LMFDB - Embedded newform 300.2.w.a.163.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [300,2,Mod(67,300)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("300.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(300, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			163.27
Character	$\chi$	$=$	300.163
Dual form			300.2.w.a.127.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33300 + 0.472333i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(1.55380 + 1.25924i) q^{4} +(1.01218 - 1.99386i) q^{5} +(-0.973281 - 1.02602i) q^{6} +(0.189838 + 0.189838i) q^{7} +(1.47645 + 2.41249i) q^{8} +(0.587785 + 0.809017i) q^{9} +(2.29101 - 2.17974i) q^{10} +(2.68290 - 3.69270i) q^{11} +(-0.812765 - 1.82741i) q^{12} +(-1.66631 - 0.263917i) q^{13} +(0.163389 + 0.342722i) q^{14} +(-1.80706 + 1.31702i) q^{15} +(0.828612 + 3.91323i) q^{16} +(2.52266 + 4.95101i) q^{17} +(0.401395 + 1.35605i) q^{18} +(-0.186788 + 0.574876i) q^{19} +(4.08349 - 1.82349i) q^{20} +(-0.0829624 - 0.255332i) q^{21} +(5.32050 - 3.65516i) q^{22} +(-3.67098 + 0.581426i) q^{23} +(-0.220276 - 2.81984i) q^{24} +(-2.95097 - 4.03631i) q^{25} +(-2.09654 - 1.13886i) q^{26} +(-0.156434 - 0.987688i) q^{27} +(0.0559189 + 0.534025i) q^{28} +(3.14920 - 1.02324i) q^{29} +(-3.03089 + 0.902066i) q^{30} +(-6.47245 - 2.10303i) q^{31} +(-0.743804 + 5.60774i) q^{32} +(-4.06693 + 2.07221i) q^{33} +(1.02420 + 7.79125i) q^{34} +(0.570663 - 0.186361i) q^{35} +(-0.105446 + 1.99722i) q^{36} +(-0.372643 + 2.35278i) q^{37} +(-0.520523 + 0.678086i) q^{38} +(1.36488 + 0.991640i) q^{39} +(6.30461 - 0.501950i) q^{40} +(-9.30874 + 6.76320i) q^{41} +(0.0100124 - 0.379545i) q^{42} +(0.00980686 - 0.00980686i) q^{43} +(8.81871 - 2.35930i) q^{44} +(2.20801 - 0.353090i) q^{45} +(-5.16806 - 0.958880i) q^{46} +(-1.17702 + 2.31002i) q^{47} +(1.03827 - 3.86290i) q^{48} -6.92792i q^{49} +(-2.02718 - 6.77426i) q^{50} -5.55664i q^{51} +(-2.25678 - 2.50836i) q^{52} +(-4.53201 + 8.89456i) q^{53} +(0.257990 - 1.39048i) q^{54} +(-4.64714 - 9.08702i) q^{55} +(-0.177697 + 0.738270i) q^{56} +(0.427418 - 0.427418i) q^{57} +(4.68120 + 0.123490i) q^{58} +(3.15728 - 2.29390i) q^{59} +(-4.46626 - 0.229128i) q^{60} +(-9.40115 - 6.83034i) q^{61} +(-7.63448 - 5.86050i) q^{62} +(-0.0419983 + 0.265167i) q^{63} +(-3.64021 + 7.12382i) q^{64} +(-2.21282 + 3.05526i) q^{65} +(-6.40001 + 0.841315i) q^{66} +(-6.49592 + 3.30984i) q^{67} +(-2.31480 + 10.8695i) q^{68} +(3.53483 + 1.14854i) q^{69} +(0.848721 + 0.0211233i) q^{70} +(12.6076 - 4.09646i) q^{71} +(-1.08391 + 2.61250i) q^{72} +(-0.770226 - 4.86301i) q^{73} +(-1.60803 + 2.96025i) q^{74} +(0.796891 + 4.93609i) q^{75} +(-1.01414 + 0.658032i) q^{76} +(1.21033 - 0.191698i) q^{77} +(1.35100 + 1.96654i) q^{78} +(4.17182 + 12.8395i) q^{79} +(8.64116 + 2.30877i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-15.6031 + 4.61855i) q^{82} +(-3.42602 - 6.72394i) q^{83} +(0.192618 - 0.501206i) q^{84} +(12.4250 - 0.0185208i) q^{85} +(0.0177047 - 0.00844049i) q^{86} +(-3.27049 - 0.517995i) q^{87} +(12.8698 + 1.02040i) q^{88} +(4.20350 - 5.78562i) q^{89} +(3.11007 + 0.572247i) q^{90} +(-0.266228 - 0.366431i) q^{91} +(-6.43614 - 3.71924i) q^{92} +(4.81224 + 4.81224i) q^{93} +(-2.66007 + 2.52333i) q^{94} +(0.957159 + 0.954310i) q^{95} +(3.20860 - 4.65885i) q^{96} +(-0.917106 - 0.467289i) q^{97} +(3.27228 - 9.23495i) q^{98} +4.56443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	1.33300	+	0.472333i	0.942577	+	0.333990i
$2$	1.33300	+	0.472333i	0.942577	+	0.333990i
$3$	−0.891007	−	0.453990i	−0.514423	−	0.262112i
$3$	−0.891007	−	0.453990i	−0.514423	−	0.262112i
$4$	1.55380	+	1.25924i	0.776902	+	0.629622i
$5$	1.01218	−	1.99386i	0.452662	−	0.891682i
$5$	1.01218	−	1.99386i	0.452662	−	0.891682i
$6$	−0.973281	−	1.02602i	−0.397340	−	0.418872i
$7$	0.189838	+	0.189838i	0.0717522	+	0.0717522i	0.742072	−	0.670320i	$-0.233843\pi$
$7$	0.189838	+	0.189838i	0.0717522	+	0.0717522i	−0.670320	+	0.742072i	$0.733843\pi$
$8$	1.47645	+	2.41249i	0.522003	+	0.852944i
$9$	0.587785	+	0.809017i	0.195928	+	0.269672i
$10$	2.29101	−	2.17974i	0.724481	−	0.689295i
$11$	2.68290	−	3.69270i	0.808925	−	1.11339i	−0.182563	−	0.983194i	$-0.558439\pi$
$11$	2.68290	−	3.69270i	0.808925	−	1.11339i	0.991488	−	0.130196i	$-0.0415607\pi$
$12$	−0.812765	−	1.82741i	−0.234625	−	0.527527i
$13$	−1.66631	−	0.263917i	−0.462151	−	0.0731975i	−0.0789825	−	0.996876i	$-0.525167\pi$
$13$	−1.66631	−	0.263917i	−0.462151	−	0.0731975i	−0.383168	+	0.923678i	$0.625167\pi$
$14$	0.163389	+	0.342722i	0.0436675	+	0.0915964i
$15$	−1.80706	+	1.31702i	−0.466580	+	0.340054i
$16$	0.828612	+	3.91323i	0.207153	+	0.978309i
$17$	2.52266	+	4.95101i	0.611836	+	1.20080i	0.964261	+	0.264955i	$0.0853572\pi$
$17$	2.52266	+	4.95101i	0.611836	+	1.20080i	−0.352425	+	0.935840i	$0.614643\pi$
$18$	0.401395	+	1.35605i	0.0946098	+	0.319625i
$19$	−0.186788	+	0.574876i	−0.0428522	+	0.131886i	−0.970194	−	0.242331i	$-0.922088\pi$
$19$	−0.186788	+	0.574876i	−0.0428522	+	0.131886i	0.927342	+	0.374216i	$0.122088\pi$
$20$	4.08349	−	1.82349i	0.913096	−	0.407744i
$21$	−0.0829624	−	0.255332i	−0.0181039	−	0.0557180i
$22$	5.32050	−	3.65516i	1.13434	−	0.779283i
$23$	−3.67098	+	0.581426i	−0.765452	+	0.121236i	−0.526939	−	0.849903i	$-0.676660\pi$
$23$	−3.67098	+	0.581426i	−0.765452	+	0.121236i	−0.238514	+	0.971139i	$0.576660\pi$
$24$	−0.220276	−	2.81984i	−0.0449636	−	0.575597i
$25$	−2.95097	−	4.03631i	−0.590194	−	0.807261i
$26$	−2.09654	−	1.13886i	−0.411165	−	0.223348i
$27$	−0.156434	−	0.987688i	−0.0301058	−	0.190081i
$28$	0.0559189	+	0.534025i	0.0105677	+	0.100921i
$29$	3.14920	−	1.02324i	0.584791	−	0.190010i	−0.00165467	−	0.999999i	$-0.500527\pi$
$29$	3.14920	−	1.02324i	0.584791	−	0.190010i	0.586446	+	0.809988i	$0.300527\pi$
$30$	−3.03089	+	0.902066i	−0.553362	+	0.164694i
$31$	−6.47245	−	2.10303i	−1.16249	−	0.377715i	−0.336653	−	0.941629i	$-0.609295\pi$
$31$	−6.47245	−	2.10303i	−1.16249	−	0.377715i	−0.825834	+	0.563914i	$0.809295\pi$
$32$	−0.743804	+	5.60774i	−0.131487	+	0.991318i
$33$	−4.06693	+	2.07221i	−0.707962	+	0.360725i
$34$	1.02420	+	7.79125i	0.175649	+	1.33619i
$35$	0.570663	−	0.186361i	0.0964596	−	0.0315007i
$36$	−0.105446	+	1.99722i	−0.0175744	+	0.332870i
$37$	−0.372643	+	2.35278i	−0.0612621	+	0.386794i	0.937938	+	0.346803i	$0.112733\pi$
$37$	−0.372643	+	2.35278i	−0.0612621	+	0.386794i	−0.999200	+	0.0399907i	$0.987267\pi$
$38$	−0.520523	+	0.678086i	−0.0844399	+	0.110000i
$39$	1.36488	+	0.991640i	0.218555	+	0.158790i
$40$	6.30461	−	0.501950i	0.996846	−	0.0793652i
$41$	−9.30874	+	6.76320i	−1.45378	+	1.05623i	−0.468852	+	0.883277i	$0.655332\pi$
$41$	−9.30874	+	6.76320i	−1.45378	+	1.05623i	−0.984929	+	0.172957i	$0.944668\pi$
$42$	0.0100124	−	0.379545i	0.00154494	−	0.0585650i
$43$	0.00980686	−	0.00980686i	0.00149553	−	0.00149553i	−0.706359	−	0.707854i	$-0.749663\pi$
$43$	0.00980686	−	0.00980686i	0.00149553	−	0.00149553i	0.707854	+	0.706359i	$0.249663\pi$
$44$	8.81871	−	2.35930i	1.32947	−	0.355678i
$45$	2.20801	−	0.353090i	0.329151	−	0.0526355i
$46$	−5.16806	−	0.958880i	−0.761989	−	0.141379i
$47$	−1.17702	+	2.31002i	−0.171685	+	0.336952i	−0.960776	−	0.277325i	$-0.910552\pi$
$47$	−1.17702	+	2.31002i	−0.171685	+	0.336952i	0.789091	+	0.614277i	$0.210552\pi$
$48$	1.03827	−	3.86290i	0.149862	−	0.557561i
$49$		−	6.92792i		−	0.989703i
$50$	−2.02718	−	6.77426i	−0.286687	−	0.958024i
$51$		−	5.55664i		−	0.778086i
$52$	−2.25678	−	2.50836i	−0.312959	−	0.347848i
$53$	−4.53201	+	8.89456i	−0.622519	+	1.22176i	0.337368	+	0.941373i	$0.390463\pi$
$53$	−4.53201	+	8.89456i	−0.622519	+	1.22176i	−0.959886	+	0.280389i	$0.909537\pi$
$54$	0.257990	−	1.39048i	0.0351079	−	0.189221i
$55$	−4.64714	−	9.08702i	−0.626621	−	1.22529i
$56$	−0.177697	+	0.738270i	−0.0237458	+	0.0986554i
$57$	0.427418	−	0.427418i	0.0566129	−	0.0566129i
$58$	4.68120	+	0.123490i	0.614672	+	0.0162150i
$59$	3.15728	−	2.29390i	0.411043	−	0.298640i	−0.362981	−	0.931797i	$-0.618241\pi$
$59$	3.15728	−	2.29390i	0.411043	−	0.298640i	0.774024	+	0.633156i	$0.218241\pi$
$60$	−4.46626	−	0.229128i	−0.576592	−	0.0295803i
$61$	−9.40115	−	6.83034i	−1.20369	−	0.874535i	−0.209051	−	0.977905i	$-0.567038\pi$
$61$	−9.40115	−	6.83034i	−1.20369	−	0.874535i	−0.994643	+	0.103369i	$0.967038\pi$
$62$	−7.63448	−	5.86050i	−0.969581	−	0.744284i
$63$	−0.0419983	+	0.265167i	−0.00529129	+	0.0334079i
$64$	−3.64021	+	7.12382i	−0.455027	+	0.890478i
$65$	−2.21282	+	3.05526i	−0.274467	+	0.378958i
$66$	−6.40001	+	0.841315i	−0.787787	+	0.103559i
$67$	−6.49592	+	3.30984i	−0.793603	+	0.404361i	−0.803287	−	0.595592i	$-0.796917\pi$
$67$	−6.49592	+	3.30984i	−0.793603	+	0.404361i	0.00968402	+	0.999953i	$0.496917\pi$
$68$	−2.31480	+	10.8695i	−0.280710	+	1.31813i
$69$	3.53483	+	1.14854i	0.425543	+	0.138267i
$70$	0.848721	+	0.0211233i	0.101442	+	0.00252471i
$71$	12.6076	−	4.09646i	1.49625	−	0.486160i	0.557326	−	0.830294i	$-0.311827\pi$
$71$	12.6076	−	4.09646i	1.49625	−	0.486160i	0.938921	+	0.344134i	$0.111827\pi$
$72$	−1.08391	+	2.61250i	−0.127740	+	0.307886i
$73$	−0.770226	−	4.86301i	−0.0901481	−	0.569173i	−0.990875	−	0.134786i	$-0.956965\pi$
$73$	−0.770226	−	4.86301i	−0.0901481	−	0.569173i	0.900727	−	0.434386i	$-0.143035\pi$
$74$	−1.60803	+	2.96025i	−0.186929	+	0.344122i
$75$	0.796891	+	4.93609i	0.0920171	+	0.569970i
$76$	−1.01414	+	0.658032i	−0.116330	+	0.0754814i
$77$	1.21033	−	0.191698i	0.137930	−	0.0218460i
$78$	1.35100	+	1.96654i	0.152971	+	0.222666i
$79$	4.17182	+	12.8395i	0.469366	+	1.44456i	0.853408	+	0.521244i	$0.174532\pi$
$79$	4.17182	+	12.8395i	0.469366	+	1.44456i	−0.384042	+	0.923316i	$0.625468\pi$
$80$	8.64116	+	2.30877i	0.966111	+	0.258128i
$81$	−0.309017	+	0.951057i	−0.0343352	+	0.105673i
$82$	−15.6031	+	4.61855i	−1.72307	+	0.510034i
$83$	−3.42602	−	6.72394i	−0.376054	−	0.738048i	0.622969	−	0.782247i	$-0.285926\pi$
$83$	−3.42602	−	6.72394i	−0.376054	−	0.738048i	−0.999023	+	0.0441989i	$0.985926\pi$
$84$	0.192618	−	0.501206i	0.0210163	−	0.0546861i
$85$	12.4250	−	0.0185208i	1.34768	−	0.00200886i
$86$	0.0177047	−	0.00844049i	0.00190915	−	0.000910161i
$87$	−3.27049	−	0.517995i	−0.350634	−	0.0555349i
$88$	12.8698	+	1.02040i	1.37192	+	0.108775i
$89$	4.20350	−	5.78562i	0.445570	−	0.613274i	−0.525869	−	0.850566i	$-0.676260\pi$
$89$	4.20350	−	5.78562i	0.445570	−	0.613274i	0.971438	+	0.237292i	$0.0762597\pi$
$90$	3.11007	+	0.572247i	0.327830	+	0.0603201i
$91$	−0.266228	−	0.366431i	−0.0279083	−	0.0384124i
$92$	−6.43614	−	3.71924i	−0.671014	−	0.387757i
$93$	4.81224	+	4.81224i	0.499007	+	0.499007i
$94$	−2.66007	+	2.52333i	−0.274365	+	0.260262i
$95$	0.957159	+	0.954310i	0.0982024	+	0.0979101i
$96$	3.20860	−	4.65885i	0.327476	−	0.475492i
$97$	−0.917106	−	0.467289i	−0.0931180	−	0.0474460i	0.406811	−	0.913512i	$-0.366641\pi$
$97$	−0.917106	−	0.467289i	−0.0931180	−	0.0474460i	−0.499929	+	0.866066i	$0.666641\pi$
$98$	3.27228	−	9.23495i	0.330551	−	0.932871i
$99$	4.56443			0.458742
$100$	0.497459	−	9.98762i	0.0497459	−	0.998762i
$101$	6.65959			0.662654			0.331327	−	0.943516i	$-0.392504\pi$
$101$	6.65959			0.662654			0.331327	+	0.943516i	$0.392504\pi$
$102$	2.62458	−	7.40703i	0.259873	−	0.733406i
$103$	−13.3848	−	6.81989i	−1.31884	−	0.671984i	−0.354107	−	0.935205i	$-0.615215\pi$
$103$	−13.3848	−	6.81989i	−1.31884	−	0.671984i	−0.964736	+	0.263221i	$0.915215\pi$
$104$	−1.82352	−	4.40961i	−0.178811	−	0.432398i
$105$	−0.593070	−	0.0930271i	−0.0578777	−	0.00907852i
$106$	−10.2424	+	9.71588i	−0.994828	+	0.943690i
$107$	11.3660	+	11.3660i	1.09880	+	1.09880i	0.994552	+	0.104243i	$0.0332420\pi$
$107$	11.3660	+	11.3660i	1.09880	+	1.09880i	0.104243	+	0.994552i	$0.466758\pi$
$108$	1.00067	−	1.73166i	0.0962897	−	0.166629i
$109$	3.89523	+	5.36133i	0.373095	+	0.513522i	0.953739	−	0.300636i	$-0.0971990\pi$
$109$	3.89523	+	5.36133i	0.373095	+	0.513522i	−0.580643	+	0.814158i	$0.697199\pi$
$110$	−1.90257	−	14.3080i	−0.181403	−	1.36422i
$111$	1.40017	−	1.92716i	0.132898	−	0.182918i
$112$	−0.585580	+	0.900185i	−0.0553321	+	0.0850595i
$113$	16.3189	+	2.58466i	1.53515	+	0.243144i	0.866024	−	0.500002i	$-0.166667\pi$
$113$	16.3189	+	2.58466i	1.53515	+	0.243144i	0.669129	+	0.743146i	$0.266667\pi$
$114$	0.771634	−	0.367867i	0.0722701	−	0.0344539i
$115$	−2.55642	+	7.90794i	−0.238387	+	0.737419i
$116$	6.18174	+	2.37570i	0.573960	+	0.220578i
$117$	−0.765918	−	1.50320i	−0.0708092	−	0.138971i
$118$	5.29216	−	1.56649i	0.487183	−	0.144207i
$119$	−0.460993	+	1.41879i	−0.0422591	+	0.130060i
$120$	−5.84532	−	2.41499i	−0.533603	−	0.220457i
$121$	−3.03887	−	9.35268i	−0.276261	−	0.850243i
$122$	−9.30559	−	13.5453i	−0.842489	−	1.22634i
$123$	11.3646	−	1.79997i	1.02471	−	0.162298i
$124$	−7.40870	−	11.4181i	−0.665321	−	1.02537i
$125$	−11.0348	+	1.79835i	−0.986979	+	0.160850i
$126$	−0.181231	+	0.333631i	−0.0161453	+	0.0297223i
$127$	0.216773	+	1.36865i	0.0192355	+	0.121448i	0.995438	−	0.0954145i	$-0.0304176\pi$
$127$	0.216773	+	1.36865i	0.0192355	+	0.121448i	−0.976202	+	0.216863i	$0.930418\pi$
$128$	−8.21724	+	7.77670i	−0.726308	+	0.687369i
$129$	−0.0131902	+	0.00428575i	−0.00116133	+	0.000377340i
$130$	−4.39280	+	3.02748i	−0.385274	+	0.265528i
$131$	18.9066	+	6.14313i	1.65188	+	0.536728i	0.979146	−	0.203158i	$-0.0651205\pi$
$131$	18.9066	+	6.14313i	1.65188	+	0.536728i	0.672732	+	0.739886i	$0.265120\pi$
$132$	−8.92863	−	1.90146i	−0.777137	−	0.165501i
$133$	−0.144593	+	0.0736739i	−0.0125378	+	0.00638834i
$134$	−10.2224	+	1.34379i	−0.883084	+	0.116086i
$135$	−2.12765	−	0.687812i	−0.183119	−	0.0591975i
$136$	−8.21967	+	13.3958i	−0.704831	+	1.14868i
$137$	−0.600835	+	3.79353i	−0.0513328	+	0.324103i	0.948637	+	0.316366i	$0.102463\pi$
$137$	−0.600835	+	3.79353i	−0.0513328	+	0.324103i	−0.999970	+	0.00773685i	$0.997537\pi$
$138$	4.16945	+	3.20062i	0.354927	+	0.272455i
$139$	14.9655	+	10.8731i	1.26936	+	0.922243i	0.999177	−	0.0405660i	$-0.0129161\pi$
$139$	14.9655	+	10.8731i	1.26936	+	0.922243i	0.270182	+	0.962809i	$0.412916\pi$
$140$	1.12137	+	0.429036i	0.0947732	+	0.0362601i
$141$	2.09746	−	1.52389i	0.176638	−	0.128335i
$142$	18.7409	+	0.494383i	1.57270	+	0.0414877i
$143$	−5.44511	+	5.44511i	−0.455343	+	0.455343i
$144$	−2.67883	+	2.97050i	−0.223236	+	0.247542i
$145$	1.14737	−	7.31477i	0.0952840	−	0.607458i
$146$	1.27025	−	6.84622i	0.105126	−	0.566597i
$147$	−3.14521	+	6.17282i	−0.259413	+	0.509126i
$148$	−3.54173	+	3.18650i	−0.291129	+	0.261929i
$149$		−	19.1283i		−	1.56705i	−0.621359	−	0.783526i	$-0.713419\pi$
$149$		−	19.1283i		−	1.56705i	0.621359	−	0.783526i	$-0.286581\pi$
$150$	−1.26922	+	6.95623i	−0.103631	+	0.567974i
$151$			0.789590i			0.0642559i	0.999484	+	0.0321280i	$0.0102284\pi$
$151$			0.789590i			0.0642559i	−0.999484	+	0.0321280i	$0.989772\pi$
$152$	−1.66267	+	0.398148i	−0.134860	+	0.0322941i
$153$	−2.52266	+	4.95101i	−0.203945	+	0.400265i
$154$	1.70393	+	0.316146i	0.137306	+	0.0254758i
$155$	−10.7445	+	10.7765i	−0.863015	+	0.865592i
$156$	0.872033	+	3.25953i	0.0698185	+	0.260971i
$157$	0.986707	−	0.986707i	0.0787478	−	0.0787478i	−0.666636	−	0.745384i	$-0.732266\pi$
$157$	0.986707	−	0.986707i	0.0787478	−	0.0787478i	0.745384	+	0.666636i	$0.232266\pi$
$158$	−0.503478	+	19.0856i	−0.0400546	+	1.51837i
$159$	8.07609	−	5.86762i	0.640476	−	0.465333i
$160$	10.4282	+	7.15910i	0.824421	+	0.565977i
$161$	−0.807270	−	0.586516i	−0.0636218	−	0.0462240i
$162$	−0.861136	+	1.12180i	−0.0676572	+	0.0881373i
$163$	1.18009	−	7.45082i	0.0924320	−	0.583593i	−0.897385	−	0.441248i	$-0.854536\pi$
$163$	1.18009	−	7.45082i	0.0924320	−	0.583593i	0.989817	−	0.142345i	$-0.0454641\pi$
$164$	−22.9805	−	1.21329i	−1.79447	−	0.0947421i
$165$	0.0152137	+	10.2064i	0.00118438	+	0.794564i
$166$	−1.39096	−	10.5813i	−0.107960	−	0.821265i
$167$	−17.5211	+	8.92744i	−1.35582	+	0.690826i	−0.972525	−	0.232799i	$-0.925212\pi$
$167$	−17.5211	+	8.92744i	−1.35582	+	0.690826i	−0.383298	+	0.923625i	$0.625212\pi$
$168$	0.493497	−	0.577130i	0.0380741	−	0.0445266i
$169$	−9.65680	−	3.13769i	−0.742831	−	0.241360i
$170$	16.5714	+	5.84405i	1.27097	+	0.448218i
$171$	−0.574876	+	0.186788i	−0.0439619	+	0.0142841i
$172$	0.0275871	−	0.00288871i	0.00210350	−	0.000220262i
$173$	−2.63941	−	16.6646i	−0.200670	−	1.26698i	−0.858106	−	0.513473i	$-0.828359\pi$
$173$	−2.63941	−	16.6646i	−0.200670	−	1.26698i	0.657435	−	0.753511i	$-0.271641\pi$
$174$	−4.11492	−	2.23525i	−0.311951	−	0.169454i
$175$	0.206038	−	1.32645i	0.0155750	−	0.100271i
$176$	16.6735	+	7.43901i	1.25681	+	0.560736i
$177$	−3.85457	+	0.610504i	−0.289727	+	0.0458883i
$178$	8.33602	−	5.72681i	0.624811	−	0.429242i
$179$	−0.708606	−	2.18087i	−0.0529637	−	0.163006i	0.921076	−	0.389383i	$-0.127312\pi$
$179$	−0.708606	−	2.18087i	−0.0529637	−	0.163006i	−0.974040	+	0.226377i	$0.927312\pi$
$180$	3.87545	+	2.23180i	0.288859	+	0.166348i
$181$	4.25840	−	13.1060i	0.316525	−	0.974163i	−0.658598	−	0.752495i	$-0.728850\pi$
$181$	4.25840	−	13.1060i	0.316525	−	0.974163i	0.975122	−	0.221667i	$-0.0711499\pi$
$182$	−0.181806	−	0.614203i	−0.0134763	−	0.0455277i
$183$	5.27558	+	10.3539i	0.389982	+	0.765383i
$184$	−6.82269	−	7.99776i	−0.502975	−	0.589603i
$185$	4.31393	+	3.12444i	0.317166	+	0.229713i
$186$	4.14177	+	8.68773i	0.303689	+	0.637015i
$187$	25.0506	+	3.96763i	1.83188	+	0.290142i
$188$	−4.73774	+	2.10717i	−0.345535	+	0.153682i
$189$	0.157804	−	0.217199i	0.0114785	−	0.0157989i
$190$	0.825146	+	1.72420i	0.0598624	+	0.125086i
$191$	−15.6587	−	21.5523i	−1.13302	−	1.55947i	−0.782200	−	0.623027i	$-0.785903\pi$
$191$	−15.6587	−	21.5523i	−1.13302	−	1.55947i	−0.350821	−	0.936443i	$-0.614097\pi$
$192$	6.47760	−	4.69475i	0.467481	−	0.338814i
$193$	6.53786	+	6.53786i	0.470605	+	0.470605i	0.902110	−	0.431505i	$-0.142017\pi$
$193$	6.53786	+	6.53786i	0.470605	+	0.470605i	−0.431505	+	0.902110i	$0.642017\pi$
$194$	−1.00179	−	1.05608i	−0.0719244	−	0.0758219i
$195$	3.35870	−	1.71765i	0.240521	−	0.123004i
$196$	8.72394	−	10.7646i	0.623139	−	0.768902i
$197$	12.1115	+	6.17110i	0.862906	+	0.439673i	0.828668	−	0.559741i	$-0.189099\pi$
$197$	12.1115	+	6.17110i	0.862906	+	0.439673i	0.0342384	+	0.999414i	$0.489099\pi$
$198$	6.08440	+	2.15593i	0.432400	+	0.153215i
$199$	7.41416			0.525576			0.262788	−	0.964854i	$-0.415358\pi$
$199$	7.41416			0.525576			0.262788	+	0.964854i	$0.415358\pi$
$200$	5.38059	−	13.0786i	0.380465	−	0.924795i
$201$	7.29054			0.514235
$202$	8.87726	+	3.14554i	0.624602	+	0.221319i
$203$	0.792088	+	0.403589i	0.0555937	+	0.0283264i
$204$	6.99717	−	8.63393i	0.489900	−	0.604496i
$205$	4.06274	+	25.4059i	0.283754	+	1.77443i
$206$	−14.6207	−	15.4130i	−1.01867	−	1.07388i
$207$	−2.62813	−	2.62813i	−0.182668	−	0.182668i
$208$	−0.347953	−	6.73934i	−0.0241262	−	0.467289i
$209$	1.62171	+	2.23209i	0.112176	+	0.154397i
$210$	−0.746626	−	0.404132i	−0.0515221	−	0.0278878i
$211$	4.85618	−	6.68396i	0.334313	−	0.460142i	−0.608457	−	0.793587i	$-0.708211\pi$
$211$	4.85618	−	6.68396i	0.334313	−	0.460142i	0.942770	+	0.333445i	$0.108211\pi$
$212$	−18.2423	+	8.11350i	−1.25288	+	0.557238i
$213$	−13.0932	−	2.07376i	−0.897132	−	0.142092i
$214$	9.78242	+	20.5195i	0.668713	+	1.40268i
$215$	−0.00962719	−	0.0294799i	−0.000656569	−	0.00201051i
$216$	2.15182	−	1.83567i	0.146413	−	0.124901i
$217$	−0.829485	−	1.62796i	−0.0563091	−	0.110513i
$218$	2.66003	+	8.98652i	0.180160	+	0.608644i
$219$	−1.52149	+	4.68265i	−0.102812	+	0.316424i
$220$	4.22202	−	19.9713i	0.284649	−	1.34647i
$221$	−2.89688	−	8.91568i	−0.194865	−	0.599733i
$222$	2.77669	−	1.90757i	0.186359	−	0.128028i
$223$	−4.16161	+	0.659135i	−0.278682	+	0.0441389i	−0.294211	−	0.955741i	$-0.595057\pi$
$223$	−4.16161	+	0.659135i	−0.278682	+	0.0441389i	0.0155288	+	0.999879i	$0.495057\pi$
$224$	−1.20577	+	0.923362i	−0.0805637	+	0.0616947i
$225$	1.53090	−	4.75987i	0.102060	−	0.317325i
$226$	20.5324	+	11.1533i	1.36579	+	0.741907i
$227$	−1.61847	−	10.2186i	−0.107421	−	0.678232i	−0.981358	−	0.192191i	$-0.938441\pi$
$227$	−1.61847	−	10.2186i	−0.107421	−	0.678232i	0.873936	−	0.486041i	$-0.161559\pi$
$228$	1.20235	−	0.125900i	0.0796274	−	0.00833796i
$229$	−1.55021	+	0.503695i	−0.102441	+	0.0332851i	−0.359789	−	0.933034i	$-0.617151\pi$
$229$	−1.55021	+	0.503695i	−0.102441	+	0.0332851i	0.257348	+	0.966319i	$0.417151\pi$
$230$	−7.14290	+	9.33384i	−0.470989	+	0.615455i
$231$	−1.16544	−	0.378676i	−0.0766806	−	0.0249150i
$232$	7.11817	+	6.08665i	0.467330	+	0.399608i
$233$	2.66801	−	1.35942i	0.174787	−	0.0890586i	−0.364408	−	0.931240i	$-0.618729\pi$
$233$	2.66801	−	1.35942i	0.174787	−	0.0890586i	0.539195	+	0.842181i	$0.318729\pi$
$234$	−0.310963	−	2.36554i	−0.0203283	−	0.154640i
$235$	3.41451	+	4.68497i	0.222738	+	0.305614i
$236$	7.79438	+	0.411517i	0.507371	+	0.0267875i
$237$	2.11191	−	13.3341i	0.137183	−	0.866141i
$238$	−1.28465	+	1.67351i	−0.0832713	+	0.108478i
$239$	−17.9159	−	13.0167i	−1.15888	−	0.841979i	−0.169248	−	0.985574i	$-0.554134\pi$
$239$	−17.9159	−	13.0167i	−1.15888	−	0.841979i	−0.989637	+	0.143595i	$0.954134\pi$
$240$	−6.65117	−	5.98013i	−0.429331	−	0.386016i
$241$	−0.0614146	+	0.0446203i	−0.00395606	+	0.00287425i	−0.589762	−	0.807577i	$-0.700778\pi$
$241$	−0.0614146	+	0.0446203i	−0.00395606	+	0.00287425i	0.585805	+	0.810452i	$0.300778\pi$
$242$	0.366748	−	13.9025i	0.0235754	−	0.893688i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−6.00649	−	22.4513i	−0.384526	−	1.43730i
$245$	−13.8133	−	7.01232i	−0.882501	−	0.448001i
$246$	15.9992	+	2.96849i	1.02007	+	0.189264i
$247$	0.462967	−	0.908624i	0.0294579	−	0.0578144i
$248$	−4.48270	−	18.7197i	−0.284652	−	1.18870i
$249$			7.54645i			0.478237i
$250$	−15.5588	−	2.81486i	−0.984025	−	0.178028i
$251$			29.9398i			1.88979i	0.327379	+	0.944893i	$0.393835\pi$
$251$			29.9398i			1.88979i	−0.327379	+	0.944893i	$0.606165\pi$
$252$	−0.399167	+	0.359131i	−0.0251451	+	0.0226231i
$253$	−7.70185	+	15.1157i	−0.484211	+	0.950318i
$254$	−0.357499	+	1.92681i	−0.0224315	+	0.120899i
$255$	−11.0792	−	5.62434i	−0.693805	−	0.352210i
$256$	−14.6268	+	6.48511i	−0.914175	+	0.405319i
$257$	14.7898	−	14.7898i	0.922565	−	0.922565i	−0.0746451	−	0.997210i	$-0.523782\pi$
$257$	14.7898	−	14.7898i	0.922565	−	0.922565i	0.997210	+	0.0746451i	$0.0237824\pi$
$258$	−0.0196069		0.000517229i	−0.00122067		3.22012e-5i
$259$	−0.517389	+	0.375905i	−0.0321490	+	0.0233576i
$260$	−7.28561	+	1.96079i	−0.451834	+	0.121603i
$261$	2.67887	+	1.94631i	0.165818	+	0.120474i
$262$	22.3010	+	17.1190i	1.37776	+	1.05762i
$263$	4.13096	−	26.0818i	0.254726	−	1.60827i	−0.446128	−	0.894969i	$-0.647197\pi$
$263$	4.13096	−	26.0818i	0.254726	−	1.60827i	0.700854	−	0.713305i	$-0.252803\pi$
$264$	−11.0038	−	6.75193i	−0.677236	−	0.415553i
$265$	13.1473	+	18.0391i	0.807633	+	1.10813i
$266$	−0.227542	+	0.0299116i	−0.0139515	+	0.00183400i
$267$	−6.37196	+	3.24667i	−0.389957	+	0.198693i
$268$	−14.2613	−	3.03711i	−0.871146	−	0.185521i
$269$	−14.2213	−	4.62080i	−0.867091	−	0.281735i	−0.158504	−	0.987358i	$-0.550667\pi$
$269$	−14.2213	−	4.62080i	−0.867091	−	0.281735i	−0.708587	+	0.705623i	$0.750667\pi$
$270$	−2.51130	−	1.92182i	−0.152833	−	0.116958i
$271$	−8.37925	+	2.72258i	−0.509003	+	0.165385i	−0.552249	−	0.833679i	$-0.686230\pi$
$271$	−8.37925	+	2.72258i	−0.509003	+	0.165385i	0.0432457	+	0.999064i	$0.486230\pi$
$272$	−17.2841	+	13.9742i	−1.04800	+	0.847313i
$273$	0.0708545	+	0.447357i	0.00428831	+	0.0270753i
$274$	−2.59272	+	4.77299i	−0.156632	+	0.288347i
$275$	−22.8220	+	0.0680375i	−1.37622	+	0.00410281i
$276$	4.04615	+	6.23581i	0.243549	+	0.375352i
$277$	−8.96925	+	1.42059i	−0.538910	+	0.0853549i	−0.419955	−	0.907545i	$-0.637954\pi$
$277$	−8.96925	+	1.42059i	−0.538910	+	0.0853549i	−0.118955	+	0.992900i	$0.537954\pi$
$278$	14.8134	+	21.5626i	0.888449	+	1.29324i
$279$	−2.10303	−	6.47245i	−0.125905	−	0.387496i
$280$	1.29215	+	1.10157i	0.0772205	+	0.0658312i
$281$	−8.89363	+	27.3718i	−0.530549	+	1.63286i	0.222525	+	0.974927i	$0.428570\pi$
$281$	−8.89363	+	27.3718i	−0.530549	+	1.63286i	−0.753074	+	0.657936i	$0.771430\pi$
$282$	3.51571	−	1.04066i	0.209357	−	0.0619703i
$283$	−8.13832	−	15.9724i	−0.483773	−	0.949458i	−0.995892	−	0.0905436i	$-0.971140\pi$
$283$	−8.13832	−	15.9724i	−0.483773	−	0.949458i	0.512120	−	0.858914i	$-0.328860\pi$
$284$	24.7482	+	9.51094i	1.46853	+	0.564371i
$285$	−0.419587	−	1.28484i	−0.0248542	−	0.0761072i
$286$	−9.83026	+	4.68646i	−0.581276	+	0.277116i
$287$	−3.05107	−	0.483242i	−0.180099	−	0.0285249i
$288$	−4.97395	+	2.69440i	−0.293093	+	0.158769i
$289$	−8.15628	+	11.2262i	−0.479781	+	0.660362i
$290$	4.98445	−	9.20868i	0.292697	−	0.540752i
$291$	0.605003	+	0.832715i	0.0354659	+	0.0488146i
$292$	4.92694	−	8.52607i	0.288327	−	0.498950i
$293$	−1.24037	−	1.24037i	−0.0724632	−	0.0724632i	0.669946	−	0.742410i	$-0.266317\pi$
$293$	−1.24037	−	1.24037i	−0.0724632	−	0.0724632i	−0.742410	+	0.669946i	$0.766317\pi$
$294$	−7.10821	+	6.74282i	−0.414559	+	0.393249i
$295$	−1.37797	−	8.61703i	−0.0802287	−	0.501703i
$296$	−6.22624	+	2.57475i	−0.361893	+	0.149654i
$297$	−4.06693	−	2.07221i	−0.235987	−	0.120242i
$298$	9.03492	−	25.4981i	0.523379	−	1.47707i
$299$	6.27044			0.362629
$300$	−4.97752	+	8.67319i	−0.287377	+	0.500747i
$301$	0.00372344			0.000214615
$302$	−0.372949	+	1.05253i	−0.0214608	+	0.0605661i
$303$	−5.93374	−	3.02339i	−0.340884	−	0.173689i
$304$	−2.40440	−	0.254598i	−0.137902	−	0.0146022i
$305$	−23.1344	+	11.8311i	−1.32467	+	0.677444i
$306$	−5.70124	+	5.40818i	−0.325918	+	0.309165i
$307$	11.6840	+	11.6840i	0.666844	+	0.666844i	0.956984	−	0.290140i	$-0.0937020\pi$
$307$	11.6840	+	11.6840i	0.666844	+	0.666844i	−0.290140	+	0.956984i	$0.593702\pi$
$308$	2.12202	+	1.22624i	0.120913	+	0.0698717i
$309$	8.82977	+	12.1531i	0.502308	+	0.691368i
$310$	−19.4125	+	9.29022i	−1.10256	+	0.527649i
$311$	3.31285	−	4.55974i	0.187854	−	0.258559i	−0.704694	−	0.709512i	$-0.748916\pi$
$311$	3.31285	−	4.55974i	0.187854	−	0.258559i	0.892548	+	0.450952i	$0.148916\pi$
$312$	−0.377156	+	4.75685i	−0.0213523	+	0.269304i
$313$	−17.7167	−	2.80604i	−1.00141	−	0.158607i	−0.365859	−	0.930670i	$-0.619225\pi$
$313$	−17.7167	−	2.80604i	−1.00141	−	0.158607i	−0.635546	+	0.772063i	$0.719225\pi$
$314$	1.78134	−	0.849231i	0.100527	−	0.0479249i
$315$	0.486196	+	0.352136i	0.0273940	+	0.0198406i
$316$	−9.68591	+	25.2034i	−0.544875	+	1.41780i
$317$	4.15260	+	8.14994i	0.233233	+	0.457746i	0.977726	−	0.209884i	$-0.0673086\pi$
$317$	4.15260	+	8.14994i	0.233233	+	0.457746i	−0.744493	+	0.667630i	$0.767309\pi$
$318$	13.5369	−	4.00697i	0.759114	−	0.224700i
$319$	4.67049	−	14.3743i	0.261497	−	0.804805i
$320$	10.5194	+	14.4687i	0.588050	+	0.808825i
$321$	−4.96713	−	15.2873i	−0.277238	−	0.853252i
$322$	−0.799064	−	1.16313i	−0.0445301	−	0.0648186i
$323$	−3.31742	+	0.525427i	−0.184586	+	0.0292356i
$324$	−1.67776	+	1.08863i	−0.0932091	+	0.0604793i
$325$	3.85198	+	7.50454i	0.213669	+	0.416277i
$326$	5.09233	−	9.37458i	0.282038	−	0.519210i
$327$	−1.03669	−	6.54537i	−0.0573288	−	0.361960i
$328$	−30.0600	−	12.4718i	−1.65979	−	0.688637i
$329$	−0.661974	+	0.215089i	−0.0364958	+	0.0118582i
$330$	−4.80051	+	13.6123i	−0.264260	+	0.749333i
$331$	−7.07411	−	2.29852i	−0.388828	−	0.126338i	0.108077	−	0.994142i	$-0.465531\pi$
$331$	−7.07411	−	2.29852i	−0.388828	−	0.126338i	−0.496906	+	0.867804i	$0.665531\pi$
$332$	3.14371	−	14.7619i	0.172534	−	0.810163i
$333$	−2.12247	+	1.08145i	−0.116311	+	0.0592632i
$334$	−27.5724	+	3.62454i	−1.50870	+	0.198326i
$335$	0.0243001	+	16.3021i	0.00132765	+	0.890680i
$336$	0.930431	−	0.536223i	0.0507592	−	0.0292534i
$337$	1.87071	−	11.8112i	0.101904	−	0.643398i	−0.882878	−	0.469603i	$-0.844397\pi$
$337$	1.87071	−	11.8112i	0.101904	−	0.643398i	0.984782	−	0.173795i	$-0.0556030\pi$
$338$	−11.3905	−	8.74377i	−0.619563	−	0.475599i
$339$	−13.3668	−	9.71158i	−0.725987	−	0.527460i
$340$	19.3294	+	15.6173i	1.04828	+	0.846969i
$341$	−25.1308	+	18.2586i	−1.36091	+	0.988759i
$342$	−0.854538	−	0.0225427i	−0.0462081	−	0.00121897i
$343$	2.64406	−	2.64406i	0.142766	−	0.142766i
$344$	0.0381382	+	0.00917964i	0.00205628	+	0.000494933i
$345$	5.86791	−	5.88543i	0.315918	−	0.316861i
$346$	4.35287	−	23.4606i	0.234012	−	1.26125i
$347$	15.3433	−	30.1129i	0.823672	−	1.61655i	0.0368882	−	0.999319i	$-0.488255\pi$
$347$	15.3433	−	30.1129i	0.823672	−	1.61655i	0.786784	−	0.617228i	$-0.211745\pi$
$348$	−4.42942	−	4.92321i	−0.237442	−	0.263912i
$349$			27.4462i			1.46916i	0.678523	+	0.734579i	$0.262620\pi$
$349$			27.4462i			1.46916i	−0.678523	+	0.734579i	$0.737380\pi$
$350$	0.901177	−	1.67085i	0.0481699	−	0.0893108i
$351$			1.68708i			0.0900496i
$352$	18.7121	+	17.7917i	0.997360	+	0.948299i
$353$	4.86385	−	9.54584i	0.258876	−	0.508074i	−0.724586	−	0.689184i	$-0.757969\pi$
$353$	4.86385	−	9.54584i	0.258876	−	0.508074i	0.983463	+	0.181110i	$0.0579691\pi$
$354$	−5.42652	−	1.00683i	−0.288416	−	0.0535126i
$355$	4.59342	−	29.2842i	0.243794	−	1.55424i
$356$	13.8169	−	3.69649i	0.732295	−	0.195913i
$357$	1.05486	−	1.05486i	0.0558294	−	0.0558294i
$358$	0.0855185	−	3.24180i	0.00451980	−	0.171335i
$359$	−10.7538	+	7.81307i	−0.567562	+	0.412358i	−0.834219	−	0.551434i	$-0.814081\pi$
$359$	−10.7538	+	7.81307i	−0.567562	+	0.412358i	0.266657	+	0.963792i	$0.414081\pi$
$360$	4.11184	+	4.80549i	0.216713	+	0.253272i
$361$	15.0757	+	10.9532i	0.793460	+	0.576482i
$362$	11.8669	−	15.4590i	0.623709	−	0.812507i
$363$	−1.53837	+	9.71291i	−0.0807437	+	0.509796i
$364$	0.0477602	−	0.904608i	0.00250332	−	0.0474143i
$365$	−10.4758	−	3.38653i	−0.548328	−	0.177259i
$366$	2.14189	+	16.2936i	0.111958	+	0.851682i
$367$	−23.2351	+	11.8389i	−1.21286	+	0.617983i	−0.939043	−	0.343799i	$-0.888286\pi$
$367$	−23.2351	+	11.8389i	−1.21286	+	0.617983i	−0.273817	+	0.961782i	$0.588286\pi$
$368$	−5.31708	−	13.8836i	−0.277172	−	0.723734i
$369$	−10.9431	−	3.55562i	−0.569674	−	0.185098i
$370$	4.27471	+	6.20250i	0.222232	+	0.322453i
$371$	−2.54888	+	0.828181i	−0.132331	+	0.0429970i
$372$	1.41750	+	13.5371i	0.0734938	+	0.701864i
$373$	−4.62618	−	29.2086i	−0.239535	−	1.51236i	−0.755156	−	0.655545i	$-0.772439\pi$
$373$	−4.62618	−	29.2086i	−0.239535	−	1.51236i	0.515621	−	0.856817i	$-0.327561\pi$
$374$	31.5186	+	17.1211i	1.62979	+	0.885311i
$375$	10.6485	+	3.40733i	0.549885	+	0.175954i
$376$	−7.31071	+	0.571087i	−0.377021	+	0.0294516i
$377$	−5.51758	+	0.873899i	−0.284170	+	0.0450081i
$378$	0.312943	−	0.214991i	0.0160961	−	0.0110579i
$379$	−5.98387	−	18.4165i	−0.307371	−	0.945990i	−0.978782	−	0.204905i	$-0.934311\pi$
$379$	−5.98387	−	18.4165i	−0.307371	−	0.945990i	0.671411	−	0.741085i	$-0.265689\pi$
$380$	0.285529	+	2.68811i	0.0146473	+	0.137897i
$381$	0.428208	−	1.31789i	0.0219378	−	0.0675175i
$382$	−10.6932	−	36.1254i	−0.547113	−	1.84834i
$383$	4.35881	+	8.55465i	0.222725	+	0.437122i	0.975147	−	0.221559i	$-0.0711146\pi$
$383$	4.35881	+	8.55465i	0.222725	+	0.437122i	−0.752422	+	0.658681i	$0.771115\pi$
$384$	10.8522	−	3.19854i	0.553797	−	0.163225i
$385$	0.842860	−	2.60727i	0.0429561	−	0.132879i
$386$	5.62695	+	11.8030i	0.286404	+	0.600759i
$387$	0.0136982	+	0.00216959i	0.000696321	+	0.000110286i
$388$	−0.836572	−	1.88093i	−0.0424705	−	0.0954900i
$389$	11.3570	−	15.6316i	0.575825	−	0.792555i	−0.417405	−	0.908721i	$-0.637060\pi$
$389$	11.3570	−	15.6316i	0.575825	−	0.792555i	0.993230	+	0.116166i	$0.0370603\pi$
$390$	5.28846	−	0.703217i	0.267792	−	0.0356088i
$391$	−12.1393	−	16.7083i	−0.613910	−	0.844975i
$392$	16.7135	−	10.2287i	0.844161	−	0.516628i
$393$	−14.0570	−	14.0570i	−0.709081	−	0.709081i
$394$	13.2298	+	13.9467i	0.666509	+	0.702627i
$395$	29.8229	+	4.67792i	1.50055	+	0.235372i
$396$	7.09222	+	5.74772i	0.356398	+	0.288834i
$397$	17.5405	+	8.93731i	0.880331	+	0.448551i	0.834890	−	0.550416i	$-0.185531\pi$
$397$	17.5405	+	8.93731i	0.880331	+	0.448551i	0.0454402	+	0.998967i	$0.485531\pi$
$398$	9.88311	+	3.50195i	0.495395	+	0.175537i
$399$	0.162281			0.00812420
$400$	13.3498	−	14.8924i	0.667490	−	0.744619i
$401$	33.9482			1.69529			0.847645	−	0.530564i	$-0.178020\pi$
$401$	33.9482			1.69529			0.847645	+	0.530564i	$0.178020\pi$
$402$	9.71833	+	3.44356i	0.484706	+	0.171749i
$403$	10.2301	+	5.21249i	0.509597	+	0.259652i
$404$	10.3477	+	8.38604i	0.514817	+	0.417221i
$405$	1.58349	+	1.57878i	0.0786844	+	0.0784502i
$406$	0.865229	+	0.912115i	0.0429406	+	0.0452675i
$407$	7.68833	+	7.68833i	0.381096	+	0.381096i
$408$	13.4053	−	8.20409i	0.663664	−	0.406163i
$409$	8.02687	+	11.0480i	0.396903	+	0.546291i	0.959963	−	0.280125i	$-0.0903760\pi$
$409$	8.02687	+	11.0480i	0.396903	+	0.546291i	−0.563060	+	0.826416i	$0.690376\pi$
$410$	−6.58441	+	35.7852i	−0.325181	+	1.76731i
$411$	2.25757	−	3.10728i	0.111358	−	0.153271i
$412$	−12.2094	−	27.4515i	−0.601516	−	1.35244i
$413$	1.03484	+	0.163903i	0.0509214	+	0.00806515i
$414$	−2.26196	−	4.74466i	−0.111169	−	0.233188i
$415$	−16.8744	+	0.0251530i	−0.828330	+	0.00123471i
$416$	2.71939	−	9.14792i	0.133329	−	0.448514i
$417$	−8.39810	−	16.4822i	−0.411257	−	0.807137i
$418$	1.10746	+	3.74137i	0.0541674	+	0.182996i
$419$	−2.10539	+	6.47973i	−0.102855	+	0.316555i	−0.989221	−	0.146430i	$-0.953222\pi$
$419$	−2.10539	+	6.47973i	−0.102855	+	0.316555i	0.886366	+	0.462985i	$0.153222\pi$
$420$	−0.804371	−	0.891366i	−0.0392493	−	0.0434942i
$421$	3.96818	+	12.2128i	0.193397	+	0.595215i	0.999992	+	0.00410979i	$0.00130819\pi$
$421$	3.96818	+	12.2128i	0.193397	+	0.595215i	−0.806594	+	0.591105i	$0.798692\pi$
$422$	9.63036	−	6.61601i	0.468799	−	0.322062i
$423$	−2.56068	+	0.405572i	−0.124505	+	0.0197196i
$424$	−28.1493	+	2.19892i	−1.36705	+	0.106789i
$425$	12.5395	−	24.7925i	0.608253	−	1.20261i
$426$	−16.4738	−	8.94868i	−0.798158	−	0.433565i
$427$	−0.488040	−	3.08136i	−0.0236179	−	0.149118i
$428$	3.34798	+	31.9732i	0.161831	+	1.54548i
$429$	7.32366	−	2.37960i	0.353590	−	0.114888i
$430$	0.00109121	−	0.0438440i	5.26226e−5	−	0.00211435i
$431$	3.23293	+	1.05044i	0.155725	+	0.0505981i	0.385842	−	0.922565i	$-0.373911\pi$
$431$	3.23293	+	1.05044i	0.155725	+	0.0505981i	−0.230117	+	0.973163i	$0.573911\pi$
$432$	3.73543	−	1.43058i	0.179721	−	0.0688286i
$433$	3.04817	−	1.55312i	0.146486	−	0.0746383i	−0.379211	−	0.925310i	$-0.623805\pi$
$433$	3.04817	−	1.55312i	0.146486	−	0.0746383i	0.525697	+	0.850672i	$0.323805\pi$
$434$	−0.336771	−	2.56187i	−0.0161655	−	0.122974i
$435$	−4.34315	+	5.99661i	−0.208238	+	0.287515i
$436$	−0.698789	+	13.2355i	−0.0334659	+	0.633865i
$437$	0.351449	−	2.21896i	0.0168121	−	0.106147i
$438$	−4.23992	+	5.52335i	−0.202591	+	0.263916i
$439$	16.2122	+	11.7788i	0.773766	+	0.562174i	0.903102	−	0.429427i	$-0.141285\pi$
$439$	16.2122	+	11.7788i	0.773766	+	0.562174i	−0.129336	+	0.991601i	$0.541285\pi$
$440$	15.0611	−	24.6277i	0.718009	−	1.17408i
$441$	5.60481	−	4.07213i	0.266896	−	0.193911i
$442$	0.349612	−	13.2529i	0.0166293	−	0.630378i
$443$	10.2267	−	10.2267i	0.485887	−	0.485887i	−0.421119	−	0.907006i	$-0.638362\pi$
$443$	10.2267	−	10.2267i	0.485887	−	0.485887i	0.907006	+	0.421119i	$0.138362\pi$
$444$	4.60235	−	1.23128i	0.218418	−	0.0584341i
$445$	−7.28102	−	14.2373i	−0.345153	−	0.674912i
$446$	−5.85878	−	1.08704i	−0.277421	−	0.0514726i
$447$	−8.68407	+	17.0434i	−0.410742	+	0.806127i
$448$	−2.04343	+	0.661323i	−0.0965429	+	0.0312446i
$449$			20.1223i			0.949629i	0.880086	+	0.474814i	$0.157485\pi$
$449$			20.1223i			0.949629i	−0.880086	+	0.474814i	$0.842515\pi$
$450$	4.28894	−	5.62183i	0.202183	−	0.265016i
$451$			52.5194i			2.47304i
$452$	22.1017	+	24.5655i	1.03957	+	1.15547i
$453$	0.358466	−	0.703530i	0.0168422	−	0.0330547i
$454$	2.66915	−	14.3859i	0.125270	−	0.675163i
$455$	−1.00008	+	0.159926i	−0.0468847	+	0.00749746i
$456$	1.66220	+	0.400082i	0.0778397	+	0.0187355i
$457$	5.50274	−	5.50274i	0.257407	−	0.257407i	−0.566591	−	0.823999i	$-0.691738\pi$
$457$	5.50274	−	5.50274i	0.257407	−	0.257407i	0.823999	+	0.566591i	$0.191738\pi$
$458$	−2.30436	−	0.0607887i	−0.107675	−	0.00284047i
$459$	4.49542	−	3.26611i	0.209828	−	0.152449i
$460$	−13.9302	+	9.06823i	−0.649499	+	0.422808i
$461$	1.99209	+	1.44734i	0.0927808	+	0.0674092i	0.633209	−	0.773981i	$-0.281738\pi$
$461$	1.99209	+	1.44734i	0.0927808	+	0.0674092i	−0.540428	+	0.841390i	$0.681738\pi$
$462$	−1.37468	−	1.05525i	−0.0639560	−	0.0490949i
$463$	−5.26029	+	33.2122i	−0.244467	+	1.54350i	0.494151	+	0.869376i	$0.335479\pi$
$463$	−5.26029	+	33.2122i	−0.244467	+	1.54350i	−0.738617	+	0.674125i	$0.764521\pi$
$464$	6.61362	+	11.4757i	0.307030	+	0.532745i
$465$	14.4658	−	4.72408i	0.670836	−	0.219074i
$466$	4.19857	−	0.551925i	0.194495	−	0.0255674i
$467$	9.58390	−	4.88324i	0.443490	−	0.225969i	−0.217962	−	0.975957i	$-0.569941\pi$
$467$	9.58390	−	4.88324i	0.443490	−	0.225969i	0.661452	+	0.749988i	$0.269941\pi$
$468$	0.702807	−	3.30015i	0.0324873	−	0.152550i
$469$	−1.86151	−	0.604841i	−0.0859565	−	0.0279290i
$470$	2.33870	+	7.85788i	0.107876	+	0.362457i
$471$	−1.32712	+	0.431207i	−0.0611504	+	0.0198690i
$472$	10.1956	+	4.23009i	0.469289	+	0.194706i
$473$	−0.00990292	−	0.0625246i	−0.000455337	−	0.00287488i
$474$	9.11330	−	16.7769i	0.418588	−	0.770587i
$475$	2.87158	−	0.942507i	0.131757	−	0.0432452i
$476$	−2.50289	+	1.62402i	−0.114720	+	0.0744368i
$477$	−9.85970	+	1.56162i	−0.451445	+	0.0715018i
$478$	−17.7338	−	25.8136i	−0.811125	−	1.18068i
$479$	7.08607	+	21.8087i	0.323771	+	0.996464i	0.971992	+	0.235012i	$0.0755131\pi$
$479$	7.08607	+	21.8087i	0.323771	+	0.996464i	−0.648221	+	0.761452i	$0.724487\pi$
$480$	−6.04143	−	11.1131i	−0.275752	−	0.507242i
$481$	1.24188	−	3.82210i	0.0566247	−	0.174273i
$482$	−0.102942	+	0.0304710i	−0.00468886	+	0.00138792i
$483$	0.453010	+	0.889083i	0.0206127	+	0.0404547i
$484$	7.05549	−	18.3589i	0.320704	−	0.834495i
$485$	−1.85999	+	1.35560i	−0.0844577	+	0.0615547i
$486$	1.27657	−	0.608587i	0.0579062	−	0.0276061i
$487$	16.6355	+	2.63480i	0.753826	+	0.119394i	0.521509	−	0.853246i	$-0.325369\pi$
$487$	16.6355	+	2.63480i	0.753826	+	0.119394i	0.232317	+	0.972640i	$0.425369\pi$
$488$	2.59782	−	32.7648i	0.117598	−	1.48319i
$489$	−4.43407	+	6.10297i	−0.200516	+	0.275986i
$490$	−15.1011	−	15.8719i	−0.682197	−	0.717021i
$491$	6.71450	+	9.24172i	0.303021	+	0.417073i	0.933189	−	0.359386i	$-0.117014\pi$
$491$	6.71450	+	9.24172i	0.303021	+	0.417073i	−0.630168	+	0.776459i	$0.717014\pi$
$492$	19.9249	+	11.5140i	0.898285	+	0.519090i
$493$	13.0104	+	13.0104i	0.585959	+	0.585959i
$494$	1.04631	−	0.992526i	0.0470757	−	0.0446558i
$495$	4.62003	−	9.10084i	0.207655	−	0.409052i
$496$	2.86649	−	27.0708i	0.128709	−	1.21552i
$497$	3.17107	+	1.61574i	0.142242	+	0.0724759i
$498$	−3.56443	+	10.0595i	−0.159726	+	0.450775i
$499$	−41.8728			−1.87448			−0.937242	−	0.348679i	$-0.886630\pi$
$499$	−41.8728			−1.87448			−0.937242	+	0.348679i	$0.886630\pi$
$500$	−19.4104	−	11.1012i	−0.868060	−	0.496459i
$501$	19.6644			0.878540
$502$	−14.1416	+	39.9100i	−0.631169	+	1.78127i
$503$	21.0178	+	10.7091i	0.937139	+	0.477496i	0.854713	−	0.519101i	$-0.173733\pi$
$503$	21.0178	+	10.7091i	0.937139	+	0.477496i	0.0824263	+	0.996597i	$0.473733\pi$
$504$	−0.701720	+	0.290184i	−0.0312571	+	0.0129258i
$505$	6.74072	−	13.2783i	0.299958	−	0.590877i
$506$	−17.4063	+	16.5115i	−0.773802	+	0.734026i
$507$	7.17979	+	7.17979i	0.318866	+	0.318866i
$508$	−1.38664	+	2.39958i	−0.0615223	+	0.106464i
$509$	−22.3651	−	30.7830i	−0.991318	−	1.36443i	−0.930504	−	0.366282i	$-0.880630\pi$
$509$	−22.3651	−	30.7830i	−0.991318	−	1.36443i	−0.0608138	−	0.998149i	$-0.519370\pi$
$510$	−12.1120	−	12.7303i	−0.536330	−	0.563708i
$511$	0.776968	−	1.06941i	0.0343711	−	0.0473077i
$512$	−22.5607	+	1.73596i	−0.997053	+	0.0767194i
$513$	0.597018	+	0.0945584i	0.0263590	+	0.00417486i
$514$	26.7007	−	12.7292i	1.17772	−	0.561461i
$515$	−27.1458	+	19.7845i	−1.19619	+	0.871807i
$516$	−0.0258918	−	0.00995044i	−0.00113982	−	0.000438044i
$517$	5.37240	+	10.5439i	0.236278	+	0.463722i
$518$	−0.867235	+	0.256704i	−0.0381041	+	0.0112789i
$519$	−5.21382	+	16.0465i	−0.228862	+	0.704363i
$520$	−10.6379	−	0.827492i	−0.466502	−	0.0362879i
$521$	2.57819	+	7.93486i	0.112953	+	0.347632i	0.991515	−	0.129996i	$-0.0414965\pi$
$521$	2.57819	+	7.93486i	0.112953	+	0.347632i	−0.878562	+	0.477629i	$0.841496\pi$
$522$	2.65164	+	3.85976i	0.116059	+	0.168937i
$523$	32.5180	−	5.15034i	1.42191	−	0.225209i	0.602365	−	0.798221i	$-0.294225\pi$
$523$	32.5180	−	5.15034i	1.42191	−	0.225209i	0.819547	+	0.573012i	$0.194225\pi$
$524$	21.6415	+	33.3532i	0.945412	+	1.45704i
$525$	−0.785779	+	1.08834i	−0.0342942	+	0.0474991i
$526$	17.8259	−	32.8160i	0.777245	−	1.43085i
$527$	−5.91572	−	37.3504i	−0.257693	−	1.62701i
$528$	−11.4789	−	14.1978i	−0.499557	−	0.617880i
$529$	−8.73626	+	2.83858i	−0.379837	+	0.123417i
$530$	9.00497	+	30.2561i	0.391151	+	1.31424i
$531$	3.71161	+	1.20597i	0.161070	+	0.0523349i
$532$	−0.317443	−	0.0676032i	−0.0137629	−	0.00293097i
$533$	17.2962	−	8.81284i	0.749180	−	0.381726i
$534$	−10.0274	+	1.31815i	−0.433926	+	0.0570419i
$535$	34.1668	−	11.1578i	1.47716	−	0.482393i
$536$	−17.5758	−	10.7845i	−0.759160	−	0.465821i
$537$	−0.358720	+	2.26487i	−0.0154799	+	0.0977362i
$538$	−16.7746	−	12.8767i	−0.723203	−	0.555156i
$539$	−25.5827	−	18.5869i	−1.10193	−	0.800596i
$540$	−2.43983	−	3.74796i	−0.104994	−	0.161287i
$541$	−7.48590	+	5.43883i	−0.321844	+	0.233833i	−0.736962	−	0.675934i	$-0.763740\pi$
$541$	−7.48590	+	5.43883i	−0.321844	+	0.233833i	0.415118	+	0.909768i	$0.363740\pi$
$542$	−12.4555	−	0.328576i	−0.535011	−	0.0141136i
$543$	−9.74427	+	9.74427i	−0.418167	+	0.418167i
$544$	−29.6403	+	10.4639i	−1.27082	+	0.448634i
$545$	14.6324	−	2.33991i	0.626784	−	0.100231i
$546$	−0.116852	+	0.629797i	−0.00500081	+	0.0269528i
$547$	6.35363	−	12.4697i	0.271662	−	0.533166i	−0.714361	−	0.699777i	$-0.753283\pi$
$547$	6.35363	−	12.4697i	0.271662	−	0.533166i	0.986023	+	0.166611i	$0.0532825\pi$
$548$	−5.71055	+	5.13780i	−0.243943	+	0.219476i
$549$		−	11.6205i		−	0.495949i
$550$	−30.4540	−	10.6889i	−1.29856	−	0.455776i
$551$			2.00153i			0.0852679i
$552$	2.44815	+	10.2235i	0.104200	+	0.435141i
$553$	−1.64547	+	3.22941i	−0.0699723	+	0.137328i
$554$	−12.6270	−	2.34282i	−0.536472	−	0.0995367i
$555$	−2.42527	−	4.74238i	−0.102947	−	0.201303i
$556$	9.56162	+	35.7399i	0.405503	+	1.51571i
$557$	2.87624	−	2.87624i	0.121870	−	0.121870i	−0.643541	−	0.765411i	$-0.722536\pi$
$557$	2.87624	−	2.87624i	0.121870	−	0.121870i	0.765411	+	0.643541i	$0.222536\pi$
$558$	0.253805	−	9.62114i	0.0107444	−	0.407295i
$559$	−0.0189295	+	0.0137531i	−0.000800630	+	0.000581692i
$560$	1.20213	+	2.07872i	0.0507993	+	0.0878418i
$561$	−20.5190	−	14.9079i	−0.866313	−	0.629413i
$562$	−24.7838	+	32.2860i	−1.04544	+	1.36190i
$563$	3.30793	−	20.8854i	0.139412	−	0.880216i	−0.814507	−	0.580153i	$-0.802993\pi$
$563$	3.30793	−	20.8854i	0.139412	−	0.880216i	0.953920	−	0.300062i	$-0.0970074\pi$
$564$	5.17799	+	0.273380i	0.218033	+	0.0115114i
$565$	21.6712	−	29.9215i	0.911713	−	1.25881i
$566$	−3.30416	−	25.1352i	−0.138884	−	1.05651i
$567$	−0.239210	+	0.121884i	−0.0100459	+	0.00511864i
$568$	28.4971	+	24.3675i	1.19571	+	1.02244i
$569$	3.40048	+	1.10488i	0.142556	+	0.0463192i	0.379426	−	0.925222i	$-0.376122\pi$
$569$	3.40048	+	1.10488i	0.142556	+	0.0463192i	−0.236870	+	0.971541i	$0.576122\pi$
$570$	0.0475586	−	1.91088i	0.00199201	−	0.0800379i
$571$	10.6049	−	3.44576i	0.443803	−	0.144200i	−0.0785864	−	0.996907i	$-0.525041\pi$
$571$	10.6049	−	3.44576i	0.443803	−	0.144200i	0.522390	+	0.852707i	$0.325041\pi$
$572$	−15.3174	+	1.60391i	−0.640451	+	0.0670630i
$573$	4.16743	+	26.3121i	0.174097	+	1.09920i
$574$	−3.83884	−	2.08529i	−0.160230	−	0.0870381i
$575$	13.1798	+	13.1014i	0.549635	+	0.546367i
$576$	−7.90296	+	1.24228i	−0.329290	+	0.0517618i
$577$	−38.4820	+	6.09495i	−1.60203	+	0.253736i	−0.892535	−	0.450979i	$-0.851075\pi$
$577$	−38.4820	+	6.09495i	−1.60203	+	0.253736i	−0.709491	+	0.704714i	$0.751075\pi$
$578$	−16.1748	+	11.1120i	−0.672785	+	0.462200i
$579$	−2.85715	−	8.79340i	−0.118739	−	0.365441i
$580$	10.9939	−	9.92089i	0.456495	−	0.411943i
$581$	0.626072	−	1.92685i	0.0259738	−	0.0799393i
$582$	0.413153	+	1.39578i	0.0171257	+	0.0578567i
$583$	20.6860	+	40.5986i	0.856727	+	1.68142i
$584$	10.5948	−	9.03814i	0.438415	−	0.374001i
$585$	−3.77242	+	0.00562319i	−0.155970	+	0.000232490i
$586$	−1.06755	−	2.23929i	−0.0441002	−	0.0925041i
$587$	15.7614	+	2.49636i	0.650542	+	0.103036i	0.472979	−	0.881074i	$-0.343179\pi$
$587$	15.7614	+	2.49636i	0.650542	+	0.103036i	0.177563	+	0.984109i	$0.443179\pi$
$588$	−12.6601	+	5.63077i	−0.522095	+	0.232209i
$589$	2.41796	−	3.32804i	0.0996303	−	0.137129i
$590$	2.23326	−	12.1374i	0.0919419	−	0.499689i
$591$	−7.98977	−	10.9970i	−0.328655	−	0.452355i
$592$	−9.51574	+	0.491299i	−0.391094	+	0.0201923i
$593$	6.24575	+	6.24575i	0.256482	+	0.256482i	0.823622	−	0.567140i	$-0.191950\pi$
$593$	6.24575	+	6.24575i	0.256482	+	0.256482i	−0.567140	+	0.823622i	$0.691950\pi$
$594$	−4.44247	−	4.68321i	−0.182277	−	0.192154i
$595$	2.36226	+	2.35523i	0.0968433	+	0.0965550i
$596$	24.0872	−	29.7216i	0.986650	−	1.21745i
$597$	−6.60606	−	3.36596i	−0.270368	−	0.137759i
$598$	8.35852	+	2.96173i	0.341805	+	0.121114i
$599$	19.3797			0.791832			0.395916	−	0.918287i	$-0.370427\pi$
$599$	19.3797			0.791832			0.395916	+	0.918287i	$0.370427\pi$
$600$	−10.7317	+	9.21036i	−0.438120	+	0.376011i
$601$	21.8893			0.892883			0.446441	−	0.894813i	$-0.352691\pi$
$601$	21.8893			0.892883			0.446441	+	0.894813i	$0.352691\pi$
$602$	0.00496336	+	0.00175870i	0.000202291	+	7.16793e-5i
$603$	−6.49592	−	3.30984i	−0.264534	−	0.134787i
$604$	−0.994286	+	1.22687i	−0.0404569	+	0.0499206i
$605$	−21.7238	−	3.40753i	−0.883199	−	0.138536i
$606$	−6.48165	−	6.83289i	−0.263299	−	0.277567i
$607$	−26.4147	−	26.4147i	−1.07214	−	1.07214i	−0.997187	−	0.0749533i	$-0.976119\pi$
$607$	−26.4147	−	26.4147i	−1.07214	−	1.07214i	−0.0749533	−	0.997187i	$-0.523881\pi$
$608$	−3.08482	−	1.47506i	−0.125106	−	0.0598214i
$609$	−0.522530	−	0.719201i	−0.0211740	−	0.0291435i
$610$	−36.4265	+	4.84370i	−1.47487	+	0.196116i
$611$	2.57093	−	3.53858i	0.104009	−	0.143156i
$612$	−10.1542	+	4.51624i	−0.410461	+	0.182558i
$613$	−23.7116	−	3.75555i	−0.957703	−	0.151685i	−0.342032	−	0.939688i	$-0.611115\pi$
$613$	−23.7116	−	3.75555i	−0.957703	−	0.151685i	−0.615671	+	0.788003i	$0.711115\pi$
$614$	10.0561	+	21.0937i	0.405833	+	0.851270i
$615$	7.91413	−	24.4813i	0.319129	−	0.987181i
$616$	2.24946	+	2.63689i	0.0906334	+	0.106243i
$617$	19.1096	+	37.5048i	0.769325	+	1.50989i	0.857900	+	0.513816i	$0.171769\pi$
$617$	19.1096	+	37.5048i	0.769325	+	1.50989i	−0.0885751	+	0.996070i	$0.528231\pi$
$618$	6.02980	+	20.3708i	0.242554	+	0.819433i
$619$	0.176865	−	0.544334i	0.00710880	−	0.0218786i	−0.947439	−	0.319936i	$-0.896339\pi$
$619$	0.176865	−	0.544334i	0.00710880	−	0.0218786i	0.954548	+	0.298057i	$0.0963386\pi$
$620$	−30.2651	+	3.21474i	−1.21547	+	0.129107i
$621$	1.14854	+	3.53483i	0.0460891	+	0.141848i
$622$	6.56976	−	4.51339i	0.263423	−	0.180971i
$623$	1.89632	−	0.300347i	0.0759744	−	0.0120332i
$624$	−2.74957	+	6.16276i	−0.110071	+	0.246708i
$625$	−7.58352	+	23.8221i	−0.303341	+	0.952882i
$626$	−22.2910	−	12.1086i	−0.890928	−	0.483958i
$627$	−0.431605	−	2.72505i	−0.0172366	−	0.108828i
$628$	2.77565	−	0.290645i	0.110761	−	0.0115980i
$629$	−12.5887	+	4.09030i	−0.501943	+	0.163091i
$630$	0.481776	+	0.699045i	0.0191944	+	0.0278506i
$631$	12.1577	+	3.95028i	0.483991	+	0.157258i	0.540842	−	0.841124i	$-0.318106\pi$
$631$	12.1577	+	3.95028i	0.483991	+	0.157258i	−0.0568504	+	0.998383i	$0.518106\pi$
$632$	−24.8158	+	29.0213i	−0.987118	+	1.15441i
$633$	−7.36134	+	3.75079i	−0.292587	+	0.149080i
$634$	1.68596	+	12.8253i	0.0669579	+	0.509359i
$635$	2.94831	+	0.953109i	0.117000	+	0.0378230i
$636$	19.9374	+	1.05263i	0.790571	+	0.0417394i
$637$	−1.82840	+	11.5441i	−0.0724438	+	0.457392i
$638$	13.0152	−	16.9550i	0.515277	−	0.671253i
$639$	10.7247	+	7.79192i	0.424261	+	0.308244i
$640$	7.18832	+	24.2555i	0.284143	+	0.958782i
$641$	−0.248557	+	0.180587i	−0.00981740	+	0.00713276i	−0.592683	−	0.805436i	$-0.701931\pi$
$641$	−0.248557	+	0.180587i	−0.00981740	+	0.00713276i	0.582866	+	0.812568i	$0.301931\pi$
$642$	0.599461	−	22.7241i	0.0236589	−	0.896850i
$643$	−16.7114	+	16.7114i	−0.659034	+	0.659034i	−0.955152	−	0.296117i	$-0.904308\pi$
$643$	−16.7114	+	16.7114i	−0.659034	+	0.659034i	0.296117	+	0.955152i	$0.404308\pi$
$644$	−0.515773	−	1.92788i	−0.0203243	−	0.0759691i
$645$	−0.00480568	+	0.0306374i	−0.000189224	+	0.00120635i
$646$	−4.67031	−	0.866527i	−0.183751	−	0.0340931i
$647$	−0.506217	+	0.993506i	−0.0199014	+	0.0390588i	−0.900743	−	0.434352i	$-0.856977\pi$
$647$	−0.506217	+	0.993506i	−0.0199014	+	0.0390588i	0.880842	+	0.473411i	$0.156977\pi$
$648$	−2.75066	+	0.658683i	−0.108056	+	0.0258755i
$649$		−	17.8132i		−	0.699229i
$650$	1.59007	+	11.8230i	0.0623676	+	0.463737i
$651$			1.82710i			0.0716096i
$652$	11.2160	−	10.0911i	0.439253	−	0.395197i
$653$	7.76292	−	15.2356i	0.303786	−	0.596214i	−0.687764	−	0.725934i	$-0.741408\pi$
$653$	7.76292	−	15.2356i	0.303786	−	0.596214i	0.991551	+	0.129720i	$0.0414077\pi$
$654$	1.70969	−	9.21467i	0.0668541	−	0.360322i
$655$	31.3855	−	31.4792i	1.22633	−	1.22999i
$656$	−34.1793	−	30.8232i	−1.33448	−	1.20344i
$657$	3.48153	−	3.48153i	0.135828	−	0.135828i
$658$	−0.984008	−	0.0259581i	−0.0383606	−	0.00101195i
$659$	−19.1442	+	13.9091i	−0.745752	+	0.541820i	−0.894507	−	0.447054i	$-0.852473\pi$
$659$	−19.1442	+	13.9091i	−0.745752	+	0.541820i	0.148755	+	0.988874i	$0.452473\pi$
$660$	−12.8286	+	15.8778i	−0.499354	+	0.618044i
$661$	11.9962	+	8.71577i	0.466599	+	0.339004i	0.796115	−	0.605146i	$-0.206885\pi$
$661$	11.9962	+	8.71577i	0.466599	+	0.339004i	−0.329515	+	0.944150i	$0.606885\pi$
$662$	−8.34416	−	6.40527i	−0.324305	−	0.248948i
$663$	−1.46649	+	9.25908i	−0.0569539	+	0.359593i
$664$	11.1631	−	18.1928i	0.433212	−	0.706016i
$665$	0.000540897		0.362870i	2.09751e−5		0.0140715i
$666$	−3.34007	+	0.439069i	−0.129425	+	0.0170136i
$667$	−10.9657	+	5.58730i	−0.424594	+	0.216341i
$668$	−38.4662	−	8.19183i	−1.48830	−	0.316951i
$669$	4.00726	+	1.30204i	0.154930	+	0.0503397i
$670$	−7.66763	+	21.7423i	−0.296227	+	0.839978i
$671$	−50.4448	+	16.3905i	−1.94740	+	0.632748i
$672$	1.49354	−	0.275315i	0.0576147	−	0.0106205i
$673$	5.11813	+	32.3146i	0.197289	+	1.24564i	0.865212	+	0.501406i	$0.167184\pi$
$673$	5.11813	+	32.3146i	0.197289	+	1.24564i	−0.667923	+	0.744231i	$0.732816\pi$
$674$	8.07250	−	14.8608i	0.310941	−	0.572417i
$675$	−3.52498	+	3.54606i	−0.135676	+	0.136488i
$676$	−11.0537	−	17.0356i	−0.425141	−	0.655216i
$677$	−16.7410	+	2.65152i	−0.643410	+	0.101906i	−0.469609	−	0.882875i	$-0.655605\pi$
$677$	−16.7410	+	2.65152i	−0.643410	+	0.101906i	−0.173801	+	0.984781i	$0.555605\pi$
$678$	−13.2310	−	19.2592i	−0.508132	−	0.739644i
$679$	−0.0853926	−	0.262811i	−0.00327707	−	0.0100858i
$680$	18.3896	+	29.9479i	0.705207	+	1.14845i
$681$	−3.19708	+	9.83960i	−0.122512	+	0.377054i
$682$	−42.1236	+	12.4687i	−1.61300	+	0.477451i
$683$	10.1740	+	19.9676i	0.389296	+	0.764037i	0.999604	−	0.0281270i	$-0.00895427\pi$
$683$	10.1740	+	19.9676i	0.389296	+	0.764037i	−0.610308	+	0.792164i	$0.708954\pi$
$684$	−1.12846	−	0.433676i	−0.0431476	−	0.0165820i
$685$	6.95561	+	5.03772i	0.265760	+	0.192482i
$686$	4.77341	−	2.27566i	0.182250	−	0.0868853i
$687$	1.60992	+	0.254987i	0.0614224	+	0.00972836i
$688$	0.0465026	+	0.0302504i	0.00177290	+	0.00115329i
$689$	9.89915	−	13.6250i	0.377128	−	0.519072i
$690$	10.6018	−	5.07370i	0.403605	−	0.193153i
$691$	−9.13509	−	12.5734i	−0.347515	−	0.478314i	0.599102	−	0.800672i	$-0.295524\pi$
$691$	−9.13509	−	12.5734i	−0.347515	−	0.478314i	−0.946618	+	0.322359i	$0.895524\pi$
$692$	16.8836	−	29.2171i	0.641819	−	1.11067i
$693$	0.866504	+	0.866504i	0.0329158	+	0.0329158i
$694$	34.6760	−	32.8936i	1.31628	−	1.24862i
$695$	36.8273	−	18.8336i	1.39694	−	0.714400i
$696$	−3.57905	−	8.65483i	−0.135664	−	0.328060i
$697$	−56.9675	−	29.0264i	−2.15780	−	1.09945i
$698$	−12.9637	+	36.5859i	−0.490684	+	1.38479i
$699$	−2.99438			−0.113258
$700$	1.99047	−	1.80160i	0.0752327	−	0.0680940i
$701$	−10.8238			−0.408809			−0.204404	−	0.978887i	$-0.565526\pi$
$701$	−10.8238			−0.408809			−0.204404	+	0.978887i	$0.565526\pi$
$702$	−0.796863	+	2.24889i	−0.0300756	+	0.0848787i
$703$	−1.28295	−	0.653695i	−0.0483873	−	0.0246546i
$704$	16.5398	+	32.5547i	0.623367	+	1.22695i
$705$	−0.915421	−	5.72450i	−0.0344767	−	0.215597i
$706$	10.9923	−	10.4273i	0.413702	−	0.392436i
$707$	1.26425	+	1.26425i	0.0475469	+	0.0475469i
$708$	−6.75802	−	3.90524i	−0.253982	−	0.146768i
$709$	1.47386	+	2.02859i	0.0553519	+	0.0761853i	0.835796	−	0.549041i	$-0.185007\pi$
$709$	1.47386	+	2.02859i	0.0553519	+	0.0761853i	−0.780444	+	0.625226i	$0.785007\pi$
$710$	19.9549	−	36.8663i	0.748895	−	1.38357i
$711$	−7.93527	+	10.9220i	−0.297596	+	0.409605i
$712$	20.1640	+	1.59874i	0.755677	+	0.0599153i
$713$	24.9830	+	3.95692i	0.935621	+	0.148188i
$714$	1.90439	−	0.907893i	0.0712699	−	0.0339770i
$715$	5.34535	+	16.3682i	0.199905	+	0.612138i
$716$	1.64521	−	4.28095i	0.0614842	−	0.159986i
$717$	10.0538	+	19.7316i	0.375464	+	0.736890i
$718$	−18.0252	+	5.33550i	−0.672694	+	0.199119i
$719$	2.03075	−	6.25002i	0.0757344	−	0.233086i	−0.906022	−	0.423231i	$-0.860896\pi$
$719$	2.03075	−	6.25002i	0.0757344	−	0.233086i	0.981756	+	0.190145i	$0.0608958\pi$
$720$	3.21131	+	8.34790i	0.119678	+	0.311108i
$721$	−1.24627	−	3.83563i	−0.0464135	−	0.142846i
$722$	14.9225	+	21.7214i	0.555357	+	0.808386i
$723$	0.0749780	−	0.0118754i	0.00278846	−	0.000441649i
$724$	23.1204	−	15.0018i	0.859262	−	0.557538i
$725$	−13.4233	−	9.69158i	−0.498528	−	0.359936i
$726$	−6.63839	+	12.2207i	−0.246374	+	0.453554i
$727$	−4.93599	−	31.1646i	−0.183066	−	1.15583i	−0.892496	−	0.451055i	$-0.851048\pi$
$727$	−4.93599	−	31.1646i	−0.183066	−	1.15583i	0.709430	−	0.704776i	$-0.248952\pi$
$728$	0.490940	−	1.18329i	0.0181955	−	0.0438556i
$729$	−0.951057	+	0.309017i	−0.0352243	+	0.0114451i
$730$	−12.3647	−	9.46232i	−0.457638	−	0.350216i
$731$	0.0732932	+	0.0238144i	0.00271085	+	0.000880808i
$732$	−4.84088	+	22.7312i	−0.178924	+	0.840169i
$733$	37.4928	−	19.1035i	1.38483	−	0.705605i	0.406691	−	0.913566i	$-0.366683\pi$
$733$	37.4928	−	19.1035i	1.38483	−	0.705605i	0.978137	+	0.207961i	$0.0666826\pi$
$734$	−36.5643	+	4.80657i	−1.34961	+	0.177414i
$735$	9.12423	+	12.5191i	0.336552	+	0.461776i
$736$	−0.529997	−	21.0184i	−0.0195359	−	0.774747i
$737$	−5.20569	+	32.8674i	−0.191754	+	1.21069i
$738$	−12.9077	−	9.90844i	−0.475141	−	0.364735i
$739$	−22.9251	−	16.6560i	−0.843313	−	0.612702i	0.0799814	−	0.996796i	$-0.474514\pi$
$739$	−22.9251	−	16.6560i	−0.843313	−	0.612702i	−0.923294	+	0.384094i	$0.874514\pi$
$740$	2.76857	+	10.2870i	0.101775	+	0.378159i
$741$	−0.825013	+	0.599407i	−0.0303076	+	0.0220198i
$742$	−3.78884	−	0.0999495i	−0.139093	−	0.00366926i
$743$	−35.9683	+	35.9683i	−1.31955	+	1.31955i	−0.405414	+	0.914133i	$0.632873\pi$
$743$	−35.9683	+	35.9683i	−1.31955	+	1.31955i	−0.914133	+	0.405414i	$0.867127\pi$
$744$	−4.50447	+	18.7145i	−0.165142	+	0.686107i
$745$	−38.1392	−	19.3613i	−1.39731	−	0.709345i
$746$	7.62943	−	41.1202i	0.279333	−	1.50552i
$747$	3.42602	−	6.72394i	0.125351	−	0.246016i
$748$	33.9276	+	37.7098i	1.24051	+	1.37881i
$749$			4.31542i			0.157682i
$750$	12.5851	+	9.57161i	0.459542	+	0.349506i
$751$			4.28864i			0.156495i	0.996934	+	0.0782473i	$0.0249324\pi$
$751$			4.28864i			0.156495i	−0.996934	+	0.0782473i	$0.975068\pi$
$752$	−10.0150	−	2.69183i	−0.365208	−	0.0981608i
$753$	13.5924	−	26.6766i	0.495335	−	0.972149i
$754$	−7.76774	−	1.44122i	−0.282884	−	0.0524862i
$755$	1.57433	+	0.799209i	0.0572959	+	0.0290862i
$756$	0.518702	−	0.138770i	0.0188650	−	0.00504703i
$757$	12.7121	−	12.7121i	0.462030	−	0.462030i	−0.437291	−	0.899320i	$-0.644062\pi$
$757$	12.7121	−	12.7121i	0.462030	−	0.462030i	0.899320	+	0.437291i	$0.144062\pi$
$758$	0.722167	−	27.3756i	0.0262303	−	0.994327i
$759$	13.7248	−	9.97165i	0.498179	−	0.361948i
$760$	−0.889069	+	3.71812i	−0.0322499	+	0.134871i
$761$	−27.1391	−	19.7177i	−0.983792	−	0.714766i	−0.0252388	−	0.999681i	$-0.508035\pi$
$761$	−27.1391	−	19.7177i	−0.983792	−	0.714766i	−0.958553	+	0.284915i	$0.908035\pi$
$762$	1.19329	−	1.55450i	0.0432282	−	0.0563135i
$763$	−0.278321	+	1.75725i	−0.0100759	+	0.0636167i
$764$	2.80910	−	53.2061i	0.101630	−	1.92493i
$765$	7.31823	+	10.0412i	0.264591	+	0.363039i
$766$	1.76968	+	13.4622i	0.0639410	+	0.486409i
$767$	−5.86641	+	2.98908i	−0.211824	+	0.107930i
$768$	15.9768	+	0.862157i	0.576511	+	0.0311104i
$769$	38.5837	+	12.5366i	1.39136	+	0.452081i	0.906388	−	0.422447i	$-0.138829\pi$
$769$	38.5837	+	12.5366i	1.39136	+	0.452081i	0.484975	+	0.874528i	$0.338829\pi$
$770$	2.35504	−	3.07740i	0.0848696	−	0.110902i
$771$	−19.8923	+	6.46340i	−0.716403	+	0.232774i
$772$	1.92579	+	18.3913i	0.0693108	+	0.661917i
$773$	1.29494	+	8.17594i	0.0465758	+	0.294068i	0.999971	−	0.00765730i	$-0.00243742\pi$
$773$	1.29494	+	8.17594i	0.0465758	+	0.294068i	−0.953395	+	0.301725i	$0.902437\pi$
$774$	0.0172351	+	0.00936220i	0.000619501	+	0.000336517i
$775$	10.6116	+	32.3308i	0.381179	+	1.16136i
$776$	−0.226728	−	2.90243i	−0.00813906	−	0.104191i
$777$	0.631655	−	0.100044i	0.0226605	−	0.00358907i
$778$	22.5223	−	15.4727i	0.807464	−	0.554724i
$779$	−2.14923	−	6.61466i	−0.0770043	−	0.236995i
$780$	7.38170	+	1.56052i	0.264307	+	0.0558757i
$781$	18.6980	−	57.5465i	0.669066	−	2.05917i
$782$	−8.28986	−	28.0060i	−0.296445	−	1.00149i
$783$	−1.50328	−	2.95036i	−0.0537229	−	0.105437i
$784$	27.1106	−	5.74056i	0.968235	−	0.205020i
$785$	−0.968630	−	2.96609i	−0.0345719	−	0.105864i
$786$	−12.0985	−	25.3776i	−0.431538	−	0.905190i
$787$	−12.9653	−	2.05351i	−0.462164	−	0.0731996i	−0.0789893	−	0.996875i	$-0.525169\pi$
$787$	−12.9653	−	2.05351i	−0.462164	−	0.0731996i	−0.383175	+	0.923676i	$0.625169\pi$
$788$	11.0479	+	24.8400i	0.393566	+	0.884887i
$789$	−15.5216	+	21.3637i	−0.552584	+	0.760567i
$790$	37.5445	+	20.3220i	1.33577	+	0.723025i
$791$	2.60729	+	3.58862i	0.0927045	+	0.127597i
$792$	6.73913	+	11.0116i	0.239465	+	0.391281i
$793$	13.8626	+	13.8626i	0.492275	+	0.492275i
$794$	19.1601	+	20.1984i	0.679968	+	0.716815i
$795$	−3.52475	−	22.0417i	−0.125010	−	0.781739i
$796$	11.5201	+	9.33623i	0.408321	+	0.330914i
$797$	−30.9282	−	15.7587i	−1.09553	−	0.558202i	−0.189702	−	0.981842i	$-0.560752\pi$
$797$	−30.9282	−	15.7587i	−1.09553	−	0.558202i	−0.905831	+	0.423640i	$0.860752\pi$
$798$	0.216321	+	0.0766505i	0.00765768	+	0.00271340i
$799$	−14.4062			−0.509653
$800$	24.8295	−	13.5461i	0.877855	−	0.478926i
$801$	7.15142			0.252683
$802$	45.2531	+	16.0348i	1.59794	+	0.566209i
$803$	−20.0241	−	10.2028i	−0.706634	−	0.360048i
$804$	11.3281	+	9.18057i	0.399510	+	0.323774i
$805$	−1.98654	+	1.01592i	−0.0700162	+	0.0358066i
$806$	11.1747	+	11.7803i	0.393613	+	0.414942i
$807$	10.5735	+	10.5735i	0.372205	+	0.372205i
$808$	9.83252	+	16.0662i	0.345907	+	0.565207i
$809$	−11.2361	−	15.4652i	−0.395042	−	0.543728i	0.564449	−	0.825468i	$-0.309089\pi$
$809$	−11.2361	−	15.4652i	−0.395042	−	0.543728i	−0.959491	+	0.281739i	$0.909089\pi$
$810$	1.36510	+	2.85246i	0.0479646	+	0.100225i
$811$	8.18655	−	11.2678i	0.287469	−	0.395667i	−0.640721	−	0.767774i	$-0.721365\pi$
$811$	8.18655	−	11.2678i	0.287469	−	0.395667i	0.928190	+	0.372107i	$0.121365\pi$
$812$	0.722533	+	1.62453i	0.0253559	+	0.0570098i
$813$	8.70199	+	1.37826i	0.305192	+	0.0483377i
$814$	6.61713	+	13.8800i	0.231930	+	0.486495i
$815$	−13.6614	−	9.89453i	−0.478539	−	0.346590i
$816$	21.7444	−	4.60430i	0.761208	−	0.161183i
$817$	0.00380592	+	0.00746953i	0.000133152	+	0.000261326i
$818$	5.48151	+	18.5185i	0.191656	+	0.647482i
$819$	0.139964	−	0.430766i	0.00489075	−	0.0150522i
$820$	−25.6796	+	44.5918i	−0.896770	+	1.55721i
$821$	5.48325	+	16.8757i	0.191367	+	0.588967i	1.00000		0.000653180i	$0.000207914\pi$
$821$	5.48325	+	16.8757i	0.191367	+	0.588967i	−0.808633	+	0.588314i	$0.799792\pi$
$822$	4.47703	−	3.07570i	0.156154	−	0.107277i
$823$	−8.33927	+	1.32081i	−0.290689	+	0.0460405i	−0.300076	−	0.953915i	$-0.597012\pi$
$823$	−8.33927	+	1.32081i	−0.290689	+	0.0460405i	0.00938714	+	0.999956i	$0.497012\pi$
$824$	−3.30900	−	42.3599i	−0.115275	−	1.47568i
$825$	20.3655	+	10.3004i	0.709034	+	0.358613i
$826$	1.30204	+	0.707275i	0.0453036	+	0.0246092i
$827$	−8.69708	−	54.9112i	−0.302427	−	1.90945i	−0.404254	−	0.914647i	$-0.632469\pi$
$827$	−8.69708	−	54.9112i	−0.302427	−	1.90945i	0.101827	−	0.994802i	$-0.467531\pi$
$828$	−0.774143	−	7.39306i	−0.0269033	−	0.256927i
$829$	19.0441	−	6.18779i	0.661428	−	0.214911i	0.0409816	−	0.999160i	$-0.486952\pi$
$829$	19.0441	−	6.18779i	0.661428	−	0.214911i	0.620446	+	0.784249i	$0.286952\pi$
$830$	−22.5055	−	7.93678i	−0.781177	−	0.275490i
$831$	8.63659	+	2.80620i	0.299600	+	0.0973460i
$832$	7.94582	−	10.9098i	0.275472	−	0.378228i
$833$	34.3002	−	17.4768i	1.18843	−	0.605536i
$834$	−3.40963	−	25.9375i	−0.118066	−	0.898144i
$835$	0.0655432	+	43.9708i	0.00226822	+	1.52167i
$836$	−0.290928	+	5.51035i	−0.0100620	+	0.190580i
$837$	−1.06462	+	6.72175i	−0.0367987	+	0.232338i
$838$	−5.86708	+	7.64306i	−0.202675	+	0.264025i
$839$	15.9259	+	11.5708i	0.549822	+	0.399469i	0.827720	−	0.561142i	$-0.189638\pi$
$839$	15.9259	+	11.5708i	0.549822	+	0.399469i	−0.277898	+	0.960611i	$0.589638\pi$
$840$	−0.651209	−	1.56813i	−0.0224689	−	0.0541055i
$841$	−14.5911	+	10.6010i	−0.503140	+	0.365553i
$842$	−0.478902	+	18.1540i	−0.0165040	+	0.625628i
$843$	20.3508	−	20.3508i	0.700919	−	0.700919i
$844$	15.9623	−	4.27045i	0.549444	−	0.146995i
$845$	−16.0306	+	16.0784i	−0.551468	+	0.553115i
$846$	−3.60497	−	0.668864i	−0.123941	−	0.0229960i
$847$	1.19860	−	2.35239i	0.0411845	−	0.0808291i
$848$	−38.5618	−	10.3647i	−1.32422	−	0.355924i
$849$			17.9262i			0.615225i
$850$	28.4255	−	27.1258i	0.974986	−	0.930406i
$851$		−	8.85366i		−	0.303499i
$852$	−17.7329	−	19.7097i	−0.607519	−	0.675245i
$853$	−3.78263	+	7.42382i	−0.129515	+	0.254187i	−0.946653	−	0.322255i	$-0.895559\pi$
$853$	−3.78263	+	7.42382i	−0.129515	+	0.254187i	0.817138	+	0.576442i	$0.195559\pi$
$854$	0.804868	−	4.33799i	0.0275420	−	0.148443i
$855$	−0.209449	+	1.33529i	−0.00716300	+	0.0456659i
$856$	−10.6391	+	44.2017i	−0.363637	+	1.51078i
$857$	−20.2813	+	20.2813i	−0.692795	+	0.692795i	−0.962846	−	0.270051i	$-0.912959\pi$
$857$	−20.2813	+	20.2813i	−0.692795	+	0.692795i	0.270051	+	0.962846i	$0.412959\pi$
$858$	10.8864	+	0.287183i	0.371657	+	0.00980428i
$859$	−7.51815	+	5.46225i	−0.256516	+	0.186370i	−0.708610	−	0.705601i	$-0.750677\pi$
$859$	−7.51815	+	5.46225i	−0.256516	+	0.186370i	0.452094	+	0.891970i	$0.350677\pi$
$860$	0.0221635	−	0.0579289i	0.000755771	−	0.00197536i
$861$	2.49914	+	1.81573i	0.0851704	+	0.0618799i
$862$	3.81336	+	2.92727i	0.129883	+	0.0997030i
$863$	1.61317	−	10.1852i	0.0549130	−	0.346707i	−0.944900	−	0.327360i	$-0.893841\pi$
$863$	1.61317	−	10.1852i	0.0549130	−	0.346707i	0.999813	−	0.0193475i	$-0.00615887\pi$
$864$	5.65506	−	0.142597i	0.192389	−	0.00485126i
$865$	−35.8984	−	11.6050i	−1.22058	−	0.394581i
$866$	4.79682	−	0.630568i	0.163003	−	0.0214276i
$867$	12.3639	−	6.29970i	0.419899	−	0.213949i
$868$	0.761136	−	3.57405i	0.0258346	−	0.121311i
$869$	58.6051	+	19.0419i	1.98804	+	0.645954i
$870$	−8.62183	+	5.94210i	−0.292307	+	0.201456i
$871$	11.6977	−	3.80082i	0.396363	−	0.128786i
$872$	−7.18304	+	17.3129i	−0.243249	+	0.586289i
$873$	−0.161017	−	1.01662i	−0.00544959	−	0.0344074i
$874$	1.51657	−	2.79189i	0.0512988	−	0.0944369i
$875$	−2.43622	−	1.75343i	−0.0823592	−	0.0592766i
$876$	−8.26069	+	5.36000i	−0.279103	+	0.181098i
$877$	−13.9619	+	2.21134i	−0.471458	+	0.0746716i	−0.387643	−	0.921810i	$-0.626711\pi$
$877$	−13.9619	+	2.21134i	−0.471458	+	0.0746716i	−0.0838154	+	0.996481i	$0.526711\pi$
$878$	16.0474	+	23.3588i	0.541573	+	0.788322i
$879$	0.542062	+	1.66829i	0.0182833	+	0.0562702i
$880$	31.7090	−	25.7150i	1.06891	−	0.866852i
$881$	−7.58893	+	23.3563i	−0.255677	+	0.786894i	0.738018	+	0.674781i	$0.235762\pi$
$881$	−7.58893	+	23.3563i	−0.255677	+	0.786894i	−0.993695	+	0.112113i	$0.964238\pi$
$882$	9.39464	−	2.78084i	0.316334	−	0.0936356i
$883$	−10.6317	−	20.8659i	−0.357786	−	0.702195i	0.640023	−	0.768356i	$-0.278925\pi$
$883$	−10.6317	−	20.8659i	−0.357786	−	0.702195i	−0.997809	+	0.0661610i	$0.978925\pi$
$884$	6.72583	−	17.5011i	0.226214	−	0.588625i
$885$	−2.68427	+	8.30342i	−0.0902307	+	0.279116i
$886$	18.4627	−	8.80187i	0.620267	−	0.295705i
$887$	9.96921	+	1.57897i	0.334733	+	0.0530166i	0.321539	−	0.946896i	$-0.395800\pi$
$887$	9.96921	+	1.57897i	0.334733	+	0.0530166i	0.0131946	+	0.999913i	$0.495800\pi$
$888$	6.71653	+	0.532533i	0.225392	+	0.0178706i
$889$	−0.218671	+	0.300974i	−0.00733398	+	0.0100944i
$890$	−2.98089	−	22.4174i	−0.0999197	−	0.751434i
$891$	2.68290	+	3.69270i	0.0898806	+	0.123710i
$892$	−7.29634	−	4.21632i	−0.244299	−	0.141173i
$893$	−1.10812	−	1.10812i	−0.0370820	−	0.0370820i
$894$	−19.6261	+	18.6172i	−0.656394	+	0.622653i
$895$	−5.06558	−	0.794571i	−0.169324	−	0.0265596i
$896$	−3.03626	−	0.0836310i	−0.101434	−	0.00279392i
$897$	−5.58700	−	2.84672i	−0.186544	−	0.0950491i
$898$	−9.50440	+	26.8231i	−0.317166	+	0.895098i
$899$	−22.5349			−0.751582
$900$	8.37255	−	5.46812i	0.279085	−	0.182271i
$901$	−55.4697			−1.84797
$902$	−24.8066	+	70.0086i	−0.825970	+	2.33103i
$903$	−0.00331761	−	0.00169041i	−0.000110403	−	5.62532e-5i
$904$	17.8585	+	43.1853i	0.593965	+	1.43632i
$905$	−21.8213	−	21.7564i	−0.725365	−	0.723206i
$906$	0.810138	−	0.768493i	0.0269150	−	0.0255315i
$907$	2.65824	+	2.65824i	0.0882653	+	0.0882653i	0.749861	−	0.661596i	$-0.230120\pi$
$907$	2.65824	+	2.65824i	0.0882653	+	0.0882653i	−0.661596	+	0.749861i	$0.730120\pi$
$908$	10.3529	−	17.9157i	0.343574	−	0.594555i
$909$	3.91441	+	5.38772i	0.129833	+	0.178699i
$910$	−1.40866	−	0.259190i	−0.0466965	−	0.00859206i
$911$	5.17032	−	7.11634i	0.171300	−	0.235775i	−0.714732	−	0.699399i	$-0.753451\pi$
$911$	5.17032	−	7.11634i	0.171300	−	0.235775i	0.886032	+	0.463624i	$0.153451\pi$
$912$	2.02675	+	1.31842i	0.0671124	+	0.0436573i
$913$	−34.0211	−	5.38842i	−1.12594	−	0.178331i
$914$	9.93430	−	4.73606i	0.328598	−	0.156655i
$915$	25.9841	−	0.0387321i	0.859009	−	0.00128044i
$916$	−3.04300	−	1.16945i	−0.100544	−	0.0386398i
$917$	2.42300	+	4.75540i	0.0800145	+	0.157037i
$918$	7.53511	−	2.23041i	0.248696	−	0.0736145i
$919$	5.44982	−	16.7728i	0.179773	−	0.553284i	−0.820046	−	0.572297i	$-0.806052\pi$
$919$	5.44982	−	16.7728i	0.179773	−	0.553284i	0.999819	+	0.0190131i	$0.00605242\pi$
$920$	−22.8522	+	5.50831i	−0.753416	+	0.181604i
$921$	−5.10612	−	15.7150i	−0.168252	−	0.517827i
$922$	1.97184	+	2.87023i	0.0649390	+	0.0945261i
$923$	−22.0893	+	3.49860i	−0.727077	+	0.115158i
$924$	−1.33403	−	2.05597i	−0.0438863	−	0.0676363i
$925$	10.5962	−	5.43888i	0.348400	−	0.178829i
$926$	−22.6992	+	41.7874i	−0.745942	+	1.37322i
$927$	−2.34997	−	14.8372i	−0.0771833	−	0.487316i
$928$	3.39566	+	18.4210i	0.111468	+	0.604698i
$929$	−35.1070	+	11.4069i	−1.15182	+	0.374250i	−0.821829	−	0.569734i	$-0.807046\pi$
$929$	−35.1070	+	11.4069i	−1.15182	+	0.374250i	−0.329993	+	0.943983i	$0.607046\pi$
$930$	21.5144	+	0.535457i	0.705483	+	0.0175583i
$931$	3.98270	+	1.29406i	0.130528	+	0.0424110i
$932$	5.85741	+	1.24741i	0.191866	+	0.0408601i
$933$	−5.02185	+	2.55876i	−0.164408	+	0.0837700i
$934$	15.0819	−	1.98260i	0.493495	−	0.0648725i
$935$	33.2667	−	45.9315i	1.08794	−	1.50212i
$936$	2.49562	−	4.06716i	0.0815717	−	0.132939i
$937$	6.89911	−	43.5592i	0.225384	−	1.42302i	−0.572350	−	0.820009i	$-0.693968\pi$
$937$	6.89911	−	43.5592i	0.225384	−	1.42302i	0.797734	−	0.603009i	$-0.206032\pi$
$938$	−2.19572	−	1.68551i	−0.0716926	−	0.0550338i
$939$	14.5118	+	10.5434i	0.473573	+	0.344071i
$940$	−0.594038	+	11.5792i	−0.0193754	+	0.377673i
$941$	8.90352	−	6.46878i	0.290246	−	0.210876i	−0.433128	−	0.901332i	$-0.642590\pi$
$941$	8.90352	−	6.46878i	0.290246	−	0.210876i	0.723374	+	0.690456i	$0.242590\pi$
$942$	−1.97273	−	0.0520404i	−0.0642749	−	0.00169557i
$943$	30.2399	−	30.2399i	0.984747	−	0.984747i
$944$	11.5927	+	10.4544i	0.377311	+	0.340263i
$945$	−0.273337	−	0.534484i	−0.00889167	−	0.0173868i
$946$	0.0163318	−	0.0880231i	0.000530991	−	0.00286188i
$947$	−23.8973	+	46.9012i	−0.776559	+	1.52408i	0.0734408	+	0.997300i	$0.476602\pi$
$947$	−23.8973	+	46.9012i	−0.776559	+	1.52408i	−0.850000	+	0.526783i	$0.823398\pi$
$948$	20.0723	−	18.0591i	0.651919	−	0.586533i
$949$			8.30656i			0.269642i
$950$	4.27301	+	0.0999751i	0.138635	+	0.00324362i
$951$		−	9.14690i		−	0.296608i
$952$	−4.10345	+	0.982627i	−0.132993	+	0.0318471i
$953$	−7.88451	+	15.4742i	−0.255404	+	0.501259i	−0.982733	−	0.185030i	$-0.940762\pi$
$953$	−7.88451	+	15.4742i	−0.255404	+	0.501259i	0.727329	+	0.686289i	$0.240762\pi$
$954$	−13.8806	−	2.57541i	−0.449402	−	0.0833819i
$955$	−58.8217	+	9.40635i	−1.90343	+	0.304382i
$956$	−11.4467	−	42.7859i	−0.370211	−	1.38379i
$957$	−10.6872	+	10.6872i	−0.345469	+	0.345469i
$958$	−0.855186	+	32.4181i	−0.0276298	+	1.04738i
$959$	−0.834219	+	0.606095i	−0.0269383	+	0.0195718i
$960$	−2.80417	−	17.6674i	−0.0905041	−	0.570213i
$961$	12.3904	+	9.00217i	0.399691	+	0.290392i
$962$	3.46073	−	4.50830i	0.111578	−	0.145354i
$963$	−2.51453	+	15.8761i	−0.0810294	+	0.511600i
$964$	−0.151614	−	0.00800471i	−0.00488316	−	0.000257814i
$965$	19.6531	−	6.41808i	0.632655	−	0.206605i
$966$	0.183922	+	1.39912i	0.00591760	+	0.0450161i
$967$	−53.2482	+	27.1313i	−1.71235	+	0.872485i	−0.730476	+	0.682939i	$0.760702\pi$
$967$	−53.2482	+	27.1313i	−1.71235	+	0.872485i	−0.981872	+	0.189546i	$0.939298\pi$
$968$	18.0765	−	21.1400i	0.581001	−	0.679464i
$969$	3.19438	+	1.03792i	0.102618	+	0.0333427i
$970$	−3.11967	+	0.928490i	−0.100166	+	0.0298120i
$971$	−39.7349	+	12.9106i	−1.27515	+	0.414322i	−0.866871	−	0.498533i	$-0.833872\pi$
$971$	−39.7349	+	12.9106i	−1.27515	+	0.414322i	−0.408283	+	0.912856i	$0.633872\pi$
$972$	1.98912	−	0.208286i	0.0638012	−	0.00668077i
$973$	0.776901	+	4.90516i	0.0249063	+	0.157252i
$974$	20.9307	+	11.3697i	0.670662	+	0.364308i
$975$	−0.0251477	−	8.43536i	−0.000805370	−	0.270148i
$976$	18.9388	−	42.4486i	0.606216	−	1.35875i
$977$	26.2795	−	4.16226i	0.840754	−	0.133162i	0.278819	−	0.960344i	$-0.410057\pi$
$977$	26.2795	−	4.16226i	0.840754	−	0.133162i	0.561935	+	0.827181i	$0.310057\pi$
$978$	−8.79327	+	6.04094i	−0.281178	+	0.193168i
$979$	−10.0870	−	31.0445i	−0.322381	−	0.992186i
$980$	−12.6330	−	28.2901i	−0.403545	−	0.903694i
$981$	−2.04784	+	6.30262i	−0.0653826	+	0.201227i
$982$	4.58530	+	15.4907i	0.146323	+	0.494329i
$983$	1.53672	+	3.01599i	0.0490138	+	0.0961950i	0.914214	−	0.405231i	$-0.132809\pi$
$983$	1.53672	+	3.01599i	0.0490138	+	0.0961950i	−0.865200	+	0.501426i	$0.832809\pi$
$984$	21.1216	+	24.7594i	0.673332	+	0.789300i
$985$	24.5633	−	17.9023i	0.782653	−	0.570415i
$986$	11.1977	+	23.4882i	0.356607	+	0.748016i
$987$	0.687472	+	0.108885i	0.0218825	+	0.00346584i
$988$	1.86354	−	0.828835i	0.0592871	−	0.0263688i
$989$	−0.0302988	+	0.0417027i	−0.000963446	+	0.00132607i
$990$	10.4571	−	9.94927i	0.332350	−	0.316208i
$991$	−29.2963	−	40.3229i	−0.930627	−	1.28090i	−0.959614	−	0.281319i	$-0.909228\pi$
$991$	−29.2963	−	40.3229i	−0.930627	−	1.28090i	0.0289870	−	0.999580i	$-0.490772\pi$
$992$	16.6075	−	34.7316i	0.527288	−	1.10273i
$993$	5.25958	+	5.25958i	0.166908	+	0.166908i
$994$	3.46389	+	3.65159i	0.109868	+	0.115821i
$995$	7.50448	−	14.7828i	0.237908	−	0.468647i
$996$	−9.50282	+	11.7257i	−0.301108	+	0.371543i
$997$	18.8621	+	9.61073i	0.597369	+	0.304375i	0.726407	−	0.687265i	$-0.241189\pi$
$997$	18.8621	+	9.61073i	0.597369	+	0.304375i	−0.129038	+	0.991640i	$0.541189\pi$
$998$	−55.8167	−	19.7779i	−1.76685	−	0.626058i
$999$	2.38210			0.0753664

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.163.27	yes	240
3.2	odd	2		900.2.bj.f.163.4		240
4.3	odd	2	inner	300.2.w.a.163.23	yes	240
12.11	even	2		900.2.bj.f.163.8		240
25.2	odd	20	inner	300.2.w.a.127.23	✓	240
75.2	even	20		900.2.bj.f.127.8		240
100.27	even	20	inner	300.2.w.a.127.27	yes	240
300.227	odd	20		900.2.bj.f.127.4		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.23	✓	240	25.2	odd	20	inner
300.2.w.a.127.27	yes	240	100.27	even	20	inner
300.2.w.a.163.23	yes	240	4.3	odd	2	inner
300.2.w.a.163.27	yes	240	1.1	even	1	trivial
900.2.bj.f.127.4		240	300.227	odd	20
900.2.bj.f.127.8		240	75.2	even	20
900.2.bj.f.163.4		240	3.2	odd	2
900.2.bj.f.163.8		240	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33300 + 0.472333i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(1.55380 + 1.25924i) q^{4} +(1.01218 - 1.99386i) q^{5} +(-0.973281 - 1.02602i) q^{6} +(0.189838 + 0.189838i) q^{7} +(1.47645 + 2.41249i) q^{8} +(0.587785 + 0.809017i) q^{9} +(2.29101 - 2.17974i) q^{10} +(2.68290 - 3.69270i) q^{11} +(-0.812765 - 1.82741i) q^{12} +(-1.66631 - 0.263917i) q^{13} +(0.163389 + 0.342722i) q^{14} +(-1.80706 + 1.31702i) q^{15} +(0.828612 + 3.91323i) q^{16} +(2.52266 + 4.95101i) q^{17} +(0.401395 + 1.35605i) q^{18} +(-0.186788 + 0.574876i) q^{19} +(4.08349 - 1.82349i) q^{20} +(-0.0829624 - 0.255332i) q^{21} +(5.32050 - 3.65516i) q^{22} +(-3.67098 + 0.581426i) q^{23} +(-0.220276 - 2.81984i) q^{24} +(-2.95097 - 4.03631i) q^{25} +(-2.09654 - 1.13886i) q^{26} +(-0.156434 - 0.987688i) q^{27} +(0.0559189 + 0.534025i) q^{28} +(3.14920 - 1.02324i) q^{29} +(-3.03089 + 0.902066i) q^{30} +(-6.47245 - 2.10303i) q^{31} +(-0.743804 + 5.60774i) q^{32} +(-4.06693 + 2.07221i) q^{33} +(1.02420 + 7.79125i) q^{34} +(0.570663 - 0.186361i) q^{35} +(-0.105446 + 1.99722i) q^{36} +(-0.372643 + 2.35278i) q^{37} +(-0.520523 + 0.678086i) q^{38} +(1.36488 + 0.991640i) q^{39} +(6.30461 - 0.501950i) q^{40} +(-9.30874 + 6.76320i) q^{41} +(0.0100124 - 0.379545i) q^{42} +(0.00980686 - 0.00980686i) q^{43} +(8.81871 - 2.35930i) q^{44} +(2.20801 - 0.353090i) q^{45} +(-5.16806 - 0.958880i) q^{46} +(-1.17702 + 2.31002i) q^{47} +(1.03827 - 3.86290i) q^{48} -6.92792i q^{49} +(-2.02718 - 6.77426i) q^{50} -5.55664i q^{51} +(-2.25678 - 2.50836i) q^{52} +(-4.53201 + 8.89456i) q^{53} +(0.257990 - 1.39048i) q^{54} +(-4.64714 - 9.08702i) q^{55} +(-0.177697 + 0.738270i) q^{56} +(0.427418 - 0.427418i) q^{57} +(4.68120 + 0.123490i) q^{58} +(3.15728 - 2.29390i) q^{59} +(-4.46626 - 0.229128i) q^{60} +(-9.40115 - 6.83034i) q^{61} +(-7.63448 - 5.86050i) q^{62} +(-0.0419983 + 0.265167i) q^{63} +(-3.64021 + 7.12382i) q^{64} +(-2.21282 + 3.05526i) q^{65} +(-6.40001 + 0.841315i) q^{66} +(-6.49592 + 3.30984i) q^{67} +(-2.31480 + 10.8695i) q^{68} +(3.53483 + 1.14854i) q^{69} +(0.848721 + 0.0211233i) q^{70} +(12.6076 - 4.09646i) q^{71} +(-1.08391 + 2.61250i) q^{72} +(-0.770226 - 4.86301i) q^{73} +(-1.60803 + 2.96025i) q^{74} +(0.796891 + 4.93609i) q^{75} +(-1.01414 + 0.658032i) q^{76} +(1.21033 - 0.191698i) q^{77} +(1.35100 + 1.96654i) q^{78} +(4.17182 + 12.8395i) q^{79} +(8.64116 + 2.30877i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-15.6031 + 4.61855i) q^{82} +(-3.42602 - 6.72394i) q^{83} +(0.192618 - 0.501206i) q^{84} +(12.4250 - 0.0185208i) q^{85} +(0.0177047 - 0.00844049i) q^{86} +(-3.27049 - 0.517995i) q^{87} +(12.8698 + 1.02040i) q^{88} +(4.20350 - 5.78562i) q^{89} +(3.11007 + 0.572247i) q^{90} +(-0.266228 - 0.366431i) q^{91} +(-6.43614 - 3.71924i) q^{92} +(4.81224 + 4.81224i) q^{93} +(-2.66007 + 2.52333i) q^{94} +(0.957159 + 0.954310i) q^{95} +(3.20860 - 4.65885i) q^{96} +(-0.917106 - 0.467289i) q^{97} +(3.27228 - 9.23495i) q^{98} +4.56443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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