LMFDB - Embedded newform 370.2.e.f.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(121,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.235342 - 0.407624i$ of defining polynomial
Character	$\chi$	$=$	370.211
Dual form			370.2.e.f.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.38923 + 2.40621i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.77846 q^{6} +(-1.65389 + 2.86462i) q^{7} +1.00000 q^{8} +(-2.35991 - 4.08749i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.38923 + 2.40621i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.77846 q^{6} +(-1.65389 + 2.86462i) q^{7} +1.00000 q^{8} +(-2.35991 - 4.08749i) q^{9} -1.00000 q^{10} +1.52932 q^{11} +(-1.38923 - 2.40621i) q^{12} +(-2.09525 + 3.62909i) q^{13} +3.30777 q^{14} +(1.38923 + 2.40621i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.90303 - 6.76024i) q^{17} +(-2.35991 + 4.08749i) q^{18} +(0.110771 - 0.191862i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.59525 - 7.95921i) q^{21} +(-0.764658 - 1.32443i) q^{22} -3.52932 q^{23} +(-1.38923 + 2.40621i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.19051 q^{26} +4.77846 q^{27} +(-1.65389 - 2.86462i) q^{28} -6.49828 q^{29} +(1.38923 - 2.40621i) q^{30} -4.41205 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.12457 + 3.67986i) q^{33} +(-3.90303 + 6.76024i) q^{34} +(1.65389 + 2.86462i) q^{35} +4.71982 q^{36} +(-2.87371 + 5.36114i) q^{37} -0.221543 q^{38} +(-5.82157 - 10.0833i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.610771 + 1.05789i) q^{41} +(-4.59525 + 7.95921i) q^{42} -0.162910 q^{43} +(-0.764658 + 1.32443i) q^{44} -4.71982 q^{45} +(1.76466 + 3.05648i) q^{46} +11.9103 q^{47} +2.77846 q^{48} +(-1.97068 - 3.41332i) q^{49} +(-0.500000 + 0.866025i) q^{50} +21.6888 q^{51} +(-2.09525 - 3.62909i) q^{52} +(1.98448 + 3.43722i) q^{53} +(-2.38923 - 4.13827i) q^{54} +(0.764658 - 1.32443i) q^{55} +(-1.65389 + 2.86462i) q^{56} +(0.307774 + 0.533080i) q^{57} +(3.24914 + 5.62768i) q^{58} +(-0.543115 - 0.940703i) q^{59} -2.77846 q^{60} +(7.24914 - 12.5559i) q^{61} +(2.20603 + 3.82095i) q^{62} +15.6121 q^{63} +1.00000 q^{64} +(2.09525 + 3.62909i) q^{65} +4.24914 q^{66} +(-3.83709 + 6.64604i) q^{67} +7.80605 q^{68} +(4.90303 - 8.49229i) q^{69} +(1.65389 - 2.86462i) q^{70} +(-7.08623 + 12.2737i) q^{71} +(-2.35991 - 4.08749i) q^{72} -7.80605 q^{73} +(6.07974 - 0.191862i) q^{74} +2.77846 q^{75} +(0.110771 + 0.191862i) q^{76} +(-2.52932 + 4.38090i) q^{77} +(-5.82157 + 10.0833i) q^{78} +(-2.52932 + 4.38090i) q^{79} -1.00000 q^{80} +(0.441367 - 0.764470i) q^{81} +1.22154 q^{82} +(4.71982 + 8.17497i) q^{83} +9.19051 q^{84} -7.80605 q^{85} +(0.0814549 + 0.141084i) q^{86} +(9.02760 - 15.6363i) q^{87} +1.52932 q^{88} +(8.66769 + 15.0129i) q^{89} +(2.35991 + 4.08749i) q^{90} +(-6.93063 - 12.0042i) q^{91} +(1.76466 - 3.05648i) q^{92} +(6.12935 - 10.6163i) q^{93} +(-5.95517 - 10.3146i) q^{94} +(-0.110771 - 0.191862i) q^{95} +(-1.38923 - 2.40621i) q^{96} +8.38101 q^{97} +(-1.97068 + 3.41332i) q^{98} +(-3.60905 - 6.25106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^9	$ 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{9} - 6 q^{10} + 10 q^{11} - 3 q^{13} + 4 q^{14} - 3 q^{16} + 2 q^{17} - 5 q^{18} + 9 q^{19} + 3 q^{20} - 18 q^{21} - 5 q^{22} - 22 q^{23} - 3 q^{25} + 6 q^{26} + 12 q^{27} - 2 q^{28} - 4 q^{29} - 24 q^{31} - 3 q^{32} - 4 q^{33} + 2 q^{34} + 2 q^{35} + 10 q^{36} + 9 q^{37} - 18 q^{38} - 2 q^{39} + 3 q^{40} - 12 q^{41} - 18 q^{42} - 16 q^{43} - 5 q^{44} - 10 q^{45} + 11 q^{46} + 34 q^{47} - 11 q^{49} - 3 q^{50} + 76 q^{51} - 3 q^{52} - 6 q^{53} - 6 q^{54} + 5 q^{55} - 2 q^{56} - 14 q^{57} + 2 q^{58} + 13 q^{59} + 26 q^{61} + 12 q^{62} - 8 q^{63} + 6 q^{64} + 3 q^{65} + 8 q^{66} - 8 q^{67} - 4 q^{68} + 4 q^{69} + 2 q^{70} - 10 q^{71} - 5 q^{72} + 4 q^{73} + 9 q^{74} + 9 q^{76} - 16 q^{77} - 2 q^{78} - 16 q^{79} - 6 q^{80} + q^{81} + 24 q^{82} + 10 q^{83} + 36 q^{84} + 4 q^{85} + 8 q^{86} + 20 q^{87} + 10 q^{88} + 27 q^{89} + 5 q^{90} + 18 q^{91} + 11 q^{92} - 12 q^{93} - 17 q^{94} - 9 q^{95} + 12 q^{97} - 11 q^{98} + 5 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^9 - 6 * q^10 + 10 * q^11 - 3 * q^13 + 4 * q^14 - 3 * q^16 + 2 * q^17 - 5 * q^18 + 9 * q^19 + 3 * q^20 - 18 * q^21 - 5 * q^22 - 22 * q^23 - 3 * q^25 + 6 * q^26 + 12 * q^27 - 2 * q^28 - 4 * q^29 - 24 * q^31 - 3 * q^32 - 4 * q^33 + 2 * q^34 + 2 * q^35 + 10 * q^36 + 9 * q^37 - 18 * q^38 - 2 * q^39 + 3 * q^40 - 12 * q^41 - 18 * q^42 - 16 * q^43 - 5 * q^44 - 10 * q^45 + 11 * q^46 + 34 * q^47 - 11 * q^49 - 3 * q^50 + 76 * q^51 - 3 * q^52 - 6 * q^53 - 6 * q^54 + 5 * q^55 - 2 * q^56 - 14 * q^57 + 2 * q^58 + 13 * q^59 + 26 * q^61 + 12 * q^62 - 8 * q^63 + 6 * q^64 + 3 * q^65 + 8 * q^66 - 8 * q^67 - 4 * q^68 + 4 * q^69 + 2 * q^70 - 10 * q^71 - 5 * q^72 + 4 * q^73 + 9 * q^74 + 9 * q^76 - 16 * q^77 - 2 * q^78 - 16 * q^79 - 6 * q^80 + q^81 + 24 * q^82 + 10 * q^83 + 36 * q^84 + 4 * q^85 + 8 * q^86 + 20 * q^87 + 10 * q^88 + 27 * q^89 + 5 * q^90 + 18 * q^91 + 11 * q^92 - 12 * q^93 - 17 * q^94 - 9 * q^95 + 12 * q^97 - 11 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−1.38923	+	2.40621i	−0.802071	+	1.38923i	0.116179	+	0.993228i	$0.462935\pi$
$3$	−1.38923	+	2.40621i	−0.802071	+	1.38923i	−0.918250	+	0.396000i	$0.870398\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	2.77846			1.13430
$7$	−1.65389	+	2.86462i	−0.625110	+	1.08272i	0.363409	+	0.931630i	$0.381613\pi$
$7$	−1.65389	+	2.86462i	−0.625110	+	1.08272i	−0.988519	+	0.151093i	$0.951721\pi$
$8$	1.00000			0.353553
$9$	−2.35991	−	4.08749i	−0.786637	−	1.36250i
$10$	−1.00000			−0.316228
$11$	1.52932			0.461106			0.230553	−	0.973060i	$-0.425946\pi$
$11$	1.52932			0.461106			0.230553	+	0.973060i	$0.425946\pi$
$12$	−1.38923	−	2.40621i	−0.401036	−	0.694614i
$13$	−2.09525	+	3.62909i	−0.581119	+	1.00653i	0.414228	+	0.910173i	$0.364052\pi$
$13$	−2.09525	+	3.62909i	−0.581119	+	1.00653i	−0.995347	+	0.0963543i	$0.969282\pi$
$14$	3.30777			0.884040
$15$	1.38923	+	2.40621i	0.358697	+	0.621282i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.90303	−	6.76024i	−0.946623	−	1.63960i	−0.752468	−	0.658629i	$-0.771137\pi$
$17$	−3.90303	−	6.76024i	−0.946623	−	1.63960i	−0.194155	−	0.980971i	$-0.562196\pi$
$18$	−2.35991	+	4.08749i	−0.556237	+	0.963430i
$19$	0.110771	−	0.191862i	0.0254127	−	0.0440161i	−0.853039	−	0.521847i	$-0.825243\pi$
$19$	0.110771	−	0.191862i	0.0254127	−	0.0440161i	0.878452	+	0.477830i	$0.158577\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−4.59525	−	7.95921i	−1.00277	−	1.73684i
$22$	−0.764658	−	1.32443i	−0.163026	−	0.282369i
$23$	−3.52932			−0.735913			−0.367957	−	0.929843i	$-0.619943\pi$
$23$	−3.52932			−0.735913			−0.367957	+	0.929843i	$0.619943\pi$
$24$	−1.38923	+	2.40621i	−0.283575	+	0.491166i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.19051			0.821826
$27$	4.77846			0.919615
$28$	−1.65389	−	2.86462i	−0.312555	−	0.541362i
$29$	−6.49828			−1.20670			−0.603350	−	0.797476i	$-0.706168\pi$
$29$	−6.49828			−1.20670			−0.603350	+	0.797476i	$0.706168\pi$
$30$	1.38923	−	2.40621i	0.253637	−	0.439313i
$31$	−4.41205			−0.792428			−0.396214	−	0.918158i	$-0.629676\pi$
$31$	−4.41205			−0.792428			−0.396214	+	0.918158i	$0.629676\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.12457	+	3.67986i	−0.369840	+	0.640582i
$34$	−3.90303	+	6.76024i	−0.669364	+	1.15937i
$35$	1.65389	+	2.86462i	0.279558	+	0.484208i
$36$	4.71982			0.786637
$37$	−2.87371	+	5.36114i	−0.472435	+	0.881365i
$37$	−2.87371	+	5.36114i	−0.472435	+	0.881365i
$38$	−0.221543			−0.0359390
$39$	−5.82157	−	10.0833i	−0.932198	−	1.61461i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−0.610771	+	1.05789i	−0.0953865	+	0.165214i	−0.909770	−	0.415113i	$-0.863742\pi$
$41$	−0.610771	+	1.05789i	−0.0953865	+	0.165214i	0.814383	+	0.580327i	$0.197075\pi$
$42$	−4.59525	+	7.95921i	−0.709063	+	1.22813i
$43$	−0.162910			−0.0248435			−0.0124217	−	0.999923i	$-0.503954\pi$
$43$	−0.162910			−0.0248435			−0.0124217	+	0.999923i	$0.503954\pi$
$44$	−0.764658	+	1.32443i	−0.115277	+	0.199665i
$45$	−4.71982			−0.703590
$46$	1.76466	+	3.05648i	0.260185	+	0.450653i
$47$	11.9103			1.73730			0.868650	−	0.495426i	$-0.164988\pi$
$47$	11.9103			1.73730			0.868650	+	0.495426i	$0.164988\pi$
$48$	2.77846			0.401036
$49$	−1.97068	−	3.41332i	−0.281526	−	0.487618i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	21.6888			3.03704
$52$	−2.09525	−	3.62909i	−0.290559	−	0.503264i
$53$	1.98448	+	3.43722i	0.272590	+	0.472139i	0.969524	−	0.244996i	$-0.0787865\pi$
$53$	1.98448	+	3.43722i	0.272590	+	0.472139i	−0.696935	+	0.717135i	$0.745453\pi$
$54$	−2.38923	−	4.13827i	−0.325133	−	0.563147i
$55$	0.764658	−	1.32443i	0.103107	−	0.178586i
$56$	−1.65389	+	2.86462i	−0.221010	+	0.382800i
$57$	0.307774	+	0.533080i	0.0407656	+	0.0706081i
$58$	3.24914	+	5.62768i	0.426633	+	0.738950i
$59$	−0.543115	−	0.940703i	−0.0707076	−	0.122469i	0.828504	−	0.559983i	$-0.189192\pi$
$59$	−0.543115	−	0.940703i	−0.0707076	−	0.122469i	−0.899212	+	0.437514i	$0.855859\pi$
$60$	−2.77846			−0.358697
$61$	7.24914	−	12.5559i	0.928157	−	1.60762i	0.141754	−	0.989902i	$-0.454726\pi$
$61$	7.24914	−	12.5559i	0.928157	−	1.60762i	0.786403	−	0.617714i	$-0.211941\pi$
$62$	2.20603	+	3.82095i	0.280165	+	0.485261i
$63$	15.6121			1.96694
$64$	1.00000			0.125000
$65$	2.09525	+	3.62909i	0.259884	+	0.450133i
$66$	4.24914			0.523033
$67$	−3.83709	+	6.64604i	−0.468775	+	0.811942i	−0.999363	−	0.0356875i	$-0.988638\pi$
$67$	−3.83709	+	6.64604i	−0.468775	+	0.811942i	0.530588	+	0.847630i	$0.321971\pi$
$68$	7.80605			0.946623
$69$	4.90303	−	8.49229i	0.590255	−	1.02235i
$70$	1.65389	−	2.86462i	0.197677	−	0.342387i
$71$	−7.08623	+	12.2737i	−0.840981	+	1.45662i	0.0480855	+	0.998843i	$0.484688\pi$
$71$	−7.08623	+	12.2737i	−0.840981	+	1.45662i	−0.889066	+	0.457778i	$0.848645\pi$
$72$	−2.35991	−	4.08749i	−0.278118	−	0.481715i
$73$	−7.80605			−0.913630			−0.456815	−	0.889562i	$-0.651010\pi$
$73$	−7.80605			−0.913630			−0.456815	+	0.889562i	$0.651010\pi$
$74$	6.07974	−	0.191862i	0.706755	−	0.0223035i
$75$	2.77846			0.320829
$76$	0.110771	+	0.191862i	0.0127064	+	0.0220081i
$77$	−2.52932	+	4.38090i	−0.288242	+	0.499250i
$78$	−5.82157	+	10.0833i	−0.659163	+	1.14170i
$79$	−2.52932	+	4.38090i	−0.284570	+	0.492890i	−0.972505	−	0.232882i	$-0.925184\pi$
$79$	−2.52932	+	4.38090i	−0.284570	+	0.492890i	0.687935	+	0.725773i	$0.258518\pi$
$80$	−1.00000			−0.111803
$81$	0.441367	−	0.764470i	0.0490408	−	0.0849411i
$82$	1.22154			0.134897
$83$	4.71982	+	8.17497i	0.518068	+	0.897320i	0.999780	+	0.0209903i	$0.00668191\pi$
$83$	4.71982	+	8.17497i	0.518068	+	0.897320i	−0.481712	+	0.876330i	$0.659985\pi$
$84$	9.19051			1.00277
$85$	−7.80605			−0.846686
$86$	0.0814549	+	0.141084i	0.00878350	+	0.0152135i
$87$	9.02760	−	15.6363i	0.967860	−	1.67638i
$88$	1.52932			0.163026
$89$	8.66769	+	15.0129i	0.918773	+	1.59136i	0.801282	+	0.598287i	$0.204152\pi$
$89$	8.66769	+	15.0129i	0.918773	+	1.59136i	0.117491	+	0.993074i	$0.462515\pi$
$90$	2.35991	+	4.08749i	0.248757	+	0.430859i
$91$	−6.93063	−	12.0042i	−0.726527	−	1.25838i
$92$	1.76466	−	3.05648i	0.183978	−	0.318660i
$93$	6.12935	−	10.6163i	0.635584	−	1.10086i
$94$	−5.95517	−	10.3146i	−0.614228	−	1.06387i
$95$	−0.110771	−	0.191862i	−0.0113649	−	0.0196846i
$96$	−1.38923	−	2.40621i	−0.141788	−	0.245583i
$97$	8.38101			0.850963			0.425482	−	0.904967i	$-0.360105\pi$
$97$	8.38101			0.850963			0.425482	+	0.904967i	$0.360105\pi$
$98$	−1.97068	+	3.41332i	−0.199069	+	0.344798i
$99$	−3.60905	−	6.25106i	−0.362723	−	0.628255i
$100$	1.00000			0.100000
$101$	−6.24914			−0.621813			−0.310906	−	0.950441i	$-0.600633\pi$
$101$	−6.24914			−0.621813			−0.310906	+	0.950441i	$0.600633\pi$
$102$	−10.8444	−	18.7830i	−1.07376	−	1.85980i
$103$	−8.96896			−0.883738			−0.441869	−	0.897080i	$-0.645684\pi$
$103$	−8.96896			−0.883738			−0.441869	+	0.897080i	$0.645684\pi$
$104$	−2.09525	+	3.62909i	−0.205457	+	0.355861i
$105$	−9.19051			−0.896902
$106$	1.98448	−	3.43722i	0.192750	−	0.333853i
$107$	4.10905	−	7.11709i	0.397237	−	0.688035i	−0.596147	−	0.802875i	$-0.703302\pi$
$107$	4.10905	−	7.11709i	0.397237	−	0.688035i	0.993384	+	0.114841i	$0.0366357\pi$
$108$	−2.38923	+	4.13827i	−0.229904	+	0.398205i
$109$	5.02760	+	8.70805i	0.481557	+	0.834080i	0.999776	−	0.0211673i	$-0.00673828\pi$
$109$	5.02760	+	8.70805i	0.481557	+	0.834080i	−0.518219	+	0.855248i	$0.673405\pi$
$110$	−1.52932			−0.145815
$111$	−8.90780	−	14.3626i	−0.845491	−	1.36324i
$112$	3.30777			0.312555
$113$	−4.36641	−	7.56284i	−0.410757	−	0.711452i	0.584216	−	0.811598i	$-0.301402\pi$
$113$	−4.36641	−	7.56284i	−0.410757	−	0.711452i	−0.994973	+	0.100146i	$0.968069\pi$
$114$	0.307774	−	0.533080i	0.0288256	−	0.0499275i
$115$	−1.76466	+	3.05648i	−0.164555	+	0.285018i
$116$	3.24914	−	5.62768i	0.301675	−	0.522517i
$117$	19.7785			1.82852
$118$	−0.543115	+	0.940703i	−0.0499978	+	0.0865988i
$119$	25.8207			2.36698
$120$	1.38923	+	2.40621i	0.126819	+	0.219656i
$121$	−8.66119			−0.787381
$122$	−14.4983			−1.31261
$123$	−1.69700	−	2.93929i	−0.153014	−	0.265027i
$124$	2.20603	−	3.82095i	0.198107	−	0.343131i
$125$	−1.00000			−0.0894427
$126$	−7.80605	−	13.5205i	−0.695419	−	1.20450i
$127$	−1.94786	−	3.37380i	−0.172845	−	0.299376i	0.766569	−	0.642163i	$-0.221963\pi$
$127$	−1.94786	−	3.37380i	−0.172845	−	0.299376i	−0.939413	+	0.342787i	$0.888629\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.226319	−	0.391996i	0.0199263	−	0.0345133i
$130$	2.09525	−	3.62909i	0.183766	−	0.318292i
$131$	2.66119	+	4.60932i	0.232509	+	0.402718i	0.958546	−	0.284938i	$-0.0919730\pi$
$131$	2.66119	+	4.60932i	0.232509	+	0.402718i	−0.726037	+	0.687656i	$0.758640\pi$
$132$	−2.12457	−	3.67986i	−0.184920	−	0.320291i
$133$	0.366407	+	0.634635i	0.0317715	+	0.0550299i
$134$	7.67418			0.662948
$135$	2.38923	−	4.13827i	0.205632	−	0.356165i
$136$	−3.90303	−	6.76024i	−0.334682	−	0.579686i
$137$	−8.01461			−0.684734			−0.342367	−	0.939566i	$-0.611229\pi$
$137$	−8.01461			−0.684734			−0.342367	+	0.939566i	$0.611229\pi$
$138$	−9.80605			−0.834747
$139$	2.32157	+	4.02108i	0.196913	+	0.341064i	0.947526	−	0.319679i	$-0.103575\pi$
$139$	2.32157	+	4.02108i	0.196913	+	0.341064i	−0.750613	+	0.660742i	$0.770242\pi$
$140$	−3.30777			−0.279558
$141$	−16.5462	+	28.6588i	−1.39344	+	2.41351i
$142$	14.1725			1.18933
$143$	−3.20431	+	5.55002i	−0.267958	+	0.464116i
$144$	−2.35991	+	4.08749i	−0.196659	+	0.340624i
$145$	−3.24914	+	5.62768i	−0.269826	+	0.467353i
$146$	3.90303	+	6.76024i	0.323017	+	0.559482i
$147$	10.9509			0.903217
$148$	−3.20603	−	5.16927i	−0.263534	−	0.424912i
$149$	21.9931			1.80175			0.900873	−	0.434082i	$-0.142927\pi$
$149$	21.9931			1.80175			0.900873	+	0.434082i	$0.142927\pi$
$150$	−1.38923	−	2.40621i	−0.113430	−	0.196467i
$151$	−10.9845	+	19.0257i	−0.893904	+	1.54829i	−0.0587499	+	0.998273i	$0.518711\pi$
$151$	−10.9845	+	19.0257i	−0.893904	+	1.54829i	−0.835155	+	0.550015i	$0.814622\pi$
$152$	0.110771	−	0.191862i	0.00898475	−	0.0155620i
$153$	−18.4216	+	31.9072i	−1.48930	+	2.57954i
$154$	5.05863			0.407636
$155$	−2.20603	+	3.82095i	−0.177192	+	0.306906i
$156$	11.6431			0.932198
$157$	8.37199	+	14.5007i	0.668158	+	1.15728i	0.978419	+	0.206632i	$0.0662502\pi$
$157$	8.37199	+	14.5007i	0.668158	+	1.15728i	−0.310261	+	0.950651i	$0.600416\pi$
$158$	5.05863			0.402443
$159$	−11.0276			−0.874545
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	5.83709	−	10.1101i	0.460027	−	0.796790i
$162$	−0.882734			−0.0693541
$163$	−3.44786	−	5.97187i	−0.270057	−	0.467753i	0.698819	−	0.715299i	$-0.253709\pi$
$163$	−3.44786	−	5.97187i	−0.270057	−	0.467753i	−0.968876	+	0.247546i	$0.920376\pi$
$164$	−0.610771	−	1.05789i	−0.0476932	−	0.0826071i
$165$	2.12457	+	3.67986i	0.165398	+	0.286477i
$166$	4.71982	−	8.17497i	0.366329	−	0.634501i
$167$	−6.52932	+	11.3091i	−0.505254	+	0.875125i	0.494728	+	0.869048i	$0.335268\pi$
$167$	−6.52932	+	11.3091i	−0.505254	+	0.875125i	−0.999982	+	0.00607710i	$0.998066\pi$
$168$	−4.59525	−	7.95921i	−0.354532	−	0.614067i
$169$	−2.28018	−	3.94938i	−0.175398	−	0.303799i
$170$	3.90303	+	6.76024i	0.299349	+	0.518487i
$171$	−1.04564			−0.0799623
$172$	0.0814549	−	0.141084i	0.00621087	−	0.0107576i
$173$	−0.0797359	−	0.138107i	−0.00606221	−	0.0105001i	0.862978	−	0.505241i	$-0.168596\pi$
$173$	−0.0797359	−	0.138107i	−0.00606221	−	0.0105001i	−0.869041	+	0.494741i	$0.835263\pi$
$174$	−18.0552			−1.36876
$175$	3.30777			0.250044
$176$	−0.764658	−	1.32443i	−0.0576383	−	0.0998324i
$177$	3.01805			0.226850
$178$	8.66769	−	15.0129i	0.649671	−	1.12526i
$179$	−18.5113			−1.38360			−0.691799	−	0.722090i	$-0.743181\pi$
$179$	−18.5113			−1.38360			−0.691799	+	0.722090i	$0.743181\pi$
$180$	2.35991	−	4.08749i	0.175897	−	0.304663i
$181$	4.93406	−	8.54605i	0.366746	−	0.635223i	−0.622309	−	0.782772i	$-0.713805\pi$
$181$	4.93406	−	8.54605i	0.366746	−	0.635223i	0.989055	+	0.147549i	$0.0471385\pi$
$182$	−6.93063	+	12.0042i	−0.513732	+	0.889810i
$183$	20.1414	+	34.8860i	1.48890	+	2.57885i
$184$	−3.52932			−0.260185
$185$	3.20603	+	5.16927i	0.235712	+	0.380053i
$186$	−12.2587			−0.898851
$187$	−5.96896	−	10.3385i	−0.436494	−	0.756030i
$188$	−5.95517	+	10.3146i	−0.434325	+	0.752273i
$189$	−7.90303	+	13.6884i	−0.574861	+	0.995688i
$190$	−0.110771	+	0.191862i	−0.00803620	+	0.0139191i
$191$	−26.9655			−1.95116			−0.975579	−	0.219651i	$-0.929508\pi$
$191$	−26.9655			−1.95116			−0.975579	+	0.219651i	$0.929508\pi$
$192$	−1.38923	+	2.40621i	−0.100259	+	0.173654i
$193$	−20.3595			−1.46551			−0.732756	−	0.680492i	$-0.761766\pi$
$193$	−20.3595			−1.46551			−0.732756	+	0.680492i	$0.761766\pi$
$194$	−4.19051	−	7.25817i	−0.300861	−	0.521106i
$195$	−11.6431			−0.833783
$196$	3.94137			0.281526
$197$	−0.427568	−	0.740570i	−0.0304630	−	0.0527634i	0.850392	−	0.526150i	$-0.176365\pi$
$197$	−0.427568	−	0.740570i	−0.0304630	−	0.0527634i	−0.880855	+	0.473386i	$0.843031\pi$
$198$	−3.60905	+	6.25106i	−0.256484	+	0.444244i
$199$	25.4346			1.80301			0.901505	−	0.432768i	$-0.142463\pi$
$199$	25.4346			1.80301			0.901505	+	0.432768i	$0.142463\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−10.6612	−	18.4657i	−0.751982	−	1.30247i
$202$	3.12457	+	5.41191i	0.219844	+	0.380781i
$203$	10.7474	−	18.6151i	0.754321	−	1.30652i
$204$	−10.8444	+	18.7830i	−0.759259	+	1.31508i
$205$	0.610771	+	1.05789i	0.0426581	+	0.0738860i
$206$	4.48448	+	7.76735i	0.312449	+	0.541177i
$207$	8.32888	+	14.4260i	0.578897	+	1.00268i
$208$	4.19051			0.290559
$209$	0.169405	−	0.293417i	0.0117180	−	0.0202961i
$210$	4.59525	+	7.95921i	0.317103	+	0.549238i
$211$	−10.8923			−0.749856			−0.374928	−	0.927054i	$-0.622333\pi$
$211$	−10.8923			−0.749856			−0.374928	+	0.927054i	$0.622333\pi$
$212$	−3.96896			−0.272590
$213$	−19.6888	−	34.1020i	−1.34905	−	2.33663i
$214$	−8.21811			−0.561778
$215$	−0.0814549	+	0.141084i	−0.00555518	+	0.00962185i
$216$	4.77846			0.325133
$217$	7.29703	−	12.6388i	0.495355	−	0.857980i
$218$	5.02760	−	8.70805i	0.340512	−	0.589784i
$219$	10.8444	−	18.7830i	0.732796	−	1.26924i
$220$	0.764658	+	1.32443i	0.0515533	+	0.0892929i
$221$	32.7113			2.20040
$222$	−7.98448	+	14.8957i	−0.535883	+	0.999733i
$223$	16.3173			1.09269			0.546344	−	0.837561i	$-0.316019\pi$
$223$	16.3173			1.09269			0.546344	+	0.837561i	$0.316019\pi$
$224$	−1.65389	−	2.86462i	−0.110505	−	0.191400i
$225$	−2.35991	+	4.08749i	−0.157327	+	0.272499i
$226$	−4.36641	+	7.56284i	−0.290449	+	0.503073i
$227$	8.66597	−	15.0099i	0.575180	−	0.996242i	−0.420842	−	0.907134i	$-0.638265\pi$
$227$	8.66597	−	15.0099i	0.575180	−	0.996242i	0.996022	−	0.0891076i	$-0.0284015\pi$
$228$	−0.615547			−0.0407656
$229$	−5.56422	+	9.63751i	−0.367694	+	0.636864i	−0.989205	−	0.146541i	$-0.953186\pi$
$229$	−5.56422	+	9.63751i	−0.367694	+	0.636864i	0.621511	+	0.783406i	$0.286519\pi$
$230$	3.52932			0.232716
$231$	−7.02760	−	12.1722i	−0.462382	−	0.800869i
$232$	−6.49828			−0.426633
$233$	−12.3664			−0.810150			−0.405075	−	0.914283i	$-0.632755\pi$
$233$	−12.3664			−0.810150			−0.405075	+	0.914283i	$0.632755\pi$
$234$	−9.88923	−	17.1286i	−0.646479	−	1.11973i
$235$	5.95517	−	10.3146i	0.388472	−	0.672854i
$236$	1.08623			0.0707076
$237$	−7.02760	−	12.1722i	−0.456492	−	0.790667i
$238$	−12.9103	−	22.3613i	−0.836852	−	1.44947i
$239$	8.19051	+	14.1864i	0.529800	+	0.917640i	0.999396	+	0.0347588i	$0.0110663\pi$
$239$	8.19051	+	14.1864i	0.529800	+	0.917640i	−0.469596	+	0.882881i	$0.655600\pi$
$240$	1.38923	−	2.40621i	0.0896743	−	0.155320i
$241$	6.35991	−	11.0157i	0.409678	−	0.709583i	−0.585176	−	0.810907i	$-0.698974\pi$
$241$	6.35991	−	11.0157i	0.409678	−	0.709583i	0.994854	+	0.101324i	$0.0323077\pi$
$242$	4.33060	+	7.50081i	0.278381	+	0.482170i
$243$	8.39400	+	14.5388i	0.538476	+	0.932667i
$244$	7.24914	+	12.5559i	0.464079	+	0.803808i
$245$	−3.94137			−0.251805
$246$	−1.69700	+	2.93929i	−0.108197	+	0.187403i
$247$	0.464189	+	0.803998i	0.0295356	+	0.0511572i
$248$	−4.41205			−0.280165
$249$	−26.2277			−1.66211
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	12.8302			0.809836			0.404918	−	0.914353i	$-0.367300\pi$
$251$	12.8302			0.809836			0.404918	+	0.914353i	$0.367300\pi$
$252$	−7.80605	+	13.5205i	−0.491735	+	0.851710i
$253$	−5.39744			−0.339334
$254$	−1.94786	+	3.37380i	−0.122220	+	0.211691i
$255$	10.8444	−	18.7830i	0.679102	−	1.17624i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.59525	−	2.76306i	−0.0995092	−	0.172355i	0.811972	−	0.583696i	$-0.198394\pi$
$257$	−1.59525	−	2.76306i	−0.0995092	−	0.172355i	−0.911482	+	0.411341i	$0.865061\pi$
$258$	−0.452638			−0.0281800
$259$	−10.6048	−	17.0988i	−0.658951	−	1.06247i
$260$	−4.19051			−0.259884
$261$	15.3354	+	26.5616i	0.949236	+	1.64412i
$262$	2.66119	−	4.60932i	0.164409	−	0.284765i
$263$	−4.17671	+	7.23427i	−0.257547	+	0.446084i	−0.965584	−	0.260091i	$-0.916248\pi$
$263$	−4.17671	+	7.23427i	−0.257547	+	0.446084i	0.708037	+	0.706175i	$0.249581\pi$
$264$	−2.12457	+	3.67986i	−0.130758	+	0.226480i
$265$	3.96896			0.243812
$266$	0.366407	−	0.634635i	0.0224658	−	0.0389120i
$267$	−48.1656			−2.94769
$268$	−3.83709	−	6.64604i	−0.234388	−	0.405971i
$269$	9.59750			0.585170			0.292585	−	0.956240i	$-0.405485\pi$
$269$	9.59750			0.585170			0.292585	+	0.956240i	$0.405485\pi$
$270$	−4.77846			−0.290808
$271$	−0.0431154	−	0.0746781i	−0.00261907	−	0.00453637i	0.864713	−	0.502266i	$-0.167500\pi$
$271$	−0.0431154	−	0.0746781i	−0.00261907	−	0.00453637i	−0.867332	+	0.497730i	$0.834167\pi$
$272$	−3.90303	+	6.76024i	−0.236656	+	0.409900i
$273$	38.5129			2.33091
$274$	4.00730	+	6.94085i	0.242090	+	0.419312i
$275$	−0.764658	−	1.32443i	−0.0461106	−	0.0798660i
$276$	4.90303	+	8.49229i	0.295128	+	0.511176i
$277$	2.39653	−	4.15092i	0.143994	−	0.249404i	−0.785003	−	0.619491i	$-0.787339\pi$
$277$	2.39653	−	4.15092i	0.143994	−	0.249404i	0.928997	+	0.370087i	$0.120672\pi$
$278$	2.32157	−	4.02108i	0.139239	−	0.241168i
$279$	10.4121	+	18.0342i	0.623353	+	1.07968i
$280$	1.65389	+	2.86462i	0.0988386	+	0.171194i
$281$	−3.52760	−	6.10998i	−0.210439	−	0.364491i	0.741413	−	0.671049i	$-0.234156\pi$
$281$	−3.52760	−	6.10998i	−0.210439	−	0.364491i	−0.951852	+	0.306558i	$0.900823\pi$
$282$	33.0923			1.97062
$283$	8.85991	−	15.3458i	0.526667	−	0.912214i	−0.472850	−	0.881143i	$-0.656775\pi$
$283$	8.85991	−	15.3458i	0.526667	−	0.912214i	0.999517	−	0.0310713i	$-0.00989189\pi$
$284$	−7.08623	−	12.2737i	−0.420490	−	0.728311i
$285$	0.615547			0.0364619
$286$	6.40861			0.378949
$287$	−2.02029	−	3.49925i	−0.119254	−	0.206554i
$288$	4.71982			0.278118
$289$	−21.9672	+	38.0484i	−1.29219	+	2.23814i
$290$	6.49828			0.381592
$291$	−11.6431	+	20.1665i	−0.682533	+	1.18218i
$292$	3.90303	−	6.76024i	0.228407	−	0.395613i
$293$	11.8427	−	20.5121i	0.691856	−	1.19833i	−0.279372	−	0.960183i	$-0.590126\pi$
$293$	11.8427	−	20.5121i	0.691856	−	1.19833i	0.971229	−	0.238148i	$-0.0765403\pi$
$294$	−5.47546	−	9.48377i	−0.319335	−	0.553105i
$295$	−1.08623			−0.0632428
$296$	−2.87371	+	5.36114i	−0.167031	+	0.311610i
$297$	7.30777			0.424040
$298$	−10.9966	−	19.0466i	−0.637014	−	1.10334i
$299$	7.39481	−	12.8082i	0.427653	−	0.740717i
$300$	−1.38923	+	2.40621i	−0.0802071	+	0.138923i
$301$	0.269434	−	0.466674i	0.0155299	−	0.0268986i
$302$	21.9690			1.26417
$303$	8.68148	−	15.0368i	0.498738	−	0.863840i
$304$	−0.221543			−0.0127064
$305$	−7.24914	−	12.5559i	−0.415085	−	0.718948i
$306$	36.8432			2.10619
$307$	−10.4526			−0.596564			−0.298282	−	0.954478i	$-0.596414\pi$
$307$	−10.4526			−0.596564			−0.298282	+	0.954478i	$0.596414\pi$
$308$	−2.52932	−	4.38090i	−0.144121	−	0.249625i
$309$	12.4599	−	21.5813i	0.708821	−	1.22771i
$310$	4.41205			0.250588
$311$	−4.70774	−	8.15405i	−0.266952	−	0.462374i	0.701121	−	0.713042i	$-0.252683\pi$
$311$	−4.70774	−	8.15405i	−0.266952	−	0.462374i	−0.968073	+	0.250668i	$0.919350\pi$
$312$	−5.82157	−	10.0833i	−0.329582	−	0.570852i
$313$	−5.27674	−	9.13958i	−0.298259	−	0.516600i	0.677479	−	0.735542i	$-0.263073\pi$
$313$	−5.27674	−	9.13958i	−0.298259	−	0.516600i	−0.975738	+	0.218943i	$0.929739\pi$
$314$	8.37199	−	14.5007i	0.472459	−	0.818323i
$315$	7.80605	−	13.5205i	0.439821	−	0.761793i
$316$	−2.52932	−	4.38090i	−0.142285	−	0.246445i
$317$	−16.4893	−	28.5602i	−0.926129	−	1.60410i	−0.789735	−	0.613448i	$-0.789782\pi$
$317$	−16.4893	−	28.5602i	−0.926129	−	1.60410i	−0.136394	−	0.990655i	$-0.543551\pi$
$318$	5.51380	+	9.55018i	0.309198	+	0.535547i
$319$	−9.93793			−0.556417
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	11.4168	+	19.7745i	0.637225	+	1.10371i
$322$	−11.6742			−0.650577
$323$	−1.72938			−0.0962250
$324$	0.441367	+	0.764470i	0.0245204	+	0.0424705i
$325$	4.19051			0.232448
$326$	−3.44786	+	5.97187i	−0.190959	+	0.330751i
$327$	−27.9379			−1.54497
$328$	−0.610771	+	1.05789i	−0.0337242	+	0.0584120i
$329$	−19.6983	+	34.1185i	−1.08600	+	1.88102i
$330$	2.12457	−	3.67986i	0.116954	−	0.202570i
$331$	−1.95860	−	3.39240i	−0.107655	−	0.186463i	0.807165	−	0.590326i	$-0.201001\pi$
$331$	−1.95860	−	3.39240i	−0.107655	−	0.186463i	−0.914820	+	0.403863i	$0.867667\pi$
$332$	−9.43965			−0.518068
$333$	28.6953	−	0.905554i	1.57249	−	0.0496240i
$334$	13.0586			0.714537
$335$	3.83709	+	6.64604i	0.209643	+	0.363112i
$336$	−4.59525	+	7.95921i	−0.250692	+	0.434211i
$337$	−3.22154	+	5.57988i	−0.175489	+	0.303955i	−0.940330	−	0.340263i	$-0.889484\pi$
$337$	−3.22154	+	5.57988i	−0.175489	+	0.303955i	0.764842	+	0.644218i	$0.222817\pi$
$338$	−2.28018	+	3.94938i	−0.124025	+	0.214818i
$339$	24.2637			1.31783
$340$	3.90303	−	6.76024i	0.211671	−	0.366626i
$341$	−6.74742			−0.365393
$342$	0.522822	+	0.905554i	0.0282710	+	0.0489667i
$343$	−10.1173			−0.546281
$344$	−0.162910			−0.00878350
$345$	−4.90303	−	8.49229i	−0.263970	−	0.457210i
$346$	−0.0797359	+	0.138107i	−0.00428663	+	0.00742466i
$347$	22.4431			1.20481			0.602404	−	0.798191i	$-0.294210\pi$
$347$	22.4431			1.20481			0.602404	+	0.798191i	$0.294210\pi$
$348$	9.02760	+	15.6363i	0.483930	+	0.838191i
$349$	10.1138	+	17.5177i	0.541381	+	0.937699i	0.998825	+	0.0484608i	$0.0154316\pi$
$349$	10.1138	+	17.5177i	0.541381	+	0.937699i	−0.457444	+	0.889238i	$0.651235\pi$
$350$	−1.65389	−	2.86462i	−0.0884040	−	0.153120i
$351$	−10.0121	+	17.3414i	−0.534405	+	0.925617i
$352$	−0.764658	+	1.32443i	−0.0407564	+	0.0705922i
$353$	2.99270	+	5.18350i	0.159285	+	0.275890i	0.934611	−	0.355671i	$-0.115748\pi$
$353$	2.99270	+	5.18350i	0.159285	+	0.275890i	−0.775326	+	0.631561i	$0.782414\pi$
$354$	−1.50902	−	2.61370i	−0.0802037	−	0.138917i
$355$	7.08623	+	12.2737i	0.376098	+	0.651421i
$356$	−17.3354			−0.918773
$357$	−35.8708	+	62.1301i	−1.89848	+	3.28827i
$358$	9.25564	+	16.0312i	0.489176	+	0.847277i
$359$	12.0242			0.634611			0.317305	−	0.948323i	$-0.397222\pi$
$359$	12.0242			0.634611			0.317305	+	0.948323i	$0.397222\pi$
$360$	−4.71982			−0.248757
$361$	9.47546	+	16.4120i	0.498708	+	0.863788i
$362$	−9.86813			−0.518657
$363$	12.0324	−	20.8407i	0.631536	−	1.09385i
$364$	13.8613			0.726527
$365$	−3.90303	+	6.76024i	−0.204294	+	0.353847i
$366$	20.1414	−	34.8860i	1.05281	−	1.82352i
$367$	10.0341	−	17.3796i	0.523775	−	0.907206i	−0.475842	−	0.879531i	$-0.657856\pi$
$367$	10.0341	−	17.3796i	0.523775	−	0.907206i	0.999617	−	0.0276746i	$-0.00881021\pi$
$368$	1.76466	+	3.05648i	0.0919892	+	0.159330i
$369$	5.76547			0.300138
$370$	2.87371	−	5.36114i	0.149397	−	0.278712i
$371$	−13.1284			−0.681594
$372$	6.12935	+	10.6163i	0.317792	+	0.550432i
$373$	−6.00902	+	10.4079i	−0.311135	+	0.538902i	−0.978608	−	0.205732i	$-0.934043\pi$
$373$	−6.00902	+	10.4079i	−0.311135	+	0.538902i	0.667473	+	0.744634i	$0.267376\pi$
$374$	−5.96896	+	10.3385i	−0.308648	+	0.534594i
$375$	1.38923	−	2.40621i	0.0717395	−	0.124256i
$376$	11.9103			0.614228
$377$	13.6155	−	23.5828i	0.701236	−	1.21458i
$378$	15.8061			0.812976
$379$	−12.2840	−	21.2766i	−0.630989	−	1.09290i	−0.987350	−	0.158556i	$-0.949316\pi$
$379$	−12.2840	−	21.2766i	−0.630989	−	1.09290i	0.356361	−	0.934348i	$-0.384017\pi$
$380$	0.221543			0.0113649
$381$	10.8241			0.554535
$382$	13.4828	+	23.3528i	0.689838	+	1.19483i
$383$	−12.4388	+	21.5447i	−0.635595	+	1.10088i	0.350794	+	0.936453i	$0.385912\pi$
$383$	−12.4388	+	21.5447i	−0.635595	+	1.10088i	−0.986389	+	0.164430i	$0.947422\pi$
$384$	2.77846			0.141788
$385$	2.52932	+	4.38090i	0.128906	+	0.223272i
$386$	10.1798	+	17.6319i	0.518136	+	0.897439i
$387$	0.384453	+	0.665891i	0.0195428	+	0.0338492i
$388$	−4.19051	+	7.25817i	−0.212741	+	0.368478i
$389$	11.4396	−	19.8141i	0.580013	−	1.00461i	−0.415464	−	0.909610i	$-0.636381\pi$
$389$	11.4396	−	19.8141i	0.580013	−	1.00461i	0.995477	−	0.0950026i	$-0.0302859\pi$
$390$	5.82157	+	10.0833i	0.294787	+	0.510586i
$391$	13.7750	+	23.8590i	0.696633	+	1.20660i
$392$	−1.97068	−	3.41332i	−0.0995345	−	0.172399i
$393$	−14.7880			−0.745956
$394$	−0.427568	+	0.740570i	−0.0215406	+	0.0373094i
$395$	2.52932	+	4.38090i	0.127264	+	0.220427i
$396$	7.21811			0.362723
$397$	25.5681			1.28323			0.641613	−	0.767029i	$-0.278266\pi$
$397$	25.5681			1.28323			0.641613	+	0.767029i	$0.278266\pi$
$398$	−12.7173	−	22.0270i	−0.637460	−	1.10411i
$399$	−2.03609			−0.101932
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	16.4232			0.820136			0.410068	−	0.912055i	$-0.365505\pi$
$401$	16.4232			0.820136			0.410068	+	0.912055i	$0.365505\pi$
$402$	−10.6612	+	18.4657i	−0.531732	+	0.920987i
$403$	9.24436	−	16.0117i	0.460495	−	0.797600i
$404$	3.12457	−	5.41191i	0.155453	−	0.269253i
$405$	−0.441367	−	0.764470i	−0.0219317	−	0.0379868i
$406$	−21.4948			−1.06677
$407$	−4.39481	+	8.19888i	−0.217843	+	0.406403i
$408$	21.6888			1.07376
$409$	−9.19528	−	15.9267i	−0.454677	−	0.787525i	0.543992	−	0.839090i	$-0.316912\pi$
$409$	−9.19528	−	15.9267i	−0.454677	−	0.787525i	−0.998670	+	0.0515658i	$0.983579\pi$
$410$	0.610771	−	1.05789i	0.0301639	−	0.0522453i
$411$	11.1341	−	19.2849i	0.549206	−	0.951252i
$412$	4.48448	−	7.76735i	0.220935	−	0.382670i
$413$	3.59301			0.176800
$414$	8.32888	−	14.4260i	0.409342	−	0.709001i
$415$	9.43965			0.463374
$416$	−2.09525	−	3.62909i	−0.102728	−	0.177931i
$417$	−12.9008			−0.631754
$418$	−0.338809			−0.0165717
$419$	17.1863	+	29.7675i	0.839604	+	1.45424i	0.890226	+	0.455519i	$0.150546\pi$
$419$	17.1863	+	29.7675i	0.839604	+	1.45424i	−0.0506225	+	0.998718i	$0.516121\pi$
$420$	4.59525	−	7.95921i	0.224225	−	0.388370i
$421$	24.5941			1.19864			0.599321	−	0.800509i	$-0.295437\pi$
$421$	24.5941			1.19864			0.599321	+	0.800509i	$0.295437\pi$
$422$	5.44614	+	9.43300i	0.265114	+	0.459191i
$423$	−28.1073	−	48.6833i	−1.36663	−	2.36706i
$424$	1.98448	+	3.43722i	0.0963750	+	0.166926i
$425$	−3.90303	+	6.76024i	−0.189325	+	0.327920i
$426$	−19.6888	+	34.1020i	−0.953925	+	1.65225i
$427$	23.9785	+	41.5320i	1.16040	+	2.00987i
$428$	4.10905	+	7.11709i	0.198619	+	0.344017i
$429$	−8.90303	−	15.4205i	−0.429842	−	0.744509i
$430$	0.162910			0.00785620
$431$	−0.808583	+	1.40051i	−0.0389481	+	0.0674600i	−0.884842	−	0.465891i	$-0.845734\pi$
$431$	−0.808583	+	1.40051i	−0.0389481	+	0.0674600i	0.845894	+	0.533351i	$0.179067\pi$
$432$	−2.38923	−	4.13827i	−0.114952	−	0.199102i
$433$	−0.234533			−0.0112709			−0.00563546	−	0.999984i	$-0.501794\pi$
$433$	−0.234533			−0.0112709			−0.00563546	+	0.999984i	$0.501794\pi$
$434$	−14.5941			−0.700537
$435$	−9.02760	−	15.6363i	−0.432840	−	0.749701i
$436$	−10.0552			−0.481557
$437$	−0.390947	+	0.677141i	−0.0187016	+	0.0323920i
$438$	−21.6888			−1.03633
$439$	−8.93884	+	15.4825i	−0.426628	+	0.738941i	−0.996571	−	0.0827435i	$-0.973632\pi$
$439$	−8.93884	+	15.4825i	−0.426628	+	0.738941i	0.569943	+	0.821684i	$0.306965\pi$
$440$	0.764658	−	1.32443i	0.0364537	−	0.0631396i
$441$	−9.30128	+	16.1103i	−0.442918	+	0.767157i
$442$	−16.3557	−	28.3288i	−0.777960	−	1.34747i
$443$	24.6612			1.17169			0.585844	−	0.810424i	$-0.300763\pi$
$443$	24.6612			1.17169			0.585844	+	0.810424i	$0.300763\pi$
$444$	16.8923	−	0.533080i	0.801672	−	0.0252988i
$445$	17.3354			0.821775
$446$	−8.15866	−	14.1312i	−0.386324	−	0.669133i
$447$	−30.5535	+	52.9202i	−1.44513	+	2.50304i
$448$	−1.65389	+	2.86462i	−0.0781388	+	0.135340i
$449$	−2.49351	+	4.31888i	−0.117676	+	0.203820i	−0.918846	−	0.394616i	$-0.870878\pi$
$449$	−2.49351	+	4.31888i	−0.117676	+	0.203820i	0.801170	+	0.598436i	$0.204211\pi$
$450$	4.71982			0.222495
$451$	−0.934063	+	1.61784i	−0.0439833	+	0.0761813i
$452$	8.73281			0.410757
$453$	−30.5199	−	52.8620i	−1.43395	−	2.48368i
$454$	−17.3319			−0.813428
$455$	−13.8613			−0.649825
$456$	0.307774	+	0.533080i	0.0144128	+	0.0249637i
$457$	14.2001	−	24.5952i	0.664251	−	1.15052i	−0.315237	−	0.949013i	$-0.602084\pi$
$457$	14.2001	−	24.5952i	0.664251	−	1.15052i	0.979488	−	0.201503i	$-0.0645826\pi$
$458$	11.1284			0.519998
$459$	−18.6504	−	32.3035i	−0.870528	−	1.50780i
$460$	−1.76466	−	3.05648i	−0.0822776	−	0.142509i
$461$	−2.30777	−	3.99718i	−0.107484	−	0.186167i	0.807267	−	0.590187i	$-0.200946\pi$
$461$	−2.30777	−	3.99718i	−0.107484	−	0.186167i	−0.914750	+	0.404020i	$0.867613\pi$
$462$	−7.02760	+	12.1722i	−0.326953	+	0.566300i
$463$	−14.6302	+	25.3402i	−0.679921	+	1.17766i	0.295083	+	0.955472i	$0.404653\pi$
$463$	−14.6302	+	25.3402i	−0.679921	+	1.17766i	−0.975004	+	0.222186i	$0.928681\pi$
$464$	3.24914	+	5.62768i	0.150838	+	0.261258i
$465$	−6.12935	−	10.6163i	−0.284242	−	0.492321i
$466$	6.18320	+	10.7096i	0.286431	+	0.496114i
$467$	−32.6543			−1.51106			−0.755531	−	0.655113i	$-0.772621\pi$
$467$	−32.6543			−1.51106			−0.755531	+	0.655113i	$0.772621\pi$
$468$	−9.88923	+	17.1286i	−0.457130	+	0.791772i
$469$	−12.6922	−	21.9836i	−0.586073	−	1.01511i
$470$	−11.9103			−0.549383
$471$	−46.5224			−2.14364
$472$	−0.543115	−	0.940703i	−0.0249989	−	0.0432994i
$473$	−0.249141			−0.0114555
$474$	−7.02760	+	12.1722i	−0.322788	+	0.559086i
$475$	−0.221543			−0.0101651
$476$	−12.9103	+	22.3613i	−0.591744	+	1.02493i
$477$	9.36641	−	16.2231i	0.428858	−	0.742804i
$478$	8.19051	−	14.1864i	0.374625	−	0.648870i
$479$	−20.8181	−	36.0581i	−0.951205	−	1.64754i	−0.742823	−	0.669488i	$-0.766514\pi$
$479$	−20.8181	−	36.0581i	−0.951205	−	1.64754i	−0.208382	−	0.978048i	$-0.566820\pi$
$480$	−2.77846			−0.126819
$481$	−13.4349	−	21.6619i	−0.612577	−	0.987697i
$482$	−12.7198			−0.579372
$483$	16.2181	+	28.0906i	0.737949	+	1.27817i
$484$	4.33060	−	7.50081i	0.196845	−	0.340946i
$485$	4.19051	−	7.25817i	0.190281	−	0.329577i
$486$	8.39400	−	14.5388i	0.380760	−	0.659495i
$487$	9.79145			0.443693			0.221846	−	0.975082i	$-0.428792\pi$
$487$	9.79145			0.443693			0.221846	+	0.975082i	$0.428792\pi$
$488$	7.24914	−	12.5559i	0.328153	−	0.568378i
$489$	19.1595			0.866421
$490$	1.97068	+	3.41332i	0.0890264	+	0.154198i
$491$	11.3569			0.512528			0.256264	−	0.966607i	$-0.417508\pi$
$491$	11.3569			0.512528			0.256264	+	0.966607i	$0.417508\pi$
$492$	3.39400			0.153014
$493$	25.3630	+	43.9300i	1.14229	+	1.97851i
$494$	0.464189	−	0.803998i	0.0208848	−	0.0361736i
$495$	−7.21811			−0.324430
$496$	2.20603	+	3.82095i	0.0990535	+	0.171566i
$497$	−23.4396	−	40.5987i	−1.05141	−	1.82110i
$498$	13.1138	+	22.7138i	0.587645	+	1.01783i
$499$	−9.32238	+	16.1468i	−0.417327	+	0.722832i	−0.995670	−	0.0929623i	$-0.970366\pi$
$499$	−9.32238	+	16.1468i	−0.417327	+	0.722832i	0.578343	+	0.815794i	$0.303700\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−18.1414	−	31.4219i	−0.810499	−	1.40383i
$502$	−6.41511	−	11.1113i	−0.286320	−	0.495921i
$503$	−10.9763	−	19.0115i	−0.489408	−	0.847679i	0.510518	−	0.859867i	$-0.329454\pi$
$503$	−10.9763	−	19.0115i	−0.489408	−	0.847679i	−0.999926	+	0.0121881i	$0.996120\pi$
$504$	15.6121			0.695419
$505$	−3.12457	+	5.41191i	−0.139042	+	0.240827i
$506$	2.69872	+	4.67432i	0.119973	+	0.207799i
$507$	12.6707			0.562727
$508$	3.89572			0.172845
$509$	−5.32807	−	9.22848i	−0.236162	−	0.409045i	0.723447	−	0.690379i	$-0.242556\pi$
$509$	−5.32807	−	9.22848i	−0.236162	−	0.409045i	−0.959610	+	0.281334i	$0.909223\pi$
$510$	−21.6888			−0.960396
$511$	12.9103	−	22.3613i	0.571119	−	0.989208i
$512$	1.00000			0.0441942
$513$	0.529317	−	0.916803i	0.0233699	−	0.0404779i
$514$	−1.59525	+	2.76306i	−0.0703636	+	0.121873i
$515$	−4.48448	+	7.76735i	−0.197610	+	0.342270i
$516$	0.226319	+	0.391996i	0.00996313	+	0.0172566i
$517$	18.2147			0.801080
$518$	−9.50559	+	17.7334i	−0.417651	+	0.779162i
$519$	0.443086			0.0194493
$520$	2.09525	+	3.62909i	0.0918830	+	0.159146i
$521$	−13.6449	+	23.6336i	−0.597792	+	1.03541i	0.395354	+	0.918529i	$0.370622\pi$
$521$	−13.6449	+	23.6336i	−0.597792	+	1.03541i	−0.993146	+	0.116878i	$0.962711\pi$
$522$	15.3354	−	26.5616i	0.671211	−	1.16257i
$523$	−17.3892	+	30.1190i	−0.760378	+	1.31701i	0.182278	+	0.983247i	$0.441653\pi$
$523$	−17.3892	+	30.1190i	−0.760378	+	1.31701i	−0.942656	+	0.333766i	$0.891680\pi$
$524$	−5.32238			−0.232509
$525$	−4.59525	+	7.95921i	−0.200553	+	0.347369i
$526$	8.35342			0.364226
$527$	17.2204	+	29.8265i	0.750130	+	1.29926i
$528$	4.24914			0.184920
$529$	−10.5439			−0.458431
$530$	−1.98448	−	3.43722i	−0.0862004	−	0.149303i
$531$	−2.56341	+	4.43995i	−0.111242	+	0.192678i
$532$	−0.732814			−0.0317715
$533$	−2.55944	−	4.43308i	−0.110862	−	0.192018i
$534$	24.0828	+	41.7126i	1.04216	+	1.80508i
$535$	−4.10905	−	7.11709i	−0.177650	−	0.307699i
$536$	−3.83709	+	6.64604i	−0.165737	+	0.287065i
$537$	25.7164	−	44.5421i	1.10974	−	1.92213i
$538$	−4.79875	−	8.31168i	−0.206889	−	0.358342i
$539$	−3.01380	−	5.22005i	−0.129814	−	0.224844i
$540$	2.38923	+	4.13827i	0.102816	+	0.178083i
$541$	−7.41043			−0.318599			−0.159300	−	0.987230i	$-0.550924\pi$
$541$	−7.41043			−0.318599			−0.159300	+	0.987230i	$0.550924\pi$
$542$	−0.0431154	+	0.0746781i	−0.00185197	+	0.00320770i
$543$	13.7091	+	23.7448i	0.588313	+	1.01899i
$544$	7.80605			0.334682
$545$	10.0552			0.430717
$546$	−19.2564	−	33.3531i	−0.824100	−	1.42738i
$547$	−2.88885			−0.123518			−0.0617591	−	0.998091i	$-0.519671\pi$
$547$	−2.88885			−0.123518			−0.0617591	+	0.998091i	$0.519671\pi$
$548$	4.00730	−	6.94085i	0.171184	−	0.296499i
$549$	−68.4293			−2.92049
$550$	−0.764658	+	1.32443i	−0.0326051	+	0.0564738i
$551$	−0.719824	+	1.24677i	−0.0306655	+	0.0531143i
$552$	4.90303	−	8.49229i	0.208687	−	0.361456i
$553$	−8.36641	−	14.4910i	−0.355776	−	0.616222i
$554$	−4.79307			−0.203638
$555$	−16.8923	+	0.533080i	−0.717038	+	0.0226280i
$556$	−4.64315			−0.196913
$557$	20.7936	+	36.0156i	0.881053	+	1.52603i	0.850172	+	0.526505i	$0.176498\pi$
$557$	20.7936	+	36.0156i	0.881053	+	1.52603i	0.0308810	+	0.999523i	$0.490169\pi$
$558$	10.4121	−	18.0342i	0.440777	−	0.763449i
$559$	0.341337	−	0.591213i	0.0144370	−	0.0250057i
$560$	1.65389	−	2.86462i	0.0698895	−	0.121052i
$561$	33.1690			1.40040
$562$	−3.52760	+	6.10998i	−0.148803	+	0.257734i
$563$	11.9639			0.504219			0.252109	−	0.967699i	$-0.418876\pi$
$563$	11.9639			0.504219			0.252109	+	0.967699i	$0.418876\pi$
$564$	−16.5462	−	28.6588i	−0.696720	−	1.20675i
$565$	−8.73281			−0.367392
$566$	−17.7198			−0.744820
$567$	1.45994	+	2.52869i	0.0613118	+	0.106195i
$568$	−7.08623	+	12.2737i	−0.297332	+	0.514994i
$569$	9.38789			0.393561			0.196780	−	0.980448i	$-0.436951\pi$
$569$	9.38789			0.393561			0.196780	+	0.980448i	$0.436951\pi$
$570$	−0.307774	−	0.533080i	−0.0128912	−	0.0223283i
$571$	4.32888	+	7.49783i	0.181158	+	0.313775i	0.942275	−	0.334840i	$-0.108682\pi$
$571$	4.32888	+	7.49783i	0.181158	+	0.313775i	−0.761117	+	0.648614i	$0.775349\pi$
$572$	−3.20431	−	5.55002i	−0.133979	−	0.232058i
$573$	37.4613	−	64.8848i	1.56497	−	2.71060i
$574$	−2.02029	+	3.49925i	−0.0843254	+	0.146056i
$575$	1.76466	+	3.05648i	0.0735913	+	0.127464i
$576$	−2.35991	−	4.08749i	−0.0983297	−	0.170312i
$577$	12.1832	+	21.1019i	0.507193	+	0.878485i	0.999965	+	0.00832623i	$0.00265035\pi$
$577$	12.1832	+	21.1019i	0.507193	+	0.878485i	−0.492772	+	0.870158i	$0.664016\pi$
$578$	43.9345			1.82743
$579$	28.2840	−	48.9894i	1.17544	−	2.03593i
$580$	−3.24914	−	5.62768i	−0.134913	−	0.233677i
$581$	−31.2242			−1.29540
$582$	23.2863			0.965248
$583$	3.03490	+	5.25660i	0.125693	+	0.217706i
$584$	−7.80605			−0.323017
$585$	9.88923	−	17.1286i	0.408869	−	0.708182i
$586$	−23.6854			−0.978433
$587$	11.2720	−	19.5236i	0.465244	−	0.805826i	−0.533969	−	0.845504i	$-0.679300\pi$
$587$	11.2720	−	19.5236i	0.465244	−	0.805826i	0.999212	+	0.0396785i	$0.0126334\pi$
$588$	−5.47546	+	9.48377i	−0.225804	+	0.391104i
$589$	−0.488729	+	0.846504i	−0.0201377	+	0.0348796i
$590$	0.543115	+	0.940703i	0.0223597	+	0.0387281i
$591$	2.37596			0.0977339
$592$	6.07974	−	0.191862i	0.249876	−	0.00788547i
$593$	6.60094			0.271068			0.135534	−	0.990773i	$-0.456725\pi$
$593$	6.60094			0.271068			0.135534	+	0.990773i	$0.456725\pi$
$594$	−3.65389	−	6.32872i	−0.149921	−	0.259670i
$595$	12.9103	−	22.3613i	0.529272	−	0.916726i
$596$	−10.9966	+	19.0466i	−0.450437	+	0.780179i
$597$	−35.3345	+	61.2011i	−1.44614	+	2.50479i
$598$	−14.7896			−0.604793
$599$	−10.8181	+	18.7376i	−0.442017	+	0.765596i	−0.997839	−	0.0657054i	$-0.979070\pi$
$599$	−10.8181	+	18.7376i	−0.442017	+	0.765596i	0.555822	+	0.831301i	$0.312404\pi$
$600$	2.77846			0.113430
$601$	9.91205	+	17.1682i	0.404321	+	0.700304i	0.994242	−	0.107156i	$-0.0341745\pi$
$601$	9.91205	+	17.1682i	0.404321	+	0.700304i	−0.589921	+	0.807461i	$0.700841\pi$
$602$	−0.538868			−0.0219626
$603$	36.2208			1.47502
$604$	−10.9845	−	19.0257i	−0.446952	−	0.774144i
$605$	−4.33060	+	7.50081i	−0.176064	+	0.304951i
$606$	−17.3630			−0.705322
$607$	−6.90647	−	11.9623i	−0.280325	−	0.485537i	0.691140	−	0.722721i	$-0.257109\pi$
$607$	−6.90647	−	11.9623i	−0.280325	−	0.485537i	−0.971465	+	0.237184i	$0.923775\pi$
$608$	0.110771	+	0.191862i	0.00449238	+	0.00778102i
$609$	29.8613	+	51.7212i	1.21004	+	2.09585i
$610$	−7.24914	+	12.5559i	−0.293509	+	0.508373i
$611$	−24.9552	+	43.2236i	−1.00958	+	1.74864i
$612$	−18.4216	−	31.9072i	−0.744649	−	1.28977i
$613$	1.39095	+	2.40919i	0.0561798	+	0.0973063i	0.892748	−	0.450557i	$-0.148775\pi$
$613$	1.39095	+	2.40919i	0.0561798	+	0.0973063i	−0.836568	+	0.547864i	$0.815441\pi$
$614$	5.22632	+	9.05225i	0.210917	+	0.365319i
$615$	−3.39400			−0.136859
$616$	−2.52932	+	4.38090i	−0.101909	+	0.176512i
$617$	−16.8061	−	29.1089i	−0.676586	−	1.17188i	−0.976003	−	0.217759i	$-0.930125\pi$
$617$	−16.8061	−	29.1089i	−0.676586	−	1.17188i	0.299416	−	0.954123i	$-0.403208\pi$
$618$	−24.9199			−1.00242
$619$	−29.1982			−1.17358			−0.586788	−	0.809740i	$-0.699608\pi$
$619$	−29.1982			−1.17358			−0.586788	+	0.809740i	$0.699608\pi$
$620$	−2.20603	−	3.82095i	−0.0885961	−	0.153453i
$621$	−16.8647			−0.676757
$622$	−4.70774	+	8.15405i	−0.188763	+	0.326948i
$623$	−57.3415			−2.29734
$624$	−5.82157	+	10.0833i	−0.233049	+	0.403653i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.27674	+	9.13958i	−0.210901	+	0.365291i
$627$	0.470683	+	0.815248i	0.0187973	+	0.0325579i
$628$	−16.7440			−0.668158
$629$	47.4588	−	1.49768i	1.89230	−	0.0597165i
$630$	−15.6121			−0.622001
$631$	15.9664	+	27.6547i	0.635614	+	1.10092i	0.986385	+	0.164454i	$0.0525862\pi$
$631$	15.9664	+	27.6547i	0.635614	+	1.10092i	−0.350771	+	0.936461i	$0.614080\pi$
$632$	−2.52932	+	4.38090i	−0.100611	+	0.174263i
$633$	15.1319	−	26.2092i	0.601438	−	1.04172i
$634$	−16.4893	+	28.5602i	−0.654872	+	1.13427i
$635$	−3.89572			−0.154597
$636$	5.51380	−	9.55018i	0.218636	−	0.378689i
$637$	16.5163			0.654401
$638$	4.96896	+	8.60650i	0.196723	+	0.340735i
$639$	66.8915			2.64619
$640$	−1.00000			−0.0395285
$641$	−17.2750	−	29.9212i	−0.682322	−	1.18182i	−0.974270	−	0.225383i	$-0.927637\pi$
$641$	−17.2750	−	29.9212i	−0.682322	−	1.18182i	0.291948	−	0.956434i	$-0.405697\pi$
$642$	11.4168	−	19.7745i	0.450586	−	0.780438i
$643$	−28.9801			−1.14286			−0.571432	−	0.820649i	$-0.693612\pi$
$643$	−28.9801			−1.14286			−0.571432	+	0.820649i	$0.693612\pi$
$644$	5.83709	+	10.1101i	0.230014	+	0.398395i
$645$	−0.226319	−	0.391996i	−0.00891130	−	0.0154348i
$646$	0.864688	+	1.49768i	0.0340207	+	0.0589256i
$647$	−9.06169	+	15.6953i	−0.356252	+	0.617046i	−0.987331	−	0.158672i	$-0.949279\pi$
$647$	−9.06169	+	15.6953i	−0.356252	+	0.617046i	0.631080	+	0.775718i	$0.282612\pi$
$648$	0.441367	−	0.764470i	0.0173385	−	0.0300312i
$649$	−0.830595	−	1.43863i	−0.0326037	−	0.0564713i
$650$	−2.09525	−	3.62909i	−0.0821826	−	0.142344i
$651$	20.2745	+	35.1164i	0.794620	+	1.37632i
$652$	6.89572			0.270057
$653$	10.0462	−	17.4005i	0.393137	−	0.680933i	−0.599724	−	0.800207i	$-0.704723\pi$
$653$	10.0462	−	17.4005i	0.393137	−	0.680933i	0.992861	+	0.119273i	$0.0380564\pi$
$654$	13.9690	+	24.1950i	0.546230	+	0.946098i
$655$	5.32238			0.207963
$656$	1.22154			0.0476932
$657$	18.4216	+	31.9072i	0.718695	+	1.24482i
$658$	39.3967			1.53584
$659$	7.04870	−	12.2087i	0.274578	−	0.475584i	−0.695450	−	0.718574i	$-0.744795\pi$
$659$	7.04870	−	12.2087i	0.274578	−	0.475584i	0.970029	+	0.242991i	$0.0781284\pi$
$660$	−4.24914			−0.165398
$661$	−23.7221	+	41.0878i	−0.922682	+	1.59813i	−0.127434	+	0.991847i	$0.540674\pi$
$661$	−23.7221	+	41.0878i	−0.922682	+	1.59813i	−0.795248	+	0.606284i	$0.792659\pi$
$662$	−1.95860	+	3.39240i	−0.0761233	+	0.131849i
$663$	−45.4435	+	78.7105i	−1.76488	+	3.05686i
$664$	4.71982	+	8.17497i	0.183165	+	0.317251i
$665$	0.732814			0.0284173
$666$	−15.1319	−	24.3981i	−0.586348	−	0.945406i
$667$	22.9345			0.888027
$668$	−6.52932	−	11.3091i	−0.252627	−	0.437563i
$669$	−22.6685	+	39.2630i	−0.876415	+	1.51799i
$670$	3.83709	−	6.64604i	0.148240	−	0.256759i
$671$	11.0862	−	19.2019i	0.427979	−	0.741282i
$672$	9.19051			0.354532
$673$	15.5056	−	26.8565i	0.597696	−	1.03524i	−0.395464	−	0.918482i	$-0.629416\pi$
$673$	15.5056	−	26.8565i	0.597696	−	1.03524i	0.993160	−	0.116759i	$-0.0372505\pi$
$674$	6.44309			0.248178
$675$	−2.38923	−	4.13827i	−0.0919615	−	0.159282i
$676$	4.56035			0.175398
$677$	−13.5630			−0.521270			−0.260635	−	0.965437i	$-0.583932\pi$
$677$	−13.5630			−0.521270			−0.260635	+	0.965437i	$0.583932\pi$
$678$	−12.1319	−	21.0130i	−0.465922	−	0.807000i
$679$	−13.8613	+	24.0084i	−0.531946	+	0.921357i
$680$	−7.80605			−0.299349
$681$	24.0780	+	41.7043i	0.922672	+	1.59811i
$682$	3.37371	+	5.84344i	0.129186	+	0.223757i
$683$	−17.8875	−	30.9821i	−0.684447	−	1.18550i	−0.973610	−	0.228217i	$-0.926711\pi$
$683$	−17.8875	−	30.9821i	−0.684447	−	1.18550i	0.289164	−	0.957280i	$-0.406623\pi$
$684$	0.522822	−	0.905554i	0.0199906	−	0.0346247i
$685$	−4.00730	+	6.94085i	−0.153111	+	0.265196i
$686$	5.05863	+	8.76181i	0.193140	+	0.334527i
$687$	−15.4599	−	26.7774i	−0.589834	−	1.02162i
$688$	0.0814549	+	0.141084i	0.00310544	+	0.00537878i
$689$	−16.6320			−0.633628
$690$	−4.90303	+	8.49229i	−0.186655	+	0.323296i
$691$	−6.91602	−	11.9789i	−0.263098	−	0.455699i	0.703966	−	0.710234i	$-0.251411\pi$
$691$	−6.91602	−	11.9789i	−0.263098	−	0.455699i	−0.967063	+	0.254535i	$0.918077\pi$
$692$	0.159472			0.00606221
$693$	23.8759			0.906969
$694$	−11.2215	−	19.4363i	−0.425964	−	0.737791i
$695$	4.64315			0.176125
$696$	9.02760	−	15.6363i	0.342190	−	0.592691i
$697$	9.53543			0.361180
$698$	10.1138	−	17.5177i	0.382814	−	0.663053i
$699$	17.1798	−	29.7562i	0.649798	−	1.12548i
$700$	−1.65389	+	2.86462i	−0.0625110	+	0.108272i
$701$	−21.9820	−	38.0739i	−0.830247	−	1.43803i	−0.897842	−	0.440317i	$-0.854866\pi$
$701$	−21.9820	−	38.0739i	−0.830247	−	1.43803i	0.0675954	−	0.997713i	$-0.478467\pi$
$702$	20.0242			0.755763
$703$	0.710272	+	1.14522i	0.0267884	+	0.0431926i
$704$	1.52932			0.0576383
$705$	16.5462	+	28.6588i	0.623165	+	1.07935i
$706$	2.99270	−	5.18350i	0.112632	−	0.195084i
$707$	10.3354	−	17.9014i	0.388702	−	0.673251i
$708$	−1.50902	+	2.61370i	−0.0567126	+	0.0982290i
$709$	−10.2277			−0.384108			−0.192054	−	0.981384i	$-0.561515\pi$
$709$	−10.2277			−0.384108			−0.192054	+	0.981384i	$0.561515\pi$
$710$	7.08623	−	12.2737i	0.265942	−	0.460624i
$711$	23.8759			0.895415
$712$	8.66769	+	15.0129i	0.324835	+	0.562631i
$713$	15.5715			0.583158
$714$	71.7416			2.68486
$715$	3.20431	+	5.55002i	0.119834	+	0.207559i
$716$	9.25564	−	16.0312i	0.345899	−	0.599115i
$717$	−45.5139			−1.69975
$718$	−6.01208	−	10.4132i	−0.224369	−	0.388618i
$719$	−13.8216	−	23.9397i	−0.515458	−	0.892799i	−0.999839	−	0.0179419i	$-0.994289\pi$
$719$	−13.8216	−	23.9397i	−0.515458	−	0.892799i	0.484381	−	0.874857i	$-0.339045\pi$
$720$	2.35991	+	4.08749i	0.0879487	+	0.152332i
$721$	14.8337	−	25.6926i	0.552434	−	0.956844i
$722$	9.47546	−	16.4120i	0.352640	−	0.610791i
$723$	17.6707	+	30.6066i	0.657182	+	1.13827i
$724$	4.93406	+	8.54605i	0.183373	+	0.317611i
$725$	3.24914	+	5.62768i	0.120670	+	0.209007i
$726$	−24.0647			−0.893127
$727$	−12.4461	+	21.5574i	−0.461602	+	0.799518i	−0.999041	−	0.0437846i	$-0.986058\pi$
$727$	−12.4461	+	21.5574i	−0.461602	+	0.799518i	0.537439	+	0.843303i	$0.319392\pi$
$728$	−6.93063	−	12.0042i	−0.256866	−	0.444905i
$729$	−43.9966			−1.62950
$730$	7.80605			0.288915
$731$	0.635841	+	1.10131i	0.0235174	+	0.0407334i
$732$	−40.2829			−1.48890
$733$	2.69872	−	4.67432i	0.0996795	−	0.172650i	−0.811872	−	0.583835i	$-0.801552\pi$
$733$	2.69872	−	4.67432i	0.0996795	−	0.172650i	0.911552	+	0.411185i	$0.134885\pi$
$734$	−20.0682			−0.740730
$735$	5.47546	−	9.48377i	0.201965	−	0.349814i
$736$	1.76466	−	3.05648i	0.0650462	−	0.112663i
$737$	−5.86813	+	10.1639i	−0.216155	+	0.374392i
$738$	−2.88273	−	4.99304i	−0.106115	−	0.183796i
$739$	−16.3794			−0.602526			−0.301263	−	0.953541i	$-0.597408\pi$
$739$	−16.3794			−0.602526			−0.301263	+	0.953541i	$0.597408\pi$
$740$	−6.07974	+	0.191862i	−0.223496	+	0.00705298i
$741$	−2.57946			−0.0947587
$742$	6.56422	+	11.3696i	0.240980	+	0.417390i
$743$	8.38021	−	14.5149i	0.307440	−	0.532502i	−0.670362	−	0.742035i	$-0.733861\pi$
$743$	8.38021	−	14.5149i	0.307440	−	0.532502i	0.977802	+	0.209533i	$0.0671944\pi$
$744$	6.12935	−	10.6163i	0.224713	−	0.389214i
$745$	10.9966	−	19.0466i	0.402883	−	0.697814i
$746$	12.0180			0.440012
$747$	22.2767	−	38.5844i	0.815063	−	1.41173i
$748$	11.9379			0.436494
$749$	13.5918	+	23.5417i	0.496634	+	0.860196i
$750$	−2.77846			−0.101455
$751$	1.15174			0.0420276			0.0210138	−	0.999779i	$-0.493311\pi$
$751$	1.15174			0.0420276			0.0210138	+	0.999779i	$0.493311\pi$
$752$	−5.95517	−	10.3146i	−0.217163	−	0.376137i
$753$	−17.8241	+	30.8722i	−0.649546	+	1.12505i
$754$	−27.2311			−0.991698
$755$	10.9845	+	19.0257i	0.399766	+	0.692415i
$756$	−7.90303	−	13.6884i	−0.287430	−	0.497844i
$757$	24.0186	+	41.6014i	0.872970	+	1.51203i	0.858910	+	0.512127i	$0.171142\pi$
$757$	24.0186	+	41.6014i	0.872970	+	1.51203i	0.0140603	+	0.999901i	$0.495524\pi$
$758$	−12.2840	+	21.2766i	−0.446177	+	0.772800i
$759$	7.49828	−	12.9874i	0.272170	−	0.471413i
$760$	−0.110771	−	0.191862i	−0.00401810	−	0.00695956i
$761$	−5.02110	−	8.69681i	−0.182015	−	0.315259i	0.760552	−	0.649277i	$-0.224929\pi$
$761$	−5.02110	−	8.69681i	−0.182015	−	0.315259i	−0.942567	+	0.334018i	$0.891595\pi$
$762$	−5.41205	−	9.37395i	−0.196058	−	0.339582i
$763$	−33.2603			−1.20410
$764$	13.4828	−	23.3528i	0.487789	−	0.844876i
$765$	18.4216	+	31.9072i	0.666034	+	1.15361i
$766$	24.8777			0.898867
$767$	4.55186			0.164358
$768$	−1.38923	−	2.40621i	−0.0501295	−	0.0868268i
$769$	45.6604			1.64656			0.823279	−	0.567638i	$-0.192142\pi$
$769$	45.6604			1.64656			0.823279	+	0.567638i	$0.192142\pi$
$770$	2.52932	−	4.38090i	0.0911502	−	0.157877i
$771$	8.86469			0.319254
$772$	10.1798	−	17.6319i	0.366378	−	0.634585i
$773$	−19.5721	+	33.8998i	−0.703958	+	1.21929i	0.263109	+	0.964766i	$0.415252\pi$
$773$	−19.5721	+	33.8998i	−0.703958	+	1.21929i	−0.967066	+	0.254524i	$0.918081\pi$
$774$	0.384453	−	0.665891i	0.0138189	−	0.0239350i
$775$	2.20603	+	3.82095i	0.0792428	+	0.137252i
$776$	8.38101			0.300861
$777$	55.8759	−	1.76331i	2.00454	−	0.0632583i
$778$	−22.8793			−0.820262
$779$	0.135312	+	0.234367i	0.00484806	+	0.00839708i
$780$	5.82157	−	10.0833i	0.208446	−	0.361039i
$781$	−10.8371	+	18.7704i	−0.387782	+	0.671657i
$782$	13.7750	−	23.8590i	0.492594	−	0.853197i
$783$	−31.0518			−1.10970
$784$	−1.97068	+	3.41332i	−0.0703816	+	0.121904i
$785$	16.7440			0.597618
$786$	7.39400	+	12.8068i	0.263735	+	0.456803i
$787$	−23.5044			−0.837841			−0.418921	−	0.908023i	$-0.637591\pi$
$787$	−23.5044			−0.837841			−0.418921	+	0.908023i	$0.637591\pi$
$788$	0.855136			0.0304630
$789$	−11.6048	−	20.1001i	−0.413142	−	0.715583i
$790$	2.52932	−	4.38090i	0.0899890	−	0.155866i
$791$	28.8862			1.02707
$792$	−3.60905	−	6.25106i	−0.128242	−	0.222122i
$793$	30.3776	+	52.6155i	1.07874	+	1.86843i
$794$	−12.7840	−	22.1426i	−0.453689	−	0.785812i
$795$	−5.51380	+	9.55018i	−0.195554	+	0.338710i
$796$	−12.7173	+	22.0270i	−0.450753	+	0.780726i
$797$	6.81852	+	11.8100i	0.241524	+	0.418332i	0.961149	−	0.276031i	$-0.0890193\pi$
$797$	6.81852	+	11.8100i	0.241524	+	0.418332i	−0.719624	+	0.694363i	$0.755686\pi$
$798$	1.01805	+	1.76331i	0.0360384	+	0.0624204i
$799$	−46.4863	−	80.5167i	−1.64457	−	2.84848i
$800$	1.00000			0.0353553
$801$	40.9100	−	70.8581i	1.44548	−	2.50365i
$802$	−8.21161	−	14.2229i	−0.289962	−	0.502229i
$803$	−11.9379			−0.421280
$804$	21.3224			0.751982
$805$	−5.83709	−	10.1101i	−0.205730	−	0.356336i
$806$	−18.4887			−0.651238
$807$	−13.3331	+	23.0936i	−0.469348	+	0.812935i
$808$	−6.24914			−0.219844
$809$	10.2294	−	17.7178i	0.359646	−	0.622925i	−0.628256	−	0.778007i	$-0.716231\pi$
$809$	10.2294	−	17.7178i	0.359646	−	0.622925i	0.987902	+	0.155082i	$0.0495642\pi$
$810$	−0.441367	+	0.764470i	−0.0155080	+	0.0268607i
$811$	19.7961	−	34.2879i	0.695136	−	1.20401i	−0.274999	−	0.961445i	$-0.588678\pi$
$811$	19.7961	−	34.2879i	0.695136	−	1.20401i	0.970135	−	0.242566i	$-0.0779891\pi$
$812$	10.7474	+	18.6151i	0.377161	+	0.653261i
$813$	0.239589			0.00840274
$814$	9.29784	−	0.293417i	0.325889	−	0.0102843i
$815$	−6.89572			−0.241547
$816$	−10.8444	−	18.7830i	−0.379630	−	0.657538i
$817$	−0.0180457	+	0.0312561i	−0.000631341	+	0.00109351i
$818$	−9.19528	+	15.9267i	−0.321506	+	0.556864i
$819$	−32.7113	+	56.6577i	−1.14303	+	1.97978i
$820$	−1.22154			−0.0426581
$821$	24.7440	−	42.8578i	0.863571	−	1.49575i	−0.00488814	−	0.999988i	$-0.501556\pi$
$821$	24.7440	−	42.8578i	0.863571	−	1.49575i	0.868459	−	0.495761i	$-0.165111\pi$
$822$	−22.2682			−0.776694
$823$	18.4565	+	31.9676i	0.643353	+	1.11432i	0.984679	+	0.174376i	$0.0557907\pi$
$823$	18.4565	+	31.9676i	0.643353	+	1.11432i	−0.341326	+	0.939945i	$0.610876\pi$
$824$	−8.96896			−0.312449
$825$	4.24914			0.147936
$826$	−1.79650	−	3.11163i	−0.0625083	−	0.108268i
$827$	−21.9966	+	38.0992i	−0.764895	+	1.32484i	0.175406	+	0.984496i	$0.443876\pi$
$827$	−21.9966	+	38.0992i	−0.764895	+	1.32484i	−0.940302	+	0.340342i	$0.889457\pi$
$828$	−16.6578			−0.578897
$829$	−5.01074	−	8.67886i	−0.174030	−	0.301429i	0.765795	−	0.643085i	$-0.222346\pi$
$829$	−5.01074	−	8.67886i	−0.174030	−	0.301429i	−0.939825	+	0.341656i	$0.889012\pi$
$830$	−4.71982	−	8.17497i	−0.163827	−	0.283758i
$831$	6.65866	+	11.5331i	0.230986	+	0.400080i
$832$	−2.09525	+	3.62909i	−0.0726399	+	0.125816i
$833$	−15.3833	+	26.6446i	−0.532998	+	0.923180i
$834$	6.45039	+	11.1724i	0.223359	+	0.386869i
$835$	6.52932	+	11.3091i	0.225956	+	0.391368i
$836$	0.169405	+	0.293417i	0.00585898	+	0.0101481i
$837$	−21.0828			−0.728728
$838$	17.1863	−	29.7675i	0.593690	−	1.02830i
$839$	1.17499	+	2.03514i	0.0405651	+	0.0702609i	0.885595	−	0.464458i	$-0.153751\pi$
$839$	1.17499	+	2.03514i	0.0405651	+	0.0702609i	−0.845030	+	0.534719i	$0.820418\pi$
$840$	−9.19051			−0.317103
$841$	13.2277			0.456126
$842$	−12.2970	−	21.2991i	−0.423784	−	0.734015i
$843$	19.6026			0.675148
$844$	5.44614	−	9.43300i	0.187464	−	0.324697i
$845$	−4.56035			−0.156881
$846$	−28.1073	+	48.6833i	−0.966350	+	1.67377i
$847$	14.3246	−	24.8110i	0.492200	−	0.852516i
$848$	1.98448	−	3.43722i	0.0681474	−	0.118035i
$849$	24.6169	+	42.6377i	0.844849	+	1.46332i
$850$	7.80605			0.267745
$851$	10.1422	−	18.9211i	0.347671	−	0.648609i
$852$	39.3776			1.34905
$853$	−10.1229	−	17.5333i	−0.346600	−	0.600329i	0.639043	−	0.769171i	$-0.279330\pi$
$853$	−10.1229	−	17.5333i	−0.346600	−	0.600329i	−0.985643	+	0.168842i	$0.945997\pi$
$854$	23.9785	−	41.5320i	0.820528	−	1.42120i
$855$	−0.522822	+	0.905554i	−0.0178801	+	0.0309693i
$856$	4.10905	−	7.11709i	0.140445	−	0.243257i
$857$	7.48711			0.255755			0.127877	−	0.991790i	$-0.459184\pi$
$857$	7.48711			0.255755			0.127877	+	0.991790i	$0.459184\pi$
$858$	−8.90303	+	15.4205i	−0.303944	+	0.526447i
$859$	−18.2508			−0.622708			−0.311354	−	0.950294i	$-0.600782\pi$
$859$	−18.2508			−0.622708			−0.311354	+	0.950294i	$0.600782\pi$
$860$	−0.0814549	−	0.141084i	−0.00277759	−	0.00481092i
$861$	11.2266			0.382601
$862$	1.61717			0.0550809
$863$	−12.5358	−	21.7127i	−0.426724	−	0.739108i	0.569856	−	0.821745i	$-0.306999\pi$
$863$	−12.5358	−	21.7127i	−0.426724	−	0.739108i	−0.996580	+	0.0826371i	$0.973666\pi$
$864$	−2.38923	+	4.13827i	−0.0812832	+	0.140787i
$865$	−0.159472			−0.00542221
$866$	0.117266	+	0.203111i	0.00398487	+	0.00690200i
$867$	−61.0350	−	105.716i	−2.07286	−	3.59030i
$868$	7.29703	+	12.6388i	0.247677	+	0.428990i
$869$	−3.86813	+	6.69979i	−0.131217	+	0.227275i
$870$	−9.02760	+	15.6363i	−0.306064	+	0.530119i
$871$	−16.0794	−	27.8503i	−0.544828	−	0.943670i
$872$	5.02760	+	8.70805i	0.170256	+	0.294892i
$873$	−19.7785	−	34.2573i	−0.669399	−	1.15943i
$874$	0.781895			0.0264480
$875$	1.65389	−	2.86462i	0.0559116	−	0.0968417i
$876$	10.8444	+	18.7830i	0.366398	+	0.634620i
$877$	3.89390			0.131488			0.0657439	−	0.997837i	$-0.479058\pi$
$877$	3.89390			0.131488			0.0657439	+	0.997837i	$0.479058\pi$
$878$	17.8777			0.603342
$879$	32.9044	+	56.9920i	1.10984	+	1.92229i
$880$	−1.52932			−0.0515533
$881$	18.0307	−	31.2300i	0.607468	−	1.05217i	−0.384188	−	0.923255i	$-0.625519\pi$
$881$	18.0307	−	31.2300i	0.607468	−	1.05217i	0.991656	−	0.128911i	$-0.0411481\pi$
$882$	18.6026			0.626381
$883$	−12.5893	+	21.8053i	−0.423663	+	0.733806i	−0.996295	−	0.0860067i	$-0.972589\pi$
$883$	−12.5893	+	21.8053i	−0.423663	+	0.733806i	0.572631	+	0.819813i	$0.305923\pi$
$884$	−16.3557	+	28.3288i	−0.550101	+	0.952802i
$885$	1.50902	−	2.61370i	0.0507252	−	0.0878587i
$886$	−12.3306	−	21.3572i	−0.414254	−	0.717510i
$887$	1.94480			0.0653002			0.0326501	−	0.999467i	$-0.489605\pi$
$887$	1.94480			0.0653002			0.0326501	+	0.999467i	$0.489605\pi$
$888$	−8.90780	−	14.3626i	−0.298926	−	0.481978i
$889$	12.8862			0.432188
$890$	−8.66769	−	15.0129i	−0.290541	−	0.503233i
$891$	0.674990	−	1.16912i	0.0226130	−	0.0391669i
$892$	−8.15866	+	14.1312i	−0.273172	+	0.473148i
$893$	1.31932	−	2.28514i	0.0441495	−	0.0764692i
$894$	61.1070			2.04372
$895$	−9.25564	+	16.0312i	−0.309382	+	0.535865i
$896$	3.30777			0.110505
$897$	20.5462	+	35.5870i	0.686017	+	1.18822i
$898$	4.98701			0.166419
$899$	28.6707			0.956223
$900$	−2.35991	−	4.08749i	−0.0786637	−	0.136250i
$901$	15.4910	−	26.8312i	0.516079	−	0.893876i
$902$	1.86813			0.0622018
$903$	0.748611	+	1.29663i	0.0249122	+	0.0431492i
$904$	−4.36641	−	7.56284i	−0.145225	−	0.251536i
$905$	−4.93406	−	8.54605i	−0.164014	−	0.284080i
$906$	−30.5199	+	52.8620i	−1.01396	+	1.75622i
$907$	0.944805	−	1.63645i	0.0313717	−	0.0543374i	−0.849913	−	0.526923i	$-0.823346\pi$
$907$	0.944805	−	1.63645i	0.0313717	−	0.0543374i	0.881285	+	0.472585i	$0.156679\pi$
$908$	8.66597	+	15.0099i	0.287590	+	0.498121i
$909$	14.7474	+	25.5433i	0.489141	+	0.847217i
$910$	6.93063	+	12.0042i	0.229748	+	0.397935i
$911$	38.3691			1.27122			0.635612	−	0.772008i	$-0.280748\pi$
$911$	38.3691			1.27122			0.635612	+	0.772008i	$0.280748\pi$
$912$	0.307774	−	0.533080i	0.0101914	−	0.0176520i
$913$	7.21811	+	12.5021i	0.238884	+	0.413760i
$914$	−28.4001			−0.939392
$915$	40.2829			1.33171
$916$	−5.56422	−	9.63751i	−0.183847	−	0.318432i
$917$	−17.6052			−0.581376
$918$	−18.6504	+	32.3035i	−0.615557	+	1.06618i
$919$	−23.3776			−0.771155			−0.385578	−	0.922675i	$-0.625998\pi$
$919$	−23.3776			−0.771155			−0.385578	+	0.922675i	$0.625998\pi$
$920$	−1.76466	+	3.05648i	−0.0581791	+	0.100769i
$921$	14.5211	−	25.1513i	0.478487	−	0.828763i
$922$	−2.30777	+	3.99718i	−0.0760025	+	0.131640i
$923$	−29.6949	−	51.4331i	−0.977420	−	1.69294i
$924$	14.0552			0.462382
$925$	6.07974	−	0.191862i	0.199900	−	0.00630838i
$926$	29.2603			0.961553
$927$	21.1660	+	36.6605i	0.695182	+	1.20409i
$928$	3.24914	−	5.62768i	0.106658	−	0.184738i
$929$	−15.6138	+	27.0439i	−0.512273	+	0.887283i	0.487626	+	0.873053i	$0.337863\pi$
$929$	−15.6138	+	27.0439i	−0.512273	+	0.887283i	−0.999899	+	0.0142302i	$0.995470\pi$
$930$	−6.12935	+	10.6163i	−0.200989	+	0.348123i
$931$	−0.873182			−0.0286174
$932$	6.18320	−	10.7096i	0.202538	−	0.350805i
$933$	26.1605			0.856457
$934$	16.3272	+	28.2795i	0.534241	+	0.925332i
$935$	−11.9379			−0.390412
$936$	19.7785			0.646479
$937$	−15.3940	−	26.6632i	−0.502900	−	0.871049i	−0.999994	−	0.00335211i	$-0.998933\pi$
$937$	−15.3940	−	26.6632i	−0.502900	−	0.871049i	0.497094	−	0.867697i	$-0.334400\pi$
$938$	−12.6922	+	21.9836i	−0.414416	+	0.717789i
$939$	29.3224			0.956900
$940$	5.95517	+	10.3146i	0.194236	+	0.336427i
$941$	−1.08398	−	1.87751i	−0.0353368	−	0.0612052i	0.847816	−	0.530290i	$-0.177917\pi$
$941$	−1.08398	−	1.87751i	−0.0353368	−	0.0612052i	−0.883153	+	0.469085i	$0.844584\pi$
$942$	23.2612	+	40.2896i	0.757892	+	1.31271i
$943$	2.15561	−	3.73362i	0.0701962	−	0.121583i
$944$	−0.543115	+	0.940703i	−0.0176769	+	0.0306173i
$945$	7.90303	+	13.6884i	0.257086	+	0.445285i
$946$	0.124570	+	0.215762i	0.00405013	+	0.00701503i
$947$	18.0876	+	31.3286i	0.587767	+	1.01804i	0.994524	+	0.104506i	$0.0333262\pi$
$947$	18.0876	+	31.3286i	0.587767	+	1.01804i	−0.406757	+	0.913536i	$0.633341\pi$
$948$	14.0552			0.456492
$949$	16.3557	−	28.3288i	0.530927	−	0.919593i
$950$	0.110771	+	0.191862i	0.00359390	+	0.00622482i
$951$	91.6294			2.97129
$952$	25.8207			0.836852
$953$	29.0574	+	50.3290i	0.941263	+	1.63032i	0.763066	+	0.646320i	$0.223693\pi$
$953$	29.0574	+	50.3290i	0.941263	+	1.63032i	0.178197	+	0.983995i	$0.442974\pi$
$954$	−18.7328			−0.606497
$955$	−13.4828	+	23.3528i	−0.436292	+	0.755680i
$956$	−16.3810			−0.529800
$957$	13.8061	−	23.9128i	0.446286	−	0.772991i
$958$	−20.8181	+	36.0581i	−0.672603	+	1.16498i
$959$	13.2553	−	22.9588i	0.428034	−	0.741377i
$960$	1.38923	+	2.40621i	0.0448372	+	0.0776602i
$961$	−11.5338			−0.372058
$962$	−12.0423	+	22.4659i	−0.388260	+	0.724329i
$963$	−38.7880			−1.24993
$964$	6.35991	+	11.0157i	0.204839	+	0.354792i
$965$	−10.1798	+	17.6319i	−0.327698	+	0.567590i
$966$	16.2181	−	28.0906i	0.521809	−	0.903800i
$967$	−1.42198	+	2.46295i	−0.0457279	+	0.0792030i	−0.887983	−	0.459875i	$-0.847894\pi$
$967$	−1.42198	+	2.46295i	−0.0457279	+	0.0792030i	0.842256	+	0.539078i	$0.181227\pi$
$968$	−8.66119			−0.278381
$969$	2.40250	−	4.16125i	0.0771794	−	0.133679i
$970$	−8.38101			−0.269098
$971$	8.40437	+	14.5568i	0.269709	+	0.467150i	0.968787	−	0.247896i	$-0.0797392\pi$
$971$	8.40437	+	14.5568i	0.269709	+	0.467150i	−0.699078	+	0.715046i	$0.746406\pi$
$972$	−16.7880			−0.538476
$973$	−15.3585			−0.492370
$974$	−4.89572	−	8.47964i	−0.156869	−	0.271705i
$975$	−5.82157	+	10.0833i	−0.186440	+	0.322923i
$976$	−14.4983			−0.464079
$977$	0.113828	+	0.197157i	0.00364170	+	0.00630760i	0.867841	−	0.496843i	$-0.165507\pi$
$977$	0.113828	+	0.197157i	0.00364170	+	0.00630760i	−0.864199	+	0.503150i	$0.832174\pi$
$978$	−9.57974	−	16.5926i	−0.306326	−	0.530573i
$979$	13.2556	+	22.9594i	0.423652	+	0.733787i
$980$	1.97068	−	3.41332i	0.0629512	−	0.109035i
$981$	23.7294	−	41.1005i	0.757621	−	1.31224i
$982$	−5.67843	−	9.83532i	−0.181206	−	0.313858i
$983$	−2.60905	−	4.51901i	−0.0832159	−	0.144134i	0.821414	−	0.570333i	$-0.193186\pi$
$983$	−2.60905	−	4.51901i	−0.0832159	−	0.144134i	−0.904630	+	0.426199i	$0.859852\pi$
$984$	−1.69700	−	2.93929i	−0.0540985	−	0.0937013i
$985$	−0.855136			−0.0272469
$986$	25.3630	−	43.9300i	0.807721	−	1.39901i
$987$	−54.7310	−	94.7969i	−1.74211	−	3.01742i
$988$	−0.928377			−0.0295356
$989$	0.574960			0.0182827
$990$	3.60905	+	6.25106i	0.114703	+	0.198672i
$991$	−7.23615			−0.229864			−0.114932	−	0.993373i	$-0.536665\pi$
$991$	−7.23615			−0.229864			−0.114932	+	0.993373i	$0.536665\pi$
$992$	2.20603	−	3.82095i	0.0700414	−	0.121315i
$993$	10.8838			0.345387
$994$	−23.4396	+	40.5987i	−0.743460	+	1.28771i
$995$	12.7173	−	22.0270i	0.403165	−	0.698303i
$996$	13.1138	−	22.7138i	0.415528	−	0.719715i
$997$	−26.6177	−	46.1032i	−0.842991	−	1.46010i	−0.887355	−	0.461088i	$-0.847459\pi$
$997$	−26.6177	−	46.1032i	−0.842991	−	1.46010i	0.0443638	−	0.999015i	$-0.485874\pi$
$998$	18.6448			0.590190
$999$	−13.7319	+	25.6180i	−0.434458	+	0.810516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.e.f.211.1	yes	6
37.10	even	3	inner	370.2.e.f.121.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.e.f.121.1	✓	6	37.10	even	3	inner
370.2.e.f.211.1	yes	6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.38923 + 2.40621i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.77846 q^{6} +(-1.65389 + 2.86462i) q^{7} +1.00000 q^{8} +(-2.35991 - 4.08749i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.38923 + 2.40621i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.77846 q^{6} +(-1.65389 + 2.86462i) q^{7} +1.00000 q^{8} +(-2.35991 - 4.08749i) q^{9} -1.00000 q^{10} +1.52932 q^{11} +(-1.38923 - 2.40621i) q^{12} +(-2.09525 + 3.62909i) q^{13} +3.30777 q^{14} +(1.38923 + 2.40621i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.90303 - 6.76024i) q^{17} +(-2.35991 + 4.08749i) q^{18} +(0.110771 - 0.191862i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.59525 - 7.95921i) q^{21} +(-0.764658 - 1.32443i) q^{22} -3.52932 q^{23} +(-1.38923 + 2.40621i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.19051 q^{26} +4.77846 q^{27} +(-1.65389 - 2.86462i) q^{28} -6.49828 q^{29} +(1.38923 - 2.40621i) q^{30} -4.41205 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.12457 + 3.67986i) q^{33} +(-3.90303 + 6.76024i) q^{34} +(1.65389 + 2.86462i) q^{35} +4.71982 q^{36} +(-2.87371 + 5.36114i) q^{37} -0.221543 q^{38} +(-5.82157 - 10.0833i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.610771 + 1.05789i) q^{41} +(-4.59525 + 7.95921i) q^{42} -0.162910 q^{43} +(-0.764658 + 1.32443i) q^{44} -4.71982 q^{45} +(1.76466 + 3.05648i) q^{46} +11.9103 q^{47} +2.77846 q^{48} +(-1.97068 - 3.41332i) q^{49} +(-0.500000 + 0.866025i) q^{50} +21.6888 q^{51} +(-2.09525 - 3.62909i) q^{52} +(1.98448 + 3.43722i) q^{53} +(-2.38923 - 4.13827i) q^{54} +(0.764658 - 1.32443i) q^{55} +(-1.65389 + 2.86462i) q^{56} +(0.307774 + 0.533080i) q^{57} +(3.24914 + 5.62768i) q^{58} +(-0.543115 - 0.940703i) q^{59} -2.77846 q^{60} +(7.24914 - 12.5559i) q^{61} +(2.20603 + 3.82095i) q^{62} +15.6121 q^{63} +1.00000 q^{64} +(2.09525 + 3.62909i) q^{65} +4.24914 q^{66} +(-3.83709 + 6.64604i) q^{67} +7.80605 q^{68} +(4.90303 - 8.49229i) q^{69} +(1.65389 - 2.86462i) q^{70} +(-7.08623 + 12.2737i) q^{71} +(-2.35991 - 4.08749i) q^{72} -7.80605 q^{73} +(6.07974 - 0.191862i) q^{74} +2.77846 q^{75} +(0.110771 + 0.191862i) q^{76} +(-2.52932 + 4.38090i) q^{77} +(-5.82157 + 10.0833i) q^{78} +(-2.52932 + 4.38090i) q^{79} -1.00000 q^{80} +(0.441367 - 0.764470i) q^{81} +1.22154 q^{82} +(4.71982 + 8.17497i) q^{83} +9.19051 q^{84} -7.80605 q^{85} +(0.0814549 + 0.141084i) q^{86} +(9.02760 - 15.6363i) q^{87} +1.52932 q^{88} +(8.66769 + 15.0129i) q^{89} +(2.35991 + 4.08749i) q^{90} +(-6.93063 - 12.0042i) q^{91} +(1.76466 - 3.05648i) q^{92} +(6.12935 - 10.6163i) q^{93} +(-5.95517 - 10.3146i) q^{94} +(-0.110771 - 0.191862i) q^{95} +(-1.38923 - 2.40621i) q^{96} +8.38101 q^{97} +(-1.97068 + 3.41332i) q^{98} +(-3.60905 - 6.25106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^9	\( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{9} - 6 q^{10} + 10 q^{11} - 3 q^{13} + 4 q^{14} - 3 q^{16} + 2 q^{17} - 5 q^{18} + 9 q^{19} + 3 q^{20} - 18 q^{21} - 5 q^{22} - 22 q^{23} - 3 q^{25} + 6 q^{26} + 12 q^{27} - 2 q^{28} - 4 q^{29} - 24 q^{31} - 3 q^{32} - 4 q^{33} + 2 q^{34} + 2 q^{35} + 10 q^{36} + 9 q^{37} - 18 q^{38} - 2 q^{39} + 3 q^{40} - 12 q^{41} - 18 q^{42} - 16 q^{43} - 5 q^{44} - 10 q^{45} + 11 q^{46} + 34 q^{47} - 11 q^{49} - 3 q^{50} + 76 q^{51} - 3 q^{52} - 6 q^{53} - 6 q^{54} + 5 q^{55} - 2 q^{56} - 14 q^{57} + 2 q^{58} + 13 q^{59} + 26 q^{61} + 12 q^{62} - 8 q^{63} + 6 q^{64} + 3 q^{65} + 8 q^{66} - 8 q^{67} - 4 q^{68} + 4 q^{69} + 2 q^{70} - 10 q^{71} - 5 q^{72} + 4 q^{73} + 9 q^{74} + 9 q^{76} - 16 q^{77} - 2 q^{78} - 16 q^{79} - 6 q^{80} + q^{81} + 24 q^{82} + 10 q^{83} + 36 q^{84} + 4 q^{85} + 8 q^{86} + 20 q^{87} + 10 q^{88} + 27 q^{89} + 5 q^{90} + 18 q^{91} + 11 q^{92} - 12 q^{93} - 17 q^{94} - 9 q^{95} + 12 q^{97} - 11 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^9 - 6 * q^10 + 10 * q^11 - 3 * q^13 + 4 * q^14 - 3 * q^16 + 2 * q^17 - 5 * q^18 + 9 * q^19 + 3 * q^20 - 18 * q^21 - 5 * q^22 - 22 * q^23 - 3 * q^25 + 6 * q^26 + 12 * q^27 - 2 * q^28 - 4 * q^29 - 24 * q^31 - 3 * q^32 - 4 * q^33 + 2 * q^34 + 2 * q^35 + 10 * q^36 + 9 * q^37 - 18 * q^38 - 2 * q^39 + 3 * q^40 - 12 * q^41 - 18 * q^42 - 16 * q^43 - 5 * q^44 - 10 * q^45 + 11 * q^46 + 34 * q^47 - 11 * q^49 - 3 * q^50 + 76 * q^51 - 3 * q^52 - 6 * q^53 - 6 * q^54 + 5 * q^55 - 2 * q^56 - 14 * q^57 + 2 * q^58 + 13 * q^59 + 26 * q^61 + 12 * q^62 - 8 * q^63 + 6 * q^64 + 3 * q^65 + 8 * q^66 - 8 * q^67 - 4 * q^68 + 4 * q^69 + 2 * q^70 - 10 * q^71 - 5 * q^72 + 4 * q^73 + 9 * q^74 + 9 * q^76 - 16 * q^77 - 2 * q^78 - 16 * q^79 - 6 * q^80 + q^81 + 24 * q^82 + 10 * q^83 + 36 * q^84 + 4 * q^85 + 8 * q^86 + 20 * q^87 + 10 * q^88 + 27 * q^89 + 5 * q^90 + 18 * q^91 + 11 * q^92 - 12 * q^93 - 17 * q^94 - 9 * q^95 + 12 * q^97 - 11 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more