LMFDB - Embedded newform 798.2.bf.a.569.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(569,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("798.569");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bf (of order $6$, degree $2$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.12
Character	$\chi$	$=$	798.569
Dual form			798.2.bf.a.683.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.556186 - 1.64032i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.60706 - 0.927835i) q^{5} +(1.69865 + 0.338490i) q^{6} +(-2.30493 + 1.29897i) q^{7} +1.00000 q^{8} +(-2.38131 + 1.82465i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.556186 - 1.64032i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.60706 - 0.927835i) q^{5} +(1.69865 + 0.338490i) q^{6} +(-2.30493 + 1.29897i) q^{7} +1.00000 q^{8} +(-2.38131 + 1.82465i) q^{9} +(1.60706 - 0.927835i) q^{10} +(0.623513 - 0.359985i) q^{11} +(-1.14247 + 1.30183i) q^{12} +4.26731i q^{13} +(0.0275240 - 2.64561i) q^{14} +(-0.628126 + 3.15214i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.18475 - 0.684017i) q^{17} +(-0.389534 - 2.97460i) q^{18} +(4.08447 + 1.52219i) q^{19} +1.85567i q^{20} +(3.41269 + 3.05835i) q^{21} +0.719971i q^{22} +(-3.10216 - 1.79104i) q^{23} +(-0.556186 - 1.64032i) q^{24} +(-0.778244 - 1.34796i) q^{25} +(-3.69560 - 2.13366i) q^{26} +(4.31746 + 2.89128i) q^{27} +(2.27740 + 1.34664i) q^{28} +5.25224 q^{29} +(-2.41577 - 2.12004i) q^{30} +(8.89311 - 5.13444i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.937281 - 0.822544i) q^{33} +1.36803i q^{34} +(4.90938 + 0.0510754i) q^{35} +(2.77085 + 1.14996i) q^{36} +(5.51689 + 3.18518i) q^{37} +(-3.36049 + 2.77616i) q^{38} +(6.99976 - 2.37342i) q^{39} +(-1.60706 - 0.927835i) q^{40} -7.90040 q^{41} +(-4.35496 + 1.42630i) q^{42} -5.96803 q^{43} +(-0.623513 - 0.359985i) q^{44} +(5.51988 - 0.722847i) q^{45} +(3.10216 - 1.79104i) q^{46} +(11.7223 + 6.76788i) q^{47} +(1.69865 + 0.338490i) q^{48} +(3.62537 - 5.98805i) q^{49} +1.55649 q^{50} +(-1.78095 - 1.56293i) q^{51} +(3.69560 - 2.13366i) q^{52} +(-0.133702 - 0.231579i) q^{53} +(-4.66265 + 2.29339i) q^{54} -1.33603 q^{55} +(-2.30493 + 1.29897i) q^{56} +(0.225160 - 7.54648i) q^{57} +(-2.62612 + 4.54857i) q^{58} +(0.0429487 + 0.0743893i) q^{59} +(3.04390 - 1.03210i) q^{60} +(1.14947 - 1.99094i) q^{61} +10.2689i q^{62} +(3.11860 - 7.29893i) q^{63} +1.00000 q^{64} +(3.95936 - 6.85781i) q^{65} +(1.18098 - 0.400438i) q^{66} +(3.81854 - 2.20464i) q^{67} +(-1.18475 - 0.684017i) q^{68} +(-1.21250 + 6.08470i) q^{69} +(-2.49892 + 4.22611i) q^{70} -0.176684 q^{71} +(-2.38131 + 1.82465i) q^{72} +(6.56246 + 11.3665i) q^{73} +(-5.51689 + 3.18518i) q^{74} +(-1.77824 + 2.02629i) q^{75} +(-0.723980 - 4.29835i) q^{76} +(-0.969542 + 1.63966i) q^{77} +(-1.44444 + 7.24868i) q^{78} +(7.75535 + 4.47755i) q^{79} +(1.60706 - 0.927835i) q^{80} +(2.34132 - 8.69012i) q^{81} +(3.95020 - 6.84195i) q^{82} +14.5654i q^{83} +(0.942266 - 4.48466i) q^{84} -2.53862 q^{85} +(2.98401 - 5.16846i) q^{86} +(-2.92122 - 8.61536i) q^{87} +(0.623513 - 0.359985i) q^{88} +(-6.60356 + 11.4377i) q^{89} +(-2.13394 + 5.14178i) q^{90} +(-5.54310 - 9.83583i) q^{91} +3.58207i q^{92} +(-13.3684 - 11.7319i) q^{93} +(-11.7223 + 6.76788i) q^{94} +(-5.15164 - 6.23597i) q^{95} +(-1.14247 + 1.30183i) q^{96} +10.2959i q^{97} +(3.37312 + 6.13368i) q^{98} +(-0.827934 + 1.99493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8}+O(q^{10}) $ 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8	$ 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8} + 4 q^{14} + 8 q^{15} - 26 q^{16} + 2 q^{19} + 2 q^{21} + 18 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} - 4 q^{30} - 26 q^{32} + 8 q^{33} + 2 q^{38} + q^{39} + 16 q^{41} + 11 q^{42} - 8 q^{43} + 14 q^{45} + 4 q^{49} - 36 q^{50} - 19 q^{51} - 24 q^{53} - 3 q^{54} + 32 q^{55} - 8 q^{56} - 4 q^{57} + 4 q^{58} + 32 q^{59} - 4 q^{60} - 20 q^{61} - 7 q^{63} + 52 q^{64} - 44 q^{65} + 8 q^{66} + 62 q^{69} - 24 q^{71} - 32 q^{73} + 16 q^{75} - 4 q^{76} - 2 q^{78} - 28 q^{81} - 8 q^{82} - 13 q^{84} + 32 q^{85} + 4 q^{86} + 34 q^{87} - 36 q^{89} - 28 q^{90} + 20 q^{93} + 30 q^{95} - 20 q^{98} - 116 q^{99}+O(q^{100}) $ 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8 + 4 * q^14 + 8 * q^15 - 26 * q^16 + 2 * q^19 + 2 * q^21 + 18 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 - 4 * q^30 - 26 * q^32 + 8 * q^33 + 2 * q^38 + q^39 + 16 * q^41 + 11 * q^42 - 8 * q^43 + 14 * q^45 + 4 * q^49 - 36 * q^50 - 19 * q^51 - 24 * q^53 - 3 * q^54 + 32 * q^55 - 8 * q^56 - 4 * q^57 + 4 * q^58 + 32 * q^59 - 4 * q^60 - 20 * q^61 - 7 * q^63 + 52 * q^64 - 44 * q^65 + 8 * q^66 + 62 * q^69 - 24 * q^71 - 32 * q^73 + 16 * q^75 - 4 * q^76 - 2 * q^78 - 28 * q^81 - 8 * q^82 - 13 * q^84 + 32 * q^85 + 4 * q^86 + 34 * q^87 - 36 * q^89 - 28 * q^90 + 20 * q^93 + 30 * q^95 - 20 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.556186	−	1.64032i	−0.321114	−	0.947041i
$3$	−0.556186	−	1.64032i	−0.321114	−	0.947041i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.60706	−	0.927835i	−0.718698	−	0.414940i	0.0955753	−	0.995422i	$-0.469531\pi$
$5$	−1.60706	−	0.927835i	−0.718698	−	0.414940i	−0.814273	+	0.580482i	$0.802864\pi$
$6$	1.69865	+	0.338490i	0.693472	+	0.138188i
$7$	−2.30493	+	1.29897i	−0.871180	+	0.490964i
$7$	−2.30493	+	1.29897i	−0.871180	+	0.490964i
$8$	1.00000			0.353553
$9$	−2.38131	+	1.82465i	−0.793772	+	0.608216i
$10$	1.60706	−	0.927835i	0.508196	−	0.293407i
$11$	0.623513	−	0.359985i	0.187996	−	0.108540i	−0.403048	−	0.915179i	$-0.632049\pi$
$11$	0.623513	−	0.359985i	0.187996	−	0.108540i	0.591044	+	0.806639i	$0.298716\pi$
$12$	−1.14247	+	1.30183i	−0.329802	+	0.375807i
$13$			4.26731i			1.18354i	0.806107	+	0.591769i	$0.201570\pi$
$13$			4.26731i			1.18354i	−0.806107	+	0.591769i	$0.798430\pi$
$14$	0.0275240	−	2.64561i	0.00735609	−	0.707069i
$15$	−0.628126	+	3.15214i	−0.162181	+	0.813879i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.18475	−	0.684017i	0.287345	−	0.165898i	−0.349399	−	0.936974i	$-0.613614\pi$
$17$	1.18475	−	0.684017i	0.287345	−	0.165898i	0.636744	+	0.771076i	$0.280281\pi$
$18$	−0.389534	−	2.97460i	−0.0918141	−	0.701121i
$19$	4.08447	+	1.52219i	0.937043	+	0.349215i
$19$	4.08447	+	1.52219i	0.937043	+	0.349215i
$20$			1.85567i			0.414940i
$21$	3.41269	+	3.05835i	0.744711	+	0.667388i
$22$			0.719971i			0.153498i
$23$	−3.10216	−	1.79104i	−0.646846	−	0.373457i	0.140401	−	0.990095i	$-0.455161\pi$
$23$	−3.10216	−	1.79104i	−0.646846	−	0.373457i	−0.787247	+	0.616638i	$0.788494\pi$
$24$	−0.556186	−	1.64032i	−0.113531	−	0.334829i
$25$	−0.778244	−	1.34796i	−0.155649	−	0.269592i
$26$	−3.69560	−	2.13366i	−0.724767	−	0.418444i
$27$	4.31746	+	2.89128i	0.830896	+	0.556427i
$28$	2.27740	+	1.34664i	0.430389	+	0.254491i
$29$	5.25224			0.975316			0.487658	−	0.873035i	$-0.337851\pi$
$29$	5.25224			0.975316			0.487658	+	0.873035i	$0.337851\pi$
$30$	−2.41577	−	2.12004i	−0.441057	−	0.387065i
$31$	8.89311	−	5.13444i	1.59725	−	0.922173i	0.605236	−	0.796046i	$-0.293079\pi$
$31$	8.89311	−	5.13444i	1.59725	−	0.922173i	0.992014	−	0.126126i	$-0.0402545\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.937281	−	0.822544i	−0.163160	−	0.143186i
$34$			1.36803i			0.234616i
$35$	4.90938	+	0.0510754i	0.829836	+	0.00863331i
$36$	2.77085	+	1.14996i	0.461808	+	0.191659i
$37$	5.51689	+	3.18518i	0.906971	+	0.523640i	0.879455	−	0.475981i	$-0.157907\pi$
$37$	5.51689	+	3.18518i	0.906971	+	0.523640i	0.0275158	+	0.999621i	$0.491240\pi$
$38$	−3.36049	+	2.77616i	−0.545144	+	0.450353i
$39$	6.99976	−	2.37342i	1.12086	−	0.380051i
$40$	−1.60706	−	0.927835i	−0.254098	−	0.146704i
$41$	−7.90040			−1.23383			−0.616917	−	0.787028i	$-0.711619\pi$
$41$	−7.90040			−1.23383			−0.616917	+	0.787028i	$0.711619\pi$
$42$	−4.35496	+	1.42630i	−0.671985	+	0.220083i
$43$	−5.96803			−0.910116			−0.455058	−	0.890462i	$-0.650381\pi$
$43$	−5.96803			−0.910116			−0.455058	+	0.890462i	$0.650381\pi$
$44$	−0.623513	−	0.359985i	−0.0939981	−	0.0542698i
$45$	5.51988	−	0.722847i	0.822855	−	0.107756i
$46$	3.10216	−	1.79104i	0.457389	−	0.264074i
$47$	11.7223	+	6.76788i	1.70987	+	0.987196i	0.934692	+	0.355459i	$0.115675\pi$
$47$	11.7223	+	6.76788i	1.70987	+	0.987196i	0.775183	+	0.631737i	$0.217658\pi$
$48$	1.69865	+	0.338490i	0.245180	+	0.0488568i
$49$	3.62537	−	5.98805i	0.517909	−	0.855435i
$50$	1.55649			0.220121
$51$	−1.78095	−	1.56293i	−0.249383	−	0.218855i
$52$	3.69560	−	2.13366i	0.512487	−	0.295885i
$53$	−0.133702	−	0.231579i	−0.0183654	−	0.0318099i	0.856697	−	0.515821i	$-0.172513\pi$
$53$	−0.133702	−	0.231579i	−0.0183654	−	0.0318099i	−0.875062	+	0.484011i	$0.839180\pi$
$54$	−4.66265	+	2.29339i	−0.634507	+	0.312091i
$55$	−1.33603			−0.180150
$56$	−2.30493	+	1.29897i	−0.308009	+	0.173582i
$57$	0.225160	−	7.54648i	0.0298232	−	0.999555i
$58$	−2.62612	+	4.54857i	−0.344826	+	0.597257i
$59$	0.0429487	+	0.0743893i	0.00559144	+	0.00968466i	0.868808	−	0.495150i	$-0.164887\pi$
$59$	0.0429487	+	0.0743893i	0.00559144	+	0.00968466i	−0.863216	+	0.504835i	$0.831554\pi$
$60$	3.04390	−	1.03210i	0.392965	−	0.133243i
$61$	1.14947	−	1.99094i	0.147174	−	0.254913i	−0.783008	−	0.622012i	$-0.786315\pi$
$61$	1.14947	−	1.99094i	0.147174	−	0.254913i	0.930182	+	0.367099i	$0.119649\pi$
$62$			10.2689i			1.30415i
$63$	3.11860	−	7.29893i	0.392906	−	0.919579i
$64$	1.00000			0.125000
$65$	3.95936	−	6.85781i	0.491098	−	0.850607i
$66$	1.18098	−	0.400438i	0.145369	−	0.0492905i
$67$	3.81854	−	2.20464i	0.466509	−	0.269339i	−0.248268	−	0.968691i	$-0.579861\pi$
$67$	3.81854	−	2.20464i	0.466509	−	0.269339i	0.714777	+	0.699352i	$0.246528\pi$
$68$	−1.18475	−	0.684017i	−0.143672	−	0.0829492i
$69$	−1.21250	+	6.08470i	−0.145967	+	0.732512i
$70$	−2.49892	+	4.22611i	−0.298678	+	0.505116i
$71$	−0.176684			−0.0209685			−0.0104842	−	0.999945i	$-0.503337\pi$
$71$	−0.176684			−0.0209685			−0.0104842	+	0.999945i	$0.503337\pi$
$72$	−2.38131	+	1.82465i	−0.280641	+	0.215037i
$73$	6.56246	+	11.3665i	0.768077	+	1.33035i	0.938604	+	0.344996i	$0.112120\pi$
$73$	6.56246	+	11.3665i	0.768077	+	1.33035i	−0.170527	+	0.985353i	$0.554547\pi$
$74$	−5.51689	+	3.18518i	−0.641325	+	0.370269i
$75$	−1.77824	+	2.02629i	−0.205333	+	0.233976i
$76$	−0.723980	−	4.29835i	−0.0830462	−	0.493055i
$77$	−0.969542	+	1.63966i	−0.110490	+	0.186857i
$78$	−1.44444	+	7.24868i	−0.163551	+	0.820752i
$79$	7.75535	+	4.47755i	0.872545	+	0.503764i	0.868193	−	0.496227i	$-0.165282\pi$
$79$	7.75535	+	4.47755i	0.872545	+	0.503764i	0.00435156	+	0.999991i	$0.498615\pi$
$80$	1.60706	−	0.927835i	0.179674	−	0.103735i
$81$	2.34132	−	8.69012i	0.260147	−	0.965569i
$82$	3.95020	−	6.84195i	0.436227	−	0.755567i
$83$			14.5654i			1.59876i	0.600828	+	0.799378i	$0.294838\pi$
$83$			14.5654i			1.59876i	−0.600828	+	0.799378i	$0.705162\pi$
$84$	0.942266	−	4.48466i	0.102810	−	0.489316i
$85$	−2.53862			−0.275352
$86$	2.98401	−	5.16846i	0.321775	−	0.557330i
$87$	−2.92122	−	8.61536i	−0.313188	−	0.923664i
$88$	0.623513	−	0.359985i	0.0664667	−	0.0383746i
$89$	−6.60356	+	11.4377i	−0.699976	+	1.21239i	0.268499	+	0.963280i	$0.413472\pi$
$89$	−6.60356	+	11.4377i	−0.699976	+	1.21239i	−0.968474	+	0.249113i	$0.919861\pi$
$90$	−2.13394	+	5.14178i	−0.224937	+	0.541991i
$91$	−5.54310	−	9.83583i	−0.581075	−	1.03108i
$92$			3.58207i			0.373457i
$93$	−13.3684	−	11.7319i	−1.38623	−	1.21654i
$94$	−11.7223	+	6.76788i	−1.20906	+	0.698053i
$95$	−5.15164	−	6.23597i	−0.528547	−	0.639797i
$96$	−1.14247	+	1.30183i	−0.116603	+	0.132868i
$97$			10.2959i			1.04540i	0.852518	+	0.522698i	$0.175074\pi$
$97$			10.2959i			1.04540i	−0.852518	+	0.522698i	$0.824926\pi$
$98$	3.37312	+	6.13368i	0.340736	+	0.619596i
$99$	−0.827934	+	1.99493i	−0.0832105	+	0.200498i
$100$	−0.778244	+	1.34796i	−0.0778244	+	0.134796i
$101$	0.399644	−	0.230734i	0.0397660	−	0.0229589i	−0.479985	−	0.877277i	$-0.659358\pi$
$101$	0.399644	−	0.230734i	0.0397660	−	0.0229589i	0.519751	+	0.854318i	$0.326025\pi$
$102$	2.24402	−	0.760881i	0.222191	−	0.0753384i
$103$	−1.86069	−	1.07427i	−0.183339	−	0.105851i	0.405521	−	0.914086i	$-0.367090\pi$
$103$	−1.86069	−	1.07427i	−0.183339	−	0.105851i	−0.588861	+	0.808235i	$0.700423\pi$
$104$			4.26731i			0.418444i
$105$	−2.64674	−	8.08137i	−0.258296	−	0.788661i
$106$	0.267405			0.0259727
$107$	−4.28479	+	7.42147i	−0.414226	+	0.717460i	−0.995347	−	0.0963569i	$-0.969281\pi$
$107$	−4.28479	+	7.42147i	−0.414226	+	0.717460i	0.581121	+	0.813817i	$0.302614\pi$
$108$	0.345190	−	5.18467i	0.0332159	−	0.498895i
$109$	−1.67618	+	0.967745i	−0.160549	+	0.0926931i	−0.578122	−	0.815950i	$-0.696214\pi$
$109$	−1.67618	+	0.967745i	−0.160549	+	0.0926931i	0.417573	+	0.908643i	$0.362881\pi$
$110$	0.668014	−	1.15703i	0.0636926	−	0.110319i
$111$	2.15630	−	10.8210i	0.204667	−	1.02709i
$112$	0.0275240	−	2.64561i	0.00260077	−	0.249986i
$113$	3.12850			0.294304			0.147152	−	0.989114i	$-0.452989\pi$
$113$	3.12850			0.294304			0.147152	+	0.989114i	$0.452989\pi$
$114$	6.42286	+	3.96823i	0.601556	+	0.371659i
$115$	3.32357	+	5.75659i	0.309925	+	0.536805i
$116$	−2.62612	−	4.54857i	−0.243829	−	0.422324i
$117$	−7.78634	−	10.1618i	−0.719847	−	0.939460i
$118$	−0.0858974			−0.00790749
$119$	−1.84225	+	3.11556i	−0.168879	+	0.285603i
$120$	−0.628126	+	3.15214i	−0.0573398	+	0.287750i
$121$	−5.24082	+	9.07737i	−0.476438	+	0.825215i
$122$	1.14947	+	1.99094i	0.104068	+	0.180251i
$123$	4.39409	+	12.9592i	0.396202	+	1.16849i
$124$	−8.89311	−	5.13444i	−0.798625	−	0.461086i
$125$			12.1667i			1.08822i
$126$	4.76176	+	6.35025i	0.424211	+	0.565725i
$127$		−	3.29174i		−	0.292095i	−0.989278	−	0.146047i	$-0.953345\pi$
$127$		−	3.29174i		−	0.292095i	0.989278	−	0.146047i	$-0.0466552\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.31933	+	9.78949i	0.292251	+	0.861917i
$130$	3.95936	+	6.85781i	0.347259	+	0.601470i
$131$	6.78992	+	3.92016i	0.593238	+	0.342506i	0.766377	−	0.642391i	$-0.222058\pi$
$131$	6.78992	+	3.92016i	0.593238	+	0.342506i	−0.173139	+	0.984897i	$0.555391\pi$
$132$	−0.243703	+	1.22298i	−0.0212116	+	0.106447i
$133$	−11.3917	+	1.79706i	−0.987785	+	0.155825i
$134$			4.40927i			0.380903i
$135$	−4.25578	−	8.65235i	−0.366279	−	0.744676i
$136$	1.18475	−	0.684017i	0.101592	−	0.0586540i
$137$	−4.86682	+	2.80986i	−0.415801	+	0.240063i	−0.693279	−	0.720669i	$-0.743835\pi$
$137$	−4.86682	+	2.80986i	−0.415801	+	0.240063i	0.277478	+	0.960732i	$0.410501\pi$
$138$	−4.66326	−	4.09240i	−0.396963	−	0.348368i
$139$	8.51437			0.722179			0.361090	−	0.932531i	$-0.382405\pi$
$139$	8.51437			0.722179			0.361090	+	0.932531i	$0.382405\pi$
$140$	−2.41046	−	4.27718i	−0.203721	−	0.361488i
$141$	4.58172	−	22.9926i	0.385850	−	1.93632i
$142$	0.0883418	−	0.153012i	0.00741348	−	0.0128405i
$143$	1.53617	+	2.66072i	0.128461	+	0.222501i
$144$	−0.389534	−	2.97460i	−0.0324612	−	0.247884i
$145$	−8.44065	−	4.87321i	−0.700958	−	0.404698i
$146$	−13.1249			−1.08623
$147$	−11.8387	−	2.61630i	−0.976440	−	0.215789i
$148$		−	6.37036i		−	0.523640i
$149$	−15.0521	−	8.69035i	−1.23312	−	0.711941i	−0.265440	−	0.964128i	$-0.585517\pi$
$149$	−15.0521	−	8.69035i	−1.23312	−	0.711941i	−0.967679	+	0.252186i	$0.918850\pi$
$150$	−0.865697	−	2.55314i	−0.0706839	−	0.208463i
$151$	9.44268	−	5.45173i	0.768434	−	0.443656i	−0.0638814	−	0.997957i	$-0.520348\pi$
$151$	9.44268	−	5.45173i	0.768434	−	0.443656i	0.832316	+	0.554302i	$0.187015\pi$
$152$	4.08447	+	1.52219i	0.331295	+	0.123466i
$153$	−1.57318	+	3.79061i	−0.127184	+	0.306453i
$154$	−0.935219	−	1.65948i	−0.0753621	−	0.133725i
$155$	−19.0557			−1.53059
$156$	−5.55532	−	4.87527i	−0.444782	−	0.390334i
$157$	−9.84522	−	17.0524i	−0.785734	−	1.36093i	−0.928559	−	0.371184i	$-0.878952\pi$
$157$	−9.84522	−	17.0524i	−0.785734	−	1.36093i	0.142825	−	0.989748i	$-0.454381\pi$
$158$	−7.75535	+	4.47755i	−0.616982	+	0.356215i
$159$	−0.305502	+	0.348116i	−0.0242278	+	0.0276074i
$160$			1.85567i			0.146704i
$161$	9.47676	+	0.0985928i	0.746873	+	0.00777020i
$162$	6.35521	+	6.37270i	0.499312	+	0.500687i
$163$	7.01980	−	12.1587i	0.549833	−	0.952339i	−0.448452	−	0.893807i	$-0.648025\pi$
$163$	7.01980	−	12.1587i	0.549833	−	0.952339i	0.998286	−	0.0585323i	$-0.0186421\pi$
$164$	3.95020	+	6.84195i	0.308459	+	0.534266i
$165$	0.743080	+	2.19152i	0.0578487	+	0.170609i
$166$	−12.6140	−	7.28268i	−0.979034	−	0.565246i
$167$	21.9168			1.69597			0.847985	−	0.530020i	$-0.177815\pi$
$167$	21.9168			1.69597			0.847985	+	0.530020i	$0.177815\pi$
$168$	3.41269	+	3.05835i	0.263295	+	0.235957i
$169$	−5.20994			−0.400764
$170$	1.26931	−	2.19851i	0.0973516	−	0.168618i
$171$	−12.5039	+	3.82791i	−0.956196	+	0.292727i
$172$	2.98401	+	5.16846i	0.227529	+	0.394092i
$173$	7.00358	−	12.1306i	0.532472	−	0.922269i	−0.466809	−	0.884358i	$-0.654596\pi$
$173$	7.00358	−	12.1306i	0.532472	−	0.922269i	0.999281	−	0.0379107i	$-0.0120703\pi$
$174$	8.92173	+	1.77783i	0.676355	+	0.134777i
$175$	3.54475	+	2.09603i	0.267958	+	0.158445i
$176$			0.719971i			0.0542698i
$177$	0.0981350	−	0.111824i	0.00737628	−	0.00840520i
$178$	−6.60356	−	11.4377i	−0.494957	−	0.857291i
$179$	6.65939	+	11.5344i	0.497746	+	0.862122i	0.999997	−	0.00260063i	$-0.000827806\pi$
$179$	6.65939	+	11.5344i	0.497746	+	0.862122i	−0.502251	+	0.864722i	$0.667494\pi$
$180$	−3.38594	−	4.41893i	−0.252373	−	0.329368i
$181$		−	2.27857i		−	0.169365i	−0.996408	−	0.0846823i	$-0.973012\pi$
$181$		−	2.27857i		−	0.169365i	0.996408	−	0.0846823i	$-0.0269875\pi$
$182$	11.2896	+	0.117453i	0.836843	+	0.00870621i
$183$	−3.90510	−	0.778167i	−0.288673	−	0.0575238i
$184$	−3.10216	−	1.79104i	−0.228695	−	0.132037i
$185$	−5.91064	−	10.2375i	−0.434559	−	0.752678i
$186$	16.8443	−	5.71141i	1.23508	−	0.418781i
$187$	0.492472	−	0.852987i	0.0360131	−	0.0623766i
$188$		−	13.5358i		−	0.987196i
$189$	−13.7071	−	1.05594i	−0.997046	−	0.0768084i
$190$	7.97633	−	1.34347i	0.578664	−	0.0974654i
$191$	9.51477	+	5.49336i	0.688465	+	0.397485i	0.803037	−	0.595930i	$-0.203216\pi$
$191$	9.51477	+	5.49336i	0.688465	+	0.397485i	−0.114572	+	0.993415i	$0.536550\pi$
$192$	−0.556186	−	1.64032i	−0.0401393	−	0.118380i
$193$	−7.11407	+	4.10731i	−0.512082	+	0.295651i	−0.733689	−	0.679485i	$-0.762203\pi$
$193$	−7.11407	+	4.10731i	−0.512082	+	0.295651i	0.221607	+	0.975136i	$0.428870\pi$
$194$	−8.91655	−	5.14797i	−0.640171	−	0.369603i
$195$	−13.4512	−	2.68041i	−0.963258	−	0.191948i
$196$	−6.99848	−	0.145635i	−0.499892	−	0.0104025i
$197$		−	23.1444i		−	1.64897i	−0.565884	−	0.824485i	$-0.691465\pi$
$197$		−	23.1444i		−	1.64897i	0.565884	−	0.824485i	$-0.308535\pi$
$198$	−1.31369	−	1.71448i	−0.0933601	−	0.121843i
$199$	6.75007	+	11.6915i	0.478500	+	0.828786i	0.999696	−	0.0246508i	$-0.00784740\pi$
$199$	6.75007	+	11.6915i	0.478500	+	0.828786i	−0.521196	+	0.853437i	$0.674514\pi$
$200$	−0.778244	−	1.34796i	−0.0550302	−	0.0953151i
$201$	−5.74013	−	5.03745i	−0.404878	−	0.355315i
$202$			0.461469i			0.0324688i
$203$	−12.1060	+	6.82249i	−0.849676	+	0.478845i
$204$	−0.463066	+	2.32382i	−0.0324211	+	0.162700i
$205$	12.6964	+	7.33027i	0.886755	+	0.511968i
$206$	1.86069	−	1.07427i	0.129640	−	0.0748479i
$207$	10.6552	−	1.39534i	0.740590	−	0.0969828i
$208$	−3.69560	−	2.13366i	−0.256244	−	0.147942i
$209$	3.09469	−	0.521244i	0.214064	−	0.0360552i
$210$	8.32204	+	1.74853i	0.574275	+	0.120660i
$211$		−	26.6370i		−	1.83377i	−0.399154	−	0.916884i	$-0.630696\pi$
$211$		−	26.6370i		−	1.83377i	0.399154	−	0.916884i	$-0.369304\pi$
$212$	−0.133702	+	0.231579i	−0.00918272	+	0.0159049i
$213$	0.0982689	+	0.289818i	0.00673327	+	0.0198580i
$214$	−4.28479	−	7.42147i	−0.292902	−	0.507321i
$215$	9.59096	+	5.53735i	0.654098	+	0.377644i
$216$	4.31746	+	2.89128i	0.293766	+	0.196727i
$217$	−13.8285	+	23.3864i	−0.938739	+	1.58757i
$218$		−	1.93549i		−	0.131088i
$219$	14.9948	−	17.0864i	1.01325	−	1.15459i
$220$	0.668014	+	1.15703i	0.0450375	+	0.0780072i
$221$	2.91891	+	5.05570i	0.196347	+	0.340083i
$222$	8.29313	+	7.27793i	0.556599	+	0.488463i
$223$			20.1285i			1.34790i	0.738775	+	0.673952i	$0.235405\pi$
$223$			20.1285i			1.34790i	−0.738775	+	0.673952i	$0.764595\pi$
$224$	2.27740	+	1.34664i	0.152165	+	0.0899762i
$225$	4.31280	+	1.78989i	0.287520	+	0.119326i
$226$	−1.56425	+	2.70936i	−0.104052	+	0.180224i
$227$	6.46489	+	11.1975i	0.429090	+	0.743206i	0.996793	−	0.0800281i	$-0.0255010\pi$
$227$	6.46489	+	11.1975i	0.429090	+	0.743206i	−0.567703	+	0.823234i	$0.692168\pi$
$228$	−6.64802	+	3.57824i	−0.440276	+	0.236975i
$229$	−7.36563	+	12.7577i	−0.486735	+	0.843049i	−0.999884	−	0.0152502i	$-0.995146\pi$
$229$	−7.36563	+	12.7577i	−0.486735	+	0.843049i	0.513149	+	0.858300i	$0.328479\pi$
$230$	−6.64714			−0.438300
$231$	3.22882	+	0.678404i	0.212441	+	0.0446357i
$232$	5.25224			0.344826
$233$	1.90160	+	1.09789i	0.124578	+	0.0719250i	0.560994	−	0.827820i	$-0.310419\pi$
$233$	1.90160	+	1.09789i	0.124578	+	0.0719250i	−0.436416	+	0.899745i	$0.643752\pi$
$234$	12.6936	−	1.66226i	0.829804	−	0.108666i
$235$	−12.5589	−	21.7527i	−0.819255	−	1.41899i
$236$	0.0429487	−	0.0743893i	0.00279572	−	0.00484233i
$237$	3.03121	−	15.2116i	0.196898	−	0.988101i
$238$	−1.77703	−	3.15322i	−0.115188	−	0.204393i
$239$		−	18.1782i		−	1.17585i	−0.808915	−	0.587926i	$-0.799945\pi$
$239$		−	18.1782i		−	1.17585i	0.808915	−	0.587926i	$-0.200055\pi$
$240$	−2.41577	−	2.12004i	−0.155937	−	0.136848i
$241$	3.51132	−	2.02726i	0.226184	−	0.130587i	−0.382627	−	0.923903i	$-0.624980\pi$
$241$	3.51132	−	2.02726i	0.226184	−	0.130587i	0.608810	+	0.793316i	$0.291647\pi$
$242$	−5.24082	−	9.07737i	−0.336893	−	0.583515i
$243$	−15.5568	+	0.992804i	−0.997970	+	0.0636884i
$244$	−2.29894			−0.147174
$245$	−11.3821	+	6.25939i	−0.727175	+	0.399898i
$246$	−13.4200	−	2.67421i	−0.855631	−	0.170501i
$247$	−6.49567	+	17.4297i	−0.413309	+	1.10903i
$248$	8.89311	−	5.13444i	0.564713	−	0.326037i
$249$	23.8919	−	8.10105i	1.51409	−	0.513383i
$250$	−10.5367	−	6.08334i	−0.666396	−	0.384744i
$251$			4.43289i			0.279802i	0.990166	+	0.139901i	$0.0446784\pi$
$251$			4.43289i			0.279802i	−0.990166	+	0.139901i	$0.955322\pi$
$252$	−7.88036	+	0.948682i	−0.496416	+	0.0597613i
$253$	−2.57899			−0.162139
$254$	2.85073	+	1.64587i	0.178871	+	0.103271i
$255$	1.41194	+	4.16415i	0.0884193	+	0.260769i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.21835	+	3.84230i	−0.138377	+	0.239676i	−0.926882	−	0.375352i	$-0.877522\pi$
$257$	−2.21835	+	3.84230i	−0.138377	+	0.239676i	0.788505	+	0.615028i	$0.210855\pi$
$258$	−10.1376	−	2.02012i	−0.631140	−	0.125767i
$259$	−16.8535	−	0.175337i	−1.04722	−	0.0108949i
$260$	−7.91872			−0.491098
$261$	−12.5072	+	9.58349i	−0.774178	+	0.593203i
$262$	−6.78992	+	3.92016i	−0.419482	+	0.242188i
$263$	−1.49894	+	0.865415i	−0.0924287	+	0.0533637i	−0.545502	−	0.838110i	$-0.683661\pi$
$263$	−1.49894	+	0.865415i	−0.0924287	+	0.0533637i	0.453073	+	0.891473i	$0.350328\pi$
$264$	−0.937281	−	0.822544i	−0.0576857	−	0.0506241i
$265$			0.496215i			0.0304823i
$266$	4.13955	−	10.7640i	0.253812	−	0.659985i
$267$	22.4343	+	4.47048i	1.37296	+	0.273589i
$268$	−3.81854	−	2.20464i	−0.233255	−	0.134670i
$269$	−11.6833	−	20.2360i	−0.712340	−	1.23381i	−0.963976	−	0.265988i	$-0.914302\pi$
$269$	−11.6833	−	20.2360i	−0.712340	−	1.23381i	0.251636	−	0.967822i	$-0.419031\pi$
$270$	9.62104	+	0.640559i	0.585518	+	0.0389832i
$271$	15.5757	−	26.9780i	0.946158	−	1.63879i	0.192744	−	0.981249i	$-0.438261\pi$
$271$	15.5757	−	26.9780i	0.946158	−	1.63879i	0.753415	−	0.657545i	$-0.228405\pi$
$272$			1.36803i			0.0829492i
$273$	−13.0509	+	14.5630i	−0.789879	+	0.881394i
$274$		−	5.61972i		−	0.339500i
$275$	−0.970491	−	0.560313i	−0.0585228	−	0.0337882i
$276$	5.87575	−	1.99230i	0.353679	−	0.119922i
$277$	−2.94049	−	5.09308i	−0.176677	−	0.306014i	0.764063	−	0.645141i	$-0.223201\pi$
$277$	−2.94049	−	5.09308i	−0.176677	−	0.306014i	−0.940740	+	0.339128i	$0.889868\pi$
$278$	−4.25718	+	7.37366i	−0.255329	+	0.442243i
$279$	−11.8088	+	28.4535i	−0.706971	+	1.70347i
$280$	4.90938	+	0.0510754i	0.293391	+	0.00305234i
$281$	−1.30594			−0.0779058			−0.0389529	−	0.999241i	$-0.512402\pi$
$281$	−1.30594			−0.0779058			−0.0389529	+	0.999241i	$0.512402\pi$
$282$	17.6213	+	15.4642i	1.04933	+	0.920878i
$283$	−8.08624	−	14.0058i	−0.480677	−	0.832557i	0.519077	−	0.854727i	$-0.326276\pi$
$283$	−8.08624	−	14.0058i	−0.480677	−	0.832557i	−0.999754	+	0.0221702i	$0.992942\pi$
$284$	0.0883418	+	0.153012i	0.00524212	+	0.00907962i
$285$	−7.36373	+	11.9187i	−0.436190	+	0.706003i
$286$	−3.07234			−0.181671
$287$	18.2098	−	10.2624i	1.07489	−	0.605768i
$288$	2.77085	+	1.14996i	0.163274	+	0.0677618i
$289$	−7.56424	+	13.1017i	−0.444955	+	0.770685i
$290$	8.44065	−	4.87321i	0.495652	−	0.286165i
$291$	16.8887	−	5.72646i	0.990032	−	0.335691i
$292$	6.56246	−	11.3665i	0.384039	−	0.665175i
$293$	13.8893			0.811421			0.405711	−	0.914002i	$-0.367024\pi$
$293$	13.8893			0.811421			0.405711	+	0.914002i	$0.367024\pi$
$294$	8.18514	−	8.94447i	0.477367	−	0.521652i
$295$		−	0.159397i		−	0.00928046i
$296$	5.51689	+	3.18518i	0.320663	+	0.185135i
$297$	3.73281	+	0.248527i	0.216600	+	0.0144210i
$298$	15.0521	−	8.69035i	0.871946	−	0.503418i
$299$	7.64290	−	13.2379i	0.442001	−	0.765567i
$300$	2.64394	+	0.526856i	0.152648	+	0.0304181i
$301$	13.7559	−	7.75228i	0.792875	−	0.446834i
$302$			10.9035i			0.627424i
$303$	−0.600755	−	0.527213i	−0.0345125	−	0.0302876i
$304$	−3.36049	+	2.77616i	−0.192738	+	0.159224i
$305$	−3.69452	+	2.13303i	−0.211548	+	0.122137i
$306$	−2.49618	−	3.25772i	−0.142697	−	0.186231i
$307$			15.4898i			0.884051i	0.897002	+	0.442025i	$0.145740\pi$
$307$			15.4898i			0.884051i	−0.897002	+	0.442025i	$0.854260\pi$
$308$	1.90476	+	0.0198164i	0.108534	+	0.00112915i
$309$	−0.727259	+	3.64962i	−0.0413723	+	0.207620i
$310$	9.52783	−	16.5027i	0.541144	−	0.937289i
$311$	−11.5454	+	6.66576i	−0.654682	+	0.377981i	−0.790248	−	0.612788i	$-0.790048\pi$
$311$	−11.5454	+	6.66576i	−0.654682	+	0.377981i	0.135566	+	0.990768i	$0.456715\pi$
$312$	6.99976	−	2.37342i	0.396284	−	0.134368i
$313$	5.12883	−	8.88340i	0.289899	−	0.502119i	−0.683887	−	0.729588i	$-0.739712\pi$
$313$	5.12883	−	8.88340i	0.289899	−	0.502119i	0.973785	+	0.227469i	$0.0730451\pi$
$314$	19.6904			1.11120
$315$	−11.7840	+	8.83626i	−0.663951	+	0.497867i
$316$		−	8.95510i		−	0.503764i
$317$	−12.7527	+	22.0884i	−0.716265	+	1.24061i	0.246204	+	0.969218i	$0.420817\pi$
$317$	−12.7527	+	22.0884i	−0.716265	+	1.24061i	−0.962469	+	0.271390i	$0.912517\pi$
$318$	−0.148727	−	0.438630i	−0.00834019	−	0.0245972i
$319$	3.27484	−	1.89073i	0.183356	−	0.105860i
$320$	−1.60706	−	0.927835i	−0.0898372	−	0.0518676i
$321$	14.5567	+	2.90072i	0.812478	+	0.161902i
$322$	−4.82376	+	8.15782i	−0.268818	+	0.454617i
$323$	5.88029	−	0.990429i	0.327188	−	0.0551089i
$324$	−8.69653	+	2.31742i	−0.483140	+	0.128745i
$325$	5.75216	−	3.32101i	0.319072	−	0.184217i
$326$	7.01980	+	12.1587i	0.388791	+	0.673405i
$327$	2.51968	+	2.21123i	0.139339	+	0.122282i
$328$	−7.90040			−0.436227
$329$	−35.8103	−	0.372558i	−1.97429	−	0.0205398i
$330$	−2.26945	−	0.452232i	−0.124929	−	0.0248946i
$331$	−7.46594	−	4.31046i	−0.410365	−	0.236924i	0.280582	−	0.959830i	$-0.409473\pi$
$331$	−7.46594	−	4.31046i	−0.410365	−	0.236924i	−0.690947	+	0.722906i	$0.742806\pi$
$332$	12.6140	−	7.28268i	0.692282	−	0.399689i
$333$	−18.9493	+	2.48147i	−1.03841	+	0.135984i
$334$	−10.9584	+	18.9805i	−0.599616	+	1.03857i
$335$	−8.18216			−0.447039
$336$	−4.35496	+	1.42630i	−0.237582	+	0.0778111i
$337$			9.30220i			0.506723i	0.967372	+	0.253362i	$0.0815363\pi$
$337$			9.30220i			0.506723i	−0.967372	+	0.253362i	$0.918464\pi$
$338$	2.60497	−	4.51194i	0.141692	−	0.245417i
$339$	−1.74002	−	5.13174i	−0.0945052	−	0.278718i
$340$	1.26931	+	2.19851i	0.0688380	+	0.119231i
$341$	3.69665	−	6.40278i	0.200185	−	0.346730i
$342$	2.93688	−	12.7426i	0.158808	−	0.689043i
$343$	−0.577920	+	18.5112i	−0.0312047	+	0.999513i
$344$	−5.96803			−0.321775
$345$	7.59415	−	8.65346i	0.408855	−	0.465887i
$346$	7.00358	+	12.1306i	0.376515	+	0.652143i
$347$	−23.9710	+	13.8397i	−1.28683	+	0.742952i	−0.978088	−	0.208193i	$-0.933242\pi$
$347$	−23.9710	+	13.8397i	−1.28683	+	0.742952i	−0.308743	+	0.951145i	$0.599908\pi$
$348$	−6.00051	+	6.83753i	−0.321661	+	0.366530i
$349$	−22.2848			−1.19288			−0.596439	−	0.802659i	$-0.703418\pi$
$349$	−22.2848			−1.19288			−0.596439	+	0.802659i	$0.703418\pi$
$350$	−3.58759	+	2.02183i	−0.191765	+	0.108071i
$351$	−12.3380	+	18.4240i	−0.658553	+	0.983398i
$352$	−0.623513	−	0.359985i	−0.0332334	−	0.0191873i
$353$	−10.1571	+	5.86420i	−0.540607	+	0.312120i	−0.745325	−	0.666701i	$-0.767706\pi$
$353$	−10.1571	+	5.86420i	−0.540607	+	0.312120i	0.204718	+	0.978821i	$0.434372\pi$
$354$	0.0477749	+	0.140899i	0.00253921	+	0.00748872i
$355$	0.283941	+	0.163933i	0.0150700	+	0.00870067i
$356$	13.2071			0.699976
$357$	6.13516	+	1.28905i	0.324707	+	0.0682238i
$358$	−13.3188			−0.703919
$359$	12.0582	+	6.96182i	0.636409	+	0.367431i	0.783230	−	0.621732i	$-0.213571\pi$
$359$	12.0582	+	6.96182i	0.636409	+	0.367431i	−0.146821	+	0.989163i	$0.546904\pi$
$360$	5.51988	−	0.722847i	0.290923	−	0.0380974i
$361$	14.3659	+	12.4347i	0.756098	+	0.654459i
$362$	1.97330	+	1.13928i	0.103714	+	0.0598794i
$363$	17.8047	+	3.54793i	0.934503	+	0.186218i
$364$	−5.74653	+	9.71838i	−0.301200	+	0.509382i
$365$		−	24.3555i		−	1.27483i
$366$	2.62646	−	2.99283i	0.137287	−	0.156438i
$367$	13.3101	+	23.0538i	0.694783	+	1.20340i	0.970254	+	0.242090i	$0.0778330\pi$
$367$	13.3101	+	23.0538i	0.694783	+	1.20340i	−0.275471	+	0.961310i	$0.588834\pi$
$368$	3.10216	−	1.79104i	0.161712	−	0.0933642i
$369$	18.8133	−	14.4154i	0.979383	−	0.750438i
$370$	11.8213			0.614559
$371$	0.608989	+	0.360098i	0.0316171	+	0.0186954i
$372$	−3.47591	+	17.4433i	−0.180218	+	0.904391i
$373$	30.0142	+	17.3287i	1.55408	+	0.897247i	0.997803	+	0.0662490i	$0.0211032\pi$
$373$	30.0142	+	17.3287i	1.55408	+	0.897247i	0.556275	+	0.830998i	$0.312230\pi$
$374$	0.492472	+	0.852987i	0.0254651	+	0.0441069i
$375$	19.9573	−	6.76693i	1.03059	−	0.349443i
$376$	11.7223	+	6.76788i	0.604532	+	0.349027i
$377$			22.4129i			1.15432i
$378$	7.76803	−	11.3427i	0.399544	−	0.583408i
$379$			9.90857i			0.508969i	0.967077	+	0.254484i	$0.0819058\pi$
$379$			9.90857i			0.508969i	−0.967077	+	0.254484i	$0.918094\pi$
$380$	−2.82469	+	7.57944i	−0.144903	+	0.388817i
$381$	−5.39952	+	1.83082i	−0.276626	+	0.0937958i
$382$	−9.51477	+	5.49336i	−0.486818	+	0.281065i
$383$	−14.1663	+	24.5367i	−0.723862	+	1.25377i	0.235578	+	0.971855i	$0.424302\pi$
$383$	−14.1663	+	24.5367i	−0.723862	+	1.25377i	−0.959441	+	0.281911i	$0.909032\pi$
$384$	1.69865	+	0.338490i	0.0866841	+	0.0172735i
$385$	3.07945	−	1.73546i	0.156943	−	0.0884471i
$386$		−	8.21463i		−	0.418113i
$387$	14.2118	−	10.8896i	0.722424	−	0.553547i
$388$	8.91655	−	5.14797i	0.452669	−	0.261349i
$389$	−15.7319	+	9.08284i	−0.797641	+	0.460518i	−0.842646	−	0.538469i	$-0.819003\pi$
$389$	−15.7319	+	9.08284i	−0.797641	+	0.460518i	0.0450047	+	0.998987i	$0.485670\pi$
$390$	9.04688	−	10.3088i	0.458107	−	0.522009i
$391$	−4.90039			−0.247824
$392$	3.62537	−	5.98805i	0.183109	−	0.302442i
$393$	2.65387	−	13.3180i	0.133870	−	0.671804i
$394$	20.0436	+	11.5722i	1.00978	+	0.582999i
$395$	−8.30886	−	14.3914i	−0.418064	−	0.724108i
$396$	2.14163	−	0.280453i	0.107621	−	0.0140933i
$397$	−3.61484	+	6.26109i	−0.181424	+	0.314235i	−0.942366	−	0.334585i	$-0.891404\pi$
$397$	−3.61484	+	6.26109i	−0.181424	+	0.314235i	0.760942	+	0.648820i	$0.224737\pi$
$398$	−13.5001			−0.676701
$399$	9.28365	+	17.6865i	0.464764	+	0.885435i
$400$	1.55649			0.0778244
$401$	7.23147	−	12.5253i	0.361123	−	0.625483i	−0.627023	−	0.779001i	$-0.715727\pi$
$401$	7.23147	−	12.5253i	0.361123	−	0.625483i	0.988146	+	0.153518i	$0.0490603\pi$
$402$	7.23263	−	2.45237i	0.360731	−	0.122313i
$403$	21.9102	+	37.9497i	1.09143	+	1.89041i
$404$	−0.399644	−	0.230734i	−0.0198830	−	0.0114795i
$405$	−11.8256	+	11.7932i	−0.587620	+	0.586007i
$406$	0.144562	−	13.8954i	0.00717451	−	0.689615i
$407$	4.58647			0.227343
$408$	−1.78095	−	1.56293i	−0.0881702	−	0.0773768i
$409$	25.2766	−	14.5935i	1.24985	−	0.721601i	0.278770	−	0.960358i	$-0.410073\pi$
$409$	25.2766	−	14.5935i	1.24985	−	0.721601i	0.971079	+	0.238757i	$0.0767399\pi$
$410$	−12.6964	+	7.33027i	−0.627030	+	0.362016i
$411$	7.31593	+	6.42035i	0.360868	+	0.316693i
$412$			2.14854i			0.105851i
$413$	−0.195623	−	0.115673i	−0.00962597	−	0.00569189i
$414$	−4.11922	+	9.92538i	−0.202449	+	0.487806i
$415$	13.5143	−	23.4074i	0.663389	−	1.14902i
$416$	3.69560	−	2.13366i	0.181192	−	0.104611i
$417$	−4.73557	−	13.9663i	−0.231902	−	0.683933i
$418$	−1.09593	+	2.94070i	−0.0536039	+	0.143834i
$419$		−	19.9873i		−	0.976446i	−0.872719	−	0.488223i	$-0.837645\pi$
$419$		−	19.9873i		−	0.976446i	0.872719	−	0.488223i	$-0.162355\pi$
$420$	−5.67530	+	6.33283i	−0.276926	+	0.309011i
$421$			11.3042i			0.550931i	0.961311	+	0.275465i	$0.0888320\pi$
$421$			11.3042i			0.550931i	−0.961311	+	0.275465i	$0.911168\pi$
$422$	23.0683	+	13.3185i	1.12295	+	0.648335i
$423$	−40.2635	+	5.27264i	−1.95768	+	0.256364i
$424$	−0.133702	−	0.231579i	−0.00649317	−	0.0112465i
$425$	−1.84405	−	1.06466i	−0.0894497	−	0.0516438i
$426$	−0.300124	−	0.0598056i	−0.0145411	−	0.00289759i
$427$	−0.0632758	+	6.08209i	−0.00306213	+	0.294333i
$428$	8.56957			0.414226
$429$	3.51005	−	3.99967i	0.169467	−	0.193106i
$430$	−9.59096	+	5.53735i	−0.462517	+	0.267035i
$431$	−13.1541	−	22.7836i	−0.633610	−	1.09745i	−0.986808	−	0.161896i	$-0.948239\pi$
$431$	−13.1541	−	22.7836i	−0.633610	−	1.09745i	0.353198	−	0.935549i	$-0.385094\pi$
$432$	−4.66265	+	2.29339i	−0.224332	+	0.110341i
$433$			1.70968i			0.0821622i	0.999156	+	0.0410811i	$0.0130802\pi$
$433$			1.70968i			0.0821622i	−0.999156	+	0.0410811i	$0.986920\pi$
$434$	−13.3389	−	23.6690i	−0.640290	−	1.13615i
$435$	−3.29907	+	16.5558i	−0.158178	+	0.793790i
$436$	1.67618	+	0.967745i	0.0802746	+	0.0463466i
$437$	−9.94441	−	12.0375i	−0.475706	−	0.575833i
$438$	7.29989	+	21.5291i	0.348802	+	1.02870i
$439$	24.5129	+	14.1525i	1.16994	+	0.675463i	0.953665	−	0.300870i	$-0.0972771\pi$
$439$	24.5129	+	14.1525i	1.16994	+	0.675463i	0.216271	+	0.976333i	$0.430610\pi$
$440$	−1.33603			−0.0636926
$441$	2.29294	+	20.8744i	0.109188	+	0.994021i
$442$	−5.83782			−0.277677
$443$	11.3257	+	6.53887i	0.538098	+	0.310671i	0.744308	−	0.667837i	$-0.232780\pi$
$443$	11.3257	+	6.53887i	0.538098	+	0.310671i	−0.206210	+	0.978508i	$0.566113\pi$
$444$	−10.4494	+	3.54310i	−0.495908	+	0.168148i
$445$	21.2246	−	12.2540i	1.00614	−	0.580896i
$446$	−17.4318	−	10.0643i	−0.825419	−	0.476556i
$447$	−5.88320	+	29.5238i	−0.278266	+	1.39643i
$448$	−2.30493	+	1.29897i	−0.108898	+	0.0613705i
$449$	−8.96199			−0.422942			−0.211471	−	0.977384i	$-0.567825\pi$
$449$	−8.96199			−0.422942			−0.211471	+	0.977384i	$0.567825\pi$
$450$	−3.70649	+	2.84004i	−0.174726	+	0.133881i
$451$	−4.92600	+	2.84403i	−0.231956	+	0.133920i
$452$	−1.56425	−	2.70936i	−0.0735760	−	0.127437i
$453$	−14.1945	−	12.4569i	−0.666915	−	0.585274i
$454$	−12.9298			−0.606825
$455$	−0.217954	+	20.9498i	−0.0102179	+	0.982143i
$456$	0.225160	−	7.54648i	0.0105441	−	0.353396i
$457$	4.07991	−	7.06661i	0.190850	−	0.330562i	−0.754682	−	0.656091i	$-0.772209\pi$
$457$	4.07991	−	7.06661i	0.190850	−	0.330562i	0.945532	+	0.325529i	$0.105542\pi$
$458$	−7.36563	−	12.7577i	−0.344173	−	0.596126i
$459$	7.09281	+	0.472232i	0.331064	+	0.0220419i
$460$	3.32357	−	5.75659i	0.154962	−	0.268403i
$461$		−	31.8022i		−	1.48118i	−0.671959	−	0.740588i	$-0.734547\pi$
$461$		−	31.8022i		−	1.48118i	0.671959	−	0.740588i	$-0.265453\pi$
$462$	−2.20193	+	2.45704i	−0.102443	+	0.114312i
$463$	−3.03009			−0.140820			−0.0704101	−	0.997518i	$-0.522431\pi$
$463$	−3.03009			−0.140820			−0.0704101	+	0.997518i	$0.522431\pi$
$464$	−2.62612	+	4.54857i	−0.121915	+	0.211162i
$465$	10.5985	+	31.2574i	0.491493	+	1.44953i
$466$	−1.90160	+	1.09789i	−0.0880898	+	0.0508587i
$467$	22.8669	+	13.2022i	1.05815	+	0.610925i	0.924921	−	0.380160i	$-0.124131\pi$
$467$	22.8669	+	13.2022i	1.05815	+	0.610925i	0.133232	+	0.991085i	$0.457464\pi$
$468$	−4.90722	+	11.8241i	−0.226836	+	0.546568i
$469$	−5.93771	+	10.0417i	−0.274178	+	0.463682i
$470$	25.1179			1.15860
$471$	−22.4957	+	25.6337i	−1.03655	+	1.18114i
$472$	0.0429487	+	0.0743893i	0.00197687	+	0.00342405i
$473$	−3.72114	+	2.14840i	−0.171098	+	0.0987837i
$474$	11.6580	+	10.2309i	0.535471	+	0.469922i
$475$	−1.12687	−	6.69034i	−0.0517042	−	0.306974i
$476$	3.61928	+	0.0376537i	0.165889	+	0.00172585i
$477$	0.740939	+	0.307504i	0.0339253	+	0.0140796i
$478$	15.7428	+	9.08912i	0.720059	+	0.415727i
$479$	19.9814	−	11.5362i	0.912972	−	0.527105i	0.0315859	−	0.999501i	$-0.489944\pi$
$479$	19.9814	−	11.5362i	0.912972	−	0.527105i	0.881386	+	0.472396i	$0.156611\pi$
$480$	3.04390	−	1.03210i	0.138934	−	0.0471086i
$481$	−13.5921	+	23.5423i	−0.619748	+	1.07344i
$482$			4.05452i			0.184678i
$483$	−5.10911	−	15.5998i	−0.232473	−	0.709814i
$484$	10.4816			0.476438
$485$	9.55294	−	16.5462i	0.433777	−	0.751323i
$486$	6.91861	−	13.9690i	0.313835	−	0.633646i
$487$	5.04979	−	2.91550i	0.228828	−	0.132114i	−0.381203	−	0.924491i	$-0.624490\pi$
$487$	5.04979	−	2.91550i	0.228828	−	0.132114i	0.610031	+	0.792377i	$0.291157\pi$
$488$	1.14947	−	1.99094i	0.0520340	−	0.0901255i
$489$	−23.8484	−	4.75227i	−1.07846	−	0.214905i
$490$	0.270251	−	12.9869i	0.0122087	−	0.586687i
$491$		−	2.13266i		−	0.0962455i	−0.998841	−	0.0481228i	$-0.984676\pi$
$491$		−	2.13266i		−	0.0962455i	0.998841	−	0.0481228i	$-0.0153239\pi$
$492$	9.02595	−	10.2850i	0.406921	−	0.463683i
$493$	6.22260	−	3.59262i	0.280252	−	0.161803i
$494$	−11.8467	−	14.3403i	−0.533010	−	0.645199i
$495$	3.18150	−	2.43778i	0.142998	−	0.109570i
$496$			10.2689i			0.461086i
$497$	0.407242	−	0.229506i	0.0182673	−	0.0102948i
$498$	−4.93023	+	24.7415i	−0.220929	+	1.10869i
$499$	3.91235	−	6.77639i	0.175141	−	0.303353i	−0.765069	−	0.643948i	$-0.777295\pi$
$499$	3.91235	−	6.77639i	0.175141	−	0.303353i	0.940210	+	0.340595i	$0.110629\pi$
$500$	10.5367	−	6.08334i	0.471213	−	0.272055i
$501$	−12.1898	−	35.9506i	−0.544600	−	1.60615i
$502$	−3.83900	−	2.21645i	−0.171343	−	0.0989249i
$503$		−	26.6994i		−	1.19047i	−0.803552	−	0.595234i	$-0.797059\pi$
$503$		−	26.6994i		−	1.19047i	0.803552	−	0.595234i	$-0.202941\pi$
$504$	3.11860	−	7.29893i	0.138913	−	0.325120i
$505$	−0.856334			−0.0381064
$506$	1.28949	−	2.23347i	0.0573250	−	0.0992898i
$507$	2.89769	+	8.54598i	0.128691	+	0.379540i
$508$	−2.85073	+	1.64587i	−0.126481	+	0.0730237i
$509$	−11.2049	+	19.4075i	−0.496650	+	0.860223i	−0.999993	−	0.00386393i	$-0.998770\pi$
$509$	−11.2049	+	19.4075i	−0.496650	+	0.860223i	0.503343	+	0.864087i	$0.332103\pi$
$510$	−4.31223	−	0.859297i	−0.190949	−	0.0380503i
$511$	−29.8907	−	17.6745i	−1.32229	−	0.781876i
$512$	1.00000			0.0441942
$513$	13.2335	+	18.3814i	0.584273	+	0.811557i
$514$	−2.21835	−	3.84230i	−0.0978474	−	0.169477i
$515$	1.99349	+	3.45282i	0.0878436	+	0.152150i
$516$	6.81828	−	7.76937i	0.300158	−	0.342027i
$517$	9.74535			0.428600
$518$	8.57858	−	14.5079i	0.376921	−	0.637439i
$519$	−23.7933	−	4.74128i	−1.04441	−	0.208119i
$520$	3.95936	−	6.85781i	0.173629	−	0.300735i
$521$	16.7809	+	29.0654i	0.735186	+	1.27338i	0.954642	+	0.297757i	$0.0962384\pi$
$521$	16.7809	+	29.0654i	0.735186	+	1.27338i	−0.219456	+	0.975622i	$0.570428\pi$
$522$	−2.04593	−	15.6233i	−0.0895477	−	0.683814i
$523$	−36.9764	−	21.3483i	−1.61686	−	0.933497i	−0.987725	−	0.156205i	$-0.950074\pi$
$523$	−36.9764	−	21.3483i	−1.61686	−	0.933497i	−0.629140	−	0.777292i	$-0.716593\pi$
$524$		−	7.84032i		−	0.342506i
$525$	1.46663	−	6.98032i	0.0640088	−	0.304646i
$526$		−	1.73083i		−	0.0754677i
$527$	7.02409	−	12.1661i	0.305974	−	0.529963i
$528$	1.18098	−	0.400438i	0.0513957	−	0.0174268i
$529$	−5.08438	−	8.80641i	−0.221060	−	0.382887i
$530$	−0.429735	−	0.248108i	−0.0186665	−	0.0107771i
$531$	−0.238009	−	0.0987781i	−0.0103287	−	0.00428661i
$532$	7.25214	+	8.96696i	0.314420	+	0.388767i
$533$		−	33.7135i		−	1.46029i
$534$	−15.0887	+	17.1934i	−0.652952	+	0.744033i
$535$	13.7718	−	7.95115i	0.595407	−	0.343758i
$536$	3.81854	−	2.20464i	0.164936	−	0.0952258i
$537$	15.2163	−	17.3388i	0.656631	−	0.748225i
$538$	23.3665			1.00740
$539$	0.104853	−	5.03870i	0.00451634	−	0.217032i
$540$	−5.36526	+	8.01179i	−0.230884	+	0.344772i
$541$	−14.4022	+	24.9453i	−0.619198	+	1.07248i	0.370435	+	0.928859i	$0.379209\pi$
$541$	−14.4022	+	24.9453i	−0.619198	+	1.07248i	−0.989632	+	0.143624i	$0.954125\pi$
$542$	15.5757	+	26.9780i	0.669035	+	1.15880i
$543$	−3.73759	+	1.26731i	−0.160395	+	0.0543854i
$544$	−1.18475	−	0.684017i	−0.0507958	−	0.0293270i
$545$	3.59163			0.153848
$546$	−6.08647	−	18.5840i	−0.260477	−	0.795320i
$547$			22.4302i			0.959048i	0.877529	+	0.479524i	$0.159191\pi$
$547$			22.4302i			0.959048i	−0.877529	+	0.479524i	$0.840809\pi$
$548$	4.86682	+	2.80986i	0.207900	+	0.120031i
$549$	0.895514	+	6.83842i	0.0382196	+	0.291857i
$550$	0.970491	−	0.560313i	0.0413819	−	0.0238918i
$551$	21.4526	+	7.99492i	0.913913	+	0.340595i
$552$	−1.21250	+	6.08470i	−0.0516072	+	0.258982i
$553$	−23.6917	−	0.246480i	−1.00747	−	0.0104814i
$554$	5.88099			0.249859
$555$	−13.5054	+	15.3893i	−0.573274	+	0.653240i
$556$	−4.25718	−	7.37366i	−0.180545	−	0.312713i
$557$	31.9713	−	18.4587i	1.35467	−	0.782118i	0.365769	−	0.930706i	$-0.380806\pi$
$557$	31.9713	−	18.4587i	1.35467	−	0.782118i	0.988899	+	0.148588i	$0.0474727\pi$
$558$	−18.7371	−	24.4534i	−0.793204	−	1.03520i
$559$		−	25.4674i		−	1.07716i
$560$	−2.49892	+	4.22611i	−0.105599	+	0.178586i
$561$	−1.67308	−	0.333394i	−0.0706375	−	0.0140759i
$562$	0.652970	−	1.13098i	0.0275439	−	0.0477074i
$563$	3.36524	+	5.82877i	0.141828	+	0.245653i	0.928185	−	0.372119i	$-0.121369\pi$
$563$	3.36524	+	5.82877i	0.141828	+	0.245653i	−0.786357	+	0.617772i	$0.788035\pi$
$564$	−22.2030	+	7.52839i	−0.934915	+	0.317003i
$565$	−5.02767	−	2.90273i	−0.211516	−	0.122119i
$566$	16.1725			0.679780
$567$	5.89162	+	23.0714i	0.247425	+	0.968907i
$568$	−0.176684			−0.00741348
$569$	13.1555	−	22.7860i	0.551508	−	0.955239i	−0.446659	−	0.894705i	$-0.647386\pi$
$569$	13.1555	−	22.7860i	0.551508	−	0.955239i	0.998166	−	0.0605346i	$-0.0192806\pi$
$570$	−6.64004	−	12.3365i	−0.278121	−	0.516720i
$571$	11.8431	+	20.5129i	0.495620	+	0.858439i	0.999987	−	0.00505011i	$-0.00160751\pi$
$571$	11.8431	+	20.5129i	0.495620	+	0.858439i	−0.504367	+	0.863489i	$0.668274\pi$
$572$	1.53617	−	2.66072i	0.0642305	−	0.111250i
$573$	3.71889	−	18.6626i	0.155359	−	0.779642i
$574$	−0.217450	+	20.9014i	−0.00907620	+	0.872406i
$575$			5.57545i			0.232512i
$576$	−2.38131	+	1.82465i	−0.0992214	+	0.0760270i
$577$	−16.4636	−	28.5158i	−0.685389	−	1.18713i	−0.973314	−	0.229476i	$-0.926299\pi$
$577$	−16.4636	−	28.5158i	−0.685389	−	1.18713i	0.287925	−	0.957653i	$-0.407035\pi$
$578$	−7.56424	−	13.1017i	−0.314631	−	0.544957i
$579$	10.6941	+	9.38495i	0.444430	+	0.390025i
$580$			9.74642i			0.404698i
$581$	−18.9199	−	33.5721i	−0.784931	−	1.39280i
$582$	−3.48508	+	17.4893i	−0.144461	+	0.724953i
$583$	−0.166730	−	0.0962619i	−0.00690527	−	0.00398676i
$584$	6.56246	+	11.3665i	0.271556	+	0.470349i
$585$	3.08461	+	23.5550i	0.127533	+	0.973881i
$586$	−6.94465	+	12.0285i	−0.286881	+	0.496892i
$587$		−	22.9114i		−	0.945653i	−0.881155	−	0.472827i	$-0.843234\pi$
$587$		−	22.9114i		−	0.945653i	0.881155	−	0.472827i	$-0.156766\pi$
$588$	3.65357	+	11.5608i	0.150671	+	0.476758i
$589$	44.1393	−	7.43446i	1.81873	−	0.306332i
$590$	0.138042	+	0.0796986i	0.00568310	+	0.00328114i
$591$	−37.9643	+	12.8726i	−1.56164	+	0.529507i
$592$	−5.51689	+	3.18518i	−0.226743	+	0.130910i
$593$	9.17417	+	5.29671i	0.376738	+	0.217510i	0.676398	−	0.736536i	$-0.263540\pi$
$593$	9.17417	+	5.29671i	0.376738	+	0.217510i	−0.299660	+	0.954046i	$0.596873\pi$
$594$	−2.08164	+	3.10845i	−0.0854106	+	0.127541i
$595$	5.85133	−	3.29758i	0.239881	−	0.135188i
$596$			17.3807i			0.711941i
$597$	15.4235	−	17.5749i	0.631241	−	0.719294i
$598$	7.64290	+	13.2379i	0.312542	+	0.541338i
$599$	−11.4929	−	19.9064i	−0.469589	−	0.813352i	0.529806	−	0.848119i	$-0.322265\pi$
$599$	−11.4929	−	19.9064i	−0.469589	−	0.813352i	−0.999395	+	0.0347664i	$0.988931\pi$
$600$	−1.77824	+	2.02629i	−0.0725963	+	0.0827228i
$601$		−	37.4887i		−	1.52919i	−0.644508	−	0.764597i	$-0.722938\pi$
$601$		−	37.4887i		−	1.52919i	0.644508	−	0.764597i	$-0.277062\pi$
$602$	−0.164264	+	15.7891i	−0.00669489	+	0.643514i
$603$	−5.07047	+	12.2174i	−0.206485	+	0.497532i
$604$	−9.44268	−	5.45173i	−0.384217	−	0.221828i
$605$	16.8446	−	9.72523i	0.684830	−	0.395387i
$606$	0.756958	−	0.256662i	0.0307493	−	0.0104262i
$607$	11.6559	+	6.72954i	0.473099	+	0.273144i	0.717536	−	0.696521i	$-0.245270\pi$
$607$	11.6559	+	6.72954i	0.473099	+	0.273144i	−0.244437	+	0.969665i	$0.578603\pi$
$608$	−0.723980	−	4.29835i	−0.0293613	−	0.174321i
$609$	17.9243	+	16.0632i	0.726328	+	0.650914i
$610$		−	4.26607i		−	0.172728i
$611$	−28.8806	+	50.0227i	−1.16839	+	2.02370i
$612$	4.06936	−	0.532896i	0.164494	−	0.0215410i
$613$	−6.74014	−	11.6743i	−0.272232	−	0.471519i	0.697201	−	0.716875i	$-0.254428\pi$
$613$	−6.74014	−	11.6743i	−0.272232	−	0.471519i	−0.969433	+	0.245356i	$0.921095\pi$
$614$	−13.4146	−	7.74491i	−0.541368	−	0.312559i
$615$	4.96245	−	24.9032i	0.200105	−	1.00419i
$616$	−0.969542	+	1.63966i	−0.0390640	+	0.0660639i
$617$		−	13.4802i		−	0.542694i	−0.962482	−	0.271347i	$-0.912531\pi$
$617$		−	13.4802i		−	0.542694i	0.962482	−	0.271347i	$-0.0874691\pi$
$618$	−2.79704	−	2.45464i	−0.112513	−	0.0987399i
$619$	−20.6759	−	35.8118i	−0.831036	−	1.43940i	−0.897217	−	0.441590i	$-0.854415\pi$
$619$	−20.6759	−	35.8118i	−0.831036	−	1.43940i	0.0661806	−	0.997808i	$-0.478919\pi$
$620$	9.52783	+	16.5027i	0.382647	+	0.662764i
$621$	−8.21510	−	16.7020i	−0.329661	−	0.670227i
$622$		−	13.3315i		−	0.534546i
$623$	0.363512	−	34.9408i	0.0145638	−	1.39988i
$624$	−1.44444	+	7.24868i	−0.0578240	+	0.290180i
$625$	7.39745	−	12.8128i	0.295898	−	0.512510i
$626$	5.12883	+	8.88340i	0.204989	+	0.355052i
$627$	−2.57623	−	4.78638i	−0.102885	−	0.191150i
$628$	−9.84522	+	17.0524i	−0.392867	+	0.680466i
$629$	8.71486			0.347484
$630$	−1.76044	−	14.6233i	−0.0701376	−	0.582608i
$631$	21.8485			0.869777			0.434888	−	0.900484i	$-0.356788\pi$
$631$	21.8485			0.869777			0.434888	+	0.900484i	$0.356788\pi$
$632$	7.75535	+	4.47755i	0.308491	+	0.178107i
$633$	−43.6933	+	14.8151i	−1.73665	+	0.588848i
$634$	−12.7527	−	22.0884i	−0.506476	−	0.877242i
$635$	−3.05419	+	5.29002i	−0.121202	+	0.209928i
$636$	0.454228	+	0.0905139i	0.0180113	+	0.00358911i
$637$	25.5529	+	15.4706i	1.01244	+	0.612966i
$638$			3.78146i			0.149709i
$639$	0.420739	−	0.322385i	0.0166442	−	0.0127534i
$640$	1.60706	−	0.927835i	0.0635245	−	0.0366759i
$641$	−4.03719	−	6.99261i	−0.159459	−	0.276192i	0.775215	−	0.631698i	$-0.217642\pi$
$641$	−4.03719	−	6.99261i	−0.159459	−	0.276192i	−0.934674	+	0.355506i	$0.884308\pi$
$642$	−9.79046	+	11.1561i	−0.386399	+	0.440298i
$643$	−25.5569			−1.00786			−0.503932	−	0.863743i	$-0.668114\pi$
$643$	−25.5569			−1.00786			−0.503932	+	0.863743i	$0.668114\pi$
$644$	−4.65299	−	8.25641i	−0.183354	−	0.325348i
$645$	3.74867	−	18.8121i	0.147604	−	0.740724i
$646$	−2.08241	+	5.58770i	−0.0819313	+	0.219845i
$647$	−30.0372	+	17.3420i	−1.18089	+	0.681784i	−0.956219	−	0.292651i	$-0.905462\pi$
$647$	−30.0372	+	17.3420i	−1.18089	+	0.681784i	−0.224666	+	0.974436i	$0.572129\pi$
$648$	2.34132	−	8.69012i	0.0919757	−	0.341380i
$649$	0.0535581	+	0.0309218i	0.00210234	+	0.00121379i
$650$			6.64202i			0.260522i
$651$	46.0524	+	9.67602i	1.80494	+	0.379233i
$652$	−14.0396			−0.549833
$653$	8.55581	+	4.93970i	0.334815	+	0.193305i	0.657977	−	0.753038i	$-0.271413\pi$
$653$	8.55581	+	4.93970i	0.334815	+	0.193305i	−0.323162	+	0.946344i	$0.604746\pi$
$654$	−3.17483	+	1.07649i	−0.124146	+	0.0420942i
$655$	−7.27452	−	12.5998i	−0.284239	−	0.492317i
$656$	3.95020	−	6.84195i	0.154229	−	0.267133i
$657$	−36.3672	−	15.0931i	−1.41882	−	0.588836i
$658$	18.2278	−	30.8264i	0.710593	−	1.20174i
$659$	39.6444			1.54433			0.772163	−	0.635425i	$-0.219175\pi$
$659$	39.6444			1.54433			0.772163	+	0.635425i	$0.219175\pi$
$660$	1.52637	−	1.73928i	0.0594138	−	0.0677016i
$661$	5.19104	−	2.99705i	0.201908	−	0.116572i	−0.395637	−	0.918407i	$-0.629476\pi$
$661$	5.19104	−	2.99705i	0.201908	−	0.116572i	0.597545	+	0.801835i	$0.296143\pi$
$662$	7.46594	−	4.31046i	0.290172	−	0.167531i
$663$	6.66953	−	7.59987i	0.259023	−	0.295154i
$664$			14.5654i			0.565246i
$665$	19.9745	+	7.68163i	0.774577	+	0.297881i
$666$	7.32562	−	17.6513i	0.283862	−	0.683974i
$667$	−16.2933	−	9.40694i	−0.630879	−	0.364238i
$668$	−10.9584	−	18.9805i	−0.423993	−	0.734377i
$669$	33.0172	−	11.1952i	1.27652	−	0.432831i
$670$	4.09108	−	7.08595i	0.158052	−	0.273754i
$671$		−	1.65517i		−	0.0638970i
$672$	0.942266	−	4.48466i	0.0363487	−	0.172999i
$673$			37.3719i			1.44058i	0.693673	+	0.720290i	$0.255991\pi$
$673$			37.3719i			1.44058i	−0.693673	+	0.720290i	$0.744009\pi$
$674$	−8.05594	−	4.65110i	−0.310303	−	0.179154i
$675$	0.537285	−	8.06989i	0.0206801	−	0.310610i
$676$	2.60497	+	4.51194i	0.100191	+	0.173536i
$677$	−17.4798	+	30.2759i	−0.671804	+	1.16360i	0.305588	+	0.952164i	$0.401147\pi$
$677$	−17.4798	+	30.2759i	−0.671804	+	1.16360i	−0.977392	+	0.211435i	$0.932186\pi$
$678$	5.31423	+	1.05896i	0.204092	+	0.0406693i
$679$	−13.3741	−	23.7314i	−0.513251	−	0.910727i
$680$	−2.53862			−0.0973516
$681$	14.7719	−	16.8324i	0.566059	−	0.645019i
$682$	3.69665	+	6.40278i	0.141552	+	0.245175i
$683$	7.72976	+	13.3883i	0.295771	+	0.512291i	0.975164	−	0.221484i	$-0.0710901\pi$
$683$	7.72976	+	13.3883i	0.295771	+	0.512291i	−0.679393	+	0.733775i	$0.737757\pi$
$684$	9.56701	+	8.91473i	0.365804	+	0.340863i
$685$	10.4283			0.398447
$686$	−15.7422	−	9.75611i	−0.601042	−	0.372490i
$687$	25.0233	+	4.98639i	0.954699	+	0.190243i
$688$	2.98401	−	5.16846i	0.113764	−	0.197046i
$689$	0.988221	−	0.570550i	0.0376482	−	0.0217362i
$690$	3.69705	+	10.9035i	0.140744	+	0.415087i
$691$	4.28039	−	7.41385i	0.162834	−	0.282036i	−0.773050	−	0.634345i	$-0.781270\pi$
$691$	4.28039	−	7.41385i	0.162834	−	0.282036i	0.935884	+	0.352309i	$0.114603\pi$
$692$	−14.0072			−0.532472
$693$	−0.683023	−	5.67363i	−0.0259459	−	0.215523i
$694$		−	27.6793i		−	1.05069i
$695$	−13.6831	−	7.89993i	−0.519029	−	0.299661i
$696$	−2.92122	−	8.61536i	−0.110729	−	0.326565i
$697$	−9.36001	+	5.40401i	−0.354536	+	0.204691i
$698$	11.1424	−	19.2992i	0.421746	−	0.730485i
$699$	0.743249	−	3.72986i	0.0281122	−	0.141076i
$700$	0.0428407	−	4.11786i	0.00161923	−	0.155640i
$701$		−	19.8926i		−	0.751334i	−0.926755	−	0.375667i	$-0.877414\pi$
$701$		−	19.8926i		−	0.751334i	0.926755	−	0.375667i	$-0.122586\pi$
$702$	−9.78662	−	19.8970i	−0.369372	−	0.750964i
$703$	17.6851	+	21.4075i	0.667008	+	0.807401i
$704$	0.623513	−	0.359985i	0.0234995	−	0.0135675i
$705$	−28.6964	+	32.6993i	−1.08077	+	1.23153i
$706$		−	11.7284i		−	0.441404i
$707$	−0.621433	+	1.05095i	−0.0233714	+	0.0395250i
$708$	−0.145910	−	0.0290754i	−0.00548363	−	0.00109272i
$709$	−7.78002	+	13.4754i	−0.292185	+	0.506079i	−0.974326	−	0.225141i	$-0.927716\pi$
$709$	−7.78002	+	13.4754i	−0.292185	+	0.506079i	0.682141	+	0.731221i	$0.261049\pi$
$710$	−0.283941	+	0.163933i	−0.0106561	+	0.00615230i
$711$	−26.6379	+	3.48832i	−0.998998	+	0.130822i
$712$	−6.60356	+	11.4377i	−0.247479	+	0.428646i
$713$	−36.7839			−1.37757
$714$	−4.18393	+	4.66868i	−0.156580	+	0.174721i
$715$		−	5.70125i		−	0.213215i
$716$	6.65939	−	11.5344i	0.248873	−	0.431061i
$717$	−29.8182	+	10.1105i	−1.11358	+	0.377583i
$718$	−12.0582	+	6.96182i	−0.450009	+	0.259813i
$719$	41.9724	+	24.2328i	1.56531	+	0.903731i	0.996704	+	0.0811195i	$0.0258495\pi$
$719$	41.9724	+	24.2328i	1.56531	+	0.903731i	0.568604	+	0.822612i	$0.307484\pi$
$720$	−2.13394	+	5.14178i	−0.0795271	+	0.191623i
$721$	5.68419	+	0.0591363i	0.211690	+	0.00220235i
$722$	−17.9517	+	6.22384i	−0.668093	+	0.231627i
$723$	−5.27830	−	4.63216i	−0.196302	−	0.172272i
$724$	−1.97330	+	1.13928i	−0.0733370	+	0.0423412i
$725$	−4.08753	−	7.07980i	−0.151807	−	0.262937i
$726$	−11.9749	+	13.6453i	−0.444432	+	0.506426i
$727$	−26.8966			−0.997538			−0.498769	−	0.866735i	$-0.666214\pi$
$727$	−26.8966			−0.997538			−0.498769	+	0.866735i	$0.666214\pi$
$728$	−5.54310	−	9.83583i	−0.205441	−	0.364540i
$729$	10.2810	+	24.9660i	0.380778	+	0.924667i
$730$	21.0925	+	12.1778i	0.780668	+	0.450719i
$731$	−7.07063	+	4.08223i	−0.261517	+	0.150987i
$732$	1.27864	+	3.77100i	0.0472597	+	0.139380i
$733$	13.2848	−	23.0099i	0.490685	−	0.849891i	−0.509258	−	0.860614i	$-0.670080\pi$
$733$	13.2848	−	23.0099i	0.490685	−	0.849891i	0.999943	+	0.0107229i	$0.00341327\pi$
$734$	−26.6203			−0.982572
$735$	16.5980	+	15.1889i	0.612226	+	0.560251i
$736$			3.58207i			0.132037i
$737$	1.58727	−	2.74924i	0.0584680	−	0.101270i
$738$	3.07747	+	23.5006i	0.113283	+	0.865067i
$739$	−6.46171	−	11.1920i	−0.237698	−	0.411705i	0.722356	−	0.691522i	$-0.243059\pi$
$739$	−6.46171	−	11.1920i	−0.237698	−	0.411705i	−0.960053	+	0.279817i	$0.909726\pi$
$740$	−5.91064	+	10.2375i	−0.217279	+	0.376339i
$741$	32.2032	+	0.960827i	1.18301	+	0.0352969i
$742$	−0.616349	+	0.347350i	−0.0226269	+	0.0127516i
$743$	27.6849			1.01566			0.507831	−	0.861457i	$-0.330448\pi$
$743$	27.6849			1.01566			0.507831	+	0.861457i	$0.330448\pi$
$744$	−13.3684	−	11.7319i	−0.490108	−	0.430111i
$745$	16.1264	+	27.9318i	0.590826	+	1.02334i
$746$	−30.0142	+	17.3287i	−1.09890	+	0.634450i
$747$	−26.5767	−	34.6847i	−0.972389	−	1.26905i
$748$	−0.984944			−0.0360131
$749$	0.235869	−	22.6717i	0.00861845	−	0.828407i
$750$	−4.11830	+	20.6670i	−0.150379	+	0.754651i
$751$	−20.3721	−	11.7618i	−0.743388	−	0.429195i	0.0799119	−	0.996802i	$-0.474536\pi$
$751$	−20.3721	−	11.7618i	−0.743388	−	0.429195i	−0.823300	+	0.567607i	$0.807869\pi$
$752$	−11.7223	+	6.76788i	−0.427469	+	0.246799i
$753$	7.27137	−	2.46551i	0.264984	−	0.0898483i
$754$	−19.4102	−	11.2065i	−0.706877	−	0.408115i
$755$	−20.2332			−0.736363
$756$	5.93909	+	12.3987i	0.216002	+	0.450936i
$757$	−31.4072			−1.14151			−0.570757	−	0.821119i	$-0.693350\pi$
$757$	−31.4072			−1.14151			−0.570757	+	0.821119i	$0.693350\pi$
$758$	−8.58107	−	4.95428i	−0.311679	−	0.179948i
$759$	1.43440	+	4.23037i	0.0520653	+	0.153553i
$760$	−5.15164	−	6.23597i	−0.186870	−	0.226202i
$761$	−4.12237	−	2.38005i	−0.149436	−	0.0862768i	0.423418	−	0.905935i	$-0.360830\pi$
$761$	−4.12237	−	2.38005i	−0.149436	−	0.0862768i	−0.572854	+	0.819658i	$0.694164\pi$
$762$	1.11422	−	5.59153i	0.0403640	−	0.202560i
$763$	2.60641	−	4.40789i	0.0943583	−	0.159576i
$764$		−	10.9867i		−	0.397485i
$765$	6.04525	−	4.63209i	0.218566	−	0.167473i
$766$	−14.1663	−	24.5367i	−0.511848	−	0.886547i
$767$	−0.317442	+	0.183275i	−0.0114622	+	0.00661769i
$768$	−1.14247	+	1.30183i	−0.0412253	+	0.0469758i
$769$	25.7360			0.928065			0.464032	−	0.885818i	$-0.346402\pi$
$769$	25.7360			0.928065			0.464032	+	0.885818i	$0.346402\pi$
$770$	−0.0367728	+	3.53461i	−0.00132520	+	0.127378i
$771$	7.53643	+	1.50178i	0.271418	+	0.0540854i
$772$	7.11407	+	4.10731i	0.256041	+	0.147825i
$773$	16.0088	+	27.7281i	0.575798	+	0.997311i	0.995954	+	0.0898594i	$0.0286418\pi$
$773$	16.0088	+	27.7281i	0.575798	+	0.997311i	−0.420157	+	0.907452i	$0.638025\pi$
$774$	2.32475	+	17.7525i	0.0835614	+	0.638101i
$775$	−13.8420	−	7.99170i	−0.497220	−	0.287070i
$776$			10.2959i			0.369603i
$777$	9.08605	+	27.7426i	0.325960	+	0.995262i
$778$		−	18.1657i		−	0.651271i
$779$	−32.2690	−	12.0259i	−1.15616	−	0.430874i
$780$	4.40428	+	12.9893i	0.157698	+	0.465090i
$781$	−0.110164	+	0.0636035i	−0.00394199	+	0.00227591i
$782$	2.45020	−	4.24387i	0.0876189	−	0.151760i
$783$	22.6763	+	15.1857i	0.810387	+	0.542692i
$784$	3.37312	+	6.13368i	0.120469	+	0.219060i
$785$			36.5390i			1.30413i
$786$	10.2068	+	8.95731i	0.364064	+	0.319497i
$787$	−14.5646	+	8.40889i	−0.519173	+	0.299745i	−0.736596	−	0.676333i	$-0.763568\pi$
$787$	−14.5646	+	8.40889i	−0.519173	+	0.299745i	0.217423	+	0.976077i	$0.430235\pi$
$788$	−20.0436	+	11.5722i	−0.714025	+	0.412243i
$789$	2.25325	+	1.97742i	0.0802178	+	0.0703979i
$790$	16.6177			0.591232
$791$	−7.21095	+	4.06381i	−0.256392	+	0.144493i
$792$	−0.827934	+	1.99493i	−0.0294194	+	0.0708868i
$793$	8.49595	+	4.90514i	0.301700	+	0.174187i
$794$	−3.61484	−	6.26109i	−0.128286	−	0.222198i
$795$	0.813953	−	0.275988i	0.0288679	−	0.00978828i
$796$	6.75007	−	11.6915i	0.239250	−	0.414393i
$797$	−12.8148			−0.453923			−0.226962	−	0.973904i	$-0.572879\pi$
$797$	−12.8148			−0.453923			−0.226962	+	0.973904i	$0.572879\pi$
$798$	−19.9588	−	0.803394i	−0.706535	−	0.0284398i
$799$	18.5174			0.655097
$800$	−0.778244	+	1.34796i	−0.0275151	+	0.0476575i
$801$	−5.14462	−	39.2859i	−0.181776	−	1.38810i
$802$	7.23147	+	12.5253i	0.255352	+	0.442283i
$803$	8.18355	+	4.72478i	0.288791	+	0.166734i
$804$	−1.49250	+	7.48983i	−0.0526363	+	0.264146i
$805$	−15.1382	−	8.95131i	−0.533552	−	0.315492i
$806$	−43.8205			−1.54351
$807$	−26.6955	+	30.4193i	−0.939725	+	1.07081i
$808$	0.399644	−	0.230734i	0.0140594	−	0.00811721i
$809$	−20.0742	+	11.5899i	−0.705773	+	0.407478i	−0.809494	−	0.587128i	$-0.800258\pi$
$809$	−20.0742	+	11.5899i	−0.705773	+	0.407478i	0.103721	+	0.994606i	$0.466925\pi$
$810$	−4.30036	−	16.1379i	−0.151099	−	0.567027i
$811$		−	26.4068i		−	0.927269i	−0.886027	−	0.463635i	$-0.846545\pi$
$811$		−	26.4068i		−	0.927269i	0.886027	−	0.463635i	$-0.153455\pi$
$812$	11.9615	+	7.07288i	0.419765	+	0.248209i
$813$	−52.9156	−	10.5445i	−1.85583	−	0.369811i
$814$	−2.29324	+	3.97200i	−0.0803778	+	0.139219i
$815$	−22.5624	+	13.0264i	−0.790328	+	0.456296i
$816$	2.24402	−	0.760881i	0.0785563	−	0.0266362i
$817$	−24.3763	−	9.08449i	−0.852817	−	0.317826i
$818$			29.1870i			1.02050i
$819$	31.1468	+	13.3080i	1.08836	+	0.465020i
$820$		−	14.6605i		−	0.511968i
$821$	29.1275	+	16.8168i	1.01656	+	0.586909i	0.913105	−	0.407725i	$-0.133678\pi$
$821$	29.1275	+	16.8168i	1.01656	+	0.586909i	0.103452	+	0.994634i	$0.467011\pi$
$822$	−9.21815	+	3.12561i	−0.321520	+	0.109018i
$823$	3.24603	+	5.62230i	0.113150	+	0.195981i	0.917039	−	0.398799i	$-0.130573\pi$
$823$	3.24603	+	5.62230i	0.113150	+	0.195981i	−0.803889	+	0.594779i	$0.797239\pi$
$824$	−1.86069	−	1.07427i	−0.0648201	−	0.0374239i
$825$	−0.379321	+	1.90356i	−0.0132063	+	0.0662733i
$826$	0.197987	−	0.111578i	0.00688885	−	0.00388229i
$827$	−40.1419			−1.39587			−0.697935	−	0.716161i	$-0.745897\pi$
$827$	−40.1419			−1.39587			−0.697935	+	0.716161i	$0.745897\pi$
$828$	−6.53602	−	8.53004i	−0.227142	−	0.296439i
$829$	−34.6064	+	19.9800i	−1.20193	+	0.693935i	−0.960984	−	0.276604i	$-0.910791\pi$
$829$	−34.6064	+	19.9800i	−1.20193	+	0.693935i	−0.240946	+	0.970539i	$0.577458\pi$
$830$	13.5143	+	23.4074i	0.469087	+	0.812482i
$831$	−6.71884	+	7.65606i	−0.233074	+	0.265586i
$832$			4.26731i			0.147942i
$833$	0.199234	−	9.57416i	0.00690304	−	0.331725i
$834$	14.4630	+	2.88203i	0.500812	+	0.0997965i
$835$	−35.2215	−	20.3351i	−1.21889	−	0.703727i
$836$	−1.99876	−	2.41946i	−0.0691284	−	0.0836787i
$837$	53.2408	+	3.54472i	1.84027	+	0.122523i
$838$	17.3095	+	9.99367i	0.597948	+	0.345226i
$839$	20.5391			0.709087			0.354544	−	0.935039i	$-0.384636\pi$
$839$	20.5391			0.709087			0.354544	+	0.935039i	$0.384636\pi$
$840$	−2.64674	−	8.08137i	−0.0913214	−	0.278834i
$841$	−1.41400			−0.0487585
$842$	−9.78969	−	5.65208i	−0.337375	−	0.194784i
$843$	0.726345	+	2.14216i	0.0250166	+	0.0737799i
$844$	−23.0683	+	13.3185i	−0.794045	+	0.458442i
$845$	8.37267	+	4.83396i	0.288029	+	0.166293i
$846$	15.5655	−	37.5055i	0.535153	−	1.28947i
$847$	0.288496	−	27.7303i	0.00991285	−	0.952825i
$848$	0.267405			0.00918272
$849$	−18.4765	+	21.0539i	−0.634113	+	0.722567i
$850$	1.84405	−	1.06466i	0.0632505	−	0.0365177i
$851$	−11.4095	−	19.7619i	−0.391114	−	0.677429i
$852$	0.201855	−	0.230012i	0.00691545	−	0.00788009i
$853$	19.5417			0.669095			0.334547	−	0.942379i	$-0.391417\pi$
$853$	19.5417			0.669095			0.334547	+	0.942379i	$0.391417\pi$
$854$	−5.23560	−	3.09584i	−0.179159	−	0.105938i
$855$	23.6461	+	5.44987i	0.808680	+	0.186382i
$856$	−4.28479	+	7.42147i	−0.146451	+	0.253660i
$857$	−9.40247	−	16.2856i	−0.321182	−	0.556304i	0.659550	−	0.751661i	$-0.270747\pi$
$857$	−9.40247	−	16.2856i	−0.321182	−	0.556304i	−0.980732	+	0.195357i	$0.937414\pi$
$858$	1.70879	+	5.03963i	0.0583372	+	0.172050i
$859$	6.20873	−	10.7538i	0.211839	−	0.366916i	−0.740451	−	0.672110i	$-0.765388\pi$
$859$	6.20873	−	10.7538i	0.211839	−	0.366916i	0.952290	+	0.305194i	$0.0987214\pi$
$860$		−	11.0747i		−	0.377644i
$861$	−26.9616	−	24.1622i	−0.918850	−	0.823446i
$862$	26.3082			0.896060
$863$	−5.22627	+	9.05217i	−0.177904	+	0.308139i	−0.941163	−	0.337954i	$-0.890265\pi$
$863$	−5.22627	+	9.05217i	−0.177904	+	0.308139i	0.763258	+	0.646094i	$0.223598\pi$
$864$	0.345190	−	5.18467i	0.0117436	−	0.176386i
$865$	−22.5103	+	12.9963i	−0.765373	+	0.441888i
$866$	−1.48063	−	0.854842i	−0.0503139	−	0.0290487i
$867$	25.6981	+	5.12084i	0.872752	+	0.173913i
$868$	27.1674	+	0.282640i	0.922123	+	0.00959343i
$869$	6.44741			0.218713
$870$	−12.6882	−	11.1350i	−0.430170	−	0.377511i
$871$	9.40787	+	16.2949i	0.318773	+	0.552132i
$872$	−1.67618	+	0.967745i	−0.0567627	+	0.0327720i
$873$	−18.7865	−	24.5179i	−0.635826	−	0.829805i
$874$	15.3970	−	2.59335i	0.520812	−	0.0877213i
$875$	−15.8041	−	28.0433i	−0.534277	−	0.948036i
$876$	−22.2947	−	4.44265i	−0.753268	−	0.150103i
$877$	−21.0446	−	12.1501i	−0.710624	−	0.410279i	0.100668	−	0.994920i	$-0.467902\pi$
$877$	−21.0446	−	12.1501i	−0.710624	−	0.410279i	−0.811292	+	0.584641i	$0.801235\pi$
$878$	−24.5129	+	14.1525i	−0.827270	+	0.477625i
$879$	−7.72503	−	22.7829i	−0.260559	−	0.768449i
$880$	0.668014	−	1.15703i	0.0225188	−	0.0390036i
$881$			58.9325i			1.98549i	0.120250	+	0.992744i	$0.461630\pi$
$881$			58.9325i			1.98549i	−0.120250	+	0.992744i	$0.538370\pi$
$882$	−19.2243	−	8.45148i	−0.647315	−	0.284576i
$883$	−24.6618			−0.829934			−0.414967	−	0.909836i	$-0.636207\pi$
$883$	−24.6618			−0.829934			−0.414967	+	0.909836i	$0.636207\pi$
$884$	2.91891	−	5.05570i	0.0981736	−	0.170042i
$885$	−0.261463	+	0.0886544i	−0.00878897	+	0.00298009i
$886$	−11.3257	+	6.53887i	−0.380493	+	0.219678i
$887$	25.0920	−	43.4606i	0.842507	−	1.45927i	−0.0452609	−	0.998975i	$-0.514412\pi$
$887$	25.0920	−	43.4606i	0.842507	−	1.45927i	0.887768	−	0.460291i	$-0.152255\pi$
$888$	2.15630	−	10.8210i	0.0723608	−	0.363130i
$889$	4.27587	+	7.58722i	0.143408	+	0.254467i
$890$			24.5080i			0.821511i
$891$	−1.66847	−	6.26124i	−0.0558960	−	0.209760i
$892$	17.4318	−	10.0643i	0.583660	−	0.336976i
$893$	37.5775	+	45.4868i	1.25748	+	1.52216i
$894$	−22.6268	−	19.8569i	−0.756752	−	0.664114i
$895$		−	24.7153i		−	0.826140i
$896$	0.0275240	−	2.64561i	0.000919511	−	0.0883836i
$897$	−25.9653	−	5.17410i	−0.866956	−	0.172758i
$898$	4.48099	−	7.76131i	0.149533	−	0.258998i
$899$	46.7087	−	26.9673i	1.55782	−	0.899410i
$900$	−0.606306	−	4.62994i	−0.0202102	−	0.154331i
$901$	−0.316808	−	0.182909i	−0.0105544	−	0.00609360i
$902$		−	5.68806i		−	0.189392i
$903$	−20.3670	−	18.2523i	−0.677773	−	0.607400i
$904$	3.12850			0.104052
$905$	−2.11414	+	3.66179i	−0.0702762	+	0.121722i
$906$	17.8852	−	6.06435i	0.594196	−	0.201475i
$907$	−3.88536	+	2.24321i	−0.129011	+	0.0744846i	−0.563117	−	0.826377i	$-0.690398\pi$
$907$	−3.88536	+	2.24321i	−0.129011	+	0.0744846i	0.434106	+	0.900862i	$0.357065\pi$
$908$	6.46489	−	11.1975i	0.214545	−	0.371603i
$909$	−0.530668	+	1.27866i	−0.0176012	+	0.0424105i
$910$	−18.0341	−	10.6637i	−0.597825	−	0.353497i
$911$	36.6425			1.21402			0.607009	−	0.794695i	$-0.292369\pi$
$911$	36.6425			1.21402			0.607009	+	0.794695i	$0.292369\pi$
$912$	6.42286	+	3.96823i	0.212682	+	0.131401i
$913$	5.24332	+	9.08169i	0.173528	+	0.300560i
$914$	4.07991	+	7.06661i	0.134951	+	0.233743i
$915$	5.55371	+	4.87385i	0.183600	+	0.161124i
$916$	14.7313			0.486735
$917$	−20.7424	−	0.215797i	−0.684975	−	0.00712623i
$918$	−3.95537	+	5.90644i	−0.130547	+	0.194941i
$919$	−21.2159	+	36.7471i	−0.699849	+	1.21217i	0.268670	+	0.963232i	$0.413416\pi$
$919$	−21.2159	+	36.7471i	−0.699849	+	1.21217i	−0.968519	+	0.248941i	$0.919917\pi$
$920$	3.32357	+	5.75659i	0.109575	+	0.189789i
$921$	25.4083	−	8.61522i	0.837232	−	0.283881i
$922$	27.5415	+	15.9011i	0.907032	+	0.523675i
$923$		−	0.753963i		−	0.0248170i
$924$	−1.02690	−	3.13544i	−0.0337824	−	0.103148i
$925$		−	9.91539i		−	0.326016i
$926$	1.51505	−	2.62414i	0.0497875	−	0.0862344i
$927$	6.39105	−	0.836929i	0.209910	−	0.0274883i
$928$	−2.62612	−	4.54857i	−0.0862066	−	0.149314i
$929$	42.0538	+	24.2798i	1.37974	+	0.796594i	0.992128	−	0.125228i	$-0.0399662\pi$
$929$	42.0538	+	24.2798i	1.37974	+	0.796594i	0.387613	+	0.921822i	$0.373300\pi$
$930$	−32.3690	−	6.45015i	−1.06142	−	0.211509i
$931$	23.9227	−	18.9395i	0.784034	−	0.620718i
$932$		−	2.19578i		−	0.0719250i
$933$	17.3554	+	15.2308i	0.568191	+	0.498635i
$934$	−22.8669	+	13.2022i	−0.748227	+	0.431989i
$935$	−1.58286	+	0.913866i	−0.0517651	+	0.0298866i
$936$	−7.78634	−	10.1618i	−0.254504	−	0.332149i
$937$	26.9977			0.881977			0.440988	−	0.897513i	$-0.354628\pi$
$937$	26.9977			0.881977			0.440988	+	0.897513i	$0.354628\pi$
$938$	−5.72750	−	10.1630i	−0.187010	−	0.331835i
$939$	−17.4242	−	3.47212i	−0.568618	−	0.113308i
$940$	−12.5589	+	21.7527i	−0.409628	+	0.709496i
$941$	15.3674	+	26.6171i	0.500962	+	0.867692i	0.999999	+	0.00111138i	$0.000353762\pi$
$941$	15.3674	+	26.6171i	0.500962	+	0.867692i	−0.499037	+	0.866581i	$0.666313\pi$
$942$	−10.9515	−	32.2987i	−0.356821	−	1.05235i
$943$	24.5083	+	14.1499i	0.798101	+	0.460784i
$944$	−0.0858974			−0.00279572
$945$	21.0484	+	14.4149i	0.684704	+	0.468917i
$946$		−	4.29681i		−	0.139701i
$947$	−25.2237	−	14.5629i	−0.819659	−	0.473231i	0.0306396	−	0.999530i	$-0.490246\pi$
$947$	−25.2237	−	14.5629i	−0.819659	−	0.473231i	−0.850299	+	0.526300i	$0.823579\pi$
$948$	−14.6893	+	4.98070i	−0.477085	+	0.161766i
$949$	−48.5044	+	28.0040i	−1.57452	+	0.909050i
$950$	6.35744	+	2.36928i	0.206263	+	0.0768695i
$951$	43.3250	+	8.63335i	1.40491	+	0.279956i
$952$	−1.84225	+	3.11556i	−0.0597076	+	0.100976i
$953$	7.19006			0.232909			0.116455	−	0.993196i	$-0.462847\pi$
$953$	7.19006			0.232909			0.116455	+	0.993196i	$0.462847\pi$
$954$	−0.636775	+	0.487920i	−0.0206164	+	0.0157970i
$955$	−10.1939	−	17.6563i	−0.329865	−	0.571344i
$956$	−15.7428	+	9.08912i	−0.509159	+	0.293963i
$957$	−4.92282	−	4.32019i	−0.159132	−	0.139652i
$958$			23.0725i			0.745439i
$959$	7.56774	−	12.7984i	0.244375	−	0.413281i
$960$	−0.628126	+	3.15214i	−0.0202727	+	0.101735i
$961$	37.2249	−	64.4755i	1.20080	−	2.07985i
$962$	−13.5921	−	23.5423i	−0.438228	−	0.759034i
$963$	−3.33814	−	25.4911i	−0.107570	−	0.821438i
$964$	−3.51132	−	2.02726i	−0.113092	−	0.0652936i
$965$	15.2436			0.490710
$966$	16.0644	+	3.37526i	0.516862	+	0.108597i
$967$	−44.7084			−1.43773			−0.718863	−	0.695152i	$-0.755337\pi$
$967$	−44.7084			−1.43773			−0.718863	+	0.695152i	$0.755337\pi$
$968$	−5.24082	+	9.07737i	−0.168446	+	0.291758i
$969$	−4.89516	−	9.09471i	−0.157255	−	0.292164i
$970$	9.55294	+	16.5462i	0.306726	+	0.531266i
$971$	18.4494	−	31.9553i	0.592069	−	1.02549i	−0.401885	−	0.915690i	$-0.631645\pi$
$971$	18.4494	−	31.9553i	0.592069	−	1.02549i	0.993953	−	0.109803i	$-0.0350219\pi$
$972$	8.63820	+	12.9762i	0.277070	+	0.416212i
$973$	−19.6250	+	11.0599i	−0.629148	+	0.354564i
$974$			5.83099i			0.186837i
$975$	−8.64680	−	7.58830i	−0.276919	−	0.243020i
$976$	1.14947	+	1.99094i	0.0367936	+	0.0637284i
$977$	0.821575	+	1.42301i	0.0262845	+	0.0455261i	0.878868	−	0.477064i	$-0.158299\pi$
$977$	0.821575	+	1.42301i	0.0262845	+	0.0455261i	−0.852584	+	0.522590i	$0.824966\pi$
$978$	16.0398	−	18.2772i	0.512896	−	0.584441i
$979$			9.50873i			0.303900i
$980$	11.1118	+	6.72748i	0.354955	+	0.214902i
$981$	2.22573	−	5.36295i	0.0710620	−	0.171226i
$982$	1.84694	+	1.06633i	0.0589381	+	0.0340279i
$983$	−13.8643	−	24.0137i	−0.442204	−	0.765919i	0.555649	−	0.831417i	$-0.312470\pi$
$983$	−13.8643	−	24.0137i	−0.442204	−	0.765919i	−0.997853	+	0.0654976i	$0.979137\pi$
$984$	4.39409	+	12.9592i	0.140078	+	0.413124i
$985$	−21.4742	+	37.1944i	−0.684224	+	1.18511i
$986$			7.18524i			0.228825i
$987$	19.3061	+	58.9477i	0.614519	+	1.87632i
$988$	18.3424	−	3.08945i	0.583550	−	0.0982884i
$989$	18.5138	+	10.6890i	0.588705	+	0.339889i
$990$	0.520429	+	3.97415i	0.0165403	+	0.126307i
$991$	2.24102	−	1.29386i	0.0711884	−	0.0411007i	−0.463983	−	0.885844i	$-0.653580\pi$
$991$	2.24102	−	1.29386i	0.0711884	−	0.0411007i	0.535172	+	0.844743i	$0.320247\pi$
$992$	−8.89311	−	5.13444i	−0.282357	−	0.163019i
$993$	−2.91810	+	14.6440i	−0.0926030	+	0.464712i
$994$	−0.00486303	+	0.467435i	−0.000154246	+	0.0148261i
$995$		−	25.0518i		−	0.794196i
$996$	−18.9617	−	16.6405i	−0.600823	−	0.527273i
$997$	23.0838	+	39.9823i	0.731071	+	1.26625i	0.956426	+	0.291976i	$0.0943126\pi$
$997$	23.0838	+	39.9823i	0.731071	+	1.26625i	−0.225355	+	0.974277i	$0.572354\pi$
$998$	3.91235	+	6.77639i	0.123843	+	0.214503i
$999$	14.6097	+	29.7028i	0.462231	+	0.939754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bf.a.569.12	yes	52
3.2	odd	2		798.2.bf.b.569.20	yes	52
7.4	even	3	inner	798.2.bf.a.683.7	yes	52
19.18	odd	2		798.2.bf.b.569.15	yes	52
21.11	odd	6		798.2.bf.b.683.15	yes	52
57.56	even	2	inner	798.2.bf.a.569.7	✓	52
133.18	odd	6		798.2.bf.b.683.20	yes	52
399.284	even	6	inner	798.2.bf.a.683.12	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bf.a.569.7	✓	52	57.56	even	2	inner
798.2.bf.a.569.12	yes	52	1.1	even	1	trivial
798.2.bf.a.683.7	yes	52	7.4	even	3	inner
798.2.bf.a.683.12	yes	52	399.284	even	6	inner
798.2.bf.b.569.15	yes	52	19.18	odd	2
798.2.bf.b.569.20	yes	52	3.2	odd	2
798.2.bf.b.683.15	yes	52	21.11	odd	6
798.2.bf.b.683.20	yes	52	133.18	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.556186 - 1.64032i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.60706 - 0.927835i) q^{5} +(1.69865 + 0.338490i) q^{6} +(-2.30493 + 1.29897i) q^{7} +1.00000 q^{8} +(-2.38131 + 1.82465i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.556186 - 1.64032i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.60706 - 0.927835i) q^{5} +(1.69865 + 0.338490i) q^{6} +(-2.30493 + 1.29897i) q^{7} +1.00000 q^{8} +(-2.38131 + 1.82465i) q^{9} +(1.60706 - 0.927835i) q^{10} +(0.623513 - 0.359985i) q^{11} +(-1.14247 + 1.30183i) q^{12} +4.26731i q^{13} +(0.0275240 - 2.64561i) q^{14} +(-0.628126 + 3.15214i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.18475 - 0.684017i) q^{17} +(-0.389534 - 2.97460i) q^{18} +(4.08447 + 1.52219i) q^{19} +1.85567i q^{20} +(3.41269 + 3.05835i) q^{21} +0.719971i q^{22} +(-3.10216 - 1.79104i) q^{23} +(-0.556186 - 1.64032i) q^{24} +(-0.778244 - 1.34796i) q^{25} +(-3.69560 - 2.13366i) q^{26} +(4.31746 + 2.89128i) q^{27} +(2.27740 + 1.34664i) q^{28} +5.25224 q^{29} +(-2.41577 - 2.12004i) q^{30} +(8.89311 - 5.13444i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.937281 - 0.822544i) q^{33} +1.36803i q^{34} +(4.90938 + 0.0510754i) q^{35} +(2.77085 + 1.14996i) q^{36} +(5.51689 + 3.18518i) q^{37} +(-3.36049 + 2.77616i) q^{38} +(6.99976 - 2.37342i) q^{39} +(-1.60706 - 0.927835i) q^{40} -7.90040 q^{41} +(-4.35496 + 1.42630i) q^{42} -5.96803 q^{43} +(-0.623513 - 0.359985i) q^{44} +(5.51988 - 0.722847i) q^{45} +(3.10216 - 1.79104i) q^{46} +(11.7223 + 6.76788i) q^{47} +(1.69865 + 0.338490i) q^{48} +(3.62537 - 5.98805i) q^{49} +1.55649 q^{50} +(-1.78095 - 1.56293i) q^{51} +(3.69560 - 2.13366i) q^{52} +(-0.133702 - 0.231579i) q^{53} +(-4.66265 + 2.29339i) q^{54} -1.33603 q^{55} +(-2.30493 + 1.29897i) q^{56} +(0.225160 - 7.54648i) q^{57} +(-2.62612 + 4.54857i) q^{58} +(0.0429487 + 0.0743893i) q^{59} +(3.04390 - 1.03210i) q^{60} +(1.14947 - 1.99094i) q^{61} +10.2689i q^{62} +(3.11860 - 7.29893i) q^{63} +1.00000 q^{64} +(3.95936 - 6.85781i) q^{65} +(1.18098 - 0.400438i) q^{66} +(3.81854 - 2.20464i) q^{67} +(-1.18475 - 0.684017i) q^{68} +(-1.21250 + 6.08470i) q^{69} +(-2.49892 + 4.22611i) q^{70} -0.176684 q^{71} +(-2.38131 + 1.82465i) q^{72} +(6.56246 + 11.3665i) q^{73} +(-5.51689 + 3.18518i) q^{74} +(-1.77824 + 2.02629i) q^{75} +(-0.723980 - 4.29835i) q^{76} +(-0.969542 + 1.63966i) q^{77} +(-1.44444 + 7.24868i) q^{78} +(7.75535 + 4.47755i) q^{79} +(1.60706 - 0.927835i) q^{80} +(2.34132 - 8.69012i) q^{81} +(3.95020 - 6.84195i) q^{82} +14.5654i q^{83} +(0.942266 - 4.48466i) q^{84} -2.53862 q^{85} +(2.98401 - 5.16846i) q^{86} +(-2.92122 - 8.61536i) q^{87} +(0.623513 - 0.359985i) q^{88} +(-6.60356 + 11.4377i) q^{89} +(-2.13394 + 5.14178i) q^{90} +(-5.54310 - 9.83583i) q^{91} +3.58207i q^{92} +(-13.3684 - 11.7319i) q^{93} +(-11.7223 + 6.76788i) q^{94} +(-5.15164 - 6.23597i) q^{95} +(-1.14247 + 1.30183i) q^{96} +10.2959i q^{97} +(3.37312 + 6.13368i) q^{98} +(-0.827934 + 1.99493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8}+O(q^{10}) \) 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8	\( 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8} + 4 q^{14} + 8 q^{15} - 26 q^{16} + 2 q^{19} + 2 q^{21} + 18 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} - 4 q^{30} - 26 q^{32} + 8 q^{33} + 2 q^{38} + q^{39} + 16 q^{41} + 11 q^{42} - 8 q^{43} + 14 q^{45} + 4 q^{49} - 36 q^{50} - 19 q^{51} - 24 q^{53} - 3 q^{54} + 32 q^{55} - 8 q^{56} - 4 q^{57} + 4 q^{58} + 32 q^{59} - 4 q^{60} - 20 q^{61} - 7 q^{63} + 52 q^{64} - 44 q^{65} + 8 q^{66} + 62 q^{69} - 24 q^{71} - 32 q^{73} + 16 q^{75} - 4 q^{76} - 2 q^{78} - 28 q^{81} - 8 q^{82} - 13 q^{84} + 32 q^{85} + 4 q^{86} + 34 q^{87} - 36 q^{89} - 28 q^{90} + 20 q^{93} + 30 q^{95} - 20 q^{98} - 116 q^{99}+O(q^{100}) \) 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8 + 4 * q^14 + 8 * q^15 - 26 * q^16 + 2 * q^19 + 2 * q^21 + 18 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 - 4 * q^30 - 26 * q^32 + 8 * q^33 + 2 * q^38 + q^39 + 16 * q^41 + 11 * q^42 - 8 * q^43 + 14 * q^45 + 4 * q^49 - 36 * q^50 - 19 * q^51 - 24 * q^53 - 3 * q^54 + 32 * q^55 - 8 * q^56 - 4 * q^57 + 4 * q^58 + 32 * q^59 - 4 * q^60 - 20 * q^61 - 7 * q^63 + 52 * q^64 - 44 * q^65 + 8 * q^66 + 62 * q^69 - 24 * q^71 - 32 * q^73 + 16 * q^75 - 4 * q^76 - 2 * q^78 - 28 * q^81 - 8 * q^82 - 13 * q^84 + 32 * q^85 + 4 * q^86 + 34 * q^87 - 36 * q^89 - 28 * q^90 + 20 * q^93 + 30 * q^95 - 20 * q^98 - 116 * q^99

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