LMFDB - Embedded newform 570.2.s.b.221.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(221,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			221.6
Character	$\chi$	$=$	570.221
Dual form			570.2.s.b.521.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.130029 - 1.72716i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.56078 - 0.750973i) q^{6} -4.16200 q^{7} -1.00000 q^{8} +(-2.96618 - 0.449163i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.130029 - 1.72716i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.56078 - 0.750973i) q^{6} -4.16200 q^{7} -1.00000 q^{8} +(-2.96618 - 0.449163i) q^{9} +(0.866025 + 0.500000i) q^{10} -2.96621i q^{11} +(1.43075 + 0.976190i) q^{12} +(-5.88671 - 3.39869i) q^{13} +(-2.08100 - 3.60440i) q^{14} +(-0.750973 - 1.56078i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.56047 - 0.900937i) q^{17} +(-1.09411 - 2.79337i) q^{18} +(0.334315 + 4.34606i) q^{19} +1.00000i q^{20} +(-0.541182 + 7.18845i) q^{21} +(2.56881 - 1.48311i) q^{22} +(-0.309948 - 0.178948i) q^{23} +(-0.130029 + 1.72716i) q^{24} +(0.500000 - 0.866025i) q^{25} -6.79738i q^{26} +(-1.16147 + 5.06468i) q^{27} +(2.08100 - 3.60440i) q^{28} +(3.63882 - 6.30262i) q^{29} +(0.976190 - 1.43075i) q^{30} -3.56783i q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.12313 - 0.385694i) q^{33} +(1.56047 + 0.900937i) q^{34} +(-3.60440 + 2.08100i) q^{35} +(1.87208 - 2.34421i) q^{36} +6.14614i q^{37} +(-3.59664 + 2.46256i) q^{38} +(-6.63554 + 9.72537i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(3.81541 + 6.60849i) q^{41} +(-6.49598 + 3.12555i) q^{42} +(-5.13659 - 8.89683i) q^{43} +(2.56881 + 1.48311i) q^{44} +(-2.79337 + 1.09411i) q^{45} -0.357897i q^{46} +(-4.46767 - 2.57941i) q^{47} +(-1.56078 + 0.750973i) q^{48} +10.3223 q^{49} +1.00000 q^{50} +(-1.35316 - 2.81233i) q^{51} +(5.88671 - 3.39869i) q^{52} +(1.75415 - 3.03828i) q^{53} +(-4.96688 + 1.52648i) q^{54} +(-1.48311 - 2.56881i) q^{55} +4.16200 q^{56} +(7.54982 - 0.0123016i) q^{57} +7.27764 q^{58} +(-4.38575 - 7.59635i) q^{59} +(1.72716 + 0.130029i) q^{60} +(1.88869 - 3.27131i) q^{61} +(3.08983 - 1.78392i) q^{62} +(12.3453 + 1.86942i) q^{63} +1.00000 q^{64} -6.79738 q^{65} +(-2.22754 - 4.62961i) q^{66} +(0.922310 + 0.532496i) q^{67} +1.80187i q^{68} +(-0.349376 + 0.512062i) q^{69} +(-3.60440 - 2.08100i) q^{70} +(-2.05789 - 3.56436i) q^{71} +(2.96618 + 0.449163i) q^{72} +(6.64377 + 11.5074i) q^{73} +(-5.32272 + 3.07307i) q^{74} +(-1.43075 - 0.976190i) q^{75} +(-3.93096 - 1.88350i) q^{76} +12.3454i q^{77} +(-11.7402 - 0.883859i) q^{78} +(1.10542 - 0.638217i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(8.59650 + 2.66460i) q^{81} +(-3.81541 + 6.60849i) q^{82} +1.93377i q^{83} +(-5.95479 - 4.06290i) q^{84} +(0.900937 - 1.56047i) q^{85} +(5.13659 - 8.89683i) q^{86} +(-10.4125 - 7.10436i) q^{87} +2.96621i q^{88} +(2.94818 - 5.10639i) q^{89} +(-2.34421 - 1.87208i) q^{90} +(24.5005 + 14.1454i) q^{91} +(0.309948 - 0.178948i) q^{92} +(-6.16223 - 0.463923i) q^{93} -5.15882i q^{94} +(2.46256 + 3.59664i) q^{95} +(-1.43075 - 0.976190i) q^{96} +(11.2544 - 6.49772i) q^{97} +(5.16113 + 8.93933i) q^{98} +(-1.33231 + 8.79833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.130029	−	1.72716i	0.0750724	−	0.997178i
$3$	0.130029	−	1.72716i	0.0750724	−	0.997178i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	1.56078	−	0.750973i	0.637186	−	0.306583i
$7$	−4.16200			−1.57309			−0.786544	−	0.617534i	$-0.788132\pi$
$7$	−4.16200			−1.57309			−0.786544	+	0.617534i	$0.788132\pi$
$8$	−1.00000			−0.353553
$9$	−2.96618	−	0.449163i	−0.988728	−	0.149721i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	2.96621i		−	0.894346i	−0.894447	−	0.447173i	$-0.852431\pi$
$11$		−	2.96621i		−	0.894346i	0.894447	−	0.447173i	$-0.147569\pi$
$12$	1.43075	+	0.976190i	0.413023	+	0.281802i
$13$	−5.88671	−	3.39869i	−1.63268	−	0.942627i	−0.983263	−	0.182194i	$-0.941680\pi$
$13$	−5.88671	−	3.39869i	−1.63268	−	0.942627i	−0.649416	−	0.760433i	$-0.724987\pi$
$14$	−2.08100	−	3.60440i	−0.556171	−	0.963316i
$15$	−0.750973	−	1.56078i	−0.193900	−	0.402992i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.56047	−	0.900937i	0.378469	−	0.218509i	−0.298683	−	0.954352i	$-0.596547\pi$
$17$	1.56047	−	0.900937i	0.378469	−	0.218509i	0.677152	+	0.735843i	$0.263214\pi$
$18$	−1.09411	−	2.79337i	−0.257883	−	0.658404i
$19$	0.334315	+	4.34606i	0.0766971	+	0.997054i
$19$	0.334315	+	4.34606i	0.0766971	+	0.997054i
$20$			1.00000i			0.223607i
$21$	−0.541182	+	7.18845i	−0.118096	+	1.56865i
$22$	2.56881	−	1.48311i	0.547673	−	0.316199i
$23$	−0.309948	−	0.178948i	−0.0646286	−	0.0373133i	0.467338	−	0.884079i	$-0.345213\pi$
$23$	−0.309948	−	0.178948i	−0.0646286	−	0.0373133i	−0.531966	+	0.846766i	$0.678547\pi$
$24$	−0.130029	+	1.72716i	−0.0265421	+	0.352556i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	6.79738i		−	1.33308i
$27$	−1.16147	+	5.06468i	−0.223525	+	0.974698i
$28$	2.08100	−	3.60440i	0.393272	−	0.681167i
$29$	3.63882	−	6.30262i	0.675712	−	1.17037i	−0.300548	−	0.953767i	$-0.597170\pi$
$29$	3.63882	−	6.30262i	0.675712	−	1.17037i	0.976260	−	0.216601i	$-0.0694971\pi$
$30$	0.976190	−	1.43075i	0.178227	−	0.261218i
$31$		−	3.56783i		−	0.640802i	−0.947282	−	0.320401i	$-0.896182\pi$
$31$		−	3.56783i		−	0.640802i	0.947282	−	0.320401i	$-0.103818\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−5.12313	−	0.385694i	−0.891823	−	0.0671407i
$34$	1.56047	+	0.900937i	0.267618	+	0.154509i
$35$	−3.60440	+	2.08100i	−0.609255	+	0.351753i
$36$	1.87208	−	2.34421i	0.312013	−	0.390702i
$37$			6.14614i			1.01042i	0.862997	+	0.505210i	$0.168585\pi$
$37$			6.14614i			1.01042i	−0.862997	+	0.505210i	$0.831415\pi$
$38$	−3.59664	+	2.46256i	−0.583452	+	0.399479i
$39$	−6.63554	+	9.72537i	−1.06254	+	1.55731i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	3.81541	+	6.60849i	0.595867	+	1.03207i	0.993424	+	0.114495i	$0.0365249\pi$
$41$	3.81541	+	6.60849i	0.595867	+	1.03207i	−0.397557	+	0.917578i	$0.630142\pi$
$42$	−6.49598	+	3.12555i	−1.00235	+	0.482283i
$43$	−5.13659	−	8.89683i	−0.783322	−	1.35675i	−0.929996	−	0.367569i	$-0.880190\pi$
$43$	−5.13659	−	8.89683i	−0.783322	−	1.35675i	0.146674	−	0.989185i	$-0.453143\pi$
$44$	2.56881	+	1.48311i	0.387263	+	0.223587i
$45$	−2.79337	+	1.09411i	−0.416411	+	0.163100i
$46$		−	0.357897i		−	0.0527690i
$47$	−4.46767	−	2.57941i	−0.651677	−	0.376246i	0.137421	−	0.990513i	$-0.456119\pi$
$47$	−4.46767	−	2.57941i	−0.651677	−	0.376246i	−0.789098	+	0.614267i	$0.789452\pi$
$48$	−1.56078	+	0.750973i	−0.225279	+	0.108394i
$49$	10.3223			1.47461
$50$	1.00000			0.141421
$51$	−1.35316	−	2.81233i	−0.189480	−	0.393805i
$52$	5.88671	−	3.39869i	0.816339	−	0.471314i
$53$	1.75415	−	3.03828i	0.240951	−	0.417340i	−0.720034	−	0.693938i	$-0.755874\pi$
$53$	1.75415	−	3.03828i	0.240951	−	0.417340i	0.960985	+	0.276599i	$0.0892073\pi$
$54$	−4.96688	+	1.52648i	−0.675906	+	0.207727i
$55$	−1.48311	−	2.56881i	−0.199982	−	0.346379i
$56$	4.16200			0.556171
$57$	7.54982	−	0.0123016i	0.999999	−	0.00162939i
$58$	7.27764			0.955601
$59$	−4.38575	−	7.59635i	−0.570976	−	0.988960i	−0.996466	−	0.0839969i	$-0.973231\pi$
$59$	−4.38575	−	7.59635i	−0.570976	−	0.988960i	0.425490	−	0.904963i	$-0.360102\pi$
$60$	1.72716	+	0.130029i	0.222976	+	0.0167867i
$61$	1.88869	−	3.27131i	0.241822	−	0.418849i	−0.719411	−	0.694585i	$-0.755588\pi$
$61$	1.88869	−	3.27131i	0.241822	−	0.418849i	0.961233	+	0.275736i	$0.0889215\pi$
$62$	3.08983	−	1.78392i	0.392409	−	0.226558i
$63$	12.3453	+	1.86942i	1.55536	+	0.235525i
$64$	1.00000			0.125000
$65$	−6.79738			−0.843112
$66$	−2.22754	−	4.62961i	−0.274192	−	0.569865i
$67$	0.922310	+	0.532496i	0.112678	+	0.0650548i	0.555280	−	0.831664i	$-0.312611\pi$
$67$	0.922310	+	0.532496i	0.112678	+	0.0650548i	−0.442602	+	0.896718i	$0.645944\pi$
$68$			1.80187i			0.218509i
$69$	−0.349376	+	0.512062i	−0.0420599	+	0.0616450i
$70$	−3.60440	−	2.08100i	−0.430808	−	0.248727i
$71$	−2.05789	−	3.56436i	−0.244226	−	0.423012i	0.717688	−	0.696365i	$-0.245201\pi$
$71$	−2.05789	−	3.56436i	−0.244226	−	0.423012i	−0.961914	+	0.273353i	$0.911867\pi$
$72$	2.96618	+	0.449163i	0.349568	+	0.0529344i
$73$	6.64377	+	11.5074i	0.777595	+	1.34683i	0.933324	+	0.359034i	$0.116894\pi$
$73$	6.64377	+	11.5074i	0.777595	+	1.34683i	−0.155729	+	0.987800i	$0.549773\pi$
$74$	−5.32272	+	3.07307i	−0.618753	+	0.357237i
$75$	−1.43075	−	0.976190i	−0.165209	−	0.112721i
$76$	−3.93096	−	1.88350i	−0.450912	−	0.216053i
$77$			12.3454i			1.40689i
$78$	−11.7402	−	0.883859i	−1.32931	−	0.100077i
$79$	1.10542	−	0.638217i	0.124370	−	0.0718050i	−0.436524	−	0.899692i	$-0.643791\pi$
$79$	1.10542	−	0.638217i	0.124370	−	0.0718050i	0.560894	+	0.827887i	$0.310457\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	8.59650	+	2.66460i	0.955167	+	0.296067i
$82$	−3.81541	+	6.60849i	−0.421342	+	0.729785i
$83$			1.93377i			0.212258i	0.994352	+	0.106129i	$0.0338457\pi$
$83$			1.93377i			0.212258i	−0.994352	+	0.106129i	$0.966154\pi$
$84$	−5.95479	−	4.06290i	−0.649721	−	0.443299i
$85$	0.900937	−	1.56047i	0.0977203	−	0.169257i
$86$	5.13659	−	8.89683i	0.553892	−	0.959370i
$87$	−10.4125	−	7.10436i	−1.11634	−	0.761668i
$88$			2.96621i			0.316199i
$89$	2.94818	−	5.10639i	0.312506	−	0.541277i	−0.666398	−	0.745596i	$-0.732165\pi$
$89$	2.94818	−	5.10639i	0.312506	−	0.541277i	0.978904	+	0.204320i	$0.0654982\pi$
$90$	−2.34421	−	1.87208i	−0.247101	−	0.197334i
$91$	24.5005	+	14.1454i	2.56835	+	1.48284i
$92$	0.309948	−	0.178948i	0.0323143	−	0.0186567i
$93$	−6.16223	−	0.463923i	−0.638993	−	0.0481065i
$94$		−	5.15882i		−	0.532092i
$95$	2.46256	+	3.59664i	0.252653	+	0.369008i
$96$	−1.43075	−	0.976190i	−0.146026	−	0.0996320i
$97$	11.2544	−	6.49772i	1.14271	−	0.659744i	0.195610	−	0.980682i	$-0.437331\pi$
$97$	11.2544	−	6.49772i	1.14271	−	0.659744i	0.947100	+	0.320938i	$0.103998\pi$
$98$	5.16113	+	8.93933i	0.521353	+	0.903009i
$99$	−1.33231	+	8.79833i	−0.133903	+	0.884265i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	3.25224	+	1.87768i	0.323610	+	0.186836i	0.653001	−	0.757357i	$-0.273510\pi$
$101$	3.25224	+	1.87768i	0.323610	+	0.186836i	−0.329391	+	0.944194i	$0.606843\pi$
$102$	1.75897	−	2.57804i	0.174164	−	0.255264i
$103$		−	2.57242i		−	0.253468i	−0.991937	−	0.126734i	$-0.959551\pi$
$103$		−	2.57242i		−	0.253468i	0.991937	−	0.126734i	$-0.0404494\pi$
$104$	5.88671	+	3.39869i	0.577239	+	0.333269i
$105$	3.12555	+	6.49598i	0.305022	+	0.633942i
$106$	3.50830			0.340756
$107$	−11.8795			−1.14844			−0.574218	−	0.818702i	$-0.694694\pi$
$107$	−11.8795			−1.14844			−0.574218	+	0.818702i	$0.694694\pi$
$108$	−3.80541	−	3.53820i	−0.366175	−	0.340464i
$109$	−11.1493	+	6.43703i	−1.06790	+	0.616555i	−0.927608	−	0.373554i	$-0.878139\pi$
$109$	−11.1493	+	6.43703i	−1.06790	+	0.616555i	−0.140297	+	0.990110i	$0.544806\pi$
$110$	1.48311	−	2.56881i	0.141409	−	0.244927i
$111$	10.6154	+	0.799178i	1.00757	+	0.0758546i
$112$	2.08100	+	3.60440i	0.196636	+	0.340584i
$113$	3.14768			0.296109			0.148055	−	0.988979i	$-0.452699\pi$
$113$	3.14768			0.296109			0.148055	+	0.988979i	$0.452699\pi$
$114$	3.78557	+	6.53219i	0.354551	+	0.611796i
$115$	−0.357897			−0.0333741
$116$	3.63882	+	6.30262i	0.337856	+	0.585184i
$117$	15.9345	+	12.7252i	1.47314	+	1.17645i
$118$	4.38575	−	7.59635i	0.403741	−	0.699300i
$119$	−6.49467	+	3.74970i	−0.595366	+	0.343734i
$120$	0.750973	+	1.56078i	0.0685541	+	0.142479i
$121$	2.20159			0.200145
$122$	3.77739			0.341989
$123$	11.9100	−	5.73054i	1.07389	−	0.516706i
$124$	3.08983	+	1.78392i	0.277475	+	0.160200i
$125$		−	1.00000i		−	0.0894427i
$126$	4.55367	+	11.6260i	0.405673	+	1.03573i
$127$	−6.05360	−	3.49505i	−0.537170	−	0.310135i	0.206761	−	0.978391i	$-0.433708\pi$
$127$	−6.05360	−	3.49505i	−0.537170	−	0.310135i	−0.743931	+	0.668256i	$0.767041\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−16.0342	+	7.71487i	−1.41173	+	0.679257i
$130$	−3.39869	−	5.88671i	−0.298085	−	0.516298i
$131$	−11.7170	+	6.76481i	−1.02372	+	0.591044i	−0.915179	−	0.403048i	$-0.867951\pi$
$131$	−11.7170	+	6.76481i	−1.02372	+	0.591044i	−0.108540	+	0.994092i	$0.534617\pi$
$132$	2.89559	−	4.24391i	0.252028	−	0.369385i
$133$	−1.39142	−	18.0883i	−0.120651	−	1.56845i
$134$			1.06499i			0.0920013i
$135$	1.52648	+	4.96688i	0.131378	+	0.427481i
$136$	−1.56047	+	0.900937i	−0.133809	+	0.0772547i
$137$	10.6066	+	6.12370i	0.906180	+	0.523183i	0.879200	−	0.476453i	$-0.158078\pi$
$137$	10.6066	+	6.12370i	0.906180	+	0.523183i	0.0269800	+	0.999636i	$0.491411\pi$
$138$	−0.618146	−	0.0465371i	−0.0526201	−	0.00396150i
$139$	5.90898	−	10.2347i	0.501193	−	0.868092i	−0.498806	−	0.866714i	$-0.666228\pi$
$139$	5.90898	−	10.2347i	0.501193	−	0.868092i	0.999999	−	0.00137828i	$-0.000438719\pi$
$140$		−	4.16200i		−	0.351753i
$141$	−5.03599	+	7.38100i	−0.424107	+	0.621592i
$142$	2.05789	−	3.56436i	0.172694	−	0.299115i
$143$	−10.0812	+	17.4612i	−0.843035	+	1.46018i
$144$	1.09411	+	2.79337i	0.0911754	+	0.232781i
$145$		−	7.27764i		−	0.604375i
$146$	−6.64377	+	11.5074i	−0.549843	+	0.952355i
$147$	1.34220	−	17.8282i	0.110702	−	1.47045i
$148$	−5.32272	−	3.07307i	−0.437524	−	0.252605i
$149$	6.23444	−	3.59946i	0.510745	−	0.294879i	−0.222395	−	0.974957i	$-0.571387\pi$
$149$	6.23444	−	3.59946i	0.510745	−	0.294879i	0.733140	+	0.680078i	$0.238054\pi$
$150$	0.130029	−	1.72716i	0.0106168	−	0.141022i
$151$			11.1275i			0.905543i	0.891627	+	0.452772i	$0.149565\pi$
$151$			11.1275i			0.905543i	−0.891627	+	0.452772i	$0.850435\pi$
$152$	−0.334315	−	4.34606i	−0.0271165	−	0.352512i
$153$	−5.03331	+	1.97144i	−0.406919	+	0.159381i
$154$	−10.6914	+	6.17269i	−0.861538	+	0.497409i
$155$	−1.78392	−	3.08983i	−0.143288	−	0.248181i
$156$	−5.10465	−	10.6092i	−0.408699	−	0.849418i
$157$	−10.7364	−	18.5960i	−0.856860	−	1.48412i	−0.874909	−	0.484287i	$-0.839079\pi$
$157$	−10.7364	−	18.5960i	−0.856860	−	1.48412i	0.0180496	−	0.999837i	$-0.494254\pi$
$158$	1.10542	+	0.638217i	0.0879428	+	0.0507738i
$159$	−5.01951	−	3.42477i	−0.398073	−	0.271602i
$160$		−	1.00000i		−	0.0790569i
$161$	1.29000	+	0.744784i	0.101667	+	0.0586972i
$162$	1.99064	+	8.77709i	0.156399	+	0.689594i
$163$	−19.4377			−1.52248			−0.761239	−	0.648471i	$-0.775409\pi$
$163$	−19.4377			−1.52248			−0.761239	+	0.648471i	$0.775409\pi$
$164$	−7.63082			−0.595867
$165$	−4.62961	+	2.22754i	−0.360414	+	0.173414i
$166$	−1.67469	+	0.966883i	−0.129981	+	0.0750447i
$167$	2.84217	−	4.92279i	0.219934	−	0.380937i	−0.734854	−	0.678226i	$-0.762749\pi$
$167$	2.84217	−	4.92279i	0.219934	−	0.380937i	0.954788	+	0.297289i	$0.0960825\pi$
$168$	0.541182	−	7.18845i	0.0417531	−	0.554601i
$169$	16.6022	+	28.7559i	1.27709	+	2.21199i
$170$	1.80187			0.138197
$171$	0.960451	−	13.0414i	0.0734475	−	0.997299i
$172$	10.2732			0.783322
$173$	−11.2154	−	19.4256i	−0.852690	−	1.47690i	−0.878772	−	0.477242i	$-0.841636\pi$
$173$	−11.2154	−	19.4256i	−0.852690	−	1.47690i	0.0260821	−	0.999660i	$-0.491697\pi$
$174$	0.946306	−	12.5697i	0.0717393	−	0.952905i
$175$	−2.08100	+	3.60440i	−0.157309	+	0.272467i
$176$	−2.56881	+	1.48311i	−0.193632	+	0.111793i
$177$	−13.6904	+	6.58716i	−1.02903	+	0.495122i
$178$	5.89635			0.441950
$179$	14.2289			1.06352			0.531758	−	0.846896i	$-0.321531\pi$
$179$	14.2289			1.06352			0.531758	+	0.846896i	$0.321531\pi$
$180$	0.449163	−	2.96618i	0.0334787	−	0.221086i
$181$	0.0315834	+	0.0182347i	0.00234757	+	0.00135537i	0.501173	−	0.865347i	$-0.332902\pi$
$181$	0.0315834	+	0.0182347i	0.00234757	+	0.00135537i	−0.498826	+	0.866702i	$0.666235\pi$
$182$			28.2907i			2.09705i
$183$	−5.40451	−	3.68745i	−0.399513	−	0.272584i
$184$	0.309948	+	0.178948i	0.0228497	+	0.0131923i
$185$	3.07307	+	5.32272i	0.225937	+	0.391334i
$186$	−2.67935	−	5.56861i	−0.196459	−	0.408310i
$187$	−2.67237	−	4.62868i	−0.195423	−	0.338482i
$188$	4.46767	−	2.57941i	0.325839	−	0.188123i
$189$	4.83404	−	21.0792i	0.351624	−	1.53329i
$190$	−1.88350	+	3.93096i	−0.136644	+	0.285181i
$191$			22.3142i			1.61460i	0.590141	+	0.807300i	$0.299072\pi$
$191$			22.3142i			1.61460i	−0.590141	+	0.807300i	$0.700928\pi$
$192$	0.130029	−	1.72716i	0.00938405	−	0.124647i
$193$	−11.5178	+	6.64983i	−0.829072	+	0.478665i	−0.853535	−	0.521036i	$-0.825546\pi$
$193$	−11.5178	+	6.64983i	−0.829072	+	0.478665i	0.0244626	+	0.999701i	$0.492213\pi$
$194$	11.2544	+	6.49772i	0.808018	+	0.466509i
$195$	−0.883859	+	11.7402i	−0.0632944	+	0.840732i
$196$	−5.16113	+	8.93933i	−0.368652	+	0.638524i
$197$		−	22.7586i		−	1.62148i	−0.585403	−	0.810742i	$-0.699064\pi$
$197$		−	22.7586i		−	1.62148i	0.585403	−	0.810742i	$-0.300936\pi$
$198$	−8.28573	+	3.24535i	−0.588841	+	0.230637i
$199$	2.34142	−	4.05546i	0.165979	−	0.287484i	−0.771023	−	0.636807i	$-0.780255\pi$
$199$	2.34142	−	4.05546i	0.165979	−	0.287484i	0.937003	+	0.349323i	$0.113588\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	1.03964	−	1.52374i	0.0733302	−	0.107476i
$202$			3.75536i			0.264226i
$203$	−15.1448	+	26.2315i	−1.06295	+	1.84109i
$204$	3.11213	+	0.234296i	0.217893	+	0.0164040i
$205$	6.60849	+	3.81541i	0.461557	+	0.266480i
$206$	2.22778	−	1.28621i	0.155217	−	0.0896144i
$207$	0.838986	+	0.670012i	0.0583135	+	0.0465690i
$208$			6.79738i			0.471314i
$209$	12.8913	−	0.991649i	0.891712	−	0.0685938i
$210$	−4.06290	+	5.95479i	−0.280367	+	0.410920i
$211$	−6.72063	+	3.88016i	−0.462667	+	0.267121i	−0.713165	−	0.700996i	$-0.752739\pi$
$211$	−6.72063	+	3.88016i	−0.462667	+	0.267121i	0.250498	+	0.968117i	$0.419406\pi$
$212$	1.75415	+	3.03828i	0.120476	+	0.208670i
$213$	−6.42382	+	3.09083i	−0.440153	+	0.211780i
$214$	−5.93976	−	10.2880i	−0.406034	−	0.703271i
$215$	−8.89683	−	5.13659i	−0.606759	−	0.350312i
$216$	1.16147	−	5.06468i	0.0790280	−	0.344608i
$217$			14.8493i			1.00804i
$218$	−11.1493	−	6.43703i	−0.755123	−	0.435970i
$219$	20.7390	−	9.97859i	1.40141	−	0.674291i
$220$	2.96621			0.199982
$221$	−12.2480			−0.823891
$222$	4.61559	+	9.59279i	0.309778	+	0.643826i
$223$	23.7955	−	13.7383i	1.59346	−	0.919987i	0.600758	−	0.799431i	$-0.294866\pi$
$223$	23.7955	−	13.7383i	1.59346	−	0.919987i	0.992707	−	0.120556i	$-0.0384678\pi$
$224$	−2.08100	+	3.60440i	−0.139043	+	0.240829i
$225$	−1.87208	+	2.34421i	−0.124805	+	0.156281i
$226$	1.57384	+	2.72597i	0.104690	+	0.181329i
$227$	25.8559			1.71612			0.858059	−	0.513551i	$-0.171670\pi$
$227$	25.8559			1.71612			0.858059	+	0.513551i	$0.171670\pi$
$228$	−3.76426	+	6.54449i	−0.249294	+	0.433419i
$229$	5.60560			0.370428			0.185214	−	0.982698i	$-0.440702\pi$
$229$	5.60560			0.370428			0.185214	+	0.982698i	$0.440702\pi$
$230$	−0.178948	−	0.309948i	−0.0117995	−	0.0204374i
$231$	21.3225	+	1.60526i	1.40292	+	0.105618i
$232$	−3.63882	+	6.30262i	−0.238900	+	0.413787i
$233$	−22.6080	+	13.0528i	−1.48110	+	0.855114i	−0.999770	−	0.0214243i	$-0.993180\pi$
$233$	−22.6080	+	13.0528i	−1.48110	+	0.855114i	−0.481331	+	0.876539i	$0.659847\pi$
$234$	−3.05314	+	20.1623i	−0.199590	+	1.31805i
$235$	−5.15882			−0.336525
$236$	8.77151			0.570976
$237$	−0.958567	−	1.99223i	−0.0622656	−	0.129409i
$238$	−6.49467	−	3.74970i	−0.420987	−	0.243057i
$239$		−	23.9431i		−	1.54875i	−0.632728	−	0.774374i	$-0.718065\pi$
$239$		−	23.9431i		−	1.54875i	0.632728	−	0.774374i	$-0.281935\pi$
$240$	−0.976190	+	1.43075i	−0.0630128	+	0.0923547i
$241$	−7.46928	−	4.31239i	−0.481139	−	0.277786i	0.239752	−	0.970834i	$-0.422934\pi$
$241$	−7.46928	−	4.31239i	−0.481139	−	0.277786i	−0.720891	+	0.693049i	$0.756267\pi$
$242$	1.10080	+	1.90663i	0.0707619	+	0.122563i
$243$	5.72000	−	14.5011i	0.366938	−	0.930245i
$244$	1.88869	+	3.27131i	0.120911	+	0.209424i
$245$	8.93933	−	5.16113i	0.571113	−	0.329732i
$246$	10.9178	+	7.44913i	0.696095	+	0.474939i
$247$	12.8029	−	26.7202i	0.814629	−	1.70017i
$248$			3.56783i			0.226558i
$249$	3.33993	+	0.251446i	0.211659	+	0.0159348i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	−11.4151	−	6.59052i	−0.720516	−	0.415990i	0.0944268	−	0.995532i	$-0.469898\pi$
$251$	−11.4151	−	6.59052i	−0.720516	−	0.415990i	−0.814942	+	0.579542i	$0.803231\pi$
$252$	−7.79160	+	9.75660i	−0.490824	+	0.614608i
$253$	−0.530799	+	0.919371i	−0.0333710	+	0.0578004i
$254$		−	6.99009i		−	0.438597i
$255$	−2.57804	−	1.75897i	−0.161443	−	0.110151i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.3200	−	23.0709i	0.830879	−	1.43913i	−0.0664625	−	0.997789i	$-0.521171\pi$
$257$	13.3200	−	23.0709i	0.830879	−	1.43913i	0.897342	−	0.441336i	$-0.145495\pi$
$258$	−14.6984	−	10.0286i	−0.915080	−	0.624351i
$259$		−	25.5803i		−	1.58948i
$260$	3.39869	−	5.88671i	0.210778	−	0.365078i
$261$	−13.6243	+	17.0603i	−0.843324	+	1.05601i
$262$	−11.7170	−	6.76481i	−0.723878	−	0.417931i
$263$	−20.1068	+	11.6087i	−1.23984	+	0.715822i	−0.969062	−	0.246819i	$-0.920615\pi$
$263$	−20.1068	+	11.6087i	−1.23984	+	0.715822i	−0.270779	+	0.962641i	$0.587281\pi$
$264$	5.12313	+	0.385694i	0.315307	+	0.0237378i
$265$		−	3.50830i		−	0.215513i
$266$	14.9692	−	10.2492i	0.917822	−	0.628416i
$267$	−8.43622	−	5.75596i	−0.516288	−	0.352259i
$268$	−0.922310	+	0.532496i	−0.0563391	+	0.0325274i
$269$	−2.52385	−	4.37144i	−0.153882	−	0.266532i	0.778769	−	0.627310i	$-0.215844\pi$
$269$	−2.52385	−	4.37144i	−0.153882	−	0.266532i	−0.932651	+	0.360779i	$0.882511\pi$
$270$	−3.53820	+	3.80541i	−0.215328	+	0.231590i
$271$	4.52551	+	7.83842i	0.274905	+	0.476150i	0.970111	−	0.242661i	$-0.0780202\pi$
$271$	4.52551	+	7.83842i	0.274905	+	0.476150i	−0.695206	+	0.718811i	$0.744687\pi$
$272$	−1.56047	−	0.900937i	−0.0946173	−	0.0546273i
$273$	27.6171	−	40.4770i	1.67146	−	2.44978i
$274$			12.2474i			0.739893i
$275$	−2.56881	−	1.48311i	−0.154905	−	0.0894346i
$276$	−0.268771	−	0.558599i	−0.0161781	−	0.0336237i
$277$	−5.33557			−0.320583			−0.160292	−	0.987070i	$-0.551243\pi$
$277$	−5.33557			−0.320583			−0.160292	+	0.987070i	$0.551243\pi$
$278$	11.8180			0.708794
$279$	−1.60254	+	10.5829i	−0.0959416	+	0.633579i
$280$	3.60440	−	2.08100i	0.215404	−	0.124364i
$281$	6.84949	−	11.8637i	0.408606	−	0.707727i	−0.586127	−	0.810219i	$-0.699348\pi$
$281$	6.84949	−	11.8637i	0.408606	−	0.707727i	0.994734	+	0.102492i	$0.0326816\pi$
$282$	−8.91013	−	0.670798i	−0.530591	−	0.0399455i
$283$	0.398146	+	0.689610i	0.0236673	+	0.0409930i	0.877616	−	0.479363i	$-0.159132\pi$
$283$	0.398146	+	0.689610i	0.0236673	+	0.0409930i	−0.853949	+	0.520356i	$0.825799\pi$
$284$	4.11577			0.244226
$285$	6.53219	−	3.78557i	0.386933	−	0.224238i
$286$	−20.1625			−1.19223
$287$	−15.8797	−	27.5045i	−0.937352	−	1.62354i
$288$	−1.87208	+	2.34421i	−0.110313	+	0.138134i
$289$	−6.87663	+	11.9107i	−0.404507	+	0.700627i
$290$	6.30262	−	3.63882i	0.370103	−	0.213679i
$291$	−9.75923	−	20.2831i	−0.572096	−	1.18901i
$292$	−13.2875			−0.777595
$293$	23.7823			1.38937			0.694687	−	0.719312i	$-0.255543\pi$
$293$	23.7823			1.38937			0.694687	+	0.719312i	$0.255543\pi$
$294$	16.1108	−	7.75173i	0.939600	−	0.452090i
$295$	−7.59635	−	4.38575i	−0.442276	−	0.255348i
$296$		−	6.14614i		−	0.357237i
$297$	15.0229	+	3.44516i	0.871718	+	0.199909i
$298$	6.23444	+	3.59946i	0.361151	+	0.208511i
$299$	1.21638	+	2.10683i	0.0703452	+	0.121841i
$300$	1.56078	−	0.750973i	0.0901118	−	0.0433574i
$301$	21.3785	+	37.0286i	1.23223	+	2.13429i
$302$	−9.63670	+	5.56375i	−0.554530	+	0.320158i
$303$	3.66595	−	5.37300i	0.210603	−	0.308671i
$304$	3.59664	−	2.46256i	0.206281	−	0.141237i
$305$		−	3.77739i		−	0.216293i
$306$	−4.22397	−	3.37325i	−0.241468	−	0.192836i
$307$	−7.52401	+	4.34399i	−0.429418	+	0.247924i	−0.699099	−	0.715025i	$-0.746415\pi$
$307$	−7.52401	+	4.34399i	−0.429418	+	0.247924i	0.269681	+	0.962950i	$0.413082\pi$
$308$	−10.6914	−	6.17269i	−0.609199	−	0.351721i
$309$	−4.44299	−	0.334490i	−0.252753	−	0.0190284i
$310$	1.78392	−	3.08983i	0.101320	−	0.175491i
$311$		−	19.4598i		−	1.10346i	−0.834021	−	0.551732i	$-0.813967\pi$
$311$		−	19.4598i		−	1.10346i	0.834021	−	0.551732i	$-0.186033\pi$
$312$	6.63554	−	9.72537i	0.375663	−	0.550591i
$313$	−7.02538	+	12.1683i	−0.397098	+	0.687793i	−0.993366	−	0.114991i	$-0.963316\pi$
$313$	−7.02538	+	12.1683i	−0.397098	+	0.687793i	0.596269	+	0.802785i	$0.296649\pi$
$314$	10.7364	−	18.5960i	0.605891	−	1.04943i
$315$	11.6260	−	4.55367i	0.655052	−	0.256570i
$316$			1.27643i			0.0718050i
$317$	6.58272	−	11.4016i	0.369722	−	0.640378i	−0.619800	−	0.784760i	$-0.712786\pi$
$317$	6.58272	−	11.4016i	0.369722	−	0.640378i	0.989522	+	0.144382i	$0.0461195\pi$
$318$	0.456182	−	6.05941i	0.0255814	−	0.339795i
$319$	−18.6949	−	10.7935i	−1.04671	−	0.604321i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−1.54468	+	20.5179i	−0.0862159	+	1.14520i
$322$			1.48957i			0.0830104i
$323$	4.43721	+	6.48069i	0.246893	+	0.360595i
$324$	−6.60587	+	6.11249i	−0.366993	+	0.339583i
$325$	−5.88671	+	3.39869i	−0.326536	+	0.188525i
$326$	−9.71885	−	16.8335i	−0.538278	−	0.932324i
$327$	9.66806	+	20.0936i	0.534645	+	1.11118i
$328$	−3.81541	−	6.60849i	−0.210671	−	0.364893i
$329$	18.5945	+	10.7355i	1.02515	+	0.591868i
$330$	−4.24391	−	2.89559i	−0.233620	−	0.159397i
$331$			4.40745i			0.242256i	0.992637	+	0.121128i	$0.0386511\pi$
$331$			4.40745i			0.242256i	−0.992637	+	0.121128i	$0.961349\pi$
$332$	−1.67469	−	0.966883i	−0.0919106	−	0.0530646i
$333$	2.76062	−	18.2306i	0.151281	−	0.999030i
$334$	5.68435			0.311034
$335$	1.06499			0.0581868
$336$	6.49598	−	3.12555i	0.354385	−	0.170513i
$337$	−4.81309	+	2.77884i	−0.262186	+	0.151373i	−0.625331	−	0.780359i	$-0.715036\pi$
$337$	−4.81309	+	2.77884i	−0.262186	+	0.151373i	0.363146	+	0.931732i	$0.381703\pi$
$338$	−16.6022	+	28.7559i	−0.903041	+	1.56411i
$339$	0.409291	−	5.43656i	0.0222296	−	0.295273i
$340$	0.900937	+	1.56047i	0.0488602	+	0.0846283i
$341$	−10.5829			−0.573099
$342$	11.7744	−	5.68891i	0.636686	−	0.307621i
$343$	−13.8272			−0.746600
$344$	5.13659	+	8.89683i	0.276946	+	0.479685i
$345$	−0.0465371	+	0.618146i	−0.00250547	+	0.0332799i
$346$	11.2154	−	19.4256i	0.602943	−	1.04433i
$347$	−2.06156	+	1.19024i	−0.110671	+	0.0638957i	−0.554314	−	0.832308i	$-0.687019\pi$
$347$	−2.06156	+	1.19024i	−0.110671	+	0.0638957i	0.443643	+	0.896204i	$0.353686\pi$
$348$	11.3588	−	5.46531i	0.608896	−	0.292971i
$349$	−21.3877			−1.14486			−0.572429	−	0.819954i	$-0.693999\pi$
$349$	−21.3877			−1.14486			−0.572429	+	0.819954i	$0.693999\pi$
$350$	−4.16200			−0.222468
$351$	24.0505	−	25.8668i	1.28372	−	1.38067i
$352$	−2.56881	−	1.48311i	−0.136918	−	0.0790498i
$353$		−	34.6235i		−	1.84282i	−0.388590	−	0.921411i	$-0.627038\pi$
$353$		−	34.6235i		−	1.84282i	0.388590	−	0.921411i	$-0.372962\pi$
$354$	−12.5499	−	8.56266i	−0.667017	−	0.455100i
$355$	−3.56436	−	2.05789i	−0.189177	−	0.109221i
$356$	2.94818	+	5.10639i	0.156253	+	0.270638i
$357$	5.63185	+	11.7049i	0.298069	+	0.619490i
$358$	7.11444	+	12.3226i	0.376010	+	0.651268i
$359$	−18.8394	+	10.8769i	−0.994305	+	0.574063i	−0.906558	−	0.422080i	$-0.861300\pi$
$359$	−18.8394	+	10.8769i	−0.994305	+	0.574063i	−0.0877470	+	0.996143i	$0.527967\pi$
$360$	2.79337	−	1.09411i	0.147224	−	0.0576644i
$361$	−18.7765	+	2.90591i	−0.988235	+	0.152942i
$362$			0.0364693i			0.00191679i
$363$	0.286271	−	3.80251i	0.0150254	−	0.199580i
$364$	−24.5005	+	14.1454i	−1.28417	+	0.741418i
$365$	11.5074	+	6.64377i	0.602322	+	0.347751i
$366$	0.491171	−	6.52416i	0.0256739	−	0.341023i
$367$	6.28744	−	10.8902i	0.328202	−	0.568462i	−0.653953	−	0.756535i	$-0.726891\pi$
$367$	6.28744	−	10.8902i	0.328202	−	0.568462i	0.982155	+	0.188073i	$0.0602241\pi$
$368$			0.357897i			0.0186567i
$369$	−8.34892	−	21.3157i	−0.434628	−	1.10965i
$370$	−3.07307	+	5.32272i	−0.159761	+	0.276715i
$371$	−7.30078	+	12.6453i	−0.379038	+	0.656512i
$372$	3.48288	−	5.10469i	0.180579	−	0.264666i
$373$			18.8039i			0.973629i	0.873505	+	0.486815i	$0.161841\pi$
$373$			18.8039i			0.973629i	−0.873505	+	0.486815i	$0.838159\pi$
$374$	2.67237	−	4.62868i	0.138185	−	0.239343i
$375$	−1.72716	−	0.130029i	−0.0891903	−	0.00671468i
$376$	4.46767	+	2.57941i	0.230403	+	0.133023i
$377$	−42.8413	+	24.7345i	−2.20644	+	1.27389i
$378$	20.6721	−	6.35320i	1.06326	−	0.326774i
$379$		−	25.0289i		−	1.28565i	−0.766014	−	0.642824i	$-0.777763\pi$
$379$		−	25.0289i		−	1.28565i	0.766014	−	0.642824i	$-0.222237\pi$
$380$	−4.34606	+	0.334315i	−0.222948	+	0.0171500i
$381$	−6.82366	+	10.0011i	−0.349587	+	0.512371i
$382$	−19.3247	+	11.1571i	−0.988737	+	0.570847i
$383$	−2.61339	−	4.52653i	−0.133538	−	0.231295i	0.791500	−	0.611169i	$-0.209301\pi$
$383$	−2.61339	−	4.52653i	−0.133538	−	0.231295i	−0.925038	+	0.379874i	$0.875967\pi$
$384$	1.56078	−	0.750973i	0.0796483	−	0.0383229i
$385$	6.17269	+	10.6914i	0.314589	+	0.544885i
$386$	−11.5178	−	6.64983i	−0.586243	−	0.338467i
$387$	11.2399	+	28.6968i	0.571358	+	1.45874i
$388$			12.9954i			0.659744i
$389$	−20.9714	−	12.1078i	−1.06329	−	0.613892i	−0.136951	−	0.990578i	$-0.543730\pi$
$389$	−20.9714	−	12.1078i	−1.06329	−	0.613892i	−0.926341	+	0.376686i	$0.877064\pi$
$390$	−10.6092	+	5.10465i	−0.537219	+	0.258484i
$391$	−0.644885			−0.0326132
$392$	−10.3223			−0.521353
$393$	10.1604	+	21.1168i	0.512523	+	1.06520i
$394$	19.7095	−	11.3793i	0.992953	−	0.573282i
$395$	0.638217	−	1.10542i	0.0321122	−	0.0556199i
$396$	−6.95342	−	5.55298i	−0.349423	−	0.279048i
$397$	12.7295	+	22.0482i	0.638877	+	1.10657i	0.985680	+	0.168629i	$0.0539341\pi$
$397$	12.7295	+	22.0482i	0.638877	+	1.10657i	−0.346803	+	0.937938i	$0.612733\pi$
$398$	4.68284			0.234730
$399$	−31.4224	+	0.0511995i	−1.57309	+	0.00256318i
$400$	−1.00000			−0.0500000
$401$	17.9661	+	31.1182i	0.897184	+	1.55397i	0.831079	+	0.556155i	$0.187724\pi$
$401$	17.9661	+	31.1182i	0.897184	+	1.55397i	0.0661050	+	0.997813i	$0.478943\pi$
$402$	1.83942	+	0.138480i	0.0917417	+	0.00690676i
$403$	−12.1260	+	21.0028i	−0.604037	+	1.04622i
$404$	−3.25224	+	1.87768i	−0.161805	+	0.0934182i
$405$	8.77709	−	1.99064i	0.436137	−	0.0989156i
$406$	−30.2896			−1.50325
$407$	18.2308			0.903665
$408$	1.35316	+	2.81233i	0.0669913	+	0.139231i
$409$	−1.54476	−	0.891867i	−0.0763834	−	0.0441000i	0.461322	−	0.887233i	$-0.347375\pi$
$409$	−1.54476	−	0.891867i	−0.0763834	−	0.0441000i	−0.537705	+	0.843133i	$0.680709\pi$
$410$			7.63082i			0.376859i
$411$	11.9558	−	17.5230i	0.589736	−	0.864346i
$412$	2.22778	+	1.28621i	0.109755	+	0.0633670i
$413$	18.2535	+	31.6160i	0.898196	+	1.55572i
$414$	−0.160754	+	1.06159i	−0.00790064	+	0.0521742i
$415$	0.966883	+	1.67469i	0.0474624	+	0.0822073i
$416$	−5.88671	+	3.39869i	−0.288620	+	0.166635i
$417$	−16.9086	−	11.5366i	−0.828017	−	0.564949i
$418$	7.30446	+	10.6684i	0.357273	+	0.521808i
$419$		−	36.2564i		−	1.77124i	−0.464409	−	0.885621i	$-0.653733\pi$
$419$		−	36.2564i		−	1.77124i	0.464409	−	0.885621i	$-0.346267\pi$
$420$	−7.18845	−	0.541182i	−0.350761	−	0.0264070i
$421$	4.43149	−	2.55852i	0.215977	−	0.124695i	−0.388109	−	0.921614i	$-0.626872\pi$
$421$	4.43149	−	2.55852i	0.215977	−	0.124695i	0.604086	+	0.796919i	$0.293538\pi$
$422$	−6.72063	−	3.88016i	−0.327155	−	0.188883i
$423$	12.0934	+	9.65773i	0.588000	+	0.469575i
$424$	−1.75415	+	3.03828i	−0.0851891	+	0.147552i
$425$		−	1.80187i		−	0.0874037i
$426$	−5.88865	−	4.01778i	−0.285306	−	0.194662i
$427$	−7.86074	+	13.6152i	−0.380408	+	0.658886i
$428$	5.93976	−	10.2880i	0.287109	−	0.497287i
$429$	28.8475	+	19.6824i	1.39277	+	0.950276i
$430$		−	10.2732i		−	0.495416i
$431$	−3.31613	+	5.74370i	−0.159732	+	0.276664i	−0.934772	−	0.355248i	$-0.884396\pi$
$431$	−3.31613	+	5.74370i	−0.159732	+	0.276664i	0.775040	+	0.631912i	$0.217730\pi$
$432$	4.96688	−	1.52648i	0.238969	−	0.0734427i
$433$	−5.22804	−	3.01841i	−0.251244	−	0.145056i	0.369090	−	0.929394i	$-0.379669\pi$
$433$	−5.22804	−	3.01841i	−0.251244	−	0.145056i	−0.620334	+	0.784338i	$0.713003\pi$
$434$	−12.8599	+	7.42466i	−0.617295	+	0.356395i
$435$	−12.5697	−	0.946306i	−0.602670	−	0.0453719i
$436$		−	12.8741i		−	0.616555i
$437$	0.674101	−	1.40688i	0.0322466	−	0.0673001i
$438$	19.0112	+	12.9712i	0.908390	+	0.619787i
$439$	10.6718	−	6.16135i	0.509336	−	0.294065i	−0.223225	−	0.974767i	$-0.571658\pi$
$439$	10.6718	−	6.16135i	0.509336	−	0.294065i	0.732561	+	0.680702i	$0.238325\pi$
$440$	1.48311	+	2.56881i	0.0707043	+	0.122463i
$441$	−30.6177	−	4.63638i	−1.45799	−	0.220780i
$442$	−6.12401	−	10.6071i	−0.291290	−	0.504528i
$443$	6.05385	+	3.49519i	0.287627	+	0.166062i	0.636871	−	0.770970i	$-0.280228\pi$
$443$	6.05385	+	3.49519i	0.287627	+	0.166062i	−0.349244	+	0.937032i	$0.613562\pi$
$444$	−5.99980	+	8.79361i	−0.284738	+	0.417326i
$445$		−	5.89635i		−	0.279514i
$446$	23.7955	+	13.7383i	1.12675	+	0.650529i
$447$	−5.40619	−	11.2359i	−0.255704	−	0.531441i
$448$	−4.16200			−0.196636
$449$	31.4802			1.48564			0.742820	−	0.669491i	$-0.233488\pi$
$449$	31.4802			1.48564			0.742820	+	0.669491i	$0.233488\pi$
$450$	−2.96618	−	0.449163i	−0.139827	−	0.0211738i
$451$	19.6022	−	11.3173i	0.923030	−	0.532912i
$452$	−1.57384	+	2.72597i	−0.0740273	+	0.128219i
$453$	19.2190	+	1.44690i	0.902988	+	0.0679813i
$454$	12.9280	+	22.3919i	0.606739	+	1.05090i
$455$	28.2907			1.32629
$456$	−7.54982	+	0.0123016i	−0.353553	+	0.000576077i
$457$	−29.5618			−1.38284			−0.691421	−	0.722452i	$-0.743015\pi$
$457$	−29.5618			−1.38284			−0.691421	+	0.722452i	$0.743015\pi$
$458$	2.80280	+	4.85459i	0.130966	+	0.226840i
$459$	2.75052	+	8.94968i	0.128383	+	0.417735i
$460$	0.178948	−	0.309948i	0.00834352	−	0.0144514i
$461$	−12.9506	+	7.47702i	−0.603169	+	0.348240i	−0.770287	−	0.637697i	$-0.779887\pi$
$461$	−12.9506	+	7.47702i	−0.603169	+	0.348240i	0.167118	+	0.985937i	$0.446554\pi$
$462$	9.27104	+	19.2684i	0.431328	+	0.896449i
$463$	−16.7492			−0.778401			−0.389200	−	0.921153i	$-0.627249\pi$
$463$	−16.7492			−0.778401			−0.389200	+	0.921153i	$0.627249\pi$
$464$	−7.27764			−0.337856
$465$	−5.56861	+	2.67935i	−0.258238	+	0.124252i
$466$	−22.6080	−	13.0528i	−1.04730	−	0.604657i
$467$			22.2847i			1.03121i	0.856825	+	0.515607i	$0.172434\pi$
$467$			22.2847i			1.03121i	−0.856825	+	0.515607i	$0.827566\pi$
$468$	−18.9876	+	7.43705i	−0.877703	+	0.343778i
$469$	−3.83866	−	2.21625i	−0.177253	−	0.102337i
$470$	−2.57941	−	4.46767i	−0.118979	−	0.206078i
$471$	−33.5144	+	16.1255i	−1.54426	+	0.743025i
$472$	4.38575	+	7.59635i	0.201871	+	0.349650i
$473$	−26.3899	+	15.2362i	−1.21341	+	0.700561i
$474$	1.24604	−	1.82626i	0.0572326	−	0.0838829i
$475$	3.93096	+	1.88350i	0.180365	+	0.0864211i
$476$		−	7.49940i		−	0.343734i
$477$	−6.56782	+	8.22420i	−0.300720	+	0.376560i
$478$	20.7353	−	11.9715i	0.948410	−	0.547565i
$479$	−24.3132	−	14.0372i	−1.11090	−	0.641377i	−0.171836	−	0.985126i	$-0.554970\pi$
$479$	−24.3132	−	14.0372i	−1.11090	−	0.641377i	−0.939062	+	0.343748i	$0.888303\pi$
$480$	−1.72716	−	0.130029i	−0.0788338	−	0.00593500i
$481$	20.8888	−	36.1805i	0.952449	−	1.64969i
$482$		−	8.62478i		−	0.392848i
$483$	1.45410	−	2.13120i	0.0661639	−	0.0969731i
$484$	−1.10080	+	1.90663i	−0.0500362	+	0.0866652i
$485$	6.49772	−	11.2544i	0.295046	−	0.511035i
$486$	15.4183	−	2.29688i	0.699389	−	0.104188i
$487$			1.65303i			0.0749058i	0.999298	+	0.0374529i	$0.0119244\pi$
$487$			1.65303i			0.0749058i	−0.999298	+	0.0374529i	$0.988076\pi$
$488$	−1.88869	+	3.27131i	−0.0854971	+	0.148085i
$489$	−2.52747	+	33.5721i	−0.114296	+	1.51818i
$490$	8.93933	+	5.16113i	0.403838	+	0.233156i
$491$	−1.30505	+	0.753470i	−0.0588960	+	0.0340036i	−0.529159	−	0.848523i	$-0.677492\pi$
$491$	−1.30505	+	0.753470i	−0.0588960	+	0.0340036i	0.470263	+	0.882526i	$0.344159\pi$
$492$	−0.992230	+	13.1797i	−0.0447332	+	0.594186i
$493$		−	13.1134i		−	0.590597i
$494$	29.5418	−	2.27247i	1.32915	−	0.102243i
$495$	3.24535	+	8.28573i	0.145868	+	0.372416i
$496$	−3.08983	+	1.78392i	−0.138738	+	0.0801002i
$497$	8.56493	+	14.8349i	0.384190	+	0.665436i
$498$	1.45221	+	3.01819i	0.0650749	+	0.135248i
$499$	10.7116	+	18.5530i	0.479517	+	0.830549i	0.999724	−	0.0234919i	$-0.00747840\pi$
$499$	10.7116	+	18.5530i	0.479517	+	0.830549i	−0.520207	+	0.854040i	$0.674145\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−8.13289	−	5.54900i	−0.363351	−	0.247911i
$502$		−	13.1810i		−	0.588299i
$503$	10.8329	+	6.25439i	0.483016	+	0.278869i	0.721672	−	0.692235i	$-0.243374\pi$
$503$	10.8329	+	6.25439i	0.483016	+	0.278869i	−0.238657	+	0.971104i	$0.576707\pi$
$504$	−12.3453	−	1.86942i	−0.549902	−	0.0832705i
$505$	3.75536			0.167111
$506$	−1.06160			−0.0471938
$507$	51.8249	−	24.9356i	2.30162	−	1.10743i
$508$	6.05360	−	3.49505i	0.268585	−	0.155068i
$509$	−12.4948	+	21.6415i	−0.553820	+	0.959245i	0.444174	+	0.895941i	$0.353497\pi$
$509$	−12.4948	+	21.6415i	−0.553820	+	0.959245i	−0.997994	+	0.0633042i	$0.979836\pi$
$510$	0.234296	−	3.11213i	0.0103748	−	0.137807i
$511$	−27.6514	−	47.8936i	−1.22323	−	2.11869i
$512$	−1.00000			−0.0441942
$513$	−22.3997	−	3.35462i	−0.988971	−	0.148110i
$514$	26.6400			1.17504
$515$	−1.28621	−	2.22778i	−0.0566771	−	0.0981677i
$516$	1.33581	−	17.7434i	0.0588059	−	0.781112i
$517$	−7.65108	+	13.2521i	−0.336494	+	0.582825i
$518$	22.1531	−	12.7901i	0.973353	−	0.561966i
$519$	−35.0095	+	16.8449i	−1.53675	+	0.739409i
$520$	6.79738			0.298085
$521$	−28.9838			−1.26980			−0.634902	−	0.772593i	$-0.718959\pi$
$521$	−28.9838			−1.26980			−0.634902	+	0.772593i	$0.718959\pi$
$522$	−21.5868	−	3.26885i	−0.944830	−	0.143074i
$523$	36.7094	+	21.1942i	1.60519	+	0.926756i	0.990426	+	0.138044i	$0.0440816\pi$
$523$	36.7094	+	21.1942i	1.60519	+	0.926756i	0.614763	+	0.788712i	$0.289252\pi$
$524$		−	13.5296i		−	0.591044i
$525$	5.95479	+	4.06290i	0.259888	+	0.177320i
$526$	−20.1068	−	11.6087i	−0.876700	−	0.506163i
$527$	−3.21439	−	5.56749i	−0.140021	−	0.242524i
$528$	2.22754	+	4.62961i	0.0969414	+	0.201478i
$529$	−11.4360	−	19.8077i	−0.497215	−	0.861202i
$530$	3.03828	−	1.75415i	0.131974	−	0.0761955i
$531$	9.59695	+	24.5021i	0.416472	+	1.06330i
$532$	16.3606	+	7.83915i	0.709324	+	0.339870i
$533$		−	51.8696i		−	2.24672i
$534$	0.766699	−	10.1840i	0.0331783	−	0.440703i
$535$	−10.2880	+	5.93976i	−0.444787	+	0.256798i
$536$	−0.922310	−	0.532496i	−0.0398377	−	0.0230003i
$537$	1.85017	−	24.5756i	0.0798408	−	1.06052i
$538$	2.52385	−	4.37144i	0.108811	−	0.188466i
$539$		−	30.6180i		−	1.31881i
$540$	−5.06468	−	1.16147i	−0.217949	−	0.0499817i
$541$	7.78025	−	13.4758i	0.334499	−	0.579369i	−0.648890	−	0.760883i	$-0.724766\pi$
$541$	7.78025	−	13.4758i	0.334499	−	0.579369i	0.983388	+	0.181513i	$0.0580996\pi$
$542$	−4.52551	+	7.83842i	−0.194387	+	0.336689i
$543$	0.0356010	−	0.0521786i	0.00152779	−	0.00223920i
$544$		−	1.80187i		−	0.0772547i
$545$	−6.43703	+	11.1493i	−0.275732	+	0.477582i
$546$	48.8627	+	3.67862i	2.09113	+	0.157430i
$547$	34.8985	+	20.1487i	1.49215	+	0.861495i	0.999960	−	0.00899064i	$-0.00286185\pi$
$547$	34.8985	+	20.1487i	1.49215	+	0.861495i	0.492194	+	0.870486i	$0.336195\pi$
$548$	−10.6066	+	6.12370i	−0.453090	+	0.261592i
$549$	−7.07157	+	8.85499i	−0.301807	+	0.377922i
$550$		−	2.96621i		−	0.126480i
$551$	28.6081	+	13.7075i	1.21875	+	0.583958i
$552$	0.349376	−	0.512062i	0.0148704	−	0.0217948i
$553$	−4.60077	+	2.65626i	−0.195645	+	0.112956i
$554$	−2.66778	−	4.62074i	−0.113343	−	0.196316i
$555$	9.59279	−	4.61559i	0.407191	−	0.195921i
$556$	5.90898	+	10.2347i	0.250597	+	0.434046i
$557$	9.13519	+	5.27420i	0.387070	+	0.223475i	0.680890	−	0.732386i	$-0.261593\pi$
$557$	9.13519	+	5.27420i	0.387070	+	0.223475i	−0.293820	+	0.955861i	$0.594927\pi$
$558$	−9.96629	+	3.90358i	−0.421907	+	0.165252i
$559$			69.8307i			2.95352i
$560$	3.60440	+	2.08100i	0.152314	+	0.0879383i
$561$	−8.34197	+	4.01375i	−0.352198	+	0.169461i
$562$	13.6990			0.577857
$563$	40.4508			1.70480			0.852399	−	0.522892i	$-0.175147\pi$
$563$	40.4508			1.70480			0.852399	+	0.522892i	$0.175147\pi$
$564$	−3.87414	−	8.05180i	−0.163131	−	0.339042i
$565$	2.72597	−	1.57384i	0.114683	−	0.0662120i
$566$	−0.398146	+	0.689610i	−0.0167353	+	0.0289864i
$567$	−35.7787	−	11.0901i	−1.50256	−	0.465740i
$568$	2.05789	+	3.56436i	0.0863470	+	0.149557i
$569$	34.8214			1.45979			0.729895	−	0.683559i	$-0.239569\pi$
$569$	34.8214			1.45979			0.729895	+	0.683559i	$0.239569\pi$
$570$	6.54449	+	3.76426i	0.274119	+	0.157667i
$571$	4.64987			0.194591			0.0972956	−	0.995256i	$-0.468981\pi$
$571$	4.64987			0.194591			0.0972956	+	0.995256i	$0.468981\pi$
$572$	−10.0812	−	17.4612i	−0.421518	−	0.730090i
$573$	38.5403	+	2.90150i	1.61004	+	0.121212i
$574$	15.8797	−	27.5045i	0.662808	−	1.14802i
$575$	−0.309948	+	0.178948i	−0.0129257	+	0.00746267i
$576$	−2.96618	−	0.449163i	−0.123591	−	0.0187151i
$577$	27.5262			1.14593			0.572966	−	0.819579i	$-0.305793\pi$
$577$	27.5262			1.14593			0.572966	+	0.819579i	$0.305793\pi$
$578$	−13.7533			−0.572060
$579$	9.98768	+	20.7579i	0.415074	+	0.862667i
$580$	6.30262	+	3.63882i	0.261702	+	0.151094i
$581$		−	8.04833i		−	0.333901i
$582$	12.6860	−	18.5933i	0.525853	−	0.770716i
$583$	−9.01218	−	5.20318i	−0.373246	−	0.215494i
$584$	−6.64377	−	11.5074i	−0.274921	−	0.476178i
$585$	20.1623	+	3.05314i	0.833608	+	0.126232i
$586$	11.8911	+	20.5960i	0.491218	+	0.850815i
$587$	−8.13311	+	4.69565i	−0.335689	+	0.193810i	−0.658364	−	0.752700i	$-0.728751\pi$
$587$	−8.13311	+	4.69565i	−0.335689	+	0.193810i	0.322675	+	0.946510i	$0.395418\pi$
$588$	14.7686	+	10.0765i	0.609046	+	0.415547i
$589$	15.5060	−	1.19278i	0.638914	−	0.0491476i
$590$		−	8.77151i		−	0.361117i
$591$	−39.3079	−	2.95929i	−1.61691	−	0.121729i
$592$	5.32272	−	3.07307i	0.218762	−	0.126302i
$593$	−4.48680	−	2.59046i	−0.184251	−	0.106377i	0.405037	−	0.914300i	$-0.367258\pi$
$593$	−4.48680	−	2.59046i	−0.184251	−	0.106377i	−0.589288	+	0.807923i	$0.700592\pi$
$594$	4.52786	+	14.7328i	0.185780	+	0.604494i
$595$	−3.74970	+	6.49467i	−0.153723	+	0.266256i
$596$			7.19891i			0.294879i
$597$	−6.69999	−	4.57135i	−0.274212	−	0.187093i
$598$	−1.21638	+	2.10683i	−0.0497415	+	0.0861549i
$599$	−8.35558	+	14.4723i	−0.341400	+	0.591322i	−0.984693	−	0.174298i	$-0.944234\pi$
$599$	−8.35558	+	14.4723i	−0.341400	+	0.591322i	0.643293	+	0.765620i	$0.277568\pi$
$600$	1.43075	+	0.976190i	0.0584102	+	0.0398528i
$601$		−	34.8345i		−	1.42093i	−0.703734	−	0.710464i	$-0.748485\pi$
$601$		−	34.8345i		−	1.42093i	0.703734	−	0.710464i	$-0.251515\pi$
$602$	−21.3785	+	37.0286i	−0.871322	+	1.50917i
$603$	−2.49657	−	1.99375i	−0.101668	−	0.0811918i
$604$	−9.63670	−	5.56375i	−0.392112	−	0.226386i
$605$	1.90663	−	1.10080i	0.0775157	−	0.0447537i
$606$	6.48612	+	0.488307i	0.263481	+	0.0198361i
$607$		−	0.510275i		−	0.0207114i	−0.999946	−	0.0103557i	$-0.996704\pi$
$607$		−	0.510275i		−	0.0207114i	0.999946	−	0.0103557i	$-0.00329639\pi$
$608$	3.93096	+	1.88350i	0.159421	+	0.0763862i
$609$	43.3369	+	29.5684i	1.75610	+	1.19817i
$610$	3.27131	−	1.88869i	0.132452	−	0.0764710i
$611$	17.5333	+	30.3685i	0.709320	+	1.22858i
$612$	0.809336	−	5.34469i	0.0327155	−	0.216046i
$613$	−1.27998	−	2.21700i	−0.0516980	−	0.0895436i	0.839018	−	0.544103i	$-0.183130\pi$
$613$	−1.27998	−	2.21700i	−0.0516980	−	0.0895436i	−0.890716	+	0.454560i	$0.849797\pi$
$614$	−7.52401	−	4.34399i	−0.303644	−	0.175309i
$615$	7.44913	−	10.9178i	0.300378	−	0.440249i
$616$		−	12.3454i		−	0.497409i
$617$	4.50617	+	2.60164i	0.181412	+	0.104738i	0.587956	−	0.808893i	$-0.299933\pi$
$617$	4.50617	+	2.60164i	0.181412	+	0.104738i	−0.406544	+	0.913631i	$0.633266\pi$
$618$	−1.93182	−	4.01498i	−0.0777090	−	0.161506i
$619$	0.708705			0.0284853			0.0142426	−	0.999899i	$-0.495466\pi$
$619$	0.708705			0.0284853			0.0142426	+	0.999899i	$0.495466\pi$
$620$	3.56783			0.143288
$621$	1.26631	−	1.36194i	0.0508153	−	0.0546529i
$622$	16.8527	−	9.72990i	0.675731	−	0.390133i
$623$	−12.2703	+	21.2528i	−0.491600	+	0.851476i
$624$	11.7402	+	0.883859i	0.469984	+	0.0353827i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−14.0508			−0.561581
$627$	−0.0364893	−	22.3944i	−0.00145724	−	0.894345i
$628$	21.4728			0.856860
$629$	5.53729	+	9.59086i	0.220786	+	0.382413i
$630$	9.75660	+	7.79160i	0.388712	+	0.310425i
$631$	−1.98291	+	3.43450i	−0.0789383	+	0.136725i	−0.902792	−	0.430077i	$-0.858486\pi$
$631$	−1.98291	+	3.43450i	−0.0789383	+	0.136725i	0.823854	+	0.566802i	$0.191820\pi$
$632$	−1.10542	+	0.638217i	−0.0439714	+	0.0253869i
$633$	5.82779	+	12.1122i	0.231634	+	0.481415i
$634$	13.1654			0.522866
$635$	−6.99009			−0.277393
$636$	5.47569	−	2.63464i	0.217125	−	0.104470i
$637$	−60.7641	−	35.0822i	−2.40756	−	1.39001i
$638$		−	21.5870i		−	0.854638i
$639$	4.50309	+	11.4969i	0.178140	+	0.454810i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	13.4779	+	23.3444i	0.532345	+	0.922048i	0.999287	+	0.0377601i	$0.0120223\pi$
$641$	13.4779	+	23.3444i	0.532345	+	0.922048i	−0.466942	+	0.884288i	$0.654644\pi$
$642$	−18.5413	+	8.92120i	−0.731768	+	0.352092i
$643$	19.5490	+	33.8598i	0.770936	+	1.33530i	0.937050	+	0.349195i	$0.113545\pi$
$643$	19.5490	+	33.8598i	0.770936	+	1.33530i	−0.166114	+	0.986107i	$0.553122\pi$
$644$	−1.29000	+	0.744784i	−0.0508333	+	0.0293486i
$645$	−10.0286	+	14.6984i	−0.394875	+	0.578748i
$646$	−3.39384	+	7.08308i	−0.133529	+	0.278680i
$647$			25.0967i			0.986652i	0.869844	+	0.493326i	$0.164219\pi$
$647$			25.0967i			0.986652i	−0.869844	+	0.493326i	$0.835781\pi$
$648$	−8.59650	−	2.66460i	−0.337703	−	0.104676i
$649$	−22.5324	+	13.0091i	−0.884473	+	0.510651i
$650$	−5.88671	−	3.39869i	−0.230896	−	0.133308i
$651$	25.6472	+	1.93085i	1.00519	+	0.0756758i
$652$	9.71885	−	16.8335i	0.380620	−	0.659253i
$653$			26.7637i			1.04734i	0.851920	+	0.523672i	$0.175438\pi$
$653$			26.7637i			1.04734i	−0.851920	+	0.523672i	$0.824562\pi$
$654$	−12.5675	+	18.4196i	−0.491429	+	0.720263i
$655$	−6.76481	+	11.7170i	−0.264323	+	0.457821i
$656$	3.81541	−	6.60849i	0.148967	−	0.258018i
$657$	−14.5380	−	37.1171i	−0.567181	−	1.44808i
$658$			21.4710i			0.837028i
$659$	4.82716	−	8.36088i	0.188039	−	0.325694i	−0.756557	−	0.653928i	$-0.773120\pi$
$659$	4.82716	−	8.36088i	0.188039	−	0.325694i	0.944596	+	0.328234i	$0.106453\pi$
$660$	0.385694	−	5.12313i	0.0150131	−	0.199418i
$661$	12.4152	+	7.16792i	0.482895	+	0.278800i	0.721622	−	0.692287i	$-0.243397\pi$
$661$	12.4152	+	7.16792i	0.482895	+	0.278800i	−0.238727	+	0.971087i	$0.576730\pi$
$662$	−3.81697	+	2.20373i	−0.148351	+	0.0856503i
$663$	−1.59260	+	21.1543i	−0.0618515	+	0.821566i
$664$		−	1.93377i		−	0.0750447i
$665$	−10.2492	−	14.9692i	−0.397445	−	0.580482i
$666$	17.1685	−	6.72453i	0.665265	−	0.260570i
$667$	−2.25569	+	1.30232i	−0.0873407	+	0.0504262i
$668$	2.84217	+	4.92279i	0.109967	+	0.190468i
$669$	−20.6342	−	42.8851i	−0.797766	−	1.65803i
$670$	0.532496	+	0.922310i	0.0205721	+	0.0356320i
$671$	−9.70340	−	5.60226i	−0.374596	−	0.216273i
$672$	5.95479	+	4.06290i	0.229711	+	0.156730i
$673$			2.57499i			0.0992586i	0.998768	+	0.0496293i	$0.0158040\pi$
$673$			2.57499i			0.0992586i	−0.998768	+	0.0496293i	$0.984196\pi$
$674$	−4.81309	−	2.77884i	−0.185393	−	0.107037i
$675$	3.80541	+	3.53820i	0.146470	+	0.136185i
$676$	−33.2044			−1.27709
$677$	−25.1278			−0.965739			−0.482870	−	0.875692i	$-0.660406\pi$
$677$	−25.1278			−0.965739			−0.482870	+	0.875692i	$0.660406\pi$
$678$	4.91284	−	2.36382i	0.188677	−	0.0907821i
$679$	−46.8408	+	27.0435i	−1.79758	+	1.03784i
$680$	−0.900937	+	1.56047i	−0.0345493	+	0.0598412i
$681$	3.36203	−	44.6574i	0.128833	−	1.71127i
$682$	−5.29147	−	9.16510i	−0.202621	−	0.350950i
$683$	17.1516			0.656289			0.328145	−	0.944627i	$-0.393577\pi$
$683$	17.1516			0.656289			0.328145	+	0.944627i	$0.393577\pi$
$684$	10.8139	+	7.35246i	0.413481	+	0.281128i
$685$	12.2474			0.467949
$686$	−6.91361	−	11.9747i	−0.263963	−	0.457197i
$687$	0.728892	−	9.68178i	0.0278090	−	0.369383i
$688$	−5.13659	+	8.89683i	−0.195831	+	0.339188i
$689$	−20.6523	+	11.9236i	−0.786792	+	0.454254i
$690$	−0.558599	+	0.268771i	−0.0212655	+	0.0102319i
$691$	−19.5888			−0.745193			−0.372597	−	0.927993i	$-0.621532\pi$
$691$	−19.5888			−0.745193			−0.372597	+	0.927993i	$0.621532\pi$
$692$	22.4308			0.852690
$693$	5.54509	−	36.6187i	0.210641	−	1.39103i
$694$	−2.06156	−	1.19024i	−0.0782559	−	0.0451811i
$695$		−	11.8180i		−	0.448281i
$696$	10.4125	+	7.10436i	0.394685	+	0.269290i
$697$	11.9077	+	6.87489i	0.451035	+	0.260405i
$698$	−10.6939	−	18.5223i	−0.404769	−	0.701080i
$699$	19.6045	+	40.7450i	0.741512	+	1.54112i
$700$	−2.08100	−	3.60440i	−0.0786544	−	0.136233i
$701$	26.3609	−	15.2194i	0.995636	−	0.574831i	0.0886817	−	0.996060i	$-0.471735\pi$
$701$	26.3609	−	15.2194i	0.995636	−	0.574831i	0.906954	+	0.421229i	$0.138401\pi$
$702$	34.4266	+	7.89495i	1.29935	+	0.297976i
$703$	−26.7115	+	2.05475i	−1.00744	+	0.0774963i
$704$		−	2.96621i		−	0.111793i
$705$	−0.670798	+	8.91013i	−0.0252637	+	0.335575i
$706$	29.9848	−	17.3117i	1.12849	−	0.651536i
$707$	−13.5358	−	7.81491i	−0.509067	−	0.293910i
$708$	1.14055	−	15.1498i	0.0428646	−	0.569365i
$709$	4.75537	−	8.23654i	0.178592	−	0.309330i	−0.762807	−	0.646626i	$-0.776179\pi$
$709$	4.75537	−	8.23654i	0.178592	−	0.309330i	0.941398	+	0.337297i	$0.109513\pi$
$710$		−	4.11577i		−	0.154462i
$711$	−3.56555	+	1.39655i	−0.133719	+	0.0523748i
$712$	−2.94818	+	5.10639i	−0.110488	+	0.191370i
$713$	−0.638458	+	1.10584i	−0.0239104	+	0.0414141i
$714$	−7.32084	+	10.7298i	−0.273976	+	0.401552i
$715$			20.1625i			0.754034i
$716$	−7.11444	+	12.3226i	−0.265879	+	0.460516i
$717$	−41.3536	−	3.11330i	−1.54438	−	0.116268i
$718$	−18.8394	−	10.8769i	−0.703080	−	0.405924i
$719$	34.4372	−	19.8823i	1.28429	−	0.741485i	0.306660	−	0.951819i	$-0.400788\pi$
$719$	34.4372	−	19.8823i	1.28429	−	0.741485i	0.977630	+	0.210334i	$0.0674551\pi$
$720$	2.34421	+	1.87208i	0.0873635	+	0.0697683i
$721$			10.7064i			0.398727i
$722$	−11.9048	−	14.8079i	−0.443052	−	0.551095i
$723$	−8.41943	+	12.3399i	−0.313122	+	0.458927i
$724$	−0.0315834	+	0.0182347i	−0.00117379	+	0.000677686i
$725$	−3.63882	−	6.30262i	−0.135142	−	0.234074i
$726$	3.43620	−	1.65334i	0.127530	−	0.0613611i
$727$	10.4980	+	18.1831i	0.389350	+	0.674374i	0.992362	−	0.123358i	$-0.0393664\pi$
$727$	10.4980	+	18.1831i	0.389350	+	0.674374i	−0.603012	+	0.797732i	$0.706033\pi$
$728$	−24.5005	−	14.1454i	−0.908048	−	0.524262i
$729$	−24.3020	−	11.7649i	−0.900073	−	0.435739i
$730$			13.2875i			0.491794i
$731$	−16.0310	−	9.25548i	−0.592926	−	0.342326i
$732$	5.89568	−	2.83672i	0.217910	−	0.104848i
$733$	9.50251			0.350983			0.175492	−	0.984481i	$-0.443849\pi$
$733$	9.50251			0.350983			0.175492	+	0.984481i	$0.443849\pi$
$734$	12.5749			0.464147
$735$	−7.75173	−	16.1108i	−0.285927	−	0.594255i
$736$	−0.309948	+	0.178948i	−0.0114248	+	0.00659613i
$737$	1.57950	−	2.73577i	0.0581815	−	0.100773i
$738$	14.2855	−	17.8882i	0.525857	−	0.658476i
$739$	−14.5149	−	25.1405i	−0.533939	−	0.924809i	−0.999214	−	0.0396431i	$-0.987378\pi$
$739$	−14.5149	−	25.1405i	−0.533939	−	0.924809i	0.465275	−	0.885166i	$-0.345955\pi$
$740$	−6.14614			−0.225937
$741$	−44.4854	−	25.5871i	−1.63421	−	0.939966i
$742$	−14.6016			−0.536040
$743$	4.08693	+	7.07877i	0.149935	+	0.259695i	0.931203	−	0.364500i	$-0.118760\pi$
$743$	4.08693	+	7.07877i	0.149935	+	0.259695i	−0.781268	+	0.624195i	$0.785427\pi$
$744$	6.16223	+	0.463923i	0.225918	+	0.0170082i
$745$	3.59946	−	6.23444i	0.131874	−	0.228412i
$746$	−16.2847	+	9.40195i	−0.596224	+	0.344230i
$747$	0.868577	−	5.73591i	0.0317796	−	0.209866i
$748$	5.34474			0.195423
$749$	49.4426			1.80659
$750$	−0.750973	−	1.56078i	−0.0274217	−	0.0569917i
$751$	0.510899	+	0.294967i	0.0186430	+	0.0107635i	0.509293	−	0.860593i	$-0.329907\pi$
$751$	0.510899	+	0.294967i	0.0186430	+	0.0107635i	−0.490650	+	0.871357i	$0.663240\pi$
$752$			5.15882i			0.188123i
$753$	−12.8672	+	18.8588i	−0.468907	+	0.687253i
$754$	−42.8413	−	24.7345i	−1.56019	−	0.900776i
$755$	5.56375	+	9.63670i	0.202486	+	0.350715i
$756$	15.8381	+	14.7260i	0.576026	+	0.535580i
$757$	−1.45489	−	2.51995i	−0.0528791	−	0.0915892i	0.838374	−	0.545095i	$-0.183506\pi$
$757$	−1.45489	−	2.51995i	−0.0528791	−	0.0915892i	−0.891253	+	0.453506i	$0.850173\pi$
$758$	21.6757	−	12.5144i	0.787295	−	0.454545i
$759$	1.51888	+	1.03632i	0.0551320	+	0.0376161i
$760$	−2.46256	−	3.59664i	−0.0893263	−	0.130464i
$761$			30.5864i			1.10876i	0.832264	+	0.554379i	$0.187044\pi$
$761$			30.5864i			1.10876i	−0.832264	+	0.554379i	$0.812956\pi$
$762$	−12.0730	−	0.908916i	−0.437360	−	0.0329266i
$763$	46.4032	−	26.7909i	1.67991	−	0.969896i
$764$	−19.3247	−	11.1571i	−0.699142	−	0.403650i
$765$	−3.37325	+	4.22397i	−0.121960	+	0.152718i
$766$	2.61339	−	4.52653i	0.0944258	−	0.163550i
$767$			59.6233i			2.15287i
$768$	1.43075	+	0.976190i	0.0516278	+	0.0352252i
$769$	12.2534	−	21.2235i	0.441869	−	0.765339i	−0.555959	−	0.831209i	$-0.687649\pi$
$769$	12.2534	−	21.2235i	0.441869	−	0.765339i	0.997828	+	0.0658703i	$0.0209824\pi$
$770$	−6.17269	+	10.6914i	−0.222448	+	0.385292i
$771$	−38.1153	−	26.0057i	−1.37269	−	0.936573i
$772$		−	13.2997i		−	0.478665i
$773$	18.2611	−	31.6291i	0.656805	−	1.13762i	−0.324632	−	0.945840i	$-0.605241\pi$
$773$	18.2611	−	31.6291i	0.656805	−	1.13762i	0.981438	−	0.191780i	$-0.0614261\pi$
$774$	−19.2322	+	24.0825i	−0.691287	+	0.865626i
$775$	−3.08983	−	1.78392i	−0.110990	−	0.0640802i
$776$	−11.2544	+	6.49772i	−0.404009	+	0.233255i
$777$	−44.1813	−	3.32618i	−1.58499	−	0.119326i
$778$		−	24.2157i		−	0.868175i
$779$	−27.4453	+	18.7913i	−0.983331	+	0.673269i
$780$	−9.72537	−	6.63554i	−0.348224	−	0.237590i
$781$	−10.5727	+	6.10413i	−0.378319	+	0.218423i
$782$	−0.322443	−	0.558487i	−0.0115305	−	0.0199715i
$783$	27.6944	+	25.7498i	0.989717	+	0.920222i
$784$	−5.16113	−	8.93933i	−0.184326	−	0.319262i
$785$	−18.5960	−	10.7364i	−0.663721	−	0.383199i
$786$	−13.2075	+	19.3575i	−0.471095	+	0.690460i
$787$		−	9.69183i		−	0.345477i	−0.984968	−	0.172738i	$-0.944739\pi$
$787$		−	9.69183i		−	0.345477i	0.984968	−	0.172738i	$-0.0552615\pi$
$788$	19.7095	+	11.3793i	0.702124	+	0.405371i
$789$	17.4356	+	36.2373i	0.620725	+	1.29008i
$790$	1.27643			0.0454135
$791$	−13.1007			−0.465806
$792$	1.33231	−	8.79833i	0.0473417	−	0.312635i
$793$	−22.2364	+	12.8382i	−0.789637	+	0.455897i
$794$	−12.7295	+	22.0482i	−0.451754	+	0.782461i
$795$	−6.05941	−	0.456182i	−0.214905	−	0.0161791i
$796$	2.34142	+	4.05546i	0.0829895	+	0.143742i
$797$	22.8396			0.809019			0.404509	−	0.914534i	$-0.367442\pi$
$797$	22.8396			0.809019			0.404509	+	0.914534i	$0.367442\pi$
$798$	−15.7555	−	27.1870i	−0.557740	−	0.962409i
$799$	−9.29555			−0.328853
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−11.0384	+	13.8223i	−0.390024	+	0.488387i
$802$	−17.9661	+	31.1182i	−0.634405	+	1.09882i
$803$	34.1332	−	19.7068i	1.20454	−	0.695439i
$804$	0.799780	+	1.66222i	0.0282061	+	0.0586220i
$805$	1.48957			0.0525004
$806$	−24.2519			−0.854238
$807$	−7.87837	+	3.79069i	−0.277332	+	0.133439i
$808$	−3.25224	−	1.87768i	−0.114413	−	0.0660566i
$809$			14.9216i			0.524616i	0.964984	+	0.262308i	$0.0844836\pi$
$809$			14.9216i			0.524616i	−0.964984	+	0.262308i	$0.915516\pi$
$810$	6.11249	+	6.60587i	0.214771	+	0.232106i
$811$	29.6318	+	17.1079i	1.04051	+	0.600740i	0.919978	−	0.391969i	$-0.128206\pi$
$811$	29.6318	+	17.1079i	1.04051	+	0.600740i	0.120534	+	0.992709i	$0.461539\pi$
$812$	−15.1448	−	26.2315i	−0.531477	−	0.920546i
$813$	14.1267	−	6.79708i	0.495444	−	0.238384i
$814$	9.11538	+	15.7883i	0.319494	+	0.553379i
$815$	−16.8335	+	9.71885i	−0.589653	+	0.340437i
$816$	−1.75897	+	2.57804i	−0.0615763	+	0.0902493i
$817$	36.9489	−	25.2983i	1.29268	−	0.885074i
$818$		−	1.78373i		−	0.0623668i
$819$	−66.3194	−	52.9625i	−2.31739	−	1.85066i
$820$	−6.60849	+	3.81541i	−0.230778	+	0.133240i
$821$	−4.44653	−	2.56720i	−0.155185	−	0.0895961i	0.420397	−	0.907340i	$-0.361891\pi$
$821$	−4.44653	−	2.56720i	−0.155185	−	0.0895961i	−0.575582	+	0.817744i	$0.695224\pi$
$822$	21.1533	+	1.59252i	0.737805	+	0.0555456i
$823$	19.8033	−	34.3004i	0.690301	−	1.19564i	−0.281439	−	0.959579i	$-0.590812\pi$
$823$	19.8033	−	34.3004i	0.690301	−	1.19564i	0.971739	−	0.236056i	$-0.0758550\pi$
$824$			2.57242i			0.0896144i
$825$	−2.89559	+	4.24391i	−0.100811	+	0.147754i
$826$	−18.2535	+	31.6160i	−0.635121	+	1.10006i
$827$	−11.4081	+	19.7595i	−0.396700	+	0.687105i	−0.993317	−	0.115422i	$-0.963178\pi$
$827$	−11.4081	+	19.7595i	−0.396700	+	0.687105i	0.596616	+	0.802527i	$0.296511\pi$
$828$	−0.999740	+	0.391577i	−0.0347434	+	0.0136082i
$829$			3.24052i			0.112548i	0.998415	+	0.0562739i	$0.0179220\pi$
$829$			3.24052i			0.112548i	−0.998415	+	0.0562739i	$0.982078\pi$
$830$	−0.966883	+	1.67469i	−0.0335610	+	0.0581293i
$831$	−0.693780	+	9.21539i	−0.0240670	+	0.319678i
$832$	−5.88671	−	3.39869i	−0.204085	−	0.117828i
$833$	16.1075	−	9.29970i	0.558094	−	0.322215i
$834$	1.53668	−	20.4115i	0.0532109	−	0.706794i
$835$		−	5.68435i		−	0.196715i
$836$	−5.58687	+	11.6600i	−0.193226	+	0.403271i
$837$	18.0699	+	4.14393i	0.624588	+	0.143235i
$838$	31.3990	−	18.1282i	1.08466	−	0.626228i
$839$	3.62615	+	6.28067i	0.125189	+	0.216833i	0.921807	−	0.387650i	$-0.126713\pi$
$839$	3.62615	+	6.28067i	0.125189	+	0.216833i	−0.796618	+	0.604483i	$0.793380\pi$
$840$	−3.12555	−	6.49598i	−0.107842	−	0.224132i
$841$	−11.9820	−	20.7535i	−0.413174	−	0.715638i
$842$	4.43149	+	2.55852i	0.152719	+	0.0881724i
$843$	−19.5999	−	13.3728i	−0.675055	−	0.460584i
$844$		−	7.76032i		−	0.267121i
$845$	28.7559	+	16.6022i	0.989232	+	0.571133i
$846$	−2.31716	+	15.3020i	−0.0796655	+	0.526095i
$847$	−9.16303			−0.314845
$848$	−3.50830			−0.120476
$849$	1.24284	−	0.597994i	0.0426541	−	0.0205231i
$850$	1.56047	−	0.900937i	0.0535236	−	0.0309019i
$851$	1.09984	−	1.90498i	0.0377021	−	0.0653020i
$852$	0.535171	−	7.10861i	0.0183347	−	0.243537i
$853$	1.50057	+	2.59906i	0.0513785	+	0.0889901i	0.890571	−	0.454845i	$-0.150305\pi$
$853$	1.50057	+	2.59906i	0.0513785	+	0.0889901i	−0.839192	+	0.543835i	$0.816972\pi$
$854$	−15.7215			−0.537978
$855$	−5.68891	−	11.7744i	−0.194557	−	0.402676i
$856$	11.8795			0.406034
$857$	−19.2846	−	33.4018i	−0.658748	−	1.14099i	−0.980940	−	0.194311i	$-0.937753\pi$
$857$	−19.2846	−	33.4018i	−0.658748	−	1.14099i	0.322192	−	0.946674i	$-0.395580\pi$
$858$	−2.62171	+	34.8239i	−0.0895038	+	1.18887i
$859$	20.8063	−	36.0376i	0.709902	−	1.22959i	−0.254991	−	0.966943i	$-0.582073\pi$
$859$	20.8063	−	36.0376i	0.709902	−	1.22959i	0.964893	−	0.262643i	$-0.0845940\pi$
$860$	8.89683	−	5.13659i	0.303379	−	0.175156i
$861$	−49.5696	+	23.8505i	−1.68933	+	0.812824i
$862$	−6.63225			−0.225895
$863$	−22.5281			−0.766866			−0.383433	−	0.923569i	$-0.625258\pi$
$863$	−22.5281			−0.766866			−0.383433	+	0.923569i	$0.625258\pi$
$864$	3.80541	+	3.53820i	0.129463	+	0.120372i
$865$	−19.4256	−	11.2154i	−0.660491	−	0.381334i
$866$		−	6.03682i		−	0.205140i
$867$	19.6775	+	13.4258i	0.668283	+	0.455964i
$868$	−12.8599	−	7.42466i	−0.436493	−	0.252009i
$869$	−1.89309	−	3.27892i	−0.0642185	−	0.111230i
$870$	−5.46531	−	11.3588i	−0.185291	−	0.385100i
$871$	−3.61958	−	6.26930i	−0.122645	−	0.212427i
$872$	11.1493	−	6.43703i	0.377561	−	0.217985i
$873$	−36.3011	+	14.2184i	−1.22861	+	0.481220i
$874$	1.55544	−	0.119650i	0.0526136	−	0.00404723i
$875$			4.16200i			0.140701i
$876$	−1.72777	+	22.9498i	−0.0583759	+	0.775401i
$877$	30.2868	−	17.4861i	1.02271	−	0.590463i	0.107824	−	0.994170i	$-0.465612\pi$
$877$	30.2868	−	17.4861i	1.02271	−	0.590463i	0.914888	+	0.403707i	$0.132278\pi$
$878$	10.6718	+	6.16135i	0.360155	+	0.207936i
$879$	3.09239	−	41.0758i	0.104304	−	1.38545i
$880$	−1.48311	+	2.56881i	−0.0499955	+	0.0865947i
$881$		−	29.7930i		−	1.00375i	−0.864939	−	0.501876i	$-0.832643\pi$
$881$		−	29.7930i		−	1.00375i	0.864939	−	0.501876i	$-0.167357\pi$
$882$	−11.2936	−	28.8339i	−0.380276	−	0.970888i
$883$	−5.90494	+	10.2276i	−0.198717	+	0.344188i	−0.948113	−	0.317935i	$-0.897011\pi$
$883$	−5.90494	+	10.2276i	−0.198717	+	0.344188i	0.749396	+	0.662122i	$0.230344\pi$
$884$	6.12401	−	10.6071i	0.205973	−	0.356755i
$885$	−8.56266	+	12.5499i	−0.287831	+	0.421859i
$886$			6.99038i			0.234847i
$887$	−6.41460	+	11.1104i	−0.215381	+	0.373051i	−0.953390	−	0.301740i	$-0.902433\pi$
$887$	−6.41460	+	11.1104i	−0.215381	+	0.373051i	0.738009	+	0.674791i	$0.235766\pi$
$888$	−10.6154	−	0.799178i	−0.356229	−	0.0268187i
$889$	25.1951	+	14.5464i	0.845016	+	0.487870i
$890$	5.10639	−	2.94818i	0.171167	−	0.0988231i
$891$	7.90378	−	25.4990i	0.264787	−	0.854250i
$892$			27.4767i			0.919987i
$893$	9.71667	−	20.2791i	0.325156	−	0.678615i
$894$	7.02751	−	10.2999i	0.235035	−	0.344479i
$895$	12.3226	−	7.11444i	0.411898	−	0.237810i
$896$	−2.08100	−	3.60440i	−0.0695214	−	0.120415i
$897$	3.79701	−	1.82694i	0.126779	−	0.0609997i
$898$	15.7401	+	27.2626i	0.525253	+	0.909765i
$899$	−22.4867	−	12.9827i	−0.749974	−	0.432997i
$900$	−1.09411	−	2.79337i	−0.0364702	−	0.0931124i
$901$		−	6.32152i		−	0.210600i
$902$	19.6022	+	11.3173i	0.652681	+	0.376825i
$903$	66.7343	−	32.1093i	2.22078	−	1.06853i
$904$	−3.14768			−0.104690
$905$	0.0364693			0.00121228
$906$	8.35645	+	17.3676i	0.277624	+	0.577000i
$907$	34.8057	−	20.0951i	1.15571	−	0.667247i	0.205434	−	0.978671i	$-0.434139\pi$
$907$	34.8057	−	20.0951i	1.15571	−	0.667247i	0.950271	+	0.311424i	$0.100806\pi$
$908$	−12.9280	+	22.3919i	−0.429029	+	0.743101i
$909$	−8.80336	−	7.03034i	−0.291989	−	0.233182i
$910$	14.1454	+	24.5005i	0.468914	+	0.812183i
$911$	26.9672			0.893462			0.446731	−	0.894668i	$-0.352588\pi$
$911$	26.9672			0.893462			0.446731	+	0.894668i	$0.352588\pi$
$912$	−3.78557	−	6.53219i	−0.125353	−	0.216302i
$913$	5.73596			0.189832
$914$	−14.7809	−	25.6013i	−0.488909	−	0.846814i
$915$	−6.52416	−	0.491171i	−0.215682	−	0.0162376i
$916$	−2.80280	+	4.85459i	−0.0926071	+	0.160400i
$917$	48.7661	−	28.1551i	1.61040	−	0.929765i
$918$	−6.37539	+	6.85686i	−0.210419	+	0.226310i
$919$	−15.1257			−0.498951			−0.249475	−	0.968381i	$-0.580258\pi$
$919$	−15.1257			−0.498951			−0.249475	+	0.968381i	$0.580258\pi$
$920$	0.357897			0.0117995
$921$	6.52443	+	13.5600i	0.214987	+	0.446818i
$922$	−12.9506	−	7.47702i	−0.426505	−	0.246243i
$923$			27.9765i			0.920857i
$924$	−12.0514	+	17.6632i	−0.396463	+	0.581076i
$925$	5.32272	+	3.07307i	0.175010	+	0.101042i
$926$	−8.37459	−	14.5052i	−0.275206	−	0.476671i
$927$	−1.15544	+	7.63027i	−0.0379495	+	0.250611i
$928$	−3.63882	−	6.30262i	−0.119450	−	0.206894i
$929$	−9.47633	+	5.47116i	−0.310908	+	0.179503i	−0.647333	−	0.762207i	$-0.724116\pi$
$929$	−9.47633	+	5.47116i	−0.310908	+	0.179503i	0.336425	+	0.941710i	$0.390782\pi$
$930$	−5.10469	−	3.48288i	−0.167389	−	0.114208i
$931$	3.45088	+	44.8611i	0.113098	+	1.47026i
$932$		−	26.1055i		−	0.855114i
$933$	−33.6102	−	2.53034i	−1.10035	−	0.0828397i
$934$	−19.2991	+	11.1424i	−0.631487	+	0.364589i
$935$	−4.62868	−	2.67237i	−0.151374	−	0.0873958i
$936$	−15.9345	−	12.7252i	−0.520835	−	0.415938i
$937$	7.80717	−	13.5224i	0.255049	−	0.441758i	−0.709860	−	0.704343i	$-0.751242\pi$
$937$	7.80717	−	13.5224i	0.255049	−	0.441758i	0.964909	+	0.262585i	$0.0845750\pi$
$938$		−	4.43250i		−	0.144726i
$939$	20.1031	+	13.7162i	0.656041	+	0.447611i
$940$	2.57941	−	4.46767i	0.0841312	−	0.145719i
$941$	10.5573	−	18.2858i	0.344158	−	0.596100i	−0.641042	−	0.767506i	$-0.721498\pi$
$941$	10.5573	−	18.2858i	0.344158	−	0.596100i	0.985200	+	0.171406i	$0.0548310\pi$
$942$	−30.7223	−	20.9616i	−1.00099	−	0.682965i
$943$		−	2.73105i		−	0.0889352i
$944$	−4.38575	+	7.59635i	−0.142744	+	0.247240i
$945$	−6.35320	−	20.6721i	−0.206670	−	0.672465i
$946$	−26.3899	−	15.2362i	−0.858009	−	0.495372i
$947$	16.7276	−	9.65770i	0.543575	−	0.313833i	−0.202952	−	0.979189i	$-0.565053\pi$
$947$	16.7276	−	9.65770i	0.543575	−	0.313833i	0.746527	+	0.665356i	$0.231720\pi$
$948$	2.20461	+	0.165974i	0.0716023	+	0.00539057i
$949$		−	90.3206i		−	2.93193i
$950$	0.334315	+	4.34606i	0.0108466	+	0.141005i
$951$	−18.8365	−	12.8520i	−0.610815	−	0.416754i
$952$	6.49467	−	3.74970i	0.210493	−	0.121528i
$953$	−2.63541	−	4.56467i	−0.0853695	−	0.147864i	0.820179	−	0.572107i	$-0.193874\pi$
$953$	−2.63541	−	4.56467i	−0.0853695	−	0.147864i	−0.905549	+	0.424243i	$0.860540\pi$
$954$	−10.4063	−	1.57580i	−0.336916	−	0.0510185i
$955$	11.1571	+	19.3247i	0.361036	+	0.625332i
$956$	20.7353	+	11.9715i	0.670627	+	0.387187i
$957$	−21.0730	+	30.8857i	−0.681195	+	0.998392i
$958$		−	28.0745i		−	0.907045i
$959$	−44.1445	−	25.4869i	−1.42550	−	0.823014i
$960$	−0.750973	−	1.56078i	−0.0242375	−	0.0503740i
$961$	18.2706			0.589373
$962$	41.7777			1.34697
$963$	35.2368	+	5.33585i	1.13549	+	0.171945i
$964$	7.46928	−	4.31239i	0.240569	−	0.138893i
$965$	−6.64983	+	11.5178i	−0.214066	+	0.370772i
$966$	2.57273	+	0.193687i	0.0827761	+	0.00623179i
$967$	−0.734029	−	1.27138i	−0.0236048	−	0.0408847i	0.853982	−	0.520303i	$-0.174181\pi$
$967$	−0.734029	−	1.27138i	−0.0236048	−	0.0408847i	−0.877586	+	0.479418i	$0.840848\pi$
$968$	−2.20159			−0.0707619
$969$	11.7702	−	6.82111i	0.378113	−	0.219126i
$970$	12.9954			0.417259
$971$	−21.9702	−	38.0536i	−0.705058	−	1.22120i	−0.966670	−	0.256024i	$-0.917587\pi$
$971$	−21.9702	−	38.0536i	−0.705058	−	1.22120i	0.261612	−	0.965173i	$-0.415746\pi$
$972$	9.69831	+	12.2042i	0.311073	+	0.391450i
$973$	−24.5932	+	42.5966i	−0.788421	+	1.36559i
$974$	−1.43156	+	0.826514i	−0.0458703	+	0.0264832i
$975$	5.10465	+	10.6092i	0.163480	+	0.339767i
$976$	−3.77739			−0.120911
$977$	−27.0036			−0.863921			−0.431961	−	0.901892i	$-0.642178\pi$
$977$	−27.0036			−0.863921			−0.431961	+	0.901892i	$0.642178\pi$
$978$	−30.3380	+	14.5972i	−0.970103	+	0.466767i
$979$	−15.1466	−	8.74492i	−0.484089	−	0.279489i
$980$			10.3223i			0.329732i
$981$	35.9620	−	14.0856i	1.14818	−	0.449718i
$982$	−1.30505	−	0.753470i	−0.0416457	−	0.0240442i
$983$	27.5611	+	47.7373i	0.879063	+	1.52258i	0.852371	+	0.522938i	$0.175164\pi$
$983$	27.5611	+	47.7373i	0.879063	+	1.52258i	0.0266924	+	0.999644i	$0.491503\pi$
$984$	−11.9100	+	5.73054i	−0.379678	+	0.182683i
$985$	−11.3793	−	19.7095i	−0.362575	−	0.627998i
$986$	11.3565	−	6.55670i	0.361666	−	0.208808i
$987$	20.9598	−	30.7197i	0.667158	−	0.977820i
$988$	16.7389	+	24.4477i	0.532536	+	0.777786i
$989$			3.67674i			0.116913i
$990$	−5.55298	+	6.95342i	−0.176485	+	0.220994i
$991$	28.0122	−	16.1729i	0.889838	−	0.513748i	0.0159483	−	0.999873i	$-0.494923\pi$
$991$	28.0122	−	16.1729i	0.889838	−	0.513748i	0.873889	+	0.486125i	$0.161590\pi$
$992$	−3.08983	−	1.78392i	−0.0981023	−	0.0566394i
$993$	7.61239	+	0.573098i	0.241572	+	0.0181867i
$994$	−8.56493	+	14.8349i	−0.271663	+	0.470534i
$995$		−	4.68284i		−	0.148456i
$996$	−1.88772	+	2.76674i	−0.0598148	+	0.0876675i
$997$	−14.9604	+	25.9122i	−0.473802	+	0.820648i	−0.999550	−	0.0299916i	$-0.990452\pi$
$997$	−14.9604	+	25.9122i	−0.473802	+	0.820648i	0.525749	+	0.850640i	$0.323785\pi$
$998$	−10.7116	+	18.5530i	−0.339070	+	0.587287i
$999$	−31.1282	−	7.13856i	−0.984854	−	0.225854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.b.221.6	yes	24
3.2	odd	2		570.2.s.a.221.10	✓	24
19.8	odd	6		570.2.s.a.521.10	yes	24
57.8	even	6	inner	570.2.s.b.521.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.10	✓	24	3.2	odd	2
570.2.s.a.521.10	yes	24	19.8	odd	6
570.2.s.b.221.6	yes	24	1.1	even	1	trivial
570.2.s.b.521.6	yes	24	57.8	even	6	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.130029 - 1.72716i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.56078 - 0.750973i) q^{6} -4.16200 q^{7} -1.00000 q^{8} +(-2.96618 - 0.449163i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.130029 - 1.72716i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.56078 - 0.750973i) q^{6} -4.16200 q^{7} -1.00000 q^{8} +(-2.96618 - 0.449163i) q^{9} +(0.866025 + 0.500000i) q^{10} -2.96621i q^{11} +(1.43075 + 0.976190i) q^{12} +(-5.88671 - 3.39869i) q^{13} +(-2.08100 - 3.60440i) q^{14} +(-0.750973 - 1.56078i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.56047 - 0.900937i) q^{17} +(-1.09411 - 2.79337i) q^{18} +(0.334315 + 4.34606i) q^{19} +1.00000i q^{20} +(-0.541182 + 7.18845i) q^{21} +(2.56881 - 1.48311i) q^{22} +(-0.309948 - 0.178948i) q^{23} +(-0.130029 + 1.72716i) q^{24} +(0.500000 - 0.866025i) q^{25} -6.79738i q^{26} +(-1.16147 + 5.06468i) q^{27} +(2.08100 - 3.60440i) q^{28} +(3.63882 - 6.30262i) q^{29} +(0.976190 - 1.43075i) q^{30} -3.56783i q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.12313 - 0.385694i) q^{33} +(1.56047 + 0.900937i) q^{34} +(-3.60440 + 2.08100i) q^{35} +(1.87208 - 2.34421i) q^{36} +6.14614i q^{37} +(-3.59664 + 2.46256i) q^{38} +(-6.63554 + 9.72537i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(3.81541 + 6.60849i) q^{41} +(-6.49598 + 3.12555i) q^{42} +(-5.13659 - 8.89683i) q^{43} +(2.56881 + 1.48311i) q^{44} +(-2.79337 + 1.09411i) q^{45} -0.357897i q^{46} +(-4.46767 - 2.57941i) q^{47} +(-1.56078 + 0.750973i) q^{48} +10.3223 q^{49} +1.00000 q^{50} +(-1.35316 - 2.81233i) q^{51} +(5.88671 - 3.39869i) q^{52} +(1.75415 - 3.03828i) q^{53} +(-4.96688 + 1.52648i) q^{54} +(-1.48311 - 2.56881i) q^{55} +4.16200 q^{56} +(7.54982 - 0.0123016i) q^{57} +7.27764 q^{58} +(-4.38575 - 7.59635i) q^{59} +(1.72716 + 0.130029i) q^{60} +(1.88869 - 3.27131i) q^{61} +(3.08983 - 1.78392i) q^{62} +(12.3453 + 1.86942i) q^{63} +1.00000 q^{64} -6.79738 q^{65} +(-2.22754 - 4.62961i) q^{66} +(0.922310 + 0.532496i) q^{67} +1.80187i q^{68} +(-0.349376 + 0.512062i) q^{69} +(-3.60440 - 2.08100i) q^{70} +(-2.05789 - 3.56436i) q^{71} +(2.96618 + 0.449163i) q^{72} +(6.64377 + 11.5074i) q^{73} +(-5.32272 + 3.07307i) q^{74} +(-1.43075 - 0.976190i) q^{75} +(-3.93096 - 1.88350i) q^{76} +12.3454i q^{77} +(-11.7402 - 0.883859i) q^{78} +(1.10542 - 0.638217i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(8.59650 + 2.66460i) q^{81} +(-3.81541 + 6.60849i) q^{82} +1.93377i q^{83} +(-5.95479 - 4.06290i) q^{84} +(0.900937 - 1.56047i) q^{85} +(5.13659 - 8.89683i) q^{86} +(-10.4125 - 7.10436i) q^{87} +2.96621i q^{88} +(2.94818 - 5.10639i) q^{89} +(-2.34421 - 1.87208i) q^{90} +(24.5005 + 14.1454i) q^{91} +(0.309948 - 0.178948i) q^{92} +(-6.16223 - 0.463923i) q^{93} -5.15882i q^{94} +(2.46256 + 3.59664i) q^{95} +(-1.43075 - 0.976190i) q^{96} +(11.2544 - 6.49772i) q^{97} +(5.16113 + 8.93933i) q^{98} +(-1.33231 + 8.79833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

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