LMFDB - Embedded newform 735.2.v.a.472.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(178,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("735.178");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.v (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			472.2
Character	$\chi$	$=$	735.472
Dual form			735.2.v.a.313.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.681344 + 2.54281i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-4.26961 - 2.46506i) q^{4} +(2.18437 + 0.478051i) q^{5} +2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.681344 + 2.54281i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-4.26961 - 2.46506i) q^{4} +(2.18437 + 0.478051i) q^{5} +2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.70390 + 5.22872i) q^{10} +(0.731395 - 1.26681i) q^{11} +(-4.76213 - 1.27601i) q^{12} +(0.887844 + 0.887844i) q^{13} +(2.23367 - 0.103594i) q^{15} +(5.22294 + 9.04639i) q^{16} +(-0.770902 - 2.87705i) q^{17} +(0.681344 + 2.54281i) q^{18} +(1.97993 + 3.42935i) q^{19} +(-8.14798 - 7.42570i) q^{20} +(2.72294 + 2.72294i) q^{22} +(5.64178 + 1.51171i) q^{23} +(3.85679 - 6.68016i) q^{24} +(4.54293 + 2.08848i) q^{25} +(-2.86255 + 1.65269i) q^{26} +(0.707107 - 0.707107i) q^{27} +5.18572i q^{29} +(-1.25848 + 5.75038i) q^{30} +(5.28575 + 3.05173i) q^{31} +(-11.6604 + 3.12439i) q^{32} +(0.378598 - 1.41295i) q^{33} +7.84104 q^{34} -4.93012 q^{36} +(0.825607 - 3.08121i) q^{37} +(-10.0692 + 2.69804i) q^{38} +(1.08738 + 0.627801i) q^{39} +(14.5217 - 9.30682i) q^{40} +0.769968i q^{41} +(-5.18572 + 5.18572i) q^{43} +(-6.24554 + 3.60587i) q^{44} +(2.13074 - 0.678180i) q^{45} +(-7.68800 + 13.3160i) q^{46} +(-11.7074 - 3.13699i) q^{47} +(7.38635 + 7.38635i) q^{48} +(-8.40592 + 10.1289i) q^{50} +(-1.48927 - 2.57949i) q^{51} +(-1.60216 - 5.97934i) q^{52} +(-0.199282 - 0.743732i) q^{53} +(1.31626 + 2.27982i) q^{54} +(2.20324 - 2.41754i) q^{55} +(2.80005 + 2.80005i) q^{57} +(-13.1863 - 3.53326i) q^{58} +(1.59816 - 2.76810i) q^{59} +(-9.79226 - 5.06382i) q^{60} +(1.23031 - 0.710320i) q^{61} +(-11.3614 + 11.3614i) q^{62} -10.8872i q^{64} +(1.51494 + 2.36381i) q^{65} +(3.33490 + 1.92541i) q^{66} +(8.10070 - 2.17058i) q^{67} +(-3.80064 + 14.1842i) q^{68} +5.84081 q^{69} +7.62611 q^{71} +(1.99642 - 7.45075i) q^{72} +(-9.30780 + 2.49402i) q^{73} +(7.27241 + 4.19873i) q^{74} +(4.92868 + 0.841520i) q^{75} -19.5226i q^{76} +(-2.33726 + 2.33726i) q^{78} +(3.91469 - 2.26015i) q^{79} +(7.08418 + 22.2575i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.95788 - 0.524613i) q^{82} +(-6.75794 - 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} +(-9.65306 - 16.7196i) q^{86} +(1.34216 + 5.00903i) q^{87} +(-2.92035 - 10.8989i) q^{88} +(-0.599954 - 1.03915i) q^{89} +(0.272713 + 5.88016i) q^{90} +(-20.3618 - 20.3618i) q^{92} +(5.89549 + 1.57969i) q^{93} +(15.9535 - 27.6323i) q^{94} +(2.68550 + 8.43747i) q^{95} +(-10.4544 + 6.03586i) q^{96} +(-8.68829 + 8.68829i) q^{97} -1.46279i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 48 q^{8}+O(q^{10}) $ 32 * q + 48 * q^8	$ 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) $ 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.681344	+	2.54281i	−0.481783	+	1.79804i	0.112345	+	0.993669i	$0.464164\pi$
$2$	−0.681344	+	2.54281i	−0.481783	+	1.79804i	−0.594128	+	0.804370i	$0.702503\pi$
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−4.26961	−	2.46506i	−2.13481	−	1.23253i
$5$	2.18437	+	0.478051i	0.976879	+	0.213791i
$5$	2.18437	+	0.478051i	0.976879	+	0.213791i
$6$			2.63251i			1.07472i
$7$		0			0
$7$		0			0
$8$	5.45433	−	5.45433i	1.92840	−	1.92840i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−2.70390	+	5.22872i	−0.855049	+	1.65347i
$11$	0.731395	−	1.26681i	0.220524	−	0.381958i	−0.734443	−	0.678670i	$-0.762557\pi$
$11$	0.731395	−	1.26681i	0.220524	−	0.381958i	0.954967	+	0.296712i	$0.0958900\pi$
$12$	−4.76213	−	1.27601i	−1.37471	−	0.368352i
$13$	0.887844	+	0.887844i	0.246244	+	0.246244i	0.819427	−	0.573183i	$-0.194292\pi$
$13$	0.887844	+	0.887844i	0.246244	+	0.246244i	−0.573183	+	0.819427i	$0.694292\pi$
$14$		0			0
$15$	2.23367	−	0.103594i	0.576730	−	0.0267479i
$16$	5.22294	+	9.04639i	1.30573	+	2.26160i
$17$	−0.770902	−	2.87705i	−0.186971	−	0.697786i	−0.994200	−	0.107547i	$-0.965700\pi$
$17$	−0.770902	−	2.87705i	−0.186971	−	0.697786i	0.807229	−	0.590239i	$-0.200966\pi$
$18$	0.681344	+	2.54281i	0.160594	+	0.599347i
$19$	1.97993	+	3.42935i	0.454228	+	0.786746i	0.998643	−	0.0520695i	$-0.0165817\pi$
$19$	1.97993	+	3.42935i	0.454228	+	0.786746i	−0.544415	+	0.838816i	$0.683248\pi$
$20$	−8.14798	−	7.42570i	−1.82194	−	1.66044i
$21$		0			0
$22$	2.72294	+	2.72294i	0.580532	+	0.580532i
$23$	5.64178	+	1.51171i	1.17639	+	0.315214i	0.793495	−	0.608577i	$-0.208259\pi$
$23$	5.64178	+	1.51171i	1.17639	+	0.315214i	0.382898	+	0.923790i	$0.374926\pi$
$24$	3.85679	−	6.68016i	0.787265	−	1.36358i
$25$	4.54293	+	2.08848i	0.908587	+	0.417696i
$26$	−2.86255	+	1.65269i	−0.561392	+	0.324120i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			5.18572i			0.962965i	0.876456	+	0.481482i	$0.159901\pi$
$29$			5.18572i			0.962965i	−0.876456	+	0.481482i	$0.840099\pi$
$30$	−1.25848	+	5.75038i	−0.229765	+	1.04987i
$31$	5.28575	+	3.05173i	0.949349	+	0.548107i	0.892879	−	0.450297i	$-0.148682\pi$
$31$	5.28575	+	3.05173i	0.949349	+	0.548107i	0.0564703	+	0.998404i	$0.482015\pi$
$32$	−11.6604	+	3.12439i	−2.06128	+	0.552319i
$33$	0.378598	−	1.41295i	0.0659054	−	0.245962i
$34$	7.84104			1.34473
$35$		0			0
$36$	−4.93012			−0.821687
$37$	0.825607	−	3.08121i	0.135729	−	0.506548i	−0.864265	−	0.503037i	$-0.832216\pi$
$37$	0.825607	−	3.08121i	0.135729	−	0.506548i	0.999994	−	0.00351049i	$-0.00111743\pi$
$38$	−10.0692	+	2.69804i	−1.63344	+	0.437679i
$39$	1.08738	+	0.627801i	0.174121	+	0.100529i
$40$	14.5217	−	9.30682i	2.29609	−	1.47154i
$41$			0.769968i			0.120249i	0.998191	+	0.0601244i	$0.0191497\pi$
$41$			0.769968i			0.120249i	−0.998191	+	0.0601244i	$0.980850\pi$
$42$		0			0
$43$	−5.18572	+	5.18572i	−0.790816	+	0.790816i	−0.981627	−	0.190811i	$-0.938888\pi$
$43$	−5.18572	+	5.18572i	−0.790816	+	0.790816i	0.190811	+	0.981627i	$0.438888\pi$
$44$	−6.24554	+	3.60587i	−0.941551	+	0.543605i
$45$	2.13074	−	0.678180i	0.317633	−	0.101097i
$46$	−7.68800	+	13.3160i	−1.13353	+	1.96334i
$47$	−11.7074	−	3.13699i	−1.70770	−	0.457577i	−0.732841	−	0.680400i	$-0.761806\pi$
$47$	−11.7074	−	3.13699i	−1.70770	−	0.457577i	−0.974859	+	0.222823i	$0.928473\pi$
$48$	7.38635	+	7.38635i	1.06613	+	1.06613i
$49$		0			0
$50$	−8.40592	+	10.1289i	−1.18878	+	1.43244i
$51$	−1.48927	−	2.57949i	−0.208539	−	0.361201i
$52$	−1.60216	−	5.97934i	−0.222180	−	0.829185i
$53$	−0.199282	−	0.743732i	−0.0273735	−	0.102159i	0.950888	−	0.309537i	$-0.100174\pi$
$53$	−0.199282	−	0.743732i	−0.0273735	−	0.102159i	−0.978261	+	0.207377i	$0.933507\pi$
$54$	1.31626	+	2.27982i	0.179120	+	0.310245i
$55$	2.20324	−	2.41754i	0.297084	−	0.325981i
$56$		0			0
$57$	2.80005	+	2.80005i	0.370876	+	0.370876i
$58$	−13.1863	−	3.53326i	−1.73145	−	0.463940i
$59$	1.59816	−	2.76810i	0.208063	−	0.360376i	−0.743041	−	0.669246i	$-0.766617\pi$
$59$	1.59816	−	2.76810i	0.208063	−	0.360376i	0.951104	+	0.308870i	$0.0999507\pi$
$60$	−9.79226	−	5.06382i	−1.26418	−	0.653736i
$61$	1.23031	−	0.710320i	0.157525	−	0.0909472i	−0.419165	−	0.907910i	$-0.637677\pi$
$61$	1.23031	−	0.710320i	0.157525	−	0.0909472i	0.576690	+	0.816963i	$0.304344\pi$
$62$	−11.3614	+	11.3614i	−1.44290	+	1.44290i
$63$		0			0
$64$		−	10.8872i		−	1.36090i
$65$	1.51494	+	2.36381i	0.187906	+	0.293195i
$66$	3.33490	+	1.92541i	0.410498	+	0.237001i
$67$	8.10070	−	2.17058i	0.989658	−	0.265178i	0.272551	−	0.962141i	$-0.412133\pi$
$67$	8.10070	−	2.17058i	0.989658	−	0.265178i	0.717107	+	0.696963i	$0.245466\pi$
$68$	−3.80064	+	14.1842i	−0.460896	+	1.72009i
$69$	5.84081			0.703150
$70$		0			0
$71$	7.62611			0.905053			0.452526	−	0.891751i	$-0.350523\pi$
$71$	7.62611			0.905053			0.452526	+	0.891751i	$0.350523\pi$
$72$	1.99642	−	7.45075i	0.235281	−	0.878080i
$73$	−9.30780	+	2.49402i	−1.08940	+	0.291903i	−0.758439	−	0.651744i	$-0.774038\pi$
$73$	−9.30780	+	2.49402i	−1.08940	+	0.291903i	−0.330956	+	0.943646i	$0.607371\pi$
$74$	7.27241	+	4.19873i	0.845401	+	0.488092i
$75$	4.92868	+	0.841520i	0.569114	+	0.0971703i
$76$		−	19.5226i		−	2.23940i
$77$		0			0
$78$	−2.33726	+	2.33726i	−0.264643	+	0.264643i
$79$	3.91469	−	2.26015i	0.440437	−	0.254286i	−0.263346	−	0.964701i	$-0.584826\pi$
$79$	3.91469	−	2.26015i	0.440437	−	0.254286i	0.703783	+	0.710415i	$0.251493\pi$
$80$	7.08418	+	22.2575i	0.792035	+	2.48846i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−1.95788	−	0.524613i	−0.216212	−	0.0579338i
$83$	−6.75794	−	6.75794i	−0.741781	−	0.741781i	0.231140	−	0.972921i	$-0.425754\pi$
$83$	−6.75794	−	6.75794i	−0.741781	−	0.741781i	−0.972921	+	0.231140i	$0.925754\pi$
$84$		0			0
$85$	−0.308559	−	6.65306i	−0.0334679	−	0.721626i
$86$	−9.65306	−	16.7196i	−1.04092	−	1.80292i
$87$	1.34216	+	5.00903i	0.143895	+	0.537024i
$88$	−2.92035	−	10.8989i	−0.311310	−	1.16182i
$89$	−0.599954	−	1.03915i	−0.0635950	−	0.110150i	0.832475	−	0.554063i	$-0.186923\pi$
$89$	−0.599954	−	1.03915i	−0.0635950	−	0.110150i	−0.896070	+	0.443913i	$0.853590\pi$
$90$	0.272713	+	5.88016i	0.0287465	+	0.619823i
$91$		0			0
$92$	−20.3618	−	20.3618i	−2.12286	−	2.12286i
$93$	5.89549	+	1.57969i	0.611334	+	0.163806i
$94$	15.9535	−	27.6323i	1.64548	−	2.85006i
$95$	2.68550	+	8.43747i	0.275527	+	0.865666i
$96$	−10.4544	+	6.03586i	−1.06700	+	0.616032i
$97$	−8.68829	+	8.68829i	−0.882162	+	0.882162i	−0.993754	−	0.111592i	$-0.964405\pi$
$97$	−8.68829	+	8.68829i	−0.882162	+	0.882162i	0.111592	+	0.993754i	$0.464405\pi$
$98$		0			0
$99$		−	1.46279i		−	0.147016i
$100$	−14.2483	−	20.1156i	−1.42483	−	2.01156i
$101$	−13.2866	−	7.67102i	−1.32207	−	0.763295i	−0.338008	−	0.941143i	$-0.609753\pi$
$101$	−13.2866	−	7.67102i	−1.32207	−	0.763295i	−0.984058	+	0.177848i	$0.943086\pi$
$102$	7.57386	−	2.02941i	0.749924	−	0.200941i
$103$	3.04085	−	11.3486i	0.299624	−	1.11821i	−0.637851	−	0.770160i	$-0.720177\pi$
$103$	3.04085	−	11.3486i	0.299624	−	1.11821i	0.937475	−	0.348052i	$-0.113157\pi$
$104$	9.68519			0.949711
$105$		0			0
$106$	2.02695			0.196875
$107$	1.60693	−	5.99715i	0.155348	−	0.579766i	−0.843727	−	0.536772i	$-0.819644\pi$
$107$	1.60693	−	5.99715i	0.155348	−	0.579766i	0.999075	−	0.0429945i	$-0.0136898\pi$
$108$	−4.76213	+	1.27601i	−0.458237	+	0.122784i
$109$	−6.44831	−	3.72294i	−0.617636	−	0.356593i	0.158312	−	0.987389i	$-0.449395\pi$
$109$	−6.44831	−	3.72294i	−0.617636	−	0.356593i	−0.775948	+	0.630797i	$0.782728\pi$
$110$	4.64619	+	7.24960i	0.442997	+	0.691222i
$111$		−	3.18990i		−	0.302772i
$112$		0			0
$113$	2.54445	−	2.54445i	0.239362	−	0.239362i	−0.577224	−	0.816586i	$-0.695864\pi$
$113$	2.54445	−	2.54445i	0.239362	−	0.239362i	0.816586	+	0.577224i	$0.195864\pi$
$114$	−9.02780	+	5.21220i	−0.845531	+	0.488168i
$115$	11.6011	+	5.99920i	1.08180	+	0.559428i
$116$	12.7831	−	22.1410i	1.18688	−	2.05574i
$117$	1.21282	+	0.324974i	0.112125	+	0.0300438i
$118$	5.94986	+	5.94986i	0.547729	+	0.547729i
$119$		0			0
$120$	11.6181	−	12.7482i	1.06058	−	1.16375i
$121$	4.43012	+	7.67320i	0.402738	+	0.697564i
$122$	0.967945	+	3.61242i	0.0876337	+	0.327053i
$123$	0.199282	+	0.743732i	0.0179687	+	0.0670600i
$124$	−15.0454	−	26.0594i	−1.35112	−	2.34020i
$125$	8.92504	+	6.73377i	0.798280	+	0.602287i
$126$		0			0
$127$	7.86025	+	7.86025i	0.697484	+	0.697484i	0.963867	−	0.266383i	$-0.0858286\pi$
$127$	7.86025	+	7.86025i	0.697484	+	0.697484i	−0.266383	+	0.963867i	$0.585829\pi$
$128$	4.36334	+	1.16915i	0.385668	+	0.103339i
$129$	−3.66686	+	6.35119i	−0.322849	+	0.559191i
$130$	−7.04293	+	2.24165i	−0.617706	+	0.196605i
$131$	5.35391	−	3.09108i	0.467773	−	0.270069i	−0.247534	−	0.968879i	$-0.579620\pi$
$131$	5.35391	−	3.09108i	0.467773	−	0.270069i	0.715307	+	0.698810i	$0.246287\pi$
$132$	−5.09947	+	5.09947i	−0.443851	+	0.443851i
$133$		0			0
$134$			22.0775i			1.90720i
$135$	1.88262	−	1.20655i	0.162030	−	0.103843i
$136$	−19.8971	−	11.4876i	−1.70616	−	0.985054i
$137$	−12.3703	+	3.31460i	−1.05686	+	0.283185i	−0.745085	−	0.666970i	$-0.767591\pi$
$137$	−12.3703	+	3.31460i	−1.05686	+	0.283185i	−0.311777	+	0.950155i	$0.600924\pi$
$138$	−3.97960	+	14.8521i	−0.338766	+	1.26429i
$139$	−11.9913			−1.01709			−0.508544	−	0.861036i	$-0.669816\pi$
$139$	−11.9913			−1.01709			−0.508544	+	0.861036i	$0.669816\pi$
$140$		0			0
$141$	−12.1204			−1.02072
$142$	−5.19601	+	19.3918i	−0.436039	+	1.62732i
$143$	1.77410	−	0.475368i	0.148357	−	0.0397523i
$144$	9.04639	+	5.22294i	0.753866	+	0.435245i
$145$	−2.47904	+	11.3275i	−0.205873	+	0.940701i
$146$		−	25.3673i		−	2.09941i
$147$		0			0
$148$	−11.1204	+	11.1204i	−0.914091	+	0.914091i
$149$	−0.0838539	+	0.0484130i	−0.00686958	+	0.00396615i	−0.503431	−	0.864036i	$-0.667929\pi$
$149$	−0.0838539	+	0.0484130i	−0.00686958	+	0.00396615i	0.496561	+	0.868002i	$0.334596\pi$
$150$	−5.49795	+	11.9593i	−0.448906	+	0.976475i
$151$	6.72748	−	11.6523i	0.547475	−	0.948254i	−0.450972	−	0.892538i	$-0.648923\pi$
$151$	6.72748	−	11.6523i	0.547475	−	0.948254i	0.998447	−	0.0557157i	$-0.0177440\pi$
$152$	29.5040	+	7.90558i	2.39309	+	0.641227i
$153$	−2.10614	−	2.10614i	−0.170272	−	0.170272i
$154$		0			0
$155$	10.0871	+	9.19296i	0.810219	+	0.738397i
$156$	−3.09513	−	5.36093i	−0.247809	−	0.429218i
$157$	0.603054	+	2.25063i	0.0481290	+	0.179620i	0.985806	−	0.167888i	$-0.0536947\pi$
$157$	0.603054	+	2.25063i	0.0481290	+	0.179620i	−0.937677	+	0.347508i	$0.887028\pi$
$158$	3.07988	+	11.4943i	0.245022	+	0.914434i
$159$	−0.384984	−	0.666812i	−0.0305312	−	0.0528816i
$160$	−26.9642	+	1.25056i	−2.13171	+	0.0988653i
$161$		0			0
$162$	1.86147	+	1.86147i	0.146251	+	0.146251i
$163$	14.0354	+	3.76077i	1.09934	+	0.294566i	0.762495	−	0.646995i	$-0.223974\pi$
$163$	14.0354	+	3.76077i	1.09934	+	0.294566i	0.336842	+	0.941561i	$0.390641\pi$
$164$	1.89802	−	3.28746i	0.148210	−	0.256708i
$165$	1.50246	−	2.90541i	0.116966	−	0.226186i
$166$	21.7887	−	12.5797i	1.69113	−	0.976373i
$167$	0.293008	−	0.293008i	0.0226737	−	0.0226737i	−0.695679	−	0.718353i	$-0.744896\pi$
$167$	0.293008	−	0.293008i	0.0226737	−	0.0226737i	0.718353	+	0.695679i	$0.244896\pi$
$168$		0			0
$169$		−	11.4235i		−	0.878728i
$170$	17.1277	+	3.74842i	1.31364	+	0.287490i
$171$	3.42935	+	1.97993i	0.262249	+	0.151409i
$172$	34.9242	−	9.35790i	2.66294	−	0.713533i
$173$	−1.26348	+	4.71537i	−0.0960606	+	0.358503i	−0.997178	−	0.0750719i	$-0.976081\pi$
$173$	−1.26348	+	4.71537i	−0.0960606	+	0.358503i	0.901118	+	0.433575i	$0.142748\pi$
$174$	−13.6515			−1.03492
$175$		0			0
$176$	15.2801			1.15178
$177$	0.827271	−	3.08742i	0.0621815	−	0.232064i
$178$	3.05114	−	0.817551i	0.228693	−	0.0612781i
$179$	1.72994	+	0.998779i	0.129302	+	0.0746523i	0.563256	−	0.826283i	$-0.309549\pi$
$179$	1.72994	+	0.998779i	0.129302	+	0.0746523i	−0.433954	+	0.900935i	$0.642882\pi$
$180$	−10.7692	−	2.35685i	−0.802689	−	0.175669i
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$		0			0
$183$	1.00454	−	1.00454i	0.0742581	−	0.0742581i
$184$	39.0175	−	22.5268i	2.87641	−	1.66070i
$185$	3.27641	−	6.33581i	0.240886	−	0.465818i
$186$	−8.03372	+	13.9148i	−0.589061	+	1.02028i
$187$	−4.20851	−	1.12767i	−0.307757	−	0.0824632i
$188$	42.2532	+	42.2532i	3.08163	+	3.08163i
$189$		0			0
$190$	−23.2847	+	1.07991i	−1.68925	+	0.0783447i
$191$	3.91712	+	6.78465i	0.283433	+	0.490920i	0.972228	−	0.234036i	$-0.0751934\pi$
$191$	3.91712	+	6.78465i	0.283433	+	0.490920i	−0.688795	+	0.724956i	$0.741860\pi$
$192$	−2.81781	−	10.5162i	−0.203358	−	0.758943i
$193$	4.96393	+	18.5257i	0.357312	+	1.33351i	0.877550	+	0.479485i	$0.159176\pi$
$193$	4.96393	+	18.5257i	0.357312	+	1.33351i	−0.520239	+	0.854021i	$0.674157\pi$
$194$	−16.1730	−	28.0124i	−1.16115	−	2.01117i
$195$	2.07512	+	1.89117i	0.148603	+	0.135430i
$196$		0			0
$197$	−11.4791	−	11.4791i	−0.817853	−	0.817853i	0.167943	−	0.985797i	$-0.446287\pi$
$197$	−11.4791	−	11.4791i	−0.817853	−	0.817853i	−0.985797	+	0.167943i	$0.946287\pi$
$198$	3.71960	+	0.996663i	0.264340	+	0.0708298i
$199$	−10.0734	+	17.4476i	−0.714084	+	1.23683i	0.249228	+	0.968445i	$0.419823\pi$
$199$	−10.0734	+	17.4476i	−0.714084	+	1.23683i	−0.963312	+	0.268384i	$0.913510\pi$
$200$	36.1699	−	13.3874i	2.55760	−	0.946632i
$201$	7.26289	−	4.19323i	0.512285	−	0.295768i
$202$	28.5587	−	28.5587i	2.00938	−	2.00938i
$203$		0			0
$204$			14.6846i			1.02812i
$205$	−0.368084	+	1.68189i	−0.0257081	+	0.117469i
$206$	26.7855	+	15.4646i	1.86623	+	1.07747i
$207$	5.64178	−	1.51171i	0.392131	−	0.105071i
$208$	−3.39463	+	12.6689i	−0.235375	+	0.878433i
$209$	5.79246			0.400673
$210$		0			0
$211$	11.9662			0.823785			0.411892	−	0.911233i	$-0.364868\pi$
$211$	11.9662			0.823785			0.411892	+	0.911233i	$0.364868\pi$
$212$	−0.982486	+	3.66669i	−0.0674774	+	0.251829i
$213$	7.36626	−	1.97378i	0.504728	−	0.135241i
$214$	14.1548	+	8.17225i	0.967599	+	0.558644i
$215$	−13.8066	+	8.84849i	−0.941601	+	0.603462i
$216$		−	7.71359i		−	0.524843i
$217$		0			0
$218$	13.8602	−	13.8602i	0.938734	−	0.938734i
$219$	−8.34514	+	4.81807i	−0.563912	+	0.325575i
$220$	−15.3664	+	4.89085i	−1.03600	+	0.329741i
$221$	1.86993	−	3.23881i	0.125785	−	0.217866i
$222$	8.11132	+	2.17342i	0.544396	+	0.145871i
$223$	−0.660910	−	0.660910i	−0.0442578	−	0.0442578i	0.684632	−	0.728889i	$-0.259963\pi$
$223$	−0.660910	−	0.660910i	−0.0442578	−	0.0442578i	−0.728889	+	0.684632i	$0.759963\pi$
$224$		0			0
$225$	4.97854	−	0.462789i	0.331902	−	0.0308526i
$226$	4.73641	+	8.20370i	0.315061	+	0.545702i
$227$	−6.35007	−	23.6988i	−0.421469	−	1.57294i	−0.771516	−	0.636210i	$-0.780501\pi$
$227$	−6.35007	−	23.6988i	−0.421469	−	1.57294i	0.350047	−	0.936732i	$-0.386166\pi$
$228$	−5.05283	−	18.8574i	−0.334632	−	1.24886i
$229$	12.5391	+	21.7184i	0.828607	+	1.43519i	0.899131	+	0.437679i	$0.144200\pi$
$229$	12.5391	+	21.7184i	0.828607	+	1.43519i	−0.0705240	+	0.997510i	$0.522467\pi$
$230$	−23.1592	+	25.4118i	−1.52707	+	1.67560i
$231$		0			0
$232$	28.2847	+	28.2847i	1.85698	+	1.85698i
$233$	−3.06178	−	0.820401i	−0.200584	−	0.0537462i	0.157128	−	0.987578i	$-0.449776\pi$
$233$	−3.06178	−	0.820401i	−0.200584	−	0.0537462i	−0.357712	+	0.933832i	$0.616443\pi$
$234$	−1.65269	+	2.86255i	−0.108040	+	0.187131i
$235$	−24.0736	−	12.4491i	−1.57039	−	0.812088i
$236$	−13.6471	+	7.87915i	−0.888350	+	0.512889i
$237$	3.19633	−	3.19633i	0.207624	−	0.207624i
$238$		0			0
$239$		−	21.3769i		−	1.38276i	−0.722492	−	0.691380i	$-0.757003\pi$
$239$		−	21.3769i		−	1.38276i	0.722492	−	0.691380i	$-0.242997\pi$
$240$	12.6035	+	19.6656i	0.813549	+	1.26941i
$241$	0.540512	+	0.312065i	0.0348174	+	0.0201018i	0.517308	−	0.855799i	$-0.326934\pi$
$241$	0.540512	+	0.312065i	0.0348174	+	0.0201018i	−0.482490	+	0.875901i	$0.660268\pi$
$242$	−22.5299	+	6.03688i	−1.44828	+	0.388065i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−7.00393			−0.448381
$245$		0			0
$246$	−2.02695			−0.129234
$247$	−1.28685	+	4.80260i	−0.0818805	+	0.305582i
$248$	45.4754	−	12.1851i	2.88769	−	0.773754i
$249$	−8.27676	−	4.77859i	−0.524518	−	0.302831i
$250$	−23.2037	+	18.1067i	−1.46753	+	1.14517i
$251$			16.3443i			1.03164i	0.856696	+	0.515822i	$0.172513\pi$
$251$			16.3443i			1.03164i	−0.856696	+	0.515822i	$0.827487\pi$
$252$		0			0
$253$	6.04143	−	6.04143i	0.379821	−	0.379821i
$254$	−25.3427	+	14.6316i	−1.59014	+	0.918068i
$255$	−2.01998	−	6.34650i	−0.126496	−	0.397433i
$256$	4.94133	−	8.55863i	0.308833	−	0.534914i
$257$	−29.1038	−	7.79833i	−1.81544	−	0.486446i	−0.819235	−	0.573458i	$-0.805602\pi$
$257$	−29.1038	−	7.79833i	−1.81544	−	0.486446i	−0.996207	+	0.0870116i	$0.972268\pi$
$258$	−13.6515	−	13.6515i	−0.849904	−	0.849904i
$259$		0			0
$260$	−0.641275	−	13.8270i	−0.0397702	−	0.857514i
$261$	2.59286	+	4.49097i	0.160494	+	0.277984i
$262$	4.21218	+	15.7201i	0.260230	+	0.971190i
$263$	−5.98263	−	22.3275i	−0.368905	−	1.37677i	−0.862049	−	0.506824i	$-0.830819\pi$
$263$	−5.98263	−	22.3275i	−0.368905	−	1.37677i	0.493145	−	0.869947i	$-0.335847\pi$
$264$	−5.64168	−	9.77167i	−0.347221	−	0.601405i
$265$	−0.0797641	−	1.71985i	−0.00489987	−	0.105650i
$266$		0			0
$267$	−0.848464	−	0.848464i	−0.0519251	−	0.0519251i
$268$	−39.9374	−	10.7012i	−2.43957	−	0.653680i
$269$	8.29515	−	14.3676i	0.505764	−	0.876009i	−0.494213	−	0.869341i	$-0.664544\pi$
$269$	8.29515	−	14.3676i	0.505764	−	0.876009i	0.999978	−	0.00666889i	$-0.00212279\pi$
$270$	1.78532	+	5.60921i	0.108651	+	0.341366i
$271$	6.73796	−	3.89016i	0.409302	−	0.236311i	−0.281188	−	0.959653i	$-0.590728\pi$
$271$	6.73796	−	3.89016i	0.409302	−	0.236311i	0.690490	+	0.723342i	$0.257395\pi$
$272$	22.0005	−	22.0005i	1.33398	−	1.33398i
$273$		0			0
$274$		−	33.7136i		−	2.03671i
$275$	5.96839	−	4.22754i	0.359908	−	0.254930i
$276$	−24.9380	−	14.3979i	−1.50109	−	0.866654i
$277$	−29.1109	+	7.80024i	−1.74910	+	0.468671i	−0.984435	−	0.175751i	$-0.943765\pi$
$277$	−29.1109	+	7.80024i	−1.74910	+	0.468671i	−0.764670	+	0.644422i	$0.777098\pi$
$278$	8.17019	−	30.4916i	0.490016	−	1.82876i
$279$	6.10346			0.365405
$280$		0			0
$281$	−21.1519			−1.26182			−0.630908	−	0.775858i	$-0.717317\pi$
$281$	−21.1519			−1.26182			−0.630908	+	0.775858i	$0.717317\pi$
$282$	8.25816	−	30.8199i	0.491766	−	1.83530i
$283$	−3.62641	+	0.971693i	−0.215567	+	0.0577611i	−0.364986	−	0.931013i	$-0.618926\pi$
$283$	−3.62641	+	0.971693i	−0.215567	+	0.0577611i	0.149419	+	0.988774i	$0.452260\pi$
$284$	−32.5605	−	18.7988i	−1.93211	−	1.11551i
$285$	4.77778	+	7.45491i	0.283011	+	0.441591i
$286$			4.83508i			0.285905i
$287$		0			0
$288$	−8.53599	+	8.53599i	−0.502988	+	0.502988i
$289$	7.03933	−	4.06416i	0.414078	−	0.239068i
$290$	−27.1147	−	14.0217i	−1.59223	−	0.823382i
$291$	−6.14355	+	10.6409i	−0.360141	+	0.623783i
$292$	45.8886	+	12.2958i	2.68543	+	0.719558i
$293$	−1.56714	−	1.56714i	−0.0915536	−	0.0915536i	0.659847	−	0.751400i	$-0.270621\pi$
$293$	−1.56714	−	1.56714i	−0.0915536	−	0.0915536i	−0.751400	+	0.659847i	$0.770621\pi$
$294$		0			0
$295$	4.81428	−	5.28255i	0.280298	−	0.307562i
$296$	−12.3028	−	21.3091i	−0.715085	−	1.23856i
$297$	−0.378598	−	1.41295i	−0.0219685	−	0.0819875i
$298$	−0.0659719	−	0.246211i	−0.00382165	−	0.0142626i
$299$	3.66686	+	6.35119i	0.212060	+	0.367299i
$300$	−18.9691	−	15.7425i	−1.09518	−	0.908891i
$301$		0			0
$302$	25.0460	+	25.0460i	1.44123	+	1.44123i
$303$	−14.8193	−	3.97081i	−0.851345	−	0.228117i
$304$	−20.6821	+	35.8225i	−1.18620	+	2.05456i
$305$	3.02702	−	0.963450i	0.173327	−	0.0551670i
$306$	6.79054	−	3.92052i	0.388189	−	0.224121i
$307$	−17.3551	+	17.3551i	−0.990510	+	0.990510i	−0.999955	−	0.00944588i	$-0.996993\pi$
$307$	−17.3551	+	17.3551i	−0.990510	+	0.990510i	0.00944588	+	0.999955i	$0.496993\pi$
$308$		0			0
$309$		−	11.7489i		−	0.668374i
$310$	−30.2488	+	19.3861i	−1.71802	+	1.10106i
$311$	−26.9029	−	15.5324i	−1.52553	−	0.880763i	−0.999542	−	0.0302685i	$-0.990364\pi$
$311$	−26.9029	−	15.5324i	−1.52553	−	0.880763i	−0.525984	−	0.850494i	$-0.676303\pi$
$312$	9.35518	−	2.50671i	0.529633	−	0.141915i
$313$	2.09522	−	7.81948i	0.118429	−	0.441983i	−0.881091	−	0.472946i	$-0.843191\pi$
$313$	2.09522	−	7.81948i	0.118429	−	0.441983i	0.999521	+	0.0309625i	$0.00985725\pi$
$314$	−6.13381			−0.346151
$315$		0			0
$316$	−22.2856			−1.25366
$317$	0.275463	−	1.02804i	0.0154715	−	0.0577406i	−0.957759	−	0.287574i	$-0.907151\pi$
$317$	0.275463	−	1.02804i	0.0154715	−	0.0577406i	0.973230	+	0.229833i	$0.0738180\pi$
$318$	1.95788	−	0.524613i	0.109793	−	0.0294188i
$319$	6.56934	+	3.79281i	0.367813	+	0.212357i
$320$	5.20464	−	23.7817i	0.290948	−	1.32943i
$321$		−	6.20871i		−	0.346536i
$322$		0			0
$323$	8.34005	−	8.34005i	0.464053	−	0.464053i
$324$	−4.26961	+	2.46506i	−0.237201	+	0.136948i
$325$	2.17917	+	5.88766i	0.120879	+	0.326589i
$326$	−19.1259	+	33.1270i	−1.05928	+	1.83473i
$327$	−7.19216	−	1.92713i	−0.397727	−	0.106571i
$328$	4.19966	+	4.19966i	0.231887	+	0.231887i
$329$		0			0
$330$	6.36421	+	5.80005i	0.350338	+	0.319282i
$331$	−7.90412	−	13.6903i	−0.434449	−	0.752489i	0.562801	−	0.826592i	$-0.309724\pi$
$331$	−7.90412	−	13.6903i	−0.434449	−	0.752489i	−0.997251	+	0.0741038i	$0.976390\pi$
$332$	12.1950	+	45.5125i	0.669290	+	2.49783i
$333$	−0.825607	−	3.08121i	−0.0452430	−	0.168849i
$334$	0.545426	+	0.944705i	0.0298444	+	0.0516920i
$335$	18.7326	−	0.868788i	1.02347	−	0.0474670i
$336$		0			0
$337$	−20.0460	−	20.0460i	−1.09197	−	1.09197i	−0.995318	−	0.0966558i	$-0.969185\pi$
$337$	−20.0460	−	20.0460i	−1.09197	−	1.09197i	−0.0966558	−	0.995318i	$-0.530815\pi$
$338$	29.0477	+	7.78331i	1.57999	+	0.423357i
$339$	1.79920	−	3.11630i	0.0977190	−	0.169254i
$340$	−15.0828	+	29.1666i	−0.817978	+	1.58178i
$341$	7.73194	−	4.46404i	0.418708	−	0.241741i
$342$	−7.37117	+	7.37117i	−0.398587	+	0.398587i
$343$		0			0
$344$			56.5693i			3.05001i
$345$	12.7585	+	2.79220i	0.686893	+	0.150327i
$346$	−11.1294	−	6.42558i	−0.598322	−	0.345441i
$347$	27.4362	−	7.35151i	1.47285	−	0.394650i	0.568945	−	0.822376i	$-0.307352\pi$
$347$	27.4362	−	7.35151i	1.47285	−	0.394650i	0.903908	+	0.427726i	$0.140685\pi$
$348$	6.61704	−	24.6951i	0.354710	−	1.32380i
$349$	14.7663			0.790420			0.395210	−	0.918591i	$-0.370672\pi$
$349$	14.7663			0.790420			0.395210	+	0.918591i	$0.370672\pi$
$350$		0			0
$351$	1.25560			0.0670190
$352$	−4.57032	+	17.0567i	−0.243599	+	0.909124i
$353$	17.0603	−	4.57130i	0.908029	−	0.243306i	0.225568	−	0.974227i	$-0.427576\pi$
$353$	17.0603	−	4.57130i	0.908029	−	0.243306i	0.682461	+	0.730922i	$0.260910\pi$
$354$	7.28706	+	4.20719i	0.387303	+	0.223610i
$355$	16.6582	+	3.64567i	0.884127	+	0.193492i
$356$			5.91570i			0.313531i
$357$		0			0
$358$	−3.71839	+	3.71839i	−0.196523	+	0.196523i
$359$	−9.12549	+	5.26861i	−0.481625	+	0.278066i	−0.721093	−	0.692838i	$-0.756360\pi$
$359$	−9.12549	+	5.26861i	−0.481625	+	0.278066i	0.239468	+	0.970904i	$0.423027\pi$
$360$	7.92277	−	15.3208i	0.417567	−	0.807477i
$361$	1.65972	−	2.87471i	0.0873535	−	0.151301i
$362$	21.5765	+	5.78140i	1.13403	+	0.303864i
$363$	6.26514	+	6.26514i	0.328835	+	0.328835i
$364$		0			0
$365$	−21.5239	+	0.998247i	−1.12661	+	0.0522507i
$366$	1.86993	+	3.23881i	0.0977427	+	0.169295i
$367$	4.09618	+	15.2871i	0.213819	+	0.797982i	0.986579	+	0.163284i	$0.0522088\pi$
$367$	4.09618	+	15.2871i	0.213819	+	0.797982i	−0.772760	+	0.634698i	$0.781125\pi$
$368$	15.7911	+	58.9334i	0.823170	+	3.07211i
$369$	0.384984	+	0.666812i	0.0200415	+	0.0347128i
$370$	13.8784	+	12.6482i	0.721505	+	0.657546i
$371$		0			0
$372$	−21.2774	−	21.2774i	−1.10318	−	1.10318i
$373$	−23.5976	−	6.32295i	−1.22184	−	0.327390i	−0.410440	−	0.911887i	$-0.634625\pi$
$373$	−23.5976	−	6.32295i	−1.22184	−	0.327390i	−0.811396	+	0.584497i	$0.801292\pi$
$374$	5.73489	−	9.93312i	0.296544	−	0.513630i
$375$	10.3638	+	4.19435i	0.535182	+	0.216595i
$376$	−80.9662	+	46.7459i	−4.17551	+	2.41073i
$377$	−4.60412	+	4.60412i	−0.237124	+	0.237124i
$378$		0			0
$379$			17.6237i			0.905267i	0.891697	+	0.452634i	$0.149515\pi$
$379$			17.6237i			0.905267i	−0.891697	+	0.452634i	$0.850485\pi$
$380$	9.33283	−	42.6447i	0.478764	−	2.18762i
$381$	9.62680	+	5.55803i	0.493196	+	0.284747i
$382$	−19.9210	+	5.33782i	−1.01925	+	0.273106i
$383$	5.90211	−	22.0270i	0.301584	−	1.12553i	−0.634263	−	0.773118i	$-0.718696\pi$
$383$	5.90211	−	22.0270i	0.301584	−	1.12553i	0.935846	−	0.352408i	$-0.114637\pi$
$384$	4.51726			0.230520
$385$		0			0
$386$	−50.4894			−2.56984
$387$	−1.89811	+	7.08383i	−0.0964862	+	0.360091i
$388$	58.5128	−	15.6785i	2.97054	−	0.795953i
$389$	−13.3377	−	7.70053i	−0.676249	−	0.390432i	0.122191	−	0.992507i	$-0.461008\pi$
$389$	−13.3377	−	7.70053i	−0.676249	−	0.390432i	−0.798440	+	0.602074i	$0.794341\pi$
$390$	−6.22277	+	3.98811i	−0.315102	+	0.201946i
$391$		−	17.3971i		−	0.879807i
$392$		0			0
$393$	4.37145	−	4.37145i	0.220510	−	0.220510i
$394$	37.0105	−	21.3680i	1.86456	−	1.07650i
$395$	9.63159	−	3.06557i	0.484618	−	0.154246i
$396$	−3.60587	+	6.24554i	−0.181202	+	0.313850i
$397$	−22.0997	−	5.92159i	−1.10915	−	0.297196i	−0.342665	−	0.939458i	$-0.611330\pi$
$397$	−22.0997	−	5.92159i	−1.10915	−	0.297196i	−0.766486	+	0.642261i	$0.777996\pi$
$398$	−37.5026	−	37.5026i	−1.87983	−	1.87983i
$399$		0			0
$400$	4.83424	+	52.0051i	0.241712	+	2.60026i
$401$	0.488797	+	0.846622i	0.0244094	+	0.0422783i	0.877972	−	0.478712i	$-0.158896\pi$
$401$	0.488797	+	0.846622i	0.0244094	+	0.0422783i	−0.853563	+	0.520990i	$0.825563\pi$
$402$	5.71407	+	21.3252i	0.284992	+	1.06360i
$403$	1.98346	+	7.40238i	0.0988033	+	0.368739i
$404$	37.8191	+	65.5046i	1.88157	+	3.25897i
$405$	1.50619	−	1.65269i	0.0748431	−	0.0821230i
$406$		0			0
$407$	−3.29947	−	3.29947i	−0.163549	−	0.163549i
$408$	−22.1923	−	5.94642i	−1.09868	−	0.294392i
$409$	−12.1586	+	21.0593i	−0.601203	+	1.04131i	0.391437	+	0.920205i	$0.371978\pi$
$409$	−12.1586	+	21.0593i	−0.601203	+	1.04131i	−0.992639	+	0.121108i	$0.961355\pi$
$410$	−4.02595	−	2.08192i	−0.198827	−	0.102819i
$411$	−11.0909	+	6.40331i	−0.547072	+	0.315852i
$412$	−40.9583	+	40.9583i	−2.01787	+	2.01787i
$413$		0			0
$414$			15.3760i			0.755689i
$415$	−11.5312	−	17.9925i	−0.566044	−	0.883216i
$416$	−13.1266	−	7.57863i	−0.643583	−	0.371573i
$417$	−11.5827	+	3.10357i	−0.567207	+	0.151983i
$418$	−3.94666	+	14.7291i	−0.193037	+	0.720425i
$419$	15.9893			0.781127			0.390563	−	0.920576i	$-0.372280\pi$
$419$	15.9893			0.781127			0.390563	+	0.920576i	$0.372280\pi$
$420$		0			0
$421$	14.7000			0.716433			0.358216	−	0.933639i	$-0.383385\pi$
$421$	14.7000			0.716433			0.358216	+	0.933639i	$0.383385\pi$
$422$	−8.15308	+	30.4277i	−0.396886	+	1.48120i
$423$	−11.7074	+	3.13699i	−0.569233	+	0.152526i
$424$	−5.14351	−	2.96961i	−0.249791	−	0.144217i
$425$	2.50650	−	14.6802i	0.121583	−	0.712096i
$426$			20.0758i			0.972677i
$427$		0			0
$428$	−21.6443	+	21.6443i	−1.04622	+	1.04622i
$429$	1.59061	−	0.918340i	0.0767955	−	0.0443379i
$430$	−13.0930	−	41.1364i	−0.631401	−	1.98377i
$431$	−11.1361	+	19.2883i	−0.536407	+	0.929084i	0.462687	+	0.886522i	$0.346885\pi$
$431$	−11.1361	+	19.2883i	−0.536407	+	0.929084i	−0.999094	+	0.0425619i	$0.986448\pi$
$432$	10.0899	+	2.70359i	0.485452	+	0.130077i
$433$	−28.0171	−	28.0171i	−1.34642	−	1.34642i	−0.889520	−	0.456896i	$-0.848961\pi$
$433$	−28.0171	−	28.0171i	−1.34642	−	1.34642i	−0.456896	−	0.889520i	$-0.651039\pi$
$434$		0			0
$435$	0.537211	+	11.5832i	0.0257573	+	0.555371i
$436$	18.3545	+	31.7910i	0.879023	+	1.52251i
$437$	5.98618	+	22.3407i	0.286358	+	1.06870i
$438$	−6.56553	−	24.5029i	−0.313713	−	1.17079i
$439$	1.17828	+	2.04084i	0.0562363	+	0.0974042i	0.892773	−	0.450507i	$-0.148757\pi$
$439$	1.17828	+	2.04084i	0.0562363	+	0.0974042i	−0.836537	+	0.547911i	$0.815423\pi$
$440$	−1.16889	−	25.2033i	−0.0557246	−	1.20152i
$441$		0			0
$442$	6.96162	+	6.96162i	0.331130	+	0.331130i
$443$	7.47553	+	2.00306i	0.355173	+	0.0951684i	0.431994	−	0.901877i	$-0.357810\pi$
$443$	7.47553	+	2.00306i	0.355173	+	0.0951684i	−0.0768206	+	0.997045i	$0.524477\pi$
$444$	−7.86331	+	13.6196i	−0.373176	+	0.646360i
$445$	−0.813754	−	2.55670i	−0.0385756	−	0.121199i
$446$	2.13088	−	1.23026i	0.100900	−	0.0582546i
$447$	−0.0684664	+	0.0684664i	−0.00323835	+	0.00323835i
$448$		0			0
$449$		−	1.20020i		−	0.0566410i	−0.999599	−	0.0283205i	$-0.990984\pi$
$449$		−	1.20020i		−	0.0566410i	0.999599	−	0.0283205i	$-0.00901591\pi$
$450$	−2.21531	+	12.9748i	−0.104431	+	0.611638i
$451$	0.975405	+	0.563150i	0.0459300	+	0.0265177i
$452$	−17.1360	+	4.59159i	−0.806011	+	0.215970i
$453$	3.48240	−	12.9965i	0.163617	−	0.610629i
$454$	64.5881			3.03127
$455$		0			0
$456$	30.5448			1.43039
$457$	−7.71489	+	28.7924i	−0.360887	+	1.34685i	0.512024	+	0.858971i	$0.328896\pi$
$457$	−7.71489	+	28.7924i	−0.360887	+	1.34685i	−0.872912	+	0.487879i	$0.837771\pi$
$458$	−63.7692	+	17.0869i	−2.97974	+	0.798418i
$459$	−2.57949	−	1.48927i	−0.120400	−	0.0695131i
$460$	−34.7436	−	54.2116i	−1.61993	−	2.52763i
$461$		−	21.9670i		−	1.02311i	−0.859252	−	0.511553i	$-0.829071\pi$
$461$		−	21.9670i		−	1.02311i	0.859252	−	0.511553i	$-0.170929\pi$
$462$		0			0
$463$	−21.6776	+	21.6776i	−1.00744	+	1.00744i	−0.00746987	+	0.999972i	$0.502378\pi$
$463$	−21.6776	+	21.6776i	−1.00744	+	1.00744i	−0.999972	+	0.00746987i	$0.997622\pi$
$464$	−46.9121	+	27.0847i	−2.17784	+	1.25738i
$465$	12.1227	+	6.26898i	0.562179	+	0.290717i
$466$	4.17225	−	7.22655i	0.193276	−	0.334763i
$467$	−9.71653	−	2.60354i	−0.449627	−	0.120477i	0.0268978	−	0.999638i	$-0.491437\pi$
$467$	−9.71653	−	2.60354i	−0.449627	−	0.120477i	−0.476525	+	0.879161i	$0.658104\pi$
$468$	−4.37718	−	4.37718i	−0.202335	−	0.202335i
$469$		0			0
$470$	48.0581	−	52.7326i	2.21676	−	2.43237i
$471$	1.16501	+	2.01786i	0.0536809	+	0.0929780i
$472$	−6.38123	−	23.8151i	−0.293720	−	1.09618i
$473$	2.77653	+	10.3622i	0.127665	+	0.476452i
$474$	5.94986	+	10.3055i	0.273286	+	0.473346i
$475$	1.83259	+	19.7144i	0.0840848	+	0.904557i
$476$		0			0
$477$	−0.544449	−	0.544449i	−0.0249286	−	0.0249286i
$478$	54.3575	+	14.5651i	2.48626	+	0.666190i
$479$	−15.8875	+	27.5179i	−0.725917	+	1.25733i	0.232678	+	0.972554i	$0.425251\pi$
$479$	−15.8875	+	27.5179i	−0.725917	+	1.25733i	−0.958595	+	0.284771i	$0.908082\pi$
$480$	−25.7217	+	8.18679i	−1.17403	+	0.373674i
$481$	3.46864	−	2.00262i	0.158157	−	0.0913117i
$482$	−1.16180	+	1.16180i	−0.0529184	+	0.0529184i
$483$		0			0
$484$		−	43.6821i		−	1.98555i
$485$	−23.1319	+	14.8250i	−1.05036	+	0.673168i
$486$	2.27982	+	1.31626i	0.103415	+	0.0597066i
$487$	6.57642	−	1.76215i	0.298006	−	0.0798505i	−0.106718	−	0.994289i	$-0.534034\pi$
$487$	6.57642	−	1.76215i	0.298006	−	0.0798505i	0.404724	+	0.914439i	$0.367368\pi$
$488$	2.83620	−	10.5848i	0.128389	−	0.479153i
$489$	14.5305			0.657092
$490$		0			0
$491$	28.3401			1.27897			0.639484	−	0.768804i	$-0.279148\pi$
$491$	28.3401			1.27897			0.639484	+	0.768804i	$0.279148\pi$
$492$	0.982486	−	3.66669i	0.0442939	−	0.165307i
$493$	14.9196	−	3.99769i	0.671943	−	0.180047i
$494$	−11.3353	−	6.54445i	−0.510000	−	0.294449i
$495$	0.699288	−	3.19527i	0.0314307	−	0.143617i
$496$			63.7559i			2.86273i
$497$		0			0
$498$	17.7904	−	17.7904i	0.797206	−	0.797206i
$499$	2.93753	−	1.69599i	0.131502	−	0.0759227i	−0.432806	−	0.901487i	$-0.642476\pi$
$499$	2.93753	−	1.69599i	0.131502	−	0.0759227i	0.564308	+	0.825564i	$0.309143\pi$
$500$	−21.5073	−	50.7514i	−0.961836	−	2.26967i
$501$	0.207188	−	0.358861i	0.00925649	−	0.0160327i
$502$	−41.5605	−	11.1361i	−1.85494	−	0.497029i
$503$	−8.32921	−	8.32921i	−0.371381	−	0.371381i	0.496599	−	0.867980i	$-0.334582\pi$
$503$	−8.32921	−	8.32921i	−0.371381	−	0.371381i	−0.867980	+	0.496599i	$0.834582\pi$
$504$		0			0
$505$	−25.3557	−	23.1080i	−1.12831	−	1.02829i
$506$	11.2459	+	19.4785i	0.499942	+	0.865925i
$507$	−2.95661	−	11.0342i	−0.131308	−	0.490047i
$508$	−14.1842	−	52.9362i	−0.629323	−	2.34866i
$509$	19.4726	+	33.7275i	0.863108	+	1.49495i	0.868914	+	0.494963i	$0.164818\pi$
$509$	19.4726	+	33.7275i	0.863108	+	1.49495i	−0.00580659	+	0.999983i	$0.501848\pi$
$510$	17.5143	−	0.812285i	0.775545	−	0.0359686i
$511$		0			0
$512$	24.7846	+	24.7846i	1.09534	+	1.09534i
$513$	3.82494	+	1.02489i	0.168875	+	0.0452500i
$514$	39.6594	−	68.6920i	1.74930	−	3.02988i
$515$	12.0676	−	23.3359i	0.531760	−	1.02830i
$516$	31.3121	−	18.0781i	1.37844	−	0.795843i
$517$	−12.5367	+	12.5367i	−0.551364	+	0.551364i
$518$		0			0
$519$			4.88171i			0.214283i
$520$	21.1560	+	4.63002i	0.927753	+	0.203040i
$521$	6.12042	+	3.53363i	0.268141	+	0.154811i	0.628042	−	0.778179i	$-0.283856\pi$
$521$	6.12042	+	3.53363i	0.268141	+	0.154811i	−0.359902	+	0.932990i	$0.617190\pi$
$522$	−13.1863	+	3.53326i	−0.577150	+	0.154647i
$523$	5.33985	−	19.9286i	0.233495	−	0.871416i	−0.745326	−	0.666700i	$-0.767706\pi$
$523$	5.33985	−	19.9286i	0.233495	−	0.871416i	0.978821	−	0.204716i	$-0.0656272\pi$
$524$	−30.4788			−1.33147
$525$		0			0
$526$	60.8508			2.65322
$527$	4.70517	−	17.5599i	0.204960	−	0.764923i
$528$	14.7595	−	3.95478i	0.642323	−	0.172110i
$529$	9.62588	+	5.55750i	0.418516	+	0.241631i
$530$	4.42761	+	0.968986i	0.192323	+	0.0420901i
$531$		−	3.19633i		−	0.138709i
$532$		0			0
$533$	−0.683611	+	0.683611i	−0.0296105	+	0.0296105i
$534$	2.73558	−	1.57939i	0.118380	−	0.0683468i
$535$	6.37708	−	12.3318i	0.275705	−	0.533150i
$536$	32.3449	−	56.0229i	1.39708	−	2.41982i
$537$	1.92949	+	0.517006i	0.0832638	+	0.0223105i
$538$	30.8823	+	30.8823i	1.33143	+	1.33143i
$539$		0			0
$540$	−11.0123	+	0.510732i	−0.473892	+	0.0219784i
$541$	−9.30063	−	16.1092i	−0.399865	−	0.692587i	0.593844	−	0.804581i	$-0.297610\pi$
$541$	−9.30063	−	16.1092i	−0.399865	−	0.692587i	−0.993709	+	0.111993i	$0.964276\pi$
$542$	5.30108	+	19.7839i	0.227701	+	0.849792i
$543$	−2.19615	−	8.19615i	−0.0942459	−	0.351731i
$544$	17.9780	+	31.1388i	0.770801	+	1.33507i
$545$	−12.3057	−	11.2149i	−0.527120	−	0.480393i
$546$		0			0
$547$	−7.22715	−	7.22715i	−0.309011	−	0.309011i	0.535515	−	0.844526i	$-0.320118\pi$
$547$	−7.22715	−	7.22715i	−0.309011	−	0.309011i	−0.844526	+	0.535515i	$0.820118\pi$
$548$	60.9869	+	16.3414i	2.60523	+	0.698069i
$549$	0.710320	−	1.23031i	0.0303157	−	0.0525084i
$550$	6.68332	+	18.0569i	0.284978	+	0.769949i
$551$	−17.7837	+	10.2674i	−0.757609	+	0.437406i
$552$	31.8577	−	31.8577i	1.35595	−	1.35595i
$553$		0			0
$554$		−	79.3382i		−	3.37076i
$555$	1.52494	−	6.96792i	0.0647300	−	0.295772i
$556$	51.1981	+	29.5593i	2.17128	+	1.25359i
$557$	0.763508	−	0.204581i	0.0323509	−	0.00866839i	−0.242607	−	0.970125i	$-0.578003\pi$
$557$	0.763508	−	0.204581i	0.0323509	−	0.00866839i	0.274958	+	0.961456i	$0.411336\pi$
$558$	−4.15856	+	15.5200i	−0.176046	+	0.657012i
$559$	−9.20823			−0.389467
$560$		0			0
$561$	−4.35697			−0.183951
$562$	14.4117	−	53.7853i	0.607922	−	2.26879i
$563$	−0.959599	+	0.257124i	−0.0404423	+	0.0108365i	−0.278983	−	0.960296i	$-0.589997\pi$
$563$	−0.959599	+	0.257124i	−0.0404423	+	0.0108365i	0.238541	+	0.971132i	$0.423331\pi$
$564$	51.7494	+	29.8775i	2.17904	+	1.25807i
$565$	6.77439	−	4.34164i	0.285001	−	0.182654i
$566$		−	9.88333i		−	0.415427i
$567$		0			0
$568$	41.5953	−	41.5953i	1.74530	−	1.74530i
$569$	8.41819	−	4.86025i	0.352909	−	0.203752i	−0.313057	−	0.949734i	$-0.601353\pi$
$569$	8.41819	−	4.86025i	0.352909	−	0.203752i	0.665966	+	0.745982i	$0.268020\pi$
$570$	−22.2117	+	7.06962i	−0.930348	+	0.296114i
$571$	0.493342	−	0.854493i	0.0206457	−	0.0357594i	−0.855518	−	0.517773i	$-0.826761\pi$
$571$	0.493342	−	0.854493i	0.0206457	−	0.0357594i	0.876164	+	0.482014i	$0.160094\pi$
$572$	−8.74652	−	2.34362i	−0.365710	−	0.0979918i
$573$	5.53964	+	5.53964i	0.231422	+	0.231422i
$574$		0			0
$575$	22.4731	+	18.6504i	0.937192	+	0.777774i
$576$	−5.44360	−	9.42859i	−0.226817	−	0.392858i
$577$	−3.78872	−	14.1397i	−0.157726	−	0.588643i	−0.998856	−	0.0478100i	$-0.984776\pi$
$577$	−3.78872	−	14.1397i	−0.157726	−	0.588643i	0.841130	−	0.540833i	$-0.181891\pi$
$578$	5.53819	+	20.6688i	0.230358	+	0.859708i
$579$	9.58958	+	16.6096i	0.398529	+	0.690273i
$580$	38.5076	−	42.2532i	1.59894	−	1.75447i
$581$		0			0
$582$	−22.8720	−	22.8720i	−0.948076	−	0.948076i
$583$	−1.08792	−	0.291508i	−0.0450572	−	0.0120730i
$584$	−37.1646	+	64.3710i	−1.53788	+	2.66369i
$585$	2.49389	+	1.28965i	0.103110	+	0.0533205i
$586$	5.05272	−	2.91719i	0.208726	−	0.120508i
$587$	−21.1413	+	21.1413i	−0.872594	+	0.872594i	−0.992755	−	0.120160i	$-0.961659\pi$
$587$	−21.1413	+	21.1413i	−0.872594	+	0.872594i	0.120160	+	0.992755i	$0.461659\pi$
$588$		0			0
$589$			24.1689i			0.995862i
$590$	10.1524	+	15.8410i	0.417966	+	0.652165i
$591$	−14.0590	−	8.11696i	−0.578310	−	0.333887i
$592$	32.1859	−	8.62419i	1.32283	−	0.354452i
$593$	2.59079	−	9.66895i	0.106391	−	0.397056i	−0.892108	−	0.451821i	$-0.850774\pi$
$593$	2.59079	−	9.66895i	0.106391	−	0.397056i	0.998499	+	0.0547654i	$0.0174411\pi$
$594$	3.85081			0.158001
$595$		0			0
$596$	0.477365			0.0195536
$597$	−5.21437	+	19.4603i	−0.213410	+	0.796457i
$598$	−18.6483	+	4.99679i	−0.762585	+	0.204334i
$599$	6.18210	+	3.56924i	0.252594	+	0.145835i	0.620951	−	0.783849i	$-0.286746\pi$
$599$	6.18210	+	3.56924i	0.252594	+	0.145835i	−0.368358	+	0.929684i	$0.620080\pi$
$600$	31.4726	−	22.2927i	1.28486	−	0.910096i
$601$			35.0829i			1.43106i	0.698580	+	0.715532i	$0.253815\pi$
$601$			35.0829i			1.43106i	−0.698580	+	0.715532i	$0.746185\pi$
$602$		0			0
$603$	5.93012	−	5.93012i	0.241493	−	0.241493i
$604$	−57.4475	+	33.1673i	−2.33750	+	1.34956i
$605$	6.00884	+	18.8789i	0.244294	+	0.767537i
$606$	20.1941	−	34.9771i	0.820328	−	1.42085i
$607$	7.32715	+	1.96330i	0.297400	+	0.0796880i	0.404434	−	0.914567i	$-0.367469\pi$
$607$	7.32715	+	1.96330i	0.297400	+	0.0796880i	−0.107034	+	0.994255i	$0.534135\pi$
$608$	−33.8014	−	33.8014i	−1.37083	−	1.37083i
$609$		0			0
$610$	0.387427	+	8.35359i	0.0156865	+	0.338227i
$611$	−7.60919	−	13.1795i	−0.307835	−	0.533186i
$612$	3.80064	+	14.1842i	0.153632	+	0.573362i
$613$	−3.83917	−	14.3280i	−0.155062	−	0.578701i	−0.999100	−	0.0424169i	$-0.986494\pi$
$613$	−3.83917	−	14.3280i	−0.155062	−	0.578701i	0.844038	−	0.536284i	$-0.180172\pi$
$614$	−32.3060	−	55.9557i	−1.30376	−	2.25819i
$615$	0.0797641	+	1.71985i	0.00321640	+	0.0693511i
$616$		0			0
$617$	19.7986	+	19.7986i	0.797060	+	0.797060i	0.982631	−	0.185571i	$-0.0594135\pi$
$617$	19.7986	+	19.7986i	0.797060	+	0.797060i	−0.185571	+	0.982631i	$0.559414\pi$
$618$	29.8754	+	8.00508i	1.20176	+	0.322011i
$619$	6.03375	−	10.4508i	0.242517	−	0.420052i	−0.718914	−	0.695099i	$-0.755360\pi$
$619$	6.03375	−	10.4508i	0.242517	−	0.420052i	0.961431	+	0.275048i	$0.0886936\pi$
$620$	−20.4070	−	64.1158i	−0.819564	−	2.57495i
$621$	5.05829	−	2.92040i	0.202982	−	0.117192i
$622$	57.8262	−	57.8262i	2.31862	−	2.31862i
$623$		0			0
$624$			13.1158i			0.525054i
$625$	16.2765	+	18.9757i	0.651060	+	0.759026i
$626$	18.4559	+	10.6555i	0.737647	+	0.425880i
$627$	5.59508	−	1.49920i	0.223446	−	0.0598722i
$628$	2.97313	−	11.0959i	0.118641	−	0.442774i
$629$	−9.50124			−0.378839
$630$		0			0
$631$	30.4435			1.21194			0.605969	−	0.795488i	$-0.292786\pi$
$631$	30.4435			1.21194			0.605969	+	0.795488i	$0.292786\pi$
$632$	9.02442	−	33.6796i	0.358972	−	1.33970i
$633$	11.5584	−	3.09707i	0.459406	−	0.123098i
$634$	2.42643	+	1.40090i	0.0963660	+	0.0556369i
$635$	13.4121	+	20.9273i	0.532242	+	0.830474i
$636$			3.79604i			0.150523i
$637$		0			0
$638$	−14.1204	+	14.1204i	−0.559032	+	0.559032i
$639$	6.60440	−	3.81305i	0.261266	−	0.150842i
$640$	8.97222	+	4.63976i	0.354658	+	0.183403i
$641$	−18.2964	+	31.6904i	−0.722666	+	1.25169i	0.237262	+	0.971446i	$0.423750\pi$
$641$	−18.2964	+	31.6904i	−0.722666	+	1.25169i	−0.959928	+	0.280248i	$0.909583\pi$
$642$	15.7876	+	4.23027i	0.623086	+	0.166955i
$643$	−12.1140	−	12.1140i	−0.477731	−	0.477731i	0.426675	−	0.904405i	$-0.359685\pi$
$643$	−12.1140	−	12.1140i	−0.477731	−	0.477731i	−0.904405	+	0.426675i	$0.859685\pi$
$644$		0			0
$645$	−11.0460	+	12.1204i	−0.434935	+	0.477240i
$646$	15.5247	+	26.8896i	0.610813	+	1.05796i
$647$	−6.99030	−	26.0881i	−0.274817	−	1.02563i	−0.955964	−	0.293484i	$-0.905185\pi$
$647$	−6.99030	−	26.0881i	−0.274817	−	1.02563i	0.681147	−	0.732147i	$-0.261481\pi$
$648$	−1.99642	−	7.45075i	−0.0784269	−	0.292693i
$649$	−2.33778	−	4.04915i	−0.0917658	−	0.158943i
$650$	−16.4560	+	1.52970i	−0.645457	+	0.0599997i
$651$		0			0
$652$	−50.6552	−	50.6552i	−1.98381	−	1.98381i
$653$	−27.8271	−	7.45625i	−1.08896	−	0.291786i	−0.330698	−	0.943737i	$-0.607284\pi$
$653$	−27.8271	−	7.45625i	−1.08896	−	0.291786i	−0.758261	+	0.651951i	$0.773951\pi$
$654$	9.80067	−	16.9753i	0.383237	−	0.663785i
$655$	13.1726	−	4.19262i	0.514696	−	0.163819i
$656$	−6.96543	+	4.02149i	−0.271954	+	0.157013i
$657$	−6.81378	+	6.81378i	−0.265831	+	0.265831i
$658$		0			0
$659$			31.4882i			1.22661i	0.789847	+	0.613304i	$0.210160\pi$
$659$			31.4882i			1.22661i	−0.789847	+	0.613304i	$0.789840\pi$
$660$	−13.5769	+	8.70131i	−0.528481	+	0.338698i
$661$	−41.7321	−	24.0940i	−1.62319	−	0.937149i	−0.986060	−	0.166392i	$-0.946788\pi$
$661$	−41.7321	−	24.0940i	−1.62319	−	0.937149i	−0.637129	−	0.770757i	$-0.719878\pi$
$662$	40.1974	−	10.7709i	1.56231	−	0.418621i
$663$	0.967945	−	3.61242i	0.0375919	−	0.140295i
$664$	−73.7201			−2.86089
$665$		0			0
$666$	8.39746			0.325395
$667$	−7.83932	+	29.2567i	−0.303540	+	1.13283i
$668$	−1.97332	+	0.528748i	−0.0763499	+	0.0204579i
$669$	−0.809446	−	0.467334i	−0.0312950	−	0.0180682i
$670$	−10.5542	+	48.2253i	−0.407743	+	1.86311i
$671$		−	2.07810i		−	0.0802241i
$672$		0			0
$673$	−30.6900	+	30.6900i	−1.18301	+	1.18301i	−0.204055	+	0.978960i	$0.565412\pi$
$673$	−30.6900	+	30.6900i	−1.18301	+	1.18301i	−0.978960	+	0.204055i	$0.934588\pi$
$674$	64.6314	−	37.3149i	2.48951	−	1.43732i
$675$	4.68912	−	1.73556i	0.180484	−	0.0668018i
$676$	−28.1595	+	48.7738i	−1.08306	+	1.87591i
$677$	2.10450	+	0.563899i	0.0808825	+	0.0216724i	0.299033	−	0.954243i	$-0.403336\pi$
$677$	2.10450	+	0.563899i	0.0808825	+	0.0216724i	−0.218151	+	0.975915i	$0.570002\pi$
$678$	6.69830	+	6.69830i	0.257246	+	0.257246i
$679$		0			0
$680$	−37.9710	−	34.6050i	−1.45612	−	1.32704i
$681$	−12.2674	−	21.2477i	−0.470087	−	0.814215i
$682$	6.08310	+	22.7024i	0.232934	+	0.869321i
$683$	5.20319	+	19.4186i	0.199094	+	0.743030i	0.991169	+	0.132606i	$0.0423345\pi$
$683$	5.20319	+	19.4186i	0.199094	+	0.743030i	−0.792074	+	0.610424i	$0.790999\pi$
$684$	−9.76132	−	16.9071i	−0.373234	−	0.646459i
$685$	−28.6057	+	1.32669i	−1.09297	+	0.0506903i
$686$		0			0
$687$	17.7330	+	17.7330i	0.676555	+	0.676555i
$688$	−73.9968	−	19.8274i	−2.82110	−	0.755912i
$689$	0.483386	−	0.837249i	0.0184155	−	0.0318967i
$690$	−15.7930	+	30.5399i	−0.601228	+	1.16264i
$691$	−8.91028	+	5.14435i	−0.338963	+	0.195700i	−0.659813	−	0.751429i	$-0.729365\pi$
$691$	−8.91028	+	5.14435i	−0.338963	+	0.195700i	0.320850	+	0.947130i	$0.396031\pi$
$692$	17.0182	−	17.0182i	0.646937	−	0.646937i
$693$		0			0
$694$			74.7741i			2.83838i
$695$	−26.1934	−	5.73245i	−0.993572	−	0.217444i
$696$	34.6415	+	20.0003i	1.31308	+	0.758108i
$697$	2.21523	−	0.593570i	0.0839079	−	0.0224831i
$698$	−10.0609	+	37.5478i	−0.380811	+	1.42121i
$699$	−3.16979			−0.119892
$700$		0			0
$701$	−44.3183			−1.67388			−0.836939	−	0.547297i	$-0.815657\pi$
$701$	−44.3183			−1.67388			−0.836939	+	0.547297i	$0.815657\pi$
$702$	−0.855497	+	3.19276i	−0.0322887	+	0.120503i
$703$	12.2012	−	3.26930i	0.460176	−	0.123304i
$704$	−13.7920	−	7.96284i	−0.519807	−	0.300111i
$705$	−26.4754	−	5.79417i	−0.997122	−	0.218221i
$706$			46.4958i			1.74989i
$707$		0			0
$708$	−11.1428	+	11.1428i	−0.418772	+	0.418772i
$709$	−0.708388	+	0.408988i	−0.0266041	+	0.0153599i	−0.513243	−	0.858243i	$-0.671556\pi$
$709$	−0.708388	+	0.408988i	−0.0266041	+	0.0153599i	0.486639	+	0.873603i	$0.338223\pi$
$710$	−20.6203	+	39.8748i	−0.773864	+	1.49647i
$711$	2.26015	−	3.91469i	0.0847621	−	0.146812i
$712$	−8.94022	−	2.39553i	−0.335049	−	0.0897761i
$713$	25.2077	+	25.2077i	0.944037	+	0.944037i
$714$		0			0
$715$	4.10253	−	0.190269i	0.153426	−	0.00711567i
$716$	−4.92411	−	8.52880i	−0.184022	−	0.318736i
$717$	−5.53276	−	20.6485i	−0.206625	−	0.771134i
$718$	−7.17947	−	26.7941i	−0.267935	−	0.999949i
$719$	−0.00381028	−	0.00659960i	−0.000142099	−	0.000246124i	0.865954	−	0.500123i	$-0.166712\pi$
$719$	−0.00381028	−	0.00659960i	−0.000142099	−	0.000246124i	−0.866096	+	0.499877i	$0.833379\pi$
$720$	17.2638	+	15.7335i	0.643385	+	0.586351i
$721$		0			0
$722$	6.17902	+	6.17902i	0.229959	+	0.229959i
$723$	0.602863	+	0.161537i	0.0224207	+	0.00600761i
$724$	−20.9167	+	36.2289i	−0.777365	+	1.34644i
$725$	−10.8303	+	23.5584i	−0.402227	+	0.874937i
$726$	−20.1998	+	11.6624i	−0.749685	+	0.432831i
$727$	28.5738	−	28.5738i	1.05974	−	1.05974i	0.0616465	−	0.998098i	$-0.480365\pi$
$727$	28.5738	−	28.5738i	1.05974	−	1.05974i	0.998098	−	0.0616465i	$-0.0196352\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	12.1269	−	55.4115i	0.448835	−	2.05087i
$731$	18.9173	+	10.9219i	0.699680	+	0.403960i
$732$	−6.76528	+	1.81275i	−0.250052	+	0.0670012i
$733$	−8.84033	+	32.9926i	−0.326525	+	1.21861i	0.586244	+	0.810134i	$0.300606\pi$
$733$	−8.84033	+	32.9926i	−0.326525	+	1.21861i	−0.912770	+	0.408475i	$0.866061\pi$
$734$	−41.6632			−1.53782
$735$		0			0
$736$	−70.5085			−2.59898
$737$	3.17510	−	11.8496i	0.116956	−	0.436486i
$738$	−1.95788	+	0.524613i	−0.0720707	+	0.0193113i
$739$	32.8676	+	18.9761i	1.20905	+	0.698047i	0.962552	−	0.271096i	$-0.0873860\pi$
$739$	32.8676	+	18.9761i	1.20905	+	0.698047i	0.246500	+	0.969143i	$0.420719\pi$
$740$	−29.6072	+	18.9749i	−1.08838	+	0.697532i
$741$			4.97202i			0.182652i
$742$		0			0
$743$	−18.8022	+	18.8022i	−0.689784	+	0.689784i	−0.962184	−	0.272400i	$-0.912183\pi$
$743$	−18.8022	+	18.8022i	−0.689784	+	0.689784i	0.272400	+	0.962184i	$0.412183\pi$
$744$	40.7721	−	23.5398i	1.49478	−	0.863010i
$745$	−0.206312	+	0.0656655i	−0.00755867	+	0.00240580i
$746$	32.1562	−	55.6961i	1.17732	−	2.03918i
$747$	−9.23152	−	2.47358i	−0.337764	−	0.0905035i
$748$	15.1889	+	15.1889i	0.555363	+	0.555363i
$749$		0			0
$750$	−17.7267	+	23.4953i	−0.647289	+	0.857927i
$751$	−0.0529576	−	0.0917252i	−0.00193245	−	0.00334710i	0.865058	−	0.501673i	$-0.167282\pi$
$751$	−0.0529576	−	0.0917252i	−0.00193245	−	0.00334710i	−0.866990	+	0.498326i	$0.833948\pi$
$752$	−32.7686	−	122.294i	−1.19495	−	4.45960i
$753$	4.23022	+	15.7874i	0.154158	+	0.575325i
$754$	−8.57041	−	14.8444i	−0.312116	−	0.540601i
$755$	20.2657	−	22.2369i	0.737545	−	0.809284i
$756$		0			0
$757$	3.14514	+	3.14514i	0.114312	+	0.114312i	0.761949	−	0.647637i	$-0.224243\pi$
$757$	3.14514	+	3.14514i	0.114312	+	0.114312i	−0.647637	+	0.761949i	$0.724243\pi$
$758$	−44.8137	−	12.0078i	−1.62771	−	0.436143i
$759$	4.27193	−	7.39921i	0.155061	−	0.268574i
$760$	60.6684	+	31.3731i	2.20067	+	1.13802i
$761$	30.4082	−	17.5562i	1.10230	−	0.636410i	0.165472	−	0.986214i	$-0.447085\pi$
$761$	30.4082	−	17.5562i	1.10230	−	0.636410i	0.936823	+	0.349804i	$0.113752\pi$
$762$	−20.6922	+	20.6922i	−0.749599	+	0.749599i
$763$		0			0
$764$		−	38.6238i		−	1.39736i
$765$	−3.59375	−	5.60744i	−0.129932	−	0.202737i
$766$	51.9891	+	30.0159i	1.87844	+	1.08452i
$767$	3.87656	−	1.03872i	0.139975	−	0.0375061i
$768$	2.55782	−	9.54591i	0.0922973	−	0.344458i
$769$	8.16835			0.294558			0.147279	−	0.989095i	$-0.452948\pi$
$769$	8.16835			0.294558			0.147279	+	0.989095i	$0.452948\pi$
$770$		0			0
$771$	−30.1304			−1.08512
$772$	24.4728	−	91.3338i	0.880796	−	3.28717i
$773$	3.43099	−	0.919332i	0.123404	−	0.0330661i	−0.196588	−	0.980486i	$-0.562986\pi$
$773$	3.43099	−	0.919332i	0.123404	−	0.0330661i	0.319993	+	0.947420i	$0.396320\pi$
$774$	−16.7196	−	9.65306i	−0.600973	−	0.346972i
$775$	17.6393	+	24.9030i	0.633624	+	0.894542i
$776$			94.7776i			3.40232i
$777$		0			0
$778$	28.6686	−	28.6686i	1.02782	−	1.02782i
$779$	−2.64049	+	1.52449i	−0.0946052	+	0.0546204i
$780$	−4.19812	−	13.1899i	−0.150317	−	0.472274i
$781$	5.57770	−	9.66085i	0.199586	−	0.345693i
$782$	44.2374	+	11.8534i	1.58193	+	0.423876i
$783$	3.66686	+	3.66686i	0.131043	+	0.131043i
$784$		0			0
$785$	0.241377	+	5.20449i	0.00861510	+	0.185756i
$786$	8.13731	+	14.0942i	0.290248	+	0.502725i
$787$	4.66123	+	17.3959i	0.166155	+	0.620098i	0.997890	+	0.0649257i	$0.0206810\pi$
$787$	4.66123	+	17.3959i	0.166155	+	0.620098i	−0.831735	+	0.555172i	$0.812652\pi$
$788$	20.7146	+	77.3081i	0.737929	+	2.75399i
$789$	−11.5576	−	20.0183i	−0.411460	−	0.712669i
$790$	1.23274	+	26.5800i	0.0438590	+	0.945675i
$791$		0			0
$792$	−7.97854	−	7.97854i	−0.283505	−	0.283505i
$793$	1.72298	+	0.461671i	0.0611847	+	0.0163944i
$794$	30.1150	−	52.1607i	1.06874	−	1.85111i
$795$	−0.522176	−	1.64060i	−0.0185197	−	0.0581862i
$796$	86.0189	−	49.6630i	3.04886	−	1.76026i
$797$	23.3462	−	23.3462i	0.826967	−	0.826967i	−0.160129	−	0.987096i	$-0.551191\pi$
$797$	23.3462	−	23.3462i	0.826967	−	0.826967i	0.987096	+	0.160129i	$0.0511912\pi$
$798$		0			0
$799$			36.1010i			1.27716i
$800$	−59.4976	−	10.1586i	−2.10356	−	0.359160i
$801$	−1.03915	−	0.599954i	−0.0367166	−	0.0211983i
$802$	−2.48584	+	0.666079i	−0.0877781	+	0.0235201i
$803$	−3.64822	+	13.6153i	−0.128743	+	0.480475i
$804$	−41.3463			−1.45817
$805$		0			0
$806$	−20.1743			−0.710609
$807$	4.29389	−	16.0250i	0.151152	−	0.564107i
$808$	−114.310	+	30.6292i	−4.02140	+	1.07753i
$809$	24.0937	+	13.9105i	0.847090	+	0.489067i	0.859668	−	0.510853i	$-0.170671\pi$
$809$	24.0937	+	13.9105i	0.847090	+	0.489067i	−0.0125781	+	0.999921i	$0.504004\pi$
$810$	3.17625	+	4.95601i	0.111602	+	0.174136i
$811$		−	5.12216i		−	0.179863i	−0.995948	−	0.0899317i	$-0.971335\pi$
$811$		−	5.12216i		−	0.179863i	0.995948	−	0.0899317i	$-0.0286649\pi$
$812$		0			0
$813$	5.50152	−	5.50152i	0.192947	−	0.192947i
$814$	10.6380	−	6.14186i	0.372862	−	0.215272i
$815$	28.8606	+	14.9246i	1.01094	+	0.522784i
$816$	15.5567	−	26.9450i	0.544594	−	0.943264i
$817$	−28.0510	−	7.51626i	−0.981382	−	0.262961i
$818$	−45.2656	−	45.2656i	−1.58267	−	1.58267i
$819$		0			0
$820$	5.71755	−	6.27368i	0.199665	−	0.219086i
$821$	13.0702	+	22.6383i	0.456154	+	0.790082i	0.998754	−	0.0499094i	$-0.0158933\pi$
$821$	13.0702	+	22.6383i	0.456154	+	0.790082i	−0.542600	+	0.839991i	$0.682560\pi$
$822$	−8.72572	−	32.5648i	−0.304345	−	1.13583i
$823$	5.02538	+	18.7550i	0.175174	+	0.653757i	0.996522	+	0.0833299i	$0.0265555\pi$
$823$	5.02538	+	18.7550i	0.175174	+	0.653757i	−0.821348	+	0.570427i	$0.806778\pi$
$824$	−45.3133	−	78.4849i	−1.57856	−	2.73415i
$825$	4.67086	−	5.62823i	0.162618	−	0.195950i
$826$		0			0
$827$	15.7484	+	15.7484i	0.547624	+	0.547624i	0.925753	−	0.378129i	$-0.123432\pi$
$827$	15.7484	+	15.7484i	0.547624	+	0.547624i	−0.378129	+	0.925753i	$0.623432\pi$
$828$	−27.8147	−	7.45292i	−0.966627	−	0.259007i
$829$	−23.6498	+	40.9627i	−0.821392	+	1.42269i	0.0832545	+	0.996528i	$0.473469\pi$
$829$	−23.6498	+	40.9627i	−0.821392	+	1.42269i	−0.904646	+	0.426164i	$0.859865\pi$
$830$	53.6082	−	17.0626i	1.86077	−	0.592251i
$831$	−26.1001	+	15.0689i	−0.905403	+	0.522735i
$832$	9.66613	−	9.66613i	0.335113	−	0.335113i
$833$		0			0
$834$		−	31.5672i		−	1.09308i
$835$	0.780111	−	0.499965i	0.0269969	−	0.0173020i
$836$	−24.7315	−	14.2788i	−0.855358	−	0.493841i
$837$	5.89549	−	1.57969i	0.203778	−	0.0546021i
$838$	−10.8942	+	40.6577i	−0.376334	+	1.40450i
$839$	10.8244			0.373699			0.186850	−	0.982389i	$-0.440172\pi$
$839$	10.8244			0.373699			0.186850	+	0.982389i	$0.440172\pi$
$840$		0			0
$841$	2.10826			0.0726986
$842$	−10.0157	+	37.3793i	−0.345165	+	1.28817i
$843$	−20.4312	+	5.47451i	−0.703686	+	0.188552i
$844$	−51.0909	−	29.4973i	−1.75862	−	1.01534i
$845$	5.46100	−	24.9531i	0.187864	−	0.858411i
$846$		−	31.9071i		−	1.09699i
$847$		0			0
$848$	5.68725	−	5.68725i	0.195301	−	0.195301i
$849$	−3.25135	+	1.87717i	−0.111586	+	0.0644242i
$850$	35.6213	+	16.3759i	1.22180	+	0.561687i
$851$	9.31580	−	16.1354i	0.319341	−	0.553116i
$852$	−36.3166	−	9.73099i	−1.24418	−	0.333378i
$853$	33.5751	+	33.5751i	1.14959	+	1.14959i	0.986633	+	0.162958i	$0.0521034\pi$
$853$	33.5751	+	33.5751i	1.14959	+	1.14959i	0.162958	+	0.986633i	$0.447897\pi$
$854$		0			0
$855$	6.54445	+	5.96431i	0.223815	+	0.203975i
$856$	−23.9457	−	41.4752i	−0.818447	−	1.41759i
$857$	3.26670	+	12.1915i	0.111588	+	0.416454i	0.999009	−	0.0445069i	$-0.0141717\pi$
$857$	3.26670	+	12.1915i	0.111588	+	0.416454i	−0.887421	+	0.460960i	$0.847505\pi$
$858$	1.25141	+	4.67033i	0.0427225	+	0.159443i
$859$	−10.1851	−	17.6410i	−0.347510	−	0.601905i	0.638297	−	0.769791i	$-0.279639\pi$
$859$	−10.1851	−	17.6410i	−0.347510	−	0.601905i	−0.985806	+	0.167886i	$0.946306\pi$
$860$	80.7608	−	3.74556i	2.75392	−	0.127723i
$861$		0			0
$862$	−41.4589	−	41.4589i	−1.41210	−	1.41210i
$863$	20.3557	+	5.45430i	0.692917	+	0.185666i	0.588056	−	0.808820i	$-0.299894\pi$
$863$	20.3557	+	5.45430i	0.692917	+	0.185666i	0.104861	+	0.994487i	$0.466560\pi$
$864$	−6.03586	+	10.4544i	−0.205344	+	0.355666i
$865$	−5.01409	+	9.69610i	−0.170484	+	0.329677i
$866$	90.3315	−	52.1529i	3.06959	−	1.77223i
$867$	5.74759	−	5.74759i	0.195198	−	0.195198i
$868$		0			0
$869$		−	6.61223i		−	0.224305i
$870$	−29.8199	−	6.52611i	−1.01099	−	0.221256i
$871$	9.11929	+	5.26503i	0.308995	+	0.178399i
$872$	−55.4773	+	14.8651i	−1.87870	+	0.503396i
$873$	−3.18013	+	11.8684i	−0.107631	+	0.401685i
$874$	−60.8869			−2.05953
$875$		0			0
$876$	47.5074			1.60512
$877$	8.58820	−	32.0516i	0.290003	−	1.08231i	−0.655103	−	0.755540i	$-0.727375\pi$
$877$	8.58820	−	32.0516i	0.290003	−	1.08231i	0.945105	−	0.326765i	$-0.105959\pi$
$878$	−5.99230	+	1.60563i	−0.202230	+	0.0541874i
$879$	−1.91935	−	1.10814i	−0.0647381	−	0.0373766i
$880$	33.3774	+	7.30468i	1.12515	+	0.246241i
$881$		−	34.9639i		−	1.17796i	−0.808147	−	0.588981i	$-0.799529\pi$
$881$		−	34.9639i		−	1.17796i	0.808147	−	0.588981i	$-0.200471\pi$
$882$		0			0
$883$	19.3814	−	19.3814i	0.652235	−	0.652235i	−0.301295	−	0.953531i	$-0.597419\pi$
$883$	19.3814	−	19.3814i	0.652235	−	0.652235i	0.953531	+	0.301295i	$0.0974190\pi$
$884$	−15.9677	+	9.21897i	−0.537053	+	0.310068i
$885$	3.28301	−	6.34858i	0.110357	−	0.213405i
$886$	−10.1868	+	17.6441i	−0.342233	+	0.592765i
$887$	26.2892	+	7.04416i	0.882704	+	0.236520i	0.671574	−	0.740938i	$-0.265619\pi$
$887$	26.2892	+	7.04416i	0.882704	+	0.236520i	0.211131	+	0.977458i	$0.432285\pi$
$888$	−17.3988	−	17.3988i	−0.583865	−	0.583865i
$889$		0			0
$890$	7.05565	−	0.327230i	0.236506	−	0.0109688i
$891$	−0.731395	−	1.26681i	−0.0245026	−	0.0424398i
$892$	1.19265	+	4.45101i	0.0399327	+	0.149031i
$893$	−12.4221	−	46.3598i	−0.415689	−	1.55137i
$894$	−0.127448	−	0.220746i	−0.00426250	−	0.00738286i
$895$	3.30135	+	3.00870i	0.110352	+	0.100570i
$896$		0			0
$897$	5.18572	+	5.18572i	0.173146	+	0.173146i
$898$	3.05189	+	0.817751i	0.101843	+	0.0272887i
$899$	−15.8254	+	27.4104i	−0.527808	+	0.914190i
$900$	−22.3972	−	10.2965i	−0.746574	−	0.343216i
$901$	−1.98612	+	1.14669i	−0.0661673	+	0.0382017i
$902$	−2.09657	+	2.09657i	−0.0698082	+	0.0698082i
$903$		0			0
$904$		−	27.7565i		−	0.923169i
$905$	4.05640	−	18.5350i	0.134839	−	0.616124i
$906$	30.6749	+	17.7102i	1.01911	+	0.588381i
$907$	20.3321	−	5.44798i	0.675117	−	0.180897i	0.0950584	−	0.995472i	$-0.469696\pi$
$907$	20.3321	−	5.44798i	0.675117	−	0.180897i	0.580059	+	0.814575i	$0.303030\pi$
$908$	−31.3066	+	116.838i	−1.03895	+	3.87740i
$909$	−15.3420			−0.508863
$910$		0			0
$911$	−23.7484			−0.786819			−0.393410	−	0.919363i	$-0.628705\pi$
$911$	−23.7484			−0.786819			−0.393410	+	0.919363i	$0.628705\pi$
$912$	−10.7059	+	39.9548i	−0.354507	+	1.32304i
$913$	−13.5038	+	3.61832i	−0.446910	+	0.119749i
$914$	−67.9570	−	39.2350i	−2.24782	−	1.29778i
$915$	2.67452	−	1.71407i	0.0884169	−	0.0566655i
$916$		−	123.639i		−	4.08514i
$917$		0			0
$918$	5.54445	−	5.54445i	0.182994	−	0.182994i
$919$	−30.9773	+	17.8848i	−1.02185	+	0.589964i	−0.914638	−	0.404273i	$-0.867525\pi$
$919$	−30.9773	+	17.8848i	−1.02185	+	0.589964i	−0.107209	+	0.994237i	$0.534191\pi$
$920$	95.9976	−	30.5544i	3.16495	−	1.00735i
$921$	−12.2719	+	21.2556i	−0.404374	+	0.700396i
$922$	55.8580	+	14.9671i	1.83958	+	0.492915i
$923$	6.77080	+	6.77080i	0.222863	+	0.222863i
$924$		0			0
$925$	10.1857	−	12.2735i	0.334905	−	0.403549i
$926$	−40.3521	−	69.8919i	−1.32605	−	2.29679i
$927$	−3.04085	−	11.3486i	−0.0998746	−	0.372737i
$928$	−16.2022	−	60.4675i	−0.531864	−	1.98494i
$929$	2.79468	+	4.84053i	0.0916905	+	0.158813i	0.908223	−	0.418487i	$-0.137440\pi$
$929$	2.79468	+	4.84053i	0.0916905	+	0.158813i	−0.816532	+	0.577300i	$0.804106\pi$
$930$	−24.2006	+	26.5545i	−0.793569	+	0.870758i
$931$		0			0
$932$	11.0503	+	11.0503i	0.361963	+	0.361963i
$933$	−30.0063	−	8.04017i	−0.982363	−	0.263223i
$934$	13.2406	−	22.9334i	0.433246	−	0.750404i
$935$	−8.65386	−	4.47513i	−0.283011	−	0.146352i
$936$	8.38762	−	4.84260i	0.274158	−	0.158285i
$937$	−20.4143	+	20.4143i	−0.666906	+	0.666906i	−0.956999	−	0.290092i	$-0.906314\pi$
$937$	−20.4143	+	20.4143i	−0.666906	+	0.666906i	0.290092	+	0.956999i	$0.406314\pi$
$938$		0			0
$939$		−	8.09533i		−	0.264181i
$940$	72.0974	+	112.496i	2.35156	+	3.66921i
$941$	14.8214	+	8.55714i	0.483164	+	0.278955i	0.721734	−	0.692170i	$-0.243345\pi$
$941$	14.8214	+	8.55714i	0.483164	+	0.278955i	−0.238570	+	0.971125i	$0.576679\pi$
$942$	−5.92481	+	1.58755i	−0.193041	+	0.0517251i
$943$	−1.16397	+	4.34399i	−0.0379040	+	0.141460i
$944$	33.3884			1.08670
$945$		0			0
$946$	−28.2408			−0.918187
$947$	2.49685	−	9.31836i	0.0811366	−	0.302806i	−0.913418	−	0.407023i	$-0.866567\pi$
$947$	2.49685	−	9.31836i	0.0811366	−	0.302806i	0.994555	+	0.104217i	$0.0332336\pi$
$948$	−21.5262	+	5.76794i	−0.699140	+	0.187334i
$949$	−10.4782	−	6.04957i	−0.340136	−	0.196378i
$950$	−51.3785	−	8.77234i	−1.66694	−	0.284612i
$951$		−	1.06431i		−	0.0345125i
$952$		0			0
$953$	30.7169	−	30.7169i	0.995017	−	0.995017i	−0.00497101	−	0.999988i	$-0.501582\pi$
$953$	30.7169	−	30.7169i	0.995017	−	0.995017i	0.999988	+	0.00497101i	$0.00158233\pi$
$954$	1.75539	−	1.01347i	0.0568328	−	0.0328125i
$955$	5.31302	+	16.6928i	0.171925	+	0.540165i
$956$	−52.6955	+	91.2712i	−1.70429	+	2.95192i
$957$	7.32715	+	1.96330i	0.236853	+	0.0634646i
$958$	−59.1480	−	59.1480i	−1.91099	−	1.91099i
$959$		0			0
$960$	−1.12785	−	24.3184i	−0.0364012	−	0.784872i
$961$	3.12611	+	5.41458i	0.100842	+	0.174664i
$962$	2.72895	+	10.1846i	0.0879849	+	0.328364i
$963$	−1.60693	−	5.99715i	−0.0517826	−	0.193255i
$964$	−1.53852	−	2.66479i	−0.0495523	−	0.0858271i
$965$	1.98685	+	42.8399i	0.0639589	+	1.37906i
$966$		0			0
$967$	24.6730	+	24.6730i	0.793431	+	0.793431i	0.982050	−	0.188619i	$-0.0604012\pi$
$967$	24.6730	+	24.6730i	0.793431	+	0.793431i	−0.188619	+	0.982050i	$0.560401\pi$
$968$	66.0155	+	17.6888i	2.12182	+	0.568540i
$969$	5.89731	−	10.2144i	0.189449	−	0.328135i
$970$	−21.9364	−	68.9209i	−0.704334	−	2.21292i
$971$	−18.3615	+	10.6010i	−0.589247	+	0.340202i	−0.764800	−	0.644268i	$-0.777162\pi$
$971$	−18.3615	+	10.6010i	−0.589247	+	0.340202i	0.175552	+	0.984470i	$0.443829\pi$
$972$	−3.48612	+	3.48612i	−0.111817	+	0.111817i
$973$		0			0
$974$			17.9232i			0.574297i
$975$	3.62876	+	5.12303i	0.116213	+	0.164068i
$976$	12.8517	+	7.41991i	0.411372	+	0.237506i
$977$	−11.1967	+	3.00015i	−0.358215	+	0.0959834i	−0.433438	−	0.901183i	$-0.642700\pi$
$977$	−11.1967	+	3.00015i	−0.358215	+	0.0959834i	0.0752233	+	0.997167i	$0.476033\pi$
$978$	−9.90028	+	36.9484i	−0.316576	+	1.18148i
$979$	−1.75521			−0.0560969
$980$		0			0
$981$	−7.44587			−0.237728
$982$	−19.3093	+	72.0634i	−0.616186	+	2.29964i
$983$	2.38938	−	0.640231i	0.0762093	−	0.0204202i	−0.220513	−	0.975384i	$-0.570773\pi$
$983$	2.38938	−	0.640231i	0.0762093	−	0.0204202i	0.296722	+	0.954964i	$0.404106\pi$
$984$	5.14351	+	2.96961i	0.163969	+	0.0946676i
$985$	−19.5870	−	30.5622i	−0.624094	−	0.973794i
$986$			40.6615i			1.29492i
$987$		0			0
$988$	17.3331	−	17.3331i	0.551438	−	0.551438i
$989$	−37.0961	+	21.4174i	−1.17959	+	0.681034i
$990$	7.64852	+	3.95524i	0.243086	+	0.125706i
$991$	18.5627	−	32.1515i	0.589662	−	1.02133i	−0.404614	−	0.914488i	$-0.632594\pi$
$991$	18.5627	−	32.1515i	0.589662	−	1.02133i	0.994276	−	0.106838i	$-0.0340725\pi$
$992$	−71.1687	−	19.0696i	−2.25961	−	0.605460i
$993$	−11.1781	−	11.1781i	−0.354727	−	0.354727i
$994$		0			0
$995$	−30.3449	+	33.2964i	−0.961996	+	1.05557i
$996$	23.5590	+	40.8054i	0.746496	+	1.29297i
$997$	−14.8437	−	55.3975i	−0.470106	−	1.75446i	−0.639382	−	0.768889i	$-0.720810\pi$
$997$	−14.8437	−	55.3975i	−0.470106	−	1.75446i	0.169277	−	0.985569i	$-0.445857\pi$
$998$	2.31110	+	8.62515i	0.0731566	+	0.273024i
$999$	−1.59495	−	2.76254i	−0.0504620	−	0.0874028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.v.a.472.2		32
5.3	odd	4	inner	735.2.v.a.178.8		32
7.2	even	3	inner	735.2.v.a.607.7		32
7.3	odd	6		105.2.m.a.97.2	yes	16
7.4	even	3		105.2.m.a.97.1	yes	16
7.5	odd	6	inner	735.2.v.a.607.8		32
7.6	odd	2	inner	735.2.v.a.472.1		32
21.11	odd	6		315.2.p.e.307.8		16
21.17	even	6		315.2.p.e.307.7		16
28.3	even	6		1680.2.cz.d.97.3		16
28.11	odd	6		1680.2.cz.d.97.6		16
35.3	even	12		105.2.m.a.13.1	✓	16
35.4	even	6		525.2.m.b.307.8		16
35.13	even	4	inner	735.2.v.a.178.7		32
35.17	even	12		525.2.m.b.118.8		16
35.18	odd	12		105.2.m.a.13.2	yes	16
35.23	odd	12	inner	735.2.v.a.313.1		32
35.24	odd	6		525.2.m.b.307.7		16
35.32	odd	12		525.2.m.b.118.7		16
35.33	even	12	inner	735.2.v.a.313.2		32
105.38	odd	12		315.2.p.e.118.8		16
105.53	even	12		315.2.p.e.118.7		16
140.3	odd	12		1680.2.cz.d.433.6		16
140.123	even	12		1680.2.cz.d.433.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.1	✓	16	35.3	even	12
105.2.m.a.13.2	yes	16	35.18	odd	12
105.2.m.a.97.1	yes	16	7.4	even	3
105.2.m.a.97.2	yes	16	7.3	odd	6
315.2.p.e.118.7		16	105.53	even	12
315.2.p.e.118.8		16	105.38	odd	12
315.2.p.e.307.7		16	21.17	even	6
315.2.p.e.307.8		16	21.11	odd	6
525.2.m.b.118.7		16	35.32	odd	12
525.2.m.b.118.8		16	35.17	even	12
525.2.m.b.307.7		16	35.24	odd	6
525.2.m.b.307.8		16	35.4	even	6
735.2.v.a.178.7		32	35.13	even	4	inner
735.2.v.a.178.8		32	5.3	odd	4	inner
735.2.v.a.313.1		32	35.23	odd	12	inner
735.2.v.a.313.2		32	35.33	even	12	inner
735.2.v.a.472.1		32	7.6	odd	2	inner
735.2.v.a.472.2		32	1.1	even	1	trivial
735.2.v.a.607.7		32	7.2	even	3	inner
735.2.v.a.607.8		32	7.5	odd	6	inner
1680.2.cz.d.97.3		16	28.3	even	6
1680.2.cz.d.97.6		16	28.11	odd	6
1680.2.cz.d.433.3		16	140.123	even	12
1680.2.cz.d.433.6		16	140.3	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.681344 + 2.54281i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-4.26961 - 2.46506i) q^{4} +(2.18437 + 0.478051i) q^{5} +2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.681344 + 2.54281i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-4.26961 - 2.46506i) q^{4} +(2.18437 + 0.478051i) q^{5} +2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.70390 + 5.22872i) q^{10} +(0.731395 - 1.26681i) q^{11} +(-4.76213 - 1.27601i) q^{12} +(0.887844 + 0.887844i) q^{13} +(2.23367 - 0.103594i) q^{15} +(5.22294 + 9.04639i) q^{16} +(-0.770902 - 2.87705i) q^{17} +(0.681344 + 2.54281i) q^{18} +(1.97993 + 3.42935i) q^{19} +(-8.14798 - 7.42570i) q^{20} +(2.72294 + 2.72294i) q^{22} +(5.64178 + 1.51171i) q^{23} +(3.85679 - 6.68016i) q^{24} +(4.54293 + 2.08848i) q^{25} +(-2.86255 + 1.65269i) q^{26} +(0.707107 - 0.707107i) q^{27} +5.18572i q^{29} +(-1.25848 + 5.75038i) q^{30} +(5.28575 + 3.05173i) q^{31} +(-11.6604 + 3.12439i) q^{32} +(0.378598 - 1.41295i) q^{33} +7.84104 q^{34} -4.93012 q^{36} +(0.825607 - 3.08121i) q^{37} +(-10.0692 + 2.69804i) q^{38} +(1.08738 + 0.627801i) q^{39} +(14.5217 - 9.30682i) q^{40} +0.769968i q^{41} +(-5.18572 + 5.18572i) q^{43} +(-6.24554 + 3.60587i) q^{44} +(2.13074 - 0.678180i) q^{45} +(-7.68800 + 13.3160i) q^{46} +(-11.7074 - 3.13699i) q^{47} +(7.38635 + 7.38635i) q^{48} +(-8.40592 + 10.1289i) q^{50} +(-1.48927 - 2.57949i) q^{51} +(-1.60216 - 5.97934i) q^{52} +(-0.199282 - 0.743732i) q^{53} +(1.31626 + 2.27982i) q^{54} +(2.20324 - 2.41754i) q^{55} +(2.80005 + 2.80005i) q^{57} +(-13.1863 - 3.53326i) q^{58} +(1.59816 - 2.76810i) q^{59} +(-9.79226 - 5.06382i) q^{60} +(1.23031 - 0.710320i) q^{61} +(-11.3614 + 11.3614i) q^{62} -10.8872i q^{64} +(1.51494 + 2.36381i) q^{65} +(3.33490 + 1.92541i) q^{66} +(8.10070 - 2.17058i) q^{67} +(-3.80064 + 14.1842i) q^{68} +5.84081 q^{69} +7.62611 q^{71} +(1.99642 - 7.45075i) q^{72} +(-9.30780 + 2.49402i) q^{73} +(7.27241 + 4.19873i) q^{74} +(4.92868 + 0.841520i) q^{75} -19.5226i q^{76} +(-2.33726 + 2.33726i) q^{78} +(3.91469 - 2.26015i) q^{79} +(7.08418 + 22.2575i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.95788 - 0.524613i) q^{82} +(-6.75794 - 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} +(-9.65306 - 16.7196i) q^{86} +(1.34216 + 5.00903i) q^{87} +(-2.92035 - 10.8989i) q^{88} +(-0.599954 - 1.03915i) q^{89} +(0.272713 + 5.88016i) q^{90} +(-20.3618 - 20.3618i) q^{92} +(5.89549 + 1.57969i) q^{93} +(15.9535 - 27.6323i) q^{94} +(2.68550 + 8.43747i) q^{95} +(-10.4544 + 6.03586i) q^{96} +(-8.68829 + 8.68829i) q^{97} -1.46279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 48 q^{8}+O(q^{10}) \) 32 * q + 48 * q^8	\( 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) \) 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Introduction

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