LMFDB - Embedded newform 735.2.v.a.607.8

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			607.8
Character	$\chi$	$=$	735.607
Dual form			735.2.v.a.178.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.54281 - 0.681344i) q^{2} +(0.258819 - 0.965926i) q^{3} +(4.26961 - 2.46506i) q^{4} +(0.678180 + 2.13074i) q^{5} -2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(2.54281 - 0.681344i) q^{2} +(0.258819 - 0.965926i) q^{3} +(4.26961 - 2.46506i) q^{4} +(0.678180 + 2.13074i) q^{5} -2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(3.17625 + 4.95601i) q^{10} +(0.731395 + 1.26681i) q^{11} +(-1.27601 - 4.76213i) q^{12} +(-0.887844 - 0.887844i) q^{13} +(2.23367 - 0.103594i) q^{15} +(5.22294 - 9.04639i) q^{16} +(-2.87705 - 0.770902i) q^{17} +(-2.54281 - 0.681344i) q^{18} +(-1.97993 + 3.42935i) q^{19} +(8.14798 + 7.42570i) q^{20} +(2.72294 + 2.72294i) q^{22} +(-1.51171 - 5.64178i) q^{23} +(-3.85679 - 6.68016i) q^{24} +(-4.08014 + 2.89006i) q^{25} +(-2.86255 - 1.65269i) q^{26} +(-0.707107 + 0.707107i) q^{27} +5.18572i q^{29} +(5.60921 - 1.78532i) q^{30} +(5.28575 - 3.05173i) q^{31} +(3.12439 - 11.6604i) q^{32} +(1.41295 - 0.378598i) q^{33} -7.84104 q^{34} -4.93012 q^{36} +(-3.08121 + 0.825607i) q^{37} +(-2.69804 + 10.0692i) q^{38} +(-1.08738 + 0.627801i) q^{39} +(15.3208 + 7.92277i) q^{40} -0.769968i q^{41} +(-5.18572 + 5.18572i) q^{43} +(6.24554 + 3.60587i) q^{44} +(0.478051 - 2.18437i) q^{45} +(-7.68800 - 13.3160i) q^{46} +(-3.13699 - 11.7074i) q^{47} +(-7.38635 - 7.38635i) q^{48} +(-8.40592 + 10.1289i) q^{50} +(-1.48927 + 2.57949i) q^{51} +(-5.97934 - 1.60216i) q^{52} +(0.743732 + 0.199282i) q^{53} +(-1.31626 + 2.27982i) q^{54} +(-2.20324 + 2.41754i) q^{55} +(2.80005 + 2.80005i) q^{57} +(3.53326 + 13.1863i) q^{58} +(-1.59816 - 2.76810i) q^{59} +(9.28153 - 5.94843i) q^{60} +(1.23031 + 0.710320i) q^{61} +(11.3614 - 11.3614i) q^{62} -10.8872i q^{64} +(1.28965 - 2.49389i) q^{65} +(3.33490 - 1.92541i) q^{66} +(-2.17058 + 8.10070i) q^{67} +(-14.1842 + 3.80064i) q^{68} -5.84081 q^{69} +7.62611 q^{71} +(-7.45075 + 1.99642i) q^{72} +(-2.49402 + 9.30780i) q^{73} +(-7.27241 + 4.19873i) q^{74} +(1.73556 + 4.68912i) q^{75} +19.5226i q^{76} +(-2.33726 + 2.33726i) q^{78} +(-3.91469 - 2.26015i) q^{79} +(22.8176 + 4.99366i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.524613 - 1.95788i) q^{82} +(6.75794 + 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} +(-9.65306 + 16.7196i) q^{86} +(5.00903 + 1.34216i) q^{87} +(10.8989 + 2.92035i) q^{88} +(0.599954 - 1.03915i) q^{89} +(-0.272713 - 5.88016i) q^{90} +(-20.3618 - 20.3618i) q^{92} +(-1.57969 - 5.89549i) q^{93} +(-15.9535 - 27.6323i) q^{94} +(-8.64982 - 1.89302i) 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.54281	−	0.681344i	1.79804	−	0.481783i	0.804370	−	0.594128i	$-0.202503\pi$
$2$	2.54281	−	0.681344i	1.79804	−	0.481783i	0.993669	+	0.112345i	$0.0358361\pi$
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	4.26961	−	2.46506i	2.13481	−	1.23253i
$5$	0.678180	+	2.13074i	0.303291	+	0.952898i
$5$	0.678180	+	2.13074i	0.303291	+	0.952898i
$6$		−	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
$10$	3.17625	+	4.95601i	1.00442	+	1.56723i
$11$	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	$0.762557\pi$
$12$	−1.27601	−	4.76213i	−0.368352	−	1.37471i
$13$	−0.887844	−	0.887844i	−0.246244	−	0.246244i	0.573183	−	0.819427i	$-0.305708\pi$
$13$	−0.887844	−	0.887844i	−0.246244	−	0.246244i	−0.819427	+	0.573183i	$0.805708\pi$
$14$		0			0
$15$	2.23367	−	0.103594i	0.576730	−	0.0267479i
$16$	5.22294	−	9.04639i	1.30573	−	2.26160i
$17$	−2.87705	−	0.770902i	−0.697786	−	0.186971i	−0.107547	−	0.994200i	$-0.534300\pi$
$17$	−2.87705	−	0.770902i	−0.697786	−	0.186971i	−0.590239	+	0.807229i	$0.700966\pi$
$18$	−2.54281	−	0.681344i	−0.599347	−	0.160594i
$19$	−1.97993	+	3.42935i	−0.454228	+	0.786746i	−0.998643	−	0.0520695i	$-0.983418\pi$
$19$	−1.97993	+	3.42935i	−0.454228	+	0.786746i	0.544415	+	0.838816i	$0.316752\pi$
$20$	8.14798	+	7.42570i	1.82194	+	1.66044i
$21$		0			0
$22$	2.72294	+	2.72294i	0.580532	+	0.580532i
$23$	−1.51171	−	5.64178i	−0.315214	−	1.17639i	−0.923790	−	0.382898i	$-0.874926\pi$
$23$	−1.51171	−	5.64178i	−0.315214	−	1.17639i	0.608577	−	0.793495i	$-0.291741\pi$
$24$	−3.85679	−	6.68016i	−0.787265	−	1.36358i
$25$	−4.08014	+	2.89006i	−0.816029	+	0.578011i
$26$	−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	$0.840099\pi$
$30$	5.60921	−	1.78532i	1.02410	−	0.325953i
$31$	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	$0.148682\pi$
$32$	3.12439	−	11.6604i	0.552319	−	2.06128i
$33$	1.41295	−	0.378598i	0.245962	−	0.0659054i
$34$	−7.84104			−1.34473
$35$		0			0
$36$	−4.93012			−0.821687
$37$	−3.08121	+	0.825607i	−0.506548	+	0.135729i	−0.503037	−	0.864265i	$-0.667784\pi$
$37$	−3.08121	+	0.825607i	−0.506548	+	0.135729i	−0.00351049	+	0.999994i	$0.501117\pi$
$38$	−2.69804	+	10.0692i	−0.437679	+	1.63344i
$39$	−1.08738	+	0.627801i	−0.174121	+	0.100529i
$40$	15.3208	+	7.92277i	2.42243	+	1.25270i
$41$		−	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	−0.981627	−	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
$45$	0.478051	−	2.18437i	0.0712637	−	0.325626i
$46$	−7.68800	−	13.3160i	−1.13353	−	1.96334i
$47$	−3.13699	−	11.7074i	−0.457577	−	1.70770i	−0.680400	−	0.732841i	$-0.738194\pi$
$47$	−3.13699	−	11.7074i	−0.457577	−	1.70770i	0.222823	−	0.974859i	$-0.428473\pi$
$48$	−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
$52$	−5.97934	−	1.60216i	−0.829185	−	0.222180i
$53$	0.743732	+	0.199282i	0.102159	+	0.0273735i	0.309537	−	0.950888i	$-0.399826\pi$
$53$	0.743732	+	0.199282i	0.102159	+	0.0273735i	−0.207377	+	0.978261i	$0.566493\pi$
$54$	−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
$58$	3.53326	+	13.1863i	0.463940	+	1.73145i
$59$	−1.59816	−	2.76810i	−0.208063	−	0.360376i	0.743041	−	0.669246i	$-0.233383\pi$
$59$	−1.59816	−	2.76810i	−0.208063	−	0.360376i	−0.951104	+	0.308870i	$0.900049\pi$
$60$	9.28153	−	5.94843i	1.19824	−	0.767939i
$61$	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
$65$	1.28965	−	2.49389i	0.159962	−	0.309329i
$66$	3.33490	−	1.92541i	0.410498	−	0.237001i
$67$	−2.17058	+	8.10070i	−0.265178	+	0.989658i	0.696963	+	0.717107i	$0.254534\pi$
$67$	−2.17058	+	8.10070i	−0.265178	+	0.989658i	−0.962141	+	0.272551i	$0.912133\pi$
$68$	−14.1842	+	3.80064i	−1.72009	+	0.460896i
$69$	−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	$0.350523\pi$
$72$	−7.45075	+	1.99642i	−0.878080	+	0.235281i
$73$	−2.49402	+	9.30780i	−0.291903	+	1.08940i	0.651744	+	0.758439i	$0.274038\pi$
$73$	−2.49402	+	9.30780i	−0.291903	+	1.08940i	−0.943646	+	0.330956i	$0.892629\pi$
$74$	−7.27241	+	4.19873i	−0.845401	+	0.488092i
$75$	1.73556	+	4.68912i	0.200405	+	0.541453i
$76$			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	$-0.415174\pi$
$79$	−3.91469	−	2.26015i	−0.440437	−	0.254286i	−0.703783	+	0.710415i	$0.748507\pi$
$80$	22.8176	+	4.99366i	2.55109	+	0.558308i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.524613	−	1.95788i	−0.0579338	−	0.216212i
$83$	6.75794	+	6.75794i	0.741781	+	0.741781i	0.972921	−	0.231140i	$-0.0742455\pi$
$83$	6.75794	+	6.75794i	0.741781	+	0.741781i	−0.231140	+	0.972921i	$0.574246\pi$
$84$		0			0
$85$	−0.308559	−	6.65306i	−0.0334679	−	0.721626i
$86$	−9.65306	+	16.7196i	−1.04092	+	1.80292i
$87$	5.00903	+	1.34216i	0.537024	+	0.143895i
$88$	10.8989	+	2.92035i	1.16182	+	0.311310i
$89$	0.599954	−	1.03915i	0.0635950	−	0.110150i	−0.832475	−	0.554063i	$-0.813077\pi$
$89$	0.599954	−	1.03915i	0.0635950	−	0.110150i	0.896070	+	0.443913i	$0.146410\pi$
$90$	−0.272713	−	5.88016i	−0.0287465	−	0.619823i
$91$		0			0
$92$	−20.3618	−	20.3618i	−2.12286	−	2.12286i
$93$	−1.57969	−	5.89549i	−0.163806	−	0.611334i
$94$	−15.9535	−	27.6323i	−1.64548	−	2.85006i
$95$	−8.64982	−	1.89302i	−0.887452	−	0.194220i
$96$	−10.4544	−	6.03586i	−1.06700	−	0.616032i
$97$	8.68829	−	8.68829i	0.882162	−	0.882162i	−0.111592	−	0.993754i	$-0.535595\pi$
$97$	8.68829	−	8.68829i	0.882162	−	0.882162i	0.993754	+	0.111592i	$0.0355950\pi$
$98$		0			0
$99$		−	1.46279i		−	0.147016i
$100$	−10.2965	+	22.3972i	−1.02965	+	2.23972i
$101$	−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	$0.609753\pi$
$102$	−2.02941	+	7.57386i	−0.200941	+	0.749924i
$103$	11.3486	−	3.04085i	1.11821	−	0.299624i	0.348052	−	0.937475i	$-0.386843\pi$
$103$	11.3486	−	3.04085i	1.11821	−	0.299624i	0.770160	+	0.637851i	$0.220177\pi$
$104$	−9.68519			−0.949711
$105$		0			0
$106$	2.02695			0.196875
$107$	−5.99715	+	1.60693i	−0.579766	+	0.155348i	−0.536772	−	0.843727i	$-0.680356\pi$
$107$	−5.99715	+	1.60693i	−0.579766	+	0.155348i	−0.0429945	+	0.999075i	$0.513690\pi$
$108$	−1.27601	+	4.76213i	−0.122784	+	0.458237i
$109$	6.44831	−	3.72294i	0.617636	−	0.356593i	−0.158312	−	0.987389i	$-0.550605\pi$
$109$	6.44831	−	3.72294i	0.617636	−	0.356593i	0.775948	+	0.630797i	$0.217272\pi$
$110$	−3.95524	+	7.64852i	−0.377117	+	0.729258i
$111$			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
$115$	10.9960	−	7.04722i	1.02538	−	0.657156i
$116$	12.7831	+	22.1410i	1.18688	+	2.05574i
$117$	0.324974	+	1.21282i	0.0300438	+	0.112125i
$118$	−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
$122$	3.61242	+	0.967945i	0.327053	+	0.0876337i
$123$	−0.743732	−	0.199282i	−0.0670600	−	0.0179687i
$124$	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	$0.585829\pi$
$128$	−1.16915	−	4.36334i	−0.103339	−	0.385668i
$129$	3.66686	+	6.35119i	0.322849	+	0.559191i
$130$	1.58014	−	7.22018i	0.138588	−	0.633252i
$131$	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
$135$	−1.98621	−	1.02712i	−0.170946	−	0.0884003i
$136$	−19.8971	+	11.4876i	−1.70616	+	0.985054i
$137$	3.31460	−	12.3703i	0.283185	−	1.05686i	−0.666970	−	0.745085i	$-0.732409\pi$
$137$	3.31460	−	12.3703i	0.283185	−	1.05686i	0.950155	−	0.311777i	$-0.100924\pi$
$138$	−14.8521	+	3.97960i	−1.26429	+	0.338766i
$139$	11.9913			1.01709			0.508544	−	0.861036i	$-0.330184\pi$
$139$	11.9913			1.01709			0.508544	+	0.861036i	$0.330184\pi$
$140$		0			0
$141$	−12.1204			−1.02072
$142$	19.3918	−	5.19601i	1.62732	−	0.436039i
$143$	0.475368	−	1.77410i	0.0397523	−	0.148357i
$144$	−9.04639	+	5.22294i	−0.753866	+	0.435245i
$145$	−11.0495	+	3.51685i	−0.917607	+	0.292059i
$146$			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	$-0.332071\pi$
$149$	0.0838539	+	0.0484130i	0.00686958	+	0.00396615i	−0.496561	+	0.868002i	$0.665404\pi$
$150$	7.60811	+	10.7410i	0.621199	+	0.877002i
$151$	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	$0.648923\pi$
$152$	7.90558	+	29.5040i	0.641227	+	2.39309i
$153$	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
$157$	2.25063	+	0.603054i	0.179620	+	0.0481290i	0.347508	−	0.937677i	$-0.387028\pi$
$157$	2.25063	+	0.603054i	0.179620	+	0.0481290i	−0.167888	+	0.985806i	$0.553695\pi$
$158$	−11.4943	−	3.07988i	−0.914434	−	0.245022i
$159$	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
$163$	−3.76077	−	14.0354i	−0.294566	−	1.09934i	−0.941561	−	0.336842i	$-0.890641\pi$
$163$	−3.76077	−	14.0354i	−0.294566	−	1.09934i	0.646995	−	0.762495i	$-0.276026\pi$
$164$	−1.89802	−	3.28746i	−0.148210	−	0.256708i
$165$	1.76493	+	2.75387i	0.137399	+	0.214388i
$166$	21.7887	+	12.5797i	1.69113	+	0.976373i
$167$	−0.293008	+	0.293008i	−0.0226737	+	0.0226737i	−0.718353	−	0.695679i	$-0.755104\pi$
$167$	−0.293008	+	0.293008i	−0.0226737	+	0.0226737i	0.695679	+	0.718353i	$0.255104\pi$
$168$		0			0
$169$		−	11.4235i		−	0.878728i
$170$	−5.31763	−	16.7072i	−0.407844	−	1.28139i
$171$	3.42935	−	1.97993i	0.262249	−	0.151409i
$172$	−9.35790	+	34.9242i	−0.713533	+	2.66294i
$173$	−4.71537	+	1.26348i	−0.358503	+	0.0960606i	−0.433575	−	0.901118i	$-0.642748\pi$
$173$	−4.71537	+	1.26348i	−0.358503	+	0.0960606i	0.0750719	+	0.997178i	$0.476081\pi$
$174$	13.6515			1.03492
$175$		0			0
$176$	15.2801			1.15178
$177$	−3.08742	+	0.827271i	−0.232064	+	0.0621815i
$178$	0.817551	−	3.05114i	0.0612781	−	0.228693i
$179$	−1.72994	+	0.998779i	−0.129302	+	0.0746523i	−0.563256	−	0.826283i	$-0.690451\pi$
$179$	−1.72994	+	0.998779i	−0.129302	+	0.0746523i	0.433954	+	0.900935i	$0.357118\pi$
$180$	−3.34351	−	10.5048i	−0.249211	−	0.782984i
$181$			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
$185$	−3.84877	−	6.00536i	−0.282967	−	0.441523i
$186$	−8.03372	−	13.9148i	−0.589061	−	1.02028i
$187$	−1.12767	−	4.20851i	−0.0824632	−	0.307757i
$188$	−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	$0.0751934\pi$
$192$	−10.5162	−	2.81781i	−0.758943	−	0.203358i
$193$	−18.5257	−	4.96393i	−1.33351	−	0.357312i	−0.479485	−	0.877550i	$-0.659176\pi$
$193$	−18.5257	−	4.96393i	−1.33351	−	0.357312i	−0.854021	+	0.520239i	$0.825843\pi$
$194$	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	$0.946287\pi$
$198$	−0.996663	−	3.71960i	−0.0708298	−	0.264340i
$199$	10.0734	+	17.4476i	0.714084	+	1.23683i	0.963312	+	0.268384i	$0.0864897\pi$
$199$	10.0734	+	17.4476i	0.714084	+	1.23683i	−0.249228	+	0.968445i	$0.580177\pi$
$200$	−6.49114	+	38.0178i	−0.458993	+	2.68826i
$201$	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
$205$	1.64060	−	0.522176i	0.114585	−	0.0364704i
$206$	26.7855	−	15.4646i	1.86623	−	1.07747i
$207$	−1.51171	+	5.64178i	−0.105071	+	0.392131i
$208$	−12.6689	+	3.39463i	−0.878433	+	0.235375i
$209$	−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	$0.364868\pi$
$212$	3.66669	−	0.982486i	0.251829	−	0.0674774i
$213$	1.97378	−	7.36626i	0.135241	−	0.504728i
$214$	−14.1548	+	8.17225i	−0.967599	+	0.558644i
$215$	−14.5663	−	7.53260i	−0.993414	−	0.513719i
$216$			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
$220$	−3.44758	+	15.7531i	−0.232436	+	1.06207i
$221$	1.86993	+	3.23881i	0.125785	+	0.217866i
$222$	2.17342	+	8.11132i	0.145871	+	0.544396i
$223$	0.660910	+	0.660910i	0.0442578	+	0.0442578i	0.728889	−	0.684632i	$-0.240037\pi$
$223$	0.660910	+	0.660910i	0.0442578	+	0.0442578i	−0.684632	+	0.728889i	$0.740037\pi$
$224$		0			0
$225$	4.97854	−	0.462789i	0.331902	−	0.0308526i
$226$	4.73641	−	8.20370i	0.315061	−	0.545702i
$227$	−23.6988	−	6.35007i	−1.57294	−	0.421469i	−0.636210	−	0.771516i	$-0.719499\pi$
$227$	−23.6988	−	6.35007i	−1.57294	−	0.421469i	−0.936732	+	0.350047i	$0.886166\pi$
$228$	18.8574	+	5.05283i	1.24886	+	0.334632i
$229$	−12.5391	+	21.7184i	−0.828607	+	1.43519i	0.0705240	+	0.997510i	$0.477533\pi$
$229$	−12.5391	+	21.7184i	−0.828607	+	1.43519i	−0.899131	+	0.437679i	$0.855800\pi$
$230$	23.1592	−	25.4118i	1.52707	−	1.67560i
$231$		0			0
$232$	28.2847	+	28.2847i	1.85698	+	1.85698i
$233$	0.820401	+	3.06178i	0.0537462	+	0.200584i	0.987578	−	0.157128i	$-0.0502236\pi$
$233$	0.820401	+	3.06178i	0.0537462	+	0.200584i	−0.933832	+	0.357712i	$0.883557\pi$
$234$	1.65269	+	2.86255i	0.108040	+	0.187131i
$235$	22.8180	−	14.6238i	1.48848	−	0.953954i
$236$	−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	$-0.242997\pi$
$240$	10.7291	−	20.7477i	0.692563	−	1.33926i
$241$	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	$0.326934\pi$
$242$	6.03688	−	22.5299i	0.388065	−	1.44828i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	7.00393			0.448381
$245$		0			0
$246$	−2.02695			−0.129234
$247$	4.80260	−	1.28685i	0.305582	−	0.0818805i
$248$	12.1851	−	45.4754i	0.773754	−	2.88769i
$249$	8.27676	−	4.77859i	0.524518	−	0.302831i
$250$	−27.2827	−	11.0417i	−1.72551	−	0.698337i
$251$		−	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
$255$	−6.50622	−	1.42389i	−0.407435	−	0.0891677i
$256$	4.94133	+	8.55863i	0.308833	+	0.534914i
$257$	−7.79833	−	29.1038i	−0.486446	−	1.81544i	−0.573458	−	0.819235i	$-0.694398\pi$
$257$	−7.79833	−	29.1038i	−0.486446	−	1.81544i	0.0870116	−	0.996207i	$-0.472268\pi$
$258$	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
$262$	15.7201	+	4.21218i	0.971190	+	0.260230i
$263$	22.3275	+	5.98263i	1.37677	+	0.368905i	0.869947	−	0.493145i	$-0.164153\pi$
$263$	22.3275	+	5.98263i	1.37677	+	0.368905i	0.506824	+	0.862049i	$0.330819\pi$
$264$	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
$268$	10.7012	+	39.9374i	0.653680	+	2.43957i
$269$	−8.29515	−	14.3676i	−0.505764	−	0.876009i	−0.999978	−	0.00666889i	$-0.997877\pi$
$269$	−8.29515	−	14.3676i	−0.505764	−	0.876009i	0.494213	−	0.869341i	$-0.335456\pi$
$270$	−5.75038	−	1.25848i	−0.349957	−	0.0765884i
$271$	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
$275$	−6.64536	−	3.05501i	−0.400730	−	0.184224i
$276$	−24.9380	+	14.3979i	−1.50109	+	0.866654i
$277$	7.80024	−	29.1109i	0.468671	−	1.74910i	−0.175751	−	0.984435i	$-0.556235\pi$
$277$	7.80024	−	29.1109i	0.468671	−	1.74910i	0.644422	−	0.764670i	$-0.277098\pi$
$278$	30.4916	−	8.17019i	1.82876	−	0.490016i
$279$	−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	$0.717317\pi$
$282$	−30.8199	+	8.25816i	−1.83530	+	0.491766i
$283$	−0.971693	+	3.62641i	−0.0577611	+	0.215567i	−0.988774	−	0.149419i	$-0.952260\pi$
$283$	−0.971693	+	3.62641i	−0.0577611	+	0.215567i	0.931013	+	0.364986i	$0.118926\pi$
$284$	32.5605	−	18.7988i	1.93211	−	1.11551i
$285$	−4.06725	+	7.86513i	−0.240923	+	0.465890i
$286$		−	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
$290$	−25.7005	+	16.4712i	−1.50919	+	0.967221i
$291$	−6.14355	−	10.6409i	−0.360141	−	0.623783i
$292$	12.2958	+	45.8886i	0.719558	+	2.68543i
$293$	1.56714	+	1.56714i	0.0915536	+	0.0915536i	0.751400	−	0.659847i	$-0.229379\pi$
$293$	1.56714	+	1.56714i	0.0915536	+	0.0915536i	−0.659847	+	0.751400i	$0.729379\pi$
$294$		0			0
$295$	4.81428	−	5.28255i	0.280298	−	0.307562i
$296$	−12.3028	+	21.3091i	−0.715085	+	1.23856i
$297$	−1.41295	−	0.378598i	−0.0819875	−	0.0219685i
$298$	0.246211	+	0.0659719i	0.0142626	+	0.00382165i
$299$	−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
$303$	3.97081	+	14.8193i	0.228117	+	0.851345i
$304$	20.6821	+	35.8225i	1.18620	+	2.05456i
$305$	−0.679139	+	3.10320i	−0.0388874	+	0.177689i
$306$	6.79054	+	3.92052i	0.388189	+	0.224121i
$307$	17.3551	−	17.3551i	0.990510	−	0.990510i	−0.00944588	−	0.999955i	$-0.503007\pi$
$307$	17.3551	−	17.3551i	0.990510	−	0.990510i	0.999955	+	0.00944588i	$0.00300676\pi$
$308$		0			0
$309$		−	11.7489i		−	0.668374i
$310$	31.9133	+	16.5032i	1.81255	+	0.937316i
$311$	−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	$0.990364\pi$
$312$	−2.50671	+	9.35518i	−0.141915	+	0.529633i
$313$	7.81948	−	2.09522i	0.441983	−	0.118429i	−0.0309625	−	0.999521i	$-0.509857\pi$
$313$	7.81948	−	2.09522i	0.441983	−	0.118429i	0.472946	+	0.881091i	$0.343191\pi$
$314$	6.13381			0.346151
$315$		0			0
$316$	−22.2856			−1.25366
$317$	−1.02804	+	0.275463i	−0.0577406	+	0.0154715i	−0.287574	−	0.957759i	$-0.592849\pi$
$317$	−1.02804	+	0.275463i	−0.0577406	+	0.0154715i	0.229833	+	0.973230i	$0.426182\pi$
$318$	0.524613	−	1.95788i	0.0294188	−	0.109793i
$319$	−6.56934	+	3.79281i	−0.367813	+	0.212357i
$320$	23.1978	−	7.38348i	1.29680	−	0.412749i
$321$			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
$325$	6.18845	+	1.05661i	0.343274	+	0.0586104i
$326$	−19.1259	−	33.1270i	−1.05928	−	1.83473i
$327$	−1.92713	−	7.19216i	−0.106571	−	0.397727i
$328$	−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	$0.309724\pi$
$332$	45.5125	+	12.1950i	2.49783	+	0.669290i
$333$	3.08121	+	0.825607i	0.168849	+	0.0452430i
$334$	−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	$-0.530815\pi$
$338$	−7.78331	−	29.0477i	−0.423357	−	1.57999i
$339$	−1.79920	−	3.11630i	−0.0977190	−	0.169254i
$340$	−17.7176	−	27.6454i	−0.960873	−	1.49928i
$341$	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
$345$	−3.96112	−	12.4453i	−0.213259	−	0.670030i
$346$	−11.1294	+	6.42558i	−0.598322	+	0.345441i
$347$	−7.35151	+	27.4362i	−0.394650	+	1.47285i	0.427726	+	0.903908i	$0.359315\pi$
$347$	−7.35151	+	27.4362i	−0.394650	+	1.47285i	−0.822376	+	0.568945i	$0.807352\pi$
$348$	24.6951	−	6.61704i	1.32380	−	0.354710i
$349$	−14.7663			−0.790420			−0.395210	−	0.918591i	$-0.629328\pi$
$349$	−14.7663			−0.790420			−0.395210	+	0.918591i	$0.629328\pi$
$350$		0			0
$351$	1.25560			0.0670190
$352$	17.0567	−	4.57032i	0.909124	−	0.243599i
$353$	4.57130	−	17.0603i	0.243306	−	0.908029i	−0.730922	−	0.682461i	$-0.760910\pi$
$353$	4.57130	−	17.0603i	0.243306	−	0.908029i	0.974227	−	0.225568i	$-0.0724238\pi$
$354$	−7.28706	+	4.20719i	−0.387303	+	0.223610i
$355$	5.17187	+	16.2493i	0.274495	+	0.862423i
$356$		−	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	$-0.243640\pi$
$359$	9.12549	+	5.26861i	0.481625	+	0.278066i	−0.239468	+	0.970904i	$0.576973\pi$
$360$	−9.30682	−	14.5217i	−0.490512	−	0.765362i
$361$	1.65972	+	2.87471i	0.0873535	+	0.151301i
$362$	5.78140	+	21.5765i	0.303864	+	1.13403i
$363$	−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
$367$	15.2871	+	4.09618i	0.797982	+	0.213819i	0.634698	−	0.772760i	$-0.281125\pi$
$367$	15.2871	+	4.09618i	0.797982	+	0.213819i	0.163284	+	0.986579i	$0.447791\pi$
$368$	−58.9334	−	15.7911i	−3.07211	−	0.823170i
$369$	−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
$373$	6.32295	+	23.5976i	0.327390	+	1.22184i	0.911887	+	0.410440i	$0.134625\pi$
$373$	6.32295	+	23.5976i	0.327390	+	1.22184i	−0.584497	+	0.811396i	$0.698708\pi$
$374$	−5.73489	−	9.93312i	−0.296544	−	0.513630i
$375$	−8.81429	+	6.87810i	−0.455168	+	0.355184i
$376$	−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	$0.850485\pi$
$380$	−41.5978	+	13.2399i	−2.13392	+	0.679191i
$381$	9.62680	−	5.55803i	0.493196	−	0.284747i
$382$	5.33782	−	19.9210i	0.273106	−	1.01925i
$383$	22.0270	−	5.90211i	1.12553	−	0.301584i	0.352408	−	0.935846i	$-0.385363\pi$
$383$	22.0270	−	5.90211i	1.12553	−	0.301584i	0.773118	+	0.634263i	$0.218696\pi$
$384$	−4.51726			−0.230520
$385$		0			0
$386$	−50.4894			−2.56984
$387$	7.08383	−	1.89811i	0.360091	−	0.0964862i
$388$	15.6785	−	58.5128i	0.795953	−	2.97054i
$389$	13.3377	−	7.70053i	0.676249	−	0.390432i	−0.122191	−	0.992507i	$-0.538992\pi$
$389$	13.3377	−	7.70053i	0.676249	−	0.390432i	0.798440	+	0.602074i	$0.205659\pi$
$390$	−6.56519	−	3.39502i	−0.332441	−	0.171914i
$391$			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
$395$	2.16093	−	9.87398i	0.108728	−	0.496814i
$396$	−3.60587	−	6.24554i	−0.181202	−	0.313850i
$397$	−5.92159	−	22.0997i	−0.297196	−	1.10915i	−0.939458	−	0.342665i	$-0.888670\pi$
$397$	−5.92159	−	22.0997i	−0.297196	−	1.10915i	0.642261	−	0.766486i	$-0.277996\pi$
$398$	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	$0.158896\pi$
$402$	21.3252	+	5.71407i	1.06360	+	0.284992i
$403$	−7.40238	−	1.98346i	−0.368739	−	0.0988033i
$404$	−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
$408$	5.94642	+	22.1923i	0.294392	+	1.09868i
$409$	12.1586	+	21.0593i	0.601203	+	1.04131i	0.992639	+	0.121108i	$0.0386449\pi$
$409$	12.1586	+	21.0593i	0.601203	+	1.04131i	−0.391437	+	0.920205i	$0.628022\pi$
$410$	3.81597	−	2.44561i	0.188457	−	0.120780i
$411$	−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
$415$	−9.81635	+	18.9825i	−0.481866	+	0.931817i
$416$	−13.1266	+	7.57863i	−0.643583	+	0.371573i
$417$	3.10357	−	11.5827i	0.151983	−	0.567207i
$418$	−14.7291	+	3.94666i	−0.720425	+	0.193037i
$419$	−15.9893			−0.781127			−0.390563	−	0.920576i	$-0.627720\pi$
$419$	−15.9893			−0.781127			−0.390563	+	0.920576i	$0.627720\pi$
$420$		0			0
$421$	14.7000			0.716433			0.358216	−	0.933639i	$-0.383385\pi$
$421$	14.7000			0.716433			0.358216	+	0.933639i	$0.383385\pi$
$422$	30.4277	−	8.15308i	1.48120	−	0.396886i
$423$	−3.13699	+	11.7074i	−0.152526	+	0.569233i
$424$	5.14351	−	2.96961i	0.249791	−	0.144217i
$425$	13.9667	−	5.16943i	0.677485	−	0.250754i
$426$		−	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
$430$	−42.1717	−	9.22932i	−2.03370	−	0.445077i
$431$	−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	$-0.346885\pi$
$432$	2.70359	+	10.0899i	0.130077	+	0.485452i
$433$	28.0171	+	28.0171i	1.34642	+	1.34642i	0.889520	+	0.456896i	$0.151039\pi$
$433$	28.0171	+	28.0171i	1.34642	+	1.34642i	0.456896	+	0.889520i	$0.348961\pi$
$434$		0			0
$435$	0.537211	+	11.5832i	0.0257573	+	0.555371i
$436$	18.3545	−	31.7910i	0.879023	−	1.52251i
$437$	22.3407	+	5.98618i	1.06870	+	0.286358i
$438$	24.5029	+	6.56553i	1.17079	+	0.313713i
$439$	−1.17828	+	2.04084i	−0.0562363	+	0.0974042i	−0.892773	−	0.450507i	$-0.851243\pi$
$439$	−1.17828	+	2.04084i	−0.0562363	+	0.0974042i	0.836537	+	0.547911i	$0.184577\pi$
$440$	1.16889	+	25.2033i	0.0557246	+	1.20152i
$441$		0			0
$442$	6.96162	+	6.96162i	0.331130	+	0.331130i
$443$	−2.00306	−	7.47553i	−0.0951684	−	0.355173i	0.901877	−	0.431994i	$-0.142190\pi$
$443$	−2.00306	−	7.47553i	−0.0951684	−	0.355173i	−0.997045	+	0.0768206i	$0.975523\pi$
$444$	7.86331	+	13.6196i	0.373176	+	0.646360i
$445$	2.62104	+	0.573618i	0.124249	+	0.0271921i
$446$	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	$-0.00901591\pi$
$450$	12.3442	−	4.56888i	0.581909	−	0.215379i
$451$	0.975405	−	0.563150i	0.0459300	−	0.0265177i
$452$	4.59159	−	17.1360i	0.215970	−	0.806011i
$453$	12.9965	−	3.48240i	0.610629	−	0.163617i
$454$	−64.5881			−3.03127
$455$		0			0
$456$	30.5448			1.43039
$457$	28.7924	−	7.71489i	1.34685	−	0.360887i	0.487879	−	0.872912i	$-0.337771\pi$
$457$	28.7924	−	7.71489i	1.34685	−	0.360887i	0.858971	+	0.512024i	$0.171104\pi$
$458$	−17.0869	+	63.7692i	−0.798418	+	2.97974i
$459$	2.57949	−	1.48927i	0.120400	−	0.0695131i
$460$	29.5768	−	57.1947i	1.37902	−	2.66672i
$461$			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	−0.00746987	+	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
$465$	11.4905	−	7.36412i	0.532858	−	0.341503i
$466$	4.17225	+	7.22655i	0.193276	+	0.334763i
$467$	−2.60354	−	9.71653i	−0.120477	−	0.449627i	0.879161	−	0.476525i	$-0.158104\pi$
$467$	−2.60354	−	9.71653i	−0.120477	−	0.449627i	−0.999638	+	0.0268978i	$0.991437\pi$
$468$	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
$472$	−23.8151	−	6.38123i	−1.09618	−	0.293720i
$473$	−10.3622	−	2.77653i	−0.476452	−	0.127665i
$474$	−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
$478$	−14.5651	−	54.3575i	−0.666190	−	2.48626i
$479$	15.8875	+	27.5179i	0.725917	+	1.25733i	0.958595	+	0.284771i	$0.0919177\pi$
$479$	15.8875	+	27.5179i	0.725917	+	1.25733i	−0.232678	+	0.972554i	$0.574749\pi$
$480$	5.77090	−	26.3691i	0.263404	−	1.20358i
$481$	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
$485$	24.4047	+	12.6203i	1.10816	+	0.573058i
$486$	2.27982	−	1.31626i	0.103415	−	0.0597066i
$487$	−1.76215	+	6.57642i	−0.0798505	+	0.298006i	−0.994289	−	0.106718i	$-0.965966\pi$
$487$	−1.76215	+	6.57642i	−0.0798505	+	0.298006i	0.914439	+	0.404724i	$0.132632\pi$
$488$	10.5848	−	2.83620i	0.479153	−	0.128389i
$489$	−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	$0.279148\pi$
$492$	−3.66669	+	0.982486i	−0.165307	+	0.0442939i
$493$	3.99769	−	14.9196i	0.180047	−	0.671943i
$494$	11.3353	−	6.54445i	0.510000	−	0.294449i
$495$	3.11683	−	0.992034i	0.140091	−	0.0445886i
$496$		−	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	$-0.357524\pi$
$499$	−2.93753	−	1.69599i	−0.131502	−	0.0759227i	−0.564308	+	0.825564i	$0.690857\pi$
$500$	−54.7056	−	6.74980i	−2.44651	−	0.301860i
$501$	0.207188	+	0.358861i	0.00925649	+	0.0160327i
$502$	−11.1361	−	41.5605i	−0.497029	−	1.85494i
$503$	8.32921	+	8.32921i	0.371381	+	0.371381i	0.867980	−	0.496599i	$-0.165418\pi$
$503$	8.32921	+	8.32921i	0.371381	+	0.371381i	−0.496599	+	0.867980i	$0.665418\pi$
$504$		0			0
$505$	−25.3557	−	23.1080i	−1.12831	−	1.02829i
$506$	11.2459	−	19.4785i	0.499942	−	0.865925i
$507$	−11.0342	−	2.95661i	−0.490047	−	0.131308i
$508$	52.9362	+	14.1842i	2.34866	+	0.629323i
$509$	−19.4726	+	33.7275i	−0.863108	+	1.49495i	0.00580659	+	0.999983i	$0.498152\pi$
$509$	−19.4726	+	33.7275i	−0.863108	+	1.49495i	−0.868914	+	0.494963i	$0.835182\pi$
$510$	−17.5143	+	0.812285i	−0.775545	+	0.0359686i
$511$		0			0
$512$	24.7846	+	24.7846i	1.09534	+	1.09534i
$513$	−1.02489	−	3.82494i	−0.0452500	−	0.168875i
$514$	−39.6594	−	68.6920i	−1.74930	−	3.02988i
$515$	14.1757	+	22.1187i	0.624655	+	0.974668i
$516$	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
$520$	−6.56830	−	20.6367i	−0.288039	−	0.904978i
$521$	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	$0.283856\pi$
$522$	3.53326	−	13.1863i	0.154647	−	0.577150i
$523$	19.9286	−	5.33985i	0.871416	−	0.233495i	0.204716	−	0.978821i	$-0.434373\pi$
$523$	19.9286	−	5.33985i	0.871416	−	0.233495i	0.666700	+	0.745326i	$0.267706\pi$
$524$	30.4788			1.33147
$525$		0			0
$526$	60.8508			2.65322
$527$	−17.5599	+	4.70517i	−0.764923	+	0.204960i
$528$	3.95478	−	14.7595i	0.172110	−	0.642323i
$529$	−9.62588	+	5.55750i	−0.418516	+	0.241631i
$530$	1.37464	+	4.31891i	0.0597104	+	0.187602i
$531$			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
$535$	−7.49111	−	11.6886i	−0.323869	−	0.505343i
$536$	32.3449	+	56.0229i	1.39708	+	2.41982i
$537$	0.517006	+	1.92949i	0.0223105	+	0.0832638i
$538$	−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	$0.297610\pi$
$542$	19.7839	+	5.30108i	0.849792	+	0.227701i
$543$	8.19615	+	2.19615i	0.351731	+	0.0942459i
$544$	−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	$0.820118\pi$
$548$	−16.3414	−	60.9869i	−0.698069	−	2.60523i
$549$	−0.710320	−	1.23031i	−0.0303157	−	0.0525084i
$550$	−18.9794	−	3.24053i	−0.809284	−	0.138177i
$551$	−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
$555$	−6.79687	+	2.16333i	−0.288511	+	0.0918281i
$556$	51.1981	−	29.5593i	2.17128	−	1.25359i
$557$	−0.204581	+	0.763508i	−0.00866839	+	0.0323509i	−0.970125	−	0.242607i	$-0.921997\pi$
$557$	−0.204581	+	0.763508i	−0.00866839	+	0.0323509i	0.961456	+	0.274958i	$0.0886640\pi$
$558$	−15.5200	+	4.15856i	−0.657012	+	0.176046i
$559$	9.20823			0.389467
$560$		0			0
$561$	−4.35697			−0.183951
$562$	−53.7853	+	14.4117i	−2.26879	+	0.607922i
$563$	−0.257124	+	0.959599i	−0.0108365	+	0.0404423i	−0.971132	−	0.238541i	$-0.923331\pi$
$563$	−0.257124	+	0.959599i	−0.0108365	+	0.0404423i	0.960296	+	0.278983i	$0.0899975\pi$
$564$	−51.7494	+	29.8775i	−2.17904	+	1.25807i
$565$	7.14717	+	3.69598i	0.300684	+	0.155491i
$566$			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	$-0.398647\pi$
$569$	−8.41819	−	4.86025i	−0.352909	−	0.203752i	−0.665966	+	0.745982i	$0.731980\pi$
$570$	−4.98340	+	22.7707i	−0.208732	+	0.953762i
$571$	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	$0.826761\pi$
$572$	−2.34362	−	8.74652i	−0.0979918	−	0.365710i
$573$	−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
$577$	−14.1397	−	3.78872i	−0.588643	−	0.157726i	−0.0478100	−	0.998856i	$-0.515224\pi$
$577$	−14.1397	−	3.78872i	−0.588643	−	0.157726i	−0.540833	+	0.841130i	$0.681891\pi$
$578$	−20.6688	−	5.53819i	−0.859708	−	0.230358i
$579$	−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
$583$	0.291508	+	1.08792i	0.0120730	+	0.0450572i
$584$	37.1646	+	64.3710i	1.53788	+	2.66369i
$585$	−2.36381	+	1.51494i	−0.0977317	+	0.0626352i
$586$	5.05272	+	2.91719i	0.208726	+	0.120508i
$587$	21.1413	−	21.1413i	0.872594	−	0.872594i	−0.120160	−	0.992755i	$-0.538341\pi$
$587$	21.1413	−	21.1413i	0.872594	−	0.872594i	0.992755	+	0.120160i	$0.0383409\pi$
$588$		0			0
$589$			24.1689i			0.995862i
$590$	8.64256	−	16.7127i	0.355809	−	0.688052i
$591$	−14.0590	+	8.11696i	−0.578310	+	0.333887i
$592$	−8.62419	+	32.1859i	−0.354452	+	1.32283i
$593$	9.66895	−	2.59079i	0.397056	−	0.106391i	−0.0547654	−	0.998499i	$-0.517441\pi$
$593$	9.66895	−	2.59079i	0.397056	−	0.106391i	0.451821	+	0.892108i	$0.350774\pi$
$594$	−3.85081			−0.158001
$595$		0			0
$596$	0.477365			0.0195536
$597$	19.4603	−	5.21437i	0.796457	−	0.213410i
$598$	−4.99679	+	18.6483i	−0.204334	+	0.762585i
$599$	−6.18210	+	3.56924i	−0.252594	+	0.145835i	−0.620951	−	0.783849i	$-0.713254\pi$
$599$	−6.18210	+	3.56924i	−0.252594	+	0.145835i	0.368358	+	0.929684i	$0.379920\pi$
$600$	35.0423	+	16.1097i	1.43060	+	0.657675i
$601$		−	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
$605$	19.3540	+	4.23565i	0.786854	+	0.172204i
$606$	20.1941	+	34.9771i	0.820328	+	1.42085i
$607$	1.96330	+	7.32715i	0.0796880	+	0.297400i	0.994255	−	0.107034i	$-0.0341353\pi$
$607$	1.96330	+	7.32715i	0.0796880	+	0.297400i	−0.914567	+	0.404434i	$0.867469\pi$
$608$	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
$612$	14.1842	+	3.80064i	0.573362	+	0.153632i
$613$	14.3280	+	3.83917i	0.578701	+	0.155062i	0.536284	−	0.844038i	$-0.319828\pi$
$613$	14.3280	+	3.83917i	0.578701	+	0.155062i	0.0424169	+	0.999100i	$0.486494\pi$
$614$	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	$0.559414\pi$
$618$	−8.00508	−	29.8754i	−0.322011	−	1.20176i
$619$	−6.03375	−	10.4508i	−0.242517	−	0.420052i	0.718914	−	0.695099i	$-0.244640\pi$
$619$	−6.03375	−	10.4508i	−0.242517	−	0.420052i	−0.961431	+	0.275048i	$0.911306\pi$
$620$	65.7294	+	14.3850i	2.63976	+	0.577714i
$621$	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
$625$	8.29516	−	23.5837i	0.331806	−	0.943348i
$626$	18.4559	−	10.6555i	0.737647	−	0.425880i
$627$	−1.49920	+	5.59508i	−0.0598722	+	0.223446i
$628$	11.0959	−	2.97313i	0.442774	−	0.118641i
$629$	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	$0.292786\pi$
$632$	−33.6796	+	9.02442i	−1.33970	+	0.358972i
$633$	3.09707	−	11.5584i	0.123098	−	0.459406i
$634$	−2.42643	+	1.40090i	−0.0963660	+	0.0556369i
$635$	−11.4175	+	22.0788i	−0.453090	+	0.876172i
$636$		−	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
$640$	8.50426	−	5.45029i	0.336160	−	0.215442i
$641$	−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	$-0.423750\pi$
$642$	4.23027	+	15.7876i	0.166955	+	0.623086i
$643$	12.1140	+	12.1140i	0.477731	+	0.477731i	0.904405	−	0.426675i	$-0.140315\pi$
$643$	12.1140	+	12.1140i	0.477731	+	0.477731i	−0.426675	+	0.904405i	$0.640315\pi$
$644$		0			0
$645$	−11.0460	+	12.1204i	−0.434935	+	0.477240i
$646$	15.5247	−	26.8896i	0.610813	−	1.05796i
$647$	−26.0881	−	6.99030i	−1.02563	−	0.274817i	−0.293484	−	0.955964i	$-0.594815\pi$
$647$	−26.0881	−	6.99030i	−1.02563	−	0.274817i	−0.732147	+	0.681147i	$0.761481\pi$
$648$	7.45075	+	1.99642i	0.292693	+	0.0784269i
$649$	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
$653$	7.45625	+	27.8271i	0.291786	+	1.08896i	0.943737	+	0.330698i	$0.107284\pi$
$653$	7.45625	+	27.8271i	0.291786	+	1.08896i	−0.651951	+	0.758261i	$0.726049\pi$
$654$	−9.80067	−	16.9753i	−0.383237	−	0.663785i
$655$	−2.95539	+	13.5041i	−0.115477	+	0.527650i
$656$	−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	$0.789840\pi$
$660$	14.3240	+	7.40730i	0.557561	+	0.288329i
$661$	−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	$0.946788\pi$
$662$	−10.7709	+	40.1974i	−0.418621	+	1.56231i
$663$	3.61242	−	0.967945i	0.140295	−	0.0375919i
$664$	73.7201			2.86089
$665$		0			0
$666$	8.39746			0.325395
$667$	29.2567	−	7.83932i	1.13283	−	0.303540i
$668$	−0.528748	+	1.97332i	−0.0204579	+	0.0763499i
$669$	0.809446	−	0.467334i	0.0312950	−	0.0180682i
$670$	−47.0414	+	14.9725i	−1.81737	+	0.578438i
$671$			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
$675$	0.841520	−	4.92868i	0.0323901	−	0.189705i
$676$	−28.1595	−	48.7738i	−1.08306	−	1.87591i
$677$	0.563899	+	2.10450i	0.0216724	+	0.0808825i	0.975915	−	0.218151i	$-0.0700025\pi$
$677$	0.563899	+	2.10450i	0.0216724	+	0.0808825i	−0.954243	+	0.299033i	$0.903336\pi$
$678$	−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
$682$	22.7024	+	6.08310i	0.869321	+	0.232934i
$683$	−19.4186	−	5.20319i	−0.743030	−	0.199094i	−0.132606	−	0.991169i	$-0.542334\pi$
$683$	−19.4186	−	5.20319i	−0.743030	−	0.199094i	−0.610424	+	0.792074i	$0.709001\pi$
$684$	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
$688$	19.8274	+	73.9968i	0.755912	+	2.82110i
$689$	−0.483386	−	0.837249i	−0.0184155	−	0.0318967i
$690$	−18.5519	−	28.9471i	−0.706258	−	1.10200i
$691$	−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
$695$	8.13225	+	25.5504i	0.308474	+	0.969180i
$696$	34.6415	−	20.0003i	1.31308	−	0.758108i
$697$	−0.593570	+	2.21523i	−0.0224831	+	0.0839079i
$698$	−37.5478	+	10.0609i	−1.42121	+	0.380811i
$699$	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	$0.815657\pi$
$702$	3.19276	−	0.855497i	0.120503	−	0.0322887i
$703$	3.26930	−	12.2012i	0.123304	−	0.460176i
$704$	13.7920	−	7.96284i	0.519807	−	0.300111i
$705$	−8.21981	−	25.8255i	−0.309576	−	0.972643i
$706$		−	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	$-0.328444\pi$
$709$	0.708388	+	0.408988i	0.0266041	+	0.0153599i	−0.486639	+	0.873603i	$0.661777\pi$
$710$	24.2225	+	37.7951i	0.909053	+	1.41842i
$711$	2.26015	+	3.91469i	0.0847621	+	0.146812i
$712$	−2.39553	−	8.94022i	−0.0897761	−	0.335049i
$713$	−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
$717$	−20.6485	−	5.53276i	−0.771134	−	0.206625i
$718$	26.7941	+	7.17947i	0.999949	+	0.267935i
$719$	0.00381028	−	0.00659960i	0.000142099	−	0.000246124i	−0.865954	−	0.500123i	$-0.833288\pi$
$719$	0.00381028	−	0.00659960i	0.000142099	−	0.000246124i	0.866096	+	0.499877i	$0.166621\pi$
$720$	−17.2638	−	15.7335i	−0.643385	−	0.586351i
$721$		0			0
$722$	6.17902	+	6.17902i	0.229959	+	0.229959i
$723$	−0.161537	−	0.602863i	−0.00600761	−	0.0224207i
$724$	20.9167	+	36.2289i	0.777365	+	1.34644i
$725$	−14.9870	−	21.1585i	−0.556604	−	0.785807i
$726$	−20.1998	−	11.6624i	−0.749685	−	0.432831i
$727$	−28.5738	+	28.5738i	−1.05974	+	1.05974i	−0.0616465	+	0.998098i	$0.519635\pi$
$727$	−28.5738	+	28.5738i	−1.05974	+	1.05974i	−0.998098	+	0.0616465i	$0.980365\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−54.0512	+	17.2036i	−2.00052	+	0.636732i
$731$	18.9173	−	10.9219i	0.699680	−	0.403960i
$732$	1.81275	−	6.76528i	0.0670012	−	0.250052i
$733$	−32.9926	+	8.84033i	−1.21861	+	0.326525i	−0.810134	−	0.586244i	$-0.800606\pi$
$733$	−32.9926	+	8.84033i	−1.21861	+	0.326525i	−0.408475	+	0.912770i	$0.633939\pi$
$734$	41.6632			1.53782
$735$		0			0
$736$	−70.5085			−2.59898
$737$	−11.8496	+	3.17510i	−0.436486	+	0.116956i
$738$	−0.524613	+	1.95788i	−0.0193113	+	0.0720707i
$739$	−32.8676	+	18.9761i	−1.20905	+	0.698047i	−0.962552	−	0.271096i	$-0.912614\pi$
$739$	−32.8676	+	18.9761i	−1.20905	+	0.698047i	−0.246500	+	0.969143i	$0.579281\pi$
$740$	−31.2363	−	16.1531i	−1.14827	−	0.593799i
$741$		−	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
$745$	−0.0462878	+	0.211504i	−0.00169586	+	0.00774890i
$746$	32.1562	+	55.6961i	1.17732	+	2.03918i
$747$	−2.47358	−	9.23152i	−0.0905035	−	0.337764i
$748$	−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	$0.167282\pi$
$752$	−122.294	−	32.7686i	−4.45960	−	1.19495i
$753$	−15.7874	−	4.23022i	−0.575325	−	0.154158i
$754$	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	$0.724243\pi$
$758$	12.0078	+	44.8137i	0.436143	+	1.62771i
$759$	−4.27193	−	7.39921i	−0.155061	−	0.268574i
$760$	−57.5041	+	36.8538i	−2.08589	+	1.33683i
$761$	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
$765$	−3.05931	+	5.91600i	−0.110610	+	0.213893i
$766$	51.9891	−	30.0159i	1.87844	−	1.08452i
$767$	−1.03872	+	3.87656i	−0.0375061	+	0.139975i
$768$	9.54591	−	2.55782i	0.344458	−	0.0922973i
$769$	−8.16835			−0.294558			−0.147279	−	0.989095i	$-0.547052\pi$
$769$	−8.16835			−0.294558			−0.147279	+	0.989095i	$0.547052\pi$
$770$		0			0
$771$	−30.1304			−1.08512
$772$	−91.3338	+	24.4728i	−3.28717	+	0.880796i
$773$	0.919332	−	3.43099i	0.0330661	−	0.123404i	−0.947420	−	0.319993i	$-0.896320\pi$
$773$	0.919332	−	3.43099i	0.0330661	−	0.123404i	0.980486	+	0.196588i	$0.0629862\pi$
$774$	16.7196	−	9.65306i	0.600973	−	0.346972i
$775$	−12.7470	+	27.7276i	−0.457884	+	0.996005i
$776$		−	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
$780$	−13.5218	−	2.95927i	−0.484159	−	0.105959i
$781$	5.57770	+	9.66085i	0.199586	+	0.345693i
$782$	11.8534	+	44.2374i	0.423876	+	1.58193i
$783$	−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
$787$	17.3959	+	4.66123i	0.620098	+	0.166155i	0.555172	−	0.831735i	$-0.312652\pi$
$787$	17.3959	+	4.66123i	0.620098	+	0.166155i	0.0649257	+	0.997890i	$0.479319\pi$
$788$	−77.3081	−	20.7146i	−2.75399	−	0.737929i
$789$	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
$793$	−0.461671	−	1.72298i	−0.0163944	−	0.0611847i
$794$	−30.1150	−	52.1607i	−1.06874	−	1.85111i
$795$	1.68189	+	0.368084i	0.0596506	+	0.0130546i
$796$	86.0189	+	49.6630i	3.04886	+	1.76026i
$797$	−23.3462	+	23.3462i	−0.826967	+	0.826967i	−0.987096	−	0.160129i	$-0.948809\pi$
$797$	−23.3462	+	23.3462i	−0.826967	+	0.826967i	0.160129	+	0.987096i	$0.448809\pi$
$798$		0			0
$799$			36.1010i			1.27716i
$800$	20.9512	+	56.6057i	0.740736	+	2.00131i
$801$	−1.03915	+	0.599954i	−0.0367166	+	0.0211983i
$802$	0.666079	−	2.48584i	0.0235201	−	0.0877781i
$803$	−13.6153	+	3.64822i	−0.480475	+	0.128743i
$804$	41.3463			1.45817
$805$		0			0
$806$	−20.1743			−0.710609
$807$	−16.0250	+	4.29389i	−0.564107	+	0.151152i
$808$	−30.6292	+	114.310i	−1.07753	+	4.02140i
$809$	−24.0937	+	13.9105i	−0.847090	+	0.489067i	−0.859668	−	0.510853i	$-0.829329\pi$
$809$	−24.0937	+	13.9105i	−0.847090	+	0.489067i	0.0125781	+	0.999921i	$0.495996\pi$
$810$	−2.70390	+	5.22872i	−0.0950054	+	0.183719i
$811$			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
$815$	27.3554	−	17.5318i	0.958217	−	0.614111i
$816$	15.5567	+	26.9450i	0.544594	+	0.943264i
$817$	−7.51626	−	28.0510i	−0.262961	−	0.981382i
$818$	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	$0.0158933\pi$
$822$	−32.5648	−	8.72572i	−1.13583	−	0.304345i
$823$	−18.7550	−	5.02538i	−0.653757	−	0.175174i	−0.0833299	−	0.996522i	$-0.526556\pi$
$823$	−18.7550	−	5.02538i	−0.653757	−	0.175174i	−0.570427	+	0.821348i	$0.693222\pi$
$824$	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	$0.623432\pi$
$828$	7.45292	+	27.8147i	0.259007	+	0.966627i
$829$	23.6498	+	40.9627i	0.821392	+	1.42269i	0.904646	+	0.426164i	$0.140135\pi$
$829$	23.6498	+	40.9627i	0.821392	+	1.42269i	−0.0832545	+	0.996528i	$0.526531\pi$
$830$	−12.0275	+	54.9574i	−0.417480	+	1.90760i
$831$	−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
$835$	−0.823038	−	0.425614i	−0.0284824	−	0.0147290i
$836$	−24.7315	+	14.2788i	−0.855358	+	0.493841i
$837$	−1.57969	+	5.89549i	−0.0546021	+	0.203778i
$838$	−40.6577	+	10.8942i	−1.40450	+	0.376334i
$839$	−10.8244			−0.373699			−0.186850	−	0.982389i	$-0.559828\pi$
$839$	−10.8244			−0.373699			−0.186850	+	0.982389i	$0.559828\pi$
$840$		0			0
$841$	2.10826			0.0726986
$842$	37.3793	−	10.0157i	1.28817	−	0.345165i
$843$	−5.47451	+	20.4312i	−0.188552	+	0.703686i
$844$	51.0909	−	29.4973i	1.75862	−	1.01534i
$845$	24.3405	−	7.74716i	0.837338	−	0.266511i
$846$			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
$850$	31.9926	−	22.6610i	1.09734	−	0.777267i
$851$	9.31580	+	16.1354i	0.319341	+	0.553116i
$852$	−9.73099	−	36.3166i	−0.333378	−	1.24418i
$853$	−33.5751	−	33.5751i	−1.14959	−	1.14959i	−0.986633	−	0.162958i	$-0.947897\pi$
$853$	−33.5751	−	33.5751i	−1.14959	−	1.14959i	−0.162958	−	0.986633i	$-0.552103\pi$
$854$		0			0
$855$	6.54445	+	5.96431i	0.223815	+	0.203975i
$856$	−23.9457	+	41.4752i	−0.818447	+	1.41759i
$857$	12.1915	+	3.26670i	0.416454	+	0.111588i	0.460960	−	0.887421i	$-0.347505\pi$
$857$	12.1915	+	3.26670i	0.416454	+	0.111588i	−0.0445069	+	0.999009i	$0.514172\pi$
$858$	−4.67033	−	1.25141i	−0.159443	−	0.0427225i
$859$	10.1851	−	17.6410i	0.347510	−	0.601905i	−0.638297	−	0.769791i	$-0.720361\pi$
$859$	10.1851	−	17.6410i	0.347510	−	0.601905i	0.985806	+	0.167886i	$0.0536940\pi$
$860$	−80.7608	+	3.74556i	−2.75392	+	0.127723i
$861$		0			0
$862$	−41.4589	−	41.4589i	−1.41210	−	1.41210i
$863$	−5.45430	−	20.3557i	−0.185666	−	0.692917i	−0.994487	−	0.104861i	$-0.966560\pi$
$863$	−5.45430	−	20.3557i	−0.185666	−	0.692917i	0.808820	−	0.588056i	$-0.200106\pi$
$864$	6.03586	+	10.4544i	0.205344	+	0.355666i
$865$	−5.89002	−	9.19038i	−0.200267	−	0.312482i
$866$	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
$870$	9.25816	+	29.0878i	0.313881	+	0.986170i
$871$	9.11929	−	5.26503i	0.308995	−	0.178399i
$872$	14.8651	−	55.4773i	0.503396	−	1.87870i
$873$	−11.8684	+	3.18013i	−0.401685	+	0.107631i
$874$	60.8869			2.05953
$875$		0			0
$876$	47.5074			1.60512
$877$	−32.0516	+	8.58820i	−1.08231	+	0.290003i	−0.755540	−	0.655103i	$-0.772625\pi$
$877$	−32.0516	+	8.58820i	−1.08231	+	0.290003i	−0.326765	+	0.945105i	$0.605959\pi$
$878$	−1.60563	+	5.99230i	−0.0541874	+	0.202230i
$879$	1.91935	−	1.10814i	0.0647381	−	0.0373766i
$880$	10.3627	+	32.5580i	0.349325	+	1.09753i
$881$			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	−0.301295	−	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
$885$	−3.85653	−	6.01746i	−0.129636	−	0.202275i
$886$	−10.1868	−	17.6441i	−0.342233	−	0.592765i
$887$	7.04416	+	26.2892i	0.236520	+	0.882704i	0.977458	+	0.211131i	$0.0677146\pi$
$887$	7.04416	+	26.2892i	0.236520	+	0.882704i	−0.740938	+	0.671574i	$0.765619\pi$
$888$	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
$892$	4.45101	+	1.19265i	0.149031	+	0.0399327i
$893$	46.3598	+	12.4221i	1.55137	+	0.415689i
$894$	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
$898$	−0.817751	−	3.05189i	−0.0272887	−	0.101843i
$899$	15.8254	+	27.4104i	0.527808	+	0.914190i
$900$	20.1156	−	14.2483i	0.670521	−	0.474944i
$901$	−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
$905$	−18.0800	+	5.75455i	−0.600998	+	0.191288i
$906$	30.6749	−	17.7102i	1.01911	−	0.588381i
$907$	−5.44798	+	20.3321i	−0.180897	+	0.675117i	0.814575	+	0.580059i	$0.196970\pi$
$907$	−5.44798	+	20.3321i	−0.180897	+	0.675117i	−0.995472	+	0.0950584i	$0.969696\pi$
$908$	−116.838	+	31.3066i	−3.87740	+	1.03895i
$909$	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	$0.628705\pi$
$912$	39.9548	−	10.7059i	1.32304	−	0.354507i
$913$	−3.61832	+	13.5038i	−0.119749	+	0.446910i
$914$	67.9570	−	39.2350i	2.24782	−	1.29778i
$915$	2.82169	+	1.45917i	0.0932822	+	0.0482385i
$916$			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	$-0.132475\pi$
$919$	30.9773	+	17.8848i	1.02185	+	0.589964i	0.107209	+	0.994237i	$0.465809\pi$
$920$	21.5379	−	98.4136i	0.710084	−	3.24460i
$921$	−12.2719	−	21.2556i	−0.404374	−	0.700396i
$922$	14.9671	+	55.8580i	0.492915	+	1.83958i
$923$	−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
$927$	−11.3486	−	3.04085i	−0.372737	−	0.0998746i
$928$	60.4675	+	16.2022i	1.98494	+	0.531864i
$929$	−2.79468	+	4.84053i	−0.0916905	+	0.158813i	−0.908223	−	0.418487i	$-0.862560\pi$
$929$	−2.79468	+	4.84053i	−0.0916905	+	0.158813i	0.816532	+	0.577300i	$0.195894\pi$
$930$	24.2006	−	26.5545i	0.793569	−	0.870758i
$931$		0			0
$932$	11.0503	+	11.0503i	0.361963	+	0.361963i
$933$	8.04017	+	30.0063i	0.263223	+	0.982363i
$934$	−13.2406	−	22.9334i	−0.433246	−	0.750404i
$935$	8.20250	−	5.25690i	0.268250	−	0.171919i
$936$	8.38762	+	4.84260i	0.274158	+	0.158285i
$937$	20.4143	−	20.4143i	0.666906	−	0.666906i	−0.290092	−	0.956999i	$-0.593686\pi$
$937$	20.4143	−	20.4143i	0.666906	−	0.666906i	0.956999	+	0.290092i	$0.0936861\pi$
$938$		0			0
$939$		−	8.09533i		−	0.264181i
$940$	61.3755	−	118.686i	2.00185	−	3.87111i
$941$	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	$0.243345\pi$
$942$	1.58755	−	5.92481i	0.0517251	−	0.193041i
$943$	−4.34399	+	1.16397i	−0.141460	+	0.0379040i
$944$	−33.3884			−1.08670
$945$		0			0
$946$	−28.2408			−0.918187
$947$	−9.31836	+	2.49685i	−0.302806	+	0.0811366i	−0.407023	−	0.913418i	$-0.633433\pi$
$947$	−9.31836	+	2.49685i	−0.302806	+	0.0811366i	0.104217	+	0.994555i	$0.466766\pi$
$948$	−5.76794	+	21.5262i	−0.187334	+	0.699140i
$949$	10.4782	−	6.04957i	0.340136	−	0.196378i
$950$	−18.0922	−	48.8813i	−0.586988	−	1.58592i
$951$			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
$955$	17.1129	+	3.74517i	0.553759	+	0.121191i
$956$	−52.6955	−	91.2712i	−1.70429	−	2.95192i
$957$	1.96330	+	7.32715i	0.0634646	+	0.236853i
$958$	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
$962$	10.1846	+	2.72895i	0.328364	+	0.0879849i
$963$	5.99715	+	1.60693i	0.193255	+	0.0517826i
$964$	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	$0.560401\pi$
$968$	−17.6888	−	66.0155i	−0.568540	−	2.12182i
$969$	−5.89731	−	10.2144i	−0.189449	−	0.328135i
$970$	70.6555	+	15.4630i	2.26861	+	0.496488i
$971$	−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
$975$	2.62230	−	5.70411i	0.0839808	−	0.182678i
$976$	12.8517	−	7.41991i	0.411372	−	0.237506i
$977$	3.00015	−	11.1967i	0.0959834	−	0.358215i	−0.901183	−	0.433438i	$-0.857300\pi$
$977$	3.00015	−	11.1967i	0.0959834	−	0.358215i	0.997167	+	0.0752233i	$0.0239670\pi$
$978$	−36.9484	+	9.90028i	−1.18148	+	0.316576i
$979$	1.75521			0.0560969
$980$		0			0
$981$	−7.44587			−0.237728
$982$	72.0634	−	19.3093i	2.29964	−	0.616186i
$983$	0.640231	−	2.38938i	0.0204202	−	0.0762093i	−0.954964	−	0.296722i	$-0.904106\pi$
$983$	0.640231	−	2.38938i	0.0204202	−	0.0762093i	0.975384	+	0.220513i	$0.0707731\pi$
$984$	−5.14351	+	2.96961i	−0.163969	+	0.0946676i
$985$	16.6742	−	32.2440i	0.531283	−	1.02738i
$986$		−	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
$990$	7.24960	−	4.64619i	0.230407	−	0.147666i
$991$	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	$0.632594\pi$
$992$	−19.0696	−	71.1687i	−0.605460	−	2.25961i
$993$	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
$997$	−55.3975	−	14.8437i	−1.75446	−	0.470106i	−0.768889	−	0.639382i	$-0.779190\pi$
$997$	−55.3975	−	14.8437i	−1.75446	−	0.470106i	−0.985569	+	0.169277i	$0.945857\pi$
$998$	−8.62515	−	2.31110i	−0.273024	−	0.0731566i
$999$	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.607.8		32
5.3	odd	4	inner	735.2.v.a.313.2		32
7.2	even	3		105.2.m.a.97.2	yes	16
7.3	odd	6	inner	735.2.v.a.472.2		32
7.4	even	3	inner	735.2.v.a.472.1		32
7.5	odd	6		105.2.m.a.97.1	yes	16
7.6	odd	2	inner	735.2.v.a.607.7		32
21.2	odd	6		315.2.p.e.307.7		16
21.5	even	6		315.2.p.e.307.8		16
28.19	even	6		1680.2.cz.d.97.6		16
28.23	odd	6		1680.2.cz.d.97.3		16
35.2	odd	12		525.2.m.b.118.8		16
35.3	even	12	inner	735.2.v.a.178.8		32
35.9	even	6		525.2.m.b.307.7		16
35.12	even	12		525.2.m.b.118.7		16
35.13	even	4	inner	735.2.v.a.313.1		32
35.18	odd	12	inner	735.2.v.a.178.7		32
35.19	odd	6		525.2.m.b.307.8		16
35.23	odd	12		105.2.m.a.13.1	✓	16
35.33	even	12		105.2.m.a.13.2	yes	16
105.23	even	12		315.2.p.e.118.8		16
105.68	odd	12		315.2.p.e.118.7		16
140.23	even	12		1680.2.cz.d.433.6		16
140.103	odd	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	35.23	odd	12
105.2.m.a.13.2	yes	16	35.33	even	12
105.2.m.a.97.1	yes	16	7.5	odd	6
105.2.m.a.97.2	yes	16	7.2	even	3
315.2.p.e.118.7		16	105.68	odd	12
315.2.p.e.118.8		16	105.23	even	12
315.2.p.e.307.7		16	21.2	odd	6
315.2.p.e.307.8		16	21.5	even	6
525.2.m.b.118.7		16	35.12	even	12
525.2.m.b.118.8		16	35.2	odd	12
525.2.m.b.307.7		16	35.9	even	6
525.2.m.b.307.8		16	35.19	odd	6
735.2.v.a.178.7		32	35.18	odd	12	inner
735.2.v.a.178.8		32	35.3	even	12	inner
735.2.v.a.313.1		32	35.13	even	4	inner
735.2.v.a.313.2		32	5.3	odd	4	inner
735.2.v.a.472.1		32	7.4	even	3	inner
735.2.v.a.472.2		32	7.3	odd	6	inner
735.2.v.a.607.7		32	7.6	odd	2	inner
735.2.v.a.607.8		32	1.1	even	1	trivial
1680.2.cz.d.97.3		16	28.23	odd	6
1680.2.cz.d.97.6		16	28.19	even	6
1680.2.cz.d.433.3		16	140.103	odd	12
1680.2.cz.d.433.6		16	140.23	even	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)

\(f(q)\)	\(=\)	\(q+(2.54281 - 0.681344i) q^{2} +(0.258819 - 0.965926i) q^{3} +(4.26961 - 2.46506i) q^{4} +(0.678180 + 2.13074i) q^{5} -2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(2.54281 - 0.681344i) q^{2} +(0.258819 - 0.965926i) q^{3} +(4.26961 - 2.46506i) q^{4} +(0.678180 + 2.13074i) q^{5} -2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(3.17625 + 4.95601i) q^{10} +(0.731395 + 1.26681i) q^{11} +(-1.27601 - 4.76213i) q^{12} +(-0.887844 - 0.887844i) q^{13} +(2.23367 - 0.103594i) q^{15} +(5.22294 - 9.04639i) q^{16} +(-2.87705 - 0.770902i) q^{17} +(-2.54281 - 0.681344i) q^{18} +(-1.97993 + 3.42935i) q^{19} +(8.14798 + 7.42570i) q^{20} +(2.72294 + 2.72294i) q^{22} +(-1.51171 - 5.64178i) q^{23} +(-3.85679 - 6.68016i) q^{24} +(-4.08014 + 2.89006i) q^{25} +(-2.86255 - 1.65269i) q^{26} +(-0.707107 + 0.707107i) q^{27} +5.18572i q^{29} +(5.60921 - 1.78532i) q^{30} +(5.28575 - 3.05173i) q^{31} +(3.12439 - 11.6604i) q^{32} +(1.41295 - 0.378598i) q^{33} -7.84104 q^{34} -4.93012 q^{36} +(-3.08121 + 0.825607i) q^{37} +(-2.69804 + 10.0692i) q^{38} +(-1.08738 + 0.627801i) q^{39} +(15.3208 + 7.92277i) q^{40} -0.769968i q^{41} +(-5.18572 + 5.18572i) q^{43} +(6.24554 + 3.60587i) q^{44} +(0.478051 - 2.18437i) q^{45} +(-7.68800 - 13.3160i) q^{46} +(-3.13699 - 11.7074i) q^{47} +(-7.38635 - 7.38635i) q^{48} +(-8.40592 + 10.1289i) q^{50} +(-1.48927 + 2.57949i) q^{51} +(-5.97934 - 1.60216i) q^{52} +(0.743732 + 0.199282i) q^{53} +(-1.31626 + 2.27982i) q^{54} +(-2.20324 + 2.41754i) q^{55} +(2.80005 + 2.80005i) q^{57} +(3.53326 + 13.1863i) q^{58} +(-1.59816 - 2.76810i) q^{59} +(9.28153 - 5.94843i) q^{60} +(1.23031 + 0.710320i) q^{61} +(11.3614 - 11.3614i) q^{62} -10.8872i q^{64} +(1.28965 - 2.49389i) q^{65} +(3.33490 - 1.92541i) q^{66} +(-2.17058 + 8.10070i) q^{67} +(-14.1842 + 3.80064i) q^{68} -5.84081 q^{69} +7.62611 q^{71} +(-7.45075 + 1.99642i) q^{72} +(-2.49402 + 9.30780i) q^{73} +(-7.27241 + 4.19873i) q^{74} +(1.73556 + 4.68912i) q^{75} +19.5226i q^{76} +(-2.33726 + 2.33726i) q^{78} +(-3.91469 - 2.26015i) q^{79} +(22.8176 + 4.99366i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.524613 - 1.95788i) q^{82} +(6.75794 + 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} +(-9.65306 + 16.7196i) q^{86} +(5.00903 + 1.34216i) q^{87} +(10.8989 + 2.92035i) q^{88} +(0.599954 - 1.03915i) q^{89} +(-0.272713 - 5.88016i) q^{90} +(-20.3618 - 20.3618i) q^{92} +(-1.57969 - 5.89549i) q^{93} +(-15.9535 - 27.6323i) q^{94} +(-8.64982 - 1.89302i) 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

L-functions

Modular forms

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