LMFDB - Embedded newform 209.2.e.b.45.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(45,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("209.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
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} - x^{17} + 14 x^{16} - 11 x^{15} + 130 x^{14} - 92 x^{13} + 629 x^{12} - 276 x^{11} + 2060 x^{10} + \cdots + 9 $ x^18 - x^17 + 14x^16 - 11x^15 + 130x^14 - 92x^13 + 629x^12 - 276x^11 + 2060x^10 - 681x^9 + 3955x^8 - 115x^7 + 4735x^6 + 105x^5 + 2904x^4 + 1230x^3 + 639x^2 + 81x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.3
Root			$-0.615930 - 1.06682i$ of defining polynomial
Character	$\chi$	$=$	209.45
Dual form			209.2.e.b.144.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615930 - 1.06682i) q^{2} +(1.01385 + 1.75603i) q^{3} +(0.241261 - 0.417876i) q^{4} +(-1.31548 - 2.27848i) q^{5} +(1.24892 - 2.16319i) q^{6} +3.75846 q^{7} -3.05812 q^{8} +(-0.555768 + 0.962618i) q^{9} +O(q^{10})$	\(q+(-0.615930 - 1.06682i) q^{2} +(1.01385 + 1.75603i) q^{3} +(0.241261 - 0.417876i) q^{4} +(-1.31548 - 2.27848i) q^{5} +(1.24892 - 2.16319i) q^{6} +3.75846 q^{7} -3.05812 q^{8} +(-0.555768 + 0.962618i) q^{9} +(-1.62049 + 2.80677i) q^{10} -1.00000 q^{11} +0.978405 q^{12} +(0.824769 - 1.42854i) q^{13} +(-2.31495 - 4.00960i) q^{14} +(2.66739 - 4.62006i) q^{15} +(1.40107 + 2.42672i) q^{16} +(0.706020 + 1.22286i) q^{17} +1.36926 q^{18} +(4.29267 - 0.756939i) q^{19} -1.26950 q^{20} +(3.81050 + 6.59997i) q^{21} +(0.615930 + 1.06682i) q^{22} +(1.21304 - 2.10105i) q^{23} +(-3.10046 - 5.37016i) q^{24} +(-0.960983 + 1.66447i) q^{25} -2.03200 q^{26} +3.82922 q^{27} +(0.906768 - 1.57057i) q^{28} +(-3.60612 + 6.24598i) q^{29} -6.57171 q^{30} -9.66660 q^{31} +(-1.33220 + 2.30744i) q^{32} +(-1.01385 - 1.75603i) q^{33} +(0.869718 - 1.50640i) q^{34} +(-4.94418 - 8.56357i) q^{35} +(0.268170 + 0.464484i) q^{36} -9.68506 q^{37} +(-3.45151 - 4.11330i) q^{38} +3.34475 q^{39} +(4.02290 + 6.96786i) q^{40} +(6.11720 + 10.5953i) q^{41} +(4.69400 - 8.13024i) q^{42} +(2.96805 + 5.14081i) q^{43} +(-0.241261 + 0.417876i) q^{44} +2.92441 q^{45} -2.98859 q^{46} +(-0.0433317 + 0.0750526i) q^{47} +(-2.84093 + 4.92063i) q^{48} +7.12599 q^{49} +2.36759 q^{50} +(-1.43159 + 2.47959i) q^{51} +(-0.397969 - 0.689302i) q^{52} +(0.599395 - 1.03818i) q^{53} +(-2.35853 - 4.08510i) q^{54} +(1.31548 + 2.27848i) q^{55} -11.4938 q^{56} +(5.68132 + 6.77066i) q^{57} +8.88446 q^{58} +(1.36140 + 2.35801i) q^{59} +(-1.28707 - 2.22928i) q^{60} +(-5.87924 + 10.1831i) q^{61} +(5.95395 + 10.3125i) q^{62} +(-2.08883 + 3.61796i) q^{63} +8.88643 q^{64} -4.33987 q^{65} +(-1.24892 + 2.16319i) q^{66} +(-2.07783 + 3.59891i) q^{67} +0.681340 q^{68} +4.91935 q^{69} +(-6.09054 + 10.5491i) q^{70} +(-1.31934 - 2.28517i) q^{71} +(1.69960 - 2.94380i) q^{72} +(-6.11642 - 10.5939i) q^{73} +(5.96532 + 10.3322i) q^{74} -3.89716 q^{75} +(0.719347 - 1.97642i) q^{76} -3.75846 q^{77} +(-2.06013 - 3.56826i) q^{78} +(-1.58868 - 2.75167i) q^{79} +(3.68615 - 6.38460i) q^{80} +(5.54955 + 9.61210i) q^{81} +(7.53553 - 13.0519i) q^{82} -1.23059 q^{83} +3.67729 q^{84} +(1.85751 - 3.21731i) q^{85} +(3.65622 - 6.33276i) q^{86} -14.6242 q^{87} +3.05812 q^{88} +(7.60245 - 13.1678i) q^{89} +(-1.80123 - 3.11982i) q^{90} +(3.09986 - 5.36911i) q^{91} +(-0.585319 - 1.01380i) q^{92} +(-9.80044 - 16.9749i) q^{93} +0.106757 q^{94} +(-7.37160 - 8.78503i) q^{95} -5.40259 q^{96} +(1.66071 + 2.87643i) q^{97} +(-4.38911 - 7.60217i) q^{98} +(0.555768 - 0.962618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) $ 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.615930	−	1.06682i	−0.435528	−	0.754357i	0.561810	−	0.827266i	$-0.310105\pi$
$2$	−0.615930	−	1.06682i	−0.435528	−	0.754357i	−0.997339	+	0.0729090i	$0.976772\pi$
$3$	1.01385	+	1.75603i	0.585344	+	1.01385i	0.994832	+	0.101531i	$0.0323740\pi$
$3$	1.01385	+	1.75603i	0.585344	+	1.01385i	−0.409488	+	0.912315i	$0.634293\pi$
$4$	0.241261	−	0.417876i	0.120630	−	0.208938i
$5$	−1.31548	−	2.27848i	−0.588301	−	1.01897i	−0.994455	−	0.105163i	$-0.966464\pi$
$5$	−1.31548	−	2.27848i	−0.588301	−	1.01897i	0.406154	−	0.913805i	$-0.366870\pi$
$6$	1.24892	−	2.16319i	0.509868	−	0.883117i
$7$	3.75846			1.42056			0.710281	−	0.703918i	$-0.248568\pi$
$7$	3.75846			1.42056			0.710281	+	0.703918i	$0.248568\pi$
$8$	−3.05812			−1.08121
$9$	−0.555768	+	0.962618i	−0.185256	+	0.320873i
$10$	−1.62049	+	2.80677i	−0.512444	+	0.887578i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	0.978405			0.282441
$13$	0.824769	−	1.42854i	0.228750	−	0.396206i	−0.728688	−	0.684846i	$-0.759870\pi$
$13$	0.824769	−	1.42854i	0.228750	−	0.396206i	0.957438	+	0.288640i	$0.0932029\pi$
$14$	−2.31495	−	4.00960i	−0.618695	−	1.07161i
$15$	2.66739	−	4.62006i	0.688718	−	1.19289i
$16$	1.40107	+	2.42672i	0.350266	+	0.606679i
$17$	0.706020	+	1.22286i	0.171235	+	0.296588i	0.938852	−	0.344321i	$-0.111891\pi$
$17$	0.706020	+	1.22286i	0.171235	+	0.296588i	−0.767617	+	0.640909i	$0.778558\pi$
$18$	1.36926			0.322737
$19$	4.29267	−	0.756939i	0.984807	−	0.173654i
$19$	4.29267	−	0.756939i	0.984807	−	0.173654i
$20$	−1.26950			−0.283868
$21$	3.81050	+	6.59997i	0.831518	+	1.44023i
$22$	0.615930	+	1.06682i	0.131317	+	0.227447i
$23$	1.21304	−	2.10105i	0.252937	−	0.438099i	−0.711396	−	0.702791i	$-0.751937\pi$
$23$	1.21304	−	2.10105i	0.252937	−	0.438099i	0.964333	+	0.264692i	$0.0852702\pi$
$24$	−3.10046	−	5.37016i	−0.632879	−	1.09618i
$25$	−0.960983	+	1.66447i	−0.192197	+	0.332894i
$26$	−2.03200			−0.398508
$27$	3.82922			0.736935
$28$	0.906768	−	1.57057i	0.171363	−	0.296809i
$29$	−3.60612	+	6.24598i	−0.669639	+	1.15985i	0.308366	+	0.951268i	$0.400218\pi$
$29$	−3.60612	+	6.24598i	−0.669639	+	1.15985i	−0.978005	+	0.208581i	$0.933116\pi$
$30$	−6.57171			−1.19982
$31$	−9.66660			−1.73617			−0.868086	−	0.496413i	$-0.834650\pi$
$31$	−9.66660			−1.73617			−0.868086	+	0.496413i	$0.834650\pi$
$32$	−1.33220	+	2.30744i	−0.235502	+	0.407902i
$33$	−1.01385	−	1.75603i	−0.176488	−	0.305686i
$34$	0.869718	−	1.50640i	0.149155	−	0.258345i
$35$	−4.94418	−	8.56357i	−0.835719	−	1.44751i
$36$	0.268170	+	0.464484i	0.0446950	+	0.0774140i
$37$	−9.68506			−1.59221			−0.796107	−	0.605156i	$-0.793111\pi$
$37$	−9.68506			−1.59221			−0.796107	+	0.605156i	$0.793111\pi$
$38$	−3.45151	−	4.11330i	−0.559908	−	0.667265i
$39$	3.34475			0.535589
$40$	4.02290	+	6.96786i	0.636076	+	1.10172i
$41$	6.11720	+	10.5953i	0.955346	+	1.65471i	0.733574	+	0.679609i	$0.237851\pi$
$41$	6.11720	+	10.5953i	0.955346	+	1.65471i	0.221772	+	0.975099i	$0.428816\pi$
$42$	4.69400	−	8.13024i	0.724299	−	1.25452i
$43$	2.96805	+	5.14081i	0.452623	+	0.783966i	0.998548	−	0.0538678i	$-0.0171549\pi$
$43$	2.96805	+	5.14081i	0.452623	+	0.783966i	−0.545925	+	0.837834i	$0.683822\pi$
$44$	−0.241261	+	0.417876i	−0.0363714	+	0.0629971i
$45$	2.92441			0.435945
$46$	−2.98859			−0.440644
$47$	−0.0433317	+	0.0750526i	−0.00632057	+	0.0109476i	−0.869168	−	0.494516i	$-0.835345\pi$
$47$	−0.0433317	+	0.0750526i	−0.00632057	+	0.0109476i	0.862848	+	0.505464i	$0.168679\pi$
$48$	−2.84093	+	4.92063i	−0.410053	+	0.710232i
$49$	7.12599			1.01800
$50$	2.36759			0.334828
$51$	−1.43159	+	2.47959i	−0.200463	+	0.347212i
$52$	−0.397969	−	0.689302i	−0.0551883	−	0.0955890i
$53$	0.599395	−	1.03818i	0.0823332	−	0.142605i	−0.821919	−	0.569605i	$-0.807096\pi$
$53$	0.599395	−	1.03818i	0.0823332	−	0.142605i	0.904252	+	0.427000i	$0.140430\pi$
$54$	−2.35853	−	4.08510i	−0.320956	−	0.555912i
$55$	1.31548	+	2.27848i	0.177379	+	0.307230i
$56$	−11.4938			−1.53592
$57$	5.68132	+	6.77066i	0.752509	+	0.896795i
$58$	8.88446			1.16659
$59$	1.36140	+	2.35801i	0.177239	+	0.306987i	0.940934	−	0.338591i	$-0.109950\pi$
$59$	1.36140	+	2.35801i	0.177239	+	0.306987i	−0.763695	+	0.645577i	$0.776617\pi$
$60$	−1.28707	−	2.22928i	−0.166160	−	0.287798i
$61$	−5.87924	+	10.1831i	−0.752760	+	1.30382i	0.193720	+	0.981057i	$0.437945\pi$
$61$	−5.87924	+	10.1831i	−0.752760	+	1.30382i	−0.946480	+	0.322762i	$0.895389\pi$
$62$	5.95395	+	10.3125i	0.756152	+	1.30969i
$63$	−2.08883	+	3.61796i	−0.263168	+	0.455820i
$64$	8.88643			1.11080
$65$	−4.33987			−0.538295
$66$	−1.24892	+	2.16319i	−0.153731	+	0.266270i
$67$	−2.07783	+	3.59891i	−0.253847	+	0.439676i	−0.964582	−	0.263784i	$-0.915029\pi$
$67$	−2.07783	+	3.59891i	−0.253847	+	0.439676i	0.710735	+	0.703460i	$0.248363\pi$
$68$	0.681340			0.0826246
$69$	4.91935			0.592220
$70$	−6.09054	+	10.5491i	−0.727958	+	1.26086i
$71$	−1.31934	−	2.28517i	−0.156577	−	0.271199i	0.777055	−	0.629433i	$-0.216713\pi$
$71$	−1.31934	−	2.28517i	−0.156577	−	0.271199i	−0.933632	+	0.358233i	$0.883379\pi$
$72$	1.69960	−	2.94380i	0.200300	−	0.346930i
$73$	−6.11642	−	10.5939i	−0.715873	−	1.23993i	−0.962622	−	0.270849i	$-0.912696\pi$
$73$	−6.11642	−	10.5939i	−0.715873	−	1.23993i	0.246749	−	0.969079i	$-0.420638\pi$
$74$	5.96532	+	10.3322i	0.693454	+	1.20110i
$75$	−3.89716			−0.450005
$76$	0.719347	−	1.97642i	0.0825147	−	0.226711i
$77$	−3.75846			−0.428316
$78$	−2.06013	−	3.56826i	−0.233264	−	0.404026i
$79$	−1.58868	−	2.75167i	−0.178740	−	0.309587i	0.762709	−	0.646742i	$-0.223869\pi$
$79$	−1.58868	−	2.75167i	−0.178740	−	0.309587i	−0.941449	+	0.337155i	$0.890535\pi$
$80$	3.68615	−	6.38460i	0.412124	−	0.713820i
$81$	5.54955	+	9.61210i	0.616616	+	1.06801i
$82$	7.53553	−	13.0519i	0.832160	−	1.44134i
$83$	−1.23059			−0.135075			−0.0675373	−	0.997717i	$-0.521514\pi$
$83$	−1.23059			−0.135075			−0.0675373	+	0.997717i	$0.521514\pi$
$84$	3.67729			0.401225
$85$	1.85751	−	3.21731i	0.201476	−	0.348966i
$86$	3.65622	−	6.33276i	0.394260	−	0.682879i
$87$	−14.6242			−1.56788
$88$	3.05812			0.325997
$89$	7.60245	−	13.1678i	0.805858	−	1.39579i	−0.109853	−	0.993948i	$-0.535038\pi$
$89$	7.60245	−	13.1678i	0.805858	−	1.39579i	0.915710	−	0.401839i	$-0.131629\pi$
$90$	−1.80123	−	3.11982i	−0.189866	−	0.328858i
$91$	3.09986	−	5.36911i	0.324953	−	0.562836i
$92$	−0.585319	−	1.01380i	−0.0610237	−	0.105696i
$93$	−9.80044	−	16.9749i	−1.01626	−	1.76021i
$94$	0.106757			0.0110112
$95$	−7.37160	−	8.78503i	−0.756311	−	0.901325i
$96$	−5.40259			−0.551400
$97$	1.66071	+	2.87643i	0.168619	+	0.292057i	0.937935	−	0.346812i	$-0.112736\pi$
$97$	1.66071	+	2.87643i	0.168619	+	0.292057i	−0.769316	+	0.638869i	$0.779403\pi$
$98$	−4.38911	−	7.60217i	−0.443367	−	0.767935i
$99$	0.555768	−	0.962618i	0.0558568	−	0.0967467i
$100$	0.463695	+	0.803143i	0.0463695	+	0.0803143i
$101$	1.63545	−	2.83268i	0.162733	−	0.281862i	−0.773115	−	0.634266i	$-0.781302\pi$
$101$	1.63545	−	2.83268i	0.162733	−	0.281862i	0.935848	+	0.352404i	$0.114636\pi$
$102$	3.52704			0.349229
$103$	−4.53533			−0.446879			−0.223439	−	0.974718i	$-0.571729\pi$
$103$	−4.53533			−0.446879			−0.223439	+	0.974718i	$0.571729\pi$
$104$	−2.52224	+	4.36865i	−0.247326	+	0.428381i
$105$	10.0253	−	17.3643i	0.978367	−	1.69458i
$106$	−1.47674			−0.143434
$107$	4.59920			0.444621			0.222311	−	0.974976i	$-0.428640\pi$
$107$	4.59920			0.444621			0.222311	+	0.974976i	$0.428640\pi$
$108$	0.923841	−	1.60014i	0.0888967	−	0.153974i
$109$	6.10959	+	10.5821i	0.585192	+	1.01358i	0.994851	+	0.101344i	$0.0323143\pi$
$109$	6.10959	+	10.5821i	0.585192	+	1.01358i	−0.409659	+	0.912239i	$0.634352\pi$
$110$	1.62049	−	2.80677i	0.154508	−	0.267615i
$111$	−9.81916	−	17.0073i	−0.931993	−	1.61426i
$112$	5.26584	+	9.12071i	0.497575	+	0.861826i
$113$	0.758905			0.0713918			0.0356959	−	0.999363i	$-0.488635\pi$
$113$	0.758905			0.0713918			0.0356959	+	0.999363i	$0.488635\pi$
$114$	3.72379	−	10.2312i	0.348765	−	0.958240i
$115$	−6.38294			−0.595212
$116$	1.74003	+	3.01382i	0.161558	+	0.279826i
$117$	0.916760	+	1.58787i	0.0847545	+	0.146799i
$118$	1.67705	−	2.90474i	0.154385	−	0.267403i
$119$	2.65355	+	4.59608i	0.243250	+	0.421322i
$120$	−8.15720	+	14.1287i	−0.744647	+	1.28977i
$121$	1.00000			0.0909091
$122$	14.4848			1.31139
$123$	−12.4038	+	21.4840i	−1.11841	+	1.93715i
$124$	−2.33217	+	4.03944i	−0.209435	+	0.362752i
$125$	−8.09819			−0.724324
$126$	5.14629			0.458468
$127$	0.564676	−	0.978047i	0.0501069	−	0.0867876i	−0.839884	−	0.542766i	$-0.817377\pi$
$127$	0.564676	−	0.978047i	0.0501069	−	0.0867876i	0.889991	+	0.455978i	$0.150710\pi$
$128$	−2.80902	−	4.86536i	−0.248284	−	0.430041i
$129$	−6.01829	+	10.4240i	−0.529881	+	0.917781i
$130$	2.67306	+	4.62987i	0.234443	+	0.406066i
$131$	−1.44107	−	2.49600i	−0.125907	−	0.218077i	0.796180	−	0.605059i	$-0.206851\pi$
$131$	−1.44107	−	2.49600i	−0.125907	−	0.218077i	−0.922087	+	0.386983i	$0.873517\pi$
$132$	−0.978405			−0.0851592
$133$	16.1338	−	2.84492i	1.39898	−	0.246686i
$134$	5.11919			0.442231
$135$	−5.03727	−	8.72482i	−0.433540	−	0.750913i
$136$	−2.15909	−	3.73966i	−0.185141	−	0.320673i
$137$	11.3615	−	19.6786i	0.970674	−	1.68126i	0.277146	−	0.960828i	$-0.410611\pi$
$137$	11.3615	−	19.6786i	0.970674	−	1.68126i	0.693528	−	0.720429i	$-0.256055\pi$
$138$	−3.02997	−	5.24807i	−0.257929	−	0.446745i
$139$	−0.653641	+	1.13214i	−0.0554411	+	0.0960267i	−0.892414	−	0.451218i	$-0.850990\pi$
$139$	−0.653641	+	1.13214i	−0.0554411	+	0.0960267i	0.836973	+	0.547244i	$0.184323\pi$
$140$	−4.77135			−0.403252
$141$	−0.175727			−0.0147988
$142$	−1.62524	+	2.81500i	−0.136387	+	0.236230i
$143$	−0.824769	+	1.42854i	−0.0689706	+	0.119461i
$144$	−3.11467			−0.259556
$145$	18.9751			1.57580
$146$	−7.53457	+	13.0503i	−0.623566	+	1.08005i
$147$	7.22466	+	12.5135i	0.595880	+	1.03209i
$148$	−2.33662	+	4.04715i	−0.192069	+	0.332674i
$149$	−2.52861	−	4.37967i	−0.207151	−	0.358797i	0.743665	−	0.668553i	$-0.233086\pi$
$149$	−2.52861	−	4.37967i	−0.207151	−	0.358797i	−0.950816	+	0.309756i	$0.899753\pi$
$150$	2.40038	+	4.15757i	0.195990	+	0.339464i
$151$	8.85980			0.721000			0.360500	−	0.932759i	$-0.382606\pi$
$151$	8.85980			0.721000			0.360500	+	0.932759i	$0.382606\pi$
$152$	−13.1275	+	2.31481i	−1.06478	+	0.187756i
$153$	−1.56953			−0.126889
$154$	2.31495	+	4.00960i	0.186544	+	0.323103i
$155$	12.7162	+	22.0252i	1.02139	+	1.76910i
$156$	0.806958	−	1.39769i	0.0646083	−	0.111905i
$157$	8.11188	+	14.0502i	0.647399	+	1.12133i	0.983742	+	0.179588i	$0.0574765\pi$
$157$	8.11188	+	14.0502i	0.647399	+	1.12133i	−0.336343	+	0.941739i	$0.609190\pi$
$158$	−1.95703	+	3.38967i	−0.155693	+	0.269668i
$159$	2.43078			0.192773
$160$	7.00995			0.554185
$161$	4.55916	−	7.89670i	0.359312	−	0.622347i
$162$	6.83626	−	11.8408i	0.537108	−	0.930298i
$163$	−21.9299			−1.71769			−0.858843	−	0.512239i	$-0.828816\pi$
$163$	−21.9299			−1.71769			−0.858843	+	0.512239i	$0.828816\pi$
$164$	5.90336			0.460975
$165$	−2.66739	+	4.62006i	−0.207656	+	0.359671i
$166$	0.757956	+	1.31282i	0.0588288	+	0.101894i
$167$	10.3598	−	17.9436i	0.801662	−	1.38852i	−0.116859	−	0.993148i	$-0.537283\pi$
$167$	10.3598	−	17.9436i	0.801662	−	1.38852i	0.918521	−	0.395371i	$-0.129384\pi$
$168$	−11.6529	−	20.1835i	−0.899044	−	1.55719i
$169$	5.13951	+	8.90190i	0.395347	+	0.684761i
$170$	−4.57639			−0.350993
$171$	−1.65709	+	4.55289i	−0.126721	+	0.348168i
$172$	2.86429			0.218400
$173$	−6.42086	−	11.1213i	−0.488169	−	0.845534i	0.511738	−	0.859141i	$-0.329002\pi$
$173$	−6.42086	−	11.1213i	−0.488169	−	0.845534i	−0.999907	+	0.0136076i	$0.995668\pi$
$174$	9.00747	+	15.6014i	0.682855	+	1.18274i
$175$	−3.61181	+	6.25585i	−0.273027	+	0.472897i
$176$	−1.40107	−	2.42672i	−0.105609	−	0.182921i
$177$	−2.76049	+	4.78132i	−0.207491	+	0.359386i
$178$	−18.7303			−1.40390
$179$	0.801793			0.0599288			0.0299644	−	0.999551i	$-0.490461\pi$
$179$	0.801793			0.0599288			0.0299644	+	0.999551i	$0.490461\pi$
$180$	0.705545	−	1.22204i	0.0525882	−	0.0910855i
$181$	5.64307	−	9.77409i	0.419446	−	0.726503i	−0.576437	−	0.817141i	$-0.695558\pi$
$181$	5.64307	−	9.77409i	0.419446	−	0.726503i	0.995884	+	0.0906388i	$0.0288909\pi$
$182$	−7.63718			−0.566105
$183$	−23.8426			−1.76250
$184$	−3.70963	+	6.42526i	−0.273477	+	0.473676i
$185$	12.7405	+	22.0672i	0.936701	+	1.62241i
$186$	−12.0728	+	20.9107i	−0.885219	+	1.53324i
$187$	−0.706020	−	1.22286i	−0.0516293	−	0.0894246i
$188$	0.0209085	+	0.0362145i	0.00152491	+	0.00264121i
$189$	14.3920			1.04686
$190$	−4.83168	+	13.2752i	−0.350527	+	0.963081i
$191$	7.65003			0.553536			0.276768	−	0.960937i	$-0.410737\pi$
$191$	7.65003			0.553536			0.276768	+	0.960937i	$0.410737\pi$
$192$	9.00948	+	15.6049i	0.650203	+	1.12618i
$193$	−4.45684	−	7.71948i	−0.320811	−	0.555660i	0.659845	−	0.751402i	$-0.270622\pi$
$193$	−4.45684	−	7.71948i	−0.320811	−	0.555660i	−0.980656	+	0.195741i	$0.937289\pi$
$194$	2.04576	−	3.54335i	0.146877	−	0.254398i
$195$	−4.39996	−	7.62096i	−0.315088	−	0.545748i
$196$	1.71922	−	2.97778i	0.122802	−	0.212699i
$197$	2.10950			0.150296			0.0751480	−	0.997172i	$-0.476057\pi$
$197$	2.10950			0.150296			0.0751480	+	0.997172i	$0.476057\pi$
$198$	−1.36926			−0.0973088
$199$	−2.75546	+	4.77260i	−0.195329	+	0.338321i	−0.947008	−	0.321209i	$-0.895911\pi$
$199$	−2.75546	+	4.77260i	−0.195329	+	0.338321i	0.751679	+	0.659529i	$0.229244\pi$
$200$	2.93880	−	5.09015i	0.207805	−	0.359928i
$201$	−8.42640			−0.594352
$202$	−4.02929			−0.283500
$203$	−13.5534	+	23.4752i	−0.951264	+	1.64764i
$204$	0.690773	+	1.19645i	0.0483638	+	0.0837686i
$205$	16.0941	−	27.8758i	1.12406	−	1.94693i
$206$	2.79344	+	4.83839i	0.194628	+	0.337106i
$207$	1.34834	+	2.33539i	0.0937160	+	0.162321i
$208$	4.62222			0.320493
$209$	−4.29267	+	0.756939i	−0.296930	+	0.0523586i
$210$	−24.6995			−1.70443
$211$	7.98080	+	13.8231i	0.549421	+	0.951625i	0.998314	+	0.0580396i	$0.0184850\pi$
$211$	7.98080	+	13.8231i	0.549421	+	0.951625i	−0.448893	+	0.893585i	$0.648182\pi$
$212$	−0.289221	−	0.500945i	−0.0198638	−	0.0344050i
$213$	2.67522	−	4.63361i	0.183303	−	0.317490i
$214$	−2.83278	−	4.90653i	−0.193645	−	0.335403i
$215$	7.80883	−	13.5253i	0.532558	−	0.922417i
$216$	−11.7102			−0.796780
$217$	−36.3315			−2.46634
$218$	7.52615	−	13.0357i	0.509735	−	0.882888i
$219$	12.4022	−	21.4813i	0.838064	−	1.45157i
$220$	1.26950			0.0855894
$221$	2.32921			0.156680
$222$	−12.0958	+	20.9506i	−0.811819	+	1.40611i
$223$	−8.56464	−	14.8344i	−0.573531	−	0.993384i	−0.996200	−	0.0870999i	$-0.972240\pi$
$223$	−8.56464	−	14.8344i	−0.573531	−	0.993384i	0.422669	−	0.906284i	$-0.361093\pi$
$224$	−5.00702	+	8.67242i	−0.334546	+	0.579451i
$225$	−1.06817	−	1.85012i	−0.0712111	−	0.123341i
$226$	−0.467433	−	0.809617i	−0.0310932	−	0.0538549i
$227$	−22.3328			−1.48228			−0.741142	−	0.671349i	$-0.765715\pi$
$227$	−22.3328			−1.48228			−0.741142	+	0.671349i	$0.765715\pi$
$228$	4.19997	−	0.740593i	0.278150	−	0.0490470i
$229$	−14.9912			−0.990645			−0.495322	−	0.868709i	$-0.664950\pi$
$229$	−14.9912			−0.990645			−0.495322	+	0.868709i	$0.664950\pi$
$230$	3.93144	+	6.80946i	0.259232	+	0.449002i
$231$	−3.81050	−	6.59997i	−0.250712	−	0.434246i
$232$	11.0279	−	19.1009i	0.724019	−	1.25404i
$233$	−0.961968	−	1.66618i	−0.0630206	−	0.109155i	0.832794	−	0.553584i	$-0.186740\pi$
$233$	−0.961968	−	1.66618i	−0.0630206	−	0.109155i	−0.895814	+	0.444429i	$0.853407\pi$
$234$	1.12932	−	1.95604i	0.0738259	−	0.127870i
$235$	0.228008			0.0148736
$236$	1.31381			0.0855215
$237$	3.22135	−	5.57953i	0.209249	−	0.362430i
$238$	3.26880	−	5.66172i	0.211885	−	0.366995i
$239$	3.30029			0.213478			0.106739	−	0.994287i	$-0.465959\pi$
$239$	3.30029			0.213478			0.106739	+	0.994287i	$0.465959\pi$
$240$	14.9488			0.964938
$241$	8.55724	−	14.8216i	0.551220	−	0.954741i	−0.446967	−	0.894551i	$-0.647496\pi$
$241$	8.55724	−	14.8216i	0.551220	−	0.954741i	0.998187	−	0.0601907i	$-0.0191709\pi$
$242$	−0.615930	−	1.06682i	−0.0395935	−	0.0685779i
$243$	−5.50894	+	9.54176i	−0.353398	+	0.612104i
$244$	2.83686	+	4.91359i	0.181611	+	0.314560i
$245$	−9.37411	−	16.2364i	−0.598890	−	1.03731i
$246$	30.5595			1.94840
$247$	2.45914	−	6.75656i	0.156472	−	0.429910i
$248$	29.5616			1.87716
$249$	−1.24763	−	2.16095i	−0.0790652	−	0.136945i
$250$	4.98792	+	8.63933i	0.315464	+	0.546399i
$251$	−6.41010	+	11.1026i	−0.404602	+	0.700791i	−0.994275	−	0.106851i	$-0.965923\pi$
$251$	−6.41010	+	11.1026i	−0.404602	+	0.700791i	0.589673	+	0.807642i	$0.299257\pi$
$252$	1.00790	+	1.74574i	0.0634920	+	0.109971i
$253$	−1.21304	+	2.10105i	−0.0762633	+	0.132092i
$254$	−1.39120			−0.0872918
$255$	7.53293			0.471730
$256$	5.42612	−	9.39832i	0.339133	−	0.587395i
$257$	−15.3049	+	26.5088i	−0.954692	+	1.65358i	−0.219621	+	0.975585i	$0.570482\pi$
$257$	−15.3049	+	26.5088i	−0.954692	+	1.65358i	−0.735071	+	0.677990i	$0.762851\pi$
$258$	14.8274			0.923112
$259$	−36.4009			−2.26184
$260$	−1.04704	+	1.81353i	−0.0649347	+	0.112470i
$261$	−4.00833	−	6.94262i	−0.248109	−	0.429738i
$262$	−1.77519	+	3.07472i	−0.109672	+	0.189957i
$263$	13.9387	+	24.1426i	0.859498	+	1.48869i	0.872408	+	0.488778i	$0.162557\pi$
$263$	13.9387	+	24.1426i	0.859498	+	1.48869i	−0.0129096	+	0.999917i	$0.504109\pi$
$264$	3.10046	+	5.37016i	0.190820	+	0.330510i
$265$	−3.15397			−0.193747
$266$	−12.9723	−	15.4596i	−0.795385	−	0.947892i
$267$	30.8308			1.88682
$268$	1.00260	+	1.73655i	0.0612434	+	0.106077i
$269$	0.778866	+	1.34904i	0.0474883	+	0.0822522i	0.888793	−	0.458310i	$-0.151545\pi$
$269$	0.778866	+	1.34904i	0.0474883	+	0.0822522i	−0.841304	+	0.540562i	$0.818212\pi$
$270$	−6.20522	+	10.7477i	−0.377637	+	0.654087i
$271$	3.00728	+	5.20875i	0.182679	+	0.316409i	0.942792	−	0.333382i	$-0.108190\pi$
$271$	3.00728	+	5.20875i	0.182679	+	0.316409i	−0.760113	+	0.649791i	$0.774856\pi$
$272$	−1.97836	+	3.42662i	−0.119956	+	0.207769i
$273$	12.5711			0.760838
$274$	−27.9914			−1.69102
$275$	0.960983	−	1.66447i	0.0579495	−	0.100371i
$276$	1.18685	−	2.05568i	0.0714397	−	0.123737i
$277$	−16.1061			−0.967724			−0.483862	−	0.875144i	$-0.660766\pi$
$277$	−16.1061			−0.967724			−0.483862	+	0.875144i	$0.660766\pi$
$278$	1.61039			0.0965846
$279$	5.37238	−	9.30524i	0.321636	−	0.557090i
$280$	15.1199	+	26.1884i	0.903586	+	1.56506i
$281$	−10.1622	+	17.6014i	−0.606226	+	1.05001i	0.385630	+	0.922653i	$0.373984\pi$
$281$	−10.1622	+	17.6014i	−0.606226	+	1.05001i	−0.991856	+	0.127361i	$0.959349\pi$
$282$	0.108235	+	0.187469i	0.00644532	+	0.0111636i
$283$	−10.8959	−	18.8722i	−0.647692	−	1.12184i	−0.983673	−	0.179967i	$-0.942401\pi$
$283$	−10.8959	−	18.8722i	−0.647692	−	1.12184i	0.335981	−	0.941869i	$-0.390932\pi$
$284$	−1.27322			−0.0755517
$285$	7.95314	−	21.8515i	0.471103	−	1.29437i
$286$	2.03200			0.120155
$287$	22.9912	+	39.8220i	1.35713	+	2.35062i
$288$	−1.48079	−	2.56480i	−0.0872564	−	0.151133i
$289$	7.50307	−	12.9957i	0.441357	−	0.764453i
$290$	−11.6873	−	20.2431i	−0.686304	−	1.18871i
$291$	−3.36740	+	5.83251i	−0.197400	+	0.341908i
$292$	−5.90261			−0.345424
$293$	−1.41230			−0.0825073			−0.0412537	−	0.999149i	$-0.513135\pi$
$293$	−1.41230			−0.0825073			−0.0412537	+	0.999149i	$0.513135\pi$
$294$	8.89977	−	15.4149i	0.519045	−	0.899012i
$295$	3.58179	−	6.20383i	0.208540	−	0.361201i
$296$	29.6181			1.72151
$297$	−3.82922			−0.222194
$298$	−3.11489	+	5.39514i	−0.180441	+	0.312532i
$299$	−2.00096	−	3.46576i	−0.115718	−	0.200430i
$300$	−0.940231	+	1.62853i	−0.0542843	+	0.0940231i
$301$	11.1553	+	19.3215i	0.642980	+	1.11367i
$302$	−5.45701	−	9.45183i	−0.314016	−	0.543891i
$303$	6.63237			0.381020
$304$	7.85119	+	9.35658i	0.450297	+	0.536637i
$305$	30.9361			1.77140
$306$	0.966722	+	1.67441i	0.0552638	+	0.0957198i
$307$	−14.4247	−	24.9844i	−0.823264	−	1.42593i	−0.903239	−	0.429137i	$-0.858818\pi$
$307$	−14.4247	−	24.9844i	−0.823264	−	1.42593i	0.0799756	−	0.996797i	$-0.474516\pi$
$308$	−0.906768	+	1.57057i	−0.0516679	+	0.0894914i
$309$	−4.59812	−	7.96418i	−0.261578	−	0.453066i
$310$	15.6646	−	27.1319i	0.889690	−	1.54099i
$311$	−14.9369			−0.846994			−0.423497	−	0.905897i	$-0.639198\pi$
$311$	−14.9369			−0.846994			−0.423497	+	0.905897i	$0.639198\pi$
$312$	−10.2287			−0.579083
$313$	−12.1615	+	21.0644i	−0.687411	+	1.19063i	0.285262	+	0.958450i	$0.407919\pi$
$313$	−12.1615	+	21.0644i	−0.687411	+	1.19063i	−0.972673	+	0.232181i	$0.925414\pi$
$314$	9.99270	−	17.3079i	0.563921	−	0.976739i
$315$	10.9913			0.619288
$316$	−1.53314			−0.0862459
$317$	8.91090	−	15.4341i	0.500486	−	0.866867i	−0.499514	−	0.866306i	$-0.666488\pi$
$317$	8.91090	−	15.4341i	0.500486	−	0.866867i	1.00000		0.000561061i	$-0.000178591\pi$
$318$	−1.49719	−	2.59320i	−0.0839581	−	0.145420i
$319$	3.60612	−	6.24598i	0.201904	−	0.349708i
$320$	−11.6899	−	20.2476i	−0.653488	−	1.13187i
$321$	4.66288	+	8.07635i	0.260257	+	0.450778i
$322$	−11.2325			−0.625963
$323$	3.95635	+	4.71494i	0.220137	+	0.262346i
$324$	5.35555			0.297531
$325$	1.58518	+	2.74561i	0.0879299	+	0.152299i
$326$	13.5073	+	23.3953i	0.748101	+	1.29575i
$327$	−12.3884	+	21.4573i	−0.685078	+	1.18659i
$328$	−18.7071	−	32.4017i	−1.03293	−	1.78908i
$329$	−0.162860	+	0.282082i	−0.00897877	+	0.0155517i
$330$	6.57171			0.361760
$331$	18.2121			1.00103			0.500513	−	0.865729i	$-0.333145\pi$
$331$	18.2121			1.00103			0.500513	+	0.865729i	$0.333145\pi$
$332$	−0.296893	+	0.514233i	−0.0162941	+	0.0282222i
$333$	5.38264	−	9.32301i	0.294967	−	0.510898i
$334$	−25.5235			−1.39659
$335$	10.9334			0.597355
$336$	−10.6775	+	18.4940i	−0.582506	+	1.00893i
$337$	14.0095	+	24.2652i	0.763147	+	1.32181i	0.941220	+	0.337793i	$0.109680\pi$
$337$	14.0095	+	24.2652i	0.763147	+	1.32181i	−0.178073	+	0.984017i	$0.556986\pi$
$338$	6.33116	−	10.9659i	0.344370	−	0.596466i
$339$	0.769413	+	1.33266i	0.0417888	+	0.0723803i
$340$	−0.896290	−	1.55242i	−0.0486081	−	0.0841918i
$341$	9.66660			0.523476
$342$	5.87777	−	1.03644i	0.317833	−	0.0560445i
$343$	0.473542			0.0255689
$344$	−9.07664	−	15.7212i	−0.489380	−	0.847631i
$345$	−6.47131	−	11.2086i	−0.348404	−	0.603453i
$346$	−7.90960	+	13.6998i	−0.425223	+	0.736508i
$347$	−14.1815	−	24.5631i	−0.761303	−	1.31862i	−0.942179	−	0.335110i	$-0.891227\pi$
$347$	−14.1815	−	24.5631i	−0.761303	−	1.31862i	0.180876	−	0.983506i	$-0.442107\pi$
$348$	−3.52824	+	6.11109i	−0.189134	+	0.327589i
$349$	−4.77221			−0.255451			−0.127725	−	0.991810i	$-0.540768\pi$
$349$	−4.77221			−0.255451			−0.127725	+	0.991810i	$0.540768\pi$
$350$	8.89850			0.475645
$351$	3.15822	−	5.47021i	0.168574	−	0.291978i
$352$	1.33220	−	2.30744i	0.0710066	−	0.122987i
$353$	−12.6727			−0.674498			−0.337249	−	0.941415i	$-0.609497\pi$
$353$	−12.6727			−0.674498			−0.337249	+	0.941415i	$0.609497\pi$
$354$	6.80108			0.361473
$355$	−3.47114	+	6.01219i	−0.184229	+	0.319094i
$356$	−3.66834	−	6.35376i	−0.194422	−	0.336748i
$357$	−5.38057	+	9.31943i	−0.284770	+	0.493236i
$358$	−0.493848	−	0.855370i	−0.0261007	−	0.0452077i
$359$	−0.624108	−	1.08099i	−0.0329391	−	0.0570523i	0.849086	−	0.528255i	$-0.177153\pi$
$359$	−0.624108	−	1.08099i	−0.0329391	−	0.0570523i	−0.882025	+	0.471203i	$0.843820\pi$
$360$	−8.94319			−0.471347
$361$	17.8541	−	6.49859i	0.939689	−	0.342031i
$362$	−13.9030			−0.730723
$363$	1.01385	+	1.75603i	0.0532131	+	0.0921678i
$364$	−1.49575	−	2.59071i	−0.0783985	−	0.135790i
$365$	−16.0921	+	27.8723i	−0.842298	+	1.45890i
$366$	14.6854	+	25.4358i	0.767616	+	1.32955i
$367$	16.9582	−	29.3725i	0.885212	−	1.53323i	0.0397409	−	0.999210i	$-0.487347\pi$
$367$	16.9582	−	29.3725i	0.885212	−	1.53323i	0.845471	−	0.534022i	$-0.179320\pi$
$368$	6.79820			0.354381
$369$	−13.5990			−0.707934
$370$	15.6945	−	27.1837i	0.815920	−	1.41321i
$371$	2.25280	−	3.90196i	0.116959	−	0.202580i
$372$	−9.45785			−0.490367
$373$	−10.3937			−0.538167			−0.269083	−	0.963117i	$-0.586721\pi$
$373$	−10.3937			−0.538167			−0.269083	+	0.963117i	$0.586721\pi$
$374$	−0.869718	+	1.50640i	−0.0449720	+	0.0778938i
$375$	−8.21032	−	14.2207i	−0.423979	−	0.734353i
$376$	0.132513	−	0.229520i	0.00683386	−	0.0118366i
$377$	5.94842	+	10.3030i	0.306359	+	0.530630i
$378$	−8.86445	−	15.3537i	−0.455938	−	0.789708i
$379$	−0.456731			−0.0234607			−0.0117303	−	0.999931i	$-0.503734\pi$
$379$	−0.456731			−0.0234607			−0.0117303	+	0.999931i	$0.503734\pi$
$380$	−5.44953	+	0.960931i	−0.279555	+	0.0492947i
$381$	2.28998			0.117319
$382$	−4.71188	−	8.16121i	−0.241081	−	0.417564i
$383$	−10.5243	−	18.2287i	−0.537768	−	0.931441i	−0.999024	−	0.0441741i	$-0.985934\pi$
$383$	−10.5243	−	18.2287i	−0.537768	−	0.931441i	0.461256	−	0.887267i	$-0.347399\pi$
$384$	5.69582	−	9.86545i	0.290664	−	0.503444i
$385$	4.94418	+	8.56357i	0.251979	+	0.436440i
$386$	−5.49021	+	9.50932i	−0.279444	+	0.484012i
$387$	−6.59818			−0.335405
$388$	1.60265			0.0813623
$389$	3.03499	−	5.25676i	0.153880	−	0.266528i	−0.778771	−	0.627309i	$-0.784156\pi$
$389$	3.03499	−	5.25676i	0.153880	−	0.266528i	0.932651	+	0.360781i	$0.117490\pi$
$390$	−5.42014	+	9.38795i	−0.274459	+	0.475377i
$391$	3.42573			0.173246
$392$	−21.7921			−1.10067
$393$	2.92204	−	5.06112i	0.147397	−	0.255300i
$394$	−1.29931	−	2.25046i	−0.0654581	−	0.113377i
$395$	−4.17975	+	7.23953i	−0.210306	+	0.364261i
$396$	−0.268170	−	0.464484i	−0.0134760	−	0.0233412i
$397$	−9.91464	−	17.1727i	−0.497601	−	0.861871i	0.502395	−	0.864638i	$-0.332452\pi$
$397$	−9.91464	−	17.1727i	−0.497601	−	0.861871i	−0.999996	+	0.00276759i	$0.999119\pi$
$398$	6.78868			0.340286
$399$	21.3530	+	25.4472i	1.06899	+	1.27395i
$400$	−5.38560			−0.269280
$401$	9.43503	+	16.3420i	0.471163	+	0.816079i	0.999456	−	0.0329838i	$-0.0105010\pi$
$401$	9.43503	+	16.3420i	0.471163	+	0.816079i	−0.528293	+	0.849062i	$0.677168\pi$
$402$	5.19007	+	8.98946i	0.258857	+	0.448354i
$403$	−7.97271	+	13.8091i	−0.397149	+	0.687882i
$404$	−0.789139	−	1.36683i	−0.0392611	−	0.0680023i
$405$	14.6007	−	25.2891i	0.725512	−	1.25662i
$406$	33.3918			1.65721
$407$	9.68506			0.480071
$408$	4.37798	−	7.58288i	0.216742	−	0.375408i
$409$	−16.3070	+	28.2445i	−0.806328	+	1.39660i	0.109063	+	0.994035i	$0.465215\pi$
$409$	−16.3070	+	28.2445i	−0.806328	+	1.39660i	−0.915391	+	0.402566i	$0.868118\pi$
$410$	−39.6514			−1.95824
$411$	46.0751			2.27271
$412$	−1.09420	+	1.89520i	−0.0539072	+	0.0933699i
$413$	5.11675	+	8.86247i	0.251779	+	0.436094i
$414$	1.66096	−	2.87687i	0.0816320	−	0.141391i
$415$	1.61882	+	2.80387i	0.0794646	+	0.137637i
$416$	2.19752	+	3.80621i	0.107742	+	0.186615i
$417$	−2.65076			−0.129808
$418$	3.45151	+	4.11330i	0.168819	+	0.201188i
$419$	−39.3439			−1.92208			−0.961039	−	0.276414i	$-0.910854\pi$
$419$	−39.3439			−1.92208			−0.961039	+	0.276414i	$0.910854\pi$
$420$	−4.83741	−	8.37864i	−0.236041	−	0.408836i
$421$	−0.302034	−	0.523138i	−0.0147202	−	0.0254962i	0.858571	−	0.512694i	$-0.171352\pi$
$421$	−0.302034	−	0.523138i	−0.0147202	−	0.0254962i	−0.873292	+	0.487198i	$0.838019\pi$
$422$	9.83123	−	17.0282i	0.478577	−	0.828919i
$423$	−0.0481647	−	0.0834237i	−0.00234185	−	0.00405620i
$424$	−1.83302	+	3.17488i	−0.0890193	+	0.154186i
$425$	−2.71389			−0.131643
$426$	−6.59099			−0.319334
$427$	−22.0969	+	38.2729i	−1.06934	+	1.85216i
$428$	1.10961	−	1.92189i	0.0536348	−	0.0928983i
$429$	−3.34475			−0.161486
$430$	−19.2388			−0.927775
$431$	7.06444	−	12.2360i	0.340282	−	0.589386i	−0.644203	−	0.764855i	$-0.722811\pi$
$431$	7.06444	−	12.2360i	0.340282	−	0.589386i	0.984485	+	0.175469i	$0.0561441\pi$
$432$	5.36499	+	9.29244i	0.258123	+	0.447083i
$433$	9.44524	−	16.3596i	0.453909	−	0.786194i	−0.544715	−	0.838621i	$-0.683362\pi$
$433$	9.44524	−	16.3596i	0.453909	−	0.786194i	0.998625	+	0.0524268i	$0.0166956\pi$
$434$	22.3777	+	38.7592i	1.07416	+	1.86050i
$435$	19.2378	+	33.3209i	0.922384	+	1.59762i
$436$	5.89601			0.282368
$437$	3.61682	−	9.93732i	0.173016	−	0.475366i
$438$	−30.5556			−1.46000
$439$	−17.4223	−	30.1763i	−0.831521	−	1.44024i	−0.896832	−	0.442371i	$-0.854137\pi$
$439$	−17.4223	−	30.1763i	−0.831521	−	1.44024i	0.0653111	−	0.997865i	$-0.479196\pi$
$440$	−4.02290	−	6.96786i	−0.191784	−	0.332180i
$441$	−3.96040	+	6.85961i	−0.188590	+	0.326648i
$442$	−1.43463	−	2.48486i	−0.0682385	−	0.118193i
$443$	2.21272	−	3.83255i	0.105130	−	0.182090i	−0.808662	−	0.588274i	$-0.799808\pi$
$443$	2.21272	−	3.83255i	0.105130	−	0.182090i	0.913791	+	0.406184i	$0.133141\pi$
$444$	−9.47591			−0.449707
$445$	−40.0035			−1.89635
$446$	−10.5504	+	18.2739i	−0.499577	+	0.865294i
$447$	5.12723	−	8.88063i	0.242510	−	0.420039i
$448$	33.3993			1.57797
$449$	27.5536			1.30033			0.650166	−	0.759792i	$-0.274699\pi$
$449$	27.5536			1.30033			0.650166	+	0.759792i	$0.274699\pi$
$450$	−1.31583	+	2.27909i	−0.0620289	+	0.107437i
$451$	−6.11720	−	10.5953i	−0.288048	−	0.498913i
$452$	0.183094	−	0.317128i	0.00861202	−	0.0149165i
$453$	8.98247	+	15.5581i	0.422033	+	0.730983i
$454$	13.7555	+	23.8252i	0.645576	+	1.11817i
$455$	−16.3112			−0.764682
$456$	−17.3741	−	20.7055i	−0.813619	−	0.969622i
$457$	30.7875			1.44018			0.720089	−	0.693881i	$-0.244101\pi$
$457$	30.7875			1.44018			0.720089	+	0.693881i	$0.244101\pi$
$458$	9.23351	+	15.9929i	0.431454	+	0.747300i
$459$	2.70351	+	4.68262i	0.126189	+	0.218566i
$460$	−1.53995	+	2.66727i	−0.0718006	+	0.124362i
$461$	12.3511	+	21.3927i	0.575248	+	0.996358i	0.996015	+	0.0891896i	$0.0284277\pi$
$461$	12.3511	+	21.3927i	0.575248	+	0.996358i	−0.420767	+	0.907169i	$0.638239\pi$
$462$	−4.69400	+	8.13024i	−0.218385	+	0.378253i
$463$	13.4674			0.625885			0.312942	−	0.949772i	$-0.398685\pi$
$463$	13.4674			0.625885			0.312942	+	0.949772i	$0.398685\pi$
$464$	−20.2096			−0.938208
$465$	−25.7846	+	44.6602i	−1.19573	+	2.07107i
$466$	−1.18501	+	2.05250i	−0.0548945	+	0.0950801i
$467$	23.5735			1.09085			0.545425	−	0.838159i	$-0.316368\pi$
$467$	23.5735			1.09085			0.545425	+	0.838159i	$0.316368\pi$
$468$	0.884712			0.0408958
$469$	−7.80943	+	13.5263i	−0.360606	+	0.624588i
$470$	−0.140437	−	0.243244i	−0.00647787	−	0.0112200i
$471$	−16.4484	+	28.4895i	−0.757902	+	1.31273i
$472$	−4.16331	−	7.21107i	−0.191632	−	0.331916i
$473$	−2.96805	−	5.14081i	−0.136471	−	0.236375i
$474$	−7.93649			−0.364535
$475$	−2.86528	+	7.87244i	−0.131468	+	0.361212i
$476$	2.56079			0.117373
$477$	0.666248	+	1.15398i	0.0305054	+	0.0528369i
$478$	−2.03275	−	3.52082i	−0.0929757	−	0.161039i
$479$	−9.28264	+	16.0780i	−0.424135	+	0.734623i	−0.996339	−	0.0854881i	$-0.972755\pi$
$479$	−9.28264	+	16.0780i	−0.424135	+	0.734623i	0.572204	+	0.820111i	$0.306088\pi$
$480$	7.10701	+	12.3097i	0.324389	+	0.561859i
$481$	−7.98793	+	13.8355i	−0.364218	+	0.630845i
$482$	−21.0826			−0.960288
$483$	18.4892			0.841286
$484$	0.241261	−	0.417876i	0.0109664	−	0.0189944i
$485$	4.36925	−	7.56777i	0.198398	−	0.343635i
$486$	13.5725			0.615660
$487$	1.97914			0.0896835			0.0448417	−	0.998994i	$-0.485722\pi$
$487$	1.97914			0.0896835			0.0448417	+	0.998994i	$0.485722\pi$
$488$	17.9794	−	31.1413i	0.813890	−	1.40970i
$489$	−22.2336	−	38.5097i	−1.00544	−	1.74147i
$490$	−11.5476	+	20.0010i	−0.521667	+	0.903554i
$491$	−10.6076	−	18.3729i	−0.478715	−	0.829159i	0.520987	−	0.853565i	$-0.325564\pi$
$491$	−10.6076	−	18.3729i	−0.478715	−	0.829159i	−0.999702	+	0.0244054i	$0.992231\pi$
$492$	5.98510	+	10.3665i	0.269829	+	0.467358i
$493$	−10.1840			−0.458663
$494$	−8.72271	+	1.53810i	−0.392453	+	0.0692024i
$495$	−2.92441			−0.131442
$496$	−13.5435	−	23.4581i	−0.608123	−	1.05330i
$497$	−4.95869	−	8.58869i	−0.222427	−	0.385256i
$498$	−1.53690	+	2.66199i	−0.0688702	+	0.119287i
$499$	−12.5623	−	21.7586i	−0.562368	−	0.974049i	−0.997289	−	0.0735811i	$-0.976557\pi$
$499$	−12.5623	−	21.7586i	−0.562368	−	0.974049i	0.434921	−	0.900468i	$-0.356776\pi$
$500$	−1.95378	+	3.38404i	−0.0873755	+	0.151339i
$501$	42.0128			1.87699
$502$	15.7927			0.704862
$503$	3.64230	−	6.30865i	0.162402	−	0.281289i	−0.773328	−	0.634007i	$-0.781409\pi$
$503$	3.64230	−	6.30865i	0.162402	−	0.281289i	0.935730	+	0.352718i	$0.114743\pi$
$504$	6.38789	−	11.0641i	0.284539	−	0.492836i
$505$	−8.60561			−0.382945
$506$	2.98859			0.132859
$507$	−10.4214	+	18.0503i	−0.462828	+	0.801642i
$508$	−0.272468	−	0.471929i	−0.0120888	−	0.0209384i
$509$	−15.1923	+	26.3138i	−0.673385	+	1.16634i	0.303553	+	0.952815i	$0.401827\pi$
$509$	−15.1923	+	26.3138i	−0.673385	+	1.16634i	−0.976938	+	0.213523i	$0.931506\pi$
$510$	−4.63976	−	8.03629i	−0.205452	−	0.355853i
$511$	−22.9883	−	39.8169i	−1.01694	−	1.76140i
$512$	−24.6045			−1.08738
$513$	16.4376	−	2.89849i	0.725738	−	0.127971i
$514$	37.7069			1.66318
$515$	5.96614	+	10.3337i	0.262899	+	0.455355i
$516$	2.90395	+	5.02979i	0.127839	+	0.221424i
$517$	0.0433317	−	0.0750526i	0.00190572	−	0.00330081i
$518$	22.4204	+	38.8332i	0.985095	+	1.70623i
$519$	13.0195	−	22.5505i	0.571494	−	0.989857i
$520$	13.2718			0.582009
$521$	−8.26667			−0.362169			−0.181085	−	0.983468i	$-0.557961\pi$
$521$	−8.26667			−0.362169			−0.181085	+	0.983468i	$0.557961\pi$
$522$	−4.93770	+	8.55234i	−0.216117	+	0.374326i
$523$	7.73795	−	13.4025i	0.338357	−	0.586052i	−0.645767	−	0.763535i	$-0.723462\pi$
$523$	7.73795	−	13.4025i	0.338357	−	0.586052i	0.984124	+	0.177483i	$0.0567955\pi$
$524$	−1.39069			−0.0607526
$525$	−14.6473			−0.639260
$526$	17.1706	−	29.7403i	0.748672	−	1.29674i
$527$	−6.82481	−	11.8209i	−0.297294	−	0.514927i
$528$	2.84093	−	4.92063i	0.123636	−	0.214143i
$529$	8.55706	+	14.8213i	0.372046	+	0.644403i
$530$	1.94262	+	3.36472i	0.0843822	+	0.146154i
$531$	−3.02648			−0.131338
$532$	2.70363	−	7.42830i	0.117217	−	0.322058i
$533$	20.1811			0.874140
$534$	−18.9896	−	32.8910i	−0.821762	−	1.42333i
$535$	−6.05016	−	10.4792i	−0.261571	−	0.453055i
$536$	6.35425	−	11.0059i	0.274462	−	0.475382i
$537$	0.812894	+	1.40797i	0.0350790	+	0.0607586i
$538$	0.959454	−	1.66182i	0.0413650	−	0.0716463i
$539$	−7.12599			−0.306938
$540$	−4.86119			−0.209192
$541$	−6.68307	+	11.5754i	−0.287328	+	0.497666i	−0.973171	−	0.230083i	$-0.926100\pi$
$541$	−6.68307	+	11.5754i	−0.287328	+	0.497666i	0.685843	+	0.727749i	$0.259434\pi$
$542$	3.70454	−	6.41646i	0.159124	−	0.275610i
$543$	22.8848			0.982082
$544$	−3.76225			−0.161305
$545$	16.0741	−	27.8411i	0.688539	−	1.19258i
$546$	−7.74292	−	13.4111i	−0.331367	−	0.573944i
$547$	−1.47815	+	2.56024i	−0.0632013	+	0.109468i	−0.895895	−	0.444266i	$-0.853464\pi$
$547$	−1.47815	+	2.56024i	−0.0632013	+	0.109468i	0.832693	+	0.553734i	$0.186798\pi$
$548$	−5.48214	−	9.49535i	−0.234186	−	0.405621i
$549$	−6.53499	−	11.3189i	−0.278907	−	0.483080i
$550$	−2.36759			−0.100955
$551$	−10.7521	+	29.5415i	−0.458053	+	1.25851i
$552$	−15.0440			−0.640313
$553$	−5.97097	−	10.3420i	−0.253911	−	0.439787i
$554$	9.92025	+	17.1824i	0.421471	+	0.730009i
$555$	−25.8338	+	44.7455i	−1.09659	+	1.89934i
$556$	0.315396	+	0.546281i	0.0133758	+	0.0231675i
$557$	−5.91940	+	10.2527i	−0.250813	+	0.434421i	−0.963750	−	0.266807i	$-0.914031\pi$
$557$	−5.91940	+	10.2527i	−0.250813	+	0.434421i	0.712937	+	0.701228i	$0.247365\pi$
$558$	−13.2360			−0.560327
$559$	9.79181			0.414150
$560$	13.8542	−	23.9962i	0.585448	−	1.01403i
$561$	1.43159	−	2.47959i	0.0604418	−	0.104688i
$562$	25.0368			1.05611
$563$	1.82512			0.0769194			0.0384597	−	0.999260i	$-0.487755\pi$
$563$	1.82512			0.0769194			0.0384597	+	0.999260i	$0.487755\pi$
$564$	−0.0423959	+	0.0734319i	−0.00178519	+	0.00309204i
$565$	−0.998326	−	1.72915i	−0.0419999	−	0.0727460i
$566$	−13.4222	+	23.2479i	−0.564176	+	0.977182i
$567$	20.8577	+	36.1267i	0.875942	+	1.51718i
$568$	4.03470	+	6.98831i	0.169292	+	0.293223i
$569$	−16.0290			−0.671971			−0.335986	−	0.941867i	$-0.609069\pi$
$569$	−16.0290			−0.671971			−0.335986	+	0.941867i	$0.609069\pi$
$570$	−28.2102	+	4.97438i	−1.18159	+	0.208354i
$571$	27.4663			1.14943			0.574714	−	0.818355i	$-0.305113\pi$
$571$	27.4663			1.14943			0.574714	+	0.818355i	$0.305113\pi$
$572$	0.397969	+	0.689302i	0.0166399	+	0.0288212i
$573$	7.75595	+	13.4337i	0.324009	+	0.561201i
$574$	28.3220	−	49.0551i	1.18214	−	2.04752i
$575$	2.33143	+	4.03815i	0.0972272	+	0.168402i
$576$	−4.93879	+	8.55424i	−0.205783	+	0.356427i
$577$	19.2841			0.802809			0.401405	−	0.915901i	$-0.368522\pi$
$577$	19.2841			0.802809			0.401405	+	0.915901i	$0.368522\pi$
$578$	−18.4855			−0.768894
$579$	9.03711	−	15.6527i	0.375569	−	0.650505i
$580$	4.57795	−	7.92924i	0.190089	−	0.329244i
$581$	−4.62511			−0.191882
$582$	8.29633			0.343894
$583$	−0.599395	+	1.03818i	−0.0248244	+	0.0429971i
$584$	18.7047	+	32.3975i	0.774007	+	1.34062i
$585$	2.41196	−	4.17764i	0.0997223	−	0.172724i
$586$	0.869877	+	1.50667i	0.0359343	+	0.0622400i
$587$	12.2148	+	21.1567i	0.504160	+	0.873231i	0.999988	+	0.00481069i	$0.00153130\pi$
$587$	12.2148	+	21.1567i	0.504160	+	0.873231i	−0.495828	+	0.868421i	$0.665135\pi$
$588$	6.97211			0.287525
$589$	−41.4955	+	7.31703i	−1.70979	+	0.301493i
$590$	−8.82451			−0.363299
$591$	2.13871	+	3.70436i	0.0879749	+	0.152377i
$592$	−13.5694	−	23.5029i	−0.557699	−	0.965963i
$593$	−0.720344	+	1.24767i	−0.0295810	+	0.0512358i	−0.880437	−	0.474163i	$-0.842751\pi$
$593$	−0.720344	+	1.24767i	−0.0295810	+	0.0512358i	0.850856	+	0.525399i	$0.176084\pi$
$594$	2.35853	+	4.08510i	0.0967718	+	0.167614i
$595$	6.98138	−	12.0921i	0.286209	−	0.495728i
$596$	−2.44021			−0.0999550
$597$	−11.1745			−0.457340
$598$	−2.46490	+	4.26933i	−0.100797	+	0.174586i
$599$	−14.7109	+	25.4800i	−0.601072	+	1.04109i	0.391588	+	0.920141i	$0.371926\pi$
$599$	−14.7109	+	25.4800i	−0.601072	+	1.04109i	−0.992659	+	0.120946i	$0.961407\pi$
$600$	11.9180			0.486549
$601$	−32.4389			−1.32321			−0.661605	−	0.749853i	$-0.730124\pi$
$601$	−32.4389			−1.32321			−0.661605	+	0.749853i	$0.730124\pi$
$602$	13.7417	−	23.8014i	0.560072	−	0.970073i
$603$	−2.30958	−	4.00031i	−0.0940534	−	0.162905i
$604$	2.13752	−	3.70229i	0.0869745	−	0.150644i
$605$	−1.31548	−	2.27848i	−0.0534819	−	0.0926334i
$606$	−4.08508	−	7.07556i	−0.165945	−	0.287425i
$607$	29.3851			1.19270			0.596352	−	0.802723i	$-0.296616\pi$
$607$	29.3851			1.19270			0.596352	+	0.802723i	$0.296616\pi$
$608$	−3.97212	+	10.9135i	−0.161091	+	0.442601i
$609$	−54.9644			−2.22727
$610$	−19.0545	−	33.0034i	−0.771494	−	1.33627i
$611$	0.0714772	+	0.123802i	0.00289166	+	0.00500850i
$612$	−0.378667	+	0.655870i	−0.0153067	+	0.0265120i
$613$	10.4192	+	18.0466i	0.420827	+	0.728894i	0.996021	−	0.0891234i	$-0.0284066\pi$
$613$	10.4192	+	18.0466i	0.420827	+	0.728894i	−0.575193	+	0.818017i	$0.695073\pi$
$614$	−17.7693	+	30.7773i	−0.717109	+	1.24207i
$615$	65.2679			2.63185
$616$	11.4938			0.463099
$617$	16.1696	−	28.0066i	0.650963	−	1.12750i	−0.331926	−	0.943305i	$-0.607699\pi$
$617$	16.1696	−	28.0066i	0.650963	−	1.12750i	0.982890	−	0.184196i	$-0.0589681\pi$
$618$	−5.66424	+	9.81076i	−0.227849	+	0.394646i
$619$	32.8773			1.32145			0.660725	−	0.750628i	$-0.270249\pi$
$619$	32.8773			1.32145			0.660725	+	0.750628i	$0.270249\pi$
$620$	12.2717			0.492844
$621$	4.64501	−	8.04539i	0.186398	−	0.322850i
$622$	9.20009	+	15.9350i	0.368890	+	0.638936i
$623$	28.5735	−	49.4907i	1.14477	−	1.98280i
$624$	4.68622	+	8.11677i	0.187599	+	0.324931i
$625$	15.4579	+	26.7739i	0.618318	+	1.07096i
$626$	29.9626			1.19755
$627$	−5.68132	−	6.77066i	−0.226890	−	0.270394i
$628$	7.82831			0.312384
$629$	−6.83785	−	11.8435i	−0.272643	−	0.472231i
$630$	−6.76985	−	11.7257i	−0.269717	−	0.467164i
$631$	13.6757	−	23.6871i	0.544422	−	0.942967i	−0.454221	−	0.890889i	$-0.650082\pi$
$631$	13.6757	−	23.6871i	0.544422	−	0.942967i	0.998643	−	0.0520781i	$-0.0165845\pi$
$632$	4.85836	+	8.41492i	0.193255	+	0.334728i
$633$	−16.1826	+	28.0291i	−0.643201	+	1.11406i
$634$	−21.9540			−0.871903
$635$	−2.97128			−0.117912
$636$	0.586451	−	1.01576i	0.0232543	−	0.0402776i
$637$	5.87730	−	10.1798i	0.232867	−	0.403337i
$638$	−8.88446			−0.351739
$639$	2.93299			0.116027
$640$	−7.39042	+	12.8006i	−0.292132	+	0.505987i
$641$	−23.1503	−	40.0975i	−0.914383	−	1.58376i	−0.807802	−	0.589454i	$-0.799343\pi$
$641$	−23.1503	−	40.0975i	−0.914383	−	1.58376i	−0.106581	−	0.994304i	$-0.533990\pi$
$642$	5.74402	−	9.94893i	0.226698	−	0.392653i
$643$	−10.3684	−	17.9586i	−0.408890	−	0.708218i	0.585876	−	0.810401i	$-0.300751\pi$
$643$	−10.3684	−	17.9586i	−0.408890	−	0.708218i	−0.994766	+	0.102183i	$0.967417\pi$
$644$	−2.19989	−	3.81033i	−0.0866880	−	0.150148i
$645$	31.6678			1.24692
$646$	2.59316	−	7.12479i	0.102027	−	0.280321i
$647$	48.7337			1.91592			0.957959	−	0.286904i	$-0.0926262\pi$
$647$	48.7337			1.91592			0.957959	+	0.286904i	$0.0926262\pi$
$648$	−16.9712	−	29.3949i	−0.666691	−	1.15474i
$649$	−1.36140	−	2.35801i	−0.0534395	−	0.0925599i
$650$	1.95272	−	3.38221i	0.0765919	−	0.132661i
$651$	−36.8345	−	63.7993i	−1.44366	−	2.50049i
$652$	−5.29083	+	9.16399i	−0.207205	+	0.358890i
$653$	−33.5147			−1.31153			−0.655765	−	0.754965i	$-0.727654\pi$
$653$	−33.5147			−1.31153			−0.655765	+	0.754965i	$0.727654\pi$
$654$	30.5214			1.19348
$655$	−3.79139	+	6.56689i	−0.148142	+	0.256589i
$656$	−17.1412	+	29.6894i	−0.669251	+	1.15918i
$657$	13.5972			0.530479
$658$	0.401242			0.0156420
$659$	−11.1783	+	19.3614i	−0.435446	+	0.754215i	−0.997332	−	0.0729999i	$-0.976743\pi$
$659$	−11.1783	+	19.3614i	−0.435446	+	0.754215i	0.561886	+	0.827215i	$0.310076\pi$
$660$	1.28707	+	2.22928i	0.0500993	+	0.0867745i
$661$	8.55175	−	14.8121i	0.332625	−	0.576123i	−0.650401	−	0.759591i	$-0.725399\pi$
$661$	8.55175	−	14.8121i	0.332625	−	0.576123i	0.983026	+	0.183468i	$0.0587325\pi$
$662$	−11.2174	−	19.4290i	−0.435975	−	0.755131i
$663$	2.36146	+	4.09017i	0.0917116	+	0.158849i
$664$	3.76329			0.146044
$665$	−27.7059	−	33.0182i	−1.07439	−	1.28039i
$666$	−13.2613			−0.513866
$667$	8.74874	+	15.1533i	0.338752	+	0.586737i
$668$	−4.99880	−	8.65818i	−0.193410	−	0.334995i
$669$	17.3664	−	30.0796i	0.671426	−	1.16294i
$670$	−6.73420	−	11.6640i	−0.260165	−	0.450619i
$671$	5.87924	−	10.1831i	0.226966	−	0.393116i
$672$	−20.3054			−0.783298
$673$	14.4175			0.555752			0.277876	−	0.960617i	$-0.410370\pi$
$673$	14.4175			0.555752			0.277876	+	0.960617i	$0.410370\pi$
$674$	17.2578	−	29.8913i	0.664744	−	1.15137i
$675$	−3.67982	+	6.37364i	−0.141636	+	0.245321i
$676$	4.95985			0.190763
$677$	26.4020			1.01471			0.507355	−	0.861737i	$-0.330623\pi$
$677$	26.4020			1.01471			0.507355	+	0.861737i	$0.330623\pi$
$678$	0.947809	−	1.64165i	0.0364004	−	0.0630473i
$679$	6.24169	+	10.8109i	0.239534	+	0.414885i
$680$	−5.68049	+	9.83890i	−0.217837	+	0.377305i
$681$	−22.6421	−	39.2172i	−0.867646	−	1.50281i
$682$	−5.95395	−	10.3125i	−0.227988	−	0.394888i
$683$	7.65175			0.292786			0.146393	−	0.989226i	$-0.453234\pi$
$683$	7.65175			0.292786			0.146393	+	0.989226i	$0.453234\pi$
$684$	1.50275	+	1.79089i	0.0574591	+	0.0684763i
$685$	−59.7831			−2.28420
$686$	−0.291669	−	0.505185i	−0.0111360	−	0.0192881i
$687$	−15.1987	−	26.3250i	−0.579868	−	1.00436i
$688$	−8.31686	+	14.4052i	−0.317077	+	0.549194i
$689$	−0.988724	−	1.71252i	−0.0376674	−	0.0652418i
$690$	−7.97175	+	13.8075i	−0.303479	+	0.525642i
$691$	−4.11843			−0.156672			−0.0783362	−	0.996927i	$-0.524961\pi$
$691$	−4.11843			−0.156672			−0.0783362	+	0.996927i	$0.524961\pi$
$692$	−6.19641			−0.235552
$693$	2.08883	−	3.61796i	0.0793480	−	0.137435i
$694$	−17.4696	+	30.2583i	−0.663138	+	1.14859i
$695$	3.43941			0.130464
$696$	44.7225			1.69520
$697$	−8.63773	+	14.9610i	−0.327177	+	0.566688i
$698$	2.93935	+	5.09110i	0.111256	+	0.192701i
$699$	1.95058	−	3.37850i	0.0737775	−	0.127786i
$700$	1.74278	+	3.01858i	0.0658708	+	0.114092i
$701$	1.74971	+	3.03060i	0.0660858	+	0.114464i	0.897175	−	0.441675i	$-0.145616\pi$
$701$	1.74971	+	3.03060i	0.0660858	+	0.114464i	−0.831089	+	0.556139i	$0.812282\pi$
$702$	−7.78098			−0.293674
$703$	−41.5748	+	7.33100i	−1.56802	+	0.276494i
$704$	−8.88643			−0.334920
$705$	0.231165	+	0.400390i	0.00870618	+	0.0150795i
$706$	7.80548	+	13.5195i	0.293763	+	0.508813i
$707$	6.14676	−	10.6465i	0.231173	−	0.400403i
$708$	1.33200	+	2.30709i	0.0500595	+	0.0867056i
$709$	−9.66080	+	16.7330i	−0.362819	+	0.628421i	−0.988424	−	0.151719i	$-0.951519\pi$
$709$	−9.66080	+	16.7330i	−0.362819	+	0.628421i	0.625605	+	0.780140i	$0.284852\pi$
$710$	8.55191			0.320947
$711$	3.53174			0.132451
$712$	−23.2492	+	40.2688i	−0.871300	+	1.50914i
$713$	−11.7260	+	20.3100i	−0.439142	+	0.760616i
$714$	13.2562			0.496102
$715$	4.33987			0.162302
$716$	0.193441	−	0.335050i	0.00722923	−	0.0125214i
$717$	3.34599	+	5.79542i	0.124958	+	0.216434i
$718$	−0.768813	+	1.33162i	−0.0286919	+	0.0496958i
$719$	−3.81014	−	6.59935i	−0.142094	−	0.246114i	0.786191	−	0.617984i	$-0.212050\pi$
$719$	−3.81014	−	6.59935i	−0.142094	−	0.246114i	−0.928285	+	0.371869i	$0.878717\pi$
$720$	4.09729	+	7.09671i	0.152697	+	0.264479i
$721$	−17.0458			−0.634820
$722$	−17.9297	−	15.0445i	−0.667274	−	0.559897i
$723$	34.7029			1.29061
$724$	−2.72290	−	4.71621i	−0.101196	−	0.175277i
$725$	−6.93084	−	12.0046i	−0.257405	−	0.445838i
$726$	1.24892	−	2.16319i	0.0463516	−	0.0802834i
$727$	3.72926	+	6.45928i	0.138311	+	0.239561i	0.926857	−	0.375414i	$-0.122499\pi$
$727$	3.72926	+	6.45928i	0.138311	+	0.239561i	−0.788547	+	0.614975i	$0.789166\pi$
$728$	−9.47973	+	16.4194i	−0.351342	+	0.608542i
$729$	10.9564			0.405794
$730$	39.6464			1.46738
$731$	−4.19100	+	7.25903i	−0.155010	+	0.268485i
$732$	−5.75228	+	9.96324i	−0.212610	+	0.368252i
$733$	25.8079			0.953237			0.476618	−	0.879110i	$-0.341862\pi$
$733$	25.8079			0.953237			0.476618	+	0.879110i	$0.341862\pi$
$734$	−41.7803			−1.54214
$735$	19.0078	−	32.9225i	0.701114	−	1.21436i
$736$	3.23203	+	5.59805i	0.119134	+	0.206347i
$737$	2.07783	−	3.59891i	0.0765378	−	0.132567i
$738$	8.37601	+	14.5077i	0.308325	+	0.534035i
$739$	9.10928	+	15.7777i	0.335090	+	0.580393i	0.983502	−	0.180896i	$-0.0578999\pi$
$739$	9.10928	+	15.7777i	0.335090	+	0.580393i	−0.648412	+	0.761290i	$0.724567\pi$
$740$	12.2951			0.451978
$741$	14.3579	−	2.53178i	0.527452	−	0.0930071i
$742$	−5.55026			−0.203757
$743$	−13.6303	−	23.6083i	−0.500047	−	0.866106i	−1.00000		5.38747e-5i	$-0.999983\pi$
$743$	−13.6303	−	23.6083i	−0.500047	−	0.866106i	0.499953	−	0.866052i	$-0.333350\pi$
$744$	29.9709	+	51.9111i	1.09879	+	1.90316i
$745$	−6.65267	+	11.5228i	−0.243735	+	0.422161i
$746$	6.40181	+	11.0883i	0.234387	+	0.405970i
$747$	0.683921	−	1.18459i	0.0250234	−	0.0433418i
$748$	−0.681340			−0.0249122
$749$	17.2859			0.631613
$750$	−10.1140	+	17.5179i	−0.369310	+	0.639663i
$751$	−5.93882	+	10.2863i	−0.216711	+	0.375354i	−0.953800	−	0.300441i	$-0.902866\pi$
$751$	−5.93882	+	10.2863i	−0.216711	+	0.375354i	0.737090	+	0.675795i	$0.236200\pi$
$752$	−0.242842			−0.00885553
$753$	−25.9954			−0.947326
$754$	7.32762	−	12.6918i	0.266856	−	0.462209i
$755$	−11.6549	−	20.1869i	−0.424165	−	0.734676i
$756$	3.47222	−	6.01406i	0.126283	−	0.218729i
$757$	11.7417	+	20.3371i	0.426758	+	0.739166i	0.996583	−	0.0825999i	$-0.0263223\pi$
$757$	11.7417	+	20.3371i	0.426758	+	0.739166i	−0.569825	+	0.821766i	$0.692989\pi$
$758$	0.281314	+	0.487250i	0.0102178	+	0.0176977i
$759$	−4.91935			−0.178561
$760$	22.5432	+	26.8657i	0.817729	+	0.974520i
$761$	−13.7958			−0.500097			−0.250049	−	0.968233i	$-0.580447\pi$
$761$	−13.7958			−0.500097			−0.250049	+	0.968233i	$0.580447\pi$
$762$	−1.41047	−	2.44300i	−0.0510958	−	0.0885005i
$763$	22.9626	+	39.7724i	0.831302	+	1.43986i
$764$	1.84565	−	3.19676i	0.0667733	−	0.115655i
$765$	2.06469	+	3.57615i	0.0746491	+	0.129296i
$766$	−12.9645	+	22.4552i	−0.468426	+	0.811338i
$767$	4.49135			0.162173
$768$	22.0050			0.794037
$769$	−17.9720	+	31.1284i	−0.648087	+	1.12252i	0.335492	+	0.942043i	$0.391097\pi$
$769$	−17.9720	+	31.1284i	−0.648087	+	1.12252i	−0.983579	+	0.180477i	$0.942236\pi$
$770$	6.09054	−	10.5491i	0.219488	−	0.380164i
$771$

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615930 - 1.06682i) q^{2} +(1.01385 + 1.75603i) q^{3} +(0.241261 - 0.417876i) q^{4} +(-1.31548 - 2.27848i) q^{5} +(1.24892 - 2.16319i) q^{6} +3.75846 q^{7} -3.05812 q^{8} +(-0.555768 + 0.962618i) q^{9} +O(q^{10})\)	\(q+(-0.615930 - 1.06682i) q^{2} +(1.01385 + 1.75603i) q^{3} +(0.241261 - 0.417876i) q^{4} +(-1.31548 - 2.27848i) q^{5} +(1.24892 - 2.16319i) q^{6} +3.75846 q^{7} -3.05812 q^{8} +(-0.555768 + 0.962618i) q^{9} +(-1.62049 + 2.80677i) q^{10} -1.00000 q^{11} +0.978405 q^{12} +(0.824769 - 1.42854i) q^{13} +(-2.31495 - 4.00960i) q^{14} +(2.66739 - 4.62006i) q^{15} +(1.40107 + 2.42672i) q^{16} +(0.706020 + 1.22286i) q^{17} +1.36926 q^{18} +(4.29267 - 0.756939i) q^{19} -1.26950 q^{20} +(3.81050 + 6.59997i) q^{21} +(0.615930 + 1.06682i) q^{22} +(1.21304 - 2.10105i) q^{23} +(-3.10046 - 5.37016i) q^{24} +(-0.960983 + 1.66447i) q^{25} -2.03200 q^{26} +3.82922 q^{27} +(0.906768 - 1.57057i) q^{28} +(-3.60612 + 6.24598i) q^{29} -6.57171 q^{30} -9.66660 q^{31} +(-1.33220 + 2.30744i) q^{32} +(-1.01385 - 1.75603i) q^{33} +(0.869718 - 1.50640i) q^{34} +(-4.94418 - 8.56357i) q^{35} +(0.268170 + 0.464484i) q^{36} -9.68506 q^{37} +(-3.45151 - 4.11330i) q^{38} +3.34475 q^{39} +(4.02290 + 6.96786i) q^{40} +(6.11720 + 10.5953i) q^{41} +(4.69400 - 8.13024i) q^{42} +(2.96805 + 5.14081i) q^{43} +(-0.241261 + 0.417876i) q^{44} +2.92441 q^{45} -2.98859 q^{46} +(-0.0433317 + 0.0750526i) q^{47} +(-2.84093 + 4.92063i) q^{48} +7.12599 q^{49} +2.36759 q^{50} +(-1.43159 + 2.47959i) q^{51} +(-0.397969 - 0.689302i) q^{52} +(0.599395 - 1.03818i) q^{53} +(-2.35853 - 4.08510i) q^{54} +(1.31548 + 2.27848i) q^{55} -11.4938 q^{56} +(5.68132 + 6.77066i) q^{57} +8.88446 q^{58} +(1.36140 + 2.35801i) q^{59} +(-1.28707 - 2.22928i) q^{60} +(-5.87924 + 10.1831i) q^{61} +(5.95395 + 10.3125i) q^{62} +(-2.08883 + 3.61796i) q^{63} +8.88643 q^{64} -4.33987 q^{65} +(-1.24892 + 2.16319i) q^{66} +(-2.07783 + 3.59891i) q^{67} +0.681340 q^{68} +4.91935 q^{69} +(-6.09054 + 10.5491i) q^{70} +(-1.31934 - 2.28517i) q^{71} +(1.69960 - 2.94380i) q^{72} +(-6.11642 - 10.5939i) q^{73} +(5.96532 + 10.3322i) q^{74} -3.89716 q^{75} +(0.719347 - 1.97642i) q^{76} -3.75846 q^{77} +(-2.06013 - 3.56826i) q^{78} +(-1.58868 - 2.75167i) q^{79} +(3.68615 - 6.38460i) q^{80} +(5.54955 + 9.61210i) q^{81} +(7.53553 - 13.0519i) q^{82} -1.23059 q^{83} +3.67729 q^{84} +(1.85751 - 3.21731i) q^{85} +(3.65622 - 6.33276i) q^{86} -14.6242 q^{87} +3.05812 q^{88} +(7.60245 - 13.1678i) q^{89} +(-1.80123 - 3.11982i) q^{90} +(3.09986 - 5.36911i) q^{91} +(-0.585319 - 1.01380i) q^{92} +(-9.80044 - 16.9749i) q^{93} +0.106757 q^{94} +(-7.37160 - 8.78503i) q^{95} -5.40259 q^{96} +(1.66071 + 2.87643i) q^{97} +(-4.38911 - 7.60217i) q^{98} +(0.555768 - 0.962618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

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