LMFDB - Embedded newform 798.2.j.l.571.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(457,798)]

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, 2, 0]))

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

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

chi := DirichletCharacter("798.457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.j (of order $3$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			571.3
Root			$2.06288i$ of defining polynomial
Character	$\chi$	$=$	798.571
Dual form			798.2.j.l.457.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.574618 + 0.995268i) q^{5} +1.00000 q^{6} +(0.00953166 - 2.64573i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.574618 + 0.995268i) q^{5} +1.00000 q^{6} +(0.00953166 - 2.64573i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.574618 + 0.995268i) q^{10} +(1.08415 - 1.87780i) q^{11} +(0.500000 + 0.866025i) q^{12} +2.29847 q^{13} +(2.29604 - 1.31461i) q^{14} +1.14924 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.49840 - 4.32735i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} -1.14924 q^{20} +(-2.28651 - 1.33112i) q^{21} +2.16830 q^{22} +(3.45783 + 5.98914i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.83963 - 3.18633i) q^{25} +(1.14924 + 1.99054i) q^{26} -1.00000 q^{27} +(2.28651 + 1.33112i) q^{28} +3.76643 q^{29} +(0.574618 + 0.995268i) q^{30} +(-2.19283 + 3.79808i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.08415 - 1.87780i) q^{33} +4.99679 q^{34} +(2.63869 - 1.51080i) q^{35} +1.00000 q^{36} +(-0.330096 - 0.571742i) q^{37} +(0.500000 - 0.866025i) q^{38} +(1.14924 - 1.99054i) q^{39} +(-0.574618 - 0.995268i) q^{40} +0.806583 q^{41} +(0.00953166 - 2.64573i) q^{42} -2.08397 q^{43} +(1.08415 + 1.87780i) q^{44} +(0.574618 - 0.995268i) q^{45} +(-3.45783 + 5.98914i) q^{46} +(1.86113 + 3.22356i) q^{47} -1.00000 q^{48} +(-6.99982 - 0.0504365i) q^{49} +3.67925 q^{50} +(-2.49840 - 4.32735i) q^{51} +(-1.14924 + 1.99054i) q^{52} +(5.63567 - 9.76126i) q^{53} +(-0.500000 - 0.866025i) q^{54} +2.49189 q^{55} +(-0.00953166 + 2.64573i) q^{56} -1.00000 q^{57} +(1.88322 + 3.26183i) q^{58} +(-5.21331 + 9.02972i) q^{59} +(-0.574618 + 0.995268i) q^{60} +(-1.28811 - 2.23107i) q^{61} -4.38565 q^{62} +(-2.29604 + 1.31461i) q^{63} +1.00000 q^{64} +(1.32075 + 2.28760i) q^{65} +(1.08415 - 1.87780i) q^{66} +(-4.44284 + 7.69523i) q^{67} +(2.49840 + 4.32735i) q^{68} +6.91567 q^{69} +(2.62774 + 1.52977i) q^{70} -0.323591 q^{71} +(0.500000 + 0.866025i) q^{72} +(2.36415 - 4.09483i) q^{73} +(0.330096 - 0.571742i) q^{74} +(-1.83963 - 3.18633i) q^{75} +1.00000 q^{76} +(-4.95783 - 2.88627i) q^{77} +2.29847 q^{78} +(3.79604 + 6.57493i) q^{79} +(0.574618 - 0.995268i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.403292 + 0.698521i) q^{82} +3.17435 q^{83} +(2.29604 - 1.31461i) q^{84} +5.74250 q^{85} +(-1.04198 - 1.80477i) q^{86} +(1.88322 - 3.26183i) q^{87} +(-1.08415 + 1.87780i) q^{88} +(-6.18879 - 10.7193i) q^{89} +1.14924 q^{90} +(0.0219083 - 6.08115i) q^{91} -6.91567 q^{92} +(2.19283 + 3.79808i) q^{93} +(-1.86113 + 3.22356i) q^{94} +(0.574618 - 0.995268i) q^{95} +(-0.500000 - 0.866025i) q^{96} -5.91567 q^{97} +(-3.45623 - 6.08724i) q^{98} -2.16830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{11} + 4 q^{12} - q^{14} - 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} - 4 q^{25} - 8 q^{27} + q^{28} - 6 q^{29} - 9 q^{31} + 4 q^{32} - 2 q^{33} - 20 q^{34} - 9 q^{35} + 8 q^{36} + 14 q^{37} + 4 q^{38} + 8 q^{41} - 2 q^{42} + 42 q^{43} + 2 q^{44} - 5 q^{46} - 7 q^{47} - 8 q^{48} - 4 q^{49} - 8 q^{50} + 10 q^{51} + 7 q^{53} - 4 q^{54} + 2 q^{56} - 8 q^{57} - 3 q^{58} - 7 q^{59} - 23 q^{61} - 18 q^{62} + q^{63} + 8 q^{64} + 48 q^{65} + 2 q^{66} - 6 q^{67} - 10 q^{68} + 10 q^{69} + 15 q^{70} + 4 q^{71} + 4 q^{72} + 5 q^{73} - 14 q^{74} + 4 q^{75} + 8 q^{76} - 17 q^{77} + 11 q^{79} - 4 q^{81} + 4 q^{82} + 28 q^{83} - q^{84} + 12 q^{85} + 21 q^{86} - 3 q^{87} - 2 q^{88} - 10 q^{89} - 48 q^{91} - 10 q^{92} + 9 q^{93} + 7 q^{94} - 4 q^{96} - 2 q^{97} + 25 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^11 + 4 * q^12 - q^14 - 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 - 4 * q^25 - 8 * q^27 + q^28 - 6 * q^29 - 9 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 - 9 * q^35 + 8 * q^36 + 14 * q^37 + 4 * q^38 + 8 * q^41 - 2 * q^42 + 42 * q^43 + 2 * q^44 - 5 * q^46 - 7 * q^47 - 8 * q^48 - 4 * q^49 - 8 * q^50 + 10 * q^51 + 7 * q^53 - 4 * q^54 + 2 * q^56 - 8 * q^57 - 3 * q^58 - 7 * q^59 - 23 * q^61 - 18 * q^62 + q^63 + 8 * q^64 + 48 * q^65 + 2 * q^66 - 6 * q^67 - 10 * q^68 + 10 * q^69 + 15 * q^70 + 4 * q^71 + 4 * q^72 + 5 * q^73 - 14 * q^74 + 4 * q^75 + 8 * q^76 - 17 * q^77 + 11 * q^79 - 4 * q^81 + 4 * q^82 + 28 * q^83 - q^84 + 12 * q^85 + 21 * q^86 - 3 * q^87 - 2 * q^88 - 10 * q^89 - 48 * q^91 - 10 * q^92 + 9 * q^93 + 7 * q^94 - 4 * q^96 - 2 * q^97 + 25 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.574618	+	0.995268i	0.256977	+	0.445098i	0.965431	−	0.260660i	$-0.0839401\pi$
$5$	0.574618	+	0.995268i	0.256977	+	0.445098i	−0.708453	+	0.705758i	$0.750607\pi$
$6$	1.00000			0.408248
$7$	0.00953166	−	2.64573i	0.00360263	−	0.999994i
$7$	0.00953166	−	2.64573i	0.00360263	−	0.999994i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.574618	+	0.995268i	−0.181710	+	0.314732i
$11$	1.08415	−	1.87780i	0.326884	−	0.566179i	−0.655008	−	0.755622i	$-0.727335\pi$
$11$	1.08415	−	1.87780i	0.326884	−	0.566179i	0.981892	+	0.189443i	$0.0606682\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	2.29847			0.637482			0.318741	−	0.947842i	$-0.396740\pi$
$13$	2.29847			0.637482			0.318741	+	0.947842i	$0.396740\pi$
$14$	2.29604	−	1.31461i	0.613642	−	0.351345i
$15$	1.14924			0.296732
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.49840	−	4.32735i	0.605950	−	1.04954i	−0.385951	−	0.922519i	$-0.626126\pi$
$17$	2.49840	−	4.32735i	0.605950	−	1.04954i	0.991901	−	0.127017i	$-0.0405402\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$	−1.14924			−0.256977
$21$	−2.28651	−	1.33112i	−0.498957	−	0.290475i
$22$	2.16830			0.462283
$23$	3.45783	+	5.98914i	0.721008	+	1.24882i	0.960596	+	0.277948i	$0.0896544\pi$
$23$	3.45783	+	5.98914i	0.721008	+	1.24882i	−0.239588	+	0.970875i	$0.577012\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	1.83963	−	3.18633i	0.367925	−	0.637266i
$26$	1.14924	+	1.99054i	0.225384	+	0.390376i
$27$	−1.00000			−0.192450
$28$	2.28651	+	1.33112i	0.432109	+	0.251558i
$29$	3.76643			0.699409			0.349704	−	0.936860i	$-0.386282\pi$
$29$	3.76643			0.699409			0.349704	+	0.936860i	$0.386282\pi$
$30$	0.574618	+	0.995268i	0.104911	+	0.181710i
$31$	−2.19283	+	3.79808i	−0.393843	+	0.682156i	−0.992953	−	0.118511i	$-0.962188\pi$
$31$	−2.19283	+	3.79808i	−0.393843	+	0.682156i	0.599110	+	0.800667i	$0.295521\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.08415	−	1.87780i	−0.188726	−	0.326884i
$34$	4.99679			0.856943
$35$	2.63869	−	1.51080i	0.446020	−	0.255372i
$36$	1.00000			0.166667
$37$	−0.330096	−	0.571742i	−0.0542674	−	0.0939938i	0.837616	−	0.546260i	$-0.183949\pi$
$37$	−0.330096	−	0.571742i	−0.0542674	−	0.0939938i	−0.891883	+	0.452266i	$0.850616\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$	1.14924	−	1.99054i	0.184025	−	0.318741i
$40$	−0.574618	−	0.995268i	−0.0908552	−	0.157366i
$41$	0.806583			0.125967			0.0629836	−	0.998015i	$-0.479938\pi$
$41$	0.806583			0.125967			0.0629836	+	0.998015i	$0.479938\pi$
$42$	0.00953166	−	2.64573i	0.00147077	−	0.408246i
$43$	−2.08397			−0.317802			−0.158901	−	0.987295i	$-0.550795\pi$
$43$	−2.08397			−0.317802			−0.158901	+	0.987295i	$0.550795\pi$
$44$	1.08415	+	1.87780i	0.163442	+	0.283089i
$45$	0.574618	−	0.995268i	0.0856591	−	0.148366i
$46$	−3.45783	+	5.98914i	−0.509830	+	0.883051i
$47$	1.86113	+	3.22356i	0.271473	+	0.470205i	0.969239	−	0.246120i	$-0.0791559\pi$
$47$	1.86113	+	3.22356i	0.271473	+	0.470205i	−0.697766	+	0.716326i	$0.745823\pi$
$48$	−1.00000			−0.144338
$49$	−6.99982	−	0.0504365i	−0.999974	−	0.00720521i
$50$	3.67925			0.520325
$51$	−2.49840	−	4.32735i	−0.349845	−	0.605950i
$52$	−1.14924	+	1.99054i	−0.159370	+	0.276038i
$53$	5.63567	−	9.76126i	0.774118	−	1.34081i	−0.161170	−	0.986927i	$-0.551527\pi$
$53$	5.63567	−	9.76126i	0.774118	−	1.34081i	0.935289	−	0.353886i	$-0.115140\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	2.49189			0.336006
$56$	−0.00953166	+	2.64573i	−0.00127372	+	0.353551i
$57$	−1.00000			−0.132453
$58$	1.88322	+	3.26183i	0.247278	+	0.428299i
$59$	−5.21331	+	9.02972i	−0.678715	+	1.17557i	0.296653	+	0.954985i	$0.404130\pi$
$59$	−5.21331	+	9.02972i	−0.678715	+	1.17557i	−0.975368	+	0.220584i	$0.929204\pi$
$60$	−0.574618	+	0.995268i	−0.0741829	+	0.128489i
$61$	−1.28811	−	2.23107i	−0.164926	−	0.285660i	0.771703	−	0.635983i	$-0.219405\pi$
$61$	−1.28811	−	2.23107i	−0.164926	−	0.285660i	−0.936629	+	0.350323i	$0.886072\pi$
$62$	−4.38565			−0.556978
$63$	−2.29604	+	1.31461i	−0.289274	+	0.165626i
$64$	1.00000			0.125000
$65$	1.32075	+	2.28760i	0.163818	+	0.283742i
$66$	1.08415	−	1.87780i	0.133450	−	0.231142i
$67$	−4.44284	+	7.69523i	−0.542779	+	0.940121i	0.455964	+	0.889998i	$0.349295\pi$
$67$	−4.44284	+	7.69523i	−0.542779	+	0.940121i	−0.998743	+	0.0501231i	$0.984039\pi$
$68$	2.49840	+	4.32735i	0.302975	+	0.524768i
$69$	6.91567			0.832549
$70$	2.62774	+	1.52977i	0.314075	+	0.182843i
$71$	−0.323591			−0.0384031			−0.0192016	−	0.999816i	$-0.506112\pi$
$71$	−0.323591			−0.0384031			−0.0192016	+	0.999816i	$0.506112\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	2.36415	−	4.09483i	0.276703	−	0.479264i	−0.693860	−	0.720110i	$-0.744091\pi$
$73$	2.36415	−	4.09483i	0.276703	−	0.479264i	0.970563	+	0.240846i	$0.0774248\pi$
$74$	0.330096	−	0.571742i	0.0383728	−	0.0664637i
$75$	−1.83963	−	3.18633i	−0.212422	−	0.367925i
$76$	1.00000			0.114708
$77$	−4.95783	−	2.88627i	−0.564998	−	0.328921i
$78$	2.29847			0.260251
$79$	3.79604	+	6.57493i	0.427088	+	0.739738i	0.996613	−	0.0822363i	$-0.0262062\pi$
$79$	3.79604	+	6.57493i	0.427088	+	0.739738i	−0.569525	+	0.821974i	$0.692873\pi$
$80$	0.574618	−	0.995268i	0.0642443	−	0.111274i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.403292	+	0.698521i	0.0445361	+	0.0771388i
$83$	3.17435			0.348431			0.174215	−	0.984708i	$-0.444261\pi$
$83$	3.17435			0.348431			0.174215	+	0.984708i	$0.444261\pi$
$84$	2.29604	−	1.31461i	0.250518	−	0.143436i
$85$	5.74250			0.622861
$86$	−1.04198	−	1.80477i	−0.112360	−	0.194613i
$87$	1.88322	−	3.26183i	0.201902	−	0.349704i
$88$	−1.08415	+	1.87780i	−0.115571	+	0.200174i
$89$	−6.18879	−	10.7193i	−0.656010	−	1.13624i	−0.981640	−	0.190745i	$-0.938910\pi$
$89$	−6.18879	−	10.7193i	−0.656010	−	1.13624i	0.325630	−	0.945497i	$-0.394424\pi$
$90$	1.14924			0.121140
$91$	0.0219083	−	6.08115i	0.00229661	−	0.637478i
$92$	−6.91567			−0.721008
$93$	2.19283	+	3.79808i	0.227385	+	0.393843i
$94$	−1.86113	+	3.22356i	−0.191960	+	0.332485i
$95$	0.574618	−	0.995268i	0.0589546	−	0.102112i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−5.91567			−0.600645			−0.300323	−	0.953838i	$-0.597094\pi$
$97$	−5.91567			−0.600645			−0.300323	+	0.953838i	$0.597094\pi$
$98$	−3.45623	−	6.08724i	−0.349132	−	0.614904i
$99$	−2.16830			−0.217922
$100$	1.83963	+	3.18633i	0.183963	+	0.318633i
$101$	6.43414	−	11.1443i	0.640221	−	1.10890i	−0.345162	−	0.938543i	$-0.612176\pi$
$101$	6.43414	−	11.1443i	0.640221	−	1.10890i	0.985383	−	0.170352i	$-0.0544905\pi$
$102$	2.49840	−	4.32735i	0.247378	−	0.428471i
$103$	−3.47791	−	6.02392i	−0.342689	−	0.593554i	0.642242	−	0.766502i	$-0.278004\pi$
$103$	−3.47791	−	6.02392i	−0.342689	−	0.593554i	−0.984931	+	0.172947i	$0.944671\pi$
$104$	−2.29847			−0.225384
$105$	0.0109541	−	3.04058i	0.00106901	−	0.296730i
$106$	11.2713			1.09477
$107$	6.19933	+	10.7376i	0.599312	+	1.03804i	0.992923	+	0.118762i	$0.0378924\pi$
$107$	6.19933	+	10.7376i	0.599312	+	1.03804i	−0.393611	+	0.919277i	$0.628774\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−9.02841	+	15.6377i	−0.864765	+	1.49782i	0.00251502	+	0.999997i	$0.499199\pi$
$109$	−9.02841	+	15.6377i	−0.864765	+	1.49782i	−0.867280	+	0.497820i	$0.834134\pi$
$110$	1.24595	+	2.15804i	0.118796	+	0.205761i
$111$	−0.660191			−0.0626626
$112$	−2.29604	+	1.31461i	−0.216955	+	0.124219i
$113$	−8.63792			−0.812587			−0.406294	−	0.913743i	$-0.633179\pi$
$113$	−8.63792			−0.812587			−0.406294	+	0.913743i	$0.633179\pi$
$114$	−0.500000	−	0.866025i	−0.0468293	−	0.0811107i
$115$	−3.97387	+	6.88295i	−0.370565	+	0.641838i
$116$	−1.88322	+	3.26183i	−0.174852	+	0.302853i
$117$	−1.14924	−	1.99054i	−0.106247	−	0.184025i
$118$	−10.4266			−0.959848
$119$	−11.4252	−	6.65134i	−1.04735	−	0.609727i
$120$	−1.14924			−0.104911
$121$	3.14924	+	5.45464i	0.286294	+	0.495876i
$122$	1.28811	−	2.23107i	0.116620	−	0.201992i
$123$	0.403292	−	0.698521i	0.0363636	−	0.0629836i
$124$	−2.19283	−	3.79808i	−0.196922	−	0.341078i
$125$	9.97452			0.892148
$126$	−2.28651	−	1.33112i	−0.203698	−	0.118586i
$127$	−13.8683			−1.23061			−0.615305	−	0.788289i	$-0.710967\pi$
$127$	−13.8683			−1.23061			−0.615305	+	0.788289i	$0.710967\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.04198	+	1.80477i	−0.0917416	+	0.158901i
$130$	−1.32075	+	2.28760i	−0.115837	+	0.200636i
$131$	−6.10565	−	10.5753i	−0.533453	−	0.923968i	−0.999237	−	0.0390690i	$-0.987561\pi$
$131$	−6.10565	−	10.5753i	−0.533453	−	0.923968i	0.465784	−	0.884899i	$-0.345773\pi$
$132$	2.16830			0.188726
$133$	−2.29604	+	1.31461i	−0.199092	+	0.113991i
$134$	−8.88568			−0.767606
$135$	−0.574618	−	0.995268i	−0.0494553	−	0.0856591i
$136$	−2.49840	+	4.32735i	−0.214236	+	0.371067i
$137$	−5.54038	+	9.59622i	−0.473347	+	0.819860i	−0.999535	−	0.0305079i	$-0.990288\pi$
$137$	−5.54038	+	9.59622i	−0.473347	+	0.819860i	0.526188	+	0.850368i	$0.323621\pi$
$138$	3.45783	+	5.98914i	0.294350	+	0.509830i
$139$	−11.0175			−0.934494			−0.467247	−	0.884127i	$-0.654754\pi$
$139$	−11.0175			−0.934494			−0.467247	+	0.884127i	$0.654754\pi$
$140$	−0.0109541	+	3.04058i	−0.000925793	+	0.256976i
$141$	3.72225			0.313470
$142$	−0.161795	−	0.280238i	−0.0135776	−	0.0235170i
$143$	2.49189	−	4.31608i	0.208382	−	0.360929i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.16426	+	3.74861i	0.179732	+	0.311305i
$146$	4.72830			0.391317
$147$	−3.54359	+	6.03680i	−0.292270	+	0.497907i
$148$	0.660191			0.0542674
$149$	10.6085	+	18.3744i	0.869082	+	1.50529i	0.862936	+	0.505312i	$0.168623\pi$
$149$	10.6085	+	18.3744i	0.869082	+	1.50529i	0.00614520	+	0.999981i	$0.498044\pi$
$150$	1.83963	−	3.18633i	0.150205	−	0.260163i
$151$	−4.70093	+	8.14226i	−0.382557	+	0.662608i	−0.991427	−	0.130662i	$-0.958290\pi$
$151$	−4.70093	+	8.14226i	−0.382557	+	0.662608i	0.608870	+	0.793270i	$0.291623\pi$
$152$	0.500000	+	0.866025i	0.0405554	+	0.0702439i
$153$	−4.99679			−0.403967
$154$	0.0206675	−	5.73675i	0.00166543	−	0.462280i
$155$	−5.04015			−0.404835
$156$	1.14924	+	1.99054i	0.0920126	+	0.159370i
$157$	−3.07361	+	5.32364i	−0.245300	+	0.424873i	−0.962216	−	0.272287i	$-0.912220\pi$
$157$	−3.07361	+	5.32364i	−0.245300	+	0.424873i	0.716916	+	0.697160i	$0.245553\pi$
$158$	−3.79604	+	6.57493i	−0.301997	+	0.523074i
$159$	−5.63567	−	9.76126i	−0.446937	−	0.774118i
$160$	1.14924			0.0908552
$161$	15.8786	−	9.09142i	1.25141	−	0.716505i
$162$	−1.00000			−0.0785674
$163$	4.30397	+	7.45469i	0.337113	+	0.583896i	0.983888	−	0.178784i	$-0.0572163\pi$
$163$	4.30397	+	7.45469i	0.337113	+	0.583896i	−0.646776	+	0.762680i	$0.723883\pi$
$164$	−0.403292	+	0.698521i	−0.0314918	+	0.0545454i
$165$	1.24595	−	2.15804i	0.0969967	−	0.168003i
$166$	1.58718	+	2.74907i	0.123189	+	0.213369i
$167$	11.9749			0.926644			0.463322	−	0.886190i	$-0.346657\pi$
$167$	11.9749			0.926644			0.463322	+	0.886190i	$0.346657\pi$
$168$	2.28651	+	1.33112i	0.176408	+	0.102698i
$169$	−7.71702			−0.593617
$170$	2.87125	+	4.97315i	0.220215	+	0.381423i
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$	1.04198	−	1.80477i	0.0794506	−	0.137612i
$173$	−4.05092	−	7.01641i	−0.307986	−	0.533448i	0.669936	−	0.742419i	$-0.266322\pi$
$173$	−4.05092	−	7.01641i	−0.307986	−	0.533448i	−0.977922	+	0.208972i	$0.932988\pi$
$174$	3.76643			0.285532
$175$	−8.41264	−	4.89754i	−0.635936	−	0.370219i
$176$	−2.16830			−0.163442
$177$	5.21331	+	9.02972i	0.391856	+	0.678715i
$178$	6.18879	−	10.7193i	0.463869	−	0.803445i
$179$	3.42378	−	5.93016i	0.255905	−	0.443241i	−0.709236	−	0.704971i	$-0.750960\pi$
$179$	3.42378	−	5.93016i	0.255905	−	0.443241i	0.965141	+	0.261731i	$0.0842932\pi$
$180$	0.574618	+	0.995268i	0.0428295	+	0.0741829i
$181$	−16.5905			−1.23316			−0.616582	−	0.787291i	$-0.711483\pi$
$181$	−16.5905			−1.23316			−0.616582	+	0.787291i	$0.711483\pi$
$182$	5.27739	−	3.02160i	0.391186	−	0.223976i
$183$	−2.57622			−0.190440
$184$	−3.45783	−	5.98914i	−0.254915	−	0.441526i
$185$	0.379358	−	0.657067i	0.0278910	−	0.0483086i
$186$	−2.19283	+	3.79808i	−0.160786	+	0.278489i
$187$	−5.41727	−	9.38299i	−0.396150	−	0.686152i
$188$	−3.72225			−0.271473
$189$	−0.00953166	+	2.64573i	−0.000693326	+	0.192449i
$190$	1.14924			0.0833744
$191$	−7.94509	−	13.7613i	−0.574887	−	0.995733i	−0.996054	−	0.0887501i	$-0.971713\pi$
$191$	−7.94509	−	13.7613i	−0.574887	−	0.995733i	0.421167	−	0.906983i	$-0.361621\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−3.24838	+	5.62636i	−0.233824	+	0.404994i	−0.958930	−	0.283642i	$-0.908457\pi$
$193$	−3.24838	+	5.62636i	−0.233824	+	0.404994i	0.725107	+	0.688637i	$0.241790\pi$
$194$	−2.95783	−	5.12312i	−0.212360	−	0.367819i
$195$	2.64149			0.189161
$196$	3.54359	−	6.03680i	0.253113	−	0.431200i
$197$	1.06491			0.0758713			0.0379357	−	0.999280i	$-0.487922\pi$
$197$	1.06491			0.0758713			0.0379357	+	0.999280i	$0.487922\pi$
$198$	−1.08415	−	1.87780i	−0.0770472	−	0.133450i
$199$	−11.7959	+	20.4310i	−0.836186	+	1.44832i	0.0568749	+	0.998381i	$0.481886\pi$
$199$	−11.7959	+	20.4310i	−0.836186	+	1.44832i	−0.893061	+	0.449936i	$0.851447\pi$
$200$	−1.83963	+	3.18633i	−0.130081	+	0.225307i
$201$	4.44284	+	7.69523i	0.313374	+	0.542779i
$202$	12.8683			0.905409
$203$	0.0359003	−	9.96498i	0.00251971	−	0.699404i
$204$	4.99679			0.349845
$205$	0.463478	+	0.802767i	0.0323707	+	0.0560677i
$206$	3.47791	−	6.02392i	0.242317	−	0.419706i
$207$	3.45783	−	5.98914i	0.240336	−	0.416274i
$208$	−1.14924	−	1.99054i	−0.0796852	−	0.138019i
$209$	−2.16830			−0.149984
$210$	2.63869	−	1.51080i	0.182087	−	0.104255i
$211$	17.8699			1.23022			0.615109	−	0.788442i	$-0.289112\pi$
$211$	17.8699			1.23022			0.615109	+	0.788442i	$0.289112\pi$
$212$	5.63567	+	9.76126i	0.387059	+	0.670406i
$213$	−0.161795	+	0.280238i	−0.0110860	+	0.0192016i
$214$	−6.19933	+	10.7376i	−0.423777	+	0.734004i
$215$	−1.19749	−	2.07411i	−0.0816679	−	0.141453i
$216$	1.00000			0.0680414
$217$	10.0278	+	5.83783i	0.680733	+	0.396298i
$218$	−18.0568			−1.22296
$219$	−2.36415	−	4.09483i	−0.159755	−	0.276703i
$220$	−1.24595	+	2.15804i	−0.0840016	+	0.145495i
$221$	5.74250	−	9.94630i	0.386282	−	0.669060i
$222$	−0.330096	−	0.571742i	−0.0221546	−	0.0383728i
$223$	4.44605			0.297729			0.148865	−	0.988858i	$-0.452438\pi$
$223$	4.44605			0.297729			0.148865	+	0.988858i	$0.452438\pi$
$224$	−2.28651	−	1.33112i	−0.152774	−	0.0889393i
$225$	−3.67925			−0.245284
$226$	−4.31896	−	7.48066i	−0.287293	−	0.497606i
$227$	−10.0469	+	17.4017i	−0.666835	+	1.15499i	0.311949	+	0.950099i	$0.399018\pi$
$227$	−10.0469	+	17.4017i	−0.666835	+	1.15499i	−0.978784	+	0.204894i	$0.934315\pi$
$228$	0.500000	−	0.866025i	0.0331133	−	0.0573539i
$229$	−8.97773	−	15.5499i	−0.593265	−	1.02757i	−0.993789	−	0.111279i	$-0.964505\pi$
$229$	−8.97773	−	15.5499i	−0.593265	−	1.02757i	0.400524	−	0.916286i	$-0.368828\pi$
$230$	−7.94774			−0.524059
$231$	−4.97850	+	2.85047i	−0.327561	+	0.187547i
$232$	−3.76643			−0.247278
$233$	−5.12697	−	8.88016i	−0.335879	−	0.581759i	0.647775	−	0.761832i	$-0.275700\pi$
$233$	−5.12697	−	8.88016i	−0.335879	−	0.581759i	−0.983653	+	0.180073i	$0.942367\pi$
$234$	1.14924	−	1.99054i	0.0751280	−	0.130125i
$235$	−2.13887	+	3.70464i	−0.139525	+	0.241664i
$236$	−5.21331	−	9.02972i	−0.339358	−	0.587785i
$237$	7.59208			0.493158
$238$	0.0476277	−	13.2202i	0.00308724	−	0.856937i
$239$	1.73965			0.112529			0.0562644	−	0.998416i	$-0.482081\pi$
$239$	1.73965			0.112529			0.0562644	+	0.998416i	$0.482081\pi$
$240$	−0.574618	−	0.995268i	−0.0370915	−	0.0642443i
$241$	10.4246	−	18.0560i	0.671508	−	1.16309i	−0.305968	−	0.952042i	$-0.598980\pi$
$241$	10.4246	−	18.0560i	0.671508	−	1.16309i	0.977476	−	0.211044i	$-0.0676865\pi$
$242$	−3.14924	+	5.45464i	−0.202441	+	0.350637i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	2.57622			0.164926
$245$	−3.97203	−	6.99568i	−0.253764	−	0.446938i
$246$	0.806583			0.0514259
$247$	−1.14924	−	1.99054i	−0.0731242	−	0.126655i
$248$	2.19283	−	3.79808i	0.139245	−	0.241179i
$249$	1.58718	−	2.74907i	0.100583	−	0.174215i
$250$	4.98726	+	8.63819i	0.315422	+	0.546327i
$251$	3.19663			0.201769			0.100885	−	0.994898i	$-0.467833\pi$
$251$	3.19663			0.201769			0.100885	+	0.994898i	$0.467833\pi$
$252$	0.00953166	−	2.64573i	0.000600438	−	0.166666i
$253$	14.9952			0.942743
$254$	−6.93414	−	12.0103i	−0.435087	−	0.753592i
$255$	2.87125	−	4.97315i	0.179805	−	0.311431i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.51095	+	13.0094i	0.468520	+	0.811501i	0.999353	−	0.0359757i	$-0.0114539\pi$
$257$	7.51095	+	13.0094i	0.468520	+	0.811501i	−0.530832	+	0.847477i	$0.678121\pi$
$258$	−2.08397			−0.129742
$259$	−1.51582	+	0.867895i	−0.0941887	+	0.0539284i
$260$	−2.64149			−0.163818
$261$	−1.88322	−	3.26183i	−0.116568	−	0.201902i
$262$	6.10565	−	10.5753i	0.377208	−	0.653344i
$263$	−5.33802	+	9.24573i	−0.329157	+	0.570116i	−0.982345	−	0.187080i	$-0.940098\pi$
$263$	−5.33802	+	9.24573i	−0.329157	+	0.570116i	0.653188	+	0.757196i	$0.273431\pi$
$264$	1.08415	+	1.87780i	0.0667248	+	0.115571i
$265$	12.9534			0.795723
$266$	−2.28651	−	1.33112i	−0.140195	−	0.0816163i
$267$	−12.3776			−0.757495
$268$	−4.44284	−	7.69523i	−0.271390	−	0.470061i
$269$	1.62453	−	2.81377i	0.0990494	−	0.171559i	−0.812242	−	0.583321i	$-0.801753\pi$
$269$	1.62453	−	2.81377i	0.0990494	−	0.171559i	0.911291	+	0.411762i	$0.135086\pi$
$270$	0.574618	−	0.995268i	0.0349702	−	0.0605701i
$271$	−9.01746	−	15.6187i	−0.547772	−	0.948768i	−0.998427	−	0.0560702i	$-0.982143\pi$
$271$	−9.01746	−	15.6187i	−0.547772	−	0.948768i	0.450655	−	0.892698i	$-0.351190\pi$
$272$	−4.99679			−0.302975
$273$	−5.25548	−	3.05955i	−0.318076	−	0.185172i
$274$	−11.0808			−0.669413
$275$	−3.98886	−	6.90892i	−0.240538	−	0.416623i
$276$	−3.45783	+	5.98914i	−0.208137	+	0.360504i
$277$	−11.1420	+	19.2984i	−0.669455	+	1.15953i	0.308601	+	0.951192i	$0.400139\pi$
$277$	−11.1420	+	19.2984i	−0.669455	+	1.15953i	−0.978057	+	0.208339i	$0.933194\pi$
$278$	−5.50876	−	9.54145i	−0.330393	−	0.572258i
$279$	4.38565			0.262562
$280$	−2.63869	+	1.51080i	−0.157692	+	0.0902876i
$281$	7.10790			0.424022			0.212011	−	0.977267i	$-0.431999\pi$
$281$	7.10790			0.424022			0.212011	+	0.977267i	$0.431999\pi$
$282$	1.86113	+	3.22356i	0.110828	+	0.191960i
$283$	7.87368	−	13.6376i	0.468042	−	0.810672i	−0.531291	−	0.847189i	$-0.678293\pi$
$283$	7.87368	−	13.6376i	0.468042	−	0.810672i	0.999333	+	0.0365169i	$0.0116263\pi$
$284$	0.161795	−	0.280238i	0.00960078	−	0.0166290i
$285$	−0.574618	−	0.995268i	−0.0340375	−	0.0589546i
$286$	4.98378			0.294697
$287$	0.00768807	−	2.13400i	0.000453813	−	0.125966i
$288$	−1.00000			−0.0589256
$289$	−3.98396	−	6.90043i	−0.234351	−	0.405907i
$290$	−2.16426	+	3.74861i	−0.127090	+	0.220126i
$291$	−2.95783	+	5.12312i	−0.173391	+	0.300323i
$292$	2.36415	+	4.09483i	0.138352	+	0.239632i
$293$	22.0139			1.28607			0.643034	−	0.765837i	$-0.277675\pi$
$293$	22.0139			1.28607			0.643034	+	0.765837i	$0.277675\pi$
$294$	−6.99982	−	0.0504365i	−0.408238	−	0.00294151i
$295$	−11.9827			−0.697657
$296$	0.330096	+	0.571742i	0.0191864	+	0.0332318i
$297$	−1.08415	+	1.87780i	−0.0629088	+	0.108961i
$298$	−10.6085	+	18.3744i	−0.614534	+	1.06440i
$299$	7.94774	+	13.7659i	0.459630	+	0.796102i
$300$	3.67925			0.212422
$301$	−0.0198637	+	5.51363i	−0.00114492	+	0.317800i
$302$	−9.40187			−0.541017
$303$	−6.43414	−	11.1443i	−0.369632	−	0.640221i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$	1.48035	−	2.56403i	0.0847643	−	0.146816i
$306$	−2.49840	−	4.32735i	−0.142824	−	0.247378i
$307$	14.3776			0.820571			0.410286	−	0.911957i	$-0.365429\pi$
$307$	14.3776			0.820571			0.410286	+	0.911957i	$0.365429\pi$
$308$	4.97850	−	2.85047i	0.283676	−	0.162421i
$309$	−6.95582			−0.395703
$310$	−2.52008	−	4.36490i	−0.143131	−	0.247910i
$311$	1.48726	−	2.57601i	0.0843348	−	0.146072i	−0.820773	−	0.571255i	$-0.806457\pi$
$311$	1.48726	−	2.57601i	0.0843348	−	0.146072i	0.905108	+	0.425183i	$0.139790\pi$
$312$	−1.14924	+	1.99054i	−0.0650627	+	0.112692i
$313$	8.37942	+	14.5136i	0.473633	+	0.820356i	0.999544	−	0.0301834i	$-0.00960914\pi$
$313$	8.37942	+	14.5136i	0.473633	+	0.820356i	−0.525912	+	0.850539i	$0.676276\pi$
$314$	−6.14721			−0.346907
$315$	−2.62774	−	1.52977i	−0.148056	−	0.0861930i
$316$	−7.59208			−0.427088
$317$	1.40531	+	2.43406i	0.0789298	+	0.136710i	0.902788	−	0.430085i	$-0.141516\pi$
$317$	1.40531	+	2.43406i	0.0789298	+	0.136710i	−0.823859	+	0.566795i	$0.808183\pi$
$318$	5.63567	−	9.76126i	0.316032	−	0.547384i
$319$	4.08338	−	7.07262i	0.228625	−	0.395990i
$320$	0.574618	+	0.995268i	0.0321221	+	0.0556372i
$321$	12.3987			0.692026
$322$	15.8127	+	9.20560i	0.881209	+	0.513008i
$323$	−4.99679			−0.278029
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	4.22834	−	7.32369i	0.234546	−	0.406245i
$326$	−4.30397	+	7.45469i	−0.238375	+	0.412877i
$327$	9.02841	+	15.6377i	0.499272	+	0.864765i
$328$	−0.806583			−0.0445361
$329$	8.54643	−	4.89332i	0.471180	−	0.269777i
$330$	2.49189			0.137174
$331$	5.06954	+	8.78069i	0.278647	+	0.482631i	0.971049	−	0.238882i	$-0.0767808\pi$
$331$	5.06954	+	8.78069i	0.278647	+	0.482631i	−0.692402	+	0.721512i	$0.743447\pi$
$332$	−1.58718	+	2.74907i	−0.0871076	+	0.150875i
$333$	−0.330096	+	0.571742i	−0.0180891	+	0.0313313i
$334$	5.98744	+	10.3706i	0.327618	+	0.567451i
$335$	−10.2118			−0.557928
$336$	−0.00953166	+	2.64573i	−0.000519994	+	0.144337i
$337$	21.4364			1.16772			0.583858	−	0.811856i	$-0.301542\pi$
$337$	21.4364			1.16772			0.583858	+	0.811856i	$0.301542\pi$
$338$	−3.85851	−	6.68313i	−0.209875	−	0.363515i
$339$	−4.31896	+	7.48066i	−0.234574	+	0.406294i
$340$	−2.87125	+	4.97315i	−0.155715	+	0.269707i
$341$	4.75470	+	8.23539i	0.257482	+	0.445971i
$342$	−1.00000			−0.0540738
$343$	−0.200161	+	18.5192i	−0.0108077	+	0.999942i
$344$	2.08397			0.112360
$345$	3.97387	+	6.88295i	0.213946	+	0.370565i
$346$	4.05092	−	7.01641i	0.217779	−	0.377204i
$347$	−14.5913	+	25.2729i	−0.783302	+	1.35672i	0.146706	+	0.989180i	$0.453133\pi$
$347$	−14.5913	+	25.2729i	−0.783302	+	1.35672i	−0.930008	+	0.367539i	$0.880200\pi$
$348$	1.88322	+	3.26183i	0.100951	+	0.174852i
$349$	9.36208			0.501141			0.250570	−	0.968098i	$-0.419382\pi$
$349$	9.36208			0.501141			0.250570	+	0.968098i	$0.419382\pi$
$350$	0.0350694	−	9.73433i	0.00187454	−	0.520322i
$351$	−2.29847			−0.122683
$352$	−1.08415	−	1.87780i	−0.0577854	−	0.100087i
$353$	−16.7997	+	29.0980i	−0.894159	+	1.54873i	−0.0593161	+	0.998239i	$0.518892\pi$
$353$	−16.7997	+	29.0980i	−0.894159	+	1.54873i	−0.834843	+	0.550489i	$0.814441\pi$
$354$	−5.21331	+	9.02972i	−0.277084	+	0.479924i
$355$	−0.185941	−	0.322059i	−0.00986873	−	0.0170931i
$356$	12.3776			0.656010
$357$	−11.4728	+	6.56884i	−0.607206	+	0.347660i
$358$	6.84755			0.361905
$359$	12.1815	+	21.0990i	0.642915	+	1.11356i	0.984779	+	0.173812i	$0.0556087\pi$
$359$	12.1815	+	21.0990i	0.642915	+	1.11356i	−0.341863	+	0.939750i	$0.611058\pi$
$360$	−0.574618	+	0.995268i	−0.0302851	+	0.0524553i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	−8.29527	−	14.3678i	−0.435989	−	0.755156i
$363$	6.29847			0.330584
$364$	5.25548	+	3.05955i	0.275462	+	0.160364i
$365$	5.43394			0.284426
$366$	−1.28811	−	2.23107i	−0.0673307	−	0.116620i
$367$	16.5786	−	28.7149i	0.865394	−	1.49891i	−0.00126140	−	0.999999i	$-0.500402\pi$
$367$	16.5786	−	28.7149i	0.865394	−	1.49891i	0.866655	−	0.498907i	$-0.166265\pi$
$368$	3.45783	−	5.98914i	0.180252	−	0.312206i
$369$	−0.403292	−	0.698521i	−0.0209945	−	0.0363636i
$370$	0.758716			0.0394438
$371$	−25.7720	−	15.0035i	−1.33801	−	0.778944i
$372$	−4.38565			−0.227385
$373$	11.2730	+	19.5254i	0.583693	+	1.01099i	0.995037	+	0.0995064i	$0.0317264\pi$
$373$	11.2730	+	19.5254i	0.583693	+	1.01099i	−0.411343	+	0.911480i	$0.634940\pi$
$374$	5.41727	−	9.38299i	0.280120	−	0.485183i
$375$	4.98726	−	8.63819i	0.257541	−	0.446074i
$376$	−1.86113	−	3.22356i	−0.0959802	−	0.166243i
$377$	8.65704			0.445860
$378$	−2.29604	+	1.31461i	−0.118095	+	0.0676164i
$379$	18.7616			0.963717			0.481858	−	0.876249i	$-0.339962\pi$
$379$	18.7616			0.963717			0.481858	+	0.876249i	$0.339962\pi$
$380$	0.574618	+	0.995268i	0.0294773	+	0.0510562i
$381$	−6.93414	+	12.0103i	−0.355247	+	0.615305i
$382$	7.94509	−	13.7613i	0.406506	−	0.704090i
$383$	4.05885	+	7.03014i	0.207398	+	0.359223i	0.950894	−	0.309517i	$-0.100167\pi$
$383$	4.05885	+	7.03014i	0.207398	+	0.359223i	−0.743496	+	0.668740i	$0.766834\pi$
$384$	1.00000			0.0510310
$385$	0.0237518	−	6.59288i	0.00121051	−	0.336004i
$386$	−6.49676			−0.330676
$387$	1.04198	+	1.80477i	0.0529670	+	0.0917416i
$388$	2.95783	−	5.12312i	0.150161	−	0.260087i
$389$	17.5017	−	30.3138i	0.887371	−	1.53697i	0.0443993	−	0.999014i	$-0.485863\pi$
$389$	17.5017	−	30.3138i	0.887371	−	1.53697i	0.842972	−	0.537958i	$-0.180804\pi$
$390$	1.32075	+	2.28760i	0.0668786	+	0.115837i
$391$	34.5562			1.74758
$392$	6.99982	+	0.0504365i	0.353544	+	0.00254743i
$393$	−12.2113			−0.615978
$394$	0.532453	+	0.922235i	0.0268246	+	0.0464615i
$395$	−4.36255	+	7.55615i	−0.219504	+	0.380191i
$396$	1.08415	−	1.87780i	0.0544806	−	0.0943632i
$397$	−7.51095	−	13.0094i	−0.376964	−	0.652921i	0.613655	−	0.789574i	$-0.289699\pi$
$397$	−7.51095	−	13.0094i	−0.376964	−	0.652921i	−0.990619	+	0.136654i	$0.956365\pi$
$398$	−23.5917			−1.18255
$399$	−0.00953166	+	2.64573i	−0.000477180	+	0.132452i
$400$	−3.67925			−0.183963
$401$	13.3143	+	23.0611i	0.664886	+	1.15162i	0.979316	+	0.202336i	$0.0648532\pi$
$401$	13.3143	+	23.0611i	0.664886	+	1.15162i	−0.314430	+	0.949281i	$0.601814\pi$
$402$	−4.44284	+	7.69523i	−0.221589	+	0.383803i
$403$	−5.04015	+	8.72980i	−0.251068	+	0.434862i
$404$	6.43414	+	11.1443i	0.320110	+	0.554448i
$405$	−1.14924			−0.0571060
$406$	8.64787	−	4.95140i	0.429187	−	0.245734i
$407$	−1.43149			−0.0709565
$408$	2.49840	+	4.32735i	0.123689	+	0.214236i
$409$	−13.8245	+	23.9447i	−0.683575	+	1.18399i	0.290307	+	0.956934i	$0.406243\pi$
$409$	−13.8245	+	23.9447i	−0.683575	+	1.18399i	−0.973882	+	0.227053i	$0.927091\pi$
$410$	−0.463478	+	0.802767i	−0.0228895	+	0.0396458i
$411$	5.54038	+	9.59622i	0.273287	+	0.473347i
$412$	6.95582			0.342689
$413$	23.8405	+	13.8791i	1.17312	+	0.682946i
$414$	6.91567			0.339887
$415$	1.82404	+	3.15933i	0.0895387	+	0.155086i
$416$	1.14924	−	1.99054i	0.0563460	−	0.0975941i
$417$	−5.50876	+	9.54145i	−0.269765	+	0.467247i
$418$	−1.08415	−	1.87780i	−0.0530275	−	0.0918464i
$419$	1.91888			0.0937433			0.0468716	−	0.998901i	$-0.485075\pi$
$419$	1.91888			0.0937433			0.0468716	+	0.998901i	$0.485075\pi$
$420$	2.62774	+	1.52977i	0.128221	+	0.0746453i
$421$	25.9815			1.26626			0.633130	−	0.774046i	$-0.281770\pi$
$421$	25.9815			1.26626			0.633130	+	0.774046i	$0.281770\pi$
$422$	8.93497	+	15.4758i	0.434948	+	0.753351i
$423$	1.86113	−	3.22356i	0.0904910	−	0.156735i
$424$	−5.63567	+	9.76126i	−0.273692	+	0.474049i
$425$	−9.19223	−	15.9214i	−0.445889	−	0.772302i
$426$	−0.323591			−0.0156780
$427$	−5.91511	+	3.38673i	−0.286252	+	0.163896i
$428$	−12.3987			−0.599312
$429$	−2.49189	−	4.31608i	−0.120310	−	0.208382i
$430$	1.19749	−	2.07411i	0.0577479	−	0.100022i
$431$	−0.482541	+	0.835785i	−0.0232432	+	0.0402584i	−0.877413	−	0.479736i	$-0.840733\pi$
$431$	−0.482541	+	0.835785i	−0.0232432	+	0.0402584i	0.854170	+	0.519994i	$0.174066\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−5.93960			−0.285439			−0.142720	−	0.989763i	$-0.545585\pi$
$433$	−5.93960			−0.285439			−0.142720	+	0.989763i	$0.545585\pi$
$434$	−0.0418025	+	11.6033i	−0.00200658	+	0.556975i
$435$	4.32852			0.207537
$436$	−9.02841	−	15.6377i	−0.432383	−	0.748909i
$437$	3.45783	−	5.98914i	0.165411	−	0.286500i
$438$	2.36415	−	4.09483i	0.112964	−	0.195659i
$439$	−10.7960	−	18.6993i	−0.515267	−	0.892468i	−0.999843	−	0.0177192i	$-0.994359\pi$
$439$	−10.7960	−	18.6993i	−0.515267	−	0.892468i	0.484576	−	0.874749i	$-0.338974\pi$
$440$	−2.49189			−0.118796
$441$	3.45623	+	6.08724i	0.164582	+	0.289869i
$442$	11.4850			0.546286
$443$	−6.96718	−	12.0675i	−0.331021	−	0.573345i	0.651691	−	0.758484i	$-0.274060\pi$
$443$	−6.96718	−	12.0675i	−0.331021	−	0.573345i	−0.982712	+	0.185139i	$0.940726\pi$
$444$	0.330096	−	0.571742i	0.0156656	−	0.0271337i
$445$	7.11238	−	12.3190i	0.337159	−	0.583977i
$446$	2.22302	+	3.85039i	0.105263	+	0.182321i
$447$	21.2170			1.00353
$448$	0.00953166	−	2.64573i	0.000450328	−	0.124999i
$449$	14.3273			0.676149			0.338074	−	0.941119i	$-0.390224\pi$
$449$	14.3273			0.676149			0.338074	+	0.941119i	$0.390224\pi$
$450$	−1.83963	−	3.18633i	−0.0867209	−	0.150205i
$451$	0.874457	−	1.51460i	0.0411766	−	0.0713199i
$452$	4.31896	−	7.48066i	0.203147	−	0.351861i
$453$	4.70093	+	8.14226i	0.220869	+	0.382557i
$454$	−20.0938			−0.943047
$455$	6.06497	−	3.47254i	0.284330	−	0.162795i
$456$	1.00000			0.0468293
$457$	−16.1491	−	27.9710i	−0.755421	−	1.30843i	−0.945165	−	0.326594i	$-0.894099\pi$
$457$	−16.1491	−	27.9710i	−0.755421	−	1.30843i	0.189744	−	0.981834i	$-0.439234\pi$
$458$	8.97773	−	15.5499i	0.419502	−	0.726598i
$459$	−2.49840	+	4.32735i	−0.116615	+	0.201983i
$460$	−3.97387	−	6.88295i	−0.185283	−	0.320919i
$461$	0.375849			0.0175050			0.00875252	−	0.999962i	$-0.497214\pi$
$461$	0.375849			0.0175050			0.00875252	+	0.999962i	$0.497214\pi$
$462$	−4.95783	−	2.88627i	−0.230659	−	0.134282i
$463$	7.80824			0.362880			0.181440	−	0.983402i	$-0.441924\pi$
$463$	7.80824			0.362880			0.181440	+	0.983402i	$0.441924\pi$
$464$	−1.88322	−	3.26183i	−0.0874261	−	0.151426i
$465$	−2.52008	+	4.36490i	−0.116866	+	0.202417i
$466$	5.12697	−	8.88016i	0.237502	−	0.411366i
$467$	6.12774	+	10.6136i	0.283558	+	0.491137i	0.972258	−	0.233909i	$-0.0751518\pi$
$467$	6.12774	+	10.6136i	0.283558	+	0.491137i	−0.688701	+	0.725046i	$0.741819\pi$
$468$	2.29847			0.106247
$469$	20.3172	+	11.8279i	0.938160	+	0.546163i
$470$	−4.27775			−0.197318
$471$	3.07361	+	5.32364i	0.141624	+	0.245300i
$472$	5.21331	−	9.02972i	0.239962	−	0.415627i
$473$	−2.25933	+	3.91328i	−0.103884	+	0.179933i
$474$	3.79604	+	6.57493i	0.174358	+	0.301997i
$475$	−3.67925			−0.168816
$476$	11.4728	−	6.56884i	0.525856	−	0.301082i
$477$	−11.2713			−0.516079
$478$	0.869826	+	1.50658i	0.0397849	+	0.0689095i
$479$	−13.5375	+	23.4477i	−0.618546	+	1.07135i	0.371206	+	0.928551i	$0.378945\pi$
$479$	−13.5375	+	23.4477i	−0.618546	+	1.07135i	−0.989751	+	0.142802i	$0.954389\pi$
$480$	0.574618	−	0.995268i	0.0262276	−	0.0454276i
$481$	−0.758716	−	1.31413i	−0.0345945	−	0.0599194i
$482$	20.8492			0.949656
$483$	0.0659178	−	18.2970i	0.00299936	−	0.832543i
$484$	−6.29847			−0.286294
$485$	−3.39925	−	5.88768i	−0.154352	−	0.267346i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−14.8749	+	25.7641i	−0.674047	+	1.16748i	0.302699	+	0.953086i	$0.402112\pi$
$487$	−14.8749	+	25.7641i	−0.674047	+	1.16748i	−0.976746	+	0.214398i	$0.931221\pi$
$488$	1.28811	+	2.23107i	0.0583101	+	0.100996i
$489$	8.60793			0.389264
$490$	4.07242	−	6.93772i	0.183973	−	0.313414i
$491$	18.4381			0.832099			0.416050	−	0.909342i	$-0.363414\pi$
$491$	18.4381			0.832099			0.416050	+	0.909342i	$0.363414\pi$
$492$	0.403292	+	0.698521i	0.0181818	+	0.0314918i
$493$	9.41004	−	16.2987i	0.423807	−	0.734055i
$494$	1.14924	−	1.99054i	0.0517066	−	0.0895585i
$495$	−1.24595	−	2.15804i	−0.0560011	−	0.0969967i
$496$	4.38565			0.196922
$497$	−0.00308435	+	0.856135i	−0.000138352	+	0.0384029i
$498$	3.17435			0.142246
$499$	−16.5785	−	28.7148i	−0.742156	−	1.28545i	−0.951512	−	0.307612i	$-0.900470\pi$
$499$	−16.5785	−	28.7148i	−0.742156	−	1.28545i	0.209356	−	0.977840i	$-0.432863\pi$
$500$	−4.98726	+	8.63819i	−0.223037	+	0.386311i
$501$	5.98744	−	10.3706i	0.267499	−	0.463322i
$502$	1.59831	+	2.76836i	0.0713362	+	0.123558i
$503$	12.8678			0.573747			0.286873	−	0.957968i	$-0.407384\pi$
$503$	12.8678			0.573747			0.286873	+	0.957968i	$0.407384\pi$
$504$	2.29604	−	1.31461i	0.102274	−	0.0585575i
$505$	14.7887			0.658089
$506$	7.49762	+	12.9863i	0.333310	+	0.577310i
$507$	−3.85851	+	6.68313i	−0.171362	+	0.296808i
$508$	6.93414	−	12.0103i	0.307653	−	0.532870i
$509$	−4.35117	−	7.53645i	−0.192862	−	0.334047i	0.753335	−	0.657637i	$-0.228444\pi$
$509$	−4.35117	−	7.53645i	−0.192862	−	0.334047i	−0.946198	+	0.323589i	$0.895110\pi$
$510$	5.74250			0.254282
$511$	−10.8113	−	6.29395i	−0.478264	−	0.278428i
$512$	−1.00000			−0.0441942
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$	−7.51095	+	13.0094i	−0.331294	+	0.573818i
$515$	3.99694	−	6.92291i	0.176126	−	0.305060i
$516$	−1.04198	−	1.80477i	−0.0458708	−	0.0794506i
$517$	8.07096			0.354960
$518$	−1.50953	−	0.878795i	−0.0663250	−	0.0386120i
$519$	−8.10185			−0.355632
$520$	−1.32075	−	2.28760i	−0.0579185	−	0.100318i
$521$	−18.8983	+	32.7328i	−0.827948	+	1.43405i	0.0716971	+	0.997426i	$0.477159\pi$
$521$	−18.8983	+	32.7328i	−0.827948	+	1.43405i	−0.899645	+	0.436622i	$0.856175\pi$
$522$	1.88322	−	3.26183i	0.0824261	−	0.142766i
$523$	−21.1682	−	36.6644i	−0.925620	−	1.60322i	−0.790561	−	0.612383i	$-0.790211\pi$
$523$	−21.1682	−	36.6644i	−0.925620	−	1.60322i	−0.135058	−	0.990838i	$-0.543122\pi$
$524$	12.2113			0.533453
$525$	−8.44771	+	4.83679i	−0.368688	+	0.211095i
$526$	−10.6760			−0.465498
$527$	10.9571	+	18.9782i	0.477298	+	0.826705i
$528$	−1.08415	+	1.87780i	−0.0471816	+	0.0817209i
$529$	−12.4132	+	21.5004i	−0.539706	+	0.934798i
$530$	6.47672	+	11.2180i	0.281331	+	0.487279i
$531$	10.4266			0.452477
$532$	0.00953166	−	2.64573i	0.000413250	−	0.114707i
$533$	1.85391			0.0803018
$534$	−6.18879	−	10.7193i	−0.267815	−	0.463869i
$535$	−7.12450	+	12.3400i	−0.308019	+	0.533505i
$536$	4.44284	−	7.69523i	0.191901	−	0.332383i
$537$	−3.42378	−	5.93016i	−0.147747	−	0.255905i
$538$	3.24906			0.140077
$539$	−7.68356	+	13.0896i	−0.330955	+	0.563809i
$540$	1.14924			0.0494553
$541$	−4.00573	−	6.93813i	−0.172220	−	0.298294i	0.766976	−	0.641676i	$-0.221761\pi$
$541$	−4.00573	−	6.93813i	−0.172220	−	0.298294i	−0.939196	+	0.343382i	$0.888427\pi$
$542$	9.01746	−	15.6187i	0.387333	−	0.670880i
$543$	−8.29527	+	14.3678i	−0.355984	+	0.616582i
$544$	−2.49840	−	4.32735i	−0.107118	−	0.185534i
$545$	−20.7516			−0.888900
$546$	0.0219083	−	6.08115i	0.000937587	−	0.260249i
$547$	−34.1587			−1.46052			−0.730260	−	0.683170i	$-0.760601\pi$
$547$	−34.1587			−1.46052			−0.730260	+	0.683170i	$0.760601\pi$
$548$	−5.54038	−	9.59622i	−0.236673	−	0.409930i
$549$	−1.28811	+	2.23107i	−0.0549753	+	0.0952199i
$550$	3.98886	−	6.90892i	0.170086	−	0.294597i
$551$	−1.88322	−	3.26183i	−0.0802277	−	0.138958i
$552$	−6.91567			−0.294350
$553$	17.4317	−	9.98064i	0.741271	−	0.424420i
$554$	−22.2839			−0.946753
$555$	−0.379358	−	0.657067i	−0.0161029	−	0.0278910i
$556$	5.50876	−	9.54145i	0.233623	−	0.404648i
$557$	20.2395	−	35.0559i	0.857576	−	1.48537i	−0.0166578	−	0.999861i	$-0.505303\pi$
$557$	20.2395	−	35.0559i	0.857576	−	1.48537i	0.874234	−	0.485505i	$-0.161364\pi$
$558$	2.19283	+	3.79808i	0.0928297	+	0.160786i
$559$	−4.78995			−0.202593
$560$	−2.62774	−	1.52977i	−0.111042	−	0.0646448i
$561$	−10.8345			−0.457435
$562$	3.55395	+	6.15562i	0.149914	+	0.259659i
$563$	−9.10220	+	15.7655i	−0.383612	+	0.664436i	−0.991576	−	0.129529i	$-0.958653\pi$
$563$	−9.10220	+	15.7655i	−0.383612	+	0.664436i	0.607964	+	0.793965i	$0.291987\pi$
$564$	−1.86113	+	3.22356i	−0.0783675	+	0.135737i
$565$	−4.96351	−	8.59705i	−0.208816	−	0.361681i
$566$	15.7474			0.661911
$567$	2.28651	+	1.33112i	0.0960243	+	0.0559019i
$568$	0.323591			0.0135776
$569$	8.01265	+	13.8783i	0.335908	+	0.581809i	0.983659	−	0.180043i	$-0.0576237\pi$
$569$	8.01265	+	13.8783i	0.335908	+	0.581809i	−0.647751	+	0.761852i	$0.724290\pi$
$570$	0.574618	−	0.995268i	0.0240681	−	0.0416872i
$571$	−3.51315	+	6.08495i	−0.147021	+	0.254647i	−0.930125	−	0.367243i	$-0.880302\pi$
$571$	−3.51315	+	6.08495i	−0.147021	+	0.254647i	0.783104	+	0.621890i	$0.213635\pi$
$572$	2.49189	+	4.31608i	0.104191	+	0.180464i
$573$	−15.8902			−0.663822
$574$	1.85195	−	1.06034i	0.0772987	−	0.0442579i
$575$	25.4445			1.06111
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−11.4555	+	19.8414i	−0.476897	+	0.826010i	−0.999649	−	0.0264748i	$-0.991572\pi$
$577$	−11.4555	+	19.8414i	−0.476897	+	0.826010i	0.522753	+	0.852484i	$0.324905\pi$
$578$	3.98396	−	6.90043i	0.165711	−	0.287020i
$579$	3.24838	+	5.62636i	0.134998	+	0.233824i
$580$	−4.32852			−0.179732
$581$	0.0302568	−	8.39850i	0.00125527	−	0.348428i
$582$	−5.91567			−0.245212
$583$	−12.2198	−	21.1653i	−0.506093	−	0.876579i
$584$	−2.36415	+	4.09483i	−0.0978293	+	0.169445i
$585$	1.32075	−	2.28760i	0.0546061	−	0.0945806i
$586$	11.0070	+	19.0646i	0.454694	+	0.787553i
$587$	−9.55395			−0.394334			−0.197167	−	0.980370i	$-0.563174\pi$
$587$	−9.55395			−0.394334			−0.197167	+	0.980370i	$0.563174\pi$
$588$	−3.45623	−	6.08724i	−0.142533	−	0.251033i
$589$	4.38565			0.180708
$590$	−5.99133	−	10.3773i	−0.246659	−	0.427226i
$591$	0.532453	−	0.922235i	0.0219022	−	0.0379357i
$592$	−0.330096	+	0.571742i	−0.0135668	+	0.0234985i
$593$	−4.05336	−	7.02062i	−0.166452	−	0.288302i	0.770718	−	0.637176i	$-0.219898\pi$
$593$	−4.05336	−	7.02062i	−0.166452	−	0.288302i	−0.937170	+	0.348874i	$0.886564\pi$
$594$	−2.16830			−0.0889664
$595$	0.0547355	−	15.1931i	0.00224394	−	0.622857i
$596$	−21.2170			−0.869082
$597$	11.7959	+	20.4310i	0.482772	+	0.836186i
$598$	−7.94774	+	13.7659i	−0.325007	+	0.562929i
$599$	9.15859	−	15.8631i	0.374210	−	0.648150i	−0.615999	−	0.787747i	$-0.711247\pi$
$599$	9.15859	−	15.8631i	0.374210	−	0.648150i	0.990208	+	0.139597i	$0.0445807\pi$
$600$	1.83963	+	3.18633i	0.0751025	+	0.130081i
$601$	15.5629			0.634824			0.317412	−	0.948288i	$-0.397186\pi$
$601$	15.5629			0.634824			0.317412	+	0.948288i	$0.397186\pi$
$602$	−4.78487	+	2.73961i	−0.195017	+	0.111658i
$603$	8.88568			0.361853
$604$	−4.70093	−	8.14226i	−0.191278	−	0.331304i
$605$	−3.61922	+	6.26867i	−0.147142	+	0.254858i
$606$	6.43414	−	11.1443i	0.261369	−	0.452705i
$607$	−14.1959	−	24.5880i	−0.576193	−	0.997996i	−0.995911	−	0.0903411i	$-0.971204\pi$
$607$	−14.1959	−	24.5880i	−0.576193	−	0.997996i	0.419718	−	0.907655i	$-0.362129\pi$
$608$	−1.00000			−0.0405554
$609$	−8.61197	−	5.01358i	−0.348975	−	0.203160i
$610$	2.96069			0.119875
$611$	4.27775	+	7.40928i	0.173059	+	0.299747i
$612$	2.49840	−	4.32735i	0.100992	−	0.174923i
$613$	17.7205	−	30.6927i	0.715723	−	1.23967i	−0.246957	−	0.969026i	$-0.579431\pi$
$613$	17.7205	−	30.6927i	0.715723	−	1.23967i	0.962680	−	0.270642i	$-0.0872360\pi$
$614$	7.18879	+	12.4513i	0.290116	+	0.502495i
$615$	0.926955			0.0373784
$616$	4.95783	+	2.88627i	0.199757	+	0.116291i
$617$	27.6964			1.11502			0.557508	−	0.830172i	$-0.311758\pi$
$617$	27.6964			1.11502			0.557508	+	0.830172i	$0.311758\pi$
$618$	−3.47791	−	6.02392i	−0.139902	−	0.242317i
$619$	13.1957	−	22.8556i	0.530380	−	0.918645i	−0.468992	−	0.883203i	$-0.655383\pi$
$619$	13.1957	−	22.8556i	0.530380	−	0.918645i	0.999372	−	0.0354425i	$-0.0112841\pi$
$620$	2.52008	−	4.36490i	0.101209	−	0.175299i
$621$	−3.45783	−	5.98914i	−0.138758	−	0.240336i
$622$	2.97452			0.119267
$623$	−28.4194	+	16.2717i	−1.13860	+	0.651912i
$624$	−2.29847			−0.0920126
$625$	−3.46659	−	6.00431i	−0.138664	−	0.240173i
$626$	−8.37942	+	14.5136i	−0.334909	+	0.580079i
$627$	−1.08415	+	1.87780i	−0.0432968	+	0.0749922i
$628$	−3.07361	−	5.32364i	−0.122650	−	0.212436i
$629$	−3.29884			−0.131533
$630$	0.0109541	−	3.04058i	0.000436423	−	0.121139i
$631$	21.3293			0.849105			0.424553	−	0.905403i	$-0.360431\pi$
$631$	21.3293			0.849105			0.424553	+	0.905403i	$0.360431\pi$
$632$	−3.79604	−	6.57493i	−0.150998	−	0.261537i
$633$	8.93497	−	15.4758i	0.355133	−	0.615109i
$634$	−1.40531	+	2.43406i	−0.0558118	+	0.0966689i
$635$	−7.96897	−	13.8027i	−0.316239	−	0.547742i
$636$	11.2713			0.446937
$637$	−16.0889	−	0.115927i	−0.637465	−	0.00459319i
$638$	8.16675			0.323325
$639$	0.161795	+	0.280238i	0.00640052	+	0.0110860i
$640$	−0.574618	+	0.995268i	−0.0227138	+	0.0393414i
$641$	−9.50348	+	16.4605i	−0.375365	+	0.650151i	−0.990382	−	0.138363i	$-0.955816\pi$
$641$	−9.50348	+	16.4605i	−0.375365	+	0.650151i	0.615017	+	0.788514i	$0.289149\pi$
$642$	6.19933	+	10.7376i	0.244668	+	0.423777i
$643$	3.46630			0.136697			0.0683487	−	0.997661i	$-0.478227\pi$
$643$	3.46630			0.136697			0.0683487	+	0.997661i	$0.478227\pi$
$644$	−0.0659178	+	18.2970i	−0.00259752	+	0.721004i
$645$	−2.39497			−0.0943020
$646$	−2.49840	−	4.32735i	−0.0982981	−	0.170257i
$647$	−6.18045	+	10.7049i	−0.242979	+	0.420851i	−0.961561	−	0.274590i	$-0.911458\pi$
$647$	−6.18045	+	10.7049i	−0.242979	+	0.420851i	0.718583	+	0.695441i	$0.244791\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	11.3040	+	19.5791i	0.443722	+	0.768549i
$650$	8.45667			0.331698
$651$	10.0696	−	5.76543i	0.394660	−	0.225965i
$652$	−8.60793			−0.337113
$653$	−25.3561	−	43.9181i	−0.992262	−	1.71865i	−0.603658	−	0.797244i	$-0.706291\pi$
$653$	−25.3561	−	43.9181i	−0.992262	−	1.71865i	−0.388605	−	0.921405i	$-0.627043\pi$
$654$	−9.02841	+	15.6377i	−0.353039	+	0.611481i
$655$	7.01684	−	12.1535i	0.274171	−	0.474877i
$656$	−0.403292	−	0.698521i	−0.0157459	−	0.0272727i
$657$	−4.72830			−0.184469
$658$	8.51095	+	4.95477i	0.331792	+	0.193157i
$659$	−29.4985			−1.14910			−0.574549	−	0.818470i	$-0.694822\pi$
$659$	−29.4985			−1.14910			−0.574549	+	0.818470i	$0.694822\pi$
$660$	1.24595	+	2.15804i	0.0484984	+	0.0840016i
$661$	18.9490	−	32.8205i	0.737029	−	1.27657i	−0.216799	−	0.976216i	$-0.569562\pi$
$661$	18.9490	−	32.8205i	0.737029	−	1.27657i	0.953827	−	0.300355i	$-0.0971051\pi$
$662$	−5.06954	+	8.78069i	−0.197033	+	0.341271i
$663$	−5.74250	−	9.94630i	−0.223020	−	0.386282i
$664$	−3.17435			−0.123189
$665$	−2.62774	−	1.52977i	−0.101899	−	0.0593221i
$666$	−0.660191			−0.0255819
$667$	13.0237	+	22.5577i	0.504279	+	0.873438i
$668$	−5.98744	+	10.3706i	−0.231661	+	0.401249i
$669$	2.22302	−	3.85039i	0.0859471	−	0.148865i
$670$	−5.10588	−	8.84364i	−0.197257	−	0.341660i
$671$	−5.58602			−0.215646
$672$	−2.29604	+	1.31461i	−0.0885716	+	0.0507123i
$673$	−0.234048			−0.00902187			−0.00451094	−	0.999990i	$-0.501436\pi$
$673$	−0.234048			−0.00902187			−0.00451094	+	0.999990i	$0.501436\pi$
$674$	10.7182	+	18.5645i	0.412850	+	0.715077i
$675$	−1.83963	+	3.18633i	−0.0708073	+	0.122642i
$676$	3.85851	−	6.68313i	0.148404	−	0.257044i
$677$	5.61173	+	9.71981i	0.215676	+	0.373562i	0.953482	−	0.301451i	$-0.0974710\pi$
$677$	5.61173	+	9.71981i	0.215676	+	0.373562i	−0.737805	+	0.675014i	$0.764138\pi$
$678$	−8.63792			−0.331737
$679$	−0.0563861	+	15.6513i	−0.00216390	+	0.600641i
$680$	−5.74250			−0.220215
$681$	10.0469	+	17.4017i	0.384997	+	0.666835i
$682$	−4.75470	+	8.23539i	−0.182067	+	0.315349i
$683$	−8.25937	+	14.3056i	−0.316036	+	0.547390i	−0.979657	−	0.200679i	$-0.935685\pi$
$683$	−8.25937	+	14.3056i	−0.316036	+	0.547390i	0.663621	+	0.748069i	$0.269019\pi$
$684$	−0.500000	−	0.866025i	−0.0191180	−	0.0331133i
$685$	−12.7344			−0.486557
$686$	−16.1382	+	9.08624i	−0.616158	+	0.346914i
$687$	−17.9555			−0.685043
$688$	1.04198	+	1.80477i	0.0397253	+	0.0688062i
$689$	12.9534	−	22.4360i	0.493486	−	0.854744i
$690$	−3.97387	+	6.88295i	−0.151283	+	0.262029i
$691$	−20.7288	−	35.9033i	−0.788559	−	1.36582i	−0.926850	−	0.375433i	$-0.877494\pi$
$691$	−20.7288	−	35.9033i	−0.788559	−	1.36582i	0.138291	−	0.990392i	$-0.455839\pi$
$692$	8.10185			0.307986
$693$	−0.0206675	+	5.73675i	−0.000785093	+	0.217921i
$694$	−29.1826			−1.10776
$695$	−6.33087	−	10.9654i	−0.240144	−	0.415941i
$696$	−1.88322	+	3.26183i	−0.0713831	+	0.123639i
$697$	2.01516	−	3.49037i	0.0763298	−	0.132207i
$698$	4.68104	+	8.10780i	0.177180	+	0.306885i
$699$	−10.2539			−0.387839
$700$	8.44771	−	4.83679i	0.319293	−	0.182814i
$701$	26.9202			1.01676			0.508380	−	0.861133i	$-0.330244\pi$
$701$	26.9202			1.01676			0.508380	+	0.861133i	$0.330244\pi$
$702$	−1.14924	−	1.99054i	−0.0433752	−	0.0751280i
$703$	−0.330096	+	0.571742i	−0.0124498	+	0.0215637i
$704$	1.08415	−	1.87780i	0.0408604	−	0.0707724i
$705$	2.13887	+	3.70464i	0.0805547	+	0.139525i
$706$	−33.5994			−1.26453
$707$	−29.4234	−	17.1292i	−1.10658	−	0.644212i
$708$	−10.4266			−0.391856
$709$	−14.8103	−	25.6522i	−0.556212	−	0.963388i	−0.997808	−	0.0661736i	$-0.978921\pi$
$709$	−14.8103	−	25.6522i	−0.556212	−	0.963388i	0.441596	−	0.897214i	$-0.354412\pi$
$710$	0.185941	−	0.322059i	0.00697825	−	0.0120867i
$711$	3.79604	−	6.57493i	0.142363	−	0.246579i
$712$	6.18879	+	10.7193i	0.231935	+	0.401722i
$713$	−30.3297			−1.13586
$714$	−11.4252	−	6.65134i	−0.427577	−	0.248920i
$715$	5.72755			0.214198
$716$	3.42378	+	5.93016i	0.127953	+	0.221620i
$717$	0.869826	−	1.50658i	0.0324843	−	0.0562644i
$718$	−12.1815	+	21.0990i	−0.454610	+	0.787407i
$719$	13.2519	+	22.9530i	0.494213	+	0.856001i	0.999978	−	0.00666979i	$-0.00212307\pi$
$719$	13.2519	+	22.9530i	0.494213	+	0.856001i	−0.505765	+	0.862671i	$0.668790\pi$
$720$	−1.14924			−0.0428295
$721$	−15.9708	+	9.14421i	−0.594785	+	0.340548i
$722$	−1.00000			−0.0372161
$723$	−10.4246	−	18.0560i	−0.387695	−	0.671508i
$724$	8.29527	−	14.3678i	0.308291	−	0.533976i
$725$	6.92883	−	12.0011i	0.257330	−	0.445709i
$726$	3.14924	+	5.45464i	0.116879	+	0.202441i
$727$	27.4510			1.01810			0.509051	−	0.860736i	$-0.329996\pi$
$727$	27.4510			1.01810			0.509051	+	0.860736i	$0.329996\pi$
$728$	−0.0219083	+	6.08115i	−0.000811974	+	0.225382i
$729$	1.00000			0.0370370
$730$	2.71697	+	4.70593i	0.100560	+	0.174174i
$731$	−5.20658	+	9.01806i	−0.192572	+	0.333545i
$732$	1.28811	−	2.23107i	0.0476100	−	0.0824629i
$733$	7.08255	+	12.2673i	0.261600	+	0.453104i	0.966667	−	0.256036i	$-0.0824166\pi$
$733$	7.08255	+	12.2673i	0.261600	+	0.453104i	−0.705067	+	0.709140i	$0.749083\pi$
$734$	33.1571			1.22385
$735$	−8.04445	−	0.0579634i	−0.296724	−	0.00213801i
$736$	6.91567			0.254915
$737$	9.63341	+	16.6856i	0.354851	+	0.614621i
$738$	0.403292	−	0.698521i	0.0148454	−	0.0257129i
$739$	−3.77009	+	6.52999i	−0.138685	+	0.240210i	−0.926999	−	0.375063i	$-0.877621\pi$
$739$	−3.77009	+	6.52999i	−0.138685	+	0.240210i	0.788314	+	0.615273i	$0.210954\pi$
$740$	0.379358	+	0.657067i	0.0139455	+	0.0241543i
$741$	−2.29847			−0.0844365
$742$	0.107434	−	29.8209i	0.00394404	−	1.09476i
$743$	−53.8226			−1.97456			−0.987279	−	0.158997i	$-0.949174\pi$
$743$	−53.8226			−1.97456			−0.987279	+	0.158997i	$0.949174\pi$
$744$	−2.19283	−	3.79808i	−0.0803929	−	0.139245i
$745$	−12.1917	+	21.1166i	−0.446668	+	0.773652i
$746$	−11.2730	+	19.5254i	−0.412734	+	0.714876i
$747$	−1.58718	−	2.74907i	−0.0580718	−	0.100583i
$748$	10.8345			0.396150
$749$	28.4678	−	16.2994i	1.04019	−	0.595568i
$750$	9.97452			0.364218
$751$	−10.3881	−	17.9927i	−0.379068	−	0.656565i	0.611859	−	0.790967i	$-0.290422\pi$
$751$	−10.3881	−	17.9927i	−0.379068	−	0.656565i	−0.990927	+	0.134402i	$0.957089\pi$
$752$	1.86113	−	3.22356i	0.0678683	−	0.117551i
$753$	1.59831	−	2.76836i	0.0582458	−	0.100885i
$754$	4.32852	+	7.49722i	0.157635	+	0.273033i
$755$	−10.8050			−0.393233
$756$	−2.28651	−	1.33112i	−0.0831595	−	0.0484124i
$757$	−15.9757			−0.580647			−0.290323	−	0.956929i	$-0.593763\pi$
$757$	−15.9757			−0.580647			−0.290323	+	0.956929i	$0.593763\pi$
$758$	9.38078	+	16.2480i	0.340725	+	0.590154i
$759$	7.49762	−	12.9863i	0.272146	−	0.471371i
$760$	−0.574618	+	0.995268i	−0.0208436	+	0.0361022i
$761$	−7.09149	−	12.2828i	−0.257066	−	0.445252i	0.708388	−	0.705823i	$-0.249422\pi$
$761$	−7.09149	−	12.2828i	−0.257066	−	0.445252i	−0.965455	+	0.260571i	$0.916089\pi$
$762$	−13.8683			−0.502395
$763$	41.2871	+	24.0358i	1.49469	+	0.870156i
$764$	15.8902			0.574887
$765$	−2.87125	−	4.97315i	−0.103810	−	0.179805i
$766$	−4.05885	+	7.03014i	−0.146652	+	0.254009i
$767$	−11.9827	+	20.7546i	−0.432669	+	0.749404i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−39.7426			−1.43316			−0.716578	−	0.697507i	$-0.754292\pi$
$769$	−39.7426			−1.43316			−0.716578	+	0.697507i	$0.754292\pi$
$770$	5.72148	−	3.27587i	0.206188	−	0.118054i
$771$	15.0219			0.541001
$772$	−3.24838	−	5.62636i	−0.116912	−	0.202497i
$773$	−0.0918959	+	0.159168i	−0.00330527	+	0.00572489i	−0.867673	−	0.497135i	$-0.834385\pi$
$773$	−0.0918959	+	0.159168i	−0.00330527	+	0.00572489i	0.864368	+	0.502860i	$0.167719\pi$
$774$	−1.04198	+	1.80477i	−0.0374533	+	0.0648711i
$775$	8.06796	+	13.9741i	0.289810	+	0.501965i
$776$	5.91567			0.212360
$777$	−0.00629271	+	1.74669i	−0.000225750	+	0.0626622i
$778$	35.0034			1.25493
$779$	−0.403292	−	0.698521i	−0.0144494	−	0.0250271i
$780$	−1.32075	+	2.28760i	−0.0472903	+	0.0819092i
$781$	−0.350821	+	0.607639i	−0.0125534	+	0.0217430i
$782$	17.2781	+	29.9265i	0.617863	+	1.07017i
$783$	−3.76643			−0.134601
$784$	3.45623	+	6.08724i	0.123437	+	0.217401i
$785$	−7.06460			−0.252146
$786$	−6.10565	−	10.5753i	−0.217781	−	0.377208i
$787$	10.1079	−	17.5074i	0.360308	−	0.624071i	−0.627704	−	0.778452i	$-0.716005\pi$
$787$	10.1079	−	17.5074i	0.360308	−	0.624071i	0.988011	+	0.154381i	$0.0493383\pi$
$788$	−0.532453	+	0.922235i	−0.0189678	+	0.0328533i
$789$	5.33802	+	9.24573i	0.190039	+	0.329157i
$790$	−8.72510			−0.310425
$791$	−0.0823337	+	22.8536i	−0.00292745	+	0.812582i
$792$	2.16830			0.0770472
$793$	−2.96069	−	5.12807i	−0.105137	−	0.182103i
$794$	7.51095	−	13.0094i	0.266554	−	0.461685i
$795$	6.47672	−	11.2180i	0.229705	−	0.397861i
$796$	−11.7959	−	20.4310i	−0.418093	−	0.724158i
$797$	−33.9377			−1.20213			−0.601067	−	0.799198i	$-0.705258\pi$
$797$	−33.9377			−1.20213			−0.601067	+	0.799198i	$0.705258\pi$
$798$	−2.29604	+	1.31461i	−0.0812789	+	0.0465368i
$799$	18.5993			0.657996
$800$	−1.83963	−	3.18633i	−0.0650406	−	0.112654i
$801$	−6.18879	+	10.7193i	−0.218670	+	0.378748i
$802$	−13.3143	+	23.0611i	−0.470145	+	0.814316i
$803$	−5.12619	−	8.87883i	−0.180899	−	0.313327i
$804$	−8.88568			−0.313374
$805$	18.1726	+	10.5794i	0.640499	+	0.372875i
$806$	−10.0803			−0.355064
$807$	−1.62453	−	2.81377i	−0.0571862	−	0.0990494i
$808$	−6.43414	+	11.1443i	−0.226352	+	0.392054i
$809$	17.3595	−	30.0676i	0.610328	−	1.05712i	−0.380857	−	0.924634i	$-0.624371\pi$
$809$	17.3595	−	30.0676i	0.610328	−	1.05712i	0.991185	−	0.132485i	$-0.0422958\pi$
$810$	−0.574618	−	0.995268i	−0.0201900	−	0.0349702i
$811$	44.1620			1.55074			0.775369	−	0.631509i	$-0.217564\pi$
$811$	44.1620			1.55074			0.775369	+	0.631509i	$0.217564\pi$
$812$	8.61197	+	5.01358i	0.302221	+	0.175942i
$813$	−18.0349			−0.632512
$814$	−0.715746	−	1.23971i	−0.0250869	−	0.0434518i
$815$	−4.94628	+	8.56720i	−0.173261	+	0.300096i
$816$	−2.49840	+	4.32735i	−0.0874613	+	0.151487i
$817$	1.04198	+	1.80477i	0.0364544	+	0.0631409i
$818$	−27.6489			−0.966721
$819$	−5.27739	+	3.02160i	−0.184407	+	0.105583i
$820$	−0.926955			−0.0323707
$821$	−6.05371	−	10.4853i	−0.211276	−	0.365941i	0.740838	−	0.671684i	$-0.234429\pi$
$821$	−6.05371	−	10.4853i	−0.211276	−	0.365941i	−0.952114	+	0.305743i	$0.901095\pi$
$822$	−5.54038	+	9.59622i	−0.193243	+	0.334707i
$823$	−1.84812	+	3.20103i	−0.0644213	+	0.111581i	−0.896437	−	0.443171i	$-0.853853\pi$
$823$	−1.84812	+	3.20103i	−0.0644213	+	0.111581i	0.832016	+	0.554752i	$0.187187\pi$
$824$	3.47791	+	6.02392i	0.121159	+	0.209853i
$825$	−7.97773			−0.277749
$826$	−0.0993830	+	27.5861i	−0.00345798	+	0.959842i
$827$	−11.8614			−0.412461			−0.206230	−	0.978503i	$-0.566120\pi$
$827$	−11.8614			−0.412461			−0.206230	+	0.978503i	$0.566120\pi$
$828$	3.45783	+	5.98914i	0.120168	+	0.208137i
$829$	−17.1460	+	29.6978i	−0.595506	+	1.03145i	0.397969	+	0.917399i	$0.369715\pi$
$829$	−17.1460	+	29.6978i	−0.595506	+	1.03145i	−0.993475	+	0.114048i	$0.963618\pi$
$830$	−1.82404	+	3.15933i	−0.0633134	+	0.109662i
$831$	11.1420	+	19.2984i	0.386510	+	0.669455i
$832$	2.29847			0.0796852
$833$	−17.7066	+	30.1646i	−0.613496	+	1.04514i
$834$	−11.0175			−0.381505
$835$	6.88099	+	11.9182i	0.238126	+	0.412447i
$836$	1.08415	−	1.87780i	0.0374961	−	0.0649452i
$837$	2.19283	−	3.79808i	0.0757951	−	0.131281i
$838$	0.959438	+	1.66180i	0.0331432	+	0.0574058i
$839$	23.5395			0.812672			0.406336	−	0.913724i	$-0.366806\pi$
$839$	23.5395			0.812672			0.406336	+	0.913724i	$0.366806\pi$
$840$	−0.0109541	+	3.04058i	−0.000377953	+	0.104910i
$841$	−14.8140			−0.510827
$842$	12.9907	+	22.5006i	0.447690	+	0.775423i
$843$	3.55395	−	6.15562i	0.122405	−	0.212011i
$844$	−8.93497	+	15.4758i	−0.307554	+	0.532700i
$845$	−4.43434	−	7.68050i	−0.152546	−	0.264217i
$846$	3.72225			0.127974
$847$	14.4615	−	8.28005i	0.496904	−	0.284506i
$848$	−11.2713			−0.387059
$849$	−7.87368	−	13.6376i	−0.270224	−	0.468042i
$850$	9.19223	−	15.9214i	0.315291	−	0.546100i
$851$	2.28283	−	3.95398i	0.0782544	−	0.135541i
$852$	−0.161795	−	0.280238i	−0.00554301	−	0.00960078i
$853$	−54.9855			−1.88267			−0.941334	−	0.337477i	$-0.890427\pi$
$853$	−54.9855			−1.88267			−0.941334	+	0.337477i	$0.890427\pi$
$854$	−5.89055	−	3.42927i	−0.201571	−	0.117347i
$855$	−1.14924			−0.0393031
$856$	−6.19933	−	10.7376i	−0.211889	−	0.367002i
$857$	−29.0666	+	50.3449i	−0.992897	+	1.71975i	−0.393412	+	0.919362i	$0.628705\pi$
$857$	−29.0666	+	50.3449i	−0.992897	+	1.71975i	−0.599485	+	0.800386i	$0.704628\pi$
$858$	2.49189	−	4.31608i	0.0850717	−	0.147349i
$859$	−5.82584	−	10.0907i	−0.198775	−	0.344289i	0.749356	−	0.662167i	$-0.230363\pi$
$859$	−5.82584	−	10.0907i	−0.198775	−	0.344289i	−0.948132	+	0.317878i	$0.897030\pi$
$860$	2.39497			0.0816679
$861$	−1.84426	−	1.07366i	−0.0628521	−	0.0365902i
$862$	−0.965082			−0.0328708
$863$	4.82235	+	8.35255i	0.164155	+	0.284324i	0.936355	−	0.351055i	$-0.114177\pi$
$863$	4.82235	+	8.35255i	0.164155	+	0.284324i	−0.772200	+	0.635379i	$0.780844\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	4.65547	−	8.06351i	0.158291	−	0.274168i
$866$	−2.96980	−	5.14385i	−0.100918	−	0.174795i
$867$	−7.96793			−0.270605
$868$	−10.0696	+	5.76543i	−0.341785	+	0.195691i
$869$	16.4619			0.558432
$870$	2.16426	+	3.74861i	0.0733753	+	0.127090i
$871$	−10.2118	+	17.6873i	−0.346012	+	0.599310i
$872$	9.02841	−	15.6377i	0.305741	−	0.529558i
$873$	2.95783	+	5.12312i	0.100108	+	0.173391i
$874$	6.91567			0.233926
$875$	0.0950737	−	26.3899i	0.00321408	−	0.892142i
$876$	4.72830			0.159755
$877$	25.9599	+	44.9639i	0.876605	+	1.51832i	0.855043	+	0.518556i	$0.173530\pi$
$877$	25.9599	+	44.9639i	0.876605	+	1.51832i	0.0215614	+	0.999768i	$0.493136\pi$
$878$	10.7960	−	18.6993i	0.364349	−	0.631070i
$879$	11.0070	−	19.0646i	0.371256	−	0.643034i
$880$	−1.24595	−	2.15804i	−0.0420008	−	0.0727475i
$881$	1.32443			0.0446213			0.0223106	−	0.999751i	$-0.492898\pi$
$881$	1.32443			0.0446213			0.0223106	+	0.999751i	$0.492898\pi$
$882$	−3.54359	+	6.03680i	−0.119319	+	0.203270i
$883$	−45.6432			−1.53602			−0.768009	−	0.640439i	$-0.778752\pi$
$883$	−45.6432			−1.53602			−0.768009	+	0.640439i	$0.778752\pi$
$884$	5.74250	+	9.94630i	0.193141	+	0.334530i
$885$	−5.99133	+	10.3773i	−0.201396	+	0.348829i
$886$	6.96718	−	12.0675i	0.234067	−	0.405416i
$887$	−2.59044	−	4.48678i	−0.0869786	−	0.150651i	0.819254	−	0.573431i	$-0.194388\pi$
$887$	−2.59044	−	4.48678i	−0.0869786	−	0.150651i	−0.906233	+	0.422779i	$0.861054\pi$
$888$	0.660191			0.0221546
$889$	−0.132188	+	36.6918i	−0.00443343	+	1.23060i
$890$	14.2248			0.476815
$891$	1.08415	+	1.87780i	0.0363204	+	0.0629088i
$892$	−2.22302	+	3.85039i	−0.0744324	+	0.128921i
$893$	1.86113	−	3.22356i	0.0622802	−	0.107872i
$894$	10.6085	+	18.3744i	0.354801	+	0.614534i
$895$	7.86946			0.263047
$896$	2.29604	−	1.31461i	0.0767053	−	0.0439181i
$897$	15.8955			0.530735
$898$	7.16367	+	12.4078i	0.239055	+	0.414055i
$899$	−8.25913	+	14.3052i	−0.275457	+	0.477106i
$900$	1.83963	−	3.18633i	0.0613209	−	0.106211i
$901$	−28.1602	−	48.7750i	−0.938154	−	1.62493i
$902$	1.74891			0.0582325
$903$	4.76501	+	2.77402i	0.158570	+	0.0923135i
$904$	8.63792			0.287293
$905$	−9.53323	−	16.5120i	−0.316895	−	0.548878i
$906$	−4.70093	+	8.14226i	−0.156178	+	0.270508i
$907$	−29.2508	+	50.6640i	−0.971258	+	1.68227i	−0.279491	+	0.960148i	$0.590166\pi$
$907$	−29.2508	+	50.6640i	−0.971258	+	1.68227i	−0.691767	+	0.722121i	$0.743168\pi$
$908$	−10.0469	−	17.4017i	−0.333418	−	0.577496i
$909$	−12.8683			−0.426814
$910$	6.03979	+	3.51615i	0.200217	+	0.116559i
$911$	23.2344			0.769790			0.384895	−	0.922960i	$-0.374238\pi$
$911$	23.2344			0.769790			0.384895	+	0.922960i	$0.374238\pi$
$912$	0.500000	+	0.866025i	0.0165567	+	0.0286770i
$913$	3.44148	−	5.96081i	0.113896	−	0.197274i
$914$	16.1491	−	27.9710i	0.534163	−	0.925198i
$915$	−1.48035	−	2.56403i	−0.0489387	−	0.0847643i
$916$	17.9555			0.593265
$917$	−28.0376	+	16.0531i	−0.925884	+	0.530121i
$918$	−4.99679			−0.164919
$919$	−8.93753	−	15.4803i	−0.294822	−	0.510647i	0.680122	−	0.733099i	$-0.261927\pi$
$919$	−8.93753	−	15.4803i	−0.294822	−	0.510647i	−0.974943	+	0.222453i	$0.928594\pi$
$920$	3.97387	−	6.88295i	0.131015	−	0.226924i
$921$	7.18879	−	12.4513i	0.236879	−	0.410286i
$922$	0.187925	+	0.325495i	0.00618897	+	0.0107196i
$923$	−0.743764			−0.0244813
$924$	0.0206675	−	5.73675i	0.000679911	−	0.188725i
$925$	−2.42901			−0.0798654
$926$	3.90412	+	6.76214i	0.128297	+	0.222218i
$927$	−3.47791	+	6.02392i	−0.114230	+	0.197851i
$928$	1.88322	−	3.26183i	0.0618196	−	0.107075i
$929$	−23.2246	−	40.2262i	−0.761974	−	1.31978i	−0.941832	−	0.336085i	$-0.890897\pi$
$929$	−23.2246	−	40.2262i	−0.761974	−	1.31978i	0.179857	−	0.983693i	$-0.442436\pi$
$930$	−5.04015			−0.165273
$931$	3.45623	+	6.08724i	0.113273	+	0.199501i
$932$	10.2539			0.335879
$933$	−1.48726	−	2.57601i	−0.0486907	−	0.0843348i
$934$	−6.12774	+	10.6136i	−0.200506	+	0.347286i
$935$	6.22573	−	10.7833i	0.203603	−	0.352651i
$936$	1.14924	+	1.99054i	0.0375640	+	0.0650627i
$937$	−42.3561			−1.38371			−0.691857	−	0.722034i	$-0.743207\pi$
$937$	−42.3561			−1.38371			−0.691857	+	0.722034i	$0.743207\pi$
$938$	−0.0846953	+	23.5092i	−0.00276540	+	0.767601i
$939$	16.7588			0.546904
$940$	−2.13887	−	3.70464i	−0.0697624	−	0.120832i
$941$	23.2485	−	40.2675i	0.757878	−	1.31268i	−0.186052	−	0.982540i	$-0.559569\pi$
$941$	23.2485	−	40.2675i	0.757878	−	1.31268i	0.943931	−	0.330144i	$-0.107097\pi$
$942$	−3.07361	+	5.32364i	−0.100143	+	0.173454i
$943$	2.78903	+	4.83074i	0.0908233	+	0.157311i
$944$	10.4266			0.339358
$945$	−2.63869	+	1.51080i	−0.0858367	+	0.0491464i
$946$	−4.51867			−0.146915
$947$	−23.6328	−	40.9333i	−0.767964	−	1.33015i	−0.938665	−	0.344830i	$-0.887937\pi$
$947$	−23.6328	−	40.9333i	−0.767964	−	1.33015i	0.170701	−	0.985323i	$-0.445397\pi$
$948$	−3.79604	+	6.57493i	−0.123290	+	0.213544i
$949$	5.43394	−	9.41186i	0.176393	−	0.305522i
$950$	−1.83963	−	3.18633i	−0.0596854	−	0.103378i
$951$	2.81061			0.0911403
$952$	11.4252	+	6.65134i	0.370293	+	0.215571i
$953$	−0.673201			−0.0218071			−0.0109036	−	0.999941i	$-0.503471\pi$
$953$	−0.673201			−0.0218071			−0.0109036	+	0.999941i	$0.503471\pi$
$954$	−5.63567	−	9.76126i	−0.182461	−	0.316032i
$955$	9.13080	−	15.8150i	0.295466	−	0.511761i
$956$	−0.869826	+	1.50658i	−0.0281322	+	0.0487264i
$957$	−4.08338	−	7.07262i	−0.131997	−	0.228625i
$958$	−27.0751			−0.874756
$959$	25.3362	+	14.7498i	0.818150	+	0.476297i
$960$	1.14924			0.0370915
$961$	5.88303	+	10.1897i	0.189775	+	0.328700i
$962$	0.758716	−	1.31413i	0.0244620	−	0.0423694i
$963$	6.19933	−	10.7376i	0.199771	−	0.346013i
$964$	10.4246	+	18.0560i	0.335754	+	0.581543i
$965$	−7.46632			−0.240349
$966$	15.8786	−	9.09142i	0.510887	−	0.292512i
$967$	1.83609			0.0590447			0.0295224	−	0.999564i	$-0.490601\pi$
$967$	1.83609			0.0590447			0.0295224	+	0.999564i	$0.490601\pi$
$968$	−3.14924	−	5.45464i	−0.101220	−	0.175319i
$969$	−2.49840	+	4.32735i	−0.0802600	+	0.139014i
$970$	3.39925	−	5.88768i	0.109143	−	0.189042i
$971$	−6.32442	−	10.9542i	−0.202960	−	0.351538i	0.746521	−	0.665362i	$-0.231723\pi$
$971$	−6.32442	−	10.9542i	−0.202960	−	0.351538i	−0.949481	+	0.313825i	$0.898390\pi$
$972$	−1.00000			−0.0320750
$973$	−0.105015	+	29.1494i	−0.00336663	+	0.934488i
$974$	−29.7498			−0.953247
$975$	−4.22834	−	7.32369i	−0.135415	−	0.234546i
$976$	−1.28811	+	2.23107i	−0.0412314	+	0.0714149i
$977$	−10.6728	+	18.4859i	−0.341454	+	0.591416i	−0.984703	−	0.174241i	$-0.944253\pi$
$977$	−10.6728	+	18.4859i	−0.341454	+	0.591416i	0.643249	+	0.765657i	$0.277586\pi$
$978$	4.30397	+	7.45469i	0.137626	+	0.238375i
$979$	−26.8383			−0.857756
$980$	8.04445	+	0.0579634i	0.256971	+	0.00185157i
$981$	18.0568			0.576510
$982$	9.21904	+	15.9679i	0.294191	+	0.509555i
$983$	−12.8634	+	22.2801i	−0.410279	+	0.710624i	−0.994920	−	0.100668i	$-0.967902\pi$
$983$	−12.8634	+	22.2801i	−0.410279	+	0.710624i	0.584641	+	0.811292i	$0.301235\pi$
$984$	−0.403292	+	0.698521i	−0.0128565	+	0.0222681i
$985$	0.611914	+	1.05987i	0.0194972	+	0.0337702i
$986$	18.8201			0.599353
$987$	0.0354792	−	9.84809i	0.00112932	−	0.313468i
$988$	2.29847			0.0731242
$989$	−7.20602	−	12.4812i	−0.229138	−	0.396879i
$990$	1.24595	−	2.15804i	0.0395987	−	0.0685870i
$991$	29.0912	−	50.3874i	0.924111	−	1.60061i	0.131126	−	0.991366i	$-0.458141\pi$
$991$	29.0912	−	50.3874i	0.924111	−	1.60061i	0.792985	−	0.609241i	$-0.208526\pi$
$992$	2.19283	+	3.79808i	0.0696223	+	0.120589i
$993$	10.1391			0.321754
$994$	−0.742976	+	0.425396i	−0.0235658	+	0.0134927i
$995$	−27.1125			−0.859523
$996$	1.58718	+	2.74907i	0.0502916	+	0.0871076i
$997$	25.6396	−	44.4091i	0.812014	−	1.40645i	−0.0994388	−	0.995044i	$-0.531705\pi$
$997$	25.6396	−	44.4091i	0.812014	−	1.40645i	0.911453	−	0.411405i	$-0.134962\pi$
$998$	16.5785	−	28.7148i	0.524783	−	0.908952i
$999$	0.330096	+	0.571742i	0.0104438	+	0.0180891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.j.l.571.3	yes	8
7.2	even	3	inner	798.2.j.l.457.3	✓	8
7.3	odd	6		5586.2.a.bz.1.3		4
7.4	even	3		5586.2.a.bw.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.l.457.3	✓	8	7.2	even	3	inner
798.2.j.l.571.3	yes	8	1.1	even	1	trivial
5586.2.a.bw.1.2		4	7.4	even	3
5586.2.a.bz.1.3		4	7.3	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.574618 + 0.995268i) q^{5} +1.00000 q^{6} +(0.00953166 - 2.64573i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.574618 + 0.995268i) q^{5} +1.00000 q^{6} +(0.00953166 - 2.64573i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.574618 + 0.995268i) q^{10} +(1.08415 - 1.87780i) q^{11} +(0.500000 + 0.866025i) q^{12} +2.29847 q^{13} +(2.29604 - 1.31461i) q^{14} +1.14924 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.49840 - 4.32735i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} -1.14924 q^{20} +(-2.28651 - 1.33112i) q^{21} +2.16830 q^{22} +(3.45783 + 5.98914i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.83963 - 3.18633i) q^{25} +(1.14924 + 1.99054i) q^{26} -1.00000 q^{27} +(2.28651 + 1.33112i) q^{28} +3.76643 q^{29} +(0.574618 + 0.995268i) q^{30} +(-2.19283 + 3.79808i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.08415 - 1.87780i) q^{33} +4.99679 q^{34} +(2.63869 - 1.51080i) q^{35} +1.00000 q^{36} +(-0.330096 - 0.571742i) q^{37} +(0.500000 - 0.866025i) q^{38} +(1.14924 - 1.99054i) q^{39} +(-0.574618 - 0.995268i) q^{40} +0.806583 q^{41} +(0.00953166 - 2.64573i) q^{42} -2.08397 q^{43} +(1.08415 + 1.87780i) q^{44} +(0.574618 - 0.995268i) q^{45} +(-3.45783 + 5.98914i) q^{46} +(1.86113 + 3.22356i) q^{47} -1.00000 q^{48} +(-6.99982 - 0.0504365i) q^{49} +3.67925 q^{50} +(-2.49840 - 4.32735i) q^{51} +(-1.14924 + 1.99054i) q^{52} +(5.63567 - 9.76126i) q^{53} +(-0.500000 - 0.866025i) q^{54} +2.49189 q^{55} +(-0.00953166 + 2.64573i) q^{56} -1.00000 q^{57} +(1.88322 + 3.26183i) q^{58} +(-5.21331 + 9.02972i) q^{59} +(-0.574618 + 0.995268i) q^{60} +(-1.28811 - 2.23107i) q^{61} -4.38565 q^{62} +(-2.29604 + 1.31461i) q^{63} +1.00000 q^{64} +(1.32075 + 2.28760i) q^{65} +(1.08415 - 1.87780i) q^{66} +(-4.44284 + 7.69523i) q^{67} +(2.49840 + 4.32735i) q^{68} +6.91567 q^{69} +(2.62774 + 1.52977i) q^{70} -0.323591 q^{71} +(0.500000 + 0.866025i) q^{72} +(2.36415 - 4.09483i) q^{73} +(0.330096 - 0.571742i) q^{74} +(-1.83963 - 3.18633i) q^{75} +1.00000 q^{76} +(-4.95783 - 2.88627i) q^{77} +2.29847 q^{78} +(3.79604 + 6.57493i) q^{79} +(0.574618 - 0.995268i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.403292 + 0.698521i) q^{82} +3.17435 q^{83} +(2.29604 - 1.31461i) q^{84} +5.74250 q^{85} +(-1.04198 - 1.80477i) q^{86} +(1.88322 - 3.26183i) q^{87} +(-1.08415 + 1.87780i) q^{88} +(-6.18879 - 10.7193i) q^{89} +1.14924 q^{90} +(0.0219083 - 6.08115i) q^{91} -6.91567 q^{92} +(2.19283 + 3.79808i) q^{93} +(-1.86113 + 3.22356i) q^{94} +(0.574618 - 0.995268i) q^{95} +(-0.500000 - 0.866025i) q^{96} -5.91567 q^{97} +(-3.45623 - 6.08724i) q^{98} -2.16830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{11} + 4 q^{12} - q^{14} - 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} - 4 q^{25} - 8 q^{27} + q^{28} - 6 q^{29} - 9 q^{31} + 4 q^{32} - 2 q^{33} - 20 q^{34} - 9 q^{35} + 8 q^{36} + 14 q^{37} + 4 q^{38} + 8 q^{41} - 2 q^{42} + 42 q^{43} + 2 q^{44} - 5 q^{46} - 7 q^{47} - 8 q^{48} - 4 q^{49} - 8 q^{50} + 10 q^{51} + 7 q^{53} - 4 q^{54} + 2 q^{56} - 8 q^{57} - 3 q^{58} - 7 q^{59} - 23 q^{61} - 18 q^{62} + q^{63} + 8 q^{64} + 48 q^{65} + 2 q^{66} - 6 q^{67} - 10 q^{68} + 10 q^{69} + 15 q^{70} + 4 q^{71} + 4 q^{72} + 5 q^{73} - 14 q^{74} + 4 q^{75} + 8 q^{76} - 17 q^{77} + 11 q^{79} - 4 q^{81} + 4 q^{82} + 28 q^{83} - q^{84} + 12 q^{85} + 21 q^{86} - 3 q^{87} - 2 q^{88} - 10 q^{89} - 48 q^{91} - 10 q^{92} + 9 q^{93} + 7 q^{94} - 4 q^{96} - 2 q^{97} + 25 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^11 + 4 * q^12 - q^14 - 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 - 4 * q^25 - 8 * q^27 + q^28 - 6 * q^29 - 9 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 - 9 * q^35 + 8 * q^36 + 14 * q^37 + 4 * q^38 + 8 * q^41 - 2 * q^42 + 42 * q^43 + 2 * q^44 - 5 * q^46 - 7 * q^47 - 8 * q^48 - 4 * q^49 - 8 * q^50 + 10 * q^51 + 7 * q^53 - 4 * q^54 + 2 * q^56 - 8 * q^57 - 3 * q^58 - 7 * q^59 - 23 * q^61 - 18 * q^62 + q^63 + 8 * q^64 + 48 * q^65 + 2 * q^66 - 6 * q^67 - 10 * q^68 + 10 * q^69 + 15 * q^70 + 4 * q^71 + 4 * q^72 + 5 * q^73 - 14 * q^74 + 4 * q^75 + 8 * q^76 - 17 * q^77 + 11 * q^79 - 4 * q^81 + 4 * q^82 + 28 * q^83 - q^84 + 12 * q^85 + 21 * q^86 - 3 * q^87 - 2 * q^88 - 10 * q^89 - 48 * q^91 - 10 * q^92 + 9 * q^93 + 7 * q^94 - 4 * q^96 - 2 * q^97 + 25 * q^98 - 4 * q^99

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