LMFDB - Embedded newform 570.2.s.a.521.10

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			521.10
Character	$\chi$	$=$	570.521
Dual form			570.2.s.a.221.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.56078 - 0.750973i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.130029 + 1.72716i) q^{6} -4.16200 q^{7} +1.00000 q^{8} +(1.87208 - 2.34421i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.56078 - 0.750973i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.130029 + 1.72716i) q^{6} -4.16200 q^{7} +1.00000 q^{8} +(1.87208 - 2.34421i) 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} +(-1.72716 - 0.130029i) 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} +(-6.49598 + 3.12555i) q^{21} +(2.56881 + 1.48311i) q^{22} +(0.309948 - 0.178948i) q^{23} +(1.56078 - 0.750973i) 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} +(-2.22754 - 4.62961i) q^{33} +(1.56047 - 0.900937i) q^{34} +(3.60440 + 2.08100i) q^{35} +(-2.96618 - 0.449163i) 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} +(0.541182 - 7.18845i) 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} +(-0.130029 + 1.72716i) q^{48} +10.3223 q^{49} -1.00000 q^{50} +(-3.11213 - 0.234296i) q^{51} +(5.88671 + 3.39869i) q^{52} +(-1.75415 - 3.03828i) q^{53} +(3.80541 + 3.53820i) q^{54} +(-1.48311 + 2.56881i) q^{55} -4.16200 q^{56} +(-2.74198 - 7.03431i) q^{57} +7.27764 q^{58} +(4.38575 - 7.59635i) q^{59} +(0.750973 + 1.56078i) q^{60} +(1.88869 + 3.27131i) q^{61} +(-3.08983 - 1.78392i) q^{62} +(-7.79160 + 9.75660i) q^{63} +1.00000 q^{64} +6.79738 q^{65} +(5.12313 + 0.385694i) 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} +(1.87208 - 2.34421i) 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} +(-5.10465 - 10.6092i) q^{78} +(1.10542 + 0.638217i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-1.99064 - 8.77709i) 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} +(0.449163 - 2.96618i) q^{90} +(24.5005 - 14.1454i) q^{91} +(-0.309948 - 0.178948i) q^{92} +(2.67935 + 5.56861i) 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} +(-6.95342 - 5.55298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 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} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 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} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * 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 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * 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 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.56078	−	0.750973i	0.901118	−	0.433574i
$3$	1.56078	−	0.750973i	0.901118	−	0.433574i
$4$	−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
$6$	−0.130029	+	1.72716i	−0.0530842	+	0.705111i
$7$	−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
$9$	1.87208	−	2.34421i	0.624026	−	0.781403i
$10$	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	−0.649416	+	0.760433i	$0.724987\pi$
$13$	−5.88671	+	3.39869i	−1.63268	+	0.942627i	−0.983263	+	0.182194i	$0.941680\pi$
$14$	2.08100	−	3.60440i	0.556171	−	0.963316i
$15$	−1.72716	−	0.130029i	−0.445952	−	0.0335734i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.56047	−	0.900937i	−0.378469	−	0.218509i	0.298683	−	0.954352i	$-0.403453\pi$
$17$	−1.56047	−	0.900937i	−0.378469	−	0.218509i	−0.677152	+	0.735843i	$0.736786\pi$
$18$	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
$21$	−6.49598	+	3.12555i	−1.41754	+	0.682051i
$22$	2.56881	+	1.48311i	0.547673	+	0.316199i
$23$	0.309948	−	0.178948i	0.0646286	−	0.0373133i	−0.467338	−	0.884079i	$-0.654787\pi$
$23$	0.309948	−	0.178948i	0.0646286	−	0.0373133i	0.531966	+	0.846766i	$0.321453\pi$
$24$	1.56078	−	0.750973i	0.318593	−	0.153292i
$25$	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	−0.976260	−	0.216601i	$-0.930503\pi$
$29$	−3.63882	−	6.30262i	−0.675712	−	1.17037i	0.300548	−	0.953767i	$-0.402830\pi$
$30$	0.976190	−	1.43075i	0.178227	−	0.261218i
$31$			3.56783i			0.640802i	0.947282	+	0.320401i	$0.103818\pi$
$31$			3.56783i			0.640802i	−0.947282	+	0.320401i	$0.896182\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.22754	−	4.62961i	−0.387766	−	0.805911i
$34$	1.56047	−	0.900937i	0.267618	−	0.154509i
$35$	3.60440	+	2.08100i	0.609255	+	0.351753i
$36$	−2.96618	−	0.449163i	−0.494364	−	0.0748606i
$37$		−	6.14614i		−	1.01042i	−0.862997	−	0.505210i	$-0.831415\pi$
$37$		−	6.14614i		−	1.01042i	0.862997	−	0.505210i	$-0.168585\pi$
$38$	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	0.397557	+	0.917578i	$0.369858\pi$
$41$	−3.81541	+	6.60849i	−0.595867	+	1.03207i	−0.993424	+	0.114495i	$0.963475\pi$
$42$	0.541182	−	7.18845i	0.0835062	−	1.10920i
$43$	−5.13659	+	8.89683i	−0.783322	+	1.35675i	0.146674	+	0.989185i	$0.453143\pi$
$43$	−5.13659	+	8.89683i	−0.783322	+	1.35675i	−0.929996	+	0.367569i	$0.880190\pi$
$44$	−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	$-0.543881\pi$
$47$	4.46767	−	2.57941i	0.651677	−	0.376246i	0.789098	+	0.614267i	$0.210548\pi$
$48$	−0.130029	+	1.72716i	−0.0187681	+	0.249295i
$49$	10.3223			1.47461
$50$	−1.00000			−0.141421
$51$	−3.11213	−	0.234296i	−0.435785	−	0.0328080i
$52$	5.88671	+	3.39869i	0.816339	+	0.471314i
$53$	−1.75415	−	3.03828i	−0.240951	−	0.417340i	0.720034	−	0.693938i	$-0.244126\pi$
$53$	−1.75415	−	3.03828i	−0.240951	−	0.417340i	−0.960985	+	0.276599i	$0.910793\pi$
$54$	3.80541	+	3.53820i	0.517850	+	0.481488i
$55$	−1.48311	+	2.56881i	−0.199982	+	0.346379i
$56$	−4.16200			−0.556171
$57$	−2.74198	−	7.03431i	−0.363184	−	0.931717i
$58$	7.27764			0.955601
$59$	4.38575	−	7.59635i	0.570976	−	0.988960i	−0.425490	−	0.904963i	$-0.639898\pi$
$59$	4.38575	−	7.59635i	0.570976	−	0.988960i	0.996466	−	0.0839969i	$-0.0267686\pi$
$60$	0.750973	+	1.56078i	0.0969502	+	0.201496i
$61$	1.88869	+	3.27131i	0.241822	+	0.418849i	0.961233	−	0.275736i	$-0.0889215\pi$
$61$	1.88869	+	3.27131i	0.241822	+	0.418849i	−0.719411	+	0.694585i	$0.755588\pi$
$62$	−3.08983	−	1.78392i	−0.392409	−	0.226558i
$63$	−7.79160	+	9.75660i	−0.981649	+	1.22922i
$64$	1.00000			0.125000
$65$	6.79738			0.843112
$66$	5.12313	+	0.385694i	0.630614	+	0.0474757i
$67$	0.922310	−	0.532496i	0.112678	−	0.0650548i	−0.442602	−	0.896718i	$-0.645944\pi$
$67$	0.922310	−	0.532496i	0.112678	−	0.0650548i	0.555280	+	0.831664i	$0.312611\pi$
$68$			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	$-0.754799\pi$
$71$	2.05789	−	3.56436i	0.244226	−	0.423012i	0.961914	+	0.273353i	$0.0881327\pi$
$72$	1.87208	−	2.34421i	0.220627	−	0.276268i
$73$	6.64377	−	11.5074i	0.777595	−	1.34683i	−0.155729	−	0.987800i	$-0.549773\pi$
$73$	6.64377	−	11.5074i	0.777595	−	1.34683i	0.933324	−	0.359034i	$-0.116894\pi$
$74$	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
$78$	−5.10465	−	10.6092i	−0.577988	−	1.20126i
$79$	1.10542	+	0.638217i	0.124370	+	0.0718050i	0.560894	−	0.827887i	$-0.310457\pi$
$79$	1.10542	+	0.638217i	0.124370	+	0.0718050i	−0.436524	+	0.899692i	$0.643791\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−1.99064	−	8.77709i	−0.221182	−	0.975233i
$82$	−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	$-0.267835\pi$
$89$	−2.94818	−	5.10639i	−0.312506	−	0.541277i	−0.978904	+	0.204320i	$0.934502\pi$
$90$	0.449163	−	2.96618i	0.0473460	−	0.312663i
$91$	24.5005	−	14.1454i	2.56835	−	1.48284i
$92$	−0.309948	−	0.178948i	−0.0323143	−	0.0186567i
$93$	2.67935	+	5.56861i	0.277835	+	0.577438i
$94$			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	0.947100	−	0.320938i	$-0.103998\pi$
$97$	11.2544	+	6.49772i	1.14271	+	0.659744i	0.195610	+	0.980682i	$0.437331\pi$
$98$	−5.16113	+	8.93933i	−0.521353	+	0.903009i
$99$	−6.95342	−	5.55298i	−0.698845	−	0.558096i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−3.25224	+	1.87768i	−0.323610	+	0.186836i	−0.653001	−	0.757357i	$-0.726490\pi$
$101$	−3.25224	+	1.87768i	−0.323610	+	0.186836i	0.329391	+	0.944194i	$0.393157\pi$
$102$	1.75897	−	2.57804i	0.174164	−	0.255264i
$103$			2.57242i			0.253468i	0.991937	+	0.126734i	$0.0404494\pi$
$103$			2.57242i			0.253468i	−0.991937	+	0.126734i	$0.959551\pi$
$104$	−5.88671	+	3.39869i	−0.577239	+	0.333269i
$105$	7.18845	+	0.541182i	0.701521	+	0.0528140i
$106$	3.50830			0.340756
$107$	11.8795			1.14844			0.574218	−	0.818702i	$-0.305306\pi$
$107$	11.8795			1.14844			0.574218	+	0.818702i	$0.305306\pi$
$108$	−4.96688	+	1.52648i	−0.477938	+	0.146885i
$109$	−11.1493	−	6.43703i	−1.06790	−	0.616555i	−0.140297	−	0.990110i	$-0.544806\pi$
$109$	−11.1493	−	6.43703i	−1.06790	−	0.616555i	−0.927608	+	0.373554i	$0.878139\pi$
$110$	−1.48311	−	2.56881i	−0.141409	−	0.244927i
$111$	−4.61559	−	9.59279i	−0.438092	−	0.910507i
$112$	2.08100	−	3.60440i	0.196636	−	0.340584i
$113$	−3.14768			−0.296109			−0.148055	−	0.988979i	$-0.547301\pi$
$113$	−3.14768			−0.296109			−0.148055	+	0.988979i	$0.547301\pi$
$114$	7.46288	+	1.14253i	0.698963	+	0.107008i
$115$	−0.357897			−0.0333741
$116$	−3.63882	+	6.30262i	−0.337856	+	0.585184i
$117$	−3.05314	+	20.1623i	−0.282263	+	1.86400i
$118$	4.38575	+	7.59635i	0.403741	+	0.699300i
$119$	6.49467	+	3.74970i	0.595366	+	0.343734i
$120$	−1.72716	−	0.130029i	−0.157668	−	0.0118700i
$121$	2.20159			0.200145
$122$	−3.77739			−0.341989
$123$	−0.992230	+	13.1797i	−0.0894664	+	1.18837i
$124$	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	−0.743931	−	0.668256i	$-0.767041\pi$
$127$	−6.05360	+	3.49505i	−0.537170	+	0.310135i	0.206761	+	0.978391i	$0.433708\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.33581	+	17.7434i	−0.117612	+	1.56222i
$130$	−3.39869	+	5.88671i	−0.298085	+	0.516298i
$131$	11.7170	+	6.76481i	1.02372	+	0.591044i	0.915179	−	0.403048i	$-0.132049\pi$
$131$	11.7170	+	6.76481i	1.02372	+	0.591044i	0.108540	+	0.994092i	$0.465383\pi$
$132$	−2.89559	+	4.24391i	−0.252028	+	0.369385i
$133$	−1.39142	+	18.0883i	−0.120651	+	1.56845i
$134$			1.06499i			0.0920013i
$135$	−3.53820	+	3.80541i	−0.304520	+	0.327517i
$136$	−1.56047	−	0.900937i	−0.133809	−	0.0772547i
$137$	−10.6066	+	6.12370i	−0.906180	+	0.523183i	−0.879200	−	0.476453i	$-0.841922\pi$
$137$	−10.6066	+	6.12370i	−0.906180	+	0.523183i	−0.0269800	+	0.999636i	$0.508589\pi$
$138$	0.268771	+	0.558599i	0.0228793	+	0.0475511i
$139$	5.90898	+	10.2347i	0.501193	+	0.868092i	0.999999	+	0.00137828i	$0.000438719\pi$
$139$	5.90898	+	10.2347i	0.501193	+	0.868092i	−0.498806	+	0.866714i	$0.666228\pi$
$140$		−	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
$147$	16.1108	−	7.75173i	1.32880	−	0.639352i
$148$	−5.32272	+	3.07307i	−0.437524	+	0.252605i
$149$	−6.23444	−	3.59946i	−0.510745	−	0.294879i	0.222395	−	0.974957i	$-0.428613\pi$
$149$	−6.23444	−	3.59946i	−0.510745	−	0.294879i	−0.733140	+	0.680078i	$0.761946\pi$
$150$	−1.56078	+	0.750973i	−0.127437	+	0.0613167i
$151$		−	11.1275i		−	0.905543i	−0.891627	−	0.452772i	$-0.850435\pi$
$151$		−	11.1275i		−	0.905543i	0.891627	−	0.452772i	$-0.149565\pi$
$152$	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
$156$	11.7402	+	0.883859i	0.939967	+	0.0707653i
$157$	−10.7364	+	18.5960i	−0.856860	+	1.48412i	0.0180496	+	0.999837i	$0.494254\pi$
$157$	−10.7364	+	18.5960i	−0.856860	+	1.48412i	−0.874909	+	0.484287i	$0.839079\pi$
$158$	−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
$162$	8.59650	+	2.66460i	0.675405	+	0.209351i
$163$	−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
$165$	−0.385694	+	5.12313i	−0.0300263	+	0.398835i
$166$	−1.67469	−	0.966883i	−0.129981	−	0.0750447i
$167$	−2.84217	−	4.92279i	−0.219934	−	0.380937i	0.734854	−	0.678226i	$-0.237251\pi$
$167$	−2.84217	−	4.92279i	−0.219934	−	0.380937i	−0.954788	+	0.297289i	$0.903918\pi$
$168$	−6.49598	+	3.12555i	−0.501175	+	0.241141i
$169$	16.6022	−	28.7559i	1.27709	−	2.21199i
$170$	−1.80187			−0.138197
$171$	−9.56221	−	8.91987i	−0.731241	−	0.682120i
$172$	10.2732			0.783322
$173$	11.2154	−	19.4256i	0.852690	−	1.47690i	−0.0260821	−	0.999660i	$-0.508303\pi$
$173$	11.2154	−	19.4256i	0.852690	−	1.47690i	0.878772	−	0.477242i	$-0.158364\pi$
$174$	11.3588	−	5.46531i	0.861109	−	0.414324i
$175$	−2.08100	−	3.60440i	−0.157309	−	0.272467i
$176$	2.56881	+	1.48311i	0.193632	+	0.111793i
$177$	1.14055	−	15.1498i	0.0857292	−	1.13873i
$178$	5.89635			0.441950
$179$	−14.2289			−1.06352			−0.531758	−	0.846896i	$-0.678469\pi$
$179$	−14.2289			−1.06352			−0.531758	+	0.846896i	$0.678469\pi$
$180$	2.34421	+	1.87208i	0.174727	+	0.139537i
$181$	0.0315834	−	0.0182347i	0.00234757	−	0.00135537i	−0.498826	−	0.866702i	$-0.666235\pi$
$181$	0.0315834	−	0.0182347i	0.00234757	−	0.00135537i	0.501173	+	0.865347i	$0.332902\pi$
$182$			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
$186$	−6.16223	−	0.463923i	−0.451837	−	0.0340165i
$187$	−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	$0.700928\pi$
$192$	1.56078	−	0.750973i	0.112640	−	0.0541968i
$193$	−11.5178	−	6.64983i	−0.829072	−	0.478665i	0.0244626	−	0.999701i	$-0.492213\pi$
$193$	−11.5178	−	6.64983i	−0.829072	−	0.478665i	−0.853535	+	0.521036i	$0.825546\pi$
$194$	−11.2544	+	6.49772i	−0.808018	+	0.466509i
$195$	10.6092	−	5.10465i	0.759743	−	0.365552i
$196$	−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	0.937003	−	0.349323i	$-0.113588\pi$
$199$	2.34142	+	4.05546i	0.165979	+	0.287484i	−0.771023	+	0.636807i	$0.780255\pi$
$200$	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
$204$	1.35316	+	2.81233i	0.0947400	+	0.196903i
$205$	6.60849	−	3.81541i	0.461557	−	0.266480i
$206$	−2.22778	−	1.28621i	−0.155217	−	0.0896144i
$207$	0.160754	−	1.06159i	0.0111732	−	0.0737855i
$208$		−	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	0.250498	−	0.968117i	$-0.419406\pi$
$211$	−6.72063	−	3.88016i	−0.462667	−	0.267121i	−0.713165	+	0.700996i	$0.752739\pi$
$212$	−1.75415	+	3.03828i	−0.120476	+	0.208670i
$213$	0.535171	−	7.10861i	0.0366693	−	0.487074i
$214$	−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
$219$	1.72777	−	22.9498i	0.116752	−	1.55080i
$220$	2.96621			0.199982
$221$	12.2480			0.823891
$222$	10.6154	+	0.799178i	0.712458	+	0.0536373i
$223$	23.7955	+	13.7383i	1.59346	+	0.919987i	0.992707	+	0.120556i	$0.0384678\pi$
$223$	23.7955	+	13.7383i	1.59346	+	0.919987i	0.600758	+	0.799431i	$0.294866\pi$
$224$	2.08100	+	3.60440i	0.139043	+	0.240829i
$225$	2.96618	+	0.449163i	0.197746	+	0.0299442i
$226$	1.57384	−	2.72597i	0.104690	−	0.181329i
$227$	−25.8559			−1.71612			−0.858059	−	0.513551i	$-0.828330\pi$
$227$	−25.8559			−1.71612			−0.858059	+	0.513551i	$0.828330\pi$
$228$	−4.72090	+	5.89178i	−0.312649	+	0.390193i
$229$	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
$231$	9.27104	+	19.2684i	0.609990	+	1.26777i
$232$	−3.63882	−	6.30262i	−0.238900	−	0.413787i
$233$	22.6080	+	13.0528i	1.48110	+	0.855114i	0.999770	−	0.0214243i	$-0.00682008\pi$
$233$	22.6080	+	13.0528i	1.48110	+	0.855114i	0.481331	+	0.876539i	$0.340153\pi$
$234$	−15.9345	−	12.7252i	−1.04167	−	0.831875i
$235$	−5.15882			−0.336525
$236$	−8.77151			−0.570976
$237$	2.20461	+	0.165974i	0.143205	+	0.0107811i
$238$	−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	−0.720891	−	0.693049i	$-0.756267\pi$
$241$	−7.46928	+	4.31239i	−0.481139	+	0.277786i	0.239752	+	0.970834i	$0.422934\pi$
$242$	−1.10080	+	1.90663i	−0.0707619	+	0.122563i
$243$	−9.69831	−	12.2042i	−0.622147	−	0.782901i
$244$	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
$249$	1.45221	+	3.01819i	0.0920298	+	0.191270i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	11.4151	−	6.59052i	0.720516	−	0.415990i	−0.0944268	−	0.995532i	$-0.530102\pi$
$251$	11.4151	−	6.59052i	0.720516	−	0.415990i	0.814942	+	0.579542i	$0.196769\pi$
$252$	12.3453	+	1.86942i	0.777679	+	0.117762i
$253$	−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	−0.897342	−	0.441336i	$-0.854505\pi$
$257$	−13.3200	−	23.0709i	−0.830879	−	1.43913i	0.0664625	−	0.997789i	$-0.478829\pi$
$258$	−14.6984	−	10.0286i	−0.915080	−	0.624351i
$259$			25.5803i			1.58948i
$260$	−3.39869	−	5.88671i	−0.210778	−	0.365078i
$261$	−21.5868	−	3.26885i	−1.33619	−	0.202337i
$262$	−11.7170	+	6.76481i	−0.723878	+	0.417931i
$263$	20.1068	+	11.6087i	1.23984	+	0.715822i	0.969062	−	0.246819i	$-0.0793853\pi$
$263$	20.1068	+	11.6087i	1.23984	+	0.715822i	0.270779	+	0.962641i	$0.412719\pi$
$264$	−2.22754	−	4.62961i	−0.137096	−	0.284933i
$265$			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	$-0.784156\pi$
$269$	2.52385	−	4.37144i	0.153882	−	0.266532i	0.932651	+	0.360779i	$0.117489\pi$
$270$	−1.52648	−	4.96688i	−0.0928985	−	0.302274i
$271$	4.52551	−	7.83842i	0.274905	−	0.476150i	−0.695206	−	0.718811i	$-0.744687\pi$
$271$	4.52551	−	7.83842i	0.274905	−	0.476150i	0.970111	+	0.242661i	$0.0780202\pi$
$272$	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
$276$	−0.618146	−	0.0465371i	−0.0372080	−	0.00280120i
$277$	−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
$279$	8.36375	+	6.67927i	0.500724	+	0.399877i
$280$	3.60440	+	2.08100i	0.215404	+	0.124364i
$281$	−6.84949	−	11.8637i	−0.408606	−	0.707727i	0.586127	−	0.810219i	$-0.300652\pi$
$281$	−6.84949	−	11.8637i	−0.408606	−	0.707727i	−0.994734	+	0.102492i	$0.967318\pi$
$282$	3.87414	+	8.05180i	0.230702	+	0.479478i
$283$	0.398146	−	0.689610i	0.0236673	−	0.0409930i	−0.853949	−	0.520356i	$-0.825799\pi$
$283$	0.398146	−	0.689610i	0.0236673	−	0.0409930i	0.877616	+	0.479363i	$0.159132\pi$
$284$	−4.11577			−0.244226
$285$	−1.14253	+	7.46288i	−0.0676777	+	0.442063i
$286$	−20.1625			−1.19223
$287$	15.8797	−	27.5045i	0.937352	−	1.62354i
$288$	−2.96618	−	0.449163i	−0.174784	−	0.0264672i
$289$	−6.87663	−	11.9107i	−0.404507	−	0.700627i
$290$	−6.30262	−	3.63882i	−0.370103	−	0.213679i
$291$	22.4453	+	1.68979i	1.31576	+	0.0990571i
$292$	−13.2875			−0.777595
$293$	−23.7823			−1.38937			−0.694687	−	0.719312i	$-0.744457\pi$
$293$	−23.7823			−1.38937			−0.694687	+	0.719312i	$0.744457\pi$
$294$	−1.34220	+	17.8282i	−0.0782784	+	1.03976i
$295$	−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
$300$	0.130029	−	1.72716i	0.00750724	−	0.0997178i
$301$	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
$306$	0.809336	−	5.34469i	0.0462666	−	0.305536i
$307$	−7.52401	−	4.34399i	−0.429418	−	0.247924i	0.269681	−	0.962950i	$-0.413082\pi$
$307$	−7.52401	−	4.34399i	−0.429418	−	0.247924i	−0.699099	+	0.715025i	$0.746415\pi$
$308$	10.6914	−	6.17269i	0.609199	−	0.351721i
$309$	1.93182	+	4.01498i	0.109897	+	0.228404i
$310$	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	0.596269	−	0.802785i	$-0.296649\pi$
$313$	−7.02538	−	12.1683i	−0.397098	−	0.687793i	−0.993366	+	0.114991i	$0.963316\pi$
$314$	−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	$-0.287214\pi$
$317$	−6.58272	−	11.4016i	−0.369722	−	0.640378i	−0.989522	+	0.144382i	$0.953881\pi$
$318$	5.47569	−	2.63464i	0.307062	−	0.147743i
$319$	−18.6949	+	10.7935i	−1.04671	+	0.604321i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	18.5413	−	8.92120i	1.03488	−	0.497933i
$322$		−	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
$327$	−22.2356	−	1.67400i	−1.22963	−	0.0925726i
$328$	−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	$-0.961349\pi$
$331$		−	4.40745i		−	0.242256i	0.992637	−	0.121128i	$-0.0386511\pi$
$332$	1.67469	−	0.966883i	0.0919106	−	0.0530646i
$333$	−14.4078	−	11.5061i	−0.789545	−	0.630529i
$334$	5.68435			0.311034
$335$	−1.06499			−0.0581868
$336$	0.541182	−	7.18845i	0.0295239	−	0.392162i
$337$	−4.81309	−	2.77884i	−0.262186	−	0.151373i	0.363146	−	0.931732i	$-0.381703\pi$
$337$	−4.81309	−	2.77884i	−0.262186	−	0.151373i	−0.625331	+	0.780359i	$0.715036\pi$
$338$	16.6022	+	28.7559i	0.903041	+	1.56411i
$339$	−4.91284	+	2.36382i	−0.266829	+	0.128385i
$340$	0.900937	−	1.56047i	0.0488602	−	0.0846283i
$341$	10.5829			0.573099
$342$	12.5059	−	3.82118i	0.676244	−	0.206626i
$343$	−13.8272			−0.746600
$344$	−5.13659	+	8.89683i	−0.276946	+	0.479685i
$345$	−0.558599	+	0.268771i	−0.0300740	+	0.0144701i
$346$	11.2154	+	19.4256i	0.602943	+	1.04433i
$347$	2.06156	+	1.19024i	0.110671	+	0.0638957i	0.554314	−	0.832308i	$-0.312981\pi$
$347$	2.06156	+	1.19024i	0.110671	+	0.0638957i	−0.443643	+	0.896204i	$0.646314\pi$
$348$	−0.946306	+	12.5697i	−0.0507273	+	0.673805i
$349$	−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
$351$	10.3761	+	33.7618i	0.553833	+	1.80207i
$352$	−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
$357$	12.9527	+	0.975141i	0.685529	+	0.0516100i
$358$	7.11444	−	12.3226i	0.376010	−	0.651268i
$359$	18.8394	+	10.8769i	0.994305	+	0.574063i	0.906558	−	0.422080i	$-0.138700\pi$
$359$	18.8394	+	10.8769i	0.994305	+	0.574063i	0.0877470	+	0.996143i	$0.472033\pi$
$360$	−2.79337	+	1.09411i	−0.147224	+	0.0576644i
$361$	−18.7765	−	2.90591i	−0.988235	−	0.152942i
$362$			0.0364693i			0.00191679i
$363$	3.43620	−	1.65334i	0.180354	−	0.0867776i
$364$	−24.5005	−	14.1454i	−1.28417	−	0.741418i
$365$	−11.5074	+	6.64377i	−0.602322	+	0.347751i
$366$	−5.89568	+	2.83672i	−0.308172	+	0.148277i
$367$	6.28744	+	10.8902i	0.328202	+	0.568462i	0.982155	−	0.188073i	$-0.0602241\pi$
$367$	6.28744	+	10.8902i	0.328202	+	0.568462i	−0.653953	+	0.756535i	$0.726891\pi$
$368$			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	$-0.838159\pi$
$373$		−	18.8039i		−	0.973629i	0.873505	−	0.486815i	$-0.161841\pi$
$374$	−2.67237	−	4.62868i	−0.138185	−	0.239343i
$375$	−0.750973	−	1.56078i	−0.0387801	−	0.0805984i
$376$	4.46767	−	2.57941i	0.230403	−	0.133023i
$377$	42.8413	+	24.7345i	2.20644	+	1.27389i
$378$	−15.8381	−	14.7260i	−0.814624	−	0.757424i
$379$			25.0289i			1.28565i	0.766014	+	0.642824i	$0.222237\pi$
$379$			25.0289i			1.28565i	−0.766014	+	0.642824i	$0.777763\pi$
$380$	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	$-0.790699\pi$
$383$	2.61339	−	4.52653i	0.133538	−	0.231295i	0.925038	+	0.379874i	$0.124033\pi$
$384$	−0.130029	+	1.72716i	−0.00663553	+	0.0881389i
$385$	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	$-0.456270\pi$
$389$	20.9714	−	12.1078i	1.06329	−	0.613892i	0.926341	+	0.376686i	$0.122936\pi$
$390$	−0.883859	+	11.7402i	−0.0447559	+	0.594488i
$391$	−0.644885			−0.0326132
$392$	10.3223			0.521353
$393$	23.3679	+	1.75925i	1.17875	+	0.0887422i
$394$	19.7095	+	11.3793i	0.992953	+	0.573282i
$395$	−0.638217	−	1.10542i	−0.0321122	−	0.0556199i
$396$	−1.33231	+	8.79833i	−0.0669513	+	0.442133i
$397$	12.7295	−	22.0482i	0.638877	−	1.10657i	−0.346803	−	0.937938i	$-0.612733\pi$
$397$	12.7295	−	22.0482i	0.638877	−	1.10657i	0.985680	−	0.168629i	$-0.0539341\pi$
$398$	−4.68284			−0.234730
$399$	11.4121	+	29.2768i	0.571321	+	1.46567i
$400$	−1.00000			−0.0500000
$401$	−17.9661	+	31.1182i	−0.897184	+	1.55397i	−0.0661050	+	0.997813i	$0.521057\pi$
$401$	−17.9661	+	31.1182i	−0.897184	+	1.55397i	−0.831079	+	0.556155i	$0.812276\pi$
$402$	0.799780	+	1.66222i	0.0398894	+	0.0829040i
$403$	−12.1260	−	21.0028i	−0.604037	−	1.04622i
$404$	3.25224	+	1.87768i	0.161805	+	0.0934182i
$405$	−2.66460	+	8.59650i	−0.132405	+	0.427164i
$406$	−30.2896			−1.50325
$407$	−18.2308			−0.903665
$408$	−3.11213	−	0.234296i	−0.154073	−	0.0115994i
$409$	−1.54476	+	0.891867i	−0.0763834	+	0.0441000i	−0.537705	−	0.843133i	$-0.680709\pi$
$409$	−1.54476	+	0.891867i	−0.0763834	+	0.0441000i	0.461322	+	0.887233i	$0.347375\pi$
$410$			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
$414$	0.838986	+	0.670012i	0.0412339	+	0.0329293i
$415$	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	$-0.346267\pi$
$420$	−3.12555	−	6.49598i	−0.152511	−	0.316971i
$421$	4.43149	+	2.55852i	0.215977	+	0.124695i	0.604086	−	0.796919i	$-0.293538\pi$
$421$	4.43149	+	2.55852i	0.215977	+	0.124695i	−0.388109	+	0.921614i	$0.626872\pi$
$422$	6.72063	−	3.88016i	0.327155	−	0.188883i
$423$	2.31716	−	15.3020i	0.112664	−	0.744010i
$424$	−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	$-0.115604\pi$
$431$	3.31613	+	5.74370i	0.159732	+	0.276664i	−0.775040	+	0.631912i	$0.782270\pi$
$432$	3.80541	+	3.53820i	0.183088	+	0.170232i
$433$	−5.22804	+	3.01841i	−0.251244	+	0.145056i	−0.620334	−	0.784338i	$-0.713003\pi$
$433$	−5.22804	+	3.01841i	−0.251244	+	0.145056i	0.369090	+	0.929394i	$0.379669\pi$
$434$	12.8599	+	7.42466i	0.617295	+	0.356395i
$435$	5.46531	+	11.3588i	0.262042	+	0.544613i
$436$			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	0.732561	−	0.680702i	$-0.238325\pi$
$439$	10.6718	+	6.16135i	0.509336	+	0.294065i	−0.223225	+	0.974767i	$0.571658\pi$
$440$	−1.48311	+	2.56881i	−0.0707043	+	0.122463i
$441$	19.3241	−	24.1975i	0.920194	−	1.15226i
$442$	−6.12401	+	10.6071i	−0.291290	+	0.504528i
$443$	−6.05385	+	3.49519i	−0.287627	+	0.166062i	−0.636871	−	0.770970i	$-0.719772\pi$
$443$	−6.05385	+	3.49519i	−0.287627	+	0.166062i	0.349244	+	0.937032i	$0.386438\pi$
$444$	−5.99980	+	8.79361i	−0.284738	+	0.417326i
$445$			5.89635i			0.279514i
$446$	−23.7955	+	13.7383i	−1.12675	+	0.650529i
$447$	−12.4337	−	0.936069i	−0.588093	−	0.0442745i
$448$	−4.16200			−0.196636
$449$	−31.4802			−1.48564			−0.742820	−	0.669491i	$-0.766512\pi$
$449$	−31.4802			−1.48564			−0.742820	+	0.669491i	$0.766512\pi$
$450$	−1.87208	+	2.34421i	−0.0882507	+	0.110507i
$451$	19.6022	+	11.3173i	0.923030	+	0.532912i
$452$	1.57384	+	2.72597i	0.0740273	+	0.128219i
$453$	−8.35645	−	17.3676i	−0.392620	−	0.816001i
$454$	12.9280	−	22.3919i	0.606739	−	1.05090i
$455$	−28.2907			−1.32629
$456$	−2.74198	−	7.03431i	−0.128405	−	0.329412i
$457$	−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
$459$	−6.37539	+	6.85686i	−0.297578	+	0.320051i
$460$	0.178948	+	0.309948i	0.00834352	+	0.0144514i
$461$	12.9506	+	7.47702i	0.603169	+	0.348240i	0.770287	−	0.637697i	$-0.220113\pi$
$461$	12.9506	+	7.47702i	0.603169	+	0.348240i	−0.167118	+	0.985937i	$0.553446\pi$
$462$	−21.3225	−	1.60526i	−0.992011	−	0.0746834i
$463$	−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
$465$	0.463923	−	6.16223i	0.0215139	−	0.285767i
$466$	−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
$471$	−2.79210	+	37.0871i	−0.128653	+	1.70888i
$472$	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
$477$	−10.4063	−	1.57580i	−0.476471	−	0.0721510i
$478$	20.7353	+	11.9715i	0.948410	+	0.547565i
$479$	24.3132	−	14.0372i	1.11090	−	0.641377i	0.171836	−	0.985126i	$-0.445030\pi$
$479$	24.3132	−	14.0372i	1.11090	−	0.641377i	0.939062	+	0.343748i	$0.111697\pi$
$480$	0.750973	+	1.56078i	0.0342771	+	0.0712396i
$481$	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	$-0.988076\pi$
$487$		−	1.65303i		−	0.0749058i	0.999298	−	0.0374529i	$-0.0119244\pi$
$488$	1.88869	+	3.27131i	0.0854971	+	0.148085i
$489$	−30.3380	+	14.5972i	−1.37193	+	0.660108i
$490$	8.93933	−	5.16113i	0.403838	−	0.233156i
$491$	1.30505	+	0.753470i	0.0588960	+	0.0340036i	0.529159	−	0.848523i	$-0.322508\pi$
$491$	1.30505	+	0.753470i	0.0588960	+	0.0340036i	−0.470263	+	0.882526i	$0.655841\pi$
$492$	11.9100	−	5.73054i	0.536946	−	0.258353i
$493$			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
$498$	−3.33993	−	0.251446i	−0.149666	−	0.0112676i
$499$	10.7116	−	18.5530i	0.479517	−	0.830549i	−0.520207	−	0.854040i	$-0.674145\pi$
$499$	10.7116	−	18.5530i	0.479517	−	0.830549i	0.999724	+	0.0234919i	$0.00747840\pi$
$500$	−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	$-0.756626\pi$
$503$	−10.8329	+	6.25439i	−0.483016	+	0.278869i	0.238657	+	0.971104i	$0.423293\pi$
$504$	−7.79160	+	9.75660i	−0.347065	+	0.434594i
$505$	3.75536			0.167111
$506$	1.06160			0.0471938
$507$	4.31755	−	57.3495i	0.191749	−	2.54698i
$508$	6.05360	+	3.49505i	0.268585	+	0.155068i
$509$	12.4948	+	21.6415i	0.553820	+	0.959245i	0.997994	+	0.0633042i	$0.0201638\pi$
$509$	12.4948	+	21.6415i	0.553820	+	0.959245i	−0.444174	+	0.895941i	$0.646503\pi$
$510$	−2.81233	+	1.35316i	−0.124532	+	0.0599189i
$511$	−27.6514	+	47.8936i	−1.22323	+	2.11869i
$512$	1.00000			0.0441942
$513$	−21.6231	−	6.74101i	−0.954683	−	0.297623i
$514$	26.6400			1.17504
$515$	1.28621	−	2.22778i	0.0566771	−	0.0981677i
$516$	16.0342	−	7.71487i	0.705865	−	0.339628i
$517$	−7.65108	−	13.2521i	−0.336494	−	0.582825i
$518$	−22.1531	−	12.7901i	−0.973353	−	0.561966i
$519$	2.91666	−	38.7416i	0.128027	−	1.70057i
$520$	6.79738			0.298085
$521$	28.9838			1.26980			0.634902	−	0.772593i	$-0.281041\pi$
$521$	28.9838			1.26980			0.634902	+	0.772593i	$0.281041\pi$
$522$	13.6243	−	17.0603i	0.596320	−	0.746710i
$523$	36.7094	−	21.1942i	1.60519	−	0.926756i	0.614763	−	0.788712i	$-0.289252\pi$
$523$	36.7094	−	21.1942i	1.60519	−	0.926756i	0.990426	−	0.138044i	$-0.0440816\pi$
$524$		−	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
$528$	5.12313	+	0.385694i	0.222956	+	0.0167852i
$529$	−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
$534$	9.20292	−	4.42800i	0.398249	−	0.191618i
$535$	−10.2880	−	5.93976i	−0.444787	−	0.256798i
$536$	0.922310	−	0.532496i	0.0398377	−	0.0230003i
$537$	−22.2082	+	10.6855i	−0.958354	+	0.461114i
$538$	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	0.983388	−	0.181513i	$-0.0580996\pi$
$541$	7.78025	+	13.4758i	0.334499	+	0.579369i	−0.648890	+	0.760883i	$0.724766\pi$
$542$	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
$546$	21.2456	+	44.1556i	0.909226	+	1.88969i
$547$	34.8985	−	20.1487i	1.49215	−	0.861495i	0.492194	−	0.870486i	$-0.336195\pi$
$547$	34.8985	−	20.1487i	1.49215	−	0.861495i	0.999960	+	0.00899064i	$0.00286185\pi$
$548$	10.6066	+	6.12370i	0.453090	+	0.261592i
$549$	11.2044	+	1.69666i	0.478193	+	0.0724119i
$550$			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
$555$	−0.799178	+	10.6154i	−0.0339232	+	0.450598i
$556$	5.90898	−	10.2347i	0.250597	−	0.434046i
$557$	−9.13519	+	5.27420i	−0.387070	+	0.223475i	−0.680890	−	0.732386i	$-0.738407\pi$
$557$	−9.13519	+	5.27420i	−0.387070	+	0.223475i	0.293820	+	0.955861i	$0.405073\pi$
$558$	−9.96629	+	3.90358i	−0.421907	+	0.165252i
$559$		−	69.8307i		−	2.95352i
$560$	−3.60440	+	2.08100i	−0.152314	+	0.0879383i
$561$	−0.694972	+	9.23123i	−0.0293418	+	0.389743i
$562$	13.6990			0.577857
$563$	−40.4508			−1.70480			−0.852399	−	0.522892i	$-0.824853\pi$
$563$	−40.4508			−1.70480			−0.852399	+	0.522892i	$0.824853\pi$
$564$	−8.91013	−	0.670798i	−0.375184	−	0.0282457i
$565$	2.72597	+	1.57384i	0.114683	+	0.0662120i
$566$	0.398146	+	0.689610i	0.0167353	+	0.0289864i
$567$	8.28504	+	36.5303i	0.347939	+	1.53413i
$568$	2.05789	−	3.56436i	0.0863470	−	0.149557i
$569$	−34.8214			−1.45979			−0.729895	−	0.683559i	$-0.760431\pi$
$569$	−34.8214			−1.45979			−0.729895	+	0.683559i	$0.760431\pi$
$570$	−5.89178	−	4.72090i	−0.246780	−	0.197737i
$571$	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
$573$	16.7574	+	34.8276i	0.700049	+	1.45494i
$574$	15.8797	+	27.5045i	0.662808	+	1.14802i
$575$	0.309948	+	0.178948i	0.0129257	+	0.00746267i
$576$	1.87208	−	2.34421i	0.0780033	−	0.0976754i
$577$	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
$579$	−22.9707	−	1.72934i	−0.954629	−	0.0718691i
$580$	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
$585$	12.7252	−	15.9345i	0.526124	−	0.658810i
$586$	11.8911	−	20.5960i	0.491218	−	0.850815i
$587$	8.13311	+	4.69565i	0.335689	+	0.193810i	0.658364	−	0.752700i	$-0.271249\pi$
$587$	8.13311	+	4.69565i	0.335689	+	0.193810i	−0.322675	+	0.946510i	$0.604582\pi$
$588$	−14.7686	−	10.0765i	−0.609046	−	0.415547i
$589$	15.5060	+	1.19278i	0.638914	+	0.0491476i
$590$		−	8.77151i		−	0.361117i
$591$	−17.0911	−	35.5212i	−0.703034	−	1.46115i
$592$	5.32272	+	3.07307i	0.218762	+	0.126302i
$593$	4.48680	−	2.59046i	0.184251	−	0.106377i	−0.405037	−	0.914300i	$-0.632742\pi$
$593$	4.48680	−	2.59046i	0.184251	−	0.106377i	0.589288	+	0.807923i	$0.299408\pi$
$594$	10.4951	−	11.2876i	0.430617	−	0.463138i
$595$	−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	$-0.0557656\pi$
$599$	8.35558	+	14.4723i	0.341400	+	0.591322i	−0.643293	+	0.765620i	$0.722432\pi$
$600$	1.43075	+	0.976190i	0.0584102	+	0.0398528i
$601$			34.8345i			1.42093i	0.703734	+	0.710464i	$0.251515\pi$
$601$			34.8345i			1.42093i	−0.703734	+	0.710464i	$0.748485\pi$
$602$	21.3785	+	37.0286i	0.871322	+	1.50917i
$603$	0.478356	−	3.15896i	0.0194802	−	0.128643i
$604$	−9.63670	+	5.56375i	−0.392112	+	0.226386i
$605$	−1.90663	−	1.10080i	−0.0775157	−	0.0447537i
$606$	−2.82018	−	5.86130i	−0.114562	−	0.238099i
$607$			0.510275i			0.0207114i	0.999946	+	0.0103557i	$0.00329639\pi$
$607$			0.510275i			0.0207114i	−0.999946	+	0.0103557i	$0.996704\pi$
$608$	−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
$612$	4.22397	+	3.37325i	0.170744	+	0.136356i
$613$	−1.27998	+	2.21700i	−0.0516980	+	0.0895436i	−0.890716	−	0.454560i	$-0.849797\pi$
$613$	−1.27998	+	2.21700i	−0.0516980	+	0.0895436i	0.839018	+	0.544103i	$0.183130\pi$
$614$	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	$-0.700067\pi$
$617$	−4.50617	+	2.60164i	−0.181412	+	0.104738i	0.406544	+	0.913631i	$0.366734\pi$
$618$	−4.44299	−	0.334490i	−0.178723	−	0.0134551i
$619$	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
$621$	−0.546322	−	1.77763i	−0.0219231	−	0.0713338i
$622$	16.8527	+	9.72990i	0.675731	+	0.390133i
$623$	12.2703	+	21.2528i	0.491600	+	0.851476i
$624$	−5.10465	−	10.6092i	−0.204350	−	0.424709i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	14.0508			0.561581
$627$	−20.8653	+	8.13329i	−0.833278	+	0.324812i
$628$	21.4728			0.856860
$629$	−5.53729	+	9.59086i	−0.220786	+	0.382413i
$630$	−1.86942	+	12.3453i	−0.0744794	+	0.491847i
$631$	−1.98291	−	3.43450i	−0.0789383	−	0.136725i	0.823854	−	0.566802i	$-0.191820\pi$
$631$	−1.98291	−	3.43450i	−0.0789383	−	0.136725i	−0.902792	+	0.430077i	$0.858486\pi$
$632$	1.10542	+	0.638217i	0.0439714	+	0.0253869i
$633$	−13.4033	−	1.00907i	−0.532735	−	0.0401069i
$634$	13.1654			0.522866
$635$	6.99009			0.277393
$636$	−0.456182	+	6.05941i	−0.0180888	+	0.240271i
$637$	−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	0.466942	+	0.884288i	$0.345356\pi$
$641$	−13.4779	+	23.3444i	−0.532345	+	0.922048i	−0.999287	+	0.0377601i	$0.987978\pi$
$642$	−1.54468	+	20.5179i	−0.0609638	+	0.809776i
$643$	19.5490	−	33.8598i	0.770936	−	1.33530i	−0.166114	−	0.986107i	$-0.553122\pi$
$643$	19.5490	−	33.8598i	0.770936	−	1.33530i	0.937050	−	0.349195i	$-0.113545\pi$
$644$	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	$0.835781\pi$
$648$	−1.99064	−	8.77709i	−0.0781996	−	0.344797i
$649$	−22.5324	−	13.0091i	−0.884473	−	0.510651i
$650$	5.88671	−	3.39869i	0.230896	−	0.133308i
$651$	−11.1514	−	23.1766i	−0.437059	−	0.908361i
$652$	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	$-0.226880\pi$
$659$	−4.82716	−	8.36088i	−0.188039	−	0.325694i	−0.944596	+	0.328234i	$0.893547\pi$
$660$	4.62961	−	2.22754i	0.180207	−	0.0867070i
$661$	12.4152	−	7.16792i	0.482895	−	0.278800i	−0.238727	−	0.971087i	$-0.576730\pi$
$661$	12.4152	−	7.16792i	0.482895	−	0.278800i	0.721622	+	0.692287i	$0.243397\pi$
$662$	3.81697	+	2.20373i	0.148351	+	0.0856503i
$663$	19.1165	−	9.19794i	0.742423	−	0.357218i
$664$			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
$669$	47.4567	+	3.57277i	1.83478	+	0.138131i
$670$	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	$-0.984196\pi$
$673$		−	2.57499i		−	0.0992586i	0.998768	−	0.0496293i	$-0.0158040\pi$
$674$	4.81309	−	2.77884i	0.185393	−	0.107037i
$675$	4.96688	−	1.52648i	0.191175	−	0.0587542i
$676$	−33.2044			−1.27709
$677$	25.1278			0.965739			0.482870	−	0.875692i	$-0.339594\pi$
$677$	25.1278			0.965739			0.482870	+	0.875692i	$0.339594\pi$
$678$	0.409291	−	5.43656i	0.0157187	−	0.208790i
$679$	−46.8408	−	27.0435i	−1.79758	−	1.03784i
$680$	0.900937	+	1.56047i	0.0345493	+	0.0598412i
$681$	−40.3554	+	19.4171i	−1.54642	+	0.744065i
$682$	−5.29147	+	9.16510i	−0.202621	+	0.350950i
$683$	−17.1516			−0.656289			−0.328145	−	0.944627i	$-0.606423\pi$
$683$	−17.1516			−0.656289			−0.328145	+	0.944627i	$0.606423\pi$
$684$	−2.94373	+	12.7411i	−0.112556	+	0.487166i
$685$	12.2474			0.467949
$686$	6.91361	−	11.9747i	0.263963	−	0.457197i
$687$	8.74911	−	4.20965i	0.333800	−	0.160608i
$688$	−5.13659	−	8.89683i	−0.195831	−	0.339188i
$689$	20.6523	+	11.9236i	0.786792	+	0.454254i
$690$	0.0465371	−	0.618146i	0.00177164	−	0.0235324i
$691$	−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
$693$	28.9401	+	23.1115i	1.09935	+	0.877934i
$694$	−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
$699$	45.0885	+	3.39448i	1.70540	+	0.128391i
$700$	−2.08100	+	3.60440i	−0.0786544	+	0.136233i
$701$	−26.3609	−	15.2194i	−0.995636	−	0.574831i	−0.0886817	−	0.996060i	$-0.528265\pi$
$701$	−26.3609	−	15.2194i	−0.995636	−	0.574831i	−0.906954	+	0.421229i	$0.861599\pi$
$702$	−34.4266	−	7.89495i	−1.29935	−	0.297976i
$703$	−26.7115	−	2.05475i	−1.00744	−	0.0774963i
$704$		−	2.96621i		−	0.111793i
$705$	−8.05180	+	3.87414i	−0.303248	+	0.145908i
$706$	29.9848	+	17.3117i	1.12849	+	0.651536i
$707$	13.5358	−	7.81491i	0.509067	−	0.293910i
$708$	−13.6904	+	6.58716i	−0.514517	+	0.247561i
$709$	4.75537	+	8.23654i	0.178592	+	0.309330i	0.941398	−	0.337297i	$-0.109513\pi$
$709$	4.75537	+	8.23654i	0.178592	+	0.309330i	−0.762807	+	0.646626i	$0.776179\pi$
$710$		−	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
$717$	−17.9806	−	37.3699i	−0.671497	−	1.39560i
$718$	−18.8394	+	10.8769i	−0.703080	+	0.405924i
$719$	−34.4372	−	19.8823i	−1.28429	−	0.741485i	−0.306660	−	0.951819i	$-0.599212\pi$
$719$	−34.4372	−	19.8823i	−1.28429	−	0.741485i	−0.977630	+	0.210334i	$0.932545\pi$
$720$	0.449163	−	2.96618i	0.0167393	−	0.110543i
$721$		−	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
$726$	−0.286271	+	3.80251i	−0.0106245	+	0.141124i
$727$	10.4980	−	18.1831i	0.389350	−	0.674374i	−0.603012	−	0.797732i	$-0.706033\pi$
$727$	10.4980	−	18.1831i	0.389350	−	0.674374i	0.992362	+	0.123358i	$0.0393664\pi$
$728$	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
$732$	0.491171	−	6.52416i	0.0181542	−	0.241140i
$733$	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
$735$	−17.8282	−	1.34220i	−0.657604	−	0.0495076i
$736$	−0.309948	−	0.178948i	−0.0114248	−	0.00659613i
$737$	−1.57950	−	2.73577i	−0.0581815	−	0.100773i
$738$	−22.6344	−	3.42749i	−0.833185	−	0.126168i
$739$	−14.5149	+	25.1405i	−0.533939	+	0.924809i	0.465275	+	0.885166i	$0.345955\pi$
$739$	−14.5149	+	25.1405i	−0.533939	+	0.924809i	−0.999214	+	0.0396431i	$0.987378\pi$
$740$	6.14614			0.225937
$741$	40.0487	+	32.0898i	1.47123	+	1.17885i
$742$	−14.6016			−0.536040
$743$	−4.08693	+	7.07877i	−0.149935	+	0.259695i	−0.931203	−	0.364500i	$-0.881240\pi$
$743$	−4.08693	+	7.07877i	−0.149935	+	0.259695i	0.781268	+	0.624195i	$0.214573\pi$
$744$	2.67935	+	5.56861i	0.0982296	+	0.204155i
$745$	3.59946	+	6.23444i	0.131874	+	0.228412i
$746$	16.2847	+	9.40195i	0.596224	+	0.344230i
$747$	4.53315	+	3.62016i	0.165859	+	0.132455i
$748$	5.34474			0.195423
$749$	−49.4426			−1.80659
$750$	1.72716	+	0.130029i	0.0630671	+	0.00474800i
$751$	0.510899	−	0.294967i	0.0186430	−	0.0107635i	−0.490650	−	0.871357i	$-0.663240\pi$
$751$	0.510899	−	0.294967i	0.0186430	−	0.0107635i	0.509293	+	0.860593i	$0.329907\pi$
$752$			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
$756$	20.6721	−	6.35320i	0.751839	−	0.231064i
$757$	−1.45489	+	2.51995i	−0.0528791	+	0.0915892i	−0.891253	−	0.453506i	$-0.850173\pi$
$757$	−1.45489	+	2.51995i	−0.0528791	+	0.0915892i	0.838374	+	0.545095i	$0.183506\pi$
$758$	−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	$0.812956\pi$
$762$	−5.24937	−	10.9100i	−0.190165	−	0.395228i
$763$	46.4032	+	26.7909i	1.67991	+	0.969896i
$764$	19.3247	−	11.1571i	0.699142	−	0.403650i
$765$	5.34469	+	0.809336i	0.193238	+	0.0292616i
$766$	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	0.997828	−	0.0658703i	$-0.0209824\pi$
$769$	12.2534	+	21.2235i	0.441869	+	0.765339i	−0.555959	+	0.831209i	$0.687649\pi$
$770$	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	−0.981438	−	0.191780i	$-0.938574\pi$
$773$	−18.2611	−	31.6291i	−0.656805	−	1.13762i	0.324632	−	0.945840i	$-0.394759\pi$
$774$	−30.4721	−	4.61433i	−1.09530	−	0.165859i
$775$	−3.08983	+	1.78392i	−0.110990	+	0.0640802i
$776$	11.2544	+	6.49772i	0.404009	+	0.233255i
$777$	19.2101	+	39.9252i	0.689158	+	1.43231i
$778$			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
$783$	−36.1472	+	11.1092i	−1.29179	+	0.397009i
$784$	−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	$0.0552615\pi$
$787$			9.69183i			0.345477i	−0.984968	+	0.172738i	$0.944739\pi$
$788$	−19.7095	+	11.3793i	−0.702124	+	0.405371i
$789$	40.1002	+	3.01894i	1.42760	+	0.107477i
$790$	1.27643			0.0454135
$791$	13.1007			0.465806
$792$	−6.95342	−	5.55298i	−0.247079	−	0.197317i
$793$	−22.2364	−	12.8382i	−0.789637	−	0.455897i
$794$	12.7295	+	22.0482i	0.451754	+	0.782461i
$795$	2.63464	+	5.47569i	0.0934411	+	0.194203i
$796$	2.34142	−	4.05546i	0.0829895	−	0.143742i
$797$	−22.8396			−0.809019			−0.404509	−	0.914534i	$-0.632558\pi$
$797$	−22.8396			−0.809019			−0.404509	+	0.914534i	$0.632558\pi$
$798$	−31.0605	−	4.75522i	−1.09953	−	0.168333i
$799$	−9.29555			−0.328853
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−17.4897	−	2.64843i	−0.617967	−	0.0935776i
$802$	−17.9661	−	31.1182i	−0.634405	−	1.09882i
$803$	−34.1332	−	19.7068i	−1.20454	−	0.695439i
$804$	−1.83942	−	0.138480i	−0.0648712	−	0.00488382i
$805$	1.48957			0.0525004
$806$	24.2519			0.854238
$807$	0.656350	−	8.71821i	0.0231046	−	0.306896i
$808$	−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	0.120534	−	0.992709i	$-0.461539\pi$
$811$	29.6318	−	17.1079i	1.04051	−	0.600740i	0.919978	+	0.391969i	$0.128206\pi$
$812$	15.1448	−	26.2315i	0.531477	−	0.920546i
$813$	1.17690	−	15.6326i	0.0412756	−	0.548259i
$814$	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
$819$	12.7072	−	83.9155i	0.444024	−	2.93224i
$820$	−6.60849	−	3.81541i	−0.230778	−	0.133240i
$821$	4.44653	−	2.56720i	0.155185	−	0.0895961i	−0.420397	−	0.907340i	$-0.638109\pi$
$821$	4.44653	−	2.56720i	0.155185	−	0.0895961i	0.575582	+	0.817744i	$0.304776\pi$
$822$	−9.19747	−	19.1155i	−0.320799	−	0.666731i
$823$	19.8033	+	34.3004i	0.690301	+	1.19564i	0.971739	+	0.236056i	$0.0758550\pi$
$823$	19.8033	+	34.3004i	0.690301	+	1.19564i	−0.281439	+	0.959579i	$0.590812\pi$
$824$			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	$-0.0368219\pi$
$827$	11.4081	+	19.7595i	0.396700	+	0.687105i	−0.596616	+	0.802527i	$0.703489\pi$
$828$	−0.999740	+	0.391577i	−0.0347434	+	0.0136082i
$829$		−	3.24052i		−	0.112548i	−0.998415	−	0.0562739i	$-0.982078\pi$
$829$		−	3.24052i		−	0.112548i	0.998415	−	0.0562739i	$-0.0179220\pi$
$830$	0.966883	+	1.67469i	0.0335610	+	0.0581293i
$831$	−8.32766	+	4.00687i	−0.288883	+	0.138997i
$832$	−5.88671	+	3.39869i	−0.204085	+	0.117828i
$833$	−16.1075	−	9.29970i	−0.558094	−	0.322215i
$834$	−18.4453	+	8.87497i	−0.638707	+	0.307315i
$835$			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	$-0.873287\pi$
$839$	−3.62615	+	6.28067i	−0.125189	+	0.216833i	0.796618	+	0.604483i	$0.206620\pi$
$840$	7.18845	+	0.541182i	0.248025	+	0.0186726i
$841$	−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
$846$	12.0934	+	9.65773i	0.415779	+	0.332040i
$847$	−9.16303			−0.314845
$848$	3.50830			0.120476
$849$	0.103541	−	1.37533i	0.00355353	−	0.0472011i
$850$	1.56047	+	0.900937i	0.0535236	+	0.0309019i
$851$	−1.09984	−	1.90498i	−0.0377021	−	0.0653020i
$852$	−6.42382	+	3.09083i	−0.220077	+	0.105890i
$853$	1.50057	−	2.59906i	0.0513785	−	0.0889901i	−0.839192	−	0.543835i	$-0.816972\pi$
$853$	1.50057	−	2.59906i	0.0513785	−	0.0889901i	0.890571	+	0.454845i	$0.150305\pi$
$854$	15.7215			0.537978
$855$	3.82118	+	12.5059i	0.130682	+	0.427694i
$856$	11.8795			0.406034
$857$	19.2846	−	33.4018i	0.658748	−	1.14099i	−0.322192	−	0.946674i	$-0.604420\pi$
$857$	19.2846	−	33.4018i	0.658748	−	1.14099i	0.980940	−	0.194311i	$-0.0622470\pi$
$858$	−31.4692	+	15.1415i	−1.07434	+	0.516921i
$859$	20.8063	+	36.0376i	0.709902	+	1.22959i	0.964893	+	0.262643i	$0.0845940\pi$
$859$	20.8063	+	36.0376i	0.709902	+	1.22959i	−0.254991	+	0.966943i	$0.582073\pi$
$860$	−8.89683	−	5.13659i	−0.303379	−	0.175156i
$861$	4.12966	−	54.8538i	0.140739	−	1.86941i
$862$	−6.63225			−0.225895
$863$	22.5281			0.766866			0.383433	−	0.923569i	$-0.374742\pi$
$863$	22.5281			0.766866			0.383433	+	0.923569i	$0.374742\pi$
$864$	−4.96688	+	1.52648i	−0.168977	+	0.0519318i
$865$	−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
$870$	−12.5697	−	0.946306i	−0.426152	−	0.0320828i
$871$	−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
$876$	−20.7390	+	9.97859i	−0.700705	+	0.337145i
$877$	30.2868	+	17.4861i	1.02271	+	0.590463i	0.914888	−	0.403707i	$-0.132278\pi$
$877$	30.2868	+	17.4861i	1.02271	+	0.590463i	0.107824	+	0.994170i	$0.465612\pi$
$878$	−10.6718	+	6.16135i	−0.360155	+	0.207936i
$879$	−37.1189	+	17.8598i	−1.25199	+	0.602397i
$880$	−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	0.749396	−	0.662122i	$-0.230344\pi$
$883$	−5.90494	−	10.2276i	−0.198717	−	0.344188i	−0.948113	+	0.317935i	$0.897011\pi$
$884$	−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	$-0.0975673\pi$
$887$	6.41460	+	11.1104i	0.215381	+	0.373051i	−0.738009	+	0.674791i	$0.764234\pi$
$888$	−4.61559	−	9.59279i	−0.154889	−	0.321913i
$889$	25.1951	−	14.5464i	0.845016	−	0.487870i
$890$	−5.10639	−	2.94818i	−0.171167	−	0.0988231i
$891$	−26.0347	+	5.90465i	−0.872196	+	0.197813i
$892$		−	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
$897$	−0.316330	+	4.20178i	−0.0105620	+	0.140293i
$898$	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
$903$	5.55966	−	73.8482i	0.185014	−	2.45752i
$904$	−3.14768			−0.104690
$905$	−0.0364693			−0.00121228
$906$	19.2190	+	1.44690i	0.638509	+	0.0480701i
$907$	34.8057	+	20.0951i	1.15571	+	0.667247i	0.950271	−	0.311424i	$-0.100806\pi$
$907$	34.8057	+	20.0951i	1.15571	+	0.667247i	0.205434	+	0.978671i	$0.434139\pi$
$908$	12.9280	+	22.3919i	0.429029	+	0.743101i
$909$	−1.68677	+	11.1391i	−0.0559467	+	0.369461i
$910$	14.1454	−	24.5005i	0.468914	−	0.812183i
$911$	−26.9672			−0.893462			−0.446731	−	0.894668i	$-0.647412\pi$
$911$	−26.9672			−0.893462			−0.446731	+	0.894668i	$0.647412\pi$
$912$	7.46288	+	1.14253i	0.247121	+	0.0378330i
$913$	5.73596			0.189832
$914$	14.7809	−	25.6013i	0.488909	−	0.846814i
$915$	−2.83672	−	5.89568i	−0.0937789	−	0.194905i
$916$	−2.80280	−	4.85459i	−0.0926071	−	0.160400i
$917$	−48.7661	−	28.1551i	−1.61040	−	0.929765i
$918$	−2.75052	−	8.94968i	−0.0907807	−	0.295384i
$919$	−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
$921$	−15.0056	−	1.12969i	−0.494450	−	0.0372246i
$922$	−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
$927$	6.03029	+	4.81577i	0.198061	+	0.158171i
$928$	−3.63882	+	6.30262i	−0.119450	+	0.206894i
$929$	9.47633	+	5.47116i	0.310908	+	0.179503i	0.647333	−	0.762207i	$-0.275884\pi$
$929$	9.47633	+	5.47116i	0.310908	+	0.179503i	−0.336425	+	0.941710i	$0.609218\pi$
$930$	5.10469	+	3.48288i	0.167389	+	0.114208i
$931$	3.45088	−	44.8611i	0.113098	−	1.47026i
$932$		−	26.1055i		−	0.855114i
$933$	−14.6138	−	30.3725i	−0.478434	−	0.994351i
$934$	−19.2991	−	11.1424i	−0.631487	−	0.364589i
$935$	4.62868	−	2.67237i	0.151374	−	0.0873958i
$936$	−3.05314	+	20.1623i	−0.0997949	+	0.659025i
$937$	7.80717	+	13.5224i	0.255049	+	0.441758i	0.964909	−	0.262585i	$-0.0845750\pi$
$937$	7.80717	+	13.5224i	0.255049	+	0.441758i	−0.709860	+	0.704343i	$0.751242\pi$
$938$		−	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	$-0.278502\pi$
$941$	−10.5573	−	18.2858i	−0.344158	−	0.596100i	−0.985200	+	0.171406i	$0.945169\pi$
$942$	−30.7223	−	20.9616i	−1.00099	−	0.682965i
$943$			2.73105i			0.0889352i
$944$	4.38575	+	7.59635i	0.142744	+	0.247240i
$945$	14.7260	−	15.8381i	0.479037	−	0.515214i
$946$	−26.3899	+	15.2362i	−0.858009	+	0.495372i
$947$	−16.7276	−	9.65770i	−0.543575	−	0.313833i	0.202952	−	0.979189i	$-0.434947\pi$
$947$	−16.7276	−	9.65770i	−0.543575	−	0.313833i	−0.746527	+	0.665356i	$0.768280\pi$
$948$	−0.958567	−	1.99223i	−0.0311328	−	0.0647047i
$949$			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	$-0.806126\pi$
$953$	2.63541	−	4.56467i	0.0853695	−	0.147864i	0.905549	+	0.424243i	$0.139460\pi$
$954$	6.56782	−	8.22420i	0.212641	−	0.266268i
$955$	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
$960$	−1.72716	−	0.130029i	−0.0557439	−	0.00419668i
$961$	18.2706			0.589373
$962$	−41.7777			−1.34697
$963$	22.2394	−	27.8481i	0.716655	−	0.897392i
$964$	7.46928	+	4.31239i	0.240569	+	0.138893i
$965$	6.64983	+	11.5178i	0.214066	+	0.370772i
$966$	−1.11863	−	2.32489i	−0.0359912	−	0.0748021i
$967$	−0.734029	+	1.27138i	−0.0236048	+	0.0408847i	−0.877586	−	0.479418i	$-0.840848\pi$
$967$	−0.734029	+	1.27138i	−0.0236048	+	0.0408847i	0.853982	+	0.520303i	$0.174181\pi$
$968$	2.20159			0.0707619
$969$	−2.05870	+	13.4472i	−0.0661349	+	0.431985i
$970$	12.9954			0.417259
$971$	21.9702	−	38.0536i	0.705058	−	1.22120i	−0.261612	−	0.965173i	$-0.584254\pi$
$971$	21.9702	−	38.0536i	0.705058	−	1.22120i	0.966670	−	0.256024i	$-0.0824126\pi$
$972$	−5.72000	+	14.5011i	−0.183469	+	0.465123i
$973$	−24.5932	−	42.5966i	−0.788421	−	1.36559i
$974$	1.43156	+	0.826514i	0.0458703	+	0.0264832i
$975$	−11.7402	−	0.883859i	−0.375987	−	0.0283061i
$976$	−3.77739			−0.120911
$977$	27.0036			0.863921			0.431961	−	0.901892i	$-0.357822\pi$
$977$	27.0036			0.863921			0.431961	+	0.901892i	$0.357822\pi$
$978$	2.52747	−	33.5721i	0.0808196	−	1.07352i
$979$	−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	−0.0266924	+	0.999644i	$0.508497\pi$
$983$	−27.5611	+	47.7373i	−0.879063	+	1.52258i	−0.852371	+	0.522938i	$0.824836\pi$
$984$	−0.992230	+	13.1797i	−0.0316311	+	0.420153i
$985$	−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
$990$	−8.79833	−	1.33231i	−0.279629	−	0.0423437i
$991$	28.0122	+	16.1729i	0.889838	+	0.513748i	0.873889	−	0.486125i	$-0.161590\pi$
$991$	28.0122	+	16.1729i	0.889838	+	0.513748i	0.0159483	+	0.999873i	$0.494923\pi$
$992$	3.08983	−	1.78392i	0.0981023	−	0.0566394i
$993$	−3.30988	−	6.87907i	−0.105036	−	0.218301i
$994$	−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	0.525749	−	0.850640i	$-0.323785\pi$
$997$	−14.9604	−	25.9122i	−0.473802	−	0.820648i	−0.999550	+	0.0299916i	$0.990452\pi$
$998$	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.a.521.10	yes	24
3.2	odd	2		570.2.s.b.521.6	yes	24
19.12	odd	6		570.2.s.b.221.6	yes	24
57.50	even	6	inner	570.2.s.a.221.10	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.10	✓	24	57.50	even	6	inner
570.2.s.a.521.10	yes	24	1.1	even	1	trivial
570.2.s.b.221.6	yes	24	19.12	odd	6
570.2.s.b.521.6	yes	24	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.56078 - 0.750973i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.130029 + 1.72716i) q^{6} -4.16200 q^{7} +1.00000 q^{8} +(1.87208 - 2.34421i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.56078 - 0.750973i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.130029 + 1.72716i) q^{6} -4.16200 q^{7} +1.00000 q^{8} +(1.87208 - 2.34421i) 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} +(-1.72716 - 0.130029i) 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} +(-6.49598 + 3.12555i) q^{21} +(2.56881 + 1.48311i) q^{22} +(0.309948 - 0.178948i) q^{23} +(1.56078 - 0.750973i) 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} +(-2.22754 - 4.62961i) q^{33} +(1.56047 - 0.900937i) q^{34} +(3.60440 + 2.08100i) q^{35} +(-2.96618 - 0.449163i) 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} +(0.541182 - 7.18845i) 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} +(-0.130029 + 1.72716i) q^{48} +10.3223 q^{49} -1.00000 q^{50} +(-3.11213 - 0.234296i) q^{51} +(5.88671 + 3.39869i) q^{52} +(-1.75415 - 3.03828i) q^{53} +(3.80541 + 3.53820i) q^{54} +(-1.48311 + 2.56881i) q^{55} -4.16200 q^{56} +(-2.74198 - 7.03431i) q^{57} +7.27764 q^{58} +(4.38575 - 7.59635i) q^{59} +(0.750973 + 1.56078i) q^{60} +(1.88869 + 3.27131i) q^{61} +(-3.08983 - 1.78392i) q^{62} +(-7.79160 + 9.75660i) q^{63} +1.00000 q^{64} +6.79738 q^{65} +(5.12313 + 0.385694i) 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} +(1.87208 - 2.34421i) 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} +(-5.10465 - 10.6092i) q^{78} +(1.10542 + 0.638217i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-1.99064 - 8.77709i) 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} +(0.449163 - 2.96618i) q^{90} +(24.5005 - 14.1454i) q^{91} +(-0.309948 - 0.178948i) q^{92} +(2.67935 + 5.56861i) 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} +(-6.95342 - 5.55298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * 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 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * 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 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

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