LMFDB - Embedded newform 273.2.j.b.100.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (of order $3$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.7
Root			$0.857510 + 1.48525i$ of defining polynomial
Character	$\chi$	$=$	273.100
Dual form			273.2.j.b.172.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.857510 + 1.48525i) q^{2} -1.00000 q^{3} +(-0.470647 + 0.815185i) q^{4} +(1.22863 - 2.12806i) q^{5} +(-0.857510 - 1.48525i) q^{6} +(2.18175 - 1.49666i) q^{7} +1.81570 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.857510 + 1.48525i) q^{2} -1.00000 q^{3} +(-0.470647 + 0.815185i) q^{4} +(1.22863 - 2.12806i) q^{5} +(-0.857510 - 1.48525i) q^{6} +(2.18175 - 1.49666i) q^{7} +1.81570 q^{8} +1.00000 q^{9} +4.21426 q^{10} -1.03816 q^{11} +(0.470647 - 0.815185i) q^{12} +(-3.36305 - 1.29996i) q^{13} +(4.09378 + 1.95704i) q^{14} +(-1.22863 + 2.12806i) q^{15} +(2.49828 + 4.32714i) q^{16} +(-1.50975 + 2.61496i) q^{17} +(0.857510 + 1.48525i) q^{18} +3.19341 q^{19} +(1.15651 + 2.00313i) q^{20} +(-2.18175 + 1.49666i) q^{21} +(-0.890235 - 1.54193i) q^{22} +(1.73601 + 3.00685i) q^{23} -1.81570 q^{24} +(-0.519081 - 0.899075i) q^{25} +(-0.953083 - 6.10970i) q^{26} -1.00000 q^{27} +(0.193220 + 2.48292i) q^{28} +(-4.01417 + 6.95275i) q^{29} -4.21426 q^{30} +(-3.48074 - 6.02882i) q^{31} +(-2.46889 + 4.27625i) q^{32} +1.03816 q^{33} -5.17850 q^{34} +(-0.504403 - 6.48172i) q^{35} +(-0.470647 + 0.815185i) q^{36} +(-1.41332 - 2.44794i) q^{37} +(2.73838 + 4.74302i) q^{38} +(3.36305 + 1.29996i) q^{39} +(2.23083 - 3.86391i) q^{40} +(-2.54107 + 4.40125i) q^{41} +(-4.09378 - 1.95704i) q^{42} +(-3.21838 - 5.57439i) q^{43} +(0.488608 - 0.846294i) q^{44} +(1.22863 - 2.12806i) q^{45} +(-2.97729 + 5.15682i) q^{46} +(4.88951 - 8.46887i) q^{47} +(-2.49828 - 4.32714i) q^{48} +(2.52003 - 6.53065i) q^{49} +(0.890235 - 1.54193i) q^{50} +(1.50975 - 2.61496i) q^{51} +(2.64252 - 2.12969i) q^{52} +(5.90947 + 10.2355i) q^{53} +(-0.857510 - 1.48525i) q^{54} +(-1.27552 + 2.20927i) q^{55} +(3.96140 - 2.71748i) q^{56} -3.19341 q^{57} -13.7688 q^{58} +(-4.47070 + 7.74348i) q^{59} +(-1.15651 - 2.00313i) q^{60} -2.60893 q^{61} +(5.96954 - 10.3396i) q^{62} +(2.18175 - 1.49666i) q^{63} +1.52470 q^{64} +(-6.89834 + 5.55958i) q^{65} +(0.890235 + 1.54193i) q^{66} -11.2200 q^{67} +(-1.42112 - 2.46145i) q^{68} +(-1.73601 - 3.00685i) q^{69} +(9.19445 - 6.30731i) q^{70} +(-1.63013 - 2.82347i) q^{71} +1.81570 q^{72} +(7.50717 + 13.0028i) q^{73} +(2.42387 - 4.19827i) q^{74} +(0.519081 + 0.899075i) q^{75} +(-1.50297 + 2.60322i) q^{76} +(-2.26501 + 1.55377i) q^{77} +(0.953083 + 6.10970i) q^{78} +(-0.211818 + 0.366880i) q^{79} +12.2779 q^{80} +1.00000 q^{81} -8.71596 q^{82} -1.34088 q^{83} +(-0.193220 - 2.48292i) q^{84} +(3.70986 + 6.42567i) q^{85} +(5.51958 - 9.56019i) q^{86} +(4.01417 - 6.95275i) q^{87} -1.88499 q^{88} +(-2.65247 - 4.59421i) q^{89} +4.21426 q^{90} +(-9.28292 + 2.19715i) q^{91} -3.26819 q^{92} +(3.48074 + 6.02882i) q^{93} +16.7712 q^{94} +(3.92353 - 6.79576i) q^{95} +(2.46889 - 4.27625i) q^{96} +(2.92406 + 5.06463i) q^{97} +(11.8606 - 1.85722i) q^{98} -1.03816 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.857510	+	1.48525i	0.606351	+	1.05023i	0.991836	+	0.127517i	$0.0407008\pi$
$2$	0.857510	+	1.48525i	0.606351	+	1.05023i	−0.385485	+	0.922714i	$0.625966\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.470647	+	0.815185i	−0.235324	+	0.407592i
$5$	1.22863	−	2.12806i	0.549462	−	0.951695i	−0.448850	−	0.893607i	$-0.648166\pi$
$5$	1.22863	−	2.12806i	0.549462	−	0.951695i	0.998311	−	0.0580883i	$-0.0185005\pi$
$6$	−0.857510	−	1.48525i	−0.350077	−	0.606351i
$7$	2.18175	−	1.49666i	0.824623	−	0.565683i
$7$	2.18175	−	1.49666i	0.824623	−	0.565683i
$8$	1.81570			0.641947
$9$	1.00000			0.333333
$10$	4.21426			1.33267
$11$	−1.03816			−0.313018			−0.156509	−	0.987677i	$-0.550024\pi$
$11$	−1.03816			−0.313018			−0.156509	+	0.987677i	$0.550024\pi$
$12$	0.470647	−	0.815185i	0.135864	−	0.235324i
$13$	−3.36305	−	1.29996i	−0.932742	−	0.360544i
$13$	−3.36305	−	1.29996i	−0.932742	−	0.360544i
$14$	4.09378	+	1.95704i	1.09411	+	0.523042i
$15$	−1.22863	+	2.12806i	−0.317232	+	0.549462i
$16$	2.49828	+	4.32714i	0.624569	+	1.08179i
$17$	−1.50975	+	2.61496i	−0.366168	+	0.634222i	−0.988963	−	0.148163i	$-0.952664\pi$
$17$	−1.50975	+	2.61496i	−0.366168	+	0.634222i	0.622795	+	0.782385i	$0.285997\pi$
$18$	0.857510	+	1.48525i	0.202117	+	0.350077i
$19$	3.19341			0.732619			0.366310	−	0.930493i	$-0.380621\pi$
$19$	3.19341			0.732619			0.366310	+	0.930493i	$0.380621\pi$
$20$	1.15651	+	2.00313i	0.258603	+	0.447913i
$21$	−2.18175	+	1.49666i	−0.476096	+	0.326597i
$22$	−0.890235	−	1.54193i	−0.189799	−	0.328741i
$23$	1.73601	+	3.00685i	0.361983	+	0.626972i	0.988287	−	0.152606i	$-0.0487666\pi$
$23$	1.73601	+	3.00685i	0.361983	+	0.626972i	−0.626304	+	0.779579i	$0.715433\pi$
$24$	−1.81570			−0.370628
$25$	−0.519081	−	0.899075i	−0.103816	−	0.179815i
$26$	−0.953083	−	6.10970i	−0.186915	−	1.19821i
$27$	−1.00000			−0.192450
$28$	0.193220	+	2.48292i	0.0365151	+	0.469229i
$29$	−4.01417	+	6.95275i	−0.745413	+	1.29109i	0.204589	+	0.978848i	$0.434414\pi$
$29$	−4.01417	+	6.95275i	−0.745413	+	1.29109i	−0.950002	+	0.312245i	$0.898919\pi$
$30$	−4.21426			−0.769416
$31$	−3.48074	−	6.02882i	−0.625160	−	1.08281i	−0.988510	−	0.151156i	$-0.951700\pi$
$31$	−3.48074	−	6.02882i	−0.625160	−	1.08281i	0.363350	−	0.931653i	$-0.381633\pi$
$32$	−2.46889	+	4.27625i	−0.436443	+	0.755941i
$33$	1.03816			0.180721
$34$	−5.17850			−0.888106
$35$	−0.504403	−	6.48172i	−0.0852598	−	1.09561i
$36$	−0.470647	+	0.815185i	−0.0784412	+	0.135864i
$37$	−1.41332	−	2.44794i	−0.232348	−	0.402439i	0.726151	−	0.687536i	$-0.241308\pi$
$37$	−1.41332	−	2.44794i	−0.232348	−	0.402439i	−0.958499	+	0.285097i	$0.907974\pi$
$38$	2.73838	+	4.74302i	0.444225	+	0.769419i
$39$	3.36305	+	1.29996i	0.538519	+	0.208160i
$40$	2.23083	−	3.86391i	0.352725	−	0.610938i
$41$	−2.54107	+	4.40125i	−0.396848	+	0.687360i	−0.993335	−	0.115262i	$-0.963229\pi$
$41$	−2.54107	+	4.40125i	−0.396848	+	0.687360i	0.596487	+	0.802622i	$0.296563\pi$
$42$	−4.09378	−	1.95704i	−0.631684	−	0.301978i
$43$	−3.21838	−	5.57439i	−0.490798	−	0.850087i	0.509146	−	0.860680i	$-0.329961\pi$
$43$	−3.21838	−	5.57439i	−0.490798	−	0.850087i	−0.999944	+	0.0105935i	$0.996628\pi$
$44$	0.488608	−	0.846294i	0.0736605	−	0.127584i
$45$	1.22863	−	2.12806i	0.183154	−	0.317232i
$46$	−2.97729	+	5.15682i	−0.438977	+	0.760331i
$47$	4.88951	−	8.46887i	0.713208	−	1.23531i	−0.250439	−	0.968132i	$-0.580575\pi$
$47$	4.88951	−	8.46887i	0.713208	−	1.23531i	0.963647	−	0.267180i	$-0.0860917\pi$
$48$	−2.49828	−	4.32714i	−0.360595	−	0.624569i
$49$	2.52003	−	6.53065i	0.360005	−	0.932950i
$50$	0.890235	−	1.54193i	0.125898	−	0.218062i
$51$	1.50975	−	2.61496i	0.211407	−	0.366168i
$52$	2.64252	−	2.12969i	0.366451	−	0.295334i
$53$	5.90947	+	10.2355i	0.811728	+	1.40595i	0.911654	+	0.410959i	$0.134806\pi$
$53$	5.90947	+	10.2355i	0.811728	+	1.40595i	−0.0999257	+	0.994995i	$0.531861\pi$
$54$	−0.857510	−	1.48525i	−0.116692	−	0.202117i
$55$	−1.27552	+	2.20927i	−0.171991	+	0.297898i
$56$	3.96140	−	2.71748i	0.529364	−	0.363139i
$57$	−3.19341			−0.422978
$58$	−13.7688			−1.80793
$59$	−4.47070	+	7.74348i	−0.582036	+	1.00812i	0.413202	+	0.910639i	$0.364410\pi$
$59$	−4.47070	+	7.74348i	−0.582036	+	1.00812i	−0.995238	+	0.0974764i	$0.968923\pi$
$60$	−1.15651	−	2.00313i	−0.149304	−	0.258603i
$61$	−2.60893			−0.334039			−0.167019	−	0.985954i	$-0.553414\pi$
$61$	−2.60893			−0.334039			−0.167019	+	0.985954i	$0.553414\pi$
$62$	5.96954	−	10.3396i	0.758133	−	1.31312i
$63$	2.18175	−	1.49666i	0.274874	−	0.188561i
$64$	1.52470			0.190588
$65$	−6.89834	+	5.55958i	−0.855634	+	0.689581i
$66$	0.890235	+	1.54193i	0.109580	+	0.189799i
$67$	−11.2200			−1.37074			−0.685371	−	0.728194i	$-0.740360\pi$
$67$	−11.2200			−1.37074			−0.685371	+	0.728194i	$0.740360\pi$
$68$	−1.42112	−	2.46145i	−0.172336	−	0.298495i
$69$	−1.73601	−	3.00685i	−0.208991	−	0.361983i
$70$	9.19445	−	6.30731i	1.09895	−	0.753867i
$71$	−1.63013	−	2.82347i	−0.193461	−	0.335085i	0.752934	−	0.658096i	$-0.228638\pi$
$71$	−1.63013	−	2.82347i	−0.193461	−	0.335085i	−0.946395	+	0.323012i	$0.895305\pi$
$72$	1.81570			0.213982
$73$	7.50717	+	13.0028i	0.878648	+	1.52186i	0.852825	+	0.522196i	$0.174887\pi$
$73$	7.50717	+	13.0028i	0.878648	+	1.52186i	0.0258228	+	0.999667i	$0.491779\pi$
$74$	2.42387	−	4.19827i	0.281769	−	0.488038i
$75$	0.519081	+	0.899075i	0.0599383	+	0.103816i
$76$	−1.50297	+	2.60322i	−0.172403	+	0.298610i
$77$	−2.26501	+	1.55377i	−0.258121	+	0.177069i
$78$	0.953083	+	6.10970i	0.107915	+	0.691788i
$79$	−0.211818	+	0.366880i	−0.0238314	+	0.0412773i	−0.877695	−	0.479219i	$-0.840920\pi$
$79$	−0.211818	+	0.366880i	−0.0238314	+	0.0412773i	0.853864	+	0.520497i	$0.174253\pi$
$80$	12.2779			1.37271
$81$	1.00000			0.111111
$82$	−8.71596			−0.962516
$83$	−1.34088			−0.147181			−0.0735904	−	0.997289i	$-0.523446\pi$
$83$	−1.34088			−0.147181			−0.0735904	+	0.997289i	$0.523446\pi$
$84$	−0.193220	−	2.48292i	−0.0210820	−	0.270909i
$85$	3.70986	+	6.42567i	0.402391	+	0.696961i
$86$	5.51958	−	9.56019i	0.595192	−	1.03090i
$87$	4.01417	−	6.95275i	0.430364	−	0.745413i
$88$	−1.88499			−0.200941
$89$	−2.65247	−	4.59421i	−0.281161	−	0.486985i	0.690510	−	0.723323i	$-0.257386\pi$
$89$	−2.65247	−	4.59421i	−0.281161	−	0.486985i	−0.971671	+	0.236338i	$0.924053\pi$
$90$	4.21426			0.444222
$91$	−9.28292	+	2.19715i	−0.973114	+	0.230324i
$92$	−3.26819			−0.340732
$93$	3.48074	+	6.02882i	0.360936	+	0.625160i
$94$	16.7712			1.72982
$95$	3.92353	−	6.79576i	0.402546	−	0.697230i
$96$	2.46889	−	4.27625i	0.251980	−	0.436443i
$97$	2.92406	+	5.06463i	0.296894	+	0.514235i	0.975424	−	0.220338i	$-0.0707159\pi$
$97$	2.92406	+	5.06463i	0.296894	+	0.514235i	−0.678530	+	0.734573i	$0.737383\pi$
$98$	11.8606	−	1.85722i	1.19810	−	0.187607i
$99$	−1.03816			−0.104339
$100$	0.977216			0.0977216
$101$	−18.5287			−1.84368			−0.921840	−	0.387572i	$-0.873314\pi$
$101$	−18.5287			−1.84368			−0.921840	+	0.387572i	$0.873314\pi$
$102$	5.17850			0.512748
$103$	−1.01571	+	1.75926i	−0.100081	+	0.173345i	−0.911718	−	0.410817i	$-0.865243\pi$
$103$	−1.01571	+	1.75926i	−0.100081	+	0.173345i	0.811637	+	0.584162i	$0.198577\pi$
$104$	−6.10629	−	2.36034i	−0.598771	−	0.231450i
$105$	0.504403	+	6.48172i	0.0492247	+	0.632551i
$106$	−10.1349	+	17.5541i	−0.984385	+	1.70500i
$107$	1.21833	+	2.11021i	0.117781	+	0.204002i	0.918888	−	0.394519i	$-0.129089\pi$
$107$	1.21833	+	2.11021i	0.117781	+	0.204002i	−0.801107	+	0.598521i	$0.795755\pi$
$108$	0.470647	−	0.815185i	0.0452881	−	0.0784412i
$109$	−7.85642	−	13.6077i	−0.752508	−	1.30338i	−0.946604	−	0.322400i	$-0.895510\pi$
$109$	−7.85642	−	13.6077i	−0.752508	−	1.30338i	0.194095	−	0.980983i	$-0.437823\pi$
$110$	−4.37509			−0.417148
$111$	1.41332	+	2.44794i	0.134146	+	0.232348i
$112$	11.9269	+	5.70166i	1.12698	+	0.538756i
$113$	2.52708	+	4.37702i	0.237727	+	0.411756i	0.960062	−	0.279788i	$-0.0902642\pi$
$113$	2.52708	+	4.37702i	0.237727	+	0.411756i	−0.722335	+	0.691544i	$0.756931\pi$
$114$	−2.73838	−	4.74302i	−0.256473	−	0.444225i
$115$	8.53167			0.795582
$116$	−3.77852	−	6.54458i	−0.350826	−	0.607649i
$117$	−3.36305	−	1.29996i	−0.310914	−	0.120181i
$118$	−15.3347			−1.41167
$119$	0.619813	+	7.96477i	0.0568182	+	0.730129i
$120$	−2.23083	+	3.86391i	−0.203646	+	0.352725i
$121$	−9.92222			−0.902020
$122$	−2.23718	−	3.87491i	−0.202545	−	0.350818i
$123$	2.54107	−	4.40125i	0.229120	−	0.396848i
$124$	6.55281			0.588459
$125$	9.73529			0.870751
$126$	4.09378	+	1.95704i	0.364703	+	0.174347i
$127$	1.84246	−	3.19124i	0.163492	−	0.283177i	−0.772627	−	0.634861i	$-0.781058\pi$
$127$	1.84246	−	3.19124i	0.163492	−	0.283177i	0.936119	+	0.351684i	$0.114391\pi$
$128$	6.24523	+	10.8171i	0.552006	+	0.956102i
$129$	3.21838	+	5.57439i	0.283362	+	0.490798i
$130$	−14.1728	−	5.47837i	−1.24303	−	0.480485i
$131$	−0.924144	+	1.60066i	−0.0807428	+	0.139851i	−0.903569	−	0.428442i	$-0.859063\pi$
$131$	−0.924144	+	1.60066i	−0.0807428	+	0.139851i	0.822826	+	0.568293i	$0.192396\pi$
$132$	−0.488608	+	0.846294i	−0.0425279	+	0.0736605i
$133$	6.96722	−	4.77944i	0.604134	−	0.414430i
$134$	−9.62127	−	16.6645i	−0.831151	−	1.43960i
$135$	−1.22863	+	2.12806i	−0.105744	+	0.183154i
$136$	−2.74126	+	4.74799i	−0.235061	+	0.407137i
$137$	−1.40759	+	2.43802i	−0.120259	+	0.208294i	−0.919870	−	0.392224i	$-0.871706\pi$
$137$	−1.40759	+	2.43802i	−0.120259	+	0.208294i	0.799611	+	0.600518i	$0.205039\pi$
$138$	2.97729	−	5.15682i	0.253444	−	0.438977i
$139$	1.87848	+	3.25363i	0.159331	+	0.275969i	0.934628	−	0.355628i	$-0.115733\pi$
$139$	1.87848	+	3.25363i	0.159331	+	0.275969i	−0.775297	+	0.631597i	$0.782400\pi$
$140$	5.52120	+	2.63942i	0.466626	+	0.223072i
$141$	−4.88951	+	8.46887i	−0.411771	+	0.713208i
$142$	2.79571	−	4.84232i	0.234611	−	0.406358i
$143$	3.49139	+	1.34957i	0.291965	+	0.112857i
$144$	2.49828	+	4.32714i	0.208190	+	0.360595i
$145$	9.86389	+	17.0848i	0.819151	+	1.41881i
$146$	−12.8750	+	22.3001i	−1.06554	+	1.84557i
$147$	−2.52003	+	6.53065i	−0.207849	+	0.538639i
$148$	2.66070			0.218708
$149$	6.73683			0.551902			0.275951	−	0.961172i	$-0.411007\pi$
$149$	6.73683			0.551902			0.275951	+	0.961172i	$0.411007\pi$
$150$	−0.890235	+	1.54193i	−0.0726873	+	0.125898i
$151$	−2.70020	−	4.67689i	−0.219739	−	0.380600i	0.734989	−	0.678079i	$-0.237187\pi$
$151$	−2.70020	−	4.67689i	−0.219739	−	0.380600i	−0.954728	+	0.297479i	$0.903854\pi$
$152$	5.79828			0.470303
$153$	−1.50975	+	2.61496i	−0.122056	+	0.211407i
$154$	−4.25001	−	2.03173i	−0.342475	−	0.163721i
$155$	−17.1062			−1.37401
$156$	−2.64252	+	2.12969i	−0.211571	+	0.170511i
$157$	−5.82721	−	10.0930i	−0.465062	−	0.805512i	0.534142	−	0.845395i	$-0.320635\pi$
$157$	−5.82721	−	10.0930i	−0.465062	−	0.805512i	−0.999204	+	0.0398832i	$0.987301\pi$
$158$	−0.726546			−0.0578009
$159$	−5.90947	−	10.2355i	−0.468651	−	0.811728i
$160$	6.06673	+	10.5079i	0.479617	+	0.830722i
$161$	8.28776	+	3.96198i	0.653167	+	0.312248i
$162$	0.857510	+	1.48525i	0.0673724	+	0.116692i
$163$	24.2516			1.89953			0.949766	−	0.312960i	$-0.101321\pi$
$163$	24.2516			1.89953			0.949766	+	0.312960i	$0.101321\pi$
$164$	−2.39189	−	4.14288i	−0.186775	−	0.323504i
$165$	1.27552	−	2.20927i	0.0992992	−	0.171991i
$166$	−1.14982	−	1.99154i	−0.0892433	−	0.154574i
$167$	8.23216	−	14.2585i	0.637024	−	1.10336i	−0.349059	−	0.937101i	$-0.613499\pi$
$167$	8.23216	−	14.2585i	0.637024	−	1.10336i	0.986083	−	0.166257i	$-0.0531680\pi$
$168$	−3.96140	+	2.71748i	−0.305629	+	0.209658i
$169$	9.62021	+	8.74366i	0.740016	+	0.672589i
$170$	−6.36248	+	11.0201i	−0.487980	+	0.845207i
$171$	3.19341			0.244206
$172$	6.05888			0.461985
$173$	−20.0405			−1.52365			−0.761827	−	0.647781i	$-0.775697\pi$
$173$	−20.0405			−1.52365			−0.761827	+	0.647781i	$0.775697\pi$
$174$	13.7688			1.04381
$175$	−2.47811	−	1.18467i	−0.187328	−	0.0895524i
$176$	−2.59362	−	4.49228i	−0.195501	−	0.338618i
$177$	4.47070	−	7.74348i	0.336039	−	0.582036i
$178$	4.54903	−	7.87915i	0.340964	−	0.590568i
$179$	−10.0951			−0.754546			−0.377273	−	0.926102i	$-0.623138\pi$
$179$	−10.0951			−0.754546			−0.377273	+	0.926102i	$0.623138\pi$
$180$	1.15651	+	2.00313i	0.0862009	+	0.149304i
$181$	19.8959			1.47885			0.739426	−	0.673238i	$-0.235097\pi$
$181$	19.8959			1.47885			0.739426	+	0.673238i	$0.235097\pi$
$182$	−11.2235	−	11.9034i	−0.831942	−	0.882337i
$183$	2.60893			0.192857
$184$	3.15207	+	5.45955i	0.232374	+	0.402483i
$185$	−6.94580			−0.510666
$186$	−5.96954	+	10.3396i	−0.437708	+	0.758133i
$187$	1.56737	−	2.71476i	0.114617	−	0.198523i
$188$	4.60246	+	7.97170i	0.335669	+	0.581396i
$189$	−2.18175	+	1.49666i	−0.158699	+	0.108866i
$190$	13.4579			0.976337
$191$	15.2774			1.10543			0.552715	−	0.833370i	$-0.313592\pi$
$191$	15.2774			1.10543			0.552715	+	0.833370i	$0.313592\pi$
$192$	−1.52470			−0.110036
$193$	25.6681			1.84763			0.923814	−	0.382843i	$-0.125055\pi$
$193$	25.6681			1.84763			0.923814	+	0.382843i	$0.125055\pi$
$194$	−5.01483	+	8.68594i	−0.360044	+	0.623614i
$195$	6.89834	−	5.55958i	0.494001	−	0.398130i
$196$	4.13764	+	5.12793i	0.295546	+	0.366281i
$197$	7.84255	−	13.5837i	0.558759	−	0.967798i	−0.438842	−	0.898564i	$-0.644611\pi$
$197$	7.84255	−	13.5837i	0.558759	−	0.967798i	0.997600	−	0.0692340i	$-0.0220555\pi$
$198$	−0.890235	−	1.54193i	−0.0632662	−	0.109580i
$199$	2.87545	−	4.98042i	0.203835	−	0.353052i	−0.745926	−	0.666029i	$-0.767993\pi$
$199$	2.87545	−	4.98042i	0.203835	−	0.353052i	0.949761	+	0.312976i	$0.101326\pi$
$200$	−0.942496	−	1.63245i	−0.0666445	−	0.115432i
$201$	11.2200			0.791398
$202$	−15.8886	−	27.5198i	−1.11792	−	1.93629i
$203$	1.64798	+	21.1770i	0.115665	+	1.48633i
$204$	1.42112	+	2.46145i	0.0994983	+	0.172336i
$205$	6.24408	+	10.8151i	0.436105	+	0.755356i
$206$	−3.48392			−0.242737
$207$	1.73601	+	3.00685i	0.120661	+	0.208991i
$208$	−2.77672	−	17.8001i	−0.192531	−	1.23421i
$209$	−3.31528			−0.229323
$210$	−9.19445	+	6.30731i	−0.634478	+	0.435246i
$211$	10.3771	−	17.9736i	0.714387	−	1.23735i	−0.248809	−	0.968553i	$-0.580039\pi$
$211$	10.3771	−	17.9736i	0.714387	−	1.23735i	0.963196	−	0.268802i	$-0.0866276\pi$
$212$	−11.1251			−0.764075
$213$	1.63013	+	2.82347i	0.111695	+	0.193461i
$214$	−2.08946	+	3.61906i	−0.142833	+	0.247394i
$215$	−15.8168			−1.07870
$216$	−1.81570			−0.123543
$217$	−16.6172	−	7.94388i	−1.12805	−	0.539266i
$218$	13.4739	−	23.3375i	0.912569	−	1.58062i
$219$	−7.50717	−	13.0028i	−0.507288	−	0.878648i
$220$	−1.20064	−	2.07957i	−0.0809472	−	0.140205i
$221$	8.47671	−	6.83164i	0.570205	−	0.459546i
$222$	−2.42387	+	4.19827i	−0.162679	+	0.281769i
$223$	5.68668	−	9.84963i	0.380809	−	0.659580i	−0.610369	−	0.792117i	$-0.708979\pi$
$223$	5.68668	−	9.84963i	0.380809	−	0.659580i	0.991178	+	0.132537i	$0.0423123\pi$
$224$	1.01358	+	13.0248i	0.0677227	+	0.870255i
$225$	−0.519081	−	0.899075i	−0.0346054	−	0.0599383i
$226$	−4.33399	+	7.50668i	−0.288292	+	0.499337i
$227$	2.71464	−	4.70189i	0.180177	−	0.312075i	−0.761764	−	0.647855i	$-0.775666\pi$
$227$	2.71464	−	4.70189i	0.180177	−	0.312075i	0.941941	+	0.335779i	$0.109000\pi$
$228$	1.50297	−	2.60322i	0.0995367	−	0.172403i
$229$	−8.67170	+	15.0198i	−0.573042	+	0.992538i	0.423209	+	0.906032i	$0.360903\pi$
$229$	−8.67170	+	15.0198i	−0.573042	+	0.992538i	−0.996251	+	0.0865059i	$0.972430\pi$
$230$	7.31599	+	12.6717i	0.482402	+	0.835545i
$231$	2.26501	−	1.55377i	0.149026	−	0.102231i
$232$	−7.28853	+	12.6241i	−0.478516	+	0.828813i
$233$	10.0164	−	17.3490i	0.656199	−	1.13657i	−0.325393	−	0.945579i	$-0.605496\pi$
$233$	10.0164	−	17.3490i	0.656199	−	1.13657i	0.981592	−	0.190991i	$-0.0611702\pi$
$234$	−0.953083	−	6.10970i	−0.0623050	−	0.399404i
$235$	−12.0148	−	20.8103i	−0.783761	−	1.35751i
$236$	−4.20825	−	7.28890i	−0.273934	−	0.474467i
$237$	0.211818	−	0.366880i	0.0137591	−	0.0238314i
$238$	−11.2982	+	7.75045i	−0.732352	+	0.502387i
$239$	−8.30497			−0.537204			−0.268602	−	0.963251i	$-0.586562\pi$
$239$	−8.30497			−0.537204			−0.268602	+	0.963251i	$0.586562\pi$
$240$	−12.2779			−0.792533
$241$	−10.2953	+	17.8320i	−0.663178	+	1.14866i	0.316597	+	0.948560i	$0.397460\pi$
$241$	−10.2953	+	17.8320i	−0.663178	+	1.14866i	−0.979776	+	0.200099i	$0.935874\pi$
$242$	−8.50840	−	14.7370i	−0.546941	−	0.947329i
$243$	−1.00000			−0.0641500
$244$	1.22788	−	2.12676i	0.0786073	−	0.136152i
$245$	−10.8014	−	13.3866i	−0.690076	−	0.855235i
$246$	8.71596			0.555709
$247$	−10.7396	−	4.15131i	−0.683345	−	0.264141i
$248$	−6.31999	−	10.9465i	−0.401320	−	0.695106i
$249$	1.34088			0.0849749
$250$	8.34811	+	14.4594i	0.527981	+	0.914490i
$251$	5.22288	+	9.04629i	0.329665	+	0.570997i	0.982445	−	0.186550i	$-0.0597308\pi$
$251$	5.22288	+	9.04629i	0.329665	+	0.570997i	−0.652780	+	0.757547i	$0.726397\pi$
$252$	0.193220	+	2.48292i	0.0121717	+	0.156410i
$253$	−1.80226	−	3.12160i	−0.113307	−	0.196253i
$254$	6.31972			0.396534
$255$	−3.70986	−	6.42567i	−0.232320	−	0.402391i
$256$	−9.18600	+	15.9106i	−0.574125	+	0.994414i
$257$	−3.61689	−	6.26463i	−0.225615	−	0.390777i	0.730889	−	0.682497i	$-0.239106\pi$
$257$	−3.61689	−	6.26463i	−0.225615	−	0.390777i	−0.956504	+	0.291720i	$0.905773\pi$
$258$	−5.51958	+	9.56019i	−0.343634	+	0.595192i
$259$	−6.74723	−	3.22553i	−0.419252	−	0.200425i
$260$	−1.28540	−	8.24003i	−0.0797173	−	0.511025i
$261$	−4.01417	+	6.95275i	−0.248471	+	0.430364i
$262$	−3.16985			−0.195834
$263$	−1.70621			−0.105209			−0.0526047	−	0.998615i	$-0.516752\pi$
$263$	−1.70621			−0.105209			−0.0526047	+	0.998615i	$0.516752\pi$
$264$	1.88499			0.116013
$265$	29.0423			1.78405
$266$	13.0731	+	6.24964i	0.801565	+	0.383190i
$267$	2.65247	+	4.59421i	0.162328	+	0.281161i
$268$	5.28067	−	9.14638i	0.322568	−	0.558704i
$269$	−10.9941	+	19.0424i	−0.670324	+	1.16104i	0.307488	+	0.951552i	$0.400512\pi$
$269$	−10.9941	+	19.0424i	−0.670324	+	1.16104i	−0.977812	+	0.209483i	$0.932822\pi$
$270$	−4.21426			−0.256472
$271$	11.8251	+	20.4817i	0.718324	+	1.24417i	0.961664	+	0.274232i	$0.0884236\pi$
$271$	11.8251	+	20.4817i	0.718324	+	1.24417i	−0.243340	+	0.969941i	$0.578243\pi$
$272$	−15.0871			−0.914790
$273$	9.28292	−	2.19715i	0.561828	−	0.132978i
$274$	−4.82810			−0.291676
$275$	0.538890	+	0.933385i	0.0324963	+	0.0562853i
$276$	3.26819			0.196722
$277$	14.9643	−	25.9190i	0.899119	−	1.55732i	0.0704974	−	0.997512i	$-0.477541\pi$
$277$	14.9643	−	25.9190i	0.899119	−	1.55732i	0.828622	−	0.559809i	$-0.189125\pi$
$278$	−3.22164	+	5.58004i	−0.193221	+	0.334669i
$279$	−3.48074	−	6.02882i	−0.208387	−	0.360936i
$280$	−0.915846	−	11.7689i	−0.0547323	−	0.703325i
$281$	−27.8636			−1.66220			−0.831102	−	0.556120i	$-0.812289\pi$
$281$	−27.8636			−1.66220			−0.831102	+	0.556120i	$0.812289\pi$
$282$	−16.7712			−0.998711
$283$	−19.4075			−1.15366			−0.576829	−	0.816865i	$-0.695710\pi$
$283$	−19.4075			−1.15366			−0.576829	+	0.816865i	$0.695710\pi$
$284$	3.06887			0.182104
$285$	−3.92353	+	6.79576i	−0.232410	+	0.402546i
$286$	0.989454	+	6.34286i	0.0585077	+	0.375061i
$287$	1.04321	+	13.4055i	0.0615787	+	0.791303i
$288$	−2.46889	+	4.27625i	−0.145481	+	0.251980i
$289$	3.94131	+	6.82655i	0.231842	+	0.401562i
$290$	−16.9168	+	29.3007i	−0.993387	+	1.72060i
$291$	−2.92406	−	5.06463i	−0.171412	−	0.296894i
$292$	−14.1329			−0.827067
$293$	−2.20711	−	3.82282i	−0.128940	−	0.223331i	0.794326	−	0.607492i	$-0.207824\pi$
$293$	−2.20711	−	3.82282i	−0.128940	−	0.223331i	−0.923266	+	0.384160i	$0.874491\pi$
$294$	−11.8606	+	1.85722i	−0.691725	+	0.108315i
$295$	10.9857	+	19.0278i	0.639613	+	1.10784i
$296$	−2.56616	−	4.44473i	−0.149155	−	0.258344i
$297$	1.03816			0.0602403
$298$	5.77690	+	10.0059i	0.334647	+	0.579625i
$299$	−1.92949	−	12.3689i	−0.111585	−	0.715314i
$300$	−0.977216			−0.0564196
$301$	−15.3646	−	7.34510i	−0.885603	−	0.423364i
$302$	4.63090	−	8.02096i	0.266479	−	0.461554i
$303$	18.5287			1.06445
$304$	7.97803	+	13.8184i	0.457571	+	0.792537i
$305$	−3.20542	+	5.55194i	−0.183542	+	0.317903i
$306$	−5.17850			−0.296035
$307$	−9.06995			−0.517649			−0.258825	−	0.965924i	$-0.583335\pi$
$307$	−9.06995			−0.517649			−0.258825	+	0.965924i	$0.583335\pi$
$308$	−0.200593	−	2.57768i	−0.0114299	−	0.146877i
$309$	1.01571	−	1.75926i	0.0577817	−	0.100081i
$310$	−14.6688	−	25.4070i	−0.833130	−	1.44302i
$311$	−11.8691	−	20.5579i	−0.673037	−	1.16573i	−0.977039	−	0.213062i	$-0.931656\pi$
$311$	−11.8691	−	20.5579i	−0.673037	−	1.16573i	0.304002	−	0.952671i	$-0.401677\pi$
$312$	6.10629	+	2.36034i	0.345701	+	0.133628i
$313$	−6.48059	+	11.2247i	−0.366304	+	0.634458i	−0.988985	−	0.148019i	$-0.952710\pi$
$313$	−6.48059	+	11.2247i	−0.366304	+	0.634458i	0.622680	+	0.782476i	$0.286044\pi$
$314$	9.99379	−	17.3098i	0.563982	−	0.976846i
$315$	−0.504403	−	6.48172i	−0.0284199	−	0.365204i
$316$	−0.199384	−	0.345342i	−0.0112162	−	0.0194270i
$317$	15.7012	−	27.1953i	0.881867	−	1.52744i	0.0326048	−	0.999468i	$-0.489620\pi$
$317$	15.7012	−	27.1953i	0.881867	−	1.52744i	0.849263	−	0.527971i	$-0.177047\pi$
$318$	10.1349	−	17.5541i	0.568335	−	0.984385i
$319$	4.16736	−	7.21808i	0.233327	−	0.404135i
$320$	1.87330	−	3.24465i	0.104721	−	0.181381i
$321$	−1.21833	−	2.11021i	−0.0680007	−	0.117781i
$322$	1.22230	+	15.7068i	0.0681159	+	0.875308i
$323$	−4.82126	+	8.35066i	−0.268262	+	0.464643i
$324$	−0.470647	+	0.815185i	−0.0261471	+	0.0452881i
$325$	0.576934	+	3.69842i	0.0320026	+	0.205151i
$326$	20.7960	+	36.0197i	1.15178	+	1.99495i
$327$	7.85642	+	13.6077i	0.434461	+	0.752508i
$328$	−4.61382	+	7.99136i	−0.254755	+	0.441249i
$329$	−2.00734	−	25.7948i	−0.110668	−	1.42212i
$330$	4.37509			0.240841
$331$	−11.5233			−0.633378			−0.316689	−	0.948529i	$-0.602571\pi$
$331$	−11.5233			−0.633378			−0.316689	+	0.948529i	$0.602571\pi$
$332$	0.631082	−	1.09307i	0.0346351	−	0.0599898i
$333$	−1.41332	−	2.44794i	−0.0774494	−	0.134146i
$334$	28.2366			1.54504
$335$	−13.7853	+	23.8768i	−0.753170	+	1.30453i
$336$	−11.9269	−	5.70166i	−0.650663	−	0.311051i
$337$	−17.7823			−0.968665			−0.484332	−	0.874884i	$-0.660937\pi$
$337$	−17.7823			−0.968665			−0.484332	+	0.874884i	$0.660937\pi$
$338$	−4.73710	+	21.7862i	−0.257664	+	1.18501i
$339$	−2.52708	−	4.37702i	−0.137252	−	0.237727i
$340$	−6.98414			−0.378768
$341$	3.61357	+	6.25890i	0.195686	+	0.338938i
$342$	2.73838	+	4.74302i	0.148075	+	0.256473i
$343$	−4.27608	−	18.0199i	−0.230886	−	0.972981i
$344$	−5.84361	−	10.1214i	−0.315066	−	0.545711i
$345$	−8.53167			−0.459330
$346$	−17.1850	−	29.7652i	−0.923869	−	1.60019i
$347$	6.16001	−	10.6694i	0.330687	−	0.572766i	−0.651960	−	0.758253i	$-0.726053\pi$
$347$	6.16001	−	10.6694i	0.330687	−	0.572766i	0.982647	+	0.185487i	$0.0593864\pi$
$348$	3.77852	+	6.54458i	0.202550	+	0.350826i
$349$	−4.29722	+	7.44301i	−0.230025	+	0.398415i	−0.957815	−	0.287385i	$-0.907214\pi$
$349$	−4.29722	+	7.44301i	−0.230025	+	0.398415i	0.727790	+	0.685800i	$0.240548\pi$
$350$	−0.365477	−	4.69648i	−0.0195356	−	0.251037i
$351$	3.36305	+	1.29996i	0.179506	+	0.0693867i
$352$	2.56311	−	4.43944i	0.136614	−	0.236623i
$353$	29.1648			1.55229			0.776144	−	0.630556i	$-0.217173\pi$
$353$	29.1648			1.55229			0.776144	+	0.630556i	$0.217173\pi$
$354$	15.3347			0.815030
$355$	−8.01135			−0.425198
$356$	4.99350			0.264655
$357$	−0.619813	−	7.96477i	−0.0328040	−	0.421540i
$358$	−8.65668	−	14.9938i	−0.457520	−	0.792448i
$359$	−1.79924	+	3.11637i	−0.0949602	+	0.164476i	−0.909592	−	0.415503i	$-0.863606\pi$
$359$	−1.79924	+	3.11637i	−0.0949602	+	0.164476i	0.814632	+	0.579979i	$0.196939\pi$
$360$	2.23083	−	3.86391i	0.117575	−	0.203646i
$361$	−8.80212			−0.463269
$362$	17.0609	+	29.5504i	0.896703	+	1.55314i
$363$	9.92222			0.520781
$364$	2.57789	−	8.60138i	0.135118	−	0.450835i
$365$	36.8943			1.93113
$366$	2.23718	+	3.87491i	0.116939	+	0.202545i
$367$	31.0655			1.62161			0.810803	−	0.585319i	$-0.199031\pi$
$367$	31.0655			1.62161			0.810803	+	0.585319i	$0.199031\pi$
$368$	−8.67406	+	15.0239i	−0.452167	+	0.783175i
$369$	−2.54107	+	4.40125i	−0.132283	+	0.229120i
$370$	−5.95610	−	10.3163i	−0.309643	−	0.536317i
$371$	28.2120	+	13.4868i	1.46469	+	0.700201i
$372$	−6.55281			−0.339747
$373$	−23.4625			−1.21484			−0.607421	−	0.794380i	$-0.707796\pi$
$373$	−23.4625			−1.21484			−0.607421	+	0.794380i	$0.707796\pi$
$374$	5.37613			0.277993
$375$	−9.73529			−0.502728
$376$	8.87788	−	15.3769i	0.457842	−	0.793005i
$377$	22.5381	−	18.1642i	1.16077	−	0.935502i
$378$	−4.09378	−	1.95704i	−0.210561	−	0.100659i
$379$	4.67032	−	8.08923i	0.239898	−	0.415516i	−0.720787	−	0.693157i	$-0.756219\pi$
$379$	4.67032	−	8.08923i	0.239898	−	0.415516i	0.960685	+	0.277641i	$0.0895526\pi$
$380$	3.69320	+	6.39681i	0.189457	+	0.328150i
$381$	−1.84246	+	3.19124i	−0.0943922	+	0.163492i
$382$	13.1005	+	22.6907i	0.670279	+	1.16096i
$383$	11.6813			0.596889			0.298444	−	0.954427i	$-0.403532\pi$
$383$	11.6813			0.596889			0.298444	+	0.954427i	$0.403532\pi$
$384$	−6.24523	−	10.8171i	−0.318701	−	0.552006i
$385$	0.523653	+	6.72908i	0.0266878	+	0.342946i
$386$	22.0106	+	38.1235i	1.12031	+	1.94044i
$387$	−3.21838	−	5.57439i	−0.163599	−	0.283362i
$388$	−5.50481			−0.279464
$389$	9.34341	+	16.1833i	0.473730	+	0.820524i	0.999548	−	0.0300730i	$-0.00957396\pi$
$389$	9.34341	+	16.1833i	0.473730	+	0.820524i	−0.525818	+	0.850597i	$0.676241\pi$
$390$	14.1728	+	5.47837i	0.717666	+	0.277408i
$391$	−10.4838			−0.530186
$392$	4.57563	−	11.8577i	0.231104	−	0.598905i
$393$	0.924144	−	1.60066i	0.0466169	−	0.0807428i
$394$	26.9003			1.35522
$395$	0.520495	+	0.901523i	0.0261889	+	0.0453605i
$396$	0.488608	−	0.846294i	0.0245535	−	0.0425279i
$397$	9.44412			0.473987			0.236993	−	0.971511i	$-0.423838\pi$
$397$	9.44412			0.473987			0.236993	+	0.971511i	$0.423838\pi$
$398$	9.86289			0.494382
$399$	−6.96722	+	4.77944i	−0.348797	+	0.239272i
$400$	2.59362	−	4.49228i	0.129681	−	0.224614i
$401$	−5.18622	−	8.98279i	−0.258987	−	0.448579i	0.706984	−	0.707230i	$-0.250055\pi$
$401$	−5.18622	−	8.98279i	−0.258987	−	0.448579i	−0.965971	+	0.258651i	$0.916722\pi$
$402$	9.62127	+	16.6645i	0.479865	+	0.831151i
$403$	3.86868	+	24.8001i	0.192713	+	1.23538i
$404$	8.72050	−	15.1044i	0.433861	−	0.751470i
$405$	1.22863	−	2.12806i	0.0610513	−	0.105744i
$406$	−30.0400	+	20.6071i	−1.49086	+	1.02271i
$407$	1.46725	+	2.54136i	0.0727291	+	0.125970i
$408$	2.74126	−	4.74799i	0.135712	−	0.235061i
$409$	−11.4435	+	19.8207i	−0.565844	+	0.980071i	0.431126	+	0.902292i	$0.358116\pi$
$409$	−11.4435	+	19.8207i	−0.565844	+	0.980071i	−0.996971	+	0.0777796i	$0.975217\pi$
$410$	−10.7087	+	18.5480i	−0.528866	+	0.916023i
$411$	1.40759	−	2.43802i	0.0694314	−	0.120259i
$412$	−0.956082	−	1.65598i	−0.0471028	−	0.0815844i
$413$	1.83540	+	23.5854i	0.0903143	+	1.16056i
$414$	−2.97729	+	5.15682i	−0.146326	+	0.253444i
$415$	−1.64745	+	2.85347i	−0.0808702	+	0.140071i
$416$	13.8620	−	11.1718i	0.679639	−	0.547742i
$417$	−1.87848	−	3.25363i	−0.0919898	−	0.159331i
$418$	−2.84289	−	4.92402i	−0.139050	−	0.240842i
$419$	4.33086	−	7.50127i	0.211576	−	0.366461i	−0.740632	−	0.671911i	$-0.765474\pi$
$419$	4.33086	−	7.50127i	0.211576	−	0.366461i	0.952208	+	0.305450i	$0.0988070\pi$
$420$	−5.52120	−	2.63942i	−0.269407	−	0.128791i
$421$	−1.15030			−0.0560620			−0.0280310	−	0.999607i	$-0.508924\pi$
$421$	−1.15030			−0.0560620			−0.0280310	+	0.999607i	$0.508924\pi$
$422$	35.5938			1.73268
$423$	4.88951	−	8.46887i	0.237736	−	0.411771i
$424$	10.7298	+	18.5846i	0.521087	+	0.902549i
$425$	3.13473			0.152057
$426$	−2.79571	+	4.84232i	−0.135453	+	0.234611i
$427$	−5.69202	+	3.90467i	−0.275456	+	0.188960i
$428$	−2.29362			−0.110866
$429$	−3.49139	−	1.34957i	−0.168566	−	0.0651578i
$430$	−13.5631	−	23.4919i	−0.654070	−	1.13288i
$431$	8.76048			0.421977			0.210989	−	0.977489i	$-0.432332\pi$
$431$	8.76048			0.421977			0.210989	+	0.977489i	$0.432332\pi$
$432$	−2.49828	−	4.32714i	−0.120198	−	0.208190i
$433$	0.463102	+	0.802117i	0.0222553	+	0.0385473i	0.876939	−	0.480603i	$-0.159582\pi$
$433$	0.463102	+	0.802117i	0.0222553	+	0.0385473i	−0.854683	+	0.519150i	$0.826249\pi$
$434$	−2.45074	−	31.4926i	−0.117639	−	1.51170i
$435$	−9.86389	−	17.0848i	−0.472937	−	0.819151i
$436$	14.7904			0.708332
$437$	5.54379	+	9.60213i	0.265195	+	0.459332i
$438$	12.8750	−	22.3001i	0.615189	−	1.06554i
$439$	−6.20418	−	10.7460i	−0.296109	−	0.512877i	0.679133	−	0.734015i	$-0.262356\pi$
$439$	−6.20418	−	10.7460i	−0.296109	−	0.512877i	−0.975242	+	0.221139i	$0.929023\pi$
$440$	−2.31597	+	4.01137i	−0.110409	+	0.191235i
$441$	2.52003	−	6.53065i	0.120002	−	0.310983i
$442$	17.4156	+	6.73185i	0.828374	+	0.320201i
$443$	−1.61468	+	2.79670i	−0.0767156	+	0.132875i	−0.901831	−	0.432089i	$-0.857777\pi$
$443$	−1.61468	+	2.79670i	−0.0767156	+	0.132875i	0.825115	+	0.564964i	$0.191110\pi$
$444$	−2.66070			−0.126271
$445$	−13.0356			−0.617948
$446$	19.5056			0.923615
$447$	−6.73683			−0.318641
$448$	3.32651	−	2.28195i	0.157163	−	0.107812i
$449$	−9.94344	−	17.2225i	−0.469260	−	0.812782i	0.530123	−	0.847921i	$-0.322146\pi$
$449$	−9.94344	−	17.2225i	−0.469260	−	0.812782i	−0.999382	+	0.0351392i	$0.988813\pi$
$450$	0.890235	−	1.54193i	0.0419661	−	0.0726873i
$451$	2.63804	−	4.56922i	0.124220	−	0.215156i
$452$	−4.75744			−0.223771
$453$	2.70020	+	4.67689i	0.126867	+	0.219739i
$454$	9.31132			0.437002
$455$	−6.72964	+	22.4541i	−0.315491	+	1.05266i
$456$	−5.79828			−0.271530
$457$	0.0394872	+	0.0683939i	0.00184713	+	0.00319933i	0.866947	−	0.498399i	$-0.166079\pi$
$457$	0.0394872	+	0.0683939i	0.00184713	+	0.00319933i	−0.865100	+	0.501599i	$0.832745\pi$
$458$	−29.7443			−1.38986
$459$	1.50975	−	2.61496i	0.0704691	−	0.122056i
$460$	−4.01541	+	6.95489i	−0.187219	+	0.324273i
$461$	2.45979	+	4.26049i	0.114564	+	0.198431i	0.917605	−	0.397493i	$-0.130120\pi$
$461$	2.45979	+	4.26049i	0.114564	+	0.198431i	−0.803041	+	0.595923i	$0.796786\pi$
$462$	4.25001	+	2.03173i	0.197728	+	0.0945245i
$463$	1.24837			0.0580166			0.0290083	−	0.999579i	$-0.490765\pi$
$463$	1.24837			0.0580166			0.0290083	+	0.999579i	$0.490765\pi$
$464$	−40.1140			−1.86225
$465$	17.1062			0.793282
$466$	34.3568			1.59155
$467$	−14.3411	+	24.8395i	−0.663628	+	1.14944i	0.316028	+	0.948750i	$0.397651\pi$
$467$	−14.3411	+	24.8395i	−0.663628	+	1.14944i	−0.979655	+	0.200687i	$0.935683\pi$
$468$	2.64252	−	2.12969i	0.122150	−	0.0984447i
$469$	−24.4792	+	16.7925i	−1.13035	+	0.775406i
$470$	20.6057	−	35.6901i	0.950468	−	1.64626i
$471$	5.82721	+	10.0930i	0.268504	+	0.465062i
$472$	−8.11746	+	14.0599i	−0.373636	+	0.647157i
$473$	3.34120	+	5.78712i	0.153628	+	0.266092i
$474$	0.726546			0.0333714
$475$	−1.65764	−	2.87112i	−0.0760577	−	0.131736i
$476$	−6.78447	−	3.24333i	−0.310966	−	0.148658i
$477$	5.90947	+	10.2355i	0.270576	+	0.468651i
$478$	−7.12159	−	12.3350i	−0.325734	−	0.564188i
$479$	−6.97871			−0.318866			−0.159433	−	0.987209i	$-0.550967\pi$
$479$	−6.97871			−0.318866			−0.159433	+	0.987209i	$0.550967\pi$
$480$	−6.06673	−	10.5079i	−0.276907	−	0.479617i
$481$	1.57084	+	10.0698i	0.0716240	+	0.459143i
$482$	−35.3133			−1.60848
$483$	−8.28776	−	3.96198i	−0.377106	−	0.180277i
$484$	4.66987	−	8.08844i	0.212267	−	0.367657i
$485$	14.3704			0.652527
$486$	−0.857510	−	1.48525i	−0.0388974	−	0.0673724i
$487$	0.964157	−	1.66997i	0.0436901	−	0.0756735i	−0.843353	−	0.537359i	$-0.819422\pi$
$487$	0.964157	−	1.66997i	0.0436901	−	0.0756735i	0.887044	+	0.461686i	$0.152755\pi$
$488$	−4.73703			−0.214435
$489$	−24.2516			−1.09670
$490$	10.6201	−	27.5219i	0.479767	−	1.24331i
$491$	14.6968	−	25.4556i	0.663256	−	1.14879i	−0.316499	−	0.948593i	$-0.602507\pi$
$491$	14.6968	−	25.4556i	0.663256	−	1.14879i	0.979755	−	0.200200i	$-0.0641592\pi$
$492$	2.39189	+	4.14288i	0.107835	+	0.186775i
$493$	−12.1208	−	20.9938i	−0.545893	−	0.945514i
$494$	−3.04359	−	19.5108i	−0.136937	−	0.877832i
$495$	−1.27552	+	2.20927i	−0.0573304	+	0.0992992i
$496$	17.3917	−	30.1233i	0.780911	−	1.35258i
$497$	−7.78231	−	3.72035i	−0.349084	−	0.166881i
$498$	1.14982	+	1.99154i	0.0515246	+	0.0892433i
$499$	−9.92902	+	17.1976i	−0.444484	+	0.769869i	−0.998016	−	0.0629592i	$-0.979946\pi$
$499$	−9.92902	+	17.1976i	−0.444484	+	0.769869i	0.553532	+	0.832828i	$0.313280\pi$
$500$	−4.58189	+	7.93607i	−0.204908	+	0.354912i
$501$	−8.23216	+	14.2585i	−0.367786	+	0.637024i
$502$	−8.95734	+	15.5146i	−0.399786	+	0.692449i
$503$	13.3790	+	23.1731i	0.596540	+	1.03324i	0.993328	+	0.115327i	$0.0367917\pi$
$503$	13.3790	+	23.1731i	0.596540	+	1.03324i	−0.396787	+	0.917911i	$0.629875\pi$
$504$	3.96140	−	2.71748i	0.176455	−	0.121046i
$505$	−22.7650	+	39.4302i	−1.01303	+	1.75462i
$506$	3.09091	−	5.35361i	0.137408	−	0.237997i
$507$	−9.62021	−	8.74366i	−0.427248	−	0.388320i
$508$	1.73430	+	3.00389i	0.0769471	+	0.133276i
$509$	−2.96465	−	5.13492i	−0.131406	−	0.227601i	0.792813	−	0.609465i	$-0.208616\pi$
$509$	−2.96465	−	5.13492i	−0.131406	−	0.227601i	−0.924219	+	0.381864i	$0.875282\pi$
$510$	6.36248	−	11.0201i	0.281736	−	0.487980i
$511$	35.8395	+	17.1332i	1.58545	+	0.757926i
$512$	−6.52743			−0.288474
$513$	−3.19341			−0.140993
$514$	6.20303	−	10.7440i	0.273604	−	0.473896i
$515$	2.49587	+	4.32297i	0.109981	+	0.190493i
$516$	−6.05888			−0.266727
$517$	−5.07610	+	8.79206i	−0.223247	+	0.386674i
$518$	−0.995096	−	12.7873i	−0.0437220	−	0.561840i
$519$	20.0405			0.879682
$520$	−12.5253	+	10.0945i	−0.549272	+	0.442675i
$521$	−16.7414	−	28.9969i	−0.733453	−	1.27038i	−0.955399	−	0.295319i	$-0.904574\pi$
$521$	−16.7414	−	28.9969i	−0.733453	−	1.27038i	0.221946	−	0.975059i	$-0.428759\pi$
$522$	−13.7688			−0.602642
$523$	−20.7273	−	35.9007i	−0.906341	−	1.56983i	−0.819107	−	0.573641i	$-0.805530\pi$
$523$	−20.7273	−	35.9007i	−0.906341	−	1.56983i	−0.0872343	−	0.996188i	$-0.527803\pi$
$524$	−0.869892	−	1.50670i	−0.0380014	−	0.0658203i
$525$	2.47811	+	1.18467i	0.108154	+	0.0517031i
$526$	−1.46309	−	2.53415i	−0.0637938	−	0.110494i
$527$	21.0202			0.915655
$528$	2.59362	+	4.49228i	0.112873	+	0.195501i
$529$	5.47255	−	9.47874i	0.237937	−	0.412119i
$530$	24.9041	+	43.1351i	1.08176	+	1.87367i
$531$	−4.47070	+	7.74348i	−0.194012	+	0.336039i
$532$	0.617030	+	7.92900i	0.0267516	+	0.343766i
$533$	14.2672	−	11.4984i	0.617980	−	0.498049i
$534$	−4.54903	+	7.87915i	−0.196856	+	0.340964i
$535$	5.98753			0.258864
$536$	−20.3722			−0.879944
$537$	10.0951			0.435637
$538$	−37.7103			−1.62581
$539$	−2.61620	+	6.77988i	−0.112688	+	0.292030i
$540$	−1.15651	−	2.00313i	−0.0497681	−	0.0862009i
$541$	−14.7605	+	25.5660i	−0.634606	+	1.09917i	0.351993	+	0.936003i	$0.385504\pi$
$541$	−14.7605	+	25.5660i	−0.634606	+	1.09917i	−0.986599	+	0.163166i	$0.947829\pi$
$542$	−20.2803	+	35.1265i	−0.871113	+	1.50881i
$543$	−19.8959			−0.853815
$544$	−7.45483	−	12.9121i	−0.319623	−	0.553603i
$545$	−38.6106			−1.65390
$546$	11.2235	+	11.9034i	0.480322	+	0.509418i
$547$	34.6619			1.48203			0.741017	−	0.671486i	$-0.234344\pi$
$547$	34.6619			1.48203			0.741017	+	0.671486i	$0.234344\pi$
$548$	−1.32496	−	2.29490i	−0.0565995	−	0.0980332i
$549$	−2.60893			−0.111346
$550$	−0.924208	+	1.60077i	−0.0394084	+	0.0682573i
$551$	−12.8189	+	22.2030i	−0.546104	+	0.945879i
$552$	−3.15207	−	5.45955i	−0.134161	−	0.232374i
$553$	0.0869600	+	1.11746i	0.00369792	+	0.0475192i
$554$	51.3283			2.18073
$555$	6.94580			0.294833
$556$	−3.53641			−0.149977
$557$	−15.0484			−0.637623			−0.318812	−	0.947818i	$-0.603284\pi$
$557$	−15.0484			−0.637623			−0.318812	+	0.947818i	$0.603284\pi$
$558$	5.96954	−	10.3396i	0.252711	−	0.437708i
$559$	3.57707	+	22.9307i	0.151294	+	0.969866i
$560$	26.7872	−	18.3758i	1.13197	−	0.776518i
$561$	−1.56737	+	2.71476i	−0.0661742	+	0.114617i
$562$	−23.8933	−	41.3845i	−1.00788	−	1.74570i
$563$	0.728725	−	1.26219i	0.0307121	−	0.0531949i	−0.850261	−	0.526362i	$-0.823556\pi$
$563$	0.728725	−	1.26219i	0.0307121	−	0.0531949i	0.880973	+	0.473167i	$0.156889\pi$
$564$	−4.60246	−	7.97170i	−0.193799	−	0.335669i
$565$	12.4194			0.522488
$566$	−16.6422	−	28.8251i	−0.699522	−	1.21161i
$567$	2.18175	−	1.49666i	0.0916247	−	0.0628537i
$568$	−2.95984	−	5.12659i	−0.124192	−	0.215107i
$569$	−2.05326	−	3.55635i	−0.0860770	−	0.149090i	0.819773	−	0.572689i	$-0.194100\pi$
$569$	−2.05326	−	3.55635i	−0.0860770	−	0.149090i	−0.905850	+	0.423599i	$0.860766\pi$
$570$	−13.4579			−0.563689
$571$	16.1753	+	28.0165i	0.676916	+	1.17245i	0.975905	+	0.218197i	$0.0700175\pi$
$571$	16.1753	+	28.0165i	0.676916	+	1.17245i	−0.298988	+	0.954257i	$0.596649\pi$
$572$	−2.74336	+	2.21096i	−0.114706	+	0.0924448i
$573$	−15.2774			−0.638221
$574$	−19.0160	+	13.0448i	−0.793713	+	0.544479i
$575$	1.80226	−	3.12160i	0.0751593	−	0.130180i
$576$	1.52470			0.0635292
$577$	3.24107	+	5.61369i	0.134927	+	0.233701i	0.925570	−	0.378577i	$-0.123587\pi$
$577$	3.24107	+	5.61369i	0.134927	+	0.233701i	−0.790642	+	0.612278i	$0.790253\pi$
$578$	−6.75942	+	11.7077i	−0.281155	+	0.486975i
$579$	−25.6681			−1.06673
$580$	−18.5696			−0.771063
$581$	−2.92546	+	2.00684i	−0.121369	+	0.0832577i
$582$	5.01483	−	8.68594i	0.207871	−	0.360044i
$583$	−6.13499	−	10.6261i	−0.254085	−	0.440088i
$584$	13.6308	+	23.6092i	0.564046	+	0.976956i
$585$	−6.89834	+	5.55958i	−0.285211	+	0.229860i
$586$	3.78523	−	6.55621i	0.156366	−	0.270835i
$587$	8.72720	−	15.1159i	0.360210	−	0.623902i	−0.627785	−	0.778387i	$-0.716038\pi$
$587$	8.72720	−	15.1159i	0.360210	−	0.623902i	0.987995	+	0.154485i	$0.0493717\pi$
$588$	−4.13764	−	5.12793i	−0.170634	−	0.211472i
$589$	−11.1154	−	19.2525i	−0.458004	−	0.793286i
$590$	−18.8407	+	32.6331i	−0.775660	+	1.34348i
$591$	−7.84255	+	13.5837i	−0.322599	+	0.558759i
$592$	7.06172	−	12.2313i	0.290235	−	0.502702i
$593$	−5.07543	+	8.79090i	−0.208423	+	0.360999i	−0.951218	−	0.308520i	$-0.900166\pi$
$593$	−5.07543	+	8.79090i	−0.208423	+	0.360999i	0.742795	+	0.669519i	$0.233500\pi$
$594$	0.890235	+	1.54193i	0.0365268	+	0.0632662i
$595$	17.7110	+	8.46678i	0.726080	+	0.347104i
$596$	−3.17067	+	5.49176i	−0.129876	+	0.224951i
$597$	−2.87545	+	4.98042i	−0.117684	+	0.203835i
$598$	16.7164	−	13.4723i	0.683585	−	0.550922i
$599$	−5.29665	−	9.17406i	−0.216415	−	0.374842i	0.737294	−	0.675572i	$-0.236103\pi$
$599$	−5.29665	−	9.17406i	−0.216415	−	0.374842i	−0.953709	+	0.300730i	$0.902770\pi$
$600$	0.942496	+	1.63245i	0.0384772	+	0.0666445i
$601$	5.08203	−	8.80234i	0.207300	−	0.359055i	−0.743563	−	0.668666i	$-0.766866\pi$
$601$	5.08203	−	8.80234i	0.207300	−	0.359055i	0.950863	+	0.309611i	$0.100199\pi$
$602$	−2.26601	−	29.1188i	−0.0923556	−	1.18680i
$603$	−11.2200			−0.456914
$604$	5.08337			0.206840
$605$	−12.1908	+	21.1150i	−0.495625	+	0.858448i
$606$	15.8886	+	27.5198i	0.645430	+	1.11792i
$607$	32.4478			1.31702			0.658508	−	0.752574i	$-0.271188\pi$
$607$	32.4478			1.31702			0.658508	+	0.752574i	$0.271188\pi$
$608$	−7.88420	+	13.6558i	−0.319746	+	0.553817i
$609$	−1.64798	−	21.1770i	−0.0667794	−	0.858134i
$610$	−10.9947			−0.445163
$611$	−27.4528	+	22.1251i	−1.11062	+	0.895085i
$612$	−1.42112	−	2.46145i	−0.0574454	−	0.0994983i
$613$	−9.83642			−0.397289			−0.198645	−	0.980072i	$-0.563654\pi$
$613$	−9.83642			−0.397289			−0.198645	+	0.980072i	$0.563654\pi$
$614$	−7.77757	−	13.4712i	−0.313877	−	0.543651i
$615$	−6.24408	−	10.8151i	−0.251785	−	0.436105i
$616$	−4.11258	+	2.82119i	−0.165700	+	0.113669i
$617$	17.6661	+	30.5985i	0.711208	+	1.23185i	0.964404	+	0.264434i	$0.0851851\pi$
$617$	17.6661	+	30.5985i	0.711208	+	1.23185i	−0.253195	+	0.967415i	$0.581482\pi$
$618$	3.48392			0.140144
$619$	−17.5126	−	30.3327i	−0.703892	−	1.21918i	−0.967090	−	0.254434i	$-0.918111\pi$
$619$	−17.5126	−	30.3327i	−0.703892	−	1.21918i	0.263198	−	0.964742i	$-0.415223\pi$
$620$	8.05100	−	13.9447i	0.323336	−	0.560034i
$621$	−1.73601	−	3.00685i	−0.0696636	−	0.120661i
$622$	20.3558	−	35.2573i	0.816193	−	1.41369i
$623$	−12.6630	−	6.05356i	−0.507331	−	0.242531i
$624$	2.77672	+	17.8001i	0.111158	+	0.712572i
$625$	14.5565	−	25.2126i	0.582261	−	1.00850i
$626$	−22.2287			−0.888437
$627$	3.31528			0.132400
$628$	10.9702			0.437761
$629$	8.53503			0.340314
$630$	9.19445	−	6.30731i	0.366316	−	0.251289i
$631$	−10.2980	−	17.8367i	−0.409959	−	0.710069i	0.584926	−	0.811087i	$-0.301124\pi$
$631$	−10.2980	−	17.8367i	−0.409959	−	0.710069i	−0.994885	+	0.101017i	$0.967790\pi$
$632$	−0.384599	+	0.666145i	−0.0152985	+	0.0264978i
$633$	−10.3771	+	17.9736i	−0.412451	+	0.714387i
$634$	53.8558			2.13889
$635$	−4.52742	−	7.84172i	−0.179665	−	0.311189i
$636$	11.1251			0.441139
$637$	−16.9646	+	18.6870i	−0.672161	+	0.740405i
$638$	14.2942			0.565913
$639$	−1.63013	−	2.82347i	−0.0644871	−	0.111695i
$640$	30.6924			1.21322
$641$	17.5384	−	30.3774i	0.692725	−	1.19983i	−0.278217	−	0.960518i	$-0.589744\pi$
$641$	17.5384	−	30.3774i	0.692725	−	1.19983i	0.970942	−	0.239316i	$-0.0769232\pi$
$642$	2.08946	−	3.61906i	0.0824646	−	0.142833i
$643$	−12.4615	−	21.5840i	−0.491435	−	0.851190i	0.508517	−	0.861052i	$-0.330194\pi$
$643$	−12.4615	−	21.5840i	−0.491435	−	0.851190i	−0.999951	+	0.00986235i	$0.996861\pi$
$644$	−7.13036	+	4.89136i	−0.280976	+	0.192747i
$645$	15.8168			0.622787
$646$	−16.5371			−0.650644
$647$	−3.35518			−0.131906			−0.0659528	−	0.997823i	$-0.521009\pi$
$647$	−3.35518			−0.131906			−0.0659528	+	0.997823i	$0.521009\pi$
$648$	1.81570			0.0713275
$649$	4.64131	−	8.03899i	0.182188	−	0.315558i
$650$	−4.99835	+	4.02832i	−0.196052	+	0.158004i
$651$	16.6172	+	7.94388i	0.651279	+	0.311345i
$652$	−11.4140	+	19.7695i	−0.447005	+	0.774235i
$653$	−2.54625	−	4.41024i	−0.0996426	−	0.172586i	0.811894	−	0.583805i	$-0.198437\pi$
$653$	−2.54625	−	4.41024i	−0.0996426	−	0.172586i	−0.911537	+	0.411219i	$0.865103\pi$
$654$	−13.4739	+	23.3375i	−0.526872	+	0.912569i
$655$	2.27087	+	3.93326i	0.0887302	+	0.153685i
$656$	−25.3931			−0.991435
$657$	7.50717	+	13.0028i	0.292883	+	0.507288i
$658$	36.5905	−	25.1007i	1.42645	−	0.978529i
$659$	−16.9148	−	29.2973i	−0.658907	−	1.14126i	−0.980899	−	0.194518i	$-0.937686\pi$
$659$	−16.9148	−	29.2973i	−0.658907	−	1.14126i	0.321992	−	0.946742i	$-0.395648\pi$
$660$	1.20064	+	2.07957i	0.0467349	+	0.0809472i
$661$	33.9014			1.31861			0.659306	−	0.751875i	$-0.270850\pi$
$661$	33.9014			1.31861			0.659306	+	0.751875i	$0.270850\pi$
$662$	−9.88135	−	17.1150i	−0.384050	−	0.665194i
$663$	−8.47671	+	6.83164i	−0.329208	+	0.265319i
$664$	−2.43464			−0.0944823
$665$	−1.61077	−	20.6988i	−0.0624629	−	0.802665i
$666$	2.42387	−	4.19827i	0.0939230	−	0.162679i
$667$	−27.8745			−1.07931
$668$	7.74889	+	13.4215i	0.299813	+	0.519292i
$669$	−5.68668	+	9.84963i	−0.219860	+	0.380809i
$670$	−47.2841			−1.82674
$671$	2.70849			0.104560
$672$	−1.01358	−	13.0248i	−0.0390997	−	0.502442i
$673$	−7.46805	+	12.9350i	−0.287872	+	0.498609i	−0.973302	−	0.229530i	$-0.926281\pi$
$673$	−7.46805	+	12.9350i	−0.287872	+	0.498609i	0.685430	+	0.728139i	$0.259614\pi$
$674$	−15.2485	−	26.4112i	−0.587351	−	1.01732i
$675$	0.519081	+	0.899075i	0.0199794	+	0.0346054i
$676$	−11.6554	+	3.72707i	−0.448286	+	0.143349i
$677$	10.8470	−	18.7875i	0.416883	−	0.722063i	−0.578741	−	0.815512i	$-0.696456\pi$
$677$	10.8470	−	18.7875i	0.416883	−	0.722063i	0.995624	+	0.0934485i	$0.0297891\pi$
$678$	4.33399	−	7.50668i	0.166446	−	0.288292i
$679$	13.9596	+	6.67341i	0.535720	+	0.256102i
$680$	6.73600	+	11.6671i	0.258314	+	0.447412i
$681$	−2.71464	+	4.70189i	−0.104025	+	0.180177i
$682$	−6.19735	+	10.7341i	−0.237309	+	0.411031i
$683$	−11.6479	+	20.1747i	−0.445694	+	0.771965i	−0.998100	−	0.0616101i	$-0.980376\pi$
$683$	−11.6479	+	20.1747i	−0.445694	+	0.771965i	0.552406	+	0.833575i	$0.313710\pi$
$684$	−1.50297	+	2.60322i	−0.0574675	+	0.0995367i
$685$	3.45883	+	5.99087i	0.132155	+	0.228900i
$686$	23.0972	−	21.8033i	0.881856	−	0.832452i
$687$	8.67170	−	15.0198i	0.330846	−	0.573042i
$688$	16.0808	−	27.8527i	0.613074	−	1.06188i
$689$	−6.56810	−	42.1046i	−0.250225	−	1.60406i
$690$	−7.31599	−	12.6717i	−0.278515	−	0.482402i
$691$	−15.6725	−	27.1456i	−0.596212	−	1.03267i	−0.993375	−	0.114921i	$-0.963339\pi$
$691$	−15.6725	−	27.1456i	−0.596212	−	1.03267i	0.397163	−	0.917748i	$-0.369995\pi$
$692$	9.43202	−	16.3367i	0.358552	−	0.621030i
$693$	−2.26501	+	1.55377i	−0.0860405	+	0.0590230i
$694$	21.1291			0.802049
$695$	9.23188			0.350185
$696$	7.28853	−	12.6241i	0.276271	−	0.478516i
$697$	−7.67275	−	13.2896i	−0.290626	−	0.503379i
$698$	−14.7397			−0.557904
$699$	−10.0164	+	17.3490i	−0.378857	+	0.656199i
$700$	2.13204	−	1.46256i	0.0805835	−	0.0552795i
$701$	−36.5409			−1.38013			−0.690066	−	0.723746i	$-0.742419\pi$
$701$	−36.5409			−1.38013			−0.690066	+	0.723746i	$0.742419\pi$
$702$	0.953083	+	6.10970i	0.0359718	+	0.230596i
$703$	−4.51331	−	7.81728i	−0.170223	−	0.294834i
$704$	−1.58289			−0.0596573
$705$	12.0148	+	20.8103i	0.452504	+	0.783761i
$706$	25.0091	+	43.3171i	0.941232	+	1.63026i
$707$	−40.4250	+	27.7312i	−1.52034	+	1.04294i
$708$	4.20825	+	7.28890i	0.158156	+	0.273934i
$709$	32.9378			1.23700			0.618502	−	0.785783i	$-0.287740\pi$
$709$	32.9378			1.23700			0.618502	+	0.785783i	$0.287740\pi$
$710$	−6.86981	−	11.8989i	−0.257819	−	0.446556i
$711$	−0.211818	+	0.366880i	−0.00794381	+	0.0137591i
$712$	−4.81609	−	8.34170i	−0.180490	−	0.312619i
$713$	12.0852	−	20.9322i	0.452594	−	0.783916i
$714$	11.2982	−	7.75045i	0.422824	−	0.290053i
$715$	7.16160	−	5.77175i	0.267829	−	0.215851i
$716$	4.75125	−	8.22941i	0.177563	−	0.307547i
$717$	8.30497			0.310155
$718$	−6.17147			−0.230317
$719$	8.58636			0.320217			0.160109	−	0.987099i	$-0.448816\pi$
$719$	8.58636			0.320217			0.160109	+	0.987099i	$0.448816\pi$
$720$	12.2779			0.457569
$721$	0.416990	+	5.35843i	0.0155295	+	0.199558i
$722$	−7.54790	−	13.0734i	−0.280904	−	0.486540i
$723$	10.2953	−	17.8320i	0.382886	−	0.663178i
$724$	−9.36395	+	16.2188i	−0.348009	+	0.602769i
$725$	8.33472			0.309544
$726$	8.50840	+	14.7370i	0.315776	+	0.546941i
$727$	31.5760			1.17109			0.585545	−	0.810640i	$-0.300881\pi$
$727$	31.5760			1.17109			0.585545	+	0.810640i	$0.300881\pi$
$728$	−16.8550	+	3.98937i	−0.624688	+	0.147856i
$729$	1.00000			0.0370370
$730$	31.6372	+	54.7972i	1.17095	+	2.02814i
$731$	19.4358			0.718858
$732$	−1.22788	+	2.12676i	−0.0453839	+	0.0786073i
$733$	7.35414	−	12.7377i	0.271631	−	0.470479i	−0.697648	−	0.716440i	$-0.745770\pi$
$733$	7.35414	−	12.7377i	0.271631	−	0.470479i	0.969280	+	0.245961i	$0.0791035\pi$
$734$	26.6390	+	46.1401i	0.983263	+	1.70306i
$735$	10.8014	+	13.3866i	0.398416	+	0.493770i
$736$	−17.1441			−0.631939
$737$	11.6482			0.429067
$738$	−8.71596			−0.320839
$739$	−14.1659			−0.521102			−0.260551	−	0.965460i	$-0.583904\pi$
$739$	−14.1659			−0.521102			−0.260551	+	0.965460i	$0.583904\pi$
$740$	3.26902	−	5.66211i	0.120172	−	0.208143i
$741$	10.7396	+	4.15131i	0.394529	+	0.152502i
$742$	4.16077	+	53.4670i	0.152747	+	1.96283i
$743$	−21.4265	+	37.1119i	−0.786063	+	1.36150i	0.142298	+	0.989824i	$0.454551\pi$
$743$	−21.4265	+	37.1119i	−0.786063	+	1.36150i	−0.928362	+	0.371678i	$0.878783\pi$
$744$	6.31999	+	10.9465i	0.231702	+	0.401320i
$745$	8.27709	−	14.3363i	0.303249	−	0.525243i
$746$	−20.1193	−	34.8477i	−0.736621	−	1.27586i
$747$	−1.34088			−0.0490603
$748$	1.47535	+	2.55539i	0.0539442	+	0.0934342i
$749$	5.81636	+	2.78052i	0.212525	+	0.101598i
$750$	−8.34811	−	14.4594i	−0.304830	−	0.527981i
$751$	0.310328	+	0.537504i	0.0113240	+	0.0196138i	0.871632	−	0.490161i	$-0.163062\pi$
$751$	0.310328	+	0.537504i	0.0113240	+	0.0196138i	−0.860308	+	0.509775i	$0.829729\pi$
$752$	48.8614			1.78179
$753$	−5.22288	−	9.04629i	−0.190332	−	0.329665i
$754$	46.3050	+	17.8988i	1.68633	+	0.651837i
$755$	−13.2702			−0.482954
$756$	−0.193220	−	2.48292i	−0.00702733	−	0.0903031i
$757$	2.21558	−	3.83750i	0.0805266	−	0.139476i	−0.822950	−	0.568114i	$-0.807673\pi$
$757$	2.21558	−	3.83750i	0.0805266	−	0.139476i	0.903476	+	0.428638i	$0.141006\pi$
$758$	16.0194			0.581851
$759$	1.80226	+	3.12160i	0.0654178	+	0.113307i
$760$	7.12397	−	12.3391i	0.258413	−	0.447585i
$761$	21.0044			0.761409			0.380704	−	0.924697i	$-0.375682\pi$
$761$	21.0044			0.761409			0.380704	+	0.924697i	$0.375682\pi$
$762$	−6.31972			−0.228939
$763$	−37.5068	−	17.9302i	−1.35784	−	0.649117i
$764$	−7.19024	+	12.4539i	−0.260134	+	0.450565i
$765$	3.70986	+	6.42567i	0.134130	+	0.232320i
$766$	10.0169	+	17.3497i	0.361924	+	0.626871i
$767$	25.1014	−	20.2300i	0.906360	−	0.730463i
$768$	9.18600	−	15.9106i	0.331471	−	0.574125i
$769$	−5.85570	+	10.1424i	−0.211162	+	0.365743i	−0.952078	−	0.305854i	$-0.901058\pi$
$769$	−5.85570	+	10.1424i	−0.211162	+	0.365743i	0.740917	+	0.671597i	$0.234391\pi$
$770$	−9.54533	+	6.54801i	−0.343990	+	0.235974i
$771$	3.61689	+	6.26463i	0.130259	+	0.225615i
$772$	−12.0806	+	20.9242i	−0.434790	+	0.753079i
$773$	−4.02075	+	6.96415i	−0.144616	+	0.250483i	−0.929230	−	0.369502i	$-0.879528\pi$
$773$	−4.02075	+	6.96415i	−0.144616	+	0.250483i	0.784613	+	0.619985i	$0.212861\pi$
$774$	5.51958	−	9.56019i	0.198397	−	0.343634i
$775$	−3.61357	+	6.25890i	−0.129803	+	0.224826i
$776$	5.30923	+	9.19585i	0.190590	+	0.330112i
$777$	6.74723	+	3.22553i	0.242055	+	0.115715i
$778$	−16.0241	+	27.7546i	−0.574493	+	0.995052i
$779$	−8.11467	+	14.0550i	−0.290738	+	0.503573i
$780$	1.28540	+	8.24003i	0.0460248	+	0.295040i
$781$	1.69234	+	2.93122i	0.0605568	+	0.104887i
$782$	−8.98993	−	15.5710i	−0.321479	−	0.556818i
$783$	4.01417	−	6.95275i	0.143455	−	0.248471i
$784$	34.5548	−	5.41083i	1.23410	−	0.193244i
$785$	−28.6380			−1.02214
$786$	3.16985			0.113065
$787$	−22.0887	+	38.2587i	−0.787377	+	1.36378i	0.140192	+	0.990124i	$0.455228\pi$
$787$	−22.0887	+	38.2587i	−0.787377	+	1.36378i	−0.927569	+	0.373653i	$0.878105\pi$
$788$	7.38215	+	12.7863i	0.262978	+	0.455492i
$789$	1.70621			0.0607426
$790$	−0.892659	+	1.54613i	−0.0317594	+	0.0550088i
$791$	12.0643	+	5.76739i	0.428959	+	0.205065i
$792$	−1.88499			−0.0669803
$793$	8.77395	+	3.39150i	0.311572	+	0.120436i
$794$	8.09843	+	14.0269i	0.287403	+	0.497796i
$795$	−29.0423			−1.03002
$796$	2.70664	+	4.68804i	0.0959343	+	0.166163i
$797$	−9.83025	−	17.0265i	−0.348205	−	0.603109i	0.637725	−	0.770264i	$-0.279875\pi$
$797$	−9.83025	−	17.0265i	−0.348205	−	0.603109i	−0.985931	+	0.167155i	$0.946542\pi$
$798$	−13.0731	−	6.24964i	−0.462784	−	0.221235i
$799$	14.7639	+	25.5718i	0.522308	+	0.904664i
$800$	5.12622			0.181239
$801$	−2.65247	−	4.59421i	−0.0937203	−	0.162328i
$802$	8.89447	−	15.4057i	0.314075	−	0.543993i
$803$	−7.79366	−	13.4990i	−0.275032	−	0.476370i
$804$	−5.28067	+	9.14638i	−0.186235	+	0.322568i
$805$	18.6139	−	12.7690i	0.656055	−	0.450048i
$806$	−33.5169	+	27.0123i	−1.18058	+	0.951466i
$807$	10.9941	−	19.0424i	0.387012	−	0.670324i
$808$	−33.6427			−1.18355
$809$	−0.872672			−0.0306815			−0.0153407	−	0.999882i	$-0.504883\pi$
$809$	−0.872672			−0.0306815			−0.0153407	+	0.999882i	$0.504883\pi$
$810$	4.21426			0.148074
$811$	35.1149			1.23305			0.616526	−	0.787335i	$-0.288540\pi$
$811$	35.1149			1.23305			0.616526	+	0.787335i	$0.288540\pi$
$812$	−18.0388	−	8.62347i	−0.633036	−	0.302625i
$813$	−11.8251	−	20.4817i	−0.414724	−	0.718324i
$814$	−2.51637	+	4.35848i	−0.0881987	+	0.152765i
$815$	29.7963	−	51.6088i	1.04372	−	1.80778i
$816$	15.0871			0.528154
$817$	−10.2776	−	17.8013i	−0.359568	−	0.622790i
$818$	−39.2517			−1.37240
$819$	−9.28292	+	2.19715i	−0.324371	+	0.0767747i
$820$	−11.7550			−0.410503
$821$	10.1024	+	17.4978i	0.352575	+	0.610678i	0.986700	−	0.162553i	$-0.0519727\pi$
$821$	10.1024	+	17.4978i	0.352575	+	0.610678i	−0.634125	+	0.773231i	$0.718639\pi$
$822$	4.82810			0.168399
$823$	−13.9713	+	24.1991i	−0.487010	+	0.843526i	−0.999888	−	0.0149350i	$-0.995246\pi$
$823$	−13.9713	+	24.1991i	−0.487010	+	0.843526i	0.512878	+	0.858461i	$0.328579\pi$
$824$	−1.84422	+	3.19429i	−0.0642466	+	0.111278i
$825$	−0.538890	−	0.933385i	−0.0187618	−	0.0324963i
$826$	−33.4564	+	22.9508i	−1.16410	+	0.798560i
$827$	−44.6141			−1.55138			−0.775692	−	0.631112i	$-0.782599\pi$
$827$	−44.6141			−1.55138			−0.775692	+	0.631112i	$0.782599\pi$
$828$	−3.26819			−0.113577
$829$	−28.1051			−0.976129			−0.488065	−	0.872807i	$-0.662297\pi$
$829$	−28.1051			−0.976129			−0.488065	+	0.872807i	$0.662297\pi$
$830$	−5.65082			−0.196143
$831$	−14.9643	+	25.9190i	−0.519107	+	0.899119i
$832$	−5.12764	−	1.98205i	−0.177769	−	0.0687152i
$833$	13.2728	+	16.4495i	0.459875	+	0.569940i
$834$	3.22164	−	5.58004i	0.111556	−	0.193221i
$835$	−20.2286	−	35.0370i	−0.700040	−	1.21251i
$836$	1.56033	−	2.70257i	0.0539651	−	0.0934702i
$837$	3.48074	+	6.02882i	0.120312	+	0.208387i
$838$	14.8550			0.513158
$839$	18.8751	+	32.6926i	0.651640	+	1.12867i	0.982725	+	0.185072i	$0.0592518\pi$
$839$	18.8751	+	32.6926i	0.651640	+	1.12867i	−0.331085	+	0.943601i	$0.607415\pi$
$840$	0.915846	+	11.7689i	0.0315997	+	0.406065i
$841$	−17.7271	−	30.7043i	−0.611280	−	1.05877i
$842$	−0.986390	−	1.70848i	−0.0339933	−	0.0588780i
$843$	27.8636			0.959674
$844$	9.76788	+	16.9185i	0.336224	+	0.582357i
$845$	30.4267	−	9.72959i	1.04671	−	0.334708i
$846$	16.7712			0.576606
$847$	−21.6478	+	14.8502i	−0.743826	+	0.510258i
$848$	−29.5270	+	51.1422i	−1.01396	+	1.75623i
$849$	19.4075			0.666065
$850$	2.68806	+	4.65586i	0.0921998	+	0.159695i
$851$	4.90706	−	8.49928i	0.168212	−	0.291352i
$852$	−3.06887			−0.105138
$853$	7.52465			0.257639			0.128820	−	0.991668i	$-0.458881\pi$
$853$	7.52465			0.257639			0.128820	+	0.991668i	$0.458881\pi$
$854$	−10.6804	−	5.10578i	−0.365475	−	0.174716i
$855$	3.92353	−	6.79576i	0.134182	−	0.232410i
$856$	2.21213	+	3.83152i	0.0756089	+	0.130959i
$857$	7.72284	+	13.3764i	0.263807	+	0.456928i	0.967250	−	0.253824i	$-0.0816884\pi$
$857$	7.72284	+	13.3764i	0.263807	+	0.456928i	−0.703443	+	0.710751i	$0.748355\pi$
$858$	−0.989454	−	6.34286i	−0.0337794	−	0.216542i
$859$	4.27437	−	7.40343i	0.145840	−	0.252602i	−0.783846	−	0.620955i	$-0.786745\pi$
$859$	4.27437	−	7.40343i	0.145840	−	0.252602i	0.929686	+	0.368353i	$0.120078\pi$
$860$	7.44414	−	12.8936i	0.253843	−	0.439669i
$861$	−1.04321	−	13.4055i	−0.0355525	−	0.456859i
$862$	7.51220	+	13.0115i	0.255866	+	0.443174i
$863$	−27.6867	+	47.9548i	−0.942468	+	1.63240i	−0.181724	+	0.983350i	$0.558168\pi$
$863$	−27.6867	+	47.9548i	−0.942468	+	1.63240i	−0.760744	+	0.649052i	$0.775166\pi$
$864$	2.46889	−	4.27625i	0.0839935	−	0.145481i
$865$	−24.6225	+	42.6474i	−0.837189	+	1.45005i
$866$	−0.794230	+	1.37565i	−0.0269890	+	0.0467464i
$867$	−3.94131	−	6.82655i	−0.133854	−	0.231842i
$868$	14.2966	−	9.80731i	0.485257	−	0.332882i
$869$	0.219902	−	0.380881i	0.00745966	−	0.0129205i
$870$	16.9168	−	29.3007i	0.573532	−	0.993387i
$871$	37.7335	+	14.5856i	1.27855	+	0.494213i
$872$	−14.2649	−	24.7075i	−0.483071	−	0.836703i
$873$	2.92406	+	5.06463i	0.0989646	+	0.171412i
$874$	−9.50771	+	16.4678i	−0.321603	+	0.557033i
$875$	21.2399	−	14.5704i	0.718041	−	0.492569i
$876$	14.1329			0.477507
$877$	49.1212			1.65870			0.829352	−	0.558726i	$-0.188710\pi$
$877$	49.1212			1.65870			0.829352	+	0.558726i	$0.188710\pi$
$878$	10.6403	−	18.4295i	0.359093	−	0.621967i
$879$	2.20711	+	3.82282i	0.0744438	+	0.128940i
$880$	−12.7464			−0.429682
$881$	−3.45324	+	5.98118i	−0.116342	+	0.201511i	−0.918316	−	0.395849i	$-0.870450\pi$
$881$	−3.45324	+	5.98118i	−0.116342	+	0.201511i	0.801973	+	0.597360i	$0.203784\pi$
$882$	11.8606	−	1.85722i	0.399368	−	0.0625358i
$883$	−25.4087			−0.855071			−0.427536	−	0.903998i	$-0.640618\pi$
$883$	−25.4087			−0.855071			−0.427536	+	0.903998i	$0.640618\pi$
$884$	1.57951	+	10.1254i	0.0531246	+	0.340553i
$885$	−10.9857	−	19.0278i	−0.369281	−	0.639613i
$886$	−5.53841			−0.186066
$887$	21.0930	+	36.5342i	0.708234	+	1.22670i	0.965512	+	0.260360i	$0.0838413\pi$
$887$	21.0930	+	36.5342i	0.708234	+	1.22670i	−0.257277	+	0.966338i	$0.582825\pi$
$888$	2.56616	+	4.44473i	0.0861148	+	0.149155i
$889$	−0.756405	−	9.72000i	−0.0253690	−	0.325998i
$890$	−11.1782	−	19.3612i	−0.374694	−	0.648989i
$891$	−1.03816			−0.0347797
$892$	5.35285	+	9.27140i	0.179227	+	0.310429i
$893$	15.6142	−	27.0446i	0.522510	−	0.905013i
$894$	−5.77690	−	10.0059i	−0.193208	−	0.334647i
$895$	−12.4032	+	21.4830i	−0.414594	+	0.718098i
$896$	29.8150	+	14.2531i	0.996048	+	0.476163i
$897$	1.92949	+	12.3689i	0.0644239	+	0.412987i
$898$	17.0532	−	29.5370i	0.569072	−	0.985662i
$899$	55.8892			1.86401
$900$	0.977216			0.0325739
$901$	−35.6873			−1.18892
$902$	9.04858			0.301285
$903$	15.3646	+	7.34510i	0.511303	+	0.244430i
$904$	4.58841	+	7.94737i	0.152608	+	0.264325i
$905$	24.4448	−	42.3396i	0.812572	−	1.40742i
$906$	−4.63090	+	8.02096i	−0.153851	+	0.266479i
$907$	27.3859			0.909335			0.454667	−	0.890661i	$-0.349758\pi$
$907$	27.3859			0.909335			0.454667	+	0.890661i	$0.349758\pi$
$908$	2.55527	+	4.42586i	0.0847997	+	0.146877i
$909$	−18.5287			−0.614560
$910$	−39.1206	+	9.25937i	−1.29684	+	0.306945i
$911$	46.0844			1.52685			0.763423	−	0.645899i	$-0.223517\pi$
$911$	46.0844			1.52685			0.763423	+	0.645899i	$0.223517\pi$
$912$	−7.97803	−	13.8184i	−0.264179	−	0.457571i
$913$	1.39205			0.0460702
$914$	−0.0677214	+	0.117297i	−0.00224002	+	0.00387984i
$915$	3.20542	−	5.55194i	0.105968	−	0.183542i
$916$	−8.16262	−	14.1381i	−0.269701	−	0.467135i
$917$	0.379398	+	4.87537i	0.0125288	+	0.160999i
$918$	5.17850			0.170916
$919$	−40.1277			−1.32369			−0.661845	−	0.749641i	$-0.730226\pi$
$919$	−40.1277			−1.32369			−0.661845	+	0.749641i	$0.730226\pi$
$920$	15.4910			0.510722
$921$	9.06995			0.298865
$922$	−4.21860	+	7.30683i	−0.138932	+	0.240638i
$923$	1.81182	+	11.6146i	0.0596367	+	0.382299i
$924$	0.200593	+	2.57768i	0.00659904	+	0.0847994i
$925$	−1.46725	+	2.54136i	−0.0482430	+	0.0835593i
$926$	1.07049	+	1.85414i	0.0351784	+	0.0609308i
$927$	−1.01571	+	1.75926i	−0.0333603	+	0.0577817i
$928$	−19.8211	−	34.3312i	−0.650660	−	1.12698i
$929$	−47.1060			−1.54550			−0.772750	−	0.634711i	$-0.781119\pi$
$929$	−47.1060			−1.54550			−0.772750	+	0.634711i	$0.781119\pi$
$930$	14.6688	+	25.4070i	0.481008	+	0.833130i
$931$	8.04751	−	20.8551i	0.263746	−	0.683497i
$932$	9.42842	+	16.3305i	0.308838	+	0.534924i
$933$	11.8691	+	20.5579i	0.388578	+	0.673037i
$934$	−49.1906			−1.60957
$935$	−3.85144	−	6.67088i	−0.125955	−	0.218161i
$936$	−6.10629	−	2.36034i	−0.199590	−	0.0771501i
$937$	43.2558			1.41310			0.706552	−	0.707661i	$-0.250249\pi$
$937$	43.2558			1.41310			0.706552	+	0.707661i	$0.250249\pi$
$938$	−45.9323	−	21.9580i	−1.49974	−	0.716955i
$939$	6.48059	−	11.2247i	0.211486	−	0.366304i
$940$	22.6190			0.737750
$941$	−21.2053	−	36.7287i	−0.691274	−	1.19732i	−0.971421	−	0.237365i	$-0.923716\pi$
$941$	−21.2053	−	36.7287i	−0.691274	−	1.19732i	0.280146	−	0.959957i	$-0.409617\pi$
$942$	−9.99379	+	17.3098i	−0.325615	+	0.563982i
$943$	−17.6452			−0.574608
$944$	−44.6762			−1.45409
$945$	0.504403	+	6.48172i	0.0164082	+	0.210850i
$946$	−5.73022	+	9.92503i	−0.186305	+	0.322691i
$947$	−21.9080	−	37.9458i	−0.711914	−	1.23307i	−0.964138	−	0.265403i	$-0.914495\pi$
$947$	−21.9080	−	37.9458i	−0.711914	−	1.23307i	0.252223	−	0.967669i	$-0.418838\pi$
$948$	0.199384	+	0.345342i	0.00647568	+	0.0112162i
$949$	−8.34387	−	53.4881i	−0.270854	−	1.73630i
$950$	2.84289	−	4.92402i	0.0922354	−	0.159756i
$951$	−15.7012	+	27.1953i	−0.509146	+	0.881867i
$952$	1.12540	+	14.4616i	0.0364743	+	0.468704i
$953$	8.09343	+	14.0182i	0.262172	+	0.454095i	0.966819	−	0.255463i	$-0.0822279\pi$
$953$	8.09343	+	14.0182i	0.262172	+	0.454095i	−0.704647	+	0.709558i	$0.748895\pi$
$954$	−10.1349	+	17.5541i	−0.328128	+	0.568335i
$955$	18.7703	−	32.5111i	0.607392	−	1.05203i
$956$	3.90871	−	6.77008i	0.126417	−	0.218960i
$957$	−4.16736	+	7.21808i	−0.134712	+	0.233327i
$958$	−5.98432	−	10.3651i	−0.193345	−	0.334883i
$959$	0.577874	+	7.42583i	0.0186605	+	0.239793i
$960$	−1.87330	+	3.24465i	−0.0604604	+	0.104721i
$961$	−8.73113	+	15.1228i	−0.281649	+	0.487831i
$962$	−13.6092	+	10.9680i	−0.438777	+	0.353624i
$963$	1.21833	+	2.11021i	0.0392602	+	0.0680007i
$964$	−9.69091	−	16.7851i	−0.312123	−	0.540613i
$965$	31.5366	−	54.6231i	1.01520	−	1.75838i
$966$	−1.22230	−	15.7068i	−0.0393268	−	0.505359i
$967$	−42.5994			−1.36990			−0.684952	−	0.728588i	$-0.740177\pi$
$967$	−42.5994			−1.36990			−0.684952	+	0.728588i	$0.740177\pi$
$968$	−18.0158			−0.579049
$969$	4.82126	−	8.35066i	0.154881	−	0.268262i
$970$	12.3228	+	21.3437i	0.395661	+	0.685304i
$971$	3.00538			0.0964472			0.0482236	−	0.998837i	$-0.484644\pi$
$971$	3.00538			0.0964472			0.0482236	+	0.998837i	$0.484644\pi$
$972$	0.470647	−	0.815185i	0.0150960	−	0.0261471i
$973$	8.96795	+	4.28715i	0.287499	+	0.137440i
$974$	3.30710			0.105966
$975$	−0.576934	−	3.69842i	−0.0184767	−	0.118444i
$976$	−6.51782	−	11.2892i	−0.208630	−	0.361359i
$977$	−40.8447			−1.30674			−0.653368	−	0.757040i	$-0.726645\pi$
$977$	−40.8447			−1.30674			−0.653368	+	0.757040i	$0.726645\pi$
$978$	−20.7960	−	36.0197i	−0.664983	−	1.15178i
$979$	2.75369	+	4.76953i	0.0880083	+	0.152435i
$980$	15.9962	−	2.50479i	0.510979	−	0.0800126i
$981$	−7.85642	−	13.6077i	−0.250836	−	0.434461i
$982$	50.4105			1.60866
$983$	30.1629	+	52.2437i	0.962047	+	1.66631i	0.717348	+	0.696715i	$0.245356\pi$
$983$	30.1629	+	52.2437i	0.962047	+	1.66631i	0.244699	+	0.969599i	$0.421311\pi$
$984$	4.61382	−	7.99136i	0.147083	−	0.254755i
$985$	−19.2712	−	33.3788i	−0.614033	−	1.06354i
$986$	20.7874	−	36.0048i	0.662006	−	1.14663i
$987$	2.00734	+	25.7948i	0.0638943	+	0.821059i
$988$	8.43865	−	6.80096i	0.268469	−	0.216367i
$989$	11.1743	−	19.3544i	0.355321	−	0.615433i
$990$	−4.37509			−0.139049
$991$	−45.9189			−1.45866			−0.729332	−	0.684160i	$-0.760169\pi$
$991$	−45.9189			−1.45866			−0.729332	+	0.684160i	$0.760169\pi$
$992$	34.3743			1.09139
$993$	11.5233			0.365681
$994$	−1.14775	−	14.7489i	−0.0364045	−	0.467808i
$995$	−7.06574	−	12.2382i	−0.223999	−	0.387978i
$996$	−0.631082	+	1.09307i	−0.0199966	+	0.0346351i
$997$	−13.2885	+	23.0163i	−0.420850	+	0.728934i	−0.996023	−	0.0890978i	$-0.971602\pi$
$997$	−13.2885	+	23.0163i	−0.420850	+	0.728934i	0.575172	+	0.818032i	$0.304935\pi$
$998$	−34.0569			−1.07805
$999$	1.41332	+	2.44794i	0.0447154	+	0.0774494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.b.100.7	✓	16
3.2	odd	2		819.2.n.e.100.2		16
7.4	even	3		273.2.l.b.256.2	yes	16
13.3	even	3		273.2.l.b.16.2	yes	16
21.11	odd	6		819.2.s.e.802.7		16
39.29	odd	6		819.2.s.e.289.7		16
91.81	even	3	inner	273.2.j.b.172.7	yes	16
273.263	odd	6		819.2.n.e.172.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.7	✓	16	1.1	even	1	trivial
273.2.j.b.172.7	yes	16	91.81	even	3	inner
273.2.l.b.16.2	yes	16	13.3	even	3
273.2.l.b.256.2	yes	16	7.4	even	3
819.2.n.e.100.2		16	3.2	odd	2
819.2.n.e.172.2		16	273.263	odd	6
819.2.s.e.289.7		16	39.29	odd	6
819.2.s.e.802.7		16	21.11	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.857510 + 1.48525i) q^{2} -1.00000 q^{3} +(-0.470647 + 0.815185i) q^{4} +(1.22863 - 2.12806i) q^{5} +(-0.857510 - 1.48525i) q^{6} +(2.18175 - 1.49666i) q^{7} +1.81570 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.857510 + 1.48525i) q^{2} -1.00000 q^{3} +(-0.470647 + 0.815185i) q^{4} +(1.22863 - 2.12806i) q^{5} +(-0.857510 - 1.48525i) q^{6} +(2.18175 - 1.49666i) q^{7} +1.81570 q^{8} +1.00000 q^{9} +4.21426 q^{10} -1.03816 q^{11} +(0.470647 - 0.815185i) q^{12} +(-3.36305 - 1.29996i) q^{13} +(4.09378 + 1.95704i) q^{14} +(-1.22863 + 2.12806i) q^{15} +(2.49828 + 4.32714i) q^{16} +(-1.50975 + 2.61496i) q^{17} +(0.857510 + 1.48525i) q^{18} +3.19341 q^{19} +(1.15651 + 2.00313i) q^{20} +(-2.18175 + 1.49666i) q^{21} +(-0.890235 - 1.54193i) q^{22} +(1.73601 + 3.00685i) q^{23} -1.81570 q^{24} +(-0.519081 - 0.899075i) q^{25} +(-0.953083 - 6.10970i) q^{26} -1.00000 q^{27} +(0.193220 + 2.48292i) q^{28} +(-4.01417 + 6.95275i) q^{29} -4.21426 q^{30} +(-3.48074 - 6.02882i) q^{31} +(-2.46889 + 4.27625i) q^{32} +1.03816 q^{33} -5.17850 q^{34} +(-0.504403 - 6.48172i) q^{35} +(-0.470647 + 0.815185i) q^{36} +(-1.41332 - 2.44794i) q^{37} +(2.73838 + 4.74302i) q^{38} +(3.36305 + 1.29996i) q^{39} +(2.23083 - 3.86391i) q^{40} +(-2.54107 + 4.40125i) q^{41} +(-4.09378 - 1.95704i) q^{42} +(-3.21838 - 5.57439i) q^{43} +(0.488608 - 0.846294i) q^{44} +(1.22863 - 2.12806i) q^{45} +(-2.97729 + 5.15682i) q^{46} +(4.88951 - 8.46887i) q^{47} +(-2.49828 - 4.32714i) q^{48} +(2.52003 - 6.53065i) q^{49} +(0.890235 - 1.54193i) q^{50} +(1.50975 - 2.61496i) q^{51} +(2.64252 - 2.12969i) q^{52} +(5.90947 + 10.2355i) q^{53} +(-0.857510 - 1.48525i) q^{54} +(-1.27552 + 2.20927i) q^{55} +(3.96140 - 2.71748i) q^{56} -3.19341 q^{57} -13.7688 q^{58} +(-4.47070 + 7.74348i) q^{59} +(-1.15651 - 2.00313i) q^{60} -2.60893 q^{61} +(5.96954 - 10.3396i) q^{62} +(2.18175 - 1.49666i) q^{63} +1.52470 q^{64} +(-6.89834 + 5.55958i) q^{65} +(0.890235 + 1.54193i) q^{66} -11.2200 q^{67} +(-1.42112 - 2.46145i) q^{68} +(-1.73601 - 3.00685i) q^{69} +(9.19445 - 6.30731i) q^{70} +(-1.63013 - 2.82347i) q^{71} +1.81570 q^{72} +(7.50717 + 13.0028i) q^{73} +(2.42387 - 4.19827i) q^{74} +(0.519081 + 0.899075i) q^{75} +(-1.50297 + 2.60322i) q^{76} +(-2.26501 + 1.55377i) q^{77} +(0.953083 + 6.10970i) q^{78} +(-0.211818 + 0.366880i) q^{79} +12.2779 q^{80} +1.00000 q^{81} -8.71596 q^{82} -1.34088 q^{83} +(-0.193220 - 2.48292i) q^{84} +(3.70986 + 6.42567i) q^{85} +(5.51958 - 9.56019i) q^{86} +(4.01417 - 6.95275i) q^{87} -1.88499 q^{88} +(-2.65247 - 4.59421i) q^{89} +4.21426 q^{90} +(-9.28292 + 2.19715i) q^{91} -3.26819 q^{92} +(3.48074 + 6.02882i) q^{93} +16.7712 q^{94} +(3.92353 - 6.79576i) q^{95} +(2.46889 - 4.27625i) q^{96} +(2.92406 + 5.06463i) q^{97} +(11.8606 - 1.85722i) q^{98} -1.03816 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more