LMFDB - Embedded newform 273.2.bl.c.88.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(88,273)]

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, 4, 5]))

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

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

chi := DirichletCharacter("273.88");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			88.2
Root			$-1.18541 + 0.771231i$ of defining polynomial
Character	$\chi$	$=$	273.88
Dual form			273.2.bl.c.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33581 - 0.771231i) q^{2} +1.00000 q^{3} +(0.189594 + 0.328387i) q^{4} +(-1.27069 + 0.733632i) q^{5} +(-1.33581 - 0.771231i) q^{6} +(1.52469 + 2.16225i) q^{7} +2.50004i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.33581 - 0.771231i) q^{2} +1.00000 q^{3} +(0.189594 + 0.328387i) q^{4} +(-1.27069 + 0.733632i) q^{5} +(-1.33581 - 0.771231i) q^{6} +(1.52469 + 2.16225i) q^{7} +2.50004i q^{8} +1.00000 q^{9} +2.26320 q^{10} +2.23204i q^{11} +(0.189594 + 0.328387i) q^{12} +(3.57691 - 0.453537i) q^{13} +(-0.369112 - 4.06424i) q^{14} +(-1.27069 + 0.733632i) q^{15} +(2.30730 - 3.99635i) q^{16} +(1.26061 + 2.18344i) q^{17} +(-1.33581 - 0.771231i) q^{18} -0.957578i q^{19} +(-0.481830 - 0.278185i) q^{20} +(1.52469 + 2.16225i) q^{21} +(1.72142 - 2.98158i) q^{22} +(1.32450 - 2.29410i) q^{23} +2.50004i q^{24} +(-1.42357 + 2.46569i) q^{25} +(-5.12786 - 2.15279i) q^{26} +1.00000 q^{27} +(-0.420980 + 0.910638i) q^{28} +(-0.728078 - 1.26107i) q^{29} +2.26320 q^{30} +(2.89114 + 1.66920i) q^{31} +(-1.83403 + 1.05888i) q^{32} +2.23204i q^{33} -3.88889i q^{34} +(-3.52370 - 1.62898i) q^{35} +(0.189594 + 0.328387i) q^{36} +(6.41759 + 3.70520i) q^{37} +(-0.738514 + 1.27914i) q^{38} +(3.57691 - 0.453537i) q^{39} +(-1.83411 - 3.17677i) q^{40} +(3.52497 - 2.03514i) q^{41} +(-0.369112 - 4.06424i) q^{42} +(3.00991 - 5.21332i) q^{43} +(-0.732971 + 0.423181i) q^{44} +(-1.27069 + 0.733632i) q^{45} +(-3.53857 + 2.04299i) q^{46} +(-9.05536 + 5.22812i) q^{47} +(2.30730 - 3.99635i) q^{48} +(-2.35062 + 6.59353i) q^{49} +(3.80323 - 2.19580i) q^{50} +(1.26061 + 2.18344i) q^{51} +(0.827097 + 1.08862i) q^{52} +(1.74412 - 3.02090i) q^{53} +(-1.33581 - 0.771231i) q^{54} +(-1.63749 - 2.83622i) q^{55} +(-5.40570 + 3.81180i) q^{56} -0.957578i q^{57} +2.24607i q^{58} +(-0.664540 + 0.383672i) q^{59} +(-0.481830 - 0.278185i) q^{60} -12.1139 q^{61} +(-2.57468 - 4.45947i) q^{62} +(1.52469 + 2.16225i) q^{63} -5.96263 q^{64} +(-4.21241 + 3.20044i) q^{65} +(1.72142 - 2.98158i) q^{66} +9.64946i q^{67} +(-0.478009 + 0.827936i) q^{68} +(1.32450 - 2.29410i) q^{69} +(3.45069 + 4.89359i) q^{70} +(-2.50519 - 1.44637i) q^{71} +2.50004i q^{72} +(-11.3623 - 6.56004i) q^{73} +(-5.71513 - 9.89889i) q^{74} +(-1.42357 + 2.46569i) q^{75} +(0.314456 - 0.181551i) q^{76} +(-4.82621 + 3.40317i) q^{77} +(-5.12786 - 2.15279i) q^{78} +(-1.88401 - 3.26320i) q^{79} +6.77083i q^{80} +1.00000 q^{81} -6.27825 q^{82} -3.89258i q^{83} +(-0.420980 + 0.910638i) q^{84} +(-3.20369 - 1.84965i) q^{85} +(-8.04135 + 4.64268i) q^{86} +(-0.728078 - 1.26107i) q^{87} -5.58018 q^{88} +(8.78828 + 5.07392i) q^{89} +2.26320 q^{90} +(6.43436 + 7.04266i) q^{91} +1.00447 q^{92} +(2.89114 + 1.66920i) q^{93} +16.1283 q^{94} +(0.702510 + 1.21678i) q^{95} +(-1.83403 + 1.05888i) q^{96} +(-5.44296 - 3.14250i) q^{97} +(8.22511 - 6.99484i) q^{98} +2.23204i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9	$ 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9} + 14 q^{10} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 27 q^{20} + 3 q^{21} + 7 q^{22} - 16 q^{23} + 10 q^{25} - q^{26} + 12 q^{27} + 24 q^{28} - 5 q^{29} + 14 q^{30} + 15 q^{31} - 6 q^{32} - 2 q^{35} + 5 q^{36} + 6 q^{37} + 24 q^{38} - q^{39} + 21 q^{40} - 15 q^{41} - 16 q^{42} - 13 q^{43} - 30 q^{44} + 6 q^{45} - 9 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} - 63 q^{50} - 55 q^{52} + 18 q^{53} - 3 q^{54} + 13 q^{55} - 21 q^{56} - 33 q^{59} - 27 q^{60} - 52 q^{61} - 13 q^{62} + 3 q^{63} - 4 q^{64} - 41 q^{65} + 7 q^{66} - 16 q^{69} - 42 q^{70} - 15 q^{71} - 18 q^{73} + 38 q^{74} + 10 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 12 q^{81} + 28 q^{82} + 24 q^{84} - 12 q^{85} - 15 q^{86} - 5 q^{87} - 32 q^{88} + 12 q^{89} + 14 q^{90} + 49 q^{91} - 40 q^{92} + 15 q^{93} + 6 q^{94} - 28 q^{95} - 6 q^{96} + 45 q^{97} + 48 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9 + 14 * q^10 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 27 * q^20 + 3 * q^21 + 7 * q^22 - 16 * q^23 + 10 * q^25 - q^26 + 12 * q^27 + 24 * q^28 - 5 * q^29 + 14 * q^30 + 15 * q^31 - 6 * q^32 - 2 * q^35 + 5 * q^36 + 6 * q^37 + 24 * q^38 - q^39 + 21 * q^40 - 15 * q^41 - 16 * q^42 - 13 * q^43 - 30 * q^44 + 6 * q^45 - 9 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 - 63 * q^50 - 55 * q^52 + 18 * q^53 - 3 * q^54 + 13 * q^55 - 21 * q^56 - 33 * q^59 - 27 * q^60 - 52 * q^61 - 13 * q^62 + 3 * q^63 - 4 * q^64 - 41 * q^65 + 7 * q^66 - 16 * q^69 - 42 * q^70 - 15 * q^71 - 18 * q^73 + 38 * q^74 + 10 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 12 * q^81 + 28 * q^82 + 24 * q^84 - 12 * q^85 - 15 * q^86 - 5 * q^87 - 32 * q^88 + 12 * q^89 + 14 * q^90 + 49 * q^91 - 40 * q^92 + 15 * q^93 + 6 * q^94 - 28 * q^95 - 6 * q^96 + 45 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.33581	−	0.771231i	−0.944561	−	0.545343i	−0.0531739	−	0.998585i	$-0.516934\pi$
$2$	−1.33581	−	0.771231i	−0.944561	−	0.545343i	−0.891387	+	0.453243i	$0.850267\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.189594	+	0.328387i	0.0947971	+	0.164193i
$5$	−1.27069	+	0.733632i	−0.568269	+	0.328090i	−0.756458	−	0.654043i	$-0.773072\pi$
$5$	−1.27069	+	0.733632i	−0.568269	+	0.328090i	0.188189	+	0.982133i	$0.439738\pi$
$6$	−1.33581	−	0.771231i	−0.545343	−	0.314854i
$7$	1.52469	+	2.16225i	0.576280	+	0.817252i
$7$	1.52469	+	2.16225i	0.576280	+	0.817252i
$8$			2.50004i			0.883898i
$9$	1.00000			0.333333
$10$	2.26320			0.715686
$11$			2.23204i			0.672985i	0.941686	+	0.336492i	$0.109241\pi$
$11$			2.23204i			0.672985i	−0.941686	+	0.336492i	$0.890759\pi$
$12$	0.189594	+	0.328387i	0.0547311	+	0.0947971i
$13$	3.57691	−	0.453537i	0.992057	−	0.125789i
$13$	3.57691	−	0.453537i	0.992057	−	0.125789i
$14$	−0.369112	−	4.06424i	−0.0986493	−	1.08621i
$15$	−1.27069	+	0.733632i	−0.328090	+	0.189423i
$16$	2.30730	−	3.99635i	0.576824	−	0.999089i
$17$	1.26061	+	2.18344i	0.305743	+	0.529563i	0.977427	−	0.211276i	$-0.0677617\pi$
$17$	1.26061	+	2.18344i	0.305743	+	0.529563i	−0.671683	+	0.740838i	$0.734428\pi$
$18$	−1.33581	−	0.771231i	−0.314854	−	0.181781i
$19$		−	0.957578i		−	0.219684i	−0.993949	−	0.109842i	$-0.964966\pi$
$19$		−	0.957578i		−	0.219684i	0.993949	−	0.109842i	$-0.0350344\pi$
$20$	−0.481830	−	0.278185i	−0.107740	−	0.0622040i
$21$	1.52469	+	2.16225i	0.332715	+	0.471841i
$22$	1.72142	−	2.98158i	0.367007	−	0.635675i
$23$	1.32450	−	2.29410i	0.276178	−	0.478354i	−0.694254	−	0.719730i	$-0.744266\pi$
$23$	1.32450	−	2.29410i	0.276178	−	0.478354i	0.970432	+	0.241376i	$0.0775989\pi$
$24$			2.50004i			0.510319i
$25$	−1.42357	+	2.46569i	−0.284713	+	0.493138i
$26$	−5.12786	−	2.15279i	−1.00566	−	0.422196i
$27$	1.00000			0.192450
$28$	−0.420980	+	0.910638i	−0.0795577	+	0.172094i
$29$	−0.728078	−	1.26107i	−0.135201	−	0.234175i	0.790473	−	0.612496i	$-0.209835\pi$
$29$	−0.728078	−	1.26107i	−0.135201	−	0.234175i	−0.925674	+	0.378322i	$0.876501\pi$
$30$	2.26320			0.413202
$31$	2.89114	+	1.66920i	0.519264	+	0.299797i	0.736633	−	0.676292i	$-0.236414\pi$
$31$	2.89114	+	1.66920i	0.519264	+	0.299797i	−0.217369	+	0.976089i	$0.569748\pi$
$32$	−1.83403	+	1.05888i	−0.324213	+	0.187185i
$33$			2.23204i			0.388548i
$34$		−	3.88889i		−	0.666939i
$35$	−3.52370	−	1.62898i	−0.595615	−	0.275347i
$36$	0.189594	+	0.328387i	0.0315990	+	0.0547311i
$37$	6.41759	+	3.70520i	1.05505	+	0.609131i	0.924058	−	0.382253i	$-0.124852\pi$
$37$	6.41759	+	3.70520i	1.05505	+	0.609131i	0.130988	+	0.991384i	$0.458185\pi$
$38$	−0.738514	+	1.27914i	−0.119803	+	0.207505i
$39$	3.57691	−	0.453537i	0.572764	−	0.0726241i
$40$	−1.83411	−	3.17677i	−0.289998	−	0.502292i
$41$	3.52497	−	2.03514i	0.550507	−	0.317835i	−0.198819	−	0.980036i	$-0.563711\pi$
$41$	3.52497	−	2.03514i	0.550507	−	0.317835i	0.749327	+	0.662201i	$0.230377\pi$
$42$	−0.369112	−	4.06424i	−0.0569552	−	0.627126i
$43$	3.00991	−	5.21332i	0.459008	−	0.795024i	−0.539901	−	0.841728i	$-0.681538\pi$
$43$	3.00991	−	5.21332i	0.459008	−	0.795024i	0.998909	+	0.0467040i	$0.0148718\pi$
$44$	−0.732971	+	0.423181i	−0.110500	+	0.0637970i
$45$	−1.27069	+	0.733632i	−0.189423	+	0.109363i
$46$	−3.53857	+	2.04299i	−0.521733	+	0.301223i
$47$	−9.05536	+	5.22812i	−1.32086	+	0.762599i	−0.983866	−	0.178907i	$-0.942744\pi$
$47$	−9.05536	+	5.22812i	−1.32086	+	0.762599i	−0.336995	+	0.941507i	$0.609410\pi$
$48$	2.30730	−	3.99635i	0.333030	−	0.576824i
$49$	−2.35062	+	6.59353i	−0.335803	+	0.941932i
$50$	3.80323	−	2.19580i	0.537859	−	0.310533i
$51$	1.26061	+	2.18344i	0.176521	+	0.305743i
$52$	0.827097	+	1.08862i	0.114698	+	0.150965i
$53$	1.74412	−	3.02090i	0.239573	−	0.414953i	−0.721019	−	0.692916i	$-0.756326\pi$
$53$	1.74412	−	3.02090i	0.239573	−	0.414953i	0.960592	+	0.277963i	$0.0896592\pi$
$54$	−1.33581	−	0.771231i	−0.181781	−	0.104951i
$55$	−1.63749	−	2.83622i	−0.220800	−	0.382436i
$56$	−5.40570	+	3.81180i	−0.722367	+	0.509373i
$57$		−	0.957578i		−	0.126834i
$58$			2.24607i			0.294923i
$59$	−0.664540	+	0.383672i	−0.0865157	+	0.0499499i	−0.542634	−	0.839969i	$-0.682573\pi$
$59$	−0.664540	+	0.383672i	−0.0865157	+	0.0499499i	0.456118	+	0.889919i	$0.349239\pi$
$60$	−0.481830	−	0.278185i	−0.0622040	−	0.0359135i
$61$	−12.1139			−1.55103			−0.775513	−	0.631332i	$-0.782509\pi$
$61$	−12.1139			−1.55103			−0.775513	+	0.631332i	$0.782509\pi$
$62$	−2.57468	−	4.45947i	−0.326984	−	0.566354i
$63$	1.52469	+	2.16225i	0.192093	+	0.272417i
$64$	−5.96263			−0.745329
$65$	−4.21241	+	3.20044i	−0.522485	+	0.396966i
$66$	1.72142	−	2.98158i	0.211892	−	0.367007i
$67$			9.64946i			1.17887i	0.807816	+	0.589434i	$0.200649\pi$
$67$			9.64946i			1.17887i	−0.807816	+	0.589434i	$0.799351\pi$
$68$	−0.478009	+	0.827936i	−0.0579671	+	0.100402i
$69$	1.32450	−	2.29410i	0.159451	−	0.276178i
$70$	3.45069	+	4.89359i	0.412436	+	0.584896i
$71$	−2.50519	−	1.44637i	−0.297311	−	0.171652i	0.343923	−	0.938998i	$-0.388244\pi$
$71$	−2.50519	−	1.44637i	−0.297311	−	0.171652i	−0.641234	+	0.767345i	$0.721577\pi$
$72$			2.50004i			0.294633i
$73$	−11.3623	−	6.56004i	−1.32986	−	0.767795i	−0.344582	−	0.938756i	$-0.611979\pi$
$73$	−11.3623	−	6.56004i	−1.32986	−	0.767795i	−0.985278	+	0.170962i	$0.945313\pi$
$74$	−5.71513	−	9.89889i	−0.664370	−	1.15072i
$75$	−1.42357	+	2.46569i	−0.164379	+	0.284713i
$76$	0.314456	−	0.181551i	0.0360706	−	0.0208254i
$77$	−4.82621	+	3.40317i	−0.549998	+	0.387828i
$78$	−5.12786	−	2.15279i	−0.580616	−	0.243755i
$79$	−1.88401	−	3.26320i	−0.211968	−	0.367139i	0.740362	−	0.672208i	$-0.234654\pi$
$79$	−1.88401	−	3.26320i	−0.211968	−	0.367139i	−0.952330	+	0.305069i	$0.901321\pi$
$80$			6.77083i			0.757002i
$81$	1.00000			0.111111
$82$	−6.27825			−0.693317
$83$		−	3.89258i		−	0.427266i	−0.976914	−	0.213633i	$-0.931470\pi$
$83$		−	3.89258i		−	0.427266i	0.976914	−	0.213633i	$-0.0685296\pi$
$84$	−0.420980	+	0.910638i	−0.0459327	+	0.0993588i
$85$	−3.20369	−	1.84965i	−0.347489	−	0.200623i
$86$	−8.04135	+	4.64268i	−0.867121	+	0.500633i
$87$	−0.728078	−	1.26107i	−0.0780582	−	0.135201i
$88$	−5.58018			−0.594850
$89$	8.78828	+	5.07392i	0.931556	+	0.537834i	0.887303	−	0.461186i	$-0.152576\pi$
$89$	8.78828	+	5.07392i	0.931556	+	0.537834i	0.0442526	+	0.999020i	$0.485909\pi$
$90$	2.26320			0.238562
$91$	6.43436	+	7.04266i	0.674504	+	0.738271i
$92$	1.00447			0.104723
$93$	2.89114	+	1.66920i	0.299797	+	0.173088i
$94$	16.1283			1.66351
$95$	0.702510	+	1.21678i	0.0720760	+	0.124839i
$96$	−1.83403	+	1.05888i	−0.187185	+	0.108071i
$97$	−5.44296	−	3.14250i	−0.552649	−	0.319072i	0.197541	−	0.980295i	$-0.436705\pi$
$97$	−5.44296	−	3.14250i	−0.552649	−	0.319072i	−0.750190	+	0.661223i	$0.770038\pi$
$98$	8.22511	−	6.99484i	0.830862	−	0.706585i
$99$			2.23204i			0.224328i
$100$	−1.07960			−0.107960
$101$	2.60679			0.259385			0.129692	−	0.991554i	$-0.458601\pi$
$101$	2.60679			0.259385			0.129692	+	0.991554i	$0.458601\pi$
$102$		−	3.88889i		−	0.385058i
$103$	−6.25199	−	10.8288i	−0.616027	−	1.06699i	−0.990203	−	0.139633i	$-0.955408\pi$
$103$	−6.25199	−	10.8288i	−0.616027	−	1.06699i	0.374176	−	0.927358i	$-0.377926\pi$
$104$	1.13386	+	8.94243i	0.111184	+	0.876877i
$105$	−3.52370	−	1.62898i	−0.343878	−	0.158972i
$106$	−4.65963	+	2.69024i	−0.452583	+	0.261299i
$107$	9.12582	−	15.8064i	0.882227	−	1.52806i	0.0333667	−	0.999443i	$-0.489377\pi$
$107$	9.12582	−	15.8064i	0.882227	−	1.52806i	0.848860	−	0.528618i	$-0.177290\pi$
$108$	0.189594	+	0.328387i	0.0182437	+	0.0315990i
$109$	1.37903	+	0.796181i	0.132087	+	0.0762603i	0.564587	−	0.825373i	$-0.309035\pi$
$109$	1.37903	+	0.796181i	0.132087	+	0.0762603i	−0.432501	+	0.901634i	$0.642369\pi$
$110$			5.05155i			0.481646i
$111$	6.41759	+	3.70520i	0.609131	+	0.351682i
$112$	12.1590	−	1.10427i	1.14892	−	0.104344i
$113$	10.1371	−	17.5580i	0.953617	−	1.65171i	0.216115	−	0.976368i	$-0.430661\pi$
$113$	10.1371	−	17.5580i	0.953617	−	1.65171i	0.737502	−	0.675345i	$-0.236005\pi$
$114$	−0.738514	+	1.27914i	−0.0691682	+	0.119803i
$115$			3.88679i			0.362445i
$116$	0.276079	−	0.478182i	0.0256333	−	0.0443981i
$117$	3.57691	−	0.453537i	0.330686	−	0.0419295i
$118$	1.18360			0.108959
$119$	−2.79910	+	6.05484i	−0.256593	+	0.555046i
$120$	−1.83411	−	3.17677i	−0.167431	−	0.289998i
$121$	6.01801			0.547092
$122$	16.1819	+	9.34261i	1.46504	+	0.845840i
$123$	3.52497	−	2.03514i	0.317835	−	0.183502i
$124$			1.26588i			0.113680i
$125$		−	11.5138i		−	1.02983i
$126$	−0.369112	−	4.06424i	−0.0328831	−	0.362072i
$127$	2.15084	+	3.72537i	0.190856	+	0.330573i	0.945534	−	0.325523i	$-0.105540\pi$
$127$	2.15084	+	3.72537i	0.190856	+	0.330573i	−0.754678	+	0.656095i	$0.772207\pi$
$128$	11.6330	+	6.71632i	1.02822	+	0.593644i
$129$	3.00991	−	5.21332i	0.265008	−	0.459008i
$130$	8.09527	−	1.02644i	0.710002	−	0.0900252i
$131$	7.41308	+	12.8398i	0.647684	+	1.12182i	0.983675	+	0.179957i	$0.0575957\pi$
$131$	7.41308	+	12.8398i	0.647684	+	1.12182i	−0.335990	+	0.941865i	$0.609071\pi$
$132$	−0.732971	+	0.423181i	−0.0637970	+	0.0368332i
$133$	2.07052	−	1.46001i	0.179537	−	0.126599i
$134$	7.44196	−	12.8898i	0.642887	−	1.11351i
$135$	−1.27069	+	0.733632i	−0.109363	+	0.0631410i
$136$	−5.45870	+	3.15158i	−0.468079	+	0.270246i
$137$	4.48465	−	2.58921i	0.383149	−	0.221211i	−0.296038	−	0.955176i	$-0.595666\pi$
$137$	4.48465	−	2.58921i	0.383149	−	0.221211i	0.679188	+	0.733965i	$0.262332\pi$
$138$	−3.53857	+	2.04299i	−0.301223	+	0.173911i
$139$	−10.3510	+	17.9284i	−0.877959	+	1.52067i	−0.0243815	+	0.999703i	$0.507762\pi$
$139$	−10.3510	+	17.9284i	−0.877959	+	1.52067i	−0.853577	+	0.520966i	$0.825572\pi$
$140$	−0.133139	−	1.46598i	−0.0112523	−	0.123898i
$141$	−9.05536	+	5.22812i	−0.762599	+	0.440287i
$142$	2.23097	+	3.86415i	0.187219	+	0.324272i
$143$	1.01231	+	7.98380i	0.0846538	+	0.667639i
$144$	2.30730	−	3.99635i	0.192275	−	0.333030i
$145$	1.85032	+	1.06828i	0.153661	+	0.0887161i
$146$	10.1186	+	17.5259i	0.837422	+	1.45046i
$147$	−2.35062	+	6.59353i	−0.193876	+	0.543825i
$148$			2.80994i			0.230975i
$149$		−	17.6440i		−	1.44545i	−0.691136	−	0.722725i	$-0.742889\pi$
$149$		−	17.6440i		−	1.44545i	0.691136	−	0.722725i	$-0.257111\pi$
$150$	3.80323	−	2.19580i	0.310533	−	0.179286i
$151$	−13.1219	−	7.57592i	−1.06784	−	0.616520i	−0.140252	−	0.990116i	$-0.544791\pi$
$151$	−13.1219	−	7.57592i	−1.06784	−	0.616520i	−0.927591	+	0.373596i	$0.878125\pi$
$152$	2.39398			0.194178
$153$	1.26061	+	2.18344i	0.101914	+	0.176521i
$154$	9.07154	−	0.823871i	0.731006	−	0.0663894i
$155$	−4.89832			−0.393442
$156$	0.827097	+	1.08862i	0.0662208	+	0.0871595i
$157$	8.38350	−	14.5206i	0.669076	−	1.15887i	−0.309087	−	0.951034i	$-0.600023\pi$
$157$	8.38350	−	14.5206i	0.669076	−	1.15887i	0.978163	−	0.207840i	$-0.0666433\pi$
$158$			5.81203i			0.462380i
$159$	1.74412	−	3.02090i	0.138318	−	0.239573i
$160$	1.55365	−	2.69100i	0.122827	−	0.212743i
$161$	6.97988	−	0.633907i	0.550091	−	0.0499589i
$162$	−1.33581	−	0.771231i	−0.104951	−	0.0605936i
$163$		−	16.1554i		−	1.26539i	−0.774402	−	0.632693i	$-0.781949\pi$
$163$		−	16.1554i		−	1.26539i	0.774402	−	0.632693i	$-0.218051\pi$
$164$	1.33663	+	0.771701i	0.104373	+	0.0602597i
$165$	−1.63749	−	2.83622i	−0.127479	−	0.220800i
$166$	−3.00207	+	5.19974i	−0.233006	+	0.403578i
$167$	−17.1116	+	9.87941i	−1.32414	+	0.764492i	−0.984386	−	0.176023i	$-0.943677\pi$
$167$	−17.1116	+	9.87941i	−1.32414	+	0.764492i	−0.339752	+	0.940515i	$0.610343\pi$
$168$	−5.40570	+	3.81180i	−0.417059	+	0.294086i
$169$	12.5886	−	3.24453i	0.968354	−	0.249579i
$170$	2.85302	+	4.94157i	0.218816	+	0.379001i
$171$		−	0.957578i		−	0.0732278i
$172$	2.28265			0.174050
$173$	1.63403			0.124233			0.0621164	−	0.998069i	$-0.480215\pi$
$173$	1.63403			0.124233			0.0621164	+	0.998069i	$0.480215\pi$
$174$			2.24607i			0.170274i
$175$	−7.50194	+	0.681321i	−0.567093	+	0.0515030i
$176$	8.92001	+	5.14997i	0.672371	+	0.388194i
$177$	−0.664540	+	0.383672i	−0.0499499	+	0.0288386i
$178$	−7.82632	−	13.5556i	−0.586608	−	1.01603i
$179$	17.4631			1.30526			0.652628	−	0.757679i	$-0.273667\pi$
$179$	17.4631			1.30526			0.652628	+	0.757679i	$0.273667\pi$
$180$	−0.481830	−	0.278185i	−0.0359135	−	0.0207347i
$181$	−0.848669			−0.0630811			−0.0315405	−	0.999502i	$-0.510041\pi$
$181$	−0.848669			−0.0630811			−0.0315405	+	0.999502i	$0.510041\pi$
$182$	−3.16357	−	14.3700i	−0.234499	−	1.06518i
$183$	−12.1139			−0.895485
$184$	5.73535	+	3.31131i	0.422816	+	0.244113i
$185$	−10.8730			−0.799400
$186$	−2.57468	−	4.45947i	−0.188785	−	0.326984i
$187$	−4.87353	+	2.81373i	−0.356388	+	0.205761i
$188$	−3.43369	−	1.98244i	−0.250427	−	0.144584i
$189$	1.52469	+	2.16225i	0.110905	+	0.157280i
$190$		−	2.16719i		−	0.157225i
$191$	−27.3607			−1.97975			−0.989875	−	0.141944i	$-0.954665\pi$
$191$	−27.3607			−1.97975			−0.989875	+	0.141944i	$0.954665\pi$
$192$	−5.96263			−0.430316
$193$		−	11.7947i		−	0.849002i	−0.905427	−	0.424501i	$-0.860449\pi$
$193$		−	11.7947i		−	0.849002i	0.905427	−	0.424501i	$-0.139551\pi$
$194$	4.84718	+	8.39556i	0.348007	+	0.602766i
$195$	−4.21241	+	3.20044i	−0.301657	+	0.229188i
$196$	−2.61089	+	0.478182i	−0.186492	+	0.0341559i
$197$	7.28644	−	4.20683i	0.519137	−	0.299724i	−0.217444	−	0.976073i	$-0.569772\pi$
$197$	7.28644	−	4.20683i	0.519137	−	0.299724i	0.736582	+	0.676349i	$0.236439\pi$
$198$	1.72142	−	2.98158i	0.122336	−	0.211892i
$199$	2.53443	+	4.38977i	0.179661	+	0.311182i	0.941764	−	0.336273i	$-0.109167\pi$
$199$	2.53443	+	4.38977i	0.179661	+	0.311182i	−0.762103	+	0.647455i	$0.775833\pi$
$200$	−6.16433	−	3.55898i	−0.435884	−	0.251658i
$201$			9.64946i			0.680620i
$202$	−3.48217	−	2.01043i	−0.245005	−	0.141454i
$203$	1.61664	−	3.49703i	0.113466	−	0.245443i
$204$	−0.478009	+	0.827936i	−0.0334673	+	0.0579671i
$205$	−2.98609	+	5.17206i	−0.208557	+	0.361232i
$206$			19.2869i			1.34378i
$207$	1.32450	−	2.29410i	0.0920592	−	0.159451i
$208$	6.44050	−	15.3411i	0.446568	−	1.06371i
$209$	2.13735			0.147844
$210$	3.45069	+	4.89359i	0.238120	+	0.337690i
$211$	10.2926	+	17.8273i	0.708570	+	1.22728i	0.965388	+	0.260820i	$0.0839928\pi$
$211$	10.2926	+	17.8273i	0.708570	+	1.22728i	−0.256817	+	0.966460i	$0.582674\pi$
$212$	1.32270			0.0908433
$213$	−2.50519	−	1.44637i	−0.171652	−	0.0991036i
$214$	−24.3807	+	14.0762i	−1.66663	+	0.962231i
$215$			8.83268i			0.602384i
$216$			2.50004i			0.170106i
$217$	0.798881	+	8.79637i	0.0542315	+	0.597137i
$218$	−1.22808	−	2.12709i	−0.0831760	−	0.144065i
$219$	−11.3623	−	6.56004i	−0.767795	−	0.443286i
$220$	0.620919	−	1.07546i	0.0418623	−	0.0725077i
$221$	5.49937	+	7.23825i	0.369928	+	0.486898i
$222$	−5.71513	−	9.89889i	−0.383574	−	0.664370i
$223$	7.09390	−	4.09566i	0.475042	−	0.274266i	−0.243306	−	0.969950i	$-0.578232\pi$
$223$	7.09390	−	4.09566i	0.475042	−	0.274266i	0.718348	+	0.695684i	$0.244898\pi$
$224$	−5.08588	−	2.35116i	−0.339815	−	0.157093i
$225$	−1.42357	+	2.46569i	−0.0949045	+	0.164379i
$226$	−27.0825	+	15.6361i	−1.80150	+	1.04010i
$227$	−19.8119	+	11.4384i	−1.31496	+	0.759193i	−0.982913	−	0.184069i	$-0.941073\pi$
$227$	−19.8119	+	11.4384i	−1.31496	+	0.759193i	−0.332048	+	0.943262i	$0.607740\pi$
$228$	0.314456	−	0.181551i	0.0208254	−	0.0120235i
$229$	12.3924	−	7.15476i	0.818913	−	0.472800i	−0.0311285	−	0.999515i	$-0.509910\pi$
$229$	12.3924	−	7.15476i	0.818913	−	0.472800i	0.850041	+	0.526716i	$0.176577\pi$
$230$	2.99761	−	5.19201i	0.197657	−	0.342351i
$231$	−4.82621	+	3.40317i	−0.317542	+	0.223912i
$232$	3.15272	−	1.82023i	0.206986	−	0.119504i
$233$	5.03403	+	8.71920i	0.329790	+	0.571213i	0.982470	−	0.186420i	$-0.0596886\pi$
$233$	5.03403	+	8.71920i	0.329790	+	0.571213i	−0.652680	+	0.757634i	$0.726355\pi$
$234$	−5.12786	−	2.15279i	−0.335219	−	0.140732i
$235$	7.67103	−	13.2866i	0.500403	−	0.866723i
$236$	−0.251986	−	0.145484i	−0.0164029	−	0.00947020i
$237$	−1.88401	−	3.26320i	−0.122380	−	0.211968i
$238$	8.40874	−	5.92937i	0.545058	−	0.384344i
$239$		−	27.8817i		−	1.80351i	−0.432242	−	0.901757i	$-0.642278\pi$
$239$		−	27.8817i		−	1.80351i	0.432242	−	0.901757i	$-0.357722\pi$
$240$			6.77083i			0.437055i
$241$	−10.5053	+	6.06521i	−0.676703	+	0.390695i	−0.798612	−	0.601847i	$-0.794432\pi$
$241$	−10.5053	+	6.06521i	−0.676703	+	0.390695i	0.121909	+	0.992541i	$0.461099\pi$
$242$	−8.03892	−	4.64127i	−0.516762	−	0.298352i
$243$	1.00000			0.0641500
$244$	−2.29672	−	3.97804i	−0.147033	−	0.254668i
$245$	−1.85032	−	10.1028i	−0.118213	−	0.645445i
$246$	−6.27825			−0.400287
$247$	−0.434297	−	3.42517i	−0.0276337	−	0.217939i
$248$	−4.17307	+	7.22796i	−0.264990	+	0.458976i
$249$		−	3.89258i		−	0.246682i
$250$	−8.87982	+	15.3803i	−0.561609	+	0.972735i
$251$	−5.86315	+	10.1553i	−0.370079	+	0.640995i	−0.989577	−	0.144003i	$-0.954003\pi$
$251$	−5.86315	+	10.1553i	−0.370079	+	0.640995i	0.619499	+	0.784998i	$0.287336\pi$
$252$	−0.420980	+	0.910638i	−0.0265192	+	0.0573648i
$253$	5.12052	+	2.95634i	0.321925	+	0.185863i
$254$		−	6.63518i		−	0.416328i
$255$	−3.20369	−	1.84965i	−0.200623	−	0.115830i
$256$	−4.39703	−	7.61588i	−0.274815	−	0.475993i
$257$	11.2305	−	19.4518i	0.700541	−	1.21337i	−0.267736	−	0.963492i	$-0.586275\pi$
$257$	11.2305	−	19.4518i	0.700541	−	1.21337i	0.968277	−	0.249880i	$-0.0803912\pi$
$258$	−8.04135	+	4.64268i	−0.500633	+	0.289040i
$259$	1.77331	+	19.5257i	0.110188	+	1.21327i
$260$	−1.84963	−	0.776515i	−0.114709	−	0.0481574i
$261$	−0.728078	−	1.26107i	−0.0450669	−	0.0780582i
$262$		−	22.8688i		−	1.41284i
$263$	−14.1477			−0.872387			−0.436194	−	0.899853i	$-0.643674\pi$
$263$	−14.1477			−0.872387			−0.436194	+	0.899853i	$0.643674\pi$
$264$	−5.58018			−0.343437
$265$			5.11817i			0.314406i
$266$	−3.89183	+	0.353453i	−0.238624	+	0.0216716i
$267$	8.78828	+	5.07392i	0.537834	+	0.310519i
$268$	−3.16875	+	1.82948i	−0.193562	+	0.111753i
$269$	−6.37047	−	11.0340i	−0.388415	−	0.672754i	0.603822	−	0.797119i	$-0.293644\pi$
$269$	−6.37047	−	11.0340i	−0.388415	−	0.672754i	−0.992236	+	0.124365i	$0.960311\pi$
$270$	2.26320			0.137734
$271$	−3.25356	−	1.87844i	−0.197639	−	0.114107i	0.397914	−	0.917423i	$-0.369734\pi$
$271$	−3.25356	−	1.87844i	−0.197639	−	0.114107i	−0.595554	+	0.803315i	$0.703067\pi$
$272$	11.6344			0.705440
$273$	6.43436	+	7.04266i	0.389425	+	0.426241i
$274$	−7.98752			−0.482544
$275$	−5.50351	−	3.17746i	−0.331874	−	0.191608i
$276$	1.00447			0.0604620
$277$	−2.46101	−	4.26260i	−0.147868	−	0.256115i	0.782571	−	0.622561i	$-0.213908\pi$
$277$	−2.46101	−	4.26260i	−0.147868	−	0.256115i	−0.930439	+	0.366446i	$0.880574\pi$
$278$	27.6539	−	15.9660i	1.65857	−	0.957577i
$279$	2.89114	+	1.66920i	0.173088	+	0.0999324i
$280$	4.07251	−	8.80940i	0.243379	−	0.526462i
$281$			21.9099i			1.30703i	0.756912	+	0.653516i	$0.226707\pi$
$281$			21.9099i			1.30703i	−0.756912	+	0.653516i	$0.773293\pi$
$282$	16.1283			0.960429
$283$	30.4171			1.80811			0.904055	−	0.427416i	$-0.140576\pi$
$283$	30.4171			1.80811			0.904055	+	0.427416i	$0.140576\pi$
$284$		−	1.09689i		−	0.0650886i
$285$	0.702510	+	1.21678i	0.0416131	+	0.0720760i
$286$	4.80510	−	11.4456i	0.284131	−	0.676791i
$287$	9.77497	+	4.51888i	0.576998	+	0.266741i
$288$	−1.83403	+	1.05888i	−0.108071	+	0.0623949i
$289$	5.32172	−	9.21748i	0.313042	−	0.542205i
$290$	−1.64779	−	2.85405i	−0.0967614	−	0.167596i
$291$	−5.44296	−	3.14250i	−0.319072	−	0.184216i
$292$		−	4.97498i		−	0.291139i
$293$	−9.06140	−	5.23160i	−0.529372	−	0.305633i	0.211388	−	0.977402i	$-0.432202\pi$
$293$	−9.06140	−	5.23160i	−0.529372	−	0.305633i	−0.740761	+	0.671769i	$0.765535\pi$
$294$	8.22511	−	6.99484i	0.479698	−	0.407947i
$295$	0.562949	−	0.975056i	0.0327761	−	0.0567699i
$296$	−9.26315	+	16.0442i	−0.538409	+	0.932552i
$297$			2.23204i			0.129516i
$298$	−13.6076	+	23.5690i	−0.788266	+	1.36532i
$299$	3.69716	−	8.80652i	0.213813	−	0.509294i
$300$	−1.07960			−0.0623307
$301$	15.8617	−	1.44055i	0.914252	−	0.0830318i
$302$	11.6856	+	20.2400i	0.672429	+	1.16468i
$303$	2.60679			0.149756
$304$	−3.82682	−	2.20942i	−0.219483	−	0.126719i
$305$	15.3930	−	8.88715i	0.881400	−	0.508877i
$306$		−	3.88889i		−	0.222313i
$307$		−	11.2995i		−	0.644896i	−0.946587	−	0.322448i	$-0.895494\pi$
$307$		−	11.2995i		−	0.644896i	0.946587	−	0.322448i	$-0.104506\pi$
$308$	−2.03258	−	0.939643i	−0.115817	−	0.0535411i
$309$	−6.25199	−	10.8288i	−0.355664	−	0.616027i
$310$	6.54322	+	3.77773i	0.371630	+	0.214561i
$311$	−3.38424	+	5.86168i	−0.191903	+	0.332385i	−0.945881	−	0.324514i	$-0.894799\pi$
$311$	−3.38424	+	5.86168i	−0.191903	+	0.332385i	0.753978	+	0.656900i	$0.228132\pi$
$312$	1.13386	+	8.94243i	0.0641922	+	0.506265i
$313$	1.36847	+	2.37027i	0.0773507	+	0.133975i	0.902106	−	0.431514i	$-0.142021\pi$
$313$	1.36847	+	2.37027i	0.0773507	+	0.133975i	−0.824755	+	0.565490i	$0.808687\pi$
$314$	−22.3975	+	12.9312i	−1.26397	+	0.729751i
$315$	−3.52370	−	1.62898i	−0.198538	−	0.0917824i
$316$	0.714395	−	1.23737i	0.0401879	−	0.0696074i
$317$	13.0303	−	7.52306i	0.731856	−	0.422537i	−0.0872447	−	0.996187i	$-0.527806\pi$
$317$	13.0303	−	7.52306i	0.731856	−	0.422537i	0.819101	+	0.573650i	$0.194473\pi$
$318$	−4.65963	+	2.69024i	−0.261299	+	0.150861i
$319$	2.81475	−	1.62510i	0.157596	−	0.0909880i
$320$	7.57665	−	4.37438i	0.423548	−	0.244535i
$321$	9.12582	−	15.8064i	0.509354	−	0.882227i
$322$	−9.81268	−	4.53631i	−0.546839	−	0.252799i
$323$	2.09082	−	1.20713i	0.116336	−	0.0671668i
$324$	0.189594	+	0.328387i	0.0105330	+	0.0182437i
$325$	−3.97369	+	9.46520i	−0.220421	+	0.525035i
$326$	−12.4595	+	21.5805i	−0.690069	+	1.19523i
$327$	1.37903	+	0.796181i	0.0762603	+	0.0440289i
$328$	5.08793	+	8.81256i	0.280934	+	0.486592i
$329$	−25.1111	−	11.6086i	−1.38442	−	0.640006i
$330$			5.05155i			0.278078i
$331$			5.77162i			0.317237i	0.987340	+	0.158619i	$0.0507040\pi$
$331$			5.77162i			0.317237i	−0.987340	+	0.158619i	$0.949296\pi$
$332$	1.27827	−	0.738009i	0.0701542	−	0.0405035i
$333$	6.41759	+	3.70520i	0.351682	+	0.203044i
$334$	30.4772			1.66764
$335$	−7.07915	−	12.2615i	−0.386775	−	0.669915i
$336$	12.1590	−	1.10427i	0.663329	−	0.0602431i
$337$	−26.5503			−1.44628			−0.723142	−	0.690699i	$-0.757303\pi$
$337$	−26.5503			−1.44628			−0.723142	+	0.690699i	$0.757303\pi$
$338$	−19.3183	−	5.37465i	−1.05078	−	0.292342i
$339$	10.1371	−	17.5580i	0.550571	−	0.953617i
$340$		−	1.40273i		−	0.0760738i
$341$	−3.72572	+	6.45313i	−0.201759	+	0.349457i
$342$	−0.738514	+	1.27914i	−0.0399343	+	0.0691682i
$343$	−17.8408	+	4.97049i	−0.963313	+	0.268381i
$344$	13.0335	+	7.52491i	0.702720	+	0.405716i
$345$			3.88679i			0.209258i
$346$	−2.18275	−	1.26021i	−0.117345	−	0.0677494i
$347$	5.97470	+	10.3485i	0.320739	+	0.555536i	0.980641	−	0.195816i	$-0.0627355\pi$
$347$	5.97470	+	10.3485i	0.320739	+	0.555536i	−0.659902	+	0.751352i	$0.729402\pi$
$348$	0.276079	−	0.478182i	0.0147994	−	0.0256333i
$349$	−30.8266	+	17.7977i	−1.65011	+	0.952692i	−0.673086	+	0.739564i	$0.735032\pi$
$349$	−30.8266	+	17.7977i	−1.65011	+	0.952692i	−0.977024	+	0.213127i	$0.931635\pi$
$350$	10.5466	+	4.87561i	0.563741	+	0.260612i
$351$	3.57691	−	0.453537i	0.190921	−	0.0242080i
$352$	−2.36345	−	4.09362i	−0.125972	−	0.218191i
$353$		−	32.8928i		−	1.75070i	−0.483486	−	0.875352i	$-0.660629\pi$
$353$		−	32.8928i		−	1.75070i	0.483486	−	0.875352i	$-0.339371\pi$
$354$	1.18360			0.0629076
$355$	4.24441			0.225270
$356$			3.84794i			0.203940i
$357$	−2.79910	+	6.05484i	−0.148144	+	0.320456i
$358$	−23.3274	−	13.4681i	−1.23289	−	0.711812i
$359$	−9.62271	+	5.55567i	−0.507867	+	0.293217i	−0.731956	−	0.681351i	$-0.761393\pi$
$359$	−9.62271	+	5.55567i	−0.507867	+	0.293217i	0.224089	+	0.974569i	$0.428059\pi$
$360$	−1.83411	−	3.17677i	−0.0966661	−	0.167431i
$361$	18.0830			0.951739
$362$	1.13366	+	0.654520i	0.0595839	+	0.0344008i
$363$	6.01801			0.315864
$364$	−1.09280	+	3.44820i	−0.0572783	+	0.180735i
$365$	19.2506			1.00762
$366$	16.1819	+	9.34261i	0.845840	+	0.488346i
$367$	−8.33304			−0.434981			−0.217491	−	0.976062i	$-0.569787\pi$
$367$	−8.33304			−0.434981			−0.217491	+	0.976062i	$0.569787\pi$
$368$	−6.11203	−	10.5864i	−0.318612	−	0.551852i
$369$	3.52497	−	2.03514i	0.183502	−	0.105945i
$370$	14.5243	+	8.38560i	0.755082	+	0.435947i
$371$	9.19118	−	0.834736i	0.477182	−	0.0433374i
$372$			1.26588i			0.0656329i
$373$	12.7499			0.660163			0.330082	−	0.943952i	$-0.392924\pi$
$373$	12.7499			0.660163			0.330082	+	0.943952i	$0.392924\pi$
$374$	8.68015			0.448840
$375$		−	11.5138i		−	0.594571i
$376$	−13.0705	−	22.6388i	−0.674060	−	1.16751i
$377$	−3.17621	−	4.18052i	−0.163583	−	0.215308i
$378$	−0.369112	−	4.06424i	−0.0189851	−	0.209042i
$379$	−27.6640	+	15.9718i	−1.42100	+	0.820416i	−0.996385	−	0.0849569i	$-0.972925\pi$
$379$	−27.6640	+	15.9718i	−1.42100	+	0.820416i	−0.424617	+	0.905373i	$0.639591\pi$
$380$	−0.266384	+	0.461390i	−0.0136652	+	0.0236688i
$381$	2.15084	+	3.72537i	0.110191	+	0.190856i
$382$	36.5487	+	21.1014i	1.86999	+	1.07964i
$383$			16.9775i			0.867510i	0.901031	+	0.433755i	$0.142812\pi$
$383$			16.9775i			0.867510i	−0.901031	+	0.433755i	$0.857188\pi$
$384$	11.6330	+	6.71632i	0.593644	+	0.342741i
$385$	3.63594	−	7.86504i	0.185304	−	0.400840i
$386$	−9.09645	+	15.7555i	−0.462997	+	0.801934i
$387$	3.00991	−	5.21332i	0.153003	−	0.265008i
$388$		−	2.38319i		−	0.120988i
$389$	0.862649	−	1.49415i	0.0437381	−	0.0757565i	−0.843328	−	0.537400i	$-0.819407\pi$
$389$	0.862649	−	1.49415i	0.0437381	−	0.0757565i	0.887066	+	0.461643i	$0.152740\pi$
$390$	8.09527	−	1.02644i	0.409920	−	0.0519761i
$391$	6.67873			0.337758
$392$	−16.4841	−	5.87664i	−0.832572	−	0.296815i
$393$	7.41308	+	12.8398i	0.373941	+	0.647684i
$394$	−12.9777			−0.653809
$395$	4.78798	+	2.76434i	0.240910	+	0.139089i
$396$	−0.732971	+	0.423181i	−0.0368332	+	0.0212657i
$397$			3.10919i			0.156046i	0.996952	+	0.0780229i	$0.0248607\pi$
$397$			3.10919i			0.156046i	−0.996952	+	0.0780229i	$0.975139\pi$
$398$		−	7.81853i		−	0.391907i
$399$	2.07052	−	1.46001i	0.103656	−	0.0730921i
$400$	6.56918	+	11.3782i	0.328459	+	0.568908i
$401$	−26.4530	−	15.2726i	−1.32100	−	0.762679i	−0.337111	−	0.941465i	$-0.609450\pi$
$401$	−26.4530	−	15.2726i	−1.32100	−	0.762679i	−0.983888	+	0.178785i	$0.942783\pi$
$402$	7.44196	−	12.8898i	0.371171	−	0.642887i
$403$	11.0984	+	4.65934i	0.552851	+	0.232098i
$404$	0.494231	+	0.856034i	0.0245889	+	0.0425893i
$405$	−1.27069	+	0.733632i	−0.0631410	+	0.0364545i
$406$	−4.85655	+	3.42456i	−0.241026	+	0.169958i
$407$	−8.27014	+	14.3243i	−0.409936	+	0.710029i
$408$	−5.45870	+	3.15158i	−0.270246	+	0.156026i
$409$	6.36394	−	3.67422i	0.314677	−	0.181679i	−0.334341	−	0.942452i	$-0.608514\pi$
$409$	6.36394	−	3.67422i	0.314677	−	0.181679i	0.649017	+	0.760774i	$0.275180\pi$
$410$	7.97770	−	4.60593i	0.393991	−	0.227471i
$411$	4.48465	−	2.58921i	0.221211	−	0.127716i
$412$	2.37068	−	4.10614i	0.116795	−	0.202295i
$413$	−1.84281	−	0.851916i	−0.0906789	−	0.0419200i
$414$	−3.53857	+	2.04299i	−0.173911	+	0.100408i
$415$	2.85572	+	4.94625i	0.140182	+	0.242802i
$416$	−6.07992	+	4.61931i	−0.298092	+	0.226480i
$417$	−10.3510	+	17.9284i	−0.506890	+	0.877959i
$418$	−2.85510	−	1.64839i	−0.139647	−	0.0806254i
$419$	5.78350	+	10.0173i	0.282542	+	0.489378i	0.972010	−	0.234938i	$-0.0754889\pi$
$419$	5.78350	+	10.0173i	0.282542	+	0.489378i	−0.689468	+	0.724316i	$0.742156\pi$
$420$	−0.133139	−	1.46598i	−0.00649654	−	0.0715326i
$421$			7.57918i			0.369386i	0.982796	+	0.184693i	$0.0591291\pi$
$421$			7.57918i			0.369386i	−0.982796	+	0.184693i	$0.940871\pi$
$422$		−	31.7518i		−	1.54565i
$423$	−9.05536	+	5.22812i	−0.440287	+	0.254200i
$424$	7.55238	+	4.36037i	0.366776	+	0.211758i
$425$	−7.17826			−0.348197
$426$	2.23097	+	3.86415i	0.108091	+	0.187219i
$427$	−18.4700	−	26.1932i	−0.893825	−	1.26758i
$428$	6.92081			0.334530
$429$	1.01231	+	7.98380i	0.0488749	+	0.385462i
$430$	6.81203	−	11.7988i	0.328505	−	0.568988i
$431$			2.47579i			0.119255i	0.998221	+	0.0596274i	$0.0189913\pi$
$431$			2.47579i			0.119255i	−0.998221	+	0.0596274i	$0.981009\pi$
$432$	2.30730	−	3.99635i	0.111010	−	0.192275i
$433$	0.513211	−	0.888908i	0.0246634	−	0.0427182i	−0.853430	−	0.521207i	$-0.825482\pi$
$433$	0.513211	−	0.888908i	0.0246634	−	0.0427182i	0.878094	+	0.478489i	$0.158815\pi$
$434$	5.71688	−	12.3664i	0.274419	−	0.593607i
$435$	1.85032	+	1.06828i	0.0887161	+	0.0512203i
$436$			0.603805i			0.0289170i
$437$	−2.19678	−	1.26831i	−0.105086	−	0.0606717i
$438$	10.1186	+	17.5259i	0.483486	+	0.837422i
$439$	4.53785	−	7.85978i	0.216580	−	0.375127i	−0.737180	−	0.675696i	$-0.763843\pi$
$439$	4.53785	−	7.85978i	0.216580	−	0.375127i	0.953760	+	0.300569i	$0.0971766\pi$
$440$	7.09067	−	4.09380i	0.338035	−	0.195164i
$441$	−2.35062	+	6.59353i	−0.111934	+	0.313977i
$442$	−1.76376	−	13.9102i	−0.0838933	−	0.661642i
$443$	12.9878	+	22.4955i	0.617069	+	1.06879i	0.990018	+	0.140943i	$0.0450134\pi$
$443$	12.9878	+	22.4955i	0.617069	+	1.06879i	−0.372949	+	0.927852i	$0.621653\pi$
$444$			2.80994i			0.133354i
$445$	−14.8896			−0.705833
$446$	−12.6348			−0.598276
$447$		−	17.6440i		−	0.834531i
$448$	−9.09119	−	12.8927i	−0.429518	−	0.609122i
$449$	27.6762	+	15.9789i	1.30612	+	0.754089i	0.981446	−	0.191737i	$-0.0614120\pi$
$449$	27.6762	+	15.9789i	1.30612	+	0.754089i	0.324674	+	0.945826i	$0.394745\pi$
$450$	3.80323	−	2.19580i	0.179286	−	0.103511i
$451$	4.54251	+	7.86786i	0.213898	+	0.370483i
$452$	7.68773			0.361600
$453$	−13.1219	−	7.57592i	−0.616520	−	0.355948i
$454$	35.2866			1.65608
$455$	−13.3428	−	4.22858i	−0.625519	−	0.198239i
$456$	2.39398			0.112109
$457$	35.6329	+	20.5727i	1.66684	+	0.962349i	0.969327	+	0.245775i	$0.0790423\pi$
$457$	35.6329	+	20.5727i	1.66684	+	0.962349i	0.697510	+	0.716575i	$0.254291\pi$
$458$	−22.0719			−1.03135
$459$	1.26061	+	2.18344i	0.0588403	+	0.101914i
$460$	−1.27637	+	0.736912i	−0.0595110	+	0.0343587i
$461$	5.19415	+	2.99884i	0.241916	+	0.139670i	0.616057	−	0.787702i	$-0.288729\pi$
$461$	5.19415	+	2.99884i	0.241916	+	0.139670i	−0.374141	+	0.927372i	$0.622062\pi$
$462$	9.07154	−	0.823871i	0.422046	−	0.0383300i
$463$			27.1770i			1.26302i	0.775367	+	0.631511i	$0.217565\pi$
$463$			27.1770i			1.26302i	−0.775367	+	0.631511i	$0.782435\pi$
$464$	−6.71957			−0.311948
$465$	−4.89832			−0.227154
$466$		−	15.5296i		−	0.719395i
$467$	2.29607	+	3.97690i	0.106249	+	0.184029i	0.914248	−	0.405155i	$-0.132783\pi$
$467$	2.29607	+	3.97690i	0.106249	+	0.184029i	−0.807999	+	0.589184i	$0.799449\pi$
$468$	0.827097	+	1.08862i	0.0382326	+	0.0503216i
$469$	−20.8645	+	14.7125i	−0.963433	+	0.679359i
$470$	−20.4941	+	11.8323i	−0.945322	+	0.545782i
$471$	8.38350	−	14.5206i	0.386291	−	0.669076i
$472$	−0.959196	−	1.66138i	−0.0441506	−	0.0764710i
$473$	11.6363	+	6.71824i	0.535039	+	0.308905i
$474$			5.81203i			0.266955i
$475$	2.36109	+	1.36318i	0.108334	+	0.0625469i
$476$	−2.51902	+	0.228776i	−0.115459	+	0.0104859i
$477$	1.74412	−	3.02090i	0.0798577	−	0.138318i
$478$	−21.5032	+	37.2446i	−0.983533	+	1.70353i
$479$			8.51732i			0.389166i	0.980886	+	0.194583i	$0.0623354\pi$
$479$			8.51732i			0.389166i	−0.980886	+	0.194583i	$0.937665\pi$
$480$	1.55365	−	2.69100i	0.0709142	−	0.122827i
$481$	24.6356	+	10.3426i	1.12329	+	0.471580i
$482$	18.7107			0.852250
$483$	6.97988	−	0.633907i	0.317595	−	0.0288438i
$484$	1.14098	+	1.97623i	0.0518627	+	0.0898288i
$485$	9.22174			0.418738
$486$	−1.33581	−	0.771231i	−0.0605936	−	0.0349837i
$487$	5.66099	−	3.26838i	0.256524	−	0.148104i	−0.366224	−	0.930527i	$-0.619350\pi$
$487$	5.66099	−	3.26838i	0.256524	−	0.148104i	0.622748	+	0.782423i	$0.286016\pi$
$488$		−	30.2852i		−	1.37095i
$489$		−	16.1554i		−	0.730571i
$490$	−5.31992	+	14.9225i	−0.240329	+	0.674128i
$491$	−18.2580	−	31.6237i	−0.823970	−	1.42716i	−0.902704	−	0.430263i	$-0.858421\pi$
$491$	−18.2580	−	31.6237i	−0.823970	−	1.42716i	0.0787336	−	0.996896i	$-0.474912\pi$
$492$	1.33663	+	0.771701i	0.0602597	+	0.0347910i
$493$	1.83565	−	3.17944i	0.0826734	−	0.143195i
$494$	−2.06146	+	4.91033i	−0.0927495	+	0.220926i
$495$	−1.63749	−	2.83622i	−0.0735999	−	0.127479i
$496$	13.3414	−	7.70268i	0.599048	−	0.345860i
$497$	−0.692234	−	7.62210i	−0.0310509	−	0.341898i
$498$	−3.00207	+	5.19974i	−0.134526	+	0.233006i
$499$	19.5923	−	11.3116i	0.877070	−	0.506377i	0.00737889	−	0.999973i	$-0.497651\pi$
$499$	19.5923	−	11.3116i	0.877070	−	0.506377i	0.869691	+	0.493596i	$0.164318\pi$
$500$	3.78099	−	2.18295i	0.169091	−	0.0976246i
$501$	−17.1116	+	9.87941i	−0.764492	+	0.441380i
$502$	15.6641	−	9.04368i	0.699124	−	0.403639i
$503$	−6.05831	+	10.4933i	−0.270127	+	0.467873i	−0.968894	−	0.247476i	$-0.920399\pi$
$503$	−6.05831	+	10.4933i	−0.270127	+	0.467873i	0.698767	+	0.715349i	$0.253732\pi$
$504$	−5.40570	+	3.81180i	−0.240789	+	0.169791i
$505$	−3.31241	+	1.91242i	−0.147400	+	0.0851017i
$506$	−4.56004	−	7.89821i	−0.202718	−	0.351118i
$507$	12.5886	−	3.24453i	0.559080	−	0.144094i
$508$	−0.815574	+	1.41262i	−0.0361852	+	0.0626747i
$509$	−16.1106	−	9.30147i	−0.714091	−	0.412280i	0.0984831	−	0.995139i	$-0.468601\pi$
$509$	−16.1106	−	9.30147i	−0.714091	−	0.412280i	−0.812574	+	0.582858i	$0.801934\pi$
$510$	2.85302	+	4.94157i	0.126334	+	0.218816i
$511$	−3.13964	−	34.5702i	−0.138890	−	1.52930i
$512$		−	13.3008i		−	0.587816i
$513$		−	0.957578i		−	0.0422781i
$514$	−30.0037	+	17.3227i	−1.32341	+	0.764070i
$515$	15.8887	+	9.17333i	0.700139	+	0.404225i
$516$	2.28265			0.100488
$517$	−11.6694	−	20.2119i	−0.513218	−	0.888919i
$518$	12.6900	−	27.4503i	0.557567	−	1.20610i
$519$	1.63403			0.0717258
$520$	−8.00124	−	10.5312i	−0.350877	−	0.461824i
$521$	2.14960	−	3.72321i	0.0941756	−	0.163117i	−0.815089	−	0.579336i	$-0.803312\pi$
$521$	2.14960	−	3.72321i	0.0941756	−	0.163117i	0.909264	+	0.416219i	$0.136645\pi$
$522$			2.24607i			0.0983076i
$523$	−3.11732	+	5.39935i	−0.136311	+	0.236097i	−0.926097	−	0.377284i	$-0.876858\pi$
$523$	−3.11732	+	5.39935i	−0.136311	+	0.236097i	0.789787	+	0.613382i	$0.210191\pi$
$524$	−2.81095	+	4.86872i	−0.122797	+	0.212691i
$525$	−7.50194	+	0.681321i	−0.327411	+	0.0297353i
$526$	18.8987	+	10.9112i	0.824023	+	0.475750i
$527$			8.41685i			0.366644i
$528$	8.92001	+	5.14997i	0.388194	+	0.224124i
$529$	7.99139	+	13.8415i	0.347452	+	0.601804i
$530$	3.94729	−	6.83690i	0.171459	−	0.296976i
$531$	−0.664540	+	0.383672i	−0.0288386	+	0.0166500i
$532$	0.872008	+	0.403121i	0.0378063	+	0.0174775i
$533$	11.6855	−	8.87822i	0.506154	−	0.384558i
$534$	−7.82632	−	13.5556i	−0.338678	−	0.586608i
$535$			26.7800i			1.15780i
$536$	−24.1240			−1.04200
$537$	17.4631			0.753590
$538$			19.6524i			0.847276i
$539$	−14.7170	−	5.24667i	−0.633906	−	0.225990i
$540$	−0.481830	−	0.278185i	−0.0207347	−	0.0119712i
$541$	4.56161	−	2.63365i	0.196119	−	0.113229i	−0.398725	−	0.917071i	$-0.630547\pi$
$541$	4.56161	−	2.63365i	0.196119	−	0.113229i	0.594844	+	0.803841i	$0.297214\pi$
$542$	2.89742	+	5.01849i	0.124455	+	0.215562i
$543$	−0.848669			−0.0364199
$544$	−4.62399	−	2.66966i	−0.198252	−	0.114461i
$545$	−2.33642			−0.100081
$546$	−3.16357	−	14.3700i	−0.135388	−	0.614981i
$547$	3.35409			0.143411			0.0717053	−	0.997426i	$-0.477156\pi$
$547$	3.35409			0.143411			0.0717053	+	0.997426i	$0.477156\pi$
$548$	1.70053	+	0.981799i	0.0726429	+	0.0419404i
$549$	−12.1139			−0.517009
$550$	4.90110	+	8.48896i	0.208984	+	0.361971i
$551$	−1.20757	+	0.697192i	−0.0514443	+	0.0297014i
$552$	5.73535	+	3.31131i	0.244113	+	0.140939i
$553$	4.18331	−	9.04908i	0.177892	−	0.384806i
$554$			7.59203i			0.322555i
$555$	−10.8730			−0.461534
$556$	−7.84994			−0.332912
$557$			8.00516i			0.339189i	0.985514	+	0.169595i	$0.0542459\pi$
$557$			8.00516i			0.339189i	−0.985514	+	0.169595i	$0.945754\pi$
$558$	−2.57468	−	4.45947i	−0.108995	−	0.188785i
$559$	8.40176	−	20.0127i	0.355357	−	0.846447i
$560$	−14.6402	+	10.3234i	−0.618661	+	0.436245i
$561$	−4.87353	+	2.81373i	−0.205761	+	0.118796i
$562$	16.8976	−	29.2674i	0.712781	−	1.23457i
$563$	17.3033	+	29.9701i	0.729246	+	1.26309i	0.957202	+	0.289420i	$0.0934623\pi$
$563$	17.3033	+	29.9701i	0.729246	+	1.26309i	−0.227956	+	0.973671i	$0.573204\pi$
$564$	−3.43369	−	1.98244i	−0.144584	−	0.0834758i
$565$			29.7476i			1.25149i
$566$	−40.6315	−	23.4586i	−1.70787	−	0.986040i
$567$	1.52469	+	2.16225i	0.0640311	+	0.0908058i
$568$	3.61598	−	6.26306i	0.151723	−	0.262792i
$569$	2.38320	−	4.12782i	0.0999089	−	0.173047i	−0.811738	−	0.584022i	$-0.801478\pi$
$569$	2.38320	−	4.12782i	0.0999089	−	0.173047i	0.911647	+	0.410975i	$0.134812\pi$
$570$		−	2.16719i		−	0.0907736i
$571$	17.3388	−	30.0317i	0.725607	−	1.25679i	−0.233117	−	0.972449i	$-0.574893\pi$
$571$	17.3388	−	30.0317i	0.725607	−	1.25679i	0.958724	−	0.284339i	$-0.0917741\pi$
$572$	−2.42985	+	1.84611i	−0.101597	+	0.0771898i
$573$	−27.3607			−1.14301
$574$	−9.57241	−	13.5751i	−0.399545	−	0.566615i
$575$	3.77103	+	6.53162i	0.157263	+	0.272387i
$576$	−5.96263			−0.248443
$577$	−33.2462	−	19.1947i	−1.38406	−	0.799085i	−0.391419	−	0.920213i	$-0.628016\pi$
$577$	−33.2462	−	19.1947i	−1.38406	−	0.799085i	−0.992637	+	0.121128i	$0.961349\pi$
$578$	−14.2176	+	8.20854i	−0.591375	+	0.341430i
$579$		−	11.7947i		−	0.490172i
$580$			0.810161i			0.0336401i
$581$	8.41671	−	5.93498i	0.349184	−	0.246225i
$582$	4.84718	+	8.39556i	0.200922	+	0.348007i
$583$	6.74277	+	3.89294i	0.279257	+	0.161229i
$584$	16.4004	−	28.4063i	0.678652	−	1.17546i
$585$	−4.21241	+	3.20044i	−0.174162	+	0.132322i
$586$	8.06954	+	13.9769i	0.333350	+	0.577379i
$587$	13.2140	−	7.62912i	0.545401	−	0.314887i	−0.201864	−	0.979414i	$-0.564700\pi$
$587$	13.2140	−	7.62912i	0.545401	−	0.314887i	0.747265	+	0.664526i	$0.231367\pi$
$588$	−2.61089	+	0.478182i	−0.107671	+	0.0197199i
$589$	1.59839	−	2.76849i	0.0658605	−	0.114074i
$590$	−1.50399	+	0.868327i	−0.0619181	+	0.0357484i
$591$	7.28644	−	4.20683i	0.299724	−	0.173046i
$592$	29.6146	−	17.0980i	1.21715	−	0.702723i
$593$	−36.2229	+	20.9133i	−1.48750	+	0.858807i	−0.999898	−	0.0142607i	$-0.995461\pi$
$593$	−36.2229	+	20.9133i	−1.48750	+	0.858807i	−0.487599	+	0.873068i	$0.662127\pi$
$594$	1.72142	−	2.98158i	0.0706306	−	0.122336i
$595$	−0.885244	−	9.74732i	−0.0362915	−	0.399601i
$596$	5.79404	−	3.34519i	0.237333	−	0.137024i
$597$	2.53443	+	4.38977i	0.103727	+	0.179661i
$598$	−11.7306	+	8.91248i	−0.479699	+	0.364458i
$599$	−21.7048	+	37.5937i	−0.886832	+	1.53604i	−0.0432328	+	0.999065i	$0.513766\pi$
$599$	−21.7048	+	37.5937i	−0.886832	+	1.53604i	−0.843599	+	0.536973i	$0.819568\pi$
$600$	−6.16433	−	3.55898i	−0.251658	−	0.145295i
$601$	−12.1988	−	21.1289i	−0.497599	−	0.861866i	0.502398	−	0.864637i	$-0.332451\pi$
$601$	−12.1988	−	21.1289i	−0.497599	−	0.861866i	−0.999996	+	0.00277068i	$0.999118\pi$
$602$	−22.2992	−	10.3087i	−0.908848	−	0.420152i
$603$			9.64946i			0.392956i
$604$		−	5.74540i		−	0.233777i
$605$	−7.64701	+	4.41501i	−0.310895	+	0.179495i
$606$	−3.48217	−	2.01043i	−0.141454	−	0.0816683i
$607$	0.468035			0.0189969			0.00949847	−	0.999955i	$-0.496976\pi$
$607$	0.468035			0.0189969			0.00949847	+	0.999955i	$0.496976\pi$
$608$	1.01396	+	1.75623i	0.0411214	+	0.0712243i
$609$	1.61664	−	3.49703i	0.0655097	−	0.141707i
$610$	−27.4162			−1.11005
$611$	−30.0191	+	22.8075i	−1.21444	+	0.922691i
$612$	−0.478009	+	0.827936i	−0.0193224	+	0.0334673i
$613$		−	34.3967i		−	1.38927i	−0.719363	−	0.694635i	$-0.755566\pi$
$613$		−	34.3967i		−	1.38927i	0.719363	−	0.694635i	$-0.244434\pi$
$614$	−8.71451	+	15.0940i	−0.351689	+	0.609143i
$615$	−2.98609	+	5.17206i	−0.120411	+	0.208557i
$616$	−8.50807	−	12.0657i	−0.342800	−	0.486142i
$617$	8.47087	+	4.89066i	0.341024	+	0.196890i	0.660725	−	0.750628i	$-0.270249\pi$
$617$	8.47087	+	4.89066i	0.341024	+	0.196890i	−0.319701	+	0.947519i	$0.603582\pi$
$618$			19.2869i			0.775834i
$619$	−18.7382	−	10.8185i	−0.753152	−	0.434833i	0.0736794	−	0.997282i	$-0.476526\pi$
$619$	−18.7382	−	10.8185i	−0.753152	−	0.434833i	−0.826832	+	0.562449i	$0.809859\pi$
$620$	−0.928692	−	1.60854i	−0.0372972	−	0.0646006i
$621$	1.32450	−	2.29410i	0.0531504	−	0.0920592i
$622$	9.04142	−	5.22006i	0.362528	−	0.209305i
$623$	2.42838	+	26.7386i	0.0972910	+	1.07126i
$624$	6.44050	−	15.3411i	0.257826	−	0.614134i
$625$	1.32907	+	2.30202i	0.0531630	+	0.0920810i
$626$		−	4.22164i		−	0.168731i
$627$	2.13735			0.0853576
$628$	6.35785			0.253706
$629$			18.6833i			0.744951i
$630$	3.45069	+	4.89359i	0.137479	+	0.194965i
$631$	−12.0447	−	6.95404i	−0.479494	−	0.276836i	0.240712	−	0.970597i	$-0.422619\pi$
$631$	−12.0447	−	6.95404i	−0.479494	−	0.276836i	−0.720206	+	0.693761i	$0.755953\pi$
$632$	8.15814	−	4.71010i	0.324513	−	0.187358i
$633$	10.2926	+	17.8273i	0.409093	+	0.708570i
$634$	−23.2081			−0.921710
$635$	−5.46610	−	3.15585i	−0.216916	−	0.125236i
$636$	1.32270			0.0524484
$637$	−5.41755	+	24.6506i	−0.214651	+	0.976691i
$638$	−5.01330			−0.198479
$639$	−2.50519	−	1.44637i	−0.0991036	−	0.0572175i
$640$	−19.7092			−0.779076
$641$	11.8350	+	20.4988i	0.467454	+	0.809654i	0.999309	−	0.0371818i	$-0.0118381\pi$
$641$	11.8350	+	20.4988i	0.467454	+	0.809654i	−0.531855	+	0.846836i	$0.678505\pi$
$642$	−24.3807	+	14.0762i	−0.962231	+	0.555545i
$643$	19.6315	+	11.3342i	0.774190	+	0.446979i	0.834367	−	0.551209i	$-0.185833\pi$
$643$	19.6315	+	11.3342i	0.774190	+	0.446979i	−0.0601776	+	0.998188i	$0.519167\pi$
$644$	1.53151	+	2.17191i	0.0603500	+	0.0855854i
$645$			8.83268i			0.347786i
$646$	−3.72392			−0.146516
$647$	−23.5710			−0.926671			−0.463336	−	0.886183i	$-0.653348\pi$
$647$	−23.5710			−0.926671			−0.463336	+	0.886183i	$0.653348\pi$
$648$			2.50004i			0.0982109i
$649$	−0.856371	−	1.48328i	−0.0336155	−	0.0582237i
$650$	12.6080	−	9.57909i	0.494525	−	0.375723i
$651$	0.798881	+	8.79637i	0.0313106	+	0.344757i
$652$	5.30521	−	3.06296i	0.207768	−	0.119955i
$653$	−4.45538	+	7.71695i	−0.174353	+	0.301987i	−0.939937	−	0.341348i	$-0.889117\pi$
$653$	−4.45538	+	7.71695i	−0.174353	+	0.301987i	0.765584	+	0.643335i	$0.222450\pi$
$654$	−1.22808	−	2.12709i	−0.0480217	−	0.0831760i
$655$	−18.8394	−	10.8770i	−0.736118	−	0.424998i
$656$		−	18.7827i		−	0.733341i
$657$	−11.3623	−	6.56004i	−0.443286	−	0.255932i
$658$	24.5908	+	34.8734i	0.958648	+	1.35951i
$659$	−4.92457	+	8.52960i	−0.191834	+	0.332266i	−0.945858	−	0.324581i	$-0.894777\pi$
$659$	−4.92457	+	8.52960i	−0.191834	+	0.332266i	0.754024	+	0.656847i	$0.228110\pi$
$660$	0.620919	−	1.07546i	0.0241692	−	0.0418623i
$661$			0.444867i			0.0173033i	0.999963	+	0.00865166i	$0.00275394\pi$
$661$			0.444867i			0.0173033i	−0.999963	+	0.00865166i	$0.997246\pi$
$662$	4.45125	−	7.70980i	0.173003	−	0.299650i
$663$	5.49937	+	7.23825i	0.213578	+	0.281110i
$664$	9.73159			0.377659
$665$	−1.55987	+	3.37422i	−0.0604893	+	0.130847i
$666$	−5.71513	−	9.89889i	−0.221457	−	0.383574i
$667$	−3.85736			−0.149358
$668$	−6.48853	−	3.74616i	−0.251049	−	0.144943i
$669$	7.09390	−	4.09566i	0.274266	−	0.158347i
$670$			21.8386i			0.843700i
$671$		−	27.0387i		−	1.04382i
$672$	−5.08588	−	2.35116i	−0.196192	−	0.0906979i
$673$	2.77793	+	4.81152i	0.107081	+	0.185470i	0.914587	−	0.404390i	$-0.132516\pi$
$673$	2.77793	+	4.81152i	0.107081	+	0.185470i	−0.807505	+	0.589860i	$0.799183\pi$
$674$	35.4661	+	20.4764i	1.36610	+	0.788721i
$675$	−1.42357	+	2.46569i	−0.0547931	+	0.0949045i
$676$	3.45219	+	3.51879i	0.132776	+	0.135338i
$677$	4.65253	+	8.05842i	0.178811	+	0.309710i	0.941474	−	0.337087i	$-0.109442\pi$
$677$	4.65253	+	8.05842i	0.178811	+	0.309710i	−0.762662	+	0.646797i	$0.776108\pi$
$678$	−27.0825	+	15.6361i	−1.04010	+	0.600500i
$679$	−1.50400	−	16.5604i	−0.0577183	−	0.635529i
$680$	4.62420	−	8.00935i	0.177330	−	0.307145i
$681$	−19.8119	+	11.4384i	−0.759193	+	0.438321i
$682$	9.95371	−	5.74678i	0.381147	−	0.220055i
$683$	18.8883	−	10.9052i	0.722741	−	0.417275i	−0.0930198	−	0.995664i	$-0.529652\pi$
$683$	18.8883	−	10.9052i	0.722741	−	0.417275i	0.815761	+	0.578390i	$0.196319\pi$
$684$	0.314456	−	0.181551i	0.0120235	−	0.00694178i
$685$	−3.79906	+	6.58017i	−0.145155	+	0.251415i
$686$	27.6653	+	7.11973i	1.05627	+	0.271833i
$687$	12.3924	−	7.15476i	0.472800	−	0.272971i
$688$	−13.8895	−	24.0574i	−0.529533	−	0.917178i
$689$	4.86847	−	11.5965i	0.185474	−	0.441792i
$690$	2.99761	−	5.19201i	0.114117	−	0.197657i
$691$	7.03659	+	4.06258i	0.267685	+	0.154548i	0.627835	−	0.778346i	$-0.283941\pi$
$691$	7.03659	+	4.06258i	0.267685	+	0.154548i	−0.360150	+	0.932894i	$0.617275\pi$
$692$	0.309802	+	0.536593i	0.0117769	+	0.0203982i
$693$	−4.82621	+	3.40317i	−0.183333	+	0.129276i
$694$		−	18.4315i		−	0.699650i
$695$		−	30.3753i		−	1.15220i
$696$	3.15272	−	1.82023i	0.119504	−	0.0689955i
$697$	8.88723	+	5.13104i	0.336628	+	0.194352i
$698$	54.9047			2.07817
$699$	5.03403	+	8.71920i	0.190404	+	0.329790i
$700$	−1.64606	−	2.33436i	−0.0622152	−	0.0882306i
$701$	−28.5599			−1.07869			−0.539347	−	0.842084i	$-0.681329\pi$
$701$	−28.5599			−1.07869			−0.539347	+	0.842084i	$0.681329\pi$
$702$	−5.12786	−	2.15279i	−0.193539	−	0.0812517i
$703$	3.54802	−	6.14535i	0.133816	−	0.231776i
$704$		−	13.3088i		−	0.501595i
$705$	7.67103	−	13.2866i	0.288908	−	0.500403i
$706$	−25.3679	+	43.9385i	−0.954734	+	1.65365i
$707$	3.97455	+	5.63651i	0.149478	+	0.211983i
$708$	−0.251986	−	0.145484i	−0.00947020	−	0.00546762i
$709$			35.6413i			1.33854i	0.743020	+	0.669269i	$0.233393\pi$
$709$			35.6413i			1.33854i	−0.743020	+	0.669269i	$0.766607\pi$
$710$	−5.66973	−	3.27342i	−0.212781	−	0.122849i
$711$	−1.88401	−	3.26320i	−0.0706559	−	0.122380i
$712$	−12.6850	+	21.9711i	−0.475390	+	0.823400i
$713$	7.65864	−	4.42172i	0.286818	−	0.165595i
$714$	8.40874	−	5.92937i	0.314689	−	0.221901i
$715$	−7.14351	−	9.40226i	−0.267152	−	0.351625i
$716$	3.31091	+	5.73466i	0.123734	+	0.214314i
$717$		−	27.8817i		−	1.04126i
$718$	17.1388			0.639615
$719$	15.0838			0.562529			0.281265	−	0.959630i	$-0.409246\pi$
$719$	15.0838			0.562529			0.281265	+	0.959630i	$0.409246\pi$
$720$			6.77083i			0.252334i
$721$	13.8821	−	30.0289i	0.516996	−	1.11834i
$722$	−24.1555	−	13.9462i	−0.898976	−	0.519024i
$723$	−10.5053	+	6.06521i	−0.390695	+	0.225568i
$724$	−0.160903	−	0.278692i	−0.00597990	−	0.0103575i
$725$	4.14587			0.153974
$726$	−8.03892	−	4.64127i	−0.298352	−	0.172254i
$727$	40.1445			1.48888			0.744439	−	0.667690i	$-0.232717\pi$
$727$	40.1445			1.48888			0.744439	+	0.667690i	$0.232717\pi$
$728$	−17.6069	+	16.0861i	−0.652556	+	0.596192i
$729$	1.00000			0.0370370
$730$	−25.7152	−	14.8467i	−0.951762	−	0.549500i
$731$	15.1773			0.561354
$732$	−2.29672	−	3.97804i	−0.0848894	−	0.147033i
$733$	−24.3833	+	14.0777i	−0.900619	+	0.519973i	−0.877401	−	0.479758i	$-0.840725\pi$
$733$	−24.3833	+	14.0777i	−0.900619	+	0.519973i	−0.0232181	+	0.999730i	$0.507391\pi$
$734$	11.1314	+	6.42670i	0.410866	+	0.237214i
$735$	−1.85032	−	10.1028i	−0.0682501	−	0.372648i
$736$			5.60993i			0.206785i
$737$	−21.5379			−0.793360
$738$	−6.27825			−0.231106
$739$		−	23.4124i		−	0.861239i	−0.902534	−	0.430619i	$-0.858295\pi$
$739$		−	23.4124i		−	0.861239i	0.902534	−	0.430619i	$-0.141705\pi$
$740$	−2.06146	−	3.57055i	−0.0757808	−	0.131256i
$741$	−0.434297	−	3.42517i	−0.0159543	−	0.125827i
$742$	−12.9215	−	5.97347i	−0.474362	−	0.219293i
$743$	27.8733	−	16.0926i	1.02257	−	0.590382i	0.107723	−	0.994181i	$-0.465644\pi$
$743$	27.8733	−	16.0926i	1.02257	−	0.590382i	0.914848	+	0.403799i	$0.132311\pi$
$744$	−4.17307	+	7.22796i	−0.152992	+	0.264990i
$745$	12.9442	+	22.4200i	0.474238	+	0.821405i
$746$	−17.0314	−	9.83310i	−0.623565	−	0.360015i
$747$		−	3.89258i		−	0.142422i
$748$	−1.84798	−	1.06693i	−0.0675690	−	0.0390110i
$749$	48.0914	−	4.36763i	1.75722	−	0.159590i
$750$	−8.87982	+	15.3803i	−0.324245	+	0.561609i
$751$	−8.62667	+	14.9418i	−0.314791	+	0.545235i	−0.979393	−	0.201963i	$-0.935268\pi$
$751$	−8.62667	+	14.9418i	−0.314791	+	0.545235i	0.664602	+	0.747198i	$0.268601\pi$
$752$			48.2513i			1.75954i
$753$	−5.86315	+	10.1553i	−0.213665	+	0.370079i
$754$	1.01867	+	8.03398i	0.0370979	+	0.292580i
$755$	22.2318			0.809097
$756$	−0.420980	+	0.910638i	−0.0153109	+	0.0331196i
$757$	0.137120	+	0.237499i	0.00498371	+	0.00863204i	0.868507	−	0.495678i	$-0.165080\pi$
$757$	0.137120	+	0.237499i	0.00498371	+	0.00863204i	−0.863523	+	0.504310i	$0.831747\pi$
$758$	49.2718			1.78963
$759$	5.12052	+	2.95634i	0.185863	+	0.107308i
$760$	−3.04201	+	1.75630i	−0.110345	+	0.0637078i
$761$		−	0.838696i		−	0.0304027i	−0.999884	−	0.0152013i	$-0.995161\pi$
$761$		−	0.838696i		−	0.0304027i	0.999884	−	0.0152013i	$-0.00483893\pi$
$762$		−	6.63518i		−	0.240367i
$763$	0.381053	+	4.19572i	0.0137950	+	0.151895i
$764$	−5.18742	−	8.98488i	−0.187674	−	0.325062i
$765$	−3.20369	−	1.84965i	−0.115830	−	0.0668743i
$766$	13.0936	−	22.6787i	0.473090	−	0.819416i
$767$	−2.20299	+	1.67376i	−0.0795454	+	0.0604358i
$768$	−4.39703	−	7.61588i	−0.158664	−	0.274815i
$769$	−19.0211	+	10.9818i	−0.685918	+	0.396015i	−0.802081	−	0.597215i	$-0.796274\pi$
$769$	−19.0211	+	10.9818i	−0.685918	+	0.396015i	0.116163	+	0.993230i	$0.462941\pi$
$770$	−10.9227	+	7.70206i	−0.393626	+	0.277563i
$771$	11.2305	−	19.4518i	0.404458	−	0.700541i
$772$	3.87323	−	2.23621i	0.139401	−	0.0804829i
$773$	46.1042	−	26.6183i	1.65825	−	0.957394i	0.684734	−	0.728793i	$-0.259918\pi$
$773$	46.1042	−	26.6183i	1.65825	−	0.957394i	0.973520	−	0.228600i	$-0.0734149\pi$
$774$	−8.04135	+	4.64268i	−0.289040	+	0.166878i
$775$	−8.23146	+	4.75244i	−0.295683	+	0.170713i
$776$	7.85636	−	13.6076i	0.282027	−	0.488485i
$777$	1.77331	+	19.5257i	0.0636172	+	0.700481i
$778$	−2.30467	+	1.33060i	−0.0826265	+	0.0477044i
$779$	−1.94881	−	3.37543i	−0.0698232	−	0.120937i
$780$	−1.84963	−	0.776515i	−0.0662274	−	0.0278037i
$781$	3.22835	−	5.59167i	0.115519	−	0.200086i
$782$	−8.92152	−	5.15084i	−0.319033	−	0.184194i
$783$	−0.728078	−	1.26107i	−0.0260194	−	0.0450669i
$784$	20.9265	+	24.6071i	0.747375	+	0.878826i
$785$			24.6016i			0.878069i
$786$		−	22.8688i		−	0.815703i
$787$	−15.8836	+	9.17041i	−0.566190	+	0.326890i	−0.755626	−	0.655003i	$-0.772667\pi$
$787$	−15.8836	+	9.17041i	−0.566190	+	0.326890i	0.189436	+	0.981893i	$0.439334\pi$
$788$	2.76293	+	1.59518i	0.0984254	+	0.0568259i
$789$	−14.1477			−0.503673
$790$	−4.26389	−	7.38528i	−0.151702	−	0.262756i
$791$	53.4206	−	4.85162i	1.89942	−	0.172504i
$792$	−5.58018			−0.198283
$793$	−43.3304	+	5.49410i	−1.53871	+	0.195101i
$794$	2.39790	−	4.15329i	0.0850984	−	0.147395i
$795$			5.11817i			0.181523i
$796$	−0.961027	+	1.66455i	−0.0340627	+	0.0589983i
$797$	−14.8967	+	25.8018i	−0.527667	+	0.913945i	0.471813	+	0.881698i	$0.343600\pi$
$797$	−14.8967	+	25.8018i	−0.527667	+	0.913945i	−0.999480	+	0.0322469i	$0.989734\pi$
$798$	−3.89183	+	0.353453i	−0.137769	+	0.0125121i
$799$	−22.8306	−	13.1813i	−0.807688	−	0.466319i
$800$		−	6.02953i		−	0.213176i
$801$	8.78828	+	5.07392i	0.310519	+	0.179278i
$802$	23.5575	+	40.8027i	0.831843	+	1.44079i
$803$	14.6423	−	25.3611i	0.516714	−	0.894975i
$804$	−3.16875	+	1.82948i	−0.111753	+	0.0645208i
$805$	−8.40419	+	5.92616i	−0.296209	+	0.208870i
$806$	−11.2319	−	14.7834i	−0.395628	−	0.520724i
$807$	−6.37047	−	11.0340i	−0.224251	−	0.388415i
$808$			6.51707i			0.229270i
$809$	−26.0992			−0.917598			−0.458799	−	0.888540i	$-0.651720\pi$
$809$	−26.0992			−0.917598			−0.458799	+	0.888540i	$0.651720\pi$
$810$	2.26320			0.0795207
$811$		−	29.8679i		−	1.04880i	−0.851471	−	0.524402i	$-0.824289\pi$
$811$		−	29.8679i		−	1.04880i	0.851471	−	0.524402i	$-0.175711\pi$
$812$	1.45488	−	0.132132i	0.0510564	−	0.00463691i
$813$	−3.25356	−	1.87844i	−0.114107	−	0.0658798i
$814$	22.0947	−	12.7564i	0.774419	−	0.447111i
$815$	11.8521	+	20.5284i	0.415161	+	0.719080i
$816$	11.6344			0.407286
$817$	−4.99217	−	2.88223i	−0.174654	−	0.100836i
$818$	−11.3347			−0.396308
$819$	6.43436	+	7.04266i	0.224835	+	0.246090i
$820$	−2.26458			−0.0790825
$821$	40.5657	+	23.4206i	1.41575	+	0.817384i	0.995922	−	0.0902186i	$-0.0287566\pi$
$821$	40.5657	+	23.4206i	1.41575	+	0.817384i	0.419829	+	0.907603i	$0.362090\pi$
$822$	−7.98752			−0.278597
$823$	−8.93720	−	15.4797i	−0.311531	−	0.539588i	0.667163	−	0.744912i	$-0.267508\pi$
$823$	−8.93720	−	15.4797i	−0.311531	−	0.539588i	−0.978694	+	0.205324i	$0.934175\pi$
$824$	27.0724	−	15.6302i	0.943111	−	0.544505i
$825$	−5.50351	−	3.17746i	−0.191608	−	0.110625i
$826$	1.80463	+	2.55923i	0.0627910	+	0.0890471i
$827$			23.3454i			0.811799i	0.913918	+	0.405899i	$0.133042\pi$
$827$			23.3454i			0.811799i	−0.913918	+	0.405899i	$0.866958\pi$
$828$	1.00447			0.0349078
$829$	55.7461			1.93614			0.968071	−	0.250676i	$-0.0806530\pi$
$829$	55.7461			1.93614			0.968071	+	0.250676i	$0.0806530\pi$
$830$		−	8.80967i		−	0.305788i
$831$	−2.46101	−	4.26260i	−0.0853715	−	0.147868i
$832$	−21.3278	+	2.70428i	−0.739409	+	0.0937539i
$833$	−17.3598	+	3.17944i	−0.601482	+	0.110161i
$834$	27.6539	−	15.9660i	0.957577	−	0.552857i
$835$	14.4957	−	25.1073i	0.501645	−	0.868874i
$836$	0.405229	+	0.701877i	0.0140151	+	0.0242749i
$837$	2.89114	+	1.66920i	0.0999324	+	0.0576960i
$838$		−	17.8417i		−	0.616330i
$839$	−16.1000	−	9.29535i	−0.555834	−	0.320911i	0.195638	−	0.980676i	$-0.437322\pi$
$839$	−16.1000	−	9.29535i	−0.555834	−	0.320911i	−0.751472	+	0.659765i	$0.770656\pi$
$840$	4.07251	−	8.80940i	0.140515	−	0.303953i
$841$	13.4398	−	23.2784i	0.463442	−	0.802704i
$842$	5.84529	−	10.1243i	0.201442	−	0.348908i
$843$			21.9099i			0.754616i
$844$	−3.90282	+	6.75989i	−0.134341	+	0.232685i
$845$	−13.6159	+	13.3582i	−0.468402	+	0.459536i
$846$	16.1283			0.554504
$847$	9.17562	+	13.0124i	0.315278	+	0.447112i
$848$	−8.04840	−	13.9402i	−0.276383	−	0.478710i
$849$	30.4171			1.04391
$850$	9.58880	+	5.53610i	0.328893	+	0.189887i
$851$	17.0002	−	9.81508i	0.582760	−	0.336457i
$852$		−	1.09689i		−	0.0375789i
$853$			31.4429i			1.07659i	0.842758	+	0.538293i	$0.180931\pi$
$853$			31.4429i			1.07659i	−0.842758	+	0.538293i	$0.819069\pi$
$854$	4.47138	+	49.2338i	0.153008	+	1.68475i
$855$	0.702510	+	1.21678i	0.0240253	+	0.0416131i
$856$	39.5166	+	22.8149i	1.35065	+	0.779798i
$857$	28.3523	−	49.1076i	0.968495	−	1.67748i	0.268579	−	0.963258i	$-0.413446\pi$
$857$	28.3523	−	49.1076i	0.968495	−	1.67748i	0.699916	−	0.714225i	$-0.253221\pi$
$858$	4.80510	−	11.4456i	0.164043	−	0.390746i
$859$	−0.915541	−	1.58576i	−0.0312379	−	0.0541056i	0.849984	−	0.526809i	$-0.176612\pi$
$859$	−0.915541	−	1.58576i	−0.0312379	−	0.0541056i	−0.881222	+	0.472703i	$0.843278\pi$
$860$	−2.90053	+	1.67462i	−0.0989074	+	0.0571042i
$861$	9.77497	+	4.51888i	0.333130	+	0.154003i
$862$	1.90941	−	3.30719i	0.0650347	−	0.112643i
$863$	−19.2517	+	11.1150i	−0.655336	+	0.378358i	−0.790497	−	0.612465i	$-0.790178\pi$
$863$	−19.2517	+	11.1150i	−0.655336	+	0.378358i	0.135162	+	0.990824i	$0.456845\pi$
$864$	−1.83403	+	1.05888i	−0.0623949	+	0.0360237i
$865$	−2.07634	+	1.19878i	−0.0705977	+	0.0407596i
$866$	−1.37111	+	0.791609i	−0.0465921	+	0.0269000i
$867$	5.32172	−	9.21748i	0.180735	−	0.313042i
$868$	−2.73715	+	1.93008i	−0.0929049	+	0.0655113i
$869$	7.28359	−	4.20518i	0.247079	−	0.142651i
$870$	−1.64779	−	2.85405i	−0.0558652	−	0.0967614i
$871$	4.37639	+	34.5153i	0.148288	+	1.16950i
$872$	−1.99048	+	3.44762i	−0.0674063	+	0.116751i
$873$	−5.44296	−	3.14250i	−0.184216	−	0.106357i
$874$	1.95633	+	3.38845i	0.0661737	+	0.114616i
$875$	24.8957	−	17.5551i	0.841629	−	0.593469i
$876$		−	4.97498i		−	0.168089i
$877$		−	22.4439i		−	0.757877i	−0.925422	−	0.378939i	$-0.876289\pi$
$877$		−	22.4439i		−	0.757877i	0.925422	−	0.378939i	$-0.123711\pi$
$878$	−12.1234	+	6.99945i	−0.409145	+	0.236220i
$879$	−9.06140	−	5.23160i	−0.305633	−	0.176457i
$880$	−15.1127			−0.509450
$881$	16.2431	+	28.1338i	0.547242	+	0.947852i	0.998462	+	0.0554388i	$0.0176558\pi$
$881$	16.2431	+	28.1338i	0.547242	+	0.947852i	−0.451220	+	0.892413i	$0.649011\pi$
$882$	8.22511	−	6.99484i	0.276954	−	0.235528i
$883$	16.1468			0.543383			0.271691	−	0.962384i	$-0.412417\pi$
$883$	16.1468			0.543383			0.271691	+	0.962384i	$0.412417\pi$
$884$	−1.33430	+	3.17825i	−0.0448773	+	0.106896i
$885$	0.562949	−	0.975056i	0.0189233	−	0.0327761i
$886$		−	40.0664i		−	1.34606i
$887$	−5.99350	+	10.3811i	−0.201242	+	0.348562i	−0.948929	−	0.315490i	$-0.897831\pi$
$887$	−5.99350	+	10.3811i	−0.201242	+	0.348562i	0.747687	+	0.664052i	$0.231164\pi$
$888$	−9.26315	+	16.0442i	−0.310851	+	0.538409i
$889$	−4.77579	+	10.3307i	−0.160175	+	0.346480i
$890$	19.8896	+	11.4833i	0.666702	+	0.384921i
$891$			2.23204i			0.0747761i
$892$	2.68992	+	1.55303i	0.0900653	+	0.0519992i
$893$	5.00633	+	8.67122i	0.167530	+	0.290171i
$894$	−13.6076	+	23.5690i	−0.455105	+	0.788266i
$895$	−22.1902	+	12.8115i	−0.741737	+	0.428242i
$896$	3.21444	+	35.3938i	0.107387	+	1.18242i
$897$	3.69716	−	8.80652i	0.123445	−	0.294041i
$898$	−24.6468	−	42.6895i	−0.822474	−	1.42457i
$899$		−	4.86123i		−	0.162131i
$900$	−1.07960			−0.0359867
$901$	8.79463			0.292991
$902$		−	14.0133i		−	0.466592i
$903$	15.8617	−	1.44055i	0.527844	−	0.0479384i
$904$	43.8956	+	25.3431i	1.45995	+	0.842900i
$905$	1.07839	−	0.622611i	0.0358470	−	0.0206963i
$906$	11.6856	+	20.2400i	0.388227	+	0.672429i
$907$	−16.7985			−0.557787			−0.278893	−	0.960322i	$-0.589968\pi$
$907$	−16.7985			−0.557787			−0.278893	+	0.960322i	$0.589968\pi$
$908$	−7.51244	−	4.33731i	−0.249309	−	0.143939i
$909$	2.60679			0.0864616
$910$	14.5622	+	15.9389i	0.482733	+	0.528371i
$911$	18.7103			0.619899			0.309949	−	0.950753i	$-0.399688\pi$
$911$	18.7103			0.619899			0.309949	+	0.950753i	$0.399688\pi$
$912$	−3.82682	−	2.20942i	−0.126719	−	0.0731611i
$913$	8.68837			0.287543
$914$	−31.7326	−	54.9624i	−1.04962	−	1.81799i
$915$	15.3930	−	8.88715i	0.508877	−	0.293800i
$916$	4.69905	+	2.71300i	0.155261	+	0.0896400i
$917$	−16.4602	+	35.6057i	−0.543564	+	1.17580i
$918$		−	3.88889i		−	0.128353i
$919$	−13.4950			−0.445158			−0.222579	−	0.974915i	$-0.571448\pi$
$919$	−13.4950			−0.445158			−0.222579	+	0.974915i	$0.571448\pi$
$920$	−9.71712			−0.320364
$921$		−	11.2995i		−	0.372331i
$922$	−4.62560	−	8.01177i	−0.152336	−	0.263854i
$923$	−9.61681	−	4.03734i	−0.316541	−	0.132891i
$924$	−2.03258	−	0.939643i	−0.0668669	−	0.0309120i
$925$	−18.2718	+	10.5492i	−0.600771	+	0.346856i
$926$	20.9597	−	36.3033i	0.688779	−	1.19300i
$927$	−6.25199	−	10.8288i	−0.205342	−	0.355664i
$928$	2.67063	+	1.54189i	0.0876678	+	0.0506150i
$929$		−	23.2962i		−	0.764324i	−0.924095	−	0.382162i	$-0.875180\pi$
$929$		−	23.2962i		−	0.764324i	0.924095	−	0.382162i	$-0.124820\pi$
$930$	6.54322	+	3.77773i	0.214561	+	0.123877i
$931$	6.31382	+	2.25090i	0.206927	+	0.0737703i
$932$	−1.90884	+	3.30622i	−0.0625263	+	0.108299i
$933$	−3.38424	+	5.86168i	−0.110795	+	0.191903i
$934$		−	7.08319i		−	0.231769i
$935$	4.12849	−	7.15075i	0.135016	−	0.233855i
$936$	1.13386	+	8.94243i	0.0370614	+	0.292292i
$937$	−46.4351			−1.51697			−0.758484	−	0.651692i	$-0.774060\pi$
$937$	−46.4351			−1.51697			−0.758484	+	0.651692i	$0.774060\pi$
$938$	39.2177	−	3.56173i	1.28050	−	0.116295i
$939$	1.36847	+	2.37027i	0.0446585	+	0.0773507i
$940$	5.81753			0.189747
$941$	25.5347	+	14.7424i	0.832406	+	0.480590i	0.854676	−	0.519162i	$-0.173756\pi$
$941$	25.5347	+	14.7424i	0.832406	+	0.480590i	−0.0222695	+	0.999752i	$0.507089\pi$
$942$	−22.3975	+	12.9312i	−0.729751	+	0.421322i
$943$		−	10.7822i		−	0.351116i
$944$			3.54098i			0.115249i
$945$	−3.52370	−	1.62898i	−0.114626	−	0.0529906i
$946$	−10.3626	−	17.9486i	−0.336918	−	0.583559i
$947$	34.5999	+	19.9763i	1.12435	+	0.649142i	0.942507	−	0.334186i	$-0.108461\pi$
$947$	34.5999	+	19.9763i	1.12435	+	0.649142i	0.181840	+	0.983328i	$0.441795\pi$
$948$	0.714395	−	1.23737i	0.0232025	−	0.0401879i
$949$	−43.6173	−	18.3115i	−1.41588	−	0.594415i
$950$	−2.10265	−	3.64189i	−0.0682189	−	0.118159i
$951$	13.0303	−	7.52306i	0.422537	−	0.243952i
$952$	−15.1373	−	6.99785i	−0.490604	−	0.226802i
$953$	1.93532	−	3.35208i	0.0626913	−	0.108584i	−0.832976	−	0.553309i	$-0.813365\pi$
$953$	1.93532	−	3.35208i	0.0626913	−	0.108584i	0.895668	+	0.444724i	$0.146698\pi$
$954$	−4.65963	+	2.69024i	−0.150861	+	0.0870996i
$955$	34.7669	−	20.0727i	1.12503	−	0.649537i
$956$	9.15597	−	5.28620i	0.296125	−	0.170968i
$957$	2.81475	−	1.62510i	0.0909880	−	0.0525320i
$958$	6.56882	−	11.3775i	0.212229	−	0.367591i
$959$	12.4362	+	5.74916i	0.401587	+	0.185650i
$960$	7.57665	−	4.37438i	0.244535	−	0.141183i
$961$	−9.92754	−	17.1950i	−0.320243	−	0.554678i
$962$	−24.9320	−	32.8154i	−0.803841	−	1.05801i
$963$	9.12582	−	15.8064i	0.294076	−	0.509354i
$964$	−3.98347	−	2.29986i	−0.128299	−	0.0740734i
$965$	8.65298	+	14.9874i	0.278549	+	0.482462i
$966$	−9.81268	−	4.53631i	−0.315718	−	0.145954i
$967$		−	29.8554i		−	0.960086i	−0.877245	−	0.480043i	$-0.840621\pi$
$967$		−	29.8554i		−	0.960086i	0.877245	−	0.480043i	$-0.159379\pi$
$968$			15.0453i			0.483573i
$969$	2.09082	−	1.20713i	0.0671668	−	0.0387788i
$970$	−12.3185	−	7.11209i	−0.395523	−	0.228356i
$971$	−46.5168			−1.49279			−0.746397	−	0.665500i	$-0.768218\pi$
$971$	−46.5168			−1.49279			−0.746397	+	0.665500i	$0.768218\pi$
$972$	0.189594	+	0.328387i	0.00608123	+	0.0105330i
$973$	−54.5477	+	4.95399i	−1.74872	+	0.158818i
$974$	−10.0827			−0.323070
$975$	−3.97369	+	9.46520i	−0.127260	+	0.303129i
$976$	−27.9504	+	48.4114i	−0.894669	+	1.54961i
$977$		−	2.35636i		−	0.0753866i	−0.999289	−	0.0376933i	$-0.987999\pi$
$977$		−	2.35636i		−	0.0753866i	0.999289	−	0.0376933i	$-0.0120010\pi$
$978$	−12.4595	+	21.5805i	−0.398412	+	0.690069i
$979$	−11.3252	+	19.6158i	−0.361954	+	0.626923i
$980$	2.96682	−	2.52305i	0.0947715	−	0.0805960i
$981$	1.37903	+	0.796181i	0.0440289	+	0.0254201i
$982$			56.3244i			1.79738i
$983$	−24.9474	−	14.4034i	−0.795697	−	0.459396i	0.0462672	−	0.998929i	$-0.485267\pi$
$983$	−24.9474	−	14.4034i	−0.795697	−	0.459396i	−0.841964	+	0.539533i	$0.818601\pi$
$984$	5.08793	+	8.81256i	0.162197	+	0.280934i
$985$	−6.17253	+	10.6911i	−0.196673	+	0.340648i
$986$	−4.90416	+	2.83142i	−0.156180	+	0.0901707i
$987$	−25.1111	−	11.6086i	−0.799296	−	0.369507i
$988$	1.04244	−	0.792010i	0.0331645	−	0.0251972i
$989$	−7.97327	−	13.8101i	−0.253535	−	0.439136i
$990$			5.05155i			0.160549i
$991$	−44.8689			−1.42531			−0.712654	−	0.701516i	$-0.752507\pi$
$991$	−44.8689			−1.42531			−0.712654	+	0.701516i	$0.752507\pi$
$992$	−7.06991			−0.224470
$993$			5.77162i			0.183157i
$994$	−4.95370	+	10.7156i	−0.157122	+	0.339877i
$995$	−6.44095	−	3.71868i	−0.204192	−	0.117890i
$996$	1.27827	−	0.738009i	0.0405035	−	0.0233847i
$997$	−14.5426	−	25.1885i	−0.460568	−	0.797727i	0.538421	−	0.842676i	$-0.319021\pi$
$997$	−14.5426	−	25.1885i	−0.460568	−	0.797727i	−0.998989	+	0.0449488i	$0.985688\pi$
$998$	−34.8954			−1.10460
$999$	6.41759	+	3.70520i	0.203044	+	0.117227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bl.c.88.2	yes	12
3.2	odd	2		819.2.do.f.361.5		12
7.2	even	3		273.2.t.c.205.5	yes	12
13.4	even	6		273.2.t.c.4.2	✓	12
21.2	odd	6		819.2.bm.e.478.2		12
39.17	odd	6		819.2.bm.e.550.5		12
91.30	even	6	inner	273.2.bl.c.121.2	yes	12
273.212	odd	6		819.2.do.f.667.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.2	✓	12	13.4	even	6
273.2.t.c.205.5	yes	12	7.2	even	3
273.2.bl.c.88.2	yes	12	1.1	even	1	trivial
273.2.bl.c.121.2	yes	12	91.30	even	6	inner
819.2.bm.e.478.2		12	21.2	odd	6
819.2.bm.e.550.5		12	39.17	odd	6
819.2.do.f.361.5		12	3.2	odd	2
819.2.do.f.667.5		12	273.212	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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33581 - 0.771231i) q^{2} +1.00000 q^{3} +(0.189594 + 0.328387i) q^{4} +(-1.27069 + 0.733632i) q^{5} +(-1.33581 - 0.771231i) q^{6} +(1.52469 + 2.16225i) q^{7} +2.50004i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.33581 - 0.771231i) q^{2} +1.00000 q^{3} +(0.189594 + 0.328387i) q^{4} +(-1.27069 + 0.733632i) q^{5} +(-1.33581 - 0.771231i) q^{6} +(1.52469 + 2.16225i) q^{7} +2.50004i q^{8} +1.00000 q^{9} +2.26320 q^{10} +2.23204i q^{11} +(0.189594 + 0.328387i) q^{12} +(3.57691 - 0.453537i) q^{13} +(-0.369112 - 4.06424i) q^{14} +(-1.27069 + 0.733632i) q^{15} +(2.30730 - 3.99635i) q^{16} +(1.26061 + 2.18344i) q^{17} +(-1.33581 - 0.771231i) q^{18} -0.957578i q^{19} +(-0.481830 - 0.278185i) q^{20} +(1.52469 + 2.16225i) q^{21} +(1.72142 - 2.98158i) q^{22} +(1.32450 - 2.29410i) q^{23} +2.50004i q^{24} +(-1.42357 + 2.46569i) q^{25} +(-5.12786 - 2.15279i) q^{26} +1.00000 q^{27} +(-0.420980 + 0.910638i) q^{28} +(-0.728078 - 1.26107i) q^{29} +2.26320 q^{30} +(2.89114 + 1.66920i) q^{31} +(-1.83403 + 1.05888i) q^{32} +2.23204i q^{33} -3.88889i q^{34} +(-3.52370 - 1.62898i) q^{35} +(0.189594 + 0.328387i) q^{36} +(6.41759 + 3.70520i) q^{37} +(-0.738514 + 1.27914i) q^{38} +(3.57691 - 0.453537i) q^{39} +(-1.83411 - 3.17677i) q^{40} +(3.52497 - 2.03514i) q^{41} +(-0.369112 - 4.06424i) q^{42} +(3.00991 - 5.21332i) q^{43} +(-0.732971 + 0.423181i) q^{44} +(-1.27069 + 0.733632i) q^{45} +(-3.53857 + 2.04299i) q^{46} +(-9.05536 + 5.22812i) q^{47} +(2.30730 - 3.99635i) q^{48} +(-2.35062 + 6.59353i) q^{49} +(3.80323 - 2.19580i) q^{50} +(1.26061 + 2.18344i) q^{51} +(0.827097 + 1.08862i) q^{52} +(1.74412 - 3.02090i) q^{53} +(-1.33581 - 0.771231i) q^{54} +(-1.63749 - 2.83622i) q^{55} +(-5.40570 + 3.81180i) q^{56} -0.957578i q^{57} +2.24607i q^{58} +(-0.664540 + 0.383672i) q^{59} +(-0.481830 - 0.278185i) q^{60} -12.1139 q^{61} +(-2.57468 - 4.45947i) q^{62} +(1.52469 + 2.16225i) q^{63} -5.96263 q^{64} +(-4.21241 + 3.20044i) q^{65} +(1.72142 - 2.98158i) q^{66} +9.64946i q^{67} +(-0.478009 + 0.827936i) q^{68} +(1.32450 - 2.29410i) q^{69} +(3.45069 + 4.89359i) q^{70} +(-2.50519 - 1.44637i) q^{71} +2.50004i q^{72} +(-11.3623 - 6.56004i) q^{73} +(-5.71513 - 9.89889i) q^{74} +(-1.42357 + 2.46569i) q^{75} +(0.314456 - 0.181551i) q^{76} +(-4.82621 + 3.40317i) q^{77} +(-5.12786 - 2.15279i) q^{78} +(-1.88401 - 3.26320i) q^{79} +6.77083i q^{80} +1.00000 q^{81} -6.27825 q^{82} -3.89258i q^{83} +(-0.420980 + 0.910638i) q^{84} +(-3.20369 - 1.84965i) q^{85} +(-8.04135 + 4.64268i) q^{86} +(-0.728078 - 1.26107i) q^{87} -5.58018 q^{88} +(8.78828 + 5.07392i) q^{89} +2.26320 q^{90} +(6.43436 + 7.04266i) q^{91} +1.00447 q^{92} +(2.89114 + 1.66920i) q^{93} +16.1283 q^{94} +(0.702510 + 1.21678i) q^{95} +(-1.83403 + 1.05888i) q^{96} +(-5.44296 - 3.14250i) q^{97} +(8.22511 - 6.99484i) q^{98} +2.23204i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9	\( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9} + 14 q^{10} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 27 q^{20} + 3 q^{21} + 7 q^{22} - 16 q^{23} + 10 q^{25} - q^{26} + 12 q^{27} + 24 q^{28} - 5 q^{29} + 14 q^{30} + 15 q^{31} - 6 q^{32} - 2 q^{35} + 5 q^{36} + 6 q^{37} + 24 q^{38} - q^{39} + 21 q^{40} - 15 q^{41} - 16 q^{42} - 13 q^{43} - 30 q^{44} + 6 q^{45} - 9 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} - 63 q^{50} - 55 q^{52} + 18 q^{53} - 3 q^{54} + 13 q^{55} - 21 q^{56} - 33 q^{59} - 27 q^{60} - 52 q^{61} - 13 q^{62} + 3 q^{63} - 4 q^{64} - 41 q^{65} + 7 q^{66} - 16 q^{69} - 42 q^{70} - 15 q^{71} - 18 q^{73} + 38 q^{74} + 10 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 12 q^{81} + 28 q^{82} + 24 q^{84} - 12 q^{85} - 15 q^{86} - 5 q^{87} - 32 q^{88} + 12 q^{89} + 14 q^{90} + 49 q^{91} - 40 q^{92} + 15 q^{93} + 6 q^{94} - 28 q^{95} - 6 q^{96} + 45 q^{97} + 48 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9 + 14 * q^10 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 27 * q^20 + 3 * q^21 + 7 * q^22 - 16 * q^23 + 10 * q^25 - q^26 + 12 * q^27 + 24 * q^28 - 5 * q^29 + 14 * q^30 + 15 * q^31 - 6 * q^32 - 2 * q^35 + 5 * q^36 + 6 * q^37 + 24 * q^38 - q^39 + 21 * q^40 - 15 * q^41 - 16 * q^42 - 13 * q^43 - 30 * q^44 + 6 * q^45 - 9 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 - 63 * q^50 - 55 * q^52 + 18 * q^53 - 3 * q^54 + 13 * q^55 - 21 * q^56 - 33 * q^59 - 27 * q^60 - 52 * q^61 - 13 * q^62 + 3 * q^63 - 4 * q^64 - 41 * q^65 + 7 * q^66 - 16 * q^69 - 42 * q^70 - 15 * q^71 - 18 * q^73 + 38 * q^74 + 10 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 12 * q^81 + 28 * q^82 + 24 * q^84 - 12 * q^85 - 15 * q^86 - 5 * q^87 - 32 * q^88 + 12 * q^89 + 14 * q^90 + 49 * q^91 - 40 * q^92 + 15 * q^93 + 6 * q^94 - 28 * q^95 - 6 * q^96 + 45 * q^97 + 48 * q^98

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