LMFDB - Embedded newform 418.2.h.b.373.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(65,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("418.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 $ x^20 + 41x^18 + 707x^16 + 6667x^14 + 37400x^12 + 126976x^10 + 253280x^8 + 273276x^6 + 137476x^4 + 30336*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.9
Root			$2.96323i$ of defining polynomial
Character	$\chi$	$=$	418.373
Dual form			418.2.h.b.65.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(2.56624 - 1.48162i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.17566 - 2.03631i) q^{5} +(2.56624 + 1.48162i) q^{6} +0.571027i q^{7} -1.00000 q^{8} +(2.89038 - 5.00628i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(2.56624 - 1.48162i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.17566 - 2.03631i) q^{5} +(2.56624 + 1.48162i) q^{6} +0.571027i q^{7} -1.00000 q^{8} +(2.89038 - 5.00628i) q^{9} +(1.17566 - 2.03631i) q^{10} +(2.06324 - 2.59674i) q^{11} +2.96323i q^{12} +(-0.952833 + 1.65036i) q^{13} +(-0.494524 + 0.285514i) q^{14} +(-6.03405 - 3.48376i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.01614 - 0.586670i) q^{17} +5.78076 q^{18} +(3.45037 + 2.66364i) q^{19} +2.35132 q^{20} +(0.846044 + 1.46539i) q^{21} +(3.28046 + 0.488448i) q^{22} +(-3.18044 + 5.50869i) q^{23} +(-2.56624 + 1.48162i) q^{24} +(-0.264361 + 0.457887i) q^{25} -1.90567 q^{26} -8.24003i q^{27} +(-0.494524 - 0.285514i) q^{28} +(-1.27997 + 2.21698i) q^{29} -6.96752i q^{30} +0.329657i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.44738 - 9.72077i) q^{33} +(1.01614 + 0.586670i) q^{34} +(1.16279 - 0.671335i) q^{35} +(2.89038 + 5.00628i) q^{36} +4.43422i q^{37} +(-0.581595 + 4.31992i) q^{38} +5.64694i q^{39} +(1.17566 + 2.03631i) q^{40} +(-4.57346 - 7.92146i) q^{41} +(-0.846044 + 1.46539i) q^{42} +(-9.13597 + 5.27465i) q^{43} +(1.21722 + 3.08519i) q^{44} -13.5924 q^{45} -6.36088 q^{46} +(-2.95016 + 5.10983i) q^{47} +(-2.56624 - 1.48162i) q^{48} +6.67393 q^{49} -0.528723 q^{50} +(1.73844 - 3.01107i) q^{51} +(-0.952833 - 1.65036i) q^{52} +(-1.52439 - 0.880108i) q^{53} +(7.13608 - 4.12002i) q^{54} +(-7.71342 - 1.14850i) q^{55} -0.571027i q^{56} +(12.8009 + 1.72340i) q^{57} -2.55995 q^{58} +(-5.24172 + 3.02631i) q^{59} +(6.03405 - 3.48376i) q^{60} +(10.9859 + 6.34273i) q^{61} +(-0.285491 + 0.164828i) q^{62} +(2.85872 + 1.65048i) q^{63} +1.00000 q^{64} +4.48084 q^{65} +(9.14213 - 3.60691i) q^{66} +(2.24569 + 1.29655i) q^{67} +1.17334i q^{68} +18.8488i q^{69} +(1.16279 + 0.671335i) q^{70} +(11.4097 - 6.58739i) q^{71} +(-2.89038 + 5.00628i) q^{72} +(-13.3662 + 7.71696i) q^{73} +(-3.84014 + 2.21711i) q^{74} +1.56673i q^{75} +(-4.03196 + 1.65629i) q^{76} +(1.48281 + 1.17817i) q^{77} +(-4.89039 + 2.82347i) q^{78} +(-0.838320 - 1.45201i) q^{79} +(-1.17566 + 2.03631i) q^{80} +(-3.53744 - 6.12702i) q^{81} +(4.57346 - 7.92146i) q^{82} -8.73822i q^{83} -1.69209 q^{84} +(-2.38928 - 1.37945i) q^{85} +(-9.13597 - 5.27465i) q^{86} +7.58572i q^{87} +(-2.06324 + 2.59674i) q^{88} +(8.10707 + 4.68062i) q^{89} +(-6.79621 - 11.7714i) q^{90} +(-0.942398 - 0.544094i) q^{91} +(-3.18044 - 5.50869i) q^{92} +(0.488425 + 0.845977i) q^{93} -5.90032 q^{94} +(1.36752 - 10.1575i) q^{95} -2.96323i q^{96} +(-13.4133 + 7.74414i) q^{97} +(3.33696 + 5.77979i) q^{98} +(-7.03646 - 17.8347i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	2.56624	−	1.48162i	1.48162	−	0.855412i	0.481834	−	0.876262i	$-0.339971\pi$
$3$	2.56624	−	1.48162i	1.48162	−	0.855412i	0.999783	+	0.0208503i	$0.00663733\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.17566	−	2.03631i	−0.525772	−	0.910664i	−0.999549	−	0.0300191i	$-0.990443\pi$
$5$	−1.17566	−	2.03631i	−0.525772	−	0.910664i	0.473777	−	0.880645i	$-0.342890\pi$
$6$	2.56624	+	1.48162i	1.04766	+	0.604868i
$7$			0.571027i			0.215828i	0.994160	+	0.107914i	$0.0344171\pi$
$7$			0.571027i			0.215828i	−0.994160	+	0.107914i	$0.965583\pi$
$8$	−1.00000			−0.353553
$9$	2.89038	−	5.00628i	0.963459	−	1.66876i
$10$	1.17566	−	2.03631i	0.371777	−	0.643936i
$11$	2.06324	−	2.59674i	0.622090	−	0.782946i
$11$	2.06324	−	2.59674i	0.622090	−	0.782946i
$12$			2.96323i			0.855412i
$13$	−0.952833	+	1.65036i	−0.264268	+	0.457726i	−0.967372	−	0.253361i	$-0.918464\pi$
$13$	−0.952833	+	1.65036i	−0.264268	+	0.457726i	0.703103	+	0.711088i	$0.251797\pi$
$14$	−0.494524	+	0.285514i	−0.132167	+	0.0763067i
$15$	−6.03405	−	3.48376i	−1.55799	−	0.899503i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.01614	−	0.586670i	0.246451	−	0.142288i	−0.371687	−	0.928358i	$-0.621221\pi$
$17$	1.01614	−	0.586670i	0.246451	−	0.142288i	0.618138	+	0.786070i	$0.287887\pi$
$18$	5.78076			1.36254
$19$	3.45037	+	2.66364i	0.791568	+	0.611081i
$19$	3.45037	+	2.66364i	0.791568	+	0.611081i
$20$	2.35132			0.525772
$21$	0.846044	+	1.46539i	0.184622	+	0.319774i
$22$	3.28046	+	0.488448i	0.699396	+	0.104137i
$23$	−3.18044	+	5.50869i	−0.663168	+	1.14864i	0.316610	+	0.948556i	$0.397455\pi$
$23$	−3.18044	+	5.50869i	−0.663168	+	1.14864i	−0.979779	+	0.200085i	$0.935878\pi$
$24$	−2.56624	+	1.48162i	−0.523831	+	0.302434i
$25$	−0.264361	+	0.457887i	−0.0528723	+	0.0915774i
$26$	−1.90567			−0.373732
$27$		−	8.24003i		−	1.58579i
$28$	−0.494524	−	0.285514i	−0.0934563	−	0.0539570i
$29$	−1.27997	+	2.21698i	−0.237685	+	0.411683i	−0.960050	−	0.279830i	$-0.909722\pi$
$29$	−1.27997	+	2.21698i	−0.237685	+	0.411683i	0.722365	+	0.691512i	$0.243055\pi$
$30$		−	6.96752i		−	1.27209i
$31$			0.329657i			0.0592081i	0.999562	+	0.0296041i	$0.00942464\pi$
$31$			0.329657i			0.0592081i	−0.999562	+	0.0296041i	$0.990575\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.44738	−	9.72077i	0.251957	−	1.69217i
$34$	1.01614	+	0.586670i	0.174267	+	0.100613i
$35$	1.16279	−	0.671335i	0.196547	−	0.113476i
$36$	2.89038	+	5.00628i	0.481730	+	0.834380i
$37$			4.43422i			0.728981i	0.931207	+	0.364490i	$0.118757\pi$
$37$			4.43422i			0.728981i	−0.931207	+	0.364490i	$0.881243\pi$
$38$	−0.581595	+	4.31992i	−0.0943472	+	0.700784i
$39$			5.64694i			0.904233i
$40$	1.17566	+	2.03631i	0.185888	+	0.321968i
$41$	−4.57346	−	7.92146i	−0.714254	−	1.23712i	−0.963247	−	0.268619i	$-0.913433\pi$
$41$	−4.57346	−	7.92146i	−0.714254	−	1.23712i	0.248993	−	0.968505i	$-0.419901\pi$
$42$	−0.846044	+	1.46539i	−0.130547	+	0.226115i
$43$	−9.13597	+	5.27465i	−1.39322	+	0.804377i	−0.993671	−	0.112334i	$-0.964167\pi$
$43$	−9.13597	+	5.27465i	−1.39322	+	0.804377i	−0.399552	+	0.916711i	$0.630834\pi$
$44$	1.21722	+	3.08519i	0.183503	+	0.465109i
$45$	−13.5924			−2.02624
$46$	−6.36088			−0.937861
$47$	−2.95016	+	5.10983i	−0.430325	+	0.745345i	−0.996901	−	0.0786647i	$-0.974934\pi$
$47$	−2.95016	+	5.10983i	−0.430325	+	0.745345i	0.566576	+	0.824009i	$0.308268\pi$
$48$	−2.56624	−	1.48162i	−0.370404	−	0.213853i
$49$	6.67393			0.953418
$50$	−0.528723			−0.0747727
$51$	1.73844	−	3.01107i	0.243430	−	0.421634i
$52$	−0.952833	−	1.65036i	−0.132134	−	0.228863i
$53$	−1.52439	−	0.880108i	−0.209391	−	0.120892i	0.391637	−	0.920120i	$-0.371909\pi$
$53$	−1.52439	−	0.880108i	−0.209391	−	0.120892i	−0.601028	+	0.799228i	$0.705242\pi$
$54$	7.13608	−	4.12002i	0.971097	−	0.560663i
$55$	−7.71342	−	1.14850i	−1.04008	−	0.154864i
$56$		−	0.571027i		−	0.0763067i
$57$	12.8009	+	1.72340i	1.69553	+	0.228270i
$58$	−2.55995			−0.336137
$59$	−5.24172	+	3.02631i	−0.682414	+	0.393992i	−0.800764	−	0.598980i	$-0.795573\pi$
$59$	−5.24172	+	3.02631i	−0.682414	+	0.393992i	0.118350	+	0.992972i	$0.462240\pi$
$60$	6.03405	−	3.48376i	0.778993	−	0.449752i
$61$	10.9859	+	6.34273i	1.40660	+	0.812104i	0.995059	−	0.0992855i	$-0.0316557\pi$
$61$	10.9859	+	6.34273i	1.40660	+	0.812104i	0.411546	+	0.911389i	$0.364989\pi$
$62$	−0.285491	+	0.164828i	−0.0362574	+	0.0209332i
$63$	2.85872	+	1.65048i	0.360165	+	0.207942i
$64$	1.00000			0.125000
$65$	4.48084			0.555780
$66$	9.14213	−	3.60691i	1.12532	−	0.443980i
$67$	2.24569	+	1.29655i	0.274354	+	0.158399i	0.630865	−	0.775893i	$-0.282700\pi$
$67$	2.24569	+	1.29655i	0.274354	+	0.158399i	−0.356510	+	0.934291i	$0.616034\pi$
$68$			1.17334i			0.142288i
$69$			18.8488i			2.26913i
$70$	1.16279	+	0.671335i	0.138980	+	0.0802399i
$71$	11.4097	−	6.58739i	1.35408	−	0.781779i	0.365263	−	0.930904i	$-0.380979\pi$
$71$	11.4097	−	6.58739i	1.35408	−	0.781779i	0.988818	+	0.149125i	$0.0476458\pi$
$72$	−2.89038	+	5.00628i	−0.340634	+	0.589996i
$73$	−13.3662	+	7.71696i	−1.56439	+	0.903202i	−0.567588	+	0.823312i	$0.692124\pi$
$73$	−13.3662	+	7.71696i	−1.56439	+	0.903202i	−0.996804	+	0.0798898i	$0.974543\pi$
$74$	−3.84014	+	2.21711i	−0.446408	+	0.257734i
$75$			1.56673i			0.180910i
$76$	−4.03196	+	1.65629i	−0.462498	+	0.189989i
$77$	1.48281	+	1.17817i	0.168982	+	0.134264i
$78$	−4.89039	+	2.82347i	−0.553728	+	0.319695i
$79$	−0.838320	−	1.45201i	−0.0943184	−	0.163364i	0.815006	−	0.579453i	$-0.196734\pi$
$79$	−0.838320	−	1.45201i	−0.0943184	−	0.163364i	−0.909324	+	0.416089i	$0.863401\pi$
$80$	−1.17566	+	2.03631i	−0.131443	+	0.227666i
$81$	−3.53744	−	6.12702i	−0.393049	−	0.680780i
$82$	4.57346	−	7.92146i	0.505054	−	0.874779i
$83$		−	8.73822i		−	0.959144i	−0.877503	−	0.479572i	$-0.840792\pi$
$83$		−	8.73822i		−	0.959144i	0.877503	−	0.479572i	$-0.159208\pi$
$84$	−1.69209			−0.184622
$85$	−2.38928	−	1.37945i	−0.259154	−	0.149622i
$86$	−9.13597	−	5.27465i	−0.985157	−	0.568781i
$87$			7.58572i			0.813275i
$88$	−2.06324	+	2.59674i	−0.219942	+	0.276813i
$89$	8.10707	+	4.68062i	0.859348	+	0.496145i	0.863794	−	0.503845i	$-0.168082\pi$
$89$	8.10707	+	4.68062i	0.859348	+	0.496145i	−0.00444609	+	0.999990i	$0.501415\pi$
$90$	−6.79621	−	11.7714i	−0.716384	−	1.24081i
$91$	−0.942398	−	0.544094i	−0.0987901	−	0.0570365i
$92$	−3.18044	−	5.50869i	−0.331584	−	0.574320i
$93$	0.488425	+	0.845977i	0.0506473	+	0.0877238i
$94$	−5.90032			−0.608571
$95$	1.36752	−	10.1575i	0.140304	−	1.04214i
$96$		−	2.96323i		−	0.302434i
$97$	−13.4133	+	7.74414i	−1.36191	+	0.786299i	−0.989878	−	0.141921i	$-0.954672\pi$
$97$	−13.4133	+	7.74414i	−1.36191	+	0.786299i	−0.372031	+	0.928220i	$0.621339\pi$
$98$	3.33696	+	5.77979i	0.337084	+	0.583847i
$99$	−7.03646	−	17.8347i	−0.707191	−	1.79246i
$100$	−0.264361	−	0.457887i	−0.0264361	−	0.0457887i
$101$	−1.86595	−	1.07731i	−0.185669	−	0.107196i	0.404284	−	0.914633i	$-0.367521\pi$
$101$	−1.86595	−	1.07731i	−0.185669	−	0.107196i	−0.589954	+	0.807437i	$0.700854\pi$
$102$	3.47688			0.344263
$103$		−	0.811899i		−	0.0799988i	−0.999200	−	0.0399994i	$-0.987264\pi$
$103$		−	0.811899i		−	0.0799988i	0.999200	−	0.0399994i	$-0.0127356\pi$
$104$	0.952833	−	1.65036i	0.0934330	−	0.161831i
$105$	1.98932	−	3.44561i	0.194138	−	0.336257i
$106$		−	1.76022i		−	0.170967i
$107$	7.61400			0.736073			0.368037	−	0.929811i	$-0.380030\pi$
$107$	7.61400			0.736073			0.368037	+	0.929811i	$0.380030\pi$
$108$	7.13608	+	4.12002i	0.686669	+	0.396449i
$109$	−7.07435	−	12.2531i	−0.677600	−	1.17364i	−0.975702	−	0.219104i	$-0.929687\pi$
$109$	−7.07435	−	12.2531i	−0.677600	−	1.17364i	0.298101	−	0.954534i	$-0.403647\pi$
$110$	−2.86208	−	7.25427i	−0.272889	−	0.691667i
$111$	6.56981	+	11.3792i	0.623579	+	1.08007i
$112$	0.494524	−	0.285514i	0.0467281	−	0.0269785i
$113$		−	6.92610i		−	0.651553i	−0.945447	−	0.325776i	$-0.894374\pi$
$113$		−	6.92610i		−	0.651553i	0.945447	−	0.325776i	$-0.105626\pi$
$114$	4.90796	+	11.9476i	0.459673	+	1.11900i
$115$	14.9565			1.39470
$116$	−1.27997	−	2.21698i	−0.118843	−	0.205841i
$117$	5.50810	+	9.54030i	0.509224	+	0.882001i
$118$	−5.24172	−	3.02631i	−0.482540	−	0.278594i
$119$	0.335005	+	0.580245i	0.0307098	+	0.0531910i
$120$	6.03405	+	3.48376i	0.550831	+	0.318022i
$121$	−2.48610	−	10.7154i	−0.226009	−	0.974125i
$122$			12.6855i			1.14849i
$123$	−23.4731	−	13.5522i	−2.11650	−	1.22196i
$124$	−0.285491	−	0.164828i	−0.0256379	−	0.0148020i
$125$	−10.5134			−0.940349
$126$			3.30097i			0.294074i
$127$	0.292083	−	0.505902i	0.0259181	−	0.0448915i	−0.852775	−	0.522278i	$-0.825082\pi$
$127$	0.292083	−	0.505902i	0.0259181	−	0.0448915i	0.878694	+	0.477386i	$0.158416\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−15.6300	+	27.0720i	−1.37615	+	2.38356i
$130$	2.24042	+	3.88052i	0.196498	+	0.340344i
$131$	2.97205	−	1.71591i	0.259669	−	0.149920i	−0.364514	−	0.931198i	$-0.618765\pi$
$131$	2.97205	−	1.71591i	0.259669	−	0.149920i	0.624184	+	0.781278i	$0.285432\pi$
$132$	7.69474	+	6.11386i	0.669741	+	0.532143i
$133$	−1.52101	+	1.97025i	−0.131888	+	0.170843i
$134$			2.59310i			0.224009i
$135$	−16.7792	+	9.68749i	−1.44413	+	0.833766i
$136$	−1.01614	+	0.586670i	−0.0871335	+	0.0503065i
$137$	5.60961	−	9.71612i	0.479261	−	0.830104i	−0.520456	−	0.853888i	$-0.674238\pi$
$137$	5.60961	−	9.71612i	0.479261	−	0.830104i	0.999717	+	0.0237840i	$0.00757140\pi$
$138$	−16.3235	+	9.42439i	−1.38955	+	0.802258i
$139$	−10.9788	−	6.33862i	−0.931211	−	0.537635i	−0.0440167	−	0.999031i	$-0.514015\pi$
$139$	−10.9788	−	6.33862i	−0.931211	−	0.537635i	−0.887194	+	0.461396i	$0.847349\pi$
$140$			1.34267i			0.113476i
$141$			17.4840i			1.47242i
$142$	11.4097	+	6.58739i	0.957480	+	0.552801i
$143$	2.31962	+	5.87933i	0.193976	+	0.491655i
$144$	−5.78076			−0.481730
$145$	6.01926			0.499873
$146$	−13.3662	−	7.71696i	−1.10619	−	0.638660i
$147$	17.1269	−	9.88821i	1.41260	−	0.815565i
$148$	−3.84014	−	2.21711i	−0.315658	−	0.182245i
$149$	0.267192	−	0.154263i	0.0218892	−	0.0126378i	−0.489015	−	0.872275i	$-0.662644\pi$
$149$	0.267192	−	0.154263i	0.0218892	−	0.0126378i	0.510905	+	0.859637i	$0.329311\pi$
$150$	−1.35683	+	0.783364i	−0.110784	+	0.0639614i
$151$	−0.718265			−0.0584515			−0.0292258	−	0.999573i	$-0.509304\pi$
$151$	−0.718265			−0.0584515			−0.0292258	+	0.999573i	$0.509304\pi$
$152$	−3.45037	−	2.66364i	−0.279862	−	0.216050i
$153$		−	6.78279i		−	0.548356i
$154$	−0.278917	+	1.87323i	−0.0224758	+	0.150949i
$155$	0.671282	−	0.387565i	0.0539187	−	0.0311300i
$156$	−4.89039	−	2.82347i	−0.391545	−	0.226058i
$157$	−11.5664	−	20.0336i	−0.923100	−	1.59886i	−0.794589	−	0.607148i	$-0.792313\pi$
$157$	−11.5664	−	20.0336i	−0.923100	−	1.59886i	−0.128512	−	0.991708i	$-0.541020\pi$
$158$	0.838320	−	1.45201i	0.0666932	−	0.115516i
$159$	−5.21593			−0.413650
$160$	−2.35132			−0.185888
$161$	−3.14561	−	1.81612i	−0.247909	−	0.143130i
$162$	3.53744	−	6.12702i	0.277927	−	0.481384i
$163$	4.45286			0.348775			0.174387	−	0.984677i	$-0.444206\pi$
$163$	4.45286			0.348775			0.174387	+	0.984677i	$0.444206\pi$
$164$	9.14691			0.714254
$165$	−21.4961	+	8.48102i	−1.67347	+	0.660247i
$166$	7.56752	−	4.36911i	0.587353	−	0.339109i
$167$	11.6550	−	20.1871i	0.901894	−	1.56213i	0.0768604	−	0.997042i	$-0.475510\pi$
$167$	11.6550	−	20.1871i	0.901894	−	1.56213i	0.825033	−	0.565084i	$-0.191156\pi$
$168$	−0.846044	−	1.46539i	−0.0652737	−	0.113057i
$169$	4.68422	+	8.11330i	0.360324	+	0.624100i
$170$		−	2.75890i		−	0.211598i
$171$	23.3078	−	9.57459i	1.78239	−	0.732187i
$172$		−	10.5493i		−	0.804377i
$173$	7.83241	+	13.5661i	0.595487	+	1.03141i	0.993478	+	0.114025i	$0.0363744\pi$
$173$	7.83241	+	13.5661i	0.595487	+	1.03141i	−0.397991	+	0.917390i	$0.630292\pi$
$174$	−6.56943	+	3.79286i	−0.498027	+	0.287536i
$175$	−0.261466	−	0.150957i	−0.0197650	−	0.0114113i
$176$	−3.28046	−	0.488448i	−0.247274	−	0.0368181i
$177$	−8.96766	+	15.5325i	−0.674051	+	1.16749i
$178$			9.36124i			0.701654i
$179$			3.16369i			0.236465i	0.992986	+	0.118233i	$0.0377228\pi$
$179$			3.16369i			0.236465i	−0.992986	+	0.118233i	$0.962277\pi$
$180$	6.79621	−	11.7714i	0.506560	−	0.877388i
$181$	−20.2505	−	11.6916i	−1.50521	−	0.869033i	−0.999982	−	0.00604749i	$-0.998075\pi$
$181$	−20.2505	−	11.6916i	−1.50521	−	0.869033i	−0.505228	−	0.862986i	$-0.668592\pi$
$182$		−	1.08819i		−	0.0806618i
$183$	37.5900			2.77873
$184$	3.18044	−	5.50869i	0.234465	−	0.406106i
$185$	9.02942	−	5.21314i	0.663856	−	0.383278i
$186$	−0.488425	+	0.845977i	−0.0358131	+	0.0620301i
$187$	0.573115	−	3.84910i	0.0419103	−	0.281474i
$188$	−2.95016	−	5.10983i	−0.215162	−	0.372672i
$189$	4.70528			0.342259
$190$	9.48045	−	3.89446i	0.687784	−	0.282534i
$191$	6.05197			0.437906			0.218953	−	0.975735i	$-0.429736\pi$
$191$	6.05197			0.437906			0.218953	+	0.975735i	$0.429736\pi$
$192$	2.56624	−	1.48162i	0.185202	−	0.106927i
$193$	8.80236	+	15.2461i	0.633608	+	1.09744i	0.986808	+	0.161893i	$0.0517600\pi$
$193$	8.80236	+	15.2461i	0.633608	+	1.09744i	−0.353201	+	0.935548i	$0.614907\pi$
$194$	−13.4133	−	7.74414i	−0.963015	−	0.555997i
$195$	11.4989	−	6.63889i	0.823453	−	0.475421i
$196$	−3.33696	+	5.77979i	−0.238355	+	0.412842i
$197$		−	4.55312i		−	0.324397i	−0.986758	−	0.162198i	$-0.948142\pi$
$197$		−	4.55312i		−	0.324397i	0.986758	−	0.162198i	$-0.0518584\pi$
$198$	11.9271	−	15.0111i	0.847620	−	1.06679i
$199$	−8.44623	+	14.6293i	−0.598737	+	1.03704i	0.394270	+	0.918995i	$0.370997\pi$
$199$	−8.44623	+	14.6293i	−0.598737	+	1.03704i	−0.993008	+	0.118049i	$0.962336\pi$
$200$	0.264361	−	0.457887i	0.0186932	−	0.0323775i
$201$	7.68395			0.541984
$202$		−	2.15462i		−	0.151598i
$203$	−1.26596	−	0.730900i	−0.0888526	−	0.0512991i
$204$	1.73844	+	3.01107i	0.121715	+	0.210817i
$205$	−10.7537	+	18.6259i	−0.751069	+	1.30089i
$206$	0.703125	−	0.405949i	0.0489890	−	0.0282838i
$207$	18.3854	+	31.8444i	1.27787	+	2.21334i
$208$	1.90567			0.132134
$209$	14.0357	−	3.46398i	0.970870	−	0.239608i
$210$	3.97864			0.274553
$211$	0.152226	+	0.263664i	0.0104797	+	0.0181514i	0.871218	−	0.490897i	$-0.163331\pi$
$211$	0.152226	+	0.263664i	0.0104797	+	0.0181514i	−0.860738	+	0.509048i	$0.829997\pi$
$212$	1.52439	−	0.880108i	0.104696	−	0.0604460i
$213$	19.5200	−	33.8096i	1.33749	−	2.31659i
$214$	3.80700	+	6.59392i	0.260241	+	0.450751i
$215$	21.4816	+	12.4024i	1.46503	+	0.845838i
$216$			8.24003i			0.560663i
$217$	−0.188243			−0.0127788
$218$	7.07435	−	12.2531i	0.479136	−	0.829887i
$219$	−22.8672	+	39.6071i	−1.54522	+	2.67640i
$220$	4.85134	−	6.10577i	0.327077	−	0.411651i
$221$			2.23599i			0.150409i
$222$	−6.56981	+	11.3792i	−0.440937	+	0.763725i
$223$	14.3317	−	8.27439i	0.959719	−	0.554094i	0.0636323	−	0.997973i	$-0.479732\pi$
$223$	14.3317	−	8.27439i	0.959719	−	0.554094i	0.896086	+	0.443880i	$0.146398\pi$
$224$	0.494524	+	0.285514i	0.0330418	+	0.0190767i
$225$	1.52821	+	2.64693i	0.101881	+	0.176462i
$226$	5.99818	−	3.46305i	0.398993	−	0.230359i
$227$	29.7240			1.97285			0.986425	−	0.164212i	$-0.0525081\pi$
$227$	29.7240			1.97285			0.986425	+	0.164212i	$0.0525081\pi$
$228$	−7.89298	+	10.2242i	−0.522726	+	0.677117i
$229$	−6.16727			−0.407545			−0.203772	−	0.979018i	$-0.565320\pi$
$229$	−6.16727			−0.407545			−0.203772	+	0.979018i	$0.565320\pi$
$230$	7.47825	+	12.9527i	0.493101	+	0.854076i
$231$	5.55083	+	0.826496i	0.365217	+	0.0543795i
$232$	1.27997	−	2.21698i	0.0840344	−	0.145552i
$233$	17.9328	−	10.3535i	1.17482	−	0.678282i	0.220009	−	0.975498i	$-0.429391\pi$
$233$	17.9328	−	10.3535i	1.17482	−	0.678282i	0.954810	+	0.297215i	$0.0960579\pi$
$234$	−5.50810	+	9.54030i	−0.360076	+	0.623669i
$235$	13.8736			0.905011
$236$		−	6.05262i		−	0.393992i
$237$	−4.30265	−	2.48414i	−0.279487	−	0.161362i
$238$	−0.335005	+	0.580245i	−0.0217151	+	0.0376117i
$239$		−	11.5876i		−	0.749541i	−0.927118	−	0.374771i	$-0.877721\pi$
$239$		−	11.5876i		−	0.749541i	0.927118	−	0.374771i	$-0.122279\pi$
$240$			6.96752i			0.449752i
$241$	1.65754	−	2.87095i	0.106772	−	0.184934i	−0.807689	−	0.589609i	$-0.799282\pi$
$241$	1.65754	−	2.87095i	0.106772	−	0.184934i	0.914461	+	0.404675i	$0.132615\pi$
$242$	8.03674	−	7.51071i	0.516621	−	0.482807i
$243$	3.25243	+	1.87779i	0.208644	+	0.120460i
$244$	−10.9859	+	6.34273i	−0.703302	+	0.406052i
$245$	−7.84628	−	13.5902i	−0.501281	−	0.868243i
$246$		−	27.1044i		−	1.72812i
$247$	−7.68357	+	3.15633i	−0.488894	+	0.200832i
$248$		−	0.329657i		−	0.0209332i
$249$	−12.9467	−	22.4243i	−0.820463	−	1.42108i
$250$	−5.25671	−	9.10489i	−0.332464	−	0.575844i
$251$	−4.44899	+	7.70588i	−0.280818	+	0.486391i	−0.971586	−	0.236685i	$-0.923939\pi$
$251$	−4.44899	+	7.70588i	−0.280818	+	0.486391i	0.690769	+	0.723076i	$0.257272\pi$
$252$	−2.85872	+	1.65048i	−0.180083	+	0.103971i
$253$	7.74261	+	19.6245i	0.486774	+	1.23378i
$254$	0.584165			0.0366538
$255$	−8.17527			−0.511955
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−16.0999	−	9.29526i	−1.00428	−	0.579823i	−0.0947697	−	0.995499i	$-0.530211\pi$
$257$	−16.0999	−	9.29526i	−1.00428	−	0.579823i	−0.909512	+	0.415677i	$0.863545\pi$
$258$	−31.2601			−1.94617
$259$	−2.53206			−0.157334
$260$	−2.24042	+	3.88052i	−0.138945	+	0.240660i
$261$	7.39921	+	12.8158i	0.458000	+	0.793279i
$262$	2.97205	+	1.71591i	0.183614	+	0.106010i
$263$	−2.99687	+	1.73024i	−0.184795	+	0.106691i	−0.589544	−	0.807737i	$-0.700692\pi$
$263$	−2.99687	+	1.73024i	−0.184795	+	0.106691i	0.404749	+	0.914428i	$0.367359\pi$
$264$	−1.44738	+	9.72077i	−0.0890804	+	0.598272i
$265$			4.13884i			0.254247i
$266$	−2.46679	−	0.332107i	−0.151249	−	0.0203628i
$267$	27.7395			1.69763
$268$	−2.24569	+	1.29655i	−0.137177	+	0.0791993i
$269$	−13.0396	+	7.52841i	−0.795038	+	0.459015i	−0.841733	−	0.539894i	$-0.818464\pi$
$269$	−13.0396	+	7.52841i	−0.795038	+	0.459015i	0.0466953	+	0.998909i	$0.485131\pi$
$270$	−16.7792	−	9.68749i	−1.02115	−	0.589562i
$271$	24.8322	−	14.3369i	1.50845	−	0.870904i	0.508499	−	0.861063i	$-0.330201\pi$
$271$	24.8322	−	14.3369i	1.50845	−	0.870904i	0.999952	−	0.00984145i	$-0.00313268\pi$
$272$	−1.01614	−	0.586670i	−0.0616127	−	0.0355721i
$273$	−3.22455			−0.195159
$274$	11.2192			0.677777
$275$	0.643573	+	1.63121i	0.0388089	+	0.0983655i
$276$	−16.3235	−	9.42439i	−0.982561	−	0.567282i
$277$			22.3703i			1.34410i	0.740506	+	0.672050i	$0.234586\pi$
$277$			22.3703i			1.34410i	−0.740506	+	0.672050i	$0.765414\pi$
$278$		−	12.6772i		−	0.760331i
$279$	1.65036	+	0.952833i	0.0988042	+	0.0570446i
$280$	−1.16279	+	0.671335i	−0.0694898	+	0.0401199i
$281$	−2.83619	+	4.91242i	−0.169193	+	0.293050i	−0.938136	−	0.346266i	$-0.887449\pi$
$281$	−2.83619	+	4.91242i	−0.169193	+	0.293050i	0.768944	+	0.639317i	$0.220783\pi$
$282$	−15.1416	+	8.74201i	−0.901670	+	0.520579i
$283$	3.04939	−	1.76057i	0.181268	−	0.104655i	−0.406620	−	0.913597i	$-0.633293\pi$
$283$	3.04939	−	1.76057i	0.181268	−	0.104655i	0.587888	+	0.808942i	$0.299960\pi$
$284$			13.1748i			0.781779i
$285$	−11.5402	−	28.0928i	−0.683583	−	1.66407i
$286$	−3.93184	+	4.94852i	−0.232495	+	0.292612i
$287$	4.52337	−	2.61157i	0.267006	−	0.154156i
$288$	−2.89038	−	5.00628i	−0.170317	−	0.294998i
$289$	−7.81164	+	13.5302i	−0.459508	+	0.795891i
$290$	3.00963	+	5.21283i	0.176732	+	0.306108i
$291$	−22.9477	+	39.7466i	−1.34522	+	2.32999i
$292$		−	15.4339i		−	0.903202i
$293$	−26.2492			−1.53350			−0.766748	−	0.641948i	$-0.778127\pi$
$293$	−26.2492			−1.53350			−0.766748	+	0.641948i	$0.778127\pi$
$294$	17.1269	+	9.88821i	0.998860	+	0.576692i
$295$	12.3250	+	7.11583i	0.717588	+	0.414300i
$296$		−	4.43422i		−	0.257734i
$297$	−21.3972	−	17.0011i	−1.24159	−	0.986507i
$298$	0.267192	+	0.154263i	0.0154780	+	0.00893624i
$299$	−6.06086	−	10.4977i	−0.350509	−	0.607099i
$300$	−1.35683	−	0.783364i	−0.0783364	−	0.0452276i
$301$	−3.01197	−	5.21689i	−0.173607	−	0.300696i
$302$	−0.359132	−	0.622035i	−0.0206657	−	0.0357941i
$303$	−6.38464			−0.366788
$304$	0.581595	−	4.31992i	0.0333568	−	0.247765i
$305$		−	29.8276i		−	1.70793i
$306$	5.87407	−	3.39140i	0.335798	−	0.193873i
$307$	−13.8879	−	24.0546i	−0.792625	−	1.37287i	−0.924337	−	0.381578i	$-0.875381\pi$
$307$	−13.8879	−	24.0546i	−0.792625	−	1.37287i	0.131712	−	0.991288i	$-0.457953\pi$
$308$	−1.76173	+	0.695067i	−0.100384	+	0.0396051i
$309$	−1.20292	−	2.08352i	−0.0684319	−	0.118528i
$310$	0.671282	+	0.387565i	0.0381263	+	0.0220122i
$311$	1.86204			0.105587			0.0527933	−	0.998605i	$-0.483188\pi$
$311$	1.86204			0.105587			0.0527933	+	0.998605i	$0.483188\pi$
$312$		−	5.64694i		−	0.319695i
$313$	−10.9434	+	18.9545i	−0.618557	+	1.07137i	0.371192	+	0.928556i	$0.378949\pi$
$313$	−10.9434	+	18.9545i	−0.618557	+	1.07137i	−0.989749	+	0.142816i	$0.954384\pi$
$314$	11.5664	−	20.0336i	0.652730	−	1.13056i
$315$		−	7.76165i		−	0.437319i
$316$	1.67664			0.0943184
$317$	−20.1001	−	11.6048i	−1.12893	−	0.651790i	−0.185266	−	0.982688i	$-0.559315\pi$
$317$	−20.1001	−	11.6048i	−1.12893	−	0.651790i	−0.943666	+	0.330899i	$0.892648\pi$
$318$	−2.60796	−	4.51713i	−0.146247	−	0.253308i
$319$	3.11602	+	7.89791i	0.174464	+	0.442198i
$320$	−1.17566	−	2.03631i	−0.0657215	−	0.113833i
$321$	19.5393	−	11.2810i	1.09058	−	0.629646i
$322$		−	3.63224i		−	0.202417i
$323$	5.06874	+	0.682409i	0.282032	+	0.0379702i
$324$	7.07488			0.393049
$325$	−0.503784	−	0.872580i	−0.0279449	−	0.0484020i
$326$	2.22643	+	3.85629i	0.123310	+	0.213580i
$327$	−36.3089	−	20.9630i	−2.00789	−	1.15925i
$328$	4.57346	+	7.92146i	0.252527	+	0.437389i
$329$	−2.91785	−	1.68462i	−0.160866	−	0.0928762i
$330$	−18.0928	−	14.3757i	−0.995977	−	0.791354i
$331$		−	19.1420i		−	1.05214i	−0.850441	−	0.526070i	$-0.823665\pi$
$331$		−	19.1420i		−	1.05214i	0.850441	−	0.526070i	$-0.176335\pi$
$332$	7.56752	+	4.36911i	0.415322	+	0.239786i
$333$	22.1989	+	12.8166i	1.21649	+	0.702343i
$334$	23.3101			1.27547
$335$		−	6.09721i		−	0.333126i
$336$	0.846044	−	1.46539i	0.0461555	−	0.0799436i
$337$	11.3437	+	19.6478i	0.617929	+	1.07028i	0.989863	+	0.142026i	$0.0453616\pi$
$337$	11.3437	+	19.6478i	0.617929	+	1.07028i	−0.371934	+	0.928259i	$0.621305\pi$
$338$	−4.68422	+	8.11330i	−0.254788	+	0.441306i
$339$	−10.2618	−	17.7740i	−0.557346	−	0.965351i
$340$	2.38928	−	1.37945i	0.129577	−	0.0748112i
$341$	0.856032	+	0.680161i	0.0463568	+	0.0368328i
$342$	19.9457	+	15.3978i	1.07854	+	0.832620i
$343$			7.80819i			0.421602i
$344$	9.13597	−	5.27465i	0.492578	−	0.284390i
$345$	38.3819	−	22.1598i	2.06641	−	1.19304i
$346$	−7.83241	+	13.5661i	−0.421073	+	0.729320i
$347$	−23.1209	+	13.3489i	−1.24120	+	0.716605i	−0.969338	−	0.245733i	$-0.920971\pi$
$347$	−23.1209	+	13.3489i	−1.24120	+	0.716605i	−0.271858	+	0.962337i	$0.587638\pi$
$348$	−6.56943	−	3.79286i	−0.352158	−	0.203319i
$349$			18.4451i			0.987344i	0.869648	+	0.493672i	$0.164346\pi$
$349$			18.4451i			0.987344i	−0.869648	+	0.493672i	$0.835654\pi$
$350$		−	0.301915i		−	0.0161380i
$351$	13.5990	+	7.85138i	0.725860	+	0.419075i
$352$	−1.21722	−	3.08519i	−0.0648781	−	0.164441i
$353$	−17.7251			−0.943414			−0.471707	−	0.881755i	$-0.656362\pi$
$353$	−17.7251			−0.943414			−0.471707	+	0.881755i	$0.656362\pi$
$354$	−17.9353			−0.953252
$355$	−26.8279	−	15.4891i	−1.42388	−	0.822075i
$356$	−8.10707	+	4.68062i	−0.429674	+	0.248072i
$357$	1.71940	+	0.992697i	0.0910004	+	0.0525391i
$358$	−2.73983	+	1.58184i	−0.144805	+	0.0836030i
$359$	−1.29550	+	0.747959i	−0.0683740	+	0.0394758i	−0.533797	−	0.845612i	$-0.679235\pi$
$359$	−1.29550	+	0.747959i	−0.0683740	+	0.0394758i	0.465423	+	0.885088i	$0.345902\pi$
$360$	13.5924			0.716384
$361$	4.81006	+	18.3811i	0.253161	+	0.967424i
$362$		−	23.3833i		−	1.22900i
$363$	−22.2560	−	23.8147i	−1.16814	−	1.24995i
$364$	0.942398	−	0.544094i	0.0493951	−	0.0285183i
$365$	31.4282	+	18.1451i	1.64503	+	0.949757i
$366$	18.7950	+	32.5539i	0.982430	+	1.70162i
$367$	15.6822	−	27.1624i	0.818606	−	1.41787i	−0.0881040	−	0.996111i	$-0.528081\pi$
$367$	15.6822	−	27.1624i	0.818606	−	1.41787i	0.906710	−	0.421755i	$-0.138586\pi$
$368$	6.36088			0.331584
$369$	−52.8761			−2.75262
$370$	9.02942	+	5.21314i	0.469417	+	0.271018i
$371$	0.502565	−	0.870469i	0.0260919	−	0.0451925i
$372$	−0.976850			−0.0506473
$373$	−8.87474			−0.459517			−0.229758	−	0.973248i	$-0.573794\pi$
$373$	−8.87474			−0.459517			−0.229758	+	0.973248i	$0.573794\pi$
$374$	3.61997	−	1.42822i	0.187184	−	0.0738513i
$375$	−26.9799	+	15.5769i	−1.39324	+	0.804386i
$376$	2.95016	−	5.10983i	0.152143	−	0.263519i
$377$	−2.43920	−	4.22482i	−0.125625	−	0.217589i
$378$	2.35264	+	4.07489i	0.121007	+	0.209590i
$379$		−	32.8522i		−	1.68750i	−0.536733	−	0.843752i	$-0.680342\pi$
$379$		−	32.8522i		−	1.68750i	0.536733	−	0.843752i	$-0.319658\pi$
$380$	8.11293	+	6.26308i	0.416184	+	0.321289i
$381$		−	1.73102i		−	0.0886828i
$382$	3.02599	+	5.24116i	0.154823	+	0.268161i
$383$	−14.5080	+	8.37617i	−0.741322	+	0.428002i	−0.822550	−	0.568693i	$-0.807449\pi$
$383$	−14.5080	+	8.37617i	−0.741322	+	0.428002i	0.0812278	+	0.996696i	$0.474116\pi$
$384$	2.56624	+	1.48162i	0.130958	+	0.0756085i
$385$	0.655824	−	4.40457i	0.0334239	−	0.224478i
$386$	−8.80236	+	15.2461i	−0.448028	+	0.776008i
$387$			60.9830i			3.09994i
$388$		−	15.4883i		−	0.786299i
$389$	−7.05992	+	12.2281i	−0.357952	+	0.619991i	−0.987619	−	0.156874i	$-0.949858\pi$
$389$	−7.05992	+	12.2281i	−0.357952	+	0.619991i	0.629667	+	0.776866i	$0.283192\pi$
$390$	11.4989	+	6.63889i	0.582269	+	0.336173i
$391$			7.46348i			0.377444i
$392$	−6.67393			−0.337084
$393$	5.08466	−	8.80689i	0.256487	−	0.444249i
$394$	3.94312	−	2.27656i	0.198652	−	0.114692i
$395$	−1.97116	+	3.41415i	−0.0991799	+	0.171785i
$396$	18.9635	+	2.82360i	0.952954	+	0.141891i
$397$	13.8657	+	24.0162i	0.695902	+	1.20534i	0.969876	+	0.243600i	$0.0783283\pi$
$397$	13.8657	+	24.0162i	0.695902	+	1.20534i	−0.273974	+	0.961737i	$0.588338\pi$
$398$	−16.8925			−0.846743
$399$	−0.984110	+	7.30969i	−0.0492671	+	0.365942i
$400$	0.528723			0.0264361
$401$	4.75221	−	2.74369i	0.237314	−	0.137013i	−0.376628	−	0.926365i	$-0.622916\pi$
$401$	4.75221	−	2.74369i	0.237314	−	0.137013i	0.613942	+	0.789351i	$0.289583\pi$
$402$	3.84198	+	6.65450i	0.191620	+	0.331896i
$403$	−0.544051	−	0.314108i	−0.0271011	−	0.0156468i
$404$	1.86595	−	1.07731i	0.0928347	−	0.0535982i
$405$	−8.31766	+	14.4066i	−0.413308	+	0.715870i
$406$		−	1.46180i		−	0.0725479i
$407$	11.5145	+	9.14884i	0.570752	+	0.453491i
$408$	−1.73844	+	3.01107i	−0.0860656	+	0.149070i
$409$	17.0930	−	29.6060i	0.845196	−	1.46392i	−0.0402542	−	0.999189i	$-0.512817\pi$
$409$	17.0930	−	29.6060i	0.845196	−	1.46392i	0.885451	−	0.464734i	$-0.153850\pi$
$410$	−21.5074			−1.06217
$411$		−	33.2452i		−	1.63986i
$412$	0.703125	+	0.405949i	0.0346405	+	0.0199997i
$413$	−1.72811	−	2.99317i	−0.0850345	−	0.147284i
$414$	−18.3854	+	31.8444i	−0.903591	+	1.56507i
$415$	−17.7937	+	10.2732i	−0.873458	+	0.504291i
$416$	0.952833	+	1.65036i	0.0467165	+	0.0809153i
$417$	−37.5656			−1.83960
$418$	10.0177	+	10.4233i	0.489984	+	0.509819i
$419$	−0.593149			−0.0289772			−0.0144886	−	0.999895i	$-0.504612\pi$
$419$	−0.593149			−0.0289772			−0.0144886	+	0.999895i	$0.504612\pi$
$420$	1.98932	+	3.44561i	0.0970690	+	0.168128i
$421$	16.1128	−	9.30270i	0.785288	−	0.453386i	−0.0530133	−	0.998594i	$-0.516883\pi$
$421$	16.1128	−	9.30270i	0.785288	−	0.453386i	0.838301	+	0.545208i	$0.183549\pi$
$422$	−0.152226	+	0.263664i	−0.00741026	+	0.0128350i
$423$	17.0542	+	29.5387i	0.829201	+	1.43622i
$424$	1.52439	+	0.880108i	0.0740310	+	0.0427418i
$425$			0.620371i			0.0300924i
$426$	39.0399			1.89149
$427$	−3.62187	+	6.27327i	−0.175275	+	0.303585i
$428$	−3.80700	+	6.59392i	−0.184018	+	0.318729i
$429$	14.6636	+	11.6510i	0.707966	+	0.562514i
$430$			24.8048i			1.19620i
$431$	−3.62863	+	6.28497i	−0.174785	+	0.302736i	−0.940087	−	0.340935i	$-0.889256\pi$
$431$	−3.62863	+	6.28497i	−0.174785	+	0.302736i	0.765302	+	0.643671i	$0.222590\pi$
$432$	−7.13608	+	4.12002i	−0.343335	+	0.198224i
$433$	8.82071	+	5.09264i	0.423896	+	0.244737i	0.696743	−	0.717321i	$-0.254632\pi$
$433$	8.82071	+	5.09264i	0.423896	+	0.244737i	−0.272847	+	0.962058i	$0.587965\pi$
$434$	−0.0941215	−	0.163023i	−0.00451798	−	0.00782537i
$435$	15.4468	−	8.91824i	0.740620	−	0.427597i
$436$	14.1487			0.677600
$437$	−25.6468	+	10.5354i	−1.22685	+	0.503979i
$438$	−45.7343			−2.18527
$439$	9.13873	+	15.8287i	0.436168	+	0.755465i	0.997390	−	0.0722004i	$-0.0230021\pi$
$439$	9.13873	+	15.8287i	0.436168	+	0.755465i	−0.561222	+	0.827665i	$0.689669\pi$
$440$	7.71342	+	1.14850i	0.367723	+	0.0547525i
$441$	19.2902	−	33.4116i	0.918580	−	1.59103i
$442$	−1.93643	+	1.11800i	−0.0921065	+	0.0531777i
$443$	11.1838	−	19.3709i	0.531357	−	0.920338i	−0.467973	−	0.883743i	$-0.655015\pi$
$443$	11.1838	−	19.3709i	0.531357	−	0.920338i	0.999330	−	0.0365951i	$-0.0116512\pi$
$444$	−13.1396			−0.623579
$445$		−	22.0113i		−	1.04344i
$446$	14.3317	+	8.27439i	0.678624	+	0.391804i
$447$	0.457119	−	0.791753i	0.0216210	−	0.0374486i
$448$			0.571027i			0.0269785i
$449$		−	16.6227i		−	0.784473i	−0.919864	−	0.392237i	$-0.871701\pi$
$449$		−	16.6227i		−	0.784473i	0.919864	−	0.392237i	$-0.128299\pi$
$450$	−1.52821	+	2.64693i	−0.0720404	+	0.124778i
$451$	−30.0061	−	4.46779i	−1.41293	−	0.210380i
$452$	5.99818	+	3.46305i	0.282131	+	0.162888i
$453$	−1.84324	+	1.06419i	−0.0866028	+	0.0500002i
$454$	14.8620	+	25.7417i	0.697508	+	1.20812i
$455$			2.55868i			0.119953i
$456$	−12.8009	−	1.72340i	−0.599459	−	0.0807057i
$457$			21.7360i			1.01677i	0.861131	+	0.508383i	$0.169757\pi$
$457$			21.7360i			1.01677i	−0.861131	+	0.508383i	$0.830243\pi$
$458$	−3.08363	−	5.34101i	−0.144089	−	0.249569i
$459$	−4.83418	−	8.37304i	−0.225640	−	0.390820i
$460$	−7.47825	+	12.9527i	−0.348675	+	0.603923i
$461$	35.7720	−	20.6530i	1.66607	−	0.961906i	0.696345	−	0.717708i	$-0.254809\pi$
$461$	35.7720	−	20.6530i	1.66607	−	0.961906i	0.969725	−	0.244198i	$-0.0785248\pi$
$462$	2.05965	+	5.22040i	0.0958234	+	0.242875i
$463$	4.17685			0.194115			0.0970574	−	0.995279i	$-0.469057\pi$
$463$	4.17685			0.194115			0.0970574	+	0.995279i	$0.469057\pi$
$464$	2.55995			0.118843
$465$	1.14845	−	1.98917i	0.0532579	−	0.0922454i
$466$	17.9328	+	10.3535i	0.830723	+	0.479618i
$467$	−9.10403			−0.421284			−0.210642	−	0.977563i	$-0.567555\pi$
$467$	−9.10403			−0.421284			−0.210642	+	0.977563i	$0.567555\pi$
$468$	−11.0162			−0.509224
$469$	−0.740364	+	1.28235i	−0.0341869	+	0.0592134i
$470$	6.93678	+	12.0149i	0.319970	+	0.554204i
$471$	−59.3643	−	34.2740i	−2.73536	−	1.57926i
$472$	5.24172	−	3.02631i	0.241270	−	0.139297i
$473$	−5.15278	+	34.6066i	−0.236925	+	1.59121i
$474$		−	4.96828i		−	0.228201i
$475$	−2.13179	+	0.875716i	−0.0978132	+	0.0401806i
$476$	−0.670009			−0.0307098
$477$	−8.81213	+	5.08769i	−0.403480	+	0.232949i
$478$	10.0352	−	5.79381i	0.458998	−	0.265003i
$479$	−20.1644	−	11.6419i	−0.921333	−	0.531932i	−0.0372730	−	0.999305i	$-0.511867\pi$
$479$	−20.1644	−	11.6419i	−0.921333	−	0.531932i	−0.884060	+	0.467373i	$0.845200\pi$
$480$	−6.03405	+	3.48376i	−0.275415	+	0.159011i
$481$	−7.31803	−	4.22507i	−0.333674	−	0.192647i
$482$	3.31508			0.150998
$483$	−10.7632			−0.489741
$484$	10.5228	+	3.20467i	0.478311	+	0.145667i
$485$	31.5389	+	18.2090i	1.43211	+	0.826828i
$486$			3.75558i			0.170357i
$487$		−	10.8112i		−	0.489901i	−0.969536	−	0.244951i	$-0.921228\pi$
$487$		−	10.8112i		−	0.489901i	0.969536	−	0.244951i	$-0.0787718\pi$
$488$	−10.9859	−	6.34273i	−0.497310	−	0.287122i
$489$	11.4271	−	6.59743i	0.516750	−	0.298346i
$490$	7.84628	−	13.5902i	0.354459	−	0.613941i
$491$	−19.7756	+	11.4174i	−0.892459	+	0.515261i	−0.874746	−	0.484582i	$-0.838972\pi$
$491$	−19.7756	+	11.4174i	−0.892459	+	0.515261i	−0.0177127	+	0.999843i	$0.505638\pi$
$492$	23.4731	−	13.5522i	1.05825	−	0.610981i
$493$			3.00369i			0.135279i
$494$	−6.57525	−	5.07601i	−0.295834	−	0.228380i
$495$	−28.0444	+	35.2960i	−1.26050	+	1.58644i
$496$	0.285491	−	0.164828i	0.0128189	−	0.00740101i
$497$	3.76158	+	6.51524i	0.168730	+	0.292249i
$498$	12.9467	−	22.4243i	0.580155	−	1.00486i
$499$	12.4626	+	21.5859i	0.557904	+	0.966317i	0.997671	+	0.0682059i	$0.0217275\pi$
$499$	12.4626	+	21.5859i	0.557904	+	0.966317i	−0.439768	+	0.898112i	$0.644939\pi$
$500$	5.25671	−	9.10489i	0.235087	−	0.407183i
$501$		−	69.0732i		−	3.08596i
$502$	−8.89798			−0.397136
$503$	−15.9585	−	9.21367i	−0.711556	−	0.410817i	0.100081	−	0.994979i	$-0.468090\pi$
$503$	−15.9585	−	9.21367i	−0.711556	−	0.410817i	−0.811637	+	0.584162i	$0.801423\pi$
$504$	−2.85872	−	1.65048i	−0.127338	−	0.0735184i
$505$			5.06621i			0.225443i
$506$	−13.1240	+	16.5176i	−0.583434	+	0.734295i
$507$	24.0416	+	13.8804i	1.06773	+	0.616452i
$508$	0.292083	+	0.505902i	0.0129591	+	0.0224458i
$509$	−10.9129	−	6.30058i	−0.483707	−	0.279268i	0.238253	−	0.971203i	$-0.423425\pi$
$509$	−10.9129	−	6.30058i	−0.483707	−	0.279268i	−0.721960	+	0.691935i	$0.756759\pi$
$510$	−4.08764	−	7.07999i	−0.181004	−	0.313507i
$511$	−4.40660	−	7.63245i	−0.194936	−	0.337640i
$512$	−1.00000			−0.0441942
$513$	21.9485	−	28.4311i	0.969048	−	1.25527i
$514$		−	18.5905i		−	0.819993i
$515$	−1.65327	+	0.954518i	−0.0728520	+	0.0420611i
$516$	−15.6300	−	27.0720i	−0.688074	−	1.19178i
$517$	7.18200	+	18.2036i	0.315864	+	0.800592i
$518$	−1.26603	−	2.19283i	−0.0556261	−	0.0963473i
$519$	40.1996	+	23.2093i	1.76457	+	1.01877i
$520$	−4.48084			−0.196498
$521$		−	10.4206i		−	0.456534i	−0.973599	−	0.228267i	$-0.926694\pi$
$521$		−	10.4206i		−	0.456534i	0.973599	−	0.228267i	$-0.0733059\pi$
$522$	−7.39921	+	12.8158i	−0.323855	+	0.560933i
$523$	16.0021	−	27.7165i	0.699724	−	1.21196i	−0.268838	−	0.963185i	$-0.586640\pi$
$523$	16.0021	−	27.7165i	0.699724	−	1.21196i	0.968562	−	0.248772i	$-0.0800270\pi$
$524$			3.43183i			0.149920i
$525$	−0.894645			−0.0390455
$526$	−2.99687	−	1.73024i	−0.130670	−	0.0754422i
$527$	0.193400	+	0.334978i	0.00842463	+	0.0145919i
$528$	−9.14213	+	3.60691i	−0.397860	+	0.156971i
$529$	−8.73043	−	15.1215i	−0.379584	−	0.657458i
$530$	−3.58434	+	2.06942i	−0.155694	+	0.0898898i
$531$			34.9887i			1.51838i
$532$	−0.945784	−	2.30236i	−0.0410050	−	0.0998200i
$533$	17.4310			0.755019
$534$	13.8698	+	24.0231i	0.600204	+	1.03958i
$535$	−8.95149	−	15.5044i	−0.387007	−	0.670315i
$536$	−2.24569	−	1.29655i	−0.0969989	−	0.0560024i
$537$	4.68737	+	8.11877i	0.202275	+	0.350351i
$538$	−13.0396	−	7.52841i	−0.562177	−	0.324573i
$539$	13.7699	−	17.3304i	0.593112	−	0.746475i
$540$		−	19.3750i		−	0.833766i
$541$	−8.72259	−	5.03599i	−0.375013	−	0.216514i	0.300633	−	0.953740i	$-0.402802\pi$
$541$	−8.72259	−	5.03599i	−0.375013	−	0.216514i	−0.675646	+	0.737226i	$0.736135\pi$
$542$	24.8322	+	14.3369i	1.06664	+	0.615822i
$543$	−69.2902			−2.97353
$544$		−	1.17334i		−	0.0503065i
$545$	−16.6341	+	28.8111i	−0.712526	+	1.23413i
$546$	−1.61228	−	2.79255i	−0.0689991	−	0.119510i
$547$	−4.81191	+	8.33448i	−0.205743	+	0.356357i	−0.950369	−	0.311125i	$-0.899294\pi$
$547$	−4.81191	+	8.33448i	−0.205743	+	0.356357i	0.744626	+	0.667481i	$0.232628\pi$
$548$	5.60961	+	9.71612i	0.239631	+	0.415052i
$549$	63.5070	−	36.6658i	2.71041	−	1.56486i
$550$	−1.09088	+	1.37295i	−0.0465153	+	0.0585430i
$551$	−10.3216	+	4.24000i	−0.439715	+	0.180630i
$552$		−	18.8488i		−	0.802258i
$553$	0.829139	−	0.478704i	0.0352586	−	0.0203566i
$554$	−19.3732	+	11.1851i	−0.823089	+	0.475211i
$555$	15.4477	−	26.7563i	0.655720	−	1.13574i
$556$	10.9788	−	6.33862i	0.465606	−	0.268817i
$557$	−34.0009	−	19.6304i	−1.44066	−	0.831768i	−0.442771	−	0.896635i	$-0.646005\pi$
$557$	−34.0009	−	19.6304i	−1.44066	−	0.831768i	−0.997894	+	0.0648665i	$0.979338\pi$
$558$			1.90567i			0.0806733i
$559$		−	20.1035i		−	0.850286i
$560$	−1.16279	−	0.671335i	−0.0491367	−	0.0283691i
$561$	−4.23214	−	10.7268i	−0.178681	−	0.452887i
$562$	−5.67237			−0.239275
$563$	−4.97386			−0.209623			−0.104812	−	0.994492i	$-0.533424\pi$
$563$	−4.97386			−0.209623			−0.104812	+	0.994492i	$0.533424\pi$
$564$	−15.1416	−	8.74201i	−0.637577	−	0.368105i
$565$	−14.1037	+	8.14275i	−0.593345	+	0.342568i
$566$	3.04939	+	1.76057i	0.128176	+	0.0740022i
$567$	3.49870	−	2.01997i	0.146931	−	0.0848309i
$568$	−11.4097	+	6.58739i	−0.478740	+	0.276401i
$569$	4.10783			0.172209			0.0861045	−	0.996286i	$-0.472558\pi$
$569$	4.10783			0.172209			0.0861045	+	0.996286i	$0.472558\pi$
$570$	18.5590	−	24.0405i	0.777349	−	1.00695i
$571$			24.3435i			1.01874i	0.860547	+	0.509371i	$0.170122\pi$
$571$			24.3435i			1.01874i	−0.860547	+	0.509371i	$0.829878\pi$
$572$	−6.25146	−	0.930818i	−0.261387	−	0.0389195i
$573$	15.5308	−	8.96671i	0.648808	−	0.374590i
$574$	4.52337	+	2.61157i	0.188802	+	0.109005i
$575$	−1.68157	−	2.91257i	−0.0701264	−	0.121462i
$576$	2.89038	−	5.00628i	0.120432	−	0.208595i
$577$	−28.7147			−1.19541			−0.597705	−	0.801716i	$-0.703921\pi$
$577$	−28.7147			−1.19541			−0.597705	+	0.801716i	$0.703921\pi$
$578$	−15.6233			−0.649842
$579$	45.1779	+	26.0834i	1.87753	+	1.08399i
$580$	−3.00963	+	5.21283i	−0.124968	+	0.216451i
$581$	4.98976			0.207010
$582$	−45.8954			−1.90243
$583$	−5.43059	+	2.14257i	−0.224912	+	0.0887363i
$584$	13.3662	−	7.71696i	0.553096	−	0.319330i
$585$	12.9513	−	22.4323i	0.535471	−	0.927463i
$586$	−13.1246	−	22.7325i	−0.542173	−	0.939071i
$587$	−3.11979	−	5.40363i	−0.128767	−	0.223032i	0.794432	−	0.607353i	$-0.207769\pi$
$587$	−3.11979	−	5.40363i	−0.128767	−	0.223032i	−0.923199	+	0.384322i	$0.874435\pi$
$588$			19.7764i			0.815565i
$589$	−0.878087	+	1.13744i	−0.0361809	+	0.0468673i
$590$			14.2317i			0.585908i
$591$	−6.74599	−	11.6844i	−0.277493	−	0.480632i
$592$	3.84014	−	2.21711i	0.157829	−	0.0911226i
$593$	11.9809	+	6.91715i	0.491995	+	0.284053i	0.725402	−	0.688326i	$-0.241654\pi$
$593$	11.9809	+	6.91715i	0.491995	+	0.284053i	−0.233407	+	0.972379i	$0.574987\pi$
$594$	4.02482	−	27.0311i	0.165141	−	1.10910i
$595$	0.787704	−	1.36434i	0.0322927	−	0.0559326i
$596$			0.308527i			0.0126378i
$597$			50.0563i			2.04867i
$598$	6.06086	−	10.4977i	0.247847	−	0.429284i
$599$	7.08898	+	4.09282i	0.289648	+	0.167228i	0.637783	−	0.770216i	$-0.279852\pi$
$599$	7.08898	+	4.09282i	0.289648	+	0.167228i	−0.348135	+	0.937444i	$0.613185\pi$
$600$		−	1.56673i		−	0.0639614i
$601$	7.75979			0.316528			0.158264	−	0.987397i	$-0.449410\pi$
$601$	7.75979			0.316528			0.158264	+	0.987397i	$0.449410\pi$
$602$	3.01197	−	5.21689i	0.122759	−	0.212624i
$603$	12.9818	−	7.49503i	0.528659	−	0.305221i
$604$	0.359132	−	0.622035i	0.0146129	−	0.0253103i
$605$	−18.8970	+	17.6601i	−0.768271	+	0.717986i
$606$	−3.19232	−	5.52926i	−0.129679	−	0.224611i
$607$	−40.1815			−1.63092			−0.815458	−	0.578816i	$-0.803515\pi$
$607$	−40.1815			−1.63092			−0.815458	+	0.578816i	$0.803515\pi$
$608$	4.03196	−	1.65629i	0.163518	−	0.0671713i
$609$	−4.33165			−0.175527
$610$	25.8315	−	14.9138i	1.04589	−	0.603843i
$611$	−5.62202	−	9.73762i	−0.227443	−	0.393942i
$612$	5.87407	+	3.39140i	0.237445	+	0.137089i
$613$	13.0915	−	7.55835i	0.528759	−	0.305279i	−0.211752	−	0.977323i	$-0.567917\pi$
$613$	13.0915	−	7.55835i	0.528759	−	0.305279i	0.740511	+	0.672044i	$0.234584\pi$
$614$	13.8879	−	24.0546i	0.560470	−	0.970763i
$615$			63.7313i			2.56989i
$616$	−1.48281	−	1.17817i	−0.0597440	−	0.0474696i
$617$	−22.8377	+	39.5560i	−0.919411	+	1.59247i	−0.119099	+	0.992882i	$0.538000\pi$
$617$	−22.8377	+	39.5560i	−0.919411	+	1.59247i	−0.800312	+	0.599584i	$0.795333\pi$
$618$	1.20292	−	2.08352i	0.0483887	−	0.0838116i
$619$	15.5372			0.624492			0.312246	−	0.950001i	$-0.398919\pi$
$619$	15.5372			0.624492			0.312246	+	0.950001i	$0.398919\pi$
$620$			0.775130i			0.0311300i
$621$	45.3918	+	26.2069i	1.82151	+	1.05165i
$622$	0.931020	+	1.61257i	0.0373305	+	0.0646583i
$623$	−2.67276	+	4.62936i	−0.107082	+	0.185471i
$624$	4.89039	−	2.82347i	0.195772	−	0.113029i
$625$	13.6820	+	23.6980i	0.547281	+	0.947919i
$626$	−21.8868			−0.874772
$627$	30.8866	−	29.6849i	1.23349	−	1.18550i
$628$	23.1328			0.923100
$629$	2.60142	+	4.50579i	0.103725	+	0.179658i
$630$	6.72178	−	3.88082i	0.267802	−	0.154616i
$631$	−21.0961	+	36.5396i	−0.839823	+	1.45462i	0.0502186	+	0.998738i	$0.484008\pi$
$631$	−21.0961	+	36.5396i	−0.839823	+	1.45462i	−0.890042	+	0.455879i	$0.849325\pi$
$632$	0.838320	+	1.45201i	0.0333466	+	0.0577580i
$633$	0.781298	+	0.451082i	0.0310538	+	0.0179289i
$634$		−	23.2096i		−	0.921770i
$635$	−1.37356			−0.0545081
$636$	2.60796	−	4.51713i	0.103413	−	0.179116i
$637$	−6.35914	+	11.0144i	−0.251958	+	0.436405i
$638$	−5.28178	+	6.64751i	−0.209108	+	0.263177i
$639$		−	76.1602i		−	3.01285i
$640$	1.17566	−	2.03631i	0.0464721	−	0.0804921i
$641$	17.4295	−	10.0629i	0.688425	−	0.397462i	−0.114597	−	0.993412i	$-0.536558\pi$
$641$	17.4295	−	10.0629i	0.688425	−	0.397462i	0.803022	+	0.595950i	$0.203224\pi$
$642$	19.5393	+	11.2810i	0.771156	+	0.445227i
$643$	−9.14326	−	15.8366i	−0.360575	−	0.624535i	0.627480	−	0.778632i	$-0.284086\pi$
$643$	−9.14326	−	15.8366i	−0.360575	−	0.624535i	−0.988056	+	0.154098i	$0.950753\pi$
$644$	3.14561	−	1.81612i	0.123954	−	0.0715651i
$645$	73.5025			2.89416
$646$	1.94339	+	4.73086i	0.0764615	+	0.186133i
$647$	48.4379			1.90429			0.952145	−	0.305645i	$-0.0988721\pi$
$647$	48.4379			1.90429			0.952145	+	0.305645i	$0.0988721\pi$
$648$	3.53744	+	6.12702i	0.138964	+	0.240692i
$649$	−2.95639	+	19.8554i	−0.116048	+	0.779392i
$650$	0.503784	−	0.872580i	0.0197601	−	0.0342254i
$651$	−0.483076	+	0.278904i	−0.0189332	+	0.0109311i
$652$	−2.22643	+	3.85629i	−0.0871937	+	0.151024i
$653$	10.9972			0.430353			0.215176	−	0.976575i	$-0.430967\pi$
$653$	10.9972			0.430353			0.215176	+	0.976575i	$0.430967\pi$
$654$		−	41.9259i		−	1.63943i
$655$	−6.98826	−	4.03467i	−0.273054	−	0.157648i
$656$	−4.57346	+	7.92146i	−0.178563	+	0.309281i
$657$			89.2198i			3.48079i
$658$		−	3.36924i		−	0.131347i
$659$	−17.3040	+	29.9715i	−0.674070	+	1.16752i	0.302670	+	0.953095i	$0.402122\pi$
$659$	−17.3040	+	29.9715i	−0.674070	+	1.16752i	−0.976740	+	0.214427i	$0.931211\pi$
$660$	3.40327	−	22.8567i	0.132472	−	0.889695i
$661$	−40.0132	−	23.1016i	−1.55633	−	0.898548i	−0.997603	−	0.0691974i	$-0.977956\pi$
$661$	−40.0132	−	23.1016i	−1.55633	−	0.898548i	−0.558728	−	0.829351i	$-0.688711\pi$
$662$	16.5775	−	9.57101i	0.644302	−	0.371988i
$663$	3.31289	+	5.73809i	0.128662	+	0.222849i
$664$			8.73822i			0.339109i
$665$	5.80023	+	0.780890i	0.224923	+	0.0302816i
$666$			25.6331i			0.993263i
$667$	−8.14176	−	14.1019i	−0.315250	−	0.546030i
$668$	11.6550	+	20.1871i	0.450947	+	0.781063i
$669$	24.5189	−	42.4681i	0.947957	−	1.64191i
$670$	5.28034	−	3.04860i	0.203997	−	0.117778i
$671$	39.1370	−	15.4410i	1.51087	−	0.596094i
$672$	1.69209			0.0652737
$673$	21.9541			0.846267			0.423133	−	0.906067i	$-0.360930\pi$
$673$	21.9541			0.846267			0.423133	+	0.906067i	$0.360930\pi$
$674$	−11.3437	+	19.6478i	−0.436942	+	0.756806i
$675$	3.77300	+	2.17835i	0.145223	+	0.0838446i
$676$	−9.36844			−0.360324
$677$	−19.9705			−0.767530			−0.383765	−	0.923431i	$-0.625373\pi$
$677$	−19.9705			−0.767530			−0.383765	+	0.923431i	$0.625373\pi$
$678$	10.2618	−	17.7740i	0.394103	−	0.682607i
$679$	−4.42212	−	7.65933i	−0.169705	−	0.293938i
$680$	2.38928	+	1.37945i	0.0916247	+	0.0528995i
$681$	76.2788	−	44.0396i	2.92301	−	1.68760i
$682$	−0.161020	+	1.08143i	−0.00616578	+	0.0414099i
$683$			9.79903i			0.374949i	0.982269	+	0.187475i	$0.0600302\pi$
$683$			9.79903i			0.374949i	−0.982269	+	0.187475i	$0.939970\pi$
$684$	−3.36206	+	24.9724i	−0.128552	+	0.954845i
$685$	−26.3800			−1.00793
$686$	−6.76209	+	3.90409i	−0.258178	+	0.149059i
$687$	−15.8267	+	9.13753i	−0.603825	+	0.348619i
$688$	9.13597	+	5.27465i	0.348306	+	0.201094i
$689$	2.90498	−	1.67719i	0.110671	−	0.0638959i
$690$	38.3819	+	22.1598i	1.46117	+	0.843609i
$691$	39.7207			1.51105			0.755524	−	0.655121i	$-0.227382\pi$
$691$	39.7207			1.51105			0.755524	+	0.655121i	$0.227382\pi$
$692$	−15.6648			−0.595487
$693$	10.1841	−	4.01801i	0.386862	−	0.152632i
$694$	−23.1209	−	13.3489i	−0.877658	−	0.506716i
$695$			29.8083i			1.13069i
$696$		−	7.58572i		−	0.287536i
$697$	−9.29457	−	5.36622i	−0.352057	−	0.203260i
$698$	−15.9739	+	9.22256i	−0.604623	+	0.349079i
$699$	30.6799	−	53.1392i	1.16042	−	2.00991i
$700$	0.261466	−	0.150957i	0.00988249	−	0.00570566i
$701$	−23.6836	+	13.6737i	−0.894516	+	0.516449i	−0.875417	−	0.483369i	$-0.839413\pi$
$701$	−23.6836	+	13.6737i	−0.894516	+	0.516449i	−0.0190988	+	0.999818i	$0.506080\pi$
$702$			15.7028i			0.592662i
$703$	−11.8111	+	15.2997i	−0.445466	+	0.577038i
$704$	2.06324	−	2.59674i	0.0777612	−	0.0978682i
$705$	35.6028	−	20.5553i	1.34088	−	0.774157i
$706$	−8.86257	−	15.3504i	−0.333547	−	0.577720i
$707$	0.615173	−	1.06551i	0.0231360	−	0.0400727i
$708$	−8.96766	−	15.5325i	−0.337025	−	0.583745i
$709$	7.22573	−	12.5153i	0.271368	−	0.470023i	−0.697844	−	0.716249i	$-0.745857\pi$
$709$	7.22573	−	12.5153i	0.271368	−	0.470023i	0.969212	+	0.246226i	$0.0791906\pi$
$710$		−	30.9782i		−	1.16259i
$711$	−9.69225			−0.363488
$712$	−8.10707	−	4.68062i	−0.303825	−	0.175414i
$713$	−1.81598	−	1.04845i	−0.0680089	−	0.0392649i
$714$			1.98539i			0.0743015i
$715$	9.24504	−	11.6356i	0.345745	−	0.435145i
$716$	−2.73983	−	1.58184i	−0.102392	−	0.0591163i
$717$	−17.1684	−	29.7366i	−0.641167	−	1.11053i
$718$	−1.29550	−	0.747959i	−0.0483477	−	0.0279136i
$719$	14.2784	+	24.7310i	0.532496	+	0.922310i	0.999280	+	0.0379388i	$0.0120792\pi$
$719$	14.2784	+	24.7310i	0.532496	+	0.922310i	−0.466784	+	0.884371i	$0.654587\pi$
$720$	6.79621	+	11.7714i	0.253280	+	0.438694i
$721$	0.463616			0.0172660
$722$	−13.5134	+	13.3562i	−0.502918	+	0.497065i
$723$		−	9.82337i		−	0.365335i
$724$	20.2505	−	11.6916i	0.752605	−	0.434517i
$725$	−0.676751	−	1.17217i	−0.0251339	−	0.0435332i
$726$	9.49618	−	31.1816i	0.352436	−	1.15726i
$727$	3.39248	+	5.87594i	0.125820	+	0.217927i	0.922053	−	0.387063i	$-0.126511\pi$
$727$	3.39248	+	5.87594i	0.125820	+	0.217927i	−0.796233	+	0.604990i	$0.793177\pi$
$728$	0.942398	+	0.544094i	0.0349276	+	0.0201655i
$729$	32.3533			1.19827
$730$			36.2902i			1.34316i
$731$	−6.18896	+	10.7196i	−0.228907	+	0.396479i
$732$	−18.7950	+	32.5539i	−0.694683	+	1.20323i
$733$		−	16.1981i		−	0.598291i	−0.954207	−	0.299146i	$-0.903298\pi$
$733$		−	16.1981i		−	0.598291i	0.954207	−	0.299146i	$-0.0967016\pi$
$734$	31.3645			1.15768
$735$	−40.2708	−	23.2504i	−1.48541	−	0.857603i
$736$	3.18044	+	5.50869i	0.117233	+	0.203053i
$737$	8.00018	−	3.15637i	0.294691	−	0.116267i
$738$	−26.4380	−	45.7920i	−0.973198	−	1.68563i
$739$	34.2010	−	19.7459i	1.25810	−	0.726366i	0.285397	−	0.958409i	$-0.407875\pi$
$739$	34.2010	−	19.7459i	1.25810	−	0.726366i	0.972705	+	0.232044i	$0.0745412\pi$
$740$			10.4263i			0.383278i
$741$	−15.0414	+	19.4840i	−0.552559	+	0.715763i
$742$	1.00513			0.0368995
$743$	2.60404	+	4.51032i	0.0955328	+	0.165468i	0.909831	−	0.414979i	$-0.136211\pi$
$743$	2.60404	+	4.51032i	0.0955328	+	0.165468i	−0.814298	+	0.580447i	$0.802878\pi$
$744$	−0.488425	−	0.845977i	−0.0179065	−	0.0310150i
$745$	−0.628255	−	0.362723i	−0.0230175	−	0.0132892i
$746$	−4.43737	−	7.68575i	−0.162464	−	0.281395i
$747$	−43.7460	−	25.2568i	−1.60058	−	0.924096i
$748$	3.04686	+	2.42088i	0.111404	+	0.0885161i
$749$			4.34780i			0.158865i
$750$	−26.9799	−	15.5769i	−0.985167	−	0.568787i
$751$	−44.2511	−	25.5484i	−1.61474	−	0.932273i	−0.988250	−	0.152847i	$-0.951156\pi$
$751$	−44.2511	−	25.5484i	−1.61474	−	0.932273i	−0.626494	−	0.779426i	$-0.715511\pi$
$752$	5.90032			0.215162
$753$			26.3668i			0.960860i
$754$	2.43920	−	4.22482i	0.0888305	−	0.153859i
$755$	0.844436	+	1.46261i	0.0307322	+	0.0532297i
$756$	−2.35264	+	4.07489i	−0.0855647	+	0.148202i
$757$	15.2839	+	26.4726i	0.555505	+	0.962162i	0.997864	+	0.0653244i	$0.0208082\pi$
$757$	15.2839	+	26.4726i	0.555505	+	0.962162i	−0.442359	+	0.896838i	$0.645858\pi$
$758$	28.4508	−	16.4261i	1.03338	−	0.596623i
$759$	48.9454	+	38.8895i	1.77660	+	1.41160i
$760$	−1.36752	+	10.1575i	−0.0496051	+	0.368453i
$761$		−	36.3854i		−	1.31897i	−0.751717	−	0.659486i	$-0.770774\pi$
$761$		−	36.3854i		−	1.31897i	0.751717	−	0.659486i	$-0.229226\pi$
$762$	1.49911	−	0.865509i	0.0543069	−	0.0313541i
$763$	6.99688	−	4.03965i	0.253304	−	0.146245i
$764$	−3.02599	+	5.24116i	−0.109476	+	0.189619i
$765$	−13.8118	+	7.97427i	−0.499368	+	0.288310i
$766$	−14.5080	−	8.37617i	−0.524194	−	0.302643i
$767$		−	11.5343i		−	0.416479i
$768$			2.96323i			0.106927i
$769$	−7.54747	−	4.35753i	−0.272169	−	0.157137i	0.357704	−	0.933835i	$-0.383560\pi$
$769$	−7.54747	−	4.35753i	−0.272169	−	0.157137i	−0.629873	+	0.776698i	$0.716893\pi$
$770$	4.14239	−	1.63433i	0.149281	−	0.0588971i
$771$	−55.0881			−1.98395
$772$	−17.6047			−0.633608
$773$	13.3224	+	7.69169i	0.479174	+	0.276651i	0.720072	−	0.693899i	$-0.244109\pi$
$773$	13.3224	+	7.69169i	0.479174	+	0.276651i	−0.240898	+	0.970550i	$0.577442\pi$
$774$	−52.8128	+	30.4915i	−1.89832	+	1.09599i
$775$	−0.150946	−	0.0871485i	−0.00542213	−	0.00313047i
$776$	13.4133	−	7.74414i	0.481508	−	0.277999i
$777$	−6.49786	+	3.75154i	−0.233109	+	0.134586i
$778$	−14.1198			−0.506221
$779$	5.31980	−	39.5140i	0.190602	−	1.41574i
$780$			13.2778i			0.475421i
$781$	6.43519	−	43.2193i	0.230269	−	1.54651i
$782$	−6.46356	+	3.73174i	−0.231137	+	0.133447i
$783$	18.2680	+	10.5470i	0.652844	+	0.376920i
$784$	−3.33696	−	5.77979i	−0.119177	−	0.206421i
$785$	−27.1964	+	47.1055i	−0.970680	+	1.68127i
$786$	10.1693			0.362727
$787$	−19.0111			−0.677672			−0.338836	−	0.940845i	$-0.610033\pi$
$787$	−19.0111			−0.677672			−0.338836	+	0.940845i	$0.610033\pi$
$788$	3.94312	+	2.27656i	0.140468	+	0.0810992i
$789$	−5.12712	+	8.88043i	−0.182530	+	0.316152i
$790$	−3.94232			−0.140262
$791$	3.95499			0.140623
$792$	7.03646	+	17.8347i	0.250030	+	0.633729i
$793$	−20.9355	+	12.0871i	−0.743442	+	0.429227i
$794$	−13.8657	+	24.0162i	−0.492077	+	0.852302i
$795$	6.13217	+	10.6212i	0.217486	+	0.376696i
$796$	−8.44623	−	14.6293i	−0.299369	−	0.518522i
$797$		−	25.9444i		−	0.918997i	−0.888179	−	0.459498i	$-0.848029\pi$
$797$		−	25.9444i		−	0.918997i	0.888179	−	0.459498i	$-0.151971\pi$
$798$	−6.82243	+	2.80258i	−0.241511	+	0.0992103i
$799$			6.92308i			0.244921i
$800$	0.264361	+	0.457887i	0.00934658	+	0.0161888i
$801$	46.8650	−	27.0575i	1.65589	−	0.956030i
$802$	4.75221	+	2.74369i	0.167806	+	0.0968830i
$803$	−7.53867	+	50.6304i	−0.266034	+	1.78671i
$804$	−3.84198	+	6.65450i	−0.135496	+	0.234686i
$805$			8.54057i			0.301015i
$806$		−	0.628216i		−	0.0221280i
$807$	−22.3084	+	38.6394i	−0.785294	+	1.36017i
$808$	1.86595	+	1.07731i	0.0656441	+	0.0378996i
$809$			40.3675i			1.41925i	0.704581	+	0.709623i	$0.251135\pi$
$809$			40.3675i			1.41925i	−0.704581	+	0.709623i	$0.748865\pi$
$810$	−16.6353			−0.584506
$811$	−9.99986	+	17.3203i	−0.351142	+	0.608197i	−0.986450	−	0.164063i	$-0.947540\pi$
$811$	−9.99986	+	17.3203i	−0.351142	+	0.608197i	0.635307	+	0.772259i	$0.280873\pi$
$812$	1.26596	−	0.730900i	0.0444263	−	0.0256495i
$813$	42.4836	−	73.5837i	1.48996	−	2.58069i
$814$	−2.16588	+	14.5463i	−0.0759141	+	0.509846i
$815$	−5.23505	−	9.06738i	−0.183376	−	0.317616i
$816$	−3.47688			−0.121715
$817$	−45.5722	−	6.13543i	−1.59437	−	0.214651i
$818$	34.1861			1.19529
$819$	−5.44777	+	3.14527i	−0.190361	+	0.109905i
$820$	−10.7537	−	18.6259i	−0.375535	−	0.650445i
$821$	−22.2401	−	12.8404i	−0.776186	−	0.448131i	0.0588907	−	0.998264i	$-0.481244\pi$
$821$	−22.2401	−	12.8404i	−0.776186	−	0.448131i	−0.835077	+	0.550133i	$0.814577\pi$
$822$	28.7911	−	16.6226i	1.00421	−	0.579779i
$823$	−16.0854	+	27.8607i	−0.560701	+	0.971162i	0.436735	+	0.899590i	$0.356135\pi$
$823$	−16.0854	+	27.8607i	−0.560701	+	0.971162i	−0.997435	+	0.0715718i	$0.977199\pi$
$824$			0.811899i			0.0282838i
$825$	4.06838	+	3.23253i	0.141643	+	0.112542i
$826$	1.72811	−	2.99317i	0.0601285	−	0.104146i
$827$	11.2205	−	19.4344i	0.390174	−	0.675801i	−0.602298	−	0.798271i	$-0.705748\pi$
$827$	11.2205	−	19.4344i	0.390174	−	0.675801i	0.992472	+	0.122470i	$0.0390816\pi$
$828$	−36.7707			−1.27787
$829$			30.8679i			1.07209i	0.844191	+	0.536043i	$0.180081\pi$
$829$			30.8679i			1.07209i	−0.844191	+	0.536043i	$0.819919\pi$
$830$	−17.7937	−	10.2732i	−0.617628	−	0.356588i
$831$	33.1442	+	57.4074i	1.14976	+	1.99144i
$832$	−0.952833	+	1.65036i	−0.0330335	+	0.0572158i
$833$	6.78166	−	3.91539i	0.234971	−	0.135660i
$834$	−18.7828	−	32.5328i	−0.650396	−	1.12652i
$835$	−54.8095			−1.89676
$836$	−4.01796	+	13.8873i	−0.138964	+	0.480301i
$837$	2.71638			0.0938919
$838$	−0.296574	−	0.513682i	−0.0102450	−	0.0177448i
$839$	−34.5555	+	19.9506i	−1.19299	+	0.688772i	−0.958983	−	0.283463i	$-0.908517\pi$
$839$	−34.5555	+	19.9506i	−1.19299	+	0.688772i	−0.234005	+	0.972235i	$0.575183\pi$
$840$	−1.98932	+	3.44561i	−0.0686381	+	0.118885i
$841$	11.2233	+	19.4394i	0.387012	+	0.670324i
$842$	16.1128	+	9.30270i	0.555282	+	0.320592i
$843$			16.8086i			0.578918i
$844$	−0.304453			−0.0104797
$845$	11.0141	−	19.0770i	0.378897	−	0.656269i
$846$	−17.0542	+	29.5387i	−0.586334	+	1.01556i
$847$	6.11877	−	1.41963i	0.210244	−	0.0487790i
$848$			1.76022i			0.0604460i
$849$	5.21698	−	9.03607i	0.179046	−	0.310117i
$850$	−0.537257	+	0.310186i	−0.0184278	+	0.0106393i
$851$	−24.4267	−	14.1028i	−0.837337	−	0.483437i
$852$	19.5200	+	33.8096i	0.668743	+	1.15830i
$853$	−21.3409	+	12.3212i	−0.730698	+	0.421869i	−0.818677	−	0.574254i	$-0.805292\pi$
$853$	−21.3409	+	12.3212i	−0.730698	+	0.421869i	0.0879795	+	0.996122i	$0.471959\pi$
$854$	−7.24375			−0.247876
$855$	−46.8989	−	36.2053i	−1.60391	−	1.23820i
$856$	−7.61400			−0.260241
$857$	21.9461	+	38.0117i	0.749664	+	1.29846i	0.947984	+	0.318318i	$0.103118\pi$
$857$	21.9461	+	38.0117i	0.749664	+	1.29846i	−0.198320	+	0.980137i	$0.563549\pi$
$858$	−2.75823	+	18.5245i	−0.0941645	+	0.632418i
$859$	8.89495	−	15.4065i	0.303492	−	0.525663i	−0.673433	−	0.739249i	$-0.735181\pi$
$859$	8.89495	−	15.4065i	0.303492	−	0.525663i	0.976924	+	0.213585i	$0.0685141\pi$
$860$	−21.4816	+	12.4024i	−0.732517	+	0.422919i
$861$	7.73869	−	13.4038i	0.263734	−	0.456800i
$862$	−7.25726			−0.247183
$863$		−	27.3368i		−	0.930555i	−0.885165	−	0.465277i	$-0.845955\pi$
$863$		−	27.3368i		−	0.930555i	0.885165	−	0.465277i	$-0.154045\pi$
$864$	−7.13608	−	4.12002i	−0.242774	−	0.140166i
$865$	18.4165	−	31.8984i	0.626181	−	1.08458i
$866$			10.1853i			0.346110i
$867$			46.2954i			1.57227i
$868$	0.0941215	−	0.163023i	0.00319469	−	0.00553337i
$869$	−5.50015	−	0.818951i	−0.186580	−	0.0277810i
$870$	15.4468	+	8.91824i	0.523697	+	0.302357i
$871$	−4.27953	+	2.47079i	−0.145006	+	0.0837195i
$872$	7.07435	+	12.2531i	0.239568	+	0.414944i
$873$			89.5340i			3.03027i
$874$	−21.9474	−	16.9431i	−0.742381	−	0.573109i
$875$		−	6.00345i		−	0.202954i
$876$	−22.8672	−	39.6071i	−0.772610	−	1.33820i
$877$	4.43862	+	7.68792i	0.149882	+	0.259603i	0.931184	−	0.364551i	$-0.118777\pi$
$877$	4.43862	+	7.68792i	0.149882	+	0.259603i	−0.781302	+	0.624153i	$0.785444\pi$
$878$	−9.13873	+	15.8287i	−0.308417	+	0.534194i
$879$	−67.3617	+	38.8913i	−2.27206	+	1.31177i
$880$	2.86208	+	7.25427i	0.0964808	+	0.244541i
$881$	3.45031			0.116244			0.0581219	−	0.998309i	$-0.481489\pi$
$881$	3.45031			0.116244			0.0581219	+	0.998309i	$0.481489\pi$
$882$	38.5804			1.29907
$883$	18.2821	−	31.6655i	0.615241	−	1.06563i	−0.375102	−	0.926984i	$-0.622392\pi$
$883$	18.2821	−	31.6655i	0.615241	−	1.06563i	0.990342	−	0.138644i	$-0.0442745\pi$
$884$	−1.93643	−	1.11800i	−0.0651291	−	0.0376023i
$885$	42.1718			1.41759
$886$	22.3676			0.751453
$887$	−9.39004	+	16.2640i	−0.315287	+	0.546093i	−0.979498	−	0.201452i	$-0.935434\pi$
$887$	−9.39004	+	16.2640i	−0.315287	+	0.546093i	0.664212	+	0.747545i	$0.268767\pi$
$888$	−6.56981	−	11.3792i	−0.220468	−	0.381862i
$889$	0.288884	+	0.166787i	0.00968885	+	0.00559386i
$890$	19.0623	−	11.0057i	0.638971	−	0.368910i
$891$	−23.2088	−	3.45571i	−0.777526	−	0.115771i
$892$			16.5488i			0.554094i
$893$	−23.7899	+	9.77262i	−0.796097	+	0.327028i
$894$	0.914237			0.0305767
$895$	6.44223	−	3.71943i	0.215340	−	0.124327i
$896$	−0.494524	+	0.285514i	−0.0165209	+	0.00953834i
$897$	−31.1072	−	17.9598i	−1.03864	−	0.599659i
$898$	14.3957	−	8.31135i	0.480390	−	0.277353i
$899$	−0.730842	−	0.421952i	−0.0243750	−	0.0140729i
$900$	−3.05642			−0.101881
$901$	−2.06533			−0.0688061
$902$	−11.1338	−	28.2199i	−0.370716	−	0.939621i
$903$	−15.4589	−	8.92518i	−0.514439	−	0.297011i
$904$			6.92610i			0.230359i
$905$			54.9817i			1.82765i
$906$	−1.84324	−	1.06419i	−0.0612374	−	0.0353554i
$907$	1.50209	−	0.867230i	0.0498760	−	0.0287959i	−0.474855	−	0.880064i	$-0.657499\pi$
$907$	1.50209	−	0.867230i	0.0498760	−	0.0287959i	0.524731	+	0.851268i	$0.324166\pi$
$908$	−14.8620	+	25.7417i	−0.493213	+	0.854269i
$909$	−10.7866	+	6.22766i	−0.357770	+	0.206559i
$910$	−2.21588	+	1.27934i	−0.0734558	+	0.0424097i
$911$			13.1554i			0.435858i	0.975965	+	0.217929i	$0.0699302\pi$
$911$			13.1554i			0.435858i	−0.975965	+	0.217929i	$0.930070\pi$
$912$	−4.90796	−	11.9476i	−0.162519	−	0.395626i
$913$	−22.6909	−	18.0290i	−0.750958	−	0.596674i
$914$	−18.8239	+	10.8680i	−0.622640	+	0.359481i
$915$	−44.1931	−	76.5447i	−1.46098	−	2.53049i
$916$	3.08363	−	5.34101i	0.101886	−	0.176472i
$917$	0.979834	+	1.69712i	0.0323570	+	0.0560439i
$918$	4.83418	−	8.37304i	0.159552	−	0.276352i
$919$		−	32.6922i		−	1.07842i	−0.842173	−	0.539208i	$-0.818724\pi$
$919$		−	32.6922i		−	1.07842i	0.842173	−	0.539208i	$-0.181276\pi$
$920$	−14.9565			−0.493101
$921$	−71.2793	−	41.1531i	−2.34873	−	1.35604i
$922$	35.7720	+	20.6530i	1.17809	+	0.680170i
$923$			25.1067i			0.826398i
$924$	−3.49118	+	4.39391i	−0.114851	+	0.144549i
$925$	−2.03037	−	1.17223i	−0.0667582	−	0.0385428i
$926$	2.08843	+	3.61726i	0.0686299	+	0.118871i
$927$	−4.06459	−	2.34669i	−0.133499	−	0.0770756i
$928$	1.27997	+	2.21698i	0.0420172	+	0.0727759i
$929$	−12.4514	−	21.5665i	−0.408518	−	0.707574i	0.586206	−	0.810162i	$-0.300621\pi$
$929$	−12.4514	−	21.5665i	−0.408518	−	0.707574i	−0.994724	+	0.102588i	$0.967288\pi$
$930$	2.29689			0.0753180
$931$	23.0275	+	17.7769i	0.754696	+	0.582615i
$932$			20.7071i			0.678282i
$933$	4.77843	−	2.75883i	0.156439	−	0.0903200i
$934$	−4.55202	−	7.88432i	−0.148947	−	0.257983i
$935$	−8.51172	+	3.35820i	−0.278363	+	0.109825i
$936$	−5.50810	−	9.54030i	−0.180038	−	0.311835i
$937$	14.2140	+	8.20648i	0.464353	+	0.268094i	0.713873	−	0.700276i	$-0.246940\pi$
$937$	14.2140	+	8.20648i	0.464353	+	0.268094i	−0.249520	+	0.968370i	$0.580273\pi$
$938$	−1.48073			−0.0483475
$939$			64.8557i			2.11648i
$940$	−6.93678	+	12.0149i	−0.226253	+	0.391881i
$941$	−7.30722	+	12.6565i	−0.238209	+	0.412590i	−0.960200	−	0.279312i	$-0.909894\pi$
$941$	−7.30722	+	12.6565i	−0.238209	+	0.412590i	0.721992	+	0.691902i	$0.243227\pi$
$942$		−	68.5480i		−	2.23341i
$943$	58.1825			1.89468
$944$	5.24172	+	3.02631i	0.170604	+	0.0984980i
$945$	−5.53182	−	9.58140i	−0.179950	−	0.311683i
$946$	−32.5466	+	12.8408i	−1.05818	+	0.417492i
$947$	25.6660	+	44.4548i	0.834033	+	1.44459i	0.894815	+	0.446437i	$0.147307\pi$
$947$	25.6660	+	44.4548i	0.834033	+	1.44459i	−0.0607821	+	0.998151i	$0.519359\pi$
$948$	4.30265	−	2.48414i	0.139744	−	0.0806811i
$949$		−	29.4119i		−	0.954751i
$950$	−1.82429	−	1.40833i	−0.0591877	−	0.0456921i
$951$	−68.7754			−2.23019
$952$	−0.335005	−	0.580245i	−0.0108576	−	0.0188058i
$953$	27.4861	+	47.6073i	0.890362	+	1.54215i	0.839442	+	0.543449i	$0.182882\pi$
$953$	27.4861	+	47.6073i	0.890362	+	1.54215i	0.0509196	+	0.998703i	$0.483785\pi$
$954$	−8.81213	−	5.08769i	−0.285303	−	0.164720i
$955$	−7.11508	−	12.3237i	−0.230238	−	0.398785i
$956$	10.0352	+	5.79381i	0.324561	+	0.187385i
$957$	19.6981	+	15.6511i	0.636750	+	0.505930i
$958$		−	23.2838i		−	0.752265i
$959$	5.54817	+	3.20324i	0.179160	+	0.103438i
$960$	−6.03405	−	3.48376i	−0.194748	−	0.112438i
$961$	30.8913			0.996494
$962$		−	8.45014i		−	0.272443i
$963$	22.0073	−	38.1178i	0.709177	−	1.22833i
$964$	1.65754	+	2.87095i	0.0533858	+	0.0924669i
$965$	20.6972	−	35.8486i	0.666266	−	1.15401i
$966$	−5.38159	−	9.32118i	−0.173150	−	0.299904i
$967$	33.0295	−	19.0696i	1.06216	−	0.613236i	0.136128	−	0.990691i	$-0.456534\pi$
$967$	33.0295	−	19.0696i	1.06216	−	0.613236i	0.926028	+	0.377455i	$0.123201\pi$
$968$	2.48610	+	10.7154i	0.0799062	+	0.344405i
$969$	14.0187	−	5.75871i	0.450344	−	0.184996i
$970$			36.4180i			1.16931i
$971$	−19.2048	+	11.0879i	−0.616312	+	0.355828i	−0.775432	−	0.631432i	$-0.782468\pi$
$971$	−19.2048	+	11.0879i	−0.616312	+	0.355828i	0.159120	+	0.987259i	$0.449134\pi$
$972$	−3.25243	+	1.87779i	−0.104322	+	0.0602302i
$973$	3.61953	−	6.26920i	0.116037	−	0.200981i
$974$	9.36275	−	5.40559i	0.300002	−	0.173206i
$975$	−2.58566	−	1.49283i	−0.0828074	−	0.0478089i
$976$		−	12.6855i		−	0.406052i
$977$		−	31.5966i		−	1.01087i	−0.862866	−	0.505433i	$-0.831333\pi$
$977$		−	31.5966i		−	1.01087i	0.862866	−	0.505433i	$-0.168667\pi$
$978$	11.4271	+	6.59743i	0.365398	+	0.210962i
$979$	28.8812	−	11.3947i	0.923046	−	0.364176i
$980$	15.6926			0.501281
$981$	−81.7902			−2.61136
$982$	−19.7756	−	11.4174i	−0.631064	−	0.364345i
$983$	17.5091	−	10.1089i	0.558453	−	0.322423i	−0.194072	−	0.980987i	$-0.562169\pi$
$983$	17.5091	−	10.1089i	0.558453	−	0.322423i	0.752524	+	0.658565i	$0.228836\pi$
$984$	23.4731	+	13.5522i	0.748296	+	0.432029i
$985$	−9.27155	+	5.35293i	−0.295416	+	0.170559i
$986$	−2.60127	+	1.50184i	−0.0828413	+	0.0478285i
$987$	−9.98385			−0.317790
$988$	1.10833	−	8.23233i	0.0352606	−	0.261905i
$989$		−	67.1029i		−	2.13375i
$990$	−44.5894	−	6.63919i	−1.41714	−	0.211007i
$991$	7.77688	−	4.48998i	0.247041	−	0.142629i	−0.371368	−	0.928486i	$-0.621111\pi$
$991$	7.77688	−	4.48998i	0.247041	−	0.142629i	0.618408	+	0.785857i	$0.287778\pi$
$992$	0.285491	+	0.164828i	0.00906436	+	0.00523331i
$993$	−28.3611	−	49.1229i	−0.900014	−	1.55887i
$994$	−3.76158	+	6.51524i	−0.119310	+	0.206651i
$995$	39.7196			1.25920
$996$	25.8934			0.820463
$997$	27.2627	+	15.7401i	0.863419	+	0.498495i	0.865156	−	0.501503i	$-0.167219\pi$
$997$	27.2627	+	15.7401i	0.863419	+	0.498495i	−0.00173643	+	0.999998i	$0.500553\pi$
$998$	−12.4626	+	21.5859i	−0.394497	+	0.683290i
$999$	36.5381			1.15601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.h.b.373.9	yes	20
11.10	odd	2		418.2.h.a.373.9	yes	20
19.8	odd	6		418.2.h.a.65.9	✓	20
209.65	even	6	inner	418.2.h.b.65.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.h.a.65.9	✓	20	19.8	odd	6
418.2.h.a.373.9	yes	20	11.10	odd	2
418.2.h.b.65.9	yes	20	209.65	even	6	inner
418.2.h.b.373.9	yes	20	1.1	even	1	trivial

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.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(2.56624 - 1.48162i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.17566 - 2.03631i) q^{5} +(2.56624 + 1.48162i) q^{6} +0.571027i q^{7} -1.00000 q^{8} +(2.89038 - 5.00628i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(2.56624 - 1.48162i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.17566 - 2.03631i) q^{5} +(2.56624 + 1.48162i) q^{6} +0.571027i q^{7} -1.00000 q^{8} +(2.89038 - 5.00628i) q^{9} +(1.17566 - 2.03631i) q^{10} +(2.06324 - 2.59674i) q^{11} +2.96323i q^{12} +(-0.952833 + 1.65036i) q^{13} +(-0.494524 + 0.285514i) q^{14} +(-6.03405 - 3.48376i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.01614 - 0.586670i) q^{17} +5.78076 q^{18} +(3.45037 + 2.66364i) q^{19} +2.35132 q^{20} +(0.846044 + 1.46539i) q^{21} +(3.28046 + 0.488448i) q^{22} +(-3.18044 + 5.50869i) q^{23} +(-2.56624 + 1.48162i) q^{24} +(-0.264361 + 0.457887i) q^{25} -1.90567 q^{26} -8.24003i q^{27} +(-0.494524 - 0.285514i) q^{28} +(-1.27997 + 2.21698i) q^{29} -6.96752i q^{30} +0.329657i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.44738 - 9.72077i) q^{33} +(1.01614 + 0.586670i) q^{34} +(1.16279 - 0.671335i) q^{35} +(2.89038 + 5.00628i) q^{36} +4.43422i q^{37} +(-0.581595 + 4.31992i) q^{38} +5.64694i q^{39} +(1.17566 + 2.03631i) q^{40} +(-4.57346 - 7.92146i) q^{41} +(-0.846044 + 1.46539i) q^{42} +(-9.13597 + 5.27465i) q^{43} +(1.21722 + 3.08519i) q^{44} -13.5924 q^{45} -6.36088 q^{46} +(-2.95016 + 5.10983i) q^{47} +(-2.56624 - 1.48162i) q^{48} +6.67393 q^{49} -0.528723 q^{50} +(1.73844 - 3.01107i) q^{51} +(-0.952833 - 1.65036i) q^{52} +(-1.52439 - 0.880108i) q^{53} +(7.13608 - 4.12002i) q^{54} +(-7.71342 - 1.14850i) q^{55} -0.571027i q^{56} +(12.8009 + 1.72340i) q^{57} -2.55995 q^{58} +(-5.24172 + 3.02631i) q^{59} +(6.03405 - 3.48376i) q^{60} +(10.9859 + 6.34273i) q^{61} +(-0.285491 + 0.164828i) q^{62} +(2.85872 + 1.65048i) q^{63} +1.00000 q^{64} +4.48084 q^{65} +(9.14213 - 3.60691i) q^{66} +(2.24569 + 1.29655i) q^{67} +1.17334i q^{68} +18.8488i q^{69} +(1.16279 + 0.671335i) q^{70} +(11.4097 - 6.58739i) q^{71} +(-2.89038 + 5.00628i) q^{72} +(-13.3662 + 7.71696i) q^{73} +(-3.84014 + 2.21711i) q^{74} +1.56673i q^{75} +(-4.03196 + 1.65629i) q^{76} +(1.48281 + 1.17817i) q^{77} +(-4.89039 + 2.82347i) q^{78} +(-0.838320 - 1.45201i) q^{79} +(-1.17566 + 2.03631i) q^{80} +(-3.53744 - 6.12702i) q^{81} +(4.57346 - 7.92146i) q^{82} -8.73822i q^{83} -1.69209 q^{84} +(-2.38928 - 1.37945i) q^{85} +(-9.13597 - 5.27465i) q^{86} +7.58572i q^{87} +(-2.06324 + 2.59674i) q^{88} +(8.10707 + 4.68062i) q^{89} +(-6.79621 - 11.7714i) q^{90} +(-0.942398 - 0.544094i) q^{91} +(-3.18044 - 5.50869i) q^{92} +(0.488425 + 0.845977i) q^{93} -5.90032 q^{94} +(1.36752 - 10.1575i) q^{95} -2.96323i q^{96} +(-13.4133 + 7.74414i) q^{97} +(3.33696 + 5.77979i) q^{98} +(-7.03646 - 17.8347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

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