LMFDB - Embedded newform 735.2.y.g.557.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(128,735)]

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([6, 9, 4]))

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

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

chi := DirichletCharacter("735.128");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.y (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:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.12
Character	$\chi$	$=$	735.557
Dual form			735.2.y.g.128.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.45834 + 0.658710i) q^{2} +(-1.25586 + 1.19281i) q^{3} +(3.87749 + 2.23867i) q^{4} +(1.98846 + 1.02275i) q^{5} +(-3.87306 + 2.10509i) q^{6} +(4.45829 + 4.45829i) q^{8} +(0.154393 - 2.99602i) q^{9} +(4.21463 + 3.82408i) q^{10} +(1.35854 + 0.784351i) q^{11} +(-7.53991 + 1.81365i) q^{12} +(-2.21881 + 2.21881i) q^{13} +(-3.71719 + 1.08744i) q^{15} +(3.54593 + 6.14174i) q^{16} +(-1.32034 - 4.92759i) q^{17} +(2.35306 - 7.26355i) q^{18} +(1.45527 - 0.840200i) q^{19} +(5.42066 + 8.41719i) q^{20} +(2.82308 + 2.82308i) q^{22} +(0.364506 - 1.36036i) q^{23} +(-10.9169 - 0.281103i) q^{24} +(2.90798 + 4.06739i) q^{25} +(-6.91613 + 3.99303i) q^{26} +(3.37980 + 3.94676i) q^{27} -8.91955 q^{29} +(-9.85442 + 0.224740i) q^{30} +(1.37417 - 2.38013i) q^{31} +(1.40779 + 5.25396i) q^{32} +(-2.64172 + 0.635440i) q^{33} -12.9834i q^{34} +(7.30576 - 11.2714i) q^{36} +(0.161183 - 0.601543i) q^{37} +(4.13100 - 1.10690i) q^{38} +(0.139900 - 5.43314i) q^{39} +(4.30546 + 13.4248i) q^{40} -6.44292i q^{41} +(-5.47734 + 5.47734i) q^{43} +(3.51180 + 6.08262i) q^{44} +(3.37118 - 5.79958i) q^{45} +(1.79216 - 3.10412i) q^{46} +(5.04552 + 1.35194i) q^{47} +(-11.7792 - 3.48356i) q^{48} +(4.46958 + 11.9145i) q^{50} +(7.53587 + 4.61346i) q^{51} +(-13.5706 + 3.63622i) q^{52} +(-3.87074 + 1.03716i) q^{53} +(5.70892 + 11.9288i) q^{54} +(1.89921 + 2.94909i) q^{55} +(-0.825420 + 2.79104i) q^{57} +(-21.9273 - 5.87540i) q^{58} +(2.77436 - 4.80533i) q^{59} +(-16.8478 - 4.10503i) q^{60} +(3.70333 + 6.41435i) q^{61} +(4.94599 - 4.94599i) q^{62} -0.340400i q^{64} +(-6.68129 + 2.14274i) q^{65} +(-6.91282 - 0.178000i) q^{66} +(5.12587 - 1.37347i) q^{67} +(5.91162 - 22.0625i) q^{68} +(1.16488 + 2.14321i) q^{69} -3.61943i q^{71} +(14.0455 - 12.6688i) q^{72} +(2.15859 + 8.05596i) q^{73} +(0.792485 - 1.37262i) q^{74} +(-8.50367 - 1.63941i) q^{75} +7.52372 q^{76} +(3.92279 - 13.2644i) q^{78} +(14.7720 - 8.52862i) q^{79} +(0.769530 + 15.8392i) q^{80} +(-8.95233 - 0.925133i) q^{81} +(4.24402 - 15.8389i) q^{82} +(-3.21312 - 3.21312i) q^{83} +(2.41421 - 11.1487i) q^{85} +(-17.0731 + 9.85718i) q^{86} +(11.2017 - 10.6394i) q^{87} +(2.55988 + 9.55360i) q^{88} +(-4.70137 - 8.14301i) q^{89} +(12.1077 - 12.0367i) q^{90} +(4.45876 - 4.45876i) q^{92} +(1.11328 + 4.62825i) q^{93} +(11.5131 + 6.64707i) q^{94} +(3.75306 - 0.182338i) q^{95} +(-8.03498 - 4.91902i) q^{96} +(-4.39640 - 4.39640i) q^{97} +(2.55968 - 3.94911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 16 q^{10} + 16 q^{12} + 16 q^{13} - 32 q^{15} + 16 q^{16} + 20 q^{18} + 16 q^{22} + 16 q^{25} + 32 q^{27} - 20 q^{30} + 28 q^{33} + 32 q^{36} + 16 q^{37} + 64 q^{40} - 80 q^{43} + 20 q^{45}+ \cdots - 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 + 16 * q^13 - 32 * q^15 + 16 * q^16 + 20 * q^18 + 16 * q^22 + 16 * q^25 + 32 * q^27 - 20 * q^30 + 28 * q^33 + 32 * q^36 + 16 * q^37 + 64 * q^40 - 80 * q^43 + 20 * q^45 + 64 * q^46 - 32 * q^48 + 20 * q^51 - 80 * q^55 + 8 * q^57 - 40 * q^58 - 32 * q^60 + 32 * q^61 - 16 * q^66 - 24 * q^67 + 8 * q^72 + 32 * q^73 - 60 * q^75 - 64 * q^76 + 120 * q^78 - 52 * q^81 - 80 * q^82 + 48 * q^85 + 4 * q^87 - 96 * q^88 + 48 * q^90 + 76 * q^93 - 96 * q^96 - 48 * q^97

Character values

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

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	2.45834	+	0.658710i	1.73831	+	0.465779i	0.982070	−	0.188517i	$-0.0603680\pi$
$2$	2.45834	+	0.658710i	1.73831	+	0.465779i	0.756239	+	0.654295i	$0.227035\pi$
$3$	−1.25586	+	1.19281i	−0.725074	+	0.688671i
$3$	−1.25586	+	1.19281i	−0.725074	+	0.688671i
$4$	3.87749	+	2.23867i	1.93874	+	1.11933i
$5$	1.98846	+	1.02275i	0.889268	+	0.457386i
$5$	1.98846	+	1.02275i	0.889268	+	0.457386i
$6$	−3.87306	+	2.10509i	−1.58117	+	0.859399i
$7$		0			0
$7$		0			0
$8$	4.45829	+	4.45829i	1.57624	+	1.57624i
$9$	0.154393	−	2.99602i	0.0514645	−	0.998675i
$10$	4.21463	+	3.82408i	1.33278	+	1.20928i
$11$	1.35854	+	0.784351i	0.409614	+	0.236491i	0.690624	−	0.723214i	$-0.257336\pi$
$11$	1.35854	+	0.784351i	0.409614	+	0.236491i	−0.281010	+	0.959705i	$0.590669\pi$
$12$	−7.53991	+	1.81365i	−2.17659	+	0.523556i
$13$	−2.21881	+	2.21881i	−0.615386	+	0.615386i	−0.944345	−	0.328958i	$-0.893303\pi$
$13$	−2.21881	+	2.21881i	−0.615386	+	0.615386i	0.328958	+	0.944345i	$0.393303\pi$
$14$		0			0
$15$	−3.71719	+	1.08744i	−0.959774	+	0.280775i
$16$	3.54593	+	6.14174i	0.886484	+	1.53543i
$17$	−1.32034	−	4.92759i	−0.320230	−	1.19512i	−0.919020	−	0.394210i	$-0.871018\pi$
$17$	−1.32034	−	4.92759i	−0.320230	−	1.19512i	0.598790	−	0.800906i	$-0.295648\pi$
$18$	2.35306	−	7.26355i	0.554622	−	1.71203i
$19$	1.45527	−	0.840200i	0.333862	−	0.192755i	−0.323693	−	0.946162i	$-0.604924\pi$
$19$	1.45527	−	0.840200i	0.333862	−	0.192755i	0.657554	+	0.753407i	$0.271591\pi$
$20$	5.42066	+	8.41719i	1.21210	+	1.88214i
$21$		0			0
$22$	2.82308	+	2.82308i	0.601883	+	0.601883i
$23$	0.364506	−	1.36036i	0.0760049	−	0.283654i	−0.917454	−	0.397841i	$-0.869760\pi$
$23$	0.364506	−	1.36036i	0.0760049	−	0.283654i	0.993459	+	0.114187i	$0.0364263\pi$
$24$	−10.9169	−	0.281103i	−2.22841	−	0.0573799i
$25$	2.90798	+	4.06739i	0.581597	+	0.813477i
$26$	−6.91613	+	3.99303i	−1.35637	+	0.783098i
$27$	3.37980	+	3.94676i	0.650443	+	0.759555i
$28$		0			0
$29$	−8.91955			−1.65632			−0.828159	−	0.560493i	$-0.810612\pi$
$29$	−8.91955			−1.65632			−0.828159	+	0.560493i	$0.810612\pi$
$30$	−9.85442	+	0.224740i	−1.79916	+	0.0410317i
$31$	1.37417	−	2.38013i	0.246808	−	0.427484i	−0.715830	−	0.698274i	$-0.753952\pi$
$31$	1.37417	−	2.38013i	0.246808	−	0.427484i	0.962638	+	0.270790i	$0.0872850\pi$
$32$	1.40779	+	5.25396i	0.248865	+	0.928777i
$33$	−2.64172	+	0.635440i	−0.459865	+	0.110616i
$34$		−	12.9834i		−	2.22664i
$35$		0			0
$36$	7.30576	−	11.2714i	1.21763	−	1.87857i
$37$	0.161183	−	0.601543i	0.0264983	−	0.0988930i	−0.951410	−	0.307926i	$-0.900365\pi$
$37$	0.161183	−	0.601543i	0.0264983	−	0.0988930i	0.977909	+	0.209033i	$0.0670317\pi$
$38$	4.13100	−	1.10690i	0.670136	−	0.179562i
$39$	0.139900	−	5.43314i	0.0224019	−	0.869999i
$40$	4.30546	+	13.4248i	0.680752	+	2.12265i
$41$		−	6.44292i		−	1.00622i	−0.864224	−	0.503108i	$-0.832190\pi$
$41$		−	6.44292i		−	1.00622i	0.864224	−	0.503108i	$-0.167810\pi$
$42$		0			0
$43$	−5.47734	+	5.47734i	−0.835286	+	0.835286i	−0.988234	−	0.152948i	$-0.951123\pi$
$43$	−5.47734	+	5.47734i	−0.835286	+	0.835286i	0.152948	+	0.988234i	$0.451123\pi$
$44$	3.51180	+	6.08262i	0.529424	+	0.916989i
$45$	3.37118	−	5.79958i	0.502545	−	0.864551i
$46$	1.79216	−	3.10412i	0.264240	−	0.457677i
$47$	5.04552	+	1.35194i	0.735965	+	0.197201i	0.607284	−	0.794485i	$-0.292259\pi$
$47$	5.04552	+	1.35194i	0.735965	+	0.197201i	0.128681	+	0.991686i	$0.458926\pi$
$48$	−11.7792	−	3.48356i	−1.70018	−	0.502808i
$49$		0			0
$50$	4.46958	+	11.9145i	0.632095	+	1.68497i
$51$	7.53587	+	4.61346i	1.05523	+	0.646014i
$52$	−13.5706	+	3.63622i	−1.88190	+	0.504253i
$53$	−3.87074	+	1.03716i	−0.531687	+	0.142465i	−0.514667	−	0.857390i	$-0.672084\pi$
$53$	−3.87074	+	1.03716i	−0.531687	+	0.142465i	−0.0170196	+	0.999855i	$0.505418\pi$
$54$	5.70892	+	11.9288i	0.776886	+	1.62330i
$55$	1.89921	+	2.94909i	0.256089	+	0.397655i
$56$		0			0
$57$	−0.825420	+	2.79104i	−0.109330	+	0.369683i
$58$	−21.9273	−	5.87540i	−2.87919	−	0.771478i
$59$	2.77436	−	4.80533i	0.361191	−	0.625600i	−0.626967	−	0.779046i	$-0.715704\pi$
$59$	2.77436	−	4.80533i	0.361191	−	0.625600i	0.988157	+	0.153446i	$0.0490371\pi$
$60$	−16.8478	−	4.10503i	−2.17504	−	0.529957i
$61$	3.70333	+	6.41435i	0.474162	+	0.821273i	0.999562	−	0.0295820i	$-0.00941760\pi$
$61$	3.70333	+	6.41435i	0.474162	+	0.821273i	−0.525400	+	0.850855i	$0.676084\pi$
$62$	4.94599	−	4.94599i	0.628141	−	0.628141i
$63$		0			0
$64$		−	0.340400i		−	0.0425500i
$65$	−6.68129	+	2.14274i	−0.828713	+	0.265775i
$66$	−6.91282	−	0.178000i	−0.850909	−	0.0219103i
$67$	5.12587	−	1.37347i	0.626225	−	0.167797i	0.0682690	−	0.997667i	$-0.478252\pi$
$67$	5.12587	−	1.37347i	0.626225	−	0.167797i	0.557956	+	0.829870i	$0.311586\pi$
$68$	5.91162	−	22.0625i	0.716890	−	2.67547i
$69$	1.16488	+	2.14321i	0.140235	+	0.258012i
$70$		0			0
$71$		−	3.61943i		−	0.429548i	−0.976664	−	0.214774i	$-0.931099\pi$
$71$		−	3.61943i		−	0.429548i	0.976664	−	0.214774i	$-0.0689015\pi$
$72$	14.0455	−	12.6688i	1.65527	−	1.49303i
$73$	2.15859	+	8.05596i	0.252644	+	0.942878i	0.969386	+	0.245541i	$0.0789655\pi$
$73$	2.15859	+	8.05596i	0.252644	+	0.942878i	−0.716743	+	0.697338i	$0.754368\pi$
$74$	0.792485	−	1.37262i	0.0921245	−	0.159564i
$75$	−8.50367	−	1.63941i	−0.981919	−	0.189302i
$76$	7.52372			0.863030
$77$		0			0
$78$	3.92279	−	13.2644i	0.444168	−	1.50189i
$79$	14.7720	−	8.52862i	1.66198	−	0.959544i	0.690211	−	0.723608i	$-0.257518\pi$
$79$	14.7720	−	8.52862i	1.66198	−	0.959544i	0.971769	−	0.235936i	$-0.0758156\pi$
$80$	0.769530	+	15.8392i	0.0860361	+	1.77088i
$81$	−8.95233	−	0.925133i	−0.994703	−	0.102793i
$82$	4.24402	−	15.8389i	0.468674	−	1.74911i
$83$	−3.21312	−	3.21312i	−0.352686	−	0.352686i	0.508422	−	0.861108i	$-0.330229\pi$
$83$	−3.21312	−	3.21312i	−0.352686	−	0.352686i	−0.861108	+	0.508422i	$0.830229\pi$
$84$		0			0
$85$	2.41421	−	11.1487i	0.261858	−	1.20925i
$86$	−17.0731	+	9.85718i	−1.84104	+	1.06293i
$87$	11.2017	−	10.6394i	1.20095	−	1.14066i
$88$	2.55988	+	9.55360i	0.272884	+	1.01842i
$89$	−4.70137	−	8.14301i	−0.498344	−	0.863157i	0.501654	−	0.865068i	$-0.332725\pi$
$89$	−4.70137	−	8.14301i	−0.498344	−	0.863157i	−0.999998	+	0.00191126i	$0.999392\pi$
$90$	12.1077	−	12.0367i	1.27627	−	1.26878i
$91$		0			0
$92$	4.45876	−	4.45876i	0.464858	−	0.464858i
$93$	1.11328	+	4.62825i	0.115442	+	0.479927i
$94$	11.5131	+	6.64707i	1.18748	+	0.685593i
$95$	3.75306	−	0.182338i	0.385056	−	0.0187075i
$96$	−8.03498	−	4.91902i	−0.820067	−	0.502046i
$97$	−4.39640	−	4.39640i	−0.446386	−	0.446386i	0.447765	−	0.894151i	$-0.352220\pi$
$97$	−4.39640	−	4.39640i	−0.446386	−	0.446386i	−0.894151	+	0.447765i	$0.852220\pi$
$98$		0			0
$99$	2.55968	−	3.94911i	0.257258	−	0.396900i
$100$	2.17014	+	22.2812i	0.217014	+	2.22812i
$101$	0.875832	+	0.505662i	0.0871485	+	0.0503152i	0.542941	−	0.839771i	$-0.317311\pi$
$101$	0.875832	+	0.505662i	0.0871485	+	0.0503152i	−0.455792	+	0.890086i	$0.650644\pi$
$102$	15.4868	+	16.3054i	1.53342	+	1.61448i
$103$	−5.50588	−	1.47530i	−0.542511	−	0.145365i	−0.0228513	−	0.999739i	$-0.507274\pi$
$103$	−5.50588	−	1.47530i	−0.542511	−	0.145365i	−0.519659	+	0.854374i	$0.673941\pi$
$104$	−19.7842			−1.94000
$105$		0			0
$106$	−10.1988			−0.990593
$107$	−3.84892	−	1.03131i	−0.372089	−	0.0997009i	0.0679285	−	0.997690i	$-0.478361\pi$
$107$	−3.84892	−	1.03131i	−0.372089	−	0.0997009i	−0.440017	+	0.897989i	$0.645028\pi$
$108$	4.26963	+	22.8698i	0.410846	+	2.20065i
$109$	5.56202	+	3.21123i	0.532744	+	0.307580i	0.742133	−	0.670252i	$-0.233814\pi$
$109$	5.56202	+	3.21123i	0.532744	+	0.307580i	−0.209389	+	0.977832i	$0.567147\pi$
$110$	2.72630	+	8.50089i	0.259943	+	0.810528i
$111$	0.515104	+	0.947718i	0.0488915	+	0.0899534i
$112$		0			0
$113$	3.29246	+	3.29246i	0.309729	+	0.309729i	0.844804	−	0.535075i	$-0.179717\pi$
$113$	3.29246	+	3.29246i	0.309729	+	0.309729i	−0.535075	+	0.844804i	$0.679717\pi$
$114$	−3.86765	+	6.31762i	−0.362239	+	0.591699i
$115$	2.11611	−	2.33222i	0.197328	−	0.217481i
$116$	−34.5854	−	19.9679i	−3.21118	−	1.85397i
$117$	6.30503	+	6.99017i	0.582900	+	0.646241i
$118$	9.98563	−	9.98563i	0.919252	−	0.919252i
$119$		0			0
$120$	−21.4204	−	11.7242i	−1.95541	−	1.07027i
$121$	−4.26959	−	7.39514i	−0.388144	−	0.672286i
$122$	4.87884	+	18.2081i	0.441709	+	1.64848i
$123$	7.68520	+	8.09144i	0.692951	+	0.729581i
$124$	10.6566	−	6.15262i	0.956995	−	0.552521i
$125$	1.62252	+	11.0620i	0.145123	+	0.989414i
$126$		0			0
$127$	14.2818	+	14.2818i	1.26730	+	1.26730i	0.947476	+	0.319826i	$0.103624\pi$
$127$	14.2818	+	14.2818i	1.26730	+	1.26730i	0.319826	+	0.947476i	$0.396376\pi$
$128$	3.03981	−	11.3447i	0.268684	−	1.00274i
$129$	0.345356	−	13.4122i	0.0304069	−	1.18088i
$130$	−17.8363	+	0.866558i	−1.56435	+	0.0760022i
$131$	4.24118	−	2.44864i	0.370553	−	0.213939i	−0.303147	−	0.952944i	$-0.598037\pi$
$131$	4.24118	−	2.44864i	0.370553	−	0.213939i	0.673700	+	0.739005i	$0.264704\pi$
$132$	−11.6658	−	3.45002i	−1.01538	−	0.300286i
$133$		0			0
$134$	13.5059			1.16673
$135$	2.68408	+	11.3047i	0.231009	+	0.972952i
$136$	16.0821	−	27.8551i	1.37903	−	2.38856i
$137$	−1.66864	−	6.22744i	−0.142561	−	0.532046i	−0.999852	−	0.0172133i	$-0.994521\pi$
$137$	−1.66864	−	6.22744i	−0.142561	−	0.532046i	0.857290	−	0.514833i	$-0.172146\pi$
$138$	1.45192	+	6.03606i	0.123595	+	0.513824i
$139$			10.2045i			0.865536i	0.901505	+	0.432768i	$0.142463\pi$
$139$			10.2045i			0.865536i	−0.901505	+	0.432768i	$0.857537\pi$
$140$		0			0
$141$	−7.94911	+	4.32050i	−0.669435	+	0.363852i
$142$	2.38416	−	8.89780i	0.200074	−	0.746687i
$143$	−4.75465	+	1.27400i	−0.397604	+	0.106538i
$144$	18.9483	−	9.67546i	1.57902	−	0.806289i
$145$	−17.7362	−	9.12243i	−1.47291	−	0.757576i
$146$			21.2262i			1.75669i
$147$		0			0
$148$	1.97164	−	1.97164i	0.162068	−	0.162068i
$149$	0.461562	+	0.799449i	0.0378126	+	0.0654934i	0.884312	−	0.466896i	$-0.154628\pi$
$149$	0.461562	+	0.799449i	0.0378126	+	0.0654934i	−0.846500	+	0.532389i	$0.821294\pi$
$150$	−19.8250	−	9.63167i	−1.61871	−	0.786423i
$151$	6.86549	−	11.8914i	0.558705	−	0.967706i	−0.438900	−	0.898536i	$-0.644632\pi$
$151$	6.86549	−	11.8914i	0.558705	−	0.967706i	0.997605	−	0.0691699i	$-0.0220350\pi$
$152$	10.2339	+	2.74216i	0.830077	+	0.222418i
$153$	−14.9670	+	3.19499i	−1.21001	+	0.258300i
$154$		0			0
$155$	5.16675	−	3.32738i	0.415004	−	0.267262i
$156$	12.7055	−	20.7538i	1.01725	−	1.66163i
$157$	−18.7434	+	5.02228i	−1.49589	+	0.400822i	−0.911720	−	0.410812i	$-0.865245\pi$
$157$	−18.7434	+	5.02228i	−1.49589	+	0.400822i	−0.584166	+	0.811634i	$0.698578\pi$
$158$	41.9325	−	11.2358i	3.33597	−	0.893870i
$159$	3.62398	−	5.91960i	0.287401	−	0.469455i
$160$	−2.57411	+	11.8871i	−0.203501	+	0.939759i
$161$		0			0
$162$	−21.3985	−	8.17128i	−1.68122	−	0.641997i
$163$	−9.02349	−	2.41784i	−0.706775	−	0.189380i	−0.112512	−	0.993650i	$-0.535890\pi$
$163$	−9.02349	−	2.41784i	−0.706775	−	0.189380i	−0.594263	+	0.804271i	$0.702556\pi$
$164$	14.4236	−	24.9823i	1.12629	−	1.95079i
$165$	−5.90286	−	1.43826i	−0.459537	−	0.111968i
$166$	−5.78243	−	10.0155i	−0.448804	−	0.777350i
$167$	3.11442	−	3.11442i	0.241001	−	0.241001i	−0.576263	−	0.817264i	$-0.695490\pi$
$167$	3.11442	−	3.11442i	0.241001	−	0.241001i	0.817264	+	0.576263i	$0.195490\pi$
$168$		0			0
$169$			3.15379i			0.242599i
$170$	13.2787	−	25.8171i	1.01843	−	1.98008i
$171$	−2.29258	−	4.48975i	−0.175318	−	0.343339i
$172$	−33.5002	+	8.97636i	−2.55437	+	0.684441i
$173$	−2.97531	+	11.1040i	−0.226209	+	0.844222i	0.755708	+	0.654909i	$0.227293\pi$
$173$	−2.97531	+	11.1040i	−0.226209	+	0.844222i	−0.981917	+	0.189313i	$0.939374\pi$
$174$	34.5460	−	18.7764i	2.61892	−	1.42344i
$175$		0			0
$176$			11.1250i			0.838580i
$177$	2.24764	+	9.34413i	0.168943	+	0.702348i
$178$	−6.19368	−	23.1151i	−0.464236	−	1.73255i
$179$	−8.29901	+	14.3743i	−0.620297	+	1.07439i	0.369133	+	0.929377i	$0.379655\pi$
$179$	−8.29901	+	14.3743i	−0.620297	+	1.07439i	−0.989430	+	0.145010i	$0.953679\pi$
$180$	26.0550	−	14.9409i	1.94203	−	1.11363i
$181$	−11.6532			−0.866174			−0.433087	−	0.901352i	$-0.642576\pi$
$181$	−11.6532			−0.866174			−0.433087	+	0.901352i	$0.642576\pi$
$182$		0			0
$183$	−12.3020	−	3.63818i	−0.909390	−	0.268942i
$184$	7.68994	−	4.43979i	0.566910	−	0.327306i
$185$	0.935732	−	1.03130i	0.0687964	−	0.0758225i
$186$	−0.311853	+	12.1111i	−0.0228662	+	0.888032i
$187$	2.07123	−	7.72992i	0.151463	−	0.565268i
$188$	16.5374	+	16.5374i	1.20611	+	1.20611i
$189$		0			0
$190$	9.34642	+	2.02393i	0.678060	+	0.146831i
$191$	11.1322	−	6.42717i	0.805497	−	0.465054i	−0.0398927	−	0.999204i	$-0.512702\pi$
$191$	11.1322	−	6.42717i	0.805497	−	0.465054i	0.845390	+	0.534150i	$0.179368\pi$
$192$	0.406034	+	0.427497i	0.0293030	+	0.0308519i
$193$	−2.95074	−	11.0123i	−0.212399	−	0.792684i	−0.987066	−	0.160315i	$-0.948749\pi$
$193$	−2.95074	−	11.0123i	−0.212399	−	0.792684i	0.774667	−	0.632370i	$-0.217918\pi$
$194$	−7.91189	−	13.7038i	−0.568040	−	0.983875i
$195$	5.83491	−	10.6605i	0.417847	−	0.763417i
$196$		0			0
$197$	−18.7512	+	18.7512i	−1.33597	+	1.33597i	−0.436036	+	0.899929i	$0.643618\pi$
$197$	−18.7512	+	18.7512i	−1.33597	+	1.33597i	−0.899929	+	0.436036i	$0.856382\pi$
$198$	8.89389	−	8.02216i	0.632061	−	0.570110i
$199$	−3.64362	−	2.10364i	−0.258289	−	0.149123i	0.365265	−	0.930904i	$-0.380978\pi$
$199$	−3.64362	−	2.10364i	−0.258289	−	0.149123i	−0.623554	+	0.781780i	$0.714312\pi$
$200$	−5.16895	+	31.0982i	−0.365500	+	2.19898i
$201$	−4.79911	+	7.83911i	−0.338503	+	0.552928i
$202$	1.82001	+	1.82001i	0.128055	+	0.128055i
$203$		0			0
$204$	18.8922	+	34.7590i	1.32272	+	2.43361i
$205$	6.58947	−	12.8115i	0.460229	−	0.894796i
$206$	−12.5635	−	7.25356i	−0.875343	−	0.505380i
$207$	−4.01938	−	1.30210i	−0.279367	−	0.0905022i
$208$	−21.4951	−	5.75959i	−1.49042	−	0.399356i
$209$	2.63605			0.182339
$210$		0			0
$211$	−21.5211			−1.48158			−0.740788	−	0.671739i	$-0.765548\pi$
$211$	−21.5211			−1.48158			−0.740788	+	0.671739i	$0.765548\pi$
$212$	−17.3306	−	4.64372i	−1.19027	−	0.318932i
$213$	4.31731	+	4.54552i	0.295817	+	0.311454i
$214$	−8.78261	−	5.07064i	−0.600367	−	0.346622i
$215$	−16.4934	+	5.28957i	−1.12484	+	0.360746i
$216$	−2.52769	+	32.6639i	−0.171988	+	2.22250i
$217$		0			0
$218$	11.5581	+	11.5581i	0.782810	+	0.782810i
$219$	−12.3201	−	7.54240i	−0.832518	−	0.509668i
$220$	0.762123	+	15.6868i	0.0513823	+	1.05760i
$221$	13.8630	+	8.00378i	0.932524	+	0.538393i
$222$	0.642030	+	2.66912i	0.0430902	+	0.179139i
$223$	−12.4001	+	12.4001i	−0.830375	+	0.830375i	−0.987568	−	0.157193i	$-0.949756\pi$
$223$	−12.4001	+	12.4001i	−0.830375	+	0.830375i	0.157193	+	0.987568i	$0.449756\pi$
$224$		0			0
$225$	12.6350	−	8.08441i	0.842331	−	0.538961i
$226$	5.92522	+	10.2628i	0.394139	+	0.682670i
$227$	3.18646	+	11.8920i	0.211493	+	0.789301i	0.987372	+	0.158420i	$0.0506399\pi$
$227$	3.18646	+	11.8920i	0.211493	+	0.789301i	−0.775879	+	0.630881i	$0.782693\pi$
$228$	−9.44878	+	8.97439i	−0.625761	+	0.594344i
$229$	3.86544	−	2.23171i	0.255435	−	0.147476i	−0.366815	−	0.930294i	$-0.619552\pi$
$229$	3.86544	−	2.23171i	0.255435	−	0.147476i	0.622251	+	0.782818i	$0.286219\pi$
$230$	6.73837	−	4.33950i	0.444315	−	0.286138i
$231$		0			0
$232$	−39.7659	−	39.7659i	−2.61076	−	2.61076i
$233$	−2.06497	+	7.70659i	−0.135281	+	0.504875i	0.864716	+	0.502262i	$0.167499\pi$
$233$	−2.06497	+	7.70659i	−0.135281	+	0.504875i	−0.999997	+	0.00261362i	$0.999168\pi$
$234$	10.8954	+	21.3374i	0.712256	+	1.39487i
$235$	8.65014	+	7.84857i	0.564273	+	0.511984i
$236$	21.5151	−	12.4217i	1.40051	−	0.808586i
$237$	−8.37859	+	28.3310i	−0.544248	+	1.84030i
$238$		0			0
$239$	11.8594			0.767124			0.383562	−	0.923515i	$-0.374697\pi$
$239$	11.8594			0.767124			0.383562	+	0.923515i	$0.374697\pi$
$240$	−19.8597	−	18.9740i	−1.28194	−	1.22477i
$241$	−9.03617	+	15.6511i	−0.582071	+	1.00818i	0.413163	+	0.910657i	$0.364424\pi$
$241$	−9.03617	+	15.6511i	−0.582071	+	1.00818i	−0.995234	+	0.0975190i	$0.968909\pi$
$242$	−5.62484	−	20.9922i	−0.361579	−	1.34943i
$243$	12.3464	−	9.51661i	0.792023	−	0.610491i
$244$			33.1621i			2.12298i
$245$		0			0
$246$	13.5629	+	24.9538i	0.864741	+	1.59100i
$247$	−1.36472	+	5.09321i	−0.0868351	+	0.324073i
$248$	16.7378	−	4.48487i	1.06285	−	0.284789i
$249$	7.86790	+	0.202593i	0.498608	+	0.0128388i
$250$	−3.29793	+	28.2629i	−0.208579	+	1.78750i
$251$			3.19253i			0.201511i	0.994911	+	0.100755i	$0.0321259\pi$
$251$			3.19253i			0.201511i	−0.994911	+	0.100755i	$0.967874\pi$
$252$		0			0
$253$	1.56219	−	1.56219i	0.0982141	−	0.0982141i
$254$	25.7019	+	44.5170i	1.61268	+	2.79324i
$255$	10.2664	+	16.8810i	0.642907	+	1.05713i
$256$	14.6054	−	25.2973i	0.912836	−	1.58108i
$257$	16.1352	+	4.32342i	1.00649	+	0.269687i	0.724161	−	0.689631i	$-0.242227\pi$
$257$	16.1352	+	4.32342i	1.00649	+	0.269687i	0.282326	+	0.959319i	$0.408894\pi$
$258$	9.68378	−	32.7443i	0.602886	−	2.03857i
$259$		0			0
$260$	−30.7035	−	6.64874i	−1.90415	−	0.412337i
$261$	−1.37712	+	26.7232i	−0.0852416	+	1.65412i
$262$	12.0392	−	3.22589i	0.743784	−	0.199296i
$263$	−17.9635	+	4.81330i	−1.10768	+	0.296801i	−0.765886	−	0.642976i	$-0.777699\pi$
$263$	−17.9635	+	4.81330i	−1.10768	+	0.296801i	−0.341789	+	0.939777i	$0.611033\pi$
$264$	−14.6105	−	8.94458i	−0.899216	−	0.550501i
$265$	−8.75757	−	1.89642i	−0.537974	−	0.116496i
$266$		0			0
$267$	15.6174	+	4.61866i	0.955767	+	0.282658i
$268$	22.9503	+	6.14950i	1.40191	+	0.375641i
$269$	−14.6703	+	25.4096i	−0.894461	+	1.54925i	−0.0599909	+	0.998199i	$0.519107\pi$
$269$	−14.6703	+	25.4096i	−0.894461	+	1.54925i	−0.834470	+	0.551053i	$0.814226\pi$
$270$	−0.848131	+	29.5588i	−0.0516156	+	1.79889i
$271$	1.59183	+	2.75713i	0.0966968	+	0.167484i	0.910316	−	0.413915i	$-0.135839\pi$
$271$	1.59183	+	2.75713i	0.0966968	+	0.167484i	−0.813619	+	0.581399i	$0.802506\pi$
$272$	25.5821	−	25.5821i	1.55114	−	1.55114i
$273$		0			0
$274$		−	16.4083i		−	0.991263i
$275$	0.760341	+	7.80657i	0.0458503	+	0.470754i
$276$	−0.281132	+	10.9181i	−0.0169222	+	0.657190i
$277$	−23.0361	+	6.17251i	−1.38411	+	0.370870i	−0.872611	−	0.488416i	$-0.837575\pi$
$277$	−23.0361	+	6.17251i	−1.38411	+	0.370870i	−0.511495	+	0.859286i	$0.670908\pi$
$278$	−6.72182	+	25.0862i	−0.403148	+	1.50457i
$279$	−6.91877	−	4.48452i	−0.414216	−	0.268481i
$280$		0			0
$281$		−	24.8052i		−	1.47975i	−0.672742	−	0.739877i	$-0.734884\pi$
$281$		−	24.8052i		−	1.47975i	0.672742	−	0.739877i	$-0.265116\pi$
$282$	−22.3876	+	5.38511i	−1.33316	+	0.320679i
$283$	−1.98356	−	7.40274i	−0.117910	−	0.440047i	0.881578	−	0.472039i	$-0.156482\pi$
$283$	−1.98356	−	7.40274i	−0.117910	−	0.440047i	−0.999488	+	0.0319914i	$0.989815\pi$
$284$	8.10271	−	14.0343i	0.480807	−	0.832783i
$285$	−4.49585	+	4.70570i	−0.266311	+	0.278741i
$286$	−12.5277			−0.740781
$287$		0			0
$288$	15.9583	−	3.40661i	0.940354	−	0.200736i
$289$	−7.81541	+	4.51223i	−0.459730	+	0.265425i
$290$	−37.5926	−	34.1091i	−2.20751	−	2.00295i
$291$	10.7654	+	0.277201i	0.631077	+	0.0162498i
$292$	−9.66472	+	36.0692i	−0.565585	+	2.11079i
$293$	−8.60739	−	8.60739i	−0.502849	−	0.502849i	0.409473	−	0.912322i	$-0.365712\pi$
$293$	−8.60739	−	8.60739i	−0.502849	−	0.502849i	−0.912322	+	0.409473i	$0.865712\pi$
$294$		0			0
$295$	10.4313	−	6.71776i	0.607336	−	0.391123i
$296$	3.40045	−	1.96325i	0.197647	−	0.114112i
$297$	1.49593	+	8.01277i	0.0868027	+	0.464948i
$298$	0.608072	+	2.26935i	0.0352246	+	0.131460i
$299$	2.20960	+	3.82714i	0.127784	+	0.221329i
$300$	−29.3028	−	25.3937i	−1.69180	−	1.46610i
$301$		0			0
$302$	24.7107	−	24.7107i	1.42194	−	1.42194i
$303$	−1.70309	+	0.409661i	−0.0978397	+	0.0235344i
$304$	10.3206	+	5.95859i	0.591926	+	0.341749i
$305$	0.803687	+	16.5423i	0.0460190	+	0.947208i
$306$	−38.8986	−	2.00456i	−2.22369	−	0.114593i
$307$	11.8525	+	11.8525i	0.676457	+	0.676457i	0.959197	−	0.282740i	$-0.0912434\pi$
$307$	11.8525	+	11.8525i	0.676457	+	0.676457i	−0.282740	+	0.959197i	$0.591243\pi$
$308$		0			0
$309$	8.67440	−	4.71471i	0.493469	−	0.268211i
$310$	14.8934	−	4.77644i	0.845889	−	0.271283i
$311$	25.3572	+	14.6400i	1.43788	+	0.830158i	0.997702	−	0.0677541i	$-0.0215833\pi$
$311$	25.3572	+	14.6400i	1.43788	+	0.830158i	0.440174	+	0.897912i	$0.354917\pi$
$312$	24.8462	−	23.5988i	1.40664	−	1.33602i
$313$	1.67444	+	0.448664i	0.0946448	+	0.0253600i	0.305831	−	0.952086i	$-0.401066\pi$
$313$	1.67444	+	0.448664i	0.0946448	+	0.0253600i	−0.211186	+	0.977446i	$0.567733\pi$
$314$	−49.3859			−2.78701
$315$		0			0
$316$	76.3710			4.29620
$317$	5.87608	+	1.57449i	0.330034	+	0.0884322i	0.420031	−	0.907510i	$-0.362019\pi$
$317$	5.87608	+	1.57449i	0.330034	+	0.0884322i	−0.0899974	+	0.995942i	$0.528686\pi$
$318$	12.8083	−	12.1652i	0.718253	−	0.682192i
$319$	−12.1175	−	6.99605i	−0.678451	−	0.391704i
$320$	0.348143	−	0.676874i	0.0194618	−	0.0378384i
$321$	6.06388	−	3.29585i	0.338453	−	0.183956i
$322$		0			0
$323$	−6.06162	−	6.06162i	−0.337278	−	0.337278i
$324$	−32.6415	−	23.6285i	−1.81341	−	1.31269i
$325$	−15.4770	−	2.57249i	−0.858510	−	0.142696i
$326$	−20.5902	−	11.8877i	−1.14038	−	0.658401i
$327$	−10.8155	+	2.60157i	−0.598101	+	0.143867i
$328$	28.7244	−	28.7244i	1.58604	−	1.58604i
$329$		0			0
$330$	−13.5638	−	7.42400i	−0.746665	−	0.408678i
$331$	−16.6301	−	28.8042i	−0.914074	−	1.58322i	−0.808252	−	0.588837i	$-0.799586\pi$
$331$	−16.6301	−	28.8042i	−0.914074	−	1.58322i	−0.105822	−	0.994385i	$-0.533747\pi$
$332$	−5.26572	−	19.6519i	−0.288994	−	1.07854i
$333$	−1.77735	−	0.575782i	−0.0973983	−	0.0315527i
$334$	9.70781	−	5.60481i	0.531188	−	0.306681i
$335$	11.5973	+	2.51136i	0.633630	+	0.137210i
$336$		0			0
$337$	10.3056	+	10.3056i	0.561383	+	0.561383i	0.929700	−	0.368317i	$-0.120066\pi$
$337$	10.3056	+	10.3056i	0.561383	+	0.561383i	−0.368317	+	0.929700i	$0.620066\pi$
$338$	−2.07743	+	7.75309i	−0.112997	+	0.421712i
$339$	−8.06218	−	0.207596i	−0.437878	−	0.0112750i
$340$	34.3194	−	37.8244i	1.86123	−	2.05131i
$341$	3.73371	−	2.15566i	0.202192	−	0.116736i
$342$	−2.67849	−	12.5475i	−0.144836	−	0.678489i
$343$		0			0
$344$	−48.8391			−2.63323
$345$	0.124363	+	5.45308i	0.00669548	+	0.293584i
$346$	−14.6286	+	25.3376i	−0.786441	+	1.36216i
$347$	7.03650	+	26.2606i	0.377739	+	1.40974i	0.849301	+	0.527909i	$0.177024\pi$
$347$	7.03650	+	26.2606i	0.377739	+	1.40974i	−0.471562	+	0.881833i	$0.656309\pi$
$348$	67.2526	−	16.1770i	3.60512	−	0.867176i
$349$		−	30.1301i		−	1.61283i	−0.591353	−	0.806413i	$-0.701406\pi$
$349$		−	30.1301i		−	1.61283i	0.591353	−	0.806413i	$-0.298594\pi$
$350$		0			0
$351$	−16.2562	−	1.25799i	−0.867694	−	0.0671463i
$352$	−2.20841	+	8.24189i	−0.117708	+	0.439294i
$353$	−23.2688	+	6.23486i	−1.23847	+	0.331848i	−0.817873	−	0.575398i	$-0.804847\pi$
$353$	−23.2688	+	6.23486i	−1.23847	+	0.331848i	−0.420600	+	0.907246i	$0.638180\pi$
$354$	−0.629612	+	24.4516i	−0.0334635	+	1.29959i
$355$	3.70176	−	7.19712i	0.196469	−	0.381983i
$356$		−	42.0992i		−	2.23125i
$357$		0			0
$358$	−29.8703	+	29.8703i	−1.57869	+	1.57869i
$359$	−0.368991	−	0.639111i	−0.0194746	−	0.0337310i	0.856124	−	0.516771i	$-0.172866\pi$
$359$	−0.368991	−	0.639111i	−0.0194746	−	0.0337310i	−0.875598	+	0.483040i	$0.839533\pi$
$360$	40.8859	−	10.8265i	2.15488	−	0.570609i
$361$	−8.08813	+	14.0090i	−0.425691	+	0.737318i
$362$	−28.6475	−	7.67607i	−1.50568	−	0.403445i
$363$	14.1831	+	4.19448i	0.744417	+	0.220153i
$364$		0			0
$365$	−3.94692	+	18.2267i	−0.206591	+	0.954028i
$366$	−27.8460	−	17.0473i	−1.45553	−	0.891079i
$367$	31.8179	−	8.52557i	1.66088	−	0.445031i	0.698250	−	0.715854i	$-0.253962\pi$
$367$	31.8179	−	8.52557i	1.66088	−	0.445031i	0.962629	+	0.270822i	$0.0872956\pi$
$368$	9.64747	−	2.58503i	0.502909	−	0.134754i
$369$	−19.3032	−	0.994745i	−1.00488	−	0.0517844i
$370$	2.97967	−	1.91890i	0.154906	−	0.0997591i
$371$		0			0
$372$	−6.04438	+	20.4382i	−0.313387	+	1.05967i
$373$	7.21411	+	1.93302i	0.373533	+	0.100088i	0.440701	−	0.897654i	$-0.354730\pi$
$373$	7.21411	+	1.93302i	0.373533	+	0.100088i	−0.0671685	+	0.997742i	$0.521397\pi$
$374$	10.1836	−	17.6384i	0.526579	−	0.912062i
$375$	−15.2325	−	11.9570i	−0.786605	−	0.617456i
$376$	16.4670	+	28.5217i	0.849222	+	1.47090i
$377$	19.7908	−	19.7908i	1.01928	−	1.01928i
$378$		0			0
$379$			3.38353i			0.173800i	0.996217	+	0.0869000i	$0.0276961\pi$
$379$			3.38353i			0.173800i	−0.996217	+	0.0869000i	$0.972304\pi$
$380$	14.9607	+	7.69485i	0.767465	+	0.394738i
$381$	−34.9715	−	0.900491i	−1.79164	−	0.0461335i
$382$	31.6004	−	8.46729i	1.61681	−	0.433224i
$383$	−1.04955	+	3.91696i	−0.0536293	+	0.200147i	−0.987542	−	0.157353i	$-0.949704\pi$
$383$	−1.04955	+	3.91696i	−0.0536293	+	0.200147i	0.933913	+	0.357500i	$0.116371\pi$
$384$	9.71455	+	17.8734i	0.495744	+	0.912097i
$385$		0			0
$386$		−	29.0157i		−	1.47686i
$387$	15.5646	+	17.2559i	0.791192	+	0.877167i
$388$	−7.20490	−	26.8890i	−0.365773	−	1.36508i
$389$	5.10508	−	8.84225i	0.258838	−	0.448320i	−0.707093	−	0.707120i	$-0.749994\pi$
$389$	5.10508	−	8.84225i	0.258838	−	0.448320i	0.965931	+	0.258800i	$0.0833272\pi$
$390$	21.3664	−	22.3637i	1.08193	−	1.13243i
$391$	−7.18455			−0.363339
$392$		0			0
$393$	−2.40557	+	8.13410i	−0.121345	+	0.410311i
$394$	−58.4483	+	33.7452i	−2.94458	+	1.70006i
$395$	38.0962	−	1.85086i	1.91683	−	0.0931269i
$396$	18.7659	−	9.58233i	0.943021	−	0.481530i
$397$	8.80417	−	32.8576i	0.441869	−	1.64908i	−0.282205	−	0.959354i	$-0.591066\pi$
$397$	8.80417	−	32.8576i	0.441869	−	1.64908i	0.724074	−	0.689723i	$-0.242268\pi$
$398$	−7.57156	−	7.57156i	−0.379528	−	0.379528i
$399$		0			0
$400$	−14.6693	+	32.2828i	−0.733465	+	1.61414i
$401$	17.3995	−	10.0456i	0.868891	−	0.501654i	0.00191140	−	0.999998i	$-0.499392\pi$
$401$	17.3995	−	10.0456i	0.868891	−	0.501654i	0.866980	+	0.498344i	$0.166058\pi$
$402$	−16.9615	+	16.1100i	−0.845965	+	0.803492i
$403$	2.23203	+	8.33007i	0.111186	+	0.414950i
$404$	2.26402	+	3.92139i	0.112639	+	0.195097i
$405$	−16.8552	−	10.9955i	−0.837542	−	0.546373i
$406$		0			0
$407$	0.690793	−	0.690793i	0.0342413	−	0.0342413i
$408$	13.0289	+	54.1652i	0.645028	+	2.68158i
$409$	−29.0207	−	16.7551i	−1.43498	−	0.828487i	−0.437487	−	0.899225i	$-0.644131\pi$
$409$	−29.0207	−	16.7551i	−1.43498	−	0.828487i	−0.997495	+	0.0707377i	$0.977465\pi$
$410$	24.6382	−	27.1545i	1.21680	−	1.34107i
$411$	9.52376	+	5.83045i	0.469772	+	0.287595i
$412$	−18.0463	−	18.0463i	−0.889077	−	0.889077i
$413$		0			0
$414$	−9.02331	−	5.84862i	−0.443471	−	0.287444i
$415$	−3.10297	−	9.67538i	−0.152319	−	0.474946i
$416$	−14.7811	−	8.53389i	−0.724705	−	0.418408i
$417$	−12.1721	−	12.8155i	−0.596070	−	0.627578i
$418$	6.48030	+	1.73639i	0.316962	+	0.0849297i
$419$	−25.8773			−1.26419			−0.632093	−	0.774892i	$-0.717804\pi$
$419$	−25.8773			−1.26419			−0.632093	+	0.774892i	$0.717804\pi$
$420$		0			0
$421$	10.4030			0.507013			0.253507	−	0.967334i	$-0.418416\pi$
$421$	10.4030			0.507013			0.253507	+	0.967334i	$0.418416\pi$
$422$	−52.9063	−	14.1762i	−2.57544	−	0.690086i
$423$	4.82945	−	14.9078i	0.234816	−	0.724840i
$424$	−21.8808	−	12.6329i	−1.06263	−	0.613508i
$425$	16.2029	−	19.6997i	0.785955	−	0.955576i
$426$	7.61923	+	14.0183i	0.369153	+	0.679188i
$427$		0			0
$428$	−12.6154	−	12.6154i	−0.609786	−	0.609786i
$429$	4.45155	−	7.27139i	0.214923	−	0.351066i
$430$	−44.0307	+	2.13918i	−2.12335	+	0.103160i
$431$	0.388850	+	0.224503i	0.0187303	+	0.0108139i	0.509336	−	0.860568i	$-0.329891\pi$
$431$	0.388850	+	0.224503i	0.0187303	+	0.0108139i	−0.490606	+	0.871382i	$0.663224\pi$
$432$	−12.2554	+	34.7528i	−0.589641	+	1.67205i
$433$	17.7813	−	17.7813i	0.854517	−	0.854517i	−0.136169	−	0.990686i	$-0.543479\pi$
$433$	17.7813	−	17.7813i	0.854517	−	0.854517i	0.990686	+	0.136169i	$0.0434790\pi$
$434$		0			0
$435$	33.1556	−	9.69944i	1.58969	−	0.465053i
$436$	14.3778	+	24.9030i	0.688570	+	1.19264i
$437$	−0.612517	−	2.28594i	−0.0293007	−	0.109352i
$438$	−25.3189	−	26.6572i	−1.20978	−	1.27373i
$439$	−25.5732	+	14.7647i	−1.22054	+	0.704679i	−0.965033	−	0.262128i	$-0.915576\pi$
$439$	−25.5732	+	14.7647i	−1.22054	+	0.704679i	−0.255507	+	0.966807i	$0.582243\pi$
$440$	−4.68067	+	21.6151i	−0.223142	+	1.03046i
$441$		0			0
$442$	28.8077	+	28.8077i	1.37024	+	1.37024i
$443$	−5.69694	+	21.2613i	−0.270670	+	1.01015i	0.688018	+	0.725693i	$0.258481\pi$
$443$	−5.69694	+	21.2613i	−0.270670	+	1.01015i	−0.958688	+	0.284460i	$0.908186\pi$
$444$	−0.124315	+	4.82791i	−0.00589975	+	0.229123i
$445$	−1.02028	−	21.0004i	−0.0483659	−	0.995514i
$446$	−38.6519	+	22.3157i	−1.83022	+	1.05668i
$447$	−1.53325	−	0.453443i	−0.0725204	−	0.0214471i
$448$		0			0
$449$	16.3214			0.770252			0.385126	−	0.922864i	$-0.374158\pi$
$449$	16.3214			0.770252			0.385126	+	0.922864i	$0.374158\pi$
$450$	36.3863	−	11.5515i	1.71527	−	0.544541i
$451$	5.05351	−	8.75294i	0.237961	−	0.412160i
$452$	5.39575	+	20.1372i	0.253795	+	0.947175i
$453$	5.56206	+	23.1232i	0.261328	+	1.08642i
$454$			31.3336i			1.47056i
$455$		0			0
$456$	−16.1232	+	8.76332i	−0.755040	+	0.410380i
$457$	−7.55108	+	28.1810i	−0.353225	+	1.31825i	0.529479	+	0.848323i	$0.322387\pi$
$457$	−7.55108	+	28.1810i	−0.353225	+	1.31825i	−0.882704	+	0.469929i	$0.844279\pi$
$458$	10.9726	−	2.94010i	0.512717	−	0.137382i
$459$	14.9855	−	21.8654i	0.699465	−	1.02059i
$460$	13.4263	−	4.30591i	0.626002	−	0.200764i
$461$		−	15.2893i		−	0.712094i	−0.934468	−	0.356047i	$-0.884124\pi$
$461$		−	15.2893i		−	0.712094i	0.934468	−	0.356047i	$-0.115876\pi$
$462$		0			0
$463$	0.492195	−	0.492195i	0.0228743	−	0.0228743i	−0.695577	−	0.718451i	$-0.744851\pi$
$463$	0.492195	−	0.492195i	0.0228743	−	0.0228743i	0.718451	+	0.695577i	$0.244851\pi$
$464$	−31.6281	−	54.7815i	−1.46830	−	2.54317i
$465$	−2.51980	+	10.3417i	−0.116853	+	0.479585i
$466$	−10.1528	+	17.5852i	−0.470320	+	0.814619i
$467$	−12.2948	−	3.29439i	−0.568937	−	0.152446i	−0.0371280	−	0.999311i	$-0.511821\pi$
$467$	−12.2948	−	3.29439i	−0.568937	−	0.152446i	−0.531809	+	0.846864i	$0.678488\pi$
$468$	8.79901	+	41.2192i	0.406734	+	1.90536i
$469$		0			0
$470$	16.0951	+	24.9924i	0.742410	+	1.15281i
$471$	17.5485	−	28.6647i	0.808594	−	1.32080i
$472$	33.7924	−	9.05465i	1.55542	−	0.416774i
$473$	−11.7373	+	3.14500i	−0.539682	+	0.144607i
$474$	−39.2594	+	64.1282i	−1.80324	+	2.94551i
$475$	7.64932	+	3.47586i	0.350975	+	0.159483i
$476$		0			0
$477$	2.50974	+	11.7570i	0.114913	+	0.538314i
$478$	29.1546	+	7.81194i	1.33350	+	0.357310i
$479$	−11.3786	+	19.7083i	−0.519901	+	0.900496i	0.479831	+	0.877361i	$0.340698\pi$
$479$	−11.3786	+	19.7083i	−0.519901	+	0.900496i	−0.999732	+	0.0231347i	$0.992635\pi$
$480$	−10.9464	−	17.9990i	−0.499631	−	0.821540i
$481$	0.977074	+	1.69234i	0.0445507	+	0.0771641i
$482$	−32.5235	+	32.5235i	−1.48141	+	1.48141i
$483$		0			0
$484$		−	38.2328i		−	1.73785i
$485$	−4.24568	−	13.2385i	−0.192787	−	0.601128i
$486$	36.6204	−	15.2623i	1.66113	−	0.692314i
$487$	15.6982	−	4.20631i	0.711352	−	0.190606i	0.115042	−	0.993361i	$-0.463300\pi$
$487$	15.6982	−	4.20631i	0.711352	−	0.190606i	0.596310	+	0.802754i	$0.296633\pi$
$488$	−12.0865	+	45.1075i	−0.547131	+	2.04192i
$489$	14.2163	−	7.72687i	0.642884	−	0.349421i
$490$		0			0
$491$			0.301729i			0.0136168i	0.999977	+	0.00680841i	$0.00216720\pi$
$491$			0.301729i			0.0136168i	−0.999977	+	0.00680841i	$0.997833\pi$
$492$	11.6852	+	48.5791i	0.526811	+	2.19011i
$493$	11.7769	+	43.9519i	0.530404	+	1.97949i
$494$	−6.70989	+	11.6219i	−0.301892	+	0.522893i
$495$	9.12877	−	5.23475i	0.410308	−	0.235285i
$496$	19.4909			0.875165
$497$		0			0
$498$	19.2085	+	5.68071i	0.860754	+	0.254559i
$499$	17.5116	−	10.1103i	0.783928	−	0.452601i	−0.0538926	−	0.998547i	$-0.517163\pi$
$499$	17.5116	−	10.1103i	0.783928	−	0.452601i	0.837821	+	0.545946i	$0.183830\pi$
$500$	−18.4728	+	46.5250i	−0.826129	+	2.08066i
$501$	−0.196370	+	7.62622i	−0.00877315	+	0.340714i
$502$	−2.10295	+	7.84832i	−0.0938593	+	0.350288i
$503$	23.8859	+	23.8859i	1.06502	+	1.06502i	0.997734	+	0.0672882i	$0.0214347\pi$
$503$	23.8859	+	23.8859i	1.06502	+	1.06502i	0.0672882	+	0.997734i	$0.478565\pi$
$504$		0			0
$505$	1.22440	+	1.90124i	0.0544850	+	0.0846042i
$506$	4.86943	−	2.81137i	0.216473	−	0.124980i
$507$	−3.76188	−	3.96073i	−0.167071	−	0.175902i
$508$	23.4052	+	87.3495i	1.03844	+	3.87551i
$509$	−5.88603	−	10.1949i	−0.260894	−	0.451881i	0.705586	−	0.708624i	$-0.250684\pi$
$509$	−5.88603	−	10.1949i	−0.260894	−	0.451881i	−0.966480	+	0.256743i	$0.917351\pi$
$510$	14.1186	+	48.2618i	0.625184	+	2.13707i
$511$		0			0
$512$	35.9587	−	35.9587i	1.58917	−	1.58917i
$513$	8.23459	+	2.90390i	0.363566	+	0.128210i
$514$	36.8179	+	21.2569i	1.62397	+	0.937600i
$515$	−9.43940	−	8.56469i	−0.415950	−	0.377405i
$516$	31.3647	−	51.2326i	1.38075	−	2.25539i
$517$	5.79412	+	5.79412i	0.254825	+	0.254825i
$518$		0			0
$519$	−9.50842	−	17.4941i	−0.417373	−	0.767907i
$520$	−39.3401	−	20.2342i	−1.72518	−	0.887327i
$521$	−25.7965	−	14.8936i	−1.13016	−	0.652500i	−0.186187	−	0.982514i	$-0.559613\pi$
$521$	−25.7965	−	14.8936i	−1.13016	−	0.652500i	−0.943976	+	0.330014i	$0.892947\pi$
$522$	−20.9883	+	64.7876i	−0.918632	+	2.83567i
$523$	23.8608	+	6.39348i	1.04336	+	0.279567i	0.739505	−	0.673151i	$-0.235060\pi$
$523$	23.8608	+	6.39348i	1.04336	+	0.279567i	0.303854	+	0.952719i	$0.401726\pi$
$524$	21.9268			0.957877
$525$		0			0
$526$	−47.3309			−2.06373
$527$	−13.5427	−	3.62875i	−0.589929	−	0.158071i
$528$	−13.2701	−	13.9715i	−0.577506	−	0.608033i
$529$	18.2009	+	10.5083i	0.791343	+	0.456882i
$530$	−20.2799	−	10.4308i	−0.880903	−	0.453083i
$531$	−13.9685	−	9.05395i	−0.606183	−	0.392908i
$532$		0			0
$533$	14.2956	+	14.2956i	0.619211	+	0.619211i
$534$	35.3504	+	21.6416i	1.52976	+	0.936522i
$535$	−6.59866	−	5.98719i	−0.285285	−	0.258849i
$536$	28.9760	+	16.7293i	1.25157	+	0.722595i
$537$	−6.72343	−	27.9514i	−0.290137	−	1.20619i
$538$	−52.8021	+	52.8021i	−2.27646	+	2.27646i
$539$		0			0
$540$	−14.8999	+	49.8425i	−0.641192	+	2.14488i
$541$	11.5559	+	20.0153i	0.496825	+	0.860526i	0.999993	−	0.00366246i	$-0.00116580\pi$
$541$	11.5559	+	20.0153i	0.496825	+	0.860526i	−0.503168	+	0.864188i	$0.667832\pi$
$542$	2.09711	+	7.82652i	0.0900786	+	0.336178i
$543$	14.6348	−	13.9001i	0.628040	−	0.596509i
$544$	24.0306	−	13.8741i	1.03030	−	0.594845i
$545$	7.77560	+	12.0739i	0.333070	+	0.517191i
$546$		0			0
$547$	−25.6689	−	25.6689i	−1.09752	−	1.09752i	−0.994700	−	0.102823i	$-0.967213\pi$
$547$	−25.6689	−	25.6689i	−1.09752	−	1.09752i	−0.102823	−	0.994700i	$-0.532787\pi$
$548$	7.47105	−	27.8824i	0.319148	−	1.19108i
$549$	19.7893	−	10.1049i	0.844588	−	0.431268i
$550$	−3.27309	+	19.6920i	−0.139565	+	0.839671i
$551$	−12.9804	+	7.49421i	−0.552982	+	0.319264i
$552$	−4.36169	+	14.7484i	−0.185646	+	0.627735i
$553$		0			0
$554$	−60.6965			−2.57875
$555$	0.0549927	+	2.41132i	0.00233431	+	0.102355i
$556$	−22.8445	+	39.5679i	−0.968824	+	1.67805i
$557$	−3.87177	−	14.4497i	−0.164052	−	0.612252i	−0.998159	−	0.0606487i	$-0.980683\pi$
$557$	−3.87177	−	14.4497i	−0.164052	−	0.612252i	0.834107	−	0.551603i	$-0.185984\pi$
$558$	−14.0547	−	15.5819i	−0.594982	−	0.659636i
$559$		−	24.3063i		−	1.02805i
$560$		0			0
$561$	6.61917	+	12.1783i	0.279462	+	0.514169i
$562$	16.3394	−	60.9796i	0.689238	−	2.57227i
$563$	−14.9192	+	3.99759i	−0.628769	+	0.168478i	−0.559111	−	0.829093i	$-0.688857\pi$
$563$	−14.9192	+	3.99759i	−0.628769	+	0.168478i	−0.0696580	+	0.997571i	$0.522191\pi$
$564$	−40.4947	−	1.04271i	−1.70514	−	0.0439061i
$565$	3.17959	+	9.91430i	0.133767	+	0.417098i
$566$		−	19.5050i		−	0.819858i
$567$		0			0
$568$	16.1365	−	16.1365i	0.677072	−	0.677072i
$569$	−21.0355	−	36.4346i	−0.881854	−	1.52742i	−0.849277	−	0.527947i	$-0.822962\pi$
$569$	−21.0355	−	36.4346i	−0.881854	−	1.52742i	−0.0325765	−	0.999469i	$-0.510371\pi$
$570$	−14.1520	+	8.60674i	−0.592762	+	0.360497i
$571$	−5.41712	+	9.38272i	−0.226699	+	0.392655i	−0.956828	−	0.290655i	$-0.906127\pi$
$571$	−5.41712	+	9.38272i	−0.226699	+	0.392655i	0.730129	+	0.683310i	$0.239460\pi$
$572$	−21.2882	−	5.70415i	−0.890103	−	0.238502i
$573$	−6.31411	+	21.3503i	−0.263776	+	0.891921i
$574$		0			0
$575$	6.59308	−	2.47331i	0.274950	−	0.103144i
$576$	−1.01985	−	0.0525556i	−0.0424936	−	0.00218982i
$577$	20.0772	−	5.37966i	0.835823	−	0.223958i	0.184571	−	0.982819i	$-0.440911\pi$
$577$	20.0772	−	5.37966i	0.835823	−	0.223958i	0.651253	+	0.758861i	$0.274244\pi$
$578$	−22.1852	+	5.94450i	−0.922782	+	0.247259i
$579$	16.8414	+	10.3103i	0.699904	+	0.428482i
$580$	−48.3498	−	75.0776i	−2.00762	−	3.11743i
$581$		0			0
$582$	26.2823	+	7.77271i	1.08944	+	0.322189i
$583$	−6.07203	−	1.62700i	−0.251478	−	0.0673833i
$584$	−26.2922	+	45.5394i	−1.08798	+	1.88443i
$585$	5.38817	+	20.3481i	0.222773	+	0.841292i
$586$	−15.4901	−	26.8297i	−0.639891	−	1.10832i
$587$	−4.89737	+	4.89737i	−0.202136	+	0.202136i	−0.800915	−	0.598779i	$-0.795653\pi$
$587$	−4.89737	+	4.89737i	−0.202136	+	0.202136i	0.598779	+	0.800915i	$0.295653\pi$
$588$		0			0
$589$		−	4.61831i		−	0.190294i
$590$	30.0688	−	9.64332i	1.23791	−	0.397009i
$591$	1.18229	−	45.9156i	0.0486331	−	1.88871i
$592$	4.26606	−	1.14309i	0.175334	−	0.0469806i
$593$	8.25882	−	30.8223i	0.339149	−	1.26572i	−0.560151	−	0.828390i	$-0.689257\pi$
$593$	8.25882	−	30.8223i	0.339149	−	1.26572i	0.899300	−	0.437331i	$-0.144076\pi$
$594$	−1.60059	+	20.6835i	−0.0656729	+	0.848654i
$595$		0			0
$596$			4.13314i			0.169300i
$597$	7.08514	−	1.70426i	0.289976	−	0.0697508i
$598$	2.91097	+	10.8639i	0.119039	+	0.444258i
$599$	−3.40986	+	5.90604i	−0.139323	+	0.241314i	−0.927241	−	0.374466i	$-0.877826\pi$
$599$	−3.40986	+	5.90604i	−0.139323	+	0.241314i	0.787918	+	0.615781i	$0.211159\pi$
$600$	−30.6029	−	45.2208i	−1.24936	−	1.84613i
$601$	8.46733			0.345390			0.172695	−	0.984975i	$-0.444753\pi$
$601$	8.46733			0.345390			0.172695	+	0.984975i	$0.444753\pi$
$602$		0			0
$603$	−3.32356	−	15.5693i	−0.135346	−	0.634031i
$604$	53.2417	−	30.7391i	2.16637	−	1.25076i
$605$	−0.926576	−	19.0717i	−0.0376707	−	0.775374i
$606$	−4.45661	−	0.114755i	−0.181038	−	0.00466159i
$607$	−2.30704	+	8.60998i	−0.0936398	+	0.349468i	−0.996810	−	0.0798148i	$-0.974567\pi$
$607$	−2.30704	+	8.60998i	−0.0936398	+	0.349468i	0.903170	+	0.429283i	$0.141234\pi$
$608$	6.46309	+	6.46309i	0.262113	+	0.262113i
$609$		0			0
$610$	−8.92083	+	41.1959i	−0.361194	+	1.66797i
$611$	−14.1947	+	8.19533i	−0.574258	+	0.331548i
$612$	−65.1870	−	21.1177i	−2.63503	−	0.853631i
$613$	−1.92064	−	7.16791i	−0.0775738	−	0.289509i	0.916231	−	0.400651i	$-0.131216\pi$
$613$	−1.92064	−	7.16791i	−0.0775738	−	0.289509i	−0.993805	+	0.111142i	$0.964549\pi$
$614$	21.3301	+	36.9448i	0.860812	+	1.49097i
$615$	7.00627	+	23.9496i	0.282520	+	0.965739i
$616$		0			0
$617$	−2.10719	+	2.10719i	−0.0848323	+	0.0848323i	−0.748250	−	0.663417i	$-0.769105\pi$
$617$	−2.10719	+	2.10719i	−0.0848323	+	0.0848323i	0.663417	+	0.748250i	$0.269105\pi$
$618$	24.4302	−	5.87646i	0.982729	−	0.236386i
$619$	18.2501	+	10.5367i	0.733534	+	0.423506i	0.819714	−	0.572773i	$-0.194133\pi$
$619$	18.2501	+	10.5367i	0.733534	+	0.423506i	−0.0861795	+	0.996280i	$0.527466\pi$
$620$	27.4829	−	1.33523i	1.10374	−	0.0536240i
$621$	6.60097	−	3.15911i	0.264888	−	0.126771i
$622$	52.6932	+	52.6932i	2.11280	+	2.11280i
$623$		0			0
$624$	33.8650	−	18.4063i	1.35569	−	0.736844i
$625$	−8.08726	+	23.6558i	−0.323491	+	0.946231i
$626$	3.82080	+	2.20594i	0.152710	+	0.0881670i
$627$	−3.31052	+	3.14431i	−0.132209	+	0.125572i
$628$	−83.9205	−	22.4864i	−3.34879	−	0.897306i
$629$	−3.17697			−0.126674
$630$		0			0
$631$	−11.6376			−0.463287			−0.231643	−	0.972801i	$-0.574410\pi$
$631$	−11.6376			−0.463287			−0.231643	+	0.972801i	$0.574410\pi$
$632$	103.881	+	27.8348i	4.13216	+	1.10721i
$633$	27.0276	−	25.6707i	1.07425	−	1.02032i
$634$	13.4083	+	7.74127i	0.532511	+	0.307445i
$635$	13.7922	+	43.0054i	0.547326	+	1.70662i
$636$	27.3040	−	14.8403i	1.08267	−	0.588455i
$637$		0			0
$638$	−25.1806	−	25.1806i	−0.996910	−	0.996910i
$639$	−10.8439	−	0.558817i	−0.428979	−	0.0221065i
$640$	17.6473	−	19.4496i	0.697572	−	0.768815i
$641$	31.2666	+	18.0518i	1.23496	+	0.713003i	0.968059	−	0.250722i	$-0.0806680\pi$
$641$	31.2666	+	18.0518i	1.23496	+	0.713003i	0.266898	+	0.963725i	$0.414001\pi$
$642$	17.0781	−	4.10797i	0.674019	−	0.162129i
$643$	21.0115	−	21.0115i	0.828614	−	0.828614i	−0.158711	−	0.987325i	$-0.550734\pi$
$643$	21.0115	−	21.0115i	0.828614	−	0.828614i	0.987325	+	0.158711i	$0.0507337\pi$
$644$		0			0
$645$	14.4040	−	26.3165i	0.567158	−	1.03621i
$646$	−10.9087	−	18.8944i	−0.429196	−	0.743389i
$647$	−6.91879	−	25.8213i	−0.272006	−	1.01514i	−0.957821	−	0.287364i	$-0.907221\pi$
$647$	−6.91879	−	25.8213i	−0.272006	−	1.01514i	0.685816	−	0.727775i	$-0.259446\pi$
$648$	−35.7875	−	44.0366i	−1.40587	−	1.72992i
$649$	7.53812	−	4.35214i	0.295897	−	0.170836i
$650$	−36.3532	−	16.5189i	−1.42589	−	0.647925i
$651$		0			0
$652$	−29.5757	−	29.5757i	−1.15828	−	1.15828i
$653$	4.49712	−	16.7835i	0.175986	−	0.656788i	−0.820396	−	0.571796i	$-0.806247\pi$
$653$	4.49712	−	16.7835i	0.175986	−	0.656788i	0.996382	−	0.0849922i	$-0.0270865\pi$
$654$	−28.3020	−	0.728756i	−1.10669	−	0.0284966i
$655$	10.9378	−	0.531399i	0.427374	−	0.0207635i
$656$	39.5707	−	22.8462i	1.54498	−	0.891994i
$657$	24.4691	−	5.22339i	0.954631	−	0.203784i
$658$		0			0
$659$	0.708622			0.0276040			0.0138020	−	0.999905i	$-0.495607\pi$
$659$	0.708622			0.0276040			0.0138020	+	0.999905i	$0.495607\pi$
$660$	−19.6685	−	18.7914i	−0.765595	−	0.731453i
$661$	8.71029	−	15.0867i	0.338791	−	0.586803i	−0.645414	−	0.763833i	$-0.723315\pi$
$661$	8.71029	−	15.0867i	0.338791	−	0.586803i	0.984206	+	0.177029i	$0.0566487\pi$
$662$	−21.9089	−	81.7650i	−0.851512	−	3.17789i
$663$	−26.9570	+	6.48425i	−1.04692	+	0.251827i
$664$		−	28.6500i		−	1.11184i
$665$		0			0
$666$	−3.99006	−	2.58623i	−0.154612	−	0.100214i
$667$	−3.25123	+	12.1338i	−0.125888	+	0.469821i
$668$	19.0483	−	5.10397i	0.737000	−	0.197479i
$669$	0.781851	−	30.3640i	0.0302281	−	1.17394i
$670$	26.8559	+	13.8131i	1.03754	+	0.533645i
$671$			11.6188i			0.448540i
$672$		0			0
$673$	−8.20389	+	8.20389i	−0.316237	+	0.316237i	−0.847320	−	0.531083i	$-0.821785\pi$
$673$	−8.20389	+	8.20389i	−0.316237	+	0.316237i	0.531083	+	0.847320i	$0.321785\pi$
$674$	18.5463	+	32.1231i	0.714377	+	1.23734i
$675$	−6.22461	+	25.2241i	−0.239585	+	0.970875i
$676$	−7.06029	+	12.2288i	−0.271550	+	0.470338i
$677$	44.8882	+	12.0278i	1.72519	+	0.462264i	0.979067	−	0.203539i	$-0.0652442\pi$
$677$	44.8882	+	12.0278i	1.72519	+	0.462264i	0.746128	+	0.665803i	$0.231911\pi$
$678$	−19.6828	−	5.82098i	−0.755915	−	0.223554i
$679$		0			0
$680$	60.4675	−	38.9409i	2.31882	−	1.49332i
$681$	−18.1867	−	11.1339i	−0.696917	−	0.426653i
$682$	10.5987	−	2.83991i	0.405845	−	0.108746i
$683$	38.9287	−	10.4309i	1.48957	−	0.399128i	0.579975	−	0.814634i	$-0.303062\pi$
$683$	38.9287	−	10.4309i	1.48957	−	0.399128i	0.909590	+	0.415506i	$0.136396\pi$
$684$	1.16161	−	22.5413i	0.0444154	−	0.861886i
$685$	3.05106	−	14.0896i	0.116575	−	0.538338i
$686$		0			0
$687$	−2.19245	+	7.41347i	−0.0836473	+	0.282842i
$688$	−53.0626	−	14.2181i	−2.02299	−	0.542060i
$689$	6.28716	−	10.8897i	0.239522	−	0.414864i
$690$	−3.28627	+	13.4874i	−0.125106	+	0.513458i
$691$	2.89969	+	5.02242i	0.110310	+	0.191062i	0.915895	−	0.401418i	$-0.131482\pi$
$691$	2.89969	+	5.02242i	0.110310	+	0.191062i	−0.805586	+	0.592480i	$0.798149\pi$
$692$	−36.3949	+	36.3949i	−1.38353	+	1.38353i
$693$		0			0
$694$			69.1925i			2.62651i
$695$	−10.4366	+	20.2913i	−0.395884	+	0.769694i
$696$	97.3740	+	2.50731i	3.69095	+	0.0950394i
$697$	−31.7481	+	8.50687i	−1.20254	+	0.322221i
$698$	19.8470	−	74.0699i	0.751219	−	2.80359i
$699$	−6.59919	−	12.1416i	−0.249604	−	0.459236i
$700$		0			0
$701$			4.92775i			0.186118i	0.995661	+	0.0930592i	$0.0296646\pi$
$701$			4.92775i			0.186118i	−0.995661	+	0.0930592i	$0.970335\pi$
$702$	−39.1347	−	13.8007i	−1.47704	−	0.520874i
$703$	−0.270852	−	1.01083i	−0.0102154	−	0.0381243i
$704$	0.266993	−	0.462446i	0.0100627	−	0.0174291i
$705$	−20.2253	+	0.461258i	−0.761729	+	0.0173720i
$706$	−61.3096			−2.30742
$707$		0			0
$708$	−12.2032	+	41.2635i	−0.458625	+	1.55078i
$709$	−14.8889	+	8.59609i	−0.559163	+	0.322833i	−0.752809	−	0.658239i	$-0.771302\pi$
$709$	−14.8889	+	8.59609i	−0.559163	+	0.322833i	0.193647	+	0.981071i	$0.437968\pi$
$710$	13.8410	−	15.2546i	0.519443	−	0.572494i
$711$	−23.2712	−	45.5740i	−0.872740	−	1.70916i
$712$	15.3438	−	57.2639i	0.575034	−	2.14606i
$713$	−2.73693	−	2.73693i	−0.102499	−	0.102499i
$714$		0			0
$715$	−10.7574	−	2.32948i	−0.402305	−	0.0871177i
$716$	−64.3586	+	37.1575i	−2.40519	+	1.38864i
$717$	−14.8939	+	14.1461i	−0.556221	+	0.528296i
$718$	−0.486116	−	1.81421i	−0.0181417	−	0.0677057i
$719$	6.12782	+	10.6137i	0.228529	+	0.395824i	0.957372	−	0.288856i	$-0.0932750\pi$
$719$	6.12782	+	10.6137i	0.228529	+	0.395824i	−0.728843	+	0.684681i	$0.759942\pi$
$720$	47.5735	+	0.139941i	1.77296	+	0.00521528i
$721$		0			0
$722$	−29.1113	+	29.1113i	−1.08341	+	1.08341i
$723$	−7.32063	−	30.4341i	−0.272257	−	1.13186i
$724$	−45.1850	−	26.0876i	−1.67929	−	0.969538i
$725$	−25.9379	−	36.2792i	−0.963309	−	1.34738i
$726$	32.1038	+	19.6540i	1.19148	+	0.729428i
$727$	−5.83842	−	5.83842i	−0.216535	−	0.216535i	0.590501	−	0.807037i	$-0.298930\pi$
$727$	−5.83842	−	5.83842i	−0.216535	−	0.216535i	−0.807037	+	0.590501i	$0.798930\pi$
$728$		0			0
$729$	−4.15390	+	26.6786i	−0.153848	+	0.988094i
$730$	−21.7090	+	42.2075i	−0.803485	+	1.56217i
$731$	34.2220	+	19.7581i	1.26575	+	0.730780i
$732$	−39.5562	−	41.6471i	−1.46204	−	1.53932i
$733$	18.5697	+	4.97574i	0.685888	+	0.183783i	0.584901	−	0.811105i	$-0.301133\pi$
$733$	18.5697	+	4.97574i	0.685888	+	0.183783i	0.100987	+	0.994888i	$0.467800\pi$
$734$	83.8351			3.09441
$735$		0			0
$736$	7.66040			0.282366
$737$	8.04096	+	2.15457i	0.296193	+	0.0793646i
$738$	−46.7985	−	15.1606i	−1.72268	−	0.558070i
$739$	13.1464	+	7.59007i	0.483598	+	0.279205i	0.721915	−	0.691982i	$-0.243262\pi$
$739$	13.1464	+	7.59007i	0.483598	+	0.279205i	−0.238317	+	0.971187i	$0.576596\pi$
$740$	5.93702	−	1.90405i	0.218249	−	0.0699943i
$741$	−4.36134	−	8.02424i	−0.160218	−	0.294778i
$742$		0			0
$743$	−34.4215	−	34.4215i	−1.26280	−	1.26280i	−0.949729	−	0.313073i	$-0.898642\pi$
$743$	−34.4215	−	34.4215i	−1.26280	−	1.26280i	−0.313073	−	0.949729i	$-0.601358\pi$
$744$	−15.6707	+	25.5974i	−0.574517	+	0.938446i
$745$	0.100167	+	2.06174i	0.00366984	+	0.0755362i
$746$	16.4614	+	9.50402i	0.602696	+	0.347967i
$747$	−10.1227	+	9.13050i	−0.370369	+	0.334068i
$748$	25.3359	−	25.3359i	0.926371	−	0.926371i
$749$		0			0
$750$	−29.5706	−	39.4282i	−1.07977	−	1.43971i
$751$	11.1258	+	19.2704i	0.405985	+	0.703186i	0.994436	−	0.105347i	$-0.0335952\pi$
$751$	11.1258	+	19.2704i	0.405985	+	0.703186i	−0.588451	+	0.808533i	$0.700262\pi$
$752$	9.58780	+	35.7822i	0.349631	+	1.30484i
$753$	−3.80809	−	4.00939i	−0.138775	−	0.146110i
$754$	61.6888	−	35.6160i	2.24657	−	1.29706i
$755$	25.8136	−	16.6239i	0.939454	−	0.605007i
$756$		0			0
$757$	−1.88407	−	1.88407i	−0.0684777	−	0.0684777i	0.672038	−	0.740516i	$-0.265419\pi$
$757$	−1.88407	−	1.88407i	−0.0684777	−	0.0684777i	−0.740516	+	0.672038i	$0.765419\pi$
$758$	−2.22876	+	8.31786i	−0.0809523	+	0.302118i
$759$	−0.0984989	+	3.82530i	−0.00357529	+	0.138850i
$760$	17.5452	+	15.9193i	0.636430	+	0.577455i
$761$	−30.8889	+	17.8337i	−1.11972	+	0.646472i	−0.941330	−	0.337488i	$-0.890423\pi$
$761$	−30.8889	+	17.8337i	−1.11972	+	0.646472i	−0.178392	+	0.983960i	$0.557089\pi$
$762$	−85.3786	−	25.2498i	−3.09294	−	0.914703i
$763$		0			0
$764$	57.5532			2.08220
$765$	−33.0291	−	8.95433i	−1.19417	−	0.323745i
$766$	−5.16028	+	8.93787i	−0.186449	+	0.322938i
$767$	4.50633	+	16.8179i	0.162714	+	0.607258i
$768$	11.8325	+	49.1914i	0.426969	+	1.77504i
$769$			31.7331i			1.14432i	0.820141	+	0.572162i	$0.193895\pi$
$769$			31.7331i			1.14432i	−0.820141	+	0.572162i	$0.806105\pi$
$770$		0			0
$771$	−25.4207	+	13.8167i	−0.915503	+	0.497595i
$772$	13.2115	−	49.3059i	0.475491	−	1.77456i
$773$	6.80067	−	1.82223i	0.244603	−	0.0655412i	−0.134434	−	0.990922i	$-0.542922\pi$
$773$	6.80067	−	1.82223i	0.244603	−	0.0655412i	0.379038	+	0.925381i	$0.376255\pi$
$774$	26.8964	+	52.6734i	0.966770	+	1.89331i
$775$	13.6770	−	1.33210i	0.491291	−	0.0478506i
$776$		−	39.2008i		−	1.40723i
$777$		0			0
$778$	18.3745	−	18.3745i	0.658758	−	0.658758i
$779$	−5.41335	−	9.37619i	−0.193953	−	0.335937i
$780$	46.4902	−	28.2737i	1.66462	−	1.01236i
$781$	2.83891	−	4.91713i	0.101584	−	0.175949i
$782$	−17.6621	−	4.73254i	−0.631595	−	0.169235i
$783$	−30.1463	−	35.2034i	−1.07734	−	1.25807i
$784$		0			0
$785$	−42.4071	−	9.18310i	−1.51357	−	0.327759i
$786$	−11.2717	+	18.4118i	−0.402049	+	0.656727i
$787$	25.6203	−	6.86494i	0.913266	−	0.244709i	0.228561	−	0.973530i	$-0.426598\pi$
$787$	25.6203	−	6.86494i	0.913266	−	0.244709i	0.684705	+	0.728821i	$0.259931\pi$
$788$	−114.685	+	30.7298i	−4.08549	+	1.09470i
$789$	16.8183	−	27.4719i	0.598748	−	0.978026i
$790$	94.8726	+	20.5443i	3.37542	+	0.730934i
$791$		0			0
$792$	29.0181	−	6.19445i	1.03111	−	0.220110i
$793$	−22.4492	−	6.01524i	−0.797194	−	0.213607i
$794$	43.2873	−	74.9758i	1.53621	−	2.66079i
$795$	13.2604	−	8.06450i	0.470298	−	0.286018i
$796$	−9.41871	−	16.3137i	−0.333837	−	0.578223i
$797$	7.92792	−	7.92792i	0.280821	−	0.280821i	−0.552615	−	0.833437i	$-0.686370\pi$
$797$	7.92792	−	7.92792i	0.280821	−	0.280821i	0.833437	+	0.552615i	$0.186370\pi$
$798$		0			0
$799$		−	26.6473i		−	0.942713i
$800$	−17.2760	+	21.0045i	−0.610800	+	0.742620i
$801$	−25.1225	+	12.8282i	−0.887660	+	0.453262i
$802$	49.3911	−	13.2343i	1.74406	−	0.467320i
$803$	−3.38618	+	12.6374i	−0.119496	+	0.445964i
$804$	−36.1576	+	19.6524i	−1.27518	+	0.693088i
$805$		0			0
$806$			21.9484i			0.773099i
$807$	−11.8851	−	49.4099i	−0.418375	−	1.73931i
$808$	1.65032	+	6.15910i	0.0580582	+	0.216676i
$809$	−16.6141	+	28.7764i	−0.584119	+	1.01172i	0.410865	+	0.911696i	$0.365227\pi$
$809$	−16.6141	+	28.7764i	−0.584119	+	1.01172i	−0.994985	+	0.100028i	$0.968107\pi$
$810$	−34.1930	−	38.1335i	−1.20142	−	1.33987i
$811$	49.8680			1.75110			0.875550	−	0.483127i	$-0.160499\pi$
$811$	49.8680			1.75110			0.875550	+	0.483127i	$0.160499\pi$
$812$		0			0
$813$	−5.28787	−	1.56383i	−0.185454	−	0.0548458i
$814$	2.15324	−	1.24317i	0.0754709	−	0.0435732i
$815$	−15.4701	−	14.0365i	−0.541893	−	0.491678i
$816$	−1.61300	+	62.6424i	−0.0564662	+	2.19292i
$817$	−3.36894	+	12.5731i	−0.117864	+	0.439876i
$818$	−60.3060	−	60.3060i	−2.10855	−	2.10855i
$819$		0			0
$820$	54.2313	−	34.9249i	1.89384	−	1.21963i
$821$	28.0956	−	16.2210i	0.980542	−	0.566116i	0.0781084	−	0.996945i	$-0.475112\pi$
$821$	28.0956	−	16.2210i	0.980542	−	0.566116i	0.902434	+	0.430829i	$0.141779\pi$
$822$	19.5721	+	20.6066i	0.682654	+	0.718739i
$823$	−11.9776	−	44.7011i	−0.417514	−	1.55818i	−0.779747	−	0.626095i	$-0.784652\pi$
$823$	−11.9776	−	44.7011i	−0.417514	−	1.55818i	0.362233	−	0.932088i	$-0.382015\pi$
$824$	−17.9695	−	31.1241i	−0.625998	−	1.08426i
$825$	−10.2667	−	8.89705i	−0.357439	−	0.309755i
$826$		0			0
$827$	−36.7198	+	36.7198i	−1.27687	+	1.27687i	−0.334465	+	0.942408i	$0.608556\pi$
$827$	−36.7198	+	36.7198i	−1.27687	+	1.27687i	−0.942408	+	0.334465i	$0.891444\pi$
$828$	−12.6701	−	14.0469i	−0.440318	−	0.488165i
$829$	12.3817	+	7.14860i	0.430036	+	0.248281i	0.699362	−	0.714768i	$-0.253468\pi$
$829$	12.3817	+	7.14860i	0.430036	+	0.248281i	−0.269326	+	0.963049i	$0.586801\pi$
$830$	−1.25489	−	25.8293i	−0.0435578	−	0.896550i
$831$	21.5676	−	35.2296i	0.748172	−	1.22210i
$832$	0.755282	+	0.755282i	0.0261847	+	0.0261847i
$833$		0			0
$834$	−21.4814	−	39.5227i	−0.743841	−	1.36856i
$835$	9.37818	−	3.00766i	0.324545	−	0.104084i
$836$	10.2212	+	5.90123i	0.353509	+	0.204098i
$837$	14.0382	−	2.62084i	0.485232	−	0.0905896i
$838$	−63.6151	−	17.0456i	−2.19755	−	0.588831i
$839$	33.6309			1.16107			0.580534	−	0.814236i	$-0.302844\pi$
$839$	33.6309			1.16107			0.580534	+	0.814236i	$0.302844\pi$
$840$		0			0
$841$	50.5583			1.74339
$842$	25.5742	+	6.85259i	0.881346	+	0.236156i
$843$	29.5880	+	31.1520i	1.01906	+	1.07293i
$844$	−83.4479	−	48.1787i	−2.87240	−	1.65838i
$845$	−3.22552	+	6.27120i	−0.110961	+	0.215736i
$846$	21.6923	−	33.4672i	0.745798	−	1.15062i
$847$		0			0
$848$	−20.0953	−	20.0953i	−0.690077	−	0.690077i
$849$	11.3212	+	6.93083i	0.388542	+	0.237865i
$850$	52.8086	−	37.7556i	1.81132	−	1.29501i
$851$	−0.759561	−	0.438533i	−0.0260374	−	0.0150327i
$852$	6.56440	+	27.2902i	0.224893	+	0.934947i
$853$	−26.5544	+	26.5544i	−0.909206	+	0.909206i	−0.996208	−	0.0870025i	$-0.972271\pi$
$853$	−26.5544	+	26.5544i	−0.909206	+	0.909206i	0.0870025	+	0.996208i	$0.472271\pi$
$854$		0			0
$855$	0.0331586	−	11.2724i	0.00113400	−	0.385509i
$856$	−12.5617	−	21.7575i	−0.429350	−	0.743655i
$857$	−8.44459	−	31.5157i	−0.288462	−	1.07655i	−0.946272	−	0.323371i	$-0.895184\pi$
$857$	−8.44459	−	31.5157i	−0.288462	−	1.07655i	0.657810	−	0.753184i	$-0.271483\pi$
$858$	15.7332	−	14.9433i	0.537121	−	0.510155i
$859$	−15.0032	+	8.66212i	−0.511903	+	0.295548i	−0.733616	−	0.679565i	$-0.762169\pi$
$859$	−15.0032	+	8.66212i	−0.511903	+	0.295548i	0.221712	+	0.975112i	$0.428835\pi$
$860$	−75.7946	−	16.4130i	−2.58457	−	0.559680i
$861$		0			0
$862$	0.808044	+	0.808044i	0.0275221	+	0.0275221i
$863$	−3.31336	+	12.3656i	−0.112788	+	0.420931i	−0.999112	−	0.0421348i	$-0.986584\pi$
$863$	−3.31336	+	12.3656i	−0.112788	+	0.420931i	0.886324	+	0.463066i	$0.153251\pi$
$864$	−15.9781	+	23.3135i	−0.543585	+	0.793143i
$865$	−17.2729	+	19.0369i	−0.587295	+	0.647275i
$866$	55.4253	−	31.9998i	1.88343	−	1.08740i
$867$	4.43285	−	14.9891i	0.150548	−	0.509056i
$868$		0			0
$869$	26.7577			0.907693
$870$	87.8970	−	2.00458i	2.97999	−	0.0679616i
$871$	−8.32585	+	14.4208i	−0.282111	+	0.488630i
$872$	10.4805	+	39.1137i	0.354914	+	1.32456i
$873$	−13.8505	+	12.4929i	−0.468768	+	0.422822i
$874$		−	6.02310i		−	0.203734i
$875$		0			0
$876$	−30.8863	−	56.8263i	−1.04355	−	1.91998i
$877$	5.65985	−	21.1228i	0.191119	−	0.713267i	−0.802118	−	0.597166i	$-0.796293\pi$
$877$	5.65985	−	21.1228i	0.191119	−	0.713267i	0.993237	−	0.116102i	$-0.0370399\pi$
$878$	−72.5932	+	19.4513i	−2.44990	+	0.656449i
$879$	21.0767	+	0.542711i	0.710900	+	0.0183052i
$880$	−11.3781	+	22.1217i	−0.383555	+	0.745723i
$881$			3.93409i			0.132543i	0.997802	+	0.0662714i	$0.0211103\pi$
$881$			3.93409i			0.132543i	−0.997802	+	0.0662714i	$0.978890\pi$
$882$		0			0
$883$	13.5688	−	13.5688i	0.456625	−	0.456625i	−0.440921	−	0.897546i	$-0.645348\pi$
$883$	13.5688	−	13.5688i	0.456625	−	0.456625i	0.897546	+	0.440921i	$0.145348\pi$
$884$	35.8356	+	62.0691i	1.20528	+	2.08761i
$885$	−5.08732	+	20.8792i	−0.171008	+	0.701848i
$886$	−28.0100	+	48.5148i	−0.941015	+	1.62989i
$887$	6.72756	+	1.80264i	0.225889	+	0.0605269i	0.369988	−	0.929036i	$-0.379362\pi$
$887$	6.72756	+	1.80264i	0.225889	+	0.0605269i	−0.144099	+	0.989563i	$0.546028\pi$
$888$	−1.92872	+	6.52168i	−0.0647235	+	0.218853i
$889$		0			0
$890$	11.3250	−	52.2982i	0.379614	−	1.75304i
$891$	−11.4364	−	8.27859i	−0.383134	−	0.277343i
$892$	−75.8412	+	20.3216i	−2.53935	+	0.680417i
$893$	8.47850	−	2.27181i	0.283722	−	0.0760231i
$894$	−3.47057	−	2.12469i	−0.116073	−	0.0710601i
$895$	−31.2035	+	20.0950i	−1.04302	+	0.671703i
$896$		0			0
$897$	−7.34002	−	2.17073i	−0.245076	−	0.0724786i
$898$	40.1234	+	10.7510i	1.33894	+	0.358767i
$899$	−12.2570	+	21.2297i	−0.408793	+	0.708050i
$900$	67.0902	−	3.06171i	2.23634	−	0.102057i
$901$	10.2214	+	17.7040i	0.340524	+	0.589806i
$902$	18.1889	−	18.1889i	0.605624	−	0.605624i
$903$		0			0
$904$			29.3575i			0.976416i
$905$	−23.1719	−	11.9182i	−0.770261	−	0.396176i
$906$	−1.55805	+	60.5085i	−0.0517628	+	2.01026i
$907$	25.9978	−	6.96610i	0.863244	−	0.231305i	0.200080	−	0.979780i	$-0.435880\pi$
$907$	25.9978	−	6.96610i	0.863244	−	0.231305i	0.663164	+	0.748474i	$0.269213\pi$
$908$	−14.2668	+	53.2446i	−0.473462	+	1.76698i
$909$	1.65020	−	2.54594i	0.0547336	−	0.0844436i
$910$		0			0
$911$			17.7669i			0.588644i	0.955706	+	0.294322i	$0.0950938\pi$
$911$			17.7669i			0.588644i	−0.955706	+	0.294322i	$0.904906\pi$
$912$	−20.0687	+	4.82734i	−0.664543	+	0.159849i
$913$	−1.84492	−	6.88535i	−0.0610581	−	0.227872i
$914$	−37.1263	+	64.3046i	−1.22803	+	2.12701i
$915$	−20.7412	−	19.8162i	−0.685682	−	0.655104i
$916$	19.9842			0.660298
$917$		0			0
$918$	51.2425	−	43.8814i	1.69125	−	1.44830i
$919$	7.36529	−	4.25235i	0.242958	−	0.140272i	−0.373577	−	0.927599i	$-0.621869\pi$
$919$	7.36529	−	4.25235i	0.242958	−	0.140272i	0.616536	+	0.787327i	$0.288536\pi$
$920$	19.8319	−	0.963512i	0.653840	−	0.0317661i
$921$	−29.0229	−	0.747320i	−0.956337	−	0.0246250i
$922$	10.0712	−	37.5863i	0.331678	−	1.23784i
$923$	8.03083	+	8.03083i	0.264338	+	0.264338i
$924$		0			0
$925$	2.91542	−	1.09368i	0.0958586	−	0.0359601i
$926$	1.53420	−	0.885769i	0.0504169	−	0.0291082i
$927$	−5.27010	+	16.2680i	−0.173093	+	0.534310i
$928$	−12.5569	−	46.8629i	−0.412200	−	1.53835i
$929$	−7.07945	−	12.2620i	−0.232269	−	0.402302i	0.726206	−	0.687477i	$-0.241282\pi$
$929$	−7.07945	−	12.2620i	−0.232269	−	0.402302i	−0.958476	+	0.285175i	$0.907948\pi$
$930$	−13.0067	+	23.7636i	−0.426507	+	0.779240i
$931$		0			0
$932$	−25.2594	+	25.2594i	−0.827399	+	0.827399i
$933$	−49.3080	+	11.8606i	−1.61427	+	0.388298i
$934$	−28.0548	−	16.1975i	−0.917982	−	0.529997i
$935$	12.0243	−	13.2523i	0.393237	−	0.433398i
$936$	−3.05455	+	59.2739i	−0.0998410	+	1.93743i
$937$	−28.7165	−	28.7165i	−0.938127	−	0.938127i	0.0600678	−	0.998194i	$-0.480868\pi$
$937$	−28.7165	−	28.7165i	−0.938127	−	0.938127i	−0.998194	+	0.0600678i	$0.980868\pi$
$938$		0			0
$939$	−2.63804	+	1.43383i	−0.0860891	+	0.0467912i
$940$	15.9705	+	49.7975i	0.520899	+	1.62422i
$941$	−15.0690	−	8.70007i	−0.491234	−	0.283614i	0.233852	−	0.972272i	$-0.424867\pi$
$941$	−15.0690	−	8.70007i	−0.491234	−	0.283614i	−0.725086	+	0.688658i	$0.758200\pi$
$942$	62.0220	−	58.9081i	2.02079	−	1.91933i
$943$	−8.76467	−	2.34849i	−0.285417	−	0.0764773i
$944$	39.3508			1.28076
$945$		0			0
$946$	−30.9259			−1.00549
$947$	11.1426	+	2.98564i	0.362085	+	0.0970204i	0.435275	−	0.900298i	$-0.356651\pi$
$947$	11.1426	+	2.98564i	0.362085	+	0.0970204i	−0.0731898	+	0.997318i	$0.523318\pi$
$948$	−95.9116	+	91.0963i	−3.11506	+	2.95867i
$949$	−22.6641	−	13.0851i	−0.735708	−	0.424761i
$950$	16.5151	+	13.5835i	0.535819	+	0.440708i
$951$	−9.25764	+	5.03172i	−0.300199	+	0.163165i
$952$		0			0
$953$	38.6159	+	38.6159i	1.25089	+	1.25089i	0.955321	+	0.295569i	$0.0955091\pi$
$953$	38.6159	+	38.6159i	1.25089	+	1.25089i	0.295569	+	0.955321i	$0.404491\pi$
$954$	−1.57462	+	30.5558i	−0.0509804	+	0.989280i
$955$	28.7093	−	1.39481i	0.929012	−	0.0451350i
$956$	45.9848	+	26.5494i	1.48726	+	0.858668i
$957$	23.5630	−	5.66784i	0.761682	−	0.183215i
$958$	−40.9545	+	40.9545i	−1.32318	+	1.32318i
$959$		0			0
$960$	0.370164	+	1.26533i	0.0119470	+	0.0408384i
$961$	11.7233	+	20.3054i	0.378172	+	0.655012i
$962$	1.28722	+	4.80396i	0.0415015	+	0.154886i
$963$	−3.68409	+	11.3722i	−0.118718	+	0.366465i
$964$	−70.0753	+	40.4580i	−2.25697	+	1.30306i
$965$	5.39535	−	24.9155i	0.173683	−	0.802058i
$966$		0			0
$967$	−18.6836	−	18.6836i	−0.600824	−	0.600824i	0.339707	−	0.940531i	$-0.389672\pi$
$967$	−18.6836	−	18.6836i	−0.600824	−	0.600824i	−0.940531	+	0.339707i	$0.889672\pi$
$968$	13.9346	−	52.0047i	0.447876	−	1.67150i
$969$	14.8430	+	0.382196i	0.476825	+	0.0122779i
$970$	−1.71702	−	35.3414i	−0.0551302	−	1.13474i
$971$	49.7947	−	28.7490i	1.59799	−	0.922599i	0.606114	−	0.795378i	$-0.292728\pi$
$971$	49.7947	−	28.7490i	1.59799	−	0.922599i	0.991874	−	0.127221i	$-0.0406057\pi$
$972$	69.1776	−	9.26098i	2.21887	−	0.297046i
$973$		0			0
$974$	41.3622			1.32533
$975$	22.5055	−	15.2305i	0.720754	−	0.487765i
$976$	−26.2635	+	45.4897i	−0.840674	+	1.45609i
$977$	−0.763219	−	2.84837i	−0.0244175	−	0.0911275i	0.952642	−	0.304095i	$-0.0983539\pi$
$977$	−0.763219	−	2.84837i	−0.0244175	−	0.0911275i	−0.977059	+	0.212967i	$0.931687\pi$
$978$	40.0383	−	9.63083i	1.28028	−	0.307960i
$979$		−	14.7501i		−	0.471415i
$980$		0			0
$981$	10.4797	−	16.1681i	0.334590	−	0.516209i
$982$	−0.198752	+	0.741751i	−0.00634242	+	0.0236702i
$983$	15.8515	−	4.24741i	0.505585	−	0.135471i	0.00299438	−	0.999996i	$-0.499047\pi$
$983$	15.8515	−	4.24741i	0.505585	−	0.135471i	0.502591	+	0.864524i	$0.332380\pi$
$984$	−1.81113	+	70.3368i	−0.0577366	+	2.24226i
$985$	−56.4637	+	18.1084i	−1.79908	+	0.576980i
$986$			115.806i			3.68802i
$987$		0			0
$988$	−16.6937	+	16.6937i	−0.531097	+	0.531097i
$989$	5.45461	+	9.44766i	0.173446	+	0.300418i
$990$	25.8898	−	6.85559i	0.822832	−	0.217885i
$991$	3.17062	−	5.49168i	0.100718	−	0.174449i	−0.811263	−	0.584682i	$-0.801219\pi$
$991$	3.17062	−	5.49168i	0.100718	−	0.174449i	0.911981	+	0.410233i	$0.134553\pi$
$992$	14.4396	+	3.86909i	0.458459	+	0.122844i
$993$	55.2432	+	16.3376i	1.75309	+	0.518457i
$994$		0			0
$995$	−5.09371	−	7.90951i	−0.161481	−	0.250748i
$996$	30.0541	+	18.3992i	0.952302	+	0.583000i
$997$	2.59062	−	0.694156i	0.0820459	−	0.0219841i	−0.217563	−	0.976046i	$-0.569811\pi$
$997$	2.59062	−	0.694156i	0.0820459	−	0.0219841i	0.299608	+	0.954062i	$0.403144\pi$
$998$	49.7093	−	13.3196i	1.57352	−	0.421624i
$999$	2.91891	−	1.39694i	0.0923504	−	0.0441973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.y.g.557.12		48
3.2	odd	2	inner	735.2.y.g.557.1		48
5.3	odd	4	inner	735.2.y.g.263.12		48
7.2	even	3	inner	735.2.y.g.422.1		48
7.3	odd	6		105.2.j.a.92.1	yes	24
7.4	even	3		735.2.j.h.197.1		24
7.5	odd	6		735.2.y.j.422.1		48
7.6	odd	2		735.2.y.j.557.12		48
15.8	even	4	inner	735.2.y.g.263.1		48
21.2	odd	6	inner	735.2.y.g.422.12		48
21.5	even	6		735.2.y.j.422.12		48
21.11	odd	6		735.2.j.h.197.12		24
21.17	even	6		105.2.j.a.92.12	yes	24
21.20	even	2		735.2.y.j.557.1		48
35.3	even	12		105.2.j.a.8.12	yes	24
35.13	even	4		735.2.y.j.263.12		48
35.17	even	12		525.2.j.b.218.1		24
35.18	odd	12		735.2.j.h.638.12		24
35.23	odd	12	inner	735.2.y.g.128.1		48
35.24	odd	6		525.2.j.b.407.12		24
35.33	even	12		735.2.y.j.128.1		48
105.17	odd	12		525.2.j.b.218.12		24
105.23	even	12	inner	735.2.y.g.128.12		48
105.38	odd	12		105.2.j.a.8.1	✓	24
105.53	even	12		735.2.j.h.638.1		24
105.59	even	6		525.2.j.b.407.1		24
105.68	odd	12		735.2.y.j.128.12		48
105.83	odd	4		735.2.y.j.263.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.1	✓	24	105.38	odd	12
105.2.j.a.8.12	yes	24	35.3	even	12
105.2.j.a.92.1	yes	24	7.3	odd	6
105.2.j.a.92.12	yes	24	21.17	even	6
525.2.j.b.218.1		24	35.17	even	12
525.2.j.b.218.12		24	105.17	odd	12
525.2.j.b.407.1		24	105.59	even	6
525.2.j.b.407.12		24	35.24	odd	6
735.2.j.h.197.1		24	7.4	even	3
735.2.j.h.197.12		24	21.11	odd	6
735.2.j.h.638.1		24	105.53	even	12
735.2.j.h.638.12		24	35.18	odd	12
735.2.y.g.128.1		48	35.23	odd	12	inner
735.2.y.g.128.12		48	105.23	even	12	inner
735.2.y.g.263.1		48	15.8	even	4	inner
735.2.y.g.263.12		48	5.3	odd	4	inner
735.2.y.g.422.1		48	7.2	even	3	inner
735.2.y.g.422.12		48	21.2	odd	6	inner
735.2.y.g.557.1		48	3.2	odd	2	inner
735.2.y.g.557.12		48	1.1	even	1	trivial
735.2.y.j.128.1		48	35.33	even	12
735.2.y.j.128.12		48	105.68	odd	12
735.2.y.j.263.1		48	105.83	odd	4
735.2.y.j.263.12		48	35.13	even	4
735.2.y.j.422.1		48	7.5	odd	6
735.2.y.j.422.12		48	21.5	even	6
735.2.y.j.557.1		48	21.20	even	2
735.2.y.j.557.12		48	7.6	odd	2

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.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.45834 + 0.658710i) q^{2} +(-1.25586 + 1.19281i) q^{3} +(3.87749 + 2.23867i) q^{4} +(1.98846 + 1.02275i) q^{5} +(-3.87306 + 2.10509i) q^{6} +(4.45829 + 4.45829i) q^{8} +(0.154393 - 2.99602i) q^{9} +(4.21463 + 3.82408i) q^{10} +(1.35854 + 0.784351i) q^{11} +(-7.53991 + 1.81365i) q^{12} +(-2.21881 + 2.21881i) q^{13} +(-3.71719 + 1.08744i) q^{15} +(3.54593 + 6.14174i) q^{16} +(-1.32034 - 4.92759i) q^{17} +(2.35306 - 7.26355i) q^{18} +(1.45527 - 0.840200i) q^{19} +(5.42066 + 8.41719i) q^{20} +(2.82308 + 2.82308i) q^{22} +(0.364506 - 1.36036i) q^{23} +(-10.9169 - 0.281103i) q^{24} +(2.90798 + 4.06739i) q^{25} +(-6.91613 + 3.99303i) q^{26} +(3.37980 + 3.94676i) q^{27} -8.91955 q^{29} +(-9.85442 + 0.224740i) q^{30} +(1.37417 - 2.38013i) q^{31} +(1.40779 + 5.25396i) q^{32} +(-2.64172 + 0.635440i) q^{33} -12.9834i q^{34} +(7.30576 - 11.2714i) q^{36} +(0.161183 - 0.601543i) q^{37} +(4.13100 - 1.10690i) q^{38} +(0.139900 - 5.43314i) q^{39} +(4.30546 + 13.4248i) q^{40} -6.44292i q^{41} +(-5.47734 + 5.47734i) q^{43} +(3.51180 + 6.08262i) q^{44} +(3.37118 - 5.79958i) q^{45} +(1.79216 - 3.10412i) q^{46} +(5.04552 + 1.35194i) q^{47} +(-11.7792 - 3.48356i) q^{48} +(4.46958 + 11.9145i) q^{50} +(7.53587 + 4.61346i) q^{51} +(-13.5706 + 3.63622i) q^{52} +(-3.87074 + 1.03716i) q^{53} +(5.70892 + 11.9288i) q^{54} +(1.89921 + 2.94909i) q^{55} +(-0.825420 + 2.79104i) q^{57} +(-21.9273 - 5.87540i) q^{58} +(2.77436 - 4.80533i) q^{59} +(-16.8478 - 4.10503i) q^{60} +(3.70333 + 6.41435i) q^{61} +(4.94599 - 4.94599i) q^{62} -0.340400i q^{64} +(-6.68129 + 2.14274i) q^{65} +(-6.91282 - 0.178000i) q^{66} +(5.12587 - 1.37347i) q^{67} +(5.91162 - 22.0625i) q^{68} +(1.16488 + 2.14321i) q^{69} -3.61943i q^{71} +(14.0455 - 12.6688i) q^{72} +(2.15859 + 8.05596i) q^{73} +(0.792485 - 1.37262i) q^{74} +(-8.50367 - 1.63941i) q^{75} +7.52372 q^{76} +(3.92279 - 13.2644i) q^{78} +(14.7720 - 8.52862i) q^{79} +(0.769530 + 15.8392i) q^{80} +(-8.95233 - 0.925133i) q^{81} +(4.24402 - 15.8389i) q^{82} +(-3.21312 - 3.21312i) q^{83} +(2.41421 - 11.1487i) q^{85} +(-17.0731 + 9.85718i) q^{86} +(11.2017 - 10.6394i) q^{87} +(2.55988 + 9.55360i) q^{88} +(-4.70137 - 8.14301i) q^{89} +(12.1077 - 12.0367i) q^{90} +(4.45876 - 4.45876i) q^{92} +(1.11328 + 4.62825i) q^{93} +(11.5131 + 6.64707i) q^{94} +(3.75306 - 0.182338i) q^{95} +(-8.03498 - 4.91902i) q^{96} +(-4.39640 - 4.39640i) q^{97} +(2.55968 - 3.94911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 16 q^{10} + 16 q^{12} + 16 q^{13} - 32 q^{15} + 16 q^{16} + 20 q^{18} + 16 q^{22} + 16 q^{25} + 32 q^{27} - 20 q^{30} + 28 q^{33} + 32 q^{36} + 16 q^{37} + 64 q^{40} - 80 q^{43} + 20 q^{45}+ \cdots - 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 + 16 * q^13 - 32 * q^15 + 16 * q^16 + 20 * q^18 + 16 * q^22 + 16 * q^25 + 32 * q^27 - 20 * q^30 + 28 * q^33 + 32 * q^36 + 16 * q^37 + 64 * q^40 - 80 * q^43 + 20 * q^45 + 64 * q^46 - 32 * q^48 + 20 * q^51 - 80 * q^55 + 8 * q^57 - 40 * q^58 - 32 * q^60 + 32 * q^61 - 16 * q^66 - 24 * q^67 + 8 * q^72 + 32 * q^73 - 60 * q^75 - 64 * q^76 + 120 * q^78 - 52 * q^81 - 80 * q^82 + 48 * q^85 + 4 * q^87 - 96 * q^88 + 48 * q^90 + 76 * q^93 - 96 * q^96 - 48 * q^97

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