LMFDB - Embedded newform 420.2.l.e.239.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(239,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("420.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.l (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.386672896.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 $ x^8 - x^6 - 2x^5 + 2x^4 - 4x^3 - 4x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.3
Root			$-0.835949 + 1.14070i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.e.239.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.835949 - 1.14070i) q^{2} +(1.10238 + 1.33595i) q^{3} +(-0.602380 + 1.90713i) q^{4} +(-1.00000 + 2.00000i) q^{5} +(0.602380 - 2.37427i) q^{6} +1.00000 q^{7} +(2.67901 - 0.907128i) q^{8} +(-0.569517 + 2.94545i) q^{9} +O(q^{10})$	\(q+(-0.835949 - 1.14070i) q^{2} +(1.10238 + 1.33595i) q^{3} +(-0.602380 + 1.90713i) q^{4} +(-1.00000 + 2.00000i) q^{5} +(0.602380 - 2.37427i) q^{6} +1.00000 q^{7} +(2.67901 - 0.907128i) q^{8} +(-0.569517 + 2.94545i) q^{9} +(3.11734 - 0.531200i) q^{10} -2.20476 q^{11} +(-3.21188 + 1.29763i) q^{12} -1.89089i q^{13} +(-0.835949 - 1.14070i) q^{14} +(-3.77428 + 0.868811i) q^{15} +(-3.27428 - 2.29763i) q^{16} -1.13903 q^{17} +(3.83595 - 1.81259i) q^{18} +8.56279i q^{19} +(-3.21188 - 3.11189i) q^{20} +(1.10238 + 1.33595i) q^{21} +(1.84307 + 2.51496i) q^{22} +3.21899i q^{23} +(4.16517 + 2.57903i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(-2.15693 + 1.58069i) q^{26} +(-4.56279 + 2.48615i) q^{27} +(-0.602380 + 1.90713i) q^{28} -1.89089i q^{29} +(4.14615 + 3.57903i) q^{30} +5.90658i q^{31} +(0.116226 + 5.65566i) q^{32} +(-2.43048 - 2.94545i) q^{33} +(0.952175 + 1.29929i) q^{34} +(-1.00000 + 2.00000i) q^{35} +(-5.27428 - 2.86042i) q^{36} +0.409519i q^{37} +(9.76755 - 7.15805i) q^{38} +(2.52613 - 2.08448i) q^{39} +(-0.864758 + 6.26516i) q^{40} -4.40952i q^{41} +(0.602380 - 2.37427i) q^{42} -0.934275 q^{43} +(1.32810 - 4.20476i) q^{44} +(-5.32137 - 4.08448i) q^{45} +(3.67190 - 2.69091i) q^{46} -2.67190i q^{47} +(-0.539980 - 6.90713i) q^{48} +1.00000 q^{49} +(-2.05494 + 6.76589i) q^{50} +(-1.25565 - 1.52169i) q^{51} +(3.60617 + 1.13903i) q^{52} +6.81904 q^{53} +(6.65021 + 3.12646i) q^{54} +(2.20476 - 4.40952i) q^{55} +(2.67901 - 0.907128i) q^{56} +(-11.4394 + 9.43945i) q^{57} +(-2.15693 + 1.58069i) q^{58} +13.5351 q^{59} +(0.616614 - 7.72139i) q^{60} +12.4694 q^{61} +(6.73762 - 4.93760i) q^{62} +(-0.569517 + 2.94545i) q^{63} +(6.35424 - 4.86042i) q^{64} +(3.78178 + 1.89089i) q^{65} +(-1.32810 + 5.23469i) q^{66} -10.8475 q^{67} +(0.686132 - 2.17229i) q^{68} +(-4.30041 + 3.54855i) q^{69} +(3.11734 - 0.531200i) q^{70} +8.00000 q^{71} +(1.14615 + 8.40752i) q^{72} +8.00000i q^{73} +(0.467138 - 0.342337i) q^{74} +(2.03665 - 8.41737i) q^{75} +(-16.3303 - 5.15805i) q^{76} -2.20476 q^{77} +(-4.48948 - 1.13903i) q^{78} -3.76609i q^{79} +(7.86954 - 4.25092i) q^{80} +(-8.35130 - 3.35496i) q^{81} +(-5.02993 + 3.68613i) q^{82} +6.84086i q^{83} +(-3.21188 + 1.29763i) q^{84} +(1.13903 - 2.27807i) q^{85} +(0.781006 + 1.06572i) q^{86} +(2.52613 - 2.08448i) q^{87} +(-5.90658 + 2.00000i) q^{88} -16.1913i q^{89} +(-0.210760 + 9.48449i) q^{90} -1.89089i q^{91} +(-6.13903 - 1.93906i) q^{92} +(-7.89089 + 6.51130i) q^{93} +(-3.04783 + 2.23357i) q^{94} +(-17.1256 - 8.56279i) q^{95} +(-7.42755 + 6.38996i) q^{96} -18.4917i q^{97} +(-0.835949 - 1.14070i) q^{98} +(1.25565 - 6.49400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 2 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 2 * q^4 - 8 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9	$ 8 q + 2 q^{3} + 2 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9} - 4 q^{10} - 4 q^{11} - 10 q^{12} - 10 q^{15} - 6 q^{16} + 4 q^{17} + 24 q^{18} - 10 q^{20} + 2 q^{21} + 6 q^{22} - 18 q^{24} - 24 q^{25} - 26 q^{26} + 8 q^{27} + 2 q^{28} + 18 q^{30} + 30 q^{32} - 26 q^{33} + 30 q^{34} - 8 q^{35} - 22 q^{36} + 20 q^{38} - 18 q^{39} - 14 q^{40} - 2 q^{42} - 8 q^{43} + 24 q^{44} - 18 q^{45} + 16 q^{46} - 2 q^{48} + 8 q^{49} + 8 q^{50} + 14 q^{51} + 16 q^{52} + 24 q^{54} + 4 q^{55} + 6 q^{56} - 20 q^{57} - 26 q^{58} - 8 q^{59} - 6 q^{60} - 16 q^{61} + 40 q^{62} + 2 q^{63} + 26 q^{64} - 32 q^{65} - 24 q^{66} - 24 q^{67} - 12 q^{68} + 24 q^{69} - 4 q^{70} + 64 q^{71} - 6 q^{72} + 4 q^{74} + 10 q^{75} - 28 q^{76} - 4 q^{77} - 4 q^{78} + 38 q^{80} + 2 q^{81} + 4 q^{82} - 10 q^{84} - 4 q^{85} + 24 q^{86} - 18 q^{87} + 24 q^{88} - 44 q^{90} - 36 q^{92} - 32 q^{93} - 2 q^{94} - 48 q^{95} - 22 q^{96} - 14 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^4 - 8 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9 - 4 * q^10 - 4 * q^11 - 10 * q^12 - 10 * q^15 - 6 * q^16 + 4 * q^17 + 24 * q^18 - 10 * q^20 + 2 * q^21 + 6 * q^22 - 18 * q^24 - 24 * q^25 - 26 * q^26 + 8 * q^27 + 2 * q^28 + 18 * q^30 + 30 * q^32 - 26 * q^33 + 30 * q^34 - 8 * q^35 - 22 * q^36 + 20 * q^38 - 18 * q^39 - 14 * q^40 - 2 * q^42 - 8 * q^43 + 24 * q^44 - 18 * q^45 + 16 * q^46 - 2 * q^48 + 8 * q^49 + 8 * q^50 + 14 * q^51 + 16 * q^52 + 24 * q^54 + 4 * q^55 + 6 * q^56 - 20 * q^57 - 26 * q^58 - 8 * q^59 - 6 * q^60 - 16 * q^61 + 40 * q^62 + 2 * q^63 + 26 * q^64 - 32 * q^65 - 24 * q^66 - 24 * q^67 - 12 * q^68 + 24 * q^69 - 4 * q^70 + 64 * q^71 - 6 * q^72 + 4 * q^74 + 10 * q^75 - 28 * q^76 - 4 * q^77 - 4 * q^78 + 38 * q^80 + 2 * q^81 + 4 * q^82 - 10 * q^84 - 4 * q^85 + 24 * q^86 - 18 * q^87 + 24 * q^88 - 44 * q^90 - 36 * q^92 - 32 * q^93 - 2 * q^94 - 48 * q^95 - 22 * q^96 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	−0.835949	−	1.14070i	−0.591105	−	0.806595i
$2$	−0.835949	−	1.14070i	−0.591105	−	0.806595i
$3$	1.10238	+	1.33595i	0.636459	+	0.771310i
$3$	1.10238	+	1.33595i	0.636459	+	0.771310i
$4$	−0.602380	+	1.90713i	−0.301190	+	0.953564i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$	0.602380	−	2.37427i	0.245921	−	0.969290i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.67901	−	0.907128i	0.947175	−	0.320718i
$9$	−0.569517	+	2.94545i	−0.189839	+	0.981815i
$10$	3.11734	−	0.531200i	0.985790	−	0.167980i
$11$	−2.20476			−0.664760			−0.332380	−	0.943146i	$-0.607852\pi$
$11$	−2.20476			−0.664760			−0.332380	+	0.943146i	$0.607852\pi$
$12$	−3.21188	+	1.29763i	−0.927189	+	0.374594i
$13$		−	1.89089i		−	0.524439i	−0.965008	−	0.262219i	$-0.915546\pi$
$13$		−	1.89089i		−	0.524439i	0.965008	−	0.262219i	$-0.0844544\pi$
$14$	−0.835949	−	1.14070i	−0.223417	−	0.304864i
$15$	−3.77428	+	0.868811i	−0.974514	+	0.224326i
$16$	−3.27428	−	2.29763i	−0.818569	−	0.574408i
$17$	−1.13903			−0.276257			−0.138128	−	0.990414i	$-0.544109\pi$
$17$	−1.13903			−0.276257			−0.138128	+	0.990414i	$0.544109\pi$
$18$	3.83595	−	1.81259i	0.904142	−	0.427233i
$19$			8.56279i			1.96444i	0.187738	+	0.982219i	$0.439885\pi$
$19$			8.56279i			1.96444i	−0.187738	+	0.982219i	$0.560115\pi$
$20$	−3.21188	−	3.11189i	−0.718197	−	0.695839i
$21$	1.10238	+	1.33595i	0.240559	+	0.291528i
$22$	1.84307	+	2.51496i	0.392943	+	0.536192i
$23$			3.21899i			0.671207i	0.942003	+	0.335603i	$0.108940\pi$
$23$			3.21899i			0.671207i	−0.942003	+	0.335603i	$0.891060\pi$
$24$	4.16517	+	2.57903i	0.850211	+	0.526441i
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	−2.15693	+	1.58069i	−0.423010	+	0.309998i
$27$	−4.56279	+	2.48615i	−0.878109	+	0.478461i
$28$	−0.602380	+	1.90713i	−0.113839	+	0.360413i
$29$		−	1.89089i		−	0.351130i	−0.984468	−	0.175565i	$-0.943825\pi$
$29$		−	1.89089i		−	0.351130i	0.984468	−	0.175565i	$-0.0561752\pi$
$30$	4.14615	+	3.57903i	0.756980	+	0.653438i
$31$			5.90658i			1.06085i	0.847731	+	0.530427i	$0.177968\pi$
$31$			5.90658i			1.06085i	−0.847731	+	0.530427i	$0.822032\pi$
$32$	0.116226	+	5.65566i	0.0205460	+	0.999789i
$33$	−2.43048	−	2.94545i	−0.423093	−	0.512736i
$34$	0.952175	+	1.29929i	0.163297	+	0.222827i
$35$	−1.00000	+	2.00000i	−0.169031	+	0.338062i
$36$	−5.27428	−	2.86042i	−0.879046	−	0.476737i
$37$			0.409519i			0.0673246i	0.999433	+	0.0336623i	$0.0107171\pi$
$37$			0.409519i			0.0673246i	−0.999433	+	0.0336623i	$0.989283\pi$
$38$	9.76755	−	7.15805i	1.58451	−	1.16119i
$39$	2.52613	−	2.08448i	0.404505	−	0.333784i
$40$	−0.864758	+	6.26516i	−0.136730	+	0.990608i
$41$		−	4.40952i		−	0.688651i	−0.938850	−	0.344326i	$-0.888108\pi$
$41$		−	4.40952i		−	0.688651i	0.938850	−	0.344326i	$-0.111892\pi$
$42$	0.602380	−	2.37427i	0.0929492	−	0.366357i
$43$	−0.934275			−0.142476			−0.0712378	−	0.997459i	$-0.522695\pi$
$43$	−0.934275			−0.142476			−0.0712378	+	0.997459i	$0.522695\pi$
$44$	1.32810	−	4.20476i	0.200219	−	0.633891i
$45$	−5.32137	−	4.08448i	−0.793264	−	0.608878i
$46$	3.67190	−	2.69091i	0.541392	−	0.396754i
$47$		−	2.67190i		−	0.389736i	−0.980829	−	0.194868i	$-0.937572\pi$
$47$		−	2.67190i		−	0.389736i	0.980829	−	0.194868i	$-0.0624279\pi$
$48$	−0.539980	−	6.90713i	−0.0779393	−	0.996958i
$49$	1.00000			0.142857
$50$	−2.05494	+	6.76589i	−0.290613	+	0.956841i
$51$	−1.25565	−	1.52169i	−0.175826	−	0.213079i
$52$	3.60617	+	1.13903i	0.500086	+	0.157956i
$53$	6.81904			0.936667			0.468334	−	0.883552i	$-0.344855\pi$
$53$	6.81904			0.936667			0.468334	+	0.883552i	$0.344855\pi$
$54$	6.65021	+	3.12646i	0.904978	+	0.425458i
$55$	2.20476	−	4.40952i	0.297290	−	0.594579i
$56$	2.67901	−	0.907128i	0.357998	−	0.121220i
$57$	−11.4394	+	9.43945i	−1.51519	+	1.25029i
$58$	−2.15693	+	1.58069i	−0.283219	+	0.207554i
$59$	13.5351			1.76212			0.881060	−	0.473005i	$-0.156831\pi$
$59$	13.5351			1.76212			0.881060	+	0.473005i	$0.156831\pi$
$60$	0.616614	−	7.72139i	0.0796046	−	0.996827i
$61$	12.4694			1.59654			0.798270	−	0.602300i	$-0.205749\pi$
$61$	12.4694			1.59654			0.798270	+	0.602300i	$0.205749\pi$
$62$	6.73762	−	4.93760i	0.855679	−	0.627076i
$63$	−0.569517	+	2.94545i	−0.0717524	+	0.371091i
$64$	6.35424	−	4.86042i	0.794280	−	0.607552i
$65$	3.78178	+	1.89089i	0.469072	+	0.234536i
$66$	−1.32810	+	5.23469i	−0.163478	+	0.644345i
$67$	−10.8475			−1.32523			−0.662617	−	0.748958i	$-0.730554\pi$
$67$	−10.8475			−1.32523			−0.662617	+	0.748958i	$0.730554\pi$
$68$	0.686132	−	2.17229i	0.0832057	−	0.263428i
$69$	−4.30041	+	3.54855i	−0.517709	+	0.427196i
$70$	3.11734	−	0.531200i	0.372594	−	0.0634906i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	1.14615	+	8.40752i	0.135075	+	0.990835i
$73$			8.00000i			0.936329i	0.883641	+	0.468165i	$0.155085\pi$
$73$			8.00000i			0.936329i	−0.883641	+	0.468165i	$0.844915\pi$
$74$	0.467138	−	0.342337i	0.0543036	−	0.0397959i
$75$	2.03665	−	8.41737i	0.235173	−	0.971954i
$76$	−16.3303	−	5.15805i	−1.87322	−	0.591669i
$77$	−2.20476			−0.251256
$78$	−4.48948	−	1.13903i	−0.508333	−	0.128970i
$79$		−	3.76609i		−	0.423718i	−0.977300	−	0.211859i	$-0.932048\pi$
$79$		−	3.76609i		−	0.423718i	0.977300	−	0.211859i	$-0.0679518\pi$
$80$	7.86954	−	4.25092i	0.879841	−	0.475268i
$81$	−8.35130	−	3.35496i	−0.927922	−	0.372774i
$82$	−5.02993	+	3.68613i	−0.555462	+	0.407065i
$83$			6.84086i			0.750882i	0.926846	+	0.375441i	$0.122509\pi$
$83$			6.84086i			0.750882i	−0.926846	+	0.375441i	$0.877491\pi$
$84$	−3.21188	+	1.29763i	−0.350444	+	0.141583i
$85$	1.13903	−	2.27807i	0.123546	−	0.247091i
$86$	0.781006	+	1.06572i	0.0842180	+	0.114920i
$87$	2.52613	−	2.08448i	0.270830	−	0.223480i
$88$	−5.90658	+	2.00000i	−0.629644	+	0.213201i
$89$		−	16.1913i		−	1.71627i	−0.513420	−	0.858137i	$-0.671622\pi$
$89$		−	16.1913i		−	1.71627i	0.513420	−	0.858137i	$-0.328378\pi$
$90$	−0.210760	+	9.48449i	−0.0222160	+	0.999753i
$91$		−	1.89089i		−	0.198219i
$92$	−6.13903	−	1.93906i	−0.640039	−	0.202161i
$93$	−7.89089	+	6.51130i	−0.818247	+	0.675190i
$94$	−3.04783	+	2.23357i	−0.314359	+	0.230375i
$95$	−17.1256	−	8.56279i	−1.75705	−	0.878524i
$96$	−7.42755	+	6.38996i	−0.758071	+	0.652172i
$97$		−	18.4917i		−	1.87755i	−0.344532	−	0.938774i	$-0.611962\pi$
$97$		−	18.4917i		−	1.87755i	0.344532	−	0.938774i	$-0.388038\pi$
$98$	−0.835949	−	1.14070i	−0.0844436	−	0.115228i
$99$	1.25565	−	6.49400i	0.126197	−	0.652672i
$100$	9.43565	−	3.31187i	0.943565	−	0.331187i
$101$			14.8789i			1.48050i	0.672329	+	0.740252i	$0.265294\pi$
$101$			14.8789i			1.48050i	−0.672329	+	0.740252i	$0.734706\pi$
$102$	−0.686132	+	2.70437i	−0.0679371	+	0.267773i
$103$	14.9208			1.47019			0.735096	−	0.677963i	$-0.237137\pi$
$103$	14.9208			1.47019			0.735096	+	0.677963i	$0.237137\pi$
$104$	−1.71528	−	5.06572i	−0.168197	−	0.496735i
$105$	−3.77428	+	0.868811i	−0.368332	+	0.0847873i
$106$	−5.70037	−	7.77846i	−0.553668	−	0.755511i
$107$			0.371487i			0.0359130i	0.999839	+	0.0179565i	$0.00571603\pi$
$107$			0.371487i			0.0359130i	−0.999839	+	0.0179565i	$0.994284\pi$
$108$	−1.99288	−	10.1994i	−0.191765	−	0.981441i
$109$	2.86097			0.274031			0.137015	−	0.990569i	$-0.456249\pi$
$109$	2.86097			0.274031			0.137015	+	0.990569i	$0.456249\pi$
$110$	−6.87299	+	1.17117i	−0.655314	+	0.111667i
$111$	−0.547097	+	0.451446i	−0.0519281	+	0.0428493i
$112$	−3.27428	−	2.29763i	−0.309390	−	0.217106i
$113$	−14.1913			−1.33501			−0.667503	−	0.744607i	$-0.732637\pi$
$113$	−14.1913			−1.33501			−0.667503	+	0.744607i	$0.732637\pi$
$114$	20.3303	+	5.15805i	1.90411	+	0.483096i
$115$	−6.43799	−	3.21899i	−0.600345	−	0.300173i
$116$	3.60617	+	1.13903i	0.334825	+	0.105757i
$117$	5.56952	+	1.07690i	0.514902	+	0.0995590i
$118$	−11.3146	−	15.4394i	−1.04160	−	1.42132i
$119$	−1.13903			−0.104415
$120$	−9.32322	+	5.75131i	−0.851090	+	0.525020i
$121$	−6.13903			−0.558094
$122$	−10.4238	−	14.2238i	−0.943722	−	1.28776i
$123$	5.89089	−	4.86097i	0.531164	−	0.438298i
$124$	−11.2646	−	3.55801i	−1.01159	−	0.319518i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	3.83595	−	1.81259i	0.341733	−	0.161479i
$127$	3.59048			0.318604			0.159302	−	0.987230i	$-0.449076\pi$
$127$	3.59048			0.318604			0.159302	+	0.987230i	$0.449076\pi$
$128$	−10.8561	−	3.18520i	−0.959551	−	0.281534i
$129$	−1.02993	−	1.24814i	−0.0906799	−	0.109893i
$130$	−1.00444	−	5.89456i	−0.0880954	−	0.516987i
$131$	4.52476			0.395330			0.197665	−	0.980270i	$-0.436664\pi$
$131$	4.52476			0.395330			0.197665	+	0.980270i	$0.436664\pi$
$132$	7.08142	−	2.86097i	0.616358	−	0.249015i
$133$			8.56279i			0.742488i
$134$	9.06796	+	12.3737i	0.783352	+	1.06893i
$135$	−0.409519	−	11.6117i	−0.0352458	−	0.999379i
$136$	−3.05149	+	1.03325i	−0.261663	+	0.0886005i
$137$	16.4694			1.40707			0.703537	−	0.710659i	$-0.251603\pi$
$137$	16.4694			1.40707			0.703537	+	0.710659i	$0.251603\pi$
$138$	7.64275	+	1.93906i	0.650594	+	0.165064i
$139$			12.9723i			1.10030i	0.835067	+	0.550148i	$0.185429\pi$
$139$			12.9723i			1.10030i	−0.835067	+	0.550148i	$0.814571\pi$
$140$	−3.21188	−	3.11189i	−0.271453	−	0.263003i
$141$	3.56952	−	2.94545i	0.300608	−	0.248051i
$142$	−6.68759	−	9.12558i	−0.561210	−	0.765801i
$143$			4.16896i			0.348626i
$144$	8.63231	−	8.33566i	0.719359	−	0.694639i
$145$	3.78178	+	1.89089i	0.314060	+	0.157030i
$146$	9.12558	−	6.68759i	0.755238	−	0.553469i
$147$	1.10238	+	1.33595i	0.0909228	+	0.110187i
$148$	−0.781006	−	0.246686i	−0.0641983	−	0.0202775i
$149$			12.8190i			1.05018i	0.851048	+	0.525088i	$0.175968\pi$
$149$			12.8190i			1.05018i	−0.851048	+	0.525088i	$0.824032\pi$
$150$	−11.3042	+	4.71328i	−0.922984	+	0.384838i
$151$		−	5.63464i		−	0.458541i	−0.973363	−	0.229270i	$-0.926366\pi$
$151$		−	5.63464i		−	0.458541i	0.973363	−	0.229270i	$-0.0736340\pi$
$152$	7.76755	+	22.9398i	0.630031	+	1.86067i
$153$	0.648700	−	3.35496i	0.0524443	−	0.271233i
$154$	1.84307	+	2.51496i	0.148518	+	0.202661i
$155$	−11.8132	−	5.90658i	−0.948856	−	0.474428i
$156$	2.45368	+	6.07331i	0.196452	+	0.486254i
$157$		−	12.8190i		−	1.02307i	−0.859262	−	0.511535i	$-0.829077\pi$
$157$		−	12.8190i		−	1.02307i	0.859262	−	0.511535i	$-0.170923\pi$
$158$	−4.29597	+	3.14826i	−0.341769	+	0.250462i
$159$	7.51717	+	9.10989i	0.596150	+	0.722461i
$160$	−11.4275	−	5.42321i	−0.903427	−	0.428742i
$161$			3.21899i			0.253692i
$162$	3.15426	+	12.3309i	0.247822	+	0.968806i
$163$	5.53510			0.433542			0.216771	−	0.976222i	$-0.430447\pi$
$163$	5.53510			0.433542			0.216771	+	0.976222i	$0.430447\pi$
$164$	8.40952	+	2.65621i	0.656673	+	0.207415i
$165$	8.32137	−	1.91552i	0.647818	−	0.149123i
$166$	7.80335	−	5.71861i	0.605657	−	0.443850i
$167$		−	16.3222i		−	1.26305i	−0.775355	−	0.631526i	$-0.782429\pi$
$167$		−	16.3222i		−	1.26305i	0.775355	−	0.631526i	$-0.217571\pi$
$168$	4.16517	+	2.57903i	0.321350	+	0.198976i
$169$	9.42453			0.724964
$170$	−3.55076	+	0.605055i	−0.272331	+	0.0464056i
$171$	−25.2212	−	4.87666i	−1.92872	−	0.372927i
$172$	0.562788	−	1.78178i	0.0429122	−	0.135860i
$173$	−5.13903			−0.390714			−0.195357	−	0.980732i	$-0.562586\pi$
$173$	−5.13903			−0.390714			−0.195357	+	0.980732i	$0.562586\pi$
$174$	−4.48948	−	1.13903i	−0.340346	−	0.0863500i
$175$	−3.00000	−	4.00000i	−0.226779	−	0.302372i
$176$	7.21899	+	5.06572i	0.544152	+	0.381843i
$177$	14.9208	+	18.0822i	1.12152	+	1.35914i
$178$	−18.4694	+	13.5351i	−1.38434	+	1.01450i
$179$	−14.4380			−1.07915			−0.539573	−	0.841939i	$-0.681414\pi$
$179$	−14.4380			−1.07915			−0.539573	+	0.841939i	$0.681414\pi$
$180$	10.9951	−	7.68813i	0.819528	−	0.573040i
$181$	8.68759			0.645743			0.322872	−	0.946443i	$-0.395352\pi$
$181$	8.68759			0.645743			0.322872	+	0.946443i	$0.395352\pi$
$182$	−2.15693	+	1.58069i	−0.159883	+	0.117168i
$183$	13.7460	+	16.6584i	1.01613	+	1.23143i
$184$	2.92004	+	8.62373i	0.215268	+	0.635750i
$185$	−0.819039	−	0.409519i	−0.0602169	−	0.0301085i
$186$	14.0238	+	3.55801i	1.02827	+	0.260886i
$187$	2.51130			0.183644
$188$	5.09565	+	1.60950i	0.371639	+	0.117385i
$189$	−4.56279	+	2.48615i	−0.331894	+	0.180841i
$190$	4.54855	+	26.6931i	0.329987	+	1.93652i
$191$	−11.7668			−0.851414			−0.425707	−	0.904861i	$-0.639975\pi$
$191$	−11.7668			−0.851414			−0.425707	+	0.904861i	$0.639975\pi$
$192$	13.4981	+	3.13090i	0.974138	+	0.225954i
$193$			18.0599i			1.29998i	0.759944	+	0.649988i	$0.225226\pi$
$193$			18.0599i			1.29998i	−0.759944	+	0.649988i	$0.774774\pi$
$194$	−21.0934	+	15.4581i	−1.51442	+	1.10983i
$195$	1.64283	+	7.13675i	0.117645	+	0.511073i
$196$	−0.602380	+	1.90713i	−0.0430271	+	0.136223i
$197$	16.0599			1.14422			0.572109	−	0.820178i	$-0.306126\pi$
$197$	16.0599			1.14422			0.572109	+	0.820178i	$0.306126\pi$
$198$	−8.45734	+	3.99633i	−0.601037	+	0.284007i
$199$		−	6.84086i		−	0.484936i	−0.970159	−	0.242468i	$-0.922043\pi$
$199$		−	6.84086i		−	0.484936i	0.970159	−	0.242468i	$-0.0779569\pi$
$200$	−11.6656	−	7.99467i	−0.824879	−	0.565309i
$201$	−11.9581	−	14.4917i	−0.843457	−	1.02217i
$202$	16.9723	−	12.4380i	1.19417	−	0.875134i
$203$		−	1.89089i		−	0.132715i
$204$	3.65844	−	1.47805i	0.256142	−	0.103484i
$205$	8.81904	+	4.40952i	0.615948	+	0.307974i
$206$	−12.4730	−	17.0201i	−0.869038	−	1.18585i
$207$	−9.48137	−	1.83327i	−0.659001	−	0.127421i
$208$	−4.34457	+	6.19130i	−0.301242	+	0.429290i
$209$		−	18.8789i		−	1.30588i
$210$	4.14615	+	3.57903i	0.286112	+	0.246976i
$211$			16.3222i			1.12367i	0.827250	+	0.561834i	$0.189904\pi$
$211$			16.3222i			1.12367i	−0.827250	+	0.561834i	$0.810096\pi$
$212$	−4.10765	+	13.0048i	−0.282115	+	0.893172i
$213$	8.81904	+	10.6876i	0.604271	+	0.732302i
$214$	0.423754	−	0.310544i	0.0289672	−	0.0212283i
$215$	0.934275	−	1.86855i	0.0637170	−	0.127434i
$216$	−9.96852	+	10.7995i	−0.678272	+	0.734811i
$217$			5.90658i			0.400965i
$218$	−2.39162	−	3.26349i	−0.161981	−	0.221032i
$219$	−10.6876	+	8.81904i	−0.722200	+	0.595935i
$220$	7.08142	+	6.86097i	0.477429	+	0.462566i
$221$			2.15379i			0.144880i
$222$	0.972308	+	0.246686i	0.0652570	+	0.0165565i
$223$	18.4274			1.23399			0.616996	−	0.786966i	$-0.288349\pi$
$223$	18.4274			1.23399			0.616996	+	0.786966i	$0.288349\pi$
$224$	0.116226	+	5.65566i	0.00776567	+	0.377885i
$225$	13.4903	−	6.55827i	0.899356	−	0.437218i
$226$	11.8632	+	16.1880i	0.789128	+	1.07681i
$227$			2.67190i			0.177340i	0.996061	+	0.0886700i	$0.0282617\pi$
$227$			2.67190i			0.177340i	−0.996061	+	0.0886700i	$0.971738\pi$
$228$	−11.1113	−	27.5026i	−0.735867	−	1.82141i
$229$	17.9284			1.18474			0.592371	−	0.805665i	$-0.298192\pi$
$229$	17.9284			1.18474			0.592371	+	0.805665i	$0.298192\pi$
$230$	1.70993	+	10.0347i	0.112749	+	0.661669i
$231$	−2.43048	−	2.94545i	−0.159914	−	0.193796i
$232$	−1.71528	−	5.06572i	−0.112614	−	0.332581i
$233$	−17.9731			−1.17746			−0.588728	−	0.808331i	$-0.700371\pi$
$233$	−17.9731			−1.17746			−0.588728	+	0.808331i	$0.700371\pi$
$234$	−3.42742	−	7.25336i	−0.224057	−	0.474167i
$235$	5.34379	+	2.67190i	0.348591	+	0.174295i
$236$	−8.15327	+	25.8132i	−0.530733	+	1.68029i
$237$	5.03130	−	4.15166i	0.326818	−	0.269679i
$238$	0.952175	+	1.29929i	0.0617203	+	0.0842207i
$239$	24.7055			1.59807			0.799033	−	0.601287i	$-0.205345\pi$
$239$	24.7055			1.59807			0.799033	+	0.601287i	$0.205345\pi$
$240$	14.3542	+	5.82717i	0.926562	+	0.376142i
$241$	−1.31533			−0.0847276			−0.0423638	−	0.999102i	$-0.513489\pi$
$241$	−1.31533			−0.0847276			−0.0423638	+	0.999102i	$0.513489\pi$
$242$	5.13192	+	7.00278i	0.329892	+	0.450156i
$243$	−4.72424	−	14.8554i	−0.303060	−	0.952971i
$244$	−7.51130	+	23.7807i	−0.480862	+	1.52240i
$245$	−1.00000	+	2.00000i	−0.0638877	+	0.127775i
$246$	−10.4694	−	2.65621i	−0.667503	−	0.169353i
$247$	16.1913			1.03023
$248$	5.35803	+	15.8238i	0.340235	+	1.00481i
$249$	−9.13903	+	7.54122i	−0.579163	+	0.477906i
$250$	−11.4768	−	10.8758i	−0.725858	−	0.687844i
$251$	13.5351			0.854328			0.427164	−	0.904174i	$-0.359513\pi$
$251$	13.5351			0.854328			0.427164	+	0.904174i	$0.359513\pi$
$252$	−5.27428	−	2.86042i	−0.332248	−	0.180190i
$253$		−	7.09711i		−	0.446191i
$254$	−3.00146	−	4.09565i	−0.188328	−	0.256984i
$255$	4.29903	−	0.989606i	0.269216	−	0.0619715i
$256$	5.44178	+	15.0462i	0.340111	+	0.940385i
$257$	−22.3826			−1.39619			−0.698094	−	0.716006i	$-0.745968\pi$
$257$	−22.3826			−1.39619			−0.698094	+	0.716006i	$0.745968\pi$
$258$	−0.562788	+	2.21822i	−0.0350377	+	0.138100i
$259$			0.409519i			0.0254463i
$260$	−5.88424	+	6.07331i	−0.364925	+	0.376651i
$261$	5.56952	+	1.07690i	0.344744	+	0.0666582i
$262$	−3.78246	−	5.16138i	−0.233681	−	0.318871i
$263$			9.49706i			0.585614i	0.956172	+	0.292807i	$0.0945893\pi$
$263$			9.49706i			0.585614i	−0.956172	+	0.292807i	$0.905411\pi$
$264$	−9.18320	−	5.68613i	−0.565187	−	0.349957i
$265$	−6.81904	+	13.6381i	−0.418890	+	0.837780i
$266$	9.76755	−	7.15805i	0.598887	−	0.438888i
$267$	21.6307	−	17.8490i	1.32378	−	1.09234i
$268$	6.53432	−	20.6876i	0.399147	−	1.26370i
$269$		−	8.60082i		−	0.524401i	−0.965013	−	0.262201i	$-0.915552\pi$
$269$		−	8.60082i		−	0.524401i	0.965013	−	0.262201i	$-0.0844482\pi$
$270$	−12.9031	+	10.1739i	−0.785260	+	0.619167i
$271$		−	12.5059i		−	0.759676i	−0.925053	−	0.379838i	$-0.875980\pi$
$271$		−	12.5059i		−	0.759676i	0.925053	−	0.379838i	$-0.124020\pi$
$272$	3.72952	+	2.61708i	0.226135	+	0.158684i
$273$	2.52613	−	2.08448i	0.152889	−	0.126158i
$274$	−13.7675	−	18.7866i	−0.831728	−	1.13494i
$275$	6.61428	+	8.81904i	0.398856	+	0.531808i
$276$	−4.17707	−	10.3390i	−0.251430	−	0.622335i
$277$		−	19.2884i		−	1.15893i	−0.814998	−	0.579464i	$-0.803262\pi$
$277$		−	19.2884i		−	1.15893i	0.814998	−	0.579464i	$-0.196738\pi$
$278$	14.7975	−	10.8442i	0.887494	−	0.650391i
$279$	−17.3975	−	3.36390i	−1.04156	−	0.201392i
$280$	−0.864758	+	6.26516i	−0.0516792	+	0.374415i
$281$		−	2.92815i		−	0.174679i	−0.996179	−	0.0873393i	$-0.972164\pi$
$281$		−	2.92815i		−	0.174679i	0.996179	−	0.0873393i	$-0.0278364\pi$
$282$	−6.34379	−	1.60950i	−0.377767	−	0.0958442i
$283$	7.51717			0.446849			0.223425	−	0.974721i	$-0.428276\pi$
$283$	7.51717			0.446849			0.223425	+	0.974721i	$0.428276\pi$
$284$	−4.81904	+	15.2570i	−0.285957	+	0.905338i
$285$	−7.43945	−	32.3183i	−0.440675	−	1.91437i
$286$	4.75552	−	3.48504i	0.281200	−	0.206075i
$287$		−	4.40952i		−	0.260286i
$288$	−16.7246	−	2.87866i	−0.985508	−	0.169627i
$289$	−15.7026			−0.923682
$290$	−1.00444	−	5.89456i	−0.0589828	−	0.346140i
$291$	24.7040	−	20.3849i	1.44817	−	1.19498i
$292$	−15.2570	−	4.81904i	−0.892850	−	0.282013i
$293$	−14.4245			−0.842690			−0.421345	−	0.906900i	$-0.638442\pi$
$293$	−14.4245			−0.842690			−0.421345	+	0.906900i	$0.638442\pi$
$294$	0.602380	−	2.37427i	0.0351315	−	0.138470i
$295$	−13.5351	+	27.0702i	−0.788044	+	1.57609i
$296$	0.371487	+	1.09711i	0.0215922	+	0.0637681i
$297$	10.0599	−	5.48137i	0.583732	−	0.318061i
$298$	14.6226	−	10.7161i	0.847067	−	0.620765i
$299$	6.08677			0.352007
$300$	14.8262	+	8.95461i	0.855989	+	0.516995i
$301$	−0.934275			−0.0538507
$302$	−6.42742	+	4.71027i	−0.369856	+	0.271046i
$303$	−19.8774	+	16.4022i	−1.14193	+	0.942281i
$304$	19.6741	−	28.0369i	1.12839	−	1.60803i
$305$	−12.4694	+	24.9387i	−0.713994	+	1.42799i
$306$	−4.36928	+	2.06461i	−0.249775	+	0.118026i
$307$	−21.7114			−1.23913			−0.619567	−	0.784944i	$-0.712692\pi$
$307$	−21.7114			−1.23913			−0.619567	+	0.784944i	$0.712692\pi$
$308$	1.32810	−	4.20476i	0.0756757	−	0.239588i
$309$	16.4484	+	19.9334i	0.935717	+	1.13397i
$310$	3.13758	+	18.4128i	0.178202	+	1.04578i
$311$	−19.9284			−1.13004			−0.565018	−	0.825079i	$-0.691131\pi$
$311$	−19.9284			−1.13004			−0.565018	+	0.825079i	$0.691131\pi$
$312$	4.87666	−	7.87588i	0.276086	−	0.445884i
$313$			18.9281i			1.06988i	0.844889	+	0.534941i	$0.179666\pi$
$313$			18.9281i			1.06988i	−0.844889	+	0.534941i	$0.820334\pi$
$314$	−14.6226	+	10.7161i	−0.825203	+	0.604742i
$315$	−5.32137	−	4.08448i	−0.299825	−	0.230134i
$316$	7.18242	+	2.26862i	0.404043	+	0.127620i
$317$	−0.278070			−0.0156179			−0.00780897	−	0.999970i	$-0.502486\pi$
$317$	−0.278070			−0.0156179			−0.00780897	+	0.999970i	$0.502486\pi$
$318$	4.10765	−	16.1902i	0.230346	−	0.907902i
$319$			4.16896i			0.233417i
$320$	3.36660	+	17.5689i	0.188199	+	0.982131i
$321$	−0.496287	+	0.409519i	−0.0277000	+	0.0228571i
$322$	3.67190	−	2.69091i	0.204627	−	0.149959i
$323$		−	9.75331i		−	0.542689i
$324$	11.4290	−	13.9060i	0.634945	−	0.772558i
$325$	−7.56357	+	5.67267i	−0.419551	+	0.314663i
$326$	−4.62706	−	6.31387i	−0.256269	−	0.349693i
$327$	3.15387	+	3.82210i	0.174409	+	0.211363i
$328$	−4.00000	−	11.8132i	−0.220863	−	0.652273i
$329$		−	2.67190i		−	0.147306i
$330$	−9.14127	−	7.89089i	−0.503210	−	0.434379i
$331$		−	13.2788i		−	0.729871i	−0.931033	−	0.364936i	$-0.881091\pi$
$331$		−	13.2788i		−	0.729871i	0.931033	−	0.364936i	$-0.118909\pi$
$332$	−13.0464	−	4.12079i	−0.716014	−	0.226158i
$333$	−1.20622	−	0.233228i	−0.0661003	−	0.0127808i
$334$	−18.6187	+	13.6445i	−1.01877	+	0.746596i
$335$	10.8475	−	21.6950i	0.592663	−	1.18533i
$336$	−0.539980	−	6.90713i	−0.0294583	−	0.376815i
$337$		−	24.3379i		−	1.32577i	−0.748721	−	0.662886i	$-0.769332\pi$
$337$		−	24.3379i		−	1.32577i	0.748721	−	0.662886i	$-0.230668\pi$
$338$	−7.87842	−	10.7505i	−0.428530	−	0.584752i
$339$	−15.6442	−	18.9589i	−0.849677	−	1.02970i
$340$	3.65844	+	3.54455i	0.198407	+	0.192230i
$341$		−	13.0226i		−	0.705213i
$342$	15.5209	+	32.8464i	0.839272	+	1.77613i
$343$	1.00000			0.0539949
$344$	−2.50294	+	0.847507i	−0.134949	+	0.0456945i
$345$	−2.79670	−	12.1494i	−0.150569	−	0.654100i
$346$	4.29597	+	5.86208i	0.230953	+	0.315147i
$347$			35.2951i			1.89474i	0.320144	+	0.947369i	$0.396269\pi$
$347$			35.2951i			1.89474i	−0.320144	+	0.947369i	$0.603731\pi$
$348$	2.45368	+	6.07331i	0.131531	+	0.325564i
$349$	−11.0942			−0.593859			−0.296929	−	0.954899i	$-0.595963\pi$
$349$	−11.0942			−0.593859			−0.296929	+	0.954899i	$0.595963\pi$
$350$	−2.05494	+	6.76589i	−0.109841	+	0.361652i
$351$	4.70105	+	8.62774i	0.250923	+	0.460515i
$352$	−0.256250	−	12.4694i	−0.0136582	−	0.664620i
$353$	21.5216			1.14548			0.572741	−	0.819737i	$-0.305880\pi$
$353$	21.5216			1.14548			0.572741	+	0.819737i	$0.305880\pi$
$354$	8.15327	−	32.1359i	0.433341	−	1.70800i
$355$	−8.00000	+	16.0000i	−0.424596	+	0.849192i
$356$	30.8789	+	9.75331i	1.63658	+	0.516925i
$357$	−1.25565	−	1.52169i	−0.0664560	−	0.0805365i
$358$	12.0694	+	16.4694i	0.637888	+	0.870433i
$359$	−15.5636			−0.821414			−0.410707	−	0.911767i	$-0.634718\pi$
$359$	−15.5636			−0.821414			−0.410707	+	0.911767i	$0.634718\pi$
$360$	−17.9612	−	6.11521i	−0.946638	−	0.322300i
$361$	−54.3213			−2.85902
$362$	−7.26238	−	9.90991i	−0.381702	−	0.520853i
$363$	−6.76755	−	8.20143i	−0.355204	−	0.430464i
$364$	3.60617	+	1.13903i	0.189015	+	0.0597016i
$365$	−16.0000	−	8.00000i	−0.837478	−	0.418739i
$366$	7.51130	−	29.6056i	0.392622	−	1.54751i
$367$	−35.7129			−1.86420			−0.932100	−	0.362201i	$-0.882026\pi$
$367$	−35.7129			−1.86420			−0.932100	+	0.362201i	$0.882026\pi$
$368$	7.39606	−	10.5399i	0.385546	−	0.549429i
$369$	12.9880	+	2.51130i	0.676128	+	0.130733i
$370$	0.217537	+	1.27661i	0.0113092	+	0.0663679i
$371$	6.81904			0.354027
$372$	−7.66457	−	18.9712i	−0.397389	−	0.983612i
$373$		−	29.0103i		−	1.50210i	−0.660246	−	0.751049i	$-0.729548\pi$
$373$		−	29.0103i		−	1.50210i	0.660246	−	0.751049i	$-0.270452\pi$
$374$	−2.09932	−	2.86463i	−0.108553	−	0.148127i
$375$	14.7981	+	12.4907i	0.764169	+	0.645016i
$376$	−2.42375	−	7.15805i	−0.124996	−	0.369148i
$377$	−3.57547			−0.184146
$378$	6.65021	+	3.12646i	0.342050	+	0.160808i
$379$		−	23.3534i		−	1.19958i	−0.800157	−	0.599791i	$-0.795250\pi$
$379$		−	23.3534i		−	1.19958i	0.800157	−	0.599791i	$-0.204750\pi$
$380$	26.6464	−	27.5026i	1.36693	−	1.41085i
$381$	3.95807	+	4.79670i	0.202778	+	0.245742i
$382$	9.83642	+	13.4223i	0.503275	+	0.686746i
$383$			14.9169i			0.762219i	0.924530	+	0.381110i	$0.124458\pi$
$383$			14.9169i			0.762219i	−0.924530	+	0.381110i	$0.875542\pi$
$384$	−7.71227	−	18.0145i	−0.393565	−	0.919297i
$385$	2.20476	−	4.40952i	0.112365	−	0.224730i
$386$	20.6008	−	15.0971i	1.04855	−	0.768423i
$387$	0.532086	−	2.75186i	0.0270474	−	0.139885i
$388$	35.2661	+	11.1390i	1.79036	+	0.565499i
$389$			19.5290i			0.990158i	0.868848	+	0.495079i	$0.164861\pi$
$389$			19.5290i			0.990158i	−0.868848	+	0.495079i	$0.835139\pi$
$390$	6.76755	−	7.83992i	0.342688	−	0.396990i
$391$		−	3.66655i		−	0.185425i
$392$	2.67901	−	0.907128i	0.135311	−	0.0458169i
$393$	4.98800	+	6.04484i	0.251611	+	0.304922i
$394$	−13.4252	−	18.3194i	−0.676352	−	0.922919i
$395$	7.53218	+	3.76609i	0.378985	+	0.189493i
$396$	11.6285	+	6.30654i	0.584355	+	0.316915i
$397$			3.48429i			0.174871i	0.996170	+	0.0874357i	$0.0278672\pi$
$397$			3.48429i			0.174871i	−0.996170	+	0.0874357i	$0.972133\pi$
$398$	−7.80335	+	5.71861i	−0.391146	+	0.286648i
$399$	−11.4394	+	9.43945i	−0.572689	+	0.472563i
$400$	0.632306	+	19.9900i	0.0316153	+	0.999500i
$401$			19.2661i			0.962102i	0.876693	+	0.481051i	$0.159745\pi$
$401$			19.2661i			0.962102i	−0.876693	+	0.481051i	$0.840255\pi$
$402$	−6.53432	+	25.7549i	−0.325902	+	1.28454i
$403$	11.1687			0.556353
$404$	−28.3760	−	8.96274i	−1.41176	−	0.445913i
$405$	15.0612	−	13.3476i	0.748399	−	0.663249i
$406$	−2.15693	+	1.58069i	−0.107047	+	0.0784482i
$407$		−	0.902892i		−	0.0447547i
$408$	−4.74427	−	2.93760i	−0.234876	−	0.145433i
$409$	−3.45903			−0.171038			−0.0855190	−	0.996337i	$-0.527255\pi$
$409$	−3.45903			−0.171038			−0.0855190	+	0.996337i	$0.527255\pi$
$410$	−2.34234	−	13.7460i	−0.115680	−	0.678866i
$411$	18.1555	+	22.0022i	0.895545	+	1.08529i
$412$	−8.98800	+	28.4559i	−0.442807	+	1.40192i
$413$	13.5351			0.666019
$414$	5.83473	+	12.3479i	0.286761	+	0.606866i
$415$	−13.6817	−	6.84086i	−0.671609	−	0.335805i
$416$	10.6942	−	0.219771i	0.524328	−	0.0107751i
$417$	−17.3303	+	14.3004i	−0.848670	+	0.700294i
$418$	−21.5351	+	15.7818i	−1.05332	+	0.771912i
$419$	11.2839			0.551257			0.275628	−	0.961264i	$-0.411114\pi$
$419$	11.2839			0.551257			0.275628	+	0.961264i	$0.411114\pi$
$420$	0.616614	−	7.72139i	0.0300877	−	0.376765i
$421$	9.95807			0.485327			0.242663	−	0.970111i	$-0.421979\pi$
$421$	9.95807			0.485327			0.242663	+	0.970111i	$0.421979\pi$
$422$	18.6187	−	13.6445i	0.906345	−	0.664206i
$423$	7.86993	+	1.52169i	0.382649	+	0.0739872i
$424$	18.2683	−	6.18574i	0.887187	−	0.300406i
$425$	3.41710	+	4.55614i	0.165754	+	0.221005i
$426$	4.81904	−	18.9941i	0.233483	−	0.920268i
$427$	12.4694			0.603435
$428$	−0.708473	−	0.223776i	−0.0342453	−	0.0108166i
$429$	−5.56952	+	4.59578i	−0.268899	+	0.221886i
$430$	−2.91246	+	0.496287i	−0.140451	+	0.0239331i
$431$	1.69226			0.0815133			0.0407566	−	0.999169i	$-0.487023\pi$
$431$	1.69226			0.0815133			0.0407566	+	0.999169i	$0.487023\pi$
$432$	20.6521	+	2.34325i	0.993625	+	0.112740i
$433$			12.9387i			0.621796i	0.950443	+	0.310898i	$0.100630\pi$
$433$			12.9387i			0.621796i	−0.950443	+	0.310898i	$0.899370\pi$
$434$	6.73762	−	4.93760i	0.323416	−	0.237012i
$435$	1.64283	+	7.13675i	0.0787675	+	0.342181i
$436$	−1.72339	+	5.45623i	−0.0825353	+	0.261306i
$437$	−27.5636			−1.31854
$438$	18.9941	+	4.81904i	0.907575	+	0.230263i
$439$		−	3.10376i		−	0.148134i	−0.997253	−	0.0740671i	$-0.976402\pi$
$439$		−	3.10376i		−	0.148134i	0.997253	−	0.0740671i	$-0.0235979\pi$
$440$	1.90658	−	13.8132i	0.0908928	−	0.658517i
$441$	−0.569517	+	2.94545i	−0.0271199	+	0.140259i
$442$	2.45682	−	1.80046i	0.116859	−	0.0856391i
$443$			14.6942i			0.698144i	0.937096	+	0.349072i	$0.113503\pi$
$443$			14.6942i			0.698144i	−0.937096	+	0.349072i	$0.886497\pi$
$444$	−0.531405	−	1.31533i	−0.0252194	−	0.0624226i
$445$	32.3826	+	16.1913i	1.53508	+	0.767541i
$446$	−15.4044	−	21.0201i	−0.729419	−	0.995332i
$447$	−17.1256	+	14.1314i	−0.810012	+	0.668395i
$448$	6.35424	−	4.86042i	0.300209	−	0.229633i
$449$		−	23.8669i		−	1.12635i	−0.826338	−	0.563174i	$-0.809580\pi$
$449$		−	23.8669i		−	1.12635i	0.826338	−	0.563174i	$-0.190420\pi$
$450$	−18.7582	−	9.90601i	−0.884271	−	0.466974i
$451$			9.72193i			0.457788i
$452$	8.54855	−	27.0646i	0.402090	−	1.27301i
$453$	7.52759	−	6.21151i	0.353677	−	0.291842i
$454$	3.04783	−	2.23357i	0.143042	−	0.104827i
$455$	3.78178	+	1.89089i	0.177293	+	0.0886463i
$456$	−22.0837	+	35.6655i	−1.03416	+	1.67019i
$457$			28.4723i			1.33188i	0.746006	+	0.665939i	$0.231969\pi$
$457$			28.4723i			1.33188i	−0.746006	+	0.665939i	$0.768031\pi$
$458$	−14.9872	−	20.4509i	−0.700307	−	0.955607i
$459$	5.19717	−	2.83182i	0.242583	−	0.132178i
$460$	10.0171	−	10.3390i	0.467052	−	0.482059i
$461$			23.3007i			1.08522i	0.839985	+	0.542610i	$0.182564\pi$
$461$			23.3007i			1.08522i	−0.839985	+	0.542610i	$0.817436\pi$
$462$	−1.32810	+	5.23469i	−0.0617889	+	0.243540i
$463$	−31.7549			−1.47577			−0.737887	−	0.674924i	$-0.764176\pi$
$463$	−31.7549			−1.47577			−0.737887	+	0.674924i	$0.764176\pi$
$464$	−4.34457	+	6.19130i	−0.201692	+	0.287424i
$465$	−5.13170	−	22.2931i	−0.237977	−	1.03382i
$466$	15.0246	+	20.5018i	0.696000	+	0.949730i
$467$		−	6.14714i		−	0.284456i	−0.989834	−	0.142228i	$-0.954573\pi$
$467$		−	6.14714i		−	0.284456i	0.989834	−	0.142228i	$-0.0454266\pi$
$468$	−5.40874	+	9.97308i	−0.250019	+	0.461006i
$469$	−10.8475			−0.500891
$470$	−1.41931	−	8.32922i	−0.0654680	−	0.384198i
$471$	17.1256	−	14.1314i	0.789105	−	0.651143i
$472$	36.2607	−	12.2781i	1.66903	−	0.565144i
$473$	2.05985			0.0947121
$474$	−8.94170	−	2.26862i	−0.410706	−	0.104201i
$475$	34.2512	−	25.6884i	1.57155	−	1.17866i
$476$	0.686132	−	2.17229i	0.0314488	−	0.0995665i
$477$	−3.88356	+	20.0851i	−0.177816	+	0.919634i
$478$	−20.6525	−	28.1815i	−0.944625	−	1.28899i
$479$	8.33792			0.380969			0.190485	−	0.981690i	$-0.438994\pi$
$479$	8.33792			0.380969			0.190485	+	0.981690i	$0.438994\pi$
$480$	−5.35237	−	21.2450i	−0.244301	−	0.969699i
$481$	0.774357			0.0353076
$482$	1.09954	+	1.50039i	0.0500829	+	0.0683408i
$483$	−4.30041	+	3.54855i	−0.195675	+	0.161465i
$484$	3.69803	−	11.7079i	0.168092	−	0.532179i
$485$	36.9834	+	18.4917i	1.67933	+	0.839665i
$486$	−12.9962	+	17.8072i	−0.589521	+	0.807753i
$487$	−19.6532			−0.890574			−0.445287	−	0.895388i	$-0.646898\pi$
$487$	−19.6532			−0.890574			−0.445287	+	0.895388i	$0.646898\pi$
$488$	33.4056	−	11.3113i	1.51220	−	0.512039i
$489$	6.10178	+	7.39460i	0.275932	+	0.334396i
$490$	3.11734	−	0.531200i	0.140827	−	0.0239972i
$491$	−14.7609			−0.666150			−0.333075	−	0.942900i	$-0.608086\pi$
$491$	−14.7609			−0.666150			−0.333075	+	0.942900i	$0.608086\pi$
$492$	5.72193	+	14.1628i	0.257965	+	0.638510i
$493$			2.15379i			0.0970019i
$494$	−13.5351	−	18.4694i	−0.608973	−	0.830976i
$495$	11.7324	+	9.00530i	0.527330	+	0.404758i
$496$	13.5711	−	19.3398i	0.609363	−	0.868382i
$497$	8.00000			0.358849
$498$	16.2420	+	4.12079i	0.727822	+	0.184657i
$499$		−	16.8347i		−	0.753626i	−0.926289	−	0.376813i	$-0.877020\pi$
$499$		−	16.8347i		−	0.753626i	0.926289	−	0.376813i	$-0.122980\pi$
$500$	−2.81192	+	22.1832i	−0.125753	+	0.992062i
$501$	21.8057	−	17.9933i	0.974205	−	0.803881i
$502$	−11.3146	−	15.4394i	−0.504997	−	0.689096i
$503$			1.38504i			0.0617559i	0.999523	+	0.0308779i	$0.00983032\pi$
$503$			1.38504i			0.0617559i	−0.999523	+	0.0308779i	$0.990170\pi$
$504$	1.14615	+	8.40752i	0.0510537	+	0.374501i
$505$	−29.7578	−	14.8789i	−1.32420	−	0.662102i
$506$	−8.09565	+	5.93282i	−0.359896	+	0.263746i
$507$	10.3894	+	12.5907i	0.461410	+	0.559172i
$508$	−2.16283	+	6.84751i	−0.0959602	+	0.303809i
$509$			0.218217i			0.00967232i	0.999988	+	0.00483616i	$0.00153940\pi$
$509$			0.218217i			0.00967232i	−0.999988	+	0.00483616i	$0.998461\pi$
$510$	−4.72261	−	4.07663i	−0.209121	−	0.180516i
$511$			8.00000i			0.353899i
$512$	12.6141	−	18.7852i	0.557468	−	0.830198i
$513$	−21.2884	−	39.0702i	−0.939906	−	1.72499i
$514$	18.7107	+	25.5318i	0.825294	+	1.12616i
$515$	−14.9208	+	29.8416i	−0.657490	+	1.31498i
$516$	3.00078	−	1.21234i	0.132102	−	0.0533705i
$517$			5.89089i			0.259081i
$518$	0.467138	−	0.342337i	0.0205248	−	0.0150414i
$519$	−5.66517	−	6.86549i	−0.248673	−	0.301361i
$520$	11.8467	+	1.63516i	0.519514	+	0.0717066i
$521$		−	1.44678i		−	0.0633844i	−0.999498	−	0.0316922i	$-0.989910\pi$
$521$		−	1.44678i		−	0.0633844i	0.999498	−	0.0316922i	$-0.0100896\pi$
$522$	−3.42742	−	7.25336i	−0.150014	−	0.317471i
$523$	−6.93719			−0.303342			−0.151671	−	0.988431i	$-0.548465\pi$
$523$	−6.93719			−0.303342			−0.151671	+	0.988431i	$0.548465\pi$
$524$	−2.72562	+	8.62929i	−0.119069	+	0.376972i
$525$	2.03665	−	8.41737i	0.0888869	−	0.367364i
$526$	10.8333	−	7.93906i	0.472353	−	0.346159i
$527$		−	6.72780i		−	0.293068i
$528$	1.19053	+	15.2286i	0.0518110	+	0.662738i
$529$	12.6381			0.549482
$530$	21.2573	−	3.62227i	0.923357	−	0.157342i
$531$	−7.70847	+	39.8669i	−0.334519	+	1.73008i
$532$	−16.3303	−	5.15805i	−0.708010	−	0.223630i
$533$	−8.33792			−0.361155
$534$	−38.4425	−	9.75331i	−1.66357	−	0.422067i
$535$	−0.742973	−	0.371487i	−0.0321215	−	0.0160608i
$536$	−29.0606	+	9.84008i	−1.25523	+	0.425027i
$537$	−15.9161	−	19.2884i	−0.686832	−	0.832356i
$538$	−9.81093	+	7.18984i	−0.422979	+	0.309976i
$539$	−2.20476			−0.0949657
$540$	22.3917	+	6.21367i	0.963587	+	0.267394i
$541$	−19.7997			−0.851256			−0.425628	−	0.904898i	$-0.639947\pi$
$541$	−19.7997			−0.851256			−0.425628	+	0.904898i	$0.639947\pi$
$542$	−14.2654	+	10.4542i	−0.612751	+	0.449048i
$543$	9.57702	+	11.6062i	0.410989	+	0.498069i
$544$	−0.132385	−	6.44199i	−0.00567598	−	0.276198i
$545$	−2.86097	+	5.72193i	−0.122550	+	0.245101i
$546$	−4.48948	−	1.13903i	−0.192132	−	0.0487462i
$547$	−19.1854			−0.820310			−0.410155	−	0.912016i	$-0.634525\pi$
$547$	−19.1854			−0.820310			−0.410155	+	0.912016i	$0.634525\pi$
$548$	−9.92082	+	31.4092i	−0.423796	+	1.34173i
$549$	−7.10152	+	36.7279i	−0.303086	+	1.56751i
$550$	4.53065	−	14.9172i	0.193188	−	0.636070i
$551$	16.1913			0.689773
$552$	−8.30187	+	13.4077i	−0.353351	+	0.570668i
$553$		−	3.76609i		−	0.160150i
$554$	−22.0022	+	16.1241i	−0.934785	+	0.685048i
$555$	−0.355795	−	1.54564i	−0.0151027	−	0.0656087i
$556$	−24.7399	−	7.81426i	−1.04920	−	0.331398i
$557$	−21.6532			−0.917478			−0.458739	−	0.888571i	$-0.651699\pi$
$557$	−21.6532			−0.917478			−0.458739	+	0.888571i	$0.651699\pi$
$558$	10.7062	+	22.6573i	0.453231	+	0.959162i
$559$			1.76661i			0.0747198i
$560$	7.86954	−	4.25092i	0.332549	−	0.179634i
$561$	2.76840	+	3.35496i	0.116882	+	0.141647i
$562$	−3.34013	+	2.44778i	−0.140895	+	0.103253i
$563$		−	20.8424i		−	0.878403i	−0.898389	−	0.439201i	$-0.855261\pi$
$563$		−	20.8424i		−	0.878403i	0.898389	−	0.439201i	$-0.144739\pi$
$564$	3.46714	+	8.58180i	0.145993	+	0.361359i
$565$	14.1913	−	28.3826i	0.597033	−	1.19407i
$566$	−6.28397	−	8.57482i	−0.264135	−	0.360426i
$567$	−8.35130	−	3.35496i	−0.350722	−	0.140895i
$568$	21.4321	−	7.25703i	0.899272	−	0.304498i
$569$		−	38.1942i		−	1.60118i	−0.599209	−	0.800592i	$-0.704518\pi$
$569$		−	38.1942i		−	1.60118i	0.599209	−	0.800592i	$-0.295482\pi$
$570$	−30.6464	+	35.5026i	−1.28364	+	1.48704i
$571$		−	12.8962i		−	0.539691i	−0.962904	−	0.269845i	$-0.913027\pi$
$571$		−	12.8962i		−	0.539691i	0.962904	−	0.269845i	$-0.0869726\pi$
$572$	−7.95074	−	2.51130i	−0.332437	−	0.105003i
$573$	−12.9715	−	15.7198i	−0.541890	−	0.656704i
$574$	−5.02993	+	3.68613i	−0.209945	+	0.153856i
$575$	12.8760	−	9.65698i	0.536965	−	0.402724i
$576$	10.6973	+	21.4842i	0.445719	+	0.895173i
$577$			5.07185i			0.211144i	0.994412	+	0.105572i	$0.0336673\pi$
$577$			5.07185i			0.211144i	−0.994412	+	0.105572i	$0.966333\pi$
$578$	13.1266	+	17.9119i	0.545993	+	0.745037i
$579$	−24.1270	+	19.9088i	−1.00269	+	0.827382i
$580$	−5.88424	+	6.07331i	−0.244330	+	0.252180i
$581$			6.84086i			0.283807i
$582$	−43.9042	−	11.1390i	−1.81989	−	0.461728i
$583$	−15.0343			−0.622659
$584$	7.25703	+	21.4321i	0.300298	+	0.886867i
$585$	−7.72331	+	10.0621i	−0.319319	+	0.416018i
$586$	12.0582	+	16.4540i	0.498118	+	0.679709i
$587$			15.5971i			0.643762i	0.946780	+	0.321881i	$0.104315\pi$
$587$			15.5971i			0.643762i	−0.946780	+	0.321881i	$0.895685\pi$
$588$	−3.21188	+	1.29763i	−0.132456	+	0.0535134i
$589$	−50.5768			−2.08398
$590$	42.1935	−	7.18984i	1.73708	−	0.296001i
$591$	17.7041	+	21.4551i	0.728248	+	0.882546i
$592$	0.940924	−	1.34088i	0.0386718	−	0.0551098i
$593$	24.9655			1.02521			0.512605	−	0.858624i	$-0.328681\pi$
$593$	24.9655			1.02521			0.512605	+	0.858624i	$0.328681\pi$
$594$	−14.6621	−	6.89310i	−0.601593	−	0.282827i
$595$	1.13903	−	2.27807i	0.0466959	−	0.0933917i
$596$	−24.4476	−	7.72193i	−1.00141	−	0.316303i
$597$	9.13903	−	7.54122i	0.374036	−	0.308642i
$598$	−5.08822	−	6.94316i	−0.208073	−	0.283927i
$599$	−12.0866			−0.493845			−0.246923	−	0.969035i	$-0.579419\pi$
$599$	−12.0866			−0.493845			−0.246923	+	0.969035i	$0.579419\pi$
$600$	−2.17940	−	24.3977i	−0.0889737	−	0.996034i
$601$	43.6681			1.78126			0.890629	−	0.454730i	$-0.150264\pi$
$601$	43.6681			1.78126			0.890629	+	0.454730i	$0.150264\pi$
$602$	0.781006	+	1.06572i	0.0318314	+	0.0434357i
$603$	6.17784	−	31.9507i	0.251581	−	1.30113i
$604$	10.7460	+	3.39419i	0.437248	+	0.138108i
$605$	6.13903	−	12.2781i	0.249587	−	0.499175i
$606$	35.3264	+	8.96274i	1.43504	+	0.364087i
$607$	40.7055			1.65219			0.826093	−	0.563534i	$-0.190559\pi$
$607$	40.7055			1.65219			0.826093	+	0.563534i	$0.190559\pi$
$608$	−48.4282	+	0.995218i	−1.96402	+	0.0403614i
$609$	2.52613	−	2.08448i	0.102364	−	0.0844674i
$610$	38.8713	−	6.62373i	1.57385	−	0.268187i
$611$	−5.05227			−0.204393
$612$	6.00758	+	3.25812i	0.242842	+	0.131702i
$613$			2.95049i			0.119169i	0.998223	+	0.0595846i	$0.0189776\pi$
$613$			2.95049i			0.119169i	−0.998223	+	0.0595846i	$0.981022\pi$
$614$	18.1496	+	24.7661i	0.732458	+	0.999479i
$615$	3.83104	+	16.6427i	0.154482	+	0.671100i
$616$	−5.90658	+	2.00000i	−0.237983	+	0.0805823i
$617$	15.3124			0.616454			0.308227	−	0.951313i	$-0.400264\pi$
$617$	15.3124			0.616454			0.308227	+	0.951313i	$0.400264\pi$
$618$	8.98800	−	35.4260i	0.361550	−	1.42504i
$619$		−	0.967840i		−	0.0389008i	−0.999811	−	0.0194504i	$-0.993808\pi$
$619$		−	0.967840i		−	0.0389008i	0.999811	−	0.0194504i	$-0.00619164\pi$
$620$	18.3806	−	18.9712i	0.738184	−	0.761902i
$621$	−8.00291	−	14.6876i	−0.321146	−	0.589393i
$622$	16.6591	+	22.7323i	0.667970	+	0.911481i
$623$		−	16.1913i		−	0.648691i
$624$	−13.0606	+	1.02104i	−0.522844	+	0.0408744i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	21.5913	−	15.8230i	0.862961	−	0.632413i
$627$	25.2212	−	20.8117i	1.00724	−	0.831140i
$628$	24.4476	+	7.72193i	0.975564	+	0.308139i
$629$		−	0.466457i		−	0.0185988i
$630$	−0.210760	+	9.48449i	−0.00839688	+	0.377871i
$631$			5.37278i			0.213887i	0.994265	+	0.106944i	$0.0341064\pi$
$631$			5.37278i			0.213887i	−0.994265	+	0.106944i	$0.965894\pi$
$632$	−3.41633	−	10.0894i	−0.135894	−	0.401335i
$633$	−21.8057	+	17.9933i	−0.866697	+	0.715169i
$634$	0.232452	+	0.317193i	0.00923184	+	0.0125973i
$635$	−3.59048	+	7.18096i	−0.142484	+	0.284968i
$636$	−21.9019	+	8.84860i	−0.868467	+	0.350870i
$637$		−	1.89089i		−	0.0749198i
$638$	4.75552	−	3.48504i	0.188273	−	0.137974i
$639$	−4.55614	+	23.5636i	−0.180238	+	0.932160i
$640$	17.2265	−	18.5270i	0.680936	−	0.732343i
$641$		−	22.3081i		−	0.881117i	−0.897724	−	0.440558i	$-0.854781\pi$
$641$		−	22.3081i		−	0.881117i	0.897724	−	0.440558i	$-0.145219\pi$
$642$	0.882008	+	0.223776i	0.0348101	+	0.00883174i
$643$	0.949286			0.0374362			0.0187181	−	0.999825i	$-0.494041\pi$
$643$	0.949286			0.0374362			0.0187181	+	0.999825i	$0.494041\pi$
$644$	−6.13903	−	1.93906i	−0.241912	−	0.0764096i
$645$	3.52621	−	0.811709i	0.138845	−	0.0319610i
$646$	−11.1256	+	8.15327i	−0.437730	+	0.320786i
$647$		−	30.1740i		−	1.18626i	−0.805107	−	0.593130i	$-0.797892\pi$
$647$		−	30.1740i		−	1.18626i	0.805107	−	0.593130i	$-0.202108\pi$
$648$	−25.4166	−	1.41230i	−0.998460	−	0.0554803i
$649$	−29.8416			−1.17139
$650$	12.7936	+	3.88567i	0.501804	+	0.152409i
$651$	−7.89089	+	6.51130i	−0.309268	+	0.255198i
$652$	−3.33423	+	10.5561i	−0.130579	+	0.413410i
$653$	−2.04468			−0.0800146			−0.0400073	−	0.999199i	$-0.512738\pi$
$653$	−2.04468			−0.0800146			−0.0400073	+	0.999199i	$0.512738\pi$
$654$	1.72339	−	6.79269i	0.0673898	−	0.265615i
$655$	−4.52476	+	9.04951i	−0.176797	+	0.353594i
$656$	−10.1314	+	14.4380i	−0.395567	+	0.563709i
$657$	−23.5636	−	4.55614i	−0.919302	−	0.177752i
$658$	−3.04783	+	2.23357i	−0.118817	+	0.0870736i
$659$	13.5054			0.526097			0.263048	−	0.964783i	$-0.415272\pi$
$659$	13.5054			0.526097			0.263048	+	0.964783i	$0.415272\pi$
$660$	−1.35949	+	17.0238i	−0.0529179	+	0.662650i
$661$	11.2286			0.436740			0.218370	−	0.975866i	$-0.429926\pi$
$661$	11.2286			0.436740			0.218370	+	0.975866i	$0.429926\pi$
$662$	−15.1471	+	11.1004i	−0.588710	+	0.431431i
$663$	−2.87735	+	2.37430i	−0.111747	+	0.0922100i
$664$	6.20554	+	18.3268i	0.240822	+	0.711216i
$665$	−17.1256	−	8.56279i	−0.664101	−	0.332051i
$666$	0.742292	+	1.57090i	0.0287632	+	0.0608710i
$667$	6.08677			0.235681
$668$	31.1286	+	9.83218i	1.20440	+	0.380419i
$669$	20.3140	+	24.6181i	0.785386	+	0.951791i
$670$	−33.8154	+	5.76220i	−1.30640	+	0.222613i
$671$	−27.4920			−1.06132
$672$	−7.42755	+	6.38996i	−0.286524	+	0.246498i
$673$		−	24.6905i		−	0.951749i	−0.879513	−	0.475874i	$-0.842132\pi$
$673$		−	24.6905i		−	0.951749i	0.879513	−	0.475874i	$-0.157868\pi$
$674$	−27.7622	+	20.3453i	−1.06936	+	0.783670i
$675$	23.6330	+	10.7927i	0.909634	+	0.415411i
$676$	−5.67715	+	17.9738i	−0.218352	+	0.691300i
$677$	26.7771			1.02913			0.514564	−	0.857452i	$-0.327954\pi$
$677$	26.7771			1.02913			0.514564	+	0.857452i	$0.327954\pi$
$678$	−8.54855	+	33.6939i	−0.328305	+	1.29401i
$679$		−	18.4917i		−	0.709647i
$680$	0.984989	−	7.13623i	0.0377726	−	0.273662i
$681$	−3.56952	+	2.94545i	−0.136784	+	0.112870i
$682$	−14.8548	+	10.8862i	−0.568821	+	0.416855i
$683$		−	16.4329i		−	0.628787i	−0.949293	−	0.314394i	$-0.898199\pi$
$683$		−	16.4329i		−	0.628787i	0.949293	−	0.314394i	$-0.101801\pi$
$684$	24.4932	−	45.1625i	0.936520	−	1.72683i
$685$	−16.4694	+	32.9387i	−0.629262	+	1.25852i
$686$	−0.835949	−	1.14070i	−0.0319167	−	0.0435520i
$687$	19.7639	+	23.9514i	0.754040	+	0.913804i
$688$	3.05908	+	2.14662i	0.116626	+	0.0818391i
$689$		−	12.8941i		−	0.491225i
$690$	−11.5209	+	13.3464i	−0.438592	+	0.508090i
$691$		−	16.6780i		−	0.634462i	−0.948348	−	0.317231i	$-0.897247\pi$
$691$		−	16.6780i		−	0.634462i	0.948348	−	0.317231i	$-0.102753\pi$
$692$	3.09565	−	9.80080i	0.117679	−	0.372570i
$693$	1.25565	−	6.49400i	0.0476982	−	0.246687i
$694$	40.2610	−	29.5049i	1.52829	−	1.11999i
$695$	−25.9446	−	12.9723i	−0.984135	−	0.492068i
$696$	4.87666	−	7.87588i	0.184849	−	0.298534i
$697$			5.02260i			0.190244i
$698$	9.27418	+	12.6551i	0.351033	+	0.479003i
$699$	−19.8132	−	24.0111i	−0.749403	−	0.908184i
$700$	9.43565	−	3.31187i	0.356634	−	0.125177i
$701$		−	14.1538i		−	0.534581i	−0.963616	−	0.267291i	$-0.913872\pi$
$701$		−	14.1538i		−	0.534581i	0.963616	−	0.267291i	$-0.0861284\pi$
$702$	5.91180	−	12.5748i	0.223127	−	0.474606i
$703$	−3.50663			−0.132255
$704$	−14.0096	+	10.7161i	−0.528005	+	0.403877i
$705$	2.32137	+	10.0845i	0.0874280	+	0.379804i
$706$	−17.9910	−	24.5497i	−0.677100	−	0.923939i
$707$			14.8789i			0.559578i
$708$	−43.4731	+	17.5636i	−1.63382	+	0.660079i
$709$	28.4397			1.06808			0.534038	−	0.845461i	$-0.320674\pi$
$709$	28.4397			1.06808			0.534038	+	0.845461i	$0.320674\pi$
$710$	24.9387	−	4.24960i	0.935934	−	0.159485i
$711$	11.0928	+	2.14485i	0.416013	+	0.0804383i
$712$	−14.6876	−	43.3767i	−0.550441	−	1.62561i
$713$	−19.0133			−0.712052
$714$	−0.686132	+	2.70437i	−0.0256778	+	0.101209i
$715$	−8.33792	−	4.16896i	−0.311821	−	0.155910i
$716$	8.69715	−	27.5351i	0.325028	−	1.02903i
$717$	27.2349	+	33.0053i	1.01710	+	1.23261i
$718$	13.0103	+	17.7533i	0.485542	+	0.662548i
$719$	−35.3453			−1.31816			−0.659080	−	0.752073i	$-0.729054\pi$
$719$	−35.3453			−1.31816			−0.659080	+	0.752073i	$0.729054\pi$
$720$	8.03902	+	25.6003i	0.299597	+	0.954066i
$721$	14.9208			0.555680
$722$	45.4099	+	61.9642i	1.68998	+	2.30607i
$723$	−1.44999	−	1.75721i	−0.0539257	−	0.0653513i
$724$	−5.23323	+	16.5683i	−0.194491	+	0.615758i
$725$	−7.56357	+	5.67267i	−0.280904	+	0.210678i
$726$	−3.69803	+	14.5757i	−0.137247	+	0.540955i
$727$	15.5636			0.577221			0.288610	−	0.957447i	$-0.406807\pi$
$727$	15.5636			0.577221			0.288610	+	0.957447i	$0.406807\pi$
$728$	−1.71528	−	5.06572i	−0.0635725	−	0.187748i
$729$	14.6381	−	22.6876i	0.542151	−	0.840281i
$730$	4.24960	+	24.9387i	0.157285	+	0.923024i
$731$	1.06417			0.0393598
$732$	−40.0501	+	16.1806i	−1.48029	+	0.598054i
$733$			15.2661i			0.563865i	0.959434	+	0.281933i	$0.0909754\pi$
$733$			15.2661i			0.563865i	−0.959434	+	0.281933i	$0.909025\pi$
$734$	29.8542	+	40.7376i	1.10194	+	1.50365i
$735$	−3.77428	+	0.868811i	−0.139216	+	0.0320466i
$736$	−18.2055	+	0.374131i	−0.671065	+	0.0137906i
$737$	23.9161			0.880963
$738$	−7.99267	−	16.9147i	−0.294214	−	0.622638i
$739$		−	9.17265i		−	0.337421i	−0.985666	−	0.168711i	$-0.946040\pi$
$739$		−	9.17265i		−	0.337421i	0.985666	−	0.168711i	$-0.0539604\pi$
$740$	1.27438	−	1.31533i	0.0468471	−	0.0483523i
$741$	17.8490	+	21.6307i	0.655698	+	0.794625i
$742$	−5.70037	−	7.77846i	−0.209267	−	0.285556i
$743$			22.9169i			0.840740i	0.907353	+	0.420370i	$0.138100\pi$
$743$			22.9169i			0.840740i	−0.907353	+	0.420370i	$0.861900\pi$
$744$	−15.2332	+	24.6019i	−0.558477	+	0.901950i
$745$	−25.6381	−	12.8190i	−0.939306	−	0.469653i
$746$	−33.0920	+	24.2512i	−1.21158	+	0.887898i
$747$	−20.1494	−	3.89599i	−0.737227	−	0.142547i
$748$	−1.51276	+	4.78937i	−0.0553118	+	0.175117i
$749$			0.371487i			0.0135738i
$750$	1.87765	−	27.3217i	0.0685620	−	0.997647i
$751$			33.2173i			1.21212i	0.795420	+	0.606059i	$0.207250\pi$
$751$			33.2173i			1.21212i	−0.795420	+	0.606059i	$0.792750\pi$
$752$	−6.13903	+	8.74853i	−0.223868	+	0.319026i
$753$	14.9208	+	18.0822i	0.543745	+	0.658952i
$754$	2.98891	+	4.07853i	0.108850	+	0.148531i
$755$	11.2693	+	5.63464i	0.410131	+	0.205066i
$756$	−1.99288	−	10.1994i	−0.0724804	−	0.370950i
$757$			24.8760i			0.904133i	0.891984	+	0.452066i	$0.149313\pi$
$757$			24.8760i			0.904133i	−0.891984	+	0.452066i	$0.850687\pi$
$758$	−26.6391	+	19.5222i	−0.967576	+	0.709079i
$759$	9.48137	−	7.82371i	0.344152	−	0.283983i
$760$	−53.6472	−	7.40474i	−1.94599	−	0.268598i
$761$			3.15405i			0.114334i	0.998365	+	0.0571670i	$0.0182068\pi$
$761$			3.15405i			0.114334i	−0.998365	+	0.0571670i	$0.981793\pi$
$762$	2.16283	−	8.52476i	0.0783512	−	0.308819i
$763$	2.86097			0.103574
$764$	7.08807	−	22.4407i	0.256437	−	0.811878i
$765$	6.06123	+	4.65237i	0.219144	+	0.168207i
$766$	17.0157	−	12.4698i	0.614802	−	0.450552i
$767$		−	25.5934i		−	0.924124i
$768$	−14.1020	+	23.8565i	−0.508862	+	0.860848i
$769$	34.7352			1.25258			0.626291	−	0.779589i	$-0.284572\pi$
$769$	34.7352			1.25258			0.626291	+	0.779589i	$0.284572\pi$
$770$	−6.87299	+	1.17117i	−0.247685	+	0.0422060i
$771$	−24.6741	−	29.9020i	−0.888617	−	1.07689i
$772$	−34.4425	−	10.8789i	−1.23961	−	0.391540i
$773$	46.5442			1.67408			0.837040	−	0.547142i	$-0.184284\pi$
$773$	46.5442			1.67408			0.837040	+	0.547142i	$0.184284\pi$
$774$	−3.58383	+	1.69346i	−0.128818	+	0.0608702i
$775$	23.6263	−	17.7197i	0.848683	−	0.636512i
$776$	−16.7744	−	49.5396i	−0.602164	−	1.77837i
$777$	−0.547097	+	0.451446i	−0.0196270	+	0.0161955i
$778$	22.2766	−	16.3252i	0.798656	−	0.585287i
$779$	37.7578			1.35281
$780$	−14.6003	−	1.16595i	−0.522775	−	0.0417477i
$781$	−17.6381			−0.631140
$782$	−4.18242	+	3.06504i	−0.149563	+	0.109606i
$783$	4.70105	+	8.62774i	0.168002	+	0.308330i
$784$	−3.27428	−	2.29763i	−0.116938	−	0.0820583i
$785$	25.6381	+	12.8190i	0.915062	+	0.457531i
$786$	2.72562	−	10.7430i	0.0972197	−	0.383189i
$787$	17.6845			0.630383			0.315192	−	0.949028i	$-0.397931\pi$
$787$	17.6845			0.630383			0.315192	+	0.949028i	$0.397931\pi$
$788$	−9.67413	+	30.6282i	−0.344627	+	1.09108i
$789$	−12.6876	+	10.4694i	−0.451690	+	0.372719i
$790$	−2.00055	−	11.7402i	−0.0711763	−	0.417697i
$791$	−14.1913			−0.504585
$792$	−2.52699	−	18.5366i	−0.0897927	−	0.658668i
$793$		−	23.5782i		−	0.837287i
$794$	3.97452	−	2.91268i	0.141050	−	0.103367i
$795$	−25.7369	+	5.92446i	−0.912795	+	0.210119i
$796$	13.0464	+	4.12079i	0.462417	+	0.146058i
$797$	27.5368			0.975404			0.487702	−	0.873010i	$-0.337835\pi$
$797$	27.5368			0.975404			0.487702	+	0.873010i	$0.337835\pi$
$798$	20.3303	+	5.15805i	0.719686	+	0.182593i
$799$			3.04338i			0.107667i
$800$	22.2740	−	17.4319i	0.787504	−	0.616310i
$801$	47.6906	+	9.22123i	1.68506	+	0.325816i
$802$	21.9767	−	16.1054i	0.776026	−	0.568703i
$803$		−	17.6381i		−	0.622434i
$804$	34.8409	−	14.0761i	1.22874	−	0.496425i
$805$	−6.43799	−	3.21899i	−0.226909	−	0.113455i
$806$	−9.33646	−	12.7401i	−0.328863	−	0.448751i
$807$	11.4903	−	9.48137i	0.404476	−	0.333760i
$808$	13.4971	+	39.8608i	0.474825	+	1.40230i
$809$		−	2.15379i		−	0.0757233i	−0.999283	−	0.0378616i	$-0.987945\pi$
$809$		−	2.15379i		−	0.0757233i	0.999283	−	0.0378616i	$-0.0120546\pi$
$810$	−27.8160	−	6.02236i	−0.977355	−	0.211604i
$811$		−	21.0484i		−	0.739108i	−0.929209	−	0.369554i	$-0.879510\pi$
$811$		−	21.0484i		−	0.739108i	0.929209	−	0.369554i	$-0.120490\pi$
$812$	3.60617	+	1.13903i	0.126552	+	0.0399723i
$813$	16.7072	−	13.7862i	0.585946	−	0.483503i
$814$	−1.02993	+	0.754771i	−0.0360989	+	0.0264547i
$815$	−5.53510	+	11.0702i	−0.193886	+	0.387772i
$816$	0.615056	+	7.86746i	0.0215313	+	0.275416i
$817$		−	8.00000i		−	0.279885i
$818$	2.89157	+	3.94571i	0.101101	+	0.137958i
$819$	5.56952	+	1.07690i	0.194615	+	0.0376298i
$820$	−13.7219	+	14.1628i	−0.479191	+	0.494588i
$821$		−	44.2048i		−	1.54276i	−0.636376	−	0.771379i	$-0.719567\pi$
$821$		−	44.2048i		−	1.54276i	0.636376	−	0.771379i	$-0.280433\pi$
$822$	9.92082	−	39.1027i	0.346028	−	1.36386i
$823$	−39.0579			−1.36147			−0.680737	−	0.732528i	$-0.738340\pi$
$823$	−39.0579			−1.36147			−0.680737	+	0.732528i	$0.738340\pi$
$824$	39.9731	−	13.5351i	1.39253	−	0.471517i
$825$	−4.49033	+	18.5583i	−0.156333	+	0.646116i
$826$	−11.3146	−	15.4394i	−0.393687	−	0.537207i
$827$		−	5.48481i		−	0.190725i	−0.995443	−	0.0953627i	$-0.969599\pi$
$827$		−	5.48481i		−	0.190725i	0.995443	−	0.0953627i	$-0.0304011\pi$
$828$	9.20767	−	16.9779i	0.319989	−	0.590022i
$829$	−24.3855			−0.846944			−0.423472	−	0.905909i	$-0.639189\pi$
$829$	−24.3855			−0.846944			−0.423472	+	0.905909i	$0.639189\pi$
$830$	3.63386	+	21.3253i	0.126133	+	0.740212i
$831$	25.7683	−	21.2632i	0.893893	−	0.737611i
$832$	−9.19053	−	12.0152i	−0.318624	−	0.416551i
$833$	−1.13903			−0.0394652
$834$	30.7997	+	7.81426i	1.06651	+	0.270586i
$835$	32.6445	+	16.3222i	1.12971	+	0.564854i
$836$	36.0045	+	11.3723i	1.24524	+	0.393318i
$837$	−14.6847	−	26.9505i	−0.507577	−	0.931545i
$838$	−9.43280	−	12.8716i	−0.325851	−	0.444641i
$839$	37.5965			1.29798			0.648988	−	0.760799i	$-0.275193\pi$
$839$	37.5965			1.29798			0.648988	+	0.760799i	$0.275193\pi$
$840$	−9.32322	+	5.75131i	−0.321682	+	0.198439i
$841$	25.4245			0.876708
$842$	−8.32444	−	11.3591i	−0.286879	−	0.391462i
$843$	3.91185	−	3.22793i	0.134731	−	0.111176i
$844$	−31.1286	−	9.83218i	−1.07149	−	0.338438i
$845$	−9.42453	+	18.8491i	−0.324214	+	0.648427i
$846$	−4.84307	−	10.2493i	−0.166508	−	0.352377i
$847$	−6.13903			−0.210940
$848$	−22.3274	−	15.6676i	−0.766727	−	0.538029i
$849$	8.28678	+	10.0426i	0.284401	+	0.344660i
$850$	2.34065	−	7.70658i	0.0802837	−	0.264333i
$851$	−1.31824			−0.0451887
$852$	−25.6950	+	10.3811i	−0.880297	+	0.355649i
$853$			32.9387i			1.12780i	0.825843	+	0.563901i	$0.190700\pi$
$853$			32.9387i			1.12780i	−0.825843	+	0.563901i	$0.809300\pi$
$854$	−10.4238	−	14.2238i	−0.356694	−	0.486728i
$855$	34.9745	−	45.5658i	1.19610	−	1.55832i
$856$	0.336986	+	0.995218i	0.0115179	+	0.0340159i
$857$	−41.6833			−1.42387			−0.711937	−	0.702244i	$-0.752182\pi$
$857$	−41.6833			−1.42387			−0.711937	+	0.702244i	$0.752182\pi$
$858$	9.89822	+	2.51130i	0.337920	+	0.0857343i
$859$			2.44600i			0.0834564i	0.999129	+	0.0417282i	$0.0132864\pi$
$859$			2.44600i			0.0834564i	−0.999129	+	0.0417282i	$0.986714\pi$
$860$	3.00078	+	2.90736i	0.102326	+	0.0991401i
$861$	5.89089	−	4.86097i	0.200761	−	0.165661i
$862$	−1.41464	−	1.93036i	−0.0481829	−	0.0657482i
$863$		−	45.2264i		−	1.53952i	−0.638331	−	0.769762i	$-0.720375\pi$
$863$		−	45.2264i		−	1.53952i	0.638331	−	0.769762i	$-0.279625\pi$
$864$	−14.5912	−	25.5166i	−0.496401	−	0.868093i
$865$	5.13903	−	10.2781i	0.174732	−	0.349465i
$866$	14.7592	−	10.8161i	0.501538	−	0.367547i
$867$	−17.3102	−	20.9779i	−0.587886	−	0.712446i
$868$	−11.2646	−	3.55801i	−0.382346	−	0.120767i
$869$			8.30333i			0.281671i
$870$	6.76755	−	7.83992i	0.229441	−	0.265798i
$871$			20.5115i			0.695004i
$872$	7.66457	−	2.59526i	0.259555	−	0.0878867i
$873$	54.4663	+	10.5314i	1.84341	+	0.356432i
$874$	23.0417	+	31.4417i	0.779398	+	1.06353i
$875$	11.0000	−	2.00000i	0.371868	−	0.0676123i
$876$	−10.3811	−	25.6950i	−0.350743	−	0.868154i
$877$			11.3723i			0.384014i	0.981394	+	0.192007i	$0.0614996\pi$
$877$			11.3723i			0.384014i	−0.981394	+	0.192007i	$0.938500\pi$
$878$	−3.54045	+	2.59458i	−0.119484	+	0.0875629i
$879$	−15.9013	−	19.2704i	−0.536338	−	0.649976i
$880$	−17.3504	+	9.37226i	−0.584883	+	0.315939i
$881$			16.8818i			0.568762i	0.958711	+	0.284381i	$0.0917881\pi$
$881$			16.8818i			0.568762i	−0.958711	+	0.284381i	$0.908212\pi$
$882$	3.83595	−	1.81259i	0.129163	−	0.0610332i
$883$	−44.3871			−1.49374			−0.746872	−	0.664968i	$-0.768445\pi$
$883$	−44.3871			−1.49374			−0.746872	+	0.664968i	$0.768445\pi$
$884$	−4.10756	−	1.29740i	−0.138152	−	0.0436363i
$885$	−51.0852	+	11.7594i	−1.71721	+	0.395289i
$886$	16.7617	−	12.2836i	0.563119	−	0.412677i
$887$		−	10.8978i		−	0.365912i	−0.983121	−	0.182956i	$-0.941433\pi$
$887$		−	10.8978i		−	0.365912i	0.983121	−	0.182956i	$-0.0585666\pi$
$888$	−1.05616	+	1.70572i	−0.0354424	+	0.0572401i
$889$	3.59048			0.120421
$890$	−8.60082	−	50.4738i	−0.288300	−	1.69189i
$891$	18.4126	+	7.39689i	0.616846	+	0.247805i
$892$	−11.1003	+	35.1435i	−0.371666	+	1.17669i
$893$	22.8789			0.765613
$894$	30.4358	+	7.72193i	1.01793	+	0.258260i
$895$	14.4380	−	28.8760i	0.482609	−	0.965217i
$896$	−10.8561	−	3.18520i	−0.362676	−	0.106410i
$897$	6.70993	+	8.13161i	0.224038	+	0.271507i
$898$	−27.2249	+	19.9515i	−0.908506	+	0.665790i
$899$	11.1687			0.372497
$900$	4.38115	+	29.6784i	0.146038	+	0.989279i
$901$	−7.76712			−0.258760
$902$	11.0898	−	8.12703i	0.369249	−	0.270601i
$903$	−1.02993	−	1.24814i	−0.0342738	−	0.0415356i
$904$	−38.0187	+	12.8733i	−1.26448	+	0.428161i
$905$	−8.68759	+	17.3752i	−0.288785	+	0.577570i
$906$	−13.3781	−	3.39419i	−0.444459	−	0.112765i
$907$	25.4635			0.845502			0.422751	−	0.906246i	$-0.361065\pi$
$907$	25.4635			0.845502			0.422751	+	0.906246i	$0.361065\pi$
$908$	−5.09565	−	1.60950i	−0.169105	−	0.0534130i
$909$	−43.8250	−	8.47379i	−1.45358	−	0.281058i
$910$	−1.00444	−	5.89456i	−0.0332969	−	0.195403i
$911$	−44.4395			−1.47235			−0.736174	−	0.676792i	$-0.763369\pi$
$911$	−44.4395			−1.47235			−0.736174	+	0.676792i	$0.763369\pi$
$912$	59.1443	−	4.62373i	1.95846	−	0.153107i
$913$		−	15.0824i		−	0.499156i
$914$	32.4783	−	23.8014i	1.07429	−	0.787279i
$915$	−47.0629	+	10.8335i	−1.55585	+	0.358145i
$916$	−10.7997	+	34.1918i	−0.356832	+	1.12973i
$917$	4.52476			0.149421
$918$	−7.57482	−	3.56115i	−0.250006	−	0.117535i
$919$			4.50906i			0.148740i	0.997231	+	0.0743701i	$0.0236946\pi$
$919$			4.50906i			0.148740i	−0.997231	+	0.0743701i	$0.976305\pi$
$920$	−20.1675	−	2.78365i	−0.664903	−	0.0917742i
$921$	−23.9342	−	29.0053i	−0.788659	−	0.955757i
$922$	26.5790	−	19.4782i	0.875333	−	0.641479i
$923$		−	15.1271i		−	0.497916i
$924$	7.08142	−	2.86097i	0.232962	−	0.0941188i
$925$	1.63808	−	1.22856i	0.0538597	−	0.0403947i
$926$	26.5454	+	36.2227i	0.872337	+	1.19035i
$927$	−8.49766	+	43.9485i	−0.279100	+	1.44346i
$928$	10.6942	−	0.219771i	0.351056	−	0.00721432i
$929$			10.7323i			0.352114i	0.984380	+	0.176057i	$0.0563344\pi$
$929$			10.7323i			0.352114i	−0.984380	+	0.176057i	$0.943666\pi$
$930$	−21.1398	+	24.4896i	−0.693202	+	0.803045i
$931$			8.56279i			0.280634i
$932$	10.8266	−	34.2770i	0.354638	−	1.12278i
$933$	−21.9687	−	26.6233i	−0.719222	−	0.871608i
$934$	−7.01203	+	5.13869i	−0.229441	+	0.168143i
$935$	−2.51130	+	5.02260i	−0.0821282	+	0.164256i
$936$	15.8977	−	2.16725i	0.519633	−	0.0708387i
$937$			33.6727i			1.10004i	0.835152	+	0.550019i	$0.185380\pi$
$937$			33.6727i			1.10004i	−0.835152	+	0.550019i	$0.814620\pi$
$938$	9.06796	+	12.3737i	0.296079	+	0.404016i
$939$	−25.2870	+	20.8660i	−0.825211	+	0.680936i
$940$	−8.31464	+	8.58180i	−0.271194	+	0.279908i
$941$			3.98534i			0.129918i	0.997888	+	0.0649592i	$0.0206917\pi$
$941$			3.98534i			0.129918i	−0.997888	+	0.0649592i	$0.979308\pi$
$942$	−30.4358	−	7.72193i	−0.991652	−	0.251594i
$943$	14.1942			0.462227
$944$	−44.3177	−	31.0987i	−1.44242	−	1.01218i
$945$	−0.409519	−	11.6117i	−0.0133217	−	0.377730i
$946$	−1.72193	−	2.34967i	−0.0559848	−	0.0763943i
$947$		−	2.78256i		−	0.0904210i	−0.998977	−	0.0452105i	$-0.985604\pi$
$947$		−	2.78256i		−	0.0904210i	0.998977	−	0.0452105i	$-0.0143959\pi$
$948$	4.88700	+	12.0962i	0.158722	+	0.392867i
$949$	15.1271			0.491047
$950$	−57.9348	−	17.5960i	−1.87965	−	0.570891i
$951$	−0.306538	−	0.371487i	−0.00994018	−	0.0120463i
$952$	−3.05149	+	1.03325i	−0.0988994	+	0.0334878i
$953$	−7.44678			−0.241225			−0.120612	−	0.992700i	$-0.538486\pi$
$953$	−7.44678			−0.241225			−0.120612	+	0.992700i	$0.538486\pi$
$954$	26.1575	−	12.3602i	0.846880	−	0.400175i
$955$	11.7668	−	23.5335i	0.380764	−	0.761528i
$956$	−14.8821	+	47.1166i	−0.481322	+	1.52386i
$957$	−5.56952	+	4.59578i	−0.180037	+	0.148560i
$958$	−6.97007	−	9.51104i	−0.225193	−	0.307288i
$959$	16.4694			0.531824
$960$	−19.7599	+	23.8652i	−0.637747	+	0.770246i
$961$	−3.88772			−0.125410
$962$	−0.647322	−	0.883306i	−0.0208705	−	0.0284789i
$963$	−1.09419	−	0.211568i	−0.0352599	−	0.00681769i
$964$	0.792326	−	2.50849i	0.0255191	−	0.0807932i
$965$	−36.1197	−	18.0599i	−1.16273	−	0.581367i
$966$	7.64275	+	1.93906i	0.245901	+	0.0623881i
$967$	9.25547			0.297636			0.148818	−	0.988865i	$-0.452453\pi$
$967$	9.25547			0.297636			0.148818	+	0.988865i	$0.452453\pi$
$968$	−16.4466	+	5.56889i	−0.528613	+	0.178991i
$969$	13.0299	−	10.7519i	0.418582	−	0.345399i
$970$	−9.82280	−	57.6450i	−0.315391	−	1.85087i
$971$	−30.9819			−0.994256			−0.497128	−	0.867677i	$-0.665612\pi$
$971$	−30.9819			−0.994256			−0.497128	+	0.867677i	$0.665612\pi$
$972$	31.1769	−	0.0611740i	0.999998	−	0.00196216i
$973$			12.9723i			0.415873i
$974$	16.4291	+	22.4184i	0.526422	+	0.718332i
$975$	−15.9163	−	3.85109i	−0.509730	−	0.123334i
$976$	−40.8282	−	28.6500i	−1.30688	−	0.917065i
$977$	5.02551			0.160780			0.0803902	−	0.996763i	$-0.474383\pi$
$977$	5.02551			0.160780			0.0803902	+	0.996763i	$0.474383\pi$
$978$	3.33423	−	13.1418i	0.106617	−	0.420228i
$979$			35.6979i			1.14091i
$980$	−3.21188	−	3.11189i	−0.102600	−	0.0994056i
$981$	−1.62937	+	8.42682i	−0.0520218	+	0.269048i
$982$	12.3394	+	16.8377i	0.393765	+	0.537313i
$983$		−	37.6974i		−	1.20236i	−0.799113	−	0.601180i	$-0.794697\pi$
$983$		−	37.6974i		−	1.20236i	0.799113	−	0.601180i	$-0.205303\pi$
$984$	11.3723	−	18.3664i	0.362535	−	0.585499i
$985$	−16.0599	+	32.1197i	−0.511709	+	1.02342i
$986$	2.45682	−	1.80046i	0.0782412	−	0.0573383i
$987$	3.56952	−	2.94545i	0.113619	−	0.0937546i
$988$	−9.75331	+	30.8789i	−0.310294	+	0.982388i
$989$		−	3.00743i		−	0.0956306i
$990$	0.464675	−	20.9110i	0.0147683	−	0.664596i
$991$		−	42.3475i		−	1.34521i	−0.740001	−	0.672606i	$-0.765175\pi$
$991$		−	42.3475i		−	1.34521i	0.740001	−	0.672606i	$-0.234825\pi$
$992$	−33.4056	+	0.686498i	−1.06063	+	0.0217963i
$993$	17.7399	−	14.6383i	0.562957	−	0.464533i
$994$	−6.68759	−	9.12558i	−0.212117	−	0.289446i
$995$	13.6817	+	6.84086i	0.433740	+	0.216870i
$996$	−8.87691	−	21.9720i	−0.281276	−	0.696209i
$997$		−	30.7850i		−	0.974969i	−0.873132	−	0.487485i	$-0.837915\pi$
$997$		−	30.7850i		−	0.974969i	0.873132	−	0.487485i	$-0.162085\pi$
$998$	−19.2033	+	14.0730i	−0.607871	+	0.445472i
$999$	−1.01813	−	1.86855i	−0.0322121	−	0.0591183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.l.e.239.3	yes	8
3.2	odd	2		420.2.l.f.239.6	yes	8
4.3	odd	2		420.2.l.c.239.4	yes	8
5.4	even	2		420.2.l.d.239.6	yes	8
12.11	even	2		420.2.l.d.239.5	yes	8
15.14	odd	2		420.2.l.c.239.3	✓	8
20.19	odd	2		420.2.l.f.239.5	yes	8
60.59	even	2	inner	420.2.l.e.239.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.l.c.239.3	✓	8	15.14	odd	2
420.2.l.c.239.4	yes	8	4.3	odd	2
420.2.l.d.239.5	yes	8	12.11	even	2
420.2.l.d.239.6	yes	8	5.4	even	2
420.2.l.e.239.3	yes	8	1.1	even	1	trivial
420.2.l.e.239.4	yes	8	60.59	even	2	inner
420.2.l.f.239.5	yes	8	20.19	odd	2
420.2.l.f.239.6	yes	8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.835949 - 1.14070i) q^{2} +(1.10238 + 1.33595i) q^{3} +(-0.602380 + 1.90713i) q^{4} +(-1.00000 + 2.00000i) q^{5} +(0.602380 - 2.37427i) q^{6} +1.00000 q^{7} +(2.67901 - 0.907128i) q^{8} +(-0.569517 + 2.94545i) q^{9} +O(q^{10})\)	\(q+(-0.835949 - 1.14070i) q^{2} +(1.10238 + 1.33595i) q^{3} +(-0.602380 + 1.90713i) q^{4} +(-1.00000 + 2.00000i) q^{5} +(0.602380 - 2.37427i) q^{6} +1.00000 q^{7} +(2.67901 - 0.907128i) q^{8} +(-0.569517 + 2.94545i) q^{9} +(3.11734 - 0.531200i) q^{10} -2.20476 q^{11} +(-3.21188 + 1.29763i) q^{12} -1.89089i q^{13} +(-0.835949 - 1.14070i) q^{14} +(-3.77428 + 0.868811i) q^{15} +(-3.27428 - 2.29763i) q^{16} -1.13903 q^{17} +(3.83595 - 1.81259i) q^{18} +8.56279i q^{19} +(-3.21188 - 3.11189i) q^{20} +(1.10238 + 1.33595i) q^{21} +(1.84307 + 2.51496i) q^{22} +3.21899i q^{23} +(4.16517 + 2.57903i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(-2.15693 + 1.58069i) q^{26} +(-4.56279 + 2.48615i) q^{27} +(-0.602380 + 1.90713i) q^{28} -1.89089i q^{29} +(4.14615 + 3.57903i) q^{30} +5.90658i q^{31} +(0.116226 + 5.65566i) q^{32} +(-2.43048 - 2.94545i) q^{33} +(0.952175 + 1.29929i) q^{34} +(-1.00000 + 2.00000i) q^{35} +(-5.27428 - 2.86042i) q^{36} +0.409519i q^{37} +(9.76755 - 7.15805i) q^{38} +(2.52613 - 2.08448i) q^{39} +(-0.864758 + 6.26516i) q^{40} -4.40952i q^{41} +(0.602380 - 2.37427i) q^{42} -0.934275 q^{43} +(1.32810 - 4.20476i) q^{44} +(-5.32137 - 4.08448i) q^{45} +(3.67190 - 2.69091i) q^{46} -2.67190i q^{47} +(-0.539980 - 6.90713i) q^{48} +1.00000 q^{49} +(-2.05494 + 6.76589i) q^{50} +(-1.25565 - 1.52169i) q^{51} +(3.60617 + 1.13903i) q^{52} +6.81904 q^{53} +(6.65021 + 3.12646i) q^{54} +(2.20476 - 4.40952i) q^{55} +(2.67901 - 0.907128i) q^{56} +(-11.4394 + 9.43945i) q^{57} +(-2.15693 + 1.58069i) q^{58} +13.5351 q^{59} +(0.616614 - 7.72139i) q^{60} +12.4694 q^{61} +(6.73762 - 4.93760i) q^{62} +(-0.569517 + 2.94545i) q^{63} +(6.35424 - 4.86042i) q^{64} +(3.78178 + 1.89089i) q^{65} +(-1.32810 + 5.23469i) q^{66} -10.8475 q^{67} +(0.686132 - 2.17229i) q^{68} +(-4.30041 + 3.54855i) q^{69} +(3.11734 - 0.531200i) q^{70} +8.00000 q^{71} +(1.14615 + 8.40752i) q^{72} +8.00000i q^{73} +(0.467138 - 0.342337i) q^{74} +(2.03665 - 8.41737i) q^{75} +(-16.3303 - 5.15805i) q^{76} -2.20476 q^{77} +(-4.48948 - 1.13903i) q^{78} -3.76609i q^{79} +(7.86954 - 4.25092i) q^{80} +(-8.35130 - 3.35496i) q^{81} +(-5.02993 + 3.68613i) q^{82} +6.84086i q^{83} +(-3.21188 + 1.29763i) q^{84} +(1.13903 - 2.27807i) q^{85} +(0.781006 + 1.06572i) q^{86} +(2.52613 - 2.08448i) q^{87} +(-5.90658 + 2.00000i) q^{88} -16.1913i q^{89} +(-0.210760 + 9.48449i) q^{90} -1.89089i q^{91} +(-6.13903 - 1.93906i) q^{92} +(-7.89089 + 6.51130i) q^{93} +(-3.04783 + 2.23357i) q^{94} +(-17.1256 - 8.56279i) q^{95} +(-7.42755 + 6.38996i) q^{96} -18.4917i q^{97} +(-0.835949 - 1.14070i) q^{98} +(1.25565 - 6.49400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 2 * q^4 - 8 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9	\( 8 q + 2 q^{3} + 2 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9} - 4 q^{10} - 4 q^{11} - 10 q^{12} - 10 q^{15} - 6 q^{16} + 4 q^{17} + 24 q^{18} - 10 q^{20} + 2 q^{21} + 6 q^{22} - 18 q^{24} - 24 q^{25} - 26 q^{26} + 8 q^{27} + 2 q^{28} + 18 q^{30} + 30 q^{32} - 26 q^{33} + 30 q^{34} - 8 q^{35} - 22 q^{36} + 20 q^{38} - 18 q^{39} - 14 q^{40} - 2 q^{42} - 8 q^{43} + 24 q^{44} - 18 q^{45} + 16 q^{46} - 2 q^{48} + 8 q^{49} + 8 q^{50} + 14 q^{51} + 16 q^{52} + 24 q^{54} + 4 q^{55} + 6 q^{56} - 20 q^{57} - 26 q^{58} - 8 q^{59} - 6 q^{60} - 16 q^{61} + 40 q^{62} + 2 q^{63} + 26 q^{64} - 32 q^{65} - 24 q^{66} - 24 q^{67} - 12 q^{68} + 24 q^{69} - 4 q^{70} + 64 q^{71} - 6 q^{72} + 4 q^{74} + 10 q^{75} - 28 q^{76} - 4 q^{77} - 4 q^{78} + 38 q^{80} + 2 q^{81} + 4 q^{82} - 10 q^{84} - 4 q^{85} + 24 q^{86} - 18 q^{87} + 24 q^{88} - 44 q^{90} - 36 q^{92} - 32 q^{93} - 2 q^{94} - 48 q^{95} - 22 q^{96} - 14 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^4 - 8 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9 - 4 * q^10 - 4 * q^11 - 10 * q^12 - 10 * q^15 - 6 * q^16 + 4 * q^17 + 24 * q^18 - 10 * q^20 + 2 * q^21 + 6 * q^22 - 18 * q^24 - 24 * q^25 - 26 * q^26 + 8 * q^27 + 2 * q^28 + 18 * q^30 + 30 * q^32 - 26 * q^33 + 30 * q^34 - 8 * q^35 - 22 * q^36 + 20 * q^38 - 18 * q^39 - 14 * q^40 - 2 * q^42 - 8 * q^43 + 24 * q^44 - 18 * q^45 + 16 * q^46 - 2 * q^48 + 8 * q^49 + 8 * q^50 + 14 * q^51 + 16 * q^52 + 24 * q^54 + 4 * q^55 + 6 * q^56 - 20 * q^57 - 26 * q^58 - 8 * q^59 - 6 * q^60 - 16 * q^61 + 40 * q^62 + 2 * q^63 + 26 * q^64 - 32 * q^65 - 24 * q^66 - 24 * q^67 - 12 * q^68 + 24 * q^69 - 4 * q^70 + 64 * q^71 - 6 * q^72 + 4 * q^74 + 10 * q^75 - 28 * q^76 - 4 * q^77 - 4 * q^78 + 38 * q^80 + 2 * q^81 + 4 * q^82 - 10 * q^84 - 4 * q^85 + 24 * q^86 - 18 * q^87 + 24 * q^88 - 44 * q^90 - 36 * q^92 - 32 * q^93 - 2 * q^94 - 48 * q^95 - 22 * q^96 - 14 * q^99

Introduction

L-functions

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