LMFDB - Embedded newform 735.2.v.a.313.2

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			313.2
Character	$\chi$	$=$	735.313
Dual form			735.2.v.a.472.2

$q$-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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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	−0.594128	−	0.804370i	$-0.702503\pi$
$2$	−0.681344	−	2.54281i	−0.481783	−	1.79804i	0.112345	−	0.993669i	$-0.464164\pi$
$3$	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	0.954967	−	0.296712i	$-0.0958900\pi$
$11$	0.731395	+	1.26681i	0.220524	+	0.381958i	−0.734443	+	0.678670i	$0.762557\pi$
$12$	−4.76213	+	1.27601i	−1.37471	+	0.368352i
$13$	0.887844	−	0.887844i	0.246244	−	0.246244i	−0.573183	−	0.819427i	$-0.694292\pi$
$13$	0.887844	−	0.887844i	0.246244	−	0.246244i	0.819427	+	0.573183i	$0.194292\pi$
$14$		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	0.807229	+	0.590239i	$0.200966\pi$
$17$	−0.770902	+	2.87705i	−0.186971	+	0.697786i	−0.994200	+	0.107547i	$0.965700\pi$
$18$	0.681344	−	2.54281i	0.160594	−	0.599347i
$19$	1.97993	−	3.42935i	0.454228	−	0.786746i	−0.544415	−	0.838816i	$-0.683248\pi$
$19$	1.97993	−	3.42935i	0.454228	−	0.786746i	0.998643	+	0.0520695i	$0.0165817\pi$
$20$	−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	0.382898	−	0.923790i	$-0.374926\pi$
$23$	5.64178	−	1.51171i	1.17639	−	0.315214i	0.793495	+	0.608577i	$0.208259\pi$
$24$	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	$-0.840099\pi$
$29$		−	5.18572i		−	0.962965i	0.876456	−	0.481482i	$-0.159901\pi$
$30$	−1.25848	−	5.75038i	−0.229765	−	1.04987i
$31$	5.28575	−	3.05173i	0.949349	−	0.548107i	0.0564703	−	0.998404i	$-0.482015\pi$
$31$	5.28575	−	3.05173i	0.949349	−	0.548107i	0.892879	+	0.450297i	$0.148682\pi$
$32$	−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	0.999994	+	0.00351049i	$0.00111743\pi$
$37$	0.825607	+	3.08121i	0.135729	+	0.506548i	−0.864265	+	0.503037i	$0.832216\pi$
$38$	−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	$-0.980850\pi$
$41$		−	0.769968i		−	0.120249i	0.998191	−	0.0601244i	$-0.0191497\pi$
$42$		0			0
$43$	−5.18572	−	5.18572i	−0.790816	−	0.790816i	0.190811	−	0.981627i	$-0.438888\pi$
$43$	−5.18572	−	5.18572i	−0.790816	−	0.790816i	−0.981627	+	0.190811i	$0.938888\pi$
$44$	−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	−0.974859	−	0.222823i	$-0.928473\pi$
$47$	−11.7074	+	3.13699i	−1.70770	+	0.457577i	−0.732841	+	0.680400i	$0.761806\pi$
$48$	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	−0.978261	−	0.207377i	$-0.933507\pi$
$53$	−0.199282	+	0.743732i	−0.0273735	+	0.102159i	0.950888	+	0.309537i	$0.100174\pi$
$54$	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	0.951104	−	0.308870i	$-0.0999507\pi$
$59$	1.59816	+	2.76810i	0.208063	+	0.360376i	−0.743041	+	0.669246i	$0.766617\pi$
$60$	−9.79226	+	5.06382i	−1.26418	+	0.653736i
$61$	1.23031	+	0.710320i	0.157525	+	0.0909472i	0.576690	−	0.816963i	$-0.304344\pi$
$61$	1.23031	+	0.710320i	0.157525	+	0.0909472i	−0.419165	+	0.907910i	$0.637677\pi$
$62$	−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	0.717107	−	0.696963i	$-0.245466\pi$
$67$	8.10070	+	2.17058i	0.989658	+	0.265178i	0.272551	+	0.962141i	$0.412133\pi$
$68$	−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	−0.330956	−	0.943646i	$-0.607371\pi$
$73$	−9.30780	−	2.49402i	−1.08940	−	0.291903i	−0.758439	+	0.651744i	$0.774038\pi$
$74$	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	0.703783	−	0.710415i	$-0.251493\pi$
$79$	3.91469	+	2.26015i	0.440437	+	0.254286i	−0.263346	+	0.964701i	$0.584826\pi$
$80$	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	−0.972921	−	0.231140i	$-0.925754\pi$
$83$	−6.75794	+	6.75794i	−0.741781	+	0.741781i	0.231140	+	0.972921i	$0.425754\pi$
$84$		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	−0.896070	−	0.443913i	$-0.853590\pi$
$89$	−0.599954	+	1.03915i	−0.0635950	+	0.110150i	0.832475	+	0.554063i	$0.186923\pi$
$90$	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	0.111592	−	0.993754i	$-0.464405\pi$
$97$	−8.68829	−	8.68829i	−0.882162	−	0.882162i	−0.993754	+	0.111592i	$0.964405\pi$
$98$		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	−0.984058	−	0.177848i	$-0.943086\pi$
$101$	−13.2866	+	7.67102i	−1.32207	+	0.763295i	−0.338008	+	0.941143i	$0.609753\pi$
$102$	7.57386	+	2.02941i	0.749924	+	0.200941i
$103$	3.04085	+	11.3486i	0.299624	+	1.11821i	0.937475	+	0.348052i	$0.113157\pi$
$103$	3.04085	+	11.3486i	0.299624	+	1.11821i	−0.637851	+	0.770160i	$0.720177\pi$
$104$	9.68519			0.949711
$105$		0			0
$106$	2.02695			0.196875
$107$	1.60693	+	5.99715i	0.155348	+	0.579766i	0.999075	+	0.0429945i	$0.0136898\pi$
$107$	1.60693	+	5.99715i	0.155348	+	0.579766i	−0.843727	+	0.536772i	$0.819644\pi$
$108$	−4.76213	−	1.27601i	−0.458237	−	0.122784i
$109$	−6.44831	+	3.72294i	−0.617636	+	0.356593i	−0.775948	−	0.630797i	$-0.782728\pi$
$109$	−6.44831	+	3.72294i	−0.617636	+	0.356593i	0.158312	+	0.987389i	$0.449395\pi$
$110$	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	0.816586	−	0.577224i	$-0.195864\pi$
$113$	2.54445	+	2.54445i	0.239362	+	0.239362i	−0.577224	+	0.816586i	$0.695864\pi$
$114$	−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	−0.266383	−	0.963867i	$-0.585829\pi$
$127$	7.86025	−	7.86025i	0.697484	−	0.697484i	0.963867	+	0.266383i	$0.0858286\pi$
$128$	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	0.715307	−	0.698810i	$-0.246287\pi$
$131$	5.35391	+	3.09108i	0.467773	+	0.270069i	−0.247534	+	0.968879i	$0.579620\pi$
$132$	−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	−0.311777	−	0.950155i	$-0.600924\pi$
$137$	−12.3703	−	3.31460i	−1.05686	−	0.283185i	−0.745085	+	0.666970i	$0.767591\pi$
$138$	−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	0.496561	−	0.868002i	$-0.334596\pi$
$149$	−0.0838539	−	0.0484130i	−0.00686958	−	0.00396615i	−0.503431	+	0.864036i	$0.667929\pi$
$150$	−5.49795	−	11.9593i	−0.448906	−	0.976475i
$151$	6.72748	+	11.6523i	0.547475	+	0.948254i	0.998447	+	0.0557157i	$0.0177440\pi$
$151$	6.72748	+	11.6523i	0.547475	+	0.948254i	−0.450972	+	0.892538i	$0.648923\pi$
$152$	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	−0.937677	−	0.347508i	$-0.887028\pi$
$157$	0.603054	−	2.25063i	0.0481290	−	0.179620i	0.985806	+	0.167888i	$0.0536947\pi$
$158$	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	0.336842	−	0.941561i	$-0.390641\pi$
$163$	14.0354	−	3.76077i	1.09934	−	0.294566i	0.762495	+	0.646995i	$0.223974\pi$
$164$	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	0.718353	−	0.695679i	$-0.244896\pi$
$167$	0.293008	+	0.293008i	0.0226737	+	0.0226737i	−0.695679	+	0.718353i	$0.744896\pi$
$168$		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	0.901118	−	0.433575i	$-0.142748\pi$
$173$	−1.26348	−	4.71537i	−0.0960606	−	0.358503i	−0.997178	+	0.0750719i	$0.976081\pi$
$174$	−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	−0.433954	−	0.900935i	$-0.642882\pi$
$179$	1.72994	−	0.998779i	0.129302	−	0.0746523i	0.563256	+	0.826283i	$0.309549\pi$
$180$	−10.7692	+	2.35685i	−0.802689	+	0.175669i
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$		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	−0.688795	−	0.724956i	$-0.741860\pi$
$191$	3.91712	−	6.78465i	0.283433	−	0.490920i	0.972228	+	0.234036i	$0.0751934\pi$
$192$	−2.81781	+	10.5162i	−0.203358	+	0.758943i
$193$	4.96393	−	18.5257i	0.357312	−	1.33351i	−0.520239	−	0.854021i	$-0.674157\pi$
$193$	4.96393	−	18.5257i	0.357312	−	1.33351i	0.877550	−	0.479485i	$-0.159176\pi$
$194$	−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	−0.985797	−	0.167943i	$-0.946287\pi$
$197$	−11.4791	+	11.4791i	−0.817853	+	0.817853i	0.167943	+	0.985797i	$0.446287\pi$
$198$	3.71960	−	0.996663i	0.264340	−	0.0708298i
$199$	−10.0734	−	17.4476i	−0.714084	−	1.23683i	−0.963312	−	0.268384i	$-0.913510\pi$
$199$	−10.0734	−	17.4476i	−0.714084	−	1.23683i	0.249228	−	0.968445i	$-0.419823\pi$
$200$	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	−0.728889	−	0.684632i	$-0.759963\pi$
$223$	−0.660910	+	0.660910i	−0.0442578	+	0.0442578i	0.684632	+	0.728889i	$0.259963\pi$
$224$		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	0.350047	+	0.936732i	$0.386166\pi$
$227$	−6.35007	+	23.6988i	−0.421469	+	1.57294i	−0.771516	+	0.636210i	$0.780501\pi$
$228$	−5.05283	+	18.8574i	−0.334632	+	1.24886i
$229$	12.5391	−	21.7184i	0.828607	−	1.43519i	−0.0705240	−	0.997510i	$-0.522467\pi$
$229$	12.5391	−	21.7184i	0.828607	−	1.43519i	0.899131	−	0.437679i	$-0.144200\pi$
$230$	−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	−0.357712	−	0.933832i	$-0.616443\pi$
$233$	−3.06178	+	0.820401i	−0.200584	+	0.0537462i	0.157128	+	0.987578i	$0.449776\pi$
$234$	−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	$0.242997\pi$
$239$			21.3769i			1.38276i	−0.722492	+	0.691380i	$0.757003\pi$
$240$	12.6035	−	19.6656i	0.813549	−	1.26941i
$241$	0.540512	−	0.312065i	0.0348174	−	0.0201018i	−0.482490	−	0.875901i	$-0.660268\pi$
$241$	0.540512	−	0.312065i	0.0348174	−	0.0201018i	0.517308	+	0.855799i	$0.326934\pi$
$242$	−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	$-0.827487\pi$
$251$		−	16.3443i		−	1.03164i	0.856696	−	0.515822i	$-0.172513\pi$
$252$		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	−0.996207	−	0.0870116i	$-0.972268\pi$
$257$	−29.1038	+	7.79833i	−1.81544	+	0.486446i	−0.819235	+	0.573458i	$0.805602\pi$
$258$	−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	0.493145	+	0.869947i	$0.335847\pi$
$263$	−5.98263	+	22.3275i	−0.368905	+	1.37677i	−0.862049	+	0.506824i	$0.830819\pi$
$264$	−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	0.999978	+	0.00666889i	$0.00212279\pi$
$269$	8.29515	+	14.3676i	0.505764	+	0.876009i	−0.494213	+	0.869341i	$0.664544\pi$
$270$	1.78532	−	5.60921i	0.108651	−	0.341366i
$271$	6.73796	+	3.89016i	0.409302	+	0.236311i	0.690490	−	0.723342i	$-0.257395\pi$
$271$	6.73796	+	3.89016i	0.409302	+	0.236311i	−0.281188	+	0.959653i	$0.590728\pi$
$272$	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	−0.764670	−	0.644422i	$-0.777098\pi$
$277$	−29.1109	−	7.80024i	−1.74910	−	0.468671i	−0.984435	+	0.175751i	$0.943765\pi$
$278$	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	0.149419	−	0.988774i	$-0.452260\pi$
$283$	−3.62641	−	0.971693i	−0.215567	−	0.0577611i	−0.364986	+	0.931013i	$0.618926\pi$
$284$	−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	−0.751400	−	0.659847i	$-0.770621\pi$
$293$	−1.56714	+	1.56714i	−0.0915536	+	0.0915536i	0.659847	+	0.751400i	$0.270621\pi$
$294$		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	0.00944588	−	0.999955i	$-0.496993\pi$
$307$	−17.3551	−	17.3551i	−0.990510	−	0.990510i	−0.999955	+	0.00944588i	$0.996993\pi$
$308$		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	−0.525984	+	0.850494i	$0.676303\pi$
$311$	−26.9029	+	15.5324i	−1.52553	+	0.880763i	−0.999542	+	0.0302685i	$0.990364\pi$
$312$	9.35518	+	2.50671i	0.529633	+	0.141915i
$313$	2.09522	+	7.81948i	0.118429	+	0.441983i	0.999521	−	0.0309625i	$-0.00985725\pi$
$313$	2.09522	+	7.81948i	0.118429	+	0.441983i	−0.881091	+	0.472946i	$0.843191\pi$
$314$	−6.13381			−0.346151
$315$		0			0
$316$	−22.2856			−1.25366
$317$	0.275463	+	1.02804i	0.0154715	+	0.0577406i	0.973230	−	0.229833i	$-0.0738180\pi$
$317$	0.275463	+	1.02804i	0.0154715	+	0.0577406i	−0.957759	+	0.287574i	$0.907151\pi$
$318$	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	−0.997251	−	0.0741038i	$-0.976390\pi$
$331$	−7.90412	+	13.6903i	−0.434449	+	0.752489i	0.562801	+	0.826592i	$0.309724\pi$
$332$	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	−0.0966558	+	0.995318i	$0.530815\pi$
$337$	−20.0460	+	20.0460i	−1.09197	+	1.09197i	−0.995318	+	0.0966558i	$0.969185\pi$
$338$	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	0.903908	−	0.427726i	$-0.140685\pi$
$347$	27.4362	+	7.35151i	1.47285	+	0.394650i	0.568945	+	0.822376i	$0.307352\pi$
$348$	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	0.682461	−	0.730922i	$-0.260910\pi$
$353$	17.0603	+	4.57130i	0.908029	+	0.243306i	0.225568	+	0.974227i	$0.427576\pi$
$354$	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	0.239468	−	0.970904i	$-0.423027\pi$
$359$	−9.12549	−	5.26861i	−0.481625	−	0.278066i	−0.721093	+	0.692838i	$0.756360\pi$
$360$	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	−0.772760	−	0.634698i	$-0.781125\pi$
$367$	4.09618	−	15.2871i	0.213819	−	0.797982i	0.986579	−	0.163284i	$-0.0522088\pi$
$368$	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	−0.811396	−	0.584497i	$-0.801292\pi$
$373$	−23.5976	+	6.32295i	−1.22184	+	0.327390i	−0.410440	+	0.911887i	$0.634625\pi$
$374$	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	$-0.850485\pi$
$379$		−	17.6237i		−	0.905267i	0.891697	−	0.452634i	$-0.149515\pi$
$380$	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	0.935846	+	0.352408i	$0.114637\pi$
$383$	5.90211	+	22.0270i	0.301584	+	1.12553i	−0.634263	+	0.773118i	$0.718696\pi$
$384$	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	−0.798440	−	0.602074i	$-0.794341\pi$
$389$	−13.3377	+	7.70053i	−0.676249	+	0.390432i	0.122191	+	0.992507i	$0.461008\pi$
$390$	−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	−0.766486	−	0.642261i	$-0.777996\pi$
$397$	−22.0997	+	5.92159i	−1.10915	+	0.297196i	−0.342665	+	0.939458i	$0.611330\pi$
$398$	−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	−0.853563	−	0.520990i	$-0.825563\pi$
$401$	0.488797	−	0.846622i	0.0244094	−	0.0422783i	0.877972	+	0.478712i	$0.158896\pi$
$402$	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	−0.992639	−	0.121108i	$-0.961355\pi$
$409$	−12.1586	−	21.0593i	−0.601203	−	1.04131i	0.391437	−	0.920205i	$-0.371978\pi$
$410$	−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	−0.999094	−	0.0425619i	$-0.986448\pi$
$431$	−11.1361	−	19.2883i	−0.536407	−	0.929084i	0.462687	−	0.886522i	$-0.346885\pi$
$432$	10.0899	−	2.70359i	0.485452	−	0.130077i
$433$	−28.0171	+	28.0171i	−1.34642	+	1.34642i	−0.456896	+	0.889520i	$0.651039\pi$
$433$	−28.0171	+	28.0171i	−1.34642	+	1.34642i	−0.889520	+	0.456896i	$0.848961\pi$
$434$		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	−0.836537	−	0.547911i	$-0.815423\pi$
$439$	1.17828	−	2.04084i	0.0562363	−	0.0974042i	0.892773	+	0.450507i	$0.148757\pi$
$440$	−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	−0.0768206	−	0.997045i	$-0.524477\pi$
$443$	7.47553	−	2.00306i	0.355173	−	0.0951684i	0.431994	+	0.901877i	$0.357810\pi$
$444$	−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	$0.00901591\pi$
$449$			1.20020i			0.0566410i	−0.999599	+	0.0283205i	$0.990984\pi$
$450$	−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	−0.872912	−	0.487879i	$-0.837771\pi$
$457$	−7.71489	−	28.7924i	−0.360887	−	1.34685i	0.512024	−	0.858971i	$-0.328896\pi$
$458$	−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	$0.170929\pi$
$461$			21.9670i			1.02311i	−0.859252	+	0.511553i	$0.829071\pi$
$462$		0			0
$463$	−21.6776	−	21.6776i	−1.00744	−	1.00744i	−0.999972	−	0.00746987i	$-0.997622\pi$
$463$	−21.6776	−	21.6776i	−1.00744	−	1.00744i	−0.00746987	−	0.999972i	$-0.502378\pi$
$464$	−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	−0.476525	−	0.879161i	$-0.658104\pi$
$467$	−9.71653	+	2.60354i	−0.449627	+	0.120477i	0.0268978	+	0.999638i	$0.491437\pi$
$468$	−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	−0.958595	−	0.284771i	$-0.908082\pi$
$479$	−15.8875	−	27.5179i	−0.725917	−	1.25733i	0.232678	−	0.972554i	$-0.425251\pi$
$480$	−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	0.404724	−	0.914439i	$-0.367368\pi$
$487$	6.57642	+	1.76215i	0.298006	+	0.0798505i	−0.106718	+	0.994289i	$0.534034\pi$
$488$	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	0.564308	−	0.825564i	$-0.309143\pi$
$499$	2.93753	+	1.69599i	0.131502	+	0.0759227i	−0.432806	+	0.901487i	$0.642476\pi$
$500$	−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	−0.867980	−	0.496599i	$-0.834582\pi$
$503$	−8.32921	+	8.32921i	−0.371381	+	0.371381i	0.496599	+	0.867980i	$0.334582\pi$
$504$		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	−0.00580659	−	0.999983i	$-0.501848\pi$
$509$	19.4726	−	33.7275i	0.863108	−	1.49495i	0.868914	−	0.494963i	$-0.164818\pi$
$510$	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	−0.359902	−	0.932990i	$-0.617190\pi$
$521$	6.12042	−	3.53363i	0.268141	−	0.154811i	0.628042	+	0.778179i	$0.283856\pi$
$522$	−13.1863	−	3.53326i	−0.577150	−	0.154647i
$523$	5.33985	+	19.9286i	0.233495	+	0.871416i	0.978821	+	0.204716i	$0.0656272\pi$
$523$	5.33985	+	19.9286i	0.233495	+	0.871416i	−0.745326	+	0.666700i	$0.767706\pi$
$524$	−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	−0.993709	−	0.111993i	$-0.964276\pi$
$541$	−9.30063	+	16.1092i	−0.399865	+	0.692587i	0.593844	+	0.804581i	$0.297610\pi$
$542$	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	−0.844526	−	0.535515i	$-0.820118\pi$
$547$	−7.22715	+	7.22715i	−0.309011	+	0.309011i	0.535515	+	0.844526i	$0.320118\pi$
$548$	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	0.274958	−	0.961456i	$-0.411336\pi$
$557$	0.763508	+	0.204581i	0.0323509	+	0.00866839i	−0.242607	+	0.970125i	$0.578003\pi$
$558$	−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	0.238541	−	0.971132i	$-0.423331\pi$
$563$	−0.959599	−	0.257124i	−0.0404423	−	0.0108365i	−0.278983	+	0.960296i	$0.589997\pi$
$564$	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	0.665966	−	0.745982i	$-0.268020\pi$
$569$	8.41819	+	4.86025i	0.352909	+	0.203752i	−0.313057	+	0.949734i	$0.601353\pi$
$570$	−22.2117	−	7.06962i	−0.930348	−	0.296114i
$571$	0.493342	+	0.854493i	0.0206457	+	0.0357594i	0.876164	−	0.482014i	$-0.160094\pi$
$571$	0.493342	+	0.854493i	0.0206457	+	0.0357594i	−0.855518	+	0.517773i	$0.826761\pi$
$572$	−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	0.841130	+	0.540833i	$0.181891\pi$
$577$	−3.78872	+	14.1397i	−0.157726	+	0.588643i	−0.998856	+	0.0478100i	$0.984776\pi$
$578$	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	0.120160	−	0.992755i	$-0.461659\pi$
$587$	−21.1413	−	21.1413i	−0.872594	−	0.872594i	−0.992755	+	0.120160i	$0.961659\pi$
$588$		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	0.998499	−	0.0547654i	$-0.0174411\pi$
$593$	2.59079	+	9.66895i	0.106391	+	0.397056i	−0.892108	+	0.451821i	$0.850774\pi$
$594$	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	−0.368358	−	0.929684i	$-0.620080\pi$
$599$	6.18210	−	3.56924i	0.252594	−	0.145835i	0.620951	+	0.783849i	$0.286746\pi$
$600$	31.4726	+	22.2927i	1.28486	+	0.910096i
$601$		−	35.0829i		−	1.43106i	−0.698580	−	0.715532i	$-0.746185\pi$
$601$		−	35.0829i		−	1.43106i	0.698580	−	0.715532i	$-0.253815\pi$
$602$		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	−0.107034	−	0.994255i	$-0.534135\pi$
$607$	7.32715	−	1.96330i	0.297400	−	0.0796880i	0.404434	+	0.914567i	$0.367469\pi$
$608$	−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	0.844038	+	0.536284i	$0.180172\pi$
$613$	−3.83917	+	14.3280i	−0.155062	+	0.578701i	−0.999100	+	0.0424169i	$0.986494\pi$
$614$	−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	−0.185571	−	0.982631i	$-0.559414\pi$
$617$	19.7986	−	19.7986i	0.797060	−	0.797060i	0.982631	+	0.185571i	$0.0594135\pi$
$618$	29.8754	−	8.00508i	1.20176	−	0.322011i
$619$	6.03375	+	10.4508i	0.242517	+	0.420052i	0.961431	−	0.275048i	$-0.0886936\pi$
$619$	6.03375	+	10.4508i	0.242517	+	0.420052i	−0.718914	+	0.695099i	$0.755360\pi$
$620$	−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	−0.959928	−	0.280248i	$-0.909583\pi$
$641$	−18.2964	−	31.6904i	−0.722666	−	1.25169i	0.237262	−	0.971446i	$-0.423750\pi$
$642$	15.7876	−	4.23027i	0.623086	−	0.166955i
$643$	−12.1140	+	12.1140i	−0.477731	+	0.477731i	−0.904405	−	0.426675i	$-0.859685\pi$
$643$	−12.1140	+	12.1140i	−0.477731	+	0.477731i	0.426675	+	0.904405i	$0.359685\pi$
$644$		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	0.681147	+	0.732147i	$0.261481\pi$
$647$	−6.99030	+	26.0881i	−0.274817	+	1.02563i	−0.955964	+	0.293484i	$0.905185\pi$
$648$	−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	−0.758261	−	0.651951i	$-0.773951\pi$
$653$	−27.8271	+	7.45625i	−1.08896	+	0.291786i	−0.330698	+	0.943737i	$0.607284\pi$
$654$	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	$-0.789840\pi$
$659$		−	31.4882i		−	1.22661i	0.789847	−	0.613304i	$-0.210160\pi$
$660$	−13.5769	−	8.70131i	−0.528481	−	0.338698i
$661$	−41.7321	+	24.0940i	−1.62319	+	0.937149i	−0.637129	+	0.770757i	$0.719878\pi$
$661$	−41.7321	+	24.0940i	−1.62319	+	0.937149i	−0.986060	+	0.166392i	$0.946788\pi$
$662$	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	−0.978960	−	0.204055i	$-0.934588\pi$
$673$	−30.6900	−	30.6900i	−1.18301	−	1.18301i	−0.204055	−	0.978960i	$-0.565412\pi$
$674$	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	−0.218151	−	0.975915i	$-0.570002\pi$
$677$	2.10450	−	0.563899i	0.0808825	−	0.0216724i	0.299033	+	0.954243i	$0.403336\pi$
$678$	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	−0.792074	−	0.610424i	$-0.790999\pi$
$683$	5.20319	−	19.4186i	0.199094	−	0.743030i	0.991169	−	0.132606i	$-0.0423345\pi$
$684$	−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	0.320850	−	0.947130i	$-0.396031\pi$
$691$	−8.91028	−	5.14435i	−0.338963	−	0.195700i	−0.659813	+	0.751429i	$0.729365\pi$
$692$	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	0.486639	−	0.873603i	$-0.338223\pi$
$709$	−0.708388	−	0.408988i	−0.0266041	−	0.0153599i	−0.513243	+	0.858243i	$0.671556\pi$
$710$	−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	−0.866096	−	0.499877i	$-0.833379\pi$
$719$	−0.00381028	+	0.00659960i	−0.000142099	+	0.000246124i	0.865954	+	0.500123i	$0.166712\pi$
$720$	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	0.998098	+	0.0616465i	$0.0196352\pi$
$727$	28.5738	+	28.5738i	1.05974	+	1.05974i	0.0616465	+	0.998098i	$0.480365\pi$
$728$		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	−0.912770	−	0.408475i	$-0.866061\pi$
$733$	−8.84033	−	32.9926i	−0.326525	−	1.21861i	0.586244	−	0.810134i	$-0.300606\pi$
$734$	−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	0.246500	−	0.969143i	$-0.420719\pi$
$739$	32.8676	−	18.9761i	1.20905	−	0.698047i	0.962552	+	0.271096i	$0.0873860\pi$
$740$	−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	0.272400	−	0.962184i	$-0.412183\pi$
$743$	−18.8022	−	18.8022i	−0.689784	−	0.689784i	−0.962184	+	0.272400i	$0.912183\pi$
$744$	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	−0.866990	−	0.498326i	$-0.833948\pi$
$751$	−0.0529576	+	0.0917252i	−0.00193245	+	0.00334710i	0.865058	+	0.501673i	$0.167282\pi$
$752$	−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	−0.647637	−	0.761949i	$-0.724243\pi$
$757$	3.14514	−	3.14514i	0.114312	−	0.114312i	0.761949	+	0.647637i	$0.224243\pi$
$758$	−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	0.936823	−	0.349804i	$-0.113752\pi$
$761$	30.4082	+	17.5562i	1.10230	+	0.636410i	0.165472	+	0.986214i	$0.447085\pi$
$762$	−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	0.319993	−	0.947420i	$-0.396320\pi$
$773$	3.43099	+	0.919332i	0.123404	+	0.0330661i	−0.196588	+	0.980486i	$0.562986\pi$
$774$	−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	−0.831735	−	0.555172i	$-0.812652\pi$
$787$	4.66123	−	17.3959i	0.166155	−	0.620098i	0.997890	−	0.0649257i	$-0.0206810\pi$
$788$	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	0.987096	−	0.160129i	$-0.0511912\pi$
$797$	23.3462	+	23.3462i	0.826967	+	0.826967i	−0.160129	+	0.987096i	$0.551191\pi$
$798$		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	−0.0125781	−	0.999921i	$-0.504004\pi$
$809$	24.0937	−	13.9105i	0.847090	−	0.489067i	0.859668	+	0.510853i	$0.170671\pi$
$810$	3.17625	−	4.95601i	0.111602	−	0.174136i
$811$			5.12216i			0.179863i	0.995948	+	0.0899317i	$0.0286649\pi$
$811$			5.12216i			0.179863i	−0.995948	+	0.0899317i	$0.971335\pi$
$812$		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	−0.542600	−	0.839991i	$-0.682560\pi$
$821$	13.0702	−	22.6383i	0.456154	−	0.790082i	0.998754	+	0.0499094i	$0.0158933\pi$
$822$	−8.72572	+	32.5648i	−0.304345	+	1.13583i
$823$	5.02538	−	18.7550i	0.175174	−	0.653757i	−0.821348	−	0.570427i	$-0.806778\pi$
$823$	5.02538	−	18.7550i	0.175174	−	0.653757i	0.996522	−	0.0833299i	$-0.0265555\pi$
$824$	−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	−0.378129	−	0.925753i	$-0.623432\pi$
$827$	15.7484	−	15.7484i	0.547624	−	0.547624i	0.925753	+	0.378129i	$0.123432\pi$
$828$	−27.8147	+	7.45292i	−0.966627	+	0.259007i
$829$	−23.6498	−	40.9627i	−0.821392	−	1.42269i	−0.904646	−	0.426164i	$-0.859865\pi$
$829$	−23.6498	−	40.9627i	−0.821392	−	1.42269i	0.0832545	−	0.996528i	$-0.473469\pi$
$830$	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	0.162958	−	0.986633i	$-0.447897\pi$
$853$	33.5751	−	33.5751i	1.14959	−	1.14959i	0.986633	−	0.162958i	$-0.0521034\pi$
$854$		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	−0.887421	−	0.460960i	$-0.847505\pi$
$857$	3.26670	−	12.1915i	0.111588	−	0.416454i	0.999009	+	0.0445069i	$0.0141717\pi$
$858$	1.25141	−	4.67033i	0.0427225	−	0.159443i
$859$	−10.1851	+	17.6410i	−0.347510	+	0.601905i	−0.985806	−	0.167886i	$-0.946306\pi$
$859$	−10.1851	+	17.6410i	−0.347510	+	0.601905i	0.638297	+	0.769791i	$0.279639\pi$
$860$	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	0.104861	−	0.994487i	$-0.466560\pi$
$863$	20.3557	−	5.45430i	0.692917	−	0.185666i	0.588056	+	0.808820i	$0.299894\pi$
$864$	−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	0.945105	+	0.326765i	$0.105959\pi$
$877$	8.58820	+	32.0516i	0.290003	+	1.08231i	−0.655103	+	0.755540i	$0.727375\pi$
$878$	−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	$0.200471\pi$
$881$			34.9639i			1.17796i	−0.808147	+	0.588981i	$0.799529\pi$
$882$		0			0
$883$	19.3814	+	19.3814i	0.652235	+	0.652235i	0.953531	−	0.301295i	$-0.0974190\pi$
$883$	19.3814	+	19.3814i	0.652235	+	0.652235i	−0.301295	+	0.953531i	$0.597419\pi$
$884$	−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	0.211131	−	0.977458i	$-0.432285\pi$
$887$	26.2892	−	7.04416i	0.882704	−	0.236520i	0.671574	+	0.740938i	$0.265619\pi$
$888$	−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	0.580059	−	0.814575i	$-0.303030\pi$
$907$	20.3321	+	5.44798i	0.675117	+	0.180897i	0.0950584	+	0.995472i	$0.469696\pi$
$908$	−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	−0.107209	−	0.994237i	$-0.534191\pi$
$919$	−30.9773	−	17.8848i	−1.02185	−	0.589964i	−0.914638	+	0.404273i	$0.867525\pi$
$920$	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	−0.816532	−	0.577300i	$-0.804106\pi$
$929$	2.79468	−	4.84053i	0.0916905	−	0.158813i	0.908223	+	0.418487i	$0.137440\pi$
$930$	−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	0.290092	−	0.956999i	$-0.406314\pi$
$937$	−20.4143	−	20.4143i	−0.666906	−	0.666906i	−0.956999	+	0.290092i	$0.906314\pi$
$938$		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	−0.238570	−	0.971125i	$-0.576679\pi$
$941$	14.8214	−	8.55714i	0.483164	−	0.278955i	0.721734	+	0.692170i	$0.243345\pi$
$942$	−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	0.994555	−	0.104217i	$-0.0332336\pi$
$947$	2.49685	+	9.31836i	0.0811366	+	0.302806i	−0.913418	+	0.407023i	$0.866567\pi$
$948$	−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	0.999988	−	0.00497101i	$-0.00158233\pi$
$953$	30.7169	+	30.7169i	0.995017	+	0.995017i	−0.00497101	+	0.999988i	$0.501582\pi$
$954$	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	−0.188619	−	0.982050i	$-0.560401\pi$
$967$	24.6730	−	24.6730i	0.793431	−	0.793431i	0.982050	+	0.188619i	$0.0604012\pi$
$968$	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	0.175552	−	0.984470i	$-0.443829\pi$
$971$	−18.3615	−	10.6010i	−0.589247	−	0.340202i	−0.764800	+	0.644268i	$0.777162\pi$
$972$	−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	0.0752233	−	0.997167i	$-0.476033\pi$
$977$	−11.1967	−	3.00015i	−0.358215	−	0.0959834i	−0.433438	+	0.901183i	$0.642700\pi$
$978$	−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	0.296722	−	0.954964i	$-0.404106\pi$
$983$	2.38938	+	0.640231i	0.0762093	+	0.0204202i	−0.220513	+	0.975384i	$0.570773\pi$
$984$	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	0.994276	+	0.106838i	$0.0340725\pi$
$991$	18.5627	+	32.1515i	0.589662	+	1.02133i	−0.404614	+	0.914488i	$0.632594\pi$
$992$	−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	0.169277	+	0.985569i	$0.445857\pi$
$997$	−14.8437	+	55.3975i	−0.470106	+	1.75446i	−0.639382	+	0.768889i	$0.720810\pi$
$998$	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.313.2		32
5.2	odd	4	inner	735.2.v.a.607.8		32
7.2	even	3		105.2.m.a.13.1	✓	16
7.3	odd	6	inner	735.2.v.a.178.8		32
7.4	even	3	inner	735.2.v.a.178.7		32
7.5	odd	6		105.2.m.a.13.2	yes	16
7.6	odd	2	inner	735.2.v.a.313.1		32
21.2	odd	6		315.2.p.e.118.8		16
21.5	even	6		315.2.p.e.118.7		16
28.19	even	6		1680.2.cz.d.433.3		16
28.23	odd	6		1680.2.cz.d.433.6		16
35.2	odd	12		105.2.m.a.97.2	yes	16
35.9	even	6		525.2.m.b.118.8		16
35.12	even	12		105.2.m.a.97.1	yes	16
35.17	even	12	inner	735.2.v.a.472.2		32
35.19	odd	6		525.2.m.b.118.7		16
35.23	odd	12		525.2.m.b.307.7		16
35.27	even	4	inner	735.2.v.a.607.7		32
35.32	odd	12	inner	735.2.v.a.472.1		32
35.33	even	12		525.2.m.b.307.8		16
105.2	even	12		315.2.p.e.307.7		16
105.47	odd	12		315.2.p.e.307.8		16
140.47	odd	12		1680.2.cz.d.97.6		16
140.107	even	12		1680.2.cz.d.97.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.1	✓	16	7.2	even	3
105.2.m.a.13.2	yes	16	7.5	odd	6
105.2.m.a.97.1	yes	16	35.12	even	12
105.2.m.a.97.2	yes	16	35.2	odd	12
315.2.p.e.118.7		16	21.5	even	6
315.2.p.e.118.8		16	21.2	odd	6
315.2.p.e.307.7		16	105.2	even	12
315.2.p.e.307.8		16	105.47	odd	12
525.2.m.b.118.7		16	35.19	odd	6
525.2.m.b.118.8		16	35.9	even	6
525.2.m.b.307.7		16	35.23	odd	12
525.2.m.b.307.8		16	35.33	even	12
735.2.v.a.178.7		32	7.4	even	3	inner
735.2.v.a.178.8		32	7.3	odd	6	inner
735.2.v.a.313.1		32	7.6	odd	2	inner
735.2.v.a.313.2		32	1.1	even	1	trivial
735.2.v.a.472.1		32	35.32	odd	12	inner
735.2.v.a.472.2		32	35.17	even	12	inner
735.2.v.a.607.7		32	35.27	even	4	inner
735.2.v.a.607.8		32	5.2	odd	4	inner
1680.2.cz.d.97.3		16	140.107	even	12
1680.2.cz.d.97.6		16	140.47	odd	12
1680.2.cz.d.433.3		16	28.19	even	6
1680.2.cz.d.433.6		16	28.23	odd	6

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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