LMFDB - Embedded newform 418.2.f.g.115.1

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			115.1
Root			$-2.04714 - 1.48734i$ of defining polynomial
Character	$\chi$	$=$	418.115
Dual form			418.2.f.g.229.1

$q$-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 $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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	−0.189532	−	0.981874i	$-0.560697\pi$
$3$	−2.04714	−	1.48734i	−1.18192	−	0.858715i	−0.992387	+	0.123160i	$0.960697\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.0815989	−	0.251136i	0.0364921	−	0.112311i	−0.931151	−	0.364633i	$-0.881194\pi$
$5$	0.0815989	−	0.251136i	0.0364921	−	0.112311i	0.967643	+	0.252322i	$0.0811943\pi$
$6$	−0.781939	+	2.40656i	−0.319225	+	0.982475i
$7$	−3.52166	+	2.55863i	−1.33106	+	0.967073i	−0.331339	+	0.943512i	$0.607500\pi$
$7$	−3.52166	+	2.55863i	−1.33106	+	0.967073i	−0.999722	+	0.0235608i	$0.992500\pi$
$8$	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	0.820623	+	0.571470i	$0.193627\pi$
$13$	1.77619	+	5.46655i	0.492627	+	1.51615i	−0.327996	+	0.944679i	$0.606373\pi$
$14$	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	−0.621645	−	0.783299i	$-0.713535\pi$
$17$	1.40882	−	4.33589i	0.341688	−	1.05161i	0.963333	−	0.268309i	$-0.0864647\pi$
$18$	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	−0.143771	−	0.989611i	$-0.545923\pi$
$29$	4.05491	−	2.94606i	0.752977	−	0.547070i	0.896748	+	0.442541i	$0.145923\pi$
$30$	0.540568	+	0.392746i	0.0986938	+	0.0717052i
$31$	1.94290	+	5.97963i	0.348955	+	1.07397i	0.959432	+	0.281939i	$0.0909777\pi$
$31$	1.94290	+	5.97963i	0.348955	+	1.07397i	−0.610477	+	0.792034i	$0.709022\pi$
$32$	−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	−0.822007	−	0.569477i	$-0.807146\pi$
$37$	−3.25073	+	2.36179i	−0.534416	+	0.388276i	0.287591	+	0.957753i	$0.407146\pi$
$38$	−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	0.626568	−	0.779367i	$-0.284459\pi$
$41$	0.505632	+	0.367363i	0.0789665	+	0.0573725i	−0.547602	+	0.836739i	$0.684459\pi$
$42$	−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	0.996097	−	0.0882656i	$-0.0281324\pi$
$47$	8.36364	+	6.07654i	1.21996	+	0.886354i	0.223865	+	0.974620i	$0.428132\pi$
$48$	−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	0.545108	+	0.838366i	$0.316489\pi$
$53$	4.34539	+	13.3737i	0.596885	+	1.83702i	0.0517771	+	0.998659i	$0.483511\pi$
$54$	−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	−0.667779	−	0.744359i	$-0.732755\pi$
$59$	−1.27666	+	0.927548i	−0.166207	+	0.120756i	0.501572	+	0.865116i	$0.332755\pi$
$60$	0.206479	−	0.635476i	0.0266563	−	0.0820396i
$61$	−1.56697	+	4.82262i	−0.200629	+	0.617474i	0.799235	+	0.601018i	$0.205238\pi$
$61$	−1.56697	+	4.82262i	−0.200629	+	0.617474i	−0.999865	+	0.0164554i	$0.994762\pi$
$62$	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	−0.988268	−	0.152727i	$-0.951194\pi$
$71$	−0.833950	+	2.56664i	−0.0989717	+	0.304604i	0.889297	+	0.457331i	$0.151194\pi$
$72$	−1.05158	+	3.23642i	−0.123929	+	0.381415i
$73$	−5.24552	+	3.81110i	−0.613942	+	0.446055i	−0.850800	−	0.525489i	$-0.823882\pi$
$73$	−5.24552	+	3.81110i	−0.613942	+	0.446055i	0.236858	+	0.971544i	$0.423882\pi$
$74$	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	0.828500	−	0.559989i	$-0.189195\pi$
$79$	−1.51921	−	4.67564i	−0.170924	−	0.526050i	−0.999424	+	0.0339391i	$0.989195\pi$
$80$	−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	0.681428	+	0.731885i	$0.261359\pi$
$83$	−2.73359	+	8.41312i	−0.300050	+	0.923460i	−0.981478	+	0.191574i	$0.938641\pi$
$84$	−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	0.961004	+	0.276535i	$0.0891860\pi$
$97$	3.40848	+	10.4902i	0.346078	+	1.06512i	−0.614926	+	0.788585i	$0.710814\pi$
$98$	−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	0.992755	−	0.120155i	$-0.0383390\pi$
$101$	1.19568	+	3.67991i	0.118974	+	0.366165i	−0.873781	+	0.486320i	$0.838339\pi$
$102$	9.33298	+	6.78081i	0.924103	+	0.671400i
$103$	2.87689	−	2.09019i	0.283469	−	0.205952i	−0.436960	−	0.899481i	$-0.643945\pi$
$103$	2.87689	−	2.09019i	0.283469	−	0.205952i	0.720429	+	0.693529i	$0.243945\pi$
$104$	−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	0.651046	−	0.759038i	$-0.274330\pi$
$107$	1.34827	+	0.979577i	0.130342	+	0.0946992i	−0.520704	+	0.853737i	$0.674330\pi$
$108$	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	0.924106	−	0.382137i	$-0.124812\pi$
$113$	8.99561	+	6.53569i	0.846236	+	0.614826i	−0.0778697	+	0.996964i	$0.524812\pi$
$114$	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	−0.955292	−	0.295663i	$-0.904460\pi$
$127$	−0.0975759	+	0.300308i	−0.00865846	+	0.0266480i	0.946634	+	0.322311i	$0.104460\pi$
$128$	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	−0.641466	−	0.767151i	$-0.721674\pi$
$137$	3.84395	−	11.8305i	0.328411	−	1.01074i	0.969877	−	0.243594i	$-0.0783264\pi$
$138$	5.37323	−	16.5371i	0.457399	−	1.40773i
$139$	5.17472	−	3.75966i	0.438914	−	0.318890i	−0.346289	−	0.938128i	$-0.612558\pi$
$139$	5.17472	−	3.75966i	0.438914	−	0.318890i	0.785203	+	0.619238i	$0.212558\pi$
$140$	−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	−0.733012	−	0.680215i	$-0.761886\pi$
$149$	3.17160	−	9.76118i	0.259828	−	0.799667i	0.992840	−	0.119452i	$-0.0381138\pi$
$150$	−10.0930	+	7.33298i	−0.824088	+	0.598735i
$151$	11.1053	+	8.06848i	0.903737	+	0.656604i	0.939423	−	0.342759i	$-0.111362\pi$
$151$	11.1053	+	8.06848i	0.903737	+	0.656604i	−0.0356858	+	0.999363i	$0.511362\pi$
$152$	−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	0.355044	−	0.934850i	$-0.384466\pi$
$157$	−5.31692	−	3.86297i	−0.424337	−	0.308299i	−0.779380	+	0.626551i	$0.784466\pi$
$158$	−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	−0.877457	−	0.479656i	$-0.840761\pi$
$163$	−5.73901	−	17.6629i	−0.449514	−	1.38346i	0.427943	−	0.903806i	$-0.359239\pi$
$164$	−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	−0.931823	−	0.362912i	$-0.881783\pi$
$167$	−5.05641	−	15.5620i	−0.391277	−	1.20423i	0.540547	−	0.841314i	$-0.318217\pi$
$168$	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	0.208760	−	0.977967i	$-0.433057\pi$
$173$	−8.63927	−	6.27680i	−0.656832	−	0.477216i	−0.865591	+	0.500751i	$0.833057\pi$
$174$	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	0.854916	−	0.518766i	$-0.173609\pi$
$179$	8.37161	+	6.08233i	0.625724	+	0.454615i	−0.229192	+	0.973381i	$0.573609\pi$
$180$	−0.726972	+	0.528176i	−0.0541853	+	0.0393679i
$181$	−7.17826	+	22.0924i	−0.533556	+	1.64212i	0.213192	+	0.977010i	$0.431614\pi$
$181$	−7.17826	+	22.0924i	−0.533556	+	1.64212i	−0.746748	+	0.665107i	$0.768386\pi$
$182$	−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	−0.681935	−	0.731413i	$-0.738861\pi$
$191$	−2.72327	+	1.97857i	−0.197049	+	0.143164i	0.484886	+	0.874577i	$0.338861\pi$
$192$	0.781939	−	2.40656i	0.0564316	−	0.173679i
$193$	2.10922	−	6.49152i	0.151825	−	0.467270i	−0.846000	−	0.533183i	$-0.820996\pi$
$193$	2.10922	−	6.49152i	0.151825	−	0.467270i	0.997825	+	0.0659127i	$0.0209959\pi$
$194$	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	0.960157	−	0.279461i	$-0.0901558\pi$
$211$	0.277596	+	0.854352i	0.0191105	+	0.0588160i	−0.941046	+	0.338277i	$0.890156\pi$
$212$	−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	0.518349	−	0.855169i	$-0.326547\pi$
$223$	−2.01279	−	1.46238i	−0.134787	−	0.0979281i	−0.653136	+	0.757241i	$0.726547\pi$
$224$	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	−0.994345	−	0.106193i	$-0.966134\pi$
$227$	−18.0892	+	13.1425i	−1.20062	+	0.872301i	−0.206274	+	0.978494i	$0.566134\pi$
$228$	−2.04714	−	1.48734i	−0.135575	−	0.0985013i
$229$	4.65007	+	14.3114i	0.307285	+	0.945726i	0.978815	+	0.204748i	$0.0656376\pi$
$229$	4.65007	+	14.3114i	0.307285	+	0.945726i	−0.671530	+	0.740978i	$0.734362\pi$
$230$	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	0.940095	−	0.340912i	$-0.110736\pi$
$233$	−0.318121	−	0.979076i	−0.0208408	−	0.0641414i	−0.960936	+	0.276771i	$0.910736\pi$
$234$	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	0.123331	−	0.992366i	$-0.460642\pi$
$239$	−12.0949	−	8.78746i	−0.782354	−	0.568414i	−0.905685	+	0.423952i	$0.860642\pi$
$240$	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	0.995428	+	0.0955169i	$0.0304504\pi$
$251$	3.90138	+	12.0072i	0.246253	+	0.757889i	−0.749175	+	0.662373i	$0.769550\pi$
$252$	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	−0.570874	−	0.821038i	$-0.693396\pi$
$257$	0.538155	−	0.390992i	0.0335692	−	0.0243894i	0.604443	+	0.796648i	$0.293396\pi$
$258$	−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	0.517302	+	0.855803i	$0.326936\pi$
$269$	−6.62991	+	20.4048i	−0.404233	+	1.24410i	−0.921534	+	0.388297i	$0.873064\pi$
$270$	−0.0832049	+	0.256078i	−0.00506369	+	0.0155844i
$271$	−8.46068	+	6.14704i	−0.513950	+	0.373406i	−0.814320	−	0.580416i	$-0.802890\pi$
$271$	−8.46068	+	6.14704i	−0.513950	+	0.373406i	0.300370	+	0.953823i	$0.402890\pi$
$272$	−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	−0.856190	−	0.516661i	$-0.827175\pi$
$277$	−7.77581	−	23.9315i	−0.467203	−	1.43790i	0.388987	−	0.921243i	$-0.372825\pi$
$278$	−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	−0.615147	−	0.788413i	$-0.710903\pi$
$281$	5.79892	−	17.8472i	0.345935	−	1.06468i	0.961082	−	0.276265i	$-0.0890967\pi$
$282$	−21.1634	+	15.3761i	−1.26026	+	0.915635i
$283$	22.7450	+	16.5252i	1.35205	+	0.982320i	0.998907	+	0.0467493i	$0.0148862\pi$
$283$	22.7450	+	16.5252i	1.35205	+	0.982320i	0.353140	+	0.935570i	$0.385114\pi$
$284$	−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	−0.475470	−	0.879732i	$-0.657722\pi$
$293$	3.66782	−	2.66483i	0.214276	−	0.155681i	0.689746	+	0.724051i	$0.257722\pi$
$294$	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	0.677247	−	0.735755i	$-0.263173\pi$
$311$	3.29396	+	2.39320i	0.186783	+	0.135706i	−0.490464	+	0.871461i	$0.663173\pi$
$312$	11.7667	−	8.54903i	0.666160	−	0.483993i
$313$	4.02926	−	12.4008i	0.227747	−	0.700934i	−0.770254	−	0.637737i	$-0.779871\pi$
$313$	4.02926	−	12.4008i	0.227747	−	0.700934i	0.998001	−	0.0631965i	$-0.0201295\pi$
$314$	−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	−0.962394	−	0.271658i	$-0.912428\pi$
$317$	−6.11544	−	18.8214i	−0.343477	−	1.05711i	0.618916	−	0.785457i	$-0.287572\pi$
$318$	−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	−0.592970	−	0.805225i	$-0.702045\pi$
$337$	−0.190798	+	0.138623i	−0.0103935	+	0.00755129i	0.582576	+	0.812776i	$0.302045\pi$
$338$	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	−0.873470	−	0.486877i	$-0.838136\pi$
$347$	2.22346	−	6.84309i	0.119361	−	0.367356i	0.992832	+	0.119521i	$0.0381359\pi$
$348$	10.2606	−	7.45474i	0.550025	−	0.399616i
$349$	−1.11145	−	0.807517i	−0.0594947	−	0.0432254i	0.557640	−	0.830083i	$-0.311707\pi$
$349$	−1.11145	−	0.807517i	−0.0594947	−	0.0432254i	−0.617135	+	0.786857i	$0.711707\pi$
$350$	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	−0.644785	−	0.764364i	$-0.723053\pi$
$359$	−2.21837	+	1.61174i	−0.117081	+	0.0850644i	0.527704	+	0.849428i	$0.323053\pi$
$360$	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	−0.256387	−	0.966574i	$-0.582532\pi$
$367$	11.1812	−	8.12360i	0.583652	−	0.424048i	0.840039	+	0.542526i	$0.182532\pi$
$368$	−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	0.736936	+	0.675962i	$0.236272\pi$
$379$	−4.99505	+	15.3732i	−0.256578	+	0.789667i	−0.993515	+	0.113705i	$0.963728\pi$
$380$	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	0.959681	+	0.281092i	$0.0906966\pi$
$383$	6.82037	+	20.9909i	0.348504	+	1.07259i	−0.611176	+	0.791494i	$0.709303\pi$
$384$	−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	−0.950702	−	0.310105i	$-0.899636\pi$
$389$	−18.7282	+	13.6068i	−0.949559	+	0.689895i	0.00114386	+	0.999999i	$0.499636\pi$
$390$	−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	−0.980453	−	0.196754i	$-0.936960\pi$
$401$	−1.43381	+	4.41281i	−0.0716010	+	0.220365i	0.908852	+	0.417119i	$0.136960\pi$
$402$	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	0.908417	−	0.418066i	$-0.137292\pi$
$409$	−1.46098	−	4.49644i	−0.0722410	−	0.222335i	−0.980658	+	0.195731i	$0.937292\pi$
$410$	−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	0.418062	−	0.908419i	$-0.362710\pi$
$421$	−6.49830	−	4.72129i	−0.316708	−	0.230102i	−0.734769	+	0.678317i	$0.762710\pi$
$422$	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	0.988631	+	0.150361i	$0.0480437\pi$
$431$	5.75465	+	17.7110i	0.277192	+	0.853109i	−0.711439	+	0.702748i	$0.751956\pi$
$432$	−0.824940	−	0.599354i	−0.0396899	−	0.0288364i
$433$	−9.23110	+	6.70679i	−0.443618	+	0.322308i	−0.787071	−	0.616862i	$-0.788403\pi$
$433$	−9.23110	+	6.70679i	−0.443618	+	0.322308i	0.343453	+	0.939170i	$0.388403\pi$
$434$	−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	0.841331	−	0.540521i	$-0.181773\pi$
$443$	12.3602	+	8.98020i	0.587250	+	0.426662i	−0.254080	+	0.967183i	$0.581773\pi$
$444$	−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	0.818306	−	0.574783i	$-0.194914\pi$
$449$	−3.84733	−	11.8409i	−0.181567	−	0.558804i	−0.999872	+	0.0159787i	$0.994914\pi$
$450$	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	−0.950435	−	0.310922i	$-0.899362\pi$
$457$	0.0264727	−	0.0814747i	0.00123834	−	0.00381122i	0.951674	+	0.307111i	$0.0993622\pi$
$458$	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	−0.927215	−	0.374529i	$-0.877804\pi$
$467$	0.930542	−	2.86391i	0.0430603	−	0.132526i	0.970275	+	0.242003i	$0.0778044\pi$
$468$	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	−0.486144	−	0.873879i	$-0.661597\pi$
$479$	9.20983	−	28.3449i	0.420808	−	1.29511i	0.906952	−	0.421234i	$-0.138403\pi$
$480$	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	0.193582	−	0.981084i	$-0.437990\pi$
$487$	−14.9989	−	10.8973i	−0.679665	−	0.493806i	−0.873247	+	0.487279i	$0.837990\pi$
$488$	−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	−0.580888	−	0.813983i	$-0.697295\pi$
$491$	0.304704	−	0.221380i	0.0137511	−	0.00999075i	0.594640	+	0.803992i	$0.297295\pi$
$492$	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	−0.193637	−	0.981073i	$-0.562028\pi$
$499$	15.1807	−	11.0294i	0.679583	−	0.493746i	0.873219	+	0.487328i	$0.162028\pi$
$500$	−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	0.949432	−	0.313973i	$-0.101660\pi$
$503$	21.1766	+	15.3857i	0.944216	+	0.686013i	−0.00521566	+	0.999986i	$0.501660\pi$
$504$	−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	0.317784	−	0.948163i	$-0.397061\pi$
$509$	−10.9595	−	7.96255i	−0.485772	−	0.352934i	−0.803556	+	0.595229i	$0.797061\pi$
$510$	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	−0.744361	−	0.667777i	$-0.767246\pi$
$521$	−7.74439	+	5.62663i	−0.339288	+	0.246507i	0.405073	+	0.914284i	$0.367246\pi$
$522$	5.27065	−	16.2214i	0.230690	−	0.709991i
$523$	9.34626	−	28.7648i	0.408683	−	1.25780i	−0.509097	−	0.860709i	$-0.670020\pi$
$523$	9.34626	−	28.7648i	0.408683	−	1.25780i	0.917780	−	0.397089i	$-0.129980\pi$
$524$	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	0.999445	+	0.0333137i	$0.0106060\pi$
$541$	4.89514	+	15.0657i	0.210458	+	0.647724i	−0.788987	+	0.614410i	$0.789394\pi$
$542$	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	0.851587	−	0.524214i	$-0.175641\pi$
$547$	14.4113	+	10.4704i	0.616184	+	0.447684i	−0.235403	+	0.971898i	$0.575641\pi$
$548$	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	−0.111278	−	0.993789i	$-0.535494\pi$
$557$	18.8685	−	13.7088i	0.799485	−	0.580860i	0.910763	+	0.412929i	$0.135494\pi$
$558$	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	0.946982	+	0.321286i	$0.104115\pi$
$563$	8.77222	+	26.9981i	0.369705	+	1.13783i	−0.577277	+	0.816548i	$0.695885\pi$
$564$	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	−0.159192	−	0.987248i	$-0.550889\pi$
$569$	−27.3677	−	19.8838i	−1.14731	−	0.833572i	−0.988121	+	0.153676i	$0.950889\pi$
$570$	−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	−0.883097	−	0.469191i	$-0.844546\pi$
$577$	2.57327	−	7.91972i	0.107127	−	0.329702i	0.990224	+	0.139488i	$0.0445457\pi$
$578$	−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	−0.389122	−	0.921186i	$-0.627221\pi$
$587$	8.88525	−	6.45551i	0.366733	−	0.266447i	0.755855	+	0.654739i	$0.227221\pi$
$588$	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	−0.909668	−	0.415336i	$-0.863664\pi$
$599$	1.72293	−	5.30263i	0.0703969	−	0.216660i	0.980065	+	0.198676i	$0.0636642\pi$
$600$	3.85517	−	11.8650i	0.157387	−	0.484387i
$601$	−19.5817	+	14.2270i	−0.798756	+	0.580330i	−0.910549	−	0.413401i	$-0.864341\pi$
$601$	−19.5817	+	14.2270i	−0.798756	+	0.580330i	0.111793	+	0.993732i	$0.464341\pi$
$602$	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	0.961608	−	0.274427i	$-0.0884882\pi$
$607$	0.550562	+	1.69446i	0.0223466	+	0.0687759i	−0.939261	+	0.343203i	$0.888488\pi$
$608$	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	−0.0972277	−	0.995262i	$-0.530998\pi$
$613$	−26.5866	−	19.3163i	−1.07382	−	0.780178i	−0.976596	+	0.215084i	$0.930998\pi$
$614$	−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	6.16107e−5	−	1.00000i	$-0.499980\pi$
$619$	−23.6600	−	17.1900i	−0.950976	−	0.690924i	−0.951037	+	0.309076i	$0.899980\pi$
$620$	−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	0.349997	−	0.936751i	$-0.386183\pi$
$631$	33.8879	−	24.6210i	1.34905	−	0.980146i	0.999058	−	0.0433949i	$-0.0138174\pi$
$632$	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	0.991710	−	0.128496i	$-0.0410149\pi$
$641$	29.7729	+	21.6313i	1.17596	+	0.854384i	0.184248	+	0.982880i	$0.441015\pi$
$642$	−3.41168	+	2.47873i	−0.134648	+	0.0978277i
$643$	−11.1912	+	34.4431i	−0.441339	+	1.35830i	0.445110	+	0.895476i	$0.353165\pi$
$643$	−11.1912	+	34.4431i	−0.441339	+	1.35830i	−0.886449	+	0.462826i	$0.846835\pi$
$644$	−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	0.886611	−	0.462517i	$-0.153053\pi$
$647$	−2.60805	−	8.02675i	−0.102533	−	0.315564i	−0.989144	+	0.146953i	$0.953053\pi$
$648$	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	0.712457	−	0.701716i	$-0.247582\pi$
$653$	40.8859	−	29.7054i	1.59999	−	1.16246i	0.887533	−	0.460745i	$-0.152418\pi$
$654$	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	0.822319	−	0.569027i	$-0.192680\pi$
$673$	−4.60260	−	14.1653i	−0.177417	−	0.546034i	−0.999736	+	0.0229938i	$0.992680\pi$
$674$	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	−0.995971	−	0.0896813i	$-0.971415\pi$
$677$	−3.57765	+	11.0109i	−0.137500	+	0.423182i	0.858470	+	0.512863i	$0.171415\pi$
$678$	−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	0.990020	+	0.140929i	$0.0450088\pi$
$691$	7.14774	+	21.9985i	0.271913	+	0.836861i	−0.718107	+	0.695933i	$0.754991\pi$
$692$	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	0.997909	−	0.0646370i	$-0.0205890\pi$
$701$	32.9580	+	23.9454i	1.24481	+	0.904405i	0.246897	+	0.969042i	$0.420589\pi$
$702$	−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	0.428867	+	0.903368i	$0.358913\pi$
$709$	−11.9577	+	36.8020i	−0.449080	+	1.38213i	−0.877947	+	0.478759i	$0.841087\pi$
$710$	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	−0.387342	−	0.921936i	$-0.626607\pi$
$719$	9.91522	−	7.20383i	0.369775	−	0.268658i	0.757118	+	0.653278i	$0.226607\pi$
$720$	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	−0.536729	−	0.843755i	$-0.680340\pi$
$733$	2.70389	−	1.96449i	0.0998706	−	0.0725602i	0.636600	+	0.771194i	$0.280340\pi$
$734$	−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	0.963580	+	0.267419i	$0.0861708\pi$
$739$	9.27571	+	28.5477i	0.341212	+	1.05014i	−0.622368	+	0.782725i	$0.713829\pi$
$740$	−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	−0.899789	−	0.436326i	$-0.856279\pi$
$743$	2.30662	−	7.09904i	0.0846216	−	0.260438i	0.984410	+	0.175887i	$0.0562795\pi$
$744$	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	−0.0411072	−	0.999155i	$-0.513089\pi$
$751$	−27.5157	−	19.9913i	−1.00406	−	0.729494i	−0.962955	+	0.269661i	$0.913089\pi$
$752$	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	0.840524	−	0.541775i	$-0.182247\pi$
$757$	−4.34499	−	13.3725i	−0.157922	−	0.486032i	−0.998445	+	0.0557424i	$0.982247\pi$
$758$	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	−0.598508	−	0.801117i	$-0.704240\pi$
$761$	−16.1432	−	49.6836i	−0.585190	−	1.80103i	0.0133185	−	0.999911i	$-0.495760\pi$
$762$	−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	0.321608	−	0.946873i	$-0.395777\pi$
$773$	−13.3326	−	9.68670i	−0.479540	−	0.348406i	−0.801148	+	0.598467i	$0.795777\pi$
$774$	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	0.390926	+	0.920422i	$0.372155\pi$
$787$	−13.0828	+	40.2646i	−0.466350	+	1.43528i	−0.857276	+	0.514857i	$0.827845\pi$
$788$	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	−0.624268	−	0.781210i	$-0.714603\pi$
$797$	9.59745	−	29.5379i	0.339959	−	1.04629i	0.964227	−	0.265077i	$-0.0853972\pi$
$798$	−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	−0.906619	−	0.421950i	$-0.861346\pi$
$809$	2.12944	−	6.55374i	0.0748671	−	0.230417i	0.981486	+	0.191533i	$0.0613458\pi$
$810$	−1.62971	+	1.18405i	−0.0572622	+	0.0416034i
$811$	−28.2400	−	20.5176i	−0.991641	−	0.720469i	−0.0313611	−	0.999508i	$-0.509984\pi$
$811$	−28.2400	−	20.5176i	−0.991641	−	0.720469i	−0.960280	+	0.279039i	$0.909984\pi$
$812$	−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	−0.130484	−	0.991450i	$-0.541653\pi$
$821$	22.1236	−	16.0738i	0.772120	−	0.560978i	0.902604	+	0.430473i	$0.141653\pi$
$822$	25.4650	+	18.5014i	0.888194	+	0.645311i
$823$	−5.65131	−	17.3930i	−0.196992	−	0.606280i	−0.999948	−	0.0102408i	$-0.996740\pi$
$823$	−5.65131	−	17.3930i	−0.196992	−	0.606280i	0.802955	−	0.596039i	$-0.203260\pi$
$824$	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	0.999892	+	0.0147180i	$0.00468506\pi$
$827$	5.74040	+	17.6671i	0.199613	+	0.614347i	−0.800278	+	0.599629i	$0.795315\pi$
$828$	18.9181	+	13.7448i	0.657450	+	0.477665i
$829$	−17.3746	+	12.6234i	−0.603445	+	0.438428i	−0.847100	−	0.531434i	$-0.821653\pi$
$829$	−17.3746	+	12.6234i	−0.603445	+	0.438428i	0.243655	+	0.969862i	$0.421653\pi$
$830$	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	0.508824	−	0.860870i	$-0.330080\pi$
$839$	−4.42235	−	3.21303i	−0.152677	−	0.110926i	−0.661501	+	0.749944i	$0.730080\pi$
$840$	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	−0.708567	−	0.705643i	$-0.750658\pi$
$853$	8.16144	−	25.1183i	0.279442	−	0.860035i	0.988010	−	0.154392i	$-0.0493418\pi$
$854$	−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	−0.377731	−	0.925915i	$-0.623296\pi$
$863$	13.8688	−	42.6837i	0.472099	−	1.45297i	0.849830	−	0.527056i	$-0.176704\pi$
$864$	−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	0.575286	−	0.817953i	$-0.304891\pi$
$877$	−0.736228	−	0.534901i	−0.0248606	−	0.0180623i	−0.600146	+	0.799890i	$0.704891\pi$
$878$	−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	0.953049	+	0.302815i	$0.0979264\pi$
$883$	45.6294	+	33.1517i	1.53555	+	1.11564i	0.582503	+	0.812829i	$0.302074\pi$
$884$	−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	0.497977	−	0.867190i	$-0.334076\pi$
$887$	43.9771	−	31.9512i	1.47661	−	1.07282i	0.978630	−	0.205628i	$-0.0659236\pi$
$888$	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	−0.993964	−	0.109709i	$-0.965008\pi$
$907$	−3.77493	+	11.6181i	−0.125345	+	0.385771i	0.868619	+	0.495480i	$0.165008\pi$
$908$	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	0.999656	−	0.0262348i	$-0.00835175\pi$
$911$	5.29698	+	16.3024i	0.175497	+	0.540124i	−0.824159	+	0.566359i	$0.808352\pi$
$912$	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	−0.962556	−	0.271084i	$-0.912618\pi$
$919$	−0.742502	+	2.28519i	−0.0244929	+	0.0753813i	0.938063	+	0.346465i	$0.112618\pi$
$920$	−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	−0.984871	−	0.173292i	$-0.944560\pi$
$929$	−2.62840	+	8.08939i	−0.0862351	+	0.265404i	0.898635	+	0.438696i	$0.144560\pi$
$930$	−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	−0.808234	−	0.588862i	$-0.799576\pi$
$937$	−15.3200	−	47.1502i	−0.500483	−	1.54033i	0.307750	−	0.951467i	$-0.400424\pi$
$938$	−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	−0.165718	−	0.986173i	$-0.552994\pi$
$941$	16.8106	−	51.7376i	0.548009	−	1.68660i	0.713727	−	0.700424i	$-0.247006\pi$
$942$	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	−0.677571	−	0.735458i	$-0.736967\pi$
$953$	−5.78794	+	4.20519i	−0.187490	+	0.136219i	0.490081	+	0.871677i	$0.336967\pi$
$954$	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	0.674113	−	0.738629i	$-0.264526\pi$
$971$	5.60731	+	4.07395i	0.179947	+	0.130739i	−0.494165	+	0.869368i	$0.664526\pi$
$972$	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	0.897456	−	0.441104i	$-0.145413\pi$
$977$	−2.74674	−	8.45359i	−0.0878759	−	0.270454i	−0.985332	+	0.170650i	$0.945413\pi$
$978$	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	−0.296753	−	0.954954i	$-0.595904\pi$
$983$	16.2960	−	11.8397i	0.519761	−	0.377629i	0.816514	+	0.577326i	$0.195904\pi$
$984$	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	−0.947584	−	0.319507i	$-0.896483\pi$
$997$	−29.5714	+	21.4848i	−0.936534	+	0.680432i	0.0110498	+	0.999939i	$0.496483\pi$
$998$	−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.115.1	✓	16
11.3	even	5		4598.2.a.bw.1.8		8
11.8	odd	10		4598.2.a.bz.1.8		8
11.9	even	5	inner	418.2.f.g.229.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.g.115.1	✓	16	1.1	even	1	trivial
418.2.f.g.229.1	yes	16	11.9	even	5	inner
4598.2.a.bw.1.8		8	11.3	even	5
4598.2.a.bz.1.8		8	11.8	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

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