LMFDB - Embedded newform 900.2.r.g.551.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(551,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.551"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,2,0,0,0,0,12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.7
Character	$\chi$	$=$	900.551
Dual form			900.2.r.g.851.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.992675 - 1.00727i) q^{2} +(1.14213 - 1.30213i) q^{3} +(-0.0291929 + 1.99979i) q^{4} +(-2.44536 + 0.142161i) q^{6} +(2.87089 + 1.65751i) q^{7} +(2.04331 - 1.95573i) q^{8} +(-0.391092 - 2.97440i) q^{9} +(1.17952 - 2.04298i) q^{11} +(2.57064 + 2.32202i) q^{12} +(2.20004 + 3.81058i) q^{13} +(-1.18030 - 4.53714i) q^{14} +(-3.99830 - 0.116759i) q^{16} -0.889368i q^{17} +(-2.60780 + 3.34655i) q^{18} +3.03537i q^{19} +(5.43722 - 1.84519i) q^{21} +(-3.22872 + 0.839925i) q^{22} +(3.63703 + 6.29952i) q^{23} +(-0.212904 - 4.89435i) q^{24} +(1.65437 - 5.99870i) q^{26} +(-4.31973 - 2.88789i) q^{27} +(-3.39848 + 5.69278i) q^{28} +(-1.03714 - 0.598791i) q^{29} +(0.205172 - 0.118456i) q^{31} +(3.85140 + 4.14327i) q^{32} +(-1.31308 - 3.86923i) q^{33} +(-0.895835 + 0.882853i) q^{34} +(5.95958 - 0.695270i) q^{36} +11.4975 q^{37} +(3.05745 - 3.01314i) q^{38} +(7.47460 + 1.48743i) q^{39} +(2.45213 - 1.41574i) q^{41} +(-7.25600 - 3.64508i) q^{42} +(-7.23369 - 4.17637i) q^{43} +(4.05110 + 2.41842i) q^{44} +(2.73494 - 9.91686i) q^{46} +(3.78624 - 6.55796i) q^{47} +(-4.71860 + 5.07295i) q^{48} +(1.99467 + 3.45488i) q^{49} +(-1.15807 - 1.01577i) q^{51} +(-7.68457 + 4.28837i) q^{52} -0.772055i q^{53} +(1.37920 + 7.21788i) q^{54} +(9.10776 - 2.22789i) q^{56} +(3.95246 + 3.46678i) q^{57} +(0.426394 + 1.63908i) q^{58} +(-1.06446 - 1.84370i) q^{59} +(1.91303 - 3.31346i) q^{61} +(-0.322986 - 0.0890754i) q^{62} +(3.80731 - 9.18741i) q^{63} +(0.350216 - 7.99233i) q^{64} +(-2.59391 + 5.16352i) q^{66} +(-5.49472 + 3.17238i) q^{67} +(1.77855 + 0.0259632i) q^{68} +(12.3568 + 2.45896i) q^{69} -11.7244 q^{71} +(-6.61625 - 5.31274i) q^{72} +6.10889 q^{73} +(-11.4133 - 11.5811i) q^{74} +(-6.07010 - 0.0886114i) q^{76} +(6.77253 - 3.91012i) q^{77} +(-5.92160 - 9.00548i) q^{78} +(-8.94873 - 5.16655i) q^{79} +(-8.69409 + 2.32653i) q^{81} +(-3.86020 - 1.06459i) q^{82} +(-1.29963 + 2.25103i) q^{83} +(3.53126 + 10.9271i) q^{84} +(2.97396 + 11.4321i) q^{86} +(-1.96425 + 0.666593i) q^{87} +(-1.58541 - 6.48127i) q^{88} -4.68130i q^{89} +14.5863i q^{91} +(-12.7039 + 7.08939i) q^{92} +(0.0800869 - 0.402452i) q^{93} +(-10.3642 + 2.69615i) q^{94} +(9.79387 - 0.282883i) q^{96} +(-3.08700 + 5.34684i) q^{97} +(1.49994 - 5.43875i) q^{98} +(-6.53795 - 2.70936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−0.992675	−	1.00727i	−0.701927	−	0.712249i
$2$	−0.992675	−	1.00727i	−0.701927	−	0.712249i
$3$	1.14213	−	1.30213i	0.659407	−	0.751786i
$3$	1.14213	−	1.30213i	0.659407	−	0.751786i
$4$	−0.0291929	+	1.99979i	−0.0145965	+	0.999893i
$5$		0			0
$5$		0			0
$6$	−2.44536	+	0.142161i	−0.998314	+	0.0580370i
$7$	2.87089	+	1.65751i	1.08509	+	0.626480i	0.932266	−	0.361773i	$-0.117828\pi$
$7$	2.87089	+	1.65751i	1.08509	+	0.626480i	0.152828	+	0.988253i	$0.451162\pi$
$8$	2.04331	−	1.95573i	0.722418	−	0.691456i
$9$	−0.391092	−	2.97440i	−0.130364	−	0.991466i
$10$		0			0
$11$	1.17952	−	2.04298i	0.355638	−	0.615983i	−0.631589	−	0.775303i	$-0.717597\pi$
$11$	1.17952	−	2.04298i	0.355638	−	0.615983i	0.987227	+	0.159320i	$0.0509303\pi$
$12$	2.57064	+	2.32202i	0.742081	+	0.670310i
$13$	2.20004	+	3.81058i	0.610181	+	1.05686i	0.991210	+	0.132301i	$0.0422366\pi$
$13$	2.20004	+	3.81058i	0.610181	+	1.05686i	−0.381029	+	0.924563i	$0.624430\pi$
$14$	−1.18030	−	4.53714i	−0.315448	−	1.21260i
$15$		0			0
$16$	−3.99830	−	0.116759i	−0.999574	−	0.0291898i
$17$		−	0.889368i		−	0.215703i	−0.994167	−	0.107852i	$-0.965603\pi$
$17$		−	0.889368i		−	0.215703i	0.994167	−	0.107852i	$-0.0343972\pi$
$18$	−2.60780	+	3.34655i	−0.614664	+	0.788789i
$19$			3.03537i			0.696363i	0.937427	+	0.348181i	$0.113201\pi$
$19$			3.03537i			0.696363i	−0.937427	+	0.348181i	$0.886799\pi$
$20$		0			0
$21$	5.43722	−	1.84519i	1.18650	−	0.402654i
$22$	−3.22872	+	0.839925i	−0.688365	+	0.179073i
$23$	3.63703	+	6.29952i	0.758374	+	1.31354i	0.943680	+	0.330861i	$0.107339\pi$
$23$	3.63703	+	6.29952i	0.758374	+	1.31354i	−0.185306	+	0.982681i	$0.559328\pi$
$24$	−0.212904	−	4.89435i	−0.0434589	−	0.999055i
$25$		0			0
$26$	1.65437	−	5.99870i	0.324448	−	1.17644i
$27$	−4.31973	−	2.88789i	−0.831333	−	0.555774i
$28$	−3.39848	+	5.69278i	−0.642251	+	1.07583i
$29$	−1.03714	−	0.598791i	−0.192592	−	0.111193i	0.400604	−	0.916251i	$-0.368800\pi$
$29$	−1.03714	−	0.598791i	−0.192592	−	0.111193i	−0.593195	+	0.805059i	$0.702134\pi$
$30$		0			0
$31$	0.205172	−	0.118456i	0.0368499	−	0.0212753i	−0.481462	−	0.876467i	$-0.659894\pi$
$31$	0.205172	−	0.118456i	0.0368499	−	0.0212753i	0.518312	+	0.855192i	$0.326561\pi$
$32$	3.85140	+	4.14327i	0.680838	+	0.732434i
$33$	−1.31308	−	3.86923i	−0.228577	−	0.673547i
$34$	−0.895835	+	0.882853i	−0.153634	+	0.151408i
$35$		0			0
$36$	5.95958	−	0.695270i	0.993263	−	0.115878i
$37$	11.4975			1.89018			0.945091	−	0.326807i	$-0.105973\pi$
$37$	11.4975			1.89018			0.945091	+	0.326807i	$0.105973\pi$
$38$	3.05745	−	3.01314i	0.495983	−	0.488796i
$39$	7.47460	+	1.48743i	1.19689	+	0.238179i
$40$		0			0
$41$	2.45213	−	1.41574i	0.382958	−	0.221101i	−0.296146	−	0.955143i	$-0.595702\pi$
$41$	2.45213	−	1.41574i	0.382958	−	0.221101i	0.679105	+	0.734042i	$0.262368\pi$
$42$	−7.25600	−	3.64508i	−1.11962	−	0.562448i
$43$	−7.23369	−	4.17637i	−1.10313	−	0.636891i	−0.166087	−	0.986111i	$-0.553113\pi$
$43$	−7.23369	−	4.17637i	−1.10313	−	0.636891i	−0.937041	+	0.349220i	$0.886447\pi$
$44$	4.05110	+	2.41842i	0.610726	+	0.364591i
$45$		0			0
$46$	2.73494	−	9.91686i	0.403245	−	1.46216i
$47$	3.78624	−	6.55796i	0.552280	−	0.956577i	−0.445829	−	0.895118i	$-0.647091\pi$
$47$	3.78624	−	6.55796i	0.552280	−	0.956577i	0.998110	−	0.0614594i	$-0.0195755\pi$
$48$	−4.71860	+	5.07295i	−0.681071	+	0.732218i
$49$	1.99467	+	3.45488i	0.284954	+	0.493554i
$50$		0			0
$51$	−1.15807	−	1.01577i	−0.162163	−	0.142236i
$52$	−7.68457	+	4.28837i	−1.06566	+	0.594689i
$53$		−	0.772055i		−	0.106050i	−0.998593	−	0.0530249i	$-0.983114\pi$
$53$		−	0.772055i		−	0.106050i	0.998593	−	0.0530249i	$-0.0168863\pi$
$54$	1.37920	+	7.21788i	0.187686	+	0.982229i
$55$		0			0
$56$	9.10776	−	2.22789i	1.21708	−	0.297715i
$57$	3.95246	+	3.46678i	0.523516	+	0.459187i
$58$	0.426394	+	1.63908i	0.0559883	+	0.215222i
$59$	−1.06446	−	1.84370i	−0.138581	−	0.240029i	0.788379	−	0.615190i	$-0.210921\pi$
$59$	−1.06446	−	1.84370i	−0.138581	−	0.240029i	−0.926960	+	0.375161i	$0.877587\pi$
$60$		0			0
$61$	1.91303	−	3.31346i	0.244938	−	0.424245i	−0.717176	−	0.696892i	$-0.754566\pi$
$61$	1.91303	−	3.31346i	0.244938	−	0.424245i	0.962114	+	0.272647i	$0.0878990\pi$
$62$	−0.322986	−	0.0890754i	−0.0410193	−	0.0113126i
$63$	3.80731	−	9.18741i	0.479676	−	1.15751i
$64$	0.350216	−	7.99233i	0.0437769	−	0.999041i
$65$		0			0
$66$	−2.59391	+	5.16352i	−0.319289	+	0.635585i
$67$	−5.49472	+	3.17238i	−0.671287	+	0.387567i	−0.796564	−	0.604554i	$-0.793351\pi$
$67$	−5.49472	+	3.17238i	−0.671287	+	0.387567i	0.125277	+	0.992122i	$0.460018\pi$
$68$	1.77855	+	0.0259632i	0.215680	+	0.00314851i
$69$	12.3568	+	2.45896i	1.48758	+	0.296024i
$70$		0			0
$71$	−11.7244			−1.39143			−0.695717	−	0.718316i	$-0.744913\pi$
$71$	−11.7244			−1.39143			−0.695717	+	0.718316i	$0.744913\pi$
$72$	−6.61625	−	5.31274i	−0.779733	−	0.626112i
$73$	6.10889			0.714992			0.357496	−	0.933915i	$-0.383631\pi$
$73$	6.10889			0.714992			0.357496	+	0.933915i	$0.383631\pi$
$74$	−11.4133	−	11.5811i	−1.32677	−	1.34628i
$75$		0			0
$76$	−6.07010	−	0.0886114i	−0.696288	−	0.0101644i
$77$	6.77253	−	3.91012i	0.771802	−	0.445600i
$78$	−5.92160	−	9.00548i	−0.670490	−	1.01967i
$79$	−8.94873	−	5.16655i	−1.00681	−	0.581283i	−0.0965546	−	0.995328i	$-0.530782\pi$
$79$	−8.94873	−	5.16655i	−1.00681	−	0.581283i	−0.910256	+	0.414045i	$0.864116\pi$
$80$		0			0
$81$	−8.69409	+	2.32653i	−0.966010	+	0.258503i
$82$	−3.86020	−	1.06459i	−0.426288	−	0.117565i
$83$	−1.29963	+	2.25103i	−0.142653	+	0.247083i	−0.928495	−	0.371345i	$-0.878897\pi$
$83$	−1.29963	+	2.25103i	−0.142653	+	0.247083i	0.785842	+	0.618428i	$0.212230\pi$
$84$	3.53126	+	10.9271i	0.385292	+	1.19225i
$85$		0			0
$86$	2.97396	+	11.4321i	0.320690	+	1.23275i
$87$	−1.96425	+	0.666593i	−0.210589	+	0.0714663i
$88$	−1.58541	−	6.48127i	−0.169006	−	0.690906i
$89$		−	4.68130i		−	0.496217i	−0.968732	−	0.248108i	$-0.920191\pi$
$89$		−	4.68130i		−	0.496217i	0.968732	−	0.248108i	$-0.0798089\pi$
$90$		0			0
$91$			14.5863i			1.52906i
$92$	−12.7039	+	7.08939i	−1.32447	+	0.739120i
$93$	0.0800869	−	0.402452i	0.00830463	−	0.0417324i
$94$	−10.3642	+	2.69615i	−1.06898	+	0.278087i
$95$		0			0
$96$	9.79387	−	0.282883i	0.999583	−	0.0288716i
$97$	−3.08700	+	5.34684i	−0.313438	+	0.542890i	−0.979104	−	0.203360i	$-0.934814\pi$
$97$	−3.08700	+	5.34684i	−0.313438	+	0.542890i	0.665667	+	0.746249i	$0.268147\pi$
$98$	1.49994	−	5.43875i	0.151517	−	0.549397i
$99$	−6.53795	−	2.70936i	−0.657089	−	0.272301i
$100$		0			0
$101$	−6.72336	−	3.88174i	−0.669000	−	0.386247i	0.126698	−	0.991941i	$-0.459562\pi$
$101$	−6.72336	−	3.88174i	−0.669000	−	0.386247i	−0.795697	+	0.605694i	$0.792895\pi$
$102$	0.126433	+	2.17482i	0.0125188	+	0.215340i
$103$	−11.3975	+	6.58033i	−1.12302	+	0.648379i	−0.942171	−	0.335131i	$-0.891219\pi$
$103$	−11.3975	+	6.58033i	−1.12302	+	0.648379i	−0.180853	+	0.983510i	$0.557886\pi$
$104$	11.9478	+	3.48350i	1.17158	+	0.341585i
$105$		0			0
$106$	−0.777669	+	0.766400i	−0.0755339	+	0.0744393i
$107$	−0.252175			−0.0243786			−0.0121893	−	0.999926i	$-0.503880\pi$
$107$	−0.252175			−0.0243786			−0.0121893	+	0.999926i	$0.503880\pi$
$108$	5.90127	−	8.55424i	0.567850	−	0.823132i
$109$	−0.459068			−0.0439708			−0.0219854	−	0.999758i	$-0.506999\pi$
$109$	−0.459068			−0.0439708			−0.0219854	+	0.999758i	$0.506999\pi$
$110$		0			0
$111$	13.1316	−	14.9713i	1.24640	−	1.42101i
$112$	−11.2851	−	6.96242i	−1.06635	−	0.657886i
$113$	15.0958	−	8.71557i	1.42009	−	0.819892i	0.423788	−	0.905761i	$-0.360700\pi$
$113$	15.0958	−	8.71557i	1.42009	−	0.819892i	0.996306	+	0.0858696i	$0.0273669\pi$
$114$	−0.431512	−	7.42259i	−0.0404148	−	0.695189i
$115$		0			0
$116$	1.22773	−	2.05657i	0.113992	−	0.190948i
$117$	10.4738	−	8.03408i	0.968300	−	0.742751i
$118$	−0.800444	+	2.90240i	−0.0736868	+	0.267187i
$119$	1.47414	−	2.55328i	0.135134	−	0.234059i
$120$		0			0
$121$	2.71748	+	4.70681i	0.247043	+	0.427891i
$122$	−5.23657	+	1.36225i	−0.474097	+	0.123332i
$123$	0.957167	−	4.80995i	0.0863048	−	0.433698i
$124$	0.230897	+	0.413758i	0.0207352	+	0.0371565i
$125$		0			0
$126$	−13.0336	+	5.28512i	−1.16113	+	0.470836i
$127$		−	10.5666i		−	0.937635i	−0.883295	−	0.468817i	$-0.844680\pi$
$127$		−	10.5666i		−	0.937635i	0.883295	−	0.468817i	$-0.155320\pi$
$128$	−8.39810	+	7.58102i	−0.742294	+	0.670074i
$129$	−13.7000	+	4.64927i	−1.20622	+	0.409345i
$130$		0			0
$131$	−8.12900	−	14.0798i	−0.710234	−	1.23016i	−0.964769	−	0.263098i	$-0.915256\pi$
$131$	−8.12900	−	14.0798i	−0.710234	−	1.23016i	0.254535	−	0.967064i	$-0.418078\pi$
$132$	7.77598	−	2.51292i	0.676812	−	0.218721i
$133$	−5.03116	+	8.71423i	−0.436257	+	0.755619i
$134$	8.64991	+	2.38554i	0.747239	+	0.206079i
$135$		0			0
$136$	−1.73937	−	1.81725i	−0.149149	−	0.155828i
$137$	11.4244	+	6.59587i	0.976051	+	0.563523i	0.901076	−	0.433662i	$-0.142779\pi$
$137$	11.4244	+	6.59587i	0.976051	+	0.563523i	0.0749753	+	0.997185i	$0.476112\pi$
$138$	−9.78940	−	14.8876i	−0.833329	−	1.26731i
$139$	5.61535	−	3.24202i	0.476288	−	0.274985i	−0.242580	−	0.970131i	$-0.577994\pi$
$139$	5.61535	−	3.24202i	0.476288	−	0.274985i	0.718868	+	0.695146i	$0.244660\pi$
$140$		0			0
$141$	−4.21496	−	12.4202i	−0.354964	−	1.04597i
$142$	11.6385	+	11.8097i	0.976685	+	0.991047i
$143$	10.3799			0.868014
$144$	1.21641	+	11.9382i	0.101368	+	0.994849i
$145$		0			0
$146$	−6.06415	−	6.15332i	−0.501872	−	0.509252i
$147$	6.77688	+	1.34858i	0.558947	+	0.111229i
$148$	−0.335646	+	22.9926i	−0.0275900	+	1.88998i
$149$	−7.25009	+	4.18584i	−0.593950	+	0.342917i	−0.766658	−	0.642056i	$-0.778082\pi$
$149$	−7.25009	+	4.18584i	−0.593950	+	0.342917i	0.172708	+	0.984973i	$0.444748\pi$
$150$		0			0
$151$	14.2008	+	8.19886i	1.15565	+	0.667214i	0.950257	−	0.311466i	$-0.100820\pi$
$151$	14.2008	+	8.19886i	1.15565	+	0.667214i	0.205391	+	0.978680i	$0.434153\pi$
$152$	5.93638	+	6.20220i	0.481504	+	0.503065i
$153$	−2.64533	+	0.347825i	−0.213863	+	0.0281200i
$154$	−10.6615	−	2.94030i	−0.859127	−	0.236936i
$155$		0			0
$156$	−3.19274	+	14.9042i	−0.255624	+	1.19329i
$157$	−5.35608	−	9.27700i	−0.427462	−	0.740386i	0.569185	−	0.822209i	$-0.307259\pi$
$157$	−5.35608	−	9.27700i	−0.427462	−	0.740386i	−0.996647	+	0.0818239i	$0.973925\pi$
$158$	3.67906	+	14.1425i	0.292690	+	1.12512i
$159$	−1.00532	−	0.881785i	−0.0797268	−	0.0699301i
$160$		0			0
$161$			24.1137i			1.90042i
$162$	10.9739	+	6.44783i	0.862187	+	0.506589i
$163$			1.33584i			0.104631i	0.998631	+	0.0523153i	$0.0166601\pi$
$163$			1.33584i			0.104631i	−0.998631	+	0.0523153i	$0.983340\pi$
$164$	2.75959	+	4.94507i	0.215488	+	0.386145i
$165$		0			0
$166$	3.55752	−	0.925458i	0.276117	−	0.0718295i
$167$	3.58501	+	6.20942i	0.277417	+	0.480500i	0.970742	−	0.240125i	$-0.0771884\pi$
$167$	3.58501	+	6.20942i	0.277417	+	0.480500i	−0.693325	+	0.720625i	$0.743855\pi$
$168$	7.50121	−	14.4040i	0.578731	−	1.11130i
$169$	−3.18034	+	5.50851i	−0.244641	+	0.423731i
$170$		0			0
$171$	9.02841	−	1.18711i	0.690420	−	0.0907806i
$172$	8.56303	−	14.3439i	0.652925	−	1.09371i
$173$	2.23027	+	1.28765i	0.169564	+	0.0978979i	0.582380	−	0.812916i	$-0.302121\pi$
$173$	2.23027	+	1.28765i	0.169564	+	0.0978979i	−0.412816	+	0.910814i	$0.635455\pi$
$174$	2.62130	+	1.31682i	0.198720	+	0.0998279i
$175$		0			0
$176$	−4.95460	+	8.03074i	−0.373467	+	0.605340i
$177$	−3.61649	−	0.719672i	−0.271832	−	0.0540939i
$178$	−4.71534	+	4.64701i	−0.353430	+	0.348308i
$179$	−10.1847			−0.761243			−0.380622	−	0.924731i	$-0.624290\pi$
$179$	−10.1847			−0.761243			−0.380622	+	0.924731i	$0.624290\pi$
$180$		0			0
$181$	4.17537			0.310353			0.155176	−	0.987887i	$-0.450405\pi$
$181$	4.17537			0.310353			0.155176	+	0.987887i	$0.450405\pi$
$182$	14.6924	−	14.4795i	1.08907	−	1.07329i
$183$	−2.12964	−	6.27541i	−0.157428	−	0.463891i
$184$	19.7518	+	5.75880i	1.45612	+	0.424545i
$185$		0			0
$186$	−0.484879	+	0.318835i	−0.0355531	+	0.0233781i
$187$	−1.81696	−	1.04902i	−0.132870	−	0.0767123i
$188$	13.0040	+	7.76312i	0.948414	+	0.566184i
$189$	−7.61478	−	15.4508i	−0.553894	−	1.12388i
$190$		0			0
$191$	−12.5152	+	21.6770i	−0.905570	+	1.56849i	−0.0854186	+	0.996345i	$0.527223\pi$
$191$	−12.5152	+	21.6770i	−0.905570	+	1.56849i	−0.820151	+	0.572147i	$0.806111\pi$
$192$	−10.0071	−	9.58428i	−0.722198	−	0.691686i
$193$	−9.45871	−	16.3830i	−0.680853	−	1.17927i	−0.974721	−	0.223426i	$-0.928276\pi$
$193$	−9.45871	−	16.3830i	−0.680853	−	1.17927i	0.293868	−	0.955846i	$-0.405057\pi$
$194$	8.45011	−	2.19823i	0.606683	−	0.157824i
$195$		0			0
$196$	−6.96725	+	3.88807i	−0.497661	+	0.277719i
$197$		−	5.25418i		−	0.374345i	−0.982327	−	0.187172i	$-0.940068\pi$
$197$		−	5.25418i		−	0.374345i	0.982327	−	0.187172i	$-0.0599323\pi$
$198$	3.76100	+	9.27501i	0.267282	+	0.659146i
$199$			18.8487i			1.33615i	0.744095	+	0.668074i	$0.232881\pi$
$199$			18.8487i			1.33615i	−0.744095	+	0.668074i	$0.767119\pi$
$200$		0			0
$201$	−2.14481	+	10.7781i	−0.151284	+	0.760229i
$202$	2.76415	+	10.6256i	0.194485	+	0.747612i
$203$	−1.98500	−	3.43813i	−0.139320	−	0.241309i
$204$	2.06513	−	2.28625i	0.144588	−	0.160069i
$205$		0			0
$206$	17.9421	+	4.94821i	1.25009	+	0.344758i
$207$	17.3149	−	13.2817i	1.20347	−	0.923140i
$208$	−8.35148	−	15.4927i	−0.579071	−	1.07423i
$209$	6.20122	+	3.58028i	0.428948	+	0.247653i
$210$		0			0
$211$	−3.96081	+	2.28678i	−0.272674	+	0.157428i	−0.630102	−	0.776512i	$-0.716987\pi$
$211$	−3.96081	+	2.28678i	−0.272674	+	0.157428i	0.357428	+	0.933941i	$0.383654\pi$
$212$	1.54395	+	0.0225385i	0.106039	+	0.00154795i
$213$	−13.3908	+	15.2667i	−0.917521	+	1.04606i
$214$	0.250327	+	0.254008i	0.0171120	+	0.0173636i
$215$		0			0
$216$	−14.4745	+	2.54740i	−0.984864	+	0.173329i
$217$	0.785367			0.0533142
$218$	0.455706	+	0.462407i	0.0308643	+	0.0313181i
$219$	6.97713	−	7.95458i	0.471471	−	0.537521i
$220$		0			0
$221$	3.38900	−	1.95664i	0.227969	−	0.131618i
$222$	−28.1156	+	1.63450i	−1.88700	+	0.109700i
$223$	20.5711	+	11.8767i	1.37754	+	0.795323i	0.991863	−	0.127310i	$-0.0406344\pi$
$223$	20.5711	+	11.8767i	1.37754	+	0.795323i	0.385677	+	0.922634i	$0.373968\pi$
$224$	4.18943	+	18.2786i	0.279918	+	1.22129i
$225$		0			0
$226$	−23.7642	−	6.55386i	−1.58077	−	0.435956i
$227$	−13.9287	+	24.1252i	−0.924478	+	1.60124i	−0.132081	+	0.991239i	$0.542166\pi$
$227$	−13.9287	+	24.1252i	−0.924478	+	1.60124i	−0.792398	+	0.610005i	$0.791168\pi$
$228$	−7.04821	+	7.80286i	−0.466779	+	0.516757i
$229$	−8.35991	−	14.4798i	−0.552439	−	0.956852i	−0.998098	−	0.0616492i	$-0.980364\pi$
$229$	−8.35991	−	14.4798i	−0.552439	−	0.956852i	0.445659	−	0.895203i	$-0.352969\pi$
$230$		0			0
$231$	2.64360	−	13.2846i	0.173936	−	0.874061i
$232$	−3.29027	+	0.804848i	−0.216017	+	0.0528409i
$233$		−	1.67938i		−	0.110020i	−0.998486	−	0.0550101i	$-0.982481\pi$
$233$		−	1.67938i		−	0.110020i	0.998486	−	0.0550101i	$-0.0175191\pi$
$234$	−18.4895	−	2.57470i	−1.20870	−	0.168313i
$235$		0			0
$236$	3.71808	−	2.07487i	0.242027	−	0.135063i
$237$	−16.9481	+	5.75157i	−1.10090	+	0.373604i
$238$	−4.03518	+	1.04972i	−0.261562	+	0.0680432i
$239$	−5.41085	−	9.37186i	−0.349999	−	0.606215i	0.636250	−	0.771483i	$-0.280485\pi$
$239$	−5.41085	−	9.37186i	−0.349999	−	0.606215i	−0.986249	+	0.165267i	$0.947151\pi$
$240$		0			0
$241$	−5.45657	+	9.45105i	−0.351488	+	0.608796i	−0.986510	−	0.163698i	$-0.947658\pi$
$241$	−5.45657	+	9.45105i	−0.351488	+	0.608796i	0.635022	+	0.772494i	$0.280991\pi$
$242$	2.04346	−	7.40957i	0.131359	−	0.476305i
$243$	−6.90031	+	13.9780i	−0.442655	+	0.896692i
$244$	6.57037	+	3.92238i	0.420625	+	0.251104i
$245$		0			0
$246$	−5.79508	+	3.81059i	−0.369481	+	0.242954i
$247$	−11.5665	+	6.67794i	−0.735961	+	0.424907i
$248$	0.187561	−	0.643303i	0.0119101	−	0.0408498i
$249$	1.44679	+	4.26326i	0.0916867	+	0.270173i
$250$		0			0
$251$	−5.05766			−0.319237			−0.159618	−	0.987179i	$-0.551026\pi$
$251$	−5.05766			−0.319237			−0.159618	+	0.987179i	$0.551026\pi$
$252$	18.2617	+	7.88202i	1.15038	+	0.496520i
$253$	17.1598			1.07883
$254$	−10.6434	+	10.4892i	−0.667829	+	0.658151i
$255$		0			0
$256$	15.9727	+	0.933676i	0.998296	+	0.0583548i
$257$	−11.5968	+	6.69541i	−0.723388	+	0.417649i	−0.815999	−	0.578054i	$-0.803812\pi$
$257$	−11.5968	+	6.69541i	−0.723388	+	0.417649i	0.0926101	+	0.995702i	$0.470479\pi$
$258$	18.2827	+	9.18439i	1.13823	+	0.571795i
$259$	33.0081	+	19.0573i	2.05103	+	1.18416i
$260$		0			0
$261$	−1.37543	+	3.31904i	−0.0851369	+	0.205444i
$262$	−6.11278	+	22.1648i	−0.377649	+	1.36935i
$263$	5.44564	−	9.43213i	0.335793	−	0.581610i	−0.647844	−	0.761773i	$-0.724329\pi$
$263$	5.44564	−	9.43213i	0.335793	−	0.581610i	0.983637	+	0.180163i	$0.0576626\pi$
$264$	−10.2502	−	5.33801i	−0.630857	−	0.328532i
$265$		0			0
$266$	13.7719	−	3.58265i	0.844410	−	0.219666i
$267$	−6.09567	−	5.34664i	−0.373049	−	0.327209i
$268$	−6.18367	−	11.0809i	−0.377728	−	0.676872i
$269$			21.5020i			1.31100i	0.755195	+	0.655500i	$0.227542\pi$
$269$			21.5020i			1.31100i	−0.755195	+	0.655500i	$0.772458\pi$
$270$		0			0
$271$			18.9445i			1.15080i	0.817873	+	0.575399i	$0.195153\pi$
$271$			18.9445i			1.15080i	−0.817873	+	0.575399i	$0.804847\pi$
$272$	−0.103842	+	3.55595i	−0.00629634	+	0.215611i
$273$	18.9933	+	16.6594i	1.14953	+	1.00828i
$274$	−4.69686	−	18.0550i	−0.283748	−	1.09074i
$275$		0			0
$276$	−5.27813	+	24.6391i	−0.317706	+	1.48310i
$277$	−9.33092	+	16.1616i	−0.560641	+	0.971058i	0.436800	+	0.899559i	$0.356112\pi$
$277$	−9.33092	+	16.1616i	−0.560641	+	0.971058i	−0.997441	+	0.0714994i	$0.977222\pi$
$278$	−8.83982	−	2.43791i	−0.530177	−	0.146216i
$279$	−0.432576	−	0.563935i	−0.0258977	−	0.0337619i
$280$		0			0
$281$	−5.84683	−	3.37567i	−0.348792	−	0.201375i	0.315361	−	0.948972i	$-0.397874\pi$
$281$	−5.84683	−	3.37567i	−0.348792	−	0.201375i	−0.664153	+	0.747596i	$0.731208\pi$
$282$	−8.32644	+	16.5748i	−0.495832	+	0.987018i
$283$	−4.56374	+	2.63488i	−0.271286	+	0.156627i	−0.629472	−	0.777023i	$-0.716729\pi$
$283$	−4.56374	+	2.63488i	−0.271286	+	0.156627i	0.358186	+	0.933650i	$0.383395\pi$
$284$	0.342270	−	23.4464i	0.0203100	−	1.39129i
$285$		0			0
$286$	−10.3039	−	10.4554i	−0.609283	−	0.618242i
$287$	9.38639			0.554061
$288$	10.8175	−	13.0760i	0.637427	−	0.770511i
$289$	16.2090			0.953472
$290$		0			0
$291$	3.43655	+	10.1265i	0.201454	+	0.593623i
$292$	−0.178336	+	12.2165i	−0.0104364	+	0.714916i
$293$	−19.3041	+	11.1453i	−1.12776	+	0.651113i	−0.943371	−	0.331741i	$-0.892364\pi$
$293$	−19.3041	+	11.1453i	−1.12776	+	0.651113i	−0.184390	+	0.982853i	$0.559031\pi$
$294$	−5.36885	−	8.16486i	−0.313118	−	0.476184i
$295$		0			0
$296$	23.4930	−	22.4861i	1.36550	−	1.30698i
$297$	−10.9951	+	5.41884i	−0.638001	+	0.314433i
$298$	11.4133	+	3.14763i	0.661153	+	0.182337i
$299$	−16.0032	+	27.7184i	−0.925490	+	1.60300i
$300$		0			0
$301$	−13.8448	−	23.9798i	−0.797999	−	1.38217i
$302$	−5.83834	−	22.4429i	−0.335959	−	1.29144i
$303$	−12.7335	+	4.32127i	−0.731518	+	0.248250i
$304$	0.354408	−	12.1363i	0.0203267	−	0.696066i
$305$		0			0
$306$	2.97631	+	2.31929i	0.170144	+	0.132585i
$307$			0.415414i			0.0237089i	0.999930	+	0.0118545i	$0.00377348\pi$
$307$			0.415414i			0.0237089i	−0.999930	+	0.0118545i	$0.996227\pi$
$308$	7.62170	+	13.6578i	0.434287	+	0.778224i
$309$	−4.44890	+	22.3566i	−0.253089	+	1.27182i
$310$		0			0
$311$	−0.284562	−	0.492876i	−0.0161360	−	0.0279484i	0.857845	−	0.513909i	$-0.171803\pi$
$311$	−0.284562	−	0.492876i	−0.0161360	−	0.0279484i	−0.873981	+	0.485961i	$0.838470\pi$
$312$	18.1819	−	11.5790i	1.02935	−	0.655535i
$313$	−14.0312	+	24.3028i	−0.793091	+	1.37367i	0.130954	+	0.991388i	$0.458196\pi$
$313$	−14.0312	+	24.3028i	−0.793091	+	1.37367i	−0.924044	+	0.382285i	$0.875137\pi$
$314$	−4.02762	+	14.6041i	−0.227292	+	0.824156i
$315$		0			0
$316$	10.5932	−	17.7447i	0.595917	−	0.998219i
$317$	−11.4952	−	6.63676i	−0.645635	−	0.372758i	0.141147	−	0.989989i	$-0.454921\pi$
$317$	−11.4952	−	6.63676i	−0.645635	−	0.372758i	−0.786782	+	0.617231i	$0.788254\pi$
$318$	0.109756	+	1.88795i	0.00615481	+	0.105871i
$319$	−2.44664	+	1.41257i	−0.136986	+	0.0790887i
$320$		0			0
$321$	−0.288015	+	0.328364i	−0.0160754	+	0.0183275i
$322$	24.2890	−	23.9370i	1.35357	−	1.33396i
$323$	2.69956			0.150208
$324$	−4.39875	−	17.4543i	−0.244375	−	0.969681i
$325$		0			0
$326$	1.34555	−	1.32605i	0.0745231	−	0.0734431i
$327$	−0.524314	+	0.597767i	−0.0289947	+	0.0330566i
$328$	2.24165	−	7.68850i	0.123774	−	0.424526i
$329$	21.7398	−	12.5515i	1.19855	−	0.691985i
$330$		0			0
$331$	7.43989	+	4.29542i	0.408933	+	0.236098i	0.690331	−	0.723493i	$-0.257465\pi$
$331$	7.43989	+	4.29542i	0.408933	+	0.236098i	−0.281398	+	0.959591i	$0.590798\pi$
$332$	−4.46364	−	2.66471i	−0.244974	−	0.146245i
$333$	−4.49659	−	34.1982i	−0.246412	−	1.87405i
$334$	2.69583	−	9.77502i	0.147509	−	0.534865i
$335$		0			0
$336$	−21.9550	+	6.74277i	−1.19775	+	0.367848i
$337$	0.527708	+	0.914017i	0.0287461	+	0.0497897i	0.880041	−	0.474899i	$-0.157515\pi$
$337$	0.527708	+	0.914017i	0.0287461	+	0.0497897i	−0.851294	+	0.524688i	$0.824182\pi$
$338$	8.70561	−	2.26469i	0.473523	−	0.123183i
$339$	5.89251	−	29.6110i	0.320037	−	1.60825i
$340$		0			0
$341$		−	0.558884i		−	0.0302652i
$342$	−10.1580	−	7.91565i	−0.549283	−	0.428029i
$343$		−	9.98036i		−	0.538889i
$344$	−22.9485	+	5.61355i	−1.23730	+	0.302662i
$345$		0			0
$346$	−0.916922	−	3.52470i	−0.0492940	−	0.189489i
$347$	−3.45165	−	5.97844i	−0.185294	−	0.320939i	0.758381	−	0.651811i	$-0.225991\pi$
$347$	−3.45165	−	5.97844i	−0.185294	−	0.320939i	−0.943676	+	0.330872i	$0.892657\pi$
$348$	−1.27570	−	3.94754i	−0.0683848	−	0.211610i
$349$	15.5145	−	26.8719i	0.830473	−	1.43842i	−0.0671899	−	0.997740i	$-0.521403\pi$
$349$	15.5145	−	26.8719i	0.830473	−	1.43842i	0.897663	−	0.440682i	$-0.145263\pi$
$350$		0			0
$351$	1.50094	−	22.8142i	0.0801142	−	1.21773i
$352$	13.0074	−	2.98128i	0.693299	−	0.158903i
$353$	−13.2995	−	7.67847i	−0.707861	−	0.408684i	0.102408	−	0.994743i	$-0.467345\pi$
$353$	−13.2995	−	7.67847i	−0.707861	−	0.408684i	−0.810269	+	0.586059i	$0.800679\pi$
$354$	2.86509	+	4.35719i	0.152278	+	0.231582i
$355$		0			0
$356$	9.36161	+	0.136661i	0.496164	+	0.00724301i
$357$	−1.64105	−	4.83568i	−0.0868537	−	0.255932i
$358$	10.1101	+	10.2588i	0.534337	+	0.542194i
$359$	8.51196			0.449244			0.224622	−	0.974446i	$-0.427885\pi$
$359$	8.51196			0.449244			0.224622	+	0.974446i	$0.427885\pi$
$360$		0			0
$361$	9.78650			0.515079
$362$	−4.14478	−	4.20573i	−0.217845	−	0.221048i
$363$	9.23258	+	1.83726i	0.484585	+	0.0964311i
$364$	−29.1696	−	0.425818i	−1.52890	−	0.0223189i
$365$		0			0
$366$	−4.20700	+	8.37456i	−0.219903	+	0.437746i
$367$	1.11984	+	0.646542i	0.0584553	+	0.0337492i	0.528943	−	0.848657i	$-0.322589\pi$
$367$	1.11984	+	0.646542i	0.0584553	+	0.0337492i	−0.470488	+	0.882407i	$0.655922\pi$
$368$	−13.8064	−	25.6120i	−0.719708	−	1.33512i
$369$	−5.16998	−	6.73993i	−0.269138	−	0.350867i
$370$		0			0
$371$	1.27969	−	2.21648i	0.0664381	−	0.115074i
$372$	0.802481	+	0.171906i	0.0416067	+	0.00891289i
$373$	−8.18898	−	14.1837i	−0.424010	−	0.734406i	0.572318	−	0.820032i	$-0.306044\pi$
$373$	−8.18898	−	14.1837i	−0.424010	−	0.734406i	−0.996327	+	0.0856259i	$0.972711\pi$
$374$	0.747002	+	2.87152i	0.0386265	+	0.148483i
$375$		0			0
$376$	−5.08917	−	20.8048i	−0.262454	−	1.07293i
$377$		−	5.26946i		−	0.271391i
$378$	−8.00416	+	23.0078i	−0.411689	+	1.18339i
$379$		−	11.7940i		−	0.605818i	−0.953020	−	0.302909i	$-0.902042\pi$
$379$		−	11.7940i		−	0.605818i	0.953020	−	0.302909i	$-0.0979578\pi$
$380$		0			0
$381$	−13.7591	−	12.0684i	−0.704901	−	0.618283i
$382$	34.2582	−	8.91198i	1.75280	−	0.455977i
$383$	−5.63455	−	9.75933i	−0.287912	−	0.498678i	0.685399	−	0.728168i	$-0.259628\pi$
$383$	−5.63455	−	9.75933i	−0.287912	−	0.498678i	−0.973311	+	0.229489i	$0.926294\pi$
$384$	0.279794	+	19.5939i	0.0142782	+	0.999898i
$385$		0			0
$386$	−7.11268	+	25.7905i	−0.362026	+	1.31270i
$387$	−9.59316	+	23.1492i	−0.487648	+	1.17674i
$388$	−10.6024	−	6.32944i	−0.538257	−	0.321328i
$389$	−17.4583	−	10.0796i	−0.885172	−	0.511054i	−0.0128115	−	0.999918i	$-0.504078\pi$
$389$	−17.4583	−	10.0796i	−0.885172	−	0.511054i	−0.872360	+	0.488864i	$0.837411\pi$
$390$		0			0
$391$	5.60259	−	3.23466i	0.283335	−	0.163584i
$392$	10.8326	+	3.15833i	0.547127	+	0.159520i
$393$	−27.6182	−	5.49594i	−1.39315	−	0.277234i
$394$	−5.29239	+	5.21569i	−0.266627	+	0.262763i
$395$		0			0
$396$	5.60901	−	12.9954i	0.281863	−	0.653044i
$397$	−5.11859			−0.256895			−0.128447	−	0.991716i	$-0.540999\pi$
$397$	−5.11859			−0.256895			−0.128447	+	0.991716i	$0.540999\pi$
$398$	18.9858	−	18.7106i	0.951670	−	0.937879i
$399$	5.60084	+	16.5040i	0.280393	+	0.826233i
$400$		0			0
$401$	9.58291	−	5.53269i	0.478548	−	0.276290i	−0.241263	−	0.970460i	$-0.577562\pi$
$401$	9.58291	−	5.53269i	0.478548	−	0.276290i	0.719811	+	0.694170i	$0.244228\pi$
$402$	12.9856	−	8.53874i	0.647662	−	0.425874i
$403$	0.902771	+	0.521215i	0.0449702	+	0.0259636i
$404$	7.95892	−	13.3320i	0.395971	−	0.663291i
$405$		0			0
$406$	−1.49267	+	5.41238i	−0.0740798	+	0.268612i
$407$	13.5615	−	23.4893i	0.672221	−	1.16432i
$408$	−4.35288	+	0.189350i	−0.215500	+	0.00937423i
$409$	8.08315	+	14.0004i	0.399686	+	0.692276i	0.993687	−	0.112188i	$-0.0357858\pi$
$409$	8.08315	+	14.0004i	0.399686	+	0.692276i	−0.594001	+	0.804464i	$0.702452\pi$
$410$		0			0
$411$	21.6368	−	7.34273i	1.06726	−	0.362190i
$412$	−12.8265	−	22.9846i	−0.631917	−	1.13237i
$413$		−	7.05742i		−	0.347273i
$414$	−30.5663	−	4.25640i	−1.50225	−	0.209191i
$415$		0			0
$416$	−7.31504	+	23.7914i	−0.358650	+	1.16647i
$417$	2.19190	−	11.0147i	0.107338	−	0.539394i
$418$	−2.54949	−	9.80037i	−0.124699	−	0.479352i
$419$	−3.65564	−	6.33176i	−0.178590	−	0.309327i	0.762808	−	0.646625i	$-0.223820\pi$
$419$	−3.65564	−	6.33176i	−0.178590	−	0.309327i	−0.941398	+	0.337298i	$0.890487\pi$
$420$		0			0
$421$	14.9731	−	25.9341i	0.729742	−	1.26395i	−0.227250	−	0.973836i	$-0.572973\pi$
$421$	14.9731	−	25.9341i	0.729742	−	1.26395i	0.956992	−	0.290114i	$-0.0936932\pi$
$422$	6.23521	+	1.71959i	0.303525	+	0.0837083i
$423$	−20.9868	−	8.69702i	−1.02041	−	0.422864i
$424$	−1.50993	−	1.57755i	−0.0733288	−	0.0766124i
$425$		0			0
$426$	28.6705	−	1.66676i	1.38909	−	0.0807546i
$427$	10.9842	−	6.34172i	0.531562	−	0.306897i
$428$	0.00736171	−	0.504295i	0.000355842	−	0.0243760i
$429$	11.8552	−	13.5160i	0.572375	−	0.652561i
$430$		0			0
$431$	−30.7505			−1.48120			−0.740599	−	0.671947i	$-0.765458\pi$
$431$	−30.7505			−1.48120			−0.740599	+	0.671947i	$0.765458\pi$
$432$	16.9344	+	12.0510i	0.814756	+	0.579804i
$433$	29.3734			1.41160			0.705798	−	0.708413i	$-0.250589\pi$
$433$	29.3734			1.41160			0.705798	+	0.708413i	$0.250589\pi$
$434$	−0.779614	−	0.791078i	−0.0374227	−	0.0379730i
$435$		0			0
$436$	0.0134016	−	0.918039i	0.000641818	−	0.0439661i
$437$	−19.1214	+	11.0398i	−0.914701	+	0.528103i
$438$	−14.9384	+	0.868446i	−0.713787	+	0.0414960i
$439$	−6.77418	−	3.91108i	−0.323314	−	0.186665i	0.329555	−	0.944136i	$-0.393101\pi$
$439$	−6.77418	−	3.91108i	−0.323314	−	0.186665i	−0.652869	+	0.757471i	$0.726435\pi$
$440$		0			0
$441$	9.49608	−	7.28413i	0.452194	−	0.346863i
$442$	−5.33505	−	1.47134i	−0.253763	−	0.0699844i
$443$	−13.3520	+	23.1263i	−0.634371	+	1.09876i	0.352277	+	0.935896i	$0.385408\pi$
$443$	−13.3520	+	23.1263i	−0.634371	+	1.09876i	−0.986648	+	0.162867i	$0.947926\pi$
$444$	29.5560	+	26.6975i	1.40267	+	1.26701i
$445$		0			0
$446$	−8.45731	−	32.5104i	−0.400465	−	1.53941i
$447$	−2.83001	+	14.2213i	−0.133855	+	0.672646i
$448$	14.2528	−	22.3646i	0.673381	−	1.05663i
$449$			23.8441i			1.12527i	0.826704	+	0.562637i	$0.190213\pi$
$449$			23.8441i			1.12527i	−0.826704	+	0.562637i	$0.809787\pi$
$450$		0			0
$451$		−	6.67955i		−	0.314528i
$452$	16.9886	+	30.4428i	0.799076	+	1.43191i
$453$	26.8952	−	9.12722i	1.26364	−	0.428834i
$454$	38.1272	−	9.91849i	1.78940	−	0.465498i
$455$		0			0
$456$	14.8562	−	0.646244i	0.695705	−	0.0302632i
$457$	7.87798	−	13.6451i	0.368516	−	0.638289i	−0.620817	−	0.783955i	$-0.713199\pi$
$457$	7.87798	−	13.6451i	0.368516	−	0.638289i	0.989334	+	0.145666i	$0.0465325\pi$
$458$	−6.28641	+	22.7944i	−0.293745	+	1.06511i
$459$	−2.56839	+	3.84183i	−0.119882	+	0.179321i
$460$		0			0
$461$	9.24515	+	5.33769i	0.430590	+	0.248601i	0.699598	−	0.714537i	$-0.253363\pi$
$461$	9.24515	+	5.33769i	0.430590	+	0.248601i	−0.269008	+	0.963138i	$0.586696\pi$
$462$	−16.0054	+	10.5245i	−0.744640	+	0.489642i
$463$	5.50175	−	3.17644i	0.255688	−	0.147622i	−0.366678	−	0.930348i	$-0.619505\pi$
$463$	5.50175	−	3.17644i	0.255688	−	0.147622i	0.622366	+	0.782726i	$0.286172\pi$
$464$	4.07687	+	2.51524i	0.189264	+	0.116767i
$465$		0			0
$466$	−1.69160	+	1.66708i	−0.0783617	+	0.0772261i
$467$	−7.76191			−0.359179			−0.179589	−	0.983742i	$-0.557477\pi$
$467$	−7.76191			−0.359179			−0.179589	+	0.983742i	$0.557477\pi$
$468$	15.7607	+	21.1798i	0.728538	+	0.979038i
$469$	−21.0330			−0.971213
$470$		0			0
$471$	−18.1972	−	3.62120i	−0.838483	−	0.166856i
$472$	−5.78081	−	1.68545i	−0.266083	−	0.0775790i
$473$	−17.0645	+	9.85221i	−0.784628	+	0.453005i
$474$	22.6174	+	11.3619i	1.03885	+	0.521871i
$475$		0			0
$476$	5.06298	+	3.02249i	0.232061	+	0.138536i
$477$	−2.29640	+	0.301945i	−0.105145	+	0.0138251i
$478$	−4.06880	+	14.7534i	−0.186103	+	0.674805i
$479$	3.56565	−	6.17588i	0.162919	−	0.282183i	−0.772996	−	0.634411i	$-0.781243\pi$
$479$	3.56565	−	6.17588i	0.162919	−	0.282183i	0.935914	+	0.352228i	$0.114576\pi$
$480$		0			0
$481$	25.2950	+	43.8122i	1.15335	+	1.99767i
$482$	14.9364	−	3.88558i	0.680333	−	0.176983i
$483$	31.3992	+	27.5409i	1.42871	+	1.25315i
$484$	−9.49194	+	5.29697i	−0.431452	+	0.240771i
$485$		0			0
$486$	20.9295	−	6.92516i	0.949379	−	0.314132i
$487$			15.1089i			0.684649i	0.939582	+	0.342325i	$0.111214\pi$
$487$			15.1089i			0.684649i	−0.939582	+	0.342325i	$0.888786\pi$
$488$	−2.57134	−	10.5118i	−0.116399	−	0.475846i
$489$	1.73943	+	1.52569i	0.0786599	+	0.0689942i
$490$		0			0
$491$	−14.7215	−	25.4984i	−0.664372	−	1.15073i	−0.979455	−	0.201662i	$-0.935366\pi$
$491$	−14.7215	−	25.4984i	−0.664372	−	1.15073i	0.315083	−	0.949064i	$-0.397968\pi$
$492$	9.59093	+	2.05455i	0.432392	+	0.0926261i
$493$	−0.532546	+	0.922396i	−0.0239847	+	0.0415426i
$494$	18.2083	+	5.02162i	0.819230	+	0.225933i
$495$		0			0
$496$	−0.834168	+	0.449666i	−0.0374552	+	0.0201906i
$497$	−33.6595	−	19.4333i	−1.50984	−	0.871705i
$498$	2.85807	−	5.68934i	0.128073	−	0.254946i
$499$	−18.0795	+	10.4382i	−0.809351	+	0.467279i	−0.846730	−	0.532022i	$-0.821432\pi$
$499$	−18.0795	+	10.4382i	−0.809351	+	0.467279i	0.0373795	+	0.999301i	$0.488099\pi$
$500$		0			0
$501$	12.1800	+	2.42379i	0.544163	+	0.108287i
$502$	5.02061	+	5.09444i	0.224081	+	0.227376i
$503$	−22.6713			−1.01086			−0.505431	−	0.862867i	$-0.668667\pi$
$503$	−22.6713			−1.01086			−0.505431	+	0.862867i	$0.668667\pi$
$504$	−10.1886	−	26.2188i	−0.453837	−	1.16788i
$505$		0			0
$506$	−17.0341	−	17.2846i	−0.757257	−	0.768392i
$507$	3.54045	+	10.4326i	0.157237	+	0.463330i
$508$	21.1310	+	0.308470i	0.937535	+	0.0136862i
$509$	23.5593	−	13.6020i	1.04425	−	0.602896i	0.123213	−	0.992380i	$-0.460680\pi$
$509$	23.5593	−	13.6020i	1.04425	−	0.602896i	0.921033	+	0.389484i	$0.127347\pi$
$510$		0			0
$511$	17.5380	+	10.1255i	0.775834	+	0.447928i
$512$	−14.9153	−	17.0157i	−0.659168	−	0.751996i
$513$	8.76582	−	13.1120i	0.387020	−	0.578909i
$514$	18.2560	+	5.03476i	0.805236	+	0.222074i
$515$		0			0
$516$	−8.89760	−	27.5328i	−0.391695	−	1.21206i
$517$	−8.93188	−	15.4705i	−0.392824	−	0.680390i
$518$	−13.5705	−	52.1658i	−0.596254	−	2.29204i
$519$	4.22393	−	1.43345i	0.185410	−	0.0629213i
$520$		0			0
$521$			2.18176i			0.0955847i	0.998857	+	0.0477924i	$0.0152186\pi$
$521$			2.18176i			0.0955847i	−0.998857	+	0.0477924i	$0.984781\pi$
$522$	4.70853	−	1.90930i	0.206087	−	0.0835678i
$523$		−	28.8185i		−	1.26014i	−0.776537	−	0.630071i	$-0.783026\pi$
$523$		−	28.8185i		−	1.26014i	0.776537	−	0.630071i	$-0.216974\pi$
$524$	28.3940	−	15.8452i	1.24040	−	0.692203i
$525$		0			0
$526$	−14.9065	+	3.87779i	−0.649953	+	0.169080i
$527$	−0.105351	−	0.182473i	−0.00458916	−	0.00794865i
$528$	4.79829	+	15.6237i	0.208819	+	0.679932i
$529$	−14.9560	+	25.9046i	−0.650261	+	1.12629i
$530$		0			0
$531$	−5.06760	+	3.88719i	−0.219915	+	0.168690i
$532$	−17.2797	−	10.3156i	−0.749171	−	0.447240i
$533$	10.7896	+	6.22935i	0.467348	+	0.269823i
$534$	0.665498	+	11.4475i	0.0287989	+	0.495381i
$535$		0			0
$536$	−5.02308	+	17.2283i	−0.216964	+	0.744151i
$537$	−11.6323	+	13.2619i	−0.501969	+	0.572292i
$538$	21.6584	−	21.3445i	0.933759	−	0.920227i
$539$	9.41102			0.405361
$540$		0			0
$541$	3.32257			0.142848			0.0714242	−	0.997446i	$-0.477246\pi$
$541$	3.32257			0.142848			0.0714242	+	0.997446i	$0.477246\pi$
$542$	19.0823	−	18.8058i	0.819655	−	0.807777i
$543$	4.76880	−	5.43688i	0.204649	−	0.233319i
$544$	3.68489	−	3.42531i	0.157989	−	0.146859i
$545$		0			0
$546$	−2.07361	−	35.6689i	−0.0887422	−	1.52649i
$547$	24.0231	+	13.8697i	1.02715	+	0.593027i	0.916168	−	0.400795i	$-0.131266\pi$
$547$	24.0231	+	13.8697i	1.02715	+	0.593027i	0.110986	+	0.993822i	$0.464599\pi$
$548$	−13.5238	+	22.6538i	−0.577710	+	0.967721i
$549$	−10.6037	−	4.39424i	−0.452556	−	0.187541i
$550$		0			0
$551$	1.81756	−	3.14810i	0.0774305	−	0.134114i
$552$	30.0577	−	19.1421i	1.27934	−	0.814742i
$553$	−17.1272	−	29.6652i	−0.728323	−	1.26149i
$554$	25.5417	−	6.64447i	1.08516	−	0.282296i
$555$		0			0
$556$	6.31943	+	11.3241i	0.268003	+	0.480251i
$557$			30.0401i			1.27284i	0.771344	+	0.636419i	$0.219585\pi$
$557$			30.0401i			1.27284i	−0.771344	+	0.636419i	$0.780415\pi$
$558$	−0.138628	+	0.995526i	−0.00586861	+	0.0421440i
$559$		−	36.7527i		−	1.55447i
$560$		0			0
$561$	−3.44117	+	1.16781i	−0.145286	+	0.0493048i
$562$	2.40378	+	9.24028i	0.101398	+	0.389778i
$563$	−0.883109	−	1.52959i	−0.0372186	−	0.0644645i	0.846816	−	0.531886i	$-0.178516\pi$
$563$	−0.883109	−	1.52959i	−0.0372186	−	0.0644645i	−0.884035	+	0.467421i	$0.845183\pi$
$564$	24.9608	−	8.06644i	1.05104	−	0.339658i
$565$		0			0
$566$	7.18435	+	1.98135i	0.301981	+	0.0832824i
$567$	−28.8160	−	7.73134i	−1.21016	−	0.324686i
$568$	−23.9566	+	22.9298i	−1.00520	+	0.962115i
$569$	−31.9951	−	18.4724i	−1.34131	−	0.774403i	−0.354306	−	0.935129i	$-0.615283\pi$
$569$	−31.9951	−	18.4724i	−1.34131	−	0.774403i	−0.986999	+	0.160726i	$0.948616\pi$
$570$		0			0
$571$	−26.5164	+	15.3092i	−1.10968	+	0.640672i	−0.938745	−	0.344612i	$-0.888011\pi$
$571$	−26.5164	+	15.3092i	−1.10968	+	0.640672i	−0.170930	+	0.985283i	$0.554677\pi$
$572$	−0.303021	+	20.7577i	−0.0126699	+	0.867922i
$573$	13.9323	+	41.0543i	0.582031	+	1.71507i
$574$	−9.31764	−	9.45465i	−0.388911	−	0.394629i
$575$		0			0
$576$	−23.9093	+	2.08406i	−0.996223	+	0.0868357i
$577$	−23.6405			−0.984168			−0.492084	−	0.870548i	$-0.663765\pi$
$577$	−23.6405			−0.984168			−0.492084	+	0.870548i	$0.663765\pi$
$578$	−16.0903	−	16.3269i	−0.669268	−	0.679109i
$579$	−32.1358	−	6.39495i	−1.33552	−	0.265765i
$580$		0			0
$581$	−7.46221	+	4.30831i	−0.309585	+	0.178739i
$582$	6.78872	−	13.5138i	0.281402	−	0.560166i
$583$	−1.57730	−	0.910652i	−0.0653249	−	0.0377154i
$584$	12.4824	−	11.9474i	0.516523	−	0.494385i
$585$		0			0
$586$	30.3890	+	8.38091i	1.25536	+	0.346212i
$587$	−0.0296509	+	0.0513568i	−0.00122382	+	0.00211972i	−0.866637	−	0.498940i	$-0.833723\pi$
$587$	−0.0296509	+	0.0513568i	−0.00122382	+	0.00211972i	0.865413	+	0.501059i	$0.167056\pi$
$588$	−2.89471	+	13.5129i	−0.119376	+	0.557264i
$589$	0.359558	+	0.622773i	0.0148153	+	0.0256609i
$590$		0			0
$591$	−6.84163	−	6.00094i	−0.281427	−	0.246846i
$592$	−45.9705	−	1.34244i	−1.88938	−	0.0551741i
$593$			44.6245i			1.83251i	0.400596	+	0.916255i	$0.368803\pi$
$593$			44.6245i			1.83251i	−0.400596	+	0.916255i	$0.631197\pi$
$594$	16.3728	+	5.69592i	0.671785	+	0.233707i
$595$		0			0
$596$	−8.15914	−	14.6208i	−0.334211	−	0.598893i
$597$	24.5435	+	21.5276i	1.00450	+	0.881066i
$598$	43.8059	−	11.3958i	1.79136	−	0.466007i
$599$	−11.5001	−	19.9187i	−0.469881	−	0.813857i	0.529526	−	0.848294i	$-0.322370\pi$
$599$	−11.5001	−	19.9187i	−0.469881	−	0.813857i	−0.999407	+	0.0344362i	$0.989036\pi$
$600$		0			0
$601$	0.981232	−	1.69954i	0.0400253	−	0.0693259i	−0.845319	−	0.534262i	$-0.820589\pi$
$601$	0.981232	−	1.69954i	0.0400253	−	0.0693259i	0.885344	+	0.464936i	$0.153923\pi$
$602$	−10.4109	+	37.7496i	−0.424315	+	1.53856i
$603$	11.5849	+	15.1028i	0.471772	+	0.615033i
$604$	−16.8105	+	28.1593i	−0.684011	+	1.14579i
$605$		0			0
$606$	16.9929	+	8.53645i	0.690289	+	0.346769i
$607$	17.5023	−	10.1049i	0.710394	−	0.410146i	−0.100813	−	0.994905i	$-0.532144\pi$
$607$	17.5023	−	10.1049i	0.710394	−	0.410146i	0.811207	+	0.584759i	$0.198811\pi$
$608$	−12.5764	+	11.6904i	−0.510040	+	0.474110i
$609$	−6.74402	−	1.34204i	−0.273282	−	0.0543823i
$610$		0			0
$611$	33.3195			1.34796
$612$	−0.618350	−	5.30026i	−0.0249953	−	0.214250i
$613$	−24.8672			−1.00438			−0.502189	−	0.864758i	$-0.667472\pi$
$613$	−24.8672			−1.00438			−0.502189	+	0.864758i	$0.667472\pi$
$614$	0.418434	−	0.412371i	0.0168866	−	0.0166419i
$615$		0			0
$616$	6.19121	−	21.2349i	0.249451	−	0.855577i
$617$	28.3549	−	16.3707i	1.14152	−	0.659059i	0.194717	−	0.980860i	$-0.437621\pi$
$617$	28.3549	−	16.3707i	1.14152	−	0.659059i	0.946808	+	0.321800i	$0.104288\pi$
$618$	26.9354	−	17.7115i	1.08350	−	0.712463i
$619$	−11.9754	−	6.91400i	−0.481332	−	0.277897i	0.239640	−	0.970862i	$-0.422971\pi$
$619$	−11.9754	−	6.91400i	−0.481332	−	0.277897i	−0.720971	+	0.692965i	$0.756304\pi$
$620$		0			0
$621$	2.48130	−	37.7156i	0.0995713	−	1.51348i
$622$	−0.213982	+	0.775897i	−0.00857991	+	0.0311106i
$623$	7.75930	−	13.4395i	0.310870	−	0.538442i
$624$	−29.7120	−	6.81989i	−1.18943	−	0.273014i
$625$		0			0
$626$	38.4079	−	9.99151i	1.53509	−	0.399341i
$627$	11.7446	−	3.98568i	0.469033	−	0.159173i
$628$	18.7084	−	10.4402i	0.746546	−	0.416609i
$629$		−	10.2255i		−	0.407719i
$630$		0			0
$631$		−	0.298908i		−	0.0118994i	−0.999982	−	0.00594968i	$-0.998106\pi$
$631$		−	0.298908i		−	0.0118994i	0.999982	−	0.00594968i	$-0.00189385\pi$
$632$	−28.3894	+	6.94447i	−1.12927	+	0.276236i
$633$	−1.54607	+	7.76929i	−0.0614507	+	0.308802i
$634$	4.72598	+	18.1669i	0.187693	+	0.721501i
$635$		0			0
$636$	1.79273	−	1.98468i	0.0710864	−	0.0786976i
$637$	−8.77672	+	15.2017i	−0.347746	+	0.602314i
$638$	3.85156	+	1.06221i	0.152485	+	0.0420534i
$639$	4.58533	+	34.8731i	0.181393	+	1.37956i
$640$		0			0
$641$	12.2453	+	7.06982i	0.483660	+	0.279241i	0.721940	−	0.691955i	$-0.243250\pi$
$641$	12.2453	+	7.06982i	0.483660	+	0.279241i	−0.238281	+	0.971196i	$0.576584\pi$
$642$	0.616658	−	0.0358494i	0.0243375	−	0.00141486i
$643$	31.6633	−	18.2808i	1.24868	−	0.720925i	0.277833	−	0.960629i	$-0.410384\pi$
$643$	31.6633	−	18.2808i	1.24868	−	0.720925i	0.970846	+	0.239704i	$0.0770505\pi$
$644$	−48.2222	−	0.703948i	−1.90022	−	0.0277394i
$645$		0			0
$646$	−2.67979	−	2.71919i	−0.105435	−	0.106985i
$647$	−25.4645			−1.00111			−0.500556	−	0.865704i	$-0.666871\pi$
$647$	−25.4645			−1.00111			−0.500556	+	0.865704i	$0.666871\pi$
$648$	−13.2146	+	21.7571i	−0.519120	+	0.854701i
$649$	−5.02220			−0.197139
$650$		0			0
$651$	0.896989	−	1.02265i	0.0351558	−	0.0400809i
$652$	−2.67139	−	0.0389969i	−0.104620	−	0.00152724i
$653$	19.4203	−	11.2123i	0.759976	−	0.438772i	−0.0693112	−	0.997595i	$-0.522080\pi$
$653$	19.4203	−	11.2123i	0.759976	−	0.438772i	0.829287	+	0.558823i	$0.188747\pi$
$654$	1.12259	−	0.0652616i	0.0438967	−	0.00255193i
$655$		0			0
$656$	−9.96964	+	5.37423i	−0.389249	+	0.209828i
$657$	−2.38914	−	18.1703i	−0.0932092	−	0.708890i
$658$	−34.2233	−	9.43834i	−1.33416	−	0.367945i
$659$	−3.28193	+	5.68446i	−0.127846	+	0.221435i	−0.922842	−	0.385179i	$-0.874140\pi$
$659$	−3.28193	+	5.68446i	−0.127846	+	0.221435i	0.794996	+	0.606615i	$0.207473\pi$
$660$		0			0
$661$	−9.44856	−	16.3654i	−0.367506	−	0.636540i	0.621669	−	0.783280i	$-0.286455\pi$
$661$	−9.44856	−	16.3654i	−0.367506	−	0.636540i	−0.989175	+	0.146741i	$0.953122\pi$
$662$	−3.05873	−	11.7579i	−0.118881	−	0.456986i
$663$	1.32287	−	6.64766i	0.0513759	−	0.258174i
$664$	1.74687	+	7.14129i	0.0677915	+	0.277136i
$665$		0			0
$666$	−29.9833	+	38.4770i	−1.16183	+	1.49095i
$667$		−	8.71129i		−	0.337303i
$668$	−12.5222	+	6.98799i	−0.484498	+	0.270373i
$669$	38.9598	−	13.2215i	1.50627	−	0.511173i
$670$		0			0
$671$	−4.51290	−	7.81657i	−0.174219	−	0.301755i
$672$	28.5860	+	15.4213i	1.10273	+	0.594890i
$673$	−15.6611	+	27.1258i	−0.603690	+	1.04562i	0.388567	+	0.921420i	$0.372970\pi$
$673$	−15.6611	+	27.1258i	−0.603690	+	1.04562i	−0.992257	+	0.124201i	$0.960363\pi$
$674$	0.396821	−	1.43887i	0.0152850	−	0.0554231i
$675$		0			0
$676$	−10.9230	−	6.52081i	−0.420115	−	0.250800i
$677$	35.4936	+	20.4922i	1.36413	+	0.787580i	0.990171	−	0.139866i	$-0.0446670\pi$
$677$	35.4936	+	20.4922i	1.36413	+	0.787580i	0.373958	+	0.927446i	$0.378000\pi$
$678$	−35.6757	+	23.4587i	−1.37012	+	0.900928i
$679$	−17.7249	+	10.2335i	−0.680219	+	0.392724i
$680$		0			0
$681$	15.5058	+	45.6910i	0.594185	+	1.75088i
$682$	−0.562948	+	0.554790i	−0.0215564	+	0.0212440i
$683$	−42.0703			−1.60978			−0.804888	−	0.593427i	$-0.797775\pi$
$683$	−42.0703			−1.60978			−0.804888	+	0.593427i	$0.797775\pi$
$684$	2.11040	+	18.0896i	0.0806933	+	0.691671i
$685$		0			0
$686$	−10.0529	+	9.90726i	−0.383823	+	0.378261i
$687$	−28.4027	−	5.65206i	−1.08363	−	0.215639i
$688$	28.4348	+	17.5430i	1.08407	+	0.668820i
$689$	2.94198	−	1.69855i	0.112080	−	0.0647096i
$690$		0			0
$691$	−30.3277	−	17.5097i	−1.15372	−	0.666101i	−0.203930	−	0.978986i	$-0.565371\pi$
$691$	−30.3277	−	17.5097i	−1.15372	−	0.666101i	−0.949791	+	0.312885i	$0.898705\pi$
$692$	−2.64012	+	4.42247i	−0.100362	+	0.168117i
$693$	−14.2789	−	18.6150i	−0.542412	−	0.707125i
$694$	−2.59554	+	9.41140i	−0.0985255	+	0.357252i
$695$		0			0
$696$	−2.70988	+	5.20360i	−0.102718	+	0.197242i
$697$	−1.25911	−	2.18084i	−0.0476922	−	0.0826054i
$698$	−42.4682	+	11.0478i	−1.60745	+	0.418164i
$699$	−2.18678	−	1.91807i	−0.0827116	−	0.0725481i
$700$		0			0
$701$		−	41.5315i		−	1.56862i	−0.620366	−	0.784312i	$-0.713016\pi$
$701$		−	41.5315i		−	1.56862i	0.620366	−	0.784312i	$-0.286984\pi$
$702$	−24.4700	+	21.1352i	−0.923560	+	0.797696i
$703$			34.8993i			1.31625i
$704$	−15.9151	−	10.1426i	−0.599824	−	0.382263i
$705$		0			0
$706$	5.46777	+	21.0184i	0.205782	+	0.791039i
$707$	−12.8680	−	22.2881i	−0.483952	−	0.838229i
$708$	1.54477	−	7.21120i	0.0580559	−	0.271013i
$709$	−5.69139	+	9.85778i	−0.213745	+	0.370217i	−0.952883	−	0.303337i	$-0.901899\pi$
$709$	−5.69139	+	9.85778i	−0.213745	+	0.370217i	0.739139	+	0.673553i	$0.235233\pi$
$710$		0			0
$711$	−11.8676	+	28.6377i	−0.445070	+	1.07400i
$712$	−9.15538	−	9.56534i	−0.343112	−	0.358476i
$713$	1.49243	+	0.861656i	0.0558920	+	0.0322693i
$714$	−3.24182	+	6.45325i	−0.121322	+	0.241507i
$715$		0			0
$716$	0.297322	−	20.3673i	0.0111115	−	0.761162i
$717$	−18.3833	−	3.65822i	−0.686536	−	0.136619i
$718$	−8.44961	−	8.57386i	−0.315337	−	0.319974i
$719$	24.0599			0.897282			0.448641	−	0.893712i	$-0.351908\pi$
$719$	24.0599			0.897282			0.448641	+	0.893712i	$0.351908\pi$
$720$		0			0
$721$	−43.6278			−1.62478
$722$	−9.71482	−	9.85767i	−0.361548	−	0.366864i
$723$	6.07442	+	17.8995i	0.225910	+	0.665689i
$724$	−0.121891	+	8.34985i	−0.00453005	+	0.310320i
$725$		0			0
$726$	−7.31433	−	11.1235i	−0.271460	−	0.412833i
$727$	−4.94944	−	2.85756i	−0.183565	−	0.105981i	0.405402	−	0.914139i	$-0.367132\pi$
$727$	−4.94944	−	2.85756i	−0.183565	−	0.105981i	−0.588966	+	0.808158i	$0.700465\pi$
$728$	28.5270	+	29.8044i	1.05728	+	1.10462i
$729$	10.3202	+	24.9498i	0.382230	+	0.924067i
$730$		0			0
$731$	−3.71433	+	6.43341i	−0.137380	+	0.237948i
$732$	12.6116	−	4.07563i	0.466140	−	0.150640i
$733$	−12.9269	−	22.3900i	−0.477465	−	0.826994i	0.522201	−	0.852822i	$-0.325111\pi$
$733$	−12.9269	−	22.3900i	−0.477465	−	0.826994i	−0.999666	+	0.0258286i	$0.991778\pi$
$734$	−0.460397	−	1.76979i	−0.0169936	−	0.0653242i
$735$		0			0
$736$	−12.0930	+	39.3312i	−0.445754	+	1.44977i
$737$			14.9675i			0.551335i
$738$	−1.65683	+	11.8981i	−0.0609888	+	0.437976i
$739$			18.0774i			0.664989i	0.943105	+	0.332495i	$0.107890\pi$
$739$			18.0774i			0.664989i	−0.943105	+	0.332495i	$0.892110\pi$
$740$		0			0
$741$	−4.51489	+	22.6882i	−0.165859	+	0.833472i
$742$	−3.50292	+	0.911255i	−0.128596	+	0.0334532i
$743$	9.00512	+	15.5973i	0.330366	+	0.572210i	0.982584	−	0.185821i	$-0.0594946\pi$
$743$	9.00512	+	15.5973i	0.330366	+	0.572210i	−0.652218	+	0.758032i	$0.726161\pi$
$744$	−0.623447	−	0.978963i	−0.0228567	−	0.0358905i
$745$		0			0
$746$	−6.15788	+	22.3284i	−0.225456	+	0.817500i
$747$	7.20374	+	2.98527i	0.263571	+	0.109225i
$748$	2.15087	−	3.60292i	0.0786435	−	0.131736i
$749$	−0.723965	−	0.417982i	−0.0264531	−	0.0152727i
$750$		0			0
$751$	35.2487	−	20.3509i	1.28624	−	0.742613i	0.308262	−	0.951302i	$-0.400253\pi$
$751$	35.2487	−	20.3509i	1.28624	−	0.742613i	0.977982	+	0.208689i	$0.0669195\pi$
$752$	−15.9042	+	25.7786i	−0.579967	+	0.940049i
$753$	−5.77649	+	6.58574i	−0.210507	+	0.239998i
$754$	−5.30778	+	5.23086i	−0.193298	+	0.190497i
$755$		0			0
$756$	31.1206	−	14.7769i	1.13185	−	0.537430i
$757$	35.4823			1.28963			0.644813	−	0.764340i	$-0.276935\pi$
$757$	35.4823			1.28963			0.644813	+	0.764340i	$0.276935\pi$
$758$	−11.8798	+	11.7076i	−0.431493	+	0.425240i
$759$	19.5986	−	22.3443i	0.711386	−	0.811046i
$760$		0			0
$761$	−34.0009	+	19.6304i	−1.23253	+	0.711602i	−0.967557	−	0.252654i	$-0.918697\pi$
$761$	−34.0009	+	19.6304i	−1.23253	+	0.711602i	−0.264974	+	0.964256i	$0.585363\pi$
$762$	1.50216	+	25.8392i	0.0544175	+	0.936054i
$763$	−1.31794	−	0.760910i	−0.0477125	−	0.0275468i
$764$	−42.9840	−	25.6606i	−1.55511	−	0.928367i
$765$		0			0
$766$	−4.23702	+	15.3634i	−0.153090	+	0.555101i
$767$	4.68371	−	8.11242i	0.169119	−	0.292923i
$768$	19.4587	−	19.7322i	0.702154	−	0.712025i
$769$	3.27941	+	5.68011i	0.118259	+	0.204830i	0.919078	−	0.394076i	$-0.128935\pi$
$769$	3.27941	+	5.68011i	0.118259	+	0.204830i	−0.800819	+	0.598906i	$0.795602\pi$
$770$		0			0
$771$	−4.52671	+	22.7476i	−0.163025	+	0.819234i
$772$	33.0386	−	18.4371i	1.18908	−	0.663567i
$773$		−	34.2118i		−	1.23051i	−0.788327	−	0.615256i	$-0.789053\pi$
$773$		−	34.2118i		−	1.23051i	0.788327	−	0.615256i	$-0.210947\pi$
$774$	32.8405	−	13.3167i	1.18043	−	0.478660i
$775$		0			0
$776$	4.14930	+	16.9626i	0.148951	+	0.608922i
$777$	62.5146	−	21.2151i	2.24270	−	0.761089i
$778$	7.17757	+	27.5910i	0.257328	+	0.989185i
$779$	4.29729	+	7.44313i	0.153967	+	0.266678i
$780$		0			0
$781$	−13.8292	+	23.9528i	−0.494847	+	0.857099i
$782$	−8.81973	−	2.43237i	−0.315393	−	0.0869813i
$783$	2.75092	+	5.58176i	0.0983097	+	0.199476i
$784$	−7.57191	−	14.0465i	−0.270425	−	0.501661i
$785$		0			0
$786$	21.8800	+	33.2747i	0.780432	+	1.18687i
$787$	15.0505	−	8.68943i	0.536494	−	0.309745i	−0.207163	−	0.978306i	$-0.566423\pi$
$787$	15.0505	−	8.68943i	0.536494	−	0.309745i	0.743657	+	0.668562i	$0.233090\pi$
$788$	10.5072	+	0.153385i	0.374305	+	0.00546411i
$789$	−6.06225	−	17.8636i	−0.215822	−	0.635962i
$790$		0			0
$791$	57.7846			2.05458
$792$	−18.6578	+	7.25043i	−0.662977	+	0.257633i
$793$	16.8349			0.597826
$794$	5.08109	+	5.15581i	0.180321	+	0.182973i
$795$		0			0
$796$	−37.6934	−	0.550249i	−1.33601	−	0.0195030i
$797$	−6.07314	+	3.50633i	−0.215122	+	0.124201i	−0.603689	−	0.797220i	$-0.706303\pi$
$797$	−6.07314	+	3.50633i	−0.215122	+	0.124201i	0.388568	+	0.921420i	$0.372970\pi$
$798$	11.0642	−	22.0247i	0.391668	−	0.779665i
$799$	−5.83244	−	3.36736i	−0.206337	−	0.119129i
$800$		0			0
$801$	−13.9241	+	1.83082i	−0.491982	+	0.0646889i
$802$	−15.0856	−	4.16042i	−0.532692	−	0.146910i
$803$	7.20555	−	12.4804i	0.254278	−	0.440423i
$804$	−21.4913	−	4.60381i	−0.757939	−	0.162364i
$805$		0			0
$806$	−0.371153	−	1.42673i	−0.0130733	−	0.0502545i
$807$	27.9984	+	24.5580i	0.985592	+	0.864483i
$808$	−21.3295	+	5.21752i	−0.750371	+	0.183552i
$809$			38.9234i			1.36847i	0.729261	+	0.684236i	$0.239864\pi$
$809$			38.9234i			1.36847i	−0.729261	+	0.684236i	$0.760136\pi$
$810$		0			0
$811$		−	35.7891i		−	1.25673i	−0.777920	−	0.628363i	$-0.783725\pi$
$811$		−	35.7891i		−	1.25673i	0.777920	−	0.628363i	$-0.216275\pi$
$812$	6.93347	−	3.86922i	0.243317	−	0.135783i
$813$	24.6683	+	21.6371i	0.865154	+	0.758845i
$814$	−37.1223	+	9.65706i	−1.30114	+	0.338480i
$815$		0			0
$816$	4.51172	+	4.19657i	0.157942	+	0.146909i
$817$	12.6769	−	21.9570i	0.443507	−	0.768177i
$818$	6.07829	−	22.0398i	0.212523	−	0.770604i
$819$	43.3856	−	5.70460i	1.51601	−	0.199335i
$820$		0			0
$821$	−27.8765	−	16.0945i	−0.972895	−	0.561701i	−0.0727775	−	0.997348i	$-0.523186\pi$
$821$	−27.8765	−	16.0945i	−0.972895	−	0.561701i	−0.900118	+	0.435647i	$0.856520\pi$
$822$	−28.8744	−	14.5052i	−1.00711	−	0.505926i
$823$	−14.9963	+	8.65813i	−0.522739	+	0.301804i	−0.738055	−	0.674741i	$-0.764255\pi$
$823$	−14.9963	+	8.65813i	−0.522739	+	0.301804i	0.215315	+	0.976545i	$0.430922\pi$
$824$	−10.4192	+	35.7360i	−0.362969	+	1.24492i
$825$		0			0
$826$	−7.10874	+	7.00572i	−0.247345	+	0.243760i
$827$	15.5363			0.540249			0.270124	−	0.962825i	$-0.412935\pi$
$827$	15.5363			0.540249			0.270124	+	0.962825i	$0.412935\pi$
$828$	26.0551	+	35.0138i	0.905476	+	1.21681i
$829$	27.4645			0.953882			0.476941	−	0.878935i	$-0.341746\pi$
$829$	27.4645			0.953882			0.476941	+	0.878935i	$0.341746\pi$
$830$		0			0
$831$	10.3875	+	30.6087i	0.360337	+	1.06180i
$832$	31.2259	−	16.2489i	1.08256	−	0.563330i
$833$	3.07266	−	1.77400i	0.106461	−	0.0614654i
$834$	−13.2707	+	8.72620i	−0.459526	+	0.302164i
$835$		0			0
$836$	−7.34082	+	12.2966i	−0.253888	+	0.425287i
$837$	−1.22837	−	0.0808146i	−0.0424588	−	0.00279336i
$838$	−2.74894	+	9.96761i	−0.0949605	+	0.344325i
$839$	6.91476	−	11.9767i	0.238724	−	0.413482i	−0.721624	−	0.692285i	$-0.756604\pi$
$839$	6.91476	−	11.9767i	0.238724	−	0.413482i	0.960348	+	0.278803i	$0.0899376\pi$
$840$		0			0
$841$	−13.7829	−	23.8727i	−0.475272	−	0.823196i
$842$	−40.9861	+	10.6622i	−1.41247	+	0.367443i
$843$	−11.0734	+	3.75790i	−0.381387	+	0.129429i
$844$	−4.45744	−	7.98754i	−0.153431	−	0.274943i
$845$		0			0
$846$	12.0728	+	29.7727i	0.415070	+	1.02361i
$847$			18.0170i			0.619070i
$848$	−0.0901446	+	3.08690i	−0.00309558	+	0.106005i
$849$	−1.78142	+	8.95196i	−0.0611380	+	0.307230i
$850$		0			0
$851$	41.8169	+	72.4290i	1.43346	+	2.48283i
$852$	−30.1393	−	27.2244i	−1.03256	−	0.932692i
$853$	18.0633	−	31.2866i	0.618476	−	1.07123i	−0.371288	−	0.928518i	$-0.621084\pi$
$853$	18.0633	−	31.2866i	0.618476	−	1.07123i	0.989764	−	0.142714i	$-0.0455829\pi$
$854$	−17.2916	−	4.76879i	−0.591705	−	0.163185i
$855$		0			0
$856$	−0.515270	+	0.493186i	−0.0176116	+	0.0168568i
$857$	6.41713	+	3.70493i	0.219205	+	0.126558i	0.605582	−	0.795783i	$-0.292940\pi$
$857$	6.41713	+	3.70493i	0.219205	+	0.126558i	−0.386377	+	0.922341i	$0.626274\pi$
$858$	−25.3827	+	1.47562i	−0.866551	+	0.0503769i
$859$	35.7586	−	20.6452i	1.22007	−	0.704407i	0.255136	−	0.966905i	$-0.417880\pi$
$859$	35.7586	−	20.6452i	1.22007	−	0.704407i	0.964932	+	0.262499i	$0.0845465\pi$
$860$		0			0
$861$	10.7205	−	12.2223i	0.365352	−	0.416535i
$862$	30.5252	+	30.9741i	1.03969	+	1.05498i
$863$	46.7922			1.59282			0.796412	−	0.604754i	$-0.206729\pi$
$863$	46.7922			1.59282			0.796412	+	0.604754i	$0.206729\pi$
$864$	−4.67171	−	29.0203i	−0.158935	−	0.987289i
$865$		0			0
$866$	−29.1583	−	29.5870i	−0.990838	−	1.00541i
$867$	18.5128	−	21.1063i	0.628726	−	0.716807i
$868$	−0.0229272	+	1.57057i	−0.000778199	+	0.0533085i
$869$	−21.1104	+	12.1881i	−0.716120	+	0.413452i
$870$		0			0
$871$	−24.1772	−	13.9587i	−0.819213	−	0.472973i
$872$	−0.938018	+	0.897815i	−0.0317653	+	0.0304039i
$873$	17.1109	+	7.09086i	0.579118	+	0.239989i
$874$	30.1014	+	8.30157i	1.01819	+	0.280805i
$875$		0			0
$876$	15.7038	+	14.1850i	0.530582	+	0.479267i
$877$	−7.07692	−	12.2576i	−0.238970	−	0.413909i	0.721449	−	0.692468i	$-0.243477\pi$
$877$	−7.07692	−	12.2576i	−0.238970	−	0.413909i	−0.960419	+	0.278559i	$0.910143\pi$
$878$	2.78504	+	10.7059i	0.0939907	+	0.361306i
$879$	−7.53520	+	37.8658i	−0.254156	+	1.27718i
$880$		0			0
$881$			13.5705i			0.457200i	0.973520	+	0.228600i	$0.0734148\pi$
$881$			13.5705i			0.457200i	−0.973520	+	0.228600i	$0.926585\pi$
$882$	−16.7636	−	2.33436i	−0.564461	−	0.0786020i
$883$		−	46.0353i		−	1.54921i	−0.632444	−	0.774606i	$-0.717948\pi$
$883$		−	46.0353i		−	1.54921i	0.632444	−	0.774606i	$-0.282052\pi$
$884$	3.81393	+	6.83441i	0.128276	+	0.229866i
$885$		0			0
$886$	36.5486	−	9.50783i	1.22788	−	0.319422i
$887$	9.90855	+	17.1621i	0.332696	+	0.576247i	0.983040	−	0.183393i	$-0.0587082\pi$
$887$	9.90855	+	17.1621i	0.332696	+	0.576247i	−0.650343	+	0.759641i	$0.725375\pi$
$888$	−2.44787	−	56.2729i	−0.0821453	−	1.88840i
$889$	17.5143	−	30.3356i	0.587409	−	1.01742i
$890$		0			0
$891$	−5.50178	+	20.5061i	−0.184316	+	0.686980i
$892$	−24.3514	+	40.7910i	−0.815346	+	1.36578i
$893$	19.9059	+	11.4927i	0.666125	+	0.384587i
$894$	17.1340	−	11.2666i	0.573047	−	0.376811i
$895$		0			0
$896$	−36.6756	+	7.84436i	−1.22525	+	0.262062i
$897$	17.8153	+	52.4962i	0.594835	+	1.75280i
$898$	24.0175	−	23.6695i	0.801475	−	0.789860i
$899$	−0.283722			−0.00946265
$900$		0			0
$901$	−0.686641			−0.0228753
$902$	−6.72812	+	6.63062i	−0.224022	+	0.220776i
$903$	−47.0374	−	9.36031i	−1.56531	−	0.311492i
$904$	13.8001	−	47.3320i	0.458983	−	1.57424i
$905$		0			0
$906$	−35.8917	−	18.0304i	−1.19242	−	0.599019i
$907$	−42.3752	−	24.4653i	−1.40705	−	0.812358i	−0.411943	−	0.911209i	$-0.635150\pi$
$907$	−42.3752	−	24.4653i	−1.40705	−	0.812358i	−0.995102	+	0.0988513i	$0.968483\pi$
$908$	−47.8386	−	28.5587i	−1.58758	−	0.947752i
$909$	−8.91637	+	21.5161i	−0.295737	+	0.713643i
$910$		0			0
$911$	16.0978	−	27.8822i	0.533343	−	0.923778i	−0.465898	−	0.884838i	$-0.654269\pi$
$911$	16.0978	−	27.8822i	0.533343	−	0.923778i	0.999242	−	0.0389396i	$-0.0123980\pi$
$912$	−15.3983	−	14.3227i	−0.509889	−	0.474272i
$913$	3.06588	+	5.31026i	0.101466	+	0.175744i
$914$	−21.5646	+	5.60985i	−0.713292	+	0.185557i
$915$		0			0
$916$	29.2006	−	16.2953i	0.964814	−	0.538413i
$917$		−	53.8956i		−	1.77979i
$918$	6.41935	−	1.22662i	0.211870	−	0.0404845i
$919$			37.8553i			1.24873i	0.781133	+	0.624365i	$0.214642\pi$
$919$			37.8553i			1.24873i	−0.781133	+	0.624365i	$0.785358\pi$
$920$		0			0
$921$	0.540923	+	0.474455i	0.0178240	+	0.0156338i
$922$	−3.80093	−	14.6110i	−0.125177	−	0.481187i
$923$	−25.7942	−	44.6768i	−0.849026	−	1.47056i
$924$	26.4892	+	5.67445i	0.871429	+	0.186676i
$925$		0			0
$926$	−8.66098	−	2.38859i	−0.284618	−	0.0784939i
$927$	24.0300	+	31.3271i	0.789248	+	1.02892i
$928$	−1.51347	−	6.60333i	−0.0496822	−	0.216765i
$929$	−14.4535	−	8.34474i	−0.474205	−	0.273782i	0.243794	−	0.969827i	$-0.421608\pi$
$929$	−14.4535	−	8.34474i	−0.474205	−	0.273782i	−0.717998	+	0.696045i	$0.754941\pi$
$930$		0			0
$931$	−10.4868	+	6.05458i	−0.343693	+	0.198431i
$932$	3.35841	+	0.0490261i	0.110008	+	0.00160590i
$933$	−0.966795	−	0.192390i	−0.0316514	−	0.00629855i
$934$	7.70506	+	7.81836i	0.252117	+	0.255824i
$935$		0			0
$936$	5.68861	−	36.9000i	0.185938	−	1.20611i
$937$	41.7514			1.36396			0.681979	−	0.731372i	$-0.261120\pi$
$937$	41.7514			1.36396			0.681979	+	0.731372i	$0.261120\pi$
$938$	20.8789	+	21.1859i	0.681721	+	0.691745i
$939$	15.6200	+	46.0273i	0.509739	+	1.50204i
$940$		0			0
$941$	9.78882	−	5.65158i	0.319106	−	0.184236i	−0.331888	−	0.943319i	$-0.607686\pi$
$941$	9.78882	−	5.65158i	0.319106	−	0.184236i	0.650994	+	0.759083i	$0.274352\pi$
$942$	14.4164	+	21.9242i	0.469711	+	0.714329i
$943$	17.8369	+	10.2982i	0.580851	+	0.335354i
$944$	4.04076	+	7.49595i	0.131516	+	0.243972i
$945$		0			0
$946$	26.8634	+	7.40858i	0.873404	+	0.240874i
$947$	−2.56935	+	4.45025i	−0.0834928	+	0.144614i	−0.904748	−	0.425947i	$-0.859941\pi$
$947$	−2.56935	+	4.45025i	−0.0834928	+	0.144614i	0.821255	+	0.570561i	$0.193274\pi$
$948$	−11.0071	−	34.0605i	−0.357495	−	1.10623i
$949$	13.4398	+	23.2784i	0.436274	+	0.755649i
$950$		0			0
$951$	−21.7709	+	7.38824i	−0.705970	+	0.239580i
$952$	−1.98142	−	8.10015i	−0.0642181	−	0.262527i
$953$		−	22.9718i		−	0.744131i	−0.928206	−	0.372066i	$-0.878650\pi$
$953$		−	22.9718i		−	0.744131i	0.928206	−	0.372066i	$-0.121350\pi$
$954$	2.58372	+	2.01336i	0.0836510	+	0.0651851i
$955$		0			0
$956$	18.8997	−	10.5470i	0.611260	−	0.341113i
$957$	−0.955025	+	4.79919i	−0.0308716	+	0.155136i
$958$	−9.76032	+	2.53907i	−0.315342	+	0.0820336i
$959$	21.8654	+	37.8720i	0.706072	+	1.22295i
$960$		0			0
$961$	−15.4719	+	26.7982i	−0.499095	+	0.864457i
$962$	19.0211	−	68.9703i	0.613265	−	2.22369i
$963$	0.0986235	+	0.750067i	0.00317810	+	0.0241706i
$964$	−18.7408	−	11.1879i	−0.603601	−	0.360337i
$965$		0			0
$966$	−3.42802	−	58.9666i	−0.110295	−	1.89722i
$967$	−36.5239	+	21.0871i	−1.17453	+	0.678115i	−0.954743	−	0.297433i	$-0.903869\pi$
$967$	−36.5239	+	21.0871i	−1.17453	+	0.678115i	−0.219787	+	0.975548i	$0.570536\pi$
$968$	14.7579	+	4.30280i	0.474337	+	0.138297i
$969$	3.08324	−	3.51519i	0.0990481	−	0.112924i
$970$		0			0
$971$	−29.9678			−0.961712			−0.480856	−	0.876799i	$-0.659674\pi$
$971$	−29.9678			−0.961712			−0.480856	+	0.876799i	$0.659674\pi$
$972$	−27.7517	−	14.2072i	−0.890135	−	0.455697i
$973$	21.4947			0.689090
$974$	15.2188	−	14.9982i	0.487641	−	0.480574i
$975$		0			0
$976$	−8.03573	+	13.0248i	−0.257217	+	0.416915i
$977$	32.1452	−	18.5590i	1.02842	−	0.593756i	0.111885	−	0.993721i	$-0.464311\pi$
$977$	32.1452	−	18.5590i	1.02842	−	0.593756i	0.916530	+	0.399965i	$0.130978\pi$
$978$	−0.189904	−	3.26660i	−0.00607245	−	0.104454i
$979$	−9.56383	−	5.52168i	−0.305661	−	0.176474i
$980$		0			0
$981$	0.179538	+	1.36545i	0.00573221	+	0.0435955i
$982$	−11.0701	+	40.1402i	−0.353262	+	1.28092i
$983$	14.3704	−	24.8903i	0.458345	−	0.793876i	−0.540529	−	0.841325i	$-0.681776\pi$
$983$	14.3704	−	24.8903i	0.458345	−	0.793876i	0.998874	+	0.0474493i	$0.0151093\pi$
$984$	−7.45119	−	11.7002i	−0.237535	−	0.372988i
$985$		0			0
$986$	1.45775	−	0.379221i	0.0464242	−	0.0120769i
$987$	8.48593	−	42.6434i	0.270110	−	1.35735i
$988$	−13.0168	−	23.3255i	−0.414119	−	0.742084i
$989$		−	60.7584i		−	1.93201i
$990$		0			0
$991$		−	5.20653i		−	0.165391i	−0.996575	−	0.0826954i	$-0.973647\pi$
$991$		−	5.20653i		−	0.165391i	0.996575	−	0.0826954i	$-0.0263529\pi$
$992$	1.28099	+	0.393862i	0.0406716	+	0.0125051i
$993$	14.0905	−	4.78180i	0.447149	−	0.151746i
$994$	13.8383	+	53.1953i	0.438925	+	1.68725i
$995$		0			0
$996$	−8.56784	+	2.76882i	−0.271483	+	0.0877334i
$997$	−10.4918	+	18.1724i	−0.332279	+	0.575525i	−0.982958	−	0.183828i	$-0.941151\pi$
$997$	−10.4918	+	18.1724i	−0.332279	+	0.575525i	0.650679	+	0.759353i	$0.274484\pi$
$998$	28.4612	+	7.84924i	0.900924	+	0.248463i
$999$	−49.6663	−	33.2036i	−1.57137	−	1.05051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.g.551.7		48
4.3	odd	2	inner	900.2.r.g.551.3		48
5.2	odd	4		180.2.n.d.119.19	yes	48
5.3	odd	4		180.2.n.d.119.6	yes	48
5.4	even	2	inner	900.2.r.g.551.18		48
9.5	odd	6	inner	900.2.r.g.851.3		48
15.2	even	4		540.2.n.d.359.6		48
15.8	even	4		540.2.n.d.359.19		48
20.3	even	4		180.2.n.d.119.10	yes	48
20.7	even	4		180.2.n.d.119.15	yes	48
20.19	odd	2	inner	900.2.r.g.551.22		48
36.23	even	6	inner	900.2.r.g.851.7		48
45.13	odd	12		540.2.n.d.179.10		48
45.14	odd	6	inner	900.2.r.g.851.22		48
45.22	odd	12		540.2.n.d.179.15		48
45.23	even	12		180.2.n.d.59.15	yes	48
45.32	even	12		180.2.n.d.59.10	yes	48
60.23	odd	4		540.2.n.d.359.15		48
60.47	odd	4		540.2.n.d.359.10		48
180.23	odd	12		180.2.n.d.59.19	yes	48
180.59	even	6	inner	900.2.r.g.851.18		48
180.67	even	12		540.2.n.d.179.19		48
180.103	even	12		540.2.n.d.179.6		48
180.167	odd	12		180.2.n.d.59.6	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.6	✓	48	180.167	odd	12
180.2.n.d.59.10	yes	48	45.32	even	12
180.2.n.d.59.15	yes	48	45.23	even	12
180.2.n.d.59.19	yes	48	180.23	odd	12
180.2.n.d.119.6	yes	48	5.3	odd	4
180.2.n.d.119.10	yes	48	20.3	even	4
180.2.n.d.119.15	yes	48	20.7	even	4
180.2.n.d.119.19	yes	48	5.2	odd	4
540.2.n.d.179.6		48	180.103	even	12
540.2.n.d.179.10		48	45.13	odd	12
540.2.n.d.179.15		48	45.22	odd	12
540.2.n.d.179.19		48	180.67	even	12
540.2.n.d.359.6		48	15.2	even	4
540.2.n.d.359.10		48	60.47	odd	4
540.2.n.d.359.15		48	60.23	odd	4
540.2.n.d.359.19		48	15.8	even	4
900.2.r.g.551.3		48	4.3	odd	2	inner
900.2.r.g.551.7		48	1.1	even	1	trivial
900.2.r.g.551.18		48	5.4	even	2	inner
900.2.r.g.551.22		48	20.19	odd	2	inner
900.2.r.g.851.3		48	9.5	odd	6	inner
900.2.r.g.851.7		48	36.23	even	6	inner
900.2.r.g.851.18		48	180.59	even	6	inner
900.2.r.g.851.22		48	45.14	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.992675 - 1.00727i) q^{2} +(1.14213 - 1.30213i) q^{3} +(-0.0291929 + 1.99979i) q^{4} +(-2.44536 + 0.142161i) q^{6} +(2.87089 + 1.65751i) q^{7} +(2.04331 - 1.95573i) q^{8} +(-0.391092 - 2.97440i) q^{9} +(1.17952 - 2.04298i) q^{11} +(2.57064 + 2.32202i) q^{12} +(2.20004 + 3.81058i) q^{13} +(-1.18030 - 4.53714i) q^{14} +(-3.99830 - 0.116759i) q^{16} -0.889368i q^{17} +(-2.60780 + 3.34655i) q^{18} +3.03537i q^{19} +(5.43722 - 1.84519i) q^{21} +(-3.22872 + 0.839925i) q^{22} +(3.63703 + 6.29952i) q^{23} +(-0.212904 - 4.89435i) q^{24} +(1.65437 - 5.99870i) q^{26} +(-4.31973 - 2.88789i) q^{27} +(-3.39848 + 5.69278i) q^{28} +(-1.03714 - 0.598791i) q^{29} +(0.205172 - 0.118456i) q^{31} +(3.85140 + 4.14327i) q^{32} +(-1.31308 - 3.86923i) q^{33} +(-0.895835 + 0.882853i) q^{34} +(5.95958 - 0.695270i) q^{36} +11.4975 q^{37} +(3.05745 - 3.01314i) q^{38} +(7.47460 + 1.48743i) q^{39} +(2.45213 - 1.41574i) q^{41} +(-7.25600 - 3.64508i) q^{42} +(-7.23369 - 4.17637i) q^{43} +(4.05110 + 2.41842i) q^{44} +(2.73494 - 9.91686i) q^{46} +(3.78624 - 6.55796i) q^{47} +(-4.71860 + 5.07295i) q^{48} +(1.99467 + 3.45488i) q^{49} +(-1.15807 - 1.01577i) q^{51} +(-7.68457 + 4.28837i) q^{52} -0.772055i q^{53} +(1.37920 + 7.21788i) q^{54} +(9.10776 - 2.22789i) q^{56} +(3.95246 + 3.46678i) q^{57} +(0.426394 + 1.63908i) q^{58} +(-1.06446 - 1.84370i) q^{59} +(1.91303 - 3.31346i) q^{61} +(-0.322986 - 0.0890754i) q^{62} +(3.80731 - 9.18741i) q^{63} +(0.350216 - 7.99233i) q^{64} +(-2.59391 + 5.16352i) q^{66} +(-5.49472 + 3.17238i) q^{67} +(1.77855 + 0.0259632i) q^{68} +(12.3568 + 2.45896i) q^{69} -11.7244 q^{71} +(-6.61625 - 5.31274i) q^{72} +6.10889 q^{73} +(-11.4133 - 11.5811i) q^{74} +(-6.07010 - 0.0886114i) q^{76} +(6.77253 - 3.91012i) q^{77} +(-5.92160 - 9.00548i) q^{78} +(-8.94873 - 5.16655i) q^{79} +(-8.69409 + 2.32653i) q^{81} +(-3.86020 - 1.06459i) q^{82} +(-1.29963 + 2.25103i) q^{83} +(3.53126 + 10.9271i) q^{84} +(2.97396 + 11.4321i) q^{86} +(-1.96425 + 0.666593i) q^{87} +(-1.58541 - 6.48127i) q^{88} -4.68130i q^{89} +14.5863i q^{91} +(-12.7039 + 7.08939i) q^{92} +(0.0800869 - 0.402452i) q^{93} +(-10.3642 + 2.69615i) q^{94} +(9.79387 - 0.282883i) q^{96} +(-3.08700 + 5.34684i) q^{97} +(1.49994 - 5.43875i) q^{98} +(-6.53795 - 2.70936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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