LMFDB - Embedded newform 209.2.e.b.45.4

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			45.4
Root			$-0.198213 - 0.343315i$ of defining polynomial
Character	$\chi$	$=$	209.45
Dual form			209.2.e.b.144.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.198213 - 0.343315i) q^{2} +(-0.634005 - 1.09813i) q^{3} +(0.921423 - 1.59595i) q^{4} +(-0.220960 - 0.382715i) q^{5} +(-0.251336 + 0.435327i) q^{6} -0.667657 q^{7} -1.52341 q^{8} +(0.696076 - 1.20564i) q^{9} +O(q^{10})$	\(q+(-0.198213 - 0.343315i) q^{2} +(-0.634005 - 1.09813i) q^{3} +(0.921423 - 1.59595i) q^{4} +(-0.220960 - 0.382715i) q^{5} +(-0.251336 + 0.435327i) q^{6} -0.667657 q^{7} -1.52341 q^{8} +(0.696076 - 1.20564i) q^{9} +(-0.0875945 + 0.151718i) q^{10} -1.00000 q^{11} -2.33675 q^{12} +(-0.802426 + 1.38984i) q^{13} +(0.132338 + 0.229217i) q^{14} +(-0.280180 + 0.485286i) q^{15} +(-1.54089 - 2.66890i) q^{16} +(-2.02772 - 3.51212i) q^{17} -0.551886 q^{18} +(2.81513 + 3.32792i) q^{19} -0.814392 q^{20} +(0.423298 + 0.733173i) q^{21} +(0.198213 + 0.343315i) q^{22} +(0.187443 - 0.324661i) q^{23} +(0.965846 + 1.67289i) q^{24} +(2.40235 - 4.16100i) q^{25} +0.636205 q^{26} -5.56929 q^{27} +(-0.615195 + 1.06555i) q^{28} +(1.28039 - 2.21770i) q^{29} +0.222141 q^{30} +9.01266 q^{31} +(-2.13425 + 3.69663i) q^{32} +(0.634005 + 1.09813i) q^{33} +(-0.803843 + 1.39230i) q^{34} +(0.147526 + 0.255522i) q^{35} +(-1.28276 - 2.22181i) q^{36} +7.24253 q^{37} +(0.584530 - 1.62611i) q^{38} +2.03497 q^{39} +(0.336612 + 0.583030i) q^{40} +(2.54306 + 4.40471i) q^{41} +(0.167806 - 0.290649i) q^{42} +(5.01170 + 8.68051i) q^{43} +(-0.921423 + 1.59595i) q^{44} -0.615222 q^{45} -0.148615 q^{46} +(-1.03598 + 1.79437i) q^{47} +(-1.95386 + 3.38418i) q^{48} -6.55423 q^{49} -1.90471 q^{50} +(-2.57117 + 4.45340i) q^{51} +(1.47875 + 2.56126i) q^{52} +(0.163017 - 0.282353i) q^{53} +(1.10391 + 1.91202i) q^{54} +(0.220960 + 0.382715i) q^{55} +1.01711 q^{56} +(1.86968 - 5.20129i) q^{57} -1.01516 q^{58} +(6.93879 + 12.0183i) q^{59} +(0.516328 + 0.894307i) q^{60} +(5.53232 - 9.58226i) q^{61} +(-1.78643 - 3.09418i) q^{62} +(-0.464740 + 0.804954i) q^{63} -4.47140 q^{64} +0.709217 q^{65} +(0.251336 - 0.435327i) q^{66} +(4.06006 - 7.03224i) q^{67} -7.47357 q^{68} -0.475359 q^{69} +(0.0584831 - 0.101296i) q^{70} +(-3.19012 - 5.52545i) q^{71} +(-1.06041 + 1.83668i) q^{72} +(0.0659932 + 0.114304i) q^{73} +(-1.43556 - 2.48647i) q^{74} -6.09241 q^{75} +(7.90512 - 1.42639i) q^{76} +0.667657 q^{77} +(-0.403357 - 0.698635i) q^{78} +(-0.134657 - 0.233233i) q^{79} +(-0.680950 + 1.17944i) q^{80} +(1.44273 + 2.49887i) q^{81} +(1.00814 - 1.74614i) q^{82} -5.76350 q^{83} +1.56015 q^{84} +(-0.896094 + 1.55208i) q^{85} +(1.98677 - 3.44118i) q^{86} -3.24709 q^{87} +1.52341 q^{88} +(-0.492968 + 0.853846i) q^{89} +(0.121945 + 0.211215i) q^{90} +(0.535745 - 0.927938i) q^{91} +(-0.345429 - 0.598300i) q^{92} +(-5.71407 - 9.89706i) q^{93} +0.821379 q^{94} +(0.651612 - 1.81273i) q^{95} +5.41251 q^{96} +(1.68899 + 2.92541i) q^{97} +(1.29914 + 2.25017i) q^{98} +(-0.696076 + 1.20564i) 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 $

$2$	−0.198213	−	0.343315i	−0.140158	−	0.242760i	0.787398	−	0.616445i	$-0.211428\pi$
$2$	−0.198213	−	0.343315i	−0.140158	−	0.242760i	−0.927556	+	0.373684i	$0.878094\pi$
$3$	−0.634005	−	1.09813i	−0.366043	−	0.634005i	0.622900	−	0.782301i	$-0.285954\pi$
$3$	−0.634005	−	1.09813i	−0.366043	−	0.634005i	−0.988943	+	0.148297i	$0.952621\pi$
$4$	0.921423	−	1.59595i	0.460712	−	0.797976i
$5$	−0.220960	−	0.382715i	−0.0988165	−	0.171155i	0.812379	−	0.583130i	$-0.198172\pi$
$5$	−0.220960	−	0.382715i	−0.0988165	−	0.171155i	−0.911195	+	0.411975i	$0.864839\pi$
$6$	−0.251336	+	0.435327i	−0.102608	+	0.177721i
$7$	−0.667657			−0.252351			−0.126175	−	0.992008i	$-0.540270\pi$
$7$	−0.667657			−0.252351			−0.126175	+	0.992008i	$0.540270\pi$
$8$	−1.52341			−0.538605
$9$	0.696076	−	1.20564i	0.232025	−	0.401880i
$10$	−0.0875945	+	0.151718i	−0.0276998	+	0.0479775i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	−2.33675			−0.674560
$13$	−0.802426	+	1.38984i	−0.222553	+	0.385473i	−0.955582	−	0.294724i	$-0.904772\pi$
$13$	−0.802426	+	1.38984i	−0.222553	+	0.385473i	0.733030	+	0.680197i	$0.238106\pi$
$14$	0.132338	+	0.229217i	0.0353689	+	0.0612608i
$15$	−0.280180	+	0.485286i	−0.0723421	+	0.125300i
$16$	−1.54089	−	2.66890i	−0.385222	−	0.667224i
$17$	−2.02772	−	3.51212i	−0.491795	−	0.851815i	0.508160	−	0.861263i	$-0.330326\pi$
$17$	−2.02772	−	3.51212i	−0.491795	−	0.851815i	−0.999955	+	0.00944813i	$0.996993\pi$
$18$	−0.551886			−0.130081
$19$	2.81513	+	3.32792i	0.645835	+	0.763477i
$19$	2.81513	+	3.32792i	0.645835	+	0.763477i
$20$	−0.814392			−0.182104
$21$	0.423298	+	0.733173i	0.0923711	+	0.159991i
$22$	0.198213	+	0.343315i	0.0422592	+	0.0731950i
$23$	0.187443	−	0.324661i	0.0390846	−	0.0676965i	−0.845821	−	0.533466i	$-0.820889\pi$
$23$	0.187443	−	0.324661i	0.0390846	−	0.0676965i	0.884906	+	0.465770i	$0.154222\pi$
$24$	0.965846	+	1.67289i	0.197152	+	0.341478i
$25$	2.40235	−	4.16100i	0.480471	−	0.832199i
$26$	0.636205			0.124770
$27$	−5.56929			−1.07181
$28$	−0.615195	+	1.06555i	−0.116261	+	0.201370i
$29$	1.28039	−	2.21770i	0.237762	−	0.411817i	−0.722309	−	0.691570i	$-0.756919\pi$
$29$	1.28039	−	2.21770i	0.237762	−	0.411817i	0.960072	+	0.279753i	$0.0902527\pi$
$30$	0.222141			0.0405573
$31$	9.01266			1.61872			0.809361	−	0.587311i	$-0.199814\pi$
$31$	9.01266			1.61872			0.809361	+	0.587311i	$0.199814\pi$
$32$	−2.13425	+	3.69663i	−0.377286	+	0.653479i
$33$	0.634005	+	1.09813i	0.110366	+	0.191160i
$34$	−0.803843	+	1.39230i	−0.137858	+	0.238777i
$35$	0.147526	+	0.255522i	0.0249364	+	0.0431911i
$36$	−1.28276	−	2.22181i	−0.213794	−	0.370301i
$37$	7.24253			1.19066			0.595332	−	0.803480i	$-0.297020\pi$
$37$	7.24253			1.19066			0.595332	+	0.803480i	$0.297020\pi$
$38$	0.584530	−	1.62611i	0.0948232	−	0.263790i
$39$	2.03497			0.325855
$40$	0.336612	+	0.583030i	0.0532231	+	0.0921851i
$41$	2.54306	+	4.40471i	0.397159	+	0.687900i	0.993374	−	0.114925i	$-0.0366627\pi$
$41$	2.54306	+	4.40471i	0.397159	+	0.687900i	−0.596215	+	0.802825i	$0.703329\pi$
$42$	0.167806	−	0.290649i	0.0258931	−	0.0448481i
$43$	5.01170	+	8.68051i	0.764277	+	1.32377i	0.940628	+	0.339439i	$0.110237\pi$
$43$	5.01170	+	8.68051i	0.764277	+	1.32377i	−0.176352	+	0.984327i	$0.556430\pi$
$44$	−0.921423	+	1.59595i	−0.138910	+	0.240599i
$45$	−0.615222			−0.0917118
$46$	−0.148615			−0.0219120
$47$	−1.03598	+	1.79437i	−0.151113	+	0.261736i	−0.931637	−	0.363390i	$-0.881619\pi$
$47$	−1.03598	+	1.79437i	−0.151113	+	0.261736i	0.780524	+	0.625126i	$0.214952\pi$
$48$	−1.95386	+	3.38418i	−0.282015	+	0.488465i
$49$	−6.55423			−0.936319
$50$	−1.90471			−0.269367
$51$	−2.57117	+	4.45340i	−0.360036	+	0.623601i
$52$	1.47875	+	2.56126i	0.205065	+	0.355183i
$53$	0.163017	−	0.282353i	0.0223921	−	0.0387842i	−0.854612	−	0.519267i	$-0.826205\pi$
$53$	0.163017	−	0.282353i	0.0223921	−	0.0387842i	0.877004	+	0.480483i	$0.159538\pi$
$54$	1.10391	+	1.91202i	0.150223	+	0.260193i
$55$	0.220960	+	0.382715i	0.0297943	+	0.0516053i
$56$	1.01711			0.135917
$57$	1.86968	−	5.20129i	0.247645	−	0.688928i
$58$	−1.01516			−0.133297
$59$	6.93879	+	12.0183i	0.903353	+	1.56465i	0.823113	+	0.567878i	$0.192236\pi$
$59$	6.93879	+	12.0183i	0.903353	+	1.56465i	0.0802407	+	0.996776i	$0.474431\pi$
$60$	0.516328	+	0.894307i	0.0666577	+	0.115455i
$61$	5.53232	−	9.58226i	0.708341	−	1.22688i	−0.257131	−	0.966377i	$-0.582777\pi$
$61$	5.53232	−	9.58226i	0.708341	−	1.22688i	0.965472	−	0.260506i	$-0.0838894\pi$
$62$	−1.78643	−	3.09418i	−0.226877	−	0.392962i
$63$	−0.464740	+	0.804954i	−0.0585518	+	0.101415i
$64$	−4.47140			−0.558925
$65$	0.709217			0.0879676
$66$	0.251336	−	0.435327i	0.0309373	−	0.0535850i
$67$	4.06006	−	7.03224i	0.496016	−	0.859125i	−0.503974	−	0.863719i	$-0.668129\pi$
$67$	4.06006	−	7.03224i	0.496016	−	0.859125i	0.999989	+	0.00459440i	$0.00146245\pi$
$68$	−7.47357			−0.906303
$69$	−0.475359			−0.0572265
$70$	0.0584831	−	0.101296i	0.00699007	−	0.0121072i
$71$	−3.19012	−	5.52545i	−0.378598	−	0.655751i	0.612261	−	0.790656i	$-0.290260\pi$
$71$	−3.19012	−	5.52545i	−0.378598	−	0.655751i	−0.990859	+	0.134905i	$0.956927\pi$
$72$	−1.06041	+	1.83668i	−0.124970	+	0.216455i
$73$	0.0659932	+	0.114304i	0.00772392	+	0.0133782i	0.869862	−	0.493296i	$-0.164208\pi$
$73$	0.0659932	+	0.114304i	0.00772392	+	0.0133782i	−0.862138	+	0.506674i	$0.830875\pi$
$74$	−1.43556	−	2.48647i	−0.166881	−	0.289046i
$75$	−6.09241			−0.703491
$76$	7.90512	−	1.42639i	0.906780	−	0.163618i
$77$	0.667657			0.0760866
$78$	−0.403357	−	0.698635i	−0.0456712	−	0.0791048i
$79$	−0.134657	−	0.233233i	−0.0151501	−	0.0262408i	0.858351	−	0.513063i	$-0.171489\pi$
$79$	−0.134657	−	0.233233i	−0.0151501	−	0.0262408i	−0.873501	+	0.486822i	$0.838156\pi$
$80$	−0.680950	+	1.17944i	−0.0761326	+	0.131865i
$81$	1.44273	+	2.49887i	0.160303	+	0.277653i
$82$	1.00814	−	1.74614i	0.111330	−	0.192829i
$83$	−5.76350			−0.632626			−0.316313	−	0.948655i	$-0.602445\pi$
$83$	−5.76350			−0.632626			−0.316313	+	0.948655i	$0.602445\pi$
$84$	1.56015			0.170226
$85$	−0.896094	+	1.55208i	−0.0971950	+	0.168347i
$86$	1.98677	−	3.44118i	0.214239	−	0.371072i
$87$	−3.24709			−0.348125
$88$	1.52341			0.162396
$89$	−0.492968	+	0.853846i	−0.0522545	+	0.0905075i	−0.890970	−	0.454063i	$-0.849974\pi$
$89$	−0.492968	+	0.853846i	−0.0522545	+	0.0905075i	0.838715	+	0.544571i	$0.183307\pi$
$90$	0.121945	+	0.211215i	0.0128541	+	0.0222640i
$91$	0.535745	−	0.927938i	0.0561614	−	0.0972743i
$92$	−0.345429	−	0.598300i	−0.0360134	−	0.0623771i
$93$	−5.71407	−	9.89706i	−0.592521	−	1.02628i
$94$	0.821379			0.0847187
$95$	0.651612	−	1.81273i	0.0668539	−	0.185982i
$96$	5.41251			0.552411
$97$	1.68899	+	2.92541i	0.171491	+	0.297031i	0.938941	−	0.344077i	$-0.111808\pi$
$97$	1.68899	+	2.92541i	0.171491	+	0.297031i	−0.767450	+	0.641108i	$0.778475\pi$
$98$	1.29914	+	2.25017i	0.131232	+	0.227301i
$99$	−0.696076	+	1.20564i	−0.0699583	+	0.121171i
$100$	−4.42717	−	7.66808i	−0.442717	−	0.766808i
$101$	3.37624	−	5.84781i	0.335948	−	0.581879i	−0.647718	−	0.761880i	$-0.724277\pi$
$101$	3.37624	−	5.84781i	0.335948	−	0.581879i	0.983666	+	0.180001i	$0.0576100\pi$
$102$	2.03856			0.201848
$103$	−9.88932			−0.974424			−0.487212	−	0.873284i	$-0.661986\pi$
$103$	−9.88932			−0.974424			−0.487212	+	0.873284i	$0.661986\pi$
$104$	1.22242	−	2.11729i	0.119868	−	0.207618i
$105$	0.187064	−	0.324005i	0.0182556	−	0.0316196i
$106$	−0.129248			−0.0125537
$107$	0.528111			0.0510544			0.0255272	−	0.999674i	$-0.491874\pi$
$107$	0.528111			0.0510544			0.0255272	+	0.999674i	$0.491874\pi$
$108$	−5.13167	+	8.88832i	−0.493795	+	0.855279i
$109$	1.27111	+	2.20163i	0.121750	+	0.210877i	0.920458	−	0.390842i	$-0.127816\pi$
$109$	1.27111	+	2.20163i	0.121750	+	0.210877i	−0.798708	+	0.601719i	$0.794483\pi$
$110$	0.0875945	−	0.151718i	0.00835181	−	0.0144658i
$111$	−4.59180	−	7.95322i	−0.435834	−	0.754887i
$112$	1.02878	+	1.78191i	0.0972110	+	0.168374i
$113$	−16.5799			−1.55971			−0.779855	−	0.625960i	$-0.784707\pi$
$113$	−16.5799			−1.55971			−0.779855	+	0.625960i	$0.784707\pi$
$114$	−2.15628	+	0.389075i	−0.201954	+	0.0364402i
$115$	−0.165670			−0.0154488
$116$	−2.35956	−	4.08688i	−0.219080	−	0.379457i
$117$	1.11710	+	1.93487i	0.103276	+	0.178879i
$118$	2.75072	−	4.76438i	0.253224	−	0.438597i
$119$	1.35382	+	2.34489i	0.124105	+	0.214956i
$120$	0.426827	−	0.739287i	0.0389638	−	0.0674873i
$121$	1.00000			0.0909091
$122$	−4.38631			−0.397118
$123$	3.22462	−	5.58521i	0.290755	−	0.503602i
$124$	8.30448	−	14.3838i	0.745764	−	1.29170i
$125$	−4.33291			−0.387547
$126$	0.368471			0.0328260
$127$	−4.61960	+	8.00138i	−0.409923	+	0.710008i	−0.994881	−	0.101056i	$-0.967778\pi$
$127$	−4.61960	+	8.00138i	−0.409923	+	0.710008i	0.584957	+	0.811064i	$0.301111\pi$
$128$	5.15480	+	8.92837i	0.455624	+	0.789164i
$129$	6.35488	−	11.0070i	0.559516	−	0.969110i
$130$	−0.140576	−	0.243485i	−0.0123293	−	0.0213551i
$131$	7.39831	+	12.8142i	0.646393	+	1.11959i	0.983978	+	0.178291i	$0.0570568\pi$
$131$	7.39831	+	12.8142i	0.646393	+	1.11959i	−0.337584	+	0.941295i	$0.609610\pi$
$132$	2.33675			0.203388
$133$	−1.87954	−	2.22191i	−0.162977	−	0.192664i
$134$	−3.21903			−0.278082
$135$	1.23059	+	2.13145i	0.105913	+	0.183446i
$136$	3.08905	+	5.35038i	0.264883	+	0.458792i
$137$	−1.25376	+	2.17158i	−0.107116	+	0.185531i	−0.914601	−	0.404358i	$-0.867495\pi$
$137$	−1.25376	+	2.17158i	−0.107116	+	0.185531i	0.807485	+	0.589889i	$0.200828\pi$
$138$	0.0942224	+	0.163198i	0.00802075	+	0.0138923i
$139$	−1.62007	+	2.80604i	−0.137412	+	0.238005i	−0.926516	−	0.376255i	$-0.877212\pi$
$139$	−1.62007	+	2.80604i	−0.137412	+	0.238005i	0.789104	+	0.614259i	$0.210545\pi$
$140$	0.543735			0.0459540
$141$	2.62726			0.221255
$142$	−1.26465	+	2.19043i	−0.106127	+	0.183817i
$143$	0.802426	−	1.38984i	0.0671022	−	0.116224i
$144$	−4.29030			−0.357525
$145$	−1.13166			−0.0939794
$146$	0.0261614	−	0.0453129i	0.00216513	−	0.00375012i
$147$	4.15541	+	7.19739i	0.342733	+	0.593631i
$148$	6.67343	−	11.5587i	0.548553	−	0.950121i
$149$	−11.7001	−	20.2651i	−0.958508	−	1.66018i	−0.726129	−	0.687558i	$-0.758683\pi$
$149$	−11.7001	−	20.2651i	−0.958508	−	1.66018i	−0.232379	−	0.972625i	$-0.574651\pi$
$150$	1.20760	+	2.09162i	0.0985998	+	0.170780i
$151$	−8.86774			−0.721647			−0.360823	−	0.932634i	$-0.617504\pi$
$151$	−8.86774			−0.721647			−0.360823	+	0.932634i	$0.617504\pi$
$152$	−4.28858	−	5.06977i	−0.347850	−	0.411213i
$153$	−5.64580			−0.456436
$154$	−0.132338	−	0.229217i	−0.0106641	−	0.0184708i
$155$	−1.99144	−	3.44928i	−0.159956	−	0.277053i
$156$	1.87506	−	3.24771i	0.150125	−	0.260025i
$157$	3.24906	+	5.62753i	0.259303	+	0.449126i	0.966055	−	0.258335i	$-0.0831738\pi$
$157$	3.24906	+	5.62753i	0.259303	+	0.449126i	−0.706752	+	0.707461i	$0.749840\pi$
$158$	−0.0533816	+	0.0924597i	−0.00424681	+	0.00735570i
$159$	−0.413413			−0.0327858
$160$	1.88634			0.149128
$161$	−0.125148	+	0.216762i	−0.00986302	+	0.0170833i
$162$	0.571934	−	0.990619i	0.0449354	−	0.0778304i
$163$	−10.6557			−0.834619			−0.417310	−	0.908764i	$-0.637027\pi$
$163$	−10.6557			−0.834619			−0.417310	+	0.908764i	$0.637027\pi$
$164$	9.37294			0.731904
$165$	0.280180	−	0.485286i	0.0218120	−	0.0377795i
$166$	1.14240	+	1.97870i	0.0886675	+	0.153577i
$167$	−6.82309	+	11.8179i	−0.527987	+	0.914500i	0.471481	+	0.881876i	$0.343720\pi$
$167$	−6.82309	+	11.8179i	−0.527987	+	0.914500i	−0.999468	+	0.0326235i	$0.989614\pi$
$168$	−0.644854	−	1.11692i	−0.0497516	−	0.0861722i
$169$	5.21223	+	9.02784i	0.400941	+	0.694449i
$170$	0.710470			0.0544906
$171$	5.97182	−	1.07755i	0.456676	−	0.0824020i
$172$	18.4716			1.40844
$173$	11.3068	+	19.5840i	0.859643	+	1.48895i	0.872269	+	0.489026i	$0.162648\pi$
$173$	11.3068	+	19.5840i	0.859643	+	1.48895i	−0.0126258	+	0.999920i	$0.504019\pi$
$174$	0.643616	+	1.11478i	0.0487924	+	0.0845110i
$175$	−1.60395	+	2.77812i	−0.121247	+	0.210006i
$176$	1.54089	+	2.66890i	0.116149	+	0.201176i
$177$	8.79845	−	15.2394i	0.661332	−	1.14546i
$178$	0.390851			0.0292955
$179$	−2.55941			−0.191299			−0.0956497	−	0.995415i	$-0.530493\pi$
$179$	−2.55941			−0.191299			−0.0956497	+	0.995415i	$0.530493\pi$
$180$	−0.566879	+	0.981864i	−0.0422527	+	0.0731838i
$181$	1.32662	−	2.29777i	0.0986069	−	0.170792i	−0.812501	−	0.582959i	$-0.801895\pi$
$181$	1.32662	−	2.29777i	0.0986069	−	0.170792i	0.911108	+	0.412167i	$0.135228\pi$
$182$	−0.424767			−0.0314858
$183$	−14.0301			−1.03713
$184$	−0.285552	+	0.494590i	−0.0210512	+	0.0364617i
$185$	−1.60031	−	2.77182i	−0.117657	−	0.203788i
$186$	−2.26521	+	3.92345i	−0.166093	+	0.287682i
$187$	2.02772	+	3.51212i	0.148282	+	0.256832i
$188$	1.90915	+	3.30675i	0.139239	+	0.241169i
$189$	3.71838			0.270472
$190$	−0.751496	+	0.135599i	−0.0545192	+	0.00983737i
$191$	6.90666			0.499748			0.249874	−	0.968278i	$-0.419611\pi$
$191$	6.90666			0.499748			0.249874	+	0.968278i	$0.419611\pi$
$192$	2.83489	+	4.91017i	0.204591	+	0.354361i
$193$	2.93315	+	5.08036i	0.211132	+	0.365692i	0.952069	−	0.305883i	$-0.0989515\pi$
$193$	2.93315	+	5.08036i	0.211132	+	0.365692i	−0.740937	+	0.671575i	$0.765618\pi$
$194$	0.669560	−	1.15971i	0.0480716	−	0.0832624i
$195$	−0.449647	−	0.778811i	−0.0321999	−	0.0557718i
$196$	−6.03922	+	10.4602i	−0.431373	+	0.747160i
$197$	19.8898			1.41709			0.708543	−	0.705667i	$-0.249353\pi$
$197$	19.8898			1.41709			0.708543	+	0.705667i	$0.249353\pi$
$198$	0.551886			0.0392208
$199$	−7.03701	+	12.1885i	−0.498841	+	0.864017i	−0.999999	−	0.00133827i	$-0.999574\pi$
$199$	−7.03701	+	12.1885i	−0.498841	+	0.864017i	0.501159	+	0.865355i	$0.332907\pi$
$200$	−3.65976	+	6.33888i	−0.258784	+	0.448227i
$201$	−10.2964			−0.726252
$202$	−2.67686			−0.188343
$203$	−0.854862	+	1.48066i	−0.0599995	+	0.103922i
$204$	4.73828	+	8.20694i	0.331746	+	0.574600i
$205$	1.12383	−	1.94653i	0.0784918	−	0.135952i
$206$	1.96019	+	3.39515i	0.136573	+	0.236552i
$207$	−0.260949	−	0.451978i	−0.0181372	−	0.0314146i
$208$	4.94579			0.342929
$209$	−2.81513	−	3.32792i	−0.194727	−	0.230197i
$210$	−0.148314			−0.0102347
$211$	8.08162	+	13.9978i	0.556362	+	0.963646i	0.997796	+	0.0663531i	$0.0211364\pi$
$211$	8.08162	+	13.9978i	0.556362	+	0.963646i	−0.441435	+	0.897293i	$0.645530\pi$
$212$	−0.300415	−	0.520334i	−0.0206326	−	0.0357367i
$213$	−4.04510	+	7.00633i	−0.277166	+	0.480066i
$214$	−0.104678	−	0.181308i	−0.00715567	−	0.0123940i
$215$	2.21477	−	3.83610i	0.151046	−	0.261620i
$216$	8.48428			0.577282
$217$	−6.01737			−0.408486
$218$	0.503901	−	0.872782i	0.0341285	−	0.0591123i
$219$	0.0836800	−	0.144938i	0.00565457	−	0.00979400i
$220$	0.814392			0.0549063
$221$	6.50839			0.437802
$222$	−1.82031	+	3.15287i	−0.122171	+	0.211607i
$223$	−3.12201	−	5.40749i	−0.209066	−	0.362112i	0.742355	−	0.670007i	$-0.233709\pi$
$223$	−3.12201	−	5.40749i	−0.209066	−	0.362112i	−0.951420	+	0.307895i	$0.900376\pi$
$224$	1.42495	−	2.46808i	0.0952084	−	0.164906i
$225$	−3.34444	−	5.79274i	−0.222963	−	0.386183i
$226$	3.28636	+	5.69215i	0.218606	+	0.378636i
$227$	5.75444			0.381936			0.190968	−	0.981596i	$-0.438837\pi$
$227$	5.75444			0.381936			0.190968	+	0.981596i	$0.438837\pi$
$228$	−6.57824	−	7.77650i	−0.435655	−	0.515011i
$229$	14.0825			0.930599			0.465300	−	0.885153i	$-0.345947\pi$
$229$	14.0825			0.930599			0.465300	+	0.885153i	$0.345947\pi$
$230$	0.0328380	+	0.0568771i	0.00216527	+	0.00375036i
$231$	−0.423298	−	0.733173i	−0.0278509	−	0.0482393i
$232$	−1.95055	+	3.37846i	−0.128060	+	0.221807i
$233$	−9.79670	−	16.9684i	−0.641803	−	1.11164i	−0.985030	−	0.172383i	$-0.944853\pi$
$233$	−9.79670	−	16.9684i	−0.641803	−	1.11164i	0.343227	−	0.939252i	$-0.388480\pi$
$234$	0.442847	−	0.767034i	0.0289498	−	0.0501426i
$235$	0.915642			0.0597299
$236$	25.5742			1.66474
$237$	−0.170747	+	0.295742i	−0.0110912	+	0.0192105i
$238$	0.536692	−	0.929577i	0.0347885	−	0.0602555i
$239$	−14.8597			−0.961192			−0.480596	−	0.876942i	$-0.659580\pi$
$239$	−14.8597			−0.961192			−0.480596	+	0.876942i	$0.659580\pi$
$240$	1.72690			0.111471
$241$	−6.97637	+	12.0834i	−0.449388	+	0.778362i	−0.998346	−	0.0574873i	$-0.981691\pi$
$241$	−6.97637	+	12.0834i	−0.449388	+	0.778362i	0.548959	+	0.835850i	$0.315024\pi$
$242$	−0.198213	−	0.343315i	−0.0127416	−	0.0220691i
$243$	−6.52455	+	11.3008i	−0.418550	+	0.724949i
$244$	−10.1952	−	17.6586i	−0.652682	−	1.13048i
$245$	1.44823	+	2.50840i	0.0925238	+	0.160256i
$246$	−2.55665			−0.163006
$247$	−6.88421	+	1.24218i	−0.438032	+	0.0790378i
$248$	−13.7299			−0.871852
$249$	3.65408	+	6.32906i	0.231568	+	0.401088i
$250$	0.858839	+	1.48755i	0.0543177	+	0.0940811i
$251$	6.88758	−	11.9296i	0.434740	−	0.752992i	−0.562534	−	0.826774i	$-0.690173\pi$
$251$	6.88758	−	11.9296i	0.434740	−	0.752992i	0.997274	+	0.0737817i	$0.0235068\pi$
$252$	0.856445	+	1.48341i	0.0539510	+	0.0934458i
$253$	−0.187443	+	0.324661i	−0.0117844	+	0.0204113i
$254$	3.66266			0.229816
$255$	2.27251			0.142310
$256$	−2.42791	+	4.20526i	−0.151744	+	0.262828i
$257$	4.03246	−	6.98443i	0.251538	−	0.435677i	−0.712411	−	0.701762i	$-0.752397\pi$
$257$	4.03246	−	6.98443i	0.251538	−	0.435677i	0.963949	+	0.266085i	$0.0857303\pi$
$258$	−5.03848			−0.313682
$259$	−4.83553			−0.300465
$260$	0.653489	−	1.13188i	0.0405277	−	0.0701960i
$261$	−1.78250	−	3.08738i	−0.110334	−	0.191104i
$262$	2.93288	−	5.07990i	0.181194	−	0.313838i
$263$	−11.2342	−	19.4583i	−0.692732	−	1.19985i	−0.970939	−	0.239326i	$-0.923073\pi$
$263$	−11.2342	−	19.4583i	−0.692732	−	1.19985i	0.278207	−	0.960521i	$-0.410260\pi$
$264$	−0.965846	−	1.67289i	−0.0594437	−	0.102960i
$265$	−0.144081			−0.00885083
$266$	−0.390265	+	1.08569i	−0.0239287	+	0.0665677i
$267$	1.25018			0.0765096
$268$	−7.48208	−	12.9593i	−0.457040	−	0.791617i
$269$	7.25896	+	12.5729i	0.442587	+	0.766582i	0.997881	−	0.0650717i	$-0.0207276\pi$
$269$	7.25896	+	12.5729i	0.442587	+	0.766582i	−0.555294	+	0.831654i	$0.687394\pi$
$270$	0.487839	−	0.844962i	0.0296890	−	0.0514228i
$271$	−9.77021	−	16.9225i	−0.593498	−	1.02797i	−0.993757	−	0.111567i	$-0.964413\pi$
$271$	−9.77021	−	16.9225i	−0.593498	−	1.02797i	0.400259	−	0.916402i	$-0.368920\pi$
$272$	−6.24899	+	10.8236i	−0.378901	+	0.656275i
$273$	−1.35866			−0.0822298
$274$	0.994049			0.0600527
$275$	−2.40235	+	4.16100i	−0.144867	+	0.250918i
$276$	−0.438007	+	0.758650i	−0.0263649	+	0.0456654i
$277$	16.4062			0.985750			0.492875	−	0.870100i	$-0.335946\pi$
$277$	16.4062			0.985750			0.492875	+	0.870100i	$0.335946\pi$
$278$	1.28447			0.0770376
$279$	6.27350	−	10.8660i	0.375585	−	0.650532i
$280$	−0.224742	−	0.389264i	−0.0134309	−	0.0232630i
$281$	5.27958	−	9.14450i	0.314953	−	0.545515i	−0.664474	−	0.747311i	$-0.731345\pi$
$281$	5.27958	−	9.14450i	0.314953	−	0.545515i	0.979428	+	0.201796i	$0.0646778\pi$
$282$	−0.520758	−	0.901979i	−0.0310107	−	0.0537121i
$283$	6.81481	+	11.8036i	0.405098	+	0.701651i	0.994333	−	0.106311i	$-0.0339040\pi$
$283$	6.81481	+	11.8036i	0.405098	+	0.701651i	−0.589235	+	0.807962i	$0.700571\pi$
$284$	−11.7578			−0.697698
$285$	−2.40373	+	0.433726i	−0.142385	+	0.0256917i
$286$	−0.636205			−0.0376196
$287$	−1.69789	−	2.94084i	−0.100223	−	0.173592i
$288$	2.97121	+	5.14628i	0.175080	+	0.303248i
$289$	0.276669	−	0.479205i	0.0162747	−	0.0281885i
$290$	0.224310	+	0.388517i	0.0131720	+	0.0228145i
$291$	2.14165	−	3.70945i	0.125546	−	0.217452i
$292$	0.243231			0.0142340
$293$	−29.3909			−1.71704			−0.858518	−	0.512784i	$-0.828614\pi$
$293$	−29.3909			−1.71704			−0.858518	+	0.512784i	$0.828614\pi$
$294$	1.64732	−	2.85323i	0.0960734	−	0.166404i
$295$	3.06640	−	5.31115i	0.178532	−	0.309227i
$296$	−11.0333			−0.641298
$297$	5.56929			0.323163
$298$	−4.63822	+	8.03363i	−0.268685	+	0.465376i
$299$	0.300818	+	0.521033i	0.0173968	+	0.0301321i
$300$	−5.61369	+	9.72319i	−0.324106	+	0.561369i
$301$	−3.34610	−	5.79561i	−0.192866	−	0.334053i
$302$	1.75770	+	3.04443i	0.101144	+	0.175187i
$303$	−8.56220			−0.491885
$304$	4.54407	−	12.6412i	0.260620	−	0.725025i
$305$	−4.88970			−0.279983
$306$	1.11907	+	1.93829i	0.0639731	+	0.110805i
$307$	−15.8419	−	27.4389i	−0.904143	−	1.56602i	−0.822064	−	0.569395i	$-0.807177\pi$
$307$	−15.8419	−	27.4389i	−0.904143	−	1.56602i	−0.0820790	−	0.996626i	$-0.526156\pi$
$308$	0.615195	−	1.06555i	0.0350540	−	0.0607153i
$309$	6.26987	+	10.8597i	0.356681	+	0.617789i
$310$	−0.789460	+	1.36738i	−0.0448383	+	0.0776622i
$311$	26.7120			1.51470			0.757348	−	0.653011i	$-0.226495\pi$
$311$	26.7120			1.51470			0.757348	+	0.653011i	$0.226495\pi$
$312$	−3.10008			−0.175507
$313$	−9.43495	+	16.3418i	−0.533295	+	0.923694i	0.465949	+	0.884812i	$0.345713\pi$
$313$	−9.43495	+	16.3418i	−0.533295	+	0.923694i	−0.999244	+	0.0388824i	$0.987620\pi$
$314$	1.28801	−	2.23090i	0.0726867	−	0.125897i
$315$	0.410757			0.0231435
$316$	−0.496305			−0.0279193
$317$	14.5166	−	25.1435i	0.815335	−	1.41220i	−0.0937527	−	0.995596i	$-0.529886\pi$
$317$	14.5166	−	25.1435i	0.815335	−	1.41220i	0.909087	−	0.416606i	$-0.136780\pi$
$318$	0.0819440	+	0.141931i	0.00459519	+	0.00795910i
$319$	−1.28039	+	2.21770i	−0.0716881	+	0.124167i
$320$	0.988003	+	1.71127i	0.0552311	+	0.0956630i
$321$	−0.334824	−	0.579933i	−0.0186881	−	0.0323687i
$322$	0.0992237			0.00552952
$323$	5.97975	−	16.6352i	0.332722	−	0.925606i
$324$	5.31744			0.295414
$325$	3.85542	+	6.67778i	0.213860	+	0.370417i
$326$	2.11210	+	3.65827i	0.116978	+	0.202613i
$327$	1.61178	−	2.79168i	0.0891315	−	0.154380i
$328$	−3.87411	−	6.71016i	−0.213912	−	0.370506i
$329$	0.691679	−	1.19802i	0.0381335	−	0.0660492i
$330$	−0.222141			−0.0122285
$331$	−18.5242			−1.01818			−0.509091	−	0.860712i	$-0.670019\pi$
$331$	−18.5242			−1.01818			−0.509091	+	0.860712i	$0.670019\pi$
$332$	−5.31062	+	9.19827i	−0.291458	+	0.504820i
$333$	5.04135	−	8.73188i	0.276264	−	0.478504i
$334$	5.40970			0.296006
$335$	−3.58846			−0.196058
$336$	1.30451	−	2.25947i	0.0711668	−	0.123264i
$337$	−3.19606	−	5.53574i	−0.174101	−	0.301551i	0.765749	−	0.643139i	$-0.222368\pi$
$337$	−3.19606	−	5.53574i	−0.174101	−	0.301551i	−0.939850	+	0.341588i	$0.889035\pi$
$338$	2.06626	−	3.57887i	0.112390	−	0.194665i
$339$	10.5118	+	18.2069i	0.570921	+	0.988863i
$340$	1.65136	+	2.86024i	0.0895577	+	0.155119i
$341$	−9.01266			−0.488063
$342$	−1.55363	−	1.83663i	−0.0840107	−	0.0993137i
$343$	9.04958			0.488631
$344$	−7.63484	−	13.2239i	−0.411643	−	0.712987i
$345$	0.105036	+	0.181927i	0.00565493	+	0.00979462i
$346$	4.48233	−	7.76362i	0.240972	−	0.417375i
$347$	15.1980	+	26.3238i	0.815873	+	1.41313i	0.908700	+	0.417451i	$0.137076\pi$
$347$	15.1980	+	26.3238i	0.815873	+	1.41313i	−0.0928267	+	0.995682i	$0.529590\pi$
$348$	−2.99195	+	5.18220i	−0.160385	+	0.277795i
$349$	−21.8950			−1.17201			−0.586007	−	0.810306i	$-0.699301\pi$
$349$	−21.8950			−1.17201			−0.586007	+	0.810306i	$0.699301\pi$
$350$	1.27169			0.0679749
$351$	4.46894	−	7.74043i	0.238534	−	0.413154i
$352$	2.13425	−	3.69663i	0.113756	−	0.197031i
$353$	24.2146			1.28881			0.644406	−	0.764684i	$-0.277105\pi$
$353$	24.2146			1.28881			0.644406	+	0.764684i	$0.277105\pi$
$354$	−6.97587			−0.370763
$355$	−1.40978	+	2.44181i	−0.0748235	+	0.129598i
$356$	0.908465	+	1.57351i	0.0481485	+	0.0833957i
$357$	1.71666	−	2.97335i	0.0908554	−	0.157366i
$358$	0.507309	+	0.878685i	0.0268121	+	0.0464399i
$359$	−9.04762	−	15.6709i	−0.477515	−	0.827080i	0.522153	−	0.852852i	$-0.325129\pi$
$359$	−9.04762	−	15.6709i	−0.477515	−	0.827080i	−0.999668	+	0.0257718i	$0.991796\pi$
$360$	0.937232			0.0493964
$361$	−3.15009	+	18.7370i	−0.165794	+	0.986160i
$362$	−1.05181			−0.0552821
$363$	−0.634005	−	1.09813i	−0.0332766	−	0.0576368i
$364$	−0.987296	−	1.71005i	−0.0517484	−	0.0896308i
$365$	0.0291638	−	0.0505131i	0.00152650	−	0.00264398i
$366$	2.78094	+	4.81673i	0.145362	+	0.251775i
$367$	9.07821	−	15.7239i	0.473879	−	0.820782i	−0.525674	−	0.850686i	$-0.676187\pi$
$367$	9.07821	−	15.7239i	0.473879	−	0.820782i	0.999553	+	0.0299039i	$0.00952011\pi$
$368$	−1.15532			−0.0602250
$369$	7.08066			0.368604
$370$	−0.634406	+	1.09882i	−0.0329812	+	0.0571251i
$371$	−0.108839	+	0.188515i	−0.00565065	+	0.00978722i
$372$	−21.0603			−1.09193
$373$	−25.2547			−1.30764			−0.653819	−	0.756651i	$-0.726834\pi$
$373$	−25.2547			−1.30764			−0.653819	+	0.756651i	$0.726834\pi$
$374$	0.803843	−	1.39230i	0.0415657	−	0.0719940i
$375$	2.74708	+	4.75808i	0.141859	+	0.245706i
$376$	1.57822	−	2.73355i	0.0813903	−	0.140972i
$377$	2.05484	+	3.55908i	0.105829	+	0.183302i
$378$	−0.737031	−	1.27658i	−0.0379088	−	0.0656599i
$379$	−20.6962			−1.06309			−0.531545	−	0.847030i	$-0.678388\pi$
$379$	−20.6962			−1.06309			−0.531545	+	0.847030i	$0.678388\pi$
$380$	−2.29262	−	2.71023i	−0.117609	−	0.139032i
$381$	11.7154			0.600198
$382$	−1.36899	−	2.37116i	−0.0700436	−	0.121319i
$383$	11.1426	+	19.2995i	0.569359	+	0.986158i	0.996630	+	0.0820343i	$0.0261417\pi$
$383$	11.1426	+	19.2995i	0.569359	+	0.986158i	−0.427271	+	0.904124i	$0.640525\pi$
$384$	6.53633	−	11.3213i	0.333556	−	0.577735i
$385$	−0.147526	−	0.255522i	−0.00751861	−	0.0130226i
$386$	1.16278	−	2.01399i	0.0591837	−	0.102509i
$387$	13.9541			0.709327
$388$	6.22509			0.316031
$389$	−0.491555	+	0.851399i	−0.0249229	+	0.0431676i	−0.878218	−	0.478261i	$-0.841267\pi$
$389$	−0.491555	+	0.851399i	−0.0249229	+	0.0431676i	0.853295	+	0.521429i	$0.174601\pi$
$390$	−0.178252	+	0.308741i	−0.00902613	+	0.0156337i
$391$	−1.52033			−0.0768865
$392$	9.98475			0.504306
$393$	9.38112	−	16.2486i	0.473215	−	0.819633i
$394$	−3.94241	−	6.82846i	−0.198616	−	0.344013i
$395$	−0.0595078	+	0.103071i	−0.00299416	+	0.00518604i
$396$	1.28276	+	2.22181i	0.0644612	+	0.111650i
$397$	3.17284	+	5.49552i	0.159240	+	0.275812i	0.934595	−	0.355714i	$-0.115762\pi$
$397$	3.17284	+	5.49552i	0.159240	+	0.275812i	−0.775355	+	0.631526i	$0.782429\pi$
$398$	5.57931			0.279666
$399$	−1.24830	+	3.47268i	−0.0624933	+	0.173851i
$400$	−14.8070			−0.740351
$401$	10.5666	+	18.3018i	0.527669	+	0.913949i	0.999480	+	0.0322492i	$0.0102670\pi$
$401$	10.5666	+	18.3018i	0.527669	+	0.913949i	−0.471811	+	0.881700i	$0.656400\pi$
$402$	2.04088	+	3.53491i	0.101790	+	0.176305i
$403$	−7.23199	+	12.5262i	−0.360251	+	0.623973i
$404$	−6.22189	−	10.7766i	−0.309550	−	0.536157i
$405$	0.637571	−	1.10431i	0.0316812	−	0.0548734i
$406$	0.677779			0.0336376
$407$	−7.24253			−0.358999
$408$	3.91694	−	6.78433i	0.193917	−	0.335875i
$409$	−4.92644	+	8.53284i	−0.243597	+	0.421922i	−0.961736	−	0.273977i	$-0.911661\pi$
$409$	−4.92644	+	8.53284i	−0.243597	+	0.421922i	0.718139	+	0.695899i	$0.244994\pi$
$410$	−0.891033			−0.0440050
$411$	3.17957			0.156836
$412$	−9.11225	+	15.7829i	−0.448928	+	0.777567i
$413$	−4.63273	−	8.02413i	−0.227962	−	0.394841i
$414$	−0.103447	+	0.179176i	−0.00508415	+	0.00880601i
$415$	1.27351	+	2.20578i	0.0625139	+	0.108277i
$416$	−3.42516	−	5.93255i	−0.167932	−	0.290867i
$417$	4.10852			0.201195
$418$	−0.584530	+	1.62611i	−0.0285903	+	0.0795358i
$419$	33.3872			1.63107			0.815535	−	0.578708i	$-0.196443\pi$
$419$	33.3872			1.63107			0.815535	+	0.578708i	$0.196443\pi$
$420$	−0.344730	−	0.597091i	−0.0168211	−	0.0291350i
$421$	−7.13493	−	12.3581i	−0.347735	−	0.602295i	0.638112	−	0.769944i	$-0.279716\pi$
$421$	−7.13493	−	12.3581i	−0.347735	−	0.602295i	−0.985847	+	0.167649i	$0.946382\pi$
$422$	3.20377	−	5.54908i	0.155957	−	0.270125i
$423$	1.44224	+	2.49804i	0.0701242	+	0.121459i
$424$	−0.248340	+	0.430138i	−0.0120605	+	0.0208894i
$425$	−19.4852			−0.945173
$426$	3.20717			0.155388
$427$	−3.69369	+	6.39767i	−0.178750	+	0.309605i
$428$	0.486613	−	0.842839i	0.0235213	−	0.0407402i
$429$	−2.03497			−0.0982491
$430$	−1.75599			−0.0846813
$431$	−2.07207	+	3.58892i	−0.0998079	+	0.172872i	−0.911605	−	0.411067i	$-0.865156\pi$
$431$	−2.07207	+	3.58892i	−0.0998079	+	0.172872i	0.811797	+	0.583940i	$0.198489\pi$
$432$	8.58165	+	14.8639i	0.412885	+	0.715137i
$433$	4.01930	−	6.96163i	0.193155	−	0.334554i	−0.753139	−	0.657861i	$-0.771461\pi$
$433$	4.01930	−	6.96163i	0.193155	−	0.334554i	0.946294	+	0.323307i	$0.104795\pi$
$434$	1.19272	+	2.06585i	0.0572525	+	0.0991642i
$435$	0.717479	+	1.24271i	0.0344005	+	0.0595834i
$436$	4.68492			0.224367
$437$	1.60812	−	0.290167i	0.0769269	−	0.0138806i
$438$	−0.0663459			−0.00317013
$439$	−6.81758	−	11.8084i	−0.325385	−	0.563584i	0.656205	−	0.754583i	$-0.272161\pi$
$439$	−6.81758	−	11.8084i	−0.325385	−	0.563584i	−0.981590	+	0.190999i	$0.938827\pi$
$440$	−0.336612	−	0.583030i	−0.0160474	−	0.0277948i
$441$	−4.56225	+	7.90204i	−0.217250	+	0.376288i
$442$	−1.29005	−	2.23443i	−0.0613613	−	0.106281i
$443$	−12.2950	+	21.2955i	−0.584152	+	1.01178i	0.410829	+	0.911712i	$0.365239\pi$
$443$	−12.2950	+	21.2955i	−0.584152	+	1.01178i	−0.994981	+	0.100068i	$0.968094\pi$
$444$	−16.9239			−0.803175
$445$	0.435706			0.0206544
$446$	−1.23765	+	2.14367i	−0.0586043	+	0.101506i
$447$	−14.8358	+	25.6964i	−0.701709	+	1.21540i
$448$	2.98536			0.141045
$449$	35.6469			1.68228			0.841141	−	0.540815i	$-0.181884\pi$
$449$	35.6469			1.68228			0.841141	+	0.540815i	$0.181884\pi$
$450$	−1.32582	+	2.29640i	−0.0625000	+	0.108253i
$451$	−2.54306	−	4.40471i	−0.119748	−	0.207410i
$452$	−15.2771	+	26.4608i	−0.718577	+	1.24461i
$453$	5.62219	+	9.73792i	0.264154	+	0.457527i
$454$	−1.14061	−	1.97559i	−0.0535313	−	0.0927189i
$455$	−0.473514			−0.0221987
$456$	−2.84828	+	7.92367i	−0.133383	+	0.371060i
$457$	−5.94149			−0.277931			−0.138966	−	0.990297i	$-0.544378\pi$
$457$	−5.94149			−0.277931			−0.138966	+	0.990297i	$0.544378\pi$
$458$	−2.79134	−	4.83474i	−0.130431	−	0.225913i
$459$	11.2930	+	19.5600i	0.527111	+	0.912984i
$460$	−0.152652	+	0.264401i	−0.00711745	+	0.0123278i
$461$	11.2066	+	19.4103i	0.521941	+	0.904029i	0.999674	+	0.0255237i	$0.00812534\pi$
$461$	11.2066	+	19.4103i	0.521941	+	0.904029i	−0.477733	+	0.878505i	$0.658541\pi$
$462$	−0.167806	+	0.290649i	−0.00780706	+	0.0135222i
$463$	12.7180			0.591055			0.295528	−	0.955334i	$-0.404505\pi$
$463$	12.7180			0.591055			0.295528	+	0.955334i	$0.404505\pi$
$464$	−7.89175			−0.366365
$465$	−2.52517	+	4.37372i	−0.117102	+	0.202826i
$466$	−3.88367	+	6.72671i	−0.179907	+	0.311609i
$467$	19.6469			0.909150			0.454575	−	0.890708i	$-0.349791\pi$
$467$	19.6469			0.909150			0.454575	+	0.890708i	$0.349791\pi$
$468$	4.11728			0.190321
$469$	−2.71073	+	4.69512i	−0.125170	+	0.216801i
$470$	−0.181492	−	0.314354i	−0.00837161	−	0.0145001i
$471$	4.11984	−	7.13576i	0.189832	−	0.328799i
$472$	−10.5706	−	18.3088i	−0.486551	−	0.842730i
$473$	−5.01170	−	8.68051i	−0.230438	−	0.399130i
$474$	0.135377			0.00621806
$475$	20.6104	−	3.71891i	0.945670	−	0.170635i
$476$	4.98978			0.228706
$477$	−0.226944	−	0.393079i	−0.0103911	−	0.0179978i
$478$	2.94538	+	5.10155i	0.134719	+	0.233339i
$479$	−11.2330	+	19.4561i	−0.513249	+	0.888973i	0.486633	+	0.873606i	$0.338225\pi$
$479$	−11.2330	+	19.4561i	−0.513249	+	0.888973i	−0.999882	+	0.0153667i	$0.995108\pi$
$480$	−1.19595	−	2.07145i	−0.0545874	−	0.0945481i
$481$	−5.81159	+	10.0660i	−0.264986	+	0.458969i
$482$	5.53123			0.251941
$483$	0.317377			0.0144412
$484$	0.921423	−	1.59595i	0.0418829	−	0.0725433i
$485$	0.746400	−	1.29280i	0.0338923	−	0.0587031i
$486$	5.17300			0.234652
$487$	32.2789			1.46270			0.731348	−	0.682005i	$-0.238892\pi$
$487$	32.2789			1.46270			0.731348	+	0.682005i	$0.238892\pi$
$488$	−8.42797	+	14.5977i	−0.381516	+	0.660805i
$489$	6.75577	+	11.7013i	0.305506	+	0.529153i
$490$	0.574115	−	0.994396i	0.0259359	−	0.0449223i
$491$	15.2924	+	26.4873i	0.690138	+	1.19535i	0.971792	+	0.235838i	$0.0757834\pi$
$491$	15.2924	+	26.4873i	0.690138	+	1.19535i	−0.281655	+	0.959516i	$0.590883\pi$
$492$	−5.94249	−	10.2927i	−0.267908	−	0.464030i
$493$	−10.3851			−0.467722
$494$	1.79100	+	2.11724i	0.0805809	+	0.0952591i
$495$	0.615222			0.0276522
$496$	−13.8875	−	24.0539i	−0.623567	−	1.08005i
$497$	2.12991	+	3.68911i	0.0955394	+	0.165479i
$498$	1.44857	−	2.50901i	0.0649122	−	0.112431i
$499$	−12.2293	−	21.1817i	−0.547457	−	0.948223i	−0.998448	−	0.0556942i	$-0.982263\pi$
$499$	−12.2293	−	21.1817i	−0.547457	−	0.948223i	0.450991	−	0.892528i	$-0.351071\pi$
$500$	−3.99244	+	6.91511i	−0.178547	+	0.309253i
$501$	17.3035			0.773063
$502$	−5.46084			−0.243729
$503$	21.7050	−	37.5941i	0.967777	−	1.67624i	0.265814	−	0.964024i	$-0.414359\pi$
$503$	21.7050	−	37.5941i	0.967777	−	1.67624i	0.701962	−	0.712214i	$-0.252308\pi$
$504$	0.707988	−	1.22627i	0.0315363	−	0.0546225i
$505$	−2.98406			−0.132789
$506$	0.148615			0.00660673
$507$	6.60915	−	11.4474i	0.293523	−	0.508396i
$508$	8.51322	+	14.7453i	0.377713	+	0.654218i
$509$	−20.0017	+	34.6439i	−0.886558	+	1.53556i	−0.0426411	+	0.999090i	$0.513577\pi$
$509$	−20.0017	+	34.6439i	−0.886558	+	1.53556i	−0.843917	+	0.536473i	$0.819756\pi$
$510$	−0.450441	−	0.780187i	−0.0199459	−	0.0345473i
$511$	−0.0440608	−	0.0763156i	−0.00194914	−	0.00337600i
$512$	22.5442			0.996320
$513$	−15.6783	−	18.5341i	−0.692213	−	0.818303i
$514$	−3.19715			−0.141020
$515$	2.18515	+	3.78479i	0.0962892	+	0.166778i
$516$	−11.7111	−	20.2842i	−0.515551	−	0.892960i
$517$	1.03598	−	1.79437i	0.0455623	−	0.0789162i
$518$	0.958465	+	1.66011i	0.0421125	+	0.0729410i
$519$	14.3372	−	24.8327i	0.629332	−	1.09004i
$520$	−1.08043			−0.0473798
$521$	−5.90795			−0.258832			−0.129416	−	0.991590i	$-0.541310\pi$
$521$	−5.90795			−0.258832			−0.129416	+	0.991590i	$0.541310\pi$
$522$	−0.706629	+	1.22392i	−0.0309283	+	0.0535694i
$523$	−10.2888	+	17.8208i	−0.449899	+	0.779249i	−0.998379	−	0.0569153i	$-0.981873\pi$
$523$	−10.2888	+	17.8208i	−0.449899	+	0.779249i	0.548480	+	0.836164i	$0.315207\pi$
$524$	27.2679			1.19120
$525$	4.06764			0.177526
$526$	−4.45354	+	7.71376i	−0.194184	+	0.336336i
$527$	−18.2752	−	31.6536i	−0.796080	−	1.37885i
$528$	1.95386	−	3.38418i	0.0850308	−	0.147278i
$529$	11.4297	+	19.7969i	0.496945	+	0.860734i
$530$	0.0285587	+	0.0494652i	0.00124051	+	0.00214863i
$531$	19.3197			0.838404
$532$	−5.27791	+	0.952339i	−0.228827	+	0.0412891i
$533$	−8.16247			−0.353556
$534$	−0.247801	−	0.429205i	−0.0107234	−	0.0185735i
$535$	−0.116692	−	0.202116i	−0.00504502	−	0.00873822i
$536$	−6.18512	+	10.7129i	−0.267157	+	0.462729i
$537$	1.62268	+	2.81056i	0.0700237	+	0.121285i
$538$	2.87764	−	4.98422i	0.124064	−	0.214885i
$539$	6.55423			0.282311
$540$	4.53559			0.195181
$541$	0.749977	−	1.29900i	0.0322440	−	0.0558483i	−0.849453	−	0.527664i	$-0.823068\pi$
$541$	0.749977	−	1.29900i	0.0322440	−	0.0558483i	0.881697	+	0.471816i	$0.156401\pi$
$542$	−3.87317	+	6.70852i	−0.166367	+	0.288156i
$543$	−3.36433			−0.144377
$544$	17.3107			0.742190
$545$	0.561730	−	0.972944i	0.0240619	−	0.0416764i
$546$	0.269304	+	0.466448i	0.0115252	+	0.0199621i
$547$	21.2762	−	36.8514i	0.909704	−	1.57565i	0.0952292	−	0.995455i	$-0.469642\pi$
$547$	21.2762	−	36.8514i	0.909704	−	1.57565i	0.814475	−	0.580199i	$-0.197025\pi$
$548$	2.31049	+	4.00189i	0.0986993	+	0.170952i
$549$	−7.70184	−	13.3400i	−0.328706	−	0.569336i
$550$	1.90471			0.0812172
$551$	10.9848	−	1.98208i	0.467968	−	0.0844394i
$552$	0.724165			0.0308225
$553$	0.0899048	+	0.155720i	0.00382314	+	0.00662188i
$554$	−3.25192	−	5.63248i	−0.138161	−	0.239301i
$555$	−2.02921	+	3.51470i	−0.0861352	+	0.149191i
$556$	2.98553	+	5.17109i	0.126615	+	0.219303i
$557$	16.8716	−	29.2224i	0.714872	−	1.23819i	−0.248138	−	0.968725i	$-0.579818\pi$
$557$	16.8716	−	29.2224i	0.714872	−	1.23819i	0.963009	−	0.269469i	$-0.0868482\pi$
$558$	−4.97396			−0.210565
$559$	−16.0861			−0.680368
$560$	0.454641	−	0.787462i	0.0192121	−	0.0332763i
$561$	2.57117	−	4.45340i	0.108555	−	0.188023i
$562$	−4.18593			−0.176573
$563$	−22.0555			−0.929530			−0.464765	−	0.885434i	$-0.653861\pi$
$563$	−22.0555			−0.929530			−0.464765	+	0.885434i	$0.653861\pi$
$564$	2.42082	−	4.19298i	0.101935	−	0.176556i
$565$	3.66351	+	6.34539i	0.154125	+	0.266953i
$566$	2.70157	−	4.67925i	0.113555	−	0.196684i
$567$	−0.963246	−	1.66839i	−0.0404525	−	0.0700659i
$568$	4.85985	+	8.41750i	0.203915	+	0.353191i
$569$	−4.55061			−0.190772			−0.0953858	−	0.995440i	$-0.530408\pi$
$569$	−4.55061			−0.190772			−0.0953858	+	0.995440i	$0.530408\pi$
$570$	0.625357	+	0.739268i	0.0261933	+	0.0309645i
$571$	−35.7886			−1.49770			−0.748852	−	0.662737i	$-0.769395\pi$
$571$	−35.7886			−1.49770			−0.748852	+	0.662737i	$0.769395\pi$
$572$	−1.47875	−	2.56126i	−0.0618295	−	0.107092i
$573$	−4.37885	−	7.58440i	−0.182929	−	0.316843i
$574$	−0.673089	+	1.16582i	−0.0280942	+	0.0486606i
$575$	−0.900609	−	1.55990i	−0.0375580	−	0.0650524i
$576$	−3.11244	+	5.39090i	−0.129685	+	0.224621i
$577$	−16.7446			−0.697088			−0.348544	−	0.937292i	$-0.613324\pi$
$577$	−16.7446			−0.697088			−0.348544	+	0.937292i	$0.613324\pi$
$578$	−0.219358			−0.00912408
$579$	3.71926	−	6.44194i	0.154567	−	0.267718i
$580$	−1.04274	+	1.80608i	−0.0432974	+	0.0749933i
$581$	3.84804			0.159644
$582$	−1.69802			−0.0703850
$583$	−0.163017	+	0.282353i	−0.00675146	+	0.0116939i
$584$	−0.100534	−	0.174131i	−0.00416014	−	0.00720557i
$585$	0.493669	−	0.855061i	0.0204107	−	0.0353524i
$586$	5.82566	+	10.0903i	0.240656	+	0.416828i
$587$	−6.95821	−	12.0520i	−0.287196	−	0.497438i	0.685943	−	0.727655i	$-0.259390\pi$
$587$	−6.95821	−	12.0520i	−0.287196	−	0.497438i	−0.973139	+	0.230217i	$0.926056\pi$
$588$	15.3156			0.631604
$589$	25.3718	+	29.9934i	1.04543	+	1.23586i
$590$	−2.43120			−0.100091
$591$	−12.6102	−	21.8415i	−0.518714	−	0.898439i
$592$	−11.1599	−	19.3295i	−0.458670	−	0.794440i
$593$	6.53052	−	11.3112i	0.268176	−	0.464495i	−0.700215	−	0.713932i	$-0.746912\pi$
$593$	6.53052	−	11.3112i	0.268176	−	0.464495i	0.968391	+	0.249437i	$0.0802457\pi$
$594$	−1.10391	−	1.91202i	−0.0452938	−	0.0784512i
$595$	0.598283	−	1.03626i	0.0245272	−	0.0424824i
$596$	−43.1229			−1.76638
$597$	17.8460			0.730388
$598$	0.119252	−	0.206551i	0.00487659	−	0.00844650i
$599$	−1.92295	+	3.33064i	−0.0785695	+	0.136086i	−0.902633	−	0.430411i	$-0.858369\pi$
$599$	−1.92295	+	3.33064i	−0.0785695	+	0.136086i	0.824063	+	0.566497i	$0.191702\pi$
$600$	9.28121			0.378904
$601$	−21.5715			−0.879921			−0.439960	−	0.898017i	$-0.645007\pi$
$601$	−21.5715			−0.879921			−0.439960	+	0.898017i	$0.645007\pi$
$602$	−1.32648	+	2.29753i	−0.0540633	+	0.0936404i
$603$	−5.65223	−	9.78995i	−0.230177	−	0.398678i
$604$	−8.17094	+	14.1525i	−0.332471	+	0.575857i
$605$	−0.220960	−	0.382715i	−0.00898332	−	0.0155596i
$606$	1.69714	+	2.93953i	0.0689416	+	0.119410i
$607$	−12.6381			−0.512964			−0.256482	−	0.966549i	$-0.582563\pi$
$607$	−12.6381			−0.512964			−0.256482	+	0.966549i	$0.582563\pi$
$608$	−18.3103	+	3.30388i	−0.742581	+	0.133990i
$609$	2.16794			0.0878496
$610$	0.969202	+	1.67871i	0.0392418	+	0.0679689i
$611$	−1.66259	−	2.87969i	−0.0672613	−	0.116500i
$612$	−5.20217	+	9.01043i	−0.210285	+	0.364225i
$613$	0.675587	+	1.17015i	0.0272867	+	0.0472620i	0.879346	−	0.476183i	$-0.157980\pi$
$613$	0.675587	+	1.17015i	0.0272867	+	0.0472620i	−0.852060	+	0.523445i	$0.824647\pi$
$614$	−6.28013	+	10.8775i	−0.253445	+	0.438980i
$615$	−2.85006			−0.114925
$616$	−1.01711			−0.0409806
$617$	−12.5262	+	21.6960i	−0.504285	+	0.873446i	0.495703	+	0.868492i	$0.334910\pi$
$617$	−12.5262	+	21.6960i	−0.504285	+	0.873446i	−0.999988	+	0.00495444i	$0.998423\pi$
$618$	2.48554	−	4.30509i	0.0999832	−	0.173176i
$619$	−3.72477			−0.149711			−0.0748556	−	0.997194i	$-0.523850\pi$
$619$	−3.72477			−0.149711			−0.0748556	+	0.997194i	$0.523850\pi$
$620$	−7.33984			−0.294775
$621$	−1.04393	+	1.80813i	−0.0418913	+	0.0725578i
$622$	−5.29466	−	9.17062i	−0.212297	−	0.367708i
$623$	0.329134	−	0.570076i	0.0131865	−	0.0228396i
$624$	−3.13565	−	5.43111i	−0.125527	−	0.217418i
$625$	−11.0544	−	19.1467i	−0.442175	−	0.765869i
$626$	7.48052			0.298982
$627$	−1.86968	+	5.20129i	−0.0746677	+	0.207719i
$628$	11.9750			0.477856
$629$	−14.6858	−	25.4366i	−0.585563	−	1.01423i
$630$	−0.0814174	−	0.141019i	−0.00324375	−	0.00561834i
$631$	3.66665	−	6.35082i	0.145967	−	0.252822i	−0.783766	−	0.621056i	$-0.786704\pi$
$631$	3.66665	−	6.35082i	0.145967	−	0.252822i	0.929733	+	0.368234i	$0.120037\pi$
$632$	0.205137	+	0.355308i	0.00815993	+	0.0141334i
$633$	10.2476	−	17.7493i	0.407304	−	0.705472i
$634$	−11.5095			−0.457102
$635$	4.08300			0.162029
$636$	−0.380929	+	0.659788i	−0.0151048	+	0.0261623i
$637$	5.25928	−	9.10935i	0.208380	−	0.360926i
$638$	1.01516			0.0401906
$639$	−8.88228			−0.351377
$640$	2.27801	−	3.94563i	0.0900464	−	0.155965i
$641$	−12.3107	−	21.3228i	−0.486243	−	0.842198i	0.513632	−	0.858011i	$-0.328300\pi$
$641$	−12.3107	−	21.3228i	−0.486243	−	0.842198i	−0.999875	+	0.0158126i	$0.994966\pi$
$642$	−0.132733	+	0.229901i	−0.00523856	+	0.00907346i
$643$	14.5028	+	25.1196i	0.571934	+	0.990619i	0.996367	+	0.0851598i	$0.0271401\pi$
$643$	14.5028	+	25.1196i	0.571934	+	0.990619i	−0.424433	+	0.905459i	$0.639527\pi$
$644$	0.230628	+	0.399460i	0.00908802	+	0.0157409i
$645$	−5.61671			−0.221158
$646$	−6.89637	+	1.24437i	−0.271334	+	0.0489591i
$647$	−27.3908			−1.07684			−0.538421	−	0.842676i	$-0.680979\pi$
$647$	−27.3908			−1.07684			−0.538421	+	0.842676i	$0.680979\pi$
$648$	−2.19786	−	3.80680i	−0.0863399	−	0.149545i
$649$	−6.93879	−	12.0183i	−0.272371	−	0.471761i
$650$	1.52839	−	2.64725i	0.0599483	−	0.103834i
$651$	3.81504	+	6.60784i	0.149523	+	0.258982i
$652$	−9.81842	+	17.0060i	−0.384519	+	0.666006i
$653$	−26.7799			−1.04798			−0.523990	−	0.851724i	$-0.675557\pi$
$653$	−26.7799			−1.04798			−0.523990	+	0.851724i	$0.675557\pi$
$654$	−1.27790			−0.0499699
$655$	3.26947	−	5.66289i	0.127749	−	0.221267i
$656$	7.83714	−	13.5743i	0.305989	−	0.529988i
$657$	0.183745			0.00716858
$658$	−0.548399			−0.0213788
$659$	9.75609	−	16.8981i	0.380043	−	0.658255i	−0.611025	−	0.791612i	$-0.709242\pi$
$659$	9.75609	−	16.8981i	0.380043	−	0.658255i	0.991068	+	0.133357i	$0.0425757\pi$
$660$	−0.516328	−	0.894307i	−0.0200981	−	0.0348109i
$661$	−11.5103	+	19.9364i	−0.447698	+	0.775436i	−0.998236	−	0.0593743i	$-0.981089\pi$
$661$	−11.5103	+	19.9364i	−0.447698	+	0.775436i	0.550538	+	0.834810i	$0.314423\pi$
$662$	3.67174	+	6.35964i	0.142706	+	0.247175i
$663$	−4.12635	−	7.14705i	−0.160254	−	0.277568i
$664$	8.78014			0.340736
$665$	−0.435053	+	1.21028i	−0.0168706	+	0.0469327i
$666$	−3.99705			−0.154883
$667$	−0.480001	−	0.831385i	−0.0185857	−	0.0321914i
$668$	12.5739	+	21.7786i	0.486499	+	0.842641i
$669$	−3.95874	+	6.85674i	−0.153054	+	0.265097i
$670$	0.711279	+	1.23197i	0.0274791	+	0.0475952i
$671$	−5.53232	+	9.58226i	−0.213573	+	0.369919i
$672$	−3.61370			−0.139401
$673$	−4.62609			−0.178323			−0.0891614	−	0.996017i	$-0.528419\pi$
$673$	−4.62609			−0.178323			−0.0891614	+	0.996017i	$0.528419\pi$
$674$	−1.26700	+	2.19451i	−0.0488031	+	0.0845295i
$675$	−13.3794	+	23.1738i	−0.514973	+	0.891960i
$676$	19.2107			0.738872
$677$	−31.2968			−1.20283			−0.601417	−	0.798935i	$-0.705397\pi$
$677$	−31.2968			−1.20283			−0.601417	+	0.798935i	$0.705397\pi$
$678$	4.16714	−	7.21769i	0.160038	−	0.277194i
$679$	−1.12767	−	1.95317i	−0.0432758	−	0.0749559i
$680$	1.36511	−	2.36445i	0.0523497	−	0.0906724i
$681$	−3.64834	−	6.31911i	−0.139805	−	0.242149i
$682$	1.78643	+	3.09418i	0.0684059	+	0.118482i
$683$	44.4872			1.70225			0.851127	−	0.524960i	$-0.175920\pi$
$683$	44.4872			1.70225			0.851127	+	0.524960i	$0.175920\pi$
$684$	3.78286	−	10.5236i	0.144641	−	0.402380i
$685$	1.10813			0.0423394
$686$	−1.79375	−	3.10686i	−0.0684855	−	0.118620i
$687$	−8.92838	−	15.4644i	−0.340639	−	0.590004i
$688$	15.4449	−	26.7514i	0.588832	−	1.01989i
$689$	0.261618	+	0.453135i	0.00996684	+	0.0172631i
$690$	0.0416389	−	0.0721206i	0.00158516	−	0.00274559i
$691$	15.7490			0.599121			0.299561	−	0.954077i	$-0.403160\pi$
$691$	15.7490			0.599121			0.299561	+	0.954077i	$0.403160\pi$
$692$	41.6736			1.58419
$693$	0.464740	−	0.804954i	0.0176540	−	0.0305777i
$694$	6.02490	−	10.4354i	0.228702	−	0.396123i
$695$	1.43188			0.0543144
$696$	4.94664			0.187502
$697$	10.3133	−	17.8631i	0.390642	−	0.676612i
$698$	4.33988	+	7.51690i	0.164267	+	0.284519i
$699$	−12.4223	+	21.5161i	−0.469855	+	0.813812i
$700$	2.95583	+	5.11965i	0.111720	+	0.193504i
$701$	−14.8487	−	25.7187i	−0.560829	−	0.971384i	−0.997424	−	0.0717259i	$-0.977149\pi$
$701$	−14.8487	−	25.7187i	−0.560829	−	0.971384i	0.436596	−	0.899658i	$-0.356184\pi$
$702$	−3.54321			−0.133730
$703$	20.3887	+	24.1025i	0.768973	+	0.909045i
$704$	4.47140			0.168522
$705$	−0.580521	−	1.00549i	−0.0218637	−	0.0378690i
$706$	−4.79965	−	8.31323i	−0.180637	−	0.312873i
$707$	−2.25417	+	3.90433i	−0.0847767	+	0.146838i
$708$	−16.2142	−	28.0838i	−0.609366	−	1.05545i
$709$	−20.6890	+	35.8343i	−0.776990	+	1.34579i	0.156679	+	0.987650i	$0.449921\pi$
$709$	−20.6890	+	35.8343i	−0.776990	+	1.34579i	−0.933669	+	0.358137i	$0.883412\pi$
$710$	1.11775			0.0419484
$711$	−0.374927			−0.0140608
$712$	0.750990	−	1.30075i	0.0281445	−	0.0487478i
$713$	1.68936	−	2.92606i	0.0632671	−	0.109582i
$714$	−1.36106			−0.0509364
$715$	−0.709217			−0.0265232
$716$	−2.35830	+	4.08470i	−0.0881338	+	0.152652i
$717$	9.42110	+	16.3178i	0.351837	+	0.609400i
$718$	−3.58671	+	6.21237i	−0.133855	+	0.231843i
$719$	4.76409	+	8.25164i	0.177671	+	0.307734i	0.941082	−	0.338178i	$-0.109811\pi$
$719$	4.76409	+	8.25164i	0.177671	+	0.307734i	−0.763412	+	0.645912i	$0.776477\pi$
$720$	0.947987	+	1.64196i	0.0353294	+	0.0611923i
$721$	6.60268			0.245896
$722$	7.05710	−	2.63245i	0.262638	−	0.0979698i
$723$	17.6922			0.657980
$724$	−2.44476	−	4.23444i	−0.0908587	−	0.157372i
$725$	−6.15190	−	10.6554i	−0.228476	−	0.395732i
$726$	−0.251336	+	0.435327i	−0.00932796	+	0.0161565i
$727$	−22.6413	−	39.2159i	−0.839719	−	1.45444i	−0.890129	−	0.455708i	$-0.849386\pi$
$727$	−22.6413	−	39.2159i	−0.839719	−	1.45444i	0.0504100	−	0.998729i	$-0.483947\pi$
$728$	−0.816157	+	1.41363i	−0.0302488	+	0.0523924i
$729$	25.2027			0.933434
$730$	−0.0231226			−0.000855805
$731$	20.3247	−	35.2034i	0.751735	−	1.30204i
$732$	−12.9276	+	22.3913i	−0.477819	+	0.827607i
$733$	52.4798			1.93838			0.969192	−	0.246306i	$-0.0792169\pi$
$733$	52.4798			1.93838			0.969192	+	0.246306i	$0.0792169\pi$
$734$	−7.19768			−0.265671
$735$	1.83636	−	3.18068i	0.0677353	−	0.117321i
$736$	0.800102	+	1.38582i	0.0294922	+	0.0510819i
$737$	−4.06006	+	7.03224i	−0.149554	+	0.259036i
$738$	−1.40348	−	2.43090i	−0.0516628	−	0.0894826i
$739$	15.6220	+	27.0581i	0.574665	+	0.995349i	0.996078	+	0.0884802i	$0.0282010\pi$
$739$	15.6220	+	27.0581i	0.574665	+	0.995349i	−0.421413	+	0.906869i	$0.638466\pi$
$740$	−5.89826			−0.216824
$741$	5.72869	+	6.77220i	0.210449	+	0.248783i
$742$	0.0862935			0.00316793
$743$	12.5085	+	21.6653i	0.458891	+	0.794822i	0.998903	−	0.0468355i	$-0.0149137\pi$
$743$	12.5085	+	21.6653i	0.458891	+	0.794822i	−0.540012	+	0.841657i	$0.681580\pi$
$744$	8.70484	+	15.0772i	0.319135	+	0.552758i
$745$	−5.17051	+	8.95558i	−0.189433	+	0.328107i
$746$	5.00581	+	8.67031i	0.183276	+	0.317443i
$747$	−4.01184	+	6.94870i	−0.146785	+	0.254240i
$748$	7.47357			0.273261
$749$	−0.352597			−0.0128836
$750$	1.08902	−	1.88623i	0.0397652	−	0.0688754i
$751$	25.1822	−	43.6169i	0.918912	−	1.59160i	0.117842	−	0.993032i	$-0.462402\pi$
$751$	25.1822	−	43.6169i	0.918912	−	1.59160i	0.801070	−	0.598570i	$-0.204264\pi$
$752$	6.38531			0.232848
$753$	−17.4670			−0.636534
$754$	0.814591	−	1.41091i	0.0296656	−	0.0513824i
$755$	1.95942	+	3.39382i	0.0713106	+	0.123514i
$756$	3.42620	−	5.93435i	0.124610	−	0.215830i
$757$	9.47616	+	16.4132i	0.344417	+	0.596548i	0.985248	−	0.171135i	$-0.0547433\pi$
$757$	9.47616	+	16.4132i	0.344417	+	0.596548i	−0.640831	+	0.767682i	$0.721410\pi$
$758$	4.10225	+	7.10530i	0.149000	+	0.258076i
$759$	0.475359			0.0172544
$760$	−0.992668	+	2.76152i	−0.0360079	+	0.100171i
$761$	−44.4460			−1.61117			−0.805583	−	0.592484i	$-0.798148\pi$
$761$	−44.4460			−1.61117			−0.805583	+	0.592484i	$0.798148\pi$
$762$	−2.32214	−	4.02207i	−0.0841224	−	0.145704i
$763$	−0.848665	−	1.46993i	−0.0307237	−	0.0532151i
$764$	6.36396	−	11.0227i	0.230240	−	0.398787i
$765$	1.24750	+	2.16073i	0.0451034	+	0.0781215i
$766$	4.41721	−	7.65082i	0.159600	−	0.276436i
$767$	−22.2714			−0.804175
$768$	6.15721			0.222179
$769$	−12.3039	+	21.3110i	−0.443691	+	0.768495i	−0.997960	−	0.0638427i	$-0.979664\pi$
$769$	−12.3039	+	21.3110i	−0.443691	+	0.768495i	0.554269	+	0.832337i	$0.312998\pi$
$770$	−0.0584831	+	0.101296i	−0.00210759

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)

\(f(q)\)	\(=\)	\(q+(-0.198213 - 0.343315i) q^{2} +(-0.634005 - 1.09813i) q^{3} +(0.921423 - 1.59595i) q^{4} +(-0.220960 - 0.382715i) q^{5} +(-0.251336 + 0.435327i) q^{6} -0.667657 q^{7} -1.52341 q^{8} +(0.696076 - 1.20564i) q^{9} +O(q^{10})\)	\(q+(-0.198213 - 0.343315i) q^{2} +(-0.634005 - 1.09813i) q^{3} +(0.921423 - 1.59595i) q^{4} +(-0.220960 - 0.382715i) q^{5} +(-0.251336 + 0.435327i) q^{6} -0.667657 q^{7} -1.52341 q^{8} +(0.696076 - 1.20564i) q^{9} +(-0.0875945 + 0.151718i) q^{10} -1.00000 q^{11} -2.33675 q^{12} +(-0.802426 + 1.38984i) q^{13} +(0.132338 + 0.229217i) q^{14} +(-0.280180 + 0.485286i) q^{15} +(-1.54089 - 2.66890i) q^{16} +(-2.02772 - 3.51212i) q^{17} -0.551886 q^{18} +(2.81513 + 3.32792i) q^{19} -0.814392 q^{20} +(0.423298 + 0.733173i) q^{21} +(0.198213 + 0.343315i) q^{22} +(0.187443 - 0.324661i) q^{23} +(0.965846 + 1.67289i) q^{24} +(2.40235 - 4.16100i) q^{25} +0.636205 q^{26} -5.56929 q^{27} +(-0.615195 + 1.06555i) q^{28} +(1.28039 - 2.21770i) q^{29} +0.222141 q^{30} +9.01266 q^{31} +(-2.13425 + 3.69663i) q^{32} +(0.634005 + 1.09813i) q^{33} +(-0.803843 + 1.39230i) q^{34} +(0.147526 + 0.255522i) q^{35} +(-1.28276 - 2.22181i) q^{36} +7.24253 q^{37} +(0.584530 - 1.62611i) q^{38} +2.03497 q^{39} +(0.336612 + 0.583030i) q^{40} +(2.54306 + 4.40471i) q^{41} +(0.167806 - 0.290649i) q^{42} +(5.01170 + 8.68051i) q^{43} +(-0.921423 + 1.59595i) q^{44} -0.615222 q^{45} -0.148615 q^{46} +(-1.03598 + 1.79437i) q^{47} +(-1.95386 + 3.38418i) q^{48} -6.55423 q^{49} -1.90471 q^{50} +(-2.57117 + 4.45340i) q^{51} +(1.47875 + 2.56126i) q^{52} +(0.163017 - 0.282353i) q^{53} +(1.10391 + 1.91202i) q^{54} +(0.220960 + 0.382715i) q^{55} +1.01711 q^{56} +(1.86968 - 5.20129i) q^{57} -1.01516 q^{58} +(6.93879 + 12.0183i) q^{59} +(0.516328 + 0.894307i) q^{60} +(5.53232 - 9.58226i) q^{61} +(-1.78643 - 3.09418i) q^{62} +(-0.464740 + 0.804954i) q^{63} -4.47140 q^{64} +0.709217 q^{65} +(0.251336 - 0.435327i) q^{66} +(4.06006 - 7.03224i) q^{67} -7.47357 q^{68} -0.475359 q^{69} +(0.0584831 - 0.101296i) q^{70} +(-3.19012 - 5.52545i) q^{71} +(-1.06041 + 1.83668i) q^{72} +(0.0659932 + 0.114304i) q^{73} +(-1.43556 - 2.48647i) q^{74} -6.09241 q^{75} +(7.90512 - 1.42639i) q^{76} +0.667657 q^{77} +(-0.403357 - 0.698635i) q^{78} +(-0.134657 - 0.233233i) q^{79} +(-0.680950 + 1.17944i) q^{80} +(1.44273 + 2.49887i) q^{81} +(1.00814 - 1.74614i) q^{82} -5.76350 q^{83} +1.56015 q^{84} +(-0.896094 + 1.55208i) q^{85} +(1.98677 - 3.44118i) q^{86} -3.24709 q^{87} +1.52341 q^{88} +(-0.492968 + 0.853846i) q^{89} +(0.121945 + 0.211215i) q^{90} +(0.535745 - 0.927938i) q^{91} +(-0.345429 - 0.598300i) q^{92} +(-5.71407 - 9.89706i) q^{93} +0.821379 q^{94} +(0.651612 - 1.81273i) q^{95} +5.41251 q^{96} +(1.68899 + 2.92541i) q^{97} +(1.29914 + 2.25017i) q^{98} +(-0.696076 + 1.20564i) 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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