LMFDB - Embedded newform 798.2.m.b.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(145,798)]

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([0, 5, 5]))

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

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

chi := DirichletCharacter("798.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.m (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Character	$\chi$	$=$	798.145
Dual form			798.2.m.b.787.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} -2.71950i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.09808 + 1.61185i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} -2.71950i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.09808 + 1.61185i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -2.71950 q^{10} +(0.624707 + 1.08202i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.99075 + 5.18013i) q^{13} +(1.61185 + 2.09808i) q^{14} +(-2.35515 - 1.35975i) q^{15} +1.00000 q^{16} +(-6.51112 - 3.75920i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-4.00092 - 1.72993i) q^{19} +2.71950i q^{20} +(0.346868 + 2.62291i) q^{21} +(1.08202 - 0.624707i) q^{22} +(-4.45865 - 7.72260i) q^{23} +(0.866025 + 0.500000i) q^{24} -2.39566 q^{25} +(5.18013 + 2.99075i) q^{26} -1.00000 q^{27} +(2.09808 - 1.61185i) q^{28} +(3.38830 + 1.95624i) q^{29} +(-1.35975 + 2.35515i) q^{30} +(3.59678 + 6.22980i) q^{31} -1.00000i q^{32} +1.24941 q^{33} +(-3.75920 + 6.51112i) q^{34} +(4.38343 + 5.70571i) q^{35} +(0.500000 + 0.866025i) q^{36} +(0.126554 + 0.0730658i) q^{37} +(-1.72993 + 4.00092i) q^{38} +(2.99075 + 5.18013i) q^{39} +2.71950 q^{40} +(4.19112 + 7.25923i) q^{41} +(2.62291 - 0.346868i) q^{42} +(-4.77135 - 8.26422i) q^{43} +(-0.624707 - 1.08202i) q^{44} +(-2.35515 + 1.35975i) q^{45} +(-7.72260 + 4.45865i) q^{46} +(1.87873 - 1.08468i) q^{47} +(0.500000 - 0.866025i) q^{48} +(1.80385 - 6.76359i) q^{49} +2.39566i q^{50} +(-6.51112 + 3.75920i) q^{51} +(2.99075 - 5.18013i) q^{52} -2.94488i q^{53} +1.00000i q^{54} +(2.94256 - 1.69889i) q^{55} +(-1.61185 - 2.09808i) q^{56} +(-3.49862 + 2.59993i) q^{57} +(1.95624 - 3.38830i) q^{58} +(1.96353 - 3.40093i) q^{59} +(2.35515 + 1.35975i) q^{60} +(-11.5009 + 6.64005i) q^{61} +(6.22980 - 3.59678i) q^{62} +(2.44495 + 1.01106i) q^{63} -1.00000 q^{64} +(14.0874 + 8.13334i) q^{65} -1.24941i q^{66} -6.35084i q^{67} +(6.51112 + 3.75920i) q^{68} -8.91729 q^{69} +(5.70571 - 4.38343i) q^{70} +(-9.48914 + 5.47856i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-2.83669 - 1.63777i) q^{73} +(0.0730658 - 0.126554i) q^{74} +(-1.19783 + 2.07470i) q^{75} +(4.00092 + 1.72993i) q^{76} +(-3.05475 - 1.26323i) q^{77} +(5.18013 - 2.99075i) q^{78} -16.2670i q^{79} -2.71950i q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.25923 - 4.19112i) q^{82} +2.14102i q^{83} +(-0.346868 - 2.62291i) q^{84} +(-10.2231 + 17.7070i) q^{85} +(-8.26422 + 4.77135i) q^{86} +(3.38830 - 1.95624i) q^{87} +(-1.08202 + 0.624707i) q^{88} +(3.88830 + 6.73473i) q^{89} +(1.35975 + 2.35515i) q^{90} +(-2.07479 - 15.6890i) q^{91} +(4.45865 + 7.72260i) q^{92} +7.19356 q^{93} +(-1.08468 - 1.87873i) q^{94} +(-4.70455 + 10.8805i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(4.59252 + 7.95448i) q^{97} +(-6.76359 - 1.80385i) q^{98} +(0.624707 - 1.08202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{3} - 28 q^{4} - 8 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 14 * q^3 - 28 * q^4 - 8 * q^7 - 14 * q^9	$ 28 q + 14 q^{3} - 28 q^{4} - 8 q^{7} - 14 q^{9} + 4 q^{10} - 14 q^{12} - 2 q^{13} - 4 q^{14} + 6 q^{15} + 28 q^{16} - 6 q^{17} + 2 q^{21} - 12 q^{22} - 12 q^{23} - 28 q^{25} + 24 q^{26} - 28 q^{27} + 8 q^{28} + 18 q^{29} + 2 q^{30} - 4 q^{31} + 4 q^{34} - 4 q^{35} + 14 q^{36} + 24 q^{37} + 18 q^{38} + 2 q^{39} - 4 q^{40} - 4 q^{41} + 4 q^{42} - 14 q^{43} + 6 q^{45} + 12 q^{46} + 24 q^{47} + 14 q^{48} - 24 q^{49} - 6 q^{51} + 2 q^{52} - 18 q^{55} + 4 q^{56} + 12 q^{57} - 2 q^{58} + 22 q^{59} - 6 q^{60} - 6 q^{61} + 12 q^{62} + 10 q^{63} - 28 q^{64} + 24 q^{65} + 6 q^{68} - 24 q^{69} + 30 q^{70} - 6 q^{71} - 42 q^{73} - 6 q^{74} - 14 q^{75} + 40 q^{77} + 24 q^{78} - 14 q^{81} - 6 q^{82} - 2 q^{84} + 28 q^{85} - 54 q^{86} + 18 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{90} - 22 q^{91} + 12 q^{92} - 8 q^{93} + 18 q^{94} + 20 q^{95} + 40 q^{97} + 32 q^{98}+O(q^{100}) $ 28 * q + 14 * q^3 - 28 * q^4 - 8 * q^7 - 14 * q^9 + 4 * q^10 - 14 * q^12 - 2 * q^13 - 4 * q^14 + 6 * q^15 + 28 * q^16 - 6 * q^17 + 2 * q^21 - 12 * q^22 - 12 * q^23 - 28 * q^25 + 24 * q^26 - 28 * q^27 + 8 * q^28 + 18 * q^29 + 2 * q^30 - 4 * q^31 + 4 * q^34 - 4 * q^35 + 14 * q^36 + 24 * q^37 + 18 * q^38 + 2 * q^39 - 4 * q^40 - 4 * q^41 + 4 * q^42 - 14 * q^43 + 6 * q^45 + 12 * q^46 + 24 * q^47 + 14 * q^48 - 24 * q^49 - 6 * q^51 + 2 * q^52 - 18 * q^55 + 4 * q^56 + 12 * q^57 - 2 * q^58 + 22 * q^59 - 6 * q^60 - 6 * q^61 + 12 * q^62 + 10 * q^63 - 28 * q^64 + 24 * q^65 + 6 * q^68 - 24 * q^69 + 30 * q^70 - 6 * q^71 - 42 * q^73 - 6 * q^74 - 14 * q^75 + 40 * q^77 + 24 * q^78 - 14 * q^81 - 6 * q^82 - 2 * q^84 + 28 * q^85 - 54 * q^86 + 18 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^90 - 22 * q^91 + 12 * q^92 - 8 * q^93 + 18 * q^94 + 20 * q^95 + 40 * q^97 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.00000			−0.500000
$5$		−	2.71950i		−	1.21620i	−0.793862	−	0.608098i	$-0.791933\pi$
$5$		−	2.71950i		−	1.21620i	0.793862	−	0.608098i	$-0.208067\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−2.09808	+	1.61185i	−0.792998	+	0.609224i
$7$	−2.09808	+	1.61185i	−0.792998	+	0.609224i
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.71950			−0.859980
$11$	0.624707	+	1.08202i	0.188356	+	0.326243i	0.944702	−	0.327929i	$-0.106351\pi$
$11$	0.624707	+	1.08202i	0.188356	+	0.326243i	−0.756346	+	0.654172i	$0.773017\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.99075	+	5.18013i	−0.829485	+	1.43671i	0.0689575	+	0.997620i	$0.478033\pi$
$13$	−2.99075	+	5.18013i	−0.829485	+	1.43671i	−0.898443	+	0.439091i	$0.855301\pi$
$14$	1.61185	+	2.09808i	0.430786	+	0.560735i
$15$	−2.35515	−	1.35975i	−0.608098	−	0.351085i
$16$	1.00000			0.250000
$17$	−6.51112	−	3.75920i	−1.57918	−	0.911740i	−0.994974	−	0.100134i	$-0.968073\pi$
$17$	−6.51112	−	3.75920i	−1.57918	−	0.911740i	−0.584205	−	0.811606i	$-0.698594\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−4.00092	−	1.72993i	−0.917873	−	0.396874i
$19$	−4.00092	−	1.72993i	−0.917873	−	0.396874i
$20$			2.71950i			0.608098i
$21$	0.346868	+	2.62291i	0.0756929	+	0.572367i
$22$	1.08202	−	0.624707i	0.230688	−	0.133188i
$23$	−4.45865	−	7.72260i	−0.929692	−	1.61027i	−0.783836	−	0.620968i	$-0.786740\pi$
$23$	−4.45865	−	7.72260i	−0.929692	−	1.61027i	−0.145856	−	0.989306i	$-0.546594\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−2.39566			−0.479132
$26$	5.18013	+	2.99075i	1.01591	+	0.586535i
$27$	−1.00000			−0.192450
$28$	2.09808	−	1.61185i	0.396499	−	0.304612i
$29$	3.38830	+	1.95624i	0.629192	+	0.363264i	0.780439	−	0.625232i	$-0.214995\pi$
$29$	3.38830	+	1.95624i	0.629192	+	0.363264i	−0.151247	+	0.988496i	$0.548329\pi$
$30$	−1.35975	+	2.35515i	−0.248255	+	0.429990i
$31$	3.59678	+	6.22980i	0.646000	+	1.11891i	0.984070	+	0.177784i	$0.0568929\pi$
$31$	3.59678	+	6.22980i	0.646000	+	1.11891i	−0.338069	+	0.941121i	$0.609774\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.24941			0.217495
$34$	−3.75920	+	6.51112i	−0.644697	+	1.11665i
$35$	4.38343	+	5.70571i	0.740935	+	0.964441i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	0.126554	+	0.0730658i	0.0208053	+	0.0120119i	0.510367	−	0.859957i	$-0.329510\pi$
$37$	0.126554	+	0.0730658i	0.0208053	+	0.0120119i	−0.489561	+	0.871969i	$0.662843\pi$
$38$	−1.72993	+	4.00092i	−0.280632	+	0.649034i
$39$	2.99075	+	5.18013i	0.478903	+	0.829485i
$40$	2.71950			0.429990
$41$	4.19112	+	7.25923i	0.654543	+	1.13370i	0.982008	+	0.188839i	$0.0604723\pi$
$41$	4.19112	+	7.25923i	0.654543	+	1.13370i	−0.327465	+	0.944863i	$0.606194\pi$
$42$	2.62291	−	0.346868i	0.404725	−	0.0535230i
$43$	−4.77135	−	8.26422i	−0.727624	−	1.26028i	−0.957885	−	0.287153i	$-0.907291\pi$
$43$	−4.77135	−	8.26422i	−0.727624	−	1.26028i	0.230261	−	0.973129i	$-0.426042\pi$
$44$	−0.624707	−	1.08202i	−0.0941781	−	0.163121i
$45$	−2.35515	+	1.35975i	−0.351085	+	0.202699i
$46$	−7.72260	+	4.45865i	−1.13864	+	0.657391i
$47$	1.87873	−	1.08468i	0.274041	−	0.158217i	−0.356682	−	0.934226i	$-0.616092\pi$
$47$	1.87873	−	1.08468i	0.274041	−	0.158217i	0.630722	+	0.776009i	$0.282759\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	1.80385	−	6.76359i	0.257693	−	0.966227i
$50$			2.39566i			0.338797i
$51$	−6.51112	+	3.75920i	−0.911740	+	0.526393i
$52$	2.99075	−	5.18013i	0.414743	−	0.718355i
$53$		−	2.94488i		−	0.404510i	−0.979333	−	0.202255i	$-0.935173\pi$
$53$		−	2.94488i		−	0.404510i	0.979333	−	0.202255i	$-0.0648269\pi$
$54$			1.00000i			0.136083i
$55$	2.94256	−	1.69889i	0.396775	−	0.229078i
$56$	−1.61185	−	2.09808i	−0.215393	−	0.280367i
$57$	−3.49862	+	2.59993i	−0.463404	+	0.344369i
$58$	1.95624	−	3.38830i	0.256867	−	0.444906i
$59$	1.96353	−	3.40093i	0.255630	−	0.442764i	−0.709437	−	0.704769i	$-0.751050\pi$
$59$	1.96353	−	3.40093i	0.255630	−	0.442764i	0.965066	+	0.262005i	$0.0843838\pi$
$60$	2.35515	+	1.35975i	0.304049	+	0.175543i
$61$	−11.5009	+	6.64005i	−1.47254	+	0.850172i	−0.999523	−	0.0308817i	$-0.990169\pi$
$61$	−11.5009	+	6.64005i	−1.47254	+	0.850172i	−0.473017	+	0.881053i	$0.656835\pi$
$62$	6.22980	−	3.59678i	0.791186	−	0.456791i
$63$	2.44495	+	1.01106i	0.308034	+	0.127382i
$64$	−1.00000			−0.125000
$65$	14.0874	+	8.13334i	1.74732	+	1.00882i
$66$		−	1.24941i		−	0.153792i
$67$		−	6.35084i		−	0.775878i	−0.921685	−	0.387939i	$-0.873187\pi$
$67$		−	6.35084i		−	0.775878i	0.921685	−	0.387939i	$-0.126813\pi$
$68$	6.51112	+	3.75920i	0.789590	+	0.455870i
$69$	−8.91729			−1.07352
$70$	5.70571	−	4.38343i	0.681963	−	0.523920i
$71$	−9.48914	+	5.47856i	−1.12615	+	0.650185i	−0.942965	−	0.332892i	$-0.891975\pi$
$71$	−9.48914	+	5.47856i	−1.12615	+	0.650185i	−0.183189	+	0.983078i	$0.558642\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−2.83669	−	1.63777i	−0.332010	−	0.191686i	0.324723	−	0.945809i	$-0.394729\pi$
$73$	−2.83669	−	1.63777i	−0.332010	−	0.191686i	−0.656733	+	0.754123i	$0.728062\pi$
$74$	0.0730658	−	0.126554i	0.00849373	−	0.0147116i
$75$	−1.19783	+	2.07470i	−0.138313	+	0.239566i
$76$	4.00092	+	1.72993i	0.458937	+	0.198437i
$77$	−3.05475	−	1.26323i	−0.348121	−	0.143959i
$78$	5.18013	−	2.99075i	0.586535	−	0.338636i
$79$		−	16.2670i		−	1.83018i	−0.403245	−	0.915092i	$-0.632118\pi$
$79$		−	16.2670i		−	1.83018i	0.403245	−	0.915092i	$-0.367882\pi$
$80$		−	2.71950i		−	0.304049i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	7.25923	−	4.19112i	0.801648	−	0.462832i
$83$			2.14102i			0.235007i	0.993072	+	0.117504i	$0.0374892\pi$
$83$			2.14102i			0.235007i	−0.993072	+	0.117504i	$0.962511\pi$
$84$	−0.346868	−	2.62291i	−0.0378464	−	0.286183i
$85$	−10.2231	+	17.7070i	−1.10885	+	1.92059i
$86$	−8.26422	+	4.77135i	−0.891154	+	0.514508i
$87$	3.38830	−	1.95624i	0.363264	−	0.209731i
$88$	−1.08202	+	0.624707i	−0.115344	+	0.0665940i
$89$	3.88830	+	6.73473i	0.412159	+	0.713880i	0.995126	−	0.0986158i	$-0.0314415\pi$
$89$	3.88830	+	6.73473i	0.412159	+	0.713880i	−0.582967	+	0.812496i	$0.698108\pi$
$90$	1.35975	+	2.35515i	0.143330	+	0.248255i
$91$	−2.07479	−	15.6890i	−0.217498	−	1.64465i
$92$	4.45865	+	7.72260i	0.464846	+	0.805137i
$93$	7.19356			0.745937
$94$	−1.08468	−	1.87873i	−0.111877	−	0.193776i
$95$	−4.70455	+	10.8805i	−0.482676	+	1.11631i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	4.59252	+	7.95448i	0.466300	+	0.807655i	0.999259	−	0.0384857i	$-0.0122534\pi$
$97$	4.59252	+	7.95448i	0.466300	+	0.807655i	−0.532959	+	0.846141i	$0.678920\pi$
$98$	−6.76359	−	1.80385i	−0.683226	−	0.182217i
$99$	0.624707	−	1.08202i	0.0627854	−	0.108748i
$100$	2.39566			0.239566
$101$		−	14.9009i		−	1.48269i	−0.671123	−	0.741346i	$-0.734188\pi$
$101$		−	14.9009i		−	1.48269i	0.671123	−	0.741346i	$-0.265812\pi$
$102$	3.75920	+	6.51112i	0.372216	+	0.644697i
$103$	1.77682	−	3.07754i	0.175075	−	0.303239i	−0.765112	−	0.643897i	$-0.777316\pi$
$103$	1.77682	−	3.07754i	0.175075	−	0.303239i	0.940187	+	0.340658i	$0.110650\pi$
$104$	−5.18013	−	2.99075i	−0.507954	−	0.293267i
$105$	7.13301	−	0.943307i	0.696110	−	0.0920574i
$106$	−2.94488			−0.286032
$107$	−5.20654	−	3.00600i	−0.503336	−	0.290601i	0.226754	−	0.973952i	$-0.427189\pi$
$107$	−5.20654	−	3.00600i	−0.503336	−	0.290601i	−0.730090	+	0.683351i	$0.760522\pi$
$108$	1.00000			0.0962250
$109$	6.53589	+	3.77350i	0.626025	+	0.361436i	0.779211	−	0.626762i	$-0.215620\pi$
$109$	6.53589	+	3.77350i	0.626025	+	0.361436i	−0.153186	+	0.988197i	$0.548953\pi$
$110$	−1.69889	−	2.94256i	−0.161983	−	0.280562i
$111$	0.126554	−	0.0730658i	0.0120119	−	0.00693510i
$112$	−2.09808	+	1.61185i	−0.198250	+	0.152306i
$113$		−	10.6689i		−	1.00364i	−0.864972	−	0.501821i	$-0.832664\pi$
$113$		−	10.6689i		−	1.00364i	0.864972	−	0.501821i	$-0.167336\pi$
$114$	2.59993	+	3.49862i	0.243506	+	0.327676i
$115$	−21.0016	+	12.1253i	−1.95841	+	1.13069i
$116$	−3.38830	−	1.95624i	−0.314596	−	0.181632i
$117$	5.98150			0.552990
$118$	−3.40093	−	1.96353i	−0.313081	−	0.180758i
$119$	19.7201	−	2.60789i	1.80774	−	0.239065i
$120$	1.35975	−	2.35515i	0.124127	−	0.214995i
$121$	4.71948	−	8.17438i	0.429044	−	0.743126i
$122$	6.64005	+	11.5009i	0.601162	+	1.04124i
$123$	8.38224			0.755801
$124$	−3.59678	−	6.22980i	−0.323000	−	0.559453i
$125$		−	7.08250i		−	0.633478i
$126$	1.01106	−	2.44495i	0.0900724	−	0.217813i
$127$	−1.76690	−	1.02012i	−0.156787	−	0.0905211i	0.419554	−	0.907731i	$-0.362187\pi$
$127$	−1.76690	−	1.02012i	−0.156787	−	0.0905211i	−0.576341	+	0.817209i	$0.695520\pi$
$128$			1.00000i			0.0883883i
$129$	−9.54270			−0.840188
$130$	8.13334	−	14.0874i	0.713341	−	1.23554i
$131$			7.61931i			0.665702i	0.942979	+	0.332851i	$0.108011\pi$
$131$			7.61931i			0.665702i	−0.942979	+	0.332851i	$0.891989\pi$
$132$	−1.24941			−0.108748
$133$	11.1826	−	2.81936i	0.969657	−	0.244470i
$134$	−6.35084			−0.548629
$135$			2.71950i			0.234057i
$136$	3.75920	−	6.51112i	0.322349	−	0.558324i
$137$	−13.1897			−1.12687			−0.563434	−	0.826161i	$-0.690520\pi$
$137$	−13.1897			−1.12687			−0.563434	+	0.826161i	$0.690520\pi$
$138$			8.91729i			0.759090i
$139$	−12.3146	−	7.10985i	−1.04451	−	0.603050i	−0.123405	−	0.992356i	$-0.539381\pi$
$139$	−12.3146	−	7.10985i	−1.04451	−	0.603050i	−0.921108	+	0.389306i	$0.872715\pi$
$140$	−4.38343	−	5.70571i	−0.370468	−	0.482221i
$141$		−	2.16937i		−	0.182694i
$142$	5.47856	+	9.48914i	0.459750	+	0.796311i
$143$	−7.47337			−0.624955
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	5.31998	−	9.21448i	0.441801	−	0.765221i
$146$	−1.63777	+	2.83669i	−0.135542	+	0.234766i
$147$	−4.95551	−	4.94398i	−0.408724	−	0.407772i
$148$	−0.126554	−	0.0730658i	−0.0104027	−	0.00600597i
$149$	6.05975			0.496434			0.248217	−	0.968704i	$-0.420155\pi$
$149$	6.05975			0.496434			0.248217	+	0.968704i	$0.420155\pi$
$150$	2.07470	+	1.19783i	0.169399	+	0.0978023i
$151$	−1.06939	+	0.617415i	−0.0870261	+	0.0502445i	−0.542882	−	0.839809i	$-0.682667\pi$
$151$	−1.06939	+	0.617415i	−0.0870261	+	0.0502445i	0.455855	+	0.890054i	$0.349333\pi$
$152$	1.72993	−	4.00092i	0.140316	−	0.324517i
$153$			7.51840i			0.607826i
$154$	−1.26323	+	3.05475i	−0.101794	+	0.246159i
$155$	16.9419	−	9.78142i	1.36081	−	0.785663i
$156$	−2.99075	−	5.18013i	−0.239452	−	0.414743i
$157$	11.7249	+	6.76935i	0.935745	+	0.540253i	0.888624	−	0.458636i	$-0.151662\pi$
$157$	11.7249	+	6.76935i	0.935745	+	0.540253i	0.0471213	+	0.998889i	$0.484995\pi$
$158$	−16.2670			−1.29414
$159$	−2.55034	−	1.47244i	−0.202255	−	0.116772i
$160$	−2.71950			−0.214995
$161$	21.8023	+	9.01592i	1.71826	+	0.710554i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	2.38467	−	4.13037i	0.186782	−	0.323516i	−0.757394	−	0.652959i	$-0.773528\pi$
$163$	2.38467	−	4.13037i	0.186782	−	0.323516i	0.944176	+	0.329443i	$0.106861\pi$
$164$	−4.19112	−	7.25923i	−0.327272	−	0.566851i
$165$		−	3.39778i		−	0.264517i
$166$	2.14102			0.166175
$167$	−5.68202	+	9.84154i	−0.439688	+	0.761562i	−0.997665	−	0.0682946i	$-0.978244\pi$
$167$	−5.68202	+	9.84154i	−0.439688	+	0.761562i	0.557977	+	0.829856i	$0.311578\pi$
$168$	−2.62291	+	0.346868i	−0.202362	+	0.0267615i
$169$	−11.3892	−	19.7267i	−0.876091	−	1.51743i
$170$	17.7070	+	10.2231i	1.35806	+	0.784078i
$171$	0.502292	+	4.32986i	0.0384113	+	0.331113i
$172$	4.77135	+	8.26422i	0.363812	+	0.630141i
$173$	5.50278			0.418368			0.209184	−	0.977876i	$-0.432919\pi$
$173$	5.50278			0.418368			0.209184	+	0.977876i	$0.432919\pi$
$174$	−1.95624	−	3.38830i	−0.148302	−	0.256867i
$175$	5.02627	−	3.86145i	0.379951	−	0.291898i
$176$	0.624707	+	1.08202i	0.0470891	+	0.0815607i
$177$	−1.96353	−	3.40093i	−0.147588	−	0.255630i
$178$	6.73473	−	3.88830i	0.504790	−	0.291440i
$179$	−7.06518	+	4.07908i	−0.528076	+	0.304885i	−0.740233	−	0.672351i	$-0.765285\pi$
$179$	−7.06518	+	4.07908i	−0.528076	+	0.304885i	0.212157	+	0.977236i	$0.431951\pi$
$180$	2.35515	−	1.35975i	0.175543	−	0.101350i
$181$	−0.0621379	+	0.107626i	−0.00461867	+	0.00799978i	−0.868326	−	0.495995i	$-0.834804\pi$
$181$	−0.0621379	+	0.107626i	−0.00461867	+	0.00799978i	0.863707	+	0.503995i	$0.168137\pi$
$182$	−15.6890	+	2.07479i	−1.16294	+	0.153794i
$183$			13.2801i			0.981694i
$184$	7.72260	−	4.45865i	0.569318	−	0.328696i
$185$	0.198702	−	0.344162i	0.0146089	−	0.0253033i
$186$		−	7.19356i		−	0.527457i
$187$		−	9.39359i		−	0.686927i
$188$	−1.87873	+	1.08468i	−0.137020	+	0.0791087i
$189$	2.09808	−	1.61185i	0.152613	−	0.117245i
$190$	10.8805	+	4.70455i	0.789353	+	0.341304i
$191$	2.14961	−	3.72323i	0.155540	−	0.269404i	−0.777715	−	0.628617i	$-0.783622\pi$
$191$	2.14961	−	3.72323i	0.155540	−	0.269404i	0.933256	+	0.359213i	$0.116955\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−8.77805	−	5.06801i	−0.631858	−	0.364803i	0.149614	−	0.988745i	$-0.452197\pi$
$193$	−8.77805	−	5.06801i	−0.631858	−	0.364803i	−0.781471	+	0.623941i	$0.785530\pi$
$194$	7.95448	−	4.59252i	0.571099	−	0.329724i
$195$	14.0874	−	8.13334i	1.00882	−	0.582440i
$196$	−1.80385	+	6.76359i	−0.128847	+	0.483113i
$197$	17.9757			1.28072			0.640359	−	0.768076i	$-0.278786\pi$
$197$	17.9757			1.28072			0.640359	+	0.768076i	$0.278786\pi$
$198$	−1.08202	−	0.624707i	−0.0768961	−	0.0443960i
$199$			10.5139i			0.745312i	0.927969	+	0.372656i	$0.121553\pi$
$199$			10.5139i			0.745312i	−0.927969	+	0.372656i	$0.878447\pi$
$200$		−	2.39566i		−	0.169399i
$201$	−5.49999	−	3.17542i	−0.387939	−	0.223977i
$202$	−14.9009			−1.04842
$203$	−10.2621	+	1.35711i	−0.720258	+	0.0952508i
$204$	6.51112	−	3.75920i	0.455870	−	0.263197i
$205$	19.7415	−	11.3977i	1.37880	−	0.796052i
$206$	−3.07754	−	1.77682i	−0.214423	−	0.123797i
$207$	−4.45865	+	7.72260i	−0.309897	+	0.536758i
$208$	−2.99075	+	5.18013i	−0.207371	+	0.359178i
$209$	−0.627571	−	5.40979i	−0.0434100	−	0.374203i
$210$	−0.943307	−	7.13301i	−0.0650944	−	0.492224i
$211$	−9.92216	+	5.72856i	−0.683070	+	0.394370i	−0.801011	−	0.598650i	$-0.795704\pi$
$211$	−9.92216	+	5.72856i	−0.683070	+	0.394370i	0.117941	+	0.993021i	$0.462371\pi$
$212$			2.94488i			0.202255i
$213$			10.9571i			0.750769i
$214$	−3.00600	+	5.20654i	−0.205486	+	0.355912i
$215$	−22.4745	+	12.9757i	−1.53275	+	0.884933i
$216$		−	1.00000i		−	0.0680414i
$217$	−17.5878	−	7.27312i	−1.19394	−	0.493732i
$218$	3.77350	−	6.53589i	0.255574	−	0.442666i
$219$	−2.83669	+	1.63777i	−0.191686	+	0.110670i
$220$	−2.94256	+	1.69889i	−0.198387	+	0.114539i
$221$	38.9463	−	22.4857i	2.61981	−	1.51255i
$222$	−0.0730658	−	0.126554i	−0.00490386	−	0.00849373i
$223$	−9.02437	−	15.6307i	−0.604317	−	1.04671i	−0.992159	−	0.124981i	$-0.960113\pi$
$223$	−9.02437	−	15.6307i	−0.604317	−	1.04671i	0.387843	−	0.921726i	$-0.373220\pi$
$224$	1.61185	+	2.09808i	0.107697	+	0.140184i
$225$	1.19783	+	2.07470i	0.0798553	+	0.138313i
$226$	−10.6689			−0.709682
$227$	−13.8476	−	23.9848i	−0.919098	−	1.59192i	−0.800788	−	0.598948i	$-0.795586\pi$
$227$	−13.8476	−	23.9848i	−0.919098	−	1.59192i	−0.118310	−	0.992977i	$-0.537748\pi$
$228$	3.49862	−	2.59993i	0.231702	−	0.172184i
$229$	−11.5882	−	6.69044i	−0.765768	−	0.442117i	0.0655946	−	0.997846i	$-0.479106\pi$
$229$	−11.5882	−	6.69044i	−0.765768	−	0.442117i	−0.831363	+	0.555730i	$0.812439\pi$
$230$	12.1253	+	21.0016i	0.799517	+	1.38480i
$231$	−2.62137	+	2.01387i	−0.172473	+	0.132503i
$232$	−1.95624	+	3.38830i	−0.128433	+	0.222453i
$233$	5.61103			0.367591			0.183795	−	0.982965i	$-0.441162\pi$
$233$	5.61103			0.367591			0.183795	+	0.982965i	$0.441162\pi$
$234$		−	5.98150i		−	0.391023i
$235$	−2.94979	−	5.10919i	−0.192423	−	0.333287i
$236$	−1.96353	+	3.40093i	−0.127815	+	0.221382i
$237$	−14.0877	−	8.13351i	−0.915092	−	0.528329i
$238$	−2.60789	−	19.7201i	−0.169045	−	1.27827i
$239$	18.7264			1.21131			0.605654	−	0.795728i	$-0.292912\pi$
$239$	18.7264			1.21131			0.605654	+	0.795728i	$0.292912\pi$
$240$	−2.35515	−	1.35975i	−0.152024	−	0.0877714i
$241$	−23.6719			−1.52484			−0.762421	−	0.647082i	$-0.775989\pi$
$241$	−23.6719			−1.52484			−0.762421	+	0.647082i	$0.775989\pi$
$242$	−8.17438	−	4.71948i	−0.525469	−	0.303380i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	11.5009	−	6.64005i	0.736270	−	0.425086i
$245$	−18.3935	−	4.90557i	−1.17512	−	0.313405i
$246$		−	8.38224i		−	0.534432i
$247$	20.9270	−	15.5515i	1.33155	−	0.989517i
$248$	−6.22980	+	3.59678i	−0.395593	+	0.228396i
$249$	1.85418	+	1.07051i	0.117504	+	0.0678408i
$250$	−7.08250			−0.447936
$251$	−13.7864	−	7.95959i	−0.870191	−	0.502405i	−0.00277914	−	0.999996i	$-0.500885\pi$
$251$	−13.7864	−	7.95959i	−0.870191	−	0.502405i	−0.867412	+	0.497591i	$0.834218\pi$
$252$	−2.44495	−	1.01106i	−0.154017	−	0.0636908i
$253$	5.57069	−	9.64873i	0.350227	−	0.606610i
$254$	−1.02012	+	1.76690i	−0.0640081	+	0.110865i
$255$	10.2231	+	17.7070i	0.640197	+	1.10885i
$256$	1.00000			0.0625000
$257$	−3.52645	−	6.10800i	−0.219974	−	0.381006i	0.734826	−	0.678256i	$-0.237264\pi$
$257$	−3.52645	−	6.10800i	−0.219974	−	0.381006i	−0.954800	+	0.297250i	$0.903931\pi$
$258$			9.54270i			0.594102i
$259$	−0.383291	+	0.0506885i	−0.0238165	+	0.00314963i
$260$	−14.0874	−	8.13334i	−0.873660	−	0.504408i
$261$		−	3.91248i		−	0.242176i
$262$	7.61931			0.470723
$263$	1.82702	−	3.16449i	0.112659	−	0.195131i	−0.804183	−	0.594382i	$-0.797397\pi$
$263$	1.82702	−	3.16449i	0.112659	−	0.195131i	0.916841	+	0.399251i	$0.130730\pi$
$264$			1.24941i			0.0768961i
$265$	−8.00858			−0.491963
$266$	−2.81936	−	11.1826i	−0.172866	−	0.685651i
$267$	7.77660			0.475920
$268$			6.35084i			0.387939i
$269$	−6.59387	+	11.4209i	−0.402036	+	0.696346i	−0.993971	−	0.109639i	$-0.965031\pi$
$269$	−6.59387	+	11.4209i	−0.402036	+	0.696346i	0.591936	+	0.805985i	$0.298364\pi$
$270$	2.71950			0.165503
$271$			29.6647i			1.80200i	0.433817	+	0.901001i	$0.357166\pi$
$271$			29.6647i			1.80200i	−0.433817	+	0.901001i	$0.642834\pi$
$272$	−6.51112	−	3.75920i	−0.394795	−	0.227935i
$273$	−14.6244	−	6.04766i	−0.885112	−	0.366021i
$274$			13.1897i			0.796817i
$275$	−1.49658	−	2.59216i	−0.0902474	−	0.156313i
$276$	8.91729			0.536758
$277$	13.7553	+	23.8249i	0.826476	+	1.43150i	0.900786	+	0.434263i	$0.142991\pi$
$277$	13.7553	+	23.8249i	0.826476	+	1.43150i	−0.0743106	+	0.997235i	$0.523676\pi$
$278$	−7.10985	+	12.3146i	−0.426421	+	0.738582i
$279$	3.59678	−	6.22980i	0.215333	−	0.372968i
$280$	−5.70571	+	4.38343i	−0.340981	+	0.261960i
$281$	−7.87266	−	4.54528i	−0.469644	−	0.271149i	0.246447	−	0.969156i	$-0.420737\pi$
$281$	−7.87266	−	4.54528i	−0.469644	−	0.271149i	−0.716091	+	0.698007i	$0.754070\pi$
$282$	−2.16937			−0.129184
$283$	9.79851	+	5.65717i	0.582461	+	0.336284i	0.762111	−	0.647447i	$-0.224163\pi$
$283$	9.79851	+	5.65717i	0.582461	+	0.336284i	−0.179650	+	0.983731i	$0.557497\pi$
$284$	9.48914	−	5.47856i	0.563077	−	0.325093i
$285$	7.07050	+	9.51449i	0.418820	+	0.563590i
$286$			7.47337i			0.441910i
$287$	−20.4941	−	8.47495i	−1.20973	−	0.500261i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	19.7632	+	34.2308i	1.16254	+	2.01358i
$290$	−9.21448	−	5.31998i	−0.541093	−	0.312400i
$291$	9.18504			0.538437
$292$	2.83669	+	1.63777i	0.166005	+	0.0958430i
$293$	18.8293			1.10002			0.550011	−	0.835157i	$-0.314624\pi$
$293$	18.8293			1.10002			0.550011	+	0.835157i	$0.314624\pi$
$294$	−4.94398	+	4.95551i	−0.288338	+	0.289011i
$295$	−9.24883	−	5.33981i	−0.538488	−	0.310896i
$296$	−0.0730658	+	0.126554i	−0.00424686	+	0.00735579i
$297$	−0.624707	−	1.08202i	−0.0362492	−	0.0627854i
$298$		−	6.05975i		−	0.351032i
$299$	53.3388			3.08466
$300$	1.19783	−	2.07470i	0.0691567	−	0.119783i
$301$	23.3314	+	9.64825i	1.34480	+	0.556116i
$302$	0.617415	+	1.06939i	0.0355282	+	0.0615367i
$303$	−12.9045	−	7.45044i	−0.741346	−	0.428016i
$304$	−4.00092	−	1.72993i	−0.229468	−	0.0992185i
$305$	18.0576	+	31.2767i	1.03397	+	1.79090i
$306$	7.51840			0.429798
$307$	5.78286	+	10.0162i	0.330046	+	0.571656i	0.982520	−	0.186155i	$-0.0596026\pi$
$307$	5.78286	+	10.0162i	0.330046	+	0.571656i	−0.652475	+	0.757810i	$0.726269\pi$
$308$	3.05475	+	1.26323i	0.174060	+	0.0719794i
$309$	−1.77682	−	3.07754i	−0.101080	−	0.175075i
$310$	−9.78142	−	16.9419i	−0.555547	−	0.962236i
$311$	−22.5801	+	13.0366i	−1.28040	+	0.739239i	−0.976921	−	0.213600i	$-0.931481\pi$
$311$	−22.5801	+	13.0366i	−1.28040	+	0.739239i	−0.303477	+	0.952839i	$0.598148\pi$
$312$	−5.18013	+	2.99075i	−0.293267	+	0.169318i
$313$	19.9015	−	11.4901i	1.12490	−	0.649460i	0.182251	−	0.983252i	$-0.441662\pi$
$313$	19.9015	−	11.4901i	1.12490	−	0.649460i	0.942647	+	0.333792i	$0.108328\pi$
$314$	6.76935	−	11.7249i	0.382016	−	0.661672i
$315$	2.74958	−	6.64902i	0.154921	−	0.374630i
$316$			16.2670i			0.915092i
$317$	18.7143	−	10.8047i	1.05110	−	0.606853i	0.128144	−	0.991756i	$-0.459098\pi$
$317$	18.7143	−	10.8047i	1.05110	−	0.606853i	0.922957	+	0.384902i	$0.125765\pi$
$318$	−1.47244	+	2.55034i	−0.0825702	+	0.143016i
$319$			4.88830i			0.273693i
$320$			2.71950i			0.152024i
$321$	−5.20654	+	3.00600i	−0.290601	+	0.167779i
$322$	9.01592	−	21.8023i	0.502438	−	1.21499i
$323$	19.5473	+	26.3040i	1.08764	+	1.46360i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	7.16482	−	12.4098i	0.397433	−	0.688373i
$326$	−4.13037	−	2.38467i	−0.228760	−	0.132075i
$327$	6.53589	−	3.77350i	0.361436	−	0.208675i
$328$	−7.25923	+	4.19112i	−0.400824	+	0.231416i
$329$	−2.19336	+	5.30398i	−0.120924	+	0.292418i
$330$	−3.39778			−0.187041
$331$	−8.97631	−	5.18247i	−0.493382	−	0.284855i	0.232594	−	0.972574i	$-0.425279\pi$
$331$	−8.97631	−	5.18247i	−0.493382	−	0.284855i	−0.725977	+	0.687719i	$0.758612\pi$
$332$		−	2.14102i		−	0.117504i
$333$		−	0.146132i		−	0.00800796i
$334$	9.84154	+	5.68202i	0.538505	+	0.310906i
$335$	−17.2711			−0.943620
$336$	0.346868	+	2.62291i	0.0189232	+	0.143092i
$337$	−24.0181	+	13.8669i	−1.30835	+	0.755376i	−0.981821	−	0.189811i	$-0.939212\pi$
$337$	−24.0181	+	13.8669i	−1.30835	+	0.755376i	−0.326529	+	0.945187i	$0.605879\pi$
$338$	−19.7267	+	11.3892i	−1.07299	+	0.619490i
$339$	−9.23950	−	5.33443i	−0.501821	−	0.289726i
$340$	10.2231	−	17.7070i	0.554427	−	0.960295i
$341$	−4.49387	+	7.78360i	−0.243356	+	0.421506i
$342$	4.32986	−	0.502292i	0.234132	−	0.0271609i
$343$	7.11730	+	17.0981i	0.384298	+	0.923209i
$344$	8.26422	−	4.77135i	0.445577	−	0.257254i
$345$			24.2505i			1.30561i
$346$		−	5.50278i		−	0.295831i
$347$	4.14276	−	7.17546i	0.222395	−	0.385199i	−0.733140	−	0.680078i	$-0.761946\pi$
$347$	4.14276	−	7.17546i	0.222395	−	0.385199i	0.955535	+	0.294879i	$0.0952793\pi$
$348$	−3.38830	+	1.95624i	−0.181632	+	0.104865i
$349$		−	11.3172i		−	0.605798i	−0.953023	−	0.302899i	$-0.902046\pi$
$349$		−	11.3172i		−	0.605798i	0.953023	−	0.302899i	$-0.0979545\pi$
$350$	−3.86145	−	5.02627i	−0.206403	−	0.268666i
$351$	2.99075	−	5.18013i	0.159634	−	0.276495i
$352$	1.08202	−	0.624707i	0.0576721	−	0.0332970i
$353$	−6.93123	+	4.00175i	−0.368912	+	0.212991i	−0.672983	−	0.739658i	$-0.734987\pi$
$353$	−6.93123	+	4.00175i	−0.368912	+	0.212991i	0.304071	+	0.952649i	$0.401654\pi$
$354$	−3.40093	+	1.96353i	−0.180758	+	0.104360i
$355$	14.8989	+	25.8057i	0.790753	+	1.36962i
$356$	−3.88830	−	6.73473i	−0.206079	−	0.356940i
$357$	7.60156	−	18.3821i	0.402317	−	0.972882i
$358$	4.07908	+	7.06518i	0.215586	+	0.373406i
$359$	−1.45916			−0.0770117			−0.0385058	−	0.999258i	$-0.512260\pi$
$359$	−1.45916			−0.0770117			−0.0385058	+	0.999258i	$0.512260\pi$
$360$	−1.35975	−	2.35515i	−0.0716650	−	0.124127i
$361$	13.0147	+	13.8426i	0.684982	+	0.728560i
$362$	0.107626	+	0.0621379i	0.00565670	+	0.00326590i
$363$	−4.71948	−	8.17438i	−0.247709	−	0.429044i
$364$	2.07479	+	15.6890i	0.108749	+	0.822326i
$365$	−4.45390	+	7.71438i	−0.233128	+	0.403789i
$366$	13.2801			0.694162
$367$		−	28.3399i		−	1.47933i	−0.672974	−	0.739666i	$-0.734983\pi$
$367$		−	28.3399i		−	1.47933i	0.672974	−	0.739666i	$-0.265017\pi$
$368$	−4.45865	−	7.72260i	−0.232423	−	0.402568i
$369$	4.19112	−	7.25923i	0.218181	−	0.377901i
$370$	−0.344162	−	0.198702i	−0.0178921	−	0.0103300i
$371$	4.74671	+	6.17858i	0.246437	+	0.320776i
$372$	−7.19356			−0.372968
$373$	3.54905	+	2.04904i	0.183763	+	0.106095i	0.589059	−	0.808090i	$-0.299498\pi$
$373$	3.54905	+	2.04904i	0.183763	+	0.106095i	−0.405297	+	0.914185i	$0.632832\pi$
$374$	−9.39359			−0.485731
$375$	−6.13362	−	3.54125i	−0.316739	−	0.182869i
$376$	1.08468	+	1.87873i	0.0559383	+	0.0968880i
$377$	−20.2672	+	11.7012i	−1.04381	+	0.602645i
$378$	−1.61185	−	2.09808i	−0.0829048	−	0.107913i
$379$		−	3.96967i		−	0.203908i	−0.994789	−	0.101954i	$-0.967490\pi$
$379$		−	3.96967i		−	0.203908i	0.994789	−	0.101954i	$-0.0325095\pi$
$380$	4.70455	−	10.8805i	0.241338	−	0.558157i
$381$	−1.76690	+	1.02012i	−0.0905211	+	0.0522624i
$382$	−3.72323	−	2.14961i	−0.190497	−	0.109984i
$383$	−9.16245			−0.468179			−0.234090	−	0.972215i	$-0.575211\pi$
$383$	−9.16245			−0.468179			−0.234090	+	0.972215i	$0.575211\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$	−3.43536	+	8.30738i	−0.175082	+	0.423383i
$386$	−5.06801	+	8.77805i	−0.257955	+	0.446791i
$387$	−4.77135	+	8.26422i	−0.242541	+	0.420094i
$388$	−4.59252	−	7.95448i	−0.233150	−	0.403828i
$389$	2.93665			0.148894			0.0744470	−	0.997225i	$-0.476281\pi$
$389$	2.93665			0.148894			0.0744470	+	0.997225i	$0.476281\pi$
$390$	−8.13334	−	14.0874i	−0.411847	−	0.713341i
$391$			67.0437i			3.39055i
$392$	6.76359	+	1.80385i	0.341613	+	0.0911083i
$393$	6.59852	+	3.80966i	0.332851	+	0.192172i
$394$		−	17.9757i		−	0.905604i
$395$	−44.2381			−2.22586
$396$	−0.624707	+	1.08202i	−0.0313927	+	0.0543738i
$397$			20.1195i			1.00977i	0.863187	+	0.504885i	$0.168465\pi$
$397$			20.1195i			1.00977i	−0.863187	+	0.504885i	$0.831535\pi$
$398$	10.5139			0.527015
$399$	3.14968	−	11.0941i	0.157681	−	0.555401i
$400$	−2.39566			−0.119783
$401$			10.2802i			0.513370i	0.966495	+	0.256685i	$0.0826303\pi$
$401$			10.2802i			0.513370i	−0.966495	+	0.256685i	$0.917370\pi$
$402$	−3.17542	+	5.49999i	−0.158375	+	0.274314i
$403$	−43.0283			−2.14339
$404$			14.9009i			0.741346i
$405$	2.35515	+	1.35975i	0.117028	+	0.0675664i
$406$	1.35711	+	10.2621i	0.0673525	+	0.509299i
$407$			0.182579i			0.00905010i
$408$	−3.75920	−	6.51112i	−0.186108	−	0.322349i
$409$	33.1567			1.63949			0.819747	−	0.572726i	$-0.194114\pi$
$409$	33.1567			1.63949			0.819747	+	0.572726i	$0.194114\pi$
$410$	−11.3977	−	19.7415i	−0.562894	−	0.974961i
$411$	−6.59483	+	11.4226i	−0.325299	+	0.563434i
$412$	−1.77682	+	3.07754i	−0.0875376	+	0.151620i
$413$	1.36217	+	10.3003i	0.0670282	+	0.506847i
$414$	7.72260	+	4.45865i	0.379545	+	0.219130i
$415$	5.82249			0.285815
$416$	5.18013	+	2.99075i	0.253977	+	0.146634i
$417$	−12.3146	+	7.10985i	−0.603050	+	0.348171i
$418$	−5.40979	+	0.627571i	−0.264602	+	0.0306955i
$419$		−	36.6140i		−	1.78871i	−0.447356	−	0.894356i	$-0.647634\pi$
$419$		−	36.6140i		−	1.78871i	0.447356	−	0.894356i	$-0.352366\pi$
$420$	−7.13301	+	0.943307i	−0.348055	+	0.0460287i
$421$	11.7219	−	6.76764i	0.571290	−	0.329834i	−0.186374	−	0.982479i	$-0.559674\pi$
$421$	11.7219	−	6.76764i	0.571290	−	0.329834i	0.757664	+	0.652644i	$0.226340\pi$
$422$	5.72856	+	9.92216i	0.278862	+	0.483003i
$423$	−1.87873	−	1.08468i	−0.0913469	−	0.0527391i
$424$	2.94488			0.143016
$425$	15.5984	+	9.00576i	0.756635	+	0.436843i
$426$	10.9571			0.530874
$427$	13.4270	−	32.4691i	0.649778	−	1.57129i
$428$	5.20654	+	3.00600i	0.251668	+	0.145301i
$429$	−3.73669	+	6.47213i	−0.180409	+	0.312477i
$430$	12.9757	+	22.4745i	0.625742	+	1.08382i
$431$			16.2642i			0.783420i	0.920089	+	0.391710i	$0.128116\pi$
$431$			16.2642i			0.783420i	−0.920089	+	0.391710i	$0.871884\pi$
$432$	−1.00000			−0.0481125
$433$	−13.7303	+	23.7816i	−0.659836	+	1.14287i	0.320822	+	0.947139i	$0.396041\pi$
$433$	−13.7303	+	23.7816i	−0.659836	+	1.14287i	−0.980658	+	0.195729i	$0.937293\pi$
$434$	−7.27312	+	17.5878i	−0.349121	+	0.844244i
$435$	−5.31998	−	9.21448i	−0.255074	−	0.441801i
$436$	−6.53589	−	3.77350i	−0.313012	−	0.180718i
$437$	4.47909	+	38.6106i	0.214264	+	1.84700i
$438$	1.63777	+	2.83669i	0.0782555	+	0.135542i
$439$	4.92053			0.234844			0.117422	−	0.993082i	$-0.462537\pi$
$439$	4.92053			0.234844			0.117422	+	0.993082i	$0.462537\pi$
$440$	1.69889	+	2.94256i	0.0809913	+	0.140281i
$441$	−6.75936	+	1.81961i	−0.321875	+	0.0866482i
$442$	−22.4857	−	38.9463i	−1.06953	−	1.85249i
$443$	−8.99249	−	15.5754i	−0.427246	−	0.740012i	0.569381	−	0.822074i	$-0.307183\pi$
$443$	−8.99249	−	15.5754i	−0.427246	−	0.740012i	−0.996627	+	0.0820618i	$0.973850\pi$
$444$	−0.126554	+	0.0730658i	−0.00600597	+	0.00346755i
$445$	18.3151	−	10.5742i	0.868218	−	0.501266i
$446$	−15.6307	+	9.02437i	−0.740134	+	0.427316i
$447$	3.02987	−	5.24790i	0.143308	−	0.248217i
$448$	2.09808	−	1.61185i	0.0991248	−	0.0761530i
$449$		−	23.8759i		−	1.12677i	−0.826193	−	0.563387i	$-0.809498\pi$
$449$		−	23.8759i		−	1.12677i	0.826193	−	0.563387i	$-0.190502\pi$
$450$	2.07470	−	1.19783i	0.0978023	−	0.0564662i
$451$	−5.23645	+	9.06979i	−0.246575	+	0.427080i
$452$			10.6689i			0.501821i
$453$			1.23483i			0.0580174i
$454$	−23.9848	+	13.8476i	−1.12566	+	0.649900i
$455$	−42.6661	+	5.64239i	−2.00022	+	0.264520i
$456$	−2.59993	−	3.49862i	−0.121753	−	0.163838i
$457$	−11.4057	+	19.7553i	−0.533538	+	0.924114i	0.465695	+	0.884945i	$0.345804\pi$
$457$	−11.4057	+	19.7553i	−0.533538	+	0.924114i	−0.999233	+	0.0391690i	$0.987529\pi$
$458$	−6.69044	+	11.5882i	−0.312624	+	0.541480i
$459$	6.51112	+	3.75920i	0.303913	+	0.175464i
$460$	21.0016	−	12.1253i	0.979204	−	0.565344i
$461$	3.72584	−	2.15112i	0.173530	−	0.100187i	−0.410719	−	0.911762i	$-0.634722\pi$
$461$	3.72584	−	2.15112i	0.173530	−	0.100187i	0.584249	+	0.811574i	$0.301389\pi$
$462$	2.01387	+	2.62137i	0.0936939	+	0.121957i
$463$	−13.3234			−0.619190			−0.309595	−	0.950869i	$-0.600193\pi$
$463$	−13.3234			−0.619190			−0.309595	+	0.950869i	$0.600193\pi$
$464$	3.38830	+	1.95624i	0.157298	+	0.0908161i
$465$		−	19.5628i		−	0.907205i
$466$		−	5.61103i		−	0.259926i
$467$	−19.4726	−	11.2425i	−0.901086	−	0.520242i	−0.0235336	−	0.999723i	$-0.507492\pi$
$467$	−19.4726	−	11.2425i	−0.901086	−	0.520242i	−0.877552	+	0.479481i	$0.840825\pi$
$468$	−5.98150			−0.276495
$469$	10.2366	+	13.3245i	0.472683	+	0.615270i
$470$	−5.10919	+	2.94979i	−0.235669	+	0.136064i
$471$	11.7249	−	6.76935i	0.540253	−	0.311915i
$472$	3.40093	+	1.96353i	0.156541	+	0.0903788i
$473$	5.96139	−	10.3254i	0.274105	−	0.474764i
$474$	−8.13351	+	14.0877i	−0.373585	+	0.647068i
$475$	9.58483	+	4.14433i	0.439782	+	0.190155i
$476$	−19.7201	+	2.60789i	−0.903870	+	0.119533i
$477$	−2.55034	+	1.47244i	−0.116772	+	0.0674183i
$478$		−	18.7264i		−	0.856524i
$479$		−	22.4939i		−	1.02777i	−0.857858	−	0.513887i	$-0.828205\pi$
$479$		−	22.4939i		−	1.02777i	0.857858	−	0.513887i	$-0.171795\pi$
$480$	−1.35975	+	2.35515i	−0.0620637	+	0.107498i
$481$	−0.756981	+	0.437043i	−0.0345154	+	0.0199275i
$482$			23.6719i			1.07823i
$483$	18.7092	−	14.3734i	0.851296	−	0.654011i
$484$	−4.71948	+	8.17438i	−0.214522	+	0.371563i
$485$	21.6322	−	12.4893i	0.982267	−	0.567112i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	6.86510	−	3.96356i	0.311087	−	0.179606i	−0.336326	−	0.941746i	$-0.609184\pi$
$487$	6.86510	−	3.96356i	0.311087	−	0.179606i	0.647413	+	0.762139i	$0.275851\pi$
$488$	−6.64005	−	11.5009i	−0.300581	−	0.520622i
$489$	−2.38467	−	4.13037i	−0.107839	−	0.186782i
$490$	−4.90557	+	18.3935i	−0.221611	+	0.830936i
$491$	12.6180	+	21.8550i	0.569441	+	0.986301i	0.996621	+	0.0821342i	$0.0261736\pi$
$491$	12.6180	+	21.8550i	0.569441	+	0.986301i	−0.427180	+	0.904166i	$0.640493\pi$
$492$	−8.38224			−0.377901
$493$	−14.7078	−	25.4746i	−0.662405	−	1.14732i
$494$	−15.5515	−	20.9270i	−0.699694	−	0.941552i
$495$	−2.94256	−	1.69889i	−0.132258	−	0.0763594i
$496$	3.59678	+	6.22980i	0.161500	+	0.279726i
$497$	11.0783	−	26.7896i	0.496930	−	1.20168i
$498$	1.07051	−	1.85418i	0.0479707	−	0.0830877i
$499$	−2.10396			−0.0941863			−0.0470931	−	0.998891i	$-0.514996\pi$
$499$	−2.10396			−0.0941863			−0.0470931	+	0.998891i	$0.514996\pi$
$500$			7.08250i			0.316739i
$501$	5.68202	+	9.84154i	0.253854	+	0.439688i
$502$	−7.95959	+	13.7864i	−0.355254	+	0.615318i
$503$	14.6623	+	8.46527i	0.653759	+	0.377448i	0.789895	−	0.613242i	$-0.210135\pi$
$503$	14.6623	+	8.46527i	0.653759	+	0.377448i	−0.136136	+	0.990690i	$0.543468\pi$
$504$	−1.01106	+	2.44495i	−0.0450362	+	0.108907i
$505$	−40.5229			−1.80324
$506$	−9.64873	−	5.57069i	−0.428938	−	0.247648i
$507$	−22.7784			−1.01162
$508$	1.76690	+	1.02012i	0.0783935	+	0.0452605i
$509$	16.5875	+	28.7304i	0.735227	+	1.27345i	0.954624	+	0.297815i	$0.0962578\pi$
$509$	16.5875	+	28.7304i	0.735227	+	1.27345i	−0.219397	+	0.975636i	$0.570409\pi$
$510$	17.7070	−	10.2231i	0.784078	−	0.452688i
$511$	8.59144	−	1.13618i	0.380063	−	0.0502616i
$512$		−	1.00000i		−	0.0441942i
$513$	4.00092	+	1.72993i	0.176645	+	0.0763784i
$514$	−6.10800	+	3.52645i	−0.269412	+	0.155545i
$515$	−8.36936	−	4.83206i	−0.368798	−	0.212926i
$516$	9.54270			0.420094
$517$	2.34731	+	1.35522i	0.103235	+	0.0596025i
$518$	0.0506885	+	0.383291i	0.00222712	+	0.0168408i
$519$	2.75139	−	4.76554i	0.120773	−	0.209184i
$520$	−8.13334	+	14.0874i	−0.356670	+	0.617771i
$521$	−1.23444	−	2.13811i	−0.0540817	−	0.0936722i	0.837717	−	0.546104i	$-0.183890\pi$
$521$	−1.23444	−	2.13811i	−0.0540817	−	0.0936722i	−0.891799	+	0.452432i	$0.850556\pi$
$522$	−3.91248			−0.171244
$523$	0.0336846	+	0.0583435i	0.00147293	+	0.00255118i	0.866761	−	0.498724i	$-0.166198\pi$
$523$	0.0336846	+	0.0583435i	0.00147293	+	0.00255118i	−0.865288	+	0.501275i	$0.832864\pi$
$524$		−	7.61931i		−	0.332851i
$525$	−0.830978	−	6.28361i	−0.0362669	−	0.274239i
$526$	−3.16449	−	1.82702i	−0.137978	−	0.0796618i
$527$		−	54.0840i		−	2.35594i
$528$	1.24941			0.0543738
$529$	−28.2590	+	48.9461i	−1.22865	+	2.12809i
$530$			8.00858i			0.347870i
$531$	−3.92706			−0.170420
$532$	−11.1826	+	2.81936i	−0.484828	+	0.122235i
$533$	−50.1384			−2.17174
$534$		−	7.77660i		−	0.336526i
$535$	−8.17481	+	14.1592i	−0.353428	+	0.612155i
$536$	6.35084			0.274314
$537$			8.15816i			0.352051i
$538$	11.4209	+	6.59387i	0.492391	+	0.284282i
$539$	8.44525	−	2.27345i	0.363762	−	0.0979244i
$540$		−	2.71950i		−	0.117028i
$541$	9.57344	+	16.5817i	0.411595	+	0.712903i	0.995064	−	0.0992322i	$-0.0316387\pi$
$541$	9.57344	+	16.5817i	0.411595	+	0.712903i	−0.583470	+	0.812135i	$0.698305\pi$
$542$	29.6647			1.27421
$543$	0.0621379	+	0.107626i	0.00266659	+	0.00461867i
$544$	−3.75920	+	6.51112i	−0.161174	+	0.279162i
$545$	10.2620	−	17.7743i	0.439576	−	0.761368i
$546$	−6.04766	+	14.6244i	−0.258816	+	0.625869i
$547$	8.95491	+	5.17012i	0.382884	+	0.221058i	0.679072	−	0.734071i	$-0.262382\pi$
$547$	8.95491	+	5.17012i	0.382884	+	0.221058i	−0.296188	+	0.955130i	$0.595716\pi$
$548$	13.1897			0.563434
$549$	11.5009	+	6.64005i	0.490847	+	0.283391i
$550$	−2.59216	+	1.49658i	−0.110530	+	0.0638146i
$551$	−10.1722	−	13.6883i	−0.433349	−	0.583141i
$552$		−	8.91729i		−	0.379545i
$553$	26.2201	+	34.1295i	1.11499	+	1.45133i
$554$	23.8249	−	13.7553i	1.01222	−	0.584407i
$555$	−0.198702	−	0.344162i	−0.00843444	−	0.0146089i
$556$	12.3146	+	7.10985i	0.522257	+	0.301525i
$557$	10.1036			0.428105			0.214053	−	0.976822i	$-0.431334\pi$
$557$	10.1036			0.428105			0.214053	+	0.976822i	$0.431334\pi$
$558$	−6.22980	−	3.59678i	−0.263729	−	0.152264i
$559$	57.0797			2.41421
$560$	4.38343	+	5.70571i	0.185234	+	0.241110i
$561$	−8.13509	−	4.69680i	−0.343464	−	0.198299i
$562$	−4.54528	+	7.87266i	−0.191731	+	0.332088i
$563$	17.1109	+	29.6369i	0.721138	+	1.24905i	0.960544	+	0.278128i	$0.0897140\pi$
$563$	17.1109	+	29.6369i	0.721138	+	1.24905i	−0.239406	+	0.970920i	$0.576953\pi$
$564$			2.16937i			0.0913469i
$565$	−29.0139			−1.22062
$566$	5.65717	−	9.79851i	0.237789	−	0.411862i
$567$	−0.346868	−	2.62291i	−0.0145671	−	0.110152i
$568$	−5.47856	−	9.48914i	−0.229875	−	0.398156i
$569$	−17.3172	−	9.99810i	−0.725975	−	0.419142i	0.0909726	−	0.995853i	$-0.471002\pi$
$569$	−17.3172	−	9.99810i	−0.725975	−	0.419142i	−0.816948	+	0.576711i	$0.804336\pi$
$570$	9.51449	−	7.07050i	0.398518	−	0.296150i
$571$	−0.654932	−	1.13438i	−0.0274081	−	0.0474722i	0.851996	−	0.523548i	$-0.175392\pi$
$571$	−0.654932	−	1.13438i	−0.0274081	−	0.0474722i	−0.879404	+	0.476076i	$0.842059\pi$
$572$	7.47337			0.312477
$573$	−2.14961	−	3.72323i	−0.0898012	−	0.155540i
$574$	−8.47495	+	20.4941i	−0.353738	+	0.855408i
$575$	10.6814	+	18.5007i	0.445445	+	0.771533i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	0.633122	−	0.365533i	0.0263572	−	0.0152173i	−0.486763	−	0.873534i	$-0.661823\pi$
$577$	0.633122	−	0.365533i	0.0263572	−	0.0152173i	0.513121	+	0.858316i	$0.328489\pi$
$578$	34.2308	−	19.7632i	1.42381	−	0.822039i
$579$	−8.77805	+	5.06801i	−0.364803	+	0.210619i
$580$	−5.31998	+	9.21448i	−0.220900	+	0.382611i
$581$	−3.45101	−	4.49202i	−0.143172	−	0.186361i
$582$		−	9.18504i		−	0.380732i
$583$	3.18643	−	1.83968i	0.131968	−	0.0761920i
$584$	1.63777	−	2.83669i	0.0677712	−	0.117383i
$585$		−	16.2667i		−	0.672544i
$586$		−	18.8293i		−	0.777833i
$587$	21.3583	−	12.3312i	0.881552	−	0.508964i	0.0103821	−	0.999946i	$-0.496695\pi$
$587$	21.3583	−	12.3312i	0.881552	−	0.508964i	0.871170	+	0.490982i	$0.163362\pi$
$588$	4.95551	+	4.94398i	0.204362	+	0.203886i
$589$	−3.61327	−	31.1471i	−0.148882	−	1.28339i
$590$	−5.33981	+	9.24883i	−0.219837	+	0.380768i
$591$	8.98787	−	15.5674i	0.369711	−	0.640359i
$592$	0.126554	+	0.0730658i	0.00520133	+	0.00300299i
$593$	−16.1149	+	9.30394i	−0.661760	+	0.382067i	−0.792947	−	0.609290i	$-0.791454\pi$
$593$	−16.1149	+	9.30394i	−0.661760	+	0.382067i	0.131187	+	0.991358i	$0.458121\pi$
$594$	−1.08202	+	0.624707i	−0.0443960	+	0.0256320i
$595$	−7.09216	−	53.6288i	−0.290750	−	2.19857i
$596$	−6.05975			−0.248217
$597$	9.10533	+	5.25696i	0.372656	+	0.215153i
$598$		−	53.3388i		−	2.18119i
$599$		−	4.08675i		−	0.166980i	−0.996509	−	0.0834900i	$-0.973393\pi$
$599$		−	4.08675i		−	0.166980i	0.996509	−	0.0834900i	$-0.0266067\pi$
$600$	−2.07470	−	1.19783i	−0.0846993	−	0.0489012i
$601$	34.8357			1.42098			0.710488	−	0.703709i	$-0.248474\pi$
$601$	34.8357			1.42098			0.710488	+	0.703709i	$0.248474\pi$
$602$	9.64825	−	23.3314i	0.393233	−	0.950916i
$603$	−5.49999	+	3.17542i	−0.223977	+	0.129313i
$604$	1.06939	−	0.617415i	0.0435130	−	0.0251223i
$605$	−22.2302	−	12.8346i	−0.903786	−	0.521801i
$606$	−7.45044	+	12.9045i	−0.302653	+	0.524211i
$607$	0.677567	−	1.17358i	0.0275016	−	0.0476342i	−0.851947	−	0.523628i	$-0.824578\pi$
$607$	0.677567	−	1.17358i	0.0275016	−	0.0476342i	0.879449	+	0.475994i	$0.157912\pi$
$608$	−1.72993	+	4.00092i	−0.0701580	+	0.162259i
$609$	−3.95575	+	9.56579i	−0.160295	+	0.387625i
$610$	31.2767	−	18.0576i	1.26636	−	0.731131i
$611$			12.9761i			0.524956i
$612$		−	7.51840i		−	0.303913i
$613$	−16.8361	+	29.1610i	−0.680005	+	1.17780i	0.294974	+	0.955505i	$0.404689\pi$
$613$	−16.8361	+	29.1610i	−0.680005	+	1.17780i	−0.974979	+	0.222298i	$0.928644\pi$
$614$	10.0162	−	5.78286i	0.404222	−	0.233377i
$615$		−	22.7955i		−	0.919202i
$616$	1.26323	−	3.05475i	0.0508971	−	0.123079i
$617$	12.7945	−	22.1607i	0.515088	−	0.892158i	−0.484759	−	0.874648i	$-0.661093\pi$
$617$	12.7945	−	22.1607i	0.515088	−	0.892158i	0.999847	−	0.0175103i	$-0.00557400\pi$
$618$	−3.07754	+	1.77682i	−0.123797	+	0.0714742i
$619$	3.30963	−	1.91082i	0.133025	−	0.0768023i	−0.432010	−	0.901869i	$-0.642196\pi$
$619$	3.30963	−	1.91082i	0.133025	−	0.0768023i	0.565036	+	0.825066i	$0.308862\pi$
$620$	−16.9419	+	9.78142i	−0.680404	+	0.392831i
$621$	4.45865	+	7.72260i	0.178919	+	0.309897i
$622$	13.0366	+	22.5801i	0.522721	+	0.905379i
$623$	−19.0134	−	7.86261i	−0.761754	−	0.315009i
$624$	2.99075	+	5.18013i	0.119726	+	0.207371i
$625$	−31.2391			−1.24956
$626$	−11.4901	−	19.9015i	−0.459238	−	0.795423i
$627$	−4.99880	−	2.16140i	−0.199633	−	0.0863181i
$628$	−11.7249	−	6.76935i	−0.467873	−	0.270126i
$629$	−0.549338	−	0.951481i	−0.0219035	−	0.0379380i
$630$	−6.64902	−	2.74958i	−0.264903	−	0.109546i
$631$	7.18413	−	12.4433i	0.285996	−	0.495359i	−0.686855	−	0.726795i	$-0.741009\pi$
$631$	7.18413	−	12.4433i	0.285996	−	0.495359i	0.972850	+	0.231436i	$0.0743424\pi$
$632$	16.2670			0.647068
$633$			11.4571i			0.455380i
$634$	−10.8047	−	18.7143i	−0.429110	−	0.743241i
$635$	−2.77421	+	4.80508i	−0.110091	+	0.190684i
$636$	2.55034	+	1.47244i	0.101127	+	0.0583860i
$637$	29.6414	+	29.5724i	1.17444	+	1.17170i
$638$	4.88830			0.193530
$639$	9.48914	+	5.47856i	0.375385	+	0.216728i
$640$	2.71950			0.107498
$641$	27.1860	+	15.6959i	1.07378	+	0.619950i	0.929213	−	0.369545i	$-0.120486\pi$
$641$	27.1860	+	15.6959i	1.07378	+	0.619950i	0.144571	+	0.989494i	$0.453820\pi$
$642$	3.00600	+	5.20654i	0.118637	+	0.205486i
$643$	19.0384	−	10.9918i	0.750802	−	0.433476i	−0.0751818	−	0.997170i	$-0.523954\pi$
$643$	19.0384	−	10.9918i	0.750802	−	0.433476i	0.825984	+	0.563694i	$0.190620\pi$
$644$	−21.8023	−	9.01592i	−0.859130	−	0.355277i
$645$			25.9513i			1.02183i
$646$	26.3040	−	19.5473i	1.03492	−	0.769078i
$647$	25.1968	−	14.5474i	0.990587	−	0.571916i	0.0851376	−	0.996369i	$-0.472867\pi$
$647$	25.1968	−	14.5474i	0.990587	−	0.571916i	0.905450	+	0.424453i	$0.139534\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	4.90653			0.192598
$650$	−12.4098	−	7.16482i	−0.486754	−	0.281027i
$651$	−15.0926	+	11.5950i	−0.591527	+	0.454442i
$652$	−2.38467	+	4.13037i	−0.0933910	+	0.161758i
$653$	−1.75651	+	3.04236i	−0.0687374	+	0.119057i	−0.898346	−	0.439289i	$-0.855230\pi$
$653$	−1.75651	+	3.04236i	−0.0687374	+	0.119057i	0.829608	+	0.558346i	$0.188564\pi$
$654$	−3.77350	−	6.53589i	−0.147555	−	0.255574i
$655$	20.7207			0.809624
$656$	4.19112	+	7.25923i	0.163636	+	0.283425i
$657$			3.27553i			0.127791i
$658$	5.30398	+	2.19336i	0.206771	+	0.0855062i
$659$	6.42019	+	3.70670i	0.250095	+	0.144393i	0.619808	−	0.784754i	$-0.287211\pi$
$659$	6.42019	+	3.70670i	0.250095	+	0.144393i	−0.369713	+	0.929146i	$0.620544\pi$
$660$			3.39778i			0.132258i
$661$	−29.6223			−1.15217			−0.576087	−	0.817389i	$-0.695421\pi$
$661$	−29.6223			−1.15217			−0.576087	+	0.817389i	$0.695421\pi$
$662$	−5.18247	+	8.97631i	−0.201423	+	0.348874i
$663$		−	44.9713i		−	1.74654i
$664$	−2.14102			−0.0830877
$665$	−7.66724	−	30.4111i	−0.297323	−	1.17929i
$666$	−0.146132			−0.00566249
$667$		−	34.8887i		−	1.35090i
$668$	5.68202	−	9.84154i	0.219844	−	0.380781i
$669$	−18.0487			−0.697805
$670$			17.2711i			0.667240i
$671$	−14.3694	−	8.29617i	−0.554724	−	0.320270i
$672$	2.62291	−	0.346868i	0.101181	−	0.0133807i
$673$			16.2117i			0.624915i	0.949932	+	0.312458i	$0.101152\pi$
$673$			16.2117i			0.624915i	−0.949932	+	0.312458i	$0.898848\pi$
$674$	13.8669	+	24.0181i	0.534131	+	0.925143i
$675$	2.39566			0.0922089
$676$	11.3892	+	19.7267i	0.438046	+	0.758717i
$677$	14.4066	−	24.9529i	0.553689	−	0.959017i	−0.444315	−	0.895870i	$-0.646553\pi$
$677$	14.4066	−	24.9529i	0.553689	−	0.959017i	0.998004	−	0.0631468i	$-0.0201136\pi$
$678$	−5.33443	+	9.23950i	−0.204868	+	0.354841i
$679$	−22.4569	−	9.28664i	−0.861818	−	0.356388i
$680$	−17.7070	−	10.2231i	−0.679031	−	0.392039i
$681$	−27.6952			−1.06128
$682$	7.78360	+	4.49387i	0.298050	+	0.172079i
$683$	2.23997	−	1.29325i	0.0857101	−	0.0494847i	−0.456532	−	0.889707i	$-0.650909\pi$
$683$	2.23997	−	1.29325i	0.0857101	−	0.0494847i	0.542242	+	0.840222i	$0.317575\pi$
$684$	−0.502292	−	4.32986i	−0.0192056	−	0.165556i
$685$			35.8692i			1.37049i
$686$	17.0981	−	7.11730i	0.652807	−	0.271740i
$687$	−11.5882	+	6.69044i	−0.442117	+	0.255256i
$688$	−4.77135	−	8.26422i	−0.181906	−	0.315070i
$689$	15.2548	+	8.80739i	0.581163	+	0.335535i
$690$	24.2505			0.923202
$691$	7.18404	+	4.14771i	0.273294	+	0.157786i	0.630384	−	0.776284i	$-0.282898\pi$
$691$	7.18404	+	4.14771i	0.273294	+	0.157786i	−0.357090	+	0.934070i	$0.616231\pi$
$692$	−5.50278			−0.209184
$693$	0.433382	+	3.27711i	0.0164628	+	0.124487i
$694$	−7.17546	−	4.14276i	−0.272377	−	0.157257i
$695$	−19.3352	+	33.4896i	−0.733427	+	1.27033i
$696$	1.95624	+	3.38830i	0.0741510	+	0.128433i
$697$		−	63.0210i		−	2.38709i
$698$	−11.3172			−0.428364
$699$	2.80552	−	4.85930i	0.106114	−	0.183795i
$700$	−5.02627	+	3.86145i	−0.189975	+	0.145949i
$701$	4.50720	+	7.80669i	0.170234	+	0.294855i	0.938502	−	0.345274i	$-0.112214\pi$
$701$	4.50720	+	7.80669i	0.170234	+	0.294855i	−0.768267	+	0.640129i	$0.778881\pi$
$702$	−5.18013	−	2.99075i	−0.195512	−	0.112879i
$703$	−0.379932	−	0.511260i	−0.0143294	−	0.0192825i
$704$	−0.624707	−	1.08202i	−0.0235445	−	0.0407803i
$705$	−5.89959			−0.222191
$706$	4.00175	+	6.93123i	0.150608	+	0.260860i
$707$	24.0180	+	31.2632i	0.903291	+	1.17577i
$708$	1.96353	+	3.40093i	0.0737940	+	0.127815i
$709$	12.3558	+	21.4009i	0.464033	+	0.803729i	0.999157	−	0.0410446i	$-0.0130686\pi$
$709$	12.3558	+	21.4009i	0.464033	+	0.803729i	−0.535124	+	0.844773i	$0.679735\pi$
$710$	25.8057	−	14.8989i	0.968470	−	0.559146i
$711$	−14.0877	+	8.13351i	−0.528329	+	0.305031i
$712$	−6.73473	+	3.88830i	−0.252395	+	0.145720i
$713$	32.0735	−	55.5530i	1.20116	−	2.08047i
$714$	−18.3821	−	7.60156i	−0.687932	−	0.284481i
$715$			20.3238i			0.760067i
$716$	7.06518	−	4.07908i	0.264038	−	0.152442i
$717$	9.36318	−	16.2175i	0.349674	−	0.605654i
$718$			1.45916i			0.0544555i
$719$		−	42.6008i		−	1.58874i	−0.607432	−	0.794372i	$-0.707800\pi$
$719$		−	42.6008i		−	1.58874i	0.607432	−	0.794372i	$-0.292200\pi$
$720$	−2.35515	+	1.35975i	−0.0877714	+	0.0506748i
$721$	1.23265	+	9.32090i	0.0459061	+	0.347128i
$722$	13.8426	−	13.0147i	0.515169	−	0.484356i
$723$	−11.8359	+	20.5005i	−0.440184	+	0.762421i
$724$	0.0621379	−	0.107626i	0.00230934	−	0.00399989i
$725$	−8.11722	−	4.68648i	−0.301466	−	0.174051i
$726$	−8.17438	+	4.71948i	−0.303380	+	0.175156i
$727$	−30.3673	+	17.5325i	−1.12626	+	0.650246i	−0.942991	−	0.332817i	$-0.892001\pi$
$727$	−30.3673	+	17.5325i	−1.12626	+	0.650246i	−0.183268	+	0.983063i	$0.558668\pi$
$728$	15.6890	−	2.07479i	0.581472	−	0.0768970i
$729$	1.00000			0.0370370
$730$	7.71438	+	4.45390i	0.285522	+	0.164846i
$731$			71.7458i			2.65361i
$732$		−	13.2801i		−	0.490847i
$733$	−43.3561	−	25.0316i	−1.60139	−	0.924565i	−0.991209	−	0.132305i	$-0.957762\pi$
$733$	−43.3561	−	25.0316i	−1.60139	−	0.924565i	−0.610184	−	0.792259i	$-0.708905\pi$
$734$	−28.3399			−1.04605
$735$	−13.4451	+	13.4765i	−0.495931	+	0.497088i
$736$	−7.72260	+	4.45865i	−0.284659	+	0.164348i
$737$	6.87176	−	3.96741i	0.253125	−	0.146142i
$738$	−7.25923	−	4.19112i	−0.267216	−	0.154277i
$739$	−0.200186	+	0.346732i	−0.00736395	+	0.0127547i	−0.869684	−	0.493609i	$-0.835677\pi$
$739$	−0.200186	+	0.346732i	−0.00736395	+	0.0127547i	0.862320	+	0.506364i	$0.169011\pi$
$740$	−0.198702	+	0.344162i	−0.00730444	+	0.0126517i
$741$	−3.00446	−	25.8991i	−0.110372	−	0.951426i
$742$	6.17858	−	4.74671i	0.226823	−	0.174257i
$743$	−36.2070	+	20.9041i	−1.32831	+	0.766898i	−0.985038	−	0.172339i	$-0.944868\pi$
$743$	−36.2070	+	20.9041i	−1.32831	+	0.766898i	−0.343269	+	0.939237i	$0.611534\pi$
$744$			7.19356i			0.263729i
$745$		−	16.4795i		−	0.603761i
$746$	2.04904	−	3.54905i	0.0750208	−	0.129940i
$747$	1.85418	−	1.07051i	0.0678408	−	0.0391679i
$748$			9.39359i			0.343464i
$749$	15.7690	−	2.08537i	0.576185	−	0.0761979i
$750$	−3.54125	+	6.13362i	−0.129308	+	0.223968i
$751$	3.98591	−	2.30127i	0.145448	−	0.0839745i	−0.425510	−	0.904954i	$-0.639905\pi$
$751$	3.98591	−	2.30127i	0.145448	−	0.0839745i	0.570958	+	0.820979i	$0.306572\pi$
$752$	1.87873	−	1.08468i	0.0685101	−	0.0395543i
$753$	−13.7864	+	7.95959i	−0.502405	+	0.290064i
$754$	11.7012	+	20.2672i	0.426134	+	0.738086i
$755$	1.67906	+	2.90821i	0.0611072	+	0.105841i
$756$	−2.09808	+	1.61185i	−0.0763063	+	0.0586226i
$757$	−5.10759	−	8.84661i	−0.185639	−	0.321535i	0.758153	−	0.652077i	$-0.226102\pi$
$757$	−5.10759	−	8.84661i	−0.185639	−	0.321535i	−0.943791	+	0.330541i	$0.892769\pi$
$758$	−3.96967			−0.144185
$759$	−5.57069	−	9.64873i	−0.202203	−	0.350227i
$760$	−10.8805	−	4.70455i	−0.394676	−	0.170652i
$761$	−34.3476	−	19.8306i	−1.24510	−	0.718859i	−0.274972	−	0.961452i	$-0.588669\pi$
$761$	−34.3476	−	19.8306i	−1.24510	−	0.718859i	−0.970128	+	0.242593i	$0.922002\pi$
$762$	1.02012	+	1.76690i	0.0369551	+	0.0640081i
$763$	−19.7951	+	2.61781i	−0.716632	+	0.0947712i
$764$	−2.14961	+	3.72323i	−0.0777701	+	0.134702i
$765$	20.4463			0.739236
$766$			9.16245i			0.331053i
$767$	11.7449	+	20.3427i	0.424082	+	0.734532i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−34.3203	−	19.8148i	−1.23762	−	0.714542i	−0.269015	−	0.963136i	$-0.586698\pi$
$769$	−34.3203	−	19.8148i	−1.23762	−	0.714542i	−0.968608	+	0.248594i	$0.920031\pi$
$770$	8.30738	+	3.43536i	0.299377	+	0.123802i
$771$	−7.05291			−0.254004
$772$	8.77805	+	5.06801i	0.315929	+	0.182402i
$773$	31.6195			1.13727			0.568637	−	0.822589i	$-0.307471\pi$
$773$	31.6195			1.13727			0.568637	+	0.822589i	$0.307471\pi$
$774$	8.26422	+	4.77135i	0.297051	+	0.171503i
$775$	−8.61665	−	14.9245i	−0.309519	−	0.536103i
$776$	−7.95448	+	4.59252i	−0.285549	+	0.164862i
$777$	−0.147748	+	0.357284i	−0.00530043	+	0.0128175i
$778$		−	2.93665i		−	0.105284i
$779$	−4.21034	−	36.2939i	−0.150851	−	1.30037i
$780$	−14.0874	+	8.13334i	−0.504408	+	0.291220i
$781$	−11.8559	−	6.84499i	−0.424236	−	0.244933i
$782$	67.0437			2.39748
$783$	−3.38830	−	1.95624i	−0.121088	−	0.0699103i
$784$	1.80385	−	6.76359i	0.0644233	−	0.241557i
$785$	18.4092	−	31.8857i	0.657053	−	1.13805i
$786$	3.80966	−	6.59852i	0.135886	−	0.235361i
$787$	−1.39380	−	2.41413i	−0.0496836	−	0.0860546i	0.840114	−	0.542410i	$-0.182488\pi$
$787$	−1.39380	−	2.41413i	−0.0496836	−	0.0860546i	−0.889798	+	0.456355i	$0.849155\pi$
$788$	−17.9757			−0.640359
$789$	−1.82702	−	3.16449i	−0.0650436	−	0.112659i
$790$			44.2381i			1.57392i
$791$	17.1966	+	22.3841i	0.611442	+	0.795886i
$792$	1.08202	+	0.624707i	0.0384481	+	0.0221980i
$793$		−	79.4350i		−	2.82082i
$794$	20.1195			0.714015
$795$	−4.00429	+	6.93563i	−0.142017	+	0.245982i
$796$		−	10.5139i		−	0.372656i
$797$	−5.77333			−0.204502			−0.102251	−	0.994759i	$-0.532604\pi$
$797$	−5.77333			−0.204502			−0.102251	+	0.994759i	$0.532604\pi$
$798$	−11.0941	−	3.14968i	−0.392728	−	0.111497i
$799$	−16.3102			−0.577012
$800$			2.39566i			0.0846993i
$801$	3.88830	−	6.73473i	0.137386	−	0.237960i
$802$	10.2802			0.363007
$803$		−	4.09250i		−	0.144421i
$804$	5.49999	+	3.17542i	0.193970	+	0.111988i
$805$	24.5188	−	59.2912i	0.864173	−	2.08974i
$806$			43.0283i			1.51561i
$807$	6.59387	+	11.4209i	0.232115	+	0.402036i
$808$	14.9009			0.524211
$809$	−4.77398	−	8.26878i	−0.167844	−	0.290715i	0.769817	−	0.638264i	$-0.220347\pi$
$809$	−4.77398	−	8.26878i	−0.167844	−	0.290715i	−0.937662	+	0.347549i	$0.887014\pi$
$810$	1.35975	−	2.35515i	0.0477767	−	0.0827516i
$811$	20.8140	−	36.0510i	0.730880	−	1.26592i	−0.225628	−	0.974214i	$-0.572443\pi$
$811$	20.8140	−	36.0510i	0.730880	−	1.26592i	0.956508	−	0.291707i	$-0.0942234\pi$
$812$	10.2621	−	1.35711i	0.360129	−	0.0476254i
$813$	25.6904	+	14.8323i	0.901001	+	0.520193i
$814$	0.182579			0.00639939
$815$	−11.2325	−	6.48511i	−0.393458	−	0.227163i
$816$	−6.51112	+	3.75920i	−0.227935	+	0.131598i
$817$	4.79322	+	41.3186i	0.167694	+	1.44555i
$818$		−	33.1567i		−	1.15930i
$819$	−12.5497	+	9.64131i	−0.438520	+	0.336895i
$820$	−19.7415	+	11.3977i	−0.689402	+	0.398026i
$821$	−5.37058	−	9.30212i	−0.187435	−	0.324646i	0.756960	−	0.653462i	$-0.226684\pi$
$821$	−5.37058	−	9.30212i	−0.187435	−	0.324646i	−0.944394	+	0.328815i	$0.893351\pi$
$822$	11.4226	+	6.59483i	0.398408	+	0.230021i
$823$	−21.5464			−0.751062			−0.375531	−	0.926810i	$-0.622540\pi$
$823$	−21.5464			−0.751062			−0.375531	+	0.926810i	$0.622540\pi$
$824$	3.07754	+	1.77682i	0.107211	+	0.0618985i
$825$	−2.99317			−0.104209
$826$	10.3003	−	1.36217i	0.358395	−	0.0473961i
$827$	−11.9231	−	6.88382i	−0.414608	−	0.239374i	0.278160	−	0.960535i	$-0.410276\pi$
$827$	−11.9231	−	6.88382i	−0.414608	−	0.239374i	−0.692768	+	0.721161i	$0.743609\pi$
$828$	4.45865	−	7.72260i	0.154949	−	0.268379i
$829$	15.2307	+	26.3803i	0.528984	+	0.916227i	0.999429	+	0.0337974i	$0.0107601\pi$
$829$	15.2307	+	26.3803i	0.528984	+	0.916227i	−0.470445	+	0.882429i	$0.655907\pi$
$830$		−	5.82249i		−	0.202102i
$831$	27.5106			0.954332
$832$	2.99075	−	5.18013i	0.103686	−	0.179589i
$833$	−37.1708	+	37.2575i	−1.28789	+	1.29090i
$834$	7.10985	+	12.3146i	0.246194	+	0.426421i
$835$	26.7640	+	15.4522i	0.926208	+	0.534746i
$836$	0.627571	+	5.40979i	0.0217050	+	0.187102i
$837$	−3.59678	−	6.22980i	−0.124323	−	0.215333i
$838$	−36.6140			−1.26481
$839$	−18.5199	−	32.0774i	−0.639379	−	1.10744i	−0.985569	−	0.169272i	$-0.945858\pi$
$839$	−18.5199	−	32.0774i	−0.639379	−	1.10744i	0.346191	−	0.938164i	$-0.387475\pi$
$840$	0.943307	+	7.13301i	0.0325472	+	0.246112i
$841$	−6.84626	−	11.8581i	−0.236078	−	0.408899i
$842$	−6.76764	−	11.7219i	−0.233228	−	0.403963i
$843$	−7.87266	+	4.54528i	−0.271149	+	0.156548i
$844$	9.92216	−	5.72856i	0.341535	−	0.197185i
$845$	−53.6465	+	30.9728i	−1.84550	+	1.06550i
$846$	−1.08468	+	1.87873i	−0.0372922	+	0.0645920i
$847$	3.27408	+	24.7576i	0.112499	+	0.850681i
$848$		−	2.94488i		−	0.101127i
$849$	9.79851	−	5.65717i	0.336284	−	0.194154i
$850$	9.00576	−	15.5984i	0.308895	−	0.535022i
$851$		−	1.30310i		−	0.0446696i
$852$		−	10.9571i		−	0.375385i
$853$	23.1048	−	13.3395i	0.791092	−	0.456737i	−0.0492551	−	0.998786i	$-0.515685\pi$
$853$	23.1048	−	13.3395i	0.791092	−	0.456737i	0.840347	+	0.542049i	$0.182351\pi$
$854$	−32.4691	−	13.4270i	−1.11107	−	0.459462i
$855$	11.7750	−	1.36598i	0.402698	−	0.0467156i
$856$	3.00600	−	5.20654i	0.102743	−	0.177956i
$857$	10.5302	−	18.2389i	0.359706	−	0.623028i	−0.628206	−	0.778047i	$-0.716210\pi$
$857$	10.5302	−	18.2389i	0.359706	−	0.623028i	0.987912	+	0.155019i	$0.0495438\pi$
$858$	6.47213	+	3.73669i	0.220955	+	0.127568i
$859$	14.9966	−	8.65829i	0.511677	−	0.295417i	−0.221846	−	0.975082i	$-0.571208\pi$
$859$	14.9966	−	8.65829i	0.511677	−	0.295417i	0.733523	+	0.679665i	$0.237875\pi$
$860$	22.4745	−	12.9757i	0.766374	−	0.442466i
$861$	−17.5866	+	13.5110i	−0.599349	+	0.460452i
$862$	16.2642			0.553961
$863$	46.8673	+	27.0588i	1.59538	+	0.921093i	0.992361	+	0.123367i	$0.0393692\pi$
$863$	46.8673	+	27.0588i	1.59538	+	0.921093i	0.603019	+	0.797727i	$0.293964\pi$
$864$			1.00000i			0.0340207i
$865$		−	14.9648i		−	0.508818i
$866$	23.7816	+	13.7303i	0.808130	+	0.466574i
$867$	39.5263			1.34238
$868$	17.5878	+	7.27312i	0.596970	+	0.246866i
$869$	17.6013	−	10.1621i	0.597084	−	0.344727i
$870$	−9.21448	+	5.31998i	−0.312400	+	0.180364i
$871$	32.8982	+	18.9938i	1.11471	+	0.643579i
$872$	−3.77350	+	6.53589i	−0.127787	+	0.221333i
$873$	4.59252	−	7.95448i	0.155433	−	0.269218i
$874$	38.6106	−	4.47909i	1.30602	−	0.151507i
$875$	11.4160	+	14.8596i	0.385930	+	0.502347i
$876$	2.83669	−	1.63777i	0.0958430	−	0.0553350i
$877$		−	8.70047i		−	0.293794i	−0.989152	−	0.146897i	$-0.953071\pi$
$877$		−	8.70047i		−	0.293794i	0.989152	−	0.146897i	$-0.0469286\pi$
$878$		−	4.92053i		−	0.166060i
$879$	9.41467	−	16.3067i	0.317549	−	0.550011i
$880$	2.94256	−	1.69889i	0.0991937	−	0.0572695i
$881$			24.0522i			0.810338i	0.914242	+	0.405169i	$0.132787\pi$
$881$			24.0522i			0.810338i	−0.914242	+	0.405169i	$0.867213\pi$
$882$	1.81961	+	6.75936i	0.0612695	+	0.227600i
$883$	7.57365	−	13.1179i	0.254873	−	0.441454i	−0.709988	−	0.704214i	$-0.751300\pi$
$883$	7.57365	−	13.1179i	0.254873	−	0.441454i	0.964861	+	0.262760i	$0.0846328\pi$
$884$	−38.9463	+	22.4857i	−1.30991	+	0.756275i
$885$	−9.24883	+	5.33981i	−0.310896	+	0.179496i
$886$	−15.5754	+	8.99249i	−0.523267	+	0.302109i
$887$	−7.27633	−	12.6030i	−0.244315	−	0.423167i	0.717624	−	0.696431i	$-0.245230\pi$
$887$	−7.27633	−	12.6030i	−0.244315	−	0.423167i	−0.961939	+	0.273265i	$0.911897\pi$
$888$	0.0730658	+	0.126554i	0.00245193	+	0.00424686i
$889$	5.35138	−	0.707695i	0.179479	−	0.0237353i
$890$	−10.5742	−	18.3151i	−0.354449	−	0.613923i
$891$	−1.24941			−0.0418569
$892$	9.02437	+	15.6307i	0.302158	+	0.523354i
$893$	−9.39306	+	1.08966i	−0.314327	+	0.0364640i
$894$	−5.24790	−	3.02987i	−0.175516	−	0.101334i
$895$	11.0930	+	19.2137i	0.370800	+	0.642244i
$896$	−1.61185	−	2.09808i	−0.0538483	−	0.0700918i
$897$	26.6694	−	46.1928i	0.890465	−	1.54233i
$898$	−23.8759			−0.796749
$899$			28.1446i			0.938676i
$900$	−1.19783	−	2.07470i	−0.0399276	−	0.0691567i
$901$	−11.0704	+	19.1744i	−0.368808	+	0.638794i
$902$	9.06979	+	5.23645i	0.301991	+	0.174355i
$903$	20.0213	−	15.3814i	0.666268	−	0.511862i
$904$	10.6689			0.354841
$905$	0.292689	+	0.168984i	0.00972930	+	0.00561721i
$906$	1.23483			0.0410245
$907$	−29.6145	−	17.0979i	−0.983334	−	0.567728i	−0.0800586	−	0.996790i	$-0.525511\pi$
$907$	−29.6145	−	17.0979i	−0.983334	−	0.567728i	−0.903275	+	0.429062i	$0.858844\pi$
$908$	13.8476	+	23.9848i	0.459549	+	0.795962i
$909$	−12.9045	+	7.45044i	−0.428016	+	0.247115i
$910$	5.64239	+	42.6661i	0.187044	+	1.41437i
$911$		−	17.3248i		−	0.573997i	−0.957931	−	0.286999i	$-0.907342\pi$
$911$		−	17.3248i		−	0.573997i	0.957931	−	0.286999i	$-0.0926575\pi$
$912$	−3.49862	+	2.59993i	−0.115851	+	0.0860922i
$913$	−2.31664	+	1.33751i	−0.0766694	+	0.0442651i
$914$	19.7553	+	11.4057i	0.653448	+	0.377268i
$915$	36.1152			1.19393
$916$	11.5882	+	6.69044i	0.382884	+	0.221058i
$917$	−12.2812	−	15.9859i	−0.405562	−	0.527901i
$918$	3.75920	−	6.51112i	0.124072	−	0.214899i
$919$	−14.1865	+	24.5717i	−0.467969	+	0.810546i	−0.999330	−	0.0365992i	$-0.988348\pi$
$919$	−14.1865	+	24.5717i	−0.467969	+	0.810546i	0.531361	+	0.847146i	$0.321681\pi$
$920$	−12.1253	−	21.0016i	−0.399758	−	0.692402i
$921$	11.5657			0.381104
$922$	−2.15112	−	3.72584i	−0.0708432	−	0.122704i
$923$		−	65.5400i		−	2.15728i
$924$	2.62137	−	2.01387i	0.0862366	−	0.0662516i
$925$	−0.303179	−	0.175041i	−0.00996848	−	0.00575530i
$926$			13.3234i			0.437833i
$927$	−3.55364			−0.116717
$928$	1.95624	−	3.38830i	0.0642167	−	0.111227i
$929$		−	22.2330i		−	0.729440i	−0.931117	−	0.364720i	$-0.881165\pi$
$929$		−	22.2330i		−	0.729440i	0.931117	−	0.364720i	$-0.118835\pi$
$930$	−19.5628			−0.641491
$931$	−18.9176	+	23.9400i	−0.620000	+	0.784602i
$932$	−5.61103			−0.183795
$933$			26.0732i			0.853599i
$934$	−11.2425	+	19.4726i	−0.367867	+	0.637164i
$935$	−25.5458			−0.835438
$936$			5.98150i			0.195512i
$937$	−9.84066	−	5.68151i	−0.321480	−	0.185607i	0.330572	−	0.943781i	$-0.392758\pi$
$937$	−9.84066	−	5.68151i	−0.321480	−	0.185607i	−0.652052	+	0.758174i	$0.726092\pi$
$938$	13.3245	−	10.2366i	0.435062	−	0.334238i
$939$		−	22.9802i		−	0.749932i
$940$	2.94979	+	5.10919i	0.0962116	+	0.166643i
$941$	−26.5046			−0.864025			−0.432012	−	0.901868i	$-0.642196\pi$
$941$	−26.5046			−0.864025			−0.432012	+	0.901868i	$0.642196\pi$
$942$	−6.76935	−	11.7249i	−0.220557	−	0.382016i
$943$	37.3734	−	64.7327i	1.21705	−	2.10799i
$944$	1.96353	−	3.40093i	0.0639075	−	0.110691i
$945$	−4.38343	−	5.70571i	−0.142593	−	0.185607i
$946$	−10.3254	−	5.96139i	−0.335709	−	0.193822i
$947$	−6.21815			−0.202063			−0.101031	−	0.994883i	$-0.532214\pi$
$947$	−6.21815			−0.202063			−0.101031	+	0.994883i	$0.532214\pi$
$948$	14.0877	+	8.13351i	0.457546	+	0.264164i
$949$	16.9677	−	9.79630i	0.550795	−	0.318001i
$950$	4.14433	−	9.58483i	0.134460	−	0.310973i
$951$		−	21.6094i		−	0.700734i
$952$	2.60789	+	19.7201i	0.0845223	+	0.639133i
$953$	−32.4451	+	18.7322i	−1.05100	+	0.606795i	−0.922929	−	0.384969i	$-0.874212\pi$
$953$	−32.4451	+	18.7322i	−1.05100	+	0.606795i	−0.128071	+	0.991765i	$0.540879\pi$
$954$	1.47244	+	2.55034i	0.0476719	+	0.0825702i
$955$	−10.1253	−	5.84585i	−0.327647	−	0.189167i
$956$	−18.7264			−0.605654
$957$	4.23340	+	2.44415i	0.136846	+	0.0790082i
$958$	−22.4939			−0.726746
$959$	27.6729	−	21.2598i	0.893605	−	0.686515i
$960$	2.35515	+	1.35975i	0.0760122	+	0.0438857i
$961$	−10.3736	+	17.9676i	−0.334633	+	0.579601i
$962$	0.437043	+	0.756981i	0.0140908	+	0.0244061i
$963$			6.01200i			0.193734i
$964$	23.6719			0.762421
$965$	−13.7824	+	23.8719i	−0.443672	+	0.768462i
$966$	−14.3734	−	18.7092i	−0.462456	−	0.601957i
$967$	3.89756	+	6.75077i	0.125337	+	0.217090i	0.921865	−	0.387512i	$-0.126665\pi$
$967$	3.89756	+	6.75077i	0.125337	+	0.217090i	−0.796528	+	0.604602i	$0.793332\pi$
$968$	8.17438	+	4.71948i	0.262735	+	0.151690i
$969$	32.5536	−	3.77643i	1.04577	−	0.121317i
$970$	−12.4893	−	21.6322i	−0.401009	−	0.694568i
$971$	−42.7017			−1.37036			−0.685182	−	0.728372i	$-0.740277\pi$
$971$	−42.7017			−1.37036			−0.685182	+	0.728372i	$0.740277\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	37.2971	−	4.93237i	1.19569	−	0.158124i
$974$	−3.96356	−	6.86510i	−0.127001	−	0.219972i
$975$	−7.16482	−	12.4098i	−0.229458	−	0.397433i
$976$	−11.5009	+	6.64005i	−0.368135	+	0.212543i
$977$	10.7842	−	6.22626i	0.345017	−	0.199196i	−0.317471	−	0.948268i	$-0.602834\pi$
$977$	10.7842	−	6.22626i	0.345017	−	0.199196i	0.662488	+	0.749072i	$0.269500\pi$
$978$	−4.13037	+	2.38467i	−0.132075	+	0.0762534i
$979$	−4.85810	+	8.41447i	−0.155265	+	0.268928i
$980$	18.3935	+	4.90557i	0.587560	+	0.156703i
$981$		−	7.54700i		−	0.240957i
$982$	21.8550	−	12.6180i	0.697420	−	0.402656i
$983$	−18.4823	+	32.0123i	−0.589495	+	1.02103i	0.404804	+	0.914403i	$0.367340\pi$
$983$	−18.4823	+	32.0123i	−0.589495	+	1.02103i	−0.994299	+	0.106631i	$0.965994\pi$
$984$			8.38224i			0.267216i
$985$		−	48.8849i		−	1.55760i
$986$	−25.4746	+	14.7078i	−0.811277	+	0.468391i
$987$	3.49670	+	4.55150i	0.111301	+	0.144876i
$988$	−20.9270	+	15.5515i	−0.665777	+	0.494759i
$989$	−42.5475	+	73.6944i	−1.35293	+	2.34335i
$990$	−1.69889	+	2.94256i	−0.0539942	+	0.0935207i
$991$	14.8831	+	8.59278i	0.472778	+	0.272959i	0.717402	−	0.696659i	$-0.245331\pi$
$991$	14.8831	+	8.59278i	0.472778	+	0.272959i	−0.244624	+	0.969618i	$0.578664\pi$
$992$	6.22980	−	3.59678i	0.197796	−	0.114198i
$993$	−8.97631	+	5.18247i	−0.284855	+	0.164461i
$994$	−26.7896	−	11.0783i	−0.849713	−	0.351383i
$995$	28.5926			0.906446
$996$	−1.85418	−	1.07051i	−0.0587519	−	0.0339204i
$997$			22.3918i			0.709155i	0.935027	+	0.354578i	$0.115375\pi$
$997$			22.3918i			0.709155i	−0.935027	+	0.354578i	$0.884625\pi$
$998$			2.10396i			0.0665997i
$999$	−0.126554	−	0.0730658i	−0.00400398	−	0.00231170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.m.b.145.2	✓	28
7.3	odd	6		798.2.bc.b.31.9	yes	28
19.8	odd	6		798.2.bc.b.103.9	yes	28
133.122	even	6	inner	798.2.m.b.787.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.m.b.145.2	✓	28	1.1	even	1	trivial
798.2.m.b.787.13	yes	28	133.122	even	6	inner
798.2.bc.b.31.9	yes	28	7.3	odd	6
798.2.bc.b.103.9	yes	28	19.8	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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} -2.71950i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.09808 + 1.61185i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} -2.71950i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.09808 + 1.61185i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -2.71950 q^{10} +(0.624707 + 1.08202i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.99075 + 5.18013i) q^{13} +(1.61185 + 2.09808i) q^{14} +(-2.35515 - 1.35975i) q^{15} +1.00000 q^{16} +(-6.51112 - 3.75920i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-4.00092 - 1.72993i) q^{19} +2.71950i q^{20} +(0.346868 + 2.62291i) q^{21} +(1.08202 - 0.624707i) q^{22} +(-4.45865 - 7.72260i) q^{23} +(0.866025 + 0.500000i) q^{24} -2.39566 q^{25} +(5.18013 + 2.99075i) q^{26} -1.00000 q^{27} +(2.09808 - 1.61185i) q^{28} +(3.38830 + 1.95624i) q^{29} +(-1.35975 + 2.35515i) q^{30} +(3.59678 + 6.22980i) q^{31} -1.00000i q^{32} +1.24941 q^{33} +(-3.75920 + 6.51112i) q^{34} +(4.38343 + 5.70571i) q^{35} +(0.500000 + 0.866025i) q^{36} +(0.126554 + 0.0730658i) q^{37} +(-1.72993 + 4.00092i) q^{38} +(2.99075 + 5.18013i) q^{39} +2.71950 q^{40} +(4.19112 + 7.25923i) q^{41} +(2.62291 - 0.346868i) q^{42} +(-4.77135 - 8.26422i) q^{43} +(-0.624707 - 1.08202i) q^{44} +(-2.35515 + 1.35975i) q^{45} +(-7.72260 + 4.45865i) q^{46} +(1.87873 - 1.08468i) q^{47} +(0.500000 - 0.866025i) q^{48} +(1.80385 - 6.76359i) q^{49} +2.39566i q^{50} +(-6.51112 + 3.75920i) q^{51} +(2.99075 - 5.18013i) q^{52} -2.94488i q^{53} +1.00000i q^{54} +(2.94256 - 1.69889i) q^{55} +(-1.61185 - 2.09808i) q^{56} +(-3.49862 + 2.59993i) q^{57} +(1.95624 - 3.38830i) q^{58} +(1.96353 - 3.40093i) q^{59} +(2.35515 + 1.35975i) q^{60} +(-11.5009 + 6.64005i) q^{61} +(6.22980 - 3.59678i) q^{62} +(2.44495 + 1.01106i) q^{63} -1.00000 q^{64} +(14.0874 + 8.13334i) q^{65} -1.24941i q^{66} -6.35084i q^{67} +(6.51112 + 3.75920i) q^{68} -8.91729 q^{69} +(5.70571 - 4.38343i) q^{70} +(-9.48914 + 5.47856i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-2.83669 - 1.63777i) q^{73} +(0.0730658 - 0.126554i) q^{74} +(-1.19783 + 2.07470i) q^{75} +(4.00092 + 1.72993i) q^{76} +(-3.05475 - 1.26323i) q^{77} +(5.18013 - 2.99075i) q^{78} -16.2670i q^{79} -2.71950i q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.25923 - 4.19112i) q^{82} +2.14102i q^{83} +(-0.346868 - 2.62291i) q^{84} +(-10.2231 + 17.7070i) q^{85} +(-8.26422 + 4.77135i) q^{86} +(3.38830 - 1.95624i) q^{87} +(-1.08202 + 0.624707i) q^{88} +(3.88830 + 6.73473i) q^{89} +(1.35975 + 2.35515i) q^{90} +(-2.07479 - 15.6890i) q^{91} +(4.45865 + 7.72260i) q^{92} +7.19356 q^{93} +(-1.08468 - 1.87873i) q^{94} +(-4.70455 + 10.8805i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(4.59252 + 7.95448i) q^{97} +(-6.76359 - 1.80385i) q^{98} +(0.624707 - 1.08202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{3} - 28 q^{4} - 8 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 14 * q^3 - 28 * q^4 - 8 * q^7 - 14 * q^9	\( 28 q + 14 q^{3} - 28 q^{4} - 8 q^{7} - 14 q^{9} + 4 q^{10} - 14 q^{12} - 2 q^{13} - 4 q^{14} + 6 q^{15} + 28 q^{16} - 6 q^{17} + 2 q^{21} - 12 q^{22} - 12 q^{23} - 28 q^{25} + 24 q^{26} - 28 q^{27} + 8 q^{28} + 18 q^{29} + 2 q^{30} - 4 q^{31} + 4 q^{34} - 4 q^{35} + 14 q^{36} + 24 q^{37} + 18 q^{38} + 2 q^{39} - 4 q^{40} - 4 q^{41} + 4 q^{42} - 14 q^{43} + 6 q^{45} + 12 q^{46} + 24 q^{47} + 14 q^{48} - 24 q^{49} - 6 q^{51} + 2 q^{52} - 18 q^{55} + 4 q^{56} + 12 q^{57} - 2 q^{58} + 22 q^{59} - 6 q^{60} - 6 q^{61} + 12 q^{62} + 10 q^{63} - 28 q^{64} + 24 q^{65} + 6 q^{68} - 24 q^{69} + 30 q^{70} - 6 q^{71} - 42 q^{73} - 6 q^{74} - 14 q^{75} + 40 q^{77} + 24 q^{78} - 14 q^{81} - 6 q^{82} - 2 q^{84} + 28 q^{85} - 54 q^{86} + 18 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{90} - 22 q^{91} + 12 q^{92} - 8 q^{93} + 18 q^{94} + 20 q^{95} + 40 q^{97} + 32 q^{98}+O(q^{100}) \) 28 * q + 14 * q^3 - 28 * q^4 - 8 * q^7 - 14 * q^9 + 4 * q^10 - 14 * q^12 - 2 * q^13 - 4 * q^14 + 6 * q^15 + 28 * q^16 - 6 * q^17 + 2 * q^21 - 12 * q^22 - 12 * q^23 - 28 * q^25 + 24 * q^26 - 28 * q^27 + 8 * q^28 + 18 * q^29 + 2 * q^30 - 4 * q^31 + 4 * q^34 - 4 * q^35 + 14 * q^36 + 24 * q^37 + 18 * q^38 + 2 * q^39 - 4 * q^40 - 4 * q^41 + 4 * q^42 - 14 * q^43 + 6 * q^45 + 12 * q^46 + 24 * q^47 + 14 * q^48 - 24 * q^49 - 6 * q^51 + 2 * q^52 - 18 * q^55 + 4 * q^56 + 12 * q^57 - 2 * q^58 + 22 * q^59 - 6 * q^60 - 6 * q^61 + 12 * q^62 + 10 * q^63 - 28 * q^64 + 24 * q^65 + 6 * q^68 - 24 * q^69 + 30 * q^70 - 6 * q^71 - 42 * q^73 - 6 * q^74 - 14 * q^75 + 40 * q^77 + 24 * q^78 - 14 * q^81 - 6 * q^82 - 2 * q^84 + 28 * q^85 - 54 * q^86 + 18 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^90 - 22 * q^91 + 12 * q^92 - 8 * q^93 + 18 * q^94 + 20 * q^95 + 40 * q^97 + 32 * q^98

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