LMFDB - Embedded newform 441.3.n.f.410.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(128,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("441.128");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.n (of order $6$, degree $2$, not 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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			410.6
Character	$\chi$	$=$	441.410
Dual form			441.3.n.f.128.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.444866 - 0.256844i) q^{2} +(-2.83879 - 0.970187i) q^{3} +(-1.86806 - 3.23558i) q^{4} +7.02462i q^{5} +(1.01370 + 1.16073i) q^{6} +3.97395i q^{8} +(7.11748 + 5.50832i) q^{9} +O(q^{10})$	\(q+(-0.444866 - 0.256844i) q^{2} +(-2.83879 - 0.970187i) q^{3} +(-1.86806 - 3.23558i) q^{4} +7.02462i q^{5} +(1.01370 + 1.16073i) q^{6} +3.97395i q^{8} +(7.11748 + 5.50832i) q^{9} +(1.80423 - 3.12502i) q^{10} -3.64877i q^{11} +(2.16392 + 10.9975i) q^{12} +(3.79085 - 6.56594i) q^{13} +(6.81519 - 19.9414i) q^{15} +(-6.45157 + 11.1744i) q^{16} +(17.5124 + 10.1108i) q^{17} +(-1.75155 - 4.27854i) q^{18} +(-13.6978 - 23.7253i) q^{19} +(22.7287 - 13.1224i) q^{20} +(-0.937164 + 1.62322i) q^{22} +3.94936i q^{23} +(3.85547 - 11.2812i) q^{24} -24.3452 q^{25} +(-3.37284 + 1.94731i) q^{26} +(-14.8609 - 22.5422i) q^{27} +(-23.7260 + 13.6982i) q^{29} +(-8.15368 + 7.12083i) q^{30} +(2.42502 + 4.20026i) q^{31} +(19.5063 - 11.2620i) q^{32} +(-3.53999 + 10.3581i) q^{33} +(-5.19377 - 8.99588i) q^{34} +(4.52670 - 33.3190i) q^{36} +(-18.7209 - 32.4256i) q^{37} +14.0728i q^{38} +(-17.1316 + 14.9615i) q^{39} -27.9155 q^{40} +(-61.1213 - 35.2884i) q^{41} +(-9.41887 - 16.3140i) q^{43} +(-11.8059 + 6.81613i) q^{44} +(-38.6938 + 49.9975i) q^{45} +(1.01437 - 1.75694i) q^{46} +(-20.7612 - 11.9865i) q^{47} +(29.1559 - 25.4627i) q^{48} +(10.8304 + 6.25292i) q^{50} +(-39.9046 - 45.6926i) q^{51} -28.3262 q^{52} +(-23.1126 - 13.3441i) q^{53} +(0.821297 + 13.8452i) q^{54} +25.6312 q^{55} +(15.8672 + 80.6406i) q^{57} +14.0732 q^{58} +(45.7350 - 26.4051i) q^{59} +(-77.2533 + 15.2007i) q^{60} +(-53.4719 + 92.6160i) q^{61} -2.49140i q^{62} +40.0422 q^{64} +(46.1232 + 26.6293i) q^{65} +(4.23524 - 3.69875i) q^{66} +(-51.0777 - 88.4692i) q^{67} -75.5502i q^{68} +(3.83161 - 11.2114i) q^{69} -138.410i q^{71} +(-21.8898 + 28.2845i) q^{72} +(34.7679 - 60.2198i) q^{73} +19.2334i q^{74} +(69.1111 + 23.6194i) q^{75} +(-51.1767 + 88.6406i) q^{76} +(11.4641 - 2.25573i) q^{78} +(-11.6077 + 20.1052i) q^{79} +(-78.4962 - 45.3198i) q^{80} +(20.3169 + 78.4106i) q^{81} +(18.1272 + 31.3973i) q^{82} +(25.9282 - 14.9697i) q^{83} +(-71.0243 + 123.018i) q^{85} +9.67670i q^{86} +(80.6431 - 15.8677i) q^{87} +14.5000 q^{88} +(135.658 - 78.3225i) q^{89} +(30.0551 - 12.3040i) q^{90} +(12.7785 - 7.37765i) q^{92} +(-2.80909 - 14.2764i) q^{93} +(6.15730 + 10.6648i) q^{94} +(166.661 - 96.2218i) q^{95} +(-66.3007 + 13.0457i) q^{96} +(-2.93155 - 5.07760i) q^{97} +(20.0986 - 25.9700i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} - 8 q^{3} + 12 q^{4} + 8 q^{6} + 20 q^{9}+O(q^{10}) $ 22 * q - 6 * q^2 - 8 * q^3 + 12 * q^4 + 8 * q^6 + 20 * q^9	$ 22 q - 6 q^{2} - 8 q^{3} + 12 q^{4} + 8 q^{6} + 20 q^{9} - 25 q^{10} + 20 q^{12} + 18 q^{13} + 53 q^{15} + 12 q^{16} - 6 q^{17} - 56 q^{18} - 3 q^{19} + 39 q^{20} - 59 q^{22} - 15 q^{24} - 114 q^{25} + 3 q^{26} + 97 q^{27} - 63 q^{29} - 20 q^{30} + 29 q^{31} + 246 q^{32} - 77 q^{33} + 99 q^{34} + 76 q^{36} - 20 q^{37} + 200 q^{39} - 210 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} - 71 q^{45} + 75 q^{46} - 261 q^{47} + 113 q^{48} + 63 q^{50} - 78 q^{51} - 92 q^{52} - 63 q^{53} + 485 q^{54} + 100 q^{55} + 224 q^{57} - 80 q^{58} + 102 q^{59} + 103 q^{60} - 78 q^{61} + 106 q^{64} - 225 q^{65} + 401 q^{66} - 132 q^{67} + 297 q^{69} - 66 q^{72} - q^{73} + 245 q^{75} - 233 q^{76} - 440 q^{78} + 140 q^{79} - 96 q^{80} + 104 q^{81} + 157 q^{82} - 255 q^{83} + 102 q^{85} + 136 q^{87} - 816 q^{88} + 720 q^{89} - 418 q^{90} - 1239 q^{92} + 210 q^{93} - 261 q^{94} + 642 q^{95} - 539 q^{96} - 178 q^{97} - 103 q^{99}+O(q^{100}) $ 22 * q - 6 * q^2 - 8 * q^3 + 12 * q^4 + 8 * q^6 + 20 * q^9 - 25 * q^10 + 20 * q^12 + 18 * q^13 + 53 * q^15 + 12 * q^16 - 6 * q^17 - 56 * q^18 - 3 * q^19 + 39 * q^20 - 59 * q^22 - 15 * q^24 - 114 * q^25 + 3 * q^26 + 97 * q^27 - 63 * q^29 - 20 * q^30 + 29 * q^31 + 246 * q^32 - 77 * q^33 + 99 * q^34 + 76 * q^36 - 20 * q^37 + 200 * q^39 - 210 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 - 71 * q^45 + 75 * q^46 - 261 * q^47 + 113 * q^48 + 63 * q^50 - 78 * q^51 - 92 * q^52 - 63 * q^53 + 485 * q^54 + 100 * q^55 + 224 * q^57 - 80 * q^58 + 102 * q^59 + 103 * q^60 - 78 * q^61 + 106 * q^64 - 225 * q^65 + 401 * q^66 - 132 * q^67 + 297 * q^69 - 66 * q^72 - q^73 + 245 * q^75 - 233 * q^76 - 440 * q^78 + 140 * q^79 - 96 * q^80 + 104 * q^81 + 157 * q^82 - 255 * q^83 + 102 * q^85 + 136 * q^87 - 816 * q^88 + 720 * q^89 - 418 * q^90 - 1239 * q^92 + 210 * q^93 - 261 * q^94 + 642 * q^95 - 539 * q^96 - 178 * q^97 - 103 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.444866	−	0.256844i	−0.222433	−	0.128422i	0.384643	−	0.923065i	$-0.374324\pi$
$2$	−0.444866	−	0.256844i	−0.222433	−	0.128422i	−0.607076	+	0.794643i	$0.707658\pi$
$3$	−2.83879	−	0.970187i	−0.946264	−	0.323396i
$3$	−2.83879	−	0.970187i	−0.946264	−	0.323396i
$4$	−1.86806	−	3.23558i	−0.467016	−	0.808895i
$5$			7.02462i			1.40492i	0.711722	+	0.702462i	$0.247916\pi$
$5$			7.02462i			1.40492i	−0.711722	+	0.702462i	$0.752084\pi$
$6$	1.01370	+	1.16073i	0.168949	+	0.193455i
$7$		0			0
$7$		0			0
$8$			3.97395i			0.496744i
$9$	7.11748	+	5.50832i	0.790831	+	0.612035i
$10$	1.80423	−	3.12502i	0.180423	−	0.312502i
$11$		−	3.64877i		−	0.331707i	−0.986150	−	0.165853i	$-0.946962\pi$
$11$		−	3.64877i		−	0.331707i	0.986150	−	0.165853i	$-0.0530378\pi$
$12$	2.16392	+	10.9975i	0.180327	+	0.916459i
$13$	3.79085	−	6.56594i	0.291604	−	0.505073i	−0.682585	−	0.730806i	$-0.739144\pi$
$13$	3.79085	−	6.56594i	0.291604	−	0.505073i	0.974189	+	0.225733i	$0.0724778\pi$
$14$		0			0
$15$	6.81519	−	19.9414i	0.454346	−	1.32943i
$16$	−6.45157	+	11.1744i	−0.403223	+	0.698403i
$17$	17.5124	+	10.1108i	1.03014	+	0.594751i	0.917024	−	0.398831i	$-0.130584\pi$
$17$	17.5124	+	10.1108i	1.03014	+	0.594751i	0.113114	+	0.993582i	$0.463917\pi$
$18$	−1.75155	−	4.27854i	−0.0973083	−	0.237697i
$19$	−13.6978	−	23.7253i	−0.720937	−	1.24870i	−0.960625	−	0.277849i	$-0.910378\pi$
$19$	−13.6978	−	23.7253i	−0.720937	−	1.24870i	0.239688	−	0.970850i	$-0.422955\pi$
$20$	22.7287	−	13.1224i	1.13644	−	0.656121i
$21$		0			0
$22$	−0.937164	+	1.62322i	−0.0425984	+	0.0737825i
$23$			3.94936i			0.171711i	0.996308	+	0.0858556i	$0.0273624\pi$
$23$			3.94936i			0.171711i	−0.996308	+	0.0858556i	$0.972638\pi$
$24$	3.85547	−	11.2812i	0.160645	−	0.470051i
$25$	−24.3452			−0.973810
$26$	−3.37284	+	1.94731i	−0.129725	+	0.0748966i
$27$	−14.8609	−	22.5422i	−0.550405	−	0.834898i
$28$		0			0
$29$	−23.7260	+	13.6982i	−0.818139	+	0.472353i	−0.849774	−	0.527147i	$-0.823262\pi$
$29$	−23.7260	+	13.6982i	−0.818139	+	0.472353i	0.0316352	+	0.999499i	$0.489929\pi$
$30$	−8.15368	+	7.12083i	−0.271789	+	0.237361i
$31$	2.42502	+	4.20026i	0.0782264	+	0.135492i	0.902485	−	0.430722i	$-0.141741\pi$
$31$	2.42502	+	4.20026i	0.0782264	+	0.135492i	−0.824258	+	0.566214i	$0.808408\pi$
$32$	19.5063	−	11.2620i	0.609573	−	0.351937i
$33$	−3.53999	+	10.3581i	−0.107272	+	0.313882i
$34$	−5.19377	−	8.99588i	−0.152758	−	0.264585i
$35$		0			0
$36$	4.52670	−	33.3190i	0.125742	−	0.925529i
$37$	−18.7209	−	32.4256i	−0.505971	−	0.876367i	−0.999976	−	0.00690796i	$-0.997801\pi$
$37$	−18.7209	−	32.4256i	−0.505971	−	0.876367i	0.494006	−	0.869459i	$-0.335532\pi$
$38$			14.0728i			0.370336i
$39$	−17.1316	+	14.9615i	−0.439272	+	0.383629i
$40$	−27.9155			−0.697887
$41$	−61.1213	−	35.2884i	−1.49076	−	0.860693i	−0.490820	−	0.871261i	$-0.663303\pi$
$41$	−61.1213	−	35.2884i	−1.49076	−	0.860693i	−0.999944	+	0.0105682i	$0.996636\pi$
$42$		0			0
$43$	−9.41887	−	16.3140i	−0.219043	−	0.379394i	0.735472	−	0.677555i	$-0.236960\pi$
$43$	−9.41887	−	16.3140i	−0.219043	−	0.379394i	−0.954516	+	0.298160i	$0.903627\pi$
$44$	−11.8059	+	6.81613i	−0.268316	+	0.154912i
$45$	−38.6938	+	49.9975i	−0.859862	+	1.11106i
$46$	1.01437	−	1.75694i	0.0220515	−	0.0381943i
$47$	−20.7612	−	11.9865i	−0.441727	−	0.255031i	0.262603	−	0.964904i	$-0.415419\pi$
$47$	−20.7612	−	11.9865i	−0.441727	−	0.255031i	−0.704330	+	0.709873i	$0.748752\pi$
$48$	29.1559	−	25.4627i	0.607416	−	0.530473i
$49$		0			0
$50$	10.8304	+	6.25292i	0.216608	+	0.125058i
$51$	−39.9046	−	45.6926i	−0.782443	−	0.895934i
$52$	−28.3262			−0.544734
$53$	−23.1126	−	13.3441i	−0.436087	−	0.251775i	0.265850	−	0.964015i	$-0.414348\pi$
$53$	−23.1126	−	13.3441i	−0.436087	−	0.251775i	−0.701936	+	0.712240i	$0.747681\pi$
$54$	0.821297	+	13.8452i	0.0152092	+	0.256393i
$55$	25.6312			0.466022
$56$		0			0
$57$	15.8672	+	80.6406i	0.278373	+	1.41475i
$58$	14.0732			0.242642
$59$	45.7350	−	26.4051i	0.775170	−	0.447545i	−0.0595458	−	0.998226i	$-0.518965\pi$
$59$	45.7350	−	26.4051i	0.775170	−	0.447545i	0.834716	+	0.550681i	$0.185632\pi$
$60$	−77.2533	+	15.2007i	−1.28755	+	0.253346i
$61$	−53.4719	+	92.6160i	−0.876588	+	1.51829i	−0.0215264	+	0.999768i	$0.506853\pi$
$61$	−53.4719	+	92.6160i	−0.876588	+	1.51829i	−0.855062	+	0.518527i	$0.826481\pi$
$62$		−	2.49140i		−	0.0401839i
$63$		0			0
$64$	40.0422			0.625660
$65$	46.1232	+	26.6293i	0.709588	+	0.409681i
$66$	4.23524	−	3.69875i	0.0641702	−	0.0560416i
$67$	−51.0777	−	88.4692i	−0.762354	−	1.32044i	−0.941634	−	0.336637i	$-0.890710\pi$
$67$	−51.0777	−	88.4692i	−0.762354	−	1.32044i	0.179281	−	0.983798i	$-0.442623\pi$
$68$		−	75.5502i		−	1.11103i
$69$	3.83161	−	11.2114i	0.0555307	−	0.162484i
$70$		0			0
$71$		−	138.410i		−	1.94944i	−0.223427	−	0.974721i	$-0.571725\pi$
$71$		−	138.410i		−	1.94944i	0.223427	−	0.974721i	$-0.428275\pi$
$72$	−21.8898	+	28.2845i	−0.304025	+	0.392840i
$73$	34.7679	−	60.2198i	0.476273	−	0.824929i	−0.523358	−	0.852113i	$-0.675321\pi$
$73$	34.7679	−	60.2198i	0.476273	−	0.824929i	0.999630	+	0.0271843i	$0.00865410\pi$
$74$			19.2334i			0.259911i
$75$	69.1111	+	23.6194i	0.921481	+	0.314926i
$76$	−51.1767	+	88.6406i	−0.673378	+	1.16632i
$77$		0			0
$78$	11.4641	−	2.25573i	0.146975	−	0.0289196i
$79$	−11.6077	+	20.1052i	−0.146933	+	0.254496i	−0.930093	−	0.367325i	$-0.880274\pi$
$79$	−11.6077	+	20.1052i	−0.146933	+	0.254496i	0.783159	+	0.621821i	$0.213607\pi$
$80$	−78.4962	−	45.3198i	−0.981202	−	0.566497i
$81$	20.3169	+	78.4106i	0.250826	+	0.968032i
$82$	18.1272	+	31.3973i	0.221064	+	0.382893i
$83$	25.9282	−	14.9697i	0.312388	−	0.180357i	−0.335606	−	0.942002i	$-0.608941\pi$
$83$	25.9282	−	14.9697i	0.312388	−	0.180357i	0.647995	+	0.761645i	$0.275608\pi$
$84$		0			0
$85$	−71.0243	+	123.018i	−0.835579	+	1.44727i
$86$			9.67670i			0.112520i
$87$	80.6431	−	15.8677i	0.926932	−	0.182388i
$88$	14.5000			0.164773
$89$	135.658	−	78.3225i	1.52425	−	0.880028i	0.524665	−	0.851309i	$-0.324191\pi$
$89$	135.658	−	78.3225i	1.52425	−	0.880028i	0.999588	−	0.0287188i	$-0.00914274\pi$
$90$	30.0551	−	12.3040i	0.333946	−	0.136711i
$91$		0			0
$92$	12.7785	−	7.37765i	0.138896	−	0.0801918i
$93$	−2.80909	−	14.2764i	−0.0302053	−	0.153509i
$94$	6.15730	+	10.6648i	0.0655032	+	0.113455i
$95$	166.661	−	96.2218i	1.75433	−	1.01286i
$96$	−66.3007	+	13.0457i	−0.690632	+	0.135892i
$97$	−2.93155	−	5.07760i	−0.0302222	−	0.0523464i	0.850519	−	0.525945i	$-0.176288\pi$
$97$	−2.93155	−	5.07760i	−0.0302222	−	0.0523464i	−0.880741	+	0.473598i	$0.842955\pi$
$98$		0			0
$99$	20.0986	−	25.9700i	0.203016	−	0.262324i
$100$	45.4784	+	78.7710i	0.454784	+	0.787710i
$101$		−	19.4750i		−	0.192822i	−0.995342	−	0.0964111i	$-0.969264\pi$
$101$		−	19.4750i		−	0.192822i	0.995342	−	0.0964111i	$-0.0307363\pi$
$102$	6.01636	+	30.5764i	0.0589839	+	0.299768i
$103$	−26.0917			−0.253317			−0.126659	−	0.991946i	$-0.540425\pi$
$103$	−26.0917			−0.253317			−0.126659	+	0.991946i	$0.540425\pi$
$104$	26.0927	+	15.0646i	0.250892	+	0.144852i
$105$		0			0
$106$	6.85468	+	11.8727i	0.0646668	+	0.112006i
$107$	−25.2215	+	14.5616i	−0.235715	+	0.136090i	−0.613206	−	0.789923i	$-0.710120\pi$
$107$	−25.2215	+	14.5616i	−0.235715	+	0.136090i	0.377491	+	0.926013i	$0.376787\pi$
$108$	−45.1761	+	90.1941i	−0.418297	+	0.835130i
$109$	50.9986	−	88.3322i	0.467877	−	0.810387i	−0.531449	−	0.847090i	$-0.678352\pi$
$109$	50.9986	−	88.3322i	0.467877	−	0.810387i	0.999326	+	0.0367034i	$0.0116857\pi$
$110$	−11.4025	−	6.58322i	−0.103659	−	0.0598474i
$111$	21.6859	+	110.212i	0.195369	+	0.992903i
$112$		0			0
$113$	−122.755	−	70.8728i	−1.08633	−	0.627193i	−0.153734	−	0.988112i	$-0.549130\pi$
$113$	−122.755	−	70.8728i	−1.08633	−	0.627193i	−0.932597	+	0.360919i	$0.882463\pi$
$114$	13.6532	−	39.9497i	0.119765	−	0.350436i
$115$	−27.7427			−0.241241
$116$	88.6434	+	51.1783i	0.764168	+	0.441192i
$117$	63.1486	−	25.8518i	0.539731	−	0.220955i
$118$	−27.1280			−0.229898
$119$		0			0
$120$	79.2462	+	27.0832i	0.660385	+	0.225694i
$121$	107.686			0.889971
$122$	47.5757	−	27.4678i	0.389964	−	0.225146i
$123$	139.274	+	159.476i	1.13231	+	1.29655i
$124$	9.06018	−	15.6927i	0.0730660	−	0.126554i
$125$			4.59944i			0.0367955i
$126$		0			0
$127$	−39.8045			−0.313421			−0.156711	−	0.987645i	$-0.550089\pi$
$127$	−39.8045			−0.313421			−0.156711	+	0.987645i	$0.550089\pi$
$128$	−95.8388	−	55.3326i	−0.748741	−	0.432286i
$129$	10.9106	+	55.4500i	0.0845784	+	0.429845i
$130$	−13.6791	−	23.6929i	−0.105224	−	0.182253i
$131$			69.5184i			0.530674i	0.964156	+	0.265337i	$0.0854833\pi$
$131$			69.5184i			0.530674i	−0.964156	+	0.265337i	$0.914517\pi$
$132$	40.1274	−	7.89567i	0.303995	−	0.0598157i
$133$		0			0
$134$			52.4759i			0.391611i
$135$	158.351	−	104.392i	1.17297	−	0.773277i
$136$	−40.1797	+	69.5932i	−0.295439	+	0.511715i
$137$			75.7533i			0.552944i	0.961022	+	0.276472i	$0.0891653\pi$
$137$			75.7533i			0.552944i	−0.961022	+	0.276472i	$0.910835\pi$
$138$	−4.58414	+	4.00345i	−0.0332184	+	0.0290105i
$139$	−37.4261	+	64.8239i	−0.269253	+	0.466359i	−0.968669	−	0.248355i	$-0.920110\pi$
$139$	−37.4261	+	64.8239i	−0.269253	+	0.466359i	0.699416	+	0.714714i	$0.253443\pi$
$140$		0			0
$141$	47.3076	+	54.1693i	0.335515	+	0.384180i
$142$	−35.5498	+	61.5741i	−0.250351	+	0.433620i
$143$	−23.9576	−	13.8319i	−0.167536	−	0.0967269i
$144$	−107.471	+	43.9965i	−0.746328	+	0.305532i
$145$	−96.2248	−	166.666i	−0.663620	−	1.14942i
$146$	−30.9342	+	17.8598i	−0.211878	+	0.122328i
$147$		0			0
$148$	−69.9437	+	121.146i	−0.472592	+	0.818554i
$149$		−	21.6822i		−	0.145518i	−0.997350	−	0.0727591i	$-0.976820\pi$
$149$		−	21.6822i		−	0.145518i	0.997350	−	0.0727591i	$-0.0231804\pi$
$150$	−24.6787	−	28.2582i	−0.164525	−	0.188388i
$151$	−171.507			−1.13580			−0.567902	−	0.823096i	$-0.692245\pi$
$151$	−171.507			−1.13580			−0.567902	+	0.823096i	$0.692245\pi$
$152$	94.2831	−	54.4344i	0.620284	−	0.358121i
$153$	68.9505	+	168.427i	0.450657	+	1.10083i
$154$		0			0
$155$	−29.5052	+	17.0348i	−0.190356	+	0.109902i
$156$	80.4121	+	27.4817i	0.515462	+	0.176165i
$157$	−40.2266	−	69.6745i	−0.256220	−	0.443787i	0.709006	−	0.705202i	$-0.249144\pi$
$157$	−40.2266	−	69.6745i	−0.256220	−	0.443787i	−0.965226	+	0.261416i	$0.915811\pi$
$158$	10.3278	−	5.96275i	0.0653657	−	0.0377389i
$159$	52.6656	+	60.3046i	0.331230	+	0.379274i
$160$	79.1112	+	137.025i	0.494445	+	0.856403i
$161$		0			0
$162$	11.1010	−	40.1005i	0.0685244	−	0.247534i
$163$	−67.6792	−	117.224i	−0.415210	−	0.719165i	0.580240	−	0.814445i	$-0.302959\pi$
$163$	−67.6792	−	117.224i	−0.415210	−	0.719165i	−0.995450	+	0.0952804i	$0.969625\pi$
$164$			263.684i			1.60783i
$165$	−72.7617	−	24.8671i	−0.440980	−	0.150710i
$166$	−15.3795			−0.0926473
$167$	−97.2491	−	56.1468i	−0.582330	−	0.336208i	0.179729	−	0.983716i	$-0.442478\pi$
$167$	−97.2491	−	56.1468i	−0.582330	−	0.336208i	−0.762059	+	0.647508i	$0.775811\pi$
$168$		0			0
$169$	55.7589	+	96.5773i	0.329934	+	0.571463i
$170$	63.1926	−	36.4843i	0.371721	−	0.214613i
$171$	33.1926	−	244.316i	0.194109	−	1.42875i
$172$	−35.1901	+	60.9510i	−0.204593	+	0.354366i
$173$	−157.656	−	91.0227i	−0.911306	−	0.526143i	−0.0304551	−	0.999536i	$-0.509696\pi$
$173$	−157.656	−	91.0227i	−0.911306	−	0.526143i	−0.880851	+	0.473393i	$0.843029\pi$
$174$	−39.9509	−	13.6536i	−0.229603	−	0.0784692i
$175$		0			0
$176$	40.7730	+	23.5403i	0.231665	+	0.133752i
$177$	−155.450	+	30.5871i	−0.878249	+	0.172809i
$178$	−80.4665			−0.452059
$179$	182.206	+	105.197i	1.01791	+	0.587691i	0.913498	−	0.406843i	$-0.133370\pi$
$179$	182.206	+	105.197i	1.01791	+	0.587691i	0.104413	+	0.994534i	$0.466704\pi$
$180$	234.053	+	31.7984i	1.30030	+	0.176658i
$181$	−104.037			−0.574791			−0.287396	−	0.957812i	$-0.592789\pi$
$181$	−104.037			−0.574791			−0.287396	+	0.957812i	$0.592789\pi$
$182$		0			0
$183$	241.650	−	211.040i	1.32049	−	1.15322i
$184$	−15.6946			−0.0852965
$185$	227.777	−	131.507i	1.23123	−	0.710850i
$186$	−2.41713	+	7.07258i	−0.0129953	+	0.0380246i
$187$	36.8919	−	63.8986i	0.197283	−	0.341704i
$188$			89.5660i			0.476415i
$189$		0			0
$190$	−98.8559			−0.520294
$191$	77.7538	+	44.8912i	0.407088	+	0.235032i	0.689538	−	0.724250i	$-0.257814\pi$
$191$	77.7538	+	44.8912i	0.407088	+	0.235032i	−0.282450	+	0.959282i	$0.591147\pi$
$192$	−113.672	−	38.8485i	−0.592040	−	0.202336i
$193$	40.0598	+	69.3855i	0.207564	+	0.359511i	0.950946	−	0.309355i	$-0.100113\pi$
$193$	40.0598	+	69.3855i	0.207564	+	0.359511i	−0.743383	+	0.668866i	$0.766780\pi$
$194$			3.01180i			0.0155248i
$195$	−105.099	−	120.343i	−0.538969	−	0.617144i
$196$		0			0
$197$			49.3712i			0.250615i	0.992118	+	0.125308i	$0.0399918\pi$
$197$			49.3712i			0.250615i	−0.992118	+	0.125308i	$0.960008\pi$
$198$	−15.6114	+	6.39100i	−0.0788456	+	0.0322778i
$199$	−1.01765	+	1.76262i	−0.00511381	+	0.00885737i	−0.868571	−	0.495565i	$-0.834961\pi$
$199$	−1.01765	+	1.76262i	−0.00511381	+	0.00885737i	0.863457	+	0.504422i	$0.168294\pi$
$200$		−	96.7468i		−	0.483734i
$201$	59.1673	+	300.700i	0.294365	+	1.49602i
$202$	−5.00204	+	8.66379i	−0.0247626	+	0.0428900i
$203$		0			0
$204$	−73.2978	+	214.471i	−0.359303	+	1.05133i
$205$	247.888	−	429.354i	1.20921	−	2.09441i
$206$	11.6073	+	6.70148i	0.0563462	+	0.0325315i
$207$	−21.7543	+	28.1095i	−0.105093	+	0.135794i
$208$	48.9138	+	84.7213i	0.235163	+	0.407314i
$209$	−86.5682	+	49.9802i	−0.414202	+	0.239139i
$210$		0			0
$211$	144.840	−	250.871i	0.686446	−	1.18896i	−0.286534	−	0.958070i	$-0.592503\pi$
$211$	144.840	−	250.871i	0.686446	−	1.18896i	0.972980	−	0.230890i	$-0.0741637\pi$
$212$			99.7102i			0.470331i
$213$	−134.284	+	392.918i	−0.630441	+	1.84469i
$214$	14.9603			0.0699078
$215$	114.599	−	66.1639i	0.533020	−	0.307739i
$216$	89.5817	−	59.0566i	0.414730	−	0.273410i
$217$		0			0
$218$	−45.3751	+	26.1973i	−0.208143	+	0.120171i
$219$	−157.123	+	137.220i	−0.717458	+	0.626576i
$220$	−47.8807	−	82.9319i	−0.217640	−	0.376963i
$221$	132.773	−	76.6568i	0.600785	−	0.346863i
$222$	18.6600	−	54.5996i	0.0840540	−	0.245944i
$223$	−67.9693	−	117.726i	−0.304795	−	0.527921i	0.672421	−	0.740169i	$-0.265255\pi$
$223$	−67.9693	−	117.726i	−0.304795	−	0.527921i	−0.977216	+	0.212249i	$0.931921\pi$
$224$		0			0
$225$	−173.277	−	134.101i	−0.770118	−	0.596006i
$226$	36.4065	+	63.0579i	0.161091	+	0.279017i
$227$		−	49.8026i		−	0.219395i	−0.993965	−	0.109697i	$-0.965012\pi$
$227$		−	49.8026i		−	0.219395i	0.993965	−	0.109697i	$-0.0349882\pi$
$228$	231.278	−	201.981i	1.01438	−	0.885883i
$229$	−142.498			−0.622261			−0.311131	−	0.950367i	$-0.600708\pi$
$229$	−142.498			−0.622261			−0.311131	+	0.950367i	$0.600708\pi$
$230$	12.3418	+	7.12555i	0.0536600	+	0.0309806i
$231$		0			0
$232$	−54.4361	−	94.2861i	−0.234638	−	0.406405i
$233$	−72.6863	+	41.9654i	−0.311958	+	0.180109i	−0.647802	−	0.761808i	$-0.724312\pi$
$233$	−72.6863	+	41.9654i	−0.311958	+	0.180109i	0.335844	+	0.941918i	$0.390978\pi$
$234$	−34.7325	−	4.71874i	−0.148430	−	0.0201656i
$235$	84.2004	−	145.839i	0.358300	−	0.620593i
$236$	−170.872	−	98.6529i	−0.724033	−	0.418021i
$237$	52.4577	−	45.8128i	0.221341	−	0.193303i
$238$		0			0
$239$	222.986	+	128.741i	0.932995	+	0.538665i	0.887758	−	0.460311i	$-0.152262\pi$
$239$	222.986	+	128.741i	0.932995	+	0.538665i	0.0452374	+	0.998976i	$0.485596\pi$
$240$	178.866	+	204.809i	0.745273	+	0.853372i
$241$	127.978			0.531030			0.265515	−	0.964107i	$-0.414458\pi$
$241$	127.978			0.531030			0.265515	+	0.964107i	$0.414458\pi$
$242$	−47.9061	−	27.6586i	−0.197959	−	0.114292i
$243$	18.3974	−	242.303i	0.0757096	−	0.997130i
$244$	399.555			1.63752
$245$		0			0
$246$	−20.9982	−	106.717i	−0.0853585	−	0.433809i
$247$	−207.705			−0.840912
$248$	−16.6916	+	9.63691i	−0.0673049	+	0.0388585i
$249$	−88.1282	+	17.3405i	−0.353928	+	0.0696407i
$250$	1.18134	−	2.04613i	0.00472535	−	0.00818454i
$251$		−	277.115i		−	1.10404i	−0.833830	−	0.552022i	$-0.813856\pi$
$251$		−	277.115i		−	1.10404i	0.833830	−	0.552022i	$-0.186144\pi$
$252$		0			0
$253$	14.4103			0.0569577
$254$	17.7077	+	10.2235i	0.0697153	+	0.0402502i
$255$	320.973	−	280.315i	1.25872	−	1.09927i
$256$	−51.6609	−	89.4792i	−0.201800	−	0.349528i
$257$			190.409i			0.740891i	0.928854	+	0.370445i	$0.120795\pi$
$257$			190.409i			0.740891i	−0.928854	+	0.370445i	$0.879205\pi$
$258$	9.38821	−	27.4701i	0.0363884	−	0.106473i
$259$		0			0
$260$		−	198.981i		−	0.765310i
$261$	−244.324	−	33.1937i	−0.936106	−	0.127179i
$262$	17.8554	−	30.9264i	0.0681502	−	0.118040i
$263$			50.8092i			0.193191i	0.995324	+	0.0965954i	$0.0307953\pi$
$263$			50.8092i			0.193191i	−0.995324	+	0.0965954i	$0.969205\pi$
$264$	−41.1626	−	14.0677i	−0.155919	−	0.0532869i
$265$	93.7369	−	162.357i	0.353724	−	0.612669i
$266$		0			0
$267$	−461.094	+	90.7271i	−1.72694	+	0.339802i
$268$	−190.833	+	330.532i	−0.712062	+	1.23333i
$269$	−15.6224	−	9.01962i	−0.0580760	−	0.0335302i	0.470681	−	0.882304i	$-0.344008\pi$
$269$	−15.6224	−	9.01962i	−0.0580760	−	0.0335302i	−0.528757	+	0.848773i	$0.677342\pi$
$270$	−97.2574	+	5.76930i	−0.360212	+	0.0213678i
$271$	85.9218	+	148.821i	0.317055	+	0.549155i	0.979872	−	0.199626i	$-0.0639728\pi$
$271$	85.9218	+	148.821i	0.317055	+	0.549155i	−0.662818	+	0.748781i	$0.730639\pi$
$272$	−225.964	+	130.461i	−0.830751	+	0.479634i
$273$		0			0
$274$	19.4568	−	33.7001i	0.0710101	−	0.122993i
$275$			88.8302i			0.323019i
$276$	−43.4331	+	8.54611i	−0.157366	+	0.0309642i
$277$	−226.589			−0.818011			−0.409006	−	0.912532i	$-0.634124\pi$
$277$	−226.589			−0.818011			−0.409006	+	0.912532i	$0.634124\pi$
$278$	33.2992	−	19.2253i	0.119781	−	0.0691558i
$279$	−5.87633	+	43.2530i	−0.0210621	+	0.155029i
$280$		0			0
$281$	−360.913	+	208.373i	−1.28439	+	0.741541i	−0.977647	−	0.210252i	$-0.932571\pi$
$281$	−360.913	+	208.373i	−1.28439	+	0.741541i	−0.306740	+	0.951793i	$0.599238\pi$
$282$	−7.13249	−	36.2488i	−0.0252925	−	0.128542i
$283$	−62.1546	−	107.655i	−0.219627	−	0.380406i	0.735067	−	0.677995i	$-0.237151\pi$
$283$	−62.1546	−	107.655i	−0.219627	−	0.380406i	−0.954694	+	0.297589i	$0.903818\pi$
$284$	−447.838	+	258.559i	−1.57689	+	0.910420i
$285$	−566.469	+	111.461i	−1.98761	+	0.391092i
$286$	7.10530	+	12.3067i	0.0248437	+	0.0430305i
$287$		0			0
$288$	200.870	+	27.2901i	0.697467	+	0.0947574i
$289$	59.9552	+	103.845i	0.207457	+	0.359327i
$290$			98.8590i			0.340893i
$291$	3.39585	+	17.2584i	0.0116696	+	0.0593072i
$292$	−259.795			−0.889708
$293$	362.584	+	209.338i	1.23749	+	0.714464i	0.968580	−	0.248702i	$-0.0800039\pi$
$293$	362.584	+	209.338i	1.23749	+	0.714464i	0.268908	+	0.963166i	$0.413337\pi$
$294$		0			0
$295$	185.486	+	321.271i	0.628766	+	1.08905i
$296$	128.858	−	74.3960i	0.435330	−	0.251338i
$297$	−82.2515	+	54.2242i	−0.276941	+	0.182573i
$298$	−5.56894	+	9.64568i	−0.0186877	+	0.0323681i
$299$	25.9313	+	14.9714i	0.0867267	+	0.0500717i
$300$	−52.6813	−	267.737i	−0.175604	−	0.892456i
$301$		0			0
$302$	76.2975	+	44.0504i	0.252641	+	0.145862i
$303$	−18.8944	+	55.2856i	−0.0623578	+	0.182461i
$304$	353.489			1.16279
$305$	−650.592	−	375.619i	−2.13309	−	1.23154i
$306$	12.5856	−	92.6369i	0.0411294	−	0.302735i
$307$	−457.334			−1.48969			−0.744843	−	0.667239i	$-0.767476\pi$
$307$	−457.334			−1.48969			−0.744843	+	0.667239i	$0.767476\pi$
$308$		0			0
$309$	74.0689	+	25.3138i	0.239705	+	0.0819217i
$310$	17.5012			0.0564554
$311$	−301.499	+	174.070i	−0.969449	+	0.559712i	−0.899068	−	0.437808i	$-0.855755\pi$
$311$	−301.499	+	174.070i	−0.969449	+	0.559712i	−0.0703809	+	0.997520i	$0.522421\pi$
$312$	−59.4563	−	68.0802i	−0.190565	−	0.218206i
$313$	−67.8539	+	117.526i	−0.216785	+	0.375483i	−0.953823	−	0.300368i	$-0.902891\pi$
$313$	−67.8539	+	117.526i	−0.216785	+	0.375483i	0.737038	+	0.675851i	$0.236224\pi$
$314$			41.3278i			0.131617i
$315$		0			0
$316$	86.7359			0.274481
$317$	−353.028	−	203.821i	−1.11365	−	0.642967i	−0.173879	−	0.984767i	$-0.555630\pi$
$317$	−353.028	−	203.821i	−1.11365	−	0.642967i	−0.939773	+	0.341800i	$0.888964\pi$
$318$	−7.94032	−	40.3543i	−0.0249695	−	0.126900i
$319$	49.9817	+	86.5709i	0.156683	+	0.271382i
$320$			281.281i			0.879005i
$321$	85.7261	−	16.8679i	0.267060	−	0.0525480i
$322$		0			0
$323$		−	553.981i		−	1.71511i
$324$	215.750	−	212.213i	0.665896	−	0.654978i
$325$	−92.2892	+	159.850i	−0.283967	+	0.491845i
$326$			69.5319i			0.213288i
$327$	−230.473	+	201.278i	−0.704811	+	0.615530i
$328$	140.234	−	242.893i	0.427544	−	0.740528i
$329$		0			0
$330$	25.9823	+	29.7509i	0.0787342	+	0.0901543i
$331$	−92.1997	+	159.695i	−0.278549	+	0.482461i	−0.971024	−	0.238981i	$-0.923187\pi$
$331$	−92.1997	+	159.695i	−0.278549	+	0.482461i	0.692475	+	0.721442i	$0.256520\pi$
$332$	−96.8711	−	55.9285i	−0.291780	−	0.168459i
$333$	45.3646	−	333.909i	0.136230	−	1.00273i
$334$	28.8419	+	49.9557i	0.0863530	+	0.149568i
$335$	621.462	−	358.801i	1.85511	−	1.07105i
$336$		0			0
$337$	121.608	−	210.631i	0.360855	−	0.625019i	−0.627247	−	0.778820i	$-0.715818\pi$
$337$	121.608	−	210.631i	0.360855	−	0.625019i	0.988102	+	0.153802i	$0.0491516\pi$
$338$		−	57.2853i		−	0.169483i
$339$	279.717	+	320.289i	0.825124	+	0.944805i
$340$	530.711			1.56091
$341$	15.3258	−	8.84834i	0.0449436	−	0.0259482i
$342$	−77.5173	+	100.163i	−0.226659	+	0.292873i
$343$		0			0
$344$	64.8308	−	37.4301i	0.188462	−	0.108808i
$345$	78.7558	+	26.9156i	0.228278	+	0.0780163i
$346$	46.7572	+	80.9859i	0.135137	+	0.234063i
$347$	291.677	−	168.400i	0.840568	−	0.485302i	−0.0168893	−	0.999857i	$-0.505376\pi$
$347$	291.677	−	168.400i	0.840568	−	0.485302i	0.857457	+	0.514555i	$0.172043\pi$
$348$	−201.988	−	231.285i	−0.580424	−	0.664613i
$349$	−239.411	−	414.673i	−0.685992	−	1.18817i	−0.973124	−	0.230282i	$-0.926035\pi$
$349$	−239.411	−	414.673i	−0.685992	−	1.18817i	0.287132	−	0.957891i	$-0.407298\pi$
$350$		0			0
$351$	−204.347	+	12.1218i	−0.582184	+	0.0345351i
$352$	−41.0924	−	71.1742i	−0.116740	−	0.202199i
$353$		−	213.029i		−	0.603481i	−0.953390	−	0.301740i	$-0.902432\pi$
$353$		−	213.029i		−	0.603481i	0.953390	−	0.301740i	$-0.0975676\pi$
$354$	77.0106	+	26.3192i	0.217544	+	0.0743480i
$355$	972.279			2.73882
$356$	−506.837	−	292.623i	−1.42370	−	0.821973i
$357$		0			0
$358$	−54.0382	−	93.5970i	−0.150945	−	0.261444i
$359$	439.984	−	254.025i	1.22558	−	0.707590i	0.259479	−	0.965749i	$-0.416449\pi$
$359$	439.984	−	254.025i	1.22558	−	0.707590i	0.966103	+	0.258159i	$0.0831157\pi$
$360$	−198.688	−	153.767i	−0.551910	−	0.427131i
$361$	−194.760	+	337.333i	−0.539500	+	0.934441i
$362$	46.2826	+	26.7213i	0.127853	+	0.0738157i
$363$	−305.699	−	104.476i	−0.842147	−	0.287813i
$364$		0			0
$365$	423.021	+	244.231i	1.15896	+	0.669127i
$366$	−161.706	+	31.8181i	−0.441821	+	0.0869348i
$367$	−39.9770			−0.108929			−0.0544646	−	0.998516i	$-0.517345\pi$
$367$	−39.9770			−0.108929			−0.0544646	+	0.998516i	$0.517345\pi$
$368$	−44.1319	−	25.4795i	−0.119924	−	0.0692379i
$369$	−240.650	−	587.840i	−0.652167	−	1.59306i
$370$	−135.107			−0.365155
$371$		0			0
$372$	−40.9448	+	35.7582i	−0.110067	+	0.0961242i
$373$	69.3676			0.185972			0.0929860	−	0.995667i	$-0.470359\pi$
$373$	69.3676			0.185972			0.0929860	+	0.995667i	$0.470359\pi$
$374$	−32.8239	+	18.9509i	−0.0877645	+	0.0506708i
$375$	4.46231	−	13.0568i	0.0118995	−	0.0348183i
$376$	47.6337	−	82.5039i	0.126685	−	0.219425i
$377$			207.712i			0.550960i
$378$		0			0
$379$	−140.172			−0.369847			−0.184924	−	0.982753i	$-0.559204\pi$
$379$	−140.172			−0.369847			−0.184924	+	0.982753i	$0.559204\pi$
$380$	−622.667	−	359.497i	−1.63860	−	0.946044i
$381$	112.997	+	38.6178i	0.296579	+	0.101359i
$382$	−23.0600	−	39.9411i	−0.0603666	−	0.104558i
$383$			523.686i			1.36733i	0.729798	+	0.683663i	$0.239614\pi$
$383$			523.686i			1.36733i	−0.729798	+	0.683663i	$0.760386\pi$
$384$	218.383	+	250.059i	0.568707	+	0.651196i
$385$		0			0
$386$		−	41.1564i		−	0.106623i
$387$	22.8239	−	167.996i	0.0589764	−	0.434099i
$388$	−10.9526	+	18.9705i	−0.0282285	+	0.0488931i
$389$			147.180i			0.378356i	0.981943	+	0.189178i	$0.0605823\pi$
$389$			147.180i			0.378356i	−0.981943	+	0.189178i	$0.939418\pi$
$390$	15.8456	+	80.5306i	0.0406298	+	0.206489i
$391$	−39.9310	+	69.1626i	−0.102125	+	0.176886i
$392$		0			0
$393$	67.4458	−	197.348i	0.171618	−	0.502158i
$394$	12.6807	−	21.9636i	0.0321845	−	0.0557452i
$395$	−141.231	−	81.5399i	−0.357547	−	0.206430i
$396$	−121.574	−	16.5169i	−0.307004	−	0.0417094i
$397$	−91.5634	−	158.592i	−0.230638	−	0.399477i	0.727358	−	0.686258i	$-0.240748\pi$
$397$	−91.5634	−	158.592i	−0.230638	−	0.399477i	−0.957996	+	0.286781i	$0.907415\pi$
$398$	0.905434	−	0.522753i	0.00227496	−	0.00131345i
$399$		0			0
$400$	157.065	−	272.044i	0.392662	−	0.680111i
$401$			614.031i			1.53125i	0.643288	+	0.765624i	$0.277570\pi$
$401$			614.031i			1.53125i	−0.643288	+	0.765624i	$0.722430\pi$
$402$	50.9115	−	148.968i	0.126645	−	0.370568i
$403$	36.7715			0.0912445
$404$	−63.0130	+	36.3806i	−0.155973	+	0.0900510i
$405$	−550.804	+	142.719i	−1.36001	+	0.352391i
$406$		0			0
$407$	−118.313	+	68.3083i	−0.290697	+	0.167834i
$408$	181.580	−	158.579i	0.445049	−	0.388674i
$409$	238.533	+	413.151i	0.583210	+	1.01015i	0.995096	+	0.0989139i	$0.0315368\pi$
$409$	238.533	+	413.151i	0.583210	+	1.01015i	−0.411886	+	0.911235i	$0.635130\pi$
$410$	−220.554	+	127.337i	−0.537936	+	0.310577i
$411$	73.4948	−	215.048i	0.178820	−	0.523231i
$412$	48.7409	+	84.4217i	0.118303	+	0.204907i
$413$		0			0
$414$	16.8975	−	6.91750i	0.0408152	−	0.0167089i
$415$	105.156	+	182.136i	0.253388	+	0.438881i
$416$		−	170.770i		−	0.410505i
$417$	169.136	−	147.711i	0.405602	−	0.354224i
$418$	51.3483			0.122843
$419$	212.402	+	122.630i	0.506926	+	0.292674i	0.731569	−	0.681767i	$-0.238788\pi$
$419$	212.402	+	122.630i	0.506926	+	0.292674i	−0.224643	+	0.974441i	$0.572122\pi$
$420$		0			0
$421$	−247.132	−	428.045i	−0.587012	−	1.01673i	−0.994621	−	0.103578i	$-0.966971\pi$
$421$	−247.132	−	428.045i	−0.587012	−	1.01673i	0.407609	−	0.913156i	$-0.366363\pi$
$422$	−128.869	+	74.4026i	−0.305377	+	0.176309i
$423$	−81.7419	−	199.673i	−0.193243	−	0.472039i
$424$	53.0287	−	91.8483i	0.125068	−	0.216623i
$425$	−426.343	−	246.149i	−1.00316	−	0.579174i
$426$	160.657	−	140.306i	0.377129	−	0.329357i
$427$		0			0
$428$	94.2307	+	54.4041i	0.220165	+	0.127112i
$429$	54.5912	+	62.5094i	0.127252	+	0.145710i
$430$	−67.9751			−0.158082
$431$	−274.768	−	158.637i	−0.637513	−	0.368068i	0.146143	−	0.989263i	$-0.453314\pi$
$431$	−274.768	−	158.637i	−0.637513	−	0.368068i	−0.783656	+	0.621195i	$0.786647\pi$
$432$	347.773	−	20.6299i	0.805031	−	0.0477544i
$433$	671.335			1.55043			0.775213	−	0.631699i	$-0.217642\pi$
$433$	671.335			1.55043			0.775213	+	0.631699i	$0.217642\pi$
$434$		0			0
$435$	111.465	+	566.487i	0.256241	+	1.30227i
$436$	−381.074			−0.874024
$437$	93.6997	−	54.0975i	0.214416	−	0.123793i
$438$	105.143	−	20.6885i	0.240053	−	0.0472339i
$439$	148.977	−	258.036i	0.339356	−	0.587782i	−0.644956	−	0.764220i	$-0.723124\pi$
$439$	148.977	−	258.036i	0.339356	−	0.587782i	0.984312	+	0.176438i	$0.0564574\pi$
$440$			101.857i			0.231494i
$441$		0			0
$442$	−78.7553			−0.178179
$443$	718.262	+	414.689i	1.62136	+	0.936092i	0.986557	+	0.163418i	$0.0522519\pi$
$443$	718.262	+	414.689i	1.62136	+	0.936092i	0.634802	+	0.772674i	$0.281081\pi$
$444$	316.090	−	276.050i	0.711914	−	0.621734i
$445$	550.185	+	952.949i	1.23637	+	2.14146i
$446$			69.8300i			0.156569i
$447$	−21.0358	+	61.5512i	−0.0470599	+	0.137699i
$448$		0			0
$449$			190.382i			0.424012i	0.977268	+	0.212006i	$0.0679997\pi$
$449$			190.382i			0.424012i	−0.977268	+	0.212006i	$0.932000\pi$
$450$	42.6419	+	104.162i	0.0947597	+	0.231471i
$451$	−128.759	+	223.018i	−0.285497	+	0.494496i
$452$			529.580i			1.17164i
$453$	486.871	+	166.393i	1.07477	+	0.367314i
$454$	−12.7915	+	22.1555i	−0.0281751	+	0.0488007i
$455$		0			0
$456$	−320.462	+	63.0556i	−0.702767	+	0.138280i
$457$	139.987	−	242.465i	0.306318	−	0.530558i	−0.671236	−	0.741243i	$-0.734236\pi$
$457$	139.987	−	242.465i	0.306318	−	0.530558i	0.977554	+	0.210686i	$0.0675697\pi$
$458$	63.3925	+	36.5997i	0.138411	+	0.0799119i
$459$	−32.3307	−	545.023i	−0.0704373	−	1.18741i
$460$	51.8252	+	89.7638i	0.112663	+	0.195139i
$461$	−132.923	+	76.7433i	−0.288337	+	0.166471i	−0.637192	−	0.770705i	$-0.719904\pi$
$461$	−132.923	+	76.7433i	−0.288337	+	0.166471i	0.348855	+	0.937177i	$0.386571\pi$
$462$		0			0
$463$	−251.599	+	435.782i	−0.543410	+	0.941215i	0.455295	+	0.890341i	$0.349534\pi$
$463$	−251.599	+	435.782i	−0.543410	+	0.941215i	−0.998705	+	0.0508737i	$0.983799\pi$
$464$		−	353.500i		−	0.761854i
$465$	100.286	−	19.7328i	0.215669	−	0.0424361i
$466$	43.1142			0.0925198
$467$	−153.150	+	88.4210i	−0.327943	+	0.189338i	−0.654928	−	0.755692i	$-0.727301\pi$
$467$	−153.150	+	88.4210i	−0.327943	+	0.189338i	0.326984	+	0.945030i	$0.393968\pi$
$468$	−201.611	−	156.030i	−0.430793	−	0.333396i
$469$		0			0
$470$	−74.9159	+	43.2527i	−0.159395	+	0.0920270i
$471$	46.5976	+	236.819i	0.0989334	+	0.502800i
$472$	104.933	+	181.749i	0.222315	+	0.385061i
$473$	−59.5259	+	34.3673i	−0.125848	+	0.0726581i
$474$	−35.1034	+	6.90712i	−0.0740578	+	0.0145720i
$475$	333.476	+	577.598i	0.702055	+	1.21600i
$476$		0			0
$477$	−91.0000	−	222.288i	−0.190776	−	0.466012i
$478$	−66.1326	−	114.545i	−0.138353	−	0.239634i
$479$			472.862i			0.987186i	0.869693	+	0.493593i	$0.164317\pi$
$479$			472.862i			0.987186i	−0.869693	+	0.493593i	$0.835683\pi$
$480$	−91.6407	−	465.737i	−0.190918	−	0.970285i
$481$	−283.873			−0.590172
$482$	−56.9332	−	32.8704i	−0.118119	−	0.0681959i
$483$		0			0
$484$	−201.165	−	348.428i	−0.415630	−	0.719893i
$485$	35.6682	−	20.5930i	0.0735426	−	0.0424599i
$486$	−70.4183	+	103.067i	−0.144894	+	0.212072i
$487$	−49.3289	+	85.4401i	−0.101291	+	0.175442i	−0.912217	−	0.409708i	$-0.865631\pi$
$487$	−49.3289	+	85.4401i	−0.101291	+	0.175442i	0.810926	+	0.585149i	$0.198964\pi$
$488$	−368.051	−	212.495i	−0.754203	−	0.435440i
$489$	78.3982	+	398.436i	0.160324	+	0.814797i
$490$		0			0
$491$	807.412	+	466.160i	1.64442	+	0.949409i	0.979234	+	0.202735i	$0.0649829\pi$
$491$	807.412	+	466.160i	1.64442	+	0.949409i	0.665190	+	0.746674i	$0.268350\pi$
$492$	255.823	−	748.543i	0.519965	−	1.52143i
$493$	−553.998			−1.12373
$494$	92.4011	+	53.3478i	0.187047	+	0.107991i
$495$	182.430	+	141.185i	0.368545	+	0.285222i
$496$	−62.5807			−0.126171
$497$		0			0
$498$	43.6591	+	14.9209i	0.0876688	+	0.0299617i
$499$	475.724			0.953354			0.476677	−	0.879079i	$-0.341841\pi$
$499$	475.724			0.953354			0.476677	+	0.879079i	$0.341841\pi$
$500$	14.8818	−	8.59204i	0.0297637	−	0.0171841i
$501$	221.597	+	253.739i	0.442310	+	0.506465i
$502$	−71.1753	+	123.279i	−0.141783	+	0.245576i
$503$			779.244i			1.54919i	0.632456	+	0.774596i	$0.282047\pi$
$503$			779.244i			1.54919i	−0.632456	+	0.774596i	$0.717953\pi$
$504$		0			0
$505$	136.805			0.270900
$506$	−6.41066	−	3.70120i	−0.0126693	−	0.00731462i
$507$	−64.5899	−	328.259i	−0.127396	−	0.647454i
$508$	74.3573	+	128.791i	0.146373	+	0.253525i
$509$			426.079i			0.837091i	0.908196	+	0.418545i	$0.137460\pi$
$509$			426.079i			0.837091i	−0.908196	+	0.418545i	$0.862540\pi$
$510$	−214.787	+	42.2626i	−0.421151	+	0.0828679i
$511$		0			0
$512$			495.735i			0.968233i
$513$	−331.259	+	661.359i	−0.645729	+	1.28920i
$514$	48.9053	−	84.7065i	0.0951466	−	0.164799i
$515$		−	183.284i		−	0.355891i
$516$	159.031	−	138.886i	0.308200	−	0.269159i
$517$	−43.7359	+	75.7528i	−0.0845956	+	0.146524i
$518$		0			0
$519$	359.243	+	411.350i	0.692184	+	0.792582i
$520$	−105.823	+	183.291i	−0.203507	+	0.352484i
$521$	−418.449	−	241.592i	−0.803166	−	0.463708i	0.0414112	−	0.999142i	$-0.486815\pi$
$521$	−418.449	−	241.592i	−0.803166	−	0.463708i	−0.844577	+	0.535434i	$0.820148\pi$
$522$	100.166	+	77.5197i	0.191888	+	0.148505i
$523$	107.843	+	186.789i	0.206200	+	0.357149i	0.950514	−	0.310680i	$-0.100557\pi$
$523$	107.843	+	186.789i	0.206200	+	0.357149i	−0.744314	+	0.667829i	$0.767224\pi$
$524$	224.932	−	129.865i	0.429260	−	0.247833i
$525$		0			0
$526$	13.0500	−	22.6033i	0.0248099	−	0.0429720i
$527$			98.0752i			0.186101i
$528$	−92.9075	−	106.383i	−0.175961	−	0.201484i
$529$	513.403			0.970515
$530$	−83.4008	+	48.1515i	−0.157360	+	0.0908519i
$531$	470.966	+	63.9851i	0.886941	+	0.120499i
$532$		0			0
$533$	−463.404	+	267.546i	−0.869425	+	0.501963i
$534$	228.428	+	78.0675i	0.427767	+	0.146194i
$535$	−102.290	−	177.171i	−0.191196	−	0.331161i
$536$	351.572	−	202.980i	0.655918	−	0.378694i
$537$	−415.185	−	475.406i	−0.773156	−	0.885299i
$538$	4.63327	+	8.02505i	0.00861202	+	0.0149165i
$539$		0			0
$540$	−633.579	−	317.344i	−1.17329	−	0.587675i
$541$	−436.156	−	755.444i	−0.806203	−	1.39638i	−0.915476	−	0.402372i	$-0.868186\pi$
$541$	−436.156	−	755.444i	−0.806203	−	1.39638i	0.109273	−	0.994012i	$-0.465148\pi$
$542$		−	88.2739i		−	0.162867i
$543$	295.340	+	100.936i	0.543904	+	0.185885i
$544$	455.469			0.837260
$545$	620.500	+	358.246i	1.13853	+	0.657331i
$546$		0			0
$547$	−151.008	−	261.554i	−0.276067	−	0.478161i	0.694337	−	0.719650i	$-0.255698\pi$
$547$	−151.008	−	261.554i	−0.276067	−	0.478161i	−0.970404	+	0.241489i	$0.922364\pi$
$548$	245.106	−	141.512i	0.447273	−	0.258233i
$549$	−890.743	+	364.652i	−1.62248	+	0.664211i
$550$	22.8155	−	39.5176i	0.0414827	−	0.0718501i
$551$	649.989	+	375.271i	1.17965	+	0.681073i
$552$	44.5536	+	15.2266i	0.0807130	+	0.0275845i
$553$		0			0
$554$	100.802	+	58.1980i	0.181953	+	0.105051i
$555$	−774.198	+	152.335i	−1.39495	+	0.274478i
$556$	279.657			0.502981
$557$	−35.2462	−	20.3494i	−0.0632787	−	0.0365340i	0.468027	−	0.883714i	$-0.344965\pi$
$557$	−35.2462	−	20.3494i	−0.0632787	−	0.0365340i	−0.531306	+	0.847180i	$0.678298\pi$
$558$	13.7234	−	17.7325i	0.0245940	−	0.0317787i
$559$	−142.822			−0.255496
$560$		0			0
$561$	−166.722	+	145.603i	−0.297187	+	0.259542i
$562$	214.077			0.380920
$563$	482.957	−	278.835i	0.857828	−	0.495267i	−0.00545641	−	0.999985i	$-0.501737\pi$
$563$	482.957	−	278.835i	0.857828	−	0.495267i	0.863284	+	0.504718i	$0.168404\pi$
$564$	86.8957	−	254.259i	0.154070	−	0.450814i
$565$	497.855	−	862.309i	0.881159	−	1.52621i
$566$			63.8560i			0.112820i
$567$		0			0
$568$	550.036			0.968373
$569$	321.583	+	185.666i	0.565173	+	0.326303i	0.755219	−	0.655472i	$-0.227530\pi$
$569$	321.583	+	185.666i	0.565173	+	0.326303i	−0.190046	+	0.981775i	$0.560864\pi$
$570$	280.631	+	95.9086i	0.492335	+	0.168261i
$571$	−202.140	−	350.117i	−0.354011	−	0.613164i	0.632938	−	0.774203i	$-0.281849\pi$
$571$	−202.140	−	350.117i	−0.354011	−	0.613164i	−0.986948	+	0.161039i	$0.948516\pi$
$572$			103.356i			0.180692i
$573$	−177.174	−	202.872i	−0.309204	−	0.354053i
$574$		0			0
$575$		−	96.1481i		−	0.167214i
$576$	285.000	+	220.565i	0.494791	+	0.382926i
$577$	416.462	−	721.333i	0.721770	−	1.25014i	−0.238519	−	0.971138i	$-0.576662\pi$
$577$	416.462	−	721.333i	0.721770	−	1.25014i	0.960290	−	0.279005i	$-0.0900047\pi$
$578$		−	61.5964i		−	0.106568i
$579$	−46.4044	−	235.837i	−0.0801457	−	0.407317i
$580$	−359.508	+	622.686i	−0.619841	+	1.07360i
$581$		0			0
$582$	2.92201	−	8.54988i	0.00502064	−	0.0146905i
$583$	−48.6895	+	84.3326i	−0.0835154	+	0.144653i
$584$	239.311	+	138.166i	0.409778	+	0.236586i
$585$	181.599	+	443.595i	0.310425	+	0.758281i
$586$	−107.534	−	186.255i	−0.183506	−	0.317841i
$587$	−464.128	+	267.964i	−0.790677	+	0.456498i	−0.840201	−	0.542275i	$-0.817563\pi$
$587$	−464.128	+	267.964i	−0.790677	+	0.456498i	0.0495236	+	0.998773i	$0.484230\pi$
$588$		0			0
$589$	66.4349	−	115.069i	0.112793	−	0.195363i
$590$		−	190.564i		−	0.322989i
$591$	47.8993	−	140.155i	0.0810479	−	0.237148i
$592$	483.117			0.816076
$593$	522.472	−	301.649i	0.881065	−	0.508683i	0.0100559	−	0.999949i	$-0.496799\pi$
$593$	522.472	−	301.649i	0.881065	−	0.508683i	0.871010	+	0.491266i	$0.163466\pi$
$594$	50.5181	−	2.99673i	0.0850472	−	0.00504499i
$595$		0			0
$596$	−70.1545	+	40.5037i	−0.117709	+	0.0679592i
$597$	4.59896	−	4.01639i	0.00770344	−	0.00672763i
$598$	−7.69063	−	13.3206i	−0.0128606	−	0.0222752i
$599$	−688.601	+	397.564i	−1.14958	+	0.663712i	−0.948786	−	0.315920i	$-0.897687\pi$
$599$	−688.601	+	397.564i	−1.14958	+	0.663712i	−0.200798	+	0.979633i	$0.564353\pi$
$600$	−93.8624	+	274.644i	−0.156437	+	0.457740i
$601$	−284.164	−	492.186i	−0.472818	−	0.818945i	0.526698	−	0.850053i	$-0.323430\pi$
$601$	−284.164	−	492.186i	−0.472818	−	0.818945i	−0.999516	+	0.0311074i	$0.990097\pi$
$602$		0			0
$603$	123.772	−	911.029i	0.205260	−	1.51083i
$604$	320.385	+	554.923i	0.530439	+	0.918747i
$605$			756.456i			1.25034i
$606$	22.6052	−	19.7418i	0.0373024	−	0.0325772i
$607$	238.174			0.392380			0.196190	−	0.980566i	$-0.437143\pi$
$607$	238.174			0.392380			0.196190	+	0.980566i	$0.437143\pi$
$608$	−534.388	−	308.529i	−0.878927	−	0.507449i
$609$		0			0
$610$	192.951	+	334.201i	0.316313	+	0.547870i
$611$	−157.405	+	90.8779i	−0.257619	+	0.148736i
$612$	416.154	−	537.727i	0.679991	−	0.878638i
$613$	−352.492	+	610.534i	−0.575028	+	0.995977i	0.421011	+	0.907056i	$0.361675\pi$
$613$	−352.492	+	610.534i	−0.575028	+	0.995977i	−0.996039	+	0.0889215i	$0.971658\pi$
$614$	203.452	+	117.463i	0.331356	+	0.191308i
$615$	−1120.25	+	978.349i	−1.82155	+	1.59081i
$616$		0			0
$617$	−722.505	−	417.138i	−1.17100	−	0.676075i	−0.217082	−	0.976153i	$-0.569654\pi$
$617$	−722.505	−	417.138i	−1.17100	−	0.676075i	−0.953915	+	0.300078i	$0.902987\pi$
$618$	−26.4490	−	30.2854i	−0.0427978	−	0.0490055i
$619$	−134.623			−0.217485			−0.108743	−	0.994070i	$-0.534682\pi$
$619$	−134.623			−0.217485			−0.108743	+	0.994070i	$0.534682\pi$
$620$	110.235	+	63.6443i	0.177799	+	0.102652i
$621$	89.0274	−	58.6912i	0.143361	−	0.0945107i
$622$	178.835			0.287517
$623$		0			0
$624$	−56.6608	−	287.962i	−0.0908025	−	0.461477i
$625$	−640.940			−1.02550
$626$	60.3718	−	34.8557i	0.0964406	−	0.0556800i
$627$	294.239	−	57.8960i	0.469281	−	0.0923380i
$628$	−150.292	+	260.313i	−0.239318	+	0.414511i
$629$		−	757.131i		−	1.20371i
$630$		0			0
$631$	951.730			1.50829			0.754144	−	0.656709i	$-0.228052\pi$
$631$	951.730			1.50829			0.754144	+	0.656709i	$0.228052\pi$
$632$	−79.8970	−	46.1286i	−0.126419	−	0.0729882i
$633$	−654.562	+	571.647i	−1.03406	+	0.903076i
$634$	104.700	+	181.346i	0.165142	+	0.286035i
$635$		−	279.611i		−	0.440333i
$636$	96.7375	−	283.056i	0.152103	−	0.445057i
$637$		0			0
$638$		−	51.3500i		−	0.0804858i
$639$	762.408	−	985.132i	1.19313	−	1.54168i
$640$	388.690	−	673.231i	0.607328	−	1.05192i
$641$			34.8141i			0.0543122i	0.999631	+	0.0271561i	$0.00864512\pi$
$641$			34.8141i			0.0543122i	−0.999631	+	0.0271561i	$0.991355\pi$
$642$	−42.4691	−	14.5142i	−0.0661512	−	0.0226079i
$643$	504.419	−	873.680i	0.784478	−	1.35876i	−0.144833	−	0.989456i	$-0.546264\pi$
$643$	504.419	−	873.680i	0.784478	−	1.35876i	0.929311	−	0.369299i	$-0.120402\pi$
$644$		0			0
$645$	−389.515	+	76.6429i	−0.603899	+	0.118826i
$646$	−142.287	+	246.448i	−0.220258	+	0.381498i
$647$	−762.764	−	440.382i	−1.17892	−	0.680653i	−0.223159	−	0.974782i	$-0.571637\pi$
$647$	−762.764	−	440.382i	−1.17892	−	0.680653i	−0.955766	+	0.294129i	$0.904970\pi$
$648$	−311.600	+	80.7384i	−0.480864	+	0.124596i
$649$	−96.3463	−	166.877i	−0.148453	−	0.257129i
$650$	82.1127	−	47.4078i	0.126327	−	0.0729350i
$651$		0			0
$652$	−252.858	+	437.963i	−0.387819	+	0.671722i
$653$		−	785.935i		−	1.20358i	−0.798656	−	0.601788i	$-0.794455\pi$
$653$		−	785.935i		−	1.20358i	0.798656	−	0.601788i	$-0.205545\pi$
$654$	154.227	−	30.3464i	0.235821	−	0.0464013i
$655$	−488.340			−0.745557
$656$	788.657	−	455.331i	1.20222	−	0.694102i
$657$	579.170	−	237.100i	0.881537	−	0.360883i
$658$		0			0
$659$	692.308	−	399.704i	1.05054	−	0.606531i	0.127741	−	0.991808i	$-0.459227\pi$
$659$	692.308	−	399.704i	1.05054	−	0.606531i	0.922801	+	0.385276i	$0.125894\pi$
$660$	55.4640	+	281.880i	0.0840364	+	0.427090i
$661$	163.861	+	283.816i	0.247899	+	0.429374i	0.962943	−	0.269706i	$-0.0869265\pi$
$661$	163.861	+	283.816i	0.247899	+	0.429374i	−0.715044	+	0.699080i	$0.753593\pi$
$662$	82.0331	−	47.3618i	0.123917	−	0.0715436i
$663$	−451.288	+	88.7976i	−0.680675	+	0.133933i
$664$	59.4887	+	103.037i	0.0895914	+	0.155177i
$665$		0			0
$666$	−105.944	+	136.893i	−0.159074	+	0.205545i
$667$	−54.0992	−	93.7026i	−0.0811083	−	0.140484i
$668$			419.543i			0.628058i
$669$	78.7342	+	400.143i	0.117689	+	0.598122i
$670$	−368.623			−0.550184
$671$	337.935	+	195.107i	0.503628	+	0.290770i
$672$		0			0
$673$	287.229	+	497.495i	0.426789	+	0.739221i	0.996586	−	0.0825652i	$-0.0263113\pi$
$673$	287.229	+	497.495i	0.426789	+	0.739221i	−0.569796	+	0.821786i	$0.692978\pi$
$674$	−108.199	+	62.4685i	−0.160532	+	0.0926833i
$675$	361.793	+	548.796i	0.535990	+	0.813031i
$676$	208.322	−	360.825i	0.308169	−	0.533764i
$677$	−194.813	−	112.476i	−0.287760	−	0.166138i	0.349171	−	0.937059i	$-0.386463\pi$
$677$	−194.813	−	112.476i	−0.287760	−	0.166138i	−0.636931	+	0.770921i	$0.719796\pi$
$678$	−42.1725	−	214.329i	−0.0622013	−	0.316120i
$679$		0			0
$680$	−488.866	−	282.247i	−0.718920	−	0.415069i
$681$	−48.3178	+	141.379i	−0.0709513	+	0.207605i
$682$	−9.09057			−0.0133293
$683$	−322.171	−	186.006i	−0.471700	−	0.272336i	0.245251	−	0.969460i	$-0.421130\pi$
$683$	−322.171	−	186.006i	−0.471700	−	0.272336i	−0.716951	+	0.697123i	$0.754463\pi$
$684$	−852.510	+	349.000i	−1.24636	+	0.510234i
$685$	−532.138			−0.776844
$686$		0			0
$687$	404.522	+	138.249i	0.588823	+	0.201236i
$688$	243.066			0.353293
$689$	−175.233	+	101.171i	−0.254329	+	0.146837i
$690$	−28.1227	−	32.2018i	−0.0407575	−	0.0466693i
$691$	−486.666	+	842.930i	−0.704292	+	1.21987i	0.262654	+	0.964890i	$0.415402\pi$
$691$	−486.666	+	842.930i	−0.704292	+	1.21987i	−0.966946	+	0.254980i	$0.917931\pi$
$692$			680.145i			0.982868i
$693$		0			0
$694$	−173.010			−0.249294
$695$	−455.363	−	262.904i	−0.655199	−	0.378279i
$696$	63.0576	+	320.472i	0.0906000	+	0.460448i
$697$	−713.586	−	1235.97i	−1.02380	−	1.77327i
$698$			245.965i			0.352386i
$699$	247.055	−	48.6119i	0.353441	−	0.0695449i
$700$		0			0
$701$			495.876i			0.707384i	0.935362	+	0.353692i	$0.115074\pi$
$701$			495.876i			0.707384i	−0.935362	+	0.353692i	$0.884926\pi$
$702$	94.0204	+	47.0926i	0.133932	+	0.0670834i
$703$	−512.871	+	888.318i	−0.729546	+	1.26361i
$704$		−	146.105i		−	0.207536i
$705$	−380.519	+	332.318i	−0.539743	+	0.471372i
$706$	−54.7151	+	94.7693i	−0.0775001	+	0.134234i
$707$		0			0
$708$	389.358	+	445.832i	0.549940	+	0.629707i
$709$	−49.0475	+	84.9528i	−0.0691785	+	0.119821i	−0.898540	−	0.438892i	$-0.855371\pi$
$709$	−49.0475	+	84.9528i	−0.0691785	+	0.119821i	0.829361	+	0.558712i	$0.188704\pi$
$710$	−432.534	−	249.724i	−0.609203	−	0.351724i
$711$	−193.363	+	79.1591i	−0.271960	+	0.111335i
$712$	311.250	+	539.100i	0.437148	+	0.757163i
$713$	−16.5883	+	9.57727i	−0.0232655	+	0.0134324i
$714$		0			0
$715$	97.1641	−	168.293i	0.135894	−	0.235375i
$716$		−	786.056i		−	1.09784i
$717$	−508.107	−	581.806i	−0.708658	−	0.811445i
$718$	−260.979			−0.363480
$719$	−256.458	+	148.066i	−0.356687	+	0.205933i	−0.667627	−	0.744496i	$-0.732690\pi$
$719$	−256.458	+	148.066i	−0.356687	+	0.205933i	0.310939	+	0.950430i	$0.399356\pi$
$720$	−309.059	−	754.944i	−0.429248	−	1.04853i
$721$		0			0
$722$	173.284	−	100.046i	0.240005	−	0.138567i
$723$	−363.304	−	124.163i	−0.502495	−	0.171733i
$724$	194.348	+	336.621i	0.268436	+	0.464946i
$725$	577.616	−	333.487i	0.796712	−	0.459982i
$726$	109.161	+	124.995i	0.150360	+	0.172169i
$727$	−12.9897	−	22.4988i	−0.0178675	−	0.0309475i	0.856953	−	0.515394i	$-0.172354\pi$
$727$	−12.9897	−	22.4988i	−0.0178675	−	0.0309475i	−0.874821	+	0.484446i	$0.839021\pi$
$728$		0			0
$729$	−287.305	+	669.998i	−0.394109	+	0.919064i
$730$	−125.459	−	217.301i	−0.171861	−	0.297672i
$731$		−	380.928i		−	0.521105i
$732$	−1134.25	−	387.643i	−1.54953	−	0.529567i
$733$	−675.530			−0.921596			−0.460798	−	0.887505i	$-0.652437\pi$
$733$	−675.530			−0.921596			−0.460798	+	0.887505i	$0.652437\pi$
$734$	17.7844	+	10.2678i	0.0242295	+	0.0139889i
$735$		0			0
$736$	44.4776	+	77.0375i	0.0604316	+	0.104671i
$737$	−322.804	+	186.371i	−0.437997	+	0.252878i
$738$	−43.9260	+	323.320i	−0.0595203	+	0.438102i
$739$	8.89120	−	15.4000i	0.0120314	−	0.0208390i	−0.859947	−	0.510383i	$-0.829504\pi$
$739$	8.89120	−	15.4000i	0.0120314	−	0.0208390i	0.871978	+	0.489544i	$0.162837\pi$
$740$	−851.004	−	491.327i	−1.15001	−	0.663956i
$741$	589.632	+	201.513i	0.795725	+	0.271947i
$742$		0			0
$743$	−748.369	−	432.071i	−1.00723	−	0.581522i	−0.0968479	−	0.995299i	$-0.530876\pi$
$743$	−748.369	−	432.071i	−1.00723	−	0.581522i	−0.910378	+	0.413777i	$0.864209\pi$
$744$	56.7336	−	11.1632i	0.0762549	−	0.0150043i
$745$	152.309			0.204442
$746$	−30.8593	−	17.8166i	−0.0413663	−	0.0238829i
$747$	267.001	+	36.2746i	0.357431	+	0.0485604i
$748$	−275.665			−0.368537
$749$		0			0
$750$	−5.33870	+	4.66243i	−0.00711827	+	0.00621658i
$751$	517.624			0.689247			0.344623	−	0.938741i	$-0.388007\pi$
$751$	517.624			0.689247			0.344623	+	0.938741i	$0.388007\pi$
$752$	267.884	−	154.663i	0.356229	−	0.205669i
$753$	−268.853	+	786.672i	−0.357043	+	1.04472i
$754$	53.3495	−	92.4040i	0.0707553	−	0.122552i
$755$		−	1204.77i		−	1.59572i
$756$		0			0
$757$	−314.752			−0.415789			−0.207895	−	0.978151i	$-0.566661\pi$
$757$	−314.752			−0.415789			−0.207895	+	0.978151i	$0.566661\pi$
$758$	62.3578	+	36.0023i	0.0822663	+	0.0474965i
$759$	−40.9079	−	13.9807i	−0.0538970	−	0.0184199i
$760$	382.381	+	662.303i	0.503132	+	0.871451i
$761$		−	590.863i		−	0.776429i	−0.921569	−	0.388215i	$-0.873092\pi$
$761$		−	590.863i		−	0.776429i	0.921569	−	0.388215i	$-0.126908\pi$
$762$	−40.3497	−	46.2023i	−0.0529524	−	0.0606329i
$763$		0			0
$764$		−	335.438i		−	0.439055i
$765$	−1183.13	+	484.351i	−1.54658	+	0.633138i
$766$	134.505	−	232.970i	0.175594	−	0.304139i
$767$		−	400.392i		−	0.522023i
$768$	59.8429	+	304.134i	0.0779204	+	0.396007i
$769$	292.620	−	506.833i	0.380521	−	0.659081i	−0.610616	−	0.791927i	$-0.709078\pi$
$769$	292.620	−	506.833i	0.380521	−	0.659081i	0.991137	+	0.132846i	$0.0424114\pi$
$770$		0			0
$771$	184.732	−	540.531i	0.239601	−	0.701078i
$772$	149.668	−	259.233i	0.193871	−	0.335794i
$773$	856.704	+	494.618i	1.10828	+	0.639869i	0.938385	−	0.345593i	$-0.112322\pi$
$773$	856.704	+	494.618i	1.10828	+	0.639869i	0.169900	+	0.985461i	$0.445655\pi$
$774$	−53.3023	+	68.8737i	−0.0688661	+	0.0889841i
$775$	−59.0377	−	102.256i	−0.0761777	−	0.131944i
$776$	20.1781	−	11.6498i	0.0260027	−	0.0150127i
$777$		0			0
$778$	37.8024	−	65.4756i	0.0485892	−	0.0841589i
$779$			1933.49i			2.48202i
$780$	−193.048	+	564.864i	−0.247498	+	0.724185i
$781$	−505.028			−0.646642
$782$	35.5279	−	20.5121i	0.0454322	−	0.0262303i
$783$	661.380	+	331.269i	0.844674	+	0.423077i
$784$		0			0
$785$	489.437	−	282.576i	0.623486	−	0.359970i
$786$	−80.6920	+	70.4705i	−0.102662	+	0.0896571i
$787$	−614.287	−	1063.98i	−0.780543	−	1.35194i	−0.931626	−	0.363419i	$-0.881609\pi$
$787$	−614.287	−	1063.98i	−0.780543	−	1.35194i	0.151083	−	0.988521i	$-0.451724\pi$
$788$	159.745	−	92.2286i	0.202722	−	0.117041i
$789$	49.2944	−	144.237i	0.0624770	−	0.182809i
$790$	41.8860	+	72.5487i	0.0530203	+	0.0918338i
$791$		0			0
$792$	103.204	+	79.8708i	0.130308	+	0.100847i
$793$	405.408	+	702.187i	0.511233	+	0.885481i
$794$			94.0699i			0.118476i
$795$	−423.616	+	369.956i	−0.532851	+	0.465353i
$796$	7.60412			0.00955291
$797$	−631.278	−	364.468i	−0.792068	−	0.457300i	0.0486223	−	0.998817i	$-0.484517\pi$
$797$	−631.278	−	364.468i	−0.792068	−	0.457300i	−0.840690	+	0.541517i	$0.817850\pi$
$798$		0			0
$799$	−242.385	−	419.823i	−0.303360	−	0.525436i
$800$	−474.886	+	274.176i	−0.593608	+	0.342720i
$801$	1396.97	+	189.792i	1.74403	+	0.236943i
$802$	157.710	−	273.162i	0.196646	−	0.340601i
$803$	−219.728	−	126.860i	−0.273634	−	0.157983i
$804$	862.412	−	753.168i	1.07265	−	0.936776i
$805$		0			0
$806$	−16.3584	−	9.44454i	−0.0202958	−	0.0117178i
$807$	35.5982	+	40.7615i	0.0441117	+	0.0505099i
$808$	77.3928			0.0957832
$809$	1007.55	+	581.707i	1.24542	+	0.719044i	0.970193	−	0.242335i	$-0.0779131\pi$
$809$	1007.55	+	581.707i	1.24542	+	0.719044i	0.275229	+	0.961379i	$0.411246\pi$
$810$	281.691	+	77.9800i	0.347766	+	0.0962716i
$811$	224.013			0.276219			0.138109	−	0.990417i	$-0.455897\pi$
$811$	224.013			0.276219			0.138109	+	0.990417i	$0.455897\pi$
$812$		0			0
$813$	−99.5300	−	505.832i	−0.122423	−	0.622179i
$814$	70.1783			0.0862141
$815$	823.453	−	475.421i	1.01037	−	0.583338i
$816$	768.037	−	151.123i	0.941221	−	0.185199i
$817$	−258.035	+	446.931i	−0.315833	+	0.547039i
$818$		−	245.063i		−	0.299588i
$819$		0			0
$820$	−1852.28			−2.25888
$821$	1162.89	+	671.396i	1.41643	+	0.817778i	0.995983	−	0.0895378i	$-0.0285390\pi$
$821$	1162.89	+	671.396i	1.41643	+	0.817778i	0.420450	+	0.907316i	$0.361872\pi$
$822$	−87.9291	+	76.7909i	−0.106970	+	0.0934195i
$823$	−665.079	−	1151.95i	−0.808115	−	1.39970i	−0.914168	−	0.405336i	$-0.867154\pi$
$823$	−665.079	−	1151.95i	−0.808115	−	1.39970i	0.106052	−	0.994361i	$-0.466179\pi$
$824$		−	103.687i		−	0.125834i
$825$	86.1819	−	252.170i	0.104463	−	0.305661i
$826$		0			0
$827$		−	863.204i		−	1.04378i	−0.853014	−	0.521889i	$-0.825228\pi$
$827$		−	863.204i		−	1.04378i	0.853014	−	0.521889i	$-0.174772\pi$
$828$	131.589	+	17.8776i	0.158924	+	0.0215913i
$829$	−288.804	+	500.224i	−0.348377	+	0.603406i	−0.985961	−	0.166974i	$-0.946600\pi$
$829$	−288.804	+	500.224i	−0.348377	+	0.603406i	0.637585	+	0.770380i	$0.279934\pi$
$830$		−	108.035i		−	0.130162i
$831$	643.239	+	219.834i	0.774055	+	0.264541i
$832$	151.794	−	262.915i	0.182445	−	0.316004i
$833$		0			0
$834$	−113.182	+	22.2702i	−0.135709	+	0.0267029i
$835$	394.410	−	683.138i	0.472347	−	0.818129i
$836$	323.429	+	186.732i	0.386877	+	0.223364i
$837$	58.6452	−	117.085i	0.0700659	−	0.139887i
$838$	−62.9937	−	109.108i	−0.0751715	−	0.130201i
$839$	264.845	−	152.908i	0.315667	−	0.182251i	−0.333792	−	0.942647i	$-0.608328\pi$
$839$	264.845	−	152.908i	0.315667	−	0.182251i	0.649460	+	0.760396i	$0.274995\pi$
$840$		0			0
$841$	−45.2169	+	78.3179i	−0.0537656	+	0.0931248i
$842$			253.897i			0.301541i
$843$	1226.72	−	241.375i	1.45518	−	0.286329i
$844$	−1082.28			−1.28232
$845$	−678.418	+	391.685i	−0.802862	+	0.463533i
$846$	−14.9204	+	109.823i	−0.0176364	+	0.129814i
$847$		0			0
$848$	298.225	−	172.180i	0.351680	−	0.203043i
$849$	71.9985	+	365.911i	0.0848039	+	0.430991i
$850$	126.444	+	219.007i	0.148757	+	0.257655i
$851$	128.060	−	73.9356i	0.150482	−	0.0868808i
$852$	1522.17	−	299.509i	1.78658	−	0.351537i
$853$	42.0979	+	72.9157i	0.0493528	+	0.0854815i	0.889646	−	0.456650i	$-0.150951\pi$
$853$	42.0979	+	72.9157i	0.0493528	+	0.0854815i	−0.840294	+	0.542131i	$0.817617\pi$
$854$		0			0
$855$	1716.23	+	233.165i	2.00728	+	0.272708i
$856$	−57.8672	−	100.229i	−0.0676019	−	0.117090i
$857$		−	237.222i		−	0.276805i	−0.990376	−	0.138402i	$-0.955803\pi$
$857$		−	237.222i		−	0.276805i	0.990376	−	0.138402i	$-0.0441967\pi$
$858$	−8.23063	−	41.8297i	−0.00959280	−	0.0487526i
$859$	−1162.19			−1.35296			−0.676479	−	0.736462i	$-0.736495\pi$
$859$	−1162.19			−1.35296			−0.676479	+	0.736462i	$0.736495\pi$
$860$	−428.157	−	247.197i	−0.497857	−	0.287438i
$861$		0			0
$862$	81.4900	+	141.145i	0.0945360	+	0.163741i
$863$	−582.552	+	336.337i	−0.675032	+	0.389730i	−0.797980	−	0.602683i	$-0.794098\pi$
$863$	−582.552	+	336.337i	−0.675032	+	0.389730i	0.122949	+	0.992413i	$0.460765\pi$
$864$	−543.753	−	272.353i	−0.629344	−	0.315223i
$865$	639.400	−	1107.47i	0.739191	−	1.28032i
$866$	−298.654	−	172.428i	−0.344866	−	0.199109i
$867$	−69.4508	−	352.963i	−0.0801047	−	0.407109i
$868$		0			0
$869$	73.3592	+	42.3540i	0.0844180	+	0.0487387i
$870$	95.9117	−	280.640i	0.110243	−	0.322575i
$871$	−774.512			−0.889221
$872$	351.028	+	202.666i	0.402555	+	0.232415i
$873$	7.10376	−	52.2876i	0.00813718	−	0.0598941i
$874$	−55.5784			−0.0635909
$875$		0			0
$876$	737.503	+	252.049i	0.841898	+	0.287727i
$877$	−751.329			−0.856703			−0.428352	−	0.903612i	$-0.640905\pi$
$877$	−751.329			−0.856703			−0.428352	+	0.903612i	$0.640905\pi$
$878$	−132.550	+	76.5278i	−0.150968	+	0.0871615i
$879$	−826.204	−	946.041i	−0.939936	−	1.07627i
$880$	−165.362	+	286.415i	−0.187911	+	0.325471i
$881$		−	696.005i		−	0.790017i	−0.918677	−	0.395009i	$-0.870742\pi$
$881$		−	696.005i		−	0.790017i	0.918677	−	0.395009i	$-0.129258\pi$
$882$		0			0
$883$	−1217.46			−1.37878			−0.689390	−	0.724390i	$-0.742121\pi$
$883$	−1217.46			−1.37878			−0.689390	+	0.724390i	$0.742121\pi$
$884$	−496.058	−	286.399i	−0.561152	−	0.323981i
$885$	−214.863	−	1091.98i	−0.242783	−	1.23387i
$886$	−213.020	−	368.962i	−0.240429	−	0.416436i
$887$		−	582.814i		−	0.657063i	−0.944493	−	0.328531i	$-0.893446\pi$
$887$		−	582.814i		−	0.657063i	0.944493	−	0.328531i	$-0.106554\pi$
$888$	−437.978	+	86.1787i	−0.493218	+	0.0970481i
$889$		0			0
$890$		−	565.246i		−	0.635108i
$891$	286.102	−	74.1318i	0.321103	−	0.0832007i
$892$	−253.942	+	439.840i	−0.284688	+	0.493094i
$893$			656.754i			0.735446i
$894$	25.1672	−	21.9792i	0.0281512	−	0.0245852i
$895$	−738.967	+	1279.93i	−0.825661	+	1.43009i
$896$		0			0
$897$	−59.0884	−	67.6589i	−0.0658733	−	0.0754280i
$898$	48.8983	−	84.6943i	0.0544524	−	0.0943144i
$899$	−115.072	−	66.4370i	−0.128000	−	0.0739010i
$900$	−110.204	+	811.160i	−0.122449	+	0.901289i
$901$	−269.837	−	467.372i	−0.299487	−	0.518726i
$902$	114.561	−	66.1421i	0.127008	−	0.0733282i
$903$		0			0
$904$	281.645	−	487.824i	0.311554	−	0.539628i
$905$		−	730.821i		−	0.807537i
$906$	−173.856	−	199.073i	−0.191894	−	0.219727i
$907$	199.160			0.219581			0.109791	−	0.993955i	$-0.464982\pi$
$907$	199.160			0.219581			0.109791	+	0.993955i	$0.464982\pi$
$908$	−161.140	+	93.0344i	−0.177467	+	0.102461i
$909$	107.275	−	138.613i	0.118014	−	0.152490i
$910$		0			0
$911$	−351.011	+	202.656i	−0.385303	+	0.222455i	−0.680123	−	0.733098i	$-0.738074\pi$
$911$	−351.011	+	202.656i	−0.385303	+	0.222455i	0.294820	+	0.955553i	$0.404740\pi$
$912$	−1003.48	−	342.950i	−1.10031	−	0.376042i
$913$	−54.6209	−	94.6062i	−0.0598257	−	0.103621i
$914$	−124.551	+	71.9096i	−0.136270	+	0.0786757i
$915$	1482.47	+	1697.50i	1.62019	+	1.85519i
$916$	266.195	+	461.063i	0.290606	+	0.503344i
$917$		0			0
$918$	−125.603	+	250.766i	−0.136822	+	0.273166i
$919$	471.303	+	816.321i	0.512843	+	0.888271i	0.999889	+	0.0148944i	$0.00474119\pi$
$919$	471.303	+	816.321i	0.512843	+	0.888271i	−0.487046	+	0.873377i	$0.661925\pi$
$920$		−	110.248i		−	0.119835i
$921$	1298.28	+	443.699i	1.40964	+	0.481758i
$922$	78.8442			0.0855143
$923$	−908.795	−	524.693i	−0.984609	−	0.568465i
$924$		0			0
$925$	455.765	+	789.408i	0.492719	+	0.853414i
$926$	223.856	−	129.243i	0.241745	−	0.139572i
$927$	−185.707	−	143.721i	−0.200331	−	0.155039i
$928$	−308.539	+	534.405i	−0.332477	+	0.575867i
$929$	1200.05	+	692.847i	1.29176	+	0.745799i	0.978966	−	0.204022i	$-0.0654013\pi$
$929$	1200.05	+	692.847i	1.29176	+	0.745799i	0.312795	+	0.949821i	$0.398735\pi$
$930$	−49.6821	−	16.9794i	−0.0534217	−	0.0182574i
$931$		0			0
$932$	271.565	+	156.788i	0.291379	+	0.168228i
$933$	1024.77	−	201.639i	1.09836	−	0.216119i
$934$	90.8415			0.0972607
$935$	448.863	+	259.151i	0.480068	+	0.277167i
$936$	102.734	+	250.949i	0.109758	+	0.268108i
$937$	93.8449			0.100155			0.0500773	−	0.998745i	$-0.484053\pi$
$937$	93.8449			0.100155			0.0500773	+	0.998745i	$0.484053\pi$
$938$		0			0
$939$	306.645	−	267.802i	0.326566	−	0.285199i
$940$	−629.167			−0.669326
$941$	−462.418	+	266.977i	−0.491411	+	0.283716i	−0.725160	−	0.688581i	$-0.758234\pi$
$941$	−462.418	+	266.977i	−0.491411	+	0.283716i	0.233749	+	0.972297i	$0.424901\pi$
$942$	40.0957	−	117.321i	0.0425644	−	0.124545i
$943$	139.367	−	241.390i	0.147791	−	0.255981i
$944$			681.418i			0.721841i
$945$		0			0
$946$	35.3081			0.0373236
$947$	−1333.62	−	769.968i	−1.40826	−	0.813060i	−0.413041	−	0.910713i	$-0.635533\pi$
$947$	−1333.62	−	769.968i	−1.40826	−	0.813060i	−0.995221	+	0.0976527i	$0.968867\pi$
$948$	−246.225	−	84.1500i	−0.259731	−	0.0887658i
$949$	−263.600	−	456.569i	−0.277766	−	0.481105i
$950$		−	342.605i		−	0.360637i
$951$	804.428	+	921.107i	0.845876	+	0.968567i
$952$		0			0
$953$			923.067i			0.968591i	0.874905	+	0.484295i	$0.160924\pi$
$953$			923.067i			0.968591i	−0.874905	+	0.484295i	$0.839076\pi$
$954$	−16.6103	+	122.261i	−0.0174112	+	0.128156i
$955$	−315.343	+	546.191i	−0.330202	+	0.571927i
$956$		−	961.984i		−	1.00626i
$957$	−57.8978	−	294.248i	−0.0604992	−	0.307469i
$958$	121.452	−	210.360i	0.126776	−	0.219583i
$959$		0			0
$960$	272.896	−	798.499i	0.284266	−	0.831770i
$961$	468.739	−	811.879i	0.487761	−	0.844827i
$962$	126.285	+	72.9109i	0.131274	+	0.0757910i
$963$	−259.724	−	35.2859i	−0.269703	−	0.0366416i
$964$	−239.072	−	414.084i	−0.248000	−	0.429548i
$965$	−487.407	+	281.404i	−0.505085	+	0.291611i
$966$		0			0
$967$	−580.540	+	1005.53i	−0.600352	+	1.03984i	0.392416	+	0.919788i	$0.371639\pi$
$967$	−580.540	+	1005.53i	−0.600352	+	1.03984i	−0.992768	+	0.120052i	$0.961694\pi$
$968$			427.941i			0.442087i
$969$	−537.465	+	1572.64i	−0.554659	+	1.62295i
$970$	−21.1568			−0.0218111
$971$	−751.650	+	433.966i	−0.774099	+	0.446926i	−0.834335	−	0.551258i	$-0.814148\pi$
$971$	−751.650	+	433.966i	−0.774099	+	0.446926i	0.0602357	+	0.998184i	$0.480815\pi$
$972$	−818.357	+	393.110i	−0.841931	+	0.404434i
$973$		0			0
$974$	43.8895	−	25.3396i	0.0450611	−	0.0260160i
$975$	417.074	−	364.242i	0.427768	−	0.373581i
$976$	−689.955	−	1195.04i	−0.706921	−	1.22442i
$977$	1386.29	−	800.376i	1.41893	−	0.819218i	0.422722	−	0.906260i	$-0.361075\pi$
$977$	1386.29	−	800.376i	1.41893	−	0.819218i	0.996205	+	0.0870419i	$0.0277414\pi$
$978$	67.4590	−	197.387i	0.0689764	−	0.201827i
$979$	−285.781	−	494.987i	−0.291911	−	0.505605i
$980$		0			0
$981$	849.543	−	347.786i	0.865997	−	0.354522i
$982$	−239.460	−	414.757i	−0.243850	−	0.422360i
$983$		−	1363.25i		−	1.38683i	−0.720541	−	0.693413i	$-0.756106\pi$
$983$		−	1363.25i		−	1.38683i	0.720541	−	0.693413i	$-0.243894\pi$
$984$	−633.748	+	553.469i	−0.644053	+	0.562469i
$985$	−346.814			−0.352095
$986$	246.455	+	142.291i	0.249955	+	0.144311i
$987$		0			0
$988$	388.006	+	672.047i	0.392719	+	0.680209i
$989$	64.4296	−	37.1985i	0.0651463	−	0.0376122i
$990$	−44.8943	−	109.664i	−0.0453478	−	0.110772i
$991$	−470.682	+	815.244i	−0.474956	+	0.822648i	−0.999589	−	0.0286806i	$-0.990869\pi$
$991$	−470.682	+	815.244i	−0.474956	+	0.822648i	0.524632	+	0.851329i	$0.324203\pi$
$992$	94.6065	+	54.6211i	0.0953695	+	0.0550616i
$993$	416.669	−	363.889i	0.419607	−	0.366454i
$994$		0			0
$995$	−12.3817	−	7.14858i	−0.0124439	−	0.00718450i
$996$	220.736	+	252.753i	0.221622	+	0.253768i
$997$	1346.49			1.35054			0.675272	−	0.737569i	$-0.264026\pi$
$997$	1346.49			1.35054			0.675272	+	0.737569i	$0.264026\pi$
$998$	−211.633	−	122.187i	−0.212058	−	0.122431i
$999$	−452.735	+	903.885i	−0.453188	+	0.904790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.n.f.410.6		22
7.2	even	3		441.3.j.f.275.6		22
7.3	odd	6		441.3.r.g.50.6		22
7.4	even	3		441.3.r.f.50.6		22
7.5	odd	6		63.3.j.b.23.6	yes	22
7.6	odd	2		63.3.n.b.32.6	yes	22
9.2	odd	6		441.3.j.f.263.6		22
21.5	even	6		189.3.j.b.44.6		22
21.20	even	2		189.3.n.b.179.6		22
63.2	odd	6	inner	441.3.n.f.128.6		22
63.11	odd	6		441.3.r.f.344.6		22
63.20	even	6		63.3.j.b.11.6	✓	22
63.34	odd	6		189.3.j.b.116.6		22
63.38	even	6		441.3.r.g.344.6		22
63.47	even	6		63.3.n.b.2.6	yes	22
63.61	odd	6		189.3.n.b.170.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.6	✓	22	63.20	even	6
63.3.j.b.23.6	yes	22	7.5	odd	6
63.3.n.b.2.6	yes	22	63.47	even	6
63.3.n.b.32.6	yes	22	7.6	odd	2
189.3.j.b.44.6		22	21.5	even	6
189.3.j.b.116.6		22	63.34	odd	6
189.3.n.b.170.6		22	63.61	odd	6
189.3.n.b.179.6		22	21.20	even	2
441.3.j.f.263.6		22	9.2	odd	6
441.3.j.f.275.6		22	7.2	even	3
441.3.n.f.128.6		22	63.2	odd	6	inner
441.3.n.f.410.6		22	1.1	even	1	trivial
441.3.r.f.50.6		22	7.4	even	3
441.3.r.f.344.6		22	63.11	odd	6
441.3.r.g.50.6		22	7.3	odd	6
441.3.r.g.344.6		22	63.38	even	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.444866 - 0.256844i) q^{2} +(-2.83879 - 0.970187i) q^{3} +(-1.86806 - 3.23558i) q^{4} +7.02462i q^{5} +(1.01370 + 1.16073i) q^{6} +3.97395i q^{8} +(7.11748 + 5.50832i) q^{9} +O(q^{10})\)	\(q+(-0.444866 - 0.256844i) q^{2} +(-2.83879 - 0.970187i) q^{3} +(-1.86806 - 3.23558i) q^{4} +7.02462i q^{5} +(1.01370 + 1.16073i) q^{6} +3.97395i q^{8} +(7.11748 + 5.50832i) q^{9} +(1.80423 - 3.12502i) q^{10} -3.64877i q^{11} +(2.16392 + 10.9975i) q^{12} +(3.79085 - 6.56594i) q^{13} +(6.81519 - 19.9414i) q^{15} +(-6.45157 + 11.1744i) q^{16} +(17.5124 + 10.1108i) q^{17} +(-1.75155 - 4.27854i) q^{18} +(-13.6978 - 23.7253i) q^{19} +(22.7287 - 13.1224i) q^{20} +(-0.937164 + 1.62322i) q^{22} +3.94936i q^{23} +(3.85547 - 11.2812i) q^{24} -24.3452 q^{25} +(-3.37284 + 1.94731i) q^{26} +(-14.8609 - 22.5422i) q^{27} +(-23.7260 + 13.6982i) q^{29} +(-8.15368 + 7.12083i) q^{30} +(2.42502 + 4.20026i) q^{31} +(19.5063 - 11.2620i) q^{32} +(-3.53999 + 10.3581i) q^{33} +(-5.19377 - 8.99588i) q^{34} +(4.52670 - 33.3190i) q^{36} +(-18.7209 - 32.4256i) q^{37} +14.0728i q^{38} +(-17.1316 + 14.9615i) q^{39} -27.9155 q^{40} +(-61.1213 - 35.2884i) q^{41} +(-9.41887 - 16.3140i) q^{43} +(-11.8059 + 6.81613i) q^{44} +(-38.6938 + 49.9975i) q^{45} +(1.01437 - 1.75694i) q^{46} +(-20.7612 - 11.9865i) q^{47} +(29.1559 - 25.4627i) q^{48} +(10.8304 + 6.25292i) q^{50} +(-39.9046 - 45.6926i) q^{51} -28.3262 q^{52} +(-23.1126 - 13.3441i) q^{53} +(0.821297 + 13.8452i) q^{54} +25.6312 q^{55} +(15.8672 + 80.6406i) q^{57} +14.0732 q^{58} +(45.7350 - 26.4051i) q^{59} +(-77.2533 + 15.2007i) q^{60} +(-53.4719 + 92.6160i) q^{61} -2.49140i q^{62} +40.0422 q^{64} +(46.1232 + 26.6293i) q^{65} +(4.23524 - 3.69875i) q^{66} +(-51.0777 - 88.4692i) q^{67} -75.5502i q^{68} +(3.83161 - 11.2114i) q^{69} -138.410i q^{71} +(-21.8898 + 28.2845i) q^{72} +(34.7679 - 60.2198i) q^{73} +19.2334i q^{74} +(69.1111 + 23.6194i) q^{75} +(-51.1767 + 88.6406i) q^{76} +(11.4641 - 2.25573i) q^{78} +(-11.6077 + 20.1052i) q^{79} +(-78.4962 - 45.3198i) q^{80} +(20.3169 + 78.4106i) q^{81} +(18.1272 + 31.3973i) q^{82} +(25.9282 - 14.9697i) q^{83} +(-71.0243 + 123.018i) q^{85} +9.67670i q^{86} +(80.6431 - 15.8677i) q^{87} +14.5000 q^{88} +(135.658 - 78.3225i) q^{89} +(30.0551 - 12.3040i) q^{90} +(12.7785 - 7.37765i) q^{92} +(-2.80909 - 14.2764i) q^{93} +(6.15730 + 10.6648i) q^{94} +(166.661 - 96.2218i) q^{95} +(-66.3007 + 13.0457i) q^{96} +(-2.93155 - 5.07760i) q^{97} +(20.0986 - 25.9700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} - 8 q^{3} + 12 q^{4} + 8 q^{6} + 20 q^{9}+O(q^{10}) \) 22 * q - 6 * q^2 - 8 * q^3 + 12 * q^4 + 8 * q^6 + 20 * q^9	\( 22 q - 6 q^{2} - 8 q^{3} + 12 q^{4} + 8 q^{6} + 20 q^{9} - 25 q^{10} + 20 q^{12} + 18 q^{13} + 53 q^{15} + 12 q^{16} - 6 q^{17} - 56 q^{18} - 3 q^{19} + 39 q^{20} - 59 q^{22} - 15 q^{24} - 114 q^{25} + 3 q^{26} + 97 q^{27} - 63 q^{29} - 20 q^{30} + 29 q^{31} + 246 q^{32} - 77 q^{33} + 99 q^{34} + 76 q^{36} - 20 q^{37} + 200 q^{39} - 210 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} - 71 q^{45} + 75 q^{46} - 261 q^{47} + 113 q^{48} + 63 q^{50} - 78 q^{51} - 92 q^{52} - 63 q^{53} + 485 q^{54} + 100 q^{55} + 224 q^{57} - 80 q^{58} + 102 q^{59} + 103 q^{60} - 78 q^{61} + 106 q^{64} - 225 q^{65} + 401 q^{66} - 132 q^{67} + 297 q^{69} - 66 q^{72} - q^{73} + 245 q^{75} - 233 q^{76} - 440 q^{78} + 140 q^{79} - 96 q^{80} + 104 q^{81} + 157 q^{82} - 255 q^{83} + 102 q^{85} + 136 q^{87} - 816 q^{88} + 720 q^{89} - 418 q^{90} - 1239 q^{92} + 210 q^{93} - 261 q^{94} + 642 q^{95} - 539 q^{96} - 178 q^{97} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 - 8 * q^3 + 12 * q^4 + 8 * q^6 + 20 * q^9 - 25 * q^10 + 20 * q^12 + 18 * q^13 + 53 * q^15 + 12 * q^16 - 6 * q^17 - 56 * q^18 - 3 * q^19 + 39 * q^20 - 59 * q^22 - 15 * q^24 - 114 * q^25 + 3 * q^26 + 97 * q^27 - 63 * q^29 - 20 * q^30 + 29 * q^31 + 246 * q^32 - 77 * q^33 + 99 * q^34 + 76 * q^36 - 20 * q^37 + 200 * q^39 - 210 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 - 71 * q^45 + 75 * q^46 - 261 * q^47 + 113 * q^48 + 63 * q^50 - 78 * q^51 - 92 * q^52 - 63 * q^53 + 485 * q^54 + 100 * q^55 + 224 * q^57 - 80 * q^58 + 102 * q^59 + 103 * q^60 - 78 * q^61 + 106 * q^64 - 225 * q^65 + 401 * q^66 - 132 * q^67 + 297 * q^69 - 66 * q^72 - q^73 + 245 * q^75 - 233 * q^76 - 440 * q^78 + 140 * q^79 - 96 * q^80 + 104 * q^81 + 157 * q^82 - 255 * q^83 + 102 * q^85 + 136 * q^87 - 816 * q^88 + 720 * q^89 - 418 * q^90 - 1239 * q^92 + 210 * q^93 - 261 * q^94 + 642 * q^95 - 539 * q^96 - 178 * q^97 - 103 * q^99

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