LMFDB - Embedded newform 735.2.y.j.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.j.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	−0.328958	−	0.944345i	$-0.606697\pi$
$13$	2.21881	−	2.21881i	0.615386	−	0.615386i	0.944345	+	0.328958i	$0.106697\pi$
$14$		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	$0.128982\pi$
$17$	1.32034	+	4.92759i	0.320230	+	1.19512i	−0.598790	+	0.800906i	$0.704352\pi$
$18$	2.35306	−	7.26355i	0.554622	−	1.71203i
$19$	−1.45527	+	0.840200i	−0.333862	+	0.192755i	−0.657554	−	0.753407i	$-0.728409\pi$
$19$	−1.45527	+	0.840200i	−0.333862	+	0.192755i	0.323693	+	0.946162i	$0.395076\pi$
$20$	−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	−0.962638	−	0.270790i	$-0.912715\pi$
$31$	−1.37417	+	2.38013i	−0.246808	+	0.427484i	0.715830	+	0.698274i	$0.246048\pi$
$32$	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	$0.167810\pi$
$41$			6.44292i			1.00622i	−0.864224	+	0.503108i	$0.832190\pi$
$42$		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	−0.128681	−	0.991686i	$-0.541074\pi$
$47$	−5.04552	−	1.35194i	−0.735965	−	0.197201i	−0.607284	+	0.794485i	$0.707741\pi$
$48$	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	−0.988157	−	0.153446i	$-0.950963\pi$
$59$	−2.77436	+	4.80533i	−0.361191	+	0.625600i	0.626967	+	0.779046i	$0.284296\pi$
$60$	−16.8478	−	4.10503i	−2.17504	−	0.529957i
$61$	−3.70333	−	6.41435i	−0.474162	−	0.821273i	0.525400	−	0.850855i	$-0.323916\pi$
$61$	−3.70333	−	6.41435i	−0.474162	−	0.821273i	−0.999562	+	0.0295820i	$0.990582\pi$
$62$	−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	$-0.921034\pi$
$73$	−2.15859	−	8.05596i	−0.252644	−	0.942878i	0.716743	−	0.697338i	$-0.245632\pi$
$74$	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	0.861108	−	0.508422i	$-0.169771\pi$
$83$	3.21312	+	3.21312i	0.352686	+	0.352686i	−0.508422	+	0.861108i	$0.669771\pi$
$84$		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	0.999998	−	0.00191126i	$-0.000608372\pi$
$89$	4.70137	+	8.14301i	0.498344	+	0.863157i	−0.501654	+	0.865068i	$0.667275\pi$
$90$	−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	0.894151	−	0.447765i	$-0.147780\pi$
$97$	4.39640	+	4.39640i	0.446386	+	0.446386i	−0.447765	+	0.894151i	$0.647780\pi$
$98$		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	0.455792	−	0.890086i	$-0.349356\pi$
$101$	−0.875832	−	0.505662i	−0.0871485	−	0.0503152i	−0.542941	+	0.839771i	$0.682689\pi$
$102$	15.4868	+	16.3054i	1.53342	+	1.61448i
$103$	5.50588	+	1.47530i	0.542511	+	0.145365i	0.519659	−	0.854374i	$-0.326059\pi$
$103$	5.50588	+	1.47530i	0.542511	+	0.145365i	0.0228513	+	0.999739i	$0.492726\pi$
$104$	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	−0.673700	−	0.739005i	$-0.735296\pi$
$131$	−4.24118	+	2.44864i	−0.370553	+	0.213939i	0.303147	+	0.952944i	$0.401963\pi$
$132$	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	$-0.857537\pi$
$139$		−	10.2045i		−	0.865536i	0.901505	−	0.432768i	$-0.142463\pi$
$140$		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	0.584166	−	0.811634i	$-0.301422\pi$
$157$	18.7434	−	5.02228i	1.49589	−	0.400822i	0.911720	+	0.410812i	$0.134755\pi$
$158$	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	−0.817264	−	0.576263i	$-0.804510\pi$
$167$	−3.11442	+	3.11442i	−0.241001	+	0.241001i	0.576263	+	0.817264i	$0.304510\pi$
$168$		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	$-0.772707\pi$
$173$	2.97531	−	11.1040i	0.226209	−	0.844222i	0.981917	−	0.189313i	$-0.0606262\pi$
$174$	−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	$-0.357424\pi$
$181$	11.6532			0.866174			0.433087	+	0.901352i	$0.357424\pi$
$182$		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	0.623554	−	0.781780i	$-0.285688\pi$
$199$	3.64362	+	2.10364i	0.258289	+	0.149123i	−0.365265	+	0.930904i	$0.619022\pi$
$200$	−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	−0.157193	−	0.987568i	$-0.550244\pi$
$223$	12.4001	−	12.4001i	0.830375	−	0.830375i	0.987568	+	0.157193i	$0.0502445\pi$
$224$		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	$-0.949360\pi$
$227$	−3.18646	−	11.8920i	−0.211493	−	0.789301i	0.775879	−	0.630881i	$-0.217307\pi$
$228$	−9.44878	+	8.97439i	−0.625761	+	0.594344i
$229$	−3.86544	+	2.23171i	−0.255435	+	0.147476i	−0.622251	−	0.782818i	$-0.713781\pi$
$229$	−3.86544	+	2.23171i	−0.255435	+	0.147476i	0.366815	+	0.930294i	$0.380448\pi$
$230$	−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	$-0.635576\pi$
$241$	9.03617	−	15.6511i	0.582071	−	1.00818i	0.995234	−	0.0975190i	$-0.0310907\pi$
$242$	−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	$-0.967874\pi$
$251$		−	3.19253i		−	0.201511i	0.994911	−	0.100755i	$-0.0321259\pi$
$252$		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	−0.282326	−	0.959319i	$-0.591106\pi$
$257$	−16.1352	−	4.32342i	−1.00649	−	0.269687i	−0.724161	+	0.689631i	$0.757773\pi$
$258$	−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	$-0.480893\pi$
$269$	14.6703	−	25.4096i	0.894461	−	1.54925i	0.834470	−	0.551053i	$-0.185774\pi$
$270$	−0.848131	+	29.5588i	−0.0516156	+	1.79889i
$271$	−1.59183	−	2.75713i	−0.0966968	−	0.167484i	0.813619	−	0.581399i	$-0.197494\pi$
$271$	−1.59183	−	2.75713i	−0.0966968	−	0.167484i	−0.910316	+	0.413915i	$0.864161\pi$
$272$	−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	0.999488	−	0.0319914i	$-0.0101849\pi$
$283$	1.98356	+	7.40274i	0.117910	+	0.440047i	−0.881578	+	0.472039i	$0.843518\pi$
$284$	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	0.912322	−	0.409473i	$-0.134288\pi$
$293$	8.60739	+	8.60739i	0.502849	+	0.502849i	−0.409473	+	0.912322i	$0.634288\pi$
$294$		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	0.282740	−	0.959197i	$-0.408757\pi$
$307$	−11.8525	−	11.8525i	−0.676457	−	0.676457i	−0.959197	+	0.282740i	$0.908757\pi$
$308$		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	−0.440174	−	0.897912i	$-0.645083\pi$
$311$	−25.3572	−	14.6400i	−1.43788	−	0.830158i	−0.997702	+	0.0677541i	$0.978417\pi$
$312$	24.8462	−	23.5988i	1.40664	−	1.33602i
$313$	−1.67444	−	0.448664i	−0.0946448	−	0.0253600i	0.211186	−	0.977446i	$-0.432267\pi$
$313$	−1.67444	−	0.448664i	−0.0946448	−	0.0253600i	−0.305831	+	0.952086i	$0.598934\pi$
$314$	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	$0.298594\pi$
$349$			30.1301i			1.61283i	−0.591353	+	0.806413i	$0.701406\pi$
$350$		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	0.420600	−	0.907246i	$-0.361820\pi$
$353$	23.2688	−	6.23486i	1.23847	−	0.331848i	0.817873	+	0.575398i	$0.195153\pi$
$354$	−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	−0.962629	−	0.270822i	$-0.912704\pi$
$367$	−31.8179	+	8.52557i	−1.66088	+	0.445031i	−0.698250	+	0.715854i	$0.746038\pi$
$368$	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	−0.933913	−	0.357500i	$-0.883629\pi$
$383$	1.04955	−	3.91696i	0.0536293	−	0.200147i	0.987542	+	0.157353i	$0.0502959\pi$
$384$	−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	$0.408934\pi$
$397$	−8.80417	+	32.8576i	−0.441869	+	1.64908i	−0.724074	+	0.689723i	$0.757732\pi$
$398$	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	0.997495	−	0.0707377i	$-0.0225353\pi$
$409$	29.0207	+	16.7551i	1.43498	+	0.828487i	0.437487	+	0.899225i	$0.355869\pi$
$410$	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	$-0.282196\pi$
$419$	25.8773			1.26419			0.632093	+	0.774892i	$0.282196\pi$
$420$		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	−0.990686	−	0.136169i	$-0.956521\pi$
$433$	−17.7813	+	17.7813i	−0.854517	+	0.854517i	0.136169	+	0.990686i	$0.456521\pi$
$434$		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	0.255507	−	0.966807i	$-0.417757\pi$
$439$	25.5732	−	14.7647i	1.22054	−	0.704679i	0.965033	+	0.262128i	$0.0844241\pi$
$440$	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	$0.115876\pi$
$461$			15.2893i			0.712094i	−0.934468	+	0.356047i	$0.884124\pi$
$462$		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	0.531809	−	0.846864i	$-0.321512\pi$
$467$	12.2948	+	3.29439i	0.568937	+	0.152446i	0.0371280	+	0.999311i	$0.488179\pi$
$468$	−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	$-0.659302\pi$
$479$	11.3786	−	19.7083i	0.519901	−	0.900496i	0.999732	−	0.0231347i	$-0.00736465\pi$
$480$	−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	$-0.978565\pi$
$503$	−23.8859	−	23.8859i	−1.06502	−	1.06502i	−0.0672882	−	0.997734i	$-0.521435\pi$
$504$		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	0.966480	−	0.256743i	$-0.0826494\pi$
$509$	5.88603	+	10.1949i	0.260894	+	0.451881i	−0.705586	+	0.708624i	$0.749316\pi$
$510$	−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	0.943976	−	0.330014i	$-0.107053\pi$
$521$	25.7965	+	14.8936i	1.13016	+	0.652500i	0.186187	+	0.982514i	$0.440387\pi$
$522$	−20.9883	+	64.7876i	−0.918632	+	2.83567i
$523$	−23.8608	−	6.39348i	−1.04336	−	0.279567i	−0.303854	−	0.952719i	$-0.598274\pi$
$523$	−23.8608	−	6.39348i	−1.04336	−	0.279567i	−0.739505	+	0.673151i	$0.764940\pi$
$524$	−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	0.0696580	−	0.997571i	$-0.477809\pi$
$563$	14.9192	−	3.99759i	0.628769	−	0.168478i	0.559111	+	0.829093i	$0.311143\pi$
$564$	−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	−0.651253	−	0.758861i	$-0.725756\pi$
$577$	−20.0772	+	5.37966i	−0.835823	+	0.223958i	−0.184571	+	0.982819i	$0.559089\pi$
$578$	−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	−0.598779	−	0.800915i	$-0.704347\pi$
$587$	4.89737	−	4.89737i	0.202136	−	0.202136i	0.800915	+	0.598779i	$0.204347\pi$
$588$		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	$0.310743\pi$
$593$	−8.25882	+	30.8223i	−0.339149	+	1.26572i	−0.899300	+	0.437331i	$0.855924\pi$
$594$	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	$-0.555247\pi$
$601$	−8.46733			−0.345390			−0.172695	+	0.984975i	$0.555247\pi$
$602$		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	−0.903170	−	0.429283i	$-0.858766\pi$
$607$	2.30704	−	8.60998i	0.0936398	−	0.349468i	0.996810	+	0.0798148i	$0.0254329\pi$
$608$	−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	0.0861795	−	0.996280i	$-0.472534\pi$
$619$	−18.2501	−	10.5367i	−0.733534	−	0.423506i	−0.819714	+	0.572773i	$0.805867\pi$
$620$	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	−0.987325	−	0.158711i	$-0.949266\pi$
$643$	−21.0115	+	21.0115i	−0.828614	+	0.828614i	0.158711	+	0.987325i	$0.449266\pi$
$644$		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	$0.0927789\pi$
$647$	6.91879	+	25.8213i	0.272006	+	1.01514i	−0.685816	+	0.727775i	$0.740554\pi$
$648$	−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	−0.984206	−	0.177029i	$-0.943351\pi$
$661$	−8.71029	+	15.0867i	−0.338791	+	0.586803i	0.645414	+	0.763833i	$0.276685\pi$
$662$	−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	−0.746128	−	0.665803i	$-0.768089\pi$
$677$	−44.8882	−	12.0278i	−1.72519	−	0.462264i	−0.979067	+	0.203539i	$0.934756\pi$
$678$	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	0.805586	−	0.592480i	$-0.201851\pi$
$691$	−2.89969	−	5.02242i	−0.110310	−	0.191062i	−0.915895	+	0.401418i	$0.868518\pi$
$692$	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	0.728843	−	0.684681i	$-0.240058\pi$
$719$	−6.12782	−	10.6137i	−0.228529	−	0.395824i	−0.957372	+	0.288856i	$0.906725\pi$
$720$	−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	0.807037	−	0.590501i	$-0.201070\pi$
$727$	5.83842	+	5.83842i	0.216535	+	0.216535i	−0.590501	+	0.807037i	$0.701070\pi$
$728$		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	−0.100987	−	0.994888i	$-0.532200\pi$
$733$	−18.5697	−	4.97574i	−0.685888	−	0.183783i	−0.584901	+	0.811105i	$0.698867\pi$
$734$	−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	0.178392	−	0.983960i	$-0.442911\pi$
$761$	30.8889	−	17.8337i	1.11972	−	0.646472i	0.941330	+	0.337488i	$0.109577\pi$
$762$	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	$-0.806105\pi$
$769$		−	31.7331i		−	1.14432i	0.820141	−	0.572162i	$-0.193895\pi$
$770$		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	−0.379038	−	0.925381i	$-0.623745\pi$
$773$	−6.80067	+	1.82223i	−0.244603	+	0.0655412i	0.134434	+	0.990922i	$0.457078\pi$
$774$	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	−0.684705	−	0.728821i	$-0.740069\pi$
$787$	−25.6203	+	6.86494i	−0.913266	+	0.244709i	−0.228561	+	0.973530i	$0.573402\pi$
$788$	−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	−0.833437	−	0.552615i	$-0.813630\pi$
$797$	−7.92792	+	7.92792i	−0.280821	+	0.280821i	0.552615	+	0.833437i	$0.313630\pi$
$798$		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	$-0.839501\pi$
$811$	−49.8680			−1.75110			−0.875550	+	0.483127i	$0.839501\pi$
$812$		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	0.269326	−	0.963049i	$-0.413199\pi$
$829$	−12.3817	−	7.14860i	−0.430036	−	0.248281i	−0.699362	+	0.714768i	$0.746532\pi$
$830$	−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	$-0.697156\pi$
$839$	−33.6309			−1.16107			−0.580534	+	0.814236i	$0.697156\pi$
$840$		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	−0.0870025	−	0.996208i	$-0.527729\pi$
$853$	26.5544	−	26.5544i	0.909206	−	0.909206i	0.996208	+	0.0870025i	$0.0277288\pi$
$854$		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	$0.104816\pi$
$857$	8.44459	+	31.5157i	0.288462	+	1.07655i	−0.657810	+	0.753184i	$0.728517\pi$
$858$	15.7332	−	14.9433i	0.537121	−	0.510155i
$859$	15.0032	−	8.66212i	0.511903	−	0.295548i	−0.221712	−	0.975112i	$-0.571165\pi$
$859$	15.0032	−	8.66212i	0.511903	−	0.295548i	0.733616	+	0.679565i	$0.237831\pi$
$860$	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	$-0.978890\pi$
$881$		−	3.93409i		−	0.132543i	0.997802	−	0.0662714i	$-0.0211103\pi$
$882$		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	0.144099	−	0.989563i	$-0.453972\pi$
$887$	−6.72756	−	1.80264i	−0.225889	−	0.0605269i	−0.369988	+	0.929036i	$0.620638\pi$
$888$	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	0.958476	−	0.285175i	$-0.0920517\pi$
$929$	7.07945	+	12.2620i	0.232269	+	0.402302i	−0.726206	+	0.687477i	$0.758718\pi$
$930$	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	0.998194	−	0.0600678i	$-0.0191317\pi$
$937$	28.7165	+	28.7165i	0.938127	+	0.938127i	−0.0600678	+	0.998194i	$0.519132\pi$
$938$		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	0.725086	−	0.688658i	$-0.241800\pi$
$941$	15.0690	+	8.70007i	0.491234	+	0.283614i	−0.233852	+	0.972272i	$0.575133\pi$
$942$	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	$0.707272\pi$
$971$	−49.7947	+	28.7490i	−1.59799	+	0.922599i	−0.991874	+	0.127221i	$0.959394\pi$
$972$	−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	−0.502591	−	0.864524i	$-0.667620\pi$
$983$	−15.8515	+	4.24741i	−0.505585	+	0.135471i	−0.00299438	+	0.999996i	$0.500953\pi$
$984$	−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	−0.299608	−	0.954062i	$-0.596856\pi$
$997$	−2.59062	+	0.694156i	−0.0820459	+	0.0219841i	0.217563	+	0.976046i	$0.430189\pi$
$998$	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.j.557.12		48
3.2	odd	2	inner	735.2.y.j.557.1		48
5.3	odd	4	inner	735.2.y.j.263.12		48
7.2	even	3	inner	735.2.y.j.422.1		48
7.3	odd	6		735.2.j.h.197.1		24
7.4	even	3		105.2.j.a.92.1	yes	24
7.5	odd	6		735.2.y.g.422.1		48
7.6	odd	2		735.2.y.g.557.12		48
15.8	even	4	inner	735.2.y.j.263.1		48
21.2	odd	6	inner	735.2.y.j.422.12		48
21.5	even	6		735.2.y.g.422.12		48
21.11	odd	6		105.2.j.a.92.12	yes	24
21.17	even	6		735.2.j.h.197.12		24
21.20	even	2		735.2.y.g.557.1		48
35.3	even	12		735.2.j.h.638.12		24
35.4	even	6		525.2.j.b.407.12		24
35.13	even	4		735.2.y.g.263.12		48
35.18	odd	12		105.2.j.a.8.12	yes	24
35.23	odd	12	inner	735.2.y.j.128.1		48
35.32	odd	12		525.2.j.b.218.1		24
35.33	even	12		735.2.y.g.128.1		48
105.23	even	12	inner	735.2.y.j.128.12		48
105.32	even	12		525.2.j.b.218.12		24
105.38	odd	12		735.2.j.h.638.1		24
105.53	even	12		105.2.j.a.8.1	✓	24
105.68	odd	12		735.2.y.g.128.12		48
105.74	odd	6		525.2.j.b.407.1		24
105.83	odd	4		735.2.y.g.263.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.1	✓	24	105.53	even	12
105.2.j.a.8.12	yes	24	35.18	odd	12
105.2.j.a.92.1	yes	24	7.4	even	3
105.2.j.a.92.12	yes	24	21.11	odd	6
525.2.j.b.218.1		24	35.32	odd	12
525.2.j.b.218.12		24	105.32	even	12
525.2.j.b.407.1		24	105.74	odd	6
525.2.j.b.407.12		24	35.4	even	6
735.2.j.h.197.1		24	7.3	odd	6
735.2.j.h.197.12		24	21.17	even	6
735.2.j.h.638.1		24	105.38	odd	12
735.2.j.h.638.12		24	35.3	even	12
735.2.y.g.128.1		48	35.33	even	12
735.2.y.g.128.12		48	105.68	odd	12
735.2.y.g.263.1		48	105.83	odd	4
735.2.y.g.263.12		48	35.13	even	4
735.2.y.g.422.1		48	7.5	odd	6
735.2.y.g.422.12		48	21.5	even	6
735.2.y.g.557.1		48	21.20	even	2
735.2.y.g.557.12		48	7.6	odd	2
735.2.y.j.128.1		48	35.23	odd	12	inner
735.2.y.j.128.12		48	105.23	even	12	inner
735.2.y.j.263.1		48	15.8	even	4	inner
735.2.y.j.263.12		48	5.3	odd	4	inner
735.2.y.j.422.1		48	7.2	even	3	inner
735.2.y.j.422.12		48	21.2	odd	6	inner
735.2.y.j.557.1		48	3.2	odd	2	inner
735.2.y.j.557.12		48	1.1	even	1	trivial

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more