0859805	−	0.0496409i
$261$	−18.6013	−	17.4947i	−1.15139	−	1.08290i
$262$	−15.4938	−	8.94536i	−0.957211	−	0.552646i
$263$	4.56467	−	12.5413i	0.281470	−	0.773331i	−0.715718	−	0.698389i	$-0.753901\pi$
$263$	4.56467	−	12.5413i	0.281470	−	0.773331i	0.997188	−	0.0749421i	$-0.0238772\pi$
$264$	32.2317	−	7.66558i	1.98373	−	0.471784i
$265$	3.21744	+	0.567321i	0.197646	+	0.0348503i
$266$	−23.0168	+	14.0734i	−1.41125	+	0.862896i
$267$	16.7652	−	11.0454i	1.02602	−	0.675966i
$268$	−14.9385	+	12.5349i	−0.912515	+	0.765691i
$269$	12.4472	+	21.5591i	0.758916	+	1.31448i	0.943404	+	0.331647i	$0.107604\pi$
$269$	12.4472	+	21.5591i	0.758916	+	1.31448i	−0.184487	+	0.982835i	$0.559062\pi$
$270$	−4.56312	+	0.815598i	−0.277703	+	0.0496357i
$271$	7.54919	+	4.35853i	0.458581	+	0.264762i	0.711447	−	0.702739i	$-0.248040\pi$
$271$	7.54919	+	4.35853i	0.458581	+	0.264762i	−0.252867	+	0.967501i	$0.581373\pi$
$272$	−29.6085	−	10.7766i	−1.79528	−	0.653427i
$273$	3.42233	+	3.44376i	0.207129	+	0.208426i
$274$	7.11889	+	5.97346i	0.430068	+	0.360870i
$275$	−10.7823	+	12.8499i	−0.650200	+	0.774878i
$276$	11.4745	−	10.8425i	0.690684	−	0.652644i
$277$	21.1896	+	7.71239i	1.27316	+	0.463393i	0.888165	−	0.459525i	$-0.151980\pi$
$277$	21.1896	+	7.71239i	1.27316	+	0.463393i	0.384996	+	0.922918i	$0.374203\pi$
$278$	34.4835			2.06819
$279$	6.20792	−	9.47078i	0.371658	−	0.567001i
$280$	−4.98192	−	1.67241i	−0.297727	−	0.0999457i
$281$	11.7861	−	2.07821i	0.703099	−	0.123975i	0.189342	−	0.981911i	$-0.439364\pi$
$281$	11.7861	−	2.07821i	0.703099	−	0.123975i	0.513757	+	0.857936i	$0.328253\pi$
$282$	−6.11208	+	52.6477i	−0.363969	+	3.13513i
$283$	−13.6417	+	16.2575i	−0.810915	+	0.966411i	−0.999879	−	0.0155731i	$-0.995043\pi$
$283$	−13.6417	+	16.2575i	−0.810915	+	0.966411i	0.188964	+	0.981984i	$0.439487\pi$
$284$	22.7156	−	27.0714i	1.34792	−	1.60639i
$285$	0.291806	−	2.51353i	0.0172851	−	0.148889i
$286$	8.96361	−	1.58053i	0.530029	−	0.0934584i
$287$	11.7130	−	2.37097i	0.691398	−	0.139954i
$288$	7.15541	+	0.405574i	0.421637	+	0.0238987i
$289$	16.9154			0.995025
$290$	7.13544	+	2.59709i	0.419008	+	0.152506i
$291$	−5.69726	+	5.38348i	−0.333979	+	0.315585i
$292$	20.2429	−	24.1245i	1.18463	−	1.41178i
$293$	17.6180	+	14.7833i	1.02926	+	0.863649i	0.990762	−	0.135610i	$-0.0432994\pi$
$293$	17.6180	+	14.7833i	1.02926	+	0.863649i	0.0384944	+	0.999259i	$0.487744\pi$
$294$	25.1595	+	16.8018i	1.46733	+	0.979900i
$295$	1.38547	+	0.504269i	0.0806650	+	0.0293597i
$296$	9.01703	+	5.20598i	0.524104	+	0.302592i
$297$	11.4672	−	13.7311i	0.665397	−	0.796762i
$298$	−11.7633	−	20.3746i	−0.681428	−	1.18027i
$299$	1.75022	−	1.46861i	0.101218	−	0.0849319i
$300$	−29.7841	+	19.6226i	−1.71959	+	1.13291i
$301$	−0.479417	−	19.0279i	−0.0276331	−	1.09675i
$302$	11.3569	+	2.00252i	0.653513	+	0.115232i
$303$	3.63342	−	0.864125i	0.208734	−	0.0496427i
$304$	−7.56185	+	20.7760i	−0.433702	+	1.19159i
$305$	−4.11546	−	2.37606i	−0.235651	−	0.136053i
$306$	−41.7446	+	12.5684i	−2.38638	+	0.718487i
$307$	−28.4532	−	16.4275i	−1.62391	−	0.937565i	−0.985860	−	0.167571i	$-0.946408\pi$
$307$	−28.4532	−	16.4275i	−1.62391	−	0.937565i	−0.638051	−	0.769994i	$-0.720259\pi$
$308$	35.8344	−	14.0746i	2.04186	−	0.801975i
$309$	0.892161	−	7.68482i	0.0507533	−	0.437174i
$310$	−0.584735	+	3.31620i	−0.0332107	+	0.188347i
$311$	7.37844	+	6.19125i	0.418393	+	0.351073i	0.827551	−	0.561390i	$-0.189733\pi$
$311$	7.37844	+	6.19125i	0.418393	+	0.351073i	−0.409158	+	0.912463i	$0.634178\pi$
$312$	10.1272	+	1.17571i	0.573340	+	0.0665613i
$313$	−3.68536	+	10.1254i	−0.208309	+	0.572324i	−0.999215	−	0.0396135i	$-0.987387\pi$
$313$	−3.68536	+	10.1254i	−0.208309	+	0.572324i	0.790906	+	0.611937i	$0.209610\pi$
$314$	1.45652	−	2.52277i	0.0821962	−	0.142368i
$315$	−2.69569	+	0.886254i	−0.151885	+	0.0499348i
$316$	−28.3492	−	49.1022i	−1.59477	−	2.76221i
$317$	−4.34468	+	0.766085i	−0.244022	+	0.0430276i	−0.294321	−	0.955707i	$-0.595094\pi$
$317$	−4.34468	+	0.766085i	−0.244022	+	0.0430276i	0.0502994	+	0.998734i	$0.483982\pi$
$318$	−38.4245	+	9.13839i	−2.15474	+	0.512455i
$319$	−27.5381	+	10.0230i	−1.54184	+	0.561183i
$320$	1.63259	−	0.594216i	0.0912648	−	0.0332177i
$321$	−8.33428	+	0.491929i	−0.465174	+	0.0274568i
$322$	8.87387	−	11.1334i	0.494522	−	0.620437i
$323$		−	23.7982i		−	1.32417i
$324$	31.7156	−	21.0015i	1.76198	−	1.16675i
$325$	−4.47035	+	2.58096i	−0.247970	+	0.143166i
$326$	−17.3553	+	3.06020i	−0.961219	+	0.169489i
$327$	31.2487	+	15.6632i	1.72806	+	0.866178i
$328$	16.1308	−	19.2240i	0.890676	−	1.06147i
$329$	0.817217	+	32.4351i	0.0450546	+	1.78820i
$330$	−1.52175	+	5.09745i	−0.0837697	+	0.280605i
$331$	−2.39714	−	13.5948i	−0.131759	−	0.747240i	−0.977062	−	0.212954i	$-0.931692\pi$
$331$	−2.39714	−	13.5948i	−0.131759	−	0.747240i	0.845304	−	0.534286i	$-0.179420\pi$
$332$	−8.56626	+	14.8372i	−0.470134	+	0.814297i
$333$	5.58315	−	0.661392i	0.305954	−	0.0362441i
$334$	−35.8189	+	20.6801i	−1.95992	+	1.13156i
$335$	−0.286436	−	1.62446i	−0.0156496	−	0.0887535i
$336$	24.7060	−	2.08384i	1.34782	−	0.113683i
$337$	6.81432	−	2.48021i	0.371200	−	0.135106i	−0.149683	−	0.988734i	$-0.547825\pi$
$337$	6.81432	−	2.48021i	0.371200	−	0.135106i	0.520882	+	0.853628i	$0.325603\pi$
$338$	−29.1877	−	5.14658i	−1.58760	−	0.279937i
$339$	−20.1565	+	8.71329i	−1.09475	+	0.473241i
$340$	6.74096	−	5.65633i	0.365580	−	0.306758i
$341$	−6.49788	−	11.2547i	−0.351880	−	0.609474i
$342$	8.81913	+	29.2918i	0.476884	+	1.58392i
$343$	16.6924	+	8.02278i	0.901303	+	0.433189i
$344$	−25.6919	−	30.6184i	−1.38521	−	1.65083i
$345$	0.308967	+	1.29913i	0.0166342	+	0.0699426i
$346$	−2.76505	−	7.59691i	−0.148650	−	0.408412i
$347$	−17.6016	−	3.10363i	−0.944901	−	0.166611i	−0.320089	−	0.947387i	$-0.603713\pi$
$347$	−17.6016	−	3.10363i	−0.944901	−	0.166611i	−0.624811	+	0.780776i	$0.714824\pi$
$348$	−62.2035	+	3.67155i	−3.33446	+	0.196816i
$349$	−11.7174	+	32.1932i	−0.627217	+	1.72326i	0.0613741	+	0.998115i	$0.480452\pi$
$349$	−11.7174	+	32.1932i	−0.627217	+	1.72326i	−0.688591	+	0.725150i	$0.741770\pi$
$350$	−24.1119	+	21.2899i	−1.28884	+	1.13799i
$351$	4.76115	−	2.76370i	0.254132	−	0.147516i
$352$	4.11246	−	7.12299i	0.219195	−	0.379657i
$353$	−2.82122	−	15.9999i	−0.150158	−	0.851589i	−0.963080	−	0.269216i	$-0.913235\pi$
$353$	−2.82122	−	15.9999i	−0.150158	−	0.851589i	0.812922	−	0.582373i	$-0.197876\pi$
$354$	−17.7931	+	1.05024i	−0.945694	+	0.0558194i
$355$	1.02238	+	2.80896i	0.0542621	+	0.149084i
$356$	8.50716	−	48.2465i	0.450878	−	2.55706i
$357$	−24.2222	+	11.2031i	−1.28197	+	0.592932i
$358$	9.78764	−	8.21280i	0.517293	−	0.434060i
$359$			17.5252i			0.924947i	0.886633	+	0.462473i	$0.153038\pi$
$359$			17.5252i			0.924947i	−0.886633	+	0.462473i	$0.846962\pi$
$360$	−3.26664	+	4.98357i	−0.172167	+	0.262657i
$361$	2.30103			0.121107
$362$	9.76155	+	3.55291i	0.513056	+	0.186737i
$363$	−0.586520	−	1.35680i	−0.0307843	−	0.0712136i
$364$	11.8435	−	0.298403i	0.620769	−	0.0156406i
$365$	0.911088	+	2.50319i	0.0476885	+	0.131023i
$366$	57.0661	+	6.62503i	2.98289	+	0.346296i
$367$	−5.56009	−	6.62625i	−0.290234	−	0.345888i	0.601150	−	0.799136i	$-0.294709\pi$
$367$	−5.56009	−	6.62625i	−0.290234	−	0.345888i	−0.891384	+	0.453249i	$0.850265\pi$
$368$		−	11.6677i		−	0.608218i
$369$	0.766832	−	13.5290i	0.0399197	−	0.704291i
$370$	−1.44785	+	0.835916i	−0.0752701	+	0.0434572i
$371$	−22.5045	+	8.83902i	−1.16837	+	0.458899i
$372$	−6.39348	−	26.8829i	−0.331486	−	1.39381i
$373$	0.481953	+	0.404407i	0.0249546	+	0.0209394i	0.655180	−	0.755473i	$-0.272593\pi$
$373$	0.481953	+	0.404407i	0.0249546	+	0.0209394i	−0.630225	+	0.776413i	$0.717037\pi$
$374$	−8.68787	+	49.2713i	−0.449239	+	2.54776i
$375$	−0.360197	−	6.10246i	−0.0186005	−	0.315130i
$376$	43.7945	+	52.1923i	2.25853	+	2.69161i
$377$	−9.01807			−0.464454
$378$	25.6621	−	22.7656i	1.31991	−	1.17093i
$379$	−5.41656			−0.278230			−0.139115	−	0.990276i	$-0.544426\pi$
$379$	−5.41656			−0.278230			−0.139115	+	0.990276i	$0.544426\pi$
$380$	−3.96900	−	4.73007i	−0.203605	−	0.242648i
$381$	−11.5242	−	5.77644i	−0.590403	−	0.295936i
$382$	1.30070	−	7.37661i	0.0665494	−	0.377420i
$383$	−12.5526	−	10.5329i	−0.641409	−	0.538206i	0.263042	−	0.964784i	$-0.415274\pi$
$383$	−12.5526	−	10.5329i	−0.641409	−	0.538206i	−0.904450	+	0.426579i	$0.859719\pi$
$384$	−21.2811	+	20.1091i	−1.08600	+	1.02619i
$385$	−0.484535	+	3.22029i	−0.0246942	+	0.164121i
$386$	35.7182	−	20.6219i	1.81801	−	1.04963i
$387$	−21.0084	−	4.94453i	−1.06792	−	0.251345i
$388$			19.1271i			0.971033i
$389$	10.0311	+	11.9546i	0.508598	+	0.606124i	0.957846	−	0.287284i	$-0.0927523\pi$
$389$	10.0311	+	11.9546i	0.508598	+	0.606124i	−0.449247	+	0.893407i	$0.648308\pi$
$390$	−0.976543	+	1.31386i	−0.0494492	+	0.0665299i
$391$	4.29539	+	11.8015i	0.217227	+	0.596827i
$392$	37.9113	−	8.67350i	1.91481	−	0.438078i
$393$	−7.40800	+	9.96686i	−0.373684	+	0.502762i
$394$	7.95742	+	2.89627i	0.400889	+	0.145912i
$395$	4.79594			0.241310
$396$	−5.13547	−	43.3510i	−0.258067	−	2.17847i
$397$			6.56653i			0.329565i	0.986330	+	0.164782i	$0.0526921\pi$
$397$			6.56653i			0.329565i	−0.986330	+	0.164782i	$0.947308\pi$
$398$	8.04189	−	6.74795i	0.403104	−	0.338244i
$399$	7.86113	+	16.9965i	0.393549	+	0.850889i
$400$	−4.57747	+	25.9601i	−0.228874	+	1.29801i
$401$	−12.0749	−	33.1756i	−0.602993	−	1.65671i	−0.745176	−	0.666868i	$-0.767634\pi$
$401$	−12.0749	−	33.1756i	−0.602993	−	1.65671i	0.142183	−	0.989840i	$-0.454588\pi$
$402$	10.9709	+	16.6522i	0.547179	+	0.830536i
$403$	−0.694444	−	3.93839i	−0.0345927	−	0.196185i
$404$	4.55675	−	7.89252i	0.226707	−	0.392668i
$405$	0.197090	+	3.21153i	0.00979350	+	0.159582i
$406$	−55.0780	+	11.1490i	−2.73347	+	0.553315i
$407$	2.20677	−	6.06305i	0.109386	−	0.300534i
$408$	−25.1123	+	50.0999i	−1.24324	+	2.48032i
$409$	17.1446	+	3.02306i	0.847748	+	0.149481i	0.580615	−	0.814179i	$-0.302812\pi$
$409$	17.1446	+	3.02306i	0.847748	+	0.149481i	0.267134	+	0.963659i	$0.413923\pi$
$410$	1.37816	+	3.78647i	0.0680627	+	0.187001i
$411$	4.68851	−	4.43029i	0.231267	−	0.218530i
$412$	−12.1347	−	14.4616i	−0.597836	−	0.712473i
$413$	−10.6943	+	2.16476i	−0.526233	+	0.106521i
$414$	−9.66035	−	12.9340i	−0.474780	−	0.635671i
$415$	−0.724594	−	1.25503i	−0.0355689	−	0.0616071i
$416$	1.93888	−	1.62691i	0.0950614	−	0.0797660i
$417$	2.76027	−	23.7762i	0.135171	−	1.16433i
$418$	34.5733	+	6.09620i	1.69103	+	0.298175i
$419$	16.1147	−	5.86527i	0.787254	−	0.286537i	0.0830600	−	0.996545i	$-0.473531\pi$
$419$	16.1147	−	5.86527i	0.787254	−	0.286537i	0.704194	+	0.710007i	$0.251308\pi$
$420$	−2.94592	+	6.26643i	−0.143746	+	0.305770i
$421$	4.49987	+	25.5201i	0.219310	+	1.24377i	0.873268	+	0.487240i	$0.161996\pi$
$421$	4.49987	+	25.5201i	0.219310	+	1.24377i	−0.653958	+	0.756531i	$0.726893\pi$
$422$	38.6673	−	22.3246i	1.88230	−	1.08674i
$423$	35.8111	+	8.42849i	1.74119	+	0.409807i
$424$	−25.3858	+	43.9696i	−1.23285	+	2.13535i
$425$	−4.92712	−	27.9431i	−0.239000	−	1.35544i
$426$	−24.8194	−	26.2661i	−1.20251	−	1.27259i
$427$	35.1571	−	0.885801i	1.70137	−	0.0428669i
$428$	−13.0952	+	15.6063i	−0.632981	+	0.754358i
$429$	−0.372262	−	6.30687i	−0.0179730	−	0.304499i
$430$	6.32032	−	1.11444i	0.304793	−	0.0537432i
$431$	10.4907	−	6.05678i	0.505317	−	0.291745i	−0.225590	−	0.974222i	$-0.572431\pi$
$431$	10.4907	−	6.05678i	0.505317	−	0.291745i	0.730907	+	0.682478i	$0.239098\pi$
$432$	4.81714	−	27.6976i	0.231765	−	1.33260i
$433$			31.6375i			1.52040i	0.649689	+	0.760200i	$0.274899\pi$
$433$			31.6375i			1.52040i	−0.649689	+	0.760200i	$0.725101\pi$
$434$	−9.11034	−	23.1952i	−0.437310	−	1.11341i
$435$	2.36184	−	4.71196i	0.113242	−	0.225921i
$436$	80.1514	−	29.1727i	3.83856	−	1.39712i
$437$	8.28100	−	3.01404i	0.396134	−	0.144181i
$438$	−22.1177	−	23.4069i	−1.05683	−	1.11842i
$439$	3.83395	−	0.676028i	0.182984	−	0.0322651i	−0.0814050	−	0.996681i	$-0.525941\pi$
$439$	3.83395	−	0.676028i	0.182984	−	0.0322651i	0.264389	+	0.964416i	$0.414830\pi$
$440$	3.41922	+	5.92226i	0.163005	+	0.282333i
$441$	13.5987	−	16.0024i	0.647555	−	0.762019i
$442$	−7.69801	+	13.3333i	−0.366157	+	0.634202i
$443$	−0.0712478	+	0.195752i	−0.00338509	+	0.00930045i	−0.941374	−	0.337366i	$-0.890464\pi$
$443$	−0.0712478	+	0.195752i	−0.00338509	+	0.00930045i	0.937989	+	0.346666i	$0.112686\pi$
$444$	8.18394	−	11.0108i	0.388392	−	0.522551i
$445$	3.17447	+	2.66370i	0.150484	+	0.126271i
$446$	−5.67084	+	32.1610i	−0.268522	+	1.52287i
$447$	−14.9898	+	6.47981i	−0.708992	+	0.306484i
$448$	−8.01391	+	10.0544i	−0.378622	+	0.475027i
$449$	−11.7985	−	6.81187i	−0.556806	−	0.321472i	0.195057	−	0.980792i	$-0.437511\pi$
$449$	−11.7985	−	6.81187i	−0.556806	−	0.321472i	−0.751862	+	0.659320i	$0.770844\pi$
$450$	16.4197	+	32.5677i	0.774030	+	1.53525i
$451$	−13.4677	−	7.77556i	−0.634168	−	0.366137i
$452$	−18.3269	+	50.3529i	−0.862027	+	2.36840i
$453$	2.28980	−	7.67019i	0.107584	−	0.360377i
$454$	−2.75724	−	0.486176i	−0.129404	−	0.0228174i
$455$	−0.479044	+	0.880211i	−0.0224579	+	0.0412649i
$456$	35.1547	+	17.6211i	1.64627	+	0.825183i
$457$	15.2178	−	12.7693i	0.711859	−	0.597320i	−0.213261	−	0.976995i	$-0.568409\pi$
$457$	15.2178	−	12.7693i	0.711859	−	0.597320i	0.925120	+	0.379675i	$0.123964\pi$
$458$	−1.59153	−	2.75662i	−0.0743675	−	0.128808i
$459$	5.32434	+	29.7887i	0.248519	+	1.39042i
$460$	2.82197	+	1.62926i	0.131575	+	0.0759648i
$461$	5.61005	+	2.04189i	0.261286	+	0.0951003i	0.469342	−	0.883017i	$-0.344491\pi$
$461$	5.61005	+	2.04189i	0.261286	+	0.0951003i	−0.208056	+	0.978117i	$0.566714\pi$
$462$	−10.0707	−	38.0591i	−0.468533	−	1.77067i
$463$	21.0832	+	17.6909i	0.979822	+	0.822168i	0.984062	−	0.177823i	$-0.0569055\pi$
$463$	21.0832	+	17.6909i	0.979822	+	0.822168i	−0.00424088	+	0.999991i	$0.501350\pi$
$464$	−29.6023	+	35.2786i	−1.37425	+	1.63777i
$465$	2.23969	+	0.668620i	0.103863	+	0.0310065i
$466$	44.0077	+	16.0175i	2.03862	+	0.741996i
$467$	−15.8827			−0.734962			−0.367481	−	0.930031i	$-0.619780\pi$
$467$	−15.8827			−0.734962			−0.367481	+	0.930031i	$0.619780\pi$
$468$	3.07763	−	13.0763i	0.142263	−	0.604451i
$469$	8.07975	+	9.15073i	0.373088	+	0.422541i
$470$	−10.7737	+	1.89969i	−0.496952	+	0.0876261i
$471$	−1.62285	−	1.20620i	−0.0747768	−	0.0555788i
$472$	−14.7279	+	17.5520i	−0.677907	+	0.807898i
$473$	−15.9209	+	18.9738i	−0.732045	+	0.872417i
$474$	−53.2193	+	23.0058i	−2.44445	+	1.05669i
$475$	−19.6074	+	3.45732i	−0.899650	+	0.158633i
$476$	−20.7248	+	61.7366i	−0.949918	+	2.82969i
$477$	3.22514	+	27.2250i	0.147669	+	1.24655i
$478$	−31.1049			−1.42270
$479$	10.0828	+	3.66985i	0.460696	+	0.167680i	0.561933	−	0.827183i	$-0.310058\pi$
$479$	10.0828	+	3.66985i	0.460696	+	0.167680i	−0.101237	+	0.994862i	$0.532280\pi$
$480$	0.342271	+	1.43916i	0.0156225	+	0.0656884i
$481$	1.27626	−	1.52098i	0.0581923	−	0.0693509i
$482$	39.3846	+	33.0476i	1.79392	+	1.50528i
$483$	−6.96607	−	7.00967i	−0.316967	−	0.318951i
$484$	−3.38942	−	1.23365i	−0.154064	−	0.0560749i
$485$	−1.40115	−	0.808953i	−0.0636228	−	0.0367326i
$486$	−17.5925	−	34.6922i	−0.798014	−	1.57367i
$487$	−4.54921	−	7.87946i	−0.206144	−	0.357052i	0.744352	−	0.667787i	$-0.232758\pi$
$487$	−4.54921	−	7.87946i	−0.206144	−	0.357052i	−0.950497	+	0.310735i	$0.899425\pi$
$488$	56.5725	−	47.4699i	2.56091	−	2.14886i
$489$	0.720771	+	12.2113i	0.0325944	+	0.552215i
$490$	−1.83757	+	5.96815i	−0.0830130	+	0.269613i
$491$	2.90320	+	0.511913i	0.131020	+	0.0231023i	0.238773	−	0.971075i	$-0.423255\pi$
$491$	2.90320	+	0.511913i	0.131020	+	0.0231023i	−0.107754	+	0.994178i	$0.534366\pi$
$492$	−22.7101	−	24.0338i	−1.02385	−	1.08353i
$493$	16.9542	−	46.5812i	0.763578	−	2.09791i
$494$	9.35589	+	5.40163i	0.420941	+	0.243031i
$495$	3.39285	+	1.45727i	0.152497	+	0.0654994i
$496$	−17.6865	−	10.2113i	−0.794148	−	0.458501i
$497$	−17.2991	−	13.7883i	−0.775972	−	0.618491i
$498$	14.0609	+	10.4510i	0.630086	+	0.468319i
$499$	1.84999	−	10.4918i	0.0828171	−	0.469679i	−0.914989	−	0.403478i	$-0.867801\pi$
$499$	1.84999	−	10.4918i	0.0828171	−	0.469679i	0.997806	−	0.0662008i	$-0.0210878\pi$
$500$	−11.4271	−	9.58848i	−0.511036	−	0.428810i
$501$	11.3916	+	26.3523i	0.508940	+	1.17733i
$502$	8.08933	−	22.2253i	0.361045	−	0.991962i
$503$	8.22192	−	14.2408i	0.366597	−	0.634965i	−0.622434	−	0.782672i	$-0.713856\pi$
$503$	8.22192	−	14.2408i	0.366597	−	0.634965i	0.989031	+	0.147707i	$0.0471893\pi$
$504$	1.38577	−	44.0763i	0.0617272	−	1.96331i
$505$	0.385441	+	0.667604i	0.0171519	+	0.0297080i
$506$	−18.2452	+	3.21712i	−0.811097	+	0.143018i
$507$	−5.88491	+	19.7128i	−0.261358	+	0.875477i
$508$	−29.5591	+	10.7586i	−1.31147	+	0.477337i
$509$	−13.7090	+	4.98966i	−0.607640	+	0.221163i	−0.627470	−	0.778641i	$-0.715910\pi$
$509$	−13.7090	+	4.98966i	−0.607640	+	0.221163i	0.0198304	+	0.999803i	$0.493687\pi$
$510$	−4.95059	−	7.51425i	−0.219216	−	0.332737i
$511$	−15.4161	−	12.2874i	−0.681966	−	0.543564i
$512$			47.1935i			2.08568i
$513$	20.9025	−	3.73605i	0.922867	−	0.164950i
$514$	34.6889	−	20.0277i	1.53006	−	0.883383i
$515$	1.57260	−	0.277292i	0.0692970	−	0.0122189i
$516$	−43.9785	+	28.9742i	−1.93604	+	1.27552i
$517$	27.1389	−	32.3429i	1.19357	−	1.42244i
$518$	5.91438	−	10.8673i	0.259863	−	0.477480i
$519$	−5.45936	+	1.29838i	−0.239639	+	0.0569927i
$520$	0.365420	+	2.07240i	0.0160247	+	0.0908808i
$521$	8.47444	−	14.6782i	0.371272	−	0.643062i	−0.618489	−	0.785793i	$-0.712255\pi$
$521$	8.47444	−	14.6782i	0.371272	−	0.643062i	0.989762	+	0.142731i	$0.0455884\pi$
$522$	−3.60586	+	63.6171i	−0.157824	+	2.78444i
$523$	27.0509	−	15.6178i	1.18285	−	0.682920i	0.226180	−	0.974085i	$-0.427376\pi$
$523$	27.0509	−	15.6178i	1.18285	−	0.682920i	0.956673	+	0.291165i	$0.0940429\pi$
$524$	5.26209	+	29.8428i	0.229875	+	1.30369i
$525$	12.7492	+	18.3292i	0.556421	+	0.799952i
$526$	−31.2944	+	11.3902i	−1.36450	+	0.496637i
$527$	21.6486	+	3.81724i	0.943029	+	0.166281i
$528$	−25.8944	−	19.2464i	−1.12691	−	0.837590i
$529$	14.0565	−	11.7948i	0.611152	−	0.512817i
$530$	−4.07616	−	7.06012i	−0.177057	−	0.306672i
$531$	−0.700139	+	12.3523i	−0.0303835	+	0.536046i
$532$	43.3201	+	14.5424i	1.87816	+	0.630492i
$533$	−3.07606	−	3.66591i	−0.133239	−	0.158788i
$534$	−48.0039	−	14.3307i	−2.07733	−	0.620150i
$535$	−0.589387	−	1.61933i	−0.0254814	−	0.0700096i
$536$	25.2447	+	4.45133i	1.09041	+	0.192268i
$537$	−4.87922	−	7.40593i	−0.210554	−	0.319589i
$538$	21.2459	−	58.3725i	0.915974	−	2.51662i
$539$	−9.37274	−	22.2029i	−0.403713	−	0.956346i
$540$	6.02635	+	5.03276i	0.259333	+	0.216576i
$541$	19.0672	−	33.0253i	0.819762	−	1.41987i	−0.0860957	−	0.996287i	$-0.527439\pi$
$541$	19.0672	−	33.0253i	0.819762	−	1.41987i	0.905858	−	0.423582i	$-0.139228\pi$
$542$	−3.77714	−	21.4212i	−0.162242	−	0.920120i
$543$	3.23109	−	6.44614i	0.138659	−	0.276630i
$544$	4.75839	+	13.0736i	0.204014	+	0.560525i
$545$	−1.25285	+	7.10526i	−0.0536662	+	0.304356i
$546$	1.09353	−	12.0654i	0.0467988	−	0.516353i
$547$	−26.5978	+	22.3182i	−1.13724	+	0.954257i	−0.999345	−	0.0361899i	$-0.988478\pi$
$547$	−26.5978	+	22.3182i	−1.13724	+	0.954257i	−0.137894	+	0.990447i	$0.544033\pi$
$548$		−	15.7405i		−	0.672401i
$549$	9.13584	−	38.8165i	0.389908	−	1.65665i
$550$	41.8570			1.78479
$551$	−32.6856	−	11.8966i	−1.39246	−	0.506812i
$552$	−20.6136	−	2.39312i	−0.877375	−	0.101858i
$553$	−30.2807	+	18.5148i	−1.28766	+	0.787330i
$554$	−19.2447	−	52.8744i	−0.817630	−	2.24642i
$555$	0.460465	+	1.06520i	0.0195456	+	0.0452150i
$556$	−37.5439	−	44.7431i	−1.59222	−	1.89753i
$557$			19.0242i			0.806081i	0.915182	+	0.403041i	$0.132047\pi$
$557$			19.0242i			0.806081i	−0.915182	+	0.403041i	$0.867953\pi$
$558$	−28.0607	+	3.32413i	−1.18790	+	0.140722i
$559$	−6.60080	+	3.81097i	−0.279184	+	0.161187i
$560$	1.87089	+	4.76336i	0.0790597	+	0.201289i
$561$	33.2769	+	9.93422i	1.40495	+	0.419423i
$562$	−22.8768	−	19.1959i	−0.964999	−	0.809730i
$563$	−5.42674	+	30.7766i	−0.228710	+	1.29708i	0.626755	+	0.779217i	$0.284383\pi$
$563$	−5.42674	+	30.7766i	−0.228710	+	1.29708i	−0.855465	+	0.517861i	$0.826728\pi$
$564$	74.9660	−	49.3896i	3.15664	−	2.07968i
$565$	−2.91346	−	3.47213i	−0.122570	−	0.146074i
$566$	52.9570			2.22595
$567$	−13.6426	−	19.5161i	−0.572934	−	0.819601i
$568$	−46.4539			−1.94916
$569$	5.51067	+	6.56736i	0.231019	+	0.275318i	0.869084	−	0.494665i	$-0.164709\pi$
$569$	5.51067	+	6.56736i	0.231019	+	0.275318i	−0.638065	+	0.769983i	$0.720265\pi$
$570$	−5.27268	+	3.47378i	−0.220848	+	0.145501i
$571$	2.20202	−	12.4883i	0.0921518	−	0.522619i	−0.903431	−	0.428733i	$-0.858960\pi$
$571$	2.20202	−	12.4883i	0.0921518	−	0.522619i	0.995583	−	0.0938856i	$-0.0299288\pi$
$572$	−11.8099	−	9.90966i	−0.493796	−	0.414344i
$573$	−4.98202	−	1.48729i	−0.208127	−	0.0621325i
$574$	−23.3192	−	18.5867i	−0.973326	−	0.775792i
$575$	9.09928	−	5.25347i	0.379466	−	0.219085i
$576$	8.72417	+	11.6806i	0.363507	+	0.486690i
$577$			35.7244i			1.48723i	0.668610	+	0.743613i	$0.266890\pi$
$577$			35.7244i			1.48723i	−0.668610	+	0.743613i	$0.733110\pi$
$578$	−27.1315	−	32.3340i	−1.12852	−	1.34492i
$579$	−11.3596	−	26.2782i	−0.472089	−	1.09209i
$580$	−4.39893	−	12.0860i	−0.182656	−	0.501842i
$581$	9.42003	+	5.12674i	0.390809	+	0.212693i
$582$	19.4287	+	2.25555i	0.805344	+	0.0934956i
$583$	29.5651	+	10.7608i	1.22446	+	0.445668i
$584$	−41.3972			−1.71303
$585$	0.827731	+	0.778491i	0.0342225	+	0.0321866i
$586$		−	57.3887i		−	2.37070i
$587$	23.8827	−	20.0400i	0.985744	−	0.827138i	0.000798351	−	1.00000i	$-0.499746\pi$
$587$	23.8827	−	20.0400i	0.985744	−	0.827138i	0.984946	+	0.172862i	$0.0553014\pi$
$588$	−5.59167	−	50.9378i	−0.230597	−	2.10064i
$589$	2.67852	−	15.1906i	0.110367	−	0.625920i
$590$	−1.25830	−	3.45716i	−0.0518035	−	0.142329i
$591$	2.63392	−	5.25477i	0.108345	−	0.216152i
$592$	−1.76070	−	9.98543i	−0.0723643	−	0.410398i
$593$	−7.36449	+	12.7557i	−0.302423	+	0.523812i	−0.976684	−	0.214681i	$-0.931129\pi$
$593$	−7.36449	+	12.7557i	−0.302423	+	0.523812i	0.674261	+	0.738493i	$0.264462\pi$
$594$	−44.6401	+	0.104292i	−1.83160	+	0.00427916i
$595$	−3.64596	−	4.12924i	−0.149470	−	0.169282i
$596$	−13.6292	+	37.4459i	−0.558273	+	1.53384i
$597$	−4.00895	−	6.08499i	−0.164075	−	0.249042i
$598$	−5.61453	−	0.989993i	−0.229595	−	0.0404838i
$599$	−4.92526	−	13.5320i	−0.201241	−	0.552904i	0.797487	−	0.603336i	$-0.206162\pi$
$599$	−4.92526	−	13.5320i	−0.201241	−	0.552904i	−0.998727	+	0.0504321i	$0.983940\pi$
$600$	44.9258	+	13.4118i	1.83409	+	0.547534i
$601$	23.1504	+	27.5895i	0.944324	+	1.12540i	0.991962	+	0.126537i	$0.0403861\pi$
$601$	23.1504	+	27.5895i	0.944324	+	1.12540i	−0.0476382	+	0.998865i	$0.515169\pi$
$602$	−35.6030	+	31.4361i	−1.45107	+	1.28124i
$603$	12.3598	−	6.23144i	0.503329	−	0.253764i
$604$	−9.76645	−	16.9160i	−0.397391	−	0.688302i
$605$	0.233720	−	0.196115i	0.00950209	−	0.00797320i
$606$	−7.47960	−	5.55931i	−0.303838	−	0.225831i
$607$	−2.31280	−	0.407809i	−0.0938737	−	0.0165525i	0.126514	−	0.991965i	$-0.459621\pi$
$607$	−2.31280	−	0.407809i	−0.0938737	−	0.0165525i	−0.220388	+	0.975412i	$0.570732\pi$
$608$	9.17362	−	3.33892i	0.372039	−	0.135411i
$609$	3.27838	+	38.8684i	0.132847	+	1.57503i
$610$	2.05912	+	11.6778i	0.0833712	+	0.472822i
$611$	11.2518	−	6.49622i	0.455198	−	0.262809i
$612$	61.7571	+	40.4806i	2.49638	+	1.63633i
$613$	−13.6890	+	23.7101i	−0.552895	+	0.957643i	0.445169	+	0.895447i	$0.353144\pi$
$613$	−13.6890	+	23.7101i	−0.552895	+	0.957643i	−0.998064	+	0.0621960i	$0.980190\pi$
$614$	14.2362	+	80.7374i	0.574526	+	3.25830i
$615$	2.72107	−	0.647144i	0.109724	−	0.0260954i
$616$	−44.4513	−	24.1921i	−1.79099	−	0.974727i
$617$	20.2153	−	24.0916i	0.813837	−	0.969893i	−0.186083	−	0.982534i	$-0.559579\pi$
$617$	20.2153	−	24.0916i	0.813837	−	0.969893i	0.999920	+	0.0126410i	$0.00402388\pi$
$618$	−16.1206	+	10.6207i	−0.648465	+	0.427226i
$619$	−13.5624	+	2.39142i	−0.545120	+	0.0961193i	−0.439425	−	0.898279i	$-0.644818\pi$
$619$	−13.5624	+	2.39142i	−0.545120	+	0.0961193i	−0.105695	+	0.994399i	$0.533707\pi$
$620$	4.93946	−	2.85180i	0.198374	−	0.114531i
$621$	−9.69119	+	5.62544i	−0.388894	+	0.225741i
$622$		−	24.0344i		−	0.963691i
$623$	−30.3263	−	4.56298i	−1.21500	−	0.182812i
$624$	−5.46220	−	8.29080i	−0.218663	−	0.331898i
$625$	−21.7061	+	7.90038i	−0.868244	+	0.316015i
$626$	25.2660	−	9.19607i	1.00983	−	0.367549i
$627$	6.97075	−	23.3501i	0.278385	−	0.932514i
$628$	−4.85913	+	0.856795i	−0.193900	+	0.0341899i
$629$	5.45698	+	9.45177i	0.217584	+	0.376867i
$630$	6.01782	+	3.73132i	0.239756	+	0.148660i
$631$	11.5471	−	20.0002i	0.459684	−	0.796197i	−0.539260	−	0.842140i	$-0.681296\pi$
$631$	11.5471	−	20.0002i	0.459684	−	0.796197i	0.998944	+	0.0459427i	$0.0146292\pi$
$632$	−25.4911	+	70.0362i	−1.01398	+	2.78589i
$633$	−12.2975	−	28.4479i	−0.488782	−	1.13070i
$634$	8.43303	+	7.07615i	0.334918	+	0.281030i
$635$	0.462039	−	2.62035i	0.0183354	−	0.103985i
$636$	53.6919	+	39.9072i	2.12902	+	1.58242i
$637$	−0.373476	−	7.40685i	−0.0147976	−	0.293470i
$638$	63.3288	+	36.5629i	2.50721	+	1.44754i
$639$	−20.0970	+	15.0104i	−0.795025	+	0.593801i
$640$	−5.23375	−	3.02170i	−0.206882	−	0.119443i
$641$	8.39959	−	23.0777i	0.331764	−	0.911514i	−0.655889	−	0.754857i	$-0.727706\pi$
$641$	8.39959	−	23.0777i	0.331764	−	0.911514i	0.987653	−	0.156657i	$-0.0500716\pi$
$642$	14.3081	+	15.1420i	0.564694	+	0.597608i
$643$	−37.4315	−	6.60018i	−1.47615	−	0.260286i	−0.623114	−	0.782131i	$-0.714133\pi$
$643$	−37.4315	−	6.60018i	−1.47615	−	0.260286i	−0.853040	+	0.521846i	$0.825244\pi$
$644$	−24.1072	+	0.607392i	−0.949956	+	0.0239346i
$645$	−0.262485	−	4.44704i	−0.0103354	−	0.175102i
$646$	−45.4904	+	38.1710i	−1.78980	+	1.50182i
$647$	−1.12029	−	1.94040i	−0.0440432	−	0.0762851i	0.843163	−	0.537657i	$-0.180691\pi$
$647$	−1.12029	−	1.94040i	−0.0440432	−	0.0762851i	−0.887207	+	0.461372i	$0.847357\pi$
$648$	−47.9463	−	14.1916i	−1.88351	−	0.557498i
$649$	12.2964	+	7.09931i	0.482674	+	0.278672i
$650$	12.1037	+	4.40540i	0.474748	+	0.172794i
$651$	−16.7222	+	4.42484i	−0.655396	+	0.173423i
$652$	22.8662	+	19.1870i	0.895509	+	0.751422i
$653$	−29.1222	+	34.7064i	−1.13964	+	1.35817i	−0.215321	+	0.976543i	$0.569080\pi$
$653$	−29.1222	+	34.7064i	−1.13964	+	1.35817i	−0.924317	+	0.381625i	$0.875365\pi$
$654$	−20.1809	−	84.8552i	−0.789134	−	3.31810i
$655$	−2.40867	−	0.876684i	−0.0941145	−	0.0342549i
$656$	−24.4383			−0.954157
$657$	−17.9094	+	13.3764i	−0.698711	+	0.521864i
$658$	60.6892	−	53.5863i	2.36591	−	2.08901i
$659$	−43.6553	+	7.69760i	−1.70057	+	0.299856i	−0.937893	−	0.346926i	$-0.887226\pi$
$659$	−43.6553	+	7.69760i	−1.70057	+	0.299856i	−0.762675	+	0.646782i	$0.776114\pi$
$660$	8.27085	−	3.57534i	0.321942	−	0.139170i
$661$	−16.8804	+	20.1173i	−0.656571	+	0.782470i	−0.986889	−	0.161399i	$-0.948399\pi$
$661$	−16.8804	+	20.1173i	−0.656571	+	0.782470i	0.330319	+	0.943870i	$0.392844\pi$
$662$	−22.1418	+	26.3876i	−0.860566	+	1.02558i
$663$	8.57707	+	6.37502i	0.333106	+	0.247585i
$664$	22.1788	−	3.91073i	0.860706	−	0.151766i
$665$	−2.89745	+	2.55834i	−0.112358	+	0.0992081i
$666$	−10.2193	−	9.61140i	−0.395991	−	0.372434i
$667$	18.3560			0.710748
$668$	65.8306	+	23.9604i	2.54706	+	0.927055i
$669$	21.7209	+	6.48438i	0.839778	+	0.250700i
$670$	−2.64574	+	3.15307i	−0.102214	+	0.121814i
$671$	−35.0572	−	29.4165i	−1.35337	−	1.13561i
$672$	−7.71695	−	7.76525i	−0.297688	−	0.299551i
$673$	−40.4246	−	14.7134i	−1.55825	−	0.567158i	−0.587918	−	0.808920i	$-0.700052\pi$
$673$	−40.4246	−	14.7134i	−1.55825	−	0.567158i	−0.970336	+	0.241762i	$0.922275\pi$
$674$	−15.6708	−	9.04751i	−0.603615	−	0.348497i
$675$	23.7696	−	8.71435i	0.914891	−	0.335416i
$676$	25.1003	+	43.4750i	0.965396	+	1.67212i
$677$	−31.8275	+	26.7064i	−1.22323	+	1.02641i	−0.224580	+	0.974456i	$0.572101\pi$
$677$	−31.8275	+	26.7064i	−1.22323	+	1.02641i	−0.998649	+	0.0519559i	$0.983454\pi$
$678$	48.9855	+	24.5537i	1.88128	+	0.942979i
$679$	11.9696	−	0.301579i	0.459350	−	0.0115735i
$680$	−11.3916	−	2.00865i	−0.436848	−	0.0770282i
$681$	−0.555922	+	1.86218i	−0.0213030	+	0.0713591i
$682$	−11.0911	+	30.4726i	−0.424702	+	1.16686i
$683$	7.54959	+	4.35876i	0.288877	+	0.166783i	0.637435	−	0.770504i	$-0.279995\pi$
$683$	7.54959	+	4.35876i	0.288877	+	0.166783i	−0.348558	+	0.937287i	$0.613329\pi$
$684$	28.4049	−	43.3344i	1.08609	−	1.65693i
$685$	1.15306	+	0.665721i	0.0440562	+	0.0254359i
$686$	−11.4381	−	44.7757i	−0.436707	−	1.70955i
$687$	−2.02807	+	0.876697i	−0.0773756	+	0.0334481i
$688$	−6.75897	+	38.3320i	−0.257683	+	1.46139i
$689$	7.41675	+	6.22339i	0.282556	+	0.237092i
$690$	1.98773	−	2.67433i	0.0756714	−	0.101810i
$691$	−15.2046	+	41.7744i	−0.578412	+	1.58917i	0.212445	+	0.977173i	$0.431857\pi$
$691$	−15.2046	+	41.7744i	−0.578412	+	1.58917i	−0.790857	+	0.612001i	$0.790365\pi$
$692$	−6.84670	+	11.8588i	−0.260273	+	0.450805i
$693$	−27.0477	+	3.89724i	−1.02746	+	0.148044i
$694$	22.2993	+	38.6236i	0.846472	+	1.46613i
$695$	4.86549	−	0.857918i	0.184559	−	0.0325427i
$696$	56.2563	+	59.5353i	2.13239	+	2.25668i
$697$	24.7187	−	8.99685i	0.936286	−	0.340780i
$698$	80.3318	−	29.2384i	3.04060	−	1.10669i
$699$	14.5666	−	29.0609i	0.550960	−	1.09918i
$700$	53.8759	+	8.10633i	2.03632	+	0.306391i
$701$			4.87126i			0.183985i	0.995760	+	0.0919925i	$0.0293236\pi$
$701$			4.87126i			0.183985i	−0.995760	+	0.0919925i	$0.970676\pi$
$702$	−12.9195	−	4.66816i	−0.487615	−	0.176188i
$703$	6.63222	−	3.82912i	0.250139	−	0.144418i
$704$	16.4770	−	2.90535i	0.621002	−	0.109499i
$705$	0.447435	+	7.58045i	0.0168514	+	0.285496i
$706$	−26.0589	+	31.0558i	−0.980740	+	1.16880i
$707$	−5.01091	−	2.72712i	−0.188454	−	0.102564i
$708$	20.7350	+	21.9435i	0.779267	+	0.824688i
$709$	2.93571	+	16.6492i	0.110253	+	0.625275i	0.988992	+	0.147972i	$0.0472746\pi$
$709$	2.93571	+	16.6492i	0.110253	+	0.625275i	−0.878739	+	0.477303i	$0.841614\pi$
$710$	3.72951	−	6.45971i	0.139966	−	0.242428i
$711$	11.6023	+	38.5360i	0.435122	+	1.44521i
$712$	−55.7713	+	32.1996i	−2.09012	+	1.20673i
$713$	1.41352	+	8.01648i	0.0529368	+	0.300220i
$714$	60.2660	+	28.3317i	2.25540	+	1.06029i
$715$	1.22541	−	0.446012i	0.0458276	−	0.0166799i
$716$	−21.3126	−	3.75798i	−0.796488	−	0.140442i
$717$	−2.48982	+	21.4466i	−0.0929842	+	0.800939i
$718$	33.4997	−	28.1096i	1.25020	−	1.04904i
$719$	−2.77541	−	4.80714i	−0.103505	−	0.179276i	0.809621	−	0.586953i	$-0.199673\pi$
$719$	−2.77541	−	4.80714i	−0.103505	−	0.179276i	−0.913126	+	0.407676i	$0.866339\pi$
$720$	5.76252	−	0.682642i	0.214757	−	0.0254406i
$721$	−8.85861	+	7.82182i	−0.329912	+	0.291300i
$722$	−3.69074	−	4.39845i	−0.137355	−	0.163693i
$723$	25.9387	−	24.5102i	0.964672	−	0.911542i
$724$	−6.01790	−	16.5340i	−0.223653	−	0.614483i
$725$	−40.8415	−	7.20146i	−1.51682	−	0.267456i
$726$	−1.65279	+	3.29738i	−0.0613408	+	0.122377i
$727$	11.3466	−	31.1745i	0.420822	−	1.15620i	−0.530415	−	0.847738i	$-0.677964\pi$
$727$	11.3466	−	31.1745i	0.420822	−	1.15620i	0.951237	−	0.308461i	$-0.0998139\pi$
$728$	−10.3077	−	11.6740i	−0.382030	−	0.432669i
$729$	−25.3283	+	9.35299i	−0.938084	+	0.346407i
$730$	3.32354	−	5.75654i	0.123010	−	0.213059i
$731$	−7.27525	−	41.2600i	−0.269085	−	1.52606i
$732$	−53.5345	−	81.2574i	−1.97869	−	3.00336i
$733$	−8.25356	−	22.6765i	−0.304852	−	0.837575i	−0.993639	−	0.112611i	$-0.964079\pi$
$733$	−8.25356	−	22.6765i	−0.304852	−	0.837575i	0.688787	−	0.724964i	$-0.258144\pi$
$734$	−3.74806	+	21.2563i	−0.138344	+	0.784585i
$735$	3.96791	+	1.74472i	0.146359	+	0.0643551i
$736$	−3.94654	+	3.31154i	−0.145471	+	0.122065i
$737$		−	15.8852i		−	0.585138i
$738$	−27.0907	+	20.2340i	−0.997224	+	0.744823i
$739$	26.0657			0.958843			0.479422	−	0.877585i	$-0.340846\pi$
$739$	26.0657			0.958843			0.479422	+	0.877585i	$0.340846\pi$
$740$	2.66096	+	0.968511i	0.0978189	+	0.0356032i
$741$	4.47329	−	6.01846i	0.164331	−	0.221093i
$742$	52.9919	+	28.8402i	1.94539	+	1.05876i
$743$	6.91069	+	18.9870i	0.253528	+	0.696564i	0.999531	+	0.0306207i	$0.00974840\pi$
$743$	6.91069	+	18.9870i	0.253528	+	0.696564i	−0.746003	+	0.665943i	$0.768029\pi$
$744$	−21.6683	+	29.1529i	−0.794398	+	1.06880i
$745$	−2.16665	−	2.58211i	−0.0793800	−	0.0946014i
$746$		−	1.56991i		−	0.0574783i
$747$	8.33141	−	8.85838i	0.304830	−	0.324111i
$748$	73.3895	−	42.3714i	2.68338	−	1.54925i
$749$	9.97272	+	7.94879i	0.364395	+	0.290442i
$750$	−11.0872	+	10.4765i	−0.404847	+	0.382549i
$751$	8.51983	+	7.14899i	0.310893	+	0.260870i	0.784861	−	0.619672i	$-0.212734\pi$
$751$	8.51983	+	7.14899i	0.310893	+	0.260870i	−0.473968	+	0.880542i	$0.657179\pi$
$752$	11.5214	−	65.3411i	0.420142	−	2.38274i
$753$	−14.6767	−	7.35660i	−0.534848	−	0.268089i
$754$	14.4645	+	17.2381i	0.526766	+	0.627776i
$755$	1.65223			0.0601307
$756$	−57.4783	−	8.51108i	−2.09047	−	0.309545i
$757$	52.3885			1.90409			0.952047	−	0.305952i	$-0.0989747\pi$
$757$	52.3885			1.90409			0.952047	+	0.305952i	$0.0989747\pi$
$758$	8.68788	+	10.3538i	0.315558	+	0.376067i
$759$	0.757729	+	12.8375i	0.0275038	+	0.465970i
$760$	−1.40945	+	7.99340i	−0.0511262	+	0.289951i
$761$	−9.61925	−	8.07151i	−0.348698	−	0.292592i	0.451569	−	0.892236i	$-0.350864\pi$
$761$	−9.61925	−	8.07151i	−0.348698	−	0.292592i	−0.800267	+	0.599644i	$0.795309\pi$
$762$	7.44250	+	31.2938i	0.269613	+	1.13365i
$763$	−19.5197	−	49.6980i	−0.706662	−	1.79919i
$764$	−10.9874	+	6.34360i	−0.397511	+	0.229503i
$765$	−5.57731	+	2.81192i	−0.201648	+	0.101665i
$766$			40.8887i			1.47737i
$767$	2.80853	+	3.34707i	0.101410	+	0.120856i
$768$	55.8504	+	6.48389i	2.01533	+	0.233967i
$769$	5.13723	+	14.1144i	0.185253	+	0.508979i	0.997202	−	0.0747491i	$-0.0238156\pi$
$769$	5.13723	+	14.1144i	0.185253	+	0.508979i	−0.811949	+	0.583728i	$0.801593\pi$
$770$	6.93279	−	4.23899i	0.249841	−	0.152763i
$771$	−11.0323	−	25.5210i	−0.397317	−	0.919115i
$772$	−65.6455	−	23.8930i	−2.36263	−	0.859929i
$773$	−18.8942			−0.679576			−0.339788	−	0.940502i	$-0.610355\pi$
$773$	−18.8942			−0.679576			−0.339788	+	0.940502i	$0.610355\pi$
$774$	24.2448	+	48.0885i	0.871463	+	1.72851i
$775$		−	18.3909i		−	0.660622i
$776$	19.2606	−	16.1616i	0.691415	−	0.580166i
$777$	−7.01950	−	4.94781i	−0.251823	−	0.177502i
$778$	6.76200	−	38.3492i	0.242429	−	1.37489i
$779$	−6.31301	−	17.3449i	−0.226187	−	0.621444i
$780$	2.76797	−	0.163379i	0.0991092	−	0.00584990i
$781$	4.99879	+	28.3496i	0.178871	+	1.01443i
$782$	15.6691	−	27.1396i	0.560325	−	0.970512i
$783$	43.5750	+	7.57852i	1.55724	+	0.270834i
$784$	−30.2015	−	22.8524i	−1.07863	−	0.816155i
$785$	0.142745	−	0.392190i	0.00509480	−	0.0139978i
$786$	30.9338	−	1.82586i	1.10337	−	0.0651263i
$787$	−1.36876	−	0.241349i	−0.0487910	−	0.00860317i	0.149199	−	0.988807i	$-0.452330\pi$
$787$	−1.36876	−	0.241349i	−0.0487910	−	0.00860317i	−0.197990	+	0.980204i	$0.563441\pi$
$788$	−4.90567	−	13.4782i	−0.174757	−	0.480142i
$789$	5.34850	+	22.4890i	0.190412	+	0.800631i
$790$	−7.69243	−	9.16748i	−0.273684	−	0.326164i
$791$	31.7993	+	10.6749i	1.13065	+	0.379556i
$792$	−39.3143	+	41.8010i	−1.39697	+	1.48533i
$793$	−7.04140	−	12.1961i	−0.250047	−	0.433095i
$794$	12.5520	−	10.5324i	0.445453	−	0.373780i
$795$	−5.19419	+	2.24536i	−0.184219	+	0.0796346i
$796$	−17.5112	−	3.08770i	−0.620668	−	0.109440i
$797$	−1.89028	+	0.688005i	−0.0669571	+	0.0243704i	−0.375282	−	0.926911i	$-0.622454\pi$
$797$	−1.89028	+	0.688005i	−0.0669571	+	0.0243704i	0.308324	+	0.951281i	$0.400232\pi$
$798$	19.8801	−	42.2881i	0.703749	−	1.49698i
$799$	12.4014	+	70.3321i	0.438732	+	2.48817i
$800$	10.0801	−	5.81975i	0.356385	−	0.205759i
$801$	−13.7235	+	31.9513i	−0.484895	+	1.12894i
$802$	−44.0479	+	76.2932i	−1.55539	+	2.69401i
$803$	4.45466	+	25.2636i	0.157201	+	0.891534i
$804$	9.66199	−	32.3650i	0.340752	−	1.14143i
$805$	0.975082	−	1.79165i	0.0343671	−	0.0631472i
$806$	−6.41442	+	7.64441i	−0.225938	+	0.269263i
$807$	−38.5469	−	19.3214i	−1.35692	−	0.680146i
$808$	−11.7978	+	2.08028i	−0.415047	+	0.0731840i
$809$	4.13482	−	2.38724i	0.145373	−	0.0839309i	−0.425550	−	0.904935i	$-0.639919\pi$
$809$	4.13482	−	2.38724i	0.145373	−	0.0839309i	0.570922	+	0.821004i	$0.306586\pi$
$810$	5.82275	−	5.52787i	0.204591	−	0.194230i
$811$			17.2143i			0.604475i	0.953233	+	0.302237i	$0.0977336\pi$
$811$			17.2143i			0.604475i	−0.953233	+	0.302237i	$0.902266\pi$
$812$	74.4321	+	59.3264i	2.61206	+	2.08195i
$813$	−15.0722	+	0.889631i	−0.528604	+	0.0312007i
$814$	−15.1291	+	5.50655i	−0.530276	+	0.193005i
$815$	−2.37263	+	0.863565i	−0.0831094	+	0.0302494i
$816$	53.0937	−	12.6271i	1.85865	−	0.442038i
$817$	−28.9518	+	5.10498i	−1.01289	+	0.178601i
$818$	−21.7205	−	37.6210i	−0.759439	−	1.31539i
$819$	−8.23152	−	1.71977i	−0.287632	−	0.0600938i
$820$	3.41255	−	5.91071i	0.119171	−	0.206411i
$821$	−2.98238	+	8.19401i	−0.104086	+	0.285973i	−0.980793	−	0.195051i	$-0.937513\pi$
$821$	−2.98238	+	8.19401i	−0.104086	+	0.285973i	0.876707	+	0.481024i	$0.159735\pi$
$822$	−15.9887	−	1.85619i	−0.557668	−	0.0647419i
$823$	−9.30169	−	7.80505i	−0.324237	−	0.272067i	0.466110	−	0.884727i	$-0.345655\pi$
$823$	−9.30169	−	7.80505i	−0.324237	−	0.272067i	−0.790347	+	0.612660i	$0.790100\pi$
$824$	−4.30923	+	24.4389i	−0.150119	+	0.851368i
$825$	3.35049	−	28.8602i	0.116649	−	1.00478i
$826$	21.2911	+	16.9701i	0.740812	+	0.590467i
$827$	−17.3220	−	10.0009i	−0.602346	−	0.347765i	0.167618	−	0.985852i	$-0.446393\pi$
$827$	−17.3220	−	10.0009i	−0.602346	−	0.347765i	−0.769964	+	0.638087i	$0.779726\pi$
$828$	−6.26443	+	26.6164i	−0.217704	+	0.924983i
$829$	−12.8073	−	7.39429i	−0.444815	−	0.256814i	0.260823	−	0.965387i	$-0.416006\pi$
$829$	−12.8073	−	7.39429i	−0.444815	−	0.256814i	−0.705638	+	0.708572i	$0.749340\pi$
$830$	−1.23680	+	3.39807i	−0.0429299	+	0.117949i
$831$	−37.9971	+	9.03674i	−1.31811	+	0.313481i
$832$	5.07043	+	0.894053i	0.175785	+	0.0309957i
$833$	38.9609	+	11.9959i	1.34992	+	0.415635i
$834$	−49.8758	+	32.8595i	−1.72706	+	1.13783i
$835$	−4.53941	+	3.80902i	−0.157093	+	0.131816i
$836$	−29.7317	−	51.4968i	−1.02829	−	1.78105i
$837$	0.0458234	+	19.6138i	0.00158389	+	0.677951i
$838$	−37.0586	−	21.3958i	−1.28017	−	0.739106i
$839$	−9.90483	−	3.60506i	−0.341953	−	0.124461i	0.165335	−	0.986238i	$-0.447130\pi$
$839$	−9.90483	−	3.60506i	−0.341953	−	0.124461i	−0.507287	+	0.861777i	$0.669352\pi$
$840$	8.79933	−	2.32837i	0.303606	−	0.0803365i
$841$	−33.2865	−	27.9307i	−1.14781	−	0.963127i
$842$	41.5643	−	49.5344i	1.43240	−	1.70707i
$843$	−15.0667	+	14.2369i	−0.518923	+	0.490343i
$844$	−71.0656	−	25.8658i	−2.44618	−	0.890337i
$845$	−4.24632			−0.146078
$846$	−41.3279	−	81.9721i	−1.42088	−	2.81826i
$847$	−0.718563	+	2.14051i	−0.0246901	+	0.0735489i
$848$	48.6918	−	8.58567i	1.67208	−	0.294833i
$849$	4.23901	−	36.5136i	0.145482	−	1.25314i
$850$	−45.5106	+	54.2375i	−1.56100	+	1.86033i
$851$	−2.59779	+	3.09592i	−0.0890510	+	0.106127i
$852$	−7.05861	+	60.8008i	−0.241824	+	2.08300i
$853$	−10.2716	+	1.81115i	−0.351691	+	0.0620126i	−0.346703	−	0.937975i	$-0.612699\pi$
$853$	−10.2716	+	1.81115i	−0.351691	+	0.0620126i	−0.00498807	+	0.999988i	$0.501588\pi$
$854$	−58.0834	−	65.7824i	−1.98757	−	2.25103i
$855$	1.97310	+	3.91355i	0.0674785	+	0.133841i
$856$	26.7801			0.915324
$857$	−44.2233	−	16.0960i	−1.51064	−	0.549828i	−0.551850	−	0.833943i	$-0.686078\pi$
$857$	−44.2233	−	16.0960i	−1.51064	−	0.549828i	−0.958790	+	0.284115i	$0.908300\pi$
$858$	−11.4586	+	10.8275i	−0.391189	+	0.369644i
$859$	2.65487	−	3.16395i	0.0905829	−	0.107952i	−0.718849	−	0.695166i	$-0.755331\pi$
$859$	2.65487	−	3.16395i	0.0905829	−	0.107952i	0.809432	+	0.587214i	$0.199775\pi$
$860$	−8.32726	−	6.98740i	−0.283957	−	0.238268i
$861$	−14.6820	+	14.5907i	−0.500362	+	0.497249i
$862$	−28.4040	−	10.3382i	−0.967446	−	0.352121i
$863$	24.3038	+	14.0318i	0.827311	+	0.477648i	0.852931	−	0.522024i	$-0.174823\pi$
$863$	24.3038	+	14.0318i	0.827311	+	0.477648i	−0.0256201	+	0.999672i	$0.508156\pi$
$864$	−10.7358	+	6.23181i	−0.365240	+	0.212011i
$865$	−0.579142	−	1.00310i	−0.0196914	−	0.0341065i
$866$	60.4754	−	50.7448i	2.05504	−	1.72438i
$867$	−24.4659	+	16.1188i	−0.830905	+	0.547423i
$868$	−20.1774	+	37.0746i	−0.684866	+	1.25839i
$869$	45.4842	+	8.02009i	1.54295	+	0.272063i
$870$	−12.7952	+	3.04305i	−0.433799	+	0.103169i
$871$	1.67190	−	4.59350i	0.0566500	−	0.155645i
$872$	−97.1007	−	56.0611i	−3.28824	−	1.89847i
$873$	3.11038	−	13.2154i	0.105270	−	0.447274i
$874$	−19.0437	−	10.9949i	−0.644161	−	0.371907i
$875$	−5.82020	+	7.30215i	−0.196759	+	0.246858i
$876$	−6.29025	+	54.1825i	−0.212528	+	1.83066i
$877$	2.77883	−	15.7595i	0.0938345	−	0.532162i	−0.901264	−	0.433271i	$-0.857359\pi$
$877$	2.77883	−	15.7595i	0.0938345	−	0.532162i	0.995098	−	0.0988910i	$-0.0315295\pi$
$878$	−7.44168	−	6.24431i	−0.251145	−	0.210735i
$879$	−39.5692	−	4.59374i	−1.33464	−	0.154943i
$880$	2.27767	−	6.25785i	0.0767802	−	0.210952i
$881$	−12.7246	+	22.0396i	−0.428702	+	0.742533i	−0.996758	−	0.0804564i	$-0.974362\pi$
$881$	−12.7246	+	22.0396i	−0.428702	+	0.742533i	0.568056	+	0.822990i	$0.307696\pi$
$882$	−52.4003	−	0.326971i	−1.76441	−	0.0110097i
$883$	−5.39480	−	9.34406i	−0.181549	−	0.314453i	0.760859	−	0.648917i	$-0.224778\pi$
$883$	−5.39480	−	9.34406i	−0.181549	−	0.314453i	−0.942408	+	0.334465i	$0.891445\pi$
$884$	25.6815	−	4.52834i	0.863761	−	0.152304i
$885$	−2.48441	+	0.590860i	−0.0835126	+	0.0198616i
$886$	0.488459	−	0.177785i	0.0164101	−	0.00597279i
$887$	21.1469	−	7.69684i	0.710043	−	0.258435i	0.0383505	−	0.999264i	$-0.487790\pi$
$887$	21.1469	−	7.69684i	0.710043	−	0.258435i	0.671693	+	0.740830i	$0.265567\pi$
$888$	−18.0027	+	1.06261i	−0.604132	+	0.0356588i
$889$	7.19869	+	18.3281i	0.241436	+	0.614706i
$890$		−	10.3405i		−	0.346613i
$891$	−3.50136	+	30.7874i	−0.117300	+	1.03142i
$892$	47.9036	−	27.6572i	1.60393	−	0.926030i
$893$	49.3514	−	8.70199i	1.65148	−	0.291201i
$894$	36.4290	+	18.2598i	1.21837	+	0.610700i
$895$	1.17667	−	1.40230i	0.0393318	−	0.0468738i
$896$	44.7102	−	1.12650i	1.49366	−	0.0376336i
$897$	−1.13202	+	3.79194i	−0.0377969	+	0.126609i
$898$	5.90322	+	33.4788i	0.196993	+	1.11720i
$899$	16.0648	−	27.8251i	0.535793	−	0.928020i
$900$	24.3803	−	56.7628i	0.812677	−	1.89209i
$901$	−46.0895	+	26.6098i	−1.53546	+	0.886500i
$902$	6.73837	+	38.2152i	0.224363	+	1.27243i
$903$	18.8251	+	27.0644i	0.626462	+	0.900648i
$904$	66.1897	−	24.0911i	2.20144	−	0.801257i
$905$	1.46571	+	0.258444i	0.0487218	+	0.00859097i
$906$	−18.3344	+	7.92561i	−0.609119	+	0.263311i
$907$	−13.2659	+	11.1314i	−0.440486	+	0.369611i	−0.835891	−	0.548895i	$-0.815049\pi$
$907$	−13.2659	+	11.1314i	−0.440486	+	0.369611i	0.395405	+	0.918507i	$0.370604\pi$
$908$	2.37112	+	4.10690i	0.0786883	+	0.136292i
$909$	−4.43182	+	4.71214i	−0.146994	+	0.156292i
$910$	2.45090	−	0.496115i	0.0812464	−	0.0164460i
$911$	20.4723	+	24.3979i	0.678277	+	0.808339i	0.989885	−	0.141872i	$-0.0453121\pi$
$911$	20.4723	+	24.3979i	0.678277	+	0.808339i	−0.311608	+	0.950211i	$0.600868\pi$
$912$	−8.86034	−	37.2554i	−0.293395	−	1.23365i
$913$	−4.77322	−	13.1143i	−0.157971	−	0.434021i
$914$	−48.8171	−	8.60777i	−1.61473	−	0.284720i
$915$	8.21663	−	0.484985i	0.271633	−	0.0160331i
$916$	−1.84399	+	5.06631i	−0.0609270	+	0.167396i
$917$	18.5923	−	3.76349i	0.613973	−	0.124282i
$918$	48.4015	−	57.9571i	1.59749	−	1.91287i
$919$	−9.28327	+	16.0791i	−0.306227	+	0.530401i	−0.977534	−	0.210779i	$-0.932400\pi$
$919$	−9.28327	+	16.0791i	−0.306227	+	0.530401i	0.671307	+	0.741180i	$0.265733\pi$
$920$	−0.743802	−	4.21831i	−0.0245224	−	0.139074i
$921$	56.8076	−	3.35306i	1.87187	−	0.110487i
$922$	−5.09513	−	13.9987i	−0.167799	−	0.461024i
$923$	−1.53826	+	8.72392i	−0.0506325	+	0.287151i
$924$	−38.4179	+	54.5038i	−1.26386	+	1.79304i
$925$	6.99458	−	5.86915i	0.229980	−	0.192977i
$926$		−	68.6762i		−	2.25684i
$927$	6.03251	+	11.9652i	0.198134	+	0.392989i
$928$	20.3346			0.667517
$929$	−10.2172	−	3.71876i	−0.335216	−	0.122008i	0.168928	−	0.985628i	$-0.445969\pi$
$929$	−10.2172	−	3.71876i	−0.335216	−	0.122008i	−0.504143	+	0.863620i	$0.668192\pi$
$930$	−2.31428	−	5.35363i	−0.0758881	−	0.175552i
$931$	8.41744	−	27.3385i	0.275871	−	0.895985i
$932$	−27.1303	−	74.5399i	−0.888682	−	2.44163i
$933$	−16.5716	−	1.92386i	−0.542529	−	0.0629843i
$934$	25.4749	+	30.3599i	0.833566	+	0.993405i
$935$			7.16814i			0.234423i
$936$	−15.7680	+	7.94975i	−0.515392	+	0.259846i
$937$	18.3316	−	10.5838i	0.598869	−	0.345757i	−0.169728	−	0.985491i	$-0.554289\pi$
$937$	18.3316	−	10.5838i	0.598869	−	0.345757i	0.768596	+	0.639734i	$0.220955\pi$
$938$	4.53222	−	30.1218i	0.147982	−	0.983512i
$939$	−4.31820	−	18.1569i	−0.140919	−	0.592528i
$940$	14.1947	+	11.9108i	0.462980	+	0.388487i
$941$	−0.900013	+	5.10423i	−0.0293396	+	0.166393i	−0.995957	−	0.0898309i	$-0.971367\pi$
$941$	−0.900013	+	5.10423i	−0.0293396	+	0.166393i	0.966617	+	0.256224i	$0.0824785\pi$
$942$	0.297294	+	5.03677i	0.00968638	+	0.164107i
$943$	6.26123	+	7.46185i	0.203894	+	0.242991i
$944$	22.3129			0.726223
$945$	3.05443	−	3.85058i	0.0993607	−	0.125259i
$946$	61.8050			2.00945
$947$	19.2144	+	22.8988i	0.624383	+	0.744111i	0.981818	−	0.189827i	$-0.0607928\pi$
$947$	19.2144	+	22.8988i	0.624383	+	0.744111i	−0.357434	+	0.933938i	$0.616348\pi$
$948$	87.7929	+	44.0057i	2.85138	+	1.42924i
$949$	−1.37082	+	7.77429i	−0.0444986	+	0.252364i
$950$	38.0580	+	31.9344i	1.23476	+	1.03609i
$951$	5.55400	−	5.24811i	0.180101	−	0.170182i
$952$	79.6790	−	31.2953i	2.58241	−	1.01429i
$953$	−29.6132	+	17.0972i	−0.959267	+	0.553833i	−0.895947	−	0.444160i	$-0.853502\pi$
$953$	−29.6132	+	17.0972i	−0.959267	+	0.553833i	−0.0633195	+	0.997993i	$0.520169\pi$
$954$	46.8679	−	49.8323i	1.51740	−	1.61338i
$955$		−	1.07317i		−	0.0347270i
$956$	33.8654	+	40.3592i	1.09528	+	1.30531i
$957$	30.2792	−	40.7382i	0.978786	−	1.31688i
$958$	−9.15737	−	25.1597i	−0.295861	−	0.812872i
$959$	−9.85025	+	0.248182i	−0.318081	+	0.00801421i
$960$	−1.79510	+	2.41516i	−0.0579365	+	0.0779489i
$961$	−15.7415	−	5.72945i	−0.507792	−	0.184821i
$962$	−4.95443			−0.159737
$963$	11.5857	−	8.65328i	0.373342	−	0.278848i
$964$		−	87.0829i		−	2.80475i
$965$	4.52665	−	3.79831i	0.145718	−	0.122272i
$966$	−2.22585	+	24.5588i	−0.0716155	+	0.790168i
$967$	7.82430	−	44.3738i	0.251612	−	1.42697i	−0.553008	−	0.833176i	$-0.686520\pi$
$967$	7.82430	−	44.3738i	0.251612	−	1.42697i	0.804621	−	0.593789i	$-0.202369\pi$
$968$	1.62165	+	4.45545i	0.0521218	+	0.143204i
$969$	22.6774	+	34.4208i	0.728502	+	1.10576i
$970$	0.701045	+	3.97582i	0.0225092	+	0.127656i
$971$	16.1729	−	28.0122i	0.519012	−	0.898955i	−0.480744	−	0.876861i	$-0.659633\pi$
$971$	16.1729	−	28.0122i	0.519012	−	0.898955i	0.999756	−	0.0220939i	$-0.00703328\pi$
$972$	−25.8599	+	60.5977i	−0.829457	+	1.94367i
$973$	−27.4078	+	24.2001i	−0.878654	+	0.775818i
$974$	−7.76498	+	21.3341i	−0.248806	+	0.683589i
$975$	4.00636	−	7.99283i	0.128306	−	0.255975i
$976$	−70.8247	−	12.4883i	−2.26704	−	0.399741i
$977$	10.5538	+	28.9962i	0.337645	+	0.927672i	0.986061	+	0.166386i	$0.0532096\pi$
$977$	10.5538	+	28.9962i	0.337645	+	0.927672i	−0.648416	+	0.761286i	$0.724568\pi$
$978$	22.1860	−	20.9641i	0.709430	−	0.670357i
$979$	25.6520	+	30.5708i	0.819840	+	0.977047i
$980$	9.74444	−	4.11352i	0.311275	−	0.131402i
$981$	−60.1226	+	7.12226i	−1.91957	+	0.227396i
$982$	−3.67806	−	6.37058i	−0.117371	−	0.203293i
$983$	8.84591	−	7.42260i	0.282141	−	0.236744i	−0.490724	−	0.871315i	$-0.663268\pi$
$983$	8.84591	−	7.42260i	0.282141	−	0.236744i	0.772865	+	0.634571i	$0.218823\pi$
$984$	−5.01248	+	43.1760i	−0.159792	+	1.37640i
$985$	1.19482	+	0.210679i	0.0380701	+	0.00671278i
$986$	−116.234	+	42.3058i	−3.70165	+	1.34729i
$987$	−32.0895	−	46.1342i	−1.02142	−	1.46847i
$988$	−3.17749	−	18.0205i	−0.101090	−	0.573307i
$989$	13.4357	−	7.75713i	0.427232	−	0.246662i
$990$	−2.65637	−	8.82286i	−0.0844250	−	0.280409i
$991$	7.29987	−	12.6437i	0.231888	−	0.401642i	−0.726476	−	0.687192i	$-0.758843\pi$
$991$	7.29987	−	12.6437i	0.231888	−	0.401642i	0.958364	+	0.285550i	$0.0921764\pi$
$992$	1.56589	+	8.88058i	0.0497170	+	0.281959i
$993$	16.4217	+	17.3789i	0.521128	+	0.551502i
$994$	1.39037	+	55.1832i	0.0440998	+	1.75031i
$995$	0.966797	−	1.15218i	0.0306495	−	0.0365267i
$996$	−1.74848	−	29.6228i	−0.0554028	−	0.938635i
$997$	39.4757	−	6.96063i	1.25021	−	0.220445i	0.490923	−	0.871203i	$-0.336660\pi$
$997$	39.4757	−	6.96063i	1.25021	−	0.220445i	0.759286	+	0.650758i	$0.225549\pi$
$998$	−23.0225	+	13.2921i	−0.728766	+	0.420753i
$999$	−7.44503	+	6.27682i	−0.235550	+	0.198590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.131.2	yes	132
3.2	odd	2		567.2.ba.a.341.21		132
7.3	odd	6		189.2.bd.a.185.21	yes	132
21.17	even	6		567.2.bd.a.17.2		132
27.7	even	9		567.2.bd.a.467.2		132
27.20	odd	18		189.2.bd.a.47.21	yes	132
189.101	even	18	inner	189.2.ba.a.101.2	✓	132
189.115	odd	18		567.2.ba.a.143.21		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.2	✓	132	189.101	even	18	inner
189.2.ba.a.131.2	yes	132	1.1	even	1	trivial
189.2.bd.a.47.21	yes	132	27.20	odd	18
189.2.bd.a.185.21	yes	132	7.3	odd	6
567.2.ba.a.143.21		132	189.115	odd	18
567.2.ba.a.341.21		132	3.2	odd	2
567.2.bd.a.17.2		132	21.17	even	6
567.2.bd.a.467.2		132	27.7	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60395 - 1.91151i) q^{2} +(-1.44637 + 0.952904i) q^{3} +(-0.733927 + 4.16231i) q^{4} +(-0.273867 - 0.229802i) q^{5} +(4.14138 + 1.23633i) q^{6} +(2.61630 + 0.393657i) q^{7} +(4.81149 - 2.77792i) q^{8} +(1.18395 - 2.75650i) q^{9} +0.892090i q^{10} +(-2.21304 - 2.63740i) q^{11} +(-2.90475 - 6.71958i) q^{12} +(-0.362359 - 0.995572i) q^{13} +(-3.44393 - 5.63249i) q^{14} +(0.615091 + 0.0714084i) q^{15} +(-5.08414 - 1.85047i) q^{16} +5.82370 q^{17} +(-7.16806 + 2.15815i) q^{18} -4.08644i q^{19} +(1.15751 - 0.971262i) q^{20} +(-4.15925 + 1.92371i) q^{21} +(-1.49181 + 8.46049i) q^{22} +(0.737571 + 2.02646i) q^{23} +(-4.31209 + 8.60277i) q^{24} +(-0.846047 - 4.79817i) q^{25} +(-1.32184 + 2.28950i) q^{26} +(0.914255 + 5.11509i) q^{27} +(-3.55870 + 10.6009i) q^{28} +(2.91124 - 7.99857i) q^{29} +(-0.850076 - 1.29029i) q^{30} +(3.71733 + 0.655466i) q^{31} +(0.817075 + 2.24489i) q^{32} +(5.71405 + 1.70583i) q^{33} +(-9.34090 - 11.1321i) q^{34} +(-0.626056 - 0.709041i) q^{35} +(10.6045 + 6.95102i) q^{36} +(0.937031 + 1.62298i) q^{37} +(-7.81127 + 6.55443i) q^{38} +(1.47279 + 1.09467i) q^{39} +(-1.95608 - 0.344910i) q^{40} +(4.24450 - 1.54487i) q^{41} +(10.3484 + 4.86491i) q^{42} +(-1.24925 - 7.08485i) q^{43} +(12.6019 - 7.27569i) q^{44} +(-0.957692 + 0.482841i) q^{45} +(2.69057 - 4.66021i) q^{46} +(2.12948 + 12.0769i) q^{47} +(9.11684 - 2.16823i) q^{48} +(6.69007 + 2.05985i) q^{49} +(-7.81473 + 9.31324i) q^{50} +(-8.42319 + 5.54942i) q^{51} +(4.40982 - 0.777571i) q^{52} +(-7.91413 + 4.56923i) q^{53} +(8.31113 - 9.95194i) q^{54} +1.23086i q^{55} +(13.6819 - 5.37379i) q^{56} +(3.89398 + 5.91048i) q^{57} +(-19.9588 + 7.26442i) q^{58} +(-3.87534 + 1.41051i) q^{59} +(-0.748656 + 2.50779i) q^{60} +(13.0904 - 2.30819i) q^{61} +(-4.70948 - 8.15705i) q^{62} +(4.18268 - 6.74576i) q^{63} +(-2.42983 + 4.20859i) q^{64} +(-0.129546 + 0.355925i) q^{65} +(-5.90433 - 13.6585i) q^{66} +(3.53447 + 2.96577i) q^{67} +(-4.27417 + 24.2400i) q^{68} +(-2.99782 - 2.22817i) q^{69} +(-0.351177 + 2.33398i) q^{70} +(-7.24109 - 4.18065i) q^{71} +(-1.96076 - 16.5518i) q^{72} +(-6.45287 - 3.72557i) q^{73} +(1.59940 - 4.39433i) q^{74} +(5.79589 + 6.13370i) q^{75} +(17.0090 + 2.99915i) q^{76} +(-4.75175 - 7.77140i) q^{77} +(-0.269805 - 4.57104i) q^{78} +(-10.2764 + 8.62293i) q^{79} +(0.967136 + 1.67513i) q^{80} +(-6.19654 - 6.52709i) q^{81} +(-9.76098 - 5.63551i) q^{82} +(3.80912 + 1.38640i) q^{83} +(-4.95450 - 18.7239i) q^{84} +(-1.59492 - 1.33830i) q^{85} +(-11.5390 + 13.7517i) q^{86} +(3.41115 + 14.3430i) q^{87} +(-17.9745 - 6.54218i) q^{88} -11.5913 q^{89} +(2.45904 + 1.05619i) q^{90} +(-0.556126 - 2.74736i) q^{91} +(-8.97607 + 1.58272i) q^{92} +(-6.00122 + 2.59422i) q^{93} +(19.6695 - 23.4412i) q^{94} +(-0.939071 + 1.11914i) q^{95} +(-3.32096 - 2.46834i) q^{96} +(4.45675 - 0.785845i) q^{97} +(-6.79310 - 16.0920i) q^{98} +(-9.89010 + 2.97769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

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