LMFDB - Embedded newform 273.2.bl.d.88.9

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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			88.9
Root			$2.11978i$ of defining polynomial
Character	$\chi$	$=$	273.88
Dual form			273.2.bl.d.121.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.83578 + 1.05989i) q^{2} -1.00000 q^{3} +(1.24674 + 2.15941i) q^{4} +(-3.01977 + 1.74346i) q^{5} +(-1.83578 - 1.05989i) q^{6} +(1.38962 + 2.25144i) q^{7} +1.04605i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.83578 + 1.05989i) q^{2} -1.00000 q^{3} +(1.24674 + 2.15941i) q^{4} +(-3.01977 + 1.74346i) q^{5} +(-1.83578 - 1.05989i) q^{6} +(1.38962 + 2.25144i) q^{7} +1.04605i q^{8} +1.00000 q^{9} -7.39152 q^{10} +4.16660i q^{11} +(-1.24674 - 2.15941i) q^{12} +(1.86958 + 3.08296i) q^{13} +(0.164764 + 5.60599i) q^{14} +(3.01977 - 1.74346i) q^{15} +(1.38477 - 2.39850i) q^{16} +(-1.38996 - 2.40747i) q^{17} +(1.83578 + 1.05989i) q^{18} -5.64150i q^{19} +(-7.52970 - 4.34728i) q^{20} +(-1.38962 - 2.25144i) q^{21} +(-4.41614 + 7.64898i) q^{22} +(1.83778 - 3.18313i) q^{23} -1.04605i q^{24} +(3.57933 - 6.19959i) q^{25} +(0.164539 + 7.64121i) q^{26} -1.00000 q^{27} +(-3.12928 + 5.80770i) q^{28} +(-1.07879 - 1.86851i) q^{29} +7.39152 q^{30} +(7.58870 + 4.38134i) q^{31} +(6.89610 - 3.98146i) q^{32} -4.16660i q^{33} -5.89280i q^{34} +(-8.12162 - 4.37606i) q^{35} +(1.24674 + 2.15941i) q^{36} +(3.28427 + 1.89617i) q^{37} +(5.97937 - 10.3566i) q^{38} +(-1.86958 - 3.08296i) q^{39} +(-1.82375 - 3.15883i) q^{40} +(4.80471 - 2.77400i) q^{41} +(-0.164764 - 5.60599i) q^{42} +(-2.45544 + 4.25295i) q^{43} +(-8.99739 + 5.19465i) q^{44} +(-3.01977 + 1.74346i) q^{45} +(6.74754 - 3.89569i) q^{46} +(-1.46177 + 0.843954i) q^{47} +(-1.38477 + 2.39850i) q^{48} +(-3.13792 + 6.25727i) q^{49} +(13.1418 - 7.58740i) q^{50} +(1.38996 + 2.40747i) q^{51} +(-4.32651 + 7.88083i) q^{52} +(-3.45203 + 5.97909i) q^{53} +(-1.83578 - 1.05989i) q^{54} +(-7.26432 - 12.5822i) q^{55} +(-2.35511 + 1.45361i) q^{56} +5.64150i q^{57} -4.57358i q^{58} +(-9.67955 + 5.58849i) q^{59} +(7.52970 + 4.34728i) q^{60} +3.32893 q^{61} +(9.28747 + 16.0864i) q^{62} +(1.38962 + 2.25144i) q^{63} +11.3406 q^{64} +(-11.0207 - 6.05029i) q^{65} +(4.41614 - 7.64898i) q^{66} -12.3848i q^{67} +(3.46581 - 6.00297i) q^{68} +(-1.83778 + 3.18313i) q^{69} +(-10.2714 - 16.6415i) q^{70} +(5.36500 + 3.09748i) q^{71} +1.04605i q^{72} +(-0.790069 - 0.456146i) q^{73} +(4.01947 + 6.96192i) q^{74} +(-3.57933 + 6.19959i) q^{75} +(12.1823 - 7.03346i) q^{76} +(-9.38083 + 5.78998i) q^{77} +(-0.164539 - 7.64121i) q^{78} +(-4.91596 - 8.51469i) q^{79} +9.65720i q^{80} +1.00000 q^{81} +11.7605 q^{82} -8.95699i q^{83} +(3.12928 - 5.80770i) q^{84} +(8.39469 + 4.84668i) q^{85} +(-9.01532 + 5.20500i) q^{86} +(1.07879 + 1.86851i) q^{87} -4.35847 q^{88} +(-0.00476914 - 0.00275346i) q^{89} -7.39152 q^{90} +(-4.34310 + 8.49338i) q^{91} +9.16491 q^{92} +(-7.58870 - 4.38134i) q^{93} -3.57799 q^{94} +(9.83575 + 17.0360i) q^{95} +(-6.89610 + 3.98146i) q^{96} +(12.9479 + 7.47550i) q^{97} +(-12.3926 + 8.16114i) q^{98} +4.16660i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * 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 $

$2$	1.83578	+	1.05989i	1.29810	+	0.749456i	0.980075	−	0.198628i	$-0.0636486\pi$
$2$	1.83578	+	1.05989i	1.29810	+	0.749456i	0.318020	+	0.948084i	$0.396982\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.24674	+	2.15941i	0.623368	+	1.07970i
$5$	−3.01977	+	1.74346i	−1.35048	+	0.779701i	−0.988317	−	0.152413i	$-0.951295\pi$
$5$	−3.01977	+	1.74346i	−1.35048	+	0.779701i	−0.362165	+	0.932114i	$0.617962\pi$
$6$	−1.83578	−	1.05989i	−0.749456	−	0.432698i
$7$	1.38962	+	2.25144i	0.525226	+	0.850963i
$7$	1.38962	+	2.25144i	0.525226	+	0.850963i
$8$			1.04605i			0.369834i
$9$	1.00000			0.333333
$10$	−7.39152			−2.33740
$11$			4.16660i			1.25628i	0.778101	+	0.628139i	$0.216183\pi$
$11$			4.16660i			1.25628i	−0.778101	+	0.628139i	$0.783817\pi$
$12$	−1.24674	−	2.15941i	−0.359901	−	0.623368i
$13$	1.86958	+	3.08296i	0.518528	+	0.855061i
$13$	1.86958	+	3.08296i	0.518528	+	0.855061i
$14$	0.164764	+	5.60599i	0.0440349	+	1.49826i
$15$	3.01977	−	1.74346i	0.779701	−	0.450160i
$16$	1.38477	−	2.39850i	0.346193	−	0.599624i
$17$	−1.38996	−	2.40747i	−0.337114	−	0.583898i	0.646775	−	0.762681i	$-0.276117\pi$
$17$	−1.38996	−	2.40747i	−0.337114	−	0.583898i	−0.983889	+	0.178783i	$0.942784\pi$
$18$	1.83578	+	1.05989i	0.432698	+	0.249819i
$19$		−	5.64150i		−	1.29425i	−0.762385	−	0.647124i	$-0.775971\pi$
$19$		−	5.64150i		−	1.29425i	0.762385	−	0.647124i	$-0.224029\pi$
$20$	−7.52970	−	4.34728i	−1.68369	−	0.972081i
$21$	−1.38962	−	2.25144i	−0.303240	−	0.491304i
$22$	−4.41614	+	7.64898i	−0.941524	+	1.63077i
$23$	1.83778	−	3.18313i	0.383204	−	0.663729i	−0.608314	−	0.793696i	$-0.708154\pi$
$23$	1.83778	−	3.18313i	0.383204	−	0.663729i	0.991518	+	0.129968i	$0.0414873\pi$
$24$		−	1.04605i		−	0.213524i
$25$	3.57933	−	6.19959i	0.715867	−	1.23992i
$26$	0.164539	+	7.64121i	0.0322688	+	1.49856i
$27$	−1.00000			−0.192450
$28$	−3.12928	+	5.80770i	−0.591379	+	1.09755i
$29$	−1.07879	−	1.86851i	−0.200325	−	0.346974i	0.748308	−	0.663352i	$-0.230867\pi$
$29$	−1.07879	−	1.86851i	−0.200325	−	0.346974i	−0.948633	+	0.316378i	$0.897533\pi$
$30$	7.39152			1.34950
$31$	7.58870	+	4.38134i	1.36297	+	0.786911i	0.990018	−	0.140939i	$-0.0450123\pi$
$31$	7.58870	+	4.38134i	1.36297	+	0.786911i	0.372952	+	0.927851i	$0.378346\pi$
$32$	6.89610	−	3.98146i	1.21907	−	0.703830i
$33$		−	4.16660i		−	0.725312i
$34$		−	5.89280i		−	1.01061i
$35$	−8.12162	−	4.37606i	−1.37280	−	0.739690i
$36$	1.24674	+	2.15941i	0.207789	+	0.359901i
$37$	3.28427	+	1.89617i	0.539930	+	0.311729i	0.745051	−	0.667008i	$-0.232425\pi$
$37$	3.28427	+	1.89617i	0.539930	+	0.311729i	−0.205121	+	0.978737i	$0.565759\pi$
$38$	5.97937	−	10.3566i	0.969982	−	1.68006i
$39$	−1.86958	−	3.08296i	−0.299372	−	0.493669i
$40$	−1.82375	−	3.15883i	−0.288360	−	0.499454i
$41$	4.80471	−	2.77400i	0.750370	−	0.433226i	−0.0754577	−	0.997149i	$-0.524042\pi$
$41$	4.80471	−	2.77400i	0.750370	−	0.433226i	0.825828	+	0.563923i	$0.190708\pi$
$42$	−0.164764	−	5.60599i	−0.0254236	−	0.865023i
$43$	−2.45544	+	4.25295i	−0.374451	+	0.648569i	−0.990245	−	0.139339i	$-0.955502\pi$
$43$	−2.45544	+	4.25295i	−0.374451	+	0.648569i	0.615793	+	0.787908i	$0.288836\pi$
$44$	−8.99739	+	5.19465i	−1.35641	+	0.783123i
$45$	−3.01977	+	1.74346i	−0.450160	+	0.259900i
$46$	6.74754	−	3.89569i	0.994870	−	0.574389i
$47$	−1.46177	+	0.843954i	−0.213221	+	0.123103i	−0.602808	−	0.797887i	$-0.705951\pi$
$47$	−1.46177	+	0.843954i	−0.213221	+	0.123103i	0.389586	+	0.920990i	$0.372618\pi$
$48$	−1.38477	+	2.39850i	−0.199875	+	0.346193i
$49$	−3.13792	+	6.25727i	−0.448275	+	0.893896i
$50$	13.1418	−	7.58740i	1.85853	−	1.07302i
$51$	1.38996	+	2.40747i	0.194633	+	0.337114i
$52$	−4.32651	+	7.88083i	−0.599979	+	1.09287i
$53$	−3.45203	+	5.97909i	−0.474173	+	0.821292i	−0.999563	−	0.0295700i	$-0.990586\pi$
$53$	−3.45203	+	5.97909i	−0.474173	+	0.821292i	0.525390	+	0.850862i	$0.323920\pi$
$54$	−1.83578	−	1.05989i	−0.249819	−	0.144233i
$55$	−7.26432	−	12.5822i	−0.979520	−	1.69658i
$56$	−2.35511	+	1.45361i	−0.314715	+	0.194247i
$57$			5.64150i			0.747235i
$58$		−	4.57358i		−	0.600540i
$59$	−9.67955	+	5.58849i	−1.26017	+	0.727560i	−0.973107	−	0.230352i	$-0.926012\pi$
$59$	−9.67955	+	5.58849i	−1.26017	+	0.727560i	−0.287063	+	0.957912i	$0.592679\pi$
$60$	7.52970	+	4.34728i	0.972081	+	0.561231i
$61$	3.32893			0.426226			0.213113	−	0.977028i	$-0.431640\pi$
$61$	3.32893			0.426226			0.213113	+	0.977028i	$0.431640\pi$
$62$	9.28747	+	16.0864i	1.17951	+	2.04297i
$63$	1.38962	+	2.25144i	0.175075	+	0.283654i
$64$	11.3406			1.41757
$65$	−11.0207	−	6.05029i	−1.36695	−	0.750447i
$66$	4.41614	−	7.64898i	0.543589	−	0.941524i
$67$		−	12.3848i		−	1.51305i	−0.653967	−	0.756523i	$-0.726897\pi$
$67$		−	12.3848i		−	1.51305i	0.653967	−	0.756523i	$-0.273103\pi$
$68$	3.46581	−	6.00297i	0.420292	−	0.727967i
$69$	−1.83778	+	3.18313i	−0.221243	+	0.383204i
$70$	−10.2714	−	16.6415i	−1.22767	−	1.98904i
$71$	5.36500	+	3.09748i	0.636708	+	0.367604i	0.783345	−	0.621587i	$-0.213512\pi$
$71$	5.36500	+	3.09748i	0.636708	+	0.367604i	−0.146637	+	0.989190i	$0.546845\pi$
$72$			1.04605i			0.123278i
$73$	−0.790069	−	0.456146i	−0.0924705	−	0.0533879i	0.453052	−	0.891484i	$-0.350335\pi$
$73$	−0.790069	−	0.456146i	−0.0924705	−	0.0533879i	−0.545522	+	0.838096i	$0.683669\pi$
$74$	4.01947	+	6.96192i	0.467254	+	0.809307i
$75$	−3.57933	+	6.19959i	−0.413306	+	0.715867i
$76$	12.1823	−	7.03346i	1.39741	−	0.806793i
$77$	−9.38083	+	5.78998i	−1.06905	+	0.659830i
$78$	−0.164539	−	7.64121i	−0.0186304	−	0.865196i
$79$	−4.91596	−	8.51469i	−0.553089	−	0.957977i	−0.998050	−	0.0624274i	$-0.980116\pi$
$79$	−4.91596	−	8.51469i	−0.553089	−	0.957977i	0.444961	−	0.895550i	$-0.353218\pi$
$80$			9.65720i			1.07971i
$81$	1.00000			0.111111
$82$	11.7605			1.29874
$83$		−	8.95699i		−	0.983157i	−0.870833	−	0.491579i	$-0.836420\pi$
$83$		−	8.95699i		−	0.983157i	0.870833	−	0.491579i	$-0.163580\pi$
$84$	3.12928	−	5.80770i	0.341433	−	0.633672i
$85$	8.39469	+	4.84668i	0.910532	+	0.525696i
$86$	−9.01532	+	5.20500i	−0.972147	+	0.561269i
$87$	1.07879	+	1.86851i	0.115658	+	0.200325i
$88$	−4.35847			−0.464615
$89$	−0.00476914	−	0.00275346i	−0.000505528	−	0.000291866i	0.499747	−	0.866171i	$-0.333426\pi$
$89$	−0.00476914	−	0.00275346i	−0.000505528	−	0.000291866i	−0.500253	+	0.865879i	$0.666760\pi$
$90$	−7.39152			−0.779135
$91$	−4.34310	+	8.49338i	−0.455280	+	0.890348i
$92$	9.16491			0.955508
$93$	−7.58870	−	4.38134i	−0.786911	−	0.454323i
$94$	−3.57799			−0.369042
$95$	9.83575	+	17.0360i	1.00913	+	1.74786i
$96$	−6.89610	+	3.98146i	−0.703830	+	0.406356i
$97$	12.9479	+	7.47550i	1.31466	+	0.759022i	0.982865	−	0.184328i	$-0.0590108\pi$
$97$	12.9479	+	7.47550i	1.31466	+	0.759022i	0.331800	+	0.943350i	$0.392344\pi$
$98$	−12.3926	+	8.16114i	−1.25184	+	0.824400i
$99$			4.16660i			0.418759i
$100$	17.8499			1.78499
$101$	15.7650			1.56868			0.784340	−	0.620331i	$-0.213002\pi$
$101$	15.7650			1.56868			0.784340	+	0.620331i	$0.213002\pi$
$102$			5.89280i			0.583475i
$103$	−6.01085	−	10.4111i	−0.592266	−	1.02584i	−0.993926	−	0.110046i	$-0.964900\pi$
$103$	−6.01085	−	10.4111i	−0.592266	−	1.02584i	0.401660	−	0.915789i	$-0.368433\pi$
$104$	−3.22493	+	1.95567i	−0.316231	+	0.191770i
$105$	8.12162	+	4.37606i	0.792589	+	0.427060i
$106$	−12.6744	+	7.31755i	−1.23104	+	0.710743i
$107$	−5.08615	+	8.80947i	−0.491697	+	0.851644i	−0.999954	−	0.00956139i	$-0.996956\pi$
$107$	−5.08615	+	8.80947i	−0.491697	+	0.851644i	0.508258	+	0.861205i	$0.330290\pi$
$108$	−1.24674	−	2.15941i	−0.119967	−	0.207789i
$109$	−10.3230	−	5.95999i	−0.988764	−	0.570863i	−0.0838593	−	0.996478i	$-0.526725\pi$
$109$	−10.3230	−	5.95999i	−0.988764	−	0.570863i	−0.904905	+	0.425614i	$0.860058\pi$
$110$		−	30.7975i		−	2.93643i
$111$	−3.28427	−	1.89617i	−0.311729	−	0.179977i
$112$	7.32437	−	0.215268i	0.692087	−	0.0203409i
$113$	−2.74618	+	4.75653i	−0.258339	+	0.447457i	−0.965797	−	0.259299i	$-0.916509\pi$
$113$	−2.74618	+	4.75653i	−0.258339	+	0.447457i	0.707458	+	0.706756i	$0.249842\pi$
$114$	−5.97937	+	10.3566i	−0.560019	+	0.969982i
$115$			12.8164i			1.19514i
$116$	2.68992	−	4.65908i	0.249753	−	0.432585i
$117$	1.86958	+	3.08296i	0.172843	+	0.285020i
$118$	−23.6928			−2.18109
$119$	3.48877	−	6.47487i	0.319815	−	0.593550i
$120$	1.82375	+	3.15883i	0.166485	+	0.288360i
$121$	−6.36056			−0.578233
$122$	6.11119	+	3.52830i	0.553282	+	0.319437i
$123$	−4.80471	+	2.77400i	−0.433226	+	0.250123i
$124$			21.8495i			1.96214i
$125$			7.52711i			0.673245i
$126$	0.164764	+	5.60599i	0.0146783	+	0.499421i
$127$	−10.7099	−	18.5502i	−0.950353	−	1.64606i	−0.744660	−	0.667443i	$-0.767389\pi$
$127$	−10.7099	−	18.5502i	−0.950353	−	1.64606i	−0.205693	−	0.978617i	$-0.565945\pi$
$128$	7.02664	+	4.05684i	0.621074	+	0.358577i
$129$	2.45544	−	4.25295i	0.216190	−	0.374451i
$130$	−13.8190	−	22.7878i	−1.21201	−	1.99862i
$131$	−8.41671	−	14.5782i	−0.735372	−	1.27370i	−0.954560	−	0.298019i	$-0.903674\pi$
$131$	−8.41671	−	14.5782i	−0.735372	−	1.27370i	0.219188	−	0.975683i	$-0.429659\pi$
$132$	8.99739	−	5.19465i	0.783123	−	0.452136i
$133$	12.7015	−	7.83953i	1.10136	−	0.679773i
$134$	13.1265	−	22.7358i	1.13396	−	1.96408i
$135$	3.01977	−	1.74346i	0.259900	−	0.150053i
$136$	2.51834	−	1.45396i	0.215946	−	0.124676i
$137$	0.222701	−	0.128576i	0.0190266	−	0.0109850i	−0.490457	−	0.871466i	$-0.663170\pi$
$137$	0.222701	−	0.128576i	0.0190266	−	0.0109850i	0.509483	+	0.860481i	$0.329837\pi$
$138$	−6.74754	+	3.89569i	−0.574389	+	0.331623i
$139$	7.66647	−	13.2787i	0.650262	−	1.12629i	−0.332798	−	0.942998i	$-0.607993\pi$
$139$	7.66647	−	13.2787i	0.650262	−	1.12629i	0.983059	−	0.183288i	$-0.0586740\pi$
$140$	−0.675799	−	22.9937i	−0.0571154	−	1.94332i
$141$	1.46177	−	0.843954i	0.123103	−	0.0710737i
$142$	6.56599	+	11.3726i	0.551005	+	0.954369i
$143$	−12.8455	+	7.78979i	−1.07419	+	0.651415i
$144$	1.38477	−	2.39850i	0.115398	−	0.199875i
$145$	6.51536	+	3.76165i	0.541072	+	0.312388i
$146$	−0.966930	−	1.67477i	−0.0800237	−	0.138605i
$147$	3.13792	−	6.25727i	0.258812	−	0.516091i
$148$			9.45610i			0.777287i
$149$		−	4.17042i		−	0.341654i	−0.985301	−	0.170827i	$-0.945356\pi$
$149$		−	4.17042i		−	0.341654i	0.985301	−	0.170827i	$-0.0546439\pi$
$150$	−13.1418	+	7.58740i	−1.07302	+	0.619509i
$151$	2.67494	+	1.54438i	0.217684	+	0.125680i	0.604877	−	0.796319i	$-0.293222\pi$
$151$	2.67494	+	1.54438i	0.217684	+	0.125680i	−0.387194	+	0.921998i	$0.626556\pi$
$152$	5.90129			0.478658
$153$	−1.38996	−	2.40747i	−0.112371	−	0.194633i
$154$	−23.3579	+	0.686504i	−1.88224	+	0.0553201i
$155$	−30.5548			−2.45422
$156$	4.32651	−	7.88083i	0.346398	−	0.630971i
$157$	−9.32909	+	16.1585i	−0.744543	+	1.28959i	0.205865	+	0.978580i	$0.433999\pi$
$157$	−9.32909	+	16.1585i	−0.744543	+	1.28959i	−0.950408	+	0.311005i	$0.899334\pi$
$158$		−	20.8415i		−	1.65806i
$159$	3.45203	−	5.97909i	0.273764	−	0.474173i
$160$	−13.8831	+	24.0462i	−1.09755	+	1.90102i
$161$	9.72043	−	0.285689i	0.766077	−	0.0225155i
$162$	1.83578	+	1.05989i	0.144233	+	0.0832729i
$163$			16.0522i			1.25731i	0.777685	+	0.628654i	$0.216394\pi$
$163$			16.0522i			1.25731i	−0.777685	+	0.628654i	$0.783606\pi$
$164$	11.9804	+	6.91689i	0.935513	+	0.540118i
$165$	7.26432	+	12.5822i	0.565526	+	0.979520i
$166$	9.49343	−	16.4431i	0.736833	−	1.27623i
$167$	4.32267	−	2.49570i	0.334498	−	0.193123i	−0.323338	−	0.946284i	$-0.604805\pi$
$167$	4.32267	−	2.49570i	0.334498	−	0.193123i	0.657836	+	0.753161i	$0.271472\pi$
$168$	2.35511	−	1.45361i	0.181701	−	0.112148i
$169$	−6.00935	+	11.5277i	−0.462257	+	0.886746i
$170$	10.2739	+	17.7949i	0.787972	+	1.36481i
$171$		−	5.64150i		−	0.431416i
$172$	−12.2451			−0.933684
$173$	11.2123			0.852453			0.426227	−	0.904616i	$-0.359843\pi$
$173$	11.2123			0.852453			0.426227	+	0.904616i	$0.359843\pi$
$174$			4.57358i			0.346722i
$175$	18.9319	−	0.556420i	1.43112	−	0.0420614i
$176$	9.99358	+	5.76979i	0.753294	+	0.434915i
$177$	9.67955	−	5.58849i	0.727560	−	0.420057i
$178$	−0.00583674	−	0.0101095i	−0.000437482	−	0.000757741i
$179$	−5.25921			−0.393092			−0.196546	−	0.980495i	$-0.562972\pi$
$179$	−5.25921			−0.393092			−0.196546	+	0.980495i	$0.562972\pi$
$180$	−7.52970	−	4.34728i	−0.561231	−	0.324027i
$181$	5.99931			0.445925			0.222963	−	0.974827i	$-0.428427\pi$
$181$	5.99931			0.445925			0.222963	+	0.974827i	$0.428427\pi$
$182$	−16.9750	+	10.9888i	−1.25827	+	0.814545i
$183$	−3.32893			−0.246082
$184$	3.32971	+	1.92241i	0.245470	+	0.141722i
$185$	−13.2236			−0.972221
$186$	−9.28747	−	16.0864i	−0.680991	−	1.17951i
$187$	10.0310	−	5.79139i	0.733538	−	0.423508i
$188$	−3.64488	−	2.10437i	−0.265830	−	0.153477i
$189$	−1.38962	−	2.25144i	−0.101080	−	0.163768i
$190$			41.6993i			3.02518i
$191$	4.61487			0.333920			0.166960	−	0.985964i	$-0.446605\pi$
$191$	4.61487			0.333920			0.166960	+	0.985964i	$0.446605\pi$
$192$	−11.3406			−0.818435
$193$			8.50460i			0.612175i	0.952003	+	0.306087i	$0.0990200\pi$
$193$			8.50460i			0.612175i	−0.952003	+	0.306087i	$0.900980\pi$
$194$	15.8464	+	27.4468i	1.13771	+	1.97057i
$195$	11.0207	+	6.05029i	0.789211	+	0.433271i
$196$	−17.4242	+	1.02510i	−1.24458	+	0.0732214i
$197$	−4.83680	+	2.79253i	−0.344608	+	0.198959i	−0.662308	−	0.749232i	$-0.730423\pi$
$197$	−4.83680	+	2.79253i	−0.344608	+	0.198959i	0.317700	+	0.948191i	$0.397090\pi$
$198$	−4.41614	+	7.64898i	−0.313841	+	0.543589i
$199$	−10.5428	−	18.2607i	−0.747362	−	1.29447i	−0.949083	−	0.315026i	$-0.897987\pi$
$199$	−10.5428	−	18.2607i	−0.747362	−	1.29447i	0.201721	−	0.979443i	$-0.435346\pi$
$200$	6.48508	+	3.74416i	0.458564	+	0.264752i
$201$			12.3848i			0.873557i
$202$	28.9412	+	16.7092i	2.03630	+	1.17566i
$203$	2.70773	−	5.02533i	0.190046	−	0.352709i
$204$	−3.46581	+	6.00297i	−0.242656	+	0.420292i
$205$	−9.67274	+	16.7537i	−0.675574	+	1.17013i
$206$		−	25.4834i		−	1.77551i
$207$	1.83778	−	3.18313i	0.127735	−	0.221243i
$208$	9.98342	−	0.214974i	0.692226	−	0.0149058i
$209$	23.5059			1.62594
$210$	10.2714	+	16.6415i	0.708793	+	1.14838i
$211$	2.36508	+	4.09643i	0.162819	+	0.282010i	0.935878	−	0.352323i	$-0.114608\pi$
$211$	2.36508	+	4.09643i	0.162819	+	0.282010i	−0.773060	+	0.634333i	$0.781275\pi$
$212$	−17.2151			−1.18234
$213$	−5.36500	−	3.09748i	−0.367604	−	0.212236i
$214$	−18.6741	+	10.7815i	−1.27654	+	0.737010i
$215$		−	17.1239i		−	1.16784i
$216$		−	1.04605i		−	0.0711747i
$217$	0.681094	+	23.1738i	0.0462357	+	1.57314i
$218$	−12.6339	−	21.8825i	−0.855673	−	1.48207i
$219$	0.790069	+	0.456146i	0.0533879	+	0.0308235i
$220$	18.1134	−	31.3733i	1.22120	−	2.11519i
$221$	4.82353	−	8.78615i	0.324465	−	0.591020i
$222$	−4.01947	−	6.96192i	−0.269769	−	0.467254i
$223$	4.23414	−	2.44458i	0.283539	−	0.163701i	−0.351485	−	0.936193i	$-0.614323\pi$
$223$	4.23414	−	2.44458i	0.283539	−	0.163701i	0.635025	+	0.772492i	$0.280990\pi$
$224$	18.5470	+	9.99341i	1.23922	+	0.667713i
$225$	3.57933	−	6.19959i	0.238622	−	0.413306i
$226$	−10.0828	+	5.82131i	−0.670698	+	0.387228i
$227$	−1.81353	+	1.04704i	−0.120368	+	0.0694945i	−0.558975	−	0.829184i	$-0.688805\pi$
$227$	−1.81353	+	1.04704i	−0.120368	+	0.0694945i	0.438607	+	0.898679i	$0.355472\pi$
$228$	−12.1823	+	7.03346i	−0.806793	+	0.465802i
$229$	−11.4235	+	6.59538i	−0.754888	+	0.435835i	−0.827457	−	0.561528i	$-0.810214\pi$
$229$	−11.4235	+	6.59538i	−0.754888	+	0.435835i	0.0725692	+	0.997363i	$0.476880\pi$
$230$	−13.5840	+	23.5282i	−0.895703	+	1.55140i
$231$	9.38083	−	5.78998i	0.617213	−	0.380953i
$232$	1.95456	−	1.12846i	0.128323	−	0.0740872i
$233$	−6.07282	−	10.5184i	−0.397844	−	0.689086i	0.595616	−	0.803269i	$-0.296908\pi$
$233$	−6.07282	−	10.5184i	−0.397844	−	0.689086i	−0.993460	+	0.114184i	$0.963575\pi$
$234$	0.164539	+	7.64121i	0.0107563	+	0.499521i
$235$	2.94281	−	5.09709i	0.191968	−	0.332498i
$236$	−24.1357	−	13.9347i	−1.57110	−	0.907074i
$237$	4.91596	+	8.51469i	0.319326	+	0.553089i
$238$	13.2673	−	8.18875i	0.859989	−	0.530798i
$239$		−	22.1534i		−	1.43299i	−0.697594	−	0.716494i	$-0.745746\pi$
$239$		−	22.1534i		−	1.43299i	0.697594	−	0.716494i	$-0.254254\pi$
$240$		−	9.65720i		−	0.623370i
$241$	−3.15700	+	1.82270i	−0.203360	+	0.117410i	−0.598222	−	0.801330i	$-0.704126\pi$
$241$	−3.15700	+	1.82270i	−0.203360	+	0.117410i	0.394862	+	0.918741i	$0.370793\pi$
$242$	−11.6766	−	6.74150i	−0.750601	−	0.433360i
$243$	−1.00000			−0.0641500
$244$	4.15029	+	7.18852i	0.265695	+	0.460198i
$245$	−1.43352	−	24.3664i	−0.0915844	−	1.55671i
$246$	−11.7605			−0.749825
$247$	17.3925	−	10.5472i	1.10666	−	0.671104i
$248$	−4.58310	+	7.93815i	−0.291027	+	0.504073i
$249$			8.95699i			0.567626i
$250$	−7.97792	+	13.8182i	−0.504568	+	0.873937i
$251$	−6.55659	+	11.3563i	−0.413848	+	0.716806i	−0.995307	−	0.0967699i	$-0.969149\pi$
$251$	−6.55659	+	11.3563i	−0.413848	+	0.716806i	0.581459	+	0.813576i	$0.302482\pi$
$252$	−3.12928	+	5.80770i	−0.197126	+	0.365851i
$253$	13.2628	+	7.65730i	0.833827	+	0.481410i
$254$		−	45.4054i		−	2.84899i
$255$	−8.39469	−	4.84668i	−0.525696	−	0.303511i
$256$	−2.74097	−	4.74750i	−0.171311	−	0.296719i
$257$	−2.31610	+	4.01159i	−0.144474	+	0.250236i	−0.929177	−	0.369636i	$-0.879482\pi$
$257$	−2.31610	+	4.01159i	−0.144474	+	0.250236i	0.784703	+	0.619872i	$0.212816\pi$
$258$	9.01532	−	5.20500i	0.561269	−	0.324049i
$259$	0.294766	+	10.0293i	0.0183159	+	0.623188i
$260$	−0.674879	−	31.3414i	−0.0418542	−	1.94371i
$261$	−1.07879	−	1.86851i	−0.0667751	−	0.115658i
$262$		−	35.6832i		−	2.20451i
$263$	9.09261			0.560675			0.280337	−	0.959902i	$-0.409554\pi$
$263$	9.09261			0.560675			0.280337	+	0.959902i	$0.409554\pi$
$264$	4.35847			0.268245
$265$		−	24.0740i		−	1.47885i
$266$	31.6262	−	0.929514i	1.93913	−	0.0569921i
$267$	0.00476914	+	0.00275346i	0.000291866	+	0.000168509i
$268$	26.7439	−	15.4406i	1.63364	−	0.943184i
$269$	12.3207	+	21.3401i	0.751207	+	1.30113i	0.947238	+	0.320531i	$0.103861\pi$
$269$	12.3207	+	21.3401i	0.751207	+	1.30113i	−0.196031	+	0.980598i	$0.562805\pi$
$270$	7.39152			0.449834
$271$	−6.76712	−	3.90700i	−0.411073	−	0.237333i	0.280178	−	0.959948i	$-0.409607\pi$
$271$	−6.76712	−	3.90700i	−0.411073	−	0.237333i	−0.691251	+	0.722615i	$0.742940\pi$
$272$	−7.69909			−0.466826
$273$	4.34310	−	8.49338i	0.262856	−	0.514043i
$274$	0.545107			0.0329311
$275$	25.8312	+	14.9137i	1.55768	+	0.899327i
$276$	−9.16491			−0.551663
$277$	13.4229	+	23.2491i	0.806503	+	1.39690i	0.915272	+	0.402836i	$0.131976\pi$
$277$	13.4229	+	23.2491i	0.806503	+	1.39690i	−0.108769	+	0.994067i	$0.534691\pi$
$278$	28.1480	−	16.2512i	1.68820	−	0.974684i
$279$	7.58870	+	4.38134i	0.454323	+	0.262304i
$280$	4.57758	−	8.49562i	0.273563	−	0.507710i
$281$		−	18.5953i		−	1.10931i	−0.832082	−	0.554653i	$-0.812851\pi$
$281$		−	18.5953i		−	1.10931i	0.832082	−	0.554653i	$-0.187149\pi$
$282$	3.57799			0.213066
$283$	−8.35936			−0.496913			−0.248456	−	0.968643i	$-0.579923\pi$
$283$	−8.35936			−0.496913			−0.248456	+	0.968643i	$0.579923\pi$
$284$			15.4470i			0.916609i
$285$	−9.83575	−	17.0360i	−0.582620	−	1.00913i
$286$	−31.8379	+	0.685569i	−1.88261	+	0.0405386i
$287$	12.9222	+	6.96270i	0.762773	+	0.410995i
$288$	6.89610	−	3.98146i	0.406356	−	0.234610i
$289$	4.63604	−	8.02986i	0.272709	−	0.472345i
$290$	7.97387	+	13.8111i	0.468242	+	0.811018i
$291$	−12.9479	−	7.47550i	−0.759022	−	0.438222i
$292$		−	2.27477i		−	0.133121i
$293$	1.03180	+	0.595712i	0.0602786	+	0.0348019i	0.529836	−	0.848100i	$-0.322253\pi$
$293$	1.03180	+	0.595712i	0.0602786	+	0.0348019i	−0.469558	+	0.882902i	$0.655587\pi$
$294$	12.3926	−	8.16114i	0.722749	−	0.475967i
$295$	19.4867	−	33.7519i	1.13456	−	1.96511i
$296$	−1.98349	+	3.43551i	−0.115288	+	0.199685i
$297$		−	4.16660i		−	0.241771i
$298$	4.42019	−	7.65599i	0.256055	−	0.443500i
$299$	13.2494	−	0.285300i	0.766230	−	0.0164993i
$300$	−17.8499			−1.03057
$301$	−12.9874	+	0.381707i	−0.748579	+	0.0220012i
$302$	3.27374	+	5.67029i	0.188383	+	0.326288i
$303$	−15.7650			−0.905678
$304$	−13.5311	−	7.81219i	−0.776063	−	0.448060i
$305$	−10.0526	+	5.80387i	−0.575610	+	0.332328i
$306$		−	5.89280i		−	0.336869i
$307$		−	0.450235i		−	0.0256963i	−0.999917	−	0.0128481i	$-0.995910\pi$
$307$		−	0.450235i		−	0.0256963i	0.999917	−	0.0128481i	$-0.00408980\pi$
$308$	−24.1984	−	13.0385i	−1.37883	−	0.742936i
$309$	6.01085	+	10.4111i	0.341945	+	0.592266i
$310$	−56.0920	−	32.3847i	−3.18581	−	1.83933i
$311$	2.39916	−	4.15546i	0.136044	−	0.235634i	−0.789952	−	0.613169i	$-0.789895\pi$
$311$	2.39916	−	4.15546i	0.136044	−	0.235634i	0.925996	+	0.377534i	$0.123228\pi$
$312$	3.22493	−	1.95567i	0.182576	−	0.110718i
$313$	−0.476130	−	0.824681i	−0.0269125	−	0.0466137i	0.852255	−	0.523126i	$-0.175234\pi$
$313$	−0.476130	−	0.824681i	−0.0269125	−	0.0466137i	−0.879168	+	0.476512i	$0.841901\pi$
$314$	−34.2524	+	19.7756i	−1.93297	+	1.11600i
$315$	−8.12162	−	4.37606i	−0.457601	−	0.246563i
$316$	12.2578	−	21.2311i	0.689555	−	1.19434i
$317$	0.276987	−	0.159919i	0.0155572	−	0.00898193i	−0.492201	−	0.870481i	$-0.663808\pi$
$317$	0.276987	−	0.159919i	0.0155572	−	0.00898193i	0.507758	+	0.861500i	$0.330474\pi$
$318$	12.6744	−	7.31755i	0.710743	−	0.410348i
$319$	7.78534	−	4.49487i	0.435895	−	0.251664i
$320$	−34.2459	+	19.7719i	−1.91440	+	1.10528i
$321$	5.08615	−	8.80947i	0.283881	−	0.491697i
$322$	18.1474	+	9.77812i	1.01132	+	0.544913i
$323$	−13.5818	+	7.84144i	−0.755710	+	0.436309i
$324$	1.24674	+	2.15941i	0.0692631	+	0.119967i
$325$	25.8050	−	0.555662i	1.43140	−	0.0308226i
$326$	−17.0136	+	29.4684i	−0.942297	+	1.63211i
$327$	10.3230	+	5.95999i	0.570863	+	0.329588i
$328$	2.90174	+	5.02597i	0.160222	+	0.277513i
$329$	−3.93141	−	2.11831i	−0.216746	−	0.116786i
$330$			30.7975i			1.69535i
$331$			3.39943i			0.186850i	0.995626	+	0.0934248i	$0.0297815\pi$
$331$			3.39943i			0.186850i	−0.995626	+	0.0934248i	$0.970219\pi$
$332$	19.3418	−	11.1670i	1.06152	−	0.612869i
$333$	3.28427	+	1.89617i	0.179977	+	0.103910i
$334$	10.5807			0.578948
$335$	21.5925	+	37.3993i	1.17972	+	2.04334i
$336$	−7.32437	+	0.215268i	−0.399577	+	0.0117438i
$337$	−22.7070			−1.23693			−0.618465	−	0.785812i	$-0.712245\pi$
$337$	−22.7070			−1.23693			−0.618465	+	0.785812i	$0.712245\pi$
$338$	−23.2500	+	14.7931i	−1.26463	+	0.804639i
$339$	2.74618	−	4.75653i	0.149152	−	0.258339i
$340$			24.1701i			1.31081i
$341$	−18.2553	+	31.6191i	−0.988579	+	1.71227i
$342$	5.97937	−	10.3566i	0.323327	−	0.560019i
$343$	−18.4484	+	1.63038i	−0.996118	+	0.0880324i
$344$	−4.44880	−	2.56851i	−0.239863	−	0.138485i
$345$		−	12.8164i		−	0.690013i
$346$	20.5833	+	11.8838i	1.10657	+	0.638876i
$347$	1.33328	+	2.30930i	0.0715741	+	0.123970i	0.899591	−	0.436733i	$-0.143864\pi$
$347$	1.33328	+	2.30930i	0.0715741	+	0.123970i	−0.828017	+	0.560703i	$0.810531\pi$
$348$	−2.68992	+	4.65908i	−0.144195	+	0.249753i
$349$	24.1217	−	13.9267i	1.29121	−	0.745478i	0.312338	−	0.949971i	$-0.398888\pi$
$349$	24.1217	−	13.9267i	1.29121	−	0.745478i	0.978868	+	0.204493i	$0.0655544\pi$
$350$	35.3446	+	19.0442i	1.88925	+	1.01796i
$351$	−1.86958	−	3.08296i	−0.0997908	−	0.164556i
$352$	16.5892	+	28.7333i	0.884206	+	1.53149i
$353$		−	5.20209i		−	0.276879i	−0.990371	−	0.138440i	$-0.955791\pi$
$353$		−	5.20209i		−	0.276879i	0.990371	−	0.138440i	$-0.0442087\pi$
$354$	23.6928			1.25926
$355$	−21.6014			−1.14648
$356$		−	0.0137314i		−	0.000727760i
$357$	−3.48877	+	6.47487i	−0.184645	+	0.342686i
$358$	−9.65477	−	5.57418i	−0.510270	−	0.294605i
$359$	30.3841	−	17.5423i	1.60361	−	0.925845i	0.612853	−	0.790197i	$-0.290022\pi$
$359$	30.3841	−	17.5423i	1.60361	−	0.925845i	0.990757	−	0.135648i	$-0.0433115\pi$
$360$	−1.82375	−	3.15883i	−0.0961201	−	0.166485i
$361$	−12.8265			−0.675079
$362$	11.0134	+	6.35861i	0.578853	+	0.334201i
$363$	6.36056			0.333843
$364$	−23.7554	+	1.21048i	−1.24512	+	0.0634463i
$365$	3.18110			0.166506
$366$	−6.11119	−	3.52830i	−0.319437	−	0.184427i
$367$	−29.9257			−1.56211			−0.781054	−	0.624463i	$-0.785318\pi$
$367$	−29.9257			−1.56211			−0.781054	+	0.624463i	$0.785318\pi$
$368$	−5.08982	−	8.81582i	−0.265325	−	0.459557i
$369$	4.80471	−	2.77400i	0.250123	−	0.144409i
$370$	−24.2757	−	14.0156i	−1.26204	−	0.728636i
$371$	−18.2585	+	0.536630i	−0.947937	+	0.0278604i
$372$		−	21.8495i		−	1.13284i
$373$	−5.11173			−0.264675			−0.132338	−	0.991205i	$-0.542248\pi$
$373$	−5.11173			−0.264675			−0.132338	+	0.991205i	$0.542248\pi$
$374$	24.5530			1.26960
$375$		−	7.52711i		−	0.388698i
$376$	−0.882818	−	1.52909i	−0.0455278	−	0.0788565i
$377$	3.74368	−	6.81919i	0.192809	−	0.351206i
$378$	−0.164764	−	5.60599i	−0.00847452	−	0.288341i
$379$	−5.52479	+	3.18974i	−0.283789	+	0.163846i	−0.635138	−	0.772399i	$-0.719057\pi$
$379$	−5.52479	+	3.18974i	−0.283789	+	0.163846i	0.351348	+	0.936245i	$0.385723\pi$
$380$	−24.5252	+	42.4788i	−1.25811	+	2.17912i
$381$	10.7099	+	18.5502i	0.548687	+	0.950353i
$382$	8.47191	+	4.89126i	0.433461	+	0.250259i
$383$			16.6415i			0.850340i	0.905114	+	0.425170i	$0.139786\pi$
$383$			16.6415i			0.850340i	−0.905114	+	0.425170i	$0.860214\pi$
$384$	−7.02664	−	4.05684i	−0.358577	−	0.207025i
$385$	18.2333	−	33.8395i	0.929256	−	1.72462i
$386$	−9.01395	+	15.6126i	−0.458798	+	0.794661i
$387$	−2.45544	+	4.25295i	−0.124817	+	0.216190i
$388$			37.2799i			1.89260i
$389$	17.6610	−	30.5898i	0.895451	−	1.55097i	0.0622045	−	0.998063i	$-0.480187\pi$
$389$	17.6610	−	30.5898i	0.895451	−	1.55097i	0.833246	−	0.552902i	$-0.186480\pi$
$390$	13.8190	+	22.7878i	0.699754	+	1.15391i
$391$	−10.2177			−0.516733
$392$	−6.54542	−	3.28242i	−0.330593	−	0.165787i
$393$	8.41671	+	14.5782i	0.424567	+	0.735372i
$394$	−11.8391			−0.596445
$395$	29.6901	+	17.1416i	1.49387	+	0.862487i
$396$	−8.99739	+	5.19465i	−0.452136	+	0.261041i
$397$		−	10.4263i		−	0.523279i	−0.965166	−	0.261639i	$-0.915737\pi$
$397$		−	10.4263i		−	0.523279i	0.965166	−	0.261639i	$-0.0842631\pi$
$398$		−	44.6970i		−	2.24046i
$399$	−12.7015	+	7.83953i	−0.635869	+	0.392467i
$400$	−9.91313	−	17.1700i	−0.495656	−	0.858502i
$401$	−9.73355	−	5.61967i	−0.486070	−	0.280633i	0.236873	−	0.971541i	$-0.423878\pi$
$401$	−9.73355	−	5.61967i	−0.486070	−	0.280633i	−0.722943	+	0.690908i	$0.757211\pi$
$402$	−13.1265	+	22.7358i	−0.654693	+	1.13396i
$403$	0.680166	+	31.5869i	0.0338815	+	1.57346i
$404$	19.6548	+	34.0432i	0.977865	+	1.69371i
$405$	−3.01977	+	1.74346i	−0.150053	+	0.0866334i
$406$	10.2971	−	6.35553i	0.511037	−	0.315419i
$407$	−7.90059	+	13.6842i	−0.391618	+	0.678302i
$408$	−2.51834	+	1.45396i	−0.124676	+	0.0719819i
$409$	−2.23110	+	1.28812i	−0.110321	+	0.0636936i	−0.554145	−	0.832420i	$-0.686955\pi$
$409$	−2.23110	+	1.28812i	−0.110321	+	0.0636936i	0.443824	+	0.896114i	$0.353621\pi$
$410$	−35.5141	+	20.5041i	−1.75392	+	1.01262i
$411$	−0.222701	+	0.128576i	−0.0109850	+	0.00634220i
$412$	14.9879	−	25.9597i	0.738399	−	1.27894i
$413$	−26.0330	−	14.0270i	−1.28100	−	0.690224i
$414$	6.74754	−	3.89569i	0.331623	−	0.191463i
$415$	15.6162	+	27.0480i	0.766569	+	1.32774i
$416$	25.1675	+	13.8168i	1.23394	+	0.677423i
$417$	−7.66647	+	13.2787i	−0.375429	+	0.650262i
$418$	43.1517	+	24.9136i	2.11062	+	1.21857i
$419$	−5.42812	−	9.40179i	−0.265181	−	0.459307i	0.702430	−	0.711753i	$-0.252098\pi$
$419$	−5.42812	−	9.40179i	−0.265181	−	0.459307i	−0.967611	+	0.252446i	$0.918765\pi$
$420$	0.675799	+	22.9937i	0.0329756	+	1.12198i
$421$		−	14.0587i		−	0.685180i	−0.939485	−	0.342590i	$-0.888696\pi$
$421$		−	14.0587i		−	0.685180i	0.939485	−	0.342590i	$-0.111304\pi$
$422$			10.0269i			0.488101i
$423$	−1.46177	+	0.843954i	−0.0710737	+	0.0410344i
$424$	−6.25443	−	3.61100i	−0.303742	−	0.175365i
$425$	−19.9005			−0.965314
$426$	−6.56599	−	11.3726i	−0.318123	−	0.551005i
$427$	4.62594	+	7.49487i	0.223865	+	0.362702i
$428$	−25.3643			−1.22603
$429$	12.8455	−	7.78979i	0.620186	−	0.376095i
$430$	18.1495	−	31.4358i	0.875244	−	1.51597i
$431$		−	37.7601i		−	1.81884i	−0.415881	−	0.909419i	$-0.636527\pi$
$431$		−	37.7601i		−	1.81884i	0.415881	−	0.909419i	$-0.363473\pi$
$432$	−1.38477	+	2.39850i	−0.0666249	+	0.115398i
$433$	−9.25482	+	16.0298i	−0.444758	+	0.770344i	−0.998035	−	0.0626536i	$-0.980044\pi$
$433$	−9.25482	+	16.0298i	−0.444758	+	0.770344i	0.553277	+	0.832997i	$0.313377\pi$
$434$	−23.3114	+	43.2641i	−1.11898	+	2.07674i
$435$	−6.51536	−	3.76165i	−0.312388	−	0.180357i
$436$		−	29.7221i		−	1.42343i
$437$	−17.9576	−	10.3678i	−0.859030	−	0.495961i
$438$	0.966930	+	1.67477i	0.0462017	+	0.0800237i
$439$	−12.4083	+	21.4918i	−0.592215	+	1.02575i	0.401719	+	0.915763i	$0.368413\pi$
$439$	−12.4083	+	21.4918i	−0.592215	+	1.02575i	−0.993934	+	0.109983i	$0.964920\pi$
$440$	13.1616	−	7.59884i	0.627453	−	0.362260i
$441$	−3.13792	+	6.25727i	−0.149425	+	0.297965i
$442$	18.1673	−	11.0171i	0.864131	−	0.524028i
$443$	10.6889	+	18.5137i	0.507845	+	0.879613i	0.999959	+	0.00908216i	$0.00289098\pi$
$443$	10.6889	+	18.5137i	0.507845	+	0.879613i	−0.492114	+	0.870531i	$0.663776\pi$
$444$		−	9.45610i		−	0.448767i
$445$	0.0192023			0.000910274
$446$	10.3640			0.490748
$447$			4.17042i			0.197254i
$448$	15.7591	+	25.5326i	0.744546	+	1.20630i
$449$	22.1737	+	12.8020i	1.04644	+	0.604162i	0.921651	−	0.388021i	$-0.126841\pi$
$449$	22.1737	+	12.8020i	1.04644	+	0.604162i	0.124789	+	0.992183i	$0.460174\pi$
$450$	13.1418	−	7.58740i	0.619509	−	0.357674i
$451$	11.5582	+	20.0193i	0.544252	+	0.942673i
$452$	−13.6951			−0.644162
$453$	−2.67494	−	1.54438i	−0.125680	−	0.0725612i
$454$	−4.43899			−0.208332
$455$	−1.69276	−	33.2201i	−0.0793579	−	1.55738i
$456$	−5.90129			−0.276353
$457$	−2.48814	−	1.43653i	−0.116390	−	0.0671981i	0.440675	−	0.897667i	$-0.354739\pi$
$457$	−2.48814	−	1.43653i	−0.116390	−	0.0671981i	−0.557065	+	0.830469i	$0.688073\pi$
$458$	−27.9615			−1.30656
$459$	1.38996	+	2.40747i	0.0648776	+	0.112371i
$460$	−27.6759	+	15.9787i	−1.29040	+	0.745010i
$461$	−35.5887	−	20.5472i	−1.65753	−	0.956976i	−0.973849	−	0.227198i	$-0.927044\pi$
$461$	−35.5887	−	20.5472i	−1.65753	−	0.956976i	−0.683683	−	0.729779i	$-0.739623\pi$
$462$	23.3579	−	0.686504i	1.08671	−	0.0319391i
$463$			31.6420i			1.47053i	0.677781	+	0.735264i	$0.262942\pi$
$463$			31.6420i			1.47053i	−0.677781	+	0.735264i	$0.737058\pi$
$464$	−5.97549			−0.277405
$465$	30.5548			1.41695
$466$		−	25.7461i		−	1.19267i
$467$	4.14434	+	7.17820i	0.191777	+	0.332168i	0.945839	−	0.324635i	$-0.105242\pi$
$467$	4.14434	+	7.17820i	0.191777	+	0.332168i	−0.754062	+	0.656803i	$0.771908\pi$
$468$	−4.32651	+	7.88083i	−0.199993	+	0.364291i
$469$	27.8836	−	17.2102i	1.28755	−	0.794691i
$470$	10.8047	−	6.23810i	0.498384	−	0.287742i
$471$	9.32909	−	16.1585i	0.429862	−	0.744543i
$472$	−5.84584	−	10.1253i	−0.269077	−	0.466054i
$473$	−17.7203	−	10.2308i	−0.814782	−	0.470415i
$474$			20.8415i			0.957282i
$475$	−34.9750	−	20.1928i	−1.60476	−	0.926509i
$476$	18.3315	−	0.538773i	0.840221	−	0.0246946i
$477$	−3.45203	+	5.97909i	−0.158058	+	0.273764i
$478$	23.4802	−	40.6689i	1.07396	−	1.86015i
$479$			34.8773i			1.59358i	0.604253	+	0.796792i	$0.293471\pi$
$479$			34.8773i			1.59358i	−0.604253	+	0.796792i	$0.706529\pi$
$480$	13.8831	−	24.0462i	0.633673	−	1.09755i
$481$	0.294365	+	13.6703i	0.0134219	+	0.623313i
$482$	−7.72743			−0.351975
$483$	−9.72043	+	0.285689i	−0.442295	+	0.0129993i
$484$	−7.92993	−	13.7351i	−0.360452	−	0.624320i
$485$	−52.1331			−2.36724
$486$	−1.83578	−	1.05989i	−0.0832729	−	0.0480776i
$487$	−3.93116	+	2.26966i	−0.178138	+	0.102848i	−0.586417	−	0.810009i	$-0.699462\pi$
$487$	−3.93116	+	2.26966i	−0.178138	+	0.102848i	0.408280	+	0.912857i	$0.366129\pi$
$488$			3.48223i			0.157633i
$489$		−	16.0522i		−	0.725907i
$490$	23.1940	−	46.2508i	1.04780	−	2.08940i
$491$	1.61494	+	2.79716i	0.0728811	+	0.126234i	0.900163	−	0.435553i	$-0.143447\pi$
$491$	1.61494	+	2.79716i	0.0728811	+	0.126234i	−0.827282	+	0.561787i	$0.810114\pi$
$492$	−11.9804	−	6.91689i	−0.540118	−	0.311838i
$493$	−2.99893	+	5.19430i	−0.135065	+	0.233939i
$494$	43.1079	−	0.928248i	1.93951	−	0.0417638i
$495$	−7.26432	−	12.5822i	−0.326507	−	0.565526i
$496$	21.0172	−	12.1343i	0.943702	−	0.544847i
$497$	0.481514	+	16.3833i	0.0215989	+	0.734890i
$498$	−9.49343	+	16.4431i	−0.425411	+	0.736833i
$499$	12.7104	−	7.33838i	0.568998	−	0.328511i	−0.187751	−	0.982217i	$-0.560120\pi$
$499$	12.7104	−	7.33838i	0.568998	−	0.328511i	0.756749	+	0.653706i	$0.226787\pi$
$500$	−16.2541	+	9.38432i	−0.726906	+	0.419679i
$501$	−4.32267	+	2.49570i	−0.193123	+	0.111499i
$502$	−24.0730	+	13.8985i	−1.07443	+	0.620322i
$503$	−17.1942	+	29.7813i	−0.766652	+	1.32788i	0.172716	+	0.984972i	$0.444746\pi$
$503$	−17.1942	+	29.7813i	−0.766652	+	1.32788i	−0.939369	+	0.342909i	$0.888588\pi$
$504$	−2.35511	+	1.45361i	−0.104905	+	0.0647489i
$505$	−47.6068	+	27.4858i	−2.11847	+	1.22310i
$506$	16.2318	+	28.1143i	0.721591	+	1.24983i
$507$	6.00935	−	11.5277i	0.266884	−	0.511963i
$508$	26.7049	−	46.2543i	1.18484	−	2.05220i
$509$	−10.5564	−	6.09474i	−0.467904	−	0.270145i	0.247458	−	0.968899i	$-0.420405\pi$
$509$	−10.5564	−	6.09474i	−0.467904	−	0.270145i	−0.715362	+	0.698754i	$0.753738\pi$
$510$	−10.2739	−	17.7949i	−0.454936	−	0.787972i
$511$	−0.0709095	−	2.41266i	−0.00313685	−	0.106730i
$512$		−	27.8479i		−	1.23071i
$513$			5.64150i			0.249078i
$514$	−8.50370	+	4.90961i	−0.375082	+	0.216554i
$515$	36.3027	+	20.9594i	1.59969	+	0.923581i
$516$	12.2451			0.539062
$517$	−3.51642	−	6.09062i	−0.154652	−	0.267865i
$518$	−10.0888	+	18.7240i	−0.443276	+	0.822685i
$519$	−11.2123			−0.492164
$520$	6.32891	−	11.5282i	0.277541	−	0.505547i
$521$	10.4208	−	18.0494i	0.456544	−	0.790757i	−0.542232	−	0.840229i	$-0.682420\pi$
$521$	10.4208	−	18.0494i	0.456544	−	0.790757i	0.998776	+	0.0494718i	$0.0157538\pi$
$522$		−	4.57358i		−	0.200180i
$523$	−4.99681	+	8.65472i	−0.218495	+	0.378445i	−0.954348	−	0.298697i	$-0.903448\pi$
$523$	−4.99681	+	8.65472i	−0.218495	+	0.378445i	0.735853	+	0.677141i	$0.236781\pi$
$524$	20.9868	−	36.3503i	0.916814	−	1.58797i
$525$	−18.9319	+	0.556420i	−0.826255	+	0.0242841i
$526$	16.6921	+	9.63717i	0.727809	+	0.420201i
$527$		−	24.3595i		−	1.06111i
$528$	−9.99358	−	5.76979i	−0.434915	−	0.251098i
$529$	4.74512	+	8.21879i	0.206310	+	0.357339i
$530$	25.5158	−	44.1946i	1.10833	−	1.91969i
$531$	−9.67955	+	5.58849i	−0.420057	+	0.242520i
$532$	32.7641	+	17.6539i	1.42050	+	0.765392i
$533$	17.5349	+	9.62654i	0.759522	+	0.416972i
$534$	0.00583674	+	0.0101095i	0.000252580	+	0.000437482i
$535$		−	35.4701i		−	1.53351i
$536$	12.9551			0.559576
$537$	5.25921			0.226952
$538$			52.2344i			2.25199i
$539$	−26.0715	−	13.0745i	−1.12298	−	0.563157i
$540$	7.52970	+	4.34728i	0.324027	+	0.187077i
$541$	−16.0718	+	9.27906i	−0.690981	+	0.398938i	−0.803979	−	0.594657i	$-0.797288\pi$
$541$	−16.0718	+	9.27906i	−0.690981	+	0.398938i	0.112999	+	0.993595i	$0.463954\pi$
$542$	−8.28198	−	14.3448i	−0.355742	−	0.616162i
$543$	−5.99931			−0.257455
$544$	−19.1705	−	11.0681i	−0.821930	−	0.474542i
$545$	41.5641			1.78041
$546$	16.9750	−	10.9888i	0.726465	−	0.470278i
$547$	−15.8836			−0.679135			−0.339567	−	0.940582i	$-0.610281\pi$
$547$	−15.8836			−0.679135			−0.339567	+	0.940582i	$0.610281\pi$
$548$	0.555297	+	0.320601i	0.0237211	+	0.0136954i
$549$	3.32893			0.142075
$550$	31.6137	+	54.7565i	1.34801	+	2.33482i
$551$	−10.5412	+	6.08597i	−0.449070	+	0.259271i
$552$	−3.32971	−	1.92241i	−0.141722	−	0.0818232i
$553$	12.3390	−	22.9001i	0.524706	−	0.973813i
$554$			56.9071i			2.41775i
$555$	13.2236			0.561312
$556$	38.2322			1.62141
$557$			35.2833i			1.49500i	0.664261	+	0.747501i	$0.268746\pi$
$557$			35.2833i			1.49500i	−0.664261	+	0.747501i	$0.731254\pi$
$558$	9.28747	+	16.0864i	0.393170	+	0.680991i
$559$	−17.7023	+	0.381187i	−0.748729	+	0.0161225i
$560$	−21.7426	+	13.4198i	−0.918791	+	0.567091i
$561$	−10.0310	+	5.79139i	−0.423508	+	0.244513i
$562$	19.7090	−	34.1370i	0.831375	−	1.43998i
$563$	−20.2913	−	35.1456i	−0.855178	−	1.48121i	−0.876480	−	0.481438i	$-0.840115\pi$
$563$	−20.2913	−	35.1456i	−0.855178	−	1.48121i	0.0213027	−	0.999773i	$-0.493219\pi$
$564$	3.64488	+	2.10437i	0.153477	+	0.0886101i
$565$		−	19.1515i		−	0.805709i
$566$	−15.3460	−	8.86001i	−0.645040	−	0.372414i
$567$	1.38962	+	2.25144i	0.0583585	+	0.0945514i
$568$	−3.24012	+	5.61206i	−0.135953	+	0.235477i
$569$	−9.19757	+	15.9307i	−0.385582	+	0.667848i	−0.991850	−	0.127413i	$-0.959333\pi$
$569$	−9.19757	+	15.9307i	−0.385582	+	0.667848i	0.606268	+	0.795261i	$0.292666\pi$
$570$		−	41.6993i		−	1.74659i
$571$	−14.3891	+	24.9227i	−0.602165	+	1.04298i	0.390327	+	0.920676i	$0.372362\pi$
$571$	−14.3891	+	24.9227i	−0.602165	+	1.04298i	−0.992493	+	0.122305i	$0.960971\pi$
$572$	−32.8363	−	18.0268i	−1.37295	−	0.753740i
$573$	−4.61487			−0.192789
$574$	16.3427	+	26.4781i	0.682130	+	1.10518i
$575$	−13.1561	−	22.7870i	−0.548646	−	0.950282i
$576$	11.3406			0.472524
$577$	13.2467	+	7.64799i	0.551468	+	0.318390i	0.749714	−	0.661762i	$-0.230191\pi$
$577$	13.2467	+	7.64799i	0.551468	+	0.318390i	−0.198246	+	0.980152i	$0.563524\pi$
$578$	17.0216	−	9.82740i	0.708003	−	0.408766i
$579$		−	8.50460i		−	0.353439i
$580$			18.7591i			0.778930i
$581$	20.1661	−	12.4468i	0.836630	−	0.516380i
$582$	−15.8464	−	27.4468i	−0.656855	−	1.13771i
$583$	−24.9125	−	14.3832i	−1.03177	−	0.595693i
$584$	0.477152	−	0.826451i	0.0197447	−	0.0341988i
$585$	−11.0207	−	6.05029i	−0.455651	−	0.250149i
$586$	1.26278	+	2.18720i	0.0521649	+	0.0903523i
$587$	0.0458932	−	0.0264965i	0.00189422	−	0.00109363i	−0.499053	−	0.866572i	$-0.666319\pi$
$587$	0.0458932	−	0.0264965i	0.00189422	−	0.00109363i	0.500947	+	0.865478i	$0.332985\pi$
$588$	17.4242	−	1.02510i	0.718561	−	0.0422744i
$589$	24.7173	−	42.8116i	1.01846	−	1.76402i
$590$	71.5466	−	41.3075i	2.94553	−	1.70060i
$591$	4.83680	−	2.79253i	0.198959	−	0.114869i
$592$	9.09592	−	5.25153i	0.373840	−	0.215837i
$593$	−4.58822	+	2.64901i	−0.188416	+	0.108782i	−0.591241	−	0.806495i	$-0.701362\pi$
$593$	−4.58822	+	2.64901i	−0.188416	+	0.108782i	0.402825	+	0.915277i	$0.368028\pi$
$594$	4.41614	−	7.64898i	0.181196	−	0.313841i
$595$	0.753432	+	25.6351i	0.0308877	+	1.05094i
$596$	9.00564	−	5.19941i	0.368885	−	0.212976i
$597$	10.5428	+	18.2607i	0.431490	+	0.747362i
$598$	24.6253	+	13.5191i	1.00701	+	0.552838i
$599$	7.57199	−	13.1151i	0.309383	−	0.535868i	−0.668844	−	0.743402i	$-0.733211\pi$
$599$	7.57199	−	13.1151i	0.309383	−	0.535868i	0.978228	+	0.207535i	$0.0665441\pi$
$600$	−6.48508	−	3.74416i	−0.264752	−	0.152855i
$601$	−8.40784	−	14.5628i	−0.342963	−	0.594030i	0.642018	−	0.766689i	$-0.278097\pi$
$601$	−8.40784	−	14.5628i	−0.342963	−	0.594030i	−0.984982	+	0.172660i	$0.944764\pi$
$602$	−24.2466	−	13.0645i	−0.988216	−	0.532467i
$603$		−	12.3848i		−	0.504349i
$604$			7.70172i			0.313379i
$605$	19.2074	−	11.0894i	0.780893	−	0.450849i
$606$	−28.9412	−	16.7092i	−1.17566	−	0.678766i
$607$	−38.1835			−1.54982			−0.774910	−	0.632071i	$-0.782205\pi$
$607$	−38.1835			−1.54982			−0.774910	+	0.632071i	$0.782205\pi$
$608$	−22.4614	−	38.9043i	−0.910931	−	1.57778i
$609$	−2.70773	+	5.02533i	−0.109723	+	0.203637i
$610$	−24.6059			−0.996262
$611$	−5.33478	−	2.92875i	−0.215822	−	0.118485i
$612$	3.46581	−	6.00297i	0.140097	−	0.242656i
$613$		−	6.72923i		−	0.271791i	−0.990723	−	0.135895i	$-0.956609\pi$
$613$		−	6.72923i		−	0.271791i	0.990723	−	0.135895i	$-0.0433911\pi$
$614$	0.477200	−	0.826534i	0.0192582	−	0.0333562i
$615$	9.67274	−	16.7537i	0.390043	−	0.675574i
$616$	−6.05661	−	9.81282i	−0.244028	−	0.395370i
$617$	23.3867	+	13.5023i	0.941512	+	0.543582i	0.890434	−	0.455113i	$-0.150401\pi$
$617$	23.3867	+	13.5023i	0.941512	+	0.543582i	0.0510777	+	0.998695i	$0.483734\pi$
$618$			25.4834i			1.02509i
$619$	−37.9576	−	21.9149i	−1.52565	−	0.880833i	−0.999537	−	0.0304157i	$-0.990317\pi$
$619$	−37.9576	−	21.9149i	−1.52565	−	0.880833i	−0.526109	−	0.850417i	$-0.676350\pi$
$620$	−38.0938	−	65.9803i	−1.52988	−	2.64983i
$621$	−1.83778	+	3.18313i	−0.0737476	+	0.127735i
$622$	8.80866	−	5.08568i	0.353195	−	0.203917i
$623$	−0.000428035	−	0.0145637i	−1.71489e−5	−	0.000583481i
$624$	−9.98342	+	0.214974i	−0.399657	+	0.00860587i
$625$	4.77341	+	8.26780i	0.190937	+	0.330712i
$626$		−	2.01858i		−	0.0806788i
$627$	−23.5059			−0.938734
$628$	−46.5236			−1.85650
$629$		−	10.5424i		−	0.420352i
$630$	−10.2714	−	16.6415i	−0.409222	−	0.663015i
$631$	22.6204	+	13.0599i	0.900504	+	0.519906i	0.877364	−	0.479826i	$-0.159300\pi$
$631$	22.6204	+	13.0599i	0.900504	+	0.519906i	0.0231402	+	0.999732i	$0.492634\pi$
$632$	8.90679	−	5.14234i	0.354293	−	0.204551i
$633$	−2.36508	−	4.09643i	−0.0940033	−	0.162819i
$634$	0.677985			0.0269262
$635$	64.6831	+	37.3448i	2.56687	+	1.48198i
$636$	17.2151			0.682622
$637$	−25.1575	+	2.02436i	−0.996778	+	0.0802079i
$638$	19.0563			0.754445
$639$	5.36500	+	3.09748i	0.212236	+	0.122535i
$640$	−28.2918			−1.11833
$641$	−1.84628	−	3.19784i	−0.0729235	−	0.126307i	0.827258	−	0.561822i	$-0.189900\pi$
$641$	−1.84628	−	3.19784i	−0.0729235	−	0.126307i	−0.900181	+	0.435515i	$0.856566\pi$
$642$	18.6741	−	10.7815i	0.737010	−	0.425513i
$643$	22.6645	+	13.0854i	0.893801	+	0.516036i	0.875184	−	0.483790i	$-0.160740\pi$
$643$	22.6645	+	13.0854i	0.893801	+	0.516036i	0.0186174	+	0.999827i	$0.494074\pi$
$644$	12.7357	+	20.6342i	0.501858	+	0.813101i
$645$			17.1239i			0.674253i
$646$	−33.2442			−1.30798
$647$	36.2475			1.42503			0.712517	−	0.701654i	$-0.247555\pi$
$647$	36.2475			1.42503			0.712517	+	0.701654i	$0.247555\pi$
$648$			1.04605i			0.0410927i
$649$	−23.2850	−	40.3308i	−0.914017	−	1.58312i
$650$	47.9613	+	26.3304i	1.88120	+	1.03276i
$651$	−0.681094	−	23.1738i	−0.0266942	−	0.908255i
$652$	−34.6633	+	20.0129i	−1.35752	+	0.783765i
$653$	21.3365	−	36.9558i	0.834960	−	1.44619i	−0.0591033	−	0.998252i	$-0.518824\pi$
$653$	21.3365	−	36.9558i	0.834960	−	1.44619i	0.894063	−	0.447941i	$-0.147843\pi$
$654$	12.6339	+	21.8825i	0.494023	+	0.855673i
$655$	50.8331	+	29.3485i	1.98621	+	1.14674i
$656$		−	15.3654i		−	0.599920i
$657$	−0.790069	−	0.456146i	−0.0308235	−	0.0177960i
$658$	−4.97205	−	8.05562i	−0.193831	−	0.314041i
$659$	2.47108	−	4.28004i	0.0962597	−	0.166727i	−0.813874	−	0.581041i	$-0.802645\pi$
$659$	2.47108	−	4.28004i	0.0962597	−	0.166727i	0.910134	+	0.414315i	$0.135979\pi$
$660$	−18.1134	+	31.3733i	−0.705062	+	1.22120i
$661$			0.643481i			0.0250285i	0.999922	+	0.0125143i	$0.00398351\pi$
$661$			0.643481i			0.0250285i	−0.999922	+	0.0125143i	$0.996016\pi$
$662$	−3.60302	+	6.24062i	−0.140035	+	0.242549i
$663$	−4.82353	+	8.78615i	−0.187330	+	0.341226i
$664$	9.36946			0.363605
$665$	−24.6876	+	45.8181i	−0.957343	+	1.77675i
$666$	4.01947	+	6.96192i	0.155751	+	0.269769i
$667$	−7.93029			−0.307062
$668$	10.7785	+	6.22294i	0.417031	+	0.240773i
$669$	−4.23414	+	2.44458i	−0.163701	+	0.0945131i
$670$			91.5426i			3.53660i
$671$			13.8703i			0.535458i
$672$	−18.5470	−	9.99341i	−0.715464	−	0.385504i
$673$	23.6567	+	40.9746i	0.911898	+	1.57945i	0.811381	+	0.584517i	$0.198716\pi$
$673$	23.6567	+	40.9746i	0.911898	+	1.57945i	0.100516	+	0.994935i	$0.467951\pi$
$674$	−41.6852	−	24.0670i	−1.60565	−	0.927024i
$675$	−3.57933	+	6.19959i	−0.137769	+	0.238622i
$676$	−32.3851	+	1.39535i	−1.24558	+	0.0536674i
$677$	8.57286	+	14.8486i	0.329482	+	0.570679i	0.982409	−	0.186741i	$-0.0597927\pi$
$677$	8.57286	+	14.8486i	0.329482	+	0.570679i	−0.652927	+	0.757420i	$0.726459\pi$
$678$	10.0828	−	5.82131i	0.387228	−	0.223566i
$679$	1.16209	+	39.5395i	0.0445970	+	1.51739i
$680$	−5.06986	+	8.78126i	−0.194420	+	0.336746i
$681$	1.81353	−	1.04704i	0.0694945	−	0.0401227i
$682$	−67.0255	+	38.6972i	−2.56654	+	1.48179i
$683$	11.7735	−	6.79745i	0.450502	−	0.260097i	−0.257540	−	0.966268i	$-0.582912\pi$
$683$	11.7735	−	6.79745i	0.450502	−	0.260097i	0.708042	+	0.706170i	$0.249579\pi$
$684$	12.1823	−	7.03346i	0.465802	−	0.268931i
$685$	−0.448336	+	0.776541i	−0.0171300	+	0.0296701i
$686$	−35.5952	−	16.5602i	−1.35903	−	0.632272i
$687$	11.4235	−	6.59538i	0.435835	−	0.251629i
$688$	6.80046	+	11.7787i	0.259265	+	0.449060i
$689$	−24.8872	+	0.535899i	−0.948126	+	0.0204161i
$690$	13.5840	−	23.5282i	0.517134	−	0.895703i
$691$	−7.83464	−	4.52333i	−0.298044	−	0.172076i	0.343520	−	0.939145i	$-0.388381\pi$
$691$	−7.83464	−	4.52333i	−0.298044	−	0.172076i	−0.641564	+	0.767070i	$0.721714\pi$
$692$	13.9787	+	24.2119i	0.531392	+	0.920397i
$693$	−9.38083	+	5.78998i	−0.356348	+	0.219943i
$694$			5.65251i			0.214566i
$695$			53.4649i			2.02804i
$696$	−1.95456	+	1.12846i	−0.0740872	+	0.0427743i
$697$	−13.3567	−	7.71148i	−0.505920	−	0.292093i
$698$	59.0430			2.23481
$699$	6.07282	+	10.5184i	0.229695	+	0.397844i
$700$	24.8046	+	40.1880i	0.937525	+	1.51896i
$701$	−35.4627			−1.33941			−0.669704	−	0.742629i	$-0.733579\pi$
$701$	−35.4627			−1.33941			−0.669704	+	0.742629i	$0.733579\pi$
$702$	−0.164539	−	7.64121i	−0.00621013	−	0.288399i
$703$	10.6973	−	18.5282i	0.403455	−	0.698804i
$704$			47.2516i			1.78086i
$705$	−2.94281	+	5.09709i	−0.110833	+	0.191968i
$706$	5.51364	−	9.54991i	0.207509	−	0.359415i
$707$	21.9074	+	35.4940i	0.823912	+	1.33489i
$708$	24.1357	+	13.9347i	0.907074	+	0.523700i
$709$			20.1237i			0.755763i	0.925854	+	0.377882i	$0.123347\pi$
$709$			20.1237i			0.755763i	−0.925854	+	0.377882i	$0.876653\pi$
$710$	−39.6555	−	22.8951i	−1.48825	−	0.859239i
$711$	−4.91596	−	8.51469i	−0.184363	−	0.319326i
$712$	0.00288026	−	0.00498875i	0.000107942	−	0.000186961i
$713$	27.8927	−	16.1039i	1.04459	−	0.603095i
$714$	−13.2673	+	8.18875i	−0.496515	+	0.306456i
$715$	25.2092	−	45.9190i	0.942769	−	1.71727i
$716$	−6.55684	−	11.3568i	−0.245041	−	0.424423i
$717$			22.1534i			0.827336i
$718$	74.3715			2.77552
$719$	10.7647			0.401454			0.200727	−	0.979647i	$-0.435670\pi$
$719$	10.7647			0.401454			0.200727	+	0.979647i	$0.435670\pi$
$720$			9.65720i			0.359903i
$721$	15.0871	−	28.0005i	0.561874	−	1.04279i
$722$	−23.5467	−	13.5947i	−0.876318	−	0.505942i
$723$	3.15700	−	1.82270i	0.117410	−	0.0677868i
$724$	7.47955	+	12.9550i	0.277975	+	0.481467i
$725$	−15.4453			−0.573625
$726$	11.6766	+	6.74150i	0.433360	+	0.250200i
$727$	−8.53740			−0.316634			−0.158317	−	0.987388i	$-0.550607\pi$
$727$	−8.53740			−0.316634			−0.158317	+	0.987388i	$0.550607\pi$
$728$	−8.88450	−	4.54309i	−0.329281	−	0.168378i
$729$	1.00000			0.0370370
$730$	5.83981	+	3.37162i	0.216141	+	0.124789i
$731$	13.6518			0.504931
$732$	−4.15029	−	7.18852i	−0.153399	−	0.265695i
$733$	27.9604	−	16.1429i	1.03274	−	0.596253i	0.114972	−	0.993369i	$-0.463322\pi$
$733$	27.9604	−	16.1429i	1.03274	−	0.596253i	0.917769	+	0.397116i	$0.129989\pi$
$734$	−54.9371	−	31.7180i	−2.02777	−	1.17073i
$735$	1.43352	+	24.3664i	0.0528763	+	0.898767i
$736$		−	29.2682i		−	1.07884i
$737$	51.6026			1.90081
$738$	11.7605			0.432912
$739$		−	29.5170i		−	1.08580i	−0.839797	−	0.542901i	$-0.817326\pi$
$739$		−	29.5170i		−	1.08580i	0.839797	−	0.542901i	$-0.182674\pi$
$740$	−16.4864	−	28.5552i	−0.606051	−	1.04971i
$741$	−17.3925	+	10.5472i	−0.638931	+	0.387462i
$742$	−34.0875	−	18.3669i	−1.25139	−	0.674271i
$743$	−15.1570	+	8.75088i	−0.556055	+	0.321039i	−0.751561	−	0.659664i	$-0.770699\pi$
$743$	−15.1570	+	8.75088i	−0.556055	+	0.321039i	0.195505	+	0.980703i	$0.437365\pi$
$744$	4.58310	−	7.93815i	0.168024	−	0.291027i
$745$	7.27098	+	12.5937i	0.266388	+	0.461397i
$746$	−9.38404	−	5.41788i	−0.343574	−	0.198363i
$747$		−	8.95699i		−	0.327719i
$748$	25.0120	+	14.4407i	0.914528	+	0.528003i
$749$	−26.9018	+	0.790660i	−0.982969	+	0.0288901i
$750$	7.97792	−	13.8182i	0.291312	−	0.504568i
$751$	−2.33033	+	4.03625i	−0.0850350	+	0.147285i	−0.905406	−	0.424546i	$-0.860434\pi$
$751$	−2.33033	+	4.03625i	−0.0850350	+	0.147285i	0.820371	+	0.571831i	$0.193767\pi$
$752$			4.67474i			0.170470i
$753$	6.55659	−	11.3563i	0.238935	−	0.413848i
$754$	14.1002	−	8.55067i	0.513498	−	0.311397i
$755$	−10.7703			−0.391970
$756$	3.12928	−	5.80770i	0.113811	−	0.211224i
$757$	0.211516	+	0.366357i	0.00768769	+	0.0133155i	0.869844	−	0.493327i	$-0.164220\pi$
$757$	0.211516	+	0.366357i	0.00768769	+	0.0133155i	−0.862156	+	0.506643i	$0.830886\pi$
$758$	−13.5231			−0.491181
$759$	−13.2628	−	7.65730i	−0.481410	−	0.277942i
$760$	−17.8205	+	10.2887i	−0.646418	+	0.373210i
$761$			32.2631i			1.16954i	0.811200	+	0.584768i	$0.198815\pi$
$761$			32.2631i			1.16954i	−0.811200	+	0.584768i	$0.801185\pi$
$762$			45.4054i			1.64487i
$763$	−0.926500	−	31.5237i	−0.0335416	−	1.14123i
$764$	5.75352	+	9.96540i	0.208155	+	0.360535i
$765$	8.39469	+	4.84668i	0.303511	+	0.175232i
$766$	−17.6381	+	30.5502i	−0.637292	+	1.10382i
$767$	−35.3258	−	19.3936i	−1.27554	−	0.700262i
$768$	2.74097	+	4.74750i	0.0989063	+	0.171311i
$769$	−30.6857	+	17.7164i	−1.10656	+	0.638870i	−0.937935	−	0.346811i	$-0.887265\pi$
$769$	−30.6857	+	17.7164i	−1.10656	+	0.638870i	−0.168620	+	0.985681i	$0.553931\pi$
$770$	69.3386	−	42.7968i	2.49879	−	1.54229i
$771$	2.31610	−	4.01159i	0.0834121	−	0.144474i
$772$	−18.3649	+	10.6030i	−0.660968	+	0.381610i
$773$	6.13296	−	3.54086i	0.220587	−	0.127356i	−0.385635	−	0.922651i	$-0.626018\pi$
$773$	6.13296	−	3.54086i	0.220587	−	0.127356i	0.606222	+	0.795295i	$0.292684\pi$
$774$	−9.01532	+	5.20500i	−0.324049	+	0.187090i
$775$	54.3249	−	31.3645i	1.95141	−	1.12665i
$776$	−7.81974	+	13.5442i	−0.280712	+	0.486208i
$777$	−0.294766	−	10.0293i	−0.0105747	−	0.359798i
$778$	64.8437	−	37.4375i	2.32476	−	1.34220i
$779$	−15.6495	−	27.1058i	−0.560702	−	0.971165i
$780$	0.674879	+	31.3414i	0.0241645	+	1.12220i
$781$	−12.9060	+	22.3538i	−0.461812	+	0.799882i
$782$	−18.7576	−	10.8297i	−0.670769	−	0.387269i
$783$	1.07879	+	1.86851i	0.0385526	+	0.0667751i
$784$	10.6627	+	16.1912i	0.380812	+	0.578257i
$785$		−	65.0597i		−	2.32208i
$786$			35.6832i			1.27278i
$787$	−7.06265	+	4.07762i	−0.251756	+	0.145352i	−0.620568	−	0.784152i	$-0.713098\pi$
$787$	−7.06265	+	4.07762i	−0.251756	+	0.145352i	0.368812	+	0.929504i	$0.379765\pi$
$788$	−12.0604	−	6.96309i	−0.429635	−	0.248050i
$789$	−9.09261			−0.323706
$790$	36.3364	+	62.9365i	1.29279	+	2.23918i
$791$	−14.5252	+	0.426904i	−0.516456	+	0.0151790i
$792$	−4.35847			−0.154872
$793$	6.22370	+	10.2630i	0.221010	+	0.364449i
$794$	11.0507	−	19.1404i	0.392174	−	0.679266i
$795$			24.0740i			0.853816i
$796$	26.2883	−	45.5326i	0.931762	−	1.61386i
$797$	5.11774	−	8.86419i	0.181280	−	0.313986i	−0.761037	−	0.648709i	$-0.775309\pi$
$797$	5.11774	−	8.86419i	0.181280	−	0.313986i	0.942317	+	0.334723i	$0.108643\pi$
$798$	−31.6262	+	0.929514i	−1.11956	+	0.0329044i
$799$	4.06359	+	2.34612i	0.143760	+	0.0829997i
$800$		−	57.0039i		−	2.01539i
$801$	−0.00476914	−	0.00275346i	−0.000168509	−	9.72888e-5i
$802$	−11.9125	−	20.6330i	−0.420644	−	0.728576i
$803$	1.90058	−	3.29190i	0.0670700	−	0.116169i
$804$	−26.7439	+	15.4406i	−0.943184	+	0.544547i
$805$	−28.8553	+	17.8099i	−1.01702	+	0.627717i
$806$	−32.2301	+	58.7077i	−1.13526	+	2.06789i
$807$	−12.3207	−	21.3401i	−0.433710	−	0.751207i
$808$			16.4910i			0.580152i
$809$	−15.9057			−0.559214			−0.279607	−	0.960115i	$-0.590204\pi$
$809$	−15.9057			−0.559214			−0.279607	+	0.960115i	$0.590204\pi$
$810$	−7.39152			−0.259712
$811$		−	0.179594i		−	0.00630639i	−0.999995	−	0.00315319i	$-0.998996\pi$
$811$		−	0.179594i		−	0.00630639i	0.999995	−	0.00315319i	$-0.00100369\pi$
$812$	14.2276	−	0.418157i	0.499290	−	0.0146744i
$813$	6.76712	+	3.90700i	0.237333	+	0.137024i
$814$	−29.0076	+	16.7475i	−1.01671	+	0.587000i
$815$	−27.9865	−	48.4740i	−0.980324	−	1.69797i
$816$	7.69909			0.269522
$817$	23.9930	+	13.8524i	0.839409	+	0.484633i
$818$	−5.46108			−0.190942
$819$	−4.34310	+	8.49338i	−0.151760	+	0.296783i
$820$	−48.2374			−1.68452
$821$	3.94335	+	2.27670i	0.137624	+	0.0794573i	0.567231	−	0.823559i	$-0.308015\pi$
$821$	3.94335	+	2.27670i	0.137624	+	0.0794573i	−0.429607	+	0.903016i	$0.641348\pi$
$822$	−0.545107			−0.0190128
$823$	−0.997193	−	1.72719i	−0.0347600	−	0.0602060i	0.848122	−	0.529801i	$-0.177733\pi$
$823$	−0.997193	−	1.72719i	−0.0347600	−	0.0602060i	−0.882882	+	0.469595i	$0.844400\pi$
$824$	10.8905	−	6.28764i	0.379389	−	0.219040i
$825$	−25.8312	−	14.9137i	−0.899327	−	0.519227i
$826$	−32.9239	−	53.3427i	−1.14557	−	1.85603i
$827$		−	3.91851i		−	0.136260i	−0.997676	−	0.0681299i	$-0.978297\pi$
$827$		−	3.91851i		−	0.136260i	0.997676	−	0.0681299i	$-0.0217032\pi$
$828$	9.16491			0.318503
$829$	−47.6789			−1.65596			−0.827979	−	0.560759i	$-0.810509\pi$
$829$	−47.6789			−1.65596			−0.827979	+	0.560759i	$0.810509\pi$
$830$			66.2058i			2.29804i
$831$	−13.4229	−	23.2491i	−0.465634	−	0.806503i
$832$	21.2021	+	34.9626i	0.735051	+	1.21211i
$833$	19.4258	−	1.14286i	0.673064	−	0.0395977i
$834$	−28.1480	+	16.2512i	−0.974684	+	0.562734i
$835$	−8.70231	+	15.0728i	−0.301156	+	0.521617i
$836$	29.3056	+	50.7588i	1.01356	+	1.75553i
$837$	−7.58870	−	4.38134i	−0.262304	−	0.151441i
$838$		−	23.0129i		−	0.794966i
$839$	43.1680	+	24.9231i	1.49033	+	0.860440i	0.999939	−	0.0110647i	$-0.00352207\pi$
$839$	43.1680	+	24.9231i	1.49033	+	0.860440i	0.490387	+	0.871505i	$0.336855\pi$
$840$	−4.57758	+	8.49562i	−0.157942	+	0.293127i
$841$	12.1724	−	21.0833i	0.419739	−	0.727010i
$842$	14.9007	−	25.8088i	0.513512	−	0.889429i
$843$			18.5953i			0.640458i
$844$	−5.89725	+	10.2143i	−0.202992	+	0.351592i
$845$	−1.95129	−	45.2880i	−0.0671265	−	1.55796i
$846$	−3.57799			−0.123014
$847$	−8.83875	−	14.3204i	−0.303703	−	0.492054i
$848$	9.56056	+	16.5594i	0.328311	+	0.568651i
$849$	8.35936			0.286893
$850$	−36.5330	−	21.0923i	−1.25307	−	0.723460i
$851$	12.0715	−	6.96950i	0.413807	−	0.238911i
$852$		−	15.4470i		−	0.529205i
$853$			11.8327i			0.405145i	0.979267	+	0.202572i	$0.0649301\pi$
$853$			11.8327i			0.405145i	−0.979267	+	0.202572i	$0.935070\pi$
$854$	0.548486	+	18.6619i	0.0187688	+	0.638599i
$855$	9.83575	+	17.0360i	0.336376	+	0.582620i
$856$	−9.21514	−	5.32037i	−0.314967	−	0.181846i
$857$	−2.61951	+	4.53712i	−0.0894807	+	0.154985i	−0.907292	−	0.420502i	$-0.861854\pi$
$857$	−2.61951	+	4.53712i	−0.0894807	+	0.154985i	0.817811	+	0.575487i	$0.195187\pi$
$858$	31.8379	−	0.685569i	1.08693	−	0.0234049i
$859$	−1.72249	−	2.98345i	−0.0587707	−	0.101794i	0.835143	−	0.550033i	$-0.185385\pi$
$859$	−1.72249	−	2.98345i	−0.0587707	−	0.101794i	−0.893914	+	0.448239i	$0.852051\pi$
$860$	36.9775	−	21.3490i	1.26092	−	0.727994i
$861$	−12.9222	−	6.96270i	−0.440387	−	0.237288i
$862$	40.0215	−	69.3193i	1.36314	−	2.36103i
$863$	−41.2353	+	23.8072i	−1.40366	+	0.810406i	−0.994767	−	0.102174i	$-0.967420\pi$
$863$	−41.2353	+	23.8072i	−1.40366	+	0.810406i	−0.408898	+	0.912580i	$0.634087\pi$
$864$	−6.89610	+	3.98146i	−0.234610	+	0.135452i
$865$	−33.8585	+	19.5482i	−1.15122	+	0.664658i
$866$	−33.9797	+	19.6182i	−1.15468	+	0.666653i
$867$	−4.63604	+	8.02986i	−0.157448	+	0.272709i
$868$	−49.1927	+	30.3624i	−1.66971	+	1.03057i
$869$	35.4773	−	20.4828i	1.20349	−	0.694833i
$870$	−7.97387	−	13.8111i	−0.270339	−	0.468242i
$871$	38.1819	−	23.1544i	1.29375	−	0.784557i
$872$	6.23444	−	10.7984i	0.211125	−	0.365679i
$873$	12.9479	+	7.47550i	0.438222	+	0.253007i
$874$	−21.9775	−	38.0662i	−0.743402	−	1.28761i
$875$	−16.9468	+	10.4598i	−0.572907	+	0.353606i
$876$			2.27477i			0.0768575i
$877$		−	24.1929i		−	0.816936i	−0.912773	−	0.408468i	$-0.866063\pi$
$877$		−	24.1929i		−	0.816936i	0.912773	−	0.408468i	$-0.133937\pi$
$878$	−45.5578	+	26.3028i	−1.53750	+	0.887677i
$879$	−1.03180	−	0.595712i	−0.0348019	−	0.0200929i
$880$	−40.2377			−1.35641
$881$	−18.1389	−	31.4175i	−0.611115	−	1.05848i	−0.991053	−	0.133471i	$-0.957388\pi$
$881$	−18.1389	−	31.4175i	−0.611115	−	1.05848i	0.379938	−	0.925012i	$-0.375945\pi$
$882$	−12.3926	+	8.16114i	−0.417280	+	0.274800i
$883$	−5.85958			−0.197191			−0.0985953	−	0.995128i	$-0.531435\pi$
$883$	−5.85958			−0.197191			−0.0985953	+	0.995128i	$0.531435\pi$
$884$	24.9866	−	0.538039i	0.840389	−	0.0180962i
$885$	−19.4867	+	33.7519i	−0.655037	+	1.13456i
$886$			45.3162i			1.52243i
$887$	16.1814	−	28.0269i	0.543317	−	0.941052i	−0.455394	−	0.890290i	$-0.650502\pi$
$887$	16.1814	−	28.0269i	0.543317	−	0.941052i	0.998711	−	0.0507624i	$-0.0161651\pi$
$888$	1.98349	−	3.43551i	0.0665616	−	0.115288i
$889$	26.8818	−	49.8904i	0.901585	−	1.67327i
$890$	0.0352512	+	0.0203523i	0.00118162	+	0.000682210i
$891$			4.16660i			0.139586i
$892$	10.5577	+	6.09550i	0.353498	+	0.204092i
$893$	4.76117	+	8.24658i	0.159326	+	0.275961i
$894$	−4.42019	+	7.65599i	−0.147833	+	0.256055i
$895$	15.8816	−	9.16924i	0.530863	−	0.306494i
$896$	0.630649	+	21.4575i	0.0210685	+	0.716844i
$897$	−13.2494	+	0.285300i	−0.442383	+	0.00952590i
$898$	27.1374	+	47.0033i	0.905586	+	1.56852i
$899$		−	18.9061i		−	0.630553i
$900$	17.8499			0.594997
$901$	19.1927			0.639401
$902$			49.0015i			1.63157i
$903$	12.9874	−	0.381707i	0.432193	−	0.0127024i
$904$	−4.97557	−	2.87265i	−0.165485	−	0.0955428i
$905$	−18.1165	+	10.4596i	−0.602214	+	0.347688i
$906$	−3.27374	−	5.67029i	−0.108763	−	0.188383i
$907$	12.8764			0.427553			0.213776	−	0.976883i	$-0.431424\pi$
$907$	12.8764			0.427553			0.213776	+	0.976883i	$0.431424\pi$
$908$	−4.52198	−	2.61077i	−0.150067	−	0.0866413i
$909$	15.7650			0.522894
$910$	32.1021	−	62.7790i	1.06417	−	2.08110i
$911$	−7.65130			−0.253499			−0.126749	−	0.991935i	$-0.540454\pi$
$911$	−7.65130			−0.253499			−0.126749	+	0.991935i	$0.540454\pi$
$912$	13.5311	+	7.81219i	0.448060	+	0.258688i
$913$	37.3202			1.23512
$914$	−3.04513	−	5.27432i	−0.100724	−	0.174459i
$915$	10.0526	−	5.80387i	0.332328	−	0.191870i
$916$	−28.4842	−	16.4454i	−0.941146	−	0.543371i
$917$	21.1258	−	39.2078i	0.697636	−	1.29476i
$918$			5.89280i			0.194492i
$919$	−26.3695			−0.869849			−0.434924	−	0.900467i	$-0.643225\pi$
$919$	−26.3695			−0.869849			−0.434924	+	0.900467i	$0.643225\pi$
$920$	−13.4066			−0.442003
$921$			0.450235i			0.0148357i
$922$	−43.5555	−	75.4403i	−1.43442	−	2.48449i
$923$	0.480859	+	22.3311i	0.0158277	+	0.735037i
$924$	24.1984	+	13.0385i	0.796067	+	0.428934i
$925$	23.5110	−	13.5741i	0.773036	−	0.446312i
$926$	−33.5371	+	58.0879i	−1.10210	+	1.90889i
$927$	−6.01085	−	10.4111i	−0.197422	−	0.341945i
$928$	−14.8788	−	8.59029i	−0.488421	−	0.281990i
$929$			33.1091i			1.08627i	0.839644	+	0.543137i	$0.182764\pi$
$929$			33.1091i			1.08627i	−0.839644	+	0.543137i	$0.817236\pi$
$930$	56.0920	+	32.3847i	1.83933	+	1.06194i
$931$	35.3004	+	17.7026i	1.15692	+	0.580179i
$932$	15.1424	−	26.2274i	0.496006	−	0.859107i
$933$	−2.39916	+	4.15546i	−0.0785448	+	0.136044i
$934$			17.5702i			0.574914i
$935$	−20.1942	+	34.9773i	−0.660420	+	1.14388i
$936$	−3.22493	+	1.95567i	−0.105410	+	0.0639232i
$937$	−11.4911			−0.375399			−0.187700	−	0.982226i	$-0.560103\pi$
$937$	−11.4911			−0.375399			−0.187700	+	0.982226i	$0.560103\pi$
$938$	69.4292	−	2.04057i	2.26694	−	0.0666269i
$939$	0.476130	+	0.824681i	0.0155379	+	0.0269125i
$940$	14.6756			0.478665
$941$	49.8468	+	28.7791i	1.62496	+	0.938171i	0.985566	+	0.169292i	$0.0541482\pi$
$941$	49.8468	+	28.7791i	1.62496	+	0.938171i	0.639394	+	0.768879i	$0.279185\pi$
$942$	34.2524	−	19.7756i	1.11600	−	0.644325i
$943$		−	20.3920i		−	0.664056i
$944$			30.9552i			1.00750i
$945$	8.12162	+	4.37606i	0.264196	+	0.142353i
$946$	−21.6871	−	37.5632i	−0.705110	−	1.22129i
$947$	41.2424	+	23.8113i	1.34020	+	0.773764i	0.986836	−	0.161723i	$-0.0517050\pi$
$947$	41.2424	+	23.8113i	1.34020	+	0.773764i	0.353362	+	0.935487i	$0.385038\pi$
$948$	−12.2578	+	21.2311i	−0.398115	+	0.689555i
$949$	−0.0708129	−	3.28856i	−0.00229869	−	0.106751i
$950$	−42.8043	−	74.1393i	−1.38876	−	2.40539i
$951$	−0.276987	+	0.159919i	−0.00898193	+	0.00518572i
$952$	6.77303	+	3.64942i	0.219515	+	0.118278i
$953$	−29.2194	+	50.6095i	−0.946510	+	1.63940i	−0.193811	+	0.981039i	$0.562085\pi$
$953$	−29.2194	+	50.6095i	−0.946510	+	1.63940i	−0.752699	+	0.658365i	$0.771248\pi$
$954$	−12.6744	+	7.31755i	−0.410348	+	0.236914i
$955$	−13.9358	+	8.04586i	−0.450953	+	0.260358i
$956$	47.8384	−	27.6195i	1.54720	−	0.893278i
$957$	−7.78534	+	4.49487i	−0.251664	+	0.145298i
$958$	−36.9661	+	64.0272i	−1.19432	+	2.06862i
$959$	0.598950	+	0.322724i	0.0193411	+	0.0104213i
$960$	34.2459	−	19.7719i	1.10528	−	0.638135i
$961$	22.8922	+	39.6505i	0.738459	+	1.27905i
$962$	−13.9487	+	25.4078i	−0.449723	+	0.819179i
$963$	−5.08615	+	8.80947i	−0.163899	+	0.283881i
$964$	−7.87189	−	4.54484i	−0.253537	−	0.146379i
$965$	−14.8275	−	25.6819i	−0.477313	−	0.826731i
$966$	−18.1474	−	9.77812i	−0.583883	−	0.314606i
$967$			54.1411i			1.74106i	0.492115	+	0.870530i	$0.336224\pi$
$967$			54.1411i			1.74106i	−0.492115	+	0.870530i	$0.663776\pi$
$968$		−	6.65346i		−	0.213850i
$969$	13.5818	−	7.84144i	0.436309	−	0.251903i
$970$	−95.7050	−	55.2553i	−3.07290	−	1.77414i
$971$	−5.88494			−0.188857			−0.0944283	−	0.995532i	$-0.530102\pi$
$971$	−5.88494			−0.188857			−0.0944283	+	0.995532i	$0.530102\pi$
$972$	−1.24674	−	2.15941i	−0.0399891	−	0.0692631i
$973$	40.5496	−	1.19178i	1.29996	−	0.0382067i
$974$	−9.62235			−0.308320
$975$	−25.8050	+	0.555662i	−0.826420	+	0.0177954i
$976$	4.60981	−	7.98442i	0.147556	−	0.255575i
$977$			15.7082i			0.502551i	0.967916	+	0.251275i	$0.0808500\pi$
$977$			15.7082i			0.502551i	−0.967916	+	0.251275i	$0.919150\pi$
$978$	17.0136	−	29.4684i	0.544035	−	0.942297i
$979$	0.0114726	−	0.0198711i	0.000366665	−	0.000635083i
$980$	50.8297	−	33.4740i	1.62370	−	1.06929i
$981$	−10.3230	−	5.95999i	−0.329588	−	0.190288i
$982$			6.84663i			0.218485i
$983$	−4.60292	−	2.65750i	−0.146810	−	0.0847609i	0.424796	−	0.905289i	$-0.360346\pi$
$983$	−4.60292	−	2.65750i	−0.146810	−	0.0847609i	−0.571606	+	0.820528i	$0.693679\pi$
$984$	−2.90174	−	5.02597i	−0.0925042	−	0.160222i
$985$	9.73734	−	16.8656i	0.310258	−	0.537382i
$986$	−11.0108	+	6.35707i	−0.350654	+	0.202450i
$987$	3.93141	+	2.11831i	0.125138	+	0.0674265i
$988$	44.4597	+	24.4080i	1.41445	+	0.776522i
$989$	9.02513	+	15.6320i	0.286982	+	0.497068i
$990$		−	30.7975i		−	0.978810i
$991$	33.2590			1.05651			0.528254	−	0.849087i	$-0.322847\pi$
$991$	33.2590			1.05651			0.528254	+	0.849087i	$0.322847\pi$
$992$	69.7765			2.21541
$993$		−	3.39943i		−	0.107878i
$994$	−16.4805	+	30.5865i	−0.522730	+	0.970145i
$995$	63.6738	+	36.7621i	2.01860	+	1.16544i
$996$	−19.3418	+	11.1670i	−0.612869	+	0.353840i
$997$	−2.51578	−	4.35746i	−0.0796755	−	0.138002i	0.823434	−	0.567411i	$-0.192055\pi$
$997$	−2.51578	−	4.35746i	−0.0796755	−	0.138002i	−0.903110	+	0.429409i	$0.858722\pi$
$998$	31.1115			0.984818
$999$	−3.28427	−	1.89617i	−0.103910	−	0.0599922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bl.d.88.9	yes	20
3.2	odd	2		819.2.do.g.361.2		20
7.2	even	3		273.2.t.d.205.2	yes	20
13.4	even	6		273.2.t.d.4.9	✓	20
21.2	odd	6		819.2.bm.g.478.9		20
39.17	odd	6		819.2.bm.g.550.2		20
91.30	even	6	inner	273.2.bl.d.121.9	yes	20
273.212	odd	6		819.2.do.g.667.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.9	✓	20	13.4	even	6
273.2.t.d.205.2	yes	20	7.2	even	3
273.2.bl.d.88.9	yes	20	1.1	even	1	trivial
273.2.bl.d.121.9	yes	20	91.30	even	6	inner
819.2.bm.g.478.9		20	21.2	odd	6
819.2.bm.g.550.2		20	39.17	odd	6
819.2.do.g.361.2		20	3.2	odd	2
819.2.do.g.667.2		20	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)

\(f(q)\)	\(=\)	\(q+(1.83578 + 1.05989i) q^{2} -1.00000 q^{3} +(1.24674 + 2.15941i) q^{4} +(-3.01977 + 1.74346i) q^{5} +(-1.83578 - 1.05989i) q^{6} +(1.38962 + 2.25144i) q^{7} +1.04605i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.83578 + 1.05989i) q^{2} -1.00000 q^{3} +(1.24674 + 2.15941i) q^{4} +(-3.01977 + 1.74346i) q^{5} +(-1.83578 - 1.05989i) q^{6} +(1.38962 + 2.25144i) q^{7} +1.04605i q^{8} +1.00000 q^{9} -7.39152 q^{10} +4.16660i q^{11} +(-1.24674 - 2.15941i) q^{12} +(1.86958 + 3.08296i) q^{13} +(0.164764 + 5.60599i) q^{14} +(3.01977 - 1.74346i) q^{15} +(1.38477 - 2.39850i) q^{16} +(-1.38996 - 2.40747i) q^{17} +(1.83578 + 1.05989i) q^{18} -5.64150i q^{19} +(-7.52970 - 4.34728i) q^{20} +(-1.38962 - 2.25144i) q^{21} +(-4.41614 + 7.64898i) q^{22} +(1.83778 - 3.18313i) q^{23} -1.04605i q^{24} +(3.57933 - 6.19959i) q^{25} +(0.164539 + 7.64121i) q^{26} -1.00000 q^{27} +(-3.12928 + 5.80770i) q^{28} +(-1.07879 - 1.86851i) q^{29} +7.39152 q^{30} +(7.58870 + 4.38134i) q^{31} +(6.89610 - 3.98146i) q^{32} -4.16660i q^{33} -5.89280i q^{34} +(-8.12162 - 4.37606i) q^{35} +(1.24674 + 2.15941i) q^{36} +(3.28427 + 1.89617i) q^{37} +(5.97937 - 10.3566i) q^{38} +(-1.86958 - 3.08296i) q^{39} +(-1.82375 - 3.15883i) q^{40} +(4.80471 - 2.77400i) q^{41} +(-0.164764 - 5.60599i) q^{42} +(-2.45544 + 4.25295i) q^{43} +(-8.99739 + 5.19465i) q^{44} +(-3.01977 + 1.74346i) q^{45} +(6.74754 - 3.89569i) q^{46} +(-1.46177 + 0.843954i) q^{47} +(-1.38477 + 2.39850i) q^{48} +(-3.13792 + 6.25727i) q^{49} +(13.1418 - 7.58740i) q^{50} +(1.38996 + 2.40747i) q^{51} +(-4.32651 + 7.88083i) q^{52} +(-3.45203 + 5.97909i) q^{53} +(-1.83578 - 1.05989i) q^{54} +(-7.26432 - 12.5822i) q^{55} +(-2.35511 + 1.45361i) q^{56} +5.64150i q^{57} -4.57358i q^{58} +(-9.67955 + 5.58849i) q^{59} +(7.52970 + 4.34728i) q^{60} +3.32893 q^{61} +(9.28747 + 16.0864i) q^{62} +(1.38962 + 2.25144i) q^{63} +11.3406 q^{64} +(-11.0207 - 6.05029i) q^{65} +(4.41614 - 7.64898i) q^{66} -12.3848i q^{67} +(3.46581 - 6.00297i) q^{68} +(-1.83778 + 3.18313i) q^{69} +(-10.2714 - 16.6415i) q^{70} +(5.36500 + 3.09748i) q^{71} +1.04605i q^{72} +(-0.790069 - 0.456146i) q^{73} +(4.01947 + 6.96192i) q^{74} +(-3.57933 + 6.19959i) q^{75} +(12.1823 - 7.03346i) q^{76} +(-9.38083 + 5.78998i) q^{77} +(-0.164539 - 7.64121i) q^{78} +(-4.91596 - 8.51469i) q^{79} +9.65720i q^{80} +1.00000 q^{81} +11.7605 q^{82} -8.95699i q^{83} +(3.12928 - 5.80770i) q^{84} +(8.39469 + 4.84668i) q^{85} +(-9.01532 + 5.20500i) q^{86} +(1.07879 + 1.86851i) q^{87} -4.35847 q^{88} +(-0.00476914 - 0.00275346i) q^{89} -7.39152 q^{90} +(-4.34310 + 8.49338i) q^{91} +9.16491 q^{92} +(-7.58870 - 4.38134i) q^{93} -3.57799 q^{94} +(9.83575 + 17.0360i) q^{95} +(-6.89610 + 3.98146i) q^{96} +(12.9479 + 7.47550i) q^{97} +(-12.3926 + 8.16114i) q^{98} +4.16660i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * q^98

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