LMFDB - Embedded newform 418.2.f.g.229.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, degree $4$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} + \cdots + 16 $ x^16 - x^15 + 7x^14 - 13x^13 + 51x^12 - 74x^11 + 332x^10 - 614x^9 + 1832x^8 - 2960x^7 + 5348x^6 - 6872x^5 + 8232x^4 - 6344x^3 + 3984x^2 - 400x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			229.1
Root			$-2.04714 + 1.48734i$ of defining polynomial
Character	$\chi$	$=$	418.229
Dual form			418.2.f.g.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-2.04714 + 1.48734i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.0815989 + 0.251136i) q^{5} +(-0.781939 - 2.40656i) q^{6} +(-3.52166 - 2.55863i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.05158 - 3.23642i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-2.04714 + 1.48734i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.0815989 + 0.251136i) q^{5} +(-0.781939 - 2.40656i) q^{6} +(-3.52166 - 2.55863i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.05158 - 3.23642i) q^{9} -0.264060 q^{10} +(3.09741 + 1.18578i) q^{11} +2.53041 q^{12} +(1.77619 - 5.46655i) q^{13} +(3.52166 - 2.55863i) q^{14} +(-0.540568 - 0.392746i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.40882 + 4.33589i) q^{17} +(2.75306 + 2.00022i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(0.0815989 - 0.251136i) q^{20} +11.0149 q^{21} +(-2.08490 + 2.57938i) q^{22} -6.87167 q^{23} +(-0.781939 + 2.40656i) q^{24} +(3.98867 - 2.89794i) q^{25} +(4.65013 + 3.37852i) q^{26} +(0.315099 + 0.969775i) q^{27} +(1.34515 + 4.13996i) q^{28} +(4.05491 + 2.94606i) q^{29} +(0.540568 - 0.392746i) q^{30} +(1.94290 - 5.97963i) q^{31} -1.00000 q^{32} +(-8.10449 + 2.17942i) q^{33} -4.55903 q^{34} +(0.355201 - 1.09320i) q^{35} +(-2.75306 + 2.00022i) q^{36} +(-3.25073 - 2.36179i) q^{37} +(-0.309017 - 0.951057i) q^{38} +(4.49449 + 13.8326i) q^{39} +(0.213629 + 0.155210i) q^{40} +(0.505632 - 0.367363i) q^{41} +(-3.40379 + 10.4758i) q^{42} +10.6878 q^{43} +(-1.80887 - 2.77993i) q^{44} +0.898587 q^{45} +(2.12346 - 6.53534i) q^{46} +(8.36364 - 6.07654i) q^{47} +(-2.04714 - 1.48734i) q^{48} +(3.69234 + 11.3639i) q^{49} +(1.52354 + 4.68897i) q^{50} +(-9.33298 - 6.78081i) q^{51} +(-4.65013 + 3.37852i) q^{52} +(4.34539 - 13.3737i) q^{53} -1.01968 q^{54} +(-0.0450467 + 0.874628i) q^{55} -4.35301 q^{56} +(0.781939 - 2.40656i) q^{57} +(-4.05491 + 2.94606i) q^{58} +(-1.27666 - 0.927548i) q^{59} +(0.206479 + 0.635476i) q^{60} +(-1.56697 - 4.82262i) q^{61} +(5.08658 + 3.69561i) q^{62} +(-11.9841 + 8.70696i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.51778 q^{65} +(0.431670 - 8.38131i) q^{66} -14.7605 q^{67} +(1.40882 - 4.33589i) q^{68} +(14.0673 - 10.2205i) q^{69} +(0.929928 + 0.675632i) q^{70} +(-0.833950 - 2.56664i) q^{71} +(-1.05158 - 3.23642i) q^{72} +(-5.24552 - 3.81110i) q^{73} +(3.25073 - 2.36179i) q^{74} +(-3.85517 + 11.8650i) q^{75} +1.00000 q^{76} +(-7.87403 - 12.1010i) q^{77} -14.5445 q^{78} +(-1.51921 + 4.67564i) q^{79} +(-0.213629 + 0.155210i) q^{80} +(6.17175 + 4.48404i) q^{81} +(0.193134 + 0.594406i) q^{82} +(-2.73359 - 8.41312i) q^{83} +(-8.91123 - 6.47439i) q^{84} +(-0.973939 + 0.707608i) q^{85} +(-3.30270 + 10.1647i) q^{86} -12.6828 q^{87} +(3.20284 - 0.861293i) q^{88} -7.63969 q^{89} +(-0.277679 + 0.854607i) q^{90} +(-20.2420 + 14.7067i) q^{91} +(5.55929 + 4.03906i) q^{92} +(4.91633 + 15.1309i) q^{93} +(3.19463 + 9.83205i) q^{94} +(-0.213629 - 0.155210i) q^{95} +(2.04714 - 1.48734i) q^{96} +(3.40848 - 10.4902i) q^{97} -11.9487 q^{98} +(7.09484 - 8.77756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−2.04714	+	1.48734i	−1.18192	+	0.858715i	−0.992387	−	0.123160i	$-0.960697\pi$
$3$	−2.04714	+	1.48734i	−1.18192	+	0.858715i	−0.189532	+	0.981874i	$0.560697\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.0815989	+	0.251136i	0.0364921	+	0.112311i	0.967643	−	0.252322i	$-0.0811943\pi$
$5$	0.0815989	+	0.251136i	0.0364921	+	0.112311i	−0.931151	+	0.364633i	$0.881194\pi$
$6$	−0.781939	−	2.40656i	−0.319225	−	0.982475i
$7$	−3.52166	−	2.55863i	−1.33106	−	0.967073i	−0.999722	−	0.0235608i	$-0.992500\pi$
$7$	−3.52166	−	2.55863i	−1.33106	−	0.967073i	−0.331339	−	0.943512i	$-0.607500\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	1.05158	−	3.23642i	0.350525	−	1.07881i
$10$	−0.264060			−0.0835030
$11$	3.09741	+	1.18578i	0.933903	+	0.357526i
$11$	3.09741	+	1.18578i	0.933903	+	0.357526i
$12$	2.53041			0.730466
$13$	1.77619	−	5.46655i	0.492627	−	1.51615i	−0.327996	−	0.944679i	$-0.606373\pi$
$13$	1.77619	−	5.46655i	0.492627	−	1.51615i	0.820623	−	0.571470i	$-0.193627\pi$
$14$	3.52166	−	2.55863i	0.941202	−	0.683824i
$15$	−0.540568	−	0.392746i	−0.139574	−	0.101407i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.40882	+	4.33589i	0.341688	+	1.05161i	0.963333	+	0.268309i	$0.0864647\pi$
$17$	1.40882	+	4.33589i	0.341688	+	1.05161i	−0.621645	+	0.783299i	$0.713535\pi$
$18$	2.75306	+	2.00022i	0.648903	+	0.471455i
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i
$20$	0.0815989	−	0.251136i	0.0182461	−	0.0561556i
$21$	11.0149			2.40365
$22$	−2.08490	+	2.57938i	−0.444501	+	0.549926i
$23$	−6.87167			−1.43284			−0.716421	−	0.697669i	$-0.754221\pi$
$23$	−6.87167			−1.43284			−0.716421	+	0.697669i	$0.754221\pi$
$24$	−0.781939	+	2.40656i	−0.159613	+	0.491237i
$25$	3.98867	−	2.89794i	0.797735	−	0.579588i
$26$	4.65013	+	3.37852i	0.911965	+	0.662581i
$27$	0.315099	+	0.969775i	0.0606408	+	0.186633i
$28$	1.34515	+	4.13996i	0.254210	+	0.782378i
$29$	4.05491	+	2.94606i	0.752977	+	0.547070i	0.896748	−	0.442541i	$-0.145923\pi$
$29$	4.05491	+	2.94606i	0.752977	+	0.547070i	−0.143771	+	0.989611i	$0.545923\pi$
$30$	0.540568	−	0.392746i	0.0986938	−	0.0717052i
$31$	1.94290	−	5.97963i	0.348955	−	1.07397i	−0.610477	−	0.792034i	$-0.709022\pi$
$31$	1.94290	−	5.97963i	0.348955	−	1.07397i	0.959432	−	0.281939i	$-0.0909777\pi$
$32$	−1.00000			−0.176777
$33$	−8.10449	+	2.17942i	−1.41081	+	0.379389i
$34$	−4.55903			−0.781866
$35$	0.355201	−	1.09320i	0.0600399	−	0.184784i
$36$	−2.75306	+	2.00022i	−0.458844	+	0.333369i
$37$	−3.25073	−	2.36179i	−0.534416	−	0.388276i	0.287591	−	0.957753i	$-0.407146\pi$
$37$	−3.25073	−	2.36179i	−0.534416	−	0.388276i	−0.822007	+	0.569477i	$0.807146\pi$
$38$	−0.309017	−	0.951057i	−0.0501292	−	0.154282i
$39$	4.49449	+	13.8326i	0.719694	+	2.21499i
$40$	0.213629	+	0.155210i	0.0337777	+	0.0245409i
$41$	0.505632	−	0.367363i	0.0789665	−	0.0573725i	−0.547602	−	0.836739i	$-0.684459\pi$
$41$	0.505632	−	0.367363i	0.0789665	−	0.0573725i	0.626568	+	0.779367i	$0.284459\pi$
$42$	−3.40379	+	10.4758i	−0.525216	+	1.61645i
$43$	10.6878			1.62987			0.814935	−	0.579552i	$-0.196772\pi$
$43$	10.6878			1.62987			0.814935	+	0.579552i	$0.196772\pi$
$44$	−1.80887	−	2.77993i	−0.272697	−	0.419090i
$45$	0.898587			0.133953
$46$	2.12346	−	6.53534i	0.313087	−	0.963584i
$47$	8.36364	−	6.07654i	1.21996	−	0.886354i	0.223865	−	0.974620i	$-0.428132\pi$
$47$	8.36364	−	6.07654i	1.21996	−	0.886354i	0.996097	+	0.0882656i	$0.0281324\pi$
$48$	−2.04714	−	1.48734i	−0.295480	−	0.214679i
$49$	3.69234	+	11.3639i	0.527478	+	1.62341i
$50$	1.52354	+	4.68897i	0.215461	+	0.663120i
$51$	−9.33298	−	6.78081i	−1.30688	−	0.949503i
$52$	−4.65013	+	3.37852i	−0.644857	+	0.468516i
$53$	4.34539	−	13.3737i	0.596885	−	1.83702i	0.0517771	−	0.998659i	$-0.483511\pi$
$53$	4.34539	−	13.3737i	0.596885	−	1.83702i	0.545108	−	0.838366i	$-0.316489\pi$
$54$	−1.01968			−0.138761
$55$	−0.0450467	+	0.874628i	−0.00607410	+	0.117935i
$56$	−4.35301			−0.581695
$57$	0.781939	−	2.40656i	0.103570	−	0.318757i
$58$	−4.05491	+	2.94606i	−0.532435	+	0.386837i
$59$	−1.27666	−	0.927548i	−0.166207	−	0.120756i	0.501572	−	0.865116i	$-0.332755\pi$
$59$	−1.27666	−	0.927548i	−0.166207	−	0.120756i	−0.667779	+	0.744359i	$0.732755\pi$
$60$	0.206479	+	0.635476i	0.0266563	+	0.0820396i
$61$	−1.56697	−	4.82262i	−0.200629	−	0.617474i	−0.999865	−	0.0164554i	$-0.994762\pi$
$61$	−1.56697	−	4.82262i	−0.200629	−	0.617474i	0.799235	−	0.601018i	$-0.205238\pi$
$62$	5.08658	+	3.69561i	0.645996	+	0.469343i
$63$	−11.9841	+	8.70696i	−1.50985	+	1.09697i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.51778			0.188258
$66$	0.431670	−	8.38131i	0.0531349	−	1.03167i
$67$	−14.7605			−1.80328			−0.901641	−	0.432484i	$-0.857637\pi$
$67$	−14.7605			−1.80328			−0.901641	+	0.432484i	$0.857637\pi$
$68$	1.40882	−	4.33589i	0.170844	−	0.525804i
$69$	14.0673	−	10.2205i	1.69350	−	1.23040i
$70$	0.929928	+	0.675632i	0.111148	+	0.0807535i
$71$	−0.833950	−	2.56664i	−0.0989717	−	0.304604i	0.889297	−	0.457331i	$-0.151194\pi$
$71$	−0.833950	−	2.56664i	−0.0989717	−	0.304604i	−0.988268	+	0.152727i	$0.951194\pi$
$72$	−1.05158	−	3.23642i	−0.123929	−	0.381415i
$73$	−5.24552	−	3.81110i	−0.613942	−	0.446055i	0.236858	−	0.971544i	$-0.423882\pi$
$73$	−5.24552	−	3.81110i	−0.613942	−	0.446055i	−0.850800	+	0.525489i	$0.823882\pi$
$74$	3.25073	−	2.36179i	0.377889	−	0.274553i
$75$	−3.85517	+	11.8650i	−0.445157	+	1.37005i
$76$	1.00000			0.114708
$77$	−7.87403	−	12.1010i	−0.897328	−	1.37904i
$78$	−14.5445			−1.64684
$79$	−1.51921	+	4.67564i	−0.170924	+	0.526050i	−0.999424	−	0.0339391i	$-0.989195\pi$
$79$	−1.51921	+	4.67564i	−0.170924	+	0.526050i	0.828500	+	0.559989i	$0.189195\pi$
$80$	−0.213629	+	0.155210i	−0.0238844	+	0.0173530i
$81$	6.17175	+	4.48404i	0.685750	+	0.498226i
$82$	0.193134	+	0.594406i	0.0213281	+	0.0656412i
$83$	−2.73359	−	8.41312i	−0.300050	−	0.923460i	−0.981478	−	0.191574i	$-0.938641\pi$
$83$	−2.73359	−	8.41312i	−0.300050	−	0.923460i	0.681428	−	0.731885i	$-0.261359\pi$
$84$	−8.91123	−	6.47439i	−0.972295	−	0.706414i
$85$	−0.973939	+	0.707608i	−0.105639	+	0.0767509i
$86$	−3.30270	+	10.1647i	−0.356140	+	1.09609i
$87$	−12.6828			−1.35974
$88$	3.20284	−	0.861293i	0.341424	−	0.0918142i
$89$	−7.63969			−0.809806			−0.404903	−	0.914360i	$-0.632695\pi$
$89$	−7.63969			−0.809806			−0.404903	+	0.914360i	$0.632695\pi$
$90$	−0.277679	+	0.854607i	−0.0292699	+	0.0900835i
$91$	−20.2420	+	14.7067i	−2.12194	+	1.54168i
$92$	5.55929	+	4.03906i	0.579597	+	0.421102i
$93$	4.91633	+	15.1309i	0.509800	+	1.56900i
$94$	3.19463	+	9.83205i	0.329501	+	1.01410i
$95$	−0.213629	−	0.155210i	−0.0219178	−	0.0159242i
$96$	2.04714	−	1.48734i	0.208936	−	0.151801i
$97$	3.40848	−	10.4902i	0.346078	−	1.06512i	−0.614926	−	0.788585i	$-0.710814\pi$
$97$	3.40848	−	10.4902i	0.346078	−	1.06512i	0.961004	−	0.276535i	$-0.0891860\pi$
$98$	−11.9487			−1.20700
$99$	7.09484	−	8.77756i	0.713058	−	0.882178i
$100$	−4.93027			−0.493027
$101$	1.19568	−	3.67991i	0.118974	−	0.366165i	−0.873781	−	0.486320i	$-0.838339\pi$
$101$	1.19568	−	3.67991i	0.118974	−	0.366165i	0.992755	+	0.120155i	$0.0383390\pi$
$102$	9.33298	−	6.78081i	0.924103	−	0.671400i
$103$	2.87689	+	2.09019i	0.283469	+	0.205952i	0.720429	−	0.693529i	$-0.243945\pi$
$103$	2.87689	+	2.09019i	0.283469	+	0.205952i	−0.436960	+	0.899481i	$0.643945\pi$
$104$	−1.77619	−	5.46655i	−0.174170	−	0.536040i
$105$	0.898803	+	2.76623i	0.0877142	+	0.269957i
$106$	11.3764	+	8.26543i	1.10497	+	0.802809i
$107$	1.34827	−	0.979577i	0.130342	−	0.0946992i	−0.520704	−	0.853737i	$-0.674330\pi$
$107$	1.34827	−	0.979577i	0.130342	−	0.0946992i	0.651046	+	0.759038i	$0.274330\pi$
$108$	0.315099	−	0.969775i	0.0303204	−	0.0933166i
$109$	−9.68307			−0.927470			−0.463735	−	0.885974i	$-0.653491\pi$
$109$	−9.68307			−0.927470			−0.463735	+	0.885974i	$0.653491\pi$
$110$	−0.817900	−	0.313117i	−0.0779837	−	0.0298545i
$111$	10.1675			0.965055
$112$	1.34515	−	4.13996i	0.127105	−	0.391189i
$113$	8.99561	−	6.53569i	0.846236	−	0.614826i	−0.0778697	−	0.996964i	$-0.524812\pi$
$113$	8.99561	−	6.53569i	0.846236	−	0.614826i	0.924106	+	0.382137i	$0.124812\pi$
$114$	2.04714	+	1.48734i	0.191733	+	0.139302i
$115$	−0.560721	−	1.72572i	−0.0522875	−	0.160924i
$116$	−1.54884	−	4.76683i	−0.143806	−	0.442589i
$117$	−15.8242	−	11.4970i	−1.46295	−	1.06290i
$118$	1.27666	−	0.927548i	0.117526	−	0.0853877i
$119$	6.13259	−	18.8742i	0.562173	−	1.73019i
$120$	−0.668179			−0.0609961
$121$	8.18785	+	7.34569i	0.744350	+	0.667790i
$122$	5.07081			0.459089
$123$	−0.488709	+	1.50409i	−0.0440654	+	0.135619i
$124$	−5.08658	+	3.69561i	−0.456788	+	0.331876i
$125$	2.12139	+	1.54128i	0.189743	+	0.137856i
$126$	−4.57752	−	14.0882i	−0.407798	−	1.25507i
$127$	−0.0975759	−	0.300308i	−0.00865846	−	0.0266480i	0.946634	−	0.322311i	$-0.104460\pi$
$127$	−0.0975759	−	0.300308i	−0.00865846	−	0.0266480i	−0.955292	+	0.295663i	$0.904460\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−21.8794	+	15.8963i	−1.92638	+	1.39959i
$130$	−0.469020	+	1.44350i	−0.0411358	+	0.126603i
$131$	−3.91920			−0.342422			−0.171211	−	0.985234i	$-0.554768\pi$
$131$	−3.91920			−0.342422			−0.171211	+	0.985234i	$0.554768\pi$
$132$	7.83771	+	3.00051i	0.682185	+	0.261161i
$133$	4.35301			0.377454
$134$	4.56125	−	14.0381i	0.394032	−	1.21270i
$135$	−0.217833	+	0.158265i	−0.0187481	+	0.0136213i
$136$	3.68833	+	2.67973i	0.316272	+	0.229785i
$137$	3.84395	+	11.8305i	0.328411	+	1.01074i	0.969877	+	0.243594i	$0.0783264\pi$
$137$	3.84395	+	11.8305i	0.328411	+	1.01074i	−0.641466	+	0.767151i	$0.721674\pi$
$138$	5.37323	+	16.5371i	0.457399	+	1.40773i
$139$	5.17472	+	3.75966i	0.438914	+	0.318890i	0.785203	−	0.619238i	$-0.212558\pi$
$139$	5.17472	+	3.75966i	0.438914	+	0.318890i	−0.346289	+	0.938128i	$0.612558\pi$
$140$	−0.929928	+	0.675632i	−0.0785932	+	0.0571013i
$141$	−8.08371	+	24.8791i	−0.680771	+	2.09520i
$142$	2.69872			0.226472
$143$	11.9837	−	14.8260i	1.00213	−	1.23981i
$144$	3.40297			0.283581
$145$	−0.408985	+	1.25873i	−0.0339644	+	0.104532i
$146$	5.24552	−	3.81110i	0.434123	−	0.315409i
$147$	−24.4607	−	17.7717i	−2.01748	−	1.46579i
$148$	1.24167	+	3.82146i	0.102064	+	0.314122i
$149$	3.17160	+	9.76118i	0.259828	+	0.799667i	0.992840	+	0.119452i	$0.0381138\pi$
$149$	3.17160	+	9.76118i	0.259828	+	0.799667i	−0.733012	+	0.680215i	$0.761886\pi$
$150$	−10.0930	−	7.33298i	−0.824088	−	0.598735i
$151$	11.1053	−	8.06848i	0.903737	−	0.656604i	−0.0356858	−	0.999363i	$-0.511362\pi$
$151$	11.1053	−	8.06848i	0.903737	−	0.656604i	0.939423	+	0.342759i	$0.111362\pi$
$152$	−0.309017	+	0.951057i	−0.0250646	+	0.0771409i
$153$	15.5142			1.25425
$154$	13.9420	−	3.74922i	1.12348	−	0.302120i
$155$	1.66024			0.133353
$156$	4.49449	−	13.8326i	0.359847	−	1.10750i
$157$	−5.31692	+	3.86297i	−0.424337	+	0.308299i	−0.779380	−	0.626551i	$-0.784466\pi$
$157$	−5.31692	+	3.86297i	−0.424337	+	0.308299i	0.355044	+	0.934850i	$0.384466\pi$
$158$	−3.97733	−	2.88970i	−0.316420	−	0.229892i
$159$	10.9956	+	33.8410i	0.872009	+	2.68377i
$160$	−0.0815989	−	0.251136i	−0.00645096	−	0.0198540i
$161$	24.1997	+	17.5821i	1.90720	+	1.38566i
$162$	−6.17175	+	4.48404i	−0.484898	+	0.352299i
$163$	−5.73901	+	17.6629i	−0.449514	+	1.38346i	0.427943	+	0.903806i	$0.359239\pi$
$163$	−5.73901	+	17.6629i	−0.449514	+	1.38346i	−0.877457	+	0.479656i	$0.840761\pi$
$164$	−0.624996			−0.0488040
$165$	−1.20865	−	1.85749i	−0.0940932	−	0.144605i
$166$	8.84608			0.686589
$167$	−5.05641	+	15.5620i	−0.391277	+	1.20423i	0.540547	+	0.841314i	$0.318217\pi$
$167$	−5.05641	+	15.5620i	−0.391277	+	1.20423i	−0.931823	+	0.362912i	$0.881783\pi$
$168$	8.91123	−	6.47439i	0.687517	−	0.499510i
$169$	−16.2111	−	11.7781i	−1.24701	−	0.906005i
$170$	−0.372012	−	1.14493i	−0.0285320	−	0.0878124i
$171$	1.05158	+	3.23642i	0.0804160	+	0.247495i
$172$	−8.64659	−	6.28212i	−0.659296	−	0.479007i
$173$	−8.63927	+	6.27680i	−0.656832	+	0.477216i	−0.865591	−	0.500751i	$-0.833057\pi$
$173$	−8.63927	+	6.27680i	−0.656832	+	0.477216i	0.208760	+	0.977967i	$0.433057\pi$
$174$	3.91919	−	12.0620i	0.297113	−	0.914420i
$175$	−21.4615			−1.62234
$176$	−0.170593	+	3.31223i	−0.0128589	+	0.249669i
$177$	3.99308			0.300139
$178$	2.36080	−	7.26578i	0.176949	−	0.544593i
$179$	8.37161	−	6.08233i	0.625724	−	0.454615i	−0.229192	−	0.973381i	$-0.573609\pi$
$179$	8.37161	−	6.08233i	0.625724	−	0.454615i	0.854916	+	0.518766i	$0.173609\pi$
$180$	−0.726972	−	0.528176i	−0.0541853	−	0.0393679i
$181$	−7.17826	−	22.0924i	−0.533556	−	1.64212i	−0.746748	−	0.665107i	$-0.768386\pi$
$181$	−7.17826	−	22.0924i	−0.533556	−	1.64212i	0.213192	−	0.977010i	$-0.431614\pi$
$182$	−7.73177	−	23.7959i	−0.573117	−	1.76387i
$183$	10.3807	+	7.54200i	0.767362	+	0.557521i
$184$	−5.55929	+	4.03906i	−0.409837	+	0.297764i
$185$	0.327874	−	1.00909i	0.0241058	−	0.0741900i
$186$	−15.9096			−1.16655
$187$	−0.777738	+	15.1006i	−0.0568738	+	1.10426i
$188$	−10.3380			−0.753978
$189$	1.37163	−	4.22144i	0.0997713	−	0.307064i
$190$	0.213629	−	0.155210i	0.0154983	−	0.0112601i
$191$	−2.72327	−	1.97857i	−0.197049	−	0.143164i	0.484886	−	0.874577i	$-0.338861\pi$
$191$	−2.72327	−	1.97857i	−0.197049	−	0.143164i	−0.681935	+	0.731413i	$0.738861\pi$
$192$	0.781939	+	2.40656i	0.0564316	+	0.173679i
$193$	2.10922	+	6.49152i	0.151825	+	0.467270i	0.997825	−	0.0659127i	$-0.0209959\pi$
$193$	2.10922	+	6.49152i	0.151825	+	0.467270i	−0.846000	+	0.533183i	$0.820996\pi$
$194$	8.92351	+	6.48331i	0.640670	+	0.465474i
$195$	−3.10712	+	2.25745i	−0.222505	+	0.161660i
$196$	3.69234	−	11.3639i	0.263739	−	0.811705i
$197$	−5.08696			−0.362431			−0.181216	−	0.983443i	$-0.558003\pi$
$197$	−5.08696			−0.362431			−0.181216	+	0.983443i	$0.558003\pi$
$198$	6.15553	+	9.46001i	0.437455	+	0.672294i
$199$	7.94291			0.563058			0.281529	−	0.959553i	$-0.409158\pi$
$199$	7.94291			0.563058			0.281529	+	0.959553i	$0.409158\pi$
$200$	1.52354	−	4.68897i	0.107730	−	0.331560i
$201$	30.2169	−	21.9539i	2.13133	−	1.54851i
$202$	3.13032	+	2.27431i	0.220249	+	0.160020i
$203$	−6.74210	−	20.7500i	−0.473203	−	1.45637i
$204$	3.56488	+	10.9716i	0.249592	+	0.768164i
$205$	0.133517	+	0.0970058i	0.00932524	+	0.00677518i
$206$	−2.87689	+	2.09019i	−0.200443	+	0.145630i
$207$	−7.22608	+	22.2396i	−0.502247	+	1.54576i
$208$	5.74787			0.398543
$209$	−3.20284	+	0.861293i	−0.221545	+	0.0595769i
$210$	−2.90859			−0.200712
$211$	0.277596	−	0.854352i	0.0191105	−	0.0588160i	−0.941046	−	0.338277i	$-0.890156\pi$
$211$	0.277596	−	0.854352i	0.0191105	−	0.0588160i	0.960157	+	0.279461i	$0.0901558\pi$
$212$	−11.3764	+	8.26543i	−0.781333	+	0.567672i
$213$	5.52467	+	4.01391i	0.378544	+	0.275028i
$214$	0.514994	+	1.58499i	0.0352043	+	0.108348i
$215$	0.872111	+	2.68408i	0.0594775	+	0.183053i
$216$	0.824940	+	0.599354i	0.0561300	+	0.0407809i
$217$	−22.1419	+	16.0870i	−1.50309	+	1.09206i
$218$	2.99223	−	9.20914i	0.202660	−	0.623722i
$219$	16.4067			1.10866
$220$	0.550537	−	0.681111i	0.0371172	−	0.0459205i
$221$	26.2047			1.76272
$222$	−3.14192	+	9.66985i	−0.210872	+	0.648998i
$223$	−2.01279	+	1.46238i	−0.134787	+	0.0979281i	−0.653136	−	0.757241i	$-0.726547\pi$
$223$	−2.01279	+	1.46238i	−0.134787	+	0.0979281i	0.518349	+	0.855169i	$0.326547\pi$
$224$	3.52166	+	2.55863i	0.235301	+	0.170956i
$225$	−5.18456	−	15.9564i	−0.345637	−	1.06376i
$226$	3.43602	+	10.5750i	0.228560	+	0.703437i
$227$	−18.0892	−	13.1425i	−1.20062	−	0.872301i	−0.206274	−	0.978494i	$-0.566134\pi$
$227$	−18.0892	−	13.1425i	−1.20062	−	0.872301i	−0.994345	+	0.106193i	$0.966134\pi$
$228$	−2.04714	+	1.48734i	−0.135575	+	0.0985013i
$229$	4.65007	−	14.3114i	0.307285	−	0.945726i	−0.671530	−	0.740978i	$-0.734362\pi$
$229$	4.65007	−	14.3114i	0.307285	−	0.945726i	0.978815	−	0.204748i	$-0.0656376\pi$
$230$	1.81453			0.119647
$231$	34.1176	+	13.0612i	2.24477	+	0.859367i
$232$	5.01214			0.329063
$233$	−0.318121	+	0.979076i	−0.0208408	+	0.0641414i	−0.960936	−	0.276771i	$-0.910736\pi$
$233$	−0.318121	+	0.979076i	−0.0208408	+	0.0641414i	0.940095	+	0.340912i	$0.110736\pi$
$234$	15.8242	−	11.4970i	1.03446	−	0.751582i
$235$	2.20850	+	1.60457i	0.144067	+	0.104671i
$236$	0.487641	+	1.50080i	0.0317427	+	0.0976940i
$237$	−3.84421	−	11.8313i	−0.249709	−	0.768524i
$238$	16.0553	+	11.6649i	1.04071	+	0.756122i
$239$	−12.0949	+	8.78746i	−0.782354	+	0.568414i	−0.905685	−	0.423952i	$-0.860642\pi$
$239$	−12.0949	+	8.78746i	−0.782354	+	0.568414i	0.123331	+	0.992366i	$0.460642\pi$
$240$	0.206479	−	0.635476i	0.0133281	−	0.0410198i
$241$	15.6439			1.00771			0.503857	−	0.863787i	$-0.331914\pi$
$241$	15.6439			1.00771			0.503857	+	0.863787i	$0.331914\pi$
$242$	−9.51635	+	5.51717i	−0.611734	+	0.354657i
$243$	−22.3628			−1.43457
$244$	−1.56697	+	4.82262i	−0.100315	+	0.308737i
$245$	−2.55258	+	1.85456i	−0.163078	+	0.118483i
$246$	−1.27946	−	0.929580i	−0.0815752	−	0.0592678i
$247$	1.77619	+	5.46655i	0.113016	+	0.347828i
$248$	−1.94290	−	5.97963i	−0.123374	−	0.379707i
$249$	18.1092	+	13.1571i	1.14762	+	0.833797i
$250$	−2.12139	+	1.54128i	−0.134169	+	0.0974792i
$251$	3.90138	−	12.0072i	0.246253	−	0.757889i	−0.749175	−	0.662373i	$-0.769550\pi$
$251$	3.90138	−	12.0072i	0.246253	−	0.757889i	0.995428	−	0.0955169i	$-0.0304504\pi$
$252$	14.8132			0.933141
$253$	−21.2843	−	8.14829i	−1.33814	−	0.512278i
$254$	0.315762			0.0198127
$255$	0.941341	−	2.89715i	0.0589491	−	0.181427i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	0.538155	+	0.390992i	0.0335692	+	0.0243894i	0.604443	−	0.796648i	$-0.293396\pi$
$257$	0.538155	+	0.390992i	0.0335692	+	0.0243894i	−0.570874	+	0.821038i	$0.693396\pi$
$258$	−8.35719	−	25.7208i	−0.520296	−	1.60131i
$259$	5.40498	+	16.6348i	0.335849	+	1.03364i
$260$	−1.22791	−	0.892130i	−0.0761518	−	0.0553275i
$261$	13.7987	−	10.0254i	0.854120	−	0.620555i
$262$	1.21110	−	3.72738i	0.0748219	−	0.230278i
$263$	15.1341			0.933211			0.466606	−	0.884465i	$-0.345477\pi$
$263$	15.1341			0.933211			0.466606	+	0.884465i	$0.345477\pi$
$264$	−5.27564	+	6.52689i	−0.324693	+	0.401702i
$265$	3.71320			0.228100
$266$	−1.34515	+	4.13996i	−0.0824766	+	0.253837i
$267$	15.6396	−	11.3628i	0.957125	−	0.695392i
$268$	11.9415	+	8.67601i	0.729443	+	0.529972i
$269$	−6.62991	−	20.4048i	−0.404233	−	1.24410i	−0.921534	−	0.388297i	$-0.873064\pi$
$269$	−6.62991	−	20.4048i	−0.404233	−	1.24410i	0.517302	−	0.855803i	$-0.326936\pi$
$270$	−0.0832049	−	0.256078i	−0.00506369	−	0.0155844i
$271$	−8.46068	−	6.14704i	−0.513950	−	0.373406i	0.300370	−	0.953823i	$-0.402890\pi$
$271$	−8.46068	−	6.14704i	−0.513950	−	0.373406i	−0.814320	+	0.580416i	$0.802890\pi$
$272$	−3.68833	+	2.67973i	−0.223638	+	0.162482i
$273$	19.5645	−	60.2135i	1.18410	−	3.64429i
$274$	−12.4393			−0.751485
$275$	15.7909	−	4.24641i	0.952225	−	0.256068i
$276$	−17.3881			−1.04664
$277$	−7.77581	+	23.9315i	−0.467203	+	1.43790i	0.388987	+	0.921243i	$0.372825\pi$
$277$	−7.77581	+	23.9315i	−0.467203	+	1.43790i	−0.856190	+	0.516661i	$0.827175\pi$
$278$	−5.17472	+	3.75966i	−0.310359	+	0.225489i
$279$	−17.3095	−	12.5761i	−1.03629	−	0.752910i
$280$	−0.355201	−	1.09320i	−0.0212273	−	0.0653309i
$281$	5.79892	+	17.8472i	0.345935	+	1.06468i	0.961082	+	0.276265i	$0.0890967\pi$
$281$	5.79892	+	17.8472i	0.345935	+	1.06468i	−0.615147	+	0.788413i	$0.710903\pi$
$282$	−21.1634	−	15.3761i	−1.26026	−	0.915635i
$283$	22.7450	−	16.5252i	1.35205	−	0.982320i	0.353140	−	0.935570i	$-0.385114\pi$
$283$	22.7450	−	16.5252i	1.35205	−	0.982320i	0.998907	−	0.0467493i	$-0.0148862\pi$
$284$	−0.833950	+	2.56664i	−0.0494859	+	0.152302i
$285$	0.668179			0.0395795
$286$	10.3972	+	15.9787i	0.614797	+	0.944838i
$287$	−2.72061			−0.160593
$288$	−1.05158	+	3.23642i	−0.0619647	+	0.190708i
$289$	−3.06190	+	2.22460i	−0.180112	+	0.130859i
$290$	−1.07074	−	0.777936i	−0.0628759	−	0.0456820i
$291$	8.62484	+	26.5445i	0.505597	+	1.55607i
$292$	2.00361	+	6.16648i	0.117253	+	0.360866i
$293$	3.66782	+	2.66483i	0.214276	+	0.155681i	0.689746	−	0.724051i	$-0.257722\pi$
$293$	3.66782	+	2.66483i	0.214276	+	0.155681i	−0.475470	+	0.879732i	$0.657722\pi$
$294$	24.4607	−	17.7717i	1.42657	−	1.03647i
$295$	0.128766	−	0.396302i	0.00749706	−	0.0230736i
$296$	−4.01812			−0.233548
$297$	−0.173951	+	3.37743i	−0.0100936	+	0.195978i
$298$	−10.2635			−0.594550
$299$	−12.2054	+	37.5643i	−0.705856	+	2.17240i
$300$	10.0930	−	7.33298i	0.582718	−	0.423370i
$301$	−37.6387	−	27.3461i	−2.16946	−	1.57620i
$302$	4.24185	+	13.0551i	0.244091	+	0.751235i
$303$	3.02555	+	9.31169i	0.173813	+	0.534943i
$304$	−0.809017	−	0.587785i	−0.0464003	−	0.0337118i
$305$	1.08327	−	0.787042i	0.0620279	−	0.0450659i
$306$	−4.79416	+	14.7549i	−0.274064	+	0.843482i
$307$	8.07536			0.460885			0.230442	−	0.973086i	$-0.425983\pi$
$307$	8.07536			0.460885			0.230442	+	0.973086i	$0.425983\pi$
$308$	−0.742592	+	14.4182i	−0.0423131	+	0.821552i
$309$	−8.99822			−0.511891
$310$	−0.513041	+	1.57898i	−0.0291388	+	0.0896800i
$311$	3.29396	−	2.39320i	0.186783	−	0.135706i	−0.490464	−	0.871461i	$-0.663173\pi$
$311$	3.29396	−	2.39320i	0.186783	−	0.135706i	0.677247	+	0.735755i	$0.263173\pi$
$312$	11.7667	+	8.54903i	0.666160	+	0.483993i
$313$	4.02926	+	12.4008i	0.227747	+	0.700934i	0.998001	+	0.0631965i	$0.0201295\pi$
$313$	4.02926	+	12.4008i	0.227747	+	0.700934i	−0.770254	+	0.637737i	$0.779871\pi$
$314$	−2.03088	−	6.25042i	−0.114609	−	0.352732i
$315$	−3.16452	−	2.29916i	−0.178300	−	0.129543i
$316$	3.97733	−	2.88970i	0.223743	−	0.162558i
$317$	−6.11544	+	18.8214i	−0.343477	+	1.05711i	0.618916	+	0.785457i	$0.287572\pi$
$317$	−6.11544	+	18.8214i	−0.343477	+	1.05711i	−0.962394	+	0.271658i	$0.912428\pi$
$318$	−35.5826			−1.99537
$319$	9.06631	+	13.9334i	0.507616	+	0.780120i
$320$	0.264060			0.0147614
$321$	−1.30315	+	4.01067i	−0.0727345	+	0.223854i
$322$	−24.1997	+	17.5821i	−1.34859	+	0.979811i
$323$	−3.68833	−	2.67973i	−0.205224	−	0.149104i
$324$	−2.35740	−	7.25533i	−0.130967	−	0.403074i
$325$	−8.75710	−	26.9516i	−0.485757	−	1.49501i
$326$	−15.0249	−	10.9162i	−0.832154	−	0.604595i
$327$	19.8226	−	14.4020i	1.09619	−	0.796432i
$328$	0.193134	−	0.594406i	0.0106641	−	0.0328206i
$329$	−45.0015			−2.48101
$330$	2.14007	−	0.575498i	0.117807	−	0.0316801i
$331$	27.5340			1.51340			0.756702	−	0.653760i	$-0.226809\pi$
$331$	27.5340			1.51340			0.756702	+	0.653760i	$0.226809\pi$
$332$	−2.73359	+	8.41312i	−0.150025	+	0.461730i
$333$	−11.0621	+	8.03710i	−0.606201	+	0.440431i
$334$	−13.2379	−	9.61786i	−0.724343	−	0.526266i
$335$	−1.20444	−	3.70689i	−0.0658057	−	0.202529i
$336$	3.40379	+	10.4758i	0.185692	+	0.571501i
$337$	−0.190798	−	0.138623i	−0.0103935	−	0.00755129i	0.582576	−	0.812776i	$-0.302045\pi$
$337$	−0.190798	−	0.138623i	−0.0103935	−	0.00755129i	−0.592970	+	0.805225i	$0.702045\pi$
$338$	16.2111	−	11.7781i	0.881769	−	0.640642i
$339$	−8.69453	+	26.7590i	−0.472222	+	1.45335i
$340$	1.20385			0.0652882
$341$	13.1085	−	16.2175i	0.709864	−	0.878226i
$342$	−3.40297			−0.184012
$343$	6.65673	−	20.4873i	0.359430	−	1.10621i
$344$	8.64659	−	6.28212i	0.466193	−	0.338709i
$345$	3.71460	+	2.69882i	0.199988	+	0.145299i
$346$	−3.29991	−	10.1561i	−0.177404	−	0.545994i
$347$	2.22346	+	6.84309i	0.119361	+	0.367356i	0.992832	−	0.119521i	$-0.0381359\pi$
$347$	2.22346	+	6.84309i	0.119361	+	0.367356i	−0.873470	+	0.486877i	$0.838136\pi$
$348$	10.2606	+	7.45474i	0.550025	+	0.399616i
$349$	−1.11145	+	0.807517i	−0.0594947	+	0.0432254i	−0.617135	−	0.786857i	$-0.711707\pi$
$349$	−1.11145	+	0.807517i	−0.0594947	+	0.0432254i	0.557640	+	0.830083i	$0.311707\pi$
$350$	6.63197	−	20.4111i	0.354494	−	1.09102i
$351$	5.86100			0.312837
$352$	−3.09741	−	1.18578i	−0.165092	−	0.0632023i
$353$	−15.7976			−0.840820			−0.420410	−	0.907334i	$-0.638114\pi$
$353$	−15.7976			−0.840820			−0.420410	+	0.907334i	$0.638114\pi$
$354$	−1.23393	+	3.79765i	−0.0655827	+	0.201843i
$355$	0.576524	−	0.418869i	0.0305987	−	0.0222313i
$356$	6.18064	+	4.49050i	0.327573	+	0.237996i
$357$	15.5180	+	47.7594i	0.821297	+	2.52769i
$358$	3.19767	+	9.84142i	0.169002	+	0.520135i
$359$	−2.21837	−	1.61174i	−0.117081	−	0.0850644i	0.527704	−	0.849428i	$-0.323053\pi$
$359$	−2.21837	−	1.61174i	−0.117081	−	0.0850644i	−0.644785	+	0.764364i	$0.723053\pi$
$360$	0.726972	−	0.528176i	0.0383148	−	0.0278373i
$361$	0.309017	−	0.951057i	0.0162641	−	0.0500556i
$362$	23.2293			1.22091
$363$	−27.6872	−	2.85958i	−1.45320	−	0.150089i
$364$	25.0205			1.31143
$365$	0.529073	−	1.62832i	0.0276929	−	0.0852301i
$366$	−10.3807	+	7.54200i	−0.542607	+	0.394227i
$367$	11.1812	+	8.12360i	0.583652	+	0.424048i	0.840039	−	0.542526i	$-0.182532\pi$
$367$	11.1812	+	8.12360i	0.583652	+	0.424048i	−0.256387	+	0.966574i	$0.582532\pi$
$368$	−2.12346	−	6.53534i	−0.110693	−	0.340678i
$369$	−0.657231	−	2.02275i	−0.0342141	−	0.105300i
$370$	0.858385	+	0.623654i	0.0446253	+	0.0324222i
$371$	−49.5215	+	35.9795i	−2.57103	+	1.86796i
$372$	4.91633	−	15.1309i	0.254900	−	0.784501i
$373$	−4.21399			−0.218192			−0.109096	−	0.994031i	$-0.534796\pi$
$373$	−4.21399			−0.218192			−0.109096	+	0.994031i	$0.534796\pi$
$374$	−14.1212	−	5.40600i	−0.730187	−	0.279538i
$375$	−6.63520			−0.342640
$376$	3.19463	−	9.83205i	0.164750	−	0.507049i
$377$	23.3071	−	16.9336i	1.20038	−	0.872125i
$378$	3.59097	+	2.60899i	0.184700	+	0.134192i
$379$	−4.99505	−	15.3732i	−0.256578	−	0.789667i	−0.993515	−	0.113705i	$-0.963728\pi$
$379$	−4.99505	−	15.3732i	−0.256578	−	0.789667i	0.736936	−	0.675962i	$-0.236272\pi$
$380$	0.0815989	+	0.251136i	0.00418594	+	0.0128830i
$381$	0.646411	+	0.469645i	0.0331166	+	0.0240606i
$382$	2.72327	−	1.97857i	0.139334	−	0.101232i
$383$	6.82037	−	20.9909i	0.348504	−	1.07259i	−0.611176	−	0.791494i	$-0.709303\pi$
$383$	6.82037	−	20.9909i	0.348504	−	1.07259i	0.959681	−	0.281092i	$-0.0906966\pi$
$384$	−2.53041			−0.129129
$385$	2.39649	−	2.96488i	0.122136	−	0.151104i
$386$	−6.82559			−0.347413
$387$	11.2390	−	34.5901i	0.571311	−	1.75831i
$388$	−8.92351	+	6.48331i	−0.453022	+	0.329140i
$389$	−18.7282	−	13.6068i	−0.949559	−	0.689895i	0.00114386	−	0.999999i	$-0.499636\pi$
$389$	−18.7282	−	13.6068i	−0.949559	−	0.689895i	−0.950702	+	0.310105i	$0.899636\pi$
$390$	−1.18681	−	3.65264i	−0.0600966	−	0.184958i
$391$	−9.68092	−	29.7948i	−0.489585	−	1.50679i
$392$	9.66668	+	7.02326i	0.488241	+	0.354728i
$393$	8.02316	−	5.82917i	0.404715	−	0.294043i
$394$	1.57196	−	4.83799i	0.0791941	−	0.243734i
$395$	−1.29818			−0.0653188
$396$	−10.8992	+	2.93096i	−0.547704	+	0.147286i
$397$	−33.7441			−1.69357			−0.846784	−	0.531936i	$-0.821465\pi$
$397$	−33.7441			−1.69357			−0.846784	+	0.531936i	$0.821465\pi$
$398$	−2.45449	+	7.55415i	−0.123033	+	0.378656i
$399$	−8.91123	+	6.47439i	−0.446120	+	0.324125i
$400$	3.98867	+	2.89794i	0.199434	+	0.144897i
$401$	−1.43381	−	4.41281i	−0.0716010	−	0.220365i	0.908852	−	0.417119i	$-0.136960\pi$
$401$	−1.43381	−	4.41281i	−0.0716010	−	0.220365i	−0.980453	+	0.196754i	$0.936960\pi$
$402$	11.5418	+	35.5221i	0.575654	+	1.77168i
$403$	−29.2370	−	21.2419i	−1.45640	−	1.05814i
$404$	−3.13032	+	2.27431i	−0.155739	+	0.113151i
$405$	−0.622494	+	1.91584i	−0.0309320	+	0.0951988i
$406$	21.8179			1.08280
$407$	−7.26825	−	11.1701i	−0.360274	−	0.553680i
$408$	−11.5362			−0.571127
$409$	−1.46098	+	4.49644i	−0.0722410	+	0.222335i	−0.980658	−	0.195731i	$-0.937292\pi$
$409$	−1.46098	+	4.49644i	−0.0722410	+	0.222335i	0.908417	+	0.418066i	$0.137292\pi$
$410$	−0.133517	+	0.0970058i	−0.00659394	+	0.00479078i
$411$	−25.4650	−	18.5014i	−1.25610	−	0.912608i
$412$	−1.09888	−	3.38199i	−0.0541377	−	0.166619i
$413$	2.12270	+	6.53301i	0.104451	+	0.321469i
$414$	−18.9181	−	13.7448i	−0.929775	−	0.675521i
$415$	1.88978	−	1.37300i	0.0927655	−	0.0673980i
$416$	−1.77619	+	5.46655i	−0.0870849	+	0.268020i
$417$	−16.1853			−0.792597
$418$	0.170593	−	3.31223i	0.00834397	−	0.162007i
$419$	14.0200			0.684921			0.342460	−	0.939532i	$-0.388740\pi$
$419$	14.0200			0.684921			0.342460	+	0.939532i	$0.388740\pi$
$420$	0.898803	−	2.76623i	0.0438571	−	0.134978i
$421$	−6.49830	+	4.72129i	−0.316708	+	0.230102i	−0.734769	−	0.678317i	$-0.762710\pi$
$421$	−6.49830	+	4.72129i	−0.316708	+	0.230102i	0.418062	+	0.908419i	$0.362710\pi$
$422$	0.726755	+	0.528019i	0.0353779	+	0.0257035i
$423$	−10.8712	−	33.4582i	−0.528577	−	1.62679i
$424$	−4.34539	−	13.3737i	−0.211031	−	0.649486i
$425$	18.1845	+	13.2118i	0.882076	+	0.640866i
$426$	−5.52467	+	4.01391i	−0.267671	+	0.194474i
$427$	−6.82101	+	20.9929i	−0.330092	+	1.01592i
$428$	−1.66656			−0.0805560
$429$	−2.48118	+	48.1747i	−0.119793	+	2.32590i
$430$	−2.82221			−0.136099
$431$	5.75465	−	17.7110i	0.277192	−	0.853109i	−0.711439	−	0.702748i	$-0.751956\pi$
$431$	5.75465	−	17.7110i	0.277192	−	0.853109i	0.988631	−	0.150361i	$-0.0480437\pi$
$432$	−0.824940	+	0.599354i	−0.0396899	+	0.0288364i
$433$	−9.23110	−	6.70679i	−0.443618	−	0.322308i	0.343453	−	0.939170i	$-0.388403\pi$
$433$	−9.23110	−	6.70679i	−0.443618	−	0.322308i	−0.787071	+	0.616862i	$0.788403\pi$
$434$	−8.45746	−	26.0294i	−0.405971	−	1.24945i
$435$	−1.03490	−	3.18510i	−0.0496197	−	0.152714i
$436$	7.83377	+	5.69156i	0.375169	+	0.272576i
$437$	5.55929	−	4.03906i	0.265937	−	0.193215i
$438$	−5.06996	+	15.6037i	−0.242252	+	0.745575i
$439$	7.72154			0.368529			0.184264	−	0.982877i	$-0.441010\pi$
$439$	7.72154			0.368529			0.184264	+	0.982877i	$0.441010\pi$
$440$	0.477650	+	0.734066i	0.0227711	+	0.0349952i
$441$	40.6610			1.93624
$442$	−8.09770	+	24.9222i	−0.385168	+	1.18543i
$443$	12.3602	−	8.98020i	0.587250	−	0.426662i	−0.254080	−	0.967183i	$-0.581773\pi$
$443$	12.3602	−	8.98020i	0.587250	−	0.426662i	0.841331	+	0.540521i	$0.181773\pi$
$444$	−8.22567	−	5.97630i	−0.390373	−	0.283622i
$445$	−0.623391	−	1.91860i	−0.0295516	−	0.0909503i
$446$	−0.768818	−	2.36618i	−0.0364046	−	0.112042i
$447$	−21.0109	−	15.2653i	−0.993781	−	0.722024i
$448$	−3.52166	+	2.55863i	−0.166383	+	0.120884i
$449$	−3.84733	+	11.8409i	−0.181567	+	0.558804i	−0.999872	−	0.0159787i	$-0.994914\pi$
$449$	−3.84733	+	11.8409i	−0.181567	+	0.558804i	0.818306	+	0.574783i	$0.194914\pi$
$450$	16.7776			0.790902
$451$	2.00176	−	0.538305i	0.0942592	−	0.0253478i
$452$	−11.1192			−0.523003
$453$	−10.7336	+	33.0347i	−0.504310	+	1.55211i
$454$	18.0892	−	13.1425i	0.848966	−	0.616810i
$455$	−5.34511	−	3.88345i	−0.250582	−	0.182059i
$456$	−0.781939	−	2.40656i	−0.0366177	−	0.112698i
$457$	0.0264727	+	0.0814747i	0.00123834	+	0.00381122i	0.951674	−	0.307111i	$-0.0993622\pi$
$457$	0.0264727	+	0.0814747i	0.00123834	+	0.00381122i	−0.950435	+	0.310922i	$0.899362\pi$
$458$	12.1740	+	8.84495i	0.568855	+	0.413297i
$459$	−3.76092	+	2.73247i	−0.175545	+	0.127541i
$460$	−0.560721	+	1.72572i	−0.0261437	+	0.0804621i
$461$	−6.62337			−0.308481			−0.154241	−	0.988033i	$-0.549293\pi$
$461$	−6.62337			−0.308481			−0.154241	+	0.988033i	$0.549293\pi$
$462$	−22.9649	+	28.4116i	−1.06842	+	1.32183i
$463$	3.97213			0.184600			0.0923002	−	0.995731i	$-0.470578\pi$
$463$	3.97213			0.184600			0.0923002	+	0.995731i	$0.470578\pi$
$464$	−1.54884	+	4.76683i	−0.0719029	+	0.221295i
$465$	−3.39874	+	2.46933i	−0.157613	+	0.114513i
$466$	−0.832852	−	0.605102i	−0.0385811	−	0.0280308i
$467$	0.930542	+	2.86391i	0.0430603	+	0.132526i	0.970275	−	0.242003i	$-0.0778044\pi$
$467$	0.930542	+	2.86391i	0.0430603	+	0.132526i	−0.927215	+	0.374529i	$0.877804\pi$
$468$	6.04432	+	18.6025i	0.279399	+	0.859902i
$469$	51.9814	+	37.7667i	2.40028	+	1.74391i
$470$	−2.20850	+	1.60457i	−0.101871	+	0.0740133i
$471$	5.13897	−	15.8161i	0.236791	−	0.728768i
$472$	−1.57804			−0.0726351
$473$	33.1044	+	12.6734i	1.52214	+	0.582721i
$474$	12.4401			0.571394
$475$	−1.52354	+	4.68897i	−0.0699047	+	0.215145i
$476$	−16.0553	+	11.6649i	−0.735895	+	0.534659i
$477$	−38.7135	−	28.1270i	−1.77257	−	1.28785i
$478$	−4.61984	−	14.2184i	−0.211307	−	0.650335i
$479$	9.20983	+	28.3449i	0.420808	+	1.29511i	0.906952	+	0.421234i	$0.138403\pi$
$479$	9.20983	+	28.3449i	0.420808	+	1.29511i	−0.486144	+	0.873879i	$0.661597\pi$
$480$	0.540568	+	0.392746i	0.0246734	+	0.0179263i
$481$	−18.6848	+	13.5753i	−0.851952	+	0.618979i
$482$	−4.83424	+	14.8783i	−0.220194	+	0.677686i
$483$	−75.6907			−3.44404
$484$	−2.30642	−	10.7555i	−0.104837	−	0.488886i
$485$	2.91259			0.132254
$486$	6.91048	−	21.2683i	0.313466	−	0.964748i
$487$	−14.9989	+	10.8973i	−0.679665	+	0.493806i	−0.873247	−	0.487279i	$-0.837990\pi$
$487$	−14.9989	+	10.8973i	−0.679665	+	0.493806i	0.193582	+	0.981084i	$0.437990\pi$
$488$	−4.10237	−	2.98055i	−0.185706	−	0.134923i
$489$	−14.5220	−	44.6943i	−0.656710	−	2.02114i
$490$	−0.974999	−	3.00074i	−0.0440460	−	0.135560i
$491$	0.304704	+	0.221380i	0.0137511	+	0.00999075i	0.594640	−	0.803992i	$-0.297295\pi$
$491$	0.304704	+	0.221380i	0.0137511	+	0.00999075i	−0.580888	+	0.813983i	$0.697295\pi$
$492$	1.27946	−	0.929580i	0.0576824	−	0.0419087i
$493$	−7.06119	+	21.7321i	−0.318020	+	0.978764i
$494$	−5.74787			−0.258609
$495$	2.78329	+	1.06553i	0.125100	+	0.0478919i
$496$	6.28735			0.282311
$497$	−3.63019	+	11.1726i	−0.162836	+	0.501159i
$498$	−18.1092	+	13.1571i	−0.811492	+	0.589584i
$499$	15.1807	+	11.0294i	0.679583	+	0.493746i	0.873219	−	0.487328i	$-0.162028\pi$
$499$	15.1807	+	11.0294i	0.679583	+	0.493746i	−0.193637	+	0.981073i	$0.562028\pi$
$500$	−0.810299	−	2.49385i	−0.0362377	−	0.111528i
$501$	−12.7948	−	39.3783i	−0.571629	−	1.75929i
$502$	10.2140	+	7.42087i	0.455871	+	0.331210i
$503$	21.1766	−	15.3857i	0.944216	−	0.686013i	−0.00521566	−	0.999986i	$-0.501660\pi$
$503$	21.1766	−	15.3857i	0.944216	−	0.686013i	0.949432	+	0.313973i	$0.101660\pi$
$504$	−4.57752	+	14.0882i	−0.203899	+	0.627536i
$505$	1.02172			0.0454661
$506$	14.3267	−	17.7247i	0.636900	−	0.787957i
$507$	50.7045			2.25186
$508$	−0.0975759	+	0.300308i	−0.00432923	+	0.0133240i
$509$	−10.9595	+	7.96255i	−0.485772	+	0.352934i	−0.803556	−	0.595229i	$-0.797061\pi$
$509$	−10.9595	+	7.96255i	−0.485772	+	0.352934i	0.317784	+	0.948163i	$0.397061\pi$
$510$	2.46446	+	1.79054i	0.109128	+	0.0792863i
$511$	8.72174	+	26.8428i	0.385827	+	1.18745i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−0.824940	−	0.599354i	−0.0364220	−	0.0264621i
$514$	−0.538155	+	0.390992i	−0.0237370	+	0.0172459i
$515$	−0.290169	+	0.893047i	−0.0127864	+	0.0393524i
$516$	27.0444			1.19057
$517$	33.1110	−	8.90407i	1.45622	−	0.391601i
$518$	−17.4909			−0.768506
$519$	8.35012	−	25.6990i	0.366529	−	1.12806i
$520$	1.22791	−	0.892130i	0.0538475	−	0.0391225i
$521$	−7.74439	−	5.62663i	−0.339288	−	0.246507i	0.405073	−	0.914284i	$-0.367246\pi$
$521$	−7.74439	−	5.62663i	−0.339288	−	0.246507i	−0.744361	+	0.667777i	$0.767246\pi$
$522$	5.27065	+	16.2214i	0.230690	+	0.709991i
$523$	9.34626	+	28.7648i	0.408683	+	1.25780i	0.917780	+	0.397089i	$0.129980\pi$
$523$	9.34626	+	28.7648i	0.408683	+	1.25780i	−0.509097	+	0.860709i	$0.670020\pi$
$524$	3.17070	+	2.30365i	0.138512	+	0.100635i
$525$	43.9348	−	31.9205i	1.91747	−	1.39313i
$526$	−4.67671	+	14.3934i	−0.203914	+	0.627583i
$527$	28.6642			1.24863
$528$	−4.57718	−	7.03435i	−0.199196	−	0.306131i
$529$	24.2198			1.05303
$530$	−1.14744	+	3.53146i	−0.0498417	+	0.153397i
$531$	−4.34444	+	3.15642i	−0.188533	+	0.136977i
$532$	−3.52166	−	2.55863i	−0.152683	−	0.110931i
$533$	−1.11011	−	3.41657i	−0.0480843	−	0.147988i
$534$	5.97378	+	18.3854i	0.258511	+	0.795614i
$535$	0.356024	+	0.258667i	0.0153923	+	0.0111831i
$536$	−11.9415	+	8.67601i	−0.515794	+	0.374746i
$537$	−8.09142	+	24.9028i	−0.349170	+	1.07464i
$538$	21.4548			0.924983
$539$	−2.03836	+	39.5768i	−0.0877984	+	1.70469i
$540$	0.269257			0.0115870
$541$	4.89514	−	15.0657i	0.210458	−	0.647724i	−0.788987	−	0.614410i	$-0.789394\pi$
$541$	4.89514	−	15.0657i	0.210458	−	0.647724i	0.999445	−	0.0333137i	$-0.0106060\pi$
$542$	8.46068	−	6.14704i	0.363417	−	0.264038i
$543$	47.5538	+	34.5499i	2.04073	+	1.48268i
$544$	−1.40882	−	4.33589i	−0.0604025	−	0.185900i
$545$	−0.790128	−	2.43176i	−0.0338454	−	0.104165i
$546$	51.2206	+	37.2140i	2.19204	+	1.59261i
$547$	14.4113	−	10.4704i	0.616184	−	0.447684i	−0.235403	−	0.971898i	$-0.575641\pi$
$547$	14.4113	−	10.4704i	0.616184	−	0.447684i	0.851587	+	0.524214i	$0.175641\pi$
$548$	3.84395	−	11.8305i	0.164205	−	0.505372i
$549$	−17.2558			−0.736460
$550$	−0.841070	+	16.3302i	−0.0358633	+	0.696323i
$551$	−5.01214			−0.213524
$552$	5.37323	−	16.5371i	0.228700	−	0.703865i
$553$	17.3134	−	12.5789i	0.736239	−	0.534909i
$554$	−20.3573	−	14.7905i	−0.864901	−	0.628387i
$555$	0.829656	+	2.55342i	0.0352169	+	0.108387i
$556$	−1.97657	−	6.08325i	−0.0838252	−	0.257987i
$557$	18.8685	+	13.7088i	0.799485	+	0.580860i	0.910763	−	0.412929i	$-0.135494\pi$
$557$	18.8685	+	13.7088i	0.799485	+	0.580860i	−0.111278	+	0.993789i	$0.535494\pi$
$558$	17.3095	−	12.5761i	0.732768	−	0.532387i
$559$	18.9835	−	58.4253i	0.802918	−	2.47113i
$560$	1.14945			0.0485733
$561$	−20.8675	−	32.0698i	−0.881026	−	1.35399i
$562$	−18.7657			−0.791584
$563$	8.77222	−	26.9981i	0.369705	−	1.13783i	−0.577277	−	0.816548i	$-0.695885\pi$
$563$	8.77222	−	26.9981i	0.369705	−	1.13783i	0.946982	−	0.321286i	$-0.104115\pi$
$564$	21.1634	−	15.3761i	0.891141	−	0.647452i
$565$	2.37538	+	1.72581i	0.0999329	+	0.0726055i
$566$	8.68780	+	26.7383i	0.365175	+	1.12389i
$567$	−10.2618	−	31.5825i	−0.430954	−	1.32634i
$568$	−2.18331	−	1.58627i	−0.0916097	−	0.0665583i
$569$	−27.3677	+	19.8838i	−1.14731	+	0.833572i	−0.988121	−	0.153676i	$-0.950889\pi$
$569$	−27.3677	+	19.8838i	−1.14731	+	0.833572i	−0.159192	+	0.987248i	$0.550889\pi$
$570$	−0.206479	+	0.635476i	−0.00864844	+	0.0266172i
$571$	−9.69632			−0.405778			−0.202889	−	0.979202i	$-0.565033\pi$
$571$	−9.69632			−0.405778			−0.202889	+	0.979202i	$0.565033\pi$
$572$	−18.4095	+	4.95060i	−0.769740	+	0.206995i
$573$	8.51772			0.355833
$574$	0.840715	−	2.58746i	0.0350908	−	0.107998i
$575$	−27.4088	+	19.9137i	−1.14303	+	0.830458i
$576$	−2.75306	−	2.00022i	−0.114711	−	0.0833423i
$577$	2.57327	+	7.91972i	0.107127	+	0.329702i	0.990224	−	0.139488i	$-0.0445457\pi$
$577$	2.57327	+	7.91972i	0.107127	+	0.329702i	−0.883097	+	0.469191i	$0.844546\pi$
$578$	−1.16954	−	3.59948i	−0.0486465	−	0.149718i
$579$	−13.9730	−	10.1520i	−0.580697	−	0.421901i
$580$	1.07074	−	0.777936i	0.0444600	−	0.0323020i
$581$	−11.8993	+	36.6224i	−0.493667	+	1.51935i
$582$	−27.9106			−1.15693
$583$	29.3178	−	36.2712i	1.21422	−	1.50220i
$584$	−6.48382			−0.268303
$585$	1.59606	−	4.91217i	0.0659891	−	0.203093i
$586$	−3.66782	+	2.66483i	−0.151516	+	0.110083i
$587$	8.88525	+	6.45551i	0.366733	+	0.266447i	0.755855	−	0.654739i	$-0.227221\pi$
$587$	8.88525	+	6.45551i	0.366733	+	0.266447i	−0.389122	+	0.921186i	$0.627221\pi$
$588$	9.34314	+	28.7552i	0.385305	+	1.18585i
$589$	1.94290	+	5.97963i	0.0800558	+	0.246386i
$590$	0.337114	+	0.244928i	0.0138788	+	0.0100835i
$591$	10.4137	−	7.56603i	0.428364	−	0.311225i
$592$	1.24167	−	3.82146i	0.0510322	−	0.157061i
$593$	−5.27579			−0.216651			−0.108325	−	0.994115i	$-0.534549\pi$
$593$	−5.27579			−0.216651			−0.108325	+	0.994115i	$0.534549\pi$
$594$	−3.15837	−	1.20912i	−0.129589	−	0.0496107i
$595$	5.24039			0.214835
$596$	3.17160	−	9.76118i	0.129914	−	0.399834i
$597$	−16.2603	+	11.8138i	−0.665489	+	0.483506i
$598$	−31.9541	−	23.2160i	−1.30670	−	0.949374i
$599$	1.72293	+	5.30263i	0.0703969	+	0.216660i	0.980065	−	0.198676i	$-0.0636642\pi$
$599$	1.72293	+	5.30263i	0.0703969	+	0.216660i	−0.909668	+	0.415336i	$0.863664\pi$
$600$	3.85517	+	11.8650i	0.157387	+	0.484387i
$601$	−19.5817	−	14.2270i	−0.798756	−	0.580330i	0.111793	−	0.993732i	$-0.464341\pi$
$601$	−19.5817	−	14.2270i	−0.798756	−	0.580330i	−0.910549	+	0.413401i	$0.864341\pi$
$602$	37.6387	−	27.3461i	1.53404	−	1.11454i
$603$	−15.5218	+	47.7712i	−0.632096	+	1.94539i
$604$	−13.7269			−0.558540
$605$	−1.17664	+	2.65566i	−0.0478374	+	0.107968i
$606$	−9.79089			−0.397728
$607$	0.550562	−	1.69446i	0.0223466	−	0.0687759i	−0.939261	−	0.343203i	$-0.888488\pi$
$607$	0.550562	−	1.69446i	0.0223466	−	0.0687759i	0.961608	+	0.274427i	$0.0884882\pi$
$608$	0.809017	−	0.587785i	0.0328100	−	0.0238378i
$609$	44.6644	+	32.4506i	1.80989	+	1.31496i
$610$	0.413772	+	1.27346i	0.0167532	+	0.0515609i
$611$	−18.3623	−	56.5134i	−0.742859	−	2.28629i
$612$	−12.5513	−	9.11904i	−0.507355	−	0.368615i
$613$	−26.5866	+	19.3163i	−1.07382	+	0.780178i	−0.976596	−	0.215084i	$-0.930998\pi$
$613$	−26.5866	+	19.3163i	−1.07382	+	0.780178i	−0.0972277	+	0.995262i	$0.530998\pi$
$614$	−2.49542	+	7.68012i	−0.100707	+	0.309944i
$615$	−0.417609			−0.0168396
$616$	−13.4830	−	5.16171i	−0.543247	−	0.207971i
$617$	6.13621			0.247035			0.123517	−	0.992342i	$-0.460583\pi$
$617$	6.13621			0.247035			0.123517	+	0.992342i	$0.460583\pi$
$618$	2.78060	−	8.55782i	0.111852	−	0.344246i
$619$	−23.6600	+	17.1900i	−0.950976	+	0.690924i	−0.951037	−	0.309076i	$-0.899980\pi$
$619$	−23.6600	+	17.1900i	−0.950976	+	0.690924i	6.16107e−5		1.00000i	$0.499980\pi$
$620$	−1.34316	−	0.975863i	−0.0539426	−	0.0391916i
$621$	−2.16525	−	6.66397i	−0.0868887	−	0.267416i
$622$	1.25818	+	3.87228i	0.0504484	+	0.155264i
$623$	26.9044	+	19.5472i	1.07790	+	0.783141i
$624$	−11.7667	+	8.54903i	−0.471046	+	0.342235i
$625$	7.40372	−	22.7863i	0.296149	−	0.911453i
$626$	−13.0390			−0.521142
$627$	5.27564	−	6.52689i	0.210689	−	0.260659i
$628$	6.57208			0.262254
$629$	5.66079	−	17.4221i	0.225710	−	0.694665i
$630$	3.16452	−	2.29916i	0.126077	−	0.0916006i
$631$	33.8879	+	24.6210i	1.34905	+	0.980146i	0.999058	+	0.0433949i	$0.0138174\pi$
$631$	33.8879	+	24.6210i	1.34905	+	0.980146i	0.349997	+	0.936751i	$0.386183\pi$
$632$	1.51921	+	4.67564i	0.0604308	+	0.185987i
$633$	0.702431	+	2.16186i	0.0279191	+	0.0859262i
$634$	−16.0104	−	11.6323i	−0.635856	−	0.461976i
$635$	0.0674559	−	0.0490096i	0.00267690	−	0.00194489i
$636$	10.9956	−	33.8410i	0.436005	−	1.34188i
$637$	68.6795			2.72118
$638$	−16.0531	+	4.31692i	−0.635547	+	0.170909i
$639$	−9.18367			−0.363300
$640$	−0.0815989	+	0.251136i	−0.00322548	+	0.00992701i
$641$	29.7729	−	21.6313i	1.17596	−	0.854384i	0.184248	−	0.982880i	$-0.441015\pi$
$641$	29.7729	−	21.6313i	1.17596	−	0.854384i	0.991710	+	0.128496i	$0.0410149\pi$
$642$	−3.41168	−	2.47873i	−0.134648	−	0.0978277i
$643$	−11.1912	−	34.4431i	−0.441339	−	1.35830i	−0.886449	−	0.462826i	$-0.846835\pi$
$643$	−11.1912	−	34.4431i	−0.441339	−	1.35830i	0.445110	−	0.895476i	$-0.353165\pi$
$644$	−9.24344	−	28.4484i	−0.364243	−	1.12102i
$645$	−5.77747	−	4.19758i	−0.227488	−	0.165279i
$646$	3.68833	−	2.67973i	0.145115	−	0.105432i
$647$	−2.60805	+	8.02675i	−0.102533	+	0.315564i	−0.989144	−	0.146953i	$-0.953053\pi$
$647$	−2.60805	+	8.02675i	−0.102533	+	0.315564i	0.886611	+	0.462517i	$0.153053\pi$
$648$	7.62870			0.299684
$649$	−2.85447	−	4.38683i	−0.112048	−	0.172198i
$650$	28.3386			1.11153
$651$	21.4008	−	65.8650i	0.838764	−	2.58145i
$652$	15.0249	−	10.9162i	0.588422	−	0.427513i
$653$	40.8859	+	29.7054i	1.59999	+	1.16246i	0.887533	+	0.460745i	$0.152418\pi$
$653$	40.8859	+	29.7054i	1.59999	+	1.16246i	0.712457	+	0.701716i	$0.247582\pi$
$654$	7.57157	+	23.3029i	0.296072	+	0.911216i
$655$	−0.319802	−	0.984250i	−0.0124957	−	0.0384578i
$656$	0.505632	+	0.367363i	0.0197416	+	0.0143431i
$657$	−17.8504	+	12.9691i	−0.696409	+	0.505971i
$658$	13.9062	−	42.7990i	0.542121	−	1.66848i
$659$	28.1898			1.09812			0.549060	−	0.835783i	$-0.314986\pi$
$659$	28.1898			1.09812			0.549060	+	0.835783i	$0.314986\pi$
$660$	−0.113987	+	2.21317i	−0.00443692	+	0.0861474i
$661$	40.1390			1.56123			0.780613	−	0.625015i	$-0.214907\pi$
$661$	40.1390			1.56123			0.780613	+	0.625015i	$0.214907\pi$
$662$	−8.50847	+	26.1864i	−0.330691	+	1.01776i
$663$	−53.6448	+	38.9752i	−2.08339	+	1.51367i
$664$	−7.15663	−	5.19959i	−0.277731	−	0.201783i
$665$	0.355201	+	1.09320i	0.0137741	+	0.0423923i
$666$	−4.22536	−	13.0043i	−0.163729	−	0.503907i
$667$	−27.8640	−	20.2444i	−1.07890	−	0.783865i
$668$	13.2379	−	9.61786i	0.512188	−	0.372126i
$669$	1.94542	−	5.98740i	0.0752144	−	0.231486i
$670$	3.89765			0.150580
$671$	0.865044	−	16.7957i	0.0333947	−	0.648391i
$672$	−11.0149			−0.424909
$673$	−4.60260	+	14.1653i	−0.177417	+	0.546034i	−0.999736	−	0.0229938i	$-0.992680\pi$
$673$	−4.60260	+	14.1653i	−0.177417	+	0.546034i	0.822319	+	0.569027i	$0.192680\pi$
$674$	0.190798	−	0.138623i	0.00734928	−	0.00533957i
$675$	4.06718	+	2.95498i	0.156546	+	0.113737i
$676$	6.19210	+	19.0573i	0.238158	+	0.732974i
$677$	−3.57765	−	11.0109i	−0.137500	−	0.423182i	0.858470	−	0.512863i	$-0.171415\pi$
$677$	−3.57765	−	11.0109i	−0.137500	−	0.423182i	−0.995971	+	0.0896813i	$0.971415\pi$
$678$	−22.7626	−	16.5380i	−0.874191	−	0.635137i
$679$	−38.8441	+	28.2219i	−1.49070	+	1.08306i
$680$	−0.372012	+	1.14493i	−0.0142660	+	0.0439062i
$681$	56.5785			2.16809
$682$	11.3730	+	17.4784i	0.435495	+	0.669282i
$683$	−27.6682			−1.05869			−0.529347	−	0.848405i	$-0.677563\pi$
$683$	−27.6682			−1.05869			−0.529347	+	0.848405i	$0.677563\pi$
$684$	1.05158	−	3.23642i	0.0402080	−	0.123748i
$685$	−2.65739	+	1.93071i	−0.101534	+	0.0737685i
$686$	17.4275	+	12.6618i	0.665387	+	0.483432i
$687$	11.7666	+	36.2138i	0.448923	+	1.38164i
$688$	3.30270	+	10.1647i	0.125914	+	0.387525i
$689$	−65.3900	−	47.5086i	−2.49116	−	1.80993i
$690$	−3.71460	+	2.69882i	−0.141413	+	0.102742i
$691$	7.14774	−	21.9985i	0.271913	−	0.836861i	−0.718107	−	0.695933i	$-0.754991\pi$
$691$	7.14774	−	21.9985i	0.271913	−	0.836861i	0.990020	−	0.140929i	$-0.0450088\pi$
$692$	10.6787			0.405944
$693$	−47.4442	+	12.7585i	−1.80225	+	0.484654i
$694$	−7.19525			−0.273128
$695$	−0.521932	+	1.60634i	−0.0197980	+	0.0609320i
$696$	−10.2606	+	7.45474i	−0.388926	+	0.282571i
$697$	2.30519	+	1.67482i	0.0873153	+	0.0634383i
$698$	−0.424537	−	1.30659i	−0.0160690	−	0.0494552i
$699$	−0.804977	−	2.47746i	−0.0304470	−	0.0937063i
$700$	17.3627	+	12.6148i	0.656249	+	0.476793i
$701$	32.9580	−	23.9454i	1.24481	−	0.904405i	0.246897	−	0.969042i	$-0.420589\pi$
$701$	32.9580	−	23.9454i	1.24481	−	0.904405i	0.997909	+	0.0646370i	$0.0205890\pi$
$702$	−1.81115	+	5.57414i	−0.0683574	+	0.210382i
$703$	4.01812			0.151546
$704$	2.08490	−	2.57938i	0.0785774	−	0.0972141i
$705$	−6.90765			−0.260157
$706$	4.88172	−	15.0244i	0.183726	−	0.565450i
$707$	−13.6263	+	9.90010i	−0.512470	+	0.372332i
$708$	−3.23047	−	2.34708i	−0.121409	−	0.0882085i
$709$	−11.9577	−	36.8020i	−0.449080	−	1.38213i	−0.877947	−	0.478759i	$-0.841087\pi$
$709$	−11.9577	−	36.8020i	−0.449080	−	1.38213i	0.428867	−	0.903368i	$-0.358913\pi$
$710$	0.220213	+	0.677745i	0.00826443	+	0.0254353i
$711$	13.5348	+	9.83357i	0.507593	+	0.368788i
$712$	−6.18064	+	4.49050i	−0.231629	+	0.168289i
$713$	−13.3510	+	41.0900i	−0.499997	+	1.53883i
$714$	−50.2172			−1.87933
$715$	4.70119	+	1.79976i	0.175814	+	0.0673070i
$716$	−10.3479			−0.386718
$717$	11.6901	−	35.9784i	0.436574	−	1.34364i
$718$	2.21837	−	1.61174i	0.0827889	−	0.0601496i
$719$	9.91522	+	7.20383i	0.369775	+	0.268658i	0.757118	−	0.653278i	$-0.226607\pi$
$719$	9.91522	+	7.20383i	0.369775	+	0.268658i	−0.387342	+	0.921936i	$0.626607\pi$
$720$	0.277679	+	0.854607i	0.0103485	+	0.0318493i
$721$	−4.78341	−	14.7218i	−0.178144	−	0.548270i
$722$	0.809017	+	0.587785i	0.0301085	+	0.0218751i
$723$	−32.0254	+	23.2678i	−1.19104	+	0.865339i
$724$	−7.17826	+	22.0924i	−0.266778	+	0.821058i
$725$	24.7112			0.917752
$726$	11.2754	−	25.4485i	0.418471	−	0.944481i
$727$	22.4137			0.831276			0.415638	−	0.909530i	$-0.363558\pi$
$727$	22.4137			0.831276			0.415638	+	0.909530i	$0.363558\pi$
$728$	−7.73177	+	23.7959i	−0.286558	+	0.881936i
$729$	27.2646	−	19.8089i	1.00980	−	0.733662i
$730$	1.38513	+	1.00636i	0.0512660	+	0.0372469i
$731$	15.0571	+	46.3410i	0.556907	+	1.71398i
$732$	−3.96506	−	12.2032i	−0.146553	−	0.451044i
$733$	2.70389	+	1.96449i	0.0998706	+	0.0725602i	0.636600	−	0.771194i	$-0.280340\pi$
$733$	2.70389	+	1.96449i	0.0998706	+	0.0725602i	−0.536729	+	0.843755i	$0.680340\pi$
$734$	−11.1812	+	8.12360i	−0.412705	+	0.299847i
$735$	2.46715	−	7.59310i	0.0910021	−	0.280076i
$736$	6.87167			0.253293
$737$	−45.7193	−	17.5027i	−1.68409	−	0.644721i
$738$	2.12684			0.0782902
$739$	9.27571	−	28.5477i	0.341212	−	1.05014i	−0.622368	−	0.782725i	$-0.713829\pi$
$739$	9.27571	−	28.5477i	0.341212	−	1.05014i	0.963580	−	0.267419i	$-0.0861708\pi$
$740$	−0.858385	+	0.623654i	−0.0315549	+	0.0229260i
$741$	−11.7667	−	8.54903i	−0.432261	−	0.314056i
$742$	−18.9155	−	58.2160i	−0.694411	−	2.13718i
$743$	2.30662	+	7.09904i	0.0846216	+	0.260438i	0.984410	−	0.175887i	$-0.0562795\pi$
$743$	2.30662	+	7.09904i	0.0846216	+	0.260438i	−0.899789	+	0.436326i	$0.856279\pi$
$744$	12.8711	+	9.35142i	0.471878	+	0.342840i
$745$	−2.19258	+	1.59300i	−0.0803300	+	0.0583632i
$746$	1.30220	−	4.00774i	0.0476768	−	0.146734i
$747$	−30.1029			−1.10141
$748$	9.50509	−	11.7595i	0.347541	−	0.429969i
$749$	−7.25453			−0.265075
$750$	2.05039	−	6.31045i	0.0748696	−	0.230425i
$751$	−27.5157	+	19.9913i	−1.00406	+	0.729494i	−0.962955	−	0.269661i	$-0.913089\pi$
$751$	−27.5157	+	19.9913i	−1.00406	+	0.729494i	−0.0411072	+	0.999155i	$0.513089\pi$
$752$	8.36364	+	6.07654i	0.304991	+	0.221589i
$753$	9.87210	+	30.3832i	0.359759	+	1.10723i
$754$	8.90252	+	27.3991i	0.324211	+	0.997818i
$755$	2.93246	+	2.13056i	0.106723	+	0.0775390i
$756$	−3.59097	+	2.60899i	−0.130602	+	0.0948881i
$757$	−4.34499	+	13.3725i	−0.157922	+	0.486032i	−0.998445	−	0.0557424i	$-0.982247\pi$
$757$	−4.34499	+	13.3725i	−0.157922	+	0.486032i	0.840524	+	0.541775i	$0.182247\pi$
$758$	16.1643			0.587114
$759$	55.6914	−	14.9763i	2.02147	−	0.543604i
$760$	−0.264060			−0.00957845
$761$	−16.1432	+	49.6836i	−0.585190	+	1.80103i	0.0133185	+	0.999911i	$0.495760\pi$
$761$	−16.1432	+	49.6836i	−0.585190	+	1.80103i	−0.598508	+	0.801117i	$0.704240\pi$
$762$	−0.646411	+	0.469645i	−0.0234170	+	0.0170134i
$763$	34.1004	+	24.7754i	1.23452	+	0.896930i
$764$	1.04020	+	3.20139i	0.0376330	+	0.115822i
$765$	1.26594	+	3.89618i	0.0457703	+	0.140867i
$766$	17.8560	+	12.9731i	0.645162	+	0.468737i
$767$	−7.33808	+	5.33143i	−0.264963	+	0.192507i
$768$	0.781939	−	2.40656i	0.0282158	−	0.0868393i
$769$	−19.2332			−0.693567			−0.346784	−	0.937945i	$-0.612726\pi$
$769$	−19.2332			−0.693567			−0.346784	+	0.937945i	$0.612726\pi$
$770$	2.07921	+	3.19540i	0.0749296	+	0.115154i
$771$	−1.68322			−0.0606196
$772$	2.10922	−	6.49152i	0.0759126	−	0.233635i
$773$	−13.3326	+	9.68670i	−0.479540	+	0.348406i	−0.801148	−	0.598467i	$-0.795777\pi$
$773$	−13.3326	+	9.68670i	−0.479540	+	0.348406i	0.321608	+	0.946873i	$0.395777\pi$
$774$	29.4241	+	21.3779i	1.05763	+	0.768411i
$775$	−9.57902	−	29.4812i	−0.344089	−	1.05900i
$776$	−3.40848	−	10.4902i	−0.122357	−	0.376577i
$777$	−35.8064	−	26.0149i	−1.28455	−	0.933278i
$778$	18.7282	−	13.6068i	0.671439	−	0.487829i
$779$	−0.193134	+	0.594406i	−0.00691976	+	0.0212968i
$780$	3.84061			0.137516
$781$	0.460383	−	8.93880i	0.0164738	−	0.319855i
$782$	31.3281			1.12029
$783$	−1.57932	+	4.86065i	−0.0564403	+	0.173705i
$784$	−9.66668	+	7.02326i	−0.345239	+	0.250831i
$785$	−1.40398	−	1.02005i	−0.0501104	−	0.0364073i
$786$	3.06457	+	9.43179i	0.109310	+	0.336421i
$787$	−13.0828	−	40.2646i	−0.466350	−	1.43528i	−0.857276	−	0.514857i	$-0.827845\pi$
$787$	−13.0828	−	40.2646i	−0.466350	−	1.43528i	0.390926	−	0.920422i	$-0.372155\pi$
$788$	4.11544	+	2.99004i	0.146606	+	0.106516i
$789$	−30.9818	+	22.5096i	−1.10298	+	0.801362i
$790$	0.401161	−	1.23465i	0.0142727	−	0.0439268i
$791$	−48.4019			−1.72097
$792$	0.580523	−	11.2714i	0.0206280	−	0.400513i
$793$	−29.1464			−1.03502
$794$	10.4275	−	32.0926i	0.370058	−	1.13892i
$795$	−7.60146	+	5.52278i	−0.269596	+	0.195873i
$796$	−6.42595	−	4.66872i	−0.227762	−	0.165479i
$797$	9.59745	+	29.5379i	0.339959	+	1.04629i	0.964227	+	0.265077i	$0.0853972\pi$
$797$	9.59745	+	29.5379i	0.339959	+	1.04629i	−0.624268	+	0.781210i	$0.714603\pi$
$798$	−3.40379	−	10.4758i	−0.120493	−	0.370839i
$799$	38.1300	+	27.7031i	1.34894	+	0.980065i
$800$	−3.98867	+	2.89794i	−0.141021	+	0.102458i
$801$	−8.03372	+	24.7252i	−0.283857	+	0.873623i
$802$	4.63991			0.163841
$803$	−11.7284	−	18.0246i	−0.413886	−	0.636073i
$804$	−37.3501			−1.31724
$805$	−2.44082	+	7.51207i	−0.0860276	+	0.264766i
$806$	29.2370	−	21.2419i	1.02983	−	0.748215i
$807$	43.9211	+	31.9106i	1.54610	+	1.12331i
$808$	−1.19568	−	3.67991i	−0.0420638	−	0.129459i
$809$	2.12944	+	6.55374i	0.0748671	+	0.230417i	0.981486	−	0.191533i	$-0.0613458\pi$
$809$	2.12944	+	6.55374i	0.0748671	+	0.230417i	−0.906619	+	0.421950i	$0.861346\pi$
$810$	−1.62971	−	1.18405i	−0.0572622	−	0.0416034i
$811$	−28.2400	+	20.5176i	−0.991641	+	0.720469i	−0.960280	−	0.279039i	$-0.909984\pi$
$811$	−28.2400	+	20.5176i	−0.991641	+	0.720469i	−0.0313611	+	0.999508i	$0.509984\pi$
$812$	−6.74210	+	20.7500i	−0.236601	+	0.728184i
$813$	26.4630			0.928096
$814$	12.8694	−	3.46078i	0.451072	−	0.121300i
$815$	−4.90407			−0.171782
$816$	3.56488	−	10.9716i	0.124796	−	0.384082i
$817$	−8.64659	+	6.28212i	−0.302506	+	0.219783i
$818$	−3.82490	−	2.77895i	−0.133735	−	0.0971639i
$819$	26.3110	+	80.9769i	0.919380	+	2.82956i
$820$	−0.0509990	−	0.156959i	−0.00178096	−	0.00548124i
$821$	22.1236	+	16.0738i	0.772120	+	0.560978i	0.902604	−	0.430473i	$-0.141653\pi$
$821$	22.1236	+	16.0738i	0.772120	+	0.560978i	−0.130484	+	0.991450i	$0.541653\pi$
$822$	25.4650	−	18.5014i	0.888194	−	0.645311i
$823$	−5.65131	+	17.3930i	−0.196992	+	0.606280i	0.802955	+	0.596039i	$0.203260\pi$
$823$	−5.65131	+	17.3930i	−0.196992	+	0.606280i	−0.999948	+	0.0102408i	$0.996740\pi$
$824$	3.55604			0.123880
$825$	−26.0103	+	32.1794i	−0.905564	+	1.12034i
$826$	−6.86922			−0.239011
$827$	5.74040	−	17.6671i	0.199613	−	0.614347i	−0.800278	−	0.599629i	$-0.795315\pi$
$827$	5.74040	−	17.6671i	0.199613	−	0.614347i	0.999892	−	0.0147180i	$-0.00468506\pi$
$828$	18.9181	−	13.7448i	0.657450	−	0.477665i
$829$	−17.3746	−	12.6234i	−0.603445	−	0.438428i	0.243655	−	0.969862i	$-0.421653\pi$
$829$	−17.3746	−	12.6234i	−0.603445	−	0.438428i	−0.847100	+	0.531434i	$0.821653\pi$
$830$	0.721830	+	2.22156i	0.0250551	+	0.0771116i
$831$	−19.6760	−	60.5565i	−0.682552	−	2.10068i
$832$	−4.65013	−	3.37852i	−0.161214	−	0.117129i
$833$	−44.0706	+	32.0192i	−1.52696	+	1.10940i
$834$	5.00153	−	15.3931i	0.173189	−	0.533020i
$835$	−4.32078			−0.149527
$836$	3.09741	+	1.18578i	0.107126	+	0.0410111i
$837$	6.41110			0.221600
$838$	−4.33241	+	13.3338i	−0.149661	+	0.460608i
$839$	−4.42235	+	3.21303i	−0.152677	+	0.110926i	−0.661501	−	0.749944i	$-0.730080\pi$
$839$	−4.42235	+	3.21303i	−0.152677	+	0.110926i	0.508824	+	0.860870i	$0.330080\pi$
$840$	2.35310	+	1.70963i	0.0811896	+	0.0589877i
$841$	−1.19850	−	3.68861i	−0.0413277	−	0.127194i
$842$	−2.48213	−	7.63921i	−0.0855398	−	0.263265i
$843$	−38.4161	−	27.9109i	−1.32312	−	0.961304i
$844$	−0.726755	+	0.528019i	−0.0250159	+	0.0181752i
$845$	1.63508	−	5.03227i	0.0562486	−	0.173115i
$846$	35.1800			1.20951
$847$	−10.0399	−	46.8187i	−0.344974	−	1.60871i
$848$	14.0620			0.482890
$849$	−21.9837	+	67.6588i	−0.754478	+	2.32204i
$850$	−18.1845	+	13.2118i	−0.623722	+	0.453161i
$851$	22.3379	+	16.2294i	0.765733	+	0.556338i
$852$	−2.11024	−	6.49464i	−0.0722955	−	0.222503i
$853$	8.16144	+	25.1183i	0.279442	+	0.860035i	0.988010	+	0.154392i	$0.0493418\pi$
$853$	8.16144	+	25.1183i	0.279442	+	0.860035i	−0.708567	+	0.705643i	$0.750658\pi$
$854$	−17.8576	−	12.9743i	−0.611076	−	0.443973i
$855$	−0.726972	+	0.528176i	−0.0248619	+	0.0180633i
$856$	0.514994	−	1.58499i	0.0176021	−	0.0541738i
$857$	48.6088			1.66044			0.830222	−	0.557432i	$-0.188213\pi$
$857$	48.6088			1.66044			0.830222	+	0.557432i	$0.188213\pi$
$858$	−45.0501	−	17.2465i	−1.53799	−	0.588787i
$859$	−47.7327			−1.62862			−0.814309	−	0.580432i	$-0.802884\pi$
$859$	−47.7327			−1.62862			−0.814309	+	0.580432i	$0.802884\pi$
$860$	0.872111	−	2.68408i	0.0297387	−	0.0915264i
$861$	5.56948	−	4.04647i	0.189808	−	0.137903i
$862$	15.0659	+	10.9460i	0.513146	+	0.372822i
$863$	13.8688	+	42.6837i	0.472099	+	1.45297i	0.849830	+	0.527056i	$0.176704\pi$
$863$	13.8688	+	42.6837i	0.472099	+	1.45297i	−0.377731	+	0.925915i	$0.623296\pi$
$864$	−0.315099	−	0.969775i	−0.0107199	−	0.0329924i
$865$	−2.28128	−	1.65745i	−0.0775659	−	0.0563550i
$866$	9.23110	−	6.70679i	0.313685	−	0.227906i
$867$	2.95942	−	9.10815i	0.100507	−	0.309329i
$868$	27.3689			0.928961
$869$	−10.2499	+	12.6809i	−0.347703	+	0.430170i
$870$	3.34901			0.113542
$871$	−26.2175	+	80.6891i	−0.888345	+	2.73405i
$872$	−7.83377	+	5.69156i	−0.265285	+	0.192741i
$873$	−30.3664	−	22.0625i	−1.02775	−	0.746703i
$874$	2.12346	+	6.53534i	0.0718272	+	0.221061i
$875$	−3.52724	−	10.8557i	−0.119242	−	0.366991i
$876$	−13.2733	−	9.64363i	−0.448464	−	0.325828i
$877$	−0.736228	+	0.534901i	−0.0248606	+	0.0180623i	−0.600146	−	0.799890i	$-0.704891\pi$
$877$	−0.736228	+	0.534901i	−0.0248606	+	0.0180623i	0.575286	+	0.817953i	$0.304891\pi$
$878$	−2.38609	+	7.34362i	−0.0805265	+	0.247835i
$879$	−11.4720			−0.386943
$880$	−0.845740	+	0.227433i	−0.0285099	+	0.00766676i
$881$	−8.25477			−0.278110			−0.139055	−	0.990285i	$-0.544407\pi$
$881$	−8.25477			−0.278110			−0.139055	+	0.990285i	$0.544407\pi$
$882$	−12.5649	+	38.6709i	−0.423084	+	1.30212i
$883$	45.6294	−	33.1517i	1.53555	−	1.11564i	0.582503	−	0.812829i	$-0.302074\pi$
$883$	45.6294	−	33.1517i	1.53555	−	1.11564i	0.953049	−	0.302815i	$-0.0979264\pi$
$884$	−21.2000	−	15.4027i	−0.713035	−	0.518050i
$885$	0.325831	+	1.00281i	0.0109527	+	0.0337089i
$886$	4.72117	+	14.5303i	0.158611	+	0.488154i
$887$	43.9771	+	31.9512i	1.47661	+	1.07282i	0.978630	+	0.205628i	$0.0659236\pi$
$887$	43.9771	+	31.9512i	1.47661	+	1.07282i	0.497977	+	0.867190i	$0.334076\pi$
$888$	8.22567	−	5.97630i	0.276035	−	0.200551i
$889$	−0.424749	+	1.30724i	−0.0142456	+	0.0438435i
$890$	2.01733			0.0676212
$891$	13.7993	+	21.2072i	0.462295	+	0.710469i
$892$	2.48795			0.0833026
$893$	−3.19463	+	9.83205i	−0.106904	+	0.329017i
$894$	21.0109	−	15.2653i	0.702709	−	0.510548i
$895$	2.21060	+	1.60610i	0.0738924	+	0.0536860i
$896$	−1.34515	−	4.13996i	−0.0449384	−	0.138306i
$897$	−30.8846	−	95.0531i	−1.03121	−	3.17373i
$898$	−10.0724	−	7.31805i	−0.336121	−	0.244206i
$899$	25.4946	−	18.5229i	0.850294	−	0.617775i
$900$	−5.18456	+	15.9564i	−0.172819	+	0.531881i
$901$	64.1089			2.13578
$902$	−0.106620	+	2.07013i	−0.00355005	+	0.0689279i
$903$	117.725			3.91763
$904$	3.43602	−	10.5750i	0.114280	−	0.351718i
$905$	4.96246	−	3.60544i	0.164958	−	0.119849i
$906$	−28.1010	−	20.4166i	−0.933593	−	0.678295i
$907$	−3.77493	−	11.6181i	−0.125345	−	0.385771i	0.868619	−	0.495480i	$-0.165008\pi$
$907$	−3.77493	−	11.6181i	−0.125345	−	0.385771i	−0.993964	+	0.109709i	$0.965008\pi$
$908$	6.90944	+	21.2651i	0.229298	+	0.705706i
$909$	−10.6524	−	7.73942i	−0.353318	−	0.256700i
$910$	5.34511	−	3.88345i	0.177189	−	0.128735i
$911$	5.29698	−	16.3024i	0.175497	−	0.540124i	−0.824159	−	0.566359i	$-0.808352\pi$
$911$	5.29698	−	16.3024i	0.175497	−	0.540124i	0.999656	+	0.0262348i	$0.00835175\pi$
$912$	2.53041			0.0837902
$913$	1.50908	−	29.3003i	0.0499432	−	0.969698i
$914$	−0.0856675			−0.00283363
$915$	−1.04701	+	3.22238i	−0.0346132	+	0.106528i
$916$	−12.1740	+	8.84495i	−0.402241	+	0.292245i
$917$	13.8021	+	10.0278i	0.455784	+	0.331147i
$918$	−1.43654	−	4.42123i	−0.0474130	−	0.145922i
$919$	−0.742502	−	2.28519i	−0.0244929	−	0.0753813i	0.938063	−	0.346465i	$-0.112618\pi$
$919$	−0.742502	−	2.28519i	−0.0244929	−	0.0753813i	−0.962556	+	0.271084i	$0.912618\pi$
$920$	−1.46799	−	1.06655i	−0.0483980	−	0.0351632i
$921$	−16.5314	+	12.0108i	−0.544729	+	0.395769i
$922$	2.04673	−	6.29920i	0.0674056	−	0.207453i
$923$	−15.5119			−0.510580
$924$	−19.9245	−	30.6206i	−0.655468	−	1.00734i
$925$	−19.8104			−0.651362
$926$	−1.22746	+	3.77772i	−0.0403367	+	0.124144i
$927$	9.78998	−	7.11284i	0.321545	−	0.233616i
$928$	−4.05491	−	2.94606i	−0.133109	−	0.0967093i
$929$	−2.62840	−	8.08939i	−0.0862351	−	0.265404i	0.898635	−	0.438696i	$-0.144560\pi$
$929$	−2.62840	−	8.08939i	−0.0862351	−	0.265404i	−0.984871	+	0.173292i	$0.944560\pi$
$930$	−1.29820	−	3.99546i	−0.0425698	−	0.131016i
$931$	−9.66668	−	7.02326i	−0.316813	−	0.230178i
$932$	0.832852	−	0.605102i	0.0272810	−	0.0198208i
$933$	−3.18371	+	9.79845i	−0.104230	+	0.320787i
$934$	−3.01130			−0.0985326
$935$	−3.85575	+	1.03687i	−0.126097	+	0.0339093i
$936$	−19.5598			−0.639334
$937$	−15.3200	+	47.1502i	−0.500483	+	1.54033i	0.307750	+	0.951467i	$0.400424\pi$
$937$	−15.3200	+	47.1502i	−0.500483	+	1.54033i	−0.808234	+	0.588862i	$0.799576\pi$
$938$	−51.9814	+	37.7667i	−1.69725	+	1.23313i
$939$	−26.6926	−	19.3933i	−0.871081	−	0.632877i
$940$	−0.843572	−	2.59625i	−0.0275143	−	0.0846802i
$941$	16.8106	+	51.7376i	0.548009	+	1.68660i	0.713727	+	0.700424i	$0.247006\pi$
$941$	16.8106	+	51.7376i	0.548009	+	1.68660i	−0.165718	+	0.986173i	$0.552994\pi$
$942$	13.4540	+	9.77490i	0.438355	+	0.318483i
$943$	−3.47454	+	2.52440i	−0.113146	+	0.0822057i
$944$	0.487641	−	1.50080i	0.0158714	−	0.0488470i
$945$	1.17208			0.0381277
$946$	−22.2829	+	27.5679i	−0.724479	+	0.896308i
$947$	−35.5384			−1.15484			−0.577421	−	0.816447i	$-0.695941\pi$
$947$	−35.5384			−1.15484			−0.577421	+	0.816447i	$0.695941\pi$
$948$	−3.84421	+	11.8313i	−0.124854	+	0.384262i
$949$	−30.1506	+	21.9057i	−0.978730	+	0.711089i
$950$	−3.98867	−	2.89794i	−0.129410	−	0.0940216i
$951$	−15.4746	−	47.6258i	−0.501797	−	1.54437i
$952$	−6.13259	−	18.8742i	−0.198758	−	0.611715i
$953$	−5.78794	−	4.20519i	−0.187490	−	0.136219i	0.490081	−	0.871677i	$-0.336967\pi$
$953$	−5.78794	−	4.20519i	−0.187490	−	0.136219i	−0.677571	+	0.735458i	$0.736967\pi$
$954$	38.7135	−	28.1270i	1.25340	−	0.910645i
$955$	0.274674	−	0.845359i	0.00888823	−	0.0273552i
$956$	14.9501			0.483521
$957$	−39.2837	−	15.0390i	−1.26986	−	0.486141i
$958$	−29.8036			−0.962911
$959$	16.7328	−	51.4981i	0.540329	−	1.66296i
$960$	−0.540568	+	0.392746i	−0.0174468	+	0.0126758i
$961$	−6.90159	−	5.01430i	−0.222632	−	0.161751i
$962$	−7.13694	−	21.9653i	−0.230104	−	0.708188i
$963$	−1.75251	−	5.39367i	−0.0564738	−	0.173809i
$964$	−12.6562	−	9.19527i	−0.407629	−	0.296160i
$965$	−1.45814	+	1.05940i	−0.0469392	+	0.0341034i
$966$	23.3897	−	71.9861i	0.752551	−	2.31611i
$967$	−22.5986			−0.726723			−0.363362	−	0.931648i	$-0.618371\pi$
$967$	−22.5986			−0.726723			−0.363362	+	0.931648i	$0.618371\pi$
$968$	10.9418	+	1.13009i	0.351683	+	0.0363224i
$969$	11.5362			0.370596
$970$	−0.900041	+	2.77004i	−0.0288986	+	0.0889407i
$971$	5.60731	−	4.07395i	0.179947	−	0.130739i	−0.494165	−	0.869368i	$-0.664526\pi$
$971$	5.60731	−	4.07395i	0.179947	−	0.130739i	0.674113	+	0.738629i	$0.264526\pi$
$972$	18.0919	+	13.1445i	0.580297	+	0.421610i
$973$	−8.60402	−	26.4804i	−0.275832	−	0.848924i
$974$	−5.72907	−	17.6323i	−0.183571	−	0.564974i
$975$	58.0132	+	42.1490i	1.85791	+	1.34985i
$976$	4.10237	−	2.98055i	0.131314	−	0.0954050i
$977$	−2.74674	+	8.45359i	−0.0878759	+	0.270454i	−0.985332	−	0.170650i	$-0.945413\pi$
$977$	−2.74674	+	8.45359i	−0.0878759	+	0.270454i	0.897456	+	0.441104i	$0.145413\pi$
$978$	46.9943			1.50271
$979$	−23.6632	−	9.05900i	−0.756280	−	0.289527i
$980$	3.15516			0.100788
$981$	−10.1825	+	31.3384i	−0.325102	+	1.00056i
$982$	−0.304704	+	0.221380i	−0.00972348	+	0.00706452i
$983$	16.2960	+	11.8397i	0.519761	+	0.377629i	0.816514	−	0.577326i	$-0.195904\pi$
$983$	16.2960	+	11.8397i	0.519761	+	0.377629i	−0.296753	+	0.954954i	$0.595904\pi$
$984$	0.488709	+	1.50409i	0.0155795	+	0.0479487i
$985$	−0.415091	−	1.27752i	−0.0132259	−	0.0407051i
$986$	−18.4864	−	13.4312i	−0.588728	−	0.427736i
$987$	92.1246	−	66.9324i	2.93236	−	2.13048i
$988$	1.77619	−	5.46655i	0.0565081	−	0.173914i
$989$	−73.4428			−2.33535
$990$	−1.87346	+	2.31780i	−0.0595425	+	0.0736645i
$991$	−46.8407			−1.48795			−0.743973	−	0.668210i	$-0.767061\pi$
$991$	−46.8407			−1.48795			−0.743973	+	0.668210i	$0.767061\pi$
$992$	−1.94290	+	5.97963i	−0.0616871	+	0.189853i
$993$	−56.3660	+	40.9523i	−1.78872	+	1.29958i
$994$	−9.50397	−	6.90504i	−0.301448	−	0.219014i
$995$	0.648133	+	1.99475i	0.0205472	+	0.0632377i
$996$	−6.91710	−	21.2886i	−0.219177	−	0.674556i
$997$	−29.5714	−	21.4848i	−0.936534	−	0.680432i	0.0110498	−	0.999939i	$-0.496483\pi$
$997$	−29.5714	−	21.4848i	−0.936534	−	0.680432i	−0.947584	+	0.319507i	$0.896483\pi$
$998$	−15.1807	+	11.0294i	−0.480537	+	0.349131i
$999$	1.26610	−	3.89667i	0.0400578	−	0.123285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.g.229.1	yes	16
11.4	even	5		4598.2.a.bw.1.8		8
11.5	even	5	inner	418.2.f.g.115.1	✓	16
11.7	odd	10		4598.2.a.bz.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.g.115.1	✓	16	11.5	even	5	inner
418.2.f.g.229.1	yes	16	1.1	even	1	trivial
4598.2.a.bw.1.8		8	11.4	even	5
4598.2.a.bz.1.8		8	11.7	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-2.04714 + 1.48734i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.0815989 + 0.251136i) q^{5} +(-0.781939 - 2.40656i) q^{6} +(-3.52166 - 2.55863i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.05158 - 3.23642i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-2.04714 + 1.48734i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.0815989 + 0.251136i) q^{5} +(-0.781939 - 2.40656i) q^{6} +(-3.52166 - 2.55863i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.05158 - 3.23642i) q^{9} -0.264060 q^{10} +(3.09741 + 1.18578i) q^{11} +2.53041 q^{12} +(1.77619 - 5.46655i) q^{13} +(3.52166 - 2.55863i) q^{14} +(-0.540568 - 0.392746i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.40882 + 4.33589i) q^{17} +(2.75306 + 2.00022i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(0.0815989 - 0.251136i) q^{20} +11.0149 q^{21} +(-2.08490 + 2.57938i) q^{22} -6.87167 q^{23} +(-0.781939 + 2.40656i) q^{24} +(3.98867 - 2.89794i) q^{25} +(4.65013 + 3.37852i) q^{26} +(0.315099 + 0.969775i) q^{27} +(1.34515 + 4.13996i) q^{28} +(4.05491 + 2.94606i) q^{29} +(0.540568 - 0.392746i) q^{30} +(1.94290 - 5.97963i) q^{31} -1.00000 q^{32} +(-8.10449 + 2.17942i) q^{33} -4.55903 q^{34} +(0.355201 - 1.09320i) q^{35} +(-2.75306 + 2.00022i) q^{36} +(-3.25073 - 2.36179i) q^{37} +(-0.309017 - 0.951057i) q^{38} +(4.49449 + 13.8326i) q^{39} +(0.213629 + 0.155210i) q^{40} +(0.505632 - 0.367363i) q^{41} +(-3.40379 + 10.4758i) q^{42} +10.6878 q^{43} +(-1.80887 - 2.77993i) q^{44} +0.898587 q^{45} +(2.12346 - 6.53534i) q^{46} +(8.36364 - 6.07654i) q^{47} +(-2.04714 - 1.48734i) q^{48} +(3.69234 + 11.3639i) q^{49} +(1.52354 + 4.68897i) q^{50} +(-9.33298 - 6.78081i) q^{51} +(-4.65013 + 3.37852i) q^{52} +(4.34539 - 13.3737i) q^{53} -1.01968 q^{54} +(-0.0450467 + 0.874628i) q^{55} -4.35301 q^{56} +(0.781939 - 2.40656i) q^{57} +(-4.05491 + 2.94606i) q^{58} +(-1.27666 - 0.927548i) q^{59} +(0.206479 + 0.635476i) q^{60} +(-1.56697 - 4.82262i) q^{61} +(5.08658 + 3.69561i) q^{62} +(-11.9841 + 8.70696i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.51778 q^{65} +(0.431670 - 8.38131i) q^{66} -14.7605 q^{67} +(1.40882 - 4.33589i) q^{68} +(14.0673 - 10.2205i) q^{69} +(0.929928 + 0.675632i) q^{70} +(-0.833950 - 2.56664i) q^{71} +(-1.05158 - 3.23642i) q^{72} +(-5.24552 - 3.81110i) q^{73} +(3.25073 - 2.36179i) q^{74} +(-3.85517 + 11.8650i) q^{75} +1.00000 q^{76} +(-7.87403 - 12.1010i) q^{77} -14.5445 q^{78} +(-1.51921 + 4.67564i) q^{79} +(-0.213629 + 0.155210i) q^{80} +(6.17175 + 4.48404i) q^{81} +(0.193134 + 0.594406i) q^{82} +(-2.73359 - 8.41312i) q^{83} +(-8.91123 - 6.47439i) q^{84} +(-0.973939 + 0.707608i) q^{85} +(-3.30270 + 10.1647i) q^{86} -12.6828 q^{87} +(3.20284 - 0.861293i) q^{88} -7.63969 q^{89} +(-0.277679 + 0.854607i) q^{90} +(-20.2420 + 14.7067i) q^{91} +(5.55929 + 4.03906i) q^{92} +(4.91633 + 15.1309i) q^{93} +(3.19463 + 9.83205i) q^{94} +(-0.213629 - 0.155210i) q^{95} +(2.04714 - 1.48734i) q^{96} +(3.40848 - 10.4902i) q^{97} -11.9487 q^{98} +(7.09484 - 8.77756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

Introduction

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