LMFDB - Embedded newform 370.2.o.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

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("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, 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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 25 x^{15} + 132 x^{14} - 135 x^{13} + 666 x^{12} - 297 x^{11} + 1845 x^{10} + \cdots + 9 $ x^18 - 3x^17 + 18x^16 - 25x^15 + 132x^14 - 135x^13 + 666x^12 - 297x^11 + 1845x^10 - 382x^9 + 3810x^8 - 63x^7 + 3325x^6 - 1329x^5 + 1332x^4 - 192x^3 + 117x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			81.2
Root			$0.247857 - 0.429301i$ of defining polynomial
Character	$\chi$	$=$	370.81
Dual form			370.2.o.b.201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(0.465818 + 0.169544i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{5} +0.495714 q^{6} +(-0.827523 - 4.69312i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.10989 - 1.77041i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(0.465818 + 0.169544i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{5} +0.495714 q^{6} +(-0.827523 - 4.69312i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.10989 - 1.77041i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.0178576 - 0.0309303i) q^{11} +(0.465818 - 0.169544i) q^{12} +(-2.22538 + 1.86732i) q^{13} +(-2.38276 - 4.12706i) q^{14} +(0.0860798 - 0.488183i) q^{15} +(0.173648 - 0.984808i) q^{16} +(4.81190 + 4.03767i) q^{17} +(-2.58817 - 0.942015i) q^{18} +(3.55030 + 1.29220i) q^{19} +(-0.766044 - 0.642788i) q^{20} +(0.410215 - 2.32644i) q^{21} +(0.00620188 - 0.0351726i) q^{22} +(3.32020 + 5.75075i) q^{23} +(0.379739 - 0.318639i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-1.45251 + 2.51583i) q^{26} +(-1.42623 - 2.47031i) q^{27} +(-3.65060 - 3.06322i) q^{28} +(2.13214 - 3.69298i) q^{29} +(-0.0860798 - 0.488183i) q^{30} +7.81339 q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.0135624 - 0.0113802i) q^{33} +(5.90267 + 2.14840i) q^{34} +(-4.47812 + 1.62990i) q^{35} -2.75427 q^{36} +(-2.58015 + 5.50843i) q^{37} +3.77815 q^{38} +(-1.35322 + 0.492530i) q^{39} +(-0.939693 - 0.342020i) q^{40} +(0.219681 - 0.184334i) q^{41} +(-0.410215 - 2.32644i) q^{42} -4.96135 q^{43} +(-0.00620188 - 0.0351726i) q^{44} +(-1.37713 + 2.38527i) q^{45} +(5.08684 + 4.26837i) q^{46} +(-0.0422679 - 0.0732102i) q^{47} +(0.247857 - 0.429301i) q^{48} +(-14.7627 + 5.37319i) q^{49} +(-0.766044 + 0.642788i) q^{50} +(1.55691 + 2.69665i) q^{51} +(-0.504453 + 2.86089i) q^{52} +(2.17004 - 12.3069i) q^{53} +(-2.18512 - 1.83353i) q^{54} +(-0.0335613 - 0.0122153i) q^{55} +(-4.47812 - 1.62990i) q^{56} +(1.43471 + 1.20386i) q^{57} +(0.740486 - 4.19950i) q^{58} +(-1.71578 + 9.73067i) q^{59} +(-0.247857 - 0.429301i) q^{60} +(7.41852 - 6.22488i) q^{61} +(7.34219 - 2.67234i) q^{62} +(-6.56276 + 11.3670i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.22538 + 1.86732i) q^{65} +(0.00885226 - 0.0153326i) q^{66} +(-0.0868810 - 0.492727i) q^{67} +6.28149 q^{68} +(0.571604 + 3.24173i) q^{69} +(-3.65060 + 3.06322i) q^{70} +(8.73683 + 3.17995i) q^{71} +(-2.58817 + 0.942015i) q^{72} -8.43531 q^{73} +(-0.540554 + 6.05870i) q^{74} -0.495714 q^{75} +(3.55030 - 1.29220i) q^{76} +(-0.159937 - 0.0582123i) q^{77} +(-1.10315 + 0.925654i) q^{78} +(0.728448 + 4.13123i) q^{79} -1.00000 q^{80} +(1.18928 + 6.74475i) q^{81} +(0.143387 - 0.248353i) q^{82} +(-5.25852 - 4.41243i) q^{83} +(-1.18117 - 2.04584i) q^{84} +(3.14075 - 5.43993i) q^{85} +(-4.66214 + 1.69688i) q^{86} +(1.61931 - 1.35877i) q^{87} +(-0.0178576 - 0.0309303i) q^{88} +(1.99369 - 11.3068i) q^{89} +(-0.478274 + 2.71242i) q^{90} +(10.6051 + 8.89873i) q^{91} +(6.23993 + 2.27115i) q^{92} +(3.63962 + 1.32471i) q^{93} +(-0.0647582 - 0.0543386i) q^{94} +(0.656069 - 3.72075i) q^{95} +(0.0860798 - 0.488183i) q^{96} +(2.46953 + 4.27736i) q^{97} +(-12.0347 + 10.0983i) q^{98} +(-0.0924369 + 0.0336443i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	0.465818	+	0.169544i	0.268940	+	0.0978863i	0.472970	−	0.881078i	$-0.343182\pi$
$3$	0.465818	+	0.169544i	0.268940	+	0.0978863i	−0.204030	+	0.978965i	$0.565404\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	0.495714			0.202374
$7$	−0.827523	−	4.69312i	−0.312774	−	1.77383i	−0.584437	−	0.811439i	$-0.698685\pi$
$7$	−0.827523	−	4.69312i	−0.312774	−	1.77383i	0.271662	−	0.962393i	$-0.412427\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.10989	−	1.77041i	−0.703297	−	0.590136i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	0.0178576	−	0.0309303i	0.00538427	−	0.00932583i	−0.863321	−	0.504656i	$-0.831619\pi$
$11$	0.0178576	−	0.0309303i	0.00538427	−	0.00932583i	0.868705	+	0.495330i	$0.164953\pi$
$12$	0.465818	−	0.169544i	0.134470	−	0.0489431i
$13$	−2.22538	+	1.86732i	−0.617210	+	0.517900i	−0.896925	−	0.442183i	$-0.854204\pi$
$13$	−2.22538	+	1.86732i	−0.617210	+	0.517900i	0.279715	+	0.960083i	$0.409760\pi$
$14$	−2.38276	−	4.12706i	−0.636819	−	1.10300i
$15$	0.0860798	−	0.488183i	0.0222257	−	0.126048i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	4.81190	+	4.03767i	1.16706	+	0.979278i	0.999978	−	0.00666534i	$-0.00212166\pi$
$17$	4.81190	+	4.03767i	1.16706	+	0.979278i	0.167080	+	0.985943i	$0.446566\pi$
$18$	−2.58817	−	0.942015i	−0.610036	−	0.222035i
$19$	3.55030	+	1.29220i	0.814495	+	0.296452i	0.715479	−	0.698634i	$-0.246208\pi$
$19$	3.55030	+	1.29220i	0.814495	+	0.296452i	0.0990154	+	0.995086i	$0.468431\pi$
$20$	−0.766044	−	0.642788i	−0.171293	−	0.143732i
$21$	0.410215	−	2.32644i	0.0895162	−	0.507671i
$22$	0.00620188	−	0.0351726i	0.00132225	−	0.00749883i
$23$	3.32020	+	5.75075i	0.692310	+	1.19912i	0.971079	+	0.238757i	$0.0767400\pi$
$23$	3.32020	+	5.75075i	0.692310	+	1.19912i	−0.278770	+	0.960358i	$0.589927\pi$
$24$	0.379739	−	0.318639i	0.0775138	−	0.0650418i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−1.45251	+	2.51583i	−0.284861	+	0.493395i
$27$	−1.42623	−	2.47031i	−0.274479	−	0.475411i
$28$	−3.65060	−	3.06322i	−0.689898	−	0.578893i
$29$	2.13214	−	3.69298i	0.395929	−	0.685769i	−0.597290	−	0.802025i	$-0.703756\pi$
$29$	2.13214	−	3.69298i	0.395929	−	0.685769i	0.993219	+	0.116256i	$0.0370893\pi$
$30$	−0.0860798	−	0.488183i	−0.0157159	−	0.0891295i
$31$	7.81339			1.40333			0.701664	−	0.712508i	$-0.252441\pi$
$31$	7.81339			1.40333			0.701664	+	0.712508i	$0.252441\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	0.0135624	−	0.0113802i	0.00236092	−	0.00198105i
$34$	5.90267	+	2.14840i	1.01230	+	0.368447i
$35$	−4.47812	+	1.62990i	−0.756941	+	0.275504i
$36$	−2.75427			−0.459045
$37$	−2.58015	+	5.50843i	−0.424174	+	0.905581i
$37$	−2.58015	+	5.50843i	−0.424174	+	0.905581i
$38$	3.77815			0.612897
$39$	−1.35322	+	0.492530i	−0.216688	+	0.0788680i
$40$	−0.939693	−	0.342020i	−0.148578	−	0.0540781i
$41$	0.219681	−	0.184334i	0.0343084	−	0.0287882i	−0.625472	−	0.780246i	$-0.715094\pi$
$41$	0.219681	−	0.184334i	0.0343084	−	0.0287882i	0.659781	+	0.751458i	$0.270649\pi$
$42$	−0.410215	−	2.32644i	−0.0632975	−	0.358978i
$43$	−4.96135			−0.756598			−0.378299	−	0.925683i	$-0.623491\pi$
$43$	−4.96135			−0.756598			−0.378299	+	0.925683i	$0.623491\pi$
$44$	−0.00620188	−	0.0351726i	−0.000934969	−	0.00530247i
$45$	−1.37713	+	2.38527i	−0.205291	+	0.355574i
$46$	5.08684	+	4.26837i	0.750014	+	0.629336i
$47$	−0.0422679	−	0.0732102i	−0.00616541	−	0.0106788i	0.862926	−	0.505330i	$-0.168629\pi$
$47$	−0.0422679	−	0.0732102i	−0.00616541	−	0.0106788i	−0.869092	+	0.494651i	$0.835296\pi$
$48$	0.247857	−	0.429301i	0.0357750	−	0.0619642i
$49$	−14.7627	+	5.37319i	−2.10896	+	0.767598i
$50$	−0.766044	+	0.642788i	−0.108335	+	0.0909039i
$51$	1.55691	+	2.69665i	0.218011	+	0.377606i
$52$	−0.504453	+	2.86089i	−0.0699550	+	0.396735i
$53$	2.17004	−	12.3069i	0.298078	−	1.69048i	−0.356344	−	0.934355i	$-0.615977\pi$
$53$	2.17004	−	12.3069i	0.298078	−	1.69048i	0.654422	−	0.756130i	$-0.272912\pi$
$54$	−2.18512	−	1.83353i	−0.297357	−	0.249512i
$55$	−0.0335613	−	0.0122153i	−0.00452541	−	0.00164711i
$56$	−4.47812	−	1.62990i	−0.598414	−	0.217805i
$57$	1.43471	+	1.20386i	0.190032	+	0.159456i
$58$	0.740486	−	4.19950i	0.0972305	−	0.551422i
$59$	−1.71578	+	9.73067i	−0.223375	+	1.26682i	0.642391	+	0.766377i	$0.277942\pi$
$59$	−1.71578	+	9.73067i	−0.223375	+	1.26682i	−0.865767	+	0.500448i	$0.833169\pi$
$60$	−0.247857	−	0.429301i	−0.0319982	−	0.0554225i
$61$	7.41852	−	6.22488i	0.949844	−	0.797014i	−0.0294269	−	0.999567i	$-0.509368\pi$
$61$	7.41852	−	6.22488i	0.949844	−	0.797014i	0.979271	+	0.202553i	$0.0649238\pi$
$62$	7.34219	−	2.67234i	0.932459	−	0.339387i
$63$	−6.56276	+	11.3670i	−0.826829	+	1.43211i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.22538	+	1.86732i	0.276025	+	0.231612i
$66$	0.00885226	−	0.0153326i	0.00108964	−	0.00188731i
$67$	−0.0868810	−	0.492727i	−0.0106142	−	0.0601961i	0.979041	−	0.203665i	$-0.0652854\pi$
$67$	−0.0868810	−	0.492727i	−0.0106142	−	0.0601961i	−0.989655	+	0.143469i	$0.954174\pi$
$68$	6.28149			0.761743
$69$	0.571604	+	3.24173i	0.0688130	+	0.390258i
$70$	−3.65060	+	3.06322i	−0.436330	+	0.366124i
$71$	8.73683	+	3.17995i	1.03687	+	0.377390i	0.803693	−	0.595044i	$-0.202865\pi$
$71$	8.73683	+	3.17995i	1.03687	+	0.377390i	0.233178	+	0.972434i	$0.425088\pi$
$72$	−2.58817	+	0.942015i	−0.305018	+	0.111018i
$73$	−8.43531			−0.987279			−0.493639	−	0.869667i	$-0.664334\pi$
$73$	−8.43531			−0.987279			−0.493639	+	0.869667i	$0.664334\pi$
$74$	−0.540554	+	6.05870i	−0.0628381	+	0.704309i
$75$	−0.495714			−0.0572401
$76$	3.55030	−	1.29220i	0.407247	−	0.148226i
$77$	−0.159937	−	0.0582123i	−0.0182265	−	0.00663391i
$78$	−1.10315	+	0.925654i	−0.124907	+	0.104810i
$79$	0.728448	+	4.13123i	0.0819568	+	0.464800i	0.997972	+	0.0636563i	$0.0202761\pi$
$79$	0.728448	+	4.13123i	0.0819568	+	0.464800i	−0.916015	+	0.401144i	$0.868613\pi$
$80$	−1.00000			−0.111803
$81$	1.18928	+	6.74475i	0.132142	+	0.749416i
$82$	0.143387	−	0.248353i	0.0158344	−	0.0274260i
$83$	−5.25852	−	4.41243i	−0.577198	−	0.484327i	0.306828	−	0.951765i	$-0.400732\pi$
$83$	−5.25852	−	4.41243i	−0.577198	−	0.484327i	−0.884026	+	0.467438i	$0.845177\pi$
$84$	−1.18117	−	2.04584i	−0.128876	−	0.223219i
$85$	3.14075	−	5.43993i	0.340662	−	0.590044i
$86$	−4.66214	+	1.69688i	−0.502732	+	0.182979i
$87$	1.61931	−	1.35877i	0.173609	−	0.145675i
$88$	−0.0178576	−	0.0309303i	−0.00190363	−	0.00329718i
$89$	1.99369	−	11.3068i	0.211331	−	1.19852i	−0.675830	−	0.737057i	$-0.736215\pi$
$89$	1.99369	−	11.3068i	0.211331	−	1.19852i	0.887161	−	0.461460i	$-0.152674\pi$
$90$	−0.478274	+	2.71242i	−0.0504145	+	0.285915i
$91$	10.6051	+	8.89873i	1.11172	+	0.932840i
$92$	6.23993	+	2.27115i	0.650558	+	0.236784i
$93$	3.63962	+	1.32471i	0.377411	+	0.137366i
$94$	−0.0647582	−	0.0543386i	−0.00667930	−	0.00560460i
$95$	0.656069	−	3.72075i	0.0673112	−	0.381741i
$96$	0.0860798	−	0.488183i	0.00878548	−	0.0498249i
$97$	2.46953	+	4.27736i	0.250743	+	0.434300i	0.963731	−	0.266877i	$-0.0859917\pi$
$97$	2.46953	+	4.27736i	0.250743	+	0.434300i	−0.712987	+	0.701177i	$0.752658\pi$
$98$	−12.0347	+	10.0983i	−1.21569	+	1.02008i
$99$	−0.0924369	+	0.0336443i	−0.00929025	+	0.00338138i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−6.51178	−	11.2787i	−0.647946	−	1.12228i	−0.983613	−	0.180295i	$-0.942295\pi$
$101$	−6.51178	−	11.2787i	−0.647946	−	1.12228i	0.335666	−	0.941981i	$-0.391039\pi$
$102$	2.38533	+	2.00153i	0.236182	+	0.198181i
$103$	−2.61639	+	4.53172i	−0.257800	+	0.446523i	−0.965652	−	0.259838i	$-0.916331\pi$
$103$	−2.61639	+	4.53172i	−0.257800	+	0.446523i	0.707852	+	0.706361i	$0.249664\pi$
$104$	0.504453	+	2.86089i	0.0494657	+	0.280534i
$105$	−2.36233			−0.230540
$106$	−2.17004	−	12.3069i	−0.210773	−	1.19535i
$107$	3.48167	−	2.92147i	0.336586	−	0.282429i	−0.458791	−	0.888544i	$-0.651717\pi$
$107$	3.48167	−	2.92147i	0.336586	−	0.282429i	0.795377	+	0.606115i	$0.207273\pi$
$108$	−2.68044	−	0.975602i	−0.257926	−	0.0938773i
$109$	−11.6125	+	4.22659i	−1.11227	+	0.404834i	−0.831827	−	0.555035i	$-0.812705\pi$
$109$	−11.6125	+	4.22659i	−1.11227	+	0.404834i	−0.280446	+	0.959870i	$0.590482\pi$
$110$	−0.0357152			−0.00340531
$111$	−2.13580	+	2.12848i	−0.202721	+	0.202026i
$112$	−4.76552			−0.450299
$113$	−16.3378	+	5.94648i	−1.53693	+	0.559397i	−0.965307	−	0.261118i	$-0.915909\pi$
$113$	−16.3378	+	5.94648i	−1.53693	+	0.559397i	−0.571625	+	0.820515i	$0.693687\pi$
$114$	1.75993	+	0.640563i	0.164833	+	0.0599942i
$115$	5.08684	−	4.26837i	0.474350	−	0.398027i
$116$	−0.740486	−	4.19950i	−0.0687524	−	0.389914i
$117$	8.00123			0.739714
$118$	1.71578	+	9.73067i	0.157950	+	0.895781i
$119$	14.9673	−	25.9241i	1.37205	−	2.37646i
$120$	−0.379739	−	0.318639i	−0.0346652	−	0.0290876i
$121$	5.49936	+	9.52517i	0.499942	+	0.865925i
$122$	4.84210	−	8.38676i	0.438383	−	0.759301i
$123$	0.133584	−	0.0486207i	0.0120449	−	0.00438398i
$124$	5.98541	−	5.02235i	0.537505	−	0.451021i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−2.27922	+	12.9261i	−0.203049	+	1.15155i
$127$	−3.39837	+	19.2731i	−0.301556	+	1.71021i	0.337731	+	0.941243i	$0.390341\pi$
$127$	−3.39837	+	19.2731i	−0.301556	+	1.71021i	−0.639287	+	0.768968i	$0.720770\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−2.31109	−	0.841167i	−0.203480	−	0.0740606i
$130$	2.72983	+	0.993578i	0.239422	+	0.0871426i
$131$	4.09249	+	3.43401i	0.357562	+	0.300030i	0.803818	−	0.594875i	$-0.202798\pi$
$131$	4.09249	+	3.43401i	0.357562	+	0.300030i	−0.446256	+	0.894905i	$0.647243\pi$
$132$	0.00307436	−	0.0174355i	0.000267588	−	0.00151757i
$133$	3.12651	−	17.7313i	0.271103	−	1.53750i
$134$	−0.250164	−	0.433297i	−0.0216109	−	0.0374311i
$135$	−2.18512	+	1.83353i	−0.188065	+	0.157805i
$136$	5.90267	−	2.14840i	0.506150	−	0.184224i
$137$	−3.73919	+	6.47647i	−0.319461	+	0.553322i	−0.980376	−	0.197139i	$-0.936835\pi$
$137$	−3.73919	+	6.47647i	−0.319461	+	0.553322i	0.660915	+	0.750461i	$0.270168\pi$
$138$	1.64587	+	2.85073i	0.140106	+	0.242670i
$139$	6.27727	+	5.26726i	0.532431	+	0.446763i	0.868940	−	0.494917i	$-0.164802\pi$
$139$	6.27727	+	5.26726i	0.532431	+	0.446763i	−0.336509	+	0.941680i	$0.609246\pi$
$140$	−2.38276	+	4.12706i	−0.201380	+	0.348800i
$141$	−0.00727683	−	0.0412689i	−0.000612819	−	0.00347547i
$142$	9.29754			0.780232
$143$	0.0180166	+	0.102177i	0.00150663	+	0.00854451i
$144$	−2.10989	+	1.77041i	−0.175824	+	0.147534i
$145$	−4.00712	−	1.45847i	−0.332773	−	0.121119i
$146$	−7.92660	+	2.88505i	−0.656010	+	0.238768i
$147$	−7.78773			−0.642322
$148$	1.56424	+	5.87819i	0.128580	+	0.483184i
$149$	7.89698			0.646946			0.323473	−	0.946237i	$-0.395150\pi$
$149$	7.89698			0.646946			0.323473	+	0.946237i	$0.395150\pi$
$150$	−0.465818	+	0.169544i	−0.0380339	+	0.0138432i
$151$	−5.21434	−	1.89787i	−0.424337	−	0.154446i	0.121020	−	0.992650i	$-0.461384\pi$
$151$	−5.21434	−	1.89787i	−0.424337	−	0.154446i	−0.545357	+	0.838204i	$0.683606\pi$
$152$	2.89423	−	2.42855i	0.234753	−	0.196981i
$153$	−3.00427	−	17.0381i	−0.242881	−	1.37745i
$154$	−0.170201			−0.0137152
$155$	−1.35678	−	7.69469i	−0.108979	−	0.618052i
$156$	−0.720031	+	1.24713i	−0.0576486	+	0.0998503i
$157$	−17.0032	−	14.2674i	−1.35701	−	1.13866i	−0.976894	−	0.213723i	$-0.931441\pi$
$157$	−17.0032	−	14.2674i	−1.35701	−	1.13866i	−0.380112	−	0.924941i	$-0.624114\pi$
$158$	2.09748	+	3.63295i	0.166867	+	0.289022i
$159$	3.09741	−	5.36487i	0.245641	−	0.425462i
$160$	−0.939693	+	0.342020i	−0.0742892	+	0.0270391i
$161$	24.2414	−	20.3410i	1.91049	−	1.60309i
$162$	3.42440	+	5.93123i	0.269046	+	0.466002i
$163$	0.227268	−	1.28890i	0.0178010	−	0.100955i	−0.974613	−	0.223897i	$-0.928122\pi$
$163$	0.227268	−	1.28890i	0.0178010	−	0.100955i	0.992414	+	0.122943i	$0.0392331\pi$
$164$	0.0497977	−	0.282417i	0.00388855	−	0.0220530i
$165$	−0.0135624	−	0.0113802i	−0.00105583	−	0.000885951i
$166$	−6.45053	−	2.34780i	−0.500659	−	0.182225i
$167$	−5.74310	−	2.09032i	−0.444415	−	0.161754i	0.110113	−	0.993919i	$-0.464879\pi$
$167$	−5.74310	−	2.09032i	−0.444415	−	0.161754i	−0.554528	+	0.832165i	$0.687101\pi$
$168$	−1.80965	−	1.51848i	−0.139618	−	0.117153i
$169$	−0.791977	+	4.49152i	−0.0609213	+	0.345502i
$170$	1.09077	−	6.18606i	0.0836582	−	0.474449i
$171$	−5.20302	−	9.01189i	−0.397885	−	0.689157i
$172$	−3.80061	+	3.18909i	−0.289794	+	0.243166i
$173$	−9.91493	+	3.60874i	−0.753818	+	0.274367i	−0.690211	−	0.723608i	$-0.742482\pi$
$173$	−9.91493	+	3.60874i	−0.753818	+	0.274367i	−0.0636065	+	0.997975i	$0.520260\pi$
$174$	1.05693	−	1.83066i	0.0801258	−	0.138782i
$175$	2.38276	+	4.12706i	0.180120	+	0.311976i
$176$	−0.0273594	−	0.0229573i	−0.00206230	−	0.00173047i
$177$	−2.44902	+	4.24182i	−0.184079	+	0.318835i
$178$	−1.99369	−	11.3068i	−0.149433	−	0.847479i
$179$	−4.87224			−0.364168			−0.182084	−	0.983283i	$-0.558284\pi$
$179$	−4.87224			−0.364168			−0.182084	+	0.983283i	$0.558284\pi$
$180$	0.478274	+	2.71242i	0.0356484	+	0.202172i
$181$	5.39164	−	4.52413i	0.400758	−	0.336276i	−0.420029	−	0.907511i	$-0.637980\pi$
$181$	5.39164	−	4.52413i	0.400758	−	0.336276i	0.820786	+	0.571235i	$0.193536\pi$
$182$	13.0091	+	4.73491i	0.964296	+	0.350975i
$183$	4.51108	−	1.64190i	0.333468	−	0.121373i
$184$	6.64040			0.489537
$185$	5.87279	+	1.58442i	0.431776	+	0.116489i
$186$	3.87321			0.283997
$187$	0.210815	−	0.0767305i	0.0154163	−	0.00561109i
$188$	−0.0794377	−	0.0289130i	−0.00579359	−	0.00210869i
$189$	−10.4132	+	8.73773i	−0.757450	+	0.635576i
$190$	−0.656069	−	3.72075i	−0.0475962	−	0.269932i
$191$	12.0681			0.873221			0.436610	−	0.899651i	$-0.356179\pi$
$191$	12.0681			0.873221			0.436610	+	0.899651i	$0.356179\pi$
$192$	−0.0860798	−	0.488183i	−0.00621227	−	0.0352315i
$193$	−9.20478	+	15.9431i	−0.662574	+	1.14761i	0.317362	+	0.948304i	$0.397203\pi$
$193$	−9.20478	+	15.9431i	−0.662574	+	1.14761i	−0.979937	+	0.199308i	$0.936130\pi$
$194$	3.78354	+	3.17477i	0.271643	+	0.227935i
$195$	0.720031	+	1.24713i	0.0515625	+	0.0893089i
$196$	−7.85507	+	13.6054i	−0.561077	+	0.971813i
$197$	−1.68946	+	0.614913i	−0.120369	+	0.0438107i	−0.401502	−	0.915858i	$-0.631512\pi$
$197$	−1.68946	+	0.614913i	−0.120369	+	0.0438107i	0.281133	+	0.959669i	$0.409290\pi$
$198$	−0.0753552	+	0.0632305i	−0.00535526	+	0.00449360i
$199$	1.53649	+	2.66128i	0.108919	+	0.188653i	0.915333	−	0.402699i	$-0.131928\pi$
$199$	1.53649	+	2.66128i	0.108919	+	0.188653i	−0.806414	+	0.591352i	$0.798594\pi$
$200$	−0.173648	+	0.984808i	−0.0122788	+	0.0696364i
$201$	0.0430681	−	0.244251i	0.00303779	−	0.0172282i
$202$	−9.97663	−	8.37138i	−0.701953	−	0.589009i
$203$	−19.0960	−	6.95037i	−1.34028	−	0.487820i
$204$	2.92604	+	1.06499i	0.204863	+	0.0745642i
$205$	−0.219681	−	0.184334i	−0.0153432	−	0.0128745i
$206$	−0.908662	+	5.15328i	−0.0633095	+	0.359046i
$207$	3.17593	−	18.0116i	0.220742	−	1.25189i
$208$	1.45251	+	2.51583i	0.100714	+	0.174441i
$209$	0.103368	−	0.0867361i	0.00715012	−	0.00599966i
$210$	−2.21987	+	0.807965i	−0.153185	+	0.0557549i
$211$	6.45980	−	11.1887i	0.444711	−	0.770261i	−0.553321	−	0.832968i	$-0.686640\pi$
$211$	6.45980	−	11.1887i	0.444711	−	0.770261i	0.998032	+	0.0627064i	$0.0199732\pi$
$212$	−6.24838	−	10.8225i	−0.429141	−	0.743294i
$213$	3.53063	+	2.96255i	0.241915	+	0.202991i
$214$	2.27250	−	3.93609i	0.155345	−	0.269065i
$215$	0.861529	+	4.88597i	0.0587558	+	0.333221i
$216$	−2.85247			−0.194086
$217$	−6.46577	−	36.6692i	−0.438925	−	2.48927i
$218$	−9.46657	+	7.94340i	−0.641157	+	0.537995i
$219$	−3.92932	−	1.43016i	−0.265519	−	0.0966411i
$220$	−0.0335613	+	0.0122153i	−0.00226270	+	0.000823557i
$221$	−18.2479			−1.22749
$222$	−1.27902	+	2.73060i	−0.0858419	+	0.183266i
$223$	23.4461			1.57007			0.785034	−	0.619453i	$-0.212645\pi$
$223$	23.4461			1.57007			0.785034	+	0.619453i	$0.212645\pi$
$224$	−4.47812	+	1.62990i	−0.299207	+	0.108902i
$225$	2.58817	+	0.942015i	0.172544	+	0.0628010i
$226$	−13.3187	+	11.1757i	−0.885947	+	0.743398i
$227$	2.64889	+	15.0226i	0.175813	+	0.997085i	0.937201	+	0.348789i	$0.113407\pi$
$227$	2.64889	+	15.0226i	0.175813	+	0.997085i	−0.761388	+	0.648296i	$0.775482\pi$
$228$	1.87288			0.124035
$229$	−0.885892	−	5.02414i	−0.0585414	−	0.332005i	0.941445	−	0.337166i	$-0.109468\pi$
$229$	−0.885892	−	5.02414i	−0.0585414	−	0.332005i	−0.999987	+	0.00516105i	$0.998357\pi$
$230$	3.32020	−	5.75075i	0.218927	−	0.379194i
$231$	−0.0646321	−	0.0542327i	−0.00425248	−	0.00356825i
$232$	−2.13214	−	3.69298i	−0.139982	−	0.242456i
$233$	13.3930	−	23.1973i	0.877402	−	1.51971i	0.0232206	−	0.999730i	$-0.492608\pi$
$233$	13.3930	−	23.1973i	0.877402	−	1.51971i	0.854182	−	0.519975i	$-0.174059\pi$
$234$	7.51869	−	2.73658i	0.491512	−	0.178896i
$235$	−0.0647582	+	0.0543386i	−0.00422436	+	0.00354466i
$236$	4.94039	+	8.55701i	0.321592	+	0.557014i
$237$	−0.361102	+	2.04791i	−0.0234561	+	0.133026i
$238$	5.19808	−	29.4798i	0.336942	−	1.91089i
$239$	15.1202	+	12.6874i	0.978048	+	0.820679i	0.983794	−	0.179304i	$-0.0573846\pi$
$239$	15.1202	+	12.6874i	0.978048	+	0.820679i	−0.00574617	+	0.999983i	$0.501829\pi$
$240$	−0.465818	−	0.169544i	−0.0300684	−	0.0109440i
$241$	−17.5991	−	6.40554i	−1.13366	−	0.412617i	−0.294038	−	0.955794i	$-0.594999\pi$
$241$	−17.5991	−	6.40554i	−1.13366	−	0.412617i	−0.839618	+	0.543177i	$0.817221\pi$
$242$	8.42551	+	7.06984i	0.541612	+	0.454467i
$243$	−2.07552	+	11.7709i	−0.133145	+	0.755101i
$244$	1.68164	−	9.53707i	0.107656	−	0.610548i
$245$	7.85507	+	13.6054i	0.501842	+	0.869216i
$246$	0.108899	−	0.0913771i	0.00694314	−	0.00582599i
$247$	−10.3137	+	3.75389i	−0.656246	+	0.238854i
$248$	3.90670	−	6.76660i	0.248076	−	0.429679i
$249$	−1.70142	−	2.94694i	−0.107823	−	0.186755i
$250$	0.766044	+	0.642788i	0.0484489	+	0.0406535i
$251$	5.30044	−	9.18063i	0.334561	−	0.579476i	−0.648840	−	0.760925i	$-0.724745\pi$
$251$	5.30044	−	9.18063i	0.334561	−	0.579476i	0.983400	+	0.181449i	$0.0580787\pi$
$252$	2.27922	+	12.9261i	0.143577	+	0.814268i
$253$	0.237163			0.0149103
$254$	3.39837	+	19.2731i	0.213233	+	1.20930i
$255$	2.38533	−	2.00153i	0.149375	−	0.125340i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	11.4314	−	4.16068i	0.713070	−	0.259536i	0.0400890	−	0.999196i	$-0.487236\pi$
$257$	11.4314	−	4.16068i	0.713070	−	0.259536i	0.672981	+	0.739660i	$0.265014\pi$
$258$	−2.45941			−0.153116
$259$	27.9869	+	7.55059i	1.73902	+	0.469171i
$260$	2.90503			0.180162
$261$	−11.0367	+	4.01702i	−0.683153	+	0.248647i
$262$	5.02018	+	1.82720i	0.310148	+	0.112885i
$263$	24.1996	−	20.3059i	1.49221	−	1.25211i	0.600408	−	0.799694i	$-0.295005\pi$
$263$	24.1996	−	20.3059i	1.49221	−	1.25211i	0.891804	−	0.452421i	$-0.149440\pi$
$264$	−0.00307436	−	0.0174355i	−0.000189214	−	0.00107308i
$265$	−12.4968			−0.767670
$266$	−3.12651	−	17.7313i	−0.191698	−	1.08718i
$267$	2.84570	−	4.92889i	0.174154	−	0.301643i
$268$	−0.383273	−	0.321605i	−0.0234121	−	0.0196451i
$269$	4.32236	+	7.48655i	0.263539	+	0.456463i	0.967180	−	0.254093i	$-0.0817768\pi$
$269$	4.32236	+	7.48655i	0.263539	+	0.456463i	−0.703641	+	0.710556i	$0.748443\pi$
$270$	−1.42623	+	2.47031i	−0.0867979	+	0.150338i
$271$	2.12113	−	0.772027i	0.128849	−	0.0468973i	−0.276791	−	0.960930i	$-0.589271\pi$
$271$	2.12113	−	0.772027i	0.128849	−	0.0468973i	0.405640	+	0.914033i	$0.367049\pi$
$272$	4.81190	−	4.03767i	0.291765	−	0.244819i
$273$	3.43132	+	5.94322i	0.207673	+	0.359700i
$274$	−1.29861	+	7.36477i	−0.0784518	+	0.444922i
$275$	−0.00620188	+	0.0351726i	−0.000373987	+	0.00212099i
$276$	2.52162	+	2.11589i	0.151783	+	0.127361i
$277$	−8.82907	−	3.21352i	−0.530487	−	0.193082i	0.0628685	−	0.998022i	$-0.479975\pi$
$277$	−8.82907	−	3.21352i	−0.530487	−	0.193082i	−0.593356	+	0.804940i	$0.702197\pi$
$278$	7.70021	+	2.80265i	0.461828	+	0.168092i
$279$	−16.4854	−	13.8329i	−0.986956	−	0.828154i
$280$	−0.827523	+	4.69312i	−0.0494540	+	0.280467i
$281$	−0.0250050	+	0.141810i	−0.00149167	+	0.00845969i	−0.985545	−	0.169417i	$-0.945812\pi$
$281$	−0.0250050	+	0.141810i	−0.00149167	+	0.00845969i	0.984053	+	0.177876i	$0.0569227\pi$
$282$	−0.0209528	−	0.0362913i	−0.00124772	−	0.00216111i
$283$	−20.2500	+	16.9918i	−1.20374	+	1.01006i	−0.204225	+	0.978924i	$0.565467\pi$
$283$	−20.2500	+	16.9918i	−1.20374	+	1.01006i	−0.999515	+	0.0311341i	$0.990088\pi$
$284$	8.73683	−	3.17995i	0.518435	−	0.188695i
$285$	0.936440	−	1.62196i	0.0554699	−	0.0960767i
$286$	0.0518768	+	0.0898533i	0.00306754	+	0.00531314i
$287$	−1.04689	−	0.878449i	−0.0617962	−	0.0518532i
$288$	−1.37713	+	2.38527i	−0.0811484	+	0.140553i
$289$	3.89965	+	22.1160i	0.229391	+	1.30094i
$290$	−4.26429			−0.250407
$291$	0.425154	+	2.41117i	0.0249230	+	0.141345i
$292$	−6.46183	+	5.42212i	−0.378150	+	0.317305i
$293$	12.2370	+	4.45390i	0.714893	+	0.260200i	0.673756	−	0.738954i	$-0.264680\pi$
$293$	12.2370	+	4.45390i	0.714893	+	0.260200i	0.0411366	+	0.999154i	$0.486902\pi$
$294$	−7.31808	+	2.66356i	−0.426799	+	0.155342i
$295$	9.88078			0.575281
$296$	3.48037	+	4.98869i	0.202292	+	0.289962i
$297$	−0.101877			−0.00591147
$298$	7.42073	−	2.70093i	0.429871	−	0.156460i
$299$	−18.1272	−	6.59776i	−1.04832	−	0.381558i
$300$	−0.379739	+	0.318639i	−0.0219242	+	0.0183966i
$301$	4.10563	+	23.2842i	0.236645	+	1.34208i
$302$	−5.54899			−0.319308
$303$	−1.12107	−	6.35788i	−0.0644035	−	0.365250i
$304$	1.88907	−	3.27197i	0.108346	−	0.187661i
$305$	−7.41852	−	6.22488i	−0.424783	−	0.356436i
$306$	−8.65046	−	14.9830i	−0.494514	−	0.856523i
$307$	−11.3954	+	19.7374i	−0.650369	+	1.12647i	0.332664	+	0.943045i	$0.392053\pi$
$307$	−11.3954	+	19.7374i	−0.650369	+	1.12647i	−0.983033	+	0.183427i	$0.941281\pi$
$308$	−0.159937	+	0.0582123i	−0.00911326	+	0.00331695i
$309$	−1.98709	+	1.66736i	−0.113041	+	0.0948530i
$310$	−3.90670	−	6.76660i	−0.221885	−	0.384317i
$311$	4.63208	−	26.2698i	0.262661	−	1.48963i	−0.512952	−	0.858417i	$-0.671448\pi$
$311$	4.63208	−	26.2698i	0.262661	−	1.48963i	0.775613	−	0.631209i	$-0.217441\pi$
$312$	−0.250064	+	1.41818i	−0.0141571	+	0.0802889i
$313$	−13.1588	−	11.0416i	−0.743782	−	0.624107i	0.190069	−	0.981771i	$-0.439129\pi$
$313$	−13.1588	−	11.0416i	−0.743782	−	0.624107i	−0.933850	+	0.357664i	$0.883573\pi$
$314$	−20.8576	−	7.59153i	−1.17706	−	0.428415i
$315$	12.3339	+	4.48919i	0.694939	+	0.252937i
$316$	3.21353	+	2.69647i	0.180775	+	0.151688i
$317$	−3.63150	+	20.5952i	−0.203965	+	1.15674i	0.695095	+	0.718918i	$0.255362\pi$
$317$	−3.63150	+	20.5952i	−0.203965	+	1.15674i	−0.899060	+	0.437825i	$0.855749\pi$
$318$	1.07572	−	6.10070i	0.0603233	−	0.342111i
$319$	−0.0761499	−	0.131896i	−0.00426358	−	0.00738473i
$320$	−0.766044	+	0.642788i	−0.0428232	+	0.0359329i
$321$	2.11715	−	0.770578i	0.118168	−	0.0430095i
$322$	15.8225	−	27.4053i	0.881752	−	1.52724i
$323$	11.8662	+	20.5529i	0.660254	+	1.14359i
$324$	5.24648	+	4.40232i	0.291471	+	0.244573i
$325$	1.45251	−	2.51583i	0.0805710	−	0.139553i
$326$	−0.227268	−	1.28890i	−0.0125872	−	0.0713857i
$327$	−6.12590			−0.338763
$328$	−0.0497977	−	0.282417i	−0.00274962	−	0.0155939i
$329$	−0.308606	+	0.258951i	−0.0170140	+	0.0142765i
$330$	−0.0166368	−	0.00605530i	−0.000915826	−	0.000333333i
$331$	−32.8499	+	11.9564i	−1.80559	+	0.657182i	−0.807899	+	0.589321i	$0.799395\pi$
$331$	−32.8499	+	11.9564i	−1.80559	+	0.657182i	−0.997695	+	0.0678611i	$0.978383\pi$
$332$	−6.86452			−0.376739
$333$	15.1960	−	7.05427i	0.832737	−	0.386572i
$334$	−6.11168			−0.334416
$335$	−0.470154	+	0.171122i	−0.0256873	+	0.00934940i
$336$	−2.21987	−	0.807965i	−0.121104	−	0.0440781i
$337$	−18.9211	+	15.8767i	−1.03070	+	0.864856i	−0.990934	−	0.134353i	$-0.957104\pi$
$337$	−18.9211	+	15.8767i	−1.03070	+	0.864856i	−0.0397621	+	0.999209i	$0.512660\pi$
$338$	0.791977	+	4.49152i	0.0430778	+	0.244307i
$339$	−8.61864			−0.468100
$340$	−1.09077	−	6.18606i	−0.0591553	−	0.335486i
$341$	0.139528	−	0.241670i	0.00755589	−	0.0130872i
$342$	−7.97149	−	6.68887i	−0.431049	−	0.361693i
$343$	20.7542	+	35.9473i	1.12062	+	1.94097i
$344$	−2.48067	+	4.29665i	−0.133749	+	0.231660i
$345$	3.09322	−	1.12584i	0.166533	−	0.0606132i
$346$	−8.08272	+	6.78221i	−0.434530	+	0.364614i
$347$	5.68747	+	9.85098i	0.305319	+	0.528828i	0.977332	−	0.211711i	$-0.0679035\pi$
$347$	5.68747	+	9.85098i	0.305319	+	0.528828i	−0.672013	+	0.740539i	$0.734570\pi$
$348$	0.367069	−	2.08175i	0.0196769	−	0.111594i
$349$	−1.67847	+	9.51910i	−0.0898467	+	0.509546i	0.906358	+	0.422510i	$0.138851\pi$
$349$	−1.67847	+	9.51910i	−0.0898467	+	0.509546i	−0.996205	+	0.0870362i	$0.972260\pi$
$350$	3.65060	+	3.06322i	0.195133	+	0.163736i
$351$	7.78677	+	2.83415i	0.415627	+	0.151276i
$352$	−0.0335613	−	0.0122153i	−0.00178882	−	0.000651079i
$353$	0.795845	+	0.667794i	0.0423586	+	0.0355431i	0.663721	−	0.747980i	$-0.268976\pi$
$353$	0.795845	+	0.667794i	0.0423586	+	0.0355431i	−0.621363	+	0.783523i	$0.713421\pi$
$354$	−0.850535	+	4.82362i	−0.0452054	+	0.256373i
$355$	1.61450	−	9.15629i	0.0856888	−	0.485965i
$356$	−5.74061	−	9.94302i	−0.304251	−	0.526979i
$357$	11.3673	−	9.53831i	0.601622	−	0.504821i
$358$	−4.57841	+	1.66640i	−0.241976	+	0.0880722i
$359$	−1.35539	+	2.34760i	−0.0715347	+	0.123902i	−0.899574	−	0.436768i	$-0.856123\pi$
$359$	−1.35539	+	2.34760i	−0.0715347	+	0.123902i	0.828039	+	0.560670i	$0.189456\pi$
$360$	1.37713	+	2.38527i	0.0725813	+	0.125715i
$361$	−3.62001	−	3.03755i	−0.190527	−	0.159871i
$362$	3.51915	−	6.09534i	0.184962	−	0.320364i
$363$	0.946768	+	5.36939i	0.0496924	+	0.281820i
$364$	13.8440			0.725621
$365$	1.46478	+	8.30716i	0.0766699	+	0.434817i
$366$	3.67746	−	3.08576i	0.192224	−	0.161295i
$367$	24.4423	+	8.89625i	1.27588	+	0.464381i	0.889066	−	0.457779i	$-0.151355\pi$
$367$	24.4423	+	8.89625i	1.27588	+	0.464381i	0.386809	+	0.922160i	$0.373577\pi$
$368$	6.23993	−	2.27115i	0.325279	−	0.118392i
$369$	−0.789851			−0.0411180
$370$	6.06052	−	0.519740i	0.315071	−	0.0270200i
$371$	−59.5536			−3.09187
$372$	3.63962	−	1.32471i	0.188706	−	0.0686832i
$373$	24.7555	+	9.01028i	1.28179	+	0.466534i	0.891025	−	0.453955i	$-0.149987\pi$
$373$	24.7555	+	9.01028i	1.28179	+	0.466534i	0.390768	+	0.920489i	$0.372209\pi$
$374$	0.171858	−	0.144206i	0.00888657	−	0.00745672i
$375$	0.0860798	+	0.488183i	0.00444514	+	0.0252096i
$376$	−0.0845358			−0.00435960
$377$	2.15113	+	12.1997i	0.110789	+	0.628315i
$378$	−6.79674	+	11.7723i	−0.349587	+	0.605502i
$379$	−12.7884	−	10.7307i	−0.656896	−	0.551202i	0.252258	−	0.967660i	$-0.418827\pi$
$379$	−12.7884	−	10.7307i	−0.656896	−	0.551202i	−0.909155	+	0.416458i	$0.863271\pi$
$380$	−1.88907	−	3.27197i	−0.0969075	−	0.167849i
$381$	−4.85066	+	8.40159i	−0.248507	+	0.430427i
$382$	11.3404	−	4.12755i	0.580223	−	0.211184i
$383$	−15.9173	+	13.3562i	−0.813335	+	0.682469i	−0.951401	−	0.307954i	$-0.900356\pi$
$383$	−15.9173	+	13.3562i	−0.813335	+	0.682469i	0.138066	+	0.990423i	$0.455911\pi$
$384$	−0.247857	−	0.429301i	−0.0126484	−	0.0219077i
$385$	−0.0295552	+	0.167616i	−0.00150627	+	0.00854249i
$386$	−3.19679	+	18.1299i	−0.162712	+	0.922786i
$387$	10.4679	+	8.78362i	0.532114	+	0.446496i
$388$	4.64120	+	1.68926i	0.235621	+	0.0857592i
$389$	−9.50776	−	3.46054i	−0.482063	−	0.175456i	0.0895463	−	0.995983i	$-0.471458\pi$
$389$	−9.50776	−	3.46054i	−0.482063	−	0.175456i	−0.571609	+	0.820526i	$0.693681\pi$
$390$	1.10315	+	0.925654i	0.0558602	+	0.0468723i
$391$	−7.24315	+	41.0779i	−0.366302	+	2.07740i
$392$	−2.72804	+	15.4715i	−0.137787	+	0.781428i
$393$	1.32414	+	2.29348i	0.0667941	+	0.115691i
$394$	−1.37726	+	1.15566i	−0.0693853	+	0.0582212i
$395$	3.94198	−	1.43476i	0.198342	−	0.0721907i
$396$	−0.0491846	+	0.0851903i	−0.00247162	+	0.00428097i
$397$	−10.3101	−	17.8577i	−0.517451	−	0.896251i	−0.999795	−	0.0202691i	$-0.993548\pi$
$397$	−10.3101	−	17.8577i	−0.517451	−	0.896251i	0.482344	−	0.875982i	$-0.339786\pi$
$398$	2.35404	+	1.97528i	0.117997	+	0.0990116i
$399$	4.46262	−	7.72949i	0.223410	−	0.386958i
$400$	0.173648	+	0.984808i	0.00868241	+	0.0492404i
$401$	25.2432			1.26058			0.630291	−	0.776359i	$-0.282935\pi$
$401$	25.2432			1.26058			0.630291	+	0.776359i	$0.282935\pi$
$402$	−0.0430681	−	0.244251i	−0.00214804	−	0.0121821i
$403$	−17.3878	+	14.5901i	−0.866147	+	0.726784i
$404$	−12.2381	−	4.45432i	−0.608871	−	0.221611i
$405$	6.43576	−	2.34243i	0.319796	−	0.116396i
$406$	−20.3215			−1.00854
$407$	0.124302	+	0.178172i	0.00616142	+	0.00883167i
$408$	3.11382			0.154157
$409$	9.86508	−	3.59060i	0.487797	−	0.177544i	−0.0864004	−	0.996260i	$-0.527536\pi$
$409$	9.86508	−	3.59060i	0.487797	−	0.177544i	0.574197	+	0.818717i	$0.305314\pi$
$410$	−0.269479	−	0.0980823i	−0.0133086	−	0.00484394i
$411$	−2.83983	+	2.38290i	−0.140079	+	0.117540i
$412$	0.908662	+	5.15328i	0.0447665	+	0.253884i
$413$	47.0870			2.31700
$414$	−3.17593	−	18.0116i	−0.156088	−	0.885221i
$415$	−3.43226	+	5.94484i	−0.168483	+	0.291821i
$416$	2.22538	+	1.86732i	0.109108	+	0.0915527i
$417$	2.03104	+	3.51786i	0.0994603	+	0.172270i
$418$	0.0674687	−	0.116859i	0.00330000	−	0.00571577i
$419$	22.1758	−	8.07133i	1.08336	−	0.394310i	0.262202	−	0.965013i	$-0.415551\pi$
$419$	22.1758	−	8.07133i	1.08336	−	0.394310i	0.821157	+	0.570703i	$0.193329\pi$
$420$	−1.80965	+	1.51848i	−0.0883019	+	0.0740941i
$421$	12.5494	+	21.7362i	0.611620	+	1.05936i	0.990967	+	0.134103i	$0.0428152\pi$
$421$	12.5494	+	21.7362i	0.611620	+	1.05936i	−0.379347	+	0.925254i	$0.623851\pi$
$422$	2.24346	−	12.7233i	0.109210	−	0.619361i
$423$	−0.0404313	+	0.229297i	−0.00196584	+	0.0111488i
$424$	−9.57308	−	8.03277i	−0.464910	−	0.390106i
$425$	−5.90267	−	2.14840i	−0.286322	−	0.104213i
$426$	4.33096	+	1.57634i	0.209836	+	0.0763740i
$427$	−35.3531	−	29.6648i	−1.71086	−	1.43558i
$428$	0.789231	−	4.47595i	0.0381489	−	0.216353i
$429$	−0.00893109	+	0.0506507i	−0.000431197	+	0.00244544i
$430$	2.48067	+	4.29665i	0.119629	+	0.207203i
$431$	−12.5746	+	10.5513i	−0.605696	+	0.508240i	−0.893271	−	0.449519i	$-0.851596\pi$
$431$	−12.5746	+	10.5513i	−0.605696	+	0.508240i	0.287575	+	0.957758i	$0.407151\pi$
$432$	−2.68044	+	0.975602i	−0.128963	+	0.0469387i
$433$	0.784375	−	1.35858i	0.0376946	−	0.0652890i	−0.846563	−	0.532289i	$-0.821332\pi$
$433$	0.784375	−	1.35858i	0.0376946	−	0.0652890i	0.884257	+	0.467000i	$0.154665\pi$
$434$	−18.6174	−	32.2463i	−0.893665	−	1.54787i
$435$	−1.61931	−	1.35877i	−0.0776402	−	0.0651478i
$436$	−6.17887	+	10.7021i	−0.295914	+	0.512538i
$437$	4.35656	+	24.7073i	0.208402	+	1.18191i
$438$	−4.18150			−0.199800
$439$	−3.63953	−	20.6408i	−0.173705	−	0.985132i	−0.939628	−	0.342199i	$-0.888828\pi$
$439$	−3.63953	−	20.6408i	−0.173705	−	0.985132i	0.765922	−	0.642933i	$-0.222283\pi$
$440$	−0.0273594	+	0.0229573i	−0.00130431	+	0.00109445i
$441$	40.6605	+	14.7992i	1.93621	+	0.704724i
$442$	−17.1474	+	6.24116i	−0.815620	+	0.296861i
$443$	−35.9465			−1.70787			−0.853934	−	0.520381i	$-0.825790\pi$
$443$	−35.9465			−1.70787			−0.853934	+	0.520381i	$0.825790\pi$
$444$	−0.267960	+	3.00338i	−0.0127168	+	0.142534i
$445$	−11.4812			−0.544262
$446$	22.0321	−	8.01904i	1.04325	−	0.379713i
$447$	3.67856	+	1.33889i	0.173990	+	0.0633271i
$448$	−3.65060	+	3.06322i	−0.172475	+	0.144723i
$449$	2.99657	+	16.9944i	0.141417	+	0.802015i	0.970175	+	0.242408i	$0.0779371\pi$
$449$	2.99657	+	16.9944i	0.141417	+	0.802015i	−0.828758	+	0.559608i	$0.810952\pi$
$450$	2.75427			0.129837
$451$	−0.00177853	−	0.0100866i	−8.37479e−5	−	0.000474958i
$452$	−8.69317	+	15.0570i	−0.408892	+	0.708222i
$453$	−2.10716	−	1.76812i	−0.0990032	−	0.0830736i
$454$	7.62717	+	13.2106i	0.357961	+	0.620006i
$455$	6.92198	−	11.9892i	0.324507	−	0.562063i
$456$	1.75993	−	0.640563i	0.0824163	−	0.0299971i
$457$	7.81430	−	6.55698i	0.365538	−	0.306722i	−0.441456	−	0.897283i	$-0.645538\pi$
$457$	7.81430	−	6.55698i	0.365538	−	0.306722i	0.806993	+	0.590561i	$0.201093\pi$
$458$	−2.55082	−	4.41816i	−0.119192	−	0.206447i
$459$	3.11139	−	17.6456i	0.145227	−	0.823624i
$460$	1.15309	−	6.53952i	0.0537633	−	0.304907i
$461$	−24.6352	−	20.6714i	−1.14737	−	0.962761i	−0.147719	−	0.989029i	$-0.547193\pi$
$461$	−24.6352	−	20.6714i	−1.14737	−	0.962761i	−0.999655	+	0.0262683i	$0.991638\pi$
$462$	−0.0792829	−	0.0288566i	−0.00368858	−	0.00134253i
$463$	21.6211	+	7.86944i	1.00482	+	0.365724i	0.791441	−	0.611246i	$-0.209331\pi$
$463$	21.6211	+	7.86944i	1.00482	+	0.365724i	0.213378	+	0.976970i	$0.431554\pi$
$464$	−3.26663	−	2.74103i	−0.151650	−	0.127249i
$465$	0.672575	−	3.81436i	0.0311899	−	0.176887i
$466$	4.65133	−	26.3790i	0.215469	−	1.22198i
$467$	2.65788	+	4.60358i	0.122992	+	0.213028i	0.920946	−	0.389690i	$-0.127418\pi$
$467$	2.65788	+	4.60358i	0.122992	+	0.213028i	−0.797954	+	0.602718i	$0.794084\pi$
$468$	6.12929	−	5.14309i	0.283327	−	0.237739i
$469$	−2.24053	+	0.815486i	−0.103458	+	0.0376556i
$470$	−0.0422679	+	0.0732102i	−0.00194967	+	0.00337693i
$471$	−5.50147	−	9.52882i	−0.253494	−	0.439065i
$472$	7.56912	+	6.35124i	0.348397	+	0.292340i
$473$	−0.0885978	+	0.153456i	−0.00407373	+	0.00705591i
$474$	0.361102	+	2.04791i	0.0165859	+	0.0940636i
$475$	−3.77815			−0.173353
$476$	−5.19808	−	29.4798i	−0.238254	−	1.35120i
$477$	−26.3668	+	22.1244i	−1.20725	+	1.01301i
$478$	18.5477	+	6.75082i	0.848353	+	0.308775i
$479$	−3.97224	+	1.44578i	−0.181496	+	0.0660592i	−0.431170	−	0.902271i	$-0.641899\pi$
$479$	−3.97224	+	1.44578i	−0.181496	+	0.0660592i	0.249673	+	0.968330i	$0.419677\pi$
$480$	−0.495714			−0.0226261
$481$	−4.54417	−	17.0763i	−0.207196	−	0.778613i
$482$	−18.7285			−0.853062
$483$	14.7408	−	5.36521i	0.670729	−	0.244125i
$484$	10.3354	+	3.76179i	0.469792	+	0.170990i
$485$	3.78354	−	3.17477i	0.171802	−	0.144159i
$486$	2.07552	+	11.7709i	0.0941475	+	0.533937i
$487$	−11.3349			−0.513633			−0.256816	−	0.966460i	$-0.582674\pi$
$487$	−11.3349			−0.513633			−0.256816	+	0.966460i	$0.582674\pi$
$488$	−1.68164	−	9.53707i	−0.0761244	−	0.431723i
$489$	0.324391	−	0.561862i	0.0146695	−	0.0254083i
$490$	12.0347	+	10.0983i	0.543671	+	0.456194i
$491$	−7.10326	−	12.3032i	−0.320566	−	0.555236i	0.660039	−	0.751231i	$-0.270540\pi$
$491$	−7.10326	−	12.3032i	−0.320566	−	0.555236i	−0.980605	+	0.195995i	$0.937206\pi$
$492$	0.0710788	−	0.123112i	0.00320448	−	0.00555032i
$493$	25.1707	−	9.16138i	1.13363	−	0.412608i
$494$	−8.40782	+	7.05500i	−0.378286	+	0.317419i
$495$	0.0491846	+	0.0851903i	0.00221068	+	0.00382902i
$496$	1.35678	−	7.69469i	0.0609213	−	0.345502i
$497$	7.69393	−	43.6344i	0.345120	−	1.95727i
$498$	−2.60672	−	2.18730i	−0.116810	−	0.0980152i
$499$	−35.1348	−	12.7880i	−1.57285	−	0.572471i	−0.599217	−	0.800587i	$-0.704521\pi$
$499$	−35.1348	−	12.7880i	−1.57285	−	0.572471i	−0.973634	+	0.228116i	$0.926743\pi$
$500$	0.939693	+	0.342020i	0.0420243	+	0.0152956i
$501$	−2.32084	−	1.94742i	−0.103688	−	0.0870042i
$502$	1.84082	−	10.4398i	0.0821600	−	0.465952i
$503$	2.86438	−	16.2447i	0.127716	−	0.724315i	−0.851941	−	0.523638i	$-0.824575\pi$
$503$	2.86438	−	16.2447i	0.127716	−	0.724315i	0.979657	−	0.200677i	$-0.0643143\pi$
$504$	6.56276	+	11.3670i	0.292328	+	0.506328i
$505$	−9.97663	+	8.37138i	−0.443954	+	0.372522i
$506$	0.222861	−	0.0811146i	0.00990736	−	0.00360598i
$507$	−1.13043	+	1.95796i	−0.0502041	+	0.0869560i
$508$	9.78521	+	16.9485i	0.434148	+	0.751967i
$509$	−7.38147	−	6.19379i	−0.327178	−	0.274535i	0.464371	−	0.885641i	$-0.346280\pi$
$509$	−7.38147	−	6.19379i	−0.327178	−	0.274535i	−0.791549	+	0.611106i	$0.790725\pi$
$510$	1.55691	−	2.69665i	0.0689412	−	0.119410i
$511$	6.98042	+	39.5879i	0.308796	+	1.75127i
$512$	−1.00000			−0.0441942
$513$	−1.87142	−	10.6133i	−0.0826250	−	0.468590i
$514$	9.31894	−	7.81952i	0.411041	−	0.344904i
$515$	4.91720	+	1.78971i	0.216678	+	0.0788642i
$516$	−2.31109	+	0.841167i	−0.101740	+	0.0370303i
$517$	−0.00301922			−0.000132785
$518$	28.8815	−	2.47683i	1.26898	−	0.108826i
$519$	−5.23040			−0.229589
$520$	2.72983	−	0.993578i	0.119711	−	0.0435713i
$521$	−3.16796	−	1.15304i	−0.138791	−	0.0505158i	0.271691	−	0.962385i	$-0.412417\pi$
$521$	−3.16796	−	1.15304i	−0.138791	−	0.0505158i	−0.410482	+	0.911869i	$0.634639\pi$
$522$	−8.99718	+	7.54953i	−0.393796	+	0.330434i
$523$	−7.56959	−	42.9293i	−0.330995	−	1.87717i	−0.463672	−	0.886007i	$-0.653468\pi$
$523$	−7.56959	−	42.9293i	−0.330995	−	1.87717i	0.132677	−	0.991159i	$-0.457643\pi$
$524$	5.34236			0.233382
$525$	0.410215	+	2.32644i	0.0179032	+	0.101534i
$526$	15.7952	−	27.3581i	0.688703	−	1.19287i
$527$	37.5973	+	31.5479i	1.63776	+	1.37425i
$528$	−0.00885226	−	0.0153326i	−0.000385245	−	0.000667264i
$529$	−10.5475	+	18.2687i	−0.458585	+	0.794292i
$530$	−11.7431	+	4.27415i	−0.510089	+	0.185657i
$531$	20.8474	−	17.4930i	0.904699	−	0.759133i
$532$	−9.00242	−	15.5926i	−0.390304	−	0.676027i
$533$	−0.144664	+	0.820429i	−0.00626608	+	0.0355367i
$534$	0.988300	−	5.60493i	0.0427679	−	0.242549i
$535$	−3.48167	−	2.92147i	−0.150526	−	0.126306i
$536$	−0.470154	−	0.171122i	−0.0203076	−	0.00739135i
$537$	−2.26958	−	0.826059i	−0.0979395	−	0.0356471i
$538$	6.62225	+	5.55672i	0.285505	+	0.239567i
$539$	−0.0974325	+	0.552567i	−0.00419671	+	0.0238007i
$540$	−0.495326	+	2.80913i	−0.0213154	+	0.120886i
$541$	−14.4896	−	25.0968i	−0.622958	−	1.07899i	−0.988932	−	0.148369i	$-0.952598\pi$
$541$	−14.4896	−	25.0968i	−0.622958	−	1.07899i	0.365974	−	0.930625i	$-0.380736\pi$
$542$	1.72916	−	1.45094i	0.0742737	−	0.0623230i
$543$	3.27857	−	1.19330i	0.140697	−	0.0512094i
$544$	3.14075	−	5.43993i	0.134658	−	0.233235i
$545$	6.17887	+	10.7021i	0.264674	+	0.458428i
$546$	5.25709	+	4.41122i	0.224983	+	0.188783i
$547$	−2.56162	+	4.43686i	−0.109527	+	0.189706i	−0.915579	−	0.402139i	$-0.868267\pi$
$547$	−2.56162	+	4.43686i	−0.109527	+	0.189706i	0.806052	+	0.591845i	$0.201600\pi$
$548$	1.29861	+	7.36477i	0.0554738	+	0.314608i
$549$	−26.6729			−1.13837
$550$	0.00620188	+	0.0351726i	0.000264449	+	0.00149977i
$551$	12.3418	−	10.3560i	0.525780	−	0.441181i
$552$	3.09322	+	1.12584i	0.131656	+	0.0479189i
$553$	18.7856	−	6.83738i	0.798843	−	0.290755i
$554$	−9.39570			−0.399185
$555$	2.46702	+	1.73375i	0.104719	+	0.0735935i
$556$	8.19440			0.347520
$557$	1.60035	−	0.582480i	0.0678091	−	0.0246805i	−0.307893	−	0.951421i	$-0.599624\pi$
$557$	1.60035	−	0.582480i	0.0678091	−	0.0246805i	0.375702	+	0.926741i	$0.377402\pi$
$558$	−20.2224	−	7.36034i	−0.856081	−	0.311588i
$559$	11.0409	−	9.26441i	0.466980	−	0.391843i
$560$	0.827523	+	4.69312i	0.0349692	+	0.198320i
$561$	0.111211			0.00469532
$562$	0.0250050	+	0.141810i	0.00105477	+	0.00598190i
$563$	18.6749	−	32.3460i	0.787055	−	1.36322i	−0.140708	−	0.990051i	$-0.544938\pi$
$563$	18.6749	−	32.3460i	0.787055	−	1.36322i	0.927764	−	0.373169i	$-0.121729\pi$
$564$	−0.0321015	−	0.0269364i	−0.00135172	−	0.00113423i
$565$	8.69317	+	15.0570i	0.365724	+	0.633453i
$566$	−13.2173	+	22.8930i	−0.555564	+	0.962265i
$567$	30.6697	−	11.1629i	1.28801	−	0.468797i
$568$	7.12233	−	5.97634i	0.298846	−	0.250762i
$569$	20.9872	+	36.3509i	0.879830	+	1.52391i	0.851527	+	0.524311i	$0.175677\pi$
$569$	20.9872	+	36.3509i	0.879830	+	1.52391i	0.0283028	+	0.999599i	$0.490990\pi$
$570$	0.325222	−	1.84443i	0.0136221	−	0.0772545i
$571$	4.32658	−	24.5373i	0.181062	−	1.02685i	−0.749850	−	0.661608i	$-0.769874\pi$
$571$	4.32658	−	24.5373i	0.181062	−	1.02685i	0.930912	−	0.365245i	$-0.119015\pi$
$572$	0.0794799	+	0.0666916i	0.00332322	+	0.00278852i
$573$	5.62157	+	2.04608i	0.234844	+	0.0854763i
$574$	−1.28421	−	0.467413i	−0.0536017	−	0.0195094i
$575$	−5.08684	−	4.26837i	−0.212136	−	0.178003i
$576$	−0.478274	+	2.71242i	−0.0199281	+	0.113018i
$577$	2.51562	−	14.2668i	0.104727	−	0.593934i	−0.886603	−	0.462532i	$-0.846941\pi$
$577$	2.51562	−	14.2668i	0.104727	−	0.593934i	0.991329	−	0.131402i	$-0.0419478\pi$
$578$	11.2286	+	19.4485i	0.467047	+	0.808950i
$579$	−6.99082	+	5.86599i	−0.290529	+	0.243782i
$580$	−4.00712	+	1.45847i	−0.166387	+	0.0605597i
$581$	−16.3565	+	28.3303i	−0.678581	+	1.17534i
$582$	1.22418	+	2.12034i	0.0507439	+	0.0878911i
$583$	−0.341905	−	0.286892i	−0.0141602	−	0.0118819i
$584$	−4.21766	+	7.30520i	−0.174528	+	0.302291i
$585$	−1.38940	−	7.87967i	−0.0574446	−	0.325784i
$586$	13.0223			0.537948
$587$	−3.71810	−	21.0864i	−0.153463	−	0.870329i	−0.960178	−	0.279389i	$-0.909868\pi$
$587$	−3.71810	−	21.0864i	−0.153463	−	0.870329i	0.806715	−	0.590940i	$-0.201243\pi$
$588$	−5.96575	+	5.00586i	−0.246023	+	0.206438i
$589$	27.7399	+	10.0965i	1.14300	+	0.416019i
$590$	9.28489	−	3.37943i	0.382253	−	0.139129i
$591$	−0.891236			−0.0366605
$592$	4.97671	+	3.49748i	0.204541	+	0.143746i
$593$	23.1182			0.949350			0.474675	−	0.880161i	$-0.342566\pi$
$593$	23.1182			0.949350			0.474675	+	0.880161i	$0.342566\pi$
$594$	−0.0957326	+	0.0348438i	−0.00392796	+	0.00142966i
$595$	−28.1293	−	10.2382i	−1.15319	−	0.419726i
$596$	6.04944	−	5.07608i	0.247795	−	0.207924i
$597$	0.264522	+	1.50018i	0.0108262	+	0.0613982i
$598$	−19.2905			−0.788849
$599$	−5.02215	−	28.4820i	−0.205199	−	1.16374i	−0.897126	−	0.441775i	$-0.854349\pi$
$599$	−5.02215	−	28.4820i	−0.205199	−	1.16374i	0.691926	−	0.721968i	$-0.256762\pi$
$600$	−0.247857	+	0.429301i	−0.0101187	+	0.0175261i
$601$	−5.01722	−	4.20994i	−0.204657	−	0.171727i	0.534699	−	0.845043i	$-0.320425\pi$
$601$	−5.01722	−	4.20994i	−0.204657	−	0.171727i	−0.739355	+	0.673316i	$0.764870\pi$
$602$	11.8217	+	20.4758i	0.481816	+	0.834530i
$603$	−0.689018	+	1.19341i	−0.0280590	+	0.0485996i
$604$	−5.21434	+	1.89787i	−0.212169	+	0.0772230i
$605$	8.42551	−	7.06984i	0.342546	−	0.287430i
$606$	−3.22798	−	5.59102i	−0.131128	−	0.227120i
$607$	8.41297	−	47.7123i	0.341472	−	1.93658i	−0.00886689	−	0.999961i	$-0.502822\pi$
$607$	8.41297	−	47.7123i	0.341472	−	1.93658i	0.350339	−	0.936623i	$-0.386066\pi$
$608$	0.656069	−	3.72075i	0.0266071	−	0.150896i
$609$	−7.71687	−	6.47522i	−0.312703	−	0.262389i
$610$	−9.10016	−	3.31219i	−0.368455	−	0.134107i
$611$	0.230769	+	0.0839930i	0.00933591	+	0.00339799i
$612$	−13.2533	−	11.1208i	−0.535732	−	0.449532i
$613$	6.68962	−	37.9387i	0.270191	−	1.53233i	−0.483643	−	0.875266i	$-0.660687\pi$
$613$	6.68962	−	37.9387i	0.270191	−	1.53233i	0.753834	−	0.657065i	$-0.228202\pi$
$614$	−3.95758	+	22.4445i	−0.159715	+	0.905788i
$615$	−0.0710788	−	0.123112i	−0.00286617	−	0.00496436i
$616$	−0.130382	+	0.109403i	−0.00525323	+	0.00440799i
$617$	−26.2780	+	9.56442i	−1.05791	+	0.385049i	−0.811644	−	0.584152i	$-0.801427\pi$
$617$	−26.2780	+	9.56442i	−1.05791	+	0.385049i	−0.246270	+	0.969201i	$0.579205\pi$
$618$	−1.29698	+	2.24643i	−0.0521721	+	0.0903648i
$619$	12.1022	+	20.9616i	0.486427	+	0.842517i	0.999878	−	0.0156020i	$-0.00496646\pi$
$619$	12.1022	+	20.9616i	0.486427	+	0.842517i	−0.513451	+	0.858119i	$0.671633\pi$
$620$	−5.98541	−	5.02235i	−0.240380	−	0.201703i
$621$	9.47077	−	16.4038i	0.380049	−	0.658264i
$622$	−4.63208	−	26.2698i	−0.185730	−	1.05332i
$623$	−54.7139			−2.19207
$624$	0.250064	+	1.41818i	0.0100106	+	0.0567728i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−16.1417	−	5.87510i	−0.645153	−	0.234816i
$627$	0.0628563	−	0.0228778i	0.00251024	−	0.000913653i
$628$	−22.1961			−0.885723
$629$	−34.6566	+	16.0883i	−1.38185	+	0.641481i
$630$	13.1255			0.522933
$631$	−25.1948	+	9.17015i	−1.00299	+	0.365058i	−0.790736	−	0.612157i	$-0.790302\pi$
$631$	−25.1948	+	9.17015i	−1.00299	+	0.365058i	−0.212252	+	0.977215i	$0.568080\pi$
$632$	3.94198	+	1.43476i	0.156803	+	0.0570718i
$633$	4.90607	−	4.11668i	0.194999	−	0.163623i
$634$	3.63150	+	20.5952i	0.144225	+	0.817941i
$635$	19.5704			0.776628
$636$	−1.07572	−	6.10070i	−0.0426550	−	0.241909i
$637$	22.8192	−	39.5240i	0.904130	−	1.56600i
$638$	−0.116668	−	0.0978965i	−0.00461895	−	0.00387576i
$639$	−12.8040	−	22.1771i	−0.506517	−	0.877313i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−23.1443	+	8.42383i	−0.914145	+	0.332721i	−0.755907	−	0.654680i	$-0.772804\pi$
$641$	−23.1443	+	8.42383i	−0.914145	+	0.332721i	−0.158238	+	0.987401i	$0.550581\pi$
$642$	1.72591	−	1.44821i	0.0681164	−	0.0571564i
$643$	1.01230	+	1.75336i	0.0399212	+	0.0691456i	0.885296	−	0.465029i	$-0.153956\pi$
$643$	1.01230	+	1.75336i	0.0399212	+	0.0691456i	−0.845374	+	0.534174i	$0.820623\pi$
$644$	5.49509	−	31.1642i	0.216537	−	1.22804i
$645$	−0.427072	+	2.42204i	−0.0168159	+	0.0953679i
$646$	18.1801	+	15.2549i	0.715286	+	0.600196i
$647$	−1.81973	−	0.662326i	−0.0715408	−	0.0260387i	0.306002	−	0.952031i	$-0.401009\pi$
$647$	−1.81973	−	0.662326i	−0.0715408	−	0.0260387i	−0.377543	+	0.925992i	$0.623231\pi$
$648$	6.43576	+	2.34243i	0.252821	+	0.0920192i
$649$	0.270333	+	0.226836i	0.0106115	+	0.00890409i
$650$	0.504453	−	2.86089i	0.0197863	−	0.112214i
$651$	3.20517	−	18.1774i	0.125620	−	0.712429i
$652$	−0.654392	−	1.13344i	−0.0256280	−	0.0443890i
$653$	−34.7672	+	29.1731i	−1.36054	+	1.14163i	−0.384731	+	0.923029i	$0.625706\pi$
$653$	−34.7672	+	29.1731i	−1.36054	+	1.14163i	−0.975814	+	0.218604i	$0.929850\pi$
$654$	−5.75646	+	2.09518i	−0.225095	+	0.0819280i
$655$	2.67118	−	4.62662i	0.104372	−	0.180777i
$656$	−0.143387	−	0.248353i	−0.00559831	−	0.00969656i
$657$	17.7976	+	14.9340i	0.694350	+	0.582629i
$658$	−0.201428	+	0.348884i	−0.00785250	+	0.0136009i
$659$	−1.44482	−	8.19396i	−0.0562820	−	0.319191i	0.943649	−	0.330948i	$-0.107369\pi$
$659$	−1.44482	−	8.19396i	−0.0562820	−	0.319191i	−0.999931	+	0.0117571i	$0.996258\pi$
$660$	−0.0177045			−0.000689147
$661$	2.76227	+	15.6656i	0.107440	+	0.609323i	0.990218	+	0.139531i	$0.0445596\pi$
$661$	2.76227	+	15.6656i	0.107440	+	0.609323i	−0.882778	+	0.469791i	$0.844329\pi$
$662$	−26.7795	+	22.4707i	−1.04081	+	0.873347i
$663$	−8.50022	−	3.09383i	−0.330121	−	0.120154i
$664$	−6.45053	+	2.34780i	−0.250329	+	0.0911124i
$665$	−18.0048			−0.698198
$666$	11.8669	−	11.8262i	0.459832	−	0.458256i
$667$	28.3166			1.09642
$668$	−5.74310	+	2.09032i	−0.222207	+	0.0808769i
$669$	10.9216	+	3.97515i	0.422255	+	0.153688i
$670$	−0.383273	+	0.321605i	−0.0148071	+	0.0124247i
$671$	−0.0600602	−	0.340618i	−0.00231860	−	0.0131494i
$672$	−2.36233			−0.0911289
$673$	−3.83282	−	21.7370i	−0.147744	−	0.837900i	−0.965123	−	0.261799i	$-0.915684\pi$
$673$	−3.83282	−	21.7370i	−0.147744	−	0.837900i	0.817378	−	0.576102i	$-0.195427\pi$
$674$	−12.3498	+	21.3906i	−0.475698	+	0.823933i
$675$	2.18512	+	1.83353i	0.0841052	+	0.0705727i
$676$	2.28041	+	3.94978i	0.0877079	+	0.151915i
$677$	10.2435	−	17.7423i	0.393690	−	0.681890i	−0.599243	−	0.800567i	$-0.704532\pi$
$677$	10.2435	−	17.7423i	0.393690	−	0.681890i	0.992933	+	0.118676i	$0.0378651\pi$
$678$	−8.09887	+	2.94775i	−0.311035	+	0.113208i
$679$	18.0305	−	15.1294i	0.691949	−	0.580614i
$680$	−3.14075	−	5.43993i	−0.120442	−	0.208612i
$681$	−1.31309	+	7.44690i	−0.0503177	+	0.285366i
$682$	0.0484577	−	0.274817i	0.00185554	−	0.0105233i
$683$	5.57819	+	4.68066i	0.213444	+	0.179100i	0.743241	−	0.669024i	$-0.233288\pi$
$683$	5.57819	+	4.68066i	0.213444	+	0.179100i	−0.529797	+	0.848124i	$0.677732\pi$
$684$	−9.77848	−	3.55907i	−0.373889	−	0.136085i
$685$	7.02738	+	2.55776i	0.268503	+	0.0977269i
$686$	31.7972	+	26.6811i	1.21402	+	1.01869i
$687$	0.439149	−	2.49054i	0.0167546	−	0.0950199i
$688$	−0.861529	+	4.88597i	−0.0328455	+	0.186276i
$689$	18.1517	+	31.4397i	0.691526	+	1.19776i
$690$	2.52162	−	2.11589i	0.0959963	−	0.0805505i
$691$	6.42415	−	2.33820i	0.244386	−	0.0889493i	−0.216923	−	0.976189i	$-0.569602\pi$
$691$	6.42415	−	2.33820i	0.244386	−	0.0889493i	0.461309	+	0.887239i	$0.347380\pi$
$692$	−5.27562	+	9.13765i	−0.200549	+	0.347361i
$693$	0.234390	+	0.405976i	0.00890375	+	0.0154217i
$694$	8.71371	+	7.31167i	0.330768	+	0.277547i
$695$	4.09720	−	7.09656i	0.155416	−	0.269188i
$696$	−0.367069	−	2.08175i	−0.0139137	−	0.0789085i
$697$	1.80137			0.0682316
$698$	1.67847	+	9.51910i	0.0635312	+	0.360303i
$699$	10.1717	−	8.53503i	0.384727	−	0.322824i
$700$	4.47812	+	1.62990i	0.169257	+	0.0616045i
$701$	−20.2481	+	7.36970i	−0.764759	+	0.278350i	−0.694803	−	0.719200i	$-0.744508\pi$
$701$	−20.2481	+	7.36970i	−0.764759	+	0.278350i	−0.0699565	+	0.997550i	$0.522286\pi$
$702$	8.28650			0.312754
$703$	−16.2783	+	16.2225i	−0.613948	+	0.611843i
$704$	−0.0357152			−0.00134607
$705$	−0.0393784	+	0.0143325i	−0.00148307	+	0.000539795i
$706$	0.976249	+	0.355326i	0.0367416	+	0.0133729i
$707$	−47.5438	+	39.8940i	−1.78807	+	1.50037i
$708$	0.850535	+	4.82362i	0.0319651	+	0.181283i
$709$	18.9008			0.709834			0.354917	−	0.934898i	$-0.384509\pi$
$709$	18.9008			0.709834			0.354917	+	0.934898i	$0.384509\pi$
$710$	−1.61450	−	9.15629i	−0.0605911	−	0.343629i
$711$	5.77703	−	10.0061i	0.216655	−	0.375258i
$712$	−8.79512	−	7.37998i	−0.329611	−	0.276576i
$713$	25.9420	+	44.9329i	0.971537	+	1.68275i
$714$	7.41949	−	12.8509i	0.277667	−	0.480934i
$715$	0.0974966	−	0.0354858i	0.00364616	−	0.00132710i
$716$	−3.73235	+	3.13181i	−0.139485	+	0.117041i
$717$	4.89222	+	8.47357i	0.182703	+	0.316451i
$718$	−0.470721	+	2.66959i	−0.0175672	+	0.0996283i
$719$	−3.52293	+	19.9796i	−0.131383	+	0.745112i	0.845927	+	0.533299i	$0.179048\pi$
$719$	−3.52293	+	19.9796i	−0.131383	+	0.745112i	−0.977310	+	0.211813i	$0.932063\pi$
$720$	2.10989	+	1.77041i	0.0786310	+	0.0659793i
$721$	23.4330	+	8.52891i	0.872690	+	0.317633i
$722$	−4.44060	−	1.61625i	−0.165262	−	0.0601504i
$723$	−7.11195	−	5.96764i	−0.264496	−	0.221939i
$724$	1.22219	−	6.93136i	0.0454222	−	0.257602i
$725$	−0.740486	+	4.19950i	−0.0275009	+	0.155966i
$726$	2.72611	+	4.72176i	0.101175	+	0.175241i
$727$	−24.1230	+	20.2416i	−0.894673	+	0.750720i	−0.969142	−	0.246504i	$-0.920718\pi$
$727$	−24.1230	+	20.2416i	−0.894673	+	0.750720i	0.0744689	+	0.997223i	$0.476274\pi$
$728$	13.0091	−	4.73491i	0.482148	−	0.175488i
$729$	7.31070	−	12.6625i	0.270767	−	0.468982i
$730$	4.21766	+	7.30520i	0.156102	+	0.270377i
$731$	−23.8735	−	20.0323i	−0.882994	−	0.740920i
$732$	2.40029	−	4.15743i	0.0887174	−	0.153663i
$733$	3.19189	+	18.1021i	0.117895	+	0.668618i	0.985276	+	0.170972i	$0.0546908\pi$
$733$	3.19189	+	18.1021i	0.117895	+	0.668618i	−0.867381	+	0.497645i	$0.834198\pi$
$734$	26.0109			0.960080
$735$	1.35233	+	7.66942i	0.0498813	+	0.282891i
$736$	5.08684	−	4.26837i	0.187503	−	0.157334i
$737$	−0.0167917	−	0.00611166i	−0.000618529	−	0.000225126i
$738$	−0.742217	+	0.270145i	−0.0273214	+	0.00994417i
$739$	22.0793			0.812200			0.406100	−	0.913829i	$-0.366888\pi$
$739$	22.0793			0.812200			0.406100	+	0.913829i	$0.366888\pi$
$740$	5.51726	−	2.56122i	0.202819	−	0.0941521i
$741$	−5.44077			−0.199872
$742$	−55.9620	+	20.3685i	−2.05443	+	0.747752i
$743$	−4.07813	−	1.48432i	−0.149612	−	0.0544544i	0.266129	−	0.963938i	$-0.414255\pi$
$743$	−4.07813	−	1.48432i	−0.149612	−	0.0544544i	−0.415741	+	0.909483i	$0.636478\pi$
$744$	2.96705	−	2.48965i	0.108777	−	0.0912749i
$745$	−1.37130	−	7.77700i	−0.0502404	−	0.284927i
$746$	26.3443			0.964533
$747$	3.28312	+	18.6195i	0.120123	+	0.681251i
$748$	0.112172	−	0.194288i	0.00410143	−	0.00710389i
$749$	−16.5920	−	13.9223i	−0.606258	−	0.508711i
$750$	0.247857	+	0.429301i	0.00905045	+	0.0156758i
$751$	−6.99791	+	12.1207i	−0.255357	+	0.442292i	−0.964992	−	0.262277i	$-0.915526\pi$
$751$	−6.99791	+	12.1207i	−0.255357	+	0.442292i	0.709635	+	0.704569i	$0.248860\pi$
$752$	−0.0794377	+	0.0289130i	−0.00289680	+	0.00105435i
$753$	4.02556	−	3.37785i	0.146700	−	0.123096i
$754$	6.19394	+	10.7282i	0.225570	+	0.390698i
$755$	−0.963571	+	5.46469i	−0.0350680	+	0.198880i
$756$	−2.36048	+	13.3870i	−0.0858500	+	0.486879i
$757$	18.0011	+	15.1047i	0.654261	+	0.548990i	0.908361	−	0.418188i	$-0.137335\pi$
$757$	18.0011	+	15.1047i	0.654261	+	0.548990i	−0.254099	+	0.967178i	$0.581779\pi$
$758$	−15.6873	−	5.70971i	−0.569789	−	0.207386i
$759$	0.110475	+	0.0402096i	0.00400999	+	0.00145952i
$760$	−2.89423	−	2.42855i	−0.104985	−	0.0880927i
$761$	6.86355	−	38.9251i	0.248804	−	1.41104i	−0.562687	−	0.826670i	$-0.690232\pi$
$761$	6.86355	−	38.9251i	0.248804	−	1.41104i	0.811491	−	0.584365i	$-0.198657\pi$
$762$	−1.68462	+	9.55394i	−0.0610272	+	0.346103i
$763$	29.4455	+	51.0011i	1.06600	+	1.84636i
$764$	9.24474	−	7.75726i	0.334463	−	0.280648i
$765$	−16.2575	+	5.91726i	−0.587793	+	0.213939i
$766$	−10.3893	+	17.9947i	−0.375379	+	0.650176i
$767$	−14.3520	−	24.8583i	−0.518220	−	0.897583i
$768$	−0.379739	−	0.318639i	−0.0137026	−	0.0114979i
$769$	−8.38223	+	14.5184i	−0.302271	+	0.523548i	−0.976650	−	0.214837i	$-0.931078\pi$
$769$	−8.38223	+	14.5184i	−0.302271	+	0.523548i	0.674379	+	0.738385i	$0.264411\pi$
$770$	0.0295552	+	0.167616i	0.00106509	+	0.00604045i
$771$	6.03036			0.217178
$772$	3.19679	+	18.1299i	0.115055	+	0.652508i
$773$	−28.5419	+	23.9495i	−1.02658	+	0.861405i	−0.990440	−	0.137942i	$-0.955951\pi$
$773$	−28.5419	+	23.9495i	−1.02658	+	0.861405i	−0.0361422	+	0.999347i	$0.511507\pi$
$774$	12.8408	+	4.67367i	0.461553	+	0.167991i
$775$	−7.34219	+	2.67234i	−0.263739	+	0.0959932i
$776$	4.93907			0.177302
$777$	11.7566	+	8.26221i	0.421767	+	0.296405i
$778$	−10.1179			−0.362746
$779$	1.01813	−	0.370570i	0.0364784	−	0.0132770i
$780$	1.35322	+	0.492530i	0.0484529	+	0.0176354i
$781$	0.254375	−	0.213446i	0.00910227	−	0.00763771i
$782$	7.24315	+	41.0779i	0.259014	+	1.46894i
$783$	−12.1637			−0.434697
$784$	2.72804	+	15.4715i	0.0974300	+	0.552553i
$785$	−11.0981	+	19.2224i	−0.396107	+	0.686078i
$786$	2.02870	+	1.70228i	0.0723614	+	0.0607184i
$787$	−25.0993	−	43.4732i	−0.894692	−	1.54965i	−0.834185	−	0.551485i	$-0.814062\pi$
$787$	−25.0993	−	43.4732i	−0.894692	−	1.54965i	−0.0605071	−	0.998168i	$-0.519272\pi$
$788$	−0.898942	+	1.55701i	−0.0320235	+	0.0554663i
$789$	14.7154	−	5.35596i	0.523881	−	0.190677i
$790$	3.21353	−	2.69647i	0.114332	−	0.0959361i
$791$	41.4274	+	71.7544i	1.47299	+	2.55129i
$792$	−0.0170816	+	0.0968748i	−0.000606970	+	0.00344230i
$793$	−4.88522	+	27.7055i	−0.173479	+	0.983849i
$794$	−15.7960	−	13.2545i	−0.560581	−	0.470383i
$795$	−5.82122	−	2.11875i	−0.206458	−	0.0751444i
$796$	2.88766	+	1.05102i	0.102350	+	0.0372525i
$797$	23.2632	+	19.5201i	0.824023	+	0.691438i	0.953911	−	0.300091i	$-0.0970171\pi$
$797$	23.2632	+	19.5201i	0.824023	+	0.691438i	−0.129887	+	0.991529i	$0.541462\pi$
$798$	1.54985	−	8.78965i	0.0548642	−	0.311150i
$799$	0.0922092	−	0.522944i	0.00326213	−	0.0185004i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−24.2241	+	20.3264i	−0.855917	+	0.718200i
$802$	23.7208	−	8.63367i	0.837611	−	0.304865i
$803$	−0.150634	+	0.260907i	−0.00531578	+	0.00920719i
$804$	−0.124010	−	0.214791i	−0.00437348	−	0.00757510i
$805$	−24.2414	−	20.3410i	−0.854398	−	0.716925i
$806$	−11.3491	+	19.6572i	−0.399754	+	0.692394i
$807$	0.744136	+	4.22021i	0.0261948	+	0.148558i
$808$	−13.0236			−0.458167
$809$	−2.22273	−	12.6057i	−0.0781471	−	0.443194i	−0.998626	−	0.0524020i	$-0.983312\pi$
$809$	−2.22273	−	12.6057i	−0.0781471	−	0.443194i	0.920479	−	0.390792i	$-0.127799\pi$
$810$	5.24648	−	4.40232i	0.184343	−	0.154682i
$811$	−7.45997	−	2.71521i	−0.261955	−	0.0953438i	0.207704	−	0.978192i	$-0.433401\pi$
$811$	−7.45997	−	2.71521i	−0.261955	−	0.0953438i	−0.469659	+	0.882848i	$0.655623\pi$
$812$	−19.0960	+	6.95037i	−0.670138	+	0.243910i
$813$	1.11895			0.0392434
$814$	0.177744	+	0.124913i	0.00622993	+	0.00437821i
$815$	−1.30878			−0.0458447
$816$	2.92604	−	1.06499i	0.102432	−	0.0372821i
$817$	−17.6143	−	6.41107i	−0.616245	−	0.224295i
$818$	8.04209	−	6.74811i	0.281185	−	0.235942i
$819$	−6.62120	−	37.5507i	−0.231363	−	1.31213i
$820$	−0.286773			−0.0100146
$821$	−2.77322	−	15.7277i	−0.0967859	−	0.548900i	−0.994185	−	0.107681i	$-0.965657\pi$
$821$	−2.77322	−	15.7277i	−0.0967859	−	0.548900i	0.897400	−	0.441219i	$-0.145454\pi$
$822$	−1.85357	+	3.21048i	−0.0646506	+	0.111978i
$823$	−18.7932	−	15.7694i	−0.655090	−	0.549686i	0.253521	−	0.967330i	$-0.418411\pi$
$823$	−18.7932	−	15.7694i	−0.655090	−	0.549686i	−0.908611	+	0.417644i	$0.862856\pi$
$824$	2.61639	+	4.53172i	0.0911462	+	0.157870i
$825$	−0.00885226	+	0.0153326i	−0.000308196	+	0.000533811i
$826$	44.2473	−	16.1047i	1.53956	−	0.560354i
$827$	0.0634080	−	0.0532057i	0.00220491	−	0.00185014i	−0.641684	−	0.766969i	$-0.721764\pi$
$827$	0.0634080	−	0.0532057i	0.00220491	−	0.00185014i	0.643889	+	0.765119i	$0.277320\pi$
$828$	−9.14472	−	15.8391i	−0.317801	−	0.550447i
$829$	1.55065	−	8.79419i	0.0538564	−	0.305435i	−0.945966	−	0.324265i	$-0.894883\pi$
$829$	1.55065	−	8.79419i	0.0538564	−	0.305435i	0.999823	+	0.0188301i	$0.00599417\pi$
$830$	−1.19201	+	6.76023i	−0.0413753	+	0.234651i
$831$	−3.56791	−	2.99383i	−0.123769	−	0.103855i
$832$	2.72983	+	0.993578i	0.0946400	+	0.0344461i
$833$	−92.7319	−	33.7516i	−3.21297	−	1.16943i
$834$	3.11173	+	2.61105i	0.107750	+	0.0904133i
$835$	−1.06128	+	6.01883i	−0.0367272	+	0.208290i
$836$	0.0234316	−	0.132887i	0.000810400	−	0.00459601i
$837$	−11.1437	−	19.3015i	−0.385184	−	0.667158i
$838$	18.0779	−	15.1691i	0.624490	−	0.524009i
$839$	16.1386	−	5.87396i	0.557166	−	0.202792i	−0.0480617	−	0.998844i	$-0.515304\pi$
$839$	16.1386	−	5.87396i	0.557166	−	0.202792i	0.605227	+	0.796053i	$0.293082\pi$
$840$	−1.18117	+	2.04584i	−0.0407541	+	0.0705882i
$841$	5.40793	+	9.36681i	0.186480	+	0.322994i
$842$	19.2268	+	16.1332i	0.662599	+	0.555986i
$843$	−0.0356909	+	0.0618184i	−0.00122926	+	0.00212914i
$844$	−2.24346	−	12.7233i	−0.0772232	−	0.437954i
$845$	4.56081			0.156897
$846$	0.0404313	+	0.229297i	0.00139006	+	0.00788340i
$847$	40.1519	−	33.6915i	1.37964	−	1.15765i
$848$	−11.7431	−	4.27415i	−0.403260	−	0.146775i
$849$	−12.3137	+	4.48182i	−0.422605	+	0.153816i
$850$	−6.28149			−0.215453
$851$	−40.2443	+	3.45128i	−1.37956	+	0.118308i
$852$	4.60892			0.157899
$853$	15.7256	−	5.72366i	0.538435	−	0.195974i	−0.0584657	−	0.998289i	$-0.518621\pi$
$853$	15.7256	−	5.72366i	0.538435	−	0.195974i	0.596901	+	0.802315i	$0.296399\pi$
$854$	−43.3670	−	15.7843i	−1.48399	−	0.540127i
$855$	−7.97149	+	6.68887i	−0.272619	+	0.228755i
$856$	−0.789231	−	4.47595i	−0.0269754	−	0.152985i
$857$	43.7498			1.49446			0.747232	−	0.664563i	$-0.231382\pi$
$857$	43.7498			1.49446			0.747232	+	0.664563i	$0.231382\pi$
$858$	0.00893109	+	0.0506507i	0.000304902	+	0.00172919i
$859$	−7.87654	+	13.6426i	−0.268744	+	0.465478i	−0.968538	−	0.248867i	$-0.919942\pi$
$859$	−7.87654	+	13.6426i	−0.268744	+	0.465478i	0.699794	+	0.714345i	$0.253275\pi$
$860$	3.80061	+	3.18909i	0.129600	+	0.108747i
$861$	−0.338727	−	0.586692i	−0.0115438	−	0.0199944i
$862$	−8.20748	+	14.2158i	−0.279548	+	0.484191i
$863$	−38.9938	+	14.1926i	−1.32737	+	0.483122i	−0.905811	−	0.423681i	$-0.860738\pi$
$863$	−38.9938	+	14.1926i	−1.32737	+	0.483122i	−0.421555	+	0.906803i	$0.638515\pi$
$864$	−2.18512	+	1.83353i	−0.0743392	+	0.0623780i
$865$	5.27562	+	9.13765i	0.179377	+	0.310689i
$866$	0.272410	−	1.54492i	0.00925688	−	0.0524984i
$867$	−1.93311	+	10.9632i	−0.0656518	+	0.372330i
$868$	−28.5236	−	23.9341i	−0.968153	−	0.812377i
$869$	0.140789	+	0.0512428i	0.00477592	+	0.00173829i
$870$	−1.98638	−	0.722984i	−0.0673447	−	0.0245115i
$871$	1.11342	+	0.934270i	0.0377268	+	0.0316565i
$872$	−2.14590	+	12.1700i	−0.0726693	+	0.412128i
$873$	2.36223	−	13.3968i	0.0799492	−	0.453415i
$874$	12.5442	+	21.7272i	0.424314	+	0.734934i
$875$	3.65060	−	3.06322i	0.123413	−	0.103556i
$876$	−3.92932	+	1.43016i	−0.132760	+	0.0483205i
$877$	−8.96793	+	15.5329i	−0.302826	+	0.524509i	−0.976775	−	0.214268i	$-0.931263\pi$
$877$	−8.96793	+	15.5329i	−0.302826	+	0.524509i	0.673949	+	0.738778i	$0.264597\pi$
$878$	−10.4796	−	18.1512i	−0.353670	−	0.612574i
$879$	4.94508	+	4.14942i	0.166794	+	0.139956i
$880$	−0.0178576	+	0.0309303i	−0.000601980	+	0.00104266i
$881$	−2.08200	−	11.8076i	−0.0701444	−	0.397809i	−0.999584	−	0.0288348i	$-0.990820\pi$
$881$	−2.08200	−	11.8076i	−0.0701444	−	0.397809i	0.929440	−	0.368974i	$-0.120291\pi$
$882$	43.2700			1.45698
$883$	5.22705	+	29.6441i	0.175904	+	0.997602i	0.937095	+	0.349074i	$0.113504\pi$
$883$	5.22705	+	29.6441i	0.175904	+	0.997602i	−0.761191	+	0.648528i	$0.775385\pi$
$884$	−13.9787	+	11.7295i	−0.470155	+	0.394507i
$885$	4.60265	+	1.67523i	0.154716	+	0.0563121i
$886$	−33.7786	+	12.2944i	−1.13482	+	0.413039i
$887$	−5.27048			−0.176965			−0.0884827	−	0.996078i	$-0.528202\pi$
$887$	−5.27048			−0.176965			−0.0884827	+	0.996078i	$0.528202\pi$
$888$	0.775416	+	2.91390i	0.0260213	+	0.0977841i
$889$	93.2632			3.12795
$890$	−10.7888	+	3.92681i	−0.361642	+	0.131627i
$891$	0.229855	+	0.0836602i	0.00770042	+	0.00280272i
$892$	17.9608	−	15.0709i	0.601371	−	0.504610i
$893$	−0.0554613	−	0.314537i	−0.00185594	−	0.0105256i
$894$	3.91464			0.130925
$895$	0.846055	+	4.79822i	0.0282805	+	0.160387i
$896$	−2.38276	+	4.12706i	−0.0796024	+	0.137875i
$897$	−7.32537	−	6.14671i	−0.244587	−	0.205233i
$898$	8.62828	+	14.9446i	0.287930	+	0.498709i
$899$	16.6593	−	28.8547i	0.555618	−	0.962358i
$900$	2.58817	−	0.942015i	0.0862722	−	0.0314005i
$901$	60.1332	−	50.4578i	2.00333	−	1.68099i
$902$	−0.00512109	−	0.00886998i	−0.000170514	−	0.000295338i
$903$	−2.03522	+	11.5423i	−0.0677278	+	0.384103i
$904$	−3.01910	+	17.1222i	−0.100414	+	0.569476i
$905$	−5.39164	−	4.52413i	−0.179224	−	0.150387i
$906$	−2.58482	−	0.940798i	−0.0858749	−	0.0312559i
$907$	36.9213	+	13.4383i	1.22595	+	0.446210i	0.872209	−	0.489133i	$-0.162687\pi$
$907$	36.9213	+	13.4383i	1.22595	+	0.446210i	0.353742	+	0.935343i	$0.384909\pi$
$908$	11.6855	+	9.80530i	0.387797	+	0.325400i
$909$	−6.22883	+	35.3254i	−0.206597	+	1.17167i
$910$	2.40398	−	13.6336i	0.0796911	−	0.451951i
$911$	10.9663	+	18.9942i	0.363330	+	0.629307i	0.988507	−	0.151177i	$-0.0483063\pi$
$911$	10.9663	+	18.9942i	0.363330	+	0.629307i	−0.625176	+	0.780484i	$0.714973\pi$
$912$	1.43471	−	1.20386i	0.0475080	−	0.0398639i
$913$	−0.230382	+	0.0838523i	−0.00762454	+	0.00277510i
$914$	5.10042	−	8.83419i	0.168707	−	0.292209i
$915$	−2.40029	−	4.15743i	−0.0793512	−	0.137440i
$916$	−3.90809	−	3.27928i	−0.129127	−	0.108350i
$917$	12.7296	−	22.0482i	0.420367	−	0.728097i
$918$	−3.11139	−	17.6456i	−0.102691	−	0.582390i
$919$	34.5020			1.13812			0.569058	−	0.822298i	$-0.307308\pi$
$919$	34.5020			1.13812			0.569058	+	0.822298i	$0.307308\pi$
$920$	−1.15309	−	6.53952i	−0.0380164	−	0.215601i
$921$	−8.65454	+	7.26202i	−0.285177	+	0.239292i
$922$	−30.2195	−	10.9990i	−0.995226	−	0.362233i
$923$	−25.3807	+	9.23783i	−0.835417	+	0.304067i
$924$	−0.0843712			−0.00277561
$925$	0.540554	−	6.05870i	0.0177733	−	0.199209i
$926$	23.0087			0.756113
$927$	13.5433	−	4.92935i	0.444820	−	0.161901i
$928$	−4.00712	−	1.45847i	−0.131540	−	0.0478767i
$929$	−31.6848	+	26.5867i	−1.03955	+	0.872282i	−0.991956	−	0.126585i	$-0.959598\pi$
$929$	−31.6848	+	26.5867i	−1.03955	+	0.872282i	−0.0475893	+	0.998867i	$0.515154\pi$
$930$	−0.672575	−	3.81436i	−0.0220546	−	0.125078i
$931$	−59.3553			−1.94529
$932$	−4.65133	−	26.3790i	−0.152359	−	0.864072i
$933$	6.61160	−	11.4516i	0.216454	−	0.374910i
$934$	4.07210	+	3.41690i	0.133243	+	0.111804i
$935$	−0.112172	−	0.194288i	−0.00366843	−	0.00635391i
$936$	4.00061	−	6.92927i	0.130764	−	0.226490i
$937$	−4.58543	+	1.66896i	−0.149799	+	0.0545225i	−0.415832	−	0.909442i	$-0.636509\pi$
$937$	−4.58543	+	1.66896i	−0.149799	+	0.0545225i	0.266032	+	0.963964i	$0.414287\pi$
$938$	−1.82650	+	1.53261i	−0.0596372	+	0.0500415i
$939$	−4.25760	−	7.37438i	−0.138941	−	0.240654i
$940$	−0.0146795	+	0.0832516i	−0.000478792	+	0.00271537i
$941$	−0.115739	+	0.656389i	−0.00377299	+	0.0213977i	−0.986636	−	0.162939i	$-0.947903\pi$
$941$	−0.115739	+	0.656389i	−0.00377299	+	0.0213977i	0.982863	+	0.184337i	$0.0590137\pi$
$942$	−8.42874	−	7.07255i	−0.274623	−	0.230436i
$943$	1.78945	+	0.651306i	0.0582724	+	0.0212094i
$944$	9.28489	+	3.37943i	0.302198	+	0.109991i
$945$	10.4132	+	8.73773i	0.338742	+	0.284238i
$946$	−0.0307697	+	0.174504i	−0.00100041	+	0.00567360i
$947$	−7.32205	+	41.5254i	−0.237935	+	1.34939i	0.598410	+	0.801190i	$0.295800\pi$
$947$	−7.32205	+	41.5254i	−0.237935	+	1.34939i	−0.836344	+	0.548205i	$0.815312\pi$
$948$	1.03975	+	1.80090i	0.0337695	+	0.0584905i
$949$	18.7718	−	15.7514i	0.609358	−	0.511312i
$950$	−3.55030	+	1.29220i	−0.115187	+	0.0419246i
$951$	−5.18342	+	8.97794i	−0.168084	+	0.291130i
$952$	−14.9673	−	25.9241i	−0.485092	−	0.840205i
$953$	−12.6506	−	10.6151i	−0.409794	−	0.343858i	0.414471	−	0.910063i	$-0.363967\pi$
$953$	−12.6506	−	10.6151i	−0.409794	−	0.343858i	−0.824265	+	0.566205i	$0.808411\pi$
$954$	−17.2097	+	29.8081i	−0.557185	+	0.965073i
$955$	−2.09561	−	11.8848i	−0.0678124	−	0.384583i
$956$	19.7381			0.638375
$957$	−0.0131099	−	0.0743501i	−0.000423784	−	0.00240340i
$958$	−3.23820	+	2.71717i	−0.104621	+	0.0877878i
$959$	33.4891	+	12.1890i	1.08142	+	0.393605i
$960$	−0.465818	+	0.169544i	−0.0150342	+	0.00547201i
$961$	30.0491			0.969327
$962$	−10.1106	−	14.4923i	−0.325978	−	0.467250i
$963$	−12.5182			−0.403392
$964$	−17.5991	+	6.40554i	−0.566828	+	0.206309i
$965$	17.2993	+	6.29644i	0.556885	+	0.202690i
$966$	12.0168	−	10.0833i	0.386634	−	0.324425i
$967$	−1.05533	−	5.98509i	−0.0339372	−	0.192467i	0.963126	−	0.269051i	$-0.0867100\pi$
$967$	−1.05533	−	5.98509i	−0.0339372	−	0.192467i	−0.997063	+	0.0765834i	$0.975599\pi$
$968$	10.9987			0.353512
$969$	2.04288	+	11.5858i	0.0656268	+	0.372188i
$970$	2.46953	−	4.27736i	0.0792919	−	0.137338i
$971$	13.8627	+	11.6322i	0.444876	+	0.373295i	0.837530	−	0.546391i	$-0.183999\pi$
$971$	13.8627	+	11.6322i	0.444876	+	0.373295i	−0.392654	+	0.919686i	$0.628443\pi$
$972$	5.97622	+	10.3511i	0.191687	+	0.332012i
$973$	19.5253	−	33.8188i	0.625951	−	1.08418i
$974$	−10.6513	+	3.87676i	−0.341290	+	0.124219i
$975$	1.10315	−	0.925654i	0.0353291	−	0.0296447i
$976$	−4.84210	−	8.38676i	−0.154992	−	0.268454i
$977$	−1.61248	+	9.14482i	−0.0515878	+	0.292569i	−0.999676	−	0.0254374i	$-0.991902\pi$
$977$	−1.61248	+	9.14482i	−0.0515878	+	0.292569i	0.948089	+	0.318006i	$0.103013\pi$
$978$	0.112660	−	0.638926i	0.00360247	−	0.0204306i
$979$	−0.314119	−	0.263578i	−0.0100393	−	0.00842397i
$980$	14.7627	+	5.37319i	0.471578	+	0.171640i
$981$	31.9839	+	11.6412i	1.02117	+	0.371674i
$982$	−10.8828	−	9.13178i	−0.347285	−	0.291407i
$983$	5.13729	−	29.1350i	0.163854	−	0.929263i	−0.786384	−	0.617738i	$-0.788049\pi$
$983$	5.13729	−	29.1350i	0.163854	−	0.929263i	0.950238	−	0.311525i	$-0.100840\pi$
$984$	0.0246854	−	0.139998i	0.000786942	−	0.00446297i
$985$	0.898942	+	1.55701i	0.0286427	+	0.0496106i
$986$	20.5193	−	17.2178i	0.653469	−	0.548325i
$987$	−0.187658	+	0.0683020i	−0.00597323	+	0.00217408i
$988$	−5.48782	+	9.50518i	−0.174591	+	0.302400i
$989$	−16.4727	−	28.5315i	−0.523800	−	0.907249i
$990$	0.0753552	+	0.0632305i	0.00239495	+	0.00200960i
$991$	18.8755	−	32.6933i	0.599599	−	1.03854i	−0.393281	−	0.919418i	$-0.628660\pi$
$991$	18.8755	−	32.6933i	0.599599	−	1.03854i	0.992880	−	0.119117i	$-0.0380065\pi$
$992$	−1.35678	−	7.69469i	−0.0430779	−	0.244307i
$993$	−17.3292			−0.549926
$994$	−7.69393	−	43.6344i	−0.244037	−	1.38400i
$995$	2.35404	−	1.97528i	0.0746282	−	0.0626205i
$996$	−3.19762	−	1.16384i	−0.101320	−	0.0368776i
$997$	18.3302	−	6.67165i	0.580524	−	0.211293i	−0.0350328	−	0.999386i	$-0.511154\pi$
$997$	18.3302	−	6.67165i	0.580524	−	0.211293i	0.615556	+	0.788093i	$0.288931\pi$
$998$	−37.3897			−1.18355
$999$	17.2874	−	1.48254i	0.546950	−	0.0469056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.b.81.2	✓	18
37.16	even	9	inner	370.2.o.b.201.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.b.81.2	✓	18	1.1	even	1	trivial
370.2.o.b.201.2	yes	18	37.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.465818 + 0.169544i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{5} +0.495714 q^{6} +(-0.827523 - 4.69312i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.10989 - 1.77041i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.465818 + 0.169544i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{5} +0.495714 q^{6} +(-0.827523 - 4.69312i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.10989 - 1.77041i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.0178576 - 0.0309303i) q^{11} +(0.465818 - 0.169544i) q^{12} +(-2.22538 + 1.86732i) q^{13} +(-2.38276 - 4.12706i) q^{14} +(0.0860798 - 0.488183i) q^{15} +(0.173648 - 0.984808i) q^{16} +(4.81190 + 4.03767i) q^{17} +(-2.58817 - 0.942015i) q^{18} +(3.55030 + 1.29220i) q^{19} +(-0.766044 - 0.642788i) q^{20} +(0.410215 - 2.32644i) q^{21} +(0.00620188 - 0.0351726i) q^{22} +(3.32020 + 5.75075i) q^{23} +(0.379739 - 0.318639i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-1.45251 + 2.51583i) q^{26} +(-1.42623 - 2.47031i) q^{27} +(-3.65060 - 3.06322i) q^{28} +(2.13214 - 3.69298i) q^{29} +(-0.0860798 - 0.488183i) q^{30} +7.81339 q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.0135624 - 0.0113802i) q^{33} +(5.90267 + 2.14840i) q^{34} +(-4.47812 + 1.62990i) q^{35} -2.75427 q^{36} +(-2.58015 + 5.50843i) q^{37} +3.77815 q^{38} +(-1.35322 + 0.492530i) q^{39} +(-0.939693 - 0.342020i) q^{40} +(0.219681 - 0.184334i) q^{41} +(-0.410215 - 2.32644i) q^{42} -4.96135 q^{43} +(-0.00620188 - 0.0351726i) q^{44} +(-1.37713 + 2.38527i) q^{45} +(5.08684 + 4.26837i) q^{46} +(-0.0422679 - 0.0732102i) q^{47} +(0.247857 - 0.429301i) q^{48} +(-14.7627 + 5.37319i) q^{49} +(-0.766044 + 0.642788i) q^{50} +(1.55691 + 2.69665i) q^{51} +(-0.504453 + 2.86089i) q^{52} +(2.17004 - 12.3069i) q^{53} +(-2.18512 - 1.83353i) q^{54} +(-0.0335613 - 0.0122153i) q^{55} +(-4.47812 - 1.62990i) q^{56} +(1.43471 + 1.20386i) q^{57} +(0.740486 - 4.19950i) q^{58} +(-1.71578 + 9.73067i) q^{59} +(-0.247857 - 0.429301i) q^{60} +(7.41852 - 6.22488i) q^{61} +(7.34219 - 2.67234i) q^{62} +(-6.56276 + 11.3670i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.22538 + 1.86732i) q^{65} +(0.00885226 - 0.0153326i) q^{66} +(-0.0868810 - 0.492727i) q^{67} +6.28149 q^{68} +(0.571604 + 3.24173i) q^{69} +(-3.65060 + 3.06322i) q^{70} +(8.73683 + 3.17995i) q^{71} +(-2.58817 + 0.942015i) q^{72} -8.43531 q^{73} +(-0.540554 + 6.05870i) q^{74} -0.495714 q^{75} +(3.55030 - 1.29220i) q^{76} +(-0.159937 - 0.0582123i) q^{77} +(-1.10315 + 0.925654i) q^{78} +(0.728448 + 4.13123i) q^{79} -1.00000 q^{80} +(1.18928 + 6.74475i) q^{81} +(0.143387 - 0.248353i) q^{82} +(-5.25852 - 4.41243i) q^{83} +(-1.18117 - 2.04584i) q^{84} +(3.14075 - 5.43993i) q^{85} +(-4.66214 + 1.69688i) q^{86} +(1.61931 - 1.35877i) q^{87} +(-0.0178576 - 0.0309303i) q^{88} +(1.99369 - 11.3068i) q^{89} +(-0.478274 + 2.71242i) q^{90} +(10.6051 + 8.89873i) q^{91} +(6.23993 + 2.27115i) q^{92} +(3.63962 + 1.32471i) q^{93} +(-0.0647582 - 0.0543386i) q^{94} +(0.656069 - 3.72075i) q^{95} +(0.0860798 - 0.488183i) q^{96} +(2.46953 + 4.27736i) q^{97} +(-12.0347 + 10.0983i) q^{98} +(-0.0924369 + 0.0336443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Introduction

L-functions

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